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0000000000000000000000000000000000000000..953eb4391d0ee7d3e57aab4bee8eb660f3a3daec --- /dev/null +++ b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_content_list.json @@ -0,0 +1,1771 @@ +[ + { + "type": "text", + "text": "Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance", + "text_level": 1, + "bbox": [ + 83, + 130, + 883, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Chamin Hewa Koneputugodage1 Yizhak Ben-Shabat1,2 Dylan Campbell1 Stephen Gould1", + "bbox": [ + 102, + 179, + 861, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1The Australian National University 2Technion Israel Institute of Technology", + "bbox": [ + 173, + 208, + 800, + 227 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{chamin.hewa, dylan.campbell, stephen.gould}@anu.edu.au sitzikbs@gmail.com", + "bbox": [ + 156, + 229, + 807, + 243 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 279, + 310, + 294 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A neural signed distance function (SDF) is a convenient shape representation for many tasks, such as surface reconstruction, editing and generation. However, neural SDFs are difficult to fit to raw point clouds, such as those sampled from the surface of a shape by a scanner. A major issue occurs when the shape's geometry is very different from the structural biases implicit in the network's initialization. In this case, we observe that the standard loss formulation does not guide the network towards the correct SDF values. We circumvent this problem by introducing guiding points, and use them to steer the optimization towards the true shape via small incremental changes for which the loss formulation has a good descent direction. We show that this point-guided homotopy-based optimization scheme facilitates a deformation from an easy problem to the difficult reconstruction problem. We also propose a metric to quantify the difference in surface geometry between a target shape and an initial surface, which helps indicate whether the standard loss formulation is guiding towards the target shape. Our method outperforms previous state-of-the-art approaches, with large improvements on shapes identified by this metric as particularly challenging.", + "bbox": [ + 75, + 311, + 473, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 207, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Point cloud reconstruction using a neural signed distance function (SDF) is a popular approach due to its simplicity and flexibility. Such methods show impressive performance improvements for cases with significant noise, outliers, missing regions or misalignment [20]. However, they are still unable to outperform classical methods on clean and relatively dense input data [20, 25], especially when the shape exhibits challenging geometry. For example, thin surfaces near each other (see Fig. 1 bottom) or large concave regions with small openings (see Fig. 1 top).", + "bbox": [ + 75, + 702, + 468, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We address the task of reconstruction from raw point clouds, i.e., without ground-truth normal vectors. We observe that the standard loss formulation used for the task", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/568962fbab4f03017bee74cb8c54b85aa592cebfe0a129c6eced93b2fd7b8793.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 277, + 630, + 380 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/314fa1430c52073e9e1807122b3c06b6acf3414afce1c190ba025a80c7b2fce7.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 503, + 382, + 629, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/90ed2fd69971a6d971725560340f526be3dd1c2c5f4ab4f672cfc1cf32bd20ac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 277, + 758, + 380 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d3f655f805eb6267a50b7ba88133c8a0e54bbf7cb9ad1ab81ae84f063b9db526.jpg", + "image_caption": [ + "SDF Baseline" + ], + "image_footnote": [], + "bbox": [ + 633, + 382, + 756, + 454 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e4e6965f1e6a3fbb171ec5f0f9b0ce132432aa1497383c6454b50f4313c9759.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 277, + 890, + 380 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/630c853cfb726aa5c3097518dbdad5c801e86ef4e46b0de497bc5180cf3bdb89.jpg", + "image_caption": [ + "Ours", + "Figure 1. Given a point cloud without ground-truth normals (left), neural SDF optimization for surface fitting frequently gets trapped in local minima (middle). Note that these two shapes have geometry very different to a sphere, which causes the loss right after spherical initialization to not provide a good descent direction towards the target shape (see Sec. 3.3). Our point-guided homotopy-based approach provides a principled way to avoid this issue and improve reconstruction quality (right)." + ], + "image_footnote": [], + "bbox": [ + 761, + 382, + 887, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "does not give a good descent direction towards the target SDF values, especially when the initialization does not align with the target geometry. Since most methods initialize to a sphere to bias the optimization result towards a bounded shape, and rely on this bias to find a good descent direction, their performance can be poor if the input shape has very different geometry to a sphere (see Fig. 1).", + "bbox": [ + 496, + 607, + 890, + 712 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instead we propose a point-guided SDF (PG-SDF) approach, where we introduce guiding points to represent an intermediate surface for the optimization to target. By incrementally moving the guiding points towards the sampled input and optimizing the network to their new location, we ensure that the loss formulation gives a good descent direction during optimization. We eventually converge the guiding points to the input points, leading the optimization stably towards the target SDF. We also propose", + "bbox": [ + 496, + 713, + 890, + 849 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1To avoid confusion, in this paper we use the term normal direction to refer to vectors in the normalized gradient field of the SDF and descent direction for the negative gradient of the loss function.", + "bbox": [ + 500, + 862, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21456", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e8ebb0b1e94055c8da1407da7f88459c925bf1d73f6ee2fc30e51637f273fde0.jpg", + "image_caption": [ + "No Guidance", + "Small Steps (between 2a and 2b)", + "Figure 2. Reconstructing a 2D surface using a neural SDF, without (1a-e) and with (2a-e,3a-f) our proposed point guidance. Note that our point guidance has two parts, converging to level sets (2) and taking small steps in between (3). The input points $\\mathcal{X}$ are black, the guiding points $\\mathcal{V}$ are green, and the network's level sets are drawn as contour lines with the zero level set $\\mathcal{R}$ in bold. (1a-b) The network deforms from the sphere initialization to one whose zero level set is close to $\\mathcal{X}$ . (1c) The network only makes local changes near $\\mathcal{X}$ , gradually interpolating $\\mathcal{X}$ by adding complexity. (1d-e) $\\mathcal{X}$ is fully interpolated, but the result is unsatisfactory. (2a) Our initialization. (2b-d) Our method after convergence to each intermediate level set. (2e) Our method after optimizing on the input points. (3a-f) The small steps taken by our method while reaching the first intermediate level set of radius $\\delta_0$ . Each row shows a single step, where the guiding points are first moved a short distance (left) and then the network is optimized to match this (right)." + ], + "image_footnote": [], + "bbox": [ + 80, + 102, + 893, + 311 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a metric—the percentage of self-intersecting outward normals (SION%)—to quantify the difference between the surface geometry of a target shape and that of another surface, such as the sphere initialization. We use this metric to determine which shapes are likely to be difficult for neural SDF methods, and why the optimization steps in our method are robust. Our contributions are:", + "bbox": [ + 75, + 464, + 468, + 568 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. a point-guided optimization approach for surface reconstruction from point clouds without normals;", + "2. a metric to quantify differences between surfaces, which can be used to identify the most challenging shapes to reconstruct; and", + "3. an interpretation of the algorithm as a homotopy method, providing a justification for the design decisions and insight into the failure modes of existing approaches." + ], + "bbox": [ + 76, + 570, + 468, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 707, + 218, + 722 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Surface reconstruction from point clouds is a fundamental problem in computer vision. We restrict our attention to methods that optimize using generic priors, rather than methods that learn reconstruction priors from a dataset [19, 45] and are sensitive to domain shift.", + "bbox": [ + 75, + 733, + 468, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Early approaches [1, 7, 10, 24] directly triangulated point clouds, with provable guarantees given dense input points with no defects. However, the limitation of vertices being input points make them impractical for even small levels of imperfection [6], and the result is often not watertight. A less restrictive class of approaches is implicit field methods", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[9, 22, 23, 32, 34], where an implicit function is defined over the domain to represent the reconstructed surface. Such methods often use a carefully defined set of basis functions, and optimize for an energy function with respect to the basis function parameters. However they usually rely on normal vectors as inputs, allowing efficient optimization with linear solvers, such as Poisson Surface Reconstruction [23] and its screened version [22].", + "bbox": [ + 496, + 464, + 890, + 584 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural implicit methods, which were popularised by DeepSDF [35] and Occupancy Networks [29], are promising as they provide more modeling and optimization flexibility. Rather than creating basis functions tailored to the input, the network is fixed and can adapt its representational ability through optimization. Furthermore, as they are optimized by gradient descent, they can work with any differentiable loss. This flexibility has led to learned shape spaces that allow for strong learned biases and interpolation [21, 26, 35, 47]. However, while many neural methods are able to perform better than non-neural approaches when the input has defects, they often perform worse when the data is clean and dense [20]. A major issue is that gradient descent optimization is not guaranteed to converge to a global optimum. Furthermore, many methods for the surface reconstruction task [2-4, 15, 41] use losses that are difficult for gradient descent to optimize. As the reason these losses are hard to optimize is fundamental to our method, we examine this issue and related loss formulations in Sec. 3.3.", + "bbox": [ + 496, + 590, + 892, + 878 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method follows a line of work that attempts to", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21457", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "improve upon these issues for reconstruction from points clouds without normals. There are three major methods that are competitive for this task, DiGS [5], SAP [39] and OG-INR [25]. DiGS and OG-INR are neural SDF methods. In order to avoid the difficulties of SDF optimization, DiGS [5] changes the optimization landscape by adding strong regularization at the start, and slowly annealing the regularization to gently change the optimization landscape back to the correct one. OG-INR [25] avoids local minima by first discretizing the problem and solving for inside-outside labels. It then uses this discrete solution to get an approximate SDF that makes it easier to optimize the original SDF. SAP [39] does not use neural methods or SDFs, and instead minimizes a chamfer loss on points and normals directly. This is related to our approach as we also use points and SDF-derived normals to guide our SDF optimization. However, rather than using a chamfer loss, which we find gets trapped in bad local minima, we use a more nuanced strategy to move our guiding points, outlined in Sec. 4.1.", + "bbox": [ + 75, + 90, + 472, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another highly related approach is Point2Mesh [17], which deforms an enclosing mesh onto the point cloud. Like SAP, they use a chamfer loss to guide the deformation, however they note that this loss does not easily enter concavities. To address this, they introduce a beam gap loss, which guides mesh vertices towards input points in the inward normal direction if they are not already well matched by chamfer distance. Our deformation strategy, in contrast, is based purely on explicitly matching points in the inward normal direction. Our approach also avoids a major shortcoming of Point2Mesh, the reconstruction output must have the same genus as the initial mesh.", + "bbox": [ + 75, + 378, + 472, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 573, + 217, + 588 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Notation and Definitions", + "text_level": 1, + "bbox": [ + 76, + 597, + 302, + 612 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We denote the Euclidean inner product as $\\langle p,q\\rangle = p^{\\mathsf{T}}q$ , the Euclidean distance as $d(p,q) = \\| p - q\\| _2$ , a unit vector as $\\hat{v} = v / \\| v\\|$ , the cosine similarity between two vectors as $s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle$ , and the distance from a point $p$ to a set $A$ by $d(p,A) = d_A(p) = \\inf_{q\\in A}d(p,q)$ .", + "bbox": [ + 76, + 619, + 468, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The chamfer distance $d_{C}$ is a common measure of the distance between two discrete point sets $P$ and $Q$ , defined by the average of two one-sided chamfer distances", + "bbox": [ + 75, + 696, + 468, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd _ {C} (P, Q) = \\frac {1}{2} \\left(d _ {\\vec {C}} (P, Q) + d _ {\\vec {C}} (Q, P)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 750, + 468, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "each averaging the distance over one set to the other set", + "bbox": [ + 76, + 786, + 442, + 801 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd _ {\\vec {C}} (P, Q) = \\frac {1}{| P |} \\sum_ {p \\in P} d (p, Q). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 809, + 468, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The chamfer distance can also be used between two surfaces, $A$ and $B$ , in which case the chamfer distance is taken over uniform samplings, $U_A \\sim U(A)$ and $U_B \\sim U(B)$ .", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A signed distance function (SDF) $F_{\\mathcal{V}}: \\mathcal{D} \\to \\mathbb{R}$ of a bounded, open volume $\\mathcal{V} \\subset \\mathcal{D}$ is a scalar function defined everywhere on $\\mathcal{D}$ . $F_{\\mathcal{V}}(z)$ is the distance from $z$ to the closest point on the boundary $\\partial \\mathcal{V}$ , with a negative sign if $z \\in \\mathcal{V}$", + "bbox": [ + 496, + 90, + 893, + 152 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\mathcal {V}} (z) = (- 1) ^ {[ [ z \\in \\mathcal {V} ] ]} d (z, \\partial \\mathcal {V}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 169, + 890, + 189 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the Iverson bracket $\\llbracket X\\rrbracket$ is 1 if $X$ is true and 0 otherwise. The level set $L_{a}$ is the set of points that have a signed distance of $a$ from $\\partial \\mathcal{V}$ , i.e.,", + "bbox": [ + 496, + 194, + 893, + 239 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {a} = \\{z \\in \\mathcal {D} \\mid F _ {\\mathcal {V}} (z) = a \\}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 246, + 890, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The exterior level set $\\Omega_{a}$ ( $a > 0$ ) is the subset of $L_{a}$ such that for each $p \\in L_{a}$ there is a connected path from a point on the boundary of $\\mathcal{D}$ to $p$ that only intersects $L_{a}$ at $p$ .", + "bbox": [ + 496, + 268, + 893, + 315 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 321, + 702, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal{X} = \\{x_i\\}_{i\\in I}$ be a point cloud sampled from a surface $S\\subset \\mathcal{D}$ where $\\mathcal{D}\\subset \\mathbb{R}^3$ is compact. We often refer to $S$ as the target shape, and assume that it is watertight, i.e., $S = \\partial \\mathcal{V}$ of some open volume $\\mathcal{V}\\subset \\mathcal{D}$ . We wish to reconstruct $S$ from the point cloud $\\mathcal{X} = \\{x_i\\}$ . Note that no per-point surface normals or scanner information is provided.", + "bbox": [ + 496, + 344, + 893, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We choose to represent our reconstructed surface $\\mathcal{R} \\subset \\mathcal{D}$ using an implicit neural representation $\\Phi$ . Specifically we define $\\mathcal{R} = \\{z \\in \\mathcal{D} \\mid \\Phi(z, \\theta) = 0\\}$ where $\\theta$ are the parameters of the neural network $\\Phi$ . Thus we want to minimize the chamfer distance between $\\mathcal{S}$ and $\\mathcal{R}$ . Since we do not know $\\mathcal{S}$ , we instead compute the distance to our input points $d_{C}(\\mathcal{X}, \\mathcal{R}) = d_{C}(\\mathcal{X}, U_{\\mathcal{R}})$ , where $U_{\\mathcal{R}}$ is a uniform sampling from $\\mathcal{R}$ . Furthermore we choose to optimize the implicit function $\\Phi$ to approximate the true signed distance function $F_{\\mathcal{V}}$ of the volume $\\mathcal{V}$ . As $\\mathcal{V}$ is unknown, during optimization we care about ensuring that $\\Phi$ is a valid SDF to some open volume $\\mathcal{U}$ for which $\\mathcal{X}$ is an approximate sampling, i.e., $\\Phi \\approx F_{\\mathcal{U}}$ and $d_{C}(\\mathcal{X}, \\partial \\mathcal{U})$ is small (note $\\partial \\mathcal{U} = \\mathcal{R}$ ). Thus our overall optimization problem is", + "bbox": [ + 496, + 435, + 892, + 647 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l l} \\operatorname {m i n i m i z e} _ {\\theta} & d _ {C} (\\mathcal {X}, \\partial \\mathcal {U}) \\\\ \\text {s u b j e c t t o} & \\Phi (x, \\theta) = F _ {\\mathcal {U}} (x). \\end{array} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 652, + 890, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Why SDFs? We choose SDFs over other popular implicit functions like indicator or occupancy functions [22, 23, 29, 38] or unsigned distance functions (UDFs) [12, 16, 49] for several reasons. First, SDFs and UDFs constrain the possibilities for $\\Phi$ , and are fairly smooth (unlike indicator functions). This helps with regularizing $\\mathcal{R}$ and ensures that they can be represented by neural networks, which are biased to be smooth. Previous works have shown that neural SDFs empirically perform better than neural occupancy functions [51]. Second, SDFs allow for distance and direction to the surface queries, which we make use of in our algorithm. Last, the signed aspect of SDFs guarantee the watertight criteria compared to UDF, and make it easier to mesh using algorithms like marching cubes [27].", + "bbox": [ + 496, + 688, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21458", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Neural SDF Formulation", + "text_level": 1, + "bbox": [ + 76, + 90, + 307, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since neural SDFs are coordinate networks, each coordinate is processed independently. During gradient descent each coordinate seeks to minimize its loss locally, and is only affected by changes in nearby coordinates due to the network's inherent smoothness bias. Thus information propagation through the domain (from the smoothness bias) is slow, and optimization is only effective if the loss provides clear guidance. Specifically, if the descent direction of the loss with respect to its SDF input value at a coordinate gives an approximate descent direction towards the target SDF value at that coordinate. However whether or not the loss provides a good descent direction depends on whether the geometry of the current state of the network aligns with the geometry of the target shape (see Fig. 2 top left for when they do not align and thus optimization gets stuck).", + "bbox": [ + 75, + 113, + 468, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now discuss this observation in relation to currently used neural SDF losses. When optimizing neural SDFs for point clouds without normals, the main losses are", + "bbox": [ + 75, + 340, + 468, + 385 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {X}) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) | \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 392, + 468, + 425 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {e i k}} (\\theta) = \\sum_ {z \\in \\mathcal {D}} | \\| \\nabla_ {z} \\Phi (z, \\theta) \\| _ {2} - 1 | \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 428, + 468, + 460 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| x _ {\\mathcal {R}} ^ {\\star} (z) - x _ {\\mathcal {X}} ^ {\\star} (z) \\| _ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 463, + 468, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{\\mathcal{R}}^{\\star}(z) = z - \\Phi(z)\\widehat{\\nabla_z\\Phi(z)}$ and $x_{\\mathcal{X}}^{\\star}(z) = \\arg \\min_{x\\in \\mathcal{X}}d(z,x)$ . The first two losses were proposed by IGR [15] and the last one was proposed by Neural Pull [4] (further details in the supplement). The zero level set loss $\\mathcal{L}_{\\mathrm{ZLS}}$ gives a perfect descent direction to the target SDF values for the points in $\\mathcal{X}$ . However, for other points in the domain, the loss formulation may not give a descent direction towards the target SDF value. The Eikonal loss $\\mathcal{L}_{\\mathrm{eik}}$ guides towards scaling the SDF gradient, and does not change its direction unless forced to by the optimization of nearby points. Thus for a point $z\\in \\mathcal{D}$ , if the network's current normal directions in the region around $z$ is in the opposite direction to what the target SDF normals are around $z$ , then at $z$ this loss does not guide towards the target SDF values. The neural pull loss $\\mathcal{L}_{\\mathrm{pull}}$ has two value-gradient pairs that will minimize its loss (one where the normal points towards $x_{\\mathcal{X}}^{\\star}$ and one where it points away), so the loss will guide towards the closer one, which may not be the target.", + "bbox": [ + 75, + 503, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As a result, an important part of these methods is spherical initialization [2], where the network is initialized roughly to the SDF of a sphere. If the shape's geometry is similar to a sphere, then the initialized normal directions in the network are mostly in the correct direction, so $\\mathcal{L}_{\\mathrm{eik}}$ and $\\mathcal{L}_{\\mathrm{pull}}$ guide towards the correct SDF value. When the shape's geometry is very different to a sphere resulting in large regions where the initialized normal directions are", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/010afb844fbfe24e3cf7bb6e4af5c2972544629a95bc1c4aa059ff075d825bc7.jpg", + "image_caption": [ + "Figure 3. Surface $\\mathcal{S}$ and surrounding surface $\\mathcal{R}$ , with outward normal directions for some points on $\\mathcal{S}$ shown, and which ones are SIONs relative to $\\mathcal{R}$ shown in red." + ], + "image_footnote": [], + "bbox": [ + 602, + 92, + 790, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "very different to the target normal directions, then the loss does not provide a good descent direction in those regions. As a result, optimization often converges to a local minimum close to the initialization, such as in Fig. 2 (top left).", + "bbox": [ + 498, + 287, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Shape Reachability", + "text_level": 1, + "bbox": [ + 500, + 358, + 683, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "From the analysis in the previous subsection, we are interested in whether the current state of a network provides similar normal directions to the SDF of the target shape, so that the loss provides a good descent direction towards the target SDF values. Let us assume that the current state of the network is roughly the SDF to some surface $\\mathcal{R}$ surrounding the target shape's surface $S$ . One way of quantifying whether the normal directions are similar is to determine if points on $S$ can \"reach\" $\\mathcal{R}$ by travelling in their outward normal direction (see Fig. 3). If $S$ has large concavities and the outward surface normal of most points in that concavity does not reach $\\mathcal{R}$ before it self-intersects, then the current normal directions of the network are likely to be poor.", + "bbox": [ + 498, + 382, + 890, + 577 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "More formally, if $P_{\\mathcal{S}}$ and $P_{\\mathcal{R}}$ are samplings of $\\mathcal{S}$ and $\\mathcal{R}$ and for each $p \\in P_{\\mathcal{S}}$ we have a known outward unit normal $n_p$ , then for a point $p \\in P_{\\mathcal{S}}$ we can construct around the outward normal a thin cylinder", + "bbox": [ + 498, + 578, + 890, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {C} _ {p} = \\{z \\in \\mathcal {D} \\mid \\| p + t n _ {p} - z \\| \\leq \\varepsilon , \\langle z - p, n _ {p} \\rangle \\geq 0 \\}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 647, + 890, + 666 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By the assumption of $\\mathcal{R}$ surrounding $S$ and $P_{\\mathcal{R}}$ being a dense sampling of $\\mathcal{R}$ , we note that $\\mathcal{C}_p \\cap P_{\\mathcal{R}} \\neq \\emptyset$ . Then we consider $p$ to have a self-intersecting outward normal (SION) with respect to $P_{\\mathcal{R}}$ if its normal direction intersects its own shape before it intersects $\\mathcal{R}$ : $\\exists p' \\in P_{\\mathcal{S}}$ such that $p' \\in \\mathcal{C}_p$ and $\\forall q \\in \\mathcal{C} \\cap P_{\\mathcal{R}}$ we have that $\\| p - p' \\|_2 < \\| p - q \\|$ . We then use the percentage of points in $p_{\\mathcal{S}}$ that have SIONs with respect to $P_{\\mathcal{R}}$ as a measure of how dissimilar the geometry of $S$ is to $\\mathcal{R}$ , which we denote $\\mathrm{SION}(S; \\mathcal{R})$ , where a high value indicates dissimilarity.", + "bbox": [ + 498, + 672, + 890, + 824 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When $\\mathcal{R}$ is not specified and $S$ is clear from context, we will use SION as a shorthand for $\\mathrm{SION}(S; \\mathcal{R})$ , with $\\mathcal{R}$ assumed to be any sphere surrounding $S$ . The two point clouds in Fig. 1 have a high SION, which indicates that their geometry is very different to a sphere and that optimization", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21459", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from a spherical initialization is likely to be difficult.", + "bbox": [ + 76, + 90, + 426, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Point-Guided SDF", + "text_level": 1, + "bbox": [ + 76, + 122, + 256, + 138 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The key idea of our method is to slowly converge the surface of reconstruction $\\mathcal{R}$ towards the input points $\\mathcal{X}$ until it interpolates $\\mathcal{X}$ , while maintaining $\\Phi$ as a valid SDF to the volume enclosed by $\\mathcal{R}$ (see Fig. 2). We do this by guiding $\\mathcal{R}$ towards level sets (Fig. 2:2a-e) and taking small steps towards reaching each level set (Fig. 2:3a-f, Fig. 4). At each step we move guiding points $\\mathcal{Y}$ , which represent the surface $\\mathcal{R}$ , a small distance towards $\\mathcal{X}$ (Fig. 4c) and then optimize $\\Phi$ to interpolate the new $\\mathcal{Y}$ positions, thus defining the new surface of reconstruction $\\mathcal{R}$ over which $\\mathcal{Y}$ is resampled (Fig. 4d). Our full algorithm is shown in Algorithm 1.", + "bbox": [ + 76, + 148, + 468, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since each movement of the guiding points is small, the geometry of the moved guiding points $\\mathcal{V}$ should be similar to the network's current surface $\\mathcal{R}$ , and $\\mathrm{SION}(\\mathcal{V};\\mathcal{R})$ should be low. Thus optimizing the network to reconstruct the updated $\\mathcal{V}$ should be robust (unlikely to converge to local minima) as the optimization is likely to have a clear descent direction from the loss at most points.", + "bbox": [ + 76, + 316, + 468, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In Sec. 4.1 we outline how to move the guiding points $\\mathcal{Y}$ one step closer to the input points $\\mathcal{X}$ (Fig. 4a-c). In Sec. 4.2 we outline how to optimize the network $\\Phi$ to interpolate the new guiding point locations (Fig. 4d). Finally, in Sec. 4.3 we analyze our method within the homotopy framework.", + "bbox": [ + 76, + 424, + 468, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Preprocessing $\\mathcal{X}$ . Following standard practice, we first center and (isotropically) scale the shape to fit in a centered ball. After scaling, we calculate the point cloud's approximate sampling radius $\\delta_{\\mathcal{X}}$ conservatively by calculating the distance to the four closest neighbors for each $x \\in \\mathcal{X}$ and averaging the highest $5\\%$ of all such distances. We use this radius extensively in our method.", + "bbox": [ + 76, + 507, + 468, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Initialization. We first initialize our network to the exterior level set of radius $\\delta_{\\mathrm{init}} = 16\\delta_{\\mathcal{X}}$ . We provide intuition into why we can do this robustly in Sec. 4.3, and provide details on how to make this more efficient in the supplement.", + "bbox": [ + 76, + 619, + 468, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Moving the Guiding Points", + "text_level": 1, + "bbox": [ + 76, + 693, + 320, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now describe how to move the guiding points $y \\in \\mathcal{V}$ towards the input points $\\mathcal{X}$ . At a high level, each step we move $\\mathcal{V}$ closer to an exterior level set of radius $\\delta$ , $\\Omega_{\\delta}$ , and when $\\mathcal{R}$ has converged to $\\Omega_{\\delta}$ we reduce $\\delta$ (see Algorithm 1).", + "bbox": [ + 76, + 717, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since we are moving $y \\in \\mathcal{V}$ to guide the surface $\\mathcal{R}$ , we only move each $y$ in the inwards normal direction of $\\mathcal{R}$ . Next, since we are moving towards an exterior level set $\\Omega_{\\delta}$ of $\\mathcal{X}$ , for each $y \\in \\mathcal{V}$ we find the closest input point in the inwards normal direction $x^{\\star}(y) \\in \\mathcal{X}$ , and use this to determine the target point $\\omega^{\\star}(y)$ on $\\Omega_{\\delta}$ that we move towards. Finally, since we want to move the surface $\\mathcal{R}$ slowly, we have a maximum step size for each movement.", + "bbox": [ + 75, + 780, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Closest point in the inward direction. We first define $x^{\\star}(y)$ (see Fig. 4a-b). As we are moving in the inward normal direction, i.e., $-n_y$ where $n_y = \\widehat{\\nabla_y\\Phi(y)}$ , we want to move $y$ based on the closest point $x \\in \\mathcal{X}$ in the inward normal direction $-n_y$ . We define the inward normal definition by setting a cosine similarity threshold $a_y \\geq 0$ to define a cone $C_y$ supported at $y$ emanating in the direction $-n_y$ ,", + "bbox": [ + 496, + 90, + 890, + 202 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC _ {y} = \\left\\{z \\mid s (- n _ {y}, z - y) \\geq a _ {y} \\right\\}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 209, + 890, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However as $y$ gets very close to points in $\\mathcal{X}$ , it is unlikely that any of those nearby points stay within this cone. Thus we also consider the half ball $H_{y}$ of radius $2\\delta_{\\mathcal{X}}$ containing points close to $y$", + "bbox": [ + 496, + 234, + 890, + 296 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nH _ {y} = \\left\\{z \\mid \\| x - y \\| _ {2} \\leq 2 \\delta_ {\\mathcal {X}} \\wedge s (- n _ {y}, z - y) \\geq 0 \\right\\}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 304, + 890, + 321 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus our target point $x^{\\star}(y)$ is given by", + "bbox": [ + 500, + 329, + 759, + 345 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {\\star} (y) = \\underset {x \\in \\mathcal {X} \\cap \\left(C _ {y} \\cup H _ {y}\\right)} {\\arg \\min } \\| x - y \\| _ {2}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 354, + 890, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Moving towards $\\Omega_{\\delta}$ . As $x^{\\star}(y)$ is our closest (inward) point, a reasonable location for a point in $\\Omega_{\\delta}$ can be computed by moving $\\delta$ away from $x^{\\star}$ towards $y$", + "bbox": [ + 496, + 390, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\omega^ {\\star} (y) = \\left(\\| x ^ {\\star} - y \\| _ {2} - \\delta\\right) \\widehat {\\left(x ^ {\\star} - y\\right)}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 445, + 890, + 465 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We move towards $\\omega^{\\star}$ with a maximum step size of $s_m$ so that the movement step is small and easy to optimize. Thus our final point $y^\\prime$ (see Fig. 4b) is", + "bbox": [ + 496, + 473, + 890, + 518 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny ^ {\\prime} = y - \\operatorname {c l i p} (\\langle \\omega^ {\\star} (y), - n _ {y} \\rangle , s _ {m}) n _ {y} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 527, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\operatorname{clip}(a, \\varepsilon)$ projects $a$ to the interval $[- \\varepsilon, \\varepsilon]$ .", + "bbox": [ + 496, + 553, + 823, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reducing $\\delta$ . After initialization, we set $\\delta = \\delta_0$ as our next target level set. Once $\\mathcal{V}$ has finished moving towards $\\Omega_{\\delta}$ and $\\mathcal{R}$ has converged, we decrease the current $\\delta$ by half and start moving $\\mathcal{V}$ towards the new exterior level set. We do this until $\\delta$ reaches $\\delta_f$ . We use $\\delta_0 = 4\\delta_{\\mathcal{X}}$ , $\\delta_f = \\delta_{\\mathcal{X}}$ . We then abandon $\\mathcal{V}$ and optimize directly on $\\mathcal{X}$ .", + "bbox": [ + 496, + 575, + 890, + 666 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Optimizing the Network", + "text_level": 1, + "bbox": [ + 500, + 675, + 723, + 691 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now have the points $\\mathcal{V}$ to guide where our new surface should be. Furthermore, we have an approximate normal $n_y$ for each $y\\in \\mathcal{V}$ given by $\\Phi$ , whose direction should be useful as the SION between the new position of the points relative to the previous positions is low. We use this to estimate an approximate SDF", + "bbox": [ + 496, + 698, + 890, + 789 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {F} _ {\\mathcal {V}} (z) = (- 1) ^ {[ s (z - y (z), n _ {y (z)}) \\geq 0 ]} d (z, y (z)) \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 796, + 890, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y(z) = \\arg \\min_{y\\in \\mathcal{Y}}d(z,y)$ and $s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle$ is cosine similarity. We guide towards these values using", + "bbox": [ + 496, + 825, + 890, + 857 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s d f}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| \\Phi (z, \\theta) - \\tilde {F} _ {\\mathcal {V}} (z) \\| _ {2}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 864, + 890, + 897 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21460", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f50af9a8f7141de56ff4290caeb08665cf3282a23906da5a2ee08e01ce4a8bd3.jpg", + "image_caption": [ + "Figure 4. One iteration of Algorithm 1, steps 6-8. (a) Given the current value of our network $\\Phi$ (the contours) and our guiding points $\\mathcal{V}$ (the green points), for each $y\\in \\mathcal{V}$ we calculate a half ball $H_{y}$ and a cone $C_y$ in the inside normal direction to find an input points $x\\in \\mathcal{X}$ (black points) to move towards (shown for 3 points, with one highlighted in red). (b) We find the closest input point $x^{\\star}(y)\\in \\mathcal{X}$ within $H_{y}\\cap \\mathcal{C}_{y}$ , and use this to calculate the new position $y^\\prime$ for each $y\\in \\mathcal{V}$ (shown for all points). (c) The result after each $y\\in \\mathcal{V}$ has been moved. (d) The network $\\Phi$ is optimized on the new guiding points, and $\\mathcal{V}$ is resampled to densely cover the new zero level set $\\mathcal{R}$ ." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 890, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Furthermore, our input points $\\mathcal{X}$ should be at distance $\\delta$ from $\\mathcal{Y}$ and should be inside, so we add a loss term", + "bbox": [ + 75, + 351, + 470, + 382 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) + \\delta |. \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 388, + 468, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Thus our overall loss term formulation is", + "bbox": [ + 76, + 429, + 349, + 444 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\theta , \\mathcal {X}, \\mathcal {Y}, \\delta) = \\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) + \\mathcal {L} _ {\\mathrm {e i k}} (\\theta) +\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 455, + 459, + 470 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\mathcal {L} _ {\\mathrm {s d f}}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {Y}). \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 473, + 468, + 491 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Relevant details (e.g., loss term weightings, domain sampling procedure, optimizer settings) are in the supplement.", + "bbox": [ + 75, + 500, + 468, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Finally, we resample $\\mathcal{V}$ in the new zero level set $\\mathcal{R}$ (Fig. 4f) so that it densely samples it. After this process has finished (i.e., when $\\Phi$ has converged for $\\delta = \\delta_f$ ), we optimize $\\Phi$ on the input points $\\mathcal{X}$ using the loss in Eq. (18). Here we do not use the approximate SDF term, as $\\mathcal{X}$ is likely to have more imperfections that our guiding points.", + "bbox": [ + 75, + 531, + 468, + 622 + ], + "page_idx": 5 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Point-Guided SDF" + ], + "code_body": "1: procedure PG-SDF( $\\mathcal{X}$ ) \n2: Center $\\mathcal{X}$ , scale $\\mathcal{X}$ and compute sampling radius $\\delta_{\\mathcal{X}}$ \n3: $\\mathcal{Y}, \\mathcal{N}_{\\mathcal{Y}}, \\Phi \\gets$ Initialization $(\\mathcal{X}, \\delta_{\\mathrm{init}})$ \n4: $\\delta \\gets \\delta_0$ \n5: while $\\delta \\geq \\delta_f$ do \n6: Move $\\mathcal{Y}$ using Eq. (14) \n7: Optimize $\\Phi$ to match $\\mathcal{Y}$ \n8: Resample $\\mathcal{Y}$ on new $\\mathcal{R}$ \n9: Query $\\Phi$ for normals $\\mathcal{N}_{\\mathcal{Y}}$ \n10: if $\\Phi$ 's zero level set has not changed then \n11: $\\delta \\gets \\frac{1}{2} \\delta$ \n12: end if \n13: end while \n14: Optimize $\\Phi$ on $\\mathcal{X}$ \n15: return $\\Phi$ \n16: end procedure", + "bbox": [ + 81, + 655, + 468, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Interpretation as a Homotopy Method", + "text_level": 1, + "bbox": [ + 500, + 351, + 828, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "One way to analyze this method is in the context of a homotopy method [33]. Here, we wish to solve a difficult problem $M(\\theta) = 0$ for $\\theta$ , and instead consider the homotopy map $H(\\theta, t) = tM(\\theta) + (1 - t)N(\\theta)$ where $N(\\theta) = 0$ is easy to solve and $t \\in [0,1]$ . This forms a homotopy between the problems $M(\\theta) = H(\\theta, 1)$ and $N(\\theta) = H(\\theta, 0)$ as we can now continuously deform one problem into the other by varying $t$ . By taking small steps along the zero path, the trajectory of points $(\\theta, t)$ for which $H(\\theta, t) = 0$ , we can reach the solution to $M(\\theta)$ .", + "bbox": [ + 496, + 375, + 890, + 525 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For our method, we start by solving the easier problem $\\mathcal{L}(\\theta, \\mathcal{Y}_0) = 0$ where $\\mathcal{Y}_0$ is our initial set of guiding points. Our goal is to solve the hard problem $\\mathcal{L}(\\theta, \\mathcal{X}) = 0$ . To see that our method is a homotopy method, note that our guiding points $\\mathcal{Y}$ are facilitating a topological homotopy from $\\mathcal{Y}_0$ to our input points $\\mathcal{X}$ . Thus we can parameterize our zero path using $\\mathcal{Y}$ . It is given by $(\\theta(\\mathcal{Y}), t(\\mathcal{Y}))$ where", + "bbox": [ + 498, + 526, + 890, + 632 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\theta (\\mathcal {Y}) \\text {s a t i s f i e s} \\mathcal {L} (\\theta (\\mathcal {Y}), \\mathcal {Y}) = 0 \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 642, + 890, + 659 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nt (\\mathcal {Y}) = \\frac {d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right) - d _ {C} \\left(\\mathcal {Y} , \\mathcal {X}\\right)}{d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right)}. \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 662, + 890, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that at initialization $\\mathcal{V} = \\mathcal{V}_0$ and we have $t(\\mathcal{V}_0) = 0$ , while at termination $\\mathcal{V} = \\mathcal{X}$ and we have $t(\\mathcal{X}) = 1$ . Each time we update $\\mathcal{V}$ , we are traversing the zero path. If we take $n$ steps to reach the final exterior level set of radius $\\delta_{\\mathcal{X}}$ , then we visit $n + 2$ points along the zero path parameterized by the sequence $\\mathcal{V}_0, \\mathcal{V}_1, \\ldots, \\mathcal{V}_n, \\mathcal{X}$ .", + "bbox": [ + 496, + 703, + 890, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To see why this works well in practice, we need to show that solving $H(\\theta(\\mathcal{Y}_{k+1}), t(\\mathcal{Y}_{k+1}))$ for $\\theta(\\mathcal{Y}_{k+1})$ given $\\theta(\\mathcal{Y}_k)$ is easy, and solving $H(\\theta(\\mathcal{Y}_0), t(\\mathcal{Y}_0))$ for $\\theta(\\mathcal{Y}_0)$ is easy. To see the former, note that we move our guiding points $\\mathcal{V}$ only a small distance from $\\mathcal{V}_k$ to $\\mathcal{V}_{k+1}$ , and that $\\mathrm{SION}(\\mathcal{Y}_{k+1};\\mathcal{V}_k)$ is small by construction. Thus, by the analysis in Secs. 3.3 and 3.4, the relative optimization problem is easy. To see the", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21461", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3f37c96cba253e0cec25111a07694230dd9d9b2e04f27bb1bdbdf1e1c07d8226.jpg", + "image_caption": [ + "Figure 5. Qualitative results on ShapeNet. Top: Intermediate results as our method converges to different level sets $\\Omega_{\\delta}$ . Bottom: Comparison with other methods, for challenging high SION shapes (0.40 for the car and 0.42 for the lamp)." + ], + "image_footnote": [], + "bbox": [ + 80, + 93, + 468, + 375 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "latter, when $\\delta_{\\mathrm{init}} \\gg \\delta_{\\mathcal{X}}$ we can estimate good normals for $\\mathcal{Y}_0$ by taking the displacement from the closest input point. With good normal estimates, $\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}$ is very effective, and so optimization is easy. Furthermore, we note that higher radius exterior level sets are less complex, with smaller SION to an enclosing sphere. We formalize and prove this observation in the supplement.", + "bbox": [ + 75, + 453, + 468, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 573, + 163, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dataset. We evaluate the performance of our method on ShapeNet [11], a large dataset of 3D CAD models. In this dataset, there are many shapes with complex geometries that are challenging to reconstruct, including extremely thin surfaces (sometimes string-like), hollow regions (often with small openings), and shapes with high genus. Previous works [5, 25] have shown that many neural methods fail on these shapes, even when using the ground-truth normals. We use the preprocessed watertight subset of Williams et al. [46], which consists of 13 classes with 20 shapes in each class. For each shape, 100k points are uniformly sampled from the surface and ground-truth normals are provided for each point, which are only used for those methods that require normals. We use these points as the input to our method, and for evaluating the squared chamfer metric. An additional 100k points are uniformly sampled within the domain with ground-truth labels that indicate whether the point is inside or outside the shape, allowing for the interior intersection-over-union (IoU) metric to be calculated. Further experimental details are given in the supplement.", + "bbox": [ + 75, + 598, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4716caa984dfd79357e62fdf329a7ebc97edc28374b6f13447499f348c1c706f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSquared Chamfer ↓IoU ↑
NN nxMeanMedianStdMeanMedianStd
SPSR [22]× T5.44e-51.97e-55.06e-40.99260.99560.0105
IGR [15]✓ T5.12e-41.13e-42.15e-30.81020.84800.1519
SIREN [41]✓ T1.03e-45.28e-51.93e-40.82680.90970.2329
FFN [43]✓ T9.12e-58.65e-53.36e-50.82180.83960.0989
NSP [46]× T5.36e-54.06e-53.64e-50.89730.92300.0871
DiGS+N [5]✓ T2.74e-42.32e-59.90e-40.92000.97740.1992
SDF+N†✓ T3.97e-52.22e-58.98e-50.99150.99510.0141
Ours+N✓ T2.43e-52.15e-51.66e-50.99320.99550.0076
SPSR [22]× E3.76e-34.37e-51.14e-20.71870.97610.3767
SIREN [41]✓ ×3.08e-42.58e-43.26e-40.30850.29520.2014
SAL [2]✓ ×1.14e-32.11e-43.63e-30.40300.39440.2722
DiGS [5]✓ ×1.32e-42.55e-54.73e-40.93900.97640.1262
SAP [39]× ×4.09e-42.46e-52.60e-30.91180.99230.2002
OG-S [25]✓ ×3.75e-52.17e-58.24e-50.96150.98710.1048
OG-N [25]✓ ×5.07e-52.57e-59.39e-50.95930.98700.1057
SDF†✓ ×1.84e-48.15e-42.95e-30.54900.52450.3572
SDF+N†✓ E2.48e-25.89e-55.63e-30.68170.96710.3990
Ours+N✓ E2.79e-24.79e-56.79e-20.70170.97210.3876
Ours✓ ×3.72e-52.40e-55.39e-50.97290.98960.0676
", + "bbox": [ + 498, + 88, + 890, + 362 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Surface reconstruction results on ShapeNet [11]. NN: uses a neural network. $n_x$ : uses ground-truth (T), estimated (E) or no (×) input surface normals. Suffix ‘+N’ denotes normal information added to the underlying method. † Our implementation.", + "bbox": [ + 496, + 368, + 893, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation and Baselines. Our baseline methods use the same implementation framework as our approach (see full details in the supplement) with standard loss formulations. 'SDF' uses $\\mathcal{L}_{\\mathrm{zls}}$ , $\\mathcal{L}_{\\mathrm{eik}}$ , and $\\mathcal{L}_{\\mathrm{pull}}$ while 'SDF+N' additionally uses $\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}$ and $\\mathcal{L}_{\\mathrm{normal}}$ [15]. We also evaluate our methods with estimated normals (using Open3D [50]).", + "bbox": [ + 496, + 441, + 890, + 532 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Surface Reconstruction on ShapeNet", + "text_level": 1, + "bbox": [ + 498, + 542, + 818, + 558 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on the full ShapeNet subset are given in Tab. 1, with qualitative results in Fig. 5. Our proposed method outperforms all prior normal-free methods and even demonstrates improvement when ground-truth normals are available. In particular, our approach gets a significant improvement in mean IoU, with much smaller variance, indicating that our method performs reliably well.", + "bbox": [ + 496, + 565, + 890, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Challenging High-SION Shapes", + "text_level": 1, + "bbox": [ + 498, + 680, + 779, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we analyze the performance of surface reconstruction methods with respect to the SION metric. Fig. 6 shows that the mean IoU degrades significantly as we progressively consider shapes with higher SION scores. While our method also follows this trend, performance degradation is considerably slower, indicating that our method is much more robust to challenging shapes. We report the reconstruction performance on the subset of 20 shapes with the highest SION in Tab. 2. On these most challenging shapes, our approach has a decisive advantage. This demonstrates that our structured optimization approach is able to achieve good reconstructions of the most difficult shapes, without sacrificing performance on easy shapes.", + "bbox": [ + 496, + 703, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21462", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2629c760daeac6654d94d308a61910968f8fd786c3aadcbf08e3c9b0494a5077.jpg", + "image_caption": [ + "Figure 6. Mean IoU for all shapes with a SION higher than a lower bound. The analysis from Secs. 3.3 and 3.4 predicts a significant negative correlation for existing neural SDF methods. Our method weakens this trend considerably." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 464, + 282 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/14061386cdc55fc9bcba1fcae0414483b5192cbb30307615467d4be380c7f490.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodNN\\(n_x\\)Squared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
SPSR [22]×T3.98e-53.92e-51.80e-50.97980.98480.0222
DiGS+N [5]✓T2.09e-47.42e-52.91e-40.81600.87640.2119
\\(\\text{SDF}+\\text{N}^{\\dagger}\\)✓T1.11e-44.84e-51.95e-40.97330.98540.0409
Ours+N✓T4.16e-53.89e-51.86e-50.98220.98650.0148
SPSR [22]×E5.83e-31.25e-31.16e-20.32900.18020.3445
DiGS [5]✓×4.34e-41.71e-45.34e-40.71080.81960.2536
SAP [39]××1.28e-45.84e-51.99e-40.76160.88720.2665
OG-S [25]✓×1.31e-46.50e-51.79e-40.76510.92190.2512
\\(\\text{SDF}^{\\dagger}\\)✓×1.29e-37.75e -41.43e-30.34130.26170.2292
\\(\\text{SDF}+\\text{N}^{\\dagger}\\)✓E5.32e-24.51e-37.03e-20.28960.19770.3288
Ours+N✓E4.89e-27.32e-36.25e-20.31730.23620.3259
Ours✓×5.51e-54.87e-53.12e-50.91530.95980.0906
", + "bbox": [ + 76, + 354, + 468, + 546 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/73e3c84f5cfceb9dfee1fbe8d7ed3a35567e845e31f98e5c6c93e66e5c2f59f0.jpg", + "table_caption": [ + "Table 2. Surface reconstruction results on the 20 highest SION ShapeNet shapes. NN: uses a neural network. $n_x$ : uses ground-truth (T), estimated (E) or no (X) input surface normals. Suffix ‘+N’ denotes adding normal information to the underlying method. † Our implementation." + ], + "table_footnote": [], + "table_body": "
Guidance y0 yδ0 δfSquared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
× × - -2.41e-31.18e-32.65e-30.27950.22550.2078
✓ × - -2.63e-41.91e-42.31e-40.56940.60910.2278
✓ ✓ 429.89e-57.70e-57.95e-50.86570.9163
✓ ✓ 118.08e-57.52e-55.66e-50.85380.9386
✓ ✓ 415.51e-54.87e-53.12e-50.91530.9598
", + "bbox": [ + 76, + 632, + 468, + 733 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation results on the 20 highest SION ShapeNet shapes. $\\mathcal{V}_0$ : uses our SDF initialization strategy instead of spherical initialization [15]. $\\mathcal{V}$ : uses our point guidance strategy. $\\delta_0 / \\delta_f$ : starting and final level set radii, given in multiples of $\\delta_{\\mathcal{X}}$ .", + "bbox": [ + 75, + 738, + 468, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Ablation Study and Runtime", + "text_level": 1, + "bbox": [ + 76, + 814, + 333, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "An ablation study, on the 20 highest-SION shapes of ShapeNet, is reported in Tab. 3. The performance when using a spherical initialization and optimizing with respect to the input points (row 1) is poor. It improves significantly", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c1e7de4b29b4865bd25a908524a6750fb0526d66715e27e1961c33cf06a65f65.jpg", + "image_caption": [ + "Figure 7. Runtime vs SION on ShapeNet for our method. Challenging shapes with high SION take more time to optimize. One outlier (82 min) is truncated for clarity and marked as $\\times$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 85, + 885, + 276 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "when replaced with our high exterior level set initialization (row 2). When point guidance is added (rows 3-5), the performance increases considerably. In particular, stopping point guidance early (when $\\delta_f = 2\\delta_{\\mathcal{X}}$ ) harms performance, as does guiding straight to the final level set target ( $\\delta_0 = \\delta_{\\mathcal{X}}$ ) without first converging to intermediate level set targets. Our gradual homotopy approach performs best by a significant margin, justifying the strategy.", + "bbox": [ + 496, + 340, + 890, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "An unoptimized implementation of our method takes 10 mins on average per ShapeNet shape (a median of 7.4 mins). Convergence time depends strongly on the difficulty of the shape, as shown in Fig. 7. Our implementation has 17.5M parameters: a small neural network with Fourier feature embeddings [43] and parametric embeddings [31, 42] computed using a dense feature grid ( $>99\\%$ of the parameters).", + "bbox": [ + 496, + 462, + 890, + 568 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 500, + 580, + 746, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed a point-guided optimization method for neural SDF reconstruction from raw point clouds. We also examined why neural SDF losses can be detrimental for some shapes, proposed a metric to identify these shapes, and used this analysis to justify our algorithm design. Our method outperforms prior work, with large improvements for the most challenging shapes.", + "bbox": [ + 496, + 606, + 890, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Like many methods, our approach is not robust to high outlier fractions and large noise scales, behaving similarly to the compared methods. In addition, our approach does not handle large occlusions gracefully, since it treats these regions like concavities to be explored. This could be alleviated by defining anisotropic per-point sampling radii $\\delta_{i}$ .", + "bbox": [ + 496, + 710, + 890, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. Y. Ben-Shabat is supported by the Marie Sklodowska-Curie grant agreement No. 893465 S. Gould is a recipient of an ARC Future Fellowship (proj. no. LP200100421) funded by the Australian Government. We would also like to thank Mingda Xu for discussions about homotopy methods.", + "bbox": [ + 496, + 806, + 890, + 881 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21463", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. The power crust, unions of balls, and the medial axis transform. In Computational Geometry, 2001. 2", + "[2] Matan Atzmon and Yaron Lipman. SAL: Sign Agnostic Learning of shapes from raw data. In CVPR, 2020. 2, 4, 7", + "[3] Matan Atzmon and Yaron Lipman. SALD: Sign Agnostic Learning with Derivatives. In ICLR, 2021.", + "[4] Ma Baorui, Han Zhizhong, Liu Yu-Shen, and Zwicker Matthias. 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In International Conference on 3D Vision (3DV), 2024. 3" + ], + "bbox": [ + 78, + 90, + 468, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21465", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_model.json b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ea6584ad7fab089133ae2e3b0769535cc740b07e --- /dev/null +++ b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_model.json @@ -0,0 +1,2387 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.084, + 0.131, + 0.885, + 0.152 + ], + "angle": 0, + "content": "Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.18, + 0.862, + 0.199 + ], + "angle": 0, + "content": "Chamin Hewa Koneputugodage1 Yizhak Ben-Shabat1,2 Dylan Campbell1 Stephen Gould1" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.209, + 0.801, + 0.228 + ], + "angle": 0, + "content": "1The Australian National University 2Technion Israel Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.23, + 0.808, + 0.244 + ], + "angle": 0, + "content": "{chamin.hewa, dylan.campbell, stephen.gould}@anu.edu.au sitzikbs@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.28, + 0.312, + 0.295 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.474, + 0.645 + ], + "angle": 0, + "content": "A neural signed distance function (SDF) is a convenient shape representation for many tasks, such as surface reconstruction, editing and generation. However, neural SDFs are difficult to fit to raw point clouds, such as those sampled from the surface of a shape by a scanner. A major issue occurs when the shape's geometry is very different from the structural biases implicit in the network's initialization. In this case, we observe that the standard loss formulation does not guide the network towards the correct SDF values. We circumvent this problem by introducing guiding points, and use them to steer the optimization towards the true shape via small incremental changes for which the loss formulation has a good descent direction. We show that this point-guided homotopy-based optimization scheme facilitates a deformation from an easy problem to the difficult reconstruction problem. We also propose a metric to quantify the difference in surface geometry between a target shape and an initial surface, which helps indicate whether the standard loss formulation is guiding towards the target shape. Our method outperforms previous state-of-the-art approaches, with large improvements on shapes identified by this metric as particularly challenging." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.677, + 0.208, + 0.692 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Point cloud reconstruction using a neural signed distance function (SDF) is a popular approach due to its simplicity and flexibility. Such methods show impressive performance improvements for cases with significant noise, outliers, missing regions or misalignment [20]. However, they are still unable to outperform classical methods on clean and relatively dense input data [20, 25], especially when the shape exhibits challenging geometry. For example, thin surfaces near each other (see Fig. 1 bottom) or large concave regions with small openings (see Fig. 1 top)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.899 + ], + "angle": 0, + "content": "We address the task of reconstruction from raw point clouds, i.e., without ground-truth normal vectors. We observe that the standard loss formulation used for the task" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.279, + 0.631, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.383, + 0.63, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.554, + 0.46, + 0.583, + 0.47 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.279, + 0.759, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.634, + 0.383, + 0.758, + 0.455 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.661, + 0.459, + 0.734, + 0.47 + ], + "angle": 0, + "content": "SDF Baseline" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.279, + 0.891, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.383, + 0.888, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.459, + 0.839, + 0.469 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.478, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Figure 1. Given a point cloud without ground-truth normals (left), neural SDF optimization for surface fitting frequently gets trapped in local minima (middle). Note that these two shapes have geometry very different to a sphere, which causes the loss right after spherical initialization to not provide a good descent direction towards the target shape (see Sec. 3.3). Our point-guided homotopy-based approach provides a principled way to avoid this issue and improve reconstruction quality (right)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.713 + ], + "angle": 0, + "content": "does not give a good descent direction towards the target SDF values, especially when the initialization does not align with the target geometry. Since most methods initialize to a sphere to bias the optimization result towards a bounded shape, and rely on this bias to find a good descent direction, their performance can be poor if the input shape has very different geometry to a sphere (see Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.851 + ], + "angle": 0, + "content": "Instead we propose a point-guided SDF (PG-SDF) approach, where we introduce guiding points to represent an intermediate surface for the optimization to target. By incrementally moving the guiding points towards the sampled input and optimizing the network to their new location, we ensure that the loss formulation gives a good descent direction during optimization. We eventually converge the guiding points to the input points, leading the optimization stably towards the target SDF. We also propose" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.9 + ], + "angle": 0, + "content": "1To avoid confusion, in this paper we use the term normal direction to refer to vectors in the normalized gradient field of the SDF and descent direction for the negative gradient of the loss function." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21456" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.091, + 0.153, + 0.101 + ], + "angle": 0, + "content": "No Guidance" + }, + { + "type": "image_caption", + "bbox": [ + 0.712, + 0.09, + 0.889, + 0.102 + ], + "angle": 0, + "content": "Small Steps (between 2a and 2b)" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.103, + 0.894, + 0.312 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.327, + 0.895, + 0.438 + ], + "angle": 0, + "content": "Figure 2. Reconstructing a 2D surface using a neural SDF, without (1a-e) and with (2a-e,3a-f) our proposed point guidance. Note that our point guidance has two parts, converging to level sets (2) and taking small steps in between (3). The input points \\(\\mathcal{X}\\) are black, the guiding points \\(\\mathcal{V}\\) are green, and the network's level sets are drawn as contour lines with the zero level set \\(\\mathcal{R}\\) in bold. (1a-b) The network deforms from the sphere initialization to one whose zero level set is close to \\(\\mathcal{X}\\). (1c) The network only makes local changes near \\(\\mathcal{X}\\), gradually interpolating \\(\\mathcal{X}\\) by adding complexity. (1d-e) \\(\\mathcal{X}\\) is fully interpolated, but the result is unsatisfactory. (2a) Our initialization. (2b-d) Our method after convergence to each intermediate level set. (2e) Our method after optimizing on the input points. (3a-f) The small steps taken by our method while reaching the first intermediate level set of radius \\(\\delta_0\\). Each row shows a single step, where the guiding points are first moved a short distance (left) and then the network is optimized to match this (right)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.47, + 0.569 + ], + "angle": 0, + "content": "a metric—the percentage of self-intersecting outward normals (SION%)—to quantify the difference between the surface geometry of a target shape and that of another surface, such as the sphere initialization. We use this metric to determine which shapes are likely to be difficult for neural SDF methods, and why the optimization steps in our method are robust. Our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.571, + 0.47, + 0.6 + ], + "angle": 0, + "content": "1. a point-guided optimization approach for surface reconstruction from point clouds without normals;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.601, + 0.47, + 0.646 + ], + "angle": 0, + "content": "2. a metric to quantify differences between surfaces, which can be used to identify the most challenging shapes to reconstruct; and" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.646, + 0.469, + 0.692 + ], + "angle": 0, + "content": "3. an interpretation of the algorithm as a homotopy method, providing a justification for the design decisions and insight into the failure modes of existing approaches." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.571, + 0.47, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.708, + 0.219, + 0.723 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Surface reconstruction from point clouds is a fundamental problem in computer vision. We restrict our attention to methods that optimize using generic priors, rather than methods that learn reconstruction priors from a dataset [19, 45] and are sensitive to domain shift." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Early approaches [1, 7, 10, 24] directly triangulated point clouds, with provable guarantees given dense input points with no defects. However, the limitation of vertices being input points make them impractical for even small levels of imperfection [6], and the result is often not watertight. A less restrictive class of approaches is implicit field methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.892, + 0.585 + ], + "angle": 0, + "content": "[9, 22, 23, 32, 34], where an implicit function is defined over the domain to represent the reconstructed surface. Such methods often use a carefully defined set of basis functions, and optimize for an energy function with respect to the basis function parameters. However they usually rely on normal vectors as inputs, allowing efficient optimization with linear solvers, such as Poisson Surface Reconstruction [23] and its screened version [22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.592, + 0.893, + 0.879 + ], + "angle": 0, + "content": "Neural implicit methods, which were popularised by DeepSDF [35] and Occupancy Networks [29], are promising as they provide more modeling and optimization flexibility. Rather than creating basis functions tailored to the input, the network is fixed and can adapt its representational ability through optimization. Furthermore, as they are optimized by gradient descent, they can work with any differentiable loss. This flexibility has led to learned shape spaces that allow for strong learned biases and interpolation [21, 26, 35, 47]. However, while many neural methods are able to perform better than non-neural approaches when the input has defects, they often perform worse when the data is clean and dense [20]. A major issue is that gradient descent optimization is not guaranteed to converge to a global optimum. Furthermore, many methods for the surface reconstruction task [2-4, 15, 41] use losses that are difficult for gradient descent to optimize. As the reason these losses are hard to optimize is fundamental to our method, we examine this issue and related loss formulations in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our method follows a line of work that attempts to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21457" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.379 + ], + "angle": 0, + "content": "improve upon these issues for reconstruction from points clouds without normals. There are three major methods that are competitive for this task, DiGS [5], SAP [39] and OG-INR [25]. DiGS and OG-INR are neural SDF methods. In order to avoid the difficulties of SDF optimization, DiGS [5] changes the optimization landscape by adding strong regularization at the start, and slowly annealing the regularization to gently change the optimization landscape back to the correct one. OG-INR [25] avoids local minima by first discretizing the problem and solving for inside-outside labels. It then uses this discrete solution to get an approximate SDF that makes it easier to optimize the original SDF. SAP [39] does not use neural methods or SDFs, and instead minimizes a chamfer loss on points and normals directly. This is related to our approach as we also use points and SDF-derived normals to guide our SDF optimization. However, rather than using a chamfer loss, which we find gets trapped in bad local minima, we use a more nuanced strategy to move our guiding points, outlined in Sec. 4.1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.473, + 0.56 + ], + "angle": 0, + "content": "Another highly related approach is Point2Mesh [17], which deforms an enclosing mesh onto the point cloud. Like SAP, they use a chamfer loss to guide the deformation, however they note that this loss does not easily enter concavities. To address this, they introduce a beam gap loss, which guides mesh vertices towards input points in the inward normal direction if they are not already well matched by chamfer distance. Our deformation strategy, in contrast, is based purely on explicitly matching points in the inward normal direction. Our approach also avoids a major shortcoming of Point2Mesh, the reconstruction output must have the same genus as the initial mesh." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.218, + 0.589 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.598, + 0.303, + 0.613 + ], + "angle": 0, + "content": "3.1. Notation and Definitions" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.621, + 0.47, + 0.698 + ], + "angle": 0, + "content": "We denote the Euclidean inner product as \\(\\langle p,q\\rangle = p^{\\mathsf{T}}q\\), the Euclidean distance as \\(d(p,q) = \\| p - q\\| _2\\), a unit vector as \\(\\hat{v} = v / \\| v\\|\\), the cosine similarity between two vectors as \\(s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle\\), and the distance from a point \\(p\\) to a set \\(A\\) by \\(d(p,A) = d_A(p) = \\inf_{q\\in A}d(p,q)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.47, + 0.743 + ], + "angle": 0, + "content": "The chamfer distance \\( d_{C} \\) is a common measure of the distance between two discrete point sets \\( P \\) and \\( Q \\), defined by the average of two one-sided chamfer distances" + }, + { + "type": "equation", + "bbox": [ + 0.139, + 0.75, + 0.47, + 0.78 + ], + "angle": 0, + "content": "\\[\nd _ {C} (P, Q) = \\frac {1}{2} \\left(d _ {\\vec {C}} (P, Q) + d _ {\\vec {C}} (Q, P)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.787, + 0.444, + 0.802 + ], + "angle": 0, + "content": "each averaging the distance over one set to the other set" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.81, + 0.469, + 0.847 + ], + "angle": 0, + "content": "\\[\nd _ {\\vec {C}} (P, Q) = \\frac {1}{| P |} \\sum_ {p \\in P} d (p, Q). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "The chamfer distance can also be used between two surfaces, \\( A \\) and \\( B \\), in which case the chamfer distance is taken over uniform samplings, \\( U_A \\sim U(A) \\) and \\( U_B \\sim U(B) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.153 + ], + "angle": 0, + "content": "A signed distance function (SDF) \\(F_{\\mathcal{V}}: \\mathcal{D} \\to \\mathbb{R}\\) of a bounded, open volume \\(\\mathcal{V} \\subset \\mathcal{D}\\) is a scalar function defined everywhere on \\(\\mathcal{D}\\). \\(F_{\\mathcal{V}}(z)\\) is the distance from \\(z\\) to the closest point on the boundary \\(\\partial \\mathcal{V}\\), with a negative sign if \\(z \\in \\mathcal{V}\\)" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.17, + 0.892, + 0.19 + ], + "angle": 0, + "content": "\\[\nF _ {\\mathcal {V}} (z) = (- 1) ^ {[ [ z \\in \\mathcal {V} ] ]} d (z, \\partial \\mathcal {V}) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.195, + 0.894, + 0.24 + ], + "angle": 0, + "content": "where the Iverson bracket \\(\\llbracket X\\rrbracket\\) is 1 if \\(X\\) is true and 0 otherwise. The level set \\(L_{a}\\) is the set of points that have a signed distance of \\(a\\) from \\(\\partial \\mathcal{V}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.247, + 0.892, + 0.265 + ], + "angle": 0, + "content": "\\[\nL _ {a} = \\{z \\in \\mathcal {D} \\mid F _ {\\mathcal {V}} (z) = a \\}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.269, + 0.894, + 0.316 + ], + "angle": 0, + "content": "The exterior level set \\(\\Omega_{a}\\) (\\(a > 0\\)) is the subset of \\(L_{a}\\) such that for each \\(p \\in L_{a}\\) there is a connected path from a point on the boundary of \\(\\mathcal{D}\\) to \\(p\\) that only intersects \\(L_{a}\\) at \\(p\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.322, + 0.704, + 0.337 + ], + "angle": 0, + "content": "3.2. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.894, + 0.435 + ], + "angle": 0, + "content": "Let \\(\\mathcal{X} = \\{x_i\\}_{i\\in I}\\) be a point cloud sampled from a surface \\(S\\subset \\mathcal{D}\\) where \\(\\mathcal{D}\\subset \\mathbb{R}^3\\) is compact. We often refer to \\(S\\) as the target shape, and assume that it is watertight, i.e., \\(S = \\partial \\mathcal{V}\\) of some open volume \\(\\mathcal{V}\\subset \\mathcal{D}\\). We wish to reconstruct \\(S\\) from the point cloud \\(\\mathcal{X} = \\{x_i\\}\\). Note that no per-point surface normals or scanner information is provided." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.893, + 0.648 + ], + "angle": 0, + "content": "We choose to represent our reconstructed surface \\(\\mathcal{R} \\subset \\mathcal{D}\\) using an implicit neural representation \\(\\Phi\\). Specifically we define \\(\\mathcal{R} = \\{z \\in \\mathcal{D} \\mid \\Phi(z, \\theta) = 0\\}\\) where \\(\\theta\\) are the parameters of the neural network \\(\\Phi\\). Thus we want to minimize the chamfer distance between \\(\\mathcal{S}\\) and \\(\\mathcal{R}\\). Since we do not know \\(\\mathcal{S}\\), we instead compute the distance to our input points \\(d_{C}(\\mathcal{X}, \\mathcal{R}) = d_{C}(\\mathcal{X}, U_{\\mathcal{R}})\\), where \\(U_{\\mathcal{R}}\\) is a uniform sampling from \\(\\mathcal{R}\\). Furthermore we choose to optimize the implicit function \\(\\Phi\\) to approximate the true signed distance function \\(F_{\\mathcal{V}}\\) of the volume \\(\\mathcal{V}\\). As \\(\\mathcal{V}\\) is unknown, during optimization we care about ensuring that \\(\\Phi\\) is a valid SDF to some open volume \\(\\mathcal{U}\\) for which \\(\\mathcal{X}\\) is an approximate sampling, i.e., \\(\\Phi \\approx F_{\\mathcal{U}}\\) and \\(d_{C}(\\mathcal{X}, \\partial \\mathcal{U})\\) is small (note \\(\\partial \\mathcal{U} = \\mathcal{R}\\)). Thus our overall optimization problem is" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.654, + 0.892, + 0.684 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l l} \\operatorname {m i n i m i z e} _ {\\theta} & d _ {C} (\\mathcal {X}, \\partial \\mathcal {U}) \\\\ \\text {s u b j e c t t o} & \\Phi (x, \\theta) = F _ {\\mathcal {U}} (x). \\end{array} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Why SDFs? We choose SDFs over other popular implicit functions like indicator or occupancy functions [22, 23, 29, 38] or unsigned distance functions (UDFs) [12, 16, 49] for several reasons. First, SDFs and UDFs constrain the possibilities for \\(\\Phi\\), and are fairly smooth (unlike indicator functions). This helps with regularizing \\(\\mathcal{R}\\) and ensures that they can be represented by neural networks, which are biased to be smooth. Previous works have shown that neural SDFs empirically perform better than neural occupancy functions [51]. Second, SDFs allow for distance and direction to the surface queries, which we make use of in our algorithm. Last, the signed aspect of SDFs guarantee the watertight criteria compared to UDF, and make it easier to mesh using algorithms like marching cubes [27]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21458" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.308, + 0.106 + ], + "angle": 0, + "content": "3.3. Neural SDF Formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.34 + ], + "angle": 0, + "content": "Since neural SDFs are coordinate networks, each coordinate is processed independently. During gradient descent each coordinate seeks to minimize its loss locally, and is only affected by changes in nearby coordinates due to the network's inherent smoothness bias. Thus information propagation through the domain (from the smoothness bias) is slow, and optimization is only effective if the loss provides clear guidance. Specifically, if the descent direction of the loss with respect to its SDF input value at a coordinate gives an approximate descent direction towards the target SDF value at that coordinate. However whether or not the loss provides a good descent direction depends on whether the geometry of the current state of the network aligns with the geometry of the target shape (see Fig. 2 top left for when they do not align and thus optimization gets stuck)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.47, + 0.386 + ], + "angle": 0, + "content": "We now discuss this observation in relation to currently used neural SDF losses. When optimizing neural SDFs for point clouds without normals, the main losses are" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.393, + 0.47, + 0.426 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {X}) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) | \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.429, + 0.469, + 0.461 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {e i k}} (\\theta) = \\sum_ {z \\in \\mathcal {D}} | \\| \\nabla_ {z} \\Phi (z, \\theta) \\| _ {2} - 1 | \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.464, + 0.469, + 0.496 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| x _ {\\mathcal {R}} ^ {\\star} (z) - x _ {\\mathcal {X}} ^ {\\star} (z) \\| _ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.47, + 0.78 + ], + "angle": 0, + "content": "where \\(x_{\\mathcal{R}}^{\\star}(z) = z - \\Phi(z)\\widehat{\\nabla_z\\Phi(z)}\\) and \\(x_{\\mathcal{X}}^{\\star}(z) = \\arg \\min_{x\\in \\mathcal{X}}d(z,x)\\). The first two losses were proposed by IGR [15] and the last one was proposed by Neural Pull [4] (further details in the supplement). The zero level set loss \\(\\mathcal{L}_{\\mathrm{ZLS}}\\) gives a perfect descent direction to the target SDF values for the points in \\(\\mathcal{X}\\). However, for other points in the domain, the loss formulation may not give a descent direction towards the target SDF value. The Eikonal loss \\(\\mathcal{L}_{\\mathrm{eik}}\\) guides towards scaling the SDF gradient, and does not change its direction unless forced to by the optimization of nearby points. Thus for a point \\(z\\in \\mathcal{D}\\), if the network's current normal directions in the region around \\(z\\) is in the opposite direction to what the target SDF normals are around \\(z\\), then at \\(z\\) this loss does not guide towards the target SDF values. The neural pull loss \\(\\mathcal{L}_{\\mathrm{pull}}\\) has two value-gradient pairs that will minimize its loss (one where the normal points towards \\(x_{\\mathcal{X}}^{\\star}\\) and one where it points away), so the loss will guide towards the closer one, which may not be the target." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "As a result, an important part of these methods is spherical initialization [2], where the network is initialized roughly to the SDF of a sphere. If the shape's geometry is similar to a sphere, then the initialized normal directions in the network are mostly in the correct direction, so \\(\\mathcal{L}_{\\mathrm{eik}}\\) and \\(\\mathcal{L}_{\\mathrm{pull}}\\) guide towards the correct SDF value. When the shape's geometry is very different to a sphere resulting in large regions where the initialized normal directions are" + }, + { + "type": "image", + "bbox": [ + 0.604, + 0.093, + 0.791, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.23, + 0.892, + 0.272 + ], + "angle": 0, + "content": "Figure 3. Surface \\( \\mathcal{S} \\) and surrounding surface \\( \\mathcal{R} \\), with outward normal directions for some points on \\( \\mathcal{S} \\) shown, and which ones are SIONs relative to \\( \\mathcal{R} \\) shown in red." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.289, + 0.892, + 0.351 + ], + "angle": 0, + "content": "very different to the target normal directions, then the loss does not provide a good descent direction in those regions. As a result, optimization often converges to a local minimum close to the initialization, such as in Fig. 2 (top left)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.359, + 0.684, + 0.376 + ], + "angle": 0, + "content": "3.4. Shape Reachability" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.383, + 0.892, + 0.578 + ], + "angle": 0, + "content": "From the analysis in the previous subsection, we are interested in whether the current state of a network provides similar normal directions to the SDF of the target shape, so that the loss provides a good descent direction towards the target SDF values. Let us assume that the current state of the network is roughly the SDF to some surface \\(\\mathcal{R}\\) surrounding the target shape's surface \\(S\\). One way of quantifying whether the normal directions are similar is to determine if points on \\(S\\) can \"reach\" \\(\\mathcal{R}\\) by travelling in their outward normal direction (see Fig. 3). If \\(S\\) has large concavities and the outward surface normal of most points in that concavity does not reach \\(\\mathcal{R}\\) before it self-intersects, then the current normal directions of the network are likely to be poor." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.579, + 0.892, + 0.64 + ], + "angle": 0, + "content": "More formally, if \\( P_{\\mathcal{S}} \\) and \\( P_{\\mathcal{R}} \\) are samplings of \\( \\mathcal{S} \\) and \\( \\mathcal{R} \\) and for each \\( p \\in P_{\\mathcal{S}} \\) we have a known outward unit normal \\( n_p \\), then for a point \\( p \\in P_{\\mathcal{S}} \\) we can construct around the outward normal a thin cylinder" + }, + { + "type": "equation", + "bbox": [ + 0.507, + 0.648, + 0.892, + 0.667 + ], + "angle": 0, + "content": "\\[\n\\mathcal {C} _ {p} = \\{z \\in \\mathcal {D} \\mid \\| p + t n _ {p} - z \\| \\leq \\varepsilon , \\langle z - p, n _ {p} \\rangle \\geq 0 \\}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.674, + 0.892, + 0.825 + ], + "angle": 0, + "content": "By the assumption of \\(\\mathcal{R}\\) surrounding \\(S\\) and \\(P_{\\mathcal{R}}\\) being a dense sampling of \\(\\mathcal{R}\\), we note that \\(\\mathcal{C}_p \\cap P_{\\mathcal{R}} \\neq \\emptyset\\). Then we consider \\(p\\) to have a self-intersecting outward normal (SION) with respect to \\(P_{\\mathcal{R}}\\) if its normal direction intersects its own shape before it intersects \\(\\mathcal{R}\\): \\(\\exists p' \\in P_{\\mathcal{S}}\\) such that \\(p' \\in \\mathcal{C}_p\\) and \\(\\forall q \\in \\mathcal{C} \\cap P_{\\mathcal{R}}\\) we have that \\(\\| p - p' \\|_2 < \\| p - q \\|\\). We then use the percentage of points in \\(p_{\\mathcal{S}}\\) that have SIONs with respect to \\(P_{\\mathcal{R}}\\) as a measure of how dissimilar the geometry of \\(S\\) is to \\(\\mathcal{R}\\), which we denote \\(\\mathrm{SION}(S; \\mathcal{R})\\), where a high value indicates dissimilarity." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "When \\(\\mathcal{R}\\) is not specified and \\(S\\) is clear from context, we will use SION as a shorthand for \\(\\mathrm{SION}(S; \\mathcal{R})\\), with \\(\\mathcal{R}\\) assumed to be any sphere surrounding \\(S\\). The two point clouds in Fig. 1 have a high SION, which indicates that their geometry is very different to a sphere and that optimization" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21459" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.427, + 0.107 + ], + "angle": 0, + "content": "from a spherical initialization is likely to be difficult." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.123, + 0.258, + 0.14 + ], + "angle": 0, + "content": "4. Point-Guided SDF" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.15, + 0.47, + 0.317 + ], + "angle": 0, + "content": "The key idea of our method is to slowly converge the surface of reconstruction \\(\\mathcal{R}\\) towards the input points \\(\\mathcal{X}\\) until it interpolates \\(\\mathcal{X}\\), while maintaining \\(\\Phi\\) as a valid SDF to the volume enclosed by \\(\\mathcal{R}\\) (see Fig. 2). We do this by guiding \\(\\mathcal{R}\\) towards level sets (Fig. 2:2a-e) and taking small steps towards reaching each level set (Fig. 2:3a-f, Fig. 4). At each step we move guiding points \\(\\mathcal{Y}\\), which represent the surface \\(\\mathcal{R}\\), a small distance towards \\(\\mathcal{X}\\) (Fig. 4c) and then optimize \\(\\Phi\\) to interpolate the new \\(\\mathcal{Y}\\) positions, thus defining the new surface of reconstruction \\(\\mathcal{R}\\) over which \\(\\mathcal{Y}\\) is resampled (Fig. 4d). Our full algorithm is shown in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.318, + 0.47, + 0.424 + ], + "angle": 0, + "content": "Since each movement of the guiding points is small, the geometry of the moved guiding points \\(\\mathcal{V}\\) should be similar to the network's current surface \\(\\mathcal{R}\\), and \\(\\mathrm{SION}(\\mathcal{V};\\mathcal{R})\\) should be low. Thus optimizing the network to reconstruct the updated \\(\\mathcal{V}\\) should be robust (unlikely to converge to local minima) as the optimization is likely to have a clear descent direction from the loss at most points." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.425, + 0.47, + 0.502 + ], + "angle": 0, + "content": "In Sec. 4.1 we outline how to move the guiding points \\(\\mathcal{Y}\\) one step closer to the input points \\(\\mathcal{X}\\) (Fig. 4a-c). In Sec. 4.2 we outline how to optimize the network \\(\\Phi\\) to interpolate the new guiding point locations (Fig. 4d). Finally, in Sec. 4.3 we analyze our method within the homotopy framework." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.508, + 0.47, + 0.613 + ], + "angle": 0, + "content": "Preprocessing \\(\\mathcal{X}\\). Following standard practice, we first center and (isotropically) scale the shape to fit in a centered ball. After scaling, we calculate the point cloud's approximate sampling radius \\(\\delta_{\\mathcal{X}}\\) conservatively by calculating the distance to the four closest neighbors for each \\(x \\in \\mathcal{X}\\) and averaging the highest \\(5\\%\\) of all such distances. We use this radius extensively in our method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.621, + 0.47, + 0.682 + ], + "angle": 0, + "content": "Initialization. We first initialize our network to the exterior level set of radius \\(\\delta_{\\mathrm{init}} = 16\\delta_{\\mathcal{X}}\\). We provide intuition into why we can do this robustly in Sec. 4.3, and provide details on how to make this more efficient in the supplement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.694, + 0.321, + 0.71 + ], + "angle": 0, + "content": "4.1. Moving the Guiding Points" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.718, + 0.47, + 0.78 + ], + "angle": 0, + "content": "We now describe how to move the guiding points \\(y \\in \\mathcal{V}\\) towards the input points \\(\\mathcal{X}\\). At a high level, each step we move \\(\\mathcal{V}\\) closer to an exterior level set of radius \\(\\delta\\), \\(\\Omega_{\\delta}\\), and when \\(\\mathcal{R}\\) has converged to \\(\\Omega_{\\delta}\\) we reduce \\(\\delta\\) (see Algorithm 1)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Since we are moving \\(y \\in \\mathcal{V}\\) to guide the surface \\(\\mathcal{R}\\), we only move each \\(y\\) in the inwards normal direction of \\(\\mathcal{R}\\). Next, since we are moving towards an exterior level set \\(\\Omega_{\\delta}\\) of \\(\\mathcal{X}\\), for each \\(y \\in \\mathcal{V}\\) we find the closest input point in the inwards normal direction \\(x^{\\star}(y) \\in \\mathcal{X}\\), and use this to determine the target point \\(\\omega^{\\star}(y)\\) on \\(\\Omega_{\\delta}\\) that we move towards. Finally, since we want to move the surface \\(\\mathcal{R}\\) slowly, we have a maximum step size for each movement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.203 + ], + "angle": 0, + "content": "Closest point in the inward direction. We first define \\( x^{\\star}(y) \\) (see Fig. 4a-b). As we are moving in the inward normal direction, i.e., \\( -n_y \\) where \\( n_y = \\widehat{\\nabla_y\\Phi(y)} \\), we want to move \\( y \\) based on the closest point \\( x \\in \\mathcal{X} \\) in the inward normal direction \\( -n_y \\). We define the inward normal definition by setting a cosine similarity threshold \\( a_y \\geq 0 \\) to define a cone \\( C_y \\) supported at \\( y \\) emanating in the direction \\( -n_y \\)," + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.21, + 0.892, + 0.228 + ], + "angle": 0, + "content": "\\[\nC _ {y} = \\left\\{z \\mid s (- n _ {y}, z - y) \\geq a _ {y} \\right\\}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.235, + 0.892, + 0.297 + ], + "angle": 0, + "content": "However as \\(y\\) gets very close to points in \\(\\mathcal{X}\\), it is unlikely that any of those nearby points stay within this cone. Thus we also consider the half ball \\(H_{y}\\) of radius \\(2\\delta_{\\mathcal{X}}\\) containing points close to \\(y\\)" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.305, + 0.892, + 0.323 + ], + "angle": 0, + "content": "\\[\nH _ {y} = \\left\\{z \\mid \\| x - y \\| _ {2} \\leq 2 \\delta_ {\\mathcal {X}} \\wedge s (- n _ {y}, z - y) \\geq 0 \\right\\}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.33, + 0.76, + 0.347 + ], + "angle": 0, + "content": "Thus our target point \\(x^{\\star}(y)\\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.355, + 0.892, + 0.383 + ], + "angle": 0, + "content": "\\[\nx ^ {\\star} (y) = \\underset {x \\in \\mathcal {X} \\cap \\left(C _ {y} \\cup H _ {y}\\right)} {\\arg \\min } \\| x - y \\| _ {2}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.391, + 0.892, + 0.437 + ], + "angle": 0, + "content": "Moving towards \\(\\Omega_{\\delta}\\). As \\(x^{\\star}(y)\\) is our closest (inward) point, a reasonable location for a point in \\(\\Omega_{\\delta}\\) can be computed by moving \\(\\delta\\) away from \\(x^{\\star}\\) towards \\(y\\)" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.446, + 0.892, + 0.466 + ], + "angle": 0, + "content": "\\[\n\\omega^ {\\star} (y) = \\left(\\| x ^ {\\star} - y \\| _ {2} - \\delta\\right) \\widehat {\\left(x ^ {\\star} - y\\right)}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.52 + ], + "angle": 0, + "content": "We move towards \\(\\omega^{\\star}\\) with a maximum step size of \\(s_m\\) so that the movement step is small and easy to optimize. Thus our final point \\(y^\\prime\\) (see Fig. 4b) is" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.529, + 0.892, + 0.547 + ], + "angle": 0, + "content": "\\[\ny ^ {\\prime} = y - \\operatorname {c l i p} (\\langle \\omega^ {\\star} (y), - n _ {y} \\rangle , s _ {m}) n _ {y} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.824, + 0.571 + ], + "angle": 0, + "content": "where \\(\\operatorname{clip}(a, \\varepsilon)\\) projects \\(a\\) to the interval \\([- \\varepsilon, \\varepsilon]\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.892, + 0.667 + ], + "angle": 0, + "content": "Reducing \\(\\delta\\). After initialization, we set \\(\\delta = \\delta_0\\) as our next target level set. Once \\(\\mathcal{V}\\) has finished moving towards \\(\\Omega_{\\delta}\\) and \\(\\mathcal{R}\\) has converged, we decrease the current \\(\\delta\\) by half and start moving \\(\\mathcal{V}\\) towards the new exterior level set. We do this until \\(\\delta\\) reaches \\(\\delta_f\\). We use \\(\\delta_0 = 4\\delta_{\\mathcal{X}}\\), \\(\\delta_f = \\delta_{\\mathcal{X}}\\). We then abandon \\(\\mathcal{V}\\) and optimize directly on \\(\\mathcal{X}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.676, + 0.724, + 0.692 + ], + "angle": 0, + "content": "4.2. Optimizing the Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.699, + 0.892, + 0.79 + ], + "angle": 0, + "content": "We now have the points \\(\\mathcal{V}\\) to guide where our new surface should be. Furthermore, we have an approximate normal \\(n_y\\) for each \\(y\\in \\mathcal{V}\\) given by \\(\\Phi\\), whose direction should be useful as the SION between the new position of the points relative to the previous positions is low. We use this to estimate an approximate SDF" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.797, + 0.892, + 0.818 + ], + "angle": 0, + "content": "\\[\n\\tilde {F} _ {\\mathcal {V}} (z) = (- 1) ^ {[ s (z - y (z), n _ {y (z)}) \\geq 0 ]} d (z, y (z)) \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.858 + ], + "angle": 0, + "content": "where \\( y(z) = \\arg \\min_{y\\in \\mathcal{Y}}d(z,y) \\) and \\( s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle \\) is cosine similarity. We guide towards these values using" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.866, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {s d f}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| \\Phi (z, \\theta) - \\tilde {F} _ {\\mathcal {V}} (z) \\| _ {2}. \\tag {16}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21460" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.891, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.256, + 0.895, + 0.327 + ], + "angle": 0, + "content": "Figure 4. One iteration of Algorithm 1, steps 6-8. (a) Given the current value of our network \\(\\Phi\\) (the contours) and our guiding points \\(\\mathcal{V}\\) (the green points), for each \\(y\\in \\mathcal{V}\\) we calculate a half ball \\(H_{y}\\) and a cone \\(C_y\\) in the inside normal direction to find an input points \\(x\\in \\mathcal{X}\\) (black points) to move towards (shown for 3 points, with one highlighted in red). (b) We find the closest input point \\(x^{\\star}(y)\\in \\mathcal{X}\\) within \\(H_{y}\\cap \\mathcal{C}_{y}\\), and use this to calculate the new position \\(y^\\prime\\) for each \\(y\\in \\mathcal{V}\\) (shown for all points). (c) The result after each \\(y\\in \\mathcal{V}\\) has been moved. (d) The network \\(\\Phi\\) is optimized on the new guiding points, and \\(\\mathcal{V}\\) is resampled to densely cover the new zero level set \\(\\mathcal{R}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.471, + 0.383 + ], + "angle": 0, + "content": "Furthermore, our input points \\(\\mathcal{X}\\) should be at distance \\(\\delta\\) from \\(\\mathcal{Y}\\) and should be inside, so we add a loss term" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.39, + 0.47, + 0.422 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) + \\delta |. \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.43, + 0.351, + 0.445 + ], + "angle": 0, + "content": "Thus our overall loss term formulation is" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.456, + 0.46, + 0.472 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\theta , \\mathcal {X}, \\mathcal {Y}, \\delta) = \\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) + \\mathcal {L} _ {\\mathrm {e i k}} (\\theta) +\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.474, + 0.469, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\mathcal {L} _ {\\mathrm {s d f}}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {Y}). \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.469, + 0.531 + ], + "angle": 0, + "content": "Relevant details (e.g., loss term weightings, domain sampling procedure, optimizer settings) are in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.47, + 0.623 + ], + "angle": 0, + "content": "Finally, we resample \\(\\mathcal{V}\\) in the new zero level set \\(\\mathcal{R}\\) (Fig. 4f) so that it densely samples it. After this process has finished (i.e., when \\(\\Phi\\) has converged for \\(\\delta = \\delta_f\\)), we optimize \\(\\Phi\\) on the input points \\(\\mathcal{X}\\) using the loss in Eq. (18). Here we do not use the approximate SDF term, as \\(\\mathcal{X}\\) is likely to have more imperfections that our guiding points." + }, + { + "type": "code_caption", + "bbox": [ + 0.081, + 0.638, + 0.294, + 0.651 + ], + "angle": 0, + "content": "Algorithm 1 Point-Guided SDF" + }, + { + "type": "algorithm", + "bbox": [ + 0.082, + 0.656, + 0.47, + 0.88 + ], + "angle": 0, + "content": "1: procedure PG-SDF(\\(\\mathcal{X}\\)) \n2: Center \\(\\mathcal{X}\\), scale \\(\\mathcal{X}\\) and compute sampling radius \\(\\delta_{\\mathcal{X}}\\) \n3: \\(\\mathcal{Y}, \\mathcal{N}_{\\mathcal{Y}}, \\Phi \\gets\\) Initialization \\((\\mathcal{X}, \\delta_{\\mathrm{init}})\\) \n4: \\(\\delta \\gets \\delta_0\\) \n5: while \\(\\delta \\geq \\delta_f\\) do \n6: Move \\(\\mathcal{Y}\\) using Eq. (14) \n7: Optimize \\(\\Phi\\) to match \\(\\mathcal{Y}\\) \n8: Resample \\(\\mathcal{Y}\\) on new \\(\\mathcal{R}\\) \n9: Query \\(\\Phi\\) for normals \\(\\mathcal{N}_{\\mathcal{Y}}\\) \n10: if \\(\\Phi\\)'s zero level set has not changed then \n11: \\(\\delta \\gets \\frac{1}{2} \\delta\\) \n12: end if \n13: end while \n14: Optimize \\(\\Phi\\) on \\(\\mathcal{X}\\) \n15: return \\(\\Phi\\) \n16: end procedure" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.352, + 0.83, + 0.369 + ], + "angle": 0, + "content": "4.3. Interpretation as a Homotopy Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.375, + 0.892, + 0.526 + ], + "angle": 0, + "content": "One way to analyze this method is in the context of a homotopy method [33]. Here, we wish to solve a difficult problem \\( M(\\theta) = 0 \\) for \\( \\theta \\), and instead consider the homotopy map \\( H(\\theta, t) = tM(\\theta) + (1 - t)N(\\theta) \\) where \\( N(\\theta) = 0 \\) is easy to solve and \\( t \\in [0,1] \\). This forms a homotopy between the problems \\( M(\\theta) = H(\\theta, 1) \\) and \\( N(\\theta) = H(\\theta, 0) \\) as we can now continuously deform one problem into the other by varying \\( t \\). By taking small steps along the zero path, the trajectory of points \\( (\\theta, t) \\) for which \\( H(\\theta, t) = 0 \\), we can reach the solution to \\( M(\\theta) \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.527, + 0.892, + 0.633 + ], + "angle": 0, + "content": "For our method, we start by solving the easier problem \\(\\mathcal{L}(\\theta, \\mathcal{Y}_0) = 0\\) where \\(\\mathcal{Y}_0\\) is our initial set of guiding points. Our goal is to solve the hard problem \\(\\mathcal{L}(\\theta, \\mathcal{X}) = 0\\). To see that our method is a homotopy method, note that our guiding points \\(\\mathcal{Y}\\) are facilitating a topological homotopy from \\(\\mathcal{Y}_0\\) to our input points \\(\\mathcal{X}\\). Thus we can parameterize our zero path using \\(\\mathcal{Y}\\). It is given by \\((\\theta(\\mathcal{Y}), t(\\mathcal{Y}))\\) where" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.643, + 0.891, + 0.66 + ], + "angle": 0, + "content": "\\[\n\\theta (\\mathcal {Y}) \\text {s a t i s f i e s} \\mathcal {L} (\\theta (\\mathcal {Y}), \\mathcal {Y}) = 0 \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.663, + 0.891, + 0.695 + ], + "angle": 0, + "content": "\\[\nt (\\mathcal {Y}) = \\frac {d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right) - d _ {C} \\left(\\mathcal {Y} , \\mathcal {X}\\right)}{d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right)}. \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Note that at initialization \\(\\mathcal{V} = \\mathcal{V}_0\\) and we have \\(t(\\mathcal{V}_0) = 0\\), while at termination \\(\\mathcal{V} = \\mathcal{X}\\) and we have \\(t(\\mathcal{X}) = 1\\). Each time we update \\(\\mathcal{V}\\), we are traversing the zero path. If we take \\(n\\) steps to reach the final exterior level set of radius \\(\\delta_{\\mathcal{X}}\\), then we visit \\(n + 2\\) points along the zero path parameterized by the sequence \\(\\mathcal{V}_0, \\mathcal{V}_1, \\ldots, \\mathcal{V}_n, \\mathcal{X}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To see why this works well in practice, we need to show that solving \\( H(\\theta(\\mathcal{Y}_{k+1}), t(\\mathcal{Y}_{k+1})) \\) for \\( \\theta(\\mathcal{Y}_{k+1}) \\) given \\( \\theta(\\mathcal{Y}_k) \\) is easy, and solving \\( H(\\theta(\\mathcal{Y}_0), t(\\mathcal{Y}_0)) \\) for \\( \\theta(\\mathcal{Y}_0) \\) is easy. To see the former, note that we move our guiding points \\( \\mathcal{V} \\) only a small distance from \\( \\mathcal{V}_k \\) to \\( \\mathcal{V}_{k+1} \\), and that \\( \\mathrm{SION}(\\mathcal{Y}_{k+1};\\mathcal{V}_k) \\) is small by construction. Thus, by the analysis in Secs. 3.3 and 3.4, the relative optimization problem is easy. To see the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21461" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.094, + 0.47, + 0.375 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.381, + 0.471, + 0.439 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on ShapeNet. Top: Intermediate results as our method converges to different level sets \\(\\Omega_{\\delta}\\). Bottom: Comparison with other methods, for challenging high SION shapes (0.40 for the car and 0.42 for the lamp)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.454, + 0.47, + 0.56 + ], + "angle": 0, + "content": "latter, when \\(\\delta_{\\mathrm{init}} \\gg \\delta_{\\mathcal{X}}\\) we can estimate good normals for \\(\\mathcal{Y}_0\\) by taking the displacement from the closest input point. With good normal estimates, \\(\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}\\) is very effective, and so optimization is easy. Furthermore, we note that higher radius exterior level sets are less complex, with smaller SION to an enclosing sphere. We formalize and prove this observation in the supplement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.574, + 0.164, + 0.589 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Dataset. We evaluate the performance of our method on ShapeNet [11], a large dataset of 3D CAD models. In this dataset, there are many shapes with complex geometries that are challenging to reconstruct, including extremely thin surfaces (sometimes string-like), hollow regions (often with small openings), and shapes with high genus. Previous works [5, 25] have shown that many neural methods fail on these shapes, even when using the ground-truth normals. We use the preprocessed watertight subset of Williams et al. [46], which consists of 13 classes with 20 shapes in each class. For each shape, 100k points are uniformly sampled from the surface and ground-truth normals are provided for each point, which are only used for those methods that require normals. We use these points as the input to our method, and for evaluating the squared chamfer metric. An additional 100k points are uniformly sampled within the domain with ground-truth labels that indicate whether the point is inside or outside the shape, allowing for the interior intersection-over-union (IoU) metric to be calculated. Further experimental details are given in the supplement." + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.363 + ], + "angle": 0, + "content": "
MethodSquared Chamfer ↓IoU ↑
NN nxMeanMedianStdMeanMedianStd
SPSR [22]× T5.44e-51.97e-55.06e-40.99260.99560.0105
IGR [15]✓ T5.12e-41.13e-42.15e-30.81020.84800.1519
SIREN [41]✓ T1.03e-45.28e-51.93e-40.82680.90970.2329
FFN [43]✓ T9.12e-58.65e-53.36e-50.82180.83960.0989
NSP [46]× T5.36e-54.06e-53.64e-50.89730.92300.0871
DiGS+N [5]✓ T2.74e-42.32e-59.90e-40.92000.97740.1992
SDF+N†✓ T3.97e-52.22e-58.98e-50.99150.99510.0141
Ours+N✓ T2.43e-52.15e-51.66e-50.99320.99550.0076
SPSR [22]× E3.76e-34.37e-51.14e-20.71870.97610.3767
SIREN [41]✓ ×3.08e-42.58e-43.26e-40.30850.29520.2014
SAL [2]✓ ×1.14e-32.11e-43.63e-30.40300.39440.2722
DiGS [5]✓ ×1.32e-42.55e-54.73e-40.93900.97640.1262
SAP [39]× ×4.09e-42.46e-52.60e-30.91180.99230.2002
OG-S [25]✓ ×3.75e-52.17e-58.24e-50.96150.98710.1048
OG-N [25]✓ ×5.07e-52.57e-59.39e-50.95930.98700.1057
SDF†✓ ×1.84e-48.15e-42.95e-30.54900.52450.3572
SDF+N†✓ E2.48e-25.89e-55.63e-30.68170.96710.3990
Ours+N✓ E2.79e-24.79e-56.79e-20.70170.97210.3876
Ours✓ ×3.72e-52.40e-55.39e-50.97290.98960.0676
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.369, + 0.894, + 0.426 + ], + "angle": 0, + "content": "Table 1. Surface reconstruction results on ShapeNet [11]. NN: uses a neural network. \\( n_x \\): uses ground-truth (T), estimated (E) or no (×) input surface normals. Suffix ‘+N’ denotes normal information added to the underlying method. † Our implementation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.442, + 0.892, + 0.533 + ], + "angle": 0, + "content": "Implementation and Baselines. Our baseline methods use the same implementation framework as our approach (see full details in the supplement) with standard loss formulations. 'SDF' uses \\(\\mathcal{L}_{\\mathrm{zls}}\\), \\(\\mathcal{L}_{\\mathrm{eik}}\\), and \\(\\mathcal{L}_{\\mathrm{pull}}\\) while 'SDF+N' additionally uses \\(\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}\\) and \\(\\mathcal{L}_{\\mathrm{normal}}\\) [15]. We also evaluate our methods with estimated normals (using Open3D [50])." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.543, + 0.819, + 0.559 + ], + "angle": 0, + "content": "5.1. Surface Reconstruction on ShapeNet" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.892, + 0.673 + ], + "angle": 0, + "content": "Results on the full ShapeNet subset are given in Tab. 1, with qualitative results in Fig. 5. Our proposed method outperforms all prior normal-free methods and even demonstrates improvement when ground-truth normals are available. In particular, our approach gets a significant improvement in mean IoU, with much smaller variance, indicating that our method performs reliably well." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.681, + 0.78, + 0.698 + ], + "angle": 0, + "content": "5.2. Challenging High-SION Shapes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we analyze the performance of surface reconstruction methods with respect to the SION metric. Fig. 6 shows that the mean IoU degrades significantly as we progressively consider shapes with higher SION scores. While our method also follows this trend, performance degradation is considerably slower, indicating that our method is much more robust to challenging shapes. We report the reconstruction performance on the subset of 20 shapes with the highest SION in Tab. 2. On these most challenging shapes, our approach has a decisive advantage. This demonstrates that our structured optimization approach is able to achieve good reconstructions of the most difficult shapes, without sacrificing performance on easy shapes." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21462" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.465, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.47, + 0.346 + ], + "angle": 0, + "content": "Figure 6. Mean IoU for all shapes with a SION higher than a lower bound. The analysis from Secs. 3.3 and 3.4 predicts a significant negative correlation for existing neural SDF methods. Our method weakens this trend considerably." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.356, + 0.469, + 0.547 + ], + "angle": 0, + "content": "
MethodNN\\(n_x\\)Squared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
SPSR [22]×T3.98e-53.92e-51.80e-50.97980.98480.0222
DiGS+N [5]✓T2.09e-47.42e-52.91e-40.81600.87640.2119
\\(\\text{SDF}+\\text{N}^{\\dagger}\\)✓T1.11e-44.84e-51.95e-40.97330.98540.0409
Ours+N✓T4.16e-53.89e-51.86e-50.98220.98650.0148
SPSR [22]×E5.83e-31.25e-31.16e-20.32900.18020.3445
DiGS [5]✓×4.34e-41.71e-45.34e-40.71080.81960.2536
SAP [39]××1.28e-45.84e-51.99e-40.76160.88720.2665
OG-S [25]✓×1.31e-46.50e-51.79e-40.76510.92190.2512
\\(\\text{SDF}^{\\dagger}\\)✓×1.29e-37.75e -41.43e-30.34130.26170.2292
\\(\\text{SDF}+\\text{N}^{\\dagger}\\)✓E5.32e-24.51e-37.03e-20.28960.19770.3288
Ours+N✓E4.89e-27.32e-36.25e-20.31730.23620.3259
Ours✓×5.51e-54.87e-53.12e-50.91530.95980.0906
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.623 + ], + "angle": 0, + "content": "Table 2. Surface reconstruction results on the 20 highest SION ShapeNet shapes. NN: uses a neural network. \\( n_x \\): uses ground-truth (T), estimated (E) or no (X) input surface normals. Suffix ‘+N’ denotes adding normal information to the underlying method. † Our implementation." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.633, + 0.469, + 0.734 + ], + "angle": 0, + "content": "
Guidance y0 yδ0 δfSquared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
× × - -2.41e-31.18e-32.65e-30.27950.22550.2078
✓ × - -2.63e-41.91e-42.31e-40.56940.60910.2278
✓ ✓ 429.89e-57.70e-57.95e-50.86570.9163
✓ ✓ 118.08e-57.52e-55.66e-50.85380.9386
✓ ✓ 415.51e-54.87e-53.12e-50.91530.9598
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.739, + 0.469, + 0.795 + ], + "angle": 0, + "content": "Table 3. Ablation results on the 20 highest SION ShapeNet shapes. \\(\\mathcal{V}_0\\): uses our SDF initialization strategy instead of spherical initialization [15]. \\(\\mathcal{V}\\): uses our point guidance strategy. \\(\\delta_0 / \\delta_f\\): starting and final level set radii, given in multiples of \\(\\delta_{\\mathcal{X}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.334, + 0.831 + ], + "angle": 0, + "content": "5.3. Ablation Study and Runtime" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "An ablation study, on the 20 highest-SION shapes of ShapeNet, is reported in Tab. 3. The performance when using a spherical initialization and optimizing with respect to the input points (row 1) is poor. It improves significantly" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.087, + 0.887, + 0.277 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.282, + 0.892, + 0.325 + ], + "angle": 0, + "content": "Figure 7. Runtime vs SION on ShapeNet for our method. Challenging shapes with high SION take more time to optimize. One outlier (82 min) is truncated for clarity and marked as \\(\\times\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.341, + 0.892, + 0.462 + ], + "angle": 0, + "content": "when replaced with our high exterior level set initialization (row 2). When point guidance is added (rows 3-5), the performance increases considerably. In particular, stopping point guidance early (when \\(\\delta_f = 2\\delta_{\\mathcal{X}}\\)) harms performance, as does guiding straight to the final level set target (\\(\\delta_0 = \\delta_{\\mathcal{X}}\\)) without first converging to intermediate level set targets. Our gradual homotopy approach performs best by a significant margin, justifying the strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.463, + 0.892, + 0.569 + ], + "angle": 0, + "content": "An unoptimized implementation of our method takes 10 mins on average per ShapeNet shape (a median of 7.4 mins). Convergence time depends strongly on the difficulty of the shape, as shown in Fig. 7. Our implementation has 17.5M parameters: a small neural network with Fourier feature embeddings [43] and parametric embeddings [31, 42] computed using a dense feature grid (\\(>99\\%\\) of the parameters)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.581, + 0.747, + 0.597 + ], + "angle": 0, + "content": "6. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.712 + ], + "angle": 0, + "content": "In this paper, we proposed a point-guided optimization method for neural SDF reconstruction from raw point clouds. We also examined why neural SDF losses can be detrimental for some shapes, proposed a metric to identify these shapes, and used this analysis to justify our algorithm design. Our method outperforms prior work, with large improvements for the most challenging shapes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Like many methods, our approach is not robust to high outlier fractions and large noise scales, behaving similarly to the compared methods. In addition, our approach does not handle large occlusions gracefully, since it treats these regions like concavities to be explored. This could be alleviated by defining anisotropic per-point sampling radii \\(\\delta_{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.807, + 0.892, + 0.882 + ], + "angle": 0, + "content": "Acknowledgements. Y. Ben-Shabat is supported by the Marie Sklodowska-Curie grant agreement No. 893465 S. Gould is a recipient of an ARC Future Fellowship (proj. no. LP200100421) funded by the Australian Government. We would also like to thank Mingda Xu for discussions about homotopy methods." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21463" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. The power crust, unions of balls, and the medial axis transform. In Computational Geometry, 2001. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.159, + 0.469, + 0.197 + ], + "angle": 0, + "content": "[2] Matan Atzmon and Yaron Lipman. SAL: Sign Agnostic Learning of shapes from raw data. 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In International Conference on 3D Vision (3DV), 2024. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21465" + } + ] +] \ No newline at end of file diff --git a/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_origin.pdf b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..3365ce7e63be27e5cb9956ef7f643b60257b92af --- /dev/null +++ b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:101f72b66407641d3b2f7bf5dad8653fd2e8dfff33b32627102d89cd8e424d20 +size 5071732 diff --git a/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/full.md b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2a6867e890c845c92e1fd3fb4ba1182dc15361c0 --- /dev/null +++ b/2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/full.md @@ -0,0 +1,388 @@ +# Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance + +Chamin Hewa Koneputugodage1 Yizhak Ben-Shabat1,2 Dylan Campbell1 Stephen Gould1 + +1The Australian National University 2Technion Israel Institute of Technology + +{chamin.hewa, dylan.campbell, stephen.gould}@anu.edu.au sitzikbs@gmail.com + +# Abstract + +A neural signed distance function (SDF) is a convenient shape representation for many tasks, such as surface reconstruction, editing and generation. However, neural SDFs are difficult to fit to raw point clouds, such as those sampled from the surface of a shape by a scanner. A major issue occurs when the shape's geometry is very different from the structural biases implicit in the network's initialization. In this case, we observe that the standard loss formulation does not guide the network towards the correct SDF values. We circumvent this problem by introducing guiding points, and use them to steer the optimization towards the true shape via small incremental changes for which the loss formulation has a good descent direction. We show that this point-guided homotopy-based optimization scheme facilitates a deformation from an easy problem to the difficult reconstruction problem. We also propose a metric to quantify the difference in surface geometry between a target shape and an initial surface, which helps indicate whether the standard loss formulation is guiding towards the target shape. Our method outperforms previous state-of-the-art approaches, with large improvements on shapes identified by this metric as particularly challenging. + +# 1. Introduction + +Point cloud reconstruction using a neural signed distance function (SDF) is a popular approach due to its simplicity and flexibility. Such methods show impressive performance improvements for cases with significant noise, outliers, missing regions or misalignment [20]. However, they are still unable to outperform classical methods on clean and relatively dense input data [20, 25], especially when the shape exhibits challenging geometry. For example, thin surfaces near each other (see Fig. 1 bottom) or large concave regions with small openings (see Fig. 1 top). + +We address the task of reconstruction from raw point clouds, i.e., without ground-truth normal vectors. We observe that the standard loss formulation used for the task + +![](images/568962fbab4f03017bee74cb8c54b85aa592cebfe0a129c6eced93b2fd7b8793.jpg) + +![](images/314fa1430c52073e9e1807122b3c06b6acf3414afce1c190ba025a80c7b2fce7.jpg) +Input + +![](images/90ed2fd69971a6d971725560340f526be3dd1c2c5f4ab4f672cfc1cf32bd20ac.jpg) + +![](images/d3f655f805eb6267a50b7ba88133c8a0e54bbf7cb9ad1ab81ae84f063b9db526.jpg) +SDF Baseline + +![](images/0e4e6965f1e6a3fbb171ec5f0f9b0ce132432aa1497383c6454b50f4313c9759.jpg) + +![](images/630c853cfb726aa5c3097518dbdad5c801e86ef4e46b0de497bc5180cf3bdb89.jpg) +Ours +Figure 1. Given a point cloud without ground-truth normals (left), neural SDF optimization for surface fitting frequently gets trapped in local minima (middle). Note that these two shapes have geometry very different to a sphere, which causes the loss right after spherical initialization to not provide a good descent direction towards the target shape (see Sec. 3.3). Our point-guided homotopy-based approach provides a principled way to avoid this issue and improve reconstruction quality (right). + +does not give a good descent direction towards the target SDF values, especially when the initialization does not align with the target geometry. Since most methods initialize to a sphere to bias the optimization result towards a bounded shape, and rely on this bias to find a good descent direction, their performance can be poor if the input shape has very different geometry to a sphere (see Fig. 1). + +Instead we propose a point-guided SDF (PG-SDF) approach, where we introduce guiding points to represent an intermediate surface for the optimization to target. By incrementally moving the guiding points towards the sampled input and optimizing the network to their new location, we ensure that the loss formulation gives a good descent direction during optimization. We eventually converge the guiding points to the input points, leading the optimization stably towards the target SDF. We also propose + +![](images/e8ebb0b1e94055c8da1407da7f88459c925bf1d73f6ee2fc30e51637f273fde0.jpg) +No Guidance +Small Steps (between 2a and 2b) +Figure 2. Reconstructing a 2D surface using a neural SDF, without (1a-e) and with (2a-e,3a-f) our proposed point guidance. Note that our point guidance has two parts, converging to level sets (2) and taking small steps in between (3). The input points $\mathcal{X}$ are black, the guiding points $\mathcal{V}$ are green, and the network's level sets are drawn as contour lines with the zero level set $\mathcal{R}$ in bold. (1a-b) The network deforms from the sphere initialization to one whose zero level set is close to $\mathcal{X}$ . (1c) The network only makes local changes near $\mathcal{X}$ , gradually interpolating $\mathcal{X}$ by adding complexity. (1d-e) $\mathcal{X}$ is fully interpolated, but the result is unsatisfactory. (2a) Our initialization. (2b-d) Our method after convergence to each intermediate level set. (2e) Our method after optimizing on the input points. (3a-f) The small steps taken by our method while reaching the first intermediate level set of radius $\delta_0$ . Each row shows a single step, where the guiding points are first moved a short distance (left) and then the network is optimized to match this (right). + +a metric—the percentage of self-intersecting outward normals (SION%)—to quantify the difference between the surface geometry of a target shape and that of another surface, such as the sphere initialization. We use this metric to determine which shapes are likely to be difficult for neural SDF methods, and why the optimization steps in our method are robust. Our contributions are: + +1. a point-guided optimization approach for surface reconstruction from point clouds without normals; +2. a metric to quantify differences between surfaces, which can be used to identify the most challenging shapes to reconstruct; and +3. an interpretation of the algorithm as a homotopy method, providing a justification for the design decisions and insight into the failure modes of existing approaches. + +# 2. Related Work + +Surface reconstruction from point clouds is a fundamental problem in computer vision. We restrict our attention to methods that optimize using generic priors, rather than methods that learn reconstruction priors from a dataset [19, 45] and are sensitive to domain shift. + +Early approaches [1, 7, 10, 24] directly triangulated point clouds, with provable guarantees given dense input points with no defects. However, the limitation of vertices being input points make them impractical for even small levels of imperfection [6], and the result is often not watertight. A less restrictive class of approaches is implicit field methods + +[9, 22, 23, 32, 34], where an implicit function is defined over the domain to represent the reconstructed surface. Such methods often use a carefully defined set of basis functions, and optimize for an energy function with respect to the basis function parameters. However they usually rely on normal vectors as inputs, allowing efficient optimization with linear solvers, such as Poisson Surface Reconstruction [23] and its screened version [22]. + +Neural implicit methods, which were popularised by DeepSDF [35] and Occupancy Networks [29], are promising as they provide more modeling and optimization flexibility. Rather than creating basis functions tailored to the input, the network is fixed and can adapt its representational ability through optimization. Furthermore, as they are optimized by gradient descent, they can work with any differentiable loss. This flexibility has led to learned shape spaces that allow for strong learned biases and interpolation [21, 26, 35, 47]. However, while many neural methods are able to perform better than non-neural approaches when the input has defects, they often perform worse when the data is clean and dense [20]. A major issue is that gradient descent optimization is not guaranteed to converge to a global optimum. Furthermore, many methods for the surface reconstruction task [2-4, 15, 41] use losses that are difficult for gradient descent to optimize. As the reason these losses are hard to optimize is fundamental to our method, we examine this issue and related loss formulations in Sec. 3.3. + +Our method follows a line of work that attempts to + +improve upon these issues for reconstruction from points clouds without normals. There are three major methods that are competitive for this task, DiGS [5], SAP [39] and OG-INR [25]. DiGS and OG-INR are neural SDF methods. In order to avoid the difficulties of SDF optimization, DiGS [5] changes the optimization landscape by adding strong regularization at the start, and slowly annealing the regularization to gently change the optimization landscape back to the correct one. OG-INR [25] avoids local minima by first discretizing the problem and solving for inside-outside labels. It then uses this discrete solution to get an approximate SDF that makes it easier to optimize the original SDF. SAP [39] does not use neural methods or SDFs, and instead minimizes a chamfer loss on points and normals directly. This is related to our approach as we also use points and SDF-derived normals to guide our SDF optimization. However, rather than using a chamfer loss, which we find gets trapped in bad local minima, we use a more nuanced strategy to move our guiding points, outlined in Sec. 4.1. + +Another highly related approach is Point2Mesh [17], which deforms an enclosing mesh onto the point cloud. Like SAP, they use a chamfer loss to guide the deformation, however they note that this loss does not easily enter concavities. To address this, they introduce a beam gap loss, which guides mesh vertices towards input points in the inward normal direction if they are not already well matched by chamfer distance. Our deformation strategy, in contrast, is based purely on explicitly matching points in the inward normal direction. Our approach also avoids a major shortcoming of Point2Mesh, the reconstruction output must have the same genus as the initial mesh. + +# 3. Preliminaries + +# 3.1. Notation and Definitions + +We denote the Euclidean inner product as $\langle p,q\rangle = p^{\mathsf{T}}q$ , the Euclidean distance as $d(p,q) = \| p - q\| _2$ , a unit vector as $\hat{v} = v / \| v\|$ , the cosine similarity between two vectors as $s(p,q) = \langle \hat{p},\hat{q}\rangle$ , and the distance from a point $p$ to a set $A$ by $d(p,A) = d_A(p) = \inf_{q\in A}d(p,q)$ . + +The chamfer distance $d_{C}$ is a common measure of the distance between two discrete point sets $P$ and $Q$ , defined by the average of two one-sided chamfer distances + +$$ +d _ {C} (P, Q) = \frac {1}{2} \left(d _ {\vec {C}} (P, Q) + d _ {\vec {C}} (Q, P)\right) \tag {1} +$$ + +each averaging the distance over one set to the other set + +$$ +d _ {\vec {C}} (P, Q) = \frac {1}{| P |} \sum_ {p \in P} d (p, Q). \tag {2} +$$ + +The chamfer distance can also be used between two surfaces, $A$ and $B$ , in which case the chamfer distance is taken over uniform samplings, $U_A \sim U(A)$ and $U_B \sim U(B)$ . + +A signed distance function (SDF) $F_{\mathcal{V}}: \mathcal{D} \to \mathbb{R}$ of a bounded, open volume $\mathcal{V} \subset \mathcal{D}$ is a scalar function defined everywhere on $\mathcal{D}$ . $F_{\mathcal{V}}(z)$ is the distance from $z$ to the closest point on the boundary $\partial \mathcal{V}$ , with a negative sign if $z \in \mathcal{V}$ + +$$ +F _ {\mathcal {V}} (z) = (- 1) ^ {[ [ z \in \mathcal {V} ] ]} d (z, \partial \mathcal {V}) \tag {3} +$$ + +where the Iverson bracket $\llbracket X\rrbracket$ is 1 if $X$ is true and 0 otherwise. The level set $L_{a}$ is the set of points that have a signed distance of $a$ from $\partial \mathcal{V}$ , i.e., + +$$ +L _ {a} = \{z \in \mathcal {D} \mid F _ {\mathcal {V}} (z) = a \}. \tag {4} +$$ + +The exterior level set $\Omega_{a}$ ( $a > 0$ ) is the subset of $L_{a}$ such that for each $p \in L_{a}$ there is a connected path from a point on the boundary of $\mathcal{D}$ to $p$ that only intersects $L_{a}$ at $p$ . + +# 3.2. Problem Formulation + +Let $\mathcal{X} = \{x_i\}_{i\in I}$ be a point cloud sampled from a surface $S\subset \mathcal{D}$ where $\mathcal{D}\subset \mathbb{R}^3$ is compact. We often refer to $S$ as the target shape, and assume that it is watertight, i.e., $S = \partial \mathcal{V}$ of some open volume $\mathcal{V}\subset \mathcal{D}$ . We wish to reconstruct $S$ from the point cloud $\mathcal{X} = \{x_i\}$ . Note that no per-point surface normals or scanner information is provided. + +We choose to represent our reconstructed surface $\mathcal{R} \subset \mathcal{D}$ using an implicit neural representation $\Phi$ . Specifically we define $\mathcal{R} = \{z \in \mathcal{D} \mid \Phi(z, \theta) = 0\}$ where $\theta$ are the parameters of the neural network $\Phi$ . Thus we want to minimize the chamfer distance between $\mathcal{S}$ and $\mathcal{R}$ . Since we do not know $\mathcal{S}$ , we instead compute the distance to our input points $d_{C}(\mathcal{X}, \mathcal{R}) = d_{C}(\mathcal{X}, U_{\mathcal{R}})$ , where $U_{\mathcal{R}}$ is a uniform sampling from $\mathcal{R}$ . Furthermore we choose to optimize the implicit function $\Phi$ to approximate the true signed distance function $F_{\mathcal{V}}$ of the volume $\mathcal{V}$ . As $\mathcal{V}$ is unknown, during optimization we care about ensuring that $\Phi$ is a valid SDF to some open volume $\mathcal{U}$ for which $\mathcal{X}$ is an approximate sampling, i.e., $\Phi \approx F_{\mathcal{U}}$ and $d_{C}(\mathcal{X}, \partial \mathcal{U})$ is small (note $\partial \mathcal{U} = \mathcal{R}$ ). Thus our overall optimization problem is + +$$ +\begin{array}{l l} \operatorname {m i n i m i z e} _ {\theta} & d _ {C} (\mathcal {X}, \partial \mathcal {U}) \\ \text {s u b j e c t t o} & \Phi (x, \theta) = F _ {\mathcal {U}} (x). \end{array} \tag {5} +$$ + +Why SDFs? We choose SDFs over other popular implicit functions like indicator or occupancy functions [22, 23, 29, 38] or unsigned distance functions (UDFs) [12, 16, 49] for several reasons. First, SDFs and UDFs constrain the possibilities for $\Phi$ , and are fairly smooth (unlike indicator functions). This helps with regularizing $\mathcal{R}$ and ensures that they can be represented by neural networks, which are biased to be smooth. Previous works have shown that neural SDFs empirically perform better than neural occupancy functions [51]. Second, SDFs allow for distance and direction to the surface queries, which we make use of in our algorithm. Last, the signed aspect of SDFs guarantee the watertight criteria compared to UDF, and make it easier to mesh using algorithms like marching cubes [27]. + +# 3.3. Neural SDF Formulation + +Since neural SDFs are coordinate networks, each coordinate is processed independently. During gradient descent each coordinate seeks to minimize its loss locally, and is only affected by changes in nearby coordinates due to the network's inherent smoothness bias. Thus information propagation through the domain (from the smoothness bias) is slow, and optimization is only effective if the loss provides clear guidance. Specifically, if the descent direction of the loss with respect to its SDF input value at a coordinate gives an approximate descent direction towards the target SDF value at that coordinate. However whether or not the loss provides a good descent direction depends on whether the geometry of the current state of the network aligns with the geometry of the target shape (see Fig. 2 top left for when they do not align and thus optimization gets stuck). + +We now discuss this observation in relation to currently used neural SDF losses. When optimizing neural SDFs for point clouds without normals, the main losses are + +$$ +\mathcal {L} _ {\mathrm {z l s}} (\theta , \mathcal {X}) = \sum_ {x \in \mathcal {X}} | \Phi (x, \theta) | \tag {6} +$$ + +$$ +\mathcal {L} _ {\mathrm {e i k}} (\theta) = \sum_ {z \in \mathcal {D}} | \| \nabla_ {z} \Phi (z, \theta) \| _ {2} - 1 | \tag {7} +$$ + +$$ +\mathcal {L} _ {\text {p u l l}} (\theta , \mathcal {X}) = \sum_ {z \in \mathcal {D}} \| x _ {\mathcal {R}} ^ {\star} (z) - x _ {\mathcal {X}} ^ {\star} (z) \| _ {2} \tag {8} +$$ + +where $x_{\mathcal{R}}^{\star}(z) = z - \Phi(z)\widehat{\nabla_z\Phi(z)}$ and $x_{\mathcal{X}}^{\star}(z) = \arg \min_{x\in \mathcal{X}}d(z,x)$ . The first two losses were proposed by IGR [15] and the last one was proposed by Neural Pull [4] (further details in the supplement). The zero level set loss $\mathcal{L}_{\mathrm{ZLS}}$ gives a perfect descent direction to the target SDF values for the points in $\mathcal{X}$ . However, for other points in the domain, the loss formulation may not give a descent direction towards the target SDF value. The Eikonal loss $\mathcal{L}_{\mathrm{eik}}$ guides towards scaling the SDF gradient, and does not change its direction unless forced to by the optimization of nearby points. Thus for a point $z\in \mathcal{D}$ , if the network's current normal directions in the region around $z$ is in the opposite direction to what the target SDF normals are around $z$ , then at $z$ this loss does not guide towards the target SDF values. The neural pull loss $\mathcal{L}_{\mathrm{pull}}$ has two value-gradient pairs that will minimize its loss (one where the normal points towards $x_{\mathcal{X}}^{\star}$ and one where it points away), so the loss will guide towards the closer one, which may not be the target. + +As a result, an important part of these methods is spherical initialization [2], where the network is initialized roughly to the SDF of a sphere. If the shape's geometry is similar to a sphere, then the initialized normal directions in the network are mostly in the correct direction, so $\mathcal{L}_{\mathrm{eik}}$ and $\mathcal{L}_{\mathrm{pull}}$ guide towards the correct SDF value. When the shape's geometry is very different to a sphere resulting in large regions where the initialized normal directions are + +![](images/010afb844fbfe24e3cf7bb6e4af5c2972544629a95bc1c4aa059ff075d825bc7.jpg) +Figure 3. Surface $\mathcal{S}$ and surrounding surface $\mathcal{R}$ , with outward normal directions for some points on $\mathcal{S}$ shown, and which ones are SIONs relative to $\mathcal{R}$ shown in red. + +very different to the target normal directions, then the loss does not provide a good descent direction in those regions. As a result, optimization often converges to a local minimum close to the initialization, such as in Fig. 2 (top left). + +# 3.4. Shape Reachability + +From the analysis in the previous subsection, we are interested in whether the current state of a network provides similar normal directions to the SDF of the target shape, so that the loss provides a good descent direction towards the target SDF values. Let us assume that the current state of the network is roughly the SDF to some surface $\mathcal{R}$ surrounding the target shape's surface $S$ . One way of quantifying whether the normal directions are similar is to determine if points on $S$ can "reach" $\mathcal{R}$ by travelling in their outward normal direction (see Fig. 3). If $S$ has large concavities and the outward surface normal of most points in that concavity does not reach $\mathcal{R}$ before it self-intersects, then the current normal directions of the network are likely to be poor. + +More formally, if $P_{\mathcal{S}}$ and $P_{\mathcal{R}}$ are samplings of $\mathcal{S}$ and $\mathcal{R}$ and for each $p \in P_{\mathcal{S}}$ we have a known outward unit normal $n_p$ , then for a point $p \in P_{\mathcal{S}}$ we can construct around the outward normal a thin cylinder + +$$ +\mathcal {C} _ {p} = \{z \in \mathcal {D} \mid \| p + t n _ {p} - z \| \leq \varepsilon , \langle z - p, n _ {p} \rangle \geq 0 \}. \tag {9} +$$ + +By the assumption of $\mathcal{R}$ surrounding $S$ and $P_{\mathcal{R}}$ being a dense sampling of $\mathcal{R}$ , we note that $\mathcal{C}_p \cap P_{\mathcal{R}} \neq \emptyset$ . Then we consider $p$ to have a self-intersecting outward normal (SION) with respect to $P_{\mathcal{R}}$ if its normal direction intersects its own shape before it intersects $\mathcal{R}$ : $\exists p' \in P_{\mathcal{S}}$ such that $p' \in \mathcal{C}_p$ and $\forall q \in \mathcal{C} \cap P_{\mathcal{R}}$ we have that $\| p - p' \|_2 < \| p - q \|$ . We then use the percentage of points in $p_{\mathcal{S}}$ that have SIONs with respect to $P_{\mathcal{R}}$ as a measure of how dissimilar the geometry of $S$ is to $\mathcal{R}$ , which we denote $\mathrm{SION}(S; \mathcal{R})$ , where a high value indicates dissimilarity. + +When $\mathcal{R}$ is not specified and $S$ is clear from context, we will use SION as a shorthand for $\mathrm{SION}(S; \mathcal{R})$ , with $\mathcal{R}$ assumed to be any sphere surrounding $S$ . The two point clouds in Fig. 1 have a high SION, which indicates that their geometry is very different to a sphere and that optimization + +from a spherical initialization is likely to be difficult. + +# 4. Point-Guided SDF + +The key idea of our method is to slowly converge the surface of reconstruction $\mathcal{R}$ towards the input points $\mathcal{X}$ until it interpolates $\mathcal{X}$ , while maintaining $\Phi$ as a valid SDF to the volume enclosed by $\mathcal{R}$ (see Fig. 2). We do this by guiding $\mathcal{R}$ towards level sets (Fig. 2:2a-e) and taking small steps towards reaching each level set (Fig. 2:3a-f, Fig. 4). At each step we move guiding points $\mathcal{Y}$ , which represent the surface $\mathcal{R}$ , a small distance towards $\mathcal{X}$ (Fig. 4c) and then optimize $\Phi$ to interpolate the new $\mathcal{Y}$ positions, thus defining the new surface of reconstruction $\mathcal{R}$ over which $\mathcal{Y}$ is resampled (Fig. 4d). Our full algorithm is shown in Algorithm 1. + +Since each movement of the guiding points is small, the geometry of the moved guiding points $\mathcal{V}$ should be similar to the network's current surface $\mathcal{R}$ , and $\mathrm{SION}(\mathcal{V};\mathcal{R})$ should be low. Thus optimizing the network to reconstruct the updated $\mathcal{V}$ should be robust (unlikely to converge to local minima) as the optimization is likely to have a clear descent direction from the loss at most points. + +In Sec. 4.1 we outline how to move the guiding points $\mathcal{Y}$ one step closer to the input points $\mathcal{X}$ (Fig. 4a-c). In Sec. 4.2 we outline how to optimize the network $\Phi$ to interpolate the new guiding point locations (Fig. 4d). Finally, in Sec. 4.3 we analyze our method within the homotopy framework. + +Preprocessing $\mathcal{X}$ . Following standard practice, we first center and (isotropically) scale the shape to fit in a centered ball. After scaling, we calculate the point cloud's approximate sampling radius $\delta_{\mathcal{X}}$ conservatively by calculating the distance to the four closest neighbors for each $x \in \mathcal{X}$ and averaging the highest $5\%$ of all such distances. We use this radius extensively in our method. + +Initialization. We first initialize our network to the exterior level set of radius $\delta_{\mathrm{init}} = 16\delta_{\mathcal{X}}$ . We provide intuition into why we can do this robustly in Sec. 4.3, and provide details on how to make this more efficient in the supplement. + +# 4.1. Moving the Guiding Points + +We now describe how to move the guiding points $y \in \mathcal{V}$ towards the input points $\mathcal{X}$ . At a high level, each step we move $\mathcal{V}$ closer to an exterior level set of radius $\delta$ , $\Omega_{\delta}$ , and when $\mathcal{R}$ has converged to $\Omega_{\delta}$ we reduce $\delta$ (see Algorithm 1). + +Since we are moving $y \in \mathcal{V}$ to guide the surface $\mathcal{R}$ , we only move each $y$ in the inwards normal direction of $\mathcal{R}$ . Next, since we are moving towards an exterior level set $\Omega_{\delta}$ of $\mathcal{X}$ , for each $y \in \mathcal{V}$ we find the closest input point in the inwards normal direction $x^{\star}(y) \in \mathcal{X}$ , and use this to determine the target point $\omega^{\star}(y)$ on $\Omega_{\delta}$ that we move towards. Finally, since we want to move the surface $\mathcal{R}$ slowly, we have a maximum step size for each movement. + +Closest point in the inward direction. We first define $x^{\star}(y)$ (see Fig. 4a-b). As we are moving in the inward normal direction, i.e., $-n_y$ where $n_y = \widehat{\nabla_y\Phi(y)}$ , we want to move $y$ based on the closest point $x \in \mathcal{X}$ in the inward normal direction $-n_y$ . We define the inward normal definition by setting a cosine similarity threshold $a_y \geq 0$ to define a cone $C_y$ supported at $y$ emanating in the direction $-n_y$ , + +$$ +C _ {y} = \left\{z \mid s (- n _ {y}, z - y) \geq a _ {y} \right\}. \tag {10} +$$ + +However as $y$ gets very close to points in $\mathcal{X}$ , it is unlikely that any of those nearby points stay within this cone. Thus we also consider the half ball $H_{y}$ of radius $2\delta_{\mathcal{X}}$ containing points close to $y$ + +$$ +H _ {y} = \left\{z \mid \| x - y \| _ {2} \leq 2 \delta_ {\mathcal {X}} \wedge s (- n _ {y}, z - y) \geq 0 \right\}. \tag {11} +$$ + +Thus our target point $x^{\star}(y)$ is given by + +$$ +x ^ {\star} (y) = \underset {x \in \mathcal {X} \cap \left(C _ {y} \cup H _ {y}\right)} {\arg \min } \| x - y \| _ {2}. \tag {12} +$$ + +Moving towards $\Omega_{\delta}$ . As $x^{\star}(y)$ is our closest (inward) point, a reasonable location for a point in $\Omega_{\delta}$ can be computed by moving $\delta$ away from $x^{\star}$ towards $y$ + +$$ +\omega^ {\star} (y) = \left(\| x ^ {\star} - y \| _ {2} - \delta\right) \widehat {\left(x ^ {\star} - y\right)}. \tag {13} +$$ + +We move towards $\omega^{\star}$ with a maximum step size of $s_m$ so that the movement step is small and easy to optimize. Thus our final point $y^\prime$ (see Fig. 4b) is + +$$ +y ^ {\prime} = y - \operatorname {c l i p} (\langle \omega^ {\star} (y), - n _ {y} \rangle , s _ {m}) n _ {y} \tag {14} +$$ + +where $\operatorname{clip}(a, \varepsilon)$ projects $a$ to the interval $[- \varepsilon, \varepsilon]$ . + +Reducing $\delta$ . After initialization, we set $\delta = \delta_0$ as our next target level set. Once $\mathcal{V}$ has finished moving towards $\Omega_{\delta}$ and $\mathcal{R}$ has converged, we decrease the current $\delta$ by half and start moving $\mathcal{V}$ towards the new exterior level set. We do this until $\delta$ reaches $\delta_f$ . We use $\delta_0 = 4\delta_{\mathcal{X}}$ , $\delta_f = \delta_{\mathcal{X}}$ . We then abandon $\mathcal{V}$ and optimize directly on $\mathcal{X}$ . + +# 4.2. Optimizing the Network + +We now have the points $\mathcal{V}$ to guide where our new surface should be. Furthermore, we have an approximate normal $n_y$ for each $y\in \mathcal{V}$ given by $\Phi$ , whose direction should be useful as the SION between the new position of the points relative to the previous positions is low. We use this to estimate an approximate SDF + +$$ +\tilde {F} _ {\mathcal {V}} (z) = (- 1) ^ {[ s (z - y (z), n _ {y (z)}) \geq 0 ]} d (z, y (z)) \tag {15} +$$ + +where $y(z) = \arg \min_{y\in \mathcal{Y}}d(z,y)$ and $s(p,q) = \langle \hat{p},\hat{q}\rangle$ is cosine similarity. We guide towards these values using + +$$ +\mathcal {L} _ {\mathrm {s d f}} (\theta , \mathcal {X}) = \sum_ {z \in \mathcal {D}} \| \Phi (z, \theta) - \tilde {F} _ {\mathcal {V}} (z) \| _ {2}. \tag {16} +$$ + +![](images/f50af9a8f7141de56ff4290caeb08665cf3282a23906da5a2ee08e01ce4a8bd3.jpg) +Figure 4. One iteration of Algorithm 1, steps 6-8. (a) Given the current value of our network $\Phi$ (the contours) and our guiding points $\mathcal{V}$ (the green points), for each $y\in \mathcal{V}$ we calculate a half ball $H_{y}$ and a cone $C_y$ in the inside normal direction to find an input points $x\in \mathcal{X}$ (black points) to move towards (shown for 3 points, with one highlighted in red). (b) We find the closest input point $x^{\star}(y)\in \mathcal{X}$ within $H_{y}\cap \mathcal{C}_{y}$ , and use this to calculate the new position $y^\prime$ for each $y\in \mathcal{V}$ (shown for all points). (c) The result after each $y\in \mathcal{V}$ has been moved. (d) The network $\Phi$ is optimized on the new guiding points, and $\mathcal{V}$ is resampled to densely cover the new zero level set $\mathcal{R}$ . + +Furthermore, our input points $\mathcal{X}$ should be at distance $\delta$ from $\mathcal{Y}$ and should be inside, so we add a loss term + +$$ +\mathcal {L} _ {\text {i n p u t}} (\theta , \mathcal {X}, \delta) = \sum_ {x \in \mathcal {X}} | \Phi (x, \theta) + \delta |. \tag {17} +$$ + +Thus our overall loss term formulation is + +$$ +\mathcal {L} (\theta , \mathcal {X}, \mathcal {Y}, \delta) = \mathcal {L} _ {\mathrm {z l s}} (\theta , \mathcal {Y}) + \mathcal {L} _ {\text {i n p u t}} (\theta , \mathcal {X}, \delta) + \mathcal {L} _ {\mathrm {e i k}} (\theta) + +$$ + +$$ +\widetilde {\mathcal {L} _ {\mathrm {s d f}}} (\theta , \mathcal {Y}) + \mathcal {L} _ {\text {p u l l}} (\theta , \mathcal {Y}). \tag {18} +$$ + +Relevant details (e.g., loss term weightings, domain sampling procedure, optimizer settings) are in the supplement. + +Finally, we resample $\mathcal{V}$ in the new zero level set $\mathcal{R}$ (Fig. 4f) so that it densely samples it. After this process has finished (i.e., when $\Phi$ has converged for $\delta = \delta_f$ ), we optimize $\Phi$ on the input points $\mathcal{X}$ using the loss in Eq. (18). Here we do not use the approximate SDF term, as $\mathcal{X}$ is likely to have more imperfections that our guiding points. + +Algorithm 1 Point-Guided SDF +1: procedure PG-SDF( $\mathcal{X}$ ) +2: Center $\mathcal{X}$ , scale $\mathcal{X}$ and compute sampling radius $\delta_{\mathcal{X}}$ +3: $\mathcal{Y}, \mathcal{N}_{\mathcal{Y}}, \Phi \gets$ Initialization $(\mathcal{X}, \delta_{\mathrm{init}})$ +4: $\delta \gets \delta_0$ +5: while $\delta \geq \delta_f$ do +6: Move $\mathcal{Y}$ using Eq. (14) +7: Optimize $\Phi$ to match $\mathcal{Y}$ +8: Resample $\mathcal{Y}$ on new $\mathcal{R}$ +9: Query $\Phi$ for normals $\mathcal{N}_{\mathcal{Y}}$ +10: if $\Phi$ 's zero level set has not changed then +11: $\delta \gets \frac{1}{2} \delta$ +12: end if +13: end while +14: Optimize $\Phi$ on $\mathcal{X}$ +15: return $\Phi$ +16: end procedure + +# 4.3. Interpretation as a Homotopy Method + +One way to analyze this method is in the context of a homotopy method [33]. Here, we wish to solve a difficult problem $M(\theta) = 0$ for $\theta$ , and instead consider the homotopy map $H(\theta, t) = tM(\theta) + (1 - t)N(\theta)$ where $N(\theta) = 0$ is easy to solve and $t \in [0,1]$ . This forms a homotopy between the problems $M(\theta) = H(\theta, 1)$ and $N(\theta) = H(\theta, 0)$ as we can now continuously deform one problem into the other by varying $t$ . By taking small steps along the zero path, the trajectory of points $(\theta, t)$ for which $H(\theta, t) = 0$ , we can reach the solution to $M(\theta)$ . + +For our method, we start by solving the easier problem $\mathcal{L}(\theta, \mathcal{Y}_0) = 0$ where $\mathcal{Y}_0$ is our initial set of guiding points. Our goal is to solve the hard problem $\mathcal{L}(\theta, \mathcal{X}) = 0$ . To see that our method is a homotopy method, note that our guiding points $\mathcal{Y}$ are facilitating a topological homotopy from $\mathcal{Y}_0$ to our input points $\mathcal{X}$ . Thus we can parameterize our zero path using $\mathcal{Y}$ . It is given by $(\theta(\mathcal{Y}), t(\mathcal{Y}))$ where + +$$ +\theta (\mathcal {Y}) \text {s a t i s f i e s} \mathcal {L} (\theta (\mathcal {Y}), \mathcal {Y}) = 0 \tag {19} +$$ + +$$ +t (\mathcal {Y}) = \frac {d _ {C} \left(\mathcal {Y} _ {0} , \mathcal {X}\right) - d _ {C} \left(\mathcal {Y} , \mathcal {X}\right)}{d _ {C} \left(\mathcal {Y} _ {0} , \mathcal {X}\right)}. \tag {20} +$$ + +Note that at initialization $\mathcal{V} = \mathcal{V}_0$ and we have $t(\mathcal{V}_0) = 0$ , while at termination $\mathcal{V} = \mathcal{X}$ and we have $t(\mathcal{X}) = 1$ . Each time we update $\mathcal{V}$ , we are traversing the zero path. If we take $n$ steps to reach the final exterior level set of radius $\delta_{\mathcal{X}}$ , then we visit $n + 2$ points along the zero path parameterized by the sequence $\mathcal{V}_0, \mathcal{V}_1, \ldots, \mathcal{V}_n, \mathcal{X}$ . + +To see why this works well in practice, we need to show that solving $H(\theta(\mathcal{Y}_{k+1}), t(\mathcal{Y}_{k+1}))$ for $\theta(\mathcal{Y}_{k+1})$ given $\theta(\mathcal{Y}_k)$ is easy, and solving $H(\theta(\mathcal{Y}_0), t(\mathcal{Y}_0))$ for $\theta(\mathcal{Y}_0)$ is easy. To see the former, note that we move our guiding points $\mathcal{V}$ only a small distance from $\mathcal{V}_k$ to $\mathcal{V}_{k+1}$ , and that $\mathrm{SION}(\mathcal{Y}_{k+1};\mathcal{V}_k)$ is small by construction. Thus, by the analysis in Secs. 3.3 and 3.4, the relative optimization problem is easy. To see the + +![](images/3f37c96cba253e0cec25111a07694230dd9d9b2e04f27bb1bdbdf1e1c07d8226.jpg) +Figure 5. Qualitative results on ShapeNet. Top: Intermediate results as our method converges to different level sets $\Omega_{\delta}$ . Bottom: Comparison with other methods, for challenging high SION shapes (0.40 for the car and 0.42 for the lamp). + +latter, when $\delta_{\mathrm{init}} \gg \delta_{\mathcal{X}}$ we can estimate good normals for $\mathcal{Y}_0$ by taking the displacement from the closest input point. With good normal estimates, $\mathcal{L}_{\widetilde{\mathrm{sdf}}}$ is very effective, and so optimization is easy. Furthermore, we note that higher radius exterior level sets are less complex, with smaller SION to an enclosing sphere. We formalize and prove this observation in the supplement. + +# 5. Results + +Dataset. We evaluate the performance of our method on ShapeNet [11], a large dataset of 3D CAD models. In this dataset, there are many shapes with complex geometries that are challenging to reconstruct, including extremely thin surfaces (sometimes string-like), hollow regions (often with small openings), and shapes with high genus. Previous works [5, 25] have shown that many neural methods fail on these shapes, even when using the ground-truth normals. We use the preprocessed watertight subset of Williams et al. [46], which consists of 13 classes with 20 shapes in each class. For each shape, 100k points are uniformly sampled from the surface and ground-truth normals are provided for each point, which are only used for those methods that require normals. We use these points as the input to our method, and for evaluating the squared chamfer metric. An additional 100k points are uniformly sampled within the domain with ground-truth labels that indicate whether the point is inside or outside the shape, allowing for the interior intersection-over-union (IoU) metric to be calculated. Further experimental details are given in the supplement. + +
MethodSquared Chamfer ↓IoU ↑
NN nxMeanMedianStdMeanMedianStd
SPSR [22]× T5.44e-51.97e-55.06e-40.99260.99560.0105
IGR [15]✓ T5.12e-41.13e-42.15e-30.81020.84800.1519
SIREN [41]✓ T1.03e-45.28e-51.93e-40.82680.90970.2329
FFN [43]✓ T9.12e-58.65e-53.36e-50.82180.83960.0989
NSP [46]× T5.36e-54.06e-53.64e-50.89730.92300.0871
DiGS+N [5]✓ T2.74e-42.32e-59.90e-40.92000.97740.1992
SDF+N†✓ T3.97e-52.22e-58.98e-50.99150.99510.0141
Ours+N✓ T2.43e-52.15e-51.66e-50.99320.99550.0076
SPSR [22]× E3.76e-34.37e-51.14e-20.71870.97610.3767
SIREN [41]✓ ×3.08e-42.58e-43.26e-40.30850.29520.2014
SAL [2]✓ ×1.14e-32.11e-43.63e-30.40300.39440.2722
DiGS [5]✓ ×1.32e-42.55e-54.73e-40.93900.97640.1262
SAP [39]× ×4.09e-42.46e-52.60e-30.91180.99230.2002
OG-S [25]✓ ×3.75e-52.17e-58.24e-50.96150.98710.1048
OG-N [25]✓ ×5.07e-52.57e-59.39e-50.95930.98700.1057
SDF†✓ ×1.84e-48.15e-42.95e-30.54900.52450.3572
SDF+N†✓ E2.48e-25.89e-55.63e-30.68170.96710.3990
Ours+N✓ E2.79e-24.79e-56.79e-20.70170.97210.3876
Ours✓ ×3.72e-52.40e-55.39e-50.97290.98960.0676
+ +Table 1. Surface reconstruction results on ShapeNet [11]. NN: uses a neural network. $n_x$ : uses ground-truth (T), estimated (E) or no (×) input surface normals. Suffix ‘+N’ denotes normal information added to the underlying method. † Our implementation. + +Implementation and Baselines. Our baseline methods use the same implementation framework as our approach (see full details in the supplement) with standard loss formulations. 'SDF' uses $\mathcal{L}_{\mathrm{zls}}$ , $\mathcal{L}_{\mathrm{eik}}$ , and $\mathcal{L}_{\mathrm{pull}}$ while 'SDF+N' additionally uses $\mathcal{L}_{\widetilde{\mathrm{sdf}}}$ and $\mathcal{L}_{\mathrm{normal}}$ [15]. We also evaluate our methods with estimated normals (using Open3D [50]). + +# 5.1. Surface Reconstruction on ShapeNet + +Results on the full ShapeNet subset are given in Tab. 1, with qualitative results in Fig. 5. Our proposed method outperforms all prior normal-free methods and even demonstrates improvement when ground-truth normals are available. In particular, our approach gets a significant improvement in mean IoU, with much smaller variance, indicating that our method performs reliably well. + +# 5.2. Challenging High-SION Shapes + +In this section, we analyze the performance of surface reconstruction methods with respect to the SION metric. Fig. 6 shows that the mean IoU degrades significantly as we progressively consider shapes with higher SION scores. While our method also follows this trend, performance degradation is considerably slower, indicating that our method is much more robust to challenging shapes. We report the reconstruction performance on the subset of 20 shapes with the highest SION in Tab. 2. On these most challenging shapes, our approach has a decisive advantage. This demonstrates that our structured optimization approach is able to achieve good reconstructions of the most difficult shapes, without sacrificing performance on easy shapes. + +![](images/2629c760daeac6654d94d308a61910968f8fd786c3aadcbf08e3c9b0494a5077.jpg) +Figure 6. Mean IoU for all shapes with a SION higher than a lower bound. The analysis from Secs. 3.3 and 3.4 predicts a significant negative correlation for existing neural SDF methods. Our method weakens this trend considerably. + +
MethodNN\(n_x\)Squared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
SPSR [22]×T3.98e-53.92e-51.80e-50.97980.98480.0222
DiGS+N [5]✓T2.09e-47.42e-52.91e-40.81600.87640.2119
\(\text{SDF}+\text{N}^{\dagger}\)✓T1.11e-44.84e-51.95e-40.97330.98540.0409
Ours+N✓T4.16e-53.89e-51.86e-50.98220.98650.0148
SPSR [22]×E5.83e-31.25e-31.16e-20.32900.18020.3445
DiGS [5]✓×4.34e-41.71e-45.34e-40.71080.81960.2536
SAP [39]××1.28e-45.84e-51.99e-40.76160.88720.2665
OG-S [25]✓×1.31e-46.50e-51.79e-40.76510.92190.2512
\(\text{SDF}^{\dagger}\)✓×1.29e-37.75e -41.43e-30.34130.26170.2292
\(\text{SDF}+\text{N}^{\dagger}\)✓E5.32e-24.51e-37.03e-20.28960.19770.3288
Ours+N✓E4.89e-27.32e-36.25e-20.31730.23620.3259
Ours✓×5.51e-54.87e-53.12e-50.91530.95980.0906
+ +Table 2. Surface reconstruction results on the 20 highest SION ShapeNet shapes. NN: uses a neural network. $n_x$ : uses ground-truth (T), estimated (E) or no (X) input surface normals. Suffix ‘+N’ denotes adding normal information to the underlying method. † Our implementation. + +
Guidance y0 yδ0 δfSquared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
× × - -2.41e-31.18e-32.65e-30.27950.22550.2078
✓ × - -2.63e-41.91e-42.31e-40.56940.60910.2278
✓ ✓ 429.89e-57.70e-57.95e-50.86570.9163
✓ ✓ 118.08e-57.52e-55.66e-50.85380.9386
✓ ✓ 415.51e-54.87e-53.12e-50.91530.9598
+ +Table 3. Ablation results on the 20 highest SION ShapeNet shapes. $\mathcal{V}_0$ : uses our SDF initialization strategy instead of spherical initialization [15]. $\mathcal{V}$ : uses our point guidance strategy. $\delta_0 / \delta_f$ : starting and final level set radii, given in multiples of $\delta_{\mathcal{X}}$ . + +# 5.3. Ablation Study and Runtime + +An ablation study, on the 20 highest-SION shapes of ShapeNet, is reported in Tab. 3. The performance when using a spherical initialization and optimizing with respect to the input points (row 1) is poor. It improves significantly + +![](images/c1e7de4b29b4865bd25a908524a6750fb0526d66715e27e1961c33cf06a65f65.jpg) +Figure 7. Runtime vs SION on ShapeNet for our method. Challenging shapes with high SION take more time to optimize. One outlier (82 min) is truncated for clarity and marked as $\times$ . + +when replaced with our high exterior level set initialization (row 2). When point guidance is added (rows 3-5), the performance increases considerably. In particular, stopping point guidance early (when $\delta_f = 2\delta_{\mathcal{X}}$ ) harms performance, as does guiding straight to the final level set target ( $\delta_0 = \delta_{\mathcal{X}}$ ) without first converging to intermediate level set targets. Our gradual homotopy approach performs best by a significant margin, justifying the strategy. + +An unoptimized implementation of our method takes 10 mins on average per ShapeNet shape (a median of 7.4 mins). Convergence time depends strongly on the difficulty of the shape, as shown in Fig. 7. Our implementation has 17.5M parameters: a small neural network with Fourier feature embeddings [43] and parametric embeddings [31, 42] computed using a dense feature grid ( $>99\%$ of the parameters). + +# 6. Discussion and Conclusion + +In this paper, we proposed a point-guided optimization method for neural SDF reconstruction from raw point clouds. We also examined why neural SDF losses can be detrimental for some shapes, proposed a metric to identify these shapes, and used this analysis to justify our algorithm design. Our method outperforms prior work, with large improvements for the most challenging shapes. + +Like many methods, our approach is not robust to high outlier fractions and large noise scales, behaving similarly to the compared methods. In addition, our approach does not handle large occlusions gracefully, since it treats these regions like concavities to be explored. This could be alleviated by defining anisotropic per-point sampling radii $\delta_{i}$ . + +Acknowledgements. Y. Ben-Shabat is supported by the Marie Sklodowska-Curie grant agreement No. 893465 S. Gould is a recipient of an ARC Future Fellowship (proj. no. LP200100421) funded by the Australian Government. 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Given a point cloud without ground-truth normals (left), neural SDF optimization for surface fitting frequently gets trapped in local minima (middle). Note that these two shapes have geometry very different to a sphere, which causes the loss right after spherical initialization to not provide a good descent direction towards the target shape (see Sec. 3.3). Our point-guided homotopy-based approach provides a principled way to avoid this issue and improve reconstruction quality (right)." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 481, + 545, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 564 + ], + "type": "text", + "content": "does not give a good descent direction towards the target SDF values, especially when the initialization does not align with the target geometry. Since most methods initialize to a sphere to bias the optimization result towards a bounded shape, and rely on this bias to find a good descent direction, their performance can be poor if the input shape has very different geometry to a sphere (see Fig. 1)." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 565, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 565, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 565, + 545, + 673 + ], + "type": "text", + "content": "Instead we propose a point-guided SDF (PG-SDF) approach, where we introduce guiding points to represent an intermediate surface for the optimization to target. By incrementally moving the guiding points towards the sampled input and optimizing the network to their new location, we ensure that the loss formulation gives a good descent direction during optimization. We eventually converge the guiding points to the input points, leading the optimization stably towards the target SDF. We also propose" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 712 + ], + "type": "text", + "content": "1To avoid confusion, in this paper we use the term normal direction to refer to vectors in the normalized gradient field of the SDF and descent direction for the negative gradient of the loss function." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21456" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 81, + 547, + 247 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 93, + 79 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 93, + 79 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 93, + 79 + ], + "type": "text", + "content": "No Guidance" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 435, + 71, + 544, + 80 + ], + "lines": [ + { + "bbox": [ + 435, + 71, + 544, + 80 + ], + "spans": [ + { + "bbox": [ + 435, + 71, + 544, + 80 + ], + "type": "text", + "content": "Small Steps (between 2a and 2b)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 49, + 81, + 547, + 247 + ], + "lines": [ + { + "bbox": [ + 49, + 81, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 49, + 81, + 547, + 247 + ], + "type": "image", + "image_path": "e8ebb0b1e94055c8da1407da7f88459c925bf1d73f6ee2fc30e51637f273fde0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": "Figure 2. Reconstructing a 2D surface using a neural SDF, without (1a-e) and with (2a-e,3a-f) our proposed point guidance. Note that our point guidance has two parts, converging to level sets (2) and taking small steps in between (3). The input points " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": " are black, the guiding points " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": " are green, and the network's level sets are drawn as contour lines with the zero level set " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": " in bold. (1a-b) The network deforms from the sphere initialization to one whose zero level set is close to " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": ". (1c) The network only makes local changes near " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": ", gradually interpolating " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": " by adding complexity. (1d-e) " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": " is fully interpolated, but the result is unsatisfactory. (2a) Our initialization. (2b-d) Our method after convergence to each intermediate level set. (2e) Our method after optimizing on the input points. (3a-f) The small steps taken by our method while reaching the first intermediate level set of radius " + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "inline_equation", + "content": "\\delta_0" + }, + { + "bbox": [ + 46, + 258, + 547, + 346 + ], + "type": "text", + "content": ". Each row shows a single step, where the guiding points are first moved a short distance (left) and then the network is optimized to match this (right)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 368, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 450 + ], + "type": "text", + "content": "a metric—the percentage of self-intersecting outward normals (SION%)—to quantify the difference between the surface geometry of a target shape and that of another surface, such as the sphere initialization. We use this metric to determine which shapes are likely to be difficult for neural SDF methods, and why the optimization steps in our method are robust. Our contributions are:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 452, + 287, + 548 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 452, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 287, + 475 + ], + "type": "text", + "content": "1. a point-guided optimization approach for surface reconstruction from point clouds without normals;" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "content": "2. a metric to quantify differences between surfaces, which can be used to identify the most challenging shapes to reconstruct; and" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 511, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 511, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 511, + 287, + 548 + ], + "type": "text", + "content": "3. an interpretation of the algorithm as a homotopy method, providing a justification for the design decisions and insight into the failure modes of existing approaches." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 560, + 134, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 134, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 134, + 572 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 581, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 640 + ], + "type": "text", + "content": "Surface reconstruction from point clouds is a fundamental problem in computer vision. We restrict our attention to methods that optimize using generic priors, rather than methods that learn reconstruction priors from a dataset [19, 45] and are sensitive to domain shift." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "Early approaches [1, 7, 10, 24] directly triangulated point clouds, with provable guarantees given dense input points with no defects. However, the limitation of vertices being input points make them impractical for even small levels of imperfection [6], and the result is often not watertight. A less restrictive class of approaches is implicit field methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 368, + 545, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 545, + 463 + ], + "type": "text", + "content": "[9, 22, 23, 32, 34], where an implicit function is defined over the domain to represent the reconstructed surface. Such methods often use a carefully defined set of basis functions, and optimize for an energy function with respect to the basis function parameters. However they usually rely on normal vectors as inputs, allowing efficient optimization with linear solvers, such as Poisson Surface Reconstruction [23] and its screened version [22]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 468, + 546, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 546, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 546, + 696 + ], + "type": "text", + "content": "Neural implicit methods, which were popularised by DeepSDF [35] and Occupancy Networks [29], are promising as they provide more modeling and optimization flexibility. Rather than creating basis functions tailored to the input, the network is fixed and can adapt its representational ability through optimization. Furthermore, as they are optimized by gradient descent, they can work with any differentiable loss. This flexibility has led to learned shape spaces that allow for strong learned biases and interpolation [21, 26, 35, 47]. However, while many neural methods are able to perform better than non-neural approaches when the input has defects, they often perform worse when the data is clean and dense [20]. A major issue is that gradient descent optimization is not guaranteed to converge to a global optimum. Furthermore, many methods for the surface reconstruction task [2-4, 15, 41] use losses that are difficult for gradient descent to optimize. As the reason these losses are hard to optimize is fundamental to our method, we examine this issue and related loss formulations in Sec. 3.3." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "Our method follows a line of work that attempts to" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21457" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 300 + ], + "type": "text", + "content": "improve upon these issues for reconstruction from points clouds without normals. There are three major methods that are competitive for this task, DiGS [5], SAP [39] and OG-INR [25]. DiGS and OG-INR are neural SDF methods. In order to avoid the difficulties of SDF optimization, DiGS [5] changes the optimization landscape by adding strong regularization at the start, and slowly annealing the regularization to gently change the optimization landscape back to the correct one. OG-INR [25] avoids local minima by first discretizing the problem and solving for inside-outside labels. It then uses this discrete solution to get an approximate SDF that makes it easier to optimize the original SDF. SAP [39] does not use neural methods or SDFs, and instead minimizes a chamfer loss on points and normals directly. This is related to our approach as we also use points and SDF-derived normals to guide our SDF optimization. However, rather than using a chamfer loss, which we find gets trapped in bad local minima, we use a more nuanced strategy to move our guiding points, outlined in Sec. 4.1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 289, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 289, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 289, + 443 + ], + "type": "text", + "content": "Another highly related approach is Point2Mesh [17], which deforms an enclosing mesh onto the point cloud. Like SAP, they use a chamfer loss to guide the deformation, however they note that this loss does not easily enter concavities. To address this, they introduce a beam gap loss, which guides mesh vertices towards input points in the inward normal direction if they are not already well matched by chamfer distance. Our deformation strategy, in contrast, is based purely on explicitly matching points in the inward normal direction. Our approach also avoids a major shortcoming of Point2Mesh, the reconstruction output must have the same genus as the initial mesh." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 454, + 133, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 133, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 133, + 466 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 473, + 185, + 485 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 473, + 185, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 473, + 185, + 485 + ], + "type": "text", + "content": "3.1. Notation and Definitions" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": "We denote the Euclidean inner product as " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\langle p,q\\rangle = p^{\\mathsf{T}}q" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": ", the Euclidean distance as " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "d(p,q) = \\| p - q\\| _2" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": ", a unit vector as " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\hat{v} = v / \\| v\\|" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": ", the cosine similarity between two vectors as " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": ", and the distance from a point " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": " to a set " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "inline_equation", + "content": "d(p,A) = d_A(p) = \\inf_{q\\in A}d(p,q)" + }, + { + "bbox": [ + 47, + 491, + 287, + 552 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "text", + "content": "The chamfer distance " + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "inline_equation", + "content": "d_{C}" + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "text", + "content": " is a common measure of the distance between two discrete point sets " + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 552, + 287, + 588 + ], + "type": "text", + "content": ", defined by the average of two one-sided chamfer distances" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 594, + 287, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 594, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 85, + 594, + 287, + 617 + ], + "type": "interline_equation", + "content": "d _ {C} (P, Q) = \\frac {1}{2} \\left(d _ {\\vec {C}} (P, Q) + d _ {\\vec {C}} (Q, P)\\right) \\tag {1}", + "image_path": "d649541fe9b3cfa64c27f7168acc65819404cef1a9ec6f78046de3c14b133b68.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 623, + 271, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 271, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 271, + 635 + ], + "type": "text", + "content": "each averaging the distance over one set to the other set" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 641, + 287, + 670 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 641, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 287, + 670 + ], + "type": "interline_equation", + "content": "d _ {\\vec {C}} (P, Q) = \\frac {1}{| P |} \\sum_ {p \\in P} d (p, Q). \\tag {2}", + "image_path": "1a4addc80ee9cc3e6517addc78334b038e5ae037e6875623767fd44cd2365ae5.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "The chamfer distance can also be used between two surfaces, " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": ", in which case the chamfer distance is taken over uniform samplings, " + }, + { + "bbox": [ + 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"inline_equation", + "content": "\\mathcal{V} \\subset \\mathcal{D}" + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": " is a scalar function defined everywhere on " + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{V}}(z)" + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": " is the distance from " + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": " to the closest point on the boundary " + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{V}" + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": ", with a negative sign if " + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "inline_equation", + "content": "z \\in \\mathcal{V}" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 134, + 545, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 134, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 364, + 134, + 545, + 150 + ], + "type": "interline_equation", + "content": "F _ {\\mathcal {V}} (z) = (- 1) ^ {[ [ z \\in \\mathcal {V} ] ]} d (z, \\partial \\mathcal {V}) \\tag {3}", + "image_path": "709b779021a284ef13682e559b88fda0601d4f09527870175d8525a2ad765498.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "content": "where the Iverson bracket " + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\llbracket X\\rrbracket" + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "content": " is 1 if " + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "content": " is true and 0 otherwise. The level set " + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "inline_equation", + "content": "L_{a}" + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "content": " is the set of points that have a signed distance of " + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{V}" + }, + { + "bbox": [ + 304, + 154, + 547, + 190 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 366, + 195, + 545, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 195, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 366, + 195, + 545, + 209 + ], + "type": "interline_equation", + "content": "L _ {a} = \\{z \\in \\mathcal {D} \\mid F _ {\\mathcal {V}} (z) = a \\}. \\tag {4}", + "image_path": "51b9ddaebd992fe116a5169dd6a6ea091881bec169cd076741f3feef1e6e265b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": "The exterior level set " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "\\Omega_{a}" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "a > 0" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": ") is the subset of " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "L_{a}" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": " such that for each " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "p \\in L_{a}" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": " there is a connected path from a point on the boundary of " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": " that only intersects " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "L_{a}" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 213, + 547, + 250 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 255, + 430, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 255, + 430, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 255, + 430, + 266 + ], + "type": "text", + "content": "3.2. Problem Formulation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\{x_i\\}_{i\\in I}" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " be a point cloud sampled from a surface " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "S\\subset \\mathcal{D}" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{D}\\subset \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " is compact. We often refer to " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " as the target shape, and assume that it is watertight, i.e., " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "S = \\partial \\mathcal{V}" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " of some open volume " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{V}\\subset \\mathcal{D}" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": ". We wish to reconstruct " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": " from the point cloud " + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = \\{x_i\\}" + }, + { + "bbox": [ + 304, + 273, + 547, + 344 + ], + "type": "text", + "content": ". Note that no per-point surface normals or scanner information is provided." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": "We choose to represent our reconstructed surface " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{R} \\subset \\mathcal{D}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " using an implicit neural representation " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ". Specifically we define " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\{z \\in \\mathcal{D} \\mid \\Phi(z, \\theta) = 0\\}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " are the parameters of the neural network " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ". Thus we want to minimize the chamfer distance between " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ". Since we do not know " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ", we instead compute the distance to our input points " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "d_{C}(\\mathcal{X}, \\mathcal{R}) = d_{C}(\\mathcal{X}, U_{\\mathcal{R}})" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "U_{\\mathcal{R}}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " is a uniform sampling from " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ". Furthermore we choose to optimize the implicit function " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " to approximate the true signed distance function " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "F_{\\mathcal{V}}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " of the volume " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " is unknown, during optimization we care about ensuring that " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " is a valid SDF to some open volume " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{U}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " for which " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " is an approximate sampling, i.e., " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\Phi \\approx F_{\\mathcal{U}}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "d_{C}(\\mathcal{X}, \\partial \\mathcal{U})" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": " is small (note " + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "inline_equation", + "content": "\\partial \\mathcal{U} = \\mathcal{R}" + }, + { + "bbox": [ + 304, + 345, + 546, + 513 + ], + "type": "text", + "content": "). Thus our overall optimization problem is" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 361, + 517, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 517, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 361, + 517, + 545, + 541 + ], + "type": "interline_equation", + "content": "\\begin{array}{l l} \\operatorname {m i n i m i z e} _ {\\theta} & d _ {C} (\\mathcal {X}, \\partial \\mathcal {U}) \\\\ \\text {s u b j e c t t o} & \\Phi (x, \\theta) = F _ {\\mathcal {U}} (x). \\end{array} \\tag {5}", + "image_path": "d9b90856e84facb3eb2b8b944dabd477546f8098f67edd152750d824722e262d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": "Why SDFs? We choose SDFs over other popular implicit functions like indicator or occupancy functions [22, 23, 29, 38] or unsigned distance functions (UDFs) [12, 16, 49] for several reasons. First, SDFs and UDFs constrain the possibilities for " + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": ", and are fairly smooth (unlike indicator functions). This helps with regularizing " + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 545, + 547, + 714 + ], + "type": "text", + "content": " and ensures that they can be represented by neural networks, which are biased to be smooth. Previous works have shown that neural SDFs empirically perform better than neural occupancy functions [51]. Second, SDFs allow for distance and direction to the surface queries, which we make use of in our algorithm. Last, the signed aspect of SDFs guarantee the watertight criteria compared to UDF, and make it easier to mesh using algorithms like marching cubes [27]." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21458" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 188, + 83 + ], + "type": "text", + "content": "3.3. Neural SDF Formulation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "type": "text", + "content": "Since neural SDFs are coordinate networks, each coordinate is processed independently. During gradient descent each coordinate seeks to minimize its loss locally, and is only affected by changes in nearby coordinates due to the network's inherent smoothness bias. Thus information propagation through the domain (from the smoothness bias) is slow, and optimization is only effective if the loss provides clear guidance. Specifically, if the descent direction of the loss with respect to its SDF input value at a coordinate gives an approximate descent direction towards the target SDF value at that coordinate. However whether or not the loss provides a good descent direction depends on whether the geometry of the current state of the network aligns with the geometry of the target shape (see Fig. 2 top left for when they do not align and thus optimization gets stuck)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 305 + ], + "type": "text", + "content": "We now discuss this observation in relation to currently used neural SDF losses. When optimizing neural SDFs for point clouds without normals, the main losses are" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 311, + 287, + 337 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 311, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 91, + 311, + 287, + 337 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {X}) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) | \\tag {6}", + "image_path": "48ee1f507b6fae18f72404c893731e102293f2788e5a742896fdbcb1c25afee7.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 339, + 287, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 339, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 104, + 339, + 287, + 365 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {e i k}} (\\theta) = \\sum_ {z \\in \\mathcal {D}} | \\| \\nabla_ {z} \\Phi (z, \\theta) \\| _ {2} - 1 | \\tag {7}", + "image_path": "206eb333a584409778c0f38a8ca1eb5d0611fd6b3120ecaec7deacd2ec066698.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 88, + 367, + 287, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 367, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 88, + 367, + 287, + 392 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| x _ {\\mathcal {R}} ^ {\\star} (z) - x _ {\\mathcal {X}} ^ {\\star} (z) \\| _ {2} \\tag {8}", + "image_path": "942f61ce488a0953109ecd49c46b375ad22171b63c5048b0c8241017b73a895e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "x_{\\mathcal{R}}^{\\star}(z) = z - \\Phi(z)\\widehat{\\nabla_z\\Phi(z)}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "x_{\\mathcal{X}}^{\\star}(z) = \\arg \\min_{x\\in \\mathcal{X}}d(z,x)" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": ". The first two losses were proposed by IGR [15] and the last one was proposed by Neural Pull [4] (further details in the supplement). The zero level set loss " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{ZLS}}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " gives a perfect descent direction to the target SDF values for the points in " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": ". However, for other points in the domain, the loss formulation may not give a descent direction towards the target SDF value. The Eikonal loss " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{eik}}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " guides towards scaling the SDF gradient, and does not change its direction unless forced to by the optimization of nearby points. Thus for a point " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "z\\in \\mathcal{D}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": ", if the network's current normal directions in the region around " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " is in the opposite direction to what the target SDF normals are around " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": ", then at " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " this loss does not guide towards the target SDF values. The neural pull loss " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pull}}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " has two value-gradient pairs that will minimize its loss (one where the normal points towards " + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "inline_equation", + "content": "x_{\\mathcal{X}}^{\\star}" + }, + { + "bbox": [ + 46, + 399, + 287, + 617 + ], + "type": "text", + "content": " and one where it points away), so the loss will guide towards the closer one, which may not be the target." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "As a result, an important part of these methods is spherical initialization [2], where the network is initialized roughly to the SDF of a sphere. If the shape's geometry is similar to a sphere, then the initialized normal directions in the network are mostly in the correct direction, so " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{eik}}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pull}}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " guide towards the correct SDF value. When the shape's geometry is very different to a sphere resulting in large regions where the initialized normal directions are" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 369, + 73, + 484, + 175 + ], + "blocks": [ + { + "bbox": [ + 369, + 73, + 484, + 175 + ], + "lines": [ + { + "bbox": [ + 369, + 73, + 484, + 175 + ], + "spans": [ + { + "bbox": [ + 369, + 73, + 484, + 175 + ], + "type": "image", + "image_path": "010afb844fbfe24e3cf7bb6e4af5c2972544629a95bc1c4aa059ff075d825bc7.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "lines": [ + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "spans": [ + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "text", + "content": "Figure 3. Surface " + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "text", + "content": " and surrounding surface " + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "text", + "content": ", with outward normal directions for some points on " + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "text", + "content": " shown, and which ones are SIONs relative to " + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 182, + 545, + 215 + ], + "type": "text", + "content": " shown in red." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 228, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 545, + 277 + ], + "type": "text", + "content": "very different to the target normal directions, then the loss does not provide a good descent direction in those regions. As a result, optimization often converges to a local minimum close to the initialization, such as in Fig. 2 (top left)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 284, + 418, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 284, + 418, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 284, + 418, + 297 + ], + "type": "text", + "content": "3.4. Shape Reachability" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": "From the analysis in the previous subsection, we are interested in whether the current state of a network provides similar normal directions to the SDF of the target shape, so that the loss provides a good descent direction towards the target SDF values. Let us assume that the current state of the network is roughly the SDF to some surface " + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": " surrounding the target shape's surface " + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": ". One way of quantifying whether the normal directions are similar is to determine if points on " + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": " can \"reach\" " + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": " by travelling in their outward normal direction (see Fig. 3). If " + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": " has large concavities and the outward surface normal of most points in that concavity does not reach " + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 303, + 545, + 457 + ], + "type": "text", + "content": " before it self-intersects, then the current normal directions of the network are likely to be poor." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": "More formally, if " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{S}}" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{R}}" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": " are samplings of " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{S}" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": " and for each " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "p \\in P_{\\mathcal{S}}" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": " we have a known outward unit normal " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "n_p" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": ", then for a point " + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "inline_equation", + "content": "p \\in P_{\\mathcal{S}}" + }, + { + "bbox": [ + 305, + 458, + 545, + 506 + ], + "type": "text", + "content": " we can construct around the outward normal a thin cylinder" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 513, + 545, + 528 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 513, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 310, + 513, + 545, + 528 + ], + "type": "interline_equation", + "content": "\\mathcal {C} _ {p} = \\{z \\in \\mathcal {D} \\mid \\| p + t n _ {p} - z \\| \\leq \\varepsilon , \\langle z - p, n _ {p} \\rangle \\geq 0 \\}. \\tag {9}", + "image_path": "fda0702bb33b0da574ae15d1441ec902588ee994e6957613d652110b69734cbb.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": "By the assumption of " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " surrounding " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{R}}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " being a dense sampling of " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": ", we note that " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_p \\cap P_{\\mathcal{R}} \\neq \\emptyset" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": ". Then we consider " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " to have a self-intersecting outward normal (SION) with respect to " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{R}}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " if its normal direction intersects its own shape before it intersects " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\exists p' \\in P_{\\mathcal{S}}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "p' \\in \\mathcal{C}_p" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\forall q \\in \\mathcal{C} \\cap P_{\\mathcal{R}}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " we have that " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\| p - p' \\|_2 < \\| p - q \\|" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": ". We then use the percentage of points in " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "p_{\\mathcal{S}}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " that have SIONs with respect to " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "P_{\\mathcal{R}}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " as a measure of how dissimilar the geometry of " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": " is to " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": ", which we denote " + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\mathrm{SION}(S; \\mathcal{R})" + }, + { + "bbox": [ + 305, + 533, + 545, + 653 + ], + "type": "text", + "content": ", where a high value indicates dissimilarity." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " is not specified and " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " is clear from context, we will use SION as a shorthand for " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{SION}(S; \\mathcal{R})" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": " assumed to be any sphere surrounding " + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": ". The two point clouds in Fig. 1 have a high SION, which indicates that their geometry is very different to a sphere and that optimization" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21459" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 261, + 84 + ], + "type": "text", + "content": "from a spherical initialization is likely to be difficult." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 97, + 157, + 110 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 97, + 157, + 110 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 157, + 110 + ], + "type": "text", + "content": "4. Point-Guided SDF" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": "The key idea of our method is to slowly converge the surface of reconstruction " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " towards the input points " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " until it interpolates " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": ", while maintaining " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " as a valid SDF to the volume enclosed by " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " (see Fig. 2). We do this by guiding " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " towards level sets (Fig. 2:2a-e) and taking small steps towards reaching each level set (Fig. 2:3a-f, Fig. 4). At each step we move guiding points " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": ", which represent the surface " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": ", a small distance towards " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " (Fig. 4c) and then optimize " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " to interpolate the new " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " positions, thus defining the new surface of reconstruction " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " over which " + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 47, + 118, + 287, + 251 + ], + "type": "text", + "content": " is resampled (Fig. 4d). Our full algorithm is shown in Algorithm 1." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "text", + "content": "Since each movement of the guiding points is small, the geometry of the moved guiding points " + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "text", + "content": " should be similar to the network's current surface " + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "inline_equation", + "content": "\\mathrm{SION}(\\mathcal{V};\\mathcal{R})" + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "text", + "content": " should be low. Thus optimizing the network to reconstruct the updated " + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 47, + 251, + 287, + 335 + ], + "type": "text", + "content": " should be robust (unlikely to converge to local minima) as the optimization is likely to have a clear descent direction from the loss at most points." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "text", + "content": "In Sec. 4.1 we outline how to move the guiding points " + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "text", + "content": " one step closer to the input points " + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "text", + "content": " (Fig. 4a-c). In Sec. 4.2 we outline how to optimize the network " + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 47, + 336, + 287, + 397 + ], + "type": "text", + "content": " to interpolate the new guiding point locations (Fig. 4d). Finally, in Sec. 4.3 we analyze our method within the homotopy framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "text", + "content": "Preprocessing " + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "text", + "content": ". Following standard practice, we first center and (isotropically) scale the shape to fit in a centered ball. After scaling, we calculate the point cloud's approximate sampling radius " + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "text", + "content": " conservatively by calculating the distance to the four closest neighbors for each " + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X}" + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "text", + "content": " and averaging the highest " + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 47, + 402, + 287, + 485 + ], + "type": "text", + "content": " of all such distances. We use this radius extensively in our method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "type": "text", + "content": "Initialization. We first initialize our network to the exterior level set of radius " + }, + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathrm{init}} = 16\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 47, + 491, + 287, + 540 + ], + "type": "text", + "content": ". We provide intuition into why we can do this robustly in Sec. 4.3, and provide details on how to make this more efficient in the supplement." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 549, + 196, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 196, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 196, + 562 + ], + "type": "text", + "content": "4.1. Moving the Guiding Points" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": "We now describe how to move the guiding points " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{V}" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": " towards the input points " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": ". At a high level, each step we move " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": " closer to an exterior level set of radius " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": ", and when " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": " has converged to " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": " we reduce " + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 568, + 287, + 617 + ], + "type": "text", + "content": " (see Algorithm 1)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": "Since we are moving " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " to guide the surface " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ", we only move each " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " in the inwards normal direction of " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ". Next, since we are moving towards an exterior level set " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ", for each " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " we find the closest input point in the inwards normal direction " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "x^{\\star}(y) \\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": ", and use this to determine the target point " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\omega^{\\star}(y)" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " that we move towards. Finally, since we want to move the surface " + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 618, + 288, + 714 + ], + "type": "text", + "content": " slowly, we have a maximum step size for each movement." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": "Closest point in the inward direction. We first define " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "x^{\\star}(y)" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " (see Fig. 4a-b). As we are moving in the inward normal direction, i.e., " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "-n_y" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "n_y = \\widehat{\\nabla_y\\Phi(y)}" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": ", we want to move " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " based on the closest point " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X}" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " in the inward normal direction " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "-n_y" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": ". We define the inward normal definition by setting a cosine similarity threshold " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "a_y \\geq 0" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " to define a cone " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "C_y" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " supported at " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": " emanating in the direction " + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "inline_equation", + "content": "-n_y" + }, + { + "bbox": [ + 304, + 72, + 545, + 160 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 358, + 166, + 545, + 180 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 166, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 358, + 166, + 545, + 180 + ], + "type": "interline_equation", + "content": "C _ {y} = \\left\\{z \\mid s (- n _ {y}, z - y) \\geq a _ {y} \\right\\}. \\tag {10}", + "image_path": "aec547137284def9f9ee4e1e160c969f4407059ebbd2886c9349397dfc2762c7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "text", + "content": "However as " + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "text", + "content": " gets very close to points in " + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "text", + "content": ", it is unlikely that any of those nearby points stay within this cone. Thus we also consider the half ball " + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "inline_equation", + "content": "H_{y}" + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "text", + "content": " of radius " + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "inline_equation", + "content": "2\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "text", + "content": " containing points close to " + }, + { + "bbox": [ + 304, + 186, + 545, + 235 + ], + "type": "inline_equation", + "content": "y" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 241, + 545, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 241, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 312, + 241, + 545, + 255 + ], + "type": "interline_equation", + "content": "H _ {y} = \\left\\{z \\mid \\| x - y \\| _ {2} \\leq 2 \\delta_ {\\mathcal {X}} \\wedge s (- n _ {y}, z - y) \\geq 0 \\right\\}. \\tag {11}", + "image_path": "a2fd81c03a8d9cbcc4b1e40378a4edb72717efbb1ffe25dd08c99b18fd5c4c96.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 261, + 465, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 261, + 465, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 465, + 274 + ], + "type": "text", + "content": "Thus our target point " + }, + { + "bbox": [ + 306, + 261, + 465, + 274 + ], + "type": "inline_equation", + "content": "x^{\\star}(y)" + }, + { + "bbox": [ + 306, + 261, + 465, + 274 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 356, + 281, + 545, + 303 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 281, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 356, + 281, + 545, + 303 + ], + "type": "interline_equation", + "content": "x ^ {\\star} (y) = \\underset {x \\in \\mathcal {X} \\cap \\left(C _ {y} \\cup H _ {y}\\right)} {\\arg \\min } \\| x - y \\| _ {2}. \\tag {12}", + "image_path": "9bb48c784242dfb69a71419d4cd4e0e161d599667e144070d330baa760486ea0.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "content": "Moving towards " + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "inline_equation", + "content": "x^{\\star}(y)" + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "content": " is our closest (inward) point, a reasonable location for a point in " + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "content": " can be computed by moving " + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "content": " away from " + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "inline_equation", + "content": "x^{\\star}" + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "text", + "content": " towards " + }, + { + "bbox": [ + 304, + 309, + 545, + 346 + ], + "type": "inline_equation", + "content": "y" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 351, + 353, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 353, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 351, + 353, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\omega^ {\\star} (y) = \\left(\\| x ^ {\\star} - y \\| _ {2} - \\delta\\right) \\widehat {\\left(x ^ {\\star} - y\\right)}. \\tag {13}", + "image_path": "72147b75f1910b729ee3c638e04491534efe9bcc3eeb28fbd04254d09304eca2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": "We move towards " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "\\omega^{\\star}" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": " with a maximum step size of " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "s_m" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": " so that the movement step is small and easy to optimize. Thus our final point " + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "inline_equation", + "content": "y^\\prime" + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": " (see Fig. 4b) is" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 351, + 418, + 545, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 418, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 351, + 418, + 545, + 433 + ], + "type": "interline_equation", + "content": "y ^ {\\prime} = y - \\operatorname {c l i p} (\\langle \\omega^ {\\star} (y), - n _ {y} \\rangle , s _ {m}) n _ {y} \\tag {14}", + "image_path": "9552a84ec043ecf8e4f67cf35f77a743c9c0928410f2dc0a3094266eb38dd458.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "inline_equation", + "content": "\\operatorname{clip}(a, \\varepsilon)" + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "text", + "content": " projects " + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "text", + "content": " to the interval " + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "inline_equation", + "content": "[- \\varepsilon, \\varepsilon]" + }, + { + "bbox": [ + 304, + 438, + 504, + 452 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": "Reducing " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": ". After initialization, we set " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta = \\delta_0" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " as our next target level set. Once " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " has finished moving towards " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " has converged, we decrease the current " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " by half and start moving " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " towards the new exterior level set. We do this until " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " reaches " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta_f" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": ". We use " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta_0 = 4\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\delta_f = \\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": ". We then abandon " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": " and optimize directly on " + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 456, + 545, + 528 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 535, + 443, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 535, + 443, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 535, + 443, + 548 + ], + "type": "text", + "content": "4.2. Optimizing the Network" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "text", + "content": "We now have the points " + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "text", + "content": " to guide where our new surface should be. Furthermore, we have an approximate normal " + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "inline_equation", + "content": "n_y" + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "text", + "content": " given by " + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 553, + 545, + 625 + ], + "type": "text", + "content": ", whose direction should be useful as the SION between the new position of the points relative to the previous positions is low. We use this to estimate an approximate SDF" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 328, + 631, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 631, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 328, + 631, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\tilde {F} _ {\\mathcal {V}} (z) = (- 1) ^ {[ s (z - y (z), n _ {y (z)}) \\geq 0 ]} d (z, y (z)) \\tag {15}", + "image_path": "31a0650e0a7c887e52d13b5d8fb20e1683f584945ca234435f2fe58f5ffdb85c.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "inline_equation", + "content": "y(z) = \\arg \\min_{y\\in \\mathcal{Y}}d(z,y)" + }, + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "inline_equation", + "content": "s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle" + }, + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "text", + "content": " is cosine similarity. We guide towards these values using" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 345, + 685, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 685, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 345, + 685, + 545, + 711 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {s d f}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| \\Phi (z, \\theta) - \\tilde {F} _ {\\mathcal {V}} (z) \\| _ {2}. \\tag {16}", + "image_path": "93fe8d2703895c1dffe2f722ce1c99ce8568159aa8b9c6752c32d67d33c504b1.jpg" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21460" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 545, + 198 + ], + "type": "image", + "image_path": "f50af9a8f7141de56ff4290caeb08665cf3282a23906da5a2ee08e01ce4a8bd3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": "Figure 4. One iteration of Algorithm 1, steps 6-8. (a) Given the current value of our network " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " (the contours) and our guiding points " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " (the green points), for each " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " we calculate a half ball " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "H_{y}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " and a cone " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "C_y" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " in the inside normal direction to find an input points " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "x\\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " (black points) to move towards (shown for 3 points, with one highlighted in red). (b) We find the closest input point " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "x^{\\star}(y)\\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "H_{y}\\cap \\mathcal{C}_{y}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": ", and use this to calculate the new position " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "y^\\prime" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " for each " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " (shown for all points). (c) The result after each " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "y\\in \\mathcal{V}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " has been moved. (d) The network " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " is optimized on the new guiding points, and " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": " is resampled to densely cover the new zero level set " + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 202, + 547, + 258 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "text", + "content": "Furthermore, our input points " + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "text", + "content": " should be at distance " + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 278, + 288, + 303 + ], + "type": "text", + "content": " and should be inside, so we add a loss term" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 93, + 308, + 287, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 308, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 93, + 308, + 287, + 334 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) + \\delta |. \\tag {17}", + "image_path": "0d52794e1ca2d33c5c759834682903c12bab2b7d70e22f894e04bd44db4de511.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 340, + 214, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 214, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 214, + 352 + ], + "type": "text", + "content": "Thus our overall loss term formulation is" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 361, + 281, + 373 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 361, + 281, + 373 + ], + "spans": [ + { + "bbox": [ + 53, + 361, + 281, + 373 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\theta , \\mathcal {X}, \\mathcal {Y}, \\delta) = \\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) + \\mathcal {L} _ {\\mathrm {e i k}} (\\theta) +", + "image_path": "3719a57f9835517d653f89029bf9475834ac8aac4cc03aedd0139a79d63a027e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 129, + 375, + 287, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 375, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 129, + 375, + 287, + 389 + ], + "type": "interline_equation", + "content": "\\widetilde {\\mathcal {L} _ {\\mathrm {s d f}}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {Y}). \\tag {18}", + "image_path": "f78f0f0a90725b800faa676c48453245a86437249bb821c45f48bc4a45a2b515.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 396, + 287, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 420 + ], + "type": "text", + "content": "Relevant details (e.g., loss term weightings, domain sampling procedure, optimizer settings) are in the supplement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": "Finally, we resample " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": " in the new zero level set " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": " (Fig. 4f) so that it densely samples it. After this process has finished (i.e., when " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": " has converged for " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\delta = \\delta_f" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": "), we optimize " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": " on the input points " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": " using the loss in Eq. (18). Here we do not use the approximate SDF term, as " + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 421, + 287, + 493 + ], + "type": "text", + "content": " is likely to have more imperfections that our guiding points." + } + ] + } + ], + "index": 8 + }, + { + "type": "code", + "bbox": [ + 50, + 519, + 287, + 696 + ], + "blocks": [ + { + "bbox": [ + 49, + 505, + 179, + 515 + ], + "lines": [ + { + "bbox": [ + 49, + 505, + 179, + 515 + ], + "spans": [ + { + "bbox": [ + 49, + 505, + 179, + 515 + ], + "type": "text", + "content": "Algorithm 1 Point-Guided SDF" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "lines": [ + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": "1: procedure PG-SDF(" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": ") \n2: Center " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": ", scale " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " and compute sampling radius " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n3: " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}, \\mathcal{N}_{\\mathcal{Y}}, \\Phi \\gets" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " Initialization " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "(\\mathcal{X}, \\delta_{\\mathrm{init}})" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n4: " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\delta \\gets \\delta_0" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n5: while " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\delta \\geq \\delta_f" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " do \n6: Move " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " using Eq. (14) \n7: Optimize " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " to match " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n8: Resample " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " on new " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n9: Query " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " for normals " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_{\\mathcal{Y}}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n10: if " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": "'s zero level set has not changed then \n11: " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\delta \\gets \\frac{1}{2} \\delta" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n12: end if \n13: end while \n14: Optimize " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n15: return " + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 50, + 519, + 287, + 696 + ], + "type": "text", + "content": " \n16: end procedure" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "code_body" + } + ], + "index": 10, + "sub_type": "algorithm" + }, + { + "bbox": [ + 306, + 278, + 507, + 292 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 278, + 507, + 292 + ], + "spans": [ + { + "bbox": [ + 306, + 278, + 507, + 292 + ], + "type": "text", + "content": "4.3. Interpretation as a Homotopy Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": "One way to analyze this method is in the context of a homotopy method [33]. Here, we wish to solve a difficult problem " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "M(\\theta) = 0" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": ", and instead consider the homotopy map " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "H(\\theta, t) = tM(\\theta) + (1 - t)N(\\theta)" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "N(\\theta) = 0" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": " is easy to solve and " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": ". This forms a homotopy between the problems " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "M(\\theta) = H(\\theta, 1)" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "N(\\theta) = H(\\theta, 0)" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": " as we can now continuously deform one problem into the other by varying " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": ". By taking small steps along the zero path, the trajectory of points " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "(\\theta, t)" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": " for which " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "H(\\theta, t) = 0" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": ", we can reach the solution to " + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "inline_equation", + "content": "M(\\theta)" + }, + { + "bbox": [ + 304, + 297, + 545, + 416 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": "For our method, we start by solving the easier problem " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\theta, \\mathcal{Y}_0) = 0" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_0" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": " is our initial set of guiding points. Our goal is to solve the hard problem " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\theta, \\mathcal{X}) = 0" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": ". To see that our method is a homotopy method, note that our guiding points " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": " are facilitating a topological homotopy from " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_0" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": " to our input points " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": ". Thus we can parameterize our zero path using " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": ". It is given by " + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "inline_equation", + "content": "(\\theta(\\mathcal{Y}), t(\\mathcal{Y}))" + }, + { + "bbox": [ + 305, + 417, + 545, + 501 + ], + "type": "text", + "content": " where" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 369, + 509, + 545, + 522 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 509, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 369, + 509, + 545, + 522 + ], + "type": "interline_equation", + "content": "\\theta (\\mathcal {Y}) \\text {s a t i s f i e s} \\mathcal {L} (\\theta (\\mathcal {Y}), \\mathcal {Y}) = 0 \\tag {19}", + "image_path": "97671a4399e7a09bd89516478361f06f17ab55b52c9ee523953cf7df60f435f7.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 525, + 545, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 525, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 358, + 525, + 545, + 550 + ], + "type": "interline_equation", + "content": "t (\\mathcal {Y}) = \\frac {d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right) - d _ {C} \\left(\\mathcal {Y} , \\mathcal {X}\\right)}{d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right)}. \\tag {20}", + "image_path": "e8820cae089290fd663602ccf46e63137e756704a49d8fdd9a05f206c9de68d6.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": "Note that at initialization " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\mathcal{V}_0" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": " and we have " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "t(\\mathcal{V}_0) = 0" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": ", while at termination " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\mathcal{X}" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": " and we have " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "t(\\mathcal{X}) = 1" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": ". Each time we update " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": ", we are traversing the zero path. If we take " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": " steps to reach the final exterior level set of radius " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": ", then we visit " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "n + 2" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": " points along the zero path parameterized by the sequence " + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_0, \\mathcal{V}_1, \\ldots, \\mathcal{V}_n, \\mathcal{X}" + }, + { + "bbox": [ + 304, + 557, + 545, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "To see why this works well in practice, we need to show that solving " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "H(\\theta(\\mathcal{Y}_{k+1}), t(\\mathcal{Y}_{k+1}))" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta(\\mathcal{Y}_{k+1})" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta(\\mathcal{Y}_k)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is easy, and solving " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "H(\\theta(\\mathcal{Y}_0), t(\\mathcal{Y}_0))" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta(\\mathcal{Y}_0)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is easy. To see the former, note that we move our guiding points " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " only a small distance from " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_k" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_{k+1}" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": ", and that " + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{SION}(\\mathcal{Y}_{k+1};\\mathcal{V}_k)" + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": " is small by construction. Thus, by the analysis in Secs. 3.3 and 3.4, the relative optimization problem is easy. To see the" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21461" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 74, + 287, + 297 + ], + "blocks": [ + { + "bbox": [ + 49, + 74, + 287, + 297 + ], + "lines": [ + { + "bbox": [ + 49, + 74, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 49, + 74, + 287, + 297 + ], + "type": "image", + "image_path": "3f37c96cba253e0cec25111a07694230dd9d9b2e04f27bb1bdbdf1e1c07d8226.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 301, + 288, + 347 + ], + "lines": [ + { + "bbox": [ + 46, + 301, + 288, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 288, + 347 + ], + "type": "text", + "content": "Figure 5. Qualitative results on ShapeNet. Top: Intermediate results as our method converges to different level sets " + }, + { + "bbox": [ + 46, + 301, + 288, + 347 + ], + "type": "inline_equation", + "content": "\\Omega_{\\delta}" + }, + { + "bbox": [ + 46, + 301, + 288, + 347 + ], + "type": "text", + "content": ". Bottom: Comparison with other methods, for challenging high SION shapes (0.40 for the car and 0.42 for the lamp)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "text", + "content": "latter, when " + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathrm{init}} \\gg \\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "text", + "content": " we can estimate good normals for " + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_0" + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "text", + "content": " by taking the displacement from the closest input point. With good normal estimates, " + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}" + }, + { + "bbox": [ + 46, + 359, + 287, + 443 + ], + "type": "text", + "content": " is very effective, and so optimization is easy. Furthermore, we note that higher radius exterior level sets are less complex, with smaller SION to an enclosing sphere. We formalize and prove this observation in the supplement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 454, + 100, + 466 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 454, + 100, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 454, + 100, + 466 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 288, + 713 + ], + "type": "text", + "content": "Dataset. We evaluate the performance of our method on ShapeNet [11], a large dataset of 3D CAD models. In this dataset, there are many shapes with complex geometries that are challenging to reconstruct, including extremely thin surfaces (sometimes string-like), hollow regions (often with small openings), and shapes with high genus. Previous works [5, 25] have shown that many neural methods fail on these shapes, even when using the ground-truth normals. We use the preprocessed watertight subset of Williams et al. [46], which consists of 13 classes with 20 shapes in each class. For each shape, 100k points are uniformly sampled from the surface and ground-truth normals are provided for each point, which are only used for those methods that require normals. We use these points as the input to our method, and for evaluating the squared chamfer metric. An additional 100k points are uniformly sampled within the domain with ground-truth labels that indicate whether the point is inside or outside the shape, allowing for the interior intersection-over-union (IoU) metric to be calculated. Further experimental details are given in the supplement." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 305, + 70, + 545, + 287 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 287 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 287 + ], + "type": "table", + "html": "
MethodSquared Chamfer ↓IoU ↑
NN nxMeanMedianStdMeanMedianStd
SPSR [22]× T5.44e-51.97e-55.06e-40.99260.99560.0105
IGR [15]✓ T5.12e-41.13e-42.15e-30.81020.84800.1519
SIREN [41]✓ T1.03e-45.28e-51.93e-40.82680.90970.2329
FFN [43]✓ T9.12e-58.65e-53.36e-50.82180.83960.0989
NSP [46]× T5.36e-54.06e-53.64e-50.89730.92300.0871
DiGS+N [5]✓ T2.74e-42.32e-59.90e-40.92000.97740.1992
SDF+N†✓ T3.97e-52.22e-58.98e-50.99150.99510.0141
Ours+N✓ T2.43e-52.15e-51.66e-50.99320.99550.0076
SPSR [22]× E3.76e-34.37e-51.14e-20.71870.97610.3767
SIREN [41]✓ ×3.08e-42.58e-43.26e-40.30850.29520.2014
SAL [2]✓ ×1.14e-32.11e-43.63e-30.40300.39440.2722
DiGS [5]✓ ×1.32e-42.55e-54.73e-40.93900.97640.1262
SAP [39]× ×4.09e-42.46e-52.60e-30.91180.99230.2002
OG-S [25]✓ ×3.75e-52.17e-58.24e-50.96150.98710.1048
OG-N [25]✓ ×5.07e-52.57e-59.39e-50.95930.98700.1057
SDF†✓ ×1.84e-48.15e-42.95e-30.54900.52450.3572
SDF+N†✓ E2.48e-25.89e-55.63e-30.68170.96710.3990
Ours+N✓ E2.79e-24.79e-56.79e-20.70170.97210.3876
Ours✓ ×3.72e-52.40e-55.39e-50.97290.98960.0676
", + "image_path": "4716caa984dfd79357e62fdf329a7ebc97edc28374b6f13447499f348c1c706f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 292, + 547, + 337 + ], + "lines": [ + { + "bbox": [ + 304, + 292, + 547, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 547, + 337 + ], + "type": "text", + "content": "Table 1. Surface reconstruction results on ShapeNet [11]. NN: uses a neural network. " + }, + { + "bbox": [ + 304, + 292, + 547, + 337 + ], + "type": "inline_equation", + "content": "n_x" + }, + { + "bbox": [ + 304, + 292, + 547, + 337 + ], + "type": "text", + "content": ": uses ground-truth (T), estimated (E) or no (×) input surface normals. Suffix ‘+N’ denotes normal information added to the underlying method. † Our implementation." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "content": "Implementation and Baselines. Our baseline methods use the same implementation framework as our approach (see full details in the supplement) with standard loss formulations. 'SDF' uses " + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{zls}}" + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{eik}}" + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pull}}" + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "content": " while 'SDF+N' additionally uses " + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}" + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{normal}}" + }, + { + "bbox": [ + 304, + 350, + 545, + 422 + ], + "type": "text", + "content": " [15]. We also evaluate our methods with estimated normals (using Open3D [50])." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 430, + 501, + 442 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 501, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 501, + 442 + ], + "type": "text", + "content": "5.1. Surface Reconstruction on ShapeNet" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 545, + 533 + ], + "type": "text", + "content": "Results on the full ShapeNet subset are given in Tab. 1, with qualitative results in Fig. 5. Our proposed method outperforms all prior normal-free methods and even demonstrates improvement when ground-truth normals are available. In particular, our approach gets a significant improvement in mean IoU, with much smaller variance, indicating that our method performs reliably well." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 539, + 477, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 477, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 477, + 552 + ], + "type": "text", + "content": "5.2. Challenging High-SION Shapes" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 713 + ], + "type": "text", + "content": "In this section, we analyze the performance of surface reconstruction methods with respect to the SION metric. Fig. 6 shows that the mean IoU degrades significantly as we progressively consider shapes with higher SION scores. While our method also follows this trend, performance degradation is considerably slower, indicating that our method is much more robust to challenging shapes. We report the reconstruction performance on the subset of 20 shapes with the highest SION in Tab. 2. On these most challenging shapes, our approach has a decisive advantage. This demonstrates that our structured optimization approach is able to achieve good reconstructions of the most difficult shapes, without sacrificing performance on easy shapes." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21462" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 284, + 224 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 284, + 224 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 284, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 284, + 224 + ], + "type": "image", + "image_path": "2629c760daeac6654d94d308a61910968f8fd786c3aadcbf08e3c9b0494a5077.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 287, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 287, + 274 + ], + "type": "text", + "content": "Figure 6. Mean IoU for all shapes with a SION higher than a lower bound. The analysis from Secs. 3.3 and 3.4 predicts a significant negative correlation for existing neural SDF methods. Our method weakens this trend considerably." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 281, + 287, + 433 + ], + "blocks": [ + { + "bbox": [ + 47, + 281, + 287, + 433 + ], + "lines": [ + { + "bbox": [ + 47, + 281, + 287, + 433 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 287, + 433 + ], + "type": "table", + "html": "
MethodNN\\(n_x\\)Squared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
SPSR [22]×T3.98e-53.92e-51.80e-50.97980.98480.0222
DiGS+N [5]✓T2.09e-47.42e-52.91e-40.81600.87640.2119
\\(\\text{SDF}+\\text{N}^{\\dagger}\\)✓T1.11e-44.84e-51.95e-40.97330.98540.0409
Ours+N✓T4.16e-53.89e-51.86e-50.98220.98650.0148
SPSR [22]×E5.83e-31.25e-31.16e-20.32900.18020.3445
DiGS [5]✓×4.34e-41.71e-45.34e-40.71080.81960.2536
SAP [39]××1.28e-45.84e-51.99e-40.76160.88720.2665
OG-S [25]✓×1.31e-46.50e-51.79e-40.76510.92190.2512
\\(\\text{SDF}^{\\dagger}\\)✓×1.29e-37.75e -41.43e-30.34130.26170.2292
\\(\\text{SDF}+\\text{N}^{\\dagger}\\)✓E5.32e-24.51e-37.03e-20.28960.19770.3288
Ours+N✓E4.89e-27.32e-36.25e-20.31730.23620.3259
Ours✓×5.51e-54.87e-53.12e-50.91530.95980.0906
", + "image_path": "14061386cdc55fc9bcba1fcae0414483b5192cbb30307615467d4be380c7f490.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 47, + 501, + 287, + 581 + ], + "blocks": [ + { + "bbox": [ + 46, + 437, + 287, + 493 + ], + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 493 + ], + "type": "text", + "content": "Table 2. Surface reconstruction results on the 20 highest SION ShapeNet shapes. NN: uses a neural network. " + }, + { + "bbox": [ + 46, + 437, + 287, + 493 + ], + "type": "inline_equation", + "content": "n_x" + }, + { + "bbox": [ + 46, + 437, + 287, + 493 + ], + "type": "text", + "content": ": uses ground-truth (T), estimated (E) or no (X) input surface normals. Suffix ‘+N’ denotes adding normal information to the underlying method. † Our implementation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 501, + 287, + 581 + ], + "lines": [ + { + "bbox": [ + 47, + 501, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 287, + 581 + ], + "type": "table", + "html": "
Guidance y0 yδ0 δfSquared Chamfer ↓IoU ↑
MeanMedianStdMeanMedianStd
× × - -2.41e-31.18e-32.65e-30.27950.22550.2078
✓ × - -2.63e-41.91e-42.31e-40.56940.60910.2278
✓ ✓ 429.89e-57.70e-57.95e-50.86570.9163
✓ ✓ 118.08e-57.52e-55.66e-50.85380.9386
✓ ✓ 415.51e-54.87e-53.12e-50.91530.9598
", + "image_path": "73e3c84f5cfceb9dfee1fbe8d7ed3a35567e845e31f98e5c6c93e66e5c2f59f0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "lines": [ + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "text", + "content": "Table 3. Ablation results on the 20 highest SION ShapeNet shapes. " + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_0" + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "text", + "content": ": uses our SDF initialization strategy instead of spherical initialization [15]. " + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "text", + "content": ": uses our point guidance strategy. " + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\delta_0 / \\delta_f" + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "text", + "content": ": starting and final level set radii, given in multiples of " + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 585, + 287, + 629 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 645, + 204, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 204, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 204, + 658 + ], + "type": "text", + "content": "5.3. Ablation Study and Runtime" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "An ablation study, on the 20 highest-SION shapes of ShapeNet, is reported in Tab. 3. The performance when using a spherical initialization and optimizing with respect to the input points (row 1) is poor. It improves significantly" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 68, + 542, + 219 + ], + "blocks": [ + { + "bbox": [ + 307, + 68, + 542, + 219 + ], + "lines": [ + { + "bbox": [ + 307, + 68, + 542, + 219 + ], + "spans": [ + { + "bbox": [ + 307, + 68, + 542, + 219 + ], + "type": "image", + "image_path": "c1e7de4b29b4865bd25a908524a6750fb0526d66715e27e1961c33cf06a65f65.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 223, + 545, + 257 + ], + "lines": [ + { + "bbox": [ + 304, + 223, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 304, + 223, + 545, + 257 + ], + "type": "text", + "content": "Figure 7. Runtime vs SION on ShapeNet for our method. Challenging shapes with high SION take more time to optimize. One outlier (82 min) is truncated for clarity and marked as " + }, + { + "bbox": [ + 304, + 223, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 304, + 223, + 545, + 257 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "type": "text", + "content": "when replaced with our high exterior level set initialization (row 2). When point guidance is added (rows 3-5), the performance increases considerably. In particular, stopping point guidance early (when " + }, + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\delta_f = 2\\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "type": "text", + "content": ") harms performance, as does guiding straight to the final level set target (" + }, + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\delta_0 = \\delta_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 270, + 545, + 365 + ], + "type": "text", + "content": ") without first converging to intermediate level set targets. Our gradual homotopy approach performs best by a significant margin, justifying the strategy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "type": "text", + "content": "An unoptimized implementation of our method takes 10 mins on average per ShapeNet shape (a median of 7.4 mins). Convergence time depends strongly on the difficulty of the shape, as shown in Fig. 7. Our implementation has 17.5M parameters: a small neural network with Fourier feature embeddings [43] and parametric embeddings [31, 42] computed using a dense feature grid (" + }, + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "type": "inline_equation", + "content": ">99\\%" + }, + { + "bbox": [ + 304, + 366, + 545, + 450 + ], + "type": "text", + "content": " of the parameters)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 460, + 457, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 457, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 457, + 472 + ], + "type": "text", + "content": "6. Discussion and Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 480, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 545, + 563 + ], + "type": "text", + "content": "In this paper, we proposed a point-guided optimization method for neural SDF reconstruction from raw point clouds. We also examined why neural SDF losses can be detrimental for some shapes, proposed a metric to identify these shapes, and used this analysis to justify our algorithm design. Our method outperforms prior work, with large improvements for the most challenging shapes." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "content": "Like many methods, our approach is not robust to high outlier fractions and large noise scales, behaving similarly to the compared methods. In addition, our approach does not handle large occlusions gracefully, since it treats these regions like concavities to be explored. This could be alleviated by defining anisotropic per-point sampling radii " + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "inline_equation", + "content": "\\delta_{i}" + }, + { + "bbox": [ + 304, + 563, + 545, + 635 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 639, + 545, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 639, + 545, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 639, + 545, + 698 + ], + "type": "text", + "content": "Acknowledgements. Y. Ben-Shabat is supported by the Marie Sklodowska-Curie grant agreement No. 893465 S. Gould is a recipient of an ARC Future Fellowship (proj. no. LP200100421) funded by the Australian Government. We would also like to thank Mingda Xu for discussions about homotopy methods." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21463" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Nina Amenta, Sunghee Choi, and Ravi Krishna Kolluri. 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Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR [32] to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups.", + "bbox": [ + 76, + 347, + 472, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 724, + 209, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "All of us may find ourselves within vulnerable demographics at some point. Throughout the human life span, we confront an array of challenges, whether originating from physical discomfort [12], emotional turmoil [53], or the inevitable march of aging [22], that can hinder our ability to perform even the simplest tasks that we once accomplished", + "bbox": [ + 75, + 750, + 468, + 840 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "effortlessly (e.g., lifting a heavy object). This predicament often triggers a complex emotional response. The fear of being labeled as \"special\" or \"disabled\" can evoke feelings of diminished self-esteem, reduced self-efficacy and self-sufficiency, and a sense of personal boundary violation [8, 40]. However, previous research in humanrobot interaction has primarily focused on pure cooperation [30, 38, 42, 43, 52, 57], and assistive technologies [4, 7] have been designed to simply take over everything for human users, often disregarding their emotional well-being. Considering the importance of sensitivity and consideration when offering help, we need new assistance technologies with an emphasis not only on the successful completion of the task but also on the recipient's emotional acceptance of the assistance [8, 40]. This introduces a new dimension to the concept of learning to help in AI, extending the boundaries beyond technical proficiency and into the realm of empathetic engagement.", + "bbox": [ + 500, + 316, + 893, + 589 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To tackle this issue, we propose a novel and pivotal challenge Smart Help, aiming to provide both proactive and adaptive support to human agents with diverse disabilities and dynamic goals in different tasks and environments. Fig. 1 exemplifies the concept of the Smart Help strategy as applied to an assistive robot aiding a human in a household task. The Basic Helper fails to provide proactive assistance due to its inability to infer the user's goals accurately. The Ordinary Helper successfully infers the user's goals from observations and offers proactive help, but it lacks adaptability to different user needs. Its simple \"take-over\" helping strategy can cause a feeling of discomfort in the human user. In contrast, the Smart Helper not only infers both the user's goals distribution but also reasons about the user's capability of completing each goal independently. As a result, the Smart Helper can identify critical goals that hinder task completion and provide proactive and adaptive help that selectively addresses those bottlenecks. This approach allows the user to accomplish the task successfully and joyfully.", + "bbox": [ + 496, + 593, + 893, + 881 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Leveraging AI2-THOR [32], a 3D interactive environ", + "bbox": [ + 517, + 883, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Indicates equal contribution. Work was conducted during Zhihao Cao and Zidong Wang's internships at BIGAI. Corresponding author: Lifeng Fan (lifengfan@bigai.ai). Our environment, dataset, and codes are available at https://github.com/caozh20/SmartHelp.", + "bbox": [ + 75, + 851, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18091", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b3f89d0f07362e36876a4ad1b65cee0413b83274452b376bf38200830c608548.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 80, + 885, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7d93d9a87ebe29ebf887feb218a90f501a8f7adc735bc62403b32f47422a122c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 215, + 885, + 361 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f2a6a7f28eb3050cbd9d9ab74c59fcfd911e258ed7fa64d11abfde1ae3b28949.jpg", + "image_caption": [ + "Figure 1. An example of the Smart Help strategy for an assistive robot. The top left shows the human user's capability distribution across several dimensions (e.g., weight for lifting heavy objects and height for grasping objects from high positions), as well as the current task (e.g., making coffee). The figure illustrates three types of helpers: (1) The Basic Helper merely observes the human user without inferring anything, and thus remains idle and waits until the human user fails the task, leading to frustration. (2) The Ordinary Helper infers the human user's goals through observations and always provides simple and direct assistance for each goal, taking over the entire task. While the task is successfully completed, the human user is left dissatisfied because the robot's helping strategy is overly intrusive, causing discomfort. (3) The Smart Helper infers both the human user's goals and her capability distribution. It reasons about whether the human user is capable of independently accomplishing each goal and thus identifies the bottleneck goal that hinders task completion. The proactive helper then adapts its strategy to assist solely with the bottleneck goal. As a result, the human user successfully completes the task with tailored support, feeling comfortable and satisfied." + ], + "image_footnote": [], + "bbox": [ + 81, + 361, + 885, + 505 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ment engineered for realistic home simulations, we demonstrate a concrete realization of the proposed novel challenge Smart Help. We create a multi-agent interactive environment featuring a main agent with diverse capability distributions (representing the vulnerable group) across dimensions, such as toggling, opening, closing, weight, and height. Within this environment, the main agent faces challenges in achieving dynamic goals across various tasks, and an assistive robot is introduced to assist the main agent throughout their endeavors. Unlike previous assistive tasks that were highly specialized and constrained, such as the use of a robotic arm for the disabled [10, 17, 51], our work represents, to the best of our knowledge, the first construction of a 3D home environment designed to assist the vulnerable group with various general daily household tasks.", + "bbox": [ + 75, + 657, + 468, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, we build a new benchmark model for our", + "bbox": [ + 96, + 885, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "proposed challenge, which consists of 1) an opponent modeling module that jointly optimizes goal inference and capability estimation, and 2) a helping policy module that reasons about the bottleneck, and learns an optimal Smart Help policy in an online interactive manner. To better evaluate performance in the Smart Help task, we also introduce six assessment metrics. Contrary to traditional evaluation metrics primarily focusing on cumulative reward or task completion, our metrics emphasize the helper's contribution to the task and the essentiality of assistance. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against baselines. We believe our proposed task, environment, model, and benchmark will contribute to the development of next-generation advanced home assistive robot technologies.", + "bbox": [ + 496, + 657, + 890, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions can be summarized as follows:", + "bbox": [ + 517, + 885, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18092", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel Smart Help challenge that aims at learning to provide both proactive and adaptive help to diverse human users (especially vulnerable groups) based on inferred goals and capabilities.", + "- To the best of our knowledge, we contribute the first 3D realistic home environment built upon AI2-THOR, that focuses on assisting the vulnerable group with daily household tasks in an online and interactive manner.", + "- We provide a benchmark model with a joint goal and capability inference, bottleneck reasoning, and helping policy improvement. Strict experiments and the proposed holistic evaluations validate the efficacy of our model." + ], + "bbox": [ + 76, + 90, + 467, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 286, + 217, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Assistive Robots. The domain of assistive robots encompasses a broad spectrum of research, focusing on enhancing the life quality for individuals with various needs and spanning diverse applications such as mobility aids [1, 20], companion robots [46], and robotic arms [21]. Feil-Seifer and Mataric [18] underscore that Socially Assistive Robotics entails robots assisting humans through effective interaction in tasks such as food delivery [49], healthcare [27], and other tasks necessitating social interaction. However, many of them only rely on simple rules or programs to achieve social interaction [27, 49]. The deployment of assistive robots has also raised ethical and safety considerations, particularly in terms of user autonomy, privacy, acceptance, trust, etc. [5, 6, 9, 18]. The objective of our work is to devise an effective algorithm for Socially Assistive Robotics to estimate people's goals and capabilities, thereby enabling comfortable and smart assistance.", + "bbox": [ + 76, + 311, + 467, + 566 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Embodied Multi-agent Collaboration. A series of embodied collaboration tasks have been developed recently thanks to the development of Embodied AI simulators [13, 14, 32, 33, 41, 47, 48, 50]. However, these tasks always focus on some limited task completion, such as collaborative navigation [34, 56] and collaborative furniture rearrangement [28, 29]. Watch-and-Help [42] and NOPA [43] study the cooperative tasks between two agents with the same capabilities. Our work focuses on the collaboration between agents with different capabilities and study the strategic assistance for the vulnerable group on household tasks.", + "bbox": [ + 76, + 568, + 467, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Opponent Modeling. Opponent modeling [16, 19, 24], a pivotal approach in multi-agent interaction tasks, leverages a variety of methodologies such as Inverse Reinforcement Learning [36], Bayesian methods [25, 26, 45, 52, 60], Deep Q-Networks (DQN) [23, 35], Variational AutoEncoders [39], Markov Decision Process [36], etc. This technique is especially valuable in competitive settings like games and strategic decision-making, where understanding and anticipating an opponent's behavior or unseen traits (e.g., Theory of Mind modeling [44]) can significantly influence the outcome. It enables agents to predict future en", + "bbox": [ + 76, + 734, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "vironmental state transitions and refine their strategies accordingly [58, 59]. Projects like Watch-and-Help [42] and NOPA [43] have explored estimating a main agent's goals to improve coordination. Yet, these initiatives often overlook the capabilities of the main agent, leading to a gap in developing effective support strategies for those in need. Our research addresses this gap by focusing on enhancing the acceptance of AI assistance among users, as emphasized in [9], highlighting the importance of aligning AI functionalities with user needs and preferences. Additionally, we propose to model the capability of the opponent and learn a smart, adaptive, and empathetic helping policy for vulnerable people in a challenging 3D household interactive environment with partial observation and high uncertainty.", + "bbox": [ + 496, + 90, + 890, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The Smart Help Challenge", + "text_level": 1, + "bbox": [ + 500, + 316, + 746, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 342, + 700, + 356 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We model the interaction between the main agent and the helper with a multi-agent Partially Observable Markov Decision Process (POMDP[11]), which is formally defined as a tuple $G = < S, A, O, R, T, n, \\gamma >$ . $S$ represents the state space, including physical states and mental states. $A$ is the joint action space for $n$ agents, whose local observations compose observation space $O$ . $T(s'|s, a)$ denotes the transition probability. $R(s, a)$ denotes the shared reward function and $\\gamma \\in [0, 1)$ is the discount factor. Specifically, there are $n = 2$ agents in our Smart Help Challenge, i.e., a main agent and a helper agent. The objective is to train a helper agent to assist the main agent in achieving goals, considering the emotional state of the main agent simultaneously.", + "bbox": [ + 496, + 364, + 890, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In previous work, the reward for the helper agent is:", + "bbox": [ + 517, + 563, + 861, + 577 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nR _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) + \\beta R ^ {g _ {m}} (s, a _ {h}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 589, + 890, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the $\\beta \\in (0,1)$ is a factor controlling the level of altruism of the helper. $R^{g_h}(s,a_h)$ is the reward attributed to the successful completion of the helper agent's goal at state $s$ through action $a_{h}$ . $R^{g_m}(s,a_h)$ is the same for the main agent's goal achievement. This formulation assumes equal consideration for both agents when rewarding goal completion. However, when the helper fulfills a goal of the main agent, it triggers emotional responses in the main agent. Integrating this emotional component with Eq. (1), we have:", + "bbox": [ + 496, + 618, + 890, + 755 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) \\tag {2} \\\\ + \\beta \\left(R ^ {g _ {m}} \\left(s, a _ {h}\\right) + \\lambda_ {e} R ^ {e _ {m}} \\left(s, a _ {h}\\right)\\right), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 766, + 890, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $R^{e_m}(s, a_h)$ means the reward correlated to the emotions of the main agent when the helper does the action $a_h$ , and $\\lambda_e$ is a hyper-parameter that controls the helper's sensitivity to the emotional states of the main agent. In our Smart Help challenge, the helper agent's role is solely to assist the main agent in accomplishing his/her goals, without its own", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18093", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "goals. So we omit the term $R^{g_h}(s, a_h)$ and set $\\beta = 1$ , leading to the helper's reward as:", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {h} (s, a _ {h}) = R ^ {g _ {m}} (s, a _ {h}) + \\lambda_ {e} R ^ {e _ {m}} (s, a _ {h}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 132, + 468, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Indeed, this is what sets smart Help apart from other assistance-related tasks. Through such design, we emphasize that AI agents must possess the capacity to discern not just how to aid humans, but also when their assistance is truly needed and will be valued.", + "bbox": [ + 75, + 159, + 468, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Challenge Implementation", + "text_level": 1, + "bbox": [ + 76, + 243, + 316, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We implement a tangible version of Smart Help in the AI2THOR [32] simulator, which emphasizes adaptive helping policy for individuals with various disabilities, as shown in Fig. 1. Our new environment includes a main agent that simulates human behavior in various assistive household tasks. The main agent, assigned with a new task and a capability distribution at the beginning of each round, attempts to complete the task with an expert planning policy, which utilizes complete information to divide the task into distinct goals and plan intentional actions for the goals. We also implement a low-level planner that translates the intentional action to a sequence of executable actions in the simulator, so as to enable the main agent to reach the target state indicated by the input intentional action. The workflow of the low-level planner is a loop involving the following steps:", + "bbox": [ + 75, + 266, + 468, + 493 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "1. Navigate to the relevant object by following the shortest path determined by the object's position and the room layout; or be directly teleported to the target position.", + "bbox": [ + 76, + 494, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2. Interact with the object in accordance with the goal. However, actions taken by the main agent might fail due to certain disabilities or the physical constraints of the scene. Thus, the helper agent, as in Fig. 2, based on its symbolic observations of the world, should infer both the goal and capability of the main agent and provide proactive assistance with the bottleneck for the main agent. We will introduce the detailed environment settings in the following part.", + "bbox": [ + 76, + 539, + 468, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Object State. We define object state of object $i$ as $e_i = (type_i, pos_i, w_i, attr_i, pr_i)$ , where:", + "bbox": [ + 76, + 659, + 468, + 688 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- type $i \\in \\mathbb{N}$ denotes the type of object $i$ with an index;", + "- $pos_{i} \\in \\mathbb{R}^{3}$ records the position of object $i$ 's center;", + "- $w_{i} \\in \\mathbb{R}$ represents the weight of object $i$ ;", + "- $\\text{attr}_i \\in \\{0,1\\}^{4+2}$ denotes the attributes of object $i$ , including its 4 status (i.e., whether it is picked up, opened, cooked, and toggled on) and its visibility to the 2 agents;", + "- $pr_i \\in \\mathbb{R}$ signifies the type of the parent receptacle of the object $i$ through an index; here, the parent receptacle means an object that serves as the container or the support for another subordinate object." + ], + "bbox": [ + 76, + 689, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Action Space. We employ intentional actions to construct the action space, where intentional actions represent the target state that the agent wants to achieve. It is defined as $a_{i} = (predicate_{i}, e_{i}) \\in A$ ; for instance, (PickUp, 3), where", + "bbox": [ + 75, + 840, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3 is an object index, representing \"Bread\" in our environment. There are seven kinds of different intentional actions: (Wait), (PickUp, $e_i$ ), (Put, $pr_i$ ), (ToggleOn, $e_i$ ), (ToggleOff, $e_i$ ), (Open, $e_i$ ), and (Close, $e_i$ ). In total, there are $|A| = 373$ possible intentional actions.", + "bbox": [ + 496, + 90, + 890, + 166 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Agent Capability. The variance of agent capability is manifested in the differences in the transition matrix, which means that different agents will produce different outcomes for the same action at the same state. For example, some agents may be able to pick an object up, while others cannot due to the its weight. Learning the matrix itself is impractical due to the vast size of the space. Instead, we select six parameters to represent the distinct characteristics of different matrices. Therefore, the capability of agent $i$ is represented as $\\eta_{i} = (\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})$ where:", + "bbox": [ + 496, + 167, + 890, + 318 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- The maximum height an agent can reach $\\alpha_{i} \\in [0,1]$ and the maximum weight an agent can lift $\\beta_{i} \\in [0,1]$ determine whether an agent can execute the action PickUp;", + "- $\\gamma_{i}, \\delta_{i}, \\epsilon_{i}, \\zeta_{i} \\in [0,1]$ respectively represent the agent's ability to complete the actions Open, Close, ToggleOn and ToggleOff." + ], + "bbox": [ + 500, + 318, + 890, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Agent State. We define the state of agent $i$ as $h_i = (\\eta_i, \\text{pos}_i, \\text{rot}_i, e_i, a_i, \\text{suc}_i)$ , wherein:", + "bbox": [ + 500, + 409, + 890, + 439 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $\\eta_{i} \\in C = [0,1]^{6}$ denotes the capability of agent $i$ ,", + "- $pos_i, rot_i \\in \\mathbb{R}^3$ represent agent $i$ 's position and rotation,", + "- $e_i \\in E, a_i \\in A$ , and $succ_i \\in \\{0,1\\}$ respectively represent the object held by agent $i$ , the action undertaken by agent $i$ in the last step, and whether the last action was a success or a failure." + ], + "bbox": [ + 500, + 439, + 890, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "World. The world is denoted as $W = (S, A, T)$ , wherein:", + "bbox": [ + 500, + 529, + 882, + 545 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $S = \\{e_i, h_j\\}_{i=1,\\dots,N_o, j=1,2}$ represents the world state, which encompasses the state of $N_o$ objects and 2 agents;", + "- $A = \\{a_{i}\\}$ denotes the action space;", + "- $T = P(S'|S, A; \\eta_i)$ refers to the transition matrix controlled by agent capability." + ], + "bbox": [ + 500, + 545, + 888, + 619 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Task. Given our formulation of agent capabilities, we select three everyday tasks for practical implementations of our challenge: Make Breakfast, Arrange Room, and Make Coffee. These tasks respectively involve different capabilities: $(\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})$ for Cook Potato, $(\\alpha_{i},\\beta_{i},\\gamma_{i})$ for Arrange Room, and $(\\alpha_{i},\\beta_{i},\\epsilon_{i},\\zeta_{i})$ for Make Coffee.", + "bbox": [ + 496, + 621, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Goal. Upon setting a task, the agent need to identify several key points (goals) that they must achieve. These goals are hidden from the helper, but affect the helper's reward for a particular action. Each goal is defined by the target state of the involved objects. The goal at time $t$ is represented as:", + "bbox": [ + 496, + 710, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ng ^ {t} = \\left(\\text {t a r g e t - s t a t e} ^ {t}, e ^ {t}, p r ^ {t}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 797, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Target state includes Wait, Get, On, In, KeepOpen, KeepClose, KeepOn and KeepOff, e.g., \"(In, Cup, Cabinet)\".", + "bbox": [ + 496, + 825, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation Space. The proposed environment supports both symbolic and visual observations. This dual-mode observation system enables the helper to acquire and refine", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18094", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/39ab639524dae24ba4b646746370f748b38a8df7440acaf6d8f75b3838e37c91.jpg", + "image_caption": [ + "Figure 2. This figure depicts the architecture of our smart help model and its interaction mechanisms with the environment. The model is partitioned into two primary components: an opponent modeling module and a helping policy module. The opponent modeling module is designed to estimate the goal and capability of the main agent. It adopts a sliding window paradigm and utilizes several MLP layers to generate the state feature $\\xi_{s}$ . This feature is then processed by a feature extractor to derive the capability feature $\\xi_{\\eta}$ and the goal feature $\\xi_{g}^{t}$ . The helping policy module is composed of two MLP layers to produce action decision and value estimation respectively. During interaction with the environment, the helping model outputs an intentional action, representing the target state it aims to reach. The environment employs a low-level planner to decompose the intentional action into a sequence of executable actions, which are then processed by the AI2THOR simulator, guiding the assistant toward the intended state. Finally, the simulator provides a new observation as feedback, triggering the next cycle of interaction." + ], + "image_footnote": [], + "bbox": [ + 80, + 87, + 893, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "helping behaviors in various contexts. Following previous work [42, 43], we use symbolic observations containing physical states of all perceivable objects and agents. Hidden states, like goals and capabilities, can not be observed.", + "bbox": [ + 75, + 546, + 468, + 608 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Our Model", + "text_level": 1, + "bbox": [ + 76, + 623, + 194, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our objective is to train a helper agent who can effectively adapt to main agents with varying capabilities and goals. There are two main challenges: 1) the challenge posed by the environment (e.g., partial observation and occlusion), and 2) the challenge posed by the task (i.e., how to estimate the current goal $g^{t}$ and capabilities $\\eta$ of the main agent). Given the observation $o^{0:t}$ , the action policy for the helper is formulated as:", + "bbox": [ + 75, + 648, + 468, + 770 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP (a | o ^ {0: t}) = \\sum_ {g ^ {t} \\in G, \\eta \\in C} P (a | g ^ {t}, \\eta , o ^ {0: t}) P (g ^ {t}, \\eta | o ^ {0: t}). \\quad (5)\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 792, + 468, + 828 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Therefore, as depicted in Fig. 2, our model consists of: 1) an opponent modeling module to estimate the current goal and capabilities of the main agent, i.e., $P(g^{t}, \\eta | o^{0:t})$ ; and 2) a helping policy module to learn the distribution of", + "bbox": [ + 76, + 839, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the helper's action conditioned on the predicted goal and capabilities of the main agent, i.e., $P(a|g^t,\\eta,o^{0:t})$ .", + "bbox": [ + 496, + 546, + 890, + 577 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training of our model has two stages. In the first stage, we train an opponent modeling module using the collected main agent trajectories. This stage is crucial as it enables the helper agent to understand and anticipate the behavior of the main agent effectively. In the second stage, we utilize the pre-trained opponent modeling module to train the helping policy module, which handles dynamic and complex tasks by interacting in our environment.", + "bbox": [ + 496, + 578, + 892, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. The Opponent Modeling Module", + "text_level": 1, + "bbox": [ + 498, + 709, + 789, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train this module, we collect simulated trajectories in our environment with the main agent following an expert policy and the helper moving randomly, where each frame contains the observations of the helper agent and the true labels of the main agent's goals and capabilities. Throughout data collection, we utilize a main agent with various tasks and capabilities and a helper executing random actions in the environment. See more details in the supplementary.", + "bbox": [ + 496, + 733, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use a sliding window trick when inferring goals and capabilities from the main agent's trajectory since goals are transient and typically persist for only a few steps. This", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18095", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "method enables examining a segment of the trajectory at any given time, and sliding the window as new actions are taken. It allows the helper agent to make more immediate and relevant inferences about the main agent's current goals and capabilities, enhancing its adaptability and responsiveness. Formally, we have:", + "bbox": [ + 75, + 90, + 472, + 183 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nP \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {0: t}\\right) \\approx P \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {t - w: t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 195, + 468, + 213 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $w$ is the window size.", + "bbox": [ + 76, + 219, + 266, + 232 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use an object encoder and an agent encoder to extract features from raw observations (details in supplementary). Similar to the \"class token\" in [2], we preprocess the sequence of object feature. We follow the usage of \"class token\" [2], and only retain this object token to represent the object feature $\\xi_{o}^{t}$ after the transformer [54] layer (other tokens are removed). This object feature $\\xi_{o}^{t}$ , together with the agent feature $\\xi_{a}^{t}$ , constitute the state feature $\\xi_{s}^{t}$ . As in Eq. (6), we use a window size of $w$ and the state features $\\{\\xi_{s}^{t - w},\\dots ,\\xi_{s}^{t}\\}$ are fed into an MLP layer to obtain the final state feature $\\xi_{s}$ . Furthermore, a feature extractor is employed to derive the capability feature $\\xi_{\\eta}$ and the target state feature $\\xi_{g}^{t}$ of the main agent. A transformer layer is utilized for the capability feature. As for the goal feature $\\xi_{g}^{t}$ , as detailed in Eq. (4), one transformer layer is used for the target state feature, and two MLP layers are employed for the features of the related object and its target parent receptacle.", + "bbox": [ + 75, + 233, + 472, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. The Helping Policy Module", + "text_level": 1, + "bbox": [ + 76, + 513, + 323, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our helping policy module has an actor-critic [55] architecture. At each time step $t$ , given the current observation $o^t$ , together with all the features $\\xi_{\\eta}$ and $\\xi_g^t$ from the opponent modeling module, the helper agent needs to learn the helping policy $\\pi_{\\theta}(a|o^t,\\eta ,g^t)$ . We employ an MLP layer for action selection (the \"Policy MLP\" in Fig. 2), coupled with an LSTM network for context memorization. Meanwhile, another MLP (the \"Value MLP\" in Fig. 2) is utilized for the value network to estimate the value of the current state.", + "bbox": [ + 75, + 537, + 468, + 674 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 686, + 269, + 704 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Two-stage Learning", + "text_level": 1, + "bbox": [ + 76, + 710, + 267, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We apply a two-stage training technique to train our model. In the first stage, we use four auxiliary classifiers to respectively train the capability feature $\\xi_{\\eta}$ , target state feature, object feature and parent receptacle feature (i.e., the goal feature $\\xi_g^t$ ) in a supervised learning manner. These classifiers are lightweight and efficient, utilizing MLPs, and are trained using cross-entropy loss and the Adam optimizer, with a learning rate of $1 \\times 10^{-6}$ and a batch size of 32.", + "bbox": [ + 75, + 734, + 467, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the second stage, we remove these four classifiers, keep the pre-trained opponent modeling module frozen, directly use the learnt opponent features $\\xi_{\\eta}$ and $\\xi_g^t$ , and focus", + "bbox": [ + 75, + 854, + 467, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on the training of helping policy module. We use 20 kitchen rooms for helping policy training and 10 for evaluation in AI2-THOR [32]. The RLlib [15] framework and PPO [31] algorithm are applied to train our helping policy module. Unless otherwise stated, we use the default settings of RLlib. During training, the scene is randomly initialized with a new room, a new task, and a new capability distribution of the main agent, at each episode.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We apply a progressive learning technique to train the help policy module. Firstly, we train the helper policy module for 840 epochs, with a constant learning rate of $5 \\times 10^{-5}$ without weight decay and a batch size of 128, using the reward defined in Eq. (3) with $\\lambda_{e} = 0.0$ . We find such \"warm-up\" quite important in helping the helper agent to familiarize itself with basic skills to complete goals and tasks. Secondly, we progressively train the model for 240 epochs with a learning rate of $5 \\times 10^{-7}$ and $\\lambda_{e} = 1.0$ in Eq. (3) to enhance the smart help ability. In the evaluation phase, we test the helper in 10 rooms (never used in training) and with 14 different task-capability pairs, repeating three times with different random seeds. We exclude 7 task-capability pairs as they will enable the main agent to finish the task independently. See supplementary for more details.", + "bbox": [ + 496, + 212, + 892, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Reward", + "text_level": 1, + "bbox": [ + 500, + 449, + 598, + 464 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The reward of the helper is influenced by the goal $g_{m}$ and the capability $\\eta_{m}$ of the main agent. During training, the helper agent will get a reward of 20 after finishing a goal of the main agent, corresponding to the first term in Eq. (3). The second term $R^{e_{m}}(s,a_{h})$ in Eq. (3) is influenced by the capability of the main agent. Specifically, if the helper finishes a goal that the main agent can handle independently, the helper will get a punishment: $R^{e_{m}}(s,a_{h}) = -30$ . For every step, the helper agent will get a cost of -0.12 normally and a cost of -0.5 if the action is illegal (e.g., attempting to open something that can not be opened, such as an apple) in the environment. If the task is not finished when the scenario is ended, the helper will receive a punishment of -20.", + "bbox": [ + 496, + 472, + 892, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Baselines", + "text_level": 1, + "bbox": [ + 500, + 680, + 607, + 695 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To make a fair comparison, the baselines are:", + "bbox": [ + 500, + 704, + 797, + 718 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Random. This helper randomly selects an action.", + "- End2end- $\\lambda_{e} = 0.0$ . This model generates actions directly from the observation with MLPs, trained with $\\lambda_{e} = 0.0$ in Eq. (3). We set learning rate to $5 \\times 10^{-5}$ , batch size to 128. The model is trained for 350 epochs before convergence.", + "- End2end- $\\lambda_{e} = 1.0$ . Similar to End2end- $\\lambda_{e} = 0.0$ , but with $\\lambda_{e} = 1.0$ in Eq. (3).", + "- MCTS. This model uses a Monte-Carlo Tree Search (MCTS [3]) algorithm to search for an action with the highest value, given a predicted goal from the opponent modeling module. The value of each action is estimated by the status of goal completion after rollout, discounted" + ], + "bbox": [ + 500, + 719, + 890, + 898 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18096", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by the number of steps taken to achieve this result.", + "bbox": [ + 89, + 90, + 424, + 104 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- MCTS-heuristic. This model combines the MCTS model with expert rules for the three selected tasks. Given a predicted goal from the opponent modeling module, it decides on which action to simulate at a probability $p = 0.5$ by chance and $p = 0.5$ by a rule-based selection of the next action to complete the goal.", + "- $\\mathbf{MCTS_{TG}}$ . This is an implementation to reproduce the high-level planning policy of Watch-and-Help [42]. This model knows the true goal of the main agent.", + "- $\\mathbf{MCTS}_{\\mathbf{RG}}$ . This model is almost the same as $MCTS_{TG}$ except that it follows a random goal.", + "- LLM. We use Large Language Model, i.e., gpt-3.5-turbo-instruct [37] as the helper. We compose a prompt based on the state observations from the AI2-THOR [32]. The prompt is fed into the LLM at every step. We extract the action decision generated from the LLM and evaluate its actual effectiveness in the AI2-THOR simulator. See supplementary for more details." + ], + "bbox": [ + 76, + 106, + 467, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 388, + 228, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To assess the contributions and efficacy of essential components in our method, we derive the following variants:", + "bbox": [ + 76, + 411, + 467, + 440 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- BaseModel. This model is the aforementioned helping policy model with a pre-trained parameter-frozen opponent modeling module. As in Sec. 5.1, we set $\\lambda_{e} = 0.0$ in Eq. (3), and train it for 840 epochs.", + "- BaseModel-w/o. Capability. Here we remove the capability embedding from the training of the helping policy.", + "- BaseModel- $\\lambda_{e} = 1.0$ . This model is trained with $\\lambda_{e} = 1.0$ in Eq. (3) for 840 epochs.", + "- BaseModel-PL- $\\lambda_{e} = 0.0$ . Here, \"PL\" means the Progressive Learning technique (detailed in Sec. 5.1), but with $\\lambda_{e} = 0.0$ in the second phase after the first warm-up phase. We simply continue to train the BaseModel with a smaller learning rate for 240 epochs (with no change in $\\lambda_{e} = 0.0$ ).", + "- BaseModel-PL- $\\lambda_{e} = 1.0$ (our full model). We use the correct Progressive Learning technique (detailed in Sec. 5.1), and change to $\\lambda_{e} = 1.0$ in the second phase after warming up the basic skills of the helper model." + ], + "bbox": [ + 76, + 441, + 467, + 712 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.5. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 723, + 261, + 738 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To objectively evaluate an agent's performance, we utilize six distinct metrics, where Helping Necessity (HN) and Helping Rate (HR) are first proposed in our work to better assess the Smart Help policy. Let $N$ denote the size of the test scenarios, and let each scenario $i$ be characterized by an initial room state $s_i^0$ and a goal of transitioning the room to the target state $s_i^*$ . Assuming that both the main agent and the helper require $l_i$ steps (with a maximum of 30) to reach the final state $s_i^l$ , we elaborate on these metrics as follows.", + "bbox": [ + 76, + 746, + 467, + 882 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "- Success Rate (SR and GSR). It includes Task-", + "bbox": [ + 76, + 885, + 467, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "conditioned Success Rate (SR) and Goal-conditioned Success Rate (GSR), respectively representing the completion degree of tasks and goals. The SR is defined as $SR = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}$ , where $R_{i}$ is 1 if the task is finished. For task $i$ , let $N_{g_i^m}$ denote the effective goals completed by the main agent, $N_{g_i^h}$ represent the effective goals completed by the helper, and $N_{g_i^a}$ be all the effective goals of the task. The goal-conditioned success for task $i$ is: $GS_{i} = \\frac{N_{g_{i}^{m}} + N_{g_{i}^{h}}}{N_{g_{i}^{a}}}$ . Hence, the overall GSR is defined as $GSR = \\frac{1}{N}\\sum_{i=1}^{N}GS_{i}$ . $R_{i} = 1$ if and only if $GS_{i} = 1$ .", + "bbox": [ + 511, + 90, + 890, + 256 + ], + "page_idx": 6 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Helping Necessity (HN). This metric reflects the necessity of the helper's involvement. Only when the capability required to finish the goal exceeds the main agent's capability, the helping is necessary. Let $N_{g_{\\mathrm{nec},i}^h}$ denote the necessary goals completed by the helper, the Helping Necessity is then calculated as $HN = \\frac{1}{N}\\sum_{i=1}^{N}\\frac{N_{g_{\\mathrm{nec},i}^h}}{N_{g_i^h}}R_i$ , where $R_i = 1$ if the task is completed, otherwise $R_i = 0$ . This assesses the helper's ability to swiftly identify the main agent's capability and provide necessary assistance.", + "- Helping Rate (HR). $HR$ represents the helper's initiative to help. $HR = \\frac{N_{\\text{help}}}{N_{\\text{need\\_help}}}$ , reflecting the probability of helping when the main agent needs help.", + "- Episode Length (EL). We record the average episode length to reflect the efficiency of helping policy. It is computed as: $EL = \\frac{1}{N}\\sum_{i=1}^{N}l_i$ .", + "- Success-weighted by Path Length (SPL). We also include SPL to have a comprehensive evaluation. It is computed as: $SPL = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}\\frac{d_{i}}{\\max(d_{i},l_{i})}$ , where $R_{i} \\in \\{0,1\\}$ denotes whether the task is successfully completed, $d_{i}$ represents the minimum number of steps to finish the task $i$ , and $l_{i}$ is the actual steps." + ], + "bbox": [ + 500, + 256, + 890, + 592 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Beyond these key metrics, we also incorporate the average rewards as a metric for evaluation. For the Smart Help challenge, we want to increase the $HN$ and $HR$ , while simultaneously descending the $EL$ , as well as keeping the $SR$ , $GSR$ , and $SPL$ as high as possible.", + "bbox": [ + 498, + 598, + 890, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Results and Analyses", + "text_level": 1, + "bbox": [ + 500, + 691, + 700, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with baselines. As shown in Tab. 1, our full model exhibits superior performance compared with all other baseline models without ground truth knowledge of the main agent. The Random agent, selecting random actions, and the $MCTS_{RG}$ model, following random goals, both have minimal ability to provide appropriate help. The superiority of our BaseModel compared to the End2End model underscores the value of opponent modeling in the context of assistance tasks. The LLM agent, although has the shortest $EL$ , falls short on other metrics compared with our model. The MCTS-heuristic model, which incorporates rule-based heuristics, outperforms the pure MCTS model.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18097", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/97a70cd3646284acf0182469e42abd40cab54e69897cb3439b5a2113bceb163a.jpg", + "image_caption": [ + "(a).BaseModel-PL- $\\lambda_{e} = 0$ (NormalHelp)" + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 336, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dce0e1e3b57125fde9803893f730547577590c1ad02562bcdd16806bffa0b758.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 334, + 93, + 493, + 256 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9b79d414220b59ace6c85aff8abe7809f99338497f765c95f1075c75c2e26c66.jpg", + "image_caption": [ + "(b).BaseModel-PL- $\\lambda_{\\mathrm{e}} = 1$ (Smart Help)", + "Figure 3. Qualitative results of the learned smart help policy. In this example, the main agent moves directly to finish the goal (\"(In, Potato, Microwave)\", but fails at the goal \" (Open, Microwave)\". (a) The BaseModel-PL- $\\lambda_{e} = 0.0$ model not only helps the main agent with the bottleneck \"(Open, Microwave), but also continues to help with another goal ((ToggleOff, Microwave)). (b) Our full model BaseModel-PL- $\\lambda_{e} = 1.0$ only offer necessary help with the bottleneck \"(Open, Microwave)\", and let the main agent to finish the rest goals independently, which helping policy is smarter since it considers the needs and emotional feelings of the main agent." + ], + "image_footnote": [], + "bbox": [ + 491, + 90, + 733, + 282 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0685dbefc6e918f88d9363091e12dde025dc862ded06672ce3fd140c03c14c29.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 92, + 890, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "However, our model achieves higher scores in $SR$ , $GSR$ , $HN$ , and $HR$ , while maintaining similar values for $EL$ and $SPL$ , indicating the effectiveness of its assistive action planning. The $MCTS_{TG}$ model, knowing the true goal of the main agent, achieves the best performance among all the models, serving as an upper bound for the task. Notably, while it surpasses other models in most metrics, our model demonstrates competitive performance, particularly in $HN$ . This suggests that our model achieves a balance by providing only necessary assistance and ensuring user comfort. The gap between our model and the upper bound shows potential for future research and further improvement.", + "bbox": [ + 75, + 396, + 468, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation analysis. Comparing the BaseModel with BaseModel- $\\lambda_{e} = 1.0$ , we find that setting $\\lambda_{e} = 0.0$ can augment the assisting actions of the helper. When compared with BaseModel-w/o. Capability, we find that the capability module contributes to the learning of the smart helping policy. Comparing the BaseModel-PL- $\\lambda_{e} = 0.0$ with BaseModel-PL- $\\lambda_{e} = 1.0$ , we find that after the initial \"warm-up\" of the basic skills, setting $\\lambda_{e} = 1.0$ in the second phase could greatly improve the $HN$ while maintaining competitive performances across other metrics. Thus, as in Sec. 5.1, for our full model, in the BaseModel \"warm-up\" training phase, the model learns how to complete the goals and tasks, and the assistive actions are greatly encouraged; while in the second progressive learning phase, our full model focuses on improving the assistance strategy of the helper based on the main agent's needs and feelings.", + "bbox": [ + 75, + 580, + 468, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results. Fig. 3 demonstrates two helping cases with a baseline model and our full model. The two models exhibit exploration behaviors in the scene and finally learn to solve the bottleneck problem of the main agent. In comparison, the BaseModel-PL- $\\lambda_{e} = 0.0$ only learns to", + "bbox": [ + 75, + 824, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/04513ed2510857058ff6e50ec1af87129d3b385149643d9f030cec61a7f5a4f7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodSR(↑)GSR(↑)HN(↑)HR(↑)Reward(↑)EL(↓)SPL(↑)
Random0.0740.3640.0540.057-31.33928.5670.054
End2end-λe=0.00.2670.4410.1490.315-23.21824.3430.212
End2end-λe=1.00.0670.3720.0570.057-26.18328.7260.049
LLM0.3450.5060.3820.381/22.9140.210
MCTS0.1780.4820.2660.328/26.7430.126
MCTS-heuristic0.2740.5280.3550.400/24.6920.199
MCTSTG0.5930.8040.6100.678/16.2710.541
MCTSRG0.0430.3480.0150.015/28.9500.042
BaseModel0.4190.5150.4080.412-15.17924.9450.176
BaseModel-w/o. Capability0.3740.5040.3750.379-13.85223.7480.235
BaseModel-λe=1.00.1810.4660.1930.200-17.18527.4480.122
BaseModel-PL-λe=0.00.4880.5560.4550.496-10.95924.3830.198
BaseModel-PL-λe=1.0 (Ours)0.4830.5480.4980.506-10.62524.6500.200
", + "bbox": [ + 501, + 391, + 890, + 518 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. The quantitative results of our experiments. The last ten environments in AI2-THOR are reserved for evaluation. The best results are highlighted in bold. Note that we include some oracle baselines and the upper bound performances are highlighted with underlines.", + "bbox": [ + 496, + 522, + 890, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "help all the goals it successfully infers, while our full model BaseModel-PL- $\\lambda_{e} = 1.0$ learns to decide whether to help based on its inferred goals and capabilities, i.e., only to help with \" (Open, Microwave)\".", + "bbox": [ + 496, + 604, + 890, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 686, + 617, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose the novel challenge Smart Help and build an environment and model that fosters smarter and more harmonious interaction between humans and artificial agents. We hope our challenge, environment, dataset, model and benchmark results will serve as valuable resources to future studies of this important problem.", + "bbox": [ + 496, + 715, + 890, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work is supported by the National Science and Technology Major Project (2022ZD0114900). We thank Zhenliang Zhang at BIGAI and Luyao Yuan at META for their helpful discussions.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18098", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Peter Aigner and Brennan McCarragher. Shared control framework applied to a robotic aid for the blind. IEEE Control Systems Magazine, 19(2):40-46, 1999. 3", + "[2] Dosovitskiy Alexey, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, and Mostafa Dehghani et al. An image is worth 16x16 words: Transformers for image recognition at scale. 2020. 6", + "[3] Browne Cameron B., Edward Powley, Daniel Whitehouse, Simon M. Lucas, Peter I. 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Advances in neural information processing systems, 31, 2018. 3" + ], + "bbox": [ + 78, + 90, + 470, + 685 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18101", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Smart Help_ Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households/e39ca544-b333-4b15-8b22-bd984a4f8117_model.json b/2024/Smart Help_ Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households/e39ca544-b333-4b15-8b22-bd984a4f8117_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3f73f2dc4bbeb4a1fb58fbda46d4922e67c05d2f --- /dev/null +++ b/2024/Smart Help_ Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households/e39ca544-b333-4b15-8b22-bd984a4f8117_model.json @@ -0,0 +1,2554 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.203, + 0.131, + 0.768, + 0.175 + ], + "angle": 0, + "content": "Smart Help: Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households" + }, + { + "type": "text", + "bbox": [ + 0.194, + 0.203, + 0.775, + 0.223 + ], + "angle": 0, + "content": "Zhihao Cao\\(^{1,2,*}\\), Zidong Wang\\(^{1,2,*}\\), Siwen Xie\\(^{3}\\), Anji Liu\\(^{4}\\), Lifeng Fan\\(^{1,\\boxtimes}\\)" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.224, + 0.832, + 0.239 + ], + "angle": 0, + "content": "\\(^{1}\\) State Key Laboratory of General Artificial Intelligence, Beijing Institute for General Artificial Intelligence (BIGAI)" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.241, + 0.74, + 0.256 + ], + "angle": 0, + "content": "\\(^{2}\\) Department of Automation, Tsinghua University \\(^{3}\\) Yuanpei College, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.273, + 0.259, + 0.697, + 0.274 + ], + "angle": 0, + "content": "4 Computer Science Department, University of California, Los Angeles" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.316, + 0.314, + 0.332 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.473, + 0.697 + ], + "angle": 0, + "content": "Despite the significant demand for assistive technology among vulnerable groups (e.g., the elderly, children, and the disabled) in daily tasks, research into advanced AI-driven assistive solutions that genuinely accommodate their diverse needs remains sparse. Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR [32] to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.725, + 0.21, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.842 + ], + "angle": 0, + "content": "All of us may find ourselves within vulnerable demographics at some point. Throughout the human life span, we confront an array of challenges, whether originating from physical discomfort [12], emotional turmoil [53], or the inevitable march of aging [22], that can hinder our ability to perform even the simplest tasks that we once accomplished" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.317, + 0.895, + 0.59 + ], + "angle": 0, + "content": "effortlessly (e.g., lifting a heavy object). This predicament often triggers a complex emotional response. The fear of being labeled as \"special\" or \"disabled\" can evoke feelings of diminished self-esteem, reduced self-efficacy and self-sufficiency, and a sense of personal boundary violation [8, 40]. However, previous research in humanrobot interaction has primarily focused on pure cooperation [30, 38, 42, 43, 52, 57], and assistive technologies [4, 7] have been designed to simply take over everything for human users, often disregarding their emotional well-being. Considering the importance of sensitivity and consideration when offering help, we need new assistance technologies with an emphasis not only on the successful completion of the task but also on the recipient's emotional acceptance of the assistance [8, 40]. This introduces a new dimension to the concept of learning to help in AI, extending the boundaries beyond technical proficiency and into the realm of empathetic engagement." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.895, + 0.882 + ], + "angle": 0, + "content": "To tackle this issue, we propose a novel and pivotal challenge Smart Help, aiming to provide both proactive and adaptive support to human agents with diverse disabilities and dynamic goals in different tasks and environments. Fig. 1 exemplifies the concept of the Smart Help strategy as applied to an assistive robot aiding a human in a household task. The Basic Helper fails to provide proactive assistance due to its inability to infer the user's goals accurately. The Ordinary Helper successfully infers the user's goals from observations and offers proactive help, but it lacks adaptability to different user needs. Its simple \"take-over\" helping strategy can cause a feeling of discomfort in the human user. In contrast, the Smart Helper not only infers both the user's goals distribution but also reasons about the user's capability of completing each goal independently. As a result, the Smart Helper can identify critical goals that hinder task completion and provide proactive and adaptive help that selectively addresses those bottlenecks. This approach allows the user to accomplish the task successfully and joyfully." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.885, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Leveraging AI2-THOR [32], a 3D interactive environ" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.852, + 0.47, + 0.902 + ], + "angle": 0, + "content": "*Indicates equal contribution. Work was conducted during Zhihao Cao and Zidong Wang's internships at BIGAI. Corresponding author: Lifeng Fan (lifengfan@bigai.ai). Our environment, dataset, and codes are available at https://github.com/caozh20/SmartHelp." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18091" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.081, + 0.887, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.217, + 0.887, + 0.362 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.362, + 0.887, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.508, + 0.892, + 0.646 + ], + "angle": 0, + "content": "Figure 1. An example of the Smart Help strategy for an assistive robot. The top left shows the human user's capability distribution across several dimensions (e.g., weight for lifting heavy objects and height for grasping objects from high positions), as well as the current task (e.g., making coffee). The figure illustrates three types of helpers: (1) The Basic Helper merely observes the human user without inferring anything, and thus remains idle and waits until the human user fails the task, leading to frustration. (2) The Ordinary Helper infers the human user's goals through observations and always provides simple and direct assistance for each goal, taking over the entire task. While the task is successfully completed, the human user is left dissatisfied because the robot's helping strategy is overly intrusive, causing discomfort. (3) The Smart Helper infers both the human user's goals and her capability distribution. It reasons about whether the human user is capable of independently accomplishing each goal and thus identifies the bottleneck goal that hinders task completion. The proactive helper then adapts its strategy to assist solely with the bottleneck goal. As a result, the human user successfully completes the task with tailored support, feeling comfortable and satisfied." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.884 + ], + "angle": 0, + "content": "ment engineered for realistic home simulations, we demonstrate a concrete realization of the proposed novel challenge Smart Help. We create a multi-agent interactive environment featuring a main agent with diverse capability distributions (representing the vulnerable group) across dimensions, such as toggling, opening, closing, weight, and height. Within this environment, the main agent faces challenges in achieving dynamic goals across various tasks, and an assistive robot is introduced to assist the main agent throughout their endeavors. Unlike previous assistive tasks that were highly specialized and constrained, such as the use of a robotic arm for the disabled [10, 17, 51], our work represents, to the best of our knowledge, the first construction of a 3D home environment designed to assist the vulnerable group with various general daily household tasks." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Furthermore, we build a new benchmark model for our" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.884 + ], + "angle": 0, + "content": "proposed challenge, which consists of 1) an opponent modeling module that jointly optimizes goal inference and capability estimation, and 2) a helping policy module that reasons about the bottleneck, and learns an optimal Smart Help policy in an online interactive manner. To better evaluate performance in the Smart Help task, we also introduce six assessment metrics. Contrary to traditional evaluation metrics primarily focusing on cumulative reward or task completion, our metrics emphasize the helper's contribution to the task and the essentiality of assistance. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against baselines. We believe our proposed task, environment, model, and benchmark will contribute to the development of next-generation advanced home assistive robot technologies." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Our main contributions can be summarized as follows:" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18092" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.151 + ], + "angle": 0, + "content": "- We propose a novel Smart Help challenge that aims at learning to provide both proactive and adaptive help to diverse human users (especially vulnerable groups) based on inferred goals and capabilities." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.152, + 0.468, + 0.211 + ], + "angle": 0, + "content": "- To the best of our knowledge, we contribute the first 3D realistic home environment built upon AI2-THOR, that focuses on assisting the vulnerable group with daily household tasks in an online and interactive manner." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.213, + 0.468, + 0.272 + ], + "angle": 0, + "content": "- We provide a benchmark model with a joint goal and capability inference, bottleneck reasoning, and helping policy improvement. Strict experiments and the proposed holistic evaluations validate the efficacy of our model." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.287, + 0.218, + 0.302 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.312, + 0.468, + 0.567 + ], + "angle": 0, + "content": "Assistive Robots. The domain of assistive robots encompasses a broad spectrum of research, focusing on enhancing the life quality for individuals with various needs and spanning diverse applications such as mobility aids [1, 20], companion robots [46], and robotic arms [21]. Feil-Seifer and Mataric [18] underscore that Socially Assistive Robotics entails robots assisting humans through effective interaction in tasks such as food delivery [49], healthcare [27], and other tasks necessitating social interaction. However, many of them only rely on simple rules or programs to achieve social interaction [27, 49]. The deployment of assistive robots has also raised ethical and safety considerations, particularly in terms of user autonomy, privacy, acceptance, trust, etc. [5, 6, 9, 18]. The objective of our work is to devise an effective algorithm for Socially Assistive Robotics to estimate people's goals and capabilities, thereby enabling comfortable and smart assistance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.569, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Embodied Multi-agent Collaboration. A series of embodied collaboration tasks have been developed recently thanks to the development of Embodied AI simulators [13, 14, 32, 33, 41, 47, 48, 50]. However, these tasks always focus on some limited task completion, such as collaborative navigation [34, 56] and collaborative furniture rearrangement [28, 29]. Watch-and-Help [42] and NOPA [43] study the cooperative tasks between two agents with the same capabilities. Our work focuses on the collaboration between agents with different capabilities and study the strategic assistance for the vulnerable group on household tasks." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Opponent Modeling. Opponent modeling [16, 19, 24], a pivotal approach in multi-agent interaction tasks, leverages a variety of methodologies such as Inverse Reinforcement Learning [36], Bayesian methods [25, 26, 45, 52, 60], Deep Q-Networks (DQN) [23, 35], Variational AutoEncoders [39], Markov Decision Process [36], etc. This technique is especially valuable in competitive settings like games and strategic decision-making, where understanding and anticipating an opponent's behavior or unseen traits (e.g., Theory of Mind modeling [44]) can significantly influence the outcome. It enables agents to predict future en" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.303 + ], + "angle": 0, + "content": "vironmental state transitions and refine their strategies accordingly [58, 59]. Projects like Watch-and-Help [42] and NOPA [43] have explored estimating a main agent's goals to improve coordination. Yet, these initiatives often overlook the capabilities of the main agent, leading to a gap in developing effective support strategies for those in need. Our research addresses this gap by focusing on enhancing the acceptance of AI assistance among users, as emphasized in [9], highlighting the importance of aligning AI functionalities with user needs and preferences. Additionally, we propose to model the capability of the opponent and learn a smart, adaptive, and empathetic helping policy for vulnerable people in a challenging 3D household interactive environment with partial observation and high uncertainty." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.318, + 0.748, + 0.335 + ], + "angle": 0, + "content": "3. The Smart Help Challenge" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.343, + 0.702, + 0.357 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.562 + ], + "angle": 0, + "content": "We model the interaction between the main agent and the helper with a multi-agent Partially Observable Markov Decision Process (POMDP[11]), which is formally defined as a tuple \\( G = < S, A, O, R, T, n, \\gamma > \\). \\( S \\) represents the state space, including physical states and mental states. \\( A \\) is the joint action space for \\( n \\) agents, whose local observations compose observation space \\( O \\). \\( T(s'|s, a) \\) denotes the transition probability. \\( R(s, a) \\) denotes the shared reward function and \\( \\gamma \\in [0, 1) \\) is the discount factor. Specifically, there are \\( n = 2 \\) agents in our Smart Help Challenge, i.e., a main agent and a helper agent. The objective is to train a helper agent to assist the main agent in achieving goals, considering the emotional state of the main agent simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.564, + 0.862, + 0.578 + ], + "angle": 0, + "content": "In previous work, the reward for the helper agent is:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.59, + 0.891, + 0.607 + ], + "angle": 0, + "content": "\\[\nR _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) + \\beta R ^ {g _ {m}} (s, a _ {h}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.619, + 0.892, + 0.756 + ], + "angle": 0, + "content": "where the \\(\\beta \\in (0,1)\\) is a factor controlling the level of altruism of the helper. \\(R^{g_h}(s,a_h)\\) is the reward attributed to the successful completion of the helper agent's goal at state \\(s\\) through action \\(a_{h}\\). \\(R^{g_m}(s,a_h)\\) is the same for the main agent's goal achievement. This formulation assumes equal consideration for both agents when rewarding goal completion. However, when the helper fulfills a goal of the main agent, it triggers emotional responses in the main agent. Integrating this emotional component with Eq. (1), we have:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.767, + 0.891, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) \\tag {2} \\\\ + \\beta \\left(R ^ {g _ {m}} \\left(s, a _ {h}\\right) + \\lambda_ {e} R ^ {e _ {m}} \\left(s, a _ {h}\\right)\\right), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( R^{e_m}(s, a_h) \\) means the reward correlated to the emotions of the main agent when the helper does the action \\( a_h \\), and \\( \\lambda_e \\) is a hyper-parameter that controls the helper's sensitivity to the emotional states of the main agent. In our Smart Help challenge, the helper agent's role is solely to assist the main agent in accomplishing his/her goals, without its own" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "18093" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "goals. So we omit the term \\( R^{g_h}(s, a_h) \\) and set \\( \\beta = 1 \\), leading to the helper's reward as:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.133, + 0.469, + 0.15 + ], + "angle": 0, + "content": "\\[\nR _ {h} (s, a _ {h}) = R ^ {g _ {m}} (s, a _ {h}) + \\lambda_ {e} R ^ {e _ {m}} (s, a _ {h}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.16, + 0.47, + 0.234 + ], + "angle": 0, + "content": "Indeed, this is what sets smart Help apart from other assistance-related tasks. Through such design, we emphasize that AI agents must possess the capacity to discern not just how to aid humans, but also when their assistance is truly needed and will be valued." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.244, + 0.318, + 0.26 + ], + "angle": 0, + "content": "3.2. Challenge Implementation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.47, + 0.494 + ], + "angle": 0, + "content": "We implement a tangible version of Smart Help in the AI2THOR [32] simulator, which emphasizes adaptive helping policy for individuals with various disabilities, as shown in Fig. 1. Our new environment includes a main agent that simulates human behavior in various assistive household tasks. The main agent, assigned with a new task and a capability distribution at the beginning of each round, attempts to complete the task with an expert planning policy, which utilizes complete information to divide the task into distinct goals and plan intentional actions for the goals. We also implement a low-level planner that translates the intentional action to a sequence of executable actions in the simulator, so as to enable the main agent to reach the target state indicated by the input intentional action. The workflow of the low-level planner is a loop involving the following steps:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.495, + 0.469, + 0.539 + ], + "angle": 0, + "content": "1. Navigate to the relevant object by following the shortest path determined by the object's position and the room layout; or be directly teleported to the target position." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.54, + 0.47, + 0.66 + ], + "angle": 0, + "content": "2. Interact with the object in accordance with the goal. However, actions taken by the main agent might fail due to certain disabilities or the physical constraints of the scene. Thus, the helper agent, as in Fig. 2, based on its symbolic observations of the world, should infer both the goal and capability of the main agent and provide proactive assistance with the bottleneck for the main agent. We will introduce the detailed environment settings in the following part." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.66, + 0.469, + 0.689 + ], + "angle": 0, + "content": "Object State. We define object state of object \\(i\\) as \\(e_i = (type_i, pos_i, w_i, attr_i, pr_i)\\), where:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.69, + 0.442, + 0.705 + ], + "angle": 0, + "content": "- type \\( i \\in \\mathbb{N} \\) denotes the type of object \\( i \\) with an index;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.705, + 0.428, + 0.72 + ], + "angle": 0, + "content": "- \\(pos_{i} \\in \\mathbb{R}^{3}\\) records the position of object \\(i\\)'s center;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.72, + 0.363, + 0.735 + ], + "angle": 0, + "content": "- \\(w_{i} \\in \\mathbb{R}\\) represents the weight of object \\(i\\);" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.735, + 0.469, + 0.781 + ], + "angle": 0, + "content": "- \\( \\text{attr}_i \\in \\{0,1\\}^{4+2} \\) denotes the attributes of object \\( i \\), including its 4 status (i.e., whether it is picked up, opened, cooked, and toggled on) and its visibility to the 2 agents;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.781, + 0.469, + 0.841 + ], + "angle": 0, + "content": "- \\( pr_i \\in \\mathbb{R} \\) signifies the type of the parent receptacle of the object \\( i \\) through an index; here, the parent receptacle means an object that serves as the container or the support for another subordinate object." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.841 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Action Space. We employ intentional actions to construct the action space, where intentional actions represent the target state that the agent wants to achieve. It is defined as \\( a_{i} = (predicate_{i}, e_{i}) \\in A \\); for instance, (PickUp, 3), where" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.167 + ], + "angle": 0, + "content": "3 is an object index, representing \"Bread\" in our environment. There are seven kinds of different intentional actions: (Wait), (PickUp, \\( e_i \\)), (Put, \\( pr_i \\)), (ToggleOn, \\( e_i \\)), (ToggleOff, \\( e_i \\)), (Open, \\( e_i \\)), and (Close, \\( e_i \\)). In total, there are \\( |A| = 373 \\) possible intentional actions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Agent Capability. The variance of agent capability is manifested in the differences in the transition matrix, which means that different agents will produce different outcomes for the same action at the same state. For example, some agents may be able to pick an object up, while others cannot due to the its weight. Learning the matrix itself is impractical due to the vast size of the space. Instead, we select six parameters to represent the distinct characteristics of different matrices. Therefore, the capability of agent \\( i \\) is represented as \\( \\eta_{i} = (\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i}) \\) where:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.319, + 0.892, + 0.363 + ], + "angle": 0, + "content": "- The maximum height an agent can reach \\( \\alpha_{i} \\in [0,1] \\) and the maximum weight an agent can lift \\( \\beta_{i} \\in [0,1] \\) determine whether an agent can execute the action PickUp;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.364, + 0.892, + 0.409 + ], + "angle": 0, + "content": "- \\(\\gamma_{i}, \\delta_{i}, \\epsilon_{i}, \\zeta_{i} \\in [0,1]\\) respectively represent the agent's ability to complete the actions Open, Close, ToggleOn and ToggleOff." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.319, + 0.892, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.41, + 0.892, + 0.44 + ], + "angle": 0, + "content": "Agent State. We define the state of agent \\(i\\) as \\(h_i = (\\eta_i, \\text{pos}_i, \\text{rot}_i, e_i, a_i, \\text{suc}_i)\\), wherein:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.44, + 0.843, + 0.455 + ], + "angle": 0, + "content": "- \\(\\eta_{i} \\in C = [0,1]^{6}\\) denotes the capability of agent \\(i\\)," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.456, + 0.888, + 0.47 + ], + "angle": 0, + "content": "- \\(pos_i, rot_i \\in \\mathbb{R}^3\\) represent agent \\(i\\)'s position and rotation," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.47, + 0.892, + 0.529 + ], + "angle": 0, + "content": "- \\( e_i \\in E, a_i \\in A \\), and \\( succ_i \\in \\{0,1\\} \\) respectively represent the object held by agent \\( i \\), the action undertaken by agent \\( i \\) in the last step, and whether the last action was a success or a failure." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.44, + 0.892, + 0.529 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.53, + 0.883, + 0.546 + ], + "angle": 0, + "content": "World. The world is denoted as \\( W = (S, A, T) \\), wherein:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.546, + 0.89, + 0.576 + ], + "angle": 0, + "content": "- \\( S = \\{e_i, h_j\\}_{i=1,\\dots,N_o, j=1,2} \\) represents the world state, which encompasses the state of \\( N_o \\) objects and 2 agents;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.577, + 0.75, + 0.591 + ], + "angle": 0, + "content": "- \\(A = \\{a_{i}\\}\\) denotes the action space;" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.591, + 0.89, + 0.621 + ], + "angle": 0, + "content": "- \\( T = P(S'|S, A; \\eta_i) \\) refers to the transition matrix controlled by agent capability." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.546, + 0.89, + 0.621 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.712 + ], + "angle": 0, + "content": "Task. Given our formulation of agent capabilities, we select three everyday tasks for practical implementations of our challenge: Make Breakfast, Arrange Room, and Make Coffee. These tasks respectively involve different capabilities: \\((\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})\\) for Cook Potato, \\((\\alpha_{i},\\beta_{i},\\gamma_{i})\\) for Arrange Room, and \\((\\alpha_{i},\\beta_{i},\\epsilon_{i},\\zeta_{i})\\) for Make Coffee." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.712, + 0.892, + 0.788 + ], + "angle": 0, + "content": "Goal. Upon setting a task, the agent need to identify several key points (goals) that they must achieve. These goals are hidden from the helper, but affect the helper's reward for a particular action. Each goal is defined by the target state of the involved objects. The goal at time \\( t \\) is represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.799, + 0.891, + 0.817 + ], + "angle": 0, + "content": "\\[\ng ^ {t} = \\left(\\text {t a r g e t - s t a t e} ^ {t}, e ^ {t}, p r ^ {t}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Target state includes Wait, Get, On, In, KeepOpen, KeepClose, KeepOn and KeepOff, e.g., \"(In, Cup, Cabinet)\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Observation Space. The proposed environment supports both symbolic and visual observations. This dual-mode observation system enables the helper to acquire and refine" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18094" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.088, + 0.894, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.406, + 0.895, + 0.533 + ], + "angle": 0, + "content": "Figure 2. This figure depicts the architecture of our smart help model and its interaction mechanisms with the environment. The model is partitioned into two primary components: an opponent modeling module and a helping policy module. The opponent modeling module is designed to estimate the goal and capability of the main agent. It adopts a sliding window paradigm and utilizes several MLP layers to generate the state feature \\(\\xi_{s}\\). This feature is then processed by a feature extractor to derive the capability feature \\(\\xi_{\\eta}\\) and the goal feature \\(\\xi_{g}^{t}\\). The helping policy module is composed of two MLP layers to produce action decision and value estimation respectively. During interaction with the environment, the helping model outputs an intentional action, representing the target state it aims to reach. The environment employs a low-level planner to decompose the intentional action into a sequence of executable actions, which are then processed by the AI2THOR simulator, guiding the assistant toward the intended state. Finally, the simulator provides a new observation as feedback, triggering the next cycle of interaction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.609 + ], + "angle": 0, + "content": "helping behaviors in various contexts. Following previous work [42, 43], we use symbolic observations containing physical states of all perceivable objects and agents. Hidden states, like goals and capabilities, can not be observed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.624, + 0.196, + 0.64 + ], + "angle": 0, + "content": "4. Our Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.47, + 0.771 + ], + "angle": 0, + "content": "Our objective is to train a helper agent who can effectively adapt to main agents with varying capabilities and goals. There are two main challenges: 1) the challenge posed by the environment (e.g., partial observation and occlusion), and 2) the challenge posed by the task (i.e., how to estimate the current goal \\( g^{t} \\) and capabilities \\( \\eta \\) of the main agent). Given the observation \\( o^{0:t} \\), the action policy for the helper is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.794, + 0.47, + 0.829 + ], + "angle": 0, + "content": "\\[\nP (a | o ^ {0: t}) = \\sum_ {g ^ {t} \\in G, \\eta \\in C} P (a | g ^ {t}, \\eta , o ^ {0: t}) P (g ^ {t}, \\eta | o ^ {0: t}). \\quad (5)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Therefore, as depicted in Fig. 2, our model consists of: 1) an opponent modeling module to estimate the current goal and capabilities of the main agent, i.e., \\( P(g^{t}, \\eta | o^{0:t}) \\); and 2) a helping policy module to learn the distribution of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.578 + ], + "angle": 0, + "content": "the helper's action conditioned on the predicted goal and capabilities of the main agent, i.e., \\( P(a|g^t,\\eta,o^{0:t}) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.579, + 0.893, + 0.7 + ], + "angle": 0, + "content": "The training of our model has two stages. In the first stage, we train an opponent modeling module using the collected main agent trajectories. This stage is crucial as it enables the helper agent to understand and anticipate the behavior of the main agent effectively. In the second stage, we utilize the pre-trained opponent modeling module to train the helping policy module, which handles dynamic and complex tasks by interacting in our environment." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.71, + 0.79, + 0.728 + ], + "angle": 0, + "content": "4.1. The Opponent Modeling Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.856 + ], + "angle": 0, + "content": "To train this module, we collect simulated trajectories in our environment with the main agent following an expert policy and the helper moving randomly, where each frame contains the observations of the helper agent and the true labels of the main agent's goals and capabilities. Throughout data collection, we utilize a main agent with various tasks and capabilities and a helper executing random actions in the environment. See more details in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We use a sliding window trick when inferring goals and capabilities from the main agent's trajectory since goals are transient and typically persist for only a few steps. This" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18095" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.184 + ], + "angle": 0, + "content": "method enables examining a segment of the trajectory at any given time, and sliding the window as new actions are taken. It allows the helper agent to make more immediate and relevant inferences about the main agent's current goals and capabilities, enhancing its adaptability and responsiveness. Formally, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.196, + 0.47, + 0.214 + ], + "angle": 0, + "content": "\\[\nP \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {0: t}\\right) \\approx P \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {t - w: t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.22, + 0.267, + 0.233 + ], + "angle": 0, + "content": "where \\(w\\) is the window size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.473, + 0.507 + ], + "angle": 0, + "content": "We use an object encoder and an agent encoder to extract features from raw observations (details in supplementary). Similar to the \"class token\" in [2], we preprocess the sequence of object feature. We follow the usage of \"class token\" [2], and only retain this object token to represent the object feature \\(\\xi_{o}^{t}\\) after the transformer [54] layer (other tokens are removed). This object feature \\(\\xi_{o}^{t}\\), together with the agent feature \\(\\xi_{a}^{t}\\), constitute the state feature \\(\\xi_{s}^{t}\\). As in Eq. (6), we use a window size of \\(w\\) and the state features \\(\\{\\xi_{s}^{t - w},\\dots ,\\xi_{s}^{t}\\}\\) are fed into an MLP layer to obtain the final state feature \\(\\xi_{s}\\). Furthermore, a feature extractor is employed to derive the capability feature \\(\\xi_{\\eta}\\) and the target state feature \\(\\xi_{g}^{t}\\) of the main agent. A transformer layer is utilized for the capability feature. As for the goal feature \\(\\xi_{g}^{t}\\), as detailed in Eq. (4), one transformer layer is used for the target state feature, and two MLP layers are employed for the features of the related object and its target parent receptacle." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.325, + 0.531 + ], + "angle": 0, + "content": "4.2. The Helping Policy Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.675 + ], + "angle": 0, + "content": "Our helping policy module has an actor-critic [55] architecture. At each time step \\( t \\), given the current observation \\( o^t \\), together with all the features \\( \\xi_{\\eta} \\) and \\( \\xi_g^t \\) from the opponent modeling module, the helper agent needs to learn the helping policy \\( \\pi_{\\theta}(a|o^t,\\eta ,g^t) \\). We employ an MLP layer for action selection (the \"Policy MLP\" in Fig. 2), coupled with an LSTM network for context memorization. Meanwhile, another MLP (the \"Value MLP\" in Fig. 2) is utilized for the value network to estimate the value of the current state." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.687, + 0.27, + 0.705 + ], + "angle": 0, + "content": "5. Experimental Setup" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.712, + 0.268, + 0.729 + ], + "angle": 0, + "content": "5.1. Two-stage Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.856 + ], + "angle": 0, + "content": "We apply a two-stage training technique to train our model. In the first stage, we use four auxiliary classifiers to respectively train the capability feature \\(\\xi_{\\eta}\\), target state feature, object feature and parent receptacle feature (i.e., the goal feature \\(\\xi_g^t\\)) in a supervised learning manner. These classifiers are lightweight and efficient, utilizing MLPs, and are trained using cross-entropy loss and the Adam optimizer, with a learning rate of \\(1 \\times 10^{-6}\\) and a batch size of 32." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.903 + ], + "angle": 0, + "content": "In the second stage, we remove these four classifiers, keep the pre-trained opponent modeling module frozen, directly use the learnt opponent features \\(\\xi_{\\eta}\\) and \\(\\xi_g^t\\), and focus" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "on the training of helping policy module. We use 20 kitchen rooms for helping policy training and 10 for evaluation in AI2-THOR [32]. The RLlib [15] framework and PPO [31] algorithm are applied to train our helping policy module. Unless otherwise stated, we use the default settings of RLlib. During training, the scene is randomly initialized with a new room, a new task, and a new capability distribution of the main agent, at each episode." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.213, + 0.893, + 0.44 + ], + "angle": 0, + "content": "We apply a progressive learning technique to train the help policy module. Firstly, we train the helper policy module for 840 epochs, with a constant learning rate of \\(5 \\times 10^{-5}\\) without weight decay and a batch size of 128, using the reward defined in Eq. (3) with \\(\\lambda_{e} = 0.0\\). We find such \"warm-up\" quite important in helping the helper agent to familiarize itself with basic skills to complete goals and tasks. Secondly, we progressively train the model for 240 epochs with a learning rate of \\(5 \\times 10^{-7}\\) and \\(\\lambda_{e} = 1.0\\) in Eq. (3) to enhance the smart help ability. In the evaluation phase, we test the helper in 10 rooms (never used in training) and with 14 different task-capability pairs, repeating three times with different random seeds. We exclude 7 task-capability pairs as they will enable the main agent to finish the task independently. See supplementary for more details." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.45, + 0.599, + 0.465 + ], + "angle": 0, + "content": "5.2. Reward" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.893, + 0.671 + ], + "angle": 0, + "content": "The reward of the helper is influenced by the goal \\( g_{m} \\) and the capability \\( \\eta_{m} \\) of the main agent. During training, the helper agent will get a reward of 20 after finishing a goal of the main agent, corresponding to the first term in Eq. (3). The second term \\( R^{e_{m}}(s,a_{h}) \\) in Eq. (3) is influenced by the capability of the main agent. Specifically, if the helper finishes a goal that the main agent can handle independently, the helper will get a punishment: \\( R^{e_{m}}(s,a_{h}) = -30 \\). For every step, the helper agent will get a cost of -0.12 normally and a cost of -0.5 if the action is illegal (e.g., attempting to open something that can not be opened, such as an apple) in the environment. If the task is not finished when the scenario is ended, the helper will receive a punishment of -20." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.608, + 0.696 + ], + "angle": 0, + "content": "5.3. Baselines" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.705, + 0.799, + 0.719 + ], + "angle": 0, + "content": "To make a fair comparison, the baselines are:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.72, + 0.842, + 0.735 + ], + "angle": 0, + "content": "- Random. This helper randomly selects an action." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.735, + 0.892, + 0.795 + ], + "angle": 0, + "content": "- End2end-\\(\\lambda_{e} = 0.0\\). This model generates actions directly from the observation with MLPs, trained with \\(\\lambda_{e} = 0.0\\) in Eq. (3). We set learning rate to \\(5 \\times 10^{-5}\\), batch size to 128. The model is trained for 350 epochs before convergence." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.796, + 0.891, + 0.825 + ], + "angle": 0, + "content": "- End2end-\\(\\lambda_{e} = 1.0\\). Similar to End2end-\\(\\lambda_{e} = 0.0\\), but with \\(\\lambda_{e} = 1.0\\) in Eq. (3)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.825, + 0.892, + 0.9 + ], + "angle": 0, + "content": "- MCTS. This model uses a Monte-Carlo Tree Search (MCTS [3]) algorithm to search for an action with the highest value, given a predicted goal from the opponent modeling module. The value of each action is estimated by the status of goal completion after rollout, discounted" + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.72, + 0.892, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18096" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.091, + 0.092, + 0.425, + 0.106 + ], + "angle": 0, + "content": "by the number of steps taken to achieve this result." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.107, + 0.468, + 0.197 + ], + "angle": 0, + "content": "- MCTS-heuristic. This model combines the MCTS model with expert rules for the three selected tasks. Given a predicted goal from the opponent modeling module, it decides on which action to simulate at a probability \\( p = 0.5 \\) by chance and \\( p = 0.5 \\) by a rule-based selection of the next action to complete the goal." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.198, + 0.468, + 0.242 + ], + "angle": 0, + "content": "- \\(\\mathbf{MCTS_{TG}}\\). This is an implementation to reproduce the high-level planning policy of Watch-and-Help [42]. This model knows the true goal of the main agent." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.243, + 0.468, + 0.272 + ], + "angle": 0, + "content": "- \\(\\mathbf{MCTS}_{\\mathbf{RG}}\\). This model is almost the same as \\(MCTS_{TG}\\) except that it follows a random goal." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.273, + 0.468, + 0.378 + ], + "angle": 0, + "content": "- LLM. We use Large Language Model, i.e., gpt-3.5-turbo-instruct [37] as the helper. We compose a prompt based on the state observations from the AI2-THOR [32]. The prompt is fed into the LLM at every step. We extract the action decision generated from the LLM and evaluate its actual effectiveness in the AI2-THOR simulator. See supplementary for more details." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.107, + 0.468, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.389, + 0.229, + 0.404 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.412, + 0.468, + 0.441 + ], + "angle": 0, + "content": "To assess the contributions and efficacy of essential components in our method, we derive the following variants:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.443, + 0.468, + 0.502 + ], + "angle": 0, + "content": "- BaseModel. This model is the aforementioned helping policy model with a pre-trained parameter-frozen opponent modeling module. As in Sec. 5.1, we set \\(\\lambda_{e} = 0.0\\) in Eq. (3), and train it for 840 epochs." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.503, + 0.468, + 0.533 + ], + "angle": 0, + "content": "- BaseModel-w/o. Capability. Here we remove the capability embedding from the training of the helping policy." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.533, + 0.468, + 0.562 + ], + "angle": 0, + "content": "- BaseModel-\\(\\lambda_{e} = 1.0\\). This model is trained with \\(\\lambda_{e} = 1.0\\) in Eq. (3) for 840 epochs." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.563, + 0.468, + 0.652 + ], + "angle": 0, + "content": "- BaseModel-PL-\\(\\lambda_{e} = 0.0\\). Here, \"PL\" means the Progressive Learning technique (detailed in Sec. 5.1), but with \\(\\lambda_{e} = 0.0\\) in the second phase after the first warm-up phase. We simply continue to train the BaseModel with a smaller learning rate for 240 epochs (with no change in \\(\\lambda_{e} = 0.0\\))." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.654, + 0.468, + 0.713 + ], + "angle": 0, + "content": "- BaseModel-PL-\\(\\lambda_{e} = 1.0\\) (our full model). We use the correct Progressive Learning technique (detailed in Sec. 5.1), and change to \\(\\lambda_{e} = 1.0\\) in the second phase after warming up the basic skills of the helper model." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.443, + 0.468, + 0.713 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.724, + 0.262, + 0.739 + ], + "angle": 0, + "content": "5.5. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.747, + 0.468, + 0.883 + ], + "angle": 0, + "content": "To objectively evaluate an agent's performance, we utilize six distinct metrics, where Helping Necessity (HN) and Helping Rate (HR) are first proposed in our work to better assess the Smart Help policy. Let \\(N\\) denote the size of the test scenarios, and let each scenario \\(i\\) be characterized by an initial room state \\(s_i^0\\) and a goal of transitioning the room to the target state \\(s_i^*\\). Assuming that both the main agent and the helper require \\(l_i\\) steps (with a maximum of 30) to reach the final state \\(s_i^l\\), we elaborate on these metrics as follows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.468, + 0.9 + ], + "angle": 0, + "content": "- Success Rate (SR and GSR). It includes Task-" + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "conditioned Success Rate (SR) and Goal-conditioned Success Rate (GSR), respectively representing the completion degree of tasks and goals. The SR is defined as \\( SR = \\frac{1}{N}\\sum_{i=1}^{N}R_{i} \\), where \\( R_{i} \\) is 1 if the task is finished. For task \\( i \\), let \\( N_{g_i^m} \\) denote the effective goals completed by the main agent, \\( N_{g_i^h} \\) represent the effective goals completed by the helper, and \\( N_{g_i^a} \\) be all the effective goals of the task. The goal-conditioned success for task \\( i \\) is: \\( GS_{i} = \\frac{N_{g_{i}^{m}} + N_{g_{i}^{h}}}{N_{g_{i}^{a}}} \\). Hence, the overall GSR is defined as \\( GSR = \\frac{1}{N}\\sum_{i=1}^{N}GS_{i} \\). \\( R_{i} = 1 \\) if and only if \\( GS_{i} = 1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.257, + 0.892, + 0.406 + ], + "angle": 0, + "content": "- Helping Necessity (HN). This metric reflects the necessity of the helper's involvement. Only when the capability required to finish the goal exceeds the main agent's capability, the helping is necessary. Let \\(N_{g_{\\mathrm{nec},i}^h}\\) denote the necessary goals completed by the helper, the Helping Necessity is then calculated as \\(HN = \\frac{1}{N}\\sum_{i=1}^{N}\\frac{N_{g_{\\mathrm{nec},i}^h}}{N_{g_i^h}}R_i\\), where \\(R_i = 1\\) if the task is completed, otherwise \\(R_i = 0\\). This assesses the helper's ability to swiftly identify the main agent's capability and provide necessary assistance." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.407, + 0.891, + 0.455 + ], + "angle": 0, + "content": "- Helping Rate (HR). \\( HR \\) represents the helper's initiative to help. \\( HR = \\frac{N_{\\text{help}}}{N_{\\text{need\\_help}}} \\), reflecting the probability of helping when the main agent needs help." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.455, + 0.891, + 0.5 + ], + "angle": 0, + "content": "- Episode Length (EL). We record the average episode length to reflect the efficiency of helping policy. It is computed as: \\( EL = \\frac{1}{N}\\sum_{i=1}^{N}l_i \\)." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.501, + 0.891, + 0.593 + ], + "angle": 0, + "content": "- Success-weighted by Path Length (SPL). We also include SPL to have a comprehensive evaluation. It is computed as: \\( SPL = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}\\frac{d_{i}}{\\max(d_{i},l_{i})} \\), where \\( R_{i} \\in \\{0,1\\} \\) denotes whether the task is successfully completed, \\( d_{i} \\) represents the minimum number of steps to finish the task \\( i \\), and \\( l_{i} \\) is the actual steps." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.257, + 0.892, + 0.593 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.599, + 0.892, + 0.675 + ], + "angle": 0, + "content": "Beyond these key metrics, we also incorporate the average rewards as a metric for evaluation. For the Smart Help challenge, we want to increase the \\(HN\\) and \\(HR\\), while simultaneously descending the \\(EL\\), as well as keeping the \\(SR\\), \\(GSR\\), and \\(SPL\\) as high as possible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.702, + 0.71 + ], + "angle": 0, + "content": "6. Results and Analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison with baselines. As shown in Tab. 1, our full model exhibits superior performance compared with all other baseline models without ground truth knowledge of the main agent. The Random agent, selecting random actions, and the \\(MCTS_{RG}\\) model, following random goals, both have minimal ability to provide appropriate help. The superiority of our BaseModel compared to the End2End model underscores the value of opponent modeling in the context of assistance tasks. The LLM agent, although has the shortest \\(EL\\), falls short on other metrics compared with our model. The MCTS-heuristic model, which incorporates rule-based heuristics, outperforms the pure MCTS model." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18097" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.337, + 0.284 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.287, + 0.358, + 0.304 + ], + "angle": 0, + "content": "(a).BaseModel-PL- \\(\\lambda_{e} = 0\\) (NormalHelp)" + }, + { + "type": "image", + "bbox": [ + 0.336, + 0.094, + 0.494, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.092, + 0.735, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.483, + 0.287, + 0.752, + 0.304 + ], + "angle": 0, + "content": "(b).BaseModel-PL- \\(\\lambda_{\\mathrm{e}} = 1\\) (Smart Help)" + }, + { + "type": "image", + "bbox": [ + 0.734, + 0.093, + 0.891, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.314, + 0.894, + 0.384 + ], + "angle": 0, + "content": "Figure 3. Qualitative results of the learned smart help policy. In this example, the main agent moves directly to finish the goal (\"(In, Potato, Microwave)\", but fails at the goal \" (Open, Microwave)\". (a) The BaseModel-PL- \\(\\lambda_{e} = 0.0\\) model not only helps the main agent with the bottleneck \"(Open, Microwave), but also continues to help with another goal ((ToggleOff, Microwave)). (b) Our full model BaseModel-PL- \\(\\lambda_{e} = 1.0\\) only offer necessary help with the bottleneck \"(Open, Microwave)\", and let the main agent to finish the rest goals independently, which helping policy is smarter since it considers the needs and emotional feelings of the main agent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.47, + 0.577 + ], + "angle": 0, + "content": "However, our model achieves higher scores in \\( SR \\), \\( GSR \\), \\( HN \\), and \\( HR \\), while maintaining similar values for \\( EL \\) and \\( SPL \\), indicating the effectiveness of its assistive action planning. The \\( MCTS_{TG} \\) model, knowing the true goal of the main agent, achieves the best performance among all the models, serving as an upper bound for the task. Notably, while it surpasses other models in most metrics, our model demonstrates competitive performance, particularly in \\( HN \\). This suggests that our model achieves a balance by providing only necessary assistance and ensuring user comfort. The gap between our model and the upper bound shows potential for future research and further improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.822 + ], + "angle": 0, + "content": "Ablation analysis. Comparing the BaseModel with BaseModel-\\(\\lambda_{e} = 1.0\\), we find that setting \\(\\lambda_{e} = 0.0\\) can augment the assisting actions of the helper. When compared with BaseModel-w/o. Capability, we find that the capability module contributes to the learning of the smart helping policy. Comparing the BaseModel-PL-\\(\\lambda_{e} = 0.0\\) with BaseModel-PL-\\(\\lambda_{e} = 1.0\\), we find that after the initial \"warm-up\" of the basic skills, setting \\(\\lambda_{e} = 1.0\\) in the second phase could greatly improve the \\(HN\\) while maintaining competitive performances across other metrics. Thus, as in Sec. 5.1, for our full model, in the BaseModel \"warm-up\" training phase, the model learns how to complete the goals and tasks, and the assistive actions are greatly encouraged; while in the second progressive learning phase, our full model focuses on improving the assistance strategy of the helper based on the main agent's needs and feelings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results. Fig. 3 demonstrates two helping cases with a baseline model and our full model. The two models exhibit exploration behaviors in the scene and finally learn to solve the bottleneck problem of the main agent. In comparison, the BaseModel-PL-\\(\\lambda_{e} = 0.0\\) only learns to" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.392, + 0.892, + 0.52 + ], + "angle": 0, + "content": "
MethodSR(↑)GSR(↑)HN(↑)HR(↑)Reward(↑)EL(↓)SPL(↑)
Random0.0740.3640.0540.057-31.33928.5670.054
End2end-λe=0.00.2670.4410.1490.315-23.21824.3430.212
End2end-λe=1.00.0670.3720.0570.057-26.18328.7260.049
LLM0.3450.5060.3820.381/22.9140.210
MCTS0.1780.4820.2660.328/26.7430.126
MCTS-heuristic0.2740.5280.3550.400/24.6920.199
MCTSTG0.5930.8040.6100.678/16.2710.541
MCTSRG0.0430.3480.0150.015/28.9500.042
BaseModel0.4190.5150.4080.412-15.17924.9450.176
BaseModel-w/o. Capability0.3740.5040.3750.379-13.85223.7480.235
BaseModel-λe=1.00.1810.4660.1930.200-17.18527.4480.122
BaseModel-PL-λe=0.00.4880.5560.4550.496-10.95924.3830.198
BaseModel-PL-λe=1.0 (Ours)0.4830.5480.4980.506-10.62524.6500.200
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.591 + ], + "angle": 0, + "content": "Table 1. The quantitative results of our experiments. The last ten environments in AI2-THOR are reserved for evaluation. The best results are highlighted in bold. Note that we include some oracle baselines and the upper bound performances are highlighted with underlines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.667 + ], + "angle": 0, + "content": "help all the goals it successfully infers, while our full model BaseModel-PL-\\(\\lambda_{e} = 1.0\\) learns to decide whether to help based on its inferred goals and capabilities, i.e., only to help with \" (Open, Microwave)\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.688, + 0.619, + 0.704 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.716, + 0.892, + 0.807 + ], + "angle": 0, + "content": "In this paper, we propose the novel challenge Smart Help and build an environment and model that fosters smarter and more harmonious interaction between humans and artificial agents. We hope our challenge, environment, dataset, model and benchmark results will serve as valuable resources to future studies of this important problem." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This work is supported by the National Science and Technology Major Project (2022ZD0114900). We thank Zhenliang Zhang at BIGAI and Luyao Yuan at META for their helpful discussions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18098" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Peter Aigner and Brennan McCarragher. Shared control framework applied to a robotic aid for the blind. IEEE Control Systems Magazine, 19(2):40-46, 1999. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.472, + 0.213 + ], + "angle": 0, + "content": "[2] Dosovitskiy Alexey, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, and Mostafa Dehghani et al. 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Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR [32] to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups. + +# 1. Introduction + +All of us may find ourselves within vulnerable demographics at some point. Throughout the human life span, we confront an array of challenges, whether originating from physical discomfort [12], emotional turmoil [53], or the inevitable march of aging [22], that can hinder our ability to perform even the simplest tasks that we once accomplished + +effortlessly (e.g., lifting a heavy object). This predicament often triggers a complex emotional response. The fear of being labeled as "special" or "disabled" can evoke feelings of diminished self-esteem, reduced self-efficacy and self-sufficiency, and a sense of personal boundary violation [8, 40]. However, previous research in humanrobot interaction has primarily focused on pure cooperation [30, 38, 42, 43, 52, 57], and assistive technologies [4, 7] have been designed to simply take over everything for human users, often disregarding their emotional well-being. Considering the importance of sensitivity and consideration when offering help, we need new assistance technologies with an emphasis not only on the successful completion of the task but also on the recipient's emotional acceptance of the assistance [8, 40]. This introduces a new dimension to the concept of learning to help in AI, extending the boundaries beyond technical proficiency and into the realm of empathetic engagement. + +To tackle this issue, we propose a novel and pivotal challenge Smart Help, aiming to provide both proactive and adaptive support to human agents with diverse disabilities and dynamic goals in different tasks and environments. Fig. 1 exemplifies the concept of the Smart Help strategy as applied to an assistive robot aiding a human in a household task. The Basic Helper fails to provide proactive assistance due to its inability to infer the user's goals accurately. The Ordinary Helper successfully infers the user's goals from observations and offers proactive help, but it lacks adaptability to different user needs. Its simple "take-over" helping strategy can cause a feeling of discomfort in the human user. In contrast, the Smart Helper not only infers both the user's goals distribution but also reasons about the user's capability of completing each goal independently. As a result, the Smart Helper can identify critical goals that hinder task completion and provide proactive and adaptive help that selectively addresses those bottlenecks. This approach allows the user to accomplish the task successfully and joyfully. + +Leveraging AI2-THOR [32], a 3D interactive environ + +![](images/b3f89d0f07362e36876a4ad1b65cee0413b83274452b376bf38200830c608548.jpg) + +![](images/7d93d9a87ebe29ebf887feb218a90f501a8f7adc735bc62403b32f47422a122c.jpg) + +![](images/f2a6a7f28eb3050cbd9d9ab74c59fcfd911e258ed7fa64d11abfde1ae3b28949.jpg) +Figure 1. An example of the Smart Help strategy for an assistive robot. The top left shows the human user's capability distribution across several dimensions (e.g., weight for lifting heavy objects and height for grasping objects from high positions), as well as the current task (e.g., making coffee). The figure illustrates three types of helpers: (1) The Basic Helper merely observes the human user without inferring anything, and thus remains idle and waits until the human user fails the task, leading to frustration. (2) The Ordinary Helper infers the human user's goals through observations and always provides simple and direct assistance for each goal, taking over the entire task. While the task is successfully completed, the human user is left dissatisfied because the robot's helping strategy is overly intrusive, causing discomfort. (3) The Smart Helper infers both the human user's goals and her capability distribution. It reasons about whether the human user is capable of independently accomplishing each goal and thus identifies the bottleneck goal that hinders task completion. The proactive helper then adapts its strategy to assist solely with the bottleneck goal. As a result, the human user successfully completes the task with tailored support, feeling comfortable and satisfied. + +ment engineered for realistic home simulations, we demonstrate a concrete realization of the proposed novel challenge Smart Help. We create a multi-agent interactive environment featuring a main agent with diverse capability distributions (representing the vulnerable group) across dimensions, such as toggling, opening, closing, weight, and height. Within this environment, the main agent faces challenges in achieving dynamic goals across various tasks, and an assistive robot is introduced to assist the main agent throughout their endeavors. Unlike previous assistive tasks that were highly specialized and constrained, such as the use of a robotic arm for the disabled [10, 17, 51], our work represents, to the best of our knowledge, the first construction of a 3D home environment designed to assist the vulnerable group with various general daily household tasks. + +Furthermore, we build a new benchmark model for our + +proposed challenge, which consists of 1) an opponent modeling module that jointly optimizes goal inference and capability estimation, and 2) a helping policy module that reasons about the bottleneck, and learns an optimal Smart Help policy in an online interactive manner. To better evaluate performance in the Smart Help task, we also introduce six assessment metrics. Contrary to traditional evaluation metrics primarily focusing on cumulative reward or task completion, our metrics emphasize the helper's contribution to the task and the essentiality of assistance. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against baselines. We believe our proposed task, environment, model, and benchmark will contribute to the development of next-generation advanced home assistive robot technologies. + +Our main contributions can be summarized as follows: + +- We propose a novel Smart Help challenge that aims at learning to provide both proactive and adaptive help to diverse human users (especially vulnerable groups) based on inferred goals and capabilities. +- To the best of our knowledge, we contribute the first 3D realistic home environment built upon AI2-THOR, that focuses on assisting the vulnerable group with daily household tasks in an online and interactive manner. +- We provide a benchmark model with a joint goal and capability inference, bottleneck reasoning, and helping policy improvement. Strict experiments and the proposed holistic evaluations validate the efficacy of our model. + +# 2. Related Work + +Assistive Robots. The domain of assistive robots encompasses a broad spectrum of research, focusing on enhancing the life quality for individuals with various needs and spanning diverse applications such as mobility aids [1, 20], companion robots [46], and robotic arms [21]. Feil-Seifer and Mataric [18] underscore that Socially Assistive Robotics entails robots assisting humans through effective interaction in tasks such as food delivery [49], healthcare [27], and other tasks necessitating social interaction. However, many of them only rely on simple rules or programs to achieve social interaction [27, 49]. The deployment of assistive robots has also raised ethical and safety considerations, particularly in terms of user autonomy, privacy, acceptance, trust, etc. [5, 6, 9, 18]. The objective of our work is to devise an effective algorithm for Socially Assistive Robotics to estimate people's goals and capabilities, thereby enabling comfortable and smart assistance. + +Embodied Multi-agent Collaboration. A series of embodied collaboration tasks have been developed recently thanks to the development of Embodied AI simulators [13, 14, 32, 33, 41, 47, 48, 50]. However, these tasks always focus on some limited task completion, such as collaborative navigation [34, 56] and collaborative furniture rearrangement [28, 29]. Watch-and-Help [42] and NOPA [43] study the cooperative tasks between two agents with the same capabilities. Our work focuses on the collaboration between agents with different capabilities and study the strategic assistance for the vulnerable group on household tasks. + +Opponent Modeling. Opponent modeling [16, 19, 24], a pivotal approach in multi-agent interaction tasks, leverages a variety of methodologies such as Inverse Reinforcement Learning [36], Bayesian methods [25, 26, 45, 52, 60], Deep Q-Networks (DQN) [23, 35], Variational AutoEncoders [39], Markov Decision Process [36], etc. This technique is especially valuable in competitive settings like games and strategic decision-making, where understanding and anticipating an opponent's behavior or unseen traits (e.g., Theory of Mind modeling [44]) can significantly influence the outcome. It enables agents to predict future en + +vironmental state transitions and refine their strategies accordingly [58, 59]. Projects like Watch-and-Help [42] and NOPA [43] have explored estimating a main agent's goals to improve coordination. Yet, these initiatives often overlook the capabilities of the main agent, leading to a gap in developing effective support strategies for those in need. Our research addresses this gap by focusing on enhancing the acceptance of AI assistance among users, as emphasized in [9], highlighting the importance of aligning AI functionalities with user needs and preferences. Additionally, we propose to model the capability of the opponent and learn a smart, adaptive, and empathetic helping policy for vulnerable people in a challenging 3D household interactive environment with partial observation and high uncertainty. + +# 3. The Smart Help Challenge + +# 3.1. Problem Formulation + +We model the interaction between the main agent and the helper with a multi-agent Partially Observable Markov Decision Process (POMDP[11]), which is formally defined as a tuple $G = < S, A, O, R, T, n, \gamma >$ . $S$ represents the state space, including physical states and mental states. $A$ is the joint action space for $n$ agents, whose local observations compose observation space $O$ . $T(s'|s, a)$ denotes the transition probability. $R(s, a)$ denotes the shared reward function and $\gamma \in [0, 1)$ is the discount factor. Specifically, there are $n = 2$ agents in our Smart Help Challenge, i.e., a main agent and a helper agent. The objective is to train a helper agent to assist the main agent in achieving goals, considering the emotional state of the main agent simultaneously. + +In previous work, the reward for the helper agent is: + +$$ +R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) + \beta R ^ {g _ {m}} (s, a _ {h}), \tag {1} +$$ + +where the $\beta \in (0,1)$ is a factor controlling the level of altruism of the helper. $R^{g_h}(s,a_h)$ is the reward attributed to the successful completion of the helper agent's goal at state $s$ through action $a_{h}$ . $R^{g_m}(s,a_h)$ is the same for the main agent's goal achievement. This formulation assumes equal consideration for both agents when rewarding goal completion. However, when the helper fulfills a goal of the main agent, it triggers emotional responses in the main agent. Integrating this emotional component with Eq. (1), we have: + +$$ +\begin{array}{l} R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) \tag {2} \\ + \beta \left(R ^ {g _ {m}} \left(s, a _ {h}\right) + \lambda_ {e} R ^ {e _ {m}} \left(s, a _ {h}\right)\right), \\ \end{array} +$$ + +where $R^{e_m}(s, a_h)$ means the reward correlated to the emotions of the main agent when the helper does the action $a_h$ , and $\lambda_e$ is a hyper-parameter that controls the helper's sensitivity to the emotional states of the main agent. In our Smart Help challenge, the helper agent's role is solely to assist the main agent in accomplishing his/her goals, without its own + +goals. So we omit the term $R^{g_h}(s, a_h)$ and set $\beta = 1$ , leading to the helper's reward as: + +$$ +R _ {h} (s, a _ {h}) = R ^ {g _ {m}} (s, a _ {h}) + \lambda_ {e} R ^ {e _ {m}} (s, a _ {h}). \tag {3} +$$ + +Indeed, this is what sets smart Help apart from other assistance-related tasks. Through such design, we emphasize that AI agents must possess the capacity to discern not just how to aid humans, but also when their assistance is truly needed and will be valued. + +# 3.2. Challenge Implementation + +We implement a tangible version of Smart Help in the AI2THOR [32] simulator, which emphasizes adaptive helping policy for individuals with various disabilities, as shown in Fig. 1. Our new environment includes a main agent that simulates human behavior in various assistive household tasks. The main agent, assigned with a new task and a capability distribution at the beginning of each round, attempts to complete the task with an expert planning policy, which utilizes complete information to divide the task into distinct goals and plan intentional actions for the goals. We also implement a low-level planner that translates the intentional action to a sequence of executable actions in the simulator, so as to enable the main agent to reach the target state indicated by the input intentional action. The workflow of the low-level planner is a loop involving the following steps: + +1. Navigate to the relevant object by following the shortest path determined by the object's position and the room layout; or be directly teleported to the target position. + +2. Interact with the object in accordance with the goal. However, actions taken by the main agent might fail due to certain disabilities or the physical constraints of the scene. Thus, the helper agent, as in Fig. 2, based on its symbolic observations of the world, should infer both the goal and capability of the main agent and provide proactive assistance with the bottleneck for the main agent. We will introduce the detailed environment settings in the following part. + +Object State. We define object state of object $i$ as $e_i = (type_i, pos_i, w_i, attr_i, pr_i)$ , where: + +- type $i \in \mathbb{N}$ denotes the type of object $i$ with an index; +- $pos_{i} \in \mathbb{R}^{3}$ records the position of object $i$ 's center; +- $w_{i} \in \mathbb{R}$ represents the weight of object $i$ ; +- $\text{attr}_i \in \{0,1\}^{4+2}$ denotes the attributes of object $i$ , including its 4 status (i.e., whether it is picked up, opened, cooked, and toggled on) and its visibility to the 2 agents; +- $pr_i \in \mathbb{R}$ signifies the type of the parent receptacle of the object $i$ through an index; here, the parent receptacle means an object that serves as the container or the support for another subordinate object. + +Action Space. We employ intentional actions to construct the action space, where intentional actions represent the target state that the agent wants to achieve. It is defined as $a_{i} = (predicate_{i}, e_{i}) \in A$ ; for instance, (PickUp, 3), where + +3 is an object index, representing "Bread" in our environment. There are seven kinds of different intentional actions: (Wait), (PickUp, $e_i$ ), (Put, $pr_i$ ), (ToggleOn, $e_i$ ), (ToggleOff, $e_i$ ), (Open, $e_i$ ), and (Close, $e_i$ ). In total, there are $|A| = 373$ possible intentional actions. + +Agent Capability. The variance of agent capability is manifested in the differences in the transition matrix, which means that different agents will produce different outcomes for the same action at the same state. For example, some agents may be able to pick an object up, while others cannot due to the its weight. Learning the matrix itself is impractical due to the vast size of the space. Instead, we select six parameters to represent the distinct characteristics of different matrices. Therefore, the capability of agent $i$ is represented as $\eta_{i} = (\alpha_{i},\beta_{i},\gamma_{i},\delta_{i},\epsilon_{i},\zeta_{i})$ where: + +- The maximum height an agent can reach $\alpha_{i} \in [0,1]$ and the maximum weight an agent can lift $\beta_{i} \in [0,1]$ determine whether an agent can execute the action PickUp; +- $\gamma_{i}, \delta_{i}, \epsilon_{i}, \zeta_{i} \in [0,1]$ respectively represent the agent's ability to complete the actions Open, Close, ToggleOn and ToggleOff. + +Agent State. We define the state of agent $i$ as $h_i = (\eta_i, \text{pos}_i, \text{rot}_i, e_i, a_i, \text{suc}_i)$ , wherein: + +- $\eta_{i} \in C = [0,1]^{6}$ denotes the capability of agent $i$ , +- $pos_i, rot_i \in \mathbb{R}^3$ represent agent $i$ 's position and rotation, +- $e_i \in E, a_i \in A$ , and $succ_i \in \{0,1\}$ respectively represent the object held by agent $i$ , the action undertaken by agent $i$ in the last step, and whether the last action was a success or a failure. + +World. The world is denoted as $W = (S, A, T)$ , wherein: + +- $S = \{e_i, h_j\}_{i=1,\dots,N_o, j=1,2}$ represents the world state, which encompasses the state of $N_o$ objects and 2 agents; +- $A = \{a_{i}\}$ denotes the action space; +- $T = P(S'|S, A; \eta_i)$ refers to the transition matrix controlled by agent capability. + +Task. Given our formulation of agent capabilities, we select three everyday tasks for practical implementations of our challenge: Make Breakfast, Arrange Room, and Make Coffee. These tasks respectively involve different capabilities: $(\alpha_{i},\beta_{i},\gamma_{i},\delta_{i},\epsilon_{i},\zeta_{i})$ for Cook Potato, $(\alpha_{i},\beta_{i},\gamma_{i})$ for Arrange Room, and $(\alpha_{i},\beta_{i},\epsilon_{i},\zeta_{i})$ for Make Coffee. + +Goal. Upon setting a task, the agent need to identify several key points (goals) that they must achieve. These goals are hidden from the helper, but affect the helper's reward for a particular action. Each goal is defined by the target state of the involved objects. The goal at time $t$ is represented as: + +$$ +g ^ {t} = \left(\text {t a r g e t - s t a t e} ^ {t}, e ^ {t}, p r ^ {t}\right) \tag {4} +$$ + +Target state includes Wait, Get, On, In, KeepOpen, KeepClose, KeepOn and KeepOff, e.g., "(In, Cup, Cabinet)". + +Observation Space. The proposed environment supports both symbolic and visual observations. This dual-mode observation system enables the helper to acquire and refine + +![](images/39ab639524dae24ba4b646746370f748b38a8df7440acaf6d8f75b3838e37c91.jpg) +Figure 2. This figure depicts the architecture of our smart help model and its interaction mechanisms with the environment. The model is partitioned into two primary components: an opponent modeling module and a helping policy module. The opponent modeling module is designed to estimate the goal and capability of the main agent. It adopts a sliding window paradigm and utilizes several MLP layers to generate the state feature $\xi_{s}$ . This feature is then processed by a feature extractor to derive the capability feature $\xi_{\eta}$ and the goal feature $\xi_{g}^{t}$ . The helping policy module is composed of two MLP layers to produce action decision and value estimation respectively. During interaction with the environment, the helping model outputs an intentional action, representing the target state it aims to reach. The environment employs a low-level planner to decompose the intentional action into a sequence of executable actions, which are then processed by the AI2THOR simulator, guiding the assistant toward the intended state. Finally, the simulator provides a new observation as feedback, triggering the next cycle of interaction. + +helping behaviors in various contexts. Following previous work [42, 43], we use symbolic observations containing physical states of all perceivable objects and agents. Hidden states, like goals and capabilities, can not be observed. + +# 4. Our Model + +Our objective is to train a helper agent who can effectively adapt to main agents with varying capabilities and goals. There are two main challenges: 1) the challenge posed by the environment (e.g., partial observation and occlusion), and 2) the challenge posed by the task (i.e., how to estimate the current goal $g^{t}$ and capabilities $\eta$ of the main agent). Given the observation $o^{0:t}$ , the action policy for the helper is formulated as: + +$$ +P (a | o ^ {0: t}) = \sum_ {g ^ {t} \in G, \eta \in C} P (a | g ^ {t}, \eta , o ^ {0: t}) P (g ^ {t}, \eta | o ^ {0: t}). \quad (5) +$$ + +Therefore, as depicted in Fig. 2, our model consists of: 1) an opponent modeling module to estimate the current goal and capabilities of the main agent, i.e., $P(g^{t}, \eta | o^{0:t})$ ; and 2) a helping policy module to learn the distribution of + +the helper's action conditioned on the predicted goal and capabilities of the main agent, i.e., $P(a|g^t,\eta,o^{0:t})$ . + +The training of our model has two stages. In the first stage, we train an opponent modeling module using the collected main agent trajectories. This stage is crucial as it enables the helper agent to understand and anticipate the behavior of the main agent effectively. In the second stage, we utilize the pre-trained opponent modeling module to train the helping policy module, which handles dynamic and complex tasks by interacting in our environment. + +# 4.1. The Opponent Modeling Module + +To train this module, we collect simulated trajectories in our environment with the main agent following an expert policy and the helper moving randomly, where each frame contains the observations of the helper agent and the true labels of the main agent's goals and capabilities. Throughout data collection, we utilize a main agent with various tasks and capabilities and a helper executing random actions in the environment. See more details in the supplementary. + +We use a sliding window trick when inferring goals and capabilities from the main agent's trajectory since goals are transient and typically persist for only a few steps. This + +method enables examining a segment of the trajectory at any given time, and sliding the window as new actions are taken. It allows the helper agent to make more immediate and relevant inferences about the main agent's current goals and capabilities, enhancing its adaptability and responsiveness. Formally, we have: + +$$ +P \left(\eta_ {i}, g ^ {t} \mid o ^ {0: t}\right) \approx P \left(\eta_ {i}, g ^ {t} \mid o ^ {t - w: t}\right), \tag {6} +$$ + +where $w$ is the window size. + +We use an object encoder and an agent encoder to extract features from raw observations (details in supplementary). Similar to the "class token" in [2], we preprocess the sequence of object feature. We follow the usage of "class token" [2], and only retain this object token to represent the object feature $\xi_{o}^{t}$ after the transformer [54] layer (other tokens are removed). This object feature $\xi_{o}^{t}$ , together with the agent feature $\xi_{a}^{t}$ , constitute the state feature $\xi_{s}^{t}$ . As in Eq. (6), we use a window size of $w$ and the state features $\{\xi_{s}^{t - w},\dots ,\xi_{s}^{t}\}$ are fed into an MLP layer to obtain the final state feature $\xi_{s}$ . Furthermore, a feature extractor is employed to derive the capability feature $\xi_{\eta}$ and the target state feature $\xi_{g}^{t}$ of the main agent. A transformer layer is utilized for the capability feature. As for the goal feature $\xi_{g}^{t}$ , as detailed in Eq. (4), one transformer layer is used for the target state feature, and two MLP layers are employed for the features of the related object and its target parent receptacle. + +# 4.2. The Helping Policy Module + +Our helping policy module has an actor-critic [55] architecture. At each time step $t$ , given the current observation $o^t$ , together with all the features $\xi_{\eta}$ and $\xi_g^t$ from the opponent modeling module, the helper agent needs to learn the helping policy $\pi_{\theta}(a|o^t,\eta ,g^t)$ . We employ an MLP layer for action selection (the "Policy MLP" in Fig. 2), coupled with an LSTM network for context memorization. Meanwhile, another MLP (the "Value MLP" in Fig. 2) is utilized for the value network to estimate the value of the current state. + +# 5. Experimental Setup + +# 5.1. Two-stage Learning + +We apply a two-stage training technique to train our model. In the first stage, we use four auxiliary classifiers to respectively train the capability feature $\xi_{\eta}$ , target state feature, object feature and parent receptacle feature (i.e., the goal feature $\xi_g^t$ ) in a supervised learning manner. These classifiers are lightweight and efficient, utilizing MLPs, and are trained using cross-entropy loss and the Adam optimizer, with a learning rate of $1 \times 10^{-6}$ and a batch size of 32. + +In the second stage, we remove these four classifiers, keep the pre-trained opponent modeling module frozen, directly use the learnt opponent features $\xi_{\eta}$ and $\xi_g^t$ , and focus + +on the training of helping policy module. We use 20 kitchen rooms for helping policy training and 10 for evaluation in AI2-THOR [32]. The RLlib [15] framework and PPO [31] algorithm are applied to train our helping policy module. Unless otherwise stated, we use the default settings of RLlib. During training, the scene is randomly initialized with a new room, a new task, and a new capability distribution of the main agent, at each episode. + +We apply a progressive learning technique to train the help policy module. Firstly, we train the helper policy module for 840 epochs, with a constant learning rate of $5 \times 10^{-5}$ without weight decay and a batch size of 128, using the reward defined in Eq. (3) with $\lambda_{e} = 0.0$ . We find such "warm-up" quite important in helping the helper agent to familiarize itself with basic skills to complete goals and tasks. Secondly, we progressively train the model for 240 epochs with a learning rate of $5 \times 10^{-7}$ and $\lambda_{e} = 1.0$ in Eq. (3) to enhance the smart help ability. In the evaluation phase, we test the helper in 10 rooms (never used in training) and with 14 different task-capability pairs, repeating three times with different random seeds. We exclude 7 task-capability pairs as they will enable the main agent to finish the task independently. See supplementary for more details. + +# 5.2. Reward + +The reward of the helper is influenced by the goal $g_{m}$ and the capability $\eta_{m}$ of the main agent. During training, the helper agent will get a reward of 20 after finishing a goal of the main agent, corresponding to the first term in Eq. (3). The second term $R^{e_{m}}(s,a_{h})$ in Eq. (3) is influenced by the capability of the main agent. Specifically, if the helper finishes a goal that the main agent can handle independently, the helper will get a punishment: $R^{e_{m}}(s,a_{h}) = -30$ . For every step, the helper agent will get a cost of -0.12 normally and a cost of -0.5 if the action is illegal (e.g., attempting to open something that can not be opened, such as an apple) in the environment. If the task is not finished when the scenario is ended, the helper will receive a punishment of -20. + +# 5.3. Baselines + +To make a fair comparison, the baselines are: + +- Random. This helper randomly selects an action. +- End2end- $\lambda_{e} = 0.0$ . This model generates actions directly from the observation with MLPs, trained with $\lambda_{e} = 0.0$ in Eq. (3). We set learning rate to $5 \times 10^{-5}$ , batch size to 128. The model is trained for 350 epochs before convergence. +- End2end- $\lambda_{e} = 1.0$ . Similar to End2end- $\lambda_{e} = 0.0$ , but with $\lambda_{e} = 1.0$ in Eq. (3). +- MCTS. This model uses a Monte-Carlo Tree Search (MCTS [3]) algorithm to search for an action with the highest value, given a predicted goal from the opponent modeling module. The value of each action is estimated by the status of goal completion after rollout, discounted + +by the number of steps taken to achieve this result. + +- MCTS-heuristic. This model combines the MCTS model with expert rules for the three selected tasks. Given a predicted goal from the opponent modeling module, it decides on which action to simulate at a probability $p = 0.5$ by chance and $p = 0.5$ by a rule-based selection of the next action to complete the goal. +- $\mathbf{MCTS_{TG}}$ . This is an implementation to reproduce the high-level planning policy of Watch-and-Help [42]. This model knows the true goal of the main agent. +- $\mathbf{MCTS}_{\mathbf{RG}}$ . This model is almost the same as $MCTS_{TG}$ except that it follows a random goal. +- LLM. We use Large Language Model, i.e., gpt-3.5-turbo-instruct [37] as the helper. We compose a prompt based on the state observations from the AI2-THOR [32]. The prompt is fed into the LLM at every step. We extract the action decision generated from the LLM and evaluate its actual effectiveness in the AI2-THOR simulator. See supplementary for more details. + +# 5.4. Ablation Study + +To assess the contributions and efficacy of essential components in our method, we derive the following variants: + +- BaseModel. This model is the aforementioned helping policy model with a pre-trained parameter-frozen opponent modeling module. As in Sec. 5.1, we set $\lambda_{e} = 0.0$ in Eq. (3), and train it for 840 epochs. +- BaseModel-w/o. Capability. Here we remove the capability embedding from the training of the helping policy. +- BaseModel- $\lambda_{e} = 1.0$ . This model is trained with $\lambda_{e} = 1.0$ in Eq. (3) for 840 epochs. +- BaseModel-PL- $\lambda_{e} = 0.0$ . Here, "PL" means the Progressive Learning technique (detailed in Sec. 5.1), but with $\lambda_{e} = 0.0$ in the second phase after the first warm-up phase. We simply continue to train the BaseModel with a smaller learning rate for 240 epochs (with no change in $\lambda_{e} = 0.0$ ). +- BaseModel-PL- $\lambda_{e} = 1.0$ (our full model). We use the correct Progressive Learning technique (detailed in Sec. 5.1), and change to $\lambda_{e} = 1.0$ in the second phase after warming up the basic skills of the helper model. + +# 5.5. Evaluation Metrics + +To objectively evaluate an agent's performance, we utilize six distinct metrics, where Helping Necessity (HN) and Helping Rate (HR) are first proposed in our work to better assess the Smart Help policy. Let $N$ denote the size of the test scenarios, and let each scenario $i$ be characterized by an initial room state $s_i^0$ and a goal of transitioning the room to the target state $s_i^*$ . Assuming that both the main agent and the helper require $l_i$ steps (with a maximum of 30) to reach the final state $s_i^l$ , we elaborate on these metrics as follows. + +- Success Rate (SR and GSR). It includes Task- + +conditioned Success Rate (SR) and Goal-conditioned Success Rate (GSR), respectively representing the completion degree of tasks and goals. The SR is defined as $SR = \frac{1}{N}\sum_{i=1}^{N}R_{i}$ , where $R_{i}$ is 1 if the task is finished. For task $i$ , let $N_{g_i^m}$ denote the effective goals completed by the main agent, $N_{g_i^h}$ represent the effective goals completed by the helper, and $N_{g_i^a}$ be all the effective goals of the task. The goal-conditioned success for task $i$ is: $GS_{i} = \frac{N_{g_{i}^{m}} + N_{g_{i}^{h}}}{N_{g_{i}^{a}}}$ . Hence, the overall GSR is defined as $GSR = \frac{1}{N}\sum_{i=1}^{N}GS_{i}$ . $R_{i} = 1$ if and only if $GS_{i} = 1$ . + +- Helping Necessity (HN). This metric reflects the necessity of the helper's involvement. Only when the capability required to finish the goal exceeds the main agent's capability, the helping is necessary. Let $N_{g_{\mathrm{nec},i}^h}$ denote the necessary goals completed by the helper, the Helping Necessity is then calculated as $HN = \frac{1}{N}\sum_{i=1}^{N}\frac{N_{g_{\mathrm{nec},i}^h}}{N_{g_i^h}}R_i$ , where $R_i = 1$ if the task is completed, otherwise $R_i = 0$ . This assesses the helper's ability to swiftly identify the main agent's capability and provide necessary assistance. +- Helping Rate (HR). $HR$ represents the helper's initiative to help. $HR = \frac{N_{\text{help}}}{N_{\text{need\_help}}}$ , reflecting the probability of helping when the main agent needs help. +- Episode Length (EL). We record the average episode length to reflect the efficiency of helping policy. It is computed as: $EL = \frac{1}{N}\sum_{i=1}^{N}l_i$ . +- Success-weighted by Path Length (SPL). We also include SPL to have a comprehensive evaluation. It is computed as: $SPL = \frac{1}{N}\sum_{i=1}^{N}R_{i}\frac{d_{i}}{\max(d_{i},l_{i})}$ , where $R_{i} \in \{0,1\}$ denotes whether the task is successfully completed, $d_{i}$ represents the minimum number of steps to finish the task $i$ , and $l_{i}$ is the actual steps. + +Beyond these key metrics, we also incorporate the average rewards as a metric for evaluation. For the Smart Help challenge, we want to increase the $HN$ and $HR$ , while simultaneously descending the $EL$ , as well as keeping the $SR$ , $GSR$ , and $SPL$ as high as possible. + +# 6. Results and Analyses + +Comparison with baselines. As shown in Tab. 1, our full model exhibits superior performance compared with all other baseline models without ground truth knowledge of the main agent. The Random agent, selecting random actions, and the $MCTS_{RG}$ model, following random goals, both have minimal ability to provide appropriate help. The superiority of our BaseModel compared to the End2End model underscores the value of opponent modeling in the context of assistance tasks. The LLM agent, although has the shortest $EL$ , falls short on other metrics compared with our model. The MCTS-heuristic model, which incorporates rule-based heuristics, outperforms the pure MCTS model. + +![](images/97a70cd3646284acf0182469e42abd40cab54e69897cb3439b5a2113bceb163a.jpg) +(a).BaseModel-PL- $\lambda_{e} = 0$ (NormalHelp) + +![](images/dce0e1e3b57125fde9803893f730547577590c1ad02562bcdd16806bffa0b758.jpg) + +![](images/9b79d414220b59ace6c85aff8abe7809f99338497f765c95f1075c75c2e26c66.jpg) +(b).BaseModel-PL- $\lambda_{\mathrm{e}} = 1$ (Smart Help) +Figure 3. Qualitative results of the learned smart help policy. In this example, the main agent moves directly to finish the goal ("(In, Potato, Microwave)", but fails at the goal " (Open, Microwave)". (a) The BaseModel-PL- $\lambda_{e} = 0.0$ model not only helps the main agent with the bottleneck "(Open, Microwave), but also continues to help with another goal ((ToggleOff, Microwave)). (b) Our full model BaseModel-PL- $\lambda_{e} = 1.0$ only offer necessary help with the bottleneck "(Open, Microwave)", and let the main agent to finish the rest goals independently, which helping policy is smarter since it considers the needs and emotional feelings of the main agent. + +![](images/0685dbefc6e918f88d9363091e12dde025dc862ded06672ce3fd140c03c14c29.jpg) + +However, our model achieves higher scores in $SR$ , $GSR$ , $HN$ , and $HR$ , while maintaining similar values for $EL$ and $SPL$ , indicating the effectiveness of its assistive action planning. The $MCTS_{TG}$ model, knowing the true goal of the main agent, achieves the best performance among all the models, serving as an upper bound for the task. Notably, while it surpasses other models in most metrics, our model demonstrates competitive performance, particularly in $HN$ . This suggests that our model achieves a balance by providing only necessary assistance and ensuring user comfort. The gap between our model and the upper bound shows potential for future research and further improvement. + +Ablation analysis. Comparing the BaseModel with BaseModel- $\lambda_{e} = 1.0$ , we find that setting $\lambda_{e} = 0.0$ can augment the assisting actions of the helper. When compared with BaseModel-w/o. Capability, we find that the capability module contributes to the learning of the smart helping policy. Comparing the BaseModel-PL- $\lambda_{e} = 0.0$ with BaseModel-PL- $\lambda_{e} = 1.0$ , we find that after the initial "warm-up" of the basic skills, setting $\lambda_{e} = 1.0$ in the second phase could greatly improve the $HN$ while maintaining competitive performances across other metrics. Thus, as in Sec. 5.1, for our full model, in the BaseModel "warm-up" training phase, the model learns how to complete the goals and tasks, and the assistive actions are greatly encouraged; while in the second progressive learning phase, our full model focuses on improving the assistance strategy of the helper based on the main agent's needs and feelings. + +Qualitative Results. Fig. 3 demonstrates two helping cases with a baseline model and our full model. The two models exhibit exploration behaviors in the scene and finally learn to solve the bottleneck problem of the main agent. In comparison, the BaseModel-PL- $\lambda_{e} = 0.0$ only learns to + +
MethodSR(↑)GSR(↑)HN(↑)HR(↑)Reward(↑)EL(↓)SPL(↑)
Random0.0740.3640.0540.057-31.33928.5670.054
End2end-λe=0.00.2670.4410.1490.315-23.21824.3430.212
End2end-λe=1.00.0670.3720.0570.057-26.18328.7260.049
LLM0.3450.5060.3820.381/22.9140.210
MCTS0.1780.4820.2660.328/26.7430.126
MCTS-heuristic0.2740.5280.3550.400/24.6920.199
MCTSTG0.5930.8040.6100.678/16.2710.541
MCTSRG0.0430.3480.0150.015/28.9500.042
BaseModel0.4190.5150.4080.412-15.17924.9450.176
BaseModel-w/o. Capability0.3740.5040.3750.379-13.85223.7480.235
BaseModel-λe=1.00.1810.4660.1930.200-17.18527.4480.122
BaseModel-PL-λe=0.00.4880.5560.4550.496-10.95924.3830.198
BaseModel-PL-λe=1.0 (Ours)0.4830.5480.4980.506-10.62524.6500.200
+ +Table 1. The quantitative results of our experiments. The last ten environments in AI2-THOR are reserved for evaluation. The best results are highlighted in bold. Note that we include some oracle baselines and the upper bound performances are highlighted with underlines. + +help all the goals it successfully infers, while our full model BaseModel-PL- $\lambda_{e} = 1.0$ learns to decide whether to help based on its inferred goals and capabilities, i.e., only to help with " (Open, Microwave)". + +# 7. Conclusion + +In this paper, we propose the novel challenge Smart Help and build an environment and model that fosters smarter and more harmonious interaction between humans and artificial agents. We hope our challenge, environment, dataset, model and benchmark results will serve as valuable resources to future studies of this important problem. + +Acknowledgement This work is supported by the National Science and Technology Major Project (2022ZD0114900). 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into advanced AI-driven assistive solutions that genuinely accommodate their diverse needs remains sparse. Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR [32] to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 128, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 666 + ], + "type": "text", + "content": "All of us may find ourselves within vulnerable demographics at some point. Throughout the human life span, we confront an array of challenges, whether originating from physical discomfort [12], emotional turmoil [53], or the inevitable march of aging [22], that can hinder our ability to perform even the simplest tasks that we once accomplished" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 251, + 547, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 547, + 467 + ], + "type": "text", + "content": "effortlessly (e.g., lifting a heavy object). This predicament often triggers a complex emotional response. The fear of being labeled as \"special\" or \"disabled\" can evoke feelings of diminished self-esteem, reduced self-efficacy and self-sufficiency, and a sense of personal boundary violation [8, 40]. However, previous research in humanrobot interaction has primarily focused on pure cooperation [30, 38, 42, 43, 52, 57], and assistive technologies [4, 7] have been designed to simply take over everything for human users, often disregarding their emotional well-being. Considering the importance of sensitivity and consideration when offering help, we need new assistance technologies with an emphasis not only on the successful completion of the task but also on the recipient's emotional acceptance of the assistance [8, 40]. This introduces a new dimension to the concept of learning to help in AI, extending the boundaries beyond technical proficiency and into the realm of empathetic engagement." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 470, + 547, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 547, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 547, + 698 + ], + "type": "text", + "content": "To tackle this issue, we propose a novel and pivotal challenge Smart Help, aiming to provide both proactive and adaptive support to human agents with diverse disabilities and dynamic goals in different tasks and environments. Fig. 1 exemplifies the concept of the Smart Help strategy as applied to an assistive robot aiding a human in a household task. The Basic Helper fails to provide proactive assistance due to its inability to infer the user's goals accurately. The Ordinary Helper successfully infers the user's goals from observations and offers proactive help, but it lacks adaptability to different user needs. Its simple \"take-over\" helping strategy can cause a feeling of discomfort in the human user. In contrast, the Smart Helper not only infers both the user's goals distribution but also reasons about the user's capability of completing each goal independently. As a result, the Smart Helper can identify critical goals that hinder task completion and provide proactive and adaptive help that selectively addresses those bottlenecks. This approach allows the user to accomplish the task successfully and joyfully." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 700, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 700, + 545, + 714 + ], + "type": "text", + "content": "Leveraging AI2-THOR [32], a 3D interactive environ" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 674, + 287, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 674, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 674, + 287, + 714 + ], + "type": "text", + "content": "*Indicates equal contribution. Work was conducted during Zhihao Cao and Zidong Wang's internships at BIGAI. Corresponding author: Lifeng Fan (lifengfan@bigai.ai). Our environment, dataset, and codes are available at https://github.com/caozh20/SmartHelp." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18091" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 64, + 542, + 171 + ], + "blocks": [ + { + "bbox": [ + 50, + 64, + 542, + 171 + ], + "lines": [ + { + "bbox": [ + 50, + 64, + 542, + 171 + ], + "spans": [ + { + "bbox": [ + 50, + 64, + 542, + 171 + ], + "type": "image", + "image_path": "b3f89d0f07362e36876a4ad1b65cee0413b83274452b376bf38200830c608548.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 171, + 542, + 286 + ], + "blocks": [ + { + "bbox": [ + 50, + 171, + 542, + 286 + ], + "lines": [ + { + "bbox": [ + 50, + 171, + 542, + 286 + ], + "spans": [ + { + "bbox": [ + 50, + 171, + 542, + 286 + ], + "type": "image", + "image_path": "7d93d9a87ebe29ebf887feb218a90f501a8f7adc735bc62403b32f47422a122c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 286, + 542, + 400 + ], + "blocks": [ + { + "bbox": [ + 50, + 286, + 542, + 400 + ], + "lines": [ + { + "bbox": [ + 50, + 286, + 542, + 400 + ], + "spans": [ + { + "bbox": [ + 50, + 286, + 542, + 400 + ], + "type": "image", + "image_path": "f2a6a7f28eb3050cbd9d9ab74c59fcfd911e258ed7fa64d11abfde1ae3b28949.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 402, + 545, + 511 + ], + "lines": [ + { + "bbox": [ + 46, + 402, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 545, + 511 + ], + "type": "text", + "content": "Figure 1. An example of the Smart Help strategy for an assistive robot. The top left shows the human user's capability distribution across several dimensions (e.g., weight for lifting heavy objects and height for grasping objects from high positions), as well as the current task (e.g., making coffee). The figure illustrates three types of helpers: (1) The Basic Helper merely observes the human user without inferring anything, and thus remains idle and waits until the human user fails the task, leading to frustration. (2) The Ordinary Helper infers the human user's goals through observations and always provides simple and direct assistance for each goal, taking over the entire task. While the task is successfully completed, the human user is left dissatisfied because the robot's helping strategy is overly intrusive, causing discomfort. (3) The Smart Helper infers both the human user's goals and her capability distribution. It reasons about whether the human user is capable of independently accomplishing each goal and thus identifies the bottleneck goal that hinders task completion. The proactive helper then adapts its strategy to assist solely with the bottleneck goal. As a result, the human user successfully completes the task with tailored support, feeling comfortable and satisfied." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 700 + ], + "type": "text", + "content": "ment engineered for realistic home simulations, we demonstrate a concrete realization of the proposed novel challenge Smart Help. We create a multi-agent interactive environment featuring a main agent with diverse capability distributions (representing the vulnerable group) across dimensions, such as toggling, opening, closing, weight, and height. Within this environment, the main agent faces challenges in achieving dynamic goals across various tasks, and an assistive robot is introduced to assist the main agent throughout their endeavors. Unlike previous assistive tasks that were highly specialized and constrained, such as the use of a robotic arm for the disabled [10, 17, 51], our work represents, to the best of our knowledge, the first construction of a 3D home environment designed to assist the vulnerable group with various general daily household tasks." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "content": "Furthermore, we build a new benchmark model for our" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 521, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 700 + ], + "type": "text", + "content": "proposed challenge, which consists of 1) an opponent modeling module that jointly optimizes goal inference and capability estimation, and 2) a helping policy module that reasons about the bottleneck, and learns an optimal Smart Help policy in an online interactive manner. To better evaluate performance in the Smart Help task, we also introduce six assessment metrics. Contrary to traditional evaluation metrics primarily focusing on cumulative reward or task completion, our metrics emphasize the helper's contribution to the task and the essentiality of assistance. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against baselines. We believe our proposed task, environment, model, and benchmark will contribute to the development of next-generation advanced home assistive robot technologies." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 712 + ], + "type": "text", + "content": "Our main contributions can be summarized as follows:" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18092" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 215 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 119 + ], + "type": "text", + "content": "- We propose a novel Smart Help challenge that aims at learning to provide both proactive and adaptive help to diverse human users (especially vulnerable groups) based on inferred goals and capabilities." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 120, + 286, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 120, + 286, + 167 + ], + "spans": [ + { + "bbox": [ + 47, + 120, + 286, + 167 + ], + "type": "text", + "content": "- To the best of our knowledge, we contribute the first 3D realistic home environment built upon AI2-THOR, that focuses on assisting the vulnerable group with daily household tasks in an online and interactive manner." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 168, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 168, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 168, + 286, + 215 + ], + "type": "text", + "content": "- We provide a benchmark model with a joint goal and capability inference, bottleneck reasoning, and helping policy improvement. Strict experiments and the proposed holistic evaluations validate the efficacy of our model." + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 227, + 133, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 133, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 133, + 239 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 247, + 286, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 247, + 286, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 247, + 286, + 449 + ], + "type": "text", + "content": "Assistive Robots. The domain of assistive robots encompasses a broad spectrum of research, focusing on enhancing the life quality for individuals with various needs and spanning diverse applications such as mobility aids [1, 20], companion robots [46], and robotic arms [21]. Feil-Seifer and Mataric [18] underscore that Socially Assistive Robotics entails robots assisting humans through effective interaction in tasks such as food delivery [49], healthcare [27], and other tasks necessitating social interaction. However, many of them only rely on simple rules or programs to achieve social interaction [27, 49]. The deployment of assistive robots has also raised ethical and safety considerations, particularly in terms of user autonomy, privacy, acceptance, trust, etc. [5, 6, 9, 18]. The objective of our work is to devise an effective algorithm for Socially Assistive Robotics to estimate people's goals and capabilities, thereby enabling comfortable and smart assistance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 450, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 450, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 47, + 450, + 286, + 581 + ], + "type": "text", + "content": "Embodied Multi-agent Collaboration. A series of embodied collaboration tasks have been developed recently thanks to the development of Embodied AI simulators [13, 14, 32, 33, 41, 47, 48, 50]. However, these tasks always focus on some limited task completion, such as collaborative navigation [34, 56] and collaborative furniture rearrangement [28, 29]. Watch-and-Help [42] and NOPA [43] study the cooperative tasks between two agents with the same capabilities. Our work focuses on the collaboration between agents with different capabilities and study the strategic assistance for the vulnerable group on household tasks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 286, + 713 + ], + "type": "text", + "content": "Opponent Modeling. Opponent modeling [16, 19, 24], a pivotal approach in multi-agent interaction tasks, leverages a variety of methodologies such as Inverse Reinforcement Learning [36], Bayesian methods [25, 26, 45, 52, 60], Deep Q-Networks (DQN) [23, 35], Variational AutoEncoders [39], Markov Decision Process [36], etc. This technique is especially valuable in competitive settings like games and strategic decision-making, where understanding and anticipating an opponent's behavior or unseen traits (e.g., Theory of Mind modeling [44]) can significantly influence the outcome. It enables agents to predict future en" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 239 + ], + "type": "text", + "content": "vironmental state transitions and refine their strategies accordingly [58, 59]. Projects like Watch-and-Help [42] and NOPA [43] have explored estimating a main agent's goals to improve coordination. Yet, these initiatives often overlook the capabilities of the main agent, leading to a gap in developing effective support strategies for those in need. Our research addresses this gap by focusing on enhancing the acceptance of AI assistance among users, as emphasized in [9], highlighting the importance of aligning AI functionalities with user needs and preferences. Additionally, we propose to model the capability of the opponent and learn a smart, adaptive, and empathetic helping policy for vulnerable people in a challenging 3D household interactive environment with partial observation and high uncertainty." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 251, + 457, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 251, + 457, + 265 + ], + "spans": [ + { + "bbox": [ + 306, + 251, + 457, + 265 + ], + "type": "text", + "content": "3. The Smart Help Challenge" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 271, + 429, + 282 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 271, + 429, + 282 + ], + "spans": [ + { + "bbox": [ + 306, + 271, + 429, + 282 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": "We model the interaction between the main agent and the helper with a multi-agent Partially Observable Markov Decision Process (POMDP[11]), which is formally defined as a tuple " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "G = < S, A, O, R, T, n, \\gamma >" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " represents the state space, including physical states and mental states. " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " is the joint action space for " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " agents, whose local observations compose observation space " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "T(s'|s, a)" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " denotes the transition probability. " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "R(s, a)" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " denotes the shared reward function and " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\gamma \\in [0, 1)" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " is the discount factor. Specifically, there are " + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "inline_equation", + "content": "n = 2" + }, + { + "bbox": [ + 304, + 289, + 545, + 445 + ], + "type": "text", + "content": " agents in our Smart Help Challenge, i.e., a main agent and a helper agent. The objective is to train a helper agent to assist the main agent in achieving goals, considering the emotional state of the main agent simultaneously." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 446, + 527, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 446, + 527, + 457 + ], + "spans": [ + { + "bbox": [ + 317, + 446, + 527, + 457 + ], + "type": "text", + "content": "In previous work, the reward for the helper agent is:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 341, + 467, + 545, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 467, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 341, + 467, + 545, + 480 + ], + "type": "interline_equation", + "content": "R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) + \\beta R ^ {g _ {m}} (s, a _ {h}), \\tag {1}", + "image_path": "16dc0b87cf84fe42237aba75f5732b0cf0105c66b0bdbd5a66220933c473749d.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "content": "where the " + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "inline_equation", + "content": "\\beta \\in (0,1)" + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "content": " is a factor controlling the level of altruism of the helper. " + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "inline_equation", + "content": "R^{g_h}(s,a_h)" + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "content": " is the reward attributed to the successful completion of the helper agent's goal at state " + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "content": " through action " + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "inline_equation", + "content": "a_{h}" + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "inline_equation", + "content": "R^{g_m}(s,a_h)" + }, + { + "bbox": [ + 304, + 490, + 545, + 598 + ], + "type": "text", + "content": " is the same for the main agent's goal achievement. This formulation assumes equal consideration for both agents when rewarding goal completion. However, when the helper fulfills a goal of the main agent, it triggers emotional responses in the main agent. Integrating this emotional component with Eq. (1), we have:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 332, + 607, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 607, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 332, + 607, + 545, + 635 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) \\tag {2} \\\\ + \\beta \\left(R ^ {g _ {m}} \\left(s, a _ {h}\\right) + \\lambda_ {e} R ^ {e _ {m}} \\left(s, a _ {h}\\right)\\right), \\\\ \\end{array}", + "image_path": "7f3c5a0b84b9250bedacc311320f30ab4e077c38d812dbcf8f15e612356d32e0.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "R^{e_m}(s, a_h)" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " means the reward correlated to the emotions of the main agent when the helper does the action " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "a_h" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_e" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " is a hyper-parameter that controls the helper's sensitivity to the emotional states of the main agent. In our Smart Help challenge, the helper agent's role is solely to assist the main agent in accomplishing his/her goals, without its own" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18093" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "goals. So we omit the term " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "R^{g_h}(s, a_h)" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": " and set " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": ", leading to the helper's reward as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 105, + 287, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 105, + 287, + 118 + ], + "spans": [ + { + "bbox": [ + 80, + 105, + 287, + 118 + ], + "type": "interline_equation", + "content": "R _ {h} (s, a _ {h}) = R ^ {g _ {m}} (s, a _ {h}) + \\lambda_ {e} R ^ {e _ {m}} (s, a _ {h}). \\tag {3}", + "image_path": "660eb84f2a50d69a0730cb3de1dce8a25097cb6e44f43d6fcf8dbc1025d94a4a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 126, + 287, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 126, + 287, + 185 + ], + "spans": [ + { + "bbox": [ + 46, + 126, + 287, + 185 + ], + "type": "text", + "content": "Indeed, this is what sets smart Help apart from other assistance-related tasks. Through such design, we emphasize that AI agents must possess the capacity to discern not just how to aid humans, but also when their assistance is truly needed and will be valued." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 193, + 194, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 193, + 194, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 193, + 194, + 205 + ], + "type": "text", + "content": "3.2. Challenge Implementation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 211, + 287, + 391 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 287, + 391 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 287, + 391 + ], + "type": "text", + "content": "We implement a tangible version of Smart Help in the AI2THOR [32] simulator, which emphasizes adaptive helping policy for individuals with various disabilities, as shown in Fig. 1. Our new environment includes a main agent that simulates human behavior in various assistive household tasks. The main agent, assigned with a new task and a capability distribution at the beginning of each round, attempts to complete the task with an expert planning policy, which utilizes complete information to divide the task into distinct goals and plan intentional actions for the goals. We also implement a low-level planner that translates the intentional action to a sequence of executable actions in the simulator, so as to enable the main agent to reach the target state indicated by the input intentional action. The workflow of the low-level planner is a loop involving the following steps:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 392, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 287, + 426 + ], + "type": "text", + "content": "1. Navigate to the relevant object by following the shortest path determined by the object's position and the room layout; or be directly teleported to the target position." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 427, + 287, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 427, + 287, + 522 + ], + "spans": [ + { + "bbox": [ + 47, + 427, + 287, + 522 + ], + "type": "text", + "content": "2. Interact with the object in accordance with the goal. However, actions taken by the main agent might fail due to certain disabilities or the physical constraints of the scene. Thus, the helper agent, as in Fig. 2, based on its symbolic observations of the world, should infer both the goal and capability of the main agent and provide proactive assistance with the bottleneck for the main agent. We will introduce the detailed environment settings in the following part." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "type": "text", + "content": "Object State. We define object state of object " + }, + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "type": "inline_equation", + "content": "e_i = (type_i, pos_i, w_i, attr_i, pr_i)" + }, + { + "bbox": [ + 47, + 522, + 287, + 545 + ], + "type": "text", + "content": ", where:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 546, + 287, + 666 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "type": "text", + "content": "- type " + }, + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "type": "inline_equation", + "content": "i \\in \\mathbb{N}" + }, + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "type": "text", + "content": " denotes the type of object " + }, + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 546, + 270, + 558 + ], + "type": "text", + "content": " with an index;" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "type": "inline_equation", + "content": "pos_{i} \\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "type": "text", + "content": " records the position of object " + }, + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 558, + 261, + 570 + ], + "type": "text", + "content": "'s center;" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "type": "inline_equation", + "content": "w_{i} \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "type": "text", + "content": " represents the weight of object " + }, + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 570, + 222, + 582 + ], + "type": "text", + "content": ";" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "inline_equation", + "content": "\\text{attr}_i \\in \\{0,1\\}^{4+2}" + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "content": " denotes the attributes of object " + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 582, + 287, + 618 + ], + "type": "text", + "content": ", including its 4 status (i.e., whether it is picked up, opened, cooked, and toggled on) and its visibility to the 2 agents;" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "type": "inline_equation", + "content": "pr_i \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "type": "text", + "content": " signifies the type of the parent receptacle of the object " + }, + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 618, + 287, + 666 + ], + "type": "text", + "content": " through an index; here, the parent receptacle means an object that serves as the container or the support for another subordinate object." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "content": "Action Space. We employ intentional actions to construct the action space, where intentional actions represent the target state that the agent wants to achieve. It is defined as " + }, + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "inline_equation", + "content": "a_{i} = (predicate_{i}, e_{i}) \\in A" + }, + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "content": "; for instance, (PickUp, 3), where" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "3 is an object index, representing \"Bread\" in our environment. There are seven kinds of different intentional actions: (Wait), (PickUp, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "), (Put, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "pr_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "), (ToggleOn, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "), (ToggleOff, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "), (Open, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "), and (Close, " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": "). In total, there are " + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "inline_equation", + "content": "|A| = 373" + }, + { + "bbox": [ + 304, + 72, + 545, + 132 + ], + "type": "text", + "content": " possible intentional actions." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": "Agent Capability. The variance of agent capability is manifested in the differences in the transition matrix, which means that different agents will produce different outcomes for the same action at the same state. For example, some agents may be able to pick an object up, while others cannot due to the its weight. Learning the matrix itself is impractical due to the vast size of the space. Instead, we select six parameters to represent the distinct characteristics of different matrices. Therefore, the capability of agent " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " is represented as " + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "inline_equation", + "content": "\\eta_{i} = (\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})" + }, + { + "bbox": [ + 304, + 133, + 545, + 252 + ], + "type": "text", + "content": " where:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 252, + 545, + 323 + ], + "type": "list", + "angle": 0, + "index": 19, + "blocks": [ + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "type": "text", + "content": "- The maximum height an agent can reach " + }, + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\alpha_{i} \\in [0,1]" + }, + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "type": "text", + "content": " and the maximum weight an agent can lift " + }, + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\beta_{i} \\in [0,1]" + }, + { + "bbox": [ + 306, + 252, + 545, + 287 + ], + "type": "text", + "content": " determine whether an agent can execute the action PickUp;" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 288, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 288, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 288, + 545, + 323 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 288, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\gamma_{i}, \\delta_{i}, \\epsilon_{i}, \\zeta_{i} \\in [0,1]" + }, + { + "bbox": [ + 306, + 288, + 545, + 323 + ], + "type": "text", + "content": " respectively represent the agent's ability to complete the actions Open, Close, ToggleOn and ToggleOff." + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "text", + "content": "Agent State. We define the state of agent " + }, + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "inline_equation", + "content": "h_i = (\\eta_i, \\text{pos}_i, \\text{rot}_i, e_i, a_i, \\text{suc}_i)" + }, + { + "bbox": [ + 306, + 324, + 545, + 348 + ], + "type": "text", + "content": ", wherein:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 348, + 545, + 418 + ], + "type": "list", + "angle": 0, + "index": 24, + "blocks": [ + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "type": "inline_equation", + "content": "\\eta_{i} \\in C = [0,1]^{6}" + }, + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "type": "text", + "content": " denotes the capability of agent " + }, + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 348, + 515, + 360 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "type": "inline_equation", + "content": "pos_i, rot_i \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "type": "text", + "content": " represent agent " + }, + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 361, + 543, + 372 + ], + "type": "text", + "content": "'s position and rotation," + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "inline_equation", + "content": "e_i \\in E, a_i \\in A" + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "inline_equation", + "content": "succ_i \\in \\{0,1\\}" + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "text", + "content": " respectively represent the object held by agent " + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "text", + "content": ", the action undertaken by agent " + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 372, + 545, + 418 + ], + "type": "text", + "content": " in the last step, and whether the last action was a success or a failure." + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 419, + 540, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 419, + 540, + 432 + ], + "spans": [ + { + "bbox": [ + 306, + 419, + 540, + 432 + ], + "type": "text", + "content": "World. The world is denoted as " + }, + { + "bbox": [ + 306, + 419, + 540, + 432 + ], + "type": "inline_equation", + "content": "W = (S, A, T)" + }, + { + "bbox": [ + 306, + 419, + 540, + 432 + ], + "type": "text", + "content": ", wherein:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 432, + 544, + 491 + ], + "type": "list", + "angle": 0, + "index": 29, + "blocks": [ + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "type": "inline_equation", + "content": "S = \\{e_i, h_j\\}_{i=1,\\dots,N_o, j=1,2}" + }, + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "type": "text", + "content": " represents the world state, which encompasses the state of " + }, + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "type": "inline_equation", + "content": "N_o" + }, + { + "bbox": [ + 306, + 432, + 544, + 456 + ], + "type": "text", + "content": " objects and 2 agents;" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 456, + 459, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 456, + 459, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 456, + 459, + 468 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 456, + 459, + 468 + ], + "type": "inline_equation", + "content": "A = \\{a_{i}\\}" + }, + { + "bbox": [ + 306, + 456, + 459, + 468 + ], + "type": "text", + "content": " denotes the action space;" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 468, + 544, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 544, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 544, + 491 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 468, + 544, + 491 + ], + "type": "inline_equation", + "content": "T = P(S'|S, A; \\eta_i)" + }, + { + "bbox": [ + 306, + 468, + 544, + 491 + ], + "type": "text", + "content": " refers to the transition matrix controlled by agent capability." + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "text", + "content": "Task. Given our formulation of agent capabilities, we select three everyday tasks for practical implementations of our challenge: Make Breakfast, Arrange Room, and Make Coffee. These tasks respectively involve different capabilities: " + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "inline_equation", + "content": "(\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})" + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "text", + "content": " for Cook Potato, " + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "inline_equation", + "content": "(\\alpha_{i},\\beta_{i},\\gamma_{i})" + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "text", + "content": " for Arrange Room, and " + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "inline_equation", + "content": "(\\alpha_{i},\\beta_{i},\\epsilon_{i},\\zeta_{i})" + }, + { + "bbox": [ + 304, + 492, + 545, + 563 + ], + "type": "text", + "content": " for Make Coffee." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 563, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 624 + ], + "type": "text", + "content": "Goal. Upon setting a task, the agent need to identify several key points (goals) that they must achieve. These goals are hidden from the helper, but affect the helper's reward for a particular action. Each goal is defined by the target state of the involved objects. The goal at time " + }, + { + "bbox": [ + 304, + 563, + 545, + 624 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 563, + 545, + 624 + ], + "type": "text", + "content": " is represented as:" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 369, + 632, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 632, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 369, + 632, + 545, + 647 + ], + "type": "interline_equation", + "content": "g ^ {t} = \\left(\\text {t a r g e t - s t a t e} ^ {t}, e ^ {t}, p r ^ {t}\\right) \\tag {4}", + "image_path": "f1018fd994aff02d49d6a055cadb0e59673d635f43fce4981613cf6500b09490.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "content": "Target state includes Wait, Get, On, In, KeepOpen, KeepClose, KeepOn and KeepOff, e.g., \"(In, Cup, Cabinet)\"." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Observation Space. The proposed environment supports both symbolic and visual observations. This dual-mode observation system enables the helper to acquire and refine" + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18094" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 69, + 547, + 317 + ], + "blocks": [ + { + "bbox": [ + 49, + 69, + 547, + 317 + ], + "lines": [ + { + "bbox": [ + 49, + 69, + 547, + 317 + ], + "spans": [ + { + "bbox": [ + 49, + 69, + 547, + 317 + ], + "type": "image", + "image_path": "39ab639524dae24ba4b646746370f748b38a8df7440acaf6d8f75b3838e37c91.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "lines": [ + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "text", + "content": "Figure 2. This figure depicts the architecture of our smart help model and its interaction mechanisms with the environment. The model is partitioned into two primary components: an opponent modeling module and a helping policy module. The opponent modeling module is designed to estimate the goal and capability of the main agent. It adopts a sliding window paradigm and utilizes several MLP layers to generate the state feature " + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\xi_{s}" + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "text", + "content": ". This feature is then processed by a feature extractor to derive the capability feature " + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\xi_{\\eta}" + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "text", + "content": " and the goal feature " + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "inline_equation", + "content": "\\xi_{g}^{t}" + }, + { + "bbox": [ + 46, + 321, + 547, + 422 + ], + "type": "text", + "content": ". The helping policy module is composed of two MLP layers to produce action decision and value estimation respectively. During interaction with the environment, the helping model outputs an intentional action, representing the target state it aims to reach. The environment employs a low-level planner to decompose the intentional action into a sequence of executable actions, which are then processed by the AI2THOR simulator, guiding the assistant toward the intended state. Finally, the simulator provides a new observation as feedback, triggering the next cycle of interaction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 433, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 482 + ], + "type": "text", + "content": "helping behaviors in various contexts. Following previous work [42, 43], we use symbolic observations containing physical states of all perceivable objects and agents. Hidden states, like goals and capabilities, can not be observed." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 494, + 119, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 119, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 119, + 506 + ], + "type": "text", + "content": "4. Our Model" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "text", + "content": "Our objective is to train a helper agent who can effectively adapt to main agents with varying capabilities and goals. There are two main challenges: 1) the challenge posed by the environment (e.g., partial observation and occlusion), and 2) the challenge posed by the task (i.e., how to estimate the current goal " + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "inline_equation", + "content": "g^{t}" + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "text", + "content": " and capabilities " + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "text", + "content": " of the main agent). Given the observation " + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "inline_equation", + "content": "o^{0:t}" + }, + { + "bbox": [ + 46, + 514, + 287, + 610 + ], + "type": "text", + "content": ", the action policy for the helper is formulated as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 628, + 287, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 628, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 56, + 628, + 287, + 656 + ], + "type": "interline_equation", + "content": "P (a | o ^ {0: t}) = \\sum_ {g ^ {t} \\in G, \\eta \\in C} P (a | g ^ {t}, \\eta , o ^ {0: t}) P (g ^ {t}, \\eta | o ^ {0: t}). \\quad (5)", + "image_path": "a5df1f6bd3fc0837c54ab77447446e5d77edf012b26b933d450f4aff6ba08ee4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": "Therefore, as depicted in Fig. 2, our model consists of: 1) an opponent modeling module to estimate the current goal and capabilities of the main agent, i.e., " + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "P(g^{t}, \\eta | o^{0:t})" + }, + { + "bbox": [ + 47, + 665, + 288, + 714 + ], + "type": "text", + "content": "; and 2) a helping policy module to learn the distribution of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 433, + 545, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 457 + ], + "type": "text", + "content": "the helper's action conditioned on the predicted goal and capabilities of the main agent, i.e., " + }, + { + "bbox": [ + 304, + 433, + 545, + 457 + ], + "type": "inline_equation", + "content": "P(a|g^t,\\eta,o^{0:t})" + }, + { + "bbox": [ + 304, + 433, + 545, + 457 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 458, + 546, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 458, + 546, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 458, + 546, + 554 + ], + "type": "text", + "content": "The training of our model has two stages. In the first stage, we train an opponent modeling module using the collected main agent trajectories. This stage is crucial as it enables the helper agent to understand and anticipate the behavior of the main agent effectively. In the second stage, we utilize the pre-trained opponent modeling module to train the helping policy module, which handles dynamic and complex tasks by interacting in our environment." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 562, + 483, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 483, + 576 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 483, + 576 + ], + "type": "text", + "content": "4.1. The Opponent Modeling Module" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 677 + ], + "type": "text", + "content": "To train this module, we collect simulated trajectories in our environment with the main agent following an expert policy and the helper moving randomly, where each frame contains the observations of the helper agent and the true labels of the main agent's goals and capabilities. Throughout data collection, we utilize a main agent with various tasks and capabilities and a helper executing random actions in the environment. See more details in the supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "We use a sliding window trick when inferring goals and capabilities from the main agent's trajectory since goals are transient and typically persist for only a few steps. This" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18095" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 145 + ], + "type": "text", + "content": "method enables examining a segment of the trajectory at any given time, and sliding the window as new actions are taken. It allows the helper agent to make more immediate and relevant inferences about the main agent's current goals and capabilities, enhancing its adaptability and responsiveness. Formally, we have:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 97, + 155, + 287, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 155, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 97, + 155, + 287, + 169 + ], + "type": "interline_equation", + "content": "P \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {0: t}\\right) \\approx P \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {t - w: t}\\right), \\tag {6}", + "image_path": "af1a03139a2bf09f59500b6cacbc3a88b76d0056e51523cf0cd9554d60828ecd.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 174, + 163, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 174, + 163, + 184 + ], + "spans": [ + { + "bbox": [ + 47, + 174, + 163, + 184 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 174, + 163, + 184 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 47, + 174, + 163, + 184 + ], + "type": "text", + "content": " is the window size." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": "We use an object encoder and an agent encoder to extract features from raw observations (details in supplementary). Similar to the \"class token\" in [2], we preprocess the sequence of object feature. We follow the usage of \"class token\" [2], and only retain this object token to represent the object feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{o}^{t}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": " after the transformer [54] layer (other tokens are removed). This object feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{o}^{t}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": ", together with the agent feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{a}^{t}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": ", constitute the state feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{s}^{t}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": ". As in Eq. (6), we use a window size of " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": " and the state features " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\{\\xi_{s}^{t - w},\\dots ,\\xi_{s}^{t}\\}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": " are fed into an MLP layer to obtain the final state feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{s}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": ". Furthermore, a feature extractor is employed to derive the capability feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{\\eta}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": " and the target state feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{g}^{t}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": " of the main agent. A transformer layer is utilized for the capability feature. As for the goal feature " + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "inline_equation", + "content": "\\xi_{g}^{t}" + }, + { + "bbox": [ + 46, + 185, + 289, + 401 + ], + "type": "text", + "content": ", as detailed in Eq. (4), one transformer layer is used for the target state feature, and two MLP layers are employed for the features of the related object and its target parent receptacle." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 407, + 198, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 198, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 198, + 420 + ], + "type": "text", + "content": "4.2. The Helping Policy Module" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "content": "Our helping policy module has an actor-critic [55] architecture. At each time step " + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "content": ", given the current observation " + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "inline_equation", + "content": "o^t" + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "content": ", together with all the features " + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\xi_{\\eta}" + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\xi_g^t" + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "content": " from the opponent modeling module, the helper agent needs to learn the helping policy " + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\pi_{\\theta}(a|o^t,\\eta ,g^t)" + }, + { + "bbox": [ + 46, + 426, + 287, + 534 + ], + "type": "text", + "content": ". We employ an MLP layer for action selection (the \"Policy MLP\" in Fig. 2), coupled with an LSTM network for context memorization. Meanwhile, another MLP (the \"Value MLP\" in Fig. 2) is utilized for the value network to estimate the value of the current state." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 544, + 165, + 558 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 165, + 558 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 165, + 558 + ], + "type": "text", + "content": "5. Experimental Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 563, + 164, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 563, + 164, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 563, + 164, + 577 + ], + "type": "text", + "content": "5.1. Two-stage Learning" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "text", + "content": "We apply a two-stage training technique to train our model. In the first stage, we use four auxiliary classifiers to respectively train the capability feature " + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "inline_equation", + "content": "\\xi_{\\eta}" + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "text", + "content": ", target state feature, object feature and parent receptacle feature (i.e., the goal feature " + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "inline_equation", + "content": "\\xi_g^t" + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "text", + "content": ") in a supervised learning manner. These classifiers are lightweight and efficient, utilizing MLPs, and are trained using cross-entropy loss and the Adam optimizer, with a learning rate of " + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-6}" + }, + { + "bbox": [ + 46, + 582, + 286, + 677 + ], + "type": "text", + "content": " and a batch size of 32." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "type": "text", + "content": "In the second stage, we remove these four classifiers, keep the pre-trained opponent modeling module frozen, directly use the learnt opponent features " + }, + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\xi_{\\eta}" + }, + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "type": "inline_equation", + "content": "\\xi_g^t" + }, + { + "bbox": [ + 46, + 677, + 286, + 715 + ], + "type": "text", + "content": ", and focus" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "on the training of helping policy module. We use 20 kitchen rooms for helping policy training and 10 for evaluation in AI2-THOR [32]. The RLlib [15] framework and PPO [31] algorithm are applied to train our helping policy module. Unless otherwise stated, we use the default settings of RLlib. During training, the scene is randomly initialized with a new room, a new task, and a new capability distribution of the main agent, at each episode." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "text", + "content": "We apply a progressive learning technique to train the help policy module. Firstly, we train the helper policy module for 840 epochs, with a constant learning rate of " + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "text", + "content": " without weight decay and a batch size of 128, using the reward defined in Eq. (3) with " + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "text", + "content": ". We find such \"warm-up\" quite important in helping the helper agent to familiarize itself with basic skills to complete goals and tasks. Secondly, we progressively train the model for 240 epochs with a learning rate of " + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-7}" + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 304, + 168, + 546, + 348 + ], + "type": "text", + "content": " in Eq. (3) to enhance the smart help ability. In the evaluation phase, we test the helper in 10 rooms (never used in training) and with 14 different task-capability pairs, repeating three times with different random seeds. We exclude 7 task-capability pairs as they will enable the main agent to finish the task independently. See supplementary for more details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 356, + 366, + 368 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 366, + 368 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 366, + 368 + ], + "type": "text", + "content": "5.2. Reward" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "text", + "content": "The reward of the helper is influenced by the goal " + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "inline_equation", + "content": "g_{m}" + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "text", + "content": " and the capability " + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "inline_equation", + "content": "\\eta_{m}" + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "text", + "content": " of the main agent. During training, the helper agent will get a reward of 20 after finishing a goal of the main agent, corresponding to the first term in Eq. (3). The second term " + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "inline_equation", + "content": "R^{e_{m}}(s,a_{h})" + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "text", + "content": " in Eq. (3) is influenced by the capability of the main agent. Specifically, if the helper finishes a goal that the main agent can handle independently, the helper will get a punishment: " + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "inline_equation", + "content": "R^{e_{m}}(s,a_{h}) = -30" + }, + { + "bbox": [ + 304, + 374, + 546, + 531 + ], + "type": "text", + "content": ". For every step, the helper agent will get a cost of -0.12 normally and a cost of -0.5 if the action is illegal (e.g., attempting to open something that can not be opened, such as an apple) in the environment. If the task is not finished when the scenario is ended, the helper will receive a punishment of -20." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 539, + 372, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 372, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 372, + 551 + ], + "type": "text", + "content": "5.3. Baselines" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 558, + 488, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 558, + 488, + 569 + ], + "spans": [ + { + "bbox": [ + 306, + 558, + 488, + 569 + ], + "type": "text", + "content": "To make a fair comparison, the baselines are:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 570, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 306, + 570, + 515, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 570, + 515, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 570, + 515, + 582 + ], + "type": "text", + "content": "- Random. This helper randomly selects an action." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "text", + "content": "- End2end-" + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "text", + "content": ". This model generates actions directly from the observation with MLPs, trained with " + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "text", + "content": " in Eq. (3). We set learning rate to " + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 306, + 582, + 545, + 629 + ], + "type": "text", + "content": ", batch size to 128. The model is trained for 350 epochs before convergence." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "text", + "content": "- End2end-" + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "text", + "content": ". Similar to End2end-" + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "text", + "content": ", but with " + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 306, + 630, + 545, + 653 + ], + "type": "text", + "content": " in Eq. (3)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 653, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 653, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 653, + 545, + 712 + ], + "type": "text", + "content": "- MCTS. This model uses a Monte-Carlo Tree Search (MCTS [3]) algorithm to search for an action with the highest value, given a predicted goal from the opponent modeling module. The value of each action is estimated by the status of goal completion after rollout, discounted" + } + ] + } + ], + "index": 19 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18096" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 55, + 72, + 260, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 72, + 260, + 83 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 260, + 83 + ], + "type": "text", + "content": "by the number of steps taken to achieve this result." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 84, + 286, + 299 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "type": "text", + "content": "- MCTS-heuristic. This model combines the MCTS model with expert rules for the three selected tasks. Given a predicted goal from the opponent modeling module, it decides on which action to simulate at a probability " + }, + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "type": "inline_equation", + "content": "p = 0.5" + }, + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "type": "text", + "content": " by chance and " + }, + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "type": "inline_equation", + "content": "p = 0.5" + }, + { + "bbox": [ + 47, + 84, + 286, + 156 + ], + "type": "text", + "content": " by a rule-based selection of the next action to complete the goal." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 156, + 286, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 191 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 191 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 156, + 286, + 191 + ], + "type": "inline_equation", + "content": "\\mathbf{MCTS_{TG}}" + }, + { + "bbox": [ + 47, + 156, + 286, + 191 + ], + "type": "text", + "content": ". This is an implementation to reproduce the high-level planning policy of Watch-and-Help [42]. This model knows the true goal of the main agent." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "type": "inline_equation", + "content": "\\mathbf{MCTS}_{\\mathbf{RG}}" + }, + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "type": "text", + "content": ". This model is almost the same as " + }, + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "type": "inline_equation", + "content": "MCTS_{TG}" + }, + { + "bbox": [ + 47, + 192, + 286, + 215 + ], + "type": "text", + "content": " except that it follows a random goal." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 216, + 286, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 286, + 299 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 286, + 299 + ], + "type": "text", + "content": "- LLM. We use Large Language Model, i.e., gpt-3.5-turbo-instruct [37] as the helper. We compose a prompt based on the state observations from the AI2-THOR [32]. The prompt is fed into the LLM at every step. We extract the action decision generated from the LLM and evaluate its actual effectiveness in the AI2-THOR simulator. See supplementary for more details." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 308, + 140, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 140, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 140, + 319 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 326, + 286, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 286, + 349 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 286, + 349 + ], + "type": "text", + "content": "To assess the contributions and efficacy of essential components in our method, we derive the following variants:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 350, + 286, + 564 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 47, + 350, + 286, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 286, + 397 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 286, + 397 + ], + "type": "text", + "content": "- BaseModel. This model is the aforementioned helping policy model with a pre-trained parameter-frozen opponent modeling module. As in Sec. 5.1, we set " + }, + { + "bbox": [ + 47, + 350, + 286, + 397 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 47, + 350, + 286, + 397 + ], + "type": "text", + "content": " in Eq. (3), and train it for 840 epochs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 398, + 286, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 398, + 286, + 422 + ], + "spans": [ + { + "bbox": [ + 47, + 398, + 286, + 422 + ], + "type": "text", + "content": "- BaseModel-w/o. Capability. Here we remove the capability embedding from the training of the helping policy." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "spans": [ + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "type": "text", + "content": "- BaseModel-" + }, + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "type": "text", + "content": ". This model is trained with " + }, + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 47, + 422, + 286, + 445 + ], + "type": "text", + "content": " in Eq. (3) for 840 epochs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "content": "- BaseModel-PL-" + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "content": ". Here, \"PL\" means the Progressive Learning technique (detailed in Sec. 5.1), but with " + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "content": " in the second phase after the first warm-up phase. We simply continue to train the BaseModel with a smaller learning rate for 240 epochs (with no change in " + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 47, + 445, + 286, + 516 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "type": "text", + "content": "- BaseModel-PL-" + }, + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "type": "text", + "content": " (our full model). We use the correct Progressive Learning technique (detailed in Sec. 5.1), and change to " + }, + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 47, + 517, + 286, + 564 + ], + "type": "text", + "content": " in the second phase after warming up the basic skills of the helper model." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 573, + 160, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 160, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 160, + 585 + ], + "type": "text", + "content": "5.5. Evaluation Metrics" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": "To objectively evaluate an agent's performance, we utilize six distinct metrics, where Helping Necessity (HN) and Helping Rate (HR) are first proposed in our work to better assess the Smart Help policy. Let " + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": " denote the size of the test scenarios, and let each scenario " + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": " be characterized by an initial room state " + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "inline_equation", + "content": "s_i^0" + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": " and a goal of transitioning the room to the target state " + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "inline_equation", + "content": "s_i^*" + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": ". Assuming that both the main agent and the helper require " + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": " steps (with a maximum of 30) to reach the final state " + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "inline_equation", + "content": "s_i^l" + }, + { + "bbox": [ + 47, + 591, + 286, + 699 + ], + "type": "text", + "content": ", we elaborate on these metrics as follows." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 286, + 712 + ], + "type": "text", + "content": "- Success Rate (SR and GSR). It includes Task-" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": "conditioned Success Rate (SR) and Goal-conditioned Success Rate (GSR), respectively representing the completion degree of tasks and goals. The SR is defined as " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "SR = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "R_{i}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": " is 1 if the task is finished. For task " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "N_{g_i^m}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": " denote the effective goals completed by the main agent, " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "N_{g_i^h}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": " represent the effective goals completed by the helper, and " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "N_{g_i^a}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": " be all the effective goals of the task. The goal-conditioned success for task " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": " is: " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "GS_{i} = \\frac{N_{g_{i}^{m}} + N_{g_{i}^{h}}}{N_{g_{i}^{a}}}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": ". Hence, the overall GSR is defined as " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "GSR = \\frac{1}{N}\\sum_{i=1}^{N}GS_{i}" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "R_{i} = 1" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": " if and only if " + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "GS_{i} = 1" + }, + { + "bbox": [ + 313, + 72, + 545, + 203 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 203, + 545, + 469 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "text", + "content": "- Helping Necessity (HN). This metric reflects the necessity of the helper's involvement. Only when the capability required to finish the goal exceeds the main agent's capability, the helping is necessary. Let " + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "inline_equation", + "content": "N_{g_{\\mathrm{nec},i}^h}" + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "text", + "content": " denote the necessary goals completed by the helper, the Helping Necessity is then calculated as " + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "inline_equation", + "content": "HN = \\frac{1}{N}\\sum_{i=1}^{N}\\frac{N_{g_{\\mathrm{nec},i}^h}}{N_{g_i^h}}R_i" + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "inline_equation", + "content": "R_i = 1" + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "text", + "content": " if the task is completed, otherwise " + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "inline_equation", + "content": "R_i = 0" + }, + { + "bbox": [ + 306, + 203, + 545, + 321 + ], + "type": "text", + "content": ". This assesses the helper's ability to swiftly identify the main agent's capability and provide necessary assistance." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "type": "text", + "content": "- Helping Rate (HR). " + }, + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "type": "inline_equation", + "content": "HR" + }, + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "type": "text", + "content": " represents the helper's initiative to help. " + }, + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "type": "inline_equation", + "content": "HR = \\frac{N_{\\text{help}}}{N_{\\text{need\\_help}}}" + }, + { + "bbox": [ + 306, + 322, + 545, + 360 + ], + "type": "text", + "content": ", reflecting the probability of helping when the main agent needs help." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "type": "text", + "content": "- Episode Length (EL). We record the average episode length to reflect the efficiency of helping policy. It is computed as: " + }, + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "type": "inline_equation", + "content": "EL = \\frac{1}{N}\\sum_{i=1}^{N}l_i" + }, + { + "bbox": [ + 306, + 360, + 545, + 396 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "content": "- Success-weighted by Path Length (SPL). We also include SPL to have a comprehensive evaluation. It is computed as: " + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "inline_equation", + "content": "SPL = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}\\frac{d_{i}}{\\max(d_{i},l_{i})}" + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "inline_equation", + "content": "R_{i} \\in \\{0,1\\}" + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "content": " denotes whether the task is successfully completed, " + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "content": " represents the minimum number of steps to finish the task " + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 306, + 396, + 545, + 469 + ], + "type": "text", + "content": " is the actual steps." + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": "Beyond these key metrics, we also incorporate the average rewards as a metric for evaluation. For the Smart Help challenge, we want to increase the " + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "inline_equation", + "content": "HN" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "inline_equation", + "content": "HR" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": ", while simultaneously descending the " + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "inline_equation", + "content": "EL" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": ", as well as keeping the " + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "inline_equation", + "content": "SR" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "inline_equation", + "content": "GSR" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "inline_equation", + "content": "SPL" + }, + { + "bbox": [ + 305, + 474, + 545, + 534 + ], + "type": "text", + "content": " as high as possible." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 548, + 429, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 429, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 429, + 562 + ], + "type": "text", + "content": "6. Results and Analyses" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Comparison with baselines. As shown in Tab. 1, our full model exhibits superior performance compared with all other baseline models without ground truth knowledge of the main agent. The Random agent, selecting random actions, and the " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "MCTS_{RG}" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " model, following random goals, both have minimal ability to provide appropriate help. The superiority of our BaseModel compared to the End2End model underscores the value of opponent modeling in the context of assistance tasks. The LLM agent, although has the shortest " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "EL" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ", falls short on other metrics compared with our model. The MCTS-heuristic model, which incorporates rule-based heuristics, outperforms the pure MCTS model." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18097" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 206, + 224 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 206, + 224 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 206, + 224 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 206, + 224 + ], + "type": "image", + "image_path": "97a70cd3646284acf0182469e42abd40cab54e69897cb3439b5a2113bceb163a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 227, + 219, + 240 + ], + "lines": [ + { + "bbox": [ + 48, + 227, + 219, + 240 + ], + "spans": [ + { + "bbox": [ + 48, + 227, + 219, + 240 + ], + "type": "text", + "content": "(a).BaseModel-PL- " + }, + { + "bbox": [ + 48, + 227, + 219, + 240 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0" + }, + { + "bbox": [ + 48, + 227, + 219, + 240 + ], + "type": "text", + "content": " (NormalHelp)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 205, + 74, + 302, + 203 + ], + "blocks": [ + { + "bbox": [ + 205, + 74, + 302, + 203 + ], + "lines": [ + { + "bbox": [ + 205, + 74, + 302, + 203 + ], + "spans": [ + { + "bbox": [ + 205, + 74, + 302, + 203 + ], + "type": "image", + "image_path": "dce0e1e3b57125fde9803893f730547577590c1ad02562bcdd16806bffa0b758.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 301, + 72, + 449, + 224 + ], + "blocks": [ + { + "bbox": [ + 301, + 72, + 449, + 224 + ], + "lines": [ + { + "bbox": [ + 301, + 72, + 449, + 224 + ], + "spans": [ + { + "bbox": [ + 301, + 72, + 449, + 224 + ], + "type": "image", + "image_path": "9b79d414220b59ace6c85aff8abe7809f99338497f765c95f1075c75c2e26c66.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 295, + 227, + 460, + 240 + ], + "lines": [ + { + "bbox": [ + 295, + 227, + 460, + 240 + ], + "spans": [ + { + "bbox": [ + 295, + 227, + 460, + 240 + ], + "type": "text", + "content": "(b).BaseModel-PL- " + }, + { + "bbox": [ + 295, + 227, + 460, + 240 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{e}} = 1" + }, + { + "bbox": [ + 295, + 227, + 460, + 240 + ], + "type": "text", + "content": " (Smart Help)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "type": "text", + "content": "Figure 3. Qualitative results of the learned smart help policy. In this example, the main agent moves directly to finish the goal (\"(In, Potato, Microwave)\", but fails at the goal \" (Open, Microwave)\". (a) The BaseModel-PL- " + }, + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "type": "text", + "content": " model not only helps the main agent with the bottleneck \"(Open, Microwave), but also continues to help with another goal ((ToggleOff, Microwave)). (b) Our full model BaseModel-PL- " + }, + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 46, + 248, + 547, + 304 + ], + "type": "text", + "content": " only offer necessary help with the bottleneck \"(Open, Microwave)\", and let the main agent to finish the rest goals independently, which helping policy is smarter since it considers the needs and emotional feelings of the main agent." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 449, + 73, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 449, + 73, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 449, + 73, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 449, + 73, + 545, + 190 + ], + "type": "image", + "image_path": "0685dbefc6e918f88d9363091e12dde025dc862ded06672ce3fd140c03c14c29.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": "However, our model achieves higher scores in " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "SR" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "GSR" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "HN" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "HR" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": ", while maintaining similar values for " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "EL" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "SPL" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": ", indicating the effectiveness of its assistive action planning. The " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "MCTS_{TG}" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": " model, knowing the true goal of the main agent, achieves the best performance among all the models, serving as an upper bound for the task. Notably, while it surpasses other models in most metrics, our model demonstrates competitive performance, particularly in " + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "inline_equation", + "content": "HN" + }, + { + "bbox": [ + 46, + 314, + 287, + 456 + ], + "type": "text", + "content": ". This suggests that our model achieves a balance by providing only necessary assistance and ensuring user comfort. The gap between our model and the upper bound shows potential for future research and further improvement." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": "Ablation analysis. Comparing the BaseModel with BaseModel-" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": ", we find that setting " + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": " can augment the assisting actions of the helper. When compared with BaseModel-w/o. Capability, we find that the capability module contributes to the learning of the smart helping policy. Comparing the BaseModel-PL-" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": " with BaseModel-PL-" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": ", we find that after the initial \"warm-up\" of the basic skills, setting " + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": " in the second phase could greatly improve the " + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "inline_equation", + "content": "HN" + }, + { + "bbox": [ + 46, + 460, + 287, + 651 + ], + "type": "text", + "content": " while maintaining competitive performances across other metrics. Thus, as in Sec. 5.1, for our full model, in the BaseModel \"warm-up\" training phase, the model learns how to complete the goals and tasks, and the assistive actions are greatly encouraged; while in the second progressive learning phase, our full model focuses on improving the assistance strategy of the helper based on the main agent's needs and feelings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": "Qualitative Results. Fig. 3 demonstrates two helping cases with a baseline model and our full model. The two models exhibit exploration behaviors in the scene and finally learn to solve the bottleneck problem of the main agent. In comparison, the BaseModel-PL-" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 0.0" + }, + { + "bbox": [ + 46, + 653, + 287, + 713 + ], + "type": "text", + "content": " only learns to" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 310, + 545, + 411 + ], + "blocks": [ + { + "bbox": [ + 307, + 310, + 545, + 411 + ], + "lines": [ + { + "bbox": [ + 307, + 310, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 307, + 310, + 545, + 411 + ], + "type": "table", + "html": "
MethodSR(↑)GSR(↑)HN(↑)HR(↑)Reward(↑)EL(↓)SPL(↑)
Random0.0740.3640.0540.057-31.33928.5670.054
End2end-λe=0.00.2670.4410.1490.315-23.21824.3430.212
End2end-λe=1.00.0670.3720.0570.057-26.18328.7260.049
LLM0.3450.5060.3820.381/22.9140.210
MCTS0.1780.4820.2660.328/26.7430.126
MCTS-heuristic0.2740.5280.3550.400/24.6920.199
MCTSTG0.5930.8040.6100.678/16.2710.541
MCTSRG0.0430.3480.0150.015/28.9500.042
BaseModel0.4190.5150.4080.412-15.17924.9450.176
BaseModel-w/o. Capability0.3740.5040.3750.379-13.85223.7480.235
BaseModel-λe=1.00.1810.4660.1930.200-17.18527.4480.122
BaseModel-PL-λe=0.00.4880.5560.4550.496-10.95924.3830.198
BaseModel-PL-λe=1.0 (Ours)0.4830.5480.4980.506-10.62524.6500.200
", + "image_path": "04513ed2510857058ff6e50ec1af87129d3b385149643d9f030cec61a7f5a4f7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 414, + 545, + 468 + ], + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 468 + ], + "type": "text", + "content": "Table 1. The quantitative results of our experiments. The last ten environments in AI2-THOR are reserved for evaluation. The best results are highlighted in bold. Note that we include some oracle baselines and the upper bound performances are highlighted with underlines." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 479, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 528 + ], + "type": "text", + "content": "help all the goals it successfully infers, while our full model BaseModel-PL-" + }, + { + "bbox": [ + 304, + 479, + 545, + 528 + ], + "type": "inline_equation", + "content": "\\lambda_{e} = 1.0" + }, + { + "bbox": [ + 304, + 479, + 545, + 528 + ], + "type": "text", + "content": " learns to decide whether to help based on its inferred goals and capabilities, i.e., only to help with \" (Open, Microwave)\"." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 544, + 378, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 378, + 557 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 378, + 557 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 639 + ], + "type": "text", + "content": "In this paper, we propose the novel challenge Smart Help and build an environment and model that fosters smarter and more harmonious interaction between humans and artificial agents. We hope our challenge, environment, dataset, model and benchmark results will serve as valuable resources to future studies of this important problem." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This work is supported by the National Science and Technology Major Project (2022ZD0114900). We thank Zhenliang Zhang at BIGAI and Luyao Yuan at META for their helpful discussions." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18098" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Peter Aigner and Brennan McCarragher. 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We propose SmartEdit, an instruction-based image editing model that leverages Multimodal Large Language Models (MLLMs) to enhance the understanding and reasoning capabilities of instruction-based editing methods. With the specialized design, our SmartEdit is capable of handling complex understanding (the instructions that contain various object attributes like location, relative size, color, and in or outside the mirror) and reasoning scenarios." + ], + "image_footnote": [], + "bbox": [ + 102, + 314, + 859, + 604 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 681, + 313, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current instruction-based image editing methods, such as InstructPix2Pix, often fail to produce satisfactory results in complex scenarios due to their dependence on the simple CLIP text encoder in diffusion models. To rectify this, this paper introduces SmartEdit, a novel approach of instruction-based image editing that leverages Multimodal Large Language Models (MLLMs) to enhance its understanding and reasoning capabilities. However, direct integration of these elements still faces challenges in situations requiring complex reasoning. To mitigate this, we", + "bbox": [ + 75, + 710, + 470, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "propose a Bidirectional Interaction Module (BIM) that enables comprehensive bidirectional information interactions between the input image and the MLLM output. During training, we initially incorporate perception data to boost the perception and understanding capabilities of diffusion models. Subsequently, we demonstrate that a small amount of complex instruction editing data can effectively stimulate SmartEdit's editing capabilities for more complex instructions. We further construct a new evaluation dataset, Reason-Edit, specifically tailored for complex instruction-based image editing. Both quantitative and qualitative results on this evaluation dataset indicate that our SmartEdit surpasses previous methods, paving the way for the practical application of complex instruction-based image editing.", + "bbox": [ + 500, + 681, + 893, + 895 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution † Corresponding author # Interns in ARC Lab, Tencent PCG", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8362", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 80, + 90, + 207, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-image synthesis [8, 13, 23, 26, 27, 29] has experienced significant advancements in recent years, thanks to the development of diffusion models. These methods have enabled the generation of images that are not only consistent with natural language descriptions, but also align with human perception and preferences, marking a substantial leap forward in the field. Instruction-based image editing methods [1, 36], represented by InstructPix2Pix, leverage pre-trained text-to-image diffusion models as priors. This allows users to conveniently and effortlessly modify images through natural language instructions for ordinary users.", + "bbox": [ + 80, + 114, + 467, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While existing instruction-based image editing methods can handle simple instructions effectively, they often fall short when dealing with complex scenarios, which require the model to have a more powerful understanding and reasoning capabilities. As depicted in Fig. 1, there are two common types of complex scenarios. The first is when the original image contains multiple objects, and the instruction modifies only one of these objects through certain attributes (such as location, relative size, color, in or outside the mirror). The other is when world knowledge is needed to identify the object to be edited (such as the object that can tell the time). We define these two types as complex understanding scenarios and complex reasoning scenarios, respectively. Handling these two scenarios is crucial for practical instruction editing, but existing instruction-based image editing methods probably fail in these scenarios (as shown in Fig. 2). In this paper, we attempt to identify the reasons why existing instruction-based image editing methods fail in these scenarios, and try to tackle the challenge in these scenarios.", + "bbox": [ + 80, + 281, + 467, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first reason why existing instruction-based image editing methods fail in these scenarios is that they typically rely on a simple CLIP text encoder [25] in diffusion models (e.g., Stable Diffusion) to process the instructions. Under this circumstance, these models struggle to 1) understand and reason through the instructions, and 2) integrate the image to comprehend the instructions. To address these limitations, we introduce the Multimodal Large Language Models (MLLMs) (e.g., LLaVA) [22, 39] into instruction-based editing models. Our method, SmartEdit, jointly optimizes MLLMs and diffusion models, leveraging the powerful reasoning capabilities of MLLMs to facilitate instruction-based image editing task.", + "bbox": [ + 80, + 584, + 467, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While substituting the CLIP encoder in the diffusion model with MLLMs can alleviate some problems, this approach still falls short when it comes to examples that necessitate complex understanding and reasoning. This is because the input image to edit (original image) is integrated into the UNet of the Stable Diffusion model through a straightforward concatenation, which is further interacted with MLLM outputs through a cross-attention operation. In", + "bbox": [ + 80, + 780, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "this setup, the image features serve as the query, and MLLM outputs act as the key and value. This means that the MLLM outputs unilaterally modulate and interact with the image feature, which affects the results. To alleviate this issue, we further propose a Bidirectional Interaction Module (BIM). This module reuses the image information extracted by the LLaVA's visual encoder from the input image. It also facilitates a comprehensive bidirectional information interaction between this image and the MLLM output, enabling the model to perform better in complex scenarios.", + "bbox": [ + 503, + 90, + 888, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second reason contributing to the failure of existing instruction-based editing methods is the absence of specific data. When solely training on editing datasets, such as the datasets used in Instructpix2pix [1] and MagicBrush [36], SmartEdit also struggles to handle scenarios requiring complex reasoning and understanding. This is because SmartEdit has not been exposed to data from these scenarios. One straightforward approach is to generate a substantial amount of paired data similar to those scenarios. However, this method is excessively expensive because the cost of generating data for these scenarios is high.", + "bbox": [ + 503, + 243, + 888, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we find that there are two keys to compensate the insufficiency of specific editing data. The first is to enhance the perception capabilities of UNet [28], and the second is to stimulate the model capacity in those scenarios with a few high-quality examples. Correspondingly, we 1) incorporate the perception-related data (e.g., segmentation) into the model's training. 2) synthesize a few high-quality paired data with complex instructions to fine-tune our SmartEdit (similar to LISA [19]). In this way, SmartEdit not only reduces the reliance on paired data under complex scenarios but also effectively stimulates its ability to handle these scenarios.", + "bbox": [ + 503, + 410, + 888, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Equipped with both the model designs and the data utilization strategy, SmartEdit can understand complex instructions, surpassing the scope that previous instruction editing methods can do. To better evaluate the understanding and reasoning ability of instruction-based image editing methods, we collect the Reason-Edit dataset, which contains a total of 219 image-text pairs. Note that there is no overlap between the Reason-Edit dataset and the small-amount high-quality synthesized training data pairs. Based on the Reason-Edit dataset, we evaluate existing instruction-based image editing methods comprehensively. Both the quantitative and qualitative results on the ReasonEdit dataset indicate that SmartEdit significantly outperforms previous instruction-based image editing methods.", + "bbox": [ + 503, + 593, + 888, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contributions are as follows:", + "bbox": [ + 522, + 805, + 818, + 819 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We analyze and focus on the performance of instruction-based image editing methods in more complex instructions. These complex scenarios have often been overlooked and less explored in past research.", + "2. We leverage MLLMs to better comprehend instructions." + ], + "bbox": [ + 503, + 825, + 888, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8363", + "bbox": [ + 483, + 946, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Figure 2. For more complex instructions or scenarios, InstructPix2Pix fails to follow the instructions.", + "bbox": [ + 184, + 180, + 781, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To further improve the performance, we propose a Bidirectional Interaction Module to facilitate the interaction of information between text and image features.", + "bbox": [ + 96, + 200, + 467, + 246 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "3. We propose a new dataset utilization strategy to enhance the performance of SmartEdit in complex scenarios. In addition to using conventional editing data, we introduce perception-related data to strengthen the perceptual ability of UNet in the diffusion process. Besides, we also add a small amount of synthetic editing data to further stimulate the model's reasoning ability.", + "4. An evaluation dataset, Reason-Edit, is specifically collected for evaluating the performance of instruction-based image editing tasks in complex scenarios. Both qualitative and quantitative results on Reason-Edit demonstrate the superiority of SmartEdit." + ], + "bbox": [ + 76, + 247, + 467, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 443, + 218, + 457 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Image Editing with Diffusion Models.", + "text_level": 1, + "bbox": [ + 76, + 468, + 400, + 483 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Pretrained text-to-image diffusion models [8, 13, 23, 26, 27, 29] can strongly assist image editing task. Instruction-based image editing task [1, 4, 11, 12, 16, 17, 32, 36, 38] requires users to provide an instruction, which converts the original image to a newly designed image that matches the given instruction. Some methods can achieve this by utilizing a tuning-free approach. For example, Prompt-to-Prompt [12] suggests modifying the cross-attention maps by comparing the original input caption with the revised caption. MasaCtrl [4] converts existing self-attention in diffusion models into mutual self-attention, which can help query correlated local contents and textures from source images for consistency. In addition, due to the scarcity of paired image-instruction editing datasets, the pioneering work InstructPix2Pix [1] introduces a large-scale vision-language image editing datasets created by fine-tuned GPT-3 [2] and Prompt-to-Prompt with stable diffusion, and further finetunes the UNet [28], which can edit images by providing a simple instruction. To enhance the editing effect of InstructPix2Pix on real images, MagicBrush [36] further provides a large-scale and manually annotated dataset for instruction-guided real image editing.", + "bbox": [ + 76, + 491, + 467, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The recent work, InstructDiffusion [11], also adopts the network design of InstructPix2Pix and focuses on unifying vision tasks in a joint training manner. By taking advantage of multiple different datasets, it can handle a variety of vision tasks, including understanding tasks (such as segmen", + "bbox": [ + 76, + 825, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "tation and keypoint detection) and generative tasks (such as editing and enhancement). Compared with InstructDiffusion, our primary focus is on the field of instruction-based image editing, especially for complex understanding and reasoning scenarios. In these scenarios, InstructDiffusion typically generates inferior results.", + "bbox": [ + 496, + 200, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. LLM with Diffusion Models", + "text_level": 1, + "bbox": [ + 500, + 304, + 751, + 319 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The exceptional open-sourced LLaMA [6, 31] significantly enhances the performance of vision tasks with the aid of Large Language Models (LLMs). Pioneering works such as LLaVA and MiniGPT-4 have improved image-text alignment through instruction-tuning. While numerous MLLM-based [7, 22, 24, 39] studies have demonstrated their robust capabilities across a variety of tasks, primarily those reliant on text generation (e.g., human-robot interaction, complex reasoning, science question answering, etc.), GILL [18] serves as a bridge between MLLMs and diffusion models. It learns to process images with LLMs and is capable of generating coherent images based on the input texts. SEED [9] presents an innovative image tokenizer to enable LLM to process and generate images and text concurrently. SEED-2 [10] further refines the tokenizer by aligning the generation embedding with the image embedding of unCLIP-SD, which allows for better preservation of rich visual semantics and reconstruction of more realistic images. Emu [30] can be characterized as a multimodal generalist, trained with the next-token-prediction objective. CM3Leon [35] proposes a multi-modal language model that is capable of executing text-to-image and image-to-text generation. It employs the CM3 multi-modal architecture that is fine-tuned on diverse instruction-style data, and utilizes a training method adapted from text-only language models.", + "bbox": [ + 496, + 329, + 890, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 722, + 624, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The goal of instruction-based image editing is to make specific modifications to an input image $x$ based on instructions $c_{T}$ , resulting in the target image $y$ . InstructPix2Pix, which is based on latent diffusion, is a seminal work in this field. For the target image $y$ and an encoder $\\mathcal{E}$ , the diffusion process introduces noise to the encoded latent $z = \\mathcal{E}(y)$ , resulting in a noisy latent $z_{t}$ , with the noise level increasing over timesteps $t \\in T$ . A UNet $\\epsilon_{\\delta}$ is then trained to predict the noise added to the noisy latent $z_{t}$ , given the image condition $c_{x}$ and text instruction condition $c_{T}$ , where $c_{x} = \\mathcal{E}(x)$ . The", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "\"Change the dog in mirror to a lion\"", + "bbox": [ + 192, + 90, + 325, + 99 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "\"Change the black raspberry to a tangerine\"", + "bbox": [ + 334, + 90, + 496, + 99 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "\"Please remove the tool that is used to cut cakes.\"", + "bbox": [ + 540, + 90, + 727, + 99 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "", + "bbox": [ + 192, + 102, + 326, + 175 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "中", + "bbox": [ + 331, + 104, + 501, + 172 + ], + "page_idx": 2 + }, + { + "type": "header", + "text": "", + "bbox": [ + 504, + 102, + 774, + 175 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8364", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "image condition is incorporated by directly concatenating $c_{x}$ and $z_{t}$ . The specific objective of latent diffusion is as follows:", + "bbox": [ + 76, + 90, + 468, + 133 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ], c _ {T}) \\| _ {2} ^ {2} \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 138, + 468, + 175 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon$ is the unscaled noise, $t$ is the sampling step, $z_{t}$ is latent noise at step $t$ , $\\mathcal{E}(x)$ is the image condition, and $c_{T}$ is the text instruction condition. The concat corresponds to the concatenation operation.", + "bbox": [ + 76, + 180, + 468, + 239 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although InstructPix2Pix has some effectiveness in instruction editing, its performance is limited when dealing with complex understanding and reasoning scenarios. To address this issue, we introduce a Multimodal Large Language Model (MLLM) into the network architecture and propose a Bidirectional Interaction Module (BIM) to implement bidirectional information interaction between the MLLM output and image information. In addition, we also explore the data utilization strategy and find that perception-related data and a small amount of complex editing data are crucial for enhancing model's performance. We provide detailed descriptions of these aspects in the next section.", + "bbox": [ + 75, + 239, + 468, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 434, + 168, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we introduce SmartEdit, specifically designed to handle complex instruction editing scenarios. In this section, we first provide a detailed overview of the framework of SmartEdit (Section 4.1). Then, we delve into the Bidirectional Interaction Module (Section 4.2). In Section 4.3, we discuss how to enhance the perception and understanding capabilities of UNet in the diffusion model and stimulate the ability of MLLMs to handle complex scenarios. Finally, We introduce Reason-Edit, which is primarily used to evaluate the ability of instruction-based image editing methods toward complex scenarios. (Section 4.4).", + "bbox": [ + 75, + 460, + 468, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. The Framework of SmartEdit", + "text_level": 1, + "bbox": [ + 76, + 635, + 344, + 648 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given an image $x$ and instruction $c$ , which is tokenized as $(s_1, \\dots, s_T)$ , our goal is to obtain the target image $y$ based on $c$ . As shown in Fig 3, the image $x$ is first processed by the image encoder and FC layer, resulting in $v_{\\mu}(x)$ . Then $v_{\\mu}(x)$ is sent into the LLM along with the token embedding $(s_1, \\dots, s_T)$ . The output of the LLM is discrete tokens, which cannot be used as the input for subsequent modules. Therefore, we take the hidden states corresponding to these discrete tokens as the input for the following modules. To jointly optimize LLaVA and the diffusion model, following GILL [18], we expand the original LLM vocabulary with $r$ new tokens $[\\mathrm{IMG}_1], \\dots, [\\mathrm{IMG}_r]$ and append the $r$ [IMG] tokens to the end of instruction $c$ . To be specific, we incorporate a trainable matrix $\\mathbf{E}$ into the embedding matrix of the LLM, which represents the $r$ [IMG] token embeddings. Subsequently, we minimize the negative log-likelihood of", + "bbox": [ + 75, + 659, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "generated $r$ [IMG] tokens, conditioned on tokens that have been generated previously:", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\mathrm {L L M}} (c) = - \\sum_ {i = 1} ^ {r} \\log p _ {\\{\\theta \\cup \\mathbf {E} \\}} ([ \\operatorname {I M G} _ {i} ] \\mid v _ {\\mu} (x), \\\\ \\left. s _ {1}, \\dots , s _ {T}, \\left[ \\mathrm {I M G} _ {1} \\right], \\dots , \\left[ \\mathrm {I M G} _ {i - 1} \\right]\\right) \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 125, + 890, + 179 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The majority of parameters $\\theta$ in the LLM are kept frozen and we utilize LoRA [15] to carry out efficient fine-tuning. We take the hidden states $h$ corresponding to the $r$ [IMG] tokens as the input for the next module.", + "bbox": [ + 498, + 190, + 890, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Considering the discrepancy between the feature spaces of the hidden states in the LLM and the clip text encoder, we need to align the hidden states $h$ to the clip text encoder space. Inspired by BLIP2 [20] and DETR [5], we adopt the QFormer $Q_{\\beta}$ with 6-layer transformer [33] and $n$ learnable queries, obtaining feature $f$ . Subsequently, the image feature $v$ output by the image encoder $E_{\\phi}$ interacts with $f$ through a bidirectional interaction module (BIM), resulting in $f'$ and $v'$ . The mentioned process is represented as:", + "bbox": [ + 496, + 251, + 890, + 387 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} h = \\operatorname {L L a V A} (x, c), \\\\ \\begin{array}{l} f = Q _ {\\beta} (h), \\\\ F _ {n} (h) \\end{array} \\tag {3} \\\\ v = E _ {\\phi} (x), \\\\ f ^ {\\prime}, v ^ {\\prime} = \\operatorname {B I M} (f, v) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 393, + 890, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the diffusion model, following the design of Instructpix2pix, we concat the encoded image latent $\\mathcal{E}(x)$ and noisy latent $z_{t}$ . Unlike Instructpix2pix, we use $f'$ as the key and value in UNet, and combine $v'$ into the features before entering UNet in a residual manner. The specific process can be formulated as:", + "bbox": [ + 496, + 474, + 890, + 564 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ] + v ^ {\\prime}, f ^ {\\prime}) \\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 574, + 890, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To keep consistency with equation 1, we omit the Conv operation here.", + "bbox": [ + 498, + 625, + 890, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Bidirectional Interaction Module", + "text_level": 1, + "bbox": [ + 500, + 665, + 790, + 680 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The design of BIM is depicted in Fig 4. It includes a self-attention block, two cross-attention blocks, and an MLP layer. The two inputs of BIM are the output $f$ from QFormer and the output $v$ from the image encoder. After bidirectional information interaction between $f$ and $v$ , BIM will eventually output $f'$ and $v'$ . In BIM, the process begins with $f$ undergoing a self-attention mechanism. After this, $f$ serves as a query to interact with the input $v$ , which acts as both key and value, through a cross-attention block. This interaction results in the generation of $f'$ via a pointwise MLP. Following the creation of $f'$ , it then serves as both key and value to interact with $v$ , which now acts as a query. This second cross-attention interaction leads to the production of $v'$ .", + "bbox": [ + 496, + 688, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8365", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f5c1c8473fe030a1883927546fec6f73a704f268f685ddf872dc104c62e009db.jpg", + "image_caption": [ + "Figure 3. The overall framework of SmartEdit. For the instruction, we first append the $r$ [IMG] tokens to the end of instruction $c$ . Together with image $x$ , they will be sent into LLaVA, which can then obtain the hidden states corresponding to these $r$ [IMG] tokens. Then the hidden state is sent into the QFormer and gets feature $f$ . Subsequently, the image feature $v$ output by the image encoder $E_{\\phi}$ interacts with $f$ through a bidirectional interaction module (BIM), resulting in $f'$ and $v'$ . The $f'$ and $v'$ are input into the diffusion models to achieve the instruction-based image editing task." + ], + "image_footnote": [], + "bbox": [ + 186, + 88, + 785, + 266 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/ea735c5f999e0935c5452baed4b6ecaf115dbec6013268642a1af6d0f22583d5.jpg", + "image_caption": [ + "Figure 4. The network design of the BIM Module. In this module, the input information $f$ and $v$ will undergo bidirectional information interaction through different cross-attention." + ], + "image_footnote": [], + "bbox": [ + 148, + 356, + 400, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As discussed in the introduction, the proposed BIM module reuses the image feature and inputs it as supplementary information into UNet. The implementation of two cross-attention blocks in this module facilitates a robust bidirectional information interaction between the image feature and the text feature. Compared to not adopting the BIM module or only fusing the image feature and text feature in one direction, SmartEdit which is equipped with the BIM module yields better results. The experimental comparison of different designs is shown in Section 5.3.", + "bbox": [ + 75, + 512, + 468, + 662 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Dataset Utilization Strategy", + "text_level": 1, + "bbox": [ + 76, + 678, + 326, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the training process of SmartEdit, two primary challenges emerge when solely utilizing datasets gathered from InstructPix2Pix and MagicBrush as the training set. The first challenge is that SmartEdit has a poor perception of position and concept. The second challenge is that, despite being equipped with MLLM, SmartEdit still has limited capability in scenarios that require reasoning. In summary, the effectiveness of SmartEdit in handling complex scenarios is limited if it is only trained on conventional editing datasets. After analysis, we have identified the causes of these issues. The first issue stems from the UNet in the diffusion model which lacks an understanding of perception and concepts, leading to SmartEdit's poor perception of position and con-", + "bbox": [ + 75, + 703, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "cept. The second issue is that SmartEdit has limited exposure to editing data that requires reasoning abilities, which in turn limits its reasoning capabilities.", + "bbox": [ + 496, + 359, + 890, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To tackle the first issue, we incorporate the segmentation data into the training set. Such modifications significantly enhanced the perception capabilities of the SmartEdit model. Regarding the second issue, we take inspiration from LISA [19] that a minimal amount of reasoning segmentation data can efficiently activate MLLM's reasoning capacity. Guided by this insight, we establish a data production pipeline and synthesize 476 paired data (each sample contains original image, instruction, and synthetic target image) as a supplement to the training data. This synthetic editing dataset includes two major types of scenarios: complex understanding and reasoning scenarios. For complex understanding scenarios, the original image contains multiple objects and the corresponding instruction modifies the specific object based on various attributes (i.e., location, color, relative size, and in or outside the mirror). We specifically consider the mirror attribute because it is a typical example that requires a strong understanding of the scene (both inside and outside the mirror) to perform well. For reasoning scenarios, we involve complex reasoning cases that need world knowledge to identify the specific object. The effectiveness of this synthetic editing dataset and the impact of different datasets on the model's performance are detailed in Section 5.4. The details of the data production pipeline and some visual examples are described in the supplementary material.", + "bbox": [ + 496, + 407, + 892, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Reason-Edit for Better Evaluation", + "text_level": 1, + "bbox": [ + 498, + 814, + 799, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To better evaluate existing instruction editing methods and SmartEdit's capabilities in complex understanding and reasoning scenarios, we collect an evaluation dataset, ReasonEdit. Reason-Edit consists of 219 image-text pairs. Con", + "bbox": [ + 496, + 839, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8366", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "sistent with the synthetic training data pairs, Reason-Edit is also categorized in the same manner. Note that there is no overlap between the data in Reason-Edit and the synthetic training set. With Reason-Edit, we can thoroughly test the performance of instruction-based image editing models in terms of understanding and reasoning scenarios. We hope more researchers will pay attention to the capabilities of instruction-based image editing models from these perspectives, thereby fostering the practical application of instruction-based image editing methods.", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 260, + 209, + 277 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setting", + "text_level": 1, + "bbox": [ + 76, + 286, + 277, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Process and Implementation Details. The training process and implementation details of SmartEdit can be found in the supplementary material.", + "bbox": [ + 76, + 306, + 468, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Network Architecture. For the Large Language Model with visual input (e.g., LLaVA), we choose LLaVA-1.1-7b and LLaVA-1.1-13b as the base model. During training, the weights of LLaVA are frozen and we add LoRA for efficient fine-tuning. In LoRA, the values of the two parameters, dim and alpha, are 16 and 27, respectively. We expand the original LLM vocabulary with 32 new tokens. The QFormer is composed of 6-layer transformer [33] and 77 learnable query tokens. In the BIM module, there is a self-attention block, two cross-attention blocks, and an MLP layer.", + "bbox": [ + 75, + 354, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Datasets. For the training process of SmartEdit, the training data can be divided into 4 categories: (1) segmentation datasets, which include COCOStuff [3], RefCOCO [34], GRefCOCO [21], and the reasoning segmentation dataset from LISA [19]; (2) editing datasets, which involve InstructPix2Pix and MagicBrush; (3) visual question answering (VQA) dataset, which is the LLaVA-Instruct-150k dataset [22]; (4) synthetic editing dataset, where we collect a total of 476 paired data for complex understanding and reasoning scenarios.", + "bbox": [ + 75, + 506, + 468, + 656 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. As we hope to only change the foreground of the image while keeping the background unchanged for editing, we adopt three metrics for the background area: PSNR, SSIM, and LPIPS [14, 37]. For the foreground area, we calculate CLIP Score [25] between the foreground area of the edited image and the GT label. The GT label is annotated manually. Among these four metrics, except for LPIPS where lower is better, the other three metrics are higher the better. While these metrics can reflect the performance to a certain extent, they are not entirely accurate. To provide a more accurate evaluation of the effects of edited images, we propose a metric for assessing editing accuracy. Specifically, we hire four workers to manually evaluate the results of these different methods on Reason-Edit. The evaluation criterion is whether the edited image aligns with the instruction. After obtaining the evaluation results", + "bbox": [ + 75, + 659, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "from each worker, we average all the results to get the final metric result, which is Instruction-Alignment (Ins-align).", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Comparison with State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 498, + 126, + 867, + 141 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare SmartEdit with existing SOTA instruction-based image editing methods, namely InstructPix2Pix, MagicBrush, and InstructDiffusion. Considering that these released models are trained on specific datasets, they would inevitably perform poorly if directly evaluated on ReasonEdit. To ensure a fair comparison, we fine-tune these methods on the same training set used by SmartEdit, and evaluate the fine-tuned models on Reason-Edit. The experimental results are shown in Tab. 1. From the quantitative results of the reasoning scenarios in the table, it can be observed that when we replace the clip text encoder in the diffusion model with LLaVA and adopt the proposed BIM module, both SmartEdit-7B and SmartEdit-13B achieve better results on these five metrics. This suggests that in scenarios requiring reasoning from instructions, a simple clip text encoder may struggle to understand the meaning of the instructions. However, the MLLM can fully utilize its powerful reasoning ability and world knowledge to correctly identify the corresponding objects and perform edits.", + "bbox": [ + 496, + 145, + 890, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The qualitative results further illustrate this point. As shown in Fig. 5, the first three examples are reasoning scenarios. In the first example, both SmartEdit-7B and SmartEdit-13B successfully identify the tool used for cutting fruit (knife) and remove it, while keeping the rest of the background unchanged. The second example can also be handled well by both of them. However, in the third example, we observe a difference in performance. Only SmartEdit-13B can accurately locate the object and perform the corresponding edits without altering other background areas. This suggests that in instruction-based image editing tasks that require reasoning, a more powerful MLLM model can effectively generalize its reasoning ability to this task. This observation aligns with the findings from LISA.", + "bbox": [ + 496, + 433, + 890, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "However, for understanding scenarios, we observe a difference in performance between SmartEdit-7B and SmartEdit-13B when compared to InstructDiffusion on PSNR/SSIM/LPIPS. Specifically, SmartEdit-7B performs worse than InstructDiffusion, while SmartEdit-13B outperforms InstructDiffusion on these metrics. Upon further analysis of the qualitative results, as shown in the $4_{th}$ and $5_{th}$ rows of Fig. 5, we find that from a visual perspective, both SmartEdit-7B and SmartEdit-13B appear superior to InstructDiffusion. This suggests that the three metrics do not always align with human visual perception. We confirm this phenomenon in the supplementary material. From the result of the Ins-align metric, it can be observed that SmartEdit shows a significant improvement compared to previous instruction-based image editing methods. Also, when adopting a more powerful MLLM model, SmartEdit-13B performs better than SmartEdit-7B on Ins-align.", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8367", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"What is the tool that is used to cut fruits. Remove this tool.\"", + "bbox": [ + 318, + 90, + 643, + 102 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6bc85be1f86c219aba6e3151188cda4a67ea4be65a7debd04e9f34ab0188cda4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 104, + 281, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6e3589d589ebb96025d134f94b508cb62cf34b72e4da5bcc44bf2f6922e02286.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 104, + 388, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e7d960d7226904cfbbaaf543777d81e3b6077efc3c0b044645854aa10a2cb8f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 104, + 488, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a50b8238129b0a03ceab42d0e57ca8fb04caa4e2f9d251f3af614c81584c94d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 104, + 586, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/19d204169620e369a8e8718e561eee41c5be01cdfaf0d896acd98329528b8c81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 589, + 104, + 684, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ff9e27bfcda6d1a644cd1d02cf9db3249b5e4e9b201b509ebd6304f7738c136.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 104, + 784, + 162 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Please replace food contains most vitamin with an orange.\"", + "bbox": [ + 326, + 162, + 635, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f774d92aaa7abdff996f16194a2362b9f51a6a2d3cbb5d919997507fd845591.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 174, + 279, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0d3c838fcf97c70e6113ecbad7cb13776d10669f95acbf5b9853c7c5684382c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 174, + 388, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f4578766e3262c5022e76eadbcac7ce8494874e8df2aebc2e4cb82d63b4ff8c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 174, + 486, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d689782519dfd8bcbf9cb55c7207a38c30a65ed3c93b0040db07a4395793a18d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 174, + 586, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0f71668069997a6876f717e88f133d1a0acfd20213f4ced493612ba6c97380cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 174, + 684, + 231 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/21ec1fa6696e197e1416d4810ebd7d29c7259855ef97dff24c7496e9676aa820.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 174, + 784, + 231 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Please remove the object that can be used to have meals.\"", + "bbox": [ + 328, + 231, + 635, + 242 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4c41a1b423755ec3450c5e042fcd3960f50f6c1dcd0e90c0f0a4a2e906ea1bcf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 244, + 279, + 306 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/992e0ba2a22f7f64cf611f72b1146b869ce28e0d48217b1f7d82f4168bcc9d30.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 244, + 388, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b3b2591e17801606f3a4b142808b6b3ec5aeef8511a7193830f5f8df912a2cac.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 244, + 486, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8978e8bb43ef97b1a3a6ad9a2df334d2b5fa3085ed0ed1a34e00191e5ed57a5b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 244, + 586, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b5b9030de85756f023f6991f4e7c93ff20d28b666b731d4297e77e8c0bfe9742.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 244, + 684, + 305 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/833e91e275be906d8270c274d17a70cb75118ccf78eb2ac42bdfa233625f2d30.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 244, + 784, + 305 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Change the middle panda to a cat\"", + "bbox": [ + 390, + 306, + 571, + 316 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c0a8d312101054ec2bd2bb8ae127c31450dda66fa6a95eefe28eb2c46f12957c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 181, + 316, + 279, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/711110d5cedae2dfd6e212d647012dbd105bd404131ec578f02f5f2f83128fec.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 316, + 388, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b4fb6b739a245ba0484ce270e6bf186e768d48d8ef8244388d64fe31ae108ae8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 318, + 486, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5530be603f1f4cd859944bb9a584d8f997e9907f7daf5fe0741434ddbb7a5030.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 318, + 586, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/36b37f9a4c1d8bacc82c1f2eff34b4ef8d97a97bea0a2c9fe620a2a57fa58c1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 318, + 684, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba332000f27e717434765d9db7ce7b88ecf6ca9bee74447f0cd0452ea7530477.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 318, + 784, + 377 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Change the cat in mirror to a tiger.\"", + "bbox": [ + 385, + 378, + 576, + 388 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/aa8cbbf55762203fed39f44b51cb67c5900f6048c6fdf32f378421ffaefdd07e.jpg", + "image_caption": [ + "Input Image", + "Figure 5. Qualitative comparison on Reason-Edit. When compared to several existing instruction editing methods that have undergone further fine-tuning on our synthetic editing dataset, our approach demonstrates superior editing capabilities in complex scenarios." + ], + "image_footnote": [], + "bbox": [ + 181, + 388, + 279, + 474 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/72afc780cb6a3e2710d85b807a95c02ae4ce83078e74e0c2cf5144d429118978.jpg", + "image_caption": [ + "InstructPix2Pix" + ], + "image_footnote": [], + "bbox": [ + 290, + 388, + 388, + 474 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/23bb399c88f20697a58cdc051f4c8aab6dd36a9a3a67bfef0562852dc5041db7.jpg", + "image_caption": [ + "MagicBrush" + ], + "image_footnote": [], + "bbox": [ + 390, + 388, + 486, + 474 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6a359ceb371dec36c97b12252d1148d654c1d22d6133f5c6814fcc79f6ff03b.jpg", + "image_caption": [ + "InstructDiffusion" + ], + "image_footnote": [], + "bbox": [ + 488, + 388, + 586, + 474 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3f03be9e68a14c376f13b0064166210d11bc219cbc794a0a4ed2fe68545383ed.jpg", + "image_caption": [ + "SmartEdit-7B" + ], + "image_footnote": [], + "bbox": [ + 588, + 388, + 684, + 474 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/10505587151f1a37c2aa3705e9aca3f53a3069481b7e95990dd632b46fcf13ba.jpg", + "image_caption": [ + "SmartEdit-13B" + ], + "image_footnote": [], + "bbox": [ + 686, + 388, + 784, + 474 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c707fd32c2bcd98e99975276a98b0594938ca1cd9da486ec7e0bc4cd898dd246.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
InstructPix2Pix21.5760.7210.08922.7620.53724.2340.7070.08319.4130.344
MagicBrush18.1200.680.14322.6200.29022.1010.6940.11319.7550.283
InstructDiffusion23.2580.7430.06723.0800.69721.4530.6660.11719.5230.483
SmartEdit-7B22.0490.7310.08723.6110.71225.2580.7420.05520.9500.789
SmartEdit-13B23.5960.7510.06823.5360.77125.7570.7470.05120.7770.817
", + "bbox": [ + 101, + 530, + 870, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. All the methods we compared have been fine-tuned using the same training data as that used by SmartEdit.", + "bbox": [ + 75, + 621, + 888, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"What is the object that the dog's food should be put into? Remove this object.\"", + "bbox": [ + 125, + 662, + 421, + 672 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b822ded3281a0d80947b525ea25d15bff37f7667c456219b6c2b0d94601e97bb.jpg", + "image_caption": [ + "Figure 6. Demonstration of the effectiveness of the BIM Module." + ], + "image_footnote": [], + "bbox": [ + 112, + 672, + 434, + 820 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Ablation Study on BIM", + "text_level": 1, + "bbox": [ + 76, + 847, + 292, + 863 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To validate the effectiveness of the bidirectional information interaction in our proposed BIM module, we conduct", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Please replace the animal that is lying on the grass with a fox\"", + "bbox": [ + 560, + 661, + 830, + 671 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8ec6bcbaa0d407c835ef1d35c20cd715362fe7b3e50030d2b27cfcaeb5e99c32.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 514, + 671, + 586, + 728 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2be4fdc566c0dcaf3d15f1fa675917f6949e1db66b28fcc18b85a0288bd70783.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 672, + 658, + 728 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f12255bdd968ef068497398649c39e040706aa377cf9603ddb9e7d83282dcb57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 660, + 672, + 730, + 727 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7f4d9f98dfe1bd8db79287c372f9acaddf14196de5e933be7d5536a230c0f4dd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 732, + 672, + 803, + 727 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/08794862aa30241b1998a302b1ebffa25d9475e8ef07138bd812124e064bf0a7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 805, + 672, + 877, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "\"Change the red strawberry to a white pumpkin\"", + "bbox": [ + 593, + 732, + 799, + 742 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5cdc4a37c81cf54440b9de80886ba5f1d95246442498591d68cfdb8abdcad7cc.jpg", + "image_caption": [ + "Input Image", + "Figure 7. Demonstration of the significance of joint training with multiple datasets." + ], + "image_footnote": [], + "bbox": [ + 514, + 742, + 586, + 799 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/576c36cdfa99cbc7c29ae4a4740e4d733a565cfff3c4a76ff748c3fa301beaa4.jpg", + "image_caption": [ + "Edit" + ], + "image_footnote": [], + "bbox": [ + 588, + 742, + 658, + 799 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dfb36085eba9a4b01687154d71952a07eebdb5985d8efe147afce5863f10708d.jpg", + "image_caption": [ + "Edit+Seg" + ], + "image_footnote": [], + "bbox": [ + 660, + 742, + 730, + 799 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fd7eddfa0d375c4c4659189f784d04640aa2afd84e6863fa3dc149d7b5e47bea.jpg", + "image_caption": [ + "Edit+Reason-Edit" + ], + "image_footnote": [], + "bbox": [ + 732, + 742, + 803, + 799 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/937a9798d99aa9d4fe48b25bb9ba17a3ef4926b3d20301e5a3326e1449f1ca41.jpg", + "image_caption": [ + "Total" + ], + "image_footnote": [], + "bbox": [ + 805, + 742, + 879, + 799 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "comparative experiments on the SmartEdit-7B model. The details are presented in Tab. 2. The first experiment, denoted as Exp 1, aims to verify the necessity of the information in", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8368", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/43ff37a01b8ec83eea3fa3bac6bab82f091d17d2602eb660b2e2cc1df53d2e63.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Exp IDPlainSimpleCABIMUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓20.9750.7130.10823.360.69523.8480.7250.07420.330.694
2✓19.5570.6920.12623.660.69223.5080.7160.08120.170.722
3✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
", + "bbox": [ + 81, + 88, + 890, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c113f2fc2ffa062fa9588efcad3f1da18db80bf666a6cbfe2a15495f056ed371.jpg", + "table_caption": [ + "Table 2. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B." + ], + "table_footnote": [], + "table_body": "
Exp IDEditSegmentationSynthetic editing datasetUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓17.5680.6640.17122.790.20122.4000.7060.10219.220.233
2✓✓18.9600.6900.14322.830.36121.7740.6930.11619.820.311
3✓✓19.5620.7020.11122.320.44023.5950.7150.07920.430.567
4✓✓✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
", + "bbox": [ + 81, + 186, + 890, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B.", + "bbox": [ + 76, + 252, + 892, + 280 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "teraction proposed in the BIM module. In this experiment, we remove the BIM module from the SmartEdit-7B model and directly apply the text feature output from QFormer to the diffusion model. The second experiment, denoted as Exp 2, aims to verify the necessity of the bidirectional information interaction proposed in the BIM module. Specifically, all blocks are discarded except for the cross-attention block on the image feature branch. Therefore, the information from the text feature of QFormer is unidirectionally applied to the image feature. These two experiments are designed to test the impact of removing or altering the BIM module on the performance of SmartEdit-7B in complex understanding and reasoning scenarios. As shown in Tab. 2, if the BIM module is removed, there is a significant decline in all metrics for both understanding and reasoning scenarios. When the BIM module is replaced with the SimpleCA module, we observe a noticeable decline in all metrics, except for the clip score in understanding scenarios. Further comparison of the qualitative results in Fig. 6 confirms that the introduction of the BIM indeed enhances SmartEdit's instruction editing performance. To be specific, when we do not use the BIM module (i.e., plain), the dog bowl (first row) turns into other objects (marked with a red circle), and the fork (second row) does not change at all. After using SimpleCA, it can be found that the dog bowl and fork have been partially removed. When SmartEdit is equipped with BIM, the dog bowl and fork can be well removed.", + "bbox": [ + 75, + 290, + 472, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablation Study on Dataset Usage", + "text_level": 1, + "bbox": [ + 76, + 713, + 366, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Section 4.3, we explore an efficient strategy for data utilization, aiming to enhance SmartEdit's capabilities in handling complex understanding and reasoning scenarios. During the training process of SmartEdit, we employ the common editing dataset, segmentation dataset, and the synthetic editing dataset. To validate the significance of these different data types in boosting SmartEdit's performance, we conduct a series of ablation studies, as detailed in Tab. 3. These experiments are based on the SmartEdit-7B model. In Exp 1, we train the model using only the editing data. In Exp 2, we incorporate segmentation data into the training", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "process, building upon Exp 1. In Exp 3, we further add the synthetic editing data to the basis established in Exp 1. The quantitative results of these experiments reveal that segmentation data and synthetic editing data play complementary roles in enhancing the model's performance. This is further corroborated by the visual comparison in Fig. 7. For reasoning scenarios, when adopting only the editing dataset or combining the editing dataset and the segmentation dataset, the performance of SmartEdit is inferior. When the synthetic editing data is incorporated into the editing dataset, SmartEdit can accurately locate the specific objects. However, the output of SmartEdit is also mediocre (the generated fox has obvious artifacts, and two pumpkins are generated). When all these datasets are combined as the training set, the results generated by SmartEdit have a further significant improvement in visual effects.", + "bbox": [ + 496, + 290, + 893, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 544, + 619, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, this paper presents SmartEdit, a novel approach to instruction-based image editing that enhances understanding and reasoning capabilities by incorporating the LLMs with visual inputs. By introducing the Bidirectional Interaction Module (BIM), we have overcome challenges associated with the direct integration of LLMs and diffusion models in complex reasoning scenarios. Our data utilization strategy, which incorporates perception data and complex instruction editing data, effectively enhances SmartEdit's capabilities in handling complex understanding and reasoning scenarios. Evaluation on our newly constructed dataset, Reason-Edit, shows that SmartEdit outperforms previous methods, marking a significant step towards practical applications of complex instruction-based image editing.", + "bbox": [ + 496, + 564, + 893, + 776 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement. The work is partially supported by the Young Scientists Fund of the National Natural Science Foundation of China under grant No. 62106154, the Natural Science Foundation of Guangdong Province, China (General Program) under grant No.2022A1515011524, Shenzhen Science and Technology Program JCYJ20220818103001002 and JCYJ20220818103006012, and the Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong (Shenzhen).", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8369", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tim Brooks, Aleksander Holynski, and Alexei A Efros. Instructpix2pix: Learning to follow image editing instructions. 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Minigpt-4: Enhancing vision-language" + ], + "bbox": [ + 78, + 90, + 468, + 901 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 2, 3", + "bbox": [ + 532, + 92, + 890, + 119 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8371", + "bbox": [ + 482, + 945, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_model.json b/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a3c5a7b189bc0fd33750f13f12fd5444c1ad0c14 --- /dev/null +++ b/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_model.json @@ -0,0 +1,2420 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.158, + 0.131, + 0.817, + 0.177 + ], + "angle": 0, + "content": "SmartEdit: Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models" + }, + { + "type": "text", + "bbox": [ + 0.094, + 0.209, + 0.89, + 0.298 + ], + "angle": 0, + "content": "Yuzhou Huang\\(^{1,2^{*\\#}}\\) Liangbin Xie\\(^{2,3,5^{*\\#}}\\) Xintao Wang\\(^{2,4\\dagger}\\) Ziyang Yuan\\(^{2,7^{\\#}}\\) Xiaodong Cun\\(^{4}\\) Yixiao Ge\\(^{2,4}\\) Jiantao Zhou\\(^{3}\\) Chao Dong\\(^{5,6}\\) Rui Huang\\(^{1}\\) Ruimao Zhang\\(^{1\\dagger}\\) Ying Shan\\(^{2,4}\\) \n\\(^{1}\\)The Chinese University of Hong Kong, Shenzhen (CUHK-SZ) \\(^{2}\\)ARC Lab, Tencent PCG \\(^{3}\\)University of Macau \\(^{4}\\)Tencent AI Lab Shenzhen Institute of Advanced Technology \\(^{6}\\)Shanghai Artificial Intelligence Laboratory \\(^{7}\\)Tsinghua University https://github.com/TencentARC/SmartEdit" + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.315, + 0.861, + 0.606 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.61, + 0.895, + 0.668 + ], + "angle": 0, + "content": "Figure 1. We propose SmartEdit, an instruction-based image editing model that leverages Multimodal Large Language Models (MLLMs) to enhance the understanding and reasoning capabilities of instruction-based editing methods. With the specialized design, our SmartEdit is capable of handling complex understanding (the instructions that contain various object attributes like location, relative size, color, and in or outside the mirror) and reasoning scenarios." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.682, + 0.314, + 0.698 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.711, + 0.472, + 0.864 + ], + "angle": 0, + "content": "Current instruction-based image editing methods, such as InstructPix2Pix, often fail to produce satisfactory results in complex scenarios due to their dependence on the simple CLIP text encoder in diffusion models. To rectify this, this paper introduces SmartEdit, a novel approach of instruction-based image editing that leverages Multimodal Large Language Models (MLLMs) to enhance its understanding and reasoning capabilities. However, direct integration of these elements still faces challenges in situations requiring complex reasoning. To mitigate this, we" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.683, + 0.895, + 0.896 + ], + "angle": 0, + "content": "propose a Bidirectional Interaction Module (BIM) that enables comprehensive bidirectional information interactions between the input image and the MLLM output. During training, we initially incorporate perception data to boost the perception and understanding capabilities of diffusion models. Subsequently, we demonstrate that a small amount of complex instruction editing data can effectively stimulate SmartEdit's editing capabilities for more complex instructions. We further construct a new evaluation dataset, Reason-Edit, specifically tailored for complex instruction-based image editing. Both quantitative and qualitative results on this evaluation dataset indicate that our SmartEdit surpasses previous methods, paving the way for the practical application of complex instruction-based image editing." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "* Equal contribution † Corresponding author # Interns in ARC Lab, Tencent PCG" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8362" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.081, + 0.091, + 0.208, + 0.105 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.116, + 0.468, + 0.281 + ], + "angle": 0, + "content": "Text-to-image synthesis [8, 13, 23, 26, 27, 29] has experienced significant advancements in recent years, thanks to the development of diffusion models. These methods have enabled the generation of images that are not only consistent with natural language descriptions, but also align with human perception and preferences, marking a substantial leap forward in the field. Instruction-based image editing methods [1, 36], represented by InstructPix2Pix, leverage pre-trained text-to-image diffusion models as priors. This allows users to conveniently and effortlessly modify images through natural language instructions for ordinary users." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.282, + 0.468, + 0.582 + ], + "angle": 0, + "content": "While existing instruction-based image editing methods can handle simple instructions effectively, they often fall short when dealing with complex scenarios, which require the model to have a more powerful understanding and reasoning capabilities. As depicted in Fig. 1, there are two common types of complex scenarios. The first is when the original image contains multiple objects, and the instruction modifies only one of these objects through certain attributes (such as location, relative size, color, in or outside the mirror). The other is when world knowledge is needed to identify the object to be edited (such as the object that can tell the time). We define these two types as complex understanding scenarios and complex reasoning scenarios, respectively. Handling these two scenarios is crucial for practical instruction editing, but existing instruction-based image editing methods probably fail in these scenarios (as shown in Fig. 2). In this paper, we attempt to identify the reasons why existing instruction-based image editing methods fail in these scenarios, and try to tackle the challenge in these scenarios." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.585, + 0.468, + 0.78 + ], + "angle": 0, + "content": "The first reason why existing instruction-based image editing methods fail in these scenarios is that they typically rely on a simple CLIP text encoder [25] in diffusion models (e.g., Stable Diffusion) to process the instructions. Under this circumstance, these models struggle to 1) understand and reason through the instructions, and 2) integrate the image to comprehend the instructions. To address these limitations, we introduce the Multimodal Large Language Models (MLLMs) (e.g., LLaVA) [22, 39] into instruction-based editing models. Our method, SmartEdit, jointly optimizes MLLMs and diffusion models, leveraging the powerful reasoning capabilities of MLLMs to facilitate instruction-based image editing task." + }, + { + "type": "text", + "bbox": [ + 0.081, + 0.781, + 0.468, + 0.9 + ], + "angle": 0, + "content": "While substituting the CLIP encoder in the diffusion model with MLLMs can alleviate some problems, this approach still falls short when it comes to examples that necessitate complex understanding and reasoning. This is because the input image to edit (original image) is integrated into the UNet of the Stable Diffusion model through a straightforward concatenation, which is further interacted with MLLM outputs through a cross-attention operation. In" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.092, + 0.89, + 0.242 + ], + "angle": 0, + "content": "this setup, the image features serve as the query, and MLLM outputs act as the key and value. This means that the MLLM outputs unilaterally modulate and interact with the image feature, which affects the results. To alleviate this issue, we further propose a Bidirectional Interaction Module (BIM). This module reuses the image information extracted by the LLaVA's visual encoder from the input image. It also facilitates a comprehensive bidirectional information interaction between this image and the MLLM output, enabling the model to perform better in complex scenarios." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.244, + 0.89, + 0.409 + ], + "angle": 0, + "content": "The second reason contributing to the failure of existing instruction-based editing methods is the absence of specific data. When solely training on editing datasets, such as the datasets used in Instructpix2pix [1] and MagicBrush [36], SmartEdit also struggles to handle scenarios requiring complex reasoning and understanding. This is because SmartEdit has not been exposed to data from these scenarios. One straightforward approach is to generate a substantial amount of paired data similar to those scenarios. However, this method is excessively expensive because the cost of generating data for these scenarios is high." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.411, + 0.89, + 0.59 + ], + "angle": 0, + "content": "In this paper, we find that there are two keys to compensate the insufficiency of specific editing data. The first is to enhance the perception capabilities of UNet [28], and the second is to stimulate the model capacity in those scenarios with a few high-quality examples. Correspondingly, we 1) incorporate the perception-related data (e.g., segmentation) into the model's training. 2) synthesize a few high-quality paired data with complex instructions to fine-tune our SmartEdit (similar to LISA [19]). In this way, SmartEdit not only reduces the reliance on paired data under complex scenarios but also effectively stimulates its ability to handle these scenarios." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.594, + 0.89, + 0.803 + ], + "angle": 0, + "content": "Equipped with both the model designs and the data utilization strategy, SmartEdit can understand complex instructions, surpassing the scope that previous instruction editing methods can do. To better evaluate the understanding and reasoning ability of instruction-based image editing methods, we collect the Reason-Edit dataset, which contains a total of 219 image-text pairs. Note that there is no overlap between the Reason-Edit dataset and the small-amount high-quality synthesized training data pairs. Based on the Reason-Edit dataset, we evaluate existing instruction-based image editing methods comprehensively. Both the quantitative and qualitative results on the ReasonEdit dataset indicate that SmartEdit significantly outperforms previous instruction-based image editing methods." + }, + { + "type": "text", + "bbox": [ + 0.523, + 0.806, + 0.819, + 0.82 + ], + "angle": 0, + "content": "In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.826, + 0.89, + 0.884 + ], + "angle": 0, + "content": "1. We analyze and focus on the performance of instruction-based image editing methods in more complex instructions. These complex scenarios have often been overlooked and less explored in past research." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.887, + 0.889, + 0.9 + ], + "angle": 0, + "content": "2. We leverage MLLMs to better comprehend instructions." + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.826, + 0.89, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.485, + 0.947, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8363" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.194, + 0.091, + 0.326, + 0.1 + ], + "angle": 0, + "content": "\"Change the dog in mirror to a lion\"" + }, + { + "type": "header", + "bbox": [ + 0.336, + 0.092, + 0.498, + 0.101 + ], + "angle": 0, + "content": "\"Change the black raspberry to a tangerine\"" + }, + { + "type": "header", + "bbox": [ + 0.542, + 0.092, + 0.728, + 0.1 + ], + "angle": 0, + "content": "\"Please remove the tool that is used to cut cakes.\"" + }, + { + "type": "header", + "bbox": [ + 0.194, + 0.103, + 0.328, + 0.176 + ], + "angle": 0, + "content": "" + }, + { + "type": "header", + "bbox": [ + 0.332, + 0.105, + 0.503, + 0.174 + ], + "angle": 0, + "content": "中" + }, + { + "type": "header", + "bbox": [ + 0.506, + 0.103, + 0.775, + 0.176 + ], + "angle": 0, + "content": "" + }, + { + "type": "image_caption", + "bbox": [ + 0.185, + 0.181, + 0.782, + 0.194 + ], + "angle": 0, + "content": "Figure 2. For more complex instructions or scenarios, InstructPix2Pix fails to follow the instructions." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.202, + 0.468, + 0.247 + ], + "angle": 0, + "content": "To further improve the performance, we propose a Bidirectional Interaction Module to facilitate the interaction of information between text and image features." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.248, + 0.468, + 0.352 + ], + "angle": 0, + "content": "3. We propose a new dataset utilization strategy to enhance the performance of SmartEdit in complex scenarios. In addition to using conventional editing data, we introduce perception-related data to strengthen the perceptual ability of UNet in the diffusion process. Besides, we also add a small amount of synthetic editing data to further stimulate the model's reasoning ability." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.353, + 0.468, + 0.428 + ], + "angle": 0, + "content": "4. An evaluation dataset, Reason-Edit, is specifically collected for evaluating the performance of instruction-based image editing tasks in complex scenarios. Both qualitative and quantitative results on Reason-Edit demonstrate the superiority of SmartEdit." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.248, + 0.468, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.444, + 0.219, + 0.458 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.469, + 0.401, + 0.484 + ], + "angle": 0, + "content": "2.1. Image Editing with Diffusion Models." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.492, + 0.468, + 0.825 + ], + "angle": 0, + "content": "Pretrained text-to-image diffusion models [8, 13, 23, 26, 27, 29] can strongly assist image editing task. Instruction-based image editing task [1, 4, 11, 12, 16, 17, 32, 36, 38] requires users to provide an instruction, which converts the original image to a newly designed image that matches the given instruction. Some methods can achieve this by utilizing a tuning-free approach. For example, Prompt-to-Prompt [12] suggests modifying the cross-attention maps by comparing the original input caption with the revised caption. MasaCtrl [4] converts existing self-attention in diffusion models into mutual self-attention, which can help query correlated local contents and textures from source images for consistency. In addition, due to the scarcity of paired image-instruction editing datasets, the pioneering work InstructPix2Pix [1] introduces a large-scale vision-language image editing datasets created by fine-tuned GPT-3 [2] and Prompt-to-Prompt with stable diffusion, and further finetunes the UNet [28], which can edit images by providing a simple instruction. To enhance the editing effect of InstructPix2Pix on real images, MagicBrush [36] further provides a large-scale and manually annotated dataset for instruction-guided real image editing." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The recent work, InstructDiffusion [11], also adopts the network design of InstructPix2Pix and focuses on unifying vision tasks in a joint training manner. By taking advantage of multiple different datasets, it can handle a variety of vision tasks, including understanding tasks (such as segmen" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.293 + ], + "angle": 0, + "content": "tation and keypoint detection) and generative tasks (such as editing and enhancement). Compared with InstructDiffusion, our primary focus is on the field of instruction-based image editing, especially for complex understanding and reasoning scenarios. In these scenarios, InstructDiffusion typically generates inferior results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.305, + 0.753, + 0.32 + ], + "angle": 0, + "content": "2.2. LLM with Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.33, + 0.892, + 0.707 + ], + "angle": 0, + "content": "The exceptional open-sourced LLaMA [6, 31] significantly enhances the performance of vision tasks with the aid of Large Language Models (LLMs). Pioneering works such as LLaVA and MiniGPT-4 have improved image-text alignment through instruction-tuning. While numerous MLLM-based [7, 22, 24, 39] studies have demonstrated their robust capabilities across a variety of tasks, primarily those reliant on text generation (e.g., human-robot interaction, complex reasoning, science question answering, etc.), GILL [18] serves as a bridge between MLLMs and diffusion models. It learns to process images with LLMs and is capable of generating coherent images based on the input texts. SEED [9] presents an innovative image tokenizer to enable LLM to process and generate images and text concurrently. SEED-2 [10] further refines the tokenizer by aligning the generation embedding with the image embedding of unCLIP-SD, which allows for better preservation of rich visual semantics and reconstruction of more realistic images. Emu [30] can be characterized as a multimodal generalist, trained with the next-token-prediction objective. CM3Leon [35] proposes a multi-modal language model that is capable of executing text-to-image and image-to-text generation. It employs the CM3 multi-modal architecture that is fine-tuned on diverse instruction-style data, and utilizes a training method adapted from text-only language models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.723, + 0.625, + 0.74 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The goal of instruction-based image editing is to make specific modifications to an input image \\( x \\) based on instructions \\( c_{T} \\), resulting in the target image \\( y \\). InstructPix2Pix, which is based on latent diffusion, is a seminal work in this field. For the target image \\( y \\) and an encoder \\( \\mathcal{E} \\), the diffusion process introduces noise to the encoded latent \\( z = \\mathcal{E}(y) \\), resulting in a noisy latent \\( z_{t} \\), with the noise level increasing over timesteps \\( t \\in T \\). A UNet \\( \\epsilon_{\\delta} \\) is then trained to predict the noise added to the noisy latent \\( z_{t} \\), given the image condition \\( c_{x} \\) and text instruction condition \\( c_{T} \\), where \\( c_{x} = \\mathcal{E}(x) \\). The" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8364" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.135 + ], + "angle": 0, + "content": "image condition is incorporated by directly concatenating \\( c_{x} \\) and \\( z_{t} \\). The specific objective of latent diffusion is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.139, + 0.469, + 0.176 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ], c _ {T}) \\| _ {2} ^ {2} \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.181, + 0.469, + 0.24 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is the unscaled noise, \\(t\\) is the sampling step, \\(z_{t}\\) is latent noise at step \\(t\\), \\(\\mathcal{E}(x)\\) is the image condition, and \\(c_{T}\\) is the text instruction condition. The concat corresponds to the concatenation operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.241, + 0.47, + 0.422 + ], + "angle": 0, + "content": "Although InstructPix2Pix has some effectiveness in instruction editing, its performance is limited when dealing with complex understanding and reasoning scenarios. To address this issue, we introduce a Multimodal Large Language Model (MLLM) into the network architecture and propose a Bidirectional Interaction Module (BIM) to implement bidirectional information interaction between the MLLM output and image information. In addition, we also explore the data utilization strategy and find that perception-related data and a small amount of complex editing data are crucial for enhancing model's performance. We provide detailed descriptions of these aspects in the next section." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.435, + 0.169, + 0.451 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.469, + 0.627 + ], + "angle": 0, + "content": "In this paper, we introduce SmartEdit, specifically designed to handle complex instruction editing scenarios. In this section, we first provide a detailed overview of the framework of SmartEdit (Section 4.1). Then, we delve into the Bidirectional Interaction Module (Section 4.2). In Section 4.3, we discuss how to enhance the perception and understanding capabilities of UNet in the diffusion model and stimulate the ability of MLLMs to handle complex scenarios. Finally, We introduce Reason-Edit, which is primarily used to evaluate the ability of instruction-based image editing methods toward complex scenarios. (Section 4.4)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.636, + 0.345, + 0.65 + ], + "angle": 0, + "content": "4.1. The Framework of SmartEdit" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Given an image \\( x \\) and instruction \\( c \\), which is tokenized as \\( (s_1, \\dots, s_T) \\), our goal is to obtain the target image \\( y \\) based on \\( c \\). As shown in Fig 3, the image \\( x \\) is first processed by the image encoder and FC layer, resulting in \\( v_{\\mu}(x) \\). Then \\( v_{\\mu}(x) \\) is sent into the LLM along with the token embedding \\( (s_1, \\dots, s_T) \\). The output of the LLM is discrete tokens, which cannot be used as the input for subsequent modules. Therefore, we take the hidden states corresponding to these discrete tokens as the input for the following modules. To jointly optimize LLaVA and the diffusion model, following GILL [18], we expand the original LLM vocabulary with \\( r \\) new tokens \\( [\\mathrm{IMG}_1], \\dots, [\\mathrm{IMG}_r] \\) and append the \\( r \\) [IMG] tokens to the end of instruction \\( c \\). To be specific, we incorporate a trainable matrix \\( \\mathbf{E} \\) into the embedding matrix of the LLM, which represents the \\( r \\) [IMG] token embeddings. Subsequently, we minimize the negative log-likelihood of" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "generated \\(r\\) [IMG] tokens, conditioned on tokens that have been generated previously:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.126, + 0.892, + 0.18 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\mathrm {L L M}} (c) = - \\sum_ {i = 1} ^ {r} \\log p _ {\\{\\theta \\cup \\mathbf {E} \\}} ([ \\operatorname {I M G} _ {i} ] \\mid v _ {\\mu} (x), \\\\ \\left. s _ {1}, \\dots , s _ {T}, \\left[ \\mathrm {I M G} _ {1} \\right], \\dots , \\left[ \\mathrm {I M G} _ {i - 1} \\right]\\right) \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.191, + 0.892, + 0.251 + ], + "angle": 0, + "content": "The majority of parameters \\(\\theta\\) in the LLM are kept frozen and we utilize LoRA [15] to carry out efficient fine-tuning. We take the hidden states \\(h\\) corresponding to the \\(r\\) [IMG] tokens as the input for the next module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.892, + 0.388 + ], + "angle": 0, + "content": "Considering the discrepancy between the feature spaces of the hidden states in the LLM and the clip text encoder, we need to align the hidden states \\( h \\) to the clip text encoder space. Inspired by BLIP2 [20] and DETR [5], we adopt the QFormer \\( Q_{\\beta} \\) with 6-layer transformer [33] and \\( n \\) learnable queries, obtaining feature \\( f \\). Subsequently, the image feature \\( v \\) output by the image encoder \\( E_{\\phi} \\) interacts with \\( f \\) through a bidirectional interaction module (BIM), resulting in \\( f' \\) and \\( v' \\). The mentioned process is represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.394, + 0.891, + 0.467 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} h = \\operatorname {L L a V A} (x, c), \\\\ \\begin{array}{l} f = Q _ {\\beta} (h), \\\\ F _ {n} (h) \\end{array} \\tag {3} \\\\ v = E _ {\\phi} (x), \\\\ f ^ {\\prime}, v ^ {\\prime} = \\operatorname {B I M} (f, v) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.565 + ], + "angle": 0, + "content": "For the diffusion model, following the design of Instructpix2pix, we concat the encoded image latent \\(\\mathcal{E}(x)\\) and noisy latent \\(z_{t}\\). Unlike Instructpix2pix, we use \\(f'\\) as the key and value in UNet, and combine \\(v'\\) into the features before entering UNet in a residual manner. The specific process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.575, + 0.892, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ] + v ^ {\\prime}, f ^ {\\prime}) \\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.625, + 0.892, + 0.655 + ], + "angle": 0, + "content": "To keep consistency with equation 1, we omit the Conv operation here." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.666, + 0.791, + 0.681 + ], + "angle": 0, + "content": "4.2. Bidirectional Interaction Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The design of BIM is depicted in Fig 4. It includes a self-attention block, two cross-attention blocks, and an MLP layer. The two inputs of BIM are the output \\( f \\) from QFormer and the output \\( v \\) from the image encoder. After bidirectional information interaction between \\( f \\) and \\( v \\), BIM will eventually output \\( f' \\) and \\( v' \\). In BIM, the process begins with \\( f \\) undergoing a self-attention mechanism. After this, \\( f \\) serves as a query to interact with the input \\( v \\), which acts as both key and value, through a cross-attention block. This interaction results in the generation of \\( f' \\) via a pointwise MLP. Following the creation of \\( f' \\), it then serves as both key and value to interact with \\( v \\), which now acts as a query. This second cross-attention interaction leads to the production of \\( v' \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8365" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.187, + 0.089, + 0.787, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.895, + 0.343 + ], + "angle": 0, + "content": "Figure 3. The overall framework of SmartEdit. For the instruction, we first append the \\( r \\) [IMG] tokens to the end of instruction \\( c \\). Together with image \\( x \\), they will be sent into LLaVA, which can then obtain the hidden states corresponding to these \\( r \\) [IMG] tokens. Then the hidden state is sent into the QFormer and gets feature \\( f \\). Subsequently, the image feature \\( v \\) output by the image encoder \\( E_{\\phi} \\) interacts with \\( f \\) through a bidirectional interaction module (BIM), resulting in \\( f' \\) and \\( v' \\). The \\( f' \\) and \\( v' \\) are input into the diffusion models to achieve the instruction-based image editing task." + }, + { + "type": "image", + "bbox": [ + 0.15, + 0.357, + 0.401, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.463, + 0.471, + 0.506 + ], + "angle": 0, + "content": "Figure 4. The network design of the BIM Module. In this module, the input information \\( f \\) and \\( v \\) will undergo bidirectional information interaction through different cross-attention." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.47, + 0.664 + ], + "angle": 0, + "content": "As discussed in the introduction, the proposed BIM module reuses the image feature and inputs it as supplementary information into UNet. The implementation of two cross-attention blocks in this module facilitates a robust bidirectional information interaction between the image feature and the text feature. Compared to not adopting the BIM module or only fusing the image feature and text feature in one direction, SmartEdit which is equipped with the BIM module yields better results. The experimental comparison of different designs is shown in Section 5.3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.327, + 0.696 + ], + "angle": 0, + "content": "4.3. Dataset Utilization Strategy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.901 + ], + "angle": 0, + "content": "During the training process of SmartEdit, two primary challenges emerge when solely utilizing datasets gathered from InstructPix2Pix and MagicBrush as the training set. The first challenge is that SmartEdit has a poor perception of position and concept. The second challenge is that, despite being equipped with MLLM, SmartEdit still has limited capability in scenarios that require reasoning. In summary, the effectiveness of SmartEdit in handling complex scenarios is limited if it is only trained on conventional editing datasets. After analysis, we have identified the causes of these issues. The first issue stems from the UNet in the diffusion model which lacks an understanding of perception and concepts, leading to SmartEdit's poor perception of position and con-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.406 + ], + "angle": 0, + "content": "cept. The second issue is that SmartEdit has limited exposure to editing data that requires reasoning abilities, which in turn limits its reasoning capabilities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.893, + 0.801 + ], + "angle": 0, + "content": "To tackle the first issue, we incorporate the segmentation data into the training set. Such modifications significantly enhanced the perception capabilities of the SmartEdit model. Regarding the second issue, we take inspiration from LISA [19] that a minimal amount of reasoning segmentation data can efficiently activate MLLM's reasoning capacity. Guided by this insight, we establish a data production pipeline and synthesize 476 paired data (each sample contains original image, instruction, and synthetic target image) as a supplement to the training data. This synthetic editing dataset includes two major types of scenarios: complex understanding and reasoning scenarios. For complex understanding scenarios, the original image contains multiple objects and the corresponding instruction modifies the specific object based on various attributes (i.e., location, color, relative size, and in or outside the mirror). We specifically consider the mirror attribute because it is a typical example that requires a strong understanding of the scene (both inside and outside the mirror) to perform well. For reasoning scenarios, we involve complex reasoning cases that need world knowledge to identify the specific object. The effectiveness of this synthetic editing dataset and the impact of different datasets on the model's performance are detailed in Section 5.4. The details of the data production pipeline and some visual examples are described in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.815, + 0.8, + 0.831 + ], + "angle": 0, + "content": "4.4. Reason-Edit for Better Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To better evaluate existing instruction editing methods and SmartEdit's capabilities in complex understanding and reasoning scenarios, we collect an evaluation dataset, ReasonEdit. Reason-Edit consists of 219 image-text pairs. Con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8366" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "sistent with the synthetic training data pairs, Reason-Edit is also categorized in the same manner. Note that there is no overlap between the data in Reason-Edit and the synthetic training set. With Reason-Edit, we can thoroughly test the performance of instruction-based image editing models in terms of understanding and reasoning scenarios. We hope more researchers will pay attention to the capabilities of instruction-based image editing models from these perspectives, thereby fostering the practical application of instruction-based image editing methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.261, + 0.21, + 0.278 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.287, + 0.279, + 0.303 + ], + "angle": 0, + "content": "5.1. Experimental Setting" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.308, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Training Process and Implementation Details. The training process and implementation details of SmartEdit can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.47, + 0.505 + ], + "angle": 0, + "content": "Network Architecture. For the Large Language Model with visual input (e.g., LLaVA), we choose LLaVA-1.1-7b and LLaVA-1.1-13b as the base model. During training, the weights of LLaVA are frozen and we add LoRA for efficient fine-tuning. In LoRA, the values of the two parameters, dim and alpha, are 16 and 27, respectively. We expand the original LLM vocabulary with 32 new tokens. The QFormer is composed of 6-layer transformer [33] and 77 learnable query tokens. In the BIM module, there is a self-attention block, two cross-attention blocks, and an MLP layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.657 + ], + "angle": 0, + "content": "Training Datasets. For the training process of SmartEdit, the training data can be divided into 4 categories: (1) segmentation datasets, which include COCOStuff [3], RefCOCO [34], GRefCOCO [21], and the reasoning segmentation dataset from LISA [19]; (2) editing datasets, which involve InstructPix2Pix and MagicBrush; (3) visual question answering (VQA) dataset, which is the LLaVA-Instruct-150k dataset [22]; (4) synthetic editing dataset, where we collect a total of 476 paired data for complex understanding and reasoning scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. As we hope to only change the foreground of the image while keeping the background unchanged for editing, we adopt three metrics for the background area: PSNR, SSIM, and LPIPS [14, 37]. For the foreground area, we calculate CLIP Score [25] between the foreground area of the edited image and the GT label. The GT label is annotated manually. Among these four metrics, except for LPIPS where lower is better, the other three metrics are higher the better. While these metrics can reflect the performance to a certain extent, they are not entirely accurate. To provide a more accurate evaluation of the effects of edited images, we propose a metric for assessing editing accuracy. Specifically, we hire four workers to manually evaluate the results of these different methods on Reason-Edit. The evaluation criterion is whether the edited image aligns with the instruction. After obtaining the evaluation results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "from each worker, we average all the results to get the final metric result, which is Instruction-Alignment (Ins-align)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.127, + 0.869, + 0.142 + ], + "angle": 0, + "content": "5.2. Comparison with State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.146, + 0.892, + 0.433 + ], + "angle": 0, + "content": "We compare SmartEdit with existing SOTA instruction-based image editing methods, namely InstructPix2Pix, MagicBrush, and InstructDiffusion. Considering that these released models are trained on specific datasets, they would inevitably perform poorly if directly evaluated on ReasonEdit. To ensure a fair comparison, we fine-tune these methods on the same training set used by SmartEdit, and evaluate the fine-tuned models on Reason-Edit. The experimental results are shown in Tab. 1. From the quantitative results of the reasoning scenarios in the table, it can be observed that when we replace the clip text encoder in the diffusion model with LLaVA and adopt the proposed BIM module, both SmartEdit-7B and SmartEdit-13B achieve better results on these five metrics. This suggests that in scenarios requiring reasoning from instructions, a simple clip text encoder may struggle to understand the meaning of the instructions. However, the MLLM can fully utilize its powerful reasoning ability and world knowledge to correctly identify the corresponding objects and perform edits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.892, + 0.644 + ], + "angle": 0, + "content": "The qualitative results further illustrate this point. As shown in Fig. 5, the first three examples are reasoning scenarios. In the first example, both SmartEdit-7B and SmartEdit-13B successfully identify the tool used for cutting fruit (knife) and remove it, while keeping the rest of the background unchanged. The second example can also be handled well by both of them. However, in the third example, we observe a difference in performance. Only SmartEdit-13B can accurately locate the object and perform the corresponding edits without altering other background areas. This suggests that in instruction-based image editing tasks that require reasoning, a more powerful MLLM model can effectively generalize its reasoning ability to this task. This observation aligns with the findings from LISA." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, for understanding scenarios, we observe a difference in performance between SmartEdit-7B and SmartEdit-13B when compared to InstructDiffusion on PSNR/SSIM/LPIPS. Specifically, SmartEdit-7B performs worse than InstructDiffusion, while SmartEdit-13B outperforms InstructDiffusion on these metrics. Upon further analysis of the qualitative results, as shown in the \\(4_{th}\\) and \\(5_{th}\\) rows of Fig. 5, we find that from a visual perspective, both SmartEdit-7B and SmartEdit-13B appear superior to InstructDiffusion. This suggests that the three metrics do not always align with human visual perception. We confirm this phenomenon in the supplementary material. From the result of the Ins-align metric, it can be observed that SmartEdit shows a significant improvement compared to previous instruction-based image editing methods. Also, when adopting a more powerful MLLM model, SmartEdit-13B performs better than SmartEdit-7B on Ins-align." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.319, + 0.092, + 0.645, + 0.103 + ], + "angle": 0, + "content": "\"What is the tool that is used to cut fruits. Remove this tool.\"" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.105, + 0.282, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.105, + 0.39, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.105, + 0.489, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.105, + 0.588, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.59, + 0.105, + 0.686, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.688, + 0.105, + 0.785, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.328, + 0.163, + 0.637, + 0.174 + ], + "angle": 0, + "content": "\"Please replace food contains most vitamin with an orange.\"" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.175, + 0.281, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.175, + 0.389, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.175, + 0.488, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.175, + 0.588, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.175, + 0.686, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.175, + 0.785, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.329, + 0.232, + 0.636, + 0.243 + ], + "angle": 0, + "content": "\"Please remove the object that can be used to have meals.\"" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.245, + 0.281, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.245, + 0.389, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.245, + 0.488, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.245, + 0.588, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.245, + 0.686, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.245, + 0.785, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.391, + 0.307, + 0.572, + 0.317 + ], + "angle": 0, + "content": "\"Change the middle panda to a cat\"" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.318, + 0.281, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.318, + 0.389, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.319, + 0.488, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.319, + 0.588, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.319, + 0.686, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.319, + 0.785, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.386, + 0.379, + 0.578, + 0.389 + ], + "angle": 0, + "content": "\"Change the cat in mirror to a tiger.\"" + }, + { + "type": "image", + "bbox": [ + 0.182, + 0.39, + 0.281, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.475, + 0.265, + 0.486 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.39, + 0.389, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.297, + 0.475, + 0.383, + 0.485 + ], + "angle": 0, + "content": "InstructPix2Pix" + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.39, + 0.488, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.406, + 0.475, + 0.467, + 0.485 + ], + "angle": 0, + "content": "MagicBrush" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.39, + 0.588, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.49, + 0.475, + 0.586, + 0.484 + ], + "angle": 0, + "content": "InstructDiffusion" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.39, + 0.686, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.597, + 0.475, + 0.672, + 0.484 + ], + "angle": 0, + "content": "SmartEdit-7B" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.39, + 0.785, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.695, + 0.475, + 0.774, + 0.484 + ], + "angle": 0, + "content": "SmartEdit-13B" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.49, + 0.891, + 0.518 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on Reason-Edit. When compared to several existing instruction editing methods that have undergone further fine-tuning on our synthetic editing dataset, our approach demonstrates superior editing capabilities in complex scenarios." + }, + { + "type": "table", + "bbox": [ + 0.102, + 0.531, + 0.871, + 0.62 + ], + "angle": 0, + "content": "
MethodsUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
InstructPix2Pix21.5760.7210.08922.7620.53724.2340.7070.08319.4130.344
MagicBrush18.1200.680.14322.6200.29022.1010.6940.11319.7550.283
InstructDiffusion23.2580.7430.06723.0800.69721.4530.6660.11719.5230.483
SmartEdit-7B22.0490.7310.08723.6110.71225.2580.7420.05520.9500.789
SmartEdit-13B23.5960.7510.06823.5360.77125.7570.7470.05120.7770.817
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.622, + 0.89, + 0.651 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. All the methods we compared have been fine-tuned using the same training data as that used by SmartEdit." + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.664, + 0.422, + 0.673 + ], + "angle": 0, + "content": "\"What is the object that the dog's food should be put into? Remove this object.\"" + }, + { + "type": "image", + "bbox": [ + 0.113, + 0.673, + 0.436, + 0.821 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.827, + 0.466, + 0.84 + ], + "angle": 0, + "content": "Figure 6. Demonstration of the effectiveness of the BIM Module." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.848, + 0.294, + 0.864 + ], + "angle": 0, + "content": "5.3. Ablation Study on BIM" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To validate the effectiveness of the bidirectional information interaction in our proposed BIM module, we conduct" + }, + { + "type": "text", + "bbox": [ + 0.561, + 0.662, + 0.831, + 0.672 + ], + "angle": 0, + "content": "\"Please replace the animal that is lying on the grass with a fox\"" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.672, + 0.588, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.673, + 0.66, + 0.729 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.673, + 0.732, + 0.728 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.673, + 0.805, + 0.728 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.673, + 0.878, + 0.728 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.594, + 0.733, + 0.8, + 0.743 + ], + "angle": 0, + "content": "\"Change the red strawberry to a white pumpkin\"" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.743, + 0.588, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.531, + 0.801, + 0.578, + 0.81 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.743, + 0.66, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.617, + 0.801, + 0.633, + 0.81 + ], + "angle": 0, + "content": "Edit" + }, + { + "type": "image", + "bbox": [ + 0.661, + 0.743, + 0.731, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.801, + 0.715, + 0.81 + ], + "angle": 0, + "content": "Edit+Seg" + }, + { + "type": "image", + "bbox": [ + 0.733, + 0.743, + 0.805, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.738, + 0.801, + 0.802, + 0.81 + ], + "angle": 0, + "content": "Edit+Reason-Edit" + }, + { + "type": "image", + "bbox": [ + 0.806, + 0.743, + 0.88, + 0.8 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.801, + 0.852, + 0.81 + ], + "angle": 0, + "content": "Total" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.815, + 0.891, + 0.842 + ], + "angle": 0, + "content": "Figure 7. Demonstration of the significance of joint training with multiple datasets." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.891, + 0.901 + ], + "angle": 0, + "content": "comparative experiments on the SmartEdit-7B model. The details are presented in Tab. 2. The first experiment, denoted as Exp 1, aims to verify the necessity of the information in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.956 + ], + "angle": 0, + "content": "8368" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.089, + 0.891, + 0.149 + ], + "angle": 0, + "content": "
Exp IDPlainSimpleCABIMUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓20.9750.7130.10823.360.69523.8480.7250.07420.330.694
2✓19.5570.6920.12623.660.69223.5080.7160.08120.170.722
3✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.152, + 0.893, + 0.18 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.187, + 0.891, + 0.251 + ], + "angle": 0, + "content": "
Exp IDEditSegmentationSynthetic editing datasetUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓17.5680.6640.17122.790.20122.4000.7060.10219.220.233
2✓✓18.9600.6900.14322.830.36121.7740.6930.11619.820.311
3✓✓19.5620.7020.11122.320.44023.5950.7150.07920.430.567
4✓✓✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.253, + 0.893, + 0.281 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.699 + ], + "angle": 0, + "content": "teraction proposed in the BIM module. In this experiment, we remove the BIM module from the SmartEdit-7B model and directly apply the text feature output from QFormer to the diffusion model. The second experiment, denoted as Exp 2, aims to verify the necessity of the bidirectional information interaction proposed in the BIM module. Specifically, all blocks are discarded except for the cross-attention block on the image feature branch. Therefore, the information from the text feature of QFormer is unidirectionally applied to the image feature. These two experiments are designed to test the impact of removing or altering the BIM module on the performance of SmartEdit-7B in complex understanding and reasoning scenarios. As shown in Tab. 2, if the BIM module is removed, there is a significant decline in all metrics for both understanding and reasoning scenarios. When the BIM module is replaced with the SimpleCA module, we observe a noticeable decline in all metrics, except for the clip score in understanding scenarios. Further comparison of the qualitative results in Fig. 6 confirms that the introduction of the BIM indeed enhances SmartEdit's instruction editing performance. To be specific, when we do not use the BIM module (i.e., plain), the dog bowl (first row) turns into other objects (marked with a red circle), and the fork (second row) does not change at all. After using SimpleCA, it can be found that the dog bowl and fork have been partially removed. When SmartEdit is equipped with BIM, the dog bowl and fork can be well removed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.714, + 0.367, + 0.73 + ], + "angle": 0, + "content": "5.4. Ablation Study on Dataset Usage" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In Section 4.3, we explore an efficient strategy for data utilization, aiming to enhance SmartEdit's capabilities in handling complex understanding and reasoning scenarios. During the training process of SmartEdit, we employ the common editing dataset, segmentation dataset, and the synthetic editing dataset. To validate the significance of these different data types in boosting SmartEdit's performance, we conduct a series of ablation studies, as detailed in Tab. 3. These experiments are based on the SmartEdit-7B model. In Exp 1, we train the model using only the editing data. In Exp 2, we incorporate segmentation data into the training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.895, + 0.533 + ], + "angle": 0, + "content": "process, building upon Exp 1. In Exp 3, we further add the synthetic editing data to the basis established in Exp 1. The quantitative results of these experiments reveal that segmentation data and synthetic editing data play complementary roles in enhancing the model's performance. This is further corroborated by the visual comparison in Fig. 7. For reasoning scenarios, when adopting only the editing dataset or combining the editing dataset and the segmentation dataset, the performance of SmartEdit is inferior. When the synthetic editing data is incorporated into the editing dataset, SmartEdit can accurately locate the specific objects. However, the output of SmartEdit is also mediocre (the generated fox has obvious artifacts, and two pumpkins are generated). When all these datasets are combined as the training set, the results generated by SmartEdit have a further significant improvement in visual effects." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.545, + 0.62, + 0.56 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.895, + 0.777 + ], + "angle": 0, + "content": "In conclusion, this paper presents SmartEdit, a novel approach to instruction-based image editing that enhances understanding and reasoning capabilities by incorporating the LLMs with visual inputs. By introducing the Bidirectional Interaction Module (BIM), we have overcome challenges associated with the direct integration of LLMs and diffusion models in complex reasoning scenarios. Our data utilization strategy, which incorporates perception data and complex instruction editing data, effectively enhances SmartEdit's capabilities in handling complex understanding and reasoning scenarios. Evaluation on our newly constructed dataset, Reason-Edit, shows that SmartEdit outperforms previous methods, marking a significant step towards practical applications of complex instruction-based image editing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Acknowledgement. The work is partially supported by the Young Scientists Fund of the National Natural Science Foundation of China under grant No. 62106154, the Natural Science Foundation of Guangdong Province, China (General Program) under grant No.2022A1515011524, Shenzhen Science and Technology Program JCYJ20220818103001002 and JCYJ20220818103006012, and the Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong (Shenzhen)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8369" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Tim Brooks, Aleksander Holynski, and Alexei A Efros. Instructpix2pix: Learning to follow image editing instructions. 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Minigpt-4: Enhancing vision-language" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.534, + 0.093, + 0.892, + 0.121 + ], + "angle": 0, + "content": "understanding with advanced large language models. arXiv preprint arXiv:2304.10592, 2023. 2, 3" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8371" + } + ] +] \ No newline at end of file diff --git a/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_origin.pdf b/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e63dcf7f9ead9ad346911adae0b8b0a951e362c6 --- /dev/null +++ b/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7743c1be12ff5a4108b169aab1064690d04592d9104e07ead13595305a86c223 +size 1878198 diff --git a/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/full.md b/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a7b6d80c4b208ff6b5cbaa95da186a9700aa4abd --- /dev/null +++ b/2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/full.md @@ -0,0 +1,339 @@ +# SmartEdit: Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models + +Yuzhou Huang $^{1,2^{*\#}}$ Liangbin Xie $^{2,3,5^{*\#}}$ Xintao Wang $^{2,4\dagger}$ Ziyang Yuan $^{2,7^{\#}}$ Xiaodong Cun $^{4}$ Yixiao Ge $^{2,4}$ Jiantao Zhou $^{3}$ Chao Dong $^{5,6}$ Rui Huang $^{1}$ Ruimao Zhang $^{1\dagger}$ Ying Shan $^{2,4}$ $^{1}$ The Chinese University of Hong Kong, Shenzhen (CUHK-SZ) $^{2}$ ARC Lab, Tencent PCG $^{3}$ University of Macau $^{4}$ Tencent AI Lab Shenzhen Institute of Advanced Technology $^{6}$ Shanghai Artificial Intelligence Laboratory $^{7}$ Tsinghua University https://github.com/TencentARC/SmartEdit + +![](images/0cddff250e1da8feb141963c68da27be358057cf683357a2dbb7f17c5543e8e0.jpg) +Figure 1. We propose SmartEdit, an instruction-based image editing model that leverages Multimodal Large Language Models (MLLMs) to enhance the understanding and reasoning capabilities of instruction-based editing methods. With the specialized design, our SmartEdit is capable of handling complex understanding (the instructions that contain various object attributes like location, relative size, color, and in or outside the mirror) and reasoning scenarios. + +# Abstract + +Current instruction-based image editing methods, such as InstructPix2Pix, often fail to produce satisfactory results in complex scenarios due to their dependence on the simple CLIP text encoder in diffusion models. To rectify this, this paper introduces SmartEdit, a novel approach of instruction-based image editing that leverages Multimodal Large Language Models (MLLMs) to enhance its understanding and reasoning capabilities. However, direct integration of these elements still faces challenges in situations requiring complex reasoning. To mitigate this, we + +propose a Bidirectional Interaction Module (BIM) that enables comprehensive bidirectional information interactions between the input image and the MLLM output. During training, we initially incorporate perception data to boost the perception and understanding capabilities of diffusion models. Subsequently, we demonstrate that a small amount of complex instruction editing data can effectively stimulate SmartEdit's editing capabilities for more complex instructions. We further construct a new evaluation dataset, Reason-Edit, specifically tailored for complex instruction-based image editing. Both quantitative and qualitative results on this evaluation dataset indicate that our SmartEdit surpasses previous methods, paving the way for the practical application of complex instruction-based image editing. + +# 1. Introduction + +Text-to-image synthesis [8, 13, 23, 26, 27, 29] has experienced significant advancements in recent years, thanks to the development of diffusion models. These methods have enabled the generation of images that are not only consistent with natural language descriptions, but also align with human perception and preferences, marking a substantial leap forward in the field. Instruction-based image editing methods [1, 36], represented by InstructPix2Pix, leverage pre-trained text-to-image diffusion models as priors. This allows users to conveniently and effortlessly modify images through natural language instructions for ordinary users. + +While existing instruction-based image editing methods can handle simple instructions effectively, they often fall short when dealing with complex scenarios, which require the model to have a more powerful understanding and reasoning capabilities. As depicted in Fig. 1, there are two common types of complex scenarios. The first is when the original image contains multiple objects, and the instruction modifies only one of these objects through certain attributes (such as location, relative size, color, in or outside the mirror). The other is when world knowledge is needed to identify the object to be edited (such as the object that can tell the time). We define these two types as complex understanding scenarios and complex reasoning scenarios, respectively. Handling these two scenarios is crucial for practical instruction editing, but existing instruction-based image editing methods probably fail in these scenarios (as shown in Fig. 2). In this paper, we attempt to identify the reasons why existing instruction-based image editing methods fail in these scenarios, and try to tackle the challenge in these scenarios. + +The first reason why existing instruction-based image editing methods fail in these scenarios is that they typically rely on a simple CLIP text encoder [25] in diffusion models (e.g., Stable Diffusion) to process the instructions. Under this circumstance, these models struggle to 1) understand and reason through the instructions, and 2) integrate the image to comprehend the instructions. To address these limitations, we introduce the Multimodal Large Language Models (MLLMs) (e.g., LLaVA) [22, 39] into instruction-based editing models. Our method, SmartEdit, jointly optimizes MLLMs and diffusion models, leveraging the powerful reasoning capabilities of MLLMs to facilitate instruction-based image editing task. + +While substituting the CLIP encoder in the diffusion model with MLLMs can alleviate some problems, this approach still falls short when it comes to examples that necessitate complex understanding and reasoning. This is because the input image to edit (original image) is integrated into the UNet of the Stable Diffusion model through a straightforward concatenation, which is further interacted with MLLM outputs through a cross-attention operation. In + +this setup, the image features serve as the query, and MLLM outputs act as the key and value. This means that the MLLM outputs unilaterally modulate and interact with the image feature, which affects the results. To alleviate this issue, we further propose a Bidirectional Interaction Module (BIM). This module reuses the image information extracted by the LLaVA's visual encoder from the input image. It also facilitates a comprehensive bidirectional information interaction between this image and the MLLM output, enabling the model to perform better in complex scenarios. + +The second reason contributing to the failure of existing instruction-based editing methods is the absence of specific data. When solely training on editing datasets, such as the datasets used in Instructpix2pix [1] and MagicBrush [36], SmartEdit also struggles to handle scenarios requiring complex reasoning and understanding. This is because SmartEdit has not been exposed to data from these scenarios. One straightforward approach is to generate a substantial amount of paired data similar to those scenarios. However, this method is excessively expensive because the cost of generating data for these scenarios is high. + +In this paper, we find that there are two keys to compensate the insufficiency of specific editing data. The first is to enhance the perception capabilities of UNet [28], and the second is to stimulate the model capacity in those scenarios with a few high-quality examples. Correspondingly, we 1) incorporate the perception-related data (e.g., segmentation) into the model's training. 2) synthesize a few high-quality paired data with complex instructions to fine-tune our SmartEdit (similar to LISA [19]). In this way, SmartEdit not only reduces the reliance on paired data under complex scenarios but also effectively stimulates its ability to handle these scenarios. + +Equipped with both the model designs and the data utilization strategy, SmartEdit can understand complex instructions, surpassing the scope that previous instruction editing methods can do. To better evaluate the understanding and reasoning ability of instruction-based image editing methods, we collect the Reason-Edit dataset, which contains a total of 219 image-text pairs. Note that there is no overlap between the Reason-Edit dataset and the small-amount high-quality synthesized training data pairs. Based on the Reason-Edit dataset, we evaluate existing instruction-based image editing methods comprehensively. Both the quantitative and qualitative results on the ReasonEdit dataset indicate that SmartEdit significantly outperforms previous instruction-based image editing methods. + +In summary, our contributions are as follows: + +1. We analyze and focus on the performance of instruction-based image editing methods in more complex instructions. These complex scenarios have often been overlooked and less explored in past research. +2. We leverage MLLMs to better comprehend instructions. + +Figure 2. For more complex instructions or scenarios, InstructPix2Pix fails to follow the instructions. + +To further improve the performance, we propose a Bidirectional Interaction Module to facilitate the interaction of information between text and image features. + +3. We propose a new dataset utilization strategy to enhance the performance of SmartEdit in complex scenarios. In addition to using conventional editing data, we introduce perception-related data to strengthen the perceptual ability of UNet in the diffusion process. Besides, we also add a small amount of synthetic editing data to further stimulate the model's reasoning ability. +4. An evaluation dataset, Reason-Edit, is specifically collected for evaluating the performance of instruction-based image editing tasks in complex scenarios. Both qualitative and quantitative results on Reason-Edit demonstrate the superiority of SmartEdit. + +# 2. Related Work + +# 2.1. Image Editing with Diffusion Models. + +Pretrained text-to-image diffusion models [8, 13, 23, 26, 27, 29] can strongly assist image editing task. Instruction-based image editing task [1, 4, 11, 12, 16, 17, 32, 36, 38] requires users to provide an instruction, which converts the original image to a newly designed image that matches the given instruction. Some methods can achieve this by utilizing a tuning-free approach. For example, Prompt-to-Prompt [12] suggests modifying the cross-attention maps by comparing the original input caption with the revised caption. MasaCtrl [4] converts existing self-attention in diffusion models into mutual self-attention, which can help query correlated local contents and textures from source images for consistency. In addition, due to the scarcity of paired image-instruction editing datasets, the pioneering work InstructPix2Pix [1] introduces a large-scale vision-language image editing datasets created by fine-tuned GPT-3 [2] and Prompt-to-Prompt with stable diffusion, and further finetunes the UNet [28], which can edit images by providing a simple instruction. To enhance the editing effect of InstructPix2Pix on real images, MagicBrush [36] further provides a large-scale and manually annotated dataset for instruction-guided real image editing. + +The recent work, InstructDiffusion [11], also adopts the network design of InstructPix2Pix and focuses on unifying vision tasks in a joint training manner. By taking advantage of multiple different datasets, it can handle a variety of vision tasks, including understanding tasks (such as segmen + +tation and keypoint detection) and generative tasks (such as editing and enhancement). Compared with InstructDiffusion, our primary focus is on the field of instruction-based image editing, especially for complex understanding and reasoning scenarios. In these scenarios, InstructDiffusion typically generates inferior results. + +# 2.2. LLM with Diffusion Models + +The exceptional open-sourced LLaMA [6, 31] significantly enhances the performance of vision tasks with the aid of Large Language Models (LLMs). Pioneering works such as LLaVA and MiniGPT-4 have improved image-text alignment through instruction-tuning. While numerous MLLM-based [7, 22, 24, 39] studies have demonstrated their robust capabilities across a variety of tasks, primarily those reliant on text generation (e.g., human-robot interaction, complex reasoning, science question answering, etc.), GILL [18] serves as a bridge between MLLMs and diffusion models. It learns to process images with LLMs and is capable of generating coherent images based on the input texts. SEED [9] presents an innovative image tokenizer to enable LLM to process and generate images and text concurrently. SEED-2 [10] further refines the tokenizer by aligning the generation embedding with the image embedding of unCLIP-SD, which allows for better preservation of rich visual semantics and reconstruction of more realistic images. Emu [30] can be characterized as a multimodal generalist, trained with the next-token-prediction objective. CM3Leon [35] proposes a multi-modal language model that is capable of executing text-to-image and image-to-text generation. It employs the CM3 multi-modal architecture that is fine-tuned on diverse instruction-style data, and utilizes a training method adapted from text-only language models. + +# 3. Preliminary + +The goal of instruction-based image editing is to make specific modifications to an input image $x$ based on instructions $c_{T}$ , resulting in the target image $y$ . InstructPix2Pix, which is based on latent diffusion, is a seminal work in this field. For the target image $y$ and an encoder $\mathcal{E}$ , the diffusion process introduces noise to the encoded latent $z = \mathcal{E}(y)$ , resulting in a noisy latent $z_{t}$ , with the noise level increasing over timesteps $t \in T$ . A UNet $\epsilon_{\delta}$ is then trained to predict the noise added to the noisy latent $z_{t}$ , given the image condition $c_{x}$ and text instruction condition $c_{T}$ , where $c_{x} = \mathcal{E}(x)$ . The + +image condition is incorporated by directly concatenating $c_{x}$ and $z_{t}$ . The specific objective of latent diffusion is as follows: + +$$ +\begin{array}{l} L _ {\text {d i f f u s i o n}} = \mathbb {E} _ {\mathcal {E} (y), \mathcal {E} (x), c _ {T}, \epsilon \sim \mathcal {N} (0, 1), t} [ \| \epsilon \\ - \epsilon_ {\delta} (t, \operatorname {c o n c a t} [ z _ {t}, \mathcal {E} (x) ], c _ {T}) \| _ {2} ^ {2} \tag {1} \\ \end{array} +$$ + +where $\epsilon$ is the unscaled noise, $t$ is the sampling step, $z_{t}$ is latent noise at step $t$ , $\mathcal{E}(x)$ is the image condition, and $c_{T}$ is the text instruction condition. The concat corresponds to the concatenation operation. + +Although InstructPix2Pix has some effectiveness in instruction editing, its performance is limited when dealing with complex understanding and reasoning scenarios. To address this issue, we introduce a Multimodal Large Language Model (MLLM) into the network architecture and propose a Bidirectional Interaction Module (BIM) to implement bidirectional information interaction between the MLLM output and image information. In addition, we also explore the data utilization strategy and find that perception-related data and a small amount of complex editing data are crucial for enhancing model's performance. We provide detailed descriptions of these aspects in the next section. + +# 4. Method + +In this paper, we introduce SmartEdit, specifically designed to handle complex instruction editing scenarios. In this section, we first provide a detailed overview of the framework of SmartEdit (Section 4.1). Then, we delve into the Bidirectional Interaction Module (Section 4.2). In Section 4.3, we discuss how to enhance the perception and understanding capabilities of UNet in the diffusion model and stimulate the ability of MLLMs to handle complex scenarios. Finally, We introduce Reason-Edit, which is primarily used to evaluate the ability of instruction-based image editing methods toward complex scenarios. (Section 4.4). + +# 4.1. The Framework of SmartEdit + +Given an image $x$ and instruction $c$ , which is tokenized as $(s_1, \dots, s_T)$ , our goal is to obtain the target image $y$ based on $c$ . As shown in Fig 3, the image $x$ is first processed by the image encoder and FC layer, resulting in $v_{\mu}(x)$ . Then $v_{\mu}(x)$ is sent into the LLM along with the token embedding $(s_1, \dots, s_T)$ . The output of the LLM is discrete tokens, which cannot be used as the input for subsequent modules. Therefore, we take the hidden states corresponding to these discrete tokens as the input for the following modules. To jointly optimize LLaVA and the diffusion model, following GILL [18], we expand the original LLM vocabulary with $r$ new tokens $[\mathrm{IMG}_1], \dots, [\mathrm{IMG}_r]$ and append the $r$ [IMG] tokens to the end of instruction $c$ . To be specific, we incorporate a trainable matrix $\mathbf{E}$ into the embedding matrix of the LLM, which represents the $r$ [IMG] token embeddings. Subsequently, we minimize the negative log-likelihood of + +generated $r$ [IMG] tokens, conditioned on tokens that have been generated previously: + +$$ +\begin{array}{l} L _ {\mathrm {L L M}} (c) = - \sum_ {i = 1} ^ {r} \log p _ {\{\theta \cup \mathbf {E} \}} ([ \operatorname {I M G} _ {i} ] \mid v _ {\mu} (x), \\ \left. s _ {1}, \dots , s _ {T}, \left[ \mathrm {I M G} _ {1} \right], \dots , \left[ \mathrm {I M G} _ {i - 1} \right]\right) \tag {2} \\ \end{array} +$$ + +The majority of parameters $\theta$ in the LLM are kept frozen and we utilize LoRA [15] to carry out efficient fine-tuning. We take the hidden states $h$ corresponding to the $r$ [IMG] tokens as the input for the next module. + +Considering the discrepancy between the feature spaces of the hidden states in the LLM and the clip text encoder, we need to align the hidden states $h$ to the clip text encoder space. Inspired by BLIP2 [20] and DETR [5], we adopt the QFormer $Q_{\beta}$ with 6-layer transformer [33] and $n$ learnable queries, obtaining feature $f$ . Subsequently, the image feature $v$ output by the image encoder $E_{\phi}$ interacts with $f$ through a bidirectional interaction module (BIM), resulting in $f'$ and $v'$ . The mentioned process is represented as: + +$$ +\begin{array}{l} h = \operatorname {L L a V A} (x, c), \\ \begin{array}{l} f = Q _ {\beta} (h), \\ F _ {n} (h) \end{array} \tag {3} \\ v = E _ {\phi} (x), \\ f ^ {\prime}, v ^ {\prime} = \operatorname {B I M} (f, v) \\ \end{array} +$$ + +For the diffusion model, following the design of Instructpix2pix, we concat the encoded image latent $\mathcal{E}(x)$ and noisy latent $z_{t}$ . Unlike Instructpix2pix, we use $f'$ as the key and value in UNet, and combine $v'$ into the features before entering UNet in a residual manner. The specific process can be formulated as: + +$$ +\begin{array}{l} L _ {\text {d i f f u s i o n}} = \mathbb {E} _ {\mathcal {E} (y), \mathcal {E} (x), c _ {T}, \epsilon \sim \mathcal {N} (0, 1), t} [ \| \epsilon \\ - \epsilon_ {\delta} (t, \operatorname {c o n c a t} [ z _ {t}, \mathcal {E} (x) ] + v ^ {\prime}, f ^ {\prime}) \| _ {2} ^ {2} \tag {4} \\ \end{array} +$$ + +To keep consistency with equation 1, we omit the Conv operation here. + +# 4.2. Bidirectional Interaction Module + +The design of BIM is depicted in Fig 4. It includes a self-attention block, two cross-attention blocks, and an MLP layer. The two inputs of BIM are the output $f$ from QFormer and the output $v$ from the image encoder. After bidirectional information interaction between $f$ and $v$ , BIM will eventually output $f'$ and $v'$ . In BIM, the process begins with $f$ undergoing a self-attention mechanism. After this, $f$ serves as a query to interact with the input $v$ , which acts as both key and value, through a cross-attention block. This interaction results in the generation of $f'$ via a pointwise MLP. Following the creation of $f'$ , it then serves as both key and value to interact with $v$ , which now acts as a query. This second cross-attention interaction leads to the production of $v'$ . + +![](images/f5c1c8473fe030a1883927546fec6f73a704f268f685ddf872dc104c62e009db.jpg) +Figure 3. The overall framework of SmartEdit. For the instruction, we first append the $r$ [IMG] tokens to the end of instruction $c$ . Together with image $x$ , they will be sent into LLaVA, which can then obtain the hidden states corresponding to these $r$ [IMG] tokens. Then the hidden state is sent into the QFormer and gets feature $f$ . Subsequently, the image feature $v$ output by the image encoder $E_{\phi}$ interacts with $f$ through a bidirectional interaction module (BIM), resulting in $f'$ and $v'$ . The $f'$ and $v'$ are input into the diffusion models to achieve the instruction-based image editing task. + +![](images/ea735c5f999e0935c5452baed4b6ecaf115dbec6013268642a1af6d0f22583d5.jpg) +Figure 4. The network design of the BIM Module. In this module, the input information $f$ and $v$ will undergo bidirectional information interaction through different cross-attention. + +As discussed in the introduction, the proposed BIM module reuses the image feature and inputs it as supplementary information into UNet. The implementation of two cross-attention blocks in this module facilitates a robust bidirectional information interaction between the image feature and the text feature. Compared to not adopting the BIM module or only fusing the image feature and text feature in one direction, SmartEdit which is equipped with the BIM module yields better results. The experimental comparison of different designs is shown in Section 5.3. + +# 4.3. Dataset Utilization Strategy + +During the training process of SmartEdit, two primary challenges emerge when solely utilizing datasets gathered from InstructPix2Pix and MagicBrush as the training set. The first challenge is that SmartEdit has a poor perception of position and concept. The second challenge is that, despite being equipped with MLLM, SmartEdit still has limited capability in scenarios that require reasoning. In summary, the effectiveness of SmartEdit in handling complex scenarios is limited if it is only trained on conventional editing datasets. After analysis, we have identified the causes of these issues. The first issue stems from the UNet in the diffusion model which lacks an understanding of perception and concepts, leading to SmartEdit's poor perception of position and con- + +cept. The second issue is that SmartEdit has limited exposure to editing data that requires reasoning abilities, which in turn limits its reasoning capabilities. + +To tackle the first issue, we incorporate the segmentation data into the training set. Such modifications significantly enhanced the perception capabilities of the SmartEdit model. Regarding the second issue, we take inspiration from LISA [19] that a minimal amount of reasoning segmentation data can efficiently activate MLLM's reasoning capacity. Guided by this insight, we establish a data production pipeline and synthesize 476 paired data (each sample contains original image, instruction, and synthetic target image) as a supplement to the training data. This synthetic editing dataset includes two major types of scenarios: complex understanding and reasoning scenarios. For complex understanding scenarios, the original image contains multiple objects and the corresponding instruction modifies the specific object based on various attributes (i.e., location, color, relative size, and in or outside the mirror). We specifically consider the mirror attribute because it is a typical example that requires a strong understanding of the scene (both inside and outside the mirror) to perform well. For reasoning scenarios, we involve complex reasoning cases that need world knowledge to identify the specific object. The effectiveness of this synthetic editing dataset and the impact of different datasets on the model's performance are detailed in Section 5.4. The details of the data production pipeline and some visual examples are described in the supplementary material. + +# 4.4. Reason-Edit for Better Evaluation + +To better evaluate existing instruction editing methods and SmartEdit's capabilities in complex understanding and reasoning scenarios, we collect an evaluation dataset, ReasonEdit. Reason-Edit consists of 219 image-text pairs. Con + +sistent with the synthetic training data pairs, Reason-Edit is also categorized in the same manner. Note that there is no overlap between the data in Reason-Edit and the synthetic training set. With Reason-Edit, we can thoroughly test the performance of instruction-based image editing models in terms of understanding and reasoning scenarios. We hope more researchers will pay attention to the capabilities of instruction-based image editing models from these perspectives, thereby fostering the practical application of instruction-based image editing methods. + +# 5. Experiments + +# 5.1. Experimental Setting + +Training Process and Implementation Details. The training process and implementation details of SmartEdit can be found in the supplementary material. + +Network Architecture. For the Large Language Model with visual input (e.g., LLaVA), we choose LLaVA-1.1-7b and LLaVA-1.1-13b as the base model. During training, the weights of LLaVA are frozen and we add LoRA for efficient fine-tuning. In LoRA, the values of the two parameters, dim and alpha, are 16 and 27, respectively. We expand the original LLM vocabulary with 32 new tokens. The QFormer is composed of 6-layer transformer [33] and 77 learnable query tokens. In the BIM module, there is a self-attention block, two cross-attention blocks, and an MLP layer. + +Training Datasets. For the training process of SmartEdit, the training data can be divided into 4 categories: (1) segmentation datasets, which include COCOStuff [3], RefCOCO [34], GRefCOCO [21], and the reasoning segmentation dataset from LISA [19]; (2) editing datasets, which involve InstructPix2Pix and MagicBrush; (3) visual question answering (VQA) dataset, which is the LLaVA-Instruct-150k dataset [22]; (4) synthetic editing dataset, where we collect a total of 476 paired data for complex understanding and reasoning scenarios. + +Evaluation Metrics. As we hope to only change the foreground of the image while keeping the background unchanged for editing, we adopt three metrics for the background area: PSNR, SSIM, and LPIPS [14, 37]. For the foreground area, we calculate CLIP Score [25] between the foreground area of the edited image and the GT label. The GT label is annotated manually. Among these four metrics, except for LPIPS where lower is better, the other three metrics are higher the better. While these metrics can reflect the performance to a certain extent, they are not entirely accurate. To provide a more accurate evaluation of the effects of edited images, we propose a metric for assessing editing accuracy. Specifically, we hire four workers to manually evaluate the results of these different methods on Reason-Edit. The evaluation criterion is whether the edited image aligns with the instruction. After obtaining the evaluation results + +from each worker, we average all the results to get the final metric result, which is Instruction-Alignment (Ins-align). + +# 5.2. Comparison with State-of-the-Art Methods + +We compare SmartEdit with existing SOTA instruction-based image editing methods, namely InstructPix2Pix, MagicBrush, and InstructDiffusion. Considering that these released models are trained on specific datasets, they would inevitably perform poorly if directly evaluated on ReasonEdit. To ensure a fair comparison, we fine-tune these methods on the same training set used by SmartEdit, and evaluate the fine-tuned models on Reason-Edit. The experimental results are shown in Tab. 1. From the quantitative results of the reasoning scenarios in the table, it can be observed that when we replace the clip text encoder in the diffusion model with LLaVA and adopt the proposed BIM module, both SmartEdit-7B and SmartEdit-13B achieve better results on these five metrics. This suggests that in scenarios requiring reasoning from instructions, a simple clip text encoder may struggle to understand the meaning of the instructions. However, the MLLM can fully utilize its powerful reasoning ability and world knowledge to correctly identify the corresponding objects and perform edits. + +The qualitative results further illustrate this point. As shown in Fig. 5, the first three examples are reasoning scenarios. In the first example, both SmartEdit-7B and SmartEdit-13B successfully identify the tool used for cutting fruit (knife) and remove it, while keeping the rest of the background unchanged. The second example can also be handled well by both of them. However, in the third example, we observe a difference in performance. Only SmartEdit-13B can accurately locate the object and perform the corresponding edits without altering other background areas. This suggests that in instruction-based image editing tasks that require reasoning, a more powerful MLLM model can effectively generalize its reasoning ability to this task. This observation aligns with the findings from LISA. + +However, for understanding scenarios, we observe a difference in performance between SmartEdit-7B and SmartEdit-13B when compared to InstructDiffusion on PSNR/SSIM/LPIPS. Specifically, SmartEdit-7B performs worse than InstructDiffusion, while SmartEdit-13B outperforms InstructDiffusion on these metrics. Upon further analysis of the qualitative results, as shown in the $4_{th}$ and $5_{th}$ rows of Fig. 5, we find that from a visual perspective, both SmartEdit-7B and SmartEdit-13B appear superior to InstructDiffusion. This suggests that the three metrics do not always align with human visual perception. We confirm this phenomenon in the supplementary material. From the result of the Ins-align metric, it can be observed that SmartEdit shows a significant improvement compared to previous instruction-based image editing methods. Also, when adopting a more powerful MLLM model, SmartEdit-13B performs better than SmartEdit-7B on Ins-align. + +"What is the tool that is used to cut fruits. Remove this tool." + +![](images/6bc85be1f86c219aba6e3151188cda4a67ea4be65a7debd04e9f34ab0188cda4.jpg) + +![](images/6e3589d589ebb96025d134f94b508cb62cf34b72e4da5bcc44bf2f6922e02286.jpg) + +![](images/e7d960d7226904cfbbaaf543777d81e3b6077efc3c0b044645854aa10a2cb8f0.jpg) + +![](images/a50b8238129b0a03ceab42d0e57ca8fb04caa4e2f9d251f3af614c81584c94d1.jpg) + +![](images/19d204169620e369a8e8718e561eee41c5be01cdfaf0d896acd98329528b8c81.jpg) + +![](images/7ff9e27bfcda6d1a644cd1d02cf9db3249b5e4e9b201b509ebd6304f7738c136.jpg) + +"Please replace food contains most vitamin with an orange." + +![](images/0f774d92aaa7abdff996f16194a2362b9f51a6a2d3cbb5d919997507fd845591.jpg) + +![](images/0d3c838fcf97c70e6113ecbad7cb13776d10669f95acbf5b9853c7c5684382c7.jpg) + +![](images/f4578766e3262c5022e76eadbcac7ce8494874e8df2aebc2e4cb82d63b4ff8c2.jpg) + +![](images/d689782519dfd8bcbf9cb55c7207a38c30a65ed3c93b0040db07a4395793a18d.jpg) + +![](images/0f71668069997a6876f717e88f133d1a0acfd20213f4ced493612ba6c97380cd.jpg) + +![](images/21ec1fa6696e197e1416d4810ebd7d29c7259855ef97dff24c7496e9676aa820.jpg) + +"Please remove the object that can be used to have meals." + +![](images/4c41a1b423755ec3450c5e042fcd3960f50f6c1dcd0e90c0f0a4a2e906ea1bcf.jpg) + +![](images/992e0ba2a22f7f64cf611f72b1146b869ce28e0d48217b1f7d82f4168bcc9d30.jpg) + +![](images/b3b2591e17801606f3a4b142808b6b3ec5aeef8511a7193830f5f8df912a2cac.jpg) + +![](images/8978e8bb43ef97b1a3a6ad9a2df334d2b5fa3085ed0ed1a34e00191e5ed57a5b.jpg) + +![](images/b5b9030de85756f023f6991f4e7c93ff20d28b666b731d4297e77e8c0bfe9742.jpg) + +![](images/833e91e275be906d8270c274d17a70cb75118ccf78eb2ac42bdfa233625f2d30.jpg) + +"Change the middle panda to a cat" + +![](images/c0a8d312101054ec2bd2bb8ae127c31450dda66fa6a95eefe28eb2c46f12957c.jpg) + +![](images/711110d5cedae2dfd6e212d647012dbd105bd404131ec578f02f5f2f83128fec.jpg) + +![](images/b4fb6b739a245ba0484ce270e6bf186e768d48d8ef8244388d64fe31ae108ae8.jpg) + +![](images/5530be603f1f4cd859944bb9a584d8f997e9907f7daf5fe0741434ddbb7a5030.jpg) + +![](images/36b37f9a4c1d8bacc82c1f2eff34b4ef8d97a97bea0a2c9fe620a2a57fa58c1b.jpg) + +![](images/ba332000f27e717434765d9db7ce7b88ecf6ca9bee74447f0cd0452ea7530477.jpg) + +"Change the cat in mirror to a tiger." + +![](images/aa8cbbf55762203fed39f44b51cb67c5900f6048c6fdf32f378421ffaefdd07e.jpg) +Input Image +Figure 5. Qualitative comparison on Reason-Edit. When compared to several existing instruction editing methods that have undergone further fine-tuning on our synthetic editing dataset, our approach demonstrates superior editing capabilities in complex scenarios. + +![](images/72afc780cb6a3e2710d85b807a95c02ae4ce83078e74e0c2cf5144d429118978.jpg) +InstructPix2Pix + +![](images/23bb399c88f20697a58cdc051f4c8aab6dd36a9a3a67bfef0562852dc5041db7.jpg) +MagicBrush + +![](images/b6a359ceb371dec36c97b12252d1148d654c1d22d6133f5c6814fcc79f6ff03b.jpg) +InstructDiffusion + +![](images/3f03be9e68a14c376f13b0064166210d11bc219cbc794a0a4ed2fe68545383ed.jpg) +SmartEdit-7B + +![](images/10505587151f1a37c2aa3705e9aca3f53a3069481b7e95990dd632b46fcf13ba.jpg) +SmartEdit-13B + +
MethodsUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
InstructPix2Pix21.5760.7210.08922.7620.53724.2340.7070.08319.4130.344
MagicBrush18.1200.680.14322.6200.29022.1010.6940.11319.7550.283
InstructDiffusion23.2580.7430.06723.0800.69721.4530.6660.11719.5230.483
SmartEdit-7B22.0490.7310.08723.6110.71225.2580.7420.05520.9500.789
SmartEdit-13B23.5960.7510.06823.5360.77125.7570.7470.05120.7770.817
+ +Table 1. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. All the methods we compared have been fine-tuned using the same training data as that used by SmartEdit. + +"What is the object that the dog's food should be put into? Remove this object." + +![](images/b822ded3281a0d80947b525ea25d15bff37f7667c456219b6c2b0d94601e97bb.jpg) +Figure 6. Demonstration of the effectiveness of the BIM Module. + +# 5.3. Ablation Study on BIM + +To validate the effectiveness of the bidirectional information interaction in our proposed BIM module, we conduct + +"Please replace the animal that is lying on the grass with a fox" + +![](images/8ec6bcbaa0d407c835ef1d35c20cd715362fe7b3e50030d2b27cfcaeb5e99c32.jpg) + +![](images/2be4fdc566c0dcaf3d15f1fa675917f6949e1db66b28fcc18b85a0288bd70783.jpg) + +![](images/f12255bdd968ef068497398649c39e040706aa377cf9603ddb9e7d83282dcb57.jpg) + +![](images/7f4d9f98dfe1bd8db79287c372f9acaddf14196de5e933be7d5536a230c0f4dd.jpg) + +![](images/08794862aa30241b1998a302b1ebffa25d9475e8ef07138bd812124e064bf0a7.jpg) + +"Change the red strawberry to a white pumpkin" + +![](images/5cdc4a37c81cf54440b9de80886ba5f1d95246442498591d68cfdb8abdcad7cc.jpg) +Input Image +Figure 7. Demonstration of the significance of joint training with multiple datasets. + +![](images/576c36cdfa99cbc7c29ae4a4740e4d733a565cfff3c4a76ff748c3fa301beaa4.jpg) +Edit + +![](images/dfb36085eba9a4b01687154d71952a07eebdb5985d8efe147afce5863f10708d.jpg) +Edit+Seg + +![](images/fd7eddfa0d375c4c4659189f784d04640aa2afd84e6863fa3dc149d7b5e47bea.jpg) +Edit+Reason-Edit + +![](images/937a9798d99aa9d4fe48b25bb9ba17a3ef4926b3d20301e5a3326e1449f1ca41.jpg) +Total + +comparative experiments on the SmartEdit-7B model. The details are presented in Tab. 2. The first experiment, denoted as Exp 1, aims to verify the necessity of the information in + +
Exp IDPlainSimpleCABIMUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓20.9750.7130.10823.360.69523.8480.7250.07420.330.694
2✓19.5570.6920.12623.660.69223.5080.7160.08120.170.722
3✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
+ +Table 2. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B. + +
Exp IDEditSegmentationSynthetic editing datasetUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓17.5680.6640.17122.790.20122.4000.7060.10219.220.233
2✓✓18.9600.6900.14322.830.36121.7740.6930.11619.820.311
3✓✓19.5620.7020.11122.320.44023.5950.7150.07920.430.567
4✓✓✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
+ +Table 3. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B. + +teraction proposed in the BIM module. In this experiment, we remove the BIM module from the SmartEdit-7B model and directly apply the text feature output from QFormer to the diffusion model. The second experiment, denoted as Exp 2, aims to verify the necessity of the bidirectional information interaction proposed in the BIM module. Specifically, all blocks are discarded except for the cross-attention block on the image feature branch. Therefore, the information from the text feature of QFormer is unidirectionally applied to the image feature. These two experiments are designed to test the impact of removing or altering the BIM module on the performance of SmartEdit-7B in complex understanding and reasoning scenarios. As shown in Tab. 2, if the BIM module is removed, there is a significant decline in all metrics for both understanding and reasoning scenarios. When the BIM module is replaced with the SimpleCA module, we observe a noticeable decline in all metrics, except for the clip score in understanding scenarios. Further comparison of the qualitative results in Fig. 6 confirms that the introduction of the BIM indeed enhances SmartEdit's instruction editing performance. To be specific, when we do not use the BIM module (i.e., plain), the dog bowl (first row) turns into other objects (marked with a red circle), and the fork (second row) does not change at all. After using SimpleCA, it can be found that the dog bowl and fork have been partially removed. When SmartEdit is equipped with BIM, the dog bowl and fork can be well removed. + +# 5.4. Ablation Study on Dataset Usage + +In Section 4.3, we explore an efficient strategy for data utilization, aiming to enhance SmartEdit's capabilities in handling complex understanding and reasoning scenarios. During the training process of SmartEdit, we employ the common editing dataset, segmentation dataset, and the synthetic editing dataset. To validate the significance of these different data types in boosting SmartEdit's performance, we conduct a series of ablation studies, as detailed in Tab. 3. These experiments are based on the SmartEdit-7B model. In Exp 1, we train the model using only the editing data. In Exp 2, we incorporate segmentation data into the training + +process, building upon Exp 1. In Exp 3, we further add the synthetic editing data to the basis established in Exp 1. The quantitative results of these experiments reveal that segmentation data and synthetic editing data play complementary roles in enhancing the model's performance. This is further corroborated by the visual comparison in Fig. 7. For reasoning scenarios, when adopting only the editing dataset or combining the editing dataset and the segmentation dataset, the performance of SmartEdit is inferior. When the synthetic editing data is incorporated into the editing dataset, SmartEdit can accurately locate the specific objects. However, the output of SmartEdit is also mediocre (the generated fox has obvious artifacts, and two pumpkins are generated). When all these datasets are combined as the training set, the results generated by SmartEdit have a further significant improvement in visual effects. + +# 6. Conclusion + +In conclusion, this paper presents SmartEdit, a novel approach to instruction-based image editing that enhances understanding and reasoning capabilities by incorporating the LLMs with visual inputs. By introducing the Bidirectional Interaction Module (BIM), we have overcome challenges associated with the direct integration of LLMs and diffusion models in complex reasoning scenarios. Our data utilization strategy, which incorporates perception data and complex instruction editing data, effectively enhances SmartEdit's capabilities in handling complex understanding and reasoning scenarios. Evaluation on our newly constructed dataset, Reason-Edit, shows that SmartEdit outperforms previous methods, marking a significant step towards practical applications of complex instruction-based image editing. + +Acknowledgement. The work is partially supported by the Young Scientists Fund of the National Natural Science Foundation of China under grant No. 62106154, the Natural Science Foundation of Guangdong Province, China (General Program) under grant No.2022A1515011524, Shenzhen Science and Technology Program JCYJ20220818103001002 and JCYJ20220818103006012, and the Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong (Shenzhen). + +# References + +[1] Tim Brooks, Aleksander Holynski, and Alexei A Efros. Instructpix2pix: Learning to follow image editing instructions. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 18392-18402, 2023. 2, 3 +[2] Tom Brown, Benjamin Mann, Nick Ryder, Melanie Subbiah, Jared D Kaplan, Prafulla Dhariwal, Arvind Neelakantan, Pranav Shyam, Girish Sastry, Amanda Askell, et al. Language models are few-shot learners. 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Springer, 2016. 6 +[35] Lili Yu, Bowen Shi, Ramakanth Pasunuru, Benjamin Muller, Olga Golovneva, Tianlu Wang, Arun Babu, Binh Tang, Brian Karrer, Shelly Sheynin, et al. Scaling autoregressive multimodal models: Pretraining and instruction tuning. arXiv preprint arXiv:2309.02591, 2023. 3 +[36] Kai Zhang, Lingbo Mo, Wenhu Chen, Huan Sun, and Yu Su. Magicbrush: A manually annotated dataset for instruction-guided image editing. arXiv preprint arXiv:2306.10012, 2023. 2, 3 +[37] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 586-595, 2018. 6 +[38] Enshen Zhou, Yiran Qin, Zhenfei Yin, Yuzhou Huang, Ruimao Zhang, Lu Sheng, Yu Qiao, and Jing Shao. Minedreamer: Learning to follow instructions via chain-of-imagination for simulated-world control. arXiv preprint arXiv:2403.12037, 2024. 3 +[39] Deyao Zhu, Jun Chen, Xiaoqian Shen, Xiang Li, and Mohamed Elhoseiny. 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We propose SmartEdit, an instruction-based image editing model that leverages Multimodal Large Language Models (MLLMs) to enhance the understanding and reasoning capabilities of instruction-based editing methods. With the specialized design, our SmartEdit is capable of handling complex understanding (the instructions that contain various object attributes like location, relative size, color, and in or outside the mirror) and reasoning scenarios." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 540, + 192, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 540, + 192, + 552 + ], + "spans": [ + { + "bbox": [ + 143, + 540, + 192, + 552 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 563, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 288, + 684 + ], + "type": "text", + "content": "Current instruction-based image editing methods, such as InstructPix2Pix, often fail to produce satisfactory results in complex scenarios due to their dependence on the simple CLIP text encoder in diffusion models. To rectify this, this paper introduces SmartEdit, a novel approach of instruction-based image editing that leverages Multimodal Large Language Models (MLLMs) to enhance its understanding and reasoning capabilities. However, direct integration of these elements still faces challenges in situations requiring complex reasoning. To mitigate this, we" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 540, + 547, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 547, + 709 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 547, + 709 + ], + "type": "text", + "content": "propose a Bidirectional Interaction Module (BIM) that enables comprehensive bidirectional information interactions between the input image and the MLLM output. During training, we initially incorporate perception data to boost the perception and understanding capabilities of diffusion models. Subsequently, we demonstrate that a small amount of complex instruction editing data can effectively stimulate SmartEdit's editing capabilities for more complex instructions. We further construct a new evaluation dataset, Reason-Edit, specifically tailored for complex instruction-based image editing. Both quantitative and qualitative results on this evaluation dataset indicate that our SmartEdit surpasses previous methods, paving the way for the practical application of complex instruction-based image editing." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "* Equal contribution † Corresponding author # Interns in ARC Lab, Tencent PCG" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8362" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 49, + 72, + 127, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 72, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 127, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 49, + 91, + 286, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 91, + 286, + 222 + ], + "spans": [ + { + "bbox": [ + 49, + 91, + 286, + 222 + ], + "type": "text", + "content": "Text-to-image synthesis [8, 13, 23, 26, 27, 29] has experienced significant advancements in recent years, thanks to the development of diffusion models. These methods have enabled the generation of images that are not only consistent with natural language descriptions, but also align with human perception and preferences, marking a substantial leap forward in the field. Instruction-based image editing methods [1, 36], represented by InstructPix2Pix, leverage pre-trained text-to-image diffusion models as priors. This allows users to conveniently and effortlessly modify images through natural language instructions for ordinary users." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 223, + 286, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 223, + 286, + 460 + ], + "spans": [ + { + "bbox": [ + 49, + 223, + 286, + 460 + ], + "type": "text", + "content": "While existing instruction-based image editing methods can handle simple instructions effectively, they often fall short when dealing with complex scenarios, which require the model to have a more powerful understanding and reasoning capabilities. As depicted in Fig. 1, there are two common types of complex scenarios. The first is when the original image contains multiple objects, and the instruction modifies only one of these objects through certain attributes (such as location, relative size, color, in or outside the mirror). The other is when world knowledge is needed to identify the object to be edited (such as the object that can tell the time). We define these two types as complex understanding scenarios and complex reasoning scenarios, respectively. Handling these two scenarios is crucial for practical instruction editing, but existing instruction-based image editing methods probably fail in these scenarios (as shown in Fig. 2). In this paper, we attempt to identify the reasons why existing instruction-based image editing methods fail in these scenarios, and try to tackle the challenge in these scenarios." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 49, + 463, + 286, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 463, + 286, + 617 + ], + "spans": [ + { + "bbox": [ + 49, + 463, + 286, + 617 + ], + "type": "text", + "content": "The first reason why existing instruction-based image editing methods fail in these scenarios is that they typically rely on a simple CLIP text encoder [25] in diffusion models (e.g., Stable Diffusion) to process the instructions. Under this circumstance, these models struggle to 1) understand and reason through the instructions, and 2) integrate the image to comprehend the instructions. To address these limitations, we introduce the Multimodal Large Language Models (MLLMs) (e.g., LLaVA) [22, 39] into instruction-based editing models. Our method, SmartEdit, jointly optimizes MLLMs and diffusion models, leveraging the powerful reasoning capabilities of MLLMs to facilitate instruction-based image editing task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 618, + 286, + 712 + ], + "type": "text", + "content": "While substituting the CLIP encoder in the diffusion model with MLLMs can alleviate some problems, this approach still falls short when it comes to examples that necessitate complex understanding and reasoning. This is because the input image to edit (original image) is integrated into the UNet of the Stable Diffusion model through a straightforward concatenation, which is further interacted with MLLM outputs through a cross-attention operation. In" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 308, + 72, + 544, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 72, + 544, + 191 + ], + "spans": [ + { + "bbox": [ + 308, + 72, + 544, + 191 + ], + "type": "text", + "content": "this setup, the image features serve as the query, and MLLM outputs act as the key and value. This means that the MLLM outputs unilaterally modulate and interact with the image feature, which affects the results. To alleviate this issue, we further propose a Bidirectional Interaction Module (BIM). This module reuses the image information extracted by the LLaVA's visual encoder from the input image. It also facilitates a comprehensive bidirectional information interaction between this image and the MLLM output, enabling the model to perform better in complex scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 308, + 193, + 544, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 193, + 544, + 323 + ], + "spans": [ + { + "bbox": [ + 308, + 193, + 544, + 323 + ], + "type": "text", + "content": "The second reason contributing to the failure of existing instruction-based editing methods is the absence of specific data. When solely training on editing datasets, such as the datasets used in Instructpix2pix [1] and MagicBrush [36], SmartEdit also struggles to handle scenarios requiring complex reasoning and understanding. This is because SmartEdit has not been exposed to data from these scenarios. One straightforward approach is to generate a substantial amount of paired data similar to those scenarios. However, this method is excessively expensive because the cost of generating data for these scenarios is high." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 325, + 544, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 325, + 544, + 467 + ], + "spans": [ + { + "bbox": [ + 308, + 325, + 544, + 467 + ], + "type": "text", + "content": "In this paper, we find that there are two keys to compensate the insufficiency of specific editing data. The first is to enhance the perception capabilities of UNet [28], and the second is to stimulate the model capacity in those scenarios with a few high-quality examples. Correspondingly, we 1) incorporate the perception-related data (e.g., segmentation) into the model's training. 2) synthesize a few high-quality paired data with complex instructions to fine-tune our SmartEdit (similar to LISA [19]). In this way, SmartEdit not only reduces the reliance on paired data under complex scenarios but also effectively stimulates its ability to handle these scenarios." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 308, + 470, + 544, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 470, + 544, + 635 + ], + "spans": [ + { + "bbox": [ + 308, + 470, + 544, + 635 + ], + "type": "text", + "content": "Equipped with both the model designs and the data utilization strategy, SmartEdit can understand complex instructions, surpassing the scope that previous instruction editing methods can do. To better evaluate the understanding and reasoning ability of instruction-based image editing methods, we collect the Reason-Edit dataset, which contains a total of 219 image-text pairs. Note that there is no overlap between the Reason-Edit dataset and the small-amount high-quality synthesized training data pairs. Based on the Reason-Edit dataset, we evaluate existing instruction-based image editing methods comprehensively. Both the quantitative and qualitative results on the ReasonEdit dataset indicate that SmartEdit significantly outperforms previous instruction-based image editing methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 320, + 638, + 501, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 638, + 501, + 649 + ], + "spans": [ + { + "bbox": [ + 320, + 638, + 501, + 649 + ], + "type": "text", + "content": "In summary, our contributions are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 308, + 654, + 544, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 308, + 654, + 544, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 654, + 544, + 700 + ], + "spans": [ + { + "bbox": [ + 308, + 654, + 544, + 700 + ], + "type": "text", + "content": "1. We analyze and focus on the performance of instruction-based image editing methods in more complex instructions. These complex scenarios have often been overlooked and less explored in past research." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 308, + 702, + 544, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 702, + 544, + 712 + ], + "spans": [ + { + "bbox": [ + 308, + 702, + 544, + 712 + ], + "type": "text", + "content": "2. We leverage MLLMs to better comprehend instructions." + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 750, + 314, + 757 + ], + "type": "text", + "content": "8363" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 113, + 143, + 478, + 153 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 143, + 478, + 153 + ], + "spans": [ + { + "bbox": [ + 113, + 143, + 478, + 153 + ], + "type": "text", + "content": "Figure 2. For more complex instructions or scenarios, InstructPix2Pix fails to follow the instructions." + } + ] + } + ], + "index": 6, + "type": "text" + }, + { + "bbox": [ + 59, + 159, + 286, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 159, + 286, + 195 + ], + "spans": [ + { + "bbox": [ + 59, + 159, + 286, + 195 + ], + "type": "text", + "content": "To further improve the performance, we propose a Bidirectional Interaction Module to facilitate the interaction of information between text and image features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 196, + 286, + 338 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 196, + 286, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 196, + 286, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 196, + 286, + 278 + ], + "type": "text", + "content": "3. We propose a new dataset utilization strategy to enhance the performance of SmartEdit in complex scenarios. In addition to using conventional editing data, we introduce perception-related data to strengthen the perceptual ability of UNet in the diffusion process. Besides, we also add a small amount of synthetic editing data to further stimulate the model's reasoning ability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 279, + 286, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 279, + 286, + 338 + ], + "spans": [ + { + "bbox": [ + 47, + 279, + 286, + 338 + ], + "type": "text", + "content": "4. An evaluation dataset, Reason-Edit, is specifically collected for evaluating the performance of instruction-based image editing tasks in complex scenarios. Both qualitative and quantitative results on Reason-Edit demonstrate the superiority of SmartEdit." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 351, + 134, + 362 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 351, + 134, + 362 + ], + "spans": [ + { + "bbox": [ + 47, + 351, + 134, + 362 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 371, + 245, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 371, + 245, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 245, + 383 + ], + "type": "text", + "content": "2.1. Image Editing with Diffusion Models." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 389, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 286, + 653 + ], + "type": "text", + "content": "Pretrained text-to-image diffusion models [8, 13, 23, 26, 27, 29] can strongly assist image editing task. Instruction-based image editing task [1, 4, 11, 12, 16, 17, 32, 36, 38] requires users to provide an instruction, which converts the original image to a newly designed image that matches the given instruction. Some methods can achieve this by utilizing a tuning-free approach. For example, Prompt-to-Prompt [12] suggests modifying the cross-attention maps by comparing the original input caption with the revised caption. MasaCtrl [4] converts existing self-attention in diffusion models into mutual self-attention, which can help query correlated local contents and textures from source images for consistency. In addition, due to the scarcity of paired image-instruction editing datasets, the pioneering work InstructPix2Pix [1] introduces a large-scale vision-language image editing datasets created by fine-tuned GPT-3 [2] and Prompt-to-Prompt with stable diffusion, and further finetunes the UNet [28], which can edit images by providing a simple instruction. To enhance the editing effect of InstructPix2Pix on real images, MagicBrush [36] further provides a large-scale and manually annotated dataset for instruction-guided real image editing." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 286, + 713 + ], + "type": "text", + "content": "The recent work, InstructDiffusion [11], also adopts the network design of InstructPix2Pix and focuses on unifying vision tasks in a joint training manner. By taking advantage of multiple different datasets, it can handle a variety of vision tasks, including understanding tasks (such as segmen" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "content": "tation and keypoint detection) and generative tasks (such as editing and enhancement). Compared with InstructDiffusion, our primary focus is on the field of instruction-based image editing, especially for complex understanding and reasoning scenarios. In these scenarios, InstructDiffusion typically generates inferior results." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 241, + 460, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 241, + 460, + 253 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 460, + 253 + ], + "type": "text", + "content": "2.2. LLM with Diffusion Models" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 261, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 261, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 545, + 559 + ], + "type": "text", + "content": "The exceptional open-sourced LLaMA [6, 31] significantly enhances the performance of vision tasks with the aid of Large Language Models (LLMs). Pioneering works such as LLaVA and MiniGPT-4 have improved image-text alignment through instruction-tuning. While numerous MLLM-based [7, 22, 24, 39] studies have demonstrated their robust capabilities across a variety of tasks, primarily those reliant on text generation (e.g., human-robot interaction, complex reasoning, science question answering, etc.), GILL [18] serves as a bridge between MLLMs and diffusion models. It learns to process images with LLMs and is capable of generating coherent images based on the input texts. SEED [9] presents an innovative image tokenizer to enable LLM to process and generate images and text concurrently. SEED-2 [10] further refines the tokenizer by aligning the generation embedding with the image embedding of unCLIP-SD, which allows for better preservation of rich visual semantics and reconstruction of more realistic images. Emu [30] can be characterized as a multimodal generalist, trained with the next-token-prediction objective. CM3Leon [35] proposes a multi-modal language model that is capable of executing text-to-image and image-to-text generation. It employs the CM3 multi-modal architecture that is fine-tuned on diverse instruction-style data, and utilizes a training method adapted from text-only language models." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 572, + 382, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 572, + 382, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 572, + 382, + 586 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "The goal of instruction-based image editing is to make specific modifications to an input image " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " based on instructions " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "c_{T}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", resulting in the target image " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". InstructPix2Pix, which is based on latent diffusion, is a seminal work in this field. For the target image " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " and an encoder " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{E}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", the diffusion process introduces noise to the encoded latent " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "z = \\mathcal{E}(y)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", resulting in a noisy latent " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", with the noise level increasing over timesteps " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "t \\in T" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". A UNet " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\delta}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " is then trained to predict the noise added to the noisy latent " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", given the image condition " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "c_{x}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " and text instruction condition " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "c_{T}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "c_{x} = \\mathcal{E}(x)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": ". The" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 118, + 72, + 199, + 79 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 72, + 199, + 79 + ], + "spans": [ + { + "bbox": [ + 118, + 72, + 199, + 79 + ], + "type": "text", + "content": "\"Change the dog in mirror to a lion\"" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 205, + 72, + 304, + 79 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 205, + 72, + 304, + 79 + ], + "spans": [ + { + "bbox": [ + 205, + 72, + 304, + 79 + ], + "type": "text", + "content": "\"Change the black raspberry to a tangerine\"" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 331, + 72, + 445, + 79 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 72, + 445, + 79 + ], + "spans": [ + { + "bbox": [ + 331, + 72, + 445, + 79 + ], + "type": "text", + "content": "\"Please remove the tool that is used to cut cakes.\"" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 118, + 81, + 200, + 139 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 81, + 200, + 139 + ], + "spans": [ + { + "bbox": [ + 118, + 81, + 200, + 139 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 203, + 83, + 307, + 137 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 203, + 83, + 307, + 137 + ], + "spans": [ + { + "bbox": [ + 203, + 83, + 307, + 137 + ], + "type": "text", + "content": "中" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 309, + 81, + 474, + 139 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 81, + 474, + 139 + ], + "spans": [ + { + "bbox": [ + 309, + 81, + 474, + 139 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8364" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": "image condition is incorporated by directly concatenating " + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "c_{x}" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": ". The specific objective of latent diffusion is as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 87, + 110, + 287, + 139 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 110, + 287, + 139 + ], + "spans": [ + { + "bbox": [ + 87, + 110, + 287, + 139 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ], c _ {T}) \\| _ {2} ^ {2} \\tag {1} \\\\ \\end{array}", + "image_path": "0e72e07dd156aef707b58826a9424a7e2a54caa4bc84ba3978e0d5795127e775.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": " is the unscaled noise, " + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": " is the sampling step, " + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": " is latent noise at step " + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(x)" + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": " is the image condition, and " + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "inline_equation", + "content": "c_{T}" + }, + { + "bbox": [ + 47, + 143, + 287, + 190 + ], + "type": "text", + "content": " is the text instruction condition. The concat corresponds to the concatenation operation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 190, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 334 + ], + "type": "text", + "content": "Although InstructPix2Pix has some effectiveness in instruction editing, its performance is limited when dealing with complex understanding and reasoning scenarios. To address this issue, we introduce a Multimodal Large Language Model (MLLM) into the network architecture and propose a Bidirectional Interaction Module (BIM) to implement bidirectional information interaction between the MLLM output and image information. In addition, we also explore the data utilization strategy and find that perception-related data and a small amount of complex editing data are crucial for enhancing model's performance. We provide detailed descriptions of these aspects in the next section." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 344, + 103, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 103, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 103, + 357 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 496 + ], + "type": "text", + "content": "In this paper, we introduce SmartEdit, specifically designed to handle complex instruction editing scenarios. In this section, we first provide a detailed overview of the framework of SmartEdit (Section 4.1). Then, we delve into the Bidirectional Interaction Module (Section 4.2). In Section 4.3, we discuss how to enhance the perception and understanding capabilities of UNet in the diffusion model and stimulate the ability of MLLMs to handle complex scenarios. Finally, We introduce Reason-Edit, which is primarily used to evaluate the ability of instruction-based image editing methods toward complex scenarios. (Section 4.4)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 503, + 211, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 503, + 211, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 503, + 211, + 514 + ], + "type": "text", + "content": "4.1. The Framework of SmartEdit" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": "Given an image " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and instruction " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ", which is tokenized as " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "(s_1, \\dots, s_T)" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ", our goal is to obtain the target image " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " based on " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ". As shown in Fig 3, the image " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " is first processed by the image encoder and FC layer, resulting in " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "v_{\\mu}(x)" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "v_{\\mu}(x)" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " is sent into the LLM along with the token embedding " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "(s_1, \\dots, s_T)" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ". The output of the LLM is discrete tokens, which cannot be used as the input for subsequent modules. Therefore, we take the hidden states corresponding to these discrete tokens as the input for the following modules. To jointly optimize LLaVA and the diffusion model, following GILL [18], we expand the original LLM vocabulary with " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " new tokens " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "[\\mathrm{IMG}_1], \\dots, [\\mathrm{IMG}_r]" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and append the " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " [IMG] tokens to the end of instruction " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ". To be specific, we incorporate a trainable matrix " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " into the embedding matrix of the LLM, which represents the " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " [IMG] token embeddings. Subsequently, we minimize the negative log-likelihood of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "generated " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " [IMG] tokens, conditioned on tokens that have been generated previously:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 337, + 99, + 545, + 142 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 99, + 545, + 142 + ], + "spans": [ + { + "bbox": [ + 337, + 99, + 545, + 142 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\mathrm {L L M}} (c) = - \\sum_ {i = 1} ^ {r} \\log p _ {\\{\\theta \\cup \\mathbf {E} \\}} ([ \\operatorname {I M G} _ {i} ] \\mid v _ {\\mu} (x), \\\\ \\left. s _ {1}, \\dots , s _ {T}, \\left[ \\mathrm {I M G} _ {1} \\right], \\dots , \\left[ \\mathrm {I M G} _ {i - 1} \\right]\\right) \\tag {2} \\\\ \\end{array}", + "image_path": "a5d8d0918362edd8c9bf865381d270bafaaf8b11b8f86d31a6fd9903becf9e8d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "text", + "content": "The majority of parameters " + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "text", + "content": " in the LLM are kept frozen and we utilize LoRA [15] to carry out efficient fine-tuning. We take the hidden states " + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "text", + "content": " corresponding to the " + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 151, + 545, + 198 + ], + "type": "text", + "content": " [IMG] tokens as the input for the next module." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": "Considering the discrepancy between the feature spaces of the hidden states in the LLM and the clip text encoder, we need to align the hidden states " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " to the clip text encoder space. Inspired by BLIP2 [20] and DETR [5], we adopt the QFormer " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "Q_{\\beta}" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " with 6-layer transformer [33] and " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " learnable queries, obtaining feature " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": ". Subsequently, the image feature " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " output by the image encoder " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "E_{\\phi}" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " interacts with " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " through a bidirectional interaction module (BIM), resulting in " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "inline_equation", + "content": "v'" + }, + { + "bbox": [ + 304, + 199, + 545, + 307 + ], + "type": "text", + "content": ". The mentioned process is represented as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 384, + 312, + 545, + 369 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 312, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 384, + 312, + 545, + 369 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} h = \\operatorname {L L a V A} (x, c), \\\\ \\begin{array}{l} f = Q _ {\\beta} (h), \\\\ F _ {n} (h) \\end{array} \\tag {3} \\\\ v = E _ {\\phi} (x), \\\\ f ^ {\\prime}, v ^ {\\prime} = \\operatorname {B I M} (f, v) \\\\ \\end{array}", + "image_path": "5620842d01f37aec1346904d69bce476a52a1e42b4132a4997d7d53c2b2de25c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "text", + "content": "For the diffusion model, following the design of Instructpix2pix, we concat the encoded image latent " + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(x)" + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "text", + "content": " and noisy latent " + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "inline_equation", + "content": "z_{t}" + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "text", + "content": ". Unlike Instructpix2pix, we use " + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "text", + "content": " as the key and value in UNet, and combine " + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "inline_equation", + "content": "v'" + }, + { + "bbox": [ + 304, + 376, + 545, + 447 + ], + "type": "text", + "content": " into the features before entering UNet in a residual manner. The specific process can be formulated as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 347, + 455, + 545, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 455, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 347, + 455, + 545, + 484 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ] + v ^ {\\prime}, f ^ {\\prime}) \\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}", + "image_path": "dcdc95f10e5f52366fdbd84aebab7a5f2dfe47b04081b998392e1ad71567704e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 495, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 545, + 518 + ], + "type": "text", + "content": "To keep consistency with equation 1, we omit the Conv operation here." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 527, + 484, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 527, + 484, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 527, + 484, + 539 + ], + "type": "text", + "content": "4.2. Bidirectional Interaction Module" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "The design of BIM is depicted in Fig 4. It includes a self-attention block, two cross-attention blocks, and an MLP layer. The two inputs of BIM are the output " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " from QFormer and the output " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " from the image encoder. After bidirectional information interaction between " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", BIM will eventually output " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v'" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ". In BIM, the process begins with " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " undergoing a self-attention mechanism. After this, " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " serves as a query to interact with the input " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", which acts as both key and value, through a cross-attention block. This interaction results in the generation of " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": " via a pointwise MLP. Following the creation of " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", it then serves as both key and value to interact with " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": ", which now acts as a query. This second cross-attention interaction leads to the production of " + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "inline_equation", + "content": "v'" + }, + { + "bbox": [ + 304, + 545, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8365" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 114, + 70, + 481, + 211 + ], + "blocks": [ + { + "bbox": [ + 114, + 70, + 481, + 211 + ], + "lines": [ + { + "bbox": [ + 114, + 70, + 481, + 211 + ], + "spans": [ + { + "bbox": [ + 114, + 70, + 481, + 211 + ], + "type": "image", + "image_path": "f5c1c8473fe030a1883927546fec6f73a704f268f685ddf872dc104c62e009db.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": "Figure 3. The overall framework of SmartEdit. For the instruction, we first append the " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " [IMG] tokens to the end of instruction " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": ". Together with image " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": ", they will be sent into LLaVA, which can then obtain the hidden states corresponding to these " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " [IMG] tokens. Then the hidden state is sent into the QFormer and gets feature " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": ". Subsequently, the image feature " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " output by the image encoder " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "E_{\\phi}" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " interacts with " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " through a bidirectional interaction module (BIM), resulting in " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "v'" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": ". The " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "f'" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "inline_equation", + "content": "v'" + }, + { + "bbox": [ + 46, + 216, + 547, + 271 + ], + "type": "text", + "content": " are input into the diffusion models to achieve the instruction-based image editing task." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 91, + 282, + 245, + 358 + ], + "blocks": [ + { + "bbox": [ + 91, + 282, + 245, + 358 + ], + "lines": [ + { + "bbox": [ + 91, + 282, + 245, + 358 + ], + "spans": [ + { + "bbox": [ + 91, + 282, + 245, + 358 + ], + "type": "image", + "image_path": "ea735c5f999e0935c5452baed4b6ecaf115dbec6013268642a1af6d0f22583d5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "lines": [ + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "type": "text", + "content": "Figure 4. The network design of the BIM Module. In this module, the input information " + }, + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 366, + 288, + 400 + ], + "type": "text", + "content": " will undergo bidirectional information interaction through different cross-attention." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 406, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 525 + ], + "type": "text", + "content": "As discussed in the introduction, the proposed BIM module reuses the image feature and inputs it as supplementary information into UNet. The implementation of two cross-attention blocks in this module facilitates a robust bidirectional information interaction between the image feature and the text feature. Compared to not adopting the BIM module or only fusing the image feature and text feature in one direction, SmartEdit which is equipped with the BIM module yields better results. The experimental comparison of different designs is shown in Section 5.3." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 537, + 200, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 537, + 200, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 537, + 200, + 551 + ], + "type": "text", + "content": "4.3. Dataset Utilization Strategy" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": "During the training process of SmartEdit, two primary challenges emerge when solely utilizing datasets gathered from InstructPix2Pix and MagicBrush as the training set. The first challenge is that SmartEdit has a poor perception of position and concept. The second challenge is that, despite being equipped with MLLM, SmartEdit still has limited capability in scenarios that require reasoning. In summary, the effectiveness of SmartEdit in handling complex scenarios is limited if it is only trained on conventional editing datasets. After analysis, we have identified the causes of these issues. The first issue stems from the UNet in the diffusion model which lacks an understanding of perception and concepts, leading to SmartEdit's poor perception of position and con-" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 285, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 321 + ], + "type": "text", + "content": "cept. The second issue is that SmartEdit has limited exposure to editing data that requires reasoning abilities, which in turn limits its reasoning capabilities." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 323, + 546, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 546, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 546, + 634 + ], + "type": "text", + "content": "To tackle the first issue, we incorporate the segmentation data into the training set. Such modifications significantly enhanced the perception capabilities of the SmartEdit model. Regarding the second issue, we take inspiration from LISA [19] that a minimal amount of reasoning segmentation data can efficiently activate MLLM's reasoning capacity. Guided by this insight, we establish a data production pipeline and synthesize 476 paired data (each sample contains original image, instruction, and synthetic target image) as a supplement to the training data. This synthetic editing dataset includes two major types of scenarios: complex understanding and reasoning scenarios. For complex understanding scenarios, the original image contains multiple objects and the corresponding instruction modifies the specific object based on various attributes (i.e., location, color, relative size, and in or outside the mirror). We specifically consider the mirror attribute because it is a typical example that requires a strong understanding of the scene (both inside and outside the mirror) to perform well. For reasoning scenarios, we involve complex reasoning cases that need world knowledge to identify the specific object. The effectiveness of this synthetic editing dataset and the impact of different datasets on the model's performance are detailed in Section 5.4. The details of the data production pipeline and some visual examples are described in the supplementary material." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 645, + 489, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 645, + 489, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 645, + 489, + 658 + ], + "type": "text", + "content": "4.4. Reason-Edit for Better Evaluation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": "To better evaluate existing instruction editing methods and SmartEdit's capabilities in complex understanding and reasoning scenarios, we collect an evaluation dataset, ReasonEdit. Reason-Edit consists of 219 image-text pairs. Con" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8366" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": "sistent with the synthetic training data pairs, Reason-Edit is also categorized in the same manner. Note that there is no overlap between the data in Reason-Edit and the synthetic training set. With Reason-Edit, we can thoroughly test the performance of instruction-based image editing models in terms of understanding and reasoning scenarios. We hope more researchers will pay attention to the capabilities of instruction-based image editing models from these perspectives, thereby fostering the practical application of instruction-based image editing methods." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 206, + 128, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 206, + 128, + 220 + ], + "spans": [ + { + "bbox": [ + 47, + 206, + 128, + 220 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 227, + 170, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 170, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 170, + 239 + ], + "type": "text", + "content": "5.1. Experimental Setting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 243, + 287, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 287, + 280 + ], + "type": "text", + "content": "Training Process and Implementation Details. The training process and implementation details of SmartEdit can be found in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 399 + ], + "type": "text", + "content": "Network Architecture. For the Large Language Model with visual input (e.g., LLaVA), we choose LLaVA-1.1-7b and LLaVA-1.1-13b as the base model. During training, the weights of LLaVA are frozen and we add LoRA for efficient fine-tuning. In LoRA, the values of the two parameters, dim and alpha, are 16 and 27, respectively. We expand the original LLM vocabulary with 32 new tokens. The QFormer is composed of 6-layer transformer [33] and 77 learnable query tokens. In the BIM module, there is a self-attention block, two cross-attention blocks, and an MLP layer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 287, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 520 + ], + "type": "text", + "content": "Training Datasets. For the training process of SmartEdit, the training data can be divided into 4 categories: (1) segmentation datasets, which include COCOStuff [3], RefCOCO [34], GRefCOCO [21], and the reasoning segmentation dataset from LISA [19]; (2) editing datasets, which involve InstructPix2Pix and MagicBrush; (3) visual question answering (VQA) dataset, which is the LLaVA-Instruct-150k dataset [22]; (4) synthetic editing dataset, where we collect a total of 476 paired data for complex understanding and reasoning scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 288, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. As we hope to only change the foreground of the image while keeping the background unchanged for editing, we adopt three metrics for the background area: PSNR, SSIM, and LPIPS [14, 37]. For the foreground area, we calculate CLIP Score [25] between the foreground area of the edited image and the GT label. The GT label is annotated manually. Among these four metrics, except for LPIPS where lower is better, the other three metrics are higher the better. While these metrics can reflect the performance to a certain extent, they are not entirely accurate. To provide a more accurate evaluation of the effects of edited images, we propose a metric for assessing editing accuracy. Specifically, we hire four workers to manually evaluate the results of these different methods on Reason-Edit. The evaluation criterion is whether the edited image aligns with the instruction. After obtaining the evaluation results" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "from each worker, we average all the results to get the final metric result, which is Instruction-Alignment (Ins-align)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 100, + 531, + 112 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 100, + 531, + 112 + ], + "spans": [ + { + "bbox": [ + 305, + 100, + 531, + 112 + ], + "type": "text", + "content": "5.2. Comparison with State-of-the-Art Methods" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 115, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 115, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 115, + 545, + 342 + ], + "type": "text", + "content": "We compare SmartEdit with existing SOTA instruction-based image editing methods, namely InstructPix2Pix, MagicBrush, and InstructDiffusion. Considering that these released models are trained on specific datasets, they would inevitably perform poorly if directly evaluated on ReasonEdit. To ensure a fair comparison, we fine-tune these methods on the same training set used by SmartEdit, and evaluate the fine-tuned models on Reason-Edit. The experimental results are shown in Tab. 1. From the quantitative results of the reasoning scenarios in the table, it can be observed that when we replace the clip text encoder in the diffusion model with LLaVA and adopt the proposed BIM module, both SmartEdit-7B and SmartEdit-13B achieve better results on these five metrics. This suggests that in scenarios requiring reasoning from instructions, a simple clip text encoder may struggle to understand the meaning of the instructions. However, the MLLM can fully utilize its powerful reasoning ability and world knowledge to correctly identify the corresponding objects and perform edits." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 343, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 545, + 510 + ], + "type": "text", + "content": "The qualitative results further illustrate this point. As shown in Fig. 5, the first three examples are reasoning scenarios. In the first example, both SmartEdit-7B and SmartEdit-13B successfully identify the tool used for cutting fruit (knife) and remove it, while keeping the rest of the background unchanged. The second example can also be handled well by both of them. However, in the third example, we observe a difference in performance. Only SmartEdit-13B can accurately locate the object and perform the corresponding edits without altering other background areas. This suggests that in instruction-based image editing tasks that require reasoning, a more powerful MLLM model can effectively generalize its reasoning ability to this task. This observation aligns with the findings from LISA." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "However, for understanding scenarios, we observe a difference in performance between SmartEdit-7B and SmartEdit-13B when compared to InstructDiffusion on PSNR/SSIM/LPIPS. Specifically, SmartEdit-7B performs worse than InstructDiffusion, while SmartEdit-13B outperforms InstructDiffusion on these metrics. Upon further analysis of the qualitative results, as shown in the " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "4_{th}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "5_{th}" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " rows of Fig. 5, we find that from a visual perspective, both SmartEdit-7B and SmartEdit-13B appear superior to InstructDiffusion. This suggests that the three metrics do not always align with human visual perception. We confirm this phenomenon in the supplementary material. From the result of the Ins-align metric, it can be observed that SmartEdit shows a significant improvement compared to previous instruction-based image editing methods. 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Qualitative comparison on Reason-Edit. 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MethodsUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
InstructPix2Pix21.5760.7210.08922.7620.53724.2340.7070.08319.4130.344
MagicBrush18.1200.680.14322.6200.29022.1010.6940.11319.7550.283
InstructDiffusion23.2580.7430.06723.0800.69721.4530.6660.11719.5230.483
SmartEdit-7B22.0490.7310.08723.6110.71225.2580.7420.05520.9500.789
SmartEdit-13B23.5960.7510.06823.5360.77125.7570.7470.05120.7770.817
", + "image_path": "c707fd32c2bcd98e99975276a98b0594938ca1cd9da486ec7e0bc4cd898dd246.jpg" + } + ] + } + ], + "index": 42, + "angle": 0, + "type": "table_body" + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 492, + 544, + 515 + ], + "lines": [ + { + "bbox": [ + 46, + 492, + 544, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 544, + 515 + ], + "type": "text", + "content": "Table 1. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. All the methods we compared have been fine-tuned using the same training data as that used by SmartEdit." + } + ] + } + ], + "index": 43, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 77, + 525, + 258, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 525, + 258, + 533 + ], + "spans": [ + { + "bbox": [ + 77, + 525, + 258, + 533 + ], + "type": "text", + "content": "\"What is the object that the dog's food should be put into? Remove this object.\"" + } + ] + } + ], + "index": 44 + }, + { + "type": "image", + "bbox": [ + 69, + 533, + 266, + 650 + ], + "blocks": [ + { + "bbox": [ + 69, + 533, + 266, + 650 + ], + "lines": [ + { + "bbox": [ + 69, + 533, + 266, + 650 + ], + "spans": [ + { + "bbox": [ + 69, + 533, + 266, + 650 + ], + "type": "image", + "image_path": "b822ded3281a0d80947b525ea25d15bff37f7667c456219b6c2b0d94601e97bb.jpg" + } + ] + } + ], + "index": 45, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 654, + 285, + 665 + ], + "lines": [ + { + "bbox": [ + 48, + 654, + 285, + 665 + ], + "spans": [ + { + "bbox": [ + 48, + 654, + 285, + 665 + ], + "type": "text", + "content": "Figure 6. Demonstration of the effectiveness of the BIM Module." + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "image_caption" + } + ], + "index": 45 + }, + { + "bbox": [ + 47, + 671, + 179, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 179, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 179, + 684 + ], + "type": "text", + "content": "5.3. Ablation Study on BIM" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "To validate the effectiveness of the bidirectional information interaction in our proposed BIM module, we conduct" + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 343, + 524, + 508, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 524, + 508, + 532 + ], + "spans": [ + { + "bbox": [ + 343, + 524, + 508, + 532 + ], + "type": "text", + "content": "\"Please replace the animal that is lying on the grass with a fox\"" + } + ] + } + ], + "index": 49 + }, + { + "type": "image", + "bbox": [ + 315, + 532, + 359, + 577 + ], + "blocks": [ + { + "bbox": [ + 315, + 532, + 359, + 577 + ], + "lines": [ + { + "bbox": [ + 315, + 532, + 359, + 577 + ], + "spans": [ + { + "bbox": [ + 315, + 532, + 359, + 577 + ], + "type": "image", + "image_path": "8ec6bcbaa0d407c835ef1d35c20cd715362fe7b3e50030d2b27cfcaeb5e99c32.jpg" + } + ] + } + ], + "index": 50, + "angle": 0, + "type": "image_body" + } + ], + "index": 50 + }, + { + "type": "image", + "bbox": [ + 360, + 533, + 403, + 577 + ], + "blocks": [ + { + "bbox": [ + 360, + 533, + 403, + 577 + ], + "lines": [ + { + "bbox": [ + 360, + 533, + 403, + 577 + ], + "spans": [ + { + "bbox": [ + 360, + 533, + 403, + 577 + ], + "type": "image", + "image_path": "2be4fdc566c0dcaf3d15f1fa675917f6949e1db66b28fcc18b85a0288bd70783.jpg" + } + ] + } + ], + "index": 51, + "angle": 0, + "type": "image_body" + } + ], + "index": 51 + }, + { + "type": "image", + "bbox": [ + 404, + 533, + 447, + 576 + ], + "blocks": [ + { + "bbox": [ + 404, + 533, + 447, + 576 + ], + "lines": [ + { + "bbox": [ + 404, + 533, + 447, + 576 + ], + "spans": [ + { + "bbox": [ + 404, + 533, + 447, + 576 + ], + "type": "image", + "image_path": "f12255bdd968ef068497398649c39e040706aa377cf9603ddb9e7d83282dcb57.jpg" + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_body" + } + ], + "index": 52 + }, + { + "type": "image", + "bbox": [ + 448, + 533, + 492, + 576 + ], + "blocks": [ + { + "bbox": [ + 448, + 533, + 492, + 576 + ], + "lines": [ + { + "bbox": [ + 448, + 533, + 492, + 576 + ], + "spans": [ + { + "bbox": [ + 448, + 533, + 492, + 576 + ], + "type": "image", + "image_path": "7f4d9f98dfe1bd8db79287c372f9acaddf14196de5e933be7d5536a230c0f4dd.jpg" + } + ] + } + ], + "index": 53, + "angle": 0, + "type": "image_body" + } + ], + "index": 53 + }, + { + "type": "image", + "bbox": [ + 493, + 533, + 537, + 576 + ], + "blocks": [ + { + "bbox": [ + 493, + 533, + 537, + 576 + ], + "lines": [ + { + "bbox": [ + 493, + 533, + 537, + 576 + ], + "spans": [ + { + "bbox": [ + 493, + 533, + 537, + 576 + ], + "type": "image", + "image_path": "08794862aa30241b1998a302b1ebffa25d9475e8ef07138bd812124e064bf0a7.jpg" + } + ] + } + ], + "index": 54, + "angle": 0, + "type": "image_body" + } + ], + "index": 54 + }, + { + "bbox": [ + 363, + 580, + 489, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 580, + 489, + 588 + ], + "spans": [ + { + "bbox": [ + 363, + 580, + 489, + 588 + ], + "type": "text", + "content": "\"Change the red strawberry to a white pumpkin\"" + } + ] + } + ], + "index": 55 + }, + { + "type": "image", + "bbox": [ + 315, + 588, + 359, + 633 + ], + "blocks": [ + { + "bbox": [ + 315, + 588, + 359, + 633 + ], + "lines": [ + { + "bbox": [ + 315, + 588, + 359, + 633 + ], + "spans": [ + { + "bbox": [ + 315, + 588, + 359, + 633 + ], + "type": "image", + "image_path": "5cdc4a37c81cf54440b9de80886ba5f1d95246442498591d68cfdb8abdcad7cc.jpg" + } + ] + } + ], + "index": 56, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 324, + 634, + 353, + 641 + ], + "lines": [ + { + "bbox": [ + 324, + 634, + 353, + 641 + ], + "spans": [ + { + "bbox": [ + 324, + 634, + 353, + 641 + ], + "type": "text", + "content": "Input Image" + } + ] + } + ], + "index": 57, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 645, + 545, + 666 + ], + "lines": [ + { + "bbox": [ + 306, + 645, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 545, + 666 + ], + "type": "text", + "content": "Figure 7. 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The details are presented in Tab. 2. The first experiment, denoted as Exp 1, aims to verify the necessity of the information in" + } + ] + } + ], + "index": 67 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8368" + } + ] + } + ], + "index": 68 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 70, + 545, + 118 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 545, + 118 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 545, + 118 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 545, + 118 + ], + "type": "table", + "html": "
Exp IDPlainSimpleCABIMUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓20.9750.7130.10823.360.69523.8480.7250.07420.330.694
2✓19.5570.6920.12623.660.69223.5080.7160.08120.170.722
3✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
", + "image_path": "43ff37a01b8ec83eea3fa3bac6bab82f091d17d2602eb660b2e2cc1df53d2e63.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 148, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 47, + 120, + 546, + 142 + ], + "lines": [ + { + "bbox": [ + 47, + 120, + 546, + 142 + ], + "spans": [ + { + "bbox": [ + 47, + 120, + 546, + 142 + ], + "type": "text", + "content": "Table 2. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 148, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 50, + 148, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 50, + 148, + 545, + 198 + ], + "type": "table", + "html": "
Exp IDEditSegmentationSynthetic editing datasetUnderstanding ScenariosReasoning Scenarios
PSNR(dB)↑SSIM↑LPIPS↓CLIP Score↑Ins-align↑PSNR(dB)SSIMLPIPSCLIP ScoreIns-align↑
1✓17.5680.6640.17122.790.20122.4000.7060.10219.220.233
2✓✓18.9600.6900.14322.830.36121.7740.6930.11619.820.311
3✓✓19.5620.7020.11122.320.44023.5950.7150.07920.430.567
4✓✓✓22.0490.7310.08723.610.71225.2580.7420.05520.950.789
", + "image_path": "c113f2fc2ffa062fa9588efcad3f1da18db80bf666a6cbfe2a15495f056ed371.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 200, + 546, + 222 + ], + "lines": [ + { + "bbox": [ + 47, + 200, + 546, + 222 + ], + "spans": [ + { + "bbox": [ + 47, + 200, + 546, + 222 + ], + "type": "text", + "content": "Table 3. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 230, + 289, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 553 + ], + "type": "text", + "content": "teraction proposed in the BIM module. In this experiment, we remove the BIM module from the SmartEdit-7B model and directly apply the text feature output from QFormer to the diffusion model. The second experiment, denoted as Exp 2, aims to verify the necessity of the bidirectional information interaction proposed in the BIM module. Specifically, all blocks are discarded except for the cross-attention block on the image feature branch. Therefore, the information from the text feature of QFormer is unidirectionally applied to the image feature. These two experiments are designed to test the impact of removing or altering the BIM module on the performance of SmartEdit-7B in complex understanding and reasoning scenarios. As shown in Tab. 2, if the BIM module is removed, there is a significant decline in all metrics for both understanding and reasoning scenarios. When the BIM module is replaced with the SimpleCA module, we observe a noticeable decline in all metrics, except for the clip score in understanding scenarios. Further comparison of the qualitative results in Fig. 6 confirms that the introduction of the BIM indeed enhances SmartEdit's instruction editing performance. To be specific, when we do not use the BIM module (i.e., plain), the dog bowl (first row) turns into other objects (marked with a red circle), and the fork (second row) does not change at all. After using SimpleCA, it can be found that the dog bowl and fork have been partially removed. When SmartEdit is equipped with BIM, the dog bowl and fork can be well removed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 565, + 224, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 565, + 224, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 565, + 224, + 578 + ], + "type": "text", + "content": "5.4. Ablation Study on Dataset Usage" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "In Section 4.3, we explore an efficient strategy for data utilization, aiming to enhance SmartEdit's capabilities in handling complex understanding and reasoning scenarios. During the training process of SmartEdit, we employ the common editing dataset, segmentation dataset, and the synthetic editing dataset. To validate the significance of these different data types in boosting SmartEdit's performance, we conduct a series of ablation studies, as detailed in Tab. 3. These experiments are based on the SmartEdit-7B model. In Exp 1, we train the model using only the editing data. In Exp 2, we incorporate segmentation data into the training" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 230, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 547, + 422 + ], + "type": "text", + "content": "process, building upon Exp 1. In Exp 3, we further add the synthetic editing data to the basis established in Exp 1. The quantitative results of these experiments reveal that segmentation data and synthetic editing data play complementary roles in enhancing the model's performance. This is further corroborated by the visual comparison in Fig. 7. For reasoning scenarios, when adopting only the editing dataset or combining the editing dataset and the segmentation dataset, the performance of SmartEdit is inferior. When the synthetic editing data is incorporated into the editing dataset, SmartEdit can accurately locate the specific objects. However, the output of SmartEdit is also mediocre (the generated fox has obvious artifacts, and two pumpkins are generated). When all these datasets are combined as the training set, the results generated by SmartEdit have a further significant improvement in visual effects." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 431, + 379, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 431, + 379, + 443 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 379, + 443 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 447, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 547, + 615 + ], + "type": "text", + "content": "In conclusion, this paper presents SmartEdit, a novel approach to instruction-based image editing that enhances understanding and reasoning capabilities by incorporating the LLMs with visual inputs. By introducing the Bidirectional Interaction Module (BIM), we have overcome challenges associated with the direct integration of LLMs and diffusion models in complex reasoning scenarios. Our data utilization strategy, which incorporates perception data and complex instruction editing data, effectively enhances SmartEdit's capabilities in handling complex understanding and reasoning scenarios. Evaluation on our newly constructed dataset, Reason-Edit, shows that SmartEdit outperforms previous methods, marking a significant step towards practical applications of complex instruction-based image editing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Acknowledgement. The work is partially supported by the Young Scientists Fund of the National Natural Science Foundation of China under grant No. 62106154, the Natural Science Foundation of Guangdong Province, China (General Program) under grant No.2022A1515011524, Shenzhen Science and Technology Program JCYJ20220818103001002 and JCYJ20220818103006012, and the Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong (Shenzhen)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8369" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Tim Brooks, Aleksander Holynski, and Alexei A Efros. 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"bbox": [ + 248, + 203, + 385, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Qing Liu1", + "bbox": [ + 408, + 203, + 488, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Cameron Smith1", + "bbox": [ + 511, + 203, + 643, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhe Lin", + "bbox": [ + 666, + 203, + 738, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Liang Zheng2", + "bbox": [ + 761, + 203, + 872, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 Adobe Research", + "bbox": [ + 269, + 220, + 408, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "2Australian National University", + "bbox": [ + 449, + 220, + 700, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://smartmask-gen.github.io", + "bbox": [ + 297, + 239, + 666, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Inputs", + "bbox": [ + 183, + 263, + 212, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Conventional Inpainting", + "bbox": [ + 421, + 263, + 531, + 273 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5edad89bc8a0c19452c825749f632f1cf619c964c9406c5ccca98b73422491f5.jpg", + "image_caption": [ + "Image Input" + ], + "image_footnote": [], + "bbox": [ + 99, + 273, + 194, + 345 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0ad97216176c879a3fd03279d618fb86905d73d0e7503453b20ec38365784ce5.jpg", + "image_caption": [ + "Image Input + Mask" + ], + "image_footnote": [], + "bbox": [ + 197, + 273, + 290, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/203ac10b40edbd4620f2a88796c2100fa03fe9df45c77ac99f1f087e9c0d9aaa.jpg", + "image_caption": [ + "SD - Impaint" + ], + "image_footnote": [], + "bbox": [ + 292, + 273, + 387, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bfab34a4539904c20c62a55f32d6afbe45bab18f90d513028026495f6e86d81c.jpg", + "image_caption": [ + "Blended Latent Diff." + ], + "image_footnote": [], + "bbox": [ + 388, + 273, + 483, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/078afec3fe31d0fdd55cfc394104e399c2891b698f053ae950822d3169d392a7.jpg", + "image_caption": [ + "Adobe SmartBrush" + ], + "image_footnote": [], + "bbox": [ + 486, + 273, + 581, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/30625f7b6cfc65d344ddc80fd4283fdd68fc85a13dcfc3fd53a542e8f704ddbc.jpg", + "image_caption": [ + "Adobe Gen-Fill" + ], + "image_footnote": [], + "bbox": [ + 583, + 273, + 676, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/70c87662f173dfa99ef1554f4cbafc030409602de8c2bdb6fcf15a427148a149.jpg", + "image_caption": [ + "SmartMask Prediction" + ], + "image_footnote": [], + "bbox": [ + 679, + 273, + 772, + 347 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/82c22c36a5354ba73c94f98bedf2201e3e9039b1b6600af1ea1338457b89a9fc.jpg", + "image_caption": [ + "Output (Ours)" + ], + "image_footnote": [], + "bbox": [ + 774, + 273, + 870, + 347 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(a) SmartMask for performing object insertion (\"bride\") with better background preservation.", + "bbox": [ + 238, + 362, + 728, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/eebb3be1459bb9d86a403cb6b9a746700505f87b988bbd874b0e97892695e519.jpg", + "image_caption": [ + "Input Image" + ], + "image_footnote": [], + "bbox": [ + 99, + 378, + 197, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9ec704501ee31c21e5d4f6790c7f297d5b0cff38ffeca97c2048454e9050d640.jpg", + "image_caption": [ + "SmartMask Outputs for \"woman beside a river in mountains\"" + ], + "image_footnote": [], + "bbox": [ + 197, + 378, + 292, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/82f0004ba92a745e6a71b57217acddc2245668e971ccdeab17d7fa00f3b02ef4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 378, + 388, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a3ef05fb4e7af95cebc55d17c80b2ed7811e8c46d7688f074924d8934540a831.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 378, + 483, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4dfd1e5a81bea99d21aabd238b639017a058f72749930c407ecdb90067c0c2f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 378, + 584, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c3b5419350751a7157f6d64bd620cc4279d0e3d14dcecd673197cd73a52e2ad5.jpg", + "image_caption": [ + "SmartMask Outputs for \"woman in a living room\"" + ], + "image_footnote": [], + "bbox": [ + 584, + 378, + 679, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/aa73bd545b74a30678fa3c8c3e13f89c79d1b27772e0d3d46814fe7461812b8f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 378, + 774, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/99fad521d354666b955ec2f3c9f79f196ffb2c74b17c5442343c61ea411092e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 378, + 870, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(b) SmartMask for mask-free object insertion where it provides diverse suggestions without user bounding box input.", + "bbox": [ + 176, + 470, + 792, + 484 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Input Prompt: Two children sitting in front of a cardboard tree", + "bbox": [ + 344, + 488, + 633, + 498 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/091f5ea1c6e9ee821bb8bf9614b89d3570f558daad5d13b20834476d0f3e1c6a.jpg", + "image_caption": [ + "User Scribbles" + ], + "image_footnote": [], + "bbox": [ + 99, + 498, + 194, + 570 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b1f585ffc0402011e47b71bcd8c9e7486f79e092a028d4e47876138ebce86bcd.jpg", + "image_caption": [ + "Scribble + Controlnet" + ], + "image_footnote": [], + "bbox": [ + 194, + 498, + 290, + 570 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/397d362fd1b3b280b339ec52515f9ca06a01a283d6ab4c6f762cd73e69caff81.jpg", + "image_caption": [ + "Scribble + PwW" + ], + "image_footnote": [], + "bbox": [ + 290, + 498, + 385, + 570 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c23cfd7e669319effb9926b929d7e5c3c7eca4f4d3b1625d4d3f91dbaede64e.jpg", + "image_caption": [ + "Scribble + DenseDiff" + ], + "image_footnote": [], + "bbox": [ + 387, + 498, + 480, + 570 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e717a482810ff85feb8996198ac3573252e7d85472b888840d73223c0485bc30.jpg", + "image_caption": [ + "Fine-grain Layout Generation (Ours)", + "Figure 1. Overview. We introduce SmartMask which allows a novice user to generate high-fidelity masks for fine-grained object insertion and layout control. The proposed approach can be used for object insertion (a-b) where it not only allows for image inpainting with better background preservation (a) but also provides diverse suggestions for mask-free object insertion at different positions and scales. We also find that when used iteratively SmartMask can be used for fine-grained layout design (c) for better quality semantic-to-image generation." + ], + "image_footnote": [], + "bbox": [ + 483, + 498, + 578, + 570 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/98b856e4064d94ac354783dbcb0b80aeee56b1c6408a95fc6aafb048651d6e46.jpg", + "image_caption": [ + "Ours + Controlnet" + ], + "image_footnote": [], + "bbox": [ + 774, + 498, + 867, + 570 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(c) SmartMask for fine-grain layout design for layout to image generation.", + "bbox": [ + 287, + 588, + 679, + 601 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 672, + 313, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The field of generative image inpainting and object insertion has made significant progress with the recent advent of latent diffusion models. Utilizing a precise object mask can greatly enhance these applications. However, due to the challenges users encounter in creating high-fidelity masks, there is a tendency for these methods to rely on more coarse masks (e.g., bounding box) for these applications. This results in limited control and compromised background content preservation. To overcome these limitations, we introduce SmartMask, which allows any novice user to create detailed masks for precise object insertion. Combined with a ControlNet-Inpaint model, our experiments demonstrate that SmartMask achieves superior object insertion qual", + "bbox": [ + 75, + 704, + 470, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ity, preserving the background content more effectively than previous methods. Notably, unlike prior works the proposed approach can also be used even without user-mask guidance, which allows it to perform mask-free object insertion at diverse positions and scales. Furthermore, we find that when used iteratively with a novel instruction-tuning based planning model, SmartMask can be used to design detailed layouts from scratch. As compared with user-scribble based layout design, we observe that SmartMask allows for better quality outputs with layout-to-image generation methods.", + "bbox": [ + 496, + 674, + 893, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 843, + 632, + 858 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Multi-modal object inpainting and insertion has gained widespread public attention with the recent advent of large-", + "bbox": [ + 500, + 869, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6497", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "scale language-image (LLI) models [1-3, 19, 24, 27, 30, 37, 38]. A novice user can gain significant control over the inserted object details by combining text-based conditioning with additional guidance from a coarse bounding box or user-scribble mask. The text prompt can be used to describe the object semantics, while the coarse mask provides control over the position and scale of the generated object.", + "bbox": [ + 75, + 90, + 468, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While convenient, the use of a coarse mask for object insertion suffers from two main limitations. 1) First, the use of a coarse mask can often be undesirable as it tends to also modify the background regions surrounding the inserted object [30, 37] (refer Fig. 1a). In order to minimize the background artifacts, recent works [37, 40] also explore the use of user-scribble based free-form mask instead of a bounding-box input. However, while feasible for describing coarse objects (e.g., mountains, teddy bear etc.), the generation of accurate free-form masks for objects with a number of fine-grain features (e.g., humans) can be quite challenging especially when limited to coarse user-scribbles. 2) Furthermore, generating variations in position and scale of the inserted object can also be troublesome as it requires the user to provide a new scene-aware free-form mask to satisfy the geometric constraints at the new scene location.", + "bbox": [ + 75, + 199, + 470, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these drawbacks, we introduce SmartMask, a context-aware diffusion model which allows a novice user to directly generate fine-grained mask suggestions for precise object insertion. In particular, given a semantic object description (e.g. kid) and the overall scene context, SmartMask generates scene-aware precise object masks which can then be used as input to a ControlNet-inpaint model [36, 41] to perform object insertion while preserving the contents of background image. As compared with coarse-mask based inpainting methods, we find that SmartMask provides a highly convenient and controllable method for object insertion and can be used 1) with user-inputs (bounding box, scribbles etc.): where the user can specify location and shape for the target object, or 2) in a mask-free manner: where the model automatically generates diverse suggestions for object insertion at diverse positions and scales.", + "bbox": [ + 75, + 444, + 468, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In addition to object insertion, we also find that SmartMask can be used for fine-grain layout design. Existing segmentation-to-image (S2I) generation methods (e.g. ControlNet [41]) enable the generation of controllable image outputs from user-scribble based semantic segmentation maps. However, generating a good quality semantic layout can be quite challenging if the user wants to generate a scene with objects that require fine-grain details for best description (e.g., humans, chairs etc.). To address this challenge, we show that SmartMask when used with a novel instruction-tuning [34] based planning model allows the user to iteratively generate the desired scene layout from scratch. As compared with scribble based layout generation, we find that the proposed approach allows the users to", + "bbox": [ + 75, + 688, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "better leverage existing S2I generation methods (e.g. ControlNet [41]) for higher quality output generation.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The main contributions of the paper are: 1) We propose SmartMask which allows any novice user to generate precise object masks for finegrained object insertion with better background preservation. 2) We show that unlike prior works, the proposed approach can also be used for mask-free object insertion. 3) Finally, we demonstrate that SmartMask can be used iteratively to generate detailed semantic layouts, which allows users to better leverage existing S2I generation methods for higher quality output generation.", + "bbox": [ + 498, + 121, + 893, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 273, + 640, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion based multi-modal image inpainting [1-3, 19, 24, 27, 30, 37, 38] has gained widespread attention with advent of text-conditioned diffusion models [24, 29, 30, 32, 39]. Despite their efficacy, these methods use coarse bounding box or user-scribble based masks for object inpainting which leads to poor background preservation around the inserted object. In contrast, SmartMask directly allows user to generate precise masks for the target object, which can then be combined with ControlNet-Inpaint [30, 41] to insert the target object while better preserving background contents.", + "bbox": [ + 498, + 299, + 890, + 449 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Mask-free object placement has been studied in the context of image compositing methods [9, 20, 22, 25, 35, 42, 44, 46], where given a cropped RGB object instance and a target image, the goal is to suggest different positions for the target object. In contrast, we study the problem of mask-free object insertion using text-only guidance. Lee et al. [18] propose a GAN-based approach to directly model a distribution of potential object locations. However, the learned distribution is w.r.t to a specific object class (e.g., cars) which limits its generalizability for diverse use-cases.", + "bbox": [ + 496, + 450, + 892, + 601 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Semantic layout to image generation methods have been explored to enable controllable image synthesis from user-scribble based semantic segmentation maps [8, 12, 17, 23, 26, 33, 45]. Recently, [4, 6, 14, 31] propose a cross-attention based training-free approach for controlling the overall scene layout from coarse user-scribbles using text-conditioned diffusion models. Zhang et al. [41] propose a versatile ControlNet model which allows the users to control the output layout on a more fine-grained level through an input semantic map. While effective, generating desired semantic layout with scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g., humans). SmartMask helps address this problem by allowing users to generate more fine-grained layouts to facilitate better quality S2I generation.", + "bbox": [ + 496, + 602, + 893, + 829 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Our Method", + "text_level": 1, + "bbox": [ + 500, + 844, + 629, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given an input image $\\mathcal{I}$ , object semantic label $\\mathcal{T}_{obj}$ and a textual description $\\mathcal{T}_{context}$ describing the final scene con", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6498", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bd575b2128bacfd093658cc193c7561b56e9d51632f8ab78253519898067144a.jpg", + "image_caption": [ + "Figure 2. Method Overview. A key idea behind SmartMask is to leverage semantic amodal segmentation data [28, 47] in order to obtain high-quality paired training annotations for mask-free single or multi-step object insertion. During training (top), given a training image $\\mathcal{I}$ with caption $C$ , we stack $k$ ordered instance maps $\\{A_1, A_2, \\ldots, A_k\\}$ to obtain an intermediate semantic map $S_k$ . The diffusion model is then trained to predict the instance map $A_{k+1}$ , conditional on the semantic map $S_k$ , $\\mathcal{T}_{obj} \\gets \\mathcal{O}_{k+1}$ and scene context $\\mathcal{T}_{context} \\gets C$ . During inference (bottom), given a real image $\\mathcal{I}$ , we first use a panoptic segmentation model to compute semantic map $S_I$ . The generated semantic layout is then directly used as input to the trained diffusion model in order to predict the fine-grained mask for the inserted object." + ], + "image_footnote": [], + "bbox": [ + 81, + 65, + 890, + 391 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "text, our goal is predict a fine-grained mask $\\mathcal{M}_{obj}$ for the target object. The object mask $\\mathcal{M}_{obj}$ could then be used as input to a ControlNet-Inpaint model for fine-grained object insertion (Sec. 4.1) or used to design detailed semantic layouts from scratch (Sec. 4.3). For instance, SmartMask could be used for single object insertion, where given an image $\\mathcal{I}$ depicting a man on a bench, $\\{\\mathcal{T}_{obj} : \\text{\"woman'}\\}$ and $\\{\\mathcal{T}_{\\text{context}} : \\text{\"a couple sitting on a bench'}\\}$ , our goal is to predict fine-grain binary mask $\\mathcal{M}_{woman}$ which places the 'woman' in a manner such that the resulting scene aligns with overall scene context of a 'a couple sitting on a bench'.", + "bbox": [ + 75, + 494, + 470, + 661 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similarly, SmartMask could also be used for multiple object insertion. For instance, given an image $\\mathcal{I}$ depicting a wedding, the user may wish to add multiple objects \\{'man', 'woman' and 'kid'\\} such that the final scene aligns with the $\\{\\mathcal{T}_{\\text {context }}: \\text { 'a family posing for a picture at a wedding }\\}$ . Unlike prior image inpainting methods which are limited independently adding each object to the scene, the goal of the smartmask model is to add each object in a manner such the generated 'man', 'woman' and 'kid' appear to be 'a family posing for a picture at a wedding'. (refer Fig. 2a).", + "bbox": [ + 75, + 667, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the next sections, we describe the key SmartMask components in detail. In particular, in Sec. 3.1 we discuss how SmartMask can leverage semantic amodal segmentation data in order to obtain high-quality paired annotations for mask-free object insertion. We then discuss a simple", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "data-adaptation strategy which allows the user to also control the position, shape of the inserted object using coarse inputs (bounding-box, scribbles) in Sec. 3.2. Finally, in Sec. 3.3 we propose a visual-instruction tuning [21] based planning model which when used with SmartMask, allows for generation of detailed semantic layouts from scratch.", + "bbox": [ + 496, + 494, + 890, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. SmartMask for Mask-Free Object Insertion", + "text_level": 1, + "bbox": [ + 498, + 592, + 872, + 608 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic-Space Task Formulation. Directly learning a model for our task in pixel space can be quite challenging, as it would require large-scale collection of training data for single or multi-step object insertion while maintaining background preservation. To address this key challenge, a core idea of our approach is to propose an equivalent task formulation which allows us to leverage large-scale semantic amodal segmentation data [28, 47] for generating high-quality paired training data in the semantic space (Fig. 2).", + "bbox": [ + 496, + 614, + 890, + 751 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SmartMask Training. In particular during training, given an image $\\mathcal{I}$ , with a sequence of ordered amodal semantic instance maps $\\{A_1, A_2 \\ldots A_n\\}$ and corresponding semantic object labels $\\{\\mathcal{O}_1, \\mathcal{O}_2 \\ldots \\mathcal{O}_n\\}$ , we first compute an intermediate layer semantic map as,", + "bbox": [ + 496, + 752, + 890, + 827 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS _ {k} = f _ {\\text {l a y e r}} \\left(\\left\\{A _ {1}, A _ {2} \\dots A _ {k} \\right\\}\\right) \\quad \\text {w h e r e} k \\in [ 1, n ]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 832, + 890, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $k$ is randomly chosen from $[1, n]$ and $f_{layer}$ is a layering operation which stacks the amodal semantic segmentation maps from $i \\in [1, k]$ in an ordered manner (Fig. 2).", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6499", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We next train a diffusion-based mask prediction model $\\mathcal{D}_{\\theta}$ which takes as input the above computed intermediate semantic layer map $S_{k}$ , textual description for next object $\\mathcal{T}_{obj} \\gets \\mathcal{O}_{k+1}$ , overall caption $\\mathcal{T}_{context} \\gets C_{\\mathcal{I}}$ (for image $\\mathcal{I}$ ) and learns to predict the binary mask $\\{A_{k+1}\\}$ for the next object. To this end, we first pass the intermediate semantic map $S_{k}$ through a learnable encoder $\\mathcal{E}_{\\phi}$ to obtain the encoded features $\\mathcal{E}_{\\phi}(S_{k})$ . At any timestep $t$ of the reverse diffusion process, the denoising noise prediction $\\epsilon_{t}$ is then computed conditional jointly on previous noise latent $\\mathbf{z}_{t}$ , and model inputs $\\{\\mathcal{E}_{\\theta}(S_{k}), \\mathcal{T}_{obj}, \\mathcal{T}_{context}\\}$ as,", + "bbox": [ + 76, + 90, + 472, + 258 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\epsilon} _ {p r e d} (t) = \\mathcal {U} _ {\\theta} (\\mathbf {z} _ {t}, \\mathcal {E} _ {\\phi} (S _ {k}), \\mathcal {T} _ {o b j}, \\mathcal {T} _ {\\text {c o n t e x t}}, t), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 267, + 468, + 284 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{U}_{\\theta}$ represents the U-Net of the diffusion model $\\mathcal{D}$ .", + "bbox": [ + 76, + 292, + 452, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The overall diffusion model $\\mathcal{D}$ is then trained to predict the next layer $A_{k + 1}$ using the following diffusion loss,", + "bbox": [ + 76, + 306, + 468, + 339 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} (\\theta , \\phi) = \\mathbf {E} _ {t \\sim [ 1, T ], S _ {k}, A _ {k + 1}, \\epsilon_ {t}} \\left[ \\| \\epsilon_ {t} - \\tilde {\\epsilon} _ {p r e d} (t) \\| ^ {2} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 347, + 468, + 366 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T$ is total number of reverse diffusion steps, $\\epsilon_t\\sim \\mathcal{N}(0,I)$ is sampled from a normal distribution and $A_{k + 1}$ represents ground truth binary mask for next object $\\mathcal{O}_{k + 1}$ .", + "bbox": [ + 76, + 375, + 468, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SmartMask Inference. During inference, given an input image $\\mathcal{I}$ , semantic object category $\\mathcal{T}_{obj}$ and a textual description $\\mathcal{T}_{\\text {context }}$ describing the final scene context, we first use a panoptic semantic segmentation model [15] to obtain the corresponding semantic layout map $\\mathcal{S}_{\\mathcal{I}}$ . The generated semantic layout $\\mathcal{S}_{\\mathcal{I}}$ is then directly used as input to the above trained diffusion model $\\mathcal{D}_{\\theta}$ in order to predict the fine-grained mask $\\mathcal{M}_{obj}$ for the target object,", + "bbox": [ + 75, + 420, + 468, + 541 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {o b j} = \\mathcal {D} _ {\\theta} \\left(\\mathcal {E} _ {\\phi} \\left(\\mathcal {S} _ {I}\\right), \\mathcal {T} _ {o b j}, \\mathcal {T} _ {\\text {c o n t e x t}}\\right). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 550, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Data Adaptation for Precise Mask Control", + "text_level": 1, + "bbox": [ + 76, + 584, + 439, + 599 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the diffusion model trained in Sec. 3.1, allows the user to perform mask-free object insertion at diverse positions and scales, the user may also wish to obtain more direct control over the spatial location and details of the inserted object. To this end, we propose a simple train-time data adaptation strategy which allows smartmask to be easily adapted to diverse forms of user control (Fig. 4). In particular, given the intermediate layer map $S_{k}$ computed using Eq. 1 and ground truth mask $A_{k + 1}$ for the next object, we replace the input $S_{k}$ to the diffusion model as,", + "bbox": [ + 75, + 607, + 468, + 758 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {S} _ {k} = g \\left(S _ {k}, G _ {o b j}\\right) = S _ {k} \\odot \\left(1 - \\alpha G _ {o b j}\\right) + \\alpha G _ {o b j}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 768, + 468, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $G_{obj}$ is the additional guidance input (e.g., bounding box mask, coarse scribbles etc.) provided by the user and $\\alpha = 0.7$ helps add additional guidance while still preserving the content of the original input $S_{k}$ after data adaptation.", + "bbox": [ + 76, + 794, + 468, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training. In this paper, we mainly consider four main guidance inputs $G_{obj}$ for additional mask control for adapting SmartMask. 1) Mask-free guidance: in absence of any", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "additional user inputs, we use $G_{obj} = \\mathbf{0}^{H,W}$ which prompts the model to suggest fine-grained masks for object insertion at diverse positions and scales. 2) Bounding-box guidance: we set $G_{obj}$ as a binary mask corresponding to ground truth object mask $A_{k+1}$ . 3) Coarse Spatial Guidance: Expecting the user to provide precise bounding box for object insertion is not always convenient and can lead to errors if bounding box is not correct. We therefore introduce a coarse spatial control where user may provide a coarse spatial location and the model learns to infer the best placement of the object around the suggested region (Fig. 4c). During training, the same is achieved by setting $G_{obj}$ as a coarse gaussian blob centered at the ground truth object mask $A_{k+1}$ . 4) User scribbles: Finally, we also allow the user to describe target object using free-form coarse scribbles, by setting $G_{obj}$ as the dilated mask output of ground-truth object mask $A_{k+1}$ .", + "bbox": [ + 496, + 90, + 890, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference. At inference time, the additional guidance input $G_{obj}$ (e.g. bounding box mask, coarse scribbles etc.) is directly provided by the user. Given an input image $\\mathcal{I}$ with semantic layout $S_{\\mathcal{I}}$ , we then use transformation from Eq. 5 as input to the adapted SmartMask model in order to generate object insertion suggestions with additional control.", + "bbox": [ + 496, + 333, + 890, + 425 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Global Planning for Multi-Step Inference", + "text_level": 1, + "bbox": [ + 498, + 436, + 854, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the original SmartMask model allows the user to generate fine-grained masks for single object insertion, we would also like to use SmartMask for iterative use cases such as multiple object insertion (Sec. A.1) or designing a fine-grained layout from scratch with large number $(>10)$ of scene elements. Such an iterative use of SmartMask would require the model to carefully plan the spatial location of each inserted object to allow for the final scene to be consistent with the final scene context description $\\mathcal{T}_{\\text{context}}$ .", + "bbox": [ + 496, + 460, + 890, + 597 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve this, we train a visual-instruction tuning [21] based planning model which given the input semantic layout $S_{I}$ , learns to plan the positioning of different scene elements over long sequences. Given a semantic object description $T_{obj}$ and final scene context $T_{context}$ , the global planning model provides several bounding box suggestions for object insertion. SmartMask model then uses the above predictions as coarse spatial guidance input $G_{obj}$ to provide fine-grained mask suggestions for the next object. The above process can then be repeated in an iterative manner until all objects have been added to the scene (refer Fig. 7a).", + "bbox": [ + 496, + 598, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The global planning model is trained in two stages. 1) Feature Alignment. Typical instruction tuning models are often trained on real images. In contrast, as discussed in Sec. 3.1 we would like to model our problem in semantic space as it allows us to leverage amodal segmentation data for training. To address this domain gap, we first finetune an existing LLaVA model [21] to understand the semantic inputs. To do this, given an intermediate semantic map $S_{k}$ computed using Eq. 1, we finetune the projection matrix $\\mathbf{W}$", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6500", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c845681feea1a94c6197d1c87a541ea6826a41236c4c81c83bb0db580470cb5f.jpg", + "image_caption": [ + "Figure 3. Qualitative Results for Image Inpainting. We observe that as compared to with state-of-the-art image inpainting [1, 2, 30, 37] methods, SmartMask allows the user to perform object insertion while better preserving the background around the inserted object." + ], + "image_footnote": [], + "bbox": [ + 83, + 79, + 890, + 407 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "of the LLaVA model [21] $\\mathcal{H}$ to predict the semantic object labels $\\{\\mathcal{O}_1,\\mathcal{O}_2\\ldots \\mathcal{O}_k\\}$ described in the current scene as,", + "bbox": [ + 75, + 455, + 470, + 488 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a l i g n}} (\\mathbf {W}) = \\mathcal {L} _ {C E} (< \\mathcal {O} _ {1}, \\mathcal {O} _ {2} \\dots \\mathcal {O} _ {k} >, \\mathcal {H} (S _ {k})). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 500, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2) Instruction-Tuning. Finally, keeping the visual encoder weights for LLaVA model fixed, we next finetune both project matrix $\\mathbf{W}$ and LLM weights $\\Phi$ [43] for global object planning. In particular, given an intermediate semantic map $S_{k}$ , we first compute the bounding box coordinates $\\mathcal{B}_{k+1} = \\{x_{min}, y_{min}, x_{max}, y_{max}\\}$ for the next object $\\mathcal{T}_{obj} = \\mathcal{O}_{k+1}$ using ground truth object mask $\\mathcal{A}_{k+1}$ . The LLaVA based planning model $\\mathcal{H}$ is then trained as,", + "bbox": [ + 75, + 529, + 468, + 650 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {i n s t r u c t}} (\\mathbf {W}, \\Phi) = \\mathcal {L} _ {C E} \\left(\\mathcal {B} _ {k + 1}, \\mathcal {H} \\left(S _ {k}, \\mathcal {T} _ {\\text {o b j}}, C\\right)\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 662, + 468, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $C$ represents the caption for the final scene (obtained using ground-truth image $\\mathcal{I}$ ) and provides the model context for placing different scene elements in the image.", + "bbox": [ + 75, + 691, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Data Collection. As discussed in Sec. 3, we note that a key idea behind SmartMask is to model the object insertion problem in semantic space (instead of pixel space), which allows us to leverage semantic amodal segmentation data to obtain large-scale paired training annotations for single or multiple object insertions. However, traditional datasets for semantic amodal segmentations such as COCOA [47] (2,500 images, 22,163 instances) and KINS [28]", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(7,517 images, 92,492 instances) though containing fine-grained amodal segmentation annotations may lack sufficient diversity to generalize across different use-cases.", + "bbox": [ + 496, + 455, + 890, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address this, we curate a new large-scale dataset consisting of fine-grain amodal segmentation masks for different objects in an input image. The overall dataset consists of 32785 diverse real world images and a total of 725897 object instances across more than 500 different semantic classes (e.g. man, woman, trees, furniture etc.). Each image $\\mathcal{I}$ in the dataset consists of a variable number of object instances $\\{A_1, A_2, \\ldots, A_n\\}$ , $n \\in [2, 50]$ and is annotated with an ordered sequence of semantic amodal segmentation maps $\\{S_1, S_2, \\ldots, S_n\\}$ . The detailed descriptions $C_I$ for each image are obtained using the InstructBLIP [7] model.", + "bbox": [ + 496, + 503, + 892, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SmartMask Training. In order to leverage the rich generalizable prior of T2I diffusion models, we use the weights from publicly available Stable-Diffusion-v1.5 model [30] in order to initialize the weights of the SmartMask U-Net model trained in Sec. 3.1. Similar to [5], we modify the architecture of the U-Net model to also condition the output mask predictions on segmentation layout $S_{I}$ . The SmartMask model is trained for a total of 100k iterations with a batch size of 192 and learning rate $1e - 5$ using 8 Nvidia-A100 GPUs. During inference, a panoptic semantic segmentation model finetuned on the dataset in Sec. 4 is used for converting real image $\\mathcal{L}$ to its semantic layout $S_{I}$ . ControlNet model trained with SDXL backbone was used to perform precise object insertion with SmartMask outputs. Please refer the supp. material for further training details.", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6501", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1541e367e0ddb99394b602a3e451e55245b1a75949436b7951887e38463e48ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 70, + 192, + 143 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cc25d52d8bc78c5c9b741c3ce4a0ee0f8c1f2ce428235dead328f6181c3d5efb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 192, + 70, + 313, + 143 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/eb859377da04b062180ddd715fda3d717138552a742497afdd2d256ac4e1ca86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 315, + 70, + 385, + 143 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c1e77d73c40fbb5db1ae36e87d9f31b7fa661ef3f5ac2a254e4bb8bad2e79c47.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 387, + 71, + 482, + 143 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3042c0e9452c4474ff54170db29cb210b24dbbabb8f9ecdfb5c8ba8c4ced6bfc.jpg", + "image_caption": [ + "Image Input" + ], + "image_footnote": [], + "bbox": [ + 83, + 145, + 192, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a7b3321d03121ca3e7dbd48b2383c6b317bda3785a1c41dc2ef12efb8a7ed94a.jpg", + "image_caption": [ + "SmartMask Outputs" + ], + "image_footnote": [], + "bbox": [ + 192, + 143, + 290, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7cca24f4f08be3af5a9aeaccb9c7a298a503a89cf6e19d39de0a7101641de4ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 143, + 383, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": 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"image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 70, + 890, + 143 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2cca947d733e9fa0e17b992cdd05753155595d06d57d93a646029ef144a96aea.jpg", + "image_caption": [ + "Image Input" + ], + "image_footnote": [], + "bbox": [ + 491, + 145, + 599, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0f177d283ca250dd1a99e5d7f4de447cf9194bca2e377ac281b3989705b03ce0.jpg", + "image_caption": [ + "SmartMask Outputs" + ], + "image_footnote": [], + "bbox": [ + 601, + 145, + 696, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9ddb99fdeb7a0a078fc27535fe4ef8ddc08be3f93b639af43b115bcafbf4608c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 145, + 792, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2bb685ea4685a640b3a7e09abfbf4cebb8c7b955220a6e96a2239c5bb0956840.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 145, + 890, + 215 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2b050e7dc75fac17cbd6fde107de344a7640e7e10a31ef8a949136423caa6f16.jpg", + "image_caption": [ + "(a) Mask-free object insertion" + ], + "image_footnote": [], + "bbox": [ + 83, + 246, + 191, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d5abdb25e3ffdc8ef40393ee48b5baad47bfab48ebef1abb319f5550e7d3dc1b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 192, + 247, + 289, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3286d89a27bd30c7be2da56fa92707f52547285588415474886e7d10074a1faa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 247, + 383, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e5df1655e0040e04db85e6136905bead5107740ace2e3dbd2855090c5a6c7fd4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 387, + 247, + 482, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9abad4c2de77fabd5f67c7bf325216ac6459a93f71251026d97daa77cac60c7b.jpg", + "image_caption": [ + "(c) Coarse-spatial guidance for mask generation" + ], + "image_footnote": [], + "bbox": [ + 83, + 321, + 192, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ee767df46b45577aad1d8b8566db68eb0e520ce2315ef284b7d26d0a5f899359.jpg", + "image_caption": [ + "Figure 4. Diverse User Controls. SmartMask is easily adaptable to diverse user-controls for precise mask generation for the target object." + ], + "image_footnote": [], + "bbox": [ + 192, + 321, + 289, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c536381eaf88f8b706a7f9d3b44fa0d9dd09afc80218f134d6d028d7145265f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 321, + 385, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d203fa9e54c436037dc166536aa14b39fc9c42c1c27d30d02b596062ee68eee6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 387, + 321, + 482, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/43f5155cf43a7f4e16c2fca1c04f6b1e97bbda9f6da518218bb87fbc4125596d.jpg", + "image_caption": [ + "(b) Bounding-box guidance for mask generation" + ], + "image_footnote": [], + "bbox": [ + 491, + 247, + 599, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3d2eda6e7647c2c890e6e6e6ad3707fdf848033f26727366b47ff4923a13bbeb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 247, + 697, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/df8b1f1beb4bda91833a976dd18b578e0d7aebc7193204591369aa3c246a2862.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 599, + 321, + 696, + 395 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b7971ae117e80ca52b74fabac87b02e4cee6c23e14fcdd4367354c42aae8a29d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 247, + 792, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/51b224e66510246178c91a6c9855216e8ed0b74134436504637d2d9e537215ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 247, + 890, + 320 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5316f72cb0b4ca50ecdf754f8a0c715346e1126edcb0d7e2fd97c67eaaeca5d9.jpg", + "image_caption": [ + "(d) Scribble-based object insertion" + ], + "image_footnote": [], + "bbox": [ + 493, + 321, + 599, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6672613038cc9524e177291009597b7ede8d577ddab4666a43e925328624ba8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 321, + 697, + 395 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/20b1b3bf833f8b8b4796f01e2f266375969cb76447c156a7a8450701f6ca7095.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 699, + 321, + 792, + 406 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e6b82c159d332af5c48118df2f718beabc4ad5baae34faf1f1929ac61feeecd7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 795, + 321, + 890, + 395 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. SmartMask for Object Insertion", + "text_level": 1, + "bbox": [ + 76, + 450, + 361, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. We compare the performance of our approach on object-insertion with prior works on performing multimodal image-inpainting using a textual description and coarse bounding box mask. In particular we show comparisons with SD-Inpaint [30], SDXL-Inpaint [27], Blended-Latent Diffusion [30], and Adobe SmartBrush [37]. We also compare the performance of our approach with state-of-the-art commercial inpainting tools by reporting results on recently released Generative-Fill from Adobe Firefly [1].", + "bbox": [ + 75, + 474, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. Following [37], we report the results for object insertion using 1) Local-FID [11] which measures the realism of the generated objects, 2) CLIP-Score [10] which measures the alignment between the textual description and the generated object, and 3) Norm. L2-BG: which reports the normalized L2 difference in the background regions before and after insertion, and helps capture the degree to which the background was preserved.", + "bbox": [ + 75, + 612, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Results. Results are shown in Fig. 3. We observe that when performing objectn insertion using a coarse bounding box mask, traditional inpainting methods usually lead to a lot of changes in the background regions around the inserted object (e.g. living room details in row-1&2, mountains in row-4 etc.). Adobe SmartBrush [37] which is trained to allow better background preservation, shows better performance, however, still suffers from notable changes to background regions. In contrast, by directly predicting a high-fidelity mask for the target object, the proposed approach allows the user to add new objects on the scene with", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/6b7724629f5d8cc2ce751f4dabfb6e8dfd0c88f011e585a57eccdc8c2d5b6e2f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodEvaluation Criteria
Local-FID ↓CLIP-Score ↑Norm. L2-BG ↓
SD Inpaint [30]22.310.2490.374
SDXL Inpaint [27]21.840.2350.623
Blended L-Diffusion [2]39.770.2530.451
Adobe SmartBrush [37]17.940.2620.304
Adobe Gen-Fill* [1]N/A0.2680.289
Smartmask (Ours)19.210.2610.098
", + "bbox": [ + 500, + 449, + 906, + 554 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative results for image inpainting. We observe that in comparison with state-of-art image inpainting methods, our approach leads to better preservation of background regions.", + "bbox": [ + 498, + 561, + 890, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "minimal changes to the background image. Furthermore we observe that target object masks are generated in a scene-aware manner, which helps us add new objects while interacting with already existing ones. For instance, when adding 'a man to a couch with table in front' (Fig. 3), prior works typically replace the couch and table to insert the target object ('man'). In contrast, smartmask places the 'man sitting on the couch with his leg on the table', and provides a more natural way for inserting objects in complex scenes.", + "bbox": [ + 496, + 611, + 890, + 747 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Results. In addition to qualitative results, we also report the performance of our approach quantitatively in Tab. 1. We find that similar to results in Fig. 3, the proposed approach shows better background preservation (Norm. L2-BG ↓) while performing comparably in terms of image quality (local-FID) and text-alignment (CLIP-Score).", + "bbox": [ + 496, + 748, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluating Mask Controllability and Quality", + "text_level": 1, + "bbox": [ + 498, + 847, + 879, + 863 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "A key advantage of SmartMask is the ability to generate high-quality masks for target object in a controllable man", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6502", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5afad3b15493e52d50f73742b4494c974ea3dc4b540204e1f077c5f1349d7ea0.jpg", + "image_caption": [ + "Figure 5. Comparing output mask quality with different Inpaint + HQSAM (middle) methods and SmartBrush mask output (right)." + ], + "image_footnote": [], + "bbox": [ + 81, + 75, + 467, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d1bdff23c45e9ac1d093535aeb24ccf1e869f294a72052c458f942bb7a4ef9b3.jpg", + "image_caption": [ + "Figure 6. Limitation of Inpaint + HQSAM. In addition to poor mask quality errors (Fig. 5), we observe that Inpaint+HQSAM can lead to scene-unaware masks (e.g. mask for woman sitting in air)" + ], + "image_footnote": [], + "bbox": [ + 78, + 325, + 468, + 396 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ner. In this section, we evaluate the performance of SmartMask in terms of 1) user control, & 2) output mask quality.", + "bbox": [ + 76, + 460, + 467, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "1) User Control. As shown in Fig. 4, we observe that SmartMask allows the user to control the output object mask in four main ways. 1) Mask-free insertion: where the model automatically suggests diverse positions and scales for the target object (e.g., table, woman in Fig. 4a). 2) Bounding-box guidance: which allows user to specify the exact bounding box for object insertion (potted plant, motorbike in Fig. 4b). 3) Coarse spatial guidance: (Fig. 4c) providing a precise bounding box can be challenging for cases with complex object insertions e.g., dog with owner. SmartMask allows the user to only specify a coarse location for the target object, and the model automatically adjusts the object placement (i.e. dog with head near woman's hand) to capture object interactions. 3) User-scribbles: Finally, the user may also control the output shape by providing coarse scribbles. The smartmask model can use this as guidance to automatically predict the more finegrain-masks for the target object (e.g., palm-tree, gaming chair in Fig. 4d).", + "bbox": [ + 75, + 491, + 468, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "2) Output Mask Quality. We also report results on the quality of generated masks by showing comparisons with the mask-prediction head of the SmartBrush model [37]. Furthermore, we also show comparisons combining standard inpainting methods with HQSAM [13, 16]. To this end, we first use the provided bounding-box mask to inpaint the target object. The user-provided bounding-box and the inpainted output are then used as input to the HQSAM model [13] to obtain target object-mask predictions.", + "bbox": [ + 75, + 763, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1589dc68e1186ae72b1e2ef8b0a30c15b3d1bfced3a6229e6af2102faf362fe1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodUser Study Results
Win ↑DrawLose ↓
SDInpaint + HQSAM [13, 30]92.04%5.12%2.84%
Blended L-Diff + HQSAM [2, 13]88.91%8.33%2.75%
SmartBrush + HQSAM [13, 37]63.89%27.78%8.34%
SmartBrush Mask [37]91.67%2.78%5.56%
", + "bbox": [ + 500, + 75, + 890, + 157 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. User study results. For evaluating generated mask quality. We observe that SmartMask generates higher quality masks as compared to SmartBrush and various Inpaint+HQSAM methods.", + "bbox": [ + 498, + 164, + 890, + 205 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results are shown in Fig. 5. We observe that as compared to outputs of SmartBrush [37] mask-prediction head, SmartMask generates higher-quality masks with fewer artifacts. Similarly, while using HQSAM on inpainting outputs helps achieve good mask quality for some examples (e.g. child in row-2), the HQSAM generated masks (or the inpainted image) often have accompanying artifacts which limits the quality of the output masks. In addition to poor mask quality errors, we also observe that Inpaint+HQSAM can lead to scene-unaware masks (Fig. 6). This occurs because prior inpainting methods typically add additional objects in the background when performing object insertion. For instance, when inserting woman in a living room in Fig. 6), we observe that Adobe Gen-Fill [1] adds an additional chair on which the woman is sitting. Extracting only the object mask for such inpainted outputs can lead to scene-unaware masks where 'the woman appears floating in the air' as the chair was not present in the original image.", + "bbox": [ + 496, + 232, + 890, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The above findings are also reflected in a quantitative user study (Tab. 2), where human subjects are shown a pair of object mask suggestions (ours vs baselines discussed above), and asked to the select the mask suggestion with the higher quality. As shown in Tab. 2, we observe that SmartMask outputs are preferred by majority of human subjects over SmartBrush mask [37] and Inpaint + HQSAM outputs.", + "bbox": [ + 496, + 505, + 890, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. SmartMask for Semantic Layout Design", + "text_level": 1, + "bbox": [ + 498, + 619, + 844, + 636 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In addition to object insertion, we also find that when used iteratively along with the visual-instruction tuning based planning model from Sec. 3.3, SmartMask forms a convenient approach for designing detailed semantic layouts with a large number of fine-grain objects (e.g. humans, furniture etc.). Results are shown in Fig. 7a. We observe that given a sequence of user provided scene elements (e.g. painting, sofa, chair etc.), SmartMask generates the entire scene layout from scratch. Furthermore, unlike static layouts generated by a panoptic segmentation model, SmartMask generated layouts allow the user greater control over the details of each scene element. Since each object in the final layout is represented by a distinct object mask, the final layouts are highly controllable and allow for a range of custom operations such as adding, removing, modifying or moving objects through simple layer manipulations. (refer Fig. 7b).", + "bbox": [ + 496, + 643, + 890, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Controllable S2I Generation. Layout to image gener", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6503", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Input Prompt: A living room with a couch, chair and table.", + "bbox": [ + 354, + 78, + 609, + 88 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9a46b4685407607a3a4dd885a0e476304736ef7b91251dbbf99eed3c20f367fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 89, + 194, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/42401609e3a49356bb558be9ce6cc3711ef81e043ea513177c806c87f88e4a2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 89, + 290, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/feb372a54979f3e4ddef475b45b15a2e9d2812af9905091833fd158bb8786ee7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 89, + 385, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb4df6409925b628bf3fce0d6bffc1e98563e92ac99b5ab2bc98b09cd21e6cc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 387, + 89, + 482, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/498d06a6c97e6831fd9241436f9544aa6fe8228d52129524dd4d4baf56a01291.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 89, + 578, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0c24cf0bf4e50977f1e5dca77f1b201a94687281f4a03df5f84fa4087608996d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 89, + 676, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f1465f37731e52fa4f55f8c816274ced944d7e646d294ba0280d7169074fb3d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 89, + 772, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/65a8d9d495c409fa221330d86a8a077ae9152a9cf2780a5ca36c65a75aa4ad36.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 89, + 870, + 162 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1cc3854ddd4e16a081d4e85d7756644bccfd00cc6c0efee08d579f32131b4825.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 164, + 194, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/691ec8b0fe874d7100da9ec24c916e8eea1cc54327a63ed1089b56da64e20156.jpg", + "image_caption": [ + "(a) SmartMask for designing very detailed semantic layouts from scratch." + ], + "image_footnote": [], + "bbox": [ + 194, + 164, + 290, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/33cac393520128e3b2a5adf5523e423e6deb9fb6a25f574683258155bc2b548c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 164, + 385, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/393471f832fe7b182306381cb8959634fcd3009536702fd1cf711d6569caca68.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 387, + 164, + 482, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3bd3f724decfdb3b96c4d5c8a80b646b3126c83ab7557bbdd67d2d45d2645a7e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 164, + 578, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f759e0b747b87796ad5e54703f6dcee2e0fd585616212aa8b84f802a07d9916.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 164, + 676, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc64b9d0fc9ac011c04406610b6e3281727e87b035a9d3d5a59b79d307c5b34c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 679, + 164, + 772, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a8e501849aa4a30b58c93be9302a797729fe59b796b976100fffb59ea4932c81.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 774, + 164, + 870, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fd9c13250aa29a6e5c95a11d759323ac9786ecd6e3c0f37d8d54efb60ab3703f.jpg", + "image_caption": [ + "Add new objects at different layers" + ], + "image_footnote": [], + "bbox": [ + 99, + 266, + 287, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/82442166caec084566d6368ec4ac446e284c12a2bcf4e01bf1bc8c8e63444e1a.jpg", + "image_caption": [ + "Remove objects at different layers", + "(b) Analyzing controllability of the layouts generated with SmartMask." + ], + "image_footnote": [], + "bbox": [ + 294, + 266, + 480, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f3a420db952460cda33210094ffec638cf362064923df695146d864f4caf0a9e.jpg", + "image_caption": [ + "Modify objects at different layers" + ], + "image_footnote": [], + "bbox": [ + 486, + 266, + 674, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3e4ea7cf2e425134cbf8ad24cd6f04369daf06cfb41a8a10fa0392804105f318.jpg", + "image_caption": [ + "Move objects at different layers" + ], + "image_footnote": [], + "bbox": [ + 681, + 266, + 870, + 339 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f1d2439fcd2e54c94b35bde05278a7aa0772da3c0848760bd826b8997dfcf9cc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 371, + 192, + 443 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d21a5ce8b9462d97115f12075c63124749d16aa921d3bff122829e0272994068.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 371, + 287, + 443 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a6eed146a8db20079a85b0e61b436f4d353d968fe91d62e7e294afb6aac8e678.jpg", + "image_caption": [ + "Input Prompt: Two children sitting in front of a building" + ], + "image_footnote": [], + "bbox": [ + 290, + 371, + 383, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/81c98acd29d02f877801ff8cadbd02d094c51a931f6f71ff8e7c33d993a02696.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 371, + 478, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/153b7a968c523f4262be3138bfcbcce0c3c42e0f2dbda5b91d280f15956125e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 371, + 576, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c8a7fa196d600ccd2909b9d0870f393b0a59a69fcbf79ac0bd1147679050d706.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 371, + 673, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/772a083b73e522ba74e3119bc3d9d3c79be3546c3d573bc44e4caf424919097d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 674, + 371, + 767, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c0729db918085758d6b08988f2146748ae325de7fa138f59d8b8f80b768c38f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 771, + 371, + 864, + 441 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dd8849f499a6dd8f7f33a6470413f4eb4599ad1986a168d8c12b74f168d82a84.jpg", + "image_caption": [ + "User Scribble", + "Scribble + Controlnet", + "Figure 7. Fine-grained layout design. We observe that SmartMask when used iteratively, allows the user to generate very detailed layouts from scratch (a). The generated layouts are highly controllable and allow for custom variations through simple layer manipulations (b)." + ], + "image_footnote": [], + "bbox": [ + 99, + 454, + 192, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/849c41d3cabe8ec5505da94aa55177f996fb1fe134e24a778d84f8e38b82f8bb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 454, + 287, + 498 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a0cbaeea35788f6ddc3e83aaabc566909c79c153926d24d479448fb55b9e3fc8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 194, + 498, + 287, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bd49d37d6cf74a2fcb9c459c40f6cc3dbbf893cf63f42a755bc88b67a1ec2efc.jpg", + "image_caption": [ + "Input Prompt: a woman walking with two children on the beach", + "Scribble $^+$ PwW", + "(c) Using SmartMask generated layouts for better quality layout-to-image generation." + ], + "image_footnote": [], + "bbox": [ + 290, + 454, + 383, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0dc9473c3ef4c219d05398331353f6c2b00a169885c0b3aa6d7a6757a6a1f6af.jpg", + "image_caption": [ + "Scribble + DenseDiff" + ], + "image_footnote": [], + "bbox": [ + 385, + 454, + 478, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/02a845fdbc6348c31c153bf41f477e14d1d022f7f1aa9b50f739e97459b9f259.jpg", + "image_caption": [ + "Fine-g", + "Fine-grain Layout Generation (Ours)" + ], + "image_footnote": [], + "bbox": [ + 483, + 454, + 576, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e1b08b835353c919c58970dd5de2b0ef4c55ccc9a084e2af9872909d8e46cce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 580, + 454, + 673, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fbb9453edf6597213a3d0183eba7aa4cfc355b0a75e769a600234353ebd66f5c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 674, + 454, + 767, + 525 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b6351bafcf23570078b24480b0535b58ec2cb18f1aa29b3e045f5a050a566574.jpg", + "image_caption": [ + "Ours + Controlnet" + ], + "image_footnote": [], + "bbox": [ + 777, + 454, + 864, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ation methods e.g., ControlNet [41] enable the generation of controllable image outputs from user-scribble based semantic segmentation maps or layouts. However, generating the user-desired layouts with coarse scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g. humans, chairs etc.). As shown in Fig. 7c, we find that this can lead to image outputs with either deformity artifacts (child in row-1) or incorrect description (woman and children in row-2) when using ControlNet [41]. A similar problem is also observed in other coarse-scribble based S2I methods such as DenseDiffusion [14] and Paint-with-Words (PwW) [4], which provide coarse control over object position but are unable to control finegrain details such as pose, action etc. of the target object. SmartMask helps address this problem by allowing any novice user to generate controllable (Fig. 7b) fine-grain layouts from scratch, which can allow users to better leverage existing S2I methods [41] for higher quality layout-to-image generation (refer Fig. 7c).", + "bbox": [ + 75, + 601, + 472, + 888 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 599, + 619, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we present SmartMask which allows a novice user to generate scene-aware precision masks for object insertion and finegrained layout design. Existing methods for object insertion typically rely on a coarse bounding box or user-scribble input which can lead to poor background preservation around the inserted object. To address this, we propose a novel diffusion based framework which leverages semantic amodal segmentation data in order to learn to generate fine-grained masks for precise object insertion. When used along with a ControlNet-Inpaint model, we show that the proposed approach achieves superior object-insertion performance, preserving background content more effectively than previous methods. Additionally, we show that SmartMask provides a highly controllable approach for designing detailed layouts from scratch. As compared with user-scribble based layout design, we observe that the proposed approach can allow users to better leverage existing S2I methods for higher quality layout-to-image generation.", + "bbox": [ + 496, + 625, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6504", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adobe. Adobe firefly - generative ai for everyone, 2023. 2, 5, 6, 7", + "[2] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. ACM Transactions on Graphics (TOG), 42(4):1-11, 2023. 5, 6, 7", + "[3] Omri Avrahami, Dani Lischinski, and Ohad Fried. Blended diffusion for text-driven editing of natural images. 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Impaint" + }, + { + "type": "image", + "bbox": [ + 0.39, + 0.275, + 0.485, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.349, + 0.479, + 0.359 + ], + "angle": 0, + "content": "Blended Latent Diff." + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.275, + 0.582, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.491, + 0.349, + 0.577, + 0.359 + ], + "angle": 0, + "content": "Adobe SmartBrush" + }, + { + "type": "image", + "bbox": [ + 0.584, + 0.275, + 0.678, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.595, + 0.349, + 0.665, + 0.359 + ], + "angle": 0, + "content": "Adobe Gen-Fill" + }, + { + "type": "image", + "bbox": [ + 0.681, + 0.275, + 0.774, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.681, + 0.349, + 0.781, + 0.359 + ], + "angle": 0, + "content": "SmartMask Prediction" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.275, + 0.871, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.796, + 0.349, + 0.86, + 0.359 + ], + "angle": 0, + "content": "Output (Ours)" + }, + { + "type": "text", + "bbox": [ + 0.24, + 0.363, + 0.73, + 0.376 + ], + "angle": 0, + "content": "(a) SmartMask for performing object insertion (\"bride\") with better background preservation." + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.38, + 0.199, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.459, + 0.177, + 0.468 + ], + "angle": 0, + "content": "Input Image" + }, + { + "type": "image", + "bbox": [ + 0.199, + 0.38, + 0.294, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.459, + 0.471, + 0.469 + ], + "angle": 0, + "content": "SmartMask Outputs for \"woman beside a river in mountains\"" + }, + { + "type": "image", + "bbox": [ + 0.294, + 0.38, + 0.39, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.391, + 0.38, + 0.485, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.38, + 0.585, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.585, + 0.38, + 0.68, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.38, + 0.776, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.38, + 0.871, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.627, + 0.459, + 0.837, + 0.469 + ], + "angle": 0, + "content": "SmartMask Outputs for \"woman in a living room\"" + }, + { + "type": "text", + "bbox": [ + 0.177, + 0.472, + 0.793, + 0.485 + ], + "angle": 0, + "content": "(b) SmartMask for mask-free object insertion where it provides diverse suggestions without user bounding box input." + }, + { + "type": "text", + "bbox": [ + 0.346, + 0.489, + 0.634, + 0.499 + ], + "angle": 0, + "content": "Input Prompt: Two children sitting in front of a cardboard tree" + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.499, + 0.195, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.572, + 0.18, + 0.581 + ], + "angle": 0, + "content": "User Scribbles" + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.499, + 0.291, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.572, + 0.291, + 0.581 + ], + "angle": 0, + "content": "Scribble + Controlnet" + }, + { + "type": "image", + "bbox": [ + 0.292, + 0.499, + 0.387, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.303, + 0.572, + 0.378, + 0.581 + ], + "angle": 0, + "content": "Scribble + PwW" + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.499, + 0.482, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.389, + 0.572, + 0.482, + 0.581 + ], + "angle": 0, + "content": "Scribble + DenseDiff" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.499, + 0.579, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.573, + 0.707, + 0.583 + ], + "angle": 0, + "content": "Fine-grain Layout Generation (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.499, + 0.868, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.573, + 0.865, + 0.582 + ], + "angle": 0, + "content": "Ours + Controlnet" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.589, + 0.68, + 0.602 + ], + "angle": 0, + "content": "(c) SmartMask for fine-grain layout design for layout to image generation." + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.605, + 0.893, + 0.66 + ], + "angle": 0, + "content": "Figure 1. Overview. We introduce SmartMask which allows a novice user to generate high-fidelity masks for fine-grained object insertion and layout control. The proposed approach can be used for object insertion (a-b) where it not only allows for image inpainting with better background preservation (a) but also provides diverse suggestions for mask-free object insertion at different positions and scales. We also find that when used iteratively SmartMask can be used for fine-grained layout design (c) for better quality semantic-to-image generation." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.674, + 0.314, + 0.689 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The field of generative image inpainting and object insertion has made significant progress with the recent advent of latent diffusion models. Utilizing a precise object mask can greatly enhance these applications. However, due to the challenges users encounter in creating high-fidelity masks, there is a tendency for these methods to rely on more coarse masks (e.g., bounding box) for these applications. This results in limited control and compromised background content preservation. To overcome these limitations, we introduce SmartMask, which allows any novice user to create detailed masks for precise object insertion. Combined with a ControlNet-Inpaint model, our experiments demonstrate that SmartMask achieves superior object insertion qual" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.827 + ], + "angle": 0, + "content": "ity, preserving the background content more effectively than previous methods. Notably, unlike prior works the proposed approach can also be used even without user-mask guidance, which allows it to perform mask-free object insertion at diverse positions and scales. Furthermore, we find that when used iteratively with a novel instruction-tuning based planning model, SmartMask can be used to design detailed layouts from scratch. As compared with user-scribble based layout design, we observe that SmartMask allows for better quality outputs with layout-to-image generation methods." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.844, + 0.633, + 0.859 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Multi-modal object inpainting and insertion has gained widespread public attention with the recent advent of large-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6497" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.198 + ], + "angle": 0, + "content": "scale language-image (LLI) models [1-3, 19, 24, 27, 30, 37, 38]. A novice user can gain significant control over the inserted object details by combining text-based conditioning with additional guidance from a coarse bounding box or user-scribble mask. The text prompt can be used to describe the object semantics, while the coarse mask provides control over the position and scale of the generated object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.2, + 0.471, + 0.442 + ], + "angle": 0, + "content": "While convenient, the use of a coarse mask for object insertion suffers from two main limitations. 1) First, the use of a coarse mask can often be undesirable as it tends to also modify the background regions surrounding the inserted object [30, 37] (refer Fig. 1a). In order to minimize the background artifacts, recent works [37, 40] also explore the use of user-scribble based free-form mask instead of a bounding-box input. However, while feasible for describing coarse objects (e.g., mountains, teddy bear etc.), the generation of accurate free-form masks for objects with a number of fine-grain features (e.g., humans) can be quite challenging especially when limited to coarse user-scribbles. 2) Furthermore, generating variations in position and scale of the inserted object can also be troublesome as it requires the user to provide a new scene-aware free-form mask to satisfy the geometric constraints at the new scene location." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.687 + ], + "angle": 0, + "content": "To address these drawbacks, we introduce SmartMask, a context-aware diffusion model which allows a novice user to directly generate fine-grained mask suggestions for precise object insertion. In particular, given a semantic object description (e.g. kid) and the overall scene context, SmartMask generates scene-aware precise object masks which can then be used as input to a ControlNet-inpaint model [36, 41] to perform object insertion while preserving the contents of background image. As compared with coarse-mask based inpainting methods, we find that SmartMask provides a highly convenient and controllable method for object insertion and can be used 1) with user-inputs (bounding box, scribbles etc.): where the user can specify location and shape for the target object, or 2) in a mask-free manner: where the model automatically generates diverse suggestions for object insertion at diverse positions and scales." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In addition to object insertion, we also find that SmartMask can be used for fine-grain layout design. Existing segmentation-to-image (S2I) generation methods (e.g. ControlNet [41]) enable the generation of controllable image outputs from user-scribble based semantic segmentation maps. However, generating a good quality semantic layout can be quite challenging if the user wants to generate a scene with objects that require fine-grain details for best description (e.g., humans, chairs etc.). To address this challenge, we show that SmartMask when used with a novel instruction-tuning [34] based planning model allows the user to iteratively generate the desired scene layout from scratch. As compared with scribble based layout generation, we find that the proposed approach allows the users to" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "better leverage existing S2I generation methods (e.g. ControlNet [41]) for higher quality output generation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.894, + 0.259 + ], + "angle": 0, + "content": "The main contributions of the paper are: 1) We propose SmartMask which allows any novice user to generate precise object masks for finegrained object insertion with better background preservation. 2) We show that unlike prior works, the proposed approach can also be used for mask-free object insertion. 3) Finally, we demonstrate that SmartMask can be used iteratively to generate detailed semantic layouts, which allows users to better leverage existing S2I generation methods for higher quality output generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.274, + 0.642, + 0.29 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.3, + 0.892, + 0.45 + ], + "angle": 0, + "content": "Diffusion based multi-modal image inpainting [1-3, 19, 24, 27, 30, 37, 38] has gained widespread attention with advent of text-conditioned diffusion models [24, 29, 30, 32, 39]. Despite their efficacy, these methods use coarse bounding box or user-scribble based masks for object inpainting which leads to poor background preservation around the inserted object. In contrast, SmartMask directly allows user to generate precise masks for the target object, which can then be combined with ControlNet-Inpaint [30, 41] to insert the target object while better preserving background contents." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.893, + 0.602 + ], + "angle": 0, + "content": "Mask-free object placement has been studied in the context of image compositing methods [9, 20, 22, 25, 35, 42, 44, 46], where given a cropped RGB object instance and a target image, the goal is to suggest different positions for the target object. In contrast, we study the problem of mask-free object insertion using text-only guidance. Lee et al. [18] propose a GAN-based approach to directly model a distribution of potential object locations. However, the learned distribution is w.r.t to a specific object class (e.g., cars) which limits its generalizability for diverse use-cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.603, + 0.894, + 0.83 + ], + "angle": 0, + "content": "Semantic layout to image generation methods have been explored to enable controllable image synthesis from user-scribble based semantic segmentation maps [8, 12, 17, 23, 26, 33, 45]. Recently, [4, 6, 14, 31] propose a cross-attention based training-free approach for controlling the overall scene layout from coarse user-scribbles using text-conditioned diffusion models. Zhang et al. [41] propose a versatile ControlNet model which allows the users to control the output layout on a more fine-grained level through an input semantic map. While effective, generating desired semantic layout with scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g., humans). SmartMask helps address this problem by allowing users to generate more fine-grained layouts to facilitate better quality S2I generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.63, + 0.86 + ], + "angle": 0, + "content": "3. Our Method" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Given an input image \\(\\mathcal{I}\\), object semantic label \\(\\mathcal{T}_{obj}\\) and a textual description \\(\\mathcal{T}_{context}\\) describing the final scene con" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6498" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.066, + 0.892, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.398, + 0.895, + 0.484 + ], + "angle": 0, + "content": "Figure 2. Method Overview. A key idea behind SmartMask is to leverage semantic amodal segmentation data [28, 47] in order to obtain high-quality paired training annotations for mask-free single or multi-step object insertion. During training (top), given a training image \\(\\mathcal{I}\\) with caption \\(C\\), we stack \\(k\\) ordered instance maps \\(\\{A_1, A_2, \\ldots, A_k\\}\\) to obtain an intermediate semantic map \\(S_k\\). The diffusion model is then trained to predict the instance map \\(A_{k+1}\\), conditional on the semantic map \\(S_k\\), \\(\\mathcal{T}_{obj} \\gets \\mathcal{O}_{k+1}\\) and scene context \\(\\mathcal{T}_{context} \\gets C\\). During inference (bottom), given a real image \\(\\mathcal{I}\\), we first use a panoptic segmentation model to compute semantic map \\(S_I\\). The generated semantic layout is then directly used as input to the trained diffusion model in order to predict the fine-grained mask for the inserted object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.495, + 0.471, + 0.662 + ], + "angle": 0, + "content": "text, our goal is predict a fine-grained mask \\(\\mathcal{M}_{obj}\\) for the target object. The object mask \\(\\mathcal{M}_{obj}\\) could then be used as input to a ControlNet-Inpaint model for fine-grained object insertion (Sec. 4.1) or used to design detailed semantic layouts from scratch (Sec. 4.3). For instance, SmartMask could be used for single object insertion, where given an image \\(\\mathcal{I}\\) depicting a man on a bench, \\(\\{\\mathcal{T}_{obj} : \\text{\"woman'}\\}\\) and \\(\\{\\mathcal{T}_{\\text{context}} : \\text{\"a couple sitting on a bench'}\\}\\), our goal is to predict fine-grain binary mask \\(\\mathcal{M}_{woman}\\) which places the 'woman' in a manner such that the resulting scene aligns with overall scene context of a 'a couple sitting on a bench'." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Similarly, SmartMask could also be used for multiple object insertion. For instance, given an image \\(\\mathcal{I}\\) depicting a wedding, the user may wish to add multiple objects \\{'man', 'woman' and 'kid'\\} such that the final scene aligns with the \\(\\{\\mathcal{T}_{\\text {context }}: \\text { 'a family posing for a picture at a wedding }\\}\\). Unlike prior image inpainting methods which are limited independently adding each object to the scene, the goal of the smartmask model is to add each object in a manner such the generated 'man', 'woman' and 'kid' appear to be 'a family posing for a picture at a wedding'. (refer Fig. 2a)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In the next sections, we describe the key SmartMask components in detail. In particular, in Sec. 3.1 we discuss how SmartMask can leverage semantic amodal segmentation data in order to obtain high-quality paired annotations for mask-free object insertion. We then discuss a simple" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.892, + 0.587 + ], + "angle": 0, + "content": "data-adaptation strategy which allows the user to also control the position, shape of the inserted object using coarse inputs (bounding-box, scribbles) in Sec. 3.2. Finally, in Sec. 3.3 we propose a visual-instruction tuning [21] based planning model which when used with SmartMask, allows for generation of detailed semantic layouts from scratch." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.593, + 0.874, + 0.609 + ], + "angle": 0, + "content": "3.1. SmartMask for Mask-Free Object Insertion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.616, + 0.892, + 0.752 + ], + "angle": 0, + "content": "Semantic-Space Task Formulation. Directly learning a model for our task in pixel space can be quite challenging, as it would require large-scale collection of training data for single or multi-step object insertion while maintaining background preservation. To address this key challenge, a core idea of our approach is to propose an equivalent task formulation which allows us to leverage large-scale semantic amodal segmentation data [28, 47] for generating high-quality paired training data in the semantic space (Fig. 2)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.892, + 0.828 + ], + "angle": 0, + "content": "SmartMask Training. In particular during training, given an image \\(\\mathcal{I}\\), with a sequence of ordered amodal semantic instance maps \\(\\{A_1, A_2 \\ldots A_n\\}\\) and corresponding semantic object labels \\(\\{\\mathcal{O}_1, \\mathcal{O}_2 \\ldots \\mathcal{O}_n\\}\\), we first compute an intermediate layer semantic map as," + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.833, + 0.892, + 0.851 + ], + "angle": 0, + "content": "\\[\nS _ {k} = f _ {\\text {l a y e r}} \\left(\\left\\{A _ {1}, A _ {2} \\dots A _ {k} \\right\\}\\right) \\quad \\text {w h e r e} k \\in [ 1, n ]. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.855, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\( k \\) is randomly chosen from \\( [1, n] \\) and \\( f_{layer} \\) is a layering operation which stacks the amodal semantic segmentation maps from \\( i \\in [1, k] \\) in an ordered manner (Fig. 2)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6499" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.26 + ], + "angle": 0, + "content": "We next train a diffusion-based mask prediction model \\(\\mathcal{D}_{\\theta}\\) which takes as input the above computed intermediate semantic layer map \\(S_{k}\\), textual description for next object \\(\\mathcal{T}_{obj} \\gets \\mathcal{O}_{k+1}\\), overall caption \\(\\mathcal{T}_{context} \\gets C_{\\mathcal{I}}\\) (for image \\(\\mathcal{I}\\)) and learns to predict the binary mask \\(\\{A_{k+1}\\}\\) for the next object. To this end, we first pass the intermediate semantic map \\(S_{k}\\) through a learnable encoder \\(\\mathcal{E}_{\\phi}\\) to obtain the encoded features \\(\\mathcal{E}_{\\phi}(S_{k})\\). At any timestep \\(t\\) of the reverse diffusion process, the denoising noise prediction \\(\\epsilon_{t}\\) is then computed conditional jointly on previous noise latent \\(\\mathbf{z}_{t}\\), and model inputs \\(\\{\\mathcal{E}_{\\theta}(S_{k}), \\mathcal{T}_{obj}, \\mathcal{T}_{context}\\}\\) as," + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.268, + 0.47, + 0.285 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\epsilon} _ {p r e d} (t) = \\mathcal {U} _ {\\theta} (\\mathbf {z} _ {t}, \\mathcal {E} _ {\\phi} (S _ {k}), \\mathcal {T} _ {o b j}, \\mathcal {T} _ {\\text {c o n t e x t}}, t), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.293, + 0.454, + 0.308 + ], + "angle": 0, + "content": "where \\(\\mathcal{U}_{\\theta}\\) represents the U-Net of the diffusion model \\(\\mathcal{D}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.308, + 0.47, + 0.34 + ], + "angle": 0, + "content": "The overall diffusion model \\(\\mathcal{D}\\) is then trained to predict the next layer \\(A_{k + 1}\\) using the following diffusion loss," + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.348, + 0.47, + 0.367 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} (\\theta , \\phi) = \\mathbf {E} _ {t \\sim [ 1, T ], S _ {k}, A _ {k + 1}, \\epsilon_ {t}} \\left[ \\| \\epsilon_ {t} - \\tilde {\\epsilon} _ {p r e d} (t) \\| ^ {2} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.375, + 0.469, + 0.42 + ], + "angle": 0, + "content": "where \\(T\\) is total number of reverse diffusion steps, \\(\\epsilon_t\\sim \\mathcal{N}(0,I)\\) is sampled from a normal distribution and \\(A_{k + 1}\\) represents ground truth binary mask for next object \\(\\mathcal{O}_{k + 1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.421, + 0.47, + 0.542 + ], + "angle": 0, + "content": "SmartMask Inference. During inference, given an input image \\(\\mathcal{I}\\), semantic object category \\(\\mathcal{T}_{obj}\\) and a textual description \\(\\mathcal{T}_{\\text {context }}\\) describing the final scene context, we first use a panoptic semantic segmentation model [15] to obtain the corresponding semantic layout map \\(\\mathcal{S}_{\\mathcal{I}}\\). The generated semantic layout \\(\\mathcal{S}_{\\mathcal{I}}\\) is then directly used as input to the above trained diffusion model \\(\\mathcal{D}_{\\theta}\\) in order to predict the fine-grained mask \\(\\mathcal{M}_{obj}\\) for the target object," + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.551, + 0.47, + 0.568 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {o b j} = \\mathcal {D} _ {\\theta} \\left(\\mathcal {E} _ {\\phi} \\left(\\mathcal {S} _ {I}\\right), \\mathcal {T} _ {o b j}, \\mathcal {T} _ {\\text {c o n t e x t}}\\right). \\tag {4}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.585, + 0.44, + 0.601 + ], + "angle": 0, + "content": "3.2. Data Adaptation for Precise Mask Control" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.76 + ], + "angle": 0, + "content": "While the diffusion model trained in Sec. 3.1, allows the user to perform mask-free object insertion at diverse positions and scales, the user may also wish to obtain more direct control over the spatial location and details of the inserted object. To this end, we propose a simple train-time data adaptation strategy which allows smartmask to be easily adapted to diverse forms of user control (Fig. 4). In particular, given the intermediate layer map \\( S_{k} \\) computed using Eq. 1 and ground truth mask \\( A_{k + 1} \\) for the next object, we replace the input \\( S_{k} \\) to the diffusion model as," + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.769, + 0.47, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\tilde {S} _ {k} = g \\left(S _ {k}, G _ {o b j}\\right) = S _ {k} \\odot \\left(1 - \\alpha G _ {o b j}\\right) + \\alpha G _ {o b j}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.469, + 0.856 + ], + "angle": 0, + "content": "where \\( G_{obj} \\) is the additional guidance input (e.g., bounding box mask, coarse scribbles etc.) provided by the user and \\( \\alpha = 0.7 \\) helps add additional guidance while still preserving the content of the original input \\( S_{k} \\) after data adaptation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Training. In this paper, we mainly consider four main guidance inputs \\( G_{obj} \\) for additional mask control for adapting SmartMask. 1) Mask-free guidance: in absence of any" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.333 + ], + "angle": 0, + "content": "additional user inputs, we use \\( G_{obj} = \\mathbf{0}^{H,W} \\) which prompts the model to suggest fine-grained masks for object insertion at diverse positions and scales. 2) Bounding-box guidance: we set \\( G_{obj} \\) as a binary mask corresponding to ground truth object mask \\( A_{k+1} \\). 3) Coarse Spatial Guidance: Expecting the user to provide precise bounding box for object insertion is not always convenient and can lead to errors if bounding box is not correct. We therefore introduce a coarse spatial control where user may provide a coarse spatial location and the model learns to infer the best placement of the object around the suggested region (Fig. 4c). During training, the same is achieved by setting \\( G_{obj} \\) as a coarse gaussian blob centered at the ground truth object mask \\( A_{k+1} \\). 4) User scribbles: Finally, we also allow the user to describe target object using free-form coarse scribbles, by setting \\( G_{obj} \\) as the dilated mask output of ground-truth object mask \\( A_{k+1} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.334, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Inference. At inference time, the additional guidance input \\( G_{obj} \\) (e.g. bounding box mask, coarse scribbles etc.) is directly provided by the user. Given an input image \\( \\mathcal{I} \\) with semantic layout \\( S_{\\mathcal{I}} \\), we then use transformation from Eq. 5 as input to the adapted SmartMask model in order to generate object insertion suggestions with additional control." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.437, + 0.855, + 0.453 + ], + "angle": 0, + "content": "3.3. Global Planning for Multi-Step Inference" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.461, + 0.892, + 0.598 + ], + "angle": 0, + "content": "While the original SmartMask model allows the user to generate fine-grained masks for single object insertion, we would also like to use SmartMask for iterative use cases such as multiple object insertion (Sec. A.1) or designing a fine-grained layout from scratch with large number \\((>10)\\) of scene elements. Such an iterative use of SmartMask would require the model to carefully plan the spatial location of each inserted object to allow for the final scene to be consistent with the final scene context description \\(\\mathcal{T}_{\\text{context}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.764 + ], + "angle": 0, + "content": "To achieve this, we train a visual-instruction tuning [21] based planning model which given the input semantic layout \\( S_{I} \\), learns to plan the positioning of different scene elements over long sequences. Given a semantic object description \\( T_{obj} \\) and final scene context \\( T_{context} \\), the global planning model provides several bounding box suggestions for object insertion. SmartMask model then uses the above predictions as coarse spatial guidance input \\( G_{obj} \\) to provide fine-grained mask suggestions for the next object. The above process can then be repeated in an iterative manner until all objects have been added to the scene (refer Fig. 7a)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The global planning model is trained in two stages. 1) Feature Alignment. Typical instruction tuning models are often trained on real images. In contrast, as discussed in Sec. 3.1 we would like to model our problem in semantic space as it allows us to leverage amodal segmentation data for training. To address this domain gap, we first finetune an existing LLaVA model [21] to understand the semantic inputs. To do this, given an intermediate semantic map \\( S_{k} \\) computed using Eq. 1, we finetune the projection matrix \\( \\mathbf{W} \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6500" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.08, + 0.892, + 0.409 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.415, + 0.893, + 0.444 + ], + "angle": 0, + "content": "Figure 3. Qualitative Results for Image Inpainting. We observe that as compared to with state-of-the-art image inpainting [1, 2, 30, 37] methods, SmartMask allows the user to perform object insertion while better preserving the background around the inserted object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.471, + 0.489 + ], + "angle": 0, + "content": "of the LLaVA model [21] \\(\\mathcal{H}\\) to predict the semantic object labels \\(\\{\\mathcal{O}_1,\\mathcal{O}_2\\ldots \\mathcal{O}_k\\}\\) described in the current scene as," + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.5, + 0.469, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a l i g n}} (\\mathbf {W}) = \\mathcal {L} _ {C E} (< \\mathcal {O} _ {1}, \\mathcal {O} _ {2} \\dots \\mathcal {O} _ {k} >, \\mathcal {H} (S _ {k})). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.47, + 0.651 + ], + "angle": 0, + "content": "2) Instruction-Tuning. Finally, keeping the visual encoder weights for LLaVA model fixed, we next finetune both project matrix \\(\\mathbf{W}\\) and LLM weights \\(\\Phi\\) [43] for global object planning. In particular, given an intermediate semantic map \\(S_{k}\\), we first compute the bounding box coordinates \\(\\mathcal{B}_{k+1} = \\{x_{min}, y_{min}, x_{max}, y_{max}\\}\\) for the next object \\(\\mathcal{T}_{obj} = \\mathcal{O}_{k+1}\\) using ground truth object mask \\(\\mathcal{A}_{k+1}\\). The LLaVA based planning model \\(\\mathcal{H}\\) is then trained as," + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.664, + 0.469, + 0.681 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {i n s t r u c t}} (\\mathbf {W}, \\Phi) = \\mathcal {L} _ {C E} \\left(\\mathcal {B} _ {k + 1}, \\mathcal {H} \\left(S _ {k}, \\mathcal {T} _ {\\text {o b j}}, C\\right)\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.47, + 0.74 + ], + "angle": 0, + "content": "where \\( C \\) represents the caption for the final scene (obtained using ground-truth image \\( \\mathcal{I} \\)) and provides the model context for placing different scene elements in the image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.21, + 0.772 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Training Data Collection. As discussed in Sec. 3, we note that a key idea behind SmartMask is to model the object insertion problem in semantic space (instead of pixel space), which allows us to leverage semantic amodal segmentation data to obtain large-scale paired training annotations for single or multiple object insertions. However, traditional datasets for semantic amodal segmentations such as COCOA [47] (2,500 images, 22,163 instances) and KINS [28]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.456, + 0.892, + 0.502 + ], + "angle": 0, + "content": "(7,517 images, 92,492 instances) though containing fine-grained amodal segmentation annotations may lack sufficient diversity to generalize across different use-cases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.505, + 0.893, + 0.672 + ], + "angle": 0, + "content": "To address this, we curate a new large-scale dataset consisting of fine-grain amodal segmentation masks for different objects in an input image. The overall dataset consists of 32785 diverse real world images and a total of 725897 object instances across more than 500 different semantic classes (e.g. man, woman, trees, furniture etc.). Each image \\(\\mathcal{I}\\) in the dataset consists of a variable number of object instances \\(\\{A_1, A_2, \\ldots, A_n\\}\\), \\(n \\in [2, 50]\\) and is annotated with an ordered sequence of semantic amodal segmentation maps \\(\\{S_1, S_2, \\ldots, S_n\\}\\). The detailed descriptions \\(C_I\\) for each image are obtained using the InstructBLIP [7] model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "SmartMask Training. In order to leverage the rich generalizable prior of T2I diffusion models, we use the weights from publicly available Stable-Diffusion-v1.5 model [30] in order to initialize the weights of the SmartMask U-Net model trained in Sec. 3.1. Similar to [5], we modify the architecture of the U-Net model to also condition the output mask predictions on segmentation layout \\( S_{I} \\). The SmartMask model is trained for a total of 100k iterations with a batch size of 192 and learning rate \\( 1e - 5 \\) using 8 Nvidia-A100 GPUs. During inference, a panoptic semantic segmentation model finetuned on the dataset in Sec. 4 is used for converting real image \\( \\mathcal{L} \\) to its semantic layout \\( S_{I} \\). ControlNet model trained with SDXL backbone was used to perform precise object insertion with SmartMask outputs. Please refer the supp. material for further training details." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6501" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.071, + 0.193, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.071, + 0.315, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.316, + 0.071, + 0.387, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.072, + 0.483, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.146, + 0.193, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.145, + 0.291, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.292, + 0.145, + 0.385, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.145, + 0.483, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.22, + 0.171, + 0.23 + ], + "angle": 0, + "content": "Image Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.296, + 0.22, + 0.381, + 0.229 + ], + "angle": 0, + "content": "SmartMask Outputs" + }, + { + "type": "image_caption", + "bbox": [ + 0.202, + 0.232, + 0.36, + 0.243 + ], + "angle": 0, + "content": "(a) Mask-free object insertion" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.071, + 0.6, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.601, + 0.071, + 0.697, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.071, + 0.794, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.796, + 0.071, + 0.892, + 0.145 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.146, + 0.601, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.146, + 0.697, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.146, + 0.794, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.796, + 0.146, + 0.892, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.22, + 0.58, + 0.229 + ], + "angle": 0, + "content": "Image Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.706, + 0.22, + 0.788, + 0.229 + ], + "angle": 0, + "content": "SmartMask Outputs" + }, + { + "type": "image_caption", + "bbox": [ + 0.563, + 0.232, + 0.816, + 0.244 + ], + "angle": 0, + "content": "(b) Bounding-box guidance for mask generation" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.247, + 0.192, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.193, + 0.248, + 0.29, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.248, + 0.385, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.248, + 0.483, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.322, + 0.193, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.194, + 0.322, + 0.29, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.322, + 0.386, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.322, + 0.483, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.153, + 0.41, + 0.411, + 0.422 + ], + "angle": 0, + "content": "(c) Coarse-spatial guidance for mask generation" + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.248, + 0.6, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.248, + 0.698, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.6, + 0.322, + 0.697, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.248, + 0.794, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.796, + 0.248, + 0.892, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.495, + 0.322, + 0.601, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.322, + 0.698, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.322, + 0.794, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.796, + 0.322, + 0.892, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.598, + 0.41, + 0.782, + 0.422 + ], + "angle": 0, + "content": "(d) Scribble-based object insertion" + }, + { + "type": "image_caption", + "bbox": [ + 0.078, + 0.425, + 0.89, + 0.44 + ], + "angle": 0, + "content": "Figure 4. Diverse User Controls. SmartMask is easily adaptable to diverse user-controls for precise mask generation for the target object." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.451, + 0.362, + 0.467 + ], + "angle": 0, + "content": "4.1. SmartMask for Object Insertion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.469, + 0.611 + ], + "angle": 0, + "content": "Baselines. We compare the performance of our approach on object-insertion with prior works on performing multimodal image-inpainting using a textual description and coarse bounding box mask. In particular we show comparisons with SD-Inpaint [30], SDXL-Inpaint [27], Blended-Latent Diffusion [30], and Adobe SmartBrush [37]. We also compare the performance of our approach with state-of-the-art commercial inpainting tools by reporting results on recently released Generative-Fill from Adobe Firefly [1]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Evaluation Metrics. Following [37], we report the results for object insertion using 1) Local-FID [11] which measures the realism of the generated objects, 2) CLIP-Score [10] which measures the alignment between the textual description and the generated object, and 3) Norm. L2-BG: which reports the normalized L2 difference in the background regions before and after insertion, and helps capture the degree to which the background was preserved." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Qualitative Results. Results are shown in Fig. 3. We observe that when performing objectn insertion using a coarse bounding box mask, traditional inpainting methods usually lead to a lot of changes in the background regions around the inserted object (e.g. living room details in row-1&2, mountains in row-4 etc.). Adobe SmartBrush [37] which is trained to allow better background preservation, shows better performance, however, still suffers from notable changes to background regions. In contrast, by directly predicting a high-fidelity mask for the target object, the proposed approach allows the user to add new objects on the scene with" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.45, + 0.907, + 0.555 + ], + "angle": 0, + "content": "
MethodEvaluation Criteria
Local-FID ↓CLIP-Score ↑Norm. L2-BG ↓
SD Inpaint [30]22.310.2490.374
SDXL Inpaint [27]21.840.2350.623
Blended L-Diffusion [2]39.770.2530.451
Adobe SmartBrush [37]17.940.2620.304
Adobe Gen-Fill* [1]N/A0.2680.289
Smartmask (Ours)19.210.2610.098
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.562, + 0.892, + 0.604 + ], + "angle": 0, + "content": "Table 1. Quantitative results for image inpainting. We observe that in comparison with state-of-art image inpainting methods, our approach leads to better preservation of background regions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.748 + ], + "angle": 0, + "content": "minimal changes to the background image. Furthermore we observe that target object masks are generated in a scene-aware manner, which helps us add new objects while interacting with already existing ones. For instance, when adding 'a man to a couch with table in front' (Fig. 3), prior works typically replace the couch and table to insert the target object ('man'). In contrast, smartmask places the 'man sitting on the couch with his leg on the table', and provides a more natural way for inserting objects in complex scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Quantitative Results. In addition to qualitative results, we also report the performance of our approach quantitatively in Tab. 1. We find that similar to results in Fig. 3, the proposed approach shows better background preservation (Norm. L2-BG ↓) while performing comparably in terms of image quality (local-FID) and text-alignment (CLIP-Score)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.848, + 0.88, + 0.864 + ], + "angle": 0, + "content": "4.2. Evaluating Mask Controllability and Quality" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "A key advantage of SmartMask is the ability to generate high-quality masks for target object in a controllable man" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6502" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.077, + 0.468, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.282, + 0.47, + 0.311 + ], + "angle": 0, + "content": "Figure 5. Comparing output mask quality with different Inpaint + HQSAM (middle) methods and SmartBrush mask output (right)." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.327, + 0.47, + 0.397 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.403, + 0.47, + 0.446 + ], + "angle": 0, + "content": "Figure 6. Limitation of Inpaint + HQSAM. In addition to poor mask quality errors (Fig. 5), we observe that Inpaint+HQSAM can lead to scene-unaware masks (e.g. mask for woman sitting in air)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.461, + 0.468, + 0.492 + ], + "angle": 0, + "content": "ner. In this section, we evaluate the performance of SmartMask in terms of 1) user control, & 2) output mask quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.764 + ], + "angle": 0, + "content": "1) User Control. As shown in Fig. 4, we observe that SmartMask allows the user to control the output object mask in four main ways. 1) Mask-free insertion: where the model automatically suggests diverse positions and scales for the target object (e.g., table, woman in Fig. 4a). 2) Bounding-box guidance: which allows user to specify the exact bounding box for object insertion (potted plant, motorbike in Fig. 4b). 3) Coarse spatial guidance: (Fig. 4c) providing a precise bounding box can be challenging for cases with complex object insertions e.g., dog with owner. SmartMask allows the user to only specify a coarse location for the target object, and the model automatically adjusts the object placement (i.e. dog with head near woman's hand) to capture object interactions. 3) User-scribbles: Finally, the user may also control the output shape by providing coarse scribbles. The smartmask model can use this as guidance to automatically predict the more finegrain-masks for the target object (e.g., palm-tree, gaming chair in Fig. 4d)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.902 + ], + "angle": 0, + "content": "2) Output Mask Quality. We also report results on the quality of generated masks by showing comparisons with the mask-prediction head of the SmartBrush model [37]. Furthermore, we also show comparisons combining standard inpainting methods with HQSAM [13, 16]. To this end, we first use the provided bounding-box mask to inpaint the target object. The user-provided bounding-box and the inpainted output are then used as input to the HQSAM model [13] to obtain target object-mask predictions." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.077, + 0.892, + 0.159 + ], + "angle": 0, + "content": "
MethodUser Study Results
Win ↑DrawLose ↓
SDInpaint + HQSAM [13, 30]92.04%5.12%2.84%
Blended L-Diff + HQSAM [2, 13]88.91%8.33%2.75%
SmartBrush + HQSAM [13, 37]63.89%27.78%8.34%
SmartBrush Mask [37]91.67%2.78%5.56%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.165, + 0.892, + 0.207 + ], + "angle": 0, + "content": "Table 2. User study results. For evaluating generated mask quality. We observe that SmartMask generates higher quality masks as compared to SmartBrush and various Inpaint+HQSAM methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.233, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Results are shown in Fig. 5. We observe that as compared to outputs of SmartBrush [37] mask-prediction head, SmartMask generates higher-quality masks with fewer artifacts. Similarly, while using HQSAM on inpainting outputs helps achieve good mask quality for some examples (e.g. child in row-2), the HQSAM generated masks (or the inpainted image) often have accompanying artifacts which limits the quality of the output masks. In addition to poor mask quality errors, we also observe that Inpaint+HQSAM can lead to scene-unaware masks (Fig. 6). This occurs because prior inpainting methods typically add additional objects in the background when performing object insertion. For instance, when inserting woman in a living room in Fig. 6), we observe that Adobe Gen-Fill [1] adds an additional chair on which the woman is sitting. Extracting only the object mask for such inpainted outputs can lead to scene-unaware masks where 'the woman appears floating in the air' as the chair was not present in the original image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.612 + ], + "angle": 0, + "content": "The above findings are also reflected in a quantitative user study (Tab. 2), where human subjects are shown a pair of object mask suggestions (ours vs baselines discussed above), and asked to the select the mask suggestion with the higher quality. As shown in Tab. 2, we observe that SmartMask outputs are preferred by majority of human subjects over SmartBrush mask [37] and Inpaint + HQSAM outputs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.621, + 0.845, + 0.637 + ], + "angle": 0, + "content": "4.3. SmartMask for Semantic Layout Design" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.885 + ], + "angle": 0, + "content": "In addition to object insertion, we also find that when used iteratively along with the visual-instruction tuning based planning model from Sec. 3.3, SmartMask forms a convenient approach for designing detailed semantic layouts with a large number of fine-grain objects (e.g. humans, furniture etc.). Results are shown in Fig. 7a. We observe that given a sequence of user provided scene elements (e.g. painting, sofa, chair etc.), SmartMask generates the entire scene layout from scratch. Furthermore, unlike static layouts generated by a panoptic segmentation model, SmartMask generated layouts allow the user greater control over the details of each scene element. Since each object in the final layout is represented by a distinct object mask, the final layouts are highly controllable and allow for a range of custom operations such as adding, removing, modifying or moving objects through simple layer manipulations. (refer Fig. 7b)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Controllable S2I Generation. Layout to image gener" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6503" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.356, + 0.079, + 0.61, + 0.089 + ], + "angle": 0, + "content": "Input Prompt: A living room with a couch, chair and table." + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.09, + 0.195, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.09, + 0.291, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.292, + 0.09, + 0.387, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.09, + 0.483, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.09, + 0.58, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.09, + 0.678, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.09, + 0.774, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.09, + 0.871, + 0.163 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.165, + 0.195, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.165, + 0.291, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.292, + 0.165, + 0.387, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.388, + 0.165, + 0.483, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.165, + 0.58, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.165, + 0.678, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.68, + 0.165, + 0.774, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.165, + 0.871, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.292, + 0.24, + 0.678, + 0.253 + ], + "angle": 0, + "content": "(a) SmartMask for designing very detailed semantic layouts from scratch." + }, + { + "type": "image_caption", + "bbox": [ + 0.117, + 0.257, + 0.263, + 0.267 + ], + "angle": 0, + "content": "Add new objects at different layers" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.267, + 0.288, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.319, + 0.257, + 0.46, + 0.267 + ], + "angle": 0, + "content": "Remove objects at different layers" + }, + { + "type": "image", + "bbox": [ + 0.295, + 0.267, + 0.481, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.512, + 0.257, + 0.65, + 0.267 + ], + "angle": 0, + "content": "Modify objects at different layers" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.267, + 0.675, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.71, + 0.257, + 0.842, + 0.267 + ], + "angle": 0, + "content": "Move objects at different layers" + }, + { + "type": "image", + "bbox": [ + 0.683, + 0.267, + 0.871, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.297, + 0.343, + 0.672, + 0.355 + ], + "angle": 0, + "content": "(b) Analyzing controllability of the layouts generated with SmartMask." + }, + { + "type": "image_caption", + "bbox": [ + 0.351, + 0.36, + 0.607, + 0.371 + ], + "angle": 0, + "content": "Input Prompt: Two children sitting in front of a building" + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.372, + 0.194, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.372, + 0.288, + 0.444 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.372, + 0.384, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.372, + 0.48, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.372, + 0.578, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.372, + 0.674, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.372, + 0.769, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.772, + 0.372, + 0.865, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.445, + 0.624, + 0.454 + ], + "angle": 0, + "content": "Input Prompt: a woman walking with two children on the beach" + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.455, + 0.194, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.527, + 0.178, + 0.537 + ], + "angle": 0, + "content": "User Scribble" + }, + { + "type": "image", + "bbox": [ + 0.195, + 0.455, + 0.289, + 0.499 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.499, + 0.288, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.527, + 0.29, + 0.537 + ], + "angle": 0, + "content": "Scribble + Controlnet" + }, + { + "type": "image", + "bbox": [ + 0.291, + 0.455, + 0.384, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.527, + 0.374, + 0.537 + ], + "angle": 0, + "content": "Scribble \\(^+\\) PwW" + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.455, + 0.48, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.387, + 0.527, + 0.481, + 0.537 + ], + "angle": 0, + "content": "Scribble + DenseDiff" + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.455, + 0.578, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.488, + 0.527, + 0.572, + 0.537 + ], + "angle": 0, + "content": "Fine-g" + }, + { + "type": "image", + "bbox": [ + 0.581, + 0.455, + 0.674, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.545, + 0.528, + 0.707, + 0.538 + ], + "angle": 0, + "content": "Fine-grain Layout Generation (Ours)" + }, + { + "type": "image", + "bbox": [ + 0.675, + 0.455, + 0.768, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.455, + 0.865, + 0.526 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.528, + 0.865, + 0.538 + ], + "angle": 0, + "content": "Ours + Controlnet" + }, + { + "type": "image_caption", + "bbox": [ + 0.26, + 0.542, + 0.71, + 0.555 + ], + "angle": 0, + "content": "(c) Using SmartMask generated layouts for better quality layout-to-image generation." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.557, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Figure 7. Fine-grained layout design. We observe that SmartMask when used iteratively, allows the user to generate very detailed layouts from scratch (a). The generated layouts are highly controllable and allow for custom variations through simple layer manipulations (b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.473, + 0.89 + ], + "angle": 0, + "content": "ation methods e.g., ControlNet [41] enable the generation of controllable image outputs from user-scribble based semantic segmentation maps or layouts. However, generating the user-desired layouts with coarse scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g. humans, chairs etc.). As shown in Fig. 7c, we find that this can lead to image outputs with either deformity artifacts (child in row-1) or incorrect description (woman and children in row-2) when using ControlNet [41]. A similar problem is also observed in other coarse-scribble based S2I methods such as DenseDiffusion [14] and Paint-with-Words (PwW) [4], which provide coarse control over object position but are unable to control finegrain details such as pose, action etc. of the target object. SmartMask helps address this problem by allowing any novice user to generate controllable (Fig. 7b) fine-grain layouts from scratch, which can allow users to better leverage existing S2I methods [41] for higher quality layout-to-image generation (refer Fig. 7c)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.601, + 0.62, + 0.617 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.626, + 0.892, + 0.899 + ], + "angle": 0, + "content": "In this paper, we present SmartMask which allows a novice user to generate scene-aware precision masks for object insertion and finegrained layout design. Existing methods for object insertion typically rely on a coarse bounding box or user-scribble input which can lead to poor background preservation around the inserted object. To address this, we propose a novel diffusion based framework which leverages semantic amodal segmentation data in order to learn to generate fine-grained masks for precise object insertion. When used along with a ControlNet-Inpaint model, we show that the proposed approach achieves superior object-insertion performance, preserving background content more effectively than previous methods. Additionally, we show that SmartMask provides a highly controllable approach for designing detailed layouts from scratch. As compared with user-scribble based layout design, we observe that the proposed approach can allow users to better leverage existing S2I methods for higher quality layout-to-image generation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6504" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] Adobe. Adobe firefly - generative ai for everyone, 2023. 2, 5, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.143, + 0.469, + 0.182 + ], + "angle": 0, + "content": "[2] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. 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Overview. We introduce SmartMask which allows a novice user to generate high-fidelity masks for fine-grained object insertion and layout control. The proposed approach can be used for object insertion (a-b) where it not only allows for image inpainting with better background preservation (a) but also provides diverse suggestions for mask-free object insertion at different positions and scales. We also find that when used iteratively SmartMask can be used for fine-grained layout design (c) for better quality semantic-to-image generation. + +![](images/98b856e4064d94ac354783dbcb0b80aeee56b1c6408a95fc6aafb048651d6e46.jpg) +Ours + Controlnet + +(c) SmartMask for fine-grain layout design for layout to image generation. + +# Abstract + +The field of generative image inpainting and object insertion has made significant progress with the recent advent of latent diffusion models. Utilizing a precise object mask can greatly enhance these applications. However, due to the challenges users encounter in creating high-fidelity masks, there is a tendency for these methods to rely on more coarse masks (e.g., bounding box) for these applications. This results in limited control and compromised background content preservation. To overcome these limitations, we introduce SmartMask, which allows any novice user to create detailed masks for precise object insertion. Combined with a ControlNet-Inpaint model, our experiments demonstrate that SmartMask achieves superior object insertion qual + +ity, preserving the background content more effectively than previous methods. Notably, unlike prior works the proposed approach can also be used even without user-mask guidance, which allows it to perform mask-free object insertion at diverse positions and scales. Furthermore, we find that when used iteratively with a novel instruction-tuning based planning model, SmartMask can be used to design detailed layouts from scratch. As compared with user-scribble based layout design, we observe that SmartMask allows for better quality outputs with layout-to-image generation methods. + +# 1. Introduction + +Multi-modal object inpainting and insertion has gained widespread public attention with the recent advent of large- + +scale language-image (LLI) models [1-3, 19, 24, 27, 30, 37, 38]. A novice user can gain significant control over the inserted object details by combining text-based conditioning with additional guidance from a coarse bounding box or user-scribble mask. The text prompt can be used to describe the object semantics, while the coarse mask provides control over the position and scale of the generated object. + +While convenient, the use of a coarse mask for object insertion suffers from two main limitations. 1) First, the use of a coarse mask can often be undesirable as it tends to also modify the background regions surrounding the inserted object [30, 37] (refer Fig. 1a). In order to minimize the background artifacts, recent works [37, 40] also explore the use of user-scribble based free-form mask instead of a bounding-box input. However, while feasible for describing coarse objects (e.g., mountains, teddy bear etc.), the generation of accurate free-form masks for objects with a number of fine-grain features (e.g., humans) can be quite challenging especially when limited to coarse user-scribbles. 2) Furthermore, generating variations in position and scale of the inserted object can also be troublesome as it requires the user to provide a new scene-aware free-form mask to satisfy the geometric constraints at the new scene location. + +To address these drawbacks, we introduce SmartMask, a context-aware diffusion model which allows a novice user to directly generate fine-grained mask suggestions for precise object insertion. In particular, given a semantic object description (e.g. kid) and the overall scene context, SmartMask generates scene-aware precise object masks which can then be used as input to a ControlNet-inpaint model [36, 41] to perform object insertion while preserving the contents of background image. As compared with coarse-mask based inpainting methods, we find that SmartMask provides a highly convenient and controllable method for object insertion and can be used 1) with user-inputs (bounding box, scribbles etc.): where the user can specify location and shape for the target object, or 2) in a mask-free manner: where the model automatically generates diverse suggestions for object insertion at diverse positions and scales. + +In addition to object insertion, we also find that SmartMask can be used for fine-grain layout design. Existing segmentation-to-image (S2I) generation methods (e.g. ControlNet [41]) enable the generation of controllable image outputs from user-scribble based semantic segmentation maps. However, generating a good quality semantic layout can be quite challenging if the user wants to generate a scene with objects that require fine-grain details for best description (e.g., humans, chairs etc.). To address this challenge, we show that SmartMask when used with a novel instruction-tuning [34] based planning model allows the user to iteratively generate the desired scene layout from scratch. As compared with scribble based layout generation, we find that the proposed approach allows the users to + +better leverage existing S2I generation methods (e.g. ControlNet [41]) for higher quality output generation. + +The main contributions of the paper are: 1) We propose SmartMask which allows any novice user to generate precise object masks for finegrained object insertion with better background preservation. 2) We show that unlike prior works, the proposed approach can also be used for mask-free object insertion. 3) Finally, we demonstrate that SmartMask can be used iteratively to generate detailed semantic layouts, which allows users to better leverage existing S2I generation methods for higher quality output generation. + +# 2. Related Work + +Diffusion based multi-modal image inpainting [1-3, 19, 24, 27, 30, 37, 38] has gained widespread attention with advent of text-conditioned diffusion models [24, 29, 30, 32, 39]. Despite their efficacy, these methods use coarse bounding box or user-scribble based masks for object inpainting which leads to poor background preservation around the inserted object. In contrast, SmartMask directly allows user to generate precise masks for the target object, which can then be combined with ControlNet-Inpaint [30, 41] to insert the target object while better preserving background contents. + +Mask-free object placement has been studied in the context of image compositing methods [9, 20, 22, 25, 35, 42, 44, 46], where given a cropped RGB object instance and a target image, the goal is to suggest different positions for the target object. In contrast, we study the problem of mask-free object insertion using text-only guidance. Lee et al. [18] propose a GAN-based approach to directly model a distribution of potential object locations. However, the learned distribution is w.r.t to a specific object class (e.g., cars) which limits its generalizability for diverse use-cases. + +Semantic layout to image generation methods have been explored to enable controllable image synthesis from user-scribble based semantic segmentation maps [8, 12, 17, 23, 26, 33, 45]. Recently, [4, 6, 14, 31] propose a cross-attention based training-free approach for controlling the overall scene layout from coarse user-scribbles using text-conditioned diffusion models. Zhang et al. [41] propose a versatile ControlNet model which allows the users to control the output layout on a more fine-grained level through an input semantic map. While effective, generating desired semantic layout with scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g., humans). SmartMask helps address this problem by allowing users to generate more fine-grained layouts to facilitate better quality S2I generation. + +# 3. Our Method + +Given an input image $\mathcal{I}$ , object semantic label $\mathcal{T}_{obj}$ and a textual description $\mathcal{T}_{context}$ describing the final scene con + +![](images/bd575b2128bacfd093658cc193c7561b56e9d51632f8ab78253519898067144a.jpg) +Figure 2. Method Overview. A key idea behind SmartMask is to leverage semantic amodal segmentation data [28, 47] in order to obtain high-quality paired training annotations for mask-free single or multi-step object insertion. During training (top), given a training image $\mathcal{I}$ with caption $C$ , we stack $k$ ordered instance maps $\{A_1, A_2, \ldots, A_k\}$ to obtain an intermediate semantic map $S_k$ . The diffusion model is then trained to predict the instance map $A_{k+1}$ , conditional on the semantic map $S_k$ , $\mathcal{T}_{obj} \gets \mathcal{O}_{k+1}$ and scene context $\mathcal{T}_{context} \gets C$ . During inference (bottom), given a real image $\mathcal{I}$ , we first use a panoptic segmentation model to compute semantic map $S_I$ . The generated semantic layout is then directly used as input to the trained diffusion model in order to predict the fine-grained mask for the inserted object. + +text, our goal is predict a fine-grained mask $\mathcal{M}_{obj}$ for the target object. The object mask $\mathcal{M}_{obj}$ could then be used as input to a ControlNet-Inpaint model for fine-grained object insertion (Sec. 4.1) or used to design detailed semantic layouts from scratch (Sec. 4.3). For instance, SmartMask could be used for single object insertion, where given an image $\mathcal{I}$ depicting a man on a bench, $\{\mathcal{T}_{obj} : \text{"woman'}\}$ and $\{\mathcal{T}_{\text{context}} : \text{"a couple sitting on a bench'}\}$ , our goal is to predict fine-grain binary mask $\mathcal{M}_{woman}$ which places the 'woman' in a manner such that the resulting scene aligns with overall scene context of a 'a couple sitting on a bench'. + +Similarly, SmartMask could also be used for multiple object insertion. For instance, given an image $\mathcal{I}$ depicting a wedding, the user may wish to add multiple objects \{'man', 'woman' and 'kid'\} such that the final scene aligns with the $\{\mathcal{T}_{\text {context }}: \text { 'a family posing for a picture at a wedding }\}$ . Unlike prior image inpainting methods which are limited independently adding each object to the scene, the goal of the smartmask model is to add each object in a manner such the generated 'man', 'woman' and 'kid' appear to be 'a family posing for a picture at a wedding'. (refer Fig. 2a). + +In the next sections, we describe the key SmartMask components in detail. In particular, in Sec. 3.1 we discuss how SmartMask can leverage semantic amodal segmentation data in order to obtain high-quality paired annotations for mask-free object insertion. We then discuss a simple + +data-adaptation strategy which allows the user to also control the position, shape of the inserted object using coarse inputs (bounding-box, scribbles) in Sec. 3.2. Finally, in Sec. 3.3 we propose a visual-instruction tuning [21] based planning model which when used with SmartMask, allows for generation of detailed semantic layouts from scratch. + +# 3.1. SmartMask for Mask-Free Object Insertion + +Semantic-Space Task Formulation. Directly learning a model for our task in pixel space can be quite challenging, as it would require large-scale collection of training data for single or multi-step object insertion while maintaining background preservation. To address this key challenge, a core idea of our approach is to propose an equivalent task formulation which allows us to leverage large-scale semantic amodal segmentation data [28, 47] for generating high-quality paired training data in the semantic space (Fig. 2). + +SmartMask Training. In particular during training, given an image $\mathcal{I}$ , with a sequence of ordered amodal semantic instance maps $\{A_1, A_2 \ldots A_n\}$ and corresponding semantic object labels $\{\mathcal{O}_1, \mathcal{O}_2 \ldots \mathcal{O}_n\}$ , we first compute an intermediate layer semantic map as, + +$$ +S _ {k} = f _ {\text {l a y e r}} \left(\left\{A _ {1}, A _ {2} \dots A _ {k} \right\}\right) \quad \text {w h e r e} k \in [ 1, n ]. \tag {1} +$$ + +where $k$ is randomly chosen from $[1, n]$ and $f_{layer}$ is a layering operation which stacks the amodal semantic segmentation maps from $i \in [1, k]$ in an ordered manner (Fig. 2). + +We next train a diffusion-based mask prediction model $\mathcal{D}_{\theta}$ which takes as input the above computed intermediate semantic layer map $S_{k}$ , textual description for next object $\mathcal{T}_{obj} \gets \mathcal{O}_{k+1}$ , overall caption $\mathcal{T}_{context} \gets C_{\mathcal{I}}$ (for image $\mathcal{I}$ ) and learns to predict the binary mask $\{A_{k+1}\}$ for the next object. To this end, we first pass the intermediate semantic map $S_{k}$ through a learnable encoder $\mathcal{E}_{\phi}$ to obtain the encoded features $\mathcal{E}_{\phi}(S_{k})$ . At any timestep $t$ of the reverse diffusion process, the denoising noise prediction $\epsilon_{t}$ is then computed conditional jointly on previous noise latent $\mathbf{z}_{t}$ , and model inputs $\{\mathcal{E}_{\theta}(S_{k}), \mathcal{T}_{obj}, \mathcal{T}_{context}\}$ as, + +$$ +\tilde {\epsilon} _ {p r e d} (t) = \mathcal {U} _ {\theta} (\mathbf {z} _ {t}, \mathcal {E} _ {\phi} (S _ {k}), \mathcal {T} _ {o b j}, \mathcal {T} _ {\text {c o n t e x t}}, t), \tag {2} +$$ + +where $\mathcal{U}_{\theta}$ represents the U-Net of the diffusion model $\mathcal{D}$ . + +The overall diffusion model $\mathcal{D}$ is then trained to predict the next layer $A_{k + 1}$ using the following diffusion loss, + +$$ +\mathcal {L} _ {t} (\theta , \phi) = \mathbf {E} _ {t \sim [ 1, T ], S _ {k}, A _ {k + 1}, \epsilon_ {t}} \left[ \| \epsilon_ {t} - \tilde {\epsilon} _ {p r e d} (t) \| ^ {2} \right], \tag {3} +$$ + +where $T$ is total number of reverse diffusion steps, $\epsilon_t\sim \mathcal{N}(0,I)$ is sampled from a normal distribution and $A_{k + 1}$ represents ground truth binary mask for next object $\mathcal{O}_{k + 1}$ . + +SmartMask Inference. During inference, given an input image $\mathcal{I}$ , semantic object category $\mathcal{T}_{obj}$ and a textual description $\mathcal{T}_{\text {context }}$ describing the final scene context, we first use a panoptic semantic segmentation model [15] to obtain the corresponding semantic layout map $\mathcal{S}_{\mathcal{I}}$ . The generated semantic layout $\mathcal{S}_{\mathcal{I}}$ is then directly used as input to the above trained diffusion model $\mathcal{D}_{\theta}$ in order to predict the fine-grained mask $\mathcal{M}_{obj}$ for the target object, + +$$ +\mathcal {M} _ {o b j} = \mathcal {D} _ {\theta} \left(\mathcal {E} _ {\phi} \left(\mathcal {S} _ {I}\right), \mathcal {T} _ {o b j}, \mathcal {T} _ {\text {c o n t e x t}}\right). \tag {4} +$$ + +# 3.2. Data Adaptation for Precise Mask Control + +While the diffusion model trained in Sec. 3.1, allows the user to perform mask-free object insertion at diverse positions and scales, the user may also wish to obtain more direct control over the spatial location and details of the inserted object. To this end, we propose a simple train-time data adaptation strategy which allows smartmask to be easily adapted to diverse forms of user control (Fig. 4). In particular, given the intermediate layer map $S_{k}$ computed using Eq. 1 and ground truth mask $A_{k + 1}$ for the next object, we replace the input $S_{k}$ to the diffusion model as, + +$$ +\tilde {S} _ {k} = g \left(S _ {k}, G _ {o b j}\right) = S _ {k} \odot \left(1 - \alpha G _ {o b j}\right) + \alpha G _ {o b j}, \tag {5} +$$ + +where $G_{obj}$ is the additional guidance input (e.g., bounding box mask, coarse scribbles etc.) provided by the user and $\alpha = 0.7$ helps add additional guidance while still preserving the content of the original input $S_{k}$ after data adaptation. + +Training. In this paper, we mainly consider four main guidance inputs $G_{obj}$ for additional mask control for adapting SmartMask. 1) Mask-free guidance: in absence of any + +additional user inputs, we use $G_{obj} = \mathbf{0}^{H,W}$ which prompts the model to suggest fine-grained masks for object insertion at diverse positions and scales. 2) Bounding-box guidance: we set $G_{obj}$ as a binary mask corresponding to ground truth object mask $A_{k+1}$ . 3) Coarse Spatial Guidance: Expecting the user to provide precise bounding box for object insertion is not always convenient and can lead to errors if bounding box is not correct. We therefore introduce a coarse spatial control where user may provide a coarse spatial location and the model learns to infer the best placement of the object around the suggested region (Fig. 4c). During training, the same is achieved by setting $G_{obj}$ as a coarse gaussian blob centered at the ground truth object mask $A_{k+1}$ . 4) User scribbles: Finally, we also allow the user to describe target object using free-form coarse scribbles, by setting $G_{obj}$ as the dilated mask output of ground-truth object mask $A_{k+1}$ . + +Inference. At inference time, the additional guidance input $G_{obj}$ (e.g. bounding box mask, coarse scribbles etc.) is directly provided by the user. Given an input image $\mathcal{I}$ with semantic layout $S_{\mathcal{I}}$ , we then use transformation from Eq. 5 as input to the adapted SmartMask model in order to generate object insertion suggestions with additional control. + +# 3.3. Global Planning for Multi-Step Inference + +While the original SmartMask model allows the user to generate fine-grained masks for single object insertion, we would also like to use SmartMask for iterative use cases such as multiple object insertion (Sec. A.1) or designing a fine-grained layout from scratch with large number $(>10)$ of scene elements. Such an iterative use of SmartMask would require the model to carefully plan the spatial location of each inserted object to allow for the final scene to be consistent with the final scene context description $\mathcal{T}_{\text{context}}$ . + +To achieve this, we train a visual-instruction tuning [21] based planning model which given the input semantic layout $S_{I}$ , learns to plan the positioning of different scene elements over long sequences. Given a semantic object description $T_{obj}$ and final scene context $T_{context}$ , the global planning model provides several bounding box suggestions for object insertion. SmartMask model then uses the above predictions as coarse spatial guidance input $G_{obj}$ to provide fine-grained mask suggestions for the next object. The above process can then be repeated in an iterative manner until all objects have been added to the scene (refer Fig. 7a). + +The global planning model is trained in two stages. 1) Feature Alignment. Typical instruction tuning models are often trained on real images. In contrast, as discussed in Sec. 3.1 we would like to model our problem in semantic space as it allows us to leverage amodal segmentation data for training. To address this domain gap, we first finetune an existing LLaVA model [21] to understand the semantic inputs. To do this, given an intermediate semantic map $S_{k}$ computed using Eq. 1, we finetune the projection matrix $\mathbf{W}$ + +![](images/c845681feea1a94c6197d1c87a541ea6826a41236c4c81c83bb0db580470cb5f.jpg) +Figure 3. Qualitative Results for Image Inpainting. We observe that as compared to with state-of-the-art image inpainting [1, 2, 30, 37] methods, SmartMask allows the user to perform object insertion while better preserving the background around the inserted object. + +of the LLaVA model [21] $\mathcal{H}$ to predict the semantic object labels $\{\mathcal{O}_1,\mathcal{O}_2\ldots \mathcal{O}_k\}$ described in the current scene as, + +$$ +\mathcal {L} _ {\text {a l i g n}} (\mathbf {W}) = \mathcal {L} _ {C E} (< \mathcal {O} _ {1}, \mathcal {O} _ {2} \dots \mathcal {O} _ {k} >, \mathcal {H} (S _ {k})). \tag {6} +$$ + +2) Instruction-Tuning. Finally, keeping the visual encoder weights for LLaVA model fixed, we next finetune both project matrix $\mathbf{W}$ and LLM weights $\Phi$ [43] for global object planning. In particular, given an intermediate semantic map $S_{k}$ , we first compute the bounding box coordinates $\mathcal{B}_{k+1} = \{x_{min}, y_{min}, x_{max}, y_{max}\}$ for the next object $\mathcal{T}_{obj} = \mathcal{O}_{k+1}$ using ground truth object mask $\mathcal{A}_{k+1}$ . The LLaVA based planning model $\mathcal{H}$ is then trained as, + +$$ +\mathcal {L} _ {\text {i n s t r u c t}} (\mathbf {W}, \Phi) = \mathcal {L} _ {C E} \left(\mathcal {B} _ {k + 1}, \mathcal {H} \left(S _ {k}, \mathcal {T} _ {\text {o b j}}, C\right)\right), \tag {7} +$$ + +where $C$ represents the caption for the final scene (obtained using ground-truth image $\mathcal{I}$ ) and provides the model context for placing different scene elements in the image. + +# 4. Experiments + +Training Data Collection. As discussed in Sec. 3, we note that a key idea behind SmartMask is to model the object insertion problem in semantic space (instead of pixel space), which allows us to leverage semantic amodal segmentation data to obtain large-scale paired training annotations for single or multiple object insertions. However, traditional datasets for semantic amodal segmentations such as COCOA [47] (2,500 images, 22,163 instances) and KINS [28] + +(7,517 images, 92,492 instances) though containing fine-grained amodal segmentation annotations may lack sufficient diversity to generalize across different use-cases. + +To address this, we curate a new large-scale dataset consisting of fine-grain amodal segmentation masks for different objects in an input image. The overall dataset consists of 32785 diverse real world images and a total of 725897 object instances across more than 500 different semantic classes (e.g. man, woman, trees, furniture etc.). Each image $\mathcal{I}$ in the dataset consists of a variable number of object instances $\{A_1, A_2, \ldots, A_n\}$ , $n \in [2, 50]$ and is annotated with an ordered sequence of semantic amodal segmentation maps $\{S_1, S_2, \ldots, S_n\}$ . The detailed descriptions $C_I$ for each image are obtained using the InstructBLIP [7] model. + +SmartMask Training. In order to leverage the rich generalizable prior of T2I diffusion models, we use the weights from publicly available Stable-Diffusion-v1.5 model [30] in order to initialize the weights of the SmartMask U-Net model trained in Sec. 3.1. Similar to [5], we modify the architecture of the U-Net model to also condition the output mask predictions on segmentation layout $S_{I}$ . The SmartMask model is trained for a total of 100k iterations with a batch size of 192 and learning rate $1e - 5$ using 8 Nvidia-A100 GPUs. During inference, a panoptic semantic segmentation model finetuned on the dataset in Sec. 4 is used for converting real image $\mathcal{L}$ to its semantic layout $S_{I}$ . ControlNet model trained with SDXL backbone was used to perform precise object insertion with SmartMask outputs. Please refer the supp. material for further training details. + +![](images/1541e367e0ddb99394b602a3e451e55245b1a75949436b7951887e38463e48ff.jpg) + +![](images/cc25d52d8bc78c5c9b741c3ce4a0ee0f8c1f2ce428235dead328f6181c3d5efb.jpg) + +![](images/eb859377da04b062180ddd715fda3d717138552a742497afdd2d256ac4e1ca86.jpg) + +![](images/c1e77d73c40fbb5db1ae36e87d9f31b7fa661ef3f5ac2a254e4bb8bad2e79c47.jpg) + +![](images/3042c0e9452c4474ff54170db29cb210b24dbbabb8f9ecdfb5c8ba8c4ced6bfc.jpg) +Image Input + +![](images/a7b3321d03121ca3e7dbd48b2383c6b317bda3785a1c41dc2ef12efb8a7ed94a.jpg) +SmartMask Outputs + +![](images/7cca24f4f08be3af5a9aeaccb9c7a298a503a89cf6e19d39de0a7101641de4ee.jpg) + +![](images/d4eea0a9d7fb22feaaf6eee5cc1dfb82c8d94704240b746d5b5237e9a5a2aa7a.jpg) + +![](images/af922d360658972d19853bf32c07845ff73d0614336a09dd52f0aaeab2d583bd.jpg) + +![](images/e9966b8b42b03b4dc14f33bf6bab8e18fdee1b4eebc7867b9626dc0d665b90d6.jpg) + +![](images/a22667328a345a39fdb788a827863c8004f33b300e43b2a5b9f3f37b25eed146.jpg) + +![](images/203e45e0b6477d3323c2de30afef4688aa58b3e19099f8570a98264d864b9602.jpg) + +![](images/2cca947d733e9fa0e17b992cdd05753155595d06d57d93a646029ef144a96aea.jpg) +Image Input + +![](images/0f177d283ca250dd1a99e5d7f4de447cf9194bca2e377ac281b3989705b03ce0.jpg) +SmartMask Outputs + +![](images/9ddb99fdeb7a0a078fc27535fe4ef8ddc08be3f93b639af43b115bcafbf4608c.jpg) + +![](images/2bb685ea4685a640b3a7e09abfbf4cebb8c7b955220a6e96a2239c5bb0956840.jpg) + +![](images/2b050e7dc75fac17cbd6fde107de344a7640e7e10a31ef8a949136423caa6f16.jpg) +(a) Mask-free object insertion + +![](images/d5abdb25e3ffdc8ef40393ee48b5baad47bfab48ebef1abb319f5550e7d3dc1b.jpg) + +![](images/3286d89a27bd30c7be2da56fa92707f52547285588415474886e7d10074a1faa.jpg) + +![](images/e5df1655e0040e04db85e6136905bead5107740ace2e3dbd2855090c5a6c7fd4.jpg) + +![](images/9abad4c2de77fabd5f67c7bf325216ac6459a93f71251026d97daa77cac60c7b.jpg) +(c) Coarse-spatial guidance for mask generation + +![](images/ee767df46b45577aad1d8b8566db68eb0e520ce2315ef284b7d26d0a5f899359.jpg) +Figure 4. Diverse User Controls. SmartMask is easily adaptable to diverse user-controls for precise mask generation for the target object. + +![](images/c536381eaf88f8b706a7f9d3b44fa0d9dd09afc80218f134d6d028d7145265f0.jpg) + +![](images/d203fa9e54c436037dc166536aa14b39fc9c42c1c27d30d02b596062ee68eee6.jpg) + +![](images/43f5155cf43a7f4e16c2fca1c04f6b1e97bbda9f6da518218bb87fbc4125596d.jpg) +(b) Bounding-box guidance for mask generation + +![](images/3d2eda6e7647c2c890e6e6e6ad3707fdf848033f26727366b47ff4923a13bbeb.jpg) + +![](images/df8b1f1beb4bda91833a976dd18b578e0d7aebc7193204591369aa3c246a2862.jpg) + +![](images/b7971ae117e80ca52b74fabac87b02e4cee6c23e14fcdd4367354c42aae8a29d.jpg) + +![](images/51b224e66510246178c91a6c9855216e8ed0b74134436504637d2d9e537215ef.jpg) + +![](images/5316f72cb0b4ca50ecdf754f8a0c715346e1126edcb0d7e2fd97c67eaaeca5d9.jpg) +(d) Scribble-based object insertion + +![](images/b6672613038cc9524e177291009597b7ede8d577ddab4666a43e925328624ba8.jpg) + +![](images/20b1b3bf833f8b8b4796f01e2f266375969cb76447c156a7a8450701f6ca7095.jpg) + +![](images/e6b82c159d332af5c48118df2f718beabc4ad5baae34faf1f1929ac61feeecd7.jpg) + +# 4.1. SmartMask for Object Insertion + +Baselines. We compare the performance of our approach on object-insertion with prior works on performing multimodal image-inpainting using a textual description and coarse bounding box mask. In particular we show comparisons with SD-Inpaint [30], SDXL-Inpaint [27], Blended-Latent Diffusion [30], and Adobe SmartBrush [37]. We also compare the performance of our approach with state-of-the-art commercial inpainting tools by reporting results on recently released Generative-Fill from Adobe Firefly [1]. + +Evaluation Metrics. Following [37], we report the results for object insertion using 1) Local-FID [11] which measures the realism of the generated objects, 2) CLIP-Score [10] which measures the alignment between the textual description and the generated object, and 3) Norm. L2-BG: which reports the normalized L2 difference in the background regions before and after insertion, and helps capture the degree to which the background was preserved. + +Qualitative Results. Results are shown in Fig. 3. We observe that when performing objectn insertion using a coarse bounding box mask, traditional inpainting methods usually lead to a lot of changes in the background regions around the inserted object (e.g. living room details in row-1&2, mountains in row-4 etc.). Adobe SmartBrush [37] which is trained to allow better background preservation, shows better performance, however, still suffers from notable changes to background regions. In contrast, by directly predicting a high-fidelity mask for the target object, the proposed approach allows the user to add new objects on the scene with + +
MethodEvaluation Criteria
Local-FID ↓CLIP-Score ↑Norm. L2-BG ↓
SD Inpaint [30]22.310.2490.374
SDXL Inpaint [27]21.840.2350.623
Blended L-Diffusion [2]39.770.2530.451
Adobe SmartBrush [37]17.940.2620.304
Adobe Gen-Fill* [1]N/A0.2680.289
Smartmask (Ours)19.210.2610.098
+ +Table 1. Quantitative results for image inpainting. We observe that in comparison with state-of-art image inpainting methods, our approach leads to better preservation of background regions. + +minimal changes to the background image. Furthermore we observe that target object masks are generated in a scene-aware manner, which helps us add new objects while interacting with already existing ones. For instance, when adding 'a man to a couch with table in front' (Fig. 3), prior works typically replace the couch and table to insert the target object ('man'). In contrast, smartmask places the 'man sitting on the couch with his leg on the table', and provides a more natural way for inserting objects in complex scenes. + +Quantitative Results. In addition to qualitative results, we also report the performance of our approach quantitatively in Tab. 1. We find that similar to results in Fig. 3, the proposed approach shows better background preservation (Norm. L2-BG ↓) while performing comparably in terms of image quality (local-FID) and text-alignment (CLIP-Score). + +# 4.2. Evaluating Mask Controllability and Quality + +A key advantage of SmartMask is the ability to generate high-quality masks for target object in a controllable man + +![](images/5afad3b15493e52d50f73742b4494c974ea3dc4b540204e1f077c5f1349d7ea0.jpg) +Figure 5. Comparing output mask quality with different Inpaint + HQSAM (middle) methods and SmartBrush mask output (right). + +![](images/d1bdff23c45e9ac1d093535aeb24ccf1e869f294a72052c458f942bb7a4ef9b3.jpg) +Figure 6. Limitation of Inpaint + HQSAM. In addition to poor mask quality errors (Fig. 5), we observe that Inpaint+HQSAM can lead to scene-unaware masks (e.g. mask for woman sitting in air) + +ner. In this section, we evaluate the performance of SmartMask in terms of 1) user control, & 2) output mask quality. + +1) User Control. As shown in Fig. 4, we observe that SmartMask allows the user to control the output object mask in four main ways. 1) Mask-free insertion: where the model automatically suggests diverse positions and scales for the target object (e.g., table, woman in Fig. 4a). 2) Bounding-box guidance: which allows user to specify the exact bounding box for object insertion (potted plant, motorbike in Fig. 4b). 3) Coarse spatial guidance: (Fig. 4c) providing a precise bounding box can be challenging for cases with complex object insertions e.g., dog with owner. SmartMask allows the user to only specify a coarse location for the target object, and the model automatically adjusts the object placement (i.e. dog with head near woman's hand) to capture object interactions. 3) User-scribbles: Finally, the user may also control the output shape by providing coarse scribbles. The smartmask model can use this as guidance to automatically predict the more finegrain-masks for the target object (e.g., palm-tree, gaming chair in Fig. 4d). + +2) Output Mask Quality. We also report results on the quality of generated masks by showing comparisons with the mask-prediction head of the SmartBrush model [37]. Furthermore, we also show comparisons combining standard inpainting methods with HQSAM [13, 16]. To this end, we first use the provided bounding-box mask to inpaint the target object. The user-provided bounding-box and the inpainted output are then used as input to the HQSAM model [13] to obtain target object-mask predictions. + +
MethodUser Study Results
Win ↑DrawLose ↓
SDInpaint + HQSAM [13, 30]92.04%5.12%2.84%
Blended L-Diff + HQSAM [2, 13]88.91%8.33%2.75%
SmartBrush + HQSAM [13, 37]63.89%27.78%8.34%
SmartBrush Mask [37]91.67%2.78%5.56%
+ +Table 2. User study results. For evaluating generated mask quality. We observe that SmartMask generates higher quality masks as compared to SmartBrush and various Inpaint+HQSAM methods. + +Results are shown in Fig. 5. We observe that as compared to outputs of SmartBrush [37] mask-prediction head, SmartMask generates higher-quality masks with fewer artifacts. Similarly, while using HQSAM on inpainting outputs helps achieve good mask quality for some examples (e.g. child in row-2), the HQSAM generated masks (or the inpainted image) often have accompanying artifacts which limits the quality of the output masks. In addition to poor mask quality errors, we also observe that Inpaint+HQSAM can lead to scene-unaware masks (Fig. 6). This occurs because prior inpainting methods typically add additional objects in the background when performing object insertion. For instance, when inserting woman in a living room in Fig. 6), we observe that Adobe Gen-Fill [1] adds an additional chair on which the woman is sitting. Extracting only the object mask for such inpainted outputs can lead to scene-unaware masks where 'the woman appears floating in the air' as the chair was not present in the original image. + +The above findings are also reflected in a quantitative user study (Tab. 2), where human subjects are shown a pair of object mask suggestions (ours vs baselines discussed above), and asked to the select the mask suggestion with the higher quality. As shown in Tab. 2, we observe that SmartMask outputs are preferred by majority of human subjects over SmartBrush mask [37] and Inpaint + HQSAM outputs. + +# 4.3. SmartMask for Semantic Layout Design + +In addition to object insertion, we also find that when used iteratively along with the visual-instruction tuning based planning model from Sec. 3.3, SmartMask forms a convenient approach for designing detailed semantic layouts with a large number of fine-grain objects (e.g. humans, furniture etc.). Results are shown in Fig. 7a. We observe that given a sequence of user provided scene elements (e.g. painting, sofa, chair etc.), SmartMask generates the entire scene layout from scratch. Furthermore, unlike static layouts generated by a panoptic segmentation model, SmartMask generated layouts allow the user greater control over the details of each scene element. Since each object in the final layout is represented by a distinct object mask, the final layouts are highly controllable and allow for a range of custom operations such as adding, removing, modifying or moving objects through simple layer manipulations. (refer Fig. 7b). + +Controllable S2I Generation. Layout to image gener + +Input Prompt: A living room with a couch, chair and table. + +![](images/9a46b4685407607a3a4dd885a0e476304736ef7b91251dbbf99eed3c20f367fc.jpg) + +![](images/42401609e3a49356bb558be9ce6cc3711ef81e043ea513177c806c87f88e4a2e.jpg) + +![](images/feb372a54979f3e4ddef475b45b15a2e9d2812af9905091833fd158bb8786ee7.jpg) + +![](images/cb4df6409925b628bf3fce0d6bffc1e98563e92ac99b5ab2bc98b09cd21e6cc8.jpg) + +![](images/498d06a6c97e6831fd9241436f9544aa6fe8228d52129524dd4d4baf56a01291.jpg) + +![](images/0c24cf0bf4e50977f1e5dca77f1b201a94687281f4a03df5f84fa4087608996d.jpg) + +![](images/f1465f37731e52fa4f55f8c816274ced944d7e646d294ba0280d7169074fb3d5.jpg) + +![](images/65a8d9d495c409fa221330d86a8a077ae9152a9cf2780a5ca36c65a75aa4ad36.jpg) + +![](images/1cc3854ddd4e16a081d4e85d7756644bccfd00cc6c0efee08d579f32131b4825.jpg) + +![](images/691ec8b0fe874d7100da9ec24c916e8eea1cc54327a63ed1089b56da64e20156.jpg) +(a) SmartMask for designing very detailed semantic layouts from scratch. + +![](images/33cac393520128e3b2a5adf5523e423e6deb9fb6a25f574683258155bc2b548c.jpg) + +![](images/393471f832fe7b182306381cb8959634fcd3009536702fd1cf711d6569caca68.jpg) + +![](images/3bd3f724decfdb3b96c4d5c8a80b646b3126c83ab7557bbdd67d2d45d2645a7e.jpg) + +![](images/5f759e0b747b87796ad5e54703f6dcee2e0fd585616212aa8b84f802a07d9916.jpg) + +![](images/fc64b9d0fc9ac011c04406610b6e3281727e87b035a9d3d5a59b79d307c5b34c.jpg) + +![](images/a8e501849aa4a30b58c93be9302a797729fe59b796b976100fffb59ea4932c81.jpg) + +![](images/fd9c13250aa29a6e5c95a11d759323ac9786ecd6e3c0f37d8d54efb60ab3703f.jpg) +Add new objects at different layers + +![](images/82442166caec084566d6368ec4ac446e284c12a2bcf4e01bf1bc8c8e63444e1a.jpg) +Remove objects at different layers +(b) Analyzing controllability of the layouts generated with SmartMask. + +![](images/f3a420db952460cda33210094ffec638cf362064923df695146d864f4caf0a9e.jpg) +Modify objects at different layers + +![](images/3e4ea7cf2e425134cbf8ad24cd6f04369daf06cfb41a8a10fa0392804105f318.jpg) +Move objects at different layers + +![](images/f1d2439fcd2e54c94b35bde05278a7aa0772da3c0848760bd826b8997dfcf9cc.jpg) + +![](images/d21a5ce8b9462d97115f12075c63124749d16aa921d3bff122829e0272994068.jpg) + +![](images/a6eed146a8db20079a85b0e61b436f4d353d968fe91d62e7e294afb6aac8e678.jpg) +Input Prompt: Two children sitting in front of a building + +![](images/81c98acd29d02f877801ff8cadbd02d094c51a931f6f71ff8e7c33d993a02696.jpg) + +![](images/153b7a968c523f4262be3138bfcbcce0c3c42e0f2dbda5b91d280f15956125e3.jpg) + +![](images/c8a7fa196d600ccd2909b9d0870f393b0a59a69fcbf79ac0bd1147679050d706.jpg) + +![](images/772a083b73e522ba74e3119bc3d9d3c79be3546c3d573bc44e4caf424919097d.jpg) + +![](images/c0729db918085758d6b08988f2146748ae325de7fa138f59d8b8f80b768c38f2.jpg) + +![](images/dd8849f499a6dd8f7f33a6470413f4eb4599ad1986a168d8c12b74f168d82a84.jpg) +User Scribble +Scribble + Controlnet +Figure 7. Fine-grained layout design. We observe that SmartMask when used iteratively, allows the user to generate very detailed layouts from scratch (a). The generated layouts are highly controllable and allow for custom variations through simple layer manipulations (b). + +![](images/849c41d3cabe8ec5505da94aa55177f996fb1fe134e24a778d84f8e38b82f8bb.jpg) + +![](images/a0cbaeea35788f6ddc3e83aaabc566909c79c153926d24d479448fb55b9e3fc8.jpg) + +![](images/bd49d37d6cf74a2fcb9c459c40f6cc3dbbf893cf63f42a755bc88b67a1ec2efc.jpg) +Input Prompt: a woman walking with two children on the beach +Scribble $^+$ PwW +(c) Using SmartMask generated layouts for better quality layout-to-image generation. + +![](images/0dc9473c3ef4c219d05398331353f6c2b00a169885c0b3aa6d7a6757a6a1f6af.jpg) +Scribble + DenseDiff + +![](images/02a845fdbc6348c31c153bf41f477e14d1d022f7f1aa9b50f739e97459b9f259.jpg) +Fine-g +Fine-grain Layout Generation (Ours) + +![](images/6e1b08b835353c919c58970dd5de2b0ef4c55ccc9a084e2af9872909d8e46cce.jpg) + +![](images/fbb9453edf6597213a3d0183eba7aa4cfc355b0a75e769a600234353ebd66f5c.jpg) + +![](images/b6351bafcf23570078b24480b0535b58ec2cb18f1aa29b3e045f5a050a566574.jpg) +Ours + Controlnet + +ation methods e.g., ControlNet [41] enable the generation of controllable image outputs from user-scribble based semantic segmentation maps or layouts. However, generating the user-desired layouts with coarse scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g. humans, chairs etc.). As shown in Fig. 7c, we find that this can lead to image outputs with either deformity artifacts (child in row-1) or incorrect description (woman and children in row-2) when using ControlNet [41]. A similar problem is also observed in other coarse-scribble based S2I methods such as DenseDiffusion [14] and Paint-with-Words (PwW) [4], which provide coarse control over object position but are unable to control finegrain details such as pose, action etc. of the target object. SmartMask helps address this problem by allowing any novice user to generate controllable (Fig. 7b) fine-grain layouts from scratch, which can allow users to better leverage existing S2I methods [41] for higher quality layout-to-image generation (refer Fig. 7c). + +# 5. Conclusion + +In this paper, we present SmartMask which allows a novice user to generate scene-aware precision masks for object insertion and finegrained layout design. Existing methods for object insertion typically rely on a coarse bounding box or user-scribble input which can lead to poor background preservation around the inserted object. To address this, we propose a novel diffusion based framework which leverages semantic amodal segmentation data in order to learn to generate fine-grained masks for precise object insertion. When used along with a ControlNet-Inpaint model, we show that the proposed approach achieves superior object-insertion performance, preserving background content more effectively than previous methods. Additionally, we show that SmartMask provides a highly controllable approach for designing detailed layouts from scratch. 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Overview. We introduce SmartMask which allows a novice user to generate high-fidelity masks for fine-grained object insertion and layout control. The proposed approach can be used for object insertion (a-b) where it not only allows for image inpainting with better background preservation (a) but also provides diverse suggestions for mask-free object insertion at different positions and scales. We also find that when used iteratively SmartMask can be used for fine-grained layout design (c) for better quality semantic-to-image generation." + } + ] + } + ], + "index": 57, + "angle": 0, + "type": "image_caption" + } + ], + "index": 52 + }, + { + "type": "image", + "bbox": [ + 474, + 395, + 531, + 452 + ], + "blocks": [ + { + "bbox": [ + 474, + 395, + 531, + 452 + ], + "lines": [ + { + "bbox": [ + 474, + 395, + 531, + 452 + ], + "spans": [ + { + "bbox": [ + 474, + 395, + 531, + 452 + ], + "type": "image", + "image_path": "98b856e4064d94ac354783dbcb0b80aeee56b1c6408a95fc6aafb048651d6e46.jpg" + } + ] + } + ], + "index": 54, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 477, + 453, + 529, + 460 + ], + "lines": [ + { + "bbox": [ + 477, + 453, + 529, + 460 + ], + "spans": [ + { + "bbox": [ + 477, + 453, + 529, + 460 + ], + "type": "text", + "content": "Ours + Controlnet" + } + ] + } + ], + "index": 55, + "angle": 0, + "type": "image_caption" + } + ], + "index": 54 + }, + { + "bbox": [ + 176, + 466, + 416, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 176, + 466, + 416, + 476 + ], + "spans": [ + { + "bbox": [ + 176, + 466, + 416, + 476 + ], + "type": "text", + "content": "(c) SmartMask for fine-grain layout design for layout to image generation." + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 143, + 533, + 192, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 533, + 192, + 545 + ], + "spans": [ + { + "bbox": [ + 143, + 533, + 192, + 545 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 713 + ], + "type": "text", + "content": "The field of generative image inpainting and object insertion has made significant progress with the recent advent of latent diffusion models. Utilizing a precise object mask can greatly enhance these applications. However, due to the challenges users encounter in creating high-fidelity masks, there is a tendency for these methods to rely on more coarse masks (e.g., bounding box) for these applications. This results in limited control and compromised background content preservation. To overcome these limitations, we introduce SmartMask, which allows any novice user to create detailed masks for precise object insertion. Combined with a ControlNet-Inpaint model, our experiments demonstrate that SmartMask achieves superior object insertion qual" + } + ] + } + ], + "index": 59 + }, + { + "bbox": [ + 304, + 534, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 654 + ], + "type": "text", + "content": "ity, preserving the background content more effectively than previous methods. Notably, unlike prior works the proposed approach can also be used even without user-mask guidance, which allows it to perform mask-free object insertion at diverse positions and scales. Furthermore, we find that when used iteratively with a novel instruction-tuning based planning model, SmartMask can be used to design detailed layouts from scratch. As compared with user-scribble based layout design, we observe that SmartMask allows for better quality outputs with layout-to-image generation methods." + } + ] + } + ], + "index": 60 + }, + { + "bbox": [ + 306, + 668, + 387, + 680 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 668, + 387, + 680 + ], + "spans": [ + { + "bbox": [ + 306, + 668, + 387, + 680 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 61 + }, + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 546, + 714 + ], + "type": "text", + "content": "Multi-modal object inpainting and insertion has gained widespread public attention with the recent advent of large-" + } + ] + } + ], + "index": 62 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6497" + } + ] + } + ], + "index": 63 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 156 + ], + "type": "text", + "content": "scale language-image (LLI) models [1-3, 19, 24, 27, 30, 37, 38]. A novice user can gain significant control over the inserted object details by combining text-based conditioning with additional guidance from a coarse bounding box or user-scribble mask. The text prompt can be used to describe the object semantics, while the coarse mask provides control over the position and scale of the generated object." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 158, + 288, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 158, + 288, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 288, + 350 + ], + "type": "text", + "content": "While convenient, the use of a coarse mask for object insertion suffers from two main limitations. 1) First, the use of a coarse mask can often be undesirable as it tends to also modify the background regions surrounding the inserted object [30, 37] (refer Fig. 1a). In order to minimize the background artifacts, recent works [37, 40] also explore the use of user-scribble based free-form mask instead of a bounding-box input. However, while feasible for describing coarse objects (e.g., mountains, teddy bear etc.), the generation of accurate free-form masks for objects with a number of fine-grain features (e.g., humans) can be quite challenging especially when limited to coarse user-scribbles. 2) Furthermore, generating variations in position and scale of the inserted object can also be troublesome as it requires the user to provide a new scene-aware free-form mask to satisfy the geometric constraints at the new scene location." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 544 + ], + "type": "text", + "content": "To address these drawbacks, we introduce SmartMask, a context-aware diffusion model which allows a novice user to directly generate fine-grained mask suggestions for precise object insertion. In particular, given a semantic object description (e.g. kid) and the overall scene context, SmartMask generates scene-aware precise object masks which can then be used as input to a ControlNet-inpaint model [36, 41] to perform object insertion while preserving the contents of background image. As compared with coarse-mask based inpainting methods, we find that SmartMask provides a highly convenient and controllable method for object insertion and can be used 1) with user-inputs (bounding box, scribbles etc.): where the user can specify location and shape for the target object, or 2) in a mask-free manner: where the model automatically generates diverse suggestions for object insertion at diverse positions and scales." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 713 + ], + "type": "text", + "content": "In addition to object insertion, we also find that SmartMask can be used for fine-grain layout design. Existing segmentation-to-image (S2I) generation methods (e.g. ControlNet [41]) enable the generation of controllable image outputs from user-scribble based semantic segmentation maps. However, generating a good quality semantic layout can be quite challenging if the user wants to generate a scene with objects that require fine-grain details for best description (e.g., humans, chairs etc.). To address this challenge, we show that SmartMask when used with a novel instruction-tuning [34] based planning model allows the user to iteratively generate the desired scene layout from scratch. As compared with scribble based layout generation, we find that the proposed approach allows the users to" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "better leverage existing S2I generation methods (e.g. ControlNet [41]) for higher quality output generation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 96, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 547, + 205 + ], + "type": "text", + "content": "The main contributions of the paper are: 1) We propose SmartMask which allows any novice user to generate precise object masks for finegrained object insertion with better background preservation. 2) We show that unlike prior works, the proposed approach can also be used for mask-free object insertion. 3) Finally, we demonstrate that SmartMask can be used iteratively to generate detailed semantic layouts, which allows users to better leverage existing S2I generation methods for higher quality output generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 217, + 392, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 217, + 392, + 229 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 392, + 229 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 237, + 545, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 545, + 356 + ], + "type": "text", + "content": "Diffusion based multi-modal image inpainting [1-3, 19, 24, 27, 30, 37, 38] has gained widespread attention with advent of text-conditioned diffusion models [24, 29, 30, 32, 39]. Despite their efficacy, these methods use coarse bounding box or user-scribble based masks for object inpainting which leads to poor background preservation around the inserted object. In contrast, SmartMask directly allows user to generate precise masks for the target object, which can then be combined with ControlNet-Inpaint [30, 41] to insert the target object while better preserving background contents." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 357, + 546, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 546, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 546, + 476 + ], + "type": "text", + "content": "Mask-free object placement has been studied in the context of image compositing methods [9, 20, 22, 25, 35, 42, 44, 46], where given a cropped RGB object instance and a target image, the goal is to suggest different positions for the target object. In contrast, we study the problem of mask-free object insertion using text-only guidance. Lee et al. [18] propose a GAN-based approach to directly model a distribution of potential object locations. However, the learned distribution is w.r.t to a specific object class (e.g., cars) which limits its generalizability for diverse use-cases." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 477, + 547, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 477, + 547, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 477, + 547, + 657 + ], + "type": "text", + "content": "Semantic layout to image generation methods have been explored to enable controllable image synthesis from user-scribble based semantic segmentation maps [8, 12, 17, 23, 26, 33, 45]. Recently, [4, 6, 14, 31] propose a cross-attention based training-free approach for controlling the overall scene layout from coarse user-scribbles using text-conditioned diffusion models. Zhang et al. [41] propose a versatile ControlNet model which allows the users to control the output layout on a more fine-grained level through an input semantic map. While effective, generating desired semantic layout with scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g., humans). SmartMask helps address this problem by allowing users to generate more fine-grained layouts to facilitate better quality S2I generation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 669, + 385, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 385, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 385, + 681 + ], + "type": "text", + "content": "3. Our Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Given an input image " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": ", object semantic label " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{obj}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " and a textual description " + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{context}" + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": " describing the final scene con" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6498" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 52, + 545, + 310 + ], + "blocks": [ + { + "bbox": [ + 50, + 52, + 545, + 310 + ], + "lines": [ + { + "bbox": [ + 50, + 52, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 50, + 52, + 545, + 310 + ], + "type": "image", + "image_path": "bd575b2128bacfd093658cc193c7561b56e9d51632f8ab78253519898067144a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": "Figure 2. Method Overview. A key idea behind SmartMask is to leverage semantic amodal segmentation data [28, 47] in order to obtain high-quality paired training annotations for mask-free single or multi-step object insertion. During training (top), given a training image " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": " with caption " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ", we stack " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": " ordered instance maps " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "\\{A_1, A_2, \\ldots, A_k\\}" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": " to obtain an intermediate semantic map " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "S_k" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ". The diffusion model is then trained to predict the instance map " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "A_{k+1}" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ", conditional on the semantic map " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "S_k" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{obj} \\gets \\mathcal{O}_{k+1}" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": " and scene context " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{context} \\gets C" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ". During inference (bottom), given a real image " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ", we first use a panoptic segmentation model to compute semantic map " + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "inline_equation", + "content": "S_I" + }, + { + "bbox": [ + 46, + 315, + 547, + 383 + ], + "type": "text", + "content": ". The generated semantic layout is then directly used as input to the trained diffusion model in order to predict the fine-grained mask for the inserted object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": "text, our goal is predict a fine-grained mask " + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{obj}" + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": " for the target object. The object mask " + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{obj}" + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": " could then be used as input to a ControlNet-Inpaint model for fine-grained object insertion (Sec. 4.1) or used to design detailed semantic layouts from scratch (Sec. 4.3). For instance, SmartMask could be used for single object insertion, where given an image " + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": " depicting a man on a bench, " + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{T}_{obj} : \\text{\"woman'}\\}" + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{T}_{\\text{context}} : \\text{\"a couple sitting on a bench'}\\}" + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": ", our goal is to predict fine-grain binary mask " + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{woman}" + }, + { + "bbox": [ + 46, + 392, + 288, + 524 + ], + "type": "text", + "content": " which places the 'woman' in a manner such that the resulting scene aligns with overall scene context of a 'a couple sitting on a bench'." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": "Similarly, SmartMask could also be used for multiple object insertion. For instance, given an image " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": " depicting a wedding, the user may wish to add multiple objects \\{'man', 'woman' and 'kid'\\} such that the final scene aligns with the " + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{T}_{\\text {context }}: \\text { 'a family posing for a picture at a wedding }\\}" + }, + { + "bbox": [ + 46, + 529, + 287, + 649 + ], + "type": "text", + "content": ". Unlike prior image inpainting methods which are limited independently adding each object to the scene, the goal of the smartmask model is to add each object in a manner such the generated 'man', 'woman' and 'kid' appear to be 'a family posing for a picture at a wedding'. (refer Fig. 2a)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "In the next sections, we describe the key SmartMask components in detail. In particular, in Sec. 3.1 we discuss how SmartMask can leverage semantic amodal segmentation data in order to obtain high-quality paired annotations for mask-free object insertion. We then discuss a simple" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "content": "data-adaptation strategy which allows the user to also control the position, shape of the inserted object using coarse inputs (bounding-box, scribbles) in Sec. 3.2. Finally, in Sec. 3.3 we propose a visual-instruction tuning [21] based planning model which when used with SmartMask, allows for generation of detailed semantic layouts from scratch." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 469, + 534, + 482 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 534, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 534, + 482 + ], + "type": "text", + "content": "3.1. SmartMask for Mask-Free Object Insertion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 487, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 595 + ], + "type": "text", + "content": "Semantic-Space Task Formulation. Directly learning a model for our task in pixel space can be quite challenging, as it would require large-scale collection of training data for single or multi-step object insertion while maintaining background preservation. To address this key challenge, a core idea of our approach is to propose an equivalent task formulation which allows us to leverage large-scale semantic amodal segmentation data [28, 47] for generating high-quality paired training data in the semantic space (Fig. 2)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "text", + "content": "SmartMask Training. In particular during training, given an image " + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "text", + "content": ", with a sequence of ordered amodal semantic instance maps " + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "\\{A_1, A_2 \\ldots A_n\\}" + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "text", + "content": " and corresponding semantic object labels " + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{O}_1, \\mathcal{O}_2 \\ldots \\mathcal{O}_n\\}" + }, + { + "bbox": [ + 304, + 596, + 545, + 655 + ], + "type": "text", + "content": ", we first compute an intermediate layer semantic map as," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 316, + 659, + 545, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 659, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 316, + 659, + 545, + 673 + ], + "type": "interline_equation", + "content": "S _ {k} = f _ {\\text {l a y e r}} \\left(\\left\\{A _ {1}, A _ {2} \\dots A _ {k} \\right\\}\\right) \\quad \\text {w h e r e} k \\in [ 1, n ]. \\tag {1}", + "image_path": "409d025ecd0abea022720bbd775114711b645206a499ccedba34ab2bd6e6a416.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " is randomly chosen from " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "[1, n]" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_{layer}" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " is a layering operation which stacks the amodal semantic segmentation maps from " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "i \\in [1, k]" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " in an ordered manner (Fig. 2)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6499" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": "We next train a diffusion-based mask prediction model " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " which takes as input the above computed intermediate semantic layer map " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": ", textual description for next object " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{obj} \\gets \\mathcal{O}_{k+1}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": ", overall caption " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{context} \\gets C_{\\mathcal{I}}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " (for image " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": ") and learns to predict the binary mask " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\{A_{k+1}\\}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " for the next object. To this end, we first pass the intermediate semantic map " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " through a learnable encoder " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\phi}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " to obtain the encoded features " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{E}_{\\phi}(S_{k})" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": ". At any timestep " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " of the reverse diffusion process, the denoising noise prediction " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\epsilon_{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " is then computed conditional jointly on previous noise latent " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_{t}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": ", and model inputs " + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{E}_{\\theta}(S_{k}), \\mathcal{T}_{obj}, \\mathcal{T}_{context}\\}" + }, + { + "bbox": [ + 47, + 72, + 289, + 205 + ], + "type": "text", + "content": " as," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 77, + 212, + 287, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 212, + 287, + 225 + ], + "spans": [ + { + "bbox": [ + 77, + 212, + 287, + 225 + ], + "type": "interline_equation", + "content": "\\tilde {\\epsilon} _ {p r e d} (t) = \\mathcal {U} _ {\\theta} (\\mathbf {z} _ {t}, \\mathcal {E} _ {\\phi} (S _ {k}), \\mathcal {T} _ {o b j}, \\mathcal {T} _ {\\text {c o n t e x t}}, t), \\tag {2}", + "image_path": "e4f435f83091d57325593f1bbed7cfbe198ac9185d5fa719fb2b896d632d3bb7.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{U}_{\\theta}" + }, + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "type": "text", + "content": " represents the U-Net of the diffusion model " + }, + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 232, + 277, + 243 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "type": "text", + "content": "The overall diffusion model " + }, + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "type": "text", + "content": " is then trained to predict the next layer " + }, + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "type": "inline_equation", + "content": "A_{k + 1}" + }, + { + "bbox": [ + 47, + 243, + 287, + 269 + ], + "type": "text", + "content": " using the following diffusion loss," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 61, + 275, + 287, + 290 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 275, + 287, + 290 + ], + "spans": [ + { + "bbox": [ + 61, + 275, + 287, + 290 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} (\\theta , \\phi) = \\mathbf {E} _ {t \\sim [ 1, T ], S _ {k}, A _ {k + 1}, \\epsilon_ {t}} \\left[ \\| \\epsilon_ {t} - \\tilde {\\epsilon} _ {p r e d} (t) \\| ^ {2} \\right], \\tag {3}", + "image_path": "08f8be1d96cd01b5af2f52f575cbf606ec1a871020a38cccc48d410ebdc28a5b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "text", + "content": " is total number of reverse diffusion steps, " + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "inline_equation", + "content": "\\epsilon_t\\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "text", + "content": " is sampled from a normal distribution and " + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "inline_equation", + "content": "A_{k + 1}" + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "text", + "content": " represents ground truth binary mask for next object " + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "inline_equation", + "content": "\\mathcal{O}_{k + 1}" + }, + { + "bbox": [ + 47, + 297, + 287, + 332 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": "SmartMask Inference. During inference, given an input image " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": ", semantic object category " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{obj}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": " and a textual description " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{\\text {context }}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": " describing the final scene context, we first use a panoptic semantic segmentation model [15] to obtain the corresponding semantic layout map " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_{\\mathcal{I}}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": ". The generated semantic layout " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{S}_{\\mathcal{I}}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": " is then directly used as input to the above trained diffusion model " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": " in order to predict the fine-grained mask " + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{obj}" + }, + { + "bbox": [ + 46, + 333, + 287, + 429 + ], + "type": "text", + "content": " for the target object," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 91, + 436, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 436, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 91, + 436, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {o b j} = \\mathcal {D} _ {\\theta} \\left(\\mathcal {E} _ {\\phi} \\left(\\mathcal {S} _ {I}\\right), \\mathcal {T} _ {o b j}, \\mathcal {T} _ {\\text {c o n t e x t}}\\right). \\tag {4}", + "image_path": "eba573a31f0c4da37fc182f43f9e87538683fa672058c8ddd600618c8adc7203.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 463, + 269, + 475 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 463, + 269, + 475 + ], + "spans": [ + { + "bbox": [ + 47, + 463, + 269, + 475 + ], + "type": "text", + "content": "3.2. Data Adaptation for Precise Mask Control" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "text", + "content": "While the diffusion model trained in Sec. 3.1, allows the user to perform mask-free object insertion at diverse positions and scales, the user may also wish to obtain more direct control over the spatial location and details of the inserted object. To this end, we propose a simple train-time data adaptation strategy which allows smartmask to be easily adapted to diverse forms of user control (Fig. 4). In particular, given the intermediate layer map " + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "text", + "content": " computed using Eq. 1 and ground truth mask " + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "inline_equation", + "content": "A_{k + 1}" + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "text", + "content": " for the next object, we replace the input " + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 46, + 481, + 287, + 601 + ], + "type": "text", + "content": " to the diffusion model as," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 56, + 609, + 287, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 609, + 287, + 623 + ], + "spans": [ + { + "bbox": [ + 56, + 609, + 287, + 623 + ], + "type": "interline_equation", + "content": "\\tilde {S} _ {k} = g \\left(S _ {k}, G _ {o b j}\\right) = S _ {k} \\odot \\left(1 - \\alpha G _ {o b j}\\right) + \\alpha G _ {o b j}, \\tag {5}", + "image_path": "3693c1fedf5f464c3b50aec72cb5b73cd638da0f80b7350dee702c1f921b3b8f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": " is the additional guidance input (e.g., bounding box mask, coarse scribbles etc.) provided by the user and " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\alpha = 0.7" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": " helps add additional guidance while still preserving the content of the original input " + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 47, + 629, + 287, + 677 + ], + "type": "text", + "content": " after data adaptation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "Training. In this paper, we mainly consider four main guidance inputs " + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": " for additional mask control for adapting SmartMask. 1) Mask-free guidance: in absence of any" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "additional user inputs, we use " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "G_{obj} = \\mathbf{0}^{H,W}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " which prompts the model to suggest fine-grained masks for object insertion at diverse positions and scales. 2) Bounding-box guidance: we set " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " as a binary mask corresponding to ground truth object mask " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "A_{k+1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": ". 3) Coarse Spatial Guidance: Expecting the user to provide precise bounding box for object insertion is not always convenient and can lead to errors if bounding box is not correct. We therefore introduce a coarse spatial control where user may provide a coarse spatial location and the model learns to infer the best placement of the object around the suggested region (Fig. 4c). During training, the same is achieved by setting " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " as a coarse gaussian blob centered at the ground truth object mask " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "A_{k+1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": ". 4) User scribbles: Finally, we also allow the user to describe target object using free-form coarse scribbles, by setting " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": " as the dilated mask output of ground-truth object mask " + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "inline_equation", + "content": "A_{k+1}" + }, + { + "bbox": [ + 304, + 72, + 545, + 263 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "text", + "content": "Inference. At inference time, the additional guidance input " + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "text", + "content": " (e.g. bounding box mask, coarse scribbles etc.) is directly provided by the user. Given an input image " + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "text", + "content": " with semantic layout " + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "inline_equation", + "content": "S_{\\mathcal{I}}" + }, + { + "bbox": [ + 304, + 264, + 545, + 337 + ], + "type": "text", + "content": ", we then use transformation from Eq. 5 as input to the adapted SmartMask model in order to generate object insertion suggestions with additional control." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 346, + 523, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 523, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 523, + 358 + ], + "type": "text", + "content": "3.3. Global Planning for Multi-Step Inference" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "type": "text", + "content": "While the original SmartMask model allows the user to generate fine-grained masks for single object insertion, we would also like to use SmartMask for iterative use cases such as multiple object insertion (Sec. A.1) or designing a fine-grained layout from scratch with large number " + }, + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "type": "inline_equation", + "content": "(>10)" + }, + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "type": "text", + "content": " of scene elements. Such an iterative use of SmartMask would require the model to carefully plan the spatial location of each inserted object to allow for the final scene to be consistent with the final scene context description " + }, + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{\\text{context}}" + }, + { + "bbox": [ + 304, + 365, + 545, + 473 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": "To achieve this, we train a visual-instruction tuning [21] based planning model which given the input semantic layout " + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "inline_equation", + "content": "S_{I}" + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": ", learns to plan the positioning of different scene elements over long sequences. Given a semantic object description " + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "inline_equation", + "content": "T_{obj}" + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": " and final scene context " + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "inline_equation", + "content": "T_{context}" + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": ", the global planning model provides several bounding box suggestions for object insertion. SmartMask model then uses the above predictions as coarse spatial guidance input " + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "inline_equation", + "content": "G_{obj}" + }, + { + "bbox": [ + 304, + 474, + 545, + 605 + ], + "type": "text", + "content": " to provide fine-grained mask suggestions for the next object. The above process can then be repeated in an iterative manner until all objects have been added to the scene (refer Fig. 7a)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The global planning model is trained in two stages. 1) Feature Alignment. Typical instruction tuning models are often trained on real images. In contrast, as discussed in Sec. 3.1 we would like to model our problem in semantic space as it allows us to leverage amodal segmentation data for training. To address this domain gap, we first finetune an existing LLaVA model [21] to understand the semantic inputs. To do this, given an intermediate semantic map " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " computed using Eq. 1, we finetune the projection matrix " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6500" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 63, + 545, + 323 + ], + "blocks": [ + { + "bbox": [ + 51, + 63, + 545, + 323 + ], + "lines": [ + { + "bbox": [ + 51, + 63, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 51, + 63, + 545, + 323 + ], + "type": "image", + "image_path": "c845681feea1a94c6197d1c87a541ea6826a41236c4c81c83bb0db580470cb5f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 328, + 546, + 351 + ], + "lines": [ + { + "bbox": [ + 46, + 328, + 546, + 351 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 546, + 351 + ], + "type": "text", + "content": "Figure 3. Qualitative Results for Image Inpainting. We observe that as compared to with state-of-the-art image inpainting [1, 2, 30, 37] methods, SmartMask allows the user to perform object insertion while better preserving the background around the inserted object." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "type": "text", + "content": "of the LLaVA model [21] " + }, + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "type": "text", + "content": " to predict the semantic object labels " + }, + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{O}_1,\\mathcal{O}_2\\ldots \\mathcal{O}_k\\}" + }, + { + "bbox": [ + 46, + 361, + 288, + 387 + ], + "type": "text", + "content": " described in the current scene as," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 396, + 287, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 396, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 59, + 396, + 287, + 409 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a l i g n}} (\\mathbf {W}) = \\mathcal {L} _ {C E} (< \\mathcal {O} _ {1}, \\mathcal {O} _ {2} \\dots \\mathcal {O} _ {k} >, \\mathcal {H} (S _ {k})). \\tag {6}", + "image_path": "743188112fc955583cb26ecbb53e847cf14985031747ba7f2d0fab92042621d2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": "2) Instruction-Tuning. Finally, keeping the visual encoder weights for LLaVA model fixed, we next finetune both project matrix " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathbf{W}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " and LLM weights " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " [43] for global object planning. In particular, given an intermediate semantic map " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "S_{k}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": ", we first compute the bounding box coordinates " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{k+1} = \\{x_{min}, y_{min}, x_{max}, y_{max}\\}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " for the next object " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_{obj} = \\mathcal{O}_{k+1}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " using ground truth object mask " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{A}_{k+1}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": ". The LLaVA based planning model " + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 419, + 287, + 515 + ], + "type": "text", + "content": " is then trained as," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 525, + 287, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 525, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 59, + 525, + 287, + 539 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {i n s t r u c t}} (\\mathbf {W}, \\Phi) = \\mathcal {L} _ {C E} \\left(\\mathcal {B} _ {k + 1}, \\mathcal {H} \\left(S _ {k}, \\mathcal {T} _ {\\text {o b j}}, C\\right)\\right), \\tag {7}", + "image_path": "16b762e3f604d4bb980a7b5086d3fa990c1fe0b0333a8f35fbd59d202044b507.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "type": "text", + "content": " represents the caption for the final scene (obtained using ground-truth image " + }, + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 548, + 287, + 586 + ], + "type": "text", + "content": ") and provides the model context for placing different scene elements in the image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 597, + 128, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 611 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Training Data Collection. As discussed in Sec. 3, we note that a key idea behind SmartMask is to model the object insertion problem in semantic space (instead of pixel space), which allows us to leverage semantic amodal segmentation data to obtain large-scale paired training annotations for single or multiple object insertions. However, traditional datasets for semantic amodal segmentations such as COCOA [47] (2,500 images, 22,163 instances) and KINS [28]" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 361, + 545, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 397 + ], + "type": "text", + "content": "(7,517 images, 92,492 instances) though containing fine-grained amodal segmentation annotations may lack sufficient diversity to generalize across different use-cases." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "content": "To address this, we curate a new large-scale dataset consisting of fine-grain amodal segmentation masks for different objects in an input image. The overall dataset consists of 32785 diverse real world images and a total of 725897 object instances across more than 500 different semantic classes (e.g. man, woman, trees, furniture etc.). Each image " + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "content": " in the dataset consists of a variable number of object instances " + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\{A_1, A_2, \\ldots, A_n\\}" + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "inline_equation", + "content": "n \\in [2, 50]" + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "content": " and is annotated with an ordered sequence of semantic amodal segmentation maps " + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "inline_equation", + "content": "\\{S_1, S_2, \\ldots, S_n\\}" + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "content": ". The detailed descriptions " + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "inline_equation", + "content": "C_I" + }, + { + "bbox": [ + 304, + 399, + 546, + 532 + ], + "type": "text", + "content": " for each image are obtained using the InstructBLIP [7] model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "SmartMask Training. In order to leverage the rich generalizable prior of T2I diffusion models, we use the weights from publicly available Stable-Diffusion-v1.5 model [30] in order to initialize the weights of the SmartMask U-Net model trained in Sec. 3.1. Similar to [5], we modify the architecture of the U-Net model to also condition the output mask predictions on segmentation layout " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "S_{I}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": ". The SmartMask model is trained for a total of 100k iterations with a batch size of 192 and learning rate " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "1e - 5" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " using 8 Nvidia-A100 GPUs. During inference, a panoptic semantic segmentation model finetuned on the dataset in Sec. 4 is used for converting real image " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " to its semantic layout " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "S_{I}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": ". ControlNet model trained with SDXL backbone was used to perform precise object insertion with SmartMask outputs. Please refer the supp. material for further training details." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6501" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 56, + 118, + 114 + ], + "blocks": [ + { + "bbox": [ + 51, + 56, + 118, + 114 + ], + "lines": [ + { + "bbox": [ + 51, + 56, + 118, + 114 + ], + "spans": [ + { + "bbox": [ + 51, + 56, + 118, + 114 + ], + "type": "image", + "image_path": "1541e367e0ddb99394b602a3e451e55245b1a75949436b7951887e38463e48ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 118, + 56, + 192, + 114 + 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SmartMask for Object Insertion" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 376, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 483 + ], + "type": "text", + "content": "Baselines. We compare the performance of our approach on object-insertion with prior works on performing multimodal image-inpainting using a textual description and coarse bounding box mask. In particular we show comparisons with SD-Inpaint [30], SDXL-Inpaint [27], Blended-Latent Diffusion [30], and Adobe SmartBrush [37]. We also compare the performance of our approach with state-of-the-art commercial inpainting tools by reporting results on recently released Generative-Fill from Adobe Firefly [1]." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "type": "text", + "content": "Evaluation Metrics. Following [37], we report the results for object insertion using 1) Local-FID [11] which measures the realism of the generated objects, 2) CLIP-Score [10] which measures the alignment between the textual description and the generated object, and 3) Norm. L2-BG: which reports the normalized L2 difference in the background regions before and after insertion, and helps capture the degree to which the background was preserved." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "Qualitative Results. Results are shown in Fig. 3. We observe that when performing objectn insertion using a coarse bounding box mask, traditional inpainting methods usually lead to a lot of changes in the background regions around the inserted object (e.g. living room details in row-1&2, mountains in row-4 etc.). Adobe SmartBrush [37] which is trained to allow better background preservation, shows better performance, however, still suffers from notable changes to background regions. In contrast, by directly predicting a high-fidelity mask for the target object, the proposed approach allows the user to add new objects on the scene with" + } + ] + } + ], + "index": 45 + }, + { + "type": "table", + "bbox": [ + 306, + 356, + 555, + 439 + ], + "blocks": [ + { + "bbox": [ + 306, + 356, + 555, + 439 + ], + "lines": [ + { + "bbox": [ + 306, + 356, + 555, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 555, + 439 + ], + "type": "table", + "html": "
MethodEvaluation Criteria
Local-FID ↓CLIP-Score ↑Norm. L2-BG ↓
SD Inpaint [30]22.310.2490.374
SDXL Inpaint [27]21.840.2350.623
Blended L-Diffusion [2]39.770.2530.451
Adobe SmartBrush [37]17.940.2620.304
Adobe Gen-Fill* [1]N/A0.2680.289
Smartmask (Ours)19.210.2610.098
", + "image_path": "6b7724629f5d8cc2ce751f4dabfb6e8dfd0c88f011e585a57eccdc8c2d5b6e2f.jpg" + } + ] + } + ], + "index": 46, + "angle": 0, + "type": "table_body" + } + ], + "index": 46 + }, + { + "bbox": [ + 305, + 445, + 545, + 478 + ], + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 478 + ], + "type": "text", + "content": "Table 1. Quantitative results for image inpainting. We observe that in comparison with state-of-art image inpainting methods, our approach leads to better preservation of background regions." + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 484, + 545, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 592 + ], + "type": "text", + "content": "minimal changes to the background image. Furthermore we observe that target object masks are generated in a scene-aware manner, which helps us add new objects while interacting with already existing ones. For instance, when adding 'a man to a couch with table in front' (Fig. 3), prior works typically replace the couch and table to insert the target object ('man'). In contrast, smartmask places the 'man sitting on the couch with his leg on the table', and provides a more natural way for inserting objects in complex scenes." + } + ] + } + ], + "index": 48 + }, + { + "bbox": [ + 304, + 593, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 665 + ], + "type": "text", + "content": "Quantitative Results. In addition to qualitative results, we also report the performance of our approach quantitatively in Tab. 1. We find that similar to results in Fig. 3, the proposed approach shows better background preservation (Norm. L2-BG ↓) while performing comparably in terms of image quality (local-FID) and text-alignment (CLIP-Score)." + } + ] + } + ], + "index": 49 + }, + { + "bbox": [ + 305, + 671, + 538, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 671, + 538, + 684 + ], + "spans": [ + { + "bbox": [ + 305, + 671, + 538, + 684 + ], + "type": "text", + "content": "4.2. Evaluating Mask Controllability and Quality" + } + ] + } + ], + "index": 50 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "A key advantage of SmartMask is the ability to generate high-quality masks for target object in a controllable man" + } + ] + } + ], + "index": 51 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6502" + } + ] + } + ], + "index": 52 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 60, + 286, + 220 + ], + "blocks": [ + { + "bbox": [ + 50, + 60, + 286, + 220 + ], + "lines": [ + { + "bbox": [ + 50, + 60, + 286, + 220 + ], + "spans": [ + { + "bbox": [ + 50, + 60, + 286, + 220 + ], + "type": "image", + "image_path": "5afad3b15493e52d50f73742b4494c974ea3dc4b540204e1f077c5f1349d7ea0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 223, + 287, + 246 + ], + "lines": [ + { + "bbox": [ + 47, + 223, + 287, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 223, + 287, + 246 + ], + "type": "text", + "content": "Figure 5. Comparing output mask quality with different Inpaint + HQSAM (middle) methods and SmartBrush mask output (right)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 258, + 287, + 314 + ], + "blocks": [ + { + "bbox": [ + 48, + 258, + 287, + 314 + ], + "lines": [ + { + "bbox": [ + 48, + 258, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 48, + 258, + 287, + 314 + ], + "type": "image", + "image_path": "d1bdff23c45e9ac1d093535aeb24ccf1e869f294a72052c458f942bb7a4ef9b3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 319, + 287, + 353 + ], + "lines": [ + { + "bbox": [ + 47, + 319, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 287, + 353 + ], + "type": "text", + "content": "Figure 6. Limitation of Inpaint + HQSAM. In addition to poor mask quality errors (Fig. 5), we observe that Inpaint+HQSAM can lead to scene-unaware masks (e.g. mask for woman sitting in air)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 365, + 286, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 286, + 389 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 286, + 389 + ], + "type": "text", + "content": "ner. In this section, we evaluate the performance of SmartMask in terms of 1) user control, & 2) output mask quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 389, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 605 + ], + "type": "text", + "content": "1) User Control. As shown in Fig. 4, we observe that SmartMask allows the user to control the output object mask in four main ways. 1) Mask-free insertion: where the model automatically suggests diverse positions and scales for the target object (e.g., table, woman in Fig. 4a). 2) Bounding-box guidance: which allows user to specify the exact bounding box for object insertion (potted plant, motorbike in Fig. 4b). 3) Coarse spatial guidance: (Fig. 4c) providing a precise bounding box can be challenging for cases with complex object insertions e.g., dog with owner. SmartMask allows the user to only specify a coarse location for the target object, and the model automatically adjusts the object placement (i.e. dog with head near woman's hand) to capture object interactions. 3) User-scribbles: Finally, the user may also control the output shape by providing coarse scribbles. The smartmask model can use this as guidance to automatically predict the more finegrain-masks for the target object (e.g., palm-tree, gaming chair in Fig. 4d)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 714 + ], + "type": "text", + "content": "2) Output Mask Quality. We also report results on the quality of generated masks by showing comparisons with the mask-prediction head of the SmartBrush model [37]. Furthermore, we also show comparisons combining standard inpainting methods with HQSAM [13, 16]. To this end, we first use the provided bounding-box mask to inpaint the target object. The user-provided bounding-box and the inpainted output are then used as input to the HQSAM model [13] to obtain target object-mask predictions." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 60, + 545, + 125 + ], + "blocks": [ + { + "bbox": [ + 306, + 60, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 306, + 60, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 306, + 60, + 545, + 125 + ], + "type": "table", + "html": "
MethodUser Study Results
Win ↑DrawLose ↓
SDInpaint + HQSAM [13, 30]92.04%5.12%2.84%
Blended L-Diff + HQSAM [2, 13]88.91%8.33%2.75%
SmartBrush + HQSAM [13, 37]63.89%27.78%8.34%
SmartBrush Mask [37]91.67%2.78%5.56%
", + "image_path": "1589dc68e1186ae72b1e2ef8b0a30c15b3d1bfced3a6229e6af2102faf362fe1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 130, + 545, + 163 + ], + "lines": [ + { + "bbox": [ + 305, + 130, + 545, + 163 + ], + "spans": [ + { + "bbox": [ + 305, + 130, + 545, + 163 + ], + "type": "text", + "content": "Table 2. User study results. For evaluating generated mask quality. We observe that SmartMask generates higher quality masks as compared to SmartBrush and various Inpaint+HQSAM methods." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 184, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 184, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 184, + 545, + 399 + ], + "type": "text", + "content": "Results are shown in Fig. 5. We observe that as compared to outputs of SmartBrush [37] mask-prediction head, SmartMask generates higher-quality masks with fewer artifacts. Similarly, while using HQSAM on inpainting outputs helps achieve good mask quality for some examples (e.g. child in row-2), the HQSAM generated masks (or the inpainted image) often have accompanying artifacts which limits the quality of the output masks. In addition to poor mask quality errors, we also observe that Inpaint+HQSAM can lead to scene-unaware masks (Fig. 6). This occurs because prior inpainting methods typically add additional objects in the background when performing object insertion. For instance, when inserting woman in a living room in Fig. 6), we observe that Adobe Gen-Fill [1] adds an additional chair on which the woman is sitting. Extracting only the object mask for such inpainted outputs can lead to scene-unaware masks where 'the woman appears floating in the air' as the chair was not present in the original image." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 545, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 484 + ], + "type": "text", + "content": "The above findings are also reflected in a quantitative user study (Tab. 2), where human subjects are shown a pair of object mask suggestions (ours vs baselines discussed above), and asked to the select the mask suggestion with the higher quality. As shown in Tab. 2, we observe that SmartMask outputs are preferred by majority of human subjects over SmartBrush mask [37] and Inpaint + HQSAM outputs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 491, + 517, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 491, + 517, + 504 + ], + "spans": [ + { + "bbox": [ + 305, + 491, + 517, + 504 + ], + "type": "text", + "content": "4.3. SmartMask for Semantic Layout Design" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 510, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 700 + ], + "type": "text", + "content": "In addition to object insertion, we also find that when used iteratively along with the visual-instruction tuning based planning model from Sec. 3.3, SmartMask forms a convenient approach for designing detailed semantic layouts with a large number of fine-grain objects (e.g. humans, furniture etc.). Results are shown in Fig. 7a. We observe that given a sequence of user provided scene elements (e.g. painting, sofa, chair etc.), SmartMask generates the entire scene layout from scratch. Furthermore, unlike static layouts generated by a panoptic segmentation model, SmartMask generated layouts allow the user greater control over the details of each scene element. Since each object in the final layout is represented by a distinct object mask, the final layouts are highly controllable and allow for a range of custom operations such as adding, removing, modifying or moving objects through simple layer manipulations. (refer Fig. 7b)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Controllable S2I Generation. Layout to image gener" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6503" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 217, + 62, + 373, + 70 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 217, + 62, + 373, + 70 + ], + "spans": [ + { + "bbox": [ + 217, + 62, + 373, + 70 + ], + "type": "text", + "content": "Input Prompt: A living room with a couch, chair and table." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 71, + 119, + 129 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 119, + 129 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 119, + 129 + ], + "spans": [ + { + "bbox": [ + 61, + 71, 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+ 426 + ], + "lines": [ + { + "bbox": [ + 477, + 418, + 529, + 426 + ], + "spans": [ + { + "bbox": [ + 477, + 418, + 529, + 426 + ], + "type": "text", + "content": "Ours + Controlnet" + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_caption" + } + ], + "index": 51 + }, + { + "bbox": [ + 46, + 476, + 289, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 289, + 704 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 289, + 704 + ], + "type": "text", + "content": "ation methods e.g., ControlNet [41] enable the generation of controllable image outputs from user-scribble based semantic segmentation maps or layouts. However, generating the user-desired layouts with coarse scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g. humans, chairs etc.). As shown in Fig. 7c, we find that this can lead to image outputs with either deformity artifacts (child in row-1) or incorrect description (woman and children in row-2) when using ControlNet [41]. A similar problem is also observed in other coarse-scribble based S2I methods such as DenseDiffusion [14] and Paint-with-Words (PwW) [4], which provide coarse control over object position but are unable to control finegrain details such as pose, action etc. of the target object. SmartMask helps address this problem by allowing any novice user to generate controllable (Fig. 7b) fine-grain layouts from scratch, which can allow users to better leverage existing S2I methods [41] for higher quality layout-to-image generation (refer Fig. 7c)." + } + ] + } + ], + "index": 55 + }, + { + "bbox": [ + 306, + 475, + 379, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 379, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 379, + 488 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 56 + }, + { + "bbox": [ + 304, + 495, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 712 + ], + "type": "text", + "content": "In this paper, we present SmartMask which allows a novice user to generate scene-aware precision masks for object insertion and finegrained layout design. Existing methods for object insertion typically rely on a coarse bounding box or user-scribble input which can lead to poor background preservation around the inserted object. To address this, we propose a novel diffusion based framework which leverages semantic amodal segmentation data in order to learn to generate fine-grained masks for precise object insertion. When used along with a ControlNet-Inpaint model, we show that the proposed approach achieves superior object-insertion performance, preserving background content more effectively than previous methods. Additionally, we show that SmartMask provides a highly controllable approach for designing detailed layouts from scratch. As compared with user-scribble based layout design, we observe that the proposed approach can allow users to better leverage existing S2I methods for higher quality layout-to-image generation." + } + ] + } + ], + "index": 57 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6504" + } + ] + } + ], + "index": 58 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 112 + ], + "type": "text", + "content": "[1] Adobe. 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Waslander $^{3}$ Hongsheng Li $^{2,4,5}$ Yu Liu $^{1,5}$", + "bbox": [ + 292, + 200, + 704, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ SenseTime Research $^{2}$ CUHK MMLab $^{3}$ University of Toronto $^{4}$ CPII under InnoHK $^{5}$ Shanghai Artificial Intelligence Laboratory", + "bbox": [ + 220, + 243, + 759, + 281 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 236, + 315, + 316, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission1. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage.", + "bbox": [ + 76, + 347, + 475, + 781 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 796, + 209, + 811 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently", + "bbox": [ + 75, + 821, + 475, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving.", + "bbox": [ + 491, + 316, + 890, + 599 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved.", + "bbox": [ + 491, + 601, + 890, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em", + "bbox": [ + 491, + 825, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal contribution, $\\boxtimes$ Corresponding author.", + "bbox": [ + 99, + 875, + 349, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1 November 2023.", + "bbox": [ + 99, + 887, + 202, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15281", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement.", + "bbox": [ + 75, + 90, + 473, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency.", + "bbox": [ + 75, + 210, + 475, + 554 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both.", + "bbox": [ + 75, + 555, + 475, + 704 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, the contributions of this work are threefold:", + "bbox": [ + 76, + 705, + 467, + 719 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation.", + "- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research.", + "- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi" + ], + "bbox": [ + 76, + 720, + 473, + 900 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/9acac4aa2a2e5a45881e39d8a4d4cabc47513a8ec18c7f8501a299de7829e8df.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RefineContext Selection/EncodingRefinement Iteration
AllFixed StrategyAdaptive StrategySingleMultipleScenario Adaptive
TNT [38]X
GoalNet [37]X
GANet [32]X
ProphNet [33]X
DCMS [36]✓XXX✓XX
QCNet [40]✓✓XX✓XX
R-Pred [5]✓X✓X✓XX
MTR [25]✓X✓XX✓X
SmartRefine (ours)✓XX✓XX✓
", + "bbox": [ + 496, + 94, + 888, + 224 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations.", + "bbox": [ + 491, + 236, + 890, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission.", + "bbox": [ + 504, + 321, + 890, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 493, + 445, + 633, + 460 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Goal-Conditioned Trajectory Prediction", + "text_level": 1, + "bbox": [ + 493, + 470, + 834, + 488 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con", + "bbox": [ + 490, + 496, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15282", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information.", + "bbox": [ + 75, + 90, + 475, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Refinement: Two-Stage Trajectory Prediction", + "text_level": 1, + "bbox": [ + 76, + 234, + 464, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation.", + "bbox": [ + 75, + 255, + 477, + 659 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 674, + 168, + 689 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework.", + "bbox": [ + 75, + 700, + 475, + 834 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem formulation", + "text_level": 1, + "bbox": [ + 76, + 845, + 274, + 861 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the observed states of the target agent $\\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \\dots, s_0]$ in the historic $T_h$ steps, we aim at", + "bbox": [ + 76, + 869, + 475, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "predicting its future states $\\mathbf{s}_f = [s_1,s_2,\\dots ,s_{T_f}]$ of $T_{f}$ steps and associated probabilities $\\mathbf{p}$ . Naturally, the target agent will interact with the context $\\mathbf{c} = (\\mathbf{o}_h,\\mathbf{m})$ , including historic states of surrounding agents $\\mathbf{o}_h$ , and the HD map $\\mathbf{m}$ . For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as $(\\mathbf{s}_f,\\mathbf{p}) = f(\\mathbf{s}_h,\\mathbf{c})$ , where $f$ denotes the prediction model.", + "bbox": [ + 491, + 90, + 890, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model $f_{b}$ generating initial trajectories $\\mathbf{s}_f^0$ and trajectory features $\\mathbf{h}_f^0$ , as typical prediction methods $(\\mathbf{s}_f^0, \\mathbf{h}_f^0, \\mathbf{p}) = f_b(\\mathbf{s}_h, \\mathbf{c})$ . The initial predicted trajectory $\\mathbf{s}_f^0$ is then used to select anchors $\\mathbf{a}^0$ and retrieve critical context elements $\\mathbf{c}^0$ , which are then passed along with the trajectory features $\\mathbf{h}_f^0$ into the refinement model $f_{r}$ for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the $i$ -th iteration is formulated as $(\\delta \\mathbf{s}_f^i, \\mathbf{h}_f^i, \\mathbf{p}) = f_r(\\mathbf{h}_f^{i-1}, \\mathbf{s}_f^{i-1}, \\mathbf{c}^{i-1})$ . The generated offset $\\delta \\mathbf{s}_f^i$ is added to the input trajectory $\\mathbf{s}_f^{i-1}$ for refinement.", + "bbox": [ + 491, + 241, + 890, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Scenario-Adaptive Refinement", + "text_level": 1, + "bbox": [ + 493, + 440, + 764, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Adaptive Anchor/Context Selection", + "text_level": 1, + "bbox": [ + 493, + 464, + 792, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1).", + "bbox": [ + 491, + 488, + 890, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all $T_{f}$ waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into $N < T_{f}$ segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments $N$ is designed to adapt to the prediction horizon.", + "bbox": [ + 491, + 582, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Context Retrieval. When retrieving context information $\\mathbf{c}$ around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal", + "bbox": [ + 491, + 825, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15283", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b7e67582f0dceddbaadbd8e0f4748f83f0e1af21a7a6e14c5b4014683a942acb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 90, + 883, + 253 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/c2b3b37b594d19f69e01cea0fae890585627d07023ec4c013811f998ab0c3e22.jpg", + "image_caption": [ + "Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models." + ], + "image_footnote": [], + "bbox": [ + 89, + 255, + 872, + 452 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration $i$ , because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed $v$ around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range $R$ varies by the refinement iterations $i$ and the agent's average velocity $v$ around the anchor: $R_{i,v} = \\mathcal{F}(i)\\cdot v$ . $\\mathcal{F}(i)$ can be any monotonically decreasing function of the refinement iteration $i$ , to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function $\\mathcal{F}(i) = \\beta (\\frac{1}{2})^{i - 1}$ , where $\\beta$ denotes a constant. The retrieval range is also constrained within a permissible range $[R_{\\mathrm{min}},R_{\\mathrm{max}}]$ to ensure computational stability and efficiency.", + "bbox": [ + 75, + 577, + 478, + 862 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Anchor-Centric Context Encoding", + "text_level": 1, + "bbox": [ + 491, + 577, + 787, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations $i$ , these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor $a$ , generating a set of context embeddings $\\mathbf{z}_a$ .", + "bbox": [ + 490, + 601, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15284", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.3 Recurrent and Multi-Iteration Refinement", + "text_level": 1, + "bbox": [ + 76, + 90, + 426, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into $N$ segments, and refine the trajectory $N$ times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here $N$ equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all $N$ segments finishes one iteration of refinement, and we will conduct multiple refinement iterations.", + "bbox": [ + 75, + 114, + 475, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings $\\mathbf{z}_a$ around the segment's corresponding anchor $a$ , and the target agent's future trajectory embeddings $\\mathbf{h}_f$ . We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings $\\mathbf{z}_a$ . The fused trajectory embeddings will be used to predict $\\delta s$ , the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all $N$ steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction.", + "bbox": [ + 75, + 357, + 477, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another $N$ recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss.", + "bbox": [ + 75, + 614, + 477, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2.4 Adaptive Number of Refinement Iterations", + "text_level": 1, + "bbox": [ + 76, + 830, + 429, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di", + "bbox": [ + 75, + 854, + 475, + 900 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Adaptive Inference with SmartRefine" + ], + "code_body": "Input: Backbone model $f_{b}$ , refinement model $f_{r}$ , quality score decoder $f_{d}$ , agents history trajectories $\\mathbf{s}_{h}$ , scene context $\\mathbf{c}$ , and score threshold $\\bar{q}$ , maximum refinement iteration at inference $I'$ . \nOutput: Target agent's future trajectories $\\mathbf{s}_{f}$ and corresponding probabilities $\\mathbf{p}$ . \n1: $\\mathbf{s}_{f}^{0}, \\mathbf{h}_{f}^{0}, \\mathbf{p}^{0} = f_{b}(\\mathbf{s}_{f}^{0}, \\mathbf{c})$ \n2: $q^{0} = f_{d}(\\mathbf{h}_{f}^{0})$ \n3: if $q^{0} > \\bar{q}$ then \n4: Return $\\mathbf{s}_{f}^{0}, \\mathbf{p}^{0}$ \n5: for $i = 1, 2, \\ldots, I'$ do \n6: Adaptively select anchors and contexts \n7: Adaptatively encode contexts $\\mathbf{c}^{i-1}$ (anchor-centric) \n8: Multi-segment recurrent refinement: \n $\\delta \\mathbf{s}_{f}^{i}, \\mathbf{h}_{f}^{i}, \\mathbf{p}^{i}, q^{i} = f_{r}(\\mathbf{s}_{f}^{i-1}, \\mathbf{h}_{f}^{i-1}, \\mathbf{c}^{i-1})$ $\\mathbf{s}_{f}^{i} = \\mathbf{s}_{f}^{i-1} + \\delta \\mathbf{s}_{f}^{i}$ \n9: if $q^{i} < q^{i-1}$ then \n10: Return $\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}$ \n11: Return $\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}$ \n% Reach max refinement iteration", + "bbox": [ + 493, + 109, + 890, + 421 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality.", + "bbox": [ + 491, + 449, + 890, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration $i$ is $d_{max} - d_i$ , where $d_{max}$ denotes the largest predicted error among all iterations. A small $d_i$ means that the current prediction has already been improved from the largest prediction error $d_{max}$ , and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize $d_{max} - d_i$ with $d_{max} - d_{min}$ , where $d_{min}$ denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as", + "bbox": [ + 491, + 559, + 890, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq _ {i} = \\frac {d _ {\\text {m a x}} - d _ {i}}{d _ {\\text {m a x}} - d _ {\\text {m i n}}} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 766, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score.", + "bbox": [ + 491, + 811, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15285", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency.", + "bbox": [ + 76, + 90, + 475, + 390 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.3. Training Loss", + "text_level": 1, + "bbox": [ + 76, + 400, + 220, + 416 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The training of our model considers three loss terms, and uses hyper-parameter $\\alpha$ to balance them:", + "bbox": [ + 76, + 424, + 475, + 454 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c l s}} + \\mathcal {L} _ {\\mathrm {r e g}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {s c o r e}} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 467, + 475, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{cls}}$ denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss $\\mathcal{L}_{\\mathrm{reg}}$ , as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss $\\mathcal{L}_{\\mathrm{score}}$ , in the training stage, we fix the refinement iteration as $I$ and each iteration will output a quality score. Thus for each iteration $i$ , we calculate the $\\ell_1$ loss between the predicted quality score $\\hat{q}_i$ and labeled quality score $q_i$ (see Sec 3.2.4), and average the loss over all iterations:", + "bbox": [ + 75, + 494, + 475, + 691 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s c o r e}} = \\frac {1}{I + 1} \\sum_ {i = 0} ^ {I} \\| \\hat {q} _ {i} - q _ {i} \\| _ {1} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 702, + 475, + 744 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Similarly, the score loss also only considers the modal closest to the ground truth.", + "bbox": [ + 76, + 755, + 475, + 785 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 800, + 209, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency.", + "bbox": [ + 76, + 825, + 475, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 493, + 90, + 699, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at $10\\mathrm{Hz}$ . Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at $10\\mathrm{Hz}$ . The data is split into 200k, 25k, and 25k for training, validation, and test respectively.", + "bbox": [ + 491, + 113, + 890, + 308 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics.", + "bbox": [ + 491, + 311, + 890, + 430 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material.", + "bbox": [ + 491, + 434, + 890, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Quantitative Result", + "text_level": 1, + "bbox": [ + 493, + 638, + 679, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by $6.0\\%$ , $3.7\\%$ , $5.4\\%$ , $4.3\\%$ , $3.5\\%$ respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param-", + "bbox": [ + 491, + 661, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15286", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8e0fffe301820899b0c2aa9203a23b941033347f606712e911a5797e2c24b84a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetMethodminFDE ↓minADE ↓MR ↓#Param.(M) ↓Flops(G) ↓Latency(ms) ↓
ArgoverseHiVT [39]0.9690.6610.0922.52.654±4.0
HiVT w/ Ours0.9110.6460.0832.72.767±8.4
Prophnet* [33]1.0040.6870.09315.27.859±1.7
Prophnet w/ Ours0.9670.6750.09215.47.971±6.2
mmTransformer [14]1.0810.7090.1022.61.215±4.8
mmTransformer w/ Ours1.0230.6920.0942.81.327±9.7
Argoverse 2DenseTNT [10]1.6240.9640.2331.63.61,075±199
DenseTNT w/ Ours1.5530.8340.2211.94.01,099±212
QCNet (no ref)1.3040.7290.1645.547.0338±53
QCNet (no ref) w/ Ours1.2580.7180.1575.847.4363±67
QCNet [40]1.2530.7200.1577.755.8392±54
QCNet w/ Ours1.2400.7160.1568.056.2418±68
", + "bbox": [ + 181, + 77, + 785, + 262 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "eters, flops, and latency.", + "bbox": [ + 76, + 333, + 238, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by $3.4\\%$ , $6.9\\%$ , $7.5\\%$ , $4.2\\%$ , $3.9\\%$ respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation.", + "bbox": [ + 75, + 351, + 475, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation studies", + "text_level": 1, + "bbox": [ + 76, + 525, + 238, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material.", + "bbox": [ + 75, + 547, + 475, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds $\\bar{q}$ for adaptive refinement, while a higher threshold leads to better accuracy, we find $\\bar{q} = 0.5$ achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve.", + "bbox": [ + 75, + 627, + 475, + 835 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger", + "bbox": [ + 75, + 840, + 475, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/bb0b3e90fc8ba4370093c10861cfdb446fd2766901a490858b5afa06ee324599.jpg", + "table_caption": [ + "Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency." + ], + "table_footnote": [], + "table_body": "
DatasetMethodminFDE ↓minADE ↓MR ↓
ArgoverseHiVT [39]1.170.770.13
HiVT w/ Ours1.130.770.12
ProphNet* [33]1.300.850.14
Prophnet* w/ Ours1.210.810.13
mmTransformer [14]1.340.840.15
mmTransformer w/ Ours1.240.810.14
Argoverse 2DenseTNT [10]1.660.990.23
DenseTNT w/ Ours1.590.850.22
QCNet (no ref)1.290.650.16
QCNet (no ref) w/ Ours1.240.640.15
QCNet [40]1.240.640.15
QCNet w/ Ours1.230.630.15
", + "bbox": [ + 496, + 319, + 888, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set.", + "bbox": [ + 491, + 506, + 890, + 575 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9496fb08086673546e98ca71b8e2033a6c91889faf7340ffde38fbadb692c7ff.jpg", + "image_caption": [ + "Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds $\\bar{q}$ mentioned in Algorithm 1." + ], + "image_footnote": [], + "bbox": [ + 496, + 595, + 689, + 727 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d3196a1d87945dd9b252629e27b1afd460b55245cad9a5d7d732a02fc9e1491.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 595, + 885, + 727 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "model parameters with the same or slightly worse accuracy.", + "bbox": [ + 491, + 789, + 887, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding.", + "bbox": [ + 490, + 810, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15287", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d30db22a5732690fa15161f3217c5fe39fb9dc20c8dab479a2a01db9371b9947.jpg", + "image_caption": [ + "Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions." + ], + "image_footnote": [], + "bbox": [ + 124, + 90, + 243, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/009efeb68911d1f475b6bd134b314208f8691127e9ce85a6ae778744b70e72e4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 245, + 90, + 361, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5613082faf5562bee17e6cb1e1261da00189c9503db82692e030d4c00634aa66.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 90, + 480, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/48b8669549bf53d061ae1a8eca62b12c1b8e6d3b4513b88482b80d15f4fff7b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 90, + 599, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fc6bdcd919f5e8c6d7a30e223de2663ba9bd480136b85475c82c1d121d73266a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 601, + 90, + 718, + 188 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0c47feb96f45286ccb1809164c0eddd48c09e9dc95feec5062a2754e885ffdf0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 718, + 90, + 838, + 188 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay.", + "bbox": [ + 75, + 252, + 475, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Discussion", + "text_level": 1, + "bbox": [ + 76, + 450, + 194, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about $56\\%$ of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about $44\\%$ trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the \"blue\" and \"orange\" trajectories change. Two phenomenons are observed:", + "bbox": [ + 75, + 474, + 475, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score \"blue\" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score \"orange\" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can", + "bbox": [ + 76, + 736, + 477, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/454332fb719d3d9d404ad198699c637e9bfbeccc83356a824c0512a3f8c58cf8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
#Anchor numbersminFDE#Param.
10.928134K
20.911207K
30.911280K
50.915433K
60.916509K
", + "bbox": [ + 496, + 250, + 684, + 318 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ab88055d1b341b3c443ccf1d533c48fb70f2d0ffd5848255dea148d2d3d6e674.jpg", + "table_caption": [ + "Table 4. Ablation study on the number of anchors." + ], + "table_footnote": [], + "table_body": "
Context EncodingminFDE
Agent-Centric0.941
Anchor-Centric0.911
", + "bbox": [ + 699, + 252, + 888, + 304 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a8625216a2f0975765aec214f4b5de886ca7b6cd54cb690c225a25f3b3491b27.jpg", + "table_caption": [ + "Table 5. Ablation study on how the contexts are encoded." + ], + "table_footnote": [], + "table_body": "
Retrieval RadiusminFDEFlops (M)
Fixed Radius500.9262,297
200.923722
100.921325
20.93058
Adaptive RadiusRmax=10, Rmin=2, linear0.911245
Rmax=10, Rmin=2, exp0.911130
", + "bbox": [ + 532, + 348, + 848, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius.", + "bbox": [ + 491, + 431, + 890, + 459 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "hardly be further improved, or even be pushed away from the ground truth due to over-refinement.", + "bbox": [ + 504, + 486, + 890, + 515 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance.", + "bbox": [ + 491, + 516, + 890, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "These results show the necessity of adaptive refinement.", + "bbox": [ + 491, + 593, + 862, + 607 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 491, + 621, + 611, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings.", + "bbox": [ + 490, + 646, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15288", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European conference on computer vision, pages 213-229. Springer, 2020. 3", + "[2] Yuning Chai, Benjamin Sapp, Mayank Bansal, and Dragomir Anguelov. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17863-17873, 2023. 1, 2, 3, 4, 6, 7, 11" + ], + "bbox": [ + 496, + 92, + 890, + 315 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15290", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_model.json b/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d53f7964cb845ae7238bc6276a248a4a83590a53 --- /dev/null +++ b/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_model.json @@ -0,0 +1,1903 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.168, + 0.13, + 0.804, + 0.175 + ], + "angle": 0, + "content": "SmartRefine: A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.202, + 0.705, + 0.24 + ], + "angle": 0, + "content": "Yang Zhou\\(^{1*}\\) Hao Shao\\(^{1,2*}\\) Letian Wang\\(^{3}\\) \nven L. Waslander\\(^{3}\\) Hongsheng Li\\(^{2,4,5}\\) Yu Liu\\(^{1,5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.221, + 0.244, + 0.761, + 0.282 + ], + "angle": 0, + "content": "\\(^{1}\\)SenseTime Research \\(^{2}\\)CUHK MMLab \\(^{3}\\)University of Toronto \\(^{4}\\)CPII under InnoHK \\(^{5}\\)Shanghai Artificial Intelligence Laboratory" + }, + { + "type": "title", + "bbox": [ + 0.238, + 0.316, + 0.317, + 0.332 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.477, + 0.782 + ], + "angle": 0, + "content": "Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission1. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.797, + 0.21, + 0.812 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.822, + 0.476, + 0.868 + ], + "angle": 0, + "content": "Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.317, + 0.892, + 0.601 + ], + "angle": 0, + "content": "make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.602, + 0.892, + 0.827 + ], + "angle": 0, + "content": "By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.827, + 0.892, + 0.901 + ], + "angle": 0, + "content": "While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.875, + 0.35, + 0.888 + ], + "angle": 0, + "content": "* Equal contribution, \\( \\boxtimes \\) Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.888, + 0.203, + 0.899 + ], + "angle": 0, + "content": "1 November 2023." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.875, + 0.35, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15281" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.475, + 0.211 + ], + "angle": 0, + "content": "ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.212, + 0.476, + 0.555 + ], + "angle": 0, + "content": "To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.476, + 0.705 + ], + "angle": 0, + "content": "It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.706, + 0.468, + 0.72 + ], + "angle": 0, + "content": "To summarize, the contributions of this work are threefold:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.722, + 0.475, + 0.796 + ], + "angle": 0, + "content": "- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.797, + 0.475, + 0.855 + ], + "angle": 0, + "content": "- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.856, + 0.475, + 0.901 + ], + "angle": 0, + "content": "- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.722, + 0.475, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.498, + 0.095, + 0.89, + 0.226 + ], + "angle": 0, + "content": "
RefineContext Selection/EncodingRefinement Iteration
AllFixed StrategyAdaptive StrategySingleMultipleScenario Adaptive
TNT [38]X
GoalNet [37]X
GANet [32]X
ProphNet [33]X
DCMS [36]✓XXX✓XX
QCNet [40]✓✓XX✓XX
R-Pred [5]✓X✓X✓XX
MTR [25]✓X✓XX✓X
SmartRefine (ours)✓XX✓XX✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.493, + 0.237, + 0.892, + 0.293 + ], + "angle": 0, + "content": "Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.323, + 0.892, + 0.428 + ], + "angle": 0, + "content": "ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission." + }, + { + "type": "title", + "bbox": [ + 0.494, + 0.446, + 0.635, + 0.461 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.494, + 0.472, + 0.836, + 0.489 + ], + "angle": 0, + "content": "2.1. Goal-Conditioned Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.491, + 0.497, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15282" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.477, + 0.226 + ], + "angle": 0, + "content": "text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.235, + 0.465, + 0.251 + ], + "angle": 0, + "content": "2.2. Refinement: Two-Stage Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.256, + 0.478, + 0.66 + ], + "angle": 0, + "content": "Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.675, + 0.169, + 0.69 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.476, + 0.835 + ], + "angle": 0, + "content": "SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.276, + 0.862 + ], + "angle": 0, + "content": "3.1. Problem formulation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.476, + 0.903 + ], + "angle": 0, + "content": "Given the observed states of the target agent \\( \\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \\dots, s_0] \\) in the historic \\( T_h \\) steps, we aim at" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.092, + 0.892, + 0.24 + ], + "angle": 0, + "content": "predicting its future states \\(\\mathbf{s}_f = [s_1,s_2,\\dots ,s_{T_f}]\\) of \\(T_{f}\\) steps and associated probabilities \\(\\mathbf{p}\\). Naturally, the target agent will interact with the context \\(\\mathbf{c} = (\\mathbf{o}_h,\\mathbf{m})\\), including historic states of surrounding agents \\(\\mathbf{o}_h\\), and the HD map \\(\\mathbf{m}\\). For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as \\((\\mathbf{s}_f,\\mathbf{p}) = f(\\mathbf{s}_h,\\mathbf{c})\\), where \\(f\\) denotes the prediction model." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.242, + 0.892, + 0.432 + ], + "angle": 0, + "content": "In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model \\( f_{b} \\) generating initial trajectories \\( \\mathbf{s}_f^0 \\) and trajectory features \\( \\mathbf{h}_f^0 \\), as typical prediction methods \\( (\\mathbf{s}_f^0, \\mathbf{h}_f^0, \\mathbf{p}) = f_b(\\mathbf{s}_h, \\mathbf{c}) \\). The initial predicted trajectory \\( \\mathbf{s}_f^0 \\) is then used to select anchors \\( \\mathbf{a}^0 \\) and retrieve critical context elements \\( \\mathbf{c}^0 \\), which are then passed along with the trajectory features \\( \\mathbf{h}_f^0 \\) into the refinement model \\( f_{r} \\) for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the \\( i \\)-th iteration is formulated as \\( (\\delta \\mathbf{s}_f^i, \\mathbf{h}_f^i, \\mathbf{p}) = f_r(\\mathbf{h}_f^{i-1}, \\mathbf{s}_f^{i-1}, \\mathbf{c}^{i-1}) \\). The generated offset \\( \\delta \\mathbf{s}_f^i \\) is added to the input trajectory \\( \\mathbf{s}_f^{i-1} \\) for refinement." + }, + { + "type": "title", + "bbox": [ + 0.494, + 0.441, + 0.766, + 0.456 + ], + "angle": 0, + "content": "3.2. Scenario-Adaptive Refinement" + }, + { + "type": "title", + "bbox": [ + 0.494, + 0.465, + 0.794, + 0.48 + ], + "angle": 0, + "content": "3.2.1 Adaptive Anchor/Context Selection" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.489, + 0.892, + 0.579 + ], + "angle": 0, + "content": "Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.583, + 0.892, + 0.822 + ], + "angle": 0, + "content": "Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all \\( T_{f} \\) waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into \\( N < T_{f} \\) segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments \\( N \\) is designed to adapt to the prediction horizon." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.826, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Context Retrieval. When retrieving context information \\( \\mathbf{c} \\) around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15283" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.092, + 0.885, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.091, + 0.256, + 0.874, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.463, + 0.896, + 0.561 + ], + "angle": 0, + "content": "Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.479, + 0.863 + ], + "angle": 0, + "content": "especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration \\( i \\), because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed \\( v \\) around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range \\( R \\) varies by the refinement iterations \\( i \\) and the agent's average velocity \\( v \\) around the anchor: \\( R_{i,v} = \\mathcal{F}(i)\\cdot v \\). \\( \\mathcal{F}(i) \\) can be any monotonically decreasing function of the refinement iteration \\( i \\), to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function \\( \\mathcal{F}(i) = \\beta (\\frac{1}{2})^{i - 1} \\), where \\( \\beta \\) denotes a constant. The retrieval range is also constrained within a permissible range \\( [R_{\\mathrm{min}},R_{\\mathrm{max}}] \\) to ensure computational stability and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.493, + 0.578, + 0.789, + 0.593 + ], + "angle": 0, + "content": "3.2.2 Anchor-Centric Context Encoding" + }, + { + "type": "text", + "bbox": [ + 0.491, + 0.602, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations \\( i \\), these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor \\( a \\), generating a set of context embeddings \\( \\mathbf{z}_a \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15284" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.092, + 0.427, + 0.106 + ], + "angle": 0, + "content": "3.2.3 Recurrent and Multi-Iteration Refinement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.477, + 0.355 + ], + "angle": 0, + "content": "The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into \\(N\\) segments, and refine the trajectory \\(N\\) times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here \\(N\\) equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all \\(N\\) segments finishes one iteration of refinement, and we will conduct multiple refinement iterations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.478, + 0.612 + ], + "angle": 0, + "content": "Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings \\(\\mathbf{z}_a\\) around the segment's corresponding anchor \\(a\\), and the target agent's future trajectory embeddings \\(\\mathbf{h}_f\\). We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings \\(\\mathbf{z}_a\\). The fused trajectory embeddings will be used to predict \\(\\delta s\\), the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all \\(N\\) steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.478, + 0.81 + ], + "angle": 0, + "content": "Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another \\( N \\) recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.431, + 0.847 + ], + "angle": 0, + "content": "3.2.4 Adaptive Number of Refinement Iterations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.476, + 0.901 + ], + "angle": 0, + "content": "As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di" + }, + { + "type": "code_caption", + "bbox": [ + 0.495, + 0.091, + 0.832, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Adaptive Inference with SmartRefine" + }, + { + "type": "algorithm", + "bbox": [ + 0.494, + 0.11, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Input: Backbone model \\(f_{b}\\), refinement model \\(f_{r}\\), quality score decoder \\(f_{d}\\), agents history trajectories \\(\\mathbf{s}_{h}\\), scene context \\(\\mathbf{c}\\), and score threshold \\(\\bar{q}\\), maximum refinement iteration at inference \\(I'\\). \nOutput: Target agent's future trajectories \\(\\mathbf{s}_{f}\\) and corresponding probabilities \\(\\mathbf{p}\\). \n1: \\(\\mathbf{s}_{f}^{0}, \\mathbf{h}_{f}^{0}, \\mathbf{p}^{0} = f_{b}(\\mathbf{s}_{f}^{0}, \\mathbf{c})\\) \n2: \\(q^{0} = f_{d}(\\mathbf{h}_{f}^{0})\\) \n3: if \\(q^{0} > \\bar{q}\\) then \n4: Return \\(\\mathbf{s}_{f}^{0}, \\mathbf{p}^{0}\\) \n5: for \\(i = 1, 2, \\ldots, I'\\) do \n6: Adaptively select anchors and contexts \n7: Adaptatively encode contexts \\(\\mathbf{c}^{i-1}\\) (anchor-centric) \n8: Multi-segment recurrent refinement: \n\\(\\delta \\mathbf{s}_{f}^{i}, \\mathbf{h}_{f}^{i}, \\mathbf{p}^{i}, q^{i} = f_{r}(\\mathbf{s}_{f}^{i-1}, \\mathbf{h}_{f}^{i-1}, \\mathbf{c}^{i-1})\\) \n\\(\\mathbf{s}_{f}^{i} = \\mathbf{s}_{f}^{i-1} + \\delta \\mathbf{s}_{f}^{i}\\) \n9: if \\(q^{i} < q^{i-1}\\) then \n10: Return \\(\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}\\) \n11: Return \\(\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}\\) \n% Reach max refinement iteration" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.45, + 0.892, + 0.556 + ], + "angle": 0, + "content": "minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.56, + 0.892, + 0.754 + ], + "angle": 0, + "content": "Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration \\( i \\) is \\( d_{max} - d_i \\), where \\( d_{max} \\) denotes the largest predicted error among all iterations. A small \\( d_i \\) means that the current prediction has already been improved from the largest prediction error \\( d_{max} \\), and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize \\( d_{max} - d_i \\) with \\( d_{max} - d_{min} \\), where \\( d_{min} \\) denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.767, + 0.892, + 0.8 + ], + "angle": 0, + "content": "\\[\nq _ {i} = \\frac {d _ {\\text {m a x}} - d _ {i}}{d _ {\\text {m a x}} - d _ {\\text {m i n}}} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.812, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15285" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.477, + 0.391 + ], + "angle": 0, + "content": "Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.401, + 0.221, + 0.417 + ], + "angle": 0, + "content": "3.3. Training Loss" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.425, + 0.476, + 0.455 + ], + "angle": 0, + "content": "The training of our model considers three loss terms, and uses hyper-parameter \\(\\alpha\\) to balance them:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.468, + 0.476, + 0.485 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c l s}} + \\mathcal {L} _ {\\mathrm {r e g}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {s c o r e}} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.477, + 0.692 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{cls}}\\) denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss \\(\\mathcal{L}_{\\mathrm{reg}}\\), as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss \\(\\mathcal{L}_{\\mathrm{score}}\\), in the training stage, we fix the refinement iteration as \\(I\\) and each iteration will output a quality score. Thus for each iteration \\(i\\), we calculate the \\(\\ell_1\\) loss between the predicted quality score \\(\\hat{q}_i\\) and labeled quality score \\(q_i\\) (see Sec 3.2.4), and average the loss over all iterations:" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.703, + 0.476, + 0.745 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s c o r e}} = \\frac {1}{I + 1} \\sum_ {i = 0} ^ {I} \\| \\hat {q} _ {i} - q _ {i} \\| _ {1} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.756, + 0.476, + 0.786 + ], + "angle": 0, + "content": "Similarly, the score loss also only considers the modal closest to the ground truth." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.801, + 0.21, + 0.817 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.476, + 0.902 + ], + "angle": 0, + "content": "We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency." + }, + { + "type": "title", + "bbox": [ + 0.494, + 0.091, + 0.7, + 0.108 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.114, + 0.892, + 0.309 + ], + "angle": 0, + "content": "Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at \\(10\\mathrm{Hz}\\). Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at \\(10\\mathrm{Hz}\\). The data is split into 200k, 25k, and 25k for training, validation, and test respectively." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.312, + 0.892, + 0.431 + ], + "angle": 0, + "content": "Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.435, + 0.892, + 0.63 + ], + "angle": 0, + "content": "Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.494, + 0.639, + 0.681, + 0.654 + ], + "angle": 0, + "content": "4.2. Quantitative Result" + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.662, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by \\(6.0\\%\\), \\(3.7\\%\\), \\(5.4\\%\\), \\(4.3\\%\\), \\(3.5\\%\\) respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15286" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.182, + 0.078, + 0.787, + 0.263 + ], + "angle": 0, + "content": "
DatasetMethodminFDE ↓minADE ↓MR ↓#Param.(M) ↓Flops(G) ↓Latency(ms) ↓
ArgoverseHiVT [39]0.9690.6610.0922.52.654±4.0
HiVT w/ Ours0.9110.6460.0832.72.767±8.4
Prophnet* [33]1.0040.6870.09315.27.859±1.7
Prophnet w/ Ours0.9670.6750.09215.47.971±6.2
mmTransformer [14]1.0810.7090.1022.61.215±4.8
mmTransformer w/ Ours1.0230.6920.0942.81.327±9.7
Argoverse 2DenseTNT [10]1.6240.9640.2331.63.61,075±199
DenseTNT w/ Ours1.5530.8340.2211.94.01,099±212
QCNet (no ref)1.3040.7290.1645.547.0338±53
QCNet (no ref) w/ Ours1.2580.7180.1575.847.4363±67
QCNet [40]1.2530.7200.1577.755.8392±54
QCNet w/ Ours1.2400.7160.1568.056.2418±68
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.265, + 0.895, + 0.308 + ], + "angle": 0, + "content": "Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.334, + 0.24, + 0.349 + ], + "angle": 0, + "content": "eters, flops, and latency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.477, + 0.517 + ], + "angle": 0, + "content": "Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by \\(3.4\\%\\), \\(6.9\\%\\), \\(7.5\\%\\), \\(4.2\\%\\), \\(3.9\\%\\) respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.526, + 0.24, + 0.541 + ], + "angle": 0, + "content": "4.3. Ablation studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.476, + 0.626 + ], + "angle": 0, + "content": "We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.476, + 0.837 + ], + "angle": 0, + "content": "Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds \\(\\bar{q}\\) for adaptive refinement, while a higher threshold leads to better accuracy, we find \\(\\bar{q} = 0.5\\) achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.476, + 0.902 + ], + "angle": 0, + "content": "Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger" + }, + { + "type": "table", + "bbox": [ + 0.498, + 0.32, + 0.89, + 0.504 + ], + "angle": 0, + "content": "
DatasetMethodminFDE ↓minADE ↓MR ↓
ArgoverseHiVT [39]1.170.770.13
HiVT w/ Ours1.130.770.12
ProphNet* [33]1.300.850.14
Prophnet* w/ Ours1.210.810.13
mmTransformer [14]1.340.840.15
mmTransformer w/ Ours1.240.810.14
Argoverse 2DenseTNT [10]1.660.990.23
DenseTNT w/ Ours1.590.850.22
QCNet (no ref)1.290.650.16
QCNet (no ref) w/ Ours1.240.640.15
QCNet [40]1.240.640.15
QCNet w/ Ours1.230.630.15
" + }, + { + "type": "table_caption", + "bbox": [ + 0.492, + 0.507, + 0.892, + 0.576 + ], + "angle": 0, + "content": "Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set." + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.596, + 0.691, + 0.728 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.597, + 0.887, + 0.728 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.492, + 0.73, + 0.895, + 0.772 + ], + "angle": 0, + "content": "Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds \\( \\bar{q} \\) mentioned in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.492, + 0.79, + 0.888, + 0.807 + ], + "angle": 0, + "content": "model parameters with the same or slightly worse accuracy." + }, + { + "type": "text", + "bbox": [ + 0.491, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15287" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.092, + 0.245, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.092, + 0.362, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.363, + 0.092, + 0.481, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.092, + 0.601, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.092, + 0.719, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.72, + 0.092, + 0.839, + 0.189 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.19, + 0.894, + 0.245 + ], + "angle": 0, + "content": "Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.253, + 0.477, + 0.433 + ], + "angle": 0, + "content": "Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.451, + 0.196, + 0.466 + ], + "angle": 0, + "content": "4.4. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.477, + 0.73 + ], + "angle": 0, + "content": "While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about \\(56\\%\\) of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about \\(44\\%\\) trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the \"blue\" and \"orange\" trajectories change. Two phenomenons are observed:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.737, + 0.478, + 0.902 + ], + "angle": 0, + "content": "- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score \"blue\" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score \"orange\" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can" + }, + { + "type": "table", + "bbox": [ + 0.497, + 0.251, + 0.685, + 0.319 + ], + "angle": 0, + "content": "
#Anchor numbersminFDE#Param.
10.928134K
20.911207K
30.911280K
50.915433K
60.916509K
" + }, + { + "type": "table_caption", + "bbox": [ + 0.493, + 0.32, + 0.687, + 0.345 + ], + "angle": 0, + "content": "Table 4. Ablation study on the number of anchors." + }, + { + "type": "table", + "bbox": [ + 0.7, + 0.253, + 0.889, + 0.305 + ], + "angle": 0, + "content": "
Context EncodingminFDE
Agent-Centric0.941
Anchor-Centric0.911
" + }, + { + "type": "table_caption", + "bbox": [ + 0.699, + 0.306, + 0.891, + 0.332 + ], + "angle": 0, + "content": "Table 5. Ablation study on how the contexts are encoded." + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.349, + 0.849, + 0.432 + ], + "angle": 0, + "content": "
Retrieval RadiusminFDEFlops (M)
Fixed Radius500.9262,297
200.923722
100.921325
20.93058
Adaptive RadiusRmax=10, Rmin=2, linear0.911245
Rmax=10, Rmin=2, exp0.911130
" + }, + { + "type": "table_caption", + "bbox": [ + 0.493, + 0.433, + 0.892, + 0.46 + ], + "angle": 0, + "content": "Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius." + }, + { + "type": "text", + "bbox": [ + 0.505, + 0.487, + 0.891, + 0.516 + ], + "angle": 0, + "content": "hardly be further improved, or even be pushed away from the ground truth due to over-refinement." + }, + { + "type": "text", + "bbox": [ + 0.493, + 0.517, + 0.892, + 0.591 + ], + "angle": 0, + "content": "- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance." + }, + { + "type": "text", + "bbox": [ + 0.493, + 0.594, + 0.863, + 0.608 + ], + "angle": 0, + "content": "These results show the necessity of adaptive refinement." + }, + { + "type": "title", + "bbox": [ + 0.493, + 0.622, + 0.612, + 0.637 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.491, + 0.647, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15288" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.476, + 0.17 + ], + "angle": 0, + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17863-17873, 2023. 1, 2, 3, 4, 6, 7, 11" + }, + { + "type": "list", + "bbox": [ + 0.498, + 0.093, + 0.892, + 0.316 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15290" + } + ] +] \ No newline at end of file diff --git a/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_origin.pdf b/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6e8d58424e25205b51bee9d4835ef3088672ae2c --- /dev/null +++ b/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:efda07ad583cc0de51930c15ad9349e9c2d9491d430ce1e5bce3870849ece5b5 +size 344229 diff --git a/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/full.md b/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..863f757d809f5f745adc9e0b729dda68459d47e0 --- /dev/null +++ b/2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/full.md @@ -0,0 +1,277 @@ +# SmartRefine: A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction + +Yang Zhou $^{1*}$ Hao Shao $^{1,2*}$ Letian Wang $^{3}$ +ven L. Waslander $^{3}$ Hongsheng Li $^{2,4,5}$ Yu Liu $^{1,5}$ + +$^{1}$ SenseTime Research $^{2}$ CUHK MMLab $^{3}$ University of Toronto $^{4}$ CPII under InnoHK $^{5}$ Shanghai Artificial Intelligence Laboratory + +# Abstract + +Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission1. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage. + +# 1. Introduction + +Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently + +make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving. + +By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved. + +While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em + +ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement. + +To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency. + +It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both. + +To summarize, the contributions of this work are threefold: + +- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation. +- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research. +- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi + +
RefineContext Selection/EncodingRefinement Iteration
AllFixed StrategyAdaptive StrategySingleMultipleScenario Adaptive
TNT [38]X
GoalNet [37]X
GANet [32]X
ProphNet [33]X
DCMS [36]✓XXX✓XX
QCNet [40]✓✓XX✓XX
R-Pred [5]✓X✓X✓XX
MTR [25]✓X✓XX✓X
SmartRefine (ours)✓XX✓XX✓
+ +Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations. + +ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. + +# 2. Related Work + +# 2.1. Goal-Conditioned Trajectory Prediction + +Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con + +text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information. + +# 2.2. Refinement: Two-Stage Trajectory Prediction + +Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation. + +# 3. Method + +SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework. + +# 3.1. Problem formulation + +Given the observed states of the target agent $\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \dots, s_0]$ in the historic $T_h$ steps, we aim at + +predicting its future states $\mathbf{s}_f = [s_1,s_2,\dots ,s_{T_f}]$ of $T_{f}$ steps and associated probabilities $\mathbf{p}$ . Naturally, the target agent will interact with the context $\mathbf{c} = (\mathbf{o}_h,\mathbf{m})$ , including historic states of surrounding agents $\mathbf{o}_h$ , and the HD map $\mathbf{m}$ . For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as $(\mathbf{s}_f,\mathbf{p}) = f(\mathbf{s}_h,\mathbf{c})$ , where $f$ denotes the prediction model. + +In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model $f_{b}$ generating initial trajectories $\mathbf{s}_f^0$ and trajectory features $\mathbf{h}_f^0$ , as typical prediction methods $(\mathbf{s}_f^0, \mathbf{h}_f^0, \mathbf{p}) = f_b(\mathbf{s}_h, \mathbf{c})$ . The initial predicted trajectory $\mathbf{s}_f^0$ is then used to select anchors $\mathbf{a}^0$ and retrieve critical context elements $\mathbf{c}^0$ , which are then passed along with the trajectory features $\mathbf{h}_f^0$ into the refinement model $f_{r}$ for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the $i$ -th iteration is formulated as $(\delta \mathbf{s}_f^i, \mathbf{h}_f^i, \mathbf{p}) = f_r(\mathbf{h}_f^{i-1}, \mathbf{s}_f^{i-1}, \mathbf{c}^{i-1})$ . The generated offset $\delta \mathbf{s}_f^i$ is added to the input trajectory $\mathbf{s}_f^{i-1}$ for refinement. + +# 3.2. Scenario-Adaptive Refinement + +# 3.2.1 Adaptive Anchor/Context Selection + +Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1). + +Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all $T_{f}$ waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into $N < T_{f}$ segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments $N$ is designed to adapt to the prediction horizon. + +Context Retrieval. When retrieving context information $\mathbf{c}$ around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal + +![](images/b7e67582f0dceddbaadbd8e0f4748f83f0e1af21a7a6e14c5b4014683a942acb.jpg) + +![](images/c2b3b37b594d19f69e01cea0fae890585627d07023ec4c013811f998ab0c3e22.jpg) +Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models. + +especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration $i$ , because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed $v$ around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range $R$ varies by the refinement iterations $i$ and the agent's average velocity $v$ around the anchor: $R_{i,v} = \mathcal{F}(i)\cdot v$ . $\mathcal{F}(i)$ can be any monotonically decreasing function of the refinement iteration $i$ , to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function $\mathcal{F}(i) = \beta (\frac{1}{2})^{i - 1}$ , where $\beta$ denotes a constant. The retrieval range is also constrained within a permissible range $[R_{\mathrm{min}},R_{\mathrm{max}}]$ to ensure computational stability and efficiency. + +# 3.2.2 Anchor-Centric Context Encoding + +With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations $i$ , these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor $a$ , generating a set of context embeddings $\mathbf{z}_a$ . + +# 3.2.3 Recurrent and Multi-Iteration Refinement + +The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into $N$ segments, and refine the trajectory $N$ times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here $N$ equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all $N$ segments finishes one iteration of refinement, and we will conduct multiple refinement iterations. + +Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings $\mathbf{z}_a$ around the segment's corresponding anchor $a$ , and the target agent's future trajectory embeddings $\mathbf{h}_f$ . We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings $\mathbf{z}_a$ . The fused trajectory embeddings will be used to predict $\delta s$ , the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all $N$ steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction. + +Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another $N$ recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss. + +# 3.2.4 Adaptive Number of Refinement Iterations + +As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di + +Algorithm 1 Adaptive Inference with SmartRefine +Input: Backbone model $f_{b}$ , refinement model $f_{r}$ , quality score decoder $f_{d}$ , agents history trajectories $\mathbf{s}_{h}$ , scene context $\mathbf{c}$ , and score threshold $\bar{q}$ , maximum refinement iteration at inference $I'$ . +Output: Target agent's future trajectories $\mathbf{s}_{f}$ and corresponding probabilities $\mathbf{p}$ . +1: $\mathbf{s}_{f}^{0}, \mathbf{h}_{f}^{0}, \mathbf{p}^{0} = f_{b}(\mathbf{s}_{f}^{0}, \mathbf{c})$ +2: $q^{0} = f_{d}(\mathbf{h}_{f}^{0})$ +3: if $q^{0} > \bar{q}$ then +4: Return $\mathbf{s}_{f}^{0}, \mathbf{p}^{0}$ +5: for $i = 1, 2, \ldots, I'$ do +6: Adaptively select anchors and contexts +7: Adaptatively encode contexts $\mathbf{c}^{i-1}$ (anchor-centric) +8: Multi-segment recurrent refinement: + $\delta \mathbf{s}_{f}^{i}, \mathbf{h}_{f}^{i}, \mathbf{p}^{i}, q^{i} = f_{r}(\mathbf{s}_{f}^{i-1}, \mathbf{h}_{f}^{i-1}, \mathbf{c}^{i-1})$ $\mathbf{s}_{f}^{i} = \mathbf{s}_{f}^{i-1} + \delta \mathbf{s}_{f}^{i}$ +9: if $q^{i} < q^{i-1}$ then +10: Return $\mathbf{s}_{f}^{i}, \mathbf{p}^{i}$ +11: Return $\mathbf{s}_{f}^{i}, \mathbf{p}^{i}$ +% Reach max refinement iteration + +minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality. + +Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration $i$ is $d_{max} - d_i$ , where $d_{max}$ denotes the largest predicted error among all iterations. A small $d_i$ means that the current prediction has already been improved from the largest prediction error $d_{max}$ , and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize $d_{max} - d_i$ with $d_{max} - d_{min}$ , where $d_{min}$ denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as + +$$ +q _ {i} = \frac {d _ {\text {m a x}} - d _ {i}}{d _ {\text {m a x}} - d _ {\text {m i n}}} \tag {1} +$$ + +To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score. + +Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency. + +# 3.3. Training Loss + +The training of our model considers three loss terms, and uses hyper-parameter $\alpha$ to balance them: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {c l s}} + \mathcal {L} _ {\mathrm {r e g}} + \alpha \cdot \mathcal {L} _ {\mathrm {s c o r e}} \tag {2} +$$ + +where $\mathcal{L}_{\mathrm{cls}}$ denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss $\mathcal{L}_{\mathrm{reg}}$ , as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss $\mathcal{L}_{\mathrm{score}}$ , in the training stage, we fix the refinement iteration as $I$ and each iteration will output a quality score. Thus for each iteration $i$ , we calculate the $\ell_1$ loss between the predicted quality score $\hat{q}_i$ and labeled quality score $q_i$ (see Sec 3.2.4), and average the loss over all iterations: + +$$ +\mathcal {L} _ {\text {s c o r e}} = \frac {1}{I + 1} \sum_ {i = 0} ^ {I} \| \hat {q} _ {i} - q _ {i} \| _ {1} \tag {3} +$$ + +Similarly, the score loss also only considers the modal closest to the ground truth. + +# 4. Experiments + +We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. + +# 4.1. Experimental Settings + +Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at $10\mathrm{Hz}$ . Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at $10\mathrm{Hz}$ . The data is split into 200k, 25k, and 25k for training, validation, and test respectively. + +Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics. + +Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material. + +# 4.2. Quantitative Result + +Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by $6.0\%$ , $3.7\%$ , $5.4\%$ , $4.3\%$ , $3.5\%$ respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param- + +
DatasetMethodminFDE ↓minADE ↓MR ↓#Param.(M) ↓Flops(G) ↓Latency(ms) ↓
ArgoverseHiVT [39]0.9690.6610.0922.52.654±4.0
HiVT w/ Ours0.9110.6460.0832.72.767±8.4
Prophnet* [33]1.0040.6870.09315.27.859±1.7
Prophnet w/ Ours0.9670.6750.09215.47.971±6.2
mmTransformer [14]1.0810.7090.1022.61.215±4.8
mmTransformer w/ Ours1.0230.6920.0942.81.327±9.7
Argoverse 2DenseTNT [10]1.6240.9640.2331.63.61,075±199
DenseTNT w/ Ours1.5530.8340.2211.94.01,099±212
QCNet (no ref)1.3040.7290.1645.547.0338±53
QCNet (no ref) w/ Ours1.2580.7180.1575.847.4363±67
QCNet [40]1.2530.7200.1577.755.8392±54
QCNet w/ Ours1.2400.7160.1568.056.2418±68
+ +eters, flops, and latency. + +Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by $3.4\%$ , $6.9\%$ , $7.5\%$ , $4.2\%$ , $3.9\%$ respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation. + +# 4.3. Ablation studies + +We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material. + +Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds $\bar{q}$ for adaptive refinement, while a higher threshold leads to better accuracy, we find $\bar{q} = 0.5$ achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve. + +Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger + +Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency. + +
DatasetMethodminFDE ↓minADE ↓MR ↓
ArgoverseHiVT [39]1.170.770.13
HiVT w/ Ours1.130.770.12
ProphNet* [33]1.300.850.14
Prophnet* w/ Ours1.210.810.13
mmTransformer [14]1.340.840.15
mmTransformer w/ Ours1.240.810.14
Argoverse 2DenseTNT [10]1.660.990.23
DenseTNT w/ Ours1.590.850.22
QCNet (no ref)1.290.650.16
QCNet (no ref) w/ Ours1.240.640.15
QCNet [40]1.240.640.15
QCNet w/ Ours1.230.630.15
+ +Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set. + +![](images/9496fb08086673546e98ca71b8e2033a6c91889faf7340ffde38fbadb692c7ff.jpg) +Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds $\bar{q}$ mentioned in Algorithm 1. + +![](images/6d3196a1d87945dd9b252629e27b1afd460b55245cad9a5d7d732a02fc9e1491.jpg) + +model parameters with the same or slightly worse accuracy. + +Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding. + +![](images/d30db22a5732690fa15161f3217c5fe39fb9dc20c8dab479a2a01db9371b9947.jpg) +Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions. + +![](images/009efeb68911d1f475b6bd134b314208f8691127e9ce85a6ae778744b70e72e4.jpg) + +![](images/5613082faf5562bee17e6cb1e1261da00189c9503db82692e030d4c00634aa66.jpg) + +![](images/48b8669549bf53d061ae1a8eca62b12c1b8e6d3b4513b88482b80d15f4fff7b7.jpg) + +![](images/fc6bdcd919f5e8c6d7a30e223de2663ba9bd480136b85475c82c1d121d73266a.jpg) + +![](images/0c47feb96f45286ccb1809164c0eddd48c09e9dc95feec5062a2754e885ffdf0.jpg) + +Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay. + +# 4.4. Discussion + +While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about $56\%$ of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about $44\%$ trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the "blue" and "orange" trajectories change. Two phenomenons are observed: + +- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score "blue" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score "orange" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can + +
#Anchor numbersminFDE#Param.
10.928134K
20.911207K
30.911280K
50.915433K
60.916509K
+ +Table 4. Ablation study on the number of anchors. + +
Context EncodingminFDE
Agent-Centric0.941
Anchor-Centric0.911
+ +Table 5. Ablation study on how the contexts are encoded. + +
Retrieval RadiusminFDEFlops (M)
Fixed Radius500.9262,297
200.923722
100.921325
20.93058
Adaptive RadiusRmax=10, Rmin=2, linear0.911245
Rmax=10, Rmin=2, exp0.911130
+ +Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius. + +hardly be further improved, or even be pushed away from the ground truth due to over-refinement. + +- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance. + +These results show the necessity of adaptive refinement. + +# 5. Conclusion + +In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings. + +# References + +[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. In European conference on computer vision, pages 213-229. 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Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission1. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 128, + 643 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 651, + 291, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 651, + 291, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 651, + 291, + 687 + ], + "type": "text", + "content": "Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 301, + 251, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 251, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 301, + 251, + 545, + 475 + ], + "type": "text", + "content": "make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 301, + 476, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 476, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 301, + 476, + 545, + 654 + ], + "type": "text", + "content": "By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 301, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 301, + 654, + 545, + 713 + ], + "type": "text", + "content": "While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 214, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 214, + 703 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 214, + 703 + ], + "type": "text", + "content": "* Equal contribution, " + }, + { + "bbox": [ + 61, + 693, + 214, + 703 + ], + "type": "inline_equation", + "content": "\\boxtimes" + }, + { + "bbox": [ + 61, + 693, + 214, + 703 + ], + "type": "text", + "content": " Corresponding author." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 61, + 703, + 124, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 124, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 124, + 712 + ], + "type": "text", + "content": "1 November 2023." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15281" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 290, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 290, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 290, + 167 + ], + "type": "text", + "content": "ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 167, + 291, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 291, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 291, + 439 + ], + "type": "text", + "content": "To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 440, + 291, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 291, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 291, + 558 + ], + "type": "text", + "content": "It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 559, + 286, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 286, + 570 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 286, + 570 + ], + "type": "text", + "content": "To summarize, the contributions of this work are threefold:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 571, + 290, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 571, + 290, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 290, + 630 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 290, + 630 + ], + "type": "text", + "content": "- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 631, + 290, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 631, + 290, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 631, + 290, + 677 + ], + "type": "text", + "content": "- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 290, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 290, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 290, + 713 + ], + "type": "text", + "content": "- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 304, + 75, + 544, + 178 + ], + "blocks": [ + { + "bbox": [ + 304, + 75, + 544, + 178 + ], + "lines": [ + { + "bbox": [ + 304, + 75, + 544, + 178 + ], + "spans": [ + { + "bbox": [ + 304, + 75, + 544, + 178 + ], + "type": "table", + "html": "
RefineContext Selection/EncodingRefinement Iteration
AllFixed StrategyAdaptive StrategySingleMultipleScenario Adaptive
TNT [38]X
GoalNet [37]X
GANet [32]X
ProphNet [33]X
DCMS [36]✓XXX✓XX
QCNet [40]✓✓XX✓XX
R-Pred [5]✓X✓X✓XX
MTR [25]✓X✓XX✓X
SmartRefine (ours)✓XX✓XX✓
", + "image_path": "9acac4aa2a2e5a45881e39d8a4d4cabc47513a8ec18c7f8501a299de7829e8df.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 301, + 187, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 301, + 187, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 301, + 187, + 545, + 232 + ], + "type": "text", + "content": "Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 309, + 255, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 255, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 309, + 255, + 545, + 338 + ], + "type": "text", + "content": "ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 302, + 353, + 388, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 353, + 388, + 365 + ], + "spans": [ + { + "bbox": [ + 302, + 353, + 388, + 365 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 302, + 373, + 511, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 373, + 511, + 387 + ], + "spans": [ + { + "bbox": [ + 302, + 373, + 511, + 387 + ], + "type": "text", + "content": "2.1. Goal-Conditioned Trajectory Prediction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 300, + 393, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 393, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 300, + 393, + 545, + 713 + ], + "type": "text", + "content": "Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15282" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 291, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 291, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 291, + 178 + ], + "type": "text", + "content": "text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 186, + 284, + 198 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 186, + 284, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 186, + 284, + 198 + ], + "type": "text", + "content": "2.2. Refinement: Two-Stage Trajectory Prediction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 202, + 292, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 202, + 292, + 522 + ], + "spans": [ + { + "bbox": [ + 46, + 202, + 292, + 522 + ], + "type": "text", + "content": "Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 534, + 103, + 546 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 534, + 103, + 546 + ], + "spans": [ + { + "bbox": [ + 47, + 534, + 103, + 546 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 555, + 291, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 291, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 291, + 661 + ], + "type": "text", + "content": "SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 168, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 168, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 168, + 682 + ], + "type": "text", + "content": "3.1. Problem formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "type": "text", + "content": "Given the observed states of the target agent " + }, + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \\dots, s_0]" + }, + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "type": "text", + "content": " in the historic " + }, + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "type": "inline_equation", + "content": "T_h" + }, + { + "bbox": [ + 47, + 689, + 291, + 715 + ], + "type": "text", + "content": " steps, we aim at" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": "predicting its future states " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_f = [s_1,s_2,\\dots ,s_{T_f}]" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "T_{f}" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": " steps and associated probabilities " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": ". Naturally, the target agent will interact with the context " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = (\\mathbf{o}_h,\\mathbf{m})" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": ", including historic states of surrounding agents " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_h" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": ", and the HD map " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "\\mathbf{m}" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": ". For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "(\\mathbf{s}_f,\\mathbf{p}) = f(\\mathbf{s}_h,\\mathbf{c})" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 301, + 72, + 545, + 190 + ], + "type": "text", + "content": " denotes the prediction model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": "In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "f_{b}" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " generating initial trajectories " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_f^0" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " and trajectory features " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_f^0" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": ", as typical prediction methods " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "(\\mathbf{s}_f^0, \\mathbf{h}_f^0, \\mathbf{p}) = f_b(\\mathbf{s}_h, \\mathbf{c})" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": ". The initial predicted trajectory " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_f^0" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " is then used to select anchors " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{a}^0" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " and retrieve critical context elements " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^0" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": ", which are then passed along with the trajectory features " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_f^0" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " into the refinement model " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "f_{r}" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": "-th iteration is formulated as " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "(\\delta \\mathbf{s}_f^i, \\mathbf{h}_f^i, \\mathbf{p}) = f_r(\\mathbf{h}_f^{i-1}, \\mathbf{s}_f^{i-1}, \\mathbf{c}^{i-1})" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": ". The generated offset " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\delta \\mathbf{s}_f^i" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " is added to the input trajectory " + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_f^{i-1}" + }, + { + "bbox": [ + 301, + 191, + 545, + 342 + ], + "type": "text", + "content": " for refinement." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 302, + 349, + 468, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 349, + 468, + 361 + ], + "spans": [ + { + "bbox": [ + 302, + 349, + 468, + 361 + ], + "type": "text", + "content": "3.2. Scenario-Adaptive Refinement" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 302, + 368, + 485, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 368, + 485, + 380 + ], + "spans": [ + { + "bbox": [ + 302, + 368, + 485, + 380 + ], + "type": "text", + "content": "3.2.1 Adaptive Anchor/Context Selection" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 301, + 387, + 545, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 387, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 301, + 387, + 545, + 458 + ], + "type": "text", + "content": "Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "text", + "content": "Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all " + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "inline_equation", + "content": "T_{f}" + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "text", + "content": " waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into " + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "inline_equation", + "content": "N < T_{f}" + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "text", + "content": " segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments " + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 301, + 461, + 545, + 651 + ], + "type": "text", + "content": " is designed to adapt to the prediction horizon." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 301, + 654, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 654, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 301, + 654, + 547, + 713 + ], + "type": "text", + "content": "Context Retrieval. When retrieving context information " + }, + { + "bbox": [ + 301, + 654, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 301, + 654, + 547, + 713 + ], + "type": "text", + "content": " around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15283" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 72, + 541, + 201 + ], + "blocks": [ + { + "bbox": [ + 55, + 72, + 541, + 201 + ], + "lines": [ + { + "bbox": [ + 55, + 72, + 541, + 201 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 541, + 201 + ], + "type": "image", + "image_path": "b7e67582f0dceddbaadbd8e0f4748f83f0e1af21a7a6e14c5b4014683a942acb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 55, + 202, + 534, + 358 + ], + "blocks": [ + { + "bbox": [ + 55, + 202, + 534, + 358 + ], + "lines": [ + { + "bbox": [ + 55, + 202, + 534, + 358 + ], + "spans": [ + { + "bbox": [ + 55, + 202, + 534, + 358 + ], + "type": "image", + "image_path": "c2b3b37b594d19f69e01cea0fae890585627d07023ec4c013811f998ab0c3e22.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 366, + 548, + 444 + ], + "lines": [ + { + "bbox": [ + 46, + 366, + 548, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 548, + 444 + ], + "type": "text", + "content": "Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": "especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": ", because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " varies by the refinement iterations " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " and the agent's average velocity " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " around the anchor: " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "R_{i,v} = \\mathcal{F}(i)\\cdot v" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(i)" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " can be any monotonically decreasing function of the refinement iteration " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": ", to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(i) = \\beta (\\frac{1}{2})^{i - 1}" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " denotes a constant. The retrieval range is also constrained within a permissible range " + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "inline_equation", + "content": "[R_{\\mathrm{min}},R_{\\mathrm{max}}]" + }, + { + "bbox": [ + 46, + 457, + 293, + 683 + ], + "type": "text", + "content": " to ensure computational stability and efficiency." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 301, + 457, + 482, + 469 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 457, + 482, + 469 + ], + "spans": [ + { + "bbox": [ + 301, + 457, + 482, + 469 + ], + "type": "text", + "content": "3.2.2 Anchor-Centric Context Encoding" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "text", + "content": "With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations " + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "text", + "content": ", these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor " + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "text", + "content": ", generating a set of context embeddings " + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_a" + }, + { + "bbox": [ + 300, + 476, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15284" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 261, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 261, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 261, + 83 + ], + "type": "text", + "content": "3.2.3 Recurrent and Multi-Iteration Refinement" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "text", + "content": "The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into " + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "text", + "content": " segments, and refine the trajectory " + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "text", + "content": " times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here " + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "text", + "content": " equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all " + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 91, + 291, + 281 + ], + "type": "text", + "content": " segments finishes one iteration of refinement, and we will conduct multiple refinement iterations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": "Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings " + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_a" + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": " around the segment's corresponding anchor " + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": ", and the target agent's future trajectory embeddings " + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_f" + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": ". We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings " + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_a" + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": ". The fused trajectory embeddings will be used to predict " + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "inline_equation", + "content": "\\delta s" + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": ", the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all " + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 283, + 292, + 484 + ], + "type": "text", + "content": " steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 487, + 292, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 292, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 292, + 641 + ], + "type": "text", + "content": "Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another " + }, + { + "bbox": [ + 46, + 487, + 292, + 641 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 487, + 292, + 641 + ], + "type": "text", + "content": " recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 658, + 263, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 263, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 263, + 670 + ], + "type": "text", + "content": "3.2.4 Adaptive Number of Refinement Iterations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 291, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 291, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 291, + 713 + ], + "type": "text", + "content": "As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di" + } + ] + } + ], + "index": 5 + }, + { + "type": "code", + "bbox": [ + 302, + 87, + 545, + 334 + ], + "blocks": [ + { + "bbox": [ + 302, + 72, + 509, + 84 + ], + "lines": [ + { + "bbox": [ + 302, + 72, + 509, + 84 + ], + "spans": [ + { + "bbox": [ + 302, + 72, + 509, + 84 + ], + "type": "text", + "content": "Algorithm 1 Adaptive Inference with SmartRefine" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "lines": [ + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": "Input: Backbone model " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "f_{b}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ", refinement model " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "f_{r}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ", quality score decoder " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ", agents history trajectories " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{h}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ", scene context " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ", and score threshold " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\bar{q}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ", maximum refinement iteration at inference " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "I'" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ". \nOutput: Target agent's future trajectories " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{f}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " and corresponding probabilities " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": ". \n1: " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{f}^{0}, \\mathbf{h}_{f}^{0}, \\mathbf{p}^{0} = f_{b}(\\mathbf{s}_{f}^{0}, \\mathbf{c})" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " \n2: " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "q^{0} = f_{d}(\\mathbf{h}_{f}^{0})" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " \n3: if " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "q^{0} > \\bar{q}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " then \n4: Return " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{f}^{0}, \\mathbf{p}^{0}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " \n5: for " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "i = 1, 2, \\ldots, I'" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " do \n6: Adaptively select anchors and contexts \n7: Adaptatively encode contexts " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{c}^{i-1}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " (anchor-centric) \n8: Multi-segment recurrent refinement: \n" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\delta \\mathbf{s}_{f}^{i}, \\mathbf{h}_{f}^{i}, \\mathbf{p}^{i}, q^{i} = f_{r}(\\mathbf{s}_{f}^{i-1}, \\mathbf{h}_{f}^{i-1}, \\mathbf{c}^{i-1})" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{f}^{i} = \\mathbf{s}_{f}^{i-1} + \\delta \\mathbf{s}_{f}^{i}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " \n9: if " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "q^{i} < q^{i-1}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " then \n10: Return " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " \n11: Return " + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}" + }, + { + "bbox": [ + 302, + 87, + 545, + 334 + ], + "type": "text", + "content": " \n% Reach max refinement iteration" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_body" + } + ], + "index": 7, + "sub_type": "algorithm" + }, + { + "bbox": [ + 301, + 356, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 356, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 301, + 356, + 545, + 440 + ], + "type": "text", + "content": "minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": "Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_{max} - d_i" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_{max}" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": " denotes the largest predicted error among all iterations. A small " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": " means that the current prediction has already been improved from the largest prediction error " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_{max}" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": ", and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_{max} - d_i" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_{max} - d_{min}" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "inline_equation", + "content": "d_{min}" + }, + { + "bbox": [ + 301, + 443, + 545, + 597 + ], + "type": "text", + "content": " denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 382, + 607, + 545, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 607, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 382, + 607, + 545, + 633 + ], + "type": "interline_equation", + "content": "q _ {i} = \\frac {d _ {\\text {m a x}} - d _ {i}}{d _ {\\text {m a x}} - d _ {\\text {m i n}}} \\tag {1}", + "image_path": "03eafc9d48d77edf7befa6ed1336b25035658ce1c59bc07457992f053dcdbe4d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 301, + 643, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 643, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 301, + 643, + 545, + 713 + ], + "type": "text", + "content": "To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15285" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 291, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 291, + 309 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 291, + 309 + ], + "type": "text", + "content": "Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 317, + 135, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 135, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 135, + 330 + ], + "type": "text", + "content": "3.3. Training Loss" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 336, + 291, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 336, + 291, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 336, + 291, + 360 + ], + "type": "text", + "content": "The training of our model considers three loss terms, and uses hyper-parameter " + }, + { + "bbox": [ + 47, + 336, + 291, + 360 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 336, + 291, + 360 + ], + "type": "text", + "content": " to balance them:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 111, + 370, + 291, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 370, + 291, + 384 + ], + "spans": [ + { + "bbox": [ + 111, + 370, + 291, + 384 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c l s}} + \\mathcal {L} _ {\\mathrm {r e g}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {s c o r e}} \\tag {2}", + "image_path": "3f41bacece2a22f3a8d518e82be0eaee5394d0a023407ba3ec70e4a1012f91dd.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": " denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": ", as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{score}}" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": ", in the training stage, we fix the refinement iteration as " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": " and each iteration will output a quality score. Thus for each iteration " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": ", we calculate the " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": " loss between the predicted quality score " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "\\hat{q}_i" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": " and labeled quality score " + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "inline_equation", + "content": "q_i" + }, + { + "bbox": [ + 46, + 392, + 291, + 548 + ], + "type": "text", + "content": " (see Sec 3.2.4), and average the loss over all iterations:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 107, + 556, + 291, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 556, + 291, + 590 + ], + "spans": [ + { + "bbox": [ + 107, + 556, + 291, + 590 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s c o r e}} = \\frac {1}{I + 1} \\sum_ {i = 0} ^ {I} \\| \\hat {q} _ {i} - q _ {i} \\| _ {1} \\tag {3}", + "image_path": "e3f44fe88fac8f629d10a5f0cd6f38c71de2edb25fae1f2b4c283d465476447e.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 598, + 291, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 291, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 291, + 622 + ], + "type": "text", + "content": "Similarly, the score loss also only considers the modal closest to the ground truth." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 634, + 128, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 128, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 128, + 647 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 654, + 291, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 291, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 291, + 714 + ], + "type": "text", + "content": "We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 302, + 72, + 428, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 72, + 428, + 85 + ], + "spans": [ + { + "bbox": [ + 302, + 72, + 428, + 85 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "type": "text", + "content": "Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at " + }, + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "type": "text", + "content": ". Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at " + }, + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 301, + 90, + 545, + 244 + ], + "type": "text", + "content": ". The data is split into 200k, 25k, and 25k for training, validation, and test respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 301, + 247, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 247, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 301, + 247, + 545, + 341 + ], + "type": "text", + "content": "Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 301, + 344, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 344, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 301, + 344, + 545, + 498 + ], + "type": "text", + "content": "Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 302, + 506, + 416, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 506, + 416, + 517 + ], + "spans": [ + { + "bbox": [ + 302, + 506, + 416, + 517 + ], + "type": "text", + "content": "4.2. Quantitative Result" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "content": "Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by " + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "inline_equation", + "content": "6.0\\%" + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "inline_equation", + "content": "4.3\\%" + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 301, + 524, + 545, + 713 + ], + "type": "text", + "content": " respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param-" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15286" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 111, + 61, + 481, + 208 + ], + "blocks": [ + { + "bbox": [ + 111, + 61, + 481, + 208 + ], + "lines": [ + { + "bbox": [ + 111, + 61, + 481, + 208 + ], + "spans": [ + { + "bbox": [ + 111, + 61, + 481, + 208 + ], + "type": "table", + "html": "
DatasetMethodminFDE ↓minADE ↓MR ↓#Param.(M) ↓Flops(G) ↓Latency(ms) ↓
ArgoverseHiVT [39]0.9690.6610.0922.52.654±4.0
HiVT w/ Ours0.9110.6460.0832.72.767±8.4
Prophnet* [33]1.0040.6870.09315.27.859±1.7
Prophnet w/ Ours0.9670.6750.09215.47.971±6.2
mmTransformer [14]1.0810.7090.1022.61.215±4.8
mmTransformer w/ Ours1.0230.6920.0942.81.327±9.7
Argoverse 2DenseTNT [10]1.6240.9640.2331.63.61,075±199
DenseTNT w/ Ours1.5530.8340.2211.94.01,099±212
QCNet (no ref)1.3040.7290.1645.547.0338±53
QCNet (no ref) w/ Ours1.2580.7180.1575.847.4363±67
QCNet [40]1.2530.7200.1577.755.8392±54
QCNet w/ Ours1.2400.7160.1568.056.2418±68
", + "image_path": "8e0fffe301820899b0c2aa9203a23b941033347f606712e911a5797e2c24b84a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 264, + 146, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 264, + 146, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 264, + 146, + 276 + ], + "type": "text", + "content": "eters, flops, and latency." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "content": "Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by " + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "inline_equation", + "content": "6.9\\%" + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "inline_equation", + "content": "7.5\\%" + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "inline_equation", + "content": "3.9\\%" + }, + { + "bbox": [ + 46, + 278, + 291, + 409 + ], + "type": "text", + "content": " respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 416, + 146, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 146, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 146, + 428 + ], + "type": "text", + "content": "4.3. Ablation studies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 434, + 291, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 291, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 291, + 495 + ], + "type": "text", + "content": "We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "type": "text", + "content": "Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds " + }, + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "type": "inline_equation", + "content": "\\bar{q}" + }, + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "type": "text", + "content": " for adaptive refinement, while a higher threshold leads to better accuracy, we find " + }, + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "type": "inline_equation", + "content": "\\bar{q} = 0.5" + }, + { + "bbox": [ + 46, + 497, + 291, + 662 + ], + "type": "text", + "content": " achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 666, + 291, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 291, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 291, + 714 + ], + "type": "text", + "content": "Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 304, + 253, + 544, + 399 + ], + "blocks": [ + { + "bbox": [ + 46, + 209, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 243 + ], + "type": "text", + "content": "Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 304, + 253, + 544, + 399 + ], + "lines": [ + { + "bbox": [ + 304, + 253, + 544, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 544, + 399 + ], + "type": "table", + "html": "
DatasetMethodminFDE ↓minADE ↓MR ↓
ArgoverseHiVT [39]1.170.770.13
HiVT w/ Ours1.130.770.12
ProphNet* [33]1.300.850.14
Prophnet* w/ Ours1.210.810.13
mmTransformer [14]1.340.840.15
mmTransformer w/ Ours1.240.810.14
Argoverse 2DenseTNT [10]1.660.990.23
DenseTNT w/ Ours1.590.850.22
QCNet (no ref)1.290.650.16
QCNet (no ref) w/ Ours1.240.640.15
QCNet [40]1.240.640.15
QCNet w/ Ours1.230.630.15
", + "image_path": "bb0b3e90fc8ba4370093c10861cfdb446fd2766901a490858b5afa06ee324599.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 301, + 401, + 545, + 456 + ], + "lines": [ + { + "bbox": [ + 301, + 401, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 301, + 401, + 545, + 456 + ], + "type": "text", + "content": "Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 304, + 472, + 422, + 576 + ], + "blocks": [ + { + "bbox": [ + 304, + 472, + 422, + 576 + ], + "lines": [ + { + "bbox": [ + 304, + 472, + 422, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 422, + 576 + ], + "type": "image", + "image_path": "9496fb08086673546e98ca71b8e2033a6c91889faf7340ffde38fbadb692c7ff.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 301, + 578, + 547, + 611 + ], + "lines": [ + { + "bbox": [ + 301, + 578, + 547, + 611 + ], + "spans": [ + { + "bbox": [ + 301, + 578, + 547, + 611 + ], + "type": "text", + "content": "Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds " + }, + { + "bbox": [ + 301, + 578, + 547, + 611 + ], + "type": "inline_equation", + "content": "\\bar{q}" + }, + { + "bbox": [ + 301, + 578, + 547, + 611 + ], + "type": "text", + "content": " mentioned in Algorithm 1." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 424, + 472, + 542, + 576 + ], + "blocks": [ + { + "bbox": [ + 424, + 472, + 542, + 576 + ], + "lines": [ + { + "bbox": [ + 424, + 472, + 542, + 576 + ], + "spans": [ + { + "bbox": [ + 424, + 472, + 542, + 576 + ], + "type": "image", + "image_path": "6d3196a1d87945dd9b252629e27b1afd460b55245cad9a5d7d732a02fc9e1491.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 301, + 625, + 543, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 625, + 543, + 639 + ], + "spans": [ + { + "bbox": [ + 301, + 625, + 543, + 639 + ], + "type": "text", + "content": "model parameters with the same or slightly worse accuracy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 300, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 300, + 642, + 545, + 714 + ], + "type": "text", + "content": "Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15287" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 72, + 149, + 149 + ], + "blocks": [ + { + "bbox": [ + 76, + 72, + 149, + 149 + ], + "lines": [ + { + "bbox": [ + 76, + 72, + 149, + 149 + ], + "spans": [ + { + "bbox": [ + 76, + 72, + 149, + 149 + ], + "type": "image", + "image_path": "d30db22a5732690fa15161f3217c5fe39fb9dc20c8dab479a2a01db9371b9947.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 150, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 46, + 150, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 150, + 547, + 194 + ], + "type": "text", + "content": "Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 150, + 72, + 221, + 149 + ], + "blocks": [ + { + "bbox": [ + 150, + 72, + 221, + 149 + ], + "lines": [ + { + "bbox": [ + 150, + 72, + 221, + 149 + ], + "spans": [ + { + "bbox": [ + 150, + 72, + 221, + 149 + ], + "type": "image", + "image_path": "009efeb68911d1f475b6bd134b314208f8691127e9ce85a6ae778744b70e72e4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 222, + 72, + 294, + 149 + ], + "blocks": [ + { + "bbox": [ + 222, + 72, + 294, + 149 + ], + "lines": [ + { + "bbox": [ + 222, + 72, + 294, + 149 + ], + "spans": [ + { + "bbox": [ + 222, + 72, + 294, + 149 + ], + "type": "image", + "image_path": "5613082faf5562bee17e6cb1e1261da00189c9503db82692e030d4c00634aa66.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 294, + 72, + 367, + 149 + ], + "blocks": [ + { + "bbox": [ + 294, + 72, + 367, + 149 + ], + "lines": [ + { + "bbox": [ + 294, + 72, + 367, + 149 + ], + "spans": [ + { + "bbox": [ + 294, + 72, + 367, + 149 + ], + "type": "image", + "image_path": "48b8669549bf53d061ae1a8eca62b12c1b8e6d3b4513b88482b80d15f4fff7b7.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 368, + 72, + 440, + 149 + ], + "blocks": [ + { + "bbox": [ + 368, + 72, + 440, + 149 + ], + "lines": [ + { + "bbox": [ + 368, + 72, + 440, + 149 + ], + "spans": [ + { + "bbox": [ + 368, + 72, + 440, + 149 + ], + "type": "image", + "image_path": "fc6bdcd919f5e8c6d7a30e223de2663ba9bd480136b85475c82c1d121d73266a.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 440, + 72, + 513, + 149 + ], + "blocks": [ + { + "bbox": [ + 440, + 72, + 513, + 149 + ], + "lines": [ + { + "bbox": [ + 440, + 72, + 513, + 149 + ], + "spans": [ + { + "bbox": [ + 440, + 72, + 513, + 149 + ], + "type": "image", + "image_path": "0c47feb96f45286ccb1809164c0eddd48c09e9dc95feec5062a2754e885ffdf0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 200, + 291, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 200, + 291, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 200, + 291, + 342 + ], + "type": "text", + "content": "Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 357, + 119, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 357, + 119, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 357, + 119, + 369 + ], + "type": "text", + "content": "4.4. Discussion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "type": "text", + "content": "While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about " + }, + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "type": "inline_equation", + "content": "56\\%" + }, + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "type": "text", + "content": " of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about " + }, + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "type": "inline_equation", + "content": "44\\%" + }, + { + "bbox": [ + 46, + 376, + 291, + 578 + ], + "type": "text", + "content": " trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the \"blue\" and \"orange\" trajectories change. Two phenomenons are observed:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 583, + 292, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 583, + 292, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 292, + 714 + ], + "type": "text", + "content": "- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score \"blue\" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score \"orange\" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 304, + 198, + 419, + 252 + ], + "blocks": [ + { + "bbox": [ + 304, + 198, + 419, + 252 + ], + "lines": [ + { + "bbox": [ + 304, + 198, + 419, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 419, + 252 + ], + "type": "table", + "html": "
#Anchor numbersminFDE#Param.
10.928134K
20.911207K
30.911280K
50.915433K
60.916509K
", + "image_path": "454332fb719d3d9d404ad198699c637e9bfbeccc83356a824c0512a3f8c58cf8.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 428, + 200, + 544, + 241 + ], + "blocks": [ + { + "bbox": [ + 301, + 253, + 420, + 273 + ], + "lines": [ + { + "bbox": [ + 301, + 253, + 420, + 273 + ], + "spans": [ + { + "bbox": [ + 301, + 253, + 420, + 273 + ], + "type": "text", + "content": "Table 4. Ablation study on the number of anchors." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 428, + 200, + 544, + 241 + ], + "lines": [ + { + "bbox": [ + 428, + 200, + 544, + 241 + ], + "spans": [ + { + "bbox": [ + 428, + 200, + 544, + 241 + ], + "type": "table", + "html": "
Context EncodingminFDE
Agent-Centric0.941
Anchor-Centric0.911
", + "image_path": "ab88055d1b341b3c443ccf1d533c48fb70f2d0ffd5848255dea148d2d3d6e674.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 326, + 276, + 519, + 342 + ], + "blocks": [ + { + "bbox": [ + 427, + 242, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 427, + 242, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 427, + 242, + 545, + 262 + ], + "type": "text", + "content": "Table 5. Ablation study on how the contexts are encoded." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 326, + 276, + 519, + 342 + ], + "lines": [ + { + "bbox": [ + 326, + 276, + 519, + 342 + ], + "spans": [ + { + "bbox": [ + 326, + 276, + 519, + 342 + ], + "type": "table", + "html": "
Retrieval RadiusminFDEFlops (M)
Fixed Radius500.9262,297
200.923722
100.921325
20.93058
Adaptive RadiusRmax=10, Rmin=2, linear0.911245
Rmax=10, Rmin=2, exp0.911130
", + "image_path": "a8625216a2f0975765aec214f4b5de886ca7b6cd54cb690c225a25f3b3491b27.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 301, + 342, + 545, + 364 + ], + "lines": [ + { + "bbox": [ + 301, + 342, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 301, + 342, + 545, + 364 + ], + "type": "text", + "content": "Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 309, + 385, + 545, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 385, + 545, + 408 + ], + "spans": [ + { + "bbox": [ + 309, + 385, + 545, + 408 + ], + "type": "text", + "content": "hardly be further improved, or even be pushed away from the ground truth due to over-refinement." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 301, + 409, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 409, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 301, + 409, + 545, + 468 + ], + "type": "text", + "content": "- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 301, + 470, + 528, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 470, + 528, + 481 + ], + "spans": [ + { + "bbox": [ + 301, + 470, + 528, + 481 + ], + "type": "text", + "content": "These results show the necessity of adaptive refinement." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 301, + 492, + 374, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 492, + 374, + 504 + ], + "spans": [ + { + "bbox": [ + 301, + 492, + 374, + 504 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 300, + 512, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 300, + 512, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 300, + 512, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15288" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 292, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 291, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 291, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 291, + 134 + ], + "type": "text", + "content": "[1] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17863-17873, 2023. 1, 2, 3, 4, 6, 7, 11" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "15290" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Smooth Diffusion_ Crafting Smooth Latent Spaces in Diffusion Models/88a5ba4c-516f-44e9-b601-18a2cbb929d6_content_list.json b/2024/Smooth Diffusion_ Crafting Smooth Latent Spaces in Diffusion Models/88a5ba4c-516f-44e9-b601-18a2cbb929d6_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9640c60389a89cb0408e7c34393aa875ae58f770 --- /dev/null +++ b/2024/Smooth Diffusion_ Crafting Smooth Latent Spaces in Diffusion Models/88a5ba4c-516f-44e9-b601-18a2cbb929d6_content_list.json @@ -0,0 +1,2137 @@ +[ + { + "type": "text", + "text": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models", + "text_level": 1, + "bbox": [ + 127, + 130, + 841, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiayi Guo $^{1,2*}$ , Xingqian Xu $^{1,3*}$ , Yifan Pu $^{2}$ , Zanlin Ni $^{2}$ , Chaofei Wang $^{2}$ , Manushree Vasu $^{1}$ , Shiji Song $^{2}$ , Gao Huang $^{2\\dagger}$ , Humphrey Shi $^{1,3\\dagger}$", + "bbox": [ + 138, + 179, + 828, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1SHI Labs @ Georgia Tech & UIUC 2Tsinghua University 3Picsart AI Research (PAIR)", + "bbox": [ + 215, + 217, + 754, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/SHI-Labs/Smooth-Diffusion", + "bbox": [ + 284, + 236, + 679, + 252 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c58bb6caaef4d90e82c90b483b9ec4f1161b14513a5458675026d2d00887ed51.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 93, + 268, + 879, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/77167fe2269aba28f7f569ee883a8d7e9e0ed77ed5a413d26bba31d5ddf6b533.jpg", + "image_caption": [ + "Task 2: Image Inversion and Reconstruction \"A train going back to its course filled with people", + "\"A mouse is next to a keyboard on a desk\"" + ], + "image_footnote": [], + "bbox": [ + 127, + 434, + 364, + 494 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6ff1a46c05fcaf841ee8277f1106cd9f3eda6139d5585dd216d0afd092424b3d.jpg", + "image_caption": [ + "Figure 1. Smooth Diffusion for downstream image synthesis tasks. Our method formally introduces latent space smoothness to diffusion models like Stable Diffusion [62]. This smoothness dramatically aids various tasks in: 1) improving continuity of transitions in image interpolation, 2) reducing approximation errors in image inversion, & 3) better preserving unedited contents in image editing." + ], + "image_footnote": [], + "bbox": [ + 127, + 505, + 364, + 579 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3b1bc098b1eaea86206c1aff1084cc919555c753ad317d7468975e7318140be3.jpg", + "image_caption": [ + "Task 3: Image Editing Replace Item: \"rabbit\" $\\rightarrow$ \"cat\"", + "Transfer Style: \"watercolor style\"" + ], + "image_footnote": [], + "bbox": [ + 397, + 434, + 630, + 494 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/244b9ba54ed011299b14b60bc28a751ea897ec537851415a71d2cd4e4fec6b42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 397, + 506, + 630, + 579 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f8390b4e94aea599d7843c44f8bcf0cf58f62d8064b98c3b8b72ac5b56f27540.jpg", + "image_caption": [ + "Add Item: + \"bacon\"", + "Drag Point" + ], + "image_footnote": [], + "bbox": [ + 638, + 434, + 874, + 494 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/94bf0431562377f821bc77bc9b712a4a7cb6dee9d8862d2cf70d41f4a74de779.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 638, + 505, + 874, + 579 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 652, + 313, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a", + "bbox": [ + 75, + 684, + 470, + 866 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.", + "bbox": [ + 496, + 654, + 893, + 866 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 876, + 205, + 888 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 96, + 888, + 225, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7548", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 89, + 207, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, diffusion models [12, 24, 62] have rapidly grown into very powerful tools for generative AI, particularly for text-to-image generation. The remarkable ability of diffusion models, generating high-quality photorealistic images from open-book contexts, has been highlighted in many research and commercial products. Such success has also inspired various diffusion-based downstream tasks, including image interpolation [29, 78], inversion [13, 44, 54, 71, 77], editing [21, 42, 45, 55, 69, 75, 81, 82], etc.", + "bbox": [ + 76, + 114, + 467, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the great success in the generation field, diffusion models occasionally produce low-quality results with undesirable and unpredictable behaviors. Specifically speaking, for image interpolation, the Stable Diffusion Walk (SDW) [29] test examines latent space with spherical linear interpolations, usually resulting in highly fluctuated outputs with unpredictable visual appearance. Examples can be found in Fig. 1 Task 1, in which such interpolation exhibits undesired sharp changes as well as \"cartoonization\" on photorealistic dog images, highlighted in the red box. For the image inversion task shown in Fig. 1 Task 2, a naive application of DDIM inversion [71] cannot reconstruct images faithfully from the sources. Instead, it generates incorrect colors and object orientations, and misinterprets the computer mouse as an animal mouse. For the image editing task shown in Fig. 1 Task 3, one may notice that only minor text prompt editing can lead to major updates on image contents and layouts, in which the object (i.e. the cat's pose, the horse's location, the shape of the pizza) can be wildly and incorrectly altered. Moreover, current diffusion models are unsuited to drag-based editing [69] because a fine-engineered drag method still has a noticeably large chance of breaking objects' shape and semantics.", + "bbox": [ + 76, + 251, + 467, + 598 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we step into an important but under-explored area: to improve the latent space smoothness of diffusion models. Our motivation to enhance latent smoothness comes from the real-world demand to improve the output qualities of the aforementioned downstream tasks. A smooth latent space implies a robust visual variation under a minor latent change. Therefore, enhancing such smoothness could help improve the continuity of image interpolation, expand the capacity of image inversion, and maintain correct semantics in image editing. Notably, prior works in GANs [32, 33, 68] have demonstrated that the smooth latent space of the generator can significantly improve downstream tasks' quality, offering additional evidence of the importance of this area.", + "bbox": [ + 76, + 599, + 467, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve our goal, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. We start our exploration by first formalizing the objective for Smooth Diffusion, in which fixed-size perturbations $\\Delta \\epsilon$ on a latent noise $\\epsilon$ should produce smooth visual changes $\\Delta \\widehat{x_0}$ on the", + "bbox": [ + 76, + 810, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "synthetic image $\\widehat{\\pmb{x}_0}$ , rounded to a constant ratio $C$ . Although one may think that according to the formulation, the smoothness constraint could be an accessible train-time loss. Actually, there is no direct application of such regularization from inference to training, and the challenge lies in the fact that in each training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" instead of the entire $T$ -step diffusion process.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, we introduce Step-wise Variation Regularization, a novel regularization that seamlessly incorporates our Smooth Diffusion's inference-time objective to training. This regularization aims to bound the 2-norm of output variation $\\Delta \\widehat{\\pmb{x}_0}$ given a fixed-size change $\\Delta \\pmb{x}_t$ in input $\\pmb{x}_t$ at an arbitrary step $t$ . The rationale of the reformulation is intuitive: If $\\pmb{x}_t$ and $\\widehat{\\pmb{x}_0}$ exhibit smooth changes at any $t$ , then the relation between the latent noise $\\epsilon$ (i.e. $\\pmb{x}_T$ ) and $\\widehat{\\pmb{x}_0}$ is just the accumulation of smooth variations and thus can be smooth as well. More details can be found in Sec. 3.", + "bbox": [ + 496, + 213, + 890, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In practice, our Smooth Diffusion is trained on top of a well-known text-to-image model: Stable Diffusion [62]. We examine and demonstrate that Smooth Diffusion dramatically improves the latent space smoothness over its baseline. Meanwhile, we conduct extensive research across numerous downstream tasks, including but not limited to image interpolation, inversion, editing, etc. Both qualitative and quantitative results support our conclusion that Smooth Diffusion can be the next-gen high-performing generative model not only for the baseline text-to-image task but across various downstream tasks.", + "bbox": [ + 496, + 366, + 890, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 550, + 638, + 566 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Diffusion models are initiated from a family of prior works including but not limited to [8, 66, 70, 76]. Since then, DDPM [24] introduced an image-based noise prediction model, becoming one of the most popular image generation research. Later works [12, 48, 71] extended DDPM, demonstrating that diffusion models perform on-par and even surpass GAN-based methods [15, 30-33]. Recently, generating images from text prompts (T2I) become an emerging field [11, 19, 28, 47, 62], among which diffusion models [16, 49, 59, 62, 64] have become quite visible to the public. For example, Stable Diffusion (SD) [62] consists of VAE [36] and CLIP [58], diffuses latent space, and yields an outstanding balance between quality and speed. Following SD [62], researchers also explored diffusion approaches for controls such as ControlNet [14, 26, 46, 57, 80, 85, 86, 89-91, 95] and multimodal such as Versatile Diffusion [6, 41, 73, 88]. Works from a different track reduce diffusion steps to improve speed [5, 34, 39, 43, 65, 72, 92, 96], or restrict data and domain for few-shot learning [20, 25, 40, 63], all had successfully maintained a high output quality.", + "bbox": [ + 496, + 577, + 890, + 880 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Smooth latent space was one of the prominent proper", + "bbox": [ + 500, + 885, + 888, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7549", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ties of SOTA GAN works [9, 31-33], while exploring such property went through the decade-long GAN research [3, 15], whose goals were mainly robust training. Ideas such as Wasserstein GAN [4, 17] had proved to be effective, which enforced the Lipschitz continuity on discriminator via gradient penalties. Another technique, namely path length regularization, related to the Jacobian clamping in [51], was adapted in StyleGAN2 [32] and later became a standard setting for GAN-based generators [10, 37, 87, 94]. Benefiting from the smoothness property, researchers managed to manipulate latent space in many downstream research projects. Works such as [7, 50, 68, 83] explored latent space disentanglement. GAN-inverse [1, 2, 52, 84] had also proved to be feasible, along with a family of image editing approaches [18, 53, 56, 60, 61, 74, 97]. As aforementioned, our work aims to investigate the latent space smoothness for diffusion models, which by far remains unexplored.", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 76, + 362, + 212, + 380 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first introduce preliminaries of our method, including diffusion process [24], diffusion inversion [12, 44, 71] and low-rank adaptation [25] (Sec. 3.1). Then Smooth Diffusion is proposed with its definition, objective (Sec. 3.2) and regularization function (Sec. 3.3).", + "bbox": [ + 75, + 386, + 468, + 463 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 479, + 217, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion process [24] is a kind of Markov chain that gradually adds random noise $\\epsilon_t \\sim N(0, I)$ to ground truth signal $\\pmb{x}_0 \\sim p(\\pmb{x}_0)$ , making $\\pmb{x}_T$ in a total of $T$ steps. At each step, The noisy data $\\pmb{x}_t$ is computed as:", + "bbox": [ + 75, + 505, + 468, + 566 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\quad t = 1, 2, \\dots , T, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 571, + 468, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\beta_{t}$ is the preset diffusion rate at step $t$ . By making $\\alpha_{t} = 1 - \\beta_{t}, \\overline{\\alpha_{t}} = \\prod_{t=1}^{T} \\alpha_{t}$ and $\\epsilon \\sim N(\\mathbf{0}, \\mathbf{I})$ , we have the following equivalents:", + "bbox": [ + 76, + 599, + 468, + 645 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\boldsymbol {x} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon} _ {t} \\tag {2} \\\\ = \\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\quad t = 1, 2, \\dots , T. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 654, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A diffusion model $\\epsilon_{\\theta}(\\pmb{x}_t, t)$ is then trained to estimate $\\pmb{\\epsilon}_t$ from $\\pmb{x}_t$ , by which one can predict the original signal $\\pmb{x}_0$ by gradually remove noise from the degraded $\\pmb{x}_T$ [71]. This is commonly known as the backward diffusion process:", + "bbox": [ + 75, + 700, + 468, + 763 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\boldsymbol {x} _ {t - 1}} = \\sqrt {\\frac {\\alpha_ {t - 1}}{\\alpha_ {t}}} \\widehat {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t - 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t - 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 75, + 768, + 468, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion inversion [12, 44, 71] targets to recover the exact backward diffusion process (i.e. $\\widehat{\\pmb{x}_t},\\epsilon_\\theta (\\widehat{\\pmb{x}_t},t),t = 1,\\dots,T)$ from a known final prediction $\\widehat{\\pmb{x_0}}$ . One of the common technique for such inversion is DDIM inversion [12, 71], which reverses Eq. (3) under a local linear approximation:", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {\\boldsymbol {x} _ {t + 1}} = \\sqrt {\\frac {\\alpha_ {t + 1}}{\\alpha_ {t}}} \\widetilde {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t + 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t + 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\cdot \\epsilon_ {\\theta} (\\widetilde {\\boldsymbol {x} _ {t}}, t), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 498, + 98, + 962, + 151 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\widetilde{\\boldsymbol{x}_t}$ represent the estimated $\\widehat{\\boldsymbol{x}}_t$ at time $t$ . However, DDIM inversion is only a rough estimation. For text-to-image diffusion, a more advanced technique, Null-Text Inversion [44], optimizes additional null-text embeddings $\\{\\varnothing_t\\}_{t=1}^T$ for each step $t$ , simulating the backward process with $\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\xi,\\varnothing_t)$ , where $\\xi$ is the input text embedding. The predicted null-text $\\varnothing_t$ is the null input of the classifier-free guidance [23] with a guidance scale $w$ :", + "bbox": [ + 496, + 152, + 893, + 273 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi , \\varnothing_ {t}\\right) = w \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi\\right) + (1 - w) \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\varnothing_ {t}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 287, + 890, + 318 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Low-rank adaptation (LoRA) [25] is initially proposed to efficiently adapt large pretrained models to downstream tasks. The key assumption of LoRA is that the weight changes required during adaptation maintain a low rank. Given a pretrained model weight $W_0 \\in \\mathbb{R}^{d \\times k}$ , its updated weight $\\Delta W$ is expressed as a low rank decomposition:", + "bbox": [ + 496, + 319, + 890, + 409 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nW _ {0} + \\Delta W = W _ {0} + B A, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 414, + 890, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $B \\in \\mathbb{R}^{d \\times r}$ , $A \\in \\mathbb{R}^{r \\times k}$ and $r \\ll \\min(d, k)$ . During adaptation, $W_0$ is frozen, while $B$ and $A$ are trainable.", + "bbox": [ + 496, + 435, + 893, + 467 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Smooth Diffusion", + "text_level": 1, + "bbox": [ + 500, + 479, + 669, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As previously mentioned, modern diffusion models (DM) do not guarantee latent space smoothness, creating not only research gaps between GANs and diffusions but also unexpected challenges in downstream tasks. To address these issues, we propose Smooth Diffusion, a novel class of high-performing diffusion models with enhanced smoothness over its latent space. The underlining of Smooth Diffusion is the newly proposed training scheme in which we carried out a Step-wise Variation Regularization to enhance model smoothness.", + "bbox": [ + 496, + 507, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To better explain our aims, we adopt the same terminologies from the standard inference-time diffusion process (Fig. 2a), involving a $T$ steps procedure that transforms the random noise $\\epsilon$ (i.e., $\\pmb{x}_T$ ) to the prediction $\\widehat{\\pmb{x}_0}$ . The overall objective of Smooth Diffusion can then be written in Eq. 7: in which we expect that a fixed-size change $\\Delta \\epsilon$ on $\\epsilon$ (i.e., $\\Delta \\pmb{x}_T$ on $\\pmb{x}_T$ ) will finally lead to a non-zero, fixed-size change $\\Delta \\widehat{\\pmb{x}_0}$ on $\\widehat{\\pmb{x}_0}$ , up to a constant ratio $C$ :", + "bbox": [ + 496, + 657, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\theta} \\left(\\widehat {\\boldsymbol {x} _ {t}}, t\\right). \\quad \\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {T} \\| _ {2} = C \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 473, + 781, + 890, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Notice that by definition, $\\pmb{x}_T$ is the initial input of the backward diffusion loop in Eq. 3. Since $\\pmb{x}_T$ is close to $\\epsilon \\sim N(\\mathbf{0},\\mathbf{1})$ , for simplicity, we make them equivalent in all the following equations.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Nevertheless, one may notice that our inference-time objective in Eq. 7 cannot be directly transformed into a train-", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7550", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/dbb434c32f3441287b89912a156f2fe21d026268eb991c3a1f5e99f730510003.jpg", + "image_caption": [ + "(a) Inference-time Diffusion:" + ], + "image_footnote": [], + "bbox": [ + 148, + 88, + 395, + 157 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/cb32d12ab776eed89c972d5c62bdcd8662fcc44433dcfb5de8bc64ffbb9b07af.jpg", + "image_caption": [ + "(b) Training-time Diffusion:", + "Denoising prediction at a single step $t$" + ], + "image_footnote": [], + "bbox": [ + 465, + 99, + 828, + 157 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/eb89a8343410e614f5db8e7109f04876fcf987f2919e0e6370dbec8346e03c9c.jpg", + "image_caption": [ + "Denoising prediction through $T$ steps", + "(c) Inference-time Smooth Diffusion:", + "Variation constraint through $T$ steps" + ], + "image_footnote": [], + "bbox": [ + 117, + 202, + 411, + 299 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/abbdeec74ef59c411237cf34463eb3e831cd71f2230127b59f9e9af621458a9d.jpg", + "image_caption": [ + "(d) Training-time Smooth Diffusion:", + "Variation constraint at a single step $t$", + "Figure 2. Illustration of Smooth Diffusion. Smooth Diffusion (c) enforces the ratio between the variation of the input latent $(\\|\\Delta \\epsilon\\|_2$ or $\\|\\Delta x_T\\|_2)$ and the variation of the output prediction $(\\|\\Delta \\widehat{x_0}\\|_2)$ is a constant $C$ . Training-time Diffusion (b) optimizes a \"t-step snapshot\" of the denoising prediction process in Inference-time Diffusion (a). Similarly, we propose Training-time Smooth Diffusion (d) to optimize a \"t-step snapshot\" of the variation constraint in Inference-time Smooth Diffusion (c). DM: Diffusion model." + ], + "image_footnote": [], + "bbox": [ + 428, + 218, + 846, + 300 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ing loss function. This is because, in one training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" of the diffusion process (Fig. 2b), where $t$ is uniformly sampled from 1 to $T$ . Hence, the proposed \"global\" objective (Eq. 7) for the entire $T$ -step process is not accessible in training. Therefore, we need to reformulate our global objective into a step-wise objective shown in Eq. 8, which can later be integrated into the diffusion training process as a loss function:", + "bbox": [ + 75, + 409, + 468, + 545 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {t} \\| _ {2} = C \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 551, + 468, + 569 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C$ is a non-zero constant. This step-wise objective indicates that at each training step, variations $\\Delta \\epsilon$ on $\\epsilon$ should imply variations $\\Delta x_{t}$ on $\\pmb{x}_{t}$ with a ratio proportional to $\\sqrt{1 - \\overline{\\alpha_t}}$ . The rationale of Eq. 8 is intuitive: If $\\pmb{x}_t$ and $\\widehat{\\pmb{x_0}}$ show smooth changes at any $t$ , then the relation between the latent noise $\\epsilon$ (i.e. $\\pmb{x}_T$ ) and $\\widehat{\\pmb{x_0}}$ is just the accumulation of smooth variations and thus can be smooth as well.", + "bbox": [ + 75, + 575, + 468, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Step-wise Variation Regularization", + "text_level": 1, + "bbox": [ + 76, + 699, + 382, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the motivation and formulation of the Smooth Diffusion objective are presented, how to realize such an objective remains unexplained. Therefore, in this section, we introduce Step-wise Variation Regularization to effectively integrate the step-wise objective into diffusion training.", + "bbox": [ + 75, + 724, + 468, + 801 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We draw inspiration from the regularization techniques [32, 51] adopted in GAN training. The core idea of Step-wise Variation Regularization is to bound the Jacobian matrix $\\mathbf{J}_{\\epsilon} = \\partial \\widehat{\\pmb{x}_0} / \\partial \\pmb{\\epsilon}$ of the diffusion system by minimizing the following regularization loss at any $\\pmb{x}_0, \\pmb{\\epsilon}$ , and step $t$ :", + "bbox": [ + 75, + 803, + 468, + 878 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {\\Delta \\widehat {\\boldsymbol {x} _ {0}}, \\epsilon} \\left(\\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} - a\\right) ^ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 883, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Delta \\widehat{\\mathbf{x}_0}$ is the normally sampled pixel intensities normalized to unit length, $\\epsilon$ is a normally sampled noise in Eq. 2, and $a$ is the exponential moving average of $\\sqrt{1 - \\overline{\\alpha_t}}\\| \\mathbf{J}_{\\epsilon}^{\\mathrm{T}}\\Delta \\widehat{\\mathbf{x}_0}\\| _2$ computed online during training. In practice, we compute Eq. 9 via standard backpropagation with the following identity:", + "bbox": [ + 496, + 409, + 892, + 500 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\| \\nabla_ {\\epsilon} (\\sqrt {1 - \\bar {\\alpha} _ {t}} \\widehat {\\boldsymbol {x} _ {0}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}}) \\| _ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 503, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The identity holds since $\\Delta \\widehat{\\pmb{x}_0}$ is independently sampled, and uncorrelated with $\\epsilon$ .", + "bbox": [ + 496, + 527, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we prove that the proposed objective in Eq. 9 exactly matches our optimization goal in Eq. 8. One preliminary result, proven in [32], is that in high dimensions, Eq. 9 is minimized when $\\mathbf{J}_{\\epsilon}$ is orthogonal at any $\\epsilon$ up to a global scaling factor $\\mathcal{K}$ (i.e. $\\mathbf{J}_{\\epsilon} \\cdot \\mathbf{J}_{\\epsilon}^{\\mathrm{T}} = \\mathcal{K} \\cdot \\mathbf{I}$ ). By applying the orthogonality of $\\mathbf{J}_{\\epsilon}$ , we have the following:", + "bbox": [ + 496, + 558, + 890, + 648 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\mathbf {J} _ {\\epsilon} ^ {- 1} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\frac {\\partial \\boldsymbol {\\epsilon}}{\\partial \\widehat {\\boldsymbol {x} _ {0}}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\Delta \\boldsymbol {\\epsilon}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 654, + 890, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "When $\\mathcal{L}_{\\mathrm{reg}}$ in Eq. 9 reaches its optimal, we then have:", + "bbox": [ + 500, + 686, + 857, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\na = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\mathcal {K} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 707, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Notice that $a = a\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2$ , since $\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2 = 1$ is the aforementioned random unit length vector. Hence, we can finally reformulate the expression:", + "bbox": [ + 496, + 729, + 890, + 775 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\right\\| _ {2} = \\frac {\\mathcal {K}}{a} \\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2} \\tag {13} \\\\ = \\mathcal {C} \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\epsilon \\| _ {2}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 780, + 890, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which exactly matches our proposed objective in Eq. 8.", + "bbox": [ + 498, + 834, + 864, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To summarize, during training, the Smooth Diffusion objective encompasses a combination of $\\mathcal{L}_{\\mathrm{base}}$ and $\\mathcal{L}_{\\mathrm{reg}}$ :", + "bbox": [ + 496, + 849, + 890, + 880 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {b a s e}} + \\lambda \\mathcal {L} _ {\\text {r e g}}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7551", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ae97956fef2e9c401807af508e6c4a441f9a97fb1e0044d0ca44e4ed01668be8.jpg", + "image_caption": [ + "Figure 3. Image interpolation comparison results. For Smooth Diffusion and Stable Diffusion [62], real images (Image A and B) are inverted into latents using NTI [44]. We perform spherical linear interpolations between latents (also known as Stable Diffusion Walk [29]) and concatenate the resulting images as a transition sequence. VAE Inter. performs interpolations within the VAE space of Stable Diffusion. ANID [78] first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion." + ], + "image_footnote": [], + "bbox": [ + 124, + 92, + 848, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{base}}$ denotes the basic training objective of a diffusion model and $\\lambda$ represents a ratio parameter controlling the intensity of Step-wise Variation Regularization.", + "bbox": [ + 75, + 426, + 470, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 482, + 209, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 508, + 266, + 523 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines and settings. We select the Stable Diffusion [62] as the primary baseline for all tasks. Additionally, for image interpolation, we adopt a VAE-space interpolation and ANID [78] as competitors. For image inversion, we integrate Smooth Diffusion and Stable Diffusion with DDIM inversion [71] and Null-text inversion [44]. For text-based image editing, SDEdit [42], Prompt-to-Prompt (P2P) [21], Plug-and-Play (PnP) [75], Diffusion Disentanglement (Disentangle) [82], Pix2Pix-Zero [55] and Cycle Diffusion [81] are chosen as SOTA approaches. For drag-based image editing, we compare Smooth Diffusion with Stable Diffusion within the framework of DragDiffusion [69].", + "bbox": [ + 75, + 530, + 468, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. Smooth Diffusion is trained atop pretrained Stable Diffusion-V1.5 [62], using LoRA [25] finetuning technique. The UNet of Smooth Diffusion is set as trainable with a LoRA rank of 8, while the VAE and text encoder are frozen. We leverage the LAION Aesthetics $6.5+$ as the training dataset, which contains 625K image-text pairs with predicted aesthetics scores of 6.5 or higher from LAION-5B [67]. Smooth diffusion is typically trained for 30K iterations with a batch size of 96, 3 samples per GPU, a total of 4 A100 GPUs, and a gradient accumulation of 8. The AdamW [35] optimizer is adopted with a constant learning rate of $1 \\times 10^{-4}$ and a weight decay of $1 \\times 10^{-4}$ .", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The ratio parameter $\\lambda$ in Eq. 14 is set to 1. During inference, the total number of diffusion steps is set to 50 and the classifier-free guidance [23] scale is set to 7.5.", + "bbox": [ + 496, + 426, + 890, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation metrics. To evaluate the general text-to-image generation performance, we report the popular FID [22] and CLIP Score [58] on the MS-COCO validation set [38]. To assess the latent space smoothness, we propose an interpolation standard deviation (ISTD) as an evaluation metric. In specific, we randomly draw 500 text prompts from the MS-COCO validation set. For each prompt, we sample a pair of Gaussian noises and uniformly interpolate them from one to the other 9 times with mix ratios from 0.1 to 0.9. Fed into diffusion models together with a prompt, we could obtain a total of 11 generated images, 2 from the source Gaussian noises and 9 from the interpolated noises. We calculate the standard deviation of L2 distances between every two adjacent images in the pixel space. Finally, we average the standard deviations over 500 prompts as ISTD. Ideally, a zero value of ISTD indicates that consistent and uniform visual fluctuations in the pixel space for identical fixed-size changes in the latent space, resulting in a smooth latent space. For image inversion, mean square error (MSE), LPIPS [93], SSIM [79] and PSNR [27] are adopted to evaluate the image reconstruction capability.", + "bbox": [ + 496, + 479, + 892, + 797 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Latent Space Interpolation", + "text_level": 1, + "bbox": [ + 498, + 814, + 743, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative comparison. The most straightforward way to demonstrate the smoothness of the latent space is through the observation of interpolation results between latent noises. In Fig. 3, we present interpolation compa", + "bbox": [ + 496, + 839, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7552", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "isons between Smooth Diffusion and Stable Diffusion using real images. To generate these comparisons, we utilize the NTI [44] to invert a pair of real images into latent noises $\\boldsymbol{x}_T$ , sharing the same $\\{\\varnothing_t\\}_{t=1}^T$ . We then perform uniform spherical linear interpolations between latent noises (also known as Stable Diffusion Walk [29]), resulting in 9 intermediate noises with mix ratios from 0.1 to 0.9. Subsequently, we concatenate the 11 images produced from these noises to create an image transition sequence in the figures.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Notably, as highlighted by the red boxes, Stable Diffusion exhibits significant visual fluctuations during the transition. In particular, the interpolated images may introduce new attributes that are unrelated to the source images, e.g., the undesired grasslands in the second row of Fig. 3. In contrast, our approach, Smooth Diffusion, not only avoids introducing obvious irrelevant attributes in the interpolated images but also ensures that the visual effects change smoothly throughout the transition. Additional interpolation results can be seen in supplementary materials.", + "bbox": [ + 75, + 228, + 468, + 380 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In addition to Stable Diffusion, Fig. 3 also includes two other baseline methods for comparison: 1) VAE Interpolation (VAE Inter.), which performs interpolations within the VAE space of Stable Diffusion. However, the results closely resemble pixel-space interpolations, with significant degradation of visual details, particularly in the highlighted red box area. 2) ANID [78], which first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. In Fig. 3, ANID with a 50-step scheduler exhibits highly blurred interpolation results. When ANID operates with a default 200-step scheduler, the blurring can be alleviated, but the quality of the interpolated images remains far from satisfactory.", + "bbox": [ + 75, + 381, + 470, + 578 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/db48c92c2e65abcef8e21fa658644696fea28e654345394485913daf74b7f049.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodISTD (↓)FID (↓)CLIP Score (↑)
Stable Diffusion38.6312.7031.46
Smooth Diffusion16.5412.1031.54
", + "bbox": [ + 83, + 589, + 460, + 648 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative comparison. The goal of Smooth Diffusion is to enhance the latent space smoothness without image generation performance degradation compared to Stable Diffusion. In pursuit of this goal, we employ the ISTD introduced in Sec. 4.1 to evaluate the latent space smoothness. Additionally, we utilize FID [22] and CLIP Score [58] to assess generators' overall performance. The results presented in Tab. 1 demonstrate that Smooth Diffusion significantly outperforms Stable Diffusion in terms of ISTD, indicating a substantial improvement in the latent space smoothness. Furthermore, Smooth Diffusion exhibits superior performance in both FID and CLIP Score, suggesting that the", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "\"A man using his laptop computer while a cat sits on his lap\"", + "bbox": [ + 566, + 92, + 820, + 101 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f5539feab45d8d5b4e8001fbed5189398141e688cec7f9e65a71b6d475cd7a2b.jpg", + "image_caption": [ + "\"A large tower that has a big clock at top" + ], + "image_footnote": [], + "bbox": [ + 519, + 101, + 867, + 155 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2b1f88ee370d4360c76f1e4dda4efdd708aa893003f2298ab26feecaf588a3cb.jpg", + "image_caption": [ + "\"A room with a couch, table set with dinnerware and a television\"" + ], + "image_footnote": [], + "bbox": [ + 519, + 162, + 869, + 217 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f1c57bc4847e375c6325958b4c4898f8036a149dcefe514e90e4d9c5a51f855d.jpg", + "image_caption": [ + "Source", + "Smooth Diff. +NTI (Ours)", + "able Diff.", + "+NTI", + "Smooth Diff", + "+DDIM (Ours)", + "able Diff", + "+DDIM", + "Figure 4. Image reconstruction comparison results. We integrate Smooth Diffusion and Stable Diffusion [62] with NTI [44] (column 2 & 3) and DDIM inversion [71] (column 4 & 5)." + ], + "image_footnote": [], + "bbox": [ + 519, + 224, + 869, + 277 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/5c89efb59942b5e912a76895a8b43de3bc0f359ed4f737e87bfbf88a76d5f79f.jpg", + "table_caption": [ + "Table 1. Quantitative evaluations of image interpolation and text-to-image generation. We evaluate Smooth Diffusion and Stable Diffusion [62] with ISTD, FID [22] and CLIP Score [58]. The better results are in bold." + ], + "table_footnote": [], + "table_body": "
MethodMSE (↓)LPIPS (↓)SSIM (↑)PSNR (↑)
Stable Diff. + DDIM0.17560.53850.266213.97
Smooth Diff. + DDIM0.10860.43260.341816.17
Stable Diff. + NTI0.01560.16560.606825.63
Smooth Diff. + NTI0.01530.16350.610225.74
VAE Reconstruction0.01480.15900.613625.98
", + "bbox": [ + 503, + 352, + 888, + 441 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative evaluations of image reconstruction. We integrate Stable Diffusion and Smooth Diffusion [62] with DDIM inversion [71] (row 2 & 3) and NTI [44] (row 4 & 5). MSE, LPIPS [93], SSIM [79] and PSNR [27] are evaluated. VAE Reconstruction results are provided as the optimal values.", + "bbox": [ + 498, + 449, + 890, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "enhancement of latent space smoothness and the overall image generation quality are not mutually exclusive but complement each other when the regularization term is applied with a suitable strength ratio.", + "bbox": [ + 498, + 530, + 890, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Image Inversion and Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 603, + 815, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Previous research [32] in the realm of GANs discovered that a smoother latent space has a positive impact on the accuracy of image inversion and reconstruction. We empirically validate this finding within the context of diffusion models. In specific, two representative inversion techniques, DDIM inversion [71] and Null-text inversion (NTI) [44] are adopted and integrated with Smooth Diffusion and Stable Diffusion separately. We both qualitatively and quantitatively compare the image inversion and reconstruction performance of these integrated models using 500 randomly sampled images from the MS-COCO validation set [38].", + "bbox": [ + 496, + 627, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As illustrated in the two rightmost columns of Fig. 4, when employing a straightforward DDIM inversion, Smooth Diffusion outperforms Stable Diffusion by a considerable margin in terms of reconstruction quality. This improvement is evident in various aspects, such as an accurate generation of character identities, a faithful recreation of the city view behind the tower, and a correct reproduc", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7553", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ee7827b792b76aebb68e1b4bcc082d4866ca9169f22c3f9d29a004ee262cb628.jpg", + "image_caption": [ + "Local Edit (Replace Item)" + ], + "image_footnote": [], + "bbox": [ + 194, + 99, + 267, + 157 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/612347a0c4f9d704b4e06fd85d11f4f9dafeddf20e06d16be55d69c182eca9ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 269, + 99, + 341, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ec5a3d46abc975d3d63f92cbca55efd6e2c13e0813b931b44f11d97a6bfb4a33.jpg", + "image_caption": [ + "\"A banana on the table\" $\\rightarrow$ \"A banana and an apple on the table\"" + ], + "image_footnote": [], + "bbox": [ + 344, + 99, + 415, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/68e345f4d89c403a49553365ec38af08e4931cdb4bcc3534787e7656bbeae946.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 99, + 488, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c47747b20560cc66b304444fa8dd03db99749aee61f04fc795ced15ba31a5d1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 99, + 562, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4f90cdb1c212d06eff27314789349bce0c906e1b3686e7ff6c0120ff2aa1fc43.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 563, + 101, + 632, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cbc9023170989899a322e1f84623e558439ce5ba10878d58984e6a15b090d99e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 101, + 702, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/672db70021d9d25bc33e5b31804ce0d12050656b1487e095d0f2d41937a46566.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 101, + 777, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/70d3bb033ae2fff962b47a60c921df6c9422e3ec5e57b49dd918b5948424fb86.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 101, + 848, + 156 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d18898001464a72cbd414292cd23f9d154cf0fa0fe20eddb22c0a10718dc7fb.jpg", + "image_caption": [ + "Local Edit (Add Item)" + ], + "image_footnote": [], + "bbox": [ + 196, + 164, + 267, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/20b35f1d5c67817b007983bb8fe5cd273d91f99cf414f450a29b167601eae654.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 269, + 164, + 341, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0a4358efe99e94b251c5aa2e6d594823b09f015256d5278868a32c510b117cb1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 344, + 164, + 415, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a5287125e4cc412e782b22a990b6663bf9abbe22cb272cfb77d3c05488e00bda.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 164, + 560, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/baad5f50cfc57ba3ed4b110359eaf946f4ff9982eaaa83b00903bddce3814291.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 562, + 165, + 632, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/351dfb9ecca76a7e5562f0191ee25583aac6facae37e640dc8c77624fb9d64f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 164, + 702, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b9846993c93e15d1132a84855317490e088059368757ac4aab59cdc8f26d0cbe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 164, + 777, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/abf8bd5f457bee13f39171ef1744fe8b06da3f64795962a4587d9b83d4e1a7e3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 779, + 164, + 848, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/944e58bc83b2afae72b0453b571b40c6a0d6063a883edb47e00b324a7d2026f9.jpg", + "image_caption": [ + "Global Edit (Transfer Style)", + "Source", + "Figure 5. Text-based image editing comparison results. We compare Smooth Diffusion and Stable Diffusion [62] (column 2 & 3), considering both local and global edits through the straightforward pipeline described in Sec. 4.4. Additionally, we present results from SOTA approaches, including SDEdit [42], P2P [21], PnP [75], Disentangle [82], Pix2Pix-Zero [55], and Cycle Diffusion [81], as references." + ], + "image_footnote": [], + "bbox": [ + 196, + 222, + 267, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/248e1d56594e55d016660a3773fe0af4d9a4d960522426e41e1d36e907c21c51.jpg", + "image_caption": [ + "Smooth Diff." + ], + "image_footnote": [], + "bbox": [ + 269, + 222, + 341, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6cbc0586d92939d164632d92b370a05673ebe898fa5f4a48e3b411539729f1bd.jpg", + "image_caption": [ + "Stable Diff." + ], + "image_footnote": [], + "bbox": [ + 344, + 222, + 415, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5bcfe2d4fa39a518d7b4c3895b8df511019b936493f990b9eb840539de4e3f30.jpg", + "image_caption": [ + "SDEdit" + ], + "image_footnote": [], + "bbox": [ + 416, + 222, + 488, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5857ecb9ed067d76cb4f302193b84cf7cd7f7b70f5898e88c014defd997006ab.jpg", + "image_caption": [ + "P2P" + ], + "image_footnote": [], + "bbox": [ + 491, + 222, + 562, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/387db9a95a751af37d265786cee3e6694163edfa2f435d758988c598cbe9bf64.jpg", + "image_caption": [ + "PnP" + ], + "image_footnote": [], + "bbox": [ + 563, + 222, + 633, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/114420e81f7e92fc91caa8f3fbc0c1d904043243ff42f026b457604ead82f656.jpg", + "image_caption": [ + "Disentangle" + ], + "image_footnote": [], + "bbox": [ + 633, + 222, + 704, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/222c2426f6793dd5ebe32cb66fcef44f26a3c2a153d754e3c011f5ee263e9b33.jpg", + "image_caption": [ + "Pix2Pix-Zero" + ], + "image_footnote": [], + "bbox": [ + 705, + 222, + 777, + 282 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d345b38d77f69a0f2eb74c8d793a31b4e5c35fab636f790727b5b7cec086f6b.jpg", + "image_caption": [ + "Cycle Diff." + ], + "image_footnote": [], + "bbox": [ + 779, + 222, + 848, + 282 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion of room layouts. This phenomenon underscores the fact that the latent space of Smooth Diffusion is more tolerant of the errors introduced by the local linear approximation in DDIM inversion. Consequently, the reconstruction results produced by Smooth Diffusion manage to retain the contents of the source images to a greater extent. On the other hand, when the optimization-based NTI technique is employed, the disparity between Smooth Diffusion and Stable Diffusion is not as pronounced. Nonetheless, there are still instances where Stable Diffusion exhibits subpar results, such as the ruined man's face in Fig. 4.", + "bbox": [ + 75, + 349, + 468, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To quantify the image reconstruction performance, MSE, LPIPS [93], SSIM [79] and PSNR [27] are reported in Tab. 2. Notably, the reconstruction error encompasses two components: 1) the error from different inversion methods and U-Net parameters and 2) the error from the shared pretrained VAE [36]. Hence, we included the VAE reconstruction errors as optimal values for our method. The results exhibit a consistent outperformance of Smooth Diffusion over Stable Diffusion across all metrics, whether using DDIM inversion or NTI. Moreover, \"Smooth Diffusion + NTI\" performs results close to VAE reconstruction, indicating its superiority attributed to a smoother latent space.", + "bbox": [ + 75, + 518, + 468, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Image Editing", + "text_level": 1, + "bbox": [ + 76, + 715, + 223, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The superiority of Smooth Diffusion in image inversion and reconstruction has motivated us to explore its potential for enhancing image editing tasks. In this section, we delve into two typical image editing scenarios: text-based image editing and drag-based image editing.", + "bbox": [ + 75, + 739, + 468, + 816 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Text-based image editing. There have been numerous methods [21, 42, 55, 75, 81, 82] proposed in the literature, each with its own unique designs aimed at achieving the SOTA performance. In contrast, we adopt a simpler pipeline akin to the image inversion and reconstruction pro", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cess discussed in Sec. 4.3. The key distinction lies in our approach to modify the text prompt during the later time steps of the reconstruction process. In specific, the original $\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\mathcal{C},\\varnothing_t)$ in Eq. (5) during NTI reconstruction (diffusion sampling) process is replaced with:", + "bbox": [ + 498, + 349, + 890, + 426 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C}, \\varnothing_ {t}\\right) = \\left\\{ \\begin{array}{l} \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {s r c}}, \\varnothing_ {t}\\right), t > T \\times r, \\\\ \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {t r g}}, \\varnothing_ {t}\\right), t \\leq T \\times r, \\end{array} \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 431, + 890, + 472 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where $\\mathcal{C}_{\\mathrm{src}}$ represents the source text prompt for inversion, while $\\mathcal{C}_{\\mathrm{trg}}$ corresponds to the target text prompt for editing. The parameter $r$ serves as a threshold, determining when to switch from $\\mathcal{C}_{\\mathrm{src}}$ to $\\mathcal{C}_{\\mathrm{trg}}$ . In practice, $r$ is typically chosen within $\\{0.6, 0.7, 0.8, 0.9\\}$ , with the exact value depending on the specific input images and target visual effects.", + "bbox": [ + 498, + 477, + 890, + 566 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Through this straightforward pipeline, we conducted a comparative analysis of the editing performance between Smooth Diffusion and Stable Diffusion, as presented in the three left-most columns of Fig. 5. We also included editing results obtained from SOTA methods as references. Our evaluation encompasses both local and global editing tasks. The local editing tasks involve replacing items (e.g., changing \"cream\" to \"strawberries\") and adding items (e.g., \"apple\"). On the other hand, the global editing tasks pertain to global style transfer, such as transforming an image into a \"cartoon style\". It is evident that while Stable Diffusion excels in achieving precise image reconstruction with NTI, as discussed in Sec. 4.3, even minor modifications to the text prompt can significantly impact the content of the generated images. For instance, it can affect elements like the style of the cake, the shape of the banana, and the haircut of the girl. In contrast, Smooth Diffusion not only accurately generates edited images in accordance with the target text prompts but also effectively preserves the unedited contents. Furthermore, when compared to SOTA methods, even with this straightforward pipeline, Smooth Diffusion consistently delivers competitive results across all cases.", + "bbox": [ + 496, + 569, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7554", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7841f881951452a64d3834f27f00765f86b6308cf1d148483b0328cbbd5aeaea.jpg", + "image_caption": [ + "Figure 6. Drag-based image editing comparison results. We implement Smooth Diffusion and Stable Diffusion [62] within the framework of DragDiffusion [69], respectively." + ], + "image_footnote": [], + "bbox": [ + 114, + 90, + 424, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Drag-based image editing. As an emerging research avenue in the community, drag-based image editing [45, 53, 69] has garnered considerable attention recently. DragDiffusion [69] first introduces a framework for drag-based image editing employing Stable Diffusion. In the task 3 of Fig. 1 and Fig. 6, we showcase that by integrating Smooth Diffusion into the DragDiffusion framework, some previously unsuccessful editing operations with Stable Diffusion can be enabled. As illustrated, Smooth Diffusion achieves operations such as making the tree grow taller without damaging existing branches (Fig. 1), rotating the cat head, creating a new mountain top without destroying the original one, and letting new flowers grow in the vase (Fig. 6). These operations, however, fail with Stable Diffusion, indicating the non-smoothness of its latent space.", + "bbox": [ + 75, + 366, + 472, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 604, + 241, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Regularization ratio. In Tab. 3, we examine the impact of different strength ratios $\\lambda$ in Eq. (14). This ratio adjusts the intensity of the step-wise variation regularization. Specifically, when a weaker regularization is applied (e.g., $\\lambda = 0.1$ ), we observe a slight improvement in the CLIP Score. However, there is a significant increase in ISTD, indicating a notable degradation in latent space smoothness. In contrast, employing a stronger regularization (e.g., $\\lambda = 10$ ) leads to a smoother latent space, as demonstrated by the decrease in ISTD. However, in this case, we observe an unexpected increase in FID, indicating a notable decline in the quality of generated images. Therefore, selecting an appropriate trade-off value for $\\lambda$ becomes crucial based on the specific experimental settings. In our default setting, we find that $\\lambda = 1$ serves as a suitable value.", + "bbox": [ + 75, + 628, + 468, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "LoRA rank. In Tab. 4, we examine the impact of different ranks of the LoRA component utilized in our Smooth diffusion. We discover that LoRA ranks within the range", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ce5c0e13f6a3e63ef2da5e690c8df5274a83585e05526010b63597da914c3699.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
RatioISTD (↓)FID (↓)CLIP Score (↑)
0.124.2312.1531.56
1 (default)16.5412.1131.49
1011.5117.4431.41
", + "bbox": [ + 529, + 88, + 859, + 160 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of [4,16] are all suitable values for our default setting. We select a default rank of 8 because of its lowest ISTD among the first three rows in Tab. 4. Furthermore, we train a fully finetuned model, referred to as \"full,\" which showcases a further decrease in ISTD. However, this comes at the expense of significantly degrading the quality of the generated images, as indicated by an increased FID and decreased CLIP Score. This decline in performance underscores the vulnerability of fully fine-tuned models to collapse within our default setting, emphasizing the need for additional meticulous design considerations.", + "bbox": [ + 496, + 200, + 890, + 367 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8e9e24e6f7fe5ca536eab5aa5b7c741eeff0a904405349225cc554009ea7b65e.jpg", + "table_caption": [ + "Table 3. Ablation results of different regularization ratios. The best results are in bold, and the second-best results are underlined." + ], + "table_footnote": [], + "table_body": "
RankISTD (↓)FID (↓)CLIP Score (↑)
416.7612.3631.49
8 (default)16.5412.1131.54
1616.6511.4931.61
full11.5227.2728.86
", + "bbox": [ + 527, + 375, + 859, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation results of different LoRA ranks. The best results are in bold, and the second-best results are underlined.", + "bbox": [ + 498, + 468, + 890, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 505, + 617, + 520 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this article, we explored Smooth Diffusion, an innovative diffusion model that enhances latent space smoothness for generation. Smooth Diffusion adopts the novel Stepwise Variation Regularization, which successfully maintains variation between arbitrary input latent and generated images at a more bounded range. Smooth Diffusion was trained on top of the prevailing text-to-image model, from which we carried out extensive research, including but not limited to interpolation, inversion, and editing, all of which had shown competitive performance. Through qualitative and quantitative measurements, we demonstrated that Smooth Diffusion managed to make a smoother latent space without compromising the output quality. We believe that Smooth Diffusion will become a valuable solution for other challenging tasks, such as video generation, in the future.", + "bbox": [ + 496, + 530, + 890, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 768, + 666, + 786 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported in part by the ML Center at Georgia Tech, NSF CAREER Award #2239840, and the National AI Institute for Exceptional Education (Award #2229873) by National Science Foundation and the Institute of Education Sciences, U.S. Department of Education. Huang is in part supported by the National Key R&D Program (#2021ZD0140407) and NSFC (62321005 & 42327901).", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7555", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2StyleGAN++: How to edit the embedded images? In CVPR, 2020. 3", + "[2] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. Restyle: A residual-based stylegan encoder via iterative refinement. In ICCV, 2021. 3", + "[3] Martin Arjovsky and Léon Bottou. Towards principled methods for training generative adversarial networks. arXiv:1701.04862, 2017. 3", + "[4] Martin Arjovsky, Soumith Chintala, and Léon Bottou. Wasserstein generative adversarial networks. 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Indomain gan inversion for real image editing. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.131, + 0.843, + 0.154 + ], + "angle": 0, + "content": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.139, + 0.18, + 0.83, + 0.217 + ], + "angle": 0, + "content": "Jiayi Guo\\(^{1,2*}\\), Xingqian Xu\\(^{1,3*}\\), Yifan Pu\\(^{2}\\), Zanlin Ni\\(^{2}\\), Chaofei Wang\\(^{2}\\), Manushree Vasu\\(^{1}\\), Shiji Song\\(^{2}\\), Gao Huang\\(^{2\\dagger}\\), Humphrey Shi\\(^{1,3\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.216, + 0.218, + 0.755, + 0.235 + ], + "angle": 0, + "content": "1SHI Labs @ Georgia Tech & UIUC 2Tsinghua University 3Picsart AI Research (PAIR)" + }, + { + "type": "text", + "bbox": [ + 0.285, + 0.237, + 0.68, + 0.253 + ], + "angle": 0, + "content": "https://github.com/SHI-Labs/Smooth-Diffusion" + }, + { + "type": "image", + "bbox": [ + 0.094, + 0.27, + 0.88, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.408, + 0.385, + 0.435 + ], + "angle": 0, + "content": "Task 2: Image Inversion and Reconstruction \"A train going back to its course filled with people" + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.435, + 0.365, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.13, + 0.495, + 0.367, + 0.506 + ], + "angle": 0, + "content": "\"A mouse is next to a keyboard on a desk\"" + }, + { + "type": "image", + "bbox": [ + 0.129, + 0.506, + 0.365, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.399, + 0.408, + 0.606, + 0.435 + ], + "angle": 0, + "content": "Task 3: Image Editing Replace Item: \"rabbit\" \\(\\rightarrow\\) \"cat\"" + }, + { + "type": "image", + "bbox": [ + 0.398, + 0.435, + 0.632, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.418, + 0.495, + 0.614, + 0.507 + ], + "angle": 0, + "content": "Transfer Style: \"watercolor style\"" + }, + { + "type": "image", + "bbox": [ + 0.398, + 0.507, + 0.632, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.696, + 0.422, + 0.816, + 0.434 + ], + "angle": 0, + "content": "Add Item: + \"bacon\"" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.435, + 0.875, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.725, + 0.495, + 0.791, + 0.506 + ], + "angle": 0, + "content": "Drag Point" + }, + { + "type": "image", + "bbox": [ + 0.64, + 0.506, + 0.875, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.591, + 0.894, + 0.634 + ], + "angle": 0, + "content": "Figure 1. Smooth Diffusion for downstream image synthesis tasks. Our method formally introduces latent space smoothness to diffusion models like Stable Diffusion [62]. This smoothness dramatically aids various tasks in: 1) improving continuity of transitions in image interpolation, 2) reducing approximation errors in image inversion, & 3) better preserving unedited contents in image editing." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.653, + 0.314, + 0.669 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.471, + 0.867 + ], + "angle": 0, + "content": "Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.895, + 0.867 + ], + "angle": 0, + "content": "new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.877, + 0.206, + 0.889 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.889, + 0.227, + 0.902 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.877, + 0.227, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7548" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.208, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.468, + 0.251 + ], + "angle": 0, + "content": "In recent years, diffusion models [12, 24, 62] have rapidly grown into very powerful tools for generative AI, particularly for text-to-image generation. The remarkable ability of diffusion models, generating high-quality photorealistic images from open-book contexts, has been highlighted in many research and commercial products. Such success has also inspired various diffusion-based downstream tasks, including image interpolation [29, 78], inversion [13, 44, 54, 71, 77], editing [21, 42, 45, 55, 69, 75, 81, 82], etc." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.252, + 0.468, + 0.599 + ], + "angle": 0, + "content": "Despite the great success in the generation field, diffusion models occasionally produce low-quality results with undesirable and unpredictable behaviors. Specifically speaking, for image interpolation, the Stable Diffusion Walk (SDW) [29] test examines latent space with spherical linear interpolations, usually resulting in highly fluctuated outputs with unpredictable visual appearance. Examples can be found in Fig. 1 Task 1, in which such interpolation exhibits undesired sharp changes as well as \"cartoonization\" on photorealistic dog images, highlighted in the red box. For the image inversion task shown in Fig. 1 Task 2, a naive application of DDIM inversion [71] cannot reconstruct images faithfully from the sources. Instead, it generates incorrect colors and object orientations, and misinterprets the computer mouse as an animal mouse. For the image editing task shown in Fig. 1 Task 3, one may notice that only minor text prompt editing can lead to major updates on image contents and layouts, in which the object (i.e. the cat's pose, the horse's location, the shape of the pizza) can be wildly and incorrectly altered. Moreover, current diffusion models are unsuited to drag-based editing [69] because a fine-engineered drag method still has a noticeably large chance of breaking objects' shape and semantics." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.6, + 0.468, + 0.809 + ], + "angle": 0, + "content": "In this work, we step into an important but under-explored area: to improve the latent space smoothness of diffusion models. Our motivation to enhance latent smoothness comes from the real-world demand to improve the output qualities of the aforementioned downstream tasks. A smooth latent space implies a robust visual variation under a minor latent change. Therefore, enhancing such smoothness could help improve the continuity of image interpolation, expand the capacity of image inversion, and maintain correct semantics in image editing. Notably, prior works in GANs [32, 33, 68] have demonstrated that the smooth latent space of the generator can significantly improve downstream tasks' quality, offering additional evidence of the importance of this area." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To achieve our goal, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. We start our exploration by first formalizing the objective for Smooth Diffusion, in which fixed-size perturbations \\(\\Delta \\epsilon\\) on a latent noise \\(\\epsilon\\) should produce smooth visual changes \\(\\Delta \\widehat{x_0}\\) on the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "synthetic image \\(\\widehat{\\pmb{x}_0}\\), rounded to a constant ratio \\(C\\). Although one may think that according to the formulation, the smoothness constraint could be an accessible train-time loss. Actually, there is no direct application of such regularization from inference to training, and the challenge lies in the fact that in each training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" instead of the entire \\(T\\)-step diffusion process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.214, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Therefore, we introduce Step-wise Variation Regularization, a novel regularization that seamlessly incorporates our Smooth Diffusion's inference-time objective to training. This regularization aims to bound the 2-norm of output variation \\(\\Delta \\widehat{\\pmb{x}_0}\\) given a fixed-size change \\(\\Delta \\pmb{x}_t\\) in input \\(\\pmb{x}_t\\) at an arbitrary step \\(t\\). The rationale of the reformulation is intuitive: If \\(\\pmb{x}_t\\) and \\(\\widehat{\\pmb{x}_0}\\) exhibit smooth changes at any \\(t\\), then the relation between the latent noise \\(\\epsilon\\) (i.e. \\(\\pmb{x}_T\\)) and \\(\\widehat{\\pmb{x}_0}\\) is just the accumulation of smooth variations and thus can be smooth as well. More details can be found in Sec. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.367, + 0.892, + 0.532 + ], + "angle": 0, + "content": "In practice, our Smooth Diffusion is trained on top of a well-known text-to-image model: Stable Diffusion [62]. We examine and demonstrate that Smooth Diffusion dramatically improves the latent space smoothness over its baseline. Meanwhile, we conduct extensive research across numerous downstream tasks, including but not limited to image interpolation, inversion, editing, etc. Both qualitative and quantitative results support our conclusion that Smooth Diffusion can be the next-gen high-performing generative model not only for the baseline text-to-image task but across various downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.551, + 0.64, + 0.567 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.881 + ], + "angle": 0, + "content": "Diffusion models are initiated from a family of prior works including but not limited to [8, 66, 70, 76]. Since then, DDPM [24] introduced an image-based noise prediction model, becoming one of the most popular image generation research. Later works [12, 48, 71] extended DDPM, demonstrating that diffusion models perform on-par and even surpass GAN-based methods [15, 30-33]. Recently, generating images from text prompts (T2I) become an emerging field [11, 19, 28, 47, 62], among which diffusion models [16, 49, 59, 62, 64] have become quite visible to the public. For example, Stable Diffusion (SD) [62] consists of VAE [36] and CLIP [58], diffuses latent space, and yields an outstanding balance between quality and speed. Following SD [62], researchers also explored diffusion approaches for controls such as ControlNet [14, 26, 46, 57, 80, 85, 86, 89-91, 95] and multimodal such as Versatile Diffusion [6, 41, 73, 88]. Works from a different track reduce diffusion steps to improve speed [5, 34, 39, 43, 65, 72, 92, 96], or restrict data and domain for few-shot learning [20, 25, 40, 63], all had successfully maintained a high output quality." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.89, + 0.902 + ], + "angle": 0, + "content": "Smooth latent space was one of the prominent proper" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7549" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.351 + ], + "angle": 0, + "content": "ties of SOTA GAN works [9, 31-33], while exploring such property went through the decade-long GAN research [3, 15], whose goals were mainly robust training. Ideas such as Wasserstein GAN [4, 17] had proved to be effective, which enforced the Lipschitz continuity on discriminator via gradient penalties. Another technique, namely path length regularization, related to the Jacobian clamping in [51], was adapted in StyleGAN2 [32] and later became a standard setting for GAN-based generators [10, 37, 87, 94]. Benefiting from the smoothness property, researchers managed to manipulate latent space in many downstream research projects. Works such as [7, 50, 68, 83] explored latent space disentanglement. GAN-inverse [1, 2, 52, 84] had also proved to be feasible, along with a family of image editing approaches [18, 53, 56, 60, 61, 74, 97]. As aforementioned, our work aims to investigate the latent space smoothness for diffusion models, which by far remains unexplored." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.363, + 0.214, + 0.381 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.464 + ], + "angle": 0, + "content": "In this section, we first introduce preliminaries of our method, including diffusion process [24], diffusion inversion [12, 44, 71] and low-rank adaptation [25] (Sec. 3.1). Then Smooth Diffusion is proposed with its definition, objective (Sec. 3.2) and regularization function (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.48, + 0.218, + 0.495 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.567 + ], + "angle": 0, + "content": "Diffusion process [24] is a kind of Markov chain that gradually adds random noise \\(\\epsilon_t \\sim N(0, I)\\) to ground truth signal \\(\\pmb{x}_0 \\sim p(\\pmb{x}_0)\\), making \\(\\pmb{x}_T\\) in a total of \\(T\\) steps. At each step, The noisy data \\(\\pmb{x}_t\\) is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.573, + 0.47, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\quad t = 1, 2, \\dots , T, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.6, + 0.47, + 0.646 + ], + "angle": 0, + "content": "where \\(\\beta_{t}\\) is the preset diffusion rate at step \\(t\\). By making \\(\\alpha_{t} = 1 - \\beta_{t}, \\overline{\\alpha_{t}} = \\prod_{t=1}^{T} \\alpha_{t}\\) and \\(\\epsilon \\sim N(\\mathbf{0}, \\mathbf{I})\\), we have the following equivalents:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.655, + 0.47, + 0.692 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\boldsymbol {x} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon} _ {t} \\tag {2} \\\\ = \\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\quad t = 1, 2, \\dots , T. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.764 + ], + "angle": 0, + "content": "A diffusion model \\(\\epsilon_{\\theta}(\\pmb{x}_t, t)\\) is then trained to estimate \\(\\pmb{\\epsilon}_t\\) from \\(\\pmb{x}_t\\), by which one can predict the original signal \\(\\pmb{x}_0\\) by gradually remove noise from the degraded \\(\\pmb{x}_T\\) [71]. This is commonly known as the backward diffusion process:" + }, + { + "type": "equation", + "bbox": [ + 0.076, + 0.769, + 0.469, + 0.822 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\boldsymbol {x} _ {t - 1}} = \\sqrt {\\frac {\\alpha_ {t - 1}}{\\alpha_ {t}}} \\widehat {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t - 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t - 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Diffusion inversion [12, 44, 71] targets to recover the exact backward diffusion process (i.e. \\(\\widehat{\\pmb{x}_t},\\epsilon_\\theta (\\widehat{\\pmb{x}_t},t),t = 1,\\dots,T)\\) from a known final prediction \\(\\widehat{\\pmb{x_0}}\\) . One of the common technique for such inversion is DDIM inversion [12, 71], which reverses Eq. (3) under a local linear approximation:" + }, + { + "type": "equation", + "bbox": [ + 0.499, + 0.099, + 0.964, + 0.152 + ], + "angle": 0, + "content": "\\[\n\\widetilde {\\boldsymbol {x} _ {t + 1}} = \\sqrt {\\frac {\\alpha_ {t + 1}}{\\alpha_ {t}}} \\widetilde {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t + 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t + 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\cdot \\epsilon_ {\\theta} (\\widetilde {\\boldsymbol {x} _ {t}}, t), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.894, + 0.275 + ], + "angle": 0, + "content": "where \\(\\widetilde{\\boldsymbol{x}_t}\\) represent the estimated \\(\\widehat{\\boldsymbol{x}}_t\\) at time \\(t\\). However, DDIM inversion is only a rough estimation. For text-to-image diffusion, a more advanced technique, Null-Text Inversion [44], optimizes additional null-text embeddings \\(\\{\\varnothing_t\\}_{t=1}^T\\) for each step \\(t\\), simulating the backward process with \\(\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\xi,\\varnothing_t)\\), where \\(\\xi\\) is the input text embedding. The predicted null-text \\(\\varnothing_t\\) is the null input of the classifier-free guidance [23] with a guidance scale \\(w\\):" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.288, + 0.892, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi , \\varnothing_ {t}\\right) = w \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi\\right) + (1 - w) \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\varnothing_ {t}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Low-rank adaptation (LoRA) [25] is initially proposed to efficiently adapt large pretrained models to downstream tasks. The key assumption of LoRA is that the weight changes required during adaptation maintain a low rank. Given a pretrained model weight \\( W_0 \\in \\mathbb{R}^{d \\times k} \\), its updated weight \\( \\Delta W \\) is expressed as a low rank decomposition:" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.415, + 0.892, + 0.432 + ], + "angle": 0, + "content": "\\[\nW _ {0} + \\Delta W = W _ {0} + B A, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.894, + 0.468 + ], + "angle": 0, + "content": "where \\(B \\in \\mathbb{R}^{d \\times r}\\), \\(A \\in \\mathbb{R}^{r \\times k}\\) and \\(r \\ll \\min(d, k)\\). During adaptation, \\(W_0\\) is frozen, while \\(B\\) and \\(A\\) are trainable." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.481, + 0.671, + 0.495 + ], + "angle": 0, + "content": "3.2. Smooth Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.657 + ], + "angle": 0, + "content": "As previously mentioned, modern diffusion models (DM) do not guarantee latent space smoothness, creating not only research gaps between GANs and diffusions but also unexpected challenges in downstream tasks. To address these issues, we propose Smooth Diffusion, a novel class of high-performing diffusion models with enhanced smoothness over its latent space. The underlining of Smooth Diffusion is the newly proposed training scheme in which we carried out a Step-wise Variation Regularization to enhance model smoothness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.78 + ], + "angle": 0, + "content": "To better explain our aims, we adopt the same terminologies from the standard inference-time diffusion process (Fig. 2a), involving a \\(T\\) steps procedure that transforms the random noise \\(\\epsilon\\) (i.e., \\(\\pmb{x}_T\\)) to the prediction \\(\\widehat{\\pmb{x}_0}\\). The overall objective of Smooth Diffusion can then be written in Eq. 7: in which we expect that a fixed-size change \\(\\Delta \\epsilon\\) on \\(\\epsilon\\) (i.e., \\(\\Delta \\pmb{x}_T\\) on \\(\\pmb{x}_T\\)) will finally lead to a non-zero, fixed-size change \\(\\Delta \\widehat{\\pmb{x}_0}\\) on \\(\\widehat{\\pmb{x}_0}\\), up to a constant ratio \\(C\\):" + }, + { + "type": "equation", + "bbox": [ + 0.474, + 0.782, + 0.892, + 0.804 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\theta} \\left(\\widehat {\\boldsymbol {x} _ {t}}, t\\right). \\quad \\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {T} \\| _ {2} = C \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Notice that by definition, \\( \\pmb{x}_T \\) is the initial input of the backward diffusion loop in Eq. 3. Since \\( \\pmb{x}_T \\) is close to \\( \\epsilon \\sim N(\\mathbf{0},\\mathbf{1}) \\), for simplicity, we make them equivalent in all the following equations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Nevertheless, one may notice that our inference-time objective in Eq. 7 cannot be directly transformed into a train-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7550" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.149, + 0.089, + 0.396, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.192, + 0.166, + 0.366, + 0.178 + ], + "angle": 0, + "content": "(a) Inference-time Diffusion:" + }, + { + "type": "image_caption", + "bbox": [ + 0.165, + 0.18, + 0.394, + 0.194 + ], + "angle": 0, + "content": "Denoising prediction through \\(T\\) steps" + }, + { + "type": "image", + "bbox": [ + 0.466, + 0.101, + 0.83, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.583, + 0.166, + 0.751, + 0.179 + ], + "angle": 0, + "content": "(b) Training-time Diffusion:" + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.18, + 0.784, + 0.194 + ], + "angle": 0, + "content": "Denoising prediction at a single step \\(t\\)" + }, + { + "type": "image", + "bbox": [ + 0.119, + 0.203, + 0.413, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.159, + 0.305, + 0.398, + 0.319 + ], + "angle": 0, + "content": "(c) Inference-time Smooth Diffusion:" + }, + { + "type": "image_caption", + "bbox": [ + 0.168, + 0.32, + 0.389, + 0.335 + ], + "angle": 0, + "content": "Variation constraint through \\(T\\) steps" + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.219, + 0.848, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.55, + 0.305, + 0.783, + 0.319 + ], + "angle": 0, + "content": "(d) Training-time Smooth Diffusion:" + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.321, + 0.78, + 0.334 + ], + "angle": 0, + "content": "Variation constraint at a single step \\(t\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.894, + 0.398 + ], + "angle": 0, + "content": "Figure 2. Illustration of Smooth Diffusion. Smooth Diffusion (c) enforces the ratio between the variation of the input latent \\((\\|\\Delta \\epsilon\\|_2\\) or \\(\\|\\Delta x_T\\|_2)\\) and the variation of the output prediction \\((\\|\\Delta \\widehat{x_0}\\|_2)\\) is a constant \\(C\\). Training-time Diffusion (b) optimizes a \"t-step snapshot\" of the denoising prediction process in Inference-time Diffusion (a). Similarly, we propose Training-time Smooth Diffusion (d) to optimize a \"t-step snapshot\" of the variation constraint in Inference-time Smooth Diffusion (c). DM: Diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.546 + ], + "angle": 0, + "content": "ing loss function. This is because, in one training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" of the diffusion process (Fig. 2b), where \\( t \\) is uniformly sampled from 1 to \\( T \\). Hence, the proposed \"global\" objective (Eq. 7) for the entire \\( T \\)-step process is not accessible in training. Therefore, we need to reformulate our global objective into a step-wise objective shown in Eq. 8, which can later be integrated into the diffusion training process as a loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.552, + 0.469, + 0.57 + ], + "angle": 0, + "content": "\\[\n\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {t} \\| _ {2} = C \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.682 + ], + "angle": 0, + "content": "where \\(C\\) is a non-zero constant. This step-wise objective indicates that at each training step, variations \\(\\Delta \\epsilon\\) on \\(\\epsilon\\) should imply variations \\(\\Delta x_{t}\\) on \\(\\pmb{x}_{t}\\) with a ratio proportional to \\(\\sqrt{1 - \\overline{\\alpha_t}}\\). The rationale of Eq. 8 is intuitive: If \\(\\pmb{x}_t\\) and \\(\\widehat{\\pmb{x_0}}\\) show smooth changes at any \\(t\\), then the relation between the latent noise \\(\\epsilon\\) (i.e. \\(\\pmb{x}_T\\)) and \\(\\widehat{\\pmb{x_0}}\\) is just the accumulation of smooth variations and thus can be smooth as well." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.7, + 0.383, + 0.716 + ], + "angle": 0, + "content": "3.3. Step-wise Variation Regularization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.726, + 0.469, + 0.802 + ], + "angle": 0, + "content": "While the motivation and formulation of the Smooth Diffusion objective are presented, how to realize such an objective remains unexplained. Therefore, in this section, we introduce Step-wise Variation Regularization to effectively integrate the step-wise objective into diffusion training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.88 + ], + "angle": 0, + "content": "We draw inspiration from the regularization techniques [32, 51] adopted in GAN training. The core idea of Step-wise Variation Regularization is to bound the Jacobian matrix \\(\\mathbf{J}_{\\epsilon} = \\partial \\widehat{\\pmb{x}_0} / \\partial \\pmb{\\epsilon}\\) of the diffusion system by minimizing the following regularization loss at any \\(\\pmb{x}_0, \\pmb{\\epsilon}\\), and step \\(t\\):" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.884, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {\\Delta \\widehat {\\boldsymbol {x} _ {0}}, \\epsilon} \\left(\\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} - a\\right) ^ {2}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.501 + ], + "angle": 0, + "content": "where \\(\\Delta \\widehat{\\mathbf{x}_0}\\) is the normally sampled pixel intensities normalized to unit length, \\(\\epsilon\\) is a normally sampled noise in Eq. 2, and \\(a\\) is the exponential moving average of \\(\\sqrt{1 - \\overline{\\alpha_t}}\\| \\mathbf{J}_{\\epsilon}^{\\mathrm{T}}\\Delta \\widehat{\\mathbf{x}_0}\\| _2\\) computed online during training. In practice, we compute Eq. 9 via standard backpropagation with the following identity:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.505, + 0.892, + 0.524 + ], + "angle": 0, + "content": "\\[\n\\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\| \\nabla_ {\\epsilon} (\\sqrt {1 - \\bar {\\alpha} _ {t}} \\widehat {\\boldsymbol {x} _ {0}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}}) \\| _ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.557 + ], + "angle": 0, + "content": "The identity holds since \\(\\Delta \\widehat{\\pmb{x}_0}\\) is independently sampled, and uncorrelated with \\(\\epsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.892, + 0.65 + ], + "angle": 0, + "content": "Next, we prove that the proposed objective in Eq. 9 exactly matches our optimization goal in Eq. 8. One preliminary result, proven in [32], is that in high dimensions, Eq. 9 is minimized when \\(\\mathbf{J}_{\\epsilon}\\) is orthogonal at any \\(\\epsilon\\) up to a global scaling factor \\(\\mathcal{K}\\) (i.e. \\(\\mathbf{J}_{\\epsilon} \\cdot \\mathbf{J}_{\\epsilon}^{\\mathrm{T}} = \\mathcal{K} \\cdot \\mathbf{I}\\)). By applying the orthogonality of \\(\\mathbf{J}_{\\epsilon}\\), we have the following:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.655, + 0.891, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\mathbf {J} _ {\\epsilon} ^ {- 1} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\frac {\\partial \\boldsymbol {\\epsilon}}{\\partial \\widehat {\\boldsymbol {x} _ {0}}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\Delta \\boldsymbol {\\epsilon}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.688, + 0.858, + 0.704 + ], + "angle": 0, + "content": "When \\(\\mathcal{L}_{\\mathrm{reg}}\\) in Eq. 9 reaches its optimal, we then have:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.708, + 0.891, + 0.726 + ], + "angle": 0, + "content": "\\[\na = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\mathcal {K} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.776 + ], + "angle": 0, + "content": "Notice that \\(a = a\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2\\) , since \\(\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2 = 1\\) is the aforementioned random unit length vector. Hence, we can finally reformulate the expression:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.781, + 0.891, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\right\\| _ {2} = \\frac {\\mathcal {K}}{a} \\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2} \\tag {13} \\\\ = \\mathcal {C} \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\epsilon \\| _ {2}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.835, + 0.866, + 0.849 + ], + "angle": 0, + "content": "which exactly matches our proposed objective in Eq. 8." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.85, + 0.891, + 0.881 + ], + "angle": 0, + "content": "To summarize, during training, the Smooth Diffusion objective encompasses a combination of \\(\\mathcal{L}_{\\mathrm{base}}\\) and \\(\\mathcal{L}_{\\mathrm{reg}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {b a s e}} + \\lambda \\mathcal {L} _ {\\text {r e g}}, \\tag {14}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7551" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.125, + 0.093, + 0.849, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.359, + 0.895, + 0.416 + ], + "angle": 0, + "content": "Figure 3. Image interpolation comparison results. For Smooth Diffusion and Stable Diffusion [62], real images (Image A and B) are inverted into latents using NTI [44]. We perform spherical linear interpolations between latents (also known as Stable Diffusion Walk [29]) and concatenate the resulting images as a transition sequence. VAE Inter. performs interpolations within the VAE space of Stable Diffusion. ANID [78] first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.471, + 0.473 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{base}}\\) denotes the basic training objective of a diffusion model and \\(\\lambda\\) represents a ratio parameter controlling the intensity of Step-wise Variation Regularization." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.21, + 0.5 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.509, + 0.267, + 0.525 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Baselines and settings. We select the Stable Diffusion [62] as the primary baseline for all tasks. Additionally, for image interpolation, we adopt a VAE-space interpolation and ANID [78] as competitors. For image inversion, we integrate Smooth Diffusion and Stable Diffusion with DDIM inversion [71] and Null-text inversion [44]. For text-based image editing, SDEdit [42], Prompt-to-Prompt (P2P) [21], Plug-and-Play (PnP) [75], Diffusion Disentanglement (Disentangle) [82], Pix2Pix-Zero [55] and Cycle Diffusion [81] are chosen as SOTA approaches. For drag-based image editing, we compare Smooth Diffusion with Stable Diffusion within the framework of DragDiffusion [69]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Implementation details. Smooth Diffusion is trained atop pretrained Stable Diffusion-V1.5 [62], using LoRA [25] finetuning technique. The UNet of Smooth Diffusion is set as trainable with a LoRA rank of 8, while the VAE and text encoder are frozen. We leverage the LAION Aesthetics \\(6.5+\\) as the training dataset, which contains 625K image-text pairs with predicted aesthetics scores of 6.5 or higher from LAION-5B [67]. Smooth diffusion is typically trained for 30K iterations with a batch size of 96, 3 samples per GPU, a total of 4 A100 GPUs, and a gradient accumulation of 8. The AdamW [35] optimizer is adopted with a constant learning rate of \\(1 \\times 10^{-4}\\) and a weight decay of \\(1 \\times 10^{-4}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.892, + 0.473 + ], + "angle": 0, + "content": "The ratio parameter \\(\\lambda\\) in Eq. 14 is set to 1. During inference, the total number of diffusion steps is set to 50 and the classifier-free guidance [23] scale is set to 7.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.893, + 0.799 + ], + "angle": 0, + "content": "Evaluation metrics. To evaluate the general text-to-image generation performance, we report the popular FID [22] and CLIP Score [58] on the MS-COCO validation set [38]. To assess the latent space smoothness, we propose an interpolation standard deviation (ISTD) as an evaluation metric. In specific, we randomly draw 500 text prompts from the MS-COCO validation set. For each prompt, we sample a pair of Gaussian noises and uniformly interpolate them from one to the other 9 times with mix ratios from 0.1 to 0.9. Fed into diffusion models together with a prompt, we could obtain a total of 11 generated images, 2 from the source Gaussian noises and 9 from the interpolated noises. We calculate the standard deviation of L2 distances between every two adjacent images in the pixel space. Finally, we average the standard deviations over 500 prompts as ISTD. Ideally, a zero value of ISTD indicates that consistent and uniform visual fluctuations in the pixel space for identical fixed-size changes in the latent space, resulting in a smooth latent space. For image inversion, mean square error (MSE), LPIPS [93], SSIM [79] and PSNR [27] are adopted to evaluate the image reconstruction capability." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.815, + 0.744, + 0.831 + ], + "angle": 0, + "content": "4.2. Latent Space Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Qualitative comparison. The most straightforward way to demonstrate the smoothness of the latent space is through the observation of interpolation results between latent noises. In Fig. 3, we present interpolation compa" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7552" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "isons between Smooth Diffusion and Stable Diffusion using real images. To generate these comparisons, we utilize the NTI [44] to invert a pair of real images into latent noises \\( \\boldsymbol{x}_T \\), sharing the same \\( \\{\\varnothing_t\\}_{t=1}^T \\). We then perform uniform spherical linear interpolations between latent noises (also known as Stable Diffusion Walk [29]), resulting in 9 intermediate noises with mix ratios from 0.1 to 0.9. Subsequently, we concatenate the 11 images produced from these noises to create an image transition sequence in the figures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.381 + ], + "angle": 0, + "content": "Notably, as highlighted by the red boxes, Stable Diffusion exhibits significant visual fluctuations during the transition. In particular, the interpolated images may introduce new attributes that are unrelated to the source images, e.g., the undesired grasslands in the second row of Fig. 3. In contrast, our approach, Smooth Diffusion, not only avoids introducing obvious irrelevant attributes in the interpolated images but also ensures that the visual effects change smoothly throughout the transition. Additional interpolation results can be seen in supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.471, + 0.579 + ], + "angle": 0, + "content": "In addition to Stable Diffusion, Fig. 3 also includes two other baseline methods for comparison: 1) VAE Interpolation (VAE Inter.), which performs interpolations within the VAE space of Stable Diffusion. However, the results closely resemble pixel-space interpolations, with significant degradation of visual details, particularly in the highlighted red box area. 2) ANID [78], which first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. In Fig. 3, ANID with a 50-step scheduler exhibits highly blurred interpolation results. When ANID operates with a default 200-step scheduler, the blurring can be alleviated, but the quality of the interpolated images remains far from satisfactory." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.59, + 0.462, + 0.649 + ], + "angle": 0, + "content": "
MethodISTD (↓)FID (↓)CLIP Score (↑)
Stable Diffusion38.6312.7031.46
Smooth Diffusion16.5412.1031.54
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.71 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluations of image interpolation and text-to-image generation. We evaluate Smooth Diffusion and Stable Diffusion [62] with ISTD, FID [22] and CLIP Score [58]. The better results are in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Quantitative comparison. The goal of Smooth Diffusion is to enhance the latent space smoothness without image generation performance degradation compared to Stable Diffusion. In pursuit of this goal, we employ the ISTD introduced in Sec. 4.1 to evaluate the latent space smoothness. Additionally, we utilize FID [22] and CLIP Score [58] to assess generators' overall performance. The results presented in Tab. 1 demonstrate that Smooth Diffusion significantly outperforms Stable Diffusion in terms of ISTD, indicating a substantial improvement in the latent space smoothness. Furthermore, Smooth Diffusion exhibits superior performance in both FID and CLIP Score, suggesting that the" + }, + { + "type": "text", + "bbox": [ + 0.567, + 0.093, + 0.821, + 0.102 + ], + "angle": 0, + "content": "\"A man using his laptop computer while a cat sits on his lap\"" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.102, + 0.869, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.607, + 0.156, + 0.779, + 0.165 + ], + "angle": 0, + "content": "\"A large tower that has a big clock at top" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.164, + 0.87, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.561, + 0.218, + 0.83, + 0.225 + ], + "angle": 0, + "content": "\"A room with a couch, table set with dinnerware and a television\"" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.225, + 0.87, + 0.279 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.541, + 0.281, + 0.572, + 0.291 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image_caption", + "bbox": [ + 0.596, + 0.28, + 0.655, + 0.298 + ], + "angle": 0, + "content": "Smooth Diff. +NTI (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.281, + 0.718, + 0.29 + ], + "angle": 0, + "content": "able Diff." + }, + { + "type": "image_caption", + "bbox": [ + 0.683, + 0.29, + 0.707, + 0.297 + ], + "angle": 0, + "content": "+NTI" + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.28, + 0.793, + 0.29 + ], + "angle": 0, + "content": "Smooth Diff" + }, + { + "type": "image_caption", + "bbox": [ + 0.734, + 0.29, + 0.796, + 0.297 + ], + "angle": 0, + "content": "+DDIM (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.281, + 0.854, + 0.29 + ], + "angle": 0, + "content": "able Diff" + }, + { + "type": "image_caption", + "bbox": [ + 0.818, + 0.29, + 0.852, + 0.297 + ], + "angle": 0, + "content": "+DDIM" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.3, + 0.892, + 0.342 + ], + "angle": 0, + "content": "Figure 4. Image reconstruction comparison results. We integrate Smooth Diffusion and Stable Diffusion [62] with NTI [44] (column 2 & 3) and DDIM inversion [71] (column 4 & 5)." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.353, + 0.89, + 0.443 + ], + "angle": 0, + "content": "
MethodMSE (↓)LPIPS (↓)SSIM (↑)PSNR (↑)
Stable Diff. + DDIM0.17560.53850.266213.97
Smooth Diff. + DDIM0.10860.43260.341816.17
Stable Diff. + NTI0.01560.16560.606825.63
Smooth Diff. + NTI0.01530.16350.610225.74
VAE Reconstruction0.01480.15900.613625.98
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.45, + 0.892, + 0.52 + ], + "angle": 0, + "content": "Table 2. Quantitative evaluations of image reconstruction. We integrate Stable Diffusion and Smooth Diffusion [62] with DDIM inversion [71] (row 2 & 3) and NTI [44] (row 4 & 5). MSE, LPIPS [93], SSIM [79] and PSNR [27] are evaluated. VAE Reconstruction results are provided as the optimal values." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.531, + 0.892, + 0.592 + ], + "angle": 0, + "content": "enhancement of latent space smoothness and the overall image generation quality are not mutually exclusive but complement each other when the regularization term is applied with a suitable strength ratio." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.816, + 0.62 + ], + "angle": 0, + "content": "4.3. Image Inversion and Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Previous research [32] in the realm of GANs discovered that a smoother latent space has a positive impact on the accuracy of image inversion and reconstruction. We empirically validate this finding within the context of diffusion models. In specific, two representative inversion techniques, DDIM inversion [71] and Null-text inversion (NTI) [44] are adopted and integrated with Smooth Diffusion and Stable Diffusion separately. We both qualitatively and quantitatively compare the image inversion and reconstruction performance of these integrated models using 500 randomly sampled images from the MS-COCO validation set [38]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As illustrated in the two rightmost columns of Fig. 4, when employing a straightforward DDIM inversion, Smooth Diffusion outperforms Stable Diffusion by a considerable margin in terms of reconstruction quality. This improvement is evident in various aspects, such as an accurate generation of character identities, a faithful recreation of the city view behind the tower, and a correct reproduc" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7553" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.119, + 0.195, + 0.141 + ], + "angle": 0, + "content": "Local Edit (Replace Item)" + }, + { + "type": "image", + "bbox": [ + 0.196, + 0.101, + 0.268, + 0.158 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.101, + 0.343, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.101, + 0.416, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.101, + 0.49, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.101, + 0.563, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.102, + 0.633, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.102, + 0.704, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.707, + 0.102, + 0.778, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.102, + 0.849, + 0.157 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.345, + 0.157, + 0.664, + 0.166 + ], + "angle": 0, + "content": "\"A banana on the table\" \\(\\rightarrow\\) \"A banana and an apple on the table\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.135, + 0.183, + 0.187, + 0.204 + ], + "angle": 0, + "content": "Local Edit (Add Item)" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.165, + 0.268, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.165, + 0.343, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.165, + 0.416, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.165, + 0.561, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.563, + 0.166, + 0.633, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.165, + 0.704, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.707, + 0.165, + 0.778, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.165, + 0.849, + 0.221 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.125, + 0.244, + 0.195, + 0.264 + ], + "angle": 0, + "content": "Global Edit (Transfer Style)" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.223, + 0.268, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.216, + 0.284, + 0.248, + 0.292 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image", + "bbox": [ + 0.271, + 0.223, + 0.343, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.284, + 0.341, + 0.293 + ], + "angle": 0, + "content": "Smooth Diff." + }, + { + "type": "image", + "bbox": [ + 0.345, + 0.223, + 0.416, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.353, + 0.284, + 0.406, + 0.292 + ], + "angle": 0, + "content": "Stable Diff." + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.223, + 0.49, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.438, + 0.284, + 0.473, + 0.292 + ], + "angle": 0, + "content": "SDEdit" + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.223, + 0.563, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.284, + 0.537, + 0.292 + ], + "angle": 0, + "content": "P2P" + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.223, + 0.634, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.588, + 0.284, + 0.608, + 0.292 + ], + "angle": 0, + "content": "PnP" + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.223, + 0.705, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.284, + 0.696, + 0.292 + ], + "angle": 0, + "content": "Disentangle" + }, + { + "type": "image", + "bbox": [ + 0.707, + 0.223, + 0.778, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.284, + 0.771, + 0.292 + ], + "angle": 0, + "content": "Pix2Pix-Zero" + }, + { + "type": "image", + "bbox": [ + 0.78, + 0.223, + 0.849, + 0.283 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.284, + 0.836, + 0.292 + ], + "angle": 0, + "content": "Cycle Diff." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.297, + 0.894, + 0.339 + ], + "angle": 0, + "content": "Figure 5. Text-based image editing comparison results. We compare Smooth Diffusion and Stable Diffusion [62] (column 2 & 3), considering both local and global edits through the straightforward pipeline described in Sec. 4.4. Additionally, we present results from SOTA approaches, including SDEdit [42], P2P [21], PnP [75], Disentangle [82], Pix2Pix-Zero [55], and Cycle Diffusion [81], as references." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.517 + ], + "angle": 0, + "content": "tion of room layouts. This phenomenon underscores the fact that the latent space of Smooth Diffusion is more tolerant of the errors introduced by the local linear approximation in DDIM inversion. Consequently, the reconstruction results produced by Smooth Diffusion manage to retain the contents of the source images to a greater extent. On the other hand, when the optimization-based NTI technique is employed, the disparity between Smooth Diffusion and Stable Diffusion is not as pronounced. Nonetheless, there are still instances where Stable Diffusion exhibits subpar results, such as the ruined man's face in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.47, + 0.701 + ], + "angle": 0, + "content": "To quantify the image reconstruction performance, MSE, LPIPS [93], SSIM [79] and PSNR [27] are reported in Tab. 2. Notably, the reconstruction error encompasses two components: 1) the error from different inversion methods and U-Net parameters and 2) the error from the shared pretrained VAE [36]. Hence, we included the VAE reconstruction errors as optimal values for our method. The results exhibit a consistent outperformance of Smooth Diffusion over Stable Diffusion across all metrics, whether using DDIM inversion or NTI. Moreover, \"Smooth Diffusion + NTI\" performs results close to VAE reconstruction, indicating its superiority attributed to a smoother latent space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.716, + 0.224, + 0.732 + ], + "angle": 0, + "content": "4.4. Image Editing" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.469, + 0.817 + ], + "angle": 0, + "content": "The superiority of Smooth Diffusion in image inversion and reconstruction has motivated us to explore its potential for enhancing image editing tasks. In this section, we delve into two typical image editing scenarios: text-based image editing and drag-based image editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Text-based image editing. There have been numerous methods [21, 42, 55, 75, 81, 82] proposed in the literature, each with its own unique designs aimed at achieving the SOTA performance. In contrast, we adopt a simpler pipeline akin to the image inversion and reconstruction pro" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.351, + 0.892, + 0.427 + ], + "angle": 0, + "content": "cess discussed in Sec. 4.3. The key distinction lies in our approach to modify the text prompt during the later time steps of the reconstruction process. In specific, the original \\(\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\mathcal{C},\\varnothing_t)\\) in Eq. (5) during NTI reconstruction (diffusion sampling) process is replaced with:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.433, + 0.892, + 0.473 + ], + "angle": 0, + "content": "\\[\n\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C}, \\varnothing_ {t}\\right) = \\left\\{ \\begin{array}{l} \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {s r c}}, \\varnothing_ {t}\\right), t > T \\times r, \\\\ \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {t r g}}, \\varnothing_ {t}\\right), t \\leq T \\times r, \\end{array} \\right. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.478, + 0.892, + 0.568 + ], + "angle": 0, + "content": "where \\(\\mathcal{C}_{\\mathrm{src}}\\) represents the source text prompt for inversion, while \\(\\mathcal{C}_{\\mathrm{trg}}\\) corresponds to the target text prompt for editing. The parameter \\(r\\) serves as a threshold, determining when to switch from \\(\\mathcal{C}_{\\mathrm{src}}\\) to \\(\\mathcal{C}_{\\mathrm{trg}}\\). In practice, \\(r\\) is typically chosen within \\(\\{0.6, 0.7, 0.8, 0.9\\}\\), with the exact value depending on the specific input images and target visual effects." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Through this straightforward pipeline, we conducted a comparative analysis of the editing performance between Smooth Diffusion and Stable Diffusion, as presented in the three left-most columns of Fig. 5. We also included editing results obtained from SOTA methods as references. Our evaluation encompasses both local and global editing tasks. The local editing tasks involve replacing items (e.g., changing \"cream\" to \"strawberries\") and adding items (e.g., \"apple\"). On the other hand, the global editing tasks pertain to global style transfer, such as transforming an image into a \"cartoon style\". It is evident that while Stable Diffusion excels in achieving precise image reconstruction with NTI, as discussed in Sec. 4.3, even minor modifications to the text prompt can significantly impact the content of the generated images. For instance, it can affect elements like the style of the cake, the shape of the banana, and the haircut of the girl. In contrast, Smooth Diffusion not only accurately generates edited images in accordance with the target text prompts but also effectively preserves the unedited contents. Furthermore, when compared to SOTA methods, even with this straightforward pipeline, Smooth Diffusion consistently delivers competitive results across all cases." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7554" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.092, + 0.426, + 0.308 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.358 + ], + "angle": 0, + "content": "Figure 6. Drag-based image editing comparison results. We implement Smooth Diffusion and Stable Diffusion [62] within the framework of DragDiffusion [69], respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.473, + 0.593 + ], + "angle": 0, + "content": "Drag-based image editing. As an emerging research avenue in the community, drag-based image editing [45, 53, 69] has garnered considerable attention recently. DragDiffusion [69] first introduces a framework for drag-based image editing employing Stable Diffusion. In the task 3 of Fig. 1 and Fig. 6, we showcase that by integrating Smooth Diffusion into the DragDiffusion framework, some previously unsuccessful editing operations with Stable Diffusion can be enabled. As illustrated, Smooth Diffusion achieves operations such as making the tree grow taller without damaging existing branches (Fig. 1), rotating the cat head, creating a new mountain top without destroying the original one, and letting new flowers grow in the vase (Fig. 6). These operations, however, fail with Stable Diffusion, indicating the non-smoothness of its latent space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.242, + 0.619 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Regularization ratio. In Tab. 3, we examine the impact of different strength ratios \\(\\lambda\\) in Eq. (14). This ratio adjusts the intensity of the step-wise variation regularization. Specifically, when a weaker regularization is applied (e.g., \\(\\lambda = 0.1\\)), we observe a slight improvement in the CLIP Score. However, there is a significant increase in ISTD, indicating a notable degradation in latent space smoothness. In contrast, employing a stronger regularization (e.g., \\(\\lambda = 10\\)) leads to a smoother latent space, as demonstrated by the decrease in ISTD. However, in this case, we observe an unexpected increase in FID, indicating a notable decline in the quality of generated images. Therefore, selecting an appropriate trade-off value for \\(\\lambda\\) becomes crucial based on the specific experimental settings. In our default setting, we find that \\(\\lambda = 1\\) serves as a suitable value." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "LoRA rank. In Tab. 4, we examine the impact of different ranks of the LoRA component utilized in our Smooth diffusion. We discover that LoRA ranks within the range" + }, + { + "type": "table", + "bbox": [ + 0.53, + 0.089, + 0.86, + 0.161 + ], + "angle": 0, + "content": "
RatioISTD (↓)FID (↓)CLIP Score (↑)
0.124.2312.1531.56
1 (default)16.5412.1131.49
1011.5117.4431.41
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.168, + 0.892, + 0.196 + ], + "angle": 0, + "content": "Table 3. Ablation results of different regularization ratios. The best results are in bold, and the second-best results are underlined." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.201, + 0.892, + 0.368 + ], + "angle": 0, + "content": "of [4,16] are all suitable values for our default setting. We select a default rank of 8 because of its lowest ISTD among the first three rows in Tab. 4. Furthermore, we train a fully finetuned model, referred to as \"full,\" which showcases a further decrease in ISTD. However, this comes at the expense of significantly degrading the quality of the generated images, as indicated by an increased FID and decreased CLIP Score. This decline in performance underscores the vulnerability of fully fine-tuned models to collapse within our default setting, emphasizing the need for additional meticulous design considerations." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.375, + 0.86, + 0.462 + ], + "angle": 0, + "content": "
RankISTD (↓)FID (↓)CLIP Score (↑)
416.7612.3631.49
8 (default)16.5412.1131.54
1616.6511.4931.61
full11.5227.2728.86
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.496 + ], + "angle": 0, + "content": "Table 4. Ablation results of different LoRA ranks. The best results are in bold, and the second-best results are underlined." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.619, + 0.521 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.759 + ], + "angle": 0, + "content": "In this article, we explored Smooth Diffusion, an innovative diffusion model that enhances latent space smoothness for generation. Smooth Diffusion adopts the novel Stepwise Variation Regularization, which successfully maintains variation between arbitrary input latent and generated images at a more bounded range. Smooth Diffusion was trained on top of the prevailing text-to-image model, from which we carried out extensive research, including but not limited to interpolation, inversion, and editing, all of which had shown competitive performance. Through qualitative and quantitative measurements, we demonstrated that Smooth Diffusion managed to make a smoother latent space without compromising the output quality. We believe that Smooth Diffusion will become a valuable solution for other challenging tasks, such as video generation, in the future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.667, + 0.787 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work is supported in part by the ML Center at Georgia Tech, NSF CAREER Award #2239840, and the National AI Institute for Exceptional Education (Award #2229873) by National Science Foundation and the Institute of Education Sciences, U.S. Department of Education. Huang is in part supported by the National Key R&D Program (#2021ZD0140407) and NSFC (62321005 & 42327901)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7555" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2StyleGAN++: How to edit the embedded images? In CVPR, 2020. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[2] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. Restyle: A residual-based stylegan encoder via iterative refinement. In ICCV, 2021. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.2, + 0.468, + 0.24 + ], + "angle": 0, + "content": "[3] Martin Arjovsky and Léon Bottou. 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Smooth Diffusion for downstream image synthesis tasks. Our method formally introduces latent space smoothness to diffusion models like Stable Diffusion [62]. This smoothness dramatically aids various tasks in: 1) improving continuity of transitions in image interpolation, 2) reducing approximation errors in image inversion, & 3) better preserving unedited contents in image editing. + +![](images/3b1bc098b1eaea86206c1aff1084cc919555c753ad317d7468975e7318140be3.jpg) +Task 3: Image Editing Replace Item: "rabbit" $\rightarrow$ "cat" +Transfer Style: "watercolor style" + +![](images/244b9ba54ed011299b14b60bc28a751ea897ec537851415a71d2cd4e4fec6b42.jpg) + +![](images/f8390b4e94aea599d7843c44f8bcf0cf58f62d8064b98c3b8b72ac5b56f27540.jpg) +Add Item: + "bacon" +Drag Point + +![](images/94bf0431562377f821bc77bc9b712a4a7cb6dee9d8862d2cf70d41f4a74de779.jpg) + +# Abstract + +Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a + +new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion. + +# 1. Introduction + +In recent years, diffusion models [12, 24, 62] have rapidly grown into very powerful tools for generative AI, particularly for text-to-image generation. The remarkable ability of diffusion models, generating high-quality photorealistic images from open-book contexts, has been highlighted in many research and commercial products. Such success has also inspired various diffusion-based downstream tasks, including image interpolation [29, 78], inversion [13, 44, 54, 71, 77], editing [21, 42, 45, 55, 69, 75, 81, 82], etc. + +Despite the great success in the generation field, diffusion models occasionally produce low-quality results with undesirable and unpredictable behaviors. Specifically speaking, for image interpolation, the Stable Diffusion Walk (SDW) [29] test examines latent space with spherical linear interpolations, usually resulting in highly fluctuated outputs with unpredictable visual appearance. Examples can be found in Fig. 1 Task 1, in which such interpolation exhibits undesired sharp changes as well as "cartoonization" on photorealistic dog images, highlighted in the red box. For the image inversion task shown in Fig. 1 Task 2, a naive application of DDIM inversion [71] cannot reconstruct images faithfully from the sources. Instead, it generates incorrect colors and object orientations, and misinterprets the computer mouse as an animal mouse. For the image editing task shown in Fig. 1 Task 3, one may notice that only minor text prompt editing can lead to major updates on image contents and layouts, in which the object (i.e. the cat's pose, the horse's location, the shape of the pizza) can be wildly and incorrectly altered. Moreover, current diffusion models are unsuited to drag-based editing [69] because a fine-engineered drag method still has a noticeably large chance of breaking objects' shape and semantics. + +In this work, we step into an important but under-explored area: to improve the latent space smoothness of diffusion models. Our motivation to enhance latent smoothness comes from the real-world demand to improve the output qualities of the aforementioned downstream tasks. A smooth latent space implies a robust visual variation under a minor latent change. Therefore, enhancing such smoothness could help improve the continuity of image interpolation, expand the capacity of image inversion, and maintain correct semantics in image editing. Notably, prior works in GANs [32, 33, 68] have demonstrated that the smooth latent space of the generator can significantly improve downstream tasks' quality, offering additional evidence of the importance of this area. + +To achieve our goal, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. We start our exploration by first formalizing the objective for Smooth Diffusion, in which fixed-size perturbations $\Delta \epsilon$ on a latent noise $\epsilon$ should produce smooth visual changes $\Delta \widehat{x_0}$ on the + +synthetic image $\widehat{\pmb{x}_0}$ , rounded to a constant ratio $C$ . Although one may think that according to the formulation, the smoothness constraint could be an accessible train-time loss. Actually, there is no direct application of such regularization from inference to training, and the challenge lies in the fact that in each training iteration (i.e., back-propagation), diffusion models optimize only a "t-step snapshot" instead of the entire $T$ -step diffusion process. + +Therefore, we introduce Step-wise Variation Regularization, a novel regularization that seamlessly incorporates our Smooth Diffusion's inference-time objective to training. This regularization aims to bound the 2-norm of output variation $\Delta \widehat{\pmb{x}_0}$ given a fixed-size change $\Delta \pmb{x}_t$ in input $\pmb{x}_t$ at an arbitrary step $t$ . The rationale of the reformulation is intuitive: If $\pmb{x}_t$ and $\widehat{\pmb{x}_0}$ exhibit smooth changes at any $t$ , then the relation between the latent noise $\epsilon$ (i.e. $\pmb{x}_T$ ) and $\widehat{\pmb{x}_0}$ is just the accumulation of smooth variations and thus can be smooth as well. More details can be found in Sec. 3. + +In practice, our Smooth Diffusion is trained on top of a well-known text-to-image model: Stable Diffusion [62]. We examine and demonstrate that Smooth Diffusion dramatically improves the latent space smoothness over its baseline. Meanwhile, we conduct extensive research across numerous downstream tasks, including but not limited to image interpolation, inversion, editing, etc. Both qualitative and quantitative results support our conclusion that Smooth Diffusion can be the next-gen high-performing generative model not only for the baseline text-to-image task but across various downstream tasks. + +# 2. Related Work + +Diffusion models are initiated from a family of prior works including but not limited to [8, 66, 70, 76]. Since then, DDPM [24] introduced an image-based noise prediction model, becoming one of the most popular image generation research. Later works [12, 48, 71] extended DDPM, demonstrating that diffusion models perform on-par and even surpass GAN-based methods [15, 30-33]. Recently, generating images from text prompts (T2I) become an emerging field [11, 19, 28, 47, 62], among which diffusion models [16, 49, 59, 62, 64] have become quite visible to the public. For example, Stable Diffusion (SD) [62] consists of VAE [36] and CLIP [58], diffuses latent space, and yields an outstanding balance between quality and speed. Following SD [62], researchers also explored diffusion approaches for controls such as ControlNet [14, 26, 46, 57, 80, 85, 86, 89-91, 95] and multimodal such as Versatile Diffusion [6, 41, 73, 88]. Works from a different track reduce diffusion steps to improve speed [5, 34, 39, 43, 65, 72, 92, 96], or restrict data and domain for few-shot learning [20, 25, 40, 63], all had successfully maintained a high output quality. + +Smooth latent space was one of the prominent proper + +ties of SOTA GAN works [9, 31-33], while exploring such property went through the decade-long GAN research [3, 15], whose goals were mainly robust training. Ideas such as Wasserstein GAN [4, 17] had proved to be effective, which enforced the Lipschitz continuity on discriminator via gradient penalties. Another technique, namely path length regularization, related to the Jacobian clamping in [51], was adapted in StyleGAN2 [32] and later became a standard setting for GAN-based generators [10, 37, 87, 94]. Benefiting from the smoothness property, researchers managed to manipulate latent space in many downstream research projects. Works such as [7, 50, 68, 83] explored latent space disentanglement. GAN-inverse [1, 2, 52, 84] had also proved to be feasible, along with a family of image editing approaches [18, 53, 56, 60, 61, 74, 97]. As aforementioned, our work aims to investigate the latent space smoothness for diffusion models, which by far remains unexplored. + +# 3. Methodology + +In this section, we first introduce preliminaries of our method, including diffusion process [24], diffusion inversion [12, 44, 71] and low-rank adaptation [25] (Sec. 3.1). Then Smooth Diffusion is proposed with its definition, objective (Sec. 3.2) and regularization function (Sec. 3.3). + +# 3.1. Preliminaries + +Diffusion process [24] is a kind of Markov chain that gradually adds random noise $\epsilon_t \sim N(0, I)$ to ground truth signal $\pmb{x}_0 \sim p(\pmb{x}_0)$ , making $\pmb{x}_T$ in a total of $T$ steps. At each step, The noisy data $\pmb{x}_t$ is computed as: + +$$ +\boldsymbol {x} _ {t} = \sqrt {1 - \beta_ {t}} \boldsymbol {x} _ {t - 1} + \sqrt {\beta_ {t}} \boldsymbol {\epsilon} _ {t}, \quad t = 1, 2, \dots , T, \tag {1} +$$ + +where $\beta_{t}$ is the preset diffusion rate at step $t$ . By making $\alpha_{t} = 1 - \beta_{t}, \overline{\alpha_{t}} = \prod_{t=1}^{T} \alpha_{t}$ and $\epsilon \sim N(\mathbf{0}, \mathbf{I})$ , we have the following equivalents: + +$$ +\begin{array}{l} \boldsymbol {x} _ {t} = \sqrt {\alpha_ {t}} \boldsymbol {x} _ {t - 1} + \sqrt {1 - \alpha_ {t}} \boldsymbol {\epsilon} _ {t} \tag {2} \\ = \sqrt {\bar {\alpha} _ {t}} \boldsymbol {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon}, \quad t = 1, 2, \dots , T. \\ \end{array} +$$ + +A diffusion model $\epsilon_{\theta}(\pmb{x}_t, t)$ is then trained to estimate $\pmb{\epsilon}_t$ from $\pmb{x}_t$ , by which one can predict the original signal $\pmb{x}_0$ by gradually remove noise from the degraded $\pmb{x}_T$ [71]. This is commonly known as the backward diffusion process: + +$$ +\widehat {\boldsymbol {x} _ {t - 1}} = \sqrt {\frac {\alpha_ {t - 1}}{\alpha_ {t}}} \widehat {\boldsymbol {x} _ {t}} + \sqrt {\alpha_ {t - 1}} \left(\sqrt {\frac {1}{\alpha_ {t - 1}} - 1} - \sqrt {\frac {1}{\alpha_ {t}} - 1}\right) \tag {3} +$$ + +Diffusion inversion [12, 44, 71] targets to recover the exact backward diffusion process (i.e. $\widehat{\pmb{x}_t},\epsilon_\theta (\widehat{\pmb{x}_t},t),t = 1,\dots,T)$ from a known final prediction $\widehat{\pmb{x_0}}$ . One of the common technique for such inversion is DDIM inversion [12, 71], which reverses Eq. (3) under a local linear approximation: + +$$ +\widetilde {\boldsymbol {x} _ {t + 1}} = \sqrt {\frac {\alpha_ {t + 1}}{\alpha_ {t}}} \widetilde {\boldsymbol {x} _ {t}} + \sqrt {\alpha_ {t + 1}} \left(\sqrt {\frac {1}{\alpha_ {t + 1}} - 1} - \sqrt {\frac {1}{\alpha_ {t}} - 1}\right) \cdot \epsilon_ {\theta} (\widetilde {\boldsymbol {x} _ {t}}, t), \tag {4} +$$ + +where $\widetilde{\boldsymbol{x}_t}$ represent the estimated $\widehat{\boldsymbol{x}}_t$ at time $t$ . However, DDIM inversion is only a rough estimation. For text-to-image diffusion, a more advanced technique, Null-Text Inversion [44], optimizes additional null-text embeddings $\{\varnothing_t\}_{t=1}^T$ for each step $t$ , simulating the backward process with $\epsilon_{\theta}(\boldsymbol{x}_t,t,\xi,\varnothing_t)$ , where $\xi$ is the input text embedding. The predicted null-text $\varnothing_t$ is the null input of the classifier-free guidance [23] with a guidance scale $w$ : + +$$ +\epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \xi , \varnothing_ {t}\right) = w \cdot \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \xi\right) + (1 - w) \cdot \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \varnothing_ {t}\right). \tag {5} +$$ + +Low-rank adaptation (LoRA) [25] is initially proposed to efficiently adapt large pretrained models to downstream tasks. The key assumption of LoRA is that the weight changes required during adaptation maintain a low rank. Given a pretrained model weight $W_0 \in \mathbb{R}^{d \times k}$ , its updated weight $\Delta W$ is expressed as a low rank decomposition: + +$$ +W _ {0} + \Delta W = W _ {0} + B A, \tag {6} +$$ + +where $B \in \mathbb{R}^{d \times r}$ , $A \in \mathbb{R}^{r \times k}$ and $r \ll \min(d, k)$ . During adaptation, $W_0$ is frozen, while $B$ and $A$ are trainable. + +# 3.2. Smooth Diffusion + +As previously mentioned, modern diffusion models (DM) do not guarantee latent space smoothness, creating not only research gaps between GANs and diffusions but also unexpected challenges in downstream tasks. To address these issues, we propose Smooth Diffusion, a novel class of high-performing diffusion models with enhanced smoothness over its latent space. The underlining of Smooth Diffusion is the newly proposed training scheme in which we carried out a Step-wise Variation Regularization to enhance model smoothness. + +To better explain our aims, we adopt the same terminologies from the standard inference-time diffusion process (Fig. 2a), involving a $T$ steps procedure that transforms the random noise $\epsilon$ (i.e., $\pmb{x}_T$ ) to the prediction $\widehat{\pmb{x}_0}$ . The overall objective of Smooth Diffusion can then be written in Eq. 7: in which we expect that a fixed-size change $\Delta \epsilon$ on $\epsilon$ (i.e., $\Delta \pmb{x}_T$ on $\pmb{x}_T$ ) will finally lead to a non-zero, fixed-size change $\Delta \widehat{\pmb{x}_0}$ on $\widehat{\pmb{x}_0}$ , up to a constant ratio $C$ : + +$$ +\epsilon_ {\theta} \left(\widehat {\boldsymbol {x} _ {t}}, t\right). \quad \| \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} \Leftrightarrow C \| \Delta \boldsymbol {x} _ {T} \| _ {2} = C \| \Delta \boldsymbol {\epsilon} \| _ {2}, \forall \boldsymbol {\epsilon}, \tag {7} +$$ + +Notice that by definition, $\pmb{x}_T$ is the initial input of the backward diffusion loop in Eq. 3. Since $\pmb{x}_T$ is close to $\epsilon \sim N(\mathbf{0},\mathbf{1})$ , for simplicity, we make them equivalent in all the following equations. + +Nevertheless, one may notice that our inference-time objective in Eq. 7 cannot be directly transformed into a train- + +![](images/dbb434c32f3441287b89912a156f2fe21d026268eb991c3a1f5e99f730510003.jpg) +(a) Inference-time Diffusion: + +![](images/cb32d12ab776eed89c972d5c62bdcd8662fcc44433dcfb5de8bc64ffbb9b07af.jpg) +(b) Training-time Diffusion: +Denoising prediction at a single step $t$ + +![](images/eb89a8343410e614f5db8e7109f04876fcf987f2919e0e6370dbec8346e03c9c.jpg) +Denoising prediction through $T$ steps +(c) Inference-time Smooth Diffusion: +Variation constraint through $T$ steps + +![](images/abbdeec74ef59c411237cf34463eb3e831cd71f2230127b59f9e9af621458a9d.jpg) +(d) Training-time Smooth Diffusion: +Variation constraint at a single step $t$ +Figure 2. Illustration of Smooth Diffusion. Smooth Diffusion (c) enforces the ratio between the variation of the input latent $(\|\Delta \epsilon\|_2$ or $\|\Delta x_T\|_2)$ and the variation of the output prediction $(\|\Delta \widehat{x_0}\|_2)$ is a constant $C$ . Training-time Diffusion (b) optimizes a "t-step snapshot" of the denoising prediction process in Inference-time Diffusion (a). Similarly, we propose Training-time Smooth Diffusion (d) to optimize a "t-step snapshot" of the variation constraint in Inference-time Smooth Diffusion (c). DM: Diffusion model. + +ing loss function. This is because, in one training iteration (i.e., back-propagation), diffusion models optimize only a "t-step snapshot" of the diffusion process (Fig. 2b), where $t$ is uniformly sampled from 1 to $T$ . Hence, the proposed "global" objective (Eq. 7) for the entire $T$ -step process is not accessible in training. Therefore, we need to reformulate our global objective into a step-wise objective shown in Eq. 8, which can later be integrated into the diffusion training process as a loss function: + +$$ +\| \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} \Leftrightarrow C \| \Delta \boldsymbol {x} _ {t} \| _ {2} = C \sqrt {1 - \bar {\alpha} _ {t}} \| \Delta \boldsymbol {\epsilon} \| _ {2}, \forall \boldsymbol {\epsilon}, \tag {8} +$$ + +where $C$ is a non-zero constant. This step-wise objective indicates that at each training step, variations $\Delta \epsilon$ on $\epsilon$ should imply variations $\Delta x_{t}$ on $\pmb{x}_{t}$ with a ratio proportional to $\sqrt{1 - \overline{\alpha_t}}$ . The rationale of Eq. 8 is intuitive: If $\pmb{x}_t$ and $\widehat{\pmb{x_0}}$ show smooth changes at any $t$ , then the relation between the latent noise $\epsilon$ (i.e. $\pmb{x}_T$ ) and $\widehat{\pmb{x_0}}$ is just the accumulation of smooth variations and thus can be smooth as well. + +# 3.3. Step-wise Variation Regularization + +While the motivation and formulation of the Smooth Diffusion objective are presented, how to realize such an objective remains unexplained. Therefore, in this section, we introduce Step-wise Variation Regularization to effectively integrate the step-wise objective into diffusion training. + +We draw inspiration from the regularization techniques [32, 51] adopted in GAN training. The core idea of Step-wise Variation Regularization is to bound the Jacobian matrix $\mathbf{J}_{\epsilon} = \partial \widehat{\pmb{x}_0} / \partial \pmb{\epsilon}$ of the diffusion system by minimizing the following regularization loss at any $\pmb{x}_0, \pmb{\epsilon}$ , and step $t$ : + +$$ +\mathcal {L} _ {\text {r e g}} = \mathbb {E} _ {\Delta \widehat {\boldsymbol {x} _ {0}}, \epsilon} \left(\sqrt {1 - \overline {{\alpha_ {t}}}} \| \mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} - a\right) ^ {2}, \tag {9} +$$ + +where $\Delta \widehat{\mathbf{x}_0}$ is the normally sampled pixel intensities normalized to unit length, $\epsilon$ is a normally sampled noise in Eq. 2, and $a$ is the exponential moving average of $\sqrt{1 - \overline{\alpha_t}}\| \mathbf{J}_{\epsilon}^{\mathrm{T}}\Delta \widehat{\mathbf{x}_0}\| _2$ computed online during training. In practice, we compute Eq. 9 via standard backpropagation with the following identity: + +$$ +\sqrt {1 - \bar {\alpha} _ {t}} \| \mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} = \| \nabla_ {\epsilon} (\sqrt {1 - \bar {\alpha} _ {t}} \widehat {\boldsymbol {x} _ {0}} \cdot \Delta \widehat {\boldsymbol {x} _ {0}}) \| _ {2}. \tag {10} +$$ + +The identity holds since $\Delta \widehat{\pmb{x}_0}$ is independently sampled, and uncorrelated with $\epsilon$ . + +Next, we prove that the proposed objective in Eq. 9 exactly matches our optimization goal in Eq. 8. One preliminary result, proven in [32], is that in high dimensions, Eq. 9 is minimized when $\mathbf{J}_{\epsilon}$ is orthogonal at any $\epsilon$ up to a global scaling factor $\mathcal{K}$ (i.e. $\mathbf{J}_{\epsilon} \cdot \mathbf{J}_{\epsilon}^{\mathrm{T}} = \mathcal{K} \cdot \mathbf{I}$ ). By applying the orthogonality of $\mathbf{J}_{\epsilon}$ , we have the following: + +$$ +\mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} = \mathcal {K} \mathbf {J} _ {\epsilon} ^ {- 1} \Delta \widehat {\boldsymbol {x} _ {0}} = \mathcal {K} \frac {\partial \boldsymbol {\epsilon}}{\partial \widehat {\boldsymbol {x} _ {0}}} \cdot \Delta \widehat {\boldsymbol {x} _ {0}} = \mathcal {K} \Delta \boldsymbol {\epsilon}. \tag {11} +$$ + +When $\mathcal{L}_{\mathrm{reg}}$ in Eq. 9 reaches its optimal, we then have: + +$$ +a = \sqrt {1 - \bar {\alpha} _ {t}} \| \mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} = \sqrt {1 - \bar {\alpha} _ {t}} \mathcal {K} \| \Delta \boldsymbol {\epsilon} \| _ {2}. \tag {12} +$$ + +Notice that $a = a\| \Delta \widehat{\pmb{x}_0}\| _2$ , since $\| \Delta \widehat{\pmb{x}_0}\| _2 = 1$ is the aforementioned random unit length vector. Hence, we can finally reformulate the expression: + +$$ +\begin{array}{l} \left\| \Delta \widehat {\boldsymbol {x} _ {0}} \right\| _ {2} = \frac {\mathcal {K}}{a} \sqrt {1 - \overline {{\alpha_ {t}}}} \| \Delta \boldsymbol {\epsilon} \| _ {2} \tag {13} \\ = \mathcal {C} \sqrt {1 - \bar {\alpha} _ {t}} \| \Delta \epsilon \| _ {2}, \\ \end{array} +$$ + +which exactly matches our proposed objective in Eq. 8. + +To summarize, during training, the Smooth Diffusion objective encompasses a combination of $\mathcal{L}_{\mathrm{base}}$ and $\mathcal{L}_{\mathrm{reg}}$ : + +$$ +\mathcal {L} = \mathcal {L} _ {\text {b a s e}} + \lambda \mathcal {L} _ {\text {r e g}}, \tag {14} +$$ + +![](images/ae97956fef2e9c401807af508e6c4a441f9a97fb1e0044d0ca44e4ed01668be8.jpg) +Figure 3. Image interpolation comparison results. For Smooth Diffusion and Stable Diffusion [62], real images (Image A and B) are inverted into latents using NTI [44]. We perform spherical linear interpolations between latents (also known as Stable Diffusion Walk [29]) and concatenate the resulting images as a transition sequence. VAE Inter. performs interpolations within the VAE space of Stable Diffusion. ANID [78] first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. + +where $\mathcal{L}_{\mathrm{base}}$ denotes the basic training objective of a diffusion model and $\lambda$ represents a ratio parameter controlling the intensity of Step-wise Variation Regularization. + +# 4. Experiments + +# 4.1. Experimental Setup + +Baselines and settings. We select the Stable Diffusion [62] as the primary baseline for all tasks. Additionally, for image interpolation, we adopt a VAE-space interpolation and ANID [78] as competitors. For image inversion, we integrate Smooth Diffusion and Stable Diffusion with DDIM inversion [71] and Null-text inversion [44]. For text-based image editing, SDEdit [42], Prompt-to-Prompt (P2P) [21], Plug-and-Play (PnP) [75], Diffusion Disentanglement (Disentangle) [82], Pix2Pix-Zero [55] and Cycle Diffusion [81] are chosen as SOTA approaches. For drag-based image editing, we compare Smooth Diffusion with Stable Diffusion within the framework of DragDiffusion [69]. + +Implementation details. Smooth Diffusion is trained atop pretrained Stable Diffusion-V1.5 [62], using LoRA [25] finetuning technique. The UNet of Smooth Diffusion is set as trainable with a LoRA rank of 8, while the VAE and text encoder are frozen. We leverage the LAION Aesthetics $6.5+$ as the training dataset, which contains 625K image-text pairs with predicted aesthetics scores of 6.5 or higher from LAION-5B [67]. Smooth diffusion is typically trained for 30K iterations with a batch size of 96, 3 samples per GPU, a total of 4 A100 GPUs, and a gradient accumulation of 8. The AdamW [35] optimizer is adopted with a constant learning rate of $1 \times 10^{-4}$ and a weight decay of $1 \times 10^{-4}$ . + +The ratio parameter $\lambda$ in Eq. 14 is set to 1. During inference, the total number of diffusion steps is set to 50 and the classifier-free guidance [23] scale is set to 7.5. + +Evaluation metrics. To evaluate the general text-to-image generation performance, we report the popular FID [22] and CLIP Score [58] on the MS-COCO validation set [38]. To assess the latent space smoothness, we propose an interpolation standard deviation (ISTD) as an evaluation metric. In specific, we randomly draw 500 text prompts from the MS-COCO validation set. For each prompt, we sample a pair of Gaussian noises and uniformly interpolate them from one to the other 9 times with mix ratios from 0.1 to 0.9. Fed into diffusion models together with a prompt, we could obtain a total of 11 generated images, 2 from the source Gaussian noises and 9 from the interpolated noises. We calculate the standard deviation of L2 distances between every two adjacent images in the pixel space. Finally, we average the standard deviations over 500 prompts as ISTD. Ideally, a zero value of ISTD indicates that consistent and uniform visual fluctuations in the pixel space for identical fixed-size changes in the latent space, resulting in a smooth latent space. For image inversion, mean square error (MSE), LPIPS [93], SSIM [79] and PSNR [27] are adopted to evaluate the image reconstruction capability. + +# 4.2. Latent Space Interpolation + +Qualitative comparison. The most straightforward way to demonstrate the smoothness of the latent space is through the observation of interpolation results between latent noises. In Fig. 3, we present interpolation compa + +isons between Smooth Diffusion and Stable Diffusion using real images. To generate these comparisons, we utilize the NTI [44] to invert a pair of real images into latent noises $\boldsymbol{x}_T$ , sharing the same $\{\varnothing_t\}_{t=1}^T$ . We then perform uniform spherical linear interpolations between latent noises (also known as Stable Diffusion Walk [29]), resulting in 9 intermediate noises with mix ratios from 0.1 to 0.9. Subsequently, we concatenate the 11 images produced from these noises to create an image transition sequence in the figures. + +Notably, as highlighted by the red boxes, Stable Diffusion exhibits significant visual fluctuations during the transition. In particular, the interpolated images may introduce new attributes that are unrelated to the source images, e.g., the undesired grasslands in the second row of Fig. 3. In contrast, our approach, Smooth Diffusion, not only avoids introducing obvious irrelevant attributes in the interpolated images but also ensures that the visual effects change smoothly throughout the transition. Additional interpolation results can be seen in supplementary materials. + +In addition to Stable Diffusion, Fig. 3 also includes two other baseline methods for comparison: 1) VAE Interpolation (VAE Inter.), which performs interpolations within the VAE space of Stable Diffusion. However, the results closely resemble pixel-space interpolations, with significant degradation of visual details, particularly in the highlighted red box area. 2) ANID [78], which first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. In Fig. 3, ANID with a 50-step scheduler exhibits highly blurred interpolation results. When ANID operates with a default 200-step scheduler, the blurring can be alleviated, but the quality of the interpolated images remains far from satisfactory. + +
MethodISTD (↓)FID (↓)CLIP Score (↑)
Stable Diffusion38.6312.7031.46
Smooth Diffusion16.5412.1031.54
+ +Quantitative comparison. The goal of Smooth Diffusion is to enhance the latent space smoothness without image generation performance degradation compared to Stable Diffusion. In pursuit of this goal, we employ the ISTD introduced in Sec. 4.1 to evaluate the latent space smoothness. Additionally, we utilize FID [22] and CLIP Score [58] to assess generators' overall performance. The results presented in Tab. 1 demonstrate that Smooth Diffusion significantly outperforms Stable Diffusion in terms of ISTD, indicating a substantial improvement in the latent space smoothness. Furthermore, Smooth Diffusion exhibits superior performance in both FID and CLIP Score, suggesting that the + +"A man using his laptop computer while a cat sits on his lap" + +![](images/f5539feab45d8d5b4e8001fbed5189398141e688cec7f9e65a71b6d475cd7a2b.jpg) +"A large tower that has a big clock at top + +![](images/2b1f88ee370d4360c76f1e4dda4efdd708aa893003f2298ab26feecaf588a3cb.jpg) +"A room with a couch, table set with dinnerware and a television" + +![](images/f1c57bc4847e375c6325958b4c4898f8036a149dcefe514e90e4d9c5a51f855d.jpg) +Source +Smooth Diff. +NTI (Ours) +able Diff. ++NTI +Smooth Diff ++DDIM (Ours) +able Diff ++DDIM +Figure 4. Image reconstruction comparison results. We integrate Smooth Diffusion and Stable Diffusion [62] with NTI [44] (column 2 & 3) and DDIM inversion [71] (column 4 & 5). + +Table 1. Quantitative evaluations of image interpolation and text-to-image generation. We evaluate Smooth Diffusion and Stable Diffusion [62] with ISTD, FID [22] and CLIP Score [58]. The better results are in bold. + +
MethodMSE (↓)LPIPS (↓)SSIM (↑)PSNR (↑)
Stable Diff. + DDIM0.17560.53850.266213.97
Smooth Diff. + DDIM0.10860.43260.341816.17
Stable Diff. + NTI0.01560.16560.606825.63
Smooth Diff. + NTI0.01530.16350.610225.74
VAE Reconstruction0.01480.15900.613625.98
+ +Table 2. Quantitative evaluations of image reconstruction. We integrate Stable Diffusion and Smooth Diffusion [62] with DDIM inversion [71] (row 2 & 3) and NTI [44] (row 4 & 5). MSE, LPIPS [93], SSIM [79] and PSNR [27] are evaluated. VAE Reconstruction results are provided as the optimal values. + +enhancement of latent space smoothness and the overall image generation quality are not mutually exclusive but complement each other when the regularization term is applied with a suitable strength ratio. + +# 4.3. Image Inversion and Reconstruction + +Previous research [32] in the realm of GANs discovered that a smoother latent space has a positive impact on the accuracy of image inversion and reconstruction. We empirically validate this finding within the context of diffusion models. In specific, two representative inversion techniques, DDIM inversion [71] and Null-text inversion (NTI) [44] are adopted and integrated with Smooth Diffusion and Stable Diffusion separately. We both qualitatively and quantitatively compare the image inversion and reconstruction performance of these integrated models using 500 randomly sampled images from the MS-COCO validation set [38]. + +As illustrated in the two rightmost columns of Fig. 4, when employing a straightforward DDIM inversion, Smooth Diffusion outperforms Stable Diffusion by a considerable margin in terms of reconstruction quality. This improvement is evident in various aspects, such as an accurate generation of character identities, a faithful recreation of the city view behind the tower, and a correct reproduc + +![](images/ee7827b792b76aebb68e1b4bcc082d4866ca9169f22c3f9d29a004ee262cb628.jpg) +Local Edit (Replace Item) + +![](images/612347a0c4f9d704b4e06fd85d11f4f9dafeddf20e06d16be55d69c182eca9ed.jpg) + +![](images/ec5a3d46abc975d3d63f92cbca55efd6e2c13e0813b931b44f11d97a6bfb4a33.jpg) +"A banana on the table" $\rightarrow$ "A banana and an apple on the table" + +![](images/68e345f4d89c403a49553365ec38af08e4931cdb4bcc3534787e7656bbeae946.jpg) + +![](images/5c47747b20560cc66b304444fa8dd03db99749aee61f04fc795ced15ba31a5d1.jpg) + +![](images/4f90cdb1c212d06eff27314789349bce0c906e1b3686e7ff6c0120ff2aa1fc43.jpg) + +![](images/cbc9023170989899a322e1f84623e558439ce5ba10878d58984e6a15b090d99e.jpg) + +![](images/672db70021d9d25bc33e5b31804ce0d12050656b1487e095d0f2d41937a46566.jpg) + +![](images/70d3bb033ae2fff962b47a60c921df6c9422e3ec5e57b49dd918b5948424fb86.jpg) + +![](images/9d18898001464a72cbd414292cd23f9d154cf0fa0fe20eddb22c0a10718dc7fb.jpg) +Local Edit (Add Item) + +![](images/20b35f1d5c67817b007983bb8fe5cd273d91f99cf414f450a29b167601eae654.jpg) + +![](images/0a4358efe99e94b251c5aa2e6d594823b09f015256d5278868a32c510b117cb1.jpg) + +![](images/a5287125e4cc412e782b22a990b6663bf9abbe22cb272cfb77d3c05488e00bda.jpg) + +![](images/baad5f50cfc57ba3ed4b110359eaf946f4ff9982eaaa83b00903bddce3814291.jpg) + +![](images/351dfb9ecca76a7e5562f0191ee25583aac6facae37e640dc8c77624fb9d64f8.jpg) + +![](images/b9846993c93e15d1132a84855317490e088059368757ac4aab59cdc8f26d0cbe.jpg) + +![](images/abf8bd5f457bee13f39171ef1744fe8b06da3f64795962a4587d9b83d4e1a7e3.jpg) + +![](images/944e58bc83b2afae72b0453b571b40c6a0d6063a883edb47e00b324a7d2026f9.jpg) +Global Edit (Transfer Style) +Source +Figure 5. Text-based image editing comparison results. We compare Smooth Diffusion and Stable Diffusion [62] (column 2 & 3), considering both local and global edits through the straightforward pipeline described in Sec. 4.4. Additionally, we present results from SOTA approaches, including SDEdit [42], P2P [21], PnP [75], Disentangle [82], Pix2Pix-Zero [55], and Cycle Diffusion [81], as references. + +![](images/248e1d56594e55d016660a3773fe0af4d9a4d960522426e41e1d36e907c21c51.jpg) +Smooth Diff. + +![](images/6cbc0586d92939d164632d92b370a05673ebe898fa5f4a48e3b411539729f1bd.jpg) +Stable Diff. + +![](images/5bcfe2d4fa39a518d7b4c3895b8df511019b936493f990b9eb840539de4e3f30.jpg) +SDEdit + +![](images/5857ecb9ed067d76cb4f302193b84cf7cd7f7b70f5898e88c014defd997006ab.jpg) +P2P + +![](images/387db9a95a751af37d265786cee3e6694163edfa2f435d758988c598cbe9bf64.jpg) +PnP + +![](images/114420e81f7e92fc91caa8f3fbc0c1d904043243ff42f026b457604ead82f656.jpg) +Disentangle + +![](images/222c2426f6793dd5ebe32cb66fcef44f26a3c2a153d754e3c011f5ee263e9b33.jpg) +Pix2Pix-Zero + +![](images/7d345b38d77f69a0f2eb74c8d793a31b4e5c35fab636f790727b5b7cec086f6b.jpg) +Cycle Diff. + +tion of room layouts. This phenomenon underscores the fact that the latent space of Smooth Diffusion is more tolerant of the errors introduced by the local linear approximation in DDIM inversion. Consequently, the reconstruction results produced by Smooth Diffusion manage to retain the contents of the source images to a greater extent. On the other hand, when the optimization-based NTI technique is employed, the disparity between Smooth Diffusion and Stable Diffusion is not as pronounced. Nonetheless, there are still instances where Stable Diffusion exhibits subpar results, such as the ruined man's face in Fig. 4. + +To quantify the image reconstruction performance, MSE, LPIPS [93], SSIM [79] and PSNR [27] are reported in Tab. 2. Notably, the reconstruction error encompasses two components: 1) the error from different inversion methods and U-Net parameters and 2) the error from the shared pretrained VAE [36]. Hence, we included the VAE reconstruction errors as optimal values for our method. The results exhibit a consistent outperformance of Smooth Diffusion over Stable Diffusion across all metrics, whether using DDIM inversion or NTI. Moreover, "Smooth Diffusion + NTI" performs results close to VAE reconstruction, indicating its superiority attributed to a smoother latent space. + +# 4.4. Image Editing + +The superiority of Smooth Diffusion in image inversion and reconstruction has motivated us to explore its potential for enhancing image editing tasks. In this section, we delve into two typical image editing scenarios: text-based image editing and drag-based image editing. + +Text-based image editing. There have been numerous methods [21, 42, 55, 75, 81, 82] proposed in the literature, each with its own unique designs aimed at achieving the SOTA performance. In contrast, we adopt a simpler pipeline akin to the image inversion and reconstruction pro + +cess discussed in Sec. 4.3. The key distinction lies in our approach to modify the text prompt during the later time steps of the reconstruction process. In specific, the original $\epsilon_{\theta}(\boldsymbol{x}_t,t,\mathcal{C},\varnothing_t)$ in Eq. (5) during NTI reconstruction (diffusion sampling) process is replaced with: + +$$ +\epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \mathcal {C}, \varnothing_ {t}\right) = \left\{ \begin{array}{l} \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \mathcal {C} _ {\text {s r c}}, \varnothing_ {t}\right), t > T \times r, \\ \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \mathcal {C} _ {\text {t r g}}, \varnothing_ {t}\right), t \leq T \times r, \end{array} \right. \tag {15} +$$ + +where $\mathcal{C}_{\mathrm{src}}$ represents the source text prompt for inversion, while $\mathcal{C}_{\mathrm{trg}}$ corresponds to the target text prompt for editing. The parameter $r$ serves as a threshold, determining when to switch from $\mathcal{C}_{\mathrm{src}}$ to $\mathcal{C}_{\mathrm{trg}}$ . In practice, $r$ is typically chosen within $\{0.6, 0.7, 0.8, 0.9\}$ , with the exact value depending on the specific input images and target visual effects. + +Through this straightforward pipeline, we conducted a comparative analysis of the editing performance between Smooth Diffusion and Stable Diffusion, as presented in the three left-most columns of Fig. 5. We also included editing results obtained from SOTA methods as references. Our evaluation encompasses both local and global editing tasks. The local editing tasks involve replacing items (e.g., changing "cream" to "strawberries") and adding items (e.g., "apple"). On the other hand, the global editing tasks pertain to global style transfer, such as transforming an image into a "cartoon style". It is evident that while Stable Diffusion excels in achieving precise image reconstruction with NTI, as discussed in Sec. 4.3, even minor modifications to the text prompt can significantly impact the content of the generated images. For instance, it can affect elements like the style of the cake, the shape of the banana, and the haircut of the girl. In contrast, Smooth Diffusion not only accurately generates edited images in accordance with the target text prompts but also effectively preserves the unedited contents. Furthermore, when compared to SOTA methods, even with this straightforward pipeline, Smooth Diffusion consistently delivers competitive results across all cases. + +![](images/7841f881951452a64d3834f27f00765f86b6308cf1d148483b0328cbbd5aeaea.jpg) +Figure 6. Drag-based image editing comparison results. We implement Smooth Diffusion and Stable Diffusion [62] within the framework of DragDiffusion [69], respectively. + +Drag-based image editing. As an emerging research avenue in the community, drag-based image editing [45, 53, 69] has garnered considerable attention recently. DragDiffusion [69] first introduces a framework for drag-based image editing employing Stable Diffusion. In the task 3 of Fig. 1 and Fig. 6, we showcase that by integrating Smooth Diffusion into the DragDiffusion framework, some previously unsuccessful editing operations with Stable Diffusion can be enabled. As illustrated, Smooth Diffusion achieves operations such as making the tree grow taller without damaging existing branches (Fig. 1), rotating the cat head, creating a new mountain top without destroying the original one, and letting new flowers grow in the vase (Fig. 6). These operations, however, fail with Stable Diffusion, indicating the non-smoothness of its latent space. + +# 4.5. Ablation Studies + +Regularization ratio. In Tab. 3, we examine the impact of different strength ratios $\lambda$ in Eq. (14). This ratio adjusts the intensity of the step-wise variation regularization. Specifically, when a weaker regularization is applied (e.g., $\lambda = 0.1$ ), we observe a slight improvement in the CLIP Score. However, there is a significant increase in ISTD, indicating a notable degradation in latent space smoothness. In contrast, employing a stronger regularization (e.g., $\lambda = 10$ ) leads to a smoother latent space, as demonstrated by the decrease in ISTD. However, in this case, we observe an unexpected increase in FID, indicating a notable decline in the quality of generated images. Therefore, selecting an appropriate trade-off value for $\lambda$ becomes crucial based on the specific experimental settings. In our default setting, we find that $\lambda = 1$ serves as a suitable value. + +LoRA rank. In Tab. 4, we examine the impact of different ranks of the LoRA component utilized in our Smooth diffusion. We discover that LoRA ranks within the range + +
RatioISTD (↓)FID (↓)CLIP Score (↑)
0.124.2312.1531.56
1 (default)16.5412.1131.49
1011.5117.4431.41
+ +of [4,16] are all suitable values for our default setting. We select a default rank of 8 because of its lowest ISTD among the first three rows in Tab. 4. Furthermore, we train a fully finetuned model, referred to as "full," which showcases a further decrease in ISTD. However, this comes at the expense of significantly degrading the quality of the generated images, as indicated by an increased FID and decreased CLIP Score. This decline in performance underscores the vulnerability of fully fine-tuned models to collapse within our default setting, emphasizing the need for additional meticulous design considerations. + +Table 3. Ablation results of different regularization ratios. The best results are in bold, and the second-best results are underlined. + +
RankISTD (↓)FID (↓)CLIP Score (↑)
416.7612.3631.49
8 (default)16.5412.1131.54
1616.6511.4931.61
full11.5227.2728.86
+ +Table 4. Ablation results of different LoRA ranks. The best results are in bold, and the second-best results are underlined. + +# 5. Conclusion + +In this article, we explored Smooth Diffusion, an innovative diffusion model that enhances latent space smoothness for generation. Smooth Diffusion adopts the novel Stepwise Variation Regularization, which successfully maintains variation between arbitrary input latent and generated images at a more bounded range. Smooth Diffusion was trained on top of the prevailing text-to-image model, from which we carried out extensive research, including but not limited to interpolation, inversion, and editing, all of which had shown competitive performance. Through qualitative and quantitative measurements, we demonstrated that Smooth Diffusion managed to make a smoother latent space without compromising the output quality. 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Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 518, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 547, + 686 + ], + "type": "text", + "content": "new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 694, + 126, + 704 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 694, + 126, + 704 + ], + "spans": [ + { + "bbox": [ + 58, + 694, + 126, + 704 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 59, + 704, + 138, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 704, + 138, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 704, + 138, + 714 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7548" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 127, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 286, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 286, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 286, + 198 + ], + "type": "text", + "content": "In recent years, diffusion models [12, 24, 62] have rapidly grown into very powerful tools for generative AI, particularly for text-to-image generation. The remarkable ability of diffusion models, generating high-quality photorealistic images from open-book contexts, has been highlighted in many research and commercial products. Such success has also inspired various diffusion-based downstream tasks, including image interpolation [29, 78], inversion [13, 44, 54, 71, 77], editing [21, 42, 45, 55, 69, 75, 81, 82], etc." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 199, + 286, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 199, + 286, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 286, + 474 + ], + "type": "text", + "content": "Despite the great success in the generation field, diffusion models occasionally produce low-quality results with undesirable and unpredictable behaviors. Specifically speaking, for image interpolation, the Stable Diffusion Walk (SDW) [29] test examines latent space with spherical linear interpolations, usually resulting in highly fluctuated outputs with unpredictable visual appearance. Examples can be found in Fig. 1 Task 1, in which such interpolation exhibits undesired sharp changes as well as \"cartoonization\" on photorealistic dog images, highlighted in the red box. For the image inversion task shown in Fig. 1 Task 2, a naive application of DDIM inversion [71] cannot reconstruct images faithfully from the sources. Instead, it generates incorrect colors and object orientations, and misinterprets the computer mouse as an animal mouse. For the image editing task shown in Fig. 1 Task 3, one may notice that only minor text prompt editing can lead to major updates on image contents and layouts, in which the object (i.e. the cat's pose, the horse's location, the shape of the pizza) can be wildly and incorrectly altered. Moreover, current diffusion models are unsuited to drag-based editing [69] because a fine-engineered drag method still has a noticeably large chance of breaking objects' shape and semantics." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 475, + 286, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 286, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 286, + 640 + ], + "type": "text", + "content": "In this work, we step into an important but under-explored area: to improve the latent space smoothness of diffusion models. Our motivation to enhance latent smoothness comes from the real-world demand to improve the output qualities of the aforementioned downstream tasks. A smooth latent space implies a robust visual variation under a minor latent change. Therefore, enhancing such smoothness could help improve the continuity of image interpolation, expand the capacity of image inversion, and maintain correct semantics in image editing. Notably, prior works in GANs [32, 33, 68] have demonstrated that the smooth latent space of the generator can significantly improve downstream tasks' quality, offering additional evidence of the importance of this area." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "content": "To achieve our goal, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. We start our exploration by first formalizing the objective for Smooth Diffusion, in which fixed-size perturbations " + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\epsilon" + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "content": " on a latent noise " + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "content": " should produce smooth visual changes " + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\widehat{x_0}" + }, + { + "bbox": [ + 47, + 642, + 286, + 713 + ], + "type": "text", + "content": " on the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "synthetic image " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ", rounded to a constant ratio " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": ". Although one may think that according to the formulation, the smoothness constraint could be an accessible train-time loss. Actually, there is no direct application of such regularization from inference to training, and the challenge lies in the fact that in each training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" instead of the entire " + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "-step diffusion process." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": "Therefore, we introduce Step-wise Variation Regularization, a novel regularization that seamlessly incorporates our Smooth Diffusion's inference-time objective to training. This regularization aims to bound the 2-norm of output variation " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\Delta \\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " given a fixed-size change " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\Delta \\pmb{x}_t" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " in input " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " at an arbitrary step " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": ". The rationale of the reformulation is intuitive: If " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " exhibit smooth changes at any " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": ", then the relation between the latent noise " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " (i.e. " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 169, + 545, + 289 + ], + "type": "text", + "content": " is just the accumulation of smooth variations and thus can be smooth as well. More details can be found in Sec. 3." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 290, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 290, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 290, + 545, + 421 + ], + "type": "text", + "content": "In practice, our Smooth Diffusion is trained on top of a well-known text-to-image model: Stable Diffusion [62]. We examine and demonstrate that Smooth Diffusion dramatically improves the latent space smoothness over its baseline. Meanwhile, we conduct extensive research across numerous downstream tasks, including but not limited to image interpolation, inversion, editing, etc. Both qualitative and quantitative results support our conclusion that Smooth Diffusion can be the next-gen high-performing generative model not only for the baseline text-to-image task but across various downstream tasks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 436, + 391, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 436, + 391, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 436, + 391, + 449 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 457, + 545, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 697 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 697 + ], + "type": "text", + "content": "Diffusion models are initiated from a family of prior works including but not limited to [8, 66, 70, 76]. Since then, DDPM [24] introduced an image-based noise prediction model, becoming one of the most popular image generation research. Later works [12, 48, 71] extended DDPM, demonstrating that diffusion models perform on-par and even surpass GAN-based methods [15, 30-33]. Recently, generating images from text prompts (T2I) become an emerging field [11, 19, 28, 47, 62], among which diffusion models [16, 49, 59, 62, 64] have become quite visible to the public. For example, Stable Diffusion (SD) [62] consists of VAE [36] and CLIP [58], diffuses latent space, and yields an outstanding balance between quality and speed. Following SD [62], researchers also explored diffusion approaches for controls such as ControlNet [14, 26, 46, 57, 80, 85, 86, 89-91, 95] and multimodal such as Versatile Diffusion [6, 41, 73, 88]. Works from a different track reduce diffusion steps to improve speed [5, 34, 39, 43, 65, 72, 92, 96], or restrict data and domain for few-shot learning [20, 25, 40, 63], all had successfully maintained a high output quality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 701, + 544, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 544, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 544, + 714 + ], + "type": "text", + "content": "Smooth latent space was one of the prominent proper" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7549" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "ties of SOTA GAN works [9, 31-33], while exploring such property went through the decade-long GAN research [3, 15], whose goals were mainly robust training. Ideas such as Wasserstein GAN [4, 17] had proved to be effective, which enforced the Lipschitz continuity on discriminator via gradient penalties. Another technique, namely path length regularization, related to the Jacobian clamping in [51], was adapted in StyleGAN2 [32] and later became a standard setting for GAN-based generators [10, 37, 87, 94]. Benefiting from the smoothness property, researchers managed to manipulate latent space in many downstream research projects. Works such as [7, 50, 68, 83] explored latent space disentanglement. GAN-inverse [1, 2, 52, 84] had also proved to be feasible, along with a family of image editing approaches [18, 53, 56, 60, 61, 74, 97]. As aforementioned, our work aims to investigate the latent space smoothness for diffusion models, which by far remains unexplored." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 287, + 130, + 301 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 287, + 130, + 301 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 130, + 301 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 306, + 287, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 367 + ], + "type": "text", + "content": "In this section, we first introduce preliminaries of our method, including diffusion process [24], diffusion inversion [12, 44, 71] and low-rank adaptation [25] (Sec. 3.1). Then Smooth Diffusion is proposed with its definition, objective (Sec. 3.2) and regularization function (Sec. 3.3)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 380, + 133, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 133, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 133, + 392 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "content": "Diffusion process [24] is a kind of Markov chain that gradually adds random noise " + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\epsilon_t \\sim N(0, I)" + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "content": " to ground truth signal " + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0 \\sim p(\\pmb{x}_0)" + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "content": ", making " + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "content": " in a total of " + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "content": " steps. At each step, The noisy data " + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 46, + 400, + 287, + 449 + ], + "type": "text", + "content": " is computed as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 453, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 453, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 55, + 453, + 287, + 469 + ], + "type": "interline_equation", + "content": "\\boldsymbol {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\quad t = 1, 2, \\dots , T, \\tag {1}", + "image_path": "6cd1c744d4f6aa8bb02c1c0020aa2965c62344ab1418d7973622b42ef89ab7f9.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "content": " is the preset diffusion rate at step " + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "content": ". By making " + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = 1 - \\beta_{t}, \\overline{\\alpha_{t}} = \\prod_{t=1}^{T} \\alpha_{t}" + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim N(\\mathbf{0}, \\mathbf{I})" + }, + { + "bbox": [ + 47, + 475, + 287, + 511 + ], + "type": "text", + "content": ", we have the following equivalents:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 73, + 518, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 518, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 73, + 518, + 287, + 548 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\boldsymbol {x} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon} _ {t} \\tag {2} \\\\ = \\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\quad t = 1, 2, \\dots , T. \\\\ \\end{array}", + "image_path": "f2a33bb1d972ab7fa9a897b247f7590760464f48af024dc678e7237fedd78669.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "content": "A diffusion model " + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\pmb{x}_t, t)" + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "content": " is then trained to estimate " + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\pmb{\\epsilon}_t" + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "content": ", by which one can predict the original signal " + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0" + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "content": " by gradually remove noise from the degraded " + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 46, + 555, + 287, + 605 + ], + "type": "text", + "content": " [71]. This is commonly known as the backward diffusion process:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 609, + 287, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 651 + ], + "type": "interline_equation", + "content": "\\widehat {\\boldsymbol {x} _ {t - 1}} = \\sqrt {\\frac {\\alpha_ {t - 1}}{\\alpha_ {t}}} \\widehat {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t - 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t - 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\tag {3}", + "image_path": "2ae0e2e3b3f9ffa5b06090254eaf7b96df85f4fb033c78840649a39a64f7dd69.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "Diffusion inversion [12, 44, 71] targets to recover the exact backward diffusion process (i.e. " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x}_t},\\epsilon_\\theta (\\widehat{\\pmb{x}_t},t),t = 1,\\dots,T)" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " from a known final prediction " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x_0}}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " . One of the common technique for such inversion is DDIM inversion [12, 71], which reverses Eq. (3) under a local linear approximation:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 78, + 589, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 78, + 589, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 78, + 589, + 120 + ], + "type": "interline_equation", + "content": "\\widetilde {\\boldsymbol {x} _ {t + 1}} = \\sqrt {\\frac {\\alpha_ {t + 1}}{\\alpha_ {t}}} \\widetilde {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t + 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t + 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\cdot \\epsilon_ {\\theta} (\\widetilde {\\boldsymbol {x} _ {t}}, t), \\tag {4}", + "image_path": "a71e996de5f97150adcc9b35d03f1757b2c0b2fd6e0ad237b7ec453460263cad.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\widetilde{\\boldsymbol{x}_t}" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": " represent the estimated " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\widehat{\\boldsymbol{x}}_t" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": ". However, DDIM inversion is only a rough estimation. For text-to-image diffusion, a more advanced technique, Null-Text Inversion [44], optimizes additional null-text embeddings " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\{\\varnothing_t\\}_{t=1}^T" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": " for each step " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": ", simulating the backward process with " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\xi,\\varnothing_t)" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": " is the input text embedding. The predicted null-text " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "\\varnothing_t" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": " is the null input of the classifier-free guidance [23] with a guidance scale " + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 121, + 547, + 217 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 228, + 545, + 252 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 545, + 252 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi , \\varnothing_ {t}\\right) = w \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi\\right) + (1 - w) \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\varnothing_ {t}\\right). \\tag {5}", + "image_path": "3ad6d84c734d392981cef58a867e19f5f97e44bb3c6b77129cedd9cadf42ae89.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "content": "Low-rank adaptation (LoRA) [25] is initially proposed to efficiently adapt large pretrained models to downstream tasks. The key assumption of LoRA is that the weight changes required during adaptation maintain a low rank. Given a pretrained model weight " + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "inline_equation", + "content": "W_0 \\in \\mathbb{R}^{d \\times k}" + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "content": ", its updated weight " + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "inline_equation", + "content": "\\Delta W" + }, + { + "bbox": [ + 304, + 253, + 545, + 324 + ], + "type": "text", + "content": " is expressed as a low rank decomposition:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 372, + 328, + 545, + 342 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 328, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 372, + 328, + 545, + 342 + ], + "type": "interline_equation", + "content": "W _ {0} + \\Delta W = W _ {0} + B A, \\tag {6}", + "image_path": "3fb1105e5fde44b79fabf240896974408d5e9b35a72ad80eca76498492530445.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{d \\times r}" + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{r \\times k}" + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "inline_equation", + "content": "r \\ll \\min(d, k)" + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": ". During adaptation, " + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "inline_equation", + "content": "W_0" + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": " is frozen, while " + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 345, + 547, + 370 + ], + "type": "text", + "content": " are trainable." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 380, + 410, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 410, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 410, + 392 + ], + "type": "text", + "content": "3.2. Smooth Diffusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 402, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 520 + ], + "type": "text", + "content": "As previously mentioned, modern diffusion models (DM) do not guarantee latent space smoothness, creating not only research gaps between GANs and diffusions but also unexpected challenges in downstream tasks. To address these issues, we propose Smooth Diffusion, a novel class of high-performing diffusion models with enhanced smoothness over its latent space. The underlining of Smooth Diffusion is the newly proposed training scheme in which we carried out a Step-wise Variation Regularization to enhance model smoothness." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": "To better explain our aims, we adopt the same terminologies from the standard inference-time diffusion process (Fig. 2a), involving a " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " steps procedure that transforms the random noise " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": ") to the prediction " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": ". The overall objective of Smooth Diffusion can then be written in Eq. 7: in which we expect that a fixed-size change " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\Delta \\epsilon" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\Delta \\pmb{x}_T" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": ") will finally lead to a non-zero, fixed-size change " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\Delta \\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": ", up to a constant ratio " + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 521, + 545, + 617 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 290, + 619, + 545, + 636 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 290, + 619, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 290, + 619, + 545, + 636 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\theta} \\left(\\widehat {\\boldsymbol {x} _ {t}}, t\\right). \\quad \\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {T} \\| _ {2} = C \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {7}", + "image_path": "f98d20c27a4a64e2563cc8e1cd4d10d79b5217e076603ce3a69259cb2b78985e.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "Notice that by definition, " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " is the initial input of the backward diffusion loop in Eq. 3. Since " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": " is close to " + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim N(\\mathbf{0},\\mathbf{1})" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": ", for simplicity, we make them equivalent in all the following equations." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "Nevertheless, one may notice that our inference-time objective in Eq. 7 cannot be directly transformed into a train-" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 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Illustration of Smooth Diffusion. Smooth Diffusion (c) enforces the ratio between the variation of the input latent " + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "inline_equation", + "content": "(\\|\\Delta \\epsilon\\|_2" + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "inline_equation", + "content": "\\|\\Delta x_T\\|_2)" + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "text", + "content": " and the variation of the output prediction " + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "inline_equation", + "content": "(\\|\\Delta \\widehat{x_0}\\|_2)" + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "text", + "content": " is a constant " + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 270, + 547, + 315 + ], + "type": "text", + "content": ". Training-time Diffusion (b) optimizes a \"t-step snapshot\" of the denoising prediction process in Inference-time Diffusion (a). Similarly, we propose Training-time Smooth Diffusion (d) to optimize a \"t-step snapshot\" of the variation constraint in Inference-time Smooth Diffusion (c). DM: Diffusion model." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "text", + "content": "ing loss function. This is because, in one training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" of the diffusion process (Fig. 2b), where " + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "text", + "content": " is uniformly sampled from 1 to " + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "text", + "content": ". Hence, the proposed \"global\" objective (Eq. 7) for the entire " + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 324, + 287, + 432 + ], + "type": "text", + "content": "-step process is not accessible in training. Therefore, we need to reformulate our global objective into a step-wise objective shown in Eq. 8, which can later be integrated into the diffusion training process as a loss function:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 63, + 437, + 287, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 437, + 287, + 451 + ], + "spans": [ + { + "bbox": [ + 63, + 437, + 287, + 451 + ], + "type": "interline_equation", + "content": "\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {t} \\| _ {2} = C \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {8}", + "image_path": "d99d1132fbb544aa4a6d88ea6bfb47d0107ece59cd7f0fb8ff444e98687b03e1.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " is a non-zero constant. This step-wise objective indicates that at each training step, variations " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\Delta \\epsilon" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " should imply variations " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\Delta x_{t}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{t}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " with a ratio proportional to " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\sqrt{1 - \\overline{\\alpha_t}}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": ". The rationale of Eq. 8 is intuitive: If " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x_0}}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " show smooth changes at any " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": ", then the relation between the latent noise " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " (i.e. " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\widehat{\\pmb{x_0}}" + }, + { + "bbox": [ + 46, + 456, + 287, + 540 + ], + "type": "text", + "content": " is just the accumulation of smooth variations and thus can be smooth as well." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 554, + 234, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 234, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 234, + 567 + ], + "type": "text", + "content": "3.3. Step-wise Variation Regularization" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": "While the motivation and formulation of the Smooth Diffusion objective are presented, how to realize such an objective remains unexplained. Therefore, in this section, we introduce Step-wise Variation Regularization to effectively integrate the step-wise objective into diffusion training." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "content": "We draw inspiration from the regularization techniques [32, 51] adopted in GAN training. The core idea of Step-wise Variation Regularization is to bound the Jacobian matrix " + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\epsilon} = \\partial \\widehat{\\pmb{x}_0} / \\partial \\pmb{\\epsilon}" + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "content": " of the diffusion system by minimizing the following regularization loss at any " + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "inline_equation", + "content": "\\pmb{x}_0, \\pmb{\\epsilon}" + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "content": ", and step " + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 636, + 287, + 696 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 75, + 700, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 700, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 75, + 700, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {\\Delta \\widehat {\\boldsymbol {x} _ {0}}, \\epsilon} \\left(\\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} - a\\right) ^ {2}, \\tag {9}", + "image_path": "f2c7e95edf290ce33887b0d5fffb24b3c500bf45f0c34adfa50ed0daaab1e415.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "inline_equation", + "content": "\\Delta \\widehat{\\mathbf{x}_0}" + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "text", + "content": " is the normally sampled pixel intensities normalized to unit length, " + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "text", + "content": " is a normally sampled noise in Eq. 2, and " + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "text", + "content": " is the exponential moving average of " + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "inline_equation", + "content": "\\sqrt{1 - \\overline{\\alpha_t}}\\| \\mathbf{J}_{\\epsilon}^{\\mathrm{T}}\\Delta \\widehat{\\mathbf{x}_0}\\| _2" + }, + { + "bbox": [ + 304, + 324, + 546, + 396 + ], + "type": "text", + "content": " computed online during training. In practice, we compute Eq. 9 via standard backpropagation with the following identity:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 399, + 545, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 399, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 313, + 399, + 545, + 415 + ], + "type": "interline_equation", + "content": "\\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\| \\nabla_ {\\epsilon} (\\sqrt {1 - \\bar {\\alpha} _ {t}} \\widehat {\\boldsymbol {x} _ {0}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}}) \\| _ {2}. \\tag {10}", + "image_path": "04962d8cd58e2541b60117c5dc72a2d819c27cff528aad74ff53a9738d8cdb0c.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "type": "text", + "content": "The identity holds since " + }, + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\Delta \\widehat{\\pmb{x}_0}" + }, + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "type": "text", + "content": " is independently sampled, and uncorrelated with " + }, + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 418, + 545, + 441 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": "Next, we prove that the proposed objective in Eq. 9 exactly matches our optimization goal in Eq. 8. One preliminary result, proven in [32], is that in high dimensions, Eq. 9 is minimized when " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\epsilon}" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": " is orthogonal at any " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": " up to a global scaling factor " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{K}" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": " (i.e. " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\epsilon} \\cdot \\mathbf{J}_{\\epsilon}^{\\mathrm{T}} = \\mathcal{K} \\cdot \\mathbf{I}" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": "). By applying the orthogonality of " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\mathbf{J}_{\\epsilon}" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": ", we have the following:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 318, + 518, + 545, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 518, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 318, + 518, + 545, + 542 + ], + "type": "interline_equation", + "content": "\\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\mathbf {J} _ {\\epsilon} ^ {- 1} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\frac {\\partial \\boldsymbol {\\epsilon}}{\\partial \\widehat {\\boldsymbol {x} _ {0}}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\Delta \\boldsymbol {\\epsilon}. \\tag {11}", + "image_path": "5d36bfdc95f9f5e8190ef11452f43776d352e0ad551de595aed42f254b7db3e7.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 544, + 525, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 544, + 525, + 557 + ], + "spans": [ + { + "bbox": [ + 306, + 544, + 525, + 557 + ], + "type": "text", + "content": "When " + }, + { + "bbox": [ + 306, + 544, + 525, + 557 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 306, + 544, + 525, + 557 + ], + "type": "text", + "content": " in Eq. 9 reaches its optimal, we then have:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 322, + 560, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 560, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 322, + 560, + 545, + 574 + ], + "type": "interline_equation", + "content": "a = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\mathcal {K} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}. \\tag {12}", + "image_path": "ee0ced1f15ba6b0455fd6b5c83072ebe7084bfadf2089197d2ac27d712091fac.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": "Notice that " + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "a = a\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2" + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": " , since " + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2 = 1" + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": " is the aforementioned random unit length vector. Hence, we can finally reformulate the expression:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 364, + 618, + 545, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 618, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 364, + 618, + 545, + 657 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\right\\| _ {2} = \\frac {\\mathcal {K}}{a} \\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2} \\tag {13} \\\\ = \\mathcal {C} \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\epsilon \\| _ {2}, \\\\ \\end{array}", + "image_path": "9261da756b81aea95375c0e903164415fbe2f63ee796d6492a07e8868a2cad64.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 661, + 529, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 661, + 529, + 672 + ], + "spans": [ + { + "bbox": [ + 305, + 661, + 529, + 672 + ], + "type": "text", + "content": "which exactly matches our proposed objective in Eq. 8." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "type": "text", + "content": "To summarize, during training, the Smooth Diffusion objective encompasses a combination of " + }, + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{base}}" + }, + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 304, + 673, + 545, + 697 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 383, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 383, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {b a s e}} + \\lambda \\mathcal {L} _ {\\text {r e g}}, \\tag {14}", + "image_path": "d35880fbd33e41f4ff834ba3f01e518635a2f6c0c87d942957b8a803987a6d9a.jpg" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7551" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 76, + 73, + 519, + 277 + ], + "blocks": [ + { + "bbox": [ + 76, + 73, + 519, + 277 + ], + "lines": [ + { + "bbox": [ + 76, + 73, + 519, + 277 + ], + "spans": [ + { + "bbox": [ + 76, + 73, + 519, + 277 + ], + "type": "image", + "image_path": "ae97956fef2e9c401807af508e6c4a441f9a97fb1e0044d0ca44e4ed01668be8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 284, + 547, + 329 + ], + "lines": [ + { + "bbox": [ + 46, + 284, + 547, + 329 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 547, + 329 + ], + "type": "text", + "content": "Figure 3. Image interpolation comparison results. For Smooth Diffusion and Stable Diffusion [62], real images (Image A and B) are inverted into latents using NTI [44]. We perform spherical linear interpolations between latents (also known as Stable Diffusion Walk [29]) and concatenate the resulting images as a transition sequence. VAE Inter. performs interpolations within the VAE space of Stable Diffusion. ANID [78] first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "type": "text", + "content": " denotes the basic training objective of a diffusion model and " + }, + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 338, + 288, + 374 + ], + "type": "text", + "content": " represents a ratio parameter controlling the intensity of Step-wise Variation Regularization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 382, + 128, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 128, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 128, + 396 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 403, + 163, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 163, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 163, + 415 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 420, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 564 + ], + "type": "text", + "content": "Baselines and settings. We select the Stable Diffusion [62] as the primary baseline for all tasks. Additionally, for image interpolation, we adopt a VAE-space interpolation and ANID [78] as competitors. For image inversion, we integrate Smooth Diffusion and Stable Diffusion with DDIM inversion [71] and Null-text inversion [44]. For text-based image editing, SDEdit [42], Prompt-to-Prompt (P2P) [21], Plug-and-Play (PnP) [75], Diffusion Disentanglement (Disentangle) [82], Pix2Pix-Zero [55] and Cycle Diffusion [81] are chosen as SOTA approaches. For drag-based image editing, we compare Smooth Diffusion with Stable Diffusion within the framework of DragDiffusion [69]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Implementation details. Smooth Diffusion is trained atop pretrained Stable Diffusion-V1.5 [62], using LoRA [25] finetuning technique. The UNet of Smooth Diffusion is set as trainable with a LoRA rank of 8, while the VAE and text encoder are frozen. We leverage the LAION Aesthetics " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "6.5+" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " as the training dataset, which contains 625K image-text pairs with predicted aesthetics scores of 6.5 or higher from LAION-5B [67]. Smooth diffusion is typically trained for 30K iterations with a batch size of 96, 3 samples per GPU, a total of 4 A100 GPUs, and a gradient accumulation of 8. The AdamW [35] optimizer is adopted with a constant learning rate of " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " and a weight decay of " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 338, + 545, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 338, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 338, + 545, + 374 + ], + "type": "text", + "content": "The ratio parameter " + }, + { + "bbox": [ + 304, + 338, + 545, + 374 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 338, + 545, + 374 + ], + "type": "text", + "content": " in Eq. 14 is set to 1. During inference, the total number of diffusion steps is set to 50 and the classifier-free guidance [23] scale is set to 7.5." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 380, + 546, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 546, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 546, + 632 + ], + "type": "text", + "content": "Evaluation metrics. To evaluate the general text-to-image generation performance, we report the popular FID [22] and CLIP Score [58] on the MS-COCO validation set [38]. To assess the latent space smoothness, we propose an interpolation standard deviation (ISTD) as an evaluation metric. In specific, we randomly draw 500 text prompts from the MS-COCO validation set. For each prompt, we sample a pair of Gaussian noises and uniformly interpolate them from one to the other 9 times with mix ratios from 0.1 to 0.9. Fed into diffusion models together with a prompt, we could obtain a total of 11 generated images, 2 from the source Gaussian noises and 9 from the interpolated noises. We calculate the standard deviation of L2 distances between every two adjacent images in the pixel space. Finally, we average the standard deviations over 500 prompts as ISTD. Ideally, a zero value of ISTD indicates that consistent and uniform visual fluctuations in the pixel space for identical fixed-size changes in the latent space, resulting in a smooth latent space. For image inversion, mean square error (MSE), LPIPS [93], SSIM [79] and PSNR [27] are adopted to evaluate the image reconstruction capability." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 645, + 455, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 645, + 455, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 645, + 455, + 658 + ], + "type": "text", + "content": "4.2. Latent Space Interpolation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 715 + ], + "type": "text", + "content": "Qualitative comparison. The most straightforward way to demonstrate the smoothness of the latent space is through the observation of interpolation results between latent noises. In Fig. 3, we present interpolation compa" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7552" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "isons between Smooth Diffusion and Stable Diffusion using real images. To generate these comparisons, we utilize the NTI [44] to invert a pair of real images into latent noises " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_T" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": ", sharing the same " + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "inline_equation", + "content": "\\{\\varnothing_t\\}_{t=1}^T" + }, + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": ". We then perform uniform spherical linear interpolations between latent noises (also known as Stable Diffusion Walk [29]), resulting in 9 intermediate noises with mix ratios from 0.1 to 0.9. Subsequently, we concatenate the 11 images produced from these noises to create an image transition sequence in the figures." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 181, + 287, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 301 + ], + "type": "text", + "content": "Notably, as highlighted by the red boxes, Stable Diffusion exhibits significant visual fluctuations during the transition. In particular, the interpolated images may introduce new attributes that are unrelated to the source images, e.g., the undesired grasslands in the second row of Fig. 3. In contrast, our approach, Smooth Diffusion, not only avoids introducing obvious irrelevant attributes in the interpolated images but also ensures that the visual effects change smoothly throughout the transition. Additional interpolation results can be seen in supplementary materials." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 302, + 288, + 458 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 288, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 288, + 458 + ], + "type": "text", + "content": "In addition to Stable Diffusion, Fig. 3 also includes two other baseline methods for comparison: 1) VAE Interpolation (VAE Inter.), which performs interpolations within the VAE space of Stable Diffusion. However, the results closely resemble pixel-space interpolations, with significant degradation of visual details, particularly in the highlighted red box area. 2) ANID [78], which first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. In Fig. 3, ANID with a 50-step scheduler exhibits highly blurred interpolation results. When ANID operates with a default 200-step scheduler, the blurring can be alleviated, but the quality of the interpolated images remains far from satisfactory." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 51, + 467, + 282, + 514 + ], + "blocks": [ + { + "bbox": [ + 51, + 467, + 282, + 514 + ], + "lines": [ + { + "bbox": [ + 51, + 467, + 282, + 514 + ], + "spans": [ + { + "bbox": [ + 51, + 467, + 282, + 514 + ], + "type": "table", + "html": "
MethodISTD (↓)FID (↓)CLIP Score (↑)
Stable Diffusion38.6312.7031.46
Smooth Diffusion16.5412.1031.54
", + "image_path": "db48c92c2e65abcef8e21fa658644696fea28e654345394485913daf74b7f049.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Quantitative comparison. The goal of Smooth Diffusion is to enhance the latent space smoothness without image generation performance degradation compared to Stable Diffusion. In pursuit of this goal, we employ the ISTD introduced in Sec. 4.1 to evaluate the latent space smoothness. Additionally, we utilize FID [22] and CLIP Score [58] to assess generators' overall performance. The results presented in Tab. 1 demonstrate that Smooth Diffusion significantly outperforms Stable Diffusion in terms of ISTD, indicating a substantial improvement in the latent space smoothness. Furthermore, Smooth Diffusion exhibits superior performance in both FID and CLIP Score, suggesting that the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 347, + 73, + 502, + 80 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 73, + 502, + 80 + ], + "spans": [ + { + "bbox": [ + 347, + 73, + 502, + 80 + ], + "type": "text", + "content": "\"A man using his laptop computer while a cat sits on his lap\"" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 318, + 80, + 531, + 123 + ], + "blocks": [ + { + "bbox": [ + 318, + 80, + 531, + 123 + ], + "lines": [ + { + "bbox": [ + 318, + 80, + 531, + 123 + ], + "spans": [ + { + "bbox": [ + 318, + 80, + 531, + 123 + ], + "type": "image", + "image_path": "f5539feab45d8d5b4e8001fbed5189398141e688cec7f9e65a71b6d475cd7a2b.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 371, + 123, + 476, + 130 + ], + "lines": [ + { + "bbox": [ + 371, + 123, + 476, + 130 + ], + "spans": [ + { + "bbox": [ + 371, + 123, + 476, + 130 + ], + "type": "text", + "content": "\"A large tower that has a big clock at top" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 318, + 129, + 532, + 172 + ], + "blocks": [ + { + "bbox": [ + 318, + 129, + 532, + 172 + ], + "lines": [ + { + "bbox": [ + 318, + 129, + 532, + 172 + ], + "spans": [ + { + "bbox": [ + 318, + 129, + 532, + 172 + ], + "type": "image", + "image_path": "2b1f88ee370d4360c76f1e4dda4efdd708aa893003f2298ab26feecaf588a3cb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 343, + 172, + 507, + 178 + ], + "lines": [ + { + "bbox": [ + 343, + 172, + 507, + 178 + ], + "spans": [ + { + "bbox": [ + 343, + 172, + 507, + 178 + ], + "type": "text", + "content": "\"A room with a couch, table set with dinnerware and a television\"" + } + ] + } + ], + "index": 10, + "angle": 0, + 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[ + { + "bbox": [ + 449, + 229, + 487, + 235 + ], + "spans": [ + { + "bbox": [ + 449, + 229, + 487, + 235 + ], + "type": "text", + "content": "+DDIM (Ours)" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 501, + 222, + 522, + 229 + ], + "lines": [ + { + "bbox": [ + 501, + 222, + 522, + 229 + ], + "spans": [ + { + "bbox": [ + 501, + 222, + 522, + 229 + ], + "type": "text", + "content": "able Diff" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 500, + 229, + 521, + 235 + ], + "lines": [ + { + "bbox": [ + 500, + 229, + 521, + 235 + ], + "spans": [ + { + "bbox": [ + 500, + 229, + 521, + 235 + ], + "type": "text", + "content": "+DDIM" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 237, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 306, + 237, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 306, + 237, + 545, + 270 + ], + "type": "text", + "content": "Figure 4. Image reconstruction comparison results. We integrate Smooth Diffusion and Stable Diffusion [62] with NTI [44] (column 2 & 3) and DDIM inversion [71] (column 4 & 5)." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 308, + 279, + 544, + 350 + ], + "blocks": [ + { + "bbox": [ + 46, + 518, + 287, + 562 + ], + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 562 + ], + "type": "text", + "content": "Table 1. Quantitative evaluations of image interpolation and text-to-image generation. We evaluate Smooth Diffusion and Stable Diffusion [62] with ISTD, FID [22] and CLIP Score [58]. The better results are in bold." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 279, + 544, + 350 + ], + "lines": [ + { + "bbox": [ + 308, + 279, + 544, + 350 + ], + "spans": [ + { + "bbox": [ + 308, + 279, + 544, + 350 + ], + "type": "table", + "html": "
MethodMSE (↓)LPIPS (↓)SSIM (↑)PSNR (↑)
Stable Diff. + DDIM0.17560.53850.266213.97
Smooth Diff. + DDIM0.10860.43260.341816.17
Stable Diff. + NTI0.01560.16560.606825.63
Smooth Diff. + NTI0.01530.16350.610225.74
VAE Reconstruction0.01480.15900.613625.98
", + "image_path": "5c89efb59942b5e912a76895a8b43de3bc0f359ed4f737e87bfbf88a76d5f79f.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "table_body" + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 356, + 545, + 411 + ], + "lines": [ + { + "bbox": [ + 305, + 356, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 545, + 411 + ], + "type": "text", + "content": "Table 2. Quantitative evaluations of image reconstruction. We integrate Stable Diffusion and Smooth Diffusion [62] with DDIM inversion [71] (row 2 & 3) and NTI [44] (row 4 & 5). MSE, LPIPS [93], SSIM [79] and PSNR [27] are evaluated. VAE Reconstruction results are provided as the optimal values." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 420, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 420, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 420, + 545, + 468 + ], + "type": "text", + "content": "enhancement of latent space smoothness and the overall image generation quality are not mutually exclusive but complement each other when the regularization term is applied with a suitable strength ratio." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 478, + 499, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 499, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 499, + 491 + ], + "type": "text", + "content": "4.3. Image Inversion and Reconstruction" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "type": "text", + "content": "Previous research [32] in the realm of GANs discovered that a smoother latent space has a positive impact on the accuracy of image inversion and reconstruction. We empirically validate this finding within the context of diffusion models. In specific, two representative inversion techniques, DDIM inversion [71] and Null-text inversion (NTI) [44] are adopted and integrated with Smooth Diffusion and Stable Diffusion separately. We both qualitatively and quantitatively compare the image inversion and reconstruction performance of these integrated models using 500 randomly sampled images from the MS-COCO validation set [38]." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "As illustrated in the two rightmost columns of Fig. 4, when employing a straightforward DDIM inversion, Smooth Diffusion outperforms Stable Diffusion by a considerable margin in terms of reconstruction quality. This improvement is evident in various aspects, such as an accurate generation of character identities, a faithful recreation of the city view behind the tower, and a correct reproduc" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7553" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 119, + 79, + 164, + 125 + ], + "blocks": [ + { + "bbox": [ + 77, + 94, + 119, + 111 + ], + "lines": [ + { + "bbox": [ + 77, + 94, + 119, + 111 + ], + "spans": [ + { + "bbox": [ + 77, + 94, + 119, + 111 + ], + "type": "text", + "content": "Local Edit (Replace Item)" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + 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This phenomenon underscores the fact that the latent space of Smooth Diffusion is more tolerant of the errors introduced by the local linear approximation in DDIM inversion. Consequently, the reconstruction results produced by Smooth Diffusion manage to retain the contents of the source images to a greater extent. On the other hand, when the optimization-based NTI technique is employed, the disparity between Smooth Diffusion and Stable Diffusion is not as pronounced. Nonetheless, there are still instances where Stable Diffusion exhibits subpar results, such as the ruined man's face in Fig. 4." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 287, + 555 + ], + "type": "text", + "content": "To quantify the image reconstruction performance, MSE, LPIPS [93], SSIM [79] and PSNR [27] are reported in Tab. 2. Notably, the reconstruction error encompasses two components: 1) the error from different inversion methods and U-Net parameters and 2) the error from the shared pretrained VAE [36]. Hence, we included the VAE reconstruction errors as optimal values for our method. The results exhibit a consistent outperformance of Smooth Diffusion over Stable Diffusion across all metrics, whether using DDIM inversion or NTI. Moreover, \"Smooth Diffusion + NTI\" performs results close to VAE reconstruction, indicating its superiority attributed to a smoother latent space." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 47, + 567, + 137, + 579 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 137, + 579 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 137, + 579 + ], + "type": "text", + "content": "4.4. Image Editing" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 46, + 586, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 647 + ], + "type": "text", + "content": "The superiority of Smooth Diffusion in image inversion and reconstruction has motivated us to explore its potential for enhancing image editing tasks. In this section, we delve into two typical image editing scenarios: text-based image editing and drag-based image editing." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "Text-based image editing. There have been numerous methods [21, 42, 55, 75, 81, 82] proposed in the literature, each with its own unique designs aimed at achieving the SOTA performance. In contrast, we adopt a simpler pipeline akin to the image inversion and reconstruction pro" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "content": "cess discussed in Sec. 4.3. The key distinction lies in our approach to modify the text prompt during the later time steps of the reconstruction process. In specific, the original " + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\mathcal{C},\\varnothing_t)" + }, + { + "bbox": [ + 305, + 277, + 545, + 338 + ], + "type": "text", + "content": " in Eq. (5) during NTI reconstruction (diffusion sampling) process is replaced with:" + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 313, + 342, + 545, + 374 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 342, + 545, + 374 + ], + "spans": [ + { + "bbox": [ + 313, + 342, + 545, + 374 + ], + "type": "interline_equation", + "content": "\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C}, \\varnothing_ {t}\\right) = \\left\\{ \\begin{array}{l} \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {s r c}}, \\varnothing_ {t}\\right), t > T \\times r, \\\\ \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {t r g}}, \\varnothing_ {t}\\right), t \\leq T \\times r, \\end{array} \\right. \\tag {15}", + "image_path": "d82ed138564460ae691ea7b36c94e79eb00864f2f522a3382dfa40faefcc53df.jpg" + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathrm{src}}" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " represents the source text prompt for inversion, while " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathrm{trg}}" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " corresponds to the target text prompt for editing. The parameter " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " serves as a threshold, determining when to switch from " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathrm{src}}" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{C}_{\\mathrm{trg}}" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": ". In practice, " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": " is typically chosen within " + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\{0.6, 0.7, 0.8, 0.9\\}" + }, + { + "bbox": [ + 305, + 378, + 545, + 449 + ], + "type": "text", + "content": ", with the exact value depending on the specific input images and target visual effects." + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 451, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 546, + 713 + ], + "type": "text", + "content": "Through this straightforward pipeline, we conducted a comparative analysis of the editing performance between Smooth Diffusion and Stable Diffusion, as presented in the three left-most columns of Fig. 5. We also included editing results obtained from SOTA methods as references. Our evaluation encompasses both local and global editing tasks. The local editing tasks involve replacing items (e.g., changing \"cream\" to \"strawberries\") and adding items (e.g., \"apple\"). On the other hand, the global editing tasks pertain to global style transfer, such as transforming an image into a \"cartoon style\". It is evident that while Stable Diffusion excels in achieving precise image reconstruction with NTI, as discussed in Sec. 4.3, even minor modifications to the text prompt can significantly impact the content of the generated images. For instance, it can affect elements like the style of the cake, the shape of the banana, and the haircut of the girl. In contrast, Smooth Diffusion not only accurately generates edited images in accordance with the target text prompts but also effectively preserves the unedited contents. Furthermore, when compared to SOTA methods, even with this straightforward pipeline, Smooth Diffusion consistently delivers competitive results across all cases." + } + ] + } + ], + "index": 48 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7554" + } + ] + } + ], + "index": 49 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 72, + 260, + 243 + ], + "blocks": [ + { + "bbox": [ + 70, + 72, + 260, + 243 + ], + "lines": [ + { + "bbox": [ + 70, + 72, + 260, + 243 + ], + "spans": [ + { + "bbox": [ + 70, + 72, + 260, + 243 + ], + "type": "image", + "image_path": "7841f881951452a64d3834f27f00765f86b6308cf1d148483b0328cbbd5aeaea.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 248, + 287, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 283 + ], + "type": "text", + "content": "Figure 6. Drag-based image editing comparison results. We implement Smooth Diffusion and Stable Diffusion [62] within the framework of DragDiffusion [69], respectively." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 290, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 289, + 469 + ], + "type": "text", + "content": "Drag-based image editing. As an emerging research avenue in the community, drag-based image editing [45, 53, 69] has garnered considerable attention recently. DragDiffusion [69] first introduces a framework for drag-based image editing employing Stable Diffusion. In the task 3 of Fig. 1 and Fig. 6, we showcase that by integrating Smooth Diffusion into the DragDiffusion framework, some previously unsuccessful editing operations with Stable Diffusion can be enabled. As illustrated, Smooth Diffusion achieves operations such as making the tree grow taller without damaging existing branches (Fig. 1), rotating the cat head, creating a new mountain top without destroying the original one, and letting new flowers grow in the vase (Fig. 6). These operations, however, fail with Stable Diffusion, indicating the non-smoothness of its latent space." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 479, + 148, + 490 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 148, + 490 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 148, + 490 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": "Regularization ratio. In Tab. 3, we examine the impact of different strength ratios " + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": " in Eq. (14). This ratio adjusts the intensity of the step-wise variation regularization. Specifically, when a weaker regularization is applied (e.g., " + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\lambda = 0.1" + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": "), we observe a slight improvement in the CLIP Score. However, there is a significant increase in ISTD, indicating a notable degradation in latent space smoothness. In contrast, employing a stronger regularization (e.g., " + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\lambda = 10" + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": ") leads to a smoother latent space, as demonstrated by the decrease in ISTD. However, in this case, we observe an unexpected increase in FID, indicating a notable decline in the quality of generated images. Therefore, selecting an appropriate trade-off value for " + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": " becomes crucial based on the specific experimental settings. In our default setting, we find that " + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\lambda = 1" + }, + { + "bbox": [ + 46, + 498, + 287, + 676 + ], + "type": "text", + "content": " serves as a suitable value." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "LoRA rank. In Tab. 4, we examine the impact of different ranks of the LoRA component utilized in our Smooth diffusion. We discover that LoRA ranks within the range" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 324, + 70, + 526, + 127 + ], + "blocks": [ + { + "bbox": [ + 324, + 70, + 526, + 127 + ], + "lines": [ + { + "bbox": [ + 324, + 70, + 526, + 127 + ], + "spans": [ + { + "bbox": [ + 324, + 70, + 526, + 127 + ], + "type": "table", + "html": "
RatioISTD (↓)FID (↓)CLIP Score (↑)
0.124.2312.1531.56
1 (default)16.5412.1131.49
1011.5117.4431.41
", + "image_path": "ce5c0e13f6a3e63ef2da5e690c8df5274a83585e05526010b63597da914c3699.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 159, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 291 + ], + "type": "text", + "content": "of [4,16] are all suitable values for our default setting. We select a default rank of 8 because of its lowest ISTD among the first three rows in Tab. 4. Furthermore, we train a fully finetuned model, referred to as \"full,\" which showcases a further decrease in ISTD. However, this comes at the expense of significantly degrading the quality of the generated images, as indicated by an increased FID and decreased CLIP Score. This decline in performance underscores the vulnerability of fully fine-tuned models to collapse within our default setting, emphasizing the need for additional meticulous design considerations." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 323, + 297, + 526, + 365 + ], + "blocks": [ + { + "bbox": [ + 305, + 133, + 545, + 155 + ], + "lines": [ + { + "bbox": [ + 305, + 133, + 545, + 155 + ], + "spans": [ + { + "bbox": [ + 305, + 133, + 545, + 155 + ], + "type": "text", + "content": "Table 3. Ablation results of different regularization ratios. The best results are in bold, and the second-best results are underlined." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 297, + 526, + 365 + ], + "lines": [ + { + "bbox": [ + 323, + 297, + 526, + 365 + ], + "spans": [ + { + "bbox": [ + 323, + 297, + 526, + 365 + ], + "type": "table", + "html": "
RankISTD (↓)FID (↓)CLIP Score (↑)
416.7612.3631.49
8 (default)16.5412.1131.54
1616.6511.4931.61
full11.5227.2728.86
", + "image_path": "8e9e24e6f7fe5ca536eab5aa5b7c741eeff0a904405349225cc554009ea7b65e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 371, + 545, + 392 + ], + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 392 + ], + "type": "text", + "content": "Table 4. Ablation results of different LoRA ranks. The best results are in bold, and the second-best results are underlined." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 400, + 378, + 412 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 378, + 412 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 378, + 412 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 420, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 601 + ], + "type": "text", + "content": "In this article, we explored Smooth Diffusion, an innovative diffusion model that enhances latent space smoothness for generation. Smooth Diffusion adopts the novel Stepwise Variation Regularization, which successfully maintains variation between arbitrary input latent and generated images at a more bounded range. Smooth Diffusion was trained on top of the prevailing text-to-image model, from which we carried out extensive research, including but not limited to interpolation, inversion, and editing, all of which had shown competitive performance. Through qualitative and quantitative measurements, we demonstrated that Smooth Diffusion managed to make a smoother latent space without compromising the output quality. We believe that Smooth Diffusion will become a valuable solution for other challenging tasks, such as video generation, in the future." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 609, + 408, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 408, + 623 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 408, + 623 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "This work is supported in part by the ML Center at Georgia Tech, NSF CAREER Award #2239840, and the National AI Institute for Exceptional Education (Award #2229873) by National Science Foundation and the Institute of Education Sciences, U.S. Department of Education. Huang is in part supported by the National Key R&D Program (#2021ZD0140407) and NSFC (62321005 & 42327901)." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7555" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. 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In ECCV, 2020. 3" + } + ] + } + ], + "index": 32 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7558" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_content_list.json b/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e6bf41248599604dd33c33766ad1eda4c48efa4d --- /dev/null +++ b/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_content_list.json @@ -0,0 +1,1876 @@ +[ + { + "type": "text", + "text": "SnAG: Scalable and Accurate Video Grounding", + "text_level": 1, + "bbox": [ + 241, + 130, + 727, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fangzhou Mu*, Sicheng Mo*, Yin Li \nUniversity of Wisconsin-Madison", + "bbox": [ + 336, + 180, + 630, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 255, + 313, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability — they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is $43\\%$ more accurate and $1.5 \\times$ faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos. Our code is available at https://github.com/fmu2/snag_release.", + "bbox": [ + 75, + 287, + 473, + 561 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 590, + 209, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Localizing moments within an untrimmed video based on text descriptions, also known as temporal video grounding, involves joint reasoning about visual, textual and temporal information, and thus remains a challenging problem in video understanding. Video grounding is gaining traction amid the rapid advances in vision-language learning, with a range of applications such as intelligent personal assistants, human-robot interaction, and interactive video editing.", + "bbox": [ + 75, + 616, + 468, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite recent progress, one largely overlooked aspect of video grounding is the scalability of models with respect to video duration and the number of text descriptions (i.e., queries). Previous methods (e.g., [46, 67]) are primarily designed for grounding only a few queries within short video snippets. However, the growing availability of long videos (e.g., on streaming platforms) and demand to query their rich contents introduce a paradigm shift, necessitating efficient grounding of large volumes of queries in long videos.", + "bbox": [ + 75, + 739, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b9a807416c0ebc2e4ad55975342dc123777b8a8af446635bc0de09fcd6219e94.jpg", + "image_caption": [ + "Figure 1. SnAG achieves the best accuracy and throughput simultaneously on the MAD dataset [45] for long-form video grounding." + ], + "image_footnote": [], + "bbox": [ + 558, + 257, + 828, + 426 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "On latest long-form video grounding benchmarks [16, 45], these methods struggle to scale up due to their high computational cost, and suffer major performance degradation.", + "bbox": [ + 496, + 472, + 890, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we take a principled approach to studying the problem of scalable video grounding, focusing on the design of cross-modal fusion—a key model component that combines visual and textual information. Specifically, we present an analysis that connects the computational cost of video grounding models to their fusion schemes. Our analysis and empirical results challenge the widely adopted early fusion, showing that late fusion scales better in inference by amortizing the cost of long video processing among text queries. Importantly, this insight further motivates the design of a novel, video-centric sampling scheme for scalable training, without compromising grounding accuracy.", + "bbox": [ + 496, + 520, + 892, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Following these findings, we present SnAG, a scalable and accurate model for long-form video grounding. SnAG features a minimalist, late-fusion design for scalable inference, while supporting video-centric sampling for scalable training. Notwithstanding its simplicity, SnAG achieves superior results across all benchmarks designed for long-form video grounding. Without bells and whistles, SnAG attains $13.75\\%$ R@5, tIoU=0.5 on MAD [45] with an inference speed of 45.3 queries per second on a P100 GPU (Fig. 1), $43\\%$ more accurate and $1.5\\times$ faster than the concurrent method of CONE [17]. In the meantime, SnAG is highly competitive on short-video benchmarks. It achieves $46.26\\%$ R@1, tIoU=0.7 on Charades-STA [43], outperforming the", + "bbox": [ + 496, + 703, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* indicates equal contribution", + "bbox": [ + 101, + 887, + 261, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18930", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "previous state of the art (SSRN [71]) by 3.61 absolute percentage points while being simpler in model design.", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. (1) We present one of the first studies to understand the effect of fusion schemes on the computational cost of video grounding. (2) Our analysis offers new insights and leads to a new training scheme for scalable video grounding. (3) Based on our findings, we further deliver a simple model that attains superior results across major benchmarks for long-form video grounding while achieving significant efficiency gains in both training and inference.", + "bbox": [ + 75, + 127, + 470, + 250 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 266, + 218, + 282 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video grounding. Previous works on video grounding can be categorized based on whether proposals are generated as moment candidates (two-stage vs. single-stage), and how text queries inform action localization (cross-modal fusion).", + "bbox": [ + 75, + 292, + 468, + 353 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Two-stage methods first generate temporal segments as proposals, then score their \"actionness\" and optionally refine their boundaries. Early works [1, 13] densely sample proposals using sliding windows and score them independently. One line of work [8, 28, 54-56] subsequently conditions proposal generation on sentence queries and/or video context to avoid dense sampling. By contrast, another line of work [14, 46, 50, 66, 67] takes the opposite path of enumerating all segments, yet organizes them in a 2D adjacency map to reason about their relations.", + "bbox": [ + 75, + 354, + 468, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Single-stage methods localize moments in a single shot without using proposals, and thus are often more efficient than two-stage methods. Some models decode moment boundaries from global features [23, 24, 33, 59, 70] or learnable queries [21, 25, 53]. Others densely predict onset and offset probabilities [15, 29, 34, 41, 63-65, 68], or classify and refine pre-set anchors [6, 30, 51, 58, 62] at every moment. Most relevant to our work are models that represent moment candidates as points [7, 11, 27, 31, 60]. Analogous to point-based object detectors [47], they classify every point in time and regress moment boundaries relative to the points. Despite their simplicity and efficiency, the performance of single-stage models lags behind two-stage models on standard benchmarks made up of short videos.", + "bbox": [ + 75, + 506, + 468, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Cross-modal fusion combines video and text information for video grounding. Early models [1, 13] fuse video and text representations right before final prediction. This simple, late-fusion approach is abandoned by subsequent models, which turn to early fusion (e.g., [56, 60, 62, 67]) with sophisticated model design (e.g., LSTM [6, 15, 29, 51, 56, 65], GCN [7, 27, 46], memory bank [8, 27]), feature hierarchies [14, 33, 50], losses [23, 34, 56, 66], and inference procedures [68, 70]. Early fusion is believed to strengthen cross-modal reasoning, albeit at a price of model complexity. Recent Transformer-based models [3, 21, 53, 66] inherit this early-fusion design; video features and text embeddings", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "are concatenated at input, and attention-based feature fusion is carried out throughout the model.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our method demonstrates a single-stage Transformer model with a simple late fusion mechanism based on crossattention. Late fusion allows us to amortize the cost of video processing across many sentence queries, resulting in scalable training and inference on long-form videos. Without bells and whistles, our model outperforms all prior methods on long-video benchmarks, and attains competitive performance on standard, short-video benchmarks.", + "bbox": [ + 496, + 122, + 890, + 242 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Long-form video grounding. Recent efforts [16, 45] put forth new challenges for sentence grounding in long videos. Previous methods tailored for short videos [46, 64, 67] fall short on these benchmarks. They have no access to long-range video context, require dense sliding window inference, and yield unsatisfactory results. Concurrent works [17, 36] present multi-stage approaches with sophisticated pre-processing, ranking and training procedures for efficient long-form video grounding. However, their efficiency stems from the restrictive assumption that moments are covered by short windows. By contrast, SnAG offers a simple, single-stage solution with superior accuracy, without making assumptions about moment duration.", + "bbox": [ + 496, + 250, + 890, + 445 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Localizing moments in videos. Closely related to video grounding, temporal action localization (e.g., [32, 42, 44]) aims to identify moments of actions from within a closed set of action categories. Solutions to the two tasks often evolve in tandem and share remarkably similar model design. SnAG is inspired by our prior work [61], yet extends its design for the more challenging task of video grounding, with the goal of scaling up video grounding for long videos.", + "bbox": [ + 496, + 450, + 890, + 573 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Scaling Up Video Grounding", + "text_level": 1, + "bbox": [ + 500, + 589, + 766, + 607 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our goal is to scale up video grounding for long-form videos with many queries. Denote an input video $\\mathbf{V}$ as a time-indexed sequence $[\\mathbf{v}_t]_{t=1}^T = [\\mathbf{v}_1, \\mathbf{v}_2, \\dots, \\mathbf{v}_T]$ , where $\\mathbf{v}_t$ represents a short video clip centered at time $t$ .1 $\\mathbf{V}$ is paired with $N$ sentence queries $\\{\\mathrm{Q}_j\\}_{j=1}^N$ , each describing a moment $\\mathbf{y}_j = (s_j, e_j)$ in the video.", + "bbox": [ + 496, + 616, + 890, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Long-form video grounding is characterized by a great number of time steps $T$ (e.g., tens of thousands) and text queries $N$ (hundreds) for an input video $\\mathbf{V}$ . With a large $T$ , it is no longer feasible to feed the full video $\\mathbf{V}$ into a model, and thus more viable to consider a sliding window setting. Specifically, a video $\\mathbf{V}$ is further partitioned into a set of $M$ snippets $\\{\\mathbf{V}_{i=1}^{M}\\}$ , each $\\mathbf{V}_{i} = [\\mathbf{v}_{t}]_{t=t_{i}}^{t_{i} + T_{w}}$ taken from a local time window of size $T_{w}$ that may overlap with others. We consider the learning of a function $\\mathcal{F}$ , realized in a deep", + "bbox": [ + 496, + 712, + 890, + 849 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1Like prior works, we consider video features and text embeddings extracted using pre-trained models (e.g., C3D [48] and BERT [10]). Yet the formulation can be easily extended to raw video frames and text tokens.", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18931", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/4803639b0a1f16039b839ad918d58e34425082f99caff1fafa9a2122313a6aae.jpg", + "image_caption": [ + "Figure 2. (a) Cross-modal fusion is key to a video grounding model $\\mathcal{F}$ . Models using early fusion jointly encode video and sentence query. SnAG revisits late fusion for scalable video grounding by decoupling expensive video encoding and inexpensive query encoding. (b) Video-centric model evaluation. With late fusion, the output of video encoder can be cached and re-used by queries of the same video in both training and inference. (c) Mini-batch sampling in training. Previous methods adopt query-centric sampling (query $\\rightarrow$ video) whereas SnAG resorts to video-centric sampling (video $\\rightarrow$ many queries) for efficient training. (d) Model overview. SnAG is a simple instantiation of late fusion and video-centric training for video grounding. It separately encodes a video and its queries using Transformers, applies simple cross-attention for cross-modal fusion, and decodes moments represented as points using lightweight convolutional heads." + ], + "image_footnote": [], + "bbox": [ + 83, + 93, + 387, + 296 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/24f620b34609b9f3f19062804931b668980e1121d4689609c7c691dd26f796f2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 398, + 93, + 578, + 296 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2ae59873afb84ef2c5185ee19976e539c33b58e59f038c76a8a3cd9d0b114779.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 588, + 93, + 887, + 296 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "network, to predict the start time $s_j$ and end time $e_j$ of the moment $\\mathbf{y}_j$ given a snippet $\\mathbf{V}_i$ and a query $\\mathrm{Q}_j$ .", + "bbox": [ + 75, + 417, + 468, + 448 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Background: Cross-Modal Fusion", + "text_level": 1, + "bbox": [ + 76, + 455, + 375, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We review cross-modal fusion - a key design choice of $\\mathcal{F}$ and define the notation used for the rest of the paper.", + "bbox": [ + 75, + 479, + 468, + 510 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Early fusion. A straightforward design is to fuse information from a video snippet $\\mathbf{V}_i$ and a text query $\\mathrm{Q}_j$ at input (Fig. 2(a)). This early fusion strategy is widely adopted in prior works [21, 53, 60, 62, 66, 67], and can be written as", + "bbox": [ + 75, + 513, + 468, + 573 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {E} \\left(\\mathbf {V} _ {i}, \\mathrm {Q} _ {j}\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 585, + 468, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mapsto$ defines any necessary post-processing of the model outputs (e.g., re-scaling, non-maximum suppression) in order to decode the moment $\\mathbf{y}_j$ .", + "bbox": [ + 75, + 613, + 468, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Late fusion. Another possible design is to first embed the video snippet $\\mathbf{V}_i$ and text query $\\mathrm{Q}_j$ , then fuse their features for grounding (Fig. 2(a)). This late fusion strategy follows", + "bbox": [ + 75, + 661, + 468, + 707 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {L} \\left(g \\left(\\mathbf {V} _ {i}\\right), h \\left(\\mathrm {Q} _ {j}\\right)\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 718, + 468, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $g(\\cdot)$ is the video encoder and $h(\\cdot)$ the text encoder. With slight abuse of the symbols, $\\mathcal{F}_L$ here denotes the rest part of the grounding model, including feature fusion. The key is to keep $\\mathcal{F}_L$ lightweight, i.e., its cost should be a minor portion in comparison to the rest of the model.", + "bbox": [ + 75, + 744, + 468, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Design choice. The conventional wisdom favors the design of early fusion for video grounding. Early fusion is believed to offer better interactions between visual and textual features, resulting in strong empirical results. In what follows, we analyze the computational cost of early and late fusion", + "bbox": [ + 75, + 824, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "during inference and training, and show that proper design of late fusion allows significantly improved scalability in video duration $(M)$ and number of text queries $(N)$ .", + "bbox": [ + 498, + 417, + 890, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Scalable Inference", + "text_level": 1, + "bbox": [ + 500, + 473, + 676, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We start by analyzing the computational cost of early vs. late fusion in inference. Denote the computational cost of a function by $\\mathcal{C}(\\cdot)$ . For example, $\\mathcal{C}(g)$ is the cost of the video encoder $g(\\cdot)$ , and $\\mathcal{C}(h)$ the cost of the text encoder $h(\\cdot)$ .", + "bbox": [ + 498, + 497, + 890, + 558 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Computational cost. We make two key observations regarding the computational cost of a video grounding model: (a) a lightweight $\\mathcal{F}_L$ is used for late fusion, thus $\\mathcal{C}(\\mathcal{F}_L) \\ll \\mathcal{C}(g) + \\mathcal{C}(h)$ ; and (b) the video encoder $g(\\cdot)$ has a much higher cost than the text encoder, thus $\\mathcal{C}(g) \\gg \\mathcal{C}(h)$ .", + "bbox": [ + 498, + 561, + 890, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first observation stems from the design of late fusion. To justify the second observation, it is important to notice that $\\mathcal{C}(g)$ scales w.r.t. the length of input video snippet (i.e., the local window size $T_w$ ), whereas $\\mathcal{C}(h)$ remains constant due to limited sequence length of text queries. For example, a realization of $g(\\cdot)$ using a vanilla Transformer has a complexity of $\\mathcal{O}(T_w^2)$ . Thus, using a larger local window size naturally leads to $\\mathcal{C}(g) \\gg \\mathcal{C}(h)$ .", + "bbox": [ + 496, + 638, + 890, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Cost analysis: early vs. late fusion. Evaluating an early-fusion model on a video with $M$ snippets and $N$ queries has a cost of $MN\\mathcal{C}(\\mathcal{F}_E)$ , whereas late fusion has a cost of $MN\\mathcal{C}(\\mathcal{F}_L) + MC(g) + NC(h)$ . This is because an early-fusion model has to compare each snippet to every query, yet late fusion allows re-using video features for all queries of the video (i.e., video-centric evaluation, see Fig. 2(b)).", + "bbox": [ + 496, + 763, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let us assume that the cost of both models can be controlled by setting $\\mathcal{C}(\\mathcal{F}_E) = \\mathcal{C}(\\mathcal{F}_L) + \\mathcal{C}(g) + \\mathcal{C}(h)$ , i.e., eval", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18932", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "uating either model on a pair of video snippet and sentence query has the same cost (post-processing excluded). With $\\mathcal{C}(\\mathcal{F}_L) = \\alpha (\\mathcal{C}(g) + \\mathcal{C}(h))$ for some small $\\alpha$ , the ratio between the cost of early and late fusion in inference is", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {R} _ {\\text {i n f}} = \\frac {\\mathcal {C} (\\text {i n f e r e n c e w i t h e a r l y f u s i o n})}{\\mathcal {C} (\\text {i n f e r e n c e w i t h l a t e f u s i o n})} (3) \\\\ = \\frac {M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M N \\mathcal {C} (g) + M N \\mathcal {C} (h)}{M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M \\mathcal {C} (g) + N \\mathcal {C} (h)} (4) \\\\ = \\frac {M N (1 + \\alpha)}{M N \\alpha + M \\mathbf {R} _ {g / (g + h)} + N (1 - \\mathbf {R} _ {g / (g + h)})} (5) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{N} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}N,&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&N \\rightarrow \\infty\\end{array}, \\right. (6) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 162, + 468, + 309 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{R}_{g / (g + h)} = \\mathcal{C}(g) / (\\mathcal{C}(g) + \\mathcal{C}(h))$ , and the approximation in Eq. 6 is a result of $\\mathbf{R}_{g / (g + h)} \\approx 1$ with $\\mathcal{C}(g) \\gg \\mathcal{C}(h)$ . Eq. 6 reveals that early fusion is $N$ times the cost of late fusion as snippet length grows ( $\\alpha \\to 0$ ), and is particularly inefficient for videos with many queries ( $N \\to \\infty$ ).", + "bbox": [ + 76, + 320, + 468, + 397 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Scalable Training", + "text_level": 1, + "bbox": [ + 76, + 406, + 250, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now show that late fusion further unlocks a novel training scheme that scales well for long-form video grounding.", + "bbox": [ + 76, + 430, + 468, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training and mini-batch sampling. Given a set of paired videos, text queries, and their moments $\\{\\mathbf{V}^{(k)},\\mathbf{Q}^{(k)},\\mathbf{y}^{(k)}\\}$ , training a model $\\mathcal{F}$ amounts to minimizing a loss function $\\mathcal{L}$ over mini-batches $B$ sampled from the dataset:", + "bbox": [ + 76, + 465, + 468, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma_ {(k, i, j) \\in B} \\mathcal {L} \\left(\\mathcal {F} \\left(\\mathbf {V} _ {i} ^ {(k)}, \\mathrm {Q} _ {j} ^ {(k)}\\right), \\mathbf {y} _ {j} ^ {(k)}\\right). \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 535, + 468, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A key design largely overlooked in video grounding is the mini-batch sampling scheme during training. With multiple queries associated with a video snippet, a combination of late fusion and proper sampling scheme allows us to reuse video representations in training as is done in inference.", + "bbox": [ + 76, + 566, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Query-centric sampling. Virtually all prior works sample mini-batches uniformly at random from all pairs of valid video snippets and text queries. $^{2}$ This can be interpreted as ancestral sampling: first draw a text query (and its moment), then select a video snippet covering the moment:", + "bbox": [ + 76, + 647, + 468, + 723 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathrm {Q} _ {j} ^ {(k)}, \\mathbf {y} _ {j} ^ {(k)}\\right) \\right\\} _ {j \\times k}\\right), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 732, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 758, + 393, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $U(\\cdot)$ denotes a discrete uniform distribution and $\\{(\\mathbf{V}_i^{(k')},\\mathbf{Q}_j^{(k')},\\mathbf{y}_{j'}^{(k')})_{+}\\}$ is the union of all valid triplets: a moment $\\mathbf{y}_{j'}^{(k')}$ of a text query $\\mathbf{Q}_{j'}^{(k')}$ in a video snippet $\\mathbf{V}_i^{(k')}$ .", + "bbox": [ + 76, + 791, + 468, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This sampling process is repeated $|B|$ times to construct a mini-batch, with $|B|$ the batch size. With a large", + "bbox": [ + 76, + 845, + 467, + 876 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "dataset, the resulting mini-batch will contain $|B|$ snippet-query pairs, each likely from a different video.", + "bbox": [ + 500, + 90, + 888, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Video-centric sampling. To speed up the training of late fusion models, we propose video-centric sampling that considers every video snippet $\\mathbf{V}_i^{(k)}$ as a sample. Specifically, we first draw a video based on its importance score, then sample a snippet within the video, and finally select multiple text queries associated with the snippet. This is defined as the following ancestral sampling:", + "bbox": [ + 498, + 125, + 890, + 233 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nk ^ {\\prime} \\sim P (k) = \\frac {M _ {+} ^ {(k)}}{\\Sigma_ {k} M _ {+} ^ {(k)}} \\quad i ^ {\\prime} \\sim P (i; k ^ {\\prime}) = \\frac {N _ {i} ^ {\\left(k ^ {\\prime}\\right)}}{\\Sigma_ {k} N _ {i} ^ {\\left(k ^ {\\prime}\\right)}} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 239, + 890, + 277 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\right\\} ^ {B _ {q}} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 279, + 851, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M_{+}^{(k)}$ denotes the number of valid snippets in a video $\\mathbf{V}^{(k)}$ , and $N_{i}^{(k^{\\prime})}$ the number of queries in a snippet $\\mathbf{V}_{i}^{(k^{\\prime})}$ . Importantly, a total of $B_{q}$ queries are drawn for the selected video snippet $\\mathbf{V}_{i^{\\prime}}^{(k^{\\prime})}$ .", + "bbox": [ + 500, + 311, + 890, + 382 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This sampling process is repeated $|B| / B_q$ times for a mini-batch, leading to $|B| / B_q$ video snippets, each likely from a different video yet with multiple $(B_q)$ text queries. This mini-batch thus allows us to re-use the video representations for the sampled snippets.", + "bbox": [ + 498, + 382, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cost analysis: query-centric vs. video-centric sampling. Fig. 2(c) illustrates the key difference between query-centric and video-centric sampling. Similar to our analysis in Section 3.2, it is easy to show that late fusion combined with video-centric training enables substantial speedup for long snippets $(\\alpha \\rightarrow 0)$ and large $B_{q}$ :", + "bbox": [ + 498, + 460, + 890, + 553 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {R} _ {\\text {t r a i n}} = \\frac {\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {v i d e o - c e n t r i c t r a i n i n g})}{\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {q u e y - c e n t r i c t r a i n i n g})} (10) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{B _ {q}} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}B _ {q},&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&B _ {q} \\rightarrow \\infty\\end{array}. \\right. (11) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 561, + 890, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Scalable Video Grounding: An Instantiation", + "text_level": 1, + "bbox": [ + 500, + 647, + 875, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We now present an instantiation with late fusion and video-centric training for scalable video grounding. Our instantiation, dubbed SnAG, is shown in Fig. 2(d). SnAG is a single-stage Transformer model where every time step represents a moment candidate. It combines (a) a multi-scale Transformer-based video encoder; (b) a Transformer-based text encoder; (c) cross-attentions for late fusion; and (d) convolutional heads for moment decoding.", + "bbox": [ + 498, + 670, + 890, + 791 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Video encoder $g$ . We use the ActionFormer backbone [61] as our video encoder, given its superior performance on the closely related task of temporal action localization. It transforms input video features into a multi-scale representation $[\\mathbf{Z}^{(l)}]_{l=1}^{L} = [\\mathbf{Z}^{(1)}, \\mathbf{Z}^{(2)}, \\dots, \\mathbf{Z}^{(L)}]$ using Transformer layers with local self-attentions [9]. We refer readers to the original paper [61] for more details on model architecture.", + "bbox": [ + 498, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2A video snippet without any query is often discarded during training.", + "bbox": [ + 93, + 886, + 465, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18933", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Text encoder $h$ . Our text encoder is a vanilla Transformer. It takes a query Q with $K$ tokens $[\\mathbf{q}_1, \\dots, \\mathbf{q}_K]$ and outputs their embeddings $\\mathbf{E} = [\\mathbf{e}_1, \\dots, \\mathbf{e}_K]$ . This computation is light compared to video encoding as $K \\ll T_w$ for long videos.", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross-modal late fusion $\\mathcal{F}_L$ . Our model uses a simple variant of cross-attention for fusion. Specifically, it modulates $[\\mathbf{Z}^{(l)}]_{l=1}^L$ with an affine transformation given by $\\mathbf{E}$ :", + "bbox": [ + 76, + 154, + 468, + 200 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} (\\mathbf {W}, \\mathbf {B}) ^ {(l)} = \\operatorname {M C A} (\\operatorname {L N} (\\mathbf {Z} ^ {(l)}), \\operatorname {L N} (\\mathbf {E})), \\\\ \\tilde {\\mathbf {Z}} ^ {(l)} = \\mathbf {W} ^ {(l)} \\odot \\mathbf {Z} ^ {(l)} + \\mathbf {B} ^ {(l)}, \\tag {12} \\\\ \\mathbf {X} ^ {(l)} = \\tilde {\\mathbf {c}} \\odot \\operatorname {M L P} (\\operatorname {L N} (\\bar {\\mathbf {Z}} ^ {(l)})) + \\bar {\\mathbf {Z}} ^ {(l)}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 207, + 468, + 266 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where LN is Layer Normalization [2], MLP is Multi-Layer Perceptron, and MCA is Multi-head Cross-Attention [49], whose output is split into affine weights $\\mathbf{W}^{(l)}$ and biases $\\mathbf{B}^{(l)}$ . $\\tilde{\\mathbf{c}}$ are learnable per-channel scales, and $\\mathbf{X}^{(l)}$ the modulated video representations prior to moment decoding.", + "bbox": [ + 76, + 272, + 468, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Moment decoding. After fusion, our model decodes each time step into a moment candidate, similar to previous video grounding models [7, 27, 31, 60]. Briefly, a classification head predicts a score $p_t^{(l)}$ for all $\\mathbf{x}_t^{(l)}$ within $[\\mathbf{X}^{(l)}]_{l=1}^L$ , and a regression head predicts the normalized distances from $t$ to the moment boundaries $(d_t^s, d_t^e)$ if $\\mathbf{x}_t^{(l)}$ is classified positive. Both heads are lightweight, each comprising three 1D convolutions. The decoded moment $\\hat{\\mathbf{y}} = (\\hat{s}, \\hat{e})$ is given by", + "bbox": [ + 76, + 351, + 468, + 476 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n(t, l) = \\underset {t, l} {\\arg \\max } p _ {t} ^ {(l)}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 484, + 468, + 516 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {s} = 2 ^ {l - 1} \\cdot (t - d _ {t} ^ {s}), \\quad \\hat {e} = 2 ^ {l - 1} \\cdot (t + d _ {t} ^ {e}).\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 517, + 413, + 534 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At inference time, we further apply Soft-NMS [4] to merge overlapping moment predictions.", + "bbox": [ + 76, + 542, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training and loss function. We use video-centric training as described in Section 3.3. The loss function for a pair of video snippet and text query is the sum of two terms: a Focal loss [26] $\\mathcal{L}_{cls}$ for moment classification and a Distance-IoU loss [69] $\\mathcal{L}_{reg}$ defined on positive time steps for distance regression. Formally,", + "bbox": [ + 76, + 575, + 468, + 666 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\frac {1}{C} \\left(\\mathcal {L} _ {c l s} + \\lambda_ {r e g} \\mathbb {1} _ {t} ^ {(l)} \\mathcal {L} _ {r e g}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 672, + 468, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbb{1}_t^{(l)}$ is an indicator function that evaluates to one on positive time steps, $C = \\sum_{t,l}\\mathbb{1}_t^{(l)}$ is the total number of positive samples within the snippet, and $\\lambda_{reg}$ balances the two loss terms. Center sampling [61] is used for selecting positive time steps around the center of a target moment.", + "bbox": [ + 76, + 707, + 468, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 800, + 207, + 816 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our main experiments include extensive comparisons of SnAG to strong baselines on five challenging benchmarks for video grounding. We further provide ablations on cross-modal fusion and analyze the efficiency of SnAG in both training and inference. More results are in the supplement.", + "bbox": [ + 76, + 824, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/88f4a85d6f7b967b7228f9f976dd1b4879b479a7ffcf06079a78ac26f9738e87.jpg", + "image_caption": [ + "Figure 3. Visualization of dataset statistics. Circle radius is in proportion to average number of queries per video. Long-video benchmarks (Ego4D-NLQ, MAD and TACoS) consist of longer videos with more queries and exhibit low moment coverage compared to short-video benchmarks (ANet-Captions and Charades)." + ], + "image_footnote": [], + "bbox": [ + 560, + 90, + 828, + 265 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/650f6dc82d2c841ac5f51499f1a53ecc671a5bcc24fd5f229c19556b7175f3d2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelR@1R@5
0.30.5Avg0.30.5Avg
SF + BERT2D-TAN [67]5.042.023.5312.895.889.39
VSLNet [64]5.453.124.2910.746.638.69
CONE [17]10.405.037.7222.7411.8717.31
SOONet [36]8.003.765.8822.4011.0916.75
SnAG (video-centric)9.836.838.3327.9319.2723.60
SnAG (query-centric)10.437.158.7927.5919.3323.46
EgoVLPVSLNet [64]10.846.818.8318.8413.4516.15
CONE [17]14.158.1811.1730.3318.0224.18
SnAG (video-centric)15.7210.7813.2538.3927.4432.92
SnAG (query-centric)15.8711.2613.5738.2627.1632.71
", + "bbox": [ + 503, + 357, + 888, + 507 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Results on Ego4D-NLQ. SnAG outperforms all baselines. Best results are in bold and second best underlined.", + "bbox": [ + 500, + 512, + 888, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We categorize five benchmark datasets into two groups based on their video and query statistics (Fig. 3).", + "bbox": [ + 498, + 566, + 888, + 598 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Long videos, many queries. Ego4D-NLQ [16] is a large collection of egocentric videos on daily human activities. The videos are 3.5 to 20 minutes long with an average of 11.6 queries. MAD [45] contains 1.2K hours of movies with 384K queries transcribed from audio description. The videos are 47 to 202 minutes long. TACoS [40] is a conventional benchmark with 10.1 hours of cooking videos, with an average of 143.5 queries per video. These datasets expose the scalability challenges that motivate our work and thus are the main focus of our experiments.", + "bbox": [ + 496, + 599, + 890, + 752 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Short videos, few queries. Charades-STA [43] is an action recognition dataset later annotated for video grounding [13]. The videos are $\\sim 30$ seconds long with $\\sim 2.4$ queries per video. ActivityNet-Captions [20] was collected for dense video captioning and later repurposed for video grounding. The videos are two minutes long on average with a small set of $\\sim 3.65$ queries. Several works [35, 57] advise against using these datasets as benchmarks for the", + "bbox": [ + 496, + 756, + 890, + 876 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "3All experiments are conducted using the Ego4D $\\nu I$ dataset.", + "bbox": [ + 514, + 886, + 834, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18934", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9fb014012dd588b5a1f1f657cd85e4227cdf987e63c2364b29be03978fca3c89.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelR@1R@5R@10R@50
0.10.30.50.10.30.50.10.30.50.10.30.5
CLIP [39]6.573.131.3915.059.855.4420.2614.138.3837.9228.7118.80
VLG-Net [46]3.642.761.6511.669.315.9917.3914.569.7739.7834.2724.93
Moment-DETR [21]0.310.240.161.521.140.282.792.061.2011.087.974.71
CONE [17]8.906.874.1020.5116.119.5927.2021.5312.8243.3634.7320.56
SOONet [36]11.269.005.3223.2119.6413.1430.3626.0017.8450.3244.7832.59
SnAG (video-centric)10.288.465.5524.4220.6013.7532.2327.5019.0052.2846.6835.24
SnAG (query-centric)10.188.375.4424.3020.3513.5132.0527.2518.7552.0546.5334.83
", + "bbox": [ + 119, + 88, + 846, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Results on MAD. SnAG outperforms all baselines. Best results are in bold and second best underlined.", + "bbox": [ + 150, + 233, + 815, + 247 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4f7ff842d2c213510aaad27a0c0318e2f50342257769de09c20c3dd7e2749bba.jpg", + "image_caption": [ + "Figure 4. Visualization of moment predictions. SnAG can (a) comprehend complex text queries with multiple objects and actions; (b) reason about temporal ordering of events." + ], + "image_footnote": [], + "bbox": [ + 81, + 261, + 467, + 424 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "temporal biases in their moment annotations. Nevertheless, we report results on these datasets for completeness.", + "bbox": [ + 75, + 482, + 468, + 512 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines. On TACoS, Charades and ANet-Captions, we compare to strong baselines including two-stage [28, 55, 56] and single-stage [30, 50, 70] models with various fusion operations (LSTM [29, 51], GCN [27, 46], co-attention [24, 68], etc.). On Ego4D and MAD, we compare to their official baselines (2D-TAN [67] and VSLNet [64] for Ego4D, CLIP [39] and VLG-Net [46] for MAD) as well as the concurrent method of CONE [17] and SOONet [36] that similarly address scalable video grounding. We discuss additional baselines in the supplement.", + "bbox": [ + 75, + 516, + 468, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metric. We report $\\mathrm{Recall}@\\mathbf{k}$ at various temporal intersection-over-union threshold $\\theta$ ( $\\mathbf{R}@\\mathbf{k}$ , tIoU= $\\theta$ ) for all datasets. It measures the percentage of sentence queries with at least one of the top- $k$ moment predictions whose temporal overlap with the ground-truth moment exceeds $\\theta$ .", + "bbox": [ + 75, + 671, + 468, + 746 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Long Videos, Many Queries", + "text_level": 1, + "bbox": [ + 76, + 756, + 328, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiment setup. For Ego4D, We consider (1) SlowFast [12] video features with BERT [10] text features, and (2) EgoVLP [38] video and text features. We train on the train split and report R@{1, 5}, tIoU={0.3, 0.5} on the val split. For MAD, we use CLIP [39] features for both videos and text. We train on the train split and report R@{1, 5, 10, 50}, tIoU={0.1, 0.3, 0.5} on the test split. For TACoS, we use C3D video features [48] and GloVe [37] for", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sentence embeddings. We train on the train split and report $\\mathrm{R}@\\{1,5\\}$ , tIoU=\\{0.5, 0.7\\} on the test split. We report results using both video-centric and query-centric training on all datasets.", + "bbox": [ + 496, + 261, + 890, + 320 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on Ego4D-NLQ (Table 1). SnAG sets the new state of the art, achieving mean R@1 / R@5 scores of $8.79\\% / 23.60\\%$ with SlowFast/BERT features, and $13.57\\% / 32.92\\%$ with EgoVLP features, doubling or even tripling the results of the official baselines [64, 67]. Compared to the strong baselines of CONE [17] and SOONet [36], SnAG improves mean R@1 and R@5 respectively by more than 1.05 and 6.29 absolute percentage points without taking advantage of external features. Further, SnAG demonstrates a larger performance gain on the more stringent tIoU threshold of 0.5, indicating more precise moment localization.", + "bbox": [ + 496, + 325, + 892, + 492 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on MAD (Table 2). SnAG sets new records on the challenging MAD dataset. It improves over CLIP [39] and VLG-Net [46] on mean R@1 / R@5 at tIoU=0.5 by 3.90 / 7.76 absolute percentage points. In the meantime, it outperforms CONE [17] and SOONet [36], with larger gain for more stringent tIoU thresholds. Further, SnAG achieves stronger results as input snippet length increases, reaching the best accuracy with $T_{w} = 16384$ (Supplement Fig. A). This scaling behavior highlights the strength of our scalable model design for long-form video grounding.", + "bbox": [ + 496, + 494, + 890, + 647 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results on TACoS (Table 4 (left)). SnAG achieves an R@1 / R@5 of $44.86\\%$ / $70.66\\%$ at tIoU=0.5, outperforming the strongest baseline of MATN [66] by a significant margin $(+7.5\\% \\mathrm{R} @ 1, +12.1\\% \\mathrm{R} @ 5)$ . This confirms that our simple single-stage design with late fusion is a strong alternative to multi-stage models with sophisticated fusion mechanisms. Importantly, our scalable design enables learning from full-resolution video features, whereas the baselines often aggressively reduce feature resolution to contain their training and inference cost on long-form videos. We hypothesize that full-resolution video features capture detailed event dynamics and are key to the strong performance of SnAG.", + "bbox": [ + 496, + 650, + 890, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Result visualization. We visualize predictions of SnAG and the baselines on TACoS and Ego4D-NLQ videos. In", + "bbox": [ + 496, + 835, + 890, + 864 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "4CONE [17] leverages external CLIP [39] features in several steps.", + "bbox": [ + 514, + 875, + 870, + 887 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "5MAD videos are not publicly available due to copyright issues.", + "bbox": [ + 517, + 887, + 857, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18935", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d45490b02b2602cd98d4a768e4f2caedcd7932de3e15250099104b16917fe4d8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelR@1R@5
0.30.50.30.5
(a) Fusion stage (early vs. late fusion)
No fusion10.857.8546.4631.19
SnAG-E53.3444.0179.5669.41
SnAG-EL54.8444.5481.1370.11
SnAG-M51.4140.7977.5665.71
SnAG (ours)55.1444.9481.1070.66
(b) Fusion operation (global vs. token-wise)
Cat49.3939.2477.3165.36
Add51.9141.8177.9866.51
Scale55.0143.9680.6370.11
Add + Scale53.3643.0980.4369.58
XAttn54.8445.0679.9670.08
XAttn-affine (ours)55.1444.9481.1070.66
", + "bbox": [ + 99, + 88, + 444, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablations results on TACoS. (a) Late fusion yields comparable results to early fusion (E, EL, M); (b) Fusion with tokenwise sentence embeddings (XAttn) produces better results than fusion with global sentence embeddings (Cat, Add, Scale).", + "bbox": [ + 75, + 340, + 468, + 396 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 4(a), a long query describes the complex interplay between two objects (pan and stove) and three actions (\"take from\", \"place on\", and \"turn on\"). VLG-Net [46] recognized both objects yet none of the actions, while 2D-TAN [67] identified one action (\"take from\") but at the same time missed one object (pan). By contrast, SnAG followed the query semantics and produced accurate localization. The other query in Fig. 4(b) tests the understanding of temporal context. SnAG leveraged the keyword \"before\" to identify the correct moment before the action (\"pick up\"), whereas VSLNet [64] only attended to the object (can), thus mistakenly predicting a moment after the action.", + "bbox": [ + 75, + 412, + 468, + 594 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Short Videos, Few Queries", + "text_level": 1, + "bbox": [ + 76, + 607, + 316, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiment setup. We extract video features using both C3D [48] (pretrained on Sports-1M [18]) and I3D [5] (pretrained on Kinetics [19]) for Charades-STA, and use the official C3D features for ActivityNet-Captions. We use GloVe word embeddings [37] to represent sentence queries for both datasets. We train on their respective train splits, report R@{1, 5}, tIoU={0.5, 0.7} on the test split of Charades-STA, and R@{1, 5}, tIoU={0.3, 0.5} on the val_2 split of ActivityNet-Captions. Following standard practice, we resize all video features to a uniform length of 256.", + "bbox": [ + 75, + 637, + 468, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on Charades-STA (Table 4 (middle)). SnAG outperforms all previous methods by a wide margin. It obtains $33.52\\%$ R@1 and $64.11\\%$ R@5 at tIoU=0.7 with C3D features, 2.10 and 4.52 absolute percentage points higher than the latest SSRN [71] baseline. It further attains $46.26\\%$ R@1 and $71.94\\%$ R@5 at tIoU=0.7 with I3D features, setting new state of the art on this competitive benchmark.", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results on ActivityNet-Captions (Table 4 (right)). SnAG achieves competitive results, reaching an R@1 / R@5 score of $30.56\\% / 63.41\\%$ at tIoU=0.7. It is only outperformed by a few latest models [22, 27, 71] while being much simpler.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies", + "text_level": 1, + "bbox": [ + 498, + 160, + 663, + 175 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct extensive ablations on TACoS to study key design choices for cross-modal fusion.", + "bbox": [ + 498, + 184, + 890, + 213 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Early vs. late fusion. Does late fusion enable better scalability at the expense of accuracy? We study three variants of SnAG with common early-fusion designs: (1) SnAG-E with fusion before the pyramid; (2) SnAG-EL with fusion before and after the pyramid; (3) SnAG-M with repeated fusion within the pyramid. Table 3 confirms that early and late fusion yield comparable results.", + "bbox": [ + 496, + 218, + 890, + 323 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Choice of fusion operation. We study fusion operations used by strong baselines, including point-wise addition, multiplication, and concatenation of video representations with global sentence embeddings, as well as vanilla cross-attention with token-level sentence embeddings. According to Table 3, token-level embeddings produce better results, and our cross-attention variant further boosts performance.", + "bbox": [ + 496, + 327, + 890, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Efficiency Analysis", + "text_level": 1, + "bbox": [ + 498, + 443, + 681, + 458 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we conduct an efficiency analysis of our method.", + "bbox": [ + 498, + 465, + 877, + 481 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Breakdown of model capacity. A key design choice of SnAG is to carefully balance the model capacity among its video encoder, text encoder, and moment decoder including the fusion module and the localization heads. For a detailed breakdown of model capacity, we measure their respective parameter size and MACs in percentage. Fig. 5(a) indicates that SnAG's video encoder absorbs a significant portion of parameters and compute, such that per-query evaluation (i.e., text encoding, fusion, and decoding) occupies $\\sim 50\\%$ of the total computation. This design is naturally in favor of video-centric training and inference, where the costly video encoding is shared among many queries.", + "bbox": [ + 496, + 484, + 890, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Video-centric vs. query-centric training. Fig. 5(b) presents the training time and GPU memory usage of video-centric training relative to conventional query-centric training. The results show that the amount of saving correlates with snippet length and number of queries. Video-centric training is thus preferred for long videos with many queries.", + "bbox": [ + 496, + 670, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "$B_{q}$ in video-centric training. We further study how $B_{q}$ , the number of text query samples per video, trades off accuracy for efficiency in video-centric training. On MAD, we fix the batch size $|B| = 32$ for a mini-batch $B$ , vary $B_{q}$ between 1 and $|B|$ , and report training time, GPU memory usage and test accuracy relative to query-centric training (i.e., $B_{q} = 1$ ). Fig. 5(d) reveals that test accuracy is unaffected even with a large $B_{q} = 32$ (i.e., a single video per mini-batch), while training time and GPU memory usage", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18936", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7b2e2f2420a0476bbd4d20cac505faa8c66f64acebdf9cb49634a9a2f6a4bc92.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodTACoS (C3D)Charades-STA (I3D)Charades-STA (C3D)ActivityNet-Captions (C3D)
R@1R@5R@1R@5R@1R@5R@1R@5
0.30.50.30.50.50.70.50.70.50.70.50.70.50.70.50.7
CTRL ICCV 17 [13]18.3213.3036.6925.42----23.638.8958.9229.52----
QSPN AAAI 19 [56]--------35.6015.8079.4045.4027.7013.6059.2038.30
SCDM NeurIPS 19 [58]27.6423.2740.0633.4954.9234.2676.5060.02----36.9020.2866.8442.92
2D-TAN AAAI 20 [67]45.6135.7769.1157.3156.6436.2189.1461.1341.1023.2581.5348.5546.1629.2178.8060.85
CBP AAAI 20 [51]27.3124.7943.6437.40----36.8018.8770.9450.1935.7617.8065.8946.20
DRN CVPR 20 [60]-23.17-33.3653.0931.7589.0660.0545.4026.4088.0155.3845.4524.3677.9750.30
BPNet AAAI 21 [55]25.9620.96--50.7531.64--38.2520.51--42.0724.69--
CPNet AAAI 21 [24]42.6128.29--60.2738.74--40.3222.47--40.5621.63--
SMIN CVPR 21 [50]48.0135.2465.1853.3664.0640.7589.4968.09----48.4630.3481.1662.11
CBLN CVPR 21 [29]38.9827.6573.1246.2461.1338.2290.3361.6947.9428.2288.2057.4748.1227.6079.3263.41
CPN CVPR 21 [68]47.6936.33--51.0731.54------45.1028.10--
DeNet CVPR 21 [70]----59.7038.5291.2466.83----43.79-74.13-
MATN CVPR 21 [66]48.7937.5767.6357.91--------48.0231.7878.0263.18
VLG-Net ICCVW 21 [46]45.4634.1970.3856.56--------46.3229.8277.1563.33
APGN EMNLP 21 [28]40.4727.8659.9847.1262.5838.8691.2462.1148.2029.3789.0558.4948.9228.6478.8763.19
IA-Net EMNLP 21 [30]37.9126.2757.6246.3961.2937.9189.7862.04----48.5727.9578.9963.12
RaNet EMNLP 21 [14]43.3433.5467.3355.0960.4039.6589.5764.54----45.5928.6775.9362.97
MGSL-Net AAAI 22 [30]42.5432.2763.3950.1363.9841.0393.2163.85----51.8731.4282.6066.71
MMN AAAI 22 [52]39.2426.1762.0347.39--------48.5929.2679.5064.76
SSRN EMNLP 22 [71]45.1034.3365.2651.8565.5942.6594.7665.4850.3931.4290.6859.9454.4933.1584.7268.48
G2L ICCV 23 [22]42.7430.9565.8349.86--------51.6833.3581.3267.60
SnAG (video-centric)56.4444.8681.1570.6664.6246.2692.5571.9451.7233.5292.5564.1148.5530.5681.7163.41
SnAG (query-centric)55.0144.5180.6870.1365.1345.9192.8071.7551.1031.7790.2262.1547.5529.6581.5562.21
", + "bbox": [ + 80, + 71, + 888, + 369 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Results on TACoS, Charades-STA and ActivityNet-Captions. SnAG outperforms all baselines on TACoS and Charade-STA by a large margin, while being highly competitive on ActivityNet-Captions. Best results are in bold and second best underlined.", + "bbox": [ + 75, + 375, + 892, + 402 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/034aec85e20ee7f163d3d00cae17d23a683054193ab09b09a375bc8f2fad07e0.jpg", + "image_caption": [ + "Figure 5. (a) Model capacity. T, E, M denotes TACoS, Ego4D and MAD, respectively (also in (b)). Shaded bar: % of parameters, Colored bar: % of MACs. SnAG places more parameters and compute in video encoder for less expensive per-query evaluation (fusion + decoding). (b, c) Video-centric vs. query-centric inference (b) and training (c). SnAG saves up to $50\\%$ training time, $40\\%$ GPU memory and $80\\%$ test time, and delivers up to $40\\%$ faster convergence relative to query-centric training / inference. (d) Effect of $B_{q}$ on training efficiency and test accuracy on MAD. Training on MAD is faster and takes less GPU memory as $B_{q}$ grows, while the test accuracy is unaffected." + ], + "image_footnote": [], + "bbox": [ + 81, + 417, + 261, + 534 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/afa7c78d392044d86a41785a82fcc08744cbb838a9d761b7c29ffd1e790003c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 417, + 465, + 534 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/38a25ea3e1e8cc1a63805f1c3481bb9e9b47d1bc2d05ecb0fa054fca392e1f6d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 417, + 679, + 534 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/405277267d74f9782f2007159bcbaabc91e6951ae176f18e1597779abe9490c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 420, + 888, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "drop by a significant $55\\%$ and $42\\%$ , approaching the upper bound by our analysis.", + "bbox": [ + 75, + 627, + 468, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Video-centric vs. query-centric inference. We now ask to what extent the re-use of video representations enabled by SnAG's late fusion design accelerates inference. Fig. 5(b) presents the percentage of time spent by our video-centric inference scheme relative to query-centric inference, where the full model is evaluated on each and every video-query pair. Consistent with earlier findings on video-centric training, longer videos with more queries result in more saving in inference time. On the challenging MAD dataset, this alone brings a major reduction (65%) in test time.", + "bbox": [ + 75, + 661, + 468, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inference speed. With window filtering [17], inference of SnAG on the val split of MAD takes 12 minutes on a single P100 GPU. This is $33\\%$ faster than CONE [17] ( $\\sim 18$ mins) and $63\\%$ faster than SOONet [36] ( $\\sim 32$ mins).6", + "bbox": [ + 75, + 816, + 470, + 878 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 626, + 619, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a simple and accurate model towards scaling up video grounding. We provided extensive analysis on the complexity of video grounding models from the perspective of cross-modal fusion, and argued that late fusion is key to scalability in video duration and query size. Our model, SnAG, is a simple instantiation of late fusion with minimalist design. It achieves superior accuracy and efficiency on a spectrum of challenging benchmarks and compares favorably to strong baselines including those dedicated to efficient inference on long videos. We hope our analysis and model design can shed light on video grounding and more broadly scalable video understanding.", + "bbox": [ + 496, + 652, + 890, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement: This work was partially supported by NIH grant R01OH012313, by grants from McPherson Eye Research Institute and VCGRE at UW Madison, and by the Army Research Lab under contract number W911NF-2020221.", + "bbox": [ + 496, + 840, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "$^{6}$ SOONet reports an inference time of 8.2 mins on a single A100 GPU.", + "bbox": [ + 94, + 886, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18937", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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Rethinking the video sampling and reasoning strategies for temporal sentence grounding. In EMNLP Findings, 2022. 2, 7, 8" + ], + "bbox": [ + 503, + 92, + 890, + 180 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18940", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_model.json b/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_model.json new file mode 100644 index 0000000000000000000000000000000000000000..cea43374a9414d2c675db73795d2c142abe0670d --- /dev/null +++ b/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_model.json @@ -0,0 +1,2631 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.243, + 0.131, + 0.728, + 0.154 + ], + "angle": 0, + "content": "SnAG: Scalable and Accurate Video Grounding" + }, + { + "type": "text", + "bbox": [ + 0.338, + 0.181, + 0.632, + 0.222 + ], + "angle": 0, + "content": "Fangzhou Mu*, Sicheng Mo*, Yin Li \nUniversity of Wisconsin-Madison" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.256, + 0.314, + 0.273 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.289, + 0.474, + 0.562 + ], + "angle": 0, + "content": "Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability — they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is \\(43\\%\\) more accurate and \\(1.5 \\times\\) faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos. Our code is available at https://github.com/fmu2/snag_release." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.592, + 0.21, + 0.607 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.47, + 0.739 + ], + "angle": 0, + "content": "Localizing moments within an untrimmed video based on text descriptions, also known as temporal video grounding, involves joint reasoning about visual, textual and temporal information, and thus remains a challenging problem in video understanding. Video grounding is gaining traction amid the rapid advances in vision-language learning, with a range of applications such as intelligent personal assistants, human-robot interaction, and interactive video editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.74, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Despite recent progress, one largely overlooked aspect of video grounding is the scalability of models with respect to video duration and the number of text descriptions (i.e., queries). Previous methods (e.g., [46, 67]) are primarily designed for grounding only a few queries within short video snippets. However, the growing availability of long videos (e.g., on streaming platforms) and demand to query their rich contents introduce a paradigm shift, necessitating efficient grounding of large volumes of queries in long videos." + }, + { + "type": "image", + "bbox": [ + 0.559, + 0.258, + 0.83, + 0.428 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.432, + 0.892, + 0.462 + ], + "angle": 0, + "content": "Figure 1. SnAG achieves the best accuracy and throughput simultaneously on the MAD dataset [45] for long-form video grounding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.519 + ], + "angle": 0, + "content": "On latest long-form video grounding benchmarks [16, 45], these methods struggle to scale up due to their high computational cost, and suffer major performance degradation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.893, + 0.703 + ], + "angle": 0, + "content": "In this paper, we take a principled approach to studying the problem of scalable video grounding, focusing on the design of cross-modal fusion—a key model component that combines visual and textual information. Specifically, we present an analysis that connects the computational cost of video grounding models to their fusion schemes. Our analysis and empirical results challenge the widely adopted early fusion, showing that late fusion scales better in inference by amortizing the cost of long video processing among text queries. Importantly, this insight further motivates the design of a novel, video-centric sampling scheme for scalable training, without compromising grounding accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Following these findings, we present SnAG, a scalable and accurate model for long-form video grounding. SnAG features a minimalist, late-fusion design for scalable inference, while supporting video-centric sampling for scalable training. Notwithstanding its simplicity, SnAG achieves superior results across all benchmarks designed for long-form video grounding. Without bells and whistles, SnAG attains \\(13.75\\%\\) R@5, tIoU=0.5 on MAD [45] with an inference speed of 45.3 queries per second on a P100 GPU (Fig. 1), \\(43\\%\\) more accurate and \\(1.5\\times\\) faster than the concurrent method of CONE [17]. In the meantime, SnAG is highly competitive on short-video benchmarks. It achieves \\(46.26\\%\\) R@1, tIoU=0.7 on Charades-STA [43], outperforming the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.102, + 0.888, + 0.262, + 0.9 + ], + "angle": 0, + "content": "* indicates equal contribution" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18930" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "previous state of the art (SSRN [71]) by 3.61 absolute percentage points while being simpler in model design." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.128, + 0.471, + 0.25 + ], + "angle": 0, + "content": "Contributions. (1) We present one of the first studies to understand the effect of fusion schemes on the computational cost of video grounding. (2) Our analysis offers new insights and leads to a new training scheme for scalable video grounding. (3) Based on our findings, we further deliver a simple model that attains superior results across major benchmarks for long-form video grounding while achieving significant efficiency gains in both training and inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.267, + 0.22, + 0.283 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.469, + 0.354 + ], + "angle": 0, + "content": "Video grounding. Previous works on video grounding can be categorized based on whether proposals are generated as moment candidates (two-stage vs. single-stage), and how text queries inform action localization (cross-modal fusion)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.469, + 0.505 + ], + "angle": 0, + "content": "Two-stage methods first generate temporal segments as proposals, then score their \"actionness\" and optionally refine their boundaries. Early works [1, 13] densely sample proposals using sliding windows and score them independently. One line of work [8, 28, 54-56] subsequently conditions proposal generation on sentence queries and/or video context to avoid dense sampling. By contrast, another line of work [14, 46, 50, 66, 67] takes the opposite path of enumerating all segments, yet organizes them in a 2D adjacency map to reason about their relations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.469, + 0.718 + ], + "angle": 0, + "content": "Single-stage methods localize moments in a single shot without using proposals, and thus are often more efficient than two-stage methods. Some models decode moment boundaries from global features [23, 24, 33, 59, 70] or learnable queries [21, 25, 53]. Others densely predict onset and offset probabilities [15, 29, 34, 41, 63-65, 68], or classify and refine pre-set anchors [6, 30, 51, 58, 62] at every moment. Most relevant to our work are models that represent moment candidates as points [7, 11, 27, 31, 60]. Analogous to point-based object detectors [47], they classify every point in time and regress moment boundaries relative to the points. Despite their simplicity and efficiency, the performance of single-stage models lags behind two-stage models on standard benchmarks made up of short videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Cross-modal fusion combines video and text information for video grounding. Early models [1, 13] fuse video and text representations right before final prediction. This simple, late-fusion approach is abandoned by subsequent models, which turn to early fusion (e.g., [56, 60, 62, 67]) with sophisticated model design (e.g., LSTM [6, 15, 29, 51, 56, 65], GCN [7, 27, 46], memory bank [8, 27]), feature hierarchies [14, 33, 50], losses [23, 34, 56, 66], and inference procedures [68, 70]. Early fusion is believed to strengthen cross-modal reasoning, albeit at a price of model complexity. Recent Transformer-based models [3, 21, 53, 66] inherit this early-fusion design; video features and text embeddings" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "are concatenated at input, and attention-based feature fusion is carried out throughout the model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Our method demonstrates a single-stage Transformer model with a simple late fusion mechanism based on crossattention. Late fusion allows us to amortize the cost of video processing across many sentence queries, resulting in scalable training and inference on long-form videos. Without bells and whistles, our model outperforms all prior methods on long-video benchmarks, and attains competitive performance on standard, short-video benchmarks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.25, + 0.892, + 0.446 + ], + "angle": 0, + "content": "Long-form video grounding. Recent efforts [16, 45] put forth new challenges for sentence grounding in long videos. Previous methods tailored for short videos [46, 64, 67] fall short on these benchmarks. They have no access to long-range video context, require dense sliding window inference, and yield unsatisfactory results. Concurrent works [17, 36] present multi-stage approaches with sophisticated pre-processing, ranking and training procedures for efficient long-form video grounding. However, their efficiency stems from the restrictive assumption that moments are covered by short windows. By contrast, SnAG offers a simple, single-stage solution with superior accuracy, without making assumptions about moment duration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.574 + ], + "angle": 0, + "content": "Localizing moments in videos. Closely related to video grounding, temporal action localization (e.g., [32, 42, 44]) aims to identify moments of actions from within a closed set of action categories. Solutions to the two tasks often evolve in tandem and share remarkably similar model design. SnAG is inspired by our prior work [61], yet extends its design for the more challenging task of video grounding, with the goal of scaling up video grounding for long videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.59, + 0.767, + 0.608 + ], + "angle": 0, + "content": "3. Scaling Up Video Grounding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.892, + 0.709 + ], + "angle": 0, + "content": "Our goal is to scale up video grounding for long-form videos with many queries. Denote an input video \\(\\mathbf{V}\\) as a time-indexed sequence \\([\\mathbf{v}_t]_{t=1}^T = [\\mathbf{v}_1, \\mathbf{v}_2, \\dots, \\mathbf{v}_T]\\), where \\(\\mathbf{v}_t\\) represents a short video clip centered at time \\(t\\).1 \\(\\mathbf{V}\\) is paired with \\(N\\) sentence queries \\(\\{\\mathrm{Q}_j\\}_{j=1}^N\\), each describing a moment \\(\\mathbf{y}_j = (s_j, e_j)\\) in the video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.85 + ], + "angle": 0, + "content": "Long-form video grounding is characterized by a great number of time steps \\( T \\) (e.g., tens of thousands) and text queries \\( N \\) (hundreds) for an input video \\( \\mathbf{V} \\). With a large \\( T \\), it is no longer feasible to feed the full video \\( \\mathbf{V} \\) into a model, and thus more viable to consider a sliding window setting. Specifically, a video \\( \\mathbf{V} \\) is further partitioned into a set of \\( M \\) snippets \\( \\{\\mathbf{V}_{i=1}^{M}\\} \\), each \\( \\mathbf{V}_{i} = [\\mathbf{v}_{t}]_{t=t_{i}}^{t_{i} + T_{w}} \\) taken from a local time window of size \\( T_{w} \\) that may overlap with others. We consider the learning of a function \\( \\mathcal{F} \\), realized in a deep" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1Like prior works, we consider video features and text embeddings extracted using pre-trained models (e.g., C3D [48] and BERT [10]). Yet the formulation can be easily extended to raw video frames and text tokens." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18931" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.094, + 0.388, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.094, + 0.58, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.589, + 0.094, + 0.888, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.306, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Figure 2. (a) Cross-modal fusion is key to a video grounding model \\(\\mathcal{F}\\). Models using early fusion jointly encode video and sentence query. SnAG revisits late fusion for scalable video grounding by decoupling expensive video encoding and inexpensive query encoding. (b) Video-centric model evaluation. With late fusion, the output of video encoder can be cached and re-used by queries of the same video in both training and inference. (c) Mini-batch sampling in training. Previous methods adopt query-centric sampling (query \\(\\rightarrow\\) video) whereas SnAG resorts to video-centric sampling (video \\(\\rightarrow\\) many queries) for efficient training. (d) Model overview. SnAG is a simple instantiation of late fusion and video-centric training for video grounding. It separately encodes a video and its queries using Transformers, applies simple cross-attention for cross-modal fusion, and decodes moments represented as points using lightweight convolutional heads." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.449 + ], + "angle": 0, + "content": "network, to predict the start time \\( s_j \\) and end time \\( e_j \\) of the moment \\( \\mathbf{y}_j \\) given a snippet \\( \\mathbf{V}_i \\) and a query \\( \\mathrm{Q}_j \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.457, + 0.377, + 0.472 + ], + "angle": 0, + "content": "3.1. Background: Cross-Modal Fusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.469, + 0.511 + ], + "angle": 0, + "content": "We review cross-modal fusion - a key design choice of \\(\\mathcal{F}\\) and define the notation used for the rest of the paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.469, + 0.574 + ], + "angle": 0, + "content": "Early fusion. A straightforward design is to fuse information from a video snippet \\(\\mathbf{V}_i\\) and a text query \\(\\mathrm{Q}_j\\) at input (Fig. 2(a)). This early fusion strategy is widely adopted in prior works [21, 53, 60, 62, 66, 67], and can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.586, + 0.469, + 0.603 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {E} \\left(\\mathbf {V} _ {i}, \\mathrm {Q} _ {j}\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.659 + ], + "angle": 0, + "content": "where \\(\\mapsto\\) defines any necessary post-processing of the model outputs (e.g., re-scaling, non-maximum suppression) in order to decode the moment \\(\\mathbf{y}_j\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.469, + 0.708 + ], + "angle": 0, + "content": "Late fusion. Another possible design is to first embed the video snippet \\(\\mathbf{V}_i\\) and text query \\(\\mathrm{Q}_j\\), then fuse their features for grounding (Fig. 2(a)). This late fusion strategy follows" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.719, + 0.469, + 0.736 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {L} \\left(g \\left(\\mathbf {V} _ {i}\\right), h \\left(\\mathrm {Q} _ {j}\\right)\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.469, + 0.822 + ], + "angle": 0, + "content": "where \\( g(\\cdot) \\) is the video encoder and \\( h(\\cdot) \\) the text encoder. With slight abuse of the symbols, \\( \\mathcal{F}_L \\) here denotes the rest part of the grounding model, including feature fusion. The key is to keep \\( \\mathcal{F}_L \\) lightweight, i.e., its cost should be a minor portion in comparison to the rest of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Design choice. The conventional wisdom favors the design of early fusion for video grounding. Early fusion is believed to offer better interactions between visual and textual features, resulting in strong empirical results. In what follows, we analyze the computational cost of early and late fusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.418, + 0.892, + 0.463 + ], + "angle": 0, + "content": "during inference and training, and show that proper design of late fusion allows significantly improved scalability in video duration \\((M)\\) and number of text queries \\((N)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.474, + 0.677, + 0.488 + ], + "angle": 0, + "content": "3.2. Scalable Inference" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.498, + 0.891, + 0.559 + ], + "angle": 0, + "content": "We start by analyzing the computational cost of early vs. late fusion in inference. Denote the computational cost of a function by \\(\\mathcal{C}(\\cdot)\\). For example, \\(\\mathcal{C}(g)\\) is the cost of the video encoder \\(g(\\cdot)\\), and \\(\\mathcal{C}(h)\\) the cost of the text encoder \\(h(\\cdot)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.563, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Computational cost. We make two key observations regarding the computational cost of a video grounding model: (a) a lightweight \\(\\mathcal{F}_L\\) is used for late fusion, thus \\(\\mathcal{C}(\\mathcal{F}_L) \\ll \\mathcal{C}(g) + \\mathcal{C}(h)\\); and (b) the video encoder \\(g(\\cdot)\\) has a much higher cost than the text encoder, thus \\(\\mathcal{C}(g) \\gg \\mathcal{C}(h)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.76 + ], + "angle": 0, + "content": "The first observation stems from the design of late fusion. To justify the second observation, it is important to notice that \\(\\mathcal{C}(g)\\) scales w.r.t. the length of input video snippet (i.e., the local window size \\(T_w\\)), whereas \\(\\mathcal{C}(h)\\) remains constant due to limited sequence length of text queries. For example, a realization of \\(g(\\cdot)\\) using a vanilla Transformer has a complexity of \\(\\mathcal{O}(T_w^2)\\). Thus, using a larger local window size naturally leads to \\(\\mathcal{C}(g) \\gg \\mathcal{C}(h)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Cost analysis: early vs. late fusion. Evaluating an early-fusion model on a video with \\(M\\) snippets and \\(N\\) queries has a cost of \\(MN\\mathcal{C}(\\mathcal{F}_E)\\), whereas late fusion has a cost of \\(MN\\mathcal{C}(\\mathcal{F}_L) + MC(g) + NC(h)\\). This is because an early-fusion model has to compare each snippet to every query, yet late fusion allows re-using video features for all queries of the video (i.e., video-centric evaluation, see Fig. 2(b))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Let us assume that the cost of both models can be controlled by setting \\(\\mathcal{C}(\\mathcal{F}_E) = \\mathcal{C}(\\mathcal{F}_L) + \\mathcal{C}(g) + \\mathcal{C}(h)\\), i.e., eval" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18932" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "uating either model on a pair of video snippet and sentence query has the same cost (post-processing excluded). With \\(\\mathcal{C}(\\mathcal{F}_L) = \\alpha (\\mathcal{C}(g) + \\mathcal{C}(h))\\) for some small \\(\\alpha\\), the ratio between the cost of early and late fusion in inference is" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.163, + 0.47, + 0.31 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {R} _ {\\text {i n f}} = \\frac {\\mathcal {C} (\\text {i n f e r e n c e w i t h e a r l y f u s i o n})}{\\mathcal {C} (\\text {i n f e r e n c e w i t h l a t e f u s i o n})} (3) \\\\ = \\frac {M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M N \\mathcal {C} (g) + M N \\mathcal {C} (h)}{M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M \\mathcal {C} (g) + N \\mathcal {C} (h)} (4) \\\\ = \\frac {M N (1 + \\alpha)}{M N \\alpha + M \\mathbf {R} _ {g / (g + h)} + N (1 - \\mathbf {R} _ {g / (g + h)})} (5) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{N} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}N,&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&N \\rightarrow \\infty\\end{array}, \\right. (6) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.321, + 0.469, + 0.398 + ], + "angle": 0, + "content": "where \\(\\mathbf{R}_{g / (g + h)} = \\mathcal{C}(g) / (\\mathcal{C}(g) + \\mathcal{C}(h))\\), and the approximation in Eq. 6 is a result of \\(\\mathbf{R}_{g / (g + h)} \\approx 1\\) with \\(\\mathcal{C}(g) \\gg \\mathcal{C}(h)\\). Eq. 6 reveals that early fusion is \\(N\\) times the cost of late fusion as snippet length grows (\\(\\alpha \\to 0\\)), and is particularly inefficient for videos with many queries (\\(N \\to \\infty\\))." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.407, + 0.25, + 0.423 + ], + "angle": 0, + "content": "3.3. Scalable Training" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.431, + 0.469, + 0.462 + ], + "angle": 0, + "content": "We now show that late fusion further unlocks a novel training scheme that scales well for long-form video grounding." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.466, + 0.469, + 0.526 + ], + "angle": 0, + "content": "Training and mini-batch sampling. Given a set of paired videos, text queries, and their moments \\(\\{\\mathbf{V}^{(k)},\\mathbf{Q}^{(k)},\\mathbf{y}^{(k)}\\}\\), training a model \\(\\mathcal{F}\\) amounts to minimizing a loss function \\(\\mathcal{L}\\) over mini-batches \\(B\\) sampled from the dataset:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.536, + 0.469, + 0.56 + ], + "angle": 0, + "content": "\\[\n\\Sigma_ {(k, i, j) \\in B} \\mathcal {L} \\left(\\mathcal {F} \\left(\\mathbf {V} _ {i} ^ {(k)}, \\mathrm {Q} _ {j} ^ {(k)}\\right), \\mathbf {y} _ {j} ^ {(k)}\\right). \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.568, + 0.469, + 0.645 + ], + "angle": 0, + "content": "A key design largely overlooked in video grounding is the mini-batch sampling scheme during training. With multiple queries associated with a video snippet, a combination of late fusion and proper sampling scheme allows us to reuse video representations in training as is done in inference." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.648, + 0.469, + 0.724 + ], + "angle": 0, + "content": "Query-centric sampling. Virtually all prior works sample mini-batches uniformly at random from all pairs of valid video snippets and text queries.\\(^{2}\\) This can be interpreted as ancestral sampling: first draw a text query (and its moment), then select a video snippet covering the moment:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.733, + 0.469, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathrm {Q} _ {j} ^ {(k)}, \\mathbf {y} _ {j} ^ {(k)}\\right) \\right\\} _ {j \\times k}\\right), \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.76, + 0.395, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.792, + 0.469, + 0.848 + ], + "angle": 0, + "content": "where \\(U(\\cdot)\\) denotes a discrete uniform distribution and \\(\\{(\\mathbf{V}_i^{(k')},\\mathbf{Q}_j^{(k')},\\mathbf{y}_{j'}^{(k')})_{+}\\}\\) is the union of all valid triplets: a moment \\(\\mathbf{y}_{j'}^{(k')}\\) of a text query \\(\\mathbf{Q}_{j'}^{(k')}\\) in a video snippet \\(\\mathbf{V}_i^{(k')}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.847, + 0.468, + 0.877 + ], + "angle": 0, + "content": "This sampling process is repeated \\(|B|\\) times to construct a mini-batch, with \\(|B|\\) the batch size. With a large" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.89, + 0.122 + ], + "angle": 0, + "content": "dataset, the resulting mini-batch will contain \\(|B|\\) snippet-query pairs, each likely from a different video." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.125, + 0.892, + 0.234 + ], + "angle": 0, + "content": "Video-centric sampling. To speed up the training of late fusion models, we propose video-centric sampling that considers every video snippet \\(\\mathbf{V}_i^{(k)}\\) as a sample. Specifically, we first draw a video based on its importance score, then sample a snippet within the video, and finally select multiple text queries associated with the snippet. This is defined as the following ancestral sampling:" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.24, + 0.892, + 0.279 + ], + "angle": 0, + "content": "\\[\nk ^ {\\prime} \\sim P (k) = \\frac {M _ {+} ^ {(k)}}{\\Sigma_ {k} M _ {+} ^ {(k)}} \\quad i ^ {\\prime} \\sim P (i; k ^ {\\prime}) = \\frac {N _ {i} ^ {\\left(k ^ {\\prime}\\right)}}{\\Sigma_ {k} N _ {i} ^ {\\left(k ^ {\\prime}\\right)}} \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.542, + 0.28, + 0.852, + 0.304 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\right\\} ^ {B _ {q}} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.313, + 0.892, + 0.383 + ], + "angle": 0, + "content": "where \\(M_{+}^{(k)}\\) denotes the number of valid snippets in a video \\(\\mathbf{V}^{(k)}\\), and \\(N_{i}^{(k^{\\prime})}\\) the number of queries in a snippet \\(\\mathbf{V}_{i}^{(k^{\\prime})}\\). Importantly, a total of \\(B_{q}\\) queries are drawn for the selected video snippet \\(\\mathbf{V}_{i^{\\prime}}^{(k^{\\prime})}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.383, + 0.892, + 0.459 + ], + "angle": 0, + "content": "This sampling process is repeated \\( |B| / B_q \\) times for a mini-batch, leading to \\( |B| / B_q \\) video snippets, each likely from a different video yet with multiple \\( (B_q) \\) text queries. This mini-batch thus allows us to re-use the video representations for the sampled snippets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.462, + 0.892, + 0.554 + ], + "angle": 0, + "content": "Cost analysis: query-centric vs. video-centric sampling. Fig. 2(c) illustrates the key difference between query-centric and video-centric sampling. Similar to our analysis in Section 3.2, it is easy to show that late fusion combined with video-centric training enables substantial speedup for long snippets \\((\\alpha \\rightarrow 0)\\) and large \\(B_{q}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.563, + 0.891, + 0.64 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {R} _ {\\text {t r a i n}} = \\frac {\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {v i d e o - c e n t r i c t r a i n i n g})}{\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {q u e y - c e n t r i c t r a i n i n g})} (10) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{B _ {q}} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}B _ {q},&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&B _ {q} \\rightarrow \\infty\\end{array}. \\right. (11) \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.877, + 0.664 + ], + "angle": 0, + "content": "3.4. Scalable Video Grounding: An Instantiation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.671, + 0.892, + 0.792 + ], + "angle": 0, + "content": "We now present an instantiation with late fusion and video-centric training for scalable video grounding. Our instantiation, dubbed SnAG, is shown in Fig. 2(d). SnAG is a single-stage Transformer model where every time step represents a moment candidate. It combines (a) a multi-scale Transformer-based video encoder; (b) a Transformer-based text encoder; (c) cross-attentions for late fusion; and (d) convolutional heads for moment decoding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Video encoder \\( g \\). We use the ActionFormer backbone [61] as our video encoder, given its superior performance on the closely related task of temporal action localization. It transforms input video features into a multi-scale representation \\( [\\mathbf{Z}^{(l)}]_{l=1}^{L} = [\\mathbf{Z}^{(1)}, \\mathbf{Z}^{(2)}, \\dots, \\mathbf{Z}^{(L)}] \\) using Transformer layers with local self-attentions [9]. We refer readers to the original paper [61] for more details on model architecture." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.466, + 0.901 + ], + "angle": 0, + "content": "2A video snippet without any query is often discarded during training." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18933" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "Text encoder \\( h \\). Our text encoder is a vanilla Transformer. It takes a query Q with \\( K \\) tokens \\( [\\mathbf{q}_1, \\dots, \\mathbf{q}_K] \\) and outputs their embeddings \\( \\mathbf{E} = [\\mathbf{e}_1, \\dots, \\mathbf{e}_K] \\). This computation is light compared to video encoding as \\( K \\ll T_w \\) for long videos." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.155, + 0.47, + 0.202 + ], + "angle": 0, + "content": "Cross-modal late fusion \\(\\mathcal{F}_L\\). Our model uses a simple variant of cross-attention for fusion. Specifically, it modulates \\([\\mathbf{Z}^{(l)}]_{l=1}^L\\) with an affine transformation given by \\(\\mathbf{E}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.208, + 0.469, + 0.267 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} (\\mathbf {W}, \\mathbf {B}) ^ {(l)} = \\operatorname {M C A} (\\operatorname {L N} (\\mathbf {Z} ^ {(l)}), \\operatorname {L N} (\\mathbf {E})), \\\\ \\tilde {\\mathbf {Z}} ^ {(l)} = \\mathbf {W} ^ {(l)} \\odot \\mathbf {Z} ^ {(l)} + \\mathbf {B} ^ {(l)}, \\tag {12} \\\\ \\mathbf {X} ^ {(l)} = \\tilde {\\mathbf {c}} \\odot \\operatorname {M L P} (\\operatorname {L N} (\\bar {\\mathbf {Z}} ^ {(l)})) + \\bar {\\mathbf {Z}} ^ {(l)}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.469, + 0.349 + ], + "angle": 0, + "content": "where LN is Layer Normalization [2], MLP is Multi-Layer Perceptron, and MCA is Multi-head Cross-Attention [49], whose output is split into affine weights \\(\\mathbf{W}^{(l)}\\) and biases \\(\\mathbf{B}^{(l)}\\). \\(\\tilde{\\mathbf{c}}\\) are learnable per-channel scales, and \\(\\mathbf{X}^{(l)}\\) the modulated video representations prior to moment decoding." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.352, + 0.469, + 0.477 + ], + "angle": 0, + "content": "Moment decoding. After fusion, our model decodes each time step into a moment candidate, similar to previous video grounding models [7, 27, 31, 60]. Briefly, a classification head predicts a score \\( p_t^{(l)} \\) for all \\( \\mathbf{x}_t^{(l)} \\) within \\( [\\mathbf{X}^{(l)}]_{l=1}^L \\), and a regression head predicts the normalized distances from \\( t \\) to the moment boundaries \\( (d_t^s, d_t^e) \\) if \\( \\mathbf{x}_t^{(l)} \\) is classified positive. Both heads are lightweight, each comprising three 1D convolutions. The decoded moment \\( \\hat{\\mathbf{y}} = (\\hat{s}, \\hat{e}) \\) is given by" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.485, + 0.469, + 0.517 + ], + "angle": 0, + "content": "\\[\n(t, l) = \\underset {t, l} {\\arg \\max } p _ {t} ^ {(l)}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.518, + 0.414, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\hat {s} = 2 ^ {l - 1} \\cdot (t - d _ {t} ^ {s}), \\quad \\hat {e} = 2 ^ {l - 1} \\cdot (t + d _ {t} ^ {e}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.543, + 0.469, + 0.573 + ], + "angle": 0, + "content": "At inference time, we further apply Soft-NMS [4] to merge overlapping moment predictions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.576, + 0.469, + 0.667 + ], + "angle": 0, + "content": "Training and loss function. We use video-centric training as described in Section 3.3. The loss function for a pair of video snippet and text query is the sum of two terms: a Focal loss [26] \\(\\mathcal{L}_{cls}\\) for moment classification and a Distance-IoU loss [69] \\(\\mathcal{L}_{reg}\\) defined on positive time steps for distance regression. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.674, + 0.469, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\frac {1}{C} \\left(\\mathcal {L} _ {c l s} + \\lambda_ {r e g} \\mathbb {1} _ {t} ^ {(l)} \\mathcal {L} _ {r e g}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.708, + 0.469, + 0.788 + ], + "angle": 0, + "content": "where \\(\\mathbb{1}_t^{(l)}\\) is an indicator function that evaluates to one on positive time steps, \\(C = \\sum_{t,l}\\mathbb{1}_t^{(l)}\\) is the total number of positive samples within the snippet, and \\(\\lambda_{reg}\\) balances the two loss terms. Center sampling [61] is used for selecting positive time steps around the center of a target moment." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.801, + 0.208, + 0.817 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Our main experiments include extensive comparisons of SnAG to strong baselines on five challenging benchmarks for video grounding. We further provide ablations on cross-modal fusion and analyze the efficiency of SnAG in both training and inference. More results are in the supplement." + }, + { + "type": "image", + "bbox": [ + 0.561, + 0.092, + 0.83, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.273, + 0.892, + 0.343 + ], + "angle": 0, + "content": "Figure 3. Visualization of dataset statistics. Circle radius is in proportion to average number of queries per video. Long-video benchmarks (Ego4D-NLQ, MAD and TACoS) consist of longer videos with more queries and exhibit low moment coverage compared to short-video benchmarks (ANet-Captions and Charades)." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.358, + 0.89, + 0.508 + ], + "angle": 0, + "content": "
ModelR@1R@5
0.30.5Avg0.30.5Avg
SF + BERT2D-TAN [67]5.042.023.5312.895.889.39
VSLNet [64]5.453.124.2910.746.638.69
CONE [17]10.405.037.7222.7411.8717.31
SOONet [36]8.003.765.8822.4011.0916.75
SnAG (video-centric)9.836.838.3327.9319.2723.60
SnAG (query-centric)10.437.158.7927.5919.3323.46
EgoVLPVSLNet [64]10.846.818.8318.8413.4516.15
CONE [17]14.158.1811.1730.3318.0224.18
SnAG (video-centric)15.7210.7813.2538.3927.4432.92
SnAG (query-centric)15.8711.2613.5738.2627.1632.71
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.513, + 0.89, + 0.54 + ], + "angle": 0, + "content": "Table 1. Results on Ego4D-NLQ. SnAG outperforms all baselines. Best results are in bold and second best underlined." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.568, + 0.89, + 0.599 + ], + "angle": 0, + "content": "Datasets. We categorize five benchmark datasets into two groups based on their video and query statistics (Fig. 3)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.891, + 0.753 + ], + "angle": 0, + "content": "Long videos, many queries. Ego4D-NLQ [16] is a large collection of egocentric videos on daily human activities. The videos are 3.5 to 20 minutes long with an average of 11.6 queries. MAD [45] contains 1.2K hours of movies with 384K queries transcribed from audio description. The videos are 47 to 202 minutes long. TACoS [40] is a conventional benchmark with 10.1 hours of cooking videos, with an average of 143.5 queries per video. These datasets expose the scalability challenges that motivate our work and thus are the main focus of our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.892, + 0.877 + ], + "angle": 0, + "content": "Short videos, few queries. Charades-STA [43] is an action recognition dataset later annotated for video grounding [13]. The videos are \\(\\sim 30\\) seconds long with \\(\\sim 2.4\\) queries per video. ActivityNet-Captions [20] was collected for dense video captioning and later repurposed for video grounding. The videos are two minutes long on average with a small set of \\(\\sim 3.65\\) queries. Several works [35, 57] advise against using these datasets as benchmarks for the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.887, + 0.836, + 0.9 + ], + "angle": 0, + "content": "3All experiments are conducted using the Ego4D \\(\\nu I\\) dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18934" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.847, + 0.228 + ], + "angle": 0, + "content": "
ModelR@1R@5R@10R@50
0.10.30.50.10.30.50.10.30.50.10.30.5
CLIP [39]6.573.131.3915.059.855.4420.2614.138.3837.9228.7118.80
VLG-Net [46]3.642.761.6511.669.315.9917.3914.569.7739.7834.2724.93
Moment-DETR [21]0.310.240.161.521.140.282.792.061.2011.087.974.71
CONE [17]8.906.874.1020.5116.119.5927.2021.5312.8243.3634.7320.56
SOONet [36]11.269.005.3223.2119.6413.1430.3626.0017.8450.3244.7832.59
SnAG (video-centric)10.288.465.5524.4220.6013.7532.2327.5019.0052.2846.6835.24
SnAG (query-centric)10.188.375.4424.3020.3513.5132.0527.2518.7552.0546.5334.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.151, + 0.234, + 0.816, + 0.248 + ], + "angle": 0, + "content": "Table 2. Results on MAD. SnAG outperforms all baselines. Best results are in bold and second best underlined." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.262, + 0.468, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.475 + ], + "angle": 0, + "content": "Figure 4. Visualization of moment predictions. SnAG can (a) comprehend complex text queries with multiple objects and actions; (b) reason about temporal ordering of events." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.469, + 0.513 + ], + "angle": 0, + "content": "temporal biases in their moment annotations. Nevertheless, we report results on these datasets for completeness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.469, + 0.669 + ], + "angle": 0, + "content": "Baselines. On TACoS, Charades and ANet-Captions, we compare to strong baselines including two-stage [28, 55, 56] and single-stage [30, 50, 70] models with various fusion operations (LSTM [29, 51], GCN [27, 46], co-attention [24, 68], etc.). On Ego4D and MAD, we compare to their official baselines (2D-TAN [67] and VSLNet [64] for Ego4D, CLIP [39] and VLG-Net [46] for MAD) as well as the concurrent method of CONE [17] and SOONet [36] that similarly address scalable video grounding. We discuss additional baselines in the supplement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.469, + 0.747 + ], + "angle": 0, + "content": "Evaluation metric. We report \\(\\mathrm{Recall}@\\mathbf{k}\\) at various temporal intersection-over-union threshold \\(\\theta\\) (\\(\\mathbf{R}@\\mathbf{k}\\), tIoU=\\(\\theta\\)) for all datasets. It measures the percentage of sentence queries with at least one of the top-\\(k\\) moment predictions whose temporal overlap with the ground-truth moment exceeds \\(\\theta\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.329, + 0.773 + ], + "angle": 0, + "content": "4.1. Long Videos, Many Queries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Experiment setup. For Ego4D, We consider (1) SlowFast [12] video features with BERT [10] text features, and (2) EgoVLP [38] video and text features. We train on the train split and report R@{1, 5}, tIoU={0.3, 0.5} on the val split. For MAD, we use CLIP [39] features for both videos and text. We train on the train split and report R@{1, 5, 10, 50}, tIoU={0.1, 0.3, 0.5} on the test split. For TACoS, we use C3D video features [48] and GloVe [37] for" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.321 + ], + "angle": 0, + "content": "sentence embeddings. We train on the train split and report \\(\\mathrm{R}@\\{1,5\\}\\), tIoU=\\{0.5, 0.7\\} on the test split. We report results using both video-centric and query-centric training on all datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.893, + 0.493 + ], + "angle": 0, + "content": "Results on Ego4D-NLQ (Table 1). SnAG sets the new state of the art, achieving mean R@1 / R@5 scores of \\(8.79\\% / 23.60\\%\\) with SlowFast/BERT features, and \\(13.57\\% / 32.92\\%\\) with EgoVLP features, doubling or even tripling the results of the official baselines [64, 67]. Compared to the strong baselines of CONE [17] and SOONet [36], SnAG improves mean R@1 and R@5 respectively by more than 1.05 and 6.29 absolute percentage points without taking advantage of external features. Further, SnAG demonstrates a larger performance gain on the more stringent tIoU threshold of 0.5, indicating more precise moment localization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.648 + ], + "angle": 0, + "content": "Results on MAD (Table 2). SnAG sets new records on the challenging MAD dataset. It improves over CLIP [39] and VLG-Net [46] on mean R@1 / R@5 at tIoU=0.5 by 3.90 / 7.76 absolute percentage points. In the meantime, it outperforms CONE [17] and SOONet [36], with larger gain for more stringent tIoU thresholds. Further, SnAG achieves stronger results as input snippet length increases, reaching the best accuracy with \\( T_{w} = 16384 \\) (Supplement Fig. A). This scaling behavior highlights the strength of our scalable model design for long-form video grounding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.832 + ], + "angle": 0, + "content": "Results on TACoS (Table 4 (left)). SnAG achieves an R@1 / R@5 of \\(44.86\\%\\) / \\(70.66\\%\\) at tIoU=0.5, outperforming the strongest baseline of MATN [66] by a significant margin \\((+7.5\\% \\mathrm{R} @ 1, +12.1\\% \\mathrm{R} @ 5)\\). This confirms that our simple single-stage design with late fusion is a strong alternative to multi-stage models with sophisticated fusion mechanisms. Importantly, our scalable design enables learning from full-resolution video features, whereas the baselines often aggressively reduce feature resolution to contain their training and inference cost on long-form videos. We hypothesize that full-resolution video features capture detailed event dynamics and are key to the strong performance of SnAG." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.836, + 0.892, + 0.866 + ], + "angle": 0, + "content": "Result visualization. We visualize predictions of SnAG and the baselines on TACoS and Ego4D-NLQ videos. In" + }, + { + "type": "page_footnote", + "bbox": [ + 0.516, + 0.875, + 0.871, + 0.888 + ], + "angle": 0, + "content": "4CONE [17] leverages external CLIP [39] features in several steps." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.888, + 0.858, + 0.901 + ], + "angle": 0, + "content": "5MAD videos are not publicly available due to copyright issues." + }, + { + "type": "list", + "bbox": [ + 0.516, + 0.875, + 0.871, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18935" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.1, + 0.089, + 0.445, + 0.336 + ], + "angle": 0, + "content": "
ModelR@1R@5
0.30.50.30.5
(a) Fusion stage (early vs. late fusion)
No fusion10.857.8546.4631.19
SnAG-E53.3444.0179.5669.41
SnAG-EL54.8444.5481.1370.11
SnAG-M51.4140.7977.5665.71
SnAG (ours)55.1444.9481.1070.66
(b) Fusion operation (global vs. token-wise)
Cat49.3939.2477.3165.36
Add51.9141.8177.9866.51
Scale55.0143.9680.6370.11
Add + Scale53.3643.0980.4369.58
XAttn54.8445.0679.9670.08
XAttn-affine (ours)55.1444.9481.1070.66
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.341, + 0.47, + 0.397 + ], + "angle": 0, + "content": "Table 3. Ablations results on TACoS. (a) Late fusion yields comparable results to early fusion (E, EL, M); (b) Fusion with tokenwise sentence embeddings (XAttn) produces better results than fusion with global sentence embeddings (Cat, Add, Scale)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Fig. 4(a), a long query describes the complex interplay between two objects (pan and stove) and three actions (\"take from\", \"place on\", and \"turn on\"). VLG-Net [46] recognized both objects yet none of the actions, while 2D-TAN [67] identified one action (\"take from\") but at the same time missed one object (pan). By contrast, SnAG followed the query semantics and produced accurate localization. The other query in Fig. 4(b) tests the understanding of temporal context. SnAG leveraged the keyword \"before\" to identify the correct moment before the action (\"pick up\"), whereas VSLNet [64] only attended to the object (can), thus mistakenly predicting a moment after the action." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.608, + 0.318, + 0.623 + ], + "angle": 0, + "content": "4.2. Short Videos, Few Queries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.789 + ], + "angle": 0, + "content": "Experiment setup. We extract video features using both C3D [48] (pretrained on Sports-1M [18]) and I3D [5] (pretrained on Kinetics [19]) for Charades-STA, and use the official C3D features for ActivityNet-Captions. We use GloVe word embeddings [37] to represent sentence queries for both datasets. We train on their respective train splits, report R@{1, 5}, tIoU={0.5, 0.7} on the test split of Charades-STA, and R@{1, 5}, tIoU={0.3, 0.5} on the val_2 split of ActivityNet-Captions. Following standard practice, we resize all video features to a uniform length of 256." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Results on Charades-STA (Table 4 (middle)). SnAG outperforms all previous methods by a wide margin. It obtains \\(33.52\\%\\) R@1 and \\(64.11\\%\\) R@5 at tIoU=0.7 with C3D features, 2.10 and 4.52 absolute percentage points higher than the latest SSRN [71] baseline. It further attains \\(46.26\\%\\) R@1 and \\(71.94\\%\\) R@5 at tIoU=0.7 with I3D features, setting new state of the art on this competitive benchmark." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Results on ActivityNet-Captions (Table 4 (right)). SnAG achieves competitive results, reaching an R@1 / R@5 score of \\(30.56\\% / 63.41\\%\\) at tIoU=0.7. It is only outperformed by a few latest models [22, 27, 71] while being much simpler." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.161, + 0.665, + 0.176 + ], + "angle": 0, + "content": "4.3. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.185, + 0.891, + 0.214 + ], + "angle": 0, + "content": "We conduct extensive ablations on TACoS to study key design choices for cross-modal fusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.219, + 0.892, + 0.324 + ], + "angle": 0, + "content": "Early vs. late fusion. Does late fusion enable better scalability at the expense of accuracy? We study three variants of SnAG with common early-fusion designs: (1) SnAG-E with fusion before the pyramid; (2) SnAG-EL with fusion before and after the pyramid; (3) SnAG-M with repeated fusion within the pyramid. Table 3 confirms that early and late fusion yield comparable results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Choice of fusion operation. We study fusion operations used by strong baselines, including point-wise addition, multiplication, and concatenation of video representations with global sentence embeddings, as well as vanilla cross-attention with token-level sentence embeddings. According to Table 3, token-level embeddings produce better results, and our cross-attention variant further boosts performance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.444, + 0.682, + 0.459 + ], + "angle": 0, + "content": "4.4. Efficiency Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.467, + 0.878, + 0.482 + ], + "angle": 0, + "content": "Finally, we conduct an efficiency analysis of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.668 + ], + "angle": 0, + "content": "Breakdown of model capacity. A key design choice of SnAG is to carefully balance the model capacity among its video encoder, text encoder, and moment decoder including the fusion module and the localization heads. For a detailed breakdown of model capacity, we measure their respective parameter size and MACs in percentage. Fig. 5(a) indicates that SnAG's video encoder absorbs a significant portion of parameters and compute, such that per-query evaluation (i.e., text encoding, fusion, and decoding) occupies \\(\\sim 50\\%\\) of the total computation. This design is naturally in favor of video-centric training and inference, where the costly video encoding is shared among many queries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Video-centric vs. query-centric training. Fig. 5(b) presents the training time and GPU memory usage of video-centric training relative to conventional query-centric training. The results show that the amount of saving correlates with snippet length and number of queries. Video-centric training is thus preferred for long videos with many queries." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\(B_{q}\\) in video-centric training. We further study how \\(B_{q}\\), the number of text query samples per video, trades off accuracy for efficiency in video-centric training. On MAD, we fix the batch size \\(|B| = 32\\) for a mini-batch \\(B\\), vary \\(B_{q}\\) between 1 and \\(|B|\\), and report training time, GPU memory usage and test accuracy relative to query-centric training (i.e., \\(B_{q} = 1\\)). Fig. 5(d) reveals that test accuracy is unaffected even with a large \\(B_{q} = 32\\) (i.e., a single video per mini-batch), while training time and GPU memory usage" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18936" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.072, + 0.89, + 0.37 + ], + "angle": 0, + "content": "
MethodTACoS (C3D)Charades-STA (I3D)Charades-STA (C3D)ActivityNet-Captions (C3D)
R@1R@5R@1R@5R@1R@5R@1R@5
0.30.50.30.50.50.70.50.70.50.70.50.70.50.70.50.7
CTRL ICCV 17 [13]18.3213.3036.6925.42----23.638.8958.9229.52----
QSPN AAAI 19 [56]--------35.6015.8079.4045.4027.7013.6059.2038.30
SCDM NeurIPS 19 [58]27.6423.2740.0633.4954.9234.2676.5060.02----36.9020.2866.8442.92
2D-TAN AAAI 20 [67]45.6135.7769.1157.3156.6436.2189.1461.1341.1023.2581.5348.5546.1629.2178.8060.85
CBP AAAI 20 [51]27.3124.7943.6437.40----36.8018.8770.9450.1935.7617.8065.8946.20
DRN CVPR 20 [60]-23.17-33.3653.0931.7589.0660.0545.4026.4088.0155.3845.4524.3677.9750.30
BPNet AAAI 21 [55]25.9620.96--50.7531.64--38.2520.51--42.0724.69--
CPNet AAAI 21 [24]42.6128.29--60.2738.74--40.3222.47--40.5621.63--
SMIN CVPR 21 [50]48.0135.2465.1853.3664.0640.7589.4968.09----48.4630.3481.1662.11
CBLN CVPR 21 [29]38.9827.6573.1246.2461.1338.2290.3361.6947.9428.2288.2057.4748.1227.6079.3263.41
CPN CVPR 21 [68]47.6936.33--51.0731.54------45.1028.10--
DeNet CVPR 21 [70]----59.7038.5291.2466.83----43.79-74.13-
MATN CVPR 21 [66]48.7937.5767.6357.91--------48.0231.7878.0263.18
VLG-Net ICCVW 21 [46]45.4634.1970.3856.56--------46.3229.8277.1563.33
APGN EMNLP 21 [28]40.4727.8659.9847.1262.5838.8691.2462.1148.2029.3789.0558.4948.9228.6478.8763.19
IA-Net EMNLP 21 [30]37.9126.2757.6246.3961.2937.9189.7862.04----48.5727.9578.9963.12
RaNet EMNLP 21 [14]43.3433.5467.3355.0960.4039.6589.5764.54----45.5928.6775.9362.97
MGSL-Net AAAI 22 [30]42.5432.2763.3950.1363.9841.0393.2163.85----51.8731.4282.6066.71
MMN AAAI 22 [52]39.2426.1762.0347.39--------48.5929.2679.5064.76
SSRN EMNLP 22 [71]45.1034.3365.2651.8565.5942.6594.7665.4850.3931.4290.6859.9454.4933.1584.7268.48
G2L ICCV 23 [22]42.7430.9565.8349.86--------51.6833.3581.3267.60
SnAG (video-centric)56.4444.8681.1570.6664.6246.2692.5571.9451.7233.5292.5564.1148.5530.5681.7163.41
SnAG (query-centric)55.0144.5180.6870.1365.1345.9192.8071.7551.1031.7790.2262.1547.5529.6581.5562.21
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.375, + 0.893, + 0.404 + ], + "angle": 0, + "content": "Table 4. Results on TACoS, Charades-STA and ActivityNet-Captions. SnAG outperforms all baselines on TACoS and Charade-STA by a large margin, while being highly competitive on ActivityNet-Captions. Best results are in bold and second best underlined." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.419, + 0.262, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.419, + 0.466, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.419, + 0.681, + 0.535 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.421, + 0.89, + 0.536 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.538, + 0.893, + 0.608 + ], + "angle": 0, + "content": "Figure 5. (a) Model capacity. T, E, M denotes TACoS, Ego4D and MAD, respectively (also in (b)). Shaded bar: % of parameters, Colored bar: % of MACs. SnAG places more parameters and compute in video encoder for less expensive per-query evaluation (fusion + decoding). (b, c) Video-centric vs. query-centric inference (b) and training (c). SnAG saves up to \\(50\\%\\) training time, \\(40\\%\\) GPU memory and \\(80\\%\\) test time, and delivers up to \\(40\\%\\) faster convergence relative to query-centric training / inference. (d) Effect of \\(B_{q}\\) on training efficiency and test accuracy on MAD. Training on MAD is faster and takes less GPU memory as \\(B_{q}\\) grows, while the test accuracy is unaffected." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.658 + ], + "angle": 0, + "content": "drop by a significant \\(55\\%\\) and \\(42\\%\\), approaching the upper bound by our analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.662, + 0.47, + 0.814 + ], + "angle": 0, + "content": "Video-centric vs. query-centric inference. We now ask to what extent the re-use of video representations enabled by SnAG's late fusion design accelerates inference. Fig. 5(b) presents the percentage of time spent by our video-centric inference scheme relative to query-centric inference, where the full model is evaluated on each and every video-query pair. Consistent with earlier findings on video-centric training, longer videos with more queries result in more saving in inference time. On the challenging MAD dataset, this alone brings a major reduction (65%) in test time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.817, + 0.471, + 0.879 + ], + "angle": 0, + "content": "Inference speed. With window filtering [17], inference of SnAG on the val split of MAD takes 12 minutes on a single P100 GPU. This is \\(33\\%\\) faster than CONE [17] (\\(\\sim 18\\) mins) and \\(63\\%\\) faster than SOONet [36] (\\(\\sim 32\\) mins).6" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.627, + 0.62, + 0.643 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.892, + 0.835 + ], + "angle": 0, + "content": "In this paper, we presented a simple and accurate model towards scaling up video grounding. We provided extensive analysis on the complexity of video grounding models from the perspective of cross-modal fusion, and argued that late fusion is key to scalability in video duration and query size. Our model, SnAG, is a simple instantiation of late fusion with minimalist design. It achieves superior accuracy and efficiency on a spectrum of challenging benchmarks and compares favorably to strong baselines including those dedicated to efficient inference on long videos. We hope our analysis and model design can shed light on video grounding and more broadly scalable video understanding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.894, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement: This work was partially supported by NIH grant R01OH012313, by grants from McPherson Eye Research Institute and VCGRE at UW Madison, and by the Army Research Lab under contract number W911NF-2020221." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.468, + 0.901 + ], + "angle": 0, + "content": "\\(^{6}\\)SOONet reports an inference time of 8.2 mins on a single A100 GPU." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18937" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.088, + 0.116, + 0.47, + 0.175 + ], + "angle": 0, + "content": "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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In EMNLP Findings, 2022. 2, 7, 8" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.892, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18940" + } + ] +] \ No newline at end of file diff --git a/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_origin.pdf b/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9c52d6327b145b28d6c30f114735df5e1ab33770 --- /dev/null +++ b/2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:380550266709ccd44059b724754ce81942935ead32361eb8cccc9ddb3da214a1 +size 4679104 diff --git a/2024/SnAG_ Scalable and Accurate Video Grounding/full.md b/2024/SnAG_ Scalable and Accurate Video Grounding/full.md new file mode 100644 index 0000000000000000000000000000000000000000..edda82517be1c352fc6151db0fb7983d0e27e2ea --- /dev/null +++ b/2024/SnAG_ Scalable and Accurate Video Grounding/full.md @@ -0,0 +1,372 @@ +# SnAG: Scalable and Accurate Video Grounding + +Fangzhou Mu*, Sicheng Mo*, Yin Li +University of Wisconsin-Madison + +# Abstract + +Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability — they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is $43\%$ more accurate and $1.5 \times$ faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos. Our code is available at https://github.com/fmu2/snag_release. + +# 1. Introduction + +Localizing moments within an untrimmed video based on text descriptions, also known as temporal video grounding, involves joint reasoning about visual, textual and temporal information, and thus remains a challenging problem in video understanding. Video grounding is gaining traction amid the rapid advances in vision-language learning, with a range of applications such as intelligent personal assistants, human-robot interaction, and interactive video editing. + +Despite recent progress, one largely overlooked aspect of video grounding is the scalability of models with respect to video duration and the number of text descriptions (i.e., queries). Previous methods (e.g., [46, 67]) are primarily designed for grounding only a few queries within short video snippets. However, the growing availability of long videos (e.g., on streaming platforms) and demand to query their rich contents introduce a paradigm shift, necessitating efficient grounding of large volumes of queries in long videos. + +![](images/b9a807416c0ebc2e4ad55975342dc123777b8a8af446635bc0de09fcd6219e94.jpg) +Figure 1. SnAG achieves the best accuracy and throughput simultaneously on the MAD dataset [45] for long-form video grounding. + +On latest long-form video grounding benchmarks [16, 45], these methods struggle to scale up due to their high computational cost, and suffer major performance degradation. + +In this paper, we take a principled approach to studying the problem of scalable video grounding, focusing on the design of cross-modal fusion—a key model component that combines visual and textual information. Specifically, we present an analysis that connects the computational cost of video grounding models to their fusion schemes. Our analysis and empirical results challenge the widely adopted early fusion, showing that late fusion scales better in inference by amortizing the cost of long video processing among text queries. Importantly, this insight further motivates the design of a novel, video-centric sampling scheme for scalable training, without compromising grounding accuracy. + +Following these findings, we present SnAG, a scalable and accurate model for long-form video grounding. SnAG features a minimalist, late-fusion design for scalable inference, while supporting video-centric sampling for scalable training. Notwithstanding its simplicity, SnAG achieves superior results across all benchmarks designed for long-form video grounding. Without bells and whistles, SnAG attains $13.75\%$ R@5, tIoU=0.5 on MAD [45] with an inference speed of 45.3 queries per second on a P100 GPU (Fig. 1), $43\%$ more accurate and $1.5\times$ faster than the concurrent method of CONE [17]. In the meantime, SnAG is highly competitive on short-video benchmarks. It achieves $46.26\%$ R@1, tIoU=0.7 on Charades-STA [43], outperforming the + +previous state of the art (SSRN [71]) by 3.61 absolute percentage points while being simpler in model design. + +Contributions. (1) We present one of the first studies to understand the effect of fusion schemes on the computational cost of video grounding. (2) Our analysis offers new insights and leads to a new training scheme for scalable video grounding. (3) Based on our findings, we further deliver a simple model that attains superior results across major benchmarks for long-form video grounding while achieving significant efficiency gains in both training and inference. + +# 2. Related Work + +Video grounding. Previous works on video grounding can be categorized based on whether proposals are generated as moment candidates (two-stage vs. single-stage), and how text queries inform action localization (cross-modal fusion). + +Two-stage methods first generate temporal segments as proposals, then score their "actionness" and optionally refine their boundaries. Early works [1, 13] densely sample proposals using sliding windows and score them independently. One line of work [8, 28, 54-56] subsequently conditions proposal generation on sentence queries and/or video context to avoid dense sampling. By contrast, another line of work [14, 46, 50, 66, 67] takes the opposite path of enumerating all segments, yet organizes them in a 2D adjacency map to reason about their relations. + +Single-stage methods localize moments in a single shot without using proposals, and thus are often more efficient than two-stage methods. Some models decode moment boundaries from global features [23, 24, 33, 59, 70] or learnable queries [21, 25, 53]. Others densely predict onset and offset probabilities [15, 29, 34, 41, 63-65, 68], or classify and refine pre-set anchors [6, 30, 51, 58, 62] at every moment. Most relevant to our work are models that represent moment candidates as points [7, 11, 27, 31, 60]. Analogous to point-based object detectors [47], they classify every point in time and regress moment boundaries relative to the points. Despite their simplicity and efficiency, the performance of single-stage models lags behind two-stage models on standard benchmarks made up of short videos. + +Cross-modal fusion combines video and text information for video grounding. Early models [1, 13] fuse video and text representations right before final prediction. This simple, late-fusion approach is abandoned by subsequent models, which turn to early fusion (e.g., [56, 60, 62, 67]) with sophisticated model design (e.g., LSTM [6, 15, 29, 51, 56, 65], GCN [7, 27, 46], memory bank [8, 27]), feature hierarchies [14, 33, 50], losses [23, 34, 56, 66], and inference procedures [68, 70]. Early fusion is believed to strengthen cross-modal reasoning, albeit at a price of model complexity. Recent Transformer-based models [3, 21, 53, 66] inherit this early-fusion design; video features and text embeddings + +are concatenated at input, and attention-based feature fusion is carried out throughout the model. + +Our method demonstrates a single-stage Transformer model with a simple late fusion mechanism based on crossattention. Late fusion allows us to amortize the cost of video processing across many sentence queries, resulting in scalable training and inference on long-form videos. Without bells and whistles, our model outperforms all prior methods on long-video benchmarks, and attains competitive performance on standard, short-video benchmarks. + +Long-form video grounding. Recent efforts [16, 45] put forth new challenges for sentence grounding in long videos. Previous methods tailored for short videos [46, 64, 67] fall short on these benchmarks. They have no access to long-range video context, require dense sliding window inference, and yield unsatisfactory results. Concurrent works [17, 36] present multi-stage approaches with sophisticated pre-processing, ranking and training procedures for efficient long-form video grounding. However, their efficiency stems from the restrictive assumption that moments are covered by short windows. By contrast, SnAG offers a simple, single-stage solution with superior accuracy, without making assumptions about moment duration. + +Localizing moments in videos. Closely related to video grounding, temporal action localization (e.g., [32, 42, 44]) aims to identify moments of actions from within a closed set of action categories. Solutions to the two tasks often evolve in tandem and share remarkably similar model design. SnAG is inspired by our prior work [61], yet extends its design for the more challenging task of video grounding, with the goal of scaling up video grounding for long videos. + +# 3. Scaling Up Video Grounding + +Our goal is to scale up video grounding for long-form videos with many queries. Denote an input video $\mathbf{V}$ as a time-indexed sequence $[\mathbf{v}_t]_{t=1}^T = [\mathbf{v}_1, \mathbf{v}_2, \dots, \mathbf{v}_T]$ , where $\mathbf{v}_t$ represents a short video clip centered at time $t$ .1 $\mathbf{V}$ is paired with $N$ sentence queries $\{\mathrm{Q}_j\}_{j=1}^N$ , each describing a moment $\mathbf{y}_j = (s_j, e_j)$ in the video. + +Long-form video grounding is characterized by a great number of time steps $T$ (e.g., tens of thousands) and text queries $N$ (hundreds) for an input video $\mathbf{V}$ . With a large $T$ , it is no longer feasible to feed the full video $\mathbf{V}$ into a model, and thus more viable to consider a sliding window setting. Specifically, a video $\mathbf{V}$ is further partitioned into a set of $M$ snippets $\{\mathbf{V}_{i=1}^{M}\}$ , each $\mathbf{V}_{i} = [\mathbf{v}_{t}]_{t=t_{i}}^{t_{i} + T_{w}}$ taken from a local time window of size $T_{w}$ that may overlap with others. We consider the learning of a function $\mathcal{F}$ , realized in a deep + +![](images/4803639b0a1f16039b839ad918d58e34425082f99caff1fafa9a2122313a6aae.jpg) +Figure 2. (a) Cross-modal fusion is key to a video grounding model $\mathcal{F}$ . Models using early fusion jointly encode video and sentence query. SnAG revisits late fusion for scalable video grounding by decoupling expensive video encoding and inexpensive query encoding. (b) Video-centric model evaluation. With late fusion, the output of video encoder can be cached and re-used by queries of the same video in both training and inference. (c) Mini-batch sampling in training. Previous methods adopt query-centric sampling (query $\rightarrow$ video) whereas SnAG resorts to video-centric sampling (video $\rightarrow$ many queries) for efficient training. (d) Model overview. SnAG is a simple instantiation of late fusion and video-centric training for video grounding. It separately encodes a video and its queries using Transformers, applies simple cross-attention for cross-modal fusion, and decodes moments represented as points using lightweight convolutional heads. + +![](images/24f620b34609b9f3f19062804931b668980e1121d4689609c7c691dd26f796f2.jpg) + +![](images/2ae59873afb84ef2c5185ee19976e539c33b58e59f038c76a8a3cd9d0b114779.jpg) + +network, to predict the start time $s_j$ and end time $e_j$ of the moment $\mathbf{y}_j$ given a snippet $\mathbf{V}_i$ and a query $\mathrm{Q}_j$ . + +# 3.1. Background: Cross-Modal Fusion + +We review cross-modal fusion - a key design choice of $\mathcal{F}$ and define the notation used for the rest of the paper. + +Early fusion. A straightforward design is to fuse information from a video snippet $\mathbf{V}_i$ and a text query $\mathrm{Q}_j$ at input (Fig. 2(a)). This early fusion strategy is widely adopted in prior works [21, 53, 60, 62, 66, 67], and can be written as + +$$ +\mathcal {F} _ {E} \left(\mathbf {V} _ {i}, \mathrm {Q} _ {j}\right) \mapsto \mathbf {y} _ {j}, \tag {1} +$$ + +where $\mapsto$ defines any necessary post-processing of the model outputs (e.g., re-scaling, non-maximum suppression) in order to decode the moment $\mathbf{y}_j$ . + +Late fusion. Another possible design is to first embed the video snippet $\mathbf{V}_i$ and text query $\mathrm{Q}_j$ , then fuse their features for grounding (Fig. 2(a)). This late fusion strategy follows + +$$ +\mathcal {F} _ {L} \left(g \left(\mathbf {V} _ {i}\right), h \left(\mathrm {Q} _ {j}\right)\right) \mapsto \mathbf {y} _ {j}, \tag {2} +$$ + +where $g(\cdot)$ is the video encoder and $h(\cdot)$ the text encoder. With slight abuse of the symbols, $\mathcal{F}_L$ here denotes the rest part of the grounding model, including feature fusion. The key is to keep $\mathcal{F}_L$ lightweight, i.e., its cost should be a minor portion in comparison to the rest of the model. + +Design choice. The conventional wisdom favors the design of early fusion for video grounding. Early fusion is believed to offer better interactions between visual and textual features, resulting in strong empirical results. In what follows, we analyze the computational cost of early and late fusion + +during inference and training, and show that proper design of late fusion allows significantly improved scalability in video duration $(M)$ and number of text queries $(N)$ . + +# 3.2. Scalable Inference + +We start by analyzing the computational cost of early vs. late fusion in inference. Denote the computational cost of a function by $\mathcal{C}(\cdot)$ . For example, $\mathcal{C}(g)$ is the cost of the video encoder $g(\cdot)$ , and $\mathcal{C}(h)$ the cost of the text encoder $h(\cdot)$ . + +Computational cost. We make two key observations regarding the computational cost of a video grounding model: (a) a lightweight $\mathcal{F}_L$ is used for late fusion, thus $\mathcal{C}(\mathcal{F}_L) \ll \mathcal{C}(g) + \mathcal{C}(h)$ ; and (b) the video encoder $g(\cdot)$ has a much higher cost than the text encoder, thus $\mathcal{C}(g) \gg \mathcal{C}(h)$ . + +The first observation stems from the design of late fusion. To justify the second observation, it is important to notice that $\mathcal{C}(g)$ scales w.r.t. the length of input video snippet (i.e., the local window size $T_w$ ), whereas $\mathcal{C}(h)$ remains constant due to limited sequence length of text queries. For example, a realization of $g(\cdot)$ using a vanilla Transformer has a complexity of $\mathcal{O}(T_w^2)$ . Thus, using a larger local window size naturally leads to $\mathcal{C}(g) \gg \mathcal{C}(h)$ . + +Cost analysis: early vs. late fusion. Evaluating an early-fusion model on a video with $M$ snippets and $N$ queries has a cost of $MN\mathcal{C}(\mathcal{F}_E)$ , whereas late fusion has a cost of $MN\mathcal{C}(\mathcal{F}_L) + MC(g) + NC(h)$ . This is because an early-fusion model has to compare each snippet to every query, yet late fusion allows re-using video features for all queries of the video (i.e., video-centric evaluation, see Fig. 2(b)). + +Let us assume that the cost of both models can be controlled by setting $\mathcal{C}(\mathcal{F}_E) = \mathcal{C}(\mathcal{F}_L) + \mathcal{C}(g) + \mathcal{C}(h)$ , i.e., eval + +uating either model on a pair of video snippet and sentence query has the same cost (post-processing excluded). With $\mathcal{C}(\mathcal{F}_L) = \alpha (\mathcal{C}(g) + \mathcal{C}(h))$ for some small $\alpha$ , the ratio between the cost of early and late fusion in inference is + +$$ +\begin{array}{l} \mathbf {R} _ {\text {i n f}} = \frac {\mathcal {C} (\text {i n f e r e n c e w i t h e a r l y f u s i o n})}{\mathcal {C} (\text {i n f e r e n c e w i t h l a t e f u s i o n})} (3) \\ = \frac {M N \mathcal {C} \left(\mathcal {F} _ {L}\right) + M N \mathcal {C} (g) + M N \mathcal {C} (h)}{M N \mathcal {C} \left(\mathcal {F} _ {L}\right) + M \mathcal {C} (g) + N \mathcal {C} (h)} (4) \\ = \frac {M N (1 + \alpha)}{M N \alpha + M \mathbf {R} _ {g / (g + h)} + N (1 - \mathbf {R} _ {g / (g + h)})} (5) \\ \approx \frac {1 + \alpha}{\frac {1}{N} + \alpha} \rightarrow \left\{\begin{array}{l l}N,&\alpha \rightarrow 0\\1 + \frac {1}{\alpha},&N \rightarrow \infty\end{array}, \right. (6) \\ \end{array} +$$ + +where $\mathbf{R}_{g / (g + h)} = \mathcal{C}(g) / (\mathcal{C}(g) + \mathcal{C}(h))$ , and the approximation in Eq. 6 is a result of $\mathbf{R}_{g / (g + h)} \approx 1$ with $\mathcal{C}(g) \gg \mathcal{C}(h)$ . Eq. 6 reveals that early fusion is $N$ times the cost of late fusion as snippet length grows ( $\alpha \to 0$ ), and is particularly inefficient for videos with many queries ( $N \to \infty$ ). + +# 3.3. Scalable Training + +We now show that late fusion further unlocks a novel training scheme that scales well for long-form video grounding. + +Training and mini-batch sampling. Given a set of paired videos, text queries, and their moments $\{\mathbf{V}^{(k)},\mathbf{Q}^{(k)},\mathbf{y}^{(k)}\}$ , training a model $\mathcal{F}$ amounts to minimizing a loss function $\mathcal{L}$ over mini-batches $B$ sampled from the dataset: + +$$ +\Sigma_ {(k, i, j) \in B} \mathcal {L} \left(\mathcal {F} \left(\mathbf {V} _ {i} ^ {(k)}, \mathrm {Q} _ {j} ^ {(k)}\right), \mathbf {y} _ {j} ^ {(k)}\right). \tag {7} +$$ + +A key design largely overlooked in video grounding is the mini-batch sampling scheme during training. With multiple queries associated with a video snippet, a combination of late fusion and proper sampling scheme allows us to reuse video representations in training as is done in inference. + +Query-centric sampling. Virtually all prior works sample mini-batches uniformly at random from all pairs of valid video snippets and text queries. $^{2}$ This can be interpreted as ancestral sampling: first draw a text query (and its moment), then select a video snippet covering the moment: + +$$ +\mathrm {Q} _ {j ^ {\prime}} ^ {(k ^ {\prime})}, \mathbf {y} _ {j ^ {\prime}} ^ {(k ^ {\prime})} \sim U \left(\left\{\left(\mathrm {Q} _ {j} ^ {(k)}, \mathbf {y} _ {j} ^ {(k)}\right) \right\} _ {j \times k}\right), \tag {8} +$$ + +$$ +\mathbf {V} _ {i ^ {\prime}} ^ {(k ^ {\prime})} \sim U \left(\left\{\left(\mathbf {V} _ {i} ^ {(k ^ {\prime})}, \mathrm {Q} _ {j ^ {\prime}} ^ {(k ^ {\prime})}, \mathbf {y} _ {j ^ {\prime}} ^ {(k ^ {\prime})}\right) _ {+} \right\}\right), +$$ + +where $U(\cdot)$ denotes a discrete uniform distribution and $\{(\mathbf{V}_i^{(k')},\mathbf{Q}_j^{(k')},\mathbf{y}_{j'}^{(k')})_{+}\}$ is the union of all valid triplets: a moment $\mathbf{y}_{j'}^{(k')}$ of a text query $\mathbf{Q}_{j'}^{(k')}$ in a video snippet $\mathbf{V}_i^{(k')}$ . + +This sampling process is repeated $|B|$ times to construct a mini-batch, with $|B|$ the batch size. With a large + +dataset, the resulting mini-batch will contain $|B|$ snippet-query pairs, each likely from a different video. + +Video-centric sampling. To speed up the training of late fusion models, we propose video-centric sampling that considers every video snippet $\mathbf{V}_i^{(k)}$ as a sample. Specifically, we first draw a video based on its importance score, then sample a snippet within the video, and finally select multiple text queries associated with the snippet. This is defined as the following ancestral sampling: + +$$ +k ^ {\prime} \sim P (k) = \frac {M _ {+} ^ {(k)}}{\Sigma_ {k} M _ {+} ^ {(k)}} \quad i ^ {\prime} \sim P (i; k ^ {\prime}) = \frac {N _ {i} ^ {\left(k ^ {\prime}\right)}}{\Sigma_ {k} N _ {i} ^ {\left(k ^ {\prime}\right)}} \tag {9} +$$ + +$$ +\left\{\mathrm {Q} _ {j ^ {\prime}} ^ {(k ^ {\prime})}, \mathbf {y} _ {j ^ {\prime}} ^ {(k ^ {\prime})} \right\} ^ {B _ {q}} \sim U \left(\left\{\left(\mathbf {V} _ {i ^ {\prime}} ^ {(k ^ {\prime})}, \mathrm {Q} _ {j} ^ {(k ^ {\prime})}, \mathbf {y} _ {j} ^ {(k ^ {\prime})}\right) _ {+} \right\}\right), +$$ + +where $M_{+}^{(k)}$ denotes the number of valid snippets in a video $\mathbf{V}^{(k)}$ , and $N_{i}^{(k^{\prime})}$ the number of queries in a snippet $\mathbf{V}_{i}^{(k^{\prime})}$ . Importantly, a total of $B_{q}$ queries are drawn for the selected video snippet $\mathbf{V}_{i^{\prime}}^{(k^{\prime})}$ . + +This sampling process is repeated $|B| / B_q$ times for a mini-batch, leading to $|B| / B_q$ video snippets, each likely from a different video yet with multiple $(B_q)$ text queries. This mini-batch thus allows us to re-use the video representations for the sampled snippets. + +Cost analysis: query-centric vs. video-centric sampling. Fig. 2(c) illustrates the key difference between query-centric and video-centric sampling. Similar to our analysis in Section 3.2, it is easy to show that late fusion combined with video-centric training enables substantial speedup for long snippets $(\alpha \rightarrow 0)$ and large $B_{q}$ : + +$$ +\begin{array}{l} \mathbf {R} _ {\text {t r a i n}} = \frac {\mathcal {C} (\text {l a t e f u s i o n} + \text {v i d e o - c e n t r i c t r a i n i n g})}{\mathcal {C} (\text {l a t e f u s i o n} + \text {q u e y - c e n t r i c t r a i n i n g})} (10) \\ \approx \frac {1 + \alpha}{\frac {1}{B _ {q}} + \alpha} \rightarrow \left\{\begin{array}{l l}B _ {q},&\alpha \rightarrow 0\\1 + \frac {1}{\alpha},&B _ {q} \rightarrow \infty\end{array}. \right. (11) \\ \end{array} +$$ + +# 3.4. Scalable Video Grounding: An Instantiation + +We now present an instantiation with late fusion and video-centric training for scalable video grounding. Our instantiation, dubbed SnAG, is shown in Fig. 2(d). SnAG is a single-stage Transformer model where every time step represents a moment candidate. It combines (a) a multi-scale Transformer-based video encoder; (b) a Transformer-based text encoder; (c) cross-attentions for late fusion; and (d) convolutional heads for moment decoding. + +Video encoder $g$ . We use the ActionFormer backbone [61] as our video encoder, given its superior performance on the closely related task of temporal action localization. It transforms input video features into a multi-scale representation $[\mathbf{Z}^{(l)}]_{l=1}^{L} = [\mathbf{Z}^{(1)}, \mathbf{Z}^{(2)}, \dots, \mathbf{Z}^{(L)}]$ using Transformer layers with local self-attentions [9]. We refer readers to the original paper [61] for more details on model architecture. + +Text encoder $h$ . Our text encoder is a vanilla Transformer. It takes a query Q with $K$ tokens $[\mathbf{q}_1, \dots, \mathbf{q}_K]$ and outputs their embeddings $\mathbf{E} = [\mathbf{e}_1, \dots, \mathbf{e}_K]$ . This computation is light compared to video encoding as $K \ll T_w$ for long videos. + +Cross-modal late fusion $\mathcal{F}_L$ . Our model uses a simple variant of cross-attention for fusion. Specifically, it modulates $[\mathbf{Z}^{(l)}]_{l=1}^L$ with an affine transformation given by $\mathbf{E}$ : + +$$ +\begin{array}{l} (\mathbf {W}, \mathbf {B}) ^ {(l)} = \operatorname {M C A} (\operatorname {L N} (\mathbf {Z} ^ {(l)}), \operatorname {L N} (\mathbf {E})), \\ \tilde {\mathbf {Z}} ^ {(l)} = \mathbf {W} ^ {(l)} \odot \mathbf {Z} ^ {(l)} + \mathbf {B} ^ {(l)}, \tag {12} \\ \mathbf {X} ^ {(l)} = \tilde {\mathbf {c}} \odot \operatorname {M L P} (\operatorname {L N} (\bar {\mathbf {Z}} ^ {(l)})) + \bar {\mathbf {Z}} ^ {(l)}, \\ \end{array} +$$ + +where LN is Layer Normalization [2], MLP is Multi-Layer Perceptron, and MCA is Multi-head Cross-Attention [49], whose output is split into affine weights $\mathbf{W}^{(l)}$ and biases $\mathbf{B}^{(l)}$ . $\tilde{\mathbf{c}}$ are learnable per-channel scales, and $\mathbf{X}^{(l)}$ the modulated video representations prior to moment decoding. + +Moment decoding. After fusion, our model decodes each time step into a moment candidate, similar to previous video grounding models [7, 27, 31, 60]. Briefly, a classification head predicts a score $p_t^{(l)}$ for all $\mathbf{x}_t^{(l)}$ within $[\mathbf{X}^{(l)}]_{l=1}^L$ , and a regression head predicts the normalized distances from $t$ to the moment boundaries $(d_t^s, d_t^e)$ if $\mathbf{x}_t^{(l)}$ is classified positive. Both heads are lightweight, each comprising three 1D convolutions. The decoded moment $\hat{\mathbf{y}} = (\hat{s}, \hat{e})$ is given by + +$$ +(t, l) = \underset {t, l} {\arg \max } p _ {t} ^ {(l)}, \tag {13} +$$ + +$$ +\hat {s} = 2 ^ {l - 1} \cdot (t - d _ {t} ^ {s}), \quad \hat {e} = 2 ^ {l - 1} \cdot (t + d _ {t} ^ {e}). +$$ + +At inference time, we further apply Soft-NMS [4] to merge overlapping moment predictions. + +Training and loss function. We use video-centric training as described in Section 3.3. The loss function for a pair of video snippet and text query is the sum of two terms: a Focal loss [26] $\mathcal{L}_{cls}$ for moment classification and a Distance-IoU loss [69] $\mathcal{L}_{reg}$ defined on positive time steps for distance regression. Formally, + +$$ +\mathcal {L} = \frac {1}{C} \left(\mathcal {L} _ {c l s} + \lambda_ {r e g} \mathbb {1} _ {t} ^ {(l)} \mathcal {L} _ {r e g}\right), \tag {14} +$$ + +where $\mathbb{1}_t^{(l)}$ is an indicator function that evaluates to one on positive time steps, $C = \sum_{t,l}\mathbb{1}_t^{(l)}$ is the total number of positive samples within the snippet, and $\lambda_{reg}$ balances the two loss terms. Center sampling [61] is used for selecting positive time steps around the center of a target moment. + +# 4. Experiments + +Our main experiments include extensive comparisons of SnAG to strong baselines on five challenging benchmarks for video grounding. We further provide ablations on cross-modal fusion and analyze the efficiency of SnAG in both training and inference. More results are in the supplement. + +![](images/88f4a85d6f7b967b7228f9f976dd1b4879b479a7ffcf06079a78ac26f9738e87.jpg) +Figure 3. Visualization of dataset statistics. Circle radius is in proportion to average number of queries per video. Long-video benchmarks (Ego4D-NLQ, MAD and TACoS) consist of longer videos with more queries and exhibit low moment coverage compared to short-video benchmarks (ANet-Captions and Charades). + +
ModelR@1R@5
0.30.5Avg0.30.5Avg
SF + BERT2D-TAN [67]5.042.023.5312.895.889.39
VSLNet [64]5.453.124.2910.746.638.69
CONE [17]10.405.037.7222.7411.8717.31
SOONet [36]8.003.765.8822.4011.0916.75
SnAG (video-centric)9.836.838.3327.9319.2723.60
SnAG (query-centric)10.437.158.7927.5919.3323.46
EgoVLPVSLNet [64]10.846.818.8318.8413.4516.15
CONE [17]14.158.1811.1730.3318.0224.18
SnAG (video-centric)15.7210.7813.2538.3927.4432.92
SnAG (query-centric)15.8711.2613.5738.2627.1632.71
+ +Table 1. Results on Ego4D-NLQ. SnAG outperforms all baselines. Best results are in bold and second best underlined. + +Datasets. We categorize five benchmark datasets into two groups based on their video and query statistics (Fig. 3). + +Long videos, many queries. Ego4D-NLQ [16] is a large collection of egocentric videos on daily human activities. The videos are 3.5 to 20 minutes long with an average of 11.6 queries. MAD [45] contains 1.2K hours of movies with 384K queries transcribed from audio description. The videos are 47 to 202 minutes long. TACoS [40] is a conventional benchmark with 10.1 hours of cooking videos, with an average of 143.5 queries per video. These datasets expose the scalability challenges that motivate our work and thus are the main focus of our experiments. + +Short videos, few queries. Charades-STA [43] is an action recognition dataset later annotated for video grounding [13]. The videos are $\sim 30$ seconds long with $\sim 2.4$ queries per video. ActivityNet-Captions [20] was collected for dense video captioning and later repurposed for video grounding. The videos are two minutes long on average with a small set of $\sim 3.65$ queries. Several works [35, 57] advise against using these datasets as benchmarks for the + +
ModelR@1R@5R@10R@50
0.10.30.50.10.30.50.10.30.50.10.30.5
CLIP [39]6.573.131.3915.059.855.4420.2614.138.3837.9228.7118.80
VLG-Net [46]3.642.761.6511.669.315.9917.3914.569.7739.7834.2724.93
Moment-DETR [21]0.310.240.161.521.140.282.792.061.2011.087.974.71
CONE [17]8.906.874.1020.5116.119.5927.2021.5312.8243.3634.7320.56
SOONet [36]11.269.005.3223.2119.6413.1430.3626.0017.8450.3244.7832.59
SnAG (video-centric)10.288.465.5524.4220.6013.7532.2327.5019.0052.2846.6835.24
SnAG (query-centric)10.188.375.4424.3020.3513.5132.0527.2518.7552.0546.5334.83
+ +Table 2. Results on MAD. SnAG outperforms all baselines. Best results are in bold and second best underlined. + +![](images/4f7ff842d2c213510aaad27a0c0318e2f50342257769de09c20c3dd7e2749bba.jpg) +Figure 4. Visualization of moment predictions. SnAG can (a) comprehend complex text queries with multiple objects and actions; (b) reason about temporal ordering of events. + +temporal biases in their moment annotations. Nevertheless, we report results on these datasets for completeness. + +Baselines. On TACoS, Charades and ANet-Captions, we compare to strong baselines including two-stage [28, 55, 56] and single-stage [30, 50, 70] models with various fusion operations (LSTM [29, 51], GCN [27, 46], co-attention [24, 68], etc.). On Ego4D and MAD, we compare to their official baselines (2D-TAN [67] and VSLNet [64] for Ego4D, CLIP [39] and VLG-Net [46] for MAD) as well as the concurrent method of CONE [17] and SOONet [36] that similarly address scalable video grounding. We discuss additional baselines in the supplement. + +Evaluation metric. We report $\mathrm{Recall}@\mathbf{k}$ at various temporal intersection-over-union threshold $\theta$ ( $\mathbf{R}@\mathbf{k}$ , tIoU= $\theta$ ) for all datasets. It measures the percentage of sentence queries with at least one of the top- $k$ moment predictions whose temporal overlap with the ground-truth moment exceeds $\theta$ . + +# 4.1. Long Videos, Many Queries + +Experiment setup. For Ego4D, We consider (1) SlowFast [12] video features with BERT [10] text features, and (2) EgoVLP [38] video and text features. We train on the train split and report R@{1, 5}, tIoU={0.3, 0.5} on the val split. For MAD, we use CLIP [39] features for both videos and text. We train on the train split and report R@{1, 5, 10, 50}, tIoU={0.1, 0.3, 0.5} on the test split. For TACoS, we use C3D video features [48] and GloVe [37] for + +sentence embeddings. We train on the train split and report $\mathrm{R}@\{1,5\}$ , tIoU=\{0.5, 0.7\} on the test split. We report results using both video-centric and query-centric training on all datasets. + +Results on Ego4D-NLQ (Table 1). SnAG sets the new state of the art, achieving mean R@1 / R@5 scores of $8.79\% / 23.60\%$ with SlowFast/BERT features, and $13.57\% / 32.92\%$ with EgoVLP features, doubling or even tripling the results of the official baselines [64, 67]. Compared to the strong baselines of CONE [17] and SOONet [36], SnAG improves mean R@1 and R@5 respectively by more than 1.05 and 6.29 absolute percentage points without taking advantage of external features. Further, SnAG demonstrates a larger performance gain on the more stringent tIoU threshold of 0.5, indicating more precise moment localization. + +Results on MAD (Table 2). SnAG sets new records on the challenging MAD dataset. It improves over CLIP [39] and VLG-Net [46] on mean R@1 / R@5 at tIoU=0.5 by 3.90 / 7.76 absolute percentage points. In the meantime, it outperforms CONE [17] and SOONet [36], with larger gain for more stringent tIoU thresholds. Further, SnAG achieves stronger results as input snippet length increases, reaching the best accuracy with $T_{w} = 16384$ (Supplement Fig. A). This scaling behavior highlights the strength of our scalable model design for long-form video grounding. + +Results on TACoS (Table 4 (left)). SnAG achieves an R@1 / R@5 of $44.86\%$ / $70.66\%$ at tIoU=0.5, outperforming the strongest baseline of MATN [66] by a significant margin $(+7.5\% \mathrm{R} @ 1, +12.1\% \mathrm{R} @ 5)$ . This confirms that our simple single-stage design with late fusion is a strong alternative to multi-stage models with sophisticated fusion mechanisms. Importantly, our scalable design enables learning from full-resolution video features, whereas the baselines often aggressively reduce feature resolution to contain their training and inference cost on long-form videos. We hypothesize that full-resolution video features capture detailed event dynamics and are key to the strong performance of SnAG. + +Result visualization. We visualize predictions of SnAG and the baselines on TACoS and Ego4D-NLQ videos. In + +
ModelR@1R@5
0.30.50.30.5
(a) Fusion stage (early vs. late fusion)
No fusion10.857.8546.4631.19
SnAG-E53.3444.0179.5669.41
SnAG-EL54.8444.5481.1370.11
SnAG-M51.4140.7977.5665.71
SnAG (ours)55.1444.9481.1070.66
(b) Fusion operation (global vs. token-wise)
Cat49.3939.2477.3165.36
Add51.9141.8177.9866.51
Scale55.0143.9680.6370.11
Add + Scale53.3643.0980.4369.58
XAttn54.8445.0679.9670.08
XAttn-affine (ours)55.1444.9481.1070.66
+ +Table 3. Ablations results on TACoS. (a) Late fusion yields comparable results to early fusion (E, EL, M); (b) Fusion with tokenwise sentence embeddings (XAttn) produces better results than fusion with global sentence embeddings (Cat, Add, Scale). + +Fig. 4(a), a long query describes the complex interplay between two objects (pan and stove) and three actions ("take from", "place on", and "turn on"). VLG-Net [46] recognized both objects yet none of the actions, while 2D-TAN [67] identified one action ("take from") but at the same time missed one object (pan). By contrast, SnAG followed the query semantics and produced accurate localization. The other query in Fig. 4(b) tests the understanding of temporal context. SnAG leveraged the keyword "before" to identify the correct moment before the action ("pick up"), whereas VSLNet [64] only attended to the object (can), thus mistakenly predicting a moment after the action. + +# 4.2. Short Videos, Few Queries + +Experiment setup. We extract video features using both C3D [48] (pretrained on Sports-1M [18]) and I3D [5] (pretrained on Kinetics [19]) for Charades-STA, and use the official C3D features for ActivityNet-Captions. We use GloVe word embeddings [37] to represent sentence queries for both datasets. We train on their respective train splits, report R@{1, 5}, tIoU={0.5, 0.7} on the test split of Charades-STA, and R@{1, 5}, tIoU={0.3, 0.5} on the val_2 split of ActivityNet-Captions. Following standard practice, we resize all video features to a uniform length of 256. + +Results on Charades-STA (Table 4 (middle)). SnAG outperforms all previous methods by a wide margin. It obtains $33.52\%$ R@1 and $64.11\%$ R@5 at tIoU=0.7 with C3D features, 2.10 and 4.52 absolute percentage points higher than the latest SSRN [71] baseline. It further attains $46.26\%$ R@1 and $71.94\%$ R@5 at tIoU=0.7 with I3D features, setting new state of the art on this competitive benchmark. + +Results on ActivityNet-Captions (Table 4 (right)). SnAG achieves competitive results, reaching an R@1 / R@5 score of $30.56\% / 63.41\%$ at tIoU=0.7. It is only outperformed by a few latest models [22, 27, 71] while being much simpler. + +# 4.3. Ablation Studies + +We conduct extensive ablations on TACoS to study key design choices for cross-modal fusion. + +Early vs. late fusion. Does late fusion enable better scalability at the expense of accuracy? We study three variants of SnAG with common early-fusion designs: (1) SnAG-E with fusion before the pyramid; (2) SnAG-EL with fusion before and after the pyramid; (3) SnAG-M with repeated fusion within the pyramid. Table 3 confirms that early and late fusion yield comparable results. + +Choice of fusion operation. We study fusion operations used by strong baselines, including point-wise addition, multiplication, and concatenation of video representations with global sentence embeddings, as well as vanilla cross-attention with token-level sentence embeddings. According to Table 3, token-level embeddings produce better results, and our cross-attention variant further boosts performance. + +# 4.4. Efficiency Analysis + +Finally, we conduct an efficiency analysis of our method. + +Breakdown of model capacity. A key design choice of SnAG is to carefully balance the model capacity among its video encoder, text encoder, and moment decoder including the fusion module and the localization heads. For a detailed breakdown of model capacity, we measure their respective parameter size and MACs in percentage. Fig. 5(a) indicates that SnAG's video encoder absorbs a significant portion of parameters and compute, such that per-query evaluation (i.e., text encoding, fusion, and decoding) occupies $\sim 50\%$ of the total computation. This design is naturally in favor of video-centric training and inference, where the costly video encoding is shared among many queries. + +Video-centric vs. query-centric training. Fig. 5(b) presents the training time and GPU memory usage of video-centric training relative to conventional query-centric training. The results show that the amount of saving correlates with snippet length and number of queries. Video-centric training is thus preferred for long videos with many queries. + +$B_{q}$ in video-centric training. We further study how $B_{q}$ , the number of text query samples per video, trades off accuracy for efficiency in video-centric training. On MAD, we fix the batch size $|B| = 32$ for a mini-batch $B$ , vary $B_{q}$ between 1 and $|B|$ , and report training time, GPU memory usage and test accuracy relative to query-centric training (i.e., $B_{q} = 1$ ). Fig. 5(d) reveals that test accuracy is unaffected even with a large $B_{q} = 32$ (i.e., a single video per mini-batch), while training time and GPU memory usage + +
MethodTACoS (C3D)Charades-STA (I3D)Charades-STA (C3D)ActivityNet-Captions (C3D)
R@1R@5R@1R@5R@1R@5R@1R@5
0.30.50.30.50.50.70.50.70.50.70.50.70.50.70.50.7
CTRL ICCV 17 [13]18.3213.3036.6925.42----23.638.8958.9229.52----
QSPN AAAI 19 [56]--------35.6015.8079.4045.4027.7013.6059.2038.30
SCDM NeurIPS 19 [58]27.6423.2740.0633.4954.9234.2676.5060.02----36.9020.2866.8442.92
2D-TAN AAAI 20 [67]45.6135.7769.1157.3156.6436.2189.1461.1341.1023.2581.5348.5546.1629.2178.8060.85
CBP AAAI 20 [51]27.3124.7943.6437.40----36.8018.8770.9450.1935.7617.8065.8946.20
DRN CVPR 20 [60]-23.17-33.3653.0931.7589.0660.0545.4026.4088.0155.3845.4524.3677.9750.30
BPNet AAAI 21 [55]25.9620.96--50.7531.64--38.2520.51--42.0724.69--
CPNet AAAI 21 [24]42.6128.29--60.2738.74--40.3222.47--40.5621.63--
SMIN CVPR 21 [50]48.0135.2465.1853.3664.0640.7589.4968.09----48.4630.3481.1662.11
CBLN CVPR 21 [29]38.9827.6573.1246.2461.1338.2290.3361.6947.9428.2288.2057.4748.1227.6079.3263.41
CPN CVPR 21 [68]47.6936.33--51.0731.54------45.1028.10--
DeNet CVPR 21 [70]----59.7038.5291.2466.83----43.79-74.13-
MATN CVPR 21 [66]48.7937.5767.6357.91--------48.0231.7878.0263.18
VLG-Net ICCVW 21 [46]45.4634.1970.3856.56--------46.3229.8277.1563.33
APGN EMNLP 21 [28]40.4727.8659.9847.1262.5838.8691.2462.1148.2029.3789.0558.4948.9228.6478.8763.19
IA-Net EMNLP 21 [30]37.9126.2757.6246.3961.2937.9189.7862.04----48.5727.9578.9963.12
RaNet EMNLP 21 [14]43.3433.5467.3355.0960.4039.6589.5764.54----45.5928.6775.9362.97
MGSL-Net AAAI 22 [30]42.5432.2763.3950.1363.9841.0393.2163.85----51.8731.4282.6066.71
MMN AAAI 22 [52]39.2426.1762.0347.39--------48.5929.2679.5064.76
SSRN EMNLP 22 [71]45.1034.3365.2651.8565.5942.6594.7665.4850.3931.4290.6859.9454.4933.1584.7268.48
G2L ICCV 23 [22]42.7430.9565.8349.86--------51.6833.3581.3267.60
SnAG (video-centric)56.4444.8681.1570.6664.6246.2692.5571.9451.7233.5292.5564.1148.5530.5681.7163.41
SnAG (query-centric)55.0144.5180.6870.1365.1345.9192.8071.7551.1031.7790.2262.1547.5529.6581.5562.21
+ +Table 4. Results on TACoS, Charades-STA and ActivityNet-Captions. SnAG outperforms all baselines on TACoS and Charade-STA by a large margin, while being highly competitive on ActivityNet-Captions. Best results are in bold and second best underlined. + +![](images/034aec85e20ee7f163d3d00cae17d23a683054193ab09b09a375bc8f2fad07e0.jpg) +Figure 5. (a) Model capacity. T, E, M denotes TACoS, Ego4D and MAD, respectively (also in (b)). Shaded bar: % of parameters, Colored bar: % of MACs. SnAG places more parameters and compute in video encoder for less expensive per-query evaluation (fusion + decoding). (b, c) Video-centric vs. query-centric inference (b) and training (c). SnAG saves up to $50\%$ training time, $40\%$ GPU memory and $80\%$ test time, and delivers up to $40\%$ faster convergence relative to query-centric training / inference. (d) Effect of $B_{q}$ on training efficiency and test accuracy on MAD. Training on MAD is faster and takes less GPU memory as $B_{q}$ grows, while the test accuracy is unaffected. + +![](images/afa7c78d392044d86a41785a82fcc08744cbb838a9d761b7c29ffd1e790003c8.jpg) + +![](images/38a25ea3e1e8cc1a63805f1c3481bb9e9b47d1bc2d05ecb0fa054fca392e1f6d.jpg) + +![](images/405277267d74f9782f2007159bcbaabc91e6951ae176f18e1597779abe9490c2.jpg) + +drop by a significant $55\%$ and $42\%$ , approaching the upper bound by our analysis. + +Video-centric vs. query-centric inference. We now ask to what extent the re-use of video representations enabled by SnAG's late fusion design accelerates inference. Fig. 5(b) presents the percentage of time spent by our video-centric inference scheme relative to query-centric inference, where the full model is evaluated on each and every video-query pair. Consistent with earlier findings on video-centric training, longer videos with more queries result in more saving in inference time. On the challenging MAD dataset, this alone brings a major reduction (65%) in test time. + +Inference speed. With window filtering [17], inference of SnAG on the val split of MAD takes 12 minutes on a single P100 GPU. This is $33\%$ faster than CONE [17] ( $\sim 18$ mins) and $63\%$ faster than SOONet [36] ( $\sim 32$ mins).6 + +# 5. Conclusion + +In this paper, we presented a simple and accurate model towards scaling up video grounding. We provided extensive analysis on the complexity of video grounding models from the perspective of cross-modal fusion, and argued that late fusion is key to scalability in video duration and query size. Our model, SnAG, is a simple instantiation of late fusion with minimalist design. It achieves superior accuracy and efficiency on a spectrum of challenging benchmarks and compares favorably to strong baselines including those dedicated to efficient inference on long videos. We hope our analysis and model design can shed light on video grounding and more broadly scalable video understanding. + +Acknowledgement: This work was partially supported by NIH grant R01OH012313, by grants from McPherson Eye Research Institute and VCGRE at UW Madison, and by the Army Research Lab under contract number W911NF-2020221. + +# References + +[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. Localizing moments in video with natural language. In ICCV, 2017. 2 +[2] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E Hinton. Layer normalization. arXiv preprint arXiv:1607.06450, 2016. 5 +[3] Wayner Barrios, Mattia Soldan, Alberto Mario Ceballos-Arroyo, Fabian Caba Heilbron, and Bernard Ghanem. Localizing moments in long video via multimodal guidance. In ICCV, 2023. 2 +[4] Navaneeth Bodla, Bharat Singh, Rama Chellappa, and Larry S Davis. Soft-NMS-improving object detection with one line of code. 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In EMNLP Findings, 2022. 2, 7, 8 \ No newline at end of file diff --git a/2024/SnAG_ Scalable and Accurate Video Grounding/images.zip b/2024/SnAG_ Scalable and Accurate Video Grounding/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..c0b37237fe83a057b4217a57caf2b9b6a1e4e24a --- /dev/null +++ b/2024/SnAG_ Scalable and Accurate Video Grounding/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1c50815eae34ba84d80322b52fb26783b5c187feecfd449ea85d4740b85f9a79 +size 642611 diff --git a/2024/SnAG_ Scalable and Accurate Video Grounding/layout.json b/2024/SnAG_ Scalable and Accurate Video Grounding/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..737d31b140de75032d2d452a5b2697d1885d7665 --- /dev/null +++ b/2024/SnAG_ Scalable and Accurate Video Grounding/layout.json @@ -0,0 +1,11346 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 148, + 103, + 445, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 148, + 103, + 445, + 121 + ], + "spans": [ + { + "bbox": [ + 148, + 103, + 445, + 121 + ], + "type": "text", + "content": "SnAG: Scalable and Accurate Video Grounding" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 206, + 143, + 386, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 206, + 143, + 386, + 175 + ], + "spans": [ + { + "bbox": [ + 206, + 143, + 386, + 175 + ], + "type": "text", + "content": "Fangzhou Mu*, Sicheng Mo*, Yin Li \nUniversity of Wisconsin-Madison" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 202, + 192, + 216 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 202, + 192, + 216 + ], + "spans": [ + { + "bbox": [ + 143, + 202, + 192, + 216 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": "Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability — they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is " + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "inline_equation", + "content": "43\\%" + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": " more accurate and " + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "inline_equation", + "content": "1.5 \\times" + }, + { + "bbox": [ + 46, + 228, + 290, + 445 + ], + "type": "text", + "content": " faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos. Our code is available at https://github.com/fmu2/snag_release." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 468, + 128, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 128, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 128, + 480 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 488, + 287, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 287, + 585 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 287, + 585 + ], + "type": "text", + "content": "Localizing moments within an untrimmed video based on text descriptions, also known as temporal video grounding, involves joint reasoning about visual, textual and temporal information, and thus remains a challenging problem in video understanding. Video grounding is gaining traction amid the rapid advances in vision-language learning, with a range of applications such as intelligent personal assistants, human-robot interaction, and interactive video editing." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 586, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 288, + 693 + ], + "type": "text", + "content": "Despite recent progress, one largely overlooked aspect of video grounding is the scalability of models with respect to video duration and the number of text descriptions (i.e., queries). Previous methods (e.g., [46, 67]) are primarily designed for grounding only a few queries within short video snippets. However, the growing availability of long videos (e.g., on streaming platforms) and demand to query their rich contents introduce a paradigm shift, necessitating efficient grounding of large volumes of queries in long videos." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 342, + 204, + 507, + 338 + ], + "blocks": [ + { + "bbox": [ + 342, + 204, + 507, + 338 + ], + "lines": [ + { + "bbox": [ + 342, + 204, + 507, + 338 + ], + "spans": [ + { + "bbox": [ + 342, + 204, + 507, + 338 + ], + "type": "image", + "image_path": "b9a807416c0ebc2e4ad55975342dc123777b8a8af446635bc0de09fcd6219e94.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "lines": [ + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 342, + 545, + 365 + ], + "type": "text", + "content": "Figure 1. SnAG achieves the best accuracy and throughput simultaneously on the MAD dataset [45] for long-form video grounding." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 411 + ], + "type": "text", + "content": "On latest long-form video grounding benchmarks [16, 45], these methods struggle to scale up due to their high computational cost, and suffer major performance degradation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 412, + 546, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 546, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 546, + 556 + ], + "type": "text", + "content": "In this paper, we take a principled approach to studying the problem of scalable video grounding, focusing on the design of cross-modal fusion—a key model component that combines visual and textual information. Specifically, we present an analysis that connects the computational cost of video grounding models to their fusion schemes. Our analysis and empirical results challenge the widely adopted early fusion, showing that late fusion scales better in inference by amortizing the cost of long video processing among text queries. Importantly, this insight further motivates the design of a novel, video-centric sampling scheme for scalable training, without compromising grounding accuracy." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": "Following these findings, we present SnAG, a scalable and accurate model for long-form video grounding. SnAG features a minimalist, late-fusion design for scalable inference, while supporting video-centric sampling for scalable training. Notwithstanding its simplicity, SnAG achieves superior results across all benchmarks designed for long-form video grounding. Without bells and whistles, SnAG attains " + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "13.75\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": " R@5, tIoU=0.5 on MAD [45] with an inference speed of 45.3 queries per second on a P100 GPU (Fig. 1), " + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "43\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": " more accurate and " + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "1.5\\times" + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": " faster than the concurrent method of CONE [17]. In the meantime, SnAG is highly competitive on short-video benchmarks. It achieves " + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "inline_equation", + "content": "46.26\\%" + }, + { + "bbox": [ + 304, + 557, + 547, + 714 + ], + "type": "text", + "content": " R@1, tIoU=0.7 on Charades-STA [43], outperforming the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 62, + 703, + 160, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 703, + 160, + 712 + ], + "spans": [ + { + "bbox": [ + 62, + 703, + 160, + 712 + ], + "type": "text", + "content": "* indicates equal contribution" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18930" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "previous state of the art (SSRN [71]) by 3.61 absolute percentage points while being simpler in model design." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 101, + 288, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 101, + 288, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 101, + 288, + 198 + ], + "type": "text", + "content": "Contributions. (1) We present one of the first studies to understand the effect of fusion schemes on the computational cost of video grounding. (2) Our analysis offers new insights and leads to a new training scheme for scalable video grounding. (3) Based on our findings, we further deliver a simple model that attains superior results across major benchmarks for long-form video grounding while achieving significant efficiency gains in both training and inference." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 211, + 134, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 211, + 134, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 211, + 134, + 224 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 232, + 287, + 280 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 287, + 280 + ], + "type": "text", + "content": "Video grounding. Previous works on video grounding can be categorized based on whether proposals are generated as moment candidates (two-stage vs. single-stage), and how text queries inform action localization (cross-modal fusion)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 399 + ], + "type": "text", + "content": "Two-stage methods first generate temporal segments as proposals, then score their \"actionness\" and optionally refine their boundaries. Early works [1, 13] densely sample proposals using sliding windows and score them independently. One line of work [8, 28, 54-56] subsequently conditions proposal generation on sentence queries and/or video context to avoid dense sampling. By contrast, another line of work [14, 46, 50, 66, 67] takes the opposite path of enumerating all segments, yet organizes them in a 2D adjacency map to reason about their relations." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 568 + ], + "type": "text", + "content": "Single-stage methods localize moments in a single shot without using proposals, and thus are often more efficient than two-stage methods. Some models decode moment boundaries from global features [23, 24, 33, 59, 70] or learnable queries [21, 25, 53]. Others densely predict onset and offset probabilities [15, 29, 34, 41, 63-65, 68], or classify and refine pre-set anchors [6, 30, 51, 58, 62] at every moment. Most relevant to our work are models that represent moment candidates as points [7, 11, 27, 31, 60]. Analogous to point-based object detectors [47], they classify every point in time and regress moment boundaries relative to the points. Despite their simplicity and efficiency, the performance of single-stage models lags behind two-stage models on standard benchmarks made up of short videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Cross-modal fusion combines video and text information for video grounding. Early models [1, 13] fuse video and text representations right before final prediction. This simple, late-fusion approach is abandoned by subsequent models, which turn to early fusion (e.g., [56, 60, 62, 67]) with sophisticated model design (e.g., LSTM [6, 15, 29, 51, 56, 65], GCN [7, 27, 46], memory bank [8, 27]), feature hierarchies [14, 33, 50], losses [23, 34, 56, 66], and inference procedures [68, 70]. Early fusion is believed to strengthen cross-modal reasoning, albeit at a price of model complexity. Recent Transformer-based models [3, 21, 53, 66] inherit this early-fusion design; video features and text embeddings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "are concatenated at input, and attention-based feature fusion is carried out throughout the model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 97, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 545, + 192 + ], + "type": "text", + "content": "Our method demonstrates a single-stage Transformer model with a simple late fusion mechanism based on crossattention. Late fusion allows us to amortize the cost of video processing across many sentence queries, resulting in scalable training and inference on long-form videos. Without bells and whistles, our model outperforms all prior methods on long-video benchmarks, and attains competitive performance on standard, short-video benchmarks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 545, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 353 + ], + "type": "text", + "content": "Long-form video grounding. Recent efforts [16, 45] put forth new challenges for sentence grounding in long videos. Previous methods tailored for short videos [46, 64, 67] fall short on these benchmarks. They have no access to long-range video context, require dense sliding window inference, and yield unsatisfactory results. Concurrent works [17, 36] present multi-stage approaches with sophisticated pre-processing, ranking and training procedures for efficient long-form video grounding. However, their efficiency stems from the restrictive assumption that moments are covered by short windows. By contrast, SnAG offers a simple, single-stage solution with superior accuracy, without making assumptions about moment duration." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 357, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 454 + ], + "type": "text", + "content": "Localizing moments in videos. Closely related to video grounding, temporal action localization (e.g., [32, 42, 44]) aims to identify moments of actions from within a closed set of action categories. Solutions to the two tasks often evolve in tandem and share remarkably similar model design. SnAG is inspired by our prior work [61], yet extends its design for the more challenging task of video grounding, with the goal of scaling up video grounding for long videos." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 467, + 469, + 481 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 467, + 469, + 481 + ], + "spans": [ + { + "bbox": [ + 306, + 467, + 469, + 481 + ], + "type": "text", + "content": "3. Scaling Up Video Grounding" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": "Our goal is to scale up video grounding for long-form videos with many queries. Denote an input video " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": " as a time-indexed sequence " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "[\\mathbf{v}_t]_{t=1}^T = [\\mathbf{v}_1, \\mathbf{v}_2, \\dots, \\mathbf{v}_T]" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{v}_t" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": " represents a short video clip centered at time " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": ".1 " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": " is paired with " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": " sentence queries " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{Q}_j\\}_{j=1}^N" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": ", each describing a moment " + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_j = (s_j, e_j)" + }, + { + "bbox": [ + 304, + 488, + 545, + 561 + ], + "type": "text", + "content": " in the video." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": "Long-form video grounding is characterized by a great number of time steps " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " (e.g., tens of thousands) and text queries " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " (hundreds) for an input video " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": ". With a large " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": ", it is no longer feasible to feed the full video " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " into a model, and thus more viable to consider a sliding window setting. Specifically, a video " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " is further partitioned into a set of " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " snippets " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{V}_{i=1}^{M}\\}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": ", each " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{i} = [\\mathbf{v}_{t}]_{t=t_{i}}^{t_{i} + T_{w}}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " taken from a local time window of size " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "T_{w}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": " that may overlap with others. We consider the learning of a function " + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 564, + 545, + 673 + ], + "type": "text", + "content": ", realized in a deep" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "1Like prior works, we consider video features and text embeddings extracted using pre-trained models (e.g., C3D [48] and BERT [10]). Yet the formulation can be easily extended to raw video frames and text tokens." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18931" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 74, + 237, + 235 + ], + "blocks": [ + { + "bbox": [ + 51, + 74, + 237, + 235 + ], + "lines": [ + { + "bbox": [ + 51, + 74, + 237, + 235 + ], + "spans": [ + { + "bbox": [ + 51, + 74, + 237, + 235 + ], + "type": "image", + "image_path": "4803639b0a1f16039b839ad918d58e34425082f99caff1fafa9a2122313a6aae.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "text", + "content": "Figure 2. (a) Cross-modal fusion is key to a video grounding model " + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "text", + "content": ". Models using early fusion jointly encode video and sentence query. SnAG revisits late fusion for scalable video grounding by decoupling expensive video encoding and inexpensive query encoding. (b) Video-centric model evaluation. With late fusion, the output of video encoder can be cached and re-used by queries of the same video in both training and inference. (c) Mini-batch sampling in training. Previous methods adopt query-centric sampling (query " + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "text", + "content": " video) whereas SnAG resorts to video-centric sampling (video " + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 242, + 545, + 319 + ], + "type": "text", + "content": " many queries) for efficient training. (d) Model overview. SnAG is a simple instantiation of late fusion and video-centric training for video grounding. It separately encodes a video and its queries using Transformers, applies simple cross-attention for cross-modal fusion, and decodes moments represented as points using lightweight convolutional heads." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 244, + 74, + 354, + 235 + ], + "blocks": [ + { + "bbox": [ + 244, + 74, + 354, + 235 + ], + "lines": [ + { + "bbox": [ + 244, + 74, + 354, + 235 + ], + "spans": [ + { + "bbox": [ + 244, + 74, + 354, + 235 + ], + "type": "image", + "image_path": "24f620b34609b9f3f19062804931b668980e1121d4689609c7c691dd26f796f2.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 360, + 74, + 543, + 235 + ], + "blocks": [ + { + "bbox": [ + 360, + 74, + 543, + 235 + ], + "lines": [ + { + "bbox": [ + 360, + 74, + 543, + 235 + ], + "spans": [ + { + "bbox": [ + 360, + 74, + 543, + 235 + ], + "type": "image", + "image_path": "2ae59873afb84ef2c5185ee19976e539c33b58e59f038c76a8a3cd9d0b114779.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "content": "network, to predict the start time " + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "s_j" + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "content": " and end time " + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "e_j" + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "content": " of the moment " + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_j" + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "content": " given a snippet " + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_i" + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "content": " and a query " + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "inline_equation", + "content": "\\mathrm{Q}_j" + }, + { + "bbox": [ + 46, + 331, + 287, + 355 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 361, + 230, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 230, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 230, + 373 + ], + "type": "text", + "content": "3.1. Background: Cross-Modal Fusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "text", + "content": "We review cross-modal fusion - a key design choice of " + }, + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 380, + 287, + 404 + ], + "type": "text", + "content": " and define the notation used for the rest of the paper." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "type": "text", + "content": "Early fusion. A straightforward design is to fuse information from a video snippet " + }, + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_i" + }, + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "type": "text", + "content": " and a text query " + }, + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "type": "inline_equation", + "content": "\\mathrm{Q}_j" + }, + { + "bbox": [ + 46, + 407, + 287, + 454 + ], + "type": "text", + "content": " at input (Fig. 2(a)). This early fusion strategy is widely adopted in prior works [21, 53, 60, 62, 66, 67], and can be written as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 126, + 464, + 287, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 464, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 126, + 464, + 287, + 477 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {E} \\left(\\mathbf {V} _ {i}, \\mathrm {Q} _ {j}\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {1}", + "image_path": "8678518b436950fc9f55324b6b0ddd52bf27e63e04fe3dbe375cc70b04e76c90.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mapsto" + }, + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "type": "text", + "content": " defines any necessary post-processing of the model outputs (e.g., re-scaling, non-maximum suppression) in order to decode the moment " + }, + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_j" + }, + { + "bbox": [ + 46, + 486, + 287, + 521 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "type": "text", + "content": "Late fusion. Another possible design is to first embed the video snippet " + }, + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_i" + }, + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "type": "text", + "content": " and text query " + }, + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "type": "inline_equation", + "content": "\\mathrm{Q}_j" + }, + { + "bbox": [ + 46, + 524, + 287, + 560 + ], + "type": "text", + "content": ", then fuse their features for grounding (Fig. 2(a)). This late fusion strategy follows" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 113, + 569, + 287, + 582 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 569, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 113, + 569, + 287, + 582 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {L} \\left(g \\left(\\mathbf {V} _ {i}\\right), h \\left(\\mathrm {Q} _ {j}\\right)\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {2}", + "image_path": "2eafb058c1ed390506f8f27d31f940c881c1470876c7aa000f1bf526d0bea054.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "text", + "content": " is the video encoder and " + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "text", + "content": " the text encoder. With slight abuse of the symbols, " + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_L" + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "text", + "content": " here denotes the rest part of the grounding model, including feature fusion. The key is to keep " + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_L" + }, + { + "bbox": [ + 46, + 590, + 287, + 651 + ], + "type": "text", + "content": " lightweight, i.e., its cost should be a minor portion in comparison to the rest of the model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 712 + ], + "type": "text", + "content": "Design choice. The conventional wisdom favors the design of early fusion for video grounding. Early fusion is believed to offer better interactions between visual and textual features, resulting in strong empirical results. In what follows, we analyze the computational cost of early and late fusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "text", + "content": "during inference and training, and show that proper design of late fusion allows significantly improved scalability in video duration " + }, + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "inline_equation", + "content": "(M)" + }, + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "text", + "content": " and number of text queries " + }, + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "inline_equation", + "content": "(N)" + }, + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 375, + 414, + 386 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 375, + 414, + 386 + ], + "spans": [ + { + "bbox": [ + 306, + 375, + 414, + 386 + ], + "type": "text", + "content": "3.2. Scalable Inference" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "content": "We start by analyzing the computational cost of early vs. late fusion in inference. Denote the computational cost of a function by " + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\cdot)" + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "content": ". For example, " + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(g)" + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "content": " is the cost of the video encoder " + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(h)" + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "content": " the cost of the text encoder " + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "inline_equation", + "content": "h(\\cdot)" + }, + { + "bbox": [ + 305, + 394, + 545, + 442 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "text", + "content": "Computational cost. We make two key observations regarding the computational cost of a video grounding model: (a) a lightweight " + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_L" + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "text", + "content": " is used for late fusion, thus " + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\mathcal{F}_L) \\ll \\mathcal{C}(g) + \\mathcal{C}(h)" + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "text", + "content": "; and (b) the video encoder " + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "text", + "content": " has a much higher cost than the text encoder, thus " + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(g) \\gg \\mathcal{C}(h)" + }, + { + "bbox": [ + 305, + 445, + 545, + 506 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": "The first observation stems from the design of late fusion. To justify the second observation, it is important to notice that " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(g)" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": " scales w.r.t. the length of input video snippet (i.e., the local window size " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "T_w" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": "), whereas " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(h)" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": " remains constant due to limited sequence length of text queries. For example, a realization of " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "g(\\cdot)" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": " using a vanilla Transformer has a complexity of " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(T_w^2)" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": ". Thus, using a larger local window size naturally leads to " + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(g) \\gg \\mathcal{C}(h)" + }, + { + "bbox": [ + 304, + 506, + 545, + 601 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": "Cost analysis: early vs. late fusion. Evaluating an early-fusion model on a video with " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " snippets and " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": " queries has a cost of " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "MN\\mathcal{C}(\\mathcal{F}_E)" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ", whereas late fusion has a cost of " + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "inline_equation", + "content": "MN\\mathcal{C}(\\mathcal{F}_L) + MC(g) + NC(h)" + }, + { + "bbox": [ + 304, + 605, + 545, + 689 + ], + "type": "text", + "content": ". This is because an early-fusion model has to compare each snippet to every query, yet late fusion allows re-using video features for all queries of the video (i.e., video-centric evaluation, see Fig. 2(b))." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Let us assume that the cost of both models can be controlled by setting " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\mathcal{F}_E) = \\mathcal{C}(\\mathcal{F}_L) + \\mathcal{C}(g) + \\mathcal{C}(h)" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": ", i.e., eval" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18932" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "uating either model on a pair of video snippet and sentence query has the same cost (post-processing excluded). With " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(\\mathcal{F}_L) = \\alpha (\\mathcal{C}(g) + \\mathcal{C}(h))" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " for some small " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ", the ratio between the cost of early and late fusion in inference is" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 58, + 129, + 287, + 245 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 129, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 58, + 129, + 287, + 245 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {R} _ {\\text {i n f}} = \\frac {\\mathcal {C} (\\text {i n f e r e n c e w i t h e a r l y f u s i o n})}{\\mathcal {C} (\\text {i n f e r e n c e w i t h l a t e f u s i o n})} (3) \\\\ = \\frac {M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M N \\mathcal {C} (g) + M N \\mathcal {C} (h)}{M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M \\mathcal {C} (g) + N \\mathcal {C} (h)} (4) \\\\ = \\frac {M N (1 + \\alpha)}{M N \\alpha + M \\mathbf {R} _ {g / (g + h)} + N (1 - \\mathbf {R} _ {g / (g + h)})} (5) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{N} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}N,&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&N \\rightarrow \\infty\\end{array}, \\right. (6) \\\\ \\end{array}", + "image_path": "bfceffaa6398a653ff3f054de48561d2ebf47382657372c4ea8ac6c0bc05e637.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "spans": [ + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{g / (g + h)} = \\mathcal{C}(g) / (\\mathcal{C}(g) + \\mathcal{C}(h))" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": ", and the approximation in Eq. 6 is a result of " + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_{g / (g + h)} \\approx 1" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\mathcal{C}(g) \\gg \\mathcal{C}(h)" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": ". Eq. 6 reveals that early fusion is " + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": " times the cost of late fusion as snippet length grows (" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "inline_equation", + "content": "\\alpha \\to 0" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": "), and is particularly inefficient for videos with many queries (" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "inline_equation", + "content": "N \\to \\infty" + }, + { + "bbox": [ + 47, + 254, + 287, + 315 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 322, + 153, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 322, + 153, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 322, + 153, + 335 + ], + "type": "text", + "content": "3.3. Scalable Training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 341, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 287, + 365 + ], + "type": "text", + "content": "We now show that late fusion further unlocks a novel training scheme that scales well for long-form video grounding." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "text", + "content": "Training and mini-batch sampling. Given a set of paired videos, text queries, and their moments " + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{V}^{(k)},\\mathbf{Q}^{(k)},\\mathbf{y}^{(k)}\\}" + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "text", + "content": ", training a model " + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "text", + "content": " amounts to minimizing a loss function " + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "text", + "content": " over mini-batches " + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 369, + 287, + 416 + ], + "type": "text", + "content": " sampled from the dataset:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 424, + 287, + 443 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 424, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 91, + 424, + 287, + 443 + ], + "type": "interline_equation", + "content": "\\Sigma_ {(k, i, j) \\in B} \\mathcal {L} \\left(\\mathcal {F} \\left(\\mathbf {V} _ {i} ^ {(k)}, \\mathrm {Q} _ {j} ^ {(k)}\\right), \\mathbf {y} _ {j} ^ {(k)}\\right). \\tag {7}", + "image_path": "0c052959d6a8345b2a9e248db99b8f57780460694dd62ac606c4a50e16c182f5.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 449, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 287, + 510 + ], + "type": "text", + "content": "A key design largely overlooked in video grounding is the mini-batch sampling scheme during training. With multiple queries associated with a video snippet, a combination of late fusion and proper sampling scheme allows us to reuse video representations in training as is done in inference." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "text", + "content": "Query-centric sampling. Virtually all prior works sample mini-batches uniformly at random from all pairs of valid video snippets and text queries." + }, + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 47, + 513, + 287, + 573 + ], + "type": "text", + "content": " This can be interpreted as ancestral sampling: first draw a text query (and its moment), then select a video snippet covering the moment:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 91, + 580, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 580, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 91, + 580, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathrm {Q} _ {j} ^ {(k)}, \\mathbf {y} _ {j} ^ {(k)}\\right) \\right\\} _ {j \\times k}\\right), \\tag {8}", + "image_path": "8488768f5468e34f45946a76309429cf51ce619e9ecb95df8c45b386a99e4508.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 601, + 241, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 601, + 241, + 619 + ], + "spans": [ + { + "bbox": [ + 93, + 601, + 241, + 619 + ], + "type": "interline_equation", + "content": "\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),", + "image_path": "fafa3f6c6a210bb4bab18832496cc6546c77e7af2849d6cac548354b84917fbe.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "inline_equation", + "content": "U(\\cdot)" + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "content": " denotes a discrete uniform distribution and " + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "inline_equation", + "content": "\\{(\\mathbf{V}_i^{(k')},\\mathbf{Q}_j^{(k')},\\mathbf{y}_{j'}^{(k')})_{+}\\}" + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "content": " is the union of all valid triplets: a moment " + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{j'}^{(k')}" + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "content": " of a text query " + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_{j'}^{(k')}" + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "content": " in a video snippet " + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_i^{(k')}" + }, + { + "bbox": [ + 47, + 627, + 287, + 671 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "type": "text", + "content": "This sampling process is repeated " + }, + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "type": "inline_equation", + "content": "|B|" + }, + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "type": "text", + "content": " times to construct a mini-batch, with " + }, + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "type": "inline_equation", + "content": "|B|" + }, + { + "bbox": [ + 47, + 670, + 286, + 694 + ], + "type": "text", + "content": " the batch size. With a large" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 544, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 544, + 96 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 544, + 96 + ], + "type": "text", + "content": "dataset, the resulting mini-batch will contain " + }, + { + "bbox": [ + 306, + 72, + 544, + 96 + ], + "type": "inline_equation", + "content": "|B|" + }, + { + "bbox": [ + 306, + 72, + 544, + 96 + ], + "type": "text", + "content": " snippet-query pairs, each likely from a different video." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 99, + 545, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 99, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 305, + 99, + 545, + 185 + ], + "type": "text", + "content": "Video-centric sampling. To speed up the training of late fusion models, we propose video-centric sampling that considers every video snippet " + }, + { + "bbox": [ + 305, + 99, + 545, + 185 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_i^{(k)}" + }, + { + "bbox": [ + 305, + 99, + 545, + 185 + ], + "type": "text", + "content": " as a sample. Specifically, we first draw a video based on its importance score, then sample a snippet within the video, and finally select multiple text queries associated with the snippet. This is defined as the following ancestral sampling:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 329, + 190, + 545, + 220 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 190, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 329, + 190, + 545, + 220 + ], + "type": "interline_equation", + "content": "k ^ {\\prime} \\sim P (k) = \\frac {M _ {+} ^ {(k)}}{\\Sigma_ {k} M _ {+} ^ {(k)}} \\quad i ^ {\\prime} \\sim P (i; k ^ {\\prime}) = \\frac {N _ {i} ^ {\\left(k ^ {\\prime}\\right)}}{\\Sigma_ {k} N _ {i} ^ {\\left(k ^ {\\prime}\\right)}} \\tag {9}", + "image_path": "f805ea58ecdc152d98c42b610fa516a207ba73a0ad7aef900a1460f8a3811727.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 331, + 221, + 521, + 240 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 221, + 521, + 240 + ], + "spans": [ + { + "bbox": [ + 331, + 221, + 521, + 240 + ], + "type": "interline_equation", + "content": "\\left\\{\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\right\\} ^ {B _ {q}} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),", + "image_path": "f4fc023e6a5163b3c20eee27bbfd3a8d62487066bbdb03cad77414e7a9be287d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "inline_equation", + "content": "M_{+}^{(k)}" + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": " denotes the number of valid snippets in a video " + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathbf{V}^{(k)}" + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "inline_equation", + "content": "N_{i}^{(k^{\\prime})}" + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": " the number of queries in a snippet " + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{i}^{(k^{\\prime})}" + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": ". Importantly, a total of " + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": " queries are drawn for the selected video snippet " + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_{i^{\\prime}}^{(k^{\\prime})}" + }, + { + "bbox": [ + 306, + 247, + 545, + 303 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "text", + "content": "This sampling process is repeated " + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "inline_equation", + "content": "|B| / B_q" + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "text", + "content": " times for a mini-batch, leading to " + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "inline_equation", + "content": "|B| / B_q" + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "text", + "content": " video snippets, each likely from a different video yet with multiple " + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "inline_equation", + "content": "(B_q)" + }, + { + "bbox": [ + 305, + 303, + 545, + 363 + ], + "type": "text", + "content": " text queries. This mini-batch thus allows us to re-use the video representations for the sampled snippets." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "type": "text", + "content": "Cost analysis: query-centric vs. video-centric sampling. Fig. 2(c) illustrates the key difference between query-centric and video-centric sampling. Similar to our analysis in Section 3.2, it is easy to show that late fusion combined with video-centric training enables substantial speedup for long snippets " + }, + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "type": "inline_equation", + "content": "(\\alpha \\rightarrow 0)" + }, + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "type": "text", + "content": " and large " + }, + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 305, + 365, + 545, + 438 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 320, + 445, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 445, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 320, + 445, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {R} _ {\\text {t r a i n}} = \\frac {\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {v i d e o - c e n t r i c t r a i n i n g})}{\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {q u e y - c e n t r i c t r a i n i n g})} (10) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{B _ {q}} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}B _ {q},&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&B _ {q} \\rightarrow \\infty\\end{array}. \\right. (11) \\\\ \\end{array}", + "image_path": "8bd0c454f59bca9e6f529bad7899ac020b25ac89b93314e67c1ed3cfee074fe5.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 513, + 536, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 536, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 536, + 525 + ], + "type": "text", + "content": "3.4. Scalable Video Grounding: An Instantiation" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 531, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 531, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 305, + 531, + 545, + 627 + ], + "type": "text", + "content": "We now present an instantiation with late fusion and video-centric training for scalable video grounding. Our instantiation, dubbed SnAG, is shown in Fig. 2(d). SnAG is a single-stage Transformer model where every time step represents a moment candidate. It combines (a) a multi-scale Transformer-based video encoder; (b) a Transformer-based text encoder; (c) cross-attentions for late fusion; and (d) convolutional heads for moment decoding." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": "Video encoder " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": ". We use the ActionFormer backbone [61] as our video encoder, given its superior performance on the closely related task of temporal action localization. It transforms input video features into a multi-scale representation " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "[\\mathbf{Z}^{(l)}]_{l=1}^{L} = [\\mathbf{Z}^{(1)}, \\mathbf{Z}^{(2)}, \\dots, \\mathbf{Z}^{(L)}]" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " using Transformer layers with local self-attentions [9]. We refer readers to the original paper [61] for more details on model architecture." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 702, + 285, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 285, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 285, + 713 + ], + "type": "text", + "content": "2A video snippet without any query is often discarded during training." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18933" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "Text encoder " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". Our text encoder is a vanilla Transformer. It takes a query Q with " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " tokens " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "[\\mathbf{q}_1, \\dots, \\mathbf{q}_K]" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " and outputs their embeddings " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{E} = [\\mathbf{e}_1, \\dots, \\mathbf{e}_K]" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": ". This computation is light compared to video encoding as " + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "K \\ll T_w" + }, + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": " for long videos." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "spans": [ + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "text", + "content": "Cross-modal late fusion " + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_L" + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "text", + "content": ". Our model uses a simple variant of cross-attention for fusion. Specifically, it modulates " + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "inline_equation", + "content": "[\\mathbf{Z}^{(l)}]_{l=1}^L" + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "text", + "content": " with an affine transformation given by " + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 47, + 122, + 287, + 159 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 85, + 164, + 287, + 211 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 164, + 287, + 211 + ], + "spans": [ + { + "bbox": [ + 85, + 164, + 287, + 211 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} (\\mathbf {W}, \\mathbf {B}) ^ {(l)} = \\operatorname {M C A} (\\operatorname {L N} (\\mathbf {Z} ^ {(l)}), \\operatorname {L N} (\\mathbf {E})), \\\\ \\tilde {\\mathbf {Z}} ^ {(l)} = \\mathbf {W} ^ {(l)} \\odot \\mathbf {Z} ^ {(l)} + \\mathbf {B} ^ {(l)}, \\tag {12} \\\\ \\mathbf {X} ^ {(l)} = \\tilde {\\mathbf {c}} \\odot \\operatorname {M L P} (\\operatorname {L N} (\\bar {\\mathbf {Z}} ^ {(l)})) + \\bar {\\mathbf {Z}} ^ {(l)}, \\\\ \\end{array}", + "image_path": "3afed23aae60537496a51f6cb8941be21fe88163050ab2e1efeaa258d8fc9cc4.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "content": "where LN is Layer Normalization [2], MLP is Multi-Layer Perceptron, and MCA is Multi-head Cross-Attention [49], whose output is split into affine weights " + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{(l)}" + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "content": " and biases " + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "inline_equation", + "content": "\\mathbf{B}^{(l)}" + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{c}}" + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "content": " are learnable per-channel scales, and " + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^{(l)}" + }, + { + "bbox": [ + 47, + 216, + 287, + 276 + ], + "type": "text", + "content": " the modulated video representations prior to moment decoding." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "spans": [ + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": "Moment decoding. After fusion, our model decodes each time step into a moment candidate, similar to previous video grounding models [7, 27, 31, 60]. Briefly, a classification head predicts a score " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "p_t^{(l)}" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{(l)}" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": " within " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "[\\mathbf{X}^{(l)}]_{l=1}^L" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": ", and a regression head predicts the normalized distances from " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": " to the moment boundaries " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "(d_t^s, d_t^e)" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": " if " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t^{(l)}" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": " is classified positive. Both heads are lightweight, each comprising three 1D convolutions. The decoded moment " + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{y}} = (\\hat{s}, \\hat{e})" + }, + { + "bbox": [ + 47, + 278, + 287, + 377 + ], + "type": "text", + "content": " is given by" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 384, + 287, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 384, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 123, + 384, + 287, + 409 + ], + "type": "interline_equation", + "content": "(t, l) = \\underset {t, l} {\\arg \\max } p _ {t} ^ {(l)}, \\tag {13}", + "image_path": "bf77a4d2b76ee3cc74c1345c7657171c1fb04d75c546a5510ef9a941a002b422.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 81, + 410, + 253, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 410, + 253, + 423 + ], + "spans": [ + { + "bbox": [ + 81, + 410, + 253, + 423 + ], + "type": "interline_equation", + "content": "\\hat {s} = 2 ^ {l - 1} \\cdot (t - d _ {t} ^ {s}), \\quad \\hat {e} = 2 ^ {l - 1} \\cdot (t + d _ {t} ^ {e}).", + "image_path": "51111612b01d9433e8a177a7251c260f369c41debdfb6abe32ca21c78dfef238.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 430, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 287, + 453 + ], + "type": "text", + "content": "At inference time, we further apply Soft-NMS [4] to merge overlapping moment predictions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "type": "text", + "content": "Training and loss function. We use video-centric training as described in Section 3.3. The loss function for a pair of video snippet and text query is the sum of two terms: a Focal loss [26] " + }, + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "type": "text", + "content": " for moment classification and a Distance-IoU loss [69] " + }, + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{reg}" + }, + { + "bbox": [ + 47, + 456, + 287, + 528 + ], + "type": "text", + "content": " defined on positive time steps for distance regression. Formally," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 108, + 533, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 533, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 108, + 533, + 287, + 554 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\frac {1}{C} \\left(\\mathcal {L} _ {c l s} + \\lambda_ {r e g} \\mathbb {1} _ {t} ^ {(l)} \\mathcal {L} _ {r e g}\\right), \\tag {14}", + "image_path": "7d86eb53c12d435b0c74f0d7ee5108960b2385fe5c35d2ce393be544755e016d.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\mathbb{1}_t^{(l)}" + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "text", + "content": " is an indicator function that evaluates to one on positive time steps, " + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "inline_equation", + "content": "C = \\sum_{t,l}\\mathbb{1}_t^{(l)}" + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "text", + "content": " is the total number of positive samples within the snippet, and " + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "inline_equation", + "content": "\\lambda_{reg}" + }, + { + "bbox": [ + 47, + 560, + 287, + 624 + ], + "type": "text", + "content": " balances the two loss terms. Center sampling [61] is used for selecting positive time steps around the center of a target moment." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 634, + 127, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 634, + 127, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 634, + 127, + 647 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 287, + 713 + ], + "type": "text", + "content": "Our main experiments include extensive comparisons of SnAG to strong baselines on five challenging benchmarks for video grounding. We further provide ablations on cross-modal fusion and analyze the efficiency of SnAG in both training and inference. More results are in the supplement." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 343, + 72, + 507, + 210 + ], + "blocks": [ + { + "bbox": [ + 343, + 72, + 507, + 210 + ], + "lines": [ + { + "bbox": [ + 343, + 72, + 507, + 210 + ], + "spans": [ + { + "bbox": [ + 343, + 72, + 507, + 210 + ], + "type": "image", + "image_path": "88f4a85d6f7b967b7228f9f976dd1b4879b479a7ffcf06079a78ac26f9738e87.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 216, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 305, + 216, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 305, + 216, + 545, + 271 + ], + "type": "text", + "content": "Figure 3. Visualization of dataset statistics. Circle radius is in proportion to average number of queries per video. Long-video benchmarks (Ego4D-NLQ, MAD and TACoS) consist of longer videos with more queries and exhibit low moment coverage compared to short-video benchmarks (ANet-Captions and Charades)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 308, + 283, + 544, + 402 + ], + "blocks": [ + { + "bbox": [ + 308, + 283, + 544, + 402 + ], + "lines": [ + { + "bbox": [ + 308, + 283, + 544, + 402 + ], + "spans": [ + { + "bbox": [ + 308, + 283, + 544, + 402 + ], + "type": "table", + "html": "
ModelR@1R@5
0.30.5Avg0.30.5Avg
SF + BERT2D-TAN [67]5.042.023.5312.895.889.39
VSLNet [64]5.453.124.2910.746.638.69
CONE [17]10.405.037.7222.7411.8717.31
SOONet [36]8.003.765.8822.4011.0916.75
SnAG (video-centric)9.836.838.3327.9319.2723.60
SnAG (query-centric)10.437.158.7927.5919.3323.46
EgoVLPVSLNet [64]10.846.818.8318.8413.4516.15
CONE [17]14.158.1811.1730.3318.0224.18
SnAG (video-centric)15.7210.7813.2538.3927.4432.92
SnAG (query-centric)15.8711.2613.5738.2627.1632.71
", + "image_path": "650f6dc82d2c841ac5f51499f1a53ecc671a5bcc24fd5f229c19556b7175f3d2.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 406, + 544, + 427 + ], + "lines": [ + { + "bbox": [ + 306, + 406, + 544, + 427 + ], + "spans": [ + { + "bbox": [ + 306, + 406, + 544, + 427 + ], + "type": "text", + "content": "Table 1. Results on Ego4D-NLQ. SnAG outperforms all baselines. Best results are in bold and second best underlined." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "spans": [ + { + "bbox": [ + 305, + 449, + 544, + 474 + ], + "type": "text", + "content": "Datasets. We categorize five benchmark datasets into two groups based on their video and query statistics (Fig. 3)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 475, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 596 + ], + "type": "text", + "content": "Long videos, many queries. Ego4D-NLQ [16] is a large collection of egocentric videos on daily human activities. The videos are 3.5 to 20 minutes long with an average of 11.6 queries. MAD [45] contains 1.2K hours of movies with 384K queries transcribed from audio description. The videos are 47 to 202 minutes long. TACoS [40] is a conventional benchmark with 10.1 hours of cooking videos, with an average of 143.5 queries per video. These datasets expose the scalability challenges that motivate our work and thus are the main focus of our experiments." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "text", + "content": "Short videos, few queries. Charades-STA [43] is an action recognition dataset later annotated for video grounding [13]. The videos are " + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\sim 30" + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "text", + "content": " seconds long with " + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\sim 2.4" + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "text", + "content": " queries per video. ActivityNet-Captions [20] was collected for dense video captioning and later repurposed for video grounding. The videos are two minutes long on average with a small set of " + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\sim 3.65" + }, + { + "bbox": [ + 304, + 599, + 545, + 694 + ], + "type": "text", + "content": " queries. Several works [35, 57] advise against using these datasets as benchmarks for the" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 702, + 511, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 702, + 511, + 712 + ], + "spans": [ + { + "bbox": [ + 315, + 702, + 511, + 712 + ], + "type": "text", + "content": "3All experiments are conducted using the Ego4D " + }, + { + "bbox": [ + 315, + 702, + 511, + 712 + ], + "type": "inline_equation", + "content": "\\nu I" + }, + { + "bbox": [ + 315, + 702, + 511, + 712 + ], + "type": "text", + "content": " dataset." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18934" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 518, + 180 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 518, + 180 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 518, + 180 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 518, + 180 + ], + "type": "table", + "html": "
ModelR@1R@5R@10R@50
0.10.30.50.10.30.50.10.30.50.10.30.5
CLIP [39]6.573.131.3915.059.855.4420.2614.138.3837.9228.7118.80
VLG-Net [46]3.642.761.6511.669.315.9917.3914.569.7739.7834.2724.93
Moment-DETR [21]0.310.240.161.521.140.282.792.061.2011.087.974.71
CONE [17]8.906.874.1020.5116.119.5927.2021.5312.8243.3634.7320.56
SOONet [36]11.269.005.3223.2119.6413.1430.3626.0017.8450.3244.7832.59
SnAG (video-centric)10.288.465.5524.4220.6013.7532.2327.5019.0052.2846.6835.24
SnAG (query-centric)10.188.375.4424.3020.3513.5132.0527.2518.7552.0546.5334.83
", + "image_path": "9fb014012dd588b5a1f1f657cd85e4227cdf987e63c2364b29be03978fca3c89.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 92, + 185, + 499, + 196 + ], + "lines": [ + { + "bbox": [ + 92, + 185, + 499, + 196 + ], + "spans": [ + { + "bbox": [ + 92, + 185, + 499, + 196 + ], + "type": "text", + "content": "Table 2. Results on MAD. SnAG outperforms all baselines. Best results are in bold and second best underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 207, + 286, + 336 + ], + "blocks": [ + { + "bbox": [ + 50, + 207, + 286, + 336 + ], + "lines": [ + { + "bbox": [ + 50, + 207, + 286, + 336 + ], + "spans": [ + { + "bbox": [ + 50, + 207, + 286, + 336 + ], + "type": "image", + "image_path": "4f7ff842d2c213510aaad27a0c0318e2f50342257769de09c20c3dd7e2749bba.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 342, + 287, + 376 + ], + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 376 + ], + "type": "text", + "content": "Figure 4. Visualization of moment predictions. SnAG can (a) comprehend complex text queries with multiple objects and actions; (b) reason about temporal ordering of events." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 382, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 287, + 406 + ], + "type": "text", + "content": "temporal biases in their moment annotations. Nevertheless, we report results on these datasets for completeness." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 409, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 287, + 529 + ], + "type": "text", + "content": "Baselines. On TACoS, Charades and ANet-Captions, we compare to strong baselines including two-stage [28, 55, 56] and single-stage [30, 50, 70] models with various fusion operations (LSTM [29, 51], GCN [27, 46], co-attention [24, 68], etc.). On Ego4D and MAD, we compare to their official baselines (2D-TAN [67] and VSLNet [64] for Ego4D, CLIP [39] and VLG-Net [46] for MAD) as well as the concurrent method of CONE [17] and SOONet [36] that similarly address scalable video grounding. We discuss additional baselines in the supplement." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": "Evaluation metric. We report " + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\mathrm{Recall}@\\mathbf{k}" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": " at various temporal intersection-over-union threshold " + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\mathbf{R}@\\mathbf{k}" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": ", tIoU=" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": ") for all datasets. It measures the percentage of sentence queries with at least one of the top-" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": " moment predictions whose temporal overlap with the ground-truth moment exceeds " + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 532, + 287, + 591 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 599, + 201, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 201, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 201, + 612 + ], + "type": "text", + "content": "4.1. Long Videos, Many Queries" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "Experiment setup. For Ego4D, We consider (1) SlowFast [12] video features with BERT [10] text features, and (2) EgoVLP [38] video and text features. We train on the train split and report R@{1, 5}, tIoU={0.3, 0.5} on the val split. For MAD, we use CLIP [39] features for both videos and text. We train on the train split and report R@{1, 5, 10, 50}, tIoU={0.1, 0.3, 0.5} on the test split. For TACoS, we use C3D video features [48] and GloVe [37] for" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "type": "text", + "content": "sentence embeddings. We train on the train split and report " + }, + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "type": "inline_equation", + "content": "\\mathrm{R}@\\{1,5\\}" + }, + { + "bbox": [ + 304, + 207, + 545, + 254 + ], + "type": "text", + "content": ", tIoU=\\{0.5, 0.7\\} on the test split. We report results using both video-centric and query-centric training on all datasets." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "type": "text", + "content": "Results on Ego4D-NLQ (Table 1). SnAG sets the new state of the art, achieving mean R@1 / R@5 scores of " + }, + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "type": "inline_equation", + "content": "8.79\\% / 23.60\\%" + }, + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "type": "text", + "content": " with SlowFast/BERT features, and " + }, + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "type": "inline_equation", + "content": "13.57\\% / 32.92\\%" + }, + { + "bbox": [ + 304, + 258, + 546, + 390 + ], + "type": "text", + "content": " with EgoVLP features, doubling or even tripling the results of the official baselines [64, 67]. Compared to the strong baselines of CONE [17] and SOONet [36], SnAG improves mean R@1 and R@5 respectively by more than 1.05 and 6.29 absolute percentage points without taking advantage of external features. Further, SnAG demonstrates a larger performance gain on the more stringent tIoU threshold of 0.5, indicating more precise moment localization." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 392, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 513 + ], + "type": "text", + "content": "Results on MAD (Table 2). SnAG sets new records on the challenging MAD dataset. It improves over CLIP [39] and VLG-Net [46] on mean R@1 / R@5 at tIoU=0.5 by 3.90 / 7.76 absolute percentage points. In the meantime, it outperforms CONE [17] and SOONet [36], with larger gain for more stringent tIoU thresholds. Further, SnAG achieves stronger results as input snippet length increases, reaching the best accuracy with " + }, + { + "bbox": [ + 304, + 392, + 545, + 513 + ], + "type": "inline_equation", + "content": "T_{w} = 16384" + }, + { + "bbox": [ + 304, + 392, + 545, + 513 + ], + "type": "text", + "content": " (Supplement Fig. A). This scaling behavior highlights the strength of our scalable model design for long-form video grounding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "content": "Results on TACoS (Table 4 (left)). SnAG achieves an R@1 / R@5 of " + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "inline_equation", + "content": "44.86\\%" + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "content": " / " + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "inline_equation", + "content": "70.66\\%" + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "content": " at tIoU=0.5, outperforming the strongest baseline of MATN [66] by a significant margin " + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "inline_equation", + "content": "(+7.5\\% \\mathrm{R} @ 1, +12.1\\% \\mathrm{R} @ 5)" + }, + { + "bbox": [ + 304, + 515, + 545, + 658 + ], + "type": "text", + "content": ". This confirms that our simple single-stage design with late fusion is a strong alternative to multi-stage models with sophisticated fusion mechanisms. Importantly, our scalable design enables learning from full-resolution video features, whereas the baselines often aggressively reduce feature resolution to contain their training and inference cost on long-form videos. We hypothesize that full-resolution video features capture detailed event dynamics and are key to the strong performance of SnAG." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 662, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 662, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 662, + 545, + 685 + ], + "type": "text", + "content": "Result visualization. We visualize predictions of SnAG and the baselines on TACoS and Ego4D-NLQ videos. In" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 315, + 693, + 533, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 693, + 533, + 703 + ], + "spans": [ + { + "bbox": [ + 315, + 693, + 533, + 703 + ], + "type": "text", + "content": "4CONE [17] leverages external CLIP [39] features in several steps." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 317, + 703, + 525, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 703, + 525, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 703, + 525, + 713 + ], + "type": "text", + "content": "5MAD videos are not publicly available due to copyright issues." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18935" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 70, + 272, + 266 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 272, + 266 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 272, + 266 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 272, + 266 + ], + "type": "table", + "html": "
ModelR@1R@5
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(a) Fusion stage (early vs. late fusion)
No fusion10.857.8546.4631.19
SnAG-E53.3444.0179.5669.41
SnAG-EL54.8444.5481.1370.11
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(b) Fusion operation (global vs. token-wise)
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Add51.9141.8177.9866.51
Scale55.0143.9680.6370.11
Add + Scale53.3643.0980.4369.58
XAttn54.8445.0679.9670.08
XAttn-affine (ours)55.1444.9481.1070.66
", + "image_path": "d45490b02b2602cd98d4a768e4f2caedcd7932de3e15250099104b16917fe4d8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 270, + 287, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 314 + ], + "type": "text", + "content": "Table 3. Ablations results on TACoS. (a) Late fusion yields comparable results to early fusion (E, EL, M); (b) Fusion with tokenwise sentence embeddings (XAttn) produces better results than fusion with global sentence embeddings (Cat, Add, Scale)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 327, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 287, + 471 + ], + "type": "text", + "content": "Fig. 4(a), a long query describes the complex interplay between two objects (pan and stove) and three actions (\"take from\", \"place on\", and \"turn on\"). VLG-Net [46] recognized both objects yet none of the actions, while 2D-TAN [67] identified one action (\"take from\") but at the same time missed one object (pan). By contrast, SnAG followed the query semantics and produced accurate localization. The other query in Fig. 4(b) tests the understanding of temporal context. SnAG leveraged the keyword \"before\" to identify the correct moment before the action (\"pick up\"), whereas VSLNet [64] only attended to the object (can), thus mistakenly predicting a moment after the action." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 481, + 194, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 194, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 194, + 493 + ], + "type": "text", + "content": "4.2. Short Videos, Few Queries" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 624 + ], + "type": "text", + "content": "Experiment setup. We extract video features using both C3D [48] (pretrained on Sports-1M [18]) and I3D [5] (pretrained on Kinetics [19]) for Charades-STA, and use the official C3D features for ActivityNet-Captions. We use GloVe word embeddings [37] to represent sentence queries for both datasets. We train on their respective train splits, report R@{1, 5}, tIoU={0.5, 0.7} on the test split of Charades-STA, and R@{1, 5}, tIoU={0.3, 0.5} on the val_2 split of ActivityNet-Captions. Following standard practice, we resize all video features to a uniform length of 256." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Results on Charades-STA (Table 4 (middle)). SnAG outperforms all previous methods by a wide margin. It obtains " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "33.52\\%" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " R@1 and " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "64.11\\%" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " R@5 at tIoU=0.7 with C3D features, 2.10 and 4.52 absolute percentage points higher than the latest SSRN [71] baseline. It further attains " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "46.26\\%" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " R@1 and " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "71.94\\%" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " R@5 at tIoU=0.7 with I3D features, setting new state of the art on this competitive benchmark." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "Results on ActivityNet-Captions (Table 4 (right)). SnAG achieves competitive results, reaching an R@1 / R@5 score of " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "30.56\\% / 63.41\\%" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " at tIoU=0.7. It is only outperformed by a few latest models [22, 27, 71] while being much simpler." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 127, + 406, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 127, + 406, + 139 + ], + "spans": [ + { + "bbox": [ + 305, + 127, + 406, + 139 + ], + "type": "text", + "content": "4.3. Ablation Studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 146, + 545, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 146, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 545, + 169 + ], + "type": "text", + "content": "We conduct extensive ablations on TACoS to study key design choices for cross-modal fusion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 173, + 545, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 173, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 304, + 173, + 545, + 256 + ], + "type": "text", + "content": "Early vs. late fusion. Does late fusion enable better scalability at the expense of accuracy? We study three variants of SnAG with common early-fusion designs: (1) SnAG-E with fusion before the pyramid; (2) SnAG-EL with fusion before and after the pyramid; (3) SnAG-M with repeated fusion within the pyramid. Table 3 confirms that early and late fusion yield comparable results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 259, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 545, + 344 + ], + "type": "text", + "content": "Choice of fusion operation. We study fusion operations used by strong baselines, including point-wise addition, multiplication, and concatenation of video representations with global sentence embeddings, as well as vanilla cross-attention with token-level sentence embeddings. According to Table 3, token-level embeddings produce better results, and our cross-attention variant further boosts performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 351, + 417, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 417, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 417, + 363 + ], + "type": "text", + "content": "4.4. Efficiency Analysis" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 369, + 537, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 369, + 537, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 369, + 537, + 381 + ], + "type": "text", + "content": "Finally, we conduct an efficiency analysis of our method." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 384, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 529 + ], + "type": "text", + "content": "Breakdown of model capacity. A key design choice of SnAG is to carefully balance the model capacity among its video encoder, text encoder, and moment decoder including the fusion module and the localization heads. For a detailed breakdown of model capacity, we measure their respective parameter size and MACs in percentage. Fig. 5(a) indicates that SnAG's video encoder absorbs a significant portion of parameters and compute, such that per-query evaluation (i.e., text encoding, fusion, and decoding) occupies " + }, + { + "bbox": [ + 304, + 384, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\sim 50\\%" + }, + { + "bbox": [ + 304, + 384, + 545, + 529 + ], + "type": "text", + "content": " of the total computation. This design is naturally in favor of video-centric training and inference, where the costly video encoding is shared among many queries." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 604 + ], + "type": "text", + "content": "Video-centric vs. query-centric training. Fig. 5(b) presents the training time and GPU memory usage of video-centric training relative to conventional query-centric training. The results show that the amount of saving correlates with snippet length and number of queries. Video-centric training is thus preferred for long videos with many queries." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " in video-centric training. We further study how " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", the number of text query samples per video, trades off accuracy for efficiency in video-centric training. On MAD, we fix the batch size " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "|B| = 32" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " for a mini-batch " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", vary " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " between 1 and " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "|B|" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ", and report training time, GPU memory usage and test accuracy relative to query-centric training (i.e., " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "B_{q} = 1" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "). Fig. 5(d) reveals that test accuracy is unaffected even with a large " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "B_{q} = 32" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " (i.e., a single video per mini-batch), while training time and GPU memory usage" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18936" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 57, + 544, + 293 + ], + "blocks": [ + { + "bbox": [ + 49, + 57, + 544, + 293 + ], + "lines": [ + { + "bbox": [ + 49, + 57, + 544, + 293 + ], + "spans": [ + { + "bbox": [ + 49, + 57, + 544, + 293 + ], + "type": "table", + "html": "
MethodTACoS (C3D)Charades-STA (I3D)Charades-STA (C3D)ActivityNet-Captions (C3D)
R@1R@5R@1R@5R@1R@5R@1R@5
0.30.50.30.50.50.70.50.70.50.70.50.70.50.70.50.7
CTRL ICCV 17 [13]18.3213.3036.6925.42----23.638.8958.9229.52----
QSPN AAAI 19 [56]--------35.6015.8079.4045.4027.7013.6059.2038.30
SCDM NeurIPS 19 [58]27.6423.2740.0633.4954.9234.2676.5060.02----36.9020.2866.8442.92
2D-TAN AAAI 20 [67]45.6135.7769.1157.3156.6436.2189.1461.1341.1023.2581.5348.5546.1629.2178.8060.85
CBP AAAI 20 [51]27.3124.7943.6437.40----36.8018.8770.9450.1935.7617.8065.8946.20
DRN CVPR 20 [60]-23.17-33.3653.0931.7589.0660.0545.4026.4088.0155.3845.4524.3677.9750.30
BPNet AAAI 21 [55]25.9620.96--50.7531.64--38.2520.51--42.0724.69--
CPNet AAAI 21 [24]42.6128.29--60.2738.74--40.3222.47--40.5621.63--
SMIN CVPR 21 [50]48.0135.2465.1853.3664.0640.7589.4968.09----48.4630.3481.1662.11
CBLN CVPR 21 [29]38.9827.6573.1246.2461.1338.2290.3361.6947.9428.2288.2057.4748.1227.6079.3263.41
CPN CVPR 21 [68]47.6936.33--51.0731.54------45.1028.10--
DeNet CVPR 21 [70]----59.7038.5291.2466.83----43.79-74.13-
MATN CVPR 21 [66]48.7937.5767.6357.91--------48.0231.7878.0263.18
VLG-Net ICCVW 21 [46]45.4634.1970.3856.56--------46.3229.8277.1563.33
APGN EMNLP 21 [28]40.4727.8659.9847.1262.5838.8691.2462.1148.2029.3789.0558.4948.9228.6478.8763.19
IA-Net EMNLP 21 [30]37.9126.2757.6246.3961.2937.9189.7862.04----48.5727.9578.9963.12
RaNet EMNLP 21 [14]43.3433.5467.3355.0960.4039.6589.5764.54----45.5928.6775.9362.97
MGSL-Net AAAI 22 [30]42.5432.2763.3950.1363.9841.0393.2163.85----51.8731.4282.6066.71
MMN AAAI 22 [52]39.2426.1762.0347.39--------48.5929.2679.5064.76
SSRN EMNLP 22 [71]45.1034.3365.2651.8565.5942.6594.7665.4850.3931.4290.6859.9454.4933.1584.7268.48
G2L ICCV 23 [22]42.7430.9565.8349.86--------51.6833.3581.3267.60
SnAG (video-centric)56.4444.8681.1570.6664.6246.2692.5571.9451.7233.5292.5564.1148.5530.5681.7163.41
SnAG (query-centric)55.0144.5180.6870.1365.1345.9192.8071.7551.1031.7790.2262.1547.5529.6581.5562.21
", + "image_path": "7b2e2f2420a0476bbd4d20cac505faa8c66f64acebdf9cb49634a9a2f6a4bc92.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 546, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 546, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 546, + 319 + ], + "type": "text", + "content": "Table 4. Results on TACoS, Charades-STA and ActivityNet-Captions. SnAG outperforms all baselines on TACoS and Charade-STA by a large margin, while being highly competitive on ActivityNet-Captions. Best results are in bold and second best underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 331, + 160, + 423 + ], + "blocks": [ + { + "bbox": [ + 50, + 331, + 160, + 423 + ], + "lines": [ + { + "bbox": [ + 50, + 331, + 160, + 423 + ], + "spans": [ + { + "bbox": [ + 50, + 331, + 160, + 423 + ], + "type": "image", + "image_path": "034aec85e20ee7f163d3d00cae17d23a683054193ab09b09a375bc8f2fad07e0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "lines": [ + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": "Figure 5. (a) Model capacity. T, E, M denotes TACoS, Ego4D and MAD, respectively (also in (b)). Shaded bar: % of parameters, Colored bar: % of MACs. SnAG places more parameters and compute in video encoder for less expensive per-query evaluation (fusion + decoding). (b, c) Video-centric vs. query-centric inference (b) and training (c). SnAG saves up to " + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": " training time, " + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": " GPU memory and " + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": " test time, and delivers up to " + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": " faster convergence relative to query-centric training / inference. (d) Effect of " + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": " on training efficiency and test accuracy on MAD. Training on MAD is faster and takes less GPU memory as " + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "inline_equation", + "content": "B_{q}" + }, + { + "bbox": [ + 46, + 426, + 546, + 481 + ], + "type": "text", + "content": " grows, while the test accuracy is unaffected." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 170, + 331, + 285, + 423 + ], + "blocks": [ + { + "bbox": [ + 170, + 331, + 285, + 423 + ], + "lines": [ + { + "bbox": [ + 170, + 331, + 285, + 423 + ], + "spans": [ + { + "bbox": [ + 170, + 331, + 285, + 423 + ], + "type": "image", + "image_path": "afa7c78d392044d86a41785a82fcc08744cbb838a9d761b7c29ffd1e790003c8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 294, + 331, + 416, + 423 + ], + "blocks": [ + { + "bbox": [ + 294, + 331, + 416, + 423 + ], + "lines": [ + { + "bbox": [ + 294, + 331, + 416, + 423 + ], + "spans": [ + { + "bbox": [ + 294, + 331, + 416, + 423 + ], + "type": "image", + "image_path": "38a25ea3e1e8cc1a63805f1c3481bb9e9b47d1bc2d05ecb0fa054fca392e1f6d.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 425, + 333, + 544, + 424 + ], + "blocks": [ + { + "bbox": [ + 425, + 333, + 544, + 424 + ], + "lines": [ + { + "bbox": [ + 425, + 333, + 544, + 424 + ], + "spans": [ + { + "bbox": [ + 425, + 333, + 544, + 424 + ], + "type": "image", + "image_path": "405277267d74f9782f2007159bcbaabc91e6951ae176f18e1597779abe9490c2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "type": "text", + "content": "drop by a significant " + }, + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "type": "inline_equation", + "content": "55\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "type": "inline_equation", + "content": "42\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 521 + ], + "type": "text", + "content": ", approaching the upper bound by our analysis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 524, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 524, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 46, + 524, + 287, + 644 + ], + "type": "text", + "content": "Video-centric vs. query-centric inference. We now ask to what extent the re-use of video representations enabled by SnAG's late fusion design accelerates inference. Fig. 5(b) presents the percentage of time spent by our video-centric inference scheme relative to query-centric inference, where the full model is evaluated on each and every video-query pair. Consistent with earlier findings on video-centric training, longer videos with more queries result in more saving in inference time. On the challenging MAD dataset, this alone brings a major reduction (65%) in test time." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "text", + "content": "Inference speed. With window filtering [17], inference of SnAG on the val split of MAD takes 12 minutes on a single P100 GPU. This is " + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "text", + "content": " faster than CONE [17] (" + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "inline_equation", + "content": "\\sim 18" + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "text", + "content": " mins) and " + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "inline_equation", + "content": "63\\%" + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "text", + "content": " faster than SOONet [36] (" + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "inline_equation", + "content": "\\sim 32" + }, + { + "bbox": [ + 46, + 647, + 288, + 696 + ], + "type": "text", + "content": " mins).6" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 496, + 379, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 496, + 379, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 496, + 379, + 509 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 517, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 545, + 661 + ], + "type": "text", + "content": "In this paper, we presented a simple and accurate model towards scaling up video grounding. We provided extensive analysis on the complexity of video grounding models from the perspective of cross-modal fusion, and argued that late fusion is key to scalability in video duration and query size. Our model, SnAG, is a simple instantiation of late fusion with minimalist design. It achieves superior accuracy and efficiency on a spectrum of challenging benchmarks and compares favorably to strong baselines including those dedicated to efficient inference on long videos. We hope our analysis and model design can shed light on video grounding and more broadly scalable video understanding." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 666, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 712 + ], + "type": "text", + "content": "Acknowledgement: This work was partially supported by NIH grant R01OH012313, by grants from McPherson Eye Research Institute and VCGRE at UW Madison, and by the Army Research Lab under contract number W911NF-2020221." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "inline_equation", + "content": "^{6}" + }, + { + "bbox": [ + 58, + 702, + 286, + 713 + ], + "type": "text", + "content": "SOONet reports an inference time of 8.2 mins on a single A100 GPU." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18937" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 711 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 138 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 138 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 138 + ], + "type": "text", + "content": "[1] Lisa Anne Hendricks, Oliver Wang, Eli Shechtman, Josef Sivic, Trevor Darrell, and Bryan Russell. 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Samples produced by the proposed text-to-video generation method for a selection of prompts. Thanks to joint spatiotemporal video modeling, our generator can synthesize temporally coherent videos with large motion (left) while retaining the semantic control capabilities typical of large-scale text-to-video generators (right). See the Website for additional samples." + ], + "image_footnote": [], + "bbox": [ + 78, + 297, + 483, + 537 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/506832b796cc84ccf0482793d3c8b2c44e40f92da38ae97d7274f447287a5401.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 297, + 890, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 604, + 313, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Contemporary models for generating images show remarkable quality and versatility. Swayed by these advantages, the research community repurposes them to generate videos. Since video content is highly redundant, we argue that naively bringing advances of image models to the video generation domain reduces motion fidelity, visual quality and impairs scalability. In this work, we build Snap Video, a video-first model that systematically addresses these challenges. To do that, we first extend the EDM framework to take into account spatially and temporally redundant pixels and naturally support video generation. Second, we show that a U-Net—a workhorse behind image generation—scales poorly when generating videos, requiring significant computational overhead. Hence, we propose a new transformer-based architecture that trains 3.31 times faster than U-Nets (and is $\\sim 4.5$ faster at inference). This allows us to efficiently train a text-to-video model with billions of", + "bbox": [ + 75, + 643, + 472, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "parameters for the first time, reach state-of-the-art results on a number of benchmarks, and generate videos with substantially higher quality, temporal consistency, and motion complexity. The user studies showed that our model was favored by a large margin over the most recent methods.", + "bbox": [ + 496, + 604, + 893, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 710, + 632, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Creating and sharing visual content is one of the key ways for people to express themselves in the digital world. Accessible to only professionals in the past, the capability to create [30, 40, 43, 69] and edit [6, 37, 42] images with stunning quality and realism was unlocked to everyone by the advent of large text-to-image models and their variations.", + "bbox": [ + 496, + 737, + 890, + 828 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Fueled by this progress, large-scale text-to-video models [4, 13, 21, 48, 62] are rapidly advancing too. Current large-scale diffusion-based video generation frame", + "bbox": [ + 496, + 829, + 890, + 875 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Work performed while interning at Snap Inc.", + "bbox": [ + 522, + 886, + 772, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7038", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "works are strongly rooted into their image counterparts [4, 13]. The availability of consolidated image generation architectures such as U-Nets [41] with publicly-available image-pretrained models [40] made them a logical foundation onto which to build large-scale video generators with the main architectural modifications focusing on the insertion of ad-hoc layers to capture temporal dependencies [4, 13, 21, 48, 62]. Similarly, training is performed under image-based diffusion frameworks with the model being applied both to videos and to a separate set of images to improve the diversity of the results [13, 21, 22, 48].", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We argue that such an approach is suboptimal under multiple aspects which we systematically address in this work. First, image and video modalities present intrinsic differences given by the similarity of content in successive video frames [7, 13]. By analogy, image and video compression algorithms are based on vastly different approaches [33]. To address this issue, we rewrite the EDM [25] framework with a focus on high-resolution videos. Differently from past work where videos were treated as a sequence of images, we perform joint video-image training by treating images as high frame-rate videos to avoid modality mismatches introduced by the absence of the temporal dimension within purely image-based training. Second, the widely adopted U-Net [41] architecture is required to fully processes each video frame. This increases computational overhead compared to purely text-to-image models, posing a very practical limit on model scalability. The latter is a critical factor in obtaining high-quality of results [13, 21]. Extending U-Net-based architectures to naturally support spatial and temporal dimensions requires volumetric attention operations, which have prohibitive computational demands. Inability to do so affects the outputs, resulting in dynamic images or motion artifacts being generated instead of videos with coherent and diverse actions.", + "bbox": [ + 75, + 260, + 472, + 623 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Following our compression analogy, we propose to leverage repetition between frames and introduce a scalable transformer architecture that treats spatial and temporal dimensions as a single, compressed, 1D latent vector. This highly compressed representation allows us to perform spatio-temporal computation jointly and enables modelling of complex motions. Our architecture is inspired by FIT [8], which we scale to billions of parameters for the first time. Compared to U-Nets, our model features a significant $3.31 \\times$ reduction in training time and $4.49 \\times$ reduction in inference time while achieving higher generation quality.", + "bbox": [ + 75, + 626, + 472, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate Snap Video on the widely-adopted UCF101 [55] and MSR-VTT [65] datasets. Our generator shows state-of-the-art performance across the range of benchmarks with particular regard to the quality of the generated motion. Most interestingly, we performed a number of user studies against the most recent open- and close-source methods and found that according to the participants", + "bbox": [ + 75, + 795, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of the study our model features photorealism comparable to Gen-2 [11], while being significantly better than Pika [1] and Floor33 [17]. Most excitedly, the preference of user-study participants favoured Snap Video by a large margin when text alignment and motion quality were assessed. Compared to Gen-2 [11] on prompt-video alignment our model was preferred in $81\\%$ of cases (80% against Pika [1], 81% against Floor33 [17]), generated most dynamic videos with most amount of motion (96% against Gen2 [11], 89% against Pika [1], 88% against Floor33 [17]) and had the best motion quality (79% against Gen-2 [11], 71% against Pika [1], 79% against Floor33 [17]).", + "bbox": [ + 496, + 90, + 893, + 273 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 286, + 640, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video Generation Video generation is a challenging and long-studied task. Due to its complexity, a large number of works focus on modeling narrow domains [5, 9, 12, 28, 35, 44, 47, 49, 56, 58, 59, 66, 70, 71] and adopt adversarial training [5, 9, 28, 44, 47, 49, 58, 59, 71] or autoregressive generation techniques [12, 35, 56, 66, 70]. To address the narrow domain limitation, the task of text-to-video generation was proposed [34] and both autoregressive models [23, 34, 61, 63, 64] and GANs [29] emerged.", + "bbox": [ + 496, + 311, + 893, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The recent success of diffusion models in the context of text-to-image generation [3, 40, 43] fostered tremendous progress in the task [2, 4, 13, 16, 17, 21, 22, 32, 48, 62, 67, 72]. ImagenVideo [21] and Make-A-Video [48] propose a deep cascade of temporal and spatial upsamplers to generate videos and jointly train their models on image and video datasets. PYoCo [13] introduces a correlated noise model to capture similarities between video frames. Video LDM [4] adopts a latent diffusion paradigm where a pretrained latent image generator and latent decoder are finetuned to generate temporally coherent videos.AnimateDiff [16] freezes a pre-trained latent image generator and trains only a newly inserted motion modeling module. These works employ U-Nets with separable spatial and temporal computation which poses a limitation on motion modeling capabilities. VideoFactory [62] improves upon this paradigm by proposing a Swapped Spatiotemporal CrossAttention that improves interactions between the spatial and temporal modalities along 3D windows.", + "bbox": [ + 496, + 448, + 895, + 734 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Differently from this corpus of works which adapts the U-Net [41] architecture to the video generation task, we show that employing transformer-based FIT [8] architectures results in significant training time savings, scalability improvements, and performance increase thanks to their learnable compressed video representation. In particular, we show that the global joint spatiotemporal modeling strategy enabled by our compressed video representation results in significant improvements in temporal consistency and motion modeling capabilities.", + "bbox": [ + 496, + 734, + 895, + 887 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7039", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "High-Resolution Generation Different approaches have been proposed to enable the generation of high-resolution outputs. Cascaded diffusion models [3, 13, 21, 43, 48] adopt a set of independent diffusion models designed to successively upsample the results of the previous step. Latent diffusion models [2, 4, 17, 40, 72] make use of a pretrained autoencoder to encode the input into a low-dimensional set of latent vectors and learn a diffusion model on this latent representation.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A different family of methods generates high-resolution outputs end-to-end without employing cascades of models or latent diffusion. Simple Diffusion [24] and Chen [7] directly generate high-resolution images by adapting the noise schedule of the diffusion process. f-DM [14] and RDM [57] design a diffusion process that seamlessly transitions between different resolutions. MDM [15] proposes a strategy where a single model is trained to simultaneously denoise inputs at progressively higher resolutions.", + "bbox": [ + 75, + 227, + 472, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we adopt a two-stage cascaded model out of two considerations: (i) it avoids temporal inconsistencies in the forms of flickering of high-frequency details that may be introduced by latent autoencoders [4], (ii) it increases model capacity with respect to an end-to-end model by creating two specialized models, one for the low resolution focusing on motion modeling and scene structure, and one for the high-resolution, focusing on high-frequency details.", + "bbox": [ + 75, + 363, + 472, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Frameworks Diffusion generative models are a set of techniques modeling generation as a pair of processes: a forward process progressively destructing a sample with noise, and a reverse process modeling generation as the progressive denoising of a sample. Different formulations of diffusion models have been proposed in the literature. Denoising Diffusion Probabilistic Models (DDPMs) [20, 50] formulate the forward and backward process as Markov chains. Score-based Generative Models (SGMs) [51, 52] model the score of the probability density function of a series of data distributions perturbed with increasing levels of noise, i.e. the direction of largest increase in the data log probability density function. An avenue of works [53, 54] generalizes DDPMs and SGMs to infinite noise levels through Stochastic Differential Equations (SDEs). In this work, we adopt the SGM framework of EDM [25] which we reformulate for the generation of high-resolution videos.", + "bbox": [ + 75, + 500, + 472, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 784, + 169, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose the generation of high-resolution videos by rewriting the EDM [25] diffusion framework for high-dimensional inputs and proposing an efficient transformer architecture based on FITs [8] which we scale to billions of parameters and tens of thousands input patches. Sec. 3.1 provides an introduction to the EDM framework, Sec 3.2", + "bbox": [ + 75, + 809, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "highlights the challenges of applying diffusion frameworks to high dimensional inputs and proposes a revisited EDM-based diffusion framework. Sec. 3.3 proposes a method to reduce the gap between image and video modalities for joint training. Finally, Sec. 3.4 describes our scalable video generation architecture, while Sec. 3.5 and Sec. 3.6 respectively describe the training and inference procedures.", + "bbox": [ + 496, + 90, + 893, + 198 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Introduction to EDM", + "text_level": 1, + "bbox": [ + 498, + 205, + 700, + 220 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models have achieved remarkable success in image and video generation. Among the proposed frameworks, Karras et al. [25] provide a unified view of common diffusion frameworks and formulate EDM. EDM defines a variance-exploding forward diffusion process $p(\\pmb{x}_{\\sigma}|\\pmb{x}) \\sim \\mathcal{N}(\\pmb{x}, \\pmb{\\sigma}^2\\mathbf{I})$ , where $\\pmb{\\sigma} \\in [\\pmb{\\sigma}_{\\mathrm{min}}, \\pmb{\\sigma}_{\\mathrm{max}}]$ represents the diffusion timestep coinciding with the standard deviation of the applied noise, and $x_{\\sigma}$ represents the data at the current noise level. A denoiser function $\\mathcal{D}_{\\theta}$ is learned to model the reverse process using the denoising objective:", + "bbox": [ + 496, + 229, + 893, + 381 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ \\lambda (\\boldsymbol {\\sigma}) \\| \\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - \\boldsymbol {x} \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 387, + 890, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda$ is the loss weighting function, $\\pmb{x} \\sim p_{\\mathrm{data}}$ is a data sample, $\\epsilon$ is gaussian noise, and $\\sigma \\sim p_{\\mathrm{train}}$ is sampled from a training distribution. $\\mathcal{D}_{\\theta}(\\pmb{x}_{\\sigma})$ is defined as:", + "bbox": [ + 496, + 420, + 893, + 465 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\sigma}\\right) = c _ {\\text {o u t}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}\\right) + c _ {\\text {s k i p}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 474, + 890, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{\\theta}$ is a neural network, and $c_{\\mathrm{out}}$ , $c_{\\mathrm{skip}}$ and $c_{\\mathrm{in}}$ represent scaling functions. In particular, the denoising objective $\\mathcal{L}(\\mathcal{F}_{\\theta})$ can equivalently be expressed in terms of $\\mathcal{F}_{\\theta}$ as:", + "bbox": [ + 496, + 498, + 890, + 544 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {F} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ w (\\boldsymbol {\\sigma}) \\left\\| \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - c _ {\\text {n r m}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\mathrm {t g t}} \\right\\| _ {2} ^ {2} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 551, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{\\mathrm{tgt}}$ represents the training target, $c_{\\mathrm{nm}}$ is a normalization factor, and $w$ is a weighting function. These forms, derived in Appx. E, are presented in Tab. 1.", + "bbox": [ + 496, + 580, + 890, + 626 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A second order Runge-Kutta sampler is proposed to reverse the diffusion process and produce sample $\\pmb{x}$ starting from gaussian noise $\\pmb{x}_{\\sigma_{\\mathrm{max}}} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I})$ .", + "bbox": [ + 496, + 627, + 890, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. EDM for High-Resolution Video Generation", + "text_level": 1, + "bbox": [ + 498, + 681, + 877, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "EDM is originally proposed as an image generation framework and its parameters are optimized for $64 \\times 64\\mathrm{px}$ image generation. Alterations in spatial resolution or the introduction of videos with shared content between frames allow the denoising network to trivially recover a noisy frame in the original resolution with higher signal-to-noise-ratio (SNR), which the original framework was designed to see at lower noise levels. To see why, consider a noisy video $\\boldsymbol{x}_{\\sigma} \\in \\mathbb{R}^{T \\times s \\cdot H \\times s \\cdot W} \\sim \\mathcal{N}(\\boldsymbol{x}, \\sigma^2\\mathbf{I})$ where $T$ is the number of frames and $s$ is an upsampling factor. We build the corresponding clean and noisy frames at original resolution $\\tilde{\\boldsymbol{x}}$ , $\\tilde{\\boldsymbol{x}}_{\\sigma} \\in \\mathbb{R}^{1 \\times H \\times W}$ by averaging values in each $T \\times s \\times s$ block of pixels. As a consequence of averaging, the noise", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7040", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/4ce66b533645f0c594a5fe77744b7466c20736e3fb07cab81944bbfed7d6cff7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
EDM [25]Our
Training and Losses
Forw. processxσx/σin + σεx/σin + σε
Training targetFtgtσx - σ2data ε + σ2data(σin-1)/σin x- σx + σ2data ε
Eff. loss weigh.w(σ)1(σ2 + σ2data)2/(σ2 + σ2data)2
Loss weigh.λ(σ)1/σ2data + 1/σ21/σ2data + 1/σ2
Network Parametrization
Input scalingcin(σ)1/√σ2data + σ21/√σ2data/σ2 + σ2
Output scalingcout(σ)σσ2data/√σ2+ σ2data- σinσσdata√σ2+ σ2data/σ2+ σ2
Skip scalingcskip(σ)σ2data/σ2+ σ2dataσinσ2data/σinσ2+ σ2data
Target scalingcnrm(σ)1/σdata√σ2+ σ2data1/σdata√σ2+ σ2data
", + "bbox": [ + 76, + 89, + 467, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Definitions of functions in Eq. (1), Eq. (2) and Eq. (3) for the EDM and our proposed diffusion framework as derived in Appx. E and Appx. F, where we highlight the terms induced by the input scaling factor $\\sigma_{\\mathrm{in}}$ . Our framework is equivalent to EDM for $\\sigma_{\\mathrm{in}} = 1$ but avoids the unstable term $\\frac{\\sigma_{\\mathrm{data}}^2(\\sigma_{\\mathrm{in}} - 1)}{\\sigma_{\\mathrm{in}}\\sigma} x$ induced by $\\sigma_{\\mathrm{in}} \\neq 1$ in $\\mathcal{F}_{\\mathrm{tgt}}$ . This form highlights that the train target and loss weight match the $v$ -prediction [45] framework for $\\sigma_{\\mathrm{data}} = 1$ . All other framework parameters are unaltered with respect to EDM.", + "bbox": [ + 75, + 291, + 472, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "variance is reduced by a factor $Ts^2$ , i.e. $\\tilde{x}_{\\sigma} \\sim \\mathcal{N}(\\tilde{x}, \\frac{\\sigma^2}{Ts^2}\\mathbf{I})$ , thus $\\tilde{x}_{\\sigma}$ has an increased signal-to-noise-ratio with respect to $x_{\\sigma}$ (see Fig. 2): $SNR_{\\tilde{x}_{\\sigma}} = Ts^2 SNR_{x_{\\sigma}}$ . If pixels in each block share similar content, a typical situation in high-resolution videos, then the information in the averaged frame is useful for recovering $x$ and can be exploited at training time by the denoiser function. This creates a train-inference mismatch during the initial sampling steps as the average frame does not yet contain a well-formed signal, yet the denoiser is reliant on its presence. Thus, for best performance, any alteration to $T$ or $s$ should instead maintain the same signal-to-noise ratio at the original resolution for which the diffusion framework was designed.", + "bbox": [ + 75, + 438, + 468, + 636 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To restore the optimal SNR at the original resolution, the magnitude of the input signal can be reduced [7] by a corresponding factor $\\sigma_{\\mathrm{in}} = s\\sqrt{T}$ as illustrated in Fig. 2. Consequently, we redefine the forward process as $p(\\boldsymbol{x}_{\\sigma}|\\boldsymbol{x}) \\sim \\mathcal{N}(\\boldsymbol{x} / \\sigma_{\\mathrm{in}}, \\sigma^2\\mathbf{I})$ .", + "bbox": [ + 75, + 640, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We rewrite the EDM framework to introduce the input scaling factor in Appx. F and highlight the changes in Tab. 1. We notice that a naive introduction of the scaling factor would alter the training target $\\mathcal{F}_{\\mathrm{tgt}}$ in a way that makes the objective explode for small noise values (see Appx. E). We thus leverage the training objective expressed in the form of Eq. (3) to rewrite the EDM process in a way that ensures $\\mathcal{F}_{\\mathrm{tgt}}$ remains unchanged, the effective loss weight $w(\\sigma)$ is such that it keeps the loss weight $\\lambda (\\sigma)$ unchanged, $c_{\\mathrm{in}}(\\sigma)$ and $c_{\\mathrm{nm}}(\\sigma)$ normalize the input and training target to have unit variance, and the framework is equivalent to the original EDM formulation for $\\sigma_{\\mathrm{in}} = 1$ (see Appx. F).", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9e11ee40e7d83893d84b6e8237365779c1162475aca6016c22edde858235273a.jpg", + "image_caption": [ + "Figure 2. Analysis of Signal-to-Noise Ratio (SNR). Top: noise $\\sigma$ is applied to an image. Middle: the same noise $\\sigma$ is applied to a 16-frames-long video $x$ without scaling. A clean image can be easily restored by simply taking average, indicating an increased SNR. Bottom: to maintain the original SNR, we scale down the 16 frames by $\\sigma_{\\mathrm{in}}$ before noise application. Averaging is not able to restore the images, indicating the SNR is maintained as $\\tilde{x} + \\sigma \\epsilon$ ." + ], + "image_footnote": [], + "bbox": [ + 500, + 88, + 893, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we modify the sampler according to the newly defined forward process that requires the signal component in $x_{\\sigma}$ to be scaled by $\\sigma_{\\mathrm{in}}$ . This is achieved by dividing the $\\mathcal{D}_{\\theta}(x_{\\sigma})$ by $\\sigma_{\\mathrm{in}}$ and multiplying the final denoised sample $x_0$ by $\\sigma_{\\mathrm{in}}$ to restore the signal magnitude.", + "bbox": [ + 498, + 377, + 892, + 455 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Image-Video Modality Matching", + "text_level": 1, + "bbox": [ + 500, + 464, + 787, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the limited amount of captioned video data with respect to images, joint image-video training is widely adopted [13, 21, 22, 48] with the same diffusion process typically applied to both modalities. However, as shown in Sec. 3.2, the presence of $T$ frames in videos calls for a different process with respect to an image with the same resolution. A possibility would be to adopt different input scaling factors for the two modalities. We argue that this solution is undesirable in that it increases the complexity of the framework and image training would not foster the denoising model to learn temporal reasoning, a fundamental capability of a video generator. To sidestep these issues while using a unified diffusion process, we match the image and video modalities by treating images as $T$ frames videos with infinite frame-rate and introduce a variable frame-rate training procedure blending the gap between the image and video modalities.", + "bbox": [ + 496, + 488, + 890, + 743 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Scalable Video Generator", + "text_level": 1, + "bbox": [ + 500, + 755, + 733, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "U-Nets [41] have shown success in video generation where they are typically augmented with temporal attention or convolutions for modeling the temporal dimension [4, 13, 21, 22, 48]. However, such an approach requires a full U-Net forward pass for each of the $T$ video frames, rapidly becoming prohibitively expensive (see Fig. 3a). These factors pose a practical limit on model scalability—a primary factor in achieving high generation quality [13, 17, 21, 48]—and", + "bbox": [ + 496, + 779, + 892, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7041", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2ea42f1c5e2f6813aedea4975141396e0f032cd2ae571fb1300c7fa3f2c7d101.jpg", + "image_caption": [ + "(a) Computational Paradigms for Videos" + ], + "image_footnote": [], + "bbox": [ + 83, + 93, + 428, + 256 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/561d720c549782cb403330e2642f70b63d952d23b5ee5139c84d5d4ac716c591.jpg", + "image_caption": [ + "(b) Snap Video FIT Architecture", + "Figure 3. (a-left) U-Net-based text-to-image architectures are adapted to do video generation by inserting temporal layers applied sequentially with spatial layers, creating separable spatiotemporal blocks. Spatial computation is repeated for each frame independently, limiting scalability. (a-right) Our scalable transformer-based model jointly performs spatial and temporal computation on a learnable compressed video representation for improved motion modeling and scalability. (b) The proposed Snap Video FIT architecture. Given a noisy input video $\\pmb{x}_{\\sigma}$ , the model estimates the denoised video $\\hat{\\pmb{x}}_{\\sigma}$ by recurrent application of FIT blocks. Each block reads information from the patch tokens into a small set of latent tokens on which computation is performed. The results are written to the patch tokens. Conditioning information in the form of text embeddings, noise level $\\sigma$ , frame-rate $\\nu$ and resolution $r$ is provided through an additional read operation." + ], + "image_footnote": [], + "bbox": [ + 464, + 93, + 887, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "similarly limit possibilities for joint spatio-temporal modeling [62]. We argue that treating spatial and temporal modeling in a separable way [4, 13, 21, 48] causes motion artifacts, temporal inconsistencies or generation of dynamic images rather than videos with vivid motion. Video frames, however, contain spatially and temporally redundant content that is amenable to compression [33]. We argue that learning and operating on a compressed video representation and jointly modeling the spatial and temporal dimensions are necessary steps to achieve the scalability and motion-modeling capabilities required for high-quality video generation.", + "bbox": [ + 75, + 410, + 467, + 592 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "FITs [8] are efficient transformer-based architectures that have recently been proposed for high-resolution image synthesis and video generation. Their main idea, summarized in Fig. 3 is that of learning a compressed representation of their input through a set of learnable latent tokens and of focusing computation on this learnable latent space, allowing input dimensionality to grow with little performance penalty. First, FITs perform patchification of the input and produce a sequence of patch tokens which are later divided into groups. A set of latent tokens is then instantiated and a sequence of computational blocks is applied. Each block first performs a cross attention \"read\" operation between latent tokens and conditioning signals such as the diffusion timestep, then an additional groupwise \"read\" cross attention operation between latent and patch tokens of corresponding groups to compress patch information, applies a series of self attention operations to the latent tokens, and performs a groupwise \"write\" cross attention operation that decompresses information in the latent tokens to update the patch tokens. Finally, the patch tokens are pro", + "bbox": [ + 75, + 598, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "jected back to the pixel space to form the output. Self conditioning is applied on the set of latent tokens to preserve the compressed video representation computed in previous sampling steps.", + "bbox": [ + 496, + 410, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While promising, these architectures have not yet been scaled to the billion-parameters size of state-of-the-art U-Net-based video generators, nor they have been applied to high-resolution video generation. In the following, we highlight the architectural considerations necessary to achieve these goals. Temporal modeling is a fundamental aspect of a high-quality video generator. FITs produce patch tokens by considering three dimensional patches of size $T_{p} \\times H_{p} \\times W_{p}$ spanning both the spatial and temporal dimensions. We find values of $T_{p} > 1$ to limit temporal modeling performance, so we consider patches spanning the spatial dimension only. In addition, similarly to patches, FITs group patch tokens into groups spanning both the temporal and spatial dimensions, and perform cross attention operations group by group. We observe that the temporal size of each group should be configured so that each group covers all $T$ video frames for best temporal modeling. Furthermore, videos contain more information with respect to images due to the presence of the temporal dimension, thus we increase the number of latent tokens representing the size of the compressed space in which joint spatiotemporal computation is performed. Finally, FITs make use of local layers which perform self attention operations on patch tokens corresponding to the same group. We find this operation to be computationally expensive for large amounts of patch tokens (147.456 for our largest resolution) and replace it with a feed forward module after each cross attention \"read\" or \"write\" operation.", + "bbox": [ + 496, + 477, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7042", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our model makes use of conditioning information represented by a sequence of conditioning tokens to control the generation process. In addition to the token representing the current $\\sigma$ , to enable text conditioning, we introduce a T5-11B [39] text encoder extracting text embeddings from the input text. To support variable video framereates and large differences in resolution and aspect ratios in the training data, we concatenate additional tokens representing the framerate and original resolution of the current input.", + "bbox": [ + 75, + 90, + 468, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To generate high-resolution outputs, we implement a model cascade consisting of a first-stage model producing $36 \\times 64\\mathrm{px}$ videos and a second-stage upsampling model producing $288 \\times 512\\mathrm{px}$ videos. To improve upsampling quality, we corrupt the second-stage low-resolution inputs with a variable level of noise during training [21, 43] and during inference apply a level of noise to the first-stage outputs obtained by hyperparameter search.", + "bbox": [ + 75, + 227, + 470, + 347 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We present detailed model hyperparameters in Appx. B.", + "bbox": [ + 96, + 347, + 467, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.5. Training", + "text_level": 1, + "bbox": [ + 76, + 369, + 181, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train Snap Video using the LAMB [68] optimizer with a learning rate of $5e^{-3}$ , a cosine learning schedule and a total batch size of 2048 videos and 2048 images, achievable thanks to our scalable video generator architecture. We train the first-stage model over 550k steps and finetune the second-stage model on high-resolution videos starting from the first-stage model weights for 370k iterations. Following the observations in Sec 3.2, we pose $\\sigma_{\\mathrm{in}} = s\\sqrt{T}$ . Considering videos with $T = 16$ frames and the original 64px resolution for which EDM was designed, we set $\\sigma_{\\mathrm{in}} = 4$ for the first-stage and $\\sigma_{\\mathrm{in}} = 32$ for the second-stage model.", + "bbox": [ + 75, + 393, + 468, + 559 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We present training details and parameters in Appx. C.", + "bbox": [ + 96, + 560, + 457, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.6. Inference", + "text_level": 1, + "bbox": [ + 76, + 583, + 187, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We produce video samples from gaussian noise and user-provided conditioning information using the deterministic sampler of [25] and our two-stage cascade. We use 256 sampling steps for the first-stage and 40 for the second-stage model, and employ classifier free guidance [19] to improve text-video alignment (see Appx. D.1) unless otherwise specified. We find dynamic thresholding [43] and oscillating guidance [21] to consistently improve quality.", + "bbox": [ + 75, + 606, + 468, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Evaluation", + "text_level": 1, + "bbox": [ + 76, + 739, + 192, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we perform evaluation of Snap Video against baselines and validate our design choices. Sec. 4.1 introduces the employed datasets, Sec. 4.3 shows ablations of our diffusion framework and architectural choices, Sec. 4.4 quantitatively compares our method to state-of-the-art large-scale video generators and Sec. 4.5 performs qualitative evaluation. We complement evaluation by showcasing samples in the Appendix and Website.", + "bbox": [ + 75, + 763, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f3c4b31bcee68ccdc657a825489525d685f20d9d9faa3cf631a55f9c832117bc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
FID ↓FVD ↓CLIPSIM ↑Train Thr. ↓Inf. Thr. ↓
U-Net 85M [10]8.2145.940.2319133.249.6
U-Net 284M [10]4.9023.760.2391230.3105.1
Snap Video FIT 500M3.0727.790.245969.523.4
Snap Video FIT 3.9B2.5112.310.2579526.0130.4
", + "bbox": [ + 501, + 90, + 888, + 159 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/00876750a38d64d436c139b9d91f6936b6ad643a041013b0cec07ab09e642664.jpg", + "table_caption": [ + "Table 2. Performance of different architectures and model sizes on our internal dataset in $64 \\times 36\\mathrm{px}$ resolution. We observe strong performance gains with scaling and note that FITs present better performance with improved speed with respect to U-Nets. Train and inference throughputs in ms/video/GPU." + ], + "table_footnote": [], + "table_body": "
σdataσinImgs. as VideosFID ↓FVD ↓CLIPSIM ↑
(i)0.51.0✓6.5839.950.2370
(ii)0.54.0✓4.0331.000.2449
(iv)1.02.0✓4.4534.890.2428
(iii)1.01/4.0X3.5024.880.2469
Ours1.04.0✓3.0727.790.2459
", + "bbox": [ + 513, + 265, + 879, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Ablation of different diffusion process configurations varying $\\sigma_{\\mathrm{data}}$ , input scaling $\\sigma_{\\mathrm{in}}$ , and treatment of images as infinite-framerate videos, evaluated on our internal dataset in $64 \\times 36$ px resolution.", + "bbox": [ + 496, + 396, + 890, + 453 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 479, + 601, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train our models on an internal dataset consisting of 1.265M images and 238k hours of videos, each with a corresponding text caption. Due to the difficulty in acquiring high-quality captions for videos, we develop a video captioning model that we use to produce synthetic video captions for the portion of videos in the dataset missing such annotation.", + "bbox": [ + 496, + 502, + 890, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We make use of the following datasets for evaluation which are never observed during training:", + "bbox": [ + 496, + 609, + 890, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "UCF-101 [55] is a video dataset containing 13.320 $320 \\times 240$ px Youtube videos from 101 action categories.", + "bbox": [ + 496, + 638, + 890, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MSR-VTT [65] is a dataset containing $10.000320 \\times 240\\mathrm{px}$ web-crawled videos, each manually annotated with 20 text captions. The test set contains 2.990 videos and 59.800 corresponding captions.", + "bbox": [ + 496, + 669, + 890, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Protocol", + "text_level": 1, + "bbox": [ + 500, + 755, + 689, + 770 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate the choices operated on the diffusion framework and on model architecture, present method ablations performed in $64 \\times 36\\mathrm{px}$ resolution using the first-stage model only, and compute FID [18], FVD [60] and CLIPSIM [63] metrics against the test set of our internal dataset on $50\\mathrm{k}$ generated videos.", + "bbox": [ + 496, + 779, + 890, + 869 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate our method against baselines, we follow the protocols highlighted in [4, 13, 32, 48, 62, 72] for zero-", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7043", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "shot evaluation on the UCF-101 [55] and MSR-VTT [65] datasets. We generate 16 frames videos in $512 \\times 288\\mathrm{px}$ resolution at 24fps for all settings. We evaluate both at the native $512 \\times 288\\mathrm{px}$ resolution with 16:9 aspect ratio and in the $288 \\times 288\\mathrm{px}$ square aspect ratio typically employed on these benchmarks. We note that the evaluation protocols of [4, 13, 32, 48, 62, 72] present different choices regarding the number of generated samples, distribution of class labels, choice of text prompts. We make use of the following evaluation parameters:", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Zero-shot UCF-101 [55] We generate 10,000 videos [4, 62] sampling classes with the same distribution as the original dataset. We produce a text prompt for each class label [13] and compute FVD [60] and Inception Score [46].", + "bbox": [ + 75, + 242, + 468, + 303 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Zero-shot MSR-VTT [65] We generate a video sample for each of the 59.800 test prompts [13, 48] and compute CLIP-FID [27] and CLIPSIM [63].", + "bbox": [ + 75, + 303, + 468, + 348 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To provide a more complete performance assessment and compare against state-of-the-art closed-source methods not reporting results for these benchmarks, we perform a user study evaluating photorealism, video-text-alignment and, most importantly, the quantity and quality of the generated motion, important characteristics of a video generator that may signal the generation of dynamic images, i.e. videos with dim motion, or motion artifacts rather than videos with vivid and high-quality motion.", + "bbox": [ + 75, + 349, + 468, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablations", + "text_level": 1, + "bbox": [ + 76, + 497, + 187, + 511 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the proposed FIT architecture, we consider the U-Net of [10], which we adapt to the video generation setting by interleaving temporal attention operations. We consider two U-Net variants of different capacities and a smaller variant of our FIT to evaluate the scalability of both architectures. We detail the architectures in Appx. B and show results in Tab. 2.", + "bbox": [ + 75, + 521, + 468, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Our 500M parameters FIT trains $3.31 \\times$ faster than the baseline 284M parameters U-Net, performs inference $4.49 \\times$ faster and surpasses it in terms of FID and CLIPSIM. In addition, both FITs and U-Nets show strong performance gains with scaling. Our largest FIT scales to 3.9B parameters with only a $1.24 \\times$ increase in inference time with respect to the 284M U-Net.", + "bbox": [ + 75, + 628, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate the choices operated on our diffusion framework, we ablate different configurations of the diffusion process using our 500M FIT architecture. We produce the following variations: (i) the original EDM framework, (ii) our scaled diffusion framework with EDM $\\sigma_{\\mathrm{data}}$ , (iii) our framework with a reduced value of $\\sigma_{\\mathrm{in}}$ , (iv) our framework with images not treated as infinite-frame-rate videos. Our framework improves over EDM under all metrics (i) and shows benefits in setting $\\sigma_{\\mathrm{data}} = 1$ , an effect that we attribute to the creation of a training target and loss weighting matching the widely used $v$ -prediction formulation of", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0bbcf0ef03f6ba5b256263e96334419081db5d9d109e17325f9950d1bb736b85.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
FVD ↓FID ↓IS ↑
CogVideo [23] (Chinese)751.3-23.55
CogVideo [23] (English)701.6-25.27
MagicVideo [72]655--
LVDM [17]641.8--
Video LDM [4]550.6-33.45
VideoFactory [62]410.0--
Make-A-Video [48]367.2-33.00
PYoCo [13]355.2-47.46
Snap Video (288 × 288 px)260.139.038.89
Snap Video (512 × 288 px)200.228.138.89
", + "bbox": [ + 532, + 88, + 862, + 244 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c38176274d080f1c4a77ac21fbc4cff6e1dcc85b5daf60613a0f37329beea830.jpg", + "table_caption": [ + "Table 4. Zero-shot evaluation results on UCF101 [55]." + ], + "table_footnote": [], + "table_body": "
CLIP-FID ↓FVD ↓CLIPSIM ↑
NUWA [64] (Chinese)47.68-0.2439
CogVideo [23] (Chinese)24.78-0.2614
CogVideo [23] (English)23.59-0.2631
MagicVideo [72]-998-
LVDM [17]--0.2381
Latent-Shift [2]15.23-0.2773
Video LDM [4]--0.2929
VideoFactory [62]--0.3005
Make-A-Video [48]13.17-0.3049
PYoCo [13]9.73--
Snap Video (288 × 288 px)8.48110.40.2793
Snap Video (512 × 288 px)9.35104.00.2793
", + "bbox": [ + 501, + 294, + 893, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Zero-shot evaluation results on MSR-VTT [65].", + "bbox": [ + 526, + 496, + 862, + 510 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Salimans et al. [45] (see Tab. 1). Using $\\sigma_{\\mathrm{in}} < s\\sqrt{T}$ (see Sec. 3.2) impairs performance (iii). Finally, treating images as infinite-frame-rate videos consistently improves FID.", + "bbox": [ + 498, + 535, + 890, + 582 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Quantitative Evaluation", + "text_level": 1, + "bbox": [ + 500, + 590, + 720, + 606 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform comparison of Snap Video against baselines on the UCF101 [55], and MSR-VTT [65] datasets respectively in Tab. 4 and Tab. 5. FID and FVD video quality metrics show improvements over the baselines which we attribute to the employed diffusion framework and joint spatiotemporal modeling performed by our architecture. On UCF101, our method produces the second-best IS of 38.89, demonstrating good video-text alignment. While our method surpasses Make-A-Video [48] on UCF101, we note that it produces a lower CLIPSIM score on MSR-VTT. We attribute this behavior to the use of T5 [39] text embeddings in place of the commonly used CLIP [38] embeddings which were observed [43] to produce higher text-image alignment despite similar CLIPSIM.", + "bbox": [ + 496, + 613, + 890, + 823 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To provide a comprehensive evaluation we run a user study to evaluate photorealism, video-text alignment, quantity of motion and quality of motion, important aspects of a video generator. Three publicly-accessible state-of-the-art video generators are considered: Gen-2 [11], PikaLabs [1]", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7044", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2fa82ded38c5ae7b26fc3839ffcf7eca9c46cddc346d8f0d30486611bcb9a4c6.jpg", + "image_caption": [ + "Figure 4. Qualitative results comparing Snap Video to state-of-the-art video generators on publicly available samples. While baseline methods present motion artifacts (top-left, top-right, bottom-right) or produce dynamic images (bottom-left), our method produces more temporally coherent motion. Best viewed in the Website." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 480, + 343 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/382a92480806ce18863c9abc916323b1b4c2e639fad98e114ce94840ca3bda3c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 890, + 343 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b92148db4ca1d8a1c2aa8c33531fdc2a30a80e985d078a2bf48f7a3bcb9f4906.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PhotorealismVideo-Text Align.Mot. Quant.Mot. Qual.
Gen-2 [11]44.381.096.078.7
PikaLab [1]61.580.389.270.5
Floor33 [17]76.380.988.079.1
", + "bbox": [ + 78, + 417, + 468, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. User study on photorealism, video-text alignment, motion quantity and quality against publicly-accessible video generators on 65 dynamic scene prompts. % of votes in favor of our method.", + "bbox": [ + 75, + 505, + 468, + 550 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and Floor33 [17]. We filter a set of 65 prompts from [31] describing scenes with vivid motions, and generate a video for each method with default options. We ask the participants to express preference between paired samples from Snap Video and each baseline, gathering votes from 5 users for each sample. Results are shown in Tab. 6 and video samples provided along with the employed prompt list in Appx. D.2 and in the Website. Our method produces results with photorealism comparable to Gen-2, while surpassing PikaLab and Floor33, and outperforms all baselines with respect to video-text alignment. Most importantly, we note that baselines often produce dynamic images, i.e. videos with dim motion, or videos with motion artifacts, a finding we attribute to the challenges in modeling large motion. In contrast, our method, thanks to the joint spatiotemporal modeling approach, produces vivid and high-quality motion as shown by the motion metrics.", + "bbox": [ + 75, + 566, + 472, + 824 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Qualitative Evaluation", + "text_level": 1, + "bbox": [ + 76, + 832, + 287, + 848 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section, we perform qualitative evaluation of our framework. In Fig. 4, Appx. D.3 and the Website, we present qualitative results comparing our method to state-", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of-the-art generators [4, 13, 21, 48] on samples publicly released by the authors. While such prompts might have been selected to highlight strengths of the baselines, our method produces more photorealistic samples aligned to the text descriptions. Most importantly, our samples present vivid and high-quality motion avoiding flickering artifacts that are present in the baselines due to temporal inconsistencies. We accompany qualitative evaluation with a user study performed on the same set of samples in Appx. D.2.", + "bbox": [ + 496, + 420, + 893, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 595, + 627, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we highlight the shortcomings of diffusion processes and architectures commonly used in text-to-video generation, and systematically address them by treating videos as first-class citizens. First, we propose a modification to the EDM [25] diffusion framework for the generation of high-resolution videos and treat images as high frame-rate videos to avoid image-video modality mismatches. Second, we replace U-Nets [41] with efficient transformer-based FITs [8] which we scale to billions of parameters. Thanks to their learnable compressed representation of videos, they significantly improve training times, scalability and performance with particular regards to temporal consistency and motion modeling capabilities due to the joint spatiotemporal modeling on the compressed representation. When evaluated on UCF101 [55] and MSR-VTT [65] and in user studies, Snap Video attains state-of-the-art performance with particular regard to the quality of the modeled motion.", + "bbox": [ + 496, + 628, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7045", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Pika lab discord server. https://www.pika.art/.Accessed: 2023-11-01. 2, 7, 8, 3, 6", + "[2] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Magicvideo: Efficient video generation with latent diffusion models. arXiv, 2023. 2, 3, 6, 7" + ], + "bbox": [ + 501, + 90, + 890, + 398 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7048", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Snap Video_ Scaled Spatiotemporal Transformers for Text-to-Video Synthesis/adef51ac-64f5-47cc-b577-559e45a201d6_model.json b/2024/Snap Video_ Scaled Spatiotemporal Transformers for Text-to-Video Synthesis/adef51ac-64f5-47cc-b577-559e45a201d6_model.json new file mode 100644 index 0000000000000000000000000000000000000000..78f3aa47e954466a7b21a2be7791e24545f2c4db --- /dev/null +++ b/2024/Snap Video_ Scaled Spatiotemporal Transformers for Text-to-Video Synthesis/adef51ac-64f5-47cc-b577-559e45a201d6_model.json @@ -0,0 +1,2246 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.095, + 0.131, + 0.877, + 0.155 + ], + "angle": 0, + "content": "Snap Video: Scaled Spatiotemporal Transformers for Text-to-Video Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.134, + 0.179, + 0.835, + 0.235 + ], + "angle": 0, + "content": "Willi Menapace\\(^{1,2,*}\\) Aliaksandr Siarohin\\(^{1}\\) Ivan Skorokhodov\\(^{1}\\) Ekaterina Deyneka\\(^{1}\\) Tsai-Shien Chen\\(^{1,3,*}\\) Anil Kag\\(^{1}\\) Yuwei Fang\\(^{1}\\) Aleksei Stoliar\\(^{1}\\) Elisa Ricci\\(^{2,4}\\) Jian Ren\\(^{1}\\) Sergey Tulyakov\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.171, + 0.244, + 0.799, + 0.285 + ], + "angle": 0, + "content": "Snap Inc.\\(^{1}\\) University of Trento\\(^{2}\\) UC Merced\\(^{3}\\) Fondazione Bruno Kessler\\(^{4}\\) snap-research.github.io/snapvideo" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.298, + 0.485, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.299, + 0.891, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.549, + 0.894, + 0.593 + ], + "angle": 0, + "content": "Figure 1. Samples produced by the proposed text-to-video generation method for a selection of prompts. Thanks to joint spatiotemporal video modeling, our generator can synthesize temporally coherent videos with large motion (left) while retaining the semantic control capabilities typical of large-scale text-to-video generators (right). See the Website for additional samples." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.605, + 0.314, + 0.621 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.645, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Contemporary models for generating images show remarkable quality and versatility. Swayed by these advantages, the research community repurposes them to generate videos. Since video content is highly redundant, we argue that naively bringing advances of image models to the video generation domain reduces motion fidelity, visual quality and impairs scalability. In this work, we build Snap Video, a video-first model that systematically addresses these challenges. To do that, we first extend the EDM framework to take into account spatially and temporally redundant pixels and naturally support video generation. Second, we show that a U-Net—a workhorse behind image generation—scales poorly when generating videos, requiring significant computational overhead. Hence, we propose a new transformer-based architecture that trains 3.31 times faster than U-Nets (and is \\(\\sim 4.5\\) faster at inference). This allows us to efficiently train a text-to-video model with billions of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.895, + 0.682 + ], + "angle": 0, + "content": "parameters for the first time, reach state-of-the-art results on a number of benchmarks, and generate videos with substantially higher quality, temporal consistency, and motion complexity. The user studies showed that our model was favored by a large margin over the most recent methods." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.712, + 0.633, + 0.728 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.892, + 0.829 + ], + "angle": 0, + "content": "Creating and sharing visual content is one of the key ways for people to express themselves in the digital world. Accessible to only professionals in the past, the capability to create [30, 40, 43, 69] and edit [6, 37, 42] images with stunning quality and realism was unlocked to everyone by the advent of large text-to-image models and their variations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.83, + 0.892, + 0.876 + ], + "angle": 0, + "content": "Fueled by this progress, large-scale text-to-video models [4, 13, 21, 48, 62] are rapidly advancing too. Current large-scale diffusion-based video generation frame" + }, + { + "type": "page_footnote", + "bbox": [ + 0.524, + 0.887, + 0.774, + 0.902 + ], + "angle": 0, + "content": "* Work performed while interning at Snap Inc." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7038" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "works are strongly rooted into their image counterparts [4, 13]. The availability of consolidated image generation architectures such as U-Nets [41] with publicly-available image-pretrained models [40] made them a logical foundation onto which to build large-scale video generators with the main architectural modifications focusing on the insertion of ad-hoc layers to capture temporal dependencies [4, 13, 21, 48, 62]. Similarly, training is performed under image-based diffusion frameworks with the model being applied both to videos and to a separate set of images to improve the diversity of the results [13, 21, 22, 48]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.624 + ], + "angle": 0, + "content": "We argue that such an approach is suboptimal under multiple aspects which we systematically address in this work. First, image and video modalities present intrinsic differences given by the similarity of content in successive video frames [7, 13]. By analogy, image and video compression algorithms are based on vastly different approaches [33]. To address this issue, we rewrite the EDM [25] framework with a focus on high-resolution videos. Differently from past work where videos were treated as a sequence of images, we perform joint video-image training by treating images as high frame-rate videos to avoid modality mismatches introduced by the absence of the temporal dimension within purely image-based training. Second, the widely adopted U-Net [41] architecture is required to fully processes each video frame. This increases computational overhead compared to purely text-to-image models, posing a very practical limit on model scalability. The latter is a critical factor in obtaining high-quality of results [13, 21]. Extending U-Net-based architectures to naturally support spatial and temporal dimensions requires volumetric attention operations, which have prohibitive computational demands. Inability to do so affects the outputs, resulting in dynamic images or motion artifacts being generated instead of videos with coherent and diverse actions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.473, + 0.794 + ], + "angle": 0, + "content": "Following our compression analogy, we propose to leverage repetition between frames and introduce a scalable transformer architecture that treats spatial and temporal dimensions as a single, compressed, 1D latent vector. This highly compressed representation allows us to perform spatio-temporal computation jointly and enables modelling of complex motions. Our architecture is inspired by FIT [8], which we scale to billions of parameters for the first time. Compared to U-Nets, our model features a significant \\(3.31 \\times\\) reduction in training time and \\(4.49 \\times\\) reduction in inference time while achieving higher generation quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.473, + 0.904 + ], + "angle": 0, + "content": "We evaluate Snap Video on the widely-adopted UCF101 [55] and MSR-VTT [65] datasets. Our generator shows state-of-the-art performance across the range of benchmarks with particular regard to the quality of the generated motion. Most interestingly, we performed a number of user studies against the most recent open- and close-source methods and found that according to the participants" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.275 + ], + "angle": 0, + "content": "of the study our model features photorealism comparable to Gen-2 [11], while being significantly better than Pika [1] and Floor33 [17]. Most excitedly, the preference of user-study participants favoured Snap Video by a large margin when text alignment and motion quality were assessed. Compared to Gen-2 [11] on prompt-video alignment our model was preferred in \\(81\\%\\) of cases (80% against Pika [1], 81% against Floor33 [17]), generated most dynamic videos with most amount of motion (96% against Gen2 [11], 89% against Pika [1], 88% against Floor33 [17]) and had the best motion quality (79% against Gen-2 [11], 71% against Pika [1], 79% against Floor33 [17])." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.287, + 0.642, + 0.303 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.312, + 0.895, + 0.448 + ], + "angle": 0, + "content": "Video Generation Video generation is a challenging and long-studied task. Due to its complexity, a large number of works focus on modeling narrow domains [5, 9, 12, 28, 35, 44, 47, 49, 56, 58, 59, 66, 70, 71] and adopt adversarial training [5, 9, 28, 44, 47, 49, 58, 59, 71] or autoregressive generation techniques [12, 35, 56, 66, 70]. To address the narrow domain limitation, the task of text-to-video generation was proposed [34] and both autoregressive models [23, 34, 61, 63, 64] and GANs [29] emerged." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.449, + 0.896, + 0.735 + ], + "angle": 0, + "content": "The recent success of diffusion models in the context of text-to-image generation [3, 40, 43] fostered tremendous progress in the task [2, 4, 13, 16, 17, 21, 22, 32, 48, 62, 67, 72]. ImagenVideo [21] and Make-A-Video [48] propose a deep cascade of temporal and spatial upsamplers to generate videos and jointly train their models on image and video datasets. PYoCo [13] introduces a correlated noise model to capture similarities between video frames. Video LDM [4] adopts a latent diffusion paradigm where a pretrained latent image generator and latent decoder are finetuned to generate temporally coherent videos.AnimateDiff [16] freezes a pre-trained latent image generator and trains only a newly inserted motion modeling module. These works employ U-Nets with separable spatial and temporal computation which poses a limitation on motion modeling capabilities. VideoFactory [62] improves upon this paradigm by proposing a Swapped Spatiotemporal CrossAttention that improves interactions between the spatial and temporal modalities along 3D windows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.888 + ], + "angle": 0, + "content": "Differently from this corpus of works which adapts the U-Net [41] architecture to the video generation task, we show that employing transformer-based FIT [8] architectures results in significant training time savings, scalability improvements, and performance increase thanks to their learnable compressed video representation. In particular, we show that the global joint spatiotemporal modeling strategy enabled by our compressed video representation results in significant improvements in temporal consistency and motion modeling capabilities." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7039" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "High-Resolution Generation Different approaches have been proposed to enable the generation of high-resolution outputs. Cascaded diffusion models [3, 13, 21, 43, 48] adopt a set of independent diffusion models designed to successively upsample the results of the previous step. Latent diffusion models [2, 4, 17, 40, 72] make use of a pretrained autoencoder to encode the input into a low-dimensional set of latent vectors and learn a diffusion model on this latent representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.473, + 0.363 + ], + "angle": 0, + "content": "A different family of methods generates high-resolution outputs end-to-end without employing cascades of models or latent diffusion. Simple Diffusion [24] and Chen [7] directly generate high-resolution images by adapting the noise schedule of the diffusion process. f-DM [14] and RDM [57] design a diffusion process that seamlessly transitions between different resolutions. MDM [15] proposes a strategy where a single model is trained to simultaneously denoise inputs at progressively higher resolutions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.485 + ], + "angle": 0, + "content": "In this work, we adopt a two-stage cascaded model out of two considerations: (i) it avoids temporal inconsistencies in the forms of flickering of high-frequency details that may be introduced by latent autoencoders [4], (ii) it increases model capacity with respect to an end-to-end model by creating two specialized models, one for the low resolution focusing on motion modeling and scene structure, and one for the high-resolution, focusing on high-frequency details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.5, + 0.473, + 0.772 + ], + "angle": 0, + "content": "Diffusion Frameworks Diffusion generative models are a set of techniques modeling generation as a pair of processes: a forward process progressively destructing a sample with noise, and a reverse process modeling generation as the progressive denoising of a sample. Different formulations of diffusion models have been proposed in the literature. Denoising Diffusion Probabilistic Models (DDPMs) [20, 50] formulate the forward and backward process as Markov chains. Score-based Generative Models (SGMs) [51, 52] model the score of the probability density function of a series of data distributions perturbed with increasing levels of noise, i.e. the direction of largest increase in the data log probability density function. An avenue of works [53, 54] generalizes DDPMs and SGMs to infinite noise levels through Stochastic Differential Equations (SDEs). In this work, we adopt the SGM framework of EDM [25] which we reformulate for the generation of high-resolution videos." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.17, + 0.801 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We propose the generation of high-resolution videos by rewriting the EDM [25] diffusion framework for high-dimensional inputs and proposing an efficient transformer architecture based on FITs [8] which we scale to billions of parameters and tens of thousands input patches. Sec. 3.1 provides an introduction to the EDM framework, Sec 3.2" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.199 + ], + "angle": 0, + "content": "highlights the challenges of applying diffusion frameworks to high dimensional inputs and proposes a revisited EDM-based diffusion framework. Sec. 3.3 proposes a method to reduce the gap between image and video modalities for joint training. Finally, Sec. 3.4 describes our scalable video generation architecture, while Sec. 3.5 and Sec. 3.6 respectively describe the training and inference procedures." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.207, + 0.702, + 0.221 + ], + "angle": 0, + "content": "3.1. Introduction to EDM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.23, + 0.895, + 0.382 + ], + "angle": 0, + "content": "Diffusion models have achieved remarkable success in image and video generation. Among the proposed frameworks, Karras et al. [25] provide a unified view of common diffusion frameworks and formulate EDM. EDM defines a variance-exploding forward diffusion process \\( p(\\pmb{x}_{\\sigma}|\\pmb{x}) \\sim \\mathcal{N}(\\pmb{x}, \\pmb{\\sigma}^2\\mathbf{I}) \\), where \\( \\pmb{\\sigma} \\in [\\pmb{\\sigma}_{\\mathrm{min}}, \\pmb{\\sigma}_{\\mathrm{max}}] \\) represents the diffusion timestep coinciding with the standard deviation of the applied noise, and \\( x_{\\sigma} \\) represents the data at the current noise level. A denoiser function \\( \\mathcal{D}_{\\theta} \\) is learned to model the reverse process using the denoising objective:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.388, + 0.892, + 0.415 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ \\lambda (\\boldsymbol {\\sigma}) \\| \\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - \\boldsymbol {x} \\| _ {2} ^ {2} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.467 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is the loss weighting function, \\(\\pmb{x} \\sim p_{\\mathrm{data}}\\) is a data sample, \\(\\epsilon\\) is gaussian noise, and \\(\\sigma \\sim p_{\\mathrm{train}}\\) is sampled from a training distribution. \\(\\mathcal{D}_{\\theta}(\\pmb{x}_{\\sigma})\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.475, + 0.892, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\sigma}\\right) = c _ {\\text {o u t}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}\\right) + c _ {\\text {s k i p}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.499, + 0.892, + 0.545 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{\\theta}\\) is a neural network, and \\(c_{\\mathrm{out}}\\), \\(c_{\\mathrm{skip}}\\) and \\(c_{\\mathrm{in}}\\) represent scaling functions. In particular, the denoising objective \\(\\mathcal{L}(\\mathcal{F}_{\\theta})\\) can equivalently be expressed in terms of \\(\\mathcal{F}_{\\theta}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.552, + 0.892, + 0.576 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(\\mathcal {F} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ w (\\boldsymbol {\\sigma}) \\left\\| \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - c _ {\\text {n r m}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\mathrm {t g t}} \\right\\| _ {2} ^ {2} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.627 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{\\mathrm{tgt}}\\) represents the training target, \\(c_{\\mathrm{nm}}\\) is a normalization factor, and \\(w\\) is a weighting function. These forms, derived in Appx. E, are presented in Tab. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.674 + ], + "angle": 0, + "content": "A second order Runge-Kutta sampler is proposed to reverse the diffusion process and produce sample \\( \\pmb{x} \\) starting from gaussian noise \\( \\pmb{x}_{\\sigma_{\\mathrm{max}}} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I}) \\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.682, + 0.878, + 0.698 + ], + "angle": 0, + "content": "3.2. EDM for High-Resolution Video Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "EDM is originally proposed as an image generation framework and its parameters are optimized for \\(64 \\times 64\\mathrm{px}\\) image generation. Alterations in spatial resolution or the introduction of videos with shared content between frames allow the denoising network to trivially recover a noisy frame in the original resolution with higher signal-to-noise-ratio (SNR), which the original framework was designed to see at lower noise levels. To see why, consider a noisy video \\(\\boldsymbol{x}_{\\sigma} \\in \\mathbb{R}^{T \\times s \\cdot H \\times s \\cdot W} \\sim \\mathcal{N}(\\boldsymbol{x}, \\sigma^2\\mathbf{I})\\) where \\(T\\) is the number of frames and \\(s\\) is an upsampling factor. We build the corresponding clean and noisy frames at original resolution \\(\\tilde{\\boldsymbol{x}}\\), \\(\\tilde{\\boldsymbol{x}}_{\\sigma} \\in \\mathbb{R}^{1 \\times H \\times W}\\) by averaging values in each \\(T \\times s \\times s\\) block of pixels. As a consequence of averaging, the noise" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7040" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.09, + 0.468, + 0.27 + ], + "angle": 0, + "content": "
EDM [25]Our
Training and Losses
Forw. processxσx/σin + σεx/σin + σε
Training targetFtgtσx - σ2data ε + σ2data(σin-1)/σin x- σx + σ2data ε
Eff. loss weigh.w(σ)1(σ2 + σ2data)2/(σ2 + σ2data)2
Loss weigh.λ(σ)1/σ2data + 1/σ21/σ2data + 1/σ2
Network Parametrization
Input scalingcin(σ)1/√σ2data + σ21/√σ2data/σ2 + σ2
Output scalingcout(σ)σσ2data/√σ2+ σ2data- σinσσdata√σ2+ σ2data/σ2+ σ2
Skip scalingcskip(σ)σ2data/σ2+ σ2dataσinσ2data/σinσ2+ σ2data
Target scalingcnrm(σ)1/σdata√σ2+ σ2data1/σdata√σ2+ σ2data
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.292, + 0.473, + 0.409 + ], + "angle": 0, + "content": "Table 1. Definitions of functions in Eq. (1), Eq. (2) and Eq. (3) for the EDM and our proposed diffusion framework as derived in Appx. E and Appx. F, where we highlight the terms induced by the input scaling factor \\(\\sigma_{\\mathrm{in}}\\). Our framework is equivalent to EDM for \\(\\sigma_{\\mathrm{in}} = 1\\) but avoids the unstable term \\(\\frac{\\sigma_{\\mathrm{data}}^2(\\sigma_{\\mathrm{in}} - 1)}{\\sigma_{\\mathrm{in}}\\sigma} x\\) induced by \\(\\sigma_{\\mathrm{in}} \\neq 1\\) in \\(\\mathcal{F}_{\\mathrm{tgt}}\\). This form highlights that the train target and loss weight match the \\(v\\)-prediction [45] framework for \\(\\sigma_{\\mathrm{data}} = 1\\). All other framework parameters are unaltered with respect to EDM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.47, + 0.637 + ], + "angle": 0, + "content": "variance is reduced by a factor \\(Ts^2\\), i.e. \\(\\tilde{x}_{\\sigma} \\sim \\mathcal{N}(\\tilde{x}, \\frac{\\sigma^2}{Ts^2}\\mathbf{I})\\), thus \\(\\tilde{x}_{\\sigma}\\) has an increased signal-to-noise-ratio with respect to \\(x_{\\sigma}\\) (see Fig. 2): \\(SNR_{\\tilde{x}_{\\sigma}} = Ts^2 SNR_{x_{\\sigma}}\\). If pixels in each block share similar content, a typical situation in high-resolution videos, then the information in the averaged frame is useful for recovering \\(x\\) and can be exploited at training time by the denoiser function. This creates a train-inference mismatch during the initial sampling steps as the average frame does not yet contain a well-formed signal, yet the denoiser is reliant on its presence. Thus, for best performance, any alteration to \\(T\\) or \\(s\\) should instead maintain the same signal-to-noise ratio at the original resolution for which the diffusion framework was designed." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.717 + ], + "angle": 0, + "content": "To restore the optimal SNR at the original resolution, the magnitude of the input signal can be reduced [7] by a corresponding factor \\(\\sigma_{\\mathrm{in}} = s\\sqrt{T}\\) as illustrated in Fig. 2. Consequently, we redefine the forward process as \\(p(\\boldsymbol{x}_{\\sigma}|\\boldsymbol{x}) \\sim \\mathcal{N}(\\boldsymbol{x} / \\sigma_{\\mathrm{in}}, \\sigma^2\\mathbf{I})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We rewrite the EDM framework to introduce the input scaling factor in Appx. F and highlight the changes in Tab. 1. We notice that a naive introduction of the scaling factor would alter the training target \\(\\mathcal{F}_{\\mathrm{tgt}}\\) in a way that makes the objective explode for small noise values (see Appx. E). We thus leverage the training objective expressed in the form of Eq. (3) to rewrite the EDM process in a way that ensures \\(\\mathcal{F}_{\\mathrm{tgt}}\\) remains unchanged, the effective loss weight \\(w(\\sigma)\\) is such that it keeps the loss weight \\(\\lambda (\\sigma)\\) unchanged, \\(c_{\\mathrm{in}}(\\sigma)\\) and \\(c_{\\mathrm{nm}}(\\sigma)\\) normalize the input and training target to have unit variance, and the framework is equivalent to the original EDM formulation for \\(\\sigma_{\\mathrm{in}} = 1\\) (see Appx. F)." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.895, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.253, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Figure 2. Analysis of Signal-to-Noise Ratio (SNR). Top: noise \\(\\sigma\\) is applied to an image. Middle: the same noise \\(\\sigma\\) is applied to a 16-frames-long video \\(x\\) without scaling. A clean image can be easily restored by simply taking average, indicating an increased SNR. Bottom: to maintain the original SNR, we scale down the 16 frames by \\(\\sigma_{\\mathrm{in}}\\) before noise application. Averaging is not able to restore the images, indicating the SNR is maintained as \\(\\tilde{x} + \\sigma \\epsilon\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.378, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Finally, we modify the sampler according to the newly defined forward process that requires the signal component in \\( x_{\\sigma} \\) to be scaled by \\( \\sigma_{\\mathrm{in}} \\). This is achieved by dividing the \\( \\mathcal{D}_{\\theta}(x_{\\sigma}) \\) by \\( \\sigma_{\\mathrm{in}} \\) and multiplying the final denoised sample \\( x_0 \\) by \\( \\sigma_{\\mathrm{in}} \\) to restore the signal magnitude." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.465, + 0.788, + 0.481 + ], + "angle": 0, + "content": "3.3. Image-Video Modality Matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.489, + 0.892, + 0.744 + ], + "angle": 0, + "content": "Due to the limited amount of captioned video data with respect to images, joint image-video training is widely adopted [13, 21, 22, 48] with the same diffusion process typically applied to both modalities. However, as shown in Sec. 3.2, the presence of \\( T \\) frames in videos calls for a different process with respect to an image with the same resolution. A possibility would be to adopt different input scaling factors for the two modalities. We argue that this solution is undesirable in that it increases the complexity of the framework and image training would not foster the denoising model to learn temporal reasoning, a fundamental capability of a video generator. To sidestep these issues while using a unified diffusion process, we match the image and video modalities by treating images as \\( T \\) frames videos with infinite frame-rate and introduce a variable frame-rate training procedure blending the gap between the image and video modalities." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.734, + 0.771 + ], + "angle": 0, + "content": "3.4. Scalable Video Generator" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.903 + ], + "angle": 0, + "content": "U-Nets [41] have shown success in video generation where they are typically augmented with temporal attention or convolutions for modeling the temporal dimension [4, 13, 21, 22, 48]. However, such an approach requires a full U-Net forward pass for each of the \\( T \\) video frames, rapidly becoming prohibitively expensive (see Fig. 3a). These factors pose a practical limit on model scalability—a primary factor in achieving high generation quality [13, 17, 21, 48]—and" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7041" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.094, + 0.429, + 0.257 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.148, + 0.263, + 0.361, + 0.275 + ], + "angle": 0, + "content": "(a) Computational Paradigms for Videos" + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.094, + 0.888, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.589, + 0.263, + 0.761, + 0.275 + ], + "angle": 0, + "content": "(b) Snap Video FIT Architecture" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.892, + 0.384 + ], + "angle": 0, + "content": "Figure 3. (a-left) U-Net-based text-to-image architectures are adapted to do video generation by inserting temporal layers applied sequentially with spatial layers, creating separable spatiotemporal blocks. Spatial computation is repeated for each frame independently, limiting scalability. (a-right) Our scalable transformer-based model jointly performs spatial and temporal computation on a learnable compressed video representation for improved motion modeling and scalability. (b) The proposed Snap Video FIT architecture. Given a noisy input video \\( \\pmb{x}_{\\sigma} \\), the model estimates the denoised video \\( \\hat{\\pmb{x}}_{\\sigma} \\) by recurrent application of FIT blocks. Each block reads information from the patch tokens into a small set of latent tokens on which computation is performed. The results are written to the patch tokens. Conditioning information in the form of text embeddings, noise level \\( \\sigma \\), frame-rate \\( \\nu \\) and resolution \\( r \\) is provided through an additional read operation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.468, + 0.593 + ], + "angle": 0, + "content": "similarly limit possibilities for joint spatio-temporal modeling [62]. We argue that treating spatial and temporal modeling in a separable way [4, 13, 21, 48] causes motion artifacts, temporal inconsistencies or generation of dynamic images rather than videos with vivid motion. Video frames, however, contain spatially and temporally redundant content that is amenable to compression [33]. We argue that learning and operating on a compressed video representation and jointly modeling the spatial and temporal dimensions are necessary steps to achieve the scalability and motion-modeling capabilities required for high-quality video generation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.47, + 0.901 + ], + "angle": 0, + "content": "FITs [8] are efficient transformer-based architectures that have recently been proposed for high-resolution image synthesis and video generation. Their main idea, summarized in Fig. 3 is that of learning a compressed representation of their input through a set of learnable latent tokens and of focusing computation on this learnable latent space, allowing input dimensionality to grow with little performance penalty. First, FITs perform patchification of the input and produce a sequence of patch tokens which are later divided into groups. A set of latent tokens is then instantiated and a sequence of computational blocks is applied. Each block first performs a cross attention \"read\" operation between latent tokens and conditioning signals such as the diffusion timestep, then an additional groupwise \"read\" cross attention operation between latent and patch tokens of corresponding groups to compress patch information, applies a series of self attention operations to the latent tokens, and performs a groupwise \"write\" cross attention operation that decompresses information in the latent tokens to update the patch tokens. Finally, the patch tokens are pro" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.411, + 0.892, + 0.472 + ], + "angle": 0, + "content": "jected back to the pixel space to form the output. Self conditioning is applied on the set of latent tokens to preserve the compressed video representation computed in previous sampling steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.893, + 0.901 + ], + "angle": 0, + "content": "While promising, these architectures have not yet been scaled to the billion-parameters size of state-of-the-art U-Net-based video generators, nor they have been applied to high-resolution video generation. In the following, we highlight the architectural considerations necessary to achieve these goals. Temporal modeling is a fundamental aspect of a high-quality video generator. FITs produce patch tokens by considering three dimensional patches of size \\( T_{p} \\times H_{p} \\times W_{p} \\) spanning both the spatial and temporal dimensions. We find values of \\( T_{p} > 1 \\) to limit temporal modeling performance, so we consider patches spanning the spatial dimension only. In addition, similarly to patches, FITs group patch tokens into groups spanning both the temporal and spatial dimensions, and perform cross attention operations group by group. We observe that the temporal size of each group should be configured so that each group covers all \\( T \\) video frames for best temporal modeling. Furthermore, videos contain more information with respect to images due to the presence of the temporal dimension, thus we increase the number of latent tokens representing the size of the compressed space in which joint spatiotemporal computation is performed. Finally, FITs make use of local layers which perform self attention operations on patch tokens corresponding to the same group. We find this operation to be computationally expensive for large amounts of patch tokens (147.456 for our largest resolution) and replace it with a feed forward module after each cross attention \"read\" or \"write\" operation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7042" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.227 + ], + "angle": 0, + "content": "Our model makes use of conditioning information represented by a sequence of conditioning tokens to control the generation process. In addition to the token representing the current \\(\\sigma\\), to enable text conditioning, we introduce a T5-11B [39] text encoder extracting text embeddings from the input text. To support variable video framereates and large differences in resolution and aspect ratios in the training data, we concatenate additional tokens representing the framerate and original resolution of the current input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.228, + 0.471, + 0.348 + ], + "angle": 0, + "content": "To generate high-resolution outputs, we implement a model cascade consisting of a first-stage model producing \\(36 \\times 64\\mathrm{px}\\) videos and a second-stage upsampling model producing \\(288 \\times 512\\mathrm{px}\\) videos. To improve upsampling quality, we corrupt the second-stage low-resolution inputs with a variable level of noise during training [21, 43] and during inference apply a level of noise to the first-stage outputs obtained by hyperparameter search." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.348, + 0.468, + 0.365 + ], + "angle": 0, + "content": "We present detailed model hyperparameters in Appx. B." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.371, + 0.182, + 0.387 + ], + "angle": 0, + "content": "3.5. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.47, + 0.56 + ], + "angle": 0, + "content": "We train Snap Video using the LAMB [68] optimizer with a learning rate of \\(5e^{-3}\\), a cosine learning schedule and a total batch size of 2048 videos and 2048 images, achievable thanks to our scalable video generator architecture. We train the first-stage model over 550k steps and finetune the second-stage model on high-resolution videos starting from the first-stage model weights for 370k iterations. Following the observations in Sec 3.2, we pose \\(\\sigma_{\\mathrm{in}} = s\\sqrt{T}\\). Considering videos with \\(T = 16\\) frames and the original 64px resolution for which EDM was designed, we set \\(\\sigma_{\\mathrm{in}} = 4\\) for the first-stage and \\(\\sigma_{\\mathrm{in}} = 32\\) for the second-stage model." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.561, + 0.459, + 0.577 + ], + "angle": 0, + "content": "We present training details and parameters in Appx. C." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.584, + 0.188, + 0.599 + ], + "angle": 0, + "content": "3.6. Inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.47, + 0.729 + ], + "angle": 0, + "content": "We produce video samples from gaussian noise and user-provided conditioning information using the deterministic sampler of [25] and our two-stage cascade. We use 256 sampling steps for the first-stage and 40 for the second-stage model, and employ classifier free guidance [19] to improve text-video alignment (see Appx. D.1) unless otherwise specified. We find dynamic thresholding [43] and oscillating guidance [21] to consistently improve quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.194, + 0.755 + ], + "angle": 0, + "content": "4. Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.901 + ], + "angle": 0, + "content": "In this section, we perform evaluation of Snap Video against baselines and validate our design choices. Sec. 4.1 introduces the employed datasets, Sec. 4.3 shows ablations of our diffusion framework and architectural choices, Sec. 4.4 quantitatively compares our method to state-of-the-art large-scale video generators and Sec. 4.5 performs qualitative evaluation. We complement evaluation by showcasing samples in the Appendix and Website." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.091, + 0.89, + 0.16 + ], + "angle": 0, + "content": "
FID ↓FVD ↓CLIPSIM ↑Train Thr. ↓Inf. Thr. ↓
U-Net 85M [10]8.2145.940.2319133.249.6
U-Net 284M [10]4.9023.760.2391230.3105.1
Snap Video FIT 500M3.0727.790.245969.523.4
Snap Video FIT 3.9B2.5112.310.2579526.0130.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.182, + 0.892, + 0.253 + ], + "angle": 0, + "content": "Table 2. Performance of different architectures and model sizes on our internal dataset in \\(64 \\times 36\\mathrm{px}\\) resolution. We observe strong performance gains with scaling and note that FITs present better performance with improved speed with respect to U-Nets. Train and inference throughputs in ms/video/GPU." + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.266, + 0.88, + 0.376 + ], + "angle": 0, + "content": "
σdataσinImgs. as VideosFID ↓FVD ↓CLIPSIM ↑
(i)0.51.0✓6.5839.950.2370
(ii)0.54.0✓4.0331.000.2449
(iv)1.02.0✓4.4534.890.2428
(iii)1.01/4.0X3.5024.880.2469
Ours1.04.0✓3.0727.790.2459
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.397, + 0.892, + 0.454 + ], + "angle": 0, + "content": "Table 3. Ablation of different diffusion process configurations varying \\(\\sigma_{\\mathrm{data}}\\), input scaling \\(\\sigma_{\\mathrm{in}}\\), and treatment of images as infinite-framerate videos, evaluated on our internal dataset in \\(64 \\times 36\\)px resolution." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.48, + 0.602, + 0.495 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.608 + ], + "angle": 0, + "content": "We train our models on an internal dataset consisting of 1.265M images and 238k hours of videos, each with a corresponding text caption. Due to the difficulty in acquiring high-quality captions for videos, we develop a video captioning model that we use to produce synthetic video captions for the portion of videos in the dataset missing such annotation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.64 + ], + "angle": 0, + "content": "We make use of the following datasets for evaluation which are never observed during training:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.892, + 0.669 + ], + "angle": 0, + "content": "UCF-101 [55] is a video dataset containing 13.320 \\(320 \\times 240\\)px Youtube videos from 101 action categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.892, + 0.731 + ], + "angle": 0, + "content": "MSR-VTT [65] is a dataset containing \\(10.000320 \\times 240\\mathrm{px}\\) web-crawled videos, each manually annotated with 20 text captions. The test set contains 2.990 videos and 59.800 corresponding captions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.756, + 0.691, + 0.771 + ], + "angle": 0, + "content": "4.2. Evaluation Protocol" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.87 + ], + "angle": 0, + "content": "To validate the choices operated on the diffusion framework and on model architecture, present method ablations performed in \\(64 \\times 36\\mathrm{px}\\) resolution using the first-stage model only, and compute FID [18], FVD [60] and CLIPSIM [63] metrics against the test set of our internal dataset on \\(50\\mathrm{k}\\) generated videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "To evaluate our method against baselines, we follow the protocols highlighted in [4, 13, 32, 48, 62, 72] for zero-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7043" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.242 + ], + "angle": 0, + "content": "shot evaluation on the UCF-101 [55] and MSR-VTT [65] datasets. We generate 16 frames videos in \\(512 \\times 288\\mathrm{px}\\) resolution at 24fps for all settings. We evaluate both at the native \\(512 \\times 288\\mathrm{px}\\) resolution with 16:9 aspect ratio and in the \\(288 \\times 288\\mathrm{px}\\) square aspect ratio typically employed on these benchmarks. We note that the evaluation protocols of [4, 13, 32, 48, 62, 72] present different choices regarding the number of generated samples, distribution of class labels, choice of text prompts. We make use of the following evaluation parameters:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Zero-shot UCF-101 [55] We generate 10,000 videos [4, 62] sampling classes with the same distribution as the original dataset. We produce a text prompt for each class label [13] and compute FVD [60] and Inception Score [46]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.469, + 0.349 + ], + "angle": 0, + "content": "Zero-shot MSR-VTT [65] We generate a video sample for each of the 59.800 test prompts [13, 48] and compute CLIP-FID [27] and CLIPSIM [63]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.486 + ], + "angle": 0, + "content": "To provide a more complete performance assessment and compare against state-of-the-art closed-source methods not reporting results for these benchmarks, we perform a user study evaluating photorealism, video-text-alignment and, most importantly, the quantity and quality of the generated motion, important characteristics of a video generator that may signal the generation of dynamic images, i.e. videos with dim motion, or motion artifacts rather than videos with vivid and high-quality motion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.188, + 0.512 + ], + "angle": 0, + "content": "4.3. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.627 + ], + "angle": 0, + "content": "To evaluate the proposed FIT architecture, we consider the U-Net of [10], which we adapt to the video generation setting by interleaving temporal attention operations. We consider two U-Net variants of different capacities and a smaller variant of our FIT to evaluate the scalability of both architectures. We detail the architectures in Appx. B and show results in Tab. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Our 500M parameters FIT trains \\(3.31 \\times\\) faster than the baseline 284M parameters U-Net, performs inference \\(4.49 \\times\\) faster and surpasses it in terms of FID and CLIPSIM. In addition, both FITs and U-Nets show strong performance gains with scaling. Our largest FIT scales to 3.9B parameters with only a \\(1.24 \\times\\) increase in inference time with respect to the 284M U-Net." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "To evaluate the choices operated on our diffusion framework, we ablate different configurations of the diffusion process using our 500M FIT architecture. We produce the following variations: (i) the original EDM framework, (ii) our scaled diffusion framework with EDM \\(\\sigma_{\\mathrm{data}}\\), (iii) our framework with a reduced value of \\(\\sigma_{\\mathrm{in}}\\), (iv) our framework with images not treated as infinite-frame-rate videos. Our framework improves over EDM under all metrics (i) and shows benefits in setting \\(\\sigma_{\\mathrm{data}} = 1\\), an effect that we attribute to the creation of a training target and loss weighting matching the widely used \\(v\\)-prediction formulation of" + }, + { + "type": "table", + "bbox": [ + 0.534, + 0.089, + 0.863, + 0.245 + ], + "angle": 0, + "content": "
FVD ↓FID ↓IS ↑
CogVideo [23] (Chinese)751.3-23.55
CogVideo [23] (English)701.6-25.27
MagicVideo [72]655--
LVDM [17]641.8--
Video LDM [4]550.6-33.45
VideoFactory [62]410.0--
Make-A-Video [48]367.2-33.00
PYoCo [13]355.2-47.46
Snap Video (288 × 288 px)260.139.038.89
Snap Video (512 × 288 px)200.228.138.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.534, + 0.267, + 0.857, + 0.28 + ], + "angle": 0, + "content": "Table 4. Zero-shot evaluation results on UCF101 [55]." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.295, + 0.894, + 0.475 + ], + "angle": 0, + "content": "
CLIP-FID ↓FVD ↓CLIPSIM ↑
NUWA [64] (Chinese)47.68-0.2439
CogVideo [23] (Chinese)24.78-0.2614
CogVideo [23] (English)23.59-0.2631
MagicVideo [72]-998-
LVDM [17]--0.2381
Latent-Shift [2]15.23-0.2773
Video LDM [4]--0.2929
VideoFactory [62]--0.3005
Make-A-Video [48]13.17-0.3049
PYoCo [13]9.73--
Snap Video (288 × 288 px)8.48110.40.2793
Snap Video (512 × 288 px)9.35104.00.2793
" + }, + { + "type": "table_caption", + "bbox": [ + 0.527, + 0.497, + 0.863, + 0.511 + ], + "angle": 0, + "content": "Table 5. Zero-shot evaluation results on MSR-VTT [65]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.536, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Salimans et al. [45] (see Tab. 1). Using \\(\\sigma_{\\mathrm{in}} < s\\sqrt{T}\\) (see Sec. 3.2) impairs performance (iii). Finally, treating images as infinite-frame-rate videos consistently improves FID." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.722, + 0.607 + ], + "angle": 0, + "content": "4.4. Quantitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.824 + ], + "angle": 0, + "content": "We perform comparison of Snap Video against baselines on the UCF101 [55], and MSR-VTT [65] datasets respectively in Tab. 4 and Tab. 5. FID and FVD video quality metrics show improvements over the baselines which we attribute to the employed diffusion framework and joint spatiotemporal modeling performed by our architecture. On UCF101, our method produces the second-best IS of 38.89, demonstrating good video-text alignment. While our method surpasses Make-A-Video [48] on UCF101, we note that it produces a lower CLIPSIM score on MSR-VTT. We attribute this behavior to the use of T5 [39] text embeddings in place of the commonly used CLIP [38] embeddings which were observed [43] to produce higher text-image alignment despite similar CLIPSIM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To provide a comprehensive evaluation we run a user study to evaluate photorealism, video-text alignment, quantity of motion and quality of motion, important aspects of a video generator. Three publicly-accessible state-of-the-art video generators are considered: Gen-2 [11], PikaLabs [1]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7044" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.482, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.892, + 0.344 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.352, + 0.894, + 0.396 + ], + "angle": 0, + "content": "Figure 4. Qualitative results comparing Snap Video to state-of-the-art video generators on publicly available samples. While baseline methods present motion artifacts (top-left, top-right, bottom-right) or produce dynamic images (bottom-left), our method produces more temporally coherent motion. Best viewed in the Website." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.418, + 0.47, + 0.484 + ], + "angle": 0, + "content": "
PhotorealismVideo-Text Align.Mot. Quant.Mot. Qual.
Gen-2 [11]44.381.096.078.7
PikaLab [1]61.580.389.270.5
Floor33 [17]76.380.988.079.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.551 + ], + "angle": 0, + "content": "Table 6. User study on photorealism, video-text alignment, motion quantity and quality against publicly-accessible video generators on 65 dynamic scene prompts. % of votes in favor of our method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.473, + 0.825 + ], + "angle": 0, + "content": "and Floor33 [17]. We filter a set of 65 prompts from [31] describing scenes with vivid motions, and generate a video for each method with default options. We ask the participants to express preference between paired samples from Snap Video and each baseline, gathering votes from 5 users for each sample. Results are shown in Tab. 6 and video samples provided along with the employed prompt list in Appx. D.2 and in the Website. Our method produces results with photorealism comparable to Gen-2, while surpassing PikaLab and Floor33, and outperforms all baselines with respect to video-text alignment. Most importantly, we note that baselines often produce dynamic images, i.e. videos with dim motion, or videos with motion artifacts, a finding we attribute to the challenges in modeling large motion. In contrast, our method, thanks to the joint spatiotemporal modeling approach, produces vivid and high-quality motion as shown by the motion metrics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.289, + 0.849 + ], + "angle": 0, + "content": "4.5. Qualitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "In this section, we perform qualitative evaluation of our framework. In Fig. 4, Appx. D.3 and the Website, we present qualitative results comparing our method to state-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.558 + ], + "angle": 0, + "content": "of-the-art generators [4, 13, 21, 48] on samples publicly released by the authors. While such prompts might have been selected to highlight strengths of the baselines, our method produces more photorealistic samples aligned to the text descriptions. Most importantly, our samples present vivid and high-quality motion avoiding flickering artifacts that are present in the baselines due to temporal inconsistencies. We accompany qualitative evaluation with a user study performed on the same set of samples in Appx. D.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.596, + 0.628, + 0.612 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In this work, we highlight the shortcomings of diffusion processes and architectures commonly used in text-to-video generation, and systematically address them by treating videos as first-class citizens. First, we propose a modification to the EDM [25] diffusion framework for the generation of high-resolution videos and treat images as high frame-rate videos to avoid image-video modality mismatches. Second, we replace U-Nets [41] with efficient transformer-based FITs [8] which we scale to billions of parameters. Thanks to their learnable compressed representation of videos, they significantly improve training times, scalability and performance with particular regards to temporal consistency and motion modeling capabilities due to the joint spatiotemporal modeling on the compressed representation. When evaluated on UCF101 [55] and MSR-VTT [65] and in user studies, Snap Video attains state-of-the-art performance with particular regard to the quality of the modeled motion." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7045" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.142 + ], + "angle": 0, + "content": "[1] Pika lab discord server. https://www.pika.art/.Accessed: 2023-11-01. 2, 7, 8, 3, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.47, + 0.2 + ], + "angle": 0, + "content": "[2] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Samples produced by the proposed text-to-video generation method for a selection of prompts. Thanks to joint spatiotemporal video modeling, our generator can synthesize temporally coherent videos with large motion (left) while retaining the semantic control capabilities typical of large-scale text-to-video generators (right). See the Website for additional samples. + +![](images/506832b796cc84ccf0482793d3c8b2c44e40f92da38ae97d7274f447287a5401.jpg) + +# Abstract + +Contemporary models for generating images show remarkable quality and versatility. Swayed by these advantages, the research community repurposes them to generate videos. Since video content is highly redundant, we argue that naively bringing advances of image models to the video generation domain reduces motion fidelity, visual quality and impairs scalability. In this work, we build Snap Video, a video-first model that systematically addresses these challenges. To do that, we first extend the EDM framework to take into account spatially and temporally redundant pixels and naturally support video generation. Second, we show that a U-Net—a workhorse behind image generation—scales poorly when generating videos, requiring significant computational overhead. Hence, we propose a new transformer-based architecture that trains 3.31 times faster than U-Nets (and is $\sim 4.5$ faster at inference). This allows us to efficiently train a text-to-video model with billions of + +parameters for the first time, reach state-of-the-art results on a number of benchmarks, and generate videos with substantially higher quality, temporal consistency, and motion complexity. The user studies showed that our model was favored by a large margin over the most recent methods. + +# 1. Introduction + +Creating and sharing visual content is one of the key ways for people to express themselves in the digital world. Accessible to only professionals in the past, the capability to create [30, 40, 43, 69] and edit [6, 37, 42] images with stunning quality and realism was unlocked to everyone by the advent of large text-to-image models and their variations. + +Fueled by this progress, large-scale text-to-video models [4, 13, 21, 48, 62] are rapidly advancing too. Current large-scale diffusion-based video generation frame + +works are strongly rooted into their image counterparts [4, 13]. The availability of consolidated image generation architectures such as U-Nets [41] with publicly-available image-pretrained models [40] made them a logical foundation onto which to build large-scale video generators with the main architectural modifications focusing on the insertion of ad-hoc layers to capture temporal dependencies [4, 13, 21, 48, 62]. Similarly, training is performed under image-based diffusion frameworks with the model being applied both to videos and to a separate set of images to improve the diversity of the results [13, 21, 22, 48]. + +We argue that such an approach is suboptimal under multiple aspects which we systematically address in this work. First, image and video modalities present intrinsic differences given by the similarity of content in successive video frames [7, 13]. By analogy, image and video compression algorithms are based on vastly different approaches [33]. To address this issue, we rewrite the EDM [25] framework with a focus on high-resolution videos. Differently from past work where videos were treated as a sequence of images, we perform joint video-image training by treating images as high frame-rate videos to avoid modality mismatches introduced by the absence of the temporal dimension within purely image-based training. Second, the widely adopted U-Net [41] architecture is required to fully processes each video frame. This increases computational overhead compared to purely text-to-image models, posing a very practical limit on model scalability. The latter is a critical factor in obtaining high-quality of results [13, 21]. Extending U-Net-based architectures to naturally support spatial and temporal dimensions requires volumetric attention operations, which have prohibitive computational demands. Inability to do so affects the outputs, resulting in dynamic images or motion artifacts being generated instead of videos with coherent and diverse actions. + +Following our compression analogy, we propose to leverage repetition between frames and introduce a scalable transformer architecture that treats spatial and temporal dimensions as a single, compressed, 1D latent vector. This highly compressed representation allows us to perform spatio-temporal computation jointly and enables modelling of complex motions. Our architecture is inspired by FIT [8], which we scale to billions of parameters for the first time. Compared to U-Nets, our model features a significant $3.31 \times$ reduction in training time and $4.49 \times$ reduction in inference time while achieving higher generation quality. + +We evaluate Snap Video on the widely-adopted UCF101 [55] and MSR-VTT [65] datasets. Our generator shows state-of-the-art performance across the range of benchmarks with particular regard to the quality of the generated motion. Most interestingly, we performed a number of user studies against the most recent open- and close-source methods and found that according to the participants + +of the study our model features photorealism comparable to Gen-2 [11], while being significantly better than Pika [1] and Floor33 [17]. Most excitedly, the preference of user-study participants favoured Snap Video by a large margin when text alignment and motion quality were assessed. Compared to Gen-2 [11] on prompt-video alignment our model was preferred in $81\%$ of cases (80% against Pika [1], 81% against Floor33 [17]), generated most dynamic videos with most amount of motion (96% against Gen2 [11], 89% against Pika [1], 88% against Floor33 [17]) and had the best motion quality (79% against Gen-2 [11], 71% against Pika [1], 79% against Floor33 [17]). + +# 2. Related Work + +Video Generation Video generation is a challenging and long-studied task. Due to its complexity, a large number of works focus on modeling narrow domains [5, 9, 12, 28, 35, 44, 47, 49, 56, 58, 59, 66, 70, 71] and adopt adversarial training [5, 9, 28, 44, 47, 49, 58, 59, 71] or autoregressive generation techniques [12, 35, 56, 66, 70]. To address the narrow domain limitation, the task of text-to-video generation was proposed [34] and both autoregressive models [23, 34, 61, 63, 64] and GANs [29] emerged. + +The recent success of diffusion models in the context of text-to-image generation [3, 40, 43] fostered tremendous progress in the task [2, 4, 13, 16, 17, 21, 22, 32, 48, 62, 67, 72]. ImagenVideo [21] and Make-A-Video [48] propose a deep cascade of temporal and spatial upsamplers to generate videos and jointly train their models on image and video datasets. PYoCo [13] introduces a correlated noise model to capture similarities between video frames. Video LDM [4] adopts a latent diffusion paradigm where a pretrained latent image generator and latent decoder are finetuned to generate temporally coherent videos.AnimateDiff [16] freezes a pre-trained latent image generator and trains only a newly inserted motion modeling module. These works employ U-Nets with separable spatial and temporal computation which poses a limitation on motion modeling capabilities. VideoFactory [62] improves upon this paradigm by proposing a Swapped Spatiotemporal CrossAttention that improves interactions between the spatial and temporal modalities along 3D windows. + +Differently from this corpus of works which adapts the U-Net [41] architecture to the video generation task, we show that employing transformer-based FIT [8] architectures results in significant training time savings, scalability improvements, and performance increase thanks to their learnable compressed video representation. In particular, we show that the global joint spatiotemporal modeling strategy enabled by our compressed video representation results in significant improvements in temporal consistency and motion modeling capabilities. + +High-Resolution Generation Different approaches have been proposed to enable the generation of high-resolution outputs. Cascaded diffusion models [3, 13, 21, 43, 48] adopt a set of independent diffusion models designed to successively upsample the results of the previous step. Latent diffusion models [2, 4, 17, 40, 72] make use of a pretrained autoencoder to encode the input into a low-dimensional set of latent vectors and learn a diffusion model on this latent representation. + +A different family of methods generates high-resolution outputs end-to-end without employing cascades of models or latent diffusion. Simple Diffusion [24] and Chen [7] directly generate high-resolution images by adapting the noise schedule of the diffusion process. f-DM [14] and RDM [57] design a diffusion process that seamlessly transitions between different resolutions. MDM [15] proposes a strategy where a single model is trained to simultaneously denoise inputs at progressively higher resolutions. + +In this work, we adopt a two-stage cascaded model out of two considerations: (i) it avoids temporal inconsistencies in the forms of flickering of high-frequency details that may be introduced by latent autoencoders [4], (ii) it increases model capacity with respect to an end-to-end model by creating two specialized models, one for the low resolution focusing on motion modeling and scene structure, and one for the high-resolution, focusing on high-frequency details. + +Diffusion Frameworks Diffusion generative models are a set of techniques modeling generation as a pair of processes: a forward process progressively destructing a sample with noise, and a reverse process modeling generation as the progressive denoising of a sample. Different formulations of diffusion models have been proposed in the literature. Denoising Diffusion Probabilistic Models (DDPMs) [20, 50] formulate the forward and backward process as Markov chains. Score-based Generative Models (SGMs) [51, 52] model the score of the probability density function of a series of data distributions perturbed with increasing levels of noise, i.e. the direction of largest increase in the data log probability density function. An avenue of works [53, 54] generalizes DDPMs and SGMs to infinite noise levels through Stochastic Differential Equations (SDEs). In this work, we adopt the SGM framework of EDM [25] which we reformulate for the generation of high-resolution videos. + +# 3. Method + +We propose the generation of high-resolution videos by rewriting the EDM [25] diffusion framework for high-dimensional inputs and proposing an efficient transformer architecture based on FITs [8] which we scale to billions of parameters and tens of thousands input patches. Sec. 3.1 provides an introduction to the EDM framework, Sec 3.2 + +highlights the challenges of applying diffusion frameworks to high dimensional inputs and proposes a revisited EDM-based diffusion framework. Sec. 3.3 proposes a method to reduce the gap between image and video modalities for joint training. Finally, Sec. 3.4 describes our scalable video generation architecture, while Sec. 3.5 and Sec. 3.6 respectively describe the training and inference procedures. + +# 3.1. Introduction to EDM + +Diffusion models have achieved remarkable success in image and video generation. Among the proposed frameworks, Karras et al. [25] provide a unified view of common diffusion frameworks and formulate EDM. EDM defines a variance-exploding forward diffusion process $p(\pmb{x}_{\sigma}|\pmb{x}) \sim \mathcal{N}(\pmb{x}, \pmb{\sigma}^2\mathbf{I})$ , where $\pmb{\sigma} \in [\pmb{\sigma}_{\mathrm{min}}, \pmb{\sigma}_{\mathrm{max}}]$ represents the diffusion timestep coinciding with the standard deviation of the applied noise, and $x_{\sigma}$ represents the data at the current noise level. A denoiser function $\mathcal{D}_{\theta}$ is learned to model the reverse process using the denoising objective: + +$$ +\mathcal {L} \left(\mathcal {D} _ {\theta}\right) = \mathbb {E} _ {\boldsymbol {\sigma}, \boldsymbol {x}, \boldsymbol {\epsilon}} \left[ \lambda (\boldsymbol {\sigma}) \| \mathcal {D} _ {\theta} \left(\boldsymbol {x} _ {\boldsymbol {\sigma}}\right) - \boldsymbol {x} \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $\lambda$ is the loss weighting function, $\pmb{x} \sim p_{\mathrm{data}}$ is a data sample, $\epsilon$ is gaussian noise, and $\sigma \sim p_{\mathrm{train}}$ is sampled from a training distribution. $\mathcal{D}_{\theta}(\pmb{x}_{\sigma})$ is defined as: + +$$ +\mathcal {D} _ {\theta} \left(\boldsymbol {x} _ {\sigma}\right) = c _ {\text {o u t}} (\boldsymbol {\sigma}) \mathcal {F} _ {\theta} \left(c _ {\text {i n}} (\boldsymbol {\sigma}) \boldsymbol {x} _ {\sigma}\right) + c _ {\text {s k i p}} (\boldsymbol {\sigma}) \boldsymbol {x} _ {\sigma}, \tag {2} +$$ + +where $\mathcal{F}_{\theta}$ is a neural network, and $c_{\mathrm{out}}$ , $c_{\mathrm{skip}}$ and $c_{\mathrm{in}}$ represent scaling functions. In particular, the denoising objective $\mathcal{L}(\mathcal{F}_{\theta})$ can equivalently be expressed in terms of $\mathcal{F}_{\theta}$ as: + +$$ +\mathcal {L} \left(\mathcal {F} _ {\theta}\right) = \mathbb {E} _ {\boldsymbol {\sigma}, \boldsymbol {x}, \boldsymbol {\epsilon}} \left[ w (\boldsymbol {\sigma}) \left\| \mathcal {F} _ {\theta} \left(c _ {\text {i n}} (\boldsymbol {\sigma}) \boldsymbol {x} _ {\boldsymbol {\sigma}}\right) - c _ {\text {n r m}} (\boldsymbol {\sigma}) \mathcal {F} _ {\mathrm {t g t}} \right\| _ {2} ^ {2} \right], \tag {3} +$$ + +where $\mathcal{F}_{\mathrm{tgt}}$ represents the training target, $c_{\mathrm{nm}}$ is a normalization factor, and $w$ is a weighting function. These forms, derived in Appx. E, are presented in Tab. 1. + +A second order Runge-Kutta sampler is proposed to reverse the diffusion process and produce sample $\pmb{x}$ starting from gaussian noise $\pmb{x}_{\sigma_{\mathrm{max}}} \sim \mathcal{N}(\mathbf{0}, \sigma_{\mathrm{max}}^2 \mathbf{I})$ . + +# 3.2. EDM for High-Resolution Video Generation + +EDM is originally proposed as an image generation framework and its parameters are optimized for $64 \times 64\mathrm{px}$ image generation. Alterations in spatial resolution or the introduction of videos with shared content between frames allow the denoising network to trivially recover a noisy frame in the original resolution with higher signal-to-noise-ratio (SNR), which the original framework was designed to see at lower noise levels. To see why, consider a noisy video $\boldsymbol{x}_{\sigma} \in \mathbb{R}^{T \times s \cdot H \times s \cdot W} \sim \mathcal{N}(\boldsymbol{x}, \sigma^2\mathbf{I})$ where $T$ is the number of frames and $s$ is an upsampling factor. We build the corresponding clean and noisy frames at original resolution $\tilde{\boldsymbol{x}}$ , $\tilde{\boldsymbol{x}}_{\sigma} \in \mathbb{R}^{1 \times H \times W}$ by averaging values in each $T \times s \times s$ block of pixels. As a consequence of averaging, the noise + +
EDM [25]Our
Training and Losses
Forw. processxσx/σin + σεx/σin + σε
Training targetFtgtσx - σ2data ε + σ2data(σin-1)/σin x- σx + σ2data ε
Eff. loss weigh.w(σ)1(σ2 + σ2data)2/(σ2 + σ2data)2
Loss weigh.λ(σ)1/σ2data + 1/σ21/σ2data + 1/σ2
Network Parametrization
Input scalingcin(σ)1/√σ2data + σ21/√σ2data/σ2 + σ2
Output scalingcout(σ)σσ2data/√σ2+ σ2data- σinσσdata√σ2+ σ2data/σ2+ σ2
Skip scalingcskip(σ)σ2data/σ2+ σ2dataσinσ2data/σinσ2+ σ2data
Target scalingcnrm(σ)1/σdata√σ2+ σ2data1/σdata√σ2+ σ2data
+ +Table 1. Definitions of functions in Eq. (1), Eq. (2) and Eq. (3) for the EDM and our proposed diffusion framework as derived in Appx. E and Appx. F, where we highlight the terms induced by the input scaling factor $\sigma_{\mathrm{in}}$ . Our framework is equivalent to EDM for $\sigma_{\mathrm{in}} = 1$ but avoids the unstable term $\frac{\sigma_{\mathrm{data}}^2(\sigma_{\mathrm{in}} - 1)}{\sigma_{\mathrm{in}}\sigma} x$ induced by $\sigma_{\mathrm{in}} \neq 1$ in $\mathcal{F}_{\mathrm{tgt}}$ . This form highlights that the train target and loss weight match the $v$ -prediction [45] framework for $\sigma_{\mathrm{data}} = 1$ . All other framework parameters are unaltered with respect to EDM. + +variance is reduced by a factor $Ts^2$ , i.e. $\tilde{x}_{\sigma} \sim \mathcal{N}(\tilde{x}, \frac{\sigma^2}{Ts^2}\mathbf{I})$ , thus $\tilde{x}_{\sigma}$ has an increased signal-to-noise-ratio with respect to $x_{\sigma}$ (see Fig. 2): $SNR_{\tilde{x}_{\sigma}} = Ts^2 SNR_{x_{\sigma}}$ . If pixels in each block share similar content, a typical situation in high-resolution videos, then the information in the averaged frame is useful for recovering $x$ and can be exploited at training time by the denoiser function. This creates a train-inference mismatch during the initial sampling steps as the average frame does not yet contain a well-formed signal, yet the denoiser is reliant on its presence. Thus, for best performance, any alteration to $T$ or $s$ should instead maintain the same signal-to-noise ratio at the original resolution for which the diffusion framework was designed. + +To restore the optimal SNR at the original resolution, the magnitude of the input signal can be reduced [7] by a corresponding factor $\sigma_{\mathrm{in}} = s\sqrt{T}$ as illustrated in Fig. 2. Consequently, we redefine the forward process as $p(\boldsymbol{x}_{\sigma}|\boldsymbol{x}) \sim \mathcal{N}(\boldsymbol{x} / \sigma_{\mathrm{in}}, \sigma^2\mathbf{I})$ . + +We rewrite the EDM framework to introduce the input scaling factor in Appx. F and highlight the changes in Tab. 1. We notice that a naive introduction of the scaling factor would alter the training target $\mathcal{F}_{\mathrm{tgt}}$ in a way that makes the objective explode for small noise values (see Appx. E). We thus leverage the training objective expressed in the form of Eq. (3) to rewrite the EDM process in a way that ensures $\mathcal{F}_{\mathrm{tgt}}$ remains unchanged, the effective loss weight $w(\sigma)$ is such that it keeps the loss weight $\lambda (\sigma)$ unchanged, $c_{\mathrm{in}}(\sigma)$ and $c_{\mathrm{nm}}(\sigma)$ normalize the input and training target to have unit variance, and the framework is equivalent to the original EDM formulation for $\sigma_{\mathrm{in}} = 1$ (see Appx. F). + +![](images/9e11ee40e7d83893d84b6e8237365779c1162475aca6016c22edde858235273a.jpg) +Figure 2. Analysis of Signal-to-Noise Ratio (SNR). Top: noise $\sigma$ is applied to an image. Middle: the same noise $\sigma$ is applied to a 16-frames-long video $x$ without scaling. A clean image can be easily restored by simply taking average, indicating an increased SNR. Bottom: to maintain the original SNR, we scale down the 16 frames by $\sigma_{\mathrm{in}}$ before noise application. Averaging is not able to restore the images, indicating the SNR is maintained as $\tilde{x} + \sigma \epsilon$ . + +Finally, we modify the sampler according to the newly defined forward process that requires the signal component in $x_{\sigma}$ to be scaled by $\sigma_{\mathrm{in}}$ . This is achieved by dividing the $\mathcal{D}_{\theta}(x_{\sigma})$ by $\sigma_{\mathrm{in}}$ and multiplying the final denoised sample $x_0$ by $\sigma_{\mathrm{in}}$ to restore the signal magnitude. + +# 3.3. Image-Video Modality Matching + +Due to the limited amount of captioned video data with respect to images, joint image-video training is widely adopted [13, 21, 22, 48] with the same diffusion process typically applied to both modalities. However, as shown in Sec. 3.2, the presence of $T$ frames in videos calls for a different process with respect to an image with the same resolution. A possibility would be to adopt different input scaling factors for the two modalities. We argue that this solution is undesirable in that it increases the complexity of the framework and image training would not foster the denoising model to learn temporal reasoning, a fundamental capability of a video generator. To sidestep these issues while using a unified diffusion process, we match the image and video modalities by treating images as $T$ frames videos with infinite frame-rate and introduce a variable frame-rate training procedure blending the gap between the image and video modalities. + +# 3.4. Scalable Video Generator + +U-Nets [41] have shown success in video generation where they are typically augmented with temporal attention or convolutions for modeling the temporal dimension [4, 13, 21, 22, 48]. However, such an approach requires a full U-Net forward pass for each of the $T$ video frames, rapidly becoming prohibitively expensive (see Fig. 3a). These factors pose a practical limit on model scalability—a primary factor in achieving high generation quality [13, 17, 21, 48]—and + +![](images/2ea42f1c5e2f6813aedea4975141396e0f032cd2ae571fb1300c7fa3f2c7d101.jpg) +(a) Computational Paradigms for Videos + +![](images/561d720c549782cb403330e2642f70b63d952d23b5ee5139c84d5d4ac716c591.jpg) +(b) Snap Video FIT Architecture +Figure 3. (a-left) U-Net-based text-to-image architectures are adapted to do video generation by inserting temporal layers applied sequentially with spatial layers, creating separable spatiotemporal blocks. Spatial computation is repeated for each frame independently, limiting scalability. (a-right) Our scalable transformer-based model jointly performs spatial and temporal computation on a learnable compressed video representation for improved motion modeling and scalability. (b) The proposed Snap Video FIT architecture. Given a noisy input video $\pmb{x}_{\sigma}$ , the model estimates the denoised video $\hat{\pmb{x}}_{\sigma}$ by recurrent application of FIT blocks. Each block reads information from the patch tokens into a small set of latent tokens on which computation is performed. The results are written to the patch tokens. Conditioning information in the form of text embeddings, noise level $\sigma$ , frame-rate $\nu$ and resolution $r$ is provided through an additional read operation. + +similarly limit possibilities for joint spatio-temporal modeling [62]. We argue that treating spatial and temporal modeling in a separable way [4, 13, 21, 48] causes motion artifacts, temporal inconsistencies or generation of dynamic images rather than videos with vivid motion. Video frames, however, contain spatially and temporally redundant content that is amenable to compression [33]. We argue that learning and operating on a compressed video representation and jointly modeling the spatial and temporal dimensions are necessary steps to achieve the scalability and motion-modeling capabilities required for high-quality video generation. + +FITs [8] are efficient transformer-based architectures that have recently been proposed for high-resolution image synthesis and video generation. Their main idea, summarized in Fig. 3 is that of learning a compressed representation of their input through a set of learnable latent tokens and of focusing computation on this learnable latent space, allowing input dimensionality to grow with little performance penalty. First, FITs perform patchification of the input and produce a sequence of patch tokens which are later divided into groups. A set of latent tokens is then instantiated and a sequence of computational blocks is applied. Each block first performs a cross attention "read" operation between latent tokens and conditioning signals such as the diffusion timestep, then an additional groupwise "read" cross attention operation between latent and patch tokens of corresponding groups to compress patch information, applies a series of self attention operations to the latent tokens, and performs a groupwise "write" cross attention operation that decompresses information in the latent tokens to update the patch tokens. Finally, the patch tokens are pro + +jected back to the pixel space to form the output. Self conditioning is applied on the set of latent tokens to preserve the compressed video representation computed in previous sampling steps. + +While promising, these architectures have not yet been scaled to the billion-parameters size of state-of-the-art U-Net-based video generators, nor they have been applied to high-resolution video generation. In the following, we highlight the architectural considerations necessary to achieve these goals. Temporal modeling is a fundamental aspect of a high-quality video generator. FITs produce patch tokens by considering three dimensional patches of size $T_{p} \times H_{p} \times W_{p}$ spanning both the spatial and temporal dimensions. We find values of $T_{p} > 1$ to limit temporal modeling performance, so we consider patches spanning the spatial dimension only. In addition, similarly to patches, FITs group patch tokens into groups spanning both the temporal and spatial dimensions, and perform cross attention operations group by group. We observe that the temporal size of each group should be configured so that each group covers all $T$ video frames for best temporal modeling. Furthermore, videos contain more information with respect to images due to the presence of the temporal dimension, thus we increase the number of latent tokens representing the size of the compressed space in which joint spatiotemporal computation is performed. Finally, FITs make use of local layers which perform self attention operations on patch tokens corresponding to the same group. We find this operation to be computationally expensive for large amounts of patch tokens (147.456 for our largest resolution) and replace it with a feed forward module after each cross attention "read" or "write" operation. + +Our model makes use of conditioning information represented by a sequence of conditioning tokens to control the generation process. In addition to the token representing the current $\sigma$ , to enable text conditioning, we introduce a T5-11B [39] text encoder extracting text embeddings from the input text. To support variable video framereates and large differences in resolution and aspect ratios in the training data, we concatenate additional tokens representing the framerate and original resolution of the current input. + +To generate high-resolution outputs, we implement a model cascade consisting of a first-stage model producing $36 \times 64\mathrm{px}$ videos and a second-stage upsampling model producing $288 \times 512\mathrm{px}$ videos. To improve upsampling quality, we corrupt the second-stage low-resolution inputs with a variable level of noise during training [21, 43] and during inference apply a level of noise to the first-stage outputs obtained by hyperparameter search. + +We present detailed model hyperparameters in Appx. B. + +# 3.5. Training + +We train Snap Video using the LAMB [68] optimizer with a learning rate of $5e^{-3}$ , a cosine learning schedule and a total batch size of 2048 videos and 2048 images, achievable thanks to our scalable video generator architecture. We train the first-stage model over 550k steps and finetune the second-stage model on high-resolution videos starting from the first-stage model weights for 370k iterations. Following the observations in Sec 3.2, we pose $\sigma_{\mathrm{in}} = s\sqrt{T}$ . Considering videos with $T = 16$ frames and the original 64px resolution for which EDM was designed, we set $\sigma_{\mathrm{in}} = 4$ for the first-stage and $\sigma_{\mathrm{in}} = 32$ for the second-stage model. + +We present training details and parameters in Appx. C. + +# 3.6. Inference + +We produce video samples from gaussian noise and user-provided conditioning information using the deterministic sampler of [25] and our two-stage cascade. We use 256 sampling steps for the first-stage and 40 for the second-stage model, and employ classifier free guidance [19] to improve text-video alignment (see Appx. D.1) unless otherwise specified. We find dynamic thresholding [43] and oscillating guidance [21] to consistently improve quality. + +# 4. Evaluation + +In this section, we perform evaluation of Snap Video against baselines and validate our design choices. Sec. 4.1 introduces the employed datasets, Sec. 4.3 shows ablations of our diffusion framework and architectural choices, Sec. 4.4 quantitatively compares our method to state-of-the-art large-scale video generators and Sec. 4.5 performs qualitative evaluation. We complement evaluation by showcasing samples in the Appendix and Website. + +
FID ↓FVD ↓CLIPSIM ↑Train Thr. ↓Inf. Thr. ↓
U-Net 85M [10]8.2145.940.2319133.249.6
U-Net 284M [10]4.9023.760.2391230.3105.1
Snap Video FIT 500M3.0727.790.245969.523.4
Snap Video FIT 3.9B2.5112.310.2579526.0130.4
+ +Table 2. Performance of different architectures and model sizes on our internal dataset in $64 \times 36\mathrm{px}$ resolution. We observe strong performance gains with scaling and note that FITs present better performance with improved speed with respect to U-Nets. Train and inference throughputs in ms/video/GPU. + +
σdataσinImgs. as VideosFID ↓FVD ↓CLIPSIM ↑
(i)0.51.0✓6.5839.950.2370
(ii)0.54.0✓4.0331.000.2449
(iv)1.02.0✓4.4534.890.2428
(iii)1.01/4.0X3.5024.880.2469
Ours1.04.0✓3.0727.790.2459
+ +Table 3. Ablation of different diffusion process configurations varying $\sigma_{\mathrm{data}}$ , input scaling $\sigma_{\mathrm{in}}$ , and treatment of images as infinite-framerate videos, evaluated on our internal dataset in $64 \times 36$ px resolution. + +# 4.1. Datasets + +We train our models on an internal dataset consisting of 1.265M images and 238k hours of videos, each with a corresponding text caption. Due to the difficulty in acquiring high-quality captions for videos, we develop a video captioning model that we use to produce synthetic video captions for the portion of videos in the dataset missing such annotation. + +We make use of the following datasets for evaluation which are never observed during training: + +UCF-101 [55] is a video dataset containing 13.320 $320 \times 240$ px Youtube videos from 101 action categories. + +MSR-VTT [65] is a dataset containing $10.000320 \times 240\mathrm{px}$ web-crawled videos, each manually annotated with 20 text captions. The test set contains 2.990 videos and 59.800 corresponding captions. + +# 4.2. Evaluation Protocol + +To validate the choices operated on the diffusion framework and on model architecture, present method ablations performed in $64 \times 36\mathrm{px}$ resolution using the first-stage model only, and compute FID [18], FVD [60] and CLIPSIM [63] metrics against the test set of our internal dataset on $50\mathrm{k}$ generated videos. + +To evaluate our method against baselines, we follow the protocols highlighted in [4, 13, 32, 48, 62, 72] for zero- + +shot evaluation on the UCF-101 [55] and MSR-VTT [65] datasets. We generate 16 frames videos in $512 \times 288\mathrm{px}$ resolution at 24fps for all settings. We evaluate both at the native $512 \times 288\mathrm{px}$ resolution with 16:9 aspect ratio and in the $288 \times 288\mathrm{px}$ square aspect ratio typically employed on these benchmarks. We note that the evaluation protocols of [4, 13, 32, 48, 62, 72] present different choices regarding the number of generated samples, distribution of class labels, choice of text prompts. We make use of the following evaluation parameters: + +Zero-shot UCF-101 [55] We generate 10,000 videos [4, 62] sampling classes with the same distribution as the original dataset. We produce a text prompt for each class label [13] and compute FVD [60] and Inception Score [46]. + +Zero-shot MSR-VTT [65] We generate a video sample for each of the 59.800 test prompts [13, 48] and compute CLIP-FID [27] and CLIPSIM [63]. + +To provide a more complete performance assessment and compare against state-of-the-art closed-source methods not reporting results for these benchmarks, we perform a user study evaluating photorealism, video-text-alignment and, most importantly, the quantity and quality of the generated motion, important characteristics of a video generator that may signal the generation of dynamic images, i.e. videos with dim motion, or motion artifacts rather than videos with vivid and high-quality motion. + +# 4.3. Ablations + +To evaluate the proposed FIT architecture, we consider the U-Net of [10], which we adapt to the video generation setting by interleaving temporal attention operations. We consider two U-Net variants of different capacities and a smaller variant of our FIT to evaluate the scalability of both architectures. We detail the architectures in Appx. B and show results in Tab. 2. + +Our 500M parameters FIT trains $3.31 \times$ faster than the baseline 284M parameters U-Net, performs inference $4.49 \times$ faster and surpasses it in terms of FID and CLIPSIM. In addition, both FITs and U-Nets show strong performance gains with scaling. Our largest FIT scales to 3.9B parameters with only a $1.24 \times$ increase in inference time with respect to the 284M U-Net. + +To evaluate the choices operated on our diffusion framework, we ablate different configurations of the diffusion process using our 500M FIT architecture. We produce the following variations: (i) the original EDM framework, (ii) our scaled diffusion framework with EDM $\sigma_{\mathrm{data}}$ , (iii) our framework with a reduced value of $\sigma_{\mathrm{in}}$ , (iv) our framework with images not treated as infinite-frame-rate videos. Our framework improves over EDM under all metrics (i) and shows benefits in setting $\sigma_{\mathrm{data}} = 1$ , an effect that we attribute to the creation of a training target and loss weighting matching the widely used $v$ -prediction formulation of + +
FVD ↓FID ↓IS ↑
CogVideo [23] (Chinese)751.3-23.55
CogVideo [23] (English)701.6-25.27
MagicVideo [72]655--
LVDM [17]641.8--
Video LDM [4]550.6-33.45
VideoFactory [62]410.0--
Make-A-Video [48]367.2-33.00
PYoCo [13]355.2-47.46
Snap Video (288 × 288 px)260.139.038.89
Snap Video (512 × 288 px)200.228.138.89
+ +Table 4. Zero-shot evaluation results on UCF101 [55]. + +
CLIP-FID ↓FVD ↓CLIPSIM ↑
NUWA [64] (Chinese)47.68-0.2439
CogVideo [23] (Chinese)24.78-0.2614
CogVideo [23] (English)23.59-0.2631
MagicVideo [72]-998-
LVDM [17]--0.2381
Latent-Shift [2]15.23-0.2773
Video LDM [4]--0.2929
VideoFactory [62]--0.3005
Make-A-Video [48]13.17-0.3049
PYoCo [13]9.73--
Snap Video (288 × 288 px)8.48110.40.2793
Snap Video (512 × 288 px)9.35104.00.2793
+ +Table 5. Zero-shot evaluation results on MSR-VTT [65]. + +Salimans et al. [45] (see Tab. 1). Using $\sigma_{\mathrm{in}} < s\sqrt{T}$ (see Sec. 3.2) impairs performance (iii). Finally, treating images as infinite-frame-rate videos consistently improves FID. + +# 4.4. Quantitative Evaluation + +We perform comparison of Snap Video against baselines on the UCF101 [55], and MSR-VTT [65] datasets respectively in Tab. 4 and Tab. 5. FID and FVD video quality metrics show improvements over the baselines which we attribute to the employed diffusion framework and joint spatiotemporal modeling performed by our architecture. On UCF101, our method produces the second-best IS of 38.89, demonstrating good video-text alignment. While our method surpasses Make-A-Video [48] on UCF101, we note that it produces a lower CLIPSIM score on MSR-VTT. We attribute this behavior to the use of T5 [39] text embeddings in place of the commonly used CLIP [38] embeddings which were observed [43] to produce higher text-image alignment despite similar CLIPSIM. + +To provide a comprehensive evaluation we run a user study to evaluate photorealism, video-text alignment, quantity of motion and quality of motion, important aspects of a video generator. Three publicly-accessible state-of-the-art video generators are considered: Gen-2 [11], PikaLabs [1] + +![](images/2fa82ded38c5ae7b26fc3839ffcf7eca9c46cddc346d8f0d30486611bcb9a4c6.jpg) +Figure 4. Qualitative results comparing Snap Video to state-of-the-art video generators on publicly available samples. While baseline methods present motion artifacts (top-left, top-right, bottom-right) or produce dynamic images (bottom-left), our method produces more temporally coherent motion. Best viewed in the Website. + +![](images/382a92480806ce18863c9abc916323b1b4c2e639fad98e114ce94840ca3bda3c.jpg) + +
PhotorealismVideo-Text Align.Mot. Quant.Mot. Qual.
Gen-2 [11]44.381.096.078.7
PikaLab [1]61.580.389.270.5
Floor33 [17]76.380.988.079.1
+ +Table 6. User study on photorealism, video-text alignment, motion quantity and quality against publicly-accessible video generators on 65 dynamic scene prompts. % of votes in favor of our method. + +and Floor33 [17]. We filter a set of 65 prompts from [31] describing scenes with vivid motions, and generate a video for each method with default options. We ask the participants to express preference between paired samples from Snap Video and each baseline, gathering votes from 5 users for each sample. Results are shown in Tab. 6 and video samples provided along with the employed prompt list in Appx. D.2 and in the Website. Our method produces results with photorealism comparable to Gen-2, while surpassing PikaLab and Floor33, and outperforms all baselines with respect to video-text alignment. Most importantly, we note that baselines often produce dynamic images, i.e. videos with dim motion, or videos with motion artifacts, a finding we attribute to the challenges in modeling large motion. In contrast, our method, thanks to the joint spatiotemporal modeling approach, produces vivid and high-quality motion as shown by the motion metrics. + +# 4.5. Qualitative Evaluation + +In this section, we perform qualitative evaluation of our framework. In Fig. 4, Appx. D.3 and the Website, we present qualitative results comparing our method to state- + +of-the-art generators [4, 13, 21, 48] on samples publicly released by the authors. While such prompts might have been selected to highlight strengths of the baselines, our method produces more photorealistic samples aligned to the text descriptions. Most importantly, our samples present vivid and high-quality motion avoiding flickering artifacts that are present in the baselines due to temporal inconsistencies. We accompany qualitative evaluation with a user study performed on the same set of samples in Appx. D.2. + +# 5. Conclusions + +In this work, we highlight the shortcomings of diffusion processes and architectures commonly used in text-to-video generation, and systematically address them by treating videos as first-class citizens. First, we propose a modification to the EDM [25] diffusion framework for the generation of high-resolution videos and treat images as high frame-rate videos to avoid image-video modality mismatches. Second, we replace U-Nets [41] with efficient transformer-based FITs [8] which we scale to billions of parameters. Thanks to their learnable compressed representation of videos, they significantly improve training times, scalability and performance with particular regards to temporal consistency and motion modeling capabilities due to the joint spatiotemporal modeling on the compressed representation. When evaluated on UCF101 [55] and MSR-VTT [65] and in user studies, Snap Video attains state-of-the-art performance with particular regard to the quality of the modeled motion. + +# References + +[1] Pika lab discord server. https://www.pika.art/.Accessed: 2023-11-01. 2, 7, 8, 3, 6 +[2] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. Latent-shift: Latent diffusion with temporal shift for efficient text-to-video generation. arXiv, 2023. 2, 3, 7 +[3] Yogesh Balaji, Seungjun Nah, Xun Huang, Arash Vahdat, Ji-aming Song, Qinsheng Zhang, Karsten Kreis, Miika Aittala, Timo Aila, Samuli Laine, Bryan Catanzaro, Tero Karras, and Ming-Yu Liu. ediff-i: Text-to-image diffusion models with an ensemble of expert denoisers. ArXiv, 2022. 2, 3 +[4] Andreas Blattmann, Robin Rombach, Huan Ling, Tim Dockhorn, Seung Wook Kim, Sanja Fidler, and Karsten Kreis. Align your latents: High-resolution video synthesis with latent diffusion models. 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Samples produced by the proposed text-to-video generation method for a selection of prompts. Thanks to joint spatiotemporal video modeling, our generator can synthesize temporally coherent videos with large motion (left) while retaining the semantic control capabilities typical of large-scale text-to-video generators (right). 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Swayed by these advantages, the research community repurposes them to generate videos. Since video content is highly redundant, we argue that naively bringing advances of image models to the video generation domain reduces motion fidelity, visual quality and impairs scalability. In this work, we build Snap Video, a video-first model that systematically addresses these challenges. To do that, we first extend the EDM framework to take into account spatially and temporally redundant pixels and naturally support video generation. Second, we show that a U-Net—a workhorse behind image generation—scales poorly when generating videos, requiring significant computational overhead. Hence, we propose a new transformer-based architecture that trains 3.31 times faster than U-Nets (and is " + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\sim 4.5" + }, + { + "bbox": [ + 46, + 510, + 289, + 714 + ], + "type": "text", + "content": " faster at inference). This allows us to efficiently train a text-to-video model with billions of" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 479, + 547, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 540 + ], + "type": "text", + "content": "parameters for the first time, reach state-of-the-art results on a number of benchmarks, and generate videos with substantially higher quality, temporal consistency, and motion complexity. The user studies showed that our model was favored by a large margin over the most recent methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 563, + 387, + 576 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 387, + 576 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 387, + 576 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 584, + 545, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 545, + 656 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 545, + 656 + ], + "type": "text", + "content": "Creating and sharing visual content is one of the key ways for people to express themselves in the digital world. Accessible to only professionals in the past, the capability to create [30, 40, 43, 69] and edit [6, 37, 42] images with stunning quality and realism was unlocked to everyone by the advent of large text-to-image models and their variations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 657, + 545, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 657, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 657, + 545, + 693 + ], + "type": "text", + "content": "Fueled by this progress, large-scale text-to-video models [4, 13, 21, 48, 62] are rapidly advancing too. Current large-scale diffusion-based video generation frame" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 320, + 702, + 473, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 702, + 473, + 714 + ], + "spans": [ + { + "bbox": [ + 320, + 702, + 473, + 714 + ], + "type": "text", + "content": "* Work performed while interning at Snap Inc." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7038" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "works are strongly rooted into their image counterparts [4, 13]. The availability of consolidated image generation architectures such as U-Nets [41] with publicly-available image-pretrained models [40] made them a logical foundation onto which to build large-scale video generators with the main architectural modifications focusing on the insertion of ad-hoc layers to capture temporal dependencies [4, 13, 21, 48, 62]. Similarly, training is performed under image-based diffusion frameworks with the model being applied both to videos and to a separate set of images to improve the diversity of the results [13, 21, 22, 48]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 206, + 289, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 494 + ], + "type": "text", + "content": "We argue that such an approach is suboptimal under multiple aspects which we systematically address in this work. First, image and video modalities present intrinsic differences given by the similarity of content in successive video frames [7, 13]. By analogy, image and video compression algorithms are based on vastly different approaches [33]. To address this issue, we rewrite the EDM [25] framework with a focus on high-resolution videos. Differently from past work where videos were treated as a sequence of images, we perform joint video-image training by treating images as high frame-rate videos to avoid modality mismatches introduced by the absence of the temporal dimension within purely image-based training. Second, the widely adopted U-Net [41] architecture is required to fully processes each video frame. This increases computational overhead compared to purely text-to-image models, posing a very practical limit on model scalability. The latter is a critical factor in obtaining high-quality of results [13, 21]. Extending U-Net-based architectures to naturally support spatial and temporal dimensions requires volumetric attention operations, which have prohibitive computational demands. Inability to do so affects the outputs, resulting in dynamic images or motion artifacts being generated instead of videos with coherent and diverse actions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "type": "text", + "content": "Following our compression analogy, we propose to leverage repetition between frames and introduce a scalable transformer architecture that treats spatial and temporal dimensions as a single, compressed, 1D latent vector. This highly compressed representation allows us to perform spatio-temporal computation jointly and enables modelling of complex motions. Our architecture is inspired by FIT [8], which we scale to billions of parameters for the first time. Compared to U-Nets, our model features a significant " + }, + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "type": "inline_equation", + "content": "3.31 \\times" + }, + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "type": "text", + "content": " reduction in training time and " + }, + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "type": "inline_equation", + "content": "4.49 \\times" + }, + { + "bbox": [ + 46, + 496, + 289, + 628 + ], + "type": "text", + "content": " reduction in inference time while achieving higher generation quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 289, + 715 + ], + "type": "text", + "content": "We evaluate Snap Video on the widely-adopted UCF101 [55] and MSR-VTT [65] datasets. Our generator shows state-of-the-art performance across the range of benchmarks with particular regard to the quality of the generated motion. Most interestingly, we performed a number of user studies against the most recent open- and close-source methods and found that according to the participants" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": "of the study our model features photorealism comparable to Gen-2 [11], while being significantly better than Pika [1] and Floor33 [17]. Most excitedly, the preference of user-study participants favoured Snap Video by a large margin when text alignment and motion quality were assessed. Compared to Gen-2 [11] on prompt-video alignment our model was preferred in " + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "inline_equation", + "content": "81\\%" + }, + { + "bbox": [ + 304, + 72, + 547, + 217 + ], + "type": "text", + "content": " of cases (80% against Pika [1], 81% against Floor33 [17]), generated most dynamic videos with most amount of motion (96% against Gen2 [11], 89% against Pika [1], 88% against Floor33 [17]) and had the best motion quality (79% against Gen-2 [11], 71% against Pika [1], 79% against Floor33 [17])." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 227, + 392, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 227, + 392, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 227, + 392, + 239 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 247, + 547, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 247, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 247, + 547, + 354 + ], + "type": "text", + "content": "Video Generation Video generation is a challenging and long-studied task. Due to its complexity, a large number of works focus on modeling narrow domains [5, 9, 12, 28, 35, 44, 47, 49, 56, 58, 59, 66, 70, 71] and adopt adversarial training [5, 9, 28, 44, 47, 49, 58, 59, 71] or autoregressive generation techniques [12, 35, 56, 66, 70]. To address the narrow domain limitation, the task of text-to-video generation was proposed [34] and both autoregressive models [23, 34, 61, 63, 64] and GANs [29] emerged." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 355, + 548, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 355, + 548, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 355, + 548, + 582 + ], + "type": "text", + "content": "The recent success of diffusion models in the context of text-to-image generation [3, 40, 43] fostered tremendous progress in the task [2, 4, 13, 16, 17, 21, 22, 32, 48, 62, 67, 72]. ImagenVideo [21] and Make-A-Video [48] propose a deep cascade of temporal and spatial upsamplers to generate videos and jointly train their models on image and video datasets. PYoCo [13] introduces a correlated noise model to capture similarities between video frames. Video LDM [4] adopts a latent diffusion paradigm where a pretrained latent image generator and latent decoder are finetuned to generate temporally coherent videos.AnimateDiff [16] freezes a pre-trained latent image generator and trains only a newly inserted motion modeling module. These works employ U-Nets with separable spatial and temporal computation which poses a limitation on motion modeling capabilities. VideoFactory [62] improves upon this paradigm by proposing a Swapped Spatiotemporal CrossAttention that improves interactions between the spatial and temporal modalities along 3D windows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 582, + 548, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 703 + ], + "type": "text", + "content": "Differently from this corpus of works which adapts the U-Net [41] architecture to the video generation task, we show that employing transformer-based FIT [8] architectures results in significant training time savings, scalability improvements, and performance increase thanks to their learnable compressed video representation. In particular, we show that the global joint spatiotemporal modeling strategy enabled by our compressed video representation results in significant improvements in temporal consistency and motion modeling capabilities." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7039" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "High-Resolution Generation Different approaches have been proposed to enable the generation of high-resolution outputs. Cascaded diffusion models [3, 13, 21, 43, 48] adopt a set of independent diffusion models designed to successively upsample the results of the previous step. Latent diffusion models [2, 4, 17, 40, 72] make use of a pretrained autoencoder to encode the input into a low-dimensional set of latent vectors and learn a diffusion model on this latent representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 289, + 287 + ], + "type": "text", + "content": "A different family of methods generates high-resolution outputs end-to-end without employing cascades of models or latent diffusion. Simple Diffusion [24] and Chen [7] directly generate high-resolution images by adapting the noise schedule of the diffusion process. f-DM [14] and RDM [57] design a diffusion process that seamlessly transitions between different resolutions. MDM [15] proposes a strategy where a single model is trained to simultaneously denoise inputs at progressively higher resolutions." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 288, + 289, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 384 + ], + "type": "text", + "content": "In this work, we adopt a two-stage cascaded model out of two considerations: (i) it avoids temporal inconsistencies in the forms of flickering of high-frequency details that may be introduced by latent autoencoders [4], (ii) it increases model capacity with respect to an end-to-end model by creating two specialized models, one for the low resolution focusing on motion modeling and scene structure, and one for the high-resolution, focusing on high-frequency details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 396, + 289, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 289, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 289, + 611 + ], + "type": "text", + "content": "Diffusion Frameworks Diffusion generative models are a set of techniques modeling generation as a pair of processes: a forward process progressively destructing a sample with noise, and a reverse process modeling generation as the progressive denoising of a sample. Different formulations of diffusion models have been proposed in the literature. Denoising Diffusion Probabilistic Models (DDPMs) [20, 50] formulate the forward and backward process as Markov chains. Score-based Generative Models (SGMs) [51, 52] model the score of the probability density function of a series of data distributions perturbed with increasing levels of noise, i.e. the direction of largest increase in the data log probability density function. An avenue of works [53, 54] generalizes DDPMs and SGMs to infinite noise levels through Stochastic Differential Equations (SDEs). In this work, we adopt the SGM framework of EDM [25] which we reformulate for the generation of high-resolution videos." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 621, + 104, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 104, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 104, + 634 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": "We propose the generation of high-resolution videos by rewriting the EDM [25] diffusion framework for high-dimensional inputs and proposing an efficient transformer architecture based on FITs [8] which we scale to billions of parameters and tens of thousands input patches. Sec. 3.1 provides an introduction to the EDM framework, Sec 3.2" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": "highlights the challenges of applying diffusion frameworks to high dimensional inputs and proposes a revisited EDM-based diffusion framework. Sec. 3.3 proposes a method to reduce the gap between image and video modalities for joint training. Finally, Sec. 3.4 describes our scalable video generation architecture, while Sec. 3.5 and Sec. 3.6 respectively describe the training and inference procedures." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 163, + 429, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 163, + 429, + 175 + ], + "spans": [ + { + "bbox": [ + 305, + 163, + 429, + 175 + ], + "type": "text", + "content": "3.1. Introduction to EDM" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "text", + "content": "Diffusion models have achieved remarkable success in image and video generation. Among the proposed frameworks, Karras et al. [25] provide a unified view of common diffusion frameworks and formulate EDM. EDM defines a variance-exploding forward diffusion process " + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "inline_equation", + "content": "p(\\pmb{x}_{\\sigma}|\\pmb{x}) \\sim \\mathcal{N}(\\pmb{x}, \\pmb{\\sigma}^2\\mathbf{I})" + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "inline_equation", + "content": "\\pmb{\\sigma} \\in [\\pmb{\\sigma}_{\\mathrm{min}}, \\pmb{\\sigma}_{\\mathrm{max}}]" + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "text", + "content": " represents the diffusion timestep coinciding with the standard deviation of the applied noise, and " + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "inline_equation", + "content": "x_{\\sigma}" + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "text", + "content": " represents the data at the current noise level. A denoiser function " + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}" + }, + { + "bbox": [ + 304, + 182, + 547, + 302 + ], + "type": "text", + "content": " is learned to model the reverse process using the denoising objective:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 339, + 307, + 545, + 328 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 307, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 339, + 307, + 545, + 328 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ \\lambda (\\boldsymbol {\\sigma}) \\| \\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - \\boldsymbol {x} \\| _ {2} ^ {2} \\right], \\tag {1}", + "image_path": "ec307c172d6e1bfac84981002063210525a3260ccfdbc1b9d915ba6f9d3b96e1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "content": " is the loss weighting function, " + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\sim p_{\\mathrm{data}}" + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "content": " is a data sample, " + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "content": " is gaussian noise, and " + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\sigma \\sim p_{\\mathrm{train}}" + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "content": " is sampled from a training distribution. " + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}(\\pmb{x}_{\\sigma})" + }, + { + "bbox": [ + 304, + 333, + 547, + 369 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 321, + 376, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 376, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 321, + 376, + 545, + 389 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\sigma}\\right) = c _ {\\text {o u t}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}\\right) + c _ {\\text {s k i p}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}, \\tag {2}", + "image_path": "a89f4399f0b4a6c44a9fa3455edbe54992d8df37e45841a94dd6bf1600c68e42.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta}" + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": " is a neural network, and " + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{out}}" + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{skip}}" + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": " represent scaling functions. In particular, the denoising objective " + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathcal{F}_{\\theta})" + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": " can equivalently be expressed in terms of " + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta}" + }, + { + "bbox": [ + 304, + 395, + 545, + 431 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 313, + 437, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 437, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 313, + 437, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(\\mathcal {F} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ w (\\boldsymbol {\\sigma}) \\left\\| \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - c _ {\\text {n r m}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\mathrm {t g t}} \\right\\| _ {2} ^ {2} \\right], \\tag {3}", + "image_path": "256cbbdd885a3c8603997db146a0b794640c325751cc823c76a4db41a3ff9eb5.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{tgt}}" + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "text", + "content": " represents the training target, " + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{nm}}" + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "text", + "content": " is a normalization factor, and " + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 460, + 545, + 496 + ], + "type": "text", + "content": " is a weighting function. These forms, derived in Appx. E, are presented in Tab. 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": "A second order Runge-Kutta sampler is proposed to reverse the diffusion process and produce sample " + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": " starting from gaussian noise " + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\sigma_{\\mathrm{max}}} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I})" + }, + { + "bbox": [ + 304, + 497, + 545, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 540, + 537, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 540, + 537, + 552 + ], + "spans": [ + { + "bbox": [ + 305, + 540, + 537, + 552 + ], + "type": "text", + "content": "3.2. EDM for High-Resolution Video Generation" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "EDM is originally proposed as an image generation framework and its parameters are optimized for " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "64 \\times 64\\mathrm{px}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " image generation. Alterations in spatial resolution or the introduction of videos with shared content between frames allow the denoising network to trivially recover a noisy frame in the original resolution with higher signal-to-noise-ratio (SNR), which the original framework was designed to see at lower noise levels. To see why, consider a noisy video " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_{\\sigma} \\in \\mathbb{R}^{T \\times s \\cdot H \\times s \\cdot W} \\sim \\mathcal{N}(\\boldsymbol{x}, \\sigma^2\\mathbf{I})" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " is the number of frames and " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " is an upsampling factor. We build the corresponding clean and noisy frames at original resolution " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{x}}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\tilde{\\boldsymbol{x}}_{\\sigma} \\in \\mathbb{R}^{1 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " by averaging values in each " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "T \\times s \\times s" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": " block of pixels. As a consequence of averaging, the noise" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7040" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 71, + 286, + 213 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 286, + 213 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 286, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 286, + 213 + ], + "type": "table", + "html": "
EDM [25]Our
Training and Losses
Forw. processxσx/σin + σεx/σin + σε
Training targetFtgtσx - σ2data ε + σ2data(σin-1)/σin x- σx + σ2data ε
Eff. loss weigh.w(σ)1(σ2 + σ2data)2/(σ2 + σ2data)2
Loss weigh.λ(σ)1/σ2data + 1/σ21/σ2data + 1/σ2
Network Parametrization
Input scalingcin(σ)1/√σ2data + σ21/√σ2data/σ2 + σ2
Output scalingcout(σ)σσ2data/√σ2+ σ2data- σinσσdata√σ2+ σ2data/σ2+ σ2
Skip scalingcskip(σ)σ2data/σ2+ σ2dataσinσ2data/σinσ2+ σ2data
Target scalingcnrm(σ)1/σdata√σ2+ σ2data1/σdata√σ2+ σ2data
", + "image_path": "4ce66b533645f0c594a5fe77744b7466c20736e3fb07cab81944bbfed7d6cff7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": "Table 1. Definitions of functions in Eq. (1), Eq. (2) and Eq. (3) for the EDM and our proposed diffusion framework as derived in Appx. E and Appx. F, where we highlight the terms induced by the input scaling factor " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": ". Our framework is equivalent to EDM for " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} = 1" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": " but avoids the unstable term " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\frac{\\sigma_{\\mathrm{data}}^2(\\sigma_{\\mathrm{in}} - 1)}{\\sigma_{\\mathrm{in}}\\sigma} x" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": " induced by " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} \\neq 1" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{tgt}}" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": ". This form highlights that the train target and loss weight match the " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": "-prediction [45] framework for " + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{data}} = 1" + }, + { + "bbox": [ + 46, + 231, + 289, + 323 + ], + "type": "text", + "content": ". All other framework parameters are unaltered with respect to EDM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": "variance is reduced by a factor " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "Ts^2" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": ", i.e. " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\sigma} \\sim \\mathcal{N}(\\tilde{x}, \\frac{\\sigma^2}{Ts^2}\\mathbf{I})" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": ", thus " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{\\sigma}" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": " has an increased signal-to-noise-ratio with respect to " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "x_{\\sigma}" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": " (see Fig. 2): " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "SNR_{\\tilde{x}_{\\sigma}} = Ts^2 SNR_{x_{\\sigma}}" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": ". If pixels in each block share similar content, a typical situation in high-resolution videos, then the information in the averaged frame is useful for recovering " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": " and can be exploited at training time by the denoiser function. This creates a train-inference mismatch during the initial sampling steps as the average frame does not yet contain a well-formed signal, yet the denoiser is reliant on its presence. Thus, for best performance, any alteration to " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 347, + 287, + 504 + ], + "type": "text", + "content": " should instead maintain the same signal-to-noise ratio at the original resolution for which the diffusion framework was designed." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "content": "To restore the optimal SNR at the original resolution, the magnitude of the input signal can be reduced [7] by a corresponding factor " + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} = s\\sqrt{T}" + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "content": " as illustrated in Fig. 2. Consequently, we redefine the forward process as " + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "inline_equation", + "content": "p(\\boldsymbol{x}_{\\sigma}|\\boldsymbol{x}) \\sim \\mathcal{N}(\\boldsymbol{x} / \\sigma_{\\mathrm{in}}, \\sigma^2\\mathbf{I})" + }, + { + "bbox": [ + 46, + 507, + 287, + 567 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "We rewrite the EDM framework to introduce the input scaling factor in Appx. F and highlight the changes in Tab. 1. We notice that a naive introduction of the scaling factor would alter the training target " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{tgt}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " in a way that makes the objective explode for small noise values (see Appx. E). We thus leverage the training objective expressed in the form of Eq. (3) to rewrite the EDM process in a way that ensures " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\mathrm{tgt}}" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " remains unchanged, the effective loss weight " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "w(\\sigma)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " is such that it keeps the loss weight " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\lambda (\\sigma)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " unchanged, " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{in}}(\\sigma)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "c_{\\mathrm{nm}}(\\sigma)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " normalize the input and training target to have unit variance, and the framework is equivalent to the original EDM formulation for " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} = 1" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " (see Appx. F)." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 547, + 194 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 547, + 194 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 547, + 194 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 547, + 194 + ], + "type": "image", + "image_path": "9e11ee40e7d83893d84b6e8237365779c1162475aca6016c22edde858235273a.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "text", + "content": "Figure 2. Analysis of Signal-to-Noise Ratio (SNR). Top: noise " + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "text", + "content": " is applied to an image. Middle: the same noise " + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "text", + "content": " is applied to a 16-frames-long video " + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "text", + "content": " without scaling. A clean image can be easily restored by simply taking average, indicating an increased SNR. Bottom: to maintain the original SNR, we scale down the 16 frames by " + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "text", + "content": " before noise application. Averaging is not able to restore the images, indicating the SNR is maintained as " + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\tilde{x} + \\sigma \\epsilon" + }, + { + "bbox": [ + 304, + 200, + 547, + 277 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": "Finally, we modify the sampler according to the newly defined forward process that requires the signal component in " + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "inline_equation", + "content": "x_{\\sigma}" + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": " to be scaled by " + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": ". This is achieved by dividing the " + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\theta}(x_{\\sigma})" + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": " and multiplying the final denoised sample " + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 305, + 299, + 546, + 361 + ], + "type": "text", + "content": " to restore the signal magnitude." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 368, + 482, + 380 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 368, + 482, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 368, + 482, + 380 + ], + "type": "text", + "content": "3.3. Image-Video Modality Matching" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "type": "text", + "content": "Due to the limited amount of captioned video data with respect to images, joint image-video training is widely adopted [13, 21, 22, 48] with the same diffusion process typically applied to both modalities. However, as shown in Sec. 3.2, the presence of " + }, + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "type": "text", + "content": " frames in videos calls for a different process with respect to an image with the same resolution. A possibility would be to adopt different input scaling factors for the two modalities. We argue that this solution is undesirable in that it increases the complexity of the framework and image training would not foster the denoising model to learn temporal reasoning, a fundamental capability of a video generator. To sidestep these issues while using a unified diffusion process, we match the image and video modalities by treating images as " + }, + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 387, + 545, + 589 + ], + "type": "text", + "content": " frames videos with infinite frame-rate and introduce a variable frame-rate training procedure blending the gap between the image and video modalities." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 598, + 449, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 449, + 610 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 449, + 610 + ], + "type": "text", + "content": "3.4. Scalable Video Generator" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "type": "text", + "content": "U-Nets [41] have shown success in video generation where they are typically augmented with temporal attention or convolutions for modeling the temporal dimension [4, 13, 21, 22, 48]. However, such an approach requires a full U-Net forward pass for each of the " + }, + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 617, + 546, + 715 + ], + "type": "text", + "content": " video frames, rapidly becoming prohibitively expensive (see Fig. 3a). These factors pose a practical limit on model scalability—a primary factor in achieving high generation quality [13, 17, 21, 48]—and" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7041" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 74, + 262, + 203 + ], + "blocks": [ + { + "bbox": [ + 51, + 74, + 262, + 203 + ], + "lines": [ + { + "bbox": [ + 51, + 74, + 262, + 203 + ], + "spans": [ + { + "bbox": [ + 51, + 74, + 262, + 203 + ], + "type": "image", + "image_path": "2ea42f1c5e2f6813aedea4975141396e0f032cd2ae571fb1300c7fa3f2c7d101.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 90, + 208, + 220, + 217 + ], + "lines": [ + { + "bbox": [ + 90, + 208, + 220, + 217 + ], + "spans": [ + { + "bbox": [ + 90, + 208, + 220, + 217 + ], + "type": "text", + "content": "(a) Computational Paradigms for Videos" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 284, + 74, + 543, + 202 + ], + "blocks": [ + { + "bbox": [ + 284, + 74, + 543, + 202 + ], + "lines": [ + { + "bbox": [ + 284, + 74, + 543, + 202 + ], + "spans": [ + { + "bbox": [ + 284, + 74, + 543, + 202 + ], + "type": "image", + "image_path": "561d720c549782cb403330e2642f70b63d952d23b5ee5139c84d5d4ac716c591.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 360, + 208, + 465, + 217 + ], + "lines": [ + { + "bbox": [ + 360, + 208, + 465, + 217 + ], + "spans": [ + { + "bbox": [ + 360, + 208, + 465, + 217 + ], + "type": "text", + "content": "(b) Snap Video FIT Architecture" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "text", + "content": "Figure 3. (a-left) U-Net-based text-to-image architectures are adapted to do video generation by inserting temporal layers applied sequentially with spatial layers, creating separable spatiotemporal blocks. Spatial computation is repeated for each frame independently, limiting scalability. (a-right) Our scalable transformer-based model jointly performs spatial and temporal computation on a learnable compressed video representation for improved motion modeling and scalability. (b) The proposed Snap Video FIT architecture. Given a noisy input video " + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\sigma}" + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "text", + "content": ", the model estimates the denoised video " + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{x}}_{\\sigma}" + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "text", + "content": " by recurrent application of FIT blocks. Each block reads information from the patch tokens into a small set of latent tokens on which computation is performed. The results are written to the patch tokens. Conditioning information in the form of text embeddings, noise level " + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "text", + "content": ", frame-rate " + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\nu" + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "text", + "content": " and resolution " + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 227, + 545, + 304 + ], + "type": "text", + "content": " is provided through an additional read operation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 325, + 286, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 286, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 286, + 469 + ], + "type": "text", + "content": "similarly limit possibilities for joint spatio-temporal modeling [62]. We argue that treating spatial and temporal modeling in a separable way [4, 13, 21, 48] causes motion artifacts, temporal inconsistencies or generation of dynamic images rather than videos with vivid motion. Video frames, however, contain spatially and temporally redundant content that is amenable to compression [33]. We argue that learning and operating on a compressed video representation and jointly modeling the spatial and temporal dimensions are necessary steps to achieve the scalability and motion-modeling capabilities required for high-quality video generation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "type": "text", + "content": "FITs [8] are efficient transformer-based architectures that have recently been proposed for high-resolution image synthesis and video generation. Their main idea, summarized in Fig. 3 is that of learning a compressed representation of their input through a set of learnable latent tokens and of focusing computation on this learnable latent space, allowing input dimensionality to grow with little performance penalty. First, FITs perform patchification of the input and produce a sequence of patch tokens which are later divided into groups. A set of latent tokens is then instantiated and a sequence of computational blocks is applied. Each block first performs a cross attention \"read\" operation between latent tokens and conditioning signals such as the diffusion timestep, then an additional groupwise \"read\" cross attention operation between latent and patch tokens of corresponding groups to compress patch information, applies a series of self attention operations to the latent tokens, and performs a groupwise \"write\" cross attention operation that decompresses information in the latent tokens to update the patch tokens. Finally, the patch tokens are pro" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 325, + 545, + 373 + ], + "type": "text", + "content": "jected back to the pixel space to form the output. Self conditioning is applied on the set of latent tokens to preserve the compressed video representation computed in previous sampling steps." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "text", + "content": "While promising, these architectures have not yet been scaled to the billion-parameters size of state-of-the-art U-Net-based video generators, nor they have been applied to high-resolution video generation. In the following, we highlight the architectural considerations necessary to achieve these goals. Temporal modeling is a fundamental aspect of a high-quality video generator. FITs produce patch tokens by considering three dimensional patches of size " + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "inline_equation", + "content": "T_{p} \\times H_{p} \\times W_{p}" + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "text", + "content": " spanning both the spatial and temporal dimensions. We find values of " + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "inline_equation", + "content": "T_{p} > 1" + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "text", + "content": " to limit temporal modeling performance, so we consider patches spanning the spatial dimension only. In addition, similarly to patches, FITs group patch tokens into groups spanning both the temporal and spatial dimensions, and perform cross attention operations group by group. We observe that the temporal size of each group should be configured so that each group covers all " + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 378, + 546, + 713 + ], + "type": "text", + "content": " video frames for best temporal modeling. Furthermore, videos contain more information with respect to images due to the presence of the temporal dimension, thus we increase the number of latent tokens representing the size of the compressed space in which joint spatiotemporal computation is performed. Finally, FITs make use of local layers which perform self attention operations on patch tokens corresponding to the same group. We find this operation to be computationally expensive for large amounts of patch tokens (147.456 for our largest resolution) and replace it with a feed forward module after each cross attention \"read\" or \"write\" operation." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7042" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": "Our model makes use of conditioning information represented by a sequence of conditioning tokens to control the generation process. In addition to the token representing the current " + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 72, + 287, + 179 + ], + "type": "text", + "content": ", to enable text conditioning, we introduce a T5-11B [39] text encoder extracting text embeddings from the input text. To support variable video framereates and large differences in resolution and aspect ratios in the training data, we concatenate additional tokens representing the framerate and original resolution of the current input." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "type": "text", + "content": "To generate high-resolution outputs, we implement a model cascade consisting of a first-stage model producing " + }, + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "type": "inline_equation", + "content": "36 \\times 64\\mathrm{px}" + }, + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "type": "text", + "content": " videos and a second-stage upsampling model producing " + }, + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "type": "inline_equation", + "content": "288 \\times 512\\mathrm{px}" + }, + { + "bbox": [ + 46, + 180, + 288, + 275 + ], + "type": "text", + "content": " videos. To improve upsampling quality, we corrupt the second-stage low-resolution inputs with a variable level of noise during training [21, 43] and during inference apply a level of noise to the first-stage outputs obtained by hyperparameter search." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 275, + 286, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 275, + 286, + 289 + ], + "spans": [ + { + "bbox": [ + 59, + 275, + 286, + 289 + ], + "type": "text", + "content": "We present detailed model hyperparameters in Appx. B." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 293, + 111, + 306 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 111, + 306 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 111, + 306 + ], + "type": "text", + "content": "3.5. Training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": "We train Snap Video using the LAMB [68] optimizer with a learning rate of " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "5e^{-3}" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": ", a cosine learning schedule and a total batch size of 2048 videos and 2048 images, achievable thanks to our scalable video generator architecture. We train the first-stage model over 550k steps and finetune the second-stage model on high-resolution videos starting from the first-stage model weights for 370k iterations. Following the observations in Sec 3.2, we pose " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} = s\\sqrt{T}" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": ". Considering videos with " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "T = 16" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": " frames and the original 64px resolution for which EDM was designed, we set " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} = 4" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": " for the first-stage and " + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} = 32" + }, + { + "bbox": [ + 46, + 312, + 287, + 443 + ], + "type": "text", + "content": " for the second-stage model." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 444, + 280, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 444, + 280, + 456 + ], + "spans": [ + { + "bbox": [ + 59, + 444, + 280, + 456 + ], + "type": "text", + "content": "We present training details and parameters in Appx. C." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 462, + 115, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 462, + 115, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 462, + 115, + 474 + ], + "type": "text", + "content": "3.6. Inference" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 480, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 287, + 577 + ], + "type": "text", + "content": "We produce video samples from gaussian noise and user-provided conditioning information using the deterministic sampler of [25] and our two-stage cascade. We use 256 sampling steps for the first-stage and 40 for the second-stage model, and employ classifier free guidance [19] to improve text-video alignment (see Appx. D.1) unless otherwise specified. We find dynamic thresholding [43] and oscillating guidance [21] to consistently improve quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 586, + 118, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 118, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 118, + 597 + ], + "type": "text", + "content": "4. Evaluation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 713 + ], + "type": "text", + "content": "In this section, we perform evaluation of Snap Video against baselines and validate our design choices. Sec. 4.1 introduces the employed datasets, Sec. 4.3 shows ablations of our diffusion framework and architectural choices, Sec. 4.4 quantitatively compares our method to state-of-the-art large-scale video generators and Sec. 4.5 performs qualitative evaluation. We complement evaluation by showcasing samples in the Appendix and Website." + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 72, + 544, + 126 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 544, + 126 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 544, + 126 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 544, + 126 + ], + "type": "table", + "html": "
FID ↓FVD ↓CLIPSIM ↑Train Thr. ↓Inf. Thr. ↓
U-Net 85M [10]8.2145.940.2319133.249.6
U-Net 284M [10]4.9023.760.2391230.3105.1
Snap Video FIT 500M3.0727.790.245969.523.4
Snap Video FIT 3.9B2.5112.310.2579526.0130.4
", + "image_path": "f3c4b31bcee68ccdc657a825489525d685f20d9d9faa3cf631a55f9c832117bc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 314, + 210, + 538, + 297 + ], + "blocks": [ + { + "bbox": [ + 304, + 144, + 545, + 200 + ], + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 200 + ], + "type": "text", + "content": "Table 2. Performance of different architectures and model sizes on our internal dataset in " + }, + { + "bbox": [ + 304, + 144, + 545, + 200 + ], + "type": "inline_equation", + "content": "64 \\times 36\\mathrm{px}" + }, + { + "bbox": [ + 304, + 144, + 545, + 200 + ], + "type": "text", + "content": " resolution. We observe strong performance gains with scaling and note that FITs present better performance with improved speed with respect to U-Nets. Train and inference throughputs in ms/video/GPU." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 314, + 210, + 538, + 297 + ], + "lines": [ + { + "bbox": [ + 314, + 210, + 538, + 297 + ], + "spans": [ + { + "bbox": [ + 314, + 210, + 538, + 297 + ], + "type": "table", + "html": "
σdataσinImgs. as VideosFID ↓FVD ↓CLIPSIM ↑
(i)0.51.0✓6.5839.950.2370
(ii)0.54.0✓4.0331.000.2449
(iv)1.02.0✓4.4534.890.2428
(iii)1.01/4.0X3.5024.880.2469
Ours1.04.0✓3.0727.790.2459
", + "image_path": "00876750a38d64d436c139b9d91f6936b6ad643a041013b0cec07ab09e642664.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "lines": [ + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "text", + "content": "Table 3. Ablation of different diffusion process configurations varying " + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{data}}" + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "text", + "content": ", input scaling " + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "text", + "content": ", and treatment of images as infinite-framerate videos, evaluated on our internal dataset in " + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "inline_equation", + "content": "64 \\times 36" + }, + { + "bbox": [ + 304, + 314, + 545, + 359 + ], + "type": "text", + "content": "px resolution." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 380, + 368, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 368, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 368, + 392 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 398, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 481 + ], + "type": "text", + "content": "We train our models on an internal dataset consisting of 1.265M images and 238k hours of videos, each with a corresponding text caption. Due to the difficulty in acquiring high-quality captions for videos, we develop a video captioning model that we use to produce synthetic video captions for the portion of videos in the dataset missing such annotation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 483, + 545, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 506 + ], + "type": "text", + "content": "We make use of the following datasets for evaluation which are never observed during training:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": "UCF-101 [55] is a video dataset containing 13.320 " + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "inline_equation", + "content": "320 \\times 240" + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": "px Youtube videos from 101 action categories." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "text", + "content": "MSR-VTT [65] is a dataset containing " + }, + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "inline_equation", + "content": "10.000320 \\times 240\\mathrm{px}" + }, + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "text", + "content": " web-crawled videos, each manually annotated with 20 text captions. The test set contains 2.990 videos and 59.800 corresponding captions." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 598, + 422, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 598, + 422, + 610 + ], + "spans": [ + { + "bbox": [ + 306, + 598, + 422, + 610 + ], + "type": "text", + "content": "4.2. Evaluation Protocol" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "content": "To validate the choices operated on the diffusion framework and on model architecture, present method ablations performed in " + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "inline_equation", + "content": "64 \\times 36\\mathrm{px}" + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "content": " resolution using the first-stage model only, and compute FID [18], FVD [60] and CLIPSIM [63] metrics against the test set of our internal dataset on " + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "inline_equation", + "content": "50\\mathrm{k}" + }, + { + "bbox": [ + 304, + 617, + 545, + 689 + ], + "type": "text", + "content": " generated videos." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "To evaluate our method against baselines, we follow the protocols highlighted in [4, 13, 32, 48, 62, 72] for zero-" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7043" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "shot evaluation on the UCF-101 [55] and MSR-VTT [65] datasets. We generate 16 frames videos in " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "512 \\times 288\\mathrm{px}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " resolution at 24fps for all settings. We evaluate both at the native " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "512 \\times 288\\mathrm{px}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " resolution with 16:9 aspect ratio and in the " + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "inline_equation", + "content": "288 \\times 288\\mathrm{px}" + }, + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": " square aspect ratio typically employed on these benchmarks. We note that the evaluation protocols of [4, 13, 32, 48, 62, 72] present different choices regarding the number of generated samples, distribution of class labels, choice of text prompts. We make use of the following evaluation parameters:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 287, + 240 + ], + "type": "text", + "content": "Zero-shot UCF-101 [55] We generate 10,000 videos [4, 62] sampling classes with the same distribution as the original dataset. We produce a text prompt for each class label [13] and compute FVD [60] and Inception Score [46]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 240, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 287, + 276 + ], + "type": "text", + "content": "Zero-shot MSR-VTT [65] We generate a video sample for each of the 59.800 test prompts [13, 48] and compute CLIP-FID [27] and CLIPSIM [63]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 287, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 384 + ], + "type": "text", + "content": "To provide a more complete performance assessment and compare against state-of-the-art closed-source methods not reporting results for these benchmarks, we perform a user study evaluating photorealism, video-text-alignment and, most importantly, the quantity and quality of the generated motion, important characteristics of a video generator that may signal the generation of dynamic images, i.e. videos with dim motion, or motion artifacts rather than videos with vivid and high-quality motion." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 394, + 115, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 115, + 405 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 115, + 405 + ], + "type": "text", + "content": "4.3. Ablations" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 413, + 287, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 496 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 496 + ], + "type": "text", + "content": "To evaluate the proposed FIT architecture, we consider the U-Net of [10], which we adapt to the video generation setting by interleaving temporal attention operations. We consider two U-Net variants of different capacities and a smaller variant of our FIT to evaluate the scalability of both architectures. We detail the architectures in Appx. B and show results in Tab. 2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "text", + "content": "Our 500M parameters FIT trains " + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "inline_equation", + "content": "3.31 \\times" + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "text", + "content": " faster than the baseline 284M parameters U-Net, performs inference " + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "inline_equation", + "content": "4.49 \\times" + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "text", + "content": " faster and surpasses it in terms of FID and CLIPSIM. In addition, both FITs and U-Nets show strong performance gains with scaling. Our largest FIT scales to 3.9B parameters with only a " + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "inline_equation", + "content": "1.24 \\times" + }, + { + "bbox": [ + 46, + 498, + 287, + 581 + ], + "type": "text", + "content": " increase in inference time with respect to the 284M U-Net." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "To evaluate the choices operated on our diffusion framework, we ablate different configurations of the diffusion process using our 500M FIT architecture. We produce the following variations: (i) the original EDM framework, (ii) our scaled diffusion framework with EDM " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{data}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": ", (iii) our framework with a reduced value of " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": ", (iv) our framework with images not treated as infinite-frame-rate videos. Our framework improves over EDM under all metrics (i) and shows benefits in setting " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{data}} = 1" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": ", an effect that we attribute to the creation of a training target and loss weighting matching the widely used " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "-prediction formulation of" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 326, + 70, + 528, + 194 + ], + "blocks": [ + { + "bbox": [ + 326, + 70, + 528, + 194 + ], + "lines": [ + { + "bbox": [ + 326, + 70, + 528, + 194 + ], + "spans": [ + { + "bbox": [ + 326, + 70, + 528, + 194 + ], + "type": "table", + "html": "
FVD ↓FID ↓IS ↑
CogVideo [23] (Chinese)751.3-23.55
CogVideo [23] (English)701.6-25.27
MagicVideo [72]655--
LVDM [17]641.8--
Video LDM [4]550.6-33.45
VideoFactory [62]410.0--
Make-A-Video [48]367.2-33.00
PYoCo [13]355.2-47.46
Snap Video (288 × 288 px)260.139.038.89
Snap Video (512 × 288 px)200.228.138.89
", + "image_path": "0bbcf0ef03f6ba5b256263e96334419081db5d9d109e17325f9950d1bb736b85.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 233, + 547, + 376 + ], + "blocks": [ + { + "bbox": [ + 326, + 211, + 524, + 221 + ], + "lines": [ + { + "bbox": [ + 326, + 211, + 524, + 221 + ], + "spans": [ + { + "bbox": [ + 326, + 211, + 524, + 221 + ], + "type": "text", + "content": "Table 4. Zero-shot evaluation results on UCF101 [55]." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 233, + 547, + 376 + ], + "lines": [ + { + "bbox": [ + 307, + 233, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 307, + 233, + 547, + 376 + ], + "type": "table", + "html": "
CLIP-FID ↓FVD ↓CLIPSIM ↑
NUWA [64] (Chinese)47.68-0.2439
CogVideo [23] (Chinese)24.78-0.2614
CogVideo [23] (English)23.59-0.2631
MagicVideo [72]-998-
LVDM [17]--0.2381
Latent-Shift [2]15.23-0.2773
Video LDM [4]--0.2929
VideoFactory [62]--0.3005
Make-A-Video [48]13.17-0.3049
PYoCo [13]9.73--
Snap Video (288 × 288 px)8.48110.40.2793
Snap Video (512 × 288 px)9.35104.00.2793
", + "image_path": "c38176274d080f1c4a77ac21fbc4cff6e1dcc85b5daf60613a0f37329beea830.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 322, + 393, + 528, + 404 + ], + "lines": [ + { + "bbox": [ + 322, + 393, + 528, + 404 + ], + "spans": [ + { + "bbox": [ + 322, + 393, + 528, + 404 + ], + "type": "text", + "content": "Table 5. Zero-shot evaluation results on MSR-VTT [65]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 424, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 424, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 305, + 424, + 545, + 461 + ], + "type": "text", + "content": "Salimans et al. [45] (see Tab. 1). Using " + }, + { + "bbox": [ + 305, + 424, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\sigma_{\\mathrm{in}} < s\\sqrt{T}" + }, + { + "bbox": [ + 305, + 424, + 545, + 461 + ], + "type": "text", + "content": " (see Sec. 3.2) impairs performance (iii). Finally, treating images as infinite-frame-rate videos consistently improves FID." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 468, + 441, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 441, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 441, + 480 + ], + "type": "text", + "content": "4.4. Quantitative Evaluation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 486, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 652 + ], + "type": "text", + "content": "We perform comparison of Snap Video against baselines on the UCF101 [55], and MSR-VTT [65] datasets respectively in Tab. 4 and Tab. 5. FID and FVD video quality metrics show improvements over the baselines which we attribute to the employed diffusion framework and joint spatiotemporal modeling performed by our architecture. On UCF101, our method produces the second-best IS of 38.89, demonstrating good video-text alignment. While our method surpasses Make-A-Video [48] on UCF101, we note that it produces a lower CLIPSIM score on MSR-VTT. We attribute this behavior to the use of T5 [39] text embeddings in place of the commonly used CLIP [38] embeddings which were observed [43] to produce higher text-image alignment despite similar CLIPSIM." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "To provide a comprehensive evaluation we run a user study to evaluate photorealism, video-text alignment, quantity of motion and quality of motion, important aspects of a video generator. Three publicly-accessible state-of-the-art video generators are considered: Gen-2 [11], PikaLabs [1]" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7044" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 294, + 272 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 294, + 272 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 294, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 294, + 272 + ], + "type": "image", + "image_path": "2fa82ded38c5ae7b26fc3839ffcf7eca9c46cddc346d8f0d30486611bcb9a4c6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 278, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 278, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 547, + 313 + ], + "type": "text", + "content": "Figure 4. Qualitative results comparing Snap Video to state-of-the-art video generators on publicly available samples. While baseline methods present motion artifacts (top-left, top-right, bottom-right) or produce dynamic images (bottom-left), our method produces more temporally coherent motion. Best viewed in the Website." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 545, + 272 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 545, + 272 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 545, + 272 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 545, + 272 + ], + "type": "image", + "image_path": "382a92480806ce18863c9abc916323b1b4c2e639fad98e114ce94840ca3bda3c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 331, + 287, + 383 + ], + "blocks": [ + { + "bbox": [ + 48, + 331, + 287, + 383 + ], + "lines": [ + { + "bbox": [ + 48, + 331, + 287, + 383 + ], + "spans": [ + { + "bbox": [ + 48, + 331, + 287, + 383 + ], + "type": "table", + "html": "
PhotorealismVideo-Text Align.Mot. Quant.Mot. Qual.
Gen-2 [11]44.381.096.078.7
PikaLab [1]61.580.389.270.5
Floor33 [17]76.380.988.079.1
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We filter a set of 65 prompts from [31] describing scenes with vivid motions, and generate a video for each method with default options. We ask the participants to express preference between paired samples from Snap Video and each baseline, gathering votes from 5 users for each sample. Results are shown in Tab. 6 and video samples provided along with the employed prompt list in Appx. D.2 and in the Website. Our method produces results with photorealism comparable to Gen-2, while surpassing PikaLab and Floor33, and outperforms all baselines with respect to video-text alignment. Most importantly, we note that baselines often produce dynamic images, i.e. videos with dim motion, or videos with motion artifacts, a finding we attribute to the challenges in modeling large motion. In contrast, our method, thanks to the joint spatiotemporal modeling approach, produces vivid and high-quality motion as shown by the motion metrics." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 659, + 176, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 176, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 176, + 672 + ], + "type": "text", + "content": "4.5. Qualitative Evaluation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "In this section, we perform qualitative evaluation of our framework. In Fig. 4, Appx. D.3 and the Website, we present qualitative results comparing our method to state-" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 333, + 547, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 441 + ], + "type": "text", + "content": "of-the-art generators [4, 13, 21, 48] on samples publicly released by the authors. While such prompts might have been selected to highlight strengths of the baselines, our method produces more photorealistic samples aligned to the text descriptions. Most importantly, our samples present vivid and high-quality motion avoiding flickering artifacts that are present in the baselines due to temporal inconsistencies. We accompany qualitative evaluation with a user study performed on the same set of samples in Appx. D.2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 472, + 384, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 384, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 384, + 484 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "In this work, we highlight the shortcomings of diffusion processes and architectures commonly used in text-to-video generation, and systematically address them by treating videos as first-class citizens. First, we propose a modification to the EDM [25] diffusion framework for the generation of high-resolution videos and treat images as high frame-rate videos to avoid image-video modality mismatches. Second, we replace U-Nets [41] with efficient transformer-based FITs [8] which we scale to billions of parameters. Thanks to their learnable compressed representation of videos, they significantly improve training times, scalability and performance with particular regards to temporal consistency and motion modeling capabilities due to the joint spatiotemporal modeling on the compressed representation. When evaluated on UCF101 [55] and MSR-VTT [65] and in user studies, Snap Video attains state-of-the-art performance with particular regard to the quality of the modeled motion." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7045" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "type": "text", + "content": "[1] Pika lab discord server. https://www.pika.art/.Accessed: 2023-11-01. 2, 7, 8, 3, 6" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 287, + 158 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 287, + 158 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 287, + 158 + ], + "type": "text", + "content": "[2] Jie An, Songyang Zhang, Harry Yang, Sonal Gupta, Jia-Bin Huang, Jiebo Luo, and Xi Yin. 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Magicvideo: Efficient video generation with latent diffusion models. arXiv, 2023. 2, 3, 6, 7" + } + ] + } + ], + "index": 16 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7048" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_content_list.json b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ce8cb20e027f21885c9458be11a702a0a3f488e8 --- /dev/null +++ b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_content_list.json @@ -0,0 +1,1491 @@ +[ + { + "type": "text", + "text": "Snapshot Lidar: Fourier embedding of amplitude and phase for single-image depth reconstruction", + "text_level": 1, + "bbox": [ + 96, + 130, + 872, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sarah Friday $^{1}$ , Yunzi Shi $^{1}$ , Yaswanth Cherivirala, Vishwanath Saragadam $^{2}$ , Adithya Pediredla $^{1}$ $^{1}$ Dartmouth College, $^{2}$ University of California, Riverside", + "bbox": [ + 111, + 202, + 854, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e0133742f106780c0d8fced97ce5f8dae823f929d003a9c2e6b20c16b53bc3c1.jpg", + "image_caption": [ + "Figure 1. We propose a novel snapshot Lidar imaging system that is inspired by off-axis holography techniques. $(1^{\\mathrm{st}}$ col.) Off-axis holography uses oblique illumination to separate the hologram and its twin in Fourier space. $(2^{\\mathrm{nd}}$ col.) We leverage the rolling-shutter effect of amplitude modulated continuous wave time-of-flight (AMCW-ToF) cameras to emulate the off-axis principle, thereby separating the time-of-flight hologram and its twin in Fourier space. $(3^{\\mathrm{rd}}$ col.) The conventional operation of AMCW-ToF Lidars requires four measurements, whereas our technique is $4\\mathrm{x}$ faster, improving both the data bandwidth and temporal resolution. $(4^{\\mathrm{th}}$ col.) Reconstructed phase (that encodes depth) from measurements—The reconstructions are quite similar even with $4\\mathrm{x}$ fewer measurements." + ], + "image_footnote": [], + "bbox": [ + 81, + 290, + 890, + 506 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 618, + 313, + 633 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras are finding applications as flash Li-dars in autonomous navigation, robotics, and AR/VR applications. A conventional CW-ToF camera requires illuminating the scene with a temporally varying light source and demodulating a set of quadrature measurements to recover the scene's depth and intensity. Capturing the four measurements in sequence renders the system slow, invariably causing inaccuracies in depth estimates due to motion in the scene or the camera. To mitigate this problem, we propose a snapshot Lidar that captures amplitude and phase simultaneously as a single time-of-flight hologram. Uniquely, our approach requires minimal changes to existing CW-ToF imaging hardware. To demonstrate the efficacy of the proposed system, we design and build a lab prototype, and evaluate it under varying scene geometries, illumina", + "bbox": [ + 75, + 659, + 472, + 900 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion conditions, and compare the reconstructed depth measurements against conventional techniques. We rigorously evaluate the robustness of our system on diverse real-world scenes to show that our technique results in a significant reduction in data bandwidth with minimal loss in reconstruction accuracy. As high-resolution CW-ToF cameras are becoming ubiquitous, increasing their temporal resolution by four times enables robust real-time capture of geometries of dynamic scenes.", + "bbox": [ + 496, + 619, + 895, + 755 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 784, + 632, + 800 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras, also known as correlation-based time-of-flight or indirect time-of-flight cameras, are used as flash Lidars to compute scene depth, and are used in autonomous navigation, robotics [6, 13], and augmented reality [8]. AMCW-ToF cameras operate by projecting a", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25203", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/36d7375630fd731530dac31a473d82fc97cd2e08fa355ff169bb9b8ae57904b7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
illuminationreferencephysics
holographycoherent beamplanar beamoptical interference
off-axiscoherent beamtilted beamoptical interference
CW-ToFAMCWelectronic shutterelectronic multiplication
proposedAMCWrolling shutterelectronic multiplication
", + "bbox": [ + 78, + 88, + 470, + 232 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Principles of holography, off-axis holography, CW-ToF, and proposed snapshot CW-ToF. We draw parallels between off-axis holographic setup, and our proposed Fourier embedded ToF, that allow us to show that using a rolling-shutter sensor and varying the reference phase during CW-ToF acquisition results in a snapshot capture of the \"ToF hologram\" that contains both the amplitude and depth (encoded in phase) of the scene.", + "bbox": [ + 75, + 242, + 468, + 339 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "temporally varying (often a sinusoidal) light source, and then correlating it on the sensor side with an appropriate (also often a sinusoid) decoding function. Depth is encoded in the phase of the measurements, and hence up to four measurements (quadrature) are required to robustly estimate the depth and intensity of the scene. These quadrature measurements are captured by temporal multiplexing, which invariably leads to lower frame rates and suffers from motion artifacts.", + "bbox": [ + 75, + 368, + 468, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inspired by snapshot off-axis holography techniques, we propose a snapshot CW-ToF imaging technique that measures amplitude and depth using a single capture. The key observation is that by defining the time-of-flight hologram as the complex sinusoid whose amplitude and phase are proportional to the intensity and depth of the scene, we can draw parallels between holography and CW-ToF imaging techniques. This novel formulation of the ToF hologram enables us to translate off-axis techniques to CW-ToF imaging. In particular, by using rolling-shutter CW-ToF sensors [1] and spatially varying the reference phase of the coded exposure, we can emulate the off-axis holography effect and recover the complex-valued ToF hologram. In Tab. 1, we highlight the similarities and differences between holography, off-axis holography, CW-ToF, and the proposed imaging techniques.", + "bbox": [ + 75, + 505, + 468, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve snapshot depth imaging, we leverage the image formation model of CW-ToF cameras, and demonstrate our modification to enable the capture of a ToF hologram with unipolar (all-positive decoding function) and bipolar (positive and negative decoding function) codes. We then show analytical and computational techniques to recover amplitude and depth from a rolling-shutter image and the need for optical prefiltering to prevent aliasing and noise folding.", + "bbox": [ + 75, + 748, + 468, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We design and build a hardware setup built in the lab", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with a Melexis 75027 device with region-of-interest support and a galvanometer to emulate the rolling-shutter effect. Using this device, in Sec. 6, we demonstrate that the proposed technique reduces data bandwidth and improves frame rate on various scenes containing diffuse, specular, and refractive objects. The proposed technique is robust to dead and saturated pixels, thereby enabling depth imaging with slightly faulty sensors, and extremely bright settings. We carefully evaluate design parameters including prefiltering window size, and spatial phase variation rate, and provide an experimentally optimal set of values that are agnostic to scene conditions. We empirically show that the proposed Fourier-based reconstruction technique is superior to the standard N-bucket technique for reconstruction.", + "bbox": [ + 496, + 90, + 890, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 314, + 640, + 329 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Continuous wave time-of-flight cameras. CW-ToF cameras measure depth at each spatial pixel with a temporally modulated light source. The intensity of the scene is encoded in the amplitude, and depth in the phase, of the measurements. Typically four or more images, with different phases, are required to recover both amplitude and depth. These four measurements are obtained either with a spatially multiplexed sensor (similar to a Bayer pattern), or with sequential measurements [12]. Spatial multiplexing results in severe aliasing artifacts, and is inherently expensive and cumbersome to manufacture. In contrast, sequential measurements invariably result in motion artifacts when capturing dynamic scenes.", + "bbox": [ + 496, + 339, + 890, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Advances in CWToF sensing With the increasing number of practical applications for CWToF, work has been done to enhance its capabilities and mitigate its limitations. CS-ToF [20] is a compressive ToF imaging architecture aimed at overcoming sensor resolution limitations. As compressive sensing relies on the assumption of a linear measurement process for high resolution image estimation, CS-ToF uses a phasor representation inspired by Gupta [9] and O'Toole [25] of the ToF output to create a linear model between the scene and ToF measurements. In a process similar to single pixel imaging, laser light is reflected off of an object onto a high resolution digital micro-mirror device (DMD), and then relayed onto a lower resolution ToF sensor. By changing the DMD codes across multiple exposures, CS-ToF performs spatiotemporal multiplexing of the scene's amplitude and phase; however, sacrificing temporal resolution for spatial resolution. CWToF has also been combined with other modalities such as spectrum [27], light transport [24, 31], and light fields [15] that have significantly expanded the applications of CWToF cameras. Nevertheless, it is worth noting that there are few, if any, approaches that capture CWToF data in a snapshot manner, that is crucial for dynamic scenes.", + "bbox": [ + 496, + 553, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25204", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Superheterodyned interferometry. A related technology that enables snapshot ToF sensing is superheterodyned interferometric time-of-flight (SH-ToF) [21, 22], where two closely spaced illumination wavelengths combine to produce a much larger (heterodyned) synthetic wavelength. This approach however still requires capturing two separate images (one with each wavelength) to produce the final superheterodyned measurement. Recent work by Ballester et al. [3] demonstrated that SH-ToF can be combined with the off-axis holography to obtain a snapshot ToF imaging system. We next briefly discuss off-axis holography to understand its relevance to ToF sensing.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Off-axis holography Off-axis holography [7, 19] is a widely known imaging technique for reconstructing the amplitude $(E_{s}(x,y))$ and phase $(\\phi_s(x,y))$ of a hologram with a single measurement. The experimental setup schematic is shown in the first column of Fig. 1. The measurement by the camera is given by", + "bbox": [ + 75, + 290, + 472, + 381 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I = \\left| E _ {s} (x, y) e ^ {- \\phi_ {s} (x, y)} + E _ {r} e ^ {- k \\sin (\\theta) x} \\right| ^ {2} \\\\ = \\left| E _ {s} (x, y) \\right| ^ {2} + \\left| E _ {r} \\right| ^ {2} + E _ {r} ^ {*} E _ {s} (x, y) e ^ {k \\sin (\\theta) x - \\phi_ {s} (x, y)} \\\\ + E _ {r} E _ {s} ^ {*} (x, y) e ^ {- k \\sin (\\theta) x + \\phi_ {s} (x, y)} \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 388, + 468, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Off-axis holography embeds the hologram $(E_{s}(x,y)e^{-\\phi_{s}(x,y)})$ and its twin $(E_{s}^{*}(x,y)e^{\\phi_{s}(x,y)})$ separately in the Fourier domain allowing us to recover the hologram computationally. Ballester et al. [2] showed that off-axis techniques can be used in synthetic wavelength interferometry. Specifically, the system consisted of a colocated, dual wavelength illumination source, and two, spatially separated reference beams. The separated location implied that the phasor information was encoded in different parts of the Fourier spectrum, enabling a simple frequency domain post-processing algorithm to estimate depth information with a single image. Our technique is inspired by off-axis holography. Two key observations that enable our technique are (i) expressing the time-of-flight image formation model with complex sinusoids allows us to draw parallels between holography and AMCW-ToF (ii) the rolling-shutter effect allows us to emulate off-axis technique.", + "bbox": [ + 75, + 459, + 472, + 732 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Applications of CW-ToF cameras. Beyond depth imaging, CW-ToF cameras enable a plethora of important applications in imaging. For example, Callenberg et al. [4] showed that a CW-ToF camera can enable difference imaging, that is often useful for implementing convolutional operations within sensors. Achar et al. [1] showed that ToF sensors can be used to tease out sub-surface features through epipolar gating. Similarly, Naik et al. [24] and Kadambi et al. [16] showed that a light transport matrix-based formulation of ToF measurements enabled measur", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/858b901540602697be8862ab2f107e769bd32009fed8a8a8ecd6cb7b20ba7b2c.jpg", + "image_caption": [ + "Figure 2. CW-ToF imaging systems. CW-ToF cameras use high-frequency illumination sources and exposure codes to indirectly measure the object's depth. The measurement is the product of the delayed illumination signal and programmatically phase-shifted exposure code. The delay encodes object depth and is recoverable by taking multiple measurements with varying phase-shift $(\\theta)$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 90, + 890, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing multipath interferences, that are key to measuring geometric properties of complex objects like metal and glass. Our proposed work enables a similar slew of applications beyond depth imaging, including sub-surface imaging and multipath interference reduction (via epipolar gating).", + "bbox": [ + 496, + 383, + 890, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Technical Background", + "text_level": 1, + "bbox": [ + 500, + 470, + 714, + 488 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, an amplitude-modulated continuous-wave time-of-flight camera (AMCW-ToF) has an illumination source whose amplitude $(e(t))$ varies over time at several tens of MHz. While these amplitude variations are typically sinusoidal, other modulations have been successfully demonstrated in the past [9-11] for various applications. The light received $(r(t))$ at the sensor is attenuated and delayed based on the light transport of the scene $(r(t) = Ae(t - \\tau))$ , where $\\tau$ is the total time-of-travel of the light beam. Assuming a collocated light source and sensor and no multi-bounce paths, $\\tau = 2d\\omega /c$ , where $d$ is the distance to the object, $\\omega$ is the modulation frequency, and $c$ is the speed of light. The sensor temporal exposure (s(t)) is also modulated, typically as a square wave (unipolar or bipolar) with the same frequency as the illumination. Recent sensors mostly use bipolar coding with a two-bucket architecture [30], and the exposure duration is approximated with a sinusoidal modulation. The measurement by the sensor is given by", + "bbox": [ + 496, + 496, + 890, + 784 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} m _ {\\theta} = \\frac {1}{T} \\int_ {t = 0} ^ {T} A r (t) s (t) d t \\\\ = \\frac {A}{T} \\int_ {t = 0} ^ {T} \\sin (\\omega t + \\phi) \\sin (\\omega t + \\theta) d t = \\frac {A}{2} \\cos (\\theta - \\phi). \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 790, + 890, + 876 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most hardware implementations of CWToF Lidar mea", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25205", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sure four images $m_0, m_{\\pi/2}, m_\\pi$ , and $m_{3\\pi/2}$ and compute amplitude and phase as", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA = 2 \\sqrt {(m _ {0} - m _ {\\pi}) ^ {2} + (m _ {\\pi / 2} - m _ {3 \\pi / 2}) ^ {2}}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 127, + 416, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi = \\arctan \\frac {m _ {\\pi / 2} - m _ {3 \\pi / 2}}{m _ {0} - m _ {\\pi}}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 154, + 468, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The quadrature technique is also extended to the N-tap technique [28] by taking $\\mathbf{N}$ measurements corresponding to $\\theta = \\{0, 2\\pi / N, 4\\pi / N, c \\dots, 2\\pi (N - 1) / N\\}$ and computing amplitude and phase as:", + "bbox": [ + 76, + 188, + 468, + 250 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA = \\sqrt {\\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2} + \\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2}}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 255, + 475, + 301 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi = \\arctan \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} / \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 305, + 468, + 345 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unlike these techniques, we reconstruct amplitude and phase using a single image, which we discuss next.", + "bbox": [ + 76, + 349, + 468, + 381 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Proposed Technique: Snapshot CWTof", + "text_level": 1, + "bbox": [ + 76, + 391, + 431, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The key idea for measuring amplitude and depth using a single image is to spatially vary the phase $\\theta$ linearly along rows or columns during the exposure. We can achieve this spatial variation with simple hardware modifications by either (1) changing the existing hardware design with different exposure phase offsets per row/column, (2) using a rolling-shutter camera and changing the phase offset of either the illumination or sensor during each row capture, or (3) using a fast line sensor (or hardware region-of-interest supporting camera) and scanning the scene line by line with a Galvanic mirror while changing the phase offset of each line. We used the last alternative in this paper, as the Melexis 75027 supports hardware ROI [23].", + "bbox": [ + 75, + 417, + 468, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To understand how linearly varying $\\theta$ embeds both amplitude and phase in the captured image, we follow the notation from O'Toole et al. [26], Li et al. [21], and Gupta et al. [9] and represent the amplitude and phase images with complex sinusoidal notation as $I(x,y) = A(x,y)e^{-j2d\\omega /c}$ and the Fourier Transform of this sinusoid as $\\mathcal{I}(\\omega_x,\\omega_y)$ . For brevity, we define $\\phi = 2d\\omega /c$ as the phase shift of the illumination signal. Varying $\\theta$ linearly during the measurement results in", + "bbox": [ + 75, + 614, + 468, + 748 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} m _ {\\theta = k x} (x, y) = \\frac {A (x , y)}{2} \\cos (k x - \\phi (x, y)) \\\\ = \\frac {A (x , y)}{4} \\left(e ^ {j (k x - \\phi (x, y))} + e ^ {- j (k x - \\phi (x, y))}\\right) \\tag {5} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 752, + 468, + 827 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Taking the Fourier transform on both sides, we get", + "bbox": [ + 76, + 833, + 411, + 848 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {F} _ {m _ {k x}} \\left(\\omega_ {x}, \\omega_ {y}\\right) = \\frac {1}{4} \\left(\\mathcal {I} \\left(\\omega_ {x} - k, \\omega_ {y}\\right) + \\mathcal {I} ^ {*} \\left(k - \\omega_ {x}, - \\omega_ {y}\\right)\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 853, + 468, + 895 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which is similar to the off-axis holography Eq. (1). Therefore, we will refer to the complex sinusoidal notation $(I(x,y))$ as the ToF hologram and its complex conjugate $(I^{*}(x,y))$ as the ToF twin.", + "bbox": [ + 498, + 90, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As depicted in Fig. 3, to recover the ToF hologram from the image captured by varying $\\theta$ linearly, we take the Fourier transform of the measured image, filter the ToF twin, right shift the ToF hologram, and compute the inverse Fourier transform. The amplitude and phase of the inverse Fourier transform result are the amplitude and phase of the scene.", + "bbox": [ + 496, + 152, + 890, + 255 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Extension to unipolar codes. Most recent ToF sensors use a two-bucket architecture to suppress background illumination; hence, the codes are bipolar. However, our technique is also amenable to unipolar-coded time-of-flight cameras and imperfect two-bucket architecture cameras. In this case, the measurement model becomes", + "bbox": [ + 496, + 273, + 890, + 363 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nm _ {\\theta} = \\frac {A}{2} \\cos (\\theta - \\phi) + a. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 369, + 890, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $a$ is proportional to the ambient background light intensity. In this case, the Fourier transform has a DC component that can be filtered out along with the ToF twin.", + "bbox": [ + 496, + 402, + 890, + 449 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Aliasing, noise folding, and prefiltering. From Fig. 3 (b), we notice that the ToF hologram and twin overlap in the Fourier domain. This overlap results in aliasing, where the high-frequency content of the ToF twin may appear as low-frequency content of the ToF hologram, and noise folding, where the twin's noise folds into the ToF hologram's noise.", + "bbox": [ + 496, + 465, + 890, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To mitigate aliasing and noise folding, we optically filter the high-resolution ToF hologram before the linear phase shifting and measurement. In the hardware implementation, we achieve this by simply defocusing the imaging lens in front of the sensor. This simple blurring operation reduces aliasing and noise folding artifacts (Fig. 3 (d, e)).", + "bbox": [ + 496, + 571, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, while the proposed snapshot Lidar technique can capture amplitude and phase with a single image, it does so by sacrificing spatial resolution for temporal resolution. As spatial resolutions of imaging sensors keep increasing (compare PMD vs DME660 vs. Melexis) due to better fabrication techniques, trading spatial resolution for improving temporal resolution is arguably more useful.", + "bbox": [ + 496, + 662, + 890, + 768 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Phase noise. As with any optical measurements, the recovered phase will have noise due to shot noise in the measurements. This shot noise is present even for the standard N-bucket technique [17, 18]. The standard deviation of the phase noise for the snapshot technique is", + "bbox": [ + 496, + 786, + 890, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {\\phi} ^ {2} \\approx \\frac {\\partial \\phi}{\\partial m _ {k x}} m _ {k x} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 866, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25206", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/82f479d141147271f6a5fef43b6752e959fa1bbd78127fcf9202efa2fe8bfd05.jpg", + "image_caption": [ + "(a) snapshot image" + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 250, + 263 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bb781112949977db1a30be2964b570d37f9ae631392b586de5bcf3fcdf676fc3.jpg", + "image_caption": [ + "(b) Fourier transform" + ], + "image_footnote": [], + "bbox": [ + 251, + 90, + 401, + 263 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0116208e53f9efb098138a9b858810ddb3c5756a52da370617890f66057846ed.jpg", + "image_caption": [ + "(c) filtered and shifted", + "Figure 3. Snapshot CWToF decoding, and effect of prefiltering. (a) captured snapshot CW-ToF image. (b) Fourier transform of snapshot image. (c) We filter out the twin and frequency shift the hologram in the Fourier domain to recover the ToF hologram. (d) We reconstruct the phase by computing the phase of the inverse Fourier transform of (c). (top row vs. bottom row) We prefilter the ToF hologram using a defocused imaging lens, which can decrease the overlap between the hologram and its twin. The prefiltering decreases aliasing and noise folding, resulting in a 3dB SNR gain ( $2 \\times$ smaller phase error). (e) zoomed-in offsets. (left) Without prefiltering, the high-frequency phase noise of the twin shows up as the low-frequency phase noise. (right) aliasing decreases with prefiltering." + ], + "image_footnote": [], + "bbox": [ + 403, + 90, + 552, + 263 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9eb1412beb1e5884ffd91c73034ea91a2485e48bd85359707b0260488fa7b931.jpg", + "image_caption": [ + "(d) recovered phase" + ], + "image_footnote": [], + "bbox": [ + 555, + 90, + 705, + 263 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/06156c8f4d30381cc2babfc53d103a89f08a5d6db9024d4ac46cb8597556ef80.jpg", + "image_caption": [ + "(e) zoomed in offsets" + ], + "image_footnote": [], + "bbox": [ + 705, + 88, + 885, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\phi$ is explicitly expressed as", + "bbox": [ + 76, + 390, + 303, + 406 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\phi (x, y) = \\arctan \\left(\\frac {m _ {k x} (x , y) \\sin (k x) * \\operatorname {s i n c} (k x)}{m _ {k x} (x , y) \\cos (k x) * \\operatorname {s i n c} (k x)}\\right).\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 412, + 452, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $\\circledast$ is spatial convolution. We show the derivation in the supplementary material. An analytical comparison of the noise variance between the N-bucket and snapshot techniques is not feasible. Instead, in Sec. 6, we show empirical comparison and show that the snapshot phase measurement does not result in additional phase noise.", + "bbox": [ + 75, + 454, + 470, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experimental setup", + "text_level": 1, + "bbox": [ + 76, + 558, + 266, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To implement our method, we use the EVK75027-110-940-2 evaluation kit (EVK) by Melexis which uses diffused $940\\mathrm{nm}$ VCSEL diodes for illumination and a Melexis 75027 CWToF sensor. While the sensor is a global shutter, we can create the rolling shutter effect by taking advantage of the sensor's hardware programmable ROI to reduce the per-frame capture/readout to a single row.", + "bbox": [ + 75, + 583, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For our experiments, we mount the EVK75027 to a linear 3D stage and carefully align the view to a set of 2-axis galvanic mirrors (GVS012) from Thorlabs. Then, we reduce the ROI of the camera to a single line, and steer the view of the galvos with a DAQ. Additionally, we separated the illumination board from the rest of the EVK and mounted it on top of the galvanic mirrors for approximate collocation of light source and apparent camera location. The MLX75027 module contained a firmware lock on the frame rate at 100 fps, severely limiting our capture speed when the ROI is reduced to only a single line. However, our setup demonstrates a proof-of-concept, and future versions of Melexis cameras without a firmware lock will enable a real-time operation.", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "One way to emulate snapshot measurements from our setup is to capture multiple images with varying phases and appropriately select the rows/columns in the image. In practice, we found it to be significantly simpler and convenient to conduct most of our experiments. In Fig. 4, we show the hardware prototype with fast-scanning galvonic mirrors. Additionally in Fig. 5, we compare results from an emulated versus hardware implemented snapshot capture and notice that the techniques result in the same amplitude and phase estimates. For more details about the hardware prototype and emulation method, we refer the reader to the supplemental material.", + "bbox": [ + 496, + 390, + 893, + 570 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 500, + 579, + 633, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we use the hardware setup and emulation technique described in Sec. 5 to evaluate the proposed snapshot technique systematically. We show that (1) prefiltering improves signal-to-noise ratio (SNR) and prefiltering with cylindrical lenses is better than regular lenses; (2) the optimal phase variation rate is $(k = \\frac{\\pi}{2}\\mathrm{line}^{-1})$ ; (3) the Fourier technique is superior to the N-bucket technique for snapshot images; (4) the snapshot technique does not add any additional noise and (5) is robust to saturated and dead pixels; (6) rotating the phase variation (by rotating the camera itself) decreases aliasing. In the supplementary, we show extended results and a comparison with the dual phase mode of the epc660 camera. We share our code on GitHub.", + "bbox": [ + 496, + 599, + 892, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimal prefiltering kernel. As mentioned in Sec. 4, prefiltering reduces aliasing and noise folding artifacts. As aliasing and noise folding occur in the direction of the rolling shutter, blurring the ToF hologram only in the rolling shutter direction is better than isotropic blurring as shown in Fig. 6. We can implement hardware anisotropic blurring by", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25207", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/177cc8cf5178c9d80f3da230e8ba5f6a36d86ed42c212337a748dc69c859c7d6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 90, + 250, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/548834f57c7c163227eabea55c2d0433f86eb4e93fe6ea77bbad2e737fef1e3b.jpg", + "image_caption": [ + "camera components" + ], + "image_footnote": [], + "bbox": [ + 96, + 260, + 120, + 275 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4781d74b6cf3ced22fb6781c5ae156e0e529d0f48649239e66fe28fae44228e1.jpg", + "image_caption": [ + "galvo/synchronization components" + ], + "image_footnote": [], + "bbox": [ + 256, + 90, + 421, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/965c574f4f684df40ca0ce49fd399496c1fb82bbec46a58cf0e81d159bca0eb0.jpg", + "image_caption": [ + "a. hardware setup" + ], + "image_footnote": [], + "bbox": [ + 274, + 258, + 299, + 273 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5ebd0578bf192c7f07b226dfb7482e868403baf62e87d563b8bb52b068800a89.jpg", + "image_caption": [ + "b. emulation method" + ], + "image_footnote": [], + "bbox": [ + 433, + 140, + 890, + 255 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bc1a395ae3ab4ce0a6e9b1fe922696bd070b616be4805467decec7f880c82f46.jpg", + "image_caption": [ + "Figure 4. Lab prototype, and rolling shutter encoding scheme. (a) Rolling shutter hardware prototype with the camera components outlined in yellow and galvonic mirrors/synchronization hardware outlined in blue. (b) Compositing quadrature images to create an emulated rolling shutter snapshot." + ], + "image_footnote": [], + "bbox": [ + 78, + 369, + 465, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "using a defocused cylindrical lens. Note that the optimal kernel for prefiltering is a 1D sinc function in the spatial domain (corresponding to eliminating all the overlapping frequencies). However, that is not physically possible. Designing the optimal optically-realizable kernel is beyond the scope of this paper.", + "bbox": [ + 75, + 686, + 468, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Assuming a 1D-Gaussian prefiltering kernel, we computed the effect of blur kernel size (measured in standard deviation $\\sigma$ ) on the phase reconstruction accuracy. As shown in Fig. 7 (a), for all values of $k$ , the SNR initially improves when $\\sigma$ is increased and then decreases showing that an optimal blur kernel size exists. This phenomenon occurs as prefiltering initially reduces the overlap between the ToF hologram and the twin but later reduces the frequency con", + "bbox": [ + 75, + 779, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/89fb19e5ccee86a86e4eeb78d269f1859c05757e13efa86547e49f38ece1c33d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 369, + 890, + 474 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ffefeba3148c77b7c91ea04d0df1f5f4d55ef5fd450d36d43ccc05e6ad93d1a8.jpg", + "image_caption": [ + "Figure 5. Advantages of emulated snapshot capture. Amplitude and depth reconstructed by snapshot data captured with emulations (this paper) vs. single line ROI (ideal optical setup) and galvanic mirrors. The emulated measurements and the reconstructed phase are similar to the full prototype. We hence demonstrated all experiments with an emulated setup, as it enables a faithful evaluation of a true snapshot system.", + "Figure 6. Robustness to noise due to prefiltering. Prefiltering reduces aliasing and noise folding artifacts to improve the reconstruction quality. Compared to the 2D-blur kernel, the 1D-blur kernel in the direction of rolling shutter direction results in a significantly higher-quality reconstruction. Since the ToF hologram and twin overlap occur only in the rolling shutter direction, a 1D blur kernel preserves the spatial frequencies in the direction orthogonal to rolling shutter." + ], + "image_footnote": [], + "bbox": [ + 500, + 477, + 887, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tent in the captured ToF hologram.", + "bbox": [ + 500, + 820, + 728, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Optimal phase variation rate $k$ . In Fig. 7 (b), we plot optimal $\\sigma$ value as a function of $R = 2\\pi / k$ , which represents the average number of rows required before the $\\theta$", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25208", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/24c1aa4ee3c15c6cc8289286a30a8e365a0c59ce7612da9cda2d7f4c08b2c4c5.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 264, + 237 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/78cf7a686275308789645f8694480559643bafe0490e3d32daf380819851548b.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 261, + 90, + 467, + 238 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d55e5df3a4e1e5e0b2172ab01c90a51e81106aa340e36f8b53615c292b00c8b.jpg", + "image_caption": [ + "Figure 7. Optimal prefilter size and phase variation rate. (a) We show the effect of the standard deviation of the blur kernel (blur kernel size) on the phase reconstruction accuracy for various phase variation rates $(k)$ . The optimal prefilter size depends on the phase variation rate. (b) The best phase reconstruction rate that results in best reconstruction quality is around $R = 4$ , and this is consistently observed for various scenes. $R = 4$ results in the least overlap between the ToF holography and its twin." + ], + "image_footnote": [], + "bbox": [ + 81, + 404, + 292, + 513 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/28c9620ca409e7e3a451d10660bbab5decd8a4479ef1dd06567804f095f35b97.jpg", + "image_caption": [ + "Phase" + ], + "image_footnote": [], + "bbox": [ + 302, + 420, + 460, + 513 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e0d3c3d9e8e4f0f15db8c5e06784d3fb3ddc699d229da11989d12cf872f1aa33.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 86, + 515, + 292, + 606 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c310f7b4257fd98e4898ab2f063aa804ebc5ad1240ceb8d437d8c7ddc9f4f50a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 302, + 515, + 459, + 606 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6d74681d7cd7ee3edc1cab6348769271829f2d887fa47e7dcf87fd6781e94999.jpg", + "image_caption": [ + "10² 104 106 -2 0 2" + ], + "image_footnote": [], + "bbox": [ + 80, + 609, + 295, + 702 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4d2f7a93faa60db4e1d640fdb5e36d56edb25245174a22814aaf600616d7e11a.jpg", + "image_caption": [ + "Figure 8. Visualization of the effect of changing the phase variation rate. In practice, we take the Discrete Fourier Transform which is circular. The smaller the overlap between the hologram and twin, the better we can reconstruct the phase." + ], + "image_footnote": [], + "bbox": [ + 300, + 609, + 462, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "value resets. From the graph, we can notice that the best SNR occurs at around $R = 3.5$ . While the optimal value depends on the noise and frequency content of the scene, we observed that it is always around $R = 4.0$ , and the SNR difference between the optimal and $R = 4.0$ is not signifi", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/72e36c2de69899ed3af6bcee2d812a192d341b95611786c70902778b9760d4d4.jpg", + "image_caption": [ + "Figure 9. For the snapshot image, instead of the proposed Fourier technique, we can also use the standard N-bucket technique by using neighboring rows as a proxy for the remaining phases. However, the N-bucket technique performs significantly worse compared to the Fourier technique at all the phase variation rates and cannot handle non-integer values of $R$ ." + ], + "image_footnote": [], + "bbox": [ + 500, + 90, + 883, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cant. At $R = 4$ , the overlap between the ToF hologram and the twin is minimal, and $\\sigma = 1$ corresponds to suppressing half of the higher frequency content; hence, the optimal SNR is always around $R = 4$ . When $R = 0$ , the twin and hologram are inseparable and the phase cannot be correctly recovered as shown in Fig. 8. In the rest of the paper, we use the phase variation rate of $k = \\pi /2$ and $\\sigma = 1$ .", + "bbox": [ + 496, + 354, + 890, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with N-bucket technique Instead of the Fourier reconstruction method detailed in Sec. 4, we can also use the standard N-bucket technique presented in Sec. 3 by grouping R-rows with phase variations $\\theta = \\{0,2\\pi /R,4\\pi /R,\\dots ,(R - 1) / R\\}$ . Note that the N-bucket technique does not decrease the number of effective rows, as we can always group $R / 2$ rows around the current row to get all the phase variations, in a sliding window manner. However, unlike the Fourier reconstruction method, the N-bucket technique works only for integer values of $R$ .", + "bbox": [ + 496, + 483, + 890, + 633 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In Fig. 9, we compare the N-bucket technique with the Fourier technique and observe that the Fourier technique uniformly works better than the standard N-bucket technique for snapshot phase reconstruction.", + "bbox": [ + 496, + 636, + 890, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison with conventional operation We compare the proposed snapshot technique with the conventional four-bucket method for the same exposure duration. We capture the snapshot image with an exposure duration of $T$ where $T = 100\\mu s$ while the four quadrature measurements are captured with $T / 4$ . In Fig. 10, we compare phase reconstruction results for both techniques. For a fair comparison, we have prefiltered the phasors for both the conventional and snapshot techniques. Our method has an SNR of 29.86 dB for phase reconstruction, slightly higher than 28.56 dB for the conventional method but our technique performs uniformly better than the conventional technique for all $\\sigma$", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25209", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d334c6d5286d85f8a94c67785a80e6425b2e7e60155c75a56e199f5e1738ba3c.jpg", + "image_caption": [ + "Figure 10. Comparisons against quadrature reconstruction. For the same total exposure duration and optimal kernel size, our method performs similarly or marginally better, compared to the conventional quadrature measurement technique. Importantly, however, our technique requires $4 \\times$ less bandwidth." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 467, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "values. While the proposed technique performs slightly better in this case, the required bandwidth is $4 \\times$ smaller than the conventional method as our technique requires only one image.", + "bbox": [ + 75, + 472, + 470, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Optimal phase variation direction Rotating the Fourier shift direction, implementable by rotating the camera along its optical axis, can also reduce the aliasing artifacts depending on the edges in the scene. We acquire the optimal result when the majority of the high-frequency edges are parallel to the direction of the phase shift (which is the same as being perpendicular to the phase variation direction). In Fig. 11, we demonstrate the result of reconstructing a scene made up of rectilinear block objects. To ensure the scene stays the same when rotated, we apply a circular mask when comparing the result with the ground truth and compute the SNR. As the graph shows, rotating the input at $75^{\\circ}$ yields the best result, since only a few rectilinear edges align with the vertical axis, the same orientation for the phase shift.", + "bbox": [ + 75, + 556, + 472, + 770 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusions", + "text_level": 1, + "bbox": [ + 76, + 784, + 204, + 800 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inspired by off-axis holography, we proposed a snapshot Lidar using CW-ToF cameras, which captures amplitude and depth using a single image. We showed how defining a time-of-flight hologram and using rolling-shutter cameras allows us to translate off-axis principles to CW-ToF cameras. Extensive experiments with our lab prototype demon", + "bbox": [ + 75, + 809, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3875e5faa66e806a6e41bcefe263ca9f63978f31614bd6a3d8a51a50726e144f.jpg", + "image_caption": [ + "Figure 11. Improving reconstruction by rotating the camera. Rotating the rolling shutter or phase variation direction improves the reconstruction quality. When the phase variation direction is perpendicular to the dominant edge direction, then we attain the highest SNR. We change the phase variation direction by simply rotating the camera." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 237 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "strated that our snapshot imaging approach performs as well as conventional quadrature measurement-based approaches, while requiring $4 \\times$ fewer measurements.", + "bbox": [ + 496, + 372, + 893, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As mentioned in the related work, continuous-wave time-of-flight cameras saw a proliferation of applications in the last decade. Translating the snapshot techniques proposed in this paper for non-sinusoidal codes [10], Doppler time-of-flight imaging [13, 14], frequency-based light transport probing [25], and time-gating [28], while non-trivial, can significantly improve all the applications.", + "bbox": [ + 496, + 424, + 893, + 531 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our approach relies on spatial modulation to compute the ToF hologram, which required pre-filtering to avoid aliasing. As part of future work, we will explore machine learning-based techniques to relax the aliasing requirements. Data-free techniques such as deep image priors [29], and generative approaches such as diffusion models [5] will enable us to solve the inverse problem more robustly, and without explicit anti-aliasing constraints.", + "bbox": [ + 496, + 535, + 893, + 656 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have translated snapshot off-axis imaging techniques to CWToF imaging. However, a wide variety of imaging ideas including high dynamic range imaging, light-field imaging, polarization imaging, and spectral imaging today are implemented with assorted pixels, which are expensive, prone to aliasing, or require custom demosaicking algorithms. Extending off-axis principles to create assorted frequency-embedding is an interesting future direction.", + "bbox": [ + 496, + 662, + 893, + 784 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 814, + 687, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The authors thank Jeremy Klotz for his help with the hardware prototype. The research is partially supported by a Burke Research Initiation Award.", + "bbox": [ + 496, + 844, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25210", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Supreeth Achar, Joseph R. Bartels, William L. 'Red' Whittaker, Kiriakos N. Kutulakos, and Srinivasa G. Narasimhan. Epipolar time-of-flight imaging. ACM TOG, 36(4), 2017. 2, 3", + "[2] Manuel Ballester, Heming Wang, Jiren Li, Oliver Cossairt, and Florian Willomitzer. Single-shot ToF sensing with submm precision using conventional CMOS sensors. arXiv preprint arXiv:2212.00928, 2022. 3", + "[3] Manuel Ballester, Heming Wang, Jiren Li, Oliver Cossaint, and Florian Willomitzer. 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In ECCV, 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 898 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "25211", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "ref_text", + "text": "[31] Di Wu, Andreas Velten, Matthew O'Toole, Belen Masia, Amit Agrawal, Qionghai Dai, and Ramesh Raskar. Decomposing global light transport using time of flight imaging. IJCV, 107:123-138, 2014. 2", + "bbox": [ + 78, + 90, + 468, + 147 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "25212", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_model.json b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b03aa100168f538d4c7ea0d074258a33f026c9d1 --- /dev/null +++ b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_model.json @@ -0,0 +1,1958 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.098, + 0.131, + 0.873, + 0.177 + ], + "angle": 0, + "content": "Snapshot Lidar: Fourier embedding of amplitude and phase for single-image depth reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.112, + 0.203, + 0.856, + 0.24 + ], + "angle": 0, + "content": "Sarah Friday\\(^{1}\\), Yunzi Shi\\(^{1}\\), Yaswanth Cherivirala, Vishwanath Saragadam\\(^{2}\\), Adithya Pediredla\\(^{1}\\) \n\\(^{1}\\)Dartmouth College, \\(^{2}\\)University of California, Riverside" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.291, + 0.892, + 0.507 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.522, + 0.895, + 0.607 + ], + "angle": 0, + "content": "Figure 1. We propose a novel snapshot Lidar imaging system that is inspired by off-axis holography techniques. \\((1^{\\mathrm{st}}\\) col.) Off-axis holography uses oblique illumination to separate the hologram and its twin in Fourier space. \\((2^{\\mathrm{nd}}\\) col.) We leverage the rolling-shutter effect of amplitude modulated continuous wave time-of-flight (AMCW-ToF) cameras to emulate the off-axis principle, thereby separating the time-of-flight hologram and its twin in Fourier space. \\((3^{\\mathrm{rd}}\\) col.) The conventional operation of AMCW-ToF Lidars requires four measurements, whereas our technique is \\(4\\mathrm{x}\\) faster, improving both the data bandwidth and temporal resolution. \\((4^{\\mathrm{th}}\\) col.) Reconstructed phase (that encodes depth) from measurements—The reconstructions are quite similar even with \\(4\\mathrm{x}\\) fewer measurements." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.619, + 0.314, + 0.635 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras are finding applications as flash Li-dars in autonomous navigation, robotics, and AR/VR applications. A conventional CW-ToF camera requires illuminating the scene with a temporally varying light source and demodulating a set of quadrature measurements to recover the scene's depth and intensity. Capturing the four measurements in sequence renders the system slow, invariably causing inaccuracies in depth estimates due to motion in the scene or the camera. To mitigate this problem, we propose a snapshot Lidar that captures amplitude and phase simultaneously as a single time-of-flight hologram. Uniquely, our approach requires minimal changes to existing CW-ToF imaging hardware. To demonstrate the efficacy of the proposed system, we design and build a lab prototype, and evaluate it under varying scene geometries, illumina" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.896, + 0.756 + ], + "angle": 0, + "content": "tion conditions, and compare the reconstructed depth measurements against conventional techniques. We rigorously evaluate the robustness of our system on diverse real-world scenes to show that our technique results in a significant reduction in data bandwidth with minimal loss in reconstruction accuracy. As high-resolution CW-ToF cameras are becoming ubiquitous, increasing their temporal resolution by four times enables robust real-time capture of geometries of dynamic scenes." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.785, + 0.633, + 0.801 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras, also known as correlation-based time-of-flight or indirect time-of-flight cameras, are used as flash Lidars to compute scene depth, and are used in autonomous navigation, robotics [6, 13], and augmented reality [8]. AMCW-ToF cameras operate by projecting a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "25203" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.472, + 0.233 + ], + "angle": 0, + "content": "
illuminationreferencephysics
holographycoherent beamplanar beamoptical interference
off-axiscoherent beamtilted beamoptical interference
CW-ToFAMCWelectronic shutterelectronic multiplication
proposedAMCWrolling shutterelectronic multiplication
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.243, + 0.47, + 0.34 + ], + "angle": 0, + "content": "Table 1. Principles of holography, off-axis holography, CW-ToF, and proposed snapshot CW-ToF. We draw parallels between off-axis holographic setup, and our proposed Fourier embedded ToF, that allow us to show that using a rolling-shutter sensor and varying the reference phase during CW-ToF acquisition results in a snapshot capture of the \"ToF hologram\" that contains both the amplitude and depth (encoded in phase) of the scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.369, + 0.47, + 0.504 + ], + "angle": 0, + "content": "temporally varying (often a sinusoidal) light source, and then correlating it on the sensor side with an appropriate (also often a sinusoid) decoding function. Depth is encoded in the phase of the measurements, and hence up to four measurements (quadrature) are required to robustly estimate the depth and intensity of the scene. These quadrature measurements are captured by temporal multiplexing, which invariably leads to lower frame rates and suffers from motion artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.47, + 0.749 + ], + "angle": 0, + "content": "Inspired by snapshot off-axis holography techniques, we propose a snapshot CW-ToF imaging technique that measures amplitude and depth using a single capture. The key observation is that by defining the time-of-flight hologram as the complex sinusoid whose amplitude and phase are proportional to the intensity and depth of the scene, we can draw parallels between holography and CW-ToF imaging techniques. This novel formulation of the ToF hologram enables us to translate off-axis techniques to CW-ToF imaging. In particular, by using rolling-shutter CW-ToF sensors [1] and spatially varying the reference phase of the coded exposure, we can emulate the off-axis holography effect and recover the complex-valued ToF hologram. In Tab. 1, we highlight the similarities and differences between holography, off-axis holography, CW-ToF, and the proposed imaging techniques." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.749, + 0.47, + 0.884 + ], + "angle": 0, + "content": "To achieve snapshot depth imaging, we leverage the image formation model of CW-ToF cameras, and demonstrate our modification to enable the capture of a ToF hologram with unipolar (all-positive decoding function) and bipolar (positive and negative decoding function) codes. We then show analytical and computational techniques to recover amplitude and depth from a rolling-shutter image and the need for optical prefiltering to prevent aliasing and noise folding." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We design and build a hardware setup built in the lab" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.304 + ], + "angle": 0, + "content": "with a Melexis 75027 device with region-of-interest support and a galvanometer to emulate the rolling-shutter effect. Using this device, in Sec. 6, we demonstrate that the proposed technique reduces data bandwidth and improves frame rate on various scenes containing diffuse, specular, and refractive objects. The proposed technique is robust to dead and saturated pixels, thereby enabling depth imaging with slightly faulty sensors, and extremely bright settings. We carefully evaluate design parameters including prefiltering window size, and spatial phase variation rate, and provide an experimentally optimal set of values that are agnostic to scene conditions. We empirically show that the proposed Fourier-based reconstruction technique is superior to the standard N-bucket technique for reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.315, + 0.642, + 0.33 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.892, + 0.537 + ], + "angle": 0, + "content": "Continuous wave time-of-flight cameras. CW-ToF cameras measure depth at each spatial pixel with a temporally modulated light source. The intensity of the scene is encoded in the amplitude, and depth in the phase, of the measurements. Typically four or more images, with different phases, are required to recover both amplitude and depth. These four measurements are obtained either with a spatially multiplexed sensor (similar to a Bayer pattern), or with sequential measurements [12]. Spatial multiplexing results in severe aliasing artifacts, and is inherently expensive and cumbersome to manufacture. In contrast, sequential measurements invariably result in motion artifacts when capturing dynamic scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Advances in CWToF sensing With the increasing number of practical applications for CWToF, work has been done to enhance its capabilities and mitigate its limitations. CS-ToF [20] is a compressive ToF imaging architecture aimed at overcoming sensor resolution limitations. As compressive sensing relies on the assumption of a linear measurement process for high resolution image estimation, CS-ToF uses a phasor representation inspired by Gupta [9] and O'Toole [25] of the ToF output to create a linear model between the scene and ToF measurements. In a process similar to single pixel imaging, laser light is reflected off of an object onto a high resolution digital micro-mirror device (DMD), and then relayed onto a lower resolution ToF sensor. By changing the DMD codes across multiple exposures, CS-ToF performs spatiotemporal multiplexing of the scene's amplitude and phase; however, sacrificing temporal resolution for spatial resolution. CWToF has also been combined with other modalities such as spectrum [27], light transport [24, 31], and light fields [15] that have significantly expanded the applications of CWToF cameras. Nevertheless, it is worth noting that there are few, if any, approaches that capture CWToF data in a snapshot manner, that is crucial for dynamic scenes." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25204" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "Superheterodyned interferometry. A related technology that enables snapshot ToF sensing is superheterodyned interferometric time-of-flight (SH-ToF) [21, 22], where two closely spaced illumination wavelengths combine to produce a much larger (heterodyned) synthetic wavelength. This approach however still requires capturing two separate images (one with each wavelength) to produce the final superheterodyned measurement. Recent work by Ballester et al. [3] demonstrated that SH-ToF can be combined with the off-axis holography to obtain a snapshot ToF imaging system. We next briefly discuss off-axis holography to understand its relevance to ToF sensing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.382 + ], + "angle": 0, + "content": "Off-axis holography Off-axis holography [7, 19] is a widely known imaging technique for reconstructing the amplitude \\((E_{s}(x,y))\\) and phase \\((\\phi_s(x,y))\\) of a hologram with a single measurement. The experimental setup schematic is shown in the first column of Fig. 1. The measurement by the camera is given by" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.39, + 0.469, + 0.451 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I = \\left| E _ {s} (x, y) e ^ {- \\phi_ {s} (x, y)} + E _ {r} e ^ {- k \\sin (\\theta) x} \\right| ^ {2} \\\\ = \\left| E _ {s} (x, y) \\right| ^ {2} + \\left| E _ {r} \\right| ^ {2} + E _ {r} ^ {*} E _ {s} (x, y) e ^ {k \\sin (\\theta) x - \\phi_ {s} (x, y)} \\\\ + E _ {r} E _ {s} ^ {*} (x, y) e ^ {- k \\sin (\\theta) x + \\phi_ {s} (x, y)} \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.46, + 0.473, + 0.733 + ], + "angle": 0, + "content": "Off-axis holography embeds the hologram \\((E_{s}(x,y)e^{-\\phi_{s}(x,y)})\\) and its twin \\((E_{s}^{*}(x,y)e^{\\phi_{s}(x,y)})\\) separately in the Fourier domain allowing us to recover the hologram computationally. Ballester et al. [2] showed that off-axis techniques can be used in synthetic wavelength interferometry. Specifically, the system consisted of a colocated, dual wavelength illumination source, and two, spatially separated reference beams. The separated location implied that the phasor information was encoded in different parts of the Fourier spectrum, enabling a simple frequency domain post-processing algorithm to estimate depth information with a single image. Our technique is inspired by off-axis holography. Two key observations that enable our technique are (i) expressing the time-of-flight image formation model with complex sinusoids allows us to draw parallels between holography and AMCW-ToF (ii) the rolling-shutter effect allows us to emulate off-axis technique." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Applications of CW-ToF cameras. Beyond depth imaging, CW-ToF cameras enable a plethora of important applications in imaging. For example, Callenberg et al. [4] showed that a CW-ToF camera can enable difference imaging, that is often useful for implementing convolutional operations within sensors. Achar et al. [1] showed that ToF sensors can be used to tease out sub-surface features through epipolar gating. Similarly, Naik et al. [24] and Kadambi et al. [16] showed that a light transport matrix-based formulation of ToF measurements enabled measur" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.276, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. CW-ToF imaging systems. CW-ToF cameras use high-frequency illumination sources and exposure codes to indirectly measure the object's depth. The measurement is the product of the delayed illumination signal and programmatically phase-shifted exposure code. The delay encodes object depth and is recoverable by taking multiple measurements with varying phase-shift \\((\\theta)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.892, + 0.46 + ], + "angle": 0, + "content": "ing multipath interferences, that are key to measuring geometric properties of complex objects like metal and glass. Our proposed work enables a similar slew of applications beyond depth imaging, including sub-surface imaging and multipath interference reduction (via epipolar gating)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.472, + 0.715, + 0.489 + ], + "angle": 0, + "content": "3. Technical Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.497, + 0.892, + 0.785 + ], + "angle": 0, + "content": "As shown in Fig. 2, an amplitude-modulated continuous-wave time-of-flight camera (AMCW-ToF) has an illumination source whose amplitude \\((e(t))\\) varies over time at several tens of MHz. While these amplitude variations are typically sinusoidal, other modulations have been successfully demonstrated in the past [9-11] for various applications. The light received \\((r(t))\\) at the sensor is attenuated and delayed based on the light transport of the scene \\((r(t) = Ae(t - \\tau))\\), where \\(\\tau\\) is the total time-of-travel of the light beam. Assuming a collocated light source and sensor and no multi-bounce paths, \\(\\tau = 2d\\omega /c\\), where \\(d\\) is the distance to the object, \\(\\omega\\) is the modulation frequency, and \\(c\\) is the speed of light. The sensor temporal exposure (s(t)) is also modulated, typically as a square wave (unipolar or bipolar) with the same frequency as the illumination. Recent sensors mostly use bipolar coding with a two-bucket architecture [30], and the exposure duration is approximated with a sinusoidal modulation. The measurement by the sensor is given by" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.791, + 0.892, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} m _ {\\theta} = \\frac {1}{T} \\int_ {t = 0} ^ {T} A r (t) s (t) d t \\\\ = \\frac {A}{T} \\int_ {t = 0} ^ {T} \\sin (\\omega t + \\phi) \\sin (\\omega t + \\theta) d t = \\frac {A}{2} \\cos (\\theta - \\phi). \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Most hardware implementations of CWToF Lidar mea" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25205" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "sure four images \\(m_0, m_{\\pi/2}, m_\\pi\\), and \\(m_{3\\pi/2}\\) and compute amplitude and phase as" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.128, + 0.418, + 0.152 + ], + "angle": 0, + "content": "\\[\nA = 2 \\sqrt {(m _ {0} - m _ {\\pi}) ^ {2} + (m _ {\\pi / 2} - m _ {3 \\pi / 2}) ^ {2}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.155, + 0.469, + 0.186 + ], + "angle": 0, + "content": "\\[\n\\phi = \\arctan \\frac {m _ {\\pi / 2} - m _ {3 \\pi / 2}}{m _ {0} - m _ {\\pi}}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.189, + 0.47, + 0.25 + ], + "angle": 0, + "content": "The quadrature technique is also extended to the N-tap technique [28] by taking \\( \\mathbf{N} \\) measurements corresponding to \\( \\theta = \\{0, 2\\pi / N, 4\\pi / N, c \\dots, 2\\pi (N - 1) / N\\} \\) and computing amplitude and phase as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.256, + 0.476, + 0.303 + ], + "angle": 0, + "content": "\\[\nA = \\sqrt {\\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2} + \\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2}}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.306, + 0.469, + 0.347 + ], + "angle": 0, + "content": "\\[\n\\phi = \\arctan \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} / \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.351, + 0.469, + 0.382 + ], + "angle": 0, + "content": "Unlike these techniques, we reconstruct amplitude and phase using a single image, which we discuss next." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.392, + 0.432, + 0.41 + ], + "angle": 0, + "content": "4. Proposed Technique: Snapshot CWTof" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.614 + ], + "angle": 0, + "content": "The key idea for measuring amplitude and depth using a single image is to spatially vary the phase \\(\\theta\\) linearly along rows or columns during the exposure. We can achieve this spatial variation with simple hardware modifications by either (1) changing the existing hardware design with different exposure phase offsets per row/column, (2) using a rolling-shutter camera and changing the phase offset of either the illumination or sensor during each row capture, or (3) using a fast line sensor (or hardware region-of-interest supporting camera) and scanning the scene line by line with a Galvanic mirror while changing the phase offset of each line. We used the last alternative in this paper, as the Melexis 75027 supports hardware ROI [23]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.469, + 0.749 + ], + "angle": 0, + "content": "To understand how linearly varying \\(\\theta\\) embeds both amplitude and phase in the captured image, we follow the notation from O'Toole et al. [26], Li et al. [21], and Gupta et al. [9] and represent the amplitude and phase images with complex sinusoidal notation as \\(I(x,y) = A(x,y)e^{-j2d\\omega /c}\\) and the Fourier Transform of this sinusoid as \\(\\mathcal{I}(\\omega_x,\\omega_y)\\). For brevity, we define \\(\\phi = 2d\\omega /c\\) as the phase shift of the illumination signal. Varying \\(\\theta\\) linearly during the measurement results in" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.753, + 0.469, + 0.828 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} m _ {\\theta = k x} (x, y) = \\frac {A (x , y)}{2} \\cos (k x - \\phi (x, y)) \\\\ = \\frac {A (x , y)}{4} \\left(e ^ {j (k x - \\phi (x, y))} + e ^ {- j (k x - \\phi (x, y))}\\right) \\tag {5} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.834, + 0.412, + 0.849 + ], + "angle": 0, + "content": "Taking the Fourier transform on both sides, we get" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.854, + 0.469, + 0.896 + ], + "angle": 0, + "content": "\\[\n\\mathcal {F} _ {m _ {k x}} \\left(\\omega_ {x}, \\omega_ {y}\\right) = \\frac {1}{4} \\left(\\mathcal {I} \\left(\\omega_ {x} - k, \\omega_ {y}\\right) + \\mathcal {I} ^ {*} \\left(k - \\omega_ {x}, - \\omega_ {y}\\right)\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "which is similar to the off-axis holography Eq. (1). Therefore, we will refer to the complex sinusoidal notation \\((I(x,y))\\) as the ToF hologram and its complex conjugate \\((I^{*}(x,y))\\) as the ToF twin." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.153, + 0.892, + 0.256 + ], + "angle": 0, + "content": "As depicted in Fig. 3, to recover the ToF hologram from the image captured by varying \\(\\theta\\) linearly, we take the Fourier transform of the measured image, filter the ToF twin, right shift the ToF hologram, and compute the inverse Fourier transform. The amplitude and phase of the inverse Fourier transform result are the amplitude and phase of the scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.364 + ], + "angle": 0, + "content": "Extension to unipolar codes. Most recent ToF sensors use a two-bucket architecture to suppress background illumination; hence, the codes are bipolar. However, our technique is also amenable to unipolar-coded time-of-flight cameras and imperfect two-bucket architecture cameras. In this case, the measurement model becomes" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.37, + 0.891, + 0.4 + ], + "angle": 0, + "content": "\\[\nm _ {\\theta} = \\frac {A}{2} \\cos (\\theta - \\phi) + a. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.404, + 0.892, + 0.45 + ], + "angle": 0, + "content": "where \\( a \\) is proportional to the ambient background light intensity. In this case, the Fourier transform has a DC component that can be filtered out along with the ToF twin." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.467, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Aliasing, noise folding, and prefiltering. From Fig. 3 (b), we notice that the ToF hologram and twin overlap in the Fourier domain. This overlap results in aliasing, where the high-frequency content of the ToF twin may appear as low-frequency content of the ToF hologram, and noise folding, where the twin's noise folds into the ToF hologram's noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.573, + 0.892, + 0.663 + ], + "angle": 0, + "content": "To mitigate aliasing and noise folding, we optically filter the high-resolution ToF hologram before the linear phase shifting and measurement. In the hardware implementation, we achieve this by simply defocusing the imaging lens in front of the sensor. This simple blurring operation reduces aliasing and noise folding artifacts (Fig. 3 (d, e))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.892, + 0.769 + ], + "angle": 0, + "content": "Therefore, while the proposed snapshot Lidar technique can capture amplitude and phase with a single image, it does so by sacrificing spatial resolution for temporal resolution. As spatial resolutions of imaging sensors keep increasing (compare PMD vs DME660 vs. Melexis) due to better fabrication techniques, trading spatial resolution for improving temporal resolution is arguably more useful." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.787, + 0.892, + 0.862 + ], + "angle": 0, + "content": "Phase noise. As with any optical measurements, the recovered phase will have noise due to shot noise in the measurements. This shot noise is present even for the standard N-bucket technique [17, 18]. The standard deviation of the phase noise for the snapshot technique is" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.867, + 0.891, + 0.899 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {\\phi} ^ {2} \\approx \\frac {\\partial \\phi}{\\partial m _ {k x}} m _ {k x} \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25206" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.25, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.119, + 0.266, + 0.231, + 0.278 + ], + "angle": 0, + "content": "(a) snapshot image" + }, + { + "type": "image", + "bbox": [ + 0.252, + 0.092, + 0.402, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.264, + 0.266, + 0.388, + 0.278 + ], + "angle": 0, + "content": "(b) Fourier transform" + }, + { + "type": "image", + "bbox": [ + 0.404, + 0.092, + 0.553, + 0.264 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.412, + 0.266, + 0.542, + 0.278 + ], + "angle": 0, + "content": "(c) filtered and shifted" + }, + { + "type": "image", + "bbox": [ + 0.556, + 0.091, + 0.706, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.577, + 0.266, + 0.694, + 0.278 + ], + "angle": 0, + "content": "(d) recovered phase" + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.089, + 0.887, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.747, + 0.266, + 0.871, + 0.278 + ], + "angle": 0, + "content": "(e) zoomed in offsets" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.895, + 0.374 + ], + "angle": 0, + "content": "Figure 3. Snapshot CWToF decoding, and effect of prefiltering. (a) captured snapshot CW-ToF image. (b) Fourier transform of snapshot image. (c) We filter out the twin and frequency shift the hologram in the Fourier domain to recover the ToF hologram. (d) We reconstruct the phase by computing the phase of the inverse Fourier transform of (c). (top row vs. bottom row) We prefilter the ToF hologram using a defocused imaging lens, which can decrease the overlap between the hologram and its twin. The prefiltering decreases aliasing and noise folding, resulting in a 3dB SNR gain (\\(2 \\times\\) smaller phase error). (e) zoomed-in offsets. (left) Without prefiltering, the high-frequency phase noise of the twin shows up as the low-frequency phase noise. (right) aliasing decreases with prefiltering." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.391, + 0.304, + 0.407 + ], + "angle": 0, + "content": "where \\(\\phi\\) is explicitly expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.414, + 0.453, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\phi (x, y) = \\arctan \\left(\\frac {m _ {k x} (x , y) \\sin (k x) * \\operatorname {s i n c} (k x)}{m _ {k x} (x , y) \\cos (k x) * \\operatorname {s i n c} (k x)}\\right).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.471, + 0.547 + ], + "angle": 0, + "content": "Here, \\(\\circledast\\) is spatial convolution. We show the derivation in the supplementary material. An analytical comparison of the noise variance between the N-bucket and snapshot techniques is not feasible. Instead, in Sec. 6, we show empirical comparison and show that the snapshot phase measurement does not result in additional phase noise." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.267, + 0.576 + ], + "angle": 0, + "content": "5. Experimental setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.689 + ], + "angle": 0, + "content": "To implement our method, we use the EVK75027-110-940-2 evaluation kit (EVK) by Melexis which uses diffused \\(940\\mathrm{nm}\\) VCSEL diodes for illumination and a Melexis 75027 CWToF sensor. While the sensor is a global shutter, we can create the rolling shutter effect by taking advantage of the sensor's hardware programmable ROI to reduce the per-frame capture/readout to a single row." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "For our experiments, we mount the EVK75027 to a linear 3D stage and carefully align the view to a set of 2-axis galvanic mirrors (GVS012) from Thorlabs. Then, we reduce the ROI of the camera to a single line, and steer the view of the galvos with a DAQ. Additionally, we separated the illumination board from the rest of the EVK and mounted it on top of the galvanic mirrors for approximate collocation of light source and apparent camera location. The MLX75027 module contained a firmware lock on the frame rate at 100 fps, severely limiting our capture speed when the ROI is reduced to only a single line. However, our setup demonstrates a proof-of-concept, and future versions of Melexis cameras without a firmware lock will enable a real-time operation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.391, + 0.895, + 0.571 + ], + "angle": 0, + "content": "One way to emulate snapshot measurements from our setup is to capture multiple images with varying phases and appropriately select the rows/columns in the image. In practice, we found it to be significantly simpler and convenient to conduct most of our experiments. In Fig. 4, we show the hardware prototype with fast-scanning galvonic mirrors. Additionally in Fig. 5, we compare results from an emulated versus hardware implemented snapshot capture and notice that the techniques result in the same amplitude and phase estimates. For more details about the hardware prototype and emulation method, we refer the reader to the supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.58, + 0.634, + 0.597 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.893, + 0.797 + ], + "angle": 0, + "content": "In this section, we use the hardware setup and emulation technique described in Sec. 5 to evaluate the proposed snapshot technique systematically. We show that (1) prefiltering improves signal-to-noise ratio (SNR) and prefiltering with cylindrical lenses is better than regular lenses; (2) the optimal phase variation rate is \\((k = \\frac{\\pi}{2}\\mathrm{line}^{-1})\\); (3) the Fourier technique is superior to the N-bucket technique for snapshot images; (4) the snapshot technique does not add any additional noise and (5) is robust to saturated and dead pixels; (6) rotating the phase variation (by rotating the camera itself) decreases aliasing. In the supplementary, we show extended results and a comparison with the dual phase mode of the epc660 camera. We share our code on GitHub." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Optimal prefiltering kernel. As mentioned in Sec. 4, prefiltering reduces aliasing and noise folding artifacts. As aliasing and noise folding occur in the direction of the rolling shutter, blurring the ToF hologram only in the rolling shutter direction is better than isotropic blurring as shown in Fig. 6. We can implement hardware anisotropic blurring by" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25207" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.092, + 0.251, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.261, + 0.122, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.262, + 0.231, + 0.273 + ], + "angle": 0, + "content": "camera components" + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.092, + 0.422, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.275, + 0.26, + 0.3, + 0.275 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.305, + 0.259, + 0.422, + 0.278 + ], + "angle": 0, + "content": "galvo/synchronization components" + }, + { + "type": "image_caption", + "bbox": [ + 0.201, + 0.278, + 0.322, + 0.293 + ], + "angle": 0, + "content": "a. hardware setup" + }, + { + "type": "image", + "bbox": [ + 0.434, + 0.141, + 0.891, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.605, + 0.277, + 0.748, + 0.29 + ], + "angle": 0, + "content": "b. emulation method" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.894, + 0.348 + ], + "angle": 0, + "content": "Figure 4. Lab prototype, and rolling shutter encoding scheme. (a) Rolling shutter hardware prototype with the camera components outlined in yellow and galvonic mirrors/synchronization hardware outlined in blue. (b) Compositing quadrature images to create an emulated rolling shutter snapshot." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.371, + 0.466, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.558, + 0.47, + 0.655 + ], + "angle": 0, + "content": "Figure 5. Advantages of emulated snapshot capture. Amplitude and depth reconstructed by snapshot data captured with emulations (this paper) vs. single line ROI (ideal optical setup) and galvanic mirrors. The emulated measurements and the reconstructed phase are similar to the full prototype. We hence demonstrated all experiments with an emulated setup, as it enables a faithful evaluation of a true snapshot system." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.469, + 0.779 + ], + "angle": 0, + "content": "using a defocused cylindrical lens. Note that the optimal kernel for prefiltering is a 1D sinc function in the spatial domain (corresponding to eliminating all the overlapping frequencies). However, that is not physically possible. Designing the optimal optically-realizable kernel is beyond the scope of this paper." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Assuming a 1D-Gaussian prefiltering kernel, we computed the effect of blur kernel size (measured in standard deviation \\(\\sigma\\)) on the phase reconstruction accuracy. As shown in Fig. 7 (a), for all values of \\(k\\), the SNR initially improves when \\(\\sigma\\) is increased and then decreases showing that an optimal blur kernel size exists. This phenomenon occurs as prefiltering initially reduces the overlap between the ToF hologram and the twin but later reduces the frequency con" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.371, + 0.892, + 0.476 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.478, + 0.888, + 0.671 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Figure 6. Robustness to noise due to prefiltering. Prefiltering reduces aliasing and noise folding artifacts to improve the reconstruction quality. Compared to the 2D-blur kernel, the 1D-blur kernel in the direction of rolling shutter direction results in a significantly higher-quality reconstruction. Since the ToF hologram and twin overlap occur only in the rolling shutter direction, a 1D blur kernel preserves the spatial frequencies in the direction orthogonal to rolling shutter." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.821, + 0.73, + 0.836 + ], + "angle": 0, + "content": "tent in the captured ToF hologram." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Optimal phase variation rate \\(k\\). In Fig. 7 (b), we plot optimal \\(\\sigma\\) value as a function of \\(R = 2\\pi / k\\), which represents the average number of rows required before the \\(\\theta\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25208" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.265, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.168, + 0.245, + 0.188, + 0.258 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.263, + 0.091, + 0.468, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.37, + 0.243, + 0.391, + 0.256 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.47, + 0.384 + ], + "angle": 0, + "content": "Figure 7. Optimal prefilter size and phase variation rate. (a) We show the effect of the standard deviation of the blur kernel (blur kernel size) on the phase reconstruction accuracy for various phase variation rates \\((k)\\). The optimal prefilter size depends on the phase variation rate. (b) The best phase reconstruction rate that results in best reconstruction quality is around \\(R = 4\\), and this is consistently observed for various scenes. \\(R = 4\\) results in the least overlap between the ToF holography and its twin." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.405, + 0.293, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.33, + 0.406, + 0.404, + 0.42 + ], + "angle": 0, + "content": "Phase" + }, + { + "type": "image", + "bbox": [ + 0.303, + 0.421, + 0.461, + 0.514 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.516, + 0.293, + 0.607 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.303, + 0.516, + 0.46, + 0.607 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.61, + 0.296, + 0.703 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.302, + 0.61, + 0.464, + 0.702 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.156, + 0.709, + 0.44, + 0.724 + ], + "angle": 0, + "content": "10² 104 106 -2 0 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.738, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Figure 8. Visualization of the effect of changing the phase variation rate. In practice, we take the Discrete Fourier Transform which is circular. The smaller the overlap between the hologram and twin, the better we can reconstruct the phase." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "value resets. From the graph, we can notice that the best SNR occurs at around \\( R = 3.5 \\). While the optimal value depends on the noise and frequency content of the scene, we observed that it is always around \\( R = 4.0 \\), and the SNR difference between the optimal and \\( R = 4.0 \\) is not signifi" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.091, + 0.885, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.327 + ], + "angle": 0, + "content": "Figure 9. For the snapshot image, instead of the proposed Fourier technique, we can also use the standard N-bucket technique by using neighboring rows as a proxy for the remaining phases. However, the N-bucket technique performs significantly worse compared to the Fourier technique at all the phase variation rates and cannot handle non-integer values of \\( R \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.462 + ], + "angle": 0, + "content": "cant. At \\( R = 4 \\), the overlap between the ToF hologram and the twin is minimal, and \\( \\sigma = 1 \\) corresponds to suppressing half of the higher frequency content; hence, the optimal SNR is always around \\( R = 4 \\). When \\( R = 0 \\), the twin and hologram are inseparable and the phase cannot be correctly recovered as shown in Fig. 8. In the rest of the paper, we use the phase variation rate of \\( k = \\pi /2 \\) and \\( \\sigma = 1 \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Comparison with N-bucket technique Instead of the Fourier reconstruction method detailed in Sec. 4, we can also use the standard N-bucket technique presented in Sec. 3 by grouping R-rows with phase variations \\(\\theta = \\{0,2\\pi /R,4\\pi /R,\\dots ,(R - 1) / R\\}\\). Note that the N-bucket technique does not decrease the number of effective rows, as we can always group \\(R / 2\\) rows around the current row to get all the phase variations, in a sliding window manner. However, unlike the Fourier reconstruction method, the N-bucket technique works only for integer values of \\(R\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.697 + ], + "angle": 0, + "content": "In Fig. 9, we compare the N-bucket technique with the Fourier technique and observe that the Fourier technique uniformly works better than the standard N-bucket technique for snapshot phase reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Comparison with conventional operation We compare the proposed snapshot technique with the conventional four-bucket method for the same exposure duration. We capture the snapshot image with an exposure duration of \\( T \\) where \\( T = 100\\mu s \\) while the four quadrature measurements are captured with \\( T / 4 \\). In Fig. 10, we compare phase reconstruction results for both techniques. For a fair comparison, we have prefiltered the phasors for both the conventional and snapshot techniques. Our method has an SNR of 29.86 dB for phase reconstruction, slightly higher than 28.56 dB for the conventional method but our technique performs uniformly better than the conventional technique for all \\( \\sigma \\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25209" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.468, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.447 + ], + "angle": 0, + "content": "Figure 10. Comparisons against quadrature reconstruction. For the same total exposure duration and optimal kernel size, our method performs similarly or marginally better, compared to the conventional quadrature measurement technique. Importantly, however, our technique requires \\(4 \\times\\) less bandwidth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.472, + 0.536 + ], + "angle": 0, + "content": "values. While the proposed technique performs slightly better in this case, the required bandwidth is \\(4 \\times\\) smaller than the conventional method as our technique requires only one image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.557, + 0.473, + 0.771 + ], + "angle": 0, + "content": "Optimal phase variation direction Rotating the Fourier shift direction, implementable by rotating the camera along its optical axis, can also reduce the aliasing artifacts depending on the edges in the scene. We acquire the optimal result when the majority of the high-frequency edges are parallel to the direction of the phase shift (which is the same as being perpendicular to the phase variation direction). In Fig. 11, we demonstrate the result of reconstructing a scene made up of rectilinear block objects. To ensure the scene stays the same when rotated, we apply a circular mask when comparing the result with the ground truth and compute the SNR. As the graph shows, rotating the input at \\(75^{\\circ}\\) yields the best result, since only a few rectilinear edges align with the vertical axis, the same orientation for the phase shift." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.785, + 0.205, + 0.801 + ], + "angle": 0, + "content": "7. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.473, + 0.904 + ], + "angle": 0, + "content": "Inspired by off-axis holography, we proposed a snapshot Lidar using CW-ToF cameras, which captures amplitude and depth using a single image. We showed how defining a time-of-flight hologram and using rolling-shutter cameras allows us to translate off-axis principles to CW-ToF cameras. Extensive experiments with our lab prototype demon" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.251, + 0.895, + 0.336 + ], + "angle": 0, + "content": "Figure 11. Improving reconstruction by rotating the camera. Rotating the rolling shutter or phase variation direction improves the reconstruction quality. When the phase variation direction is perpendicular to the dominant edge direction, then we attain the highest SNR. We change the phase variation direction by simply rotating the camera." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.373, + 0.895, + 0.42 + ], + "angle": 0, + "content": "strated that our snapshot imaging approach performs as well as conventional quadrature measurement-based approaches, while requiring \\(4 \\times\\) fewer measurements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.895, + 0.532 + ], + "angle": 0, + "content": "As mentioned in the related work, continuous-wave time-of-flight cameras saw a proliferation of applications in the last decade. Translating the snapshot techniques proposed in this paper for non-sinusoidal codes [10], Doppler time-of-flight imaging [13, 14], frequency-based light transport probing [25], and time-gating [28], while non-trivial, can significantly improve all the applications." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.536, + 0.895, + 0.657 + ], + "angle": 0, + "content": "Our approach relies on spatial modulation to compute the ToF hologram, which required pre-filtering to avoid aliasing. As part of future work, we will explore machine learning-based techniques to relax the aliasing requirements. Data-free techniques such as deep image priors [29], and generative approaches such as diffusion models [5] will enable us to solve the inverse problem more robustly, and without explicit anti-aliasing constraints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.663, + 0.895, + 0.785 + ], + "angle": 0, + "content": "We have translated snapshot off-axis imaging techniques to CWToF imaging. However, a wide variety of imaging ideas including high dynamic range imaging, light-field imaging, polarization imaging, and spectral imaging today are implemented with assorted pixels, which are expensive, prone to aliasing, or require custom demosaicking algorithms. Extending off-axis principles to create assorted frequency-embedding is an interesting future direction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.688, + 0.832 + ], + "angle": 0, + "content": "8. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.845, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The authors thank Jeremy Klotz for his help with the hardware prototype. The research is partially supported by a Burke Research Initiation Award." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25210" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Supreeth Achar, Joseph R. Bartels, William L. 'Red' Whittaker, Kiriakos N. Kutulakos, and Srinivasa G. Narasimhan. Epipolar time-of-flight imaging. ACM TOG, 36(4), 2017. 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.47, + 0.227 + ], + "angle": 0, + "content": "[2] Manuel Ballester, Heming Wang, Jiren Li, Oliver Cossairt, and Florian Willomitzer. 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IJCV, 107:123-138, 2014. 2" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25212" + } + ] +] \ No newline at end of file diff --git a/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_origin.pdf b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..bf014564c29cbd6d97b53f1ec432cb8229975769 --- /dev/null +++ b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/4828c6e5-d978-4f03-9ac3-919a10abf8a1_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:758b6b12e6c6fb447a829026b4f78c43b5626f4d4196d2d6b7a1d20714b043e7 +size 5113742 diff --git a/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/full.md b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..06da171e27f2e0d65bd41f14a342eed9f2697800 --- /dev/null +++ b/2024/Snapshot Lidar_ Fourier Embedding of Amplitude and Phase for Single-Image Depth Reconstruction/full.md @@ -0,0 +1,292 @@ +# Snapshot Lidar: Fourier embedding of amplitude and phase for single-image depth reconstruction + +Sarah Friday $^{1}$ , Yunzi Shi $^{1}$ , Yaswanth Cherivirala, Vishwanath Saragadam $^{2}$ , Adithya Pediredla $^{1}$ $^{1}$ Dartmouth College, $^{2}$ University of California, Riverside + +![](images/e0133742f106780c0d8fced97ce5f8dae823f929d003a9c2e6b20c16b53bc3c1.jpg) +Figure 1. We propose a novel snapshot Lidar imaging system that is inspired by off-axis holography techniques. $(1^{\mathrm{st}}$ col.) Off-axis holography uses oblique illumination to separate the hologram and its twin in Fourier space. $(2^{\mathrm{nd}}$ col.) We leverage the rolling-shutter effect of amplitude modulated continuous wave time-of-flight (AMCW-ToF) cameras to emulate the off-axis principle, thereby separating the time-of-flight hologram and its twin in Fourier space. $(3^{\mathrm{rd}}$ col.) The conventional operation of AMCW-ToF Lidars requires four measurements, whereas our technique is $4\mathrm{x}$ faster, improving both the data bandwidth and temporal resolution. $(4^{\mathrm{th}}$ col.) Reconstructed phase (that encodes depth) from measurements—The reconstructions are quite similar even with $4\mathrm{x}$ fewer measurements. + +# Abstract + +Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras are finding applications as flash Li-dars in autonomous navigation, robotics, and AR/VR applications. A conventional CW-ToF camera requires illuminating the scene with a temporally varying light source and demodulating a set of quadrature measurements to recover the scene's depth and intensity. Capturing the four measurements in sequence renders the system slow, invariably causing inaccuracies in depth estimates due to motion in the scene or the camera. To mitigate this problem, we propose a snapshot Lidar that captures amplitude and phase simultaneously as a single time-of-flight hologram. Uniquely, our approach requires minimal changes to existing CW-ToF imaging hardware. To demonstrate the efficacy of the proposed system, we design and build a lab prototype, and evaluate it under varying scene geometries, illumina + +tion conditions, and compare the reconstructed depth measurements against conventional techniques. We rigorously evaluate the robustness of our system on diverse real-world scenes to show that our technique results in a significant reduction in data bandwidth with minimal loss in reconstruction accuracy. As high-resolution CW-ToF cameras are becoming ubiquitous, increasing their temporal resolution by four times enables robust real-time capture of geometries of dynamic scenes. + +# 1. Introduction + +Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras, also known as correlation-based time-of-flight or indirect time-of-flight cameras, are used as flash Lidars to compute scene depth, and are used in autonomous navigation, robotics [6, 13], and augmented reality [8]. AMCW-ToF cameras operate by projecting a + +
illuminationreferencephysics
holographycoherent beamplanar beamoptical interference
off-axiscoherent beamtilted beamoptical interference
CW-ToFAMCWelectronic shutterelectronic multiplication
proposedAMCWrolling shutterelectronic multiplication
+ +Table 1. Principles of holography, off-axis holography, CW-ToF, and proposed snapshot CW-ToF. We draw parallels between off-axis holographic setup, and our proposed Fourier embedded ToF, that allow us to show that using a rolling-shutter sensor and varying the reference phase during CW-ToF acquisition results in a snapshot capture of the "ToF hologram" that contains both the amplitude and depth (encoded in phase) of the scene. + +temporally varying (often a sinusoidal) light source, and then correlating it on the sensor side with an appropriate (also often a sinusoid) decoding function. Depth is encoded in the phase of the measurements, and hence up to four measurements (quadrature) are required to robustly estimate the depth and intensity of the scene. These quadrature measurements are captured by temporal multiplexing, which invariably leads to lower frame rates and suffers from motion artifacts. + +Inspired by snapshot off-axis holography techniques, we propose a snapshot CW-ToF imaging technique that measures amplitude and depth using a single capture. The key observation is that by defining the time-of-flight hologram as the complex sinusoid whose amplitude and phase are proportional to the intensity and depth of the scene, we can draw parallels between holography and CW-ToF imaging techniques. This novel formulation of the ToF hologram enables us to translate off-axis techniques to CW-ToF imaging. In particular, by using rolling-shutter CW-ToF sensors [1] and spatially varying the reference phase of the coded exposure, we can emulate the off-axis holography effect and recover the complex-valued ToF hologram. In Tab. 1, we highlight the similarities and differences between holography, off-axis holography, CW-ToF, and the proposed imaging techniques. + +To achieve snapshot depth imaging, we leverage the image formation model of CW-ToF cameras, and demonstrate our modification to enable the capture of a ToF hologram with unipolar (all-positive decoding function) and bipolar (positive and negative decoding function) codes. We then show analytical and computational techniques to recover amplitude and depth from a rolling-shutter image and the need for optical prefiltering to prevent aliasing and noise folding. + +We design and build a hardware setup built in the lab + +with a Melexis 75027 device with region-of-interest support and a galvanometer to emulate the rolling-shutter effect. Using this device, in Sec. 6, we demonstrate that the proposed technique reduces data bandwidth and improves frame rate on various scenes containing diffuse, specular, and refractive objects. The proposed technique is robust to dead and saturated pixels, thereby enabling depth imaging with slightly faulty sensors, and extremely bright settings. We carefully evaluate design parameters including prefiltering window size, and spatial phase variation rate, and provide an experimentally optimal set of values that are agnostic to scene conditions. We empirically show that the proposed Fourier-based reconstruction technique is superior to the standard N-bucket technique for reconstruction. + +# 2. Related Work + +Continuous wave time-of-flight cameras. CW-ToF cameras measure depth at each spatial pixel with a temporally modulated light source. The intensity of the scene is encoded in the amplitude, and depth in the phase, of the measurements. Typically four or more images, with different phases, are required to recover both amplitude and depth. These four measurements are obtained either with a spatially multiplexed sensor (similar to a Bayer pattern), or with sequential measurements [12]. Spatial multiplexing results in severe aliasing artifacts, and is inherently expensive and cumbersome to manufacture. In contrast, sequential measurements invariably result in motion artifacts when capturing dynamic scenes. + +Advances in CWToF sensing With the increasing number of practical applications for CWToF, work has been done to enhance its capabilities and mitigate its limitations. CS-ToF [20] is a compressive ToF imaging architecture aimed at overcoming sensor resolution limitations. As compressive sensing relies on the assumption of a linear measurement process for high resolution image estimation, CS-ToF uses a phasor representation inspired by Gupta [9] and O'Toole [25] of the ToF output to create a linear model between the scene and ToF measurements. In a process similar to single pixel imaging, laser light is reflected off of an object onto a high resolution digital micro-mirror device (DMD), and then relayed onto a lower resolution ToF sensor. By changing the DMD codes across multiple exposures, CS-ToF performs spatiotemporal multiplexing of the scene's amplitude and phase; however, sacrificing temporal resolution for spatial resolution. CWToF has also been combined with other modalities such as spectrum [27], light transport [24, 31], and light fields [15] that have significantly expanded the applications of CWToF cameras. Nevertheless, it is worth noting that there are few, if any, approaches that capture CWToF data in a snapshot manner, that is crucial for dynamic scenes. + +Superheterodyned interferometry. A related technology that enables snapshot ToF sensing is superheterodyned interferometric time-of-flight (SH-ToF) [21, 22], where two closely spaced illumination wavelengths combine to produce a much larger (heterodyned) synthetic wavelength. This approach however still requires capturing two separate images (one with each wavelength) to produce the final superheterodyned measurement. Recent work by Ballester et al. [3] demonstrated that SH-ToF can be combined with the off-axis holography to obtain a snapshot ToF imaging system. We next briefly discuss off-axis holography to understand its relevance to ToF sensing. + +Off-axis holography Off-axis holography [7, 19] is a widely known imaging technique for reconstructing the amplitude $(E_{s}(x,y))$ and phase $(\phi_s(x,y))$ of a hologram with a single measurement. The experimental setup schematic is shown in the first column of Fig. 1. The measurement by the camera is given by + +$$ +\begin{array}{l} I = \left| E _ {s} (x, y) e ^ {- \phi_ {s} (x, y)} + E _ {r} e ^ {- k \sin (\theta) x} \right| ^ {2} \\ = \left| E _ {s} (x, y) \right| ^ {2} + \left| E _ {r} \right| ^ {2} + E _ {r} ^ {*} E _ {s} (x, y) e ^ {k \sin (\theta) x - \phi_ {s} (x, y)} \\ + E _ {r} E _ {s} ^ {*} (x, y) e ^ {- k \sin (\theta) x + \phi_ {s} (x, y)} \tag {1} \\ \end{array} +$$ + +Off-axis holography embeds the hologram $(E_{s}(x,y)e^{-\phi_{s}(x,y)})$ and its twin $(E_{s}^{*}(x,y)e^{\phi_{s}(x,y)})$ separately in the Fourier domain allowing us to recover the hologram computationally. Ballester et al. [2] showed that off-axis techniques can be used in synthetic wavelength interferometry. Specifically, the system consisted of a colocated, dual wavelength illumination source, and two, spatially separated reference beams. The separated location implied that the phasor information was encoded in different parts of the Fourier spectrum, enabling a simple frequency domain post-processing algorithm to estimate depth information with a single image. Our technique is inspired by off-axis holography. Two key observations that enable our technique are (i) expressing the time-of-flight image formation model with complex sinusoids allows us to draw parallels between holography and AMCW-ToF (ii) the rolling-shutter effect allows us to emulate off-axis technique. + +Applications of CW-ToF cameras. Beyond depth imaging, CW-ToF cameras enable a plethora of important applications in imaging. For example, Callenberg et al. [4] showed that a CW-ToF camera can enable difference imaging, that is often useful for implementing convolutional operations within sensors. Achar et al. [1] showed that ToF sensors can be used to tease out sub-surface features through epipolar gating. Similarly, Naik et al. [24] and Kadambi et al. [16] showed that a light transport matrix-based formulation of ToF measurements enabled measur + +![](images/858b901540602697be8862ab2f107e769bd32009fed8a8a8ecd6cb7b20ba7b2c.jpg) +Figure 2. CW-ToF imaging systems. CW-ToF cameras use high-frequency illumination sources and exposure codes to indirectly measure the object's depth. The measurement is the product of the delayed illumination signal and programmatically phase-shifted exposure code. The delay encodes object depth and is recoverable by taking multiple measurements with varying phase-shift $(\theta)$ . + +ing multipath interferences, that are key to measuring geometric properties of complex objects like metal and glass. Our proposed work enables a similar slew of applications beyond depth imaging, including sub-surface imaging and multipath interference reduction (via epipolar gating). + +# 3. Technical Background + +As shown in Fig. 2, an amplitude-modulated continuous-wave time-of-flight camera (AMCW-ToF) has an illumination source whose amplitude $(e(t))$ varies over time at several tens of MHz. While these amplitude variations are typically sinusoidal, other modulations have been successfully demonstrated in the past [9-11] for various applications. The light received $(r(t))$ at the sensor is attenuated and delayed based on the light transport of the scene $(r(t) = Ae(t - \tau))$ , where $\tau$ is the total time-of-travel of the light beam. Assuming a collocated light source and sensor and no multi-bounce paths, $\tau = 2d\omega /c$ , where $d$ is the distance to the object, $\omega$ is the modulation frequency, and $c$ is the speed of light. The sensor temporal exposure (s(t)) is also modulated, typically as a square wave (unipolar or bipolar) with the same frequency as the illumination. Recent sensors mostly use bipolar coding with a two-bucket architecture [30], and the exposure duration is approximated with a sinusoidal modulation. The measurement by the sensor is given by + +$$ +\begin{array}{l} m _ {\theta} = \frac {1}{T} \int_ {t = 0} ^ {T} A r (t) s (t) d t \\ = \frac {A}{T} \int_ {t = 0} ^ {T} \sin (\omega t + \phi) \sin (\omega t + \theta) d t = \frac {A}{2} \cos (\theta - \phi). \tag {2} \\ \end{array} +$$ + +Most hardware implementations of CWToF Lidar mea + +sure four images $m_0, m_{\pi/2}, m_\pi$ , and $m_{3\pi/2}$ and compute amplitude and phase as + +$$ +A = 2 \sqrt {(m _ {0} - m _ {\pi}) ^ {2} + (m _ {\pi / 2} - m _ {3 \pi / 2}) ^ {2}} +$$ + +$$ +\phi = \arctan \frac {m _ {\pi / 2} - m _ {3 \pi / 2}}{m _ {0} - m _ {\pi}}. \tag {3} +$$ + +The quadrature technique is also extended to the N-tap technique [28] by taking $\mathbf{N}$ measurements corresponding to $\theta = \{0, 2\pi / N, 4\pi / N, c \dots, 2\pi (N - 1) / N\}$ and computing amplitude and phase as: + +$$ +A = \sqrt {\left(\sum_ {n = 0} ^ {N - 1} m _ {\frac {2 \pi n}{N}} \cos \frac {2 \pi n}{N}\right) ^ {2} + \left(\sum_ {n = 0} ^ {N - 1} m _ {\frac {2 \pi n}{N}} \cos \frac {2 \pi n}{N}\right) ^ {2}} +$$ + +$$ +\phi = \arctan \sum_ {n = 0} ^ {N - 1} m _ {\frac {2 \pi n}{N}} \cos \frac {2 \pi n}{N} / \sum_ {n = 0} ^ {N - 1} m _ {\frac {2 \pi n}{N}} \cos \frac {2 \pi n}{N} \tag {4} +$$ + +Unlike these techniques, we reconstruct amplitude and phase using a single image, which we discuss next. + +# 4. Proposed Technique: Snapshot CWTof + +The key idea for measuring amplitude and depth using a single image is to spatially vary the phase $\theta$ linearly along rows or columns during the exposure. We can achieve this spatial variation with simple hardware modifications by either (1) changing the existing hardware design with different exposure phase offsets per row/column, (2) using a rolling-shutter camera and changing the phase offset of either the illumination or sensor during each row capture, or (3) using a fast line sensor (or hardware region-of-interest supporting camera) and scanning the scene line by line with a Galvanic mirror while changing the phase offset of each line. We used the last alternative in this paper, as the Melexis 75027 supports hardware ROI [23]. + +To understand how linearly varying $\theta$ embeds both amplitude and phase in the captured image, we follow the notation from O'Toole et al. [26], Li et al. [21], and Gupta et al. [9] and represent the amplitude and phase images with complex sinusoidal notation as $I(x,y) = A(x,y)e^{-j2d\omega /c}$ and the Fourier Transform of this sinusoid as $\mathcal{I}(\omega_x,\omega_y)$ . For brevity, we define $\phi = 2d\omega /c$ as the phase shift of the illumination signal. Varying $\theta$ linearly during the measurement results in + +$$ +\begin{array}{l} m _ {\theta = k x} (x, y) = \frac {A (x , y)}{2} \cos (k x - \phi (x, y)) \\ = \frac {A (x , y)}{4} \left(e ^ {j (k x - \phi (x, y))} + e ^ {- j (k x - \phi (x, y))}\right) \tag {5} \\ \end{array} +$$ + +Taking the Fourier transform on both sides, we get + +$$ +\mathcal {F} _ {m _ {k x}} \left(\omega_ {x}, \omega_ {y}\right) = \frac {1}{4} \left(\mathcal {I} \left(\omega_ {x} - k, \omega_ {y}\right) + \mathcal {I} ^ {*} \left(k - \omega_ {x}, - \omega_ {y}\right)\right), \tag {6} +$$ + +which is similar to the off-axis holography Eq. (1). Therefore, we will refer to the complex sinusoidal notation $(I(x,y))$ as the ToF hologram and its complex conjugate $(I^{*}(x,y))$ as the ToF twin. + +As depicted in Fig. 3, to recover the ToF hologram from the image captured by varying $\theta$ linearly, we take the Fourier transform of the measured image, filter the ToF twin, right shift the ToF hologram, and compute the inverse Fourier transform. The amplitude and phase of the inverse Fourier transform result are the amplitude and phase of the scene. + +Extension to unipolar codes. Most recent ToF sensors use a two-bucket architecture to suppress background illumination; hence, the codes are bipolar. However, our technique is also amenable to unipolar-coded time-of-flight cameras and imperfect two-bucket architecture cameras. In this case, the measurement model becomes + +$$ +m _ {\theta} = \frac {A}{2} \cos (\theta - \phi) + a. \tag {7} +$$ + +where $a$ is proportional to the ambient background light intensity. In this case, the Fourier transform has a DC component that can be filtered out along with the ToF twin. + +Aliasing, noise folding, and prefiltering. From Fig. 3 (b), we notice that the ToF hologram and twin overlap in the Fourier domain. This overlap results in aliasing, where the high-frequency content of the ToF twin may appear as low-frequency content of the ToF hologram, and noise folding, where the twin's noise folds into the ToF hologram's noise. + +To mitigate aliasing and noise folding, we optically filter the high-resolution ToF hologram before the linear phase shifting and measurement. In the hardware implementation, we achieve this by simply defocusing the imaging lens in front of the sensor. This simple blurring operation reduces aliasing and noise folding artifacts (Fig. 3 (d, e)). + +Therefore, while the proposed snapshot Lidar technique can capture amplitude and phase with a single image, it does so by sacrificing spatial resolution for temporal resolution. As spatial resolutions of imaging sensors keep increasing (compare PMD vs DME660 vs. Melexis) due to better fabrication techniques, trading spatial resolution for improving temporal resolution is arguably more useful. + +Phase noise. As with any optical measurements, the recovered phase will have noise due to shot noise in the measurements. This shot noise is present even for the standard N-bucket technique [17, 18]. The standard deviation of the phase noise for the snapshot technique is + +$$ +\sigma_ {\phi} ^ {2} \approx \frac {\partial \phi}{\partial m _ {k x}} m _ {k x} \tag {8} +$$ + +![](images/82f479d141147271f6a5fef43b6752e959fa1bbd78127fcf9202efa2fe8bfd05.jpg) +(a) snapshot image + +![](images/bb781112949977db1a30be2964b570d37f9ae631392b586de5bcf3fcdf676fc3.jpg) +(b) Fourier transform + +![](images/0116208e53f9efb098138a9b858810ddb3c5756a52da370617890f66057846ed.jpg) +(c) filtered and shifted +Figure 3. Snapshot CWToF decoding, and effect of prefiltering. (a) captured snapshot CW-ToF image. (b) Fourier transform of snapshot image. (c) We filter out the twin and frequency shift the hologram in the Fourier domain to recover the ToF hologram. (d) We reconstruct the phase by computing the phase of the inverse Fourier transform of (c). (top row vs. bottom row) We prefilter the ToF hologram using a defocused imaging lens, which can decrease the overlap between the hologram and its twin. The prefiltering decreases aliasing and noise folding, resulting in a 3dB SNR gain ( $2 \times$ smaller phase error). (e) zoomed-in offsets. (left) Without prefiltering, the high-frequency phase noise of the twin shows up as the low-frequency phase noise. (right) aliasing decreases with prefiltering. + +![](images/9eb1412beb1e5884ffd91c73034ea91a2485e48bd85359707b0260488fa7b931.jpg) +(d) recovered phase + +![](images/06156c8f4d30381cc2babfc53d103a89f08a5d6db9024d4ac46cb8597556ef80.jpg) +(e) zoomed in offsets + +where $\phi$ is explicitly expressed as + +$$ +\phi (x, y) = \arctan \left(\frac {m _ {k x} (x , y) \sin (k x) * \operatorname {s i n c} (k x)}{m _ {k x} (x , y) \cos (k x) * \operatorname {s i n c} (k x)}\right). +$$ + +Here, $\circledast$ is spatial convolution. We show the derivation in the supplementary material. An analytical comparison of the noise variance between the N-bucket and snapshot techniques is not feasible. Instead, in Sec. 6, we show empirical comparison and show that the snapshot phase measurement does not result in additional phase noise. + +# 5. Experimental setup + +To implement our method, we use the EVK75027-110-940-2 evaluation kit (EVK) by Melexis which uses diffused $940\mathrm{nm}$ VCSEL diodes for illumination and a Melexis 75027 CWToF sensor. While the sensor is a global shutter, we can create the rolling shutter effect by taking advantage of the sensor's hardware programmable ROI to reduce the per-frame capture/readout to a single row. + +For our experiments, we mount the EVK75027 to a linear 3D stage and carefully align the view to a set of 2-axis galvanic mirrors (GVS012) from Thorlabs. Then, we reduce the ROI of the camera to a single line, and steer the view of the galvos with a DAQ. Additionally, we separated the illumination board from the rest of the EVK and mounted it on top of the galvanic mirrors for approximate collocation of light source and apparent camera location. The MLX75027 module contained a firmware lock on the frame rate at 100 fps, severely limiting our capture speed when the ROI is reduced to only a single line. However, our setup demonstrates a proof-of-concept, and future versions of Melexis cameras without a firmware lock will enable a real-time operation. + +One way to emulate snapshot measurements from our setup is to capture multiple images with varying phases and appropriately select the rows/columns in the image. In practice, we found it to be significantly simpler and convenient to conduct most of our experiments. In Fig. 4, we show the hardware prototype with fast-scanning galvonic mirrors. Additionally in Fig. 5, we compare results from an emulated versus hardware implemented snapshot capture and notice that the techniques result in the same amplitude and phase estimates. For more details about the hardware prototype and emulation method, we refer the reader to the supplemental material. + +# 6. Experiments + +In this section, we use the hardware setup and emulation technique described in Sec. 5 to evaluate the proposed snapshot technique systematically. We show that (1) prefiltering improves signal-to-noise ratio (SNR) and prefiltering with cylindrical lenses is better than regular lenses; (2) the optimal phase variation rate is $(k = \frac{\pi}{2}\mathrm{line}^{-1})$ ; (3) the Fourier technique is superior to the N-bucket technique for snapshot images; (4) the snapshot technique does not add any additional noise and (5) is robust to saturated and dead pixels; (6) rotating the phase variation (by rotating the camera itself) decreases aliasing. In the supplementary, we show extended results and a comparison with the dual phase mode of the epc660 camera. We share our code on GitHub. + +Optimal prefiltering kernel. As mentioned in Sec. 4, prefiltering reduces aliasing and noise folding artifacts. As aliasing and noise folding occur in the direction of the rolling shutter, blurring the ToF hologram only in the rolling shutter direction is better than isotropic blurring as shown in Fig. 6. We can implement hardware anisotropic blurring by + +![](images/177cc8cf5178c9d80f3da230e8ba5f6a36d86ed42c212337a748dc69c859c7d6.jpg) + +![](images/548834f57c7c163227eabea55c2d0433f86eb4e93fe6ea77bbad2e737fef1e3b.jpg) +camera components + +![](images/4781d74b6cf3ced22fb6781c5ae156e0e529d0f48649239e66fe28fae44228e1.jpg) +galvo/synchronization components + +![](images/965c574f4f684df40ca0ce49fd399496c1fb82bbec46a58cf0e81d159bca0eb0.jpg) +a. hardware setup + +![](images/5ebd0578bf192c7f07b226dfb7482e868403baf62e87d563b8bb52b068800a89.jpg) +b. emulation method + +![](images/bc1a395ae3ab4ce0a6e9b1fe922696bd070b616be4805467decec7f880c82f46.jpg) +Figure 4. Lab prototype, and rolling shutter encoding scheme. (a) Rolling shutter hardware prototype with the camera components outlined in yellow and galvonic mirrors/synchronization hardware outlined in blue. (b) Compositing quadrature images to create an emulated rolling shutter snapshot. + +using a defocused cylindrical lens. Note that the optimal kernel for prefiltering is a 1D sinc function in the spatial domain (corresponding to eliminating all the overlapping frequencies). However, that is not physically possible. Designing the optimal optically-realizable kernel is beyond the scope of this paper. + +Assuming a 1D-Gaussian prefiltering kernel, we computed the effect of blur kernel size (measured in standard deviation $\sigma$ ) on the phase reconstruction accuracy. As shown in Fig. 7 (a), for all values of $k$ , the SNR initially improves when $\sigma$ is increased and then decreases showing that an optimal blur kernel size exists. This phenomenon occurs as prefiltering initially reduces the overlap between the ToF hologram and the twin but later reduces the frequency con + +![](images/89fb19e5ccee86a86e4eeb78d269f1859c05757e13efa86547e49f38ece1c33d.jpg) + +![](images/ffefeba3148c77b7c91ea04d0df1f5f4d55ef5fd450d36d43ccc05e6ad93d1a8.jpg) +Figure 5. Advantages of emulated snapshot capture. Amplitude and depth reconstructed by snapshot data captured with emulations (this paper) vs. single line ROI (ideal optical setup) and galvanic mirrors. The emulated measurements and the reconstructed phase are similar to the full prototype. We hence demonstrated all experiments with an emulated setup, as it enables a faithful evaluation of a true snapshot system. +Figure 6. Robustness to noise due to prefiltering. Prefiltering reduces aliasing and noise folding artifacts to improve the reconstruction quality. Compared to the 2D-blur kernel, the 1D-blur kernel in the direction of rolling shutter direction results in a significantly higher-quality reconstruction. Since the ToF hologram and twin overlap occur only in the rolling shutter direction, a 1D blur kernel preserves the spatial frequencies in the direction orthogonal to rolling shutter. + +tent in the captured ToF hologram. + +Optimal phase variation rate $k$ . In Fig. 7 (b), we plot optimal $\sigma$ value as a function of $R = 2\pi / k$ , which represents the average number of rows required before the $\theta$ + +![](images/24c1aa4ee3c15c6cc8289286a30a8e365a0c59ce7612da9cda2d7f4c08b2c4c5.jpg) +(a) + +![](images/78cf7a686275308789645f8694480559643bafe0490e3d32daf380819851548b.jpg) +(b) + +![](images/6d55e5df3a4e1e5e0b2172ab01c90a51e81106aa340e36f8b53615c292b00c8b.jpg) +Figure 7. Optimal prefilter size and phase variation rate. (a) We show the effect of the standard deviation of the blur kernel (blur kernel size) on the phase reconstruction accuracy for various phase variation rates $(k)$ . The optimal prefilter size depends on the phase variation rate. (b) The best phase reconstruction rate that results in best reconstruction quality is around $R = 4$ , and this is consistently observed for various scenes. $R = 4$ results in the least overlap between the ToF holography and its twin. + +![](images/28c9620ca409e7e3a451d10660bbab5decd8a4479ef1dd06567804f095f35b97.jpg) +Phase + +![](images/e0d3c3d9e8e4f0f15db8c5e06784d3fb3ddc699d229da11989d12cf872f1aa33.jpg) + +![](images/c310f7b4257fd98e4898ab2f063aa804ebc5ad1240ceb8d437d8c7ddc9f4f50a.jpg) + +![](images/6d74681d7cd7ee3edc1cab6348769271829f2d887fa47e7dcf87fd6781e94999.jpg) +10² 104 106 -2 0 2 + +![](images/4d2f7a93faa60db4e1d640fdb5e36d56edb25245174a22814aaf600616d7e11a.jpg) +Figure 8. Visualization of the effect of changing the phase variation rate. In practice, we take the Discrete Fourier Transform which is circular. The smaller the overlap between the hologram and twin, the better we can reconstruct the phase. + +value resets. From the graph, we can notice that the best SNR occurs at around $R = 3.5$ . While the optimal value depends on the noise and frequency content of the scene, we observed that it is always around $R = 4.0$ , and the SNR difference between the optimal and $R = 4.0$ is not signifi + +![](images/72e36c2de69899ed3af6bcee2d812a192d341b95611786c70902778b9760d4d4.jpg) +Figure 9. For the snapshot image, instead of the proposed Fourier technique, we can also use the standard N-bucket technique by using neighboring rows as a proxy for the remaining phases. However, the N-bucket technique performs significantly worse compared to the Fourier technique at all the phase variation rates and cannot handle non-integer values of $R$ . + +cant. At $R = 4$ , the overlap between the ToF hologram and the twin is minimal, and $\sigma = 1$ corresponds to suppressing half of the higher frequency content; hence, the optimal SNR is always around $R = 4$ . When $R = 0$ , the twin and hologram are inseparable and the phase cannot be correctly recovered as shown in Fig. 8. In the rest of the paper, we use the phase variation rate of $k = \pi /2$ and $\sigma = 1$ . + +Comparison with N-bucket technique Instead of the Fourier reconstruction method detailed in Sec. 4, we can also use the standard N-bucket technique presented in Sec. 3 by grouping R-rows with phase variations $\theta = \{0,2\pi /R,4\pi /R,\dots ,(R - 1) / R\}$ . Note that the N-bucket technique does not decrease the number of effective rows, as we can always group $R / 2$ rows around the current row to get all the phase variations, in a sliding window manner. However, unlike the Fourier reconstruction method, the N-bucket technique works only for integer values of $R$ . + +In Fig. 9, we compare the N-bucket technique with the Fourier technique and observe that the Fourier technique uniformly works better than the standard N-bucket technique for snapshot phase reconstruction. + +Comparison with conventional operation We compare the proposed snapshot technique with the conventional four-bucket method for the same exposure duration. We capture the snapshot image with an exposure duration of $T$ where $T = 100\mu s$ while the four quadrature measurements are captured with $T / 4$ . In Fig. 10, we compare phase reconstruction results for both techniques. For a fair comparison, we have prefiltered the phasors for both the conventional and snapshot techniques. Our method has an SNR of 29.86 dB for phase reconstruction, slightly higher than 28.56 dB for the conventional method but our technique performs uniformly better than the conventional technique for all $\sigma$ + +![](images/d334c6d5286d85f8a94c67785a80e6425b2e7e60155c75a56e199f5e1738ba3c.jpg) +Figure 10. Comparisons against quadrature reconstruction. For the same total exposure duration and optimal kernel size, our method performs similarly or marginally better, compared to the conventional quadrature measurement technique. Importantly, however, our technique requires $4 \times$ less bandwidth. + +values. While the proposed technique performs slightly better in this case, the required bandwidth is $4 \times$ smaller than the conventional method as our technique requires only one image. + +Optimal phase variation direction Rotating the Fourier shift direction, implementable by rotating the camera along its optical axis, can also reduce the aliasing artifacts depending on the edges in the scene. We acquire the optimal result when the majority of the high-frequency edges are parallel to the direction of the phase shift (which is the same as being perpendicular to the phase variation direction). In Fig. 11, we demonstrate the result of reconstructing a scene made up of rectilinear block objects. To ensure the scene stays the same when rotated, we apply a circular mask when comparing the result with the ground truth and compute the SNR. As the graph shows, rotating the input at $75^{\circ}$ yields the best result, since only a few rectilinear edges align with the vertical axis, the same orientation for the phase shift. + +# 7. Conclusions + +Inspired by off-axis holography, we proposed a snapshot Lidar using CW-ToF cameras, which captures amplitude and depth using a single image. We showed how defining a time-of-flight hologram and using rolling-shutter cameras allows us to translate off-axis principles to CW-ToF cameras. Extensive experiments with our lab prototype demon + +![](images/3875e5faa66e806a6e41bcefe263ca9f63978f31614bd6a3d8a51a50726e144f.jpg) +Figure 11. Improving reconstruction by rotating the camera. Rotating the rolling shutter or phase variation direction improves the reconstruction quality. When the phase variation direction is perpendicular to the dominant edge direction, then we attain the highest SNR. We change the phase variation direction by simply rotating the camera. + +strated that our snapshot imaging approach performs as well as conventional quadrature measurement-based approaches, while requiring $4 \times$ fewer measurements. + +As mentioned in the related work, continuous-wave time-of-flight cameras saw a proliferation of applications in the last decade. Translating the snapshot techniques proposed in this paper for non-sinusoidal codes [10], Doppler time-of-flight imaging [13, 14], frequency-based light transport probing [25], and time-gating [28], while non-trivial, can significantly improve all the applications. + +Our approach relies on spatial modulation to compute the ToF hologram, which required pre-filtering to avoid aliasing. As part of future work, we will explore machine learning-based techniques to relax the aliasing requirements. Data-free techniques such as deep image priors [29], and generative approaches such as diffusion models [5] will enable us to solve the inverse problem more robustly, and without explicit anti-aliasing constraints. + +We have translated snapshot off-axis imaging techniques to CWToF imaging. However, a wide variety of imaging ideas including high dynamic range imaging, light-field imaging, polarization imaging, and spectral imaging today are implemented with assorted pixels, which are expensive, prone to aliasing, or require custom demosaicking algorithms. Extending off-axis principles to create assorted frequency-embedding is an interesting future direction. + +# 8. Acknowledgements + +The authors thank Jeremy Klotz for his help with the hardware prototype. The research is partially supported by a Burke Research Initiation Award. + +# References + +[1] Supreeth Achar, Joseph R. Bartels, William L. 'Red' Whittaker, Kiriakos N. Kutulakos, and Srinivasa G. Narasimhan. 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Exploiting wavelength diversity for high resolution time-of-flight 3d imaging. 43(7):2193-2205, 2021. 3 +[23] Melexis. Melexis 75027 application note. https://media.melexis.com/ - /media/files/documents/product-flyers/mlx75027-product-flyer-melexis.pdf.4 +[24] Nikhil Naik, Achuta Kadambi, Christoph Rhemann, Shahram Izadi, Ramesh Raskar, and Sing Bing Kang. A light transport model for mitigating multipath interference in time-of-flight sensors. In CVPR, pages 73-81, 2015. 2, 3 +[25] Matthew O'Toole, Felix Heide, Lei Xiao, Matthias B Hullin, Wolfgang Heidrich, and Kiriakos N Kutulakos. Temporal frequency probing for 5D transient analysis of global light transport. ACM Transactions on Graphics (ToG), 33(4):1-11, 2014. 2, 8 +[26] Matthew O'Toole, Felix Heide, Lei Xiao, Matthias B Hullin, Wolfgang Heidrich, and Kiriakos N Kutulakos. Temporal frequency probing for 5d transient analysis of global light transport. ACM TOG, 33(4):1-11, 2014. 4 +[27] Hoover Rueda-Chacon, Juan F Floresz-Ospina, Daniel L Lau, and Gonzalo R Arce. Snapshot compressive tof+ spectral imaging via optimized color-coded apertures. 42(10):2346-2360, 2019. 2 +[28] Ryuichi Tadano, Adithya Kumar Pediredla, and Ashok Veeraraghavan. Depth selective camera: A direct, on-chip, programmable technique for depth selectivity in photography. In ICCV, 2015. 4, 8 +[29] Dmitry Ulyanov, Andrea Vedaldi, and Victor Lempitsky. Deep image prior. In CVPR, 2018. 8 +[30] Mian Wei, Navig Sarhangnejad, Zhengfan Xia, Nikita Gusev, Nikola Katic, Roman Genov, and Kiriakos N Kutulakos. Coded two-bucket cameras for computer vision. In ECCV, 2018. 3 + +[31] Di Wu, Andreas Velten, Matthew O'Toole, Belen Masia, Amit Agrawal, Qionghai Dai, and Ramesh Raskar. Decomposing global light transport using time of flight imaging. 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We propose a novel snapshot Lidar imaging system that is inspired by off-axis holography techniques. " + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "inline_equation", + "content": "(1^{\\mathrm{st}}" + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "text", + "content": " col.) Off-axis holography uses oblique illumination to separate the hologram and its twin in Fourier space. " + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "inline_equation", + "content": "(2^{\\mathrm{nd}}" + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "text", + "content": " col.) We leverage the rolling-shutter effect of amplitude modulated continuous wave time-of-flight (AMCW-ToF) cameras to emulate the off-axis principle, thereby separating the time-of-flight hologram and its twin in Fourier space. " + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "inline_equation", + "content": "(3^{\\mathrm{rd}}" + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "text", + "content": " col.) The conventional operation of AMCW-ToF Lidars requires four measurements, whereas our technique is " + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "inline_equation", + "content": "4\\mathrm{x}" + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "text", + "content": " faster, improving both the data bandwidth and temporal resolution. " + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "inline_equation", + "content": "(4^{\\mathrm{th}}" + }, + { + "bbox": [ + 45, + 413, + 547, + 480 + ], + "type": "text", + "content": " col.) 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A conventional CW-ToF camera requires illuminating the scene with a temporally varying light source and demodulating a set of quadrature measurements to recover the scene's depth and intensity. Capturing the four measurements in sequence renders the system slow, invariably causing inaccuracies in depth estimates due to motion in the scene or the camera. To mitigate this problem, we propose a snapshot Lidar that captures amplitude and phase simultaneously as a single time-of-flight hologram. Uniquely, our approach requires minimal changes to existing CW-ToF imaging hardware. To demonstrate the efficacy of the proposed system, we design and build a lab prototype, and evaluate it under varying scene geometries, illumina" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 491, + 548, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 548, + 598 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 548, + 598 + ], + "type": "text", + "content": "tion conditions, and compare the reconstructed depth measurements against conventional techniques. We rigorously evaluate the robustness of our system on diverse real-world scenes to show that our technique results in a significant reduction in data bandwidth with minimal loss in reconstruction accuracy. As high-resolution CW-ToF cameras are becoming ubiquitous, increasing their temporal resolution by four times enables robust real-time capture of geometries of dynamic scenes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 621, + 387, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 387, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 387, + 634 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras, also known as correlation-based time-of-flight or indirect time-of-flight cameras, are used as flash Lidars to compute scene depth, and are used in autonomous navigation, robotics [6, 13], and augmented reality [8]. AMCW-ToF cameras operate by projecting a" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "25203" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 288, + 184 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 288, + 184 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 288, + 184 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 288, + 184 + ], + "type": "table", + "html": "
illuminationreferencephysics
holographycoherent beamplanar beamoptical interference
off-axiscoherent beamtilted beamoptical interference
CW-ToFAMCWelectronic shutterelectronic multiplication
proposedAMCWrolling shutterelectronic multiplication
", + "image_path": "36d7375630fd731530dac31a473d82fc97cd2e08fa355ff169bb9b8ae57904b7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 287, + 269 + ], + "lines": [ + { + "bbox": [ + 46, + 192, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 287, + 269 + ], + "type": "text", + "content": "Table 1. Principles of holography, off-axis holography, CW-ToF, and proposed snapshot CW-ToF. We draw parallels between off-axis holographic setup, and our proposed Fourier embedded ToF, that allow us to show that using a rolling-shutter sensor and varying the reference phase during CW-ToF acquisition results in a snapshot capture of the \"ToF hologram\" that contains both the amplitude and depth (encoded in phase) of the scene." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 292, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 292, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 287, + 399 + ], + "type": "text", + "content": "temporally varying (often a sinusoidal) light source, and then correlating it on the sensor side with an appropriate (also often a sinusoid) decoding function. Depth is encoded in the phase of the measurements, and hence up to four measurements (quadrature) are required to robustly estimate the depth and intensity of the scene. These quadrature measurements are captured by temporal multiplexing, which invariably leads to lower frame rates and suffers from motion artifacts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 400, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 287, + 593 + ], + "type": "text", + "content": "Inspired by snapshot off-axis holography techniques, we propose a snapshot CW-ToF imaging technique that measures amplitude and depth using a single capture. The key observation is that by defining the time-of-flight hologram as the complex sinusoid whose amplitude and phase are proportional to the intensity and depth of the scene, we can draw parallels between holography and CW-ToF imaging techniques. This novel formulation of the ToF hologram enables us to translate off-axis techniques to CW-ToF imaging. In particular, by using rolling-shutter CW-ToF sensors [1] and spatially varying the reference phase of the coded exposure, we can emulate the off-axis holography effect and recover the complex-valued ToF hologram. In Tab. 1, we highlight the similarities and differences between holography, off-axis holography, CW-ToF, and the proposed imaging techniques." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 593, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 593, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 593, + 287, + 700 + ], + "type": "text", + "content": "To achieve snapshot depth imaging, we leverage the image formation model of CW-ToF cameras, and demonstrate our modification to enable the capture of a ToF hologram with unipolar (all-positive decoding function) and bipolar (positive and negative decoding function) codes. We then show analytical and computational techniques to recover amplitude and depth from a rolling-shutter image and the need for optical prefiltering to prevent aliasing and noise folding." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "We design and build a hardware setup built in the lab" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 240 + ], + "type": "text", + "content": "with a Melexis 75027 device with region-of-interest support and a galvanometer to emulate the rolling-shutter effect. Using this device, in Sec. 6, we demonstrate that the proposed technique reduces data bandwidth and improves frame rate on various scenes containing diffuse, specular, and refractive objects. The proposed technique is robust to dead and saturated pixels, thereby enabling depth imaging with slightly faulty sensors, and extremely bright settings. We carefully evaluate design parameters including prefiltering window size, and spatial phase variation rate, and provide an experimentally optimal set of values that are agnostic to scene conditions. We empirically show that the proposed Fourier-based reconstruction technique is superior to the standard N-bucket technique for reconstruction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 249, + 392, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 249, + 392, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 249, + 392, + 261 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 269, + 545, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 545, + 425 + ], + "type": "text", + "content": "Continuous wave time-of-flight cameras. CW-ToF cameras measure depth at each spatial pixel with a temporally modulated light source. The intensity of the scene is encoded in the amplitude, and depth in the phase, of the measurements. Typically four or more images, with different phases, are required to recover both amplitude and depth. These four measurements are obtained either with a spatially multiplexed sensor (similar to a Bayer pattern), or with sequential measurements [12]. Spatial multiplexing results in severe aliasing artifacts, and is inherently expensive and cumbersome to manufacture. In contrast, sequential measurements invariably result in motion artifacts when capturing dynamic scenes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "content": "Advances in CWToF sensing With the increasing number of practical applications for CWToF, work has been done to enhance its capabilities and mitigate its limitations. CS-ToF [20] is a compressive ToF imaging architecture aimed at overcoming sensor resolution limitations. As compressive sensing relies on the assumption of a linear measurement process for high resolution image estimation, CS-ToF uses a phasor representation inspired by Gupta [9] and O'Toole [25] of the ToF output to create a linear model between the scene and ToF measurements. In a process similar to single pixel imaging, laser light is reflected off of an object onto a high resolution digital micro-mirror device (DMD), and then relayed onto a lower resolution ToF sensor. By changing the DMD codes across multiple exposures, CS-ToF performs spatiotemporal multiplexing of the scene's amplitude and phase; however, sacrificing temporal resolution for spatial resolution. CWToF has also been combined with other modalities such as spectrum [27], light transport [24, 31], and light fields [15] that have significantly expanded the applications of CWToF cameras. Nevertheless, it is worth noting that there are few, if any, approaches that capture CWToF data in a snapshot manner, that is crucial for dynamic scenes." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25204" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "Superheterodyned interferometry. A related technology that enables snapshot ToF sensing is superheterodyned interferometric time-of-flight (SH-ToF) [21, 22], where two closely spaced illumination wavelengths combine to produce a much larger (heterodyned) synthetic wavelength. This approach however still requires capturing two separate images (one with each wavelength) to produce the final superheterodyned measurement. Recent work by Ballester et al. [3] demonstrated that SH-ToF can be combined with the off-axis holography to obtain a snapshot ToF imaging system. We next briefly discuss off-axis holography to understand its relevance to ToF sensing." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "type": "text", + "content": "Off-axis holography Off-axis holography [7, 19] is a widely known imaging technique for reconstructing the amplitude " + }, + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "type": "inline_equation", + "content": "(E_{s}(x,y))" + }, + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "type": "text", + "content": " and phase " + }, + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "type": "inline_equation", + "content": "(\\phi_s(x,y))" + }, + { + "bbox": [ + 46, + 230, + 289, + 302 + ], + "type": "text", + "content": " of a hologram with a single measurement. The experimental setup schematic is shown in the first column of Fig. 1. The measurement by the camera is given by" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 308, + 287, + 357 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 308, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 52, + 308, + 287, + 357 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I = \\left| E _ {s} (x, y) e ^ {- \\phi_ {s} (x, y)} + E _ {r} e ^ {- k \\sin (\\theta) x} \\right| ^ {2} \\\\ = \\left| E _ {s} (x, y) \\right| ^ {2} + \\left| E _ {r} \\right| ^ {2} + E _ {r} ^ {*} E _ {s} (x, y) e ^ {k \\sin (\\theta) x - \\phi_ {s} (x, y)} \\\\ + E _ {r} E _ {s} ^ {*} (x, y) e ^ {- k \\sin (\\theta) x + \\phi_ {s} (x, y)} \\tag {1} \\\\ \\end{array}", + "image_path": "3fd3efe539197427f2e5aecd2392bcf6efe33b177b071bcc2017e6230b03fe4e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "spans": [ + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "type": "text", + "content": "Off-axis holography embeds the hologram " + }, + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "type": "inline_equation", + "content": "(E_{s}(x,y)e^{-\\phi_{s}(x,y)})" + }, + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "type": "text", + "content": " and its twin " + }, + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "type": "inline_equation", + "content": "(E_{s}^{*}(x,y)e^{\\phi_{s}(x,y)})" + }, + { + "bbox": [ + 46, + 364, + 289, + 580 + ], + "type": "text", + "content": " separately in the Fourier domain allowing us to recover the hologram computationally. Ballester et al. [2] showed that off-axis techniques can be used in synthetic wavelength interferometry. Specifically, the system consisted of a colocated, dual wavelength illumination source, and two, spatially separated reference beams. The separated location implied that the phasor information was encoded in different parts of the Fourier spectrum, enabling a simple frequency domain post-processing algorithm to estimate depth information with a single image. Our technique is inspired by off-axis holography. Two key observations that enable our technique are (i) expressing the time-of-flight image formation model with complex sinusoids allows us to draw parallels between holography and AMCW-ToF (ii) the rolling-shutter effect allows us to emulate off-axis technique." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "Applications of CW-ToF cameras. Beyond depth imaging, CW-ToF cameras enable a plethora of important applications in imaging. For example, Callenberg et al. [4] showed that a CW-ToF camera can enable difference imaging, that is often useful for implementing convolutional operations within sensors. Achar et al. [1] showed that ToF sensors can be used to tease out sub-surface features through epipolar gating. Similarly, Naik et al. [24] and Kadambi et al. [16] showed that a light transport matrix-based formulation of ToF measurements enabled measur" + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 307, + 72, + 545, + 209 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 545, + 209 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 545, + 209 + ], + "type": "image", + "image_path": "858b901540602697be8862ab2f107e769bd32009fed8a8a8ecd6cb7b20ba7b2c.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 218, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 304, + 218, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 218, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. CW-ToF imaging systems. CW-ToF cameras use high-frequency illumination sources and exposure codes to indirectly measure the object's depth. The measurement is the product of the delayed illumination signal and programmatically phase-shifted exposure code. The delay encodes object depth and is recoverable by taking multiple measurements with varying phase-shift " + }, + { + "bbox": [ + 304, + 218, + 547, + 285 + ], + "type": "inline_equation", + "content": "(\\theta)" + }, + { + "bbox": [ + 304, + 218, + 547, + 285 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 304, + 545, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 364 + ], + "type": "text", + "content": "ing multipath interferences, that are key to measuring geometric properties of complex objects like metal and glass. Our proposed work enables a similar slew of applications beyond depth imaging, including sub-surface imaging and multipath interference reduction (via epipolar gating)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 373, + 437, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 437, + 387 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 437, + 387 + ], + "type": "text", + "content": "3. Technical Background" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": "As shown in Fig. 2, an amplitude-modulated continuous-wave time-of-flight camera (AMCW-ToF) has an illumination source whose amplitude " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "(e(t))" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": " varies over time at several tens of MHz. While these amplitude variations are typically sinusoidal, other modulations have been successfully demonstrated in the past [9-11] for various applications. The light received " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "(r(t))" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": " at the sensor is attenuated and delayed based on the light transport of the scene " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "(r(t) = Ae(t - \\tau))" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": " is the total time-of-travel of the light beam. Assuming a collocated light source and sensor and no multi-bounce paths, " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "\\tau = 2d\\omega /c" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": " is the distance to the object, " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": " is the modulation frequency, and " + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 304, + 393, + 545, + 621 + ], + "type": "text", + "content": " is the speed of light. The sensor temporal exposure (s(t)) is also modulated, typically as a square wave (unipolar or bipolar) with the same frequency as the illumination. Recent sensors mostly use bipolar coding with a two-bucket architecture [30], and the exposure duration is approximated with a sinusoidal modulation. The measurement by the sensor is given by" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 626, + 545, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 626, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 306, + 626, + 545, + 694 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} m _ {\\theta} = \\frac {1}{T} \\int_ {t = 0} ^ {T} A r (t) s (t) d t \\\\ = \\frac {A}{T} \\int_ {t = 0} ^ {T} \\sin (\\omega t + \\phi) \\sin (\\omega t + \\theta) d t = \\frac {A}{2} \\cos (\\theta - \\phi). \\tag {2} \\\\ \\end{array}", + "image_path": "3a437df8767135667b2a6bc178d4b8c0c9337d6f8ac6caeeede5572bae5e1f65.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "Most hardware implementations of CWToF Lidar mea" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25205" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "sure four images " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "m_0, m_{\\pi/2}, m_\\pi" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "m_{3\\pi/2}" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " and compute amplitude and phase as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 79, + 101, + 255, + 120 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 101, + 255, + 120 + ], + "spans": [ + { + "bbox": [ + 79, + 101, + 255, + 120 + ], + "type": "interline_equation", + "content": "A = 2 \\sqrt {(m _ {0} - m _ {\\pi}) ^ {2} + (m _ {\\pi / 2} - m _ {3 \\pi / 2}) ^ {2}}", + "image_path": "35fdf7c083472d9ce869939e223f646ad509211ff0d17704e84e59d10b5f1906.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 81, + 122, + 287, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 122, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 81, + 122, + 287, + 147 + ], + "type": "interline_equation", + "content": "\\phi = \\arctan \\frac {m _ {\\pi / 2} - m _ {3 \\pi / 2}}{m _ {0} - m _ {\\pi}}. \\tag {3}", + "image_path": "d1f560113c78680ca8903e0eaeff5fd446cc7ad7cc369014033c6e01f8775156.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "spans": [ + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "type": "text", + "content": "The quadrature technique is also extended to the N-tap technique [28] by taking " + }, + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\mathbf{N}" + }, + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "type": "text", + "content": " measurements corresponding to " + }, + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "type": "inline_equation", + "content": "\\theta = \\{0, 2\\pi / N, 4\\pi / N, c \\dots, 2\\pi (N - 1) / N\\}" + }, + { + "bbox": [ + 47, + 149, + 287, + 198 + ], + "type": "text", + "content": " and computing amplitude and phase as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 202, + 291, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 202, + 291, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 202, + 291, + 239 + ], + "type": "interline_equation", + "content": "A = \\sqrt {\\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2} + \\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2}}", + "image_path": "60b6f10c96ebc4d180560314cebca584750efdb0bfc8ed80b6ab63a200834233.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 48, + 242, + 287, + 274 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 242, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 48, + 242, + 287, + 274 + ], + "type": "interline_equation", + "content": "\\phi = \\arctan \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} / \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} \\tag {4}", + "image_path": "9fe648f41251cd8f694a6484a5e962a9685620778e02f83d1c6848baa6624654.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 277, + 287, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 277, + 287, + 302 + ], + "spans": [ + { + "bbox": [ + 47, + 277, + 287, + 302 + ], + "type": "text", + "content": "Unlike these techniques, we reconstruct amplitude and phase using a single image, which we discuss next." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 310, + 264, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 310, + 264, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 310, + 264, + 324 + ], + "type": "text", + "content": "4. Proposed Technique: Snapshot CWTof" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "content": "The key idea for measuring amplitude and depth using a single image is to spatially vary the phase " + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 331, + 287, + 486 + ], + "type": "text", + "content": " linearly along rows or columns during the exposure. We can achieve this spatial variation with simple hardware modifications by either (1) changing the existing hardware design with different exposure phase offsets per row/column, (2) using a rolling-shutter camera and changing the phase offset of either the illumination or sensor during each row capture, or (3) using a fast line sensor (or hardware region-of-interest supporting camera) and scanning the scene line by line with a Galvanic mirror while changing the phase offset of each line. We used the last alternative in this paper, as the Melexis 75027 supports hardware ROI [23]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "content": "To understand how linearly varying " + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "content": " embeds both amplitude and phase in the captured image, we follow the notation from O'Toole et al. [26], Li et al. [21], and Gupta et al. [9] and represent the amplitude and phase images with complex sinusoidal notation as " + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "inline_equation", + "content": "I(x,y) = A(x,y)e^{-j2d\\omega /c}" + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "content": " and the Fourier Transform of this sinusoid as " + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathcal{I}(\\omega_x,\\omega_y)" + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "content": ". For brevity, we define " + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\phi = 2d\\omega /c" + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "content": " as the phase shift of the illumination signal. Varying " + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 487, + 287, + 593 + ], + "type": "text", + "content": " linearly during the measurement results in" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 48, + 596, + 287, + 655 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 596, + 287, + 655 + ], + "spans": [ + { + "bbox": [ + 48, + 596, + 287, + 655 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} m _ {\\theta = k x} (x, y) = \\frac {A (x , y)}{2} \\cos (k x - \\phi (x, y)) \\\\ = \\frac {A (x , y)}{4} \\left(e ^ {j (k x - \\phi (x, y))} + e ^ {- j (k x - \\phi (x, y))}\\right) \\tag {5} \\\\ \\end{array}", + "image_path": "d0dc8767b2edb8e65c2e9a6cd066af68804af9f7e72b1be0a866abb2a0e0444d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 660, + 252, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 660, + 252, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 660, + 252, + 672 + ], + "type": "text", + "content": "Taking the Fourier transform on both sides, we get" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 48, + 676, + 287, + 709 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 676, + 287, + 709 + ], + "spans": [ + { + "bbox": [ + 48, + 676, + 287, + 709 + ], + "type": "interline_equation", + "content": "\\mathcal {F} _ {m _ {k x}} \\left(\\omega_ {x}, \\omega_ {y}\\right) = \\frac {1}{4} \\left(\\mathcal {I} \\left(\\omega_ {x} - k, \\omega_ {y}\\right) + \\mathcal {I} ^ {*} \\left(k - \\omega_ {x}, - \\omega_ {y}\\right)\\right), \\tag {6}", + "image_path": "6b0bd3f5aac2516feddaade269bc7e3d80018c9884e7dea65f48db50e8496219.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": "which is similar to the off-axis holography Eq. (1). Therefore, we will refer to the complex sinusoidal notation " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "(I(x,y))" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " as the ToF hologram and its complex conjugate " + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "(I^{*}(x,y))" + }, + { + "bbox": [ + 305, + 72, + 545, + 120 + ], + "type": "text", + "content": " as the ToF twin." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 121, + 545, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 545, + 202 + ], + "type": "text", + "content": "As depicted in Fig. 3, to recover the ToF hologram from the image captured by varying " + }, + { + "bbox": [ + 304, + 121, + 545, + 202 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 121, + 545, + 202 + ], + "type": "text", + "content": " linearly, we take the Fourier transform of the measured image, filter the ToF twin, right shift the ToF hologram, and compute the inverse Fourier transform. The amplitude and phase of the inverse Fourier transform result are the amplitude and phase of the scene." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 217, + 545, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 288 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 288 + ], + "type": "text", + "content": "Extension to unipolar codes. Most recent ToF sensors use a two-bucket architecture to suppress background illumination; hence, the codes are bipolar. However, our technique is also amenable to unipolar-coded time-of-flight cameras and imperfect two-bucket architecture cameras. In this case, the measurement model becomes" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 372, + 293, + 545, + 316 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 293, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 372, + 293, + 545, + 316 + ], + "type": "interline_equation", + "content": "m _ {\\theta} = \\frac {A}{2} \\cos (\\theta - \\phi) + a. \\tag {7}", + "image_path": "06bd1fdf19e5c5cb6046671b14c94f2cba32310bfb80cbb6fe54d3623b7b30f3.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 319, + 545, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 356 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 319, + 545, + 356 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 319, + 545, + 356 + ], + "type": "text", + "content": " is proportional to the ambient background light intensity. In this case, the Fourier transform has a DC component that can be filtered out along with the ToF twin." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 369, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 453 + ], + "type": "text", + "content": "Aliasing, noise folding, and prefiltering. From Fig. 3 (b), we notice that the ToF hologram and twin overlap in the Fourier domain. This overlap results in aliasing, where the high-frequency content of the ToF twin may appear as low-frequency content of the ToF hologram, and noise folding, where the twin's noise folds into the ToF hologram's noise." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 453, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 545, + 525 + ], + "type": "text", + "content": "To mitigate aliasing and noise folding, we optically filter the high-resolution ToF hologram before the linear phase shifting and measurement. In the hardware implementation, we achieve this by simply defocusing the imaging lens in front of the sensor. This simple blurring operation reduces aliasing and noise folding artifacts (Fig. 3 (d, e))." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 525, + 545, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 609 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 609 + ], + "type": "text", + "content": "Therefore, while the proposed snapshot Lidar technique can capture amplitude and phase with a single image, it does so by sacrificing spatial resolution for temporal resolution. As spatial resolutions of imaging sensors keep increasing (compare PMD vs DME660 vs. Melexis) due to better fabrication techniques, trading spatial resolution for improving temporal resolution is arguably more useful." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 623, + 545, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 623, + 545, + 682 + ], + "spans": [ + { + "bbox": [ + 304, + 623, + 545, + 682 + ], + "type": "text", + "content": "Phase noise. As with any optical measurements, the recovered phase will have noise due to shot noise in the measurements. This shot noise is present even for the standard N-bucket technique [17, 18]. The standard deviation of the phase noise for the snapshot technique is" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 389, + 686, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 686, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 389, + 686, + 545, + 712 + ], + "type": "interline_equation", + "content": "\\sigma_ {\\phi} ^ {2} \\approx \\frac {\\partial \\phi}{\\partial m _ {k x}} m _ {k x} \\tag {8}", + "image_path": "64eb34ac499eac0ebdcc6815bd742db8dcf5237c72402ca483a5e3804ebdc498.jpg" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25206" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 153, + 209 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 153, + 209 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 153, + 209 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 153, + 209 + ], + "type": "image", + "image_path": "82f479d141147271f6a5fef43b6752e959fa1bbd78127fcf9202efa2fe8bfd05.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 210, + 141, + 220 + ], + "lines": [ + { + "bbox": [ + 72, + 210, + 141, + 220 + ], + "spans": [ + { + "bbox": [ + 72, + 210, + 141, + 220 + ], + "type": "text", + "content": "(a) snapshot image" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 154, + 72, + 246, + 209 + ], + "blocks": [ + { + "bbox": [ + 154, + 72, + 246, + 209 + ], + "lines": [ + { + "bbox": [ + 154, + 72, + 246, + 209 + ], + "spans": [ + { + "bbox": [ + 154, + 72, + 246, + 209 + ], + "type": "image", + "image_path": "bb781112949977db1a30be2964b570d37f9ae631392b586de5bcf3fcdf676fc3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 161, + 210, + 237, + 220 + ], + "lines": [ + { + "bbox": [ + 161, + 210, + 237, + 220 + ], + "spans": [ + { + "bbox": [ + 161, + 210, + 237, + 220 + ], + "type": "text", + "content": "(b) Fourier transform" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 247, + 72, + 338, + 209 + ], + "blocks": [ + { + "bbox": [ + 247, + 72, + 338, + 209 + ], + "lines": [ + { + "bbox": [ + 247, + 72, + 338, + 209 + ], + "spans": [ + { + "bbox": [ + 247, + 72, + 338, + 209 + ], + "type": "image", + "image_path": "0116208e53f9efb098138a9b858810ddb3c5756a52da370617890f66057846ed.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 252, + 210, + 331, + 220 + ], + "lines": [ + { + "bbox": [ + 252, + 210, + 331, + 220 + ], + "spans": [ + { + "bbox": [ + 252, + 210, + 331, + 220 + ], + "type": "text", + "content": "(c) filtered and shifted" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 228, + 547, + 296 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 547, + 296 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 547, + 296 + ], + "type": "text", + "content": "Figure 3. Snapshot CWToF decoding, and effect of prefiltering. (a) captured snapshot CW-ToF image. (b) Fourier transform of snapshot image. (c) We filter out the twin and frequency shift the hologram in the Fourier domain to recover the ToF hologram. (d) We reconstruct the phase by computing the phase of the inverse Fourier transform of (c). (top row vs. bottom row) We prefilter the ToF hologram using a defocused imaging lens, which can decrease the overlap between the hologram and its twin. The prefiltering decreases aliasing and noise folding, resulting in a 3dB SNR gain (" + }, + { + "bbox": [ + 46, + 228, + 547, + 296 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 46, + 228, + 547, + 296 + ], + "type": "text", + "content": " smaller phase error). (e) zoomed-in offsets. (left) Without prefiltering, the high-frequency phase noise of the twin shows up as the low-frequency phase noise. (right) aliasing decreases with prefiltering." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 340, + 72, + 432, + 209 + ], + "blocks": [ + { + "bbox": [ + 340, + 72, + 432, + 209 + ], + "lines": [ + { + "bbox": [ + 340, + 72, + 432, + 209 + ], + "spans": [ + { + "bbox": [ + 340, + 72, + 432, + 209 + ], + "type": "image", + "image_path": "9eb1412beb1e5884ffd91c73034ea91a2485e48bd85359707b0260488fa7b931.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 353, + 210, + 424, + 220 + ], + "lines": [ + { + "bbox": [ + 353, + 210, + 424, + 220 + ], + "spans": [ + { + "bbox": [ + 353, + 210, + 424, + 220 + ], + "type": "text", + "content": "(d) recovered phase" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 432, + 70, + 542, + 209 + ], + "blocks": [ + { + "bbox": [ + 432, + 70, + 542, + 209 + ], + "lines": [ + { + "bbox": [ + 432, + 70, + 542, + 209 + ], + "spans": [ + { + "bbox": [ + 432, + 70, + 542, + 209 + ], + "type": "image", + "image_path": "06156c8f4d30381cc2babfc53d103a89f08a5d6db9024d4ac46cb8597556ef80.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 457, + 210, + 533, + 220 + ], + "lines": [ + { + "bbox": [ + 457, + 210, + 533, + 220 + ], + "spans": [ + { + "bbox": [ + 457, + 210, + 533, + 220 + ], + "type": "text", + "content": "(e) zoomed in offsets" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 309, + 186, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 309, + 186, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 309, + 186, + 322 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 309, + 186, + 322 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 309, + 186, + 322 + ], + "type": "text", + "content": " is explicitly expressed as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 56, + 327, + 277, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 327, + 277, + 355 + ], + "spans": [ + { + "bbox": [ + 56, + 327, + 277, + 355 + ], + "type": "interline_equation", + "content": "\\phi (x, y) = \\arctan \\left(\\frac {m _ {k x} (x , y) \\sin (k x) * \\operatorname {s i n c} (k x)}{m _ {k x} (x , y) \\cos (k x) * \\operatorname {s i n c} (k x)}\\right).", + "image_path": "f66db92c2ed8120351a1cc2d1b6a789a12c6d3cd25adaaa15674c2ddab9354a4.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 360, + 288, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 288, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 288, + 433 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 360, + 288, + 433 + ], + "type": "inline_equation", + "content": "\\circledast" + }, + { + "bbox": [ + 46, + 360, + 288, + 433 + ], + "type": "text", + "content": " is spatial convolution. We show the derivation in the supplementary material. An analytical comparison of the noise variance between the N-bucket and snapshot techniques is not feasible. Instead, in Sec. 6, we show empirical comparison and show that the snapshot phase measurement does not result in additional phase noise." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 442, + 163, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 163, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 163, + 456 + ], + "type": "text", + "content": "5. Experimental setup" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 462, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 545 + ], + "type": "text", + "content": "To implement our method, we use the EVK75027-110-940-2 evaluation kit (EVK) by Melexis which uses diffused " + }, + { + "bbox": [ + 46, + 462, + 287, + 545 + ], + "type": "inline_equation", + "content": "940\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 462, + 287, + 545 + ], + "type": "text", + "content": " VCSEL diodes for illumination and a Melexis 75027 CWToF sensor. While the sensor is a global shutter, we can create the rolling shutter effect by taking advantage of the sensor's hardware programmable ROI to reduce the per-frame capture/readout to a single row." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "For our experiments, we mount the EVK75027 to a linear 3D stage and carefully align the view to a set of 2-axis galvanic mirrors (GVS012) from Thorlabs. Then, we reduce the ROI of the camera to a single line, and steer the view of the galvos with a DAQ. Additionally, we separated the illumination board from the rest of the EVK and mounted it on top of the galvanic mirrors for approximate collocation of light source and apparent camera location. The MLX75027 module contained a firmware lock on the frame rate at 100 fps, severely limiting our capture speed when the ROI is reduced to only a single line. However, our setup demonstrates a proof-of-concept, and future versions of Melexis cameras without a firmware lock will enable a real-time operation." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 309, + 547, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 309, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 304, + 309, + 547, + 452 + ], + "type": "text", + "content": "One way to emulate snapshot measurements from our setup is to capture multiple images with varying phases and appropriately select the rows/columns in the image. In practice, we found it to be significantly simpler and convenient to conduct most of our experiments. In Fig. 4, we show the hardware prototype with fast-scanning galvonic mirrors. Additionally in Fig. 5, we compare results from an emulated versus hardware implemented snapshot capture and notice that the techniques result in the same amplitude and phase estimates. For more details about the hardware prototype and emulation method, we refer the reader to the supplemental material." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 459, + 388, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 388, + 472 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 388, + 472 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 475, + 546, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 546, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 546, + 631 + ], + "type": "text", + "content": "In this section, we use the hardware setup and emulation technique described in Sec. 5 to evaluate the proposed snapshot technique systematically. We show that (1) prefiltering improves signal-to-noise ratio (SNR) and prefiltering with cylindrical lenses is better than regular lenses; (2) the optimal phase variation rate is " + }, + { + "bbox": [ + 304, + 475, + 546, + 631 + ], + "type": "inline_equation", + "content": "(k = \\frac{\\pi}{2}\\mathrm{line}^{-1})" + }, + { + "bbox": [ + 304, + 475, + 546, + 631 + ], + "type": "text", + "content": "; (3) the Fourier technique is superior to the N-bucket technique for snapshot images; (4) the snapshot technique does not add any additional noise and (5) is robust to saturated and dead pixels; (6) rotating the phase variation (by rotating the camera itself) decreases aliasing. In the supplementary, we show extended results and a comparison with the dual phase mode of the epc660 camera. We share our code on GitHub." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "Optimal prefiltering kernel. As mentioned in Sec. 4, prefiltering reduces aliasing and noise folding artifacts. As aliasing and noise folding occur in the direction of the rolling shutter, blurring the ToF hologram only in the rolling shutter direction is better than isotropic blurring as shown in Fig. 6. We can implement hardware anisotropic blurring by" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25207" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 153, + 202 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 153, + 202 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 153, + 202 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 153, + 202 + ], + "type": "image", + "image_path": "177cc8cf5178c9d80f3da230e8ba5f6a36d86ed42c212337a748dc69c859c7d6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 206, + 74, + 218 + ], + "blocks": [ + { + "bbox": [ + 59, + 206, + 74, + 218 + ], + "lines": [ + { + "bbox": [ + 59, + 206, + 74, + 218 + ], + "spans": [ + { + "bbox": [ + 59, + 206, + 74, + 218 + ], + "type": "image", + "image_path": "548834f57c7c163227eabea55c2d0433f86eb4e93fe6ea77bbad2e737fef1e3b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 207, + 141, + 216 + ], + "lines": [ + { + "bbox": [ + 75, + 207, + 141, + 216 + ], + "spans": [ + { + "bbox": [ + 75, + 207, + 141, + 216 + ], + "type": "text", + "content": "camera components" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 157, + 72, + 258, + 202 + ], + "blocks": [ + { + "bbox": [ + 157, + 72, + 258, + 202 + ], + "lines": [ + { + "bbox": [ + 157, + 72, + 258, + 202 + ], + "spans": [ + { + "bbox": [ + 157, + 72, + 258, + 202 + ], + "type": "image", + "image_path": "4781d74b6cf3ced22fb6781c5ae156e0e529d0f48649239e66fe28fae44228e1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 186, + 205, + 258, + 220 + ], + "lines": [ + { + "bbox": [ + 186, + 205, + 258, + 220 + ], + "spans": [ + { + "bbox": [ + 186, + 205, + 258, + 220 + ], + "type": "text", + "content": "galvo/synchronization components" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 168, + 205, + 183, + 217 + ], + "blocks": [ + { + "bbox": [ + 168, + 205, + 183, + 217 + ], + "lines": [ + { + "bbox": [ + 168, + 205, + 183, + 217 + ], + "spans": [ + { + "bbox": [ + 168, + 205, + 183, + 217 + ], + "type": "image", + "image_path": "965c574f4f684df40ca0ce49fd399496c1fb82bbec46a58cf0e81d159bca0eb0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 123, + 220, + 197, + 232 + ], + "lines": [ + { + "bbox": [ + 123, + 220, + 197, + 232 + ], + "spans": [ + { + "bbox": [ + 123, + 220, + 197, + 232 + ], + "type": "text", + "content": "a. hardware setup" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 265, + 111, + 545, + 202 + ], + "blocks": [ + { + "bbox": [ + 265, + 111, + 545, + 202 + ], + "lines": [ + { + "bbox": [ + 265, + 111, + 545, + 202 + ], + "spans": [ + { + "bbox": [ + 265, + 111, + 545, + 202 + ], + "type": "image", + "image_path": "5ebd0578bf192c7f07b226dfb7482e868403baf62e87d563b8bb52b068800a89.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 370, + 219, + 457, + 229 + ], + "lines": [ + { + "bbox": [ + 370, + 219, + 457, + 229 + ], + "spans": [ + { + "bbox": [ + 370, + 219, + 457, + 229 + ], + "type": "text", + "content": "b. emulation method" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 48, + 293, + 285, + 434 + ], + "blocks": [ + { + "bbox": [ + 46, + 240, + 547, + 275 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 547, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 547, + 275 + ], + "type": "text", + "content": "Figure 4. Lab prototype, and rolling shutter encoding scheme. (a) Rolling shutter hardware prototype with the camera components outlined in yellow and galvonic mirrors/synchronization hardware outlined in blue. (b) Compositing quadrature images to create an emulated rolling shutter snapshot." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 293, + 285, + 434 + ], + "lines": [ + { + "bbox": [ + 48, + 293, + 285, + 434 + ], + "spans": [ + { + "bbox": [ + 48, + 293, + 285, + 434 + ], + "type": "image", + "image_path": "bc1a395ae3ab4ce0a6e9b1fe922696bd070b616be4805467decec7f880c82f46.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 616 + ], + "type": "text", + "content": "using a defocused cylindrical lens. Note that the optimal kernel for prefiltering is a 1D sinc function in the spatial domain (corresponding to eliminating all the overlapping frequencies). However, that is not physically possible. Designing the optimal optically-realizable kernel is beyond the scope of this paper." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": "Assuming a 1D-Gaussian prefiltering kernel, we computed the effect of blur kernel size (measured in standard deviation " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ") on the phase reconstruction accuracy. As shown in Fig. 7 (a), for all values of " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": ", the SNR initially improves when " + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 617, + 287, + 714 + ], + "type": "text", + "content": " is increased and then decreases showing that an optimal blur kernel size exists. This phenomenon occurs as prefiltering initially reduces the overlap between the ToF hologram and the twin but later reduces the frequency con" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 306, + 293, + 545, + 376 + ], + "blocks": [ + { + "bbox": [ + 306, + 293, + 545, + 376 + ], + "lines": [ + { + "bbox": [ + 306, + 293, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 545, + 376 + ], + "type": "image", + "image_path": "89fb19e5ccee86a86e4eeb78d269f1859c05757e13efa86547e49f38ece1c33d.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 306, + 378, + 543, + 531 + ], + "blocks": [ + { + "bbox": [ + 46, + 441, + 287, + 518 + ], + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 518 + ], + "type": "text", + "content": "Figure 5. Advantages of emulated snapshot capture. Amplitude and depth reconstructed by snapshot data captured with emulations (this paper) vs. single line ROI (ideal optical setup) and galvanic mirrors. The emulated measurements and the reconstructed phase are similar to the full prototype. We hence demonstrated all experiments with an emulated setup, as it enables a faithful evaluation of a true snapshot system." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 306, + 378, + 543, + 531 + ], + "lines": [ + { + "bbox": [ + 306, + 378, + 543, + 531 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 543, + 531 + ], + "type": "image", + "image_path": "ffefeba3148c77b7c91ea04d0df1f5f4d55ef5fd450d36d43ccc05e6ad93d1a8.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 540, + 545, + 628 + ], + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 628 + ], + "type": "text", + "content": "Figure 6. Robustness to noise due to prefiltering. Prefiltering reduces aliasing and noise folding artifacts to improve the reconstruction quality. Compared to the 2D-blur kernel, the 1D-blur kernel in the direction of rolling shutter direction results in a significantly higher-quality reconstruction. Since the ToF hologram and twin overlap occur only in the rolling shutter direction, a 1D blur kernel preserves the spatial frequencies in the direction orthogonal to rolling shutter." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 650, + 446, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 650, + 446, + 662 + ], + "spans": [ + { + "bbox": [ + 306, + 650, + 446, + 662 + ], + "type": "text", + "content": "tent in the captured ToF hologram." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Optimal phase variation rate " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": ". In Fig. 7 (b), we plot optimal " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": " value as a function of " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "R = 2\\pi / k" + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": ", which represents the average number of rows required before the " + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25208" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 162, + 188 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 162, + 188 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 162, + 188 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 162, + 188 + ], + "type": "image", + "image_path": "24c1aa4ee3c15c6cc8289286a30a8e365a0c59ce7612da9cda2d7f4c08b2c4c5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 102, + 194, + 115, + 204 + ], + "lines": [ + { + "bbox": [ + 102, + 194, + 115, + 204 + ], + "spans": [ + { + "bbox": [ + 102, + 194, + 115, + 204 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 160, + 72, + 286, + 189 + ], + "blocks": [ + { + "bbox": [ + 160, + 72, + 286, + 189 + ], + "lines": [ + { + "bbox": [ + 160, + 72, + 286, + 189 + ], + "spans": [ + { + "bbox": [ + 160, + 72, + 286, + 189 + ], + "type": "image", + "image_path": "78cf7a686275308789645f8694480559643bafe0490e3d32daf380819851548b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 226, + 192, + 239, + 202 + ], + "lines": [ + { + "bbox": [ + 226, + 192, + 239, + 202 + ], + "spans": [ + { + "bbox": [ + 226, + 192, + 239, + 202 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 320, + 179, + 407 + ], + "blocks": [ + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "text", + "content": "Figure 7. Optimal prefilter size and phase variation rate. (a) We show the effect of the standard deviation of the blur kernel (blur kernel size) on the phase reconstruction accuracy for various phase variation rates " + }, + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "inline_equation", + "content": "(k)" + }, + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "text", + "content": ". The optimal prefilter size depends on the phase variation rate. (b) The best phase reconstruction rate that results in best reconstruction quality is around " + }, + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "inline_equation", + "content": "R = 4" + }, + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "text", + "content": ", and this is consistently observed for various scenes. " + }, + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "inline_equation", + "content": "R = 4" + }, + { + "bbox": [ + 46, + 216, + 287, + 304 + ], + "type": "text", + "content": " results in the least overlap between the ToF holography and its twin." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 320, + 179, + 407 + ], + "lines": [ + { + "bbox": [ + 50, + 320, + 179, + 407 + ], + "spans": [ + { + "bbox": [ + 50, + 320, + 179, + 407 + ], + "type": "image", + "image_path": "6d55e5df3a4e1e5e0b2172ab01c90a51e81106aa340e36f8b53615c292b00c8b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 185, + 333, + 282, + 407 + ], + "blocks": [ + { + "bbox": [ + 201, + 321, + 247, + 332 + ], + "lines": [ + { + "bbox": [ + 201, + 321, + 247, + 332 + ], + "spans": [ + { + "bbox": [ + 201, + 321, + 247, + 332 + ], + "type": "text", + "content": "Phase" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 185, + 333, + 282, + 407 + ], + "lines": [ + { + "bbox": [ + 185, + 333, + 282, + 407 + ], + "spans": [ + { + "bbox": [ + 185, + 333, + 282, + 407 + ], + "type": "image", + "image_path": "28c9620ca409e7e3a451d10660bbab5decd8a4479ef1dd06567804f095f35b97.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 53, + 408, + 179, + 480 + ], + "blocks": [ + { + "bbox": [ + 53, + 408, + 179, + 480 + ], + "lines": [ + { + "bbox": [ + 53, + 408, + 179, + 480 + ], + "spans": [ + { + "bbox": [ + 53, + 408, + 179, + 480 + ], + "type": "image", + "image_path": "e0d3c3d9e8e4f0f15db8c5e06784d3fb3ddc699d229da11989d12cf872f1aa33.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 185, + 408, + 281, + 480 + ], + "blocks": [ + { + "bbox": [ + 185, + 408, + 281, + 480 + ], + "lines": [ + { + "bbox": [ + 185, + 408, + 281, + 480 + ], + "spans": [ + { + "bbox": [ + 185, + 408, + 281, + 480 + ], + "type": "image", + "image_path": "c310f7b4257fd98e4898ab2f063aa804ebc5ad1240ceb8d437d8c7ddc9f4f50a.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 49, + 483, + 181, + 556 + ], + "blocks": [ + { + "bbox": [ + 49, + 483, + 181, + 556 + ], + "lines": [ + { + "bbox": [ + 49, + 483, + 181, + 556 + ], + "spans": [ + { + "bbox": [ + 49, + 483, + 181, + 556 + ], + "type": "image", + "image_path": "6d74681d7cd7ee3edc1cab6348769271829f2d887fa47e7dcf87fd6781e94999.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 95, + 561, + 269, + 573 + ], + "lines": [ + { + "bbox": [ + 95, + 561, + 269, + 573 + ], + "spans": [ + { + "bbox": [ + 95, + 561, + 269, + 573 + ], + "type": "text", + "content": "10² 104 106 -2 0 2" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 184, + 483, + 283, + 555 + ], + "blocks": [ + { + "bbox": [ + 184, + 483, + 283, + 555 + ], + "lines": [ + { + "bbox": [ + 184, + 483, + 283, + 555 + ], + "spans": [ + { + "bbox": [ + 184, + 483, + 283, + 555 + ], + "type": "image", + "image_path": "4d2f7a93faa60db4e1d640fdb5e36d56edb25245174a22814aaf600616d7e11a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 584, + 287, + 628 + ], + "lines": [ + { + "bbox": [ + 46, + 584, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 584, + 287, + 628 + ], + "type": "text", + "content": "Figure 8. Visualization of the effect of changing the phase variation rate. In practice, we take the Discrete Fourier Transform which is circular. The smaller the overlap between the hologram and twin, the better we can reconstruct the phase." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "value resets. From the graph, we can notice that the best SNR occurs at around " + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "R = 3.5" + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": ". While the optimal value depends on the noise and frequency content of the scene, we observed that it is always around " + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "R = 4.0" + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": ", and the SNR difference between the optimal and " + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "inline_equation", + "content": "R = 4.0" + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": " is not signifi" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 306, + 72, + 541, + 182 + ], + "blocks": [ + { + "bbox": [ + 306, + 72, + 541, + 182 + ], + "lines": [ + { + "bbox": [ + 306, + 72, + 541, + 182 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 541, + 182 + ], + "type": "image", + "image_path": "72e36c2de69899ed3af6bcee2d812a192d341b95611786c70902778b9760d4d4.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 193, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 258 + ], + "type": "text", + "content": "Figure 9. For the snapshot image, instead of the proposed Fourier technique, we can also use the standard N-bucket technique by using neighboring rows as a proxy for the remaining phases. However, the N-bucket technique performs significantly worse compared to the Fourier technique at all the phase variation rates and cannot handle non-integer values of " + }, + { + "bbox": [ + 304, + 193, + 545, + 258 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 193, + 545, + 258 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": "cant. At " + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "inline_equation", + "content": "R = 4" + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": ", the overlap between the ToF hologram and the twin is minimal, and " + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\sigma = 1" + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": " corresponds to suppressing half of the higher frequency content; hence, the optimal SNR is always around " + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "inline_equation", + "content": "R = 4" + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "inline_equation", + "content": "R = 0" + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": ", the twin and hologram are inseparable and the phase cannot be correctly recovered as shown in Fig. 8. In the rest of the paper, we use the phase variation rate of " + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "inline_equation", + "content": "k = \\pi /2" + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\sigma = 1" + }, + { + "bbox": [ + 304, + 281, + 545, + 365 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "text", + "content": "Comparison with N-bucket technique Instead of the Fourier reconstruction method detailed in Sec. 4, we can also use the standard N-bucket technique presented in Sec. 3 by grouping R-rows with phase variations " + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\theta = \\{0,2\\pi /R,4\\pi /R,\\dots ,(R - 1) / R\\}" + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "text", + "content": ". Note that the N-bucket technique does not decrease the number of effective rows, as we can always group " + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "inline_equation", + "content": "R / 2" + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "text", + "content": " rows around the current row to get all the phase variations, in a sliding window manner. However, unlike the Fourier reconstruction method, the N-bucket technique works only for integer values of " + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 383, + 545, + 502 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 504, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 552 + ], + "type": "text", + "content": "In Fig. 9, we compare the N-bucket technique with the Fourier technique and observe that the Fourier technique uniformly works better than the standard N-bucket technique for snapshot phase reconstruction." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Comparison with conventional operation We compare the proposed snapshot technique with the conventional four-bucket method for the same exposure duration. We capture the snapshot image with an exposure duration of " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "T = 100\\mu s" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": " while the four quadrature measurements are captured with " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "T / 4" + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": ". In Fig. 10, we compare phase reconstruction results for both techniques. For a fair comparison, we have prefiltered the phasors for both the conventional and snapshot techniques. Our method has an SNR of 29.86 dB for phase reconstruction, slightly higher than 28.56 dB for the conventional method but our technique performs uniformly better than the conventional technique for all " + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\sigma" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25209" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 286, + 289 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 286, + 289 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 286, + 289 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 286, + 289 + ], + "type": "image", + "image_path": "d334c6d5286d85f8a94c67785a80e6425b2e7e60155c75a56e199f5e1738ba3c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "type": "text", + "content": "Figure 10. Comparisons against quadrature reconstruction. For the same total exposure duration and optimal kernel size, our method performs similarly or marginally better, compared to the conventional quadrature measurement technique. Importantly, however, our technique requires " + }, + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 297, + 287, + 354 + ], + "type": "text", + "content": " less bandwidth." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 374, + 288, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 288, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 288, + 424 + ], + "type": "text", + "content": "values. While the proposed technique performs slightly better in this case, the required bandwidth is " + }, + { + "bbox": [ + 46, + 374, + 288, + 424 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 46, + 374, + 288, + 424 + ], + "type": "text", + "content": " smaller than the conventional method as our technique requires only one image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 441, + 289, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 289, + 610 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 289, + 610 + ], + "type": "text", + "content": "Optimal phase variation direction Rotating the Fourier shift direction, implementable by rotating the camera along its optical axis, can also reduce the aliasing artifacts depending on the edges in the scene. We acquire the optimal result when the majority of the high-frequency edges are parallel to the direction of the phase shift (which is the same as being perpendicular to the phase variation direction). In Fig. 11, we demonstrate the result of reconstructing a scene made up of rectilinear block objects. To ensure the scene stays the same when rotated, we apply a circular mask when comparing the result with the ground truth and compute the SNR. As the graph shows, rotating the input at " + }, + { + "bbox": [ + 46, + 441, + 289, + 610 + ], + "type": "inline_equation", + "content": "75^{\\circ}" + }, + { + "bbox": [ + 46, + 441, + 289, + 610 + ], + "type": "text", + "content": " yields the best result, since only a few rectilinear edges align with the vertical axis, the same orientation for the phase shift." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 621, + 125, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 125, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 125, + 634 + ], + "type": "text", + "content": "7. Conclusions" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": "Inspired by off-axis holography, we proposed a snapshot Lidar using CW-ToF cameras, which captures amplitude and depth using a single image. We showed how defining a time-of-flight hologram and using rolling-shutter cameras allows us to translate off-axis principles to CW-ToF cameras. Extensive experiments with our lab prototype demon" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 188 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 188 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 188 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 188 + ], + "type": "image", + "image_path": "3875e5faa66e806a6e41bcefe263ca9f63978f31614bd6a3d8a51a50726e144f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 198, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 266 + ], + "type": "text", + "content": "Figure 11. Improving reconstruction by rotating the camera. Rotating the rolling shutter or phase variation direction improves the reconstruction quality. When the phase variation direction is perpendicular to the dominant edge direction, then we attain the highest SNR. We change the phase variation direction by simply rotating the camera." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 295, + 547, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 295, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 304, + 295, + 547, + 332 + ], + "type": "text", + "content": "strated that our snapshot imaging approach performs as well as conventional quadrature measurement-based approaches, while requiring " + }, + { + "bbox": [ + 304, + 295, + 547, + 332 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 304, + 295, + 547, + 332 + ], + "type": "text", + "content": " fewer measurements." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 336, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 547, + 421 + ], + "type": "text", + "content": "As mentioned in the related work, continuous-wave time-of-flight cameras saw a proliferation of applications in the last decade. Translating the snapshot techniques proposed in this paper for non-sinusoidal codes [10], Doppler time-of-flight imaging [13, 14], frequency-based light transport probing [25], and time-gating [28], while non-trivial, can significantly improve all the applications." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 424, + 547, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 424, + 547, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 424, + 547, + 520 + ], + "type": "text", + "content": "Our approach relies on spatial modulation to compute the ToF hologram, which required pre-filtering to avoid aliasing. As part of future work, we will explore machine learning-based techniques to relax the aliasing requirements. Data-free techniques such as deep image priors [29], and generative approaches such as diffusion models [5] will enable us to solve the inverse problem more robustly, and without explicit anti-aliasing constraints." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 525, + 547, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 547, + 621 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 547, + 621 + ], + "type": "text", + "content": "We have translated snapshot off-axis imaging techniques to CWToF imaging. However, a wide variety of imaging ideas including high dynamic range imaging, light-field imaging, polarization imaging, and spectral imaging today are implemented with assorted pixels, which are expensive, prone to aliasing, or require custom demosaicking algorithms. Extending off-axis principles to create assorted frequency-embedding is an interesting future direction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 645, + 421, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 421, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 421, + 658 + ], + "type": "text", + "content": "8. Acknowledgements" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 669, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 669, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 669, + 547, + 713 + ], + "type": "text", + "content": "The authors thank Jeremy Klotz for his help with the hardware prototype. The research is partially supported by a Burke Research Initiation Award." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25210" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Supreeth Achar, Joseph R. 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IJCV, 107:123-138, 2014. 2" + } + ] + } + ], + "index": 0 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "25212" + } + ] + } + ], + "index": 1 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_content_list.json b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6619356f04fbb42f8845e409ff1d3df576c8b197 --- /dev/null +++ b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_content_list.json @@ -0,0 +1,2155 @@ +[ + { + "type": "text", + "text": "SocialCircle: Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction", + "text_level": 1, + "bbox": [ + 114, + 130, + 854, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Conghao Wong $^{1*}$ Beihao Xia $(\\boxtimes)^{1*}$ Ziqian Zou $^{1}$ Yulong Wang $^{2}$ Xinge You $^{1,3}$ $^{1}$ Huazhong University of Science and Technology $^{2}$ Huazhong Agricultural University Research Institute of Huazhong University of Science and Technology in Shenzhen", + "bbox": [ + 138, + 202, + 828, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{conghaowong, xbh_hust, ziqianzoulive}@icloud.com, ylwang@mail.hzau.edu.cn, youxg@mail.hust.edu.cn", + "bbox": [ + 99, + 260, + 864, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 309, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Analyzing and forecasting trajectories of agents like pedestrians and cars in complex scenes has become more and more significant in many intelligent systems and applications. The diversity and uncertainty in socially interactive behaviors among a rich variety of agents make this task more challenging than other deterministic computer vision tasks. Researchers have made a lot of efforts to quantify the effects of these interactions on future trajectories through different mathematical models and network structures, but this problem has not been well solved. Inspired by marine animals that localize the positions of their companions underwater through echoes, we build a new angle-based trainable social interaction representation, named SocialCircle, for continuously reflecting the context of social interactions at different angular orientations relative to the target agent. We validate the effect of the proposed SocialCircle by training it along with several newly released trajectory prediction models, and experiments show that the SocialCircle not only quantitatively improves the prediction performance, but also qualitatively helps better simulate social interactions when forecasting pedestrian trajectories in a way that is consistent with human intuitions.", + "bbox": [ + 75, + 340, + 473, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 703, + 209, + 718 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Analyzing, understanding, and forecasting behaviors of intelligent agents have been significantly required by more and more intelligent systems and applications. Due to the ease of access and analysis of trajectories, analyzing agents' behaviors through trajectories has also become a common approach. Trajectory prediction aims at forecasting agents' all possible future trajectories during a specific period by taking into account the positions of all agents that appeared", + "bbox": [ + 75, + 744, + 468, + 864 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c6beb97077a89a46efaea5614ddbca34abe4bd5aa90bb192f44460692fdcde1c.jpg", + "image_caption": [ + "Figure 1. Motivation Illustration. Analogous to marine animals like dolphins and whales localizing other companions underwater through echolocation, we analyze agents' reactions to the potential socially interactive behaviors by assuming (1) they first Scan their interaction environment by sending signals from all angles, (2) then all neighbors feedback their Reflection signals to tell their directions, and (3) finally the target agent could make interactive decisions by the received echoes at different angular orientations." + ], + "image_footnote": [], + "bbox": [ + 501, + 308, + 893, + 570 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "in the scene [1]. It also considers the potential interactive behaviors [2, 8, 12, 33, 46] as well as the scene constraints [3, 5, 17, 25, 27, 30, 41, 47] when making predictions.", + "bbox": [ + 496, + 718, + 890, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The social interaction [1, 28] (also known as the agent-to-agent interaction) considered in trajectory prediction takes into account not only all kinds of interactive behaviors among different agents but how they affect their trajectories. Current social-interaction-modeling methods in the trajectory prediction task can be classified roughly into Model-based and Model-free two classes[49]. Model-based methods may take some particular \"rules\" [49] as the primary foundation for the prediction. For example, the Social-", + "bbox": [ + 496, + 763, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* equal contribution. Codes are available at https://github.com/cocoon2wong/SocialCircle.", + "bbox": [ + 76, + 875, + 467, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19005", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Force-based methods [9, 28] model and simulate agents' behaviors mainly according to the rules in Newtonian mechanics. Some other methods like [3, 42, 49] also turn trajectory prediction into an optimization problem by introducing their different mathematical models. However, designing a generalized \"rule\" that fits most socially interactive cases is often difficult, making them challenging to apply to complex scenes. On the contrary, model-free methods are mostly driven by data, and few manual interventions are considered. For example, graph-based methods [4, 14, 36] may build a series of spatial or temporal graph structures, thus learning to simulate agents' social interactions. Most model-free methods could fully utilize the ability of neural networks to fit data, but they may heavily rely on different network structures and pose limited explainability.", + "bbox": [ + 75, + 90, + 472, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "\"Rules\" and \"data\" play essential roles but put different limitations on these methods accordingly. A natural thought is to add several \"lite-rules\" to data-driven backbones to provide limited constraints as guidance to improve either the data-fit process or the explainability. In short, we want to constrain the learning process with relatively weak rules for social interactions rather than solid mathematical rules, thus benefiting from both rules and data-fit capabilities.", + "bbox": [ + 75, + 320, + 472, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Analyzing agents' interactive behaviors through bionics and psychology is a natural choice. Animals would not analyze others' behaviors by solving complex equations but with relatively simple judgment rules when planning trajectories. Some researchers in the social psychology area also point out that each agent in a complex multiagent system tends to behave and interact with each other according to simple rules rather than extensive computations, which inspired a series of agent-based simulation models that have been widely applied in economics and political science [35]. It is fascinating that some marine animals can locate others in the deep sea through echolocation rather than visual factors due to the weak light. They may firstly scan the environment by sending some unique signals (like ultrasounds) at different angles, which could be reflected in contact with others and produce echoes. Then, they gather echoes from different directions, thus locating, interacting, or communicating with others, and finally modifying their behaviors.", + "bbox": [ + 75, + 444, + 472, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As shown in Fig. 1, the echolocation is similar to how agents interact with others. Only a few \"rules\" are established, like the time from they send to receive the echo and the direction where it comes. This way, we bring a simple priori to model social behaviors that interactions are considered to be angle-based. In detail, all interactive behaviors are considered in a special angle space where the angle $\\theta$ (which direction the echo comes from) plays as the independent variable. We assume that most social interactions can be \"inferred\" by several simple components corresponding to each angle $\\theta$ , like the velocity of each participant (in which way the participant's position changes during two", + "bbox": [ + 75, + 719, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "echolocations) and the distance between each participant and the target agent (how long the echo arrives since scanning). Thus, we can obtain an angle-based vector function $\\mathbf{f}(\\theta)$ $(0\\leq \\theta < 2\\pi)$ to represent the current socially interactive context when forecasting trajectories. We call that angle-based social interaction representation SocialCircle.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SocialCircle can be classified as Model-based, but it is also inspired by model-free methods to fit data with relatively weak rules, i.e., simple components at different angles. Then, the observed trajectory and the angle-based SocialCircle will be analyzed together in a data-driven way, as they could be both treated as sequences, to catch the temporal-attentive portions in trajectories and the angle-attentive portions in the current interactive context simultaneously, thus establishing connections among these weak rules and agents' real-world socially interactive behaviors as well as the forecasted trajectories.", + "bbox": [ + 496, + 181, + 892, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we contribute (1) The angle-based Social-Circle representation for pedestrian trajectory prediction to model social interactive behaviors; (2) The serialized modeling strategy that treats and encodes the spatial social interactions in the temporal sequences' way along with trajectories; (3) Experiments on multiple backbone prediction models show quantitative and qualitative superiority.", + "bbox": [ + 496, + 347, + 893, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 467, + 640, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-based Social Interaction Methods. Model-based methods aim to use mathematical rules as the foundation to forecast trajectories. The classic Social Force Model [9] is proposed to model human dynamics with Newtonian mechanics. Pellegrini et al. [28] introduce Social Force factors to model social behaviors in the multi-agent tracking task. More Social-Force-based methods like [19, 24, 50] are also proposed to model crowds' interactions.", + "bbox": [ + 496, + 492, + 890, + 613 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Other mathematical tools and models are also used to simulate socially interactive behaviors when forecasting trajectories. Xie et al. [42] propose the \"Dark Matter\" model to simulate and forecast social behaviors with fields and agent-based Lagrangian Mechanics. Xia et al. [41] propose a social transfer function to model human socially interactive behaviors via a uniform way across multiple prediction scenes. Yue et al. [49] propose a neural differential equation model, in which the explicit physics model serves as a strong inductive bias in modeling pedestrian behaviors.", + "bbox": [ + 496, + 614, + 890, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, these methods are often difficult to cover all possible socially interactive cases. Even though some methods like [41, 49] draw on the advantages of data-driven approaches to make some key parameters trainable, they may still be limited by the complex mathematical rules and equations in complex prediction scenes.", + "bbox": [ + 496, + 765, + 890, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-free Social Interaction Methods. Model-free methods simulate interactive behaviors mostly through a data-driven form. Alahi et al. [1] propose the Social-", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19006", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pooling method to connect nearby sequences to share hidden states with each other, thus simulating the information-sharing process. Variations of social pooling methods like [8, 30] are proposed to pool features by considering different scales or locations simultaneously. Grid-based methods like [11] have been proposed to explore additional simple rules to enhance the capacity of pooling methods. With the quick development of graph neural networks, graph structures have been widely used to model social interactions. Graph Attention Networks (GATs) [18, 26], Graph Convolutional Networks [6, 32, 36] are employed to simulate interactions as the edges between different nodes.", + "bbox": [ + 75, + 90, + 468, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most model-free methods prefer to focus more on the structure through which to fit the data so that the predicted trajectory could reflect the effects of social interactive cues. In this process, few direct mathematical rules are constraints, making them more dependent on different network structures and high-quality data.", + "bbox": [ + 75, + 272, + 468, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The proposed SocialCircle tries to address these problems by introducing \"lite-rules\" to these trainable backbones, thus taking advantage of the data-driven approach combined with the explainability of the model-based approach to model interactive behaviors. It also avoids designing complex mathematical models or solving complex equations during the interaction modeling.", + "bbox": [ + 75, + 362, + 468, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 481, + 166, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formulations. This work only concerns trajectories of 2D coordinates $\\mathbf{p} = (x,y)^{\\top}$ . Denote the historical trajectory of agent (pedestrian) $i$ during $t_h$ observation steps as $\\mathbf{X}^i = (\\mathbf{p}_1^i,\\dots,\\mathbf{p}_{t_h}^i)^\\top$ , trajectory prediction focused in this paper aims at forecasting one or more possible future trajectories $\\hat{\\mathbf{Y}}^i = (\\hat{\\mathbf{p}}_{t_h + 1}^i,\\dots,\\hat{\\mathbf{p}}_{t_h + t_f}^i)^\\top$ through its observed $\\mathbf{X}^i$ and all its' neighbors' trajectories $\\mathcal{X}^{/i} = \\{\\mathbf{X}^j |1\\leq j\\leq N_a,j\\neq i\\}$ along with the scene image $\\mathbf{I}_{t_h}$ .", + "bbox": [ + 75, + 507, + 468, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Angle-based SocialCircle Representation. In this paper, all social-interaction-related operations are described and implemented in an \"angle\" space, where the angle $\\theta$ is the independent variable that describes the location of interactive behaviors. We first define the angle $\\theta^i (j)\\in [0,2\\pi)$ to represent the relative position of a neighbor agent $j$ to the target agent $i$ . It is computed as the \"direction\" of the vector that begins from agent $i$ and ends at agent $j$ at the current observation step $(t = t_h)$ . Formally,", + "bbox": [ + 75, + 643, + 468, + 779 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta^ {i} (j) = \\operatorname {a t a n 2} \\left(\\mathbf {p} _ {t _ {h}} ^ {j} - \\mathbf {p} _ {t _ {h}} ^ {i}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 789, + 468, + 814 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, atan2 is the \"quadrant-sensitive\" arctan function that computes angle of the input $\\mathbf{p} = (x,y)^{\\top}$ from 0 to $2\\pi$", + "bbox": [ + 75, + 824, + 468, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Agent $i$ 's SocialCircle representation (short for SocialCircle) can be treated as a head-to-tail cyclic vector function $\\mathbf{f}^i (\\theta)$ for all $\\theta \\in [0,2\\pi)$ . To make the computation", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "easier, the angle variables will be discretized into $N_{\\theta}$ \"partitions\". This way, agent $i$ 's SocialCircle can be denoted as", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} ^ {i} = \\left(\\mathbf {f} ^ {i} \\left(\\theta_ {1}\\right), \\mathbf {f} ^ {i} \\left(\\theta_ {2}\\right), \\dots , \\mathbf {f} ^ {i} \\left(\\theta_ {N _ {\\theta}}\\right)\\right) ^ {\\top}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 132, + 890, + 152 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $0 = \\theta_0 < \\theta_1 < \\ldots < \\theta_{N_\\theta} = 2\\pi$ . As shown in Fig. 2, each $\\mathbf{f}^i(\\theta_n) \\in \\mathbb{R}^{d_{\\mathrm{sc}}}$ ( $n = 1, 2, \\ldots, N_\\theta$ ) is used to represent the overall interactive effort in the $n$ th partition caused by all participants from the set $\\mathbf{N}^i(\\theta_n)$ , which satisfies", + "bbox": [ + 498, + 157, + 890, + 219 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {n - 1} \\leq \\theta^ {i} (j) < \\theta_ {n}, \\forall j \\in \\mathbf {N} ^ {i} (\\theta_ {n}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 227, + 890, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We treat agent $i$ as its self-neighbor in the 1st partition. Denote the number of agents in $\\mathbf{N}^i (\\theta_n)$ as $\\left|\\mathbf{N}^i (\\theta_n)\\right|$ , we have", + "bbox": [ + 498, + 253, + 890, + 285 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ni \\in \\mathbf {N} ^ {i} \\left(\\theta_ {1}\\right), \\quad \\sum_ {n} \\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right| = N _ {a}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 305, + 890, + 335 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SocialCircle Meta Components. Each SocialCircle partition is computed via three meta components:", + "bbox": [ + 498, + 345, + 890, + 375 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\mathrm {m e t a}} ^ {i} \\left(\\theta_ {n}\\right) = \\left(\\mathbf {f} _ {\\mathrm {v e l}} ^ {i} \\left(\\theta_ {n}\\right), \\mathbf {f} _ {\\mathrm {d i s}} ^ {i} \\left(\\theta_ {n}\\right), \\mathbf {f} _ {\\mathrm {d i r}} ^ {i} \\left(\\theta_ {n}\\right)\\right) ^ {\\top}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 383, + 890, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(a) Velocity $\\mathbf{f}_{\\mathrm{vel}}^i$ . Agents with higher velocities may pose potentially more significant dangers to others around them. SocialCircle takes the \"average velocity\" (the movement length during the observation period) of all neighbors in one partition to simulate this interactive factor. Formally,", + "bbox": [ + 498, + 412, + 890, + 489 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\mathrm {v e l}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\left\\| \\mathbf {p} _ {t _ {h}} ^ {j} - \\mathbf {p} _ {1} ^ {j} \\right\\| _ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 498, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(b) Distance $\\mathbf{f}_{\\mathrm{dis}}^i$ . Agents present different interaction preferences as the distance to the interaction participant changes. SocialCircle takes the average Euclidean distance (at $t = t_h$ moment) between the target agent and all its neighbors in one partition to model this factor. Formally,", + "bbox": [ + 498, + 545, + 890, + 622 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\mathrm {d i s}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\left\\| \\mathbf {p} _ {t _ {h}} ^ {i} - \\mathbf {p} _ {t _ {h}} ^ {j} \\right\\| _ {2}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 630, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(c) Direction $\\mathbf{f}_{\\mathrm{dir}}^i$ . Partitioning the continuous $\\theta \\in [0,2\\pi)$ may cause the loss of angle details. We use the average angles of all neighbors in one partition relative to the target agent as a compensation factor. It also acts as a positional coding term to distinguish different partitions. Formally,", + "bbox": [ + 498, + 678, + 890, + 753 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\operatorname {d i r}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\theta^ {i} (j). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 762, + 890, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Serialized Modeling of Social Interaction. SocialCircle partitions $\\{\\mathbf{f}^i (\\theta_n)\\}_{n}$ are obtained by concatenating and embedding all meta components. Formally,", + "bbox": [ + 498, + 809, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} ^ {i} \\left(\\theta_ {n}\\right) = \\left\\{ \\begin{array}{l l} g _ {\\text {e m b e d}} \\left(\\mathbf {0}\\right), & \\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right| = 0; \\\\ g _ {\\text {e m b e d}} \\left(\\mathbf {f} _ {\\text {m e t a}} ^ {i} \\left(\\theta_ {n}\\right)\\right), & \\text {O t h e r w i s e .} \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 863, + 890, + 904 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19007", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e229276ad6a18b090cce57c5975f3692e6bfb83ce244c851445f633f82b99974.jpg", + "image_caption": [ + "Figure 2. Computation pipeline of the proposed SocialCircle. Each agent's SocialCircle is different to others'. For a target agent, it first computes three meta components: velocity, distance, and direction. Then, these meta components will be averaged within each angle-based SocialCircle partition, and finally embedded into the set of high-dimensional head-to-tail cyclic representation $\\mathbf{f}^i (\\theta_n)$ $(1\\leq n\\leq N_{\\theta})$" + ], + "image_footnote": [], + "bbox": [ + 78, + 85, + 893, + 200 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f90323f00a8dc4765d892224703772dc8ee133f43bcdf165685239475b31b3ca.jpg", + "image_caption": [ + "Figure 3. The serialized modeling of social interactions. SocialCircle is treated as a \"virtual\" temporal sequence that shares the same sequence shape as the embedded trajectory by adding zero paddings, so they could be fused to forecast trajectories together." + ], + "image_footnote": [], + "bbox": [ + 78, + 277, + 467, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $g_{\\mathrm{embed}}$ is the embedding function that contains 2 fully connected layers with 64 output units. ReLU activation is used in the first layer while tanh is used in the second layer.", + "bbox": [ + 75, + 484, + 468, + 529 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SocialCircle represents the Spatial interactive context at the current step $(t = t_h)$ through a serialized form. A natural thought is to handle this sequence $\\mathbf{f}^i\\in \\mathbb{R}^{N_\\theta \\times d_{\\mathrm{sc}}}$ along with the observed trajectory $\\mathbf{X}^i\\in \\mathbb{R}^{t_h\\times 2}$ to learn the attentive portions inner these sequences simultaneously. In detail, we treat the spatial SocialCircle $\\mathbf{f}^i$ as a Virtual Temporal Sequence that shares the same sequence length as the trajectory $\\mathbf{X}^i$ or its representations. As shown in Fig. 3, $\\mathbf{f}^i$ will be padded at first (we set $N_{\\theta}\\leq t_h$ ). Formally,", + "bbox": [ + 75, + 530, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\text {p a d}} ^ {i} = \\left(\\underbrace {\\mathbf {f} ^ {i} \\left(\\theta_ {1}\\right) , \\dots , \\mathbf {f} ^ {i} \\left(\\theta_ {N _ {\\theta}}\\right)} _ {N _ {\\theta}}, \\underbrace {\\mathbf {0} , \\dots , \\mathbf {0}} _ {t _ {h} - N _ {\\theta}}\\right) ^ {\\top} \\in \\mathbb {R} ^ {t _ {h} \\times d _ {\\mathrm {s c}}}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 672, + 468, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In most previous works [1, 8], agent- $i$ 's observed trajectory $\\mathbf{X}^i$ will be first embedded into the high-dimensional $\\mathbf{f}_{\\mathrm{traj}}^i \\in \\mathbb{R}^{t_h \\times d}$ by some embedding layer $f_{\\mathrm{embed}}$ , i.e., $\\mathbf{f}_{\\mathrm{traj}}^i = f_{\\mathrm{embed}}(\\mathbf{X}^i)$ . Denote the computation of one trajectory prediction model (we call the backbone prediction model) as $B_{\\mathrm{pred}}$ , future trajectories $\\hat{\\mathbf{Y}}^i$ are usually predicted by", + "bbox": [ + 75, + 726, + 468, + 820 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {Y}} ^ {i} = B _ {\\text {p r e d}} \\left(\\mathbf {f} _ {\\text {t r a j}} ^ {i}, \\mathbf {f} _ {\\text {s o c i a l}} ^ {i}, \\mathbf {f} _ {\\text {o t h e r s}} ^ {i}\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 827, + 468, + 847 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{f}_{\\mathrm{social}}^i$ denotes the original social representations in the backbone prediction model, and $\\mathbf{f}_{\\mathrm{others}}^i$ denotes other required features (like visual features from scene image $\\mathbf{I}_{t_h}$ ).", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SocialCircle Models (the SocialCircle-lized backbone prediction models) take the fused vector $\\mathbf{f}_{\\mathrm{fuse}}^i$ containing both trajectory information and interactive context to instead the single $\\mathbf{f}_{\\mathrm{traj}}^i$ to learn the temporal-attentive portions in the observed trajectories and the angle-attentive portions in the SocialCircle simultaneously. The $\\mathbf{f}_{\\mathrm{fuse}}^i$ is fused by", + "bbox": [ + 498, + 281, + 890, + 375 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {\\text {f u s e}} ^ {i} = \\tanh \\left(\\mathbf {W} _ {\\text {f u s e}} \\operatorname {C o n c a t} \\left(\\mathbf {f} _ {\\text {t r a j}} ^ {i}, \\mathbf {f} _ {\\text {p a d}} ^ {i}\\right) + \\mathbf {b} _ {\\text {f u s e}}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 383, + 890, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\mathbf{W}_{\\mathrm{fuse}}$ and $\\mathbf{b}_{\\mathrm{fuse}}$ are the trainable weights and bias. Meanwhile, the original $\\mathbf{f}_{\\mathrm{social}}^i$ will be removed. The trajectory prediction pipeline of SocialCircle models has become", + "bbox": [ + 498, + 412, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {Y}} _ {\\mathrm {S C}} ^ {i} = B _ {\\text {p r e d}} \\left(\\mathbf {f} _ {\\text {f u s e}} ^ {i}, \\mathbf {f} _ {\\text {o t h e r s}} ^ {i}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 470, + 890, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training. SocialCircle does not introduce additional new loss functions. We take Transformer[37], MSN[40], $\\mathrm{V}^2$ -Net[38], E- $\\mathrm{V}^2$ -Net[39] as backbone trajectory prediction models to validate SocialCircle's performance in our experiments. These models will be trained with original loss functions and settings reported in their papers.", + "bbox": [ + 496, + 494, + 890, + 585 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 599, + 632, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Datasets. (a) ETH[28]-UCY[13] contains several videos captured in pedestrian walking scenes. We use the leave-one-out strategy [1] to train with $\\{t_h = 8, t_f = 12\\}$ and sample interval $\\Delta t = 0.4s$ . (b) Stanford Drone Dataset [29] (SDD) has 60 drone videos. Different categories of agents are annotated in pixels. Following [15], we split $60\\%$ videos to train, $20\\%$ to validate, and $20\\%$ to test under $(t_h, t_f, \\Delta t) = (8, 12, 0.4)$ . (c) NBA SportVU [16] (NBA) includes trajectories captured by the SportVU tracking system in NBA games. Following [43, 44], we set $(t_h, t_f, \\Delta t) = (5, 10, 0.4)$ , and sample 50K trajectories, including $65\\%$ to train, $25\\%$ to test, and $10\\%$ to validate.", + "bbox": [ + 496, + 623, + 890, + 805 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Metrics. We measure prediction accuracy with the best Average/Final Displacement Error over 20 generated trajectories (i.e., $\\min\\mathrm{ADE}_{20}/\\min\\mathrm{FDE}_{20}$ [1, 8], short for ADE/FDE). See their detailed definitions in the Appendix.", + "bbox": [ + 496, + 805, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "1Ethics Note: Datasets used in this work are publicly available and do not contain any sensitive personally identifiable information.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19008", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/0f6bee9d9ad5d86d5f526245dd7868a894406d6e394bb2c1ce130d084ac58828.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Models (ETH-UCY)ethhotelunivzara1zara2ETH-UCYModels (SDD)SDD
SHENet[25] (2022)0.41/0.610.13/0.200.25/0.430.21/0.320.15/0.260.23/0.36FlowChain[20] (2023)9.93/17.17
MID[7] (2022)0.39/0.660.13/0.220.22/0.450.17/0.300.13/0.270.21/0.38SHENet[25] (2022)9.01/13.24
EqMotion[45] (2023)0.40/0.610.12/0.180.23/0.430.18/0.320.13/0.230.21/0.35IMP[34] (2023)8.98/15.54
MSN[40] (2023)0.27/0.410.11/0.170.28/0.480.22/0.360.18/0.290.21/0.34LED[23] (2023)8.48/11.36
LED[23] (2023)0.39/0.580.11/0.170.26/0.430.18/0.260.13/0.220.21/0.33MID[7] (2022)7.91/14.50
Trajectory++[31] (2020)0.43/0.860.12/0.190.22/0.430.17/0.320.12/0.250.20/0.39Y-net[22] (2021)7.85/11.85
Agentformer[48] (2021)0.26/0.390.11/0.140.26/0.460.15/0.230.14/0.230.18/0.29MSN[40] (2023)7.69/12.16
V2-Net[38] (2022)0.23/0.370.10/0.160.21/0.350.19/0.300.14/0.240.18/0.28V2-Net[38] (2022)7.12/11.39
Y-net[22] (2021)0.28/0.330.10/0.140.24/0.410.17/0.270.13/0.220.18/0.27E-V2-Net[39] (2023)6.57/10.49
E-V2-Net[39] (2023)0.25/0.380.11/0.160.20/0.340.19/0.300.13/0.240.17/0.28NSP-SFM[49] (2022)6.52/10.61
MSN-SC (Ours)0.27/0.390.13/0.180.22/0.450.18/0.340.15/0.270.19/0.33MSN-SC (Ours)7.49/12.12
V2-Net-SC (Ours)0.25/0.370.12/0.150.21/0.350.17/0.290.13/0.220.17/0.27V2-Net-SC (Ours)6.71/10.66
E-V2-Net-SC (Ours)0.25/0.380.12/0.140.20/0.340.18/0.290.13/0.220.17/0.27E-V2-Net-SC (Ours)6.54/10.36
", + "bbox": [ + 89, + 88, + 883, + 280 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/bcfcae2dc8e63bb1c819bec33502626efb17c5249212f9cd022d79a0e8fa2551.jpg", + "table_caption": [ + "Table 1. Comparisons on ETH-UCY (left) and SDD (right) under best-of-20 and with $t_h = 8$ frames' (3.2s) observations to predict future $t_f = 12$ frames' (4.8s) trajectories. Metrics are reported as \"ADE/FDE\". Lower ADE and FDE indicate better prediction performance." + ], + "table_footnote": [], + "table_body": "
Models (NBA)Metrics@2.0sMetrics@4.0s
PECNet[21] (2020)0.96/1.691.83/ 3.41
NMMP[10] (2020)0.70/1.111.33/ 2.05
V2-Net[38] (2022)0.69/0.961.28/ 1.68
E-V2-Net[39] (2023)0.68/ 0.931.26/ 1.64
MemoNet[44] (2022)0.71/1.141.25/ 1.47
GroupNet+NMMP[43] (2022)0.69/1.081.25/ 1.80
GroupNet+CVAE[43] (2022)0.62/0.951.13/1.69
V2-Net-SC (Ours)0.67/0.921.22/1.51
E-V2-Net-SC (Ours)0.67/0.901.18/1.46
", + "bbox": [ + 88, + 340, + 460, + 484 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 2. Comparisons on NBA under best-of-20 in meters ( $t_h = 5, t_f = 10$ ). Metrics are reported as \"ADE/FDE\" at different prediction lengths, including 2.0s (5 frames) and 4.0s (10 frames).", + "bbox": [ + 75, + 494, + 470, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. Models are trained on one NVIDIA Tesla T4 GPU. SocialCircle is computed on each agent's 50 nearest neighbors to save the computation resource. For SocialCircle models, we set $N_{\\theta} = t_h^2$ , and set $\\theta_n = 2n\\pi / N_{\\theta}$ ( $n = 1, 2, \\dots, N_{\\theta}$ ). Feature dimensions $d$ and $d_{\\mathrm{sc}}$ are set to 64. Following [51], trajectories are preprocessed by moving to $(0, 0)$ . We set the learning rate to 1e-4, epochs to 600, and batch size to 1500.", + "bbox": [ + 75, + 565, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Comparisons to State-of-the-Art Methods", + "text_level": 1, + "bbox": [ + 76, + 698, + 433, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ETH-UCY. Tab. 1 illustrates that SocialCircle models are competitive. In detail, the E-V²-Net-SC has achieved a noteworthy prediction performance with $5.6\\%$ better ADE and $6.9\\%$ better FDE compared with Agentformer. Moreover, MSN-SC performs better than EqMotion with the improvement of $9.5\\%$ ADE and $5.7\\%$ FDE, even though MSN performs not as well as other new approaches.", + "bbox": [ + 75, + 720, + 468, + 828 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SDD. In Tab. 1, $\\mathrm{V}^2$ -Net-SC outperforms Y-net by $14.52\\%$ ADE and $10.04\\%$ FDE. It has also obtained $20.87\\%$ ADE and $6.16\\%$ FDE improvements compared to the newly", + "bbox": [ + 76, + 829, + 470, + 875 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/78a5727e38901797e82d0ad553a665ca6ff1c22e3dd71c4d7543a75cd080ab2b.jpg", + "image_caption": [ + "Figure 4. Loss curves (loss values after different training epochs) of the simple Transformer (left) and the corresponding Transformer-SC variation (right) during the training process on SDD with 600 epochs in total. Loss values are normalized, and each figure includes six training runs (\"nan\" loss values are not displayed). Curves are smoothed with the decay factor $= 0.8$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 340, + 694, + 435 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2972c88ad57377e5ba5b64f00152fa10f83af3960694be49fa1a6f6e7cfa50cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 340, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "published LED. In addition, $\\mathrm{E - V^2}$ -Net-SC outperforms the state-of-the-art NSP-SFM by as much as $2.36\\%$ FDE.", + "bbox": [ + 496, + 559, + 890, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "NBA. In Tab. 2, compared with GroupNet+CVAE, E-V²-Net-SC's ADE is not as well as that model (about $4.42\\%$ worse), but its FDEs (both at 2.0s and 4.0s) are better than those for about $5.26\\%$ and $13.60\\%$ . In addition, even though the FDE (4.0s) of MemoNet and E-V²-Net-SC are at the same level, E-V²-Net-SC outperforms the other for about $5.60\\%$ ADE (4.0s). Although E-V²-Net performs not as well as these newly published methods, the proposed SocialCircle makes it available to achieve competitive results.", + "bbox": [ + 496, + 590, + 892, + 727 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Ablation Studies and Quantitative Analyses", + "text_level": 1, + "bbox": [ + 500, + 739, + 870, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Overall Validation of SocialCircle. As shown in Tab. 3, SocialCircle could help even the simplest Transformer [37] (which considers nothing about agents' multimodality and interactions) improve $5.89\\%$ ADE and $4.00\\%$ FDE. SocialCircle also facilitates MSN, $\\mathrm{V}^2$ -Net, and $\\mathrm{E - V^2}$ -Net with up to $4.92\\%$ ADE gains and $8.00\\%$ FDE gains compared to their original models. In addition, we also plot loss curves $(\\ell_2$ loss) of 6 training runs of the simplest Transformer and the Transformer-SC in Fig. 4. It shows that SocialCir", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "See detailed analyses about $N_{\\theta}$ in the Appendix.", + "bbox": [ + 94, + 886, + 359, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19009", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b717f9bfc894995763f160b43713ad9a6e8f04c0d4388749d327f20ce9adff9d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 109, + 292, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0b833409cdcdcf891f320cfcb5c9d8783fb075320a7d13be2a865d1ffab466c4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 109, + 483, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fde14a8dee277cd55d3d4b4734b7b47921181904498cf20a76addf76420c0602.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 109, + 676, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/65d5f7d24e2cc76eafe9ab106821d15bdbbb21ab3a7516687e7132ff1ca5de38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 676, + 109, + 867, + 166 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/221a072e49a6f39cc0888cc359637356ef62c36cc29293126bce9a1432fa0373.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 101, + 166, + 292, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/766bbaa628bb81ece14396a9dad0e2196c6be0eca0bd5cace8ddbca5b64acf30.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 166, + 483, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4609569b814d33e9b375d663dc041da997d310810fd1edb9479532ced495ba2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 166, + 676, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/526452591ccecca722842d8a4388e42c5ca4c887662682220ea64a73d32da0a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 676, + 166, + 867, + 241 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f9aa8a9914aa28e47d0595d84aa1cc68776c134fcc235a1acf450070848e7e37.jpg", + "image_caption": [ + "Transformer-SC" + ], + "image_footnote": [], + "bbox": [ + 101, + 241, + 292, + 323 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2e8b0ebc8f0466cc3709b1208e17e39c5850b898f2318a682cfe45d0a921ee0e.jpg", + "image_caption": [ + "MSN-SC" + ], + "image_footnote": [], + "bbox": [ + 292, + 241, + 483, + 323 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/642e439ae40925667aa95ab5437c288546805e2883766f90bd4d3bfb90e49b2e.jpg", + "image_caption": [ + "V2-Net-SC", + "Figure 5. Visualized predictions of SocialCircle models with different backbone prediction models in several ETH-UCY and SDD scenes." + ], + "image_footnote": [], + "bbox": [ + 483, + 241, + 676, + 323 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f9c76372519a9d156e3ede1410c31552dab9e0710b472abaa7950d41d52c5141.jpg", + "image_caption": [ + "E-V2-Net-SC" + ], + "image_footnote": [], + "bbox": [ + 676, + 241, + 867, + 323 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9258695d593dd2aaf36a636688fd245056a30c1c6277608ad4f1037992887abe.jpg", + "image_caption": [ + "Target agents' observations" + ], + "image_footnote": [], + "bbox": [ + 114, + 397, + 364, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/07114d0c0c8881371789658bf8c62a2c8e60e0e8fe1c560e49c03bd44363f615.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 114, + 460, + 364, + 518 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e5c523cb33e104f2035c3f99c2ad8f9bc392f02b8de8a862eeef7b2a6cab9701.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 114, + 518, + 364, + 578 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dd7530e6e241d58023975d704ca0c43c1183bc00916745d9a10de8acfa575a78.jpg", + "image_caption": [ + "Figure 6. Prediction comparisons of SocialCircle models and their original models in several interactive ETH-UCY and SDD scenes." + ], + "image_footnote": [], + "bbox": [ + 114, + 578, + 364, + 638 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/040cb2dd4e0042baa59340033448b003d58d885caf7df277ee891fc070e561ed.jpg", + "image_caption": [ + "Target agents' ground truth", + "Neighbor agents' observations" + ], + "image_footnote": [], + "bbox": [ + 366, + 397, + 529, + 459 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a62b4867b6cb4f085d0c24b9c565e5fccd3453515eb8aab96024882f22752f16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 366, + 459, + 529, + 518 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/12c7986fd53bae63e878c9bd4cd7b64f816bf2bdaf4da371abd8be0ed442d0d0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 366, + 518, + 531, + 578 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/626132764b8db74a49b91434b94f3e26e24dff43bc5594381a74c47e2e4d6721.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 366, + 578, + 531, + 638 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/08e938354e2cc915a5d1b7a2eee3a363c8f57eda5e2db4eddca1b5cf45027b66.jpg", + "image_caption": [ + "Model Predictions" + ], + "image_footnote": [], + "bbox": [ + 532, + 397, + 700, + 458 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ffc858822b2331676c0789a632cc2c565167f298791bbaa8ab1bbe5c7c23749.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 534, + 458, + 700, + 518 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b4e55b94b6a78e487467ab63551c48e782c04183d7123a3e6babccff9271fbc3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 532, + 518, + 700, + 578 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/19ba49184fc0f952c80094862b9bee0281d5047435b329e9babc75371fa8a0c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 534, + 578, + 700, + 638 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fe197f4acea535486d53671785aa4e737ce545510ba7141e9d3d8517471d522c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 397, + 870, + 458 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/88735d32345888985558ac7be2c16104ef12fd4e47361cf34efe5c948d63e919.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 458, + 870, + 518 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/32fd94bc743b80e8cc503cc039b73f74a9a22ed90bf107227094e736a3da2678.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 518, + 870, + 578 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/5f23e05e306f73073dc72f36198473828cafcaf8763f6873e4977a726843ea27.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 702, + 578, + 870, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cle could help the loss drop faster for Transformer-SC with an average of $13.04\\%$ lower than that in the Transformer after 600 training epochs. Moreover, 5 out of 6 Transformer runs' loss values fall into \"nan\" due to the inappropriate gradients before 450 training epochs. As for Transformer-SC, only two runs are terminated, demonstrating that SocialCircle may also somehow act as a normalization factor, thus improving the training stability.", + "bbox": [ + 75, + 690, + 468, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Validation of SocialCircle Meta Components. As shown in Tab. 3, both $\\mathrm{V}^2$ -Net and $\\mathrm{E - V}^2$ -Net benefit further from the velocity and distance factors, each of which could provide at least $1.50\\%$ ADE and FDE gains (SC-a1 and SC-a2 variations). However, MSN-SC variations are", + "bbox": [ + 75, + 824, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "not so sensitive to these two factors (less than $1.07\\%$ ADE differences among MSN-SC, MSN-SC-a1, and MSN-SC-a2) but rely more on the direction factor (up to $3.30\\%$ FDE gain has been brought by this factor). Although these factors contribute differently to different backbone models, the combination of all these factors promotes the most, for removing each one could lead to a serious performance drop.", + "bbox": [ + 496, + 690, + 890, + 797 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Parameters & Efficiency. Please refer to the Appendix.", + "bbox": [ + 517, + 799, + 890, + 813 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Qualitative Analyses", + "text_level": 1, + "bbox": [ + 500, + 829, + 694, + 845 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visualized Predictions. Fig. 5 visualizes trajectories predicted by several SocialCircle models. We can see that all SocialCircle models' predictions present similar ways", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Target agents' observations", + "bbox": [ + 148, + 94, + 313, + 107 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Target agents' ground truth", + "bbox": [ + 331, + 94, + 490, + 106 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Neighbor agents' observations", + "bbox": [ + 506, + 94, + 684, + 106 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "#", + "bbox": [ + 697, + 93, + 722, + 109 + ], + "page_idx": 5 + }, + { + "type": "header", + "text": "Model Predictions", + "bbox": [ + 725, + 95, + 821, + 106 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19010", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/11fb60821c71a166609f219e595047e14b274e597efd2262ab972ce840c2c33e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VariationsVDRADE/FDEADE/FDE Gain (%)
Transformer*×××17.44/33.36-5.89%/-4.00%
Transformer-SC✓✓✓16.47/32.08(base)
MSN*×××7.79/13.09-4.01%/-8.00%
MSN-SC-a1×✓✓7.53/12.30-0.53%/-1.49%
MSN-SC-a2✓×✓7.57/12.40-1.07%/-2.31%
MSN-SC-a3✓✓×7.60/12.52-1.47%/-3.30%
MSN-SC✓✓✓7.49/12.12(base)
V2-Net*×××7.04/10.94-4.92%/-2.63%
V2-Net-SC-a1×✓✓6.86/10.82-2.24%/-1.50%
V2-Net-SC-a2✓×✓6.87/10.87-2.38%/-1.97%
V2-Net-SC-a3✓✓×6.78/10.71-1.04%/-0.47%
V2-Net-SC✓✓✓6.71/10.66(base)
E-V2-Net*×××6.73/10.75-2.91%/-3.76%
E-V2-Net-SC-a1×✓✓6.67/10.73-1.99%/-3.57%
E-V2-Net-SC-a2✓×✓6.64/10.55-1.53%/-1.83%
E-V2-Net-SC-a3✓✓×6.59/10.48-0.76%/-1.16%
E-V2-Net-SC✓✓✓6.54/10.36(base)
", + "bbox": [ + 84, + 88, + 460, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Ablation studies on validating SocialCircle meta components on SDD. \"V\", \"D\", and \"R\" indicate whether $\\mathbf{f}_{\\mathrm{vel}}^i$ , $\\mathbf{f}_{\\mathrm{dis}}^i$ , or $\\mathbf{f}_{\\mathrm{dir}}^i$ are included in the meta vector $\\mathbf{f}_{\\mathrm{meta}}^i$ . Models with “*” are reproduced under the same condition.", + "bbox": [ + 76, + 349, + 468, + 405 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f7559a10ca0ab057fe4174765206b171819ef3cb17ff56bbca974cd177ddd57a.jpg", + "image_caption": [ + "Figure 7. Toy Examples I: Validation of social interactions. The arrows and circles point to the same predicted trajectory that has been changed significantly due to the manual neighbor." + ], + "image_footnote": [], + "bbox": [ + 78, + 424, + 468, + 601 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "to handle social interactions. For example, predictions in Fig. 5 (a2) to (a4) all present avoidance of the group of pedestrians standing still at the roadside. Similarly, avoiding the upcoming biker about to cross the intersection has also become a major concern in (c1) to (c4). These results indicate the effectiveness of the proposed SocialCircle that works with different backbone prediction models.", + "bbox": [ + 75, + 686, + 468, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualized Social Interaction Cases. As shown in Fig. 6, we observe that predictions given by SocialCircle models seem to be more \"conservative\" with a tendency to avoid others in different social interaction situations, which looks like it is trying to avoid possible collisions or too-close social distances. For example, predictions in (a2) display heavier avoidance of the man coming from", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/89bb77240c0e739235fa0afcf49e13f458a77dc3b57f7fe9fb65f5e7e80be088.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 88, + 637, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2b7af5d8ce56d2caab12558d66738281cbb478bd3549d62f856843c10f99ae78.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 89, + 764, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/93918e0f1d11ebd88d06f48d3b81ef622e80071e2908611ec1735849fafa4b50.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 89, + 890, + 162 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/09500c2fa22959f45961508ee665748cf28765c922baf4f3d000dc780ebca4f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 167, + 637, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ba9259e853e15c8918a2488651a8e27fd4ac1556edb3cb5e66707711fdef6714.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 167, + 764, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/76ac48b64f3746d03946f198bcb5d5d82fe55bf796e8e2510735b34d5ab9f750.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 167, + 890, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/769eee2155ba861a3f3ef0f21860e3ca25dc50021428178d4bb0e45a437107a1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 244, + 637, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d2f2790bbe9d51095f153b5a928a97fab309d3899f2925212275c73db31f444a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 244, + 764, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d20f46e36babf408ffeded327f7c4630defbb0354907228451766bdfe309ec2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 244, + 890, + 321 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5c613230eaab5bf1e82dba5c82056ed35c439eee88d25a668fefc2ecbdae88cf.jpg", + "image_caption": [ + "Figure 8. Toy Examples II: Validation of SocialCircle meta components by manually changing the manual neighbor's velocity (denoted by $v_{m}$ ) and its distance to the target agent ( $d_{m}$ )." + ], + "image_footnote": [], + "bbox": [ + 506, + 324, + 637, + 398 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a8beab7d13ecbeed4c1c52e616d6a5a8b81d14a7886efd83ef8e5e427deb0c11.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 324, + 764, + 398 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/417e52aba0625f6dd870609b3ae5881569cf155b9d6ccc81d123df3f74e49ed2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 324, + 890, + 398 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0c66fca0e651e413a27a4027348e93d0c097619d517ebd121de431c75806ebd3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 503, + 474, + 617, + 571 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/282275fc74b3c3889dc8d0d6738a36afb8318f59e7bc66b1697b493044c4f225.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 476, + 733, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/72082df32dd56dd0440bddf5b19c2b9371faeca2e2b34d0b4761c8304d00cf05.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 474, + 851, + 570 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fa5ea9f1dba9b78fe3b3ec3c76eee5530ee58798f9574cbf3d3f4193aa5b42cf.jpg", + "image_caption": [ + "Figure 9. Visualized attention scores of each SocialCircle partition in the colored-ring form on several ETH-UCY prediction scenes. Partitions with higher attention scores (redder and wider) contribute more to the final predicted trajectories." + ], + "image_footnote": [], + "bbox": [ + 503, + 571, + 617, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5a22efc03eed3b2d96861310ab32c517c9e074b3a6a1e591a1b878615bec3257.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 619, + 571, + 733, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c2afcd876b8e9b86f4f4e66d19963eba2afb2bcb2ebee8b78f73ef41d17b0157.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 571, + 849, + 667 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f896882706d091209e36fefa427c926f8d0e6975e8011cdbd62d35f403993c8a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 852, + 515, + 885, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the car side than in (b2). Similarly, the potential collision between the moving biker and the focused walking pedestrian has been caught in (c3), thus representing a prediction shift (comparing the blue prediction in (c3) and the red one in (d3)). In addition, two pedestrians walk towards right together in cases (a4) and (b4). Unlike case (b4), SocialCircle model forecasts that the target agent may not crossover the other two's potential trajectories, like it \"thought\" that the agent would rather keep its relative position in the group.", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19011", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/828e955a639e09277a29e6bce4edb11d31a1f162542ee464fb3cdc9e4755eef5.jpg", + "image_caption": [ + "Figure 10. Toy Examples III: Comparisons of attention scores before and after adding manual neighbors in ETH-UCY scenes." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 470, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Note that social interactions are not only limited to these collision cases. They are common behavior patterns among agents, including scene-specific interactions like the game-related interactions in the NBA dataset. Please see the qualitative analyses of NBA interactions in the Appendix.", + "bbox": [ + 75, + 308, + 468, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Toy Examples I (Social Interactions). We design a series of toy examples on several real-world prediction scenes from ETH-UCY to verify the capacity of SocialCircle in handling social interactions in Fig. 7. We manually add new \"manual neighbors\" in different positions (partitions) to test SocialCircle model's response. Each manual neighbor's observed trajectory is simulated by linearly interpolating from the given start and end points. Comparing Fig. 7 (a1) and (b1), several predicted trajectories to the right of the target agent have changed a lot. For example, the red trajectory contracts violently to the other side, which seems quite likely to prevent possible collisions with the manual neighbor that walks towards itself. Similar phenomenons also appear in Fig. 7 (b2), whose blue and green predictions show varying degrees of avoidance tendencies, depending on where they are located. The predicted trajectories colored in blue and cyan in Fig. 7 (a3) also show a tendency to avoid the manual neighbor. These cases illustrate the adaptivity of the SocialCircle in customizing different predictions. We have provided more toy cases in the Appendix.", + "bbox": [ + 75, + 385, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Toy Examples II (SocialCircle Meta Components). Fig. 8 further shows the qualitative effect on predicted trajectories caused by the other two SocialCircle factors, velocity and distance. We first focus on the velocity factor validated in (a1) to (a3) or (a4) to (a6). When the manual neighbor has a higher velocity, the predicted trajectories will be affected by it to a greater extent, and vice versa, especially for the pink predictions in (a1) to (a3). Except for the velocity, as the distance $d_{m}$ increases in Fig. 8 (b1) to (b3) or (b4) to (b6), the influence of manual neighbors gradually becomes smaller. In contrast, the predicted trajectory may produce a heavier shift when $d_{m}$ decreases step by step. These \"social-like\" behaviors brought by different SocialCircle meta components are learned adaptively during", + "bbox": [ + 75, + 688, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training. It illustrates SocialCircle's capacity and explainability to represent potential social interaction cases and finally modify predicted trajectories socially.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Toy Examples III (SocialCircle Partitions). In Fig. 9, we visualize how each SocialCircle partition contributes by squaring-sum the feature $\\mathbf{f}_{\\mathrm{pad}}^i$ in each partition, which we call the Attention Score. Note that agent $i$ itself will be treated as its self-neighbor located in partition 1 (see Eq. (4)). We can see from these figures that SocialCircle acts far from simply locating all neighbors but tells which partitions should be paid more attention to when forecasting trajectories. In Fig. 9 (a) to (d), partition 1 catches more attention, and others present different trends according to different neighbor distributions. Similar to the phenomenon shown in Fig. 8, neighbors that are closer to the target agent elicit higher levels of attention (like partition 3 against partition 2 in (a)), and neighbors that move faster attract more attention (partition 4 compared to partition 6 in (d)). Unlike these cases, partition 8 owns a higher score than partition 1 in case (e), indicating that the SocialCircle cares more about the neighbor walking along with the target agent rather than the agent itself. It is interesting in case (e) that some partitions have also been assigned scores even though there are no neighbors.", + "bbox": [ + 496, + 136, + 892, + 453 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Furthermore, Fig. 10 shows how the attention scores change after adding manual neighbors. In case (a1), SocialCircle focuses more on partition 4. However, the scores have changed significantly in case (a2) due to the manual neighbor located between partitions 1 and 8, and partition 4 has been less focused. Cases (b1) and (b2) also show the similar trends. All these qualitative results illustrate SocialCircle's ability to describe different interactions and the effectiveness of partitioned modeling social interactions.", + "bbox": [ + 496, + 454, + 892, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. SocialCircle does not contain the directions where neighbor agents came from. It also does not directly consider the interactions among neighbor agents and how they affect the target agent, i.e., the high-order interactions. We will further study it in our subsequent works.", + "bbox": [ + 496, + 589, + 890, + 666 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 679, + 617, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work focuses on the modeling of social interactions when forecasting pedestrian trajectories. Like marine animals localizing and communicating with others through echolocation, we bring a simple priori rule to construct the angle-based social interaction representation SocialCircle, which aims to learn how three meta components modify agent trajectories. Experiments on multiple datasets show its competitiveness, and additional toy experiments also prove its effectiveness in handling social interactions.", + "bbox": [ + 496, + 704, + 890, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This project is supported by National Natural Science Foundation of China (62172177), and National Key R&D Program of China (2022YFC3301000).", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19012", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. 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IEEE transactions on pattern" + ], + "bbox": [ + 501, + 92, + 890, + 901 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19014", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "analysis and machine intelligence, 44(5):2742-2759, 2022.", + "bbox": [ + 109, + 90, + 467, + 104 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "5", + "bbox": [ + 112, + 107, + 120, + 116 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "19015", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_model.json b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e8c9c20a9ba906976efa68080b9b283ebcb0484b --- /dev/null +++ b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_model.json @@ -0,0 +1,2741 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.131, + 0.856, + 0.177 + ], + "angle": 0, + "content": "SocialCircle: Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.14, + 0.203, + 0.83, + 0.258 + ], + "angle": 0, + "content": "Conghao Wong\\(^{1*}\\) Beihao Xia\\((\\boxtimes)^{1*}\\) Ziqian Zou\\(^{1}\\) Yulong Wang\\(^{2}\\) Xinge You\\(^{1,3}\\) \n\\(^{1}\\)Huazhong University of Science and Technology \\(^{2}\\)Huazhong Agricultural University Research Institute of Huazhong University of Science and Technology in Shenzhen" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.261, + 0.866, + 0.275 + ], + "angle": 0, + "content": "{conghaowong, xbh_hust, ziqianzoulive}@icloud.com, ylwang@mail.hzau.edu.cn, youxg@mail.hust.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.31, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.675 + ], + "angle": 0, + "content": "Analyzing and forecasting trajectories of agents like pedestrians and cars in complex scenes has become more and more significant in many intelligent systems and applications. The diversity and uncertainty in socially interactive behaviors among a rich variety of agents make this task more challenging than other deterministic computer vision tasks. Researchers have made a lot of efforts to quantify the effects of these interactions on future trajectories through different mathematical models and network structures, but this problem has not been well solved. Inspired by marine animals that localize the positions of their companions underwater through echoes, we build a new angle-based trainable social interaction representation, named SocialCircle, for continuously reflecting the context of social interactions at different angular orientations relative to the target agent. We validate the effect of the proposed SocialCircle by training it along with several newly released trajectory prediction models, and experiments show that the SocialCircle not only quantitatively improves the prediction performance, but also qualitatively helps better simulate social interactions when forecasting pedestrian trajectories in a way that is consistent with human intuitions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.704, + 0.21, + 0.719 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.745, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Analyzing, understanding, and forecasting behaviors of intelligent agents have been significantly required by more and more intelligent systems and applications. Due to the ease of access and analysis of trajectories, analyzing agents' behaviors through trajectories has also become a common approach. Trajectory prediction aims at forecasting agents' all possible future trajectories during a specific period by taking into account the positions of all agents that appeared" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.309, + 0.895, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.692 + ], + "angle": 0, + "content": "Figure 1. Motivation Illustration. Analogous to marine animals like dolphins and whales localizing other companions underwater through echolocation, we analyze agents' reactions to the potential socially interactive behaviors by assuming (1) they first Scan their interaction environment by sending signals from all angles, (2) then all neighbors feedback their Reflection signals to tell their directions, and (3) finally the target agent could make interactive decisions by the received echoes at different angular orientations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.765 + ], + "angle": 0, + "content": "in the scene [1]. It also considers the potential interactive behaviors [2, 8, 12, 33, 46] as well as the scene constraints [3, 5, 17, 25, 27, 30, 41, 47] when making predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.893, + 0.902 + ], + "angle": 0, + "content": "The social interaction [1, 28] (also known as the agent-to-agent interaction) considered in trajectory prediction takes into account not only all kinds of interactive behaviors among different agents but how they affect their trajectories. Current social-interaction-modeling methods in the trajectory prediction task can be classified roughly into Model-based and Model-free two classes[49]. Model-based methods may take some particular \"rules\" [49] as the primary foundation for the prediction. For example, the Social-" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.876, + 0.468, + 0.9 + ], + "angle": 0, + "content": "* equal contribution. Codes are available at https://github.com/cocoon2wong/SocialCircle." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19005" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.318 + ], + "angle": 0, + "content": "Force-based methods [9, 28] model and simulate agents' behaviors mainly according to the rules in Newtonian mechanics. Some other methods like [3, 42, 49] also turn trajectory prediction into an optimization problem by introducing their different mathematical models. However, designing a generalized \"rule\" that fits most socially interactive cases is often difficult, making them challenging to apply to complex scenes. On the contrary, model-free methods are mostly driven by data, and few manual interventions are considered. For example, graph-based methods [4, 14, 36] may build a series of spatial or temporal graph structures, thus learning to simulate agents' social interactions. Most model-free methods could fully utilize the ability of neural networks to fit data, but they may heavily rely on different network structures and pose limited explainability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.473, + 0.442 + ], + "angle": 0, + "content": "\"Rules\" and \"data\" play essential roles but put different limitations on these methods accordingly. A natural thought is to add several \"lite-rules\" to data-driven backbones to provide limited constraints as guidance to improve either the data-fit process or the explainability. In short, we want to constrain the learning process with relatively weak rules for social interactions rather than solid mathematical rules, thus benefiting from both rules and data-fit capabilities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.473, + 0.718 + ], + "angle": 0, + "content": "Analyzing agents' interactive behaviors through bionics and psychology is a natural choice. Animals would not analyze others' behaviors by solving complex equations but with relatively simple judgment rules when planning trajectories. Some researchers in the social psychology area also point out that each agent in a complex multiagent system tends to behave and interact with each other according to simple rules rather than extensive computations, which inspired a series of agent-based simulation models that have been widely applied in economics and political science [35]. It is fascinating that some marine animals can locate others in the deep sea through echolocation rather than visual factors due to the weak light. They may firstly scan the environment by sending some unique signals (like ultrasounds) at different angles, which could be reflected in contact with others and produce echoes. Then, they gather echoes from different directions, thus locating, interacting, or communicating with others, and finally modifying their behaviors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As shown in Fig. 1, the echolocation is similar to how agents interact with others. Only a few \"rules\" are established, like the time from they send to receive the echo and the direction where it comes. This way, we bring a simple priori to model social behaviors that interactions are considered to be angle-based. In detail, all interactive behaviors are considered in a special angle space where the angle \\(\\theta\\) (which direction the echo comes from) plays as the independent variable. We assume that most social interactions can be \"inferred\" by several simple components corresponding to each angle \\(\\theta\\), like the velocity of each participant (in which way the participant's position changes during two" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "echolocations) and the distance between each participant and the target agent (how long the echo arrives since scanning). Thus, we can obtain an angle-based vector function \\(\\mathbf{f}(\\theta)\\) \\((0\\leq \\theta < 2\\pi)\\) to represent the current socially interactive context when forecasting trajectories. We call that angle-based social interaction representation SocialCircle." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.183, + 0.893, + 0.348 + ], + "angle": 0, + "content": "SocialCircle can be classified as Model-based, but it is also inspired by model-free methods to fit data with relatively weak rules, i.e., simple components at different angles. Then, the observed trajectory and the angle-based SocialCircle will be analyzed together in a data-driven way, as they could be both treated as sequences, to catch the temporal-attentive portions in trajectories and the angle-attentive portions in the current interactive context simultaneously, thus establishing connections among these weak rules and agents' real-world socially interactive behaviors as well as the forecasted trajectories." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.348, + 0.894, + 0.456 + ], + "angle": 0, + "content": "In summary, we contribute (1) The angle-based Social-Circle representation for pedestrian trajectory prediction to model social interactive behaviors; (2) The serialized modeling strategy that treats and encodes the spatial social interactions in the temporal sequences' way along with trajectories; (3) Experiments on multiple backbone prediction models show quantitative and qualitative superiority." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.642, + 0.484 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.493, + 0.892, + 0.614 + ], + "angle": 0, + "content": "Model-based Social Interaction Methods. Model-based methods aim to use mathematical rules as the foundation to forecast trajectories. The classic Social Force Model [9] is proposed to model human dynamics with Newtonian mechanics. Pellegrini et al. [28] introduce Social Force factors to model social behaviors in the multi-agent tracking task. More Social-Force-based methods like [19, 24, 50] are also proposed to model crowds' interactions." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.615, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Other mathematical tools and models are also used to simulate socially interactive behaviors when forecasting trajectories. Xie et al. [42] propose the \"Dark Matter\" model to simulate and forecast social behaviors with fields and agent-based Lagrangian Mechanics. Xia et al. [41] propose a social transfer function to model human socially interactive behaviors via a uniform way across multiple prediction scenes. Yue et al. [49] propose a neural differential equation model, in which the explicit physics model serves as a strong inductive bias in modeling pedestrian behaviors." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.766, + 0.892, + 0.855 + ], + "angle": 0, + "content": "However, these methods are often difficult to cover all possible socially interactive cases. Even though some methods like [41, 49] draw on the advantages of data-driven approaches to make some key parameters trainable, they may still be limited by the complex mathematical rules and equations in complex prediction scenes." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Model-free Social Interaction Methods. Model-free methods simulate interactive behaviors mostly through a data-driven form. Alahi et al. [1] propose the Social-" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19006" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.272 + ], + "angle": 0, + "content": "Pooling method to connect nearby sequences to share hidden states with each other, thus simulating the information-sharing process. Variations of social pooling methods like [8, 30] are proposed to pool features by considering different scales or locations simultaneously. Grid-based methods like [11] have been proposed to explore additional simple rules to enhance the capacity of pooling methods. With the quick development of graph neural networks, graph structures have been widely used to model social interactions. Graph Attention Networks (GATs) [18, 26], Graph Convolutional Networks [6, 32, 36] are employed to simulate interactions as the edges between different nodes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.469, + 0.363 + ], + "angle": 0, + "content": "Most model-free methods prefer to focus more on the structure through which to fit the data so that the predicted trajectory could reflect the effects of social interactive cues. In this process, few direct mathematical rules are constraints, making them more dependent on different network structures and high-quality data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.469, + 0.469 + ], + "angle": 0, + "content": "The proposed SocialCircle tries to address these problems by introducing \"lite-rules\" to these trainable backbones, thus taking advantage of the data-driven approach combined with the explainability of the model-based approach to model interactive behaviors. It also avoids designing complex mathematical models or solving complex equations during the interaction modeling." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.168, + 0.497 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.644 + ], + "angle": 0, + "content": "Formulations. This work only concerns trajectories of 2D coordinates \\(\\mathbf{p} = (x,y)^{\\top}\\). Denote the historical trajectory of agent (pedestrian) \\(i\\) during \\(t_h\\) observation steps as \\(\\mathbf{X}^i = (\\mathbf{p}_1^i,\\dots,\\mathbf{p}_{t_h}^i)^\\top\\), trajectory prediction focused in this paper aims at forecasting one or more possible future trajectories \\(\\hat{\\mathbf{Y}}^i = (\\hat{\\mathbf{p}}_{t_h + 1}^i,\\dots,\\hat{\\mathbf{p}}_{t_h + t_f}^i)^\\top\\) through its observed \\(\\mathbf{X}^i\\) and all its' neighbors' trajectories \\(\\mathcal{X}^{/i} = \\{\\mathbf{X}^j |1\\leq j\\leq N_a,j\\neq i\\}\\) along with the scene image \\(\\mathbf{I}_{t_h}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Angle-based SocialCircle Representation. In this paper, all social-interaction-related operations are described and implemented in an \"angle\" space, where the angle \\(\\theta\\) is the independent variable that describes the location of interactive behaviors. We first define the angle \\(\\theta^i (j)\\in [0,2\\pi)\\) to represent the relative position of a neighbor agent \\(j\\) to the target agent \\(i\\). It is computed as the \"direction\" of the vector that begins from agent \\(i\\) and ends at agent \\(j\\) at the current observation step \\((t = t_h)\\). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.79, + 0.469, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\theta^ {i} (j) = \\operatorname {a t a n 2} \\left(\\mathbf {p} _ {t _ {h}} ^ {j} - \\mathbf {p} _ {t _ {h}} ^ {i}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Here, atan2 is the \"quadrant-sensitive\" arctan function that computes angle of the input \\(\\mathbf{p} = (x,y)^{\\top}\\) from 0 to \\(2\\pi\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Agent \\(i\\)'s SocialCircle representation (short for SocialCircle) can be treated as a head-to-tail cyclic vector function \\(\\mathbf{f}^i (\\theta)\\) for all \\(\\theta \\in [0,2\\pi)\\). To make the computation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "easier, the angle variables will be discretized into \\(N_{\\theta}\\) \"partitions\". This way, agent \\(i\\) 's SocialCircle can be denoted as" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.133, + 0.891, + 0.154 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} ^ {i} = \\left(\\mathbf {f} ^ {i} \\left(\\theta_ {1}\\right), \\mathbf {f} ^ {i} \\left(\\theta_ {2}\\right), \\dots , \\mathbf {f} ^ {i} \\left(\\theta_ {N _ {\\theta}}\\right)\\right) ^ {\\top}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.158, + 0.892, + 0.22 + ], + "angle": 0, + "content": "Here, \\(0 = \\theta_0 < \\theta_1 < \\ldots < \\theta_{N_\\theta} = 2\\pi\\). As shown in Fig. 2, each \\(\\mathbf{f}^i(\\theta_n) \\in \\mathbb{R}^{d_{\\mathrm{sc}}}\\) (\\(n = 1, 2, \\ldots, N_\\theta\\)) is used to represent the overall interactive effort in the \\(n\\)th partition caused by all participants from the set \\(\\mathbf{N}^i(\\theta_n)\\), which satisfies" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.228, + 0.891, + 0.245 + ], + "angle": 0, + "content": "\\[\n\\theta_ {n - 1} \\leq \\theta^ {i} (j) < \\theta_ {n}, \\forall j \\in \\mathbf {N} ^ {i} (\\theta_ {n}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.254, + 0.892, + 0.286 + ], + "angle": 0, + "content": "We treat agent \\(i\\) as its self-neighbor in the 1st partition. Denote the number of agents in \\(\\mathbf{N}^i (\\theta_n)\\) as \\(\\left|\\mathbf{N}^i (\\theta_n)\\right|\\), we have" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.306, + 0.891, + 0.337 + ], + "angle": 0, + "content": "\\[\ni \\in \\mathbf {N} ^ {i} \\left(\\theta_ {1}\\right), \\quad \\sum_ {n} \\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right| = N _ {a}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.346, + 0.891, + 0.376 + ], + "angle": 0, + "content": "SocialCircle Meta Components. Each SocialCircle partition is computed via three meta components:" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.385, + 0.891, + 0.407 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\mathrm {m e t a}} ^ {i} \\left(\\theta_ {n}\\right) = \\left(\\mathbf {f} _ {\\mathrm {v e l}} ^ {i} \\left(\\theta_ {n}\\right), \\mathbf {f} _ {\\mathrm {d i s}} ^ {i} \\left(\\theta_ {n}\\right), \\mathbf {f} _ {\\mathrm {d i r}} ^ {i} \\left(\\theta_ {n}\\right)\\right) ^ {\\top}. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.414, + 0.892, + 0.49 + ], + "angle": 0, + "content": "(a) Velocity \\(\\mathbf{f}_{\\mathrm{vel}}^i\\). Agents with higher velocities may pose potentially more significant dangers to others around them. SocialCircle takes the \"average velocity\" (the movement length during the observation period) of all neighbors in one partition to simulate this interactive factor. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.499, + 0.891, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\mathrm {v e l}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\left\\| \\mathbf {p} _ {t _ {h}} ^ {j} - \\mathbf {p} _ {1} ^ {j} \\right\\| _ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.546, + 0.892, + 0.623 + ], + "angle": 0, + "content": "(b) Distance \\(\\mathbf{f}_{\\mathrm{dis}}^i\\). Agents present different interaction preferences as the distance to the interaction participant changes. SocialCircle takes the average Euclidean distance (at \\(t = t_h\\) moment) between the target agent and all its neighbors in one partition to model this factor. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.631, + 0.891, + 0.669 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\mathrm {d i s}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\left\\| \\mathbf {p} _ {t _ {h}} ^ {i} - \\mathbf {p} _ {t _ {h}} ^ {j} \\right\\| _ {2}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.679, + 0.892, + 0.755 + ], + "angle": 0, + "content": "(c) Direction \\(\\mathbf{f}_{\\mathrm{dir}}^i\\). Partitioning the continuous \\(\\theta \\in [0,2\\pi)\\) may cause the loss of angle details. We use the average angles of all neighbors in one partition relative to the target agent as a compensation factor. It also acts as a positional coding term to distinguish different partitions. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.763, + 0.891, + 0.802 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\operatorname {d i r}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\theta^ {i} (j). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.81, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Serialized Modeling of Social Interaction. SocialCircle partitions \\(\\{\\mathbf{f}^i (\\theta_n)\\}_{n}\\) are obtained by concatenating and embedding all meta components. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.864, + 0.891, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} ^ {i} \\left(\\theta_ {n}\\right) = \\left\\{ \\begin{array}{l l} g _ {\\text {e m b e d}} \\left(\\mathbf {0}\\right), & \\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right| = 0; \\\\ g _ {\\text {e m b e d}} \\left(\\mathbf {f} _ {\\text {m e t a}} ^ {i} \\left(\\theta_ {n}\\right)\\right), & \\text {O t h e r w i s e .} \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19007" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.086, + 0.895, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.213, + 0.893, + 0.258 + ], + "angle": 0, + "content": "Figure 2. Computation pipeline of the proposed SocialCircle. Each agent's SocialCircle is different to others'. For a target agent, it first computes three meta components: velocity, distance, and direction. Then, these meta components will be averaged within each angle-based SocialCircle partition, and finally embedded into the set of high-dimensional head-to-tail cyclic representation \\(\\mathbf{f}^i (\\theta_n)\\) \\((1\\leq n\\leq N_{\\theta})\\)" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.279, + 0.468, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.405, + 0.471, + 0.463 + ], + "angle": 0, + "content": "Figure 3. The serialized modeling of social interactions. SocialCircle is treated as a \"virtual\" temporal sequence that shares the same sequence shape as the embedded trajectory by adding zero paddings, so they could be fused to forecast trajectories together." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.469, + 0.53 + ], + "angle": 0, + "content": "Here, \\( g_{\\mathrm{embed}} \\) is the embedding function that contains 2 fully connected layers with 64 output units. ReLU activation is used in the first layer while tanh is used in the second layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.469, + 0.668 + ], + "angle": 0, + "content": "SocialCircle represents the Spatial interactive context at the current step \\((t = t_h)\\) through a serialized form. A natural thought is to handle this sequence \\(\\mathbf{f}^i\\in \\mathbb{R}^{N_\\theta \\times d_{\\mathrm{sc}}}\\) along with the observed trajectory \\(\\mathbf{X}^i\\in \\mathbb{R}^{t_h\\times 2}\\) to learn the attentive portions inner these sequences simultaneously. In detail, we treat the spatial SocialCircle \\(\\mathbf{f}^i\\) as a Virtual Temporal Sequence that shares the same sequence length as the trajectory \\(\\mathbf{X}^i\\) or its representations. As shown in Fig. 3, \\(\\mathbf{f}^i\\) will be padded at first (we set \\(N_{\\theta}\\leq t_h\\)). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.674, + 0.469, + 0.726 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\text {p a d}} ^ {i} = \\left(\\underbrace {\\mathbf {f} ^ {i} \\left(\\theta_ {1}\\right) , \\dots , \\mathbf {f} ^ {i} \\left(\\theta_ {N _ {\\theta}}\\right)} _ {N _ {\\theta}}, \\underbrace {\\mathbf {0} , \\dots , \\mathbf {0}} _ {t _ {h} - N _ {\\theta}}\\right) ^ {\\top} \\in \\mathbb {R} ^ {t _ {h} \\times d _ {\\mathrm {s c}}}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.469, + 0.821 + ], + "angle": 0, + "content": "In most previous works [1, 8], agent- \\(i\\)'s observed trajectory \\(\\mathbf{X}^i\\) will be first embedded into the high-dimensional \\(\\mathbf{f}_{\\mathrm{traj}}^i \\in \\mathbb{R}^{t_h \\times d}\\) by some embedding layer \\(f_{\\mathrm{embed}}\\), i.e., \\(\\mathbf{f}_{\\mathrm{traj}}^i = f_{\\mathrm{embed}}(\\mathbf{X}^i)\\). Denote the computation of one trajectory prediction model (we call the backbone prediction model) as \\(B_{\\mathrm{pred}}\\), future trajectories \\(\\hat{\\mathbf{Y}}^i\\) are usually predicted by" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.828, + 0.469, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {Y}} ^ {i} = B _ {\\text {p r e d}} \\left(\\mathbf {f} _ {\\text {t r a j}} ^ {i}, \\mathbf {f} _ {\\text {s o c i a l}} ^ {i}, \\mathbf {f} _ {\\text {o t h e r s}} ^ {i}\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.903 + ], + "angle": 0, + "content": "where \\(\\mathbf{f}_{\\mathrm{social}}^i\\) denotes the original social representations in the backbone prediction model, and \\(\\mathbf{f}_{\\mathrm{others}}^i\\) denotes other required features (like visual features from scene image \\(\\mathbf{I}_{t_h}\\))." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.282, + 0.892, + 0.375 + ], + "angle": 0, + "content": "SocialCircle Models (the SocialCircle-lized backbone prediction models) take the fused vector \\(\\mathbf{f}_{\\mathrm{fuse}}^i\\) containing both trajectory information and interactive context to instead the single \\(\\mathbf{f}_{\\mathrm{traj}}^i\\) to learn the temporal-attentive portions in the observed trajectories and the angle-attentive portions in the SocialCircle simultaneously. The \\(\\mathbf{f}_{\\mathrm{fuse}}^i\\) is fused by" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.384, + 0.892, + 0.404 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {\\text {f u s e}} ^ {i} = \\tanh \\left(\\mathbf {W} _ {\\text {f u s e}} \\operatorname {C o n c a t} \\left(\\mathbf {f} _ {\\text {t r a j}} ^ {i}, \\mathbf {f} _ {\\text {p a d}} ^ {i}\\right) + \\mathbf {b} _ {\\text {f u s e}}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.413, + 0.892, + 0.459 + ], + "angle": 0, + "content": "Here, \\(\\mathbf{W}_{\\mathrm{fuse}}\\) and \\(\\mathbf{b}_{\\mathrm{fuse}}\\) are the trainable weights and bias. Meanwhile, the original \\(\\mathbf{f}_{\\mathrm{social}}^i\\) will be removed. The trajectory prediction pipeline of SocialCircle models has become" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.471, + 0.891, + 0.49 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {Y}} _ {\\mathrm {S C}} ^ {i} = B _ {\\text {p r e d}} \\left(\\mathbf {f} _ {\\text {f u s e}} ^ {i}, \\mathbf {f} _ {\\text {o t h e r s}} ^ {i}\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.495, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Training. SocialCircle does not introduce additional new loss functions. We take Transformer[37], MSN[40], \\(\\mathrm{V}^2\\)-Net[38], E-\\(\\mathrm{V}^2\\)-Net[39] as backbone trajectory prediction models to validate SocialCircle's performance in our experiments. These models will be trained with original loss functions and settings reported in their papers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.6, + 0.633, + 0.617 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Datasets. (a) ETH[28]-UCY[13] contains several videos captured in pedestrian walking scenes. We use the leave-one-out strategy [1] to train with \\(\\{t_h = 8, t_f = 12\\}\\) and sample interval \\(\\Delta t = 0.4s\\). (b) Stanford Drone Dataset [29] (SDD) has 60 drone videos. Different categories of agents are annotated in pixels. Following [15], we split \\(60\\%\\) videos to train, \\(20\\%\\) to validate, and \\(20\\%\\) to test under \\((t_h, t_f, \\Delta t) = (8, 12, 0.4)\\). (c) NBA SportVU [16] (NBA) includes trajectories captured by the SportVU tracking system in NBA games. Following [43, 44], we set \\((t_h, t_f, \\Delta t) = (5, 10, 0.4)\\), and sample 50K trajectories, including \\(65\\%\\) to train, \\(25\\%\\) to test, and \\(10\\%\\) to validate." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.806, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Metrics. We measure prediction accuracy with the best Average/Final Displacement Error over 20 generated trajectories (i.e., \\(\\min\\mathrm{ADE}_{20}/\\min\\mathrm{FDE}_{20}\\) [1, 8], short for ADE/FDE). See their detailed definitions in the Appendix." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1Ethics Note: Datasets used in this work are publicly available and do not contain any sensitive personally identifiable information." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19008" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.885, + 0.281 + ], + "angle": 0, + "content": "
Models (ETH-UCY)ethhotelunivzara1zara2ETH-UCYModels (SDD)SDD
SHENet[25] (2022)0.41/0.610.13/0.200.25/0.430.21/0.320.15/0.260.23/0.36FlowChain[20] (2023)9.93/17.17
MID[7] (2022)0.39/0.660.13/0.220.22/0.450.17/0.300.13/0.270.21/0.38SHENet[25] (2022)9.01/13.24
EqMotion[45] (2023)0.40/0.610.12/0.180.23/0.430.18/0.320.13/0.230.21/0.35IMP[34] (2023)8.98/15.54
MSN[40] (2023)0.27/0.410.11/0.170.28/0.480.22/0.360.18/0.290.21/0.34LED[23] (2023)8.48/11.36
LED[23] (2023)0.39/0.580.11/0.170.26/0.430.18/0.260.13/0.220.21/0.33MID[7] (2022)7.91/14.50
Trajectory++[31] (2020)0.43/0.860.12/0.190.22/0.430.17/0.320.12/0.250.20/0.39Y-net[22] (2021)7.85/11.85
Agentformer[48] (2021)0.26/0.390.11/0.140.26/0.460.15/0.230.14/0.230.18/0.29MSN[40] (2023)7.69/12.16
V2-Net[38] (2022)0.23/0.370.10/0.160.21/0.350.19/0.300.14/0.240.18/0.28V2-Net[38] (2022)7.12/11.39
Y-net[22] (2021)0.28/0.330.10/0.140.24/0.410.17/0.270.13/0.220.18/0.27E-V2-Net[39] (2023)6.57/10.49
E-V2-Net[39] (2023)0.25/0.380.11/0.160.20/0.340.19/0.300.13/0.240.17/0.28NSP-SFM[49] (2022)6.52/10.61
MSN-SC (Ours)0.27/0.390.13/0.180.22/0.450.18/0.340.15/0.270.19/0.33MSN-SC (Ours)7.49/12.12
V2-Net-SC (Ours)0.25/0.370.12/0.150.21/0.350.17/0.290.13/0.220.17/0.27V2-Net-SC (Ours)6.71/10.66
E-V2-Net-SC (Ours)0.25/0.380.12/0.140.20/0.340.18/0.290.13/0.220.17/0.27E-V2-Net-SC (Ours)6.54/10.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.29, + 0.893, + 0.32 + ], + "angle": 0, + "content": "Table 1. Comparisons on ETH-UCY (left) and SDD (right) under best-of-20 and with \\( t_h = 8 \\) frames' (3.2s) observations to predict future \\( t_f = 12 \\) frames' (4.8s) trajectories. Metrics are reported as \"ADE/FDE\". Lower ADE and FDE indicate better prediction performance." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.342, + 0.462, + 0.485 + ], + "angle": 0, + "content": "
Models (NBA)Metrics@2.0sMetrics@4.0s
PECNet[21] (2020)0.96/1.691.83/ 3.41
NMMP[10] (2020)0.70/1.111.33/ 2.05
V2-Net[38] (2022)0.69/0.961.28/ 1.68
E-V2-Net[39] (2023)0.68/ 0.931.26/ 1.64
MemoNet[44] (2022)0.71/1.141.25/ 1.47
GroupNet+NMMP[43] (2022)0.69/1.081.25/ 1.80
GroupNet+CVAE[43] (2022)0.62/0.951.13/1.69
V2-Net-SC (Ours)0.67/0.921.22/1.51
E-V2-Net-SC (Ours)0.67/0.901.18/1.46
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.495, + 0.472, + 0.539 + ], + "angle": 0, + "content": "Table 2. Comparisons on NBA under best-of-20 in meters (\\( t_h = 5, t_f = 10 \\)). Metrics are reported as \"ADE/FDE\" at different prediction lengths, including 2.0s (5 frames) and 4.0s (10 frames)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Implementation details. Models are trained on one NVIDIA Tesla T4 GPU. SocialCircle is computed on each agent's 50 nearest neighbors to save the computation resource. For SocialCircle models, we set \\( N_{\\theta} = t_h^2 \\), and set \\( \\theta_n = 2n\\pi / N_{\\theta} \\) (\\( n = 1, 2, \\dots, N_{\\theta} \\)). Feature dimensions \\( d \\) and \\( d_{\\mathrm{sc}} \\) are set to 64. Following [51], trajectories are preprocessed by moving to \\( (0, 0) \\). We set the learning rate to 1e-4, epochs to 600, and batch size to 1500." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.699, + 0.434, + 0.715 + ], + "angle": 0, + "content": "4.1. Comparisons to State-of-the-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.722, + 0.47, + 0.829 + ], + "angle": 0, + "content": "ETH-UCY. Tab. 1 illustrates that SocialCircle models are competitive. In detail, the E-V²-Net-SC has achieved a noteworthy prediction performance with \\(5.6\\%\\) better ADE and \\(6.9\\%\\) better FDE compared with Agentformer. Moreover, MSN-SC performs better than EqMotion with the improvement of \\(9.5\\%\\) ADE and \\(5.7\\%\\) FDE, even though MSN performs not as well as other new approaches." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.471, + 0.876 + ], + "angle": 0, + "content": "SDD. In Tab. 1, \\(\\mathrm{V}^2\\)-Net-SC outperforms Y-net by \\(14.52\\%\\) ADE and \\(10.04\\%\\) FDE. It has also obtained \\(20.87\\%\\) ADE and \\(6.16\\%\\) FDE improvements compared to the newly" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.341, + 0.695, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.341, + 0.892, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.447, + 0.895, + 0.532 + ], + "angle": 0, + "content": "Figure 4. Loss curves (loss values after different training epochs) of the simple Transformer (left) and the corresponding Transformer-SC variation (right) during the training process on SDD with 600 epochs in total. Loss values are normalized, and each figure includes six training runs (\"nan\" loss values are not displayed). Curves are smoothed with the decay factor \\(= 0.8\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.56, + 0.892, + 0.59 + ], + "angle": 0, + "content": "published LED. In addition, \\(\\mathrm{E - V^2}\\) -Net-SC outperforms the state-of-the-art NSP-SFM by as much as \\(2.36\\%\\) FDE." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.591, + 0.893, + 0.728 + ], + "angle": 0, + "content": "NBA. In Tab. 2, compared with GroupNet+CVAE, E-V²-Net-SC's ADE is not as well as that model (about \\(4.42\\%\\) worse), but its FDEs (both at 2.0s and 4.0s) are better than those for about \\(5.26\\%\\) and \\(13.60\\%\\). In addition, even though the FDE (4.0s) of MemoNet and E-V²-Net-SC are at the same level, E-V²-Net-SC outperforms the other for about \\(5.60\\%\\) ADE (4.0s). Although E-V²-Net performs not as well as these newly published methods, the proposed SocialCircle makes it available to achieve competitive results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.871, + 0.758 + ], + "angle": 0, + "content": "4.2. Ablation Studies and Quantitative Analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Overall Validation of SocialCircle. As shown in Tab. 3, SocialCircle could help even the simplest Transformer [37] (which considers nothing about agents' multimodality and interactions) improve \\(5.89\\%\\) ADE and \\(4.00\\%\\) FDE. SocialCircle also facilitates MSN, \\(\\mathrm{V}^2\\)-Net, and \\(\\mathrm{E - V^2}\\)-Net with up to \\(4.92\\%\\) ADE gains and \\(8.00\\%\\) FDE gains compared to their original models. In addition, we also plot loss curves \\((\\ell_2\\) loss) of 6 training runs of the simplest Transformer and the Transformer-SC in Fig. 4. It shows that SocialCir" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.361, + 0.902 + ], + "angle": 0, + "content": "See detailed analyses about \\(N_{\\theta}\\) in the Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19009" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.149, + 0.095, + 0.314, + 0.108 + ], + "angle": 0, + "content": "Target agents' observations" + }, + { + "type": "header", + "bbox": [ + 0.332, + 0.095, + 0.491, + 0.107 + ], + "angle": 0, + "content": "Target agents' ground truth" + }, + { + "type": "header", + "bbox": [ + 0.508, + 0.095, + 0.685, + 0.107 + ], + "angle": 0, + "content": "Neighbor agents' observations" + }, + { + "type": "header", + "bbox": [ + 0.699, + 0.094, + 0.723, + 0.11 + ], + "angle": 0, + "content": "#" + }, + { + "type": "header", + "bbox": [ + 0.726, + 0.096, + 0.823, + 0.107 + ], + "angle": 0, + "content": "Model Predictions" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.111, + 0.293, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.111, + 0.484, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.111, + 0.677, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.111, + 0.869, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.167, + 0.293, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.167, + 0.484, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.167, + 0.677, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.167, + 0.869, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.242, + 0.293, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.242, + 0.484, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.485, + 0.242, + 0.677, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.678, + 0.242, + 0.869, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.326, + 0.25, + 0.338 + ], + "angle": 0, + "content": "Transformer-SC" + }, + { + "type": "image_caption", + "bbox": [ + 0.36, + 0.326, + 0.42, + 0.338 + ], + "angle": 0, + "content": "MSN-SC" + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.326, + 0.617, + 0.338 + ], + "angle": 0, + "content": "V2-Net-SC" + }, + { + "type": "image_caption", + "bbox": [ + 0.732, + 0.326, + 0.816, + 0.338 + ], + "angle": 0, + "content": "E-V2-Net-SC" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.353, + 0.891, + 0.368 + ], + "angle": 0, + "content": "Figure 5. Visualized predictions of SocialCircle models with different backbone prediction models in several ETH-UCY and SDD scenes." + }, + { + "type": "image_caption", + "bbox": [ + 0.149, + 0.383, + 0.313, + 0.396 + ], + "angle": 0, + "content": "Target agents' observations" + }, + { + "type": "image_caption", + "bbox": [ + 0.334, + 0.383, + 0.491, + 0.396 + ], + "angle": 0, + "content": "Target agents' ground truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.508, + 0.383, + 0.685, + 0.396 + ], + "angle": 0, + "content": "Neighbor agents' observations" + }, + { + "type": "image_caption", + "bbox": [ + 0.698, + 0.382, + 0.823, + 0.396 + ], + "angle": 0, + "content": "Model Predictions" + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.398, + 0.365, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.461, + 0.365, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.52, + 0.365, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.116, + 0.579, + 0.365, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.398, + 0.531, + 0.46 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.46, + 0.531, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.52, + 0.532, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.579, + 0.532, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.398, + 0.701, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.459, + 0.701, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.534, + 0.52, + 0.701, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.579, + 0.701, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.398, + 0.871, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.459, + 0.871, + 0.52 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.52, + 0.871, + 0.579 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.579, + 0.871, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.091, + 0.65, + 0.877, + 0.665 + ], + "angle": 0, + "content": "Figure 6. Prediction comparisons of SocialCircle models and their original models in several interactive ETH-UCY and SDD scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.691, + 0.47, + 0.813 + ], + "angle": 0, + "content": "cle could help the loss drop faster for Transformer-SC with an average of \\(13.04\\%\\) lower than that in the Transformer after 600 training epochs. Moreover, 5 out of 6 Transformer runs' loss values fall into \"nan\" due to the inappropriate gradients before 450 training epochs. As for Transformer-SC, only two runs are terminated, demonstrating that SocialCircle may also somehow act as a normalization factor, thus improving the training stability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Validation of SocialCircle Meta Components. As shown in Tab. 3, both \\(\\mathrm{V}^2\\)-Net and \\(\\mathrm{E - V}^2\\)-Net benefit further from the velocity and distance factors, each of which could provide at least \\(1.50\\%\\) ADE and FDE gains (SC-a1 and SC-a2 variations). However, MSN-SC variations are" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.691, + 0.892, + 0.798 + ], + "angle": 0, + "content": "not so sensitive to these two factors (less than \\(1.07\\%\\) ADE differences among MSN-SC, MSN-SC-a1, and MSN-SC-a2) but rely more on the direction factor (up to \\(3.30\\%\\) FDE gain has been brought by this factor). Although these factors contribute differently to different backbone models, the combination of all these factors promotes the most, for removing each one could lead to a serious performance drop." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.8, + 0.891, + 0.814 + ], + "angle": 0, + "content": "Parameters & Efficiency. Please refer to the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.83, + 0.695, + 0.847 + ], + "angle": 0, + "content": "4.3. Qualitative Analyses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Visualized Predictions. Fig. 5 visualizes trajectories predicted by several SocialCircle models. We can see that all SocialCircle models' predictions present similar ways" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19010" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.462, + 0.34 + ], + "angle": 0, + "content": "
VariationsVDRADE/FDEADE/FDE Gain (%)
Transformer*×××17.44/33.36-5.89%/-4.00%
Transformer-SC✓✓✓16.47/32.08(base)
MSN*×××7.79/13.09-4.01%/-8.00%
MSN-SC-a1×✓✓7.53/12.30-0.53%/-1.49%
MSN-SC-a2✓×✓7.57/12.40-1.07%/-2.31%
MSN-SC-a3✓✓×7.60/12.52-1.47%/-3.30%
MSN-SC✓✓✓7.49/12.12(base)
V2-Net*×××7.04/10.94-4.92%/-2.63%
V2-Net-SC-a1×✓✓6.86/10.82-2.24%/-1.50%
V2-Net-SC-a2✓×✓6.87/10.87-2.38%/-1.97%
V2-Net-SC-a3✓✓×6.78/10.71-1.04%/-0.47%
V2-Net-SC✓✓✓6.71/10.66(base)
E-V2-Net*×××6.73/10.75-2.91%/-3.76%
E-V2-Net-SC-a1×✓✓6.67/10.73-1.99%/-3.57%
E-V2-Net-SC-a2✓×✓6.64/10.55-1.53%/-1.83%
E-V2-Net-SC-a3✓✓×6.59/10.48-0.76%/-1.16%
E-V2-Net-SC✓✓✓6.54/10.36(base)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.351, + 0.47, + 0.406 + ], + "angle": 0, + "content": "Table 3. Ablation studies on validating SocialCircle meta components on SDD. \"V\", \"D\", and \"R\" indicate whether \\(\\mathbf{f}_{\\mathrm{vel}}^i\\), \\(\\mathbf{f}_{\\mathrm{dis}}^i\\), or \\(\\mathbf{f}_{\\mathrm{dir}}^i\\) are included in the meta vector \\(\\mathbf{f}_{\\mathrm{meta}}^i\\). Models with “*” are reproduced under the same condition." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.425, + 0.47, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Figure 7. Toy Examples I: Validation of social interactions. The arrows and circles point to the same predicted trajectory that has been changed significantly due to the manual neighbor." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.687, + 0.47, + 0.793 + ], + "angle": 0, + "content": "to handle social interactions. For example, predictions in Fig. 5 (a2) to (a4) all present avoidance of the group of pedestrians standing still at the roadside. Similarly, avoiding the upcoming biker about to cross the intersection has also become a major concern in (c1) to (c4). These results indicate the effectiveness of the proposed SocialCircle that works with different backbone prediction models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Visualized Social Interaction Cases. As shown in Fig. 6, we observe that predictions given by SocialCircle models seem to be more \"conservative\" with a tendency to avoid others in different social interaction situations, which looks like it is trying to avoid possible collisions or too-close social distances. For example, predictions in (a2) display heavier avoidance of the man coming from" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.089, + 0.638, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.09, + 0.766, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.09, + 0.892, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.168, + 0.638, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.168, + 0.766, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.168, + 0.892, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.246, + 0.638, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.246, + 0.766, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.246, + 0.892, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.325, + 0.638, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.325, + 0.766, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.325, + 0.892, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.415, + 0.892, + 0.458 + ], + "angle": 0, + "content": "Figure 8. Toy Examples II: Validation of SocialCircle meta components by manually changing the manual neighbor's velocity (denoted by \\( v_{m} \\)) and its distance to the target agent (\\( d_{m} \\))." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.475, + 0.619, + 0.572 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.477, + 0.735, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.476, + 0.852, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.573, + 0.618, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.573, + 0.735, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.573, + 0.851, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.853, + 0.516, + 0.887, + 0.63 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.68, + 0.892, + 0.737 + ], + "angle": 0, + "content": "Figure 9. Visualized attention scores of each SocialCircle partition in the colored-ring form on several ETH-UCY prediction scenes. Partitions with higher attention scores (redder and wider) contribute more to the final predicted trajectories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.903 + ], + "angle": 0, + "content": "the car side than in (b2). Similarly, the potential collision between the moving biker and the focused walking pedestrian has been caught in (c3), thus representing a prediction shift (comparing the blue prediction in (c3) and the red one in (d3)). In addition, two pedestrians walk towards right together in cases (a4) and (b4). Unlike case (b4), SocialCircle model forecasts that the target agent may not crossover the other two's potential trajectories, like it \"thought\" that the agent would rather keep its relative position in the group." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19011" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.472, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.251, + 0.47, + 0.28 + ], + "angle": 0, + "content": "Figure 10. Toy Examples III: Comparisons of attention scores before and after adding manual neighbors in ETH-UCY scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.47, + 0.384 + ], + "angle": 0, + "content": "Note that social interactions are not only limited to these collision cases. They are common behavior patterns among agents, including scene-specific interactions like the game-related interactions in the NBA dataset. Please see the qualitative analyses of NBA interactions in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.386, + 0.47, + 0.688 + ], + "angle": 0, + "content": "Toy Examples I (Social Interactions). We design a series of toy examples on several real-world prediction scenes from ETH-UCY to verify the capacity of SocialCircle in handling social interactions in Fig. 7. We manually add new \"manual neighbors\" in different positions (partitions) to test SocialCircle model's response. Each manual neighbor's observed trajectory is simulated by linearly interpolating from the given start and end points. Comparing Fig. 7 (a1) and (b1), several predicted trajectories to the right of the target agent have changed a lot. For example, the red trajectory contracts violently to the other side, which seems quite likely to prevent possible collisions with the manual neighbor that walks towards itself. Similar phenomenons also appear in Fig. 7 (b2), whose blue and green predictions show varying degrees of avoidance tendencies, depending on where they are located. The predicted trajectories colored in blue and cyan in Fig. 7 (a3) also show a tendency to avoid the manual neighbor. These cases illustrate the adaptivity of the SocialCircle in customizing different predictions. We have provided more toy cases in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Toy Examples II (SocialCircle Meta Components). Fig. 8 further shows the qualitative effect on predicted trajectories caused by the other two SocialCircle factors, velocity and distance. We first focus on the velocity factor validated in (a1) to (a3) or (a4) to (a6). When the manual neighbor has a higher velocity, the predicted trajectories will be affected by it to a greater extent, and vice versa, especially for the pink predictions in (a1) to (a3). Except for the velocity, as the distance \\( d_{m} \\) increases in Fig. 8 (b1) to (b3) or (b4) to (b6), the influence of manual neighbors gradually becomes smaller. In contrast, the predicted trajectory may produce a heavier shift when \\( d_{m} \\) decreases step by step. These \"social-like\" behaviors brought by different SocialCircle meta components are learned adaptively during" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "training. It illustrates SocialCircle's capacity and explainability to represent potential social interaction cases and finally modify predicted trajectories socially." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.893, + 0.454 + ], + "angle": 0, + "content": "Toy Examples III (SocialCircle Partitions). In Fig. 9, we visualize how each SocialCircle partition contributes by squaring-sum the feature \\(\\mathbf{f}_{\\mathrm{pad}}^i\\) in each partition, which we call the Attention Score. Note that agent \\(i\\) itself will be treated as its self-neighbor located in partition 1 (see Eq. (4)). We can see from these figures that SocialCircle acts far from simply locating all neighbors but tells which partitions should be paid more attention to when forecasting trajectories. In Fig. 9 (a) to (d), partition 1 catches more attention, and others present different trends according to different neighbor distributions. Similar to the phenomenon shown in Fig. 8, neighbors that are closer to the target agent elicit higher levels of attention (like partition 3 against partition 2 in (a)), and neighbors that move faster attract more attention (partition 4 compared to partition 6 in (d)). Unlike these cases, partition 8 owns a higher score than partition 1 in case (e), indicating that the SocialCircle cares more about the neighbor walking along with the target agent rather than the agent itself. It is interesting in case (e) that some partitions have also been assigned scores even though there are no neighbors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.893, + 0.59 + ], + "angle": 0, + "content": "Furthermore, Fig. 10 shows how the attention scores change after adding manual neighbors. In case (a1), SocialCircle focuses more on partition 4. However, the scores have changed significantly in case (a2) due to the manual neighbor located between partitions 1 and 8, and partition 4 has been less focused. Cases (b1) and (b2) also show the similar trends. All these qualitative results illustrate SocialCircle's ability to describe different interactions and the effectiveness of partitioned modeling social interactions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.892, + 0.667 + ], + "angle": 0, + "content": "Limitations. SocialCircle does not contain the directions where neighbor agents came from. It also does not directly consider the interactions among neighbor agents and how they affect the target agent, i.e., the high-order interactions. We will further study it in our subsequent works." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.619, + 0.695 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.84 + ], + "angle": 0, + "content": "This work focuses on the modeling of social interactions when forecasting pedestrian trajectories. Like marine animals localizing and communicating with others through echolocation, we bring a simple priori rule to construct the angle-based social interaction representation SocialCircle, which aims to learn how three meta components modify agent trajectories. Experiments on multiple datasets show its competitiveness, and additional toy experiments also prove its effectiveness in handling social interactions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgement This project is supported by National Natural Science Foundation of China (62172177), and National Key R&D Program of China (2022YFC3301000)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19012" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. 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IEEE transactions on pattern" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19014" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.11, + 0.092, + 0.468, + 0.106 + ], + "angle": 0, + "content": "analysis and machine intelligence, 44(5):2742-2759, 2022." + }, + { + "type": "text", + "bbox": [ + 0.113, + 0.108, + 0.122, + 0.117 + ], + "angle": 0, + "content": "5" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19015" + } + ] +] \ No newline at end of file diff --git a/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_origin.pdf b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5101be555b7eacc6f40a34279e465e776e8ac624 --- /dev/null +++ b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/5b88fdbf-49dd-42ca-9334-fda1ac3ea6a3_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:991d6dc5f5a5a0a8720d1d396ba1915b4f890831fe2e9f3a04982c1066f1c95a +size 4495711 diff --git a/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/full.md b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bd4776216e1f0bc2a6afa79fa27cfb3739f55f01 --- /dev/null +++ b/2024/SocialCircle_ Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction/full.md @@ -0,0 +1,401 @@ +# SocialCircle: Learning the Angle-based Social Interaction Representation for Pedestrian Trajectory Prediction + +Conghao Wong $^{1*}$ Beihao Xia $(\boxtimes)^{1*}$ Ziqian Zou $^{1}$ Yulong Wang $^{2}$ Xinge You $^{1,3}$ $^{1}$ Huazhong University of Science and Technology $^{2}$ Huazhong Agricultural University Research Institute of Huazhong University of Science and Technology in Shenzhen + +{conghaowong, xbh_hust, ziqianzoulive}@icloud.com, ylwang@mail.hzau.edu.cn, youxg@mail.hust.edu.cn + +# Abstract + +Analyzing and forecasting trajectories of agents like pedestrians and cars in complex scenes has become more and more significant in many intelligent systems and applications. The diversity and uncertainty in socially interactive behaviors among a rich variety of agents make this task more challenging than other deterministic computer vision tasks. Researchers have made a lot of efforts to quantify the effects of these interactions on future trajectories through different mathematical models and network structures, but this problem has not been well solved. Inspired by marine animals that localize the positions of their companions underwater through echoes, we build a new angle-based trainable social interaction representation, named SocialCircle, for continuously reflecting the context of social interactions at different angular orientations relative to the target agent. We validate the effect of the proposed SocialCircle by training it along with several newly released trajectory prediction models, and experiments show that the SocialCircle not only quantitatively improves the prediction performance, but also qualitatively helps better simulate social interactions when forecasting pedestrian trajectories in a way that is consistent with human intuitions. + +# 1. Introduction + +Analyzing, understanding, and forecasting behaviors of intelligent agents have been significantly required by more and more intelligent systems and applications. Due to the ease of access and analysis of trajectories, analyzing agents' behaviors through trajectories has also become a common approach. Trajectory prediction aims at forecasting agents' all possible future trajectories during a specific period by taking into account the positions of all agents that appeared + +![](images/c6beb97077a89a46efaea5614ddbca34abe4bd5aa90bb192f44460692fdcde1c.jpg) +Figure 1. Motivation Illustration. Analogous to marine animals like dolphins and whales localizing other companions underwater through echolocation, we analyze agents' reactions to the potential socially interactive behaviors by assuming (1) they first Scan their interaction environment by sending signals from all angles, (2) then all neighbors feedback their Reflection signals to tell their directions, and (3) finally the target agent could make interactive decisions by the received echoes at different angular orientations. + +in the scene [1]. It also considers the potential interactive behaviors [2, 8, 12, 33, 46] as well as the scene constraints [3, 5, 17, 25, 27, 30, 41, 47] when making predictions. + +The social interaction [1, 28] (also known as the agent-to-agent interaction) considered in trajectory prediction takes into account not only all kinds of interactive behaviors among different agents but how they affect their trajectories. Current social-interaction-modeling methods in the trajectory prediction task can be classified roughly into Model-based and Model-free two classes[49]. Model-based methods may take some particular "rules" [49] as the primary foundation for the prediction. For example, the Social- + +Force-based methods [9, 28] model and simulate agents' behaviors mainly according to the rules in Newtonian mechanics. Some other methods like [3, 42, 49] also turn trajectory prediction into an optimization problem by introducing their different mathematical models. However, designing a generalized "rule" that fits most socially interactive cases is often difficult, making them challenging to apply to complex scenes. On the contrary, model-free methods are mostly driven by data, and few manual interventions are considered. For example, graph-based methods [4, 14, 36] may build a series of spatial or temporal graph structures, thus learning to simulate agents' social interactions. Most model-free methods could fully utilize the ability of neural networks to fit data, but they may heavily rely on different network structures and pose limited explainability. + +"Rules" and "data" play essential roles but put different limitations on these methods accordingly. A natural thought is to add several "lite-rules" to data-driven backbones to provide limited constraints as guidance to improve either the data-fit process or the explainability. In short, we want to constrain the learning process with relatively weak rules for social interactions rather than solid mathematical rules, thus benefiting from both rules and data-fit capabilities. + +Analyzing agents' interactive behaviors through bionics and psychology is a natural choice. Animals would not analyze others' behaviors by solving complex equations but with relatively simple judgment rules when planning trajectories. Some researchers in the social psychology area also point out that each agent in a complex multiagent system tends to behave and interact with each other according to simple rules rather than extensive computations, which inspired a series of agent-based simulation models that have been widely applied in economics and political science [35]. It is fascinating that some marine animals can locate others in the deep sea through echolocation rather than visual factors due to the weak light. They may firstly scan the environment by sending some unique signals (like ultrasounds) at different angles, which could be reflected in contact with others and produce echoes. Then, they gather echoes from different directions, thus locating, interacting, or communicating with others, and finally modifying their behaviors. + +As shown in Fig. 1, the echolocation is similar to how agents interact with others. Only a few "rules" are established, like the time from they send to receive the echo and the direction where it comes. This way, we bring a simple priori to model social behaviors that interactions are considered to be angle-based. In detail, all interactive behaviors are considered in a special angle space where the angle $\theta$ (which direction the echo comes from) plays as the independent variable. We assume that most social interactions can be "inferred" by several simple components corresponding to each angle $\theta$ , like the velocity of each participant (in which way the participant's position changes during two + +echolocations) and the distance between each participant and the target agent (how long the echo arrives since scanning). Thus, we can obtain an angle-based vector function $\mathbf{f}(\theta)$ $(0\leq \theta < 2\pi)$ to represent the current socially interactive context when forecasting trajectories. We call that angle-based social interaction representation SocialCircle. + +SocialCircle can be classified as Model-based, but it is also inspired by model-free methods to fit data with relatively weak rules, i.e., simple components at different angles. Then, the observed trajectory and the angle-based SocialCircle will be analyzed together in a data-driven way, as they could be both treated as sequences, to catch the temporal-attentive portions in trajectories and the angle-attentive portions in the current interactive context simultaneously, thus establishing connections among these weak rules and agents' real-world socially interactive behaviors as well as the forecasted trajectories. + +In summary, we contribute (1) The angle-based Social-Circle representation for pedestrian trajectory prediction to model social interactive behaviors; (2) The serialized modeling strategy that treats and encodes the spatial social interactions in the temporal sequences' way along with trajectories; (3) Experiments on multiple backbone prediction models show quantitative and qualitative superiority. + +# 2. Related Work + +Model-based Social Interaction Methods. Model-based methods aim to use mathematical rules as the foundation to forecast trajectories. The classic Social Force Model [9] is proposed to model human dynamics with Newtonian mechanics. Pellegrini et al. [28] introduce Social Force factors to model social behaviors in the multi-agent tracking task. More Social-Force-based methods like [19, 24, 50] are also proposed to model crowds' interactions. + +Other mathematical tools and models are also used to simulate socially interactive behaviors when forecasting trajectories. Xie et al. [42] propose the "Dark Matter" model to simulate and forecast social behaviors with fields and agent-based Lagrangian Mechanics. Xia et al. [41] propose a social transfer function to model human socially interactive behaviors via a uniform way across multiple prediction scenes. Yue et al. [49] propose a neural differential equation model, in which the explicit physics model serves as a strong inductive bias in modeling pedestrian behaviors. + +However, these methods are often difficult to cover all possible socially interactive cases. Even though some methods like [41, 49] draw on the advantages of data-driven approaches to make some key parameters trainable, they may still be limited by the complex mathematical rules and equations in complex prediction scenes. + +Model-free Social Interaction Methods. Model-free methods simulate interactive behaviors mostly through a data-driven form. Alahi et al. [1] propose the Social- + +Pooling method to connect nearby sequences to share hidden states with each other, thus simulating the information-sharing process. Variations of social pooling methods like [8, 30] are proposed to pool features by considering different scales or locations simultaneously. Grid-based methods like [11] have been proposed to explore additional simple rules to enhance the capacity of pooling methods. With the quick development of graph neural networks, graph structures have been widely used to model social interactions. Graph Attention Networks (GATs) [18, 26], Graph Convolutional Networks [6, 32, 36] are employed to simulate interactions as the edges between different nodes. + +Most model-free methods prefer to focus more on the structure through which to fit the data so that the predicted trajectory could reflect the effects of social interactive cues. In this process, few direct mathematical rules are constraints, making them more dependent on different network structures and high-quality data. + +The proposed SocialCircle tries to address these problems by introducing "lite-rules" to these trainable backbones, thus taking advantage of the data-driven approach combined with the explainability of the model-based approach to model interactive behaviors. It also avoids designing complex mathematical models or solving complex equations during the interaction modeling. + +# 3. Method + +Formulations. This work only concerns trajectories of 2D coordinates $\mathbf{p} = (x,y)^{\top}$ . Denote the historical trajectory of agent (pedestrian) $i$ during $t_h$ observation steps as $\mathbf{X}^i = (\mathbf{p}_1^i,\dots,\mathbf{p}_{t_h}^i)^\top$ , trajectory prediction focused in this paper aims at forecasting one or more possible future trajectories $\hat{\mathbf{Y}}^i = (\hat{\mathbf{p}}_{t_h + 1}^i,\dots,\hat{\mathbf{p}}_{t_h + t_f}^i)^\top$ through its observed $\mathbf{X}^i$ and all its' neighbors' trajectories $\mathcal{X}^{/i} = \{\mathbf{X}^j |1\leq j\leq N_a,j\neq i\}$ along with the scene image $\mathbf{I}_{t_h}$ . + +Angle-based SocialCircle Representation. In this paper, all social-interaction-related operations are described and implemented in an "angle" space, where the angle $\theta$ is the independent variable that describes the location of interactive behaviors. We first define the angle $\theta^i (j)\in [0,2\pi)$ to represent the relative position of a neighbor agent $j$ to the target agent $i$ . It is computed as the "direction" of the vector that begins from agent $i$ and ends at agent $j$ at the current observation step $(t = t_h)$ . Formally, + +$$ +\theta^ {i} (j) = \operatorname {a t a n 2} \left(\mathbf {p} _ {t _ {h}} ^ {j} - \mathbf {p} _ {t _ {h}} ^ {i}\right). \tag {1} +$$ + +Here, atan2 is the "quadrant-sensitive" arctan function that computes angle of the input $\mathbf{p} = (x,y)^{\top}$ from 0 to $2\pi$ + +Agent $i$ 's SocialCircle representation (short for SocialCircle) can be treated as a head-to-tail cyclic vector function $\mathbf{f}^i (\theta)$ for all $\theta \in [0,2\pi)$ . To make the computation + +easier, the angle variables will be discretized into $N_{\theta}$ "partitions". This way, agent $i$ 's SocialCircle can be denoted as + +$$ +\mathbf {f} ^ {i} = \left(\mathbf {f} ^ {i} \left(\theta_ {1}\right), \mathbf {f} ^ {i} \left(\theta_ {2}\right), \dots , \mathbf {f} ^ {i} \left(\theta_ {N _ {\theta}}\right)\right) ^ {\top}. \tag {2} +$$ + +Here, $0 = \theta_0 < \theta_1 < \ldots < \theta_{N_\theta} = 2\pi$ . As shown in Fig. 2, each $\mathbf{f}^i(\theta_n) \in \mathbb{R}^{d_{\mathrm{sc}}}$ ( $n = 1, 2, \ldots, N_\theta$ ) is used to represent the overall interactive effort in the $n$ th partition caused by all participants from the set $\mathbf{N}^i(\theta_n)$ , which satisfies + +$$ +\theta_ {n - 1} \leq \theta^ {i} (j) < \theta_ {n}, \forall j \in \mathbf {N} ^ {i} (\theta_ {n}). \tag {3} +$$ + +We treat agent $i$ as its self-neighbor in the 1st partition. Denote the number of agents in $\mathbf{N}^i (\theta_n)$ as $\left|\mathbf{N}^i (\theta_n)\right|$ , we have + +$$ +i \in \mathbf {N} ^ {i} \left(\theta_ {1}\right), \quad \sum_ {n} \left| \mathbf {N} ^ {i} \left(\theta_ {n}\right) \right| = N _ {a}. \tag {4} +$$ + +SocialCircle Meta Components. Each SocialCircle partition is computed via three meta components: + +$$ +\mathbf {f} _ {\mathrm {m e t a}} ^ {i} \left(\theta_ {n}\right) = \left(\mathbf {f} _ {\mathrm {v e l}} ^ {i} \left(\theta_ {n}\right), \mathbf {f} _ {\mathrm {d i s}} ^ {i} \left(\theta_ {n}\right), \mathbf {f} _ {\mathrm {d i r}} ^ {i} \left(\theta_ {n}\right)\right) ^ {\top}. \tag {5} +$$ + +(a) Velocity $\mathbf{f}_{\mathrm{vel}}^i$ . Agents with higher velocities may pose potentially more significant dangers to others around them. SocialCircle takes the "average velocity" (the movement length during the observation period) of all neighbors in one partition to simulate this interactive factor. Formally, + +$$ +\mathbf {f} _ {\mathrm {v e l}} ^ {i} \left(\theta_ {n}\right) = \frac {1}{\left| \mathbf {N} ^ {i} \left(\theta_ {n}\right) \right|} \sum_ {j \in \mathbf {N} ^ {i} \left(\theta_ {n}\right)} \left\| \mathbf {p} _ {t _ {h}} ^ {j} - \mathbf {p} _ {1} ^ {j} \right\| _ {2}, \tag {6} +$$ + +(b) Distance $\mathbf{f}_{\mathrm{dis}}^i$ . Agents present different interaction preferences as the distance to the interaction participant changes. SocialCircle takes the average Euclidean distance (at $t = t_h$ moment) between the target agent and all its neighbors in one partition to model this factor. Formally, + +$$ +\mathbf {f} _ {\mathrm {d i s}} ^ {i} \left(\theta_ {n}\right) = \frac {1}{\left| \mathbf {N} ^ {i} \left(\theta_ {n}\right) \right|} \sum_ {j \in \mathbf {N} ^ {i} \left(\theta_ {n}\right)} \left\| \mathbf {p} _ {t _ {h}} ^ {i} - \mathbf {p} _ {t _ {h}} ^ {j} \right\| _ {2}. \tag {7} +$$ + +(c) Direction $\mathbf{f}_{\mathrm{dir}}^i$ . Partitioning the continuous $\theta \in [0,2\pi)$ may cause the loss of angle details. We use the average angles of all neighbors in one partition relative to the target agent as a compensation factor. It also acts as a positional coding term to distinguish different partitions. Formally, + +$$ +\mathbf {f} _ {\operatorname {d i r}} ^ {i} \left(\theta_ {n}\right) = \frac {1}{\left| \mathbf {N} ^ {i} \left(\theta_ {n}\right) \right|} \sum_ {j \in \mathbf {N} ^ {i} \left(\theta_ {n}\right)} \theta^ {i} (j). \tag {8} +$$ + +Serialized Modeling of Social Interaction. SocialCircle partitions $\{\mathbf{f}^i (\theta_n)\}_{n}$ are obtained by concatenating and embedding all meta components. Formally, + +$$ +\mathbf {f} ^ {i} \left(\theta_ {n}\right) = \left\{ \begin{array}{l l} g _ {\text {e m b e d}} \left(\mathbf {0}\right), & \left| \mathbf {N} ^ {i} \left(\theta_ {n}\right) \right| = 0; \\ g _ {\text {e m b e d}} \left(\mathbf {f} _ {\text {m e t a}} ^ {i} \left(\theta_ {n}\right)\right), & \text {O t h e r w i s e .} \end{array} \right. \tag {9} +$$ + +![](images/e229276ad6a18b090cce57c5975f3692e6bfb83ce244c851445f633f82b99974.jpg) +Figure 2. Computation pipeline of the proposed SocialCircle. Each agent's SocialCircle is different to others'. For a target agent, it first computes three meta components: velocity, distance, and direction. Then, these meta components will be averaged within each angle-based SocialCircle partition, and finally embedded into the set of high-dimensional head-to-tail cyclic representation $\mathbf{f}^i (\theta_n)$ $(1\leq n\leq N_{\theta})$ + +![](images/f90323f00a8dc4765d892224703772dc8ee133f43bcdf165685239475b31b3ca.jpg) +Figure 3. The serialized modeling of social interactions. SocialCircle is treated as a "virtual" temporal sequence that shares the same sequence shape as the embedded trajectory by adding zero paddings, so they could be fused to forecast trajectories together. + +Here, $g_{\mathrm{embed}}$ is the embedding function that contains 2 fully connected layers with 64 output units. ReLU activation is used in the first layer while tanh is used in the second layer. + +SocialCircle represents the Spatial interactive context at the current step $(t = t_h)$ through a serialized form. A natural thought is to handle this sequence $\mathbf{f}^i\in \mathbb{R}^{N_\theta \times d_{\mathrm{sc}}}$ along with the observed trajectory $\mathbf{X}^i\in \mathbb{R}^{t_h\times 2}$ to learn the attentive portions inner these sequences simultaneously. In detail, we treat the spatial SocialCircle $\mathbf{f}^i$ as a Virtual Temporal Sequence that shares the same sequence length as the trajectory $\mathbf{X}^i$ or its representations. As shown in Fig. 3, $\mathbf{f}^i$ will be padded at first (we set $N_{\theta}\leq t_h$ ). Formally, + +$$ +\mathbf {f} _ {\text {p a d}} ^ {i} = \left(\underbrace {\mathbf {f} ^ {i} \left(\theta_ {1}\right) , \dots , \mathbf {f} ^ {i} \left(\theta_ {N _ {\theta}}\right)} _ {N _ {\theta}}, \underbrace {\mathbf {0} , \dots , \mathbf {0}} _ {t _ {h} - N _ {\theta}}\right) ^ {\top} \in \mathbb {R} ^ {t _ {h} \times d _ {\mathrm {s c}}}. \tag {10} +$$ + +In most previous works [1, 8], agent- $i$ 's observed trajectory $\mathbf{X}^i$ will be first embedded into the high-dimensional $\mathbf{f}_{\mathrm{traj}}^i \in \mathbb{R}^{t_h \times d}$ by some embedding layer $f_{\mathrm{embed}}$ , i.e., $\mathbf{f}_{\mathrm{traj}}^i = f_{\mathrm{embed}}(\mathbf{X}^i)$ . Denote the computation of one trajectory prediction model (we call the backbone prediction model) as $B_{\mathrm{pred}}$ , future trajectories $\hat{\mathbf{Y}}^i$ are usually predicted by + +$$ +\hat {\mathbf {Y}} ^ {i} = B _ {\text {p r e d}} \left(\mathbf {f} _ {\text {t r a j}} ^ {i}, \mathbf {f} _ {\text {s o c i a l}} ^ {i}, \mathbf {f} _ {\text {o t h e r s}} ^ {i}\right), \tag {11} +$$ + +where $\mathbf{f}_{\mathrm{social}}^i$ denotes the original social representations in the backbone prediction model, and $\mathbf{f}_{\mathrm{others}}^i$ denotes other required features (like visual features from scene image $\mathbf{I}_{t_h}$ ). + +SocialCircle Models (the SocialCircle-lized backbone prediction models) take the fused vector $\mathbf{f}_{\mathrm{fuse}}^i$ containing both trajectory information and interactive context to instead the single $\mathbf{f}_{\mathrm{traj}}^i$ to learn the temporal-attentive portions in the observed trajectories and the angle-attentive portions in the SocialCircle simultaneously. The $\mathbf{f}_{\mathrm{fuse}}^i$ is fused by + +$$ +\mathbf {f} _ {\text {f u s e}} ^ {i} = \tanh \left(\mathbf {W} _ {\text {f u s e}} \operatorname {C o n c a t} \left(\mathbf {f} _ {\text {t r a j}} ^ {i}, \mathbf {f} _ {\text {p a d}} ^ {i}\right) + \mathbf {b} _ {\text {f u s e}}\right). \tag {12} +$$ + +Here, $\mathbf{W}_{\mathrm{fuse}}$ and $\mathbf{b}_{\mathrm{fuse}}$ are the trainable weights and bias. Meanwhile, the original $\mathbf{f}_{\mathrm{social}}^i$ will be removed. The trajectory prediction pipeline of SocialCircle models has become + +$$ +\hat {\mathbf {Y}} _ {\mathrm {S C}} ^ {i} = B _ {\text {p r e d}} \left(\mathbf {f} _ {\text {f u s e}} ^ {i}, \mathbf {f} _ {\text {o t h e r s}} ^ {i}\right). \tag {13} +$$ + +Training. SocialCircle does not introduce additional new loss functions. We take Transformer[37], MSN[40], $\mathrm{V}^2$ -Net[38], E- $\mathrm{V}^2$ -Net[39] as backbone trajectory prediction models to validate SocialCircle's performance in our experiments. These models will be trained with original loss functions and settings reported in their papers. + +# 4. Experiments + +Datasets. (a) ETH[28]-UCY[13] contains several videos captured in pedestrian walking scenes. We use the leave-one-out strategy [1] to train with $\{t_h = 8, t_f = 12\}$ and sample interval $\Delta t = 0.4s$ . (b) Stanford Drone Dataset [29] (SDD) has 60 drone videos. Different categories of agents are annotated in pixels. Following [15], we split $60\%$ videos to train, $20\%$ to validate, and $20\%$ to test under $(t_h, t_f, \Delta t) = (8, 12, 0.4)$ . (c) NBA SportVU [16] (NBA) includes trajectories captured by the SportVU tracking system in NBA games. Following [43, 44], we set $(t_h, t_f, \Delta t) = (5, 10, 0.4)$ , and sample 50K trajectories, including $65\%$ to train, $25\%$ to test, and $10\%$ to validate. + +Metrics. We measure prediction accuracy with the best Average/Final Displacement Error over 20 generated trajectories (i.e., $\min\mathrm{ADE}_{20}/\min\mathrm{FDE}_{20}$ [1, 8], short for ADE/FDE). See their detailed definitions in the Appendix. + +
Models (ETH-UCY)ethhotelunivzara1zara2ETH-UCYModels (SDD)SDD
SHENet[25] (2022)0.41/0.610.13/0.200.25/0.430.21/0.320.15/0.260.23/0.36FlowChain[20] (2023)9.93/17.17
MID[7] (2022)0.39/0.660.13/0.220.22/0.450.17/0.300.13/0.270.21/0.38SHENet[25] (2022)9.01/13.24
EqMotion[45] (2023)0.40/0.610.12/0.180.23/0.430.18/0.320.13/0.230.21/0.35IMP[34] (2023)8.98/15.54
MSN[40] (2023)0.27/0.410.11/0.170.28/0.480.22/0.360.18/0.290.21/0.34LED[23] (2023)8.48/11.36
LED[23] (2023)0.39/0.580.11/0.170.26/0.430.18/0.260.13/0.220.21/0.33MID[7] (2022)7.91/14.50
Trajectory++[31] (2020)0.43/0.860.12/0.190.22/0.430.17/0.320.12/0.250.20/0.39Y-net[22] (2021)7.85/11.85
Agentformer[48] (2021)0.26/0.390.11/0.140.26/0.460.15/0.230.14/0.230.18/0.29MSN[40] (2023)7.69/12.16
V2-Net[38] (2022)0.23/0.370.10/0.160.21/0.350.19/0.300.14/0.240.18/0.28V2-Net[38] (2022)7.12/11.39
Y-net[22] (2021)0.28/0.330.10/0.140.24/0.410.17/0.270.13/0.220.18/0.27E-V2-Net[39] (2023)6.57/10.49
E-V2-Net[39] (2023)0.25/0.380.11/0.160.20/0.340.19/0.300.13/0.240.17/0.28NSP-SFM[49] (2022)6.52/10.61
MSN-SC (Ours)0.27/0.390.13/0.180.22/0.450.18/0.340.15/0.270.19/0.33MSN-SC (Ours)7.49/12.12
V2-Net-SC (Ours)0.25/0.370.12/0.150.21/0.350.17/0.290.13/0.220.17/0.27V2-Net-SC (Ours)6.71/10.66
E-V2-Net-SC (Ours)0.25/0.380.12/0.140.20/0.340.18/0.290.13/0.220.17/0.27E-V2-Net-SC (Ours)6.54/10.36
+ +Table 1. Comparisons on ETH-UCY (left) and SDD (right) under best-of-20 and with $t_h = 8$ frames' (3.2s) observations to predict future $t_f = 12$ frames' (4.8s) trajectories. Metrics are reported as "ADE/FDE". Lower ADE and FDE indicate better prediction performance. + +
Models (NBA)Metrics@2.0sMetrics@4.0s
PECNet[21] (2020)0.96/1.691.83/ 3.41
NMMP[10] (2020)0.70/1.111.33/ 2.05
V2-Net[38] (2022)0.69/0.961.28/ 1.68
E-V2-Net[39] (2023)0.68/ 0.931.26/ 1.64
MemoNet[44] (2022)0.71/1.141.25/ 1.47
GroupNet+NMMP[43] (2022)0.69/1.081.25/ 1.80
GroupNet+CVAE[43] (2022)0.62/0.951.13/1.69
V2-Net-SC (Ours)0.67/0.921.22/1.51
E-V2-Net-SC (Ours)0.67/0.901.18/1.46
+ +Table 2. Comparisons on NBA under best-of-20 in meters ( $t_h = 5, t_f = 10$ ). Metrics are reported as "ADE/FDE" at different prediction lengths, including 2.0s (5 frames) and 4.0s (10 frames). + +Implementation details. Models are trained on one NVIDIA Tesla T4 GPU. SocialCircle is computed on each agent's 50 nearest neighbors to save the computation resource. For SocialCircle models, we set $N_{\theta} = t_h^2$ , and set $\theta_n = 2n\pi / N_{\theta}$ ( $n = 1, 2, \dots, N_{\theta}$ ). Feature dimensions $d$ and $d_{\mathrm{sc}}$ are set to 64. Following [51], trajectories are preprocessed by moving to $(0, 0)$ . We set the learning rate to 1e-4, epochs to 600, and batch size to 1500. + +# 4.1. Comparisons to State-of-the-Art Methods + +ETH-UCY. Tab. 1 illustrates that SocialCircle models are competitive. In detail, the E-V²-Net-SC has achieved a noteworthy prediction performance with $5.6\%$ better ADE and $6.9\%$ better FDE compared with Agentformer. Moreover, MSN-SC performs better than EqMotion with the improvement of $9.5\%$ ADE and $5.7\%$ FDE, even though MSN performs not as well as other new approaches. + +SDD. In Tab. 1, $\mathrm{V}^2$ -Net-SC outperforms Y-net by $14.52\%$ ADE and $10.04\%$ FDE. It has also obtained $20.87\%$ ADE and $6.16\%$ FDE improvements compared to the newly + +![](images/78a5727e38901797e82d0ad553a665ca6ff1c22e3dd71c4d7543a75cd080ab2b.jpg) +Figure 4. Loss curves (loss values after different training epochs) of the simple Transformer (left) and the corresponding Transformer-SC variation (right) during the training process on SDD with 600 epochs in total. Loss values are normalized, and each figure includes six training runs ("nan" loss values are not displayed). Curves are smoothed with the decay factor $= 0.8$ . + +![](images/2972c88ad57377e5ba5b64f00152fa10f83af3960694be49fa1a6f6e7cfa50cb.jpg) + +published LED. In addition, $\mathrm{E - V^2}$ -Net-SC outperforms the state-of-the-art NSP-SFM by as much as $2.36\%$ FDE. + +NBA. In Tab. 2, compared with GroupNet+CVAE, E-V²-Net-SC's ADE is not as well as that model (about $4.42\%$ worse), but its FDEs (both at 2.0s and 4.0s) are better than those for about $5.26\%$ and $13.60\%$ . In addition, even though the FDE (4.0s) of MemoNet and E-V²-Net-SC are at the same level, E-V²-Net-SC outperforms the other for about $5.60\%$ ADE (4.0s). Although E-V²-Net performs not as well as these newly published methods, the proposed SocialCircle makes it available to achieve competitive results. + +# 4.2. Ablation Studies and Quantitative Analyses + +Overall Validation of SocialCircle. As shown in Tab. 3, SocialCircle could help even the simplest Transformer [37] (which considers nothing about agents' multimodality and interactions) improve $5.89\%$ ADE and $4.00\%$ FDE. SocialCircle also facilitates MSN, $\mathrm{V}^2$ -Net, and $\mathrm{E - V^2}$ -Net with up to $4.92\%$ ADE gains and $8.00\%$ FDE gains compared to their original models. In addition, we also plot loss curves $(\ell_2$ loss) of 6 training runs of the simplest Transformer and the Transformer-SC in Fig. 4. It shows that SocialCir + +![](images/b717f9bfc894995763f160b43713ad9a6e8f04c0d4388749d327f20ce9adff9d.jpg) + +![](images/0b833409cdcdcf891f320cfcb5c9d8783fb075320a7d13be2a865d1ffab466c4.jpg) + +![](images/fde14a8dee277cd55d3d4b4734b7b47921181904498cf20a76addf76420c0602.jpg) + +![](images/65d5f7d24e2cc76eafe9ab106821d15bdbbb21ab3a7516687e7132ff1ca5de38.jpg) + +![](images/221a072e49a6f39cc0888cc359637356ef62c36cc29293126bce9a1432fa0373.jpg) + +![](images/766bbaa628bb81ece14396a9dad0e2196c6be0eca0bd5cace8ddbca5b64acf30.jpg) + +![](images/4609569b814d33e9b375d663dc041da997d310810fd1edb9479532ced495ba2a.jpg) + +![](images/526452591ccecca722842d8a4388e42c5ca4c887662682220ea64a73d32da0a0.jpg) + +![](images/f9aa8a9914aa28e47d0595d84aa1cc68776c134fcc235a1acf450070848e7e37.jpg) +Transformer-SC + +![](images/2e8b0ebc8f0466cc3709b1208e17e39c5850b898f2318a682cfe45d0a921ee0e.jpg) +MSN-SC + +![](images/642e439ae40925667aa95ab5437c288546805e2883766f90bd4d3bfb90e49b2e.jpg) +V2-Net-SC +Figure 5. Visualized predictions of SocialCircle models with different backbone prediction models in several ETH-UCY and SDD scenes. + +![](images/f9c76372519a9d156e3ede1410c31552dab9e0710b472abaa7950d41d52c5141.jpg) +E-V2-Net-SC + +![](images/9258695d593dd2aaf36a636688fd245056a30c1c6277608ad4f1037992887abe.jpg) +Target agents' observations + +![](images/07114d0c0c8881371789658bf8c62a2c8e60e0e8fe1c560e49c03bd44363f615.jpg) + +![](images/e5c523cb33e104f2035c3f99c2ad8f9bc392f02b8de8a862eeef7b2a6cab9701.jpg) + +![](images/dd7530e6e241d58023975d704ca0c43c1183bc00916745d9a10de8acfa575a78.jpg) +Figure 6. Prediction comparisons of SocialCircle models and their original models in several interactive ETH-UCY and SDD scenes. + +![](images/040cb2dd4e0042baa59340033448b003d58d885caf7df277ee891fc070e561ed.jpg) +Target agents' ground truth +Neighbor agents' observations + +![](images/a62b4867b6cb4f085d0c24b9c565e5fccd3453515eb8aab96024882f22752f16.jpg) + +![](images/12c7986fd53bae63e878c9bd4cd7b64f816bf2bdaf4da371abd8be0ed442d0d0.jpg) + +![](images/626132764b8db74a49b91434b94f3e26e24dff43bc5594381a74c47e2e4d6721.jpg) + +![](images/08e938354e2cc915a5d1b7a2eee3a363c8f57eda5e2db4eddca1b5cf45027b66.jpg) +Model Predictions + +![](images/1ffc858822b2331676c0789a632cc2c565167f298791bbaa8ab1bbe5c7c23749.jpg) + +![](images/b4e55b94b6a78e487467ab63551c48e782c04183d7123a3e6babccff9271fbc3.jpg) + +![](images/19ba49184fc0f952c80094862b9bee0281d5047435b329e9babc75371fa8a0c1.jpg) + +![](images/fe197f4acea535486d53671785aa4e737ce545510ba7141e9d3d8517471d522c.jpg) + +![](images/88735d32345888985558ac7be2c16104ef12fd4e47361cf34efe5c948d63e919.jpg) + +![](images/32fd94bc743b80e8cc503cc039b73f74a9a22ed90bf107227094e736a3da2678.jpg) + +![](images/5f23e05e306f73073dc72f36198473828cafcaf8763f6873e4977a726843ea27.jpg) + +cle could help the loss drop faster for Transformer-SC with an average of $13.04\%$ lower than that in the Transformer after 600 training epochs. Moreover, 5 out of 6 Transformer runs' loss values fall into "nan" due to the inappropriate gradients before 450 training epochs. As for Transformer-SC, only two runs are terminated, demonstrating that SocialCircle may also somehow act as a normalization factor, thus improving the training stability. + +Validation of SocialCircle Meta Components. As shown in Tab. 3, both $\mathrm{V}^2$ -Net and $\mathrm{E - V}^2$ -Net benefit further from the velocity and distance factors, each of which could provide at least $1.50\%$ ADE and FDE gains (SC-a1 and SC-a2 variations). However, MSN-SC variations are + +not so sensitive to these two factors (less than $1.07\%$ ADE differences among MSN-SC, MSN-SC-a1, and MSN-SC-a2) but rely more on the direction factor (up to $3.30\%$ FDE gain has been brought by this factor). Although these factors contribute differently to different backbone models, the combination of all these factors promotes the most, for removing each one could lead to a serious performance drop. + +Parameters & Efficiency. Please refer to the Appendix. + +# 4.3. Qualitative Analyses + +Visualized Predictions. Fig. 5 visualizes trajectories predicted by several SocialCircle models. We can see that all SocialCircle models' predictions present similar ways + +
VariationsVDRADE/FDEADE/FDE Gain (%)
Transformer*×××17.44/33.36-5.89%/-4.00%
Transformer-SC✓✓✓16.47/32.08(base)
MSN*×××7.79/13.09-4.01%/-8.00%
MSN-SC-a1×✓✓7.53/12.30-0.53%/-1.49%
MSN-SC-a2✓×✓7.57/12.40-1.07%/-2.31%
MSN-SC-a3✓✓×7.60/12.52-1.47%/-3.30%
MSN-SC✓✓✓7.49/12.12(base)
V2-Net*×××7.04/10.94-4.92%/-2.63%
V2-Net-SC-a1×✓✓6.86/10.82-2.24%/-1.50%
V2-Net-SC-a2✓×✓6.87/10.87-2.38%/-1.97%
V2-Net-SC-a3✓✓×6.78/10.71-1.04%/-0.47%
V2-Net-SC✓✓✓6.71/10.66(base)
E-V2-Net*×××6.73/10.75-2.91%/-3.76%
E-V2-Net-SC-a1×✓✓6.67/10.73-1.99%/-3.57%
E-V2-Net-SC-a2✓×✓6.64/10.55-1.53%/-1.83%
E-V2-Net-SC-a3✓✓×6.59/10.48-0.76%/-1.16%
E-V2-Net-SC✓✓✓6.54/10.36(base)
+ +Table 3. Ablation studies on validating SocialCircle meta components on SDD. "V", "D", and "R" indicate whether $\mathbf{f}_{\mathrm{vel}}^i$ , $\mathbf{f}_{\mathrm{dis}}^i$ , or $\mathbf{f}_{\mathrm{dir}}^i$ are included in the meta vector $\mathbf{f}_{\mathrm{meta}}^i$ . Models with “*” are reproduced under the same condition. + +![](images/f7559a10ca0ab057fe4174765206b171819ef3cb17ff56bbca974cd177ddd57a.jpg) +Figure 7. Toy Examples I: Validation of social interactions. The arrows and circles point to the same predicted trajectory that has been changed significantly due to the manual neighbor. + +to handle social interactions. For example, predictions in Fig. 5 (a2) to (a4) all present avoidance of the group of pedestrians standing still at the roadside. Similarly, avoiding the upcoming biker about to cross the intersection has also become a major concern in (c1) to (c4). These results indicate the effectiveness of the proposed SocialCircle that works with different backbone prediction models. + +Visualized Social Interaction Cases. As shown in Fig. 6, we observe that predictions given by SocialCircle models seem to be more "conservative" with a tendency to avoid others in different social interaction situations, which looks like it is trying to avoid possible collisions or too-close social distances. For example, predictions in (a2) display heavier avoidance of the man coming from + +![](images/89bb77240c0e739235fa0afcf49e13f458a77dc3b57f7fe9fb65f5e7e80be088.jpg) + +![](images/2b7af5d8ce56d2caab12558d66738281cbb478bd3549d62f856843c10f99ae78.jpg) + +![](images/93918e0f1d11ebd88d06f48d3b81ef622e80071e2908611ec1735849fafa4b50.jpg) + +![](images/09500c2fa22959f45961508ee665748cf28765c922baf4f3d000dc780ebca4f1.jpg) + +![](images/ba9259e853e15c8918a2488651a8e27fd4ac1556edb3cb5e66707711fdef6714.jpg) + +![](images/76ac48b64f3746d03946f198bcb5d5d82fe55bf796e8e2510735b34d5ab9f750.jpg) + +![](images/769eee2155ba861a3f3ef0f21860e3ca25dc50021428178d4bb0e45a437107a1.jpg) + +![](images/d2f2790bbe9d51095f153b5a928a97fab309d3899f2925212275c73db31f444a.jpg) + +![](images/d20f46e36babf408ffeded327f7c4630defbb0354907228451766bdfe309ec2e.jpg) + +![](images/5c613230eaab5bf1e82dba5c82056ed35c439eee88d25a668fefc2ecbdae88cf.jpg) +Figure 8. Toy Examples II: Validation of SocialCircle meta components by manually changing the manual neighbor's velocity (denoted by $v_{m}$ ) and its distance to the target agent ( $d_{m}$ ). + +![](images/a8beab7d13ecbeed4c1c52e616d6a5a8b81d14a7886efd83ef8e5e427deb0c11.jpg) + +![](images/417e52aba0625f6dd870609b3ae5881569cf155b9d6ccc81d123df3f74e49ed2.jpg) + +![](images/0c66fca0e651e413a27a4027348e93d0c097619d517ebd121de431c75806ebd3.jpg) + +![](images/282275fc74b3c3889dc8d0d6738a36afb8318f59e7bc66b1697b493044c4f225.jpg) + +![](images/72082df32dd56dd0440bddf5b19c2b9371faeca2e2b34d0b4761c8304d00cf05.jpg) + +![](images/fa5ea9f1dba9b78fe3b3ec3c76eee5530ee58798f9574cbf3d3f4193aa5b42cf.jpg) +Figure 9. Visualized attention scores of each SocialCircle partition in the colored-ring form on several ETH-UCY prediction scenes. Partitions with higher attention scores (redder and wider) contribute more to the final predicted trajectories. + +![](images/5a22efc03eed3b2d96861310ab32c517c9e074b3a6a1e591a1b878615bec3257.jpg) + +![](images/c2afcd876b8e9b86f4f4e66d19963eba2afb2bcb2ebee8b78f73ef41d17b0157.jpg) + +![](images/f896882706d091209e36fefa427c926f8d0e6975e8011cdbd62d35f403993c8a.jpg) + +the car side than in (b2). Similarly, the potential collision between the moving biker and the focused walking pedestrian has been caught in (c3), thus representing a prediction shift (comparing the blue prediction in (c3) and the red one in (d3)). In addition, two pedestrians walk towards right together in cases (a4) and (b4). Unlike case (b4), SocialCircle model forecasts that the target agent may not crossover the other two's potential trajectories, like it "thought" that the agent would rather keep its relative position in the group. + +![](images/828e955a639e09277a29e6bce4edb11d31a1f162542ee464fb3cdc9e4755eef5.jpg) +Figure 10. Toy Examples III: Comparisons of attention scores before and after adding manual neighbors in ETH-UCY scenes. + +Note that social interactions are not only limited to these collision cases. They are common behavior patterns among agents, including scene-specific interactions like the game-related interactions in the NBA dataset. Please see the qualitative analyses of NBA interactions in the Appendix. + +Toy Examples I (Social Interactions). We design a series of toy examples on several real-world prediction scenes from ETH-UCY to verify the capacity of SocialCircle in handling social interactions in Fig. 7. We manually add new "manual neighbors" in different positions (partitions) to test SocialCircle model's response. Each manual neighbor's observed trajectory is simulated by linearly interpolating from the given start and end points. Comparing Fig. 7 (a1) and (b1), several predicted trajectories to the right of the target agent have changed a lot. For example, the red trajectory contracts violently to the other side, which seems quite likely to prevent possible collisions with the manual neighbor that walks towards itself. Similar phenomenons also appear in Fig. 7 (b2), whose blue and green predictions show varying degrees of avoidance tendencies, depending on where they are located. The predicted trajectories colored in blue and cyan in Fig. 7 (a3) also show a tendency to avoid the manual neighbor. These cases illustrate the adaptivity of the SocialCircle in customizing different predictions. We have provided more toy cases in the Appendix. + +Toy Examples II (SocialCircle Meta Components). Fig. 8 further shows the qualitative effect on predicted trajectories caused by the other two SocialCircle factors, velocity and distance. We first focus on the velocity factor validated in (a1) to (a3) or (a4) to (a6). When the manual neighbor has a higher velocity, the predicted trajectories will be affected by it to a greater extent, and vice versa, especially for the pink predictions in (a1) to (a3). Except for the velocity, as the distance $d_{m}$ increases in Fig. 8 (b1) to (b3) or (b4) to (b6), the influence of manual neighbors gradually becomes smaller. In contrast, the predicted trajectory may produce a heavier shift when $d_{m}$ decreases step by step. These "social-like" behaviors brought by different SocialCircle meta components are learned adaptively during + +training. It illustrates SocialCircle's capacity and explainability to represent potential social interaction cases and finally modify predicted trajectories socially. + +Toy Examples III (SocialCircle Partitions). In Fig. 9, we visualize how each SocialCircle partition contributes by squaring-sum the feature $\mathbf{f}_{\mathrm{pad}}^i$ in each partition, which we call the Attention Score. Note that agent $i$ itself will be treated as its self-neighbor located in partition 1 (see Eq. (4)). We can see from these figures that SocialCircle acts far from simply locating all neighbors but tells which partitions should be paid more attention to when forecasting trajectories. In Fig. 9 (a) to (d), partition 1 catches more attention, and others present different trends according to different neighbor distributions. Similar to the phenomenon shown in Fig. 8, neighbors that are closer to the target agent elicit higher levels of attention (like partition 3 against partition 2 in (a)), and neighbors that move faster attract more attention (partition 4 compared to partition 6 in (d)). Unlike these cases, partition 8 owns a higher score than partition 1 in case (e), indicating that the SocialCircle cares more about the neighbor walking along with the target agent rather than the agent itself. It is interesting in case (e) that some partitions have also been assigned scores even though there are no neighbors. + +Furthermore, Fig. 10 shows how the attention scores change after adding manual neighbors. In case (a1), SocialCircle focuses more on partition 4. However, the scores have changed significantly in case (a2) due to the manual neighbor located between partitions 1 and 8, and partition 4 has been less focused. Cases (b1) and (b2) also show the similar trends. All these qualitative results illustrate SocialCircle's ability to describe different interactions and the effectiveness of partitioned modeling social interactions. + +Limitations. SocialCircle does not contain the directions where neighbor agents came from. It also does not directly consider the interactions among neighbor agents and how they affect the target agent, i.e., the high-order interactions. We will further study it in our subsequent works. + +# 5. Conclusion + +This work focuses on the modeling of social interactions when forecasting pedestrian trajectories. Like marine animals localizing and communicating with others through echolocation, we bring a simple priori rule to construct the angle-based social interaction representation SocialCircle, which aims to learn how three meta components modify agent trajectories. Experiments on multiple datasets show its competitiveness, and additional toy experiments also prove its effectiveness in handling social interactions. + +Acknowledgement This project is supported by National Natural Science Foundation of China (62172177), and National Key R&D Program of China (2022YFC3301000). + +# References + +[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. Social lstm: Human trajectory prediction in crowded spaces. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 961–971, 2016. 1, 2, 4 +[2] Javad Amirian, Jean-Bernard Hayet, and Julien Pettré. Social ways: Learning multi-modal distributions of pedestrian trajectories with gans. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition Workshops, pages 0–0, 2019. 1 +[3] Catarina Barata, Jacinto C. Nascimento, João M. Lemos, and Jorge S. Marques. Sparse motion fields for trajectory prediction. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 9813-9823, 2021. 5 +[49] Jiangbei Yue, Dinesh Manocha, and He Wang. Human trajectory prediction via neural social physics. In European Conference on Computer Vision, pages 376-394. Springer, 2022. 1, 2, 5 +[50] Francesco Zanlungo, Tetsushi Ikeda, and Takayuki Kanda. Social force model with explicit collision prediction. *Europhysics Letters*, 93(6):68005, 2011. 2 +[51] Pu Zhang, Jianru Xue, Pengfei Zhang, Nanning Zheng, and Wanli Ouyang. Social-aware pedestrian trajectory prediction via states refinement LSTM. 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The diversity and uncertainty in socially interactive behaviors among a rich variety of agents make this task more challenging than other deterministic computer vision tasks. Researchers have made a lot of efforts to quantify the effects of these interactions on future trajectories through different mathematical models and network structures, but this problem has not been well solved. Inspired by marine animals that localize the positions of their companions underwater through echoes, we build a new angle-based trainable social interaction representation, named SocialCircle, for continuously reflecting the context of social interactions at different angular orientations relative to the target agent. We validate the effect of the proposed SocialCircle by training it along with several newly released trajectory prediction models, and experiments show that the SocialCircle not only quantitatively improves the prediction performance, but also qualitatively helps better simulate social interactions when forecasting pedestrian trajectories in a way that is consistent with human intuitions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 557, + 128, + 569 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 557, + 128, + 569 + ], + "spans": [ + { + "bbox": [ + 47, + 557, + 128, + 569 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "type": "text", + "content": "Analyzing, understanding, and forecasting behaviors of intelligent agents have been significantly required by more and more intelligent systems and applications. Due to the ease of access and analysis of trajectories, analyzing agents' behaviors through trajectories has also become a common approach. Trajectory prediction aims at forecasting agents' all possible future trajectories during a specific period by taking into account the positions of all agents that appeared" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 244, + 547, + 452 + ], + "blocks": [ + { + "bbox": [ + 307, + 244, + 547, + 452 + ], + "lines": [ + { + "bbox": [ + 307, + 244, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 307, + 244, + 547, + 452 + ], + "type": "image", + "image_path": "c6beb97077a89a46efaea5614ddbca34abe4bd5aa90bb192f44460692fdcde1c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 459, + 547, + 548 + ], + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 548 + ], + "type": "text", + "content": "Figure 1. Motivation Illustration. Analogous to marine animals like dolphins and whales localizing other companions underwater through echolocation, we analyze agents' reactions to the potential socially interactive behaviors by assuming (1) they first Scan their interaction environment by sending signals from all angles, (2) then all neighbors feedback their Reflection signals to tell their directions, and (3) finally the target agent could make interactive decisions by the received echoes at different angular orientations." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 569, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 605 + ], + "type": "text", + "content": "in the scene [1]. It also considers the potential interactive behaviors [2, 8, 12, 33, 46] as well as the scene constraints [3, 5, 17, 25, 27, 30, 41, 47] when making predictions." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 546, + 714 + ], + "type": "text", + "content": "The social interaction [1, 28] (also known as the agent-to-agent interaction) considered in trajectory prediction takes into account not only all kinds of interactive behaviors among different agents but how they affect their trajectories. Current social-interaction-modeling methods in the trajectory prediction task can be classified roughly into Model-based and Model-free two classes[49]. Model-based methods may take some particular \"rules\" [49] as the primary foundation for the prediction. For example, the Social-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 712 + ], + "type": "text", + "content": "* equal contribution. Codes are available at https://github.com/cocoon2wong/SocialCircle." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19005" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 251 + ], + "type": "text", + "content": "Force-based methods [9, 28] model and simulate agents' behaviors mainly according to the rules in Newtonian mechanics. Some other methods like [3, 42, 49] also turn trajectory prediction into an optimization problem by introducing their different mathematical models. However, designing a generalized \"rule\" that fits most socially interactive cases is often difficult, making them challenging to apply to complex scenes. On the contrary, model-free methods are mostly driven by data, and few manual interventions are considered. For example, graph-based methods [4, 14, 36] may build a series of spatial or temporal graph structures, thus learning to simulate agents' social interactions. Most model-free methods could fully utilize the ability of neural networks to fit data, but they may heavily rely on different network structures and pose limited explainability." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 254, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 289, + 350 + ], + "type": "text", + "content": "\"Rules\" and \"data\" play essential roles but put different limitations on these methods accordingly. A natural thought is to add several \"lite-rules\" to data-driven backbones to provide limited constraints as guidance to improve either the data-fit process or the explainability. In short, we want to constrain the learning process with relatively weak rules for social interactions rather than solid mathematical rules, thus benefiting from both rules and data-fit capabilities." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 289, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 289, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 289, + 568 + ], + "type": "text", + "content": "Analyzing agents' interactive behaviors through bionics and psychology is a natural choice. Animals would not analyze others' behaviors by solving complex equations but with relatively simple judgment rules when planning trajectories. Some researchers in the social psychology area also point out that each agent in a complex multiagent system tends to behave and interact with each other according to simple rules rather than extensive computations, which inspired a series of agent-based simulation models that have been widely applied in economics and political science [35]. It is fascinating that some marine animals can locate others in the deep sea through echolocation rather than visual factors due to the weak light. They may firstly scan the environment by sending some unique signals (like ultrasounds) at different angles, which could be reflected in contact with others and produce echoes. Then, they gather echoes from different directions, thus locating, interacting, or communicating with others, and finally modifying their behaviors." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": "As shown in Fig. 1, the echolocation is similar to how agents interact with others. Only a few \"rules\" are established, like the time from they send to receive the echo and the direction where it comes. This way, we bring a simple priori to model social behaviors that interactions are considered to be angle-based. In detail, all interactive behaviors are considered in a special angle space where the angle " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": " (which direction the echo comes from) plays as the independent variable. We assume that most social interactions can be \"inferred\" by several simple components corresponding to each angle " + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 570, + 289, + 715 + ], + "type": "text", + "content": ", like the velocity of each participant (in which way the participant's position changes during two" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "echolocations) and the distance between each participant and the target agent (how long the echo arrives since scanning). Thus, we can obtain an angle-based vector function " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathbf{f}(\\theta)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "(0\\leq \\theta < 2\\pi)" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " to represent the current socially interactive context when forecasting trajectories. We call that angle-based social interaction representation SocialCircle." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 144, + 546, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 275 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 275 + ], + "type": "text", + "content": "SocialCircle can be classified as Model-based, but it is also inspired by model-free methods to fit data with relatively weak rules, i.e., simple components at different angles. Then, the observed trajectory and the angle-based SocialCircle will be analyzed together in a data-driven way, as they could be both treated as sequences, to catch the temporal-attentive portions in trajectories and the angle-attentive portions in the current interactive context simultaneously, thus establishing connections among these weak rules and agents' real-world socially interactive behaviors as well as the forecasted trajectories." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 275, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 275, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 275, + 547, + 361 + ], + "type": "text", + "content": "In summary, we contribute (1) The angle-based Social-Circle representation for pedestrian trajectory prediction to model social interactive behaviors; (2) The serialized modeling strategy that treats and encodes the spatial social interactions in the temporal sequences' way along with trajectories; (3) Experiments on multiple backbone prediction models show quantitative and qualitative superiority." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 390, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 486 + ], + "type": "text", + "content": "Model-based Social Interaction Methods. Model-based methods aim to use mathematical rules as the foundation to forecast trajectories. The classic Social Force Model [9] is proposed to model human dynamics with Newtonian mechanics. Pellegrini et al. [28] introduce Social Force factors to model social behaviors in the multi-agent tracking task. More Social-Force-based methods like [19, 24, 50] are also proposed to model crowds' interactions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 487, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 605 + ], + "type": "text", + "content": "Other mathematical tools and models are also used to simulate socially interactive behaviors when forecasting trajectories. Xie et al. [42] propose the \"Dark Matter\" model to simulate and forecast social behaviors with fields and agent-based Lagrangian Mechanics. Xia et al. [41] propose a social transfer function to model human socially interactive behaviors via a uniform way across multiple prediction scenes. Yue et al. [49] propose a neural differential equation model, in which the explicit physics model serves as a strong inductive bias in modeling pedestrian behaviors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 606, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 606, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 606, + 545, + 677 + ], + "type": "text", + "content": "However, these methods are often difficult to cover all possible socially interactive cases. Even though some methods like [41, 49] draw on the advantages of data-driven approaches to make some key parameters trainable, they may still be limited by the complex mathematical rules and equations in complex prediction scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Model-free Social Interaction Methods. Model-free methods simulate interactive behaviors mostly through a data-driven form. Alahi et al. [1] propose the Social-" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19006" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 215 + ], + "type": "text", + "content": "Pooling method to connect nearby sequences to share hidden states with each other, thus simulating the information-sharing process. Variations of social pooling methods like [8, 30] are proposed to pool features by considering different scales or locations simultaneously. Grid-based methods like [11] have been proposed to explore additional simple rules to enhance the capacity of pooling methods. With the quick development of graph neural networks, graph structures have been widely used to model social interactions. Graph Attention Networks (GATs) [18, 26], Graph Convolutional Networks [6, 32, 36] are employed to simulate interactions as the edges between different nodes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 287, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 287 + ], + "type": "text", + "content": "Most model-free methods prefer to focus more on the structure through which to fit the data so that the predicted trajectory could reflect the effects of social interactive cues. In this process, few direct mathematical rules are constraints, making them more dependent on different network structures and high-quality data." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 287, + 287, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 287, + 371 + ], + "type": "text", + "content": "The proposed SocialCircle tries to address these problems by introducing \"lite-rules\" to these trainable backbones, thus taking advantage of the data-driven approach combined with the explainability of the model-based approach to model interactive behaviors. It also avoids designing complex mathematical models or solving complex equations during the interaction modeling." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 381, + 102, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 102, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 102, + 393 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": "Formulations. This work only concerns trajectories of 2D coordinates " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = (x,y)^{\\top}" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": ". Denote the historical trajectory of agent (pedestrian) " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": " during " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "t_h" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": " observation steps as " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^i = (\\mathbf{p}_1^i,\\dots,\\mathbf{p}_{t_h}^i)^\\top" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": ", trajectory prediction focused in this paper aims at forecasting one or more possible future trajectories " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Y}}^i = (\\hat{\\mathbf{p}}_{t_h + 1}^i,\\dots,\\hat{\\mathbf{p}}_{t_h + t_f}^i)^\\top" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": " through its observed " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^i" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": " and all its' neighbors' trajectories " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^{/i} = \\{\\mathbf{X}^j |1\\leq j\\leq N_a,j\\neq i\\}" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": " along with the scene image " + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{t_h}" + }, + { + "bbox": [ + 46, + 402, + 287, + 510 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": "Angle-based SocialCircle Representation. In this paper, all social-interaction-related operations are described and implemented in an \"angle\" space, where the angle " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": " is the independent variable that describes the location of interactive behaviors. We first define the angle " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\theta^i (j)\\in [0,2\\pi)" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": " to represent the relative position of a neighbor agent " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": " to the target agent " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": ". It is computed as the \"direction\" of the vector that begins from agent " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": " and ends at agent " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": " at the current observation step " + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "inline_equation", + "content": "(t = t_h)" + }, + { + "bbox": [ + 46, + 510, + 287, + 617 + ], + "type": "text", + "content": ". Formally," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 625, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 625, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 625, + 287, + 645 + ], + "type": "interline_equation", + "content": "\\theta^ {i} (j) = \\operatorname {a t a n 2} \\left(\\mathbf {p} _ {t _ {h}} ^ {j} - \\mathbf {p} _ {t _ {h}} ^ {i}\\right). \\tag {1}", + "image_path": "7e7fba6f8be8a321717ce333f3d4d5cbe1ff2d6aaf50731692a11d2016793975.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": "Here, atan2 is the \"quadrant-sensitive\" arctan function that computes angle of the input " + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = (x,y)^{\\top}" + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": " from 0 to " + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "2\\pi" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Agent " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "'s SocialCircle representation (short for SocialCircle) can be treated as a head-to-tail cyclic vector function " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^i (\\theta)" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\theta \\in [0,2\\pi)" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": ". To make the computation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "easier, the angle variables will be discretized into " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " \"partitions\". This way, agent " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " 's SocialCircle can be denoted as" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 347, + 105, + 545, + 121 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 105, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 347, + 105, + 545, + 121 + ], + "type": "interline_equation", + "content": "\\mathbf {f} ^ {i} = \\left(\\mathbf {f} ^ {i} \\left(\\theta_ {1}\\right), \\mathbf {f} ^ {i} \\left(\\theta_ {2}\\right), \\dots , \\mathbf {f} ^ {i} \\left(\\theta_ {N _ {\\theta}}\\right)\\right) ^ {\\top}. \\tag {2}", + "image_path": "2f8c6edd116d903c0ebe46c0704c688ba6794b82cd5e843b8ffad769f18ab675.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "spans": [ + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "inline_equation", + "content": "0 = \\theta_0 < \\theta_1 < \\ldots < \\theta_{N_\\theta} = 2\\pi" + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "content": ". As shown in Fig. 2, each " + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^i(\\theta_n) \\in \\mathbb{R}^{d_{\\mathrm{sc}}}" + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "inline_equation", + "content": "n = 1, 2, \\ldots, N_\\theta" + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "content": ") is used to represent the overall interactive effort in the " + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "content": "th partition caused by all participants from the set " + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "inline_equation", + "content": "\\mathbf{N}^i(\\theta_n)" + }, + { + "bbox": [ + 305, + 125, + 545, + 174 + ], + "type": "text", + "content": ", which satisfies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 352, + 180, + 545, + 194 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 180, + 545, + 194 + ], + "spans": [ + { + "bbox": [ + 352, + 180, + 545, + 194 + ], + "type": "interline_equation", + "content": "\\theta_ {n - 1} \\leq \\theta^ {i} (j) < \\theta_ {n}, \\forall j \\in \\mathbf {N} ^ {i} (\\theta_ {n}). \\tag {3}", + "image_path": "8fc8be9fe26a70abc18001890180a2cad4bc19a0a650eb85e35940e690655a19.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "text", + "content": "We treat agent " + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "text", + "content": " as its self-neighbor in the 1st partition. Denote the number of agents in " + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\mathbf{N}^i (\\theta_n)" + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "inline_equation", + "content": "\\left|\\mathbf{N}^i (\\theta_n)\\right|" + }, + { + "bbox": [ + 305, + 201, + 545, + 226 + ], + "type": "text", + "content": ", we have" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 354, + 242, + 545, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 242, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 354, + 242, + 545, + 266 + ], + "type": "interline_equation", + "content": "i \\in \\mathbf {N} ^ {i} \\left(\\theta_ {1}\\right), \\quad \\sum_ {n} \\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right| = N _ {a}. \\tag {4}", + "image_path": "992e9878a3f283949b8c72df9d89626686dcada4f07d740aea897fc7b4af01f0.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 274, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 274, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 274, + 545, + 297 + ], + "type": "text", + "content": "SocialCircle Meta Components. Each SocialCircle partition is computed via three meta components:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 334, + 304, + 545, + 322 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 304, + 545, + 322 + ], + "spans": [ + { + "bbox": [ + 334, + 304, + 545, + 322 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\mathrm {m e t a}} ^ {i} \\left(\\theta_ {n}\\right) = \\left(\\mathbf {f} _ {\\mathrm {v e l}} ^ {i} \\left(\\theta_ {n}\\right), \\mathbf {f} _ {\\mathrm {d i s}} ^ {i} \\left(\\theta_ {n}\\right), \\mathbf {f} _ {\\mathrm {d i r}} ^ {i} \\left(\\theta_ {n}\\right)\\right) ^ {\\top}. \\tag {5}", + "image_path": "15539eee825efcdbfed972ca632e3072f9ee1944b2626b13d65b24b1fb24bedf.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 327, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 545, + 388 + ], + "type": "text", + "content": "(a) Velocity " + }, + { + "bbox": [ + 305, + 327, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{vel}}^i" + }, + { + "bbox": [ + 305, + 327, + 545, + 388 + ], + "type": "text", + "content": ". Agents with higher velocities may pose potentially more significant dangers to others around them. SocialCircle takes the \"average velocity\" (the movement length during the observation period) of all neighbors in one partition to simulate this interactive factor. Formally," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 333, + 395, + 545, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 395, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 333, + 395, + 545, + 425 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\mathrm {v e l}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\left\\| \\mathbf {p} _ {t _ {h}} ^ {j} - \\mathbf {p} _ {1} ^ {j} \\right\\| _ {2}, \\tag {6}", + "image_path": "a8bff8a10de3e47d3922cfefdc932f436f95eec8d3e7bca0077cfe38f938eda6.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "type": "text", + "content": "(b) Distance " + }, + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{dis}}^i" + }, + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "type": "text", + "content": ". Agents present different interaction preferences as the distance to the interaction participant changes. SocialCircle takes the average Euclidean distance (at " + }, + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "type": "inline_equation", + "content": "t = t_h" + }, + { + "bbox": [ + 305, + 432, + 545, + 493 + ], + "type": "text", + "content": " moment) between the target agent and all its neighbors in one partition to model this factor. Formally," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 332, + 499, + 545, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 499, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 332, + 499, + 545, + 529 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\mathrm {d i s}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\left\\| \\mathbf {p} _ {t _ {h}} ^ {i} - \\mathbf {p} _ {t _ {h}} ^ {j} \\right\\| _ {2}. \\tag {7}", + "image_path": "dd17034ae221ca5f9779c96df91a280ce59e26415e81313312d2ddf8695f87c0.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "type": "text", + "content": "(c) Direction " + }, + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{dir}}^i" + }, + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "type": "text", + "content": ". Partitioning the continuous " + }, + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\theta \\in [0,2\\pi)" + }, + { + "bbox": [ + 305, + 537, + 545, + 597 + ], + "type": "text", + "content": " may cause the loss of angle details. We use the average angles of all neighbors in one partition relative to the target agent as a compensation factor. It also acts as a positional coding term to distinguish different partitions. Formally," + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 350, + 604, + 545, + 635 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 604, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 350, + 604, + 545, + 635 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\operatorname {d i r}} ^ {i} \\left(\\theta_ {n}\\right) = \\frac {1}{\\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right|} \\sum_ {j \\in \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right)} \\theta^ {i} (j). \\tag {8}", + "image_path": "6e285e34089b9dc67ecf1ba617d1d88ef4f8b343642a9ae31cb01dbcdf2ea7be.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 641, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 641, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 641, + 545, + 677 + ], + "type": "text", + "content": "Serialized Modeling of Social Interaction. SocialCircle partitions " + }, + { + "bbox": [ + 305, + 641, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{f}^i (\\theta_n)\\}_{n}" + }, + { + "bbox": [ + 305, + 641, + 545, + 677 + ], + "type": "text", + "content": " are obtained by concatenating and embedding all meta components. Formally," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 317, + 684, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 684, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 317, + 684, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\mathbf {f} ^ {i} \\left(\\theta_ {n}\\right) = \\left\\{ \\begin{array}{l l} g _ {\\text {e m b e d}} \\left(\\mathbf {0}\\right), & \\left| \\mathbf {N} ^ {i} \\left(\\theta_ {n}\\right) \\right| = 0; \\\\ g _ {\\text {e m b e d}} \\left(\\mathbf {f} _ {\\text {m e t a}} ^ {i} \\left(\\theta_ {n}\\right)\\right), & \\text {O t h e r w i s e .} \\end{array} \\right. \\tag {9}", + "image_path": "d632f3f0b48fd89f369e0ffb64e408a1bc317f39c06e5a42c29ae6e8a572f0d1.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19007" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 68, + 547, + 159 + ], + "blocks": [ + { + "bbox": [ + 48, + 68, + 547, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 68, + 547, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 68, + 547, + 159 + ], + "type": "image", + "image_path": "e229276ad6a18b090cce57c5975f3692e6bfb83ce244c851445f633f82b99974.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 168, + 546, + 204 + ], + "lines": [ + { + "bbox": [ + 46, + 168, + 546, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 546, + 204 + ], + "type": "text", + "content": "Figure 2. Computation pipeline of the proposed SocialCircle. Each agent's SocialCircle is different to others'. For a target agent, it first computes three meta components: velocity, distance, and direction. Then, these meta components will be averaged within each angle-based SocialCircle partition, and finally embedded into the set of high-dimensional head-to-tail cyclic representation " + }, + { + "bbox": [ + 46, + 168, + 546, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^i (\\theta_n)" + }, + { + "bbox": [ + 46, + 168, + 546, + 204 + ], + "type": "inline_equation", + "content": "(1\\leq n\\leq N_{\\theta})" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 220, + 286, + 312 + ], + "blocks": [ + { + "bbox": [ + 48, + 220, + 286, + 312 + ], + "lines": [ + { + "bbox": [ + 48, + 220, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 48, + 220, + 286, + 312 + ], + "type": "image", + "image_path": "f90323f00a8dc4765d892224703772dc8ee133f43bcdf165685239475b31b3ca.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 320, + 288, + 366 + ], + "lines": [ + { + "bbox": [ + 46, + 320, + 288, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 288, + 366 + ], + "type": "text", + "content": "Figure 3. The serialized modeling of social interactions. SocialCircle is treated as a \"virtual\" temporal sequence that shares the same sequence shape as the embedded trajectory by adding zero paddings, so they could be fused to forecast trajectories together." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{embed}}" + }, + { + "bbox": [ + 46, + 384, + 287, + 419 + ], + "type": "text", + "content": " is the embedding function that contains 2 fully connected layers with 64 output units. ReLU activation is used in the first layer while tanh is used in the second layer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": "SocialCircle represents the Spatial interactive context at the current step " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "(t = t_h)" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": " through a serialized form. A natural thought is to handle this sequence " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^i\\in \\mathbb{R}^{N_\\theta \\times d_{\\mathrm{sc}}}" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": " along with the observed trajectory " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^i\\in \\mathbb{R}^{t_h\\times 2}" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": " to learn the attentive portions inner these sequences simultaneously. In detail, we treat the spatial SocialCircle " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^i" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": " as a Virtual Temporal Sequence that shares the same sequence length as the trajectory " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^i" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": " or its representations. As shown in Fig. 3, " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{f}^i" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": " will be padded at first (we set " + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "inline_equation", + "content": "N_{\\theta}\\leq t_h" + }, + { + "bbox": [ + 46, + 420, + 287, + 529 + ], + "type": "text", + "content": "). Formally," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 533, + 287, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 533, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 59, + 533, + 287, + 574 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\text {p a d}} ^ {i} = \\left(\\underbrace {\\mathbf {f} ^ {i} \\left(\\theta_ {1}\\right) , \\dots , \\mathbf {f} ^ {i} \\left(\\theta_ {N _ {\\theta}}\\right)} _ {N _ {\\theta}}, \\underbrace {\\mathbf {0} , \\dots , \\mathbf {0}} _ {t _ {h} - N _ {\\theta}}\\right) ^ {\\top} \\in \\mathbb {R} ^ {t _ {h} \\times d _ {\\mathrm {s c}}}. \\tag {10}", + "image_path": "80b705acb378995c6b4e74618d455cf092d8eb351ffc5623d94a8e127e3978df.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": "In most previous works [1, 8], agent- " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": "'s observed trajectory " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^i" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": " will be first embedded into the high-dimensional " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{traj}}^i \\in \\mathbb{R}^{t_h \\times d}" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": " by some embedding layer " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{embed}}" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{traj}}^i = f_{\\mathrm{embed}}(\\mathbf{X}^i)" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": ". Denote the computation of one trajectory prediction model (we call the backbone prediction model) as " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "B_{\\mathrm{pred}}" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": ", future trajectories " + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{Y}}^i" + }, + { + "bbox": [ + 46, + 575, + 287, + 650 + ], + "type": "text", + "content": " are usually predicted by" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 96, + 655, + 287, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 655, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 96, + 655, + 287, + 671 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {Y}} ^ {i} = B _ {\\text {p r e d}} \\left(\\mathbf {f} _ {\\text {t r a j}} ^ {i}, \\mathbf {f} _ {\\text {s o c i a l}} ^ {i}, \\mathbf {f} _ {\\text {o t h e r s}} ^ {i}\\right), \\tag {11}", + "image_path": "e7904613fec7fc950638257be108c4d6909161d9333d1e35bde7ca9eca339323.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{social}}^i" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " denotes the original social representations in the backbone prediction model, and " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{others}}^i" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": " denotes other required features (like visual features from scene image " + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{I}_{t_h}" + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "text", + "content": "SocialCircle Models (the SocialCircle-lized backbone prediction models) take the fused vector " + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{fuse}}^i" + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "text", + "content": " containing both trajectory information and interactive context to instead the single " + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{traj}}^i" + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "text", + "content": " to learn the temporal-attentive portions in the observed trajectories and the angle-attentive portions in the SocialCircle simultaneously. The " + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{fuse}}^i" + }, + { + "bbox": [ + 305, + 223, + 545, + 297 + ], + "type": "text", + "content": " is fused by" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 311, + 304, + 545, + 319 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 304, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 311, + 304, + 545, + 319 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {\\text {f u s e}} ^ {i} = \\tanh \\left(\\mathbf {W} _ {\\text {f u s e}} \\operatorname {C o n c a t} \\left(\\mathbf {f} _ {\\text {t r a j}} ^ {i}, \\mathbf {f} _ {\\text {p a d}} ^ {i}\\right) + \\mathbf {b} _ {\\text {f u s e}}\\right). \\tag {12}", + "image_path": "d00b410f35eefa64a3d896a01b2292eac65a7ea9147b4787c0358a94205cb8d1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{\\mathrm{fuse}}" + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{b}_{\\mathrm{fuse}}" + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "text", + "content": " are the trainable weights and bias. Meanwhile, the original " + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{social}}^i" + }, + { + "bbox": [ + 305, + 327, + 545, + 363 + ], + "type": "text", + "content": " will be removed. The trajectory prediction pipeline of SocialCircle models has become" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 373, + 545, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 373, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 365, + 373, + 545, + 388 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {Y}} _ {\\mathrm {S C}} ^ {i} = B _ {\\text {p r e d}} \\left(\\mathbf {f} _ {\\text {f u s e}} ^ {i}, \\mathbf {f} _ {\\text {o t h e r s}} ^ {i}\\right). \\tag {13}", + "image_path": "4a2aba63e8f731fab5d60b5b3d0438ca44e1ea1b05e1f65dc377b2f3d3b0149b.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "content": "Training. SocialCircle does not introduce additional new loss functions. We take Transformer[37], MSN[40], " + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\mathrm{V}^2" + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "content": "-Net[38], E-" + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "inline_equation", + "content": "\\mathrm{V}^2" + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "content": "-Net[39] as backbone trajectory prediction models to validate SocialCircle's performance in our experiments. These models will be trained with original loss functions and settings reported in their papers." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 475, + 387, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 387, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 387, + 488 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": "Datasets. (a) ETH[28]-UCY[13] contains several videos captured in pedestrian walking scenes. We use the leave-one-out strategy [1] to train with " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\{t_h = 8, t_f = 12\\}" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " and sample interval " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "\\Delta t = 0.4s" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": ". (b) Stanford Drone Dataset [29] (SDD) has 60 drone videos. Different categories of agents are annotated in pixels. Following [15], we split " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " videos to train, " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " to validate, and " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " to test under " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "(t_h, t_f, \\Delta t) = (8, 12, 0.4)" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": ". (c) NBA SportVU [16] (NBA) includes trajectories captured by the SportVU tracking system in NBA games. Following [43, 44], we set " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "(t_h, t_f, \\Delta t) = (5, 10, 0.4)" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": ", and sample 50K trajectories, including " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "65\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " to train, " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " to test, and " + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 494, + 545, + 638 + ], + "type": "text", + "content": " to validate." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "content": "Metrics. We measure prediction accuracy with the best Average/Final Displacement Error over 20 generated trajectories (i.e., " + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\min\\mathrm{ADE}_{20}/\\min\\mathrm{FDE}_{20}" + }, + { + "bbox": [ + 304, + 638, + 545, + 686 + ], + "type": "text", + "content": " [1, 8], short for ADE/FDE). See their detailed definitions in the Appendix." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "1Ethics Note: Datasets used in this work are publicly available and do not contain any sensitive personally identifiable information." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19008" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 541, + 222 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 541, + 222 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 541, + 222 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 541, + 222 + ], + "type": "table", + "html": "
Models (ETH-UCY)ethhotelunivzara1zara2ETH-UCYModels (SDD)SDD
SHENet[25] (2022)0.41/0.610.13/0.200.25/0.430.21/0.320.15/0.260.23/0.36FlowChain[20] (2023)9.93/17.17
MID[7] (2022)0.39/0.660.13/0.220.22/0.450.17/0.300.13/0.270.21/0.38SHENet[25] (2022)9.01/13.24
EqMotion[45] (2023)0.40/0.610.12/0.180.23/0.430.18/0.320.13/0.230.21/0.35IMP[34] (2023)8.98/15.54
MSN[40] (2023)0.27/0.410.11/0.170.28/0.480.22/0.360.18/0.290.21/0.34LED[23] (2023)8.48/11.36
LED[23] (2023)0.39/0.580.11/0.170.26/0.430.18/0.260.13/0.220.21/0.33MID[7] (2022)7.91/14.50
Trajectory++[31] (2020)0.43/0.860.12/0.190.22/0.430.17/0.320.12/0.250.20/0.39Y-net[22] (2021)7.85/11.85
Agentformer[48] (2021)0.26/0.390.11/0.140.26/0.460.15/0.230.14/0.230.18/0.29MSN[40] (2023)7.69/12.16
V2-Net[38] (2022)0.23/0.370.10/0.160.21/0.350.19/0.300.14/0.240.18/0.28V2-Net[38] (2022)7.12/11.39
Y-net[22] (2021)0.28/0.330.10/0.140.24/0.410.17/0.270.13/0.220.18/0.27E-V2-Net[39] (2023)6.57/10.49
E-V2-Net[39] (2023)0.25/0.380.11/0.160.20/0.340.19/0.300.13/0.240.17/0.28NSP-SFM[49] (2022)6.52/10.61
MSN-SC (Ours)0.27/0.390.13/0.180.22/0.450.18/0.340.15/0.270.19/0.33MSN-SC (Ours)7.49/12.12
V2-Net-SC (Ours)0.25/0.370.12/0.150.21/0.350.17/0.290.13/0.220.17/0.27V2-Net-SC (Ours)6.71/10.66
E-V2-Net-SC (Ours)0.25/0.380.12/0.140.20/0.340.18/0.290.13/0.220.17/0.27E-V2-Net-SC (Ours)6.54/10.36
", + "image_path": "0f6bee9d9ad5d86d5f526245dd7868a894406d6e394bb2c1ce130d084ac58828.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 54, + 270, + 282, + 384 + ], + "blocks": [ + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "type": "text", + "content": "Table 1. Comparisons on ETH-UCY (left) and SDD (right) under best-of-20 and with " + }, + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "type": "inline_equation", + "content": "t_h = 8" + }, + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "type": "text", + "content": " frames' (3.2s) observations to predict future " + }, + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "type": "inline_equation", + "content": "t_f = 12" + }, + { + "bbox": [ + 46, + 229, + 546, + 253 + ], + "type": "text", + "content": " frames' (4.8s) trajectories. Metrics are reported as \"ADE/FDE\". Lower ADE and FDE indicate better prediction performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 270, + 282, + 384 + ], + "lines": [ + { + "bbox": [ + 54, + 270, + 282, + 384 + ], + "spans": [ + { + "bbox": [ + 54, + 270, + 282, + 384 + ], + "type": "table", + "html": "
Models (NBA)Metrics@2.0sMetrics@4.0s
PECNet[21] (2020)0.96/1.691.83/ 3.41
NMMP[10] (2020)0.70/1.111.33/ 2.05
V2-Net[38] (2022)0.69/0.961.28/ 1.68
E-V2-Net[39] (2023)0.68/ 0.931.26/ 1.64
MemoNet[44] (2022)0.71/1.141.25/ 1.47
GroupNet+NMMP[43] (2022)0.69/1.081.25/ 1.80
GroupNet+CVAE[43] (2022)0.62/0.951.13/1.69
V2-Net-SC (Ours)0.67/0.921.22/1.51
E-V2-Net-SC (Ours)0.67/0.901.18/1.46
", + "image_path": "bcfcae2dc8e63bb1c819bec33502626efb17c5249212f9cd022d79a0e8fa2551.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 392, + 288, + 426 + ], + "lines": [ + { + "bbox": [ + 46, + 392, + 288, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 288, + 426 + ], + "type": "text", + "content": "Table 2. Comparisons on NBA under best-of-20 in meters (" + }, + { + "bbox": [ + 46, + 392, + 288, + 426 + ], + "type": "inline_equation", + "content": "t_h = 5, t_f = 10" + }, + { + "bbox": [ + 46, + 392, + 288, + 426 + ], + "type": "text", + "content": "). Metrics are reported as \"ADE/FDE\" at different prediction lengths, including 2.0s (5 frames) and 4.0s (10 frames)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": "Implementation details. Models are trained on one NVIDIA Tesla T4 GPU. SocialCircle is computed on each agent's 50 nearest neighbors to save the computation resource. For SocialCircle models, we set " + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "inline_equation", + "content": "N_{\\theta} = t_h^2" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": ", and set " + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\theta_n = 2n\\pi / N_{\\theta}" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "inline_equation", + "content": "n = 1, 2, \\dots, N_{\\theta}" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": "). Feature dimensions " + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "inline_equation", + "content": "d_{\\mathrm{sc}}" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": " are set to 64. Following [51], trajectories are preprocessed by moving to " + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "inline_equation", + "content": "(0, 0)" + }, + { + "bbox": [ + 46, + 448, + 287, + 544 + ], + "type": "text", + "content": ". We set the learning rate to 1e-4, epochs to 600, and batch size to 1500." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 553, + 265, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 553, + 265, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 553, + 265, + 566 + ], + "type": "text", + "content": "4.1. Comparisons to State-of-the-Art Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "text", + "content": "ETH-UCY. Tab. 1 illustrates that SocialCircle models are competitive. In detail, the E-V²-Net-SC has achieved a noteworthy prediction performance with " + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "inline_equation", + "content": "5.6\\%" + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "text", + "content": " better ADE and " + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "inline_equation", + "content": "6.9\\%" + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "text", + "content": " better FDE compared with Agentformer. Moreover, MSN-SC performs better than EqMotion with the improvement of " + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "inline_equation", + "content": "9.5\\%" + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "text", + "content": " ADE and " + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 46, + 571, + 287, + 656 + ], + "type": "text", + "content": " FDE, even though MSN performs not as well as other new approaches." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "content": "SDD. In Tab. 1, " + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "inline_equation", + "content": "\\mathrm{V}^2" + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "content": "-Net-SC outperforms Y-net by " + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "inline_equation", + "content": "14.52\\%" + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "content": " ADE and " + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "inline_equation", + "content": "10.04\\%" + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "content": " FDE. It has also obtained " + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "inline_equation", + "content": "20.87\\%" + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "content": " ADE and " + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "inline_equation", + "content": "6.16\\%" + }, + { + "bbox": [ + 47, + 657, + 288, + 693 + ], + "type": "text", + "content": " FDE improvements compared to the newly" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 270, + 425, + 345 + ], + "blocks": [ + { + "bbox": [ + 307, + 270, + 425, + 345 + ], + "lines": [ + { + "bbox": [ + 307, + 270, + 425, + 345 + ], + "spans": [ + { + "bbox": [ + 307, + 270, + 425, + 345 + ], + "type": "image", + "image_path": "78a5727e38901797e82d0ad553a665ca6ff1c22e3dd71c4d7543a75cd080ab2b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 354, + 547, + 421 + ], + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 421 + ], + "type": "text", + "content": "Figure 4. Loss curves (loss values after different training epochs) of the simple Transformer (left) and the corresponding Transformer-SC variation (right) during the training process on SDD with 600 epochs in total. Loss values are normalized, and each figure includes six training runs (\"nan\" loss values are not displayed). Curves are smoothed with the decay factor " + }, + { + "bbox": [ + 304, + 354, + 547, + 421 + ], + "type": "inline_equation", + "content": "= 0.8" + }, + { + "bbox": [ + 304, + 354, + 547, + 421 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 427, + 270, + 545, + 346 + ], + "blocks": [ + { + "bbox": [ + 427, + 270, + 545, + 346 + ], + "lines": [ + { + "bbox": [ + 427, + 270, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 427, + 270, + 545, + 346 + ], + "type": "image", + "image_path": "2972c88ad57377e5ba5b64f00152fa10f83af3960694be49fa1a6f6e7cfa50cb.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "content": "published LED. In addition, " + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\mathrm{E - V^2}" + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "content": " -Net-SC outperforms the state-of-the-art NSP-SFM by as much as " + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "inline_equation", + "content": "2.36\\%" + }, + { + "bbox": [ + 304, + 443, + 545, + 467 + ], + "type": "text", + "content": " FDE." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "text", + "content": "NBA. In Tab. 2, compared with GroupNet+CVAE, E-V²-Net-SC's ADE is not as well as that model (about " + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "inline_equation", + "content": "4.42\\%" + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "text", + "content": " worse), but its FDEs (both at 2.0s and 4.0s) are better than those for about " + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "inline_equation", + "content": "5.26\\%" + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "inline_equation", + "content": "13.60\\%" + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "text", + "content": ". In addition, even though the FDE (4.0s) of MemoNet and E-V²-Net-SC are at the same level, E-V²-Net-SC outperforms the other for about " + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "inline_equation", + "content": "5.60\\%" + }, + { + "bbox": [ + 304, + 468, + 546, + 576 + ], + "type": "text", + "content": " ADE (4.0s). Although E-V²-Net performs not as well as these newly published methods, the proposed SocialCircle makes it available to achieve competitive results." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 586, + 533, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 533, + 600 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 533, + 600 + ], + "type": "text", + "content": "4.2. Ablation Studies and Quantitative Analyses" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Overall Validation of SocialCircle. As shown in Tab. 3, SocialCircle could help even the simplest Transformer [37] (which considers nothing about agents' multimodality and interactions) improve " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "5.89\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " ADE and " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "4.00\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " FDE. SocialCircle also facilitates MSN, " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{V}^2" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "-Net, and " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{E - V^2}" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "-Net with up to " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "4.92\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " ADE gains and " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "8.00\\%" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " FDE gains compared to their original models. In addition, we also plot loss curves " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "(\\ell_2" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": " loss) of 6 training runs of the simplest Transformer and the Transformer-SC in Fig. 4. It shows that SocialCir" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "type": "text", + "content": "See detailed analyses about " + }, + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 58, + 702, + 220, + 714 + ], + "type": "text", + "content": " in the Appendix." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19009" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + 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Moreover, 5 out of 6 Transformer runs' loss values fall into \"nan\" due to the inappropriate gradients before 450 training epochs. As for Transformer-SC, only two runs are terminated, demonstrating that SocialCircle may also somehow act as a normalization factor, thus improving the training stability." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": "Validation of SocialCircle Meta Components. As shown in Tab. 3, both " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{V}^2" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": "-Net and " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{E - V}^2" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": "-Net benefit further from the velocity and distance factors, each of which could provide at least " + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "inline_equation", + "content": "1.50\\%" + }, + { + "bbox": [ + 46, + 653, + 288, + 713 + ], + "type": "text", + "content": " ADE and FDE gains (SC-a1 and SC-a2 variations). However, MSN-SC variations are" + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "type": "text", + "content": "not so sensitive to these two factors (less than " + }, + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "type": "inline_equation", + "content": "1.07\\%" + }, + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "type": "text", + "content": " ADE differences among MSN-SC, MSN-SC-a1, and MSN-SC-a2) but rely more on the direction factor (up to " + }, + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "type": "inline_equation", + "content": "3.30\\%" + }, + { + "bbox": [ + 304, + 547, + 545, + 632 + ], + "type": "text", + "content": " FDE gain has been brought by this factor). Although these factors contribute differently to different backbone models, the combination of all these factors promotes the most, for removing each one could lead to a serious performance drop." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 317, + 633, + 545, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 633, + 545, + 644 + ], + "spans": [ + { + "bbox": [ + 317, + 633, + 545, + 644 + ], + "type": "text", + "content": "Parameters & Efficiency. Please refer to the Appendix." + } + ] + } + ], + "index": 46 + }, + { + "bbox": [ + 306, + 657, + 425, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 657, + 425, + 670 + ], + "spans": [ + { + "bbox": [ + 306, + 657, + 425, + 670 + ], + "type": "text", + "content": "4.3. Qualitative Analyses" + } + ] + } + ], + "index": 47 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Visualized Predictions. Fig. 5 visualizes trajectories predicted by several SocialCircle models. 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VariationsVDRADE/FDEADE/FDE Gain (%)
Transformer*×××17.44/33.36-5.89%/-4.00%
Transformer-SC✓✓✓16.47/32.08(base)
MSN*×××7.79/13.09-4.01%/-8.00%
MSN-SC-a1×✓✓7.53/12.30-0.53%/-1.49%
MSN-SC-a2✓×✓7.57/12.40-1.07%/-2.31%
MSN-SC-a3✓✓×7.60/12.52-1.47%/-3.30%
MSN-SC✓✓✓7.49/12.12(base)
V2-Net*×××7.04/10.94-4.92%/-2.63%
V2-Net-SC-a1×✓✓6.86/10.82-2.24%/-1.50%
V2-Net-SC-a2✓×✓6.87/10.87-2.38%/-1.97%
V2-Net-SC-a3✓✓×6.78/10.71-1.04%/-0.47%
V2-Net-SC✓✓✓6.71/10.66(base)
E-V2-Net*×××6.73/10.75-2.91%/-3.76%
E-V2-Net-SC-a1×✓✓6.67/10.73-1.99%/-3.57%
E-V2-Net-SC-a2✓×✓6.64/10.55-1.53%/-1.83%
E-V2-Net-SC-a3✓✓×6.59/10.48-0.76%/-1.16%
E-V2-Net-SC✓✓✓6.54/10.36(base)
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Ablation studies on validating SocialCircle meta components on SDD. \"V\", \"D\", and \"R\" indicate whether " + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{vel}}^i" + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{dis}}^i" + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "text", + "content": ", or " + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{dir}}^i" + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "text", + "content": " are included in the meta vector " + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{meta}}^i" + }, + { + "bbox": [ + 47, + 277, + 287, + 321 + ], + "type": "text", + "content": ". Models with “*” are reproduced under the same condition." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 336, + 287, + 476 + ], + "blocks": [ + { + "bbox": [ + 48, + 336, + 287, + 476 + ], + "lines": [ + { + "bbox": [ + 48, + 336, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 48, + 336, + 287, + 476 + ], + "type": "image", + "image_path": "f7559a10ca0ab057fe4174765206b171819ef3cb17ff56bbca974cd177ddd57a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 485, + 287, + 519 + ], + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 519 + ], + "type": "text", + "content": "Figure 7. Toy Examples I: Validation of social interactions. The arrows and circles point to the same predicted trajectory that has been changed significantly due to the manual neighbor." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 628 + ], + "type": "text", + "content": "to handle social interactions. For example, predictions in Fig. 5 (a2) to (a4) all present avoidance of the group of pedestrians standing still at the roadside. Similarly, avoiding the upcoming biker about to cross the intersection has also become a major concern in (c1) to (c4). These results indicate the effectiveness of the proposed SocialCircle that works with different backbone prediction models." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Visualized Social Interaction Cases. As shown in Fig. 6, we observe that predictions given by SocialCircle models seem to be more \"conservative\" with a tendency to avoid others in different social interaction situations, which looks like it is trying to avoid possible collisions or too-close social distances. For example, predictions in (a2) display heavier avoidance of the man coming from" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 70, + 390, + 129 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 390, + 129 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 390, + 129 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 390, + 129 + ], + "type": "image", + "image_path": "89bb77240c0e739235fa0afcf49e13f458a77dc3b57f7fe9fb65f5e7e80be088.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 390, + 71, + 468, + 129 + ], + "blocks": [ + { + "bbox": [ + 390, + 71, + 468, + 129 + ], + "lines": [ + { + "bbox": [ + 390, + 71, + 468, + 129 + ], + "spans": [ + { + "bbox": [ + 390, + 71, + 468, + 129 + ], + "type": "image", + "image_path": "2b7af5d8ce56d2caab12558d66738281cbb478bd3549d62f856843c10f99ae78.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 468, + 71, + 545, + 129 + ], + "blocks": [ + { + "bbox": [ + 468, + 71, + 545, + 129 + ], + "lines": [ + { + "bbox": [ + 468, + 71, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 468, + 71, + 545, + 129 + ], + "type": "image", + "image_path": "93918e0f1d11ebd88d06f48d3b81ef622e80071e2908611ec1735849fafa4b50.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 133, + 390, + 191 + ], + "blocks": [ + { + "bbox": [ + 310, + 133, + 390, + 191 + ], + "lines": [ + { + "bbox": [ + 310, + 133, + 390, + 191 + ], + "spans": [ + { + "bbox": [ + 310, + 133, + 390, + 191 + ], + "type": "image", + "image_path": "09500c2fa22959f45961508ee665748cf28765c922baf4f3d000dc780ebca4f1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 390, + 133, + 468, + 191 + ], + "blocks": [ + { + "bbox": [ + 390, + 133, + 468, + 191 + ], + "lines": [ + { + "bbox": [ + 390, + 133, + 468, + 191 + ], + "spans": [ + { + "bbox": [ + 390, + 133, + 468, + 191 + ], + "type": "image", + "image_path": "ba9259e853e15c8918a2488651a8e27fd4ac1556edb3cb5e66707711fdef6714.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 468, + 133, + 545, + 191 + ], + "blocks": [ + { + "bbox": [ + 468, + 133, + 545, + 191 + ], + "lines": [ + { + "bbox": [ + 468, + 133, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 468, + 133, + 545, + 191 + ], + "type": "image", + "image_path": "76ac48b64f3746d03946f198bcb5d5d82fe55bf796e8e2510735b34d5ab9f750.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 194, + 390, + 255 + ], + "blocks": [ + { + "bbox": [ + 310, + 194, + 390, + 255 + ], + "lines": [ + { + "bbox": [ + 310, + 194, + 390, + 255 + ], + "spans": [ + { + "bbox": [ + 310, + 194, + 390, + 255 + ], + "type": "image", + "image_path": "769eee2155ba861a3f3ef0f21860e3ca25dc50021428178d4bb0e45a437107a1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 390, + 194, + 468, + 255 + ], + "blocks": [ + { + "bbox": [ + 390, + 194, + 468, + 255 + ], + "lines": [ + { + "bbox": [ + 390, + 194, + 468, + 255 + ], + "spans": [ + { + "bbox": [ + 390, + 194, + 468, + 255 + ], + "type": "image", + "image_path": "d2f2790bbe9d51095f153b5a928a97fab309d3899f2925212275c73db31f444a.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 468, + 194, + 545, + 255 + ], + "blocks": [ + { + "bbox": [ + 468, + 194, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 468, + 194, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 468, + 194, + 545, + 255 + ], + "type": "image", + "image_path": "d20f46e36babf408ffeded327f7c4630defbb0354907228451766bdfe309ec2e.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 310, + 257, + 390, + 316 + ], + "blocks": [ + { + "bbox": [ + 310, + 257, + 390, + 316 + ], + "lines": [ + { + "bbox": [ + 310, + 257, + 390, + 316 + ], + "spans": [ + { + "bbox": [ + 310, + 257, + 390, + 316 + ], + "type": "image", + "image_path": "5c613230eaab5bf1e82dba5c82056ed35c439eee88d25a668fefc2ecbdae88cf.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "lines": [ + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "spans": [ + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "type": "text", + "content": "Figure 8. Toy Examples II: Validation of SocialCircle meta components by manually changing the manual neighbor's velocity (denoted by " + }, + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "type": "inline_equation", + "content": "v_{m}" + }, + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "type": "text", + "content": ") and its distance to the target agent (" + }, + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "type": "inline_equation", + "content": "d_{m}" + }, + { + "bbox": [ + 306, + 328, + 545, + 362 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 390, + 257, + 468, + 316 + ], + "blocks": [ + { + "bbox": [ + 390, + 257, + 468, + 316 + ], + "lines": [ + { + "bbox": [ + 390, + 257, + 468, + 316 + ], + "spans": [ + { + "bbox": [ + 390, + 257, + 468, + 316 + ], + "type": "image", + "image_path": "a8beab7d13ecbeed4c1c52e616d6a5a8b81d14a7886efd83ef8e5e427deb0c11.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 468, + 257, + 545, + 316 + ], + "blocks": [ + { + "bbox": [ + 468, + 257, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 468, + 257, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 468, + 257, + 545, + 316 + ], + "type": "image", + "image_path": "417e52aba0625f6dd870609b3ae5881569cf155b9d6ccc81d123df3f74e49ed2.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 308, + 376, + 378, + 453 + ], + "blocks": [ + { + "bbox": [ + 308, + 376, + 378, + 453 + ], + "lines": [ + { + "bbox": [ + 308, + 376, + 378, + 453 + ], + "spans": [ + { + "bbox": [ + 308, + 376, + 378, + 453 + ], + "type": "image", + "image_path": "0c66fca0e651e413a27a4027348e93d0c097619d517ebd121de431c75806ebd3.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 380, + 377, + 449, + 452 + ], + "blocks": [ + { + "bbox": [ + 380, + 377, + 449, + 452 + ], + "lines": [ + { + "bbox": [ + 380, + 377, + 449, + 452 + ], + "spans": [ + { + "bbox": [ + 380, + 377, + 449, + 452 + ], + "type": "image", + "image_path": "282275fc74b3c3889dc8d0d6738a36afb8318f59e7bc66b1697b493044c4f225.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 450, + 376, + 521, + 452 + ], + "blocks": [ + { + "bbox": [ + 450, + 376, + 521, + 452 + ], + "lines": [ + { + "bbox": [ + 450, + 376, + 521, + 452 + ], + "spans": [ + { + "bbox": [ + 450, + 376, + 521, + 452 + ], + "type": "image", + "image_path": "72082df32dd56dd0440bddf5b19c2b9371faeca2e2b34d0b4761c8304d00cf05.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 308, + 453, + 378, + 529 + ], + "blocks": [ + { + "bbox": [ + 308, + 453, + 378, + 529 + ], + "lines": [ + { + "bbox": [ + 308, + 453, + 378, + 529 + ], + "spans": [ + { + "bbox": [ + 308, + 453, + 378, + 529 + ], + "type": "image", + "image_path": "fa5ea9f1dba9b78fe3b3ec3c76eee5530ee58798f9574cbf3d3f4193aa5b42cf.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 538, + 545, + 583 + ], + "lines": [ + { + "bbox": [ + 306, + 538, + 545, + 583 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 545, + 583 + ], + "type": "text", + "content": "Figure 9. Visualized attention scores of each SocialCircle partition in the colored-ring form on several ETH-UCY prediction scenes. Partitions with higher attention scores (redder and wider) contribute more to the final predicted trajectories." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 379, + 453, + 449, + 529 + ], + "blocks": [ + { + "bbox": [ + 379, + 453, + 449, + 529 + ], + "lines": [ + { + "bbox": [ + 379, + 453, + 449, + 529 + ], + "spans": [ + { + "bbox": [ + 379, + 453, + 449, + 529 + ], + "type": "image", + "image_path": "5a22efc03eed3b2d96861310ab32c517c9e074b3a6a1e591a1b878615bec3257.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 450, + 453, + 520, + 529 + ], + "blocks": [ + { + "bbox": [ + 450, + 453, + 520, + 529 + ], + "lines": [ + { + "bbox": [ + 450, + 453, + 520, + 529 + ], + "spans": [ + { + "bbox": [ + 450, + 453, + 520, + 529 + ], + "type": "image", + "image_path": "c2afcd876b8e9b86f4f4e66d19963eba2afb2bcb2ebee8b78f73ef41d17b0157.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 522, + 408, + 542, + 498 + ], + "blocks": [ + { + "bbox": [ + 522, + 408, + 542, + 498 + ], + "lines": [ + { + "bbox": [ + 522, + 408, + 542, + 498 + ], + "spans": [ + { + "bbox": [ + 522, + 408, + 542, + 498 + ], + "type": "image", + "image_path": "f896882706d091209e36fefa427c926f8d0e6975e8011cdbd62d35f403993c8a.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "the car side than in (b2). Similarly, the potential collision between the moving biker and the focused walking pedestrian has been caught in (c3), thus representing a prediction shift (comparing the blue prediction in (c3) and the red one in (d3)). In addition, two pedestrians walk towards right together in cases (a4) and (b4). Unlike case (b4), SocialCircle model forecasts that the target agent may not crossover the other two's potential trajectories, like it \"thought\" that the agent would rather keep its relative position in the group." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19011" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 288, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 288, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 288, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 288, + 190 + ], + "type": "image", + "image_path": "828e955a639e09277a29e6bce4edb11d31a1f162542ee464fb3cdc9e4755eef5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 198, + 287, + 221 + ], + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 221 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 221 + ], + "type": "text", + "content": "Figure 10. Toy Examples III: Comparisons of attention scores before and after adding manual neighbors in ETH-UCY scenes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 244, + 287, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 287, + 304 + ], + "type": "text", + "content": "Note that social interactions are not only limited to these collision cases. They are common behavior patterns among agents, including scene-specific interactions like the game-related interactions in the NBA dataset. Please see the qualitative analyses of NBA interactions in the Appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 305, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 305, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 305, + 287, + 544 + ], + "type": "text", + "content": "Toy Examples I (Social Interactions). We design a series of toy examples on several real-world prediction scenes from ETH-UCY to verify the capacity of SocialCircle in handling social interactions in Fig. 7. We manually add new \"manual neighbors\" in different positions (partitions) to test SocialCircle model's response. Each manual neighbor's observed trajectory is simulated by linearly interpolating from the given start and end points. Comparing Fig. 7 (a1) and (b1), several predicted trajectories to the right of the target agent have changed a lot. For example, the red trajectory contracts violently to the other side, which seems quite likely to prevent possible collisions with the manual neighbor that walks towards itself. Similar phenomenons also appear in Fig. 7 (b2), whose blue and green predictions show varying degrees of avoidance tendencies, depending on where they are located. The predicted trajectories colored in blue and cyan in Fig. 7 (a3) also show a tendency to avoid the manual neighbor. These cases illustrate the adaptivity of the SocialCircle in customizing different predictions. We have provided more toy cases in the Appendix." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "type": "text", + "content": "Toy Examples II (SocialCircle Meta Components). Fig. 8 further shows the qualitative effect on predicted trajectories caused by the other two SocialCircle factors, velocity and distance. We first focus on the velocity factor validated in (a1) to (a3) or (a4) to (a6). When the manual neighbor has a higher velocity, the predicted trajectories will be affected by it to a greater extent, and vice versa, especially for the pink predictions in (a1) to (a3). Except for the velocity, as the distance " + }, + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "type": "inline_equation", + "content": "d_{m}" + }, + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "type": "text", + "content": " increases in Fig. 8 (b1) to (b3) or (b4) to (b6), the influence of manual neighbors gradually becomes smaller. In contrast, the predicted trajectory may produce a heavier shift when " + }, + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "type": "inline_equation", + "content": "d_{m}" + }, + { + "bbox": [ + 46, + 545, + 287, + 714 + ], + "type": "text", + "content": " decreases step by step. These \"social-like\" behaviors brought by different SocialCircle meta components are learned adaptively during" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "training. It illustrates SocialCircle's capacity and explainability to represent potential social interaction cases and finally modify predicted trajectories socially." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "type": "text", + "content": "Toy Examples III (SocialCircle Partitions). In Fig. 9, we visualize how each SocialCircle partition contributes by squaring-sum the feature " + }, + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathrm{pad}}^i" + }, + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "type": "text", + "content": " in each partition, which we call the Attention Score. Note that agent " + }, + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 108, + 546, + 359 + ], + "type": "text", + "content": " itself will be treated as its self-neighbor located in partition 1 (see Eq. (4)). We can see from these figures that SocialCircle acts far from simply locating all neighbors but tells which partitions should be paid more attention to when forecasting trajectories. In Fig. 9 (a) to (d), partition 1 catches more attention, and others present different trends according to different neighbor distributions. Similar to the phenomenon shown in Fig. 8, neighbors that are closer to the target agent elicit higher levels of attention (like partition 3 against partition 2 in (a)), and neighbors that move faster attract more attention (partition 4 compared to partition 6 in (d)). Unlike these cases, partition 8 owns a higher score than partition 1 in case (e), indicating that the SocialCircle cares more about the neighbor walking along with the target agent rather than the agent itself. It is interesting in case (e) that some partitions have also been assigned scores even though there are no neighbors." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 360, + 546, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 546, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 546, + 467 + ], + "type": "text", + "content": "Furthermore, Fig. 10 shows how the attention scores change after adding manual neighbors. In case (a1), SocialCircle focuses more on partition 4. However, the scores have changed significantly in case (a2) due to the manual neighbor located between partitions 1 and 8, and partition 4 has been less focused. Cases (b1) and (b2) also show the similar trends. All these qualitative results illustrate SocialCircle's ability to describe different interactions and the effectiveness of partitioned modeling social interactions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 467, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 545, + 528 + ], + "type": "text", + "content": "Limitations. SocialCircle does not contain the directions where neighbor agents came from. It also does not directly consider the interactions among neighbor agents and how they affect the target agent, i.e., the high-order interactions. We will further study it in our subsequent works." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 378, + 550 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 665 + ], + "type": "text", + "content": "This work focuses on the modeling of social interactions when forecasting pedestrian trajectories. Like marine animals localizing and communicating with others through echolocation, we bring a simple priori rule to construct the angle-based social interaction representation SocialCircle, which aims to learn how three meta components modify agent trajectories. Experiments on multiple datasets show its competitiveness, and additional toy experiments also prove its effectiveness in handling social interactions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgement This project is supported by National Natural Science Foundation of China (62172177), and National Key R&D Program of China (2022YFC3301000)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19012" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Alexandre Alahi, Kratarth Goel, Vignesh Ramanathan, Alexandre Robicquet, Li Fei-Fei, and Silvio Savarese. 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Prior studies have primarily focused on probing such bias attributes individually while ignoring biases associated with intersections between social attributes. This could be due to the difficulty of collecting an exhaustive set of image-text pairs for various combinations of social attributes. To address this challenge, we employ text-to-image diffusion models to produce counterfactual examples for probing intersectional social biases at scale. Our approach utilizes Stable Diffusion with cross attention control to produce sets of counterfactual image-text pairs that are highly similar in their depiction of a subject (e.g., a given occupation) while differing only in their depiction of intersectional social attributes (e.g., race & gender). Through our over-generate-then-filter methodology, we produce SocialCounterfactuals, a high-quality dataset containing 171k image-text pairs for probing intersectional biases related to gender, race, and physical characteristics. We conduct extensive experiments to demonstrate the usefulness of our generated dataset for probing and mitigating intersectional social biases in state-of-the-art VLMs.", + "bbox": [ + 76, + 376, + 473, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 768, + 209, + 784 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Counterfactual examples, which study the impact on a response variable following a change to a causal feature, have proven valuable in natural language processing (NLP) for probing model biases and improving robustness to spurious correlation [16, 18, 26, 30, 54, 57, 60]. While counterfactual examples for VLMs have been relatively unexplored, recent work [33] has shown that text-to-image diffusion models", + "bbox": [ + 75, + 794, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "with cross attention control can effectively produce multimodal counterfactual examples for VLM training, data augmentation and evaluation. This suggests that synthetic counterfactual examples generated by diffusion models could be an effective tool for probing and mitigating biases in VLMs.", + "bbox": [ + 496, + 345, + 895, + 421 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Bias in pre-trained models can be viewed as spurious correlations, which are often attributed to the co-occurrence of non-causal (i.e., spurious) features with labels in datasets. During pre-training, models learn to exploit such correlations as shortcuts to achieving high in-domain performance on the training dataset [19]. Consequently, models which learn to rely on spurious correlations are more brittle and have worse out-of-domain (OOD) generalization [47, 58].", + "bbox": [ + 496, + 424, + 895, + 546 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Social biases are a particularly concerning type of spurious correlation learned by VLMs. Due to a lack of proportional representation for people of various races, genders, and other social attributes in image-text datasets [5, 17, 63], VLMs learn biased associations between these attributes and various subjects (e.g., occupations). For example, given a gender- and race-neutral query such as \"A photo of an attorney\", a VLM may retrieve a disproportionate number of images of one particular race due to learned spurious correlations between this specific occupation and race.", + "bbox": [ + 496, + 549, + 895, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior studies on probing social biases in VLMs [22-24, 28, 65] have primarily utilized real image-text pairs collected from existing datasets by identifying the cooccurrence of certain attributes with a target subject. However, this approach is limited by the availability of existing image-text pairs for various combinations of social attributes and subject types. Consequently, these prior studies have focused exclusively on investigating biases associated with a single social attribute at a time while ignoring the potential role of intersectional bias (e.g., particular race-gender combinations) [40], which could be attributed to the difficulty of collecting an exhaustive set of image-text examples for various combinations of social attributes. Additionally, the", + "bbox": [ + 496, + 704, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11975", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d5fe8c34870311a0384fc93ef571a69e032398b0f4e9b41ec6ff2b17ca9ec9ee.jpg", + "image_caption": [ + "A White male construction worker", + "Figure 1. Examples of our counterfactual image-text pairs for probing intersectional race-gender bias in VLMs for the \"construction worker\" occupation. See Section 7.1 in Supplementary Material for additional examples." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 212, + 191 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/dbabbdf873fa541ac1ef193142983c4bcc91842a12f6bd5bc17d0a507312068f.jpg", + "image_caption": [ + "An Asian female construction worker" + ], + "image_footnote": [], + "bbox": [ + 217, + 90, + 349, + 191 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a38481ec7c8ae4590b1013ea25c086e075b1d49b28d6bd59fdcd7b5f2518903f.jpg", + "image_caption": [ + "A Middle Eastern male construction worker" + ], + "image_footnote": [], + "bbox": [ + 352, + 90, + 482, + 191 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2f77f37b979cfe5d5c667e507badfee064a5f7f868fae21453b513ebbee7bd46.jpg", + "image_caption": [ + "A Latino female construction worker" + ], + "image_footnote": [], + "bbox": [ + 486, + 90, + 617, + 191 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/06ff31107c1c89b45f05acef60004dcedaffddd892d63e659506f87e35352467.jpg", + "image_caption": [ + "A Black male construction worker" + ], + "image_footnote": [], + "bbox": [ + 622, + 90, + 751, + 191 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f97cdf9e456a859c77c006a9c250cc26a0002d3c6a37bd7c097dfda83fdae41f.jpg", + "image_caption": [ + "An Indian female construction worker" + ], + "image_footnote": [], + "bbox": [ + 754, + 90, + 885, + 191 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "large variability in how subjects can be naturally depicted in real images complicates the task of estimating bias in VLMs because disproportionate retrieval results could be attributed to other differences in images besides the social attribute.", + "bbox": [ + 75, + 281, + 468, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We overcome these limitations by leveraging text-to-image diffusion models to produce counterfactual image-text pairs for probing and mitigating social biases in VLMs (see Figure 1 and Section 7.1 in Supplementary Material for examples). Specifically, our approach utilizes Stable Diffusion [42] with cross-attention control [25] to produce a set of highly similar counterfactual image-text examples which depict a common subject while differing only in intersectoral social attributes. Text-to-image diffusion models are particularly well-suited for this task due to their ability to generate depictions of specific subjects with various combinations of different social attributes, which might be rare or missing from existing image-text datasets. After generating candidate images, we apply three stages of filtering to ensure that only the highest-quality counterfactuals are retained.", + "bbox": [ + 75, + 342, + 468, + 568 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We apply our methodology at scale to produce Social-Counterfactuals, an extensive dataset containing over 171k counterfactual image-text pairs for probing intersectional biases related to race, gender, and physical characteristics. To the best of our knowledge, SocialCounterfactuals is the largest resource released to-date for probing bias in VLMs and the only one which considers intersectional biases. Through extensive evaluation of six VLMs, we demonstrate its usefulness for uncovering intersectional social biases. Additionally, we conduct VLM training experiments using our dataset which demonstrate its ability to reduce skewness in retrieval results for social attributes. We make our dataset1 and code2 publicly available.", + "bbox": [ + 75, + 569, + 470, + 765 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 777, + 218, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Probing bias in pre-trained models", + "text_level": 1, + "bbox": [ + 76, + 803, + 380, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Much of the prior work on probing social bias in pre-trained models has focused exclusively on language models, pro", + "bbox": [ + 75, + 825, + 470, + 857 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ducing multiple datasets for measuring stereotypical bias along different social attributes, categories, demographic axes and stigmatized groups [35, 37, 39, 49]. Gender biases associated with pronoun and coreferences have also been extensively studied [8, 43, 56, 64]. Some prior work has addressed topics related to intersectionality in bias evaluations [31, 50, 51]. Additionally, various approaches for bias detection and mitigation for vision-only models have been proposed [1, 6, 13, 27, 55].", + "bbox": [ + 500, + 281, + 892, + 417 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Approaches to generate synthetic datasets with fairness have been explored [2, 4, 15, 34, 44]. For probing biases in VLMs, VLStereoSet [65] extends the StereoSet dataset to the vision domain by sourcing images from Google search and using crowdsourced workers for annotation, resulting in a total of 1028 images. VisoGender [23] consists of 690 manually-annotated images for benchmarking occupation-related gender bias in VLMs. The MultiModal Bias dataset [28] evaluates bias in VLMs across 14 population subgroups and contains a total of 3800 human-annotated images obtained from Flickr. These datasets differ from ours primarily in their much smaller scale, their reliance on collection of data from existing sources & human annotation, and their focus on investigating only a single attribute at a time (as opposed to our investigation of intersectional biases). Bias in VLMs used for text-to-image generation have also been investigated [10, 38, 53], but such studies differ from our focus on bias in image-text retrieval settings.", + "bbox": [ + 496, + 420, + 893, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Mitigating bias in pre-trained VLMs", + "text_level": 1, + "bbox": [ + 500, + 709, + 816, + 724 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A variety of methods have been proposed for mitigating the biases observed in pre-trained VLMs. These include adversarial approaches for prompt learning [3], fair sampling methods for reducing bias learned during training [52], contrastive learning techniques for improving group robustness [62], learning additive residuals to offset image representations [45], and eliminating biased directions in the text embedding space through projection matrices [11]. Smith et al. [48] introduced an approach for debiasing VLMs using synthetically-constructed contrast sets, which they use to produce 7946 image-text pairs for gender bias. However, all", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "$^{1}$ Our dataset is available at https://huggingface.co/datasets/Intel/SocialCounterfactuals \n $^{2}$ Our code is available at our GitHub repository", + "bbox": [ + 76, + 864, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11976", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "of these prior works focus exclusively on debiasing models for a single social attribute at a time (e.g., gender) as opposed to our focus on debiasing for intersectional biases.", + "bbox": [ + 75, + 90, + 470, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Generating SocialCounterfactuals", + "text_level": 1, + "bbox": [ + 76, + 150, + 387, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our approach to creating counterfactual image-text examples for intersectional social biases consists of three steps. First, we construct sets of image captions describing a subject with counterfactual changes to intersecting social attributes. We then utilize a text-to-image diffusion model with cross attention control to over-generate sets of images corresponding to the counterfactual captions, where differences among images are isolated to the induced counterfactual change (i.e., the social attributes). Finally, we apply stringent filtering to identify only the highest-quality generations.", + "bbox": [ + 75, + 176, + 472, + 328 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Terminology", + "text_level": 1, + "bbox": [ + 76, + 337, + 210, + 353 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this work, we do not make any claims regarding gender identification or gender assignment, which we acknowledge to be unique to each individual regardless of their appearance or traits. We use perceived gender as an inference made by a human annotator or model. We acknowledge that labels used in this study may differ from an individual's gender identity and could also vary based on different annotators' interpretations. We recognize that gender and gender identity is fluid and misjudgements in a binary paradigm could arise.", + "bbox": [ + 75, + 359, + 468, + 496 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similarly, we acknowledge that the six races we discuss in this paper - White, Black, Indian, Asian, Middle Eastern and Latino, are not representative of all races. We inherit this list of races from prior work [29]. Any inference or reference to race and occupation is considered to be perceived race and perceived occupation (respectively), and does not aim to associate any bias with any groups of individuals.", + "bbox": [ + 75, + 496, + 468, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Constructing captions for probing social biases", + "text_level": 1, + "bbox": [ + 76, + 612, + 468, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider the task of creating a caption $C_{p,a_1,a_2}^s$ beginning with prefix $p$ and describing a subject $s$ which possesses a pair of attributes $a_1$ and $a_2^3$ . Given a set of prefixes $P$ , a set of subjects $S$ , and attribute sets $A_1, A_2, \\ldots, A_k$ , we populate the following template to obtain our captions:", + "bbox": [ + 75, + 635, + 468, + 712 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} C _ {p, a _ {1}, a _ {2}} ^ {s} = < p > < a _ {1} > < a _ {2} > < s > \\\\ \\forall p \\in P, s \\in S, a _ {1} \\in A _ {i}, a _ {2} \\in A _ {j}, (i, j) \\in \\{1, \\dots , k \\mid i \\neq j \\} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 75, + 723, + 472, + 760 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For example, given the prefix $A$ photo of $a$ , the subject doctor, and attribute pair (Asian, Female), we construct the caption $A$ photo of an Asian female doctor. We construct captions in this manner using a set of occupations as our subjects and three sets of attributes for measuring social bias (gender, race, and physical characteristics). Captions are grouped into counterfactual sets, where each set contains all captions", + "bbox": [ + 75, + 771, + 470, + 878 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "corresponding to a given prefix and subject. Using 260 occupations, 4 prefixes, 6 races, and 5 physical characteristics, and 2 gender terms $^{4}$ , we produced a total of 54,080 captions which were grouped into 3,120 counterfactual sets (see Section 8.4 of Supp. Material for additional details and examples). While we categorize these social attributes with the aim of probing biases, we recognize the limitations inherent to this process and acknowledge that attributes such as gender and race are not considered by all individuals to exist as discrete categories (see Section 6 for additional discussion).", + "bbox": [ + 500, + 90, + 893, + 243 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Counterfactual image generation", + "text_level": 1, + "bbox": [ + 500, + 252, + 790, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After generating sets of counterfactual captions, we use text-to-image diffusion models to produce images for each caption. In order to precisely measure the impact of social attribute differences, it is desirable for images within a counterfactual set to only differ in how the social attributes differ across captions. However, this is challenging for diffusion models as even minor changes to a prompt can result in the generation of images with significant differences. For example, changing the attributes Hispanic female to Asian male in the prompt A photo of a Hispanic female doctor may produce other undesired modifications to the image that extend beyond the induced counterfactual change (e.g., changes to the background). This complicates the task of quantifying the impact of model bias attributed to the changed social attributes on retrieval results, as other differences between the generated images could contribute to a VLM's preference for retrieving particular images.", + "bbox": [ + 498, + 275, + 893, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hertz et al. [25] proposed Prompt-to-Prompt to address this issue by injecting cross-attention maps during denoising steps to control attention between certain pixels and tokens, which enables separate generations to maintain many of the same details while isolating differences to how the text prompts differ. However, Brooks et al. [7] noted that some changes require varying the parameter $p$ in Prompt-to-Prompt, which controls the number of denoising steps with shared attention weights. For example, changes that require more substantial structural modifications to the image may necessitate less overall similarity between the resulting images and thus fewer shared attention weights. We therefore adopt their proposed approach of over-generating 100 image pairs with Prompt-to-Prompt by sampling $p \\sim U(0.1, 0.9)$ , which we then subsequently filter to retain only the highest-quality generated candidates (Section 3.4).", + "bbox": [ + 498, + 532, + 893, + 773 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We extend Prompt-to-Prompt for image pairs from Brooks et al. [7] to support batched generation of multiple images with cross attention control. This enables simultaneous generation of entire sets of counterfactual images which differ only according to the social attribute differences across prompts (e.g., Figure 1). In total, we over-generate", + "bbox": [ + 498, + 773, + 893, + 866 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "3See Section 10.2 for discussion of extension to more than two attributes", + "bbox": [ + 94, + 886, + 470, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "4We also explored the generation of other subjects and social attributes with our method. See Section 7.4 of Supplementary Material for details.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11977", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/07779d06a8bb004c9b8cc16c96775f464423fe3cefb2ba2ba3dc76a92ef72c92.jpg", + "image_caption": [ + "Figure 2. Overview of our methodology for generating SocialCounterfactuals." + ], + "image_footnote": [], + "bbox": [ + 84, + 101, + 883, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5,408,000 images for 54,080 captions.", + "bbox": [ + 76, + 313, + 331, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Three-Stage Filtering", + "text_level": 1, + "bbox": [ + 76, + 335, + 279, + 353 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CLIP image-text similarity filtering. After over-generating 100 candidate image sets for each of our templates, we first filter the candidates using CLIP [41] to ensure a minimum cosine similarity of 0.2 between the encoding of each caption and its corresponding generated image. We also apply a similar filtering criteria between pairs of images in each set, requiring the cosine similarity of CLIP image encodings within the set to be greater than 0.2. These filtering criteria help ensure that images accurately depict the subjects described in each caption while also retaining a high-degree of similarity to each other, thereby ensuring that they represent valid counterfactual examples.", + "bbox": [ + 75, + 359, + 473, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "NSFW Filtering with ViT. Manual examination of generated images revealed instances of not-safe-for-work (NSFW) content. We therefore applied a NSFW filter which uses a fine-tuned vision transformer (ViT) for NSFW image classification. This filter removes $0.9 - 2.7\\%$ of generated images (see Table 11 in Supplementary Material for details).", + "bbox": [ + 75, + 559, + 470, + 650 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CLIP Attribute Detectability Filtering. To further ensure data quality, we filter counterfactual sets based on CLIP's ability to discern targeted social attributes in each image using a two-phase approach (see Section 8.3 in Supp. Material for additional details). In the first phase, we randomly sampled 100 counterfactual sets for each pair of attribute types. For each attribute type, we then manually labeled the sampled counterfactual sets according to whether or not they should be filtered out based on a lack of detectability of the targeted attribute. Specifically, we label how many images in a counterfactual set possess their targeted attribute.", + "bbox": [ + 75, + 667, + 468, + 833 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the second phase, we develop a learnable threshold-based heuristics to automatically label whether a counterfactual set should be filtered with respect to an individual", + "bbox": [ + 75, + 834, + 470, + 878 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/fcd4e855ae97ed39596e4e278a27dfe78603e825bb5aed0a902ed21b3fb5dc57.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Attribute PairCounterfactual SetsImages Per SetTotal Images
(Race, Gender)7,9361295,232
(Physical Char., Gender)5,0521050,520
(Physical Char., Race)8363025,080
", + "bbox": [ + 503, + 310, + 888, + 366 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Details of the number of counterfactual sets, images per set, and total images which remain in our dataset after filtering", + "bbox": [ + 498, + 376, + 892, + 405 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "attribute type. These threshold-based heuristics are applied according to how many of a set's constituent images have their respective targeted attributes discernible by CLIP-based image-text similarity scores (rather than by a human annotator). Thresholds were heuristically derived to obtain high correspondence between automatic filtering with CLIP and those filtered by the manual human annotation. This process produces a separate learned threshold for each attribute type and attribute type pair combination. A counterfactual set is filtered out due to a lack of detectability for an attribute type if the number of its constituent images whose corresponding targeted attribute is discernible by CLIP is less than the corresponding learned threshold.", + "bbox": [ + 496, + 445, + 893, + 642 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To estimate the quality of our generated dataset and the impact of filtering, we randomly sampled 100 counterfactual sets depicting Race-Gender intersectional social attributes. Prior to CLIP attribute detectability filtering, we found that $90.8\\%$ of the images accurately depicted their corresponding captions. Applying attribute detectability filtering further increases this figure to $97.5\\%$ , which demonstrates the value of our filtering methodology and the high quality it ensures in our dataset (see Section 7.2 of Supp. Material for details).", + "bbox": [ + 496, + 643, + 893, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1 provides details on the total number of counterfactual sets and images which remain in our dataset after filtering. We group counterfactual sets into three dataset segments based on the pair of attribute types used to construct the captions, which are detailed in each row of Table 1. In total, our dataset consists of 13,824 counterfactual sets with 170,832 image-text pairs, which represents the largest paired image-text dataset for investigating social biases to-date.", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "5https://huggingface.co/Falconsai/nsfw_image_detector", + "bbox": [ + 93, + 886, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11978", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Probing Intersectional Biases", + "text_level": 1, + "bbox": [ + 76, + 89, + 346, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To probe intersectional social biases in VLMs, we calculate MaxSkew over our dataset. We describe this metric in Section 4.1 and detail our evaluation results in Section 4.2.", + "bbox": [ + 75, + 114, + 468, + 160 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 169, + 261, + 184 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $q$ denote a text query and $R_{K}(q)$ denote the set of top- $K$ ranked images retrieved by a VLM for $q$ . For a given attribute pair $(a_{i},a_{j})$ , we denote the desired proportion $d$ of retrieved images with the corresponding attributes as $p_{d(q),(a_i,a_j)}$ and the actual proportion as $p_{R_K(q),(a_i,a_j)}$ . Geyik et al. [20] define Skew@ $K$ for attributes $(a_{i},a_{j})$ in retrieval results $R_{K}(q)$ as:", + "bbox": [ + 75, + 191, + 468, + 299 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S k e w} _ {(a _ {i}, a _ {j})} @ K (R _ {K} (q)) = \\log \\left(\\frac {p _ {R _ {K} (q) , (a _ {i} , a _ {j})}}{p _ {d (q) , (a _ {i} , a _ {j})}}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 309, + 431, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In essence, Skew@K measures the ratio of the proportion of top-K retrieved images having a set of attributes to the desired proportion. To aggregate Skew@K over the various attributes under consideration, Geyik et al. [20] further proposed the following MaxSkew@K metric:", + "bbox": [ + 75, + 349, + 468, + 425 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\operatorname{MaxSkerw} @ K(R_K(q)) = \\max_{(a_i, a_j) \\in A} \\operatorname{Skerw}_{(a_i, a_j)} @ K(R_K(q))$", + "bbox": [ + 76, + 436, + 475, + 462 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $A$ denotes the set of all attribute pairs. We calculate MaxSkew@ $K$ by retrieving images from our counterfactual sets using prompts which are neutral with respect to the investigated attributes. For example, given a prompt constructed from the template \"A construction worker\" (Figure 1), we form its corresponding attribute-neutral prompt \"A construction worker.\"", + "bbox": [ + 75, + 470, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We construct neutral prompts in this manner for each unique combination of prefixes and subjects, averaging their text representations across different prefixes to obtain a single text embedding for each subject. Skew@ $K$ and MaxSkew@ $K$ are then calculated by retrieving the top- $K$ images for the computed text embedding from the set of all images generated for the subject which met our filtering and selection criteria. We set $K = |A_1| \\times |A_2|$ , where $A_1$ and $A_2$ are the investigated attribute sets.", + "bbox": [ + 75, + 577, + 468, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Results", + "text_level": 1, + "bbox": [ + 76, + 720, + 171, + 736 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 3 provides boxplots of the intersectional bias MaxSkew@K distribution for six state-of-the-art VLMs: ALIP [59], CLIP [41], FLAVA [46], LaCLIP [14], OpenCLIP [9], and SLIP [36]. We measure the MaxSkew@K distribution across occupations separately using the three segments of our dataset for Race-Gender (Figure 6a), Physical Characteristics-Gender (Figure 6b), and Physical Characteristics-Race (Figure 6c) intersectional biases.", + "bbox": [ + 75, + 744, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "All six evaluated VLMs exhibit significant skewness in retrieval for attribute-neutral occupation prompts, with CLIP and FLAVA having the lowest overall MaxSkew@K. Among the three segments of our dataset, Physical Characteristics-Gender intersectional biases tend to have lower MaxSkew@K scores while Race-Gender intersectional biases have the greatest amount of skewness.", + "bbox": [ + 504, + 90, + 893, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to illustrating the overall distribution of MaxSkew@K across occupations, the boxplots in Figure 3 also provides the occupation names for minimum values (green circles) and maximum values (red circles). These labels show some commonalities across models, such as FLAVA and LaCLIP both having their greatest Race-Gender MaxSkew@K values for the 'Makeup Artist' profession. We also observe that LaCLIP and OpenCLIP have their greatest skewness in retrieval from the Physical Characteristics-Race segment for the 'Barber' occupation. Notably, both CLIP and FLAVA have multiple occupations with zero skewness across all segments of the dataset, while SLIP has no occupations with zero skewness across the three segments.", + "bbox": [ + 496, + 199, + 893, + 396 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our dataset can also be used to evaluate individual (i.e., marginal) bias for a specific attribute type by filtering on the value of the other attribute depicted in a counterfactual set. MaxSkew@ $K$ can then be calculated as previously described to estimate bias in retrieval results for a single social attribute at a time. To illustrate, we estimated the marginal gender bias across occupations using images specific to each race, which we provide in Figure 4. All VLMs exhibit variation in gender bias across different races, highlighting the importance of measuring bias in the presence of other social attributes. While CLIP has lower overall skewness than other evaluated models, it also has the greatest disparity in MaxSkew@ $K$ across different races; specifically, CLIP exhibits nearly 2x more gender skewness for images depicting Indian subjects than it does for Latinos. Interestingly, both CLIP and FLAVA exhibit the greatest gender bias in retrieving images depicting Indian people, while SLIP and ALIP exhibit the greatest gender bias for Middle Eastern people.", + "bbox": [ + 496, + 398, + 893, + 671 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As a further case study in uncovering intersectional social biases in VLMs, Figure 5 provides a breakdown of the proportion of images retrieved using gender- and race-neutral prompts for the 'Doctor' occupation. The left and center plots of Figure 5 depict the marginal distributions of retrievals for each race and gender (respectively), whereas the right plot provides the distribution of retrieved images for intersectional race-gender attributes. While SLIP, OpenCLIP, LaCLIP, and ALIP exhibit strong bias for retrieving male images, this gender bias occurs along starkly different dimensions with respect to race. OpenCLIP strongly favors retrieving images of Asian male doctors when presented with a neutral text prompt, whereas the other three models prefer to retrieve images of Indian male doctors. This gender bias is inverted for CLIP, which retrieves images of women", + "bbox": [ + 496, + 674, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "6We also provide results for other evaluation metrics in Section 10.1.", + "bbox": [ + 93, + 875, + 452, + 886 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "See Section 10.4 for additional details and probing results", + "bbox": [ + 96, + 887, + 406, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11979", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/e5742b5e59b3852358005e5c64b1c043ff87b9a5910b5921c3873a7d9de96b2a.jpg", + "image_caption": [ + "(a) Race-Gender" + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 349, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/48842e4790a61fe593183fcdfe41690b2e2bfd2f7ab6e4c8820a460d402156ef.jpg", + "image_caption": [ + "(b) Physical Characteristics-Gender" + ], + "image_footnote": [], + "bbox": [ + 351, + 88, + 620, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/94eaa0990547591496ff7b4133955a17ac2a2f226d93a5b8e4b699815b8c1ce7.jpg", + "image_caption": [ + "(c) Physical Characteristics-Race" + ], + "image_footnote": [], + "bbox": [ + 622, + 89, + 890, + 239 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/223d9d682ba4c9ad5de21ef494055bcc0a0af0a835240899f1a245a690c7ca02.jpg", + "image_caption": [ + "Figure 3. Distribution of MaxSkew@ $K$ measured across occupations for (a) Race-Gender, (b) Physical Characteristics-Gender, and (c) Physical Characteristics-Race intersectional biases. Max (min) values are plotted as red (green) circles with corresponding occupation names", + "Figure 4. Mean of (marginal) gender MaxSkew@ $K$ measured across occupations for different races." + ], + "image_footnote": [], + "bbox": [ + 81, + 318, + 467, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "in a slightly higher proportion than men, but still has zero representation of certain groups (e.g., Black females). These results show that seemingly similar biases among pre-trained VLMs for social attributes such as gender can interact very differently with other attributes such as race, which highlights the importance of studying bias in the presence of intersectional social attributes.", + "bbox": [ + 75, + 601, + 468, + 705 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Mitigating Intersectional Biases", + "text_level": 1, + "bbox": [ + 76, + 720, + 366, + 738 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We investigate the suitability of our SocialCounterfactuals dataset for debiasing VLMs through additional training.", + "bbox": [ + 75, + 746, + 467, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Training Experiment Setting", + "text_level": 1, + "bbox": [ + 76, + 786, + 334, + 803 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For each of the three segments of our dataset (see Table 1), we withhold counterfactual sets associated with $20\\%$ of the occupation subjects for testing and use the remainder as a training dataset. We then separately finetune ALIP, CLIP, and FLAVA on each of these three training datasets, which we hereafter refer to as the 'debiased' variants of these mod-", + "bbox": [ + 75, + 809, + 470, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "els. To estimate the magnitude of debiasing, we evaluate each model's MaxSkew@K for intersectional bias using the withheld testing dataset containing $20\\%$ of the occupations.", + "bbox": [ + 496, + 321, + 892, + 368 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results for Intersectional Social Biases", + "text_level": 1, + "bbox": [ + 498, + 378, + 831, + 393 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2 provides the mean MaxSkew@ $K$ calculated over our withheld test sets for pre-trained and debiased variants of CLIP, ALIP, and FLAVA. Training on our dataset has the greatest overall debiasing effect on ALIP, producing up to a 0.426 absolute reduction in MaxSkew@ $K$ . Among the three segments of our dataset used for debiasing, MaxSkew@ $K$ for (Physical Char., Race) intersectional bias has the greatest amount of skewness in pre-trained models. However, training on our dataset also produces the greatest absolute reduction in skewness for this type of intersectional bias, with CLIP having an absolute reduction in MaxSkew@ $K$ of 0.327 for (Physical Char., Race) intersectional biases.", + "bbox": [ + 496, + 402, + 893, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These results show that training VLMs with our dataset produces significant debiasing effects across all three types of intersectional biases. Furthermore, the strongest intersectional biases observed in pre-trained VLMs benefit the most from debiasing. Remarkably, these debiasing effects are observed despite there being no overlap between the occupations used for training and testing, which demonstrates that the debiasing effects generalize to new subjects not seen during training. This suggests that the ability of our dataset to mitigate intersectional bias in VLMs is not limited to only the occupation subjects that we investigated.", + "bbox": [ + 496, + 585, + 893, + 751 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.3. Analysis of Race-Gender Debiased CLIP Model", + "text_level": 1, + "bbox": [ + 498, + 762, + 890, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To further understand the impact of training VLMs using our synthetic counterfactuals, we conduct analyses of CLIP after debiasing for Race-Gender intersectional bias. For simplicity, we hereafter refer to this model as Debiased CLIP.", + "bbox": [ + 496, + 787, + 893, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Skewness evaluation using other datasets with real image-text pairs. Since our dataset was synthetically generated,", + "bbox": [ + 498, + 869, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11980", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/eb4e12870aab81b4b91a95de413e33f0f6251856969c66fbc0142fa7792b9499.jpg", + "image_caption": [ + "Asian", + "Black", + "Indian", + "Latino", + "White" + ], + "image_footnote": [], + "bbox": [ + 80, + 152, + 101, + 215 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/94fbad2eb547f84aebd9dd39496bf8d5687bad5800cac51c67e4ccd99e26f70f.jpg", + "image_caption": [ + "Middle Eastern", + "Figure 5. Proportion of images retrieved $@k = 12$ using neutral prompts for the 'Doctor' occupation." + ], + "image_footnote": [], + "bbox": [ + 184, + 88, + 379, + 308 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad10c417f4def69ab974a5a37d20d7864a5e407266558df0d2d205e77a0185a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 385, + 88, + 571, + 308 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ad470fca11670b86ce7d28da121e415a6aa1aa522fd6d1b204456573a248031.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 88, + 888, + 308 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/27ab7c021197367d45336959fdf14ae5e92e6c262080cb9c7ce9d3375b7ed52a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Intersectional BiasCLIP [41]ALIP [59]FLAVA [46]
Pre-trainedDebiasedPre-trainedDebiasedPre-trainedDebiased
(Race, Gender)1.020.771.401.160.980.79
(Physical Char., Gender)0.870.711.281.020.920.81
(Physical Char., Race)1.190.871.551.131.120.97
", + "bbox": [ + 176, + 347, + 792, + 431 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "a natural question to ask is how well our observed debiasing effects extend to evaluations with real image-text pairs. Unfortunately, there are no such existing resources for measuring the intersectional social biases that we investigate in this work. However, several real image-text datasets have been proposed for evaluating (marginal) social biases for attributes such as perceived race and gender.", + "bbox": [ + 75, + 508, + 468, + 614 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To evaluate our Debiased CLIP model on such datasets, we use the Protected-Attribute Tag Association (PATA) dataset introduced in [45] for nuanced reporting of biases associated with race, age, and gender protected attributes. The PATA dataset comprises of 4,934 public images organized in 24 scenes, where the scenes represent situations in which certain groups of humans may have biases associated with them. The images are annotated with binary gender (male, female), ethnic-race labels (White, Black, Indian, East Asian, Latino-Hispanic) and two age groups (young and old). We also evaluate our Debiased CLIP model on the VisoGender dataset [23], which was curated to benchmark gender bias in image-text pronoun resolution. VisoGender consists of 690 images of people in 23 unique occupational settings.[8]", + "bbox": [ + 75, + 616, + 470, + 828 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3 provides the mean MaxSkew@ $K$ of our Debiased CLIP model on these two datasets. Despite only being", + "bbox": [ + 76, + 829, + 470, + 859 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/63e315fc2a573649161734b0b2cd736c9763b7949e93b8ac8385c736f58b9d18.jpg", + "table_caption": [ + "Table 2. Mean of MaxSkew@ $K$ for pre-trained and debiased variants of CLIP, ALIP, and FLAVA, estimated by withholding counterfactual sets for $20\\%$ of the occupations in our dataset. Best results are in bold." + ], + "table_footnote": [], + "table_body": "
ModelVisoGender [23]PATA [45]
Pre-trained CLIP0.2690.323
Debiased CLIP0.2190.283
", + "bbox": [ + 544, + 506, + 848, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. MaxSkew@ $K$ of our debiased CLIP model as well as pre-trained CLIP on the VisoGender [23] and PATA [45] datasets.", + "bbox": [ + 498, + 569, + 890, + 597 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "trained for mitigating intersectional bias using synthetic examples, our Debiased CLIP model achieves a $15\\%$ and $12\\%$ relative reductions in skewness when measured using real image-text examples from VisoGender and PATA (respectively). Both models have much lower MaxSkew@ $K$ for these datasets than for SocialCounterfactuals, which demonstrates how our dataset reveals significantly more skewness in retrieval results than existing single-attribute datasets.", + "bbox": [ + 496, + 637, + 893, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of debiasing on task-specific performance. An important question for practitioners seeking to debias VLMs is the extent to which debiasing degrades the performance of the model on other tasks. As described previously in Section 1, social biases can be viewed as a type of spurious correlation which models learn as shortcuts to achieving high performance on training datasets. Consequently, it is expected that eliminating these shortcuts may degrade the", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "8We compare SocialCounterfactuals to PATA and VisoGender using the FID and IS metrics in Section 10.3.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11981", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2d1a9667c8a91507a22674c3f71959c848913e5c55f224ffc3fac3428bd5f7cb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
CLIP ModelText RetrievalImage Retrieval
R@1R@5R@10R@1R@5R@10
Pre-trained67.18993.869.490.694.9
Debiased69.289.693.867.390.493.8
", + "bbox": [ + 81, + 89, + 465, + 157 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b2d90b25bd9babcfa807629ad4fbb405fe0ea7276e15ecb747ebe1b5fb524d00.jpg", + "table_caption": [ + "Table 4. Image & text retrieval performance of Debiased CLIP and pre-trained CLIP on Flickr30K[61]. Debiasing CLIP with our dataset results in improved performance on text retrieval and only minimal performance degradation on image retrieval." + ], + "table_footnote": [], + "table_body": "
CLIP ModelCIFAR10[32]CIFAR100[32]Caltech256[21]ImageNet[12]
Pre-trained88.8064.1783.4359.25
Debiased86.7261.4679.7255.38
", + "bbox": [ + 80, + 270, + 465, + 311 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Accuracy of our debiased CLIP model as well as pretrained CLIP on zero-shot image recognition datasets. Debiasing CLIP with our dataset results in minimal performance degradation.", + "bbox": [ + 75, + 321, + 470, + 364 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "performance of the model on other tasks to some extent.", + "bbox": [ + 75, + 421, + 447, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We estimate the magnitude of this impact by evaluating our Debiased CLIP model on image-text retrieval and zero-shot image recognition tasks. Table 4 provides the text retrieval and image retrieval performance of both pretrained CLIP and our Debiased CLIP on Flickr30K. We observe that our Debiased CLIP model achieves equivalent or better performance across all three text retrieval settings compared to pre-trained CLIP. In the image retrieval settings, our Debiased CLIP model exhibits a minor degradation in performance compared to pre-trained CLIP.", + "bbox": [ + 75, + 445, + 468, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5 measures the accuracy of pre-trained CLIP and our Debiased CLIP model on zero-shot image recognition datasets. Similar to the image retrieval evaluation, our Debiased CLIP model exhibits a minor degradation in accuracy on these datasets. These performance reductions are similar in magnitude to those observed in prior work on debiasing CLIP [45] and characterize the trade-off between model fairness and absolute performance inherent to debiasing efforts.", + "bbox": [ + 75, + 604, + 468, + 727 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Depending on the intended use case, the benefits of reducing skewness in the retrieval results of VLMs may be far more valuable than the relatively small decrease in performance observed in debiased models. Additionally, these results were obtained without any tuning of the training process for balancing task-specific performance with debiasing efforts. We hypothesize that additional attention to these task-specific performance measures during training, as well as other strategies such as mixing real data with our counterfactual examples, may produce a different balance between model debiasing and task-specific performance.", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 89, + 619, + 106 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we presented a methodology for automatically generating counterfactual examples for probing and mitigating intersectional bias in VLMs. We used our approach to construct SocialCounterfactuals, a large dataset of image-text counterfactuals depicting intersectional social attributes related to gender, race, and physical characteristics for various occupations. Our evaluations of six pre-trained VLMs showed that all exhibit significant intersectional social biases in retrieval results, with substantial variation in retrieval skewness across differing racial and gender attributes. Through training experiments, we further demonstrated that SocialCounterfactuals can be a valuable resource for mitigating skewness in VLMs. A promising direction for future work could be extending our approach to investigate intersectional social biases in VLMs for other attributes and subjects. Our SocialCounterfactuals dataset could also be a valuable resource for reducing bias in generative text-to-image diffusion models. Finally, alternative training strategies for debiasing VLMs with synthetic counterfactuals could be explored to balance bias mitigation with task-specific performance measures.", + "bbox": [ + 496, + 114, + 893, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and Ethical Considerations Despite our best efforts, the templates and methodologies we adopt may themselves contain some latent biases which could contribute to the implicit biases exhibited by VLMs. All statements pertaining to gender, race, and occupational attributes or associations should be interpreted only within the context of our experiments. Furthermore, all discussion of social attributes in this work are intended to be interpreted as perceived. We are aware that our approach only considers binary classification of genders and does not exhaustively encompass all races, physical characteristics, and occupations, which is due to data limitation rather than our value judgements.", + "bbox": [ + 496, + 454, + 893, + 635 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With the findings we present in this paper, we aim to increase the understanding of bias in VLMs and probe mitigation strategies. We acknowledge that our work does not encompass all possible social attributes and that our selected categories for gender, race, physical characteristics, and occupations may harbor stereotypes that cannot be assumed to represent their entire groups. Our aim is that the techniques presented in this work can help reduce various social disparities in VLMs and can be further extended to include more genders, races, occupations and other social characteristics. Continuing these efforts will increase confidence in the ability of VLMs to exhibit fairness with respect to differing social attributes. See Section 9 for additional discussion.", + "bbox": [ + 496, + 636, + 893, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 847, + 596, + 863 + ], + "page_idx": 7 + }, + { + "type": "ref_text", + "text": "[1] Ananthu Aniraj, Cassio F. Dantas, Dino Ienco, and Diego Marcos. Masking strategies for background bias removal in", + "bbox": [ + 506, + 872, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11982", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "computer vision models. 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Polyjuice: Generating counterfactuals for explaining, evaluating, and improving models. arXiv preprint arXiv:2101.00288, 2021. 1", + "[58] Kai Xiao, Logan Engstrom, Andrew Ilyas, and Aleksander Madry. Noise or signal: The role of image backgrounds in object recognition. arXiv preprint arXiv:2006.09994, 2020. 1", + "[59] Kaicheng Yang, Jiankang Deng, Xiang An, Jiawei Li, Ziyong Feng, Jia Guo, Jing Yang, and Tongliang Liu. Alip: Adaptive language-image pre-training with synthetic caption. arXiv preprint arXiv:2308.08428, 2023. 5, 7", + "[60] Linyi Yang, Jiazheng Li, Padraig Cunningham, Yue Zhang, Barry Smyth, and Ruihai Dong. Exploring the efficacy of automatically generated counterfactuals for sentiment analysis. arXiv preprint arXiv:2106.15231, 2021. 1", + "[61] Peter Young, Alice Lai, Micah Hodosh, and Julia Hockenmaier. From image descriptions to visual denotations: New similarity metrics for semantic inference over event descriptions. 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Association for Computational Linguistics, 2022. 1, 2" + ], + "bbox": [ + 78, + 92, + 468, + 601 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11985", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/e6b7bc50-d0f7-4de0-a9f0-f633baf42ce9_model.json b/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/e6b7bc50-d0f7-4de0-a9f0-f633baf42ce9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c8335b75177d1c38cfb73552f03bff4ff80c8369 --- /dev/null +++ b/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/e6b7bc50-d0f7-4de0-a9f0-f633baf42ce9_model.json @@ -0,0 +1,2587 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.096, + 0.13, + 0.877, + 0.177 + ], + "angle": 0, + "content": "SocialCounterfactuals: Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.204, + 0.296, + 0.222 + ], + "angle": 0, + "content": "Phillip Howard" + }, + { + "type": "text", + "bbox": [ + 0.334, + 0.204, + 0.47, + 0.221 + ], + "angle": 0, + "content": "Avinash Madasu" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.204, + 0.574, + 0.222 + ], + "angle": 0, + "content": "Tiep Le" + }, + { + "type": "text", + "bbox": [ + 0.613, + 0.204, + 0.8, + 0.222 + ], + "angle": 0, + "content": "Gustavo Lujan Moreno" + }, + { + "type": "text", + "bbox": [ + 0.34, + 0.223, + 0.53, + 0.238 + ], + "angle": 0, + "content": "Anahita Bhiwandiwalla" + }, + { + "type": "text", + "bbox": [ + 0.569, + 0.223, + 0.671, + 0.238 + ], + "angle": 0, + "content": "Vasudev Lal" + }, + { + "type": "title", + "bbox": [ + 0.443, + 0.257, + 0.528, + 0.274 + ], + "angle": 0, + "content": "Intel Labs" + }, + { + "type": "text", + "bbox": [ + 0.174, + 0.278, + 0.838, + 0.293 + ], + "angle": 0, + "content": "{phillip.r.howard, avinash.madasu, tiep.le, gustavo.lujan.moreno}@intel.com" + }, + { + "type": "text", + "bbox": [ + 0.3, + 0.296, + 0.708, + 0.31 + ], + "angle": 0, + "content": "{anahita.bhiwandiwalla, vasudev.lal}@intel.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.377, + 0.474, + 0.739 + ], + "angle": 0, + "content": "While vision-language models (VLMs) have achieved remarkable performance improvements recently, there is growing evidence that these models also possess harmful biases with respect to social attributes such as gender and race. Prior studies have primarily focused on probing such bias attributes individually while ignoring biases associated with intersections between social attributes. This could be due to the difficulty of collecting an exhaustive set of image-text pairs for various combinations of social attributes. To address this challenge, we employ text-to-image diffusion models to produce counterfactual examples for probing intersectional social biases at scale. Our approach utilizes Stable Diffusion with cross attention control to produce sets of counterfactual image-text pairs that are highly similar in their depiction of a subject (e.g., a given occupation) while differing only in their depiction of intersectional social attributes (e.g., race & gender). Through our over-generate-then-filter methodology, we produce SocialCounterfactuals, a high-quality dataset containing 171k image-text pairs for probing intersectional biases related to gender, race, and physical characteristics. We conduct extensive experiments to demonstrate the usefulness of our generated dataset for probing and mitigating intersectional social biases in state-of-the-art VLMs." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.769, + 0.21, + 0.785 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Counterfactual examples, which study the impact on a response variable following a change to a causal feature, have proven valuable in natural language processing (NLP) for probing model biases and improving robustness to spurious correlation [16, 18, 26, 30, 54, 57, 60]. While counterfactual examples for VLMs have been relatively unexplored, recent work [33] has shown that text-to-image diffusion models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.896, + 0.422 + ], + "angle": 0, + "content": "with cross attention control can effectively produce multimodal counterfactual examples for VLM training, data augmentation and evaluation. This suggests that synthetic counterfactual examples generated by diffusion models could be an effective tool for probing and mitigating biases in VLMs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.897, + 0.547 + ], + "angle": 0, + "content": "Bias in pre-trained models can be viewed as spurious correlations, which are often attributed to the co-occurrence of non-causal (i.e., spurious) features with labels in datasets. During pre-training, models learn to exploit such correlations as shortcuts to achieving high in-domain performance on the training dataset [19]. Consequently, models which learn to rely on spurious correlations are more brittle and have worse out-of-domain (OOD) generalization [47, 58]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.55, + 0.897, + 0.702 + ], + "angle": 0, + "content": "Social biases are a particularly concerning type of spurious correlation learned by VLMs. Due to a lack of proportional representation for people of various races, genders, and other social attributes in image-text datasets [5, 17, 63], VLMs learn biased associations between these attributes and various subjects (e.g., occupations). For example, given a gender- and race-neutral query such as \"A photo of an attorney\", a VLM may retrieve a disproportionate number of images of one particular race due to learned spurious correlations between this specific occupation and race." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Prior studies on probing social biases in VLMs [22-24, 28, 65] have primarily utilized real image-text pairs collected from existing datasets by identifying the cooccurrence of certain attributes with a target subject. However, this approach is limited by the availability of existing image-text pairs for various combinations of social attributes and subject types. Consequently, these prior studies have focused exclusively on investigating biases associated with a single social attribute at a time while ignoring the potential role of intersectional bias (e.g., particular race-gender combinations) [40], which could be attributed to the difficulty of collecting an exhaustive set of image-text examples for various combinations of social attributes. Additionally, the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11975" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.092, + 0.214, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.094, + 0.193, + 0.205, + 0.213 + ], + "angle": 0, + "content": "A White male construction worker" + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.092, + 0.35, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.228, + 0.193, + 0.339, + 0.213 + ], + "angle": 0, + "content": "An Asian female construction worker" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.092, + 0.483, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.356, + 0.193, + 0.48, + 0.213 + ], + "angle": 0, + "content": "A Middle Eastern male construction worker" + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.092, + 0.619, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.497, + 0.193, + 0.609, + 0.213 + ], + "angle": 0, + "content": "A Latino female construction worker" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.092, + 0.753, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.193, + 0.743, + 0.213 + ], + "angle": 0, + "content": "A Black male construction worker" + }, + { + "type": "image", + "bbox": [ + 0.756, + 0.092, + 0.887, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.767, + 0.193, + 0.878, + 0.213 + ], + "angle": 0, + "content": "An Indian female construction worker" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.227, + 0.895, + 0.256 + ], + "angle": 0, + "content": "Figure 1. Examples of our counterfactual image-text pairs for probing intersectional race-gender bias in VLMs for the \"construction worker\" occupation. See Section 7.1 in Supplementary Material for additional examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.282, + 0.469, + 0.342 + ], + "angle": 0, + "content": "large variability in how subjects can be naturally depicted in real images complicates the task of estimating bias in VLMs because disproportionate retrieval results could be attributed to other differences in images besides the social attribute." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.47, + 0.569 + ], + "angle": 0, + "content": "We overcome these limitations by leveraging text-to-image diffusion models to produce counterfactual image-text pairs for probing and mitigating social biases in VLMs (see Figure 1 and Section 7.1 in Supplementary Material for examples). Specifically, our approach utilizes Stable Diffusion [42] with cross-attention control [25] to produce a set of highly similar counterfactual image-text examples which depict a common subject while differing only in intersectoral social attributes. Text-to-image diffusion models are particularly well-suited for this task due to their ability to generate depictions of specific subjects with various combinations of different social attributes, which might be rare or missing from existing image-text datasets. After generating candidate images, we apply three stages of filtering to ensure that only the highest-quality counterfactuals are retained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.57, + 0.471, + 0.766 + ], + "angle": 0, + "content": "We apply our methodology at scale to produce Social-Counterfactuals, an extensive dataset containing over 171k counterfactual image-text pairs for probing intersectional biases related to race, gender, and physical characteristics. To the best of our knowledge, SocialCounterfactuals is the largest resource released to-date for probing bias in VLMs and the only one which considers intersectional biases. Through extensive evaluation of six VLMs, we demonstrate its usefulness for uncovering intersectional social biases. Additionally, we conduct VLM training experiments using our dataset which demonstrate its ability to reduce skewness in retrieval results for social attributes. We make our dataset1 and code2 publicly available." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.779, + 0.22, + 0.794 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.804, + 0.382, + 0.82 + ], + "angle": 0, + "content": "2.1. Probing bias in pre-trained models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.827, + 0.471, + 0.858 + ], + "angle": 0, + "content": "Much of the prior work on probing social bias in pre-trained models has focused exclusively on language models, pro" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.282, + 0.893, + 0.419 + ], + "angle": 0, + "content": "ducing multiple datasets for measuring stereotypical bias along different social attributes, categories, demographic axes and stigmatized groups [35, 37, 39, 49]. Gender biases associated with pronoun and coreferences have also been extensively studied [8, 43, 56, 64]. Some prior work has addressed topics related to intersectionality in bias evaluations [31, 50, 51]. Additionally, various approaches for bias detection and mitigation for vision-only models have been proposed [1, 6, 13, 27, 55]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.421, + 0.895, + 0.693 + ], + "angle": 0, + "content": "Approaches to generate synthetic datasets with fairness have been explored [2, 4, 15, 34, 44]. For probing biases in VLMs, VLStereoSet [65] extends the StereoSet dataset to the vision domain by sourcing images from Google search and using crowdsourced workers for annotation, resulting in a total of 1028 images. VisoGender [23] consists of 690 manually-annotated images for benchmarking occupation-related gender bias in VLMs. The MultiModal Bias dataset [28] evaluates bias in VLMs across 14 population subgroups and contains a total of 3800 human-annotated images obtained from Flickr. These datasets differ from ours primarily in their much smaller scale, their reliance on collection of data from existing sources & human annotation, and their focus on investigating only a single attribute at a time (as opposed to our investigation of intersectional biases). Bias in VLMs used for text-to-image generation have also been investigated [10, 38, 53], but such studies differ from our focus on bias in image-text retrieval settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.71, + 0.818, + 0.726 + ], + "angle": 0, + "content": "2.2. Mitigating bias in pre-trained VLMs" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": "A variety of methods have been proposed for mitigating the biases observed in pre-trained VLMs. These include adversarial approaches for prompt learning [3], fair sampling methods for reducing bias learned during training [52], contrastive learning techniques for improving group robustness [62], learning additive residuals to offset image representations [45], and eliminating biased directions in the text embedding space through projection matrices [11]. Smith et al. [48] introduced an approach for debiasing VLMs using synthetically-constructed contrast sets, which they use to produce 7946 image-text pairs for gender bias. However, all" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.865, + 0.47, + 0.901 + ], + "angle": 0, + "content": "\\(^{1}\\)Our dataset is available at https://huggingface.co/datasets/Intel/SocialCounterfactuals \n\\(^{2}\\)Our code is available at our GitHub repository" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11976" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.138 + ], + "angle": 0, + "content": "of these prior works focus exclusively on debiasing models for a single social attribute at a time (e.g., gender) as opposed to our focus on debiasing for intersectional biases." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.151, + 0.388, + 0.168 + ], + "angle": 0, + "content": "3. Generating SocialCounterfactuals" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.177, + 0.473, + 0.329 + ], + "angle": 0, + "content": "Our approach to creating counterfactual image-text examples for intersectional social biases consists of three steps. First, we construct sets of image captions describing a subject with counterfactual changes to intersecting social attributes. We then utilize a text-to-image diffusion model with cross attention control to over-generate sets of images corresponding to the counterfactual captions, where differences among images are isolated to the induced counterfactual change (i.e., the social attributes). Finally, we apply stringent filtering to identify only the highest-quality generations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.338, + 0.212, + 0.354 + ], + "angle": 0, + "content": "3.1. Terminology" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.497 + ], + "angle": 0, + "content": "In this work, we do not make any claims regarding gender identification or gender assignment, which we acknowledge to be unique to each individual regardless of their appearance or traits. We use perceived gender as an inference made by a human annotator or model. We acknowledge that labels used in this study may differ from an individual's gender identity and could also vary based on different annotators' interpretations. We recognize that gender and gender identity is fluid and misjudgements in a binary paradigm could arise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.47, + 0.603 + ], + "angle": 0, + "content": "Similarly, we acknowledge that the six races we discuss in this paper - White, Black, Indian, Asian, Middle Eastern and Latino, are not representative of all races. We inherit this list of races from prior work [29]. Any inference or reference to race and occupation is considered to be perceived race and perceived occupation (respectively), and does not aim to associate any bias with any groups of individuals." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.613, + 0.47, + 0.63 + ], + "angle": 0, + "content": "3.2. Constructing captions for probing social biases" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.713 + ], + "angle": 0, + "content": "Consider the task of creating a caption \\( C_{p,a_1,a_2}^s \\) beginning with prefix \\( p \\) and describing a subject \\( s \\) which possesses a pair of attributes \\( a_1 \\) and \\( a_2^3 \\). Given a set of prefixes \\( P \\), a set of subjects \\( S \\), and attribute sets \\( A_1, A_2, \\ldots, A_k \\), we populate the following template to obtain our captions:" + }, + { + "type": "equation", + "bbox": [ + 0.076, + 0.724, + 0.473, + 0.761 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} C _ {p, a _ {1}, a _ {2}} ^ {s} = < p > < a _ {1} > < a _ {2} > < s > \\\\ \\forall p \\in P, s \\in S, a _ {1} \\in A _ {i}, a _ {2} \\in A _ {j}, (i, j) \\in \\{1, \\dots , k \\mid i \\neq j \\} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.772, + 0.471, + 0.879 + ], + "angle": 0, + "content": "For example, given the prefix \\( A \\) photo of \\( a \\), the subject doctor, and attribute pair (Asian, Female), we construct the caption \\( A \\) photo of an Asian female doctor. We construct captions in this manner using a set of occupations as our subjects and three sets of attributes for measuring social bias (gender, race, and physical characteristics). Captions are grouped into counterfactual sets, where each set contains all captions" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.895, + 0.244 + ], + "angle": 0, + "content": "corresponding to a given prefix and subject. Using 260 occupations, 4 prefixes, 6 races, and 5 physical characteristics, and 2 gender terms\\(^{4}\\), we produced a total of 54,080 captions which were grouped into 3,120 counterfactual sets (see Section 8.4 of Supp. Material for additional details and examples). While we categorize these social attributes with the aim of probing biases, we recognize the limitations inherent to this process and acknowledge that attributes such as gender and race are not considered by all individuals to exist as discrete categories (see Section 6 for additional discussion)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.253, + 0.792, + 0.269 + ], + "angle": 0, + "content": "3.3. Counterfactual image generation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.276, + 0.895, + 0.533 + ], + "angle": 0, + "content": "After generating sets of counterfactual captions, we use text-to-image diffusion models to produce images for each caption. In order to precisely measure the impact of social attribute differences, it is desirable for images within a counterfactual set to only differ in how the social attributes differ across captions. However, this is challenging for diffusion models as even minor changes to a prompt can result in the generation of images with significant differences. For example, changing the attributes Hispanic female to Asian male in the prompt A photo of a Hispanic female doctor may produce other undesired modifications to the image that extend beyond the induced counterfactual change (e.g., changes to the background). This complicates the task of quantifying the impact of model bias attributed to the changed social attributes on retrieval results, as other differences between the generated images could contribute to a VLM's preference for retrieving particular images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.534, + 0.895, + 0.775 + ], + "angle": 0, + "content": "Hertz et al. [25] proposed Prompt-to-Prompt to address this issue by injecting cross-attention maps during denoising steps to control attention between certain pixels and tokens, which enables separate generations to maintain many of the same details while isolating differences to how the text prompts differ. However, Brooks et al. [7] noted that some changes require varying the parameter \\( p \\) in Prompt-to-Prompt, which controls the number of denoising steps with shared attention weights. For example, changes that require more substantial structural modifications to the image may necessitate less overall similarity between the resulting images and thus fewer shared attention weights. We therefore adopt their proposed approach of over-generating 100 image pairs with Prompt-to-Prompt by sampling \\( p \\sim U(0.1, 0.9) \\), which we then subsequently filter to retain only the highest-quality generated candidates (Section 3.4)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.775, + 0.894, + 0.867 + ], + "angle": 0, + "content": "We extend Prompt-to-Prompt for image pairs from Brooks et al. [7] to support batched generation of multiple images with cross attention control. This enables simultaneous generation of entire sets of counterfactual images which differ only according to the social attribute differences across prompts (e.g., Figure 1). In total, we over-generate" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.471, + 0.9 + ], + "angle": 0, + "content": "3See Section 10.2 for discussion of extension to more than two attributes" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "4We also explored the generation of other subjects and social attributes with our method. See Section 7.4 of Supplementary Material for details." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11977" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.102, + 0.885, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.273, + 0.719, + 0.288 + ], + "angle": 0, + "content": "Figure 2. Overview of our methodology for generating SocialCounterfactuals." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.314, + 0.333, + 0.33 + ], + "angle": 0, + "content": "5,408,000 images for 54,080 captions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.337, + 0.281, + 0.354 + ], + "angle": 0, + "content": "3.4. Three-Stage Filtering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.474, + 0.542 + ], + "angle": 0, + "content": "CLIP image-text similarity filtering. After over-generating 100 candidate image sets for each of our templates, we first filter the candidates using CLIP [41] to ensure a minimum cosine similarity of 0.2 between the encoding of each caption and its corresponding generated image. We also apply a similar filtering criteria between pairs of images in each set, requiring the cosine similarity of CLIP image encodings within the set to be greater than 0.2. These filtering criteria help ensure that images accurately depict the subjects described in each caption while also retaining a high-degree of similarity to each other, thereby ensuring that they represent valid counterfactual examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.56, + 0.472, + 0.651 + ], + "angle": 0, + "content": "NSFW Filtering with ViT. Manual examination of generated images revealed instances of not-safe-for-work (NSFW) content. We therefore applied a NSFW filter which uses a fine-tuned vision transformer (ViT) for NSFW image classification. This filter removes \\(0.9 - 2.7\\%\\) of generated images (see Table 11 in Supplementary Material for details)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.668, + 0.47, + 0.834 + ], + "angle": 0, + "content": "CLIP Attribute Detectability Filtering. To further ensure data quality, we filter counterfactual sets based on CLIP's ability to discern targeted social attributes in each image using a two-phase approach (see Section 8.3 in Supp. Material for additional details). In the first phase, we randomly sampled 100 counterfactual sets for each pair of attribute types. For each attribute type, we then manually labeled the sampled counterfactual sets according to whether or not they should be filtered out based on a lack of detectability of the targeted attribute. Specifically, we label how many images in a counterfactual set possess their targeted attribute." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.835, + 0.471, + 0.88 + ], + "angle": 0, + "content": "In the second phase, we develop a learnable threshold-based heuristics to automatically label whether a counterfactual set should be filtered with respect to an individual" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.311, + 0.89, + 0.367 + ], + "angle": 0, + "content": "
Attribute PairCounterfactual SetsImages Per SetTotal Images
(Race, Gender)7,9361295,232
(Physical Char., Gender)5,0521050,520
(Physical Char., Race)8363025,080
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.377, + 0.893, + 0.406 + ], + "angle": 0, + "content": "Table 1. Details of the number of counterfactual sets, images per set, and total images which remain in our dataset after filtering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.446, + 0.895, + 0.643 + ], + "angle": 0, + "content": "attribute type. These threshold-based heuristics are applied according to how many of a set's constituent images have their respective targeted attributes discernible by CLIP-based image-text similarity scores (rather than by a human annotator). Thresholds were heuristically derived to obtain high correspondence between automatic filtering with CLIP and those filtered by the manual human annotation. This process produces a separate learned threshold for each attribute type and attribute type pair combination. A counterfactual set is filtered out due to a lack of detectability for an attribute type if the number of its constituent images whose corresponding targeted attribute is discernible by CLIP is less than the corresponding learned threshold." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.895, + 0.78 + ], + "angle": 0, + "content": "To estimate the quality of our generated dataset and the impact of filtering, we randomly sampled 100 counterfactual sets depicting Race-Gender intersectional social attributes. Prior to CLIP attribute detectability filtering, we found that \\(90.8\\%\\) of the images accurately depicted their corresponding captions. Applying attribute detectability filtering further increases this figure to \\(97.5\\%\\), which demonstrates the value of our filtering methodology and the high quality it ensures in our dataset (see Section 7.2 of Supp. Material for details)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Table 1 provides details on the total number of counterfactual sets and images which remain in our dataset after filtering. We group counterfactual sets into three dataset segments based on the pair of attribute types used to construct the captions, which are detailed in each row of Table 1. In total, our dataset consists of 13,824 counterfactual sets with 170,832 image-text pairs, which represents the largest paired image-text dataset for investigating social biases to-date." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.887, + 0.47, + 0.901 + ], + "angle": 0, + "content": "5https://huggingface.co/Falconsai/nsfw_image_detector" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11978" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.09, + 0.348, + 0.108 + ], + "angle": 0, + "content": "4. Probing Intersectional Biases" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.161 + ], + "angle": 0, + "content": "To probe intersectional social biases in VLMs, we calculate MaxSkew over our dataset. We describe this metric in Section 4.1 and detail our evaluation results in Section 4.2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.17, + 0.262, + 0.185 + ], + "angle": 0, + "content": "4.1. Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.193, + 0.469, + 0.3 + ], + "angle": 0, + "content": "Let \\( q \\) denote a text query and \\( R_{K}(q) \\) denote the set of top- \\( K \\) ranked images retrieved by a VLM for \\( q \\). For a given attribute pair \\( (a_{i},a_{j}) \\), we denote the desired proportion \\( d \\) of retrieved images with the corresponding attributes as \\( p_{d(q),(a_i,a_j)} \\) and the actual proportion as \\( p_{R_K(q),(a_i,a_j)} \\). Geyik et al. [20] define Skew@ \\( K \\) for attributes \\( (a_{i},a_{j}) \\) in retrieval results \\( R_{K}(q) \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.31, + 0.432, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S k e w} _ {(a _ {i}, a _ {j})} @ K (R _ {K} (q)) = \\log \\left(\\frac {p _ {R _ {K} (q) , (a _ {i} , a _ {j})}}{p _ {d (q) , (a _ {i} , a _ {j})}}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.47, + 0.426 + ], + "angle": 0, + "content": "In essence, Skew@K measures the ratio of the proportion of top-K retrieved images having a set of attributes to the desired proportion. To aggregate Skew@K over the various attributes under consideration, Geyik et al. [20] further proposed the following MaxSkew@K metric:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.437, + 0.477, + 0.463 + ], + "angle": 0, + "content": "\\(\\operatorname{MaxSkerw} @ K(R_K(q)) = \\max_{(a_i, a_j) \\in A} \\operatorname{Skerw}_{(a_i, a_j)} @ K(R_K(q))\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.576 + ], + "angle": 0, + "content": "where \\( A \\) denotes the set of all attribute pairs. We calculate MaxSkew@\\( K \\) by retrieving images from our counterfactual sets using prompts which are neutral with respect to the investigated attributes. For example, given a prompt constructed from the template \"A construction worker\" (Figure 1), we form its corresponding attribute-neutral prompt \"A construction worker.\"" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.469, + 0.713 + ], + "angle": 0, + "content": "We construct neutral prompts in this manner for each unique combination of prefixes and subjects, averaging their text representations across different prefixes to obtain a single text embedding for each subject. Skew@ \\(K\\) and MaxSkew@ \\(K\\) are then calculated by retrieving the top- \\(K\\) images for the computed text embedding from the set of all images generated for the subject which met our filtering and selection criteria. We set \\(K = |A_1| \\times |A_2|\\), where \\(A_1\\) and \\(A_2\\) are the investigated attribute sets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.172, + 0.737 + ], + "angle": 0, + "content": "4.2. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.746, + 0.47, + 0.866 + ], + "angle": 0, + "content": "Figure 3 provides boxplots of the intersectional bias MaxSkew@K distribution for six state-of-the-art VLMs: ALIP [59], CLIP [41], FLAVA [46], LaCLIP [14], OpenCLIP [9], and SLIP [36]. We measure the MaxSkew@K distribution across occupations separately using the three segments of our dataset for Race-Gender (Figure 6a), Physical Characteristics-Gender (Figure 6b), and Physical Characteristics-Race (Figure 6c) intersectional biases." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.092, + 0.894, + 0.197 + ], + "angle": 0, + "content": "All six evaluated VLMs exhibit significant skewness in retrieval for attribute-neutral occupation prompts, with CLIP and FLAVA having the lowest overall MaxSkew@K. Among the three segments of our dataset, Physical Characteristics-Gender intersectional biases tend to have lower MaxSkew@K scores while Race-Gender intersectional biases have the greatest amount of skewness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.894, + 0.397 + ], + "angle": 0, + "content": "In addition to illustrating the overall distribution of MaxSkew@K across occupations, the boxplots in Figure 3 also provides the occupation names for minimum values (green circles) and maximum values (red circles). These labels show some commonalities across models, such as FLAVA and LaCLIP both having their greatest Race-Gender MaxSkew@K values for the 'Makeup Artist' profession. We also observe that LaCLIP and OpenCLIP have their greatest skewness in retrieval from the Physical Characteristics-Race segment for the 'Barber' occupation. Notably, both CLIP and FLAVA have multiple occupations with zero skewness across all segments of the dataset, while SLIP has no occupations with zero skewness across the three segments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.894, + 0.672 + ], + "angle": 0, + "content": "Our dataset can also be used to evaluate individual (i.e., marginal) bias for a specific attribute type by filtering on the value of the other attribute depicted in a counterfactual set. MaxSkew@ \\( K \\) can then be calculated as previously described to estimate bias in retrieval results for a single social attribute at a time. To illustrate, we estimated the marginal gender bias across occupations using images specific to each race, which we provide in Figure 4. All VLMs exhibit variation in gender bias across different races, highlighting the importance of measuring bias in the presence of other social attributes. While CLIP has lower overall skewness than other evaluated models, it also has the greatest disparity in MaxSkew@ \\( K \\) across different races; specifically, CLIP exhibits nearly 2x more gender skewness for images depicting Indian subjects than it does for Latinos. Interestingly, both CLIP and FLAVA exhibit the greatest gender bias in retrieving images depicting Indian people, while SLIP and ALIP exhibit the greatest gender bias for Middle Eastern people." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.894, + 0.901 + ], + "angle": 0, + "content": "As a further case study in uncovering intersectional social biases in VLMs, Figure 5 provides a breakdown of the proportion of images retrieved using gender- and race-neutral prompts for the 'Doctor' occupation. The left and center plots of Figure 5 depict the marginal distributions of retrievals for each race and gender (respectively), whereas the right plot provides the distribution of retrieved images for intersectional race-gender attributes. While SLIP, OpenCLIP, LaCLIP, and ALIP exhibit strong bias for retrieving male images, this gender bias occurs along starkly different dimensions with respect to race. OpenCLIP strongly favors retrieving images of Asian male doctors when presented with a neutral text prompt, whereas the other three models prefer to retrieve images of Indian male doctors. This gender bias is inverted for CLIP, which retrieves images of women" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.454, + 0.887 + ], + "angle": 0, + "content": "6We also provide results for other evaluation metrics in Section 10.1." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.407, + 0.9 + ], + "angle": 0, + "content": "See Section 10.4 for additional details and probing results" + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.454, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11979" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.35, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.17, + 0.243, + 0.26, + 0.255 + ], + "angle": 0, + "content": "(a) Race-Gender" + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.089, + 0.621, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.391, + 0.243, + 0.581, + 0.256 + ], + "angle": 0, + "content": "(b) Physical Characteristics-Gender" + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.09, + 0.891, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.669, + 0.243, + 0.844, + 0.256 + ], + "angle": 0, + "content": "(c) Physical Characteristics-Race" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.268, + 0.894, + 0.297 + ], + "angle": 0, + "content": "Figure 3. Distribution of MaxSkew@ \\(K\\) measured across occupations for (a) Race-Gender, (b) Physical Characteristics-Gender, and (c) Physical Characteristics-Race intersectional biases. Max (min) values are plotted as red (green) circles with corresponding occupation names" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.319, + 0.468, + 0.537 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Figure 4. Mean of (marginal) gender MaxSkew@ \\( K \\) measured across occupations for different races." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.602, + 0.47, + 0.707 + ], + "angle": 0, + "content": "in a slightly higher proportion than men, but still has zero representation of certain groups (e.g., Black females). These results show that seemingly similar biases among pre-trained VLMs for social attributes such as gender can interact very differently with other attributes such as race, which highlights the importance of studying bias in the presence of intersectional social attributes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.367, + 0.739 + ], + "angle": 0, + "content": "5. Mitigating Intersectional Biases" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.468, + 0.779 + ], + "angle": 0, + "content": "We investigate the suitability of our SocialCounterfactuals dataset for debiasing VLMs through additional training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.336, + 0.804 + ], + "angle": 0, + "content": "5.1. Training Experiment Setting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.9 + ], + "angle": 0, + "content": "For each of the three segments of our dataset (see Table 1), we withhold counterfactual sets associated with \\(20\\%\\) of the occupation subjects for testing and use the remainder as a training dataset. We then separately finetune ALIP, CLIP, and FLAVA on each of these three training datasets, which we hereafter refer to as the 'debiased' variants of these mod-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.322, + 0.893, + 0.369 + ], + "angle": 0, + "content": "els. To estimate the magnitude of debiasing, we evaluate each model's MaxSkew@K for intersectional bias using the withheld testing dataset containing \\(20\\%\\) of the occupations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.38, + 0.833, + 0.395 + ], + "angle": 0, + "content": "5.2. Results for Intersectional Social Biases" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Table 2 provides the mean MaxSkew@ \\( K \\) calculated over our withheld test sets for pre-trained and debiased variants of CLIP, ALIP, and FLAVA. Training on our dataset has the greatest overall debiasing effect on ALIP, producing up to a 0.426 absolute reduction in MaxSkew@ \\( K \\). Among the three segments of our dataset used for debiasing, MaxSkew@ \\( K \\) for (Physical Char., Race) intersectional bias has the greatest amount of skewness in pre-trained models. However, training on our dataset also produces the greatest absolute reduction in skewness for this type of intersectional bias, with CLIP having an absolute reduction in MaxSkew@ \\( K \\) of 0.327 for (Physical Char., Race) intersectional biases." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.586, + 0.895, + 0.752 + ], + "angle": 0, + "content": "These results show that training VLMs with our dataset produces significant debiasing effects across all three types of intersectional biases. Furthermore, the strongest intersectional biases observed in pre-trained VLMs benefit the most from debiasing. Remarkably, these debiasing effects are observed despite there being no overlap between the occupations used for training and testing, which demonstrates that the debiasing effects generalize to new subjects not seen during training. This suggests that the ability of our dataset to mitigate intersectional bias in VLMs is not limited to only the occupation subjects that we investigated." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.763, + 0.892, + 0.78 + ], + "angle": 0, + "content": "5.3. Analysis of Race-Gender Debiased CLIP Model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.788, + 0.894, + 0.848 + ], + "angle": 0, + "content": "To further understand the impact of training VLMs using our synthetic counterfactuals, we conduct analyses of CLIP after debiasing for Race-Gender intersectional bias. For simplicity, we hereafter refer to this model as Debiased CLIP." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Skewness evaluation using other datasets with real image-text pairs. Since our dataset was synthetically generated," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11980" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.153, + 0.102, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.155, + 0.137, + 0.163 + ], + "angle": 0, + "content": "Asian" + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.165, + 0.137, + 0.173 + ], + "angle": 0, + "content": "Black" + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.175, + 0.137, + 0.183 + ], + "angle": 0, + "content": "Indian" + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.185, + 0.137, + 0.193 + ], + "angle": 0, + "content": "Latino" + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.196, + 0.174, + 0.204 + ], + "angle": 0, + "content": "Middle Eastern" + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.206, + 0.137, + 0.214 + ], + "angle": 0, + "content": "White" + }, + { + "type": "list", + "bbox": [ + 0.111, + 0.155, + 0.174, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.185, + 0.089, + 0.38, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.387, + 0.089, + 0.572, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.578, + 0.089, + 0.89, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.183, + 0.321, + 0.785, + 0.336 + ], + "angle": 0, + "content": "Figure 5. Proportion of images retrieved \\(@k = 12\\) using neutral prompts for the 'Doctor' occupation." + }, + { + "type": "table", + "bbox": [ + 0.178, + 0.348, + 0.794, + 0.432 + ], + "angle": 0, + "content": "
Intersectional BiasCLIP [41]ALIP [59]FLAVA [46]
Pre-trainedDebiasedPre-trainedDebiasedPre-trainedDebiased
(Race, Gender)1.020.771.401.160.980.79
(Physical Char., Gender)0.870.711.281.020.920.81
(Physical Char., Race)1.190.871.551.131.120.97
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.442, + 0.893, + 0.47 + ], + "angle": 0, + "content": "Table 2. Mean of MaxSkew@ \\(K\\) for pre-trained and debiased variants of CLIP, ALIP, and FLAVA, estimated by withholding counterfactual sets for \\(20\\%\\) of the occupations in our dataset. Best results are in bold." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.47, + 0.616 + ], + "angle": 0, + "content": "a natural question to ask is how well our observed debiasing effects extend to evaluations with real image-text pairs. Unfortunately, there are no such existing resources for measuring the intersectional social biases that we investigate in this work. However, several real image-text datasets have been proposed for evaluating (marginal) social biases for attributes such as perceived race and gender." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.617, + 0.471, + 0.829 + ], + "angle": 0, + "content": "To evaluate our Debiased CLIP model on such datasets, we use the Protected-Attribute Tag Association (PATA) dataset introduced in [45] for nuanced reporting of biases associated with race, age, and gender protected attributes. The PATA dataset comprises of 4,934 public images organized in 24 scenes, where the scenes represent situations in which certain groups of humans may have biases associated with them. The images are annotated with binary gender (male, female), ethnic-race labels (White, Black, Indian, East Asian, Latino-Hispanic) and two age groups (young and old). We also evaluate our Debiased CLIP model on the VisoGender dataset [23], which was curated to benchmark gender bias in image-text pronoun resolution. VisoGender consists of 690 images of people in 23 unique occupational settings.[8]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.83, + 0.471, + 0.861 + ], + "angle": 0, + "content": "Table 3 provides the mean MaxSkew@ \\( K \\) of our Debiased CLIP model on these two datasets. Despite only being" + }, + { + "type": "table", + "bbox": [ + 0.545, + 0.507, + 0.849, + 0.56 + ], + "angle": 0, + "content": "
ModelVisoGender [23]PATA [45]
Pre-trained CLIP0.2690.323
Debiased CLIP0.2190.283
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.57, + 0.892, + 0.598 + ], + "angle": 0, + "content": "Table 3. MaxSkew@ \\( K \\) of our debiased CLIP model as well as pre-trained CLIP on the VisoGender [23] and PATA [45] datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.895, + 0.76 + ], + "angle": 0, + "content": "trained for mitigating intersectional bias using synthetic examples, our Debiased CLIP model achieves a \\(15\\%\\) and \\(12\\%\\) relative reductions in skewness when measured using real image-text examples from VisoGender and PATA (respectively). Both models have much lower MaxSkew@\\(K\\) for these datasets than for SocialCounterfactuals, which demonstrates how our dataset reveals significantly more skewness in retrieval results than existing single-attribute datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Impact of debiasing on task-specific performance. An important question for practitioners seeking to debias VLMs is the extent to which debiasing degrades the performance of the model on other tasks. As described previously in Section 1, social biases can be viewed as a type of spurious correlation which models learn as shortcuts to achieving high performance on training datasets. Consequently, it is expected that eliminating these shortcuts may degrade the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "8We compare SocialCounterfactuals to PATA and VisoGender using the FID and IS metrics in Section 10.3." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11981" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.082, + 0.09, + 0.467, + 0.159 + ], + "angle": 0, + "content": "
CLIP ModelText RetrievalImage Retrieval
R@1R@5R@10R@1R@5R@10
Pre-trained67.18993.869.490.694.9
Debiased69.289.693.867.390.493.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.17, + 0.472, + 0.227 + ], + "angle": 0, + "content": "Table 4. Image & text retrieval performance of Debiased CLIP and pre-trained CLIP on Flickr30K[61]. Debiasing CLIP with our dataset results in improved performance on text retrieval and only minimal performance degradation on image retrieval." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.271, + 0.466, + 0.313 + ], + "angle": 0, + "content": "
CLIP ModelCIFAR10[32]CIFAR100[32]Caltech256[21]ImageNet[12]
Pre-trained88.8064.1783.4359.25
Debiased86.7261.4679.7255.38
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.323, + 0.472, + 0.366 + ], + "angle": 0, + "content": "Table 5. Accuracy of our debiased CLIP model as well as pretrained CLIP on zero-shot image recognition datasets. Debiasing CLIP with our dataset results in minimal performance degradation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.449, + 0.439 + ], + "angle": 0, + "content": "performance of the model on other tasks to some extent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.598 + ], + "angle": 0, + "content": "We estimate the magnitude of this impact by evaluating our Debiased CLIP model on image-text retrieval and zero-shot image recognition tasks. Table 4 provides the text retrieval and image retrieval performance of both pretrained CLIP and our Debiased CLIP on Flickr30K. We observe that our Debiased CLIP model achieves equivalent or better performance across all three text retrieval settings compared to pre-trained CLIP. In the image retrieval settings, our Debiased CLIP model exhibits a minor degradation in performance compared to pre-trained CLIP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.47, + 0.728 + ], + "angle": 0, + "content": "Table 5 measures the accuracy of pre-trained CLIP and our Debiased CLIP model on zero-shot image recognition datasets. Similar to the image retrieval evaluation, our Debiased CLIP model exhibits a minor degradation in accuracy on these datasets. These performance reductions are similar in magnitude to those observed in prior work on debiasing CLIP [45] and characterize the trade-off between model fairness and absolute performance inherent to debiasing efforts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Depending on the intended use case, the benefits of reducing skewness in the retrieval results of VLMs may be far more valuable than the relatively small decrease in performance observed in debiased models. Additionally, these results were obtained without any tuning of the training process for balancing task-specific performance with debiasing efforts. We hypothesize that additional attention to these task-specific performance measures during training, as well as other strategies such as mixing real data with our counterfactual examples, may produce a different balance between model debiasing and task-specific performance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.09, + 0.62, + 0.107 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.895, + 0.433 + ], + "angle": 0, + "content": "In this work, we presented a methodology for automatically generating counterfactual examples for probing and mitigating intersectional bias in VLMs. We used our approach to construct SocialCounterfactuals, a large dataset of image-text counterfactuals depicting intersectional social attributes related to gender, race, and physical characteristics for various occupations. Our evaluations of six pre-trained VLMs showed that all exhibit significant intersectional social biases in retrieval results, with substantial variation in retrieval skewness across differing racial and gender attributes. Through training experiments, we further demonstrated that SocialCounterfactuals can be a valuable resource for mitigating skewness in VLMs. A promising direction for future work could be extending our approach to investigate intersectional social biases in VLMs for other attributes and subjects. Our SocialCounterfactuals dataset could also be a valuable resource for reducing bias in generative text-to-image diffusion models. Finally, alternative training strategies for debiasing VLMs with synthetic counterfactuals could be explored to balance bias mitigation with task-specific performance measures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.895, + 0.636 + ], + "angle": 0, + "content": "Limitations and Ethical Considerations Despite our best efforts, the templates and methodologies we adopt may themselves contain some latent biases which could contribute to the implicit biases exhibited by VLMs. All statements pertaining to gender, race, and occupational attributes or associations should be interpreted only within the context of our experiments. Furthermore, all discussion of social attributes in this work are intended to be interpreted as perceived. We are aware that our approach only considers binary classification of genders and does not exhaustively encompass all races, physical characteristics, and occupations, which is due to data limitation rather than our value judgements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.895, + 0.833 + ], + "angle": 0, + "content": "With the findings we present in this paper, we aim to increase the understanding of bias in VLMs and probe mitigation strategies. We acknowledge that our work does not encompass all possible social attributes and that our selected categories for gender, race, physical characteristics, and occupations may harbor stereotypes that cannot be assumed to represent their entire groups. Our aim is that the techniques presented in this work can help reduce various social disparities in VLMs and can be further extended to include more genders, races, occupations and other social characteristics. Continuing these efforts will increase confidence in the ability of VLMs to exhibit fairness with respect to differing social attributes. See Section 9 for additional discussion." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.848, + 0.597, + 0.864 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.873, + 0.892, + 0.901 + ], + "angle": 0, + "content": "[1] Ananthu Aniraj, Cassio F. Dantas, Dino Ienco, and Diego Marcos. Masking strategies for background bias removal in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11982" + } + ], + [ + { + "type": "ref_text", + "bbox": [ + 0.108, + 0.092, + 0.471, + 0.134 + ], + "angle": 0, + "content": "computer vision models. 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Association for Computational Linguistics, 2022. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.093, + 0.47, + 0.602 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "11985" + } + ] +] \ No newline at end of file diff --git a/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/e6b7bc50-d0f7-4de0-a9f0-f633baf42ce9_origin.pdf b/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/e6b7bc50-d0f7-4de0-a9f0-f633baf42ce9_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..52cc04cf4c88684918c397b4182cd386c783b67f --- /dev/null +++ b/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/e6b7bc50-d0f7-4de0-a9f0-f633baf42ce9_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c650890dc3c66c61af168e3108243c780ed12f7f73359a2cc991b8e40019f993 +size 5017236 diff --git a/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/full.md b/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/full.md new file mode 100644 index 0000000000000000000000000000000000000000..75a33a0ad88b2c2ffc6c77694b2a8f62f8f19566 --- /dev/null +++ b/2024/SocialCounterfactuals_ Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples/full.md @@ -0,0 +1,333 @@ +# SocialCounterfactuals: Probing and Mitigating Intersectional Social Biases in Vision-Language Models with Counterfactual Examples + +Phillip Howard + +Avinash Madasu + +Tiep Le + +Gustavo Lujan Moreno + +Anahita Bhiwandiwalla + +Vasudev Lal + +# Intel Labs + +{phillip.r.howard, avinash.madasu, tiep.le, gustavo.lujan.moreno}@intel.com + +{anahita.bhiwandiwalla, vasudev.lal}@intel.com + +# Abstract + +While vision-language models (VLMs) have achieved remarkable performance improvements recently, there is growing evidence that these models also possess harmful biases with respect to social attributes such as gender and race. Prior studies have primarily focused on probing such bias attributes individually while ignoring biases associated with intersections between social attributes. This could be due to the difficulty of collecting an exhaustive set of image-text pairs for various combinations of social attributes. To address this challenge, we employ text-to-image diffusion models to produce counterfactual examples for probing intersectional social biases at scale. Our approach utilizes Stable Diffusion with cross attention control to produce sets of counterfactual image-text pairs that are highly similar in their depiction of a subject (e.g., a given occupation) while differing only in their depiction of intersectional social attributes (e.g., race & gender). Through our over-generate-then-filter methodology, we produce SocialCounterfactuals, a high-quality dataset containing 171k image-text pairs for probing intersectional biases related to gender, race, and physical characteristics. We conduct extensive experiments to demonstrate the usefulness of our generated dataset for probing and mitigating intersectional social biases in state-of-the-art VLMs. + +# 1. Introduction + +Counterfactual examples, which study the impact on a response variable following a change to a causal feature, have proven valuable in natural language processing (NLP) for probing model biases and improving robustness to spurious correlation [16, 18, 26, 30, 54, 57, 60]. While counterfactual examples for VLMs have been relatively unexplored, recent work [33] has shown that text-to-image diffusion models + +with cross attention control can effectively produce multimodal counterfactual examples for VLM training, data augmentation and evaluation. This suggests that synthetic counterfactual examples generated by diffusion models could be an effective tool for probing and mitigating biases in VLMs. + +Bias in pre-trained models can be viewed as spurious correlations, which are often attributed to the co-occurrence of non-causal (i.e., spurious) features with labels in datasets. During pre-training, models learn to exploit such correlations as shortcuts to achieving high in-domain performance on the training dataset [19]. Consequently, models which learn to rely on spurious correlations are more brittle and have worse out-of-domain (OOD) generalization [47, 58]. + +Social biases are a particularly concerning type of spurious correlation learned by VLMs. Due to a lack of proportional representation for people of various races, genders, and other social attributes in image-text datasets [5, 17, 63], VLMs learn biased associations between these attributes and various subjects (e.g., occupations). For example, given a gender- and race-neutral query such as "A photo of an attorney", a VLM may retrieve a disproportionate number of images of one particular race due to learned spurious correlations between this specific occupation and race. + +Prior studies on probing social biases in VLMs [22-24, 28, 65] have primarily utilized real image-text pairs collected from existing datasets by identifying the cooccurrence of certain attributes with a target subject. However, this approach is limited by the availability of existing image-text pairs for various combinations of social attributes and subject types. Consequently, these prior studies have focused exclusively on investigating biases associated with a single social attribute at a time while ignoring the potential role of intersectional bias (e.g., particular race-gender combinations) [40], which could be attributed to the difficulty of collecting an exhaustive set of image-text examples for various combinations of social attributes. Additionally, the + +![](images/d5fe8c34870311a0384fc93ef571a69e032398b0f4e9b41ec6ff2b17ca9ec9ee.jpg) +A White male construction worker +Figure 1. Examples of our counterfactual image-text pairs for probing intersectional race-gender bias in VLMs for the "construction worker" occupation. See Section 7.1 in Supplementary Material for additional examples. + +![](images/dbabbdf873fa541ac1ef193142983c4bcc91842a12f6bd5bc17d0a507312068f.jpg) +An Asian female construction worker + +![](images/a38481ec7c8ae4590b1013ea25c086e075b1d49b28d6bd59fdcd7b5f2518903f.jpg) +A Middle Eastern male construction worker + +![](images/2f77f37b979cfe5d5c667e507badfee064a5f7f868fae21453b513ebbee7bd46.jpg) +A Latino female construction worker + +![](images/06ff31107c1c89b45f05acef60004dcedaffddd892d63e659506f87e35352467.jpg) +A Black male construction worker + +![](images/f97cdf9e456a859c77c006a9c250cc26a0002d3c6a37bd7c097dfda83fdae41f.jpg) +An Indian female construction worker + +large variability in how subjects can be naturally depicted in real images complicates the task of estimating bias in VLMs because disproportionate retrieval results could be attributed to other differences in images besides the social attribute. + +We overcome these limitations by leveraging text-to-image diffusion models to produce counterfactual image-text pairs for probing and mitigating social biases in VLMs (see Figure 1 and Section 7.1 in Supplementary Material for examples). Specifically, our approach utilizes Stable Diffusion [42] with cross-attention control [25] to produce a set of highly similar counterfactual image-text examples which depict a common subject while differing only in intersectoral social attributes. Text-to-image diffusion models are particularly well-suited for this task due to their ability to generate depictions of specific subjects with various combinations of different social attributes, which might be rare or missing from existing image-text datasets. After generating candidate images, we apply three stages of filtering to ensure that only the highest-quality counterfactuals are retained. + +We apply our methodology at scale to produce Social-Counterfactuals, an extensive dataset containing over 171k counterfactual image-text pairs for probing intersectional biases related to race, gender, and physical characteristics. To the best of our knowledge, SocialCounterfactuals is the largest resource released to-date for probing bias in VLMs and the only one which considers intersectional biases. Through extensive evaluation of six VLMs, we demonstrate its usefulness for uncovering intersectional social biases. Additionally, we conduct VLM training experiments using our dataset which demonstrate its ability to reduce skewness in retrieval results for social attributes. We make our dataset1 and code2 publicly available. + +# 2. Related Work + +# 2.1. Probing bias in pre-trained models + +Much of the prior work on probing social bias in pre-trained models has focused exclusively on language models, pro + +ducing multiple datasets for measuring stereotypical bias along different social attributes, categories, demographic axes and stigmatized groups [35, 37, 39, 49]. Gender biases associated with pronoun and coreferences have also been extensively studied [8, 43, 56, 64]. Some prior work has addressed topics related to intersectionality in bias evaluations [31, 50, 51]. Additionally, various approaches for bias detection and mitigation for vision-only models have been proposed [1, 6, 13, 27, 55]. + +Approaches to generate synthetic datasets with fairness have been explored [2, 4, 15, 34, 44]. For probing biases in VLMs, VLStereoSet [65] extends the StereoSet dataset to the vision domain by sourcing images from Google search and using crowdsourced workers for annotation, resulting in a total of 1028 images. VisoGender [23] consists of 690 manually-annotated images for benchmarking occupation-related gender bias in VLMs. The MultiModal Bias dataset [28] evaluates bias in VLMs across 14 population subgroups and contains a total of 3800 human-annotated images obtained from Flickr. These datasets differ from ours primarily in their much smaller scale, their reliance on collection of data from existing sources & human annotation, and their focus on investigating only a single attribute at a time (as opposed to our investigation of intersectional biases). Bias in VLMs used for text-to-image generation have also been investigated [10, 38, 53], but such studies differ from our focus on bias in image-text retrieval settings. + +# 2.2. Mitigating bias in pre-trained VLMs + +A variety of methods have been proposed for mitigating the biases observed in pre-trained VLMs. These include adversarial approaches for prompt learning [3], fair sampling methods for reducing bias learned during training [52], contrastive learning techniques for improving group robustness [62], learning additive residuals to offset image representations [45], and eliminating biased directions in the text embedding space through projection matrices [11]. Smith et al. [48] introduced an approach for debiasing VLMs using synthetically-constructed contrast sets, which they use to produce 7946 image-text pairs for gender bias. However, all + +of these prior works focus exclusively on debiasing models for a single social attribute at a time (e.g., gender) as opposed to our focus on debiasing for intersectional biases. + +# 3. Generating SocialCounterfactuals + +Our approach to creating counterfactual image-text examples for intersectional social biases consists of three steps. First, we construct sets of image captions describing a subject with counterfactual changes to intersecting social attributes. We then utilize a text-to-image diffusion model with cross attention control to over-generate sets of images corresponding to the counterfactual captions, where differences among images are isolated to the induced counterfactual change (i.e., the social attributes). Finally, we apply stringent filtering to identify only the highest-quality generations. + +# 3.1. Terminology + +In this work, we do not make any claims regarding gender identification or gender assignment, which we acknowledge to be unique to each individual regardless of their appearance or traits. We use perceived gender as an inference made by a human annotator or model. We acknowledge that labels used in this study may differ from an individual's gender identity and could also vary based on different annotators' interpretations. We recognize that gender and gender identity is fluid and misjudgements in a binary paradigm could arise. + +Similarly, we acknowledge that the six races we discuss in this paper - White, Black, Indian, Asian, Middle Eastern and Latino, are not representative of all races. We inherit this list of races from prior work [29]. Any inference or reference to race and occupation is considered to be perceived race and perceived occupation (respectively), and does not aim to associate any bias with any groups of individuals. + +# 3.2. Constructing captions for probing social biases + +Consider the task of creating a caption $C_{p,a_1,a_2}^s$ beginning with prefix $p$ and describing a subject $s$ which possesses a pair of attributes $a_1$ and $a_2^3$ . Given a set of prefixes $P$ , a set of subjects $S$ , and attribute sets $A_1, A_2, \ldots, A_k$ , we populate the following template to obtain our captions: + +$$ +\begin{array}{l} C _ {p, a _ {1}, a _ {2}} ^ {s} = < p > < a _ {1} > < a _ {2} > < s > \\ \forall p \in P, s \in S, a _ {1} \in A _ {i}, a _ {2} \in A _ {j}, (i, j) \in \{1, \dots , k \mid i \neq j \} \\ \end{array} +$$ + +For example, given the prefix $A$ photo of $a$ , the subject doctor, and attribute pair (Asian, Female), we construct the caption $A$ photo of an Asian female doctor. We construct captions in this manner using a set of occupations as our subjects and three sets of attributes for measuring social bias (gender, race, and physical characteristics). Captions are grouped into counterfactual sets, where each set contains all captions + +corresponding to a given prefix and subject. Using 260 occupations, 4 prefixes, 6 races, and 5 physical characteristics, and 2 gender terms $^{4}$ , we produced a total of 54,080 captions which were grouped into 3,120 counterfactual sets (see Section 8.4 of Supp. Material for additional details and examples). While we categorize these social attributes with the aim of probing biases, we recognize the limitations inherent to this process and acknowledge that attributes such as gender and race are not considered by all individuals to exist as discrete categories (see Section 6 for additional discussion). + +# 3.3. Counterfactual image generation + +After generating sets of counterfactual captions, we use text-to-image diffusion models to produce images for each caption. In order to precisely measure the impact of social attribute differences, it is desirable for images within a counterfactual set to only differ in how the social attributes differ across captions. However, this is challenging for diffusion models as even minor changes to a prompt can result in the generation of images with significant differences. For example, changing the attributes Hispanic female to Asian male in the prompt A photo of a Hispanic female doctor may produce other undesired modifications to the image that extend beyond the induced counterfactual change (e.g., changes to the background). This complicates the task of quantifying the impact of model bias attributed to the changed social attributes on retrieval results, as other differences between the generated images could contribute to a VLM's preference for retrieving particular images. + +Hertz et al. [25] proposed Prompt-to-Prompt to address this issue by injecting cross-attention maps during denoising steps to control attention between certain pixels and tokens, which enables separate generations to maintain many of the same details while isolating differences to how the text prompts differ. However, Brooks et al. [7] noted that some changes require varying the parameter $p$ in Prompt-to-Prompt, which controls the number of denoising steps with shared attention weights. For example, changes that require more substantial structural modifications to the image may necessitate less overall similarity between the resulting images and thus fewer shared attention weights. We therefore adopt their proposed approach of over-generating 100 image pairs with Prompt-to-Prompt by sampling $p \sim U(0.1, 0.9)$ , which we then subsequently filter to retain only the highest-quality generated candidates (Section 3.4). + +We extend Prompt-to-Prompt for image pairs from Brooks et al. [7] to support batched generation of multiple images with cross attention control. This enables simultaneous generation of entire sets of counterfactual images which differ only according to the social attribute differences across prompts (e.g., Figure 1). In total, we over-generate + +![](images/07779d06a8bb004c9b8cc16c96775f464423fe3cefb2ba2ba3dc76a92ef72c92.jpg) +Figure 2. Overview of our methodology for generating SocialCounterfactuals. + +5,408,000 images for 54,080 captions. + +# 3.4. Three-Stage Filtering + +CLIP image-text similarity filtering. After over-generating 100 candidate image sets for each of our templates, we first filter the candidates using CLIP [41] to ensure a minimum cosine similarity of 0.2 between the encoding of each caption and its corresponding generated image. We also apply a similar filtering criteria between pairs of images in each set, requiring the cosine similarity of CLIP image encodings within the set to be greater than 0.2. These filtering criteria help ensure that images accurately depict the subjects described in each caption while also retaining a high-degree of similarity to each other, thereby ensuring that they represent valid counterfactual examples. + +NSFW Filtering with ViT. Manual examination of generated images revealed instances of not-safe-for-work (NSFW) content. We therefore applied a NSFW filter which uses a fine-tuned vision transformer (ViT) for NSFW image classification. This filter removes $0.9 - 2.7\%$ of generated images (see Table 11 in Supplementary Material for details). + +CLIP Attribute Detectability Filtering. To further ensure data quality, we filter counterfactual sets based on CLIP's ability to discern targeted social attributes in each image using a two-phase approach (see Section 8.3 in Supp. Material for additional details). In the first phase, we randomly sampled 100 counterfactual sets for each pair of attribute types. For each attribute type, we then manually labeled the sampled counterfactual sets according to whether or not they should be filtered out based on a lack of detectability of the targeted attribute. Specifically, we label how many images in a counterfactual set possess their targeted attribute. + +In the second phase, we develop a learnable threshold-based heuristics to automatically label whether a counterfactual set should be filtered with respect to an individual + +
Attribute PairCounterfactual SetsImages Per SetTotal Images
(Race, Gender)7,9361295,232
(Physical Char., Gender)5,0521050,520
(Physical Char., Race)8363025,080
+ +Table 1. Details of the number of counterfactual sets, images per set, and total images which remain in our dataset after filtering + +attribute type. These threshold-based heuristics are applied according to how many of a set's constituent images have their respective targeted attributes discernible by CLIP-based image-text similarity scores (rather than by a human annotator). Thresholds were heuristically derived to obtain high correspondence between automatic filtering with CLIP and those filtered by the manual human annotation. This process produces a separate learned threshold for each attribute type and attribute type pair combination. A counterfactual set is filtered out due to a lack of detectability for an attribute type if the number of its constituent images whose corresponding targeted attribute is discernible by CLIP is less than the corresponding learned threshold. + +To estimate the quality of our generated dataset and the impact of filtering, we randomly sampled 100 counterfactual sets depicting Race-Gender intersectional social attributes. Prior to CLIP attribute detectability filtering, we found that $90.8\%$ of the images accurately depicted their corresponding captions. Applying attribute detectability filtering further increases this figure to $97.5\%$ , which demonstrates the value of our filtering methodology and the high quality it ensures in our dataset (see Section 7.2 of Supp. Material for details). + +Table 1 provides details on the total number of counterfactual sets and images which remain in our dataset after filtering. We group counterfactual sets into three dataset segments based on the pair of attribute types used to construct the captions, which are detailed in each row of Table 1. In total, our dataset consists of 13,824 counterfactual sets with 170,832 image-text pairs, which represents the largest paired image-text dataset for investigating social biases to-date. + +# 4. Probing Intersectional Biases + +To probe intersectional social biases in VLMs, we calculate MaxSkew over our dataset. We describe this metric in Section 4.1 and detail our evaluation results in Section 4.2. + +# 4.1. Evaluation Metrics + +Let $q$ denote a text query and $R_{K}(q)$ denote the set of top- $K$ ranked images retrieved by a VLM for $q$ . For a given attribute pair $(a_{i},a_{j})$ , we denote the desired proportion $d$ of retrieved images with the corresponding attributes as $p_{d(q),(a_i,a_j)}$ and the actual proportion as $p_{R_K(q),(a_i,a_j)}$ . Geyik et al. [20] define Skew@ $K$ for attributes $(a_{i},a_{j})$ in retrieval results $R_{K}(q)$ as: + +$$ +\operatorname {S k e w} _ {(a _ {i}, a _ {j})} @ K (R _ {K} (q)) = \log \left(\frac {p _ {R _ {K} (q) , (a _ {i} , a _ {j})}}{p _ {d (q) , (a _ {i} , a _ {j})}}\right) +$$ + +In essence, Skew@K measures the ratio of the proportion of top-K retrieved images having a set of attributes to the desired proportion. To aggregate Skew@K over the various attributes under consideration, Geyik et al. [20] further proposed the following MaxSkew@K metric: + +$\operatorname{MaxSkerw} @ K(R_K(q)) = \max_{(a_i, a_j) \in A} \operatorname{Skerw}_{(a_i, a_j)} @ K(R_K(q))$ + +where $A$ denotes the set of all attribute pairs. We calculate MaxSkew@ $K$ by retrieving images from our counterfactual sets using prompts which are neutral with respect to the investigated attributes. For example, given a prompt constructed from the template "A construction worker" (Figure 1), we form its corresponding attribute-neutral prompt "A construction worker." + +We construct neutral prompts in this manner for each unique combination of prefixes and subjects, averaging their text representations across different prefixes to obtain a single text embedding for each subject. Skew@ $K$ and MaxSkew@ $K$ are then calculated by retrieving the top- $K$ images for the computed text embedding from the set of all images generated for the subject which met our filtering and selection criteria. We set $K = |A_1| \times |A_2|$ , where $A_1$ and $A_2$ are the investigated attribute sets. + +# 4.2. Results + +Figure 3 provides boxplots of the intersectional bias MaxSkew@K distribution for six state-of-the-art VLMs: ALIP [59], CLIP [41], FLAVA [46], LaCLIP [14], OpenCLIP [9], and SLIP [36]. We measure the MaxSkew@K distribution across occupations separately using the three segments of our dataset for Race-Gender (Figure 6a), Physical Characteristics-Gender (Figure 6b), and Physical Characteristics-Race (Figure 6c) intersectional biases. + +All six evaluated VLMs exhibit significant skewness in retrieval for attribute-neutral occupation prompts, with CLIP and FLAVA having the lowest overall MaxSkew@K. Among the three segments of our dataset, Physical Characteristics-Gender intersectional biases tend to have lower MaxSkew@K scores while Race-Gender intersectional biases have the greatest amount of skewness. + +In addition to illustrating the overall distribution of MaxSkew@K across occupations, the boxplots in Figure 3 also provides the occupation names for minimum values (green circles) and maximum values (red circles). These labels show some commonalities across models, such as FLAVA and LaCLIP both having their greatest Race-Gender MaxSkew@K values for the 'Makeup Artist' profession. We also observe that LaCLIP and OpenCLIP have their greatest skewness in retrieval from the Physical Characteristics-Race segment for the 'Barber' occupation. Notably, both CLIP and FLAVA have multiple occupations with zero skewness across all segments of the dataset, while SLIP has no occupations with zero skewness across the three segments. + +Our dataset can also be used to evaluate individual (i.e., marginal) bias for a specific attribute type by filtering on the value of the other attribute depicted in a counterfactual set. MaxSkew@ $K$ can then be calculated as previously described to estimate bias in retrieval results for a single social attribute at a time. To illustrate, we estimated the marginal gender bias across occupations using images specific to each race, which we provide in Figure 4. All VLMs exhibit variation in gender bias across different races, highlighting the importance of measuring bias in the presence of other social attributes. While CLIP has lower overall skewness than other evaluated models, it also has the greatest disparity in MaxSkew@ $K$ across different races; specifically, CLIP exhibits nearly 2x more gender skewness for images depicting Indian subjects than it does for Latinos. Interestingly, both CLIP and FLAVA exhibit the greatest gender bias in retrieving images depicting Indian people, while SLIP and ALIP exhibit the greatest gender bias for Middle Eastern people. + +As a further case study in uncovering intersectional social biases in VLMs, Figure 5 provides a breakdown of the proportion of images retrieved using gender- and race-neutral prompts for the 'Doctor' occupation. The left and center plots of Figure 5 depict the marginal distributions of retrievals for each race and gender (respectively), whereas the right plot provides the distribution of retrieved images for intersectional race-gender attributes. While SLIP, OpenCLIP, LaCLIP, and ALIP exhibit strong bias for retrieving male images, this gender bias occurs along starkly different dimensions with respect to race. OpenCLIP strongly favors retrieving images of Asian male doctors when presented with a neutral text prompt, whereas the other three models prefer to retrieve images of Indian male doctors. This gender bias is inverted for CLIP, which retrieves images of women + +![](images/e5742b5e59b3852358005e5c64b1c043ff87b9a5910b5921c3873a7d9de96b2a.jpg) +(a) Race-Gender + +![](images/48842e4790a61fe593183fcdfe41690b2e2bfd2f7ab6e4c8820a460d402156ef.jpg) +(b) Physical Characteristics-Gender + +![](images/94eaa0990547591496ff7b4133955a17ac2a2f226d93a5b8e4b699815b8c1ce7.jpg) +(c) Physical Characteristics-Race + +![](images/223d9d682ba4c9ad5de21ef494055bcc0a0af0a835240899f1a245a690c7ca02.jpg) +Figure 3. Distribution of MaxSkew@ $K$ measured across occupations for (a) Race-Gender, (b) Physical Characteristics-Gender, and (c) Physical Characteristics-Race intersectional biases. Max (min) values are plotted as red (green) circles with corresponding occupation names +Figure 4. Mean of (marginal) gender MaxSkew@ $K$ measured across occupations for different races. + +in a slightly higher proportion than men, but still has zero representation of certain groups (e.g., Black females). These results show that seemingly similar biases among pre-trained VLMs for social attributes such as gender can interact very differently with other attributes such as race, which highlights the importance of studying bias in the presence of intersectional social attributes. + +# 5. Mitigating Intersectional Biases + +We investigate the suitability of our SocialCounterfactuals dataset for debiasing VLMs through additional training. + +# 5.1. Training Experiment Setting + +For each of the three segments of our dataset (see Table 1), we withhold counterfactual sets associated with $20\%$ of the occupation subjects for testing and use the remainder as a training dataset. We then separately finetune ALIP, CLIP, and FLAVA on each of these three training datasets, which we hereafter refer to as the 'debiased' variants of these mod- + +els. To estimate the magnitude of debiasing, we evaluate each model's MaxSkew@K for intersectional bias using the withheld testing dataset containing $20\%$ of the occupations. + +# 5.2. Results for Intersectional Social Biases + +Table 2 provides the mean MaxSkew@ $K$ calculated over our withheld test sets for pre-trained and debiased variants of CLIP, ALIP, and FLAVA. Training on our dataset has the greatest overall debiasing effect on ALIP, producing up to a 0.426 absolute reduction in MaxSkew@ $K$ . Among the three segments of our dataset used for debiasing, MaxSkew@ $K$ for (Physical Char., Race) intersectional bias has the greatest amount of skewness in pre-trained models. However, training on our dataset also produces the greatest absolute reduction in skewness for this type of intersectional bias, with CLIP having an absolute reduction in MaxSkew@ $K$ of 0.327 for (Physical Char., Race) intersectional biases. + +These results show that training VLMs with our dataset produces significant debiasing effects across all three types of intersectional biases. Furthermore, the strongest intersectional biases observed in pre-trained VLMs benefit the most from debiasing. Remarkably, these debiasing effects are observed despite there being no overlap between the occupations used for training and testing, which demonstrates that the debiasing effects generalize to new subjects not seen during training. This suggests that the ability of our dataset to mitigate intersectional bias in VLMs is not limited to only the occupation subjects that we investigated. + +# 5.3. Analysis of Race-Gender Debiased CLIP Model + +To further understand the impact of training VLMs using our synthetic counterfactuals, we conduct analyses of CLIP after debiasing for Race-Gender intersectional bias. For simplicity, we hereafter refer to this model as Debiased CLIP. + +Skewness evaluation using other datasets with real image-text pairs. Since our dataset was synthetically generated, + +![](images/eb4e12870aab81b4b91a95de413e33f0f6251856969c66fbc0142fa7792b9499.jpg) +Asian +Black +Indian +Latino +White + +![](images/94fbad2eb547f84aebd9dd39496bf8d5687bad5800cac51c67e4ccd99e26f70f.jpg) +Middle Eastern +Figure 5. Proportion of images retrieved $@k = 12$ using neutral prompts for the 'Doctor' occupation. + +![](images/ad10c417f4def69ab974a5a37d20d7864a5e407266558df0d2d205e77a0185a2.jpg) + +![](images/9ad470fca11670b86ce7d28da121e415a6aa1aa522fd6d1b204456573a248031.jpg) + +
Intersectional BiasCLIP [41]ALIP [59]FLAVA [46]
Pre-trainedDebiasedPre-trainedDebiasedPre-trainedDebiased
(Race, Gender)1.020.771.401.160.980.79
(Physical Char., Gender)0.870.711.281.020.920.81
(Physical Char., Race)1.190.871.551.131.120.97
+ +a natural question to ask is how well our observed debiasing effects extend to evaluations with real image-text pairs. Unfortunately, there are no such existing resources for measuring the intersectional social biases that we investigate in this work. However, several real image-text datasets have been proposed for evaluating (marginal) social biases for attributes such as perceived race and gender. + +To evaluate our Debiased CLIP model on such datasets, we use the Protected-Attribute Tag Association (PATA) dataset introduced in [45] for nuanced reporting of biases associated with race, age, and gender protected attributes. The PATA dataset comprises of 4,934 public images organized in 24 scenes, where the scenes represent situations in which certain groups of humans may have biases associated with them. The images are annotated with binary gender (male, female), ethnic-race labels (White, Black, Indian, East Asian, Latino-Hispanic) and two age groups (young and old). We also evaluate our Debiased CLIP model on the VisoGender dataset [23], which was curated to benchmark gender bias in image-text pronoun resolution. VisoGender consists of 690 images of people in 23 unique occupational settings.[8] + +Table 3 provides the mean MaxSkew@ $K$ of our Debiased CLIP model on these two datasets. Despite only being + +Table 2. Mean of MaxSkew@ $K$ for pre-trained and debiased variants of CLIP, ALIP, and FLAVA, estimated by withholding counterfactual sets for $20\%$ of the occupations in our dataset. Best results are in bold. + +
ModelVisoGender [23]PATA [45]
Pre-trained CLIP0.2690.323
Debiased CLIP0.2190.283
+ +Table 3. MaxSkew@ $K$ of our debiased CLIP model as well as pre-trained CLIP on the VisoGender [23] and PATA [45] datasets. + +trained for mitigating intersectional bias using synthetic examples, our Debiased CLIP model achieves a $15\%$ and $12\%$ relative reductions in skewness when measured using real image-text examples from VisoGender and PATA (respectively). Both models have much lower MaxSkew@ $K$ for these datasets than for SocialCounterfactuals, which demonstrates how our dataset reveals significantly more skewness in retrieval results than existing single-attribute datasets. + +Impact of debiasing on task-specific performance. An important question for practitioners seeking to debias VLMs is the extent to which debiasing degrades the performance of the model on other tasks. As described previously in Section 1, social biases can be viewed as a type of spurious correlation which models learn as shortcuts to achieving high performance on training datasets. Consequently, it is expected that eliminating these shortcuts may degrade the + +
CLIP ModelText RetrievalImage Retrieval
R@1R@5R@10R@1R@5R@10
Pre-trained67.18993.869.490.694.9
Debiased69.289.693.867.390.493.8
+ +Table 4. Image & text retrieval performance of Debiased CLIP and pre-trained CLIP on Flickr30K[61]. Debiasing CLIP with our dataset results in improved performance on text retrieval and only minimal performance degradation on image retrieval. + +
CLIP ModelCIFAR10[32]CIFAR100[32]Caltech256[21]ImageNet[12]
Pre-trained88.8064.1783.4359.25
Debiased86.7261.4679.7255.38
+ +Table 5. Accuracy of our debiased CLIP model as well as pretrained CLIP on zero-shot image recognition datasets. Debiasing CLIP with our dataset results in minimal performance degradation. + +performance of the model on other tasks to some extent. + +We estimate the magnitude of this impact by evaluating our Debiased CLIP model on image-text retrieval and zero-shot image recognition tasks. Table 4 provides the text retrieval and image retrieval performance of both pretrained CLIP and our Debiased CLIP on Flickr30K. We observe that our Debiased CLIP model achieves equivalent or better performance across all three text retrieval settings compared to pre-trained CLIP. In the image retrieval settings, our Debiased CLIP model exhibits a minor degradation in performance compared to pre-trained CLIP. + +Table 5 measures the accuracy of pre-trained CLIP and our Debiased CLIP model on zero-shot image recognition datasets. Similar to the image retrieval evaluation, our Debiased CLIP model exhibits a minor degradation in accuracy on these datasets. These performance reductions are similar in magnitude to those observed in prior work on debiasing CLIP [45] and characterize the trade-off between model fairness and absolute performance inherent to debiasing efforts. + +Depending on the intended use case, the benefits of reducing skewness in the retrieval results of VLMs may be far more valuable than the relatively small decrease in performance observed in debiased models. Additionally, these results were obtained without any tuning of the training process for balancing task-specific performance with debiasing efforts. We hypothesize that additional attention to these task-specific performance measures during training, as well as other strategies such as mixing real data with our counterfactual examples, may produce a different balance between model debiasing and task-specific performance. + +# 6. Conclusion + +In this work, we presented a methodology for automatically generating counterfactual examples for probing and mitigating intersectional bias in VLMs. We used our approach to construct SocialCounterfactuals, a large dataset of image-text counterfactuals depicting intersectional social attributes related to gender, race, and physical characteristics for various occupations. Our evaluations of six pre-trained VLMs showed that all exhibit significant intersectional social biases in retrieval results, with substantial variation in retrieval skewness across differing racial and gender attributes. Through training experiments, we further demonstrated that SocialCounterfactuals can be a valuable resource for mitigating skewness in VLMs. A promising direction for future work could be extending our approach to investigate intersectional social biases in VLMs for other attributes and subjects. Our SocialCounterfactuals dataset could also be a valuable resource for reducing bias in generative text-to-image diffusion models. Finally, alternative training strategies for debiasing VLMs with synthetic counterfactuals could be explored to balance bias mitigation with task-specific performance measures. + +Limitations and Ethical Considerations Despite our best efforts, the templates and methodologies we adopt may themselves contain some latent biases which could contribute to the implicit biases exhibited by VLMs. All statements pertaining to gender, race, and occupational attributes or associations should be interpreted only within the context of our experiments. Furthermore, all discussion of social attributes in this work are intended to be interpreted as perceived. We are aware that our approach only considers binary classification of genders and does not exhaustively encompass all races, physical characteristics, and occupations, which is due to data limitation rather than our value judgements. + +With the findings we present in this paper, we aim to increase the understanding of bias in VLMs and probe mitigation strategies. We acknowledge that our work does not encompass all possible social attributes and that our selected categories for gender, race, physical characteristics, and occupations may harbor stereotypes that cannot be assumed to represent their entire groups. Our aim is that the techniques presented in this work can help reduce various social disparities in VLMs and can be further extended to include more genders, races, occupations and other social characteristics. Continuing these efforts will increase confidence in the ability of VLMs to exhibit fairness with respect to differing social attributes. 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Transactions of the Association for Computational Linguistics, 2:67-78, 2014. 8 +[62] Michael Zhang and Christopher Ré. Contrastive adapters for foundation model group robustness. Advances in Neural Information Processing Systems, 35:21682-21697, 2022. 2 +[63] Dora Zhao, Angelina Wang, and Olga Russakovsky. Understanding and evaluating racial biases in image captioning. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 14830-14840, 2021. 1 +[64] Jieyu Zhao, Tianlu Wang, Mark Yatskar, Vicente Ordonez, and Kai-Wei Chang. Gender bias in coreference resolution: Evaluation and debiasing methods. arXiv preprint arXiv:1804.06876, 2018. 2 +[65] Kankan Zhou, Yibin LAI, and Jing Jiang. Vlstereoset: A study of stereotypical bias in pre-trained vision-language models. 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Prior studies have primarily focused on probing such bias attributes individually while ignoring biases associated with intersections between social attributes. This could be due to the difficulty of collecting an exhaustive set of image-text pairs for various combinations of social attributes. To address this challenge, we employ text-to-image diffusion models to produce counterfactual examples for probing intersectional social biases at scale. Our approach utilizes Stable Diffusion with cross attention control to produce sets of counterfactual image-text pairs that are highly similar in their depiction of a subject (e.g., a given occupation) while differing only in their depiction of intersectional social attributes (e.g., race & gender). Through our over-generate-then-filter methodology, we produce SocialCounterfactuals, a high-quality dataset containing 171k image-text pairs for probing intersectional biases related to gender, race, and physical characteristics. We conduct extensive experiments to demonstrate the usefulness of our generated dataset for probing and mitigating intersectional social biases in state-of-the-art VLMs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 128, + 621 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 714 + ], + "type": "text", + "content": "Counterfactual examples, which study the impact on a response variable following a change to a causal feature, have proven valuable in natural language processing (NLP) for probing model biases and improving robustness to spurious correlation [16, 18, 26, 30, 54, 57, 60]. While counterfactual examples for VLMs have been relatively unexplored, recent work [33] has shown that text-to-image diffusion models" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 274, + 548, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 548, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 548, + 334 + ], + "type": "text", + "content": "with cross attention control can effectively produce multimodal counterfactual examples for VLM training, data augmentation and evaluation. This suggests that synthetic counterfactual examples generated by diffusion models could be an effective tool for probing and mitigating biases in VLMs." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 336, + 548, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 548, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 548, + 433 + ], + "type": "text", + "content": "Bias in pre-trained models can be viewed as spurious correlations, which are often attributed to the co-occurrence of non-causal (i.e., spurious) features with labels in datasets. During pre-training, models learn to exploit such correlations as shortcuts to achieving high in-domain performance on the training dataset [19]. Consequently, models which learn to rely on spurious correlations are more brittle and have worse out-of-domain (OOD) generalization [47, 58]." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 435, + 548, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 435, + 548, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 435, + 548, + 555 + ], + "type": "text", + "content": "Social biases are a particularly concerning type of spurious correlation learned by VLMs. Due to a lack of proportional representation for people of various races, genders, and other social attributes in image-text datasets [5, 17, 63], VLMs learn biased associations between these attributes and various subjects (e.g., occupations). For example, given a gender- and race-neutral query such as \"A photo of an attorney\", a VLM may retrieve a disproportionate number of images of one particular race due to learned spurious correlations between this specific occupation and race." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 558, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 548, + 714 + ], + "type": "text", + "content": "Prior studies on probing social biases in VLMs [22-24, 28, 65] have primarily utilized real image-text pairs collected from existing datasets by identifying the cooccurrence of certain attributes with a target subject. However, this approach is limited by the availability of existing image-text pairs for various combinations of social attributes and subject types. Consequently, these prior studies have focused exclusively on investigating biases associated with a single social attribute at a time while ignoring the potential role of intersectional bias (e.g., particular race-gender combinations) [40], which could be attributed to the difficulty of collecting an exhaustive set of image-text examples for various combinations of social attributes. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11975" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 130, + 152 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 130, + 152 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 130, + 152 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 130, + 152 + ], + "type": "image", + "image_path": "d5fe8c34870311a0384fc93ef571a69e032398b0f4e9b41ec6ff2b17ca9ec9ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 57, + 152, + 125, + 168 + ], + "lines": [ + { + "bbox": [ + 57, + 152, + 125, + 168 + ], + "spans": [ + { + "bbox": [ + 57, + 152, + 125, + 168 + ], + "type": "text", + "content": "A White male construction worker" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 179, + 547, + 202 + ], + "lines": [ + { + "bbox": [ + 46, + 179, + 547, + 202 + ], + "spans": [ + { + "bbox": [ + 46, + 179, + 547, + 202 + ], + "type": "text", + "content": "Figure 1. Examples of our counterfactual image-text pairs for probing intersectional race-gender bias in VLMs for the \"construction worker\" occupation. 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Specifically, our approach utilizes Stable Diffusion [42] with cross-attention control [25] to produce a set of highly similar counterfactual image-text examples which depict a common subject while differing only in intersectoral social attributes. Text-to-image diffusion models are particularly well-suited for this task due to their ability to generate depictions of specific subjects with various combinations of different social attributes, which might be rare or missing from existing image-text datasets. After generating candidate images, we apply three stages of filtering to ensure that only the highest-quality counterfactuals are retained." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 451, + 288, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 451, + 288, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 451, + 288, + 606 + ], + "type": "text", + "content": "We apply our methodology at scale to produce Social-Counterfactuals, an extensive dataset containing over 171k counterfactual image-text pairs for probing intersectional biases related to race, gender, and physical characteristics. To the best of our knowledge, SocialCounterfactuals is the largest resource released to-date for probing bias in VLMs and the only one which considers intersectional biases. Through extensive evaluation of six VLMs, we demonstrate its usefulness for uncovering intersectional social biases. Additionally, we conduct VLM training experiments using our dataset which demonstrate its ability to reduce skewness in retrieval results for social attributes. We make our dataset1 and code2 publicly available." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 616, + 134, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 134, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 134, + 628 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 636, + 233, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 636, + 233, + 649 + ], + "spans": [ + { + "bbox": [ + 47, + 636, + 233, + 649 + ], + "type": "text", + "content": "2.1. Probing bias in pre-trained models" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 654, + 288, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 679 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 679 + ], + "type": "text", + "content": "Much of the prior work on probing social bias in pre-trained models has focused exclusively on language models, pro" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 223, + 546, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 223, + 546, + 331 + ], + "spans": [ + { + "bbox": [ + 306, + 223, + 546, + 331 + ], + "type": "text", + "content": "ducing multiple datasets for measuring stereotypical bias along different social attributes, categories, demographic axes and stigmatized groups [35, 37, 39, 49]. Gender biases associated with pronoun and coreferences have also been extensively studied [8, 43, 56, 64]. Some prior work has addressed topics related to intersectionality in bias evaluations [31, 50, 51]. Additionally, various approaches for bias detection and mitigation for vision-only models have been proposed [1, 6, 13, 27, 55]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 333, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 333, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 333, + 547, + 548 + ], + "type": "text", + "content": "Approaches to generate synthetic datasets with fairness have been explored [2, 4, 15, 34, 44]. For probing biases in VLMs, VLStereoSet [65] extends the StereoSet dataset to the vision domain by sourcing images from Google search and using crowdsourced workers for annotation, resulting in a total of 1028 images. VisoGender [23] consists of 690 manually-annotated images for benchmarking occupation-related gender bias in VLMs. The MultiModal Bias dataset [28] evaluates bias in VLMs across 14 population subgroups and contains a total of 3800 human-annotated images obtained from Flickr. These datasets differ from ours primarily in their much smaller scale, their reliance on collection of data from existing sources & human annotation, and their focus on investigating only a single attribute at a time (as opposed to our investigation of intersectional biases). Bias in VLMs used for text-to-image generation have also been investigated [10, 38, 53], but such studies differ from our focus on bias in image-text retrieval settings." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 562, + 500, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 562, + 500, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 562, + 500, + 574 + ], + "type": "text", + "content": "2.2. Mitigating bias in pre-trained VLMs" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "A variety of methods have been proposed for mitigating the biases observed in pre-trained VLMs. These include adversarial approaches for prompt learning [3], fair sampling methods for reducing bias learned during training [52], contrastive learning techniques for improving group robustness [62], learning additive residuals to offset image representations [45], and eliminating biased directions in the text embedding space through projection matrices [11]. Smith et al. [48] introduced an approach for debiasing VLMs using synthetically-constructed contrast sets, which they use to produce 7946 image-text pairs for gender bias. However, all" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 685, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 685, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 685, + 287, + 713 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 47, + 685, + 287, + 713 + ], + "type": "text", + "content": "Our dataset is available at https://huggingface.co/datasets/Intel/SocialCounterfactuals \n" + }, + { + "bbox": [ + 47, + 685, + 287, + 713 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 47, + 685, + 287, + 713 + ], + "type": "text", + "content": "Our code is available at our GitHub repository" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11976" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 109 + ], + "type": "text", + "content": "of these prior works focus exclusively on debiasing models for a single social attribute at a time (e.g., gender) as opposed to our focus on debiasing for intersectional biases." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 119, + 237, + 133 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 119, + 237, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 119, + 237, + 133 + ], + "type": "text", + "content": "3. Generating SocialCounterfactuals" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 140, + 289, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 140, + 289, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 289, + 260 + ], + "type": "text", + "content": "Our approach to creating counterfactual image-text examples for intersectional social biases consists of three steps. First, we construct sets of image captions describing a subject with counterfactual changes to intersecting social attributes. We then utilize a text-to-image diffusion model with cross attention control to over-generate sets of images corresponding to the counterfactual captions, where differences among images are isolated to the induced counterfactual change (i.e., the social attributes). Finally, we apply stringent filtering to identify only the highest-quality generations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 267, + 129, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 267, + 129, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 267, + 129, + 280 + ], + "type": "text", + "content": "3.1. Terminology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 285, + 287, + 393 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 393 + ], + "type": "text", + "content": "In this work, we do not make any claims regarding gender identification or gender assignment, which we acknowledge to be unique to each individual regardless of their appearance or traits. We use perceived gender as an inference made by a human annotator or model. We acknowledge that labels used in this study may differ from an individual's gender identity and could also vary based on different annotators' interpretations. We recognize that gender and gender identity is fluid and misjudgements in a binary paradigm could arise." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 393, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 287, + 477 + ], + "type": "text", + "content": "Similarly, we acknowledge that the six races we discuss in this paper - White, Black, Indian, Asian, Middle Eastern and Latino, are not representative of all races. We inherit this list of races from prior work [29]. Any inference or reference to race and occupation is considered to be perceived race and perceived occupation (respectively), and does not aim to associate any bias with any groups of individuals." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 485, + 287, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 485, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 485, + 287, + 498 + ], + "type": "text", + "content": "3.2. Constructing captions for probing social biases" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": "Consider the task of creating a caption " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "C_{p,a_1,a_2}^s" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": " beginning with prefix " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": " and describing a subject " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": " which possesses a pair of attributes " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "a_1" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "a_2^3" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": ". Given a set of prefixes " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": ", a set of subjects " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": ", and attribute sets " + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "inline_equation", + "content": "A_1, A_2, \\ldots, A_k" + }, + { + "bbox": [ + 46, + 503, + 287, + 564 + ], + "type": "text", + "content": ", we populate the following template to obtain our captions:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 573, + 289, + 602 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 289, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 289, + 602 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} C _ {p, a _ {1}, a _ {2}} ^ {s} = < p > < a _ {1} > < a _ {2} > < s > \\\\ \\forall p \\in P, s \\in S, a _ {1} \\in A _ {i}, a _ {2} \\in A _ {j}, (i, j) \\in \\{1, \\dots , k \\mid i \\neq j \\} \\\\ \\end{array}", + "image_path": "4b67f109c0f0a2717cd487957ec55991b8732a7a9db3c8822291d61f4ef55fae.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "text", + "content": "For example, given the prefix " + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "text", + "content": " photo of " + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "text", + "content": ", the subject doctor, and attribute pair (Asian, Female), we construct the caption " + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 611, + 288, + 696 + ], + "type": "text", + "content": " photo of an Asian female doctor. We construct captions in this manner using a set of occupations as our subjects and three sets of attributes for measuring social bias (gender, race, and physical characteristics). Captions are grouped into counterfactual sets, where each set contains all captions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 547, + 193 + ], + "type": "text", + "content": "corresponding to a given prefix and subject. Using 260 occupations, 4 prefixes, 6 races, and 5 physical characteristics, and 2 gender terms" + }, + { + "bbox": [ + 306, + 72, + 547, + 193 + ], + "type": "inline_equation", + "content": "^{4}" + }, + { + "bbox": [ + 306, + 72, + 547, + 193 + ], + "type": "text", + "content": ", we produced a total of 54,080 captions which were grouped into 3,120 counterfactual sets (see Section 8.4 of Supp. Material for additional details and examples). While we categorize these social attributes with the aim of probing biases, we recognize the limitations inherent to this process and acknowledge that attributes such as gender and race are not considered by all individuals to exist as discrete categories (see Section 6 for additional discussion)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 200, + 484, + 213 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 200, + 484, + 213 + ], + "spans": [ + { + "bbox": [ + 306, + 200, + 484, + 213 + ], + "type": "text", + "content": "3.3. Counterfactual image generation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 218, + 547, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 218, + 547, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 218, + 547, + 422 + ], + "type": "text", + "content": "After generating sets of counterfactual captions, we use text-to-image diffusion models to produce images for each caption. In order to precisely measure the impact of social attribute differences, it is desirable for images within a counterfactual set to only differ in how the social attributes differ across captions. However, this is challenging for diffusion models as even minor changes to a prompt can result in the generation of images with significant differences. For example, changing the attributes Hispanic female to Asian male in the prompt A photo of a Hispanic female doctor may produce other undesired modifications to the image that extend beyond the induced counterfactual change (e.g., changes to the background). This complicates the task of quantifying the impact of model bias attributed to the changed social attributes on retrieval results, as other differences between the generated images could contribute to a VLM's preference for retrieving particular images." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "type": "text", + "content": "Hertz et al. [25] proposed Prompt-to-Prompt to address this issue by injecting cross-attention maps during denoising steps to control attention between certain pixels and tokens, which enables separate generations to maintain many of the same details while isolating differences to how the text prompts differ. However, Brooks et al. [7] noted that some changes require varying the parameter " + }, + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "type": "text", + "content": " in Prompt-to-Prompt, which controls the number of denoising steps with shared attention weights. For example, changes that require more substantial structural modifications to the image may necessitate less overall similarity between the resulting images and thus fewer shared attention weights. We therefore adopt their proposed approach of over-generating 100 image pairs with Prompt-to-Prompt by sampling " + }, + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "type": "inline_equation", + "content": "p \\sim U(0.1, 0.9)" + }, + { + "bbox": [ + 305, + 422, + 547, + 613 + ], + "type": "text", + "content": ", which we then subsequently filter to retain only the highest-quality generated candidates (Section 3.4)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 613, + 547, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 613, + 547, + 686 + ], + "spans": [ + { + "bbox": [ + 305, + 613, + 547, + 686 + ], + "type": "text", + "content": "We extend Prompt-to-Prompt for image pairs from Brooks et al. [7] to support batched generation of multiple images with cross attention control. This enables simultaneous generation of entire sets of counterfactual images which differ only according to the social attribute differences across prompts (e.g., Figure 1). In total, we over-generate" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 288, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 288, + 712 + ], + "type": "text", + "content": "3See Section 10.2 for discussion of extension to more than two attributes" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "4We also explored the generation of other subjects and social attributes with our method. See Section 7.4 of Supplementary Material for details." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11977" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 80, + 541, + 198 + ], + "blocks": [ + { + "bbox": [ + 52, + 80, + 541, + 198 + ], + "lines": [ + { + "bbox": [ + 52, + 80, + 541, + 198 + ], + "spans": [ + { + "bbox": [ + 52, + 80, + 541, + 198 + ], + "type": "image", + "image_path": "07779d06a8bb004c9b8cc16c96775f464423fe3cefb2ba2ba3dc76a92ef72c92.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 154, + 216, + 440, + 228 + ], + "lines": [ + { + "bbox": [ + 154, + 216, + 440, + 228 + ], + "spans": [ + { + "bbox": [ + 154, + 216, + 440, + 228 + ], + "type": "text", + "content": "Figure 2. Overview of our methodology for generating SocialCounterfactuals." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 248, + 203, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 248, + 203, + 261 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 203, + 261 + ], + "type": "text", + "content": "5,408,000 images for 54,080 captions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 266, + 171, + 280 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 171, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 171, + 280 + ], + "type": "text", + "content": "3.4. Three-Stage Filtering" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 285, + 290, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 290, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 290, + 429 + ], + "type": "text", + "content": "CLIP image-text similarity filtering. After over-generating 100 candidate image sets for each of our templates, we first filter the candidates using CLIP [41] to ensure a minimum cosine similarity of 0.2 between the encoding of each caption and its corresponding generated image. We also apply a similar filtering criteria between pairs of images in each set, requiring the cosine similarity of CLIP image encodings within the set to be greater than 0.2. These filtering criteria help ensure that images accurately depict the subjects described in each caption while also retaining a high-degree of similarity to each other, thereby ensuring that they represent valid counterfactual examples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 443, + 288, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 443, + 288, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 443, + 288, + 515 + ], + "type": "text", + "content": "NSFW Filtering with ViT. Manual examination of generated images revealed instances of not-safe-for-work (NSFW) content. We therefore applied a NSFW filter which uses a fine-tuned vision transformer (ViT) for NSFW image classification. This filter removes " + }, + { + "bbox": [ + 46, + 443, + 288, + 515 + ], + "type": "inline_equation", + "content": "0.9 - 2.7\\%" + }, + { + "bbox": [ + 46, + 443, + 288, + 515 + ], + "type": "text", + "content": " of generated images (see Table 11 in Supplementary Material for details)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 529, + 287, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 287, + 660 + ], + "type": "text", + "content": "CLIP Attribute Detectability Filtering. To further ensure data quality, we filter counterfactual sets based on CLIP's ability to discern targeted social attributes in each image using a two-phase approach (see Section 8.3 in Supp. Material for additional details). In the first phase, we randomly sampled 100 counterfactual sets for each pair of attribute types. For each attribute type, we then manually labeled the sampled counterfactual sets according to whether or not they should be filtered out based on a lack of detectability of the targeted attribute. Specifically, we label how many images in a counterfactual set possess their targeted attribute." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 661, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 661, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 661, + 288, + 696 + ], + "type": "text", + "content": "In the second phase, we develop a learnable threshold-based heuristics to automatically label whether a counterfactual set should be filtered with respect to an individual" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 246, + 544, + 290 + ], + "blocks": [ + { + "bbox": [ + 308, + 246, + 544, + 290 + ], + "lines": [ + { + "bbox": [ + 308, + 246, + 544, + 290 + ], + "spans": [ + { + "bbox": [ + 308, + 246, + 544, + 290 + ], + "type": "table", + "html": "
Attribute PairCounterfactual SetsImages Per SetTotal Images
(Race, Gender)7,9361295,232
(Physical Char., Gender)5,0521050,520
(Physical Char., Race)8363025,080
", + "image_path": "fcd4e855ae97ed39596e4e278a27dfe78603e825bb5aed0a902ed21b3fb5dc57.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 298, + 546, + 321 + ], + "lines": [ + { + "bbox": [ + 305, + 298, + 546, + 321 + ], + "spans": [ + { + "bbox": [ + 305, + 298, + 546, + 321 + ], + "type": "text", + "content": "Table 1. Details of the number of counterfactual sets, images per set, and total images which remain in our dataset after filtering" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 353, + 547, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 353, + 547, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 353, + 547, + 509 + ], + "type": "text", + "content": "attribute type. These threshold-based heuristics are applied according to how many of a set's constituent images have their respective targeted attributes discernible by CLIP-based image-text similarity scores (rather than by a human annotator). Thresholds were heuristically derived to obtain high correspondence between automatic filtering with CLIP and those filtered by the manual human annotation. This process produces a separate learned threshold for each attribute type and attribute type pair combination. A counterfactual set is filtered out due to a lack of detectability for an attribute type if the number of its constituent images whose corresponding targeted attribute is discernible by CLIP is less than the corresponding learned threshold." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "type": "text", + "content": "To estimate the quality of our generated dataset and the impact of filtering, we randomly sampled 100 counterfactual sets depicting Race-Gender intersectional social attributes. Prior to CLIP attribute detectability filtering, we found that " + }, + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "type": "inline_equation", + "content": "90.8\\%" + }, + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "type": "text", + "content": " of the images accurately depicted their corresponding captions. Applying attribute detectability filtering further increases this figure to " + }, + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "type": "inline_equation", + "content": "97.5\\%" + }, + { + "bbox": [ + 304, + 510, + 547, + 617 + ], + "type": "text", + "content": ", which demonstrates the value of our filtering methodology and the high quality it ensures in our dataset (see Section 7.2 of Supp. Material for details)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Table 1 provides details on the total number of counterfactual sets and images which remain in our dataset after filtering. We group counterfactual sets into three dataset segments based on the pair of attribute types used to construct the captions, which are detailed in each row of Table 1. In total, our dataset consists of 13,824 counterfactual sets with 170,832 image-text pairs, which represents the largest paired image-text dataset for investigating social biases to-date." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 702, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 702, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 702, + 287, + 713 + ], + "type": "text", + "content": "5https://huggingface.co/Falconsai/nsfw_image_detector" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11978" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 212, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 212, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 212, + 85 + ], + "type": "text", + "content": "4. Probing Intersectional Biases" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 127 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 127 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 127 + ], + "type": "text", + "content": "To probe intersectional social biases in VLMs, we calculate MaxSkew over our dataset. We describe this metric in Section 4.1 and detail our evaluation results in Section 4.2." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 134, + 160, + 146 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 134, + 160, + 146 + ], + "spans": [ + { + "bbox": [ + 47, + 134, + 160, + 146 + ], + "type": "text", + "content": "4.1. Evaluation Metrics" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "spans": [ + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " denote a text query and " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "R_{K}(q)" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " denote the set of top- " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " ranked images retrieved by a VLM for " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": ". For a given attribute pair " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "(a_{i},a_{j})" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": ", we denote the desired proportion " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " of retrieved images with the corresponding attributes as " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "p_{d(q),(a_i,a_j)}" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " and the actual proportion as " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "p_{R_K(q),(a_i,a_j)}" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": ". Geyik et al. [20] define Skew@ " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " for attributes " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "(a_{i},a_{j})" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " in retrieval results " + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "inline_equation", + "content": "R_{K}(q)" + }, + { + "bbox": [ + 46, + 152, + 287, + 237 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 70, + 245, + 264, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 245, + 264, + 270 + ], + "spans": [ + { + "bbox": [ + 70, + 245, + 264, + 270 + ], + "type": "interline_equation", + "content": "\\operatorname {S k e w} _ {(a _ {i}, a _ {j})} @ K (R _ {K} (q)) = \\log \\left(\\frac {p _ {R _ {K} (q) , (a _ {i} , a _ {j})}}{p _ {d (q) , (a _ {i} , a _ {j})}}\\right)", + "image_path": "b575d3e8ac44c9889cad12452c858aadaf0599d98c8ff5c0b4b37b8b71ba1541.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 337 + ], + "type": "text", + "content": "In essence, Skew@K measures the ratio of the proportion of top-K retrieved images having a set of attributes to the desired proportion. To aggregate Skew@K over the various attributes under consideration, Geyik et al. [20] further proposed the following MaxSkew@K metric:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 346, + 291, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 291, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 291, + 366 + ], + "type": "inline_equation", + "content": "\\operatorname{MaxSkerw} @ K(R_K(q)) = \\max_{(a_i, a_j) \\in A} \\operatorname{Skerw}_{(a_i, a_j)} @ K(R_K(q))" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " denotes the set of all attribute pairs. We calculate MaxSkew@" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " by retrieving images from our counterfactual sets using prompts which are neutral with respect to the investigated attributes. For example, given a prompt constructed from the template \"A construction worker\" (Figure 1), we form its corresponding attribute-neutral prompt \"A construction worker.\"" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": "We construct neutral prompts in this manner for each unique combination of prefixes and subjects, averaging their text representations across different prefixes to obtain a single text embedding for each subject. Skew@ " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " and MaxSkew@ " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " are then calculated by retrieving the top- " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " images for the computed text embedding from the set of all images generated for the subject which met our filtering and selection criteria. We set " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "K = |A_1| \\times |A_2|" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "A_1" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "inline_equation", + "content": "A_2" + }, + { + "bbox": [ + 46, + 457, + 287, + 564 + ], + "type": "text", + "content": " are the investigated attribute sets." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 571, + 105, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 105, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 105, + 583 + ], + "type": "text", + "content": "4.2. Results" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 590, + 287, + 685 + ], + "type": "text", + "content": "Figure 3 provides boxplots of the intersectional bias MaxSkew@K distribution for six state-of-the-art VLMs: ALIP [59], CLIP [41], FLAVA [46], LaCLIP [14], OpenCLIP [9], and SLIP [36]. We measure the MaxSkew@K distribution across occupations separately using the three segments of our dataset for Race-Gender (Figure 6a), Physical Characteristics-Gender (Figure 6b), and Physical Characteristics-Race (Figure 6c) intersectional biases." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 72, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 72, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 309, + 72, + 547, + 156 + ], + "type": "text", + "content": "All six evaluated VLMs exhibit significant skewness in retrieval for attribute-neutral occupation prompts, with CLIP and FLAVA having the lowest overall MaxSkew@K. Among the three segments of our dataset, Physical Characteristics-Gender intersectional biases tend to have lower MaxSkew@K scores while Race-Gender intersectional biases have the greatest amount of skewness." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 158, + 547, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 547, + 314 + ], + "type": "text", + "content": "In addition to illustrating the overall distribution of MaxSkew@K across occupations, the boxplots in Figure 3 also provides the occupation names for minimum values (green circles) and maximum values (red circles). These labels show some commonalities across models, such as FLAVA and LaCLIP both having their greatest Race-Gender MaxSkew@K values for the 'Makeup Artist' profession. We also observe that LaCLIP and OpenCLIP have their greatest skewness in retrieval from the Physical Characteristics-Race segment for the 'Barber' occupation. Notably, both CLIP and FLAVA have multiple occupations with zero skewness across all segments of the dataset, while SLIP has no occupations with zero skewness across the three segments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "type": "text", + "content": "Our dataset can also be used to evaluate individual (i.e., marginal) bias for a specific attribute type by filtering on the value of the other attribute depicted in a counterfactual set. MaxSkew@ " + }, + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "type": "text", + "content": " can then be calculated as previously described to estimate bias in retrieval results for a single social attribute at a time. To illustrate, we estimated the marginal gender bias across occupations using images specific to each race, which we provide in Figure 4. All VLMs exhibit variation in gender bias across different races, highlighting the importance of measuring bias in the presence of other social attributes. While CLIP has lower overall skewness than other evaluated models, it also has the greatest disparity in MaxSkew@ " + }, + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 316, + 547, + 532 + ], + "type": "text", + "content": " across different races; specifically, CLIP exhibits nearly 2x more gender skewness for images depicting Indian subjects than it does for Latinos. Interestingly, both CLIP and FLAVA exhibit the greatest gender bias in retrieving images depicting Indian people, while SLIP and ALIP exhibit the greatest gender bias for Middle Eastern people." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 713 + ], + "type": "text", + "content": "As a further case study in uncovering intersectional social biases in VLMs, Figure 5 provides a breakdown of the proportion of images retrieved using gender- and race-neutral prompts for the 'Doctor' occupation. The left and center plots of Figure 5 depict the marginal distributions of retrievals for each race and gender (respectively), whereas the right plot provides the distribution of retrieved images for intersectional race-gender attributes. While SLIP, OpenCLIP, LaCLIP, and ALIP exhibit strong bias for retrieving male images, this gender bias occurs along starkly different dimensions with respect to race. OpenCLIP strongly favors retrieving images of Asian male doctors when presented with a neutral text prompt, whereas the other three models prefer to retrieve images of Indian male doctors. This gender bias is inverted for CLIP, which retrieves images of women" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 277, + 702 + ], + "type": "text", + "content": "6We also provide results for other evaluation metrics in Section 10.1." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 59, + 703, + 249, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 249, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 249, + 712 + ], + "type": "text", + "content": "See Section 10.4 for additional details and probing results" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11979" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 214, + 190 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 214, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 214, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 214, + 190 + ], + "type": "image", + "image_path": "e5742b5e59b3852358005e5c64b1c043ff87b9a5910b5921c3873a7d9de96b2a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 104, + 192, + 159, + 201 + ], + "lines": [ + { + "bbox": [ + 104, + 192, + 159, + 201 + ], + "spans": [ + { + "bbox": [ + 104, + 192, + 159, + 201 + ], + "type": "text", + "content": "(a) Race-Gender" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 70, + 380, + 190 + ], + "blocks": [ + { + "bbox": [ + 215, + 70, + 380, + 190 + ], + "lines": [ + { + "bbox": [ + 215, + 70, + 380, + 190 + ], + "spans": [ + { + "bbox": [ + 215, + 70, + 380, + 190 + ], + "type": "image", + "image_path": "48842e4790a61fe593183fcdfe41690b2e2bfd2f7ab6e4c8820a460d402156ef.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 239, + 192, + 355, + 202 + ], + "lines": [ + { + "bbox": [ + 239, + 192, + 355, + 202 + ], + "spans": [ + { + "bbox": [ + 239, + 192, + 355, + 202 + ], + "type": "text", + "content": "(b) Physical Characteristics-Gender" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 381, + 71, + 545, + 190 + ], + "blocks": [ + { + "bbox": [ + 381, + 71, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 381, + 71, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 381, + 71, + 545, + 190 + ], + "type": "image", + "image_path": "94eaa0990547591496ff7b4133955a17ac2a2f226d93a5b8e4b699815b8c1ce7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 409, + 192, + 516, + 202 + ], + "lines": [ + { + "bbox": [ + 409, + 192, + 516, + 202 + ], + "spans": [ + { + "bbox": [ + 409, + 192, + 516, + 202 + ], + "type": "text", + "content": "(c) Physical Characteristics-Race" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 50, + 252, + 286, + 425 + ], + "blocks": [ + { + "bbox": [ + 46, + 212, + 547, + 235 + ], + "lines": [ + { + "bbox": [ + 46, + 212, + 547, + 235 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 547, + 235 + ], + "type": "text", + "content": "Figure 3. Distribution of MaxSkew@ " + }, + { + "bbox": [ + 46, + 212, + 547, + 235 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 212, + 547, + 235 + ], + "type": "text", + "content": " measured across occupations for (a) Race-Gender, (b) Physical Characteristics-Gender, and (c) Physical Characteristics-Race intersectional biases. Max (min) values are plotted as red (green) circles with corresponding occupation names" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 252, + 286, + 425 + ], + "lines": [ + { + "bbox": [ + 50, + 252, + 286, + 425 + ], + "spans": [ + { + "bbox": [ + 50, + 252, + 286, + 425 + ], + "type": "image", + "image_path": "223d9d682ba4c9ad5de21ef494055bcc0a0af0a835240899f1a245a690c7ca02.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 433, + 287, + 456 + ], + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 456 + ], + "type": "text", + "content": "Figure 4. Mean of (marginal) gender MaxSkew@ " + }, + { + "bbox": [ + 46, + 433, + 287, + 456 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 433, + 287, + 456 + ], + "type": "text", + "content": " measured across occupations for different races." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 476, + 287, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 476, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 476, + 287, + 559 + ], + "type": "text", + "content": "in a slightly higher proportion than men, but still has zero representation of certain groups (e.g., Black females). These results show that seemingly similar biases among pre-trained VLMs for social attributes such as gender can interact very differently with other attributes such as race, which highlights the importance of studying bias in the presence of intersectional social attributes." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 571, + 224, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 224, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 224, + 585 + ], + "type": "text", + "content": "5. Mitigating Intersectional Biases" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 591, + 286, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 286, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 286, + 616 + ], + "type": "text", + "content": "We investigate the suitability of our SocialCounterfactuals dataset for debiasing VLMs through additional training." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 623, + 205, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 205, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 205, + 636 + ], + "type": "text", + "content": "5.1. Training Experiment Setting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 641, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 712 + ], + "type": "text", + "content": "For each of the three segments of our dataset (see Table 1), we withhold counterfactual sets associated with " + }, + { + "bbox": [ + 46, + 641, + 288, + 712 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 641, + 288, + 712 + ], + "type": "text", + "content": " of the occupation subjects for testing and use the remainder as a training dataset. We then separately finetune ALIP, CLIP, and FLAVA on each of these three training datasets, which we hereafter refer to as the 'debiased' variants of these mod-" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 255, + 546, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 255, + 546, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 255, + 546, + 292 + ], + "type": "text", + "content": "els. To estimate the magnitude of debiasing, we evaluate each model's MaxSkew@K for intersectional bias using the withheld testing dataset containing " + }, + { + "bbox": [ + 304, + 255, + 546, + 292 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 255, + 546, + 292 + ], + "type": "text", + "content": " of the occupations." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 300, + 509, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 509, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 509, + 312 + ], + "type": "text", + "content": "5.2. Results for Intersectional Social Biases" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "text", + "content": "Table 2 provides the mean MaxSkew@ " + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "text", + "content": " calculated over our withheld test sets for pre-trained and debiased variants of CLIP, ALIP, and FLAVA. Training on our dataset has the greatest overall debiasing effect on ALIP, producing up to a 0.426 absolute reduction in MaxSkew@ " + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "text", + "content": ". Among the three segments of our dataset used for debiasing, MaxSkew@ " + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "text", + "content": " for (Physical Char., Race) intersectional bias has the greatest amount of skewness in pre-trained models. However, training on our dataset also produces the greatest absolute reduction in skewness for this type of intersectional bias, with CLIP having an absolute reduction in MaxSkew@ " + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 319, + 547, + 462 + ], + "type": "text", + "content": " of 0.327 for (Physical Char., Race) intersectional biases." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 464, + 547, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 464, + 547, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 464, + 547, + 595 + ], + "type": "text", + "content": "These results show that training VLMs with our dataset produces significant debiasing effects across all three types of intersectional biases. Furthermore, the strongest intersectional biases observed in pre-trained VLMs benefit the most from debiasing. Remarkably, these debiasing effects are observed despite there being no overlap between the occupations used for training and testing, which demonstrates that the debiasing effects generalize to new subjects not seen during training. This suggests that the ability of our dataset to mitigate intersectional bias in VLMs is not limited to only the occupation subjects that we investigated." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 604, + 545, + 617 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 604, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 604, + 545, + 617 + ], + "type": "text", + "content": "5.3. Analysis of Race-Gender Debiased CLIP Model" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 624, + 547, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 547, + 671 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 547, + 671 + ], + "type": "text", + "content": "To further understand the impact of training VLMs using our synthetic counterfactuals, we conduct analyses of CLIP after debiasing for Race-Gender intersectional bias. For simplicity, we hereafter refer to this model as Debiased CLIP." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 714 + ], + "type": "text", + "content": "Skewness evaluation using other datasets with real image-text pairs. 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Proportion of images retrieved " + }, + { + "bbox": [ + 111, + 254, + 480, + 266 + ], + "type": "inline_equation", + "content": "@k = 12" + }, + { + "bbox": [ + 111, + 254, + 480, + 266 + ], + "type": "text", + "content": " using neutral prompts for the 'Doctor' occupation." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 236, + 70, + 350, + 244 + ], + "blocks": [ + { + "bbox": [ + 236, + 70, + 350, + 244 + ], + "lines": [ + { + "bbox": [ + 236, + 70, + 350, + 244 + ], + "spans": [ + { + "bbox": [ + 236, + 70, + 350, + 244 + ], + "type": "image", + "image_path": "ad10c417f4def69ab974a5a37d20d7864a5e407266558df0d2d205e77a0185a2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 353, + 70, + 544, + 244 + ], + "blocks": [ + { + "bbox": [ + 353, + 70, + 544, + 244 + ], + "lines": [ + { + "bbox": [ + 353, + 70, + 544, + 244 + ], + "spans": [ + { + "bbox": [ + 353, + 70, + 544, + 244 + ], + "type": "image", + "image_path": "9ad470fca11670b86ce7d28da121e415a6aa1aa522fd6d1b204456573a248031.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 108, + 275, + 485, + 342 + ], + "blocks": [ + { + "bbox": [ + 108, + 275, + 485, + 342 + ], + "lines": [ + { + "bbox": [ + 108, + 275, + 485, + 342 + ], + "spans": [ + { + "bbox": [ + 108, + 275, + 485, + 342 + ], + "type": "table", + "html": "
Intersectional BiasCLIP [41]ALIP [59]FLAVA [46]
Pre-trainedDebiasedPre-trainedDebiasedPre-trainedDebiased
(Race, Gender)1.020.771.401.160.980.79
(Physical Char., Gender)0.870.711.281.020.920.81
(Physical Char., Race)1.190.871.551.131.120.97
", + "image_path": "27ab7c021197367d45336959fdf14ae5e92e6c262080cb9c7ce9d3375b7ed52a.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 403, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 287, + 487 + ], + "type": "text", + "content": "a natural question to ask is how well our observed debiasing effects extend to evaluations with real image-text pairs. Unfortunately, there are no such existing resources for measuring the intersectional social biases that we investigate in this work. However, several real image-text datasets have been proposed for evaluating (marginal) social biases for attributes such as perceived race and gender." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 488, + 288, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 488, + 288, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 488, + 288, + 656 + ], + "type": "text", + "content": "To evaluate our Debiased CLIP model on such datasets, we use the Protected-Attribute Tag Association (PATA) dataset introduced in [45] for nuanced reporting of biases associated with race, age, and gender protected attributes. The PATA dataset comprises of 4,934 public images organized in 24 scenes, where the scenes represent situations in which certain groups of humans may have biases associated with them. The images are annotated with binary gender (male, female), ethnic-race labels (White, Black, Indian, East Asian, Latino-Hispanic) and two age groups (young and old). We also evaluate our Debiased CLIP model on the VisoGender dataset [23], which was curated to benchmark gender bias in image-text pronoun resolution. VisoGender consists of 690 images of people in 23 unique occupational settings.[8]" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 657, + 288, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 288, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 288, + 681 + ], + "type": "text", + "content": "Table 3 provides the mean MaxSkew@ " + }, + { + "bbox": [ + 47, + 657, + 288, + 681 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 657, + 288, + 681 + ], + "type": "text", + "content": " of our Debiased CLIP model on these two datasets. Despite only being" + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 333, + 401, + 519, + 443 + ], + "blocks": [ + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "lines": [ + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "type": "text", + "content": "Table 2. Mean of MaxSkew@ " + }, + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "type": "text", + "content": " for pre-trained and debiased variants of CLIP, ALIP, and FLAVA, estimated by withholding counterfactual sets for " + }, + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 350, + 546, + 372 + ], + "type": "text", + "content": " of the occupations in our dataset. Best results are in bold." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 333, + 401, + 519, + 443 + ], + "lines": [ + { + "bbox": [ + 333, + 401, + 519, + 443 + ], + "spans": [ + { + "bbox": [ + 333, + 401, + 519, + 443 + ], + "type": "table", + "html": "
ModelVisoGender [23]PATA [45]
Pre-trained CLIP0.2690.323
Debiased CLIP0.2190.283
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CLIP ModelText RetrievalImage Retrieval
R@1R@5R@10R@1R@5R@10
Pre-trained67.18993.869.490.694.9
Debiased69.289.693.867.390.493.8
", + "image_path": "2d1a9667c8a91507a22674c3f71959c848913e5c55f224ffc3fac3428bd5f7cb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 214, + 285, + 247 + ], + "blocks": [ + { + "bbox": [ + 46, + 134, + 288, + 179 + ], + "lines": [ + { + "bbox": [ + 46, + 134, + 288, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 288, + 179 + ], + "type": "text", + "content": "Table 4. Image & text retrieval performance of Debiased CLIP and pre-trained CLIP on Flickr30K[61]. Debiasing CLIP with our dataset results in improved performance on text retrieval and only minimal performance degradation on image retrieval." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 214, + 285, + 247 + ], + "lines": [ + { + "bbox": [ + 49, + 214, + 285, + 247 + ], + "spans": [ + { + "bbox": [ + 49, + 214, + 285, + 247 + ], + "type": "table", + "html": "
CLIP ModelCIFAR10[32]CIFAR100[32]Caltech256[21]ImageNet[12]
Pre-trained88.8064.1783.4359.25
Debiased86.7261.4679.7255.38
", + "image_path": "b2d90b25bd9babcfa807629ad4fbb405fe0ea7276e15ecb747ebe1b5fb524d00.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 255, + 288, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 255, + 288, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 288, + 289 + ], + "type": "text", + "content": "Table 5. Accuracy of our debiased CLIP model as well as pretrained CLIP on zero-shot image recognition datasets. Debiasing CLIP with our dataset results in minimal performance degradation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 334, + 274, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 274, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 274, + 347 + ], + "type": "text", + "content": "performance of the model on other tasks to some extent." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 353, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 473 + ], + "type": "text", + "content": "We estimate the magnitude of this impact by evaluating our Debiased CLIP model on image-text retrieval and zero-shot image recognition tasks. Table 4 provides the text retrieval and image retrieval performance of both pretrained CLIP and our Debiased CLIP on Flickr30K. We observe that our Debiased CLIP model achieves equivalent or better performance across all three text retrieval settings compared to pre-trained CLIP. In the image retrieval settings, our Debiased CLIP model exhibits a minor degradation in performance compared to pre-trained CLIP." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 479, + 287, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 576 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 576 + ], + "type": "text", + "content": "Table 5 measures the accuracy of pre-trained CLIP and our Debiased CLIP model on zero-shot image recognition datasets. Similar to the image retrieval evaluation, our Debiased CLIP model exhibits a minor degradation in accuracy on these datasets. These performance reductions are similar in magnitude to those observed in prior work on debiasing CLIP [45] and characterize the trade-off between model fairness and absolute performance inherent to debiasing efforts." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "Depending on the intended use case, the benefits of reducing skewness in the retrieval results of VLMs may be far more valuable than the relatively small decrease in performance observed in debiased models. Additionally, these results were obtained without any tuning of the training process for balancing task-specific performance with debiasing efforts. We hypothesize that additional attention to these task-specific performance measures during training, as well as other strategies such as mixing real data with our counterfactual examples, may produce a different balance between model debiasing and task-specific performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 71, + 379, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 379, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 379, + 84 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 91, + 547, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 342 + ], + "type": "text", + "content": "In this work, we presented a methodology for automatically generating counterfactual examples for probing and mitigating intersectional bias in VLMs. We used our approach to construct SocialCounterfactuals, a large dataset of image-text counterfactuals depicting intersectional social attributes related to gender, race, and physical characteristics for various occupations. Our evaluations of six pre-trained VLMs showed that all exhibit significant intersectional social biases in retrieval results, with substantial variation in retrieval skewness across differing racial and gender attributes. Through training experiments, we further demonstrated that SocialCounterfactuals can be a valuable resource for mitigating skewness in VLMs. A promising direction for future work could be extending our approach to investigate intersectional social biases in VLMs for other attributes and subjects. Our SocialCounterfactuals dataset could also be a valuable resource for reducing bias in generative text-to-image diffusion models. Finally, alternative training strategies for debiasing VLMs with synthetic counterfactuals could be explored to balance bias mitigation with task-specific performance measures." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 360, + 547, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 547, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 547, + 503 + ], + "type": "text", + "content": "Limitations and Ethical Considerations Despite our best efforts, the templates and methodologies we adopt may themselves contain some latent biases which could contribute to the implicit biases exhibited by VLMs. All statements pertaining to gender, race, and occupational attributes or associations should be interpreted only within the context of our experiments. Furthermore, all discussion of social attributes in this work are intended to be interpreted as perceived. We are aware that our approach only considers binary classification of genders and does not exhaustively encompass all races, physical characteristics, and occupations, which is due to data limitation rather than our value judgements." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 504, + 547, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 547, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 547, + 659 + ], + "type": "text", + "content": "With the findings we present in this paper, we aim to increase the understanding of bias in VLMs and probe mitigation strategies. We acknowledge that our work does not encompass all possible social attributes and that our selected categories for gender, race, physical characteristics, and occupations may harbor stereotypes that cannot be assumed to represent their entire groups. Our aim is that the techniques presented in this work can help reduce various social disparities in VLMs and can be further extended to include more genders, races, occupations and other social characteristics. Continuing these efforts will increase confidence in the ability of VLMs to exhibit fairness with respect to differing social attributes. See Section 9 for additional discussion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 671, + 365, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 365, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 365, + 684 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 691, + 545, + 713 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 691, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 310, + 691, + 545, + 713 + ], + "type": "text", + "content": "[1] Ananthu Aniraj, Cassio F. 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Association for Computational Linguistics, 2022. 1, 2" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11985" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/e8af8e09-8ccf-4c64-8c0b-738d9e4d84de_content_list.json b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/e8af8e09-8ccf-4c64-8c0b-738d9e4d84de_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..23030266570a1bc6eb7b984ac28d2a63b59b1bcc --- /dev/null +++ b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/e8af8e09-8ccf-4c64-8c0b-738d9e4d84de_content_list.json @@ -0,0 +1,1478 @@ +[ + { + "type": "text", + "text": "Soften to Defend: Towards Adversarial Robustness via Self-Guided Label Refinement", + "text_level": 1, + "bbox": [ + 207, + 130, + 759, + 172 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhuorong Li $^{1,\\ast,\\dagger}$ Daiwei Yu $^{1,*}$ Lina Wei $^{1}$ Canghong Jin $^{1}$ Yun Zhang $^{1}$ Sixian Chan $^{2}$ Hangzhou City University $^{2}$ Zhejiang University of Technology", + "bbox": [ + 107, + 202, + 857, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{lizr, weiln, jinch, yunzhang}@hzcu.edu.cn, ydw.ccm@gmail.com, sxchan@zjut.edu.cn", + "bbox": [ + 125, + 241, + 841, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Adversarial training (AT) is currently one of the most effective ways to obtain the robustness of deep neural networks against adversarial attacks. However, most AT methods suffer from robust overfitting, i.e., a significant generalization gap in adversarial robustness between the training and testing curves. In this paper, we first identify a connection between robust overfitting and the excessive memorization of noisy labels in AT from a view of gradient norm. As such label noise is mainly caused by a distribution mismatch and improper label assignments, we are motivated to propose a label refinement approach for AT. Specifically, our Self-Guided Label Refinement first self-refines a more accurate and informative label distribution from over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model and thus requiring no external teachers. Empirical results demonstrate that our method can simultaneously boost the standard accuracy and robust performance across multiple benchmark datasets, attack types, and architectures. In addition, we also provide a set of analyses from the perspectives of information theory to dive into our method and suggest the importance of soft labels for robust generalization.", + "bbox": [ + 75, + 323, + 473, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent studies have reported that deep neural networks (DNNs) are vulnerable to adversarial examples, i.e., malicious inputs perturbed by an imperceptible noise to confuse the classifier prediction [14, 25]. This vulnerability raises serious security concerns and motivates a growing body of works on defense techniques [18, 24, 39]. Adversarial training (AT) is arguably the most promising way to harden classifiers against adversarial examples, which directly augments the training set with adversarial examples [3, 18]. It", + "bbox": [ + 75, + 726, + 470, + 863 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "is formulated as a min-max problem [18] to find model parameters $w$ that minimize the adversarial risk:", + "bbox": [ + 500, + 292, + 893, + 321 + ], + "page_idx": 0 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {w} \\mathcal {L} _ {\\mathcal {S}} \\left(x ^ {\\prime}, y; w\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 330, + 893, + 353 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathcal{S}}(x',y;w) = 1 / n\\sum_{i = 1}^{|S|}\\max_{x'\\in \\mathcal{B}_r(x)}\\ell (f(x_i';w),y_i)$ and $f(\\cdot ;w)$ is a model parameterized by $w$ $\\ell (\\cdot)$ is the loss function such as cross-entropy loss, and $\\mathcal{B}_r(x)$ denotes the set of the allowed perturbations under the given metric space $M = (X,d)$ and the suitable radius $r > 0$ , i.e., $\\mathcal{B}_r(x) = \\{x + \\delta \\in \\mathcal{X}:d(x,x + \\delta) < r\\}$", + "bbox": [ + 496, + 361, + 893, + 462 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, most AT methods suffer from a dominant phenomenon that is referred to as \"robust overfitting\". That is, an adversarially trained model can reach almost $100\\%$ robust accuracy on the training set while the performance on the test set is much inferior, witnessing a significant gap of adversarial robustness [22]. Various regularization techniques including classic $\\ell_1$ , $\\ell_2$ regularization and more advanced regularizations using data augmentation, such as Mixup [38] and Cutout [9], have been attempted to mitigate robust overfitting, whereas they are reported to perform no better than a simple early stopping [22]. However, early stopping raises another concern as the checkpoint of the best robustness and that of the best standard accuracy often do not coincide [5]. To outperform data augmentations and early stopping, regularizations specifically designed for robust training are thus proposed, to name a few, loss reweighting [27, 29, 37, 40] and weight smoothing [5, 33, 36, 37]. These regularization methods are likely to restrict the change of training loss by suppressing perturbations with respect to either the inputs $x$ or the weights $w$ , whereas few explorations attempt to combat robust overfitting from the perspective of labels $y$ .", + "bbox": [ + 496, + 463, + 895, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous investigations on labels in AT [10, 35] emphasised the existence of label noise in AT to provide an understanding of robust generalization, for instance, from a classic bias-variance perspective. We take a step still further to investigate the memorization of label noise in AT, which is characterised by a non-monotonical increase of gradient norm, as illustrated in Fig. 1, resulting in robust overfitting. In light of our analyses, we are motivated to design a strategy", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 99, + 875, + 232, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* The first two authors contribute equally.", + "bbox": [ + 99, + 887, + 323, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24776", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/df0b5802ee23945c78879e8b25fe902fbf047d4fe032d4a8723f634cea1175e8.jpg", + "image_caption": [ + "(a) Gradient norm magnitude" + ], + "image_footnote": [], + "bbox": [ + 81, + 95, + 465, + 292 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d04f677b2fea59684592a610f0b73d654144165b5896168625f1297642c723eb.jpg", + "image_caption": [ + "(b) Generalization gap", + "Figure 1. In figure (a), we calculate the gradient norm of vanilla adversarially trained PreAct-ResNet 18 on CIFAR-10 for robustness against $\\ell_{\\infty}$ perturbations of radius 8/255. In figure (b), we show the robust accuracy under PGD-20 attack under the same settings with figure (a). The gradient norm keeps non-monotonically ramping up when robust overfitting happens." + ], + "image_footnote": [], + "bbox": [ + 488, + 90, + 887, + 292 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for label refinement to alleviate excessive memorization and thus the robust overfitting. To that end, we conduct an empirical experiment using different label assignments and analyse through the lens of learning curve, which is a useful indicator for the occurrence of robust overfitting. As shown in Fig. 2, the phenomenon of robust overfitting is presented, for instance, in the lower left of Fig. 2 for PGD-AT [18] with commonly used hard labels, and at a slightly reduced extent as shown in the lower middle of Fig. 2 with vanilla soft labels.", + "bbox": [ + 75, + 364, + 470, + 501 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a theoretical-grounded method to alleviate the memoization on over-confident labels during adversarial training and thus to combat robust overfitting. Our main idea is to resort to an alternative for label assignment. Particularly, motivated by the effectiveness of soft label in alleviating overfitting in standard training [26], our work generates more reliable labels automatically by incorporating predictive label distributions into the process of robust learning. It provides a promising way to inject distilled knowledge and to self-calibrate the adversarial training. Our method is conceptually simple yet significantly enhances the learning of deep models in adversarial scenarios. The key contributions are as follows:", + "bbox": [ + 75, + 501, + 473, + 698 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We first inspect the behaviour of deep models trained by AT when robust overfitting occurs. Specifically, we identify a connection between robust overfitting and the excessive memorization of noisy labels in AT through the lens of gradient norm (see Fig. 1). As such label noise is mainly due to inaccurate label distribution, we further investigate the effects of different label assignment methods on AT (see Fig. 2). These observations consistently implies a connection between robust overfitting and noisy hard labels. Exploring such connections could help to shed light on understanding and improving the robust learning of deep models.", + "- Upon the observation, we are motivated to propose a label" + ], + "bbox": [ + 81, + 703, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "refinement approach for AT. Specifically, our Self-Guided Label Refinement (SGLR) first self-refines accurate and informative label distribution from the over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model, requiring no external teacher models nor modifications to the existing architecture.", + "bbox": [ + 516, + 364, + 893, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- We verify the effectiveness of SGLR through extensive evaluations. Overall, experimental results show that the proposed method consistently improves the test accuracy over the state-of-the-art on various benchmark datasets against diverse adversaries. Moreover, our approach can achieve robust accuracy up to $56.4\\%$ and close the generalization gap to merely $0.4\\%$ , significantly mitigating the overfitting issue and thus being able to pushing up the adversarial robustness.", + "bbox": [ + 504, + 470, + 893, + 607 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. A closer look at robust overfitting", + "text_level": 1, + "bbox": [ + 500, + 633, + 805, + 651 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Robust overfitting has been prevalent across various datasets and models [22]. Then, crops of empirical and theoretical studies have emerged to analyze this phenomenon through the lens of loss value [37], training data [10] and learned features [30]. However, a comprehensive underlying mechanism of robust overfitting still remains an enigma. In this section, we revisit robust overfitting from a perspective of the established information theory and identify a \"memorization effect\" over the course of adversarial training, which is akin to standard training as observed in [6, 34]. First and foremost, we conduct some observations when robust overfitting occurs via analysing the change of the gradient norm of adversarial loss with respect to model weight, i.e., $\\| \\nabla_w L(x', y, w) \\|_2$ . As shown in Fig. 1 (a), we may note that the gradient norm holds nearly the constant and then keeps ramping up nonmonotonically. This increasing behavior of gradient norm", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24777", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/fbe753404e53dce1be123c028b2607c3d794c114dcfd9153b4539fad709f2048.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 89, + 349, + 234 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4cad22deaad17b7d5fcc92669886b371124a53caa5479c81fd1ad30750de56fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 351, + 90, + 617, + 234 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/fb89fc4c68e5775ab99c4d6a3ea0f06b7e5a12e02ab20cdef448e9c4fbf4aea9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 619, + 90, + 885, + 234 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1a33523c1fba43f31ff1f04494e469c6860ea25c8262ae8e19047975d2367594.jpg", + "image_caption": [ + "Figure 2. Robust accuracy of models employing different label assignment methods in adversarial training." + ], + "image_footnote": [], + "bbox": [ + 80, + 236, + 349, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/561c2e92403f150dd68cbedd37d9426a530c267a7c09ca950107412c1761e366.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 236, + 619, + 383 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/7dd9be1e6da23622df5700a8132ab35e95296843aba017b4fcef5e32d30824cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 236, + 887, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "encountered with the learning rate (LR) decays. So we divide the training process into two phases according to the LR decays: (1) Stationary stage; (2) Non-monotonical growth stage.", + "bbox": [ + 75, + 411, + 470, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In stationary stage, as illustrated in Fig. 1 (b), the learning curve (orange line) and test robust accuracy (blue line) ramp up at almost the same pace and maintain a very small generalization gap, i.e., the divergence between the training and test accuracy, implying that the model keeps learning efficient robust features as the training progresses and accordingly hovers a small constant gradient norm. However, a significantly expanding generalization gap can be witnessed after an inflection point, where the LR decays. We refer the period afterwards as \"Non-monotonical growth stage\", as a prominent characteristic of this stage is that the gradient norm keeps growing non-monotonically and does not converge to a constant, even after the training has ended.", + "bbox": [ + 75, + 472, + 468, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is worth noting that this trend of gradient norm greatly contradicts with that of the conventional ERM training, where zero gradient norm can be reached at the end of training. Nonetheless, such behaviour of gradient norm is in line with ERM when significant noisy labels surrounding, as observed in [11, 31]. Specifically, such growing trend is interpreted as an indicator that the training has entered a \"memorization routine\", where the model firstly fits on training samples with clean labels, then gradually over-fits samples with noisy labels. Later in this stage, the test accuracy on clean data will go down whereas the training accuracy keeps going up. Similarly, we are able to identify a non-monotonical growth in adversarial training, as depicted in Fig. 1 (a). Remarkably, this divergent gradient norm as the adversarial training progressing, exactly accompanies", + "bbox": [ + 75, + 667, + 470, + 893 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with the enlargement of generalization gap that is depicted in Fig. 1 (b), which reveals the overfitting problem. Thus, we come to a conjecture that the memorization effect is also the culprit of the increasing gradient norm in the scenario of robust training and further induces robust overfitting. To that end, we first provide proof for our hypothesis that adversarial training memorizes samples with noisy labels mainly in the non-monotonical divergence phase.", + "bbox": [ + 496, + 411, + 890, + 531 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following [1], the expected cross entropy loss could be decomposed into three terms according to PAC-Bayesian framework:", + "bbox": [ + 496, + 531, + 890, + 571 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {H} _ {f} (\\hat {y} | x, w) \\\\ = \\mathbb {E} _ {\\mathcal {S}} \\mathbb {E} _ {w \\sim Q (w | \\mathcal {S})} \\sum_ {i = 1} ^ {m} [ - \\log f (\\hat {y} _ {i} | x _ {i}, w) ] \\\\ = \\mathcal {H} (y | x) + \\mathbb {E} _ {x, w \\sim Q (w | \\mathcal {S})} \\mathrm {K L} [ p (y | x) \\| f (\\hat {y} | x, w) ] - I (w; y | x) \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 587, + 890, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In conventional ERM training, minimizing $-I(w; y|x)$ relies on the cross entropy loss between the prediction $f(\\hat{y} | x, w)$ and the true label distribution $p(y|x)$ . Noisy label viewed as the outlier of a true label distribution can provide a positive value of $I(w; y|x)$ . This term essentially quantifies the extent to which label information overlaps the weights of the model. In other words, the presence of noisy labels will reduce the finite degree of freedom with respect to weights. The reason for this reduction is that model attempts to accommodate the noise labels in the training data, inducing a potential overfitting. Different from the conventional ERM training, adversarial training requires perturbed samples $x'$ , which are usually obtained by solving a multi-step maximization problem. Accordingly, we use the notation $p(y'|x')$ for the true distribution of adversarial samples. Based on the", + "bbox": [ + 496, + 691, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24778", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Eq. (2), we have", + "bbox": [ + 76, + 90, + 189, + 104 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {H} _ {f} (\\hat {y} | x ^ {\\prime}, w) = \\mathbb {E} _ {\\mathcal {S}} \\mathbb {E} _ {w \\sim Q (w | \\mathcal {S})} \\sum_ {i = 1} ^ {m} \\left[ - \\log f \\left(\\hat {y} _ {i} \\mid x _ {i} ^ {\\prime}, w\\right) \\right] \\\\ = \\mathcal {H} \\left(y ^ {\\prime} \\mid x ^ {\\prime}\\right) - I (w; y ^ {\\prime} \\mid x ^ {\\prime}) \\\\ + \\mathbb {E} _ {x ^ {\\prime}, w \\sim Q (w | \\mathcal {S})} \\mathrm {K L} [ p (y ^ {\\prime} | x ^ {\\prime}) \\| f (\\hat {y} | x ^ {\\prime}, w) ] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 114, + 431, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As aforementioned, the adversarial perturbation causes a mismatch between the label distributions of the perturbed data and their origins, as $p(y'|x') \\neq p(y|x)$ . However, during adversarial training, $p(y'|x')$ is often simply replaced by $p(y|x')$ , that is, the perturbed labels are directly inherited from their origins. This would inevitably exert influence on the label memorization and results in performance degradation.", + "bbox": [ + 76, + 194, + 470, + 313 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We are interested in the memoization of noisy labels in adversarial training, which can be characterised by $I(w; y'|x')$ and referred to as \"Information In Weights\" (IIW). The training dynamics can also be captured through the lens of IIW. However, computing the value of $I(w; y'|x')$ is as difficult as fitting the model itself. Basing on the chain rule of mutual information, we could approach to our desired result via the upper bound, i.e., $I(\\mathcal{D}; w) = I((x, y); w) = I(x; w) + I(y; w|x)$ . By using the positivity property of mutual information, we have $I(y; w|x) \\leq I(D; w)$ . Then we could take an approximation under some Gaussian assumptions, as suggested by Wang et al. [32], to estimate $I(w; y'|x')$ and further depict the learning behaviour of model, which is illustrated by the green line in Fig. 1 (b). The increasing IIW supports our hypothesis that adversarially trained model mainly overfits the noisy labels in the non-monotonical growth stage. Upon the theoretical analysis, it is natural that we proposed to prevent models from excessively memorising noisy labels by means of IIW reductions. In this work, we propose to reduce IIW through soft labels, which is specifically effective in lowering mutual information and thus can be expected to weaken the memorization under the distribution mismatch.", + "bbox": [ + 76, + 314, + 472, + 661 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 (Soft label could reduce the IIW) Let $u$ be the uniform random variable with $p.d.f. p(u)$ . By using the composition in Eq. (2), there exists an interpolation ration $\\lambda$ between the clean label distribution and uniform distribution, such that", + "bbox": [ + 76, + 671, + 470, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI \\left(y ^ {*}; w \\mid x ^ {\\prime}\\right) \\lesssim I (y; w \\mid x ^ {\\prime}) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 757, + 468, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $p(y^{*}|x^{\\prime},w) = \\lambda \\cdot p(y|x^{\\prime},w) + (1 - \\lambda)\\cdot p(u)$ and the symbol $\\lesssim$ means that the corresponding inequality up to an $c$ -independent constant.", + "bbox": [ + 76, + 785, + 468, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The detailed proof could be found in Appendix A. Theorem 1 proves that there exists some kind of soft label that could reduces the information in weights. So the memorization effect caused by the label distribution mismatch could be", + "bbox": [ + 76, + 839, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "effectively mitigated. Thus, to better suppress the memorization effect, we should provide more underlying information about the true label distribution than uniform distribution to facilitate a better interpolation of the soft label. In the following, we introduce our solution to estimate more accurate and informative soft labels for adversarial training.", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Self-guided label refinement for adversarial training", + "text_level": 1, + "bbox": [ + 498, + 194, + 890, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Methodology", + "text_level": 1, + "bbox": [ + 500, + 237, + 637, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As discussed above, hard labels in adversarial training are uninformative but over-confident, and thus heavily impairs the generalization (see Fig. 2). To address this issue, we propose an alternative to one-hot labels for adversarial training. Specifically, our Self-Guided Label Refinement first utilizes the learned probability distributions to refine the over-confident hard labels, and then it guides the training process using the historical training model to obtain a calibrated prediction.", + "bbox": [ + 496, + 260, + 893, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We begin by softening the over-confident hard labels. It is well acknowledged that label smoothing (LS) helps to calibrate the degree of confidence of a model and it is effective in improving the robustness in noise regimes [17]. The vanilla LS for a $K$ -class classification problem can be formulated:", + "bbox": [ + 496, + 396, + 893, + 486 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = \\frac {r}{K} \\cdot \\mathbf {1} + (1 - r) \\cdot \\mathbf {y} _ {\\text {h a r d}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 494, + 890, + 521 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where, $\\mathbf{y}_{\\text {hard }}$ denotes labels encoded by a one-hot vector, the notation of 1 denotes all one vector, and $r \\in [0,1]$ controls the smooth level. It is shown that LS serves as a regularizer as well as a confidence penalty [21] and therefore improves the generalization of the model in standard training. Unfortunately, when it comes to adversarial training, a direct combination with LS cannot guarantee reliable robustness, especially in the cases of strong perturbations[4, 20]. Specifically, as the uniform distribution is unlikely to match the underlying distribution, LS tends to introduce a bias that might hurt the robust generalization. Moreover, soft labels with identical probability over the false categories cannot reveal the semantic similarity.", + "bbox": [ + 496, + 530, + 893, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To alleviate this artificial effect, we introduce our Self-Guided Label Refinement (SGLR) which utilizes the knowledge inferred by a trustworthy model itself to retains informative labels. The proposed SGLR can be formulated as:", + "bbox": [ + 496, + 726, + 893, + 787 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} = r \\cdot f \\left(x ^ {\\prime}; w\\right) + (1 - r) \\cdot \\mathbf {y} _ {h a r d} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 801, + 890, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f(x'; w)$ is the logit output of the model parameterized by $w$ on training data $x'$ . To be noticed, the model $f$ we referred to here is not pre-trained but rather on the training. Eq. (6) also in fact serves as a regularizer by integrating the knowledge extracted from the model with static information", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24779", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/70e85b23541508b5f67c54c0a41b918c5ac1b5e2a2749178987c3cd5df7327fc.jpg", + "image_caption": [ + "Figure 3. The mean confidence of model in the correct and incorrect predictions over clean and adversarial test sets." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 269, + 223 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/44dd40b47c9c4dfd10d879d7f9c74d790853a4e4bf6326cd3908c0f1abe8e20c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 90, + 457, + 223 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "that encoded by one-hot labels, thus, we suggest that this particular form of soft label has the potential to convey a better quantity of informative content.", + "bbox": [ + 76, + 262, + 468, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Furthermore, according to Sanyal et al. [23], there exists a good interpolation of the noisy training dataset that could lead to a satisfactory generalization. Consequently, we aim to establish a valid interpolation between robust and non-robust features with the expectation that it strikes a balance between accuracy and robustness, as represented by the equation:", + "bbox": [ + 75, + 308, + 468, + 398 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {f} (x, x ^ {\\prime}; w) = \\lambda \\cdot f (x; w) + (1 - \\lambda) \\cdot f (x ^ {\\prime}; w) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 407, + 468, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 3 illustrates the major trajectory of PGD-AT training on CIFAR-10 dataset in terms of the confidence in both the correct and incorrect predictions, where the model dynamics are shown by a series of colored dots with darker colours and larger areas. Gray dashed lines mark the best standard / robust accuracy of the trained model, and the red star in the bottom right corner denotes an ideal model that with a high confidence in correct classification whereas a low one in the incorrect prediction. As training processes, model tends to assign increasing confidence to its correct predictions and also to those wrong predictions, as implied by the moving of the colored dots away from the dash line. In other words, the latter prediction of the model is not better calibrated and the model in the middle training stage could be of great help to reduce the expected calibration error. Therefore, we are motivated to utilize exponential moving average (EMA) that taking the moving average of history model prediction to obtain calibrated soft label. Intuitively, EMA considers recent proposals from the current state while retaining some influence from previous information. This straightforward method is easy to deploy and incurs negligible training overhead. Then the dynamic updating of soft label could be defined as follows:", + "bbox": [ + 75, + 436, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbf {y} = r \\cdot \\widetilde {p _ {t}} + (1 - r) \\cdot \\mathbf {y} _ {\\text {h a r d}} \\tag {8} \\\\ \\widetilde {p _ {t}} = \\alpha \\cdot \\widetilde {p} _ {t - 1} + (1 - \\alpha) \\cdot \\widetilde {f} (x, x ^ {\\prime}; w _ {t}) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 791, + 468, + 828 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Connection to symmetric cross entropy", + "text_level": 1, + "bbox": [ + 76, + 847, + 413, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross Entropy (CE) is the prevalent loss function for deep learning with remarkable success. However, as the noisy", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "label is tipping the training process into overfitting, CE loss has taken a nasty blow and is prone to fitting noise. Inspired by the symmetric Kullback-Leibler (KL) Divergence, Wang et al. [28] proposed a more flexible loss, i.e., symmetric cross entropy (SCE), to strike a balance between sufficient learning and robustness to noisy labels. Moreover, it reveals that predictive distribution exploited by the model is superior to one-hot label distribution for the most part. Both SCE loss and our method utilize the informative knowledge inferred by the model and Proposition 1 provide such a close link between them.", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition.1 Let $\\ell_{sce}$ be the SCE loss function and $\\gamma$ represents the sum of CE and reverse CE loss. When $\\gamma \\rightarrow 1$ , then our methods can also be written as:", + "bbox": [ + 498, + 267, + 893, + 311 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\ell_ {s g l r} = \\ell_ {s c e} - \\alpha \\cdot \\ell_ {r k l}\n$$\n", + "text_format": "latex", + "bbox": [ + 619, + 325, + 769, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\ell_{rkl}$ denotes the reverse KL divergence between labels and model predictions, i.e., $D_{KL}(p\\parallel q)$ .", + "bbox": [ + 498, + 353, + 890, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proof of Proposition 1 can be found in Appendix A. Note that Proposition 1 indicates our method can be decomposed into two terms. The first term represents the SCE loss function when the weighted sum tends to 1. The second term indicates that our method rewards the distribution differences between predictions and labels. Though our study aims at mitigating robust overfitting, which is different from the scenario of SCE loss, there is no conflict between our method and SCE.", + "bbox": [ + 496, + 393, + 892, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Comparison to knowledge distillation", + "text_level": 1, + "bbox": [ + 500, + 539, + 821, + 556 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Knowledge distillation (KD) [16] has been proven to be an effective way to compress models, which is able to remarkably beef up the performance of lightweight models. There is a huge scope for applying KD to adversarial training to improve the efficiency of AT. A crop of works [5, 13, 29, 41] have advanced exploring KD implicitly or explicitly in conjunction with AT. The efficacy of KD is attributed to the teacher model's informative knowledge, which guides the student to acquire a more similar knowledge representation and effectively capture inter-class relationships. By enforcing consistency in probability distributions, KD facilitates better learning outcomes for the student.", + "bbox": [ + 496, + 561, + 893, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition. 2 Some $KD$ methods, which minimize the distance of the feature map between the teacher and student model, belong to the family of our method. Let $p_t$ be the prediction of the teacher model and then the $KD$ could also be written as $\\ell_{KD} = \\mathbb{E}_{\\widetilde{q}}[-\\log p] = H(\\widetilde{q},p)$ , where $\\widetilde{q} = (1 - \\alpha) \\cdot q + \\alpha \\cdot p_t$ .", + "bbox": [ + 496, + 753, + 893, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 2 shows that some KD revised the hard label via the knowledge $p_t$ learned by the teacher. The proof of Proposition 2 is presented in Appendix A. Further, we view", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24780", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/680328cc3fb23fb34980359be52d86db7c58a30b1488e6a19322476dbea79feb.jpg", + "table_caption": [ + "Table 1. Comparison between our method and other KD methods." + ], + "table_footnote": [], + "table_body": "
ARD [13]RSLAD [41]KD-SWA [5]Ous
Trained teacher models1120
Standardly teacher independent✓✓✗✓
Adversarily teacher independent✗✗✗✓
Forward times in one training iteration3342
", + "bbox": [ + 173, + 106, + 789, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "our method as special supervision, and smoothing the hard label could better reflect the similarities among classes. There are many differences between our method and other KDs in AT. The main differences are summarized in Tab. 1. Our method does not incur any extra computational cost as we do not involve teacher models, which is a boon throughout the whole training progress.", + "bbox": [ + 75, + 219, + 470, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.4. Tolerant to noisy label", + "text_level": 1, + "bbox": [ + 76, + 335, + 284, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the following part, we'd like to delve into whether the proposed method is tolerant of noisy labels. We define the symmetric noise label as that true label $y$ has probabilities $\\eta_{x,\\widetilde{y}} = p(\\widetilde{y} | y, x)$ to flip into the wrong labels uniformly. The corresponding noisy empirical risk is:", + "bbox": [ + 75, + 358, + 470, + 434 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nR _ {\\mathcal {S}} ^ {\\eta} (f) = \\mathbb {E} _ {\\mathcal {S}} (1 - \\eta_ {x}) \\cdot \\ell (f (x), y) + \\sum_ {i \\neq y} \\eta_ {x, i} \\ell (f (x), i)\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 445, + 452, + 478 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where, $\\eta_{x}$ is the noise rate. We call a loss function noisetolerant if and only if the global minimum $f_{\\eta}^{*}$ has the same probability of misclassification as that of $f^{*}$ on the noise-free data.", + "bbox": [ + 75, + 489, + 468, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Lemma. 1 Given a symmetric loss function $\\ell$ that it satisfies $\\sum_{i=1}^{k} L(f(x), i) = C$ and $C$ is some constant. Then $\\ell$ is noise tolerant under symmetric label noise if noise rate $\\eta$ meets $\\eta < 1 - \\frac{1}{K}$ .", + "bbox": [ + 75, + 560, + 468, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The loss condition theoretically guarantees the noise tolerance by risk minimization on a symmetric loss function following [12] and it shows that the global optimal classifier $f^{*}$ on noise-free data remains the optimal even with the noisy label. Further, we can also derive the noise tolerance theoretically about our method from Theorem 2.", + "bbox": [ + 75, + 630, + 468, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Theorem 2 In a $K$ -class classification problem, our method $\\widetilde{\\ell}$ is noise-tolerant under symmetric or uniform label noise if noise rate $\\eta < 1 - \\frac{1}{K}$ . And if $R(f^{*}) = 0$ , $\\widetilde{l}$ is also noise-tolerant under asymmetric or class-dependent label noise when noise rate $\\eta_{y,k} < 1 - \\eta_y$ with $\\sum_{i \\neq y} \\eta_{y,i} = \\eta_y$ , then", + "bbox": [ + 75, + 731, + 470, + 810 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nR _ {\\mathcal {S}} ^ {\\eta} (f ^ {*}) - R _ {\\mathcal {S}} ^ {\\eta} (f) \\simeq \\left(1 - \\frac {\\eta K}{K - 1}\\right) \\left(R _ {\\mathcal {S}} (f ^ {*}) - R _ {\\mathcal {S}} (f)\\right) \\leq 0\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 829, + 467, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "From Theorem 2, we can derive that our method is nearly noise-tolerant under symmetric noise and further prove the", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "robustness of the proposed method to asymmetric noise. More details can be found in Appendix B. We show a significant improvement under noise regimes empirically in experiments.", + "bbox": [ + 496, + 219, + 893, + 280 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 292, + 632, + 310 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training and evaluation setups. We conduct extensive experiments on the benchmark datasets, CIFAR-10/100. We set the perturbation budget to $\\epsilon = 8 / 255$ under the $\\ell_{\\infty}$ norm-bounded constraint. We use ResNet-18 [15] as our default network architecture unless otherwise specified. For all experiments, the model is trained using SGD with a momentum of 0.9, weight decay of $5\\times 10^{-4}$ , and an initial learning rate of 0.1 for a total of 200 epochs. The learning rate is decayed by a factor of 0.1 at the 100-th and 150-th epochs, following [22]. The evaluation of the proposed approach encompasses PGD-20 [22] and AutoAttack [7], which is recognized as the most reliable robustness evaluation up to date. AutoAttack is an ensemble of diverse attacks, including APGD-CE, APGD-DLR, FAB [8] and Square attack [2]. We quantify the robust generalization by computing the difference between the best and final checkpoints over the course of training.", + "bbox": [ + 496, + 318, + 893, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Improved robust performance across datasets. Experimental results of PGD-AT [18], TRADES [39], and the combinations of them with our proposal (denoted as PGD-AT+SGLR and TRADES+SGLR) on CIFAR-10/100 datasets are shown in Tab. 3, from which we make the following observations on our advantages: 1) Closer generalization gap. It is remarkable that the differences between the best and the final test accuracies of the combinations are reduced to around $0.5\\%$ , while the corresponding baselines (PGD-AT and TRADES) induce much larger gaps, which", + "bbox": [ + 496, + 571, + 893, + 723 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dd7a11861918aa90968198794d50a66605a110c463ab61bb7f14a9c514eb47b0.jpg", + "image_caption": [ + "Figure 4. Test accuracy $(\\%)$ on CIFAR-10 dataset (with $40\\%$ label noise). We split the training set into 1) untouched portion, where the labels of elements are left untouched; 2) corrupted portion, where the labels of elements are assigned uniformly at random." + ], + "image_footnote": [], + "bbox": [ + 503, + 744, + 697, + 849 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e64b3ea23e72d01d8c7da75ad86b2520c3fcbd724aedca5ccb6e9a00fec9aa38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 744, + 887, + 849 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24781", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/aaa946e1bc2b873d1d7355b6988a9bb3a87f9d8a61b3c8d3de1842c1c51bbeb7.jpg", + "table_caption": [ + "Table 2. Test accuracy $(\\%)$ of the proposed method and other methods on CIFAR-10 under the $\\ell_{\\infty}$ norm with $\\epsilon = 8 / 255$ based on the ResNet-18 architecture." + ], + "table_footnote": [], + "table_body": "
MethodNatural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
PGD-AT80.782.4-1.650.741.49.347.740.27.5
PGD-AT+LS82.284.3-2.153.748.94.848.444.63.9
PGD-AT+TE82.482.8-0.455.854.81.050.649.61.0
PGD-AT+SGLR82.983.0-0.156.455.90.551.250.21.0
AWP82.181.11.055.454.80.650.649.90.7
KD-AT82.985.5-2.654.653.21.449.148.80.3
KD-SWA84.785.4-0.854.953.81.149.349.4-0.1
PGD-AT + SGLR82.983.0-0.156.455.90.551.250.21.0
", + "bbox": [ + 169, + 121, + 792, + 296 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e81d6eaa5b1ae19fb23aa1e873a303782a8023398d61ff546d99b7ee6de11ccc.jpg", + "table_caption": [ + "Table 3. Clean accuracy and robust accuracy (\\%) of ResNet 18 trained on different benchmark datasets. All threat models are under $\\ell_{\\infty}$ norm with $\\epsilon = 8 / 255$ . The bold indicates the improved performance achieved by the proposed method." + ], + "table_footnote": [], + "table_body": "
DatasetMethodNatrural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
CIFAR-10AT80.782.4-1.650.741.49.347.740.27.5
+SGLR82.983.00.156.455.90.551.250.21.0
TRADES81.282.5-1.353.350.33.049.046.82.2
+SGLR82.283.3-0.955.855.40.450.750.10.6
CIFAR-100AT53.953.60.327.319.87.522.718.14.6
+SGLR56.956.60.334.534.30.227.526.70.8
TRADES57.956.31.729.927.72.224.623.41.2
+SGLR57.157.4-0.333.933.20.727.126.40.7
", + "bbox": [ + 148, + 335, + 815, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "are up to $9.3\\%$ and $3.0\\%$ on CIFAR-10 dataset when the model is threaten by PGD-20. It indicates that our method effectively alleviates robust overfitting. 2) Higher robust accuracy. As the combinations induce smaller gaps, they can approach higher robust accuracy against adversaries compared to baseline methods, as can be observed in Tab. 3. Besides, it is notable that our method is especially effective against AutoAttack [7], regarding the fundamental difficulties of simultaneously achieving the robustness against multiple adversaries. 3) Consistent improvement. Combining our label smoothing method could consistently and significantly improve the performance on all considered adversaries and also on the clean test set, and across different datasets, namely, the CIFAR-10 and CIFAR-100 datasets.", + "bbox": [ + 73, + 539, + 470, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Improved generalization under noise regimes. Moreover, we verify the self-guided label smoothing by comparing the behavior of the proposed SGLR with that of the widely used one-hot labels under different noise settings, with $40\\%$ noisy labels and fully $60\\%$ true labels, respectively. Specifically, we focus on evaluating the effectiveness of our approach in mitigating the impact of symmetric noisy labels, where the labels are resampled from a uniform distribution over all labels with a probability $\\eta$ .", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We begin by making the observations in the left of Fig. 4: 1) The generalization error (i.e., the difference between the training and test accuracy) of the proposed SGLR (almost negligible) is obviously smaller than that of the commonly used hard labels ( $>50\\%$ ). 2) The peak of the training accuracy using hard labels (blue curve) can approximate $100\\%$ even on the training set with $40\\%$ noisy labels (horizontal gray dashed denotes the portion of correct labels), which suggests that using hard labels could fit correct labels in the early stage and eventually memorizes noisy labels. On the contrary, our training curve is bounded by the untouched portion, implying that our method is able to calibrate the training process and maintain a proper fitting of training data. Then we turn to the other setting as shown in the right of Fig. 4, our test accuracy grows steadily while the baseline method fails. This observation again suggests that the double-descent phenomenon might be due to the overfitting of noise and it is hopeful to be avoided by our method.", + "bbox": [ + 496, + 539, + 893, + 810 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To give a more intuitive explanation, we further visualize the penultimate layer representations of ResNet 18 trained with (a) a hard label; (b) a soft label, and (c) the proposed soften label. As Fig. 5 shown, under all the settings of noise rate, the proposed SGLR with self-guided distribution", + "bbox": [ + 496, + 811, + 893, + 887 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24782", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a26d48146a2dafdfe89def41f1f5880ce90225f13ec80d576a1c42eb51bfb816.jpg", + "image_caption": [ + "Figure 5. Visualization of representations learned by standard training with hard/soft labels and the proposed SGLR with self-guided distribution on CIFAR-10 dataset under various levels of symmetric noisy labels $(\\eta \\in [0.0,0.2,0.4,0.6])$" + ], + "image_footnote": [], + "bbox": [ + 84, + 89, + 467, + 275 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "can consistently provide better representations, displayed with more separable clusters and tighter intra-class distance, which are very close to those of the clean setting (the leftmost column). Notably, even with a significantly increased noise rate from 0 (no noise) to 0.6 (severe noise), as illustrated from left to right in Fig. 5, our method learns representations with almost negligible variance. This also echoes our advantages of robust learning under various settings of data corruption.", + "bbox": [ + 75, + 342, + 468, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In a nutshell, we have grounds to empirically believe that our method exhibits benign tolerance to noisy labels and improves the generalization ability of the model by avoiding fitting noisy labels.", + "bbox": [ + 75, + 479, + 468, + 540 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison against other methods. Considering that our method is analogous to employing the technique of label smoothing into AT, in Tab. 2, we report robustness evaluations of AT with label smoothing (PGD-AT + LS) and temporal ensembling (PGD-AT + TE) on CIFAR-10 test set. Since excessive LS could degrade the robustness reported in [20], we implement LS with smoothing level $r = 0.2$ . We empirically found that SGLR not only can effectively alleviate robust overfitting while LS fails but also boosts the robustness even under strong AutoAttack. Further, we also report other methods (e.g., AWP [33], KD-AT [10]) in Tab. 2, which can mitigate robust overfitting through the lens of weight smoothness and the knowledge transfer of teacher model. Though robust overfitting is indeed impeded by applying these methods, our method could better narrow the generalization gap between best and final models and achieve remarkable robustness than others under AutoAttack.", + "bbox": [ + 75, + 553, + 470, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "On the impact of smoothing effect $r$ . The effectiveness of SGLR relies on the smoothing level of soft labels. Besides, as we discussed in Sec. 3.3, SGLR could be viewed as a kind of knowledge distillation without extra teacher models involved. Large temperature $T$ during distillation improves", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the smoothness of output distribution but could impair the test performance. As the temperature is vital, we could specify $f(x;w)_i$ in Eq. (7) as $\\exp (z_i / T) / \\sum_j\\exp (z_j / T)$ . We vary the smoothing level $r\\in \\{0.0,0.2,0.4,0.6,0.8\\}$ in Tab. 4 and note that an increase in $r$ initially boosts both standard accuracy and robust accuracy, followed by a decline, indicating that excessive smoothing introduces noise and hampers predictive capability. Additionally, increasing the temperature while fixing $r$ only gains slightly improvement in standard accuracy but observes degradation in robust accuracy.", + "bbox": [ + 496, + 90, + 893, + 258 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/29359ef9b3f47887af29c2ef917efdf3b710cc659b825bd53c83ad80db3c1f32.jpg", + "table_caption": [ + "Table 4. Ablation study on smoothing level $r$ and temperature $T$ ." + ], + "table_footnote": [], + "table_body": "
T/r0.00.20.40.60.8
1SA82.483.582.878.569.1
RA43.754.954.252.748.3
1.5SA83.282.983.180.674.5
RA45.755.953.250.449.8
2SA82.984.483.978.575.6
RA45.853.952.050.947.8
", + "bbox": [ + 527, + 300, + 861, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Discussion and conclusion", + "text_level": 1, + "bbox": [ + 500, + 492, + 741, + 508 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we show that label noise induced by distribution mismatch and improper label assignments would degrade the test accuracies as well as make the robust overfitting aggravated. From the view of this observation, a label assignment approach for AT, Self-Guided Label Refinement (SGLR), is proposed to weaken the memorization in AT on noisy labels and thus to mitigate the robust overfitting. Extensive experimental results demonstrate the effectiveness of the proposed SGLR. Though we circumvent over confident prediction, the model is still not well-calibrated. As we measure the calibration of model during the training over the entire dataset instead of in a sample-wise way, it may give a false sense of reweighting confidence. In the future, we will attempt to address this limitation.", + "bbox": [ + 496, + 517, + 893, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 753, + 660, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is partially supported by the National Science and Technology Major Project of China (Grant No. 2022ZD0119103), the National Natural Science Foundation of China (Grant No. 61906168), the Zhejiang Provincial Natural Science Foundation of China (Grant No.LQ21F020006, LY23F020023), and is also supported by the advanced computing resources provided by the Supercomputing Center of Hangzhou City University.", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24783", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alessandro Achille and Stefano Soatto. 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IEEE, 2021. 5, 6" + ], + "bbox": [ + 78, + 90, + 470, + 571 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24785", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/e8af8e09-8ccf-4c64-8c0b-738d9e4d84de_model.json b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/e8af8e09-8ccf-4c64-8c0b-738d9e4d84de_model.json new file mode 100644 index 0000000000000000000000000000000000000000..1868195061672314479348c765fab36b869af272 --- /dev/null +++ b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/e8af8e09-8ccf-4c64-8c0b-738d9e4d84de_model.json @@ -0,0 +1,1969 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.209, + 0.131, + 0.761, + 0.174 + ], + "angle": 0, + "content": "Soften to Defend: Towards Adversarial Robustness via Self-Guided Label Refinement" + }, + { + "type": "text", + "bbox": [ + 0.109, + 0.203, + 0.858, + 0.24 + ], + "angle": 0, + "content": "Zhuorong Li\\(^{1,\\ast,\\dagger}\\) Daiwei Yu\\(^{1,*}\\) Lina Wei\\(^{1}\\) Canghong Jin\\(^{1}\\) Yun Zhang\\(^{1}\\) Sixian Chan\\(^{2}\\) Hangzhou City University \\(^{2}\\)Zhejiang University of Technology" + }, + { + "type": "text", + "bbox": [ + 0.127, + 0.242, + 0.842, + 0.256 + ], + "angle": 0, + "content": "{lizr, weiln, jinch, yunzhang}@hzcu.edu.cn, ydw.ccm@gmail.com, sxchan@zjut.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.673 + ], + "angle": 0, + "content": "Adversarial training (AT) is currently one of the most effective ways to obtain the robustness of deep neural networks against adversarial attacks. However, most AT methods suffer from robust overfitting, i.e., a significant generalization gap in adversarial robustness between the training and testing curves. In this paper, we first identify a connection between robust overfitting and the excessive memorization of noisy labels in AT from a view of gradient norm. As such label noise is mainly caused by a distribution mismatch and improper label assignments, we are motivated to propose a label refinement approach for AT. Specifically, our Self-Guided Label Refinement first self-refines a more accurate and informative label distribution from over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model and thus requiring no external teachers. Empirical results demonstrate that our method can simultaneously boost the standard accuracy and robust performance across multiple benchmark datasets, attack types, and architectures. In addition, we also provide a set of analyses from the perspectives of information theory to dive into our method and suggest the importance of soft labels for robust generalization." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.21, + 0.717 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.471, + 0.864 + ], + "angle": 0, + "content": "Recent studies have reported that deep neural networks (DNNs) are vulnerable to adversarial examples, i.e., malicious inputs perturbed by an imperceptible noise to confuse the classifier prediction [14, 25]. This vulnerability raises serious security concerns and motivates a growing body of works on defense techniques [18, 24, 39]. Adversarial training (AT) is arguably the most promising way to harden classifiers against adversarial examples, which directly augments the training set with adversarial examples [3, 18]. It" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.293, + 0.895, + 0.323 + ], + "angle": 0, + "content": "is formulated as a min-max problem [18] to find model parameters \\( w \\) that minimize the adversarial risk:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.332, + 0.894, + 0.354 + ], + "angle": 0, + "content": "\\[\n\\min _ {w} \\mathcal {L} _ {\\mathcal {S}} \\left(x ^ {\\prime}, y; w\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.362, + 0.895, + 0.463 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathcal{S}}(x',y;w) = 1 / n\\sum_{i = 1}^{|S|}\\max_{x'\\in \\mathcal{B}_r(x)}\\ell (f(x_i';w),y_i)\\) and \\(f(\\cdot ;w)\\) is a model parameterized by \\(w\\) \\(\\ell (\\cdot)\\) is the loss function such as cross-entropy loss, and \\(\\mathcal{B}_r(x)\\) denotes the set of the allowed perturbations under the given metric space \\(M = (X,d)\\) and the suitable radius \\(r > 0\\) , i.e., \\(\\mathcal{B}_r(x) = \\{x + \\delta \\in \\mathcal{X}:d(x,x + \\delta) < r\\}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.896, + 0.78 + ], + "angle": 0, + "content": "However, most AT methods suffer from a dominant phenomenon that is referred to as \"robust overfitting\". That is, an adversarially trained model can reach almost \\(100\\%\\) robust accuracy on the training set while the performance on the test set is much inferior, witnessing a significant gap of adversarial robustness [22]. Various regularization techniques including classic \\(\\ell_1\\), \\(\\ell_2\\) regularization and more advanced regularizations using data augmentation, such as Mixup [38] and Cutout [9], have been attempted to mitigate robust overfitting, whereas they are reported to perform no better than a simple early stopping [22]. However, early stopping raises another concern as the checkpoint of the best robustness and that of the best standard accuracy often do not coincide [5]. To outperform data augmentations and early stopping, regularizations specifically designed for robust training are thus proposed, to name a few, loss reweighting [27, 29, 37, 40] and weight smoothing [5, 33, 36, 37]. These regularization methods are likely to restrict the change of training loss by suppressing perturbations with respect to either the inputs \\(x\\) or the weights \\(w\\), whereas few explorations attempt to combat robust overfitting from the perspective of labels \\(y\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Previous investigations on labels in AT [10, 35] emphasised the existence of label noise in AT to provide an understanding of robust generalization, for instance, from a classic bias-variance perspective. We take a step still further to investigate the memorization of label noise in AT, which is characterised by a non-monotonical increase of gradient norm, as illustrated in Fig. 1, resulting in robust overfitting. In light of our analyses, we are motivated to design a strategy" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.875, + 0.233, + 0.888 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.888, + 0.325, + 0.901 + ], + "angle": 0, + "content": "* The first two authors contribute equally." + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.875, + 0.325, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24776" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.096, + 0.466, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.188, + 0.297, + 0.378, + 0.312 + ], + "angle": 0, + "content": "(a) Gradient norm magnitude" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.092, + 0.888, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.62, + 0.297, + 0.766, + 0.312 + ], + "angle": 0, + "content": "(b) Generalization gap" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.895, + 0.36 + ], + "angle": 0, + "content": "Figure 1. In figure (a), we calculate the gradient norm of vanilla adversarially trained PreAct-ResNet 18 on CIFAR-10 for robustness against \\(\\ell_{\\infty}\\) perturbations of radius 8/255. In figure (b), we show the robust accuracy under PGD-20 attack under the same settings with figure (a). The gradient norm keeps non-monotonically ramping up when robust overfitting happens." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.471, + 0.502 + ], + "angle": 0, + "content": "for label refinement to alleviate excessive memorization and thus the robust overfitting. To that end, we conduct an empirical experiment using different label assignments and analyse through the lens of learning curve, which is a useful indicator for the occurrence of robust overfitting. As shown in Fig. 2, the phenomenon of robust overfitting is presented, for instance, in the lower left of Fig. 2 for PGD-AT [18] with commonly used hard labels, and at a slightly reduced extent as shown in the lower middle of Fig. 2 with vanilla soft labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.502, + 0.474, + 0.699 + ], + "angle": 0, + "content": "In this work, we propose a theoretical-grounded method to alleviate the memoization on over-confident labels during adversarial training and thus to combat robust overfitting. Our main idea is to resort to an alternative for label assignment. Particularly, motivated by the effectiveness of soft label in alleviating overfitting in standard training [26], our work generates more reliable labels automatically by incorporating predictive label distributions into the process of robust learning. It provides a promising way to inject distilled knowledge and to self-calibrate the adversarial training. Our method is conceptually simple yet significantly enhances the learning of deep models in adversarial scenarios. The key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.704, + 0.47, + 0.886 + ], + "angle": 0, + "content": "- We first inspect the behaviour of deep models trained by AT when robust overfitting occurs. Specifically, we identify a connection between robust overfitting and the excessive memorization of noisy labels in AT through the lens of gradient norm (see Fig. 1). As such label noise is mainly due to inaccurate label distribution, we further investigate the effects of different label assignment methods on AT (see Fig. 2). These observations consistently implies a connection between robust overfitting and noisy hard labels. Exploring such connections could help to shed light on understanding and improving the robust learning of deep models." + }, + { + "type": "text", + "bbox": [ + 0.082, + 0.886, + 0.469, + 0.902 + ], + "angle": 0, + "content": "- Upon the observation, we are motivated to propose a label" + }, + { + "type": "list", + "bbox": [ + 0.082, + 0.704, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.517, + 0.366, + 0.895, + 0.472 + ], + "angle": 0, + "content": "refinement approach for AT. Specifically, our Self-Guided Label Refinement (SGLR) first self-refines accurate and informative label distribution from the over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model, requiring no external teacher models nor modifications to the existing architecture." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.472, + 0.895, + 0.608 + ], + "angle": 0, + "content": "- We verify the effectiveness of SGLR through extensive evaluations. Overall, experimental results show that the proposed method consistently improves the test accuracy over the state-of-the-art on various benchmark datasets against diverse adversaries. Moreover, our approach can achieve robust accuracy up to \\(56.4\\%\\) and close the generalization gap to merely \\(0.4\\%\\), significantly mitigating the overfitting issue and thus being able to pushing up the adversarial robustness." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.807, + 0.652 + ], + "angle": 0, + "content": "2. A closer look at robust overfitting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Robust overfitting has been prevalent across various datasets and models [22]. Then, crops of empirical and theoretical studies have emerged to analyze this phenomenon through the lens of loss value [37], training data [10] and learned features [30]. However, a comprehensive underlying mechanism of robust overfitting still remains an enigma. In this section, we revisit robust overfitting from a perspective of the established information theory and identify a \"memorization effect\" over the course of adversarial training, which is akin to standard training as observed in [6, 34]. First and foremost, we conduct some observations when robust overfitting occurs via analysing the change of the gradient norm of adversarial loss with respect to model weight, i.e., \\(\\| \\nabla_w L(x', y, w) \\|_2\\). As shown in Fig. 1 (a), we may note that the gradient norm holds nearly the constant and then keeps ramping up nonmonotonically. This increasing behavior of gradient norm" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24777" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.351, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.091, + 0.619, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.62, + 0.091, + 0.887, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.237, + 0.351, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.237, + 0.62, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.237, + 0.888, + 0.385 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.167, + 0.39, + 0.8, + 0.404 + ], + "angle": 0, + "content": "Figure 2. Robust accuracy of models employing different label assignment methods in adversarial training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.471, + 0.472 + ], + "angle": 0, + "content": "encountered with the learning rate (LR) decays. So we divide the training process into two phases according to the LR decays: (1) Stationary stage; (2) Non-monotonical growth stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.669 + ], + "angle": 0, + "content": "In stationary stage, as illustrated in Fig. 1 (b), the learning curve (orange line) and test robust accuracy (blue line) ramp up at almost the same pace and maintain a very small generalization gap, i.e., the divergence between the training and test accuracy, implying that the model keeps learning efficient robust features as the training progresses and accordingly hovers a small constant gradient norm. However, a significantly expanding generalization gap can be witnessed after an inflection point, where the LR decays. We refer the period afterwards as \"Non-monotonical growth stage\", as a prominent characteristic of this stage is that the gradient norm keeps growing non-monotonically and does not converge to a constant, even after the training has ended." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.471, + 0.895 + ], + "angle": 0, + "content": "It is worth noting that this trend of gradient norm greatly contradicts with that of the conventional ERM training, where zero gradient norm can be reached at the end of training. Nonetheless, such behaviour of gradient norm is in line with ERM when significant noisy labels surrounding, as observed in [11, 31]. Specifically, such growing trend is interpreted as an indicator that the training has entered a \"memorization routine\", where the model firstly fits on training samples with clean labels, then gradually over-fits samples with noisy labels. Later in this stage, the test accuracy on clean data will go down whereas the training accuracy keeps going up. Similarly, we are able to identify a non-monotonical growth in adversarial training, as depicted in Fig. 1 (a). Remarkably, this divergent gradient norm as the adversarial training progressing, exactly accompanies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.412, + 0.892, + 0.532 + ], + "angle": 0, + "content": "with the enlargement of generalization gap that is depicted in Fig. 1 (b), which reveals the overfitting problem. Thus, we come to a conjecture that the memorization effect is also the culprit of the increasing gradient norm in the scenario of robust training and further induces robust overfitting. To that end, we first provide proof for our hypothesis that adversarial training memorizes samples with noisy labels mainly in the non-monotonical divergence phase." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.573 + ], + "angle": 0, + "content": "Following [1], the expected cross entropy loss could be decomposed into three terms according to PAC-Bayesian framework:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.588, + 0.892, + 0.675 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {H} _ {f} (\\hat {y} | x, w) \\\\ = \\mathbb {E} _ {\\mathcal {S}} \\mathbb {E} _ {w \\sim Q (w | \\mathcal {S})} \\sum_ {i = 1} ^ {m} [ - \\log f (\\hat {y} _ {i} | x _ {i}, w) ] \\\\ = \\mathcal {H} (y | x) + \\mathbb {E} _ {x, w \\sim Q (w | \\mathcal {S})} \\mathrm {K L} [ p (y | x) \\| f (\\hat {y} | x, w) ] - I (w; y | x) \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.692, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In conventional ERM training, minimizing \\(-I(w; y|x)\\) relies on the cross entropy loss between the prediction \\(f(\\hat{y} | x, w)\\) and the true label distribution \\(p(y|x)\\). Noisy label viewed as the outlier of a true label distribution can provide a positive value of \\(I(w; y|x)\\). This term essentially quantifies the extent to which label information overlaps the weights of the model. In other words, the presence of noisy labels will reduce the finite degree of freedom with respect to weights. The reason for this reduction is that model attempts to accommodate the noise labels in the training data, inducing a potential overfitting. Different from the conventional ERM training, adversarial training requires perturbed samples \\(x'\\), which are usually obtained by solving a multi-step maximization problem. Accordingly, we use the notation \\(p(y'|x')\\) for the true distribution of adversarial samples. Based on the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24778" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.191, + 0.106 + ], + "angle": 0, + "content": "Eq. (2), we have" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.116, + 0.432, + 0.188 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {H} _ {f} (\\hat {y} | x ^ {\\prime}, w) = \\mathbb {E} _ {\\mathcal {S}} \\mathbb {E} _ {w \\sim Q (w | \\mathcal {S})} \\sum_ {i = 1} ^ {m} \\left[ - \\log f \\left(\\hat {y} _ {i} \\mid x _ {i} ^ {\\prime}, w\\right) \\right] \\\\ = \\mathcal {H} \\left(y ^ {\\prime} \\mid x ^ {\\prime}\\right) - I (w; y ^ {\\prime} \\mid x ^ {\\prime}) \\\\ + \\mathbb {E} _ {x ^ {\\prime}, w \\sim Q (w | \\mathcal {S})} \\mathrm {K L} [ p (y ^ {\\prime} | x ^ {\\prime}) \\| f (\\hat {y} | x ^ {\\prime}, w) ] \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.195, + 0.471, + 0.314 + ], + "angle": 0, + "content": "As aforementioned, the adversarial perturbation causes a mismatch between the label distributions of the perturbed data and their origins, as \\( p(y'|x') \\neq p(y|x) \\). However, during adversarial training, \\( p(y'|x') \\) is often simply replaced by \\( p(y|x') \\), that is, the perturbed labels are directly inherited from their origins. This would inevitably exert influence on the label memorization and results in performance degradation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.315, + 0.473, + 0.662 + ], + "angle": 0, + "content": "We are interested in the memoization of noisy labels in adversarial training, which can be characterised by \\( I(w; y'|x') \\) and referred to as \"Information In Weights\" (IIW). The training dynamics can also be captured through the lens of IIW. However, computing the value of \\( I(w; y'|x') \\) is as difficult as fitting the model itself. Basing on the chain rule of mutual information, we could approach to our desired result via the upper bound, i.e., \\( I(\\mathcal{D}; w) = I((x, y); w) = I(x; w) + I(y; w|x) \\). By using the positivity property of mutual information, we have \\( I(y; w|x) \\leq I(D; w) \\). Then we could take an approximation under some Gaussian assumptions, as suggested by Wang et al. [32], to estimate \\( I(w; y'|x') \\) and further depict the learning behaviour of model, which is illustrated by the green line in Fig. 1 (b). The increasing IIW supports our hypothesis that adversarially trained model mainly overfits the noisy labels in the non-monotonical growth stage. Upon the theoretical analysis, it is natural that we proposed to prevent models from excessively memorising noisy labels by means of IIW reductions. In this work, we propose to reduce IIW through soft labels, which is specifically effective in lowering mutual information and thus can be expected to weaken the memorization under the distribution mismatch." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.672, + 0.471, + 0.747 + ], + "angle": 0, + "content": "Theorem 1 (Soft label could reduce the IIW) Let \\( u \\) be the uniform random variable with \\( p.d.f. p(u) \\). By using the composition in Eq. (2), there exists an interpolation ration \\( \\lambda \\) between the clean label distribution and uniform distribution, such that" + }, + { + "type": "equation", + "bbox": [ + 0.189, + 0.758, + 0.47, + 0.775 + ], + "angle": 0, + "content": "\\[\nI \\left(y ^ {*}; w \\mid x ^ {\\prime}\\right) \\lesssim I (y; w \\mid x ^ {\\prime}) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.786, + 0.47, + 0.832 + ], + "angle": 0, + "content": "where \\( p(y^{*}|x^{\\prime},w) = \\lambda \\cdot p(y|x^{\\prime},w) + (1 - \\lambda)\\cdot p(u) \\) and the symbol \\( \\lesssim \\) means that the corresponding inequality up to an \\( c \\)-independent constant." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The detailed proof could be found in Appendix A. Theorem 1 proves that there exists some kind of soft label that could reduces the information in weights. So the memorization effect caused by the label distribution mismatch could be" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.183 + ], + "angle": 0, + "content": "effectively mitigated. Thus, to better suppress the memorization effect, we should provide more underlying information about the true label distribution than uniform distribution to facilitate a better interpolation of the soft label. In the following, we introduce our solution to estimate more accurate and informative soft labels for adversarial training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.195, + 0.892, + 0.231 + ], + "angle": 0, + "content": "3. Self-guided label refinement for adversarial training" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.238, + 0.638, + 0.255 + ], + "angle": 0, + "content": "3.1. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.895, + 0.397 + ], + "angle": 0, + "content": "As discussed above, hard labels in adversarial training are uninformative but over-confident, and thus heavily impairs the generalization (see Fig. 2). To address this issue, we propose an alternative to one-hot labels for adversarial training. Specifically, our Self-Guided Label Refinement first utilizes the learned probability distributions to refine the over-confident hard labels, and then it guides the training process using the historical training model to obtain a calibrated prediction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.895, + 0.487 + ], + "angle": 0, + "content": "We begin by softening the over-confident hard labels. It is well acknowledged that label smoothing (LS) helps to calibrate the degree of confidence of a model and it is effective in improving the robustness in noise regimes [17]. The vanilla LS for a \\(K\\)-class classification problem can be formulated:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.495, + 0.892, + 0.522 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = \\frac {r}{K} \\cdot \\mathbf {1} + (1 - r) \\cdot \\mathbf {y} _ {\\text {h a r d}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.895, + 0.727 + ], + "angle": 0, + "content": "where, \\(\\mathbf{y}_{\\text {hard }}\\) denotes labels encoded by a one-hot vector, the notation of 1 denotes all one vector, and \\(r \\in [0,1]\\) controls the smooth level. It is shown that LS serves as a regularizer as well as a confidence penalty [21] and therefore improves the generalization of the model in standard training. Unfortunately, when it comes to adversarial training, a direct combination with LS cannot guarantee reliable robustness, especially in the cases of strong perturbations[4, 20]. Specifically, as the uniform distribution is unlikely to match the underlying distribution, LS tends to introduce a bias that might hurt the robust generalization. Moreover, soft labels with identical probability over the false categories cannot reveal the semantic similarity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.895, + 0.788 + ], + "angle": 0, + "content": "To alleviate this artificial effect, we introduce our Self-Guided Label Refinement (SGLR) which utilizes the knowledge inferred by a trustworthy model itself to retains informative labels. The proposed SGLR can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.803, + 0.892, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} = r \\cdot f \\left(x ^ {\\prime}; w\\right) + (1 - r) \\cdot \\mathbf {y} _ {h a r d} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.895, + 0.901 + ], + "angle": 0, + "content": "where \\( f(x'; w) \\) is the logit output of the model parameterized by \\( w \\) on training data \\( x' \\). To be noticed, the model \\( f \\) we referred to here is not pre-trained but rather on the training. Eq. (6) also in fact serves as a regularizer by integrating the knowledge extracted from the model with static information" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24779" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.27, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.092, + 0.458, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.229, + 0.47, + 0.256 + ], + "angle": 0, + "content": "Figure 3. The mean confidence of model in the correct and incorrect predictions over clean and adversarial test sets." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.263, + 0.469, + 0.308 + ], + "angle": 0, + "content": "that encoded by one-hot labels, thus, we suggest that this particular form of soft label has the potential to convey a better quantity of informative content." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.309, + 0.469, + 0.4 + ], + "angle": 0, + "content": "Furthermore, according to Sanyal et al. [23], there exists a good interpolation of the noisy training dataset that could lead to a satisfactory generalization. Consequently, we aim to establish a valid interpolation between robust and non-robust features with the expectation that it strikes a balance between accuracy and robustness, as represented by the equation:" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.408, + 0.47, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\widetilde {f} (x, x ^ {\\prime}; w) = \\lambda \\cdot f (x; w) + (1 - \\lambda) \\cdot f (x ^ {\\prime}; w) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.47, + 0.783 + ], + "angle": 0, + "content": "Fig. 3 illustrates the major trajectory of PGD-AT training on CIFAR-10 dataset in terms of the confidence in both the correct and incorrect predictions, where the model dynamics are shown by a series of colored dots with darker colours and larger areas. Gray dashed lines mark the best standard / robust accuracy of the trained model, and the red star in the bottom right corner denotes an ideal model that with a high confidence in correct classification whereas a low one in the incorrect prediction. As training processes, model tends to assign increasing confidence to its correct predictions and also to those wrong predictions, as implied by the moving of the colored dots away from the dash line. In other words, the latter prediction of the model is not better calibrated and the model in the middle training stage could be of great help to reduce the expected calibration error. Therefore, we are motivated to utilize exponential moving average (EMA) that taking the moving average of history model prediction to obtain calibrated soft label. Intuitively, EMA considers recent proposals from the current state while retaining some influence from previous information. This straightforward method is easy to deploy and incurs negligible training overhead. Then the dynamic updating of soft label could be defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.792, + 0.47, + 0.829 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbf {y} = r \\cdot \\widetilde {p _ {t}} + (1 - r) \\cdot \\mathbf {y} _ {\\text {h a r d}} \\tag {8} \\\\ \\widetilde {p _ {t}} = \\alpha \\cdot \\widetilde {p} _ {t - 1} + (1 - \\alpha) \\cdot \\widetilde {f} (x, x ^ {\\prime}; w _ {t}) \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.414, + 0.865 + ], + "angle": 0, + "content": "3.2. Connection to symmetric cross entropy" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Cross Entropy (CE) is the prevalent loss function for deep learning with remarkable success. However, as the noisy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "label is tipping the training process into overfitting, CE loss has taken a nasty blow and is prone to fitting noise. Inspired by the symmetric Kullback-Leibler (KL) Divergence, Wang et al. [28] proposed a more flexible loss, i.e., symmetric cross entropy (SCE), to strike a balance between sufficient learning and robustness to noisy labels. Moreover, it reveals that predictive distribution exploited by the model is superior to one-hot label distribution for the most part. Both SCE loss and our method utilize the informative knowledge inferred by the model and Proposition 1 provide such a close link between them." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.268, + 0.894, + 0.313 + ], + "angle": 0, + "content": "Proposition.1 Let \\(\\ell_{sce}\\) be the SCE loss function and \\(\\gamma\\) represents the sum of CE and reverse CE loss. When \\(\\gamma \\rightarrow 1\\), then our methods can also be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.62, + 0.327, + 0.771, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\ell_ {s g l r} = \\ell_ {s c e} - \\alpha \\cdot \\ell_ {r k l}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.354, + 0.892, + 0.385 + ], + "angle": 0, + "content": "where \\(\\ell_{rkl}\\) denotes the reverse KL divergence between labels and model predictions, i.e., \\(D_{KL}(p\\parallel q)\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.893, + 0.529 + ], + "angle": 0, + "content": "The proof of Proposition 1 can be found in Appendix A. Note that Proposition 1 indicates our method can be decomposed into two terms. The first term represents the SCE loss function when the weighted sum tends to 1. The second term indicates that our method rewards the distribution differences between predictions and labels. Though our study aims at mitigating robust overfitting, which is different from the scenario of SCE loss, there is no conflict between our method and SCE." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.822, + 0.557 + ], + "angle": 0, + "content": "3.3. Comparison to knowledge distillation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.894, + 0.744 + ], + "angle": 0, + "content": "Knowledge distillation (KD) [16] has been proven to be an effective way to compress models, which is able to remarkably beef up the performance of lightweight models. There is a huge scope for applying KD to adversarial training to improve the efficiency of AT. A crop of works [5, 13, 29, 41] have advanced exploring KD implicitly or explicitly in conjunction with AT. The efficacy of KD is attributed to the teacher model's informative knowledge, which guides the student to acquire a more similar knowledge representation and effectively capture inter-class relationships. By enforcing consistency in probability distributions, KD facilitates better learning outcomes for the student." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.755, + 0.894, + 0.846 + ], + "angle": 0, + "content": "Proposition. 2 Some \\(KD\\) methods, which minimize the distance of the feature map between the teacher and student model, belong to the family of our method. Let \\(p_t\\) be the prediction of the teacher model and then the \\(KD\\) could also be written as \\(\\ell_{KD} = \\mathbb{E}_{\\widetilde{q}}[-\\log p] = H(\\widetilde{q},p)\\), where \\(\\widetilde{q} = (1 - \\alpha) \\cdot q + \\alpha \\cdot p_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Proposition 2 shows that some KD revised the hard label via the knowledge \\( p_t \\) learned by the teacher. The proof of Proposition 2 is presented in Appendix A. Further, we view" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24780" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.289, + 0.09, + 0.68, + 0.103 + ], + "angle": 0, + "content": "Table 1. Comparison between our method and other KD methods." + }, + { + "type": "table", + "bbox": [ + 0.174, + 0.107, + 0.79, + 0.202 + ], + "angle": 0, + "content": "
ARD [13]RSLAD [41]KD-SWA [5]Ous
Trained teacher models1120
Standardly teacher independent✓✓✗✓
Adversarily teacher independent✗✗✗✓
Forward times in one training iteration3342
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.22, + 0.471, + 0.327 + ], + "angle": 0, + "content": "our method as special supervision, and smoothing the hard label could better reflect the similarities among classes. There are many differences between our method and other KDs in AT. The main differences are summarized in Tab. 1. Our method does not incur any extra computational cost as we do not involve teacher models, which is a boon throughout the whole training progress." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.336, + 0.285, + 0.351 + ], + "angle": 0, + "content": "3.4. Tolerant to noisy label" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.471, + 0.435 + ], + "angle": 0, + "content": "In the following part, we'd like to delve into whether the proposed method is tolerant of noisy labels. We define the symmetric noise label as that true label \\(y\\) has probabilities \\(\\eta_{x,\\widetilde{y}} = p(\\widetilde{y} | y, x)\\) to flip into the wrong labels uniformly. The corresponding noisy empirical risk is:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.446, + 0.454, + 0.479 + ], + "angle": 0, + "content": "\\[\nR _ {\\mathcal {S}} ^ {\\eta} (f) = \\mathbb {E} _ {\\mathcal {S}} (1 - \\eta_ {x}) \\cdot \\ell (f (x), y) + \\sum_ {i \\neq y} \\eta_ {x, i} \\ell (f (x), i)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.47, + 0.549 + ], + "angle": 0, + "content": "where, \\(\\eta_{x}\\) is the noise rate. We call a loss function noisetolerant if and only if the global minimum \\(f_{\\eta}^{*}\\) has the same probability of misclassification as that of \\(f^{*}\\) on the noise-free data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.624 + ], + "angle": 0, + "content": "Lemma. 1 Given a symmetric loss function \\(\\ell\\) that it satisfies \\(\\sum_{i=1}^{k} L(f(x), i) = C\\) and \\(C\\) is some constant. Then \\(\\ell\\) is noise tolerant under symmetric label noise if noise rate \\(\\eta\\) meets \\(\\eta < 1 - \\frac{1}{K}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.722 + ], + "angle": 0, + "content": "The loss condition theoretically guarantees the noise tolerance by risk minimization on a symmetric loss function following [12] and it shows that the global optimal classifier \\( f^{*} \\) on noise-free data remains the optimal even with the noisy label. Further, we can also derive the noise tolerance theoretically about our method from Theorem 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.471, + 0.811 + ], + "angle": 0, + "content": "Theorem 2 In a \\(K\\)-class classification problem, our method \\(\\widetilde{\\ell}\\) is noise-tolerant under symmetric or uniform label noise if noise rate \\(\\eta < 1 - \\frac{1}{K}\\). And if \\(R(f^{*}) = 0\\), \\(\\widetilde{l}\\) is also noise-tolerant under asymmetric or class-dependent label noise when noise rate \\(\\eta_{y,k} < 1 - \\eta_y\\) with \\(\\sum_{i \\neq y} \\eta_{y,i} = \\eta_y\\), then" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.83, + 0.468, + 0.861 + ], + "angle": 0, + "content": "\\[\nR _ {\\mathcal {S}} ^ {\\eta} (f ^ {*}) - R _ {\\mathcal {S}} ^ {\\eta} (f) \\simeq \\left(1 - \\frac {\\eta K}{K - 1}\\right) \\left(R _ {\\mathcal {S}} (f ^ {*}) - R _ {\\mathcal {S}} (f)\\right) \\leq 0\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "From Theorem 2, we can derive that our method is nearly noise-tolerant under symmetric noise and further prove the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.22, + 0.894, + 0.281 + ], + "angle": 0, + "content": "robustness of the proposed method to asymmetric noise. More details can be found in Appendix B. We show a significant improvement under noise regimes empirically in experiments." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.293, + 0.633, + 0.311 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.319, + 0.895, + 0.561 + ], + "angle": 0, + "content": "Training and evaluation setups. We conduct extensive experiments on the benchmark datasets, CIFAR-10/100. We set the perturbation budget to \\(\\epsilon = 8 / 255\\) under the \\(\\ell_{\\infty}\\) norm-bounded constraint. We use ResNet-18 [15] as our default network architecture unless otherwise specified. For all experiments, the model is trained using SGD with a momentum of 0.9, weight decay of \\(5\\times 10^{-4}\\), and an initial learning rate of 0.1 for a total of 200 epochs. The learning rate is decayed by a factor of 0.1 at the 100-th and 150-th epochs, following [22]. The evaluation of the proposed approach encompasses PGD-20 [22] and AutoAttack [7], which is recognized as the most reliable robustness evaluation up to date. AutoAttack is an ensemble of diverse attacks, including APGD-CE, APGD-DLR, FAB [8] and Square attack [2]. We quantify the robust generalization by computing the difference between the best and final checkpoints over the course of training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.572, + 0.895, + 0.724 + ], + "angle": 0, + "content": "Improved robust performance across datasets. Experimental results of PGD-AT [18], TRADES [39], and the combinations of them with our proposal (denoted as PGD-AT+SGLR and TRADES+SGLR) on CIFAR-10/100 datasets are shown in Tab. 3, from which we make the following observations on our advantages: 1) Closer generalization gap. It is remarkable that the differences between the best and the final test accuracies of the combinations are reduced to around \\(0.5\\%\\), while the corresponding baselines (PGD-AT and TRADES) induce much larger gaps, which" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.746, + 0.699, + 0.85 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.746, + 0.888, + 0.85 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.854, + 0.894, + 0.91 + ], + "angle": 0, + "content": "Figure 4. Test accuracy \\((\\%)\\) on CIFAR-10 dataset (with \\(40\\%\\) label noise). We split the training set into 1) untouched portion, where the labels of elements are left untouched; 2) corrupted portion, where the labels of elements are assigned uniformly at random." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24781" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 2. Test accuracy \\((\\%)\\) of the proposed method and other methods on CIFAR-10 under the \\(\\ell_{\\infty}\\) norm with \\(\\epsilon = 8 / 255\\) based on the ResNet-18 architecture." + }, + { + "type": "table", + "bbox": [ + 0.171, + 0.122, + 0.794, + 0.297 + ], + "angle": 0, + "content": "
MethodNatural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
PGD-AT80.782.4-1.650.741.49.347.740.27.5
PGD-AT+LS82.284.3-2.153.748.94.848.444.63.9
PGD-AT+TE82.482.8-0.455.854.81.050.649.61.0
PGD-AT+SGLR82.983.0-0.156.455.90.551.250.21.0
AWP82.181.11.055.454.80.650.649.90.7
KD-AT82.985.5-2.654.653.21.449.148.80.3
KD-SWA84.785.4-0.854.953.81.149.349.4-0.1
PGD-AT + SGLR82.983.0-0.156.455.90.551.250.21.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.303, + 0.89, + 0.334 + ], + "angle": 0, + "content": "Table 3. Clean accuracy and robust accuracy (\\%) of ResNet 18 trained on different benchmark datasets. All threat models are under \\(\\ell_{\\infty}\\) norm with \\(\\epsilon = 8 / 255\\). The bold indicates the improved performance achieved by the proposed method." + }, + { + "type": "table", + "bbox": [ + 0.15, + 0.336, + 0.816, + 0.521 + ], + "angle": 0, + "content": "
DatasetMethodNatrural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
CIFAR-10AT80.782.4-1.650.741.49.347.740.27.5
+SGLR82.983.00.156.455.90.551.250.21.0
TRADES81.282.5-1.353.350.33.049.046.82.2
+SGLR82.283.3-0.955.855.40.450.750.10.6
CIFAR-100AT53.953.60.327.319.87.522.718.14.6
+SGLR56.956.60.334.534.30.227.526.70.8
TRADES57.956.31.729.927.72.224.623.41.2
+SGLR57.157.4-0.333.933.20.727.126.40.7
" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.54, + 0.472, + 0.751 + ], + "angle": 0, + "content": "are up to \\(9.3\\%\\) and \\(3.0\\%\\) on CIFAR-10 dataset when the model is threaten by PGD-20. It indicates that our method effectively alleviates robust overfitting. 2) Higher robust accuracy. As the combinations induce smaller gaps, they can approach higher robust accuracy against adversaries compared to baseline methods, as can be observed in Tab. 3. Besides, it is notable that our method is especially effective against AutoAttack [7], regarding the fundamental difficulties of simultaneously achieving the robustness against multiple adversaries. 3) Consistent improvement. Combining our label smoothing method could consistently and significantly improve the performance on all considered adversaries and also on the clean test set, and across different datasets, namely, the CIFAR-10 and CIFAR-100 datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Improved generalization under noise regimes. Moreover, we verify the self-guided label smoothing by comparing the behavior of the proposed SGLR with that of the widely used one-hot labels under different noise settings, with \\(40\\%\\) noisy labels and fully \\(60\\%\\) true labels, respectively. Specifically, we focus on evaluating the effectiveness of our approach in mitigating the impact of symmetric noisy labels, where the labels are resampled from a uniform distribution over all labels with a probability \\(\\eta\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.54, + 0.895, + 0.811 + ], + "angle": 0, + "content": "We begin by making the observations in the left of Fig. 4: 1) The generalization error (i.e., the difference between the training and test accuracy) of the proposed SGLR (almost negligible) is obviously smaller than that of the commonly used hard labels (\\(>50\\%\\)). 2) The peak of the training accuracy using hard labels (blue curve) can approximate \\(100\\%\\) even on the training set with \\(40\\%\\) noisy labels (horizontal gray dashed denotes the portion of correct labels), which suggests that using hard labels could fit correct labels in the early stage and eventually memorizes noisy labels. On the contrary, our training curve is bounded by the untouched portion, implying that our method is able to calibrate the training process and maintain a proper fitting of training data. Then we turn to the other setting as shown in the right of Fig. 4, our test accuracy grows steadily while the baseline method fails. This observation again suggests that the double-descent phenomenon might be due to the overfitting of noise and it is hopeful to be avoided by our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.895, + 0.888 + ], + "angle": 0, + "content": "To give a more intuitive explanation, we further visualize the penultimate layer representations of ResNet 18 trained with (a) a hard label; (b) a soft label, and (c) the proposed soften label. As Fig. 5 shown, under all the settings of noise rate, the proposed SGLR with self-guided distribution" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24782" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.09, + 0.468, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.472, + 0.335 + ], + "angle": 0, + "content": "Figure 5. Visualization of representations learned by standard training with hard/soft labels and the proposed SGLR with self-guided distribution on CIFAR-10 dataset under various levels of symmetric noisy labels \\((\\eta \\in [0.0,0.2,0.4,0.6])\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.343, + 0.47, + 0.478 + ], + "angle": 0, + "content": "can consistently provide better representations, displayed with more separable clusters and tighter intra-class distance, which are very close to those of the clean setting (the leftmost column). Notably, even with a significantly increased noise rate from 0 (no noise) to 0.6 (severe noise), as illustrated from left to right in Fig. 5, our method learns representations with almost negligible variance. This also echoes our advantages of robust learning under various settings of data corruption." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.47, + 0.541 + ], + "angle": 0, + "content": "In a nutshell, we have grounds to empirically believe that our method exhibits benign tolerance to noisy labels and improves the generalization ability of the model by avoiding fitting noisy labels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.554, + 0.471, + 0.812 + ], + "angle": 0, + "content": "Comparison against other methods. Considering that our method is analogous to employing the technique of label smoothing into AT, in Tab. 2, we report robustness evaluations of AT with label smoothing (PGD-AT + LS) and temporal ensembling (PGD-AT + TE) on CIFAR-10 test set. Since excessive LS could degrade the robustness reported in [20], we implement LS with smoothing level \\( r = 0.2 \\). We empirically found that SGLR not only can effectively alleviate robust overfitting while LS fails but also boosts the robustness even under strong AutoAttack. Further, we also report other methods (e.g., AWP [33], KD-AT [10]) in Tab. 2, which can mitigate robust overfitting through the lens of weight smoothness and the knowledge transfer of teacher model. Though robust overfitting is indeed impeded by applying these methods, our method could better narrow the generalization gap between best and final models and achieve remarkable robustness than others under AutoAttack." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "On the impact of smoothing effect \\( r \\). The effectiveness of SGLR relies on the smoothing level of soft labels. Besides, as we discussed in Sec. 3.3, SGLR could be viewed as a kind of knowledge distillation without extra teacher models involved. Large temperature \\( T \\) during distillation improves" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.259 + ], + "angle": 0, + "content": "the smoothness of output distribution but could impair the test performance. As the temperature is vital, we could specify \\( f(x;w)_i \\) in Eq. (7) as \\( \\exp (z_i / T) / \\sum_j\\exp (z_j / T) \\). We vary the smoothing level \\( r\\in \\{0.0,0.2,0.4,0.6,0.8\\} \\) in Tab. 4 and note that an increase in \\( r \\) initially boosts both standard accuracy and robust accuracy, followed by a decline, indicating that excessive smoothing introduces noise and hampers predictive capability. Additionally, increasing the temperature while fixing \\( r \\) only gains slightly improvement in standard accuracy but observes degradation in robust accuracy." + }, + { + "type": "table_caption", + "bbox": [ + 0.503, + 0.282, + 0.889, + 0.296 + ], + "angle": 0, + "content": "Table 4. Ablation study on smoothing level \\( r \\) and temperature \\( T \\) ." + }, + { + "type": "table", + "bbox": [ + 0.528, + 0.301, + 0.862, + 0.442 + ], + "angle": 0, + "content": "
T/r0.00.20.40.60.8
1SA82.483.582.878.569.1
RA43.754.954.252.748.3
1.5SA83.282.983.180.674.5
RA45.755.953.250.449.8
2SA82.984.483.978.575.6
RA45.853.952.050.947.8
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.493, + 0.742, + 0.509 + ], + "angle": 0, + "content": "5. Discussion and conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.895, + 0.73 + ], + "angle": 0, + "content": "In this study, we show that label noise induced by distribution mismatch and improper label assignments would degrade the test accuracies as well as make the robust overfitting aggravated. From the view of this observation, a label assignment approach for AT, Self-Guided Label Refinement (SGLR), is proposed to weaken the memorization in AT on noisy labels and thus to mitigate the robust overfitting. Extensive experimental results demonstrate the effectiveness of the proposed SGLR. Though we circumvent over confident prediction, the model is still not well-calibrated. As we measure the calibration of model during the training over the entire dataset instead of in a sample-wise way, it may give a false sense of reweighting confidence. In the future, we will attempt to address this limitation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.755, + 0.661, + 0.772 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This work is partially supported by the National Science and Technology Major Project of China (Grant No. 2022ZD0119103), the National Natural Science Foundation of China (Grant No. 61906168), the Zhejiang Provincial Natural Science Foundation of China (Grant No.LQ21F020006, LY23F020023), and is also supported by the advanced computing resources provided by the Supercomputing Center of Hangzhou City University." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24783" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.472, + 0.156 + ], + "angle": 0, + "content": "[1] Alessandro Achille and Stefano Soatto. 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However, most AT methods suffer from robust overfitting, i.e., a significant generalization gap in adversarial robustness between the training and testing curves. In this paper, we first identify a connection between robust overfitting and the excessive memorization of noisy labels in AT from a view of gradient norm. As such label noise is mainly caused by a distribution mismatch and improper label assignments, we are motivated to propose a label refinement approach for AT. Specifically, our Self-Guided Label Refinement first self-refines a more accurate and informative label distribution from over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model and thus requiring no external teachers. Empirical results demonstrate that our method can simultaneously boost the standard accuracy and robust performance across multiple benchmark datasets, attack types, and architectures. In addition, we also provide a set of analyses from the perspectives of information theory to dive into our method and suggest the importance of soft labels for robust generalization. + +# 1. Introduction + +Recent studies have reported that deep neural networks (DNNs) are vulnerable to adversarial examples, i.e., malicious inputs perturbed by an imperceptible noise to confuse the classifier prediction [14, 25]. This vulnerability raises serious security concerns and motivates a growing body of works on defense techniques [18, 24, 39]. Adversarial training (AT) is arguably the most promising way to harden classifiers against adversarial examples, which directly augments the training set with adversarial examples [3, 18]. It + +is formulated as a min-max problem [18] to find model parameters $w$ that minimize the adversarial risk: + +$$ +\min _ {w} \mathcal {L} _ {\mathcal {S}} \left(x ^ {\prime}, y; w\right) \tag {1} +$$ + +where $\mathcal{L}_{\mathcal{S}}(x',y;w) = 1 / n\sum_{i = 1}^{|S|}\max_{x'\in \mathcal{B}_r(x)}\ell (f(x_i';w),y_i)$ and $f(\cdot ;w)$ is a model parameterized by $w$ $\ell (\cdot)$ is the loss function such as cross-entropy loss, and $\mathcal{B}_r(x)$ denotes the set of the allowed perturbations under the given metric space $M = (X,d)$ and the suitable radius $r > 0$ , i.e., $\mathcal{B}_r(x) = \{x + \delta \in \mathcal{X}:d(x,x + \delta) < r\}$ + +However, most AT methods suffer from a dominant phenomenon that is referred to as "robust overfitting". That is, an adversarially trained model can reach almost $100\%$ robust accuracy on the training set while the performance on the test set is much inferior, witnessing a significant gap of adversarial robustness [22]. Various regularization techniques including classic $\ell_1$ , $\ell_2$ regularization and more advanced regularizations using data augmentation, such as Mixup [38] and Cutout [9], have been attempted to mitigate robust overfitting, whereas they are reported to perform no better than a simple early stopping [22]. However, early stopping raises another concern as the checkpoint of the best robustness and that of the best standard accuracy often do not coincide [5]. To outperform data augmentations and early stopping, regularizations specifically designed for robust training are thus proposed, to name a few, loss reweighting [27, 29, 37, 40] and weight smoothing [5, 33, 36, 37]. These regularization methods are likely to restrict the change of training loss by suppressing perturbations with respect to either the inputs $x$ or the weights $w$ , whereas few explorations attempt to combat robust overfitting from the perspective of labels $y$ . + +Previous investigations on labels in AT [10, 35] emphasised the existence of label noise in AT to provide an understanding of robust generalization, for instance, from a classic bias-variance perspective. We take a step still further to investigate the memorization of label noise in AT, which is characterised by a non-monotonical increase of gradient norm, as illustrated in Fig. 1, resulting in robust overfitting. In light of our analyses, we are motivated to design a strategy + +![](images/df0b5802ee23945c78879e8b25fe902fbf047d4fe032d4a8723f634cea1175e8.jpg) +(a) Gradient norm magnitude + +![](images/d04f677b2fea59684592a610f0b73d654144165b5896168625f1297642c723eb.jpg) +(b) Generalization gap +Figure 1. In figure (a), we calculate the gradient norm of vanilla adversarially trained PreAct-ResNet 18 on CIFAR-10 for robustness against $\ell_{\infty}$ perturbations of radius 8/255. In figure (b), we show the robust accuracy under PGD-20 attack under the same settings with figure (a). The gradient norm keeps non-monotonically ramping up when robust overfitting happens. + +for label refinement to alleviate excessive memorization and thus the robust overfitting. To that end, we conduct an empirical experiment using different label assignments and analyse through the lens of learning curve, which is a useful indicator for the occurrence of robust overfitting. As shown in Fig. 2, the phenomenon of robust overfitting is presented, for instance, in the lower left of Fig. 2 for PGD-AT [18] with commonly used hard labels, and at a slightly reduced extent as shown in the lower middle of Fig. 2 with vanilla soft labels. + +In this work, we propose a theoretical-grounded method to alleviate the memoization on over-confident labels during adversarial training and thus to combat robust overfitting. Our main idea is to resort to an alternative for label assignment. Particularly, motivated by the effectiveness of soft label in alleviating overfitting in standard training [26], our work generates more reliable labels automatically by incorporating predictive label distributions into the process of robust learning. It provides a promising way to inject distilled knowledge and to self-calibrate the adversarial training. Our method is conceptually simple yet significantly enhances the learning of deep models in adversarial scenarios. The key contributions are as follows: + +- We first inspect the behaviour of deep models trained by AT when robust overfitting occurs. Specifically, we identify a connection between robust overfitting and the excessive memorization of noisy labels in AT through the lens of gradient norm (see Fig. 1). As such label noise is mainly due to inaccurate label distribution, we further investigate the effects of different label assignment methods on AT (see Fig. 2). These observations consistently implies a connection between robust overfitting and noisy hard labels. Exploring such connections could help to shed light on understanding and improving the robust learning of deep models. +- Upon the observation, we are motivated to propose a label + +refinement approach for AT. Specifically, our Self-Guided Label Refinement (SGLR) first self-refines accurate and informative label distribution from the over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model, requiring no external teacher models nor modifications to the existing architecture. + +- We verify the effectiveness of SGLR through extensive evaluations. Overall, experimental results show that the proposed method consistently improves the test accuracy over the state-of-the-art on various benchmark datasets against diverse adversaries. Moreover, our approach can achieve robust accuracy up to $56.4\%$ and close the generalization gap to merely $0.4\%$ , significantly mitigating the overfitting issue and thus being able to pushing up the adversarial robustness. + +# 2. A closer look at robust overfitting + +Robust overfitting has been prevalent across various datasets and models [22]. Then, crops of empirical and theoretical studies have emerged to analyze this phenomenon through the lens of loss value [37], training data [10] and learned features [30]. However, a comprehensive underlying mechanism of robust overfitting still remains an enigma. In this section, we revisit robust overfitting from a perspective of the established information theory and identify a "memorization effect" over the course of adversarial training, which is akin to standard training as observed in [6, 34]. First and foremost, we conduct some observations when robust overfitting occurs via analysing the change of the gradient norm of adversarial loss with respect to model weight, i.e., $\| \nabla_w L(x', y, w) \|_2$ . As shown in Fig. 1 (a), we may note that the gradient norm holds nearly the constant and then keeps ramping up nonmonotonically. This increasing behavior of gradient norm + +![](images/fbe753404e53dce1be123c028b2607c3d794c114dcfd9153b4539fad709f2048.jpg) + +![](images/4cad22deaad17b7d5fcc92669886b371124a53caa5479c81fd1ad30750de56fc.jpg) + +![](images/fb89fc4c68e5775ab99c4d6a3ea0f06b7e5a12e02ab20cdef448e9c4fbf4aea9.jpg) + +![](images/1a33523c1fba43f31ff1f04494e469c6860ea25c8262ae8e19047975d2367594.jpg) +Figure 2. Robust accuracy of models employing different label assignment methods in adversarial training. + +![](images/561c2e92403f150dd68cbedd37d9426a530c267a7c09ca950107412c1761e366.jpg) + +![](images/7dd9be1e6da23622df5700a8132ab35e95296843aba017b4fcef5e32d30824cb.jpg) + +encountered with the learning rate (LR) decays. So we divide the training process into two phases according to the LR decays: (1) Stationary stage; (2) Non-monotonical growth stage. + +In stationary stage, as illustrated in Fig. 1 (b), the learning curve (orange line) and test robust accuracy (blue line) ramp up at almost the same pace and maintain a very small generalization gap, i.e., the divergence between the training and test accuracy, implying that the model keeps learning efficient robust features as the training progresses and accordingly hovers a small constant gradient norm. However, a significantly expanding generalization gap can be witnessed after an inflection point, where the LR decays. We refer the period afterwards as "Non-monotonical growth stage", as a prominent characteristic of this stage is that the gradient norm keeps growing non-monotonically and does not converge to a constant, even after the training has ended. + +It is worth noting that this trend of gradient norm greatly contradicts with that of the conventional ERM training, where zero gradient norm can be reached at the end of training. Nonetheless, such behaviour of gradient norm is in line with ERM when significant noisy labels surrounding, as observed in [11, 31]. Specifically, such growing trend is interpreted as an indicator that the training has entered a "memorization routine", where the model firstly fits on training samples with clean labels, then gradually over-fits samples with noisy labels. Later in this stage, the test accuracy on clean data will go down whereas the training accuracy keeps going up. Similarly, we are able to identify a non-monotonical growth in adversarial training, as depicted in Fig. 1 (a). Remarkably, this divergent gradient norm as the adversarial training progressing, exactly accompanies + +with the enlargement of generalization gap that is depicted in Fig. 1 (b), which reveals the overfitting problem. Thus, we come to a conjecture that the memorization effect is also the culprit of the increasing gradient norm in the scenario of robust training and further induces robust overfitting. To that end, we first provide proof for our hypothesis that adversarial training memorizes samples with noisy labels mainly in the non-monotonical divergence phase. + +Following [1], the expected cross entropy loss could be decomposed into three terms according to PAC-Bayesian framework: + +$$ +\begin{array}{l} \mathcal {H} _ {f} (\hat {y} | x, w) \\ = \mathbb {E} _ {\mathcal {S}} \mathbb {E} _ {w \sim Q (w | \mathcal {S})} \sum_ {i = 1} ^ {m} [ - \log f (\hat {y} _ {i} | x _ {i}, w) ] \\ = \mathcal {H} (y | x) + \mathbb {E} _ {x, w \sim Q (w | \mathcal {S})} \mathrm {K L} [ p (y | x) \| f (\hat {y} | x, w) ] - I (w; y | x) \tag {2} \\ \end{array} +$$ + +In conventional ERM training, minimizing $-I(w; y|x)$ relies on the cross entropy loss between the prediction $f(\hat{y} | x, w)$ and the true label distribution $p(y|x)$ . Noisy label viewed as the outlier of a true label distribution can provide a positive value of $I(w; y|x)$ . This term essentially quantifies the extent to which label information overlaps the weights of the model. In other words, the presence of noisy labels will reduce the finite degree of freedom with respect to weights. The reason for this reduction is that model attempts to accommodate the noise labels in the training data, inducing a potential overfitting. Different from the conventional ERM training, adversarial training requires perturbed samples $x'$ , which are usually obtained by solving a multi-step maximization problem. Accordingly, we use the notation $p(y'|x')$ for the true distribution of adversarial samples. Based on the + +Eq. (2), we have + +$$ +\begin{array}{l} \mathcal {H} _ {f} (\hat {y} | x ^ {\prime}, w) = \mathbb {E} _ {\mathcal {S}} \mathbb {E} _ {w \sim Q (w | \mathcal {S})} \sum_ {i = 1} ^ {m} \left[ - \log f \left(\hat {y} _ {i} \mid x _ {i} ^ {\prime}, w\right) \right] \\ = \mathcal {H} \left(y ^ {\prime} \mid x ^ {\prime}\right) - I (w; y ^ {\prime} \mid x ^ {\prime}) \\ + \mathbb {E} _ {x ^ {\prime}, w \sim Q (w | \mathcal {S})} \mathrm {K L} [ p (y ^ {\prime} | x ^ {\prime}) \| f (\hat {y} | x ^ {\prime}, w) ] \\ \end{array} +$$ + +As aforementioned, the adversarial perturbation causes a mismatch between the label distributions of the perturbed data and their origins, as $p(y'|x') \neq p(y|x)$ . However, during adversarial training, $p(y'|x')$ is often simply replaced by $p(y|x')$ , that is, the perturbed labels are directly inherited from their origins. This would inevitably exert influence on the label memorization and results in performance degradation. + +We are interested in the memoization of noisy labels in adversarial training, which can be characterised by $I(w; y'|x')$ and referred to as "Information In Weights" (IIW). The training dynamics can also be captured through the lens of IIW. However, computing the value of $I(w; y'|x')$ is as difficult as fitting the model itself. Basing on the chain rule of mutual information, we could approach to our desired result via the upper bound, i.e., $I(\mathcal{D}; w) = I((x, y); w) = I(x; w) + I(y; w|x)$ . By using the positivity property of mutual information, we have $I(y; w|x) \leq I(D; w)$ . Then we could take an approximation under some Gaussian assumptions, as suggested by Wang et al. [32], to estimate $I(w; y'|x')$ and further depict the learning behaviour of model, which is illustrated by the green line in Fig. 1 (b). The increasing IIW supports our hypothesis that adversarially trained model mainly overfits the noisy labels in the non-monotonical growth stage. Upon the theoretical analysis, it is natural that we proposed to prevent models from excessively memorising noisy labels by means of IIW reductions. In this work, we propose to reduce IIW through soft labels, which is specifically effective in lowering mutual information and thus can be expected to weaken the memorization under the distribution mismatch. + +Theorem 1 (Soft label could reduce the IIW) Let $u$ be the uniform random variable with $p.d.f. p(u)$ . By using the composition in Eq. (2), there exists an interpolation ration $\lambda$ between the clean label distribution and uniform distribution, such that + +$$ +I \left(y ^ {*}; w \mid x ^ {\prime}\right) \lesssim I (y; w \mid x ^ {\prime}) \tag {4} +$$ + +where $p(y^{*}|x^{\prime},w) = \lambda \cdot p(y|x^{\prime},w) + (1 - \lambda)\cdot p(u)$ and the symbol $\lesssim$ means that the corresponding inequality up to an $c$ -independent constant. + +The detailed proof could be found in Appendix A. Theorem 1 proves that there exists some kind of soft label that could reduces the information in weights. So the memorization effect caused by the label distribution mismatch could be + +effectively mitigated. Thus, to better suppress the memorization effect, we should provide more underlying information about the true label distribution than uniform distribution to facilitate a better interpolation of the soft label. In the following, we introduce our solution to estimate more accurate and informative soft labels for adversarial training. + +# 3. Self-guided label refinement for adversarial training + +# 3.1. Methodology + +As discussed above, hard labels in adversarial training are uninformative but over-confident, and thus heavily impairs the generalization (see Fig. 2). To address this issue, we propose an alternative to one-hot labels for adversarial training. Specifically, our Self-Guided Label Refinement first utilizes the learned probability distributions to refine the over-confident hard labels, and then it guides the training process using the historical training model to obtain a calibrated prediction. + +We begin by softening the over-confident hard labels. It is well acknowledged that label smoothing (LS) helps to calibrate the degree of confidence of a model and it is effective in improving the robustness in noise regimes [17]. The vanilla LS for a $K$ -class classification problem can be formulated: + +$$ +\mathbf {y} = \frac {r}{K} \cdot \mathbf {1} + (1 - r) \cdot \mathbf {y} _ {\text {h a r d}} \tag {5} +$$ + +where, $\mathbf{y}_{\text {hard }}$ denotes labels encoded by a one-hot vector, the notation of 1 denotes all one vector, and $r \in [0,1]$ controls the smooth level. It is shown that LS serves as a regularizer as well as a confidence penalty [21] and therefore improves the generalization of the model in standard training. Unfortunately, when it comes to adversarial training, a direct combination with LS cannot guarantee reliable robustness, especially in the cases of strong perturbations[4, 20]. Specifically, as the uniform distribution is unlikely to match the underlying distribution, LS tends to introduce a bias that might hurt the robust generalization. Moreover, soft labels with identical probability over the false categories cannot reveal the semantic similarity. + +To alleviate this artificial effect, we introduce our Self-Guided Label Refinement (SGLR) which utilizes the knowledge inferred by a trustworthy model itself to retains informative labels. The proposed SGLR can be formulated as: + +$$ +\mathbf {y} = r \cdot f \left(x ^ {\prime}; w\right) + (1 - r) \cdot \mathbf {y} _ {h a r d} \tag {6} +$$ + +where $f(x'; w)$ is the logit output of the model parameterized by $w$ on training data $x'$ . To be noticed, the model $f$ we referred to here is not pre-trained but rather on the training. Eq. (6) also in fact serves as a regularizer by integrating the knowledge extracted from the model with static information + +![](images/70e85b23541508b5f67c54c0a41b918c5ac1b5e2a2749178987c3cd5df7327fc.jpg) +Figure 3. The mean confidence of model in the correct and incorrect predictions over clean and adversarial test sets. + +![](images/44dd40b47c9c4dfd10d879d7f9c74d790853a4e4bf6326cd3908c0f1abe8e20c.jpg) + +that encoded by one-hot labels, thus, we suggest that this particular form of soft label has the potential to convey a better quantity of informative content. + +Furthermore, according to Sanyal et al. [23], there exists a good interpolation of the noisy training dataset that could lead to a satisfactory generalization. Consequently, we aim to establish a valid interpolation between robust and non-robust features with the expectation that it strikes a balance between accuracy and robustness, as represented by the equation: + +$$ +\widetilde {f} (x, x ^ {\prime}; w) = \lambda \cdot f (x; w) + (1 - \lambda) \cdot f (x ^ {\prime}; w) \tag {7} +$$ + +Fig. 3 illustrates the major trajectory of PGD-AT training on CIFAR-10 dataset in terms of the confidence in both the correct and incorrect predictions, where the model dynamics are shown by a series of colored dots with darker colours and larger areas. Gray dashed lines mark the best standard / robust accuracy of the trained model, and the red star in the bottom right corner denotes an ideal model that with a high confidence in correct classification whereas a low one in the incorrect prediction. As training processes, model tends to assign increasing confidence to its correct predictions and also to those wrong predictions, as implied by the moving of the colored dots away from the dash line. In other words, the latter prediction of the model is not better calibrated and the model in the middle training stage could be of great help to reduce the expected calibration error. Therefore, we are motivated to utilize exponential moving average (EMA) that taking the moving average of history model prediction to obtain calibrated soft label. Intuitively, EMA considers recent proposals from the current state while retaining some influence from previous information. This straightforward method is easy to deploy and incurs negligible training overhead. Then the dynamic updating of soft label could be defined as follows: + +$$ +\begin{array}{l} \mathbf {y} = r \cdot \widetilde {p _ {t}} + (1 - r) \cdot \mathbf {y} _ {\text {h a r d}} \tag {8} \\ \widetilde {p _ {t}} = \alpha \cdot \widetilde {p} _ {t - 1} + (1 - \alpha) \cdot \widetilde {f} (x, x ^ {\prime}; w _ {t}) \\ \end{array} +$$ + +# 3.2. Connection to symmetric cross entropy + +Cross Entropy (CE) is the prevalent loss function for deep learning with remarkable success. However, as the noisy + +label is tipping the training process into overfitting, CE loss has taken a nasty blow and is prone to fitting noise. Inspired by the symmetric Kullback-Leibler (KL) Divergence, Wang et al. [28] proposed a more flexible loss, i.e., symmetric cross entropy (SCE), to strike a balance between sufficient learning and robustness to noisy labels. Moreover, it reveals that predictive distribution exploited by the model is superior to one-hot label distribution for the most part. Both SCE loss and our method utilize the informative knowledge inferred by the model and Proposition 1 provide such a close link between them. + +Proposition.1 Let $\ell_{sce}$ be the SCE loss function and $\gamma$ represents the sum of CE and reverse CE loss. When $\gamma \rightarrow 1$ , then our methods can also be written as: + +$$ +\ell_ {s g l r} = \ell_ {s c e} - \alpha \cdot \ell_ {r k l} +$$ + +where $\ell_{rkl}$ denotes the reverse KL divergence between labels and model predictions, i.e., $D_{KL}(p\parallel q)$ . + +The proof of Proposition 1 can be found in Appendix A. Note that Proposition 1 indicates our method can be decomposed into two terms. The first term represents the SCE loss function when the weighted sum tends to 1. The second term indicates that our method rewards the distribution differences between predictions and labels. Though our study aims at mitigating robust overfitting, which is different from the scenario of SCE loss, there is no conflict between our method and SCE. + +# 3.3. Comparison to knowledge distillation + +Knowledge distillation (KD) [16] has been proven to be an effective way to compress models, which is able to remarkably beef up the performance of lightweight models. There is a huge scope for applying KD to adversarial training to improve the efficiency of AT. A crop of works [5, 13, 29, 41] have advanced exploring KD implicitly or explicitly in conjunction with AT. The efficacy of KD is attributed to the teacher model's informative knowledge, which guides the student to acquire a more similar knowledge representation and effectively capture inter-class relationships. By enforcing consistency in probability distributions, KD facilitates better learning outcomes for the student. + +Proposition. 2 Some $KD$ methods, which minimize the distance of the feature map between the teacher and student model, belong to the family of our method. Let $p_t$ be the prediction of the teacher model and then the $KD$ could also be written as $\ell_{KD} = \mathbb{E}_{\widetilde{q}}[-\log p] = H(\widetilde{q},p)$ , where $\widetilde{q} = (1 - \alpha) \cdot q + \alpha \cdot p_t$ . + +Proposition 2 shows that some KD revised the hard label via the knowledge $p_t$ learned by the teacher. The proof of Proposition 2 is presented in Appendix A. Further, we view + +Table 1. Comparison between our method and other KD methods. + +
ARD [13]RSLAD [41]KD-SWA [5]Ous
Trained teacher models1120
Standardly teacher independent✓✓✗✓
Adversarily teacher independent✗✗✗✓
Forward times in one training iteration3342
+ +our method as special supervision, and smoothing the hard label could better reflect the similarities among classes. There are many differences between our method and other KDs in AT. The main differences are summarized in Tab. 1. Our method does not incur any extra computational cost as we do not involve teacher models, which is a boon throughout the whole training progress. + +# 3.4. Tolerant to noisy label + +In the following part, we'd like to delve into whether the proposed method is tolerant of noisy labels. We define the symmetric noise label as that true label $y$ has probabilities $\eta_{x,\widetilde{y}} = p(\widetilde{y} | y, x)$ to flip into the wrong labels uniformly. The corresponding noisy empirical risk is: + +$$ +R _ {\mathcal {S}} ^ {\eta} (f) = \mathbb {E} _ {\mathcal {S}} (1 - \eta_ {x}) \cdot \ell (f (x), y) + \sum_ {i \neq y} \eta_ {x, i} \ell (f (x), i) +$$ + +where, $\eta_{x}$ is the noise rate. We call a loss function noisetolerant if and only if the global minimum $f_{\eta}^{*}$ has the same probability of misclassification as that of $f^{*}$ on the noise-free data. + +Lemma. 1 Given a symmetric loss function $\ell$ that it satisfies $\sum_{i=1}^{k} L(f(x), i) = C$ and $C$ is some constant. Then $\ell$ is noise tolerant under symmetric label noise if noise rate $\eta$ meets $\eta < 1 - \frac{1}{K}$ . + +The loss condition theoretically guarantees the noise tolerance by risk minimization on a symmetric loss function following [12] and it shows that the global optimal classifier $f^{*}$ on noise-free data remains the optimal even with the noisy label. Further, we can also derive the noise tolerance theoretically about our method from Theorem 2. + +Theorem 2 In a $K$ -class classification problem, our method $\widetilde{\ell}$ is noise-tolerant under symmetric or uniform label noise if noise rate $\eta < 1 - \frac{1}{K}$ . And if $R(f^{*}) = 0$ , $\widetilde{l}$ is also noise-tolerant under asymmetric or class-dependent label noise when noise rate $\eta_{y,k} < 1 - \eta_y$ with $\sum_{i \neq y} \eta_{y,i} = \eta_y$ , then + +$$ +R _ {\mathcal {S}} ^ {\eta} (f ^ {*}) - R _ {\mathcal {S}} ^ {\eta} (f) \simeq \left(1 - \frac {\eta K}{K - 1}\right) \left(R _ {\mathcal {S}} (f ^ {*}) - R _ {\mathcal {S}} (f)\right) \leq 0 +$$ + +From Theorem 2, we can derive that our method is nearly noise-tolerant under symmetric noise and further prove the + +robustness of the proposed method to asymmetric noise. More details can be found in Appendix B. We show a significant improvement under noise regimes empirically in experiments. + +# 4. Experiments + +Training and evaluation setups. We conduct extensive experiments on the benchmark datasets, CIFAR-10/100. We set the perturbation budget to $\epsilon = 8 / 255$ under the $\ell_{\infty}$ norm-bounded constraint. We use ResNet-18 [15] as our default network architecture unless otherwise specified. For all experiments, the model is trained using SGD with a momentum of 0.9, weight decay of $5\times 10^{-4}$ , and an initial learning rate of 0.1 for a total of 200 epochs. The learning rate is decayed by a factor of 0.1 at the 100-th and 150-th epochs, following [22]. The evaluation of the proposed approach encompasses PGD-20 [22] and AutoAttack [7], which is recognized as the most reliable robustness evaluation up to date. AutoAttack is an ensemble of diverse attacks, including APGD-CE, APGD-DLR, FAB [8] and Square attack [2]. We quantify the robust generalization by computing the difference between the best and final checkpoints over the course of training. + +Improved robust performance across datasets. Experimental results of PGD-AT [18], TRADES [39], and the combinations of them with our proposal (denoted as PGD-AT+SGLR and TRADES+SGLR) on CIFAR-10/100 datasets are shown in Tab. 3, from which we make the following observations on our advantages: 1) Closer generalization gap. It is remarkable that the differences between the best and the final test accuracies of the combinations are reduced to around $0.5\%$ , while the corresponding baselines (PGD-AT and TRADES) induce much larger gaps, which + +![](images/dd7a11861918aa90968198794d50a66605a110c463ab61bb7f14a9c514eb47b0.jpg) +Figure 4. Test accuracy $(\%)$ on CIFAR-10 dataset (with $40\%$ label noise). We split the training set into 1) untouched portion, where the labels of elements are left untouched; 2) corrupted portion, where the labels of elements are assigned uniformly at random. + +![](images/e64b3ea23e72d01d8c7da75ad86b2520c3fcbd724aedca5ccb6e9a00fec9aa38.jpg) + +Table 2. Test accuracy $(\%)$ of the proposed method and other methods on CIFAR-10 under the $\ell_{\infty}$ norm with $\epsilon = 8 / 255$ based on the ResNet-18 architecture. + +
MethodNatural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
PGD-AT80.782.4-1.650.741.49.347.740.27.5
PGD-AT+LS82.284.3-2.153.748.94.848.444.63.9
PGD-AT+TE82.482.8-0.455.854.81.050.649.61.0
PGD-AT+SGLR82.983.0-0.156.455.90.551.250.21.0
AWP82.181.11.055.454.80.650.649.90.7
KD-AT82.985.5-2.654.653.21.449.148.80.3
KD-SWA84.785.4-0.854.953.81.149.349.4-0.1
PGD-AT + SGLR82.983.0-0.156.455.90.551.250.21.0
+ +Table 3. Clean accuracy and robust accuracy (\%) of ResNet 18 trained on different benchmark datasets. All threat models are under $\ell_{\infty}$ norm with $\epsilon = 8 / 255$ . The bold indicates the improved performance achieved by the proposed method. + +
DatasetMethodNatrural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
CIFAR-10AT80.782.4-1.650.741.49.347.740.27.5
+SGLR82.983.00.156.455.90.551.250.21.0
TRADES81.282.5-1.353.350.33.049.046.82.2
+SGLR82.283.3-0.955.855.40.450.750.10.6
CIFAR-100AT53.953.60.327.319.87.522.718.14.6
+SGLR56.956.60.334.534.30.227.526.70.8
TRADES57.956.31.729.927.72.224.623.41.2
+SGLR57.157.4-0.333.933.20.727.126.40.7
+ +are up to $9.3\%$ and $3.0\%$ on CIFAR-10 dataset when the model is threaten by PGD-20. It indicates that our method effectively alleviates robust overfitting. 2) Higher robust accuracy. As the combinations induce smaller gaps, they can approach higher robust accuracy against adversaries compared to baseline methods, as can be observed in Tab. 3. Besides, it is notable that our method is especially effective against AutoAttack [7], regarding the fundamental difficulties of simultaneously achieving the robustness against multiple adversaries. 3) Consistent improvement. Combining our label smoothing method could consistently and significantly improve the performance on all considered adversaries and also on the clean test set, and across different datasets, namely, the CIFAR-10 and CIFAR-100 datasets. + +Improved generalization under noise regimes. Moreover, we verify the self-guided label smoothing by comparing the behavior of the proposed SGLR with that of the widely used one-hot labels under different noise settings, with $40\%$ noisy labels and fully $60\%$ true labels, respectively. Specifically, we focus on evaluating the effectiveness of our approach in mitigating the impact of symmetric noisy labels, where the labels are resampled from a uniform distribution over all labels with a probability $\eta$ . + +We begin by making the observations in the left of Fig. 4: 1) The generalization error (i.e., the difference between the training and test accuracy) of the proposed SGLR (almost negligible) is obviously smaller than that of the commonly used hard labels ( $>50\%$ ). 2) The peak of the training accuracy using hard labels (blue curve) can approximate $100\%$ even on the training set with $40\%$ noisy labels (horizontal gray dashed denotes the portion of correct labels), which suggests that using hard labels could fit correct labels in the early stage and eventually memorizes noisy labels. On the contrary, our training curve is bounded by the untouched portion, implying that our method is able to calibrate the training process and maintain a proper fitting of training data. Then we turn to the other setting as shown in the right of Fig. 4, our test accuracy grows steadily while the baseline method fails. This observation again suggests that the double-descent phenomenon might be due to the overfitting of noise and it is hopeful to be avoided by our method. + +To give a more intuitive explanation, we further visualize the penultimate layer representations of ResNet 18 trained with (a) a hard label; (b) a soft label, and (c) the proposed soften label. As Fig. 5 shown, under all the settings of noise rate, the proposed SGLR with self-guided distribution + +![](images/a26d48146a2dafdfe89def41f1f5880ce90225f13ec80d576a1c42eb51bfb816.jpg) +Figure 5. Visualization of representations learned by standard training with hard/soft labels and the proposed SGLR with self-guided distribution on CIFAR-10 dataset under various levels of symmetric noisy labels $(\eta \in [0.0,0.2,0.4,0.6])$ + +can consistently provide better representations, displayed with more separable clusters and tighter intra-class distance, which are very close to those of the clean setting (the leftmost column). Notably, even with a significantly increased noise rate from 0 (no noise) to 0.6 (severe noise), as illustrated from left to right in Fig. 5, our method learns representations with almost negligible variance. This also echoes our advantages of robust learning under various settings of data corruption. + +In a nutshell, we have grounds to empirically believe that our method exhibits benign tolerance to noisy labels and improves the generalization ability of the model by avoiding fitting noisy labels. + +Comparison against other methods. Considering that our method is analogous to employing the technique of label smoothing into AT, in Tab. 2, we report robustness evaluations of AT with label smoothing (PGD-AT + LS) and temporal ensembling (PGD-AT + TE) on CIFAR-10 test set. Since excessive LS could degrade the robustness reported in [20], we implement LS with smoothing level $r = 0.2$ . We empirically found that SGLR not only can effectively alleviate robust overfitting while LS fails but also boosts the robustness even under strong AutoAttack. Further, we also report other methods (e.g., AWP [33], KD-AT [10]) in Tab. 2, which can mitigate robust overfitting through the lens of weight smoothness and the knowledge transfer of teacher model. Though robust overfitting is indeed impeded by applying these methods, our method could better narrow the generalization gap between best and final models and achieve remarkable robustness than others under AutoAttack. + +On the impact of smoothing effect $r$ . The effectiveness of SGLR relies on the smoothing level of soft labels. Besides, as we discussed in Sec. 3.3, SGLR could be viewed as a kind of knowledge distillation without extra teacher models involved. Large temperature $T$ during distillation improves + +the smoothness of output distribution but could impair the test performance. As the temperature is vital, we could specify $f(x;w)_i$ in Eq. (7) as $\exp (z_i / T) / \sum_j\exp (z_j / T)$ . We vary the smoothing level $r\in \{0.0,0.2,0.4,0.6,0.8\}$ in Tab. 4 and note that an increase in $r$ initially boosts both standard accuracy and robust accuracy, followed by a decline, indicating that excessive smoothing introduces noise and hampers predictive capability. Additionally, increasing the temperature while fixing $r$ only gains slightly improvement in standard accuracy but observes degradation in robust accuracy. + +Table 4. Ablation study on smoothing level $r$ and temperature $T$ . + +
T/r0.00.20.40.60.8
1SA82.483.582.878.569.1
RA43.754.954.252.748.3
1.5SA83.282.983.180.674.5
RA45.755.953.250.449.8
2SA82.984.483.978.575.6
RA45.853.952.050.947.8
+ +# 5. Discussion and conclusion + +In this study, we show that label noise induced by distribution mismatch and improper label assignments would degrade the test accuracies as well as make the robust overfitting aggravated. From the view of this observation, a label assignment approach for AT, Self-Guided Label Refinement (SGLR), is proposed to weaken the memorization in AT on noisy labels and thus to mitigate the robust overfitting. Extensive experimental results demonstrate the effectiveness of the proposed SGLR. Though we circumvent over confident prediction, the model is still not well-calibrated. As we measure the calibration of model during the training over the entire dataset instead of in a sample-wise way, it may give a false sense of reweighting confidence. In the future, we will attempt to address this limitation. + +# Acknowledgement + +This work is partially supported by the National Science and Technology Major Project of China (Grant No. 2022ZD0119103), the National Natural Science Foundation of China (Grant No. 61906168), the Zhejiang Provincial Natural Science Foundation of China (Grant No.LQ21F020006, LY23F020023), and is also supported by the advanced computing resources provided by the Supercomputing Center of Hangzhou City University. + +# References + +[1] Alessandro Achille and Stefano Soatto. Emergence of invariance and disentanglement in deep representations. J. Mach. Learn. Res., 19:50:1-50:34, 2018. 3 +[2] Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square attack: A query-efficient black-box adversarial attack via random search. In ECCV, pages 484-501. Springer, 2020. 6 +[3] Anish Athalye, Nicholas Carlini, and David A. Wagner. 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IEEE, 2021. 5, 6 \ No newline at end of file diff --git a/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/images.zip b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e576711b02166f6801610d02858649dceae695d2 --- /dev/null +++ b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5dcaa0a754f436a576dce8b22be18a93afa2ebdf791a03a0cc865c6015dc0643 +size 496790 diff --git a/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/layout.json b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..763683850bd3ee840299679c07e58b9b7344f15f --- /dev/null +++ b/2024/Soften to Defend_ Towards Adversarial Robustness via Self-Guided Label Refinement/layout.json @@ -0,0 +1,8297 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 127, + 103, + 465, + 137 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 103, + 465, + 137 + ], + "spans": [ + { + "bbox": [ + 127, + 103, + 465, + 137 + ], + "type": "text", + "content": "Soften to Defend: Towards Adversarial Robustness via Self-Guided Label Refinement" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "spans": [ + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": "Zhuorong Li" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{1,\\ast,\\dagger}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": " Daiwei Yu" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": " Lina Wei" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": " Canghong Jin" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": " Yun Zhang" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": " Sixian Chan" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": " Hangzhou City University " + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 66, + 160, + 525, + 190 + ], + "type": "text", + "content": "Zhejiang University of Technology" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 191, + 515, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 191, + 515, + 202 + ], + "spans": [ + { + "bbox": [ + 77, + 191, + 515, + 202 + ], + "type": "text", + "content": "{lizr, weiln, jinch, yunzhang}@hzcu.edu.cn, ydw.ccm@gmail.com, sxchan@zjut.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "type": "text", + "content": "Adversarial training (AT) is currently one of the most effective ways to obtain the robustness of deep neural networks against adversarial attacks. However, most AT methods suffer from robust overfitting, i.e., a significant generalization gap in adversarial robustness between the training and testing curves. In this paper, we first identify a connection between robust overfitting and the excessive memorization of noisy labels in AT from a view of gradient norm. As such label noise is mainly caused by a distribution mismatch and improper label assignments, we are motivated to propose a label refinement approach for AT. Specifically, our Self-Guided Label Refinement first self-refines a more accurate and informative label distribution from over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model and thus requiring no external teachers. Empirical results demonstrate that our method can simultaneously boost the standard accuracy and robust performance across multiple benchmark datasets, attack types, and architectures. In addition, we also provide a set of analyses from the perspectives of information theory to dive into our method and suggest the importance of soft labels for robust generalization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 575, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 288, + 684 + ], + "type": "text", + "content": "Recent studies have reported that deep neural networks (DNNs) are vulnerable to adversarial examples, i.e., malicious inputs perturbed by an imperceptible noise to confuse the classifier prediction [14, 25]. This vulnerability raises serious security concerns and motivates a growing body of works on defense techniques [18, 24, 39]. Adversarial training (AT) is arguably the most promising way to harden classifiers against adversarial examples, which directly augments the training set with adversarial examples [3, 18]. It" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 232, + 547, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 547, + 255 + ], + "type": "text", + "content": "is formulated as a min-max problem [18] to find model parameters " + }, + { + "bbox": [ + 306, + 232, + 547, + 255 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 306, + 232, + 547, + 255 + ], + "type": "text", + "content": " that minimize the adversarial risk:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 389, + 262, + 547, + 280 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 262, + 547, + 280 + ], + "spans": [ + { + "bbox": [ + 389, + 262, + 547, + 280 + ], + "type": "interline_equation", + "content": "\\min _ {w} \\mathcal {L} _ {\\mathcal {S}} \\left(x ^ {\\prime}, y; w\\right) \\tag {1}", + "image_path": "51ea4237f25b9c846404c893f795d0871d6c383d2d846584b154b1337a72eab1.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathcal{S}}(x',y;w) = 1 / n\\sum_{i = 1}^{|S|}\\max_{x'\\in \\mathcal{B}_r(x)}\\ell (f(x_i';w),y_i)" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "f(\\cdot ;w)" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": " is a model parameterized by " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "\\ell (\\cdot)" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": " is the loss function such as cross-entropy loss, and " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_r(x)" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": " denotes the set of the allowed perturbations under the given metric space " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "M = (X,d)" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": " and the suitable radius " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "r > 0" + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "text", + "content": " , i.e., " + }, + { + "bbox": [ + 304, + 286, + 547, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_r(x) = \\{x + \\delta \\in \\mathcal{X}:d(x,x + \\delta) < r\\}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": "However, most AT methods suffer from a dominant phenomenon that is referred to as \"robust overfitting\". That is, an adversarially trained model can reach almost " + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": " robust accuracy on the training set while the performance on the test set is much inferior, witnessing a significant gap of adversarial robustness [22]. Various regularization techniques including classic " + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": " regularization and more advanced regularizations using data augmentation, such as Mixup [38] and Cutout [9], have been attempted to mitigate robust overfitting, whereas they are reported to perform no better than a simple early stopping [22]. However, early stopping raises another concern as the checkpoint of the best robustness and that of the best standard accuracy often do not coincide [5]. To outperform data augmentations and early stopping, regularizations specifically designed for robust training are thus proposed, to name a few, loss reweighting [27, 29, 37, 40] and weight smoothing [5, 33, 36, 37]. These regularization methods are likely to restrict the change of training loss by suppressing perturbations with respect to either the inputs " + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": " or the weights " + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": ", whereas few explorations attempt to combat robust overfitting from the perspective of labels " + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 367, + 548, + 617 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "Previous investigations on labels in AT [10, 35] emphasised the existence of label noise in AT to provide an understanding of robust generalization, for instance, from a classic bias-variance perspective. We take a step still further to investigate the memorization of label noise in AT, which is characterised by a non-monotonical increase of gradient norm, as illustrated in Fig. 1, resulting in robust overfitting. In light of our analyses, we are motivated to design a strategy" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 693, + 142, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 693, + 142, + 703 + ], + "spans": [ + { + "bbox": [ + 61, + 693, + 142, + 703 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 61, + 703, + 198, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 703, + 198, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 703, + 198, + 713 + ], + "type": "text", + "content": "* The first two authors contribute equally." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24776" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 76, + 285, + 232 + ], + "blocks": [ + { + "bbox": [ + 50, + 76, + 285, + 232 + ], + "lines": [ + { + "bbox": [ + 50, + 76, + 285, + 232 + ], + "spans": [ + { + "bbox": [ + 50, + 76, + 285, + 232 + ], + "type": "image", + "image_path": "df0b5802ee23945c78879e8b25fe902fbf047d4fe032d4a8723f634cea1175e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 115, + 235, + 231, + 247 + ], + "lines": [ + { + "bbox": [ + 115, + 235, + 231, + 247 + ], + "spans": [ + { + "bbox": [ + 115, + 235, + 231, + 247 + ], + "type": "text", + "content": "(a) Gradient norm magnitude" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 299, + 72, + 543, + 232 + ], + "blocks": [ + { + "bbox": [ + 299, + 72, + 543, + 232 + ], + "lines": [ + { + "bbox": [ + 299, + 72, + 543, + 232 + ], + "spans": [ + { + "bbox": [ + 299, + 72, + 543, + 232 + ], + "type": "image", + "image_path": "d04f677b2fea59684592a610f0b73d654144165b5896168625f1297642c723eb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 379, + 235, + 468, + 247 + ], + "lines": [ + { + "bbox": [ + 379, + 235, + 468, + 247 + ], + "spans": [ + { + "bbox": [ + 379, + 235, + 468, + 247 + ], + "type": "text", + "content": "(b) Generalization gap" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": "Figure 1. In figure (a), we calculate the gradient norm of vanilla adversarially trained PreAct-ResNet 18 on CIFAR-10 for robustness against " + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 251, + 547, + 285 + ], + "type": "text", + "content": " perturbations of radius 8/255. In figure (b), we show the robust accuracy under PGD-20 attack under the same settings with figure (a). The gradient norm keeps non-monotonically ramping up when robust overfitting happens." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 288, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 288, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 288, + 397 + ], + "type": "text", + "content": "for label refinement to alleviate excessive memorization and thus the robust overfitting. To that end, we conduct an empirical experiment using different label assignments and analyse through the lens of learning curve, which is a useful indicator for the occurrence of robust overfitting. As shown in Fig. 2, the phenomenon of robust overfitting is presented, for instance, in the lower left of Fig. 2 for PGD-AT [18] with commonly used hard labels, and at a slightly reduced extent as shown in the lower middle of Fig. 2 with vanilla soft labels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 397, + 290, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 397, + 290, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 397, + 290, + 553 + ], + "type": "text", + "content": "In this work, we propose a theoretical-grounded method to alleviate the memoization on over-confident labels during adversarial training and thus to combat robust overfitting. Our main idea is to resort to an alternative for label assignment. Particularly, motivated by the effectiveness of soft label in alleviating overfitting in standard training [26], our work generates more reliable labels automatically by incorporating predictive label distributions into the process of robust learning. It provides a promising way to inject distilled knowledge and to self-calibrate the adversarial training. Our method is conceptually simple yet significantly enhances the learning of deep models in adversarial scenarios. The key contributions are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 50, + 557, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 50, + 557, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 557, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 50, + 557, + 287, + 701 + ], + "type": "text", + "content": "- We first inspect the behaviour of deep models trained by AT when robust overfitting occurs. Specifically, we identify a connection between robust overfitting and the excessive memorization of noisy labels in AT through the lens of gradient norm (see Fig. 1). As such label noise is mainly due to inaccurate label distribution, we further investigate the effects of different label assignment methods on AT (see Fig. 2). These observations consistently implies a connection between robust overfitting and noisy hard labels. Exploring such connections could help to shed light on understanding and improving the robust learning of deep models." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 50, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 50, + 701, + 287, + 714 + ], + "type": "text", + "content": "- Upon the observation, we are motivated to propose a label" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 316, + 289, + 547, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 289, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 316, + 289, + 547, + 373 + ], + "type": "text", + "content": "refinement approach for AT. Specifically, our Self-Guided Label Refinement (SGLR) first self-refines accurate and informative label distribution from the over-confident hard labels, and then it calibrates the training by dynamically incorporating knowledge from self-distilled models into the current model, requiring no external teacher models nor modifications to the existing architecture." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "spans": [ + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "type": "text", + "content": "- We verify the effectiveness of SGLR through extensive evaluations. Overall, experimental results show that the proposed method consistently improves the test accuracy over the state-of-the-art on various benchmark datasets against diverse adversaries. Moreover, our approach can achieve robust accuracy up to " + }, + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "type": "inline_equation", + "content": "56.4\\%" + }, + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "type": "text", + "content": " and close the generalization gap to merely " + }, + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "type": "inline_equation", + "content": "0.4\\%" + }, + { + "bbox": [ + 309, + 373, + 547, + 481 + ], + "type": "text", + "content": ", significantly mitigating the overfitting issue and thus being able to pushing up the adversarial robustness." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 502, + 493, + 516 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 493, + 516 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 493, + 516 + ], + "type": "text", + "content": "2. A closer look at robust overfitting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "Robust overfitting has been prevalent across various datasets and models [22]. Then, crops of empirical and theoretical studies have emerged to analyze this phenomenon through the lens of loss value [37], training data [10] and learned features [30]. However, a comprehensive underlying mechanism of robust overfitting still remains an enigma. In this section, we revisit robust overfitting from a perspective of the established information theory and identify a \"memorization effect\" over the course of adversarial training, which is akin to standard training as observed in [6, 34]. First and foremost, we conduct some observations when robust overfitting occurs via analysing the change of the gradient norm of adversarial loss with respect to model weight, i.e., " + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\| \\nabla_w L(x', y, w) \\|_2" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": ". As shown in Fig. 1 (a), we may note that the gradient norm holds nearly the constant and then keeps ramping up nonmonotonically. This increasing behavior of gradient norm" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24777" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 214, + 186 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 214, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 214, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 214, + 186 + ], + "type": "image", + "image_path": "fbe753404e53dce1be123c028b2607c3d794c114dcfd9153b4539fad709f2048.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 215, + 72, + 378, + 186 + ], + "blocks": [ + { + "bbox": [ + 215, + 72, + 378, + 186 + ], + "lines": [ + { + "bbox": [ + 215, + 72, + 378, + 186 + ], + "spans": [ + { + "bbox": [ + 215, + 72, + 378, + 186 + ], + "type": "image", + "image_path": "4cad22deaad17b7d5fcc92669886b371124a53caa5479c81fd1ad30750de56fc.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 379, + 72, + 542, + 186 + ], + "blocks": [ + { + "bbox": [ + 379, + 72, + 542, + 186 + ], + "lines": [ + { + "bbox": [ + 379, + 72, + 542, + 186 + ], + "spans": [ + { + "bbox": [ + 379, + 72, + 542, + 186 + ], + "type": "image", + "image_path": "fb89fc4c68e5775ab99c4d6a3ea0f06b7e5a12e02ab20cdef448e9c4fbf4aea9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 49, + 187, + 214, + 304 + ], + "blocks": [ + { + "bbox": [ + 49, + 187, + 214, + 304 + ], + "lines": [ + { + "bbox": [ + 49, + 187, + 214, + 304 + ], + "spans": [ + { + "bbox": [ + 49, + 187, + 214, + 304 + ], + "type": "image", + "image_path": "1a33523c1fba43f31ff1f04494e469c6860ea25c8262ae8e19047975d2367594.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 102, + 308, + 489, + 319 + ], + "lines": [ + { + "bbox": [ + 102, + 308, + 489, + 319 + ], + "spans": [ + { + "bbox": [ + 102, + 308, + 489, + 319 + ], + "type": "text", + "content": "Figure 2. Robust accuracy of models employing different label assignment methods in adversarial training." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 220, + 187, + 379, + 304 + ], + "blocks": [ + { + "bbox": [ + 220, + 187, + 379, + 304 + ], + "lines": [ + { + "bbox": [ + 220, + 187, + 379, + 304 + ], + "spans": [ + { + "bbox": [ + 220, + 187, + 379, + 304 + ], + "type": "image", + "image_path": "561c2e92403f150dd68cbedd37d9426a530c267a7c09ca950107412c1761e366.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 385, + 187, + 543, + 304 + ], + "blocks": [ + { + "bbox": [ + 385, + 187, + 543, + 304 + ], + "lines": [ + { + "bbox": [ + 385, + 187, + 543, + 304 + ], + "spans": [ + { + "bbox": [ + 385, + 187, + 543, + 304 + ], + "type": "image", + "image_path": "7dd9be1e6da23622df5700a8132ab35e95296843aba017b4fcef5e32d30824cb.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 326, + 288, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 288, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 288, + 373 + ], + "type": "text", + "content": "encountered with the learning rate (LR) decays. So we divide the training process into two phases according to the LR decays: (1) Stationary stage; (2) Non-monotonical growth stage." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 529 + ], + "type": "text", + "content": "In stationary stage, as illustrated in Fig. 1 (b), the learning curve (orange line) and test robust accuracy (blue line) ramp up at almost the same pace and maintain a very small generalization gap, i.e., the divergence between the training and test accuracy, implying that the model keeps learning efficient robust features as the training progresses and accordingly hovers a small constant gradient norm. However, a significantly expanding generalization gap can be witnessed after an inflection point, where the LR decays. We refer the period afterwards as \"Non-monotonical growth stage\", as a prominent characteristic of this stage is that the gradient norm keeps growing non-monotonically and does not converge to a constant, even after the training has ended." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 529, + 288, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 288, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 288, + 708 + ], + "type": "text", + "content": "It is worth noting that this trend of gradient norm greatly contradicts with that of the conventional ERM training, where zero gradient norm can be reached at the end of training. Nonetheless, such behaviour of gradient norm is in line with ERM when significant noisy labels surrounding, as observed in [11, 31]. Specifically, such growing trend is interpreted as an indicator that the training has entered a \"memorization routine\", where the model firstly fits on training samples with clean labels, then gradually over-fits samples with noisy labels. Later in this stage, the test accuracy on clean data will go down whereas the training accuracy keeps going up. Similarly, we are able to identify a non-monotonical growth in adversarial training, as depicted in Fig. 1 (a). Remarkably, this divergent gradient norm as the adversarial training progressing, exactly accompanies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 326, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 326, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 326, + 545, + 421 + ], + "type": "text", + "content": "with the enlargement of generalization gap that is depicted in Fig. 1 (b), which reveals the overfitting problem. Thus, we come to a conjecture that the memorization effect is also the culprit of the increasing gradient norm in the scenario of robust training and further induces robust overfitting. To that end, we first provide proof for our hypothesis that adversarial training memorizes samples with noisy labels mainly in the non-monotonical divergence phase." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 421, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 453 + ], + "type": "text", + "content": "Following [1], the expected cross entropy loss could be decomposed into three terms according to PAC-Bayesian framework:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 308, + 465, + 545, + 534 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 465, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 308, + 465, + 545, + 534 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {H} _ {f} (\\hat {y} | x, w) \\\\ = \\mathbb {E} _ {\\mathcal {S}} \\mathbb {E} _ {w \\sim Q (w | \\mathcal {S})} \\sum_ {i = 1} ^ {m} [ - \\log f (\\hat {y} _ {i} | x _ {i}, w) ] \\\\ = \\mathcal {H} (y | x) + \\mathbb {E} _ {x, w \\sim Q (w | \\mathcal {S})} \\mathrm {K L} [ p (y | x) \\| f (\\hat {y} | x, w) ] - I (w; y | x) \\tag {2} \\\\ \\end{array}", + "image_path": "da6b6b52fb4e7f6a813485498a499e72c47a4e96ce356d290478b01bab18f767.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": "In conventional ERM training, minimizing " + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "inline_equation", + "content": "-I(w; y|x)" + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": " relies on the cross entropy loss between the prediction " + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "inline_equation", + "content": "f(\\hat{y} | x, w)" + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": " and the true label distribution " + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "inline_equation", + "content": "p(y|x)" + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": ". Noisy label viewed as the outlier of a true label distribution can provide a positive value of " + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "inline_equation", + "content": "I(w; y|x)" + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": ". This term essentially quantifies the extent to which label information overlaps the weights of the model. In other words, the presence of noisy labels will reduce the finite degree of freedom with respect to weights. The reason for this reduction is that model attempts to accommodate the noise labels in the training data, inducing a potential overfitting. Different from the conventional ERM training, adversarial training requires perturbed samples " + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "inline_equation", + "content": "x'" + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": ", which are usually obtained by solving a multi-step maximization problem. Accordingly, we use the notation " + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "inline_equation", + "content": "p(y'|x')" + }, + { + "bbox": [ + 304, + 548, + 547, + 713 + ], + "type": "text", + "content": " for the true distribution of adversarial samples. Based on the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24778" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 116, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 116, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 116, + 83 + ], + "type": "text", + "content": "Eq. (2), we have" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 61, + 91, + 264, + 148 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 91, + 264, + 148 + ], + "spans": [ + { + "bbox": [ + 61, + 91, + 264, + 148 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {H} _ {f} (\\hat {y} | x ^ {\\prime}, w) = \\mathbb {E} _ {\\mathcal {S}} \\mathbb {E} _ {w \\sim Q (w | \\mathcal {S})} \\sum_ {i = 1} ^ {m} \\left[ - \\log f \\left(\\hat {y} _ {i} \\mid x _ {i} ^ {\\prime}, w\\right) \\right] \\\\ = \\mathcal {H} \\left(y ^ {\\prime} \\mid x ^ {\\prime}\\right) - I (w; y ^ {\\prime} \\mid x ^ {\\prime}) \\\\ + \\mathbb {E} _ {x ^ {\\prime}, w \\sim Q (w | \\mathcal {S})} \\mathrm {K L} [ p (y ^ {\\prime} | x ^ {\\prime}) \\| f (\\hat {y} | x ^ {\\prime}, w) ] \\\\ \\end{array}", + "image_path": "1e93fdf72c6757cb408c4c5f789b8e04fcb4690a2cc7b65aab1b5bec9894807c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "text", + "content": "As aforementioned, the adversarial perturbation causes a mismatch between the label distributions of the perturbed data and their origins, as " + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "inline_equation", + "content": "p(y'|x') \\neq p(y|x)" + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "text", + "content": ". However, during adversarial training, " + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "inline_equation", + "content": "p(y'|x')" + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "text", + "content": " is often simply replaced by " + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "inline_equation", + "content": "p(y|x')" + }, + { + "bbox": [ + 47, + 154, + 288, + 248 + ], + "type": "text", + "content": ", that is, the perturbed labels are directly inherited from their origins. This would inevitably exert influence on the label memorization and results in performance degradation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "spans": [ + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "content": "We are interested in the memoization of noisy labels in adversarial training, which can be characterised by " + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "inline_equation", + "content": "I(w; y'|x')" + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "content": " and referred to as \"Information In Weights\" (IIW). The training dynamics can also be captured through the lens of IIW. However, computing the value of " + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "inline_equation", + "content": "I(w; y'|x')" + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "content": " is as difficult as fitting the model itself. Basing on the chain rule of mutual information, we could approach to our desired result via the upper bound, i.e., " + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "inline_equation", + "content": "I(\\mathcal{D}; w) = I((x, y); w) = I(x; w) + I(y; w|x)" + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "content": ". By using the positivity property of mutual information, we have " + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "inline_equation", + "content": "I(y; w|x) \\leq I(D; w)" + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "content": ". Then we could take an approximation under some Gaussian assumptions, as suggested by Wang et al. [32], to estimate " + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "inline_equation", + "content": "I(w; y'|x')" + }, + { + "bbox": [ + 47, + 249, + 289, + 524 + ], + "type": "text", + "content": " and further depict the learning behaviour of model, which is illustrated by the green line in Fig. 1 (b). The increasing IIW supports our hypothesis that adversarially trained model mainly overfits the noisy labels in the non-monotonical growth stage. Upon the theoretical analysis, it is natural that we proposed to prevent models from excessively memorising noisy labels by means of IIW reductions. In this work, we propose to reduce IIW through soft labels, which is specifically effective in lowering mutual information and thus can be expected to weaken the memorization under the distribution mismatch." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "text", + "content": "Theorem 1 (Soft label could reduce the IIW) Let " + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "inline_equation", + "content": "u" + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "text", + "content": " be the uniform random variable with " + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "inline_equation", + "content": "p.d.f. p(u)" + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "text", + "content": ". By using the composition in Eq. (2), there exists an interpolation ration " + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 532, + 288, + 591 + ], + "type": "text", + "content": " between the clean label distribution and uniform distribution, such that" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 600, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 600, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 115, + 600, + 287, + 613 + ], + "type": "interline_equation", + "content": "I \\left(y ^ {*}; w \\mid x ^ {\\prime}\\right) \\lesssim I (y; w \\mid x ^ {\\prime}) \\tag {4}", + "image_path": "0309651aacb680bdda5297cfb72238d8918feb1451171c3cb5bd9ff8bf1bc2a0.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "inline_equation", + "content": "p(y^{*}|x^{\\prime},w) = \\lambda \\cdot p(y|x^{\\prime},w) + (1 - \\lambda)\\cdot p(u)" + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "text", + "content": " and the symbol " + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "inline_equation", + "content": "\\lesssim" + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "text", + "content": " means that the corresponding inequality up to an " + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 622, + 287, + 658 + ], + "type": "text", + "content": "-independent constant." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 713 + ], + "type": "text", + "content": "The detailed proof could be found in Appendix A. Theorem 1 proves that there exists some kind of soft label that could reduces the information in weights. So the memorization effect caused by the label distribution mismatch could be" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "effectively mitigated. Thus, to better suppress the memorization effect, we should provide more underlying information about the true label distribution than uniform distribution to facilitate a better interpolation of the soft label. In the following, we introduce our solution to estimate more accurate and informative soft labels for adversarial training." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 154, + 545, + 182 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 154, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 305, + 154, + 545, + 182 + ], + "type": "text", + "content": "3. Self-guided label refinement for adversarial training" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 188, + 390, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 390, + 201 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 390, + 201 + ], + "type": "text", + "content": "3.1. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 206, + 547, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 547, + 314 + ], + "type": "text", + "content": "As discussed above, hard labels in adversarial training are uninformative but over-confident, and thus heavily impairs the generalization (see Fig. 2). To address this issue, we propose an alternative to one-hot labels for adversarial training. Specifically, our Self-Guided Label Refinement first utilizes the learned probability distributions to refine the over-confident hard labels, and then it guides the training process using the historical training model to obtain a calibrated prediction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 314, + 547, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 547, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 547, + 385 + ], + "type": "text", + "content": "We begin by softening the over-confident hard labels. It is well acknowledged that label smoothing (LS) helps to calibrate the degree of confidence of a model and it is effective in improving the robustness in noise regimes [17]. The vanilla LS for a " + }, + { + "bbox": [ + 304, + 314, + 547, + 385 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 314, + 547, + 385 + ], + "type": "text", + "content": "-class classification problem can be formulated:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 365, + 392, + 545, + 413 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 392, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 365, + 392, + 545, + 413 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = \\frac {r}{K} \\cdot \\mathbf {1} + (1 - r) \\cdot \\mathbf {y} _ {\\text {h a r d}} \\tag {5}", + "image_path": "7b1cbebc20e4e7b56f9846ba59c22ab11f6807940a0135887b8d5b6933109b51.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_{\\text {hard }}" + }, + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "type": "text", + "content": " denotes labels encoded by a one-hot vector, the notation of 1 denotes all one vector, and " + }, + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "type": "inline_equation", + "content": "r \\in [0,1]" + }, + { + "bbox": [ + 304, + 420, + 547, + 575 + ], + "type": "text", + "content": " controls the smooth level. It is shown that LS serves as a regularizer as well as a confidence penalty [21] and therefore improves the generalization of the model in standard training. Unfortunately, when it comes to adversarial training, a direct combination with LS cannot guarantee reliable robustness, especially in the cases of strong perturbations[4, 20]. Specifically, as the uniform distribution is unlikely to match the underlying distribution, LS tends to introduce a bias that might hurt the robust generalization. Moreover, soft labels with identical probability over the false categories cannot reveal the semantic similarity." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 575, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 547, + 624 + ], + "type": "text", + "content": "To alleviate this artificial effect, we introduce our Self-Guided Label Refinement (SGLR) which utilizes the knowledge inferred by a trustworthy model itself to retains informative labels. The proposed SGLR can be formulated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 354, + 635, + 545, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 635, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 354, + 635, + 545, + 649 + ], + "type": "interline_equation", + "content": "\\mathbf {y} = r \\cdot f \\left(x ^ {\\prime}; w\\right) + (1 - r) \\cdot \\mathbf {y} _ {h a r d} \\tag {6}", + "image_path": "94157ec11976e280e6972c06e378c501b1482162bb20e38f1f0aacb76a9f6cb7.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "inline_equation", + "content": "f(x'; w)" + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": " is the logit output of the model parameterized by " + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": " on training data " + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "inline_equation", + "content": "x'" + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": ". To be noticed, the model " + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": " we referred to here is not pre-trained but rather on the training. Eq. (6) also in fact serves as a regularizer by integrating the knowledge extracted from the model with static information" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24779" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 165, + 177 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 165, + 177 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 165, + 177 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 165, + 177 + ], + "type": "image", + "image_path": "70e85b23541508b5f67c54c0a41b918c5ac1b5e2a2749178987c3cd5df7327fc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 181, + 287, + 202 + ], + "lines": [ + { + "bbox": [ + 47, + 181, + 287, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 181, + 287, + 202 + ], + "type": "text", + "content": "Figure 3. The mean confidence of model in the correct and incorrect predictions over clean and adversarial test sets." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 72, + 280, + 177 + ], + "blocks": [ + { + "bbox": [ + 167, + 72, + 280, + 177 + ], + "lines": [ + { + "bbox": [ + 167, + 72, + 280, + 177 + ], + "spans": [ + { + "bbox": [ + 167, + 72, + 280, + 177 + ], + "type": "image", + "image_path": "44dd40b47c9c4dfd10d879d7f9c74d790853a4e4bf6326cd3908c0f1abe8e20c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 208, + 287, + 243 + ], + "type": "text", + "content": "that encoded by one-hot labels, thus, we suggest that this particular form of soft label has the potential to convey a better quantity of informative content." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 244, + 287, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 244, + 287, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 244, + 287, + 316 + ], + "type": "text", + "content": "Furthermore, according to Sanyal et al. [23], there exists a good interpolation of the noisy training dataset that could lead to a satisfactory generalization. Consequently, we aim to establish a valid interpolation between robust and non-robust features with the expectation that it strikes a balance between accuracy and robustness, as represented by the equation:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 72, + 323, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 323, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 72, + 323, + 287, + 338 + ], + "type": "interline_equation", + "content": "\\widetilde {f} (x, x ^ {\\prime}; w) = \\lambda \\cdot f (x; w) + (1 - \\lambda) \\cdot f (x ^ {\\prime}; w) \\tag {7}", + "image_path": "66e062fc88a3a5b20488cdcaa38035fbe86f67b02c502c09142b2492dceb6ad4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 346, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 620 + ], + "type": "text", + "content": "Fig. 3 illustrates the major trajectory of PGD-AT training on CIFAR-10 dataset in terms of the confidence in both the correct and incorrect predictions, where the model dynamics are shown by a series of colored dots with darker colours and larger areas. Gray dashed lines mark the best standard / robust accuracy of the trained model, and the red star in the bottom right corner denotes an ideal model that with a high confidence in correct classification whereas a low one in the incorrect prediction. As training processes, model tends to assign increasing confidence to its correct predictions and also to those wrong predictions, as implied by the moving of the colored dots away from the dash line. In other words, the latter prediction of the model is not better calibrated and the model in the middle training stage could be of great help to reduce the expected calibration error. Therefore, we are motivated to utilize exponential moving average (EMA) that taking the moving average of history model prediction to obtain calibrated soft label. Intuitively, EMA considers recent proposals from the current state while retaining some influence from previous information. This straightforward method is easy to deploy and incurs negligible training overhead. Then the dynamic updating of soft label could be defined as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 91, + 627, + 287, + 656 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 627, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 91, + 627, + 287, + 656 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbf {y} = r \\cdot \\widetilde {p _ {t}} + (1 - r) \\cdot \\mathbf {y} _ {\\text {h a r d}} \\tag {8} \\\\ \\widetilde {p _ {t}} = \\alpha \\cdot \\widetilde {p} _ {t - 1} + (1 - \\alpha) \\cdot \\widetilde {f} (x, x ^ {\\prime}; w _ {t}) \\\\ \\end{array}", + "image_path": "24c21901376ffee38c8aa4dd66ed6b52d979bd5579e945b947f505044d5824c9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 671, + 253, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 253, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 253, + 685 + ], + "type": "text", + "content": "3.2. Connection to symmetric cross entropy" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Cross Entropy (CE) is the prevalent loss function for deep learning with remarkable success. However, as the noisy" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "label is tipping the training process into overfitting, CE loss has taken a nasty blow and is prone to fitting noise. Inspired by the symmetric Kullback-Leibler (KL) Divergence, Wang et al. [28] proposed a more flexible loss, i.e., symmetric cross entropy (SCE), to strike a balance between sufficient learning and robustness to noisy labels. Moreover, it reveals that predictive distribution exploited by the model is superior to one-hot label distribution for the most part. Both SCE loss and our method utilize the informative knowledge inferred by the model and Proposition 1 provide such a close link between them." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "text", + "content": "Proposition.1 Let " + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "inline_equation", + "content": "\\ell_{sce}" + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "text", + "content": " be the SCE loss function and " + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "text", + "content": " represents the sum of CE and reverse CE loss. When " + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "inline_equation", + "content": "\\gamma \\rightarrow 1" + }, + { + "bbox": [ + 305, + 212, + 547, + 247 + ], + "type": "text", + "content": ", then our methods can also be written as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 379, + 258, + 471, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 379, + 258, + 471, + 270 + ], + "spans": [ + { + "bbox": [ + 379, + 258, + 471, + 270 + ], + "type": "interline_equation", + "content": "\\ell_ {s g l r} = \\ell_ {s c e} - \\alpha \\cdot \\ell_ {r k l}", + "image_path": "6cb6d7776f299b7fe769127c5a07c89e1160777904bdee4b13e92f1dfdc448ef.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "spans": [ + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "type": "inline_equation", + "content": "\\ell_{rkl}" + }, + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "type": "text", + "content": " denotes the reverse KL divergence between labels and model predictions, i.e., " + }, + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "type": "inline_equation", + "content": "D_{KL}(p\\parallel q)" + }, + { + "bbox": [ + 305, + 280, + 545, + 304 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 312, + 546, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 546, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 546, + 418 + ], + "type": "text", + "content": "The proof of Proposition 1 can be found in Appendix A. Note that Proposition 1 indicates our method can be decomposed into two terms. The first term represents the SCE loss function when the weighted sum tends to 1. The second term indicates that our method rewards the distribution differences between predictions and labels. Though our study aims at mitigating robust overfitting, which is different from the scenario of SCE loss, there is no conflict between our method and SCE." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 427, + 503, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 503, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 503, + 441 + ], + "type": "text", + "content": "3.3. Comparison to knowledge distillation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 445, + 547, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 589 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 589 + ], + "type": "text", + "content": "Knowledge distillation (KD) [16] has been proven to be an effective way to compress models, which is able to remarkably beef up the performance of lightweight models. There is a huge scope for applying KD to adversarial training to improve the efficiency of AT. A crop of works [5, 13, 29, 41] have advanced exploring KD implicitly or explicitly in conjunction with AT. The efficacy of KD is attributed to the teacher model's informative knowledge, which guides the student to acquire a more similar knowledge representation and effectively capture inter-class relationships. By enforcing consistency in probability distributions, KD facilitates better learning outcomes for the student." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "content": "Proposition. 2 Some " + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "inline_equation", + "content": "KD" + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "content": " methods, which minimize the distance of the feature map between the teacher and student model, belong to the family of our method. Let " + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "content": " be the prediction of the teacher model and then the " + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "inline_equation", + "content": "KD" + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "content": " could also be written as " + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "inline_equation", + "content": "\\ell_{KD} = \\mathbb{E}_{\\widetilde{q}}[-\\log p] = H(\\widetilde{q},p)" + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "inline_equation", + "content": "\\widetilde{q} = (1 - \\alpha) \\cdot q + \\alpha \\cdot p_t" + }, + { + "bbox": [ + 304, + 597, + 547, + 670 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "Proposition 2 shows that some KD revised the hard label via the knowledge " + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": " learned by the teacher. The proof of Proposition 2 is presented in Appendix A. Further, we view" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24780" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 84, + 483, + 159 + ], + "blocks": [ + { + "bbox": [ + 176, + 71, + 416, + 81 + ], + "lines": [ + { + "bbox": [ + 176, + 71, + 416, + 81 + ], + "spans": [ + { + "bbox": [ + 176, + 71, + 416, + 81 + ], + "type": "text", + "content": "Table 1. Comparison between our method and other KD methods." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 106, + 84, + 483, + 159 + ], + "lines": [ + { + "bbox": [ + 106, + 84, + 483, + 159 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 483, + 159 + ], + "type": "table", + "html": "
ARD [13]RSLAD [41]KD-SWA [5]Ous
Trained teacher models1120
Standardly teacher independent✓✓✗✓
Adversarily teacher independent✗✗✗✓
Forward times in one training iteration3342
", + "image_path": "680328cc3fb23fb34980359be52d86db7c58a30b1488e6a19322476dbea79feb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 174, + 288, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 174, + 288, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 288, + 258 + ], + "type": "text", + "content": "our method as special supervision, and smoothing the hard label could better reflect the similarities among classes. There are many differences between our method and other KDs in AT. The main differences are summarized in Tab. 1. Our method does not incur any extra computational cost as we do not involve teacher models, which is a boon throughout the whole training progress." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 266, + 174, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 266, + 174, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 174, + 277 + ], + "type": "text", + "content": "3.4. Tolerant to noisy label" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "type": "text", + "content": "In the following part, we'd like to delve into whether the proposed method is tolerant of noisy labels. We define the symmetric noise label as that true label " + }, + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "type": "text", + "content": " has probabilities " + }, + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "type": "inline_equation", + "content": "\\eta_{x,\\widetilde{y}} = p(\\widetilde{y} | y, x)" + }, + { + "bbox": [ + 46, + 284, + 288, + 344 + ], + "type": "text", + "content": " to flip into the wrong labels uniformly. The corresponding noisy empirical risk is:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 353, + 277, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 353, + 277, + 379 + ], + "spans": [ + { + "bbox": [ + 56, + 353, + 277, + 379 + ], + "type": "interline_equation", + "content": "R _ {\\mathcal {S}} ^ {\\eta} (f) = \\mathbb {E} _ {\\mathcal {S}} (1 - \\eta_ {x}) \\cdot \\ell (f (x), y) + \\sum_ {i \\neq y} \\eta_ {x, i} \\ell (f (x), i)", + "image_path": "60117a664bd5800086917052403fcbba7b6e66985d3d3555fbc3c8420922d527.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "text", + "content": "where, " + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\eta_{x}" + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "text", + "content": " is the noise rate. We call a loss function noisetolerant if and only if the global minimum " + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "inline_equation", + "content": "f_{\\eta}^{*}" + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "text", + "content": " has the same probability of misclassification as that of " + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "inline_equation", + "content": "f^{*}" + }, + { + "bbox": [ + 46, + 388, + 287, + 434 + ], + "type": "text", + "content": " on the noise-free data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": "Lemma. 1 Given a symmetric loss function " + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": " that it satisfies " + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\sum_{i=1}^{k} L(f(x), i) = C" + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": " is some constant. Then " + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": " is noise tolerant under symmetric label noise if noise rate " + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": " meets " + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "inline_equation", + "content": "\\eta < 1 - \\frac{1}{K}" + }, + { + "bbox": [ + 46, + 444, + 287, + 494 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 499, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 571 + ], + "type": "text", + "content": "The loss condition theoretically guarantees the noise tolerance by risk minimization on a symmetric loss function following [12] and it shows that the global optimal classifier " + }, + { + "bbox": [ + 46, + 499, + 287, + 571 + ], + "type": "inline_equation", + "content": "f^{*}" + }, + { + "bbox": [ + 46, + 499, + 287, + 571 + ], + "type": "text", + "content": " on noise-free data remains the optimal even with the noisy label. Further, we can also derive the noise tolerance theoretically about our method from Theorem 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": "Theorem 2 In a " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": "-class classification problem, our method " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "\\widetilde{\\ell}" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": " is noise-tolerant under symmetric or uniform label noise if noise rate " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "\\eta < 1 - \\frac{1}{K}" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": ". And if " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "R(f^{*}) = 0" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "\\widetilde{l}" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": " is also noise-tolerant under asymmetric or class-dependent label noise when noise rate " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "\\eta_{y,k} < 1 - \\eta_y" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "inline_equation", + "content": "\\sum_{i \\neq y} \\eta_{y,i} = \\eta_y" + }, + { + "bbox": [ + 46, + 579, + 288, + 642 + ], + "type": "text", + "content": ", then" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 657, + 286, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 286, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 286, + 681 + ], + "type": "interline_equation", + "content": "R _ {\\mathcal {S}} ^ {\\eta} (f ^ {*}) - R _ {\\mathcal {S}} ^ {\\eta} (f) \\simeq \\left(1 - \\frac {\\eta K}{K - 1}\\right) \\left(R _ {\\mathcal {S}} (f ^ {*}) - R _ {\\mathcal {S}} (f)\\right) \\leq 0", + "image_path": "cd828253b8ba0779f488b6586cf6928b2b7d926bd178ecbbdcf0293bad0590ab.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "From Theorem 2, we can derive that our method is nearly noise-tolerant under symmetric noise and further prove the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 174, + 547, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 174, + 547, + 222 + ], + "spans": [ + { + "bbox": [ + 304, + 174, + 547, + 222 + ], + "type": "text", + "content": "robustness of the proposed method to asymmetric noise. More details can be found in Appendix B. We show a significant improvement under noise regimes empirically in experiments." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 232, + 387, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 387, + 246 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 387, + 246 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "text", + "content": "Training and evaluation setups. We conduct extensive experiments on the benchmark datasets, CIFAR-10/100. We set the perturbation budget to " + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "inline_equation", + "content": "\\epsilon = 8 / 255" + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "text", + "content": " under the " + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "text", + "content": " norm-bounded constraint. We use ResNet-18 [15] as our default network architecture unless otherwise specified. For all experiments, the model is trained using SGD with a momentum of 0.9, weight decay of " + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "inline_equation", + "content": "5\\times 10^{-4}" + }, + { + "bbox": [ + 304, + 252, + 547, + 444 + ], + "type": "text", + "content": ", and an initial learning rate of 0.1 for a total of 200 epochs. The learning rate is decayed by a factor of 0.1 at the 100-th and 150-th epochs, following [22]. The evaluation of the proposed approach encompasses PGD-20 [22] and AutoAttack [7], which is recognized as the most reliable robustness evaluation up to date. AutoAttack is an ensemble of diverse attacks, including APGD-CE, APGD-DLR, FAB [8] and Square attack [2]. We quantify the robust generalization by computing the difference between the best and final checkpoints over the course of training." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 453, + 547, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 453, + 547, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 453, + 547, + 573 + ], + "type": "text", + "content": "Improved robust performance across datasets. Experimental results of PGD-AT [18], TRADES [39], and the combinations of them with our proposal (denoted as PGD-AT+SGLR and TRADES+SGLR) on CIFAR-10/100 datasets are shown in Tab. 3, from which we make the following observations on our advantages: 1) Closer generalization gap. It is remarkable that the differences between the best and the final test accuracies of the combinations are reduced to around " + }, + { + "bbox": [ + 304, + 453, + 547, + 573 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 453, + 547, + 573 + ], + "type": "text", + "content": ", while the corresponding baselines (PGD-AT and TRADES) induce much larger gaps, which" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 308, + 590, + 427, + 673 + ], + "blocks": [ + { + "bbox": [ + 308, + 590, + 427, + 673 + ], + "lines": [ + { + "bbox": [ + 308, + 590, + 427, + 673 + ], + "spans": [ + { + "bbox": [ + 308, + 590, + 427, + 673 + ], + "type": "image", + "image_path": "dd7a11861918aa90968198794d50a66605a110c463ab61bb7f14a9c514eb47b0.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "lines": [ + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "spans": [ + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "type": "text", + "content": "Figure 4. Test accuracy " + }, + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "type": "text", + "content": " on CIFAR-10 dataset (with " + }, + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 676, + 547, + 720 + ], + "type": "text", + "content": " label noise). We split the training set into 1) untouched portion, where the labels of elements are left untouched; 2) corrupted portion, where the labels of elements are assigned uniformly at random." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 427, + 590, + 543, + 673 + ], + "blocks": [ + { + "bbox": [ + 427, + 590, + 543, + 673 + ], + "lines": [ + { + "bbox": [ + 427, + 590, + 543, + 673 + ], + "spans": [ + { + "bbox": [ + 427, + 590, + 543, + 673 + ], + "type": "image", + "image_path": "e64b3ea23e72d01d8c7da75ad86b2520c3fcbd724aedca5ccb6e9a00fec9aa38.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24781" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 104, + 96, + 485, + 235 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "text", + "content": "Table 2. Test accuracy " + }, + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "text", + "content": " of the proposed method and other methods on CIFAR-10 under the " + }, + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "text", + "content": " norm with " + }, + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "inline_equation", + "content": "\\epsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 70, + 545, + 92 + ], + "type": "text", + "content": " based on the ResNet-18 architecture." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 104, + 96, + 485, + 235 + ], + "lines": [ + { + "bbox": [ + 104, + 96, + 485, + 235 + ], + "spans": [ + { + "bbox": [ + 104, + 96, + 485, + 235 + ], + "type": "table", + "html": "
MethodNatural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
PGD-AT80.782.4-1.650.741.49.347.740.27.5
PGD-AT+LS82.284.3-2.153.748.94.848.444.63.9
PGD-AT+TE82.482.8-0.455.854.81.050.649.61.0
PGD-AT+SGLR82.983.0-0.156.455.90.551.250.21.0
AWP82.181.11.055.454.80.650.649.90.7
KD-AT82.985.5-2.654.653.21.449.148.80.3
KD-SWA84.785.4-0.854.953.81.149.349.4-0.1
PGD-AT + SGLR82.983.0-0.156.455.90.551.250.21.0
", + "image_path": "aaa946e1bc2b873d1d7355b6988a9bb3a87f9d8a61b3c8d3de1842c1c51bbeb7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 91, + 266, + 499, + 412 + ], + "blocks": [ + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "type": "text", + "content": "Table 3. Clean accuracy and robust accuracy (\\%) of ResNet 18 trained on different benchmark datasets. All threat models are under " + }, + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "type": "text", + "content": " norm with " + }, + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "type": "inline_equation", + "content": "\\epsilon = 8 / 255" + }, + { + "bbox": [ + 46, + 239, + 544, + 264 + ], + "type": "text", + "content": ". The bold indicates the improved performance achieved by the proposed method." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 91, + 266, + 499, + 412 + ], + "lines": [ + { + "bbox": [ + 91, + 266, + 499, + 412 + ], + "spans": [ + { + "bbox": [ + 91, + 266, + 499, + 412 + ], + "type": "table", + "html": "
DatasetMethodNatrural AccuracyPGD-20AutoAttack
BestFinalDiff ↓BestFinalDiff ↓BestFinalDiff ↓
CIFAR-10AT80.782.4-1.650.741.49.347.740.27.5
+SGLR82.983.00.156.455.90.551.250.21.0
TRADES81.282.5-1.353.350.33.049.046.82.2
+SGLR82.283.3-0.955.855.40.450.750.10.6
CIFAR-100AT53.953.60.327.319.87.522.718.14.6
+SGLR56.956.60.334.534.30.227.526.70.8
TRADES57.956.31.729.927.72.224.623.41.2
+SGLR57.157.4-0.333.933.20.727.126.40.7
", + "image_path": "e81d6eaa5b1ae19fb23aa1e873a303782a8023398d61ff546d99b7ee6de11ccc.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "spans": [ + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "type": "text", + "content": "are up to " + }, + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "type": "inline_equation", + "content": "9.3\\%" + }, + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "type": "inline_equation", + "content": "3.0\\%" + }, + { + "bbox": [ + 45, + 427, + 288, + 594 + ], + "type": "text", + "content": " on CIFAR-10 dataset when the model is threaten by PGD-20. It indicates that our method effectively alleviates robust overfitting. 2) Higher robust accuracy. As the combinations induce smaller gaps, they can approach higher robust accuracy against adversaries compared to baseline methods, as can be observed in Tab. 3. Besides, it is notable that our method is especially effective against AutoAttack [7], regarding the fundamental difficulties of simultaneously achieving the robustness against multiple adversaries. 3) Consistent improvement. Combining our label smoothing method could consistently and significantly improve the performance on all considered adversaries and also on the clean test set, and across different datasets, namely, the CIFAR-10 and CIFAR-100 datasets." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Improved generalization under noise regimes. Moreover, we verify the self-guided label smoothing by comparing the behavior of the proposed SGLR with that of the widely used one-hot labels under different noise settings, with " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " noisy labels and fully " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": " true labels, respectively. Specifically, we focus on evaluating the effectiveness of our approach in mitigating the impact of symmetric noisy labels, where the labels are resampled from a uniform distribution over all labels with a probability " + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "text", + "content": "We begin by making the observations in the left of Fig. 4: 1) The generalization error (i.e., the difference between the training and test accuracy) of the proposed SGLR (almost negligible) is obviously smaller than that of the commonly used hard labels (" + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "inline_equation", + "content": ">50\\%" + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "text", + "content": "). 2) The peak of the training accuracy using hard labels (blue curve) can approximate " + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "text", + "content": " even on the training set with " + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 427, + 547, + 642 + ], + "type": "text", + "content": " noisy labels (horizontal gray dashed denotes the portion of correct labels), which suggests that using hard labels could fit correct labels in the early stage and eventually memorizes noisy labels. On the contrary, our training curve is bounded by the untouched portion, implying that our method is able to calibrate the training process and maintain a proper fitting of training data. Then we turn to the other setting as shown in the right of Fig. 4, our test accuracy grows steadily while the baseline method fails. This observation again suggests that the double-descent phenomenon might be due to the overfitting of noise and it is hopeful to be avoided by our method." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 643, + 547, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 547, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 547, + 703 + ], + "type": "text", + "content": "To give a more intuitive explanation, we further visualize the penultimate layer representations of ResNet 18 trained with (a) a hard label; (b) a soft label, and (c) the proposed soften label. As Fig. 5 shown, under all the settings of noise rate, the proposed SGLR with self-guided distribution" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24782" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 71, + 286, + 218 + ], + "blocks": [ + { + "bbox": [ + 52, + 71, + 286, + 218 + ], + "lines": [ + { + "bbox": [ + 52, + 71, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 52, + 71, + 286, + 218 + ], + "type": "image", + "image_path": "a26d48146a2dafdfe89def41f1f5880ce90225f13ec80d576a1c42eb51bfb816.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 288, + 265 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 288, + 265 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 288, + 265 + ], + "type": "text", + "content": "Figure 5. Visualization of representations learned by standard training with hard/soft labels and the proposed SGLR with self-guided distribution on CIFAR-10 dataset under various levels of symmetric noisy labels " + }, + { + "bbox": [ + 46, + 220, + 288, + 265 + ], + "type": "inline_equation", + "content": "(\\eta \\in [0.0,0.2,0.4,0.6])" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 271, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 271, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 271, + 287, + 378 + ], + "type": "text", + "content": "can consistently provide better representations, displayed with more separable clusters and tighter intra-class distance, which are very close to those of the clean setting (the leftmost column). Notably, even with a significantly increased noise rate from 0 (no noise) to 0.6 (severe noise), as illustrated from left to right in Fig. 5, our method learns representations with almost negligible variance. This also echoes our advantages of robust learning under various settings of data corruption." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 380, + 287, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 428 + ], + "type": "text", + "content": "In a nutshell, we have grounds to empirically believe that our method exhibits benign tolerance to noisy labels and improves the generalization ability of the model by avoiding fitting noisy labels." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 438, + 288, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 438, + 288, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 438, + 288, + 643 + ], + "type": "text", + "content": "Comparison against other methods. Considering that our method is analogous to employing the technique of label smoothing into AT, in Tab. 2, we report robustness evaluations of AT with label smoothing (PGD-AT + LS) and temporal ensembling (PGD-AT + TE) on CIFAR-10 test set. Since excessive LS could degrade the robustness reported in [20], we implement LS with smoothing level " + }, + { + "bbox": [ + 46, + 438, + 288, + 643 + ], + "type": "inline_equation", + "content": "r = 0.2" + }, + { + "bbox": [ + 46, + 438, + 288, + 643 + ], + "type": "text", + "content": ". We empirically found that SGLR not only can effectively alleviate robust overfitting while LS fails but also boosts the robustness even under strong AutoAttack. Further, we also report other methods (e.g., AWP [33], KD-AT [10]) in Tab. 2, which can mitigate robust overfitting through the lens of weight smoothness and the knowledge transfer of teacher model. Though robust overfitting is indeed impeded by applying these methods, our method could better narrow the generalization gap between best and final models and achieve remarkable robustness than others under AutoAttack." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "On the impact of smoothing effect " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": ". The effectiveness of SGLR relies on the smoothing level of soft labels. Besides, as we discussed in Sec. 3.3, SGLR could be viewed as a kind of knowledge distillation without extra teacher models involved. Large temperature " + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": " during distillation improves" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": "the smoothness of output distribution but could impair the test performance. As the temperature is vital, we could specify " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "f(x;w)_i" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " in Eq. (7) as " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "\\exp (z_i / T) / \\sum_j\\exp (z_j / T)" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": ". We vary the smoothing level " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "r\\in \\{0.0,0.2,0.4,0.6,0.8\\}" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " in Tab. 4 and note that an increase in " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " initially boosts both standard accuracy and robust accuracy, followed by a decline, indicating that excessive smoothing introduces noise and hampers predictive capability. Additionally, increasing the temperature while fixing " + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 72, + 547, + 205 + ], + "type": "text", + "content": " only gains slightly improvement in standard accuracy but observes degradation in robust accuracy." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 323, + 238, + 527, + 350 + ], + "blocks": [ + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "lines": [ + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "spans": [ + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "type": "text", + "content": "Table 4. Ablation study on smoothing level " + }, + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "type": "text", + "content": " and temperature " + }, + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 307, + 223, + 544, + 234 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 238, + 527, + 350 + ], + "lines": [ + { + "bbox": [ + 323, + 238, + 527, + 350 + ], + "spans": [ + { + "bbox": [ + 323, + 238, + 527, + 350 + ], + "type": "table", + "html": "
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", + "image_path": "29359ef9b3f47887af29c2ef917efdf3b710cc659b825bd53c83ad80db3c1f32.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 390, + 454, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 454, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 454, + 403 + ], + "type": "text", + "content": "5. Discussion and conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 410, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 547, + 578 + ], + "type": "text", + "content": "In this study, we show that label noise induced by distribution mismatch and improper label assignments would degrade the test accuracies as well as make the robust overfitting aggravated. From the view of this observation, a label assignment approach for AT, Self-Guided Label Refinement (SGLR), is proposed to weaken the memorization in AT on noisy labels and thus to mitigate the robust overfitting. Extensive experimental results demonstrate the effectiveness of the proposed SGLR. Though we circumvent over confident prediction, the model is still not well-calibrated. As we measure the calibration of model during the training over the entire dataset instead of in a sample-wise way, it may give a false sense of reweighting confidence. In the future, we will attempt to address this limitation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 597, + 404, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 404, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 404, + 611 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "This work is partially supported by the National Science and Technology Major Project of China (Grant No. 2022ZD0119103), the National Natural Science Foundation of China (Grant No. 61906168), the Zhejiang Provincial Natural Science Foundation of China (Grant No.LQ21F020006, LY23F020023), and is also supported by the advanced computing resources provided by the Supercomputing Center of Hangzhou City University." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24783" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "text", + "content": "[1] Alessandro Achille and Stefano Soatto. 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Existing approaches often hinge on discriminative models tasked with predicting either the absolute positions of puzzle elements or the permutation actions applied to the original data. Unfortunately, these methods face limitations in effectively solving puzzles with a large number of elements. In this paper, we propose JPDVT, an innovative approach that harnesses diffusion transformers to address this challenge. Specifically, we generate positional information for image patches or video frames, conditioned on their underlying visual content. This information is then employed to accurately assemble the puzzle pieces in their correct positions, even in scenarios involving missing pieces. Our method achieves state-of-the-art performance on several datasets.", + "bbox": [ + 75, + 397, + 472, + 654 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 683, + 207, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image and video jigsaw puzzle solving involves the challenging task of reassembling image fragments or reshuffling video frames from unordered sequences into meaningful images and video sequences. This problem holds significant importance across various domains, ranging from image editing, biology, archaeology, document or photograph restoration, to photo sequencing [3].", + "bbox": [ + 75, + 709, + 468, + 816 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/303aa82eeec77f1ad261149c162e8df85db496543cc8c377e998623b0eadded4.jpg", + "image_caption": [ + "Figure 1. Top: given unordered image fragments, some of them masked, we want to reconstruct the original image. Bottom: given shuffled video frames, some of them masked, we want to reconstruct the original video." + ], + "image_footnote": [], + "bbox": [ + 501, + 359, + 893, + 597 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Past methods for solving jigsaw puzzles have commonly relied on discriminative networks, particularly in classifying the positions of image patches or video frames [11, 18]. Typically, these approaches involve feature extraction using a Convolutional Neural Network (CNN) backbone, followed by pairwise feature combinations before classification. The classifier then operates either by classifying permutations applied to the raw data or by directly predicting the positions of unordered elements. The primary emphasis in these methods is on training the feature backbone network to extract highly distinguishable positional features during the jigsaw puzzle-solving process.", + "bbox": [ + 496, + 672, + 892, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, these approaches face challenges when dealing with a large number of elements and when handling a variable number of elements. Furthermore, they often pri", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*This work was supported in part by NSF grant 2038493, ONR grant N00014-21-1-2431, NIH grant R01CA240771 from NCI, and U.S. Department of Homeland Security grant 22STESE00001-03-02. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security.", + "bbox": [ + 75, + 827, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23009", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/25270e81ae047ab0ba10f8ae8ae67aff5f9ee70e5f90ac176fbf1db34d08d148.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 94, + 88, + 457, + 223 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a94d2f6cf97dd29858cc05d3ad3e5c839d49a0cf028c031ef5f0f010cc51ac46.jpg", + "image_caption": [ + "Gaussian Noise", + "Figure 2. Top. Each piece has a positional encoding and an embedding of its visual content. The forward diffusion step (highlighted in the red box), gradually adds noise to the positional encodings. The reverse generation reconstructs the positional encodings, conditioned by the provided visual content. Bottom. Samples of 1D and 2D positional encodings, for video frames and image tiles, both in their original form and with added noise." + ], + "image_footnote": [], + "bbox": [ + 96, + 224, + 158, + 280 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f8de5380dc64aeff67c00cf648ecb32a44ff47eaeb5e2dc653aa915bf8cf5607.jpg", + "image_caption": [ + "Diffused 1-D PE", + "1-DPE" + ], + "image_footnote": [], + "bbox": [ + 163, + 226, + 227, + 279 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6d0eabdf3cd783b8c580ddb2c3cf54ecb7700042d733fdbc869a1f6007aa80f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 228, + 226, + 287, + 279 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0f386f447593d085463755297293bf46d3fcf94155fb59ea17513b46705fd858.jpg", + "image_caption": [ + "Diffused 2-D PE" + ], + "image_footnote": [], + "bbox": [ + 287, + 226, + 370, + 279 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/a2d8d51181aee9e593aaeca10f8842a52d731fd72b51a871e642c3858f816063.jpg", + "image_caption": [ + "2-D PE" + ], + "image_footnote": [], + "bbox": [ + 370, + 226, + 452, + 279 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "oritize learning order at the expense of capturing the entire structure of the data, making them less suitable for solving jigsaw puzzles when data elements are missing.", + "bbox": [ + 75, + 409, + 468, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper introduces Jigsaw Puzzles with Diffusion Vision Transformers (JPDVT), a novel approach to tackle these challenges through the utilization of a conditional diffusion denoising probabilistic model (CDDPM). The CD-DPM is designed to learn the positions of all the elements and generate the missing pieces, guided by the visual context of the available pieces, as illustrated in Figs. 1 and 2. Rigorous testing on diverse image and video datasets validates its superior performance compared to state-of-the-art models, underscoring the effectiveness of our proposed approach. The main contributions of this work are:", + "bbox": [ + 75, + 454, + 468, + 619 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. A simple unified design to solve both image and temporal puzzles with large number of pieces. The proposed model can handle missing data, finding the correct positions of the available pieces and generating plausible reconstructs for the missing ones.", + "2. State-of-the-art performance on several image and video datasets. Our code and pre-trained models are available at our GitHub project page.1" + ], + "bbox": [ + 76, + 623, + 468, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 758, + 218, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Solving image and video jigsaw puzzles have the common objective of learning (spatial or temporal) positional information from unordered elements.", + "bbox": [ + 75, + 785, + 468, + 829 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spatial Jigsaw Puzzles: Most existing approaches revolve around the reassembly of square puzzle pieces, with a focus on recreating the original image using non", + "bbox": [ + 76, + 830, + 468, + 877 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "overlapping components. Existing state-of-the-art jigsaw puzzle solvers can be broadly categorized into two streams.", + "bbox": [ + 500, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first stream, represented by algorithms like [18-20, 24, 31], leverages feature extraction or image understanding networks for encoding visual content. Subsequently, these methods engage in fragment reassembly, demonstrating effectiveness in handling fragments with large eroded gaps.", + "bbox": [ + 500, + 122, + 890, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second stream, as exemplified by [3, 14], initiates the process with fragment generation and subsequent reassembly. A neural network serves as a discriminator to verify the correct placement of fragments, yet these methods are generally limited to addressing small eroded gaps.", + "bbox": [ + 498, + 199, + 890, + 275 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While most of the prior works use CNNs, owing to their downsampling capabilities that facilitate classification, our paper advocates for using transformer models due to their equivariance to shuffling transformations.", + "bbox": [ + 498, + 276, + 890, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In terms of reassembly strategies, traditional approaches include brute force [20] or greedy methods [3]. However, these methods face scalability challenges with large-scale puzzles due to their exponentially growing complexity. Some studies propose using classifiers to predict permutations [18] or fragment positions [31]. Other sophisticated approaches involve Dijkstra's algorithm with graph-cut [19], while a recent work [24] employs reinforcement learning as the reassembly strategy. Additionally, [25] utilized a genetic algorithm to tackle the problem. In contrast, our paper introduces the novel use of diffusion generative models for reassembly, leveraging positional information learned from visual patterns encoded by a transformer model. Moreover, our approach extends beyond conventional practices, demonstrating the capability to solve jigsaw puzzles even in the presence of missing elements.", + "bbox": [ + 496, + 338, + 892, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Temporal Puzzles: Several recent works [11, 13, 15, 30, 33] propose using sorting temporal sequences as a pretext tasks for self-supervised learning for applications such as action recognition and video anomaly detection. They employ CNNs as video encoders to predict the order of shuffled videos directly. However, these methods, while effective for specific applications, are not explicitly designed to address the broader challenges of solving temporal puzzles, particularly on larger temporal scales.", + "bbox": [ + 496, + 580, + 890, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, our work draws inspiration from the paradigm set by [1, 4, 6, 16], where the emphasis lies on explicitly reshuffling temporal sequences akin to a photo sequencing problem. Unlike method [6], which learned permutation matrices by solving optimization problems enforcing low-rank structures on shuffled temporal sequences, our approach transcends the limitations of optimization-based techniques. These methods face constraints on sequence length and lose the ability to capture spatial coherence due to significant dimensionality reduction.", + "bbox": [ + 496, + 718, + 890, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This work moves beyond solving purely temporal jigsaw puzzles and tackles a more intricate problem—reshuffling", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1https://github.com/JinyangMarkLiu/JPDVT", + "bbox": [ + 94, + 886, + 410, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23010", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7d37e33933a85b814063055a00f70a15de245857875cec85e8e8c61b02bbc566.jpg", + "image_caption": [ + "Figure 3. Left: Architecture employed to train the proposed diffusion transformer model. Image patches, accompanied by their corresponding position encoding tokens, undergo permutation in a consistent manner. During forward diffusion, noise is introduced to all positional encoding tokens and a subset of embedded patch tokens. The transformer is trained to execute a reverse diffusion process, mitigating the introduced noise. Right: Inference process. During inference, the observed patches are padded with Gaussian noise to fill the entire image. Linearly embedded patch tokens are then concatenated with positional encoding tokens initialized with Gaussian noise. The transformer model is designed to reconstruct the visual content of the missing patches and to determine the positions for all patches, simultaneously." + ], + "image_footnote": [], + "bbox": [ + 81, + 88, + 480, + 300 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2b38258e8bd2c48e20ac3887a3584b5603ed0e673ba50b027a23e4fb657ab6a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 88, + 890, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "temporal sequences with temporal masks. Specifically, it aims to reconstruct a shuffled temporal sequence or video with missing frames, posing a novel and challenging extension to the temporal puzzle-solving paradigm.", + "bbox": [ + 75, + 421, + 470, + 482 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Our Approach", + "text_level": 1, + "bbox": [ + 76, + 497, + 225, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we present JPDVT, which uses a novel perspective on representing video and image data as non-ordered sets, to solve masked jigsaw puzzles. This representation enables JPDVT to harness the inherent properties of vision transformer architectures and the capabilities of conditional generative diffusion models to solve puzzles with missing pieces, as depicted in Fig. 3.", + "bbox": [ + 75, + 523, + 468, + 630 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Masked Jigsaw Transformer Diffusion", + "text_level": 1, + "bbox": [ + 76, + 640, + 408, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider an image or video, denoted as $\\mathbf{X}$ , partitioned into an unordered puzzle comprising individual pieces $\\mathbf{x}_1, \\ldots, \\mathbf{x}_N$ such that $\\mathbf{x}_i \\cap \\mathbf{x}_j = \\phi$ for all $i$ and $j$ , and $\\mathbf{X} = \\cup_{i=1}^{N} \\mathbf{x}_i$ . Our objective is to reconstruct $\\mathbf{X}$ by establishing a mapping $f(\\mathbf{x}_i) = l_i$ that assigns the correct position to each piece. Specifically, we seek a solution where $\\mathbf{X}$ is the union of the pieces placed at their designated locations, expressed as $\\mathbf{X} = \\cup_{i=1}^{N} (\\mathbf{x}_i @ l_i)$ , where $\\mathbf{x}_i @ l_i$ signifies that piece $\\mathbf{x}_i$ should be positioned at location $l_i$ .", + "bbox": [ + 75, + 662, + 468, + 800 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To achieve this goal, we propose representing the solved puzzle of $\\mathbf{X}$ as a set of pairs denoted by $\\mathbf{P} = \\{(\\mathbf{e}_1,\\gamma (l_1)),\\ldots ,(\\mathbf{e}_N,\\gamma (l_N))\\}$ . In this representation, $\\mathbf{e}_i$ is an embedding of the visual content of piece $\\mathbf{x}_i$ , and $\\gamma (l_i)$", + "bbox": [ + 76, + 801, + 470, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "is a vector containing the positional encoding of its location $l_{i}$ , as illustrated in Fig. 2. This representation is similar to the ones used by masked autoencoders (MAE) to learn to inpaint missing data [9]. However, a notable distinction lies in the fact that masked autoencoders possess knowledge of the locations of the given pieces, allowing them to directly work with the pairs $(\\mathbf{e}_i, \\gamma(l_i))$ . In our scenario, where the pieces have been shuffled, a separate treatment of the visual content $\\mathbf{e}_i$ and its corresponding location $\\gamma(l_i)$ is necessary.", + "bbox": [ + 500, + 421, + 890, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Puzzles without Missing Pieces. Given a complete set of puzzle pieces embeddings, $\\mathbf{E} = \\{\\mathbf{e}_1,\\mathbf{e}_2,\\dots ,\\mathbf{e}_N\\}$ , let $\\mathbf{L} = (\\gamma (l_1),\\gamma (l_2),\\ldots ,\\gamma (l_N))^T$ be a matrix with the sought positional encodings of the given pieces. Then, we formulate solving the jigsaw puzzle as a conditional generation problem, where the goal is to learn the joint probability of the locations $\\mathbf{L}$ , given their unsorted visual content $\\mathbf{E}$ : $\\mathbf{L}|\\mathbf{E}\\sim q(\\mathbf{L}|\\mathbf{E})$ . We propose to learn this probability by using a CDDPM as follows.", + "bbox": [ + 496, + 556, + 890, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the forward process, we diffuse the positional encodings, conditioned on the set of unsorted visual contents:", + "bbox": [ + 498, + 693, + 890, + 723 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {L} _ {t} \\mid \\mathbf {L} _ {t - 1}, \\mathbf {E}\\right) = \\mathcal {N} \\left(\\mathbf {L} _ {t} \\mid \\mathbf {E}; \\sqrt {1 - \\beta_ {t}} \\mathbf {L} _ {t - 1} \\mid \\mathbf {E}, \\beta_ {t} \\mathbf {I}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 529, + 731, + 859, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where noise is gradually added to the positional encodings of the patches (See Fig. 2), and $\\beta_{t}$ schedules the amount of noise added at each step $t$ . The distribution of $\\mathbf{L}_t$ given $\\mathbf{L}_0$ can be explicitly expressed by", + "bbox": [ + 496, + 755, + 893, + 816 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {L} _ {t} \\mid \\mathbf {L} _ {0}, \\mathbf {E}\\right) = \\mathcal {N} \\left(\\mathbf {L} _ {t} \\mid \\mathbf {E}; \\sqrt {\\alpha_ {t}} \\mathbf {L} _ {0} \\mid \\mathbf {E}, (1 - \\alpha_ {t}) \\mathbf {I}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 823, + 851, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})$", + "bbox": [ + 500, + 845, + 684, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The reverse diffusion denoising process is given by:", + "bbox": [ + 517, + 863, + 861, + 877 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(\\mathbf {L} _ {t - 1} \\mid \\mathbf {L} _ {t}, \\mathbf {E}\\right) := \\mathcal {N} \\left(\\mathbf {L} _ {t - 1} \\mid t, \\mathbf {E}; \\mu_ {\\theta} \\left(\\mathbf {L} _ {t}, t, \\mathbf {E}\\right), \\sigma_ {\\theta} \\left(\\mathbf {L} _ {t}, t, \\mathbf {E}\\right) \\mathbf {I}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 883, + 903, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2In the cases with missing pieces or with eroded pieces, we will allow $\\mathbf{X}\\supseteq \\cup_{i = 1}^{M\\leq N}(\\mathbf{x}_i@l_i)$", + "bbox": [ + 76, + 872, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23011", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The conditional diffusion model learns a network $\\epsilon_{\\theta}$ to predict the noise added to the noisy input $\\mathbf{L}_t$ with the loss:", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {\\mathbf {L} _ {0} \\sim q (\\mathbf {L} _ {0}), \\epsilon \\sim \\mathcal {N} (0, I), t, \\mathbf {E}} [ \\| \\epsilon - \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {L} _ {t}, t, \\mathbf {E}) \\| _ {2} ^ {2} ]\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 128, + 444, + 148 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{L}_t = \\sqrt{\\alpha_t}\\mathbf{L}_0 + \\sqrt{(1 - \\alpha_t)}\\epsilon$ for $\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})$ .", + "bbox": [ + 75, + 157, + 421, + 174 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Puzzles with Missing Pieces. For jigsaw puzzles with missing pieces, $\\mathbf{E} = \\mathbf{E}^g\\cup \\mathbf{E}^m$ , where $\\mathbf{E}^g$ and $\\mathbf{E}^m$ are the given and missing pieces, respectively. In this case, we generate the positional information for both the given pieces and the missing ones. For the missing pieces, it is possible to fill them up using an inpainting algorithm [28] after having their location, or alternatively, to generate the embeddings of the missing visual content simultaneously with the locations. In the later case, the conditional forward process gradually adds noise to both, the positional encodings and the visual content embeddings of the missing pieces, conditioned on the visual content of the given pieces using $q(\\mathbf{L}_t,\\mathbf{E}_t^m |\\mathbf{L}_0,\\mathbf{E}_0^m,\\mathbf{E}^g)$ and the corresponding reverse diffusion process: $p_{\\theta}(\\mathbf{L}_{t - 1},\\mathbf{E}_{t - 1}^{m}|\\mathbf{L}_{t},\\mathbf{E}_{t}^{m},\\mathbf{E}^{g})$", + "bbox": [ + 75, + 174, + 468, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 393, + 294, + 409 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we give implementation details of our models, which are rooted in the official codebase of diffusion models from [17]. Code will be provided.", + "bbox": [ + 75, + 417, + 468, + 462 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Solving image jigsaw puzzles. We implemented our diffusion transformers by modifying ViTs based on [2], following the approach in [21] for incorporating timesteps. Adaptive normalization layers are introduced before and after the multi-head attention and MLP modules to accommodate timesteps. To avoid the model reducing to a mere classification task, we anchor the positional embedding of the initial patch and represent subsequent patches using relative positional embeddings. This approach enhances the model's ability to capture spatial dependencies and ensures resilience against overreliance on absolute positional information. We utilized a linear noise schedule with $T = 1000$ diffusion steps.", + "bbox": [ + 75, + 463, + 468, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Solving temporal jigsaw puzzles. For low-resolution videos, with missing frames, we applied diffusion directly on the video pixels. For high-resolution videos, we followed [22] and first compressed each of the frames into a latent space, and subsequently applied diffusion process on these latent variables. For the reverse diffusion process, we modified the video U-Net based on [23]. In our implementation, we only use the 2D spatial convolutional layers without the temporal convolutional layer, and in the $2\\mathrm{D} + 1\\mathrm{D}$ attention layers, we removed the temporal positional embedding. We used a linear noise schedule, and we fixed diffusion steps to $T = 1000$", + "bbox": [ + 75, + 659, + 468, + 838 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Positional Encoding. We use the positional encoding:", + "bbox": [ + 96, + 839, + 455, + 854 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma_ {1 D} (l _ {n}) = \\left\\{ \\begin{array}{l} \\gamma (l _ {n}, 2 i) = \\sin \\left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\\right) \\\\ \\gamma (l _ {n}, 2 i + 1) = \\cos \\left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\\right) \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 863, + 431, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For temporal puzzles we use a 1-D positional encoding with a dimension of 16 to represent each video frame. To align with the input feature map's shape, the positional encoding undergoes an initial transformation through an MLP, ensuring it matches the size of the input feature map. Subsequently, the positional encoding is concatenated with the feature maps. For image puzzles, we employ a 2-D positional encoding with 32 dimensions to encode the position of an image patch, with the first half representing the x-coordinate and the second half representing the y-coordinate: $\\gamma_{2D}(l_x,l_y) = [\\gamma_{1D}(l_x),\\gamma_{1D}(l_y)]$ . This positional encoding is incorporated into image tokens following an MLP layer.", + "bbox": [ + 496, + 90, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 301, + 633, + 319 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, we describe the experiments we ran to validate the effectiveness of the proposed approach.", + "bbox": [ + 496, + 328, + 890, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 369, + 602, + 383 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We evaluated our approach on five datasets, consisting of both images and videos with different levels of resolution and complexity:", + "bbox": [ + 496, + 393, + 890, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "ImageNet-1k [5] contains 1,281,167 training images, and 50,000 validation images categorized into 1000 classes.", + "bbox": [ + 496, + 439, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "JPwLEG-3 [24] contains 12,000 images collected from MET [35] dataset. Each image is segmented into 9 fragments of dimensions $96 \\times 96$ , with gaps of 48 pixels between them. 9,000 images were allocated for training, 2,000 for testing, and an additional 1,000 for validation purposes.", + "bbox": [ + 496, + 470, + 890, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "MovingMNIST [27] comprises 10,000 video sequences, each containing 20 frames. Two digits move independently within each video, which has low resolution of $64 \\times 64$ pixels. We used 9,000 videos for training and tested our approach on the remaining 1,000 videos.", + "bbox": [ + 496, + 546, + 890, + 621 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "CLEVRER [34] is a diagnostic video dataset with 20,000 videos that simulate collisions among objects of different colors and shapes with $480 \\times 320$ pixels. The dataset is split into 10,000 videos for training, 5,000 for validation, and 5,000 for testing.", + "bbox": [ + 496, + 622, + 890, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$QST$ (Quick Sky Time) [36] contains 1,167 video clips extracted from 216 time-lapse 4K videos collected from YouTube, totaling 285,446 frames. The resolution of each frame exceeds $1,024 \\times 1,024$ . We downsample the frames to 256, and train on 1,000 videos, test on 167 videos.", + "bbox": [ + 496, + 699, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "UCF101 [26] is an action recognition dataset, consisting of 13,320 video clips representing 101 different human actions. Each frame has a resolution of $320 \\times 240$ pixels, with 9,537 videos for training and 3,783 videos for testing.", + "bbox": [ + 496, + 773, + 890, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Metrics", + "text_level": 1, + "bbox": [ + 500, + 845, + 596, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image Puzzle Solving Accuracy: In assessing image jigsaw solutions, we gauge solving accuracy both at", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23012", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6070c33b40a7b37a218d661fbc764b01e4d84192c241db6b4a7a4a51b89221c8.jpg", + "image_caption": [ + "Figure 4. Qualitative results for puzzles for Imagenet-1K dataset with 1, 2, and 3 missing pieces. Left: without cropping. Right: with cropping. First column shows the input puzzle, second column shows the sorted result (denoted as JPDVT-S), third column shows the sorted and inpainted result (denoted as JPDVT-SI), and last column shows the ground truth images." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 885, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the puzzle and piece levels. The puzzle-wise accuracy metric denotes the percentage of flawlessly reassembled image puzzles—essentially, the fraction of puzzles with every single piece correctly positioned, totaling $100\\%$ . On the other hand, the piece-wise accuracy metric quantifies the ratio of correctly placed pieces to the overall number of pieces in the dataset. This comprehensive evaluation framework provides a nuanced understanding of the reconstruction quality, capturing both holistic puzzle-level performance and the precision of individual pieces within the puzzle assembly.", + "bbox": [ + 75, + 632, + 472, + 785 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Video Puzzle Solving Accuracy Following [6], we measure video jigsaw puzzle solving accuracy with the average Normalized Kendall distance, based on 1,000 testing samples from each dataset. The Kendall distance, also called bubble-sort distance, scores the number of pairwise disagreements between the candidate sorting and the ground truth, which is defined as the number of elements in the set", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "constructed from two sequences $\\sigma_{1}$ and $\\sigma_{2}$ as follows:", + "bbox": [ + 498, + 632, + 857, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {G} (\\sigma_ {1}, \\sigma_ {2}) = \\{(i, j) | \\sigma_ {1} (i) < \\sigma_ {2} (j), \\sigma_ {2} (i) > \\sigma_ {1} (j) \\}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 657, + 864, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma_{1}(i)$ and $\\sigma_{2}(i)$ are the rankings of the element $i$ in the $\\sigma_{1}$ and $\\sigma_{2}$ sequences. The normalized distance is the Kendall distance, normalized by the biggest possible distance. The lower the distance is, the more similar the two sequences are, with the worst possible score being 1.", + "bbox": [ + 496, + 686, + 890, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Image Jigsaw Puzzles Experiments", + "text_level": 1, + "bbox": [ + 498, + 771, + 805, + 787 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conducted experiments on solving image jigsaw puzzles using the ImageNet-1k dataset, JPwLEG-3 [24], and the dataset used in [3]. Our models were trained separately with varying hyperparameters tailored to accommodate different numbers of puzzle pieces. To assess JPDVT's performance, we conducted comparative evaluations against state-of-the-art methods [3, 19, 24, 25, 31].", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23013", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/607efe8265f5dcf621be06b061e404abb28e17e0ac2fa7a78b57308deaef358f.jpg", + "image_caption": [ + "Figure 5. Video reshuffle results are showcased on various datasets, including 20 frames on MovingMNIST, 32 frames on CLEVRER, 32 frames on UCF101, and 32 frames on QST. Due to space limitations, only a subset of frames is presented in this illustration." + ], + "image_footnote": [], + "bbox": [ + 81, + 93, + 885, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The experiments on $\\text{ImangeNet-1k}$ follow the data preprocessing procedure from [31]. During training, each image underwent an initial resizing to $255 \\times 255$ before being divided into nine patches, each of size $85 \\times 85$ . Subsequently, every patch was randomly cropped to $64 \\times 64$ . A total of $9! = 362$ , 880 permutations were applied to these patches, and the models were trained to generate permutation indices based on the image patches. Data augmentation solely involved horizontal flipping. During testing, in con", + "bbox": [ + 75, + 762, + 472, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "trast to random cropping, we used the cropped patch from the center. The experiments on JPwLEG-3 follow the experiment setting in [24]. In the experiments with a large number of pieces, we follow the experiment setting with the largest number of pieces in [3].", + "bbox": [ + 496, + 762, + 890, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 4 presents qualitative results for puzzles with 1, 2, and 3 missing pieces, showcasing flawless reshuffling. Quantitative results for puzzles without missing pieces are provided in tables 1, 3 and 4. JPDVT achieved a $68.7\\%$", + "bbox": [ + 496, + 839, + 892, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23014", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/48160e7793821122e4d184f6fbd0ea21ad5e4ed399b0fd8e82cc6aa14da22a81.jpg", + "image_caption": [ + "Figure 6. Video reshuffle results with masks: Our diffusion model adeptly captures and reconstructs crucial latent components essential for the sequence reordering process." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 879, + 344 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2e80caa3476fe81588f2e455a84d283aaf1acdc940c0ccea367340f61e02caf4.jpg", + "table_caption": [ + "Table 1. Results of $3 \\times 3$ image puzzle solving on ImageNet-1k val split. Puzzle-level shows the percentages of flawlessly re-assembled puzzles. Fragment-level shows the fraction of correctly placed pieces of all the pieces in the dataset." + ], + "table_footnote": [], + "table_body": "
MethodPuzzle-levelPiece-level
SAJ[31]47.3%NA
Deepzzle [19]48%78%
JPDVT(Ours)68.7%83.3%
", + "bbox": [ + 120, + 464, + 426, + 525 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/32443cb9b6f2af25a5491b6018a19e5d2238e3a636032e918a4f4b113f7e0078.jpg", + "table_caption": [ + "Table 2. Results on $3 \\times 3$ puzzle recognition on ImageNet-1K val split on our proposed model on different number of missing fragments with and without eroded gaps." + ], + "table_footnote": [], + "table_body": "
% MissingWith gapWithout gap
puzzlepiecepuzzlepiece
068.7%83.3%99.4%99.6%
11.141.5%72.0%96.9%98.8%
22.221.4%61.8%82.8%95.0%
33.314.9%54.1%56.1%76.4%
", + "bbox": [ + 98, + 585, + 447, + 676 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "success rate on imagenet-1k dataset and $71.3\\%$ on JPwLEG-3 dataset for puzzles without missing pieces—an improvement of $20.7\\%$ and $11.6\\%$ , respectively, over prior state-of-the-art performances at the puzzle level. The results in table 3 show the capability of our model to handle a large number of puzzle pieces. Unlike previous methods, our approach handles puzzles with missing fragments, as demonstrated in Table 2. The performance gradually decreases with an increasing number of random missing pieces, indicating greater difficulty with eroded pieces compared to those without erosion. This suggests the architecture effectively learns to align piece boundaries, a crucial aspect in solving the puzzle.", + "bbox": [ + 75, + 710, + 468, + 906 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a4b621e01d3ecb63282642e0ad9f665fd3d3dd1ca1b46289732313b5671a0412.jpg", + "table_caption": [ + "Table 3. Results of 150 pieces puzzle solving with $7\\%$ erosion." + ], + "table_footnote": [], + "table_body": "
MethodPiece-levelPuzzle-level
SJP-ED[3]66.7%10%
JPDVT(Ours)75.9%45%
", + "bbox": [ + 540, + 424, + 846, + 470 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/db71f437a9c58add6a2ab05cdcb1521f76f361fafffe4c24d5c1dc64c0f804a1.jpg", + "table_caption": [ + "Table 4. Comparison to the SOTA of $3 \\times 3$ puzzle recognition on the JPwLEG-3 [24] dataset." + ], + "table_footnote": [], + "table_body": "
MethodVenuePiece-level
Siamese [24]AAAI-202359.7%
Puzzlet [25]ICASSP-202358.2%
SJP-ED [3]CVPR-202055.2%
Deepzzle [19]TIP-202052.3%
JPDVT(Ours)-71.3%
", + "bbox": [ + 535, + 508, + 852, + 601 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/27b7f498901db285614345f028b5f54a162d16c90e10eef5a61575e89435b61a.jpg", + "table_caption": [ + "Table 5. Normalized Kendall Distance for Temporal Puzzles without missing data measures the number of pairwise disagreements between two sequences." + ], + "table_footnote": [], + "table_body": "
DatasetsMethodNormalizedKendallDistance x 103
Size, #Pieces1, 202, 104, 5
MMNISTSTP1.40.040.01
VCOP--13.7
J-VAD1730.460
JPDVT(Ours)0.70.040
Size, #Pieces1, 322, 164, 8
CLEVRERSTP-0.150
VCOP--4.6
J-VAD268.258.20.04
JPDVT(Ours)2.60.170.04
UCFVCOP--14.5
J-VAD-164.33.8
JPDVT(Ours)26.24.21.2
QSTSTP-00
VCOP--14.5
JPDVT(Ours)7.03.00.19
", + "bbox": [ + 501, + 662, + 890, + 878 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23015", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Temporal Jigsaw Puzzles Experiments", + "text_level": 1, + "bbox": [ + 76, + 90, + 408, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We constructed temporal puzzles from videos by segmenting them, where each piece is a clip comprising one or more frames in the correct temporal order. Specifically, in the case of MovingMNIST, we built puzzles with: 20 pieces, where each piece is a single frame; 10 pieces, each comprising a pair of consecutive frames; and 5 pieces, with each piece containing four consecutive frames. Similarly, for the CLEVRER, UCF, and QST datasets, our evaluation included puzzles with 32 pieces (single frames), 16 pieces (two frames), 8 pieces (four frames), and 4 pieces (eight frames). Qualitative examples in Fig. 5 and 6 demonstrate instances where our approach adeptly resolved the puzzles without and with missing data, respectively.", + "bbox": [ + 75, + 113, + 468, + 309 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We compared the performance of our algorithm solving temporal puzzles, without missing data, against the state-of-the-art methods STP (Space-Time Puzzle) [6], VCOP (Video Clip-Order Prediction) [33], and J-VAD (Joint Video Anomaly Detection) [30], using four video datasets, whenever possible, as described below. We trained these models following the processes detailed in their respective papers, with adjustments made to network sizes to accommodate varying dataset dimensions. To ensure fair comparisons, we fixed the first frame as an anchor frame, and fully randomly shuffle the remaining frames with no mask. Detailed training hyperparameters are available in the appendix.", + "bbox": [ + 75, + 311, + 470, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "STP adapts its inputs based on video characteristics. For dynamic textures, exemplified by the QST dataset, it utilizes the PCA decomposition of pixels. However, for more structured videos, such as MovingMNIST and CLEVRER, STP requires feature correspondences across the input frames. Thus, for MovingMNIST and CLEVRER we ran experiments by providing STP ground-truth object coordinates, giving this method an unfair advantage. Regrettably, providing feature correspondences for the UCF dataset was impractical due to its complexity. Additionally, the computational demands of STP rendered unfeasible to run for puzzles with 32 pieces, since its inference time for this setting takes over 30 minutes/video. In contrast, our approach takes approximately 10 seconds/video.", + "bbox": [ + 75, + 492, + 468, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "VCOP and J-VAD, on the other hand, have faster inference times, approximately 1 sec/video. However, VCOP predicts the permutation of videos by classifying over a vast number of possibilities. For instance, with 10 clips, the model must classify among $10! = 3,628,800$ classes. As the number of video clips for ordering increases, training the model becomes impractical due to the exponential growth in classes. J-VAD, employs a 3D-CNN model coupled with a classifier to directly predict the position of each input frame or clip. However, its performance experiences a significant decline when tested on 16 and 32 clips. This phenomenon aligns with findings in [30], where performance deterioration is reported for frame numbers larger than 9,", + "bbox": [ + 75, + 704, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/733554842799d0a22fff356b9fa16d879f3329b6b1d0034a622d190577a3af79.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 88, + 694, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e0ff15a866fdc68946d34503c769fb8fc934d6ce0a588d0e8b9e959e8afd40ed.jpg", + "image_caption": [ + "Figure 7. Normalized Kendall distances vs. missing pieces. (a) CLEVRER dataset with 8 pieces, each containing 4 frames. (b) MovingMNIST dataset with 8 pieces, each with 4 frames. (c) UCF dataset with 8 pieces, each with 4 frames. (d) QST dataset with 8 pieces, each with 4 frames." + ], + "image_footnote": [], + "bbox": [ + 504, + 159, + 694, + 220 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ae8f1076430c2080f1cadc3cde1a864b04d0aa7eecb7cd5379827c4a21c9f2ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 88, + 890, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/573b6f60bba05468ffed7ed5251bf6a62a661fecd0c070c58b70b6617f469601.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 157, + 888, + 220 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "consistent with our observations.", + "bbox": [ + 500, + 308, + 718, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2 provides the quantitative results of the comparisons against the baselines. Our approach achieves State-Of-The-Art performance across the board and second best for the QST dataset. While STP has comparable performance in some settings and best performance for QST, as noted above, it uses different types of inputs depending on the video characteristics and in this case ground-truth feature correspondences, while our approach always works directly on the raw data. In addition, while our approach is an order of magnitude slower than VCOP and J-VAD, it can handle all the testing settings while the others cannot.", + "bbox": [ + 496, + 325, + 890, + 492 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, JPDVT can handle temporal puzzles with missing fragments, as shown in Fig. 6. As seen in Fig. 7, JPDVT's performance gradually decreases with an increasing number of random missing pieces. This capability allows the use of JPDVT to increase the temporal resolution of videos, as illustrated in the supplemental material.", + "bbox": [ + 496, + 494, + 890, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 609, + 617, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Solving puzzles is a fundamental task involving the re-assembly of disordered fragments, a classic problem in pattern recognition that traces its roots back to 1964 [8]. In this paper, we present JPDVT, a novel method for solving image and temporal puzzles in an unified framework. Our approach works by describing the underlying data as an unordered set of pairs, associating the (2D or 1D) positional encoding of a puzzle piece with an embedding of its visual content. This representation enables the formulation of the puzzle-solving problem as a Conditional Diffusion Denoising process, where the unknown positional encodings of the shuffled puzzle pieces are recovered through a reverse denoising process, conditioned on the visual content embeddings of the given elements. JPDVT achieves state-of-the-art performance in quantitative comparisons and produces high-quality qualitative examples, while solving image and video puzzles. Notably, it can handle missing data and solve larger puzzles than previous approaches.", + "bbox": [ + 496, + 636, + 890, + 888 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23016", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tali Basha, Yael Moses, and Shai Avidan. Photo sequencing. In Computer Vision-ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Proceedings, Part VI 12, pages 654-667. Springer, 2012. 2", + "[2] Lucas Beyer, Xiaohua Zhai, and Alexander Kolesnikov. 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Springer, 2020. 4" + ], + "bbox": [ + 78, + 90, + 468, + 696 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23018", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/f9db8bd8-d9fa-40a9-84f3-75a6cea32e88_model.json b/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/f9db8bd8-d9fa-40a9-84f3-75a6cea32e88_model.json new file mode 100644 index 0000000000000000000000000000000000000000..71eaf7d851078060a4b7422e89bede9df64f9eed --- /dev/null +++ b/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/f9db8bd8-d9fa-40a9-84f3-75a6cea32e88_model.json @@ -0,0 +1,2079 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.131, + 0.835, + 0.152 + ], + "angle": 0, + "content": "Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers *" + }, + { + "type": "text", + "bbox": [ + 0.12, + 0.182, + 0.312, + 0.233 + ], + "angle": 0, + "content": "Jinyang Liu Northeastern University Boston MA" + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.238, + 0.337, + 0.251 + ], + "angle": 0, + "content": "liu.jinyan@northeastern.edu" + }, + { + "type": "text", + "bbox": [ + 0.393, + 0.182, + 0.588, + 0.233 + ], + "angle": 0, + "content": "Wondmgezahu Teshome Northeastern University Boston MA" + }, + { + "type": "text", + "bbox": [ + 0.374, + 0.238, + 0.605, + 0.251 + ], + "angle": 0, + "content": "teshome.w@northeastern.edu" + }, + { + "type": "text", + "bbox": [ + 0.689, + 0.182, + 0.829, + 0.234 + ], + "angle": 0, + "content": "Sandesh Ghimire \nQualcomm \nSan Diego CA" + }, + { + "type": "text", + "bbox": [ + 0.643, + 0.238, + 0.875, + 0.251 + ], + "angle": 0, + "content": "drsandeshghimire@gmail.com" + }, + { + "type": "text", + "bbox": [ + 0.243, + 0.26, + 0.434, + 0.31 + ], + "angle": 0, + "content": "Mario Sznaier Northeastern University Boston MA" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.316, + 0.468, + 0.328 + ], + "angle": 0, + "content": "msznaier@coe.northeastern.edu" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.26, + 0.738, + 0.31 + ], + "angle": 0, + "content": "Octavia Camps Northeastern University Boston MA" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.316, + 0.756, + 0.329 + ], + "angle": 0, + "content": "camps@coe.northeastern.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.365, + 0.313, + 0.381 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.398, + 0.473, + 0.655 + ], + "angle": 0, + "content": "Solving image and video jigsaw puzzles poses the challenging task of rearranging image fragments or video frames from unordered sequences to restore meaningful images and video sequences. Existing approaches often hinge on discriminative models tasked with predicting either the absolute positions of puzzle elements or the permutation actions applied to the original data. Unfortunately, these methods face limitations in effectively solving puzzles with a large number of elements. In this paper, we propose JPDVT, an innovative approach that harnesses diffusion transformers to address this challenge. Specifically, we generate positional information for image patches or video frames, conditioned on their underlying visual content. This information is then employed to accurately assemble the puzzle pieces in their correct positions, even in scenarios involving missing pieces. Our method achieves state-of-the-art performance on several datasets." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.684, + 0.208, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.71, + 0.47, + 0.817 + ], + "angle": 0, + "content": "Image and video jigsaw puzzle solving involves the challenging task of reassembling image fragments or reshuffling video frames from unordered sequences into meaningful images and video sequences. This problem holds significant importance across various domains, ranging from image editing, biology, archaeology, document or photograph restoration, to photo sequencing [3]." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.828, + 0.47, + 0.901 + ], + "angle": 0, + "content": "*This work was supported in part by NSF grant 2038493, ONR grant N00014-21-1-2431, NIH grant R01CA240771 from NCI, and U.S. Department of Homeland Security grant 22STESE00001-03-02. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.361, + 0.895, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.608, + 0.893, + 0.663 + ], + "angle": 0, + "content": "Figure 1. Top: given unordered image fragments, some of them masked, we want to reconstruct the original image. Bottom: given shuffled video frames, some of them masked, we want to reconstruct the original video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.856 + ], + "angle": 0, + "content": "Past methods for solving jigsaw puzzles have commonly relied on discriminative networks, particularly in classifying the positions of image patches or video frames [11, 18]. Typically, these approaches involve feature extraction using a Convolutional Neural Network (CNN) backbone, followed by pairwise feature combinations before classification. The classifier then operates either by classifying permutations applied to the raw data or by directly predicting the positions of unordered elements. The primary emphasis in these methods is on training the feature backbone network to extract highly distinguishable positional features during the jigsaw puzzle-solving process." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "However, these approaches face challenges when dealing with a large number of elements and when handling a variable number of elements. Furthermore, they often pri" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23009" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.089, + 0.458, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.097, + 0.226, + 0.159, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.28, + 0.159, + 0.286 + ], + "angle": 0, + "content": "Gaussian Noise" + }, + { + "type": "image", + "bbox": [ + 0.164, + 0.227, + 0.228, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.164, + 0.28, + 0.23, + 0.286 + ], + "angle": 0, + "content": "Diffused 1-D PE" + }, + { + "type": "image", + "bbox": [ + 0.229, + 0.227, + 0.288, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.227, + 0.28, + 0.276, + 0.287 + ], + "angle": 0, + "content": "1-DPE" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.227, + 0.371, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.299, + 0.28, + 0.365, + 0.287 + ], + "angle": 0, + "content": "Diffused 2-D PE" + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.227, + 0.453, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.397, + 0.28, + 0.428, + 0.287 + ], + "angle": 0, + "content": "2-D PE" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.4 + ], + "angle": 0, + "content": "Figure 2. Top. Each piece has a positional encoding and an embedding of its visual content. The forward diffusion step (highlighted in the red box), gradually adds noise to the positional encodings. The reverse generation reconstructs the positional encodings, conditioned by the provided visual content. Bottom. Samples of 1D and 2D positional encodings, for video frames and image tiles, both in their original form and with added noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.455 + ], + "angle": 0, + "content": "oritize learning order at the expense of capturing the entire structure of the data, making them less suitable for solving jigsaw puzzles when data elements are missing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.621 + ], + "angle": 0, + "content": "This paper introduces Jigsaw Puzzles with Diffusion Vision Transformers (JPDVT), a novel approach to tackle these challenges through the utilization of a conditional diffusion denoising probabilistic model (CDDPM). The CD-DPM is designed to learn the positions of all the elements and generate the missing pieces, guided by the visual context of the available pieces, as illustrated in Figs. 1 and 2. Rigorous testing on diverse image and video datasets validates its superior performance compared to state-of-the-art models, underscoring the effectiveness of our proposed approach. The main contributions of this work are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.624, + 0.47, + 0.7 + ], + "angle": 0, + "content": "1. A simple unified design to solve both image and temporal puzzles with large number of pieces. The proposed model can handle missing data, finding the correct positions of the available pieces and generating plausible reconstructs for the missing ones." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.7, + 0.469, + 0.746 + ], + "angle": 0, + "content": "2. State-of-the-art performance on several image and video datasets. Our code and pre-trained models are available at our GitHub project page.1" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.624, + 0.47, + 0.746 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.76, + 0.219, + 0.775 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.469, + 0.83 + ], + "angle": 0, + "content": "Solving image and video jigsaw puzzles have the common objective of learning (spatial or temporal) positional information from unordered elements." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.832, + 0.469, + 0.878 + ], + "angle": 0, + "content": "Spatial Jigsaw Puzzles: Most existing approaches revolve around the reassembly of square puzzle pieces, with a focus on recreating the original image using non" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "overlapping components. Existing state-of-the-art jigsaw puzzle solvers can be broadly categorized into two streams." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.123, + 0.892, + 0.199 + ], + "angle": 0, + "content": "The first stream, represented by algorithms like [18-20, 24, 31], leverages feature extraction or image understanding networks for encoding visual content. Subsequently, these methods engage in fragment reassembly, demonstrating effectiveness in handling fragments with large eroded gaps." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.2, + 0.892, + 0.276 + ], + "angle": 0, + "content": "The second stream, as exemplified by [3, 14], initiates the process with fragment generation and subsequent reassembly. A neural network serves as a discriminator to verify the correct placement of fragments, yet these methods are generally limited to addressing small eroded gaps." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.277, + 0.892, + 0.337 + ], + "angle": 0, + "content": "While most of the prior works use CNNs, owing to their downsampling capabilities that facilitate classification, our paper advocates for using transformer models due to their equivariance to shuffling transformations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.893, + 0.581 + ], + "angle": 0, + "content": "In terms of reassembly strategies, traditional approaches include brute force [20] or greedy methods [3]. However, these methods face scalability challenges with large-scale puzzles due to their exponentially growing complexity. Some studies propose using classifiers to predict permutations [18] or fragment positions [31]. Other sophisticated approaches involve Dijkstra's algorithm with graph-cut [19], while a recent work [24] employs reinforcement learning as the reassembly strategy. Additionally, [25] utilized a genetic algorithm to tackle the problem. In contrast, our paper introduces the novel use of diffusion generative models for reassembly, leveraging positional information learned from visual patterns encoded by a transformer model. Moreover, our approach extends beyond conventional practices, demonstrating the capability to solve jigsaw puzzles even in the presence of missing elements." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.581, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Temporal Puzzles: Several recent works [11, 13, 15, 30, 33] propose using sorting temporal sequences as a pretext tasks for self-supervised learning for applications such as action recognition and video anomaly detection. They employ CNNs as video encoders to predict the order of shuffled videos directly. However, these methods, while effective for specific applications, are not explicitly designed to address the broader challenges of solving temporal puzzles, particularly on larger temporal scales." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.87 + ], + "angle": 0, + "content": "In contrast, our work draws inspiration from the paradigm set by [1, 4, 6, 16], where the emphasis lies on explicitly reshuffling temporal sequences akin to a photo sequencing problem. Unlike method [6], which learned permutation matrices by solving optimization problems enforcing low-rank structures on shuffled temporal sequences, our approach transcends the limitations of optimization-based techniques. These methods face constraints on sequence length and lose the ability to capture spatial coherence due to significant dimensionality reduction." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "This work moves beyond solving purely temporal jigsaw puzzles and tackles a more intricate problem—reshuffling" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.411, + 0.9 + ], + "angle": 0, + "content": "1https://github.com/JinyangMarkLiu/JPDVT" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23010" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.089, + 0.482, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.089, + 0.891, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.312, + 0.895, + 0.397 + ], + "angle": 0, + "content": "Figure 3. Left: Architecture employed to train the proposed diffusion transformer model. Image patches, accompanied by their corresponding position encoding tokens, undergo permutation in a consistent manner. During forward diffusion, noise is introduced to all positional encoding tokens and a subset of embedded patch tokens. The transformer is trained to execute a reverse diffusion process, mitigating the introduced noise. Right: Inference process. During inference, the observed patches are padded with Gaussian noise to fill the entire image. Linearly embedded patch tokens are then concatenated with positional encoding tokens initialized with Gaussian noise. The transformer model is designed to reconstruct the visual content of the missing patches and to determine the positions for all patches, simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.471, + 0.483 + ], + "angle": 0, + "content": "temporal sequences with temporal masks. Specifically, it aims to reconstruct a shuffled temporal sequence or video with missing frames, posing a novel and challenging extension to the temporal puzzle-solving paradigm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.226, + 0.515 + ], + "angle": 0, + "content": "3. Our Approach" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.524, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Here, we present JPDVT, which uses a novel perspective on representing video and image data as non-ordered sets, to solve masked jigsaw puzzles. This representation enables JPDVT to harness the inherent properties of vision transformer architectures and the capabilities of conditional generative diffusion models to solve puzzles with missing pieces, as depicted in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.641, + 0.409, + 0.657 + ], + "angle": 0, + "content": "3.1. Masked Jigsaw Transformer Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.664, + 0.47, + 0.801 + ], + "angle": 0, + "content": "Consider an image or video, denoted as \\(\\mathbf{X}\\), partitioned into an unordered puzzle comprising individual pieces \\(\\mathbf{x}_1, \\ldots, \\mathbf{x}_N\\) such that \\(\\mathbf{x}_i \\cap \\mathbf{x}_j = \\phi\\) for all \\(i\\) and \\(j\\), and \\(\\mathbf{X} = \\cup_{i=1}^{N} \\mathbf{x}_i\\). Our objective is to reconstruct \\(\\mathbf{X}\\) by establishing a mapping \\(f(\\mathbf{x}_i) = l_i\\) that assigns the correct position to each piece. Specifically, we seek a solution where \\(\\mathbf{X}\\) is the union of the pieces placed at their designated locations, expressed as \\(\\mathbf{X} = \\cup_{i=1}^{N} (\\mathbf{x}_i @ l_i)\\), where \\(\\mathbf{x}_i @ l_i\\) signifies that piece \\(\\mathbf{x}_i\\) should be positioned at location \\(l_i\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.802, + 0.471, + 0.863 + ], + "angle": 0, + "content": "To achieve this goal, we propose representing the solved puzzle of \\(\\mathbf{X}\\) as a set of pairs denoted by \\(\\mathbf{P} = \\{(\\mathbf{e}_1,\\gamma (l_1)),\\ldots ,(\\mathbf{e}_N,\\gamma (l_N))\\}\\). In this representation, \\(\\mathbf{e}_i\\) is an embedding of the visual content of piece \\(\\mathbf{x}_i\\), and \\(\\gamma (l_i)\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.422, + 0.892, + 0.558 + ], + "angle": 0, + "content": "is a vector containing the positional encoding of its location \\( l_{i} \\), as illustrated in Fig. 2. This representation is similar to the ones used by masked autoencoders (MAE) to learn to inpaint missing data [9]. However, a notable distinction lies in the fact that masked autoencoders possess knowledge of the locations of the given pieces, allowing them to directly work with the pairs \\( (\\mathbf{e}_i, \\gamma(l_i)) \\). In our scenario, where the pieces have been shuffled, a separate treatment of the visual content \\( \\mathbf{e}_i \\) and its corresponding location \\( \\gamma(l_i) \\) is necessary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.693 + ], + "angle": 0, + "content": "Puzzles without Missing Pieces. Given a complete set of puzzle pieces embeddings, \\(\\mathbf{E} = \\{\\mathbf{e}_1,\\mathbf{e}_2,\\dots ,\\mathbf{e}_N\\}\\), let \\(\\mathbf{L} = (\\gamma (l_1),\\gamma (l_2),\\ldots ,\\gamma (l_N))^T\\) be a matrix with the sought positional encodings of the given pieces. Then, we formulate solving the jigsaw puzzle as a conditional generation problem, where the goal is to learn the joint probability of the locations \\(\\mathbf{L}\\), given their unsorted visual content \\(\\mathbf{E}\\): \\(\\mathbf{L}|\\mathbf{E}\\sim q(\\mathbf{L}|\\mathbf{E})\\). We propose to learn this probability by using a CDDPM as follows." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.694, + 0.891, + 0.724 + ], + "angle": 0, + "content": "For the forward process, we diffuse the positional encodings, conditioned on the set of unsorted visual contents:" + }, + { + "type": "equation", + "bbox": [ + 0.53, + 0.732, + 0.86, + 0.75 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {L} _ {t} \\mid \\mathbf {L} _ {t - 1}, \\mathbf {E}\\right) = \\mathcal {N} \\left(\\mathbf {L} _ {t} \\mid \\mathbf {E}; \\sqrt {1 - \\beta_ {t}} \\mathbf {L} _ {t - 1} \\mid \\mathbf {E}, \\beta_ {t} \\mathbf {I}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.756, + 0.894, + 0.817 + ], + "angle": 0, + "content": "where noise is gradually added to the positional encodings of the patches (See Fig. 2), and \\(\\beta_{t}\\) schedules the amount of noise added at each step \\(t\\). The distribution of \\(\\mathbf{L}_t\\) given \\(\\mathbf{L}_0\\) can be explicitly expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.824, + 0.852, + 0.841 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {L} _ {t} \\mid \\mathbf {L} _ {0}, \\mathbf {E}\\right) = \\mathcal {N} \\left(\\mathbf {L} _ {t} \\mid \\mathbf {E}; \\sqrt {\\alpha_ {t}} \\mathbf {L} _ {0} \\mid \\mathbf {E}, (1 - \\alpha_ {t}) \\mathbf {I}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.846, + 0.686, + 0.863 + ], + "angle": 0, + "content": "where \\(\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})\\)" + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.864, + 0.862, + 0.878 + ], + "angle": 0, + "content": "The reverse diffusion denoising process is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.885, + 0.905, + 0.903 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(\\mathbf {L} _ {t - 1} \\mid \\mathbf {L} _ {t}, \\mathbf {E}\\right) := \\mathcal {N} \\left(\\mathbf {L} _ {t - 1} \\mid t, \\mathbf {E}; \\mu_ {\\theta} \\left(\\mathbf {L} _ {t}, t, \\mathbf {E}\\right), \\sigma_ {\\theta} \\left(\\mathbf {L} _ {t}, t, \\mathbf {E}\\right) \\mathbf {I}\\right)\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.873, + 0.469, + 0.903 + ], + "angle": 0, + "content": "2In the cases with missing pieces or with eroded pieces, we will allow \\(\\mathbf{X}\\supseteq \\cup_{i = 1}^{M\\leq N}(\\mathbf{x}_i@l_i)\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23011" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "The conditional diffusion model learns a network \\(\\epsilon_{\\theta}\\) to predict the noise added to the noisy input \\(\\mathbf{L}_t\\) with the loss:" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.13, + 0.445, + 0.15 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {\\mathbf {L} _ {0} \\sim q (\\mathbf {L} _ {0}), \\epsilon \\sim \\mathcal {N} (0, I), t, \\mathbf {E}} [ \\| \\epsilon - \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {L} _ {t}, t, \\mathbf {E}) \\| _ {2} ^ {2} ]\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.158, + 0.423, + 0.175 + ], + "angle": 0, + "content": "where \\(\\mathbf{L}_t = \\sqrt{\\alpha_t}\\mathbf{L}_0 + \\sqrt{(1 - \\alpha_t)}\\epsilon\\) for \\(\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.175, + 0.47, + 0.388 + ], + "angle": 0, + "content": "Puzzles with Missing Pieces. For jigsaw puzzles with missing pieces, \\(\\mathbf{E} = \\mathbf{E}^g\\cup \\mathbf{E}^m\\) , where \\(\\mathbf{E}^g\\) and \\(\\mathbf{E}^m\\) are the given and missing pieces, respectively. In this case, we generate the positional information for both the given pieces and the missing ones. For the missing pieces, it is possible to fill them up using an inpainting algorithm [28] after having their location, or alternatively, to generate the embeddings of the missing visual content simultaneously with the locations. In the later case, the conditional forward process gradually adds noise to both, the positional encodings and the visual content embeddings of the missing pieces, conditioned on the visual content of the given pieces using \\(q(\\mathbf{L}_t,\\mathbf{E}_t^m |\\mathbf{L}_0,\\mathbf{E}_0^m,\\mathbf{E}^g)\\) and the corresponding reverse diffusion process: \\(p_{\\theta}(\\mathbf{L}_{t - 1},\\mathbf{E}_{t - 1}^{m}|\\mathbf{L}_{t},\\mathbf{E}_{t}^{m},\\mathbf{E}^{g})\\)" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.395, + 0.295, + 0.41 + ], + "angle": 0, + "content": "3.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.463 + ], + "angle": 0, + "content": "In this section, we give implementation details of our models, which are rooted in the official codebase of diffusion models from [17]. Code will be provided." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.469, + 0.658 + ], + "angle": 0, + "content": "Solving image jigsaw puzzles. We implemented our diffusion transformers by modifying ViTs based on [2], following the approach in [21] for incorporating timesteps. Adaptive normalization layers are introduced before and after the multi-head attention and MLP modules to accommodate timesteps. To avoid the model reducing to a mere classification task, we anchor the positional embedding of the initial patch and represent subsequent patches using relative positional embeddings. This approach enhances the model's ability to capture spatial dependencies and ensures resilience against overreliance on absolute positional information. We utilized a linear noise schedule with \\( T = 1000 \\) diffusion steps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Solving temporal jigsaw puzzles. For low-resolution videos, with missing frames, we applied diffusion directly on the video pixels. For high-resolution videos, we followed [22] and first compressed each of the frames into a latent space, and subsequently applied diffusion process on these latent variables. For the reverse diffusion process, we modified the video U-Net based on [23]. In our implementation, we only use the 2D spatial convolutional layers without the temporal convolutional layer, and in the \\(2\\mathrm{D} + 1\\mathrm{D}\\) attention layers, we removed the temporal positional embedding. We used a linear noise schedule, and we fixed diffusion steps to \\(T = 1000\\)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.84, + 0.457, + 0.856 + ], + "angle": 0, + "content": "Positional Encoding. We use the positional encoding:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.864, + 0.432, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\gamma_ {1 D} (l _ {n}) = \\left\\{ \\begin{array}{l} \\gamma (l _ {n}, 2 i) = \\sin \\left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\\right) \\\\ \\gamma (l _ {n}, 2 i + 1) = \\cos \\left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\\right) \\end{array} \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.289 + ], + "angle": 0, + "content": "For temporal puzzles we use a 1-D positional encoding with a dimension of 16 to represent each video frame. To align with the input feature map's shape, the positional encoding undergoes an initial transformation through an MLP, ensuring it matches the size of the input feature map. Subsequently, the positional encoding is concatenated with the feature maps. For image puzzles, we employ a 2-D positional encoding with 32 dimensions to encode the position of an image patch, with the first half representing the x-coordinate and the second half representing the y-coordinate: \\(\\gamma_{2D}(l_x,l_y) = [\\gamma_{1D}(l_x),\\gamma_{1D}(l_y)]\\). This positional encoding is incorporated into image tokens following an MLP layer." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.303, + 0.634, + 0.32 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.892, + 0.361 + ], + "angle": 0, + "content": "Here, we describe the experiments we ran to validate the effectiveness of the proposed approach." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.371, + 0.603, + 0.385 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.439 + ], + "angle": 0, + "content": "We evaluated our approach on five datasets, consisting of both images and videos with different levels of resolution and complexity:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.892, + 0.47 + ], + "angle": 0, + "content": "ImageNet-1k [5] contains 1,281,167 training images, and 50,000 validation images categorized into 1000 classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.546 + ], + "angle": 0, + "content": "JPwLEG-3 [24] contains 12,000 images collected from MET [35] dataset. Each image is segmented into 9 fragments of dimensions \\(96 \\times 96\\), with gaps of 48 pixels between them. 9,000 images were allocated for training, 2,000 for testing, and an additional 1,000 for validation purposes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.622 + ], + "angle": 0, + "content": "MovingMNIST [27] comprises 10,000 video sequences, each containing 20 frames. Two digits move independently within each video, which has low resolution of \\(64 \\times 64\\) pixels. We used 9,000 videos for training and tested our approach on the remaining 1,000 videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.699 + ], + "angle": 0, + "content": "CLEVRER [34] is a diagnostic video dataset with 20,000 videos that simulate collisions among objects of different colors and shapes with \\(480 \\times 320\\) pixels. The dataset is split into 10,000 videos for training, 5,000 for validation, and 5,000 for testing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.774 + ], + "angle": 0, + "content": "\\(QST\\) (Quick Sky Time) [36] contains 1,167 video clips extracted from 216 time-lapse 4K videos collected from YouTube, totaling 285,446 frames. The resolution of each frame exceeds \\(1,024 \\times 1,024\\). We downsample the frames to 256, and train on 1,000 videos, test on 167 videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.775, + 0.892, + 0.836 + ], + "angle": 0, + "content": "UCF101 [26] is an action recognition dataset, consisting of 13,320 video clips representing 101 different human actions. Each frame has a resolution of \\(320 \\times 240\\) pixels, with 9,537 videos for training and 3,783 videos for testing." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.597, + 0.862 + ], + "angle": 0, + "content": "4.2. Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Image Puzzle Solving Accuracy: In assessing image jigsaw solutions, we gauge solving accuracy both at" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23012" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.887, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.564, + 0.893, + 0.608 + ], + "angle": 0, + "content": "Figure 4. Qualitative results for puzzles for Imagenet-1K dataset with 1, 2, and 3 missing pieces. Left: without cropping. Right: with cropping. First column shows the input puzzle, second column shows the sorted result (denoted as JPDVT-S), third column shows the sorted and inpainted result (denoted as JPDVT-SI), and last column shows the ground truth images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.633, + 0.473, + 0.786 + ], + "angle": 0, + "content": "the puzzle and piece levels. The puzzle-wise accuracy metric denotes the percentage of flawlessly reassembled image puzzles—essentially, the fraction of puzzles with every single piece correctly positioned, totaling \\(100\\%\\). On the other hand, the piece-wise accuracy metric quantifies the ratio of correctly placed pieces to the overall number of pieces in the dataset. This comprehensive evaluation framework provides a nuanced understanding of the reconstruction quality, capturing both holistic puzzle-level performance and the precision of individual pieces within the puzzle assembly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Video Puzzle Solving Accuracy Following [6], we measure video jigsaw puzzle solving accuracy with the average Normalized Kendall distance, based on 1,000 testing samples from each dataset. The Kendall distance, also called bubble-sort distance, scores the number of pairwise disagreements between the candidate sorting and the ground truth, which is defined as the number of elements in the set" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.633, + 0.859, + 0.649 + ], + "angle": 0, + "content": "constructed from two sequences \\(\\sigma_{1}\\) and \\(\\sigma_{2}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.659, + 0.866, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathcal {G} (\\sigma_ {1}, \\sigma_ {2}) = \\{(i, j) | \\sigma_ {1} (i) < \\sigma_ {2} (j), \\sigma_ {2} (i) > \\sigma_ {1} (j) \\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.892, + 0.763 + ], + "angle": 0, + "content": "where \\(\\sigma_{1}(i)\\) and \\(\\sigma_{2}(i)\\) are the rankings of the element \\(i\\) in the \\(\\sigma_{1}\\) and \\(\\sigma_{2}\\) sequences. The normalized distance is the Kendall distance, normalized by the biggest possible distance. The lower the distance is, the more similar the two sequences are, with the worst possible score being 1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.807, + 0.789 + ], + "angle": 0, + "content": "4.3. Image Jigsaw Puzzles Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conducted experiments on solving image jigsaw puzzles using the ImageNet-1k dataset, JPwLEG-3 [24], and the dataset used in [3]. Our models were trained separately with varying hyperparameters tailored to accommodate different numbers of puzzle pieces. To assess JPDVT's performance, we conducted comparative evaluations against state-of-the-art methods [3, 19, 24, 25, 31]." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23013" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.094, + 0.887, + 0.692 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.709, + 0.895, + 0.737 + ], + "angle": 0, + "content": "Figure 5. Video reshuffle results are showcased on various datasets, including 20 frames on MovingMNIST, 32 frames on CLEVRER, 32 frames on UCF101, and 32 frames on QST. Due to space limitations, only a subset of frames is presented in this illustration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.473, + 0.9 + ], + "angle": 0, + "content": "The experiments on \\( \\text{ImangeNet-1k} \\) follow the data preprocessing procedure from [31]. During training, each image underwent an initial resizing to \\( 255 \\times 255 \\) before being divided into nine patches, each of size \\( 85 \\times 85 \\). Subsequently, every patch was randomly cropped to \\( 64 \\times 64 \\). A total of \\( 9! = 362 \\), 880 permutations were applied to these patches, and the models were trained to generate permutation indices based on the image patches. Data augmentation solely involved horizontal flipping. During testing, in con" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.839 + ], + "angle": 0, + "content": "trast to random cropping, we used the cropped patch from the center. The experiments on JPwLEG-3 follow the experiment setting in [24]. In the experiments with a large number of pieces, we follow the experiment setting with the largest number of pieces in [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Fig. 4 presents qualitative results for puzzles with 1, 2, and 3 missing pieces, showcasing flawless reshuffling. Quantitative results for puzzles without missing pieces are provided in tables 1, 3 and 4. JPDVT achieved a \\(68.7\\%\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23014" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.88, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.893, + 0.385 + ], + "angle": 0, + "content": "Figure 6. Video reshuffle results with masks: Our diffusion model adeptly captures and reconstructs crucial latent components essential for the sequence reordering process." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.41, + 0.47, + 0.464 + ], + "angle": 0, + "content": "Table 1. Results of \\(3 \\times 3\\) image puzzle solving on ImageNet-1k val split. Puzzle-level shows the percentages of flawlessly re-assembled puzzles. Fragment-level shows the fraction of correctly placed pieces of all the pieces in the dataset." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.465, + 0.427, + 0.526 + ], + "angle": 0, + "content": "
MethodPuzzle-levelPiece-level
SAJ[31]47.3%NA
Deepzzle [19]48%78%
JPDVT(Ours)68.7%83.3%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.546, + 0.47, + 0.587 + ], + "angle": 0, + "content": "Table 2. Results on \\(3 \\times 3\\) puzzle recognition on ImageNet-1K val split on our proposed model on different number of missing fragments with and without eroded gaps." + }, + { + "type": "table", + "bbox": [ + 0.099, + 0.587, + 0.449, + 0.678 + ], + "angle": 0, + "content": "
% MissingWith gapWithout gap
puzzlepiecepuzzlepiece
068.7%83.3%99.4%99.6%
11.141.5%72.0%96.9%98.8%
22.221.4%61.8%82.8%95.0%
33.314.9%54.1%56.1%76.4%
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.711, + 0.47, + 0.907 + ], + "angle": 0, + "content": "success rate on imagenet-1k dataset and \\(71.3\\%\\) on JPwLEG-3 dataset for puzzles without missing pieces—an improvement of \\(20.7\\%\\) and \\(11.6\\%\\), respectively, over prior state-of-the-art performances at the puzzle level. The results in table 3 show the capability of our model to handle a large number of puzzle pieces. Unlike previous methods, our approach handles puzzles with missing fragments, as demonstrated in Table 2. The performance gradually decreases with an increasing number of random missing pieces, indicating greater difficulty with eroded pieces compared to those without erosion. This suggests the architecture effectively learns to align piece boundaries, a crucial aspect in solving the puzzle." + }, + { + "type": "table_caption", + "bbox": [ + 0.509, + 0.41, + 0.882, + 0.423 + ], + "angle": 0, + "content": "Table 3. Results of 150 pieces puzzle solving with \\(7\\%\\) erosion." + }, + { + "type": "table", + "bbox": [ + 0.542, + 0.425, + 0.847, + 0.471 + ], + "angle": 0, + "content": "
MethodPiece-levelPuzzle-level
SJP-ED[3]66.7%10%
JPDVT(Ours)75.9%45%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.481, + 0.891, + 0.508 + ], + "angle": 0, + "content": "Table 4. Comparison to the SOTA of \\(3 \\times 3\\) puzzle recognition on the JPwLEG-3 [24] dataset." + }, + { + "type": "table", + "bbox": [ + 0.536, + 0.51, + 0.853, + 0.602 + ], + "angle": 0, + "content": "
MethodVenuePiece-level
Siamese [24]AAAI-202359.7%
Puzzlet [25]ICASSP-202358.2%
SJP-ED [3]CVPR-202055.2%
Deepzzle [19]TIP-202052.3%
JPDVT(Ours)-71.3%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.615, + 0.891, + 0.657 + ], + "angle": 0, + "content": "Table 5. Normalized Kendall Distance for Temporal Puzzles without missing data measures the number of pairwise disagreements between two sequences." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.663, + 0.892, + 0.88 + ], + "angle": 0, + "content": "
DatasetsMethodNormalizedKendallDistance x 103
Size, #Pieces1, 202, 104, 5
MMNISTSTP1.40.040.01
VCOP--13.7
J-VAD1730.460
JPDVT(Ours)0.70.040
Size, #Pieces1, 322, 164, 8
CLEVRERSTP-0.150
VCOP--4.6
J-VAD268.258.20.04
JPDVT(Ours)2.60.170.04
UCFVCOP--14.5
J-VAD-164.33.8
JPDVT(Ours)26.24.21.2
QSTSTP-00
VCOP--14.5
JPDVT(Ours)7.03.00.19
" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23015" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.409, + 0.108 + ], + "angle": 0, + "content": "4.4. Temporal Jigsaw Puzzles Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.31 + ], + "angle": 0, + "content": "We constructed temporal puzzles from videos by segmenting them, where each piece is a clip comprising one or more frames in the correct temporal order. Specifically, in the case of MovingMNIST, we built puzzles with: 20 pieces, where each piece is a single frame; 10 pieces, each comprising a pair of consecutive frames; and 5 pieces, with each piece containing four consecutive frames. Similarly, for the CLEVRER, UCF, and QST datasets, our evaluation included puzzles with 32 pieces (single frames), 16 pieces (two frames), 8 pieces (four frames), and 4 pieces (eight frames). Qualitative examples in Fig. 5 and 6 demonstrate instances where our approach adeptly resolved the puzzles without and with missing data, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.471, + 0.493 + ], + "angle": 0, + "content": "We compared the performance of our algorithm solving temporal puzzles, without missing data, against the state-of-the-art methods STP (Space-Time Puzzle) [6], VCOP (Video Clip-Order Prediction) [33], and J-VAD (Joint Video Anomaly Detection) [30], using four video datasets, whenever possible, as described below. We trained these models following the processes detailed in their respective papers, with adjustments made to network sizes to accommodate varying dataset dimensions. To ensure fair comparisons, we fixed the first frame as an anchor frame, and fully randomly shuffle the remaining frames with no mask. Detailed training hyperparameters are available in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.705 + ], + "angle": 0, + "content": "STP adapts its inputs based on video characteristics. For dynamic textures, exemplified by the QST dataset, it utilizes the PCA decomposition of pixels. However, for more structured videos, such as MovingMNIST and CLEVRER, STP requires feature correspondences across the input frames. Thus, for MovingMNIST and CLEVRER we ran experiments by providing STP ground-truth object coordinates, giving this method an unfair advantage. Regrettably, providing feature correspondences for the UCF dataset was impractical due to its complexity. Additionally, the computational demands of STP rendered unfeasible to run for puzzles with 32 pieces, since its inference time for this setting takes over 30 minutes/video. In contrast, our approach takes approximately 10 seconds/video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.902 + ], + "angle": 0, + "content": "VCOP and J-VAD, on the other hand, have faster inference times, approximately 1 sec/video. However, VCOP predicts the permutation of videos by classifying over a vast number of possibilities. For instance, with 10 clips, the model must classify among \\(10! = 3,628,800\\) classes. As the number of video clips for ordering increases, training the model becomes impractical due to the exponential growth in classes. J-VAD, employs a 3D-CNN model coupled with a classifier to directly predict the position of each input frame or clip. However, its performance experiences a significant decline when tested on 16 and 32 clips. This phenomenon aligns with findings in [30], where performance deterioration is reported for frame numbers larger than 9," + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.695, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.16, + 0.695, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.089, + 0.891, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.159, + 0.889, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.224, + 0.894, + 0.294 + ], + "angle": 0, + "content": "Figure 7. Normalized Kendall distances vs. missing pieces. (a) CLEVRER dataset with 8 pieces, each containing 4 frames. (b) MovingMNIST dataset with 8 pieces, each with 4 frames. (c) UCF dataset with 8 pieces, each with 4 frames. (d) QST dataset with 8 pieces, each with 4 frames." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.309, + 0.72, + 0.323 + ], + "angle": 0, + "content": "consistent with our observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Table 2 provides the quantitative results of the comparisons against the baselines. Our approach achieves State-Of-The-Art performance across the board and second best for the QST dataset. While STP has comparable performance in some settings and best performance for QST, as noted above, it uses different types of inputs depending on the video characteristics and in this case ground-truth feature correspondences, while our approach always works directly on the raw data. In addition, while our approach is an order of magnitude slower than VCOP and J-VAD, it can handle all the testing settings while the others cannot." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Finally, JPDVT can handle temporal puzzles with missing fragments, as shown in Fig. 6. As seen in Fig. 7, JPDVT's performance gradually decreases with an increasing number of random missing pieces. This capability allows the use of JPDVT to increase the temporal resolution of videos, as illustrated in the supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.61, + 0.619, + 0.625 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.889 + ], + "angle": 0, + "content": "Solving puzzles is a fundamental task involving the re-assembly of disordered fragments, a classic problem in pattern recognition that traces its roots back to 1964 [8]. In this paper, we present JPDVT, a novel method for solving image and temporal puzzles in an unified framework. Our approach works by describing the underlying data as an unordered set of pairs, associating the (2D or 1D) positional encoding of a puzzle piece with an embedding of its visual content. This representation enables the formulation of the puzzle-solving problem as a Conditional Diffusion Denoising process, where the unknown positional encodings of the shuffled puzzle pieces are recovered through a reverse denoising process, conditioned on the visual content embeddings of the given elements. JPDVT achieves state-of-the-art performance in quantitative comparisons and produces high-quality qualitative examples, while solving image and video puzzles. Notably, it can handle missing data and solve larger puzzles than previous approaches." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23016" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Tali Basha, Yael Moses, and Shai Avidan. Photo sequencing. In Computer Vision-ECCV 2012: 12th European Conference on Computer Vision, Florence, Italy, October 7-13, 2012, Proceedings, Part VI 12, pages 654-667. Springer, 2012. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.186, + 0.472, + 0.227 + ], + "angle": 0, + "content": "[2] Lucas Beyer, Xiaohua Zhai, and Alexander Kolesnikov. 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Springer, 2020. 4" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.698 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23018" + } + ] +] \ No newline at end of file diff --git a/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/f9db8bd8-d9fa-40a9-84f3-75a6cea32e88_origin.pdf b/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/f9db8bd8-d9fa-40a9-84f3-75a6cea32e88_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..a0485925c82090491e17a5d260fe1a1b5b949ea3 --- /dev/null +++ b/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/f9db8bd8-d9fa-40a9-84f3-75a6cea32e88_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e023c106a3736a844ca26910576ee45edf9f0413241b5685e1e2849e1a4e1830 +size 5649123 diff --git a/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/full.md b/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4d7624451c49f3efd9cfcf0bbd5d06587306cac2 --- /dev/null +++ b/2024/Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers/full.md @@ -0,0 +1,301 @@ +# Solving Masked Jigsaw Puzzles with Diffusion Vision Transformers * + +Jinyang Liu Northeastern University Boston MA + +liu.jinyan@northeastern.edu + +Wondmgezahu Teshome Northeastern University Boston MA + +teshome.w@northeastern.edu + +Sandesh Ghimire +Qualcomm +San Diego CA + +drsandeshghimire@gmail.com + +Mario Sznaier Northeastern University Boston MA + +msznaier@coe.northeastern.edu + +Octavia Camps Northeastern University Boston MA + +camps@coe.northeastern.edu + +# Abstract + +Solving image and video jigsaw puzzles poses the challenging task of rearranging image fragments or video frames from unordered sequences to restore meaningful images and video sequences. Existing approaches often hinge on discriminative models tasked with predicting either the absolute positions of puzzle elements or the permutation actions applied to the original data. Unfortunately, these methods face limitations in effectively solving puzzles with a large number of elements. In this paper, we propose JPDVT, an innovative approach that harnesses diffusion transformers to address this challenge. Specifically, we generate positional information for image patches or video frames, conditioned on their underlying visual content. This information is then employed to accurately assemble the puzzle pieces in their correct positions, even in scenarios involving missing pieces. Our method achieves state-of-the-art performance on several datasets. + +# 1. Introduction + +Image and video jigsaw puzzle solving involves the challenging task of reassembling image fragments or reshuffling video frames from unordered sequences into meaningful images and video sequences. This problem holds significant importance across various domains, ranging from image editing, biology, archaeology, document or photograph restoration, to photo sequencing [3]. + +![](images/303aa82eeec77f1ad261149c162e8df85db496543cc8c377e998623b0eadded4.jpg) +Figure 1. Top: given unordered image fragments, some of them masked, we want to reconstruct the original image. Bottom: given shuffled video frames, some of them masked, we want to reconstruct the original video. + +Past methods for solving jigsaw puzzles have commonly relied on discriminative networks, particularly in classifying the positions of image patches or video frames [11, 18]. Typically, these approaches involve feature extraction using a Convolutional Neural Network (CNN) backbone, followed by pairwise feature combinations before classification. The classifier then operates either by classifying permutations applied to the raw data or by directly predicting the positions of unordered elements. The primary emphasis in these methods is on training the feature backbone network to extract highly distinguishable positional features during the jigsaw puzzle-solving process. + +However, these approaches face challenges when dealing with a large number of elements and when handling a variable number of elements. Furthermore, they often pri + +![](images/25270e81ae047ab0ba10f8ae8ae67aff5f9ee70e5f90ac176fbf1db34d08d148.jpg) + +![](images/a94d2f6cf97dd29858cc05d3ad3e5c839d49a0cf028c031ef5f0f010cc51ac46.jpg) +Gaussian Noise +Figure 2. Top. Each piece has a positional encoding and an embedding of its visual content. The forward diffusion step (highlighted in the red box), gradually adds noise to the positional encodings. The reverse generation reconstructs the positional encodings, conditioned by the provided visual content. Bottom. Samples of 1D and 2D positional encodings, for video frames and image tiles, both in their original form and with added noise. + +![](images/f8de5380dc64aeff67c00cf648ecb32a44ff47eaeb5e2dc653aa915bf8cf5607.jpg) +Diffused 1-D PE +1-DPE + +![](images/6d0eabdf3cd783b8c580ddb2c3cf54ecb7700042d733fdbc869a1f6007aa80f1.jpg) + +![](images/0f386f447593d085463755297293bf46d3fcf94155fb59ea17513b46705fd858.jpg) +Diffused 2-D PE + +![](images/a2d8d51181aee9e593aaeca10f8842a52d731fd72b51a871e642c3858f816063.jpg) +2-D PE + +oritize learning order at the expense of capturing the entire structure of the data, making them less suitable for solving jigsaw puzzles when data elements are missing. + +This paper introduces Jigsaw Puzzles with Diffusion Vision Transformers (JPDVT), a novel approach to tackle these challenges through the utilization of a conditional diffusion denoising probabilistic model (CDDPM). The CD-DPM is designed to learn the positions of all the elements and generate the missing pieces, guided by the visual context of the available pieces, as illustrated in Figs. 1 and 2. Rigorous testing on diverse image and video datasets validates its superior performance compared to state-of-the-art models, underscoring the effectiveness of our proposed approach. The main contributions of this work are: + +1. A simple unified design to solve both image and temporal puzzles with large number of pieces. The proposed model can handle missing data, finding the correct positions of the available pieces and generating plausible reconstructs for the missing ones. +2. State-of-the-art performance on several image and video datasets. Our code and pre-trained models are available at our GitHub project page.1 + +# 2. Related Work + +Solving image and video jigsaw puzzles have the common objective of learning (spatial or temporal) positional information from unordered elements. + +Spatial Jigsaw Puzzles: Most existing approaches revolve around the reassembly of square puzzle pieces, with a focus on recreating the original image using non + +overlapping components. Existing state-of-the-art jigsaw puzzle solvers can be broadly categorized into two streams. + +The first stream, represented by algorithms like [18-20, 24, 31], leverages feature extraction or image understanding networks for encoding visual content. Subsequently, these methods engage in fragment reassembly, demonstrating effectiveness in handling fragments with large eroded gaps. + +The second stream, as exemplified by [3, 14], initiates the process with fragment generation and subsequent reassembly. A neural network serves as a discriminator to verify the correct placement of fragments, yet these methods are generally limited to addressing small eroded gaps. + +While most of the prior works use CNNs, owing to their downsampling capabilities that facilitate classification, our paper advocates for using transformer models due to their equivariance to shuffling transformations. + +In terms of reassembly strategies, traditional approaches include brute force [20] or greedy methods [3]. However, these methods face scalability challenges with large-scale puzzles due to their exponentially growing complexity. Some studies propose using classifiers to predict permutations [18] or fragment positions [31]. Other sophisticated approaches involve Dijkstra's algorithm with graph-cut [19], while a recent work [24] employs reinforcement learning as the reassembly strategy. Additionally, [25] utilized a genetic algorithm to tackle the problem. In contrast, our paper introduces the novel use of diffusion generative models for reassembly, leveraging positional information learned from visual patterns encoded by a transformer model. Moreover, our approach extends beyond conventional practices, demonstrating the capability to solve jigsaw puzzles even in the presence of missing elements. + +Temporal Puzzles: Several recent works [11, 13, 15, 30, 33] propose using sorting temporal sequences as a pretext tasks for self-supervised learning for applications such as action recognition and video anomaly detection. They employ CNNs as video encoders to predict the order of shuffled videos directly. However, these methods, while effective for specific applications, are not explicitly designed to address the broader challenges of solving temporal puzzles, particularly on larger temporal scales. + +In contrast, our work draws inspiration from the paradigm set by [1, 4, 6, 16], where the emphasis lies on explicitly reshuffling temporal sequences akin to a photo sequencing problem. Unlike method [6], which learned permutation matrices by solving optimization problems enforcing low-rank structures on shuffled temporal sequences, our approach transcends the limitations of optimization-based techniques. These methods face constraints on sequence length and lose the ability to capture spatial coherence due to significant dimensionality reduction. + +This work moves beyond solving purely temporal jigsaw puzzles and tackles a more intricate problem—reshuffling + +![](images/7d37e33933a85b814063055a00f70a15de245857875cec85e8e8c61b02bbc566.jpg) +Figure 3. Left: Architecture employed to train the proposed diffusion transformer model. Image patches, accompanied by their corresponding position encoding tokens, undergo permutation in a consistent manner. During forward diffusion, noise is introduced to all positional encoding tokens and a subset of embedded patch tokens. The transformer is trained to execute a reverse diffusion process, mitigating the introduced noise. Right: Inference process. During inference, the observed patches are padded with Gaussian noise to fill the entire image. Linearly embedded patch tokens are then concatenated with positional encoding tokens initialized with Gaussian noise. The transformer model is designed to reconstruct the visual content of the missing patches and to determine the positions for all patches, simultaneously. + +![](images/2b38258e8bd2c48e20ac3887a3584b5603ed0e673ba50b027a23e4fb657ab6a0.jpg) + +temporal sequences with temporal masks. Specifically, it aims to reconstruct a shuffled temporal sequence or video with missing frames, posing a novel and challenging extension to the temporal puzzle-solving paradigm. + +# 3. Our Approach + +Here, we present JPDVT, which uses a novel perspective on representing video and image data as non-ordered sets, to solve masked jigsaw puzzles. This representation enables JPDVT to harness the inherent properties of vision transformer architectures and the capabilities of conditional generative diffusion models to solve puzzles with missing pieces, as depicted in Fig. 3. + +# 3.1. Masked Jigsaw Transformer Diffusion + +Consider an image or video, denoted as $\mathbf{X}$ , partitioned into an unordered puzzle comprising individual pieces $\mathbf{x}_1, \ldots, \mathbf{x}_N$ such that $\mathbf{x}_i \cap \mathbf{x}_j = \phi$ for all $i$ and $j$ , and $\mathbf{X} = \cup_{i=1}^{N} \mathbf{x}_i$ . Our objective is to reconstruct $\mathbf{X}$ by establishing a mapping $f(\mathbf{x}_i) = l_i$ that assigns the correct position to each piece. Specifically, we seek a solution where $\mathbf{X}$ is the union of the pieces placed at their designated locations, expressed as $\mathbf{X} = \cup_{i=1}^{N} (\mathbf{x}_i @ l_i)$ , where $\mathbf{x}_i @ l_i$ signifies that piece $\mathbf{x}_i$ should be positioned at location $l_i$ . + +To achieve this goal, we propose representing the solved puzzle of $\mathbf{X}$ as a set of pairs denoted by $\mathbf{P} = \{(\mathbf{e}_1,\gamma (l_1)),\ldots ,(\mathbf{e}_N,\gamma (l_N))\}$ . In this representation, $\mathbf{e}_i$ is an embedding of the visual content of piece $\mathbf{x}_i$ , and $\gamma (l_i)$ + +is a vector containing the positional encoding of its location $l_{i}$ , as illustrated in Fig. 2. This representation is similar to the ones used by masked autoencoders (MAE) to learn to inpaint missing data [9]. However, a notable distinction lies in the fact that masked autoencoders possess knowledge of the locations of the given pieces, allowing them to directly work with the pairs $(\mathbf{e}_i, \gamma(l_i))$ . In our scenario, where the pieces have been shuffled, a separate treatment of the visual content $\mathbf{e}_i$ and its corresponding location $\gamma(l_i)$ is necessary. + +Puzzles without Missing Pieces. Given a complete set of puzzle pieces embeddings, $\mathbf{E} = \{\mathbf{e}_1,\mathbf{e}_2,\dots ,\mathbf{e}_N\}$ , let $\mathbf{L} = (\gamma (l_1),\gamma (l_2),\ldots ,\gamma (l_N))^T$ be a matrix with the sought positional encodings of the given pieces. Then, we formulate solving the jigsaw puzzle as a conditional generation problem, where the goal is to learn the joint probability of the locations $\mathbf{L}$ , given their unsorted visual content $\mathbf{E}$ : $\mathbf{L}|\mathbf{E}\sim q(\mathbf{L}|\mathbf{E})$ . We propose to learn this probability by using a CDDPM as follows. + +For the forward process, we diffuse the positional encodings, conditioned on the set of unsorted visual contents: + +$$ +q \left(\mathbf {L} _ {t} \mid \mathbf {L} _ {t - 1}, \mathbf {E}\right) = \mathcal {N} \left(\mathbf {L} _ {t} \mid \mathbf {E}; \sqrt {1 - \beta_ {t}} \mathbf {L} _ {t - 1} \mid \mathbf {E}, \beta_ {t} \mathbf {I}\right) +$$ + +where noise is gradually added to the positional encodings of the patches (See Fig. 2), and $\beta_{t}$ schedules the amount of noise added at each step $t$ . The distribution of $\mathbf{L}_t$ given $\mathbf{L}_0$ can be explicitly expressed by + +$$ +q \left(\mathbf {L} _ {t} \mid \mathbf {L} _ {0}, \mathbf {E}\right) = \mathcal {N} \left(\mathbf {L} _ {t} \mid \mathbf {E}; \sqrt {\alpha_ {t}} \mathbf {L} _ {0} \mid \mathbf {E}, (1 - \alpha_ {t}) \mathbf {I}\right) +$$ + +where $\alpha_{t} = \prod_{s = 1}^{t}(1 - \beta_{s})$ + +The reverse diffusion denoising process is given by: + +$$ +p _ {\theta} \left(\mathbf {L} _ {t - 1} \mid \mathbf {L} _ {t}, \mathbf {E}\right) := \mathcal {N} \left(\mathbf {L} _ {t - 1} \mid t, \mathbf {E}; \mu_ {\theta} \left(\mathbf {L} _ {t}, t, \mathbf {E}\right), \sigma_ {\theta} \left(\mathbf {L} _ {t}, t, \mathbf {E}\right) \mathbf {I}\right) +$$ + +The conditional diffusion model learns a network $\epsilon_{\theta}$ to predict the noise added to the noisy input $\mathbf{L}_t$ with the loss: + +$$ +\mathcal {L} (\boldsymbol {\theta}) = \mathbb {E} _ {\mathbf {L} _ {0} \sim q (\mathbf {L} _ {0}), \epsilon \sim \mathcal {N} (0, I), t, \mathbf {E}} [ \| \epsilon - \epsilon_ {\boldsymbol {\theta}} (\mathbf {L} _ {t}, t, \mathbf {E}) \| _ {2} ^ {2} ] +$$ + +where $\mathbf{L}_t = \sqrt{\alpha_t}\mathbf{L}_0 + \sqrt{(1 - \alpha_t)}\epsilon$ for $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ . + +Puzzles with Missing Pieces. For jigsaw puzzles with missing pieces, $\mathbf{E} = \mathbf{E}^g\cup \mathbf{E}^m$ , where $\mathbf{E}^g$ and $\mathbf{E}^m$ are the given and missing pieces, respectively. In this case, we generate the positional information for both the given pieces and the missing ones. For the missing pieces, it is possible to fill them up using an inpainting algorithm [28] after having their location, or alternatively, to generate the embeddings of the missing visual content simultaneously with the locations. In the later case, the conditional forward process gradually adds noise to both, the positional encodings and the visual content embeddings of the missing pieces, conditioned on the visual content of the given pieces using $q(\mathbf{L}_t,\mathbf{E}_t^m |\mathbf{L}_0,\mathbf{E}_0^m,\mathbf{E}^g)$ and the corresponding reverse diffusion process: $p_{\theta}(\mathbf{L}_{t - 1},\mathbf{E}_{t - 1}^{m}|\mathbf{L}_{t},\mathbf{E}_{t}^{m},\mathbf{E}^{g})$ + +# 3.2. Implementation Details + +In this section, we give implementation details of our models, which are rooted in the official codebase of diffusion models from [17]. Code will be provided. + +Solving image jigsaw puzzles. We implemented our diffusion transformers by modifying ViTs based on [2], following the approach in [21] for incorporating timesteps. Adaptive normalization layers are introduced before and after the multi-head attention and MLP modules to accommodate timesteps. To avoid the model reducing to a mere classification task, we anchor the positional embedding of the initial patch and represent subsequent patches using relative positional embeddings. This approach enhances the model's ability to capture spatial dependencies and ensures resilience against overreliance on absolute positional information. We utilized a linear noise schedule with $T = 1000$ diffusion steps. + +Solving temporal jigsaw puzzles. For low-resolution videos, with missing frames, we applied diffusion directly on the video pixels. For high-resolution videos, we followed [22] and first compressed each of the frames into a latent space, and subsequently applied diffusion process on these latent variables. For the reverse diffusion process, we modified the video U-Net based on [23]. In our implementation, we only use the 2D spatial convolutional layers without the temporal convolutional layer, and in the $2\mathrm{D} + 1\mathrm{D}$ attention layers, we removed the temporal positional embedding. We used a linear noise schedule, and we fixed diffusion steps to $T = 1000$ + +Positional Encoding. We use the positional encoding: + +$$ +\gamma_ {1 D} (l _ {n}) = \left\{ \begin{array}{l} \gamma (l _ {n}, 2 i) = \sin \left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\right) \\ \gamma (l _ {n}, 2 i + 1) = \cos \left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\right) \end{array} \right. +$$ + +For temporal puzzles we use a 1-D positional encoding with a dimension of 16 to represent each video frame. To align with the input feature map's shape, the positional encoding undergoes an initial transformation through an MLP, ensuring it matches the size of the input feature map. Subsequently, the positional encoding is concatenated with the feature maps. For image puzzles, we employ a 2-D positional encoding with 32 dimensions to encode the position of an image patch, with the first half representing the x-coordinate and the second half representing the y-coordinate: $\gamma_{2D}(l_x,l_y) = [\gamma_{1D}(l_x),\gamma_{1D}(l_y)]$ . This positional encoding is incorporated into image tokens following an MLP layer. + +# 4. Experiments + +Here, we describe the experiments we ran to validate the effectiveness of the proposed approach. + +# 4.1. Datasets + +We evaluated our approach on five datasets, consisting of both images and videos with different levels of resolution and complexity: + +ImageNet-1k [5] contains 1,281,167 training images, and 50,000 validation images categorized into 1000 classes. + +JPwLEG-3 [24] contains 12,000 images collected from MET [35] dataset. Each image is segmented into 9 fragments of dimensions $96 \times 96$ , with gaps of 48 pixels between them. 9,000 images were allocated for training, 2,000 for testing, and an additional 1,000 for validation purposes. + +MovingMNIST [27] comprises 10,000 video sequences, each containing 20 frames. Two digits move independently within each video, which has low resolution of $64 \times 64$ pixels. We used 9,000 videos for training and tested our approach on the remaining 1,000 videos. + +CLEVRER [34] is a diagnostic video dataset with 20,000 videos that simulate collisions among objects of different colors and shapes with $480 \times 320$ pixels. The dataset is split into 10,000 videos for training, 5,000 for validation, and 5,000 for testing. + +$QST$ (Quick Sky Time) [36] contains 1,167 video clips extracted from 216 time-lapse 4K videos collected from YouTube, totaling 285,446 frames. The resolution of each frame exceeds $1,024 \times 1,024$ . We downsample the frames to 256, and train on 1,000 videos, test on 167 videos. + +UCF101 [26] is an action recognition dataset, consisting of 13,320 video clips representing 101 different human actions. Each frame has a resolution of $320 \times 240$ pixels, with 9,537 videos for training and 3,783 videos for testing. + +# 4.2. Metrics + +Image Puzzle Solving Accuracy: In assessing image jigsaw solutions, we gauge solving accuracy both at + +![](images/6070c33b40a7b37a218d661fbc764b01e4d84192c241db6b4a7a4a51b89221c8.jpg) +Figure 4. Qualitative results for puzzles for Imagenet-1K dataset with 1, 2, and 3 missing pieces. Left: without cropping. Right: with cropping. First column shows the input puzzle, second column shows the sorted result (denoted as JPDVT-S), third column shows the sorted and inpainted result (denoted as JPDVT-SI), and last column shows the ground truth images. + +the puzzle and piece levels. The puzzle-wise accuracy metric denotes the percentage of flawlessly reassembled image puzzles—essentially, the fraction of puzzles with every single piece correctly positioned, totaling $100\%$ . On the other hand, the piece-wise accuracy metric quantifies the ratio of correctly placed pieces to the overall number of pieces in the dataset. This comprehensive evaluation framework provides a nuanced understanding of the reconstruction quality, capturing both holistic puzzle-level performance and the precision of individual pieces within the puzzle assembly. + +Video Puzzle Solving Accuracy Following [6], we measure video jigsaw puzzle solving accuracy with the average Normalized Kendall distance, based on 1,000 testing samples from each dataset. The Kendall distance, also called bubble-sort distance, scores the number of pairwise disagreements between the candidate sorting and the ground truth, which is defined as the number of elements in the set + +constructed from two sequences $\sigma_{1}$ and $\sigma_{2}$ as follows: + +$$ +\mathcal {G} (\sigma_ {1}, \sigma_ {2}) = \{(i, j) | \sigma_ {1} (i) < \sigma_ {2} (j), \sigma_ {2} (i) > \sigma_ {1} (j) \} +$$ + +where $\sigma_{1}(i)$ and $\sigma_{2}(i)$ are the rankings of the element $i$ in the $\sigma_{1}$ and $\sigma_{2}$ sequences. The normalized distance is the Kendall distance, normalized by the biggest possible distance. The lower the distance is, the more similar the two sequences are, with the worst possible score being 1. + +# 4.3. Image Jigsaw Puzzles Experiments + +We conducted experiments on solving image jigsaw puzzles using the ImageNet-1k dataset, JPwLEG-3 [24], and the dataset used in [3]. Our models were trained separately with varying hyperparameters tailored to accommodate different numbers of puzzle pieces. To assess JPDVT's performance, we conducted comparative evaluations against state-of-the-art methods [3, 19, 24, 25, 31]. + +![](images/607efe8265f5dcf621be06b061e404abb28e17e0ac2fa7a78b57308deaef358f.jpg) +Figure 5. Video reshuffle results are showcased on various datasets, including 20 frames on MovingMNIST, 32 frames on CLEVRER, 32 frames on UCF101, and 32 frames on QST. Due to space limitations, only a subset of frames is presented in this illustration. + +The experiments on $\text{ImangeNet-1k}$ follow the data preprocessing procedure from [31]. During training, each image underwent an initial resizing to $255 \times 255$ before being divided into nine patches, each of size $85 \times 85$ . Subsequently, every patch was randomly cropped to $64 \times 64$ . A total of $9! = 362$ , 880 permutations were applied to these patches, and the models were trained to generate permutation indices based on the image patches. Data augmentation solely involved horizontal flipping. During testing, in con + +trast to random cropping, we used the cropped patch from the center. The experiments on JPwLEG-3 follow the experiment setting in [24]. In the experiments with a large number of pieces, we follow the experiment setting with the largest number of pieces in [3]. + +Fig. 4 presents qualitative results for puzzles with 1, 2, and 3 missing pieces, showcasing flawless reshuffling. Quantitative results for puzzles without missing pieces are provided in tables 1, 3 and 4. JPDVT achieved a $68.7\%$ + +![](images/48160e7793821122e4d184f6fbd0ea21ad5e4ed399b0fd8e82cc6aa14da22a81.jpg) +Figure 6. Video reshuffle results with masks: Our diffusion model adeptly captures and reconstructs crucial latent components essential for the sequence reordering process. + +Table 1. Results of $3 \times 3$ image puzzle solving on ImageNet-1k val split. Puzzle-level shows the percentages of flawlessly re-assembled puzzles. Fragment-level shows the fraction of correctly placed pieces of all the pieces in the dataset. + +
MethodPuzzle-levelPiece-level
SAJ[31]47.3%NA
Deepzzle [19]48%78%
JPDVT(Ours)68.7%83.3%
+ +Table 2. Results on $3 \times 3$ puzzle recognition on ImageNet-1K val split on our proposed model on different number of missing fragments with and without eroded gaps. + +
% MissingWith gapWithout gap
puzzlepiecepuzzlepiece
068.7%83.3%99.4%99.6%
11.141.5%72.0%96.9%98.8%
22.221.4%61.8%82.8%95.0%
33.314.9%54.1%56.1%76.4%
+ +success rate on imagenet-1k dataset and $71.3\%$ on JPwLEG-3 dataset for puzzles without missing pieces—an improvement of $20.7\%$ and $11.6\%$ , respectively, over prior state-of-the-art performances at the puzzle level. The results in table 3 show the capability of our model to handle a large number of puzzle pieces. Unlike previous methods, our approach handles puzzles with missing fragments, as demonstrated in Table 2. The performance gradually decreases with an increasing number of random missing pieces, indicating greater difficulty with eroded pieces compared to those without erosion. This suggests the architecture effectively learns to align piece boundaries, a crucial aspect in solving the puzzle. + +Table 3. Results of 150 pieces puzzle solving with $7\%$ erosion. + +
MethodPiece-levelPuzzle-level
SJP-ED[3]66.7%10%
JPDVT(Ours)75.9%45%
+ +Table 4. Comparison to the SOTA of $3 \times 3$ puzzle recognition on the JPwLEG-3 [24] dataset. + +
MethodVenuePiece-level
Siamese [24]AAAI-202359.7%
Puzzlet [25]ICASSP-202358.2%
SJP-ED [3]CVPR-202055.2%
Deepzzle [19]TIP-202052.3%
JPDVT(Ours)-71.3%
+ +Table 5. Normalized Kendall Distance for Temporal Puzzles without missing data measures the number of pairwise disagreements between two sequences. + +
DatasetsMethodNormalizedKendallDistance x 103
Size, #Pieces1, 202, 104, 5
MMNISTSTP1.40.040.01
VCOP--13.7
J-VAD1730.460
JPDVT(Ours)0.70.040
Size, #Pieces1, 322, 164, 8
CLEVRERSTP-0.150
VCOP--4.6
J-VAD268.258.20.04
JPDVT(Ours)2.60.170.04
UCFVCOP--14.5
J-VAD-164.33.8
JPDVT(Ours)26.24.21.2
QSTSTP-00
VCOP--14.5
JPDVT(Ours)7.03.00.19
+ +# 4.4. Temporal Jigsaw Puzzles Experiments + +We constructed temporal puzzles from videos by segmenting them, where each piece is a clip comprising one or more frames in the correct temporal order. Specifically, in the case of MovingMNIST, we built puzzles with: 20 pieces, where each piece is a single frame; 10 pieces, each comprising a pair of consecutive frames; and 5 pieces, with each piece containing four consecutive frames. Similarly, for the CLEVRER, UCF, and QST datasets, our evaluation included puzzles with 32 pieces (single frames), 16 pieces (two frames), 8 pieces (four frames), and 4 pieces (eight frames). Qualitative examples in Fig. 5 and 6 demonstrate instances where our approach adeptly resolved the puzzles without and with missing data, respectively. + +We compared the performance of our algorithm solving temporal puzzles, without missing data, against the state-of-the-art methods STP (Space-Time Puzzle) [6], VCOP (Video Clip-Order Prediction) [33], and J-VAD (Joint Video Anomaly Detection) [30], using four video datasets, whenever possible, as described below. We trained these models following the processes detailed in their respective papers, with adjustments made to network sizes to accommodate varying dataset dimensions. To ensure fair comparisons, we fixed the first frame as an anchor frame, and fully randomly shuffle the remaining frames with no mask. Detailed training hyperparameters are available in the appendix. + +STP adapts its inputs based on video characteristics. For dynamic textures, exemplified by the QST dataset, it utilizes the PCA decomposition of pixels. However, for more structured videos, such as MovingMNIST and CLEVRER, STP requires feature correspondences across the input frames. Thus, for MovingMNIST and CLEVRER we ran experiments by providing STP ground-truth object coordinates, giving this method an unfair advantage. Regrettably, providing feature correspondences for the UCF dataset was impractical due to its complexity. Additionally, the computational demands of STP rendered unfeasible to run for puzzles with 32 pieces, since its inference time for this setting takes over 30 minutes/video. In contrast, our approach takes approximately 10 seconds/video. + +VCOP and J-VAD, on the other hand, have faster inference times, approximately 1 sec/video. However, VCOP predicts the permutation of videos by classifying over a vast number of possibilities. For instance, with 10 clips, the model must classify among $10! = 3,628,800$ classes. As the number of video clips for ordering increases, training the model becomes impractical due to the exponential growth in classes. J-VAD, employs a 3D-CNN model coupled with a classifier to directly predict the position of each input frame or clip. However, its performance experiences a significant decline when tested on 16 and 32 clips. This phenomenon aligns with findings in [30], where performance deterioration is reported for frame numbers larger than 9, + +![](images/733554842799d0a22fff356b9fa16d879f3329b6b1d0034a622d190577a3af79.jpg) + +![](images/e0ff15a866fdc68946d34503c769fb8fc934d6ce0a588d0e8b9e959e8afd40ed.jpg) +Figure 7. Normalized Kendall distances vs. missing pieces. (a) CLEVRER dataset with 8 pieces, each containing 4 frames. (b) MovingMNIST dataset with 8 pieces, each with 4 frames. (c) UCF dataset with 8 pieces, each with 4 frames. (d) QST dataset with 8 pieces, each with 4 frames. + +![](images/ae8f1076430c2080f1cadc3cde1a864b04d0aa7eecb7cd5379827c4a21c9f2ca.jpg) + +![](images/573b6f60bba05468ffed7ed5251bf6a62a661fecd0c070c58b70b6617f469601.jpg) + +consistent with our observations. + +Table 2 provides the quantitative results of the comparisons against the baselines. Our approach achieves State-Of-The-Art performance across the board and second best for the QST dataset. While STP has comparable performance in some settings and best performance for QST, as noted above, it uses different types of inputs depending on the video characteristics and in this case ground-truth feature correspondences, while our approach always works directly on the raw data. In addition, while our approach is an order of magnitude slower than VCOP and J-VAD, it can handle all the testing settings while the others cannot. + +Finally, JPDVT can handle temporal puzzles with missing fragments, as shown in Fig. 6. As seen in Fig. 7, JPDVT's performance gradually decreases with an increasing number of random missing pieces. This capability allows the use of JPDVT to increase the temporal resolution of videos, as illustrated in the supplemental material. + +# 5. Conclusion + +Solving puzzles is a fundamental task involving the re-assembly of disordered fragments, a classic problem in pattern recognition that traces its roots back to 1964 [8]. In this paper, we present JPDVT, a novel method for solving image and temporal puzzles in an unified framework. Our approach works by describing the underlying data as an unordered set of pairs, associating the (2D or 1D) positional encoding of a puzzle piece with an embedding of its visual content. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 10334-10343, 2019. 2, 8, 5 +[34] Kexin Yi, Chuang Gan, Yunzhu Li, Pushmeet Kohli, Jiajun Wu, Antonio Torralba, and Joshua B Tenenbaum. Clevrer: Collision events for video representation and reasoning. arXiv preprint arXiv:1910.01442, 2019. 4 +[35] Nikolaos-Antonios Ypsilantis, Noa Garcia, Guangxing Han, Sarah Ibrahimi, Nanne Van Noord, and Giorgos Tolias. The met dataset: Instance-level recognition for artworks. In Thirty-fifth Conference on Neural Information Processing Systems Datasets and Benchmarks Track (Round 2), 2021. 4 +[36] Jiangning Zhang, Chao Xu, Liang Liu, Mengmeng Wang, Xia Wu, Yong Liu, and Yunliang Jiang. Dtvnet: Dynamic time-lapse video generation via single still image. In Computer Vision-ECCV 2020: 16th European Conference, Glasgow, UK, August 23-28, 2020, Proceedings, Part V 16, pages 300-315. 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puzzles poses the challenging task of rearranging image fragments or video frames from unordered sequences to restore meaningful images and video sequences. Existing approaches often hinge on discriminative models tasked with predicting either the absolute positions of puzzle elements or the permutation actions applied to the original data. Unfortunately, these methods face limitations in effectively solving puzzles with a large number of elements. In this paper, we propose JPDVT, an innovative approach that harnesses diffusion transformers to address this challenge. Specifically, we generate positional information for image patches or video frames, conditioned on their underlying visual content. This information is then employed to accurately assemble the puzzle pieces in their correct positions, even in scenarios involving missing pieces. 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Bottom: given shuffled video frames, some of them masked, we want to reconstruct the original video." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 533, + 546, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 677 + ], + "type": "text", + "content": "Past methods for solving jigsaw puzzles have commonly relied on discriminative networks, particularly in classifying the positions of image patches or video frames [11, 18]. Typically, these approaches involve feature extraction using a Convolutional Neural Network (CNN) backbone, followed by pairwise feature combinations before classification. The classifier then operates either by classifying permutations applied to the raw data or by directly predicting the positions of unordered elements. The primary emphasis in these methods is on training the feature backbone network to extract highly distinguishable positional features during the jigsaw puzzle-solving process." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "However, these approaches face challenges when dealing with a large number of elements and when handling a variable number of elements. Furthermore, they often pri" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 655, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 655, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 655, + 287, + 713 + ], + "type": "text", + "content": "*This work was supported in part by NSF grant 2038493, ONR grant N00014-21-1-2431, NIH grant R01CA240771 from NCI, and U.S. Department of Homeland Security grant 22STESE00001-03-02. The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of the U.S. Department of Homeland Security." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23009" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 280, + 177 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 280, + 177 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 280, + 177 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 280, + 177 + ], + "type": "image", + "image_path": "25270e81ae047ab0ba10f8ae8ae67aff5f9ee70e5f90ac176fbf1db34d08d148.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 59, + 178, + 97, + 222 + ], + "blocks": [ + { + "bbox": [ + 59, + 178, + 97, + 222 + ], + "lines": [ + { + "bbox": [ + 59, + 178, + 97, + 222 + ], + "spans": [ + { + "bbox": [ + 59, + 178, + 97, + 222 + ], + "type": "image", + "image_path": "a94d2f6cf97dd29858cc05d3ad3e5c839d49a0cf028c031ef5f0f010cc51ac46.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 221, + 97, + 226 + ], + "lines": [ + { + "bbox": [ + 58, + 221, + 97, + 226 + ], + "spans": [ + { + "bbox": [ + 58, + 221, + 97, + 226 + ], + "type": "text", + "content": "Gaussian Noise" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 239, + 289, + 316 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 316 + ], + "type": "text", + "content": "Figure 2. 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The CD-DPM is designed to learn the positions of all the elements and generate the missing pieces, guided by the visual context of the available pieces, as illustrated in Figs. 1 and 2. Rigorous testing on diverse image and video datasets validates its superior performance compared to state-of-the-art models, underscoring the effectiveness of our proposed approach. The main contributions of this work are:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 494, + 287, + 590 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 47, + 494, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 494, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 47, + 494, + 287, + 554 + ], + "type": "text", + "content": "1. A simple unified design to solve both image and temporal puzzles with large number of pieces. The proposed model can handle missing data, finding the correct positions of the available pieces and generating plausible reconstructs for the missing ones." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 554, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 554, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 47, + 554, + 287, + 590 + ], + "type": "text", + "content": "2. State-of-the-art performance on several image and video datasets. Our code and pre-trained models are available at our GitHub project page.1" + } + ] + } + ], + "index": 15 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 601, + 134, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 134, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 134, + 613 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 622, + 287, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 287, + 657 + ], + "type": "text", + "content": "Solving image and video jigsaw puzzles have the common objective of learning (spatial or temporal) positional information from unordered elements." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 47, + 658, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 287, + 695 + ], + "type": "text", + "content": "Spatial Jigsaw Puzzles: Most existing approaches revolve around the reassembly of square puzzle pieces, with a focus on recreating the original image using non" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "content": "overlapping components. Existing state-of-the-art jigsaw puzzle solvers can be broadly categorized into two streams." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 97, + 545, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 97, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 306, + 97, + 545, + 157 + ], + "type": "text", + "content": "The first stream, represented by algorithms like [18-20, 24, 31], leverages feature extraction or image understanding networks for encoding visual content. Subsequently, these methods engage in fragment reassembly, demonstrating effectiveness in handling fragments with large eroded gaps." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 158, + 545, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 158, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 305, + 158, + 545, + 218 + ], + "type": "text", + "content": "The second stream, as exemplified by [3, 14], initiates the process with fragment generation and subsequent reassembly. A neural network serves as a discriminator to verify the correct placement of fragments, yet these methods are generally limited to addressing small eroded gaps." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 219, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 219, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 219, + 545, + 266 + ], + "type": "text", + "content": "While most of the prior works use CNNs, owing to their downsampling capabilities that facilitate classification, our paper advocates for using transformer models due to their equivariance to shuffling transformations." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 268, + 546, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 546, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 546, + 460 + ], + "type": "text", + "content": "In terms of reassembly strategies, traditional approaches include brute force [20] or greedy methods [3]. However, these methods face scalability challenges with large-scale puzzles due to their exponentially growing complexity. Some studies propose using classifiers to predict permutations [18] or fragment positions [31]. Other sophisticated approaches involve Dijkstra's algorithm with graph-cut [19], while a recent work [24] employs reinforcement learning as the reassembly strategy. Additionally, [25] utilized a genetic algorithm to tackle the problem. In contrast, our paper introduces the novel use of diffusion generative models for reassembly, leveraging positional information learned from visual patterns encoded by a transformer model. Moreover, our approach extends beyond conventional practices, demonstrating the capability to solve jigsaw puzzles even in the presence of missing elements." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 568 + ], + "type": "text", + "content": "Temporal Puzzles: Several recent works [11, 13, 15, 30, 33] propose using sorting temporal sequences as a pretext tasks for self-supervised learning for applications such as action recognition and video anomaly detection. They employ CNNs as video encoders to predict the order of shuffled videos directly. However, these methods, while effective for specific applications, are not explicitly designed to address the broader challenges of solving temporal puzzles, particularly on larger temporal scales." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 569, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 689 + ], + "type": "text", + "content": "In contrast, our work draws inspiration from the paradigm set by [1, 4, 6, 16], where the emphasis lies on explicitly reshuffling temporal sequences akin to a photo sequencing problem. Unlike method [6], which learned permutation matrices by solving optimization problems enforcing low-rank structures on shuffled temporal sequences, our approach transcends the limitations of optimization-based techniques. These methods face constraints on sequence length and lose the ability to capture spatial coherence due to significant dimensionality reduction." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "This work moves beyond solving purely temporal jigsaw puzzles and tackles a more intricate problem—reshuffling" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 251, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 251, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 251, + 712 + ], + "type": "text", + "content": "1https://github.com/JinyangMarkLiu/JPDVT" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23010" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 70, + 294, + 238 + ], + "blocks": [ + { + "bbox": [ + 50, + 70, + 294, + 238 + ], + "lines": [ + { + "bbox": [ + 50, + 70, + 294, + 238 + ], + "spans": [ + { + "bbox": [ + 50, + 70, + 294, + 238 + ], + "type": "image", + "image_path": "7d37e33933a85b814063055a00f70a15de245857875cec85e8e8c61b02bbc566.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 547, + 314 + ], + "type": "text", + "content": "Figure 3. Left: Architecture employed to train the proposed diffusion transformer model. Image patches, accompanied by their corresponding position encoding tokens, undergo permutation in a consistent manner. During forward diffusion, noise is introduced to all positional encoding tokens and a subset of embedded patch tokens. The transformer is trained to execute a reverse diffusion process, mitigating the introduced noise. Right: Inference process. During inference, the observed patches are padded with Gaussian noise to fill the entire image. Linearly embedded patch tokens are then concatenated with positional encoding tokens initialized with Gaussian noise. The transformer model is designed to reconstruct the visual content of the missing patches and to determine the positions for all patches, simultaneously." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 300, + 70, + 545, + 238 + ], + "blocks": [ + { + "bbox": [ + 300, + 70, + 545, + 238 + ], + "lines": [ + { + "bbox": [ + 300, + 70, + 545, + 238 + ], + "spans": [ + { + "bbox": [ + 300, + 70, + 545, + 238 + ], + "type": "image", + "image_path": "2b38258e8bd2c48e20ac3887a3584b5603ed0e673ba50b027a23e4fb657ab6a0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 334, + 288, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 288, + 382 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 288, + 382 + ], + "type": "text", + "content": "temporal sequences with temporal masks. Specifically, it aims to reconstruct a shuffled temporal sequence or video with missing frames, posing a novel and challenging extension to the temporal puzzle-solving paradigm." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 394, + 138, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 138, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 138, + 407 + ], + "type": "text", + "content": "3. Our Approach" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 415, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 415, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 415, + 287, + 499 + ], + "type": "text", + "content": "Here, we present JPDVT, which uses a novel perspective on representing video and image data as non-ordered sets, to solve masked jigsaw puzzles. This representation enables JPDVT to harness the inherent properties of vision transformer architectures and the capabilities of conditional generative diffusion models to solve puzzles with missing pieces, as depicted in Fig. 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 507, + 250, + 520 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 507, + 250, + 520 + ], + "spans": [ + { + "bbox": [ + 47, + 507, + 250, + 520 + ], + "type": "text", + "content": "3.1. Masked Jigsaw Transformer Diffusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": "Consider an image or video, denoted as " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": ", partitioned into an unordered puzzle comprising individual pieces " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_1, \\ldots, \\mathbf{x}_N" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\cap \\mathbf{x}_j = \\phi" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\cup_{i=1}^{N} \\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": ". Our objective is to reconstruct " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " by establishing a mapping " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "f(\\mathbf{x}_i) = l_i" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " that assigns the correct position to each piece. Specifically, we seek a solution where " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " is the union of the pieces placed at their designated locations, expressed as " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\cup_{i=1}^{N} (\\mathbf{x}_i @ l_i)" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i @ l_i" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " signifies that piece " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " should be positioned at location " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "text", + "content": "To achieve this goal, we propose representing the solved puzzle of " + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "text", + "content": " as a set of pairs denoted by " + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = \\{(\\mathbf{e}_1,\\gamma (l_1)),\\ldots ,(\\mathbf{e}_N,\\gamma (l_N))\\}" + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "text", + "content": ". In this representation, " + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "text", + "content": " is an embedding of the visual content of piece " + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 635, + 288, + 683 + ], + "type": "inline_equation", + "content": "\\gamma (l_i)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "text", + "content": "is a vector containing the positional encoding of its location " + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "text", + "content": ", as illustrated in Fig. 2. This representation is similar to the ones used by masked autoencoders (MAE) to learn to inpaint missing data [9]. However, a notable distinction lies in the fact that masked autoencoders possess knowledge of the locations of the given pieces, allowing them to directly work with the pairs " + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "inline_equation", + "content": "(\\mathbf{e}_i, \\gamma(l_i))" + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "text", + "content": ". In our scenario, where the pieces have been shuffled, a separate treatment of the visual content " + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\mathbf{e}_i" + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "text", + "content": " and its corresponding location " + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\gamma(l_i)" + }, + { + "bbox": [ + 306, + 334, + 545, + 441 + ], + "type": "text", + "content": " is necessary." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "content": "Puzzles without Missing Pieces. Given a complete set of puzzle pieces embeddings, " + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{E} = \\{\\mathbf{e}_1,\\mathbf{e}_2,\\dots ,\\mathbf{e}_N\\}" + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{L} = (\\gamma (l_1),\\gamma (l_2),\\ldots ,\\gamma (l_N))^T" + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "content": " be a matrix with the sought positional encodings of the given pieces. Then, we formulate solving the jigsaw puzzle as a conditional generation problem, where the goal is to learn the joint probability of the locations " + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{L}" + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "content": ", given their unsorted visual content " + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "inline_equation", + "content": "\\mathbf{L}|\\mathbf{E}\\sim q(\\mathbf{L}|\\mathbf{E})" + }, + { + "bbox": [ + 304, + 441, + 545, + 548 + ], + "type": "text", + "content": ". We propose to learn this probability by using a CDDPM as follows." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 549, + 545, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 549, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 305, + 549, + 545, + 573 + ], + "type": "text", + "content": "For the forward process, we diffuse the positional encodings, conditioned on the set of unsorted visual contents:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 324, + 579, + 526, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 324, + 579, + 526, + 594 + ], + "spans": [ + { + "bbox": [ + 324, + 579, + 526, + 594 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {L} _ {t} \\mid \\mathbf {L} _ {t - 1}, \\mathbf {E}\\right) = \\mathcal {N} \\left(\\mathbf {L} _ {t} \\mid \\mathbf {E}; \\sqrt {1 - \\beta_ {t}} \\mathbf {L} _ {t - 1} \\mid \\mathbf {E}, \\beta_ {t} \\mathbf {I}\\right)", + "image_path": "dd21e66e332aa0960cf2dc27616881a1fac53f9d4942fc3e356bb179b123f8cb.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "text", + "content": "where noise is gradually added to the positional encodings of the patches (See Fig. 2), and " + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "text", + "content": " schedules the amount of noise added at each step " + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "text", + "content": ". The distribution of " + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_t" + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "text", + "content": " given " + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_0" + }, + { + "bbox": [ + 304, + 598, + 547, + 647 + ], + "type": "text", + "content": " can be explicitly expressed by" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 329, + 652, + 521, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 652, + 521, + 666 + ], + "spans": [ + { + "bbox": [ + 329, + 652, + 521, + 666 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {L} _ {t} \\mid \\mathbf {L} _ {0}, \\mathbf {E}\\right) = \\mathcal {N} \\left(\\mathbf {L} _ {t} \\mid \\mathbf {E}; \\sqrt {\\alpha_ {t}} \\mathbf {L} _ {0} \\mid \\mathbf {E}, (1 - \\alpha_ {t}) \\mathbf {I}\\right)", + "image_path": "5e1cab0202479397c2d4fb789be978c7dbdb3d2098df088ad3bd63be3ed018f2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 670, + 419, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 419, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 419, + 683 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 670, + 419, + 683 + ], + "type": "inline_equation", + "content": "\\alpha_{t} = \\prod_{s = 1}^{t}(1 - \\beta_{s})" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 684, + 527, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 684, + 527, + 695 + ], + "spans": [ + { + "bbox": [ + 317, + 684, + 527, + 695 + ], + "type": "text", + "content": "The reverse diffusion denoising process is given by:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 700, + 553, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 700, + 553, + 715 + ], + "spans": [ + { + "bbox": [ + 306, + 700, + 553, + 715 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(\\mathbf {L} _ {t - 1} \\mid \\mathbf {L} _ {t}, \\mathbf {E}\\right) := \\mathcal {N} \\left(\\mathbf {L} _ {t - 1} \\mid t, \\mathbf {E}; \\mu_ {\\theta} \\left(\\mathbf {L} _ {t}, t, \\mathbf {E}\\right), \\sigma_ {\\theta} \\left(\\mathbf {L} _ {t}, t, \\mathbf {E}\\right) \\mathbf {I}\\right)", + "image_path": "48de37a2cefd9c465fba8d865f8aaf85afc73d5fac3a6fd9be216260434ca1e0.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 691, + 287, + 715 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 691, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 691, + 287, + 715 + ], + "type": "text", + "content": "2In the cases with missing pieces or with eroded pieces, we will allow " + }, + { + "bbox": [ + 47, + 691, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\supseteq \\cup_{i = 1}^{M\\leq N}(\\mathbf{x}_i@l_i)" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23011" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "The conditional diffusion model learns a network " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": " to predict the noise added to the noisy input " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_t" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": " with the loss:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 102, + 272, + 118 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 102, + 272, + 118 + ], + "spans": [ + { + "bbox": [ + 62, + 102, + 272, + 118 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\boldsymbol {\\theta}) = \\mathbb {E} _ {\\mathbf {L} _ {0} \\sim q (\\mathbf {L} _ {0}), \\epsilon \\sim \\mathcal {N} (0, I), t, \\mathbf {E}} [ \\| \\epsilon - \\epsilon_ {\\boldsymbol {\\theta}} (\\mathbf {L} _ {t}, t, \\mathbf {E}) \\| _ {2} ^ {2} ]", + "image_path": "6699fb8c634d61c80631a55a07bf7eed69fc3f92c30033b1024000ef270b56fd.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "spans": [ + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_t = \\sqrt{\\alpha_t}\\mathbf{L}_0 + \\sqrt{(1 - \\alpha_t)}\\epsilon" + }, + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "type": "inline_equation", + "content": "\\epsilon \\sim \\mathcal{N}(0,\\mathbf{I})" + }, + { + "bbox": [ + 46, + 125, + 258, + 138 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "text", + "content": "Puzzles with Missing Pieces. For jigsaw puzzles with missing pieces, " + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{E} = \\mathbf{E}^g\\cup \\mathbf{E}^m" + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "text", + "content": " , where " + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{E}^g" + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{E}^m" + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "text", + "content": " are the given and missing pieces, respectively. In this case, we generate the positional information for both the given pieces and the missing ones. For the missing pieces, it is possible to fill them up using an inpainting algorithm [28] after having their location, or alternatively, to generate the embeddings of the missing visual content simultaneously with the locations. In the later case, the conditional forward process gradually adds noise to both, the positional encodings and the visual content embeddings of the missing pieces, conditioned on the visual content of the given pieces using " + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "inline_equation", + "content": "q(\\mathbf{L}_t,\\mathbf{E}_t^m |\\mathbf{L}_0,\\mathbf{E}_0^m,\\mathbf{E}^g)" + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "text", + "content": " and the corresponding reverse diffusion process: " + }, + { + "bbox": [ + 46, + 138, + 287, + 307 + ], + "type": "inline_equation", + "content": "p_{\\theta}(\\mathbf{L}_{t - 1},\\mathbf{E}_{t - 1}^{m}|\\mathbf{L}_{t},\\mathbf{E}_{t}^{m},\\mathbf{E}^{g})" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 312, + 180, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 180, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 180, + 324 + ], + "type": "text", + "content": "3.2. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 331, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 366 + ], + "type": "text", + "content": "In this section, we give implementation details of our models, which are rooted in the official codebase of diffusion models from [17]. Code will be provided." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 367, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 287, + 521 + ], + "type": "text", + "content": "Solving image jigsaw puzzles. We implemented our diffusion transformers by modifying ViTs based on [2], following the approach in [21] for incorporating timesteps. Adaptive normalization layers are introduced before and after the multi-head attention and MLP modules to accommodate timesteps. To avoid the model reducing to a mere classification task, we anchor the positional embedding of the initial patch and represent subsequent patches using relative positional embeddings. This approach enhances the model's ability to capture spatial dependencies and ensures resilience against overreliance on absolute positional information. We utilized a linear noise schedule with " + }, + { + "bbox": [ + 46, + 367, + 287, + 521 + ], + "type": "inline_equation", + "content": "T = 1000" + }, + { + "bbox": [ + 46, + 367, + 287, + 521 + ], + "type": "text", + "content": " diffusion steps." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 664 + ], + "type": "text", + "content": "Solving temporal jigsaw puzzles. For low-resolution videos, with missing frames, we applied diffusion directly on the video pixels. For high-resolution videos, we followed [22] and first compressed each of the frames into a latent space, and subsequently applied diffusion process on these latent variables. For the reverse diffusion process, we modified the video U-Net based on [23]. In our implementation, we only use the 2D spatial convolutional layers without the temporal convolutional layer, and in the " + }, + { + "bbox": [ + 46, + 522, + 287, + 664 + ], + "type": "inline_equation", + "content": "2\\mathrm{D} + 1\\mathrm{D}" + }, + { + "bbox": [ + 46, + 522, + 287, + 664 + ], + "type": "text", + "content": " attention layers, we removed the temporal positional embedding. We used a linear noise schedule, and we fixed diffusion steps to " + }, + { + "bbox": [ + 46, + 522, + 287, + 664 + ], + "type": "inline_equation", + "content": "T = 1000" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 665, + 279, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 665, + 279, + 677 + ], + "spans": [ + { + "bbox": [ + 59, + 665, + 279, + 677 + ], + "type": "text", + "content": "Positional Encoding. We use the positional encoding:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 684, + 264, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 684, + 264, + 717 + ], + "spans": [ + { + "bbox": [ + 59, + 684, + 264, + 717 + ], + "type": "interline_equation", + "content": "\\gamma_ {1 D} (l _ {n}) = \\left\\{ \\begin{array}{l} \\gamma (l _ {n}, 2 i) = \\sin \\left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\\right) \\\\ \\gamma (l _ {n}, 2 i + 1) = \\cos \\left(l _ {n} / 1 0 0 0 ^ {(2 i / 1 6)}\\right) \\end{array} \\right.", + "image_path": "1c46cc34abe1d62df5e6345cd5558a283cd2ee4f4c03ba76f0bdb35cd1d39d58.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": "For temporal puzzles we use a 1-D positional encoding with a dimension of 16 to represent each video frame. To align with the input feature map's shape, the positional encoding undergoes an initial transformation through an MLP, ensuring it matches the size of the input feature map. Subsequently, the positional encoding is concatenated with the feature maps. For image puzzles, we employ a 2-D positional encoding with 32 dimensions to encode the position of an image patch, with the first half representing the x-coordinate and the second half representing the y-coordinate: " + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\gamma_{2D}(l_x,l_y) = [\\gamma_{1D}(l_x),\\gamma_{1D}(l_y)]" + }, + { + "bbox": [ + 304, + 72, + 545, + 228 + ], + "type": "text", + "content": ". This positional encoding is incorporated into image tokens following an MLP layer." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 239, + 388, + 253 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 388, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 388, + 253 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 260, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 545, + 285 + ], + "type": "text", + "content": "Here, we describe the experiments we ran to validate the effectiveness of the proposed approach." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 293, + 369, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 293, + 369, + 304 + ], + "spans": [ + { + "bbox": [ + 306, + 293, + 369, + 304 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 312, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 347 + ], + "type": "text", + "content": "We evaluated our approach on five datasets, consisting of both images and videos with different levels of resolution and complexity:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 348, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 545, + 372 + ], + "type": "text", + "content": "ImageNet-1k [5] contains 1,281,167 training images, and 50,000 validation images categorized into 1000 classes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 373, + 545, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 432 + ], + "type": "text", + "content": "JPwLEG-3 [24] contains 12,000 images collected from MET [35] dataset. Each image is segmented into 9 fragments of dimensions " + }, + { + "bbox": [ + 304, + 373, + 545, + 432 + ], + "type": "inline_equation", + "content": "96 \\times 96" + }, + { + "bbox": [ + 304, + 373, + 545, + 432 + ], + "type": "text", + "content": ", with gaps of 48 pixels between them. 9,000 images were allocated for training, 2,000 for testing, and an additional 1,000 for validation purposes." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 433, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 492 + ], + "type": "text", + "content": "MovingMNIST [27] comprises 10,000 video sequences, each containing 20 frames. Two digits move independently within each video, which has low resolution of " + }, + { + "bbox": [ + 304, + 433, + 545, + 492 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 433, + 545, + 492 + ], + "type": "text", + "content": " pixels. We used 9,000 videos for training and tested our approach on the remaining 1,000 videos." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "type": "text", + "content": "CLEVRER [34] is a diagnostic video dataset with 20,000 videos that simulate collisions among objects of different colors and shapes with " + }, + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "type": "inline_equation", + "content": "480 \\times 320" + }, + { + "bbox": [ + 304, + 493, + 545, + 553 + ], + "type": "text", + "content": " pixels. The dataset is split into 10,000 videos for training, 5,000 for validation, and 5,000 for testing." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "inline_equation", + "content": "QST" + }, + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "text", + "content": " (Quick Sky Time) [36] contains 1,167 video clips extracted from 216 time-lapse 4K videos collected from YouTube, totaling 285,446 frames. The resolution of each frame exceeds " + }, + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "inline_equation", + "content": "1,024 \\times 1,024" + }, + { + "bbox": [ + 304, + 554, + 545, + 613 + ], + "type": "text", + "content": ". We downsample the frames to 256, and train on 1,000 videos, test on 167 videos." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 613, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 613, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 613, + 545, + 662 + ], + "type": "text", + "content": "UCF101 [26] is an action recognition dataset, consisting of 13,320 video clips representing 101 different human actions. Each frame has a resolution of " + }, + { + "bbox": [ + 304, + 613, + 545, + 662 + ], + "type": "inline_equation", + "content": "320 \\times 240" + }, + { + "bbox": [ + 304, + 613, + 545, + 662 + ], + "type": "text", + "content": " pixels, with 9,537 videos for training and 3,783 videos for testing." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 670, + 365, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 365, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 365, + 682 + ], + "type": "text", + "content": "4.2. Metrics" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "Image Puzzle Solving Accuracy: In assessing image jigsaw solutions, we gauge solving accuracy both at" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23012" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 542, + 437 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 542, + 437 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 542, + 437 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 542, + 437 + ], + "type": "image", + "image_path": "6070c33b40a7b37a218d661fbc764b01e4d84192c241db6b4a7a4a51b89221c8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 446, + 546, + 481 + ], + "lines": [ + { + "bbox": [ + 46, + 446, + 546, + 481 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 546, + 481 + ], + "type": "text", + "content": "Figure 4. Qualitative results for puzzles for Imagenet-1K dataset with 1, 2, and 3 missing pieces. Left: without cropping. Right: with cropping. First column shows the input puzzle, second column shows the sorted result (denoted as JPDVT-S), third column shows the sorted and inpainted result (denoted as JPDVT-SI), and last column shows the ground truth images." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 501, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 501, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 501, + 289, + 622 + ], + "type": "text", + "content": "the puzzle and piece levels. The puzzle-wise accuracy metric denotes the percentage of flawlessly reassembled image puzzles—essentially, the fraction of puzzles with every single piece correctly positioned, totaling " + }, + { + "bbox": [ + 46, + 501, + 289, + 622 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 501, + 289, + 622 + ], + "type": "text", + "content": ". On the other hand, the piece-wise accuracy metric quantifies the ratio of correctly placed pieces to the overall number of pieces in the dataset. This comprehensive evaluation framework provides a nuanced understanding of the reconstruction quality, capturing both holistic puzzle-level performance and the precision of individual pieces within the puzzle assembly." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "Video Puzzle Solving Accuracy Following [6], we measure video jigsaw puzzle solving accuracy with the average Normalized Kendall distance, based on 1,000 testing samples from each dataset. The Kendall distance, also called bubble-sort distance, scores the number of pairwise disagreements between the candidate sorting and the ground truth, which is defined as the number of elements in the set" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "spans": [ + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "type": "text", + "content": "constructed from two sequences " + }, + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "type": "inline_equation", + "content": "\\sigma_{1}" + }, + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "type": "inline_equation", + "content": "\\sigma_{2}" + }, + { + "bbox": [ + 305, + 501, + 525, + 514 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 321, + 521, + 529, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 521, + 529, + 536 + ], + "spans": [ + { + "bbox": [ + 321, + 521, + 529, + 536 + ], + "type": "interline_equation", + "content": "\\mathcal {G} (\\sigma_ {1}, \\sigma_ {2}) = \\{(i, j) | \\sigma_ {1} (i) < \\sigma_ {2} (j), \\sigma_ {2} (i) > \\sigma_ {1} (j) \\}", + "image_path": "301d46e2b658f39a7e751bc28f9ab94e6a271c0fce65076b214935fe30116cd1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\sigma_{1}(i)" + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\sigma_{2}(i)" + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "content": " are the rankings of the element " + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\sigma_{1}" + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "inline_equation", + "content": "\\sigma_{2}" + }, + { + "bbox": [ + 304, + 544, + 545, + 604 + ], + "type": "text", + "content": " sequences. The normalized distance is the Kendall distance, normalized by the biggest possible distance. The lower the distance is, the more similar the two sequences are, with the worst possible score being 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 611, + 493, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 493, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 493, + 624 + ], + "type": "text", + "content": "4.3. Image Jigsaw Puzzles Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "We conducted experiments on solving image jigsaw puzzles using the ImageNet-1k dataset, JPwLEG-3 [24], and the dataset used in [3]. Our models were trained separately with varying hyperparameters tailored to accommodate different numbers of puzzle pieces. To assess JPDVT's performance, we conducted comparative evaluations against state-of-the-art methods [3, 19, 24, 25, 31]." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23013" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 74, + 542, + 548 + ], + "blocks": [ + { + "bbox": [ + 50, + 74, + 542, + 548 + ], + "lines": [ + { + "bbox": [ + 50, + 74, + 542, + 548 + ], + "spans": [ + { + "bbox": [ + 50, + 74, + 542, + 548 + ], + "type": "image", + "image_path": "607efe8265f5dcf621be06b061e404abb28e17e0ac2fa7a78b57308deaef358f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 561, + 547, + 583 + ], + "lines": [ + { + "bbox": [ + 46, + 561, + 547, + 583 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 547, + 583 + ], + "type": "text", + "content": "Figure 5. Video reshuffle results are showcased on various datasets, including 20 frames on MovingMNIST, 32 frames on CLEVRER, 32 frames on UCF101, and 32 frames on QST. Due to space limitations, only a subset of frames is presented in this illustration." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "content": "The experiments on " + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "inline_equation", + "content": "\\text{ImangeNet-1k}" + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "content": " follow the data preprocessing procedure from [31]. During training, each image underwent an initial resizing to " + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "inline_equation", + "content": "255 \\times 255" + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "content": " before being divided into nine patches, each of size " + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "inline_equation", + "content": "85 \\times 85" + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "content": ". Subsequently, every patch was randomly cropped to " + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "content": ". A total of " + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "inline_equation", + "content": "9! = 362" + }, + { + "bbox": [ + 46, + 604, + 289, + 712 + ], + "type": "text", + "content": ", 880 permutations were applied to these patches, and the models were trained to generate permutation indices based on the image patches. Data augmentation solely involved horizontal flipping. During testing, in con" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 604, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 664 + ], + "type": "text", + "content": "trast to random cropping, we used the cropped patch from the center. The experiments on JPwLEG-3 follow the experiment setting in [24]. In the experiments with a large number of pieces, we follow the experiment setting with the largest number of pieces in [3]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "text", + "content": "Fig. 4 presents qualitative results for puzzles with 1, 2, and 3 missing pieces, showcasing flawless reshuffling. Quantitative results for puzzles without missing pieces are provided in tables 1, 3 and 4. JPDVT achieved a " + }, + { + "bbox": [ + 304, + 665, + 546, + 715 + ], + "type": "inline_equation", + "content": "68.7\\%" + } + ] + } + ], + "index": 4 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23014" + } + ] + } + ], + "index": 5 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 538, + 273 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 538, + 273 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 538, + 273 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 538, + 273 + ], + "type": "image", + "image_path": "48160e7793821122e4d184f6fbd0ea21ad5e4ed399b0fd8e82cc6aa14da22a81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 546, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 546, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 546, + 304 + ], + "type": "text", + "content": "Figure 6. Video reshuffle results with masks: Our diffusion model adeptly captures and reconstructs crucial latent components essential for the sequence reordering process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 74, + 368, + 261, + 416 + ], + "blocks": [ + { + "bbox": [ + 47, + 324, + 287, + 367 + ], + "lines": [ + { + "bbox": [ + 47, + 324, + 287, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 287, + 367 + ], + "type": "text", + "content": "Table 1. Results of " + }, + { + "bbox": [ + 47, + 324, + 287, + 367 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 47, + 324, + 287, + 367 + ], + "type": "text", + "content": " image puzzle solving on ImageNet-1k val split. Puzzle-level shows the percentages of flawlessly re-assembled puzzles. Fragment-level shows the fraction of correctly placed pieces of all the pieces in the dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 368, + 261, + 416 + ], + "lines": [ + { + "bbox": [ + 74, + 368, + 261, + 416 + ], + "spans": [ + { + "bbox": [ + 74, + 368, + 261, + 416 + ], + "type": "table", + "html": "
MethodPuzzle-levelPiece-level
SAJ[31]47.3%NA
Deepzzle [19]48%78%
JPDVT(Ours)68.7%83.3%
", + "image_path": "2e80caa3476fe81588f2e455a84d283aaf1acdc940c0ccea367340f61e02caf4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 60, + 464, + 274, + 536 + ], + "blocks": [ + { + "bbox": [ + 47, + 432, + 287, + 464 + ], + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 464 + ], + "type": "text", + "content": "Table 2. Results on " + }, + { + "bbox": [ + 47, + 432, + 287, + 464 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 47, + 432, + 287, + 464 + ], + "type": "text", + "content": " puzzle recognition on ImageNet-1K val split on our proposed model on different number of missing fragments with and without eroded gaps." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 60, + 464, + 274, + 536 + ], + "lines": [ + { + "bbox": [ + 60, + 464, + 274, + 536 + ], + "spans": [ + { + "bbox": [ + 60, + 464, + 274, + 536 + ], + "type": "table", + "html": "
% MissingWith gapWithout gap
puzzlepiecepuzzlepiece
068.7%83.3%99.4%99.6%
11.141.5%72.0%96.9%98.8%
22.221.4%61.8%82.8%95.0%
33.314.9%54.1%56.1%76.4%
", + "image_path": "32443cb9b6f2af25a5491b6018a19e5d2238e3a636032e918a4f4b113f7e0078.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "spans": [ + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "text", + "content": "success rate on imagenet-1k dataset and " + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "inline_equation", + "content": "71.3\\%" + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "text", + "content": " on JPwLEG-3 dataset for puzzles without missing pieces—an improvement of " + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "inline_equation", + "content": "20.7\\%" + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "inline_equation", + "content": "11.6\\%" + }, + { + "bbox": [ + 46, + 563, + 287, + 718 + ], + "type": "text", + "content": ", respectively, over prior state-of-the-art performances at the puzzle level. The results in table 3 show the capability of our model to handle a large number of puzzle pieces. Unlike previous methods, our approach handles puzzles with missing fragments, as demonstrated in Table 2. The performance gradually decreases with an increasing number of random missing pieces, indicating greater difficulty with eroded pieces compared to those without erosion. This suggests the architecture effectively learns to align piece boundaries, a crucial aspect in solving the puzzle." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 331, + 336, + 518, + 373 + ], + "blocks": [ + { + "bbox": [ + 311, + 324, + 539, + 335 + ], + "lines": [ + { + "bbox": [ + 311, + 324, + 539, + 335 + ], + "spans": [ + { + "bbox": [ + 311, + 324, + 539, + 335 + ], + "type": "text", + "content": "Table 3. Results of 150 pieces puzzle solving with " + }, + { + "bbox": [ + 311, + 324, + 539, + 335 + ], + "type": "inline_equation", + "content": "7\\%" + }, + { + "bbox": [ + 311, + 324, + 539, + 335 + ], + "type": "text", + "content": " erosion." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 336, + 518, + 373 + ], + "lines": [ + { + "bbox": [ + 331, + 336, + 518, + 373 + ], + "spans": [ + { + "bbox": [ + 331, + 336, + 518, + 373 + ], + "type": "table", + "html": "
MethodPiece-levelPuzzle-level
SJP-ED[3]66.7%10%
JPDVT(Ours)75.9%45%
", + "image_path": "a4b621e01d3ecb63282642e0ad9f665fd3d3dd1ca1b46289732313b5671a0412.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 328, + 403, + 522, + 476 + ], + "blocks": [ + { + "bbox": [ + 306, + 380, + 545, + 402 + ], + "lines": [ + { + "bbox": [ + 306, + 380, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 545, + 402 + ], + "type": "text", + "content": "Table 4. Comparison to the SOTA of " + }, + { + "bbox": [ + 306, + 380, + 545, + 402 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 306, + 380, + 545, + 402 + ], + "type": "text", + "content": " puzzle recognition on the JPwLEG-3 [24] dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 328, + 403, + 522, + 476 + ], + "lines": [ + { + "bbox": [ + 328, + 403, + 522, + 476 + ], + "spans": [ + { + "bbox": [ + 328, + 403, + 522, + 476 + ], + "type": "table", + "html": "
MethodVenuePiece-level
Siamese [24]AAAI-202359.7%
Puzzlet [25]ICASSP-202358.2%
SJP-ED [3]CVPR-202055.2%
Deepzzle [19]TIP-202052.3%
JPDVT(Ours)-71.3%
", + "image_path": "db71f437a9c58add6a2ab05cdcb1521f76f361fafffe4c24d5c1dc64c0f804a1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 307, + 525, + 545, + 696 + ], + "blocks": [ + { + "bbox": [ + 306, + 487, + 545, + 520 + ], + "lines": [ + { + "bbox": [ + 306, + 487, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 545, + 520 + ], + "type": "text", + "content": "Table 5. Normalized Kendall Distance for Temporal Puzzles without missing data measures the number of pairwise disagreements between two sequences." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 525, + 545, + 696 + ], + "lines": [ + { + "bbox": [ + 307, + 525, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 307, + 525, + 545, + 696 + ], + "type": "table", + "html": "
DatasetsMethodNormalizedKendallDistance x 103
Size, #Pieces1, 202, 104, 5
MMNISTSTP1.40.040.01
VCOP--13.7
J-VAD1730.460
JPDVT(Ours)0.70.040
Size, #Pieces1, 322, 164, 8
CLEVRERSTP-0.150
VCOP--4.6
J-VAD268.258.20.04
JPDVT(Ours)2.60.170.04
UCFVCOP--14.5
J-VAD-164.33.8
JPDVT(Ours)26.24.21.2
QSTSTP-00
VCOP--14.5
JPDVT(Ours)7.03.00.19
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Temporal Jigsaw Puzzles Experiments" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 245 + ], + "type": "text", + "content": "We constructed temporal puzzles from videos by segmenting them, where each piece is a clip comprising one or more frames in the correct temporal order. Specifically, in the case of MovingMNIST, we built puzzles with: 20 pieces, where each piece is a single frame; 10 pieces, each comprising a pair of consecutive frames; and 5 pieces, with each piece containing four consecutive frames. Similarly, for the CLEVRER, UCF, and QST datasets, our evaluation included puzzles with 32 pieces (single frames), 16 pieces (two frames), 8 pieces (four frames), and 4 pieces (eight frames). Qualitative examples in Fig. 5 and 6 demonstrate instances where our approach adeptly resolved the puzzles without and with missing data, respectively." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 247, + 288, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 288, + 390 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 288, + 390 + ], + "type": "text", + "content": "We compared the performance of our algorithm solving temporal puzzles, without missing data, against the state-of-the-art methods STP (Space-Time Puzzle) [6], VCOP (Video Clip-Order Prediction) [33], and J-VAD (Joint Video Anomaly Detection) [30], using four video datasets, whenever possible, as described below. We trained these models following the processes detailed in their respective papers, with adjustments made to network sizes to accommodate varying dataset dimensions. To ensure fair comparisons, we fixed the first frame as an anchor frame, and fully randomly shuffle the remaining frames with no mask. Detailed training hyperparameters are available in the appendix." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 390, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 558 + ], + "type": "text", + "content": "STP adapts its inputs based on video characteristics. For dynamic textures, exemplified by the QST dataset, it utilizes the PCA decomposition of pixels. However, for more structured videos, such as MovingMNIST and CLEVRER, STP requires feature correspondences across the input frames. Thus, for MovingMNIST and CLEVRER we ran experiments by providing STP ground-truth object coordinates, giving this method an unfair advantage. Regrettably, providing feature correspondences for the UCF dataset was impractical due to its complexity. Additionally, the computational demands of STP rendered unfeasible to run for puzzles with 32 pieces, since its inference time for this setting takes over 30 minutes/video. In contrast, our approach takes approximately 10 seconds/video." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": "VCOP and J-VAD, on the other hand, have faster inference times, approximately 1 sec/video. However, VCOP predicts the permutation of videos by classifying over a vast number of possibilities. For instance, with 10 clips, the model must classify among " + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "inline_equation", + "content": "10! = 3,628,800" + }, + { + "bbox": [ + 46, + 558, + 288, + 714 + ], + "type": "text", + "content": " classes. As the number of video clips for ordering increases, training the model becomes impractical due to the exponential growth in classes. J-VAD, employs a 3D-CNN model coupled with a classifier to directly predict the position of each input frame or clip. However, its performance experiences a significant decline when tested on 16 and 32 clips. This phenomenon aligns with findings in [30], where performance deterioration is reported for frame numbers larger than 9," + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 425, + 125 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 425, + 125 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 425, + 125 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 425, + 125 + ], + "type": "image", + "image_path": "733554842799d0a22fff356b9fa16d879f3329b6b1d0034a622d190577a3af79.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 309, + 126, + 425, + 175 + ], + "blocks": [ + { + "bbox": [ + 309, + 126, + 425, + 175 + ], + "lines": [ + { + "bbox": [ + 309, + 126, + 425, + 175 + ], + "spans": [ + { + "bbox": [ + 309, + 126, + 425, + 175 + ], + "type": "image", + "image_path": "e0ff15a866fdc68946d34503c769fb8fc934d6ce0a588d0e8b9e959e8afd40ed.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 177, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 232 + ], + "type": "text", + "content": "Figure 7. Normalized Kendall distances vs. missing pieces. (a) CLEVRER dataset with 8 pieces, each containing 4 frames. (b) MovingMNIST dataset with 8 pieces, each with 4 frames. (c) UCF dataset with 8 pieces, each with 4 frames. (d) QST dataset with 8 pieces, each with 4 frames." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 427, + 70, + 545, + 125 + ], + "blocks": [ + { + "bbox": [ + 427, + 70, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 427, + 70, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 427, + 70, + 545, + 125 + ], + "type": "image", + "image_path": "ae8f1076430c2080f1cadc3cde1a864b04d0aa7eecb7cd5379827c4a21c9f2ca.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 427, + 125, + 544, + 175 + ], + "blocks": [ + { + "bbox": [ + 427, + 125, + 544, + 175 + ], + "lines": [ + { + "bbox": [ + 427, + 125, + 544, + 175 + ], + "spans": [ + { + "bbox": [ + 427, + 125, + 544, + 175 + ], + "type": "image", + "image_path": "573b6f60bba05468ffed7ed5251bf6a62a661fecd0c070c58b70b6617f469601.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 244, + 440, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 244, + 440, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 244, + 440, + 255 + ], + "type": "text", + "content": "consistent with our observations." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 258, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 390 + ], + "type": "text", + "content": "Table 2 provides the quantitative results of the comparisons against the baselines. Our approach achieves State-Of-The-Art performance across the board and second best for the QST dataset. While STP has comparable performance in some settings and best performance for QST, as noted above, it uses different types of inputs depending on the video characteristics and in this case ground-truth feature correspondences, while our approach always works directly on the raw data. In addition, while our approach is an order of magnitude slower than VCOP and J-VAD, it can handle all the testing settings while the others cannot." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 464 + ], + "type": "text", + "content": "Finally, JPDVT can handle temporal puzzles with missing fragments, as shown in Fig. 6. As seen in Fig. 7, JPDVT's performance gradually decreases with an increasing number of random missing pieces. This capability allows the use of JPDVT to increase the temporal resolution of videos, as illustrated in the supplemental material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 483, + 378, + 495 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 504, + 545, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 704 + ], + "type": "text", + "content": "Solving puzzles is a fundamental task involving the re-assembly of disordered fragments, a classic problem in pattern recognition that traces its roots back to 1964 [8]. In this paper, we present JPDVT, a novel method for solving image and temporal puzzles in an unified framework. Our approach works by describing the underlying data as an unordered set of pairs, associating the (2D or 1D) positional encoding of a puzzle piece with an embedding of its visual content. This representation enables the formulation of the puzzle-solving problem as a Conditional Diffusion Denoising process, where the unknown positional encodings of the shuffled puzzle pieces are recovered through a reverse denoising process, conditioned on the visual content embeddings of the given elements. JPDVT achieves state-of-the-art performance in quantitative comparisons and produces high-quality qualitative examples, while solving image and video puzzles. Notably, it can handle missing data and solve larger puzzles than previous approaches." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23016" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Tali Basha, Yael Moses, and Shai Avidan. 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Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LeGOCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback-Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, e.g., delivering a $7.74\\%$ and $2.51\\%$ accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD.", + "bbox": [ + 75, + 378, + 473, + 847 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3619d89db8d68a4da5c915be7f18240b4a13ee8bb6bec033bbd2938194dc7112.jpg", + "image_caption": [ + "(a) Baseline SimGCD [39]" + ], + "image_footnote": [], + "bbox": [ + 506, + 347, + 694, + 472 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c538abaa230281ec7f7edcc33191d06dba75f264058cf9eaa21d896ba111770d.jpg", + "image_caption": [ + "(b) Ours LegoGCD", + "Figure 1. Visualization of the accuracy results in unlabeled dataset on CUB dataset [37] during training. (a) shows a decrease in the accuracy of known (Old) classes (green) in the baseline as the accuracy of novel (New) classes (orange) increases. (b) demonstrates that LegoGCD solves the catastrophic forgetting problem and surpasses the baseline by a significant margin of 7.74." + ], + "image_footnote": [], + "bbox": [ + 699, + 347, + 887, + 472 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 613, + 633, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning have achieved superior performance on computer vision tasks [4, 11, 24, 25, 30, 34], particularly on image classification [10, 12, 27, 28, 51]. However, conventional methods work in a close-world setting, where all training data comes with pre-defined classes. Consequently, deploying these models in real-world scenarios with potential novel classes becomes a considerable challenge. Furthermore, these achievements rely heavily on large-scale annotated dataset, which is not easily accessible in realistic scenarios. To address these challenges, a new paradigm of Generalized Category Discovery (GCD) [1, 7, 9, 23, 36, 39, 45, 46] has been proposed and attracts increasing attention in recent years.", + "bbox": [ + 496, + 641, + 892, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The goal of GCD is to train a classification model capable of recognizing both known and novel categories within unlabeled data. To be clear, GCD distinguishes itself from the Novel Class Discovery (NCD) [8], which relies on an", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal Contribution.", + "bbox": [ + 94, + 875, + 209, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Joint Corresponding Authors.", + "bbox": [ + 96, + 887, + 259, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "16880", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "unrealistic assumption that all unlabeled data exclusively belongs to entirely new classes or patterns. In contrast, GCD adopts a more pragmatic assumption, acknowledging that unlabeled data encompasses a mixture of both known and novel categories. Consequently, GCD is more realistic compared to NCD, especially in real-world scenarios.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since GCD is partially based on the learned patterns, an intuitive idea is to classify the unlabeled data through a clustering-based approach [36] i.e. $k$ -means. However, as the scale of datasets increases, the computational costs for clustering in the original GCD grow exponentially. To tackle this issue, Wen et al. introduce SimGCD [39], which replaces the clustering approach with a classifier. Specifically, SimGCD trains the classifier using a pseudo-labeling strategy, a technique that has demonstrated remarkable effectiveness in Semi-supervised Learning (SSL) [3, 45]. Nevertheless, the pseudo labels of novel samples tend to be assigned as known classes due to the absence of guidance for novel class samples. In response, Wen et al. further propose to adopt class mean entropy to encourage the model to focus on novel categories, consequently generating high-quality pseudo labels for classifier training. As a result, SimGCD has achieved state-of-the-art performance and established itself as a robust baseline solution in the GCD setting.", + "bbox": [ + 75, + 184, + 470, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, SimGCD [39] still has a significant drawback. It encourages the model to focus more on novel classes by employing an entropy regularization, which unfortunately comes at the cost of known class accuracy, resulting in a catastrophic forgetting problem in known categories. To illustrate this issue, we have tracked the classification accuracy of known and novel categories on unlabeled data during each training epoch on CUB [37]. As shown in Fig. 1a, the green curve represents the accuracy of known (Old) classes, while the orange curve represents the accuracy of novel (New) classes. Notably, we can easily observe this phenomenon, with the accuracy of novel classes improving, the accuracy of known categories initially increases to approximately $74\\%$ after 20 epochs but then drops to $64.44\\%$ in the end. We thus conclude that SimGCD faces catastrophic forgetting in known categories during training.", + "bbox": [ + 75, + 474, + 468, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above issue, we propose a novel Local Entropy Regularization (LER) to preserve the knowledge of known categories. In particular, we first identify potential known samples using a threshold on their logits prediction like FixMatch [29]. Then, we employ the information entropy function to encourage the predictions of above selected known samples close to a uniform distribution, thereby maintaining the prediction stability of known classes. Consequently, this LER prevents known samples from being misclassified as novel classes and therefore preserves the knowledge related to known categories during", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "learning novel categories.", + "bbox": [ + 498, + 90, + 671, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "It's worth noting that the model may occasionally miss potential known samples or select incorrect (novel) samples for LER. For example, when we have two augmentation view samples, $\\pmb{x}_i$ and $\\pmb{x}_i'$ , from the same image, and $\\pmb{x}_i$ has higher logits than the threshold while $\\pmb{x}_i'$ falls below it. In such cases, we can't be certain whether the original image belongs to known classes, and this uncertainty may impact the effectiveness of LER. We argue that the predictions of the two view samples should be correctly aligned to ensure the quality of the chosen known samples. Therefore, we further propose a dual-view alignment scheme called Dual-views Kullback-Leibler divergence constraint (DKL), which employs Kullback-Leibler (KL) divergence to encourage the consistency of two views from the same image.", + "bbox": [ + 496, + 111, + 890, + 324 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, we propose a novel approach named LegoGCD, which integrates SimGCD [39] with our proposed LER and DKL to address the problem of catastrophic forgetting. To validate the effectiveness of LegoGCD, we conduct extensive experiments on eight datasets, including generic datasets such as CIFAR10/100 [15], ImageNet-1k [5], and fine-grained datasets CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Intuitively, we also visualize the classification accuracy of known and novel categories on CUB [37]. These results are shown in Fig. 1b. The green curve represents the accuracy of known (Old) categories, while the orange curve indicates the accuracy of novel (New) classes. Clearly, LegoGCD effectively prevents the decline in known classes and achieves an accuracy of $72.18\\%$ , surpassing SimGCD by a margin of 7.74. Clearly, the results indicate that LegoGCD solves the catastrophic forgetting problem of known categories effectively. Moreover, our method can be easily placed onto SimGCD like Lego, requiring only a few lines of code on the implementation without introducing any additional parameters or altering the internal network structure of SimGCD.", + "bbox": [ + 496, + 328, + 892, + 645 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our key contributions are as follows:", + "bbox": [ + 517, + 651, + 846, + 665 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a novel constraint named Local Entropy Regularization (LER), which is designed to mitigate the catastrophic forgetting problem of known classes by preserving the knowledge of known categories during learning novel classes.", + "- We propose a Dual-views Kullback-Leibler divergence constraint (DKL) that ensures the prediction distribution of one view approximates that of another, maintaining consistency between dual views augmented from the same image.", + "- The proposed LegoGCD is effective and can be simply integrated from SimGCD without any extra parameter addition. Extensive results demonstrate our method exhibits significant performance improvement on known classes, e.g., a $7.74\\%$ increase in CUB [37]." + ], + "bbox": [ + 500, + 671, + 890, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "16881", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Generalized Category Discovery", + "text_level": 1, + "bbox": [ + 76, + 114, + 362, + 130 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GCD was first formulated by Vaze et al. [36], presents a unique challenge distinct from Semi-supervised Learning (SSL) [3, 17, 22, 32, 47]. While SSL assumes that unlabeled data belongs to the same class set as the labeled data, GCD tackles a more realistic scenario where the unlabeled data may include classes not present in the labeled set, which is the same setting in Novel Category Discovery (NCD) [7-9, 13, 18, 19, 40, 41, 49]. Therefore, GCD can be viewed as an extension of NCD, with the main difference being that GCD seeks to identify specific categories within novel classes, while NCD focuses on grouping novel classes into a single category. The original GCD approach employs contrastive and SSL, which uses clustering during inference and incurs significant computational costs. To address this challenge, Wen et al. [39] introduce SimGCD with a classifier to replace clustering, offering a robust baseline for the GCD problem. However, it's important to note that SimGCD introduces a drawback, leading to a decrease in the classification accuracy of known classes during the intense learning of novel categories.", + "bbox": [ + 76, + 137, + 472, + 441 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Entropy regularization", + "text_level": 1, + "bbox": [ + 76, + 446, + 292, + 463 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "It is a widely used technique in image classification, especially in the context of cross-entropy, which aims to align prediction distributions with the standard label distribution. However, in scenarios such as Semi-supervised Learning (SSL) [3, 17, 22, 32, 47], where true labels are unknown, pseudo labels take the place of actual labels in standard cross-entropy. This form of entropy regularization minimizes output differences between various views of unlabeled data. Notably, Data Augmentations [43, 44] have proven effective, contributing to substantial successes in pseudo-supervised learning. For instance, in SimGCD [39], an augmentation strategy generates two views of data, establishing training targets in one view and enforcing prediction consistency with the other view during unlabeled data training. Another form of entropy, information entropy, measures the amount of information within a set of events. In SimGCD, information entropy is employed to minimize class mean entropy, promoting more uniform class predictions in each iteration to ensure the visibility of novel classes. However, due to the absence of protection for the knowledge of known classes, class mean entropy has led to a degeneration in known categories.", + "bbox": [ + 76, + 470, + 472, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 814, + 168, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we first formulate the GCD task (Sec. 3.1) and present the overview of the baseline SimGCD [39] (Sec. 3.2). Then, we introduce how to mitigate the degradation of SimGCD by the proposed LegoGCD. At last, we", + "bbox": [ + 76, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "describe the details of the proposed Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) in Sec. 3.3 and Sec. 3.4, respectively.", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Formulation", + "text_level": 1, + "bbox": [ + 500, + 146, + 702, + 161 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Traditional image classification tasks are typically developed using a labeled dataset, denoted as $\\mathcal{D}^l = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_l$ . This dataset contains only samples from known classes, represented by $\\mathcal{V}_l$ . In contrast, Generalized Category Discovery (GCD) aims to recognize unlabeled data, denoted as $\\mathcal{D}^u = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_u$ . This dataset comprises both known and novel class samples, where $\\mathcal{V}_l$ is a subset of $\\mathcal{V}_u$ . The goal of GCD is to develop a model that can identify both known and novel classes using the labels from known categories $(\\mathcal{V}_l)$ and unlabeled data $(\\mathcal{D}_u)$ without access to class labels. It's important to note that the total number of categories is represented as $K = |\\mathcal{V}_l\\cup \\mathcal{V}_u|$ . We assume prior knowledge of this total category count, as done in previous works [7, 9, 48, 50].", + "bbox": [ + 498, + 169, + 893, + 382 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 391, + 640, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the fundamental structure of SimGCD [39] baseline program as shown in Fig. 2. This program primarily consists of two key components: Representation learning and Parametric Classification.", + "bbox": [ + 498, + 415, + 893, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Representation Learning", + "text_level": 1, + "bbox": [ + 500, + 494, + 728, + 511 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The representation learning process in our framework follows GCD [36] and SimGCD [39]. It employs a Vision Transformer (ViT-B/16) [6] pretrained with DINO self-supervision [4] on ImageNet [5] as the backbone. This process includes supervised contrastive learning on labeled data and unsupervised contrastive learning on all data, encompassing both labeled and unlabeled data.", + "bbox": [ + 498, + 518, + 890, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, given two views (random augmentations) $\\pmb{x}_i$ and $\\pmb{x}_i'$ of the same image in a mini-batch $B$ , the unsupervised contrastive loss is written as:", + "bbox": [ + 498, + 626, + 890, + 670 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e p}} ^ {u} = \\frac {1}{| B |} \\sum_ {i \\in B} - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {i} ^ {\\prime} / \\tau_ {u}\\right)}{\\sum_ {i} ^ {i \\neq n} \\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {n} ^ {\\prime} / \\tau_ {u}\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 678, + 890, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\boldsymbol{z}_i = \\phi(f(\\boldsymbol{x}_i))$ and $\\boldsymbol{z}_i' = \\phi(f(\\boldsymbol{x}_i'))$ , $f$ is the feature backbone, $\\phi$ is a multi-layer perceptron (MLP) projection head, $\\tau_u$ is a unsupervised temperature.", + "bbox": [ + 498, + 729, + 890, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The objective of the supervised contrastive loss is to encourage the model to bring samples with the same class label closer in the feature space, formally written as:", + "bbox": [ + 498, + 777, + 890, + 821 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {r e p}} ^ {s} = \\frac {1}{| B ^ {l} |} \\sum_ {i \\in B ^ {l}} \\frac {1}{| \\mathcal {N} _ {i} |} \\sum_ {q \\in N _ {i}} - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {q} ^ {\\prime} / \\tau_ {c}\\right)}{\\sum_ {i} ^ {i \\neq n} \\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {n} ^ {\\prime} / \\tau_ {c}\\right)}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 833, + 890, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{N}_i$ is the indices of images share the same label with", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "16882", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/552586c6d7fe99680abe9149bfc524821f4a9229926b32026237a2e280de7a92.jpg", + "image_caption": [ + "Figure 2. Illustration of our proposed LegoGCD. LegoGCD is mainly composed of SimGCD and our proposed LER and DKL. (a) Representation learning and Mean Entropy in SimGCD (Sec. 3.2). (b) Local Entropy Regularization (LER) (Sec. 3.3) for discovering potential known samples in unlabeled data and preserving the knowledge of known classes. (c) Dual-views Kullback-Leibler divergence (DKL) (Sec. 3.4) to ensure consistent predictions for two view samples." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 893, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\pmb{x}_i$ in the mini-batch $B$ . Finally, the total loss in representation learning is constructed as:", + "bbox": [ + 76, + 467, + 470, + 497 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {r e p}} = (1 - \\lambda) \\mathcal {L} _ {\\text {r e p}} ^ {u} + \\lambda \\mathcal {L} _ {\\text {r e p}} ^ {s}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 505, + 468, + 523 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $B^l$ is the labeled subset of $B$ and $\\lambda$ is a weight factor.", + "bbox": [ + 76, + 531, + 468, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 Parametric Classification", + "text_level": 1, + "bbox": [ + 76, + 564, + 307, + 578 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from the GCD [36] that uses $k$ -means, SimGCD [39] employs a more efficient classifier based on self-distillation [2, 4]. Formally, the classifier is denoted as a set of prototypes $\\mathcal{C} = \\{c_1,\\dots ,c_K\\}$ , where $K = |\\mathcal{Y}_l\\cup \\mathcal{Y}_u|$ . During training, the soft label of each view $\\pmb{x}_i$ is obtained by applying softmax on cosine similarity between hidden feature $\\pmb{h}_i = f(\\pmb{x}_i)$ and prototypes $\\mathcal{C}$ , scaled by $1 / \\tau_{s}$ :", + "bbox": [ + 76, + 587, + 468, + 694 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {p} _ {i} ^ {(k)} = \\frac {\\exp \\left(\\frac {1}{\\tau_ {s}} \\left(\\boldsymbol {h} _ {i} / \\| \\boldsymbol {h} _ {i} \\| _ {2}\\right) ^ {\\top} \\left(\\boldsymbol {c} _ {k} / \\| \\boldsymbol {c} _ {k} \\| _ {2}\\right)\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(\\frac {1}{\\tau_ {s}} \\left(\\boldsymbol {h} _ {i} / \\| \\boldsymbol {h} _ {i} \\| _ {2}\\right) ^ {\\top} \\left(\\boldsymbol {c} _ {k ^ {\\prime}} / \\| \\boldsymbol {c} _ {k ^ {\\prime}} \\| _ {2}\\right)\\right)}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 700, + 468, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The soft pseudo label $\\pmb{q}_i'$ for view $\\pmb{x}_i'$ is similarly generated. Then, it employs a cross-entropy loss $\\ell(\\pmb{q}',\\pmb{p}) = -\\sum_k \\pmb{q}'^{(k)} \\log \\pmb{p}^{(k)}$ to supervise the learning of prediction with pseudo labels or ground-truth labels:", + "bbox": [ + 76, + 758, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c l s}} ^ {u} = \\frac {1}{| B |} \\sum_ {i \\in B} \\ell \\left(\\boldsymbol {q} _ {i} ^ {\\prime}, \\boldsymbol {p} _ {i}\\right), \\mathcal {L} _ {\\mathrm {c l s}} ^ {s} = \\frac {1}{| B |} \\sum_ {i \\in B} \\ell \\left(\\boldsymbol {y} _ {i}, \\boldsymbol {p} _ {i}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 827, + 468, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{cls}}^u$ and $\\mathcal{L}_{\\mathrm{cls}}^s$ are unsupervised and supervised classification losses for all and labeled data, respectively. To", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "regulate unsupervised learning, SimGCD adopts a class mean entropy regulariser [2]: $H(\\overline{\\boldsymbol{p}}) = -\\sum_{k}\\overline{\\boldsymbol{p}}^{(k)}\\log \\overline{\\boldsymbol{p}}^{(k)}$ , where $\\overline{\\boldsymbol{p}}$ is the mean prediction of each class in a batch $\\overline{\\boldsymbol{p}} = \\frac{1}{2|B|}\\sum_{i\\in B}(\\boldsymbol {p}_i + \\boldsymbol {p}_i')$ . Then the classification objective is: $\\mathcal{L}_{\\mathrm{cls}} = (1 - \\lambda)(\\mathcal{L}_{\\mathrm{cls}}^u -\\varepsilon H(\\overline{\\boldsymbol{p}})) + \\lambda \\mathcal{L}_{\\mathrm{cls}}^s$ . Finally, the overall objective in baseline SimGCD is $\\mathcal{L}_{\\mathrm{rep}} + \\mathcal{L}_{\\mathrm{cls}}$ .", + "bbox": [ + 496, + 467, + 890, + 561 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Local Entropy Regularization", + "text_level": 1, + "bbox": [ + 500, + 573, + 766, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Motivation. Although the baseline SimGCD [39] has improved accuracy and computational efficiency compared to GCD [36], it faces catastrophic forgetting in known (Old) classes during training, as shown in Fig. 1a. This is due to SimGCD relying on class mean entropy, causing a shift in focus to novel classes and resulting in information loss in known classes. We argue that retaining knowledge of known classes should be prioritized. Fig. 3a displays potential known class samples in each epoch on the FGVC-Aircraft [21] dataset. Evidently, LegoGCD recognizes nearly 10 more potential known samples than SimGCD in the end. Fig. 3b illustrates the maximum number of potential known samples in various datasets, confirming that LegoGCD with LER excels at preserving the recognition ability of known categories. Concretely, we propose a Local Entropy Regularization (LER) to preserve the knowledge of known categories, solving the problem of catastrophic forgetting. In contrast to the class mean entropy, which primarily shifts the network's focus to novel classes, we argue that the network should also maintain its ability to recognize", + "bbox": [ + 496, + 598, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "16883", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a26441a944c5723a5f04e093501f04e0ac5d3812b4766218bbb4c6144f41e71f.jpg", + "image_caption": [ + "(a) FGVC-Aircraft [21]", + "Figure 3. Comparison of potential known samples in SimGCD [39] and LegoGCD. (a) LegoGCD recognizes almost 10 more high-confidence samples than SimGCD in the end on the FGVC-Aircraft dataset. (b) LegoGCD with LER produces more high-confidence known samples in various generic and fine-grained datasets compared to SimGCD without LER." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 269, + 215 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/88af60ff24eadc72014b75e9cf4eb946b497b0b09c337afc124045afbcb5b0ed.jpg", + "image_caption": [ + "(b) Maximum numbers" + ], + "image_footnote": [], + "bbox": [ + 272, + 89, + 464, + 215 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "known samples as it did before. Specifically, we choose known samples based on a confidence threshold $\\delta$ in unlabeled data and utilize entropy regularization to ensure the stability of these known classes associated with the selected known samples.", + "bbox": [ + 75, + 353, + 468, + 428 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The training dataset, denoted as $\\mathcal{D} = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}$ , comprises both labeled and unlabeled samples represented as $x_{i}$ within a batch $B$ . To distinguish between labeled and unlabeled samples in a batch, we utilize a binary mask vector $M = [m_1,m_2,\\dots ,m_i]\\subseteq \\{0,1\\}$ , where each $m_{i}$ can be either 0 (indicating an unlabeled sample) or 1 (indicating a labeled sample). Consequently, the unlabeled samples in a batch are obtained by applying this mask $M = 0$ .", + "bbox": [ + 75, + 429, + 468, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Next, let $\\pmb{p}_i = [p_i^1, p_i^2, \\dots, p_i^k]$ as the prediction vector for sample $\\pmb{x}_i$ , where $K$ represents the total number of categories. We use $S = [s_1, s_2, \\dots, s_i] \\subseteq \\{0, 1\\}$ as a binary vector to denote the high-confidence sample. When $s_i = 1$ , it indicates that $\\pmb{x}_i$ is a potential high-confidence sample. This can be expressed as follows:", + "bbox": [ + 75, + 549, + 468, + 641 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} = \\mathbb {1} (\\max \\left(\\boldsymbol {p} _ {i}\\right) \\geq \\delta), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 652, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\delta$ represents the confidence threshold. Then, we let $\\mathcal{Y} = [y_1,y_2,\\dots ,y_i]\\in \\{1,2,\\dots ,K\\}$ denotes the potential class label corresponding to $\\pmb {x}_i$ . $y_{i}$ is determined by the index of the maximum value in $\\pmb{p}_i$ :", + "bbox": [ + 76, + 676, + 468, + 739 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ny _ {i} = \\arg \\max _ {j} \\left(\\boldsymbol {p} _ {i}\\right) _ {j}, \\quad i = 1, 2, \\dots , b \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 750, + 468, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $b$ denotes the number of batch sizes. We also introduce $\\mathcal{O} = [o_1, o_2, \\ldots, o_i] \\subseteq \\{0, 1\\}$ as a binary vector, and $o_i = 1$ signifying potential known samples with high-confidence in unlabeled data. This calculation can be performed as follows:", + "bbox": [ + 75, + 781, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\no _ {i} = \\underbrace {\\mathbb {1} (m _ {i} = 0)} _ {\\text {U n l a b e l e d}} \\cdot \\underbrace {\\mathbb {1} (s _ {i} = 1)} _ {\\text {H i g h - c o n f i d e n c e}} \\cdot \\underbrace {\\mathbb {1} (y _ {i} \\in \\mathcal {Y} _ {l})} _ {\\text {K n o w n}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 867, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{Y}_l$ represents the known class set. Next, we use information entropy to assess the stability of the known categories during training, which is expressed as follows:", + "bbox": [ + 500, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {e n t r o p y}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\mathbb {1} \\left(o _ {i} = 1\\right) \\cdot H \\left(\\frac {1}{\\tau_ {o}} \\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 148, + 890, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau_{o}$ is a temperature, $H$ is an entropy regulariser [2] used in Sec. 3.2.2. Additionally, to further enhance the margins between the categories, we replace the vanilla information loss with a Margin-aware Pattern (MAP) [38, 42], and the final LER loss can be formulated as:", + "bbox": [ + 498, + 200, + 890, + 275 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L E R} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\mathbb {1} (o _ {i} = 1) \\cdot H \\left(\\frac {1}{\\tau_ {o}} \\boldsymbol {p} (\\boldsymbol {x} _ {i}), \\frac {1}{\\tau_ {o}} \\boldsymbol {p} (\\boldsymbol {x} _ {i}) - \\Delta_ {j}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 285, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Delta_j = \\lambda_{ler}\\log \\left(\\frac{1}{\\tilde{p}_j}\\right)$ , $j\\in \\{1,\\dots ,K\\}$ , $\\lambda_{ler} = 0.4$ and $\\tilde{p}_j$ is the average model prediction updated at each iteration through an exponential moving average.", + "bbox": [ + 498, + 340, + 890, + 391 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total process is divided into three steps: 1) Applying the label mask $M$ to select samples from unlabeled data; 2) Using the threshold $\\delta$ to select high-confidence samples from all training data; 3) Identifying high-confidence known samples from all training samples. Furthermore, we provide an intuitive representation of the entire process in the top-right corner of Fig. 2.", + "bbox": [ + 498, + 392, + 890, + 497 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 3b compares the quantity of high-confidence known samples across various datasets. Clearly, the numbers increase with the introduction of LER, proving our method with LER retains more knowledge about known classes.", + "bbox": [ + 498, + 498, + 890, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Dual-views Kullback-Leibler divergence", + "text_level": 1, + "bbox": [ + 500, + 568, + 843, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It's crucial to note that the model might mistakenly identify incorrect samples as known ones when considering two views of the same image for LER. For instance, if $\\boldsymbol{x}_i$ and $\\boldsymbol{x}_i'$ are misaligned, and $\\boldsymbol{x}_i$ exceeds the confidence threshold $\\delta$ while $\\boldsymbol{x}_i'$ falls below it, uncertainty arises about whether the image of the two views is a potential known one. Thus, we might erroneously select $\\boldsymbol{x}_i$ or miss $\\boldsymbol{x}_i'$ for LER. In other words, we can confidently select both $\\boldsymbol{x}_i$ and $\\boldsymbol{x}_i'$ as known samples only when both $\\boldsymbol{x}_i$ and $\\boldsymbol{x}_i'$ exceed the threshold $\\delta$ .", + "bbox": [ + 498, + 592, + 890, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In general, an ideal approach is to push the alignment of two view samples $\\pmb{x}_i$ and $\\pmb{x}_i'$ and both belong to the known or novel sample set. To achieve this, we propose a dual-view alignment technique named Dual-views Kullback-Leibler divergence constraint (DKL).", + "bbox": [ + 498, + 729, + 890, + 803 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Formally, given wo cosine similarity $\\pmb{p}_i$ and $\\pmb{p}_i^\\prime$ from Sec. 3.2.2 of two view samples $\\pmb{x}_i$ and $\\pmb{x}_i^\\prime$ in a mini-batch $B$ , the DKL can be formulated as:", + "bbox": [ + 500, + 804, + 890, + 848 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD _ {K L} \\left(\\boldsymbol {p} _ {i} \\| \\boldsymbol {p} _ {i} ^ {\\prime}\\right) = \\frac {1}{B / 2} \\sum_ {i = 1} ^ {B / 2} \\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right) \\cdot \\log \\frac {\\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right)}{\\boldsymbol {p} \\left(\\boldsymbol {x} _ {i} ^ {\\prime}\\right)}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 861, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "16884", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In summary, DKL aligns the predictions of two view samples, enhancing the creation of more reliable potential known samples for LER. Finally, the ultimate classification loss can be updated as:", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {c l s}} = (1 - \\lambda) \\left(\\mathcal {L} _ {\\mathrm {c l s}} ^ {u} - \\varepsilon H (\\bar {\\boldsymbol {p}}) + D _ {K L} \\left(\\boldsymbol {p} _ {i} \\| \\boldsymbol {p} _ {i} ^ {\\prime}\\right)\\right) + \\lambda \\mathcal {L} _ {\\mathrm {c l s}} ^ {s}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 160, + 468, + 178 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda$ is a weight factor to control the balance between supervised and unsupervised classification learning.", + "bbox": [ + 76, + 186, + 468, + 215 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "By simply integrating the Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) into SimGCD, we propose a new paragraph named LegoGCD. The overall loss for training our model can be formulated as:", + "bbox": [ + 75, + 215, + 468, + 291 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\alpha \\cdot \\left(\\mathcal {L} _ {\\text {r e p}} + \\mathcal {L} _ {\\text {c l s}}\\right) + \\beta \\cdot \\mathcal {L} _ {\\text {L E R}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 301, + 468, + 318 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\beta$ is a control factor to assign the weight to remember known classes. Aligning with SimGCD, we set $\\alpha$ to 1 and simultaneously adjust $\\beta$ (see Tab. 7). Notably, the DKL is plugged into classification loss $\\mathcal{L}_{cls}$ . Algorithm 1 in appendix describes one training step of LegoGCD.", + "bbox": [ + 76, + 325, + 468, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 415, + 200, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 439, + 267, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We evaluate the effectiveness of our approach on eight datasets, consistent with SimGCD [39]. These datasets encompass generic image recognition datasets like CIFAR10/100 [15] and ImageNet-100 [33], as well as Semantic Shit [35] datasets, including CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Additionally, we include two more challenging datasets: Herbarium 19 [31] and ImageNet-1k [26]. For each dataset, we follow the GCD [36] and SimGCD [39] protocols by sub-sampling $50\\%$ of known class images to form the labeled set $\\mathcal{D}^l$ within the training set. The remaining images from known and novel classes constitute the unlabeled data $\\mathcal{D}^u$ . Tab. 1 provides details of the datasets used in our experiments.", + "bbox": [ + 75, + 462, + 468, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation protocol. During training, we use dataset $\\mathcal{D}$ combined by $\\mathcal{D}^l$ and $\\mathcal{D}^u$ to train the models. For evaluation, we use clustering accuracy (ACC) [36, 39] to evaluate the model performance. Specifically, ACC is computed as follows: given the ground-truth label $y^{*}$ and the model's prediction $\\hat{y}_i$ , $ACC = \\frac{1}{M}\\sum_{i=1}^{M}\\mathbb{1}(y_i^* = p(\\hat{y}_i))$ , where $M = |\\mathcal{D}^u|$ , and $p$ is determined using the Hungarian optimal assignment algorithm [16].", + "bbox": [ + 75, + 659, + 468, + 779 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. Following [36, 39], we conduct our experiments using ViT-B/16 backbone [6], which was pre-trained with DINO [4], and only fine-tune the last attention block of the backbone for all models. We use the [CLS] token output as the image feature and input for classifier training in SimGCD. Our training regimen includes an initial learning rate of 0.1, decay using a cosine schedule. For a fair comparison, we use a batch size of 128 and", + "bbox": [ + 75, + 780, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/475ed16ecccadb97ff58f3eb076278ee3a4b33be59cb36ebc700ab03d2795f26.jpg", + "table_caption": [ + "Table 1. Overview of the datasets used in our experiments. We list the specific number of labeled and unlabeled images $(\\mathcal{D}^l,\\mathcal{D}^u)$ and their corresponding class assignments (Old and New)." + ], + "table_footnote": [], + "table_body": "
DatasetBalanceLabeled DlUnlabeled Du
ImagesOldImagesNew
CIFAR10 [15]✓12.5k537.5k10
CIFAR100 [15]✓20.0k8030.0k100
ImageNet-100 [33]✓31.9k5095.3k100
CUB [37]✓1.5k1004.5k200
Stanford Cars [14]✓2.0k986.1k196
FGVC-Aircraft [21]✓1.7k505.0k100
Herbarium 19 [31]X8.9k34125.4k683
ImageNet-1K [26]✓321k500960k1000
", + "bbox": [ + 504, + 132, + 890, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "train the models for 200 epochs, setting $\\lambda = 0.35$ in the loss function (see Eq. (5)). Temperature values $\\tau_{u} = 0.07$ and $\\tau_{c} = 1.0$ are employed in representation learning. As for training the classifier in SimGCD, we follow the same settings, including $\\tau_{s} = 0.1$ and initial $\\tau_{t} = 0.07$ which is warmed up to 0.04 with a cosine schedule within the first 30 epochs. In LegoGCD, we set $\\tau_{o} = 0.05$ (see Eq. (9)). All experiments are conducted using PyTorch and trained on Nvidia Tesla V100 GPUs.", + "bbox": [ + 496, + 301, + 890, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with the baselines", + "text_level": 1, + "bbox": [ + 498, + 449, + 769, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our approach with Generalized Category Discovery methods like $k$ -means [20], ORCA[19], GCD [36], SimGCD [39], and strong baselines derived from Novel Category Discovery, including RS+ [9] and UNO+[7]. For a fair comparison, we reproduce SimGCD (denoted as SimGCD*) using the same random seed (i.e. seed=0) as our method. Tab. 2 shows results on SSB datasets [35] and Herbarium 19 [31], Tab. 3 and Tab. 4 present results on generic recognition datasets, including the challenging ImageNet-1k [26].", + "bbox": [ + 496, + 472, + 890, + 623 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall, our method effectively mitigates catastrophic forgetting and achieves superior performance compared to the GCD and SimGCD baseline, particularly in recognizing \"Old\" categories. Specifically, it outperforms the baseline by $3.5\\% / 2.1\\%$ on CIFAR100 and ImageNet-100 and shows significant improvements in fine-grained evaluations with $5.4\\%$ in CUB and $5.1\\%$ in Stanford Cars. Additionally, it surpasses the baseline by $0.4\\% / 0.5\\%$ on the challenging datasets ImageNet-1k and Herbarium 19. In addressing the forgetting problem, our approach also competes well with SimGCD on \"New\" classes, achieving $3.4\\%$ in Stanford Cars, $1.0\\%$ in CIFAR100, and $3.5\\%$ in ImageNet-100.", + "bbox": [ + 496, + 625, + 890, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 816, + 651, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we conduct ablation studies to validate the effectiveness of LER and DKL in LegoGCD. The datasets considered include fine-grained datasets like CUB and Stanford Cars, as well as generic image recognition datasets CI", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "16885", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9c349374b5c163a527624fd9a54f99a663027e6165a334415a44c140ff354f59.jpg", + "table_caption": [ + "Table 2. Classification results on Semantic Shift Benchmark [35] datasets and Herbarium 19 [31]. Bold represent our results, $\\Delta$ indicates the margin ahead of the baseline SimGCD, and red signifies improvement in known categories." + ], + "table_footnote": [], + "table_body": "
MethodCUBStanford CarsFGVC-AircraftHerbarium 19
AllOldNewAllOldNewAllOldNewAllOldNew
k-means[20]34.338.932.112.810.613.816.014.416.813.012.213.4
RS+[9]33.351.624.228.361.812.126.936.422.227.955.812.8
UNO+[7]35.149.028.135.570.518.640.356.432.228.353.714.7
ORCA[19]35.345.630.223.550.110.722.031.817.120.930.915.5
GCD [36]51.356.648.739.057.629.945.041.146.935.451.027.0
SimGCD [39]60.365.657.753.871.945.054.259.151.844.058.036.4
SimGCD* [39]61.966.559.653.470.645.054.661.451.144.956.938.4
Ours63.871.959.857.375.748.455.061.551.745.157.438.4
Δ1.95.40.23.95.13.40.40.10.60.20.50.0
", + "bbox": [ + 99, + 119, + 870, + 316 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/35871b7c11b0927d18fbc3138815b78b34ef5613b16196f16561d89f1092ecc0.jpg", + "image_caption": [ + "Figure 4. Step by step, we integrate LER and DKL into the baseline SimGCD [39]. Initially, the addition of LER increases accuracy in the \"Old\" category while decreasing accuracy in the \"New\" category. Subsequently, the introduction of a Margin-aware Pattern (MAP) widens margins between novel categories, ultimately achieving the best performance when embedding with DKL." + ], + "image_footnote": [], + "bbox": [ + 78, + 329, + 282, + 479 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/14e055423539b63fd2cf5454bf9030b7eee2289d0f1413028c8aaa064f09b678.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 329, + 483, + 479 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9fd546375ed948da3a5664a911d4b82b84f153b2dad5e66238568019219269a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 496, + 329, + 687, + 479 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/28040163a6db1c2d23d88d6c9820d1fd5e073eafa53d728216849b8283adcbb0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 700, + 343, + 890, + 479 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/52eb9fd07dad6c64db22a9023485209a2661891af2ec157263d4b4c1cbb1d7a8.jpg", + "table_caption": [ + "Table 3. Classification results on the generic image recognition datasets, CIFAR10 [15] and CIFAR100 [15]." + ], + "table_footnote": [], + "table_body": "
MethodCIFAR10CIFAR100
AllOldNewAllOldNew
k-means[20]83.685.782.552.052.250.8
RS+[9]46.819.260.558.277.619.3
UNO+[7]68.698.353.869.580.647.2
ORCA[19]81.886.279.669.077.452.0
GCD [36]91.597.988.273.076.266.5
SimGCD [39]97.195.198.180.181.277.8
SimGCD* [39]96.993.898.579.077.981.5
Ours97.194.398.581.881.482.5
Δ0.20.50.02.83.51.0
", + "bbox": [ + 81, + 587, + 468, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FAR100 and ImageNet-100.", + "text_level": 1, + "bbox": [ + 76, + 791, + 266, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Local Entropy Regularization (LER). We conduct ablation studies on LER as shown in Fig. 4. Firstly, the SimGCD baseline with LER (without Margin-aware Pattern, MAP) notably enhances \"Old\" Categories (see green curves). However, using raw LER alone may impact accuracy in \"New\" classes (see orange curves). This is be", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/4d1067b40db14fecb993bbb4cbd680e818024c5c802eaf613d2a360310426ef5.jpg", + "table_caption": [ + "Table 4. Classification results on the generic image recognition ImageNet-100 [33] and the challenging ImageNet-1k [26]." + ], + "table_footnote": [], + "table_body": "
MethodImageNet-100ImageNet-1k
AllOldNewAllOldNew
k-means[20]72.775.571.3---
RS+[9]37.161.624.8---
UNO+[7]70.395.057.9---
ORCA[19]73.592.663.9---
GCD [36]74.189.866.352.572.542.2
SimGCD [39]83.093.177.957.177.346.9
SimGCD* [39]83.392.478.662.379.153.8
Ours86.394.582.162.479.553.8
Δ3.02.13.50.10.40.0
", + "bbox": [ + 504, + 587, + 890, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cause it primarily encourages the network to remember known classes, consequently influencing the learning of novel ones. To mitigate this, we incorporate MAP (see Eq. (10)) to encourage the network to simultaneously enhance the margins of all classes, particularly novel classes. Finally, the inclusion of MAP in LER leads to improvements in both the \"Old\" and \"New\" categories.", + "bbox": [ + 496, + 795, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "16886", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b247e4780d68abcb07a1f89103fa42cf399c9644f8a5b5a7c688e8ca6fb429c4.jpg", + "table_caption": [ + "Table 5. Ablation study on different combinations of our algorithms on CUB. Bold indicates the best results." + ], + "table_footnote": [], + "table_body": "
SimGCDLERMAPDKLCUB
AllOld ↑New
✓61.966.559.6
✓✓62.567.360.2
✓✓63.471.059.6
✓✓✓63.772.058.5
✓✓✓✓63.871.959.8
", + "bbox": [ + 81, + 118, + 468, + 237 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b4e369d2c71a15d6406b129d5659f2b8a1b6d93ce824cd76e469d5b68cf65b22.jpg", + "table_caption": [ + "Table 6. Ablation study on $\\alpha$ and $\\beta$ was conducted on CUB and CIFAR100. Bold indicates the best results. The underline denotes the selected $\\beta$ ." + ], + "table_footnote": [], + "table_body": "
αβCUBCIFAR100
AllOld ↑NewAllOld ↑New
0.061.966.559.679.077.981.5
0.563.069.559.780.880.481.5
1.063.669.760.681.881.482.5
1.01.563.471.259.881.481.780.8
2.063.871.959.881.782.180.9
", + "bbox": [ + 81, + 301, + 468, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dual-views Kullback-Leibler divergence (DKL). DKL is designed to improve the quality of known samples for LER by aligning the predictions of two views from the same image. The results in Tab. 5 indicate that incorporating DKL into raw SimGCD led to improvements in both \"Old\" and \"New\" category accuracies by $1.8\\%$ and $0.6\\%$ , respectively (67.3% vs. 66.5%, 60.2% vs. 59.6%). This success proves beneficial for self-distillation learning in SimGCD. Additionally, from Fig. 4 and Tab. 5, we can see that our method becomes more effective with DKL, particularly in \"Old\" classes, while maintaining performance on \"New\" classes.", + "bbox": [ + 75, + 449, + 468, + 630 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different $\\alpha$ and $\\beta$ . The coefficient $\\beta$ is crucial for balancing knowledge preservation of known classes and facilitating effective learning of novel classes. As depicted in Tab. 6 with $\\alpha = 1.0$ aligned to SimGCD, accuracy on \"Old\" categories consistently surpasses SimGCD ( $\\beta = 0.0$ ) across different $\\beta$ values. Optimal equilibrium is achieved with $\\beta = 2.0$ in CUB and $\\beta = 1.0$ in CIFAR100.", + "bbox": [ + 75, + 636, + 468, + 743 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Different confidence threshold $\\delta$ . We compare accuracy with different $\\delta$ in Tab. 7. Results show varying responses across datasets. In Stanford Cars, \"Old\" accuracy initially increases, then slightly decreases, while \"New\" accuracy decreases but remains above SimGCD at $45.5\\%$ . In contrast, in CIFAR100, \"Old\" accuracy decreases but consistently surpasses SimGCD at $77.9\\%$ . Our goal is to prioritize high \"Old\" accuracy and ensure \"New\" equals or exceeds SimGCD. Therefore, we choose $\\delta = 0.85$ for both Stanford Cars and CIFAR100.", + "bbox": [ + 75, + 750, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/caa71524a20c8f92fbc9d92b8141cdacfa47c565e1f734e2c55068e10bd3d704.jpg", + "table_caption": [ + "Table 7. Ablation study on confidence threshold $\\delta$ was conducted on Stanford Cars and CIFAR100. Bold indicates the best results. The underline denotes the selected threshold." + ], + "table_footnote": [], + "table_body": "
δStanford CarsCIFAR100
AllOld ↑NewAllOld ↓New
0.7055.366.849.880.383.374.3
0.7555.872.347.980.983.376.3
0.8056.573.048.581.382.778.5
0.8557.375.748.481.881.482.5
0.9056.475.347.379.080.576.0
", + "bbox": [ + 504, + 132, + 890, + 262 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 276, + 619, + 292 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose LegoGCD, a novel approach to mitigate the issue of catastrophic forgetting in known categories. The core of our design is to preserve knowledge of known classes while maintaining the accuracy of novel classes. To achieve this, we develop two techniques: Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). LER explicitly regularizes high-confidence potential known class samples to retain the knowledge of known categories. To ensure the accurate selection of these samples, we employ DKL to align the distribution of two view samples for LER. Both LER and DKL can be seamlessly integrated into baseline SimGCD resembling Lego blocks, without introducing new parameters or altering the internal network structure. Extensive experiments demonstrate that LegoGCD significantly enhances performance in known classes, effectively addressing the catastrophic forgetting problem.", + "bbox": [ + 496, + 301, + 890, + 559 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 573, + 687, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is supported by the National Key R&D Program of China (2021YFB0301300), and also received supported from programs: the Major Program of Guangdong Basic and Applied Research (2019B030302002), the Key-Area Research and Development Program of Guangdong Province (2021B0101400002), the Major Key Project of PCL PCL2021A13 and Peng Cheng Cloud-Brain, and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (23xkjc016).", + "bbox": [ + 496, + 598, + 890, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 750, + 596, + 763 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Wenbin An, Feng Tian, Qinghua Zheng, Wei Ding, QianYing Wang, and Ping Chen. 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In Proceedings of IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8697-8710, 2018. 1" + ], + "bbox": [ + 501, + 92, + 890, + 893 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "16889", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Solving the Catastrophic Forgetting Problem in Generalized Category Discovery/6bc5b6dc-66ef-4cae-bd24-fa6ae8788463_model.json b/2024/Solving the Catastrophic Forgetting Problem in Generalized Category Discovery/6bc5b6dc-66ef-4cae-bd24-fa6ae8788463_model.json new file mode 100644 index 0000000000000000000000000000000000000000..445931e3fd50a1fa0d3b7c987953403ca6a25ec4 --- /dev/null +++ b/2024/Solving the Catastrophic Forgetting Problem in Generalized Category Discovery/6bc5b6dc-66ef-4cae-bd24-fa6ae8788463_model.json @@ -0,0 +1,2310 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.131, + 0.89, + 0.154 + ], + "angle": 0, + "content": "Solving the Catastrophic Forgetting Problem in Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.18, + 0.761, + 0.218 + ], + "angle": 0, + "content": "Xinzi Cao\\(^{1,2*}\\), Xiawu Zheng\\(^{2,3*}\\), Guanhong Wang\\(^{4}\\) \nWeijiang Yu\\(^{1}\\), Yunhang Shen\\(^{6}\\), Ke Li\\(^{6}\\), Yutong Lu\\(^{1\\dagger}\\), Yonghong Tian\\(^{2,8\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.199, + 0.22, + 0.772, + 0.257 + ], + "angle": 0, + "content": "1 Sun Yat-sen University, 2 Peng Cheng Laboratory, 3 Xiamen University \n4 Zhejiang University, 5 Tecnt Youtu Lab, 6 Peking University" + }, + { + "type": "text", + "bbox": [ + 0.164, + 0.262, + 0.806, + 0.278 + ], + "angle": 0, + "content": "caoxz@mail2.sysu.edu.cn zhengxiawu@xmu.edu.cn guanhongwang@zju.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.28, + 0.758, + 0.294 + ], + "angle": 0, + "content": "{weijiangyu8, shenyunhang01}@gmail.com tristanli@tencent.com" + }, + { + "type": "text", + "bbox": [ + 0.286, + 0.298, + 0.684, + 0.312 + ], + "angle": 0, + "content": "luyutong@mail.sysu.edu.cn yhtian@pku.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.347, + 0.314, + 0.362 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.474, + 0.848 + ], + "angle": 0, + "content": "Generalized Category Discovery (GCD) aims to identify a mix of known and novel categories within unlabeled data sets, providing a more realistic setting for image recognition. Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LeGOCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback-Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, e.g., delivering a \\(7.74\\%\\) and \\(2.51\\%\\) accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.348, + 0.695, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.529, + 0.476, + 0.672, + 0.489 + ], + "angle": 0, + "content": "(a) Baseline SimGCD [39]" + }, + { + "type": "image", + "bbox": [ + 0.7, + 0.348, + 0.888, + 0.473 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.476, + 0.846, + 0.489 + ], + "angle": 0, + "content": "(b) Ours LegoGCD" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.5, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Figure 1. Visualization of the accuracy results in unlabeled dataset on CUB dataset [37] during training. (a) shows a decrease in the accuracy of known (Old) classes (green) in the baseline as the accuracy of novel (New) classes (orange) increases. (b) demonstrates that LegoGCD solves the catastrophic forgetting problem and surpasses the baseline by a significant margin of 7.74." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.614, + 0.634, + 0.63 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.893, + 0.839 + ], + "angle": 0, + "content": "Deep learning have achieved superior performance on computer vision tasks [4, 11, 24, 25, 30, 34], particularly on image classification [10, 12, 27, 28, 51]. However, conventional methods work in a close-world setting, where all training data comes with pre-defined classes. Consequently, deploying these models in real-world scenarios with potential novel classes becomes a considerable challenge. Furthermore, these achievements rely heavily on large-scale annotated dataset, which is not easily accessible in realistic scenarios. To address these challenges, a new paradigm of Generalized Category Discovery (GCD) [1, 7, 9, 23, 36, 39, 45, 46] has been proposed and attracts increasing attention in recent years." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "The goal of GCD is to train a classification model capable of recognizing both known and novel categories within unlabeled data. To be clear, GCD distinguishes itself from the Novel Class Discovery (NCD) [8], which relies on an" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.21, + 0.888 + ], + "angle": 0, + "content": "*Equal Contribution." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.26, + 0.9 + ], + "angle": 0, + "content": "† Joint Corresponding Authors." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.26, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16880" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "unrealistic assumption that all unlabeled data exclusively belongs to entirely new classes or patterns. In contrast, GCD adopts a more pragmatic assumption, acknowledging that unlabeled data encompasses a mixture of both known and novel categories. Consequently, GCD is more realistic compared to NCD, especially in real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.185, + 0.471, + 0.472 + ], + "angle": 0, + "content": "Since GCD is partially based on the learned patterns, an intuitive idea is to classify the unlabeled data through a clustering-based approach [36] i.e. \\(k\\)-means. However, as the scale of datasets increases, the computational costs for clustering in the original GCD grow exponentially. To tackle this issue, Wen et al. introduce SimGCD [39], which replaces the clustering approach with a classifier. Specifically, SimGCD trains the classifier using a pseudo-labeling strategy, a technique that has demonstrated remarkable effectiveness in Semi-supervised Learning (SSL) [3, 45]. Nevertheless, the pseudo labels of novel samples tend to be assigned as known classes due to the absence of guidance for novel class samples. In response, Wen et al. further propose to adopt class mean entropy to encourage the model to focus on novel categories, consequently generating high-quality pseudo labels for classifier training. As a result, SimGCD has achieved state-of-the-art performance and established itself as a robust baseline solution in the GCD setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.47, + 0.732 + ], + "angle": 0, + "content": "However, SimGCD [39] still has a significant drawback. It encourages the model to focus more on novel classes by employing an entropy regularization, which unfortunately comes at the cost of known class accuracy, resulting in a catastrophic forgetting problem in known categories. To illustrate this issue, we have tracked the classification accuracy of known and novel categories on unlabeled data during each training epoch on CUB [37]. As shown in Fig. 1a, the green curve represents the accuracy of known (Old) classes, while the orange curve represents the accuracy of novel (New) classes. Notably, we can easily observe this phenomenon, with the accuracy of novel classes improving, the accuracy of known categories initially increases to approximately \\(74\\%\\) after 20 epochs but then drops to \\(64.44\\%\\) in the end. We thus conclude that SimGCD faces catastrophic forgetting in known categories during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To address the above issue, we propose a novel Local Entropy Regularization (LER) to preserve the knowledge of known categories. In particular, we first identify potential known samples using a threshold on their logits prediction like FixMatch [29]. Then, we employ the information entropy function to encourage the predictions of above selected known samples close to a uniform distribution, thereby maintaining the prediction stability of known classes. Consequently, this LER prevents known samples from being misclassified as novel classes and therefore preserves the knowledge related to known categories during" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.673, + 0.107 + ], + "angle": 0, + "content": "learning novel categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.112, + 0.892, + 0.325 + ], + "angle": 0, + "content": "It's worth noting that the model may occasionally miss potential known samples or select incorrect (novel) samples for LER. For example, when we have two augmentation view samples, \\( \\pmb{x}_i \\) and \\( \\pmb{x}_i' \\), from the same image, and \\( \\pmb{x}_i \\) has higher logits than the threshold while \\( \\pmb{x}_i' \\) falls below it. In such cases, we can't be certain whether the original image belongs to known classes, and this uncertainty may impact the effectiveness of LER. We argue that the predictions of the two view samples should be correctly aligned to ensure the quality of the chosen known samples. Therefore, we further propose a dual-view alignment scheme called Dual-views Kullback-Leibler divergence constraint (DKL), which employs Kullback-Leibler (KL) divergence to encourage the consistency of two views from the same image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.893, + 0.646 + ], + "angle": 0, + "content": "To summarize, we propose a novel approach named LegoGCD, which integrates SimGCD [39] with our proposed LER and DKL to address the problem of catastrophic forgetting. To validate the effectiveness of LegoGCD, we conduct extensive experiments on eight datasets, including generic datasets such as CIFAR10/100 [15], ImageNet-1k [5], and fine-grained datasets CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Intuitively, we also visualize the classification accuracy of known and novel categories on CUB [37]. These results are shown in Fig. 1b. The green curve represents the accuracy of known (Old) categories, while the orange curve indicates the accuracy of novel (New) classes. Clearly, LegoGCD effectively prevents the decline in known classes and achieves an accuracy of \\(72.18\\%\\), surpassing SimGCD by a margin of 7.74. Clearly, the results indicate that LegoGCD solves the catastrophic forgetting problem of known categories effectively. Moreover, our method can be easily placed onto SimGCD like Lego, requiring only a few lines of code on the implementation without introducing any additional parameters or altering the internal network structure of SimGCD." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.652, + 0.848, + 0.666 + ], + "angle": 0, + "content": "In summary, our key contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.672, + 0.891, + 0.746 + ], + "angle": 0, + "content": "- We introduce a novel constraint named Local Entropy Regularization (LER), which is designed to mitigate the catastrophic forgetting problem of known classes by preserving the knowledge of known categories during learning novel classes." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.748, + 0.891, + 0.821 + ], + "angle": 0, + "content": "- We propose a Dual-views Kullback-Leibler divergence constraint (DKL) that ensures the prediction distribution of one view approximates that of another, maintaining consistency between dual views augmented from the same image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.823, + 0.892, + 0.898 + ], + "angle": 0, + "content": "- The proposed LegoGCD is effective and can be simply integrated from SimGCD without any extra parameter addition. Extensive results demonstrate our method exhibits significant performance improvement on known classes, e.g., a \\(7.74\\%\\) increase in CUB [37]." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.672, + 0.892, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "16881" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.363, + 0.131 + ], + "angle": 0, + "content": "2.1. Generalized Category Discovery" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.138, + 0.473, + 0.442 + ], + "angle": 0, + "content": "GCD was first formulated by Vaze et al. [36], presents a unique challenge distinct from Semi-supervised Learning (SSL) [3, 17, 22, 32, 47]. While SSL assumes that unlabeled data belongs to the same class set as the labeled data, GCD tackles a more realistic scenario where the unlabeled data may include classes not present in the labeled set, which is the same setting in Novel Category Discovery (NCD) [7-9, 13, 18, 19, 40, 41, 49]. Therefore, GCD can be viewed as an extension of NCD, with the main difference being that GCD seeks to identify specific categories within novel classes, while NCD focuses on grouping novel classes into a single category. The original GCD approach employs contrastive and SSL, which uses clustering during inference and incurs significant computational costs. To address this challenge, Wen et al. [39] introduce SimGCD with a classifier to replace clustering, offering a robust baseline for the GCD problem. However, it's important to note that SimGCD introduces a drawback, leading to a decrease in the classification accuracy of known classes during the intense learning of novel categories." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.448, + 0.293, + 0.464 + ], + "angle": 0, + "content": "2.2. Entropy regularization" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.471, + 0.473, + 0.805 + ], + "angle": 0, + "content": "It is a widely used technique in image classification, especially in the context of cross-entropy, which aims to align prediction distributions with the standard label distribution. However, in scenarios such as Semi-supervised Learning (SSL) [3, 17, 22, 32, 47], where true labels are unknown, pseudo labels take the place of actual labels in standard cross-entropy. This form of entropy regularization minimizes output differences between various views of unlabeled data. Notably, Data Augmentations [43, 44] have proven effective, contributing to substantial successes in pseudo-supervised learning. For instance, in SimGCD [39], an augmentation strategy generates two views of data, establishing training targets in one view and enforcing prediction consistency with the other view during unlabeled data training. Another form of entropy, information entropy, measures the amount of information within a set of events. In SimGCD, information entropy is employed to minimize class mean entropy, promoting more uniform class predictions in each iteration to ensure the visibility of novel classes. However, due to the absence of protection for the knowledge of known classes, class mean entropy has led to a degeneration in known categories." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.815, + 0.169, + 0.831 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.472, + 0.903 + ], + "angle": 0, + "content": "In this section, we first formulate the GCD task (Sec. 3.1) and present the overview of the baseline SimGCD [39] (Sec. 3.2). Then, we introduce how to mitigate the degradation of SimGCD by the proposed LegoGCD. At last, we" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "describe the details of the proposed Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) in Sec. 3.3 and Sec. 3.4, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.147, + 0.704, + 0.162 + ], + "angle": 0, + "content": "3.1. Problem Formulation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.17, + 0.895, + 0.383 + ], + "angle": 0, + "content": "Traditional image classification tasks are typically developed using a labeled dataset, denoted as \\(\\mathcal{D}^l = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_l\\). This dataset contains only samples from known classes, represented by \\(\\mathcal{V}_l\\). In contrast, Generalized Category Discovery (GCD) aims to recognize unlabeled data, denoted as \\(\\mathcal{D}^u = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_u\\). This dataset comprises both known and novel class samples, where \\(\\mathcal{V}_l\\) is a subset of \\(\\mathcal{V}_u\\). The goal of GCD is to develop a model that can identify both known and novel classes using the labels from known categories \\((\\mathcal{V}_l)\\) and unlabeled data \\((\\mathcal{D}_u)\\) without access to class labels. It's important to note that the total number of categories is represented as \\(K = |\\mathcal{V}_l\\cup \\mathcal{V}_u|\\). We assume prior knowledge of this total category count, as done in previous works [7, 9, 48, 50]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.392, + 0.642, + 0.407 + ], + "angle": 0, + "content": "3.2. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.416, + 0.894, + 0.476 + ], + "angle": 0, + "content": "In this section, we introduce the fundamental structure of SimGCD [39] baseline program as shown in Fig. 2. This program primarily consists of two key components: Representation learning and Parametric Classification." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.496, + 0.729, + 0.512 + ], + "angle": 0, + "content": "3.2.1 Representation Learning" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.52, + 0.892, + 0.626 + ], + "angle": 0, + "content": "The representation learning process in our framework follows GCD [36] and SimGCD [39]. It employs a Vision Transformer (ViT-B/16) [6] pretrained with DINO self-supervision [4] on ImageNet [5] as the backbone. This process includes supervised contrastive learning on labeled data and unsupervised contrastive learning on all data, encompassing both labeled and unlabeled data." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.627, + 0.892, + 0.671 + ], + "angle": 0, + "content": "Formally, given two views (random augmentations) \\( \\pmb{x}_i \\) and \\( \\pmb{x}_i' \\) of the same image in a mini-batch \\( B \\), the unsupervised contrastive loss is written as:" + }, + { + "type": "equation", + "bbox": [ + 0.525, + 0.679, + 0.892, + 0.72 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r e p}} ^ {u} = \\frac {1}{| B |} \\sum_ {i \\in B} - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {i} ^ {\\prime} / \\tau_ {u}\\right)}{\\sum_ {i} ^ {i \\neq n} \\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {n} ^ {\\prime} / \\tau_ {u}\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.731, + 0.892, + 0.776 + ], + "angle": 0, + "content": "where \\( \\boldsymbol{z}_i = \\phi(f(\\boldsymbol{x}_i)) \\) and \\( \\boldsymbol{z}_i' = \\phi(f(\\boldsymbol{x}_i')) \\), \\( f \\) is the feature backbone, \\( \\phi \\) is a multi-layer perceptron (MLP) projection head, \\( \\tau_u \\) is a unsupervised temperature." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.778, + 0.892, + 0.823 + ], + "angle": 0, + "content": "The objective of the supervised contrastive loss is to encourage the model to bring samples with the same class label closer in the feature space, formally written as:" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.834, + 0.892, + 0.875 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {r e p}} ^ {s} = \\frac {1}{| B ^ {l} |} \\sum_ {i \\in B ^ {l}} \\frac {1}{| \\mathcal {N} _ {i} |} \\sum_ {q \\in N _ {i}} - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {q} ^ {\\prime} / \\tau_ {c}\\right)}{\\sum_ {i} ^ {i \\neq n} \\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {n} ^ {\\prime} / \\tau_ {c}\\right)}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{N}_i\\) is the indices of images share the same label with" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16882" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.895, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.385, + 0.895, + 0.442 + ], + "angle": 0, + "content": "Figure 2. Illustration of our proposed LegoGCD. LegoGCD is mainly composed of SimGCD and our proposed LER and DKL. (a) Representation learning and Mean Entropy in SimGCD (Sec. 3.2). (b) Local Entropy Regularization (LER) (Sec. 3.3) for discovering potential known samples in unlabeled data and preserving the knowledge of known classes. (c) Dual-views Kullback-Leibler divergence (DKL) (Sec. 3.4) to ensure consistent predictions for two view samples." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.468, + 0.471, + 0.498 + ], + "angle": 0, + "content": "\\(\\pmb{x}_i\\) in the mini-batch \\(B\\). Finally, the total loss in representation learning is constructed as:" + }, + { + "type": "equation", + "bbox": [ + 0.173, + 0.506, + 0.47, + 0.525 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {r e p}} = (1 - \\lambda) \\mathcal {L} _ {\\text {r e p}} ^ {u} + \\lambda \\mathcal {L} _ {\\text {r e p}} ^ {s}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.532, + 0.47, + 0.549 + ], + "angle": 0, + "content": "where \\(B^l\\) is the labeled subset of \\(B\\) and \\(\\lambda\\) is a weight factor." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.565, + 0.308, + 0.579 + ], + "angle": 0, + "content": "3.2.2 Parametric Classification" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.588, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Different from the GCD [36] that uses \\(k\\)-means, SimGCD [39] employs a more efficient classifier based on self-distillation [2, 4]. Formally, the classifier is denoted as a set of prototypes \\(\\mathcal{C} = \\{c_1,\\dots ,c_K\\}\\), where \\(K = |\\mathcal{Y}_l\\cup \\mathcal{Y}_u|\\). During training, the soft label of each view \\(\\pmb{x}_i\\) is obtained by applying softmax on cosine similarity between hidden feature \\(\\pmb{h}_i = f(\\pmb{x}_i)\\) and prototypes \\(\\mathcal{C}\\), scaled by \\(1 / \\tau_{s}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.701, + 0.47, + 0.755 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {p} _ {i} ^ {(k)} = \\frac {\\exp \\left(\\frac {1}{\\tau_ {s}} \\left(\\boldsymbol {h} _ {i} / \\| \\boldsymbol {h} _ {i} \\| _ {2}\\right) ^ {\\top} \\left(\\boldsymbol {c} _ {k} / \\| \\boldsymbol {c} _ {k} \\| _ {2}\\right)\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(\\frac {1}{\\tau_ {s}} \\left(\\boldsymbol {h} _ {i} / \\| \\boldsymbol {h} _ {i} \\| _ {2}\\right) ^ {\\top} \\left(\\boldsymbol {c} _ {k ^ {\\prime}} / \\| \\boldsymbol {c} _ {k ^ {\\prime}} \\| _ {2}\\right)\\right)}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.76, + 0.469, + 0.822 + ], + "angle": 0, + "content": "The soft pseudo label \\( \\pmb{q}_i' \\) for view \\( \\pmb{x}_i' \\) is similarly generated. Then, it employs a cross-entropy loss \\( \\ell(\\pmb{q}',\\pmb{p}) = -\\sum_k \\pmb{q}'^{(k)} \\log \\pmb{p}^{(k)} \\) to supervise the learning of prediction with pseudo labels or ground-truth labels:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.828, + 0.47, + 0.864 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c l s}} ^ {u} = \\frac {1}{| B |} \\sum_ {i \\in B} \\ell \\left(\\boldsymbol {q} _ {i} ^ {\\prime}, \\boldsymbol {p} _ {i}\\right), \\mathcal {L} _ {\\mathrm {c l s}} ^ {s} = \\frac {1}{| B |} \\sum_ {i \\in B} \\ell \\left(\\boldsymbol {y} _ {i}, \\boldsymbol {p} _ {i}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{cls}}^u\\) and \\(\\mathcal{L}_{\\mathrm{cls}}^s\\) are unsupervised and supervised classification losses for all and labeled data, respectively. To" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.562 + ], + "angle": 0, + "content": "regulate unsupervised learning, SimGCD adopts a class mean entropy regulariser [2]: \\( H(\\overline{\\boldsymbol{p}}) = -\\sum_{k}\\overline{\\boldsymbol{p}}^{(k)}\\log \\overline{\\boldsymbol{p}}^{(k)} \\), where \\( \\overline{\\boldsymbol{p}} \\) is the mean prediction of each class in a batch \\( \\overline{\\boldsymbol{p}} = \\frac{1}{2|B|}\\sum_{i\\in B}(\\boldsymbol {p}_i + \\boldsymbol {p}_i') \\). Then the classification objective is: \\( \\mathcal{L}_{\\mathrm{cls}} = (1 - \\lambda)(\\mathcal{L}_{\\mathrm{cls}}^u -\\varepsilon H(\\overline{\\boldsymbol{p}})) + \\lambda \\mathcal{L}_{\\mathrm{cls}}^s \\). Finally, the overall objective in baseline SimGCD is \\( \\mathcal{L}_{\\mathrm{rep}} + \\mathcal{L}_{\\mathrm{cls}} \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.767, + 0.591 + ], + "angle": 0, + "content": "3.3. Local Entropy Regularization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Motivation. Although the baseline SimGCD [39] has improved accuracy and computational efficiency compared to GCD [36], it faces catastrophic forgetting in known (Old) classes during training, as shown in Fig. 1a. This is due to SimGCD relying on class mean entropy, causing a shift in focus to novel classes and resulting in information loss in known classes. We argue that retaining knowledge of known classes should be prioritized. Fig. 3a displays potential known class samples in each epoch on the FGVC-Aircraft [21] dataset. Evidently, LegoGCD recognizes nearly 10 more potential known samples than SimGCD in the end. Fig. 3b illustrates the maximum number of potential known samples in various datasets, confirming that LegoGCD with LER excels at preserving the recognition ability of known categories. Concretely, we propose a Local Entropy Regularization (LER) to preserve the knowledge of known categories, solving the problem of catastrophic forgetting. In contrast to the class mean entropy, which primarily shifts the network's focus to novel classes, we argue that the network should also maintain its ability to recognize" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16883" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.27, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.221, + 0.238, + 0.234 + ], + "angle": 0, + "content": "(a) FGVC-Aircraft [21]" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.09, + 0.465, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.308, + 0.221, + 0.433, + 0.234 + ], + "angle": 0, + "content": "(b) Maximum numbers" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.47, + 0.329 + ], + "angle": 0, + "content": "Figure 3. Comparison of potential known samples in SimGCD [39] and LegoGCD. (a) LegoGCD recognizes almost 10 more high-confidence samples than SimGCD in the end on the FGVC-Aircraft dataset. (b) LegoGCD with LER produces more high-confidence known samples in various generic and fine-grained datasets compared to SimGCD without LER." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.469, + 0.429 + ], + "angle": 0, + "content": "known samples as it did before. Specifically, we choose known samples based on a confidence threshold \\(\\delta\\) in unlabeled data and utilize entropy regularization to ensure the stability of these known classes associated with the selected known samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.469, + 0.55 + ], + "angle": 0, + "content": "The training dataset, denoted as \\(\\mathcal{D} = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}\\), comprises both labeled and unlabeled samples represented as \\(x_{i}\\) within a batch \\(B\\). To distinguish between labeled and unlabeled samples in a batch, we utilize a binary mask vector \\(M = [m_1,m_2,\\dots ,m_i]\\subseteq \\{0,1\\}\\), where each \\(m_{i}\\) can be either 0 (indicating an unlabeled sample) or 1 (indicating a labeled sample). Consequently, the unlabeled samples in a batch are obtained by applying this mask \\(M = 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.469, + 0.642 + ], + "angle": 0, + "content": "Next, let \\( \\pmb{p}_i = [p_i^1, p_i^2, \\dots, p_i^k] \\) as the prediction vector for sample \\( \\pmb{x}_i \\), where \\( K \\) represents the total number of categories. We use \\( S = [s_1, s_2, \\dots, s_i] \\subseteq \\{0, 1\\} \\) as a binary vector to denote the high-confidence sample. When \\( s_i = 1 \\), it indicates that \\( \\pmb{x}_i \\) is a potential high-confidence sample. This can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.653, + 0.469, + 0.669 + ], + "angle": 0, + "content": "\\[\ns _ {i} = \\mathbb {1} (\\max \\left(\\boldsymbol {p} _ {i}\\right) \\geq \\delta), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.678, + 0.469, + 0.74 + ], + "angle": 0, + "content": "where \\(\\delta\\) represents the confidence threshold. Then, we let \\(\\mathcal{Y} = [y_1,y_2,\\dots ,y_i]\\in \\{1,2,\\dots ,K\\}\\) denotes the potential class label corresponding to \\(\\pmb {x}_i\\). \\(y_{i}\\) is determined by the index of the maximum value in \\(\\pmb{p}_i\\):" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.75, + 0.469, + 0.773 + ], + "angle": 0, + "content": "\\[\ny _ {i} = \\arg \\max _ {j} \\left(\\boldsymbol {p} _ {i}\\right) _ {j}, \\quad i = 1, 2, \\dots , b \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.469, + 0.857 + ], + "angle": 0, + "content": "where \\( b \\) denotes the number of batch sizes. We also introduce \\( \\mathcal{O} = [o_1, o_2, \\ldots, o_i] \\subseteq \\{0, 1\\} \\) as a binary vector, and \\( o_i = 1 \\) signifying potential known samples with high-confidence in unlabeled data. This calculation can be performed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.868, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\no _ {i} = \\underbrace {\\mathbb {1} (m _ {i} = 0)} _ {\\text {U n l a b e l e d}} \\cdot \\underbrace {\\mathbb {1} (s _ {i} = 1)} _ {\\text {H i g h - c o n f i d e n c e}} \\cdot \\underbrace {\\mathbb {1} (y _ {i} \\in \\mathcal {Y} _ {l})} _ {\\text {K n o w n}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "where \\(\\mathcal{Y}_l\\) represents the known class set. Next, we use information entropy to assess the stability of the known categories during training, which is expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.149, + 0.892, + 0.19 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {e n t r o p y}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\mathbb {1} \\left(o _ {i} = 1\\right) \\cdot H \\left(\\frac {1}{\\tau_ {o}} \\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.201, + 0.892, + 0.276 + ], + "angle": 0, + "content": "where \\(\\tau_{o}\\) is a temperature, \\(H\\) is an entropy regulariser [2] used in Sec. 3.2.2. Additionally, to further enhance the margins between the categories, we replace the vanilla information loss with a Margin-aware Pattern (MAP) [38, 42], and the final LER loss can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.286, + 0.892, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L E R} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\mathbb {1} (o _ {i} = 1) \\cdot H \\left(\\frac {1}{\\tau_ {o}} \\boldsymbol {p} (\\boldsymbol {x} _ {i}), \\frac {1}{\\tau_ {o}} \\boldsymbol {p} (\\boldsymbol {x} _ {i}) - \\Delta_ {j}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.341, + 0.891, + 0.392 + ], + "angle": 0, + "content": "where \\(\\Delta_j = \\lambda_{ler}\\log \\left(\\frac{1}{\\tilde{p}_j}\\right)\\), \\(j\\in \\{1,\\dots ,K\\}\\), \\(\\lambda_{ler} = 0.4\\) and \\(\\tilde{p}_j\\) is the average model prediction updated at each iteration through an exponential moving average." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.393, + 0.892, + 0.498 + ], + "angle": 0, + "content": "The total process is divided into three steps: 1) Applying the label mask \\( M \\) to select samples from unlabeled data; 2) Using the threshold \\( \\delta \\) to select high-confidence samples from all training data; 3) Identifying high-confidence known samples from all training samples. Furthermore, we provide an intuitive representation of the entire process in the top-right corner of Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.499, + 0.892, + 0.559 + ], + "angle": 0, + "content": "Fig. 3b compares the quantity of high-confidence known samples across various datasets. Clearly, the numbers increase with the introduction of LER, proving our method with LER retains more knowledge about known classes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.569, + 0.844, + 0.586 + ], + "angle": 0, + "content": "3.4. Dual-views Kullback-Leibler divergence" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.593, + 0.892, + 0.729 + ], + "angle": 0, + "content": "It's crucial to note that the model might mistakenly identify incorrect samples as known ones when considering two views of the same image for LER. For instance, if \\( \\boldsymbol{x}_i \\) and \\( \\boldsymbol{x}_i' \\) are misaligned, and \\( \\boldsymbol{x}_i \\) exceeds the confidence threshold \\( \\delta \\) while \\( \\boldsymbol{x}_i' \\) falls below it, uncertainty arises about whether the image of the two views is a potential known one. Thus, we might erroneously select \\( \\boldsymbol{x}_i \\) or miss \\( \\boldsymbol{x}_i' \\) for LER. In other words, we can confidently select both \\( \\boldsymbol{x}_i \\) and \\( \\boldsymbol{x}_i' \\) as known samples only when both \\( \\boldsymbol{x}_i \\) and \\( \\boldsymbol{x}_i' \\) exceed the threshold \\( \\delta \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.73, + 0.892, + 0.804 + ], + "angle": 0, + "content": "In general, an ideal approach is to push the alignment of two view samples \\( \\pmb{x}_i \\) and \\( \\pmb{x}_i' \\) and both belong to the known or novel sample set. To achieve this, we propose a dual-view alignment technique named Dual-views Kullback-Leibler divergence constraint (DKL)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.805, + 0.892, + 0.849 + ], + "angle": 0, + "content": "Formally, given wo cosine similarity \\(\\pmb{p}_i\\) and \\(\\pmb{p}_i^\\prime\\) from Sec. 3.2.2 of two view samples \\(\\pmb{x}_i\\) and \\(\\pmb{x}_i^\\prime\\) in a mini-batch \\(B\\), the DKL can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.862, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nD _ {K L} \\left(\\boldsymbol {p} _ {i} \\| \\boldsymbol {p} _ {i} ^ {\\prime}\\right) = \\frac {1}{B / 2} \\sum_ {i = 1} ^ {B / 2} \\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right) \\cdot \\log \\frac {\\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right)}{\\boldsymbol {p} \\left(\\boldsymbol {x} _ {i} ^ {\\prime}\\right)}. \\tag {11}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "16884" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "In summary, DKL aligns the predictions of two view samples, enhancing the creation of more reliable potential known samples for LER. Finally, the ultimate classification loss can be updated as:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.161, + 0.469, + 0.179 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {c l s}} = (1 - \\lambda) \\left(\\mathcal {L} _ {\\mathrm {c l s}} ^ {u} - \\varepsilon H (\\bar {\\boldsymbol {p}}) + D _ {K L} \\left(\\boldsymbol {p} _ {i} \\| \\boldsymbol {p} _ {i} ^ {\\prime}\\right)\\right) + \\lambda \\mathcal {L} _ {\\mathrm {c l s}} ^ {s}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.187, + 0.469, + 0.217 + ], + "angle": 0, + "content": "where \\(\\lambda\\) is a weight factor to control the balance between supervised and unsupervised classification learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.217, + 0.469, + 0.292 + ], + "angle": 0, + "content": "By simply integrating the Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) into SimGCD, we propose a new paragraph named LegoGCD. The overall loss for training our model can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.302, + 0.469, + 0.319 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\alpha \\cdot \\left(\\mathcal {L} _ {\\text {r e p}} + \\mathcal {L} _ {\\text {c l s}}\\right) + \\beta \\cdot \\mathcal {L} _ {\\text {L E R}}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.327, + 0.469, + 0.403 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a control factor to assign the weight to remember known classes. Aligning with SimGCD, we set \\(\\alpha\\) to 1 and simultaneously adjust \\(\\beta\\) (see Tab. 7). Notably, the DKL is plugged into classification loss \\(\\mathcal{L}_{cls}\\). Algorithm 1 in appendix describes one training step of LegoGCD." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.416, + 0.202, + 0.433 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.44, + 0.268, + 0.457 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.469, + 0.659 + ], + "angle": 0, + "content": "Dataset. We evaluate the effectiveness of our approach on eight datasets, consistent with SimGCD [39]. These datasets encompass generic image recognition datasets like CIFAR10/100 [15] and ImageNet-100 [33], as well as Semantic Shit [35] datasets, including CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Additionally, we include two more challenging datasets: Herbarium 19 [31] and ImageNet-1k [26]. For each dataset, we follow the GCD [36] and SimGCD [39] protocols by sub-sampling \\(50\\%\\) of known class images to form the labeled set \\(\\mathcal{D}^l\\) within the training set. The remaining images from known and novel classes constitute the unlabeled data \\(\\mathcal{D}^u\\). Tab. 1 provides details of the datasets used in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Evaluation protocol. During training, we use dataset \\(\\mathcal{D}\\) combined by \\(\\mathcal{D}^l\\) and \\(\\mathcal{D}^u\\) to train the models. For evaluation, we use clustering accuracy (ACC) [36, 39] to evaluate the model performance. Specifically, ACC is computed as follows: given the ground-truth label \\(y^{*}\\) and the model's prediction \\(\\hat{y}_i\\), \\(ACC = \\frac{1}{M}\\sum_{i=1}^{M}\\mathbb{1}(y_i^* = p(\\hat{y}_i))\\), where \\(M = |\\mathcal{D}^u|\\), and \\(p\\) is determined using the Hungarian optimal assignment algorithm [16]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Implementation details. Following [36, 39], we conduct our experiments using ViT-B/16 backbone [6], which was pre-trained with DINO [4], and only fine-tune the last attention block of the backbone for all models. We use the [CLS] token output as the image feature and input for classifier training in SimGCD. Our training regimen includes an initial learning rate of 0.1, decay using a cosine schedule. For a fair comparison, we use a batch size of 128 and" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.131 + ], + "angle": 0, + "content": "Table 1. Overview of the datasets used in our experiments. We list the specific number of labeled and unlabeled images \\((\\mathcal{D}^l,\\mathcal{D}^u)\\) and their corresponding class assignments (Old and New)." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.133, + 0.892, + 0.276 + ], + "angle": 0, + "content": "
DatasetBalanceLabeled DlUnlabeled Du
ImagesOldImagesNew
CIFAR10 [15]✓12.5k537.5k10
CIFAR100 [15]✓20.0k8030.0k100
ImageNet-100 [33]✓31.9k5095.3k100
CUB [37]✓1.5k1004.5k200
Stanford Cars [14]✓2.0k986.1k196
FGVC-Aircraft [21]✓1.7k505.0k100
Herbarium 19 [31]X8.9k34125.4k683
ImageNet-1K [26]✓321k500960k1000
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.892, + 0.437 + ], + "angle": 0, + "content": "train the models for 200 epochs, setting \\(\\lambda = 0.35\\) in the loss function (see Eq. (5)). Temperature values \\(\\tau_{u} = 0.07\\) and \\(\\tau_{c} = 1.0\\) are employed in representation learning. As for training the classifier in SimGCD, we follow the same settings, including \\(\\tau_{s} = 0.1\\) and initial \\(\\tau_{t} = 0.07\\) which is warmed up to 0.04 with a cosine schedule within the first 30 epochs. In LegoGCD, we set \\(\\tau_{o} = 0.05\\) (see Eq. (9)). All experiments are conducted using PyTorch and trained on Nvidia Tesla V100 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.45, + 0.771, + 0.466 + ], + "angle": 0, + "content": "4.2. Comparison with the baselines" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.624 + ], + "angle": 0, + "content": "We compare our approach with Generalized Category Discovery methods like \\( k \\)-means [20], ORCA[19], GCD [36], SimGCD [39], and strong baselines derived from Novel Category Discovery, including RS+ [9] and UNO+[7]. For a fair comparison, we reproduce SimGCD (denoted as SimGCD*) using the same random seed (i.e. seed=0) as our method. Tab. 2 shows results on SSB datasets [35] and Herbarium 19 [31], Tab. 3 and Tab. 4 present results on generic recognition datasets, including the challenging ImageNet-1k [26]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Overall, our method effectively mitigates catastrophic forgetting and achieves superior performance compared to the GCD and SimGCD baseline, particularly in recognizing \"Old\" categories. Specifically, it outperforms the baseline by \\(3.5\\% / 2.1\\%\\) on CIFAR100 and ImageNet-100 and shows significant improvements in fine-grained evaluations with \\(5.4\\%\\) in CUB and \\(5.1\\%\\) in Stanford Cars. Additionally, it surpasses the baseline by \\(0.4\\% / 0.5\\%\\) on the challenging datasets ImageNet-1k and Herbarium 19. In addressing the forgetting problem, our approach also competes well with SimGCD on \"New\" classes, achieving \\(3.4\\%\\) in Stanford Cars, \\(1.0\\%\\) in CIFAR100, and \\(3.5\\%\\) in ImageNet-100." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.652, + 0.833 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we conduct ablation studies to validate the effectiveness of LER and DKL in LegoGCD. The datasets considered include fine-grained datasets like CUB and Stanford Cars, as well as generic image recognition datasets CI" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "16885" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 2. Classification results on Semantic Shift Benchmark [35] datasets and Herbarium 19 [31]. Bold represent our results, \\(\\Delta\\) indicates the margin ahead of the baseline SimGCD, and red signifies improvement in known categories." + }, + { + "type": "table", + "bbox": [ + 0.1, + 0.12, + 0.871, + 0.317 + ], + "angle": 0, + "content": "
MethodCUBStanford CarsFGVC-AircraftHerbarium 19
AllOldNewAllOldNewAllOldNewAllOldNew
k-means[20]34.338.932.112.810.613.816.014.416.813.012.213.4
RS+[9]33.351.624.228.361.812.126.936.422.227.955.812.8
UNO+[7]35.149.028.135.570.518.640.356.432.228.353.714.7
ORCA[19]35.345.630.223.550.110.722.031.817.120.930.915.5
GCD [36]51.356.648.739.057.629.945.041.146.935.451.027.0
SimGCD [39]60.365.657.753.871.945.054.259.151.844.058.036.4
SimGCD* [39]61.966.559.653.470.645.054.661.451.144.956.938.4
Ours63.871.959.857.375.748.455.061.551.745.157.438.4
Δ1.95.40.23.95.13.40.40.10.60.20.50.0
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.33, + 0.283, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.33, + 0.484, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.33, + 0.688, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.702, + 0.344, + 0.891, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.492, + 0.893, + 0.534 + ], + "angle": 0, + "content": "Figure 4. Step by step, we integrate LER and DKL into the baseline SimGCD [39]. Initially, the addition of LER increases accuracy in the \"Old\" category while decreasing accuracy in the \"New\" category. Subsequently, the introduction of a Margin-aware Pattern (MAP) widens margins between novel categories, ultimately achieving the best performance when embedding with DKL." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.559, + 0.47, + 0.587 + ], + "angle": 0, + "content": "Table 3. Classification results on the generic image recognition datasets, CIFAR10 [15] and CIFAR100 [15]." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.588, + 0.47, + 0.759 + ], + "angle": 0, + "content": "
MethodCIFAR10CIFAR100
AllOldNewAllOldNew
k-means[20]83.685.782.552.052.250.8
RS+[9]46.819.260.558.277.619.3
UNO+[7]68.698.353.869.580.647.2
ORCA[19]81.886.279.669.077.452.0
GCD [36]91.597.988.273.076.266.5
SimGCD [39]97.195.198.180.181.277.8
SimGCD* [39]96.993.898.579.077.981.5
Ours97.194.398.581.881.482.5
Δ0.20.50.02.83.51.0
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.792, + 0.267, + 0.807 + ], + "angle": 0, + "content": "FAR100 and ImageNet-100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Local Entropy Regularization (LER). We conduct ablation studies on LER as shown in Fig. 4. Firstly, the SimGCD baseline with LER (without Margin-aware Pattern, MAP) notably enhances \"Old\" Categories (see green curves). However, using raw LER alone may impact accuracy in \"New\" classes (see orange curves). This is be" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.559, + 0.892, + 0.587 + ], + "angle": 0, + "content": "Table 4. Classification results on the generic image recognition ImageNet-100 [33] and the challenging ImageNet-1k [26]." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.588, + 0.892, + 0.759 + ], + "angle": 0, + "content": "
MethodImageNet-100ImageNet-1k
AllOldNewAllOldNew
k-means[20]72.775.571.3---
RS+[9]37.161.624.8---
UNO+[7]70.395.057.9---
ORCA[19]73.592.663.9---
GCD [36]74.189.866.352.572.542.2
SimGCD [39]83.093.177.957.177.346.9
SimGCD* [39]83.392.478.662.379.153.8
Ours86.394.582.162.479.553.8
Δ3.02.13.50.10.40.0
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.893, + 0.902 + ], + "angle": 0, + "content": "cause it primarily encourages the network to remember known classes, consequently influencing the learning of novel ones. To mitigate this, we incorporate MAP (see Eq. (10)) to encourage the network to simultaneously enhance the margins of all classes, particularly novel classes. Finally, the inclusion of MAP in LER leads to improvements in both the \"Old\" and \"New\" categories." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "16886" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.117 + ], + "angle": 0, + "content": "Table 5. Ablation study on different combinations of our algorithms on CUB. Bold indicates the best results." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.119, + 0.47, + 0.238 + ], + "angle": 0, + "content": "
SimGCDLERMAPDKLCUB
AllOld ↑New
✓61.966.559.6
✓✓62.567.360.2
✓✓63.471.059.6
✓✓✓63.772.058.5
✓✓✓✓63.871.959.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.258, + 0.47, + 0.3 + ], + "angle": 0, + "content": "Table 6. Ablation study on \\( \\alpha \\) and \\( \\beta \\) was conducted on CUB and CIFAR100. Bold indicates the best results. The underline denotes the selected \\( \\beta \\)." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.302, + 0.469, + 0.421 + ], + "angle": 0, + "content": "
αβCUBCIFAR100
AllOld ↑NewAllOld ↑New
0.061.966.559.679.077.981.5
0.563.069.559.780.880.481.5
1.063.669.760.681.881.482.5
1.01.563.471.259.881.481.780.8
2.063.871.959.881.782.180.9
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.45, + 0.47, + 0.631 + ], + "angle": 0, + "content": "Dual-views Kullback-Leibler divergence (DKL). DKL is designed to improve the quality of known samples for LER by aligning the predictions of two views from the same image. The results in Tab. 5 indicate that incorporating DKL into raw SimGCD led to improvements in both \"Old\" and \"New\" category accuracies by \\(1.8\\%\\) and \\(0.6\\%\\), respectively (67.3% vs. 66.5%, 60.2% vs. 59.6%). This success proves beneficial for self-distillation learning in SimGCD. Additionally, from Fig. 4 and Tab. 5, we can see that our method becomes more effective with DKL, particularly in \"Old\" classes, while maintaining performance on \"New\" classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Different \\(\\alpha\\) and \\(\\beta\\). The coefficient \\(\\beta\\) is crucial for balancing knowledge preservation of known classes and facilitating effective learning of novel classes. As depicted in Tab. 6 with \\(\\alpha = 1.0\\) aligned to SimGCD, accuracy on \"Old\" categories consistently surpasses SimGCD (\\(\\beta = 0.0\\)) across different \\(\\beta\\) values. Optimal equilibrium is achieved with \\(\\beta = 2.0\\) in CUB and \\(\\beta = 1.0\\) in CIFAR100." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Different confidence threshold \\(\\delta\\). We compare accuracy with different \\(\\delta\\) in Tab. 7. Results show varying responses across datasets. In Stanford Cars, \"Old\" accuracy initially increases, then slightly decreases, while \"New\" accuracy decreases but remains above SimGCD at \\(45.5\\%\\). In contrast, in CIFAR100, \"Old\" accuracy decreases but consistently surpasses SimGCD at \\(77.9\\%\\). Our goal is to prioritize high \"Old\" accuracy and ensure \"New\" equals or exceeds SimGCD. Therefore, we choose \\(\\delta = 0.85\\) for both Stanford Cars and CIFAR100." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.131 + ], + "angle": 0, + "content": "Table 7. Ablation study on confidence threshold \\(\\delta\\) was conducted on Stanford Cars and CIFAR100. Bold indicates the best results. The underline denotes the selected threshold." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.133, + 0.892, + 0.263 + ], + "angle": 0, + "content": "
δStanford CarsCIFAR100
AllOld ↑NewAllOld ↓New
0.7055.366.849.880.383.374.3
0.7555.872.347.980.983.376.3
0.8056.573.048.581.382.778.5
0.8557.375.748.481.881.482.5
0.9056.475.347.379.080.576.0
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.277, + 0.62, + 0.293 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.302, + 0.892, + 0.56 + ], + "angle": 0, + "content": "In this paper, we propose LegoGCD, a novel approach to mitigate the issue of catastrophic forgetting in known categories. The core of our design is to preserve knowledge of known classes while maintaining the accuracy of novel classes. To achieve this, we develop two techniques: Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). LER explicitly regularizes high-confidence potential known class samples to retain the knowledge of known categories. To ensure the accurate selection of these samples, we employ DKL to align the distribution of two view samples for LER. Both LER and DKL can be seamlessly integrated into baseline SimGCD resembling Lego blocks, without introducing new parameters or altering the internal network structure. Extensive experiments demonstrate that LegoGCD significantly enhances performance in known classes, effectively addressing the catastrophic forgetting problem." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.688, + 0.591 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.736 + ], + "angle": 0, + "content": "This research is supported by the National Key R&D Program of China (2021YFB0301300), and also received supported from programs: the Major Program of Guangdong Basic and Applied Research (2019B030302002), the Key-Area Research and Development Program of Guangdong Province (2021B0101400002), the Major Key Project of PCL PCL2021A13 and Peng Cheng Cloud-Brain, and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (23xkjc016)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.75, + 0.597, + 0.765 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.774, + 0.894, + 0.843 + ], + "angle": 0, + "content": "[1] Wenbin An, Feng Tian, Qinghua Zheng, Wei Ding, QianYing Wang, and Ping Chen. Generalized category discovery with decoupled prototypical network. 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Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LeGOCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback-Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, e.g., delivering a $7.74\%$ and $2.51\%$ accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD. + +![](images/3619d89db8d68a4da5c915be7f18240b4a13ee8bb6bec033bbd2938194dc7112.jpg) +(a) Baseline SimGCD [39] + +![](images/c538abaa230281ec7f7edcc33191d06dba75f264058cf9eaa21d896ba111770d.jpg) +(b) Ours LegoGCD +Figure 1. Visualization of the accuracy results in unlabeled dataset on CUB dataset [37] during training. (a) shows a decrease in the accuracy of known (Old) classes (green) in the baseline as the accuracy of novel (New) classes (orange) increases. (b) demonstrates that LegoGCD solves the catastrophic forgetting problem and surpasses the baseline by a significant margin of 7.74. + +# 1. Introduction + +Deep learning have achieved superior performance on computer vision tasks [4, 11, 24, 25, 30, 34], particularly on image classification [10, 12, 27, 28, 51]. However, conventional methods work in a close-world setting, where all training data comes with pre-defined classes. Consequently, deploying these models in real-world scenarios with potential novel classes becomes a considerable challenge. Furthermore, these achievements rely heavily on large-scale annotated dataset, which is not easily accessible in realistic scenarios. To address these challenges, a new paradigm of Generalized Category Discovery (GCD) [1, 7, 9, 23, 36, 39, 45, 46] has been proposed and attracts increasing attention in recent years. + +The goal of GCD is to train a classification model capable of recognizing both known and novel categories within unlabeled data. To be clear, GCD distinguishes itself from the Novel Class Discovery (NCD) [8], which relies on an + +unrealistic assumption that all unlabeled data exclusively belongs to entirely new classes or patterns. In contrast, GCD adopts a more pragmatic assumption, acknowledging that unlabeled data encompasses a mixture of both known and novel categories. Consequently, GCD is more realistic compared to NCD, especially in real-world scenarios. + +Since GCD is partially based on the learned patterns, an intuitive idea is to classify the unlabeled data through a clustering-based approach [36] i.e. $k$ -means. However, as the scale of datasets increases, the computational costs for clustering in the original GCD grow exponentially. To tackle this issue, Wen et al. introduce SimGCD [39], which replaces the clustering approach with a classifier. Specifically, SimGCD trains the classifier using a pseudo-labeling strategy, a technique that has demonstrated remarkable effectiveness in Semi-supervised Learning (SSL) [3, 45]. Nevertheless, the pseudo labels of novel samples tend to be assigned as known classes due to the absence of guidance for novel class samples. In response, Wen et al. further propose to adopt class mean entropy to encourage the model to focus on novel categories, consequently generating high-quality pseudo labels for classifier training. As a result, SimGCD has achieved state-of-the-art performance and established itself as a robust baseline solution in the GCD setting. + +However, SimGCD [39] still has a significant drawback. It encourages the model to focus more on novel classes by employing an entropy regularization, which unfortunately comes at the cost of known class accuracy, resulting in a catastrophic forgetting problem in known categories. To illustrate this issue, we have tracked the classification accuracy of known and novel categories on unlabeled data during each training epoch on CUB [37]. As shown in Fig. 1a, the green curve represents the accuracy of known (Old) classes, while the orange curve represents the accuracy of novel (New) classes. Notably, we can easily observe this phenomenon, with the accuracy of novel classes improving, the accuracy of known categories initially increases to approximately $74\%$ after 20 epochs but then drops to $64.44\%$ in the end. We thus conclude that SimGCD faces catastrophic forgetting in known categories during training. + +To address the above issue, we propose a novel Local Entropy Regularization (LER) to preserve the knowledge of known categories. In particular, we first identify potential known samples using a threshold on their logits prediction like FixMatch [29]. Then, we employ the information entropy function to encourage the predictions of above selected known samples close to a uniform distribution, thereby maintaining the prediction stability of known classes. Consequently, this LER prevents known samples from being misclassified as novel classes and therefore preserves the knowledge related to known categories during + +learning novel categories. + +It's worth noting that the model may occasionally miss potential known samples or select incorrect (novel) samples for LER. For example, when we have two augmentation view samples, $\pmb{x}_i$ and $\pmb{x}_i'$ , from the same image, and $\pmb{x}_i$ has higher logits than the threshold while $\pmb{x}_i'$ falls below it. In such cases, we can't be certain whether the original image belongs to known classes, and this uncertainty may impact the effectiveness of LER. We argue that the predictions of the two view samples should be correctly aligned to ensure the quality of the chosen known samples. Therefore, we further propose a dual-view alignment scheme called Dual-views Kullback-Leibler divergence constraint (DKL), which employs Kullback-Leibler (KL) divergence to encourage the consistency of two views from the same image. + +To summarize, we propose a novel approach named LegoGCD, which integrates SimGCD [39] with our proposed LER and DKL to address the problem of catastrophic forgetting. To validate the effectiveness of LegoGCD, we conduct extensive experiments on eight datasets, including generic datasets such as CIFAR10/100 [15], ImageNet-1k [5], and fine-grained datasets CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Intuitively, we also visualize the classification accuracy of known and novel categories on CUB [37]. These results are shown in Fig. 1b. The green curve represents the accuracy of known (Old) categories, while the orange curve indicates the accuracy of novel (New) classes. Clearly, LegoGCD effectively prevents the decline in known classes and achieves an accuracy of $72.18\%$ , surpassing SimGCD by a margin of 7.74. Clearly, the results indicate that LegoGCD solves the catastrophic forgetting problem of known categories effectively. Moreover, our method can be easily placed onto SimGCD like Lego, requiring only a few lines of code on the implementation without introducing any additional parameters or altering the internal network structure of SimGCD. + +In summary, our key contributions are as follows: + +- We introduce a novel constraint named Local Entropy Regularization (LER), which is designed to mitigate the catastrophic forgetting problem of known classes by preserving the knowledge of known categories during learning novel classes. +- We propose a Dual-views Kullback-Leibler divergence constraint (DKL) that ensures the prediction distribution of one view approximates that of another, maintaining consistency between dual views augmented from the same image. +- The proposed LegoGCD is effective and can be simply integrated from SimGCD without any extra parameter addition. Extensive results demonstrate our method exhibits significant performance improvement on known classes, e.g., a $7.74\%$ increase in CUB [37]. + +# 2. Related Work + +# 2.1. Generalized Category Discovery + +GCD was first formulated by Vaze et al. [36], presents a unique challenge distinct from Semi-supervised Learning (SSL) [3, 17, 22, 32, 47]. While SSL assumes that unlabeled data belongs to the same class set as the labeled data, GCD tackles a more realistic scenario where the unlabeled data may include classes not present in the labeled set, which is the same setting in Novel Category Discovery (NCD) [7-9, 13, 18, 19, 40, 41, 49]. Therefore, GCD can be viewed as an extension of NCD, with the main difference being that GCD seeks to identify specific categories within novel classes, while NCD focuses on grouping novel classes into a single category. The original GCD approach employs contrastive and SSL, which uses clustering during inference and incurs significant computational costs. To address this challenge, Wen et al. [39] introduce SimGCD with a classifier to replace clustering, offering a robust baseline for the GCD problem. However, it's important to note that SimGCD introduces a drawback, leading to a decrease in the classification accuracy of known classes during the intense learning of novel categories. + +# 2.2. Entropy regularization + +It is a widely used technique in image classification, especially in the context of cross-entropy, which aims to align prediction distributions with the standard label distribution. However, in scenarios such as Semi-supervised Learning (SSL) [3, 17, 22, 32, 47], where true labels are unknown, pseudo labels take the place of actual labels in standard cross-entropy. This form of entropy regularization minimizes output differences between various views of unlabeled data. Notably, Data Augmentations [43, 44] have proven effective, contributing to substantial successes in pseudo-supervised learning. For instance, in SimGCD [39], an augmentation strategy generates two views of data, establishing training targets in one view and enforcing prediction consistency with the other view during unlabeled data training. Another form of entropy, information entropy, measures the amount of information within a set of events. In SimGCD, information entropy is employed to minimize class mean entropy, promoting more uniform class predictions in each iteration to ensure the visibility of novel classes. However, due to the absence of protection for the knowledge of known classes, class mean entropy has led to a degeneration in known categories. + +# 3. Method + +In this section, we first formulate the GCD task (Sec. 3.1) and present the overview of the baseline SimGCD [39] (Sec. 3.2). Then, we introduce how to mitigate the degradation of SimGCD by the proposed LegoGCD. At last, we + +describe the details of the proposed Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) in Sec. 3.3 and Sec. 3.4, respectively. + +# 3.1. Problem Formulation + +Traditional image classification tasks are typically developed using a labeled dataset, denoted as $\mathcal{D}^l = \{(x_i,y_i)\} \in \mathcal{X}\times \mathcal{Y}_l$ . This dataset contains only samples from known classes, represented by $\mathcal{V}_l$ . In contrast, Generalized Category Discovery (GCD) aims to recognize unlabeled data, denoted as $\mathcal{D}^u = \{(x_i,y_i)\} \in \mathcal{X}\times \mathcal{Y}_u$ . This dataset comprises both known and novel class samples, where $\mathcal{V}_l$ is a subset of $\mathcal{V}_u$ . The goal of GCD is to develop a model that can identify both known and novel classes using the labels from known categories $(\mathcal{V}_l)$ and unlabeled data $(\mathcal{D}_u)$ without access to class labels. It's important to note that the total number of categories is represented as $K = |\mathcal{V}_l\cup \mathcal{V}_u|$ . We assume prior knowledge of this total category count, as done in previous works [7, 9, 48, 50]. + +# 3.2. Preliminaries + +In this section, we introduce the fundamental structure of SimGCD [39] baseline program as shown in Fig. 2. This program primarily consists of two key components: Representation learning and Parametric Classification. + +# 3.2.1 Representation Learning + +The representation learning process in our framework follows GCD [36] and SimGCD [39]. It employs a Vision Transformer (ViT-B/16) [6] pretrained with DINO self-supervision [4] on ImageNet [5] as the backbone. This process includes supervised contrastive learning on labeled data and unsupervised contrastive learning on all data, encompassing both labeled and unlabeled data. + +Formally, given two views (random augmentations) $\pmb{x}_i$ and $\pmb{x}_i'$ of the same image in a mini-batch $B$ , the unsupervised contrastive loss is written as: + +$$ +\mathcal {L} _ {\mathrm {r e p}} ^ {u} = \frac {1}{| B |} \sum_ {i \in B} - \log \frac {\exp \left(\boldsymbol {z} _ {i} ^ {\top} \cdot \boldsymbol {z} _ {i} ^ {\prime} / \tau_ {u}\right)}{\sum_ {i} ^ {i \neq n} \exp \left(\boldsymbol {z} _ {i} ^ {\top} \cdot \boldsymbol {z} _ {n} ^ {\prime} / \tau_ {u}\right)}, \tag {1} +$$ + +where $\boldsymbol{z}_i = \phi(f(\boldsymbol{x}_i))$ and $\boldsymbol{z}_i' = \phi(f(\boldsymbol{x}_i'))$ , $f$ is the feature backbone, $\phi$ is a multi-layer perceptron (MLP) projection head, $\tau_u$ is a unsupervised temperature. + +The objective of the supervised contrastive loss is to encourage the model to bring samples with the same class label closer in the feature space, formally written as: + +$$ +\mathcal {L} _ {\mathrm {r e p}} ^ {s} = \frac {1}{| B ^ {l} |} \sum_ {i \in B ^ {l}} \frac {1}{| \mathcal {N} _ {i} |} \sum_ {q \in N _ {i}} - \log \frac {\exp \left(\boldsymbol {z} _ {i} ^ {\top} \cdot \boldsymbol {z} _ {q} ^ {\prime} / \tau_ {c}\right)}{\sum_ {i} ^ {i \neq n} \exp \left(\boldsymbol {z} _ {i} ^ {\top} \cdot \boldsymbol {z} _ {n} ^ {\prime} / \tau_ {c}\right)}, \tag {2} +$$ + +where $\mathcal{N}_i$ is the indices of images share the same label with + +![](images/552586c6d7fe99680abe9149bfc524821f4a9229926b32026237a2e280de7a92.jpg) +Figure 2. Illustration of our proposed LegoGCD. LegoGCD is mainly composed of SimGCD and our proposed LER and DKL. (a) Representation learning and Mean Entropy in SimGCD (Sec. 3.2). (b) Local Entropy Regularization (LER) (Sec. 3.3) for discovering potential known samples in unlabeled data and preserving the knowledge of known classes. (c) Dual-views Kullback-Leibler divergence (DKL) (Sec. 3.4) to ensure consistent predictions for two view samples. + +$\pmb{x}_i$ in the mini-batch $B$ . Finally, the total loss in representation learning is constructed as: + +$$ +\mathcal {L} _ {\text {r e p}} = (1 - \lambda) \mathcal {L} _ {\text {r e p}} ^ {u} + \lambda \mathcal {L} _ {\text {r e p}} ^ {s}, \tag {3} +$$ + +where $B^l$ is the labeled subset of $B$ and $\lambda$ is a weight factor. + +# 3.2.2 Parametric Classification + +Different from the GCD [36] that uses $k$ -means, SimGCD [39] employs a more efficient classifier based on self-distillation [2, 4]. Formally, the classifier is denoted as a set of prototypes $\mathcal{C} = \{c_1,\dots ,c_K\}$ , where $K = |\mathcal{Y}_l\cup \mathcal{Y}_u|$ . During training, the soft label of each view $\pmb{x}_i$ is obtained by applying softmax on cosine similarity between hidden feature $\pmb{h}_i = f(\pmb{x}_i)$ and prototypes $\mathcal{C}$ , scaled by $1 / \tau_{s}$ : + +$$ +\boldsymbol {p} _ {i} ^ {(k)} = \frac {\exp \left(\frac {1}{\tau_ {s}} \left(\boldsymbol {h} _ {i} / \| \boldsymbol {h} _ {i} \| _ {2}\right) ^ {\top} \left(\boldsymbol {c} _ {k} / \| \boldsymbol {c} _ {k} \| _ {2}\right)\right)}{\sum_ {k ^ {\prime}} \exp \left(\frac {1}{\tau_ {s}} \left(\boldsymbol {h} _ {i} / \| \boldsymbol {h} _ {i} \| _ {2}\right) ^ {\top} \left(\boldsymbol {c} _ {k ^ {\prime}} / \| \boldsymbol {c} _ {k ^ {\prime}} \| _ {2}\right)\right)}, \tag {4} +$$ + +The soft pseudo label $\pmb{q}_i'$ for view $\pmb{x}_i'$ is similarly generated. Then, it employs a cross-entropy loss $\ell(\pmb{q}',\pmb{p}) = -\sum_k \pmb{q}'^{(k)} \log \pmb{p}^{(k)}$ to supervise the learning of prediction with pseudo labels or ground-truth labels: + +$$ +\mathcal {L} _ {\mathrm {c l s}} ^ {u} = \frac {1}{| B |} \sum_ {i \in B} \ell \left(\boldsymbol {q} _ {i} ^ {\prime}, \boldsymbol {p} _ {i}\right), \mathcal {L} _ {\mathrm {c l s}} ^ {s} = \frac {1}{| B |} \sum_ {i \in B} \ell \left(\boldsymbol {y} _ {i}, \boldsymbol {p} _ {i}\right), \tag {5} +$$ + +where $\mathcal{L}_{\mathrm{cls}}^u$ and $\mathcal{L}_{\mathrm{cls}}^s$ are unsupervised and supervised classification losses for all and labeled data, respectively. To + +regulate unsupervised learning, SimGCD adopts a class mean entropy regulariser [2]: $H(\overline{\boldsymbol{p}}) = -\sum_{k}\overline{\boldsymbol{p}}^{(k)}\log \overline{\boldsymbol{p}}^{(k)}$ , where $\overline{\boldsymbol{p}}$ is the mean prediction of each class in a batch $\overline{\boldsymbol{p}} = \frac{1}{2|B|}\sum_{i\in B}(\boldsymbol {p}_i + \boldsymbol {p}_i')$ . Then the classification objective is: $\mathcal{L}_{\mathrm{cls}} = (1 - \lambda)(\mathcal{L}_{\mathrm{cls}}^u -\varepsilon H(\overline{\boldsymbol{p}})) + \lambda \mathcal{L}_{\mathrm{cls}}^s$ . Finally, the overall objective in baseline SimGCD is $\mathcal{L}_{\mathrm{rep}} + \mathcal{L}_{\mathrm{cls}}$ . + +# 3.3. Local Entropy Regularization + +Motivation. Although the baseline SimGCD [39] has improved accuracy and computational efficiency compared to GCD [36], it faces catastrophic forgetting in known (Old) classes during training, as shown in Fig. 1a. This is due to SimGCD relying on class mean entropy, causing a shift in focus to novel classes and resulting in information loss in known classes. We argue that retaining knowledge of known classes should be prioritized. Fig. 3a displays potential known class samples in each epoch on the FGVC-Aircraft [21] dataset. Evidently, LegoGCD recognizes nearly 10 more potential known samples than SimGCD in the end. Fig. 3b illustrates the maximum number of potential known samples in various datasets, confirming that LegoGCD with LER excels at preserving the recognition ability of known categories. Concretely, we propose a Local Entropy Regularization (LER) to preserve the knowledge of known categories, solving the problem of catastrophic forgetting. In contrast to the class mean entropy, which primarily shifts the network's focus to novel classes, we argue that the network should also maintain its ability to recognize + +![](images/a26441a944c5723a5f04e093501f04e0ac5d3812b4766218bbb4c6144f41e71f.jpg) +(a) FGVC-Aircraft [21] +Figure 3. Comparison of potential known samples in SimGCD [39] and LegoGCD. (a) LegoGCD recognizes almost 10 more high-confidence samples than SimGCD in the end on the FGVC-Aircraft dataset. (b) LegoGCD with LER produces more high-confidence known samples in various generic and fine-grained datasets compared to SimGCD without LER. + +![](images/88af60ff24eadc72014b75e9cf4eb946b497b0b09c337afc124045afbcb5b0ed.jpg) +(b) Maximum numbers + +known samples as it did before. Specifically, we choose known samples based on a confidence threshold $\delta$ in unlabeled data and utilize entropy regularization to ensure the stability of these known classes associated with the selected known samples. + +The training dataset, denoted as $\mathcal{D} = \{(x_i,y_i)\} \in \mathcal{X}\times \mathcal{Y}$ , comprises both labeled and unlabeled samples represented as $x_{i}$ within a batch $B$ . To distinguish between labeled and unlabeled samples in a batch, we utilize a binary mask vector $M = [m_1,m_2,\dots ,m_i]\subseteq \{0,1\}$ , where each $m_{i}$ can be either 0 (indicating an unlabeled sample) or 1 (indicating a labeled sample). Consequently, the unlabeled samples in a batch are obtained by applying this mask $M = 0$ . + +Next, let $\pmb{p}_i = [p_i^1, p_i^2, \dots, p_i^k]$ as the prediction vector for sample $\pmb{x}_i$ , where $K$ represents the total number of categories. We use $S = [s_1, s_2, \dots, s_i] \subseteq \{0, 1\}$ as a binary vector to denote the high-confidence sample. When $s_i = 1$ , it indicates that $\pmb{x}_i$ is a potential high-confidence sample. This can be expressed as follows: + +$$ +s _ {i} = \mathbb {1} (\max \left(\boldsymbol {p} _ {i}\right) \geq \delta), \tag {6} +$$ + +where $\delta$ represents the confidence threshold. Then, we let $\mathcal{Y} = [y_1,y_2,\dots ,y_i]\in \{1,2,\dots ,K\}$ denotes the potential class label corresponding to $\pmb {x}_i$ . $y_{i}$ is determined by the index of the maximum value in $\pmb{p}_i$ : + +$$ +y _ {i} = \arg \max _ {j} \left(\boldsymbol {p} _ {i}\right) _ {j}, \quad i = 1, 2, \dots , b \tag {7} +$$ + +where $b$ denotes the number of batch sizes. We also introduce $\mathcal{O} = [o_1, o_2, \ldots, o_i] \subseteq \{0, 1\}$ as a binary vector, and $o_i = 1$ signifying potential known samples with high-confidence in unlabeled data. This calculation can be performed as follows: + +$$ +o _ {i} = \underbrace {\mathbb {1} (m _ {i} = 0)} _ {\text {U n l a b e l e d}} \cdot \underbrace {\mathbb {1} (s _ {i} = 1)} _ {\text {H i g h - c o n f i d e n c e}} \cdot \underbrace {\mathbb {1} (y _ {i} \in \mathcal {Y} _ {l})} _ {\text {K n o w n}}, \tag {8} +$$ + +where $\mathcal{Y}_l$ represents the known class set. Next, we use information entropy to assess the stability of the known categories during training, which is expressed as follows: + +$$ +\mathcal {L} _ {\text {e n t r o p y}} = - \frac {1}{B} \sum_ {i = 1} ^ {B} \mathbb {1} \left(o _ {i} = 1\right) \cdot H \left(\frac {1}{\tau_ {o}} \boldsymbol {p} \left(\boldsymbol {x} _ {i}\right)\right), \tag {9} +$$ + +where $\tau_{o}$ is a temperature, $H$ is an entropy regulariser [2] used in Sec. 3.2.2. Additionally, to further enhance the margins between the categories, we replace the vanilla information loss with a Margin-aware Pattern (MAP) [38, 42], and the final LER loss can be formulated as: + +$$ +\mathcal {L} _ {L E R} = - \frac {1}{B} \sum_ {i = 1} ^ {B} \mathbb {1} (o _ {i} = 1) \cdot H \left(\frac {1}{\tau_ {o}} \boldsymbol {p} (\boldsymbol {x} _ {i}), \frac {1}{\tau_ {o}} \boldsymbol {p} (\boldsymbol {x} _ {i}) - \Delta_ {j}\right), \tag {10} +$$ + +where $\Delta_j = \lambda_{ler}\log \left(\frac{1}{\tilde{p}_j}\right)$ , $j\in \{1,\dots ,K\}$ , $\lambda_{ler} = 0.4$ and $\tilde{p}_j$ is the average model prediction updated at each iteration through an exponential moving average. + +The total process is divided into three steps: 1) Applying the label mask $M$ to select samples from unlabeled data; 2) Using the threshold $\delta$ to select high-confidence samples from all training data; 3) Identifying high-confidence known samples from all training samples. Furthermore, we provide an intuitive representation of the entire process in the top-right corner of Fig. 2. + +Fig. 3b compares the quantity of high-confidence known samples across various datasets. Clearly, the numbers increase with the introduction of LER, proving our method with LER retains more knowledge about known classes. + +# 3.4. Dual-views Kullback-Leibler divergence + +It's crucial to note that the model might mistakenly identify incorrect samples as known ones when considering two views of the same image for LER. For instance, if $\boldsymbol{x}_i$ and $\boldsymbol{x}_i'$ are misaligned, and $\boldsymbol{x}_i$ exceeds the confidence threshold $\delta$ while $\boldsymbol{x}_i'$ falls below it, uncertainty arises about whether the image of the two views is a potential known one. Thus, we might erroneously select $\boldsymbol{x}_i$ or miss $\boldsymbol{x}_i'$ for LER. In other words, we can confidently select both $\boldsymbol{x}_i$ and $\boldsymbol{x}_i'$ as known samples only when both $\boldsymbol{x}_i$ and $\boldsymbol{x}_i'$ exceed the threshold $\delta$ . + +In general, an ideal approach is to push the alignment of two view samples $\pmb{x}_i$ and $\pmb{x}_i'$ and both belong to the known or novel sample set. To achieve this, we propose a dual-view alignment technique named Dual-views Kullback-Leibler divergence constraint (DKL). + +Formally, given wo cosine similarity $\pmb{p}_i$ and $\pmb{p}_i^\prime$ from Sec. 3.2.2 of two view samples $\pmb{x}_i$ and $\pmb{x}_i^\prime$ in a mini-batch $B$ , the DKL can be formulated as: + +$$ +D _ {K L} \left(\boldsymbol {p} _ {i} \| \boldsymbol {p} _ {i} ^ {\prime}\right) = \frac {1}{B / 2} \sum_ {i = 1} ^ {B / 2} \boldsymbol {p} \left(\boldsymbol {x} _ {i}\right) \cdot \log \frac {\boldsymbol {p} \left(\boldsymbol {x} _ {i}\right)}{\boldsymbol {p} \left(\boldsymbol {x} _ {i} ^ {\prime}\right)}. \tag {11} +$$ + +In summary, DKL aligns the predictions of two view samples, enhancing the creation of more reliable potential known samples for LER. Finally, the ultimate classification loss can be updated as: + +$$ +\mathcal {L} _ {\mathrm {c l s}} = (1 - \lambda) \left(\mathcal {L} _ {\mathrm {c l s}} ^ {u} - \varepsilon H (\bar {\boldsymbol {p}}) + D _ {K L} \left(\boldsymbol {p} _ {i} \| \boldsymbol {p} _ {i} ^ {\prime}\right)\right) + \lambda \mathcal {L} _ {\mathrm {c l s}} ^ {s}. \tag {12} +$$ + +where $\lambda$ is a weight factor to control the balance between supervised and unsupervised classification learning. + +By simply integrating the Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) into SimGCD, we propose a new paragraph named LegoGCD. The overall loss for training our model can be formulated as: + +$$ +\mathcal {L} = \alpha \cdot \left(\mathcal {L} _ {\text {r e p}} + \mathcal {L} _ {\text {c l s}}\right) + \beta \cdot \mathcal {L} _ {\text {L E R}}, \tag {13} +$$ + +where $\beta$ is a control factor to assign the weight to remember known classes. Aligning with SimGCD, we set $\alpha$ to 1 and simultaneously adjust $\beta$ (see Tab. 7). Notably, the DKL is plugged into classification loss $\mathcal{L}_{cls}$ . Algorithm 1 in appendix describes one training step of LegoGCD. + +# 4. Experiment + +# 4.1. Experimental Setup + +Dataset. We evaluate the effectiveness of our approach on eight datasets, consistent with SimGCD [39]. These datasets encompass generic image recognition datasets like CIFAR10/100 [15] and ImageNet-100 [33], as well as Semantic Shit [35] datasets, including CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Additionally, we include two more challenging datasets: Herbarium 19 [31] and ImageNet-1k [26]. For each dataset, we follow the GCD [36] and SimGCD [39] protocols by sub-sampling $50\%$ of known class images to form the labeled set $\mathcal{D}^l$ within the training set. The remaining images from known and novel classes constitute the unlabeled data $\mathcal{D}^u$ . Tab. 1 provides details of the datasets used in our experiments. + +Evaluation protocol. During training, we use dataset $\mathcal{D}$ combined by $\mathcal{D}^l$ and $\mathcal{D}^u$ to train the models. For evaluation, we use clustering accuracy (ACC) [36, 39] to evaluate the model performance. Specifically, ACC is computed as follows: given the ground-truth label $y^{*}$ and the model's prediction $\hat{y}_i$ , $ACC = \frac{1}{M}\sum_{i=1}^{M}\mathbb{1}(y_i^* = p(\hat{y}_i))$ , where $M = |\mathcal{D}^u|$ , and $p$ is determined using the Hungarian optimal assignment algorithm [16]. + +Implementation details. Following [36, 39], we conduct our experiments using ViT-B/16 backbone [6], which was pre-trained with DINO [4], and only fine-tune the last attention block of the backbone for all models. We use the [CLS] token output as the image feature and input for classifier training in SimGCD. Our training regimen includes an initial learning rate of 0.1, decay using a cosine schedule. For a fair comparison, we use a batch size of 128 and + +Table 1. Overview of the datasets used in our experiments. We list the specific number of labeled and unlabeled images $(\mathcal{D}^l,\mathcal{D}^u)$ and their corresponding class assignments (Old and New). + +
DatasetBalanceLabeled DlUnlabeled Du
ImagesOldImagesNew
CIFAR10 [15]✓12.5k537.5k10
CIFAR100 [15]✓20.0k8030.0k100
ImageNet-100 [33]✓31.9k5095.3k100
CUB [37]✓1.5k1004.5k200
Stanford Cars [14]✓2.0k986.1k196
FGVC-Aircraft [21]✓1.7k505.0k100
Herbarium 19 [31]X8.9k34125.4k683
ImageNet-1K [26]✓321k500960k1000
+ +train the models for 200 epochs, setting $\lambda = 0.35$ in the loss function (see Eq. (5)). Temperature values $\tau_{u} = 0.07$ and $\tau_{c} = 1.0$ are employed in representation learning. As for training the classifier in SimGCD, we follow the same settings, including $\tau_{s} = 0.1$ and initial $\tau_{t} = 0.07$ which is warmed up to 0.04 with a cosine schedule within the first 30 epochs. In LegoGCD, we set $\tau_{o} = 0.05$ (see Eq. (9)). All experiments are conducted using PyTorch and trained on Nvidia Tesla V100 GPUs. + +# 4.2. Comparison with the baselines + +We compare our approach with Generalized Category Discovery methods like $k$ -means [20], ORCA[19], GCD [36], SimGCD [39], and strong baselines derived from Novel Category Discovery, including RS+ [9] and UNO+[7]. For a fair comparison, we reproduce SimGCD (denoted as SimGCD*) using the same random seed (i.e. seed=0) as our method. Tab. 2 shows results on SSB datasets [35] and Herbarium 19 [31], Tab. 3 and Tab. 4 present results on generic recognition datasets, including the challenging ImageNet-1k [26]. + +Overall, our method effectively mitigates catastrophic forgetting and achieves superior performance compared to the GCD and SimGCD baseline, particularly in recognizing "Old" categories. Specifically, it outperforms the baseline by $3.5\% / 2.1\%$ on CIFAR100 and ImageNet-100 and shows significant improvements in fine-grained evaluations with $5.4\%$ in CUB and $5.1\%$ in Stanford Cars. Additionally, it surpasses the baseline by $0.4\% / 0.5\%$ on the challenging datasets ImageNet-1k and Herbarium 19. In addressing the forgetting problem, our approach also competes well with SimGCD on "New" classes, achieving $3.4\%$ in Stanford Cars, $1.0\%$ in CIFAR100, and $3.5\%$ in ImageNet-100. + +# 4.3. Ablation Study + +In this section, we conduct ablation studies to validate the effectiveness of LER and DKL in LegoGCD. The datasets considered include fine-grained datasets like CUB and Stanford Cars, as well as generic image recognition datasets CI + +Table 2. Classification results on Semantic Shift Benchmark [35] datasets and Herbarium 19 [31]. Bold represent our results, $\Delta$ indicates the margin ahead of the baseline SimGCD, and red signifies improvement in known categories. + +
MethodCUBStanford CarsFGVC-AircraftHerbarium 19
AllOldNewAllOldNewAllOldNewAllOldNew
k-means[20]34.338.932.112.810.613.816.014.416.813.012.213.4
RS+[9]33.351.624.228.361.812.126.936.422.227.955.812.8
UNO+[7]35.149.028.135.570.518.640.356.432.228.353.714.7
ORCA[19]35.345.630.223.550.110.722.031.817.120.930.915.5
GCD [36]51.356.648.739.057.629.945.041.146.935.451.027.0
SimGCD [39]60.365.657.753.871.945.054.259.151.844.058.036.4
SimGCD* [39]61.966.559.653.470.645.054.661.451.144.956.938.4
Ours63.871.959.857.375.748.455.061.551.745.157.438.4
Δ1.95.40.23.95.13.40.40.10.60.20.50.0
+ +![](images/35871b7c11b0927d18fbc3138815b78b34ef5613b16196f16561d89f1092ecc0.jpg) +Figure 4. Step by step, we integrate LER and DKL into the baseline SimGCD [39]. Initially, the addition of LER increases accuracy in the "Old" category while decreasing accuracy in the "New" category. Subsequently, the introduction of a Margin-aware Pattern (MAP) widens margins between novel categories, ultimately achieving the best performance when embedding with DKL. + +![](images/14e055423539b63fd2cf5454bf9030b7eee2289d0f1413028c8aaa064f09b678.jpg) + +![](images/9fd546375ed948da3a5664a911d4b82b84f153b2dad5e66238568019219269a0.jpg) + +![](images/28040163a6db1c2d23d88d6c9820d1fd5e073eafa53d728216849b8283adcbb0.jpg) + +Table 3. Classification results on the generic image recognition datasets, CIFAR10 [15] and CIFAR100 [15]. + +
MethodCIFAR10CIFAR100
AllOldNewAllOldNew
k-means[20]83.685.782.552.052.250.8
RS+[9]46.819.260.558.277.619.3
UNO+[7]68.698.353.869.580.647.2
ORCA[19]81.886.279.669.077.452.0
GCD [36]91.597.988.273.076.266.5
SimGCD [39]97.195.198.180.181.277.8
SimGCD* [39]96.993.898.579.077.981.5
Ours97.194.398.581.881.482.5
Δ0.20.50.02.83.51.0
+ +# FAR100 and ImageNet-100. + +Local Entropy Regularization (LER). We conduct ablation studies on LER as shown in Fig. 4. Firstly, the SimGCD baseline with LER (without Margin-aware Pattern, MAP) notably enhances "Old" Categories (see green curves). However, using raw LER alone may impact accuracy in "New" classes (see orange curves). This is be + +Table 4. Classification results on the generic image recognition ImageNet-100 [33] and the challenging ImageNet-1k [26]. + +
MethodImageNet-100ImageNet-1k
AllOldNewAllOldNew
k-means[20]72.775.571.3---
RS+[9]37.161.624.8---
UNO+[7]70.395.057.9---
ORCA[19]73.592.663.9---
GCD [36]74.189.866.352.572.542.2
SimGCD [39]83.093.177.957.177.346.9
SimGCD* [39]83.392.478.662.379.153.8
Ours86.394.582.162.479.553.8
Δ3.02.13.50.10.40.0
+ +cause it primarily encourages the network to remember known classes, consequently influencing the learning of novel ones. To mitigate this, we incorporate MAP (see Eq. (10)) to encourage the network to simultaneously enhance the margins of all classes, particularly novel classes. Finally, the inclusion of MAP in LER leads to improvements in both the "Old" and "New" categories. + +Table 5. Ablation study on different combinations of our algorithms on CUB. Bold indicates the best results. + +
SimGCDLERMAPDKLCUB
AllOld ↑New
✓61.966.559.6
✓✓62.567.360.2
✓✓63.471.059.6
✓✓✓63.772.058.5
✓✓✓✓63.871.959.8
+ +Table 6. Ablation study on $\alpha$ and $\beta$ was conducted on CUB and CIFAR100. Bold indicates the best results. The underline denotes the selected $\beta$ . + +
αβCUBCIFAR100
AllOld ↑NewAllOld ↑New
0.061.966.559.679.077.981.5
0.563.069.559.780.880.481.5
1.063.669.760.681.881.482.5
1.01.563.471.259.881.481.780.8
2.063.871.959.881.782.180.9
+ +Dual-views Kullback-Leibler divergence (DKL). DKL is designed to improve the quality of known samples for LER by aligning the predictions of two views from the same image. The results in Tab. 5 indicate that incorporating DKL into raw SimGCD led to improvements in both "Old" and "New" category accuracies by $1.8\%$ and $0.6\%$ , respectively (67.3% vs. 66.5%, 60.2% vs. 59.6%). This success proves beneficial for self-distillation learning in SimGCD. Additionally, from Fig. 4 and Tab. 5, we can see that our method becomes more effective with DKL, particularly in "Old" classes, while maintaining performance on "New" classes. + +Different $\alpha$ and $\beta$ . The coefficient $\beta$ is crucial for balancing knowledge preservation of known classes and facilitating effective learning of novel classes. As depicted in Tab. 6 with $\alpha = 1.0$ aligned to SimGCD, accuracy on "Old" categories consistently surpasses SimGCD ( $\beta = 0.0$ ) across different $\beta$ values. Optimal equilibrium is achieved with $\beta = 2.0$ in CUB and $\beta = 1.0$ in CIFAR100. + +Different confidence threshold $\delta$ . We compare accuracy with different $\delta$ in Tab. 7. Results show varying responses across datasets. In Stanford Cars, "Old" accuracy initially increases, then slightly decreases, while "New" accuracy decreases but remains above SimGCD at $45.5\%$ . In contrast, in CIFAR100, "Old" accuracy decreases but consistently surpasses SimGCD at $77.9\%$ . Our goal is to prioritize high "Old" accuracy and ensure "New" equals or exceeds SimGCD. Therefore, we choose $\delta = 0.85$ for both Stanford Cars and CIFAR100. + +Table 7. Ablation study on confidence threshold $\delta$ was conducted on Stanford Cars and CIFAR100. Bold indicates the best results. The underline denotes the selected threshold. + +
δStanford CarsCIFAR100
AllOld ↑NewAllOld ↓New
0.7055.366.849.880.383.374.3
0.7555.872.347.980.983.376.3
0.8056.573.048.581.382.778.5
0.8557.375.748.481.881.482.5
0.9056.475.347.379.080.576.0
+ +# 5. Conclusion + +In this paper, we propose LegoGCD, a novel approach to mitigate the issue of catastrophic forgetting in known categories. The core of our design is to preserve knowledge of known classes while maintaining the accuracy of novel classes. To achieve this, we develop two techniques: Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). LER explicitly regularizes high-confidence potential known class samples to retain the knowledge of known categories. To ensure the accurate selection of these samples, we employ DKL to align the distribution of two view samples for LER. Both LER and DKL can be seamlessly integrated into baseline SimGCD resembling Lego blocks, without introducing new parameters or altering the internal network structure. Extensive experiments demonstrate that LegoGCD significantly enhances performance in known classes, effectively addressing the catastrophic forgetting problem. + +# 6. Acknowledgements + +This research is supported by the National Key R&D Program of China (2021YFB0301300), and also received supported from programs: the Major Program of Guangdong Basic and Applied Research (2019B030302002), the Key-Area Research and Development Program of Guangdong Province (2021B0101400002), the Major Key Project of PCL PCL2021A13 and Peng Cheng Cloud-Brain, and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (23xkjc016). + +# References + +[1] Wenbin An, Feng Tian, Qinghua Zheng, Wei Ding, QianYing Wang, and Ping Chen. Generalized category discovery with decoupled prototypical network. In Proceedings of the AAAI Conference on Artificial Intelligence (AAAI), pages 12527-12535, 2023. 1 +[2] Mahmoud Assran, Mathilde Caron, Ishan Misra, Piotr Bojanowski, Florian Bordes, Pascal Vincent, Armand Joulin, Mike Rabbat, and Nicolas Ballas. Masked siamese networks for label-efficient learning. 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Essentially, GCD needs to remember existing patterns thoroughly to recognize novel categories. Recent state-of-the-art method SimGCD transfers the knowledge from known-class data to the learning of novel classes through debiased learning. However, some patterns are catastrophically forgot during adaptation and thus lead to poor performance in novel categories classification. To address this issue, we propose a novel learning approach, LeGOCD, which is seamlessly integrated into previous methods to enhance the discrimination of novel classes while maintaining performance on previously encountered known classes. Specifically, we design two types of techniques termed as Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). The LER optimizes the distribution of potential known class samples in unlabeled data, thus ensuring the preservation of knowledge related to known categories while learning novel classes. Meanwhile, DKL introduces Kullback-Leibler divergence to encourage the model to produce a similar prediction distribution of two view samples from the same image. In this way, it successfully avoids mismatched prediction and generates more reliable potential known class samples simultaneously. Extensive experiments validate that the proposed LegoGCD effectively addresses the known category forgetting issue across all datasets, e.g., delivering a " + }, + { + "bbox": [ + 46, + 300, + 290, + 671 + ], + "type": "inline_equation", + "content": "7.74\\%" + }, + { + "bbox": [ + 46, + 300, + 290, + 671 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 300, + 290, + 671 + ], + "type": "inline_equation", + "content": "2.51\\%" + }, + { + "bbox": [ + 46, + 300, + 290, + 671 + ], + "type": "text", + "content": " accuracy boost on known and novel classes in CUB, respectively. Our code is available at: https://github.com/Cliffia123/LegoGCD." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 310, + 275, + 425, + 374 + ], + "blocks": [ + { + "bbox": [ + 310, + 275, + 425, + 374 + ], + "lines": [ + { + "bbox": [ + 310, + 275, + 425, + 374 + ], + "spans": [ + { + "bbox": [ + 310, + 275, + 425, + 374 + ], + "type": "image", + "image_path": "3619d89db8d68a4da5c915be7f18240b4a13ee8bb6bec033bbd2938194dc7112.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 323, + 376, + 411, + 387 + ], + "lines": [ + { + "bbox": [ + 323, + 376, + 411, + 387 + ], + "spans": [ + { + "bbox": [ + 323, + 376, + 411, + 387 + ], + "type": "text", + "content": "(a) Baseline SimGCD [39]" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 428, + 275, + 543, + 374 + ], + "blocks": [ + { + "bbox": [ + 428, + 275, + 543, + 374 + ], + "lines": [ + { + "bbox": [ + 428, + 275, + 543, + 374 + ], + "spans": [ + { + "bbox": [ + 428, + 275, + 543, + 374 + ], + "type": "image", + "image_path": "c538abaa230281ec7f7edcc33191d06dba75f264058cf9eaa21d896ba111770d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 453, + 376, + 517, + 387 + ], + "lines": [ + { + "bbox": [ + 453, + 376, + 517, + 387 + ], + "spans": [ + { + "bbox": [ + 453, + 376, + 517, + 387 + ], + "type": "text", + "content": "(b) Ours LegoGCD" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 396, + 547, + 462 + ], + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 462 + ], + "type": "text", + "content": "Figure 1. Visualization of the accuracy results in unlabeled dataset on CUB dataset [37] during training. (a) shows a decrease in the accuracy of known (Old) classes (green) in the baseline as the accuracy of novel (New) classes (orange) increases. (b) demonstrates that LegoGCD solves the catastrophic forgetting problem and surpasses the baseline by a significant margin of 7.74." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 486, + 388, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 486, + 388, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 486, + 388, + 498 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 508, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 546, + 664 + ], + "type": "text", + "content": "Deep learning have achieved superior performance on computer vision tasks [4, 11, 24, 25, 30, 34], particularly on image classification [10, 12, 27, 28, 51]. However, conventional methods work in a close-world setting, where all training data comes with pre-defined classes. Consequently, deploying these models in real-world scenarios with potential novel classes becomes a considerable challenge. Furthermore, these achievements rely heavily on large-scale annotated dataset, which is not easily accessible in realistic scenarios. To address these challenges, a new paradigm of Generalized Category Discovery (GCD) [1, 7, 9, 23, 36, 39, 45, 46] has been proposed and attracts increasing attention in recent years." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "The goal of GCD is to train a classification model capable of recognizing both known and novel categories within unlabeled data. To be clear, GCD distinguishes itself from the Novel Class Discovery (NCD) [8], which relies on an" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 128, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 128, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 128, + 703 + ], + "type": "text", + "content": "*Equal Contribution." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 59, + 703, + 159, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 159, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 159, + 712 + ], + "type": "text", + "content": "† Joint Corresponding Authors." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16880" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "unrealistic assumption that all unlabeled data exclusively belongs to entirely new classes or patterns. In contrast, GCD adopts a more pragmatic assumption, acknowledging that unlabeled data encompasses a mixture of both known and novel categories. Consequently, GCD is more realistic compared to NCD, especially in real-world scenarios." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 288, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 146, + 288, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 288, + 373 + ], + "type": "text", + "content": "Since GCD is partially based on the learned patterns, an intuitive idea is to classify the unlabeled data through a clustering-based approach [36] i.e. " + }, + { + "bbox": [ + 46, + 146, + 288, + 373 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 146, + 288, + 373 + ], + "type": "text", + "content": "-means. However, as the scale of datasets increases, the computational costs for clustering in the original GCD grow exponentially. To tackle this issue, Wen et al. introduce SimGCD [39], which replaces the clustering approach with a classifier. Specifically, SimGCD trains the classifier using a pseudo-labeling strategy, a technique that has demonstrated remarkable effectiveness in Semi-supervised Learning (SSL) [3, 45]. Nevertheless, the pseudo labels of novel samples tend to be assigned as known classes due to the absence of guidance for novel class samples. In response, Wen et al. further propose to adopt class mean entropy to encourage the model to focus on novel categories, consequently generating high-quality pseudo labels for classifier training. As a result, SimGCD has achieved state-of-the-art performance and established itself as a robust baseline solution in the GCD setting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "text", + "content": "However, SimGCD [39] still has a significant drawback. It encourages the model to focus more on novel classes by employing an entropy regularization, which unfortunately comes at the cost of known class accuracy, resulting in a catastrophic forgetting problem in known categories. To illustrate this issue, we have tracked the classification accuracy of known and novel categories on unlabeled data during each training epoch on CUB [37]. As shown in Fig. 1a, the green curve represents the accuracy of known (Old) classes, while the orange curve represents the accuracy of novel (New) classes. Notably, we can easily observe this phenomenon, with the accuracy of novel classes improving, the accuracy of known categories initially increases to approximately " + }, + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "inline_equation", + "content": "74\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "text", + "content": " after 20 epochs but then drops to " + }, + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "inline_equation", + "content": "64.44\\%" + }, + { + "bbox": [ + 46, + 376, + 287, + 579 + ], + "type": "text", + "content": " in the end. We thus conclude that SimGCD faces catastrophic forgetting in known categories during training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "To address the above issue, we propose a novel Local Entropy Regularization (LER) to preserve the knowledge of known categories. In particular, we first identify potential known samples using a threshold on their logits prediction like FixMatch [29]. Then, we employ the information entropy function to encourage the predictions of above selected known samples close to a uniform distribution, thereby maintaining the prediction stability of known classes. Consequently, this LER prevents known samples from being misclassified as novel classes and therefore preserves the knowledge related to known categories during" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 72, + 411, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 411, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 411, + 84 + ], + "type": "text", + "content": "learning novel categories." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "spans": [ + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "text", + "content": "It's worth noting that the model may occasionally miss potential known samples or select incorrect (novel) samples for LER. For example, when we have two augmentation view samples, " + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i'" + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "text", + "content": ", from the same image, and " + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "text", + "content": " has higher logits than the threshold while " + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i'" + }, + { + "bbox": [ + 304, + 88, + 545, + 257 + ], + "type": "text", + "content": " falls below it. In such cases, we can't be certain whether the original image belongs to known classes, and this uncertainty may impact the effectiveness of LER. We argue that the predictions of the two view samples should be correctly aligned to ensure the quality of the chosen known samples. Therefore, we further propose a dual-view alignment scheme called Dual-views Kullback-Leibler divergence constraint (DKL), which employs Kullback-Leibler (KL) divergence to encourage the consistency of two views from the same image." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 260, + 546, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 546, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 546, + 511 + ], + "type": "text", + "content": "To summarize, we propose a novel approach named LegoGCD, which integrates SimGCD [39] with our proposed LER and DKL to address the problem of catastrophic forgetting. To validate the effectiveness of LegoGCD, we conduct extensive experiments on eight datasets, including generic datasets such as CIFAR10/100 [15], ImageNet-1k [5], and fine-grained datasets CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Intuitively, we also visualize the classification accuracy of known and novel categories on CUB [37]. These results are shown in Fig. 1b. The green curve represents the accuracy of known (Old) categories, while the orange curve indicates the accuracy of novel (New) classes. Clearly, LegoGCD effectively prevents the decline in known classes and achieves an accuracy of " + }, + { + "bbox": [ + 304, + 260, + 546, + 511 + ], + "type": "inline_equation", + "content": "72.18\\%" + }, + { + "bbox": [ + 304, + 260, + 546, + 511 + ], + "type": "text", + "content": ", surpassing SimGCD by a margin of 7.74. Clearly, the results indicate that LegoGCD solves the catastrophic forgetting problem of known categories effectively. Moreover, our method can be easily placed onto SimGCD like Lego, requiring only a few lines of code on the implementation without introducing any additional parameters or altering the internal network structure of SimGCD." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 317, + 516, + 518, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 516, + 518, + 527 + ], + "spans": [ + { + "bbox": [ + 317, + 516, + 518, + 527 + ], + "type": "text", + "content": "In summary, our key contributions are as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 532, + 545, + 711 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 532, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 532, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 306, + 532, + 545, + 590 + ], + "type": "text", + "content": "- We introduce a novel constraint named Local Entropy Regularization (LER), which is designed to mitigate the catastrophic forgetting problem of known classes by preserving the knowledge of known categories during learning novel classes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 592, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 592, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 306, + 592, + 545, + 650 + ], + "type": "text", + "content": "- We propose a Dual-views Kullback-Leibler divergence constraint (DKL) that ensures the prediction distribution of one view approximates that of another, maintaining consistency between dual views augmented from the same image." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "type": "text", + "content": "- The proposed LegoGCD is effective and can be simply integrated from SimGCD without any extra parameter addition. Extensive results demonstrate our method exhibits significant performance improvement on known classes, e.g., a " + }, + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "type": "inline_equation", + "content": "7.74\\%" + }, + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "type": "text", + "content": " increase in CUB [37]." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16881" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 222, + 103 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 222, + 103 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 222, + 103 + ], + "type": "text", + "content": "2.1. Generalized Category Discovery" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 109, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 109, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 47, + 109, + 289, + 350 + ], + "type": "text", + "content": "GCD was first formulated by Vaze et al. [36], presents a unique challenge distinct from Semi-supervised Learning (SSL) [3, 17, 22, 32, 47]. While SSL assumes that unlabeled data belongs to the same class set as the labeled data, GCD tackles a more realistic scenario where the unlabeled data may include classes not present in the labeled set, which is the same setting in Novel Category Discovery (NCD) [7-9, 13, 18, 19, 40, 41, 49]. Therefore, GCD can be viewed as an extension of NCD, with the main difference being that GCD seeks to identify specific categories within novel classes, while NCD focuses on grouping novel classes into a single category. The original GCD approach employs contrastive and SSL, which uses clustering during inference and incurs significant computational costs. To address this challenge, Wen et al. [39] introduce SimGCD with a classifier to replace clustering, offering a robust baseline for the GCD problem. However, it's important to note that SimGCD introduces a drawback, leading to a decrease in the classification accuracy of known classes during the intense learning of novel categories." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 354, + 179, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 354, + 179, + 367 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 179, + 367 + ], + "type": "text", + "content": "2.2. Entropy regularization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 373, + 289, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 373, + 289, + 637 + ], + "spans": [ + { + "bbox": [ + 47, + 373, + 289, + 637 + ], + "type": "text", + "content": "It is a widely used technique in image classification, especially in the context of cross-entropy, which aims to align prediction distributions with the standard label distribution. However, in scenarios such as Semi-supervised Learning (SSL) [3, 17, 22, 32, 47], where true labels are unknown, pseudo labels take the place of actual labels in standard cross-entropy. This form of entropy regularization minimizes output differences between various views of unlabeled data. Notably, Data Augmentations [43, 44] have proven effective, contributing to substantial successes in pseudo-supervised learning. For instance, in SimGCD [39], an augmentation strategy generates two views of data, establishing training targets in one view and enforcing prediction consistency with the other view during unlabeled data training. Another form of entropy, information entropy, measures the amount of information within a set of events. In SimGCD, information entropy is employed to minimize class mean entropy, promoting more uniform class predictions in each iteration to ensure the visibility of novel classes. However, due to the absence of protection for the knowledge of known classes, class mean entropy has led to a degeneration in known categories." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 645, + 103, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 103, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 103, + 658 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 288, + 715 + ], + "type": "text", + "content": "In this section, we first formulate the GCD task (Sec. 3.1) and present the overview of the baseline SimGCD [39] (Sec. 3.2). Then, we introduce how to mitigate the degradation of SimGCD by the proposed LegoGCD. At last, we" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": "describe the details of the proposed Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) in Sec. 3.3 and Sec. 3.4, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 116, + 430, + 128 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 116, + 430, + 128 + ], + "spans": [ + { + "bbox": [ + 306, + 116, + 430, + 128 + ], + "type": "text", + "content": "3.1. Problem Formulation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "spans": [ + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": "Traditional image classification tasks are typically developed using a labeled dataset, denoted as " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_l" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": ". This dataset contains only samples from known classes, represented by " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_l" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": ". In contrast, Generalized Category Discovery (GCD) aims to recognize unlabeled data, denoted as " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}_u" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": ". This dataset comprises both known and novel class samples, where " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_l" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": " is a subset of " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_u" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": ". The goal of GCD is to develop a model that can identify both known and novel classes using the labels from known categories " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "(\\mathcal{V}_l)" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": " and unlabeled data " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}_u)" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": " without access to class labels. It's important to note that the total number of categories is represented as " + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "inline_equation", + "content": "K = |\\mathcal{V}_l\\cup \\mathcal{V}_u|" + }, + { + "bbox": [ + 305, + 134, + 547, + 303 + ], + "type": "text", + "content": ". We assume prior knowledge of this total category count, as done in previous works [7, 9, 48, 50]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 310, + 392, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 310, + 392, + 322 + ], + "spans": [ + { + "bbox": [ + 306, + 310, + 392, + 322 + ], + "type": "text", + "content": "3.2. Preliminaries" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 329, + 547, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 329, + 547, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 547, + 376 + ], + "type": "text", + "content": "In this section, we introduce the fundamental structure of SimGCD [39] baseline program as shown in Fig. 2. This program primarily consists of two key components: Representation learning and Parametric Classification." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 392, + 446, + 405 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 392, + 446, + 405 + ], + "spans": [ + { + "bbox": [ + 306, + 392, + 446, + 405 + ], + "type": "text", + "content": "3.2.1 Representation Learning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 411, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 411, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 545, + 495 + ], + "type": "text", + "content": "The representation learning process in our framework follows GCD [36] and SimGCD [39]. It employs a Vision Transformer (ViT-B/16) [6] pretrained with DINO self-supervision [4] on ImageNet [5] as the backbone. This process includes supervised contrastive learning on labeled data and unsupervised contrastive learning on all data, encompassing both labeled and unlabeled data." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "text", + "content": "Formally, given two views (random augmentations) " + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i'" + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "text", + "content": " of the same image in a mini-batch " + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 496, + 545, + 531 + ], + "type": "text", + "content": ", the unsupervised contrastive loss is written as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 321, + 537, + 545, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 537, + 545, + 570 + ], + "spans": [ + { + "bbox": [ + 321, + 537, + 545, + 570 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r e p}} ^ {u} = \\frac {1}{| B |} \\sum_ {i \\in B} - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {i} ^ {\\prime} / \\tau_ {u}\\right)}{\\sum_ {i} ^ {i \\neq n} \\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {n} ^ {\\prime} / \\tau_ {u}\\right)}, \\tag {1}", + "image_path": "ac32a58c0a4533c48adc86f3c5820916af3be451717f5ee0dce1b09d2372f068.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_i = \\phi(f(\\boldsymbol{x}_i))" + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\boldsymbol{z}_i' = \\phi(f(\\boldsymbol{x}_i'))" + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "content": " is the feature backbone, " + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "content": " is a multi-layer perceptron (MLP) projection head, " + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\tau_u" + }, + { + "bbox": [ + 305, + 578, + 545, + 614 + ], + "type": "text", + "content": " is a unsupervised temperature." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 616, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 616, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 305, + 616, + 545, + 651 + ], + "type": "text", + "content": "The objective of the supervised contrastive loss is to encourage the model to bring samples with the same class label closer in the feature space, formally written as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 311, + 660, + 545, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 660, + 545, + 693 + ], + "spans": [ + { + "bbox": [ + 311, + 660, + 545, + 693 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {r e p}} ^ {s} = \\frac {1}{| B ^ {l} |} \\sum_ {i \\in B ^ {l}} \\frac {1}{| \\mathcal {N} _ {i} |} \\sum_ {q \\in N _ {i}} - \\log \\frac {\\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {q} ^ {\\prime} / \\tau_ {c}\\right)}{\\sum_ {i} ^ {i \\neq n} \\exp \\left(\\boldsymbol {z} _ {i} ^ {\\top} \\cdot \\boldsymbol {z} _ {n} ^ {\\prime} / \\tau_ {c}\\right)}, \\tag {2}", + "image_path": "6905bb2abf6c5757442d482b6551475010782e08b58edfc18f6d76d0cd34b903.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}_i" + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": " is the indices of images share the same label with" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "16882" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 547, + 297 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 547, + 297 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 547, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 547, + 297 + ], + "type": "image", + "image_path": "552586c6d7fe99680abe9149bfc524821f4a9229926b32026237a2e280de7a92.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 304, + 547, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 547, + 350 + ], + "type": "text", + "content": "Figure 2. Illustration of our proposed LegoGCD. LegoGCD is mainly composed of SimGCD and our proposed LER and DKL. (a) Representation learning and Mean Entropy in SimGCD (Sec. 3.2). (b) Local Entropy Regularization (LER) (Sec. 3.3) for discovering potential known samples in unlabeled data and preserving the knowledge of known classes. (c) Dual-views Kullback-Leibler divergence (DKL) (Sec. 3.4) to ensure consistent predictions for two view samples." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 370, + 288, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 370, + 288, + 394 + ], + "spans": [ + { + "bbox": [ + 47, + 370, + 288, + 394 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 47, + 370, + 288, + 394 + ], + "type": "text", + "content": " in the mini-batch " + }, + { + "bbox": [ + 47, + 370, + 288, + 394 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 370, + 288, + 394 + ], + "type": "text", + "content": ". Finally, the total loss in representation learning is constructed as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 400, + 287, + 415 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 400, + 287, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 287, + 415 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {r e p}} = (1 - \\lambda) \\mathcal {L} _ {\\text {r e p}} ^ {u} + \\lambda \\mathcal {L} _ {\\text {r e p}} ^ {s}, \\tag {3}", + "image_path": "d9eb9d629999c084a76b429f7713ca0c3e01e191414444ea068e1528642c9065.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "inline_equation", + "content": "B^l" + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "text", + "content": " is the labeled subset of " + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 421, + 287, + 434 + ], + "type": "text", + "content": " is a weight factor." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 447, + 188, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 188, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 188, + 458 + ], + "type": "text", + "content": "3.2.2 Parametric Classification" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": "Different from the GCD [36] that uses " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": "-means, SimGCD [39] employs a more efficient classifier based on self-distillation [2, 4]. Formally, the classifier is denoted as a set of prototypes " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = \\{c_1,\\dots ,c_K\\}" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "K = |\\mathcal{Y}_l\\cup \\mathcal{Y}_u|" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": ". During training, the soft label of each view " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": " is obtained by applying softmax on cosine similarity between hidden feature " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\pmb{h}_i = f(\\pmb{x}_i)" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": " and prototypes " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": ", scaled by " + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "inline_equation", + "content": "1 / \\tau_{s}" + }, + { + "bbox": [ + 47, + 465, + 287, + 550 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 555, + 287, + 597 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 555, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 55, + 555, + 287, + 597 + ], + "type": "interline_equation", + "content": "\\boldsymbol {p} _ {i} ^ {(k)} = \\frac {\\exp \\left(\\frac {1}{\\tau_ {s}} \\left(\\boldsymbol {h} _ {i} / \\| \\boldsymbol {h} _ {i} \\| _ {2}\\right) ^ {\\top} \\left(\\boldsymbol {c} _ {k} / \\| \\boldsymbol {c} _ {k} \\| _ {2}\\right)\\right)}{\\sum_ {k ^ {\\prime}} \\exp \\left(\\frac {1}{\\tau_ {s}} \\left(\\boldsymbol {h} _ {i} / \\| \\boldsymbol {h} _ {i} \\| _ {2}\\right) ^ {\\top} \\left(\\boldsymbol {c} _ {k ^ {\\prime}} / \\| \\boldsymbol {c} _ {k ^ {\\prime}} \\| _ {2}\\right)\\right)}, \\tag {4}", + "image_path": "e9a68ac6af39501afd8e5ee7ec47602559263ffdfd26d8ba13608160f3c6429f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "text", + "content": "The soft pseudo label " + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\pmb{q}_i'" + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "text", + "content": " for view " + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i'" + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "text", + "content": " is similarly generated. Then, it employs a cross-entropy loss " + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\ell(\\pmb{q}',\\pmb{p}) = -\\sum_k \\pmb{q}'^{(k)} \\log \\pmb{p}^{(k)}" + }, + { + "bbox": [ + 47, + 601, + 287, + 651 + ], + "type": "text", + "content": " to supervise the learning of prediction with pseudo labels or ground-truth labels:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 655, + 287, + 684 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 655, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 53, + 655, + 287, + 684 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c l s}} ^ {u} = \\frac {1}{| B |} \\sum_ {i \\in B} \\ell \\left(\\boldsymbol {q} _ {i} ^ {\\prime}, \\boldsymbol {p} _ {i}\\right), \\mathcal {L} _ {\\mathrm {c l s}} ^ {s} = \\frac {1}{| B |} \\sum_ {i \\in B} \\ell \\left(\\boldsymbol {y} _ {i}, \\boldsymbol {p} _ {i}\\right), \\tag {5}", + "image_path": "2327e23c8255ad469397f472b5b6510be45bd7612eb6c728b144d286ce914503.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}^u" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}^s" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " are unsupervised and supervised classification losses for all and labeled data, respectively. To" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "content": "regulate unsupervised learning, SimGCD adopts a class mean entropy regulariser [2]: " + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "inline_equation", + "content": "H(\\overline{\\boldsymbol{p}}) = -\\sum_{k}\\overline{\\boldsymbol{p}}^{(k)}\\log \\overline{\\boldsymbol{p}}^{(k)}" + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\overline{\\boldsymbol{p}}" + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "content": " is the mean prediction of each class in a batch " + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\overline{\\boldsymbol{p}} = \\frac{1}{2|B|}\\sum_{i\\in B}(\\boldsymbol {p}_i + \\boldsymbol {p}_i')" + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "content": ". Then the classification objective is: " + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}} = (1 - \\lambda)(\\mathcal{L}_{\\mathrm{cls}}^u -\\varepsilon H(\\overline{\\boldsymbol{p}})) + \\lambda \\mathcal{L}_{\\mathrm{cls}}^s" + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "content": ". Finally, the overall objective in baseline SimGCD is " + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{rep}} + \\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 370, + 545, + 445 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 454, + 469, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 469, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 469, + 468 + ], + "type": "text", + "content": "3.3. Local Entropy Regularization" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 713 + ], + "type": "text", + "content": "Motivation. Although the baseline SimGCD [39] has improved accuracy and computational efficiency compared to GCD [36], it faces catastrophic forgetting in known (Old) classes during training, as shown in Fig. 1a. This is due to SimGCD relying on class mean entropy, causing a shift in focus to novel classes and resulting in information loss in known classes. We argue that retaining knowledge of known classes should be prioritized. Fig. 3a displays potential known class samples in each epoch on the FGVC-Aircraft [21] dataset. Evidently, LegoGCD recognizes nearly 10 more potential known samples than SimGCD in the end. Fig. 3b illustrates the maximum number of potential known samples in various datasets, confirming that LegoGCD with LER excels at preserving the recognition ability of known categories. Concretely, we propose a Local Entropy Regularization (LER) to preserve the knowledge of known categories, solving the problem of catastrophic forgetting. In contrast to the class mean entropy, which primarily shifts the network's focus to novel classes, we argue that the network should also maintain its ability to recognize" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16883" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 165, + 171 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 165, + 171 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 165, + 171 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 165, + 171 + ], + "type": "image", + "image_path": "a26441a944c5723a5f04e093501f04e0ac5d3812b4766218bbb4c6144f41e71f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 69, + 175, + 145, + 185 + ], + "lines": [ + { + "bbox": [ + 69, + 175, + 145, + 185 + ], + "spans": [ + { + "bbox": [ + 69, + 175, + 145, + 185 + ], + "type": "text", + "content": "(a) FGVC-Aircraft [21]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 194, + 287, + 260 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 260 + ], + "type": "text", + "content": "Figure 3. Comparison of potential known samples in SimGCD [39] and LegoGCD. (a) LegoGCD recognizes almost 10 more high-confidence samples than SimGCD in the end on the FGVC-Aircraft dataset. (b) LegoGCD with LER produces more high-confidence known samples in various generic and fine-grained datasets compared to SimGCD without LER." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 167, + 71, + 284, + 171 + ], + "blocks": [ + { + "bbox": [ + 167, + 71, + 284, + 171 + ], + "lines": [ + { + "bbox": [ + 167, + 71, + 284, + 171 + ], + "spans": [ + { + "bbox": [ + 167, + 71, + 284, + 171 + ], + "type": "image", + "image_path": "88af60ff24eadc72014b75e9cf4eb946b497b0b09c337afc124045afbcb5b0ed.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 188, + 175, + 264, + 185 + ], + "lines": [ + { + "bbox": [ + 188, + 175, + 264, + 185 + ], + "spans": [ + { + "bbox": [ + 188, + 175, + 264, + 185 + ], + "type": "text", + "content": "(b) Maximum numbers" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 280, + 287, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 287, + 339 + ], + "type": "text", + "content": "known samples as it did before. Specifically, we choose known samples based on a confidence threshold " + }, + { + "bbox": [ + 46, + 280, + 287, + 339 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 280, + 287, + 339 + ], + "type": "text", + "content": " in unlabeled data and utilize entropy regularization to ensure the stability of these known classes associated with the selected known samples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": "The training dataset, denoted as " + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "inline_equation", + "content": "\\mathcal{D} = \\{(x_i,y_i)\\} \\in \\mathcal{X}\\times \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": ", comprises both labeled and unlabeled samples represented as " + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": " within a batch " + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": ". To distinguish between labeled and unlabeled samples in a batch, we utilize a binary mask vector " + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "inline_equation", + "content": "M = [m_1,m_2,\\dots ,m_i]\\subseteq \\{0,1\\}" + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": ", where each " + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "inline_equation", + "content": "m_{i}" + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": " can be either 0 (indicating an unlabeled sample) or 1 (indicating a labeled sample). Consequently, the unlabeled samples in a batch are obtained by applying this mask " + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "inline_equation", + "content": "M = 0" + }, + { + "bbox": [ + 46, + 340, + 287, + 435 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": "Next, let " + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i = [p_i^1, p_i^2, \\dots, p_i^k]" + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": " as the prediction vector for sample " + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": " represents the total number of categories. We use " + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "inline_equation", + "content": "S = [s_1, s_2, \\dots, s_i] \\subseteq \\{0, 1\\}" + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": " as a binary vector to denote the high-confidence sample. When " + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "inline_equation", + "content": "s_i = 1" + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": ", it indicates that " + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 46, + 435, + 287, + 508 + ], + "type": "text", + "content": " is a potential high-confidence sample. This can be expressed as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 117, + 517, + 287, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 517, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 117, + 517, + 287, + 529 + ], + "type": "interline_equation", + "content": "s _ {i} = \\mathbb {1} (\\max \\left(\\boldsymbol {p} _ {i}\\right) \\geq \\delta), \\tag {6}", + "image_path": "ed8db16282538194118357b0dc70f7ee76ccd67be7a787743cc5827d132bfa8e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "content": " represents the confidence threshold. Then, we let " + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = [y_1,y_2,\\dots ,y_i]\\in \\{1,2,\\dots ,K\\}" + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "content": " denotes the potential class label corresponding to " + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\pmb {x}_i" + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "content": " is determined by the index of the maximum value in " + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i" + }, + { + "bbox": [ + 47, + 536, + 287, + 586 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 89, + 594, + 287, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 594, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 89, + 594, + 287, + 612 + ], + "type": "interline_equation", + "content": "y _ {i} = \\arg \\max _ {j} \\left(\\boldsymbol {p} _ {i}\\right) _ {j}, \\quad i = 1, 2, \\dots , b \\tag {7}", + "image_path": "f6e21b77a6ab9b958839ee8723391d53915bb46ed1faacd5739bf7ed7664fa8f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": " denotes the number of batch sizes. We also introduce " + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mathcal{O} = [o_1, o_2, \\ldots, o_i] \\subseteq \\{0, 1\\}" + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": " as a binary vector, and " + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "inline_equation", + "content": "o_i = 1" + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": " signifying potential known samples with high-confidence in unlabeled data. This calculation can be performed as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 78, + 687, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 687, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 78, + 687, + 287, + 715 + ], + "type": "interline_equation", + "content": "o _ {i} = \\underbrace {\\mathbb {1} (m _ {i} = 0)} _ {\\text {U n l a b e l e d}} \\cdot \\underbrace {\\mathbb {1} (s _ {i} = 1)} _ {\\text {H i g h - c o n f i d e n c e}} \\cdot \\underbrace {\\mathbb {1} (y _ {i} \\in \\mathcal {Y} _ {l})} _ {\\text {K n o w n}}, \\tag {8}", + "image_path": "7d908db0bc1d22668adeaef8ef1cc8f01177bbdd64b93a6e25b95c02b81b0b05.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 109 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_l" + }, + { + "bbox": [ + 306, + 72, + 545, + 109 + ], + "type": "text", + "content": " represents the known class set. Next, we use information entropy to assess the stability of the known categories during training, which is expressed as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 319, + 118, + 545, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 118, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 319, + 118, + 545, + 150 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {e n t r o p y}} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\mathbb {1} \\left(o _ {i} = 1\\right) \\cdot H \\left(\\frac {1}{\\tau_ {o}} \\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right)\\right), \\tag {9}", + "image_path": "5459e6ffdc96d191c15d00ac8f637668065b9d8c1714c8faec6448c7805f20c5.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "type": "inline_equation", + "content": "\\tau_{o}" + }, + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "type": "text", + "content": " is a temperature, " + }, + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 305, + 159, + 545, + 218 + ], + "type": "text", + "content": " is an entropy regulariser [2] used in Sec. 3.2.2. Additionally, to further enhance the margins between the categories, we replace the vanilla information loss with a Margin-aware Pattern (MAP) [38, 42], and the final LER loss can be formulated as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 307, + 226, + 545, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 226, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 307, + 226, + 545, + 258 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L E R} = - \\frac {1}{B} \\sum_ {i = 1} ^ {B} \\mathbb {1} (o _ {i} = 1) \\cdot H \\left(\\frac {1}{\\tau_ {o}} \\boldsymbol {p} (\\boldsymbol {x} _ {i}), \\frac {1}{\\tau_ {o}} \\boldsymbol {p} (\\boldsymbol {x} _ {i}) - \\Delta_ {j}\\right), \\tag {10}", + "image_path": "6012f479645ea9428ea13b8200aeb38ebccb61e5a2bef3432fa0eea94e5c76ee.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "inline_equation", + "content": "\\Delta_j = \\lambda_{ler}\\log \\left(\\frac{1}{\\tilde{p}_j}\\right)" + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "inline_equation", + "content": "j\\in \\{1,\\dots ,K\\}" + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "inline_equation", + "content": "\\lambda_{ler} = 0.4" + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "inline_equation", + "content": "\\tilde{p}_j" + }, + { + "bbox": [ + 305, + 270, + 545, + 310 + ], + "type": "text", + "content": " is the average model prediction updated at each iteration through an exponential moving average." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "type": "text", + "content": "The total process is divided into three steps: 1) Applying the label mask " + }, + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "type": "text", + "content": " to select samples from unlabeled data; 2) Using the threshold " + }, + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 311, + 545, + 394 + ], + "type": "text", + "content": " to select high-confidence samples from all training data; 3) Identifying high-confidence known samples from all training samples. Furthermore, we provide an intuitive representation of the entire process in the top-right corner of Fig. 2." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 395, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 395, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 305, + 395, + 545, + 442 + ], + "type": "text", + "content": "Fig. 3b compares the quantity of high-confidence known samples across various datasets. Clearly, the numbers increase with the introduction of LER, proving our method with LER retains more knowledge about known classes." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 450, + 516, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 450, + 516, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 450, + 516, + 464 + ], + "type": "text", + "content": "3.4. Dual-views Kullback-Leibler divergence" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": "It's crucial to note that the model might mistakenly identify incorrect samples as known ones when considering two views of the same image for LER. For instance, if " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i'" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " are misaligned, and " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " exceeds the confidence threshold " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " while " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i'" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " falls below it, uncertainty arises about whether the image of the two views is a potential known one. Thus, we might erroneously select " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " or miss " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i'" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " for LER. In other words, we can confidently select both " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i'" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " as known samples only when both " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_i'" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": " exceed the threshold " + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 469, + 545, + 577 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "type": "text", + "content": "In general, an ideal approach is to push the alignment of two view samples " + }, + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i'" + }, + { + "bbox": [ + 305, + 578, + 545, + 636 + ], + "type": "text", + "content": " and both belong to the known or novel sample set. To achieve this, we propose a dual-view alignment technique named Dual-views Kullback-Leibler divergence constraint (DKL)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "content": "Formally, given wo cosine similarity " + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i" + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i^\\prime" + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "content": " from Sec. 3.2.2 of two view samples " + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i" + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\pmb{x}_i^\\prime" + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "content": " in a mini-batch " + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 306, + 637, + 545, + 672 + ], + "type": "text", + "content": ", the DKL can be formulated as:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 325, + 682, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 682, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 325, + 682, + 545, + 715 + ], + "type": "interline_equation", + "content": "D _ {K L} \\left(\\boldsymbol {p} _ {i} \\| \\boldsymbol {p} _ {i} ^ {\\prime}\\right) = \\frac {1}{B / 2} \\sum_ {i = 1} ^ {B / 2} \\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right) \\cdot \\log \\frac {\\boldsymbol {p} \\left(\\boldsymbol {x} _ {i}\\right)}{\\boldsymbol {p} \\left(\\boldsymbol {x} _ {i} ^ {\\prime}\\right)}. \\tag {11}", + "image_path": "612e0fa0d76d0c58f37cd2ae40a2c28e0895f9b3e782344f04ad55795101316a.jpg" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16884" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "In summary, DKL aligns the predictions of two view samples, enhancing the creation of more reliable potential known samples for LER. Finally, the ultimate classification loss can be updated as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 52, + 127, + 287, + 141 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 127, + 287, + 141 + ], + "spans": [ + { + "bbox": [ + 52, + 127, + 287, + 141 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {c l s}} = (1 - \\lambda) \\left(\\mathcal {L} _ {\\mathrm {c l s}} ^ {u} - \\varepsilon H (\\bar {\\boldsymbol {p}}) + D _ {K L} \\left(\\boldsymbol {p} _ {i} \\| \\boldsymbol {p} _ {i} ^ {\\prime}\\right)\\right) + \\lambda \\mathcal {L} _ {\\mathrm {c l s}} ^ {s}. \\tag {12}", + "image_path": "d9e50d2a3a78dadd4ad8ca04c93ed6aed3f6db4b412130802f8d75211a69a5f5.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 148, + 287, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 148, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 148, + 287, + 171 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 148, + 287, + 171 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 47, + 148, + 287, + 171 + ], + "type": "text", + "content": " is a weight factor to control the balance between supervised and unsupervised classification learning." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 171, + 287, + 231 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 231 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 231 + ], + "type": "text", + "content": "By simply integrating the Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL) into SimGCD, we propose a new paragraph named LegoGCD. The overall loss for training our model can be formulated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 239, + 287, + 252 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 239, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 93, + 239, + 287, + 252 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\alpha \\cdot \\left(\\mathcal {L} _ {\\text {r e p}} + \\mathcal {L} _ {\\text {c l s}}\\right) + \\beta \\cdot \\mathcal {L} _ {\\text {L E R}}, \\tag {13}", + "image_path": "008f31ca1d31750865b3b5df15538d298cefe35bfee2990debf492b44f2774f3.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "text", + "content": " is a control factor to assign the weight to remember known classes. Aligning with SimGCD, we set " + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "text", + "content": " to 1 and simultaneously adjust " + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "text", + "content": " (see Tab. 7). Notably, the DKL is plugged into classification loss " + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{cls}" + }, + { + "bbox": [ + 47, + 258, + 287, + 319 + ], + "type": "text", + "content": ". Algorithm 1 in appendix describes one training step of LegoGCD." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 329, + 123, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 329, + 123, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 329, + 123, + 342 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 348, + 164, + 361 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 348, + 164, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 348, + 164, + 361 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "text", + "content": "Dataset. We evaluate the effectiveness of our approach on eight datasets, consistent with SimGCD [39]. These datasets encompass generic image recognition datasets like CIFAR10/100 [15] and ImageNet-100 [33], as well as Semantic Shit [35] datasets, including CUB [37], Stanford Cars [14], and FGVC-Aircraft [21]. Additionally, we include two more challenging datasets: Herbarium 19 [31] and ImageNet-1k [26]. For each dataset, we follow the GCD [36] and SimGCD [39] protocols by sub-sampling " + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "text", + "content": " of known class images to form the labeled set " + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l" + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "text", + "content": " within the training set. The remaining images from known and novel classes constitute the unlabeled data " + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 46, + 366, + 287, + 521 + ], + "type": "text", + "content": ". Tab. 1 provides details of the datasets used in our experiments." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": "Evaluation protocol. During training, we use dataset " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": " combined by " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^l" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^u" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": " to train the models. For evaluation, we use clustering accuracy (ACC) [36, 39] to evaluate the model performance. Specifically, ACC is computed as follows: given the ground-truth label " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "y^{*}" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": " and the model's prediction " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\hat{y}_i" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "ACC = \\frac{1}{M}\\sum_{i=1}^{M}\\mathbb{1}(y_i^* = p(\\hat{y}_i))" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "M = |\\mathcal{D}^u|" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 522, + 287, + 617 + ], + "type": "text", + "content": " is determined using the Hungarian optimal assignment algorithm [16]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 287, + 713 + ], + "type": "text", + "content": "Implementation details. Following [36, 39], we conduct our experiments using ViT-B/16 backbone [6], which was pre-trained with DINO [4], and only fine-tune the last attention block of the backbone for all models. We use the [CLS] token output as the image feature and input for classifier training in SimGCD. Our training regimen includes an initial learning rate of 0.1, decay using a cosine schedule. For a fair comparison, we use a batch size of 128 and" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 105, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 545, + 103 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 103 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 103 + ], + "type": "text", + "content": "Table 1. Overview of the datasets used in our experiments. We list the specific number of labeled and unlabeled images " + }, + { + "bbox": [ + 305, + 71, + 545, + 103 + ], + "type": "inline_equation", + "content": "(\\mathcal{D}^l,\\mathcal{D}^u)" + }, + { + "bbox": [ + 305, + 71, + 545, + 103 + ], + "type": "text", + "content": " and their corresponding class assignments (Old and New)." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 105, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 309, + 105, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 309, + 105, + 545, + 218 + ], + "type": "table", + "html": "
DatasetBalanceLabeled DlUnlabeled Du
ImagesOldImagesNew
CIFAR10 [15]✓12.5k537.5k10
CIFAR100 [15]✓20.0k8030.0k100
ImageNet-100 [33]✓31.9k5095.3k100
CUB [37]✓1.5k1004.5k200
Stanford Cars [14]✓2.0k986.1k196
FGVC-Aircraft [21]✓1.7k505.0k100
Herbarium 19 [31]X8.9k34125.4k683
ImageNet-1K [26]✓321k500960k1000
", + "image_path": "475ed16ecccadb97ff58f3eb076278ee3a4b33be59cb36ebc700ab03d2795f26.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": "train the models for 200 epochs, setting " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\lambda = 0.35" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " in the loss function (see Eq. (5)). Temperature values " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\tau_{u} = 0.07" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\tau_{c} = 1.0" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " are employed in representation learning. As for training the classifier in SimGCD, we follow the same settings, including " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\tau_{s} = 0.1" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " and initial " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\tau_{t} = 0.07" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " which is warmed up to 0.04 with a cosine schedule within the first 30 epochs. In LegoGCD, we set " + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\tau_{o} = 0.05" + }, + { + "bbox": [ + 304, + 239, + 545, + 346 + ], + "type": "text", + "content": " (see Eq. (9)). All experiments are conducted using PyTorch and trained on Nvidia Tesla V100 GPUs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 356, + 471, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 356, + 471, + 369 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 471, + 369 + ], + "type": "text", + "content": "4.2. Comparison with the baselines" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "type": "text", + "content": "We compare our approach with Generalized Category Discovery methods like " + }, + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 374, + 545, + 494 + ], + "type": "text", + "content": "-means [20], ORCA[19], GCD [36], SimGCD [39], and strong baselines derived from Novel Category Discovery, including RS+ [9] and UNO+[7]. For a fair comparison, we reproduce SimGCD (denoted as SimGCD*) using the same random seed (i.e. seed=0) as our method. Tab. 2 shows results on SSB datasets [35] and Herbarium 19 [31], Tab. 3 and Tab. 4 present results on generic recognition datasets, including the challenging ImageNet-1k [26]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": "Overall, our method effectively mitigates catastrophic forgetting and achieves superior performance compared to the GCD and SimGCD baseline, particularly in recognizing \"Old\" categories. Specifically, it outperforms the baseline by " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "3.5\\% / 2.1\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " on CIFAR100 and ImageNet-100 and shows significant improvements in fine-grained evaluations with " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "5.4\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " in CUB and " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " in Stanford Cars. Additionally, it surpasses the baseline by " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "0.4\\% / 0.5\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " on the challenging datasets ImageNet-1k and Herbarium 19. In addressing the forgetting problem, our approach also competes well with SimGCD on \"New\" classes, achieving " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "3.4\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " in Stanford Cars, " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " in CIFAR100, and " + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 304, + 495, + 545, + 638 + ], + "type": "text", + "content": " in ImageNet-100." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 647, + 399, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 399, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 399, + 659 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "In this section, we conduct ablation studies to validate the effectiveness of LER and DKL in LegoGCD. The datasets considered include fine-grained datasets like CUB and Stanford Cars, as well as generic image recognition datasets CI" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "16885" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 61, + 95, + 533, + 251 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 2. Classification results on Semantic Shift Benchmark [35] datasets and Herbarium 19 [31]. Bold represent our results, " + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 47, + 70, + 545, + 93 + ], + "type": "text", + "content": " indicates the margin ahead of the baseline SimGCD, and red signifies improvement in known categories." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 61, + 95, + 533, + 251 + ], + "lines": [ + { + "bbox": [ + 61, + 95, + 533, + 251 + ], + "spans": [ + { + "bbox": [ + 61, + 95, + 533, + 251 + ], + "type": "table", + "html": "
MethodCUBStanford CarsFGVC-AircraftHerbarium 19
AllOldNewAllOldNewAllOldNewAllOldNew
k-means[20]34.338.932.112.810.613.816.014.416.813.012.213.4
RS+[9]33.351.624.228.361.812.126.936.422.227.955.812.8
UNO+[7]35.149.028.135.570.518.640.356.432.228.353.714.7
ORCA[19]35.345.630.223.550.110.722.031.817.120.930.915.5
GCD [36]51.356.648.739.057.629.945.041.146.935.451.027.0
SimGCD [39]60.365.657.753.871.945.054.259.151.844.058.036.4
SimGCD* [39]61.966.559.653.470.645.054.661.451.144.956.938.4
Ours63.871.959.857.375.748.455.061.551.745.157.438.4
Δ1.95.40.23.95.13.40.40.10.60.20.50.0
", + "image_path": "9c349374b5c163a527624fd9a54f99a663027e6165a334415a44c140ff354f59.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 261, + 173, + 380 + ], + "blocks": [ + { + "bbox": [ + 48, + 261, + 173, + 380 + ], + "lines": [ + { + "bbox": [ + 48, + 261, + 173, + 380 + ], + "spans": [ + { + "bbox": [ + 48, + 261, + 173, + 380 + ], + "type": "image", + "image_path": "35871b7c11b0927d18fbc3138815b78b34ef5613b16196f16561d89f1092ecc0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 389, + 546, + 422 + ], + "lines": [ + { + "bbox": [ + 46, + 389, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 546, + 422 + ], + "type": "text", + "content": "Figure 4. Step by step, we integrate LER and DKL into the baseline SimGCD [39]. Initially, the addition of LER increases accuracy in the \"Old\" category while decreasing accuracy in the \"New\" category. Subsequently, the introduction of a Margin-aware Pattern (MAP) widens margins between novel categories, ultimately achieving the best performance when embedding with DKL." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 179, + 261, + 296, + 380 + ], + "blocks": [ + { + "bbox": [ + 179, + 261, + 296, + 380 + ], + "lines": [ + { + "bbox": [ + 179, + 261, + 296, + 380 + ], + "spans": [ + { + "bbox": [ + 179, + 261, + 296, + 380 + ], + "type": "image", + "image_path": "14e055423539b63fd2cf5454bf9030b7eee2289d0f1413028c8aaa064f09b678.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 304, + 261, + 421, + 380 + ], + "blocks": [ + { + "bbox": [ + 304, + 261, + 421, + 380 + ], + "lines": [ + { + "bbox": [ + 304, + 261, + 421, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 261, + 421, + 380 + ], + "type": "image", + "image_path": "9fd546375ed948da3a5664a911d4b82b84f153b2dad5e66238568019219269a0.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 429, + 272, + 545, + 380 + ], + "blocks": [ + { + "bbox": [ + 429, + 272, + 545, + 380 + ], + "lines": [ + { + "bbox": [ + 429, + 272, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 429, + 272, + 545, + 380 + ], + "type": "image", + "image_path": "28040163a6db1c2d23d88d6c9820d1fd5e073eafa53d728216849b8283adcbb0.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 50, + 465, + 287, + 601 + ], + "blocks": [ + { + "bbox": [ + 47, + 442, + 287, + 464 + ], + "lines": [ + { + "bbox": [ + 47, + 442, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 287, + 464 + ], + "type": "text", + "content": "Table 3. Classification results on the generic image recognition datasets, CIFAR10 [15] and CIFAR100 [15]." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 465, + 287, + 601 + ], + "lines": [ + { + "bbox": [ + 50, + 465, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 50, + 465, + 287, + 601 + ], + "type": "table", + "html": "
MethodCIFAR10CIFAR100
AllOldNewAllOldNew
k-means[20]83.685.782.552.052.250.8
RS+[9]46.819.260.558.277.619.3
UNO+[7]68.698.353.869.580.647.2
ORCA[19]81.886.279.669.077.452.0
GCD [36]91.597.988.273.076.266.5
SimGCD [39]97.195.198.180.181.277.8
SimGCD* [39]96.993.898.579.077.981.5
Ours97.194.398.581.881.482.5
Δ0.20.50.02.83.51.0
", + "image_path": "52eb9fd07dad6c64db22a9023485209a2661891af2ec157263d4b4c1cbb1d7a8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 627, + 163, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 163, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 163, + 639 + ], + "type": "text", + "content": "FAR100 and ImageNet-100." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Local Entropy Regularization (LER). We conduct ablation studies on LER as shown in Fig. 4. Firstly, the SimGCD baseline with LER (without Margin-aware Pattern, MAP) notably enhances \"Old\" Categories (see green curves). However, using raw LER alone may impact accuracy in \"New\" classes (see orange curves). This is be" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 465, + 545, + 601 + ], + "blocks": [ + { + "bbox": [ + 306, + 442, + 545, + 464 + ], + "lines": [ + { + "bbox": [ + 306, + 442, + 545, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 545, + 464 + ], + "type": "text", + "content": "Table 4. Classification results on the generic image recognition ImageNet-100 [33] and the challenging ImageNet-1k [26]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 465, + 545, + 601 + ], + "lines": [ + { + "bbox": [ + 309, + 465, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 309, + 465, + 545, + 601 + ], + "type": "table", + "html": "
MethodImageNet-100ImageNet-1k
AllOldNewAllOldNew
k-means[20]72.775.571.3---
RS+[9]37.161.624.8---
UNO+[7]70.395.057.9---
ORCA[19]73.592.663.9---
GCD [36]74.189.866.352.572.542.2
SimGCD [39]83.093.177.957.177.346.9
SimGCD* [39]83.392.478.662.379.153.8
Ours86.394.582.162.479.553.8
Δ3.02.13.50.10.40.0
", + "image_path": "4d1067b40db14fecb993bbb4cbd680e818024c5c802eaf613d2a360310426ef5.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 630, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 546, + 714 + ], + "type": "text", + "content": "cause it primarily encourages the network to remember known classes, consequently influencing the learning of novel ones. To mitigate this, we incorporate MAP (see Eq. (10)) to encourage the network to simultaneously enhance the margins of all classes, particularly novel classes. Finally, the inclusion of MAP in LER leads to improvements in both the \"Old\" and \"New\" categories." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "16886" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 94, + 287, + 188 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 92 + ], + "type": "text", + "content": "Table 5. Ablation study on different combinations of our algorithms on CUB. Bold indicates the best results." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 94, + 287, + 188 + ], + "lines": [ + { + "bbox": [ + 50, + 94, + 287, + 188 + ], + "spans": [ + { + "bbox": [ + 50, + 94, + 287, + 188 + ], + "type": "table", + "html": "
SimGCDLERMAPDKLCUB
AllOld ↑New
✓61.966.559.6
✓✓62.567.360.2
✓✓63.471.059.6
✓✓✓63.772.058.5
✓✓✓✓63.871.959.8
", + "image_path": "b247e4780d68abcb07a1f89103fa42cf399c9644f8a5b5a7c688e8ca6fb429c4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 239, + 287, + 333 + ], + "blocks": [ + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "lines": [ + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "text", + "content": "Table 6. Ablation study on " + }, + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "text", + "content": " was conducted on CUB and CIFAR100. Bold indicates the best results. The underline denotes the selected " + }, + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 47, + 204, + 287, + 237 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 239, + 287, + 333 + ], + "lines": [ + { + "bbox": [ + 50, + 239, + 287, + 333 + ], + "spans": [ + { + "bbox": [ + 50, + 239, + 287, + 333 + ], + "type": "table", + "html": "
αβCUBCIFAR100
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0.061.966.559.679.077.981.5
0.563.069.559.780.880.481.5
1.063.669.760.681.881.482.5
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", + "image_path": "b4e369d2c71a15d6406b129d5659f2b8a1b6d93ce824cd76e469d5b68cf65b22.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": "Dual-views Kullback-Leibler divergence (DKL). DKL is designed to improve the quality of known samples for LER by aligning the predictions of two views from the same image. The results in Tab. 5 indicate that incorporating DKL into raw SimGCD led to improvements in both \"Old\" and \"New\" category accuracies by " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "inline_equation", + "content": "0.6\\%" + }, + { + "bbox": [ + 46, + 356, + 287, + 499 + ], + "type": "text", + "content": ", respectively (67.3% vs. 66.5%, 60.2% vs. 59.6%). This success proves beneficial for self-distillation learning in SimGCD. Additionally, from Fig. 4 and Tab. 5, we can see that our method becomes more effective with DKL, particularly in \"Old\" classes, while maintaining performance on \"New\" classes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": "Different " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": ". The coefficient " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": " is crucial for balancing knowledge preservation of known classes and facilitating effective learning of novel classes. As depicted in Tab. 6 with " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\alpha = 1.0" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": " aligned to SimGCD, accuracy on \"Old\" categories consistently surpasses SimGCD (" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\beta = 0.0" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": ") across different " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": " values. Optimal equilibrium is achieved with " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\beta = 2.0" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": " in CUB and " + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\beta = 1.0" + }, + { + "bbox": [ + 46, + 504, + 287, + 589 + ], + "type": "text", + "content": " in CIFAR100." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": "Different confidence threshold " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": ". We compare accuracy with different " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": " in Tab. 7. Results show varying responses across datasets. In Stanford Cars, \"Old\" accuracy initially increases, then slightly decreases, while \"New\" accuracy decreases but remains above SimGCD at " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "45.5\\%" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": ". In contrast, in CIFAR100, \"Old\" accuracy decreases but consistently surpasses SimGCD at " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "77.9\\%" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": ". Our goal is to prioritize high \"Old\" accuracy and ensure \"New\" equals or exceeds SimGCD. Therefore, we choose " + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\delta = 0.85" + }, + { + "bbox": [ + 46, + 594, + 288, + 713 + ], + "type": "text", + "content": " for both Stanford Cars and CIFAR100." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 309, + 105, + 545, + 208 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "type": "text", + "content": "Table 7. Ablation study on confidence threshold " + }, + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 70, + 545, + 103 + ], + "type": "text", + "content": " was conducted on Stanford Cars and CIFAR100. Bold indicates the best results. The underline denotes the selected threshold." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 105, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 309, + 105, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 309, + 105, + 545, + 208 + ], + "type": "table", + "html": "
δStanford CarsCIFAR100
AllOld ↑NewAllOld ↓New
0.7055.366.849.880.383.374.3
0.7555.872.347.980.983.376.3
0.8056.573.048.581.382.778.5
0.8557.375.748.481.881.482.5
0.9056.475.347.379.080.576.0
", + "image_path": "caa71524a20c8f92fbc9d92b8141cdacfa47c565e1f734e2c55068e10bd3d704.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 219, + 379, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 219, + 379, + 232 + ], + "spans": [ + { + "bbox": [ + 306, + 219, + 379, + 232 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 239, + 545, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 443 + ], + "type": "text", + "content": "In this paper, we propose LegoGCD, a novel approach to mitigate the issue of catastrophic forgetting in known categories. The core of our design is to preserve knowledge of known classes while maintaining the accuracy of novel classes. To achieve this, we develop two techniques: Local Entropy Regularization (LER) and Dual-views Kullback-Leibler divergence constraint (DKL). LER explicitly regularizes high-confidence potential known class samples to retain the knowledge of known categories. To ensure the accurate selection of these samples, we employ DKL to align the distribution of two view samples for LER. Both LER and DKL can be seamlessly integrated into baseline SimGCD resembling Lego blocks, without introducing new parameters or altering the internal network structure. Extensive experiments demonstrate that LegoGCD significantly enhances performance in known classes, effectively addressing the catastrophic forgetting problem." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 454, + 421, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 421, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 421, + 468 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 474, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 582 + ], + "type": "text", + "content": "This research is supported by the National Key R&D Program of China (2021YFB0301300), and also received supported from programs: the Major Program of Guangdong Basic and Applied Research (2019B030302002), the Key-Area Research and Development Program of Guangdong Province (2021B0101400002), the Major Key Project of PCL PCL2021A13 and Peng Cheng Cloud-Brain, and the Fundamental Research Funds for the Central Universities, Sun Yat-sen University (23xkjc016)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 594, + 365, + 605 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 365, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 365, + 605 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 310, + 613, + 547, + 714 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 310, + 613, + 547, + 667 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 613, + 547, + 667 + ], + "spans": [ + { + "bbox": [ + 310, + 613, + 547, + 667 + ], + "type": "text", + "content": "[1] Wenbin An, Feng Tian, Qinghua Zheng, Wei Ding, QianYing Wang, and Ping Chen. 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In Proceedings of IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 8697-8710, 2018. 1" + } + ] + } + ], + "index": 25 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "16889" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_content_list.json b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7dcff622bac8049e5e10aa459b250dfe36b4482e --- /dev/null +++ b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_content_list.json @@ -0,0 +1,1387 @@ +[ + { + "type": "text", + "text": "SonicVisionLM: Playing Sound with Vision Language Models", + "text_level": 1, + "bbox": [ + 173, + 130, + 795, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhifeng Xie $^{1,2}$ , Shengye Yu $^{1}$ , Qile He $^{1}$ , Mengtian Li $^{1,2\\dagger}$ $^{1}$ Shanghai University", + "bbox": [ + 264, + 179, + 709, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Shanghai Engineering Research Center of Motion Picture Special Effects", + "bbox": [ + 191, + 217, + 777, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhifeng_xie,yussisy,shu_hql,mtli}@shu.edu.cn", + "bbox": [ + 289, + 236, + 679, + 251 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There has been a growing interest in the task of generating sound for silent videos, primarily because of its practicality in streamlining video post-production. However, existing methods for video-sound generation attempt to directly create sound from visual representations, which can be challenging due to the difficulty of aligning visual representations with audio representations. In this paper, we present SonicVisionLM, a novel framework aimed at generating a wide range of sound effects by leveraging vision-language models(VLMs). Instead of generating audio directly from video, we use the capabilities of powerful VLMs. When provided with a silent video, our approach first identifies events within the video using a VLM to suggest possible sounds that match the video content. This shift in approach transforms the challenging task of aligning image and audio into more well-studied sub-problems of aligning image-to-text and text-to-audio through the popular diffusion models. To improve the quality of audio recommendations with LLMs, we have collected an extensive dataset that maps text descriptions to specific sound effects and developed a time-controlled audio adapter. Our approach surpasses current state-of-the-art methods for converting video to audio, enhancing synchronization with the visuals, and improving alignment between audio and video components. Project page: https://yusiissy.github.io/SonicVisionLM.github.io/", + "bbox": [ + 76, + 318, + 473, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 734, + 209, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The sound effects artists work with various types of sounds, including those visible on-screen (like footsteps or a car passing) and those audible but not visible (like background noises and heartbeats can enhance the video's authenticity and narrative). On-screen sounds match what is happening in the video, while off-screen sounds establish the ambience and provide additional information. Creating soundtracks for videos is a vital aspect of video produc", + "bbox": [ + 75, + 753, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4bbd06805daadfdfae81d8e85519c1d3b0b7eee92413b32129e7f8e5f6db61d1.jpg", + "image_caption": [ + "Figure 1. A model implements the automatic detection of on-screen sound generation and accepts the user's editing of text and time in the off-screen section. On-screen sound refers to audio that originates from visible actions within the video frame. Off-screen sound is not directly observable on the screen." + ], + "image_footnote": [], + "bbox": [ + 501, + 284, + 893, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion, but it can be labour-intensive for artists. Therefore, the video-sound generation task has gained notable attention.", + "bbox": [ + 498, + 537, + 890, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although the recent approaches have made great efforts, the video-sound generation task is still challenging. For onscreen sounds, achieving semantic relevance and maintaining temporal synchronization continues to be a complex issue. It is hard to edit off-screen sounds. Current methods [14, 25, 32] primarily focus on the visual content to generate the corresponding sound, a subset of these methods [7, 9] considers editability. Nonetheless, the alignment between video and audio features is tricky, leading to deficiencies including 1) incorrect sound meanings and mismatched timing, 2) monotonous sound effects, and a lack of complex scenarios. Both lead to unsatisfactory results in the videosound generation task.", + "bbox": [ + 496, + 568, + 892, + 763 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a novel framework named SonicVisionLM to solve the above deficiency, as shown in Fig. 1. SonicVisionLM is proposed by introducing three key components: video-to-text, text-based interaction, and text-to-audio generation. First, the video-to-text component focuses on generating sound effects for on-screen events. This step uses a VLM to identify appropriate sound descriptions from the input silent video. Following this, a timestamp detection network is trained to extract specific temporal information", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26866", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/00caee69593690197395fbfbf327a758c565f0ff7f84769475aba3a4865645d5.jpg", + "image_caption": [ + "Figure 2. SonicVisionLM's framework. SonicVisionLM presents a composite framework designed to automatically recognize on-screen sounds coupled with a user-interactive module for editing off-screen sounds. The blue dashed box and arrows in the figure represent the visual automation workflow: First, a silent video goes into the system to determine the occurring events (text) and their timing (time). Then, this information conditions the generation of sounds matching the screen. The purple dotted box and arrows show how users can modify or add off-screen sounds." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 893, + 372 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "from the video. A key innovation within this framework is the design of a time-conditioned embedding, which is utilized to guide an audio adapter. After that, the text-based interaction component allows users to change the text and timestamps from a previous video-to-text component or to input new corresponding text-timestamp pairs for personalized sound design. Finally, the text-to-audio generation component accepts the text and timestamp conditions and inputs them into the LDM and adapter to generate diverse, time-synchronized, and controllable sounds. Simultaneously, We collect a text-to-single-sound dataset, named CondPromptBank, for sound effects caption and timing cues, comprising over ten thousand data points, covering 23 categories. The main contributions of this work are:", + "bbox": [ + 75, + 452, + 472, + 664 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel framework called SonicVisionLM and collect a dataset CondPromptBank specifically for training a time-controllable adapter. It ensures the generated sound aligns perfectly with our text input and maintains precise timing control.", + "- We introduce three pioneering components: video-to-text, text-based interaction, and text-to-audio generation. This unique combination facilitates the automatic recognition of on-screen sounds while enabling user customization of off-screen sounds.", + "- The proposed framework achieves state-of-the-art results on conditional and unconditional video-sound generation tasks. The conditional task can be noticeably enhanced in all metrics. (IoU: $22.4 \\rightarrow 39.7$ )" + ], + "bbox": [ + 76, + 686, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 450, + 640, + 467 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Audio Generation can be broadly classified into two categories. The Text-to-Audio Generation field includes Text-to-Speech (TTS) and Text-to-Music (TTM). Leading TTS models, such as FastSpeech2 [29] and NaturalSpeech [33], now produce speech virtually indistinguishable from human speech. In TTM, MusicLM [1], Noise2Music [12], MusicGen [6] and MeLoDy [21] are aimed to generate music segments from text, bringing innovation to music composition and synthesis. Models like AudioGen [19], AudioLDM [24], Tango [10], and Make-an-Audio [13] focuses on universal audio generation modeling. AudioGen [19] treats audio generation as a conditional language modelling task, while the other three models employ latent diffusion methods to accomplish sound generation. Current methods use datasets including sound effects, voices, and music, but practical applications use these elements separately. As the textual descriptions of time are subjective, videos are more intuitive and precise, so V2A requires more accurate semantic features and time control than T2A. Therefore, we have created a text-to-single-sound dataset called CondPromptBank with detailed semantic segmentation and temporal annotations that help models produce high-quality sound effects for videos. In Video-to-Audio Generation task, SpecVQGAN [14] utilizes a Transformer-based autoregressive model, drawing on ResNet50 or RGB+Flow features to generate sound. Im2Wav [32] uses a dual-transformer model conditioned on CLIP features for sound generation. CondFoleyGen [9] and VARIETYSOUND [7]", + "bbox": [ + 496, + 477, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26867", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "introduce tasks for controllable timbre generation. Diff-foley [25] uses contrastive audio-visual pretraining to align audio and visual features. ClipSonic [8] learns the text-audio correspondence by leveraging the audio-visual correspondences in videos and the multi-modal representation learned by pre-trained VLMs. However, the sounds generated by these methods often suffer from poor audio-visual synchronization, noticeable noises, and lack of editability. Unlike the works above, our model ensures audio-visual synchronization, enriches diversity, and supports personalized user edits. Our model provides a more comprehensive sound solution for video production.", + "bbox": [ + 75, + 90, + 472, + 271 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Model has been utilized for generating both mel-spectrogram generation [4, 28], and waveform generation [3, 20, 22]. However, their iterative generation process can be slow for high-dimensional data. Models such as AudioLDM [24], Make-An-Audio [13], and Tango [10] have successfully trained diffusion models within a continuous latent space. Nevertheless, achieving satisfactory results in controlling LDM for audio generation tasks remains challenging. This paper aims to introduce time control to ensure audio-visual synchronization.", + "bbox": [ + 75, + 272, + 472, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision Language Models like ChatGPT-4, which demonstrated advanced multi-modal abilities and inspired vision-language LLMs. Vision-LLM [36] and LLaVA [34] focus on aligning image inputs with large language models Vicuna[5] exhibit similar multi-modal capabilities. Recent developments in this field include MiniGPT-v2 [2]. Kosmos-2 [27] demonstrates multi-modal LLMs' ability to perform visual grounding. In this paper, we first introduce the VLMs to the audio generation task.", + "bbox": [ + 75, + 422, + 472, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 575, + 171, + 590 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 599, + 187, + 616 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we introduce the framework of SonicVisionLM, as shown in Fig. 2. Before delving into the specific design details, we first briefly overview the preliminary knowledge (Sec. 3.2). Then, we introduce the Visual-to-Audio Event Detection Module (Sec. 3.3), which obtains textual descriptions of on-screen sounds through VLMs. Subsequently, we present the Sound Event Timestamp Detection Module (Sec. 3.4), designed to accurately detect the timing information through network architecture. Finally, we introduce the proposed time-controllable adapter as an extension of the audio diffusion model (Sec. 3.5), enabling the generation of multiple sounds that are semantically coherent and temporally aligned.", + "bbox": [ + 75, + 623, + 472, + 821 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 830, + 218, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Audio Diffusion Model. The text-prompt encoder encodes the input description $\\tau \\in R^{L\\times d_t}$ of the sound, where $L$ is the token count and $d_{t}$ and is the token-embedding size.", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The latent diffusion model (LDM) is used to construct the audio prior $z_0$ with the guidance of text encoding $\\tau$ . This essentially reduces to approximating the true prior $q(z_0 \\mid \\tau)$ with parameterized $p(z_0 \\mid \\tau)$ . LDM can achieve the above through forward and reverse diffusion processes. The forward diffusion is a Markov chain of Gaussian distributions with scheduled noise parameters $0 < \\beta_1 < \\beta_2 < \\dots < \\beta_N < 1$ to sample noisier versions of $z_0$ , where $N$ is the number of forward diffusion steps. For each step $n$ , we define $\\alpha_n = 1 - \\beta_n$ , and calculate the cumulative product $\\bar{\\alpha}_n = \\prod_{i=1}^n \\alpha_n$ . The diffusion equations are described as follows:", + "bbox": [ + 496, + 90, + 893, + 271 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(z _ {n} \\mid z _ {n - 1}\\right) = \\mathcal {N} \\left(\\sqrt {1 - \\beta_ {n}} z _ {n - 1}, \\beta_ {n} \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 272, + 890, + 299 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(z _ {n} \\mid z _ {0}\\right) = \\mathcal {N} \\left(\\sqrt {\\bar {\\alpha} _ {n}} z _ {0}, \\left(1 - \\bar {\\alpha} _ {n}\\right) \\mathbf {I}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 304, + 890, + 323 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the noise term $\\epsilon$ and the final step of the forward process yields $z_{N}$ follow a Gaussian distribution, specifically $\\epsilon ,z_{N}\\sim \\mathcal{N}(0,I)$ . The reverse process denoises and reconstructs $z_{0}$ through text-guided noise estimation $(\\hat{\\epsilon}_{\\theta})$ using following loss function:", + "bbox": [ + 496, + 328, + 893, + 404 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {D M} = \\sum_ {n = 1} ^ {N} \\gamma_ {n} \\mathbb {E} _ {\\epsilon_ {n} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}), z _ {0}} \\left\\| \\epsilon_ {n} - \\hat {\\epsilon} _ {\\theta} ^ {(n)} (z _ {n}, \\tau) \\right\\| _ {2} ^ {2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 407, + 890, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After training LDM, we generate audio latent by sampling through the reverse process with $z_{N} \\sim \\mathcal{N}(0,I)$ , conditioned on the given textual representation $\\tau$ . Its reverse dynamics are shown below:", + "bbox": [ + 496, + 459, + 893, + 517 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\theta} \\left(z _ {n - 1} \\mid z _ {n}, \\tau\\right) = \\mathcal {N} \\left(\\mu_ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right), \\tilde {\\beta} ^ {(n)}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 517, + 890, + 542 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right) = \\frac {1}{\\sqrt {\\alpha_ {n}}} \\left[ z _ {n} - \\frac {1 - \\alpha_ {n}}{\\sqrt {1 - \\bar {\\alpha} _ {n}}} \\hat {\\epsilon} _ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right) \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 556, + 890, + 592 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\beta} ^ {(n)} = \\frac {1 - \\bar {\\alpha} _ {n - 1}}{1 - \\bar {\\alpha} _ {n}} \\beta_ {n}. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 597, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The noise estimation $(\\hat{\\epsilon}_{\\theta})$ is parameterized with U-Net framework [30] with a cross-attention component to include the text guidance $\\tau$ .", + "bbox": [ + 496, + 633, + 893, + 678 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After that, the decoder of audio VAE [18] constructs a mel-spectrogram feature from the latent audio representation $\\hat{z}_0$ . This mel-spectrogram feature is conveyed to a vocoder to generate the final audio.", + "bbox": [ + 496, + 679, + 893, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Visual-to-Audio Event Understanding Module", + "text_level": 1, + "bbox": [ + 498, + 744, + 890, + 761 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The diversity of sound is influenced by various factors such as its source, actions, the environment, and more. At the same time, these factors are often included in the description of visual images. Inspired by the widespread use of VLMs [23, 37, 39], we chose MiniGPT-v2 [2] to process visual information and generate descriptions of sounds. Recognizing that MiniGPT-v2 was initially developed for single-image understanding and its limitations in conveying dynamic information, we have adapted the", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26868", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LLaMA-2 [34] conversation template design to suit a multimodal instructional framework. To not miss sound events, we encoded four random video frames with time-sensitive prompts (temporal cues):", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": "First, >$ ImageFeature $>>$ Img>. Then, >$ ImageFeature $>>$ Img>. After that, >$ ImageFeature $>>$ Img>. Finally, >$ ImageFeature $>>$ Img>. [Task Identifier] Instruction", + "guess_lang": "erlang", + "bbox": [ + 73, + 154, + 472, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Sound Event Timestamp Detection Module", + "text_level": 1, + "bbox": [ + 76, + 236, + 444, + 252 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In practice, sound artists need to manually determine the point in time when a sound event starts and ends and then adjust the appropriate sound effect to the correct position. This judgment is usually based on current visual information. To simplify the process, we use the sound event timestamp detection module to detect the timestamp of the sound event in the video inspired by the CondFoleyGen [9]. Instead of using a hand-crafted approach to transfer sounds from the conditional audio, We use a ResNet(2+1)-D18 [35] visual network to capture timestamps as time-conditional inputs to the LDM, trained on paired video and timestamp.", + "bbox": [ + 75, + 256, + 468, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The workflow begins with feeding a sequence of silent video frames $V_{f}$ into the detection network. The network then outputs a binary vector $V_{ct}$ representing predictions for each frame, derived from a fully connected layer post-pooling. The ground truth $V_{ct}$ is obtained: Function $P$ detects audio $a$ in each frame, applying a threshold $x$ to reduce noise effects. Sounds within 0.02s across consecutive frames are considered a single event. This method identifies the start $x_{start}$ and end points $x_{end}$ of sound segments, as delineated in Eq. 7. Based on timestamps, we construct $T_{ct}$ , as depicted in Eq. 8, where 1 indicates the presence of sound, and 0 indicates the absence. The process equations are as follows:", + "bbox": [ + 75, + 422, + 468, + 617 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {\\text {s t a r t}}, x _ {\\text {e n d}} = P \\left(a _ {c}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 618, + 467, + 632 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nT _ {c t} = \\left\\{ \\begin{array}{l l} 1, i f t i n [ x _ {\\text {s t a r t}}, x _ {\\text {e n d}} ], \\\\ 0, e l s e. \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 633, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, $T_{ct}$ is adjusted to correspond with the video frames' duration, represented as $V_{ct}$ . We employ binary cross-entropy loss to penalize inaccuracies in time prediction. Given that an input video may contain multiple sound events, each sound event's weights are based on its duration relative to the total sound duration in the video. The binary vector $T_{ct}$ serves as input for the Time-controllable Latent Diffusion Model. The whole process and network structure are shown in Fig. 3.", + "bbox": [ + 75, + 674, + 468, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Time-controllable Latent Diffusion Model", + "text_level": 1, + "bbox": [ + 76, + 816, + 433, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our experimentation, we observed that the results generated were semantically inaccurate and temporally unsynchronized. This issue often arose when utilizing audio-visual datasets to train end-to-end models, limiting the", + "bbox": [ + 75, + 840, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9aa7556e896714aabe96004f88cf17ba553d548f048d5ebdb1acbbb4f130c9db.jpg", + "image_caption": [ + "Figure 3. Sound Event Timestamp Detection Module. The network analyzes the video's features to output a binary vector corresponding to the video's frame count. Within this vector, sections marked in white (value of 1) mean sound presence, and those in black (value of 0) indicate sound absence." + ], + "image_footnote": [], + "bbox": [ + 514, + 88, + 880, + 251 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "task's practical application. We attribute these shortcomings to the complexity of the sound sources and the poor audio quality of the audio-visual dataset used for training. To address this, we use text to bridge audio and video and then introduce time control in the T2A generation model. In the visual domain, many works are based on the ControlNet [40] architecture, which can finer control the generation of images or videos by manipulating the input image conditions of neural network blocks. However, unlike the visual domain's inherent intuitiveness, audio features exhibit temporal continuity and are inherently more complex and abstract. Thus, selecting appropriate audio features to guide the generation process poses a greater challenge.", + "bbox": [ + 496, + 342, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this paper, we propose a embedding called Audio Time-condition Embedding, denote as $A_{ct}$ , which is constructed through the following procedure: During the training phase, the adapter extracted Mel-spectrogram features from audio waveform $a$ and then normalized it, denoted as $a_{mel} = mel(a)$ . For $a_{c} = \\max (mel(a), T_{ct})$ , we then initialize $a_{c}$ to match $a_{mel}$ 's dimensions but with zero values, then fill $a_{c}$ 's Mel channels with the maximum values based on the corresponding frames where $T_{ct}$ equals 1. Finally, $A_{ct}$ is derived by encoding the embedding of $a_{c}$ via the encoder $E_{a}$ , and described as follows:", + "bbox": [ + 498, + 539, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nA _ {c t} = E _ {a} \\left(\\max \\left(\\operatorname {m e l} \\left(a _ {c}\\right), T _ {c t}\\right)\\right). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 708, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by ControlNet [40], we have developed a network architecture named Time-controllable Adapter. Then, we integrate the audio time-condition embedding $A_{ct}$ with the text embedding $\\tau$ and target audio embedding into the neural network block. This integration facilitates joint training for the time-controllable adapter. $A_{ct}$ is fed solely into the adapter, while text embedding $\\tau$ inputs into both Tango and the adapter.", + "bbox": [ + 496, + 734, + 890, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Tango's denoising model, akin to UNet, includes encoder $F$ , middle block $M$ , and decoder $G$ . $F$ and $G$ have 12 corresponding blocks. Tango's outputs of the encoder's", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26869", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$i - th$ block and decoder's $j - th$ block are $f_{i}$ and $g_{j}$ , with $m$ for the single middle block. The adapter mimics Tango's encoder and middle layers as $F'$ and $M'$ . Adapter's outputs, like $f_{i}'$ and $m'$ , are marked with $(')$ . Following this, the output of the time-controllable adapter is concatenated with the output of the corresponding decoder block during the decoding process. For example, $f_{1}$ from the 1st encoder layer adds to $g_{12}$ of the decoder, making $i + j = 13$ . To achieve it, we ensure that all Tango's elements are kept frozen while modifying the input of the $i - th$ block of the decoder as:", + "bbox": [ + 75, + 90, + 472, + 243 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\text {C o n c a t} \\left(m + m ^ {\\prime}, f _ {j} + z e r o \\left(f _ {j} ^ {\\prime}\\right)\\right) i = 1, j = 1 2. \\\\ \\text {C o n c a t} \\left(g _ {i - 1}, f _ {j} + z e r o \\left(f _ {j} ^ {\\prime}\\right)\\right) 2 \\leqslant i \\leqslant 1 2, i + j = 1 3. \\end{array} \\right. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 253, + 468, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "zero(\\cdot) is one zero convolutional layer, facilitating trainable and fixed neural network block connections. Its weights evolve from zero to optimized values during training. This approach not only retains the Tango's capability for generating audio, trained on billions of audio-text pairs, but also enables the model to comprehend the guidance provided by the time control embedding, resulting in temporally controllable outcomes.", + "bbox": [ + 75, + 309, + 468, + 430 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/def8aa30eabec00c627e46503ee9699789aea175fb55e8afebda23ef7e6592fa.jpg", + "table_caption": [ + "Table 1. Distribution of CondPromptBank Categories" + ], + "table_footnote": [], + "table_body": "
Category%Category%Category%
Household Daily14.11Transportation Vehicles10.42Impacts Crashes10.10
Foley8.24Human Elements7.77Industrial6.58
Weapons War5.83Cartoon Comical4.90Sports4.43
Animals Insects4.04Instruments3.68Water Liquid3.27
Technology2.70Horror2.41Emergency2.20
Public Places1.87Sound Design Effects1.69Doors Windows1.56
Fire Explosions1.49Nature Weather1.02Leisure0.84
Multimedia0.47Bells0.37
", + "bbox": [ + 80, + 450, + 465, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 550, + 209, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 76, + 575, + 269, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. Since Tango's training datasets include varied audio types like speech, sound effects, and music, it tends to produce mixed audio outputs. Our task requires distinct handling of these audio types, ensuring each sound event is separate. To meet our specific needs, we developed CondPromptBank, a high-quality dataset of single sound effects crafted for training time-controlled adapters. This dataset consists of 10,276 individual data entries, each with a sound effect, title, and start/end timestamps. Each sound is typically 10 seconds or shorter, sourced from freely available sound effect libraries and websites. During the collection, we focused on 23 common categories of sound effects and manually filtered out low-quality data with noise and mixed sources. The category distribution shows Tab. 1. To enhance the textual descriptions with precise details, we further annotated the sound effect text labels with fine-grained information based on sound characteristics. Now, each label not only identifies the audio source but also describes the associated actions in detail. We believe the division into single audio sources is crucial, as videos provide a more concrete", + "bbox": [ + 75, + 598, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "expression of content than text, thus requiring more precise sound representation.", + "bbox": [ + 496, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. To train our complete model, we first train the adapter on CondPromtBank, then train the timestamps detection net on Greatest Hits [26] and Countix-AV dataset [41]. We trained the adapter for approximately 200 epochs with a batch size 32 and a learning rate of $3.0 \\times 10^{-5}$ using Adam [17]. Our model has two versions: small and full. The difference between them is the version of pre-trained parameters used for Tango. We trained the timestamps detection net for 70 epochs with a batch size of 24 and a learning rate of $1.0 \\times 10^{-5}$ . The training of the adapter takes approximately five days, and the training of the timestamps detection network requires approximately one day using one NVIDIA A6000 GPU.", + "bbox": [ + 496, + 122, + 893, + 318 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Conditional Generation Task Results", + "text_level": 1, + "bbox": [ + 498, + 330, + 820, + 345 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We tested our model using the Greatest Hits [26] dataset, which has 977 videos of drumsticks interacting with different objects, lasting 11 hours. This dataset is divided into two types of actions and 17 types of materials. This detailed categorization helps check if our model can change sound types based on these details but still match the target action. We used the same test settings as CondFoleyGen [9] and compared our results with theirs.", + "bbox": [ + 496, + 354, + 890, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. For the conditional generation task, we use the following five objective metrics to evaluate the performance of the model: CLAP-top, Onset Acc [9], Onset AP [9], Time Acc, and IoU.", + "bbox": [ + 496, + 476, + 890, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Quantitative Results. SonicVisionLM-full demonstrates superior performance over CondFoleyGen across all metrics, as seen in Tab. 2. It achieves leading scores of $36.8\\%$ and $42.8\\%$ on CLAP-top versions, exceeding any CondFoleyGen model by more than $20\\%$ . This result suggests that it is better at matching sounds to text prompts. Our model significantly surpasses CondFoleyGen in audio-visual synchronization, evidenced by an $11\\%$ improvement in Onset AP and a $16\\%$ rise in IoU. Moreover, we see a $6\\%$ enhancement in onset accuracy and an $8.3\\%$ increase in timing precision. These advancements illustrate our model's outstanding accuracy in sound event detection and its effectiveness in synchronizing generated sounds with the input video. We think CondFoleyGen relies on the audio-visual synchronization module [15] to improve time accuracy, requiring many samples to re-ranking the sounds. In contrast, our model gets higher synchronization during the generation process with fewer samples.", + "bbox": [ + 496, + 537, + 893, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Qualitative Results. As shown in Fig. 4 (row 4, 6, 7), we compare the timestamped positional distance to the target sound. Our results closely match the target sound, demonstrating a high degree of accuracy. However, CondFoleyGen often produces results with the wrong number of sounds and with a large difference in the positional distance.", + "bbox": [ + 496, + 810, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26870", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/019b1814d7c9fe01d4aa233d0e452693c90e085f412473c419cca9d2e67c36a4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCLAP - topgeneral↑CLAP - topunfused↑Onset Acc ↑Onset AP↑Time Acc↑IoU↑
CondFoleyGen(old)* [9]17.315.621.667.035.523.3
CondFoleyGen(new) * [9]16.313.619.268.637.422.4
Ours-small29.628.019.477.0327.835.6
Ours-full36.842.827.678.143.839.7
", + "bbox": [ + 78, + 88, + 898, + 167 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Conditional Generation Task Quantitative Results. CLAP-top metric evaluates a model's ability to control sound content. It calculates the percentage of times the sound samples generated by all models ranked in the top 1 according to the CLAP ranking, divided by the total number of samples. We used two versions of the CLAP models for evaluation: $CLAP_{general}$ and $CLAP_{unfused}$ . Onset Acc and Time Acc are both metrics based on the number of sound occurrences, with Onset Acc focusing on the onset count and Time Acc on the count of time intervals. We measure the average accuracy of predicting onsets within 0.1s of ground truth to assess the timing of generated onsets. IoU is calculated by computing the intersection and union of these vectors. These metrics collectively allow us to comprehensively evaluate the accuracy of the generated sounds in terms of both timing and content. The variant \"old\" corresponds to the prior codebook, while variant \"new\" matches the updated codebook. The old model was trained on 192-width spectrograms, and the new one was trained on 2s waveforms. \\*\\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. The six metrics are all measured in percentage.", + "bbox": [ + 75, + 175, + 893, + 316 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3081aef1559e8b0e08d194c805a3f92bba882fa2651c733f7c6e52369a57db11.jpg", + "image_caption": [ + "Figure 4. Conditional Generation Task Qualitative Results. The red dashed boxes are the conditional audio inputs and generated results for CondFoleyGen, and the blue dashed boxes are the conditional text inputs and results corresponding to SonicVisionLM." + ], + "image_footnote": [], + "bbox": [ + 78, + 321, + 890, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This indicates that our model has a higher visual-audio synchronization than CondFoleyGen. As shown in Fig. 4 (column 3, 7), we compare the sound shape to the conditional sound. Even though our model has not learned any timbre on the Greatest Hits dataset, our results are still very similar to the conditional sound. As shown in Fig. 4 (column 1, 7), The mel-spectrograms of the CondFoleyGen results do not produce sounds that are similar to, and sometimes blurred.", + "bbox": [ + 75, + 704, + 470, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Unconditional Generation", + "text_level": 1, + "bbox": [ + 76, + 844, + 313, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To evaluate the task of unconditional sound generation, considering that our LDM has not been trained on", + "bbox": [ + 76, + 869, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "audio-visual datasets, we have chosen to perform quantitative evaluation and qualitative evaluation on two datasets: Greatest Hits [26] and CountixAV [41], which are zero-shot tasks for all models. We use two state-of-the-art V2A models as baselines: SpecVQGAN [14] and DIFF-FOLEY [25].", + "bbox": [ + 496, + 704, + 892, + 780 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics. For objective evaluation, we have employed three metrics as [14, 25]: Inception Score (IS) [31], Frechet Distance (FID) [11], and Mean KL Divergence (MKL) [14]. For subjective evaluation, as the [9], we conduct user evaluations for the three critical components: overall audio quality (OVL), alignment with the input video (REL), and time synchronization (Time-sync).", + "bbox": [ + 496, + 794, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26871", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/080c0376050ac049141d085e03a36fe16514c64b42a4cddfe0d42be13bfe0b3f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Metric
Dataset MethodGreatest HitsCountix-AV
MKL↓FID ↓IS↑IoU↑MKL↓FID ↓IS↑IoU ↑
\\(SpecVQGAN^* [14]\\)6.8082.42.1725.87.3934.15.334.9
DIFF-FOLEY†[25]5.6820.03.8422.04.915.95.231.3
Ours-small6.4631.93.8836.610.021.715.137.5
Ours-full4.6724.93.2639.59.7119.712.742
", + "bbox": [ + 78, + 89, + 883, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/75e5efff9a493a163ecfccd6effd1147605f9261dd7f290efe31ddd6017d64c3.jpg", + "image_caption": [ + "Figure 5. Unconditional Generation Task Qualitative Results. The left example is from CountixAV, and the right one is from Greatest Hits. We're comparing them side by side. The dashed box highlights examples of both good and bad results we generated." + ], + "image_footnote": [], + "bbox": [ + 81, + 270, + 890, + 513 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d3260d9d2e3bf4f8b14933c88947d4886524a476a4f7b13ab77223826a35772c.jpg", + "table_caption": [ + "Table 3. Unconditional Sound Generation Quantitative Results. IS assesses the quality and diversity of generated samples, FID measures distribution-level similarity, and MKL measures paired sample-level similarity. \\*\\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. \\*\\* denotes that data is obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage." + ], + "table_footnote": [], + "table_body": "
MethodOVL↑REL↑Time-sync ↑
SpecVQGAN* [14]372531
DIFF-FOLEY† [25]486458
Ours756987
", + "bbox": [ + 78, + 563, + 468, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Subjective Results. Following [9], we invited the 300 English-proficient evaluators to rate 30 randomly selected audio samples from three perspectives: OVL, REL, and Time-sync. Scores were averaged on a 1-100 scale. “**” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. “†” denotes data obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance.", + "bbox": [ + 75, + 642, + 468, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Results. In our experiments, the choice of vocoder significantly influenced the FID metric. We upgraded from DIFF-FOLEY's weak Griffin-Lim vocoder to the superior MelGAN to ensure fairness. Despite our model using 64 Mel filters compared to MelGAN's 80, our performance on the Greatest Hits dataset excels in MKL, IS, and IoU metrics, as shown in Tab. 3. This underscores our model's precise time control and high-quality sound generation, demonstrating its exceptional capability to produce", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sounds that align closely with the ground truth. In the CountixAV dataset, SonicVisionLM-small outperforms baselines by nearly 10 points in the IS metric, highlighting its exceptional sound quality. Despite slightly lower MKL and FID scores compared to baselines, we do not view this as a drawback. Unlike the Greatest Hits dataset, which was recorded in high quality with specialized recording equipment, the CountixAV dataset is sourced from diverse YouTube videos. It often includes sounds marred by low-quality background noise or mixed sound sources, especially human vocals. MKL and FID metrics emphasize similarity to the ground truth. Since DIFF-FOLEY was trained on similar audiovisual data, its tendency to mix multiple sounds in response to complex visual information explains its advantage in these metrics. Our model, targeting sound events from specific actions and filtering out irrelevant auditory information, diverges from the ground truth, a deliberate choice to enhance sound event relevance. The IoU metrics show that our model makes sound at the correct times and remains silent otherwise. To further argue our point, we conducted a subjective assessment of three aspects of OVL, REL, and Time-sync. As shown in Tab. 4, our model performed sig", + "bbox": [ + 496, + 566, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26872", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/63fff4b4786a542a78e611a541ba0f4d01bd898c64fe05fd69acebf4f3a4e3c2.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFD↓FAD↓KL↓IoU↑
tango-small* [10]44.911.53.4741.3
Ours-small26.22.052.3071.6
tango-full* [10]44.310.873.1439.3
Ours-full25.43.192.3265.7
", + "bbox": [ + 78, + 88, + 470, + 174 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Time Condition Ablation Results. “*” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage.", + "bbox": [ + 75, + 184, + 470, + 253 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e48b0da71d8c895f44e1cec6fc105fd9acd1348a161c0358e6ab84737f82890f.jpg", + "image_caption": [ + "Figure 6. Conditioning-scale Ablation Study. In the chart, the higher the indicators are, the better they are. The brightness of the colour also represents a good or bad performance." + ], + "image_footnote": [], + "bbox": [ + 102, + 273, + 457, + 398 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d1d59b20e8dcd0a285f2964737226da410b9dde3e9a00707ddd358b8346b1c5b.jpg", + "image_caption": [ + "Silent Video", + "Figure 7. Multi-soundtracks generation example. In the video, the blue and green masks show different soundtracks. The timing of on-screen sounds (corresponding to visible actions) aligns accurately with their occurrence in the frames. Conversely, off-screen sounds (not visible in the video) lack precise timing." + ], + "image_footnote": [], + "bbox": [ + 78, + 459, + 468, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "nificantly better than the baseline models in all metrics.", + "bbox": [ + 75, + 734, + 441, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Qualitative Results. For clearer time point comparison, we denoised the data from the CountixAV. Fig. 5 reveals our generated sounds are more precise than the baseline models. Furthermore, our model can capture finer-grained visual transformations, capturing the signal despite sudden changes in the frequency of movement and producing the correct sound. In contrast, SpecVQGAN results are full of noise. DIFF-FOLEY can sometimes generate clear sounds, but it is not aligned with the visual-sound synchronization.", + "bbox": [ + 73, + 750, + 468, + 885 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 90, + 653, + 107 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Time condition. Evaluation Metrics. We employed objective metrics from Tango [10], such as the Frechet Audio Distance (FAD) [16] and Frechet Distance(FD) [24] to measure the distribution difference between generated audio and ground truth without the need for any reference audio samples. KL divergence [19, 38] assesses their similarity based on the broad concepts present in the original and the generated audio signals.", + "bbox": [ + 496, + 113, + 890, + 233 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Result. we compared our model with the Tango [10]. As shown in Tab. 5, both in the small and full versions, our model outperforms Tango in terms of IoU, which validates the effectiveness of the time-controllable adapter.", + "bbox": [ + 496, + 234, + 890, + 294 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conditioning-scale. As seen in the Fig. 6. The sound quality improves in the range from 0.6 to 2.0 on the conditioning scale as it lines up better with the IoU. But at 3.0, control goes down a lot. The best mix of good sound quality and steadiness is found at a conditioning scale equal to 2.0.", + "bbox": [ + 496, + 294, + 890, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Multi-soundtracks generation", + "text_level": 1, + "bbox": [ + 498, + 378, + 764, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Fig. 7, SonicVisionLM works like a sound designer in traditional video post-production. First, it looks at the visual information to find the key sounds needed. For example, it picks out the hissing of cooking meat and the clinking of pots. Then, if the story needs it, the sound designer adds off-screen sounds. This might include extra kitchen sounds like distant chopping, simmering pots, or the buzz of kitchen machines, making it feel more natural. Lastly, SonicVisionLM puts these audio tracks in the right place on the video timeline. This ensures the sounds match perfectly with what is happening in the video, creating a smooth audio-visual experience. More detailed results can be found in the Supplementary Materials.", + "bbox": [ + 496, + 402, + 890, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 612, + 617, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose SonicVisionLM, which utilizes the capabilities of powerful vision-language models (VLMs). When provided with a silent video, SonicVisionLM first identifies events within the video using a VLM to suggest possible sounds that match the video content. SonicVisionLM demonstrates outstanding performance in both conditional and unconditional generation tasks. Further, we tested its efficacy in post-production, focusing on automatic recognition of on-screen sounds and personalized editing for off-screen sounds. Extensive experiments show the superior performance of our method.", + "bbox": [ + 496, + 636, + 890, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. While SonicVisionLM has achieved adequate results, refinements in the visual understanding and times-tamp detection parts are still required. Regarding various multimedia contexts, expanding the diversity and range of audio generation control are still the key demands of applications. Thus, the model should enrich the audio-visual experience and broaden applicability in future attempts.", + "bbox": [ + 496, + 789, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26873", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Andrea Agostinelli, Timo I Denk, Zalán Borsos, Jesse Engel, Mauro Verzetti, Antoine Caillon, Qingqing Huang, Aren Jansen, Adam Roberts, Marco Tagliasacchi, et al. Musicl: Generating music from text. arXiv preprint arXiv:2301.11325, 2023. 2", + "[2] Jun Chen, Deyao Zhu, Xiaogian Shen, Xiang Li, Zechun Liu, Pengchuan Zhang, Raghuraman Krishnamoorthi, Vikas Chandra, Yunyang Xiong, and Mohamed Elhoseiny. 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In CVPR, pages 14070-14079, 2021. 5, 6" + ], + "bbox": [ + 78, + 90, + 468, + 742 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "26875", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_model.json b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4f7652692b171bf325bcbaa22c256bb51ebca784 --- /dev/null +++ b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_model.json @@ -0,0 +1,1870 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.174, + 0.131, + 0.797, + 0.154 + ], + "angle": 0, + "content": "SonicVisionLM: Playing Sound with Vision Language Models" + }, + { + "type": "text", + "bbox": [ + 0.266, + 0.18, + 0.71, + 0.218 + ], + "angle": 0, + "content": "Zhifeng Xie\\(^{1,2}\\), Shengye Yu\\(^{1}\\), Qile He\\(^{1}\\), Mengtian Li\\(^{1,2\\dagger}\\) \n\\(^{1}\\)Shanghai University" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.218, + 0.778, + 0.235 + ], + "angle": 0, + "content": "\\(^{2}\\)Shanghai Engineering Research Center of Motion Picture Special Effects" + }, + { + "type": "text", + "bbox": [ + 0.29, + 0.237, + 0.681, + 0.252 + ], + "angle": 0, + "content": "{zhifeng_xie,yussisy,shu_hql,mtli}@shu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.712 + ], + "angle": 0, + "content": "There has been a growing interest in the task of generating sound for silent videos, primarily because of its practicality in streamlining video post-production. However, existing methods for video-sound generation attempt to directly create sound from visual representations, which can be challenging due to the difficulty of aligning visual representations with audio representations. In this paper, we present SonicVisionLM, a novel framework aimed at generating a wide range of sound effects by leveraging vision-language models(VLMs). Instead of generating audio directly from video, we use the capabilities of powerful VLMs. When provided with a silent video, our approach first identifies events within the video using a VLM to suggest possible sounds that match the video content. This shift in approach transforms the challenging task of aligning image and audio into more well-studied sub-problems of aligning image-to-text and text-to-audio through the popular diffusion models. To improve the quality of audio recommendations with LLMs, we have collected an extensive dataset that maps text descriptions to specific sound effects and developed a time-controlled audio adapter. Our approach surpasses current state-of-the-art methods for converting video to audio, enhancing synchronization with the visuals, and improving alignment between audio and video components. Project page: https://yusiissy.github.io/SonicVisionLM.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.736, + 0.21, + 0.751 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.47, + 0.876 + ], + "angle": 0, + "content": "The sound effects artists work with various types of sounds, including those visible on-screen (like footsteps or a car passing) and those audible but not visible (like background noises and heartbeats can enhance the video's authenticity and narrative). On-screen sounds match what is happening in the video, while off-screen sounds establish the ambience and provide additional information. Creating soundtracks for videos is a vital aspect of video produc" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.285, + 0.895, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.462, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 1. A model implements the automatic detection of on-screen sound generation and accepts the user's editing of text and time in the off-screen section. On-screen sound refers to audio that originates from visible actions within the video frame. Off-screen sound is not directly observable on the screen." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.538, + 0.892, + 0.568 + ], + "angle": 0, + "content": "tion, but it can be labour-intensive for artists. Therefore, the video-sound generation task has gained notable attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.893, + 0.764 + ], + "angle": 0, + "content": "Although the recent approaches have made great efforts, the video-sound generation task is still challenging. For onscreen sounds, achieving semantic relevance and maintaining temporal synchronization continues to be a complex issue. It is hard to edit off-screen sounds. Current methods [14, 25, 32] primarily focus on the visual content to generate the corresponding sound, a subset of these methods [7, 9] considers editability. Nonetheless, the alignment between video and audio features is tricky, leading to deficiencies including 1) incorrect sound meanings and mismatched timing, 2) monotonous sound effects, and a lack of complex scenarios. Both lead to unsatisfactory results in the videosound generation task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "We propose a novel framework named SonicVisionLM to solve the above deficiency, as shown in Fig. 1. SonicVisionLM is proposed by introducing three key components: video-to-text, text-based interaction, and text-to-audio generation. First, the video-to-text component focuses on generating sound effects for on-screen events. This step uses a VLM to identify appropriate sound descriptions from the input silent video. Following this, a timestamp detection network is trained to extract specific temporal information" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26866" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.895, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.378, + 0.895, + 0.448 + ], + "angle": 0, + "content": "Figure 2. SonicVisionLM's framework. SonicVisionLM presents a composite framework designed to automatically recognize on-screen sounds coupled with a user-interactive module for editing off-screen sounds. The blue dashed box and arrows in the figure represent the visual automation workflow: First, a silent video goes into the system to determine the occurring events (text) and their timing (time). Then, this information conditions the generation of sounds matching the screen. The purple dotted box and arrows show how users can modify or add off-screen sounds." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.473, + 0.665 + ], + "angle": 0, + "content": "from the video. A key innovation within this framework is the design of a time-conditioned embedding, which is utilized to guide an audio adapter. After that, the text-based interaction component allows users to change the text and timestamps from a previous video-to-text component or to input new corresponding text-timestamp pairs for personalized sound design. Finally, the text-to-audio generation component accepts the text and timestamp conditions and inputs them into the LDM and adapter to generate diverse, time-synchronized, and controllable sounds. Simultaneously, We collect a text-to-single-sound dataset, named CondPromptBank, for sound effects caption and timing cues, comprising over ten thousand data points, covering 23 categories. The main contributions of this work are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.687, + 0.47, + 0.763 + ], + "angle": 0, + "content": "- We propose a novel framework called SonicVisionLM and collect a dataset CondPromptBank specifically for training a time-controllable adapter. It ensures the generated sound aligns perfectly with our text input and maintains precise timing control." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.763, + 0.47, + 0.837 + ], + "angle": 0, + "content": "- We introduce three pioneering components: video-to-text, text-based interaction, and text-to-audio generation. This unique combination facilitates the automatic recognition of on-screen sounds while enabling user customization of off-screen sounds." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.839, + 0.47, + 0.899 + ], + "angle": 0, + "content": "- The proposed framework achieves state-of-the-art results on conditional and unconditional video-sound generation tasks. The conditional task can be noticeably enhanced in all metrics. (IoU: \\(22.4 \\rightarrow 39.7\\))" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.687, + 0.47, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.451, + 0.642, + 0.468 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Audio Generation can be broadly classified into two categories. The Text-to-Audio Generation field includes Text-to-Speech (TTS) and Text-to-Music (TTM). Leading TTS models, such as FastSpeech2 [29] and NaturalSpeech [33], now produce speech virtually indistinguishable from human speech. In TTM, MusicLM [1], Noise2Music [12], MusicGen [6] and MeLoDy [21] are aimed to generate music segments from text, bringing innovation to music composition and synthesis. Models like AudioGen [19], AudioLDM [24], Tango [10], and Make-an-Audio [13] focuses on universal audio generation modeling. AudioGen [19] treats audio generation as a conditional language modelling task, while the other three models employ latent diffusion methods to accomplish sound generation. Current methods use datasets including sound effects, voices, and music, but practical applications use these elements separately. As the textual descriptions of time are subjective, videos are more intuitive and precise, so V2A requires more accurate semantic features and time control than T2A. Therefore, we have created a text-to-single-sound dataset called CondPromptBank with detailed semantic segmentation and temporal annotations that help models produce high-quality sound effects for videos. In Video-to-Audio Generation task, SpecVQGAN [14] utilizes a Transformer-based autoregressive model, drawing on ResNet50 or RGB+Flow features to generate sound. Im2Wav [32] uses a dual-transformer model conditioned on CLIP features for sound generation. CondFoleyGen [9] and VARIETYSOUND [7]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26867" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.272 + ], + "angle": 0, + "content": "introduce tasks for controllable timbre generation. Diff-foley [25] uses contrastive audio-visual pretraining to align audio and visual features. ClipSonic [8] learns the text-audio correspondence by leveraging the audio-visual correspondences in videos and the multi-modal representation learned by pre-trained VLMs. However, the sounds generated by these methods often suffer from poor audio-visual synchronization, noticeable noises, and lack of editability. Unlike the works above, our model ensures audio-visual synchronization, enriches diversity, and supports personalized user edits. Our model provides a more comprehensive sound solution for video production." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.473, + 0.424 + ], + "angle": 0, + "content": "Diffusion Model has been utilized for generating both mel-spectrogram generation [4, 28], and waveform generation [3, 20, 22]. However, their iterative generation process can be slow for high-dimensional data. Models such as AudioLDM [24], Make-An-Audio [13], and Tango [10] have successfully trained diffusion models within a continuous latent space. Nevertheless, achieving satisfactory results in controlling LDM for audio generation tasks remains challenging. This paper aims to introduce time control to ensure audio-visual synchronization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.473, + 0.561 + ], + "angle": 0, + "content": "Vision Language Models like ChatGPT-4, which demonstrated advanced multi-modal abilities and inspired vision-language LLMs. Vision-LLM [36] and LLaVA [34] focus on aligning image inputs with large language models Vicuna[5] exhibit similar multi-modal capabilities. Recent developments in this field include MiniGPT-v2 [2]. Kosmos-2 [27] demonstrates multi-modal LLMs' ability to perform visual grounding. In this paper, we first introduce the VLMs to the audio generation task." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.172, + 0.592 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.601, + 0.189, + 0.617 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.473, + 0.822 + ], + "angle": 0, + "content": "In this section, we introduce the framework of SonicVisionLM, as shown in Fig. 2. Before delving into the specific design details, we first briefly overview the preliminary knowledge (Sec. 3.2). Then, we introduce the Visual-to-Audio Event Detection Module (Sec. 3.3), which obtains textual descriptions of on-screen sounds through VLMs. Subsequently, we present the Sound Event Timestamp Detection Module (Sec. 3.4), designed to accurately detect the timing information through network architecture. Finally, we introduce the proposed time-controllable adapter as an extension of the audio diffusion model (Sec. 3.5), enabling the generation of multiple sounds that are semantically coherent and temporally aligned." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.22, + 0.848 + ], + "angle": 0, + "content": "3.2. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Audio Diffusion Model. The text-prompt encoder encodes the input description \\(\\tau \\in R^{L\\times d_t}\\) of the sound, where \\(L\\) is the token count and \\(d_{t}\\) and is the token-embedding size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.272 + ], + "angle": 0, + "content": "The latent diffusion model (LDM) is used to construct the audio prior \\( z_0 \\) with the guidance of text encoding \\( \\tau \\). This essentially reduces to approximating the true prior \\( q(z_0 \\mid \\tau) \\) with parameterized \\( p(z_0 \\mid \\tau) \\). LDM can achieve the above through forward and reverse diffusion processes. The forward diffusion is a Markov chain of Gaussian distributions with scheduled noise parameters \\( 0 < \\beta_1 < \\beta_2 < \\dots < \\beta_N < 1 \\) to sample noisier versions of \\( z_0 \\), where \\( N \\) is the number of forward diffusion steps. For each step \\( n \\), we define \\( \\alpha_n = 1 - \\beta_n \\), and calculate the cumulative product \\( \\bar{\\alpha}_n = \\prod_{i=1}^n \\alpha_n \\). The diffusion equations are described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.273, + 0.892, + 0.3 + ], + "angle": 0, + "content": "\\[\nq \\left(z _ {n} \\mid z _ {n - 1}\\right) = \\mathcal {N} \\left(\\sqrt {1 - \\beta_ {n}} z _ {n - 1}, \\beta_ {n} \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.305, + 0.892, + 0.324 + ], + "angle": 0, + "content": "\\[\nq \\left(z _ {n} \\mid z _ {0}\\right) = \\mathcal {N} \\left(\\sqrt {\\bar {\\alpha} _ {n}} z _ {0}, \\left(1 - \\bar {\\alpha} _ {n}\\right) \\mathbf {I}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.895, + 0.405 + ], + "angle": 0, + "content": "where the noise term \\(\\epsilon\\) and the final step of the forward process yields \\(z_{N}\\) follow a Gaussian distribution, specifically \\(\\epsilon ,z_{N}\\sim \\mathcal{N}(0,I)\\). The reverse process denoises and reconstructs \\(z_{0}\\) through text-guided noise estimation \\((\\hat{\\epsilon}_{\\theta})\\) using following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.408, + 0.892, + 0.45 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {D M} = \\sum_ {n = 1} ^ {N} \\gamma_ {n} \\mathbb {E} _ {\\epsilon_ {n} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}), z _ {0}} \\left\\| \\epsilon_ {n} - \\hat {\\epsilon} _ {\\theta} ^ {(n)} (z _ {n}, \\tau) \\right\\| _ {2} ^ {2}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.518 + ], + "angle": 0, + "content": "After training LDM, we generate audio latent by sampling through the reverse process with \\( z_{N} \\sim \\mathcal{N}(0,I) \\), conditioned on the given textual representation \\( \\tau \\). Its reverse dynamics are shown below:" + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.518, + 0.892, + 0.543 + ], + "angle": 0, + "content": "\\[\np _ {\\theta} \\left(z _ {n - 1} \\mid z _ {n}, \\tau\\right) = \\mathcal {N} \\left(\\mu_ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right), \\tilde {\\beta} ^ {(n)}\\right), \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.558, + 0.892, + 0.593 + ], + "angle": 0, + "content": "\\[\n\\mu_ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right) = \\frac {1}{\\sqrt {\\alpha_ {n}}} \\left[ z _ {n} - \\frac {1 - \\alpha_ {n}}{\\sqrt {1 - \\bar {\\alpha} _ {n}}} \\hat {\\epsilon} _ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right) \\right], \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.598, + 0.892, + 0.63 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\beta} ^ {(n)} = \\frac {1 - \\bar {\\alpha} _ {n - 1}}{1 - \\bar {\\alpha} _ {n}} \\beta_ {n}. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.634, + 0.895, + 0.679 + ], + "angle": 0, + "content": "The noise estimation \\((\\hat{\\epsilon}_{\\theta})\\) is parameterized with U-Net framework [30] with a cross-attention component to include the text guidance \\(\\tau\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.895, + 0.74 + ], + "angle": 0, + "content": "After that, the decoder of audio VAE [18] constructs a mel-spectrogram feature from the latent audio representation \\(\\hat{z}_0\\). This mel-spectrogram feature is conveyed to a vocoder to generate the final audio." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.745, + 0.891, + 0.762 + ], + "angle": 0, + "content": "3.3. Visual-to-Audio Event Understanding Module" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The diversity of sound is influenced by various factors such as its source, actions, the environment, and more. At the same time, these factors are often included in the description of visual images. Inspired by the widespread use of VLMs [23, 37, 39], we chose MiniGPT-v2 [2] to process visual information and generate descriptions of sounds. Recognizing that MiniGPT-v2 was initially developed for single-image understanding and its limitations in conveying dynamic information, we have adapted the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26868" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "LLaMA-2 [34] conversation template design to suit a multimodal instructional framework. To not miss sound events, we encoded four random video frames with time-sensitive prompts (temporal cues):" + }, + { + "type": "code", + "bbox": [ + 0.075, + 0.155, + 0.473, + 0.232 + ], + "angle": 0, + "content": "First, >\\) ImageFeature \\(>>\\) Img>. Then, >\\) ImageFeature \\(>>\\) Img>. After that, >\\) ImageFeature \\(>>\\) Img>. Finally, >\\) ImageFeature \\(>>\\) Img>. [Task Identifier] Instruction" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.237, + 0.445, + 0.253 + ], + "angle": 0, + "content": "3.4. Sound Event Timestamp Detection Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.257, + 0.47, + 0.422 + ], + "angle": 0, + "content": "In practice, sound artists need to manually determine the point in time when a sound event starts and ends and then adjust the appropriate sound effect to the correct position. This judgment is usually based on current visual information. To simplify the process, we use the sound event timestamp detection module to detect the timestamp of the sound event in the video inspired by the CondFoleyGen [9]. Instead of using a hand-crafted approach to transfer sounds from the conditional audio, We use a ResNet(2+1)-D18 [35] visual network to capture timestamps as time-conditional inputs to the LDM, trained on paired video and timestamp." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.423, + 0.47, + 0.618 + ], + "angle": 0, + "content": "The workflow begins with feeding a sequence of silent video frames \\( V_{f} \\) into the detection network. The network then outputs a binary vector \\( V_{ct} \\) representing predictions for each frame, derived from a fully connected layer post-pooling. The ground truth \\( V_{ct} \\) is obtained: Function \\( P \\) detects audio \\( a \\) in each frame, applying a threshold \\( x \\) to reduce noise effects. Sounds within 0.02s across consecutive frames are considered a single event. This method identifies the start \\( x_{start} \\) and end points \\( x_{end} \\) of sound segments, as delineated in Eq. 7. Based on timestamps, we construct \\( T_{ct} \\), as depicted in Eq. 8, where 1 indicates the presence of sound, and 0 indicates the absence. The process equations are as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.619, + 0.468, + 0.633 + ], + "angle": 0, + "content": "\\[\nx _ {\\text {s t a r t}}, x _ {\\text {e n d}} = P \\left(a _ {c}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.634, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\nT _ {c t} = \\left\\{ \\begin{array}{l l} 1, i f t i n [ x _ {\\text {s t a r t}}, x _ {\\text {e n d}} ], \\\\ 0, e l s e. \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Finally, \\( T_{ct} \\) is adjusted to correspond with the video frames' duration, represented as \\( V_{ct} \\). We employ binary cross-entropy loss to penalize inaccuracies in time prediction. Given that an input video may contain multiple sound events, each sound event's weights are based on its duration relative to the total sound duration in the video. The binary vector \\( T_{ct} \\) serves as input for the Time-controllable Latent Diffusion Model. The whole process and network structure are shown in Fig. 3." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.818, + 0.434, + 0.833 + ], + "angle": 0, + "content": "3.5. Time-controllable Latent Diffusion Model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.841, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In our experimentation, we observed that the results generated were semantically inaccurate and temporally unsynchronized. This issue often arose when utilizing audio-visual datasets to train end-to-end models, limiting the" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.089, + 0.882, + 0.252 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.262, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Figure 3. Sound Event Timestamp Detection Module. The network analyzes the video's features to output a binary vector corresponding to the video's frame count. Within this vector, sections marked in white (value of 1) mean sound presence, and those in black (value of 0) indicate sound absence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.343, + 0.892, + 0.539 + ], + "angle": 0, + "content": "task's practical application. We attribute these shortcomings to the complexity of the sound sources and the poor audio quality of the audio-visual dataset used for training. To address this, we use text to bridge audio and video and then introduce time control in the T2A generation model. In the visual domain, many works are based on the ControlNet [40] architecture, which can finer control the generation of images or videos by manipulating the input image conditions of neural network blocks. However, unlike the visual domain's inherent intuitiveness, audio features exhibit temporal continuity and are inherently more complex and abstract. Thus, selecting appropriate audio features to guide the generation process poses a greater challenge." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.54, + 0.892, + 0.704 + ], + "angle": 0, + "content": "In this paper, we propose a embedding called Audio Time-condition Embedding, denote as \\( A_{ct} \\), which is constructed through the following procedure: During the training phase, the adapter extracted Mel-spectrogram features from audio waveform \\( a \\) and then normalized it, denoted as \\( a_{mel} = mel(a) \\). For \\( a_{c} = \\max (mel(a), T_{ct}) \\), we then initialize \\( a_{c} \\) to match \\( a_{mel} \\)'s dimensions but with zero values, then fill \\( a_{c} \\)'s Mel channels with the maximum values based on the corresponding frames where \\( T_{ct} \\) equals 1. Finally, \\( A_{ct} \\) is derived by encoding the embedding of \\( a_{c} \\) via the encoder \\( E_{a} \\), and described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.709, + 0.891, + 0.726 + ], + "angle": 0, + "content": "\\[\nA _ {c t} = E _ {a} \\left(\\max \\left(\\operatorname {m e l} \\left(a _ {c}\\right), T _ {c t}\\right)\\right). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Inspired by ControlNet [40], we have developed a network architecture named Time-controllable Adapter. Then, we integrate the audio time-condition embedding \\( A_{ct} \\) with the text embedding \\( \\tau \\) and target audio embedding into the neural network block. This integration facilitates joint training for the time-controllable adapter. \\( A_{ct} \\) is fed solely into the adapter, while text embedding \\( \\tau \\) inputs into both Tango and the adapter." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Tango's denoising model, akin to UNet, includes encoder \\( F \\), middle block \\( M \\), and decoder \\( G \\). \\( F \\) and \\( G \\) have 12 corresponding blocks. Tango's outputs of the encoder's" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26869" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.244 + ], + "angle": 0, + "content": "\\(i - th\\) block and decoder's \\(j - th\\) block are \\(f_{i}\\) and \\(g_{j}\\), with \\(m\\) for the single middle block. The adapter mimics Tango's encoder and middle layers as \\(F'\\) and \\(M'\\). Adapter's outputs, like \\(f_{i}'\\) and \\(m'\\), are marked with \\((')\\). Following this, the output of the time-controllable adapter is concatenated with the output of the corresponding decoder block during the decoding process. For example, \\(f_{1}\\) from the 1st encoder layer adds to \\(g_{12}\\) of the decoder, making \\(i + j = 13\\). To achieve it, we ensure that all Tango's elements are kept frozen while modifying the input of the \\(i - th\\) block of the decoder as:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.254, + 0.47, + 0.302 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\text {C o n c a t} \\left(m + m ^ {\\prime}, f _ {j} + z e r o \\left(f _ {j} ^ {\\prime}\\right)\\right) i = 1, j = 1 2. \\\\ \\text {C o n c a t} \\left(g _ {i - 1}, f _ {j} + z e r o \\left(f _ {j} ^ {\\prime}\\right)\\right) 2 \\leqslant i \\leqslant 1 2, i + j = 1 3. \\end{array} \\right. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.47, + 0.431 + ], + "angle": 0, + "content": "zero(\\cdot) is one zero convolutional layer, facilitating trainable and fixed neural network block connections. Its weights evolve from zero to optimized values during training. This approach not only retains the Tango's capability for generating audio, trained on billions of audio-text pairs, but also enables the model to comprehend the guidance provided by the time control embedding, resulting in temporally controllable outcomes." + }, + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.439, + 0.432, + 0.452 + ], + "angle": 0, + "content": "Table 1. Distribution of CondPromptBank Categories" + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.452, + 0.466, + 0.538 + ], + "angle": 0, + "content": "
Category%Category%Category%
Household Daily14.11Transportation Vehicles10.42Impacts Crashes10.10
Foley8.24Human Elements7.77Industrial6.58
Weapons War5.83Cartoon Comical4.90Sports4.43
Animals Insects4.04Instruments3.68Water Liquid3.27
Technology2.70Horror2.41Emergency2.20
Public Places1.87Sound Design Effects1.69Doors Windows1.56
Fire Explosions1.49Nature Weather1.02Leisure0.84
Multimedia0.47Bells0.37
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.551, + 0.21, + 0.568 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.576, + 0.271, + 0.592 + ], + "angle": 0, + "content": "4.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Dataset. Since Tango's training datasets include varied audio types like speech, sound effects, and music, it tends to produce mixed audio outputs. Our task requires distinct handling of these audio types, ensuring each sound event is separate. To meet our specific needs, we developed CondPromptBank, a high-quality dataset of single sound effects crafted for training time-controlled adapters. This dataset consists of 10,276 individual data entries, each with a sound effect, title, and start/end timestamps. Each sound is typically 10 seconds or shorter, sourced from freely available sound effect libraries and websites. During the collection, we focused on 23 common categories of sound effects and manually filtered out low-quality data with noise and mixed sources. The category distribution shows Tab. 1. To enhance the textual descriptions with precise details, we further annotated the sound effect text labels with fine-grained information based on sound characteristics. Now, each label not only identifies the audio source but also describes the associated actions in detail. We believe the division into single audio sources is crucial, as videos provide a more concrete" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "expression of content than text, thus requiring more precise sound representation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.895, + 0.319 + ], + "angle": 0, + "content": "Implementation details. To train our complete model, we first train the adapter on CondPromtBank, then train the timestamps detection net on Greatest Hits [26] and Countix-AV dataset [41]. We trained the adapter for approximately 200 epochs with a batch size 32 and a learning rate of \\(3.0 \\times 10^{-5}\\) using Adam [17]. Our model has two versions: small and full. The difference between them is the version of pre-trained parameters used for Tango. We trained the timestamps detection net for 70 epochs with a batch size of 24 and a learning rate of \\(1.0 \\times 10^{-5}\\). The training of the adapter takes approximately five days, and the training of the timestamps detection network requires approximately one day using one NVIDIA A6000 GPU." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.331, + 0.821, + 0.346 + ], + "angle": 0, + "content": "4.2. Conditional Generation Task Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.476 + ], + "angle": 0, + "content": "We tested our model using the Greatest Hits [26] dataset, which has 977 videos of drumsticks interacting with different objects, lasting 11 hours. This dataset is divided into two types of actions and 17 types of materials. This detailed categorization helps check if our model can change sound types based on these details but still match the target action. We used the same test settings as CondFoleyGen [9] and compared our results with theirs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Evaluation Metrics. For the conditional generation task, we use the following five objective metrics to evaluate the performance of the model: CLAP-top, Onset Acc [9], Onset AP [9], Time Acc, and IoU." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.895, + 0.809 + ], + "angle": 0, + "content": "Quantitative Results. SonicVisionLM-full demonstrates superior performance over CondFoleyGen across all metrics, as seen in Tab. 2. It achieves leading scores of \\(36.8\\%\\) and \\(42.8\\%\\) on CLAP-top versions, exceeding any CondFoleyGen model by more than \\(20\\%\\). This result suggests that it is better at matching sounds to text prompts. Our model significantly surpasses CondFoleyGen in audio-visual synchronization, evidenced by an \\(11\\%\\) improvement in Onset AP and a \\(16\\%\\) rise in IoU. Moreover, we see a \\(6\\%\\) enhancement in onset accuracy and an \\(8.3\\%\\) increase in timing precision. These advancements illustrate our model's outstanding accuracy in sound event detection and its effectiveness in synchronizing generated sounds with the input video. We think CondFoleyGen relies on the audio-visual synchronization module [15] to improve time accuracy, requiring many samples to re-ranking the sounds. In contrast, our model gets higher synchronization during the generation process with fewer samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results. As shown in Fig. 4 (row 4, 6, 7), we compare the timestamped positional distance to the target sound. Our results closely match the target sound, demonstrating a high degree of accuracy. However, CondFoleyGen often produces results with the wrong number of sounds and with a large difference in the positional distance." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26870" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.089, + 0.899, + 0.168 + ], + "angle": 0, + "content": "
MethodCLAP - topgeneral↑CLAP - topunfused↑Onset Acc ↑Onset AP↑Time Acc↑IoU↑
CondFoleyGen(old)* [9]17.315.621.667.035.523.3
CondFoleyGen(new) * [9]16.313.619.268.637.422.4
Ours-small29.628.019.477.0327.835.6
Ours-full36.842.827.678.143.839.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.176, + 0.894, + 0.317 + ], + "angle": 0, + "content": "Table 2. Conditional Generation Task Quantitative Results. CLAP-top metric evaluates a model's ability to control sound content. It calculates the percentage of times the sound samples generated by all models ranked in the top 1 according to the CLAP ranking, divided by the total number of samples. We used two versions of the CLAP models for evaluation: \\(CLAP_{general}\\) and \\(CLAP_{unfused}\\). Onset Acc and Time Acc are both metrics based on the number of sound occurrences, with Onset Acc focusing on the onset count and Time Acc on the count of time intervals. We measure the average accuracy of predicting onsets within 0.1s of ground truth to assess the timing of generated onsets. IoU is calculated by computing the intersection and union of these vectors. These metrics collectively allow us to comprehensively evaluate the accuracy of the generated sounds in terms of both timing and content. The variant \"old\" corresponds to the prior codebook, while variant \"new\" matches the updated codebook. The old model was trained on 192-width spectrograms, and the new one was trained on 2s waveforms. \\*\\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. The six metrics are all measured in percentage." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.323, + 0.891, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.664, + 0.893, + 0.694 + ], + "angle": 0, + "content": "Figure 4. Conditional Generation Task Qualitative Results. The red dashed boxes are the conditional audio inputs and generated results for CondFoleyGen, and the blue dashed boxes are the conditional text inputs and results corresponding to SonicVisionLM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.826 + ], + "angle": 0, + "content": "This indicates that our model has a higher visual-audio synchronization than CondFoleyGen. As shown in Fig. 4 (column 3, 7), we compare the sound shape to the conditional sound. Even though our model has not learned any timbre on the Greatest Hits dataset, our results are still very similar to the conditional sound. As shown in Fig. 4 (column 1, 7), The mel-spectrograms of the CondFoleyGen results do not produce sounds that are similar to, and sometimes blurred." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.315, + 0.86 + ], + "angle": 0, + "content": "4.3. Unconditional Generation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To evaluate the task of unconditional sound generation, considering that our LDM has not been trained on" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.781 + ], + "angle": 0, + "content": "audio-visual datasets, we have chosen to perform quantitative evaluation and qualitative evaluation on two datasets: Greatest Hits [26] and CountixAV [41], which are zero-shot tasks for all models. We use two state-of-the-art V2A models as baselines: SpecVQGAN [14] and DIFF-FOLEY [25]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Evaluation Metrics. For objective evaluation, we have employed three metrics as [14, 25]: Inception Score (IS) [31], Frechet Distance (FID) [11], and Mean KL Divergence (MKL) [14]. For subjective evaluation, as the [9], we conduct user evaluations for the three critical components: overall audio quality (OVL), alignment with the input video (REL), and time synchronization (Time-sync)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26871" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.09, + 0.885, + 0.201 + ], + "angle": 0, + "content": "
Metric
Dataset MethodGreatest HitsCountix-AV
MKL↓FID ↓IS↑IoU↑MKL↓FID ↓IS↑IoU ↑
\\(SpecVQGAN^* [14]\\)6.8082.42.1725.87.3934.15.334.9
DIFF-FOLEY†[25]5.6820.03.8422.04.915.95.231.3
Ours-small6.4631.93.8836.610.021.715.137.5
Ours-full4.6724.93.2639.59.7119.712.742
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.211, + 0.893, + 0.268 + ], + "angle": 0, + "content": "Table 3. Unconditional Sound Generation Quantitative Results. IS assesses the quality and diversity of generated samples, FID measures distribution-level similarity, and MKL measures paired sample-level similarity. \\*\\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. \\*\\* denotes that data is obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.271, + 0.891, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.526, + 0.893, + 0.556 + ], + "angle": 0, + "content": "Figure 5. Unconditional Generation Task Qualitative Results. The left example is from CountixAV, and the right one is from Greatest Hits. We're comparing them side by side. The dashed box highlights examples of both good and bad results we generated." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.564, + 0.47, + 0.633 + ], + "angle": 0, + "content": "
MethodOVL↑REL↑Time-sync ↑
SpecVQGAN* [14]372531
DIFF-FOLEY† [25]486458
Ours756987
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.754 + ], + "angle": 0, + "content": "Table 4. Subjective Results. Following [9], we invited the 300 English-proficient evaluators to rate 30 randomly selected audio samples from three perspectives: OVL, REL, and Time-sync. Scores were averaged on a 1-100 scale. “**” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. “†” denotes data obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Quantitative Results. In our experiments, the choice of vocoder significantly influenced the FID metric. We upgraded from DIFF-FOLEY's weak Griffin-Lim vocoder to the superior MelGAN to ensure fairness. Despite our model using 64 Mel filters compared to MelGAN's 80, our performance on the Greatest Hits dataset excels in MKL, IS, and IoU metrics, as shown in Tab. 3. This underscores our model's precise time control and high-quality sound generation, demonstrating its exceptional capability to produce" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.895, + 0.901 + ], + "angle": 0, + "content": "sounds that align closely with the ground truth. In the CountixAV dataset, SonicVisionLM-small outperforms baselines by nearly 10 points in the IS metric, highlighting its exceptional sound quality. Despite slightly lower MKL and FID scores compared to baselines, we do not view this as a drawback. Unlike the Greatest Hits dataset, which was recorded in high quality with specialized recording equipment, the CountixAV dataset is sourced from diverse YouTube videos. It often includes sounds marred by low-quality background noise or mixed sound sources, especially human vocals. MKL and FID metrics emphasize similarity to the ground truth. Since DIFF-FOLEY was trained on similar audiovisual data, its tendency to mix multiple sounds in response to complex visual information explains its advantage in these metrics. Our model, targeting sound events from specific actions and filtering out irrelevant auditory information, diverges from the ground truth, a deliberate choice to enhance sound event relevance. The IoU metrics show that our model makes sound at the correct times and remains silent otherwise. To further argue our point, we conducted a subjective assessment of three aspects of OVL, REL, and Time-sync. As shown in Tab. 4, our model performed sig" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26872" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.472, + 0.175 + ], + "angle": 0, + "content": "
MethodFD↓FAD↓KL↓IoU↑
tango-small* [10]44.911.53.4741.3
Ours-small26.22.052.3071.6
tango-full* [10]44.310.873.1439.3
Ours-full25.43.192.3265.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.185, + 0.471, + 0.255 + ], + "angle": 0, + "content": "Table 5. Time Condition Ablation Results. “*” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.274, + 0.458, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.448 + ], + "angle": 0, + "content": "Figure 6. Conditioning-scale Ablation Study. In the chart, the higher the indicators are, the better they are. The brightness of the colour also represents a good or bad performance." + }, + { + "type": "image_caption", + "bbox": [ + 0.08, + 0.451, + 0.141, + 0.46 + ], + "angle": 0, + "content": "Silent Video" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.46, + 0.47, + 0.642 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.725 + ], + "angle": 0, + "content": "Figure 7. Multi-soundtracks generation example. In the video, the blue and green masks show different soundtracks. The timing of on-screen sounds (corresponding to visible actions) aligns accurately with their occurrence in the frames. Conversely, off-screen sounds (not visible in the video) lack precise timing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.442, + 0.749 + ], + "angle": 0, + "content": "nificantly better than the baseline models in all metrics." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.75, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Qualitative Results. For clearer time point comparison, we denoised the data from the CountixAV. Fig. 5 reveals our generated sounds are more precise than the baseline models. Furthermore, our model can capture finer-grained visual transformations, capturing the signal despite sudden changes in the frequency of movement and producing the correct sound. In contrast, SpecVQGAN results are full of noise. DIFF-FOLEY can sometimes generate clear sounds, but it is not aligned with the visual-sound synchronization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.655, + 0.108 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.234 + ], + "angle": 0, + "content": "Time condition. Evaluation Metrics. We employed objective metrics from Tango [10], such as the Frechet Audio Distance (FAD) [16] and Frechet Distance(FD) [24] to measure the distribution difference between generated audio and ground truth without the need for any reference audio samples. KL divergence [19, 38] assesses their similarity based on the broad concepts present in the original and the generated audio signals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.235, + 0.892, + 0.295 + ], + "angle": 0, + "content": "Result. we compared our model with the Tango [10]. As shown in Tab. 5, both in the small and full versions, our model outperforms Tango in terms of IoU, which validates the effectiveness of the time-controllable adapter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.372 + ], + "angle": 0, + "content": "Conditioning-scale. As seen in the Fig. 6. The sound quality improves in the range from 0.6 to 2.0 on the conditioning scale as it lines up better with the IoU. But at 3.0, control goes down a lot. The best mix of good sound quality and steadiness is found at a conditioning scale equal to 2.0." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.38, + 0.766, + 0.396 + ], + "angle": 0, + "content": "4.5. Multi-soundtracks generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.6 + ], + "angle": 0, + "content": "As shown in Fig. 7, SonicVisionLM works like a sound designer in traditional video post-production. First, it looks at the visual information to find the key sounds needed. For example, it picks out the hissing of cooking meat and the clinking of pots. Then, if the story needs it, the sound designer adds off-screen sounds. This might include extra kitchen sounds like distant chopping, simmering pots, or the buzz of kitchen machines, making it feel more natural. Lastly, SonicVisionLM puts these audio tracks in the right place on the video timeline. This ensures the sounds match perfectly with what is happening in the video, creating a smooth audio-visual experience. More detailed results can be found in the Supplementary Materials." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.613, + 0.619, + 0.629 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.637, + 0.892, + 0.789 + ], + "angle": 0, + "content": "In this paper, we propose SonicVisionLM, which utilizes the capabilities of powerful vision-language models (VLMs). When provided with a silent video, SonicVisionLM first identifies events within the video using a VLM to suggest possible sounds that match the video content. SonicVisionLM demonstrates outstanding performance in both conditional and unconditional generation tasks. Further, we tested its efficacy in post-production, focusing on automatic recognition of on-screen sounds and personalized editing for off-screen sounds. Extensive experiments show the superior performance of our method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.892, + 0.888 + ], + "angle": 0, + "content": "Limitations. While SonicVisionLM has achieved adequate results, refinements in the visual understanding and times-tamp detection parts are still required. Regarding various multimedia contexts, expanding the diversity and range of audio generation control are still the key demands of applications. 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In CVPR, pages 14070-14079, 2021. 5, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "26875" + } + ] +] \ No newline at end of file diff --git a/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_origin.pdf b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..cc5a0b9c0ddd07eaed2cdf02072719aa04e1d97e --- /dev/null +++ b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/578ceece-2af8-4d00-b6af-84640cb38a96_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5d782fa340da2cdcdfb7c4cbac1633e5b7e94177485c4480f5eb4a1be8f70c07 +size 3782639 diff --git a/2024/SonicVisionLM_ Playing Sound with Vision Language Models/full.md b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/full.md new file mode 100644 index 0000000000000000000000000000000000000000..42b4f48f15b2996986fa342e5ec795b6cef7ce3c --- /dev/null +++ b/2024/SonicVisionLM_ Playing Sound with Vision Language Models/full.md @@ -0,0 +1,275 @@ +# SonicVisionLM: Playing Sound with Vision Language Models + +Zhifeng Xie $^{1,2}$ , Shengye Yu $^{1}$ , Qile He $^{1}$ , Mengtian Li $^{1,2\dagger}$ $^{1}$ Shanghai University + +$^{2}$ Shanghai Engineering Research Center of Motion Picture Special Effects + +{zhifeng_xie,yussisy,shu_hql,mtli}@shu.edu.cn + +# Abstract + +There has been a growing interest in the task of generating sound for silent videos, primarily because of its practicality in streamlining video post-production. However, existing methods for video-sound generation attempt to directly create sound from visual representations, which can be challenging due to the difficulty of aligning visual representations with audio representations. In this paper, we present SonicVisionLM, a novel framework aimed at generating a wide range of sound effects by leveraging vision-language models(VLMs). Instead of generating audio directly from video, we use the capabilities of powerful VLMs. When provided with a silent video, our approach first identifies events within the video using a VLM to suggest possible sounds that match the video content. This shift in approach transforms the challenging task of aligning image and audio into more well-studied sub-problems of aligning image-to-text and text-to-audio through the popular diffusion models. To improve the quality of audio recommendations with LLMs, we have collected an extensive dataset that maps text descriptions to specific sound effects and developed a time-controlled audio adapter. Our approach surpasses current state-of-the-art methods for converting video to audio, enhancing synchronization with the visuals, and improving alignment between audio and video components. Project page: https://yusiissy.github.io/SonicVisionLM.github.io/ + +# 1. Introduction + +The sound effects artists work with various types of sounds, including those visible on-screen (like footsteps or a car passing) and those audible but not visible (like background noises and heartbeats can enhance the video's authenticity and narrative). On-screen sounds match what is happening in the video, while off-screen sounds establish the ambience and provide additional information. Creating soundtracks for videos is a vital aspect of video produc + +![](images/4bbd06805daadfdfae81d8e85519c1d3b0b7eee92413b32129e7f8e5f6db61d1.jpg) +Figure 1. A model implements the automatic detection of on-screen sound generation and accepts the user's editing of text and time in the off-screen section. On-screen sound refers to audio that originates from visible actions within the video frame. Off-screen sound is not directly observable on the screen. + +tion, but it can be labour-intensive for artists. Therefore, the video-sound generation task has gained notable attention. + +Although the recent approaches have made great efforts, the video-sound generation task is still challenging. For onscreen sounds, achieving semantic relevance and maintaining temporal synchronization continues to be a complex issue. It is hard to edit off-screen sounds. Current methods [14, 25, 32] primarily focus on the visual content to generate the corresponding sound, a subset of these methods [7, 9] considers editability. Nonetheless, the alignment between video and audio features is tricky, leading to deficiencies including 1) incorrect sound meanings and mismatched timing, 2) monotonous sound effects, and a lack of complex scenarios. Both lead to unsatisfactory results in the videosound generation task. + +We propose a novel framework named SonicVisionLM to solve the above deficiency, as shown in Fig. 1. SonicVisionLM is proposed by introducing three key components: video-to-text, text-based interaction, and text-to-audio generation. First, the video-to-text component focuses on generating sound effects for on-screen events. This step uses a VLM to identify appropriate sound descriptions from the input silent video. Following this, a timestamp detection network is trained to extract specific temporal information + +![](images/00caee69593690197395fbfbf327a758c565f0ff7f84769475aba3a4865645d5.jpg) +Figure 2. SonicVisionLM's framework. SonicVisionLM presents a composite framework designed to automatically recognize on-screen sounds coupled with a user-interactive module for editing off-screen sounds. The blue dashed box and arrows in the figure represent the visual automation workflow: First, a silent video goes into the system to determine the occurring events (text) and their timing (time). Then, this information conditions the generation of sounds matching the screen. The purple dotted box and arrows show how users can modify or add off-screen sounds. + +from the video. A key innovation within this framework is the design of a time-conditioned embedding, which is utilized to guide an audio adapter. After that, the text-based interaction component allows users to change the text and timestamps from a previous video-to-text component or to input new corresponding text-timestamp pairs for personalized sound design. Finally, the text-to-audio generation component accepts the text and timestamp conditions and inputs them into the LDM and adapter to generate diverse, time-synchronized, and controllable sounds. Simultaneously, We collect a text-to-single-sound dataset, named CondPromptBank, for sound effects caption and timing cues, comprising over ten thousand data points, covering 23 categories. The main contributions of this work are: + +- We propose a novel framework called SonicVisionLM and collect a dataset CondPromptBank specifically for training a time-controllable adapter. It ensures the generated sound aligns perfectly with our text input and maintains precise timing control. +- We introduce three pioneering components: video-to-text, text-based interaction, and text-to-audio generation. This unique combination facilitates the automatic recognition of on-screen sounds while enabling user customization of off-screen sounds. +- The proposed framework achieves state-of-the-art results on conditional and unconditional video-sound generation tasks. The conditional task can be noticeably enhanced in all metrics. (IoU: $22.4 \rightarrow 39.7$ ) + +# 2. Related Work + +Audio Generation can be broadly classified into two categories. The Text-to-Audio Generation field includes Text-to-Speech (TTS) and Text-to-Music (TTM). Leading TTS models, such as FastSpeech2 [29] and NaturalSpeech [33], now produce speech virtually indistinguishable from human speech. In TTM, MusicLM [1], Noise2Music [12], MusicGen [6] and MeLoDy [21] are aimed to generate music segments from text, bringing innovation to music composition and synthesis. Models like AudioGen [19], AudioLDM [24], Tango [10], and Make-an-Audio [13] focuses on universal audio generation modeling. AudioGen [19] treats audio generation as a conditional language modelling task, while the other three models employ latent diffusion methods to accomplish sound generation. Current methods use datasets including sound effects, voices, and music, but practical applications use these elements separately. As the textual descriptions of time are subjective, videos are more intuitive and precise, so V2A requires more accurate semantic features and time control than T2A. Therefore, we have created a text-to-single-sound dataset called CondPromptBank with detailed semantic segmentation and temporal annotations that help models produce high-quality sound effects for videos. In Video-to-Audio Generation task, SpecVQGAN [14] utilizes a Transformer-based autoregressive model, drawing on ResNet50 or RGB+Flow features to generate sound. Im2Wav [32] uses a dual-transformer model conditioned on CLIP features for sound generation. CondFoleyGen [9] and VARIETYSOUND [7] + +introduce tasks for controllable timbre generation. Diff-foley [25] uses contrastive audio-visual pretraining to align audio and visual features. ClipSonic [8] learns the text-audio correspondence by leveraging the audio-visual correspondences in videos and the multi-modal representation learned by pre-trained VLMs. However, the sounds generated by these methods often suffer from poor audio-visual synchronization, noticeable noises, and lack of editability. Unlike the works above, our model ensures audio-visual synchronization, enriches diversity, and supports personalized user edits. Our model provides a more comprehensive sound solution for video production. + +Diffusion Model has been utilized for generating both mel-spectrogram generation [4, 28], and waveform generation [3, 20, 22]. However, their iterative generation process can be slow for high-dimensional data. Models such as AudioLDM [24], Make-An-Audio [13], and Tango [10] have successfully trained diffusion models within a continuous latent space. Nevertheless, achieving satisfactory results in controlling LDM for audio generation tasks remains challenging. This paper aims to introduce time control to ensure audio-visual synchronization. + +Vision Language Models like ChatGPT-4, which demonstrated advanced multi-modal abilities and inspired vision-language LLMs. Vision-LLM [36] and LLaVA [34] focus on aligning image inputs with large language models Vicuna[5] exhibit similar multi-modal capabilities. Recent developments in this field include MiniGPT-v2 [2]. Kosmos-2 [27] demonstrates multi-modal LLMs' ability to perform visual grounding. In this paper, we first introduce the VLMs to the audio generation task. + +# 3. Method + +# 3.1. Overview + +In this section, we introduce the framework of SonicVisionLM, as shown in Fig. 2. Before delving into the specific design details, we first briefly overview the preliminary knowledge (Sec. 3.2). Then, we introduce the Visual-to-Audio Event Detection Module (Sec. 3.3), which obtains textual descriptions of on-screen sounds through VLMs. Subsequently, we present the Sound Event Timestamp Detection Module (Sec. 3.4), designed to accurately detect the timing information through network architecture. Finally, we introduce the proposed time-controllable adapter as an extension of the audio diffusion model (Sec. 3.5), enabling the generation of multiple sounds that are semantically coherent and temporally aligned. + +# 3.2. Preliminaries + +Audio Diffusion Model. The text-prompt encoder encodes the input description $\tau \in R^{L\times d_t}$ of the sound, where $L$ is the token count and $d_{t}$ and is the token-embedding size. + +The latent diffusion model (LDM) is used to construct the audio prior $z_0$ with the guidance of text encoding $\tau$ . This essentially reduces to approximating the true prior $q(z_0 \mid \tau)$ with parameterized $p(z_0 \mid \tau)$ . LDM can achieve the above through forward and reverse diffusion processes. The forward diffusion is a Markov chain of Gaussian distributions with scheduled noise parameters $0 < \beta_1 < \beta_2 < \dots < \beta_N < 1$ to sample noisier versions of $z_0$ , where $N$ is the number of forward diffusion steps. For each step $n$ , we define $\alpha_n = 1 - \beta_n$ , and calculate the cumulative product $\bar{\alpha}_n = \prod_{i=1}^n \alpha_n$ . The diffusion equations are described as follows: + +$$ +q \left(z _ {n} \mid z _ {n - 1}\right) = \mathcal {N} \left(\sqrt {1 - \beta_ {n}} z _ {n - 1}, \beta_ {n} \mathbf {I}\right), \tag {1} +$$ + +$$ +q \left(z _ {n} \mid z _ {0}\right) = \mathcal {N} \left(\sqrt {\bar {\alpha} _ {n}} z _ {0}, \left(1 - \bar {\alpha} _ {n}\right) \mathbf {I}\right), \tag {2} +$$ + +where the noise term $\epsilon$ and the final step of the forward process yields $z_{N}$ follow a Gaussian distribution, specifically $\epsilon ,z_{N}\sim \mathcal{N}(0,I)$ . The reverse process denoises and reconstructs $z_{0}$ through text-guided noise estimation $(\hat{\epsilon}_{\theta})$ using following loss function: + +$$ +\mathcal {L} _ {D M} = \sum_ {n = 1} ^ {N} \gamma_ {n} \mathbb {E} _ {\epsilon_ {n} \sim \mathcal {N} (\mathbf {0}, \mathbf {I}), z _ {0}} \left\| \epsilon_ {n} - \hat {\epsilon} _ {\theta} ^ {(n)} (z _ {n}, \tau) \right\| _ {2} ^ {2}, \tag {3} +$$ + +After training LDM, we generate audio latent by sampling through the reverse process with $z_{N} \sim \mathcal{N}(0,I)$ , conditioned on the given textual representation $\tau$ . Its reverse dynamics are shown below: + +$$ +p _ {\theta} \left(z _ {n - 1} \mid z _ {n}, \tau\right) = \mathcal {N} \left(\mu_ {\theta} ^ {(n)} \left(z _ {n}, \tau\right), \tilde {\beta} ^ {(n)}\right), \tag {4} +$$ + +$$ +\mu_ {\theta} ^ {(n)} \left(z _ {n}, \tau\right) = \frac {1}{\sqrt {\alpha_ {n}}} \left[ z _ {n} - \frac {1 - \alpha_ {n}}{\sqrt {1 - \bar {\alpha} _ {n}}} \hat {\epsilon} _ {\theta} ^ {(n)} \left(z _ {n}, \tau\right) \right], \tag {5} +$$ + +$$ +\tilde {\beta} ^ {(n)} = \frac {1 - \bar {\alpha} _ {n - 1}}{1 - \bar {\alpha} _ {n}} \beta_ {n}. \tag {6} +$$ + +The noise estimation $(\hat{\epsilon}_{\theta})$ is parameterized with U-Net framework [30] with a cross-attention component to include the text guidance $\tau$ . + +After that, the decoder of audio VAE [18] constructs a mel-spectrogram feature from the latent audio representation $\hat{z}_0$ . This mel-spectrogram feature is conveyed to a vocoder to generate the final audio. + +# 3.3. Visual-to-Audio Event Understanding Module + +The diversity of sound is influenced by various factors such as its source, actions, the environment, and more. At the same time, these factors are often included in the description of visual images. Inspired by the widespread use of VLMs [23, 37, 39], we chose MiniGPT-v2 [2] to process visual information and generate descriptions of sounds. Recognizing that MiniGPT-v2 was initially developed for single-image understanding and its limitations in conveying dynamic information, we have adapted the + +LLaMA-2 [34] conversation template design to suit a multimodal instructional framework. To not miss sound events, we encoded four random video frames with time-sensitive prompts (temporal cues): + +```erlang +First, >$ ImageFeature $>>$ Img>. Then, >$ ImageFeature $>>$ Img>. After that, >$ ImageFeature $>>$ Img>. Finally, >$ ImageFeature $>>$ Img>. [Task Identifier] Instruction +``` + +# 3.4. Sound Event Timestamp Detection Module + +In practice, sound artists need to manually determine the point in time when a sound event starts and ends and then adjust the appropriate sound effect to the correct position. This judgment is usually based on current visual information. To simplify the process, we use the sound event timestamp detection module to detect the timestamp of the sound event in the video inspired by the CondFoleyGen [9]. Instead of using a hand-crafted approach to transfer sounds from the conditional audio, We use a ResNet(2+1)-D18 [35] visual network to capture timestamps as time-conditional inputs to the LDM, trained on paired video and timestamp. + +The workflow begins with feeding a sequence of silent video frames $V_{f}$ into the detection network. The network then outputs a binary vector $V_{ct}$ representing predictions for each frame, derived from a fully connected layer post-pooling. The ground truth $V_{ct}$ is obtained: Function $P$ detects audio $a$ in each frame, applying a threshold $x$ to reduce noise effects. Sounds within 0.02s across consecutive frames are considered a single event. This method identifies the start $x_{start}$ and end points $x_{end}$ of sound segments, as delineated in Eq. 7. Based on timestamps, we construct $T_{ct}$ , as depicted in Eq. 8, where 1 indicates the presence of sound, and 0 indicates the absence. The process equations are as follows: + +$$ +x _ {\text {s t a r t}}, x _ {\text {e n d}} = P \left(a _ {c}\right), \tag {7} +$$ + +$$ +T _ {c t} = \left\{ \begin{array}{l l} 1, i f t i n [ x _ {\text {s t a r t}}, x _ {\text {e n d}} ], \\ 0, e l s e. \end{array} \right. \tag {8} +$$ + +Finally, $T_{ct}$ is adjusted to correspond with the video frames' duration, represented as $V_{ct}$ . We employ binary cross-entropy loss to penalize inaccuracies in time prediction. Given that an input video may contain multiple sound events, each sound event's weights are based on its duration relative to the total sound duration in the video. The binary vector $T_{ct}$ serves as input for the Time-controllable Latent Diffusion Model. The whole process and network structure are shown in Fig. 3. + +# 3.5. Time-controllable Latent Diffusion Model + +In our experimentation, we observed that the results generated were semantically inaccurate and temporally unsynchronized. This issue often arose when utilizing audio-visual datasets to train end-to-end models, limiting the + +![](images/9aa7556e896714aabe96004f88cf17ba553d548f048d5ebdb1acbbb4f130c9db.jpg) +Figure 3. Sound Event Timestamp Detection Module. The network analyzes the video's features to output a binary vector corresponding to the video's frame count. Within this vector, sections marked in white (value of 1) mean sound presence, and those in black (value of 0) indicate sound absence. + +task's practical application. We attribute these shortcomings to the complexity of the sound sources and the poor audio quality of the audio-visual dataset used for training. To address this, we use text to bridge audio and video and then introduce time control in the T2A generation model. In the visual domain, many works are based on the ControlNet [40] architecture, which can finer control the generation of images or videos by manipulating the input image conditions of neural network blocks. However, unlike the visual domain's inherent intuitiveness, audio features exhibit temporal continuity and are inherently more complex and abstract. Thus, selecting appropriate audio features to guide the generation process poses a greater challenge. + +In this paper, we propose a embedding called Audio Time-condition Embedding, denote as $A_{ct}$ , which is constructed through the following procedure: During the training phase, the adapter extracted Mel-spectrogram features from audio waveform $a$ and then normalized it, denoted as $a_{mel} = mel(a)$ . For $a_{c} = \max (mel(a), T_{ct})$ , we then initialize $a_{c}$ to match $a_{mel}$ 's dimensions but with zero values, then fill $a_{c}$ 's Mel channels with the maximum values based on the corresponding frames where $T_{ct}$ equals 1. Finally, $A_{ct}$ is derived by encoding the embedding of $a_{c}$ via the encoder $E_{a}$ , and described as follows: + +$$ +A _ {c t} = E _ {a} \left(\max \left(\operatorname {m e l} \left(a _ {c}\right), T _ {c t}\right)\right). \tag {9} +$$ + +Inspired by ControlNet [40], we have developed a network architecture named Time-controllable Adapter. Then, we integrate the audio time-condition embedding $A_{ct}$ with the text embedding $\tau$ and target audio embedding into the neural network block. This integration facilitates joint training for the time-controllable adapter. $A_{ct}$ is fed solely into the adapter, while text embedding $\tau$ inputs into both Tango and the adapter. + +Tango's denoising model, akin to UNet, includes encoder $F$ , middle block $M$ , and decoder $G$ . $F$ and $G$ have 12 corresponding blocks. Tango's outputs of the encoder's + +$i - th$ block and decoder's $j - th$ block are $f_{i}$ and $g_{j}$ , with $m$ for the single middle block. The adapter mimics Tango's encoder and middle layers as $F'$ and $M'$ . Adapter's outputs, like $f_{i}'$ and $m'$ , are marked with $(')$ . Following this, the output of the time-controllable adapter is concatenated with the output of the corresponding decoder block during the decoding process. For example, $f_{1}$ from the 1st encoder layer adds to $g_{12}$ of the decoder, making $i + j = 13$ . To achieve it, we ensure that all Tango's elements are kept frozen while modifying the input of the $i - th$ block of the decoder as: + +$$ +\left\{ \begin{array}{l} \text {C o n c a t} \left(m + m ^ {\prime}, f _ {j} + z e r o \left(f _ {j} ^ {\prime}\right)\right) i = 1, j = 1 2. \\ \text {C o n c a t} \left(g _ {i - 1}, f _ {j} + z e r o \left(f _ {j} ^ {\prime}\right)\right) 2 \leqslant i \leqslant 1 2, i + j = 1 3. \end{array} \right. \tag {10} +$$ + +zero(\cdot) is one zero convolutional layer, facilitating trainable and fixed neural network block connections. Its weights evolve from zero to optimized values during training. This approach not only retains the Tango's capability for generating audio, trained on billions of audio-text pairs, but also enables the model to comprehend the guidance provided by the time control embedding, resulting in temporally controllable outcomes. + +Table 1. Distribution of CondPromptBank Categories + +
Category%Category%Category%
Household Daily14.11Transportation Vehicles10.42Impacts Crashes10.10
Foley8.24Human Elements7.77Industrial6.58
Weapons War5.83Cartoon Comical4.90Sports4.43
Animals Insects4.04Instruments3.68Water Liquid3.27
Technology2.70Horror2.41Emergency2.20
Public Places1.87Sound Design Effects1.69Doors Windows1.56
Fire Explosions1.49Nature Weather1.02Leisure0.84
Multimedia0.47Bells0.37
+ +# 4. Experiments + +# 4.1. Experiment Settings + +Dataset. Since Tango's training datasets include varied audio types like speech, sound effects, and music, it tends to produce mixed audio outputs. Our task requires distinct handling of these audio types, ensuring each sound event is separate. To meet our specific needs, we developed CondPromptBank, a high-quality dataset of single sound effects crafted for training time-controlled adapters. This dataset consists of 10,276 individual data entries, each with a sound effect, title, and start/end timestamps. Each sound is typically 10 seconds or shorter, sourced from freely available sound effect libraries and websites. During the collection, we focused on 23 common categories of sound effects and manually filtered out low-quality data with noise and mixed sources. The category distribution shows Tab. 1. To enhance the textual descriptions with precise details, we further annotated the sound effect text labels with fine-grained information based on sound characteristics. Now, each label not only identifies the audio source but also describes the associated actions in detail. We believe the division into single audio sources is crucial, as videos provide a more concrete + +expression of content than text, thus requiring more precise sound representation. + +Implementation details. To train our complete model, we first train the adapter on CondPromtBank, then train the timestamps detection net on Greatest Hits [26] and Countix-AV dataset [41]. We trained the adapter for approximately 200 epochs with a batch size 32 and a learning rate of $3.0 \times 10^{-5}$ using Adam [17]. Our model has two versions: small and full. The difference between them is the version of pre-trained parameters used for Tango. We trained the timestamps detection net for 70 epochs with a batch size of 24 and a learning rate of $1.0 \times 10^{-5}$ . The training of the adapter takes approximately five days, and the training of the timestamps detection network requires approximately one day using one NVIDIA A6000 GPU. + +# 4.2. Conditional Generation Task Results + +We tested our model using the Greatest Hits [26] dataset, which has 977 videos of drumsticks interacting with different objects, lasting 11 hours. This dataset is divided into two types of actions and 17 types of materials. This detailed categorization helps check if our model can change sound types based on these details but still match the target action. We used the same test settings as CondFoleyGen [9] and compared our results with theirs. + +Evaluation Metrics. For the conditional generation task, we use the following five objective metrics to evaluate the performance of the model: CLAP-top, Onset Acc [9], Onset AP [9], Time Acc, and IoU. + +Quantitative Results. SonicVisionLM-full demonstrates superior performance over CondFoleyGen across all metrics, as seen in Tab. 2. It achieves leading scores of $36.8\%$ and $42.8\%$ on CLAP-top versions, exceeding any CondFoleyGen model by more than $20\%$ . This result suggests that it is better at matching sounds to text prompts. Our model significantly surpasses CondFoleyGen in audio-visual synchronization, evidenced by an $11\%$ improvement in Onset AP and a $16\%$ rise in IoU. Moreover, we see a $6\%$ enhancement in onset accuracy and an $8.3\%$ increase in timing precision. These advancements illustrate our model's outstanding accuracy in sound event detection and its effectiveness in synchronizing generated sounds with the input video. We think CondFoleyGen relies on the audio-visual synchronization module [15] to improve time accuracy, requiring many samples to re-ranking the sounds. In contrast, our model gets higher synchronization during the generation process with fewer samples. + +Qualitative Results. As shown in Fig. 4 (row 4, 6, 7), we compare the timestamped positional distance to the target sound. Our results closely match the target sound, demonstrating a high degree of accuracy. However, CondFoleyGen often produces results with the wrong number of sounds and with a large difference in the positional distance. + +
MethodCLAP - topgeneral↑CLAP - topunfused↑Onset Acc ↑Onset AP↑Time Acc↑IoU↑
CondFoleyGen(old)* [9]17.315.621.667.035.523.3
CondFoleyGen(new) * [9]16.313.619.268.637.422.4
Ours-small29.628.019.477.0327.835.6
Ours-full36.842.827.678.143.839.7
+ +Table 2. Conditional Generation Task Quantitative Results. CLAP-top metric evaluates a model's ability to control sound content. It calculates the percentage of times the sound samples generated by all models ranked in the top 1 according to the CLAP ranking, divided by the total number of samples. We used two versions of the CLAP models for evaluation: $CLAP_{general}$ and $CLAP_{unfused}$ . Onset Acc and Time Acc are both metrics based on the number of sound occurrences, with Onset Acc focusing on the onset count and Time Acc on the count of time intervals. We measure the average accuracy of predicting onsets within 0.1s of ground truth to assess the timing of generated onsets. IoU is calculated by computing the intersection and union of these vectors. These metrics collectively allow us to comprehensively evaluate the accuracy of the generated sounds in terms of both timing and content. The variant "old" corresponds to the prior codebook, while variant "new" matches the updated codebook. The old model was trained on 192-width spectrograms, and the new one was trained on 2s waveforms. \*\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. The six metrics are all measured in percentage. + +![](images/3081aef1559e8b0e08d194c805a3f92bba882fa2651c733f7c6e52369a57db11.jpg) +Figure 4. Conditional Generation Task Qualitative Results. The red dashed boxes are the conditional audio inputs and generated results for CondFoleyGen, and the blue dashed boxes are the conditional text inputs and results corresponding to SonicVisionLM. + +This indicates that our model has a higher visual-audio synchronization than CondFoleyGen. As shown in Fig. 4 (column 3, 7), we compare the sound shape to the conditional sound. Even though our model has not learned any timbre on the Greatest Hits dataset, our results are still very similar to the conditional sound. As shown in Fig. 4 (column 1, 7), The mel-spectrograms of the CondFoleyGen results do not produce sounds that are similar to, and sometimes blurred. + +# 4.3. Unconditional Generation + +To evaluate the task of unconditional sound generation, considering that our LDM has not been trained on + +audio-visual datasets, we have chosen to perform quantitative evaluation and qualitative evaluation on two datasets: Greatest Hits [26] and CountixAV [41], which are zero-shot tasks for all models. We use two state-of-the-art V2A models as baselines: SpecVQGAN [14] and DIFF-FOLEY [25]. + +Evaluation Metrics. For objective evaluation, we have employed three metrics as [14, 25]: Inception Score (IS) [31], Frechet Distance (FID) [11], and Mean KL Divergence (MKL) [14]. For subjective evaluation, as the [9], we conduct user evaluations for the three critical components: overall audio quality (OVL), alignment with the input video (REL), and time synchronization (Time-sync). + +
Metric
Dataset MethodGreatest HitsCountix-AV
MKL↓FID ↓IS↑IoU↑MKL↓FID ↓IS↑IoU ↑
\(SpecVQGAN^* [14]\)6.8082.42.1725.87.3934.15.334.9
DIFF-FOLEY†[25]5.6820.03.8422.04.915.95.231.3
Ours-small6.4631.93.8836.610.021.715.137.5
Ours-full4.6724.93.2639.59.7119.712.742
+ +![](images/75e5efff9a493a163ecfccd6effd1147605f9261dd7f290efe31ddd6017d64c3.jpg) +Figure 5. Unconditional Generation Task Qualitative Results. The left example is from CountixAV, and the right one is from Greatest Hits. We're comparing them side by side. The dashed box highlights examples of both good and bad results we generated. + +Table 3. Unconditional Sound Generation Quantitative Results. IS assesses the quality and diversity of generated samples, FID measures distribution-level similarity, and MKL measures paired sample-level similarity. \*\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. \*\* denotes that data is obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage. + +
MethodOVL↑REL↑Time-sync ↑
SpecVQGAN* [14]372531
DIFF-FOLEY† [25]486458
Ours756987
+ +Table 4. Subjective Results. Following [9], we invited the 300 English-proficient evaluators to rate 30 randomly selected audio samples from three perspectives: OVL, REL, and Time-sync. Scores were averaged on a 1-100 scale. “**” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. “†” denotes data obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance. + +Quantitative Results. In our experiments, the choice of vocoder significantly influenced the FID metric. We upgraded from DIFF-FOLEY's weak Griffin-Lim vocoder to the superior MelGAN to ensure fairness. Despite our model using 64 Mel filters compared to MelGAN's 80, our performance on the Greatest Hits dataset excels in MKL, IS, and IoU metrics, as shown in Tab. 3. This underscores our model's precise time control and high-quality sound generation, demonstrating its exceptional capability to produce + +sounds that align closely with the ground truth. In the CountixAV dataset, SonicVisionLM-small outperforms baselines by nearly 10 points in the IS metric, highlighting its exceptional sound quality. Despite slightly lower MKL and FID scores compared to baselines, we do not view this as a drawback. Unlike the Greatest Hits dataset, which was recorded in high quality with specialized recording equipment, the CountixAV dataset is sourced from diverse YouTube videos. It often includes sounds marred by low-quality background noise or mixed sound sources, especially human vocals. MKL and FID metrics emphasize similarity to the ground truth. Since DIFF-FOLEY was trained on similar audiovisual data, its tendency to mix multiple sounds in response to complex visual information explains its advantage in these metrics. Our model, targeting sound events from specific actions and filtering out irrelevant auditory information, diverges from the ground truth, a deliberate choice to enhance sound event relevance. The IoU metrics show that our model makes sound at the correct times and remains silent otherwise. To further argue our point, we conducted a subjective assessment of three aspects of OVL, REL, and Time-sync. As shown in Tab. 4, our model performed sig + +
MethodFD↓FAD↓KL↓IoU↑
tango-small* [10]44.911.53.4741.3
Ours-small26.22.052.3071.6
tango-full* [10]44.310.873.1439.3
Ours-full25.43.192.3265.7
+ +Table 5. Time Condition Ablation Results. “*” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage. + +![](images/e48b0da71d8c895f44e1cec6fc105fd9acd1348a161c0358e6ab84737f82890f.jpg) +Figure 6. Conditioning-scale Ablation Study. In the chart, the higher the indicators are, the better they are. The brightness of the colour also represents a good or bad performance. + +![](images/d1d59b20e8dcd0a285f2964737226da410b9dde3e9a00707ddd358b8346b1c5b.jpg) +Silent Video +Figure 7. Multi-soundtracks generation example. In the video, the blue and green masks show different soundtracks. The timing of on-screen sounds (corresponding to visible actions) aligns accurately with their occurrence in the frames. Conversely, off-screen sounds (not visible in the video) lack precise timing. + +nificantly better than the baseline models in all metrics. + +Qualitative Results. For clearer time point comparison, we denoised the data from the CountixAV. Fig. 5 reveals our generated sounds are more precise than the baseline models. Furthermore, our model can capture finer-grained visual transformations, capturing the signal despite sudden changes in the frequency of movement and producing the correct sound. In contrast, SpecVQGAN results are full of noise. DIFF-FOLEY can sometimes generate clear sounds, but it is not aligned with the visual-sound synchronization. + +# 4.4. Ablation Study + +Time condition. Evaluation Metrics. We employed objective metrics from Tango [10], such as the Frechet Audio Distance (FAD) [16] and Frechet Distance(FD) [24] to measure the distribution difference between generated audio and ground truth without the need for any reference audio samples. KL divergence [19, 38] assesses their similarity based on the broad concepts present in the original and the generated audio signals. + +Result. we compared our model with the Tango [10]. As shown in Tab. 5, both in the small and full versions, our model outperforms Tango in terms of IoU, which validates the effectiveness of the time-controllable adapter. + +Conditioning-scale. As seen in the Fig. 6. The sound quality improves in the range from 0.6 to 2.0 on the conditioning scale as it lines up better with the IoU. But at 3.0, control goes down a lot. The best mix of good sound quality and steadiness is found at a conditioning scale equal to 2.0. + +# 4.5. Multi-soundtracks generation + +As shown in Fig. 7, SonicVisionLM works like a sound designer in traditional video post-production. First, it looks at the visual information to find the key sounds needed. For example, it picks out the hissing of cooking meat and the clinking of pots. Then, if the story needs it, the sound designer adds off-screen sounds. This might include extra kitchen sounds like distant chopping, simmering pots, or the buzz of kitchen machines, making it feel more natural. Lastly, SonicVisionLM puts these audio tracks in the right place on the video timeline. This ensures the sounds match perfectly with what is happening in the video, creating a smooth audio-visual experience. More detailed results can be found in the Supplementary Materials. + +# 5. Conclusion + +In this paper, we propose SonicVisionLM, which utilizes the capabilities of powerful vision-language models (VLMs). When provided with a silent video, SonicVisionLM first identifies events within the video using a VLM to suggest possible sounds that match the video content. SonicVisionLM demonstrates outstanding performance in both conditional and unconditional generation tasks. Further, we tested its efficacy in post-production, focusing on automatic recognition of on-screen sounds and personalized editing for off-screen sounds. Extensive experiments show the superior performance of our method. + +Limitations. While SonicVisionLM has achieved adequate results, refinements in the visual understanding and times-tamp detection parts are still required. Regarding various multimedia contexts, expanding the diversity and range of audio generation control are still the key demands of applications. Thus, the model should enrich the audio-visual experience and broaden applicability in future attempts. + +# References + +[1] Andrea Agostinelli, Timo I Denk, Zalán Borsos, Jesse Engel, Mauro Verzetti, Antoine Caillon, Qingqing Huang, Aren Jansen, Adam Roberts, Marco Tagliasacchi, et al. 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However, existing methods for video-sound generation attempt to directly create sound from visual representations, which can be challenging due to the difficulty of aligning visual representations with audio representations. In this paper, we present SonicVisionLM, a novel framework aimed at generating a wide range of sound effects by leveraging vision-language models(VLMs). Instead of generating audio directly from video, we use the capabilities of powerful VLMs. When provided with a silent video, our approach first identifies events within the video using a VLM to suggest possible sounds that match the video content. This shift in approach transforms the challenging task of aligning image and audio into more well-studied sub-problems of aligning image-to-text and text-to-audio through the popular diffusion models. 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Creating soundtracks for videos is a vital aspect of video produc" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 225, + 547, + 361 + ], + "blocks": [ + { + "bbox": [ + 307, + 225, + 547, + 361 + ], + "lines": [ + { + "bbox": [ + 307, + 225, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 307, + 225, + 547, + 361 + ], + "type": "image", + "image_path": "4bbd06805daadfdfae81d8e85519c1d3b0b7eee92413b32129e7f8e5f6db61d1.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 365, + 546, + 420 + ], + "lines": [ + { + "bbox": [ + 305, + 365, + 546, + 420 + ], + "spans": [ + { + "bbox": [ + 305, + 365, + 546, + 420 + ], + "type": "text", + "content": "Figure 1. A model implements the automatic detection of on-screen sound generation and accepts the user's editing of text and time in the off-screen section. On-screen sound refers to audio that originates from visible actions within the video frame. Off-screen sound is not directly observable on the screen." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 426, + 545, + 449 + ], + "type": "text", + "content": "tion, but it can be labour-intensive for artists. Therefore, the video-sound generation task has gained notable attention." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 450, + 546, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 546, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 546, + 605 + ], + "type": "text", + "content": "Although the recent approaches have made great efforts, the video-sound generation task is still challenging. For onscreen sounds, achieving semantic relevance and maintaining temporal synchronization continues to be a complex issue. It is hard to edit off-screen sounds. Current methods [14, 25, 32] primarily focus on the visual content to generate the corresponding sound, a subset of these methods [7, 9] considers editability. Nonetheless, the alignment between video and audio features is tricky, leading to deficiencies including 1) incorrect sound meanings and mismatched timing, 2) monotonous sound effects, and a lack of complex scenarios. Both lead to unsatisfactory results in the videosound generation task." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "We propose a novel framework named SonicVisionLM to solve the above deficiency, as shown in Fig. 1. SonicVisionLM is proposed by introducing three key components: video-to-text, text-based interaction, and text-to-audio generation. First, the video-to-text component focuses on generating sound effects for on-screen events. This step uses a VLM to identify appropriate sound descriptions from the input silent video. Following this, a timestamp detection network is trained to extract specific temporal information" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "† Corresponding author." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "26866" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 547, + 295 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 547, + 295 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 547, + 295 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 547, + 295 + ], + "type": "image", + "image_path": "00caee69593690197395fbfbf327a758c565f0ff7f84769475aba3a4865645d5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 299, + 547, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 299, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 547, + 354 + ], + "type": "text", + "content": "Figure 2. SonicVisionLM's framework. SonicVisionLM presents a composite framework designed to automatically recognize on-screen sounds coupled with a user-interactive module for editing off-screen sounds. The blue dashed box and arrows in the figure represent the visual automation workflow: First, a silent video goes into the system to determine the occurring events (text) and their timing (time). Then, this information conditions the generation of sounds matching the screen. The purple dotted box and arrows show how users can modify or add off-screen sounds." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 358, + 289, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 289, + 526 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 289, + 526 + ], + "type": "text", + "content": "from the video. A key innovation within this framework is the design of a time-conditioned embedding, which is utilized to guide an audio adapter. After that, the text-based interaction component allows users to change the text and timestamps from a previous video-to-text component or to input new corresponding text-timestamp pairs for personalized sound design. Finally, the text-to-audio generation component accepts the text and timestamp conditions and inputs them into the LDM and adapter to generate diverse, time-synchronized, and controllable sounds. Simultaneously, We collect a text-to-single-sound dataset, named CondPromptBank, for sound effects caption and timing cues, comprising over ten thousand data points, covering 23 categories. The main contributions of this work are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 544, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 544, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 544, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 544, + 287, + 604 + ], + "type": "text", + "content": "- We propose a novel framework called SonicVisionLM and collect a dataset CondPromptBank specifically for training a time-controllable adapter. It ensures the generated sound aligns perfectly with our text input and maintains precise timing control." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 604, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 604, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 604, + 287, + 662 + ], + "type": "text", + "content": "- We introduce three pioneering components: video-to-text, text-based interaction, and text-to-audio generation. This unique combination facilitates the automatic recognition of on-screen sounds while enabling user customization of off-screen sounds." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 664, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 664, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 664, + 287, + 712 + ], + "type": "text", + "content": "- The proposed framework achieves state-of-the-art results on conditional and unconditional video-sound generation tasks. The conditional task can be noticeably enhanced in all metrics. (IoU: " + }, + { + "bbox": [ + 47, + 664, + 287, + 712 + ], + "type": "inline_equation", + "content": "22.4 \\rightarrow 39.7" + }, + { + "bbox": [ + 47, + 664, + 287, + 712 + ], + "type": "text", + "content": ")" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 357, + 392, + 370 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 392, + 370 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 392, + 370 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 378, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 547, + 715 + ], + "type": "text", + "content": "Audio Generation can be broadly classified into two categories. The Text-to-Audio Generation field includes Text-to-Speech (TTS) and Text-to-Music (TTM). Leading TTS models, such as FastSpeech2 [29] and NaturalSpeech [33], now produce speech virtually indistinguishable from human speech. In TTM, MusicLM [1], Noise2Music [12], MusicGen [6] and MeLoDy [21] are aimed to generate music segments from text, bringing innovation to music composition and synthesis. Models like AudioGen [19], AudioLDM [24], Tango [10], and Make-an-Audio [13] focuses on universal audio generation modeling. AudioGen [19] treats audio generation as a conditional language modelling task, while the other three models employ latent diffusion methods to accomplish sound generation. Current methods use datasets including sound effects, voices, and music, but practical applications use these elements separately. As the textual descriptions of time are subjective, videos are more intuitive and precise, so V2A requires more accurate semantic features and time control than T2A. Therefore, we have created a text-to-single-sound dataset called CondPromptBank with detailed semantic segmentation and temporal annotations that help models produce high-quality sound effects for videos. In Video-to-Audio Generation task, SpecVQGAN [14] utilizes a Transformer-based autoregressive model, drawing on ResNet50 or RGB+Flow features to generate sound. Im2Wav [32] uses a dual-transformer model conditioned on CLIP features for sound generation. CondFoleyGen [9] and VARIETYSOUND [7]" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26867" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 215 + ], + "type": "text", + "content": "introduce tasks for controllable timbre generation. Diff-foley [25] uses contrastive audio-visual pretraining to align audio and visual features. ClipSonic [8] learns the text-audio correspondence by leveraging the audio-visual correspondences in videos and the multi-modal representation learned by pre-trained VLMs. However, the sounds generated by these methods often suffer from poor audio-visual synchronization, noticeable noises, and lack of editability. Unlike the works above, our model ensures audio-visual synchronization, enriches diversity, and supports personalized user edits. Our model provides a more comprehensive sound solution for video production." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 216, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 289, + 335 + ], + "type": "text", + "content": "Diffusion Model has been utilized for generating both mel-spectrogram generation [4, 28], and waveform generation [3, 20, 22]. However, their iterative generation process can be slow for high-dimensional data. Models such as AudioLDM [24], Make-An-Audio [13], and Tango [10] have successfully trained diffusion models within a continuous latent space. Nevertheless, achieving satisfactory results in controlling LDM for audio generation tasks remains challenging. This paper aims to introduce time control to ensure audio-visual synchronization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 289, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 444 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 444 + ], + "type": "text", + "content": "Vision Language Models like ChatGPT-4, which demonstrated advanced multi-modal abilities and inspired vision-language LLMs. Vision-LLM [36] and LLaVA [34] focus on aligning image inputs with large language models Vicuna[5] exhibit similar multi-modal capabilities. Recent developments in this field include MiniGPT-v2 [2]. Kosmos-2 [27] demonstrates multi-modal LLMs' ability to perform visual grounding. In this paper, we first introduce the VLMs to the audio generation task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 456, + 105, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 105, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 105, + 468 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 475, + 115, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 115, + 488 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 115, + 488 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 494, + 289, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 289, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 289, + 651 + ], + "type": "text", + "content": "In this section, we introduce the framework of SonicVisionLM, as shown in Fig. 2. Before delving into the specific design details, we first briefly overview the preliminary knowledge (Sec. 3.2). Then, we introduce the Visual-to-Audio Event Detection Module (Sec. 3.3), which obtains textual descriptions of on-screen sounds through VLMs. Subsequently, we present the Sound Event Timestamp Detection Module (Sec. 3.4), designed to accurately detect the timing information through network architecture. Finally, we introduce the proposed time-controllable adapter as an extension of the audio diffusion model (Sec. 3.5), enabling the generation of multiple sounds that are semantically coherent and temporally aligned." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 134, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 134, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 134, + 671 + ], + "type": "text", + "content": "3.2. Preliminaries" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Audio Diffusion Model. The text-prompt encoder encodes the input description " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\tau \\in R^{L\\times d_t}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " of the sound, where " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " is the token count and " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "d_{t}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " and is the token-embedding size." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": "The latent diffusion model (LDM) is used to construct the audio prior " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " with the guidance of text encoding " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ". This essentially reduces to approximating the true prior " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "q(z_0 \\mid \\tau)" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " with parameterized " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "p(z_0 \\mid \\tau)" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ". LDM can achieve the above through forward and reverse diffusion processes. The forward diffusion is a Markov chain of Gaussian distributions with scheduled noise parameters " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "0 < \\beta_1 < \\beta_2 < \\dots < \\beta_N < 1" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " to sample noisier versions of " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "z_0" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": " is the number of forward diffusion steps. For each step " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ", we define " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\alpha_n = 1 - \\beta_n" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ", and calculate the cumulative product " + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_n = \\prod_{i=1}^n \\alpha_n" + }, + { + "bbox": [ + 304, + 72, + 547, + 215 + ], + "type": "text", + "content": ". The diffusion equations are described as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 332, + 216, + 545, + 237 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 216, + 545, + 237 + ], + "spans": [ + { + "bbox": [ + 332, + 216, + 545, + 237 + ], + "type": "interline_equation", + "content": "q \\left(z _ {n} \\mid z _ {n - 1}\\right) = \\mathcal {N} \\left(\\sqrt {1 - \\beta_ {n}} z _ {n - 1}, \\beta_ {n} \\mathbf {I}\\right), \\tag {1}", + "image_path": "a467e367c8d52bb2d519f8bf10167f0773f3c1e237ed03b83fa881d98aebb486.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 341, + 241, + 545, + 256 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 241, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 341, + 241, + 545, + 256 + ], + "type": "interline_equation", + "content": "q \\left(z _ {n} \\mid z _ {0}\\right) = \\mathcal {N} \\left(\\sqrt {\\bar {\\alpha} _ {n}} z _ {0}, \\left(1 - \\bar {\\alpha} _ {n}\\right) \\mathbf {I}\\right), \\tag {2}", + "image_path": "898670c44f2ea58dc94538ba7753c1ef4b548ef4324ba86c4b2b987f99981b11.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "content": "where the noise term " + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "content": " and the final step of the forward process yields " + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "inline_equation", + "content": "z_{N}" + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "content": " follow a Gaussian distribution, specifically " + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "inline_equation", + "content": "\\epsilon ,z_{N}\\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "content": ". The reverse process denoises and reconstructs " + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "inline_equation", + "content": "z_{0}" + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "content": " through text-guided noise estimation " + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "inline_equation", + "content": "(\\hat{\\epsilon}_{\\theta})" + }, + { + "bbox": [ + 304, + 260, + 547, + 320 + ], + "type": "text", + "content": " using following loss function:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 314, + 323, + 545, + 356 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 323, + 545, + 356 + ], + "spans": [ + { + "bbox": [ + 314, + 323, + 545, + 356 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {D M} = \\sum_ {n = 1} ^ {N} \\gamma_ {n} \\mathbb {E} _ {\\epsilon_ {n} \\sim \\mathcal {N} (\\mathbf {0}, \\mathbf {I}), z _ {0}} \\left\\| \\epsilon_ {n} - \\hat {\\epsilon} _ {\\theta} ^ {(n)} (z _ {n}, \\tau) \\right\\| _ {2} ^ {2}, \\tag {3}", + "image_path": "a16ed092bad0b441074cc92b9c8848a071eabc90bf4956f639a31e65c7d5cec6.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "type": "text", + "content": "After training LDM, we generate audio latent by sampling through the reverse process with " + }, + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "type": "inline_equation", + "content": "z_{N} \\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "type": "text", + "content": ", conditioned on the given textual representation " + }, + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 364, + 547, + 410 + ], + "type": "text", + "content": ". Its reverse dynamics are shown below:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 334, + 410, + 545, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 410, + 545, + 430 + ], + "spans": [ + { + "bbox": [ + 334, + 410, + 545, + 430 + ], + "type": "interline_equation", + "content": "p _ {\\theta} \\left(z _ {n - 1} \\mid z _ {n}, \\tau\\right) = \\mathcal {N} \\left(\\mu_ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right), \\tilde {\\beta} ^ {(n)}\\right), \\tag {4}", + "image_path": "38bdc337d9734b948c8f630c708790a896b89a59c155c394833c4f3f75a81427.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 314, + 441, + 545, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 441, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 314, + 441, + 545, + 469 + ], + "type": "interline_equation", + "content": "\\mu_ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right) = \\frac {1}{\\sqrt {\\alpha_ {n}}} \\left[ z _ {n} - \\frac {1 - \\alpha_ {n}}{\\sqrt {1 - \\bar {\\alpha} _ {n}}} \\hat {\\epsilon} _ {\\theta} ^ {(n)} \\left(z _ {n}, \\tau\\right) \\right], \\tag {5}", + "image_path": "b4c6d1c1ad6e219c7c11b3b7578d1f4ab38ff7aef3868e594164d431d214cd90.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 376, + 473, + 545, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 473, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 376, + 473, + 545, + 498 + ], + "type": "interline_equation", + "content": "\\tilde {\\beta} ^ {(n)} = \\frac {1 - \\bar {\\alpha} _ {n - 1}}{1 - \\bar {\\alpha} _ {n}} \\beta_ {n}. \\tag {6}", + "image_path": "9ea710559cdc799be655c77e343bd5b0cc40f3a20d990bafcfc94fd923345926.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "type": "text", + "content": "The noise estimation " + }, + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "type": "inline_equation", + "content": "(\\hat{\\epsilon}_{\\theta})" + }, + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "type": "text", + "content": " is parameterized with U-Net framework [30] with a cross-attention component to include the text guidance " + }, + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 502, + 547, + 537 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 538, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 547, + 586 + ], + "type": "text", + "content": "After that, the decoder of audio VAE [18] constructs a mel-spectrogram feature from the latent audio representation " + }, + { + "bbox": [ + 304, + 538, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\hat{z}_0" + }, + { + "bbox": [ + 304, + 538, + 547, + 586 + ], + "type": "text", + "content": ". This mel-spectrogram feature is conveyed to a vocoder to generate the final audio." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 590, + 545, + 603 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 590, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 305, + 590, + 545, + 603 + ], + "type": "text", + "content": "3.3. Visual-to-Audio Event Understanding Module" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "The diversity of sound is influenced by various factors such as its source, actions, the environment, and more. At the same time, these factors are often included in the description of visual images. Inspired by the widespread use of VLMs [23, 37, 39], we chose MiniGPT-v2 [2] to process visual information and generate descriptions of sounds. Recognizing that MiniGPT-v2 was initially developed for single-image understanding and its limitations in conveying dynamic information, we have adapted the" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26868" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "LLaMA-2 [34] conversation template design to suit a multimodal instructional framework. To not miss sound events, we encoded four random video frames with time-sensitive prompts (temporal cues):" + } + ] + } + ], + "index": 0 + }, + { + "type": "code", + "bbox": [ + 45, + 122, + 289, + 183 + ], + "blocks": [ + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "lines": [ + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "spans": [ + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": "First, >" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " ImageFeature " + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "inline_equation", + "content": ">>" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " Img>. Then, >" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " ImageFeature " + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "inline_equation", + "content": ">>" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " Img>. After that, >" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " ImageFeature " + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "inline_equation", + "content": ">>" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " Img>. Finally, >" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " ImageFeature " + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "inline_equation", + "content": ">>" + }, + { + "bbox": [ + 45, + 122, + 289, + 183 + ], + "type": "text", + "content": " Img>. [Task Identifier] Instruction" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "code", + "guess_lang": "erlang" + }, + { + "bbox": [ + 47, + 187, + 272, + 200 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 187, + 272, + 200 + ], + "spans": [ + { + "bbox": [ + 47, + 187, + 272, + 200 + ], + "type": "text", + "content": "3.4. Sound Event Timestamp Detection Module" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 203, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 203, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 287, + 334 + ], + "type": "text", + "content": "In practice, sound artists need to manually determine the point in time when a sound event starts and ends and then adjust the appropriate sound effect to the correct position. This judgment is usually based on current visual information. To simplify the process, we use the sound event timestamp detection module to detect the timestamp of the sound event in the video inspired by the CondFoleyGen [9]. Instead of using a hand-crafted approach to transfer sounds from the conditional audio, We use a ResNet(2+1)-D18 [35] visual network to capture timestamps as time-conditional inputs to the LDM, trained on paired video and timestamp." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": "The workflow begins with feeding a sequence of silent video frames " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "V_{f}" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " into the detection network. The network then outputs a binary vector " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "V_{ct}" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " representing predictions for each frame, derived from a fully connected layer post-pooling. The ground truth " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "V_{ct}" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " is obtained: Function " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " detects audio " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " in each frame, applying a threshold " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " to reduce noise effects. Sounds within 0.02s across consecutive frames are considered a single event. This method identifies the start " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "x_{start}" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " and end points " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "x_{end}" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": " of sound segments, as delineated in Eq. 7. Based on timestamps, we construct " + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "inline_equation", + "content": "T_{ct}" + }, + { + "bbox": [ + 46, + 335, + 287, + 489 + ], + "type": "text", + "content": ", as depicted in Eq. 8, where 1 indicates the presence of sound, and 0 indicates the absence. The process equations are as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 118, + 490, + 286, + 501 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 490, + 286, + 501 + ], + "spans": [ + { + "bbox": [ + 118, + 490, + 286, + 501 + ], + "type": "interline_equation", + "content": "x _ {\\text {s t a r t}}, x _ {\\text {e n d}} = P \\left(a _ {c}\\right), \\tag {7}", + "image_path": "b8b2156a8cecfaea68a264410e04c205923dc0593c34750d3e57011099941b32.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 85, + 502, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 502, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 85, + 502, + 287, + 533 + ], + "type": "interline_equation", + "content": "T _ {c t} = \\left\\{ \\begin{array}{l l} 1, i f t i n [ x _ {\\text {s t a r t}}, x _ {\\text {e n d}} ], \\\\ 0, e l s e. \\end{array} \\right. \\tag {8}", + "image_path": "9711e4cd63b9ad025d3d604a239ed556730d09155041e178134cd59cd47e658d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": "Finally, " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "T_{ct}" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " is adjusted to correspond with the video frames' duration, represented as " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "V_{ct}" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": ". We employ binary cross-entropy loss to penalize inaccuracies in time prediction. Given that an input video may contain multiple sound events, each sound event's weights are based on its duration relative to the total sound duration in the video. The binary vector " + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "inline_equation", + "content": "T_{ct}" + }, + { + "bbox": [ + 46, + 534, + 287, + 641 + ], + "type": "text", + "content": " serves as input for the Time-controllable Latent Diffusion Model. The whole process and network structure are shown in Fig. 3." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 647, + 265, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 265, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 265, + 659 + ], + "type": "text", + "content": "3.5. Time-controllable Latent Diffusion Model" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 713 + ], + "type": "text", + "content": "In our experimentation, we observed that the results generated were semantically inaccurate and temporally unsynchronized. This issue often arose when utilizing audio-visual datasets to train end-to-end models, limiting the" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 315, + 70, + 539, + 199 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 539, + 199 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 539, + 199 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 539, + 199 + ], + "type": "image", + "image_path": "9aa7556e896714aabe96004f88cf17ba553d548f048d5ebdb1acbbb4f130c9db.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 207, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 305, + 207, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 207, + 545, + 262 + ], + "type": "text", + "content": "Figure 3. Sound Event Timestamp Detection Module. The network analyzes the video's features to output a binary vector corresponding to the video's frame count. Within this vector, sections marked in white (value of 1) mean sound presence, and those in black (value of 0) indicate sound absence." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 271, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 271, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 271, + 545, + 426 + ], + "type": "text", + "content": "task's practical application. We attribute these shortcomings to the complexity of the sound sources and the poor audio quality of the audio-visual dataset used for training. To address this, we use text to bridge audio and video and then introduce time control in the T2A generation model. In the visual domain, many works are based on the ControlNet [40] architecture, which can finer control the generation of images or videos by manipulating the input image conditions of neural network blocks. However, unlike the visual domain's inherent intuitiveness, audio features exhibit temporal continuity and are inherently more complex and abstract. Thus, selecting appropriate audio features to guide the generation process poses a greater challenge." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": "In this paper, we propose a embedding called Audio Time-condition Embedding, denote as " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "A_{ct}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": ", which is constructed through the following procedure: During the training phase, the adapter extracted Mel-spectrogram features from audio waveform " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": " and then normalized it, denoted as " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a_{mel} = mel(a)" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a_{c} = \\max (mel(a), T_{ct})" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": ", we then initialize " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a_{c}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": " to match " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a_{mel}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": "'s dimensions but with zero values, then fill " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a_{c}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": "'s Mel channels with the maximum values based on the corresponding frames where " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "T_{ct}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": " equals 1. Finally, " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "A_{ct}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": " is derived by encoding the embedding of " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "a_{c}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": " via the encoder " + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "inline_equation", + "content": "E_{a}" + }, + { + "bbox": [ + 305, + 427, + 545, + 557 + ], + "type": "text", + "content": ", and described as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 356, + 561, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 561, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 356, + 561, + 545, + 574 + ], + "type": "interline_equation", + "content": "A _ {c t} = E _ {a} \\left(\\max \\left(\\operatorname {m e l} \\left(a _ {c}\\right), T _ {c t}\\right)\\right). \\tag {9}", + "image_path": "0451065ac53a0f9dbae2a74f4467c3ad64db1404b1290928400d3c541e5188e6.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": "Inspired by ControlNet [40], we have developed a network architecture named Time-controllable Adapter. Then, we integrate the audio time-condition embedding " + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "inline_equation", + "content": "A_{ct}" + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": " with the text embedding " + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": " and target audio embedding into the neural network block. This integration facilitates joint training for the time-controllable adapter. " + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "inline_equation", + "content": "A_{ct}" + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": " is fed solely into the adapter, while text embedding " + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": " inputs into both Tango and the adapter." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Tango's denoising model, akin to UNet, includes encoder " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ", middle block " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ", and decoder " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": " have 12 corresponding blocks. Tango's outputs of the encoder's" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26869" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "i - th" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " block and decoder's " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "j - th" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " block are " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "g_{j}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " for the single middle block. The adapter mimics Tango's encoder and middle layers as " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "F'" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "M'" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ". Adapter's outputs, like " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "f_{i}'" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "m'" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ", are marked with " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "(')" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ". Following this, the output of the time-controllable adapter is concatenated with the output of the corresponding decoder block during the decoding process. For example, " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "f_{1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " from the 1st encoder layer adds to " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "g_{12}" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " of the decoder, making " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "i + j = 13" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": ". To achieve it, we ensure that all Tango's elements are kept frozen while modifying the input of the " + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "inline_equation", + "content": "i - th" + }, + { + "bbox": [ + 46, + 72, + 289, + 193 + ], + "type": "text", + "content": " block of the decoder as:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 201, + 287, + 239 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 201, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 59, + 201, + 287, + 239 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\text {C o n c a t} \\left(m + m ^ {\\prime}, f _ {j} + z e r o \\left(f _ {j} ^ {\\prime}\\right)\\right) i = 1, j = 1 2. \\\\ \\text {C o n c a t} \\left(g _ {i - 1}, f _ {j} + z e r o \\left(f _ {j} ^ {\\prime}\\right)\\right) 2 \\leqslant i \\leqslant 1 2, i + j = 1 3. \\end{array} \\right. \\tag {10}", + "image_path": "57f6135d8cda3e7d5ad928c6e8d06cb8db079d216178d7de9253c409312d9506.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 245, + 287, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 287, + 341 + ], + "type": "text", + "content": "zero(\\cdot) is one zero convolutional layer, facilitating trainable and fixed neural network block connections. Its weights evolve from zero to optimized values during training. This approach not only retains the Tango's capability for generating audio, trained on billions of audio-text pairs, but also enables the model to comprehend the guidance provided by the time control embedding, resulting in temporally controllable outcomes." + } + ] + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 49, + 357, + 285, + 426 + ], + "blocks": [ + { + "bbox": [ + 69, + 347, + 264, + 357 + ], + "lines": [ + { + "bbox": [ + 69, + 347, + 264, + 357 + ], + "spans": [ + { + "bbox": [ + 69, + 347, + 264, + 357 + ], + "type": "text", + "content": "Table 1. Distribution of CondPromptBank Categories" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 357, + 285, + 426 + ], + "lines": [ + { + "bbox": [ + 49, + 357, + 285, + 426 + ], + "spans": [ + { + "bbox": [ + 49, + 357, + 285, + 426 + ], + "type": "table", + "html": "
Category%Category%Category%
Household Daily14.11Transportation Vehicles10.42Impacts Crashes10.10
Foley8.24Human Elements7.77Industrial6.58
Weapons War5.83Cartoon Comical4.90Sports4.43
Animals Insects4.04Instruments3.68Water Liquid3.27
Technology2.70Horror2.41Emergency2.20
Public Places1.87Sound Design Effects1.69Doors Windows1.56
Fire Explosions1.49Nature Weather1.02Leisure0.84
Multimedia0.47Bells0.37
", + "image_path": "def8aa30eabec00c627e46503ee9699789aea175fb55e8afebda23ef7e6592fa.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 128, + 449 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 456, + 165, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 165, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 165, + 468 + ], + "type": "text", + "content": "4.1. Experiment Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 474, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 289, + 714 + ], + "type": "text", + "content": "Dataset. Since Tango's training datasets include varied audio types like speech, sound effects, and music, it tends to produce mixed audio outputs. Our task requires distinct handling of these audio types, ensuring each sound event is separate. To meet our specific needs, we developed CondPromptBank, a high-quality dataset of single sound effects crafted for training time-controlled adapters. This dataset consists of 10,276 individual data entries, each with a sound effect, title, and start/end timestamps. Each sound is typically 10 seconds or shorter, sourced from freely available sound effect libraries and websites. During the collection, we focused on 23 common categories of sound effects and manually filtered out low-quality data with noise and mixed sources. The category distribution shows Tab. 1. To enhance the textual descriptions with precise details, we further annotated the sound effect text labels with fine-grained information based on sound characteristics. Now, each label not only identifies the audio source but also describes the associated actions in detail. We believe the division into single audio sources is crucial, as videos provide a more concrete" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 95 + ], + "type": "text", + "content": "expression of content than text, thus requiring more precise sound representation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "type": "text", + "content": "Implementation details. To train our complete model, we first train the adapter on CondPromtBank, then train the timestamps detection net on Greatest Hits [26] and Countix-AV dataset [41]. We trained the adapter for approximately 200 epochs with a batch size 32 and a learning rate of " + }, + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "type": "inline_equation", + "content": "3.0 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "type": "text", + "content": " using Adam [17]. Our model has two versions: small and full. The difference between them is the version of pre-trained parameters used for Tango. We trained the timestamps detection net for 70 epochs with a batch size of 24 and a learning rate of " + }, + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "type": "inline_equation", + "content": "1.0 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 97, + 547, + 252 + ], + "type": "text", + "content": ". The training of the adapter takes approximately five days, and the training of the timestamps detection network requires approximately one day using one NVIDIA A6000 GPU." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 262, + 502, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 262, + 502, + 274 + ], + "spans": [ + { + "bbox": [ + 305, + 262, + 502, + 274 + ], + "type": "text", + "content": "4.2. Conditional Generation Task Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "type": "text", + "content": "We tested our model using the Greatest Hits [26] dataset, which has 977 videos of drumsticks interacting with different objects, lasting 11 hours. This dataset is divided into two types of actions and 17 types of materials. This detailed categorization helps check if our model can change sound types based on these details but still match the target action. We used the same test settings as CondFoleyGen [9] and compared our results with theirs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 377, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 424 + ], + "type": "text", + "content": "Evaluation Metrics. For the conditional generation task, we use the following five objective metrics to evaluate the performance of the model: CLAP-top, Onset Acc [9], Onset AP [9], Time Acc, and IoU." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": "Quantitative Results. SonicVisionLM-full demonstrates superior performance over CondFoleyGen across all metrics, as seen in Tab. 2. It achieves leading scores of " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "36.8\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "42.8\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": " on CLAP-top versions, exceeding any CondFoleyGen model by more than " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": ". This result suggests that it is better at matching sounds to text prompts. Our model significantly surpasses CondFoleyGen in audio-visual synchronization, evidenced by an " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "11\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": " improvement in Onset AP and a " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "16\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": " rise in IoU. Moreover, we see a " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": " enhancement in onset accuracy and an " + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "inline_equation", + "content": "8.3\\%" + }, + { + "bbox": [ + 304, + 426, + 547, + 640 + ], + "type": "text", + "content": " increase in timing precision. These advancements illustrate our model's outstanding accuracy in sound event detection and its effectiveness in synchronizing generated sounds with the input video. We think CondFoleyGen relies on the audio-visual synchronization module [15] to improve time accuracy, requiring many samples to re-ranking the sounds. In contrast, our model gets higher synchronization during the generation process with fewer samples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 713 + ], + "type": "text", + "content": "Qualitative Results. As shown in Fig. 4 (row 4, 6, 7), we compare the timestamped positional distance to the target sound. Our results closely match the target sound, demonstrating a high degree of accuracy. However, CondFoleyGen often produces results with the wrong number of sounds and with a large difference in the positional distance." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "26870" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 550, + 133 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 550, + 133 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 550, + 133 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 550, + 133 + ], + "type": "table", + "html": "
MethodCLAP - topgeneral↑CLAP - topunfused↑Onset Acc ↑Onset AP↑Time Acc↑IoU↑
CondFoleyGen(old)* [9]17.315.621.667.035.523.3
CondFoleyGen(new) * [9]16.313.619.268.637.422.4
Ours-small29.628.019.477.0327.835.6
Ours-full36.842.827.678.143.839.7
", + "image_path": "019b1814d7c9fe01d4aa233d0e452693c90e085f412473c419cca9d2e67c36a4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "type": "text", + "content": "Table 2. Conditional Generation Task Quantitative Results. CLAP-top metric evaluates a model's ability to control sound content. It calculates the percentage of times the sound samples generated by all models ranked in the top 1 according to the CLAP ranking, divided by the total number of samples. We used two versions of the CLAP models for evaluation: " + }, + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "type": "inline_equation", + "content": "CLAP_{general}" + }, + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "type": "inline_equation", + "content": "CLAP_{unfused}" + }, + { + "bbox": [ + 46, + 139, + 547, + 251 + ], + "type": "text", + "content": ". Onset Acc and Time Acc are both metrics based on the number of sound occurrences, with Onset Acc focusing on the onset count and Time Acc on the count of time intervals. We measure the average accuracy of predicting onsets within 0.1s of ground truth to assess the timing of generated onsets. IoU is calculated by computing the intersection and union of these vectors. These metrics collectively allow us to comprehensively evaluate the accuracy of the generated sounds in terms of both timing and content. The variant \"old\" corresponds to the prior codebook, while variant \"new\" matches the updated codebook. The old model was trained on 192-width spectrograms, and the new one was trained on 2s waveforms. \\*\\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. The six metrics are all measured in percentage." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 48, + 255, + 545, + 517 + ], + "blocks": [ + { + "bbox": [ + 48, + 255, + 545, + 517 + ], + "lines": [ + { + "bbox": [ + 48, + 255, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 48, + 255, + 545, + 517 + ], + "type": "image", + "image_path": "3081aef1559e8b0e08d194c805a3f92bba882fa2651c733f7c6e52369a57db11.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 525, + 546, + 549 + ], + "lines": [ + { + "bbox": [ + 46, + 525, + 546, + 549 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 546, + 549 + ], + "type": "text", + "content": "Figure 4. Conditional Generation Task Qualitative Results. The red dashed boxes are the conditional audio inputs and generated results for CondFoleyGen, and the blue dashed boxes are the conditional text inputs and results corresponding to SonicVisionLM." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 558, + 288, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 654 + ], + "type": "text", + "content": "This indicates that our model has a higher visual-audio synchronization than CondFoleyGen. As shown in Fig. 4 (column 3, 7), we compare the sound shape to the conditional sound. Even though our model has not learned any timbre on the Greatest Hits dataset, our results are still very similar to the conditional sound. As shown in Fig. 4 (column 1, 7), The mel-spectrograms of the CondFoleyGen results do not produce sounds that are similar to, and sometimes blurred." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 192, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 192, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 192, + 681 + ], + "type": "text", + "content": "4.3. Unconditional Generation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 713 + ], + "type": "text", + "content": "To evaluate the task of unconditional sound generation, considering that our LDM has not been trained on" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 558, + 546, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 618 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 618 + ], + "type": "text", + "content": "audio-visual datasets, we have chosen to perform quantitative evaluation and qualitative evaluation on two datasets: Greatest Hits [26] and CountixAV [41], which are zero-shot tasks for all models. We use two state-of-the-art V2A models as baselines: SpecVQGAN [14] and DIFF-FOLEY [25]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": "Evaluation Metrics. For objective evaluation, we have employed three metrics as [14, 25]: Inception Score (IS) [31], Frechet Distance (FID) [11], and Mean KL Divergence (MKL) [14]. For subjective evaluation, as the [9], we conduct user evaluations for the three critical components: overall audio quality (OVL), alignment with the input video (REL), and time synchronization (Time-sync)." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26871" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 541, + 159 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 541, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 541, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 541, + 159 + ], + "type": "table", + "html": "
Metric
Dataset MethodGreatest HitsCountix-AV
MKL↓FID ↓IS↑IoU↑MKL↓FID ↓IS↑IoU ↑
\\(SpecVQGAN^* [14]\\)6.8082.42.1725.87.3934.15.334.9
DIFF-FOLEY†[25]5.6820.03.8422.04.915.95.231.3
Ours-small6.4631.93.8836.610.021.715.137.5
Ours-full4.6724.93.2639.59.7119.712.742
", + "image_path": "080c0376050ac049141d085e03a36fe16514c64b42a4cddfe0d42be13bfe0b3f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 214, + 545, + 407 + ], + "blocks": [ + { + "bbox": [ + 50, + 214, + 545, + 407 + ], + "lines": [ + { + "bbox": [ + 50, + 214, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 50, + 214, + 545, + 407 + ], + "type": "image", + "image_path": "75e5efff9a493a163ecfccd6effd1147605f9261dd7f290efe31ddd6017d64c3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 416, + 546, + 440 + ], + "lines": [ + { + "bbox": [ + 46, + 416, + 546, + 440 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 546, + 440 + ], + "type": "text", + "content": "Figure 5. Unconditional Generation Task Qualitative Results. The left example is from CountixAV, and the right one is from Greatest Hits. We're comparing them side by side. The dashed box highlights examples of both good and bad results we generated." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 446, + 287, + 501 + ], + "blocks": [ + { + "bbox": [ + 46, + 167, + 546, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 167, + 546, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 546, + 212 + ], + "type": "text", + "content": "Table 3. Unconditional Sound Generation Quantitative Results. IS assesses the quality and diversity of generated samples, FID measures distribution-level similarity, and MKL measures paired sample-level similarity. \\*\\* denotes the data sourced from the official code and is based on experiments conducted with our local configurations. \\*\\* denotes that data is obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 446, + 287, + 501 + ], + "lines": [ + { + "bbox": [ + 48, + 446, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 48, + 446, + 287, + 501 + ], + "type": "table", + "html": "
MethodOVL↑REL↑Time-sync ↑
SpecVQGAN* [14]372531
DIFF-FOLEY† [25]486458
Ours756987
", + "image_path": "d3260d9d2e3bf4f8b14933c88947d4886524a476a4f7b13ab77223826a35772c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 287, + 597 + ], + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 597 + ], + "type": "text", + "content": "Table 4. Subjective Results. Following [9], we invited the 300 English-proficient evaluators to rate 30 randomly selected audio samples from three perspectives: OVL, REL, and Time-sync. Scores were averaged on a 1-100 scale. “**” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. “†” denotes data obtained from our adjusted official code. Underline denotes the worst performance. Boldface denotes the best performance." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Quantitative Results. In our experiments, the choice of vocoder significantly influenced the FID metric. We upgraded from DIFF-FOLEY's weak Griffin-Lim vocoder to the superior MelGAN to ensure fairness. Despite our model using 64 Mel filters compared to MelGAN's 80, our performance on the Greatest Hits dataset excels in MKL, IS, and IoU metrics, as shown in Tab. 3. This underscores our model's precise time control and high-quality sound generation, demonstrating its exceptional capability to produce" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 449, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 713 + ], + "type": "text", + "content": "sounds that align closely with the ground truth. In the CountixAV dataset, SonicVisionLM-small outperforms baselines by nearly 10 points in the IS metric, highlighting its exceptional sound quality. Despite slightly lower MKL and FID scores compared to baselines, we do not view this as a drawback. Unlike the Greatest Hits dataset, which was recorded in high quality with specialized recording equipment, the CountixAV dataset is sourced from diverse YouTube videos. It often includes sounds marred by low-quality background noise or mixed sound sources, especially human vocals. MKL and FID metrics emphasize similarity to the ground truth. Since DIFF-FOLEY was trained on similar audiovisual data, its tendency to mix multiple sounds in response to complex visual information explains its advantage in these metrics. Our model, targeting sound events from specific actions and filtering out irrelevant auditory information, diverges from the ground truth, a deliberate choice to enhance sound event relevance. The IoU metrics show that our model makes sound at the correct times and remains silent otherwise. To further argue our point, we conducted a subjective assessment of three aspects of OVL, REL, and Time-sync. As shown in Tab. 4, our model performed sig" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26872" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 288, + 138 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 288, + 138 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 288, + 138 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 288, + 138 + ], + "type": "table", + "html": "
MethodFD↓FAD↓KL↓IoU↑
tango-small* [10]44.911.53.4741.3
Ours-small26.22.052.3071.6
tango-full* [10]44.310.873.1439.3
Ours-full25.43.192.3265.7
", + "image_path": "63fff4b4786a542a78e611a541ba0f4d01bd898c64fe05fd69acebf4f3a4e3c2.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 146, + 288, + 201 + ], + "lines": [ + { + "bbox": [ + 46, + 146, + 288, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 146, + 288, + 201 + ], + "type": "text", + "content": "Table 5. Time Condition Ablation Results. “*” denotes the data sourced from the official code and is based on experiments conducted with our local configurations. Underline denotes the worst performance. Boldface denotes the best performance. IoU metric is measured in percentage." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 63, + 217, + 280, + 316 + ], + "blocks": [ + { + "bbox": [ + 63, + 217, + 280, + 316 + ], + "lines": [ + { + "bbox": [ + 63, + 217, + 280, + 316 + ], + "spans": [ + { + "bbox": [ + 63, + 217, + 280, + 316 + ], + "type": "image", + "image_path": "e48b0da71d8c895f44e1cec6fc105fd9acd1348a161c0358e6ab84737f82890f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 322, + 287, + 354 + ], + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 354 + ], + "type": "text", + "content": "Figure 6. Conditioning-scale Ablation Study. In the chart, the higher the indicators are, the better they are. The brightness of the colour also represents a good or bad performance." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 48, + 364, + 287, + 508 + ], + "blocks": [ + { + "bbox": [ + 48, + 357, + 86, + 364 + ], + "lines": [ + { + "bbox": [ + 48, + 357, + 86, + 364 + ], + "spans": [ + { + "bbox": [ + 48, + 357, + 86, + 364 + ], + "type": "text", + "content": "Silent Video" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 48, + 364, + 287, + 508 + ], + "lines": [ + { + "bbox": [ + 48, + 364, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 48, + 364, + 287, + 508 + ], + "type": "image", + "image_path": "d1d59b20e8dcd0a285f2964737226da410b9dde3e9a00707ddd358b8346b1c5b.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 518, + 287, + 574 + ], + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 574 + ], + "type": "text", + "content": "Figure 7. Multi-soundtracks generation example. In the video, the blue and green masks show different soundtracks. The timing of on-screen sounds (corresponding to visible actions) aligns accurately with their occurrence in the frames. Conversely, off-screen sounds (not visible in the video) lack precise timing." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 270, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 270, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 270, + 593 + ], + "type": "text", + "content": "nificantly better than the baseline models in all metrics." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 594, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 594, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 45, + 594, + 287, + 701 + ], + "type": "text", + "content": "Qualitative Results. For clearer time point comparison, we denoised the data from the CountixAV. Fig. 5 reveals our generated sounds are more precise than the baseline models. Furthermore, our model can capture finer-grained visual transformations, capturing the signal despite sudden changes in the frequency of movement and producing the correct sound. In contrast, SpecVQGAN results are full of noise. DIFF-FOLEY can sometimes generate clear sounds, but it is not aligned with the visual-sound synchronization." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 400, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 400, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 400, + 85 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 90, + 545, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 185 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 185 + ], + "type": "text", + "content": "Time condition. Evaluation Metrics. We employed objective metrics from Tango [10], such as the Frechet Audio Distance (FAD) [16] and Frechet Distance(FD) [24] to measure the distribution difference between generated audio and ground truth without the need for any reference audio samples. KL divergence [19, 38] assesses their similarity based on the broad concepts present in the original and the generated audio signals." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 186, + 545, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 233 + ], + "type": "text", + "content": "Result. we compared our model with the Tango [10]. As shown in Tab. 5, both in the small and full versions, our model outperforms Tango in terms of IoU, which validates the effectiveness of the time-controllable adapter." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 233, + 545, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 294 + ], + "type": "text", + "content": "Conditioning-scale. As seen in the Fig. 6. The sound quality improves in the range from 0.6 to 2.0 on the conditioning scale as it lines up better with the IoU. But at 3.0, control goes down a lot. The best mix of good sound quality and steadiness is found at a conditioning scale equal to 2.0." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 300, + 468, + 313 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 300, + 468, + 313 + ], + "spans": [ + { + "bbox": [ + 305, + 300, + 468, + 313 + ], + "type": "text", + "content": "4.5. Multi-soundtracks generation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 319, + 545, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 475 + ], + "type": "text", + "content": "As shown in Fig. 7, SonicVisionLM works like a sound designer in traditional video post-production. First, it looks at the visual information to find the key sounds needed. For example, it picks out the hissing of cooking meat and the clinking of pots. Then, if the story needs it, the sound designer adds off-screen sounds. This might include extra kitchen sounds like distant chopping, simmering pots, or the buzz of kitchen machines, making it feel more natural. Lastly, SonicVisionLM puts these audio tracks in the right place on the video timeline. This ensures the sounds match perfectly with what is happening in the video, creating a smooth audio-visual experience. More detailed results can be found in the Supplementary Materials." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 485, + 378, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 485, + 378, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 485, + 378, + 498 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 504, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 504, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 504, + 545, + 624 + ], + "type": "text", + "content": "In this paper, we propose SonicVisionLM, which utilizes the capabilities of powerful vision-language models (VLMs). When provided with a silent video, SonicVisionLM first identifies events within the video using a VLM to suggest possible sounds that match the video content. SonicVisionLM demonstrates outstanding performance in both conditional and unconditional generation tasks. Further, we tested its efficacy in post-production, focusing on automatic recognition of on-screen sounds and personalized editing for off-screen sounds. Extensive experiments show the superior performance of our method." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 625, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 545, + 703 + ], + "type": "text", + "content": "Limitations. While SonicVisionLM has achieved adequate results, refinements in the visual understanding and times-tamp detection parts are still required. Regarding various multimedia contexts, expanding the diversity and range of audio generation control are still the key demands of applications. Thus, the model should enrich the audio-visual experience and broaden applicability in future attempts." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26873" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Andrea Agostinelli, Timo I Denk, Zalán Borsos, Jesse Engel, Mauro Verzetti, Antoine Caillon, Qingqing Huang, Aren Jansen, Adam Roberts, Marco Tagliasacchi, et al. 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In CVPR, pages 14070-14079, 2021. 5, 6" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "26875" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_content_list.json b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e282bfe43c842a307381dc20577ce0b79467eefa --- /dev/null +++ b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_content_list.json @@ -0,0 +1,1694 @@ +[ + { + "type": "text", + "text": "SoundingActions: Learning How Actions Sound from Narrated Egocentric Videos", + "text_level": 1, + "bbox": [ + 76, + 130, + 893, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Changan Chen $^{1}$ Kumar Ashutosh $^{1,2}$ Rohit Girdhar $^{2}$ David Harwath $^{1}$ Kristen Grauman $^{1,2}$ $^{1}$ University of Texas at Austin ${}^{2}$ FAIR, Meta", + "bbox": [ + 107, + 179, + 861, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 313, + 267 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We propose a novel self-supervised embedding to learn how actions sound from narrated in-the-wild egocentric videos. Whereas existing methods rely on curated data with known audio-visual correspondence, our multimodal contrastive-consensus coding (MC3) embedding reinforces the associations between audio, language, and vision when all modality pairs agree, while diminishing those associations when any one pair does not. We show our approach can successfully discover how the long tail of human actions sound from egocentric video, outperforming an array of recent multimodal embedding techniques on two datasets (Ego4D and EPIC-Sounds) and multiple cross-modal tasks.", + "bbox": [ + 75, + 282, + 473, + 465 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 511, + 209, + 526 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Human activity often produces sounds. Closing a door, chopping vegetables, typing on a keyboard, talking with a friend—our interactions with the objects and people around us generate audio that reveals our physical behaviors. These sounds can be strongly associated with the subjects of our activity and how we perform it. For example, opening a water bottle sounds different than opening a cabinet; chopping sweet potatoes sounds different than chopping onions; chopping onions sounds different than mincing onions (the same object). Understanding the link between sounds and actions is valuable for a number of applications, such as multimodal activity recognition, cross-modal retrieval, content generation, or forecasting the physical effects of a person's actions.", + "bbox": [ + 75, + 537, + 470, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "How should AI learn about sounding actions? Existing work typically curates annotated datasets for supervised learning [9, 22, 28, 45], taking care to select events or actions that have associated sounds (e.g., lawnmowing, chopping), while others deliberately collect videos of object collisions (e.g., striking objects with a drumstick [43] or crashing into them with a robot [10, 17]), or develop physics-based simulations [16]. On the one hand, these approaches are appealing for their ability to focus on meaningful audio-visual correspondences. On the other hand, their curated nature risks limiting the scope of sounding actions that can be learned.", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Action: C moves a metal cutting machine with hands.", + "bbox": [ + 500, + 252, + 630, + 290 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Does the action sound?", + "bbox": [ + 501, + 301, + 635, + 313 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6d6a4a6a781495d237d8a7ca94de18d4281de8cfd6143cdaf55793c2b76a41b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 328, + 560, + 345 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Action: C digs the soil with a hoe.", + "bbox": [ + 501, + 357, + 604, + 381 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Does the action sound?", + "bbox": [ + 501, + 400, + 635, + 411 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0b8d9a7d05e976e624a887d30acb37300c896e8daf6422135115c00554de9adf.jpg", + "image_caption": [ + "Figure 1. We aim to distinguish sounds that are directly caused by human actions (bottom) from those that are not (top). Given egocentric training videos with language descriptions of the camera wearer's (\"C\") current action, we learn an embedding where the audio and visual features of any given clip are best aligned only when both are also consistent with the language. This allows discerning clips where the audio and vision may be correlated (e.g., the cutting machine running making loud noise in top row) versus those where the sounds are driven by human action (digging in bottom row)—importantly, without language at inference time." + ], + "image_footnote": [], + "bbox": [ + 504, + 431, + 560, + 448 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/76dd2112a7e9914204785da4a979af634217ba87f46887bb3d4b099a5c4d3226.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 250, + 758, + 323 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b093e1674ba0dd5e6841140fc140d729bb958b05444e237524c722bc06978e16.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 250, + 890, + 323 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/97958cccd0161c87aac033022a51d514126c86b00756c799cf2295f59b9a954d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 324, + 890, + 349 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/69f5653cd42e3a1268bc42468bbe8afe56840b149c58096f764162763bdf259c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 352, + 758, + 424 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b9f94bf0c4355b63560251d13935aae243c149a9108102af87f018770f746cc7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 766, + 352, + 890, + 424 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3cd993d8955896feeaefbb852e29c0b9037572582a12f056f86d1e54675718b9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 426, + 890, + 452 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instead, we aim to learn how human actions sound from narrated in-the-wild egocentric videos. See Figure 1. Given a pool of videos of everyday human activity, the goal is to learn a cross-modal representation where sounding actions cluster together based on how they look and sound. By sampling the videos freely, we can broaden the scope to discover the breadth of sounding actions without having to rely on a closed, pre-defined set of action categories. In particular, by focusing on unscripted egocentric video from wearable cameras in daily-life settings [11, 26], we aim to include subtle and long-tail scenarios unavailable in curated datasets, such as sounds of keys jangling when unlocking a door, scissors snipping when cutting the dog's fur, or fingernails scratching on one's own arm. Egocentric video is a particularly attractive source here because 1) human interaction sounds are more audible in near-field egocentric recordings and 2) passively captured long-form ego-video simply covers more", + "bbox": [ + 496, + 643, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "27252", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4d012ad5e17f8f882c8298bb77a0b08f86721fd70cb21fe59c2f952331c2cbe5.jpg", + "image_caption": [ + "Figure 2. Main idea. On the left, the Venn diagram illustrates different ways audio $(A)$ , video $(V)$ and language $(L)$ modalities can overlap in the content they capture. C refers to the camera wearer. Regions II, III, IV are information that is only shared between two modalities but not the third, e.g., the racing game in $①$ where the game sounds correlate with the vision, yet are not about the camera wearer's described action (using hands on laptop), the lifting action in $③$ , where the visuals and language agree but the action is inaudible, and the off-screen talking action in $④$ , where talking is heard and described, but the camera wearer cannot be seen speaking. Region I is the information that corresponds to all modalities agreeing, e.g., the visible and audible plastering action in $②$ . Our model's \"align\" phase detects any such (dis)agreements via pairwise contrastive learning on the modalities. In the \"refine\" phase, we use the intersection of that agreement (region I) to refine the embedding. For example, on the right, we show what the three modality embeddings should look like after the \"align\" stage for examples 1 and 2. Embeddings of instances where all modalities agree will be closer in the embedding space and apart otherwise. In other words, for example 1, yellow (video) cannot be close to blue (audio) unless green is too (language)." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 263, + 277 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/15d118388b5b8b7713a64344599219dc7501703ab835d915110efcf20d77fcd1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 259, + 88, + 496, + 279 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c3cdb3f9bbfb7d6b65d9cdb02854f54ed8d1a84da7aa87a66a35c49177bde73f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 88, + 686, + 279 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7205e41e9eb5db7adf746ff81007a0b398811eaef9e2067a1320ea012e65c401.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 705, + 88, + 892, + 277 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "everyday sounds, including the rare ones.", + "bbox": [ + 76, + 455, + 352, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, the learning task is challenging because some visible actions do not make any sound, and some sounds are the result of off-screen actions. Finally, other sounds may be correlated with on-screen objects (such as traffic noise and a city street), but are not directly related to the video by a salient and visible camera wearer action. For this reason, although existing self-supervised audio-visual methods [3, 5, 6, 20, 23, 33, 35, 42] are good at detecting audio-visual correspondences, they tend to capture general correlations rather than the action-specific correspondence.", + "bbox": [ + 75, + 473, + 468, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address this challenge, we propose a novel multimodal consensus embedding approach. Importantly, we suppose the in-the-wild egocentric training videos are accompanied by free-form natural language descriptions describing the actions of the camera wearer, as provided in the \"narrations\" of existing large-scale ego-video datasets [11, 26]. The main idea is to seek video samples where there is semantic agreement between all three modalities—the audio, visual, and language—while distancing those that do not. This intersection of the modalities with language assures that correspondences in the audio and visual streams stem from alignment on the sounding action.", + "bbox": [ + 75, + 627, + 470, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To achieve this, the proposed model first aligns a preliminary embedding from contrastive losses imposed per instance on each pair of modalities. Next, we refine those embeddings with a consensus objective that targets a minimum (bottleneck) pairwise similarity. The latter pushes all pairs of inter-modality agreement towards this consensus—or lack", + "bbox": [ + 75, + 810, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "thereof—while jointly continuing to optimize the paired-modalities' contrastive losses. In this way, we overcome the simplifying assumption made by existing multimodal embeddings that require all modalities to agree [1, 23, 55]. See Figure 2.", + "bbox": [ + 496, + 455, + 893, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We demonstrate our approach by training with in-the-wild data from Ego4D [26] without audio labels and testing on both Ego4D and EPIC-Sounds [28]. To allow a formal large-scale evaluation of sounding actions, we introduce a dataset of professional annotations on 33K video clips spanning Ego4D. Our model successfully discovers sounding actions that agree with ground truth labels on both datasets. Compared to existing multimodal embedding paradigms [14, 23, 35, 55], our model not only better discovers sounding actions and learns embeddings for cross-modality retrieval, but also generalizes better to the audio classification benchmark on EPIC-Sounds. To our knowledge, this is the first result of its kind to show sounding actions discovered organically from narrated in-the-wild video.", + "bbox": [ + 496, + 531, + 895, + 757 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 768, + 640, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Action/interaction/impact sound. Some work [21, 30, 40] leverages audio to improve activity recognition on video datasets such as UCF101 [52] and ActivityNet [15], which have visual labels but no audio labels. Existing audio datasets such as AudioSet [22] and VGG-Sound [9] target general sound classes such as music, speech, and sports. EPIC-Sounds [28] provides an audio classification bench-", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "27253", + "bbox": [ + 478, + 924, + 517, + 936 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "mark for actions in kitchen environments, but it has no labels for the correspondence between the visual action and the sound. The Greatest Hits dataset [43] contains videos where people hit and scratch object surfaces with a drumstick, which enables audio synthesis from videos. Interaction sound has also been studied in robotics, e.g., using a robotic platform to collect sounds and study the synergy between action and sounds [10, 17]. Impact sounds are modeled in a physics-based simulator [16]. Throughout, the existing work assumes a fixed, given taxonomy of action classes or audio labels of interest. In contrast, we learn how actions make sounds from in-the-wild narrated egocentric videos, without relying on a taxonomy of discrete labels for the audio events.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Audio-visual learning. As naturally co-occurring data, there are rich correspondences between video and audio, such as spatial correspondence [18, 29, 38], acoustic correspondence [8, 51], semantic correspondence [5, 6], and lip motion [19, 49]. Existing work typically either learns one type of correspondences by manually creating misalignment, e.g., shifting audio temporally to create temporal supervision [5, 33, 42] or down-mixing audio channels to create spatial supervision [18, 38], or it picks up any correspondence that emerges from the learning process [37, 39] (e.g., actions, objects, environments). In contrast, we aim to learn action-specific correspondence by leveraging the semantic grounding from human narrations.", + "bbox": [ + 75, + 295, + 472, + 491 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Language+X learning. Language can provide semantic grounding for what we see or hear. Prior work exploring language with another modality includes image/video captioning [57], visual question answering [4], and audio captioning [36]. Recent results with large-scale image-text datasets show that language is excellent for guiding the learning of image features (such as CLIP [47]), video features [34, 59], or audio features [27]. However, there is limited work studying binding language to more than one modality, as we propose. Some recent work [1, 58] explores self-supervised learning with language, vision, and sound, where the language is typically the transcription of the audio. They construct self-supervised objectives under the assumption that modalities agree with each other. In contrast, we use language that is different from the speech transcription and we explore modality agreement in training.", + "bbox": [ + 75, + 500, + 472, + 742 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Multi-modal/view representation learning. Recent work builds multimodal models using more than two modalities (e.g., audio, video, and language) for improving the representations of one modality [1, 2, 50], while others explore modality-invariant or view-invariant features [23, 53, 55]. For example, ImageBind [23] binds the visual features with other modalities in sequence, while CMC [55] proposes a contrastive multi-view loss that maximizes the mutual information between different views of the same scene. These methods assume there exists shared information among all", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "modalities, which does not address how to find these examples. Our method implicitly discovers the shared information by analyzing the multimodal consensus, or lack thereof.", + "bbox": [ + 496, + 90, + 893, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Task Formulation", + "text_level": 1, + "bbox": [ + 498, + 145, + 676, + 161 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We define a sounding action as a human-initiated action that produces sound during its execution due to interactions with the surrounding environment. We are particularly interested in learning how subtle and long-tail daily human actions sound. If hypothetically we were given a clip with audio $a$ , video $v$ , and label $y$ indicating whether the clip contains a sounding action, our objective would be to minimize the distance between audio-visual embeddings if $y = 1$ and maximize the distance between them if $y = 0$ , i.e., minimizing $(-1)^{y}\\mathcal{D}(e_{a},e_{v})$ , where $\\mathcal{D}$ measures the distance and $e_{a,v}$ are their embeddings. However, we do not assume access to any such direct supervision; labeling sounding actions is expensive, both because many actions do not produce sounds, and because many clips do not contain actions. Instead, we aim to discover sounding actions in a weakly supervised fashion, while simultaneously learning multimodal embeddings that capture them well.", + "bbox": [ + 496, + 166, + 893, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To this end, we leverage \"narrations\", a form of language description that is collected in recent egocentric video datasets such as Ego4D [26] and EPIC-Kitchens [11]. These narrations are timestamped free-form sentences describing the current action being performed by the camera-wearer. See Figure 2 for examples. Note that there may be other events in the video, too (e.g., a TV is playing), but these are not narrated. This is significant: the language specifically addresses near-field human interactions with objects, people, and the environment. The narrations offer two key benefits: 1) the timestamps provide temporal grounding of actions that occur in the video, indicating where potentially interesting clips are and 2) the language provides semantic grounding of actions—which our multimodal consensus idea will exploit to learn action-specific audio-visual correspondence.", + "bbox": [ + 496, + 424, + 893, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Formally, given a video with frames $v \\in \\mathcal{R}^{T \\times H \\times W \\times C}$ , audio $a \\in \\mathcal{R}^S$ , and language narration $l$ , where $T$ and $S$ are the number of frames for video and audio respectively, the goal is to learn embeddings $e_v$ and $e_a$ that are close in the embedding space if both $a$ and $v$ capture the same human action described in $l$ , and distant otherwise. If we plot how the three modalities overlap in a Venn diagram (Figure 2), we can see that what we are interested in learning is exactly region I, i.e., a camera-wearer action that sounds. From an information-theory perspective, this is equivalent to learning modality-invariant embeddings.", + "bbox": [ + 496, + 648, + 893, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Multimodal Contrastive-Consensus Coding", + "text_level": 1, + "bbox": [ + 498, + 829, + 887, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next we present our solution MC3 (Multimodal Contrastive-Consensus Coding) for learning modality-invariant embeddings, which consists of an inter-sample contrastive loss and", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "27254", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2752579371699c03b33bc24d64854cdfec2db944d263b0e91d34a8319b1a1462.jpg", + "image_caption": [ + "Figure 3. Multimodal contrastive-consensus loss. (a): Given three modality embeddings $e_i^t, e_j^t, e_k^t$ , multimodal contrastive coding pulls each pair of modalities closer while pushing modality pairs from another sample further away. (b): However, not all modalities agree on how close they should be depending on the instance. Thus we set the furthest distance a feature has with respect to the anchor feature as the consensus and push the remaining embeddings away to meet this consensus." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 468, + 189 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "an intra-sample consensus loss. See Fig. 3. We first present the two-stage training framework in Sec. 4.1 and then discuss the two losses in Sec. 4.2 and Sec. 4.3. For simplicity, we denote the $n$ input modalities as $M_{i}, i \\in [1,n]$ .", + "bbox": [ + 75, + 338, + 470, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Align-Refine Two-stage Training", + "text_level": 1, + "bbox": [ + 76, + 407, + 362, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We design a two-stage training paradigm. The high-level idea is to first optimize the pairwise agreement in an \"align\" stage, and then refine these embeddings with global consensus in the \"refine\" stage. See Fig. 2.", + "bbox": [ + 75, + 430, + 470, + 491 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the first stage, we train modality encoders with a contrastive loss $\\mathcal{L}_{\\mathrm{contrastive}}$ , which guides modality embeddings to have a good initial alignment that captures the pairwise similarity between modalities that capture the same underlying action, as opposed to random initialization.", + "bbox": [ + 75, + 491, + 470, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the second stage, we refine the pairwise-aligned embeddings with a globally established consensus. Specifically, we train the model with a consensus loss $\\mathcal{L}_{\\mathrm{consensus}}$ that pushes all intra-sample modality agreement towards this consensus, while jointly optimizing the contrastive loss $\\mathcal{L}_{\\mathrm{contrastive}}$ , to maximally capture the shared information across modalities. The MC3 loss $\\mathcal{L}_{\\mathrm{MC3}}$ combines the contrastive and consensus losses, and will be detailed below. We confirm experimentally that it is important to keep the contrastive loss in the second stage, although the main purpose of this stage is to refine embeddings with consensus.", + "bbox": [ + 75, + 566, + 470, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Multimodal Contrastive Coding", + "text_level": 1, + "bbox": [ + 76, + 741, + 359, + 758 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Cross-modal contrastive learning has been shown to discover representations where modalities are informative of each other [39]. Prior work [46, 56] shows that minimizing the contrastive loss between $M_{i}$ and $M_{j}$ maximizes the lower bound on the mutual information $I(M_{i};M_{j})$ . Inspired by this, we first use contrastive learning to optimize the pairwise similarities $S(e_i,e_j) = e_i e_j$ , where $e_{i,j}$ is the latent embedding normalized on the unit sphere for modality pair $i,j$ . We use the InfoNCE [41] loss to optimize each individual", + "bbox": [ + 75, + 763, + 472, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{S}(e_i,e_j)$ as follows:", + "bbox": [ + 500, + 90, + 638, + 107 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i, j} = - \\frac {1}{| \\mathcal {B} |} \\sum_ {t \\in \\mathcal {B}} \\log \\frac {\\exp \\left(e _ {i} ^ {t} e _ {j} ^ {t} / \\tau\\right)}{\\sum_ {l \\in \\mathcal {B}} \\exp \\left(e _ {i} ^ {t} e _ {j} ^ {l} / \\tau\\right)}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 121, + 893, + 161 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{B}$ is the batch and $\\tau$ is the temperature. This loss treats modalities from the same sample as positive pairs and pulls them closer and it treats modalities from different samples as negative pairs and pushes them apart. See Fig. 3 (a). The total loss is the sum of losses enumerated over all pairs of modalities, i.e., $\\mathcal{L}_{\\text{contrastive}} = \\sum_{i,j} \\mathcal{L}_{i,j}$ .", + "bbox": [ + 496, + 175, + 893, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Multimodal Consensus Coding", + "text_level": 1, + "bbox": [ + 498, + 281, + 774, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The contrastive loss above attempts to bring all temporally co-occurring modalities closer assuming there are strong correspondences among them in the input space. However, naively doing so would be problematic for instances where not all modalities agree (cf. Figure 2). To tackle this issue, we propose a novel objective that leverages the consensus of inter-sample modalities discovered from the contrastive coding as additional supervision.", + "bbox": [ + 496, + 306, + 893, + 428 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "First of all, we choose an anchor modality $M_{a}$ , which serves as the point of comparison for other modalities $M_{i}, i \\in [1, n], i \\neq a$ . With the normalized embedding $e_{i}^{t}$ of modality $i$ and sample $t$ , we then compute the cosine similarity score between each non-anchor modality and the anchor modality. Now, these similarity scores may or may not agree with each other. To only learn embeddings shared across all modalities, we set the consensus score as the minimum (bottleneck) score:", + "bbox": [ + 496, + 429, + 893, + 565 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc ^ {t} = \\mathcal {K} ^ {- 1} (\\min _ {i, i \\neq a} (\\mathcal {K} _ {1} (e _ {1} ^ {t} e _ {a} ^ {t}), \\dots , \\mathcal {K} _ {n} (e _ {n} ^ {t} e _ {a} ^ {t}))), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 579, + 892, + 604 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{K}_i(x) = ((x + 1) / 2)^{\\alpha_i}, x \\in [-1,1]$ is a modality-specific scaling function that first maps scores to $[0,1]$ and then adjusts the distribution with a tunable parameter $\\alpha_i$ . $\\mathcal{K}^{-1}$ is the inverse function that maps the scaled score back to the original space. The intuition behind $\\mathcal{K}_i(x)$ is that different modalities carry different amounts of information and we want to normalize the score distributions among the different modality pairs, making them comparable.", + "bbox": [ + 496, + 619, + 893, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The consensus score $c^t$ is high if and only if all pairwise scores are high, and it is low if there exists at least one modality that does not agree with the anchor modality. After obtaining the consensus score, we design a loss that forces all modalities to follow this consensus, as follows:", + "bbox": [ + 496, + 742, + 893, + 818 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c o n s e n u s}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {t \\in \\mathcal {B}} \\sum_ {i, i \\neq a} \\left\\| e _ {i} ^ {t} e _ {a} ^ {t} - c ^ {t} \\right\\| _ {2} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 830, + 892, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The total loss $\\mathcal{L}_{\\mathrm{MC3}}$ is the sum of the contrastive loss", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "27255", + "bbox": [ + 478, + 924, + 519, + 936 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Eq.1) and the consensus loss (Eq.3):", + "bbox": [ + 76, + 90, + 331, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {M C 3}} = - \\frac {1}{| \\mathcal {B} |} \\left(\\sum_ {t \\in \\mathcal {B}} \\underbrace {\\sum_ {i , j} \\log \\frac {\\exp \\left(e _ {i} ^ {t} e _ {j} ^ {t} / \\tau\\right)}{\\sum_ {l \\in \\mathcal {B}} \\exp \\left(e _ {i} ^ {t} e _ {j} ^ {l} / \\tau\\right)}} _ {\\text {I n t e r - s a m p l e}}\\right) \\tag {4} \\\\ - \\underbrace{\\sum_{i,i\\neq a}||e_{i}^{t}e_{a}^{t} - c^{t}||_{2})}_{\\text{Intra-sample}}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 114, + 468, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This loss pushes embeddings with a low consensus score apart while pulling together embeddings with a high consensus score, and thus aligns embeddings better in the joint embedding space. See Fig. 3.", + "bbox": [ + 75, + 241, + 468, + 301 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimizing this loss is not trivial since it has both contrastive and reconstruction objectives. Indeed, directly optimizing the loss does not work well as shown in the ablation study (Sec. 6.1). The proposed two-stage training paradigm (Sec. 4.1) helps train the model stably.", + "bbox": [ + 75, + 301, + 468, + 377 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 386, + 294, + 401 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our modalities of interest are $M_{1} = A$ (audio), $M_{2} = V$ (vision), and $M_{3} = L$ (language). There are six pairwise contrastive losses for three modalities. When computing the modality consensus, we empirically find using audio as the anchor leads to the best results in our task (cf. Sec. 6). We set the scaling parameters $\\alpha_{l}$ and $\\alpha_{v}$ to 1 and 0.5 respectively, based on a hyperparameter search on the validation set. See ablations in Supp.", + "bbox": [ + 75, + 409, + 468, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For extracting the feature representations, we use TimeSformer [7] as our video encoder, DistillBERT [48] as our text encoder, and AST [24] as our audio encoder. We initialize the video and language encoders with embeddings from [34], and the audio encoder with embeddings pretrained on ImageNet [13]. We train all encoders. We choose these initial encoders due to their good results in the literature; however, our MC3 loss is not specific to the choice of these encoders and others could be swapped in.", + "bbox": [ + 75, + 530, + 468, + 665 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train all models on 8 A40 GPUs with a learning rate of $3\\mathrm{e} - 5$ and batch size of 256 for 5 epochs for both stages, and take the final checkpoint for evaluation. We use the Adam optimizer [32]. Our implementation is based on the codebase from [34].", + "bbox": [ + 75, + 666, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Training and Eval Data for Sounding Actions", + "text_level": 1, + "bbox": [ + 76, + 753, + 468, + 771 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. Ego4D [26] is a large-scale egocentric video dataset that has more than 3,600 hours of video recordings depicting hundreds of daily activities—and 2,113 of those hours have audio available. As discussed, it also has timestamped narrations that are free-form sentences describing the current activity performed by the camera-wearer. However, Ego4D has no annotation of whether an action makes sounds, what sounds an action makes, or whether there exists", + "bbox": [ + 75, + 779, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1c6a340e7fe760f69c7659188d4b2ce98291543dc12f75ce50b6eae6974e0c7c.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Example verb groups and how frequently they sound" + ], + "table_body": "
WashCloseCutDropStirWipeRubTouchLiftHold
0.900.820.770.640.640.530.390.270.190.09
", + "bbox": [ + 506, + 90, + 883, + 132 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "other (non-action) sounds. It is thus non-trivial to detect if an action in the clip makes sound based on simple heuristics, e.g., the burst of sound energy, since many actions could produce continuous sounds with ambient-sound characteristics, e.g., wiping tables or sawing wood.", + "bbox": [ + 496, + 162, + 893, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We construct the training dataset by extracting clips from each Ego4D video based on the narration timestamps. These clips cover a wide range of daily activities and environments, including construction sites, cooking, arts and crafts, shopping, farming, and many others. Since the timestamp is only an approximate point for where an action occurs, we sample the clip from 0.5 s before to 1 s after the timestamp (1.5 s duration) so that the clip is likely long enough to capture the action sound, if there is any, without introducing visuals that stray from the narrated action. See ablations on the duration in Supp. We sample a training set of 250K clips from 1,876 hours of video. From their narrations, we find there are 6,114 unique nouns (objects) and 2,819 unique verbs (actions).", + "bbox": [ + 496, + 238, + 892, + 435 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ground truth annotations for evaluation. Today's egocentric video datasets lack annotations for sounding actions. Thus, to determine how well our model learns long-tail sounding actions and facilitate future research, we collect a large ground truth evaluation set for Ego4D using professional annotators trained for the task. It consists of 33K clips manually labeled as to whether or not the camera wearer's action sounds, i.e., indicating whether the action described in the narration is both visible and audible in the clip.", + "bbox": [ + 496, + 440, + 893, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To ensure annotation quality, in addition to providing concrete examples and annotation guidelines (see Supp.) and iterating with quality control feedback to the professional annotators, we assign three annotators per clip and take the majority vote as the correct answer. We split the 33K obtained annotations into 3K for validation and 30K for test. We stress that this is an eval set only; our training data (above) has no manual labels about sound, only free-form language narrations.", + "bbox": [ + 496, + 577, + 892, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Action type analysis. In total, among the 33,000 resulting ground truth clips, 17,693 are positive and 15,307 are negative. The fact that only half of this in-the-wild clip distribution consists of sounding actions underscores the need for models that can tell the difference between audio that co-occurs with human action and actions that sound. To gain insight into the annotations, we group them by semantic similarity and analyze them at a group level. While narrations provide semantic descriptions of actions, using them for grouping would be too noisy since the same action could be described in different ways. To reduce the influence of narration variance, we utilize the taxonomy defined in Ego4D (for", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "27256", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b85e16c7dc5034f3e5ce07fd21920c048850563879f74d0c98246c1314c734fa.jpg", + "image_caption": [ + "Figure 4. Long-tail distribution of sounding actions." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 472, + 200 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "analysis only, not training). For example, \"check\", \"examine\", and \"inspect\" should belong to the same group (taxon). We first group these clips by verb alone, i.e., extracting verbs from narrations and then applying the taxonomy, which results in 106 unique groups. We then compute the percentage of clips in each group that make sounds. Tab. 1 shows 10 examples. We see that actions involving more significant human motions (wash, close, cut) are more often sounding, whereas more subtle movements (lift, hold) are often not. Importantly, there is not a one-to-one mapping between an action verb and its sounding label—how actions sound is scenario-dependent and hence must be mined from the data.", + "bbox": [ + 75, + 232, + 472, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "While grouping by verbs provides some insights, how actions make sounds also depends on the object that they interact with, e.g., cutting a carrot sounds different from cutting bread. To this end, we further group the 17K sounding clips by both verbs and nouns, which results in 2,388 unique action groups. We plot the long-tail distribution of them in Fig. 4 and show examples sampled from this distribution. This plot shows the diverse and long-tail nature of sounding actions and our test set annotations, which is not present in existing action datasets [10, 15, 17, 28, 43, 52].", + "bbox": [ + 75, + 415, + 470, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 76, + 587, + 209, + 604 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our model with several baselines and ablations on three tasks: sounding action discovery (on Ego4D), sounding action retrieval (on Ego4D), and audio event classification (on EPIC-Sounds). We show our model outperforms an array of existing learning methods.", + "bbox": [ + 75, + 609, + 470, + 686 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SotA Baselines. We consider two baselines that only use a contrastive loss for two modalities: CLAP [14] for audio-language and CM-ACC [35] for audio-video. For more than two modalities, we consider two more baselines: CMC [55] uses contrastive objectives between all pairs of viewpoints (modalities in our case), representing the joint training paradigm; ImageBind [23] learns the joint embedding by first performing vision-language pretraining and then freezing the vision encoder and training the vision-audio modality pair. This represents strategies that align modalities sequentially. For a fair comparison, we equip all baselines with the same encoder and the same initialization as ours (see Sec. 4.4) while keeping their original losses.", + "bbox": [ + 75, + 704, + 472, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c20786d68e0b71dc7a36cf131f0b40a54729881153ce9bc18e860aa678672581.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AVAL
ROCPRROCPR
RandomXXX0.5000.5590.5000.559
CLAP [14]✓X✓--0.6370.695
CM-ACC [35]✓✓X0.5400.590--
CMC [55]✓✓✓0.5500.6010.6350.693
ImageBind [23]✓✓✓0.5540.6050.6420.685
w/o Lconsensus✓✓✓0.5630.6150.6350.694
w/o Lcontrastive✓✓✓0.4360.4930.5840.620
w/o align-stage✓✓✓0.4480.5070.4640.521
MC3✓✓✓0.5980.6660.6580.715
", + "bbox": [ + 500, + 88, + 897, + 276 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Sounding action discovery. Area-under-curve (AUC) values are reported for both ROC and precision-recall (PR) curves, for audio-vision (AV) and audio-language (AL). Both are the higher the better. We train our model five times with different seeds; the standard deviation is always within 0.01.", + "bbox": [ + 496, + 279, + 893, + 349 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f4496dc1b89ed142fa35b18bf1097481b64843c6e3489f047d2be87da2141298.jpg", + "image_caption": [ + "Figure 5. Sounding action discovery accuracy" + ], + "image_footnote": [], + "bbox": [ + 506, + 353, + 689, + 464 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dd6e4870f002203b3a97ea3b1cf9a792aa546b7dbbd3085030925edfdb755232.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 352, + 885, + 465 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Sounding Action Discovery", + "text_level": 1, + "bbox": [ + 498, + 493, + 743, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Human interactions with objects in our daily lives are complex and subtle. Due to many incidental background sounds, recognizing whether actions make sound is not trivial but can be useful for applications like multimodal video generation, e.g., verifying the generated action video and audio match. Towards this goal, we answer the question \"what actions sound?\" by performing sounding action discovery. In this experiment, we take the per-modality encoders learned on the narrated 250K Ego4D clips and apply them to the 30K test clips. Given a test clip, we feed the video and audio through their corresponding modality encoders, and compute the cosine similarity between the output embeddings. That score indicates how likely it is that the action in the video sounds. For completeness, instead of defining a hard threshold for positives, we plot the ROC and precision-recall (PR) curves by varying the positive threshold, and calculate the area-under-curve (AUC) values for them—common metrics for classification [12, 54] that are invariant to the absolute score values. For both metrics, higher values are better, indicating the model learns meaningful embeddings of sounding actions. Similarly, we can also evaluate discovery for audio-language, if narrations are available.", + "bbox": [ + 496, + 516, + 895, + 849 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Table 2 shows the results for sounding action discovery. We first look at discovery with audio-visual modalities alone at test time (\"AV\" columns). CM-ACC [35]", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "27257", + "bbox": [ + 478, + 925, + 517, + 936 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ffde83a21d1589c41ddaea81e7a543e5eb7b7026d008af7012579f227d2352b.jpg", + "image_caption": [ + "Figure 6. Example visual embedding cluster from our model" + ], + "image_footnote": [], + "bbox": [ + 114, + 88, + 426, + 210 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "discover soundsounding actions much better than random chance, showing that audio-visual contrastive learning captures both visual action embeddings and action sound embeddings. CMC [55] and ImageBind [23] do better—benefiting (like us) from the language modality at training time. However, neither the joint nor sequential training paradigm exploits modality agreement, resulting in weak cross-modal constraints, and thus only marginal performance improvement. In comparison, our model MC3 explicitly models the modality consensus and improves the discovery result substantially by learning embeddings most relevant to sounding actions.", + "bbox": [ + 75, + 237, + 472, + 402 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also report the discovery result from using audiolanguage modalities (\"AL\" columns). Since narrations provide action specifications, the discovery performance is better than $AV$ , e.g., CLAP [14] vs CM-ACC [35]. While CMC's [55] and ImageBind's [23] joint training results are not much better than CLAP [14], our model improves the \"AL\" discovery by leveraging the video modality and imposing the trimodal consensus constraint.", + "bbox": [ + 75, + 404, + 470, + 523 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 5 plots the precision-recall curves. For the audio-visual curve, our model always has higher precision compared to baselines, especially when recall is low. This is strong evidence of our model learning features of sounding actions, whereas baselines are limited to capturing general audio-visual correspondence—whether action-based or not. We observe a similar trend for audio-language discovery.", + "bbox": [ + 75, + 525, + 470, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablations. To study the importance of each loss and the two-stage training, we first ablate the consensus loss in the second stage (\"w/o $\\mathcal{L}_{\\mathrm{consensus}}$ in Table 2), which trains the model contrastively for both stages. The model performance drops significantly, showing that exploring the modality consensus is key to learning how actions sound. We then ablate the contrastive loss in the second stage (\"w/o $\\mathcal{L}_{\\mathrm{contrastive}}$ ), which harms performance even more. This suggests that $\\mathcal{L}_{\\mathrm{consensus}}$ functions like a regularization term that forces the $\\mathcal{L}_{\\mathrm{contrastive}}$ to learn sounding action embeddings. Lastly, we ablate the two-stage training strategy by removing the align stage (\"w/o align-stage\"), which optimizes $\\mathcal{L}_{\\mathrm{MC3}}$ directly; this model fails badly. Aligning embeddings first is critical to making MC3's training stable.", + "bbox": [ + 75, + 637, + 472, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Clustering. To visualize the learned embeddings, we group video embeddings in the test set with agglomerative clustering into 20 clusters. Fig. 6 shows the top 8 examples", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9b5db632bc8dc8adf5ced69800202167ff57c62a76c9471e6e7c61d3953382f1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
V→A@5 @10A→V@5 @10L→A@5 @10A→L@5 @10
Random0.10.10.10.10.10.10.10.1
CLAP [14]----49.887.634.067.1
CM-ACC [35]34.663.530.957.7----
CMC [55]36.567.933.863.744.181.832.864.3
ImageBind [23]32.861.529.757.942.676.530.660.5
w/o Lconsensus33.963.030.056.145.084.732.965.8
w/o Lcontrastive3.33.76.412.53.14.73.38.0
w/o align-stage10.019.45.911.811.620.96.512.6
MC338.472.834.466.346.288.537.573.8
", + "bbox": [ + 506, + 88, + 885, + 276 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Sounding action retrieval. We report Recall @5 and @10 for different query-retrieval modalities. See R@1 results in Supp.", + "bbox": [ + 500, + 279, + 890, + 306 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "of one cluster (more in Supp.). This cluster clearly captures the sound of water running, despite varying types of camera-wearer movement. Not only does it group videos with similar actions that make this sound, but also it shows the learned embeddings are agnostic of the background (the bathroom example).", + "bbox": [ + 496, + 316, + 893, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Sounding Action Retrieval", + "text_level": 1, + "bbox": [ + 500, + 417, + 740, + 434 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Retrieving a different modality given a video, audio, or description is another useful application, such as adding sound effects to silent videos or retrieving captions for action sounds. To explore this setting, we answer the question \"how do different actions sound?\" by evaluating the cross-modal retrieval performance of long-tail sounding actions from the same category. Different from the binary classification task above, here we aim to retrieve other examples of the same action.", + "bbox": [ + 496, + 443, + 893, + 577 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To do this, we utilize the action groups constructed in Sec. 5 based on verbs and nouns, and only keep groups that have more than two instances of sounding actions (such that there will be at least one true positive to retrieve for each query). We then divide each action group equally into a query pool of 7,559 examples and a retrieval pool of 7,032 examples. Given a query modality $M_{i}$ of instance $A$ , we compute its distance to other modalities $M_{j}$ of all instances in the retrieval pool. A retrieval is correct if the retrieved instance $B$ and $A$ belong to the same action group.", + "bbox": [ + 496, + 579, + 893, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Results. Table 3 shows the results for four different query-retrieval modality settings. For audio-visual retrieval, we observe that all models can retrieve video with audio (or audio with video) for similar actions with much higher recall than random chance. Our model strongly outperforms the baselines and ablations, benefiting from modeling the modality consensus explicitly. We also observe that retrieving audio with video is easier than the opposite, likely because audio can be vague sometimes, e.g., a collision sound might occur due to various actions while seeing a cutting action indicates the likely sound. For audio-language retrieval, our", + "bbox": [ + 496, + 734, + 895, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "27258", + "bbox": [ + 478, + 925, + 519, + 936 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bdcabbcbb9c8b881bb18beb504ca7b7d9d0ca8ccff2c82be25f3647fa033be39.jpg", + "image_caption": [ + "Figure 7. Qualitative examples for retrieval. The first row is video-to-audio retrieval, motivated by adding audio effects for silent videos. The second row is audio-to-text retrieval, motivated by audio captioning applications. For each row, we show three correct retrieval examples along with their text (gray indicates the text is not observed by the model). For the retrieved item, we show the ground truth rank as the superscript. All examples are long-tail sounding actions, showing how our model learns to capture the features of how actions sound." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 370, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/01323f3b33133d1cfcce45e595e445b0ac270d0ba9098f355d5dfe696b61e601.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 372, + 88, + 500, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8095ba9044315a7e51ae8e522448f28b8328ab89ebc19c6a9b63b89cf46e06e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 88, + 630, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2dbce9d96889fc51a8f32ff29573f75b1f9ba9c3428312a4bc1cf333d9fa53fa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 89, + 759, + 329 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3338f23177776111e0e50111987a3108c9df78b0763e6dfc0a7fb7cd284c9b3c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 761, + 89, + 890, + 329 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "model similarly outperforms the baselines by large margins. Qualitative examples. In Fig 7, we show examples for video-to-audio and audio-to-language retrieval. Even though these actions are subtle, our model retrieves audio or captions that are very relevant. Listen to examples in Supp. video.", + "bbox": [ + 75, + 410, + 470, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. Audio Classification on EPIC-Sounds", + "text_level": 1, + "bbox": [ + 76, + 498, + 400, + 513 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we evaluate our learned representation on a standard audio benchmark. To assess the impact of our model's action sounds representation, we consider EPIC-Sounds [28], a challenging audio classification benchmark for sounds in kitchen environments. To our knowledge, EPIC-Sounds represents the only large-scale benchmark for audio in egocentric video. Note, this classification task is different from the sounding action discovery task in Sec. 6.1 in that here the model only takes an audio clip as input.", + "bbox": [ + 75, + 522, + 468, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We consider both linear-probe and fine-tuning settings. In the linear-probe setup, we freeze the model weights and only train the last classification layer, which evaluates the quality of the pre-trained representations. In the fine-tuning setup, we fine-tune both the encoder and the last layer.", + "bbox": [ + 75, + 657, + 468, + 734 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4 shows the results. We compare with two SotA methods reported in EPIC-Sounds: SSAST [25] and ASF [31]. SSAST is pretrained on LibriSpeech [44] and shares the same network architecture as ours, while ASF is trained on VGG-Sound with supervised learning. With linear-probe, our model strongly outperforms SSAST [25], which, like us, is also pretrained in a self-supervised fashion with no audio labels. ASF [31] does better than both, likely due to its advantage of supervised audio classification pretraining. When fine-tuning, our model outperforms both prior methods in all but one metric when following the same", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1f77010623a4b680f8abe2c54037d83208d8cd1f75a8dcc40569e10832c4aed5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Top-1Top-5mCAMAPmAUC
Random-7.7130.952.290.0230.500
ASF [31]*L45.5379.3313.480.1720.789
SSAST [25]L28.7464.847.140.0790.755
MC3L42.4478.7612.790.1530.818
ASF [31]*F53.7584.5420.110.2540.873
SSAST [25]F53.4784.5620.220.2350.879
MC3F55.9785.8621.650.2420.885
", + "bbox": [ + 503, + 407, + 887, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Results of classification on EPIC-Sounds. L: Linear-Probe; F: Fine-tuning. * denotes pretraining with supervised audio classification while the rest are pretrained in a self-supervised fashion.", + "bbox": [ + 498, + 556, + 893, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "fine-tuning and evaluation protocol. This shows our MC3 audio encoder—trained for sounding action discovery—learns generalizable action sound embeddings, improving the state of the art. The margins are naturally smaller in the fine-tuning regime, as is typical, since all models have time to adapt to the new domain.", + "bbox": [ + 496, + 613, + 893, + 704 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 714, + 619, + 729 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We explored learning how first-person actions sound from inthe-wild, narrated egocentric videos—without audio labels. Training with 250K clips from Ego4D, we show the promise of our novel multimodal consensus framework for accurately aligning representations to capture the long-tail of sounding actions in novel (unnarrated) videos, with clear impact on sounding action discovery, retrieval, and pre-training for audio classification. In the future, we plan to explore multimodal consensus from asynchronous multimodal streams.", + "bbox": [ + 496, + 736, + 893, + 871 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: UT Austin is supported in part by the IFML NSF AI Institute. 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In CVPR, 2023. 3" + ], + "bbox": [ + 78, + 90, + 467, + 246 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "27262", + "bbox": [ + 478, + 926, + 517, + 936 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_model.json b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ea3ee0d50247b0e33a4aadbc30b2ee0130a79c59 --- /dev/null +++ b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_model.json @@ -0,0 +1,2301 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.131, + 0.895, + 0.155 + ], + "angle": 0, + "content": "SoundingActions: Learning How Actions Sound from Narrated Egocentric Videos" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.18, + 0.862, + 0.218 + ], + "angle": 0, + "content": "Changan Chen\\(^{1}\\) Kumar Ashutosh\\(^{1,2}\\) Rohit Girdhar\\(^{2}\\) David Harwath\\(^{1}\\) Kristen Grauman\\(^{1,2}\\) \n\\(^{1}\\)University of Texas at Austin \\({}^{2}\\)FAIR, Meta" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.314, + 0.268 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.474, + 0.466 + ], + "angle": 0, + "content": "We propose a novel self-supervised embedding to learn how actions sound from narrated in-the-wild egocentric videos. Whereas existing methods rely on curated data with known audio-visual correspondence, our multimodal contrastive-consensus coding (MC3) embedding reinforces the associations between audio, language, and vision when all modality pairs agree, while diminishing those associations when any one pair does not. We show our approach can successfully discover how the long tail of human actions sound from egocentric video, outperforming an array of recent multimodal embedding techniques on two datasets (Ego4D and EPIC-Sounds) and multiple cross-modal tasks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.512, + 0.21, + 0.527 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.472, + 0.734 + ], + "angle": 0, + "content": "Human activity often produces sounds. Closing a door, chopping vegetables, typing on a keyboard, talking with a friend—our interactions with the objects and people around us generate audio that reveals our physical behaviors. These sounds can be strongly associated with the subjects of our activity and how we perform it. For example, opening a water bottle sounds different than opening a cabinet; chopping sweet potatoes sounds different than chopping onions; chopping onions sounds different than mincing onions (the same object). Understanding the link between sounds and actions is valuable for a number of applications, such as multimodal activity recognition, cross-modal retrieval, content generation, or forecasting the physical effects of a person's actions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.472, + 0.902 + ], + "angle": 0, + "content": "How should AI learn about sounding actions? Existing work typically curates annotated datasets for supervised learning [9, 22, 28, 45], taking care to select events or actions that have associated sounds (e.g., lawnmowing, chopping), while others deliberately collect videos of object collisions (e.g., striking objects with a drumstick [43] or crashing into them with a robot [10, 17]), or develop physics-based simulations [16]. On the one hand, these approaches are appealing for their ability to focus on meaningful audio-visual correspondences. On the other hand, their curated nature risks limiting the scope of sounding actions that can be learned." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.253, + 0.631, + 0.291 + ], + "angle": 0, + "content": "Action: C moves a metal cutting machine with hands." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.303, + 0.636, + 0.314 + ], + "angle": 0, + "content": "Does the action sound?" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.329, + 0.561, + 0.347 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.358, + 0.605, + 0.382 + ], + "angle": 0, + "content": "Action: C digs the soil with a hoe." + }, + { + "type": "text", + "bbox": [ + 0.503, + 0.401, + 0.636, + 0.412 + ], + "angle": 0, + "content": "Does the action sound?" + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.432, + 0.561, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.25, + 0.759, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.251, + 0.891, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.325, + 0.891, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.353, + 0.759, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.767, + 0.353, + 0.891, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.427, + 0.891, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.466, + 0.895, + 0.606 + ], + "angle": 0, + "content": "Figure 1. We aim to distinguish sounds that are directly caused by human actions (bottom) from those that are not (top). Given egocentric training videos with language descriptions of the camera wearer's (\"C\") current action, we learn an embedding where the audio and visual features of any given clip are best aligned only when both are also consistent with the language. This allows discerning clips where the audio and vision may be correlated (e.g., the cutting machine running making loud noise in top row) versus those where the sounds are driven by human action (digging in bottom row)—importantly, without language at inference time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Instead, we aim to learn how human actions sound from narrated in-the-wild egocentric videos. See Figure 1. Given a pool of videos of everyday human activity, the goal is to learn a cross-modal representation where sounding actions cluster together based on how they look and sound. By sampling the videos freely, we can broaden the scope to discover the breadth of sounding actions without having to rely on a closed, pre-defined set of action categories. In particular, by focusing on unscripted egocentric video from wearable cameras in daily-life settings [11, 26], we aim to include subtle and long-tail scenarios unavailable in curated datasets, such as sounds of keys jangling when unlocking a door, scissors snipping when cutting the dog's fur, or fingernails scratching on one's own arm. Egocentric video is a particularly attractive source here because 1) human interaction sounds are more audible in near-field egocentric recordings and 2) passively captured long-form ego-video simply covers more" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "27252" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.264, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.26, + 0.089, + 0.498, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.089, + 0.687, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.706, + 0.089, + 0.893, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.895, + 0.43 + ], + "angle": 0, + "content": "Figure 2. Main idea. On the left, the Venn diagram illustrates different ways audio \\((A)\\), video \\((V)\\) and language \\((L)\\) modalities can overlap in the content they capture. C refers to the camera wearer. Regions II, III, IV are information that is only shared between two modalities but not the third, e.g., the racing game in \\(①\\) where the game sounds correlate with the vision, yet are not about the camera wearer's described action (using hands on laptop), the lifting action in \\(③\\), where the visuals and language agree but the action is inaudible, and the off-screen talking action in \\(④\\), where talking is heard and described, but the camera wearer cannot be seen speaking. Region I is the information that corresponds to all modalities agreeing, e.g., the visible and audible plastering action in \\(②\\). Our model's \"align\" phase detects any such (dis)agreements via pairwise contrastive learning on the modalities. In the \"refine\" phase, we use the intersection of that agreement (region I) to refine the embedding. For example, on the right, we show what the three modality embeddings should look like after the \"align\" stage for examples 1 and 2. Embeddings of instances where all modalities agree will be closer in the embedding space and apart otherwise. In other words, for example 1, yellow (video) cannot be close to blue (audio) unless green is too (language)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.457, + 0.353, + 0.471 + ], + "angle": 0, + "content": "everyday sounds, including the rare ones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.625 + ], + "angle": 0, + "content": "However, the learning task is challenging because some visible actions do not make any sound, and some sounds are the result of off-screen actions. Finally, other sounds may be correlated with on-screen objects (such as traffic noise and a city street), but are not directly related to the video by a salient and visible camera wearer action. For this reason, although existing self-supervised audio-visual methods [3, 5, 6, 20, 23, 33, 35, 42] are good at detecting audio-visual correspondences, they tend to capture general correlations rather than the action-specific correspondence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.471, + 0.809 + ], + "angle": 0, + "content": "To address this challenge, we propose a novel multimodal consensus embedding approach. Importantly, we suppose the in-the-wild egocentric training videos are accompanied by free-form natural language descriptions describing the actions of the camera wearer, as provided in the \"narrations\" of existing large-scale ego-video datasets [11, 26]. The main idea is to seek video samples where there is semantic agreement between all three modalities—the audio, visual, and language—while distancing those that do not. This intersection of the modalities with language assures that correspondences in the audio and visual streams stem from alignment on the sounding action." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.901 + ], + "angle": 0, + "content": "To achieve this, the proposed model first aligns a preliminary embedding from contrastive losses imposed per instance on each pair of modalities. Next, we refine those embeddings with a consensus objective that targets a minimum (bottleneck) pairwise similarity. The latter pushes all pairs of inter-modality agreement towards this consensus—or lack" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.895, + 0.532 + ], + "angle": 0, + "content": "thereof—while jointly continuing to optimize the paired-modalities' contrastive losses. In this way, we overcome the simplifying assumption made by existing multimodal embeddings that require all modalities to agree [1, 23, 55]. See Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.896, + 0.758 + ], + "angle": 0, + "content": "We demonstrate our approach by training with in-the-wild data from Ego4D [26] without audio labels and testing on both Ego4D and EPIC-Sounds [28]. To allow a formal large-scale evaluation of sounding actions, we introduce a dataset of professional annotations on 33K video clips spanning Ego4D. Our model successfully discovers sounding actions that agree with ground truth labels on both datasets. Compared to existing multimodal embedding paradigms [14, 23, 35, 55], our model not only better discovers sounding actions and learns embeddings for cross-modality retrieval, but also generalizes better to the audio classification benchmark on EPIC-Sounds. To our knowledge, this is the first result of its kind to show sounding actions discovered organically from narrated in-the-wild video." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.642, + 0.785 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Action/interaction/impact sound. Some work [21, 30, 40] leverages audio to improve activity recognition on video datasets such as UCF101 [52] and ActivityNet [15], which have visual labels but no audio labels. Existing audio datasets such as AudioSet [22] and VGG-Sound [9] target general sound classes such as music, speech, and sports. EPIC-Sounds [28] provides an audio classification bench-" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.925, + 0.519, + 0.937 + ], + "angle": 0, + "content": "27253" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "mark for actions in kitchen environments, but it has no labels for the correspondence between the visual action and the sound. The Greatest Hits dataset [43] contains videos where people hit and scratch object surfaces with a drumstick, which enables audio synthesis from videos. Interaction sound has also been studied in robotics, e.g., using a robotic platform to collect sounds and study the synergy between action and sounds [10, 17]. Impact sounds are modeled in a physics-based simulator [16]. Throughout, the existing work assumes a fixed, given taxonomy of action classes or audio labels of interest. In contrast, we learn how actions make sounds from in-the-wild narrated egocentric videos, without relying on a taxonomy of discrete labels for the audio events." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.296, + 0.473, + 0.492 + ], + "angle": 0, + "content": "Audio-visual learning. As naturally co-occurring data, there are rich correspondences between video and audio, such as spatial correspondence [18, 29, 38], acoustic correspondence [8, 51], semantic correspondence [5, 6], and lip motion [19, 49]. Existing work typically either learns one type of correspondences by manually creating misalignment, e.g., shifting audio temporally to create temporal supervision [5, 33, 42] or down-mixing audio channels to create spatial supervision [18, 38], or it picks up any correspondence that emerges from the learning process [37, 39] (e.g., actions, objects, environments). In contrast, we aim to learn action-specific correspondence by leveraging the semantic grounding from human narrations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.473, + 0.743 + ], + "angle": 0, + "content": "Language+X learning. Language can provide semantic grounding for what we see or hear. Prior work exploring language with another modality includes image/video captioning [57], visual question answering [4], and audio captioning [36]. Recent results with large-scale image-text datasets show that language is excellent for guiding the learning of image features (such as CLIP [47]), video features [34, 59], or audio features [27]. However, there is limited work studying binding language to more than one modality, as we propose. Some recent work [1, 58] explores self-supervised learning with language, vision, and sound, where the language is typically the transcription of the audio. They construct self-supervised objectives under the assumption that modalities agree with each other. In contrast, we use language that is different from the speech transcription and we explore modality agreement in training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Multi-modal/view representation learning. Recent work builds multimodal models using more than two modalities (e.g., audio, video, and language) for improving the representations of one modality [1, 2, 50], while others explore modality-invariant or view-invariant features [23, 53, 55]. For example, ImageBind [23] binds the visual features with other modalities in sequence, while CMC [55] proposes a contrastive multi-view loss that maximizes the mutual information between different views of the same scene. These methods assume there exists shared information among all" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.138 + ], + "angle": 0, + "content": "modalities, which does not address how to find these examples. Our method implicitly discovers the shared information by analyzing the multimodal consensus, or lack thereof." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.146, + 0.677, + 0.162 + ], + "angle": 0, + "content": "3. Task Formulation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.167, + 0.895, + 0.424 + ], + "angle": 0, + "content": "We define a sounding action as a human-initiated action that produces sound during its execution due to interactions with the surrounding environment. We are particularly interested in learning how subtle and long-tail daily human actions sound. If hypothetically we were given a clip with audio \\(a\\), video \\(v\\), and label \\(y\\) indicating whether the clip contains a sounding action, our objective would be to minimize the distance between audio-visual embeddings if \\(y = 1\\) and maximize the distance between them if \\(y = 0\\), i.e., minimizing \\((-1)^{y}\\mathcal{D}(e_{a},e_{v})\\), where \\(\\mathcal{D}\\) measures the distance and \\(e_{a,v}\\) are their embeddings. However, we do not assume access to any such direct supervision; labeling sounding actions is expensive, both because many actions do not produce sounds, and because many clips do not contain actions. Instead, we aim to discover sounding actions in a weakly supervised fashion, while simultaneously learning multimodal embeddings that capture them well." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.895, + 0.649 + ], + "angle": 0, + "content": "To this end, we leverage \"narrations\", a form of language description that is collected in recent egocentric video datasets such as Ego4D [26] and EPIC-Kitchens [11]. These narrations are timestamped free-form sentences describing the current action being performed by the camera-wearer. See Figure 2 for examples. Note that there may be other events in the video, too (e.g., a TV is playing), but these are not narrated. This is significant: the language specifically addresses near-field human interactions with objects, people, and the environment. The narrations offer two key benefits: 1) the timestamps provide temporal grounding of actions that occur in the video, indicating where potentially interesting clips are and 2) the language provides semantic grounding of actions—which our multimodal consensus idea will exploit to learn action-specific audio-visual correspondence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.895, + 0.817 + ], + "angle": 0, + "content": "Formally, given a video with frames \\( v \\in \\mathcal{R}^{T \\times H \\times W \\times C} \\), audio \\( a \\in \\mathcal{R}^S \\), and language narration \\( l \\), where \\( T \\) and \\( S \\) are the number of frames for video and audio respectively, the goal is to learn embeddings \\( e_v \\) and \\( e_a \\) that are close in the embedding space if both \\( a \\) and \\( v \\) capture the same human action described in \\( l \\), and distant otherwise. If we plot how the three modalities overlap in a Venn diagram (Figure 2), we can see that what we are interested in learning is exactly region I, i.e., a camera-wearer action that sounds. From an information-theory perspective, this is equivalent to learning modality-invariant embeddings." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.83, + 0.888, + 0.848 + ], + "angle": 0, + "content": "4. Multimodal Contrastive-Consensus Coding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Next we present our solution MC3 (Multimodal Contrastive-Consensus Coding) for learning modality-invariant embeddings, which consists of an inter-sample contrastive loss and" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "27254" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.47, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.201, + 0.473, + 0.314 + ], + "angle": 0, + "content": "Figure 3. Multimodal contrastive-consensus loss. (a): Given three modality embeddings \\( e_i^t, e_j^t, e_k^t \\), multimodal contrastive coding pulls each pair of modalities closer while pushing modality pairs from another sample further away. (b): However, not all modalities agree on how close they should be depending on the instance. Thus we set the furthest distance a feature has with respect to the anchor feature as the consensus and push the remaining embeddings away to meet this consensus." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.471, + 0.4 + ], + "angle": 0, + "content": "an intra-sample consensus loss. See Fig. 3. We first present the two-stage training framework in Sec. 4.1 and then discuss the two losses in Sec. 4.2 and Sec. 4.3. For simplicity, we denote the \\( n \\) input modalities as \\( M_{i}, i \\in [1,n] \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.408, + 0.364, + 0.423 + ], + "angle": 0, + "content": "4.1. Align-Refine Two-stage Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.471, + 0.492 + ], + "angle": 0, + "content": "We design a two-stage training paradigm. The high-level idea is to first optimize the pairwise agreement in an \"align\" stage, and then refine these embeddings with global consensus in the \"refine\" stage. See Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.472, + 0.567 + ], + "angle": 0, + "content": "In the first stage, we train modality encoders with a contrastive loss \\(\\mathcal{L}_{\\mathrm{contrastive}}\\), which guides modality embeddings to have a good initial alignment that captures the pairwise similarity between modalities that capture the same underlying action, as opposed to random initialization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.472, + 0.734 + ], + "angle": 0, + "content": "In the second stage, we refine the pairwise-aligned embeddings with a globally established consensus. Specifically, we train the model with a consensus loss \\(\\mathcal{L}_{\\mathrm{consensus}}\\) that pushes all intra-sample modality agreement towards this consensus, while jointly optimizing the contrastive loss \\(\\mathcal{L}_{\\mathrm{contrastive}}\\), to maximally capture the shared information across modalities. The MC3 loss \\(\\mathcal{L}_{\\mathrm{MC3}}\\) combines the contrastive and consensus losses, and will be detailed below. We confirm experimentally that it is important to keep the contrastive loss in the second stage, although the main purpose of this stage is to refine embeddings with consensus." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.36, + 0.759 + ], + "angle": 0, + "content": "4.2. Multimodal Contrastive Coding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Cross-modal contrastive learning has been shown to discover representations where modalities are informative of each other [39]. Prior work [46, 56] shows that minimizing the contrastive loss between \\( M_{i} \\) and \\( M_{j} \\) maximizes the lower bound on the mutual information \\( I(M_{i};M_{j}) \\). Inspired by this, we first use contrastive learning to optimize the pairwise similarities \\( S(e_i,e_j) = e_i e_j \\), where \\( e_{i,j} \\) is the latent embedding normalized on the unit sphere for modality pair \\( i,j \\). We use the InfoNCE [41] loss to optimize each individual" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.64, + 0.108 + ], + "angle": 0, + "content": "\\(\\mathcal{S}(e_i,e_j)\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.122, + 0.894, + 0.162 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i, j} = - \\frac {1}{| \\mathcal {B} |} \\sum_ {t \\in \\mathcal {B}} \\log \\frac {\\exp \\left(e _ {i} ^ {t} e _ {j} ^ {t} / \\tau\\right)}{\\sum_ {l \\in \\mathcal {B}} \\exp \\left(e _ {i} ^ {t} e _ {j} ^ {l} / \\tau\\right)}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.176, + 0.894, + 0.27 + ], + "angle": 0, + "content": "where \\(\\mathcal{B}\\) is the batch and \\(\\tau\\) is the temperature. This loss treats modalities from the same sample as positive pairs and pulls them closer and it treats modalities from different samples as negative pairs and pushes them apart. See Fig. 3 (a). The total loss is the sum of losses enumerated over all pairs of modalities, i.e., \\(\\mathcal{L}_{\\text{contrastive}} = \\sum_{i,j} \\mathcal{L}_{i,j}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.282, + 0.776, + 0.299 + ], + "angle": 0, + "content": "4.3. Multimodal Consensus Coding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.307, + 0.895, + 0.429 + ], + "angle": 0, + "content": "The contrastive loss above attempts to bring all temporally co-occurring modalities closer assuming there are strong correspondences among them in the input space. However, naively doing so would be problematic for instances where not all modalities agree (cf. Figure 2). To tackle this issue, we propose a novel objective that leverages the consensus of inter-sample modalities discovered from the contrastive coding as additional supervision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.895, + 0.566 + ], + "angle": 0, + "content": "First of all, we choose an anchor modality \\( M_{a} \\), which serves as the point of comparison for other modalities \\( M_{i}, i \\in [1, n], i \\neq a \\). With the normalized embedding \\( e_{i}^{t} \\) of modality \\( i \\) and sample \\( t \\), we then compute the cosine similarity score between each non-anchor modality and the anchor modality. Now, these similarity scores may or may not agree with each other. To only learn embeddings shared across all modalities, we set the consensus score as the minimum (bottleneck) score:" + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.58, + 0.893, + 0.605 + ], + "angle": 0, + "content": "\\[\nc ^ {t} = \\mathcal {K} ^ {- 1} (\\min _ {i, i \\neq a} (\\mathcal {K} _ {1} (e _ {1} ^ {t} e _ {a} ^ {t}), \\dots , \\mathcal {K} _ {n} (e _ {n} ^ {t} e _ {a} ^ {t}))), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.894, + 0.741 + ], + "angle": 0, + "content": "where \\(\\mathcal{K}_i(x) = ((x + 1) / 2)^{\\alpha_i}, x \\in [-1,1]\\) is a modality-specific scaling function that first maps scores to \\([0,1]\\) and then adjusts the distribution with a tunable parameter \\(\\alpha_i\\). \\(\\mathcal{K}^{-1}\\) is the inverse function that maps the scaled score back to the original space. The intuition behind \\(\\mathcal{K}_i(x)\\) is that different modalities carry different amounts of information and we want to normalize the score distributions among the different modality pairs, making them comparable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.743, + 0.894, + 0.819 + ], + "angle": 0, + "content": "The consensus score \\( c^t \\) is high if and only if all pairwise scores are high, and it is low if there exists at least one modality that does not agree with the anchor modality. After obtaining the consensus score, we design a loss that forces all modalities to follow this consensus, as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.832, + 0.893, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c o n s e n u s}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {t \\in \\mathcal {B}} \\sum_ {i, i \\neq a} \\left\\| e _ {i} ^ {t} e _ {a} ^ {t} - c ^ {t} \\right\\| _ {2} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The total loss \\(\\mathcal{L}_{\\mathrm{MC3}}\\) is the sum of the contrastive loss" + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.925, + 0.521, + 0.937 + ], + "angle": 0, + "content": "27255" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.332, + 0.107 + ], + "angle": 0, + "content": "Eq.1) and the consensus loss (Eq.3):" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.115, + 0.47, + 0.233 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {M C 3}} = - \\frac {1}{| \\mathcal {B} |} \\left(\\sum_ {t \\in \\mathcal {B}} \\underbrace {\\sum_ {i , j} \\log \\frac {\\exp \\left(e _ {i} ^ {t} e _ {j} ^ {t} / \\tau\\right)}{\\sum_ {l \\in \\mathcal {B}} \\exp \\left(e _ {i} ^ {t} e _ {j} ^ {l} / \\tau\\right)}} _ {\\text {I n t e r - s a m p l e}}\\right) \\tag {4} \\\\ - \\underbrace{\\sum_{i,i\\neq a}||e_{i}^{t}e_{a}^{t} - c^{t}||_{2})}_{\\text{Intra-sample}}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.242, + 0.47, + 0.302 + ], + "angle": 0, + "content": "This loss pushes embeddings with a low consensus score apart while pulling together embeddings with a high consensus score, and thus aligns embeddings better in the joint embedding space. See Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.47, + 0.378 + ], + "angle": 0, + "content": "Optimizing this loss is not trivial since it has both contrastive and reconstruction objectives. Indeed, directly optimizing the loss does not work well as shown in the ablation study (Sec. 6.1). The proposed two-stage training paradigm (Sec. 4.1) helps train the model stably." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.387, + 0.295, + 0.402 + ], + "angle": 0, + "content": "4.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.47, + 0.53 + ], + "angle": 0, + "content": "Our modalities of interest are \\( M_{1} = A \\) (audio), \\( M_{2} = V \\) (vision), and \\( M_{3} = L \\) (language). There are six pairwise contrastive losses for three modalities. When computing the modality consensus, we empirically find using audio as the anchor leads to the best results in our task (cf. Sec. 6). We set the scaling parameters \\( \\alpha_{l} \\) and \\( \\alpha_{v} \\) to 1 and 0.5 respectively, based on a hyperparameter search on the validation set. See ablations in Supp." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.531, + 0.47, + 0.666 + ], + "angle": 0, + "content": "For extracting the feature representations, we use TimeSformer [7] as our video encoder, DistillBERT [48] as our text encoder, and AST [24] as our audio encoder. We initialize the video and language encoders with embeddings from [34], and the audio encoder with embeddings pretrained on ImageNet [13]. We train all encoders. We choose these initial encoders due to their good results in the literature; however, our MC3 loss is not specific to the choice of these encoders and others could be swapped in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.47, + 0.743 + ], + "angle": 0, + "content": "We train all models on 8 A40 GPUs with a learning rate of \\(3\\mathrm{e} - 5\\) and batch size of 256 for 5 epochs for both stages, and take the final checkpoint for evaluation. We use the Adam optimizer [32]. Our implementation is based on the codebase from [34]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.755, + 0.469, + 0.772 + ], + "angle": 0, + "content": "5. Training and Eval Data for Sounding Actions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Dataset. Ego4D [26] is a large-scale egocentric video dataset that has more than 3,600 hours of video recordings depicting hundreds of daily activities—and 2,113 of those hours have audio available. As discussed, it also has timestamped narrations that are free-form sentences describing the current activity performed by the camera-wearer. However, Ego4D has no annotation of whether an action makes sounds, what sounds an action makes, or whether there exists" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.092, + 0.885, + 0.133 + ], + "angle": 0, + "content": "
WashCloseCutDropStirWipeRubTouchLiftHold
0.900.820.770.640.640.530.390.270.190.09
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.511, + 0.135, + 0.88, + 0.15 + ], + "angle": 0, + "content": "Table 1. Example verb groups and how frequently they sound" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.163, + 0.894, + 0.238 + ], + "angle": 0, + "content": "other (non-action) sounds. It is thus non-trivial to detect if an action in the clip makes sound based on simple heuristics, e.g., the burst of sound energy, since many actions could produce continuous sounds with ambient-sound characteristics, e.g., wiping tables or sawing wood." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.239, + 0.893, + 0.436 + ], + "angle": 0, + "content": "We construct the training dataset by extracting clips from each Ego4D video based on the narration timestamps. These clips cover a wide range of daily activities and environments, including construction sites, cooking, arts and crafts, shopping, farming, and many others. Since the timestamp is only an approximate point for where an action occurs, we sample the clip from 0.5 s before to 1 s after the timestamp (1.5 s duration) so that the clip is likely long enough to capture the action sound, if there is any, without introducing visuals that stray from the narrated action. See ablations on the duration in Supp. We sample a training set of 250K clips from 1,876 hours of video. From their narrations, we find there are 6,114 unique nouns (objects) and 2,819 unique verbs (actions)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.894, + 0.577 + ], + "angle": 0, + "content": "Ground truth annotations for evaluation. Today's egocentric video datasets lack annotations for sounding actions. Thus, to determine how well our model learns long-tail sounding actions and facilitate future research, we collect a large ground truth evaluation set for Ego4D using professional annotators trained for the task. It consists of 33K clips manually labeled as to whether or not the camera wearer's action sounds, i.e., indicating whether the action described in the narration is both visible and audible in the clip." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.893, + 0.713 + ], + "angle": 0, + "content": "To ensure annotation quality, in addition to providing concrete examples and annotation guidelines (see Supp.) and iterating with quality control feedback to the professional annotators, we assign three annotators per clip and take the majority vote as the correct answer. We split the 33K obtained annotations into 3K for validation and 30K for test. We stress that this is an eval set only; our training data (above) has no manual labels about sound, only free-form language narrations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Action type analysis. In total, among the 33,000 resulting ground truth clips, 17,693 are positive and 15,307 are negative. The fact that only half of this in-the-wild clip distribution consists of sounding actions underscores the need for models that can tell the difference between audio that co-occurs with human action and actions that sound. To gain insight into the annotations, we group them by semantic similarity and analyze them at a group level. While narrations provide semantic descriptions of actions, using them for grouping would be too noisy since the same action could be described in different ways. To reduce the influence of narration variance, we utilize the taxonomy defined in Ego4D (for" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "27256" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.473, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.118, + 0.205, + 0.428, + 0.22 + ], + "angle": 0, + "content": "Figure 4. Long-tail distribution of sounding actions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.233, + 0.473, + 0.414 + ], + "angle": 0, + "content": "analysis only, not training). For example, \"check\", \"examine\", and \"inspect\" should belong to the same group (taxon). We first group these clips by verb alone, i.e., extracting verbs from narrations and then applying the taxonomy, which results in 106 unique groups. We then compute the percentage of clips in each group that make sounds. Tab. 1 shows 10 examples. We see that actions involving more significant human motions (wash, close, cut) are more often sounding, whereas more subtle movements (lift, hold) are often not. Importantly, there is not a one-to-one mapping between an action verb and its sounding label—how actions sound is scenario-dependent and hence must be mined from the data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.472, + 0.568 + ], + "angle": 0, + "content": "While grouping by verbs provides some insights, how actions make sounds also depends on the object that they interact with, e.g., cutting a carrot sounds different from cutting bread. To this end, we further group the 17K sounding clips by both verbs and nouns, which results in 2,388 unique action groups. We plot the long-tail distribution of them in Fig. 4 and show examples sampled from this distribution. This plot shows the diverse and long-tail nature of sounding actions and our test set annotations, which is not present in existing action datasets [10, 15, 17, 28, 43, 52]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.588, + 0.21, + 0.605 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.472, + 0.687 + ], + "angle": 0, + "content": "We compare our model with several baselines and ablations on three tasks: sounding action discovery (on Ego4D), sounding action retrieval (on Ego4D), and audio event classification (on EPIC-Sounds). We show our model outperforms an array of existing learning methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.901 + ], + "angle": 0, + "content": "SotA Baselines. We consider two baselines that only use a contrastive loss for two modalities: CLAP [14] for audio-language and CM-ACC [35] for audio-video. For more than two modalities, we consider two more baselines: CMC [55] uses contrastive objectives between all pairs of viewpoints (modalities in our case), representing the joint training paradigm; ImageBind [23] learns the joint embedding by first performing vision-language pretraining and then freezing the vision encoder and training the vision-audio modality pair. This represents strategies that align modalities sequentially. For a fair comparison, we equip all baselines with the same encoder and the same initialization as ours (see Sec. 4.4) while keeping their original losses." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.898, + 0.277 + ], + "angle": 0, + "content": "
AVAL
ROCPRROCPR
RandomXXX0.5000.5590.5000.559
CLAP [14]✓X✓--0.6370.695
CM-ACC [35]✓✓X0.5400.590--
CMC [55]✓✓✓0.5500.6010.6350.693
ImageBind [23]✓✓✓0.5540.6050.6420.685
w/o Lconsensus✓✓✓0.5630.6150.6350.694
w/o Lcontrastive✓✓✓0.4360.4930.5840.620
w/o align-stage✓✓✓0.4480.5070.4640.521
MC3✓✓✓0.5980.6660.6580.715
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.28, + 0.895, + 0.351 + ], + "angle": 0, + "content": "Table 2. Sounding action discovery. Area-under-curve (AUC) values are reported for both ROC and precision-recall (PR) curves, for audio-vision (AV) and audio-language (AL). Both are the higher the better. We train our model five times with different seeds; the standard deviation is always within 0.01." + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.354, + 0.69, + 0.465 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.353, + 0.886, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.558, + 0.47, + 0.833, + 0.485 + ], + "angle": 0, + "content": "Figure 5. Sounding action discovery accuracy" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.494, + 0.745, + 0.51 + ], + "angle": 0, + "content": "6.1. Sounding Action Discovery" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.896, + 0.85 + ], + "angle": 0, + "content": "Human interactions with objects in our daily lives are complex and subtle. Due to many incidental background sounds, recognizing whether actions make sound is not trivial but can be useful for applications like multimodal video generation, e.g., verifying the generated action video and audio match. Towards this goal, we answer the question \"what actions sound?\" by performing sounding action discovery. In this experiment, we take the per-modality encoders learned on the narrated 250K Ego4D clips and apply them to the 30K test clips. Given a test clip, we feed the video and audio through their corresponding modality encoders, and compute the cosine similarity between the output embeddings. That score indicates how likely it is that the action in the video sounds. For completeness, instead of defining a hard threshold for positives, we plot the ROC and precision-recall (PR) curves by varying the positive threshold, and calculate the area-under-curve (AUC) values for them—common metrics for classification [12, 54] that are invariant to the absolute score values. For both metrics, higher values are better, indicating the model learns meaningful embeddings of sounding actions. Similarly, we can also evaluate discovery for audio-language, if narrations are available." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Results. Table 2 shows the results for sounding action discovery. We first look at discovery with audio-visual modalities alone at test time (\"AV\" columns). CM-ACC [35]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.519, + 0.938 + ], + "angle": 0, + "content": "27257" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.116, + 0.089, + 0.428, + 0.211 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.213, + 0.454, + 0.227 + ], + "angle": 0, + "content": "Figure 6. Example visual embedding cluster from our model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.238, + 0.473, + 0.404 + ], + "angle": 0, + "content": "discover soundsounding actions much better than random chance, showing that audio-visual contrastive learning captures both visual action embeddings and action sound embeddings. CMC [55] and ImageBind [23] do better—benefiting (like us) from the language modality at training time. However, neither the joint nor sequential training paradigm exploits modality agreement, resulting in weak cross-modal constraints, and thus only marginal performance improvement. In comparison, our model MC3 explicitly models the modality consensus and improves the discovery result substantially by learning embeddings most relevant to sounding actions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.472, + 0.525 + ], + "angle": 0, + "content": "We also report the discovery result from using audiolanguage modalities (\"AL\" columns). Since narrations provide action specifications, the discovery performance is better than \\(AV\\), e.g., CLAP [14] vs CM-ACC [35]. While CMC's [55] and ImageBind's [23] joint training results are not much better than CLAP [14], our model improves the \"AL\" discovery by leveraging the video modality and imposing the trimodal consensus constraint." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.526, + 0.472, + 0.633 + ], + "angle": 0, + "content": "Fig. 5 plots the precision-recall curves. For the audio-visual curve, our model always has higher precision compared to baselines, especially when recall is low. This is strong evidence of our model learning features of sounding actions, whereas baselines are limited to capturing general audio-visual correspondence—whether action-based or not. We observe a similar trend for audio-language discovery." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.473, + 0.851 + ], + "angle": 0, + "content": "Ablations. To study the importance of each loss and the two-stage training, we first ablate the consensus loss in the second stage (\"w/o \\(\\mathcal{L}_{\\mathrm{consensus}}\\) in Table 2), which trains the model contrastively for both stages. The model performance drops significantly, showing that exploring the modality consensus is key to learning how actions sound. We then ablate the contrastive loss in the second stage (\"w/o \\(\\mathcal{L}_{\\mathrm{contrastive}}\\)), which harms performance even more. This suggests that \\(\\mathcal{L}_{\\mathrm{consensus}}\\) functions like a regularization term that forces the \\(\\mathcal{L}_{\\mathrm{contrastive}}\\) to learn sounding action embeddings. Lastly, we ablate the two-stage training strategy by removing the align stage (\"w/o align-stage\"), which optimizes \\(\\mathcal{L}_{\\mathrm{MC3}}\\) directly; this model fails badly. Aligning embeddings first is critical to making MC3's training stable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Clustering. To visualize the learned embeddings, we group video embeddings in the test set with agglomerative clustering into 20 clusters. Fig. 6 shows the top 8 examples" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.089, + 0.887, + 0.277 + ], + "angle": 0, + "content": "
V→A@5 @10A→V@5 @10L→A@5 @10A→L@5 @10
Random0.10.10.10.10.10.10.10.1
CLAP [14]----49.887.634.067.1
CM-ACC [35]34.663.530.957.7----
CMC [55]36.567.933.863.744.181.832.864.3
ImageBind [23]32.861.529.757.942.676.530.660.5
w/o Lconsensus33.963.030.056.145.084.732.965.8
w/o Lcontrastive3.33.76.412.53.14.73.38.0
w/o align-stage10.019.45.911.811.620.96.512.6
MC338.472.834.466.346.288.537.573.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.28, + 0.892, + 0.308 + ], + "angle": 0, + "content": "Table 3. Sounding action retrieval. We report Recall @5 and @10 for different query-retrieval modalities. See R@1 results in Supp." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.895, + 0.409 + ], + "angle": 0, + "content": "of one cluster (more in Supp.). This cluster clearly captures the sound of water running, despite varying types of camera-wearer movement. Not only does it group videos with similar actions that make this sound, but also it shows the learned embeddings are agnostic of the background (the bathroom example)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.419, + 0.741, + 0.435 + ], + "angle": 0, + "content": "6.2. Sounding Action Retrieval" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.895, + 0.578 + ], + "angle": 0, + "content": "Retrieving a different modality given a video, audio, or description is another useful application, such as adding sound effects to silent videos or retrieving captions for action sounds. To explore this setting, we answer the question \"how do different actions sound?\" by evaluating the cross-modal retrieval performance of long-tail sounding actions from the same category. Different from the binary classification task above, here we aim to retrieve other examples of the same action." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.732 + ], + "angle": 0, + "content": "To do this, we utilize the action groups constructed in Sec. 5 based on verbs and nouns, and only keep groups that have more than two instances of sounding actions (such that there will be at least one true positive to retrieve for each query). We then divide each action group equally into a query pool of 7,559 examples and a retrieval pool of 7,032 examples. Given a query modality \\( M_{i} \\) of instance \\( A \\), we compute its distance to other modalities \\( M_{j} \\) of all instances in the retrieval pool. A retrieval is correct if the retrieved instance \\( B \\) and \\( A \\) belong to the same action group." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.901 + ], + "angle": 0, + "content": "Results. Table 3 shows the results for four different query-retrieval modality settings. For audio-visual retrieval, we observe that all models can retrieve video with audio (or audio with video) for similar actions with much higher recall than random chance. Our model strongly outperforms the baselines and ablations, benefiting from modeling the modality consensus explicitly. We also observe that retrieving audio with video is easier than the opposite, likely because audio can be vague sometimes, e.g., a collision sound might occur due to various actions while seeing a cutting action indicates the likely sound. For audio-language retrieval, our" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.926, + 0.521, + 0.938 + ], + "angle": 0, + "content": "27258" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.372, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.373, + 0.089, + 0.501, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.631, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.632, + 0.09, + 0.761, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.762, + 0.09, + 0.891, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.338, + 0.894, + 0.395 + ], + "angle": 0, + "content": "Figure 7. Qualitative examples for retrieval. The first row is video-to-audio retrieval, motivated by adding audio effects for silent videos. The second row is audio-to-text retrieval, motivated by audio captioning applications. For each row, we show three correct retrieval examples along with their text (gray indicates the text is not observed by the model). For the retrieved item, we show the ground truth rank as the superscript. All examples are long-tail sounding actions, showing how our model learns to capture the features of how actions sound." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.471, + 0.489 + ], + "angle": 0, + "content": "model similarly outperforms the baselines by large margins. Qualitative examples. In Fig 7, we show examples for video-to-audio and audio-to-language retrieval. Even though these actions are subtle, our model retrieves audio or captions that are very relevant. Listen to examples in Supp. video." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.499, + 0.401, + 0.515 + ], + "angle": 0, + "content": "6.3. Audio Classification on EPIC-Sounds" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.659 + ], + "angle": 0, + "content": "Finally, we evaluate our learned representation on a standard audio benchmark. To assess the impact of our model's action sounds representation, we consider EPIC-Sounds [28], a challenging audio classification benchmark for sounds in kitchen environments. To our knowledge, EPIC-Sounds represents the only large-scale benchmark for audio in egocentric video. Note, this classification task is different from the sounding action discovery task in Sec. 6.1 in that here the model only takes an audio clip as input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.659, + 0.47, + 0.735 + ], + "angle": 0, + "content": "We consider both linear-probe and fine-tuning settings. In the linear-probe setup, we freeze the model weights and only train the last classification layer, which evaluates the quality of the pre-trained representations. In the fine-tuning setup, we fine-tune both the encoder and the last layer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Table 4 shows the results. We compare with two SotA methods reported in EPIC-Sounds: SSAST [25] and ASF [31]. SSAST is pretrained on LibriSpeech [44] and shares the same network architecture as ours, while ASF is trained on VGG-Sound with supervised learning. With linear-probe, our model strongly outperforms SSAST [25], which, like us, is also pretrained in a self-supervised fashion with no audio labels. ASF [31] does better than both, likely due to its advantage of supervised audio classification pretraining. When fine-tuning, our model outperforms both prior methods in all but one metric when following the same" + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.408, + 0.888, + 0.553 + ], + "angle": 0, + "content": "
Top-1Top-5mCAMAPmAUC
Random-7.7130.952.290.0230.500
ASF [31]*L45.5379.3313.480.1720.789
SSAST [25]L28.7464.847.140.0790.755
MC3L42.4478.7612.790.1530.818
ASF [31]*F53.7584.5420.110.2540.873
SSAST [25]F53.4784.5620.220.2350.879
MC3F55.9785.8621.650.2420.885
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.558, + 0.895, + 0.601 + ], + "angle": 0, + "content": "Table 4. Results of classification on EPIC-Sounds. L: Linear-Probe; F: Fine-tuning. * denotes pretraining with supervised audio classification while the rest are pretrained in a self-supervised fashion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.705 + ], + "angle": 0, + "content": "fine-tuning and evaluation protocol. This shows our MC3 audio encoder—trained for sounding action discovery—learns generalizable action sound embeddings, improving the state of the art. The margins are naturally smaller in the fine-tuning regime, as is typical, since all models have time to adapt to the new domain." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.715, + 0.62, + 0.731 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.895, + 0.872 + ], + "angle": 0, + "content": "We explored learning how first-person actions sound from inthe-wild, narrated egocentric videos—without audio labels. Training with 250K clips from Ego4D, we show the promise of our novel multimodal consensus framework for accurately aligning representations to capture the long-tail of sounding actions in novel (unnarrated) videos, with clear impact on sounding action discovery, retrieval, and pre-training for audio classification. In the future, we plan to explore multimodal consensus from asynchronous multimodal streams." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.873, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements: UT Austin is supported in part by the IFML NSF AI Institute. 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In CVPR, 2023. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.927, + 0.519, + 0.938 + ], + "angle": 0, + "content": "27262" + } + ] +] \ No newline at end of file diff --git a/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_origin.pdf b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b3e621cf940dc875db82f2a7244df999271ce8b8 --- /dev/null +++ b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/87979a59-b194-4c7b-8bc8-5f7988336f66_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5c1882dc05b2f024d3c09775b67354c841800f6e7a8d87f7573a77dc243052f7 +size 3263534 diff --git a/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/full.md b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..df71919f2afc90bf6110155d4161df0a17cf8fe1 --- /dev/null +++ b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/full.md @@ -0,0 +1,323 @@ +# SoundingActions: Learning How Actions Sound from Narrated Egocentric Videos + +Changan Chen $^{1}$ Kumar Ashutosh $^{1,2}$ Rohit Girdhar $^{2}$ David Harwath $^{1}$ Kristen Grauman $^{1,2}$ $^{1}$ University of Texas at Austin ${}^{2}$ FAIR, Meta + +# Abstract + +We propose a novel self-supervised embedding to learn how actions sound from narrated in-the-wild egocentric videos. Whereas existing methods rely on curated data with known audio-visual correspondence, our multimodal contrastive-consensus coding (MC3) embedding reinforces the associations between audio, language, and vision when all modality pairs agree, while diminishing those associations when any one pair does not. We show our approach can successfully discover how the long tail of human actions sound from egocentric video, outperforming an array of recent multimodal embedding techniques on two datasets (Ego4D and EPIC-Sounds) and multiple cross-modal tasks. + +# 1. Introduction + +Human activity often produces sounds. Closing a door, chopping vegetables, typing on a keyboard, talking with a friend—our interactions with the objects and people around us generate audio that reveals our physical behaviors. These sounds can be strongly associated with the subjects of our activity and how we perform it. For example, opening a water bottle sounds different than opening a cabinet; chopping sweet potatoes sounds different than chopping onions; chopping onions sounds different than mincing onions (the same object). Understanding the link between sounds and actions is valuable for a number of applications, such as multimodal activity recognition, cross-modal retrieval, content generation, or forecasting the physical effects of a person's actions. + +How should AI learn about sounding actions? Existing work typically curates annotated datasets for supervised learning [9, 22, 28, 45], taking care to select events or actions that have associated sounds (e.g., lawnmowing, chopping), while others deliberately collect videos of object collisions (e.g., striking objects with a drumstick [43] or crashing into them with a robot [10, 17]), or develop physics-based simulations [16]. On the one hand, these approaches are appealing for their ability to focus on meaningful audio-visual correspondences. On the other hand, their curated nature risks limiting the scope of sounding actions that can be learned. + +Action: C moves a metal cutting machine with hands. + +Does the action sound? + +![](images/6d6a4a6a781495d237d8a7ca94de18d4281de8cfd6143cdaf55793c2b76a41b2.jpg) + +Action: C digs the soil with a hoe. + +Does the action sound? + +![](images/0b8d9a7d05e976e624a887d30acb37300c896e8daf6422135115c00554de9adf.jpg) +Figure 1. We aim to distinguish sounds that are directly caused by human actions (bottom) from those that are not (top). Given egocentric training videos with language descriptions of the camera wearer's ("C") current action, we learn an embedding where the audio and visual features of any given clip are best aligned only when both are also consistent with the language. This allows discerning clips where the audio and vision may be correlated (e.g., the cutting machine running making loud noise in top row) versus those where the sounds are driven by human action (digging in bottom row)—importantly, without language at inference time. + +![](images/76dd2112a7e9914204785da4a979af634217ba87f46887bb3d4b099a5c4d3226.jpg) + +![](images/b093e1674ba0dd5e6841140fc140d729bb958b05444e237524c722bc06978e16.jpg) + +![](images/97958cccd0161c87aac033022a51d514126c86b00756c799cf2295f59b9a954d.jpg) + +![](images/69f5653cd42e3a1268bc42468bbe8afe56840b149c58096f764162763bdf259c.jpg) + +![](images/b9f94bf0c4355b63560251d13935aae243c149a9108102af87f018770f746cc7.jpg) + +![](images/3cd993d8955896feeaefbb852e29c0b9037572582a12f056f86d1e54675718b9.jpg) + +Instead, we aim to learn how human actions sound from narrated in-the-wild egocentric videos. See Figure 1. Given a pool of videos of everyday human activity, the goal is to learn a cross-modal representation where sounding actions cluster together based on how they look and sound. By sampling the videos freely, we can broaden the scope to discover the breadth of sounding actions without having to rely on a closed, pre-defined set of action categories. In particular, by focusing on unscripted egocentric video from wearable cameras in daily-life settings [11, 26], we aim to include subtle and long-tail scenarios unavailable in curated datasets, such as sounds of keys jangling when unlocking a door, scissors snipping when cutting the dog's fur, or fingernails scratching on one's own arm. Egocentric video is a particularly attractive source here because 1) human interaction sounds are more audible in near-field egocentric recordings and 2) passively captured long-form ego-video simply covers more + +![](images/4d012ad5e17f8f882c8298bb77a0b08f86721fd70cb21fe59c2f952331c2cbe5.jpg) +Figure 2. Main idea. On the left, the Venn diagram illustrates different ways audio $(A)$ , video $(V)$ and language $(L)$ modalities can overlap in the content they capture. C refers to the camera wearer. Regions II, III, IV are information that is only shared between two modalities but not the third, e.g., the racing game in $①$ where the game sounds correlate with the vision, yet are not about the camera wearer's described action (using hands on laptop), the lifting action in $③$ , where the visuals and language agree but the action is inaudible, and the off-screen talking action in $④$ , where talking is heard and described, but the camera wearer cannot be seen speaking. Region I is the information that corresponds to all modalities agreeing, e.g., the visible and audible plastering action in $②$ . Our model's "align" phase detects any such (dis)agreements via pairwise contrastive learning on the modalities. In the "refine" phase, we use the intersection of that agreement (region I) to refine the embedding. For example, on the right, we show what the three modality embeddings should look like after the "align" stage for examples 1 and 2. Embeddings of instances where all modalities agree will be closer in the embedding space and apart otherwise. In other words, for example 1, yellow (video) cannot be close to blue (audio) unless green is too (language). + +![](images/15d118388b5b8b7713a64344599219dc7501703ab835d915110efcf20d77fcd1.jpg) + +![](images/c3cdb3f9bbfb7d6b65d9cdb02854f54ed8d1a84da7aa87a66a35c49177bde73f.jpg) + +![](images/7205e41e9eb5db7adf746ff81007a0b398811eaef9e2067a1320ea012e65c401.jpg) + +everyday sounds, including the rare ones. + +However, the learning task is challenging because some visible actions do not make any sound, and some sounds are the result of off-screen actions. Finally, other sounds may be correlated with on-screen objects (such as traffic noise and a city street), but are not directly related to the video by a salient and visible camera wearer action. For this reason, although existing self-supervised audio-visual methods [3, 5, 6, 20, 23, 33, 35, 42] are good at detecting audio-visual correspondences, they tend to capture general correlations rather than the action-specific correspondence. + +To address this challenge, we propose a novel multimodal consensus embedding approach. Importantly, we suppose the in-the-wild egocentric training videos are accompanied by free-form natural language descriptions describing the actions of the camera wearer, as provided in the "narrations" of existing large-scale ego-video datasets [11, 26]. The main idea is to seek video samples where there is semantic agreement between all three modalities—the audio, visual, and language—while distancing those that do not. This intersection of the modalities with language assures that correspondences in the audio and visual streams stem from alignment on the sounding action. + +To achieve this, the proposed model first aligns a preliminary embedding from contrastive losses imposed per instance on each pair of modalities. Next, we refine those embeddings with a consensus objective that targets a minimum (bottleneck) pairwise similarity. The latter pushes all pairs of inter-modality agreement towards this consensus—or lack + +thereof—while jointly continuing to optimize the paired-modalities' contrastive losses. In this way, we overcome the simplifying assumption made by existing multimodal embeddings that require all modalities to agree [1, 23, 55]. See Figure 2. + +We demonstrate our approach by training with in-the-wild data from Ego4D [26] without audio labels and testing on both Ego4D and EPIC-Sounds [28]. To allow a formal large-scale evaluation of sounding actions, we introduce a dataset of professional annotations on 33K video clips spanning Ego4D. Our model successfully discovers sounding actions that agree with ground truth labels on both datasets. Compared to existing multimodal embedding paradigms [14, 23, 35, 55], our model not only better discovers sounding actions and learns embeddings for cross-modality retrieval, but also generalizes better to the audio classification benchmark on EPIC-Sounds. To our knowledge, this is the first result of its kind to show sounding actions discovered organically from narrated in-the-wild video. + +# 2. Related Work + +Action/interaction/impact sound. Some work [21, 30, 40] leverages audio to improve activity recognition on video datasets such as UCF101 [52] and ActivityNet [15], which have visual labels but no audio labels. Existing audio datasets such as AudioSet [22] and VGG-Sound [9] target general sound classes such as music, speech, and sports. EPIC-Sounds [28] provides an audio classification bench- + +mark for actions in kitchen environments, but it has no labels for the correspondence between the visual action and the sound. The Greatest Hits dataset [43] contains videos where people hit and scratch object surfaces with a drumstick, which enables audio synthesis from videos. Interaction sound has also been studied in robotics, e.g., using a robotic platform to collect sounds and study the synergy between action and sounds [10, 17]. Impact sounds are modeled in a physics-based simulator [16]. Throughout, the existing work assumes a fixed, given taxonomy of action classes or audio labels of interest. In contrast, we learn how actions make sounds from in-the-wild narrated egocentric videos, without relying on a taxonomy of discrete labels for the audio events. + +Audio-visual learning. As naturally co-occurring data, there are rich correspondences between video and audio, such as spatial correspondence [18, 29, 38], acoustic correspondence [8, 51], semantic correspondence [5, 6], and lip motion [19, 49]. Existing work typically either learns one type of correspondences by manually creating misalignment, e.g., shifting audio temporally to create temporal supervision [5, 33, 42] or down-mixing audio channels to create spatial supervision [18, 38], or it picks up any correspondence that emerges from the learning process [37, 39] (e.g., actions, objects, environments). In contrast, we aim to learn action-specific correspondence by leveraging the semantic grounding from human narrations. + +Language+X learning. Language can provide semantic grounding for what we see or hear. Prior work exploring language with another modality includes image/video captioning [57], visual question answering [4], and audio captioning [36]. Recent results with large-scale image-text datasets show that language is excellent for guiding the learning of image features (such as CLIP [47]), video features [34, 59], or audio features [27]. However, there is limited work studying binding language to more than one modality, as we propose. Some recent work [1, 58] explores self-supervised learning with language, vision, and sound, where the language is typically the transcription of the audio. They construct self-supervised objectives under the assumption that modalities agree with each other. In contrast, we use language that is different from the speech transcription and we explore modality agreement in training. + +Multi-modal/view representation learning. Recent work builds multimodal models using more than two modalities (e.g., audio, video, and language) for improving the representations of one modality [1, 2, 50], while others explore modality-invariant or view-invariant features [23, 53, 55]. For example, ImageBind [23] binds the visual features with other modalities in sequence, while CMC [55] proposes a contrastive multi-view loss that maximizes the mutual information between different views of the same scene. These methods assume there exists shared information among all + +modalities, which does not address how to find these examples. Our method implicitly discovers the shared information by analyzing the multimodal consensus, or lack thereof. + +# 3. Task Formulation + +We define a sounding action as a human-initiated action that produces sound during its execution due to interactions with the surrounding environment. We are particularly interested in learning how subtle and long-tail daily human actions sound. If hypothetically we were given a clip with audio $a$ , video $v$ , and label $y$ indicating whether the clip contains a sounding action, our objective would be to minimize the distance between audio-visual embeddings if $y = 1$ and maximize the distance between them if $y = 0$ , i.e., minimizing $(-1)^{y}\mathcal{D}(e_{a},e_{v})$ , where $\mathcal{D}$ measures the distance and $e_{a,v}$ are their embeddings. However, we do not assume access to any such direct supervision; labeling sounding actions is expensive, both because many actions do not produce sounds, and because many clips do not contain actions. Instead, we aim to discover sounding actions in a weakly supervised fashion, while simultaneously learning multimodal embeddings that capture them well. + +To this end, we leverage "narrations", a form of language description that is collected in recent egocentric video datasets such as Ego4D [26] and EPIC-Kitchens [11]. These narrations are timestamped free-form sentences describing the current action being performed by the camera-wearer. See Figure 2 for examples. Note that there may be other events in the video, too (e.g., a TV is playing), but these are not narrated. This is significant: the language specifically addresses near-field human interactions with objects, people, and the environment. The narrations offer two key benefits: 1) the timestamps provide temporal grounding of actions that occur in the video, indicating where potentially interesting clips are and 2) the language provides semantic grounding of actions—which our multimodal consensus idea will exploit to learn action-specific audio-visual correspondence. + +Formally, given a video with frames $v \in \mathcal{R}^{T \times H \times W \times C}$ , audio $a \in \mathcal{R}^S$ , and language narration $l$ , where $T$ and $S$ are the number of frames for video and audio respectively, the goal is to learn embeddings $e_v$ and $e_a$ that are close in the embedding space if both $a$ and $v$ capture the same human action described in $l$ , and distant otherwise. If we plot how the three modalities overlap in a Venn diagram (Figure 2), we can see that what we are interested in learning is exactly region I, i.e., a camera-wearer action that sounds. From an information-theory perspective, this is equivalent to learning modality-invariant embeddings. + +# 4. Multimodal Contrastive-Consensus Coding + +Next we present our solution MC3 (Multimodal Contrastive-Consensus Coding) for learning modality-invariant embeddings, which consists of an inter-sample contrastive loss and + +![](images/2752579371699c03b33bc24d64854cdfec2db944d263b0e91d34a8319b1a1462.jpg) +Figure 3. Multimodal contrastive-consensus loss. (a): Given three modality embeddings $e_i^t, e_j^t, e_k^t$ , multimodal contrastive coding pulls each pair of modalities closer while pushing modality pairs from another sample further away. (b): However, not all modalities agree on how close they should be depending on the instance. Thus we set the furthest distance a feature has with respect to the anchor feature as the consensus and push the remaining embeddings away to meet this consensus. + +an intra-sample consensus loss. See Fig. 3. We first present the two-stage training framework in Sec. 4.1 and then discuss the two losses in Sec. 4.2 and Sec. 4.3. For simplicity, we denote the $n$ input modalities as $M_{i}, i \in [1,n]$ . + +# 4.1. Align-Refine Two-stage Training + +We design a two-stage training paradigm. The high-level idea is to first optimize the pairwise agreement in an "align" stage, and then refine these embeddings with global consensus in the "refine" stage. See Fig. 2. + +In the first stage, we train modality encoders with a contrastive loss $\mathcal{L}_{\mathrm{contrastive}}$ , which guides modality embeddings to have a good initial alignment that captures the pairwise similarity between modalities that capture the same underlying action, as opposed to random initialization. + +In the second stage, we refine the pairwise-aligned embeddings with a globally established consensus. Specifically, we train the model with a consensus loss $\mathcal{L}_{\mathrm{consensus}}$ that pushes all intra-sample modality agreement towards this consensus, while jointly optimizing the contrastive loss $\mathcal{L}_{\mathrm{contrastive}}$ , to maximally capture the shared information across modalities. The MC3 loss $\mathcal{L}_{\mathrm{MC3}}$ combines the contrastive and consensus losses, and will be detailed below. We confirm experimentally that it is important to keep the contrastive loss in the second stage, although the main purpose of this stage is to refine embeddings with consensus. + +# 4.2. Multimodal Contrastive Coding + +Cross-modal contrastive learning has been shown to discover representations where modalities are informative of each other [39]. Prior work [46, 56] shows that minimizing the contrastive loss between $M_{i}$ and $M_{j}$ maximizes the lower bound on the mutual information $I(M_{i};M_{j})$ . Inspired by this, we first use contrastive learning to optimize the pairwise similarities $S(e_i,e_j) = e_i e_j$ , where $e_{i,j}$ is the latent embedding normalized on the unit sphere for modality pair $i,j$ . We use the InfoNCE [41] loss to optimize each individual + +$\mathcal{S}(e_i,e_j)$ as follows: + +$$ +\mathcal {L} _ {i, j} = - \frac {1}{| \mathcal {B} |} \sum_ {t \in \mathcal {B}} \log \frac {\exp \left(e _ {i} ^ {t} e _ {j} ^ {t} / \tau\right)}{\sum_ {l \in \mathcal {B}} \exp \left(e _ {i} ^ {t} e _ {j} ^ {l} / \tau\right)}, \tag {1} +$$ + +where $\mathcal{B}$ is the batch and $\tau$ is the temperature. This loss treats modalities from the same sample as positive pairs and pulls them closer and it treats modalities from different samples as negative pairs and pushes them apart. See Fig. 3 (a). The total loss is the sum of losses enumerated over all pairs of modalities, i.e., $\mathcal{L}_{\text{contrastive}} = \sum_{i,j} \mathcal{L}_{i,j}$ . + +# 4.3. Multimodal Consensus Coding + +The contrastive loss above attempts to bring all temporally co-occurring modalities closer assuming there are strong correspondences among them in the input space. However, naively doing so would be problematic for instances where not all modalities agree (cf. Figure 2). To tackle this issue, we propose a novel objective that leverages the consensus of inter-sample modalities discovered from the contrastive coding as additional supervision. + +First of all, we choose an anchor modality $M_{a}$ , which serves as the point of comparison for other modalities $M_{i}, i \in [1, n], i \neq a$ . With the normalized embedding $e_{i}^{t}$ of modality $i$ and sample $t$ , we then compute the cosine similarity score between each non-anchor modality and the anchor modality. Now, these similarity scores may or may not agree with each other. To only learn embeddings shared across all modalities, we set the consensus score as the minimum (bottleneck) score: + +$$ +c ^ {t} = \mathcal {K} ^ {- 1} (\min _ {i, i \neq a} (\mathcal {K} _ {1} (e _ {1} ^ {t} e _ {a} ^ {t}), \dots , \mathcal {K} _ {n} (e _ {n} ^ {t} e _ {a} ^ {t}))), \tag {2} +$$ + +where $\mathcal{K}_i(x) = ((x + 1) / 2)^{\alpha_i}, x \in [-1,1]$ is a modality-specific scaling function that first maps scores to $[0,1]$ and then adjusts the distribution with a tunable parameter $\alpha_i$ . $\mathcal{K}^{-1}$ is the inverse function that maps the scaled score back to the original space. The intuition behind $\mathcal{K}_i(x)$ is that different modalities carry different amounts of information and we want to normalize the score distributions among the different modality pairs, making them comparable. + +The consensus score $c^t$ is high if and only if all pairwise scores are high, and it is low if there exists at least one modality that does not agree with the anchor modality. After obtaining the consensus score, we design a loss that forces all modalities to follow this consensus, as follows: + +$$ +\mathcal {L} _ {\text {c o n s e n u s}} = \frac {1}{| \mathcal {B} |} \sum_ {t \in \mathcal {B}} \sum_ {i, i \neq a} \left\| e _ {i} ^ {t} e _ {a} ^ {t} - c ^ {t} \right\| _ {2} \tag {3} +$$ + +The total loss $\mathcal{L}_{\mathrm{MC3}}$ is the sum of the contrastive loss + +Eq.1) and the consensus loss (Eq.3): + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {M C 3}} = - \frac {1}{| \mathcal {B} |} \left(\sum_ {t \in \mathcal {B}} \underbrace {\sum_ {i , j} \log \frac {\exp \left(e _ {i} ^ {t} e _ {j} ^ {t} / \tau\right)}{\sum_ {l \in \mathcal {B}} \exp \left(e _ {i} ^ {t} e _ {j} ^ {l} / \tau\right)}} _ {\text {I n t e r - s a m p l e}}\right) \tag {4} \\ - \underbrace{\sum_{i,i\neq a}||e_{i}^{t}e_{a}^{t} - c^{t}||_{2})}_{\text{Intra-sample}}. \\ \end{array} +$$ + +This loss pushes embeddings with a low consensus score apart while pulling together embeddings with a high consensus score, and thus aligns embeddings better in the joint embedding space. See Fig. 3. + +Optimizing this loss is not trivial since it has both contrastive and reconstruction objectives. Indeed, directly optimizing the loss does not work well as shown in the ablation study (Sec. 6.1). The proposed two-stage training paradigm (Sec. 4.1) helps train the model stably. + +# 4.4. Implementation Details + +Our modalities of interest are $M_{1} = A$ (audio), $M_{2} = V$ (vision), and $M_{3} = L$ (language). There are six pairwise contrastive losses for three modalities. When computing the modality consensus, we empirically find using audio as the anchor leads to the best results in our task (cf. Sec. 6). We set the scaling parameters $\alpha_{l}$ and $\alpha_{v}$ to 1 and 0.5 respectively, based on a hyperparameter search on the validation set. See ablations in Supp. + +For extracting the feature representations, we use TimeSformer [7] as our video encoder, DistillBERT [48] as our text encoder, and AST [24] as our audio encoder. We initialize the video and language encoders with embeddings from [34], and the audio encoder with embeddings pretrained on ImageNet [13]. We train all encoders. We choose these initial encoders due to their good results in the literature; however, our MC3 loss is not specific to the choice of these encoders and others could be swapped in. + +We train all models on 8 A40 GPUs with a learning rate of $3\mathrm{e} - 5$ and batch size of 256 for 5 epochs for both stages, and take the final checkpoint for evaluation. We use the Adam optimizer [32]. Our implementation is based on the codebase from [34]. + +# 5. Training and Eval Data for Sounding Actions + +Dataset. Ego4D [26] is a large-scale egocentric video dataset that has more than 3,600 hours of video recordings depicting hundreds of daily activities—and 2,113 of those hours have audio available. As discussed, it also has timestamped narrations that are free-form sentences describing the current activity performed by the camera-wearer. However, Ego4D has no annotation of whether an action makes sounds, what sounds an action makes, or whether there exists + +
WashCloseCutDropStirWipeRubTouchLiftHold
0.900.820.770.640.640.530.390.270.190.09
+ +Table 1. Example verb groups and how frequently they sound + +other (non-action) sounds. It is thus non-trivial to detect if an action in the clip makes sound based on simple heuristics, e.g., the burst of sound energy, since many actions could produce continuous sounds with ambient-sound characteristics, e.g., wiping tables or sawing wood. + +We construct the training dataset by extracting clips from each Ego4D video based on the narration timestamps. These clips cover a wide range of daily activities and environments, including construction sites, cooking, arts and crafts, shopping, farming, and many others. Since the timestamp is only an approximate point for where an action occurs, we sample the clip from 0.5 s before to 1 s after the timestamp (1.5 s duration) so that the clip is likely long enough to capture the action sound, if there is any, without introducing visuals that stray from the narrated action. See ablations on the duration in Supp. We sample a training set of 250K clips from 1,876 hours of video. From their narrations, we find there are 6,114 unique nouns (objects) and 2,819 unique verbs (actions). + +Ground truth annotations for evaluation. Today's egocentric video datasets lack annotations for sounding actions. Thus, to determine how well our model learns long-tail sounding actions and facilitate future research, we collect a large ground truth evaluation set for Ego4D using professional annotators trained for the task. It consists of 33K clips manually labeled as to whether or not the camera wearer's action sounds, i.e., indicating whether the action described in the narration is both visible and audible in the clip. + +To ensure annotation quality, in addition to providing concrete examples and annotation guidelines (see Supp.) and iterating with quality control feedback to the professional annotators, we assign three annotators per clip and take the majority vote as the correct answer. We split the 33K obtained annotations into 3K for validation and 30K for test. We stress that this is an eval set only; our training data (above) has no manual labels about sound, only free-form language narrations. + +Action type analysis. In total, among the 33,000 resulting ground truth clips, 17,693 are positive and 15,307 are negative. The fact that only half of this in-the-wild clip distribution consists of sounding actions underscores the need for models that can tell the difference between audio that co-occurs with human action and actions that sound. To gain insight into the annotations, we group them by semantic similarity and analyze them at a group level. While narrations provide semantic descriptions of actions, using them for grouping would be too noisy since the same action could be described in different ways. To reduce the influence of narration variance, we utilize the taxonomy defined in Ego4D (for + +![](images/b85e16c7dc5034f3e5ce07fd21920c048850563879f74d0c98246c1314c734fa.jpg) +Figure 4. Long-tail distribution of sounding actions. + +analysis only, not training). For example, "check", "examine", and "inspect" should belong to the same group (taxon). We first group these clips by verb alone, i.e., extracting verbs from narrations and then applying the taxonomy, which results in 106 unique groups. We then compute the percentage of clips in each group that make sounds. Tab. 1 shows 10 examples. We see that actions involving more significant human motions (wash, close, cut) are more often sounding, whereas more subtle movements (lift, hold) are often not. Importantly, there is not a one-to-one mapping between an action verb and its sounding label—how actions sound is scenario-dependent and hence must be mined from the data. + +While grouping by verbs provides some insights, how actions make sounds also depends on the object that they interact with, e.g., cutting a carrot sounds different from cutting bread. To this end, we further group the 17K sounding clips by both verbs and nouns, which results in 2,388 unique action groups. We plot the long-tail distribution of them in Fig. 4 and show examples sampled from this distribution. This plot shows the diverse and long-tail nature of sounding actions and our test set annotations, which is not present in existing action datasets [10, 15, 17, 28, 43, 52]. + +# 6. Experiments + +We compare our model with several baselines and ablations on three tasks: sounding action discovery (on Ego4D), sounding action retrieval (on Ego4D), and audio event classification (on EPIC-Sounds). We show our model outperforms an array of existing learning methods. + +SotA Baselines. We consider two baselines that only use a contrastive loss for two modalities: CLAP [14] for audio-language and CM-ACC [35] for audio-video. For more than two modalities, we consider two more baselines: CMC [55] uses contrastive objectives between all pairs of viewpoints (modalities in our case), representing the joint training paradigm; ImageBind [23] learns the joint embedding by first performing vision-language pretraining and then freezing the vision encoder and training the vision-audio modality pair. This represents strategies that align modalities sequentially. For a fair comparison, we equip all baselines with the same encoder and the same initialization as ours (see Sec. 4.4) while keeping their original losses. + +
AVAL
ROCPRROCPR
RandomXXX0.5000.5590.5000.559
CLAP [14]✓X✓--0.6370.695
CM-ACC [35]✓✓X0.5400.590--
CMC [55]✓✓✓0.5500.6010.6350.693
ImageBind [23]✓✓✓0.5540.6050.6420.685
w/o Lconsensus✓✓✓0.5630.6150.6350.694
w/o Lcontrastive✓✓✓0.4360.4930.5840.620
w/o align-stage✓✓✓0.4480.5070.4640.521
MC3✓✓✓0.5980.6660.6580.715
+ +Table 2. Sounding action discovery. Area-under-curve (AUC) values are reported for both ROC and precision-recall (PR) curves, for audio-vision (AV) and audio-language (AL). Both are the higher the better. We train our model five times with different seeds; the standard deviation is always within 0.01. + +![](images/f4496dc1b89ed142fa35b18bf1097481b64843c6e3489f047d2be87da2141298.jpg) +Figure 5. Sounding action discovery accuracy + +![](images/dd6e4870f002203b3a97ea3b1cf9a792aa546b7dbbd3085030925edfdb755232.jpg) + +# 6.1. Sounding Action Discovery + +Human interactions with objects in our daily lives are complex and subtle. Due to many incidental background sounds, recognizing whether actions make sound is not trivial but can be useful for applications like multimodal video generation, e.g., verifying the generated action video and audio match. Towards this goal, we answer the question "what actions sound?" by performing sounding action discovery. In this experiment, we take the per-modality encoders learned on the narrated 250K Ego4D clips and apply them to the 30K test clips. Given a test clip, we feed the video and audio through their corresponding modality encoders, and compute the cosine similarity between the output embeddings. That score indicates how likely it is that the action in the video sounds. For completeness, instead of defining a hard threshold for positives, we plot the ROC and precision-recall (PR) curves by varying the positive threshold, and calculate the area-under-curve (AUC) values for them—common metrics for classification [12, 54] that are invariant to the absolute score values. For both metrics, higher values are better, indicating the model learns meaningful embeddings of sounding actions. Similarly, we can also evaluate discovery for audio-language, if narrations are available. + +Results. Table 2 shows the results for sounding action discovery. We first look at discovery with audio-visual modalities alone at test time ("AV" columns). CM-ACC [35] + +![](images/1ffde83a21d1589c41ddaea81e7a543e5eb7b7026d008af7012579f227d2352b.jpg) +Figure 6. Example visual embedding cluster from our model + +discover soundsounding actions much better than random chance, showing that audio-visual contrastive learning captures both visual action embeddings and action sound embeddings. CMC [55] and ImageBind [23] do better—benefiting (like us) from the language modality at training time. However, neither the joint nor sequential training paradigm exploits modality agreement, resulting in weak cross-modal constraints, and thus only marginal performance improvement. In comparison, our model MC3 explicitly models the modality consensus and improves the discovery result substantially by learning embeddings most relevant to sounding actions. + +We also report the discovery result from using audiolanguage modalities ("AL" columns). Since narrations provide action specifications, the discovery performance is better than $AV$ , e.g., CLAP [14] vs CM-ACC [35]. While CMC's [55] and ImageBind's [23] joint training results are not much better than CLAP [14], our model improves the "AL" discovery by leveraging the video modality and imposing the trimodal consensus constraint. + +Fig. 5 plots the precision-recall curves. For the audio-visual curve, our model always has higher precision compared to baselines, especially when recall is low. This is strong evidence of our model learning features of sounding actions, whereas baselines are limited to capturing general audio-visual correspondence—whether action-based or not. We observe a similar trend for audio-language discovery. + +Ablations. To study the importance of each loss and the two-stage training, we first ablate the consensus loss in the second stage ("w/o $\mathcal{L}_{\mathrm{consensus}}$ in Table 2), which trains the model contrastively for both stages. The model performance drops significantly, showing that exploring the modality consensus is key to learning how actions sound. We then ablate the contrastive loss in the second stage ("w/o $\mathcal{L}_{\mathrm{contrastive}}$ ), which harms performance even more. This suggests that $\mathcal{L}_{\mathrm{consensus}}$ functions like a regularization term that forces the $\mathcal{L}_{\mathrm{contrastive}}$ to learn sounding action embeddings. Lastly, we ablate the two-stage training strategy by removing the align stage ("w/o align-stage"), which optimizes $\mathcal{L}_{\mathrm{MC3}}$ directly; this model fails badly. Aligning embeddings first is critical to making MC3's training stable. + +Clustering. To visualize the learned embeddings, we group video embeddings in the test set with agglomerative clustering into 20 clusters. Fig. 6 shows the top 8 examples + +
V→A@5 @10A→V@5 @10L→A@5 @10A→L@5 @10
Random0.10.10.10.10.10.10.10.1
CLAP [14]----49.887.634.067.1
CM-ACC [35]34.663.530.957.7----
CMC [55]36.567.933.863.744.181.832.864.3
ImageBind [23]32.861.529.757.942.676.530.660.5
w/o Lconsensus33.963.030.056.145.084.732.965.8
w/o Lcontrastive3.33.76.412.53.14.73.38.0
w/o align-stage10.019.45.911.811.620.96.512.6
MC338.472.834.466.346.288.537.573.8
+ +Table 3. Sounding action retrieval. We report Recall @5 and @10 for different query-retrieval modalities. See R@1 results in Supp. + +of one cluster (more in Supp.). This cluster clearly captures the sound of water running, despite varying types of camera-wearer movement. Not only does it group videos with similar actions that make this sound, but also it shows the learned embeddings are agnostic of the background (the bathroom example). + +# 6.2. Sounding Action Retrieval + +Retrieving a different modality given a video, audio, or description is another useful application, such as adding sound effects to silent videos or retrieving captions for action sounds. To explore this setting, we answer the question "how do different actions sound?" by evaluating the cross-modal retrieval performance of long-tail sounding actions from the same category. Different from the binary classification task above, here we aim to retrieve other examples of the same action. + +To do this, we utilize the action groups constructed in Sec. 5 based on verbs and nouns, and only keep groups that have more than two instances of sounding actions (such that there will be at least one true positive to retrieve for each query). We then divide each action group equally into a query pool of 7,559 examples and a retrieval pool of 7,032 examples. Given a query modality $M_{i}$ of instance $A$ , we compute its distance to other modalities $M_{j}$ of all instances in the retrieval pool. A retrieval is correct if the retrieved instance $B$ and $A$ belong to the same action group. + +Results. Table 3 shows the results for four different query-retrieval modality settings. For audio-visual retrieval, we observe that all models can retrieve video with audio (or audio with video) for similar actions with much higher recall than random chance. Our model strongly outperforms the baselines and ablations, benefiting from modeling the modality consensus explicitly. We also observe that retrieving audio with video is easier than the opposite, likely because audio can be vague sometimes, e.g., a collision sound might occur due to various actions while seeing a cutting action indicates the likely sound. For audio-language retrieval, our + +![](images/bdcabbcbb9c8b881bb18beb504ca7b7d9d0ca8ccff2c82be25f3647fa033be39.jpg) +Figure 7. Qualitative examples for retrieval. The first row is video-to-audio retrieval, motivated by adding audio effects for silent videos. The second row is audio-to-text retrieval, motivated by audio captioning applications. For each row, we show three correct retrieval examples along with their text (gray indicates the text is not observed by the model). For the retrieved item, we show the ground truth rank as the superscript. All examples are long-tail sounding actions, showing how our model learns to capture the features of how actions sound. + +![](images/01323f3b33133d1cfcce45e595e445b0ac270d0ba9098f355d5dfe696b61e601.jpg) + +![](images/8095ba9044315a7e51ae8e522448f28b8328ab89ebc19c6a9b63b89cf46e06e0.jpg) + +![](images/2dbce9d96889fc51a8f32ff29573f75b1f9ba9c3428312a4bc1cf333d9fa53fa.jpg) + +![](images/3338f23177776111e0e50111987a3108c9df78b0763e6dfc0a7fb7cd284c9b3c.jpg) + +model similarly outperforms the baselines by large margins. Qualitative examples. In Fig 7, we show examples for video-to-audio and audio-to-language retrieval. Even though these actions are subtle, our model retrieves audio or captions that are very relevant. Listen to examples in Supp. video. + +# 6.3. Audio Classification on EPIC-Sounds + +Finally, we evaluate our learned representation on a standard audio benchmark. To assess the impact of our model's action sounds representation, we consider EPIC-Sounds [28], a challenging audio classification benchmark for sounds in kitchen environments. To our knowledge, EPIC-Sounds represents the only large-scale benchmark for audio in egocentric video. Note, this classification task is different from the sounding action discovery task in Sec. 6.1 in that here the model only takes an audio clip as input. + +We consider both linear-probe and fine-tuning settings. In the linear-probe setup, we freeze the model weights and only train the last classification layer, which evaluates the quality of the pre-trained representations. In the fine-tuning setup, we fine-tune both the encoder and the last layer. + +Table 4 shows the results. We compare with two SotA methods reported in EPIC-Sounds: SSAST [25] and ASF [31]. SSAST is pretrained on LibriSpeech [44] and shares the same network architecture as ours, while ASF is trained on VGG-Sound with supervised learning. With linear-probe, our model strongly outperforms SSAST [25], which, like us, is also pretrained in a self-supervised fashion with no audio labels. ASF [31] does better than both, likely due to its advantage of supervised audio classification pretraining. When fine-tuning, our model outperforms both prior methods in all but one metric when following the same + +
Top-1Top-5mCAMAPmAUC
Random-7.7130.952.290.0230.500
ASF [31]*L45.5379.3313.480.1720.789
SSAST [25]L28.7464.847.140.0790.755
MC3L42.4478.7612.790.1530.818
ASF [31]*F53.7584.5420.110.2540.873
SSAST [25]F53.4784.5620.220.2350.879
MC3F55.9785.8621.650.2420.885
+ +Table 4. Results of classification on EPIC-Sounds. L: Linear-Probe; F: Fine-tuning. * denotes pretraining with supervised audio classification while the rest are pretrained in a self-supervised fashion. + +fine-tuning and evaluation protocol. This shows our MC3 audio encoder—trained for sounding action discovery—learns generalizable action sound embeddings, improving the state of the art. The margins are naturally smaller in the fine-tuning regime, as is typical, since all models have time to adapt to the new domain. + +# 7. Conclusion + +We explored learning how first-person actions sound from inthe-wild, narrated egocentric videos—without audio labels. Training with 250K clips from Ego4D, we show the promise of our novel multimodal consensus framework for accurately aligning representations to capture the long-tail of sounding actions in novel (unnarrated) videos, with clear impact on sounding action discovery, retrieval, and pre-training for audio classification. 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In CVPR, 2023. 3 \ No newline at end of file diff --git a/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/images.zip b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..2d03cac40972fd0396797df959ec04b5c7852bbb --- /dev/null +++ b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:36048d4b13e94823dbb4c55d717762e31fd120e08468b7776c16a4880ebf362b +size 517103 diff --git a/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/layout.json b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..73d4e0be753037644533fd7a3a72cef31d815072 --- /dev/null +++ b/2024/SoundingActions_ Learning How Actions Sound from Narrated Egocentric Videos/layout.json @@ -0,0 +1,8723 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 47, + 103, + 547, + 122 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 103, + 547, + 122 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 547, + 122 + ], + "type": "text", + "content": "SoundingActions: Learning How Actions Sound from Narrated Egocentric Videos" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "spans": [ + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": "Changan Chen" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": " Kumar Ashutosh" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": " Rohit Girdhar" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": " David Harwath" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": " Kristen Grauman" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": "University of Texas at Austin " + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "inline_equation", + "content": "{}^{2}" + }, + { + "bbox": [ + 66, + 142, + 527, + 172 + ], + "type": "text", + "content": "FAIR, Meta" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 192, + 212 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 224, + 290, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 290, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 290, + 369 + ], + "type": "text", + "content": "We propose a novel self-supervised embedding to learn how actions sound from narrated in-the-wild egocentric videos. Whereas existing methods rely on curated data with known audio-visual correspondence, our multimodal contrastive-consensus coding (MC3) embedding reinforces the associations between audio, language, and vision when all modality pairs agree, while diminishing those associations when any one pair does not. We show our approach can successfully discover how the long tail of human actions sound from egocentric video, outperforming an array of recent multimodal embedding techniques on two datasets (Ego4D and EPIC-Sounds) and multiple cross-modal tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 405, + 128, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 405, + 128, + 417 + ], + "spans": [ + { + "bbox": [ + 47, + 405, + 128, + 417 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 426, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 581 + ], + "type": "text", + "content": "Human activity often produces sounds. Closing a door, chopping vegetables, typing on a keyboard, talking with a friend—our interactions with the objects and people around us generate audio that reveals our physical behaviors. These sounds can be strongly associated with the subjects of our activity and how we perform it. For example, opening a water bottle sounds different than opening a cabinet; chopping sweet potatoes sounds different than chopping onions; chopping onions sounds different than mincing onions (the same object). Understanding the link between sounds and actions is valuable for a number of applications, such as multimodal activity recognition, cross-modal retrieval, content generation, or forecasting the physical effects of a person's actions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "How should AI learn about sounding actions? Existing work typically curates annotated datasets for supervised learning [9, 22, 28, 45], taking care to select events or actions that have associated sounds (e.g., lawnmowing, chopping), while others deliberately collect videos of object collisions (e.g., striking objects with a drumstick [43] or crashing into them with a robot [10, 17]), or develop physics-based simulations [16]. On the one hand, these approaches are appealing for their ability to focus on meaningful audio-visual correspondences. On the other hand, their curated nature risks limiting the scope of sounding actions that can be learned." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 200, + 386, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 200, + 386, + 230 + ], + "spans": [ + { + "bbox": [ + 306, + 200, + 386, + 230 + ], + "type": "text", + "content": "Action: C moves a metal cutting machine with hands." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 307, + 239, + 389, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 239, + 389, + 248 + ], + "spans": [ + { + "bbox": [ + 307, + 239, + 389, + 248 + ], + "type": "text", + "content": "Does the action sound?" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 260, + 343, + 274 + ], + "blocks": [ + { + "bbox": [ + 309, + 260, + 343, + 274 + ], + "lines": [ + { + "bbox": [ + 309, + 260, + 343, + 274 + ], + "spans": [ + { + "bbox": [ + 309, + 260, + 343, + 274 + ], + "type": "image", + "image_path": "6d6a4a6a781495d237d8a7ca94de18d4281de8cfd6143cdaf55793c2b76a41b2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 307, + 283, + 370, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 283, + 370, + 302 + ], + "spans": [ + { + "bbox": [ + 307, + 283, + 370, + 302 + ], + "type": "text", + "content": "Action: C digs the soil with a hoe." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 307, + 317, + 389, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 317, + 389, + 326 + ], + "spans": [ + { + "bbox": [ + 307, + 317, + 389, + 326 + ], + "type": "text", + "content": "Does the action sound?" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 309, + 342, + 343, + 355 + ], + "blocks": [ + { + "bbox": [ + 309, + 342, + 343, + 355 + ], + "lines": [ + { + "bbox": [ + 309, + 342, + 343, + 355 + ], + "spans": [ + { + "bbox": [ + 309, + 342, + 343, + 355 + ], + "type": "image", + "image_path": "0b8d9a7d05e976e624a887d30acb37300c896e8daf6422135115c00554de9adf.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 369, + 547, + 479 + ], + "lines": [ + { + "bbox": [ + 304, + 369, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 547, + 479 + ], + "type": "text", + "content": "Figure 1. We aim to distinguish sounds that are directly caused by human actions (bottom) from those that are not (top). Given egocentric training videos with language descriptions of the camera wearer's (\"C\") current action, we learn an embedding where the audio and visual features of any given clip are best aligned only when both are also consistent with the language. This allows discerning clips where the audio and vision may be correlated (e.g., the cutting machine running making loud noise in top row) versus those where the sounds are driven by human action (digging in bottom row)—importantly, without language at inference time." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 389, + 198, + 464, + 256 + ], + "blocks": [ + { + "bbox": [ + 389, + 198, + 464, + 256 + ], + "lines": [ + { + "bbox": [ + 389, + 198, + 464, + 256 + ], + "spans": [ + { + "bbox": [ + 389, + 198, + 464, + 256 + ], + "type": "image", + "image_path": "76dd2112a7e9914204785da4a979af634217ba87f46887bb3d4b099a5c4d3226.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 468, + 198, + 545, + 256 + ], + "blocks": [ + { + "bbox": [ + 468, + 198, + 545, + 256 + ], + "lines": [ + { + "bbox": [ + 468, + 198, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 468, + 198, + 545, + 256 + ], + "type": "image", + "image_path": "b093e1674ba0dd5e6841140fc140d729bb958b05444e237524c722bc06978e16.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 389, + 257, + 545, + 277 + ], + "blocks": [ + { + "bbox": [ + 389, + 257, + 545, + 277 + ], + "lines": [ + { + "bbox": [ + 389, + 257, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 389, + 257, + 545, + 277 + ], + "type": "image", + "image_path": "97958cccd0161c87aac033022a51d514126c86b00756c799cf2295f59b9a954d.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 389, + 279, + 464, + 336 + ], + "blocks": [ + { + "bbox": [ + 389, + 279, + 464, + 336 + ], + "lines": [ + { + "bbox": [ + 389, + 279, + 464, + 336 + ], + "spans": [ + { + "bbox": [ + 389, + 279, + 464, + 336 + ], + "type": "image", + "image_path": "69f5653cd42e3a1268bc42468bbe8afe56840b149c58096f764162763bdf259c.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 469, + 279, + 545, + 336 + ], + "blocks": [ + { + "bbox": [ + 469, + 279, + 545, + 336 + ], + "lines": [ + { + "bbox": [ + 469, + 279, + 545, + 336 + ], + "spans": [ + { + "bbox": [ + 469, + 279, + 545, + 336 + ], + "type": "image", + "image_path": "b9f94bf0c4355b63560251d13935aae243c149a9108102af87f018770f746cc7.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 389, + 338, + 545, + 358 + ], + "blocks": [ + { + "bbox": [ + 389, + 338, + 545, + 358 + ], + "lines": [ + { + "bbox": [ + 389, + 338, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 389, + 338, + 545, + 358 + ], + "type": "image", + "image_path": "3cd993d8955896feeaefbb852e29c0b9037572582a12f056f86d1e54675718b9.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 548, + 715 + ], + "type": "text", + "content": "Instead, we aim to learn how human actions sound from narrated in-the-wild egocentric videos. See Figure 1. Given a pool of videos of everyday human activity, the goal is to learn a cross-modal representation where sounding actions cluster together based on how they look and sound. By sampling the videos freely, we can broaden the scope to discover the breadth of sounding actions without having to rely on a closed, pre-defined set of action categories. In particular, by focusing on unscripted egocentric video from wearable cameras in daily-life settings [11, 26], we aim to include subtle and long-tail scenarios unavailable in curated datasets, such as sounds of keys jangling when unlocking a door, scissors snipping when cutting the dog's fur, or fingernails scratching on one's own arm. Egocentric video is a particularly attractive source here because 1) human interaction sounds are more audible in near-field egocentric recordings and 2) passively captured long-form ego-video simply covers more" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "27252" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 161, + 220 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 161, + 220 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 161, + 220 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 161, + 220 + ], + "type": "image", + "image_path": "4d012ad5e17f8f882c8298bb77a0b08f86721fd70cb21fe59c2f952331c2cbe5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "lines": [ + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": "Figure 2. Main idea. On the left, the Venn diagram illustrates different ways audio " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "(A)" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": ", video " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "(V)" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": " and language " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "(L)" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": " modalities can overlap in the content they capture. C refers to the camera wearer. Regions II, III, IV are information that is only shared between two modalities but not the third, e.g., the racing game in " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "①" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": " where the game sounds correlate with the vision, yet are not about the camera wearer's described action (using hands on laptop), the lifting action in " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "③" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": ", where the visuals and language agree but the action is inaudible, and the off-screen talking action in " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "④" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": ", where talking is heard and described, but the camera wearer cannot be seen speaking. Region I is the information that corresponds to all modalities agreeing, e.g., the visible and audible plastering action in " + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "inline_equation", + "content": "②" + }, + { + "bbox": [ + 46, + 230, + 547, + 340 + ], + "type": "text", + "content": ". Our model's \"align\" phase detects any such (dis)agreements via pairwise contrastive learning on the modalities. In the \"refine\" phase, we use the intersection of that agreement (region I) to refine the embedding. For example, on the right, we show what the three modality embeddings should look like after the \"align\" stage for examples 1 and 2. Embeddings of instances where all modalities agree will be closer in the embedding space and apart otherwise. In other words, for example 1, yellow (video) cannot be close to blue (audio) unless green is too (language)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 159, + 70, + 304, + 221 + ], + "blocks": [ + { + "bbox": [ + 159, + 70, + 304, + 221 + ], + "lines": [ + { + "bbox": [ + 159, + 70, + 304, + 221 + ], + "spans": [ + { + "bbox": [ + 159, + 70, + 304, + 221 + ], + "type": "image", + "image_path": "15d118388b5b8b7713a64344599219dc7501703ab835d915110efcf20d77fcd1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 420, + 221 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 420, + 221 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 420, + 221 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 420, + 221 + ], + "type": "image", + "image_path": "c3cdb3f9bbfb7d6b65d9cdb02854f54ed8d1a84da7aa87a66a35c49177bde73f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 432, + 70, + 546, + 220 + ], + "blocks": [ + { + "bbox": [ + 432, + 70, + 546, + 220 + ], + "lines": [ + { + "bbox": [ + 432, + 70, + 546, + 220 + ], + "spans": [ + { + "bbox": [ + 432, + 70, + 546, + 220 + ], + "type": "image", + "image_path": "7205e41e9eb5db7adf746ff81007a0b398811eaef9e2067a1320ea012e65c401.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 361, + 216, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 361, + 216, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 361, + 216, + 373 + ], + "type": "text", + "content": "everyday sounds, including the rare ones." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 375, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 495 + ], + "type": "text", + "content": "However, the learning task is challenging because some visible actions do not make any sound, and some sounds are the result of off-screen actions. Finally, other sounds may be correlated with on-screen objects (such as traffic noise and a city street), but are not directly related to the video by a salient and visible camera wearer action. For this reason, although existing self-supervised audio-visual methods [3, 5, 6, 20, 23, 33, 35, 42] are good at detecting audio-visual correspondences, they tend to capture general correlations rather than the action-specific correspondence." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 497, + 288, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 288, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 288, + 640 + ], + "type": "text", + "content": "To address this challenge, we propose a novel multimodal consensus embedding approach. Importantly, we suppose the in-the-wild egocentric training videos are accompanied by free-form natural language descriptions describing the actions of the camera wearer, as provided in the \"narrations\" of existing large-scale ego-video datasets [11, 26]. The main idea is to seek video samples where there is semantic agreement between all three modalities—the audio, visual, and language—while distancing those that do not. This intersection of the modalities with language assures that correspondences in the audio and visual streams stem from alignment on the sounding action." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 713 + ], + "type": "text", + "content": "To achieve this, the proposed model first aligns a preliminary embedding from contrastive losses imposed per instance on each pair of modalities. Next, we refine those embeddings with a consensus objective that targets a minimum (bottleneck) pairwise similarity. The latter pushes all pairs of inter-modality agreement towards this consensus—or lack" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 361, + 547, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 547, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 547, + 421 + ], + "type": "text", + "content": "thereof—while jointly continuing to optimize the paired-modalities' contrastive losses. In this way, we overcome the simplifying assumption made by existing multimodal embeddings that require all modalities to agree [1, 23, 55]. See Figure 2." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 421, + 548, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 548, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 548, + 600 + ], + "type": "text", + "content": "We demonstrate our approach by training with in-the-wild data from Ego4D [26] without audio labels and testing on both Ego4D and EPIC-Sounds [28]. To allow a formal large-scale evaluation of sounding actions, we introduce a dataset of professional annotations on 33K video clips spanning Ego4D. Our model successfully discovers sounding actions that agree with ground truth labels on both datasets. Compared to existing multimodal embedding paradigms [14, 23, 35, 55], our model not only better discovers sounding actions and learns embeddings for cross-modality retrieval, but also generalizes better to the audio classification benchmark on EPIC-Sounds. To our knowledge, this is the first result of its kind to show sounding actions discovered organically from narrated in-the-wild video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 609, + 392, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 392, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 392, + 621 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "Action/interaction/impact sound. Some work [21, 30, 40] leverages audio to improve activity recognition on video datasets such as UCF101 [52] and ActivityNet [15], which have visual labels but no audio labels. Existing audio datasets such as AudioSet [22] and VGG-Sound [9] target general sound classes such as music, speech, and sports. EPIC-Sounds [28] provides an audio classification bench-" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 317, + 742 + ], + "type": "text", + "content": "27253" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "mark for actions in kitchen environments, but it has no labels for the correspondence between the visual action and the sound. The Greatest Hits dataset [43] contains videos where people hit and scratch object surfaces with a drumstick, which enables audio synthesis from videos. Interaction sound has also been studied in robotics, e.g., using a robotic platform to collect sounds and study the synergy between action and sounds [10, 17]. Impact sounds are modeled in a physics-based simulator [16]. Throughout, the existing work assumes a fixed, given taxonomy of action classes or audio labels of interest. In contrast, we learn how actions make sounds from in-the-wild narrated egocentric videos, without relying on a taxonomy of discrete labels for the audio events." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 234, + 289, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 234, + 289, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 234, + 289, + 389 + ], + "type": "text", + "content": "Audio-visual learning. As naturally co-occurring data, there are rich correspondences between video and audio, such as spatial correspondence [18, 29, 38], acoustic correspondence [8, 51], semantic correspondence [5, 6], and lip motion [19, 49]. Existing work typically either learns one type of correspondences by manually creating misalignment, e.g., shifting audio temporally to create temporal supervision [5, 33, 42] or down-mixing audio channels to create spatial supervision [18, 38], or it picks up any correspondence that emerges from the learning process [37, 39] (e.g., actions, objects, environments). In contrast, we aim to learn action-specific correspondence by leveraging the semantic grounding from human narrations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 396, + 289, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 289, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 289, + 588 + ], + "type": "text", + "content": "Language+X learning. Language can provide semantic grounding for what we see or hear. Prior work exploring language with another modality includes image/video captioning [57], visual question answering [4], and audio captioning [36]. Recent results with large-scale image-text datasets show that language is excellent for guiding the learning of image features (such as CLIP [47]), video features [34, 59], or audio features [27]. However, there is limited work studying binding language to more than one modality, as we propose. Some recent work [1, 58] explores self-supervised learning with language, vision, and sound, where the language is typically the transcription of the audio. They construct self-supervised objectives under the assumption that modalities agree with each other. In contrast, we use language that is different from the speech transcription and we explore modality agreement in training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Multi-modal/view representation learning. Recent work builds multimodal models using more than two modalities (e.g., audio, video, and language) for improving the representations of one modality [1, 2, 50], while others explore modality-invariant or view-invariant features [23, 53, 55]. For example, ImageBind [23] binds the visual features with other modalities in sequence, while CMC [55] proposes a contrastive multi-view loss that maximizes the mutual information between different views of the same scene. These methods assume there exists shared information among all" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 109 + ], + "type": "text", + "content": "modalities, which does not address how to find these examples. Our method implicitly discovers the shared information by analyzing the multimodal consensus, or lack thereof." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 115, + 414, + 128 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 115, + 414, + 128 + ], + "spans": [ + { + "bbox": [ + 305, + 115, + 414, + 128 + ], + "type": "text", + "content": "3. Task Formulation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": "We define a sounding action as a human-initiated action that produces sound during its execution due to interactions with the surrounding environment. We are particularly interested in learning how subtle and long-tail daily human actions sound. If hypothetically we were given a clip with audio " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": ", video " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": ", and label " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": " indicating whether the clip contains a sounding action, our objective would be to minimize the distance between audio-visual embeddings if " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "y = 1" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": " and maximize the distance between them if " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "y = 0" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": ", i.e., minimizing " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "(-1)^{y}\\mathcal{D}(e_{a},e_{v})" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": " measures the distance and " + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "inline_equation", + "content": "e_{a,v}" + }, + { + "bbox": [ + 304, + 132, + 547, + 335 + ], + "type": "text", + "content": " are their embeddings. However, we do not assume access to any such direct supervision; labeling sounding actions is expensive, both because many actions do not produce sounds, and because many clips do not contain actions. Instead, we aim to discover sounding actions in a weakly supervised fashion, while simultaneously learning multimodal embeddings that capture them well." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 336, + 547, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 547, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 547, + 514 + ], + "type": "text", + "content": "To this end, we leverage \"narrations\", a form of language description that is collected in recent egocentric video datasets such as Ego4D [26] and EPIC-Kitchens [11]. These narrations are timestamped free-form sentences describing the current action being performed by the camera-wearer. See Figure 2 for examples. Note that there may be other events in the video, too (e.g., a TV is playing), but these are not narrated. This is significant: the language specifically addresses near-field human interactions with objects, people, and the environment. The narrations offer two key benefits: 1) the timestamps provide temporal grounding of actions that occur in the video, indicating where potentially interesting clips are and 2) the language provides semantic grounding of actions—which our multimodal consensus idea will exploit to learn action-specific audio-visual correspondence." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": "Formally, given a video with frames " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "v \\in \\mathcal{R}^{T \\times H \\times W \\times C}" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": ", audio " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "a \\in \\mathcal{R}^S" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": ", and language narration " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": " are the number of frames for video and audio respectively, the goal is to learn embeddings " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "e_v" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "e_a" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": " that are close in the embedding space if both " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": " capture the same human action described in " + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 514, + 547, + 647 + ], + "type": "text", + "content": ", and distant otherwise. If we plot how the three modalities overlap in a Venn diagram (Figure 2), we can see that what we are interested in learning is exactly region I, i.e., a camera-wearer action that sounds. From an information-theory perspective, this is equivalent to learning modality-invariant embeddings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 657, + 543, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 657, + 543, + 671 + ], + "spans": [ + { + "bbox": [ + 305, + 657, + 543, + 671 + ], + "type": "text", + "content": "4. Multimodal Contrastive-Consensus Coding" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Next we present our solution MC3 (Multimodal Contrastive-Consensus Coding) for learning modality-invariant embeddings, which consists of an inter-sample contrastive loss and" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "27254" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 287, + 150 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 287, + 150 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 287, + 150 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 287, + 150 + ], + "type": "image", + "image_path": "2752579371699c03b33bc24d64854cdfec2db944d263b0e91d34a8319b1a1462.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 159, + 289, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 159, + 289, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 289, + 248 + ], + "type": "text", + "content": "Figure 3. Multimodal contrastive-consensus loss. (a): Given three modality embeddings " + }, + { + "bbox": [ + 46, + 159, + 289, + 248 + ], + "type": "inline_equation", + "content": "e_i^t, e_j^t, e_k^t" + }, + { + "bbox": [ + 46, + 159, + 289, + 248 + ], + "type": "text", + "content": ", multimodal contrastive coding pulls each pair of modalities closer while pushing modality pairs from another sample further away. (b): However, not all modalities agree on how close they should be depending on the instance. Thus we set the furthest distance a feature has with respect to the anchor feature as the consensus and push the remaining embeddings away to meet this consensus." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "type": "text", + "content": "an intra-sample consensus loss. See Fig. 3. We first present the two-stage training framework in Sec. 4.1 and then discuss the two losses in Sec. 4.2 and Sec. 4.3. For simplicity, we denote the " + }, + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "type": "text", + "content": " input modalities as " + }, + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "type": "inline_equation", + "content": "M_{i}, i \\in [1,n]" + }, + { + "bbox": [ + 46, + 268, + 288, + 316 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 222, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 222, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 222, + 335 + ], + "type": "text", + "content": "4.1. Align-Refine Two-stage Training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 341, + 288, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 288, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 288, + 389 + ], + "type": "text", + "content": "We design a two-stage training paradigm. The high-level idea is to first optimize the pairwise agreement in an \"align\" stage, and then refine these embeddings with global consensus in the \"refine\" stage. See Fig. 2." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 389, + 288, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 288, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 288, + 449 + ], + "type": "text", + "content": "In the first stage, we train modality encoders with a contrastive loss " + }, + { + "bbox": [ + 46, + 389, + 288, + 449 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{contrastive}}" + }, + { + "bbox": [ + 46, + 389, + 288, + 449 + ], + "type": "text", + "content": ", which guides modality embeddings to have a good initial alignment that captures the pairwise similarity between modalities that capture the same underlying action, as opposed to random initialization." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "text", + "content": "In the second stage, we refine the pairwise-aligned embeddings with a globally established consensus. Specifically, we train the model with a consensus loss " + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{consensus}}" + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "text", + "content": " that pushes all intra-sample modality agreement towards this consensus, while jointly optimizing the contrastive loss " + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{contrastive}}" + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "text", + "content": ", to maximally capture the shared information across modalities. The MC3 loss " + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MC3}}" + }, + { + "bbox": [ + 46, + 449, + 288, + 581 + ], + "type": "text", + "content": " combines the contrastive and consensus losses, and will be detailed below. We confirm experimentally that it is important to keep the contrastive loss in the second stage, although the main purpose of this stage is to refine embeddings with consensus." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 587, + 220, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 220, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 220, + 601 + ], + "type": "text", + "content": "4.2. Multimodal Contrastive Coding" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": "Cross-modal contrastive learning has been shown to discover representations where modalities are informative of each other [39]. Prior work [46, 56] shows that minimizing the contrastive loss between " + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "inline_equation", + "content": "M_{j}" + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": " maximizes the lower bound on the mutual information " + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "inline_equation", + "content": "I(M_{i};M_{j})" + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": ". Inspired by this, we first use contrastive learning to optimize the pairwise similarities " + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "inline_equation", + "content": "S(e_i,e_j) = e_i e_j" + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "inline_equation", + "content": "e_{i,j}" + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": " is the latent embedding normalized on the unit sphere for modality pair " + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "inline_equation", + "content": "i,j" + }, + { + "bbox": [ + 46, + 605, + 289, + 714 + ], + "type": "text", + "content": ". We use the InfoNCE [41] loss to optimize each individual" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 391, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 391, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 391, + 85 + ], + "type": "inline_equation", + "content": "\\mathcal{S}(e_i,e_j)" + }, + { + "bbox": [ + 306, + 72, + 391, + 85 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 340, + 96, + 547, + 128 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 96, + 547, + 128 + ], + "spans": [ + { + "bbox": [ + 340, + 96, + 547, + 128 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i, j} = - \\frac {1}{| \\mathcal {B} |} \\sum_ {t \\in \\mathcal {B}} \\log \\frac {\\exp \\left(e _ {i} ^ {t} e _ {j} ^ {t} / \\tau\\right)}{\\sum_ {l \\in \\mathcal {B}} \\exp \\left(e _ {i} ^ {t} e _ {j} ^ {l} / \\tau\\right)}, \\tag {1}", + "image_path": "55d9af97da3c817d4cc749a9614c6d1fb8dd2642a0d50a395ff1167d9a3d51f6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "text", + "content": " is the batch and " + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "text", + "content": " is the temperature. This loss treats modalities from the same sample as positive pairs and pulls them closer and it treats modalities from different samples as negative pairs and pushes them apart. See Fig. 3 (a). The total loss is the sum of losses enumerated over all pairs of modalities, i.e., " + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\text{contrastive}} = \\sum_{i,j} \\mathcal{L}_{i,j}" + }, + { + "bbox": [ + 304, + 139, + 547, + 213 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 223, + 474, + 236 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 223, + 474, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 223, + 474, + 236 + ], + "type": "text", + "content": "4.3. Multimodal Consensus Coding" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 243, + 547, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 339 + ], + "type": "text", + "content": "The contrastive loss above attempts to bring all temporally co-occurring modalities closer assuming there are strong correspondences among them in the input space. However, naively doing so would be problematic for instances where not all modalities agree (cf. Figure 2). To tackle this issue, we propose a novel objective that leverages the consensus of inter-sample modalities discovered from the contrastive coding as additional supervision." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "content": "First of all, we choose an anchor modality " + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "inline_equation", + "content": "M_{a}" + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "content": ", which serves as the point of comparison for other modalities " + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "inline_equation", + "content": "M_{i}, i \\in [1, n], i \\neq a" + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "content": ". With the normalized embedding " + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "inline_equation", + "content": "e_{i}^{t}" + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "content": " of modality " + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "content": " and sample " + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 340, + 547, + 448 + ], + "type": "text", + "content": ", we then compute the cosine similarity score between each non-anchor modality and the anchor modality. Now, these similarity scores may or may not agree with each other. To only learn embeddings shared across all modalities, we set the consensus score as the minimum (bottleneck) score:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 337, + 459, + 546, + 479 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 459, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 337, + 459, + 546, + 479 + ], + "type": "interline_equation", + "content": "c ^ {t} = \\mathcal {K} ^ {- 1} (\\min _ {i, i \\neq a} (\\mathcal {K} _ {1} (e _ {1} ^ {t} e _ {a} ^ {t}), \\dots , \\mathcal {K} _ {n} (e _ {n} ^ {t} e _ {a} ^ {t}))), \\tag {2}", + "image_path": "50cf3a755f2db0e3db557f43a740ecf3b108b9518b0792e062c2ba88bdb402e7.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_i(x) = ((x + 1) / 2)^{\\alpha_i}, x \\in [-1,1]" + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "content": " is a modality-specific scaling function that first maps scores to " + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "content": " and then adjusts the distribution with a tunable parameter " + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\alpha_i" + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{K}^{-1}" + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "content": " is the inverse function that maps the scaled score back to the original space. The intuition behind " + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_i(x)" + }, + { + "bbox": [ + 304, + 491, + 547, + 586 + ], + "type": "text", + "content": " is that different modalities carry different amounts of information and we want to normalize the score distributions among the different modality pairs, making them comparable." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 588, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 588, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 588, + 547, + 648 + ], + "type": "text", + "content": "The consensus score " + }, + { + "bbox": [ + 304, + 588, + 547, + 648 + ], + "type": "inline_equation", + "content": "c^t" + }, + { + "bbox": [ + 304, + 588, + 547, + 648 + ], + "type": "text", + "content": " is high if and only if all pairwise scores are high, and it is low if there exists at least one modality that does not agree with the anchor modality. After obtaining the consensus score, we design a loss that forces all modalities to follow this consensus, as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 347, + 658, + 546, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 658, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 347, + 658, + 546, + 689 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c o n s e n u s}} = \\frac {1}{| \\mathcal {B} |} \\sum_ {t \\in \\mathcal {B}} \\sum_ {i, i \\neq a} \\left\\| e _ {i} ^ {t} e _ {a} ^ {t} - c ^ {t} \\right\\| _ {2} \\tag {3}", + "image_path": "4b232c328a90bb3770f04cb6f3bb150de962467cc955c11488e8b69a5461a5a1.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "The total loss " + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MC3}}" + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": " is the sum of the contrastive loss" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 732, + 318, + 742 + ], + "type": "text", + "content": "27255" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 203, + 84 + ], + "type": "text", + "content": "Eq.1) and the consensus loss (Eq.3):" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 70, + 91, + 287, + 184 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 91, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 70, + 91, + 287, + 184 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {M C 3}} = - \\frac {1}{| \\mathcal {B} |} \\left(\\sum_ {t \\in \\mathcal {B}} \\underbrace {\\sum_ {i , j} \\log \\frac {\\exp \\left(e _ {i} ^ {t} e _ {j} ^ {t} / \\tau\\right)}{\\sum_ {l \\in \\mathcal {B}} \\exp \\left(e _ {i} ^ {t} e _ {j} ^ {l} / \\tau\\right)}} _ {\\text {I n t e r - s a m p l e}}\\right) \\tag {4} \\\\ - \\underbrace{\\sum_{i,i\\neq a}||e_{i}^{t}e_{a}^{t} - c^{t}||_{2})}_{\\text{Intra-sample}}. \\\\ \\end{array}", + "image_path": "1177cef0bb0eea347ced580fc03d8a9e16cd1bb5ff7129dc8d8b042bc34c2fb0.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 191, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 191, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 191, + 287, + 239 + ], + "type": "text", + "content": "This loss pushes embeddings with a low consensus score apart while pulling together embeddings with a high consensus score, and thus aligns embeddings better in the joint embedding space. See Fig. 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 287, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 299 + ], + "type": "text", + "content": "Optimizing this loss is not trivial since it has both contrastive and reconstruction objectives. Indeed, directly optimizing the loss does not work well as shown in the ablation study (Sec. 6.1). The proposed two-stage training paradigm (Sec. 4.1) helps train the model stably." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 306, + 180, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 180, + 318 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 180, + 318 + ], + "type": "text", + "content": "4.4. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "content": "Our modalities of interest are " + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "inline_equation", + "content": "M_{1} = A" + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "content": " (audio), " + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "inline_equation", + "content": "M_{2} = V" + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "content": " (vision), and " + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "inline_equation", + "content": "M_{3} = L" + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "content": " (language). There are six pairwise contrastive losses for three modalities. When computing the modality consensus, we empirically find using audio as the anchor leads to the best results in our task (cf. Sec. 6). We set the scaling parameters " + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "inline_equation", + "content": "\\alpha_{l}" + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "inline_equation", + "content": "\\alpha_{v}" + }, + { + "bbox": [ + 46, + 324, + 287, + 419 + ], + "type": "text", + "content": " to 1 and 0.5 respectively, based on a hyperparameter search on the validation set. See ablations in Supp." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 420, + 287, + 527 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 420, + 287, + 527 + ], + "spans": [ + { + "bbox": [ + 46, + 420, + 287, + 527 + ], + "type": "text", + "content": "For extracting the feature representations, we use TimeSformer [7] as our video encoder, DistillBERT [48] as our text encoder, and AST [24] as our audio encoder. We initialize the video and language encoders with embeddings from [34], and the audio encoder with embeddings pretrained on ImageNet [13]. We train all encoders. We choose these initial encoders due to their good results in the literature; however, our MC3 loss is not specific to the choice of these encoders and others could be swapped in." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 528, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 287, + 588 + ], + "type": "text", + "content": "We train all models on 8 A40 GPUs with a learning rate of " + }, + { + "bbox": [ + 46, + 528, + 287, + 588 + ], + "type": "inline_equation", + "content": "3\\mathrm{e} - 5" + }, + { + "bbox": [ + 46, + 528, + 287, + 588 + ], + "type": "text", + "content": " and batch size of 256 for 5 epochs for both stages, and take the final checkpoint for evaluation. We use the Adam optimizer [32]. Our implementation is based on the codebase from [34]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 597, + 287, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 287, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 287, + 611 + ], + "type": "text", + "content": "5. Training and Eval Data for Sounding Actions" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 712 + ], + "type": "text", + "content": "Dataset. Ego4D [26] is a large-scale egocentric video dataset that has more than 3,600 hours of video recordings depicting hundreds of daily activities—and 2,113 of those hours have audio available. As discussed, it also has timestamped narrations that are free-form sentences describing the current activity performed by the camera-wearer. However, Ego4D has no annotation of whether an action makes sounds, what sounds an action makes, or whether there exists" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 310, + 72, + 541, + 105 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 541, + 105 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 541, + 105 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 541, + 105 + ], + "type": "table", + "html": "
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", + "image_path": "1c6a340e7fe760f69c7659188d4b2ce98291543dc12f75ce50b6eae6974e0c7c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 312, + 106, + 538, + 118 + ], + "lines": [ + { + "bbox": [ + 312, + 106, + 538, + 118 + ], + "spans": [ + { + "bbox": [ + 312, + 106, + 538, + 118 + ], + "type": "text", + "content": "Table 1. Example verb groups and how frequently they sound" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 129, + 547, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 129, + 547, + 188 + ], + "spans": [ + { + "bbox": [ + 304, + 129, + 547, + 188 + ], + "type": "text", + "content": "other (non-action) sounds. It is thus non-trivial to detect if an action in the clip makes sound based on simple heuristics, e.g., the burst of sound energy, since many actions could produce continuous sounds with ambient-sound characteristics, e.g., wiping tables or sawing wood." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 189, + 546, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 189, + 546, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 189, + 546, + 345 + ], + "type": "text", + "content": "We construct the training dataset by extracting clips from each Ego4D video based on the narration timestamps. These clips cover a wide range of daily activities and environments, including construction sites, cooking, arts and crafts, shopping, farming, and many others. Since the timestamp is only an approximate point for where an action occurs, we sample the clip from 0.5 s before to 1 s after the timestamp (1.5 s duration) so that the clip is likely long enough to capture the action sound, if there is any, without introducing visuals that stray from the narrated action. See ablations on the duration in Supp. We sample a training set of 250K clips from 1,876 hours of video. From their narrations, we find there are 6,114 unique nouns (objects) and 2,819 unique verbs (actions)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 349, + 547, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 547, + 456 + ], + "type": "text", + "content": "Ground truth annotations for evaluation. Today's egocentric video datasets lack annotations for sounding actions. Thus, to determine how well our model learns long-tail sounding actions and facilitate future research, we collect a large ground truth evaluation set for Ego4D using professional annotators trained for the task. It consists of 33K clips manually labeled as to whether or not the camera wearer's action sounds, i.e., indicating whether the action described in the narration is both visible and audible in the clip." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 457, + 546, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 546, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 546, + 564 + ], + "type": "text", + "content": "To ensure annotation quality, in addition to providing concrete examples and annotation guidelines (see Supp.) and iterating with quality control feedback to the professional annotators, we assign three annotators per clip and take the majority vote as the correct answer. We split the 33K obtained annotations into 3K for validation and 30K for test. We stress that this is an eval set only; our training data (above) has no manual labels about sound, only free-form language narrations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Action type analysis. In total, among the 33,000 resulting ground truth clips, 17,693 are positive and 15,307 are negative. The fact that only half of this in-the-wild clip distribution consists of sounding actions underscores the need for models that can tell the difference between audio that co-occurs with human action and actions that sound. To gain insight into the annotations, we group them by semantic similarity and analyze them at a group level. While narrations provide semantic descriptions of actions, using them for grouping would be too noisy since the same action could be described in different ways. To reduce the influence of narration variance, we utilize the taxonomy defined in Ego4D (for" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "27256" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 289, + 159 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 289, + 159 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 289, + 159 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 289, + 159 + ], + "type": "image", + "image_path": "b85e16c7dc5034f3e5ce07fd21920c048850563879f74d0c98246c1314c734fa.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 72, + 162, + 261, + 174 + ], + "lines": [ + { + "bbox": [ + 72, + 162, + 261, + 174 + ], + "spans": [ + { + "bbox": [ + 72, + 162, + 261, + 174 + ], + "type": "text", + "content": "Figure 4. Long-tail distribution of sounding actions." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 184, + 289, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 184, + 289, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 184, + 289, + 327 + ], + "type": "text", + "content": "analysis only, not training). For example, \"check\", \"examine\", and \"inspect\" should belong to the same group (taxon). We first group these clips by verb alone, i.e., extracting verbs from narrations and then applying the taxonomy, which results in 106 unique groups. We then compute the percentage of clips in each group that make sounds. Tab. 1 shows 10 examples. We see that actions involving more significant human motions (wash, close, cut) are more often sounding, whereas more subtle movements (lift, hold) are often not. Importantly, there is not a one-to-one mapping between an action verb and its sounding label—how actions sound is scenario-dependent and hence must be mined from the data." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 329, + 288, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 288, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 288, + 449 + ], + "type": "text", + "content": "While grouping by verbs provides some insights, how actions make sounds also depends on the object that they interact with, e.g., cutting a carrot sounds different from cutting bread. To this end, we further group the 17K sounding clips by both verbs and nouns, which results in 2,388 unique action groups. We plot the long-tail distribution of them in Fig. 4 and show examples sampled from this distribution. This plot shows the diverse and long-tail nature of sounding actions and our test set annotations, which is not present in existing action datasets [10, 15, 17, 28, 43, 52]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 465, + 128, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 128, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 128, + 479 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 483, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 288, + 544 + ], + "type": "text", + "content": "We compare our model with several baselines and ablations on three tasks: sounding action discovery (on Ego4D), sounding action retrieval (on Ego4D), and audio event classification (on EPIC-Sounds). We show our model outperforms an array of existing learning methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 713 + ], + "type": "text", + "content": "SotA Baselines. We consider two baselines that only use a contrastive loss for two modalities: CLAP [14] for audio-language and CM-ACC [35] for audio-video. For more than two modalities, we consider two more baselines: CMC [55] uses contrastive objectives between all pairs of viewpoints (modalities in our case), representing the joint training paradigm; ImageBind [23] learns the joint embedding by first performing vision-language pretraining and then freezing the vision encoder and training the vision-audio modality pair. This represents strategies that align modalities sequentially. For a fair comparison, we equip all baselines with the same encoder and the same initialization as ours (see Sec. 4.4) while keeping their original losses." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 549, + 219 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 549, + 219 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 549, + 219 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 549, + 219 + ], + "type": "table", + "html": "
AVAL
ROCPRROCPR
RandomXXX0.5000.5590.5000.559
CLAP [14]✓X✓--0.6370.695
CM-ACC [35]✓✓X0.5400.590--
CMC [55]✓✓✓0.5500.6010.6350.693
ImageBind [23]✓✓✓0.5540.6050.6420.685
w/o Lconsensus✓✓✓0.5630.6150.6350.694
w/o Lcontrastive✓✓✓0.4360.4930.5840.620
w/o align-stage✓✓✓0.4480.5070.4640.521
MC3✓✓✓0.5980.6660.6580.715
", + "image_path": "c20786d68e0b71dc7a36cf131f0b40a54729881153ce9bc18e860aa678672581.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 221, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 304, + 221, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 547, + 277 + ], + "type": "text", + "content": "Table 2. Sounding action discovery. Area-under-curve (AUC) values are reported for both ROC and precision-recall (PR) curves, for audio-vision (AV) and audio-language (AL). Both are the higher the better. We train our model five times with different seeds; the standard deviation is always within 0.01." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 280, + 422, + 368 + ], + "blocks": [ + { + "bbox": [ + 310, + 280, + 422, + 368 + ], + "lines": [ + { + "bbox": [ + 310, + 280, + 422, + 368 + ], + "spans": [ + { + "bbox": [ + 310, + 280, + 422, + 368 + ], + "type": "image", + "image_path": "f4496dc1b89ed142fa35b18bf1097481b64843c6e3489f047d2be87da2141298.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 341, + 372, + 509, + 384 + ], + "lines": [ + { + "bbox": [ + 341, + 372, + 509, + 384 + ], + "spans": [ + { + "bbox": [ + 341, + 372, + 509, + 384 + ], + "type": "text", + "content": "Figure 5. Sounding action discovery accuracy" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 426, + 279, + 542, + 369 + ], + "blocks": [ + { + "bbox": [ + 426, + 279, + 542, + 369 + ], + "lines": [ + { + "bbox": [ + 426, + 279, + 542, + 369 + ], + "spans": [ + { + "bbox": [ + 426, + 279, + 542, + 369 + ], + "type": "image", + "image_path": "dd6e4870f002203b3a97ea3b1cf9a792aa546b7dbbd3085030925edfdb755232.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 391, + 455, + 403 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 391, + 455, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 391, + 455, + 403 + ], + "type": "text", + "content": "6.1. Sounding Action Discovery" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 409, + 548, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 548, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 548, + 673 + ], + "type": "text", + "content": "Human interactions with objects in our daily lives are complex and subtle. Due to many incidental background sounds, recognizing whether actions make sound is not trivial but can be useful for applications like multimodal video generation, e.g., verifying the generated action video and audio match. Towards this goal, we answer the question \"what actions sound?\" by performing sounding action discovery. In this experiment, we take the per-modality encoders learned on the narrated 250K Ego4D clips and apply them to the 30K test clips. Given a test clip, we feed the video and audio through their corresponding modality encoders, and compute the cosine similarity between the output embeddings. That score indicates how likely it is that the action in the video sounds. For completeness, instead of defining a hard threshold for positives, we plot the ROC and precision-recall (PR) curves by varying the positive threshold, and calculate the area-under-curve (AUC) values for them—common metrics for classification [12, 54] that are invariant to the absolute score values. For both metrics, higher values are better, indicating the model learns meaningful embeddings of sounding actions. Similarly, we can also evaluate discovery for audio-language, if narrations are available." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Results. Table 2 shows the results for sounding action discovery. We first look at discovery with audio-visual modalities alone at test time (\"AV\" columns). CM-ACC [35]" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 317, + 742 + ], + "type": "text", + "content": "27257" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 70, + 70, + 261, + 167 + ], + "blocks": [ + { + "bbox": [ + 70, + 70, + 261, + 167 + ], + "lines": [ + { + "bbox": [ + 70, + 70, + 261, + 167 + ], + "spans": [ + { + "bbox": [ + 70, + 70, + 261, + 167 + ], + "type": "image", + "image_path": "1ffde83a21d1589c41ddaea81e7a543e5eb7b7026d008af7012579f227d2352b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 168, + 277, + 179 + ], + "lines": [ + { + "bbox": [ + 56, + 168, + 277, + 179 + ], + "spans": [ + { + "bbox": [ + 56, + 168, + 277, + 179 + ], + "type": "text", + "content": "Figure 6. Example visual embedding cluster from our model" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 188, + 289, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 188, + 289, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 188, + 289, + 319 + ], + "type": "text", + "content": "discover soundsounding actions much better than random chance, showing that audio-visual contrastive learning captures both visual action embeddings and action sound embeddings. CMC [55] and ImageBind [23] do better—benefiting (like us) from the language modality at training time. However, neither the joint nor sequential training paradigm exploits modality agreement, resulting in weak cross-modal constraints, and thus only marginal performance improvement. In comparison, our model MC3 explicitly models the modality consensus and improves the discovery result substantially by learning embeddings most relevant to sounding actions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 320, + 288, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 288, + 415 + ], + "type": "text", + "content": "We also report the discovery result from using audiolanguage modalities (\"AL\" columns). Since narrations provide action specifications, the discovery performance is better than " + }, + { + "bbox": [ + 46, + 320, + 288, + 415 + ], + "type": "inline_equation", + "content": "AV" + }, + { + "bbox": [ + 46, + 320, + 288, + 415 + ], + "type": "text", + "content": ", e.g., CLAP [14] vs CM-ACC [35]. While CMC's [55] and ImageBind's [23] joint training results are not much better than CLAP [14], our model improves the \"AL\" discovery by leveraging the video modality and imposing the trimodal consensus constraint." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 416, + 288, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 416, + 288, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 416, + 288, + 501 + ], + "type": "text", + "content": "Fig. 5 plots the precision-recall curves. For the audio-visual curve, our model always has higher precision compared to baselines, especially when recall is low. This is strong evidence of our model learning features of sounding actions, whereas baselines are limited to capturing general audio-visual correspondence—whether action-based or not. We observe a similar trend for audio-language discovery." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "content": "Ablations. To study the importance of each loss and the two-stage training, we first ablate the consensus loss in the second stage (\"w/o " + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{consensus}}" + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "content": " in Table 2), which trains the model contrastively for both stages. The model performance drops significantly, showing that exploring the modality consensus is key to learning how actions sound. We then ablate the contrastive loss in the second stage (\"w/o " + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{contrastive}}" + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "content": "), which harms performance even more. This suggests that " + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{consensus}}" + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "content": " functions like a regularization term that forces the " + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{contrastive}}" + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "content": " to learn sounding action embeddings. Lastly, we ablate the two-stage training strategy by removing the align stage (\"w/o align-stage\"), which optimizes " + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{MC3}}" + }, + { + "bbox": [ + 46, + 505, + 289, + 673 + ], + "type": "text", + "content": " directly; this model fails badly. Aligning embeddings first is critical to making MC3's training stable." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Clustering. To visualize the learned embeddings, we group video embeddings in the test set with agglomerative clustering into 20 clusters. Fig. 6 shows the top 8 examples" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 310, + 70, + 542, + 219 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 542, + 219 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 542, + 219 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 542, + 219 + ], + "type": "table", + "html": "
V→A@5 @10A→V@5 @10L→A@5 @10A→L@5 @10
Random0.10.10.10.10.10.10.10.1
CLAP [14]----49.887.634.067.1
CM-ACC [35]34.663.530.957.7----
CMC [55]36.567.933.863.744.181.832.864.3
ImageBind [23]32.861.529.757.942.676.530.660.5
w/o Lconsensus33.963.030.056.145.084.732.965.8
w/o Lcontrastive3.33.76.412.53.14.73.38.0
w/o align-stage10.019.45.911.811.620.96.512.6
MC338.472.834.466.346.288.537.573.8
", + "image_path": "9b5db632bc8dc8adf5ced69800202167ff57c62a76c9471e6e7c61d3953382f1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 221, + 545, + 243 + ], + "lines": [ + { + "bbox": [ + 306, + 221, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 221, + 545, + 243 + ], + "type": "text", + "content": "Table 3. Sounding action retrieval. We report Recall @5 and @10 for different query-retrieval modalities. See R@1 results in Supp." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 251, + 547, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 547, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 547, + 323 + ], + "type": "text", + "content": "of one cluster (more in Supp.). This cluster clearly captures the sound of water running, despite varying types of camera-wearer movement. Not only does it group videos with similar actions that make this sound, but also it shows the learned embeddings are agnostic of the background (the bathroom example)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 331, + 453, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 453, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 453, + 344 + ], + "type": "text", + "content": "6.2. Sounding Action Retrieval" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 351, + 547, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 547, + 457 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 547, + 457 + ], + "type": "text", + "content": "Retrieving a different modality given a video, audio, or description is another useful application, such as adding sound effects to silent videos or retrieving captions for action sounds. To explore this setting, we answer the question \"how do different actions sound?\" by evaluating the cross-modal retrieval performance of long-tail sounding actions from the same category. Different from the binary classification task above, here we aim to retrieve other examples of the same action." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "content": "To do this, we utilize the action groups constructed in Sec. 5 based on verbs and nouns, and only keep groups that have more than two instances of sounding actions (such that there will be at least one true positive to retrieve for each query). We then divide each action group equally into a query pool of 7,559 examples and a retrieval pool of 7,032 examples. Given a query modality " + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "inline_equation", + "content": "M_{i}" + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "content": " of instance " + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "content": ", we compute its distance to other modalities " + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "inline_equation", + "content": "M_{j}" + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "content": " of all instances in the retrieval pool. A retrieval is correct if the retrieved instance " + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 459, + 547, + 579 + ], + "type": "text", + "content": " belong to the same action group." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 713 + ], + "type": "text", + "content": "Results. Table 3 shows the results for four different query-retrieval modality settings. For audio-visual retrieval, we observe that all models can retrieve video with audio (or audio with video) for similar actions with much higher recall than random chance. Our model strongly outperforms the baselines and ablations, benefiting from modeling the modality consensus explicitly. We also observe that retrieving audio with video is easier than the opposite, likely because audio can be vague sometimes, e.g., a collision sound might occur due to various actions while seeing a cutting action indicates the likely sound. For audio-language retrieval, our" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "27258" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 227, + 261 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 227, + 261 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 227, + 261 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 227, + 261 + ], + "type": "image", + "image_path": "bdcabbcbb9c8b881bb18beb504ca7b7d9d0ca8ccff2c82be25f3647fa033be39.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 267, + 547, + 312 + ], + "lines": [ + { + "bbox": [ + 46, + 267, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 547, + 312 + ], + "type": "text", + "content": "Figure 7. Qualitative examples for retrieval. The first row is video-to-audio retrieval, motivated by adding audio effects for silent videos. The second row is audio-to-text retrieval, motivated by audio captioning applications. For each row, we show three correct retrieval examples along with their text (gray indicates the text is not observed by the model). For the retrieved item, we show the ground truth rank as the superscript. All examples are long-tail sounding actions, showing how our model learns to capture the features of how actions sound." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 228, + 70, + 306, + 261 + ], + "blocks": [ + { + "bbox": [ + 228, + 70, + 306, + 261 + ], + "lines": [ + { + "bbox": [ + 228, + 70, + 306, + 261 + ], + "spans": [ + { + "bbox": [ + 228, + 70, + 306, + 261 + ], + "type": "image", + "image_path": "01323f3b33133d1cfcce45e595e445b0ac270d0ba9098f355d5dfe696b61e601.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 386, + 261 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 386, + 261 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 386, + 261 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 386, + 261 + ], + "type": "image", + "image_path": "8095ba9044315a7e51ae8e522448f28b8328ab89ebc19c6a9b63b89cf46e06e0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 386, + 71, + 465, + 261 + ], + "blocks": [ + { + "bbox": [ + 386, + 71, + 465, + 261 + ], + "lines": [ + { + "bbox": [ + 386, + 71, + 465, + 261 + ], + "spans": [ + { + "bbox": [ + 386, + 71, + 465, + 261 + ], + "type": "image", + "image_path": "2dbce9d96889fc51a8f32ff29573f75b1f9ba9c3428312a4bc1cf333d9fa53fa.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 466, + 71, + 545, + 261 + ], + "blocks": [ + { + "bbox": [ + 466, + 71, + 545, + 261 + ], + "lines": [ + { + "bbox": [ + 466, + 71, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 466, + 71, + 545, + 261 + ], + "type": "image", + "image_path": "3338f23177776111e0e50111987a3108c9df78b0763e6dfc0a7fb7cd284c9b3c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 325, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 288, + 387 + ], + "type": "text", + "content": "model similarly outperforms the baselines by large margins. Qualitative examples. In Fig 7, we show examples for video-to-audio and audio-to-language retrieval. Even though these actions are subtle, our model retrieves audio or captions that are very relevant. Listen to examples in Supp. video." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 395, + 245, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 395, + 245, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 395, + 245, + 407 + ], + "type": "text", + "content": "6.3. Audio Classification on EPIC-Sounds" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 414, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 521 + ], + "type": "text", + "content": "Finally, we evaluate our learned representation on a standard audio benchmark. To assess the impact of our model's action sounds representation, we consider EPIC-Sounds [28], a challenging audio classification benchmark for sounds in kitchen environments. To our knowledge, EPIC-Sounds represents the only large-scale benchmark for audio in egocentric video. Note, this classification task is different from the sounding action discovery task in Sec. 6.1 in that here the model only takes an audio clip as input." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 582 + ], + "type": "text", + "content": "We consider both linear-probe and fine-tuning settings. In the linear-probe setup, we freeze the model weights and only train the last classification layer, which evaluates the quality of the pre-trained representations. In the fine-tuning setup, we fine-tune both the encoder and the last layer." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Table 4 shows the results. We compare with two SotA methods reported in EPIC-Sounds: SSAST [25] and ASF [31]. SSAST is pretrained on LibriSpeech [44] and shares the same network architecture as ours, while ASF is trained on VGG-Sound with supervised learning. With linear-probe, our model strongly outperforms SSAST [25], which, like us, is also pretrained in a self-supervised fashion with no audio labels. ASF [31] does better than both, likely due to its advantage of supervised audio classification pretraining. When fine-tuning, our model outperforms both prior methods in all but one metric when following the same" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 308, + 323, + 543, + 437 + ], + "blocks": [ + { + "bbox": [ + 308, + 323, + 543, + 437 + ], + "lines": [ + { + "bbox": [ + 308, + 323, + 543, + 437 + ], + "spans": [ + { + "bbox": [ + 308, + 323, + 543, + 437 + ], + "type": "table", + "html": "
Top-1Top-5mCAMAPmAUC
Random-7.7130.952.290.0230.500
ASF [31]*L45.5379.3313.480.1720.789
SSAST [25]L28.7464.847.140.0790.755
MC3L42.4478.7612.790.1530.818
ASF [31]*F53.7584.5420.110.2540.873
SSAST [25]F53.4784.5620.220.2350.879
MC3F55.9785.8621.650.2420.885
", + "image_path": "1f77010623a4b680f8abe2c54037d83208d8cd1f75a8dcc40569e10832c4aed5.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 441, + 547, + 475 + ], + "lines": [ + { + "bbox": [ + 305, + 441, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 305, + 441, + 547, + 475 + ], + "type": "text", + "content": "Table 4. Results of classification on EPIC-Sounds. L: Linear-Probe; F: Fine-tuning. * denotes pretraining with supervised audio classification while the rest are pretrained in a self-supervised fashion." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 486, + 547, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 558 + ], + "type": "text", + "content": "fine-tuning and evaluation protocol. This shows our MC3 audio encoder—trained for sounding action discovery—learns generalizable action sound embeddings, improving the state of the art. The margins are naturally smaller in the fine-tuning regime, as is typical, since all models have time to adapt to the new domain." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 566, + 379, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 566, + 379, + 578 + ], + "spans": [ + { + "bbox": [ + 306, + 566, + 379, + 578 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 583, + 547, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 583, + 547, + 690 + ], + "spans": [ + { + "bbox": [ + 304, + 583, + 547, + 690 + ], + "type": "text", + "content": "We explored learning how first-person actions sound from inthe-wild, narrated egocentric videos—without audio labels. Training with 250K clips from Ego4D, we show the promise of our novel multimodal consensus framework for accurately aligning representations to capture the long-tail of sounding actions in novel (unnarrated) videos, with clear impact on sounding action discovery, retrieval, and pre-training for audio classification. In the future, we plan to explore multimodal consensus from asynchronous multimodal streams." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements: UT Austin is supported in part by the IFML NSF AI Institute. KG is paid as a research scientist by Meta." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 733, + 318, + 742 + ], + "type": "text", + "content": "27259" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 134 + ], + "type": "text", + "content": "[1] Hassan Akbari, Liangzhe Yuan, Rui Qian, Wei-Hong Chuang, Shih-Fu Chang, Yin Cui, and Boqing Gong. 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In CVPR, 2023. 3" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "spans": [ + { + "bbox": [ + 293, + 734, + 317, + 742 + ], + "type": "text", + "content": "27262" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_content_list.json b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..4fea64a2a3d1f32d703d7f2539aab16e6447d5ed --- /dev/null +++ b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_content_list.json @@ -0,0 +1,1712 @@ +[ + { + "type": "text", + "text": "Source-Free Domain Adaptation with Frozen Multimodal Foundation Model", + "text_level": 1, + "bbox": [ + 98, + 130, + 870, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Song Tang $^{1,2,3}$ , Wenxin Su $^{1}$ , Mao Ye $^{*4}$ , and Xiatian Zhu $^{*5}$", + "bbox": [ + 254, + 191, + 712, + 210 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1University of Shanghai for Science and Technology 2Universität Hamburg 3ComOriginMat Inc.", + "bbox": [ + 106, + 210, + 864, + 227 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "4University of Electronic Science and Technology of China 5University of Surrey", + "bbox": [ + 163, + 228, + 803, + 244 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tangs@usst.edu.cn, {suwenxin43, cvlab.uestc}@gmail.com, xiatian.zhu@surrey.ac.uk", + "bbox": [ + 130, + 248, + 844, + 262 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 324 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Source-Free Domain Adaptation (SFDA) aims to adapt a source model for a target domain, with only access to unlabeled target training data and the source model pretrained on a supervised source domain. Relying on pseudo labeling and/or auxiliary supervision, conventional methods are inevitably error-prone. To mitigate this limitation, in this work we for the first time explore the potentials of off-the-shelf vision-language (ViL) multimodal models (e.g., CLIP) with rich whilst heterogeneous knowledge. We find that directly applying the ViL model to the target domain in a zero-shot fashion is unsatisfactory, as it is not specialized for this particular task but largely generic. To make it task specific, we propose a novel Distilling multiModal Foundation mOdel (DIFO) approach. Specifically, DIFO alternates between two steps during adaptation: (i) Customizing the ViL model by maximizing the mutual information with the target model in a prompt learning manner, (ii) Distilling the knowledge of this customized ViL model to the target model. For more fine-grained and reliable distillation, we further introduce two effective regularization terms, namely most-likely category encouragement and predictive consistency. Extensive experiments show that DIFO significantly outperforms the state-of-the-art alternatives. Code is here.", + "bbox": [ + 75, + 340, + 473, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 722, + 209, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation (UDA) relies on both well-annotated source data and unannotated target data. However, due to heightened safety and privacy concerns, accessing source data freely has become difficult [18, 23]. In response, Source-Free Domain Adaptation (SFDA) has gained attention as a more practical solution, aiming to transfer a pretrained source model to the target domain using only unlabeled target data.", + "bbox": [ + 75, + 750, + 470, + 869 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33090923e17fc171744e1617cc9c005cfb6532ee449e37016a7c6c94710d50ab.jpg", + "image_caption": [ + "Figure 1. We expand beyond traditional SFDA methods that rely solely on a pretrained source model and unlabeled target data. Instead, we innovate by exploring off-the-shelf multimodal foundation models, such as CLIP, in an unsupervised manner (marked by the box with blue background)." + ], + "image_footnote": [], + "bbox": [ + 522, + 308, + 867, + 468 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Due to the absence of source samples, traditional distribution matching approaches are no longer viable [7, 14]. The predominant alternative is self-supervised learning, which generates or mines auxiliary information to facilitate unsupervised adaptation. Two main approaches exist: constructing a pseudo source domain to leverage established UDA methods such as adversarial learning [16, 41] or domain shift minimization based on distribution measurement [5, 15, 37] and mining extra supervision from the source model [11, 18, 40] or target data [34, 42, 43]. In the presence of domain distribution shift, applying the source model to the target domain introduces inevitable errors in pseudo-labeling or auxiliary supervision, thereby limiting adaptation performance.", + "bbox": [ + 496, + 568, + 893, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address identified limitations, we pioneer the exploration of off-the-shelf multimodal foundation models, such as the vision-language (ViL) model CLIP [24], transcending the constraints of both the source model and target data knowledge. However, direct application of the ViL model proves unsatisfactory, lacking specialization for specific tasks. To overcome this, we propose a novel task-specific distillation approach named Distilling multiModal", + "bbox": [ + 496, + 779, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23711", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Foundation mOdel (DIFO). Initially, we customize the ViL model through unsupervised prompt learning for imposing task-specific information. Subsequently, we distil the knowledge from this customized ViL model to the target model, with joint supervision through two designed regularization terms: (1) most-likely category encouragement for coarse-grained distillation and (2) predictive consistency for fine-grained distillation.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are summarized as follows. (1) Pioneering the use of generic but heterogeneous knowledge sources (e.g., the off-the-shelf ViL model) for the SFDA problem, transcending the limited knowledge boundary of a pretrained source model and unlabeled target data. (2) Development of the novel DIFO approach to effectively distill useful task-specific knowledge from the general-purpose ViL model. (3) Extensive evaluation on standard benchmarks, demonstrating the significant superiority of our DIFO over previous state-of-the-art alternatives under conventional closed-set settings, as well as more challenging partial-set and open-set settings.", + "bbox": [ + 75, + 212, + 472, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 404, + 218, + 420 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Source-free domain adaptation. Existing SFDA approaches fall into three distinct categories. The first explicitly aligns the pseudo source domain with the target domain, treating SFDA as a specialized case of unsupervised domain adaptation. This alignment is achieved by constructing the pseudo source domain through a generative model [21, 38] or by splitting the target domain based on prior source hypotheses [6].", + "bbox": [ + 75, + 429, + 472, + 549 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second group extracts cross-domain factors from the source domain and transfers them in successive model adaptation for aligning feature distributions across the two domains. For example, [31] establishes a mapping relationship from a sample and its exemplar Support Vector Machine (SVM) (an individual classifier) on the source domain to ensure individual classification on the target domain. Some approaches leverage pre-trained source models to generate auxiliary factors, such as multi-hypothesis [18], prototypes [36], source distribution estimation [5], or hard samples [20] to aid in feature alignment.", + "bbox": [ + 75, + 551, + 472, + 715 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The third group incorporates auxiliary information refined from the unlabeled target domain. In addition to widely used pseudo-labels [3, 24], geometry information, such as intrinsic neighborhood structure [33] and target data manifold [34], has also been exploited.", + "bbox": [ + 75, + 717, + 472, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite continual advancements, these methods are limited by the knowledge derived solely from the pretrained source model and unlabeled target data. We break this limitation by tapping into the rich knowledge encoded in off-the-shelf multimodal foundation models.", + "bbox": [ + 75, + 792, + 472, + 867 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Large multimodal model. Multimodal vision-language (ViL) models, such as CLIP [28] and ALIGN [13], have", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "shown promise across various mono-modal and multimodal tasks by capturing modality-invariant features. Approaches in this domain can be broadly categorized into two lines.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The first line focuses on enhancing ViL model performance. For instance, in [8, 46], prompt learning optimizes the text encoder through the use of tailored, learnable prompts designed for specific scenarios. Other efforts aim to improve data efficiency by repurposing noisy data [1].", + "bbox": [ + 496, + 137, + 893, + 213 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The second line utilizes ViL models as external knowledge to enhance downstream tasks, as demonstrated in this paper. Previous work in knowledge transfer primarily falls into two frameworks. For the first scheme, where the ViL model is directly applied to the target task in a zero-shot fashion [22], domain generality is leveraged without task-specific refinement. The second scheme does not focus on source model adaptation. Instead, it fine-tunes the ViL model to the target domain through prompt or adaptor learning with an amount of manal labels [4].", + "bbox": [ + 496, + 214, + 893, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A relevant method to our DIFO is the UDA method DAPL [8]. Although both adopt CLIP, they differ significantly in problem setting and methodology. DAPL employs CLIP to learn domain-specific prompts, aiming to disentangle domain and category information in CLIP's visual features. In contrast, DIFO aligns target features to a progressively customized vision-language latent space in a memory-aware fashion. Importantly, DAPL requires labeled source data, making it inapplicable in SFDA.", + "bbox": [ + 496, + 367, + 895, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 520, + 635, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Problem statement. In the context of two distinct yet interrelated domains—namely, the labeled source domain and the unlabeled target domain—both characterized by the same set of $C$ categories, the following notation is employed. The source samples and their corresponding labels are represented as $\\mathcal{X}_s$ and $\\mathcal{Y}_s$ respectively. Similarly, the target samples and their true labels are denoted as $\\mathcal{X}_t = \\{\\pmb{x}_i\\}_{i=1}^n$ and $\\mathcal{Y}_t = \\{y_i\\}_{i=1}^n$ , where $n$ signifies the number of samples.", + "bbox": [ + 496, + 546, + 893, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We aim to learn a target model $\\theta_t: \\mathcal{X}_t \\to \\mathcal{Y}_t$ . This involves utilizing (1) a pre-trained source model $\\theta_s: \\mathcal{X}_s \\to \\mathcal{Y}_s$ , (2) unlabeled target data, and (3) a Visual-Language (ViL) model denoted as $\\theta_v$ .", + "bbox": [ + 496, + 669, + 893, + 729 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Overview. As depicted in Fig. 2, the proposed DIFO framework alternates between two distinct steps to customize and distill the off-the-shelf ViL knowledge.", + "bbox": [ + 496, + 732, + 893, + 777 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the first step, we engage in prompt learning on the ViL model for the purpose of task-specific customization. This serves to mitigate the guidance error within the ViL model. In particular, we adopt a mutual information-based alignment approach. This approach is characterized by its richness in context and interaction between the target model and the ViL model, as opposed to placing blind trust in either model alone as conventional methods.", + "bbox": [ + 496, + 780, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23712", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b9a880d506f08b86ecaf952ad0b735640344cbcc9c7c29ab5f95679bbae724ee.jpg", + "image_caption": [ + "Figure 2. Overview of our DIFO: The process involves two alternating steps. First, we perform (a) task-specific customization of a ViL model through task-specific prompt learning ( $L_{\\mathrm{TSC}}$ ). This is achieved under soft predictive guidance using mutual information maximization. Second, we undertake (b) memory-aware knowledge adaptation, incorporating two regularizations: most-likely category encouragement ( $L_{\\mathrm{MCE}}$ ) predicted by our dynamic memory-aware predictor, along with the typical predictive consistency ( $L_{\\mathrm{PC}}$ ). These regularizations are designed to facilitate a coarse-to-fine adaptation." + ], + "image_footnote": [], + "bbox": [ + 122, + 90, + 849, + 252 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the second step, knowledge adaptation takes place within a unique constraint that encourages the identification of the most probable category labels in the logit space, while concurrently maintaining the typical predictive consistency. The most likely category labels are determined by a carefully designed memory-aware predictor, which dynamically integrates knowledge from both the target model and the ViL model in a cumulative fashion.", + "bbox": [ + 75, + 354, + 473, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task-Specific ViL Model Customization", + "text_level": 1, + "bbox": [ + 76, + 481, + 419, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We adopt the prompt learning framework for ViL model customization, with all the parameters of the ViL model frozen throughout. The only learnable part in customization is the prompts each assigned for a specific class. To optimize these prompts, we need a useful supervision. In SFDA, however, it is challenging to customize such a domain-generic ViL model towards the target domain, at the absence of a well-trained target domain model. This is because, none of them can reasonably make predictions. That means there is no clearly good supervision signals available.", + "bbox": [ + 75, + 505, + 470, + 655 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address this challenge, we propose to explore the wisdom of the crowd by leveraging their predictive interaction as the supervision. Formally, we denote the predictions by the target model and the ViL model as $\\theta_t(\\boldsymbol{x}_i)$ and $\\theta_v(\\boldsymbol{x}_i)$ , respectively, given an unlabeled target sample $\\boldsymbol{x}_k$ . We conduct the customization by maximizing the mutual information of their predictions as:", + "bbox": [ + 75, + 656, + 470, + 762 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {T S C}} = - \\min _ {\\boldsymbol {v}} \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\chi_ {t}} \\mathrm {I} \\left(\\theta_ {t} \\left(\\boldsymbol {x} _ {i}\\right), \\theta_ {v} \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {v}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 768, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\pmb{v}$ is the prompt context to be learned and the function $\\mathrm{I}(\\cdot ,\\cdot)$ measures the mutual information [12].", + "bbox": [ + 76, + 795, + 468, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This alignment design differs significantly from the conventional adoption of the Kullback-Leibler (KL) divergence. First of all, the mutual information is a lower optimization bound than KL divergence, facilitating deeper alignment (see Theorem 1 with the proof provided in Supplementary).", + "bbox": [ + 75, + 825, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Theorem 1 Given two random variables $X, Y$ . Their mutual information $I(X,Y)$ and KL divergence $D_{\\mathrm{KL}}(X||Y)$ satisfy the unequal relationship as follows.", + "bbox": [ + 498, + 354, + 895, + 400 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n- \\mathrm {I} (X, Y) \\leq D _ {\\mathrm {K L}} (X, Y). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 411, + 892, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Crucially, the KL divergence exhibits an inherent bias towards a specific prediction, making it less suitable for our context where none of the predictions holds a significant advantage. On the contrary, mutual information considers the joint distribution or correlation between the two predictions. This distinction arises from their respective definitions: $-\\mathrm{I}(X,Y) = -H(X) + H(X|Y)$ and $D_{\\mathrm{KL}}(X,Y) = -H(X) + H(X:Y)$ , where", + "bbox": [ + 498, + 446, + 893, + 570 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH (X \\mid Y) = - \\sum_ {\\leftarrow} p (\\boldsymbol {x}, \\boldsymbol {y}) \\log p (\\boldsymbol {x} \\mid \\boldsymbol {y}) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 580, + 893, + 611 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nH \\left(X: Y\\right) = - \\sum p (\\boldsymbol {x}) \\log p (\\boldsymbol {y}).\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 604, + 797, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The conditional entropy component $H(X|Y)$ of mutual information explicitly captures the joint distributions, a feature absent in KL divergence. Empirically, we also confirm the significance of incorporating this joint distribution-based interaction between the two predictions during the customization of the ViL model (see ablation study in Tab. 6 and task-specific knowledge adaptation analysis in Section 4.3).", + "bbox": [ + 496, + 640, + 895, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Memory-Aware Knowledge Adaptation", + "text_level": 1, + "bbox": [ + 500, + 756, + 838, + 772 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As previously mentioned, even with customization for the target domain, the ViL model may not be fully adapted due to no robust target model available in prior. This limitation hinders effective knowledge adaptation at this stage. To address this issue, we propose the incorporation of a specialized memory-aware predictor to provide additional learning guidance – most-likely category encouragement, complementing the conventional predictive consistency constraint.", + "bbox": [ + 496, + 780, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23713", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most-likely category encouragement. The rationale behind incorporating this learning constraint is to harness the collective knowledge of both the target model and the ViL model in order to enhance the discernment of probable category labels for each sample. Given the sluggish nature of this search process, it has been devised to function as a form of learning regularization. An illustration of this regularization process is presented in Fig. 3. Specifically, it is realized through two distinct steps as detailed below.", + "bbox": [ + 75, + 90, + 472, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(I) Memory-aware predictor. We initiate the process by generating pseudo-labels that represent the most likely category distribution, utilizing historical information stored in a prediction bank. The prediction bank archives two types of historical data for all samples in the target domain: (1) predictions from the target model denoted by $\\{p_i\\}_{i = 1}^n$ and (2) predictions from the ViL model denoted by $\\{p_i'\\}_{i = 1}^n$ .", + "bbox": [ + 75, + 228, + 468, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Throughout the adaptation process, the predictions from the target model are updated iteratively. At the end of each training iteration, the newly predicted labels for the training batch from the target model replace their counterparts in the prediction bank. In contrast, predictions from the ViL model are updated collectively in an epoch-wise manner, triggering updates every $M$ iterations. This mixed-update strategy is designed to strike a balance between maintaining the stability of the customized ViL model's guidance and capturing the task-specific dynamics inherent in the adaptation process.", + "bbox": [ + 75, + 335, + 468, + 487 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the provided prediction bank, the creation of a pseudo-label for the most probable category involves a historical prediction fusion process as:", + "bbox": [ + 75, + 488, + 470, + 532 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\boldsymbol {p}} _ {i} = \\omega \\boldsymbol {p} _ {i} + (1 - \\omega) \\boldsymbol {p} _ {i} ^ {\\prime}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 550, + 468, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, the weight $\\omega$ , drawn from an Exponential distribution with parameter $\\lambda$ , is a crucial factor. This fusion introduces dynamic bias rectification (represented by $\\pmb{p}_i$ ) based on the guidance from the customized ViL model $(\\pmb{p}_i')$ . The role of $\\pmb{p}_i$ is to provide adjustments, leading us to adopt an asymmetric random weighting approach represented by $\\omega$ .", + "bbox": [ + 75, + 583, + 468, + 672 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(II) Category attention calibration. Subsequently, we formulate a regularization technique employing pseudo-labels acquired through category attention calibration. Specifically, we begin by identifying the top- $N$ most probable categories using $\\bar{p}_i$ . The indices of these identified categories are denoted by $\\mathcal{M}_i = \\{m_k\\}_{k=1}^N$ . With $\\mathcal{M}_i$ , the target model's logit of a target domain sample $x_i$ , denoted as $l_i$ , is segregated into positive and negative category groups. We define this regularization as:", + "bbox": [ + 75, + 675, + 470, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L _ {\\mathrm {M C E}} = \\min _ {\\theta t} \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\mathcal {X} _ {t}} \\log \\frac {\\exp \\left(a _ {i} / \\tau\\right)}{\\sum_ {j \\neq \\mathcal {M} _ {i}} \\exp \\left(b _ {i} \\cdot l _ {i , j} / \\tau\\right)} \\tag {5} \\\\ a _ {i} = \\prod_ {k = 1} ^ {N} \\boldsymbol {l} _ {i, m _ {k}}, \\quad b _ {i} = \\sum_ {k = 1} ^ {N} \\boldsymbol {l} _ {i, m _ {k}} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 98, + 825, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/102c3302efd2d097288c9fa34db29e0e59f88101a106c60a01080c5074051551.jpg", + "image_caption": [ + "Figure 3. Illustration of most-likely category encouragement. In contrast to the conventional approach that assigns equal importance to all categories (depicted by the gray line), our approach (represented by the black line) introduces additional supervision by incorporating extra knowledge about the two most likely categories." + ], + "image_footnote": [], + "bbox": [ + 514, + 90, + 880, + 241 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $l_{i,a}$ denotes the $a$ -th element of $l_{i}$ and $\\tau$ is the temperature parameter.", + "bbox": [ + 496, + 338, + 893, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In Eq. (5), we note that the product operation with $a_{i}$ in the numerator amplifies penalties for the probability decrease on the most likely categories compared to the sum form. Similarly, the sum with $b_{i}$ in the denominator serves as an increasing weighting parameter to enhance suppression of values at other locations. Moreover, $a_{i}$ is more sensitive to changes than $b_{i}$ due to $\\frac{\\partial a_{i}}{\\partial m_{k}} \\propto O(n^{N - 1})$ and $\\frac{\\partial b_{i}}{\\partial m_{k}} \\propto O(1)$ . By combining the use of $a_{i}$ and $b_{i}$ , we globally impose a calibration effect on the elements corresponding to the most likely categories within the logit $l_{i}$ . Essentially, attention is introduced to these potential categories, as illustrated in the box with a yellow background in Fig. 3.", + "bbox": [ + 496, + 369, + 893, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Predictive Consistency. For the purpose of knowledge adaptation, we incorporate the conventional predictive consistency loss as:", + "bbox": [ + 496, + 554, + 893, + 597 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {P C}} = \\min _ {\\theta_ {t}} \\left[ - \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\mathcal {X} _ {t}} \\mathrm {I} \\left(\\theta_ {t} (\\boldsymbol {x} _ {i}), \\theta_ {v} (\\boldsymbol {x} _ {i}, \\boldsymbol {v} *)\\right) + \\alpha L _ {B} \\right], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 608, + 890, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta_t(\\pmb{x}_i)$ represents the target prediction, $\\theta_v(\\pmb{x}_i, \\pmb{v})$ denotes the ViL prediction, and $\\pmb{v}$ is the prompt context learned during the initial phase of task-specific customization. The function $\\mathrm{I}(\\cdot, \\cdot)$ corresponds to the mutual information function. The parameter $\\alpha$ serves as a trade-off parameter, and the category balance term $L_{\\mathrm{B}} = \\mathrm{KL}(\\bar{\\pmb{q}} || \\frac{1}{C})$ aligns with previous approaches [35, 42], preventing solution collapse by ensuring the empirical label distribution $\\bar{\\pmb{q}}$ matches the uniform distribution $\\frac{1}{C}$ . For the reasons elaborated in Section 3.1, we employ mutual information for alignment.", + "bbox": [ + 496, + 638, + 893, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Model training", + "text_level": 1, + "bbox": [ + 500, + 816, + 653, + 832 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To systematically distill and leverage task-specific knowledge from the ViL model, we adopt an epoch-wise training approach for DIFO. The training process is divided into $T$ epochs, each comprising two stages aligned with the two", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23714", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Training of DIFO", + "text_level": 1, + "bbox": [ + 78, + 90, + 285, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Pre-trained source model $\\theta_{s}$ , target model $\\theta_{t}$ , ViL model $\\theta_{v}$ , unlabelled target domain $\\mathcal{X}_{t}$ , learnable prompt context $\\boldsymbol{v}$ , #epoch $T$ , #iteration per epoch $M$ .", + "bbox": [ + 76, + 107, + 454, + 152 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: The adapted target model $\\theta_t$ .", + "bbox": [ + 78, + 154, + 328, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Procedure:", + "text_level": 1, + "bbox": [ + 78, + 169, + 156, + 181 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Initialisation: Set $\\theta_{t} = \\theta_{s}$ and $\\pmb{v} = a$ photo of a [CLS].", + "2: for $t = 1:T$ do", + "3: Update ViL predictions in the prediction bank.", + "4: Step1", + "5: for $m = 1:M$ do", + "6: Sample a batch from $\\mathcal{X}_t$ ;", + "7: Forward prompt $\\pmb{v}$ and this batch $\\mathcal{X}_t^b$ through $\\theta_v$ ;", + "8: Forward this batch data through $\\theta_t$ ;", + "9: Customize $\\theta_v$ by optimizing $L_{\\mathrm{TSC}}$ (Eq. (1)) and obtain task-specific prompt context $\\pmb{v}^{*}$ .", + "10: end for", + "11: Step2", + "12: for $m = 1:M$ do", + "13: Sample a batch from $\\mathcal{X}_t$ ;", + "14: Forward the $\\pmb{v}^{*}$ and this batch through $\\theta_{\\upsilon}$", + "15: Forward this batch data through $\\theta_{t}$", + "16: Discover most-likely category (Eq. (4));", + "17: Update model $\\theta_{t}$ by optimizing $L_{\\mathrm{MKA}}$ (Eq. (7)).", + "18: Update target predictions in the prediction bank.", + "19: end for", + "20: Set $\\pmb{v} = \\pmb{v}^{*}$", + "21: end for", + "22: return Adapted model $\\theta_{t}$" + ], + "bbox": [ + 86, + 185, + 464, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "steps in the DIFO framework (Fig. 2). During the first stage, training is governed by the objective $L_{\\mathrm{TSC}}$ , and in the subsequent second stage, the objective function transitions to", + "bbox": [ + 75, + 561, + 470, + 608 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {M K A}} = L _ {\\mathrm {P C}} + \\beta L _ {\\mathrm {M C E}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 619, + 468, + 635 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta$ is a trade-off parameter. We summarize the whole training procedure of DIFO in Algorithm 1.", + "bbox": [ + 75, + 645, + 468, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 688, + 207, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate four standard benchmarks: Office-31 [29], Office-Home [39], VisDA [26] and DomainNet-126 [27]. Among them, Office-31 is a small-scaled dataset; Office-Home is a medium-scale dataset; VisDA and DomainNet-126 are both large-scale datasets. The details of the four datasets are provided in Supplementary.", + "bbox": [ + 75, + 714, + 470, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Competitor. We compare DIFO with 18 existing top-performing methods into three groups. (1) The first group contains Source (the source model's results), CLIP [28] and Source+CLIP where Source+CLIP directly average the results of the source model and CLIP. (2) The second group includes three state-of-the-art UDA methods", + "bbox": [ + 75, + 809, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8b47cc14db011ec6371fa7fbacdae87b5e03f71b5c8c5d8619e79b79411a21f4.jpg", + "table_caption": [ + "Table 1. Closed-set SFDA on Office-31 (%)" + ], + "table_footnote": [], + "table_body": "
MethodVenueA→DA→WD→AD→WW→AW→DAvg.
Source-79.176.659.995.561.498.878.6
SHOT [24]ICML2093.791.174.298.274.6100.88.6
NRC [42]NIPS2196.090.875.399.075.0100.89.4
GKD [32]IROS2194.691.675.198.775.1100.89.2
HCL [11]NIPS2194.792.575.998.277.7100.89.8
AaD [43]NIPS2296.492.175.099.176.5100.89.9
AdaCon [2]CVPR2287.783.173.791.377.672.881.0
CoWA [19]ICML2294.495.276.298.577.699.890.3
SCLM [34]NN2295.890.075.598.975.599.889.4
ELR [44]ICLR2393.893.376.298.076.9100.89.6
PLUE [25]CVPR2389.288.472.897.169.697.985.8
TPDS [35]IJCV2397.194.575.798.775.599.890.2
DIFO-C-RN-93.692.178.595.778.897.089.3
DIFO-C-B32-97.295.583.097.283.298.892.5
", + "bbox": [ + 501, + 114, + 890, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DAPL [8], PADCLIP [17] and ADCLIP [30] that are also multimodal guiding-based. (3) The third group comprises 13 current state-of-the-art SFDA models: SHOT [24], NRC [42], GKD [32], HCL [11], AaD [43], AdaCon [2], CoWA [19], SCLM [34], ELR [44], PLUE [25], TPDS [35] and CRS [45].", + "bbox": [ + 496, + 306, + 893, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For comprehensive comparisons, we implement DIFO in two variants: (1) DIFO-C-RN (weak version) and (2) DIFO-C-B32 (strong version). The key distinction lies in the backbone of the CLIP image-encoder. Specifically, for DIFO-C-RN, ResNet101 [10] is employed on the VisDA dataset, while ResNet50 [10] is used on the other three datasets. On the other hand, DIFO-C-B32 adopts ViT-B/32 [9] as the backbone across all datasets.", + "bbox": [ + 496, + 400, + 893, + 520 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "SFDA settings. We consider three distinct settings: the conventional closed-set SFDA setting, the partial-set and the open-set SFDA settings. The experiment implementation details are provided in Supplementary.", + "bbox": [ + 496, + 527, + 890, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Comparison Results", + "text_level": 1, + "bbox": [ + 500, + 604, + 691, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison on Closed-set SFDA setting. The comparisons of the four evaluation datasets are listed in Tab. 1~3. DIFO-C-B32 surpasses the previous best method CoWA (on Office-31), TPDS (on Office-Home) and PLUE (on VisDA) and GKD (on DomainNet-126) by $2.2\\%$ , $9.6\\%$ $2.0\\%$ and $11.3\\%$ in average accuracy respectively. Specifically, DIFO-C-B32 obtains the best results on 4 out of 6 tasks on Office-31 while surpassing previous methods on all tasks of the other three datasets. As for DIFO-C-RN, besides Office-31, it obtains the second-best results and beat the previous best methods by $5.9\\%$ , $0.5\\%$ and $8.0\\%$ on Office-Home, VisDA and DomainNet-126 in average accuracy. The comparison of DIFO-C-RN shows that our method can still perform well despite using a weaker CLIP. Based on a strong CLIP (see results of DIFO-C-B32), our method's performance can improve further as we expected. All of the results indicate that the DIFO can boost the cross-domain performance in closed-set SFDA setting.", + "bbox": [ + 496, + 628, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23715", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/43537830b4bbe76f353d55ac4c2cd5cb01581102ce86a46159f6a18b4c389a48.jpg", + "table_caption": [ + "Table 2. Closed-set SFDA on Office-Home and VisDA (%). SF and M means source-free and multimodal, respectively; the full results on VisDA are in Supplementary." + ], + "table_footnote": [], + "table_body": "
MethodVenueSF MOffice-HomeVisDASy→Re
Ar→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg.
Source--43.767.073.949.960.162.551.740.972.664.246.378.159.249.2
DAPL-RN [8]TNNLS23X √54.184.384.874.483.785.074.554.684.875.254.783.874.586.9
PADCLIP-RN [17]ICCV23X √57.584.083.877.885.584.776.359.285.478.160.286.776.688.5
ADCLIP-RN [30]ICCVW23X √55.485.285.676.185.886.276.756.185.476.856.185.575.987.7
SHOT [24]ICML20√ X56.777.980.668.078.079.467.954.582.374.258.684.571.982.7
NRC [42]NIPS21√ X57.780.382.068.179.878.665.356.483.071.058.685.672.285.9
GKD [32]IROS21√ X56.578.281.868.778.979.167.654.882.674.458.584.872.283.0
AaD [43]NIPS22√ X59.379.382.168.979.879.567.257.483.172.158.585.472.788.0
AdaCon [2]CVPR22√ X47.275.175.560.773.373.260.245.276.665.648.379.165.086.8
CoWA [19]ICML22√ X56.978.481.069.180.079.967.757.282.472.860.584.572.586.9
SCLM [34]NN22√ X58.280.381.569.379.080.769.056.882.774.760.685.073.085.3
ELR [44]ICLR23√ X58.478.781.569.279.579.366.358.082.673.459.885.172.685.8
PLUE [25]CVPR23√ X49.173.578.262.973.574.562.248.378.668.651.881.566.988.3
TPDS [35]IJCV23√ X59.380.382.170.679.480.969.856.882.174.561.285.373.587.6
DIFO-C-RN-√ √62.687.587.179.587.987.478.363.488.180.063.387.779.488.8
DIFO-C-B32-√ √70.690.688.882.590.688.880.970.188.983.470.591.283.190.3
", + "bbox": [ + 78, + 128, + 890, + 321 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/7ce10d786dd1534b64b228c8ba95118f362c46399df7dc69193bbdc8856f3452.jpg", + "table_caption": [ + "Table 3. Closed-set SFDA on DomainNet-126 (\\%). SF and M means source-free and multimodal, respectively." + ], + "table_footnote": [], + "table_body": "
MethodVenueSFMC→PC→RC→SP→CP→RP→SR→CR→PR→SS→CS→PS→RAvg.
Source---44.659.847.553.375.346.255.362.746.455.150.759.554.7
DAPL-RN [8]TNNLS23✗✓72.487.665.972.787.665.673.272.466.273.872.987.874.8
ADCLIP-RN [30]ICCVW23✗✓71.788.166.073.286.965.273.673.068.472.374.289.375.2
SHOT [24]ICML20✓✗63.578.259.567.981.361.767.767.657.870.264.078.068.1
GKD [32]IROS21✓✗61.477.460.369.681.463.268.368.459.571.565.277.668.7
NRC [42]NIPS21✓✗62.677.158.362.981.360.764.769.458.769.465.878.767.5
AdaCon [2]CVPR22✓✗60.874.855.962.278.358.263.168.155.667.166.075.465.4
CoWA [19]ICML22✓✗64.680.660.666.279.860.869.067.260.069.065.879.968.6
PLUE [25]CVPR23✓✗59.874.056.061.678.557.961.665.953.867.564.376.064.7
TPDS [35]IJCV23✓✗62.977.159.865.679.061.566.467.058.268.664.375.367.1
DIFO-C-RN-✓✓73.889.069.474.088.770.174.874.669.674.774.388.076.7
DIFO-C-B32-✓✓76.687.274.980.087.475.680.877.375.580.576.787.380.0
", + "bbox": [ + 78, + 359, + 890, + 507 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/80299e001c22f733dd14e620a86da90967f52c020d00a1c0ff17df600b691346.jpg", + "table_caption": [ + "Table 4. Results (%) of CLIP and Source+CLIP on the four evaluation datasets. The backbone of CLIP image-encoder in CLP-C-RN and CLP-C-B32 are the same as DIFO-C-RN and DIFO-C-B32, respectively. The full results are provided in Supplementary." + ], + "table_footnote": [], + "table_body": "
MethodVenueOffice-31Office-HomeVisDASy→ReDomainNet-126
→A→D→W→Avg.→Ar→Cl→Pr→Rw→Avg.→C→P→R→S→Avg.
CLIP-RN [28]ICML2173.173.967.071.472.551.981.582.572.183.767.970.287.165.472.7
Source+CLIP-RN-76.390.484.083.675.457.484.485.775.782.071.871.487.366.574.3
DIFO-C-RN-78.695.393.989.379.363.187.787.579.488.874.574.288.569.776.7
CLIP-B32 [28]ICML2176.082.780.679.874.659.884.385.576.182.974.773.585.771.276.3
Source+CLIP-B32-78.593.089.687.078.962.586.187.778.882.076.873.786.070.876.8
DIFO-C-B32-83.198.096.492.582.370.490.888.883.190.380.476.987.375.380.0
", + "bbox": [ + 81, + 559, + 890, + 655 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison to CLIP based prediction results. The original CLIP model can conduct general image classification. We carry out a quantitative comparison between DIFO's adaptation performance and CLIP's performance on the four datasets, averaging the adaptation results of DIFO grouped by the target domain name.", + "bbox": [ + 75, + 680, + 470, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As presented in the bottom of Tab. 4, DIFO-C-B32 outperforms CLIP-B32 on all tasks. On average accuracy, DIFO-C-B32 increases the performance by $12.7\\%$ , $7.0\\%$ , $7.4\\%$ and $3.7\\%$ in Office-31, Office-Home, VisDA and DomainNet-126, respectively. Regarding the weak version, as reported in the top, DIFO-C-RN maintains similar advantages with the increase of $17.9\\%$ , $7.3\\%$ , $5.1\\%$ and $4.0\\%$ . The result shows that the domain generality of the original CLIP model", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cannot fully excel to the target domain, and task-specific customization is needed.", + "bbox": [ + 498, + 680, + 890, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Interestingly, compared with CLIP-B32, except for VisDA with a tiny gap of $0.9\\%$ , Source+CLIP-B32 averagely improve by $7.2\\%$ at most on the other datasets. Meanwhile, Source+CLIP-B32 is beaten by DIFO-C-B32 with an increase of $3.2\\%$ at least. In the group of DIFO-C-RN, we have the same observation. These results imply that directly weighting the source model and CLIP is an intuitive knowledge adaptation scheme, but it is hard to perform adaptation deeply. Considering Source+CLIP is an average version, we conduct a comprehensive comparison with the weighting strategy where the weighting coefficient of CLIP prediction varies from 0.0 to 1.0. Here, we conduct this experiment", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23716", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3b26860047386a85e932091f20117cf811ba115c02bf5c3524b93519673a1edb.jpg", + "image_caption": [ + "Figure 4. The performance of the scheme directly weighting the source model and CLIP-B32. All results are normalized by corresponding DIFO-C-B32 accuracies for a clear view." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 459, + 224 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "based on more challenging CLIP-B32 due to its large performance gap with Source (see the first row in Tab. $1 \\sim 3$ ). For a clear view, all weighted accuracies are normalized by the corresponding DIFO-C-B32 accuracies, respectively. As shown in Fig. 4, no result can exceed the value of 1.0. This indicates that weighting the source model and CLIP in a zero-shot manner cannot obtain desirable task-specific fusion, and a carefully designed distilling is necessary.", + "bbox": [ + 73, + 284, + 470, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on Partial-set and Open-set SFDA settings. These are the variations of traditional Closed-set SFDA setting, following the same as SHOT [24] (the detailed setting introduction is provided in Supplementary). As reported in Tab. 5, compared with previous best method CoWA (Partial-set) and CRS (Open-set), our DIFO-C-B32 improves by $2.4\\%$ and $2.7\\%$ , respectively.", + "bbox": [ + 75, + 409, + 470, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Model Analysis", + "text_level": 1, + "bbox": [ + 76, + 523, + 232, + 540 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature distribution visualization. Taking task $\\mathrm{Ar} \\rightarrow \\mathrm{Cl}$ in Office-Home as a toy experiment, we visualize feature distribution using t-SNE tool. Meanwhile, we choose 5 comparisons, including the source model (termed Source), CLIP-B32's zero shot (termed CLIP), SHOT, TPDS and Oracle (trained on domain Cl with the real labels). As shown at the top of Fig. 5, from Souce to DIFO-C-B32, category aliasing gradually relieves. Compared with Oracle, DIFO-C-B32 has the most similar distribution shape. To verify this point, we also give the 3D Density chart results arranged at the bottom of Fig. 5. These results confirm the effectiveness of our DIFO-C-B32 in terms of Feature distribution.", + "bbox": [ + 73, + 547, + 470, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablataion study. We evaluate the (1) effect of $L_{\\mathrm{TSC}}$ , $L_{\\mathrm{MCE}}$ and $L_{\\mathrm{PC}}$ , (2) effect of optimization of mutual information, (3) effect of task-specific customization and (4) effect of historical prediction fusion.", + "bbox": [ + 75, + 734, + 470, + 794 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For this first issue, we conduct a progressive experiment to isolate the loss's effects. The top four rows of Tab. 6 list the ablation study results. For convenience comparison, the baseline (the first row) is the source model results. When single $L_{\\mathrm{TSP}}$ or $L_{\\mathrm{MCE}}$ works, the accuracy largely increases on the three datasets with an improvement of about $20\\%$ in average accuracy compared with the baseline. As both of them", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/2ada8ae08f9b4963fe0057f575eb38cc39b76d0f5301a344e14d722d2cb1a406.jpg", + "table_caption": [ + "Table 5. Partial-set SFDA and Open-set SFDA on Office-Home $(\\%)$ . The full results are provided in Supplementary." + ], + "table_footnote": [], + "table_body": "
Partial-set SFDAVenueAvg.Open-set SFDAVenueAvg.
Source-62.8Source-46.6
SHOT [24]ICML2079.3SHOT [24]ICML2072.8
HCL [11]NIPS2179.6HCL [11]NIPS2172.6
CoWA [19]ICML2283.2CoWA [19]ICML2273.2
AaD [43]NIPS2279.7AaD [43]NIPS2271.8
CRS [45]CVPR2380.6CRS [45]CVPR2373.2
DIFO-C-B32-85.6DIFO-C-B32-75.9
", + "bbox": [ + 511, + 128, + 879, + 222 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dc83c3e2ce2cc1eee4cb1db8bf4be7c155a1aa81048b471df2a16e9309c99242.jpg", + "table_caption": [ + "Table 6. Classification results of ablation study (%) on Office-31 Office-Home and VisDA." + ], + "table_footnote": [], + "table_body": "
L TSCL MCEL PCOffice-31Office-HomeVisDAAvg.
XXX78.659.249.262.3
✓XX82.477.484.481.4
X✓X82.176.588.682.4
✓✓X87.080.088.385.1
✓✓✓92.583.190.388.6
DIFO-C-B32 w/ KL90.481.589.087.0
DIFO-C-B32 w/ CLIP90.781.188.886.8
DIFO-C-B32 w/o p i'89.873.587.083.4
DIFO-C-B32 w/o p i88.982.288.986.7
", + "bbox": [ + 514, + 281, + 874, + 395 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "are adopted, the accuracy evident increase (3.7% in average, the fourth row) on the top of the case of only $L_{\\mathrm{TSC}}$ and further enhanced by adopting of item $L_{\\mathrm{PC}}$ (3.5% in average, the fifth row). The results indicate: (1) all objective components positively affect the final performance, (2) $L_{\\mathrm{MCE}}$ , $L_{\\mathrm{PC}}$ is crucial due to providing a new soft supervision for coarse-to-fine adaptation.", + "bbox": [ + 496, + 426, + 893, + 531 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the second and third issues, we propose two variation methods of DIFO-C-B32 to evaluate the effect. One is DIFO-C-B32 w/ KL where the mutual information maximization loss in $L_{\\mathrm{TSC}}$ , $L_{\\mathrm{PC}}$ are replaced by KL divergence loss. The other one is DIFO-C-B32 w/ CLIP where the prompt learning-based customization for CLIP is cancelled, and the inputted prompt is set to the fixed template of \"a photo of a [CLS].\" during the entire adaptation. As presented in the last two rows in Tab. 6, DIFO-C-B32 (the fifth row) beats DIFO-C-B32 w/ KL and DIFO-C-B32 w/ CLIP with average improvement of $1.6\\%$ at least, respectively confirming the effect of adopting mutual information optimization and task-specific customization. As for the fourth issue, its effect is verified by the performance decreases $(3.4\\%$ in average at most) in the variation methods (the last two rows), which remove $p_i'$ and $p_i$ from the fusion respectively.", + "bbox": [ + 496, + 532, + 895, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Task-Specific Knowledge Adaptation Analysis", + "text_level": 1, + "bbox": [ + 498, + 785, + 887, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this part, we give a feature space shift analysis using the measure of MMD (maximum mean discrepancy) distance [47] to verify whether the proposed method ensures a task-specific knowledge adaptation.", + "bbox": [ + 496, + 809, + 893, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this experiment, we first train a domain-invariant Oracle model over all Office-Home data with real labels, and use", + "bbox": [ + 498, + 869, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23717", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/48a4d1c6bf2a835975c7ebb9ca66ef7ecc80b1cc9925114736e11ae7c184f4b3.jpg", + "image_caption": [ + "Source" + ], + "image_footnote": [], + "bbox": [ + 107, + 87, + 233, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/80bb58617f83c1e2f218badbda1f1316fe9012ceb00d70a371917ba91ed5f77f.jpg", + "image_caption": [ + "CLIP" + ], + "image_footnote": [], + "bbox": [ + 236, + 88, + 357, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dd63f2cc23b49daa9938726837fbc62f7a4c03a47b55cef1e4f74dc53a17f267.jpg", + "image_caption": [ + "SHOT" + ], + "image_footnote": [], + "bbox": [ + 359, + 88, + 482, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d2ad274d62cdddc32062fe802e18501fa327fcaa4171d78988d644e8476db72f.jpg", + "image_caption": [ + "TPDS" + ], + "image_footnote": [], + "bbox": [ + 486, + 88, + 609, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/54774a514d15f060b5a43eba493d2f7397d2efd44c030b3a89f06f5413ffba13.jpg", + "image_caption": [ + "DIFO-C-B32" + ], + "image_footnote": [], + "bbox": [ + 612, + 88, + 733, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4dcf522eb9519db170790167fd023ce1f48cef83ef6e98e1dc191ae44c763fd7.jpg", + "image_caption": [ + "Oracle" + ], + "image_footnote": [], + "bbox": [ + 736, + 88, + 859, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b62710b1931928333c312cc66bcc8e12d60de47f024cfb883dc2a53202f3811b.jpg", + "image_caption": [ + "Figure 5. Feature distribution visualization comparison on transfer task $\\mathrm{Ar}\\rightarrow \\mathrm{Cl}$ in Office-Home. Oracle is trained on target domain Cl using the ground-truth labels. Different colors stand for different categories. Top: t-SNE feature distribution over 65 categories. Bottom: The corresponding 3D density charts. For easy view, the first 10 categories were used in this plot." + ], + "image_footnote": [], + "bbox": [ + 106, + 191, + 228, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0326ec4ee1cb4e723da4874897b37c4ba2b2776a28bc5ec29512388bd0a81637.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 233, + 191, + 352, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ea5c48a06ab0a1643857b0024221b51d96cfdf6b648895c2c2e7ef0bb40c3ae8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 359, + 191, + 478, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2ef10853082fa9699bbd21b2f10c627f83ea8163fb5541dce5820ee12427fcd3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 482, + 191, + 604, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/00bb252782872160b32b1fa71cd361a53840792a8432ce8cc50853e66dbee666.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 607, + 191, + 730, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/532d1b5bc35f812ce1202298bdaf0abfe68e99b8cbd509bd7b902dcc336da1a4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 733, + 191, + 856, + 292 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c139258b696aaf76993dec4b07e0e7d1696ff1c094a31398b6fd5814118c49f3.jpg", + "image_caption": [ + "Figure 6. The evolving dynamics of MMD distance during adaption of $\\mathrm{Ar} \\rightarrow \\mathrm{Cl}$ in Office-Home. Left and Right present the varying curves of MMD distance and accuracy, respectively" + ], + "image_footnote": [], + "bbox": [ + 78, + 364, + 272, + 508 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3092ad539664b52a52d77b8af8750bba8d39eefc87c973bb67f83d85e7862982.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 272, + 364, + 467, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the logits to express the ideal task-specific space $\\mathcal{O}$ . After that, an analysis is conducted on the transfer task $\\mathrm{Ar} \\to \\mathrm{Cl}$ . During this adaptation, there are $T$ (epoch number) intermediate target models and customized CLIP models. We feedforward the target data through each intermediate model and take the logits as a space. Thus, we obtain $T$ intermediate target feature spaces $\\{\\mathcal{U}_k\\}_{k=1}^T$ and $T$ intermediate customized CLIP feature spaces $\\{\\mathcal{V}\\}_{k=1}^T$ . Within this context, these intermediate spaces can depict the task-specific distillation to $\\mathcal{O}$ . In practice, the CLIP image encoder's backbone is set to ViT-B/32.", + "bbox": [ + 75, + 593, + 468, + 758 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the left of Fig. 6, we give the MMD distance change curve of $\\{\\mathcal{U}_k\\}_{k=1}^T$ (in red, termed TGT) and $\\{\\mathcal{V}\\}_{k=1}^T$ (in blue, termed CUS-CLIP), taking $\\mathcal{O}$ as the original space. It is seen that at early epochs ( $1 \\sim 4$ ), TGT and CUS-CLIP sharply decrease and then maintain a gradual decrease in the following epochs. Meanwhile, this change is consistent with the accuracy varying shown in the right of Fig. 6.", + "bbox": [ + 75, + 762, + 470, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "These results indicate that our DIFO encourages task-specific knowledge adaptation due to converging the ideal", + "bbox": [ + 76, + 869, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "task-specific space. Besides, we observe two details. First, after epoch 1, CUS-CLIP's distance reduces by 2.2, which is 58.6 time of TGT's decrease of 0.038. This is because CLIP represents a heterogeneous space of vision-language, much different from the vision space $\\mathcal{O}$ . Furthermore, the large distance decrease confirms the effect of customization. Second, the synchronized distance reductions of CUS-CLIP and TGT indicate the interaction between the target model and CLIP is a crucial design for task-specific distillation.", + "bbox": [ + 496, + 369, + 893, + 506 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 518, + 619, + 535 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present an innovative approach, referred to as DIFO, designed to tackle the SFDA problem. To the best of our knowledge, this marks the initial endeavor to address SFDA by leveraging a pretrained ViL foundation model, departing from previous approaches that predominantly concentrated on self-mining auxiliary information. DIFO is featured with alternating between customization of the ViL model and the transfer of task-specific knowledge from the customized ViL model. We introduce two pivotal designs: a mutual information-based alignment for ViL customization and a most-likely category encouragement for more precise adaptation of task-specific knowledge. Our method's effectiveness is validated by state-of-the-art experimental results across four challenging datasets.", + "bbox": [ + 496, + 544, + 893, + 756 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 768, + 660, + 787 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by the German Research Foundation (DFG) and National Natural Science Foundation of China (NSFC) in project Crossmodal Learning under contract Sonderforschungsbereich Transregio 169, the Hamburg Landesforschungsforderungsprojekt Cross, NSFC (61773083); NSFC (62206168, 62276048). Shanghai SAST Funding (202410013).", + "bbox": [ + 496, + 794, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23718", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alex Andonian, Shixing Chen, and Raffay Hamid. Robust cross-modal representation learning with progressive self-distillation. In CVPR, 2022. 2", + "[2] Dian Chen, Dequan Wang, Trevor Darrell, and Sayna Ebrahimi. Contrastive test-time adaptation. In CVPR, 2022. 5, 6", + "[3] Weijie Chen, Luojun Lin, Shicai Yang, Di Xie, Shiliang Pu, and Yueting Zhuang. Self-supervised noisy label learning for source-free unsupervised domain adaptation. In IROS, 2022. 2", + "[4] Junhyeong Cho, Gilhyun Nam, Sungyeon Kim, Hunmin Yang, and Suha Kwak. 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International Journal of Computer Vision, pages 1-19, 2023. 4, 5, 6", + "[36] Korawat Tanwisuth, Xinjie Fan, Huangjie Zheng, Shujian Zhang, Hao Zhang, Bo Chen, and Mingyuan Zhou. A prototype-oriented framework for unsupervised domain adaptation. In NeurIPS, 2021. 2", + "[37] Jiayi Tian, Jing Zhang, Wen Li, and Dong Xu. Vdm-da: Virtual domain modeling for source data-free domain adaptation. IEEE Transactions on Circuits and Systems for Video Technology, 32(6):3749-3760, 2021. 1", + "[38] Jiayi Tian, Jing Zhang, Wen Li, and Dong Xu. Vdm-da: Virtual domain modeling for source data-free domain adaptation. IEEE Transactions on Circuits and Systems for Video Technology, 32(6):3749-3760, 2021. 2", + "[39] Hemanth Venkateswara, Jose Eusebio, Shayok Chakraborty, and Sethuraman Panchanathan. Deep hashing network for unsupervised domain adaptation. In CVPR, 2017. 5", + "[40] Fan Wang, Zhongyi Han, Yongshun Gong, and Yilong Yin. Exploring domain-invariant parameters for source free domain adaptation. In CVPR, 2022. 1", + "[41] Haifeng Xia, Handong Zhao, and Zhengming Ding. Adaptive adversarial network for source-free domain adaptation. In CVPR, 2021. 1", + "[42] Shiqi Yang, Joost van de Weijer, Luis Herranz, Shangling Jui, et al. Exploiting the intrinsic neighborhood structure for source-free domain adaptation. In NeurIPS, 2021. 1, 4, 5, 6", + "[43] Shiqi Yang, Yaxing Wang, Kai Wang, Shangling Jui, et al. Attracting and dispersing: A simple approach for source-free domain adaptation. In NeurIPS, 2022. 1, 5, 6, 7", + "[44] Li Yi, Gezheng Xu, Pengcheng Xu, Jiaqi Li, Ruizhi Pu, Charles Ling, A Ian McLeod, and Boyu Wang. When source-free domain adaptation meets learning with noisy labels. In ICLR, 2023. 5, 6", + "[45] Yixin Zhang, Zilei Wang, and Weinan He. Class relationship embedded learning for source-free unsupervised domain adaptation. In CVPR, 2023. 5, 7", + "[46] Kaiyang Zhou, Jingkang Yang, Chen Change Loy, and Ziwei Liu. Learning to prompt for vision-language models. International Journal of Computer Vision, 130(9):2337-2348, 2022. 2", + "[47] ZongxianLee. A pytorch implementation of maximum mean discrepancies (MMD) loss. https://github.com/ZongxianLee/MMD_Loss.Pytorch, 2019. 7" + ], + "bbox": [ + 78, + 90, + 470, + 871 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "23720", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_model.json b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ae373441be34704690aeb13681570586c9e9e467 --- /dev/null +++ b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_model.json @@ -0,0 +1,2497 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.099, + 0.131, + 0.872, + 0.152 + ], + "angle": 0, + "content": "Source-Free Domain Adaptation with Frozen Multimodal Foundation Model" + }, + { + "type": "text", + "bbox": [ + 0.255, + 0.193, + 0.713, + 0.211 + ], + "angle": 0, + "content": "Song Tang\\(^{1,2,3}\\), Wenxin Su\\(^{1}\\), Mao Ye\\(^{*4}\\), and Xiatian Zhu\\(^{*5}\\)" + }, + { + "type": "text", + "bbox": [ + 0.107, + 0.211, + 0.865, + 0.228 + ], + "angle": 0, + "content": "1University of Shanghai for Science and Technology 2Universität Hamburg 3ComOriginMat Inc." + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.229, + 0.805, + 0.246 + ], + "angle": 0, + "content": "4University of Electronic Science and Technology of China 5University of Surrey" + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.249, + 0.846, + 0.263 + ], + "angle": 0, + "content": "tangs@usst.edu.cn, {suwenxin43, cvlab.uestc}@gmail.com, xiatian.zhu@surrey.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.325 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.691 + ], + "angle": 0, + "content": "Source-Free Domain Adaptation (SFDA) aims to adapt a source model for a target domain, with only access to unlabeled target training data and the source model pretrained on a supervised source domain. Relying on pseudo labeling and/or auxiliary supervision, conventional methods are inevitably error-prone. To mitigate this limitation, in this work we for the first time explore the potentials of off-the-shelf vision-language (ViL) multimodal models (e.g., CLIP) with rich whilst heterogeneous knowledge. We find that directly applying the ViL model to the target domain in a zero-shot fashion is unsatisfactory, as it is not specialized for this particular task but largely generic. To make it task specific, we propose a novel Distilling multiModal Foundation mOdel (DIFO) approach. Specifically, DIFO alternates between two steps during adaptation: (i) Customizing the ViL model by maximizing the mutual information with the target model in a prompt learning manner, (ii) Distilling the knowledge of this customized ViL model to the target model. For more fine-grained and reliable distillation, we further introduce two effective regularization terms, namely most-likely category encouragement and predictive consistency. Extensive experiments show that DIFO significantly outperforms the state-of-the-art alternatives. Code is here." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.723, + 0.21, + 0.739 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.472, + 0.871 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation (UDA) relies on both well-annotated source data and unannotated target data. However, due to heightened safety and privacy concerns, accessing source data freely has become difficult [18, 23]. In response, Source-Free Domain Adaptation (SFDA) has gained attention as a more practical solution, aiming to transfer a pretrained source model to the target domain using only unlabeled target data." + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.309, + 0.868, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.478, + 0.895, + 0.548 + ], + "angle": 0, + "content": "Figure 1. We expand beyond traditional SFDA methods that rely solely on a pretrained source model and unlabeled target data. Instead, we innovate by exploring off-the-shelf multimodal foundation models, such as CLIP, in an unsupervised manner (marked by the box with blue background)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.895, + 0.78 + ], + "angle": 0, + "content": "Due to the absence of source samples, traditional distribution matching approaches are no longer viable [7, 14]. The predominant alternative is self-supervised learning, which generates or mines auxiliary information to facilitate unsupervised adaptation. Two main approaches exist: constructing a pseudo source domain to leverage established UDA methods such as adversarial learning [16, 41] or domain shift minimization based on distribution measurement [5, 15, 37] and mining extra supervision from the source model [11, 18, 40] or target data [34, 42, 43]. In the presence of domain distribution shift, applying the source model to the target domain introduces inevitable errors in pseudo-labeling or auxiliary supervision, thereby limiting adaptation performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.896, + 0.902 + ], + "angle": 0, + "content": "To address identified limitations, we pioneer the exploration of off-the-shelf multimodal foundation models, such as the vision-language (ViL) model CLIP [24], transcending the constraints of both the source model and target data knowledge. However, direct application of the ViL model proves unsatisfactory, lacking specialization for specific tasks. To overcome this, we propose a novel task-specific distillation approach named Distilling multiModal" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.221, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23711" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "Foundation mOdel (DIFO). Initially, we customize the ViL model through unsupervised prompt learning for imposing task-specific information. Subsequently, we distil the knowledge from this customized ViL model to the target model, with joint supervision through two designed regularization terms: (1) most-likely category encouragement for coarse-grained distillation and (2) predictive consistency for fine-grained distillation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.213, + 0.473, + 0.395 + ], + "angle": 0, + "content": "Our contributions are summarized as follows. (1) Pioneering the use of generic but heterogeneous knowledge sources (e.g., the off-the-shelf ViL model) for the SFDA problem, transcending the limited knowledge boundary of a pretrained source model and unlabeled target data. (2) Development of the novel DIFO approach to effectively distill useful task-specific knowledge from the general-purpose ViL model. (3) Extensive evaluation on standard benchmarks, demonstrating the significant superiority of our DIFO over previous state-of-the-art alternatives under conventional closed-set settings, as well as more challenging partial-set and open-set settings." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.405, + 0.22, + 0.421 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.473, + 0.55 + ], + "angle": 0, + "content": "Source-free domain adaptation. Existing SFDA approaches fall into three distinct categories. The first explicitly aligns the pseudo source domain with the target domain, treating SFDA as a specialized case of unsupervised domain adaptation. This alignment is achieved by constructing the pseudo source domain through a generative model [21, 38] or by splitting the target domain based on prior source hypotheses [6]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.473, + 0.717 + ], + "angle": 0, + "content": "The second group extracts cross-domain factors from the source domain and transfers them in successive model adaptation for aligning feature distributions across the two domains. For example, [31] establishes a mapping relationship from a sample and its exemplar Support Vector Machine (SVM) (an individual classifier) on the source domain to ensure individual classification on the target domain. Some approaches leverage pre-trained source models to generate auxiliary factors, such as multi-hypothesis [18], prototypes [36], source distribution estimation [5], or hard samples [20] to aid in feature alignment." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.473, + 0.793 + ], + "angle": 0, + "content": "The third group incorporates auxiliary information refined from the unlabeled target domain. In addition to widely used pseudo-labels [3, 24], geometry information, such as intrinsic neighborhood structure [33] and target data manifold [34], has also been exploited." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.473, + 0.868 + ], + "angle": 0, + "content": "Despite continual advancements, these methods are limited by the knowledge derived solely from the pretrained source model and unlabeled target data. We break this limitation by tapping into the rich knowledge encoded in off-the-shelf multimodal foundation models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Large multimodal model. Multimodal vision-language (ViL) models, such as CLIP [28] and ALIGN [13], have" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "shown promise across various mono-modal and multimodal tasks by capturing modality-invariant features. Approaches in this domain can be broadly categorized into two lines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.138, + 0.895, + 0.214 + ], + "angle": 0, + "content": "The first line focuses on enhancing ViL model performance. For instance, in [8, 46], prompt learning optimizes the text encoder through the use of tailored, learnable prompts designed for specific scenarios. Other efforts aim to improve data efficiency by repurposing noisy data [1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.215, + 0.895, + 0.366 + ], + "angle": 0, + "content": "The second line utilizes ViL models as external knowledge to enhance downstream tasks, as demonstrated in this paper. Previous work in knowledge transfer primarily falls into two frameworks. For the first scheme, where the ViL model is directly applied to the target task in a zero-shot fashion [22], domain generality is leveraged without task-specific refinement. The second scheme does not focus on source model adaptation. Instead, it fine-tunes the ViL model to the target domain through prompt or adaptor learning with an amount of manal labels [4]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.897, + 0.504 + ], + "angle": 0, + "content": "A relevant method to our DIFO is the UDA method DAPL [8]. Although both adopt CLIP, they differ significantly in problem setting and methodology. DAPL employs CLIP to learn domain-specific prompts, aiming to disentangle domain and category information in CLIP's visual features. In contrast, DIFO aligns target features to a progressively customized vision-language latent space in a memory-aware fashion. Importantly, DAPL requires labeled source data, making it inapplicable in SFDA." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.521, + 0.636, + 0.538 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.895, + 0.669 + ], + "angle": 0, + "content": "Problem statement. In the context of two distinct yet interrelated domains—namely, the labeled source domain and the unlabeled target domain—both characterized by the same set of \\( C \\) categories, the following notation is employed. The source samples and their corresponding labels are represented as \\( \\mathcal{X}_s \\) and \\( \\mathcal{Y}_s \\) respectively. Similarly, the target samples and their true labels are denoted as \\( \\mathcal{X}_t = \\{\\pmb{x}_i\\}_{i=1}^n \\) and \\( \\mathcal{Y}_t = \\{y_i\\}_{i=1}^n \\), where \\( n \\) signifies the number of samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.895, + 0.731 + ], + "angle": 0, + "content": "We aim to learn a target model \\(\\theta_t: \\mathcal{X}_t \\to \\mathcal{Y}_t\\). This involves utilizing (1) a pre-trained source model \\(\\theta_s: \\mathcal{X}_s \\to \\mathcal{Y}_s\\), (2) unlabeled target data, and (3) a Visual-Language (ViL) model denoted as \\(\\theta_v\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.895, + 0.779 + ], + "angle": 0, + "content": "Overview. As depicted in Fig. 2, the proposed DIFO framework alternates between two distinct steps to customize and distill the off-the-shelf ViL knowledge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In the first step, we engage in prompt learning on the ViL model for the purpose of task-specific customization. This serves to mitigate the guidance error within the ViL model. In particular, we adopt a mutual information-based alignment approach. This approach is characterized by its richness in context and interaction between the target model and the ViL model, as opposed to placing blind trust in either model alone as conventional methods." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23712" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.123, + 0.092, + 0.85, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.264, + 0.897, + 0.337 + ], + "angle": 0, + "content": "Figure 2. Overview of our DIFO: The process involves two alternating steps. First, we perform (a) task-specific customization of a ViL model through task-specific prompt learning (\\( L_{\\mathrm{TSC}} \\)). This is achieved under soft predictive guidance using mutual information maximization. Second, we undertake (b) memory-aware knowledge adaptation, incorporating two regularizations: most-likely category encouragement (\\( L_{\\mathrm{MCE}} \\)) predicted by our dynamic memory-aware predictor, along with the typical predictive consistency (\\( L_{\\mathrm{PC}} \\)). These regularizations are designed to facilitate a coarse-to-fine adaptation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.475, + 0.475 + ], + "angle": 0, + "content": "In the second step, knowledge adaptation takes place within a unique constraint that encourages the identification of the most probable category labels in the logit space, while concurrently maintaining the typical predictive consistency. The most likely category labels are determined by a carefully designed memory-aware predictor, which dynamically integrates knowledge from both the target model and the ViL model in a cumulative fashion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.482, + 0.421, + 0.499 + ], + "angle": 0, + "content": "3.1. Task-Specific ViL Model Customization" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.656 + ], + "angle": 0, + "content": "We adopt the prompt learning framework for ViL model customization, with all the parameters of the ViL model frozen throughout. The only learnable part in customization is the prompts each assigned for a specific class. To optimize these prompts, we need a useful supervision. In SFDA, however, it is challenging to customize such a domain-generic ViL model towards the target domain, at the absence of a well-trained target domain model. This is because, none of them can reasonably make predictions. That means there is no clearly good supervision signals available." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.472, + 0.763 + ], + "angle": 0, + "content": "To address this challenge, we propose to explore the wisdom of the crowd by leveraging their predictive interaction as the supervision. Formally, we denote the predictions by the target model and the ViL model as \\(\\theta_t(\\boldsymbol{x}_i)\\) and \\(\\theta_v(\\boldsymbol{x}_i)\\), respectively, given an unlabeled target sample \\(\\boldsymbol{x}_k\\). We conduct the customization by maximizing the mutual information of their predictions as:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.769, + 0.47, + 0.79 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {T S C}} = - \\min _ {\\boldsymbol {v}} \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\chi_ {t}} \\mathrm {I} \\left(\\theta_ {t} \\left(\\boldsymbol {x} _ {i}\\right), \\theta_ {v} \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {v}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.796, + 0.47, + 0.825 + ], + "angle": 0, + "content": "where \\(\\pmb{v}\\) is the prompt context to be learned and the function \\(\\mathrm{I}(\\cdot ,\\cdot)\\) measures the mutual information [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.902 + ], + "angle": 0, + "content": "This alignment design differs significantly from the conventional adoption of the Kullback-Leibler (KL) divergence. First of all, the mutual information is a lower optimization bound than KL divergence, facilitating deeper alignment (see Theorem 1 with the proof provided in Supplementary)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.355, + 0.896, + 0.401 + ], + "angle": 0, + "content": "Theorem 1 Given two random variables \\( X, Y \\). Their mutual information \\( I(X,Y) \\) and KL divergence \\( D_{\\mathrm{KL}}(X||Y) \\) satisfy the unequal relationship as follows." + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.412, + 0.893, + 0.43 + ], + "angle": 0, + "content": "\\[\n- \\mathrm {I} (X, Y) \\leq D _ {\\mathrm {K L}} (X, Y). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.448, + 0.895, + 0.571 + ], + "angle": 0, + "content": "Crucially, the KL divergence exhibits an inherent bias towards a specific prediction, making it less suitable for our context where none of the predictions holds a significant advantage. On the contrary, mutual information considers the joint distribution or correlation between the two predictions. This distinction arises from their respective definitions: \\(-\\mathrm{I}(X,Y) = -H(X) + H(X|Y)\\) and \\(D_{\\mathrm{KL}}(X,Y) = -H(X) + H(X:Y)\\), where" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.581, + 0.895, + 0.612 + ], + "angle": 0, + "content": "\\[\nH (X \\mid Y) = - \\sum_ {\\leftarrow} p (\\boldsymbol {x}, \\boldsymbol {y}) \\log p (\\boldsymbol {x} \\mid \\boldsymbol {y}) \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.606, + 0.799, + 0.629 + ], + "angle": 0, + "content": "\\[\nH \\left(X: Y\\right) = - \\sum p (\\boldsymbol {x}) \\log p (\\boldsymbol {y}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.896, + 0.747 + ], + "angle": 0, + "content": "The conditional entropy component \\( H(X|Y) \\) of mutual information explicitly captures the joint distributions, a feature absent in KL divergence. Empirically, we also confirm the significance of incorporating this joint distribution-based interaction between the two predictions during the customization of the ViL model (see ablation study in Tab. 6 and task-specific knowledge adaptation analysis in Section 4.3)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.839, + 0.773 + ], + "angle": 0, + "content": "3.2. Memory-Aware Knowledge Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.895, + 0.901 + ], + "angle": 0, + "content": "As previously mentioned, even with customization for the target domain, the ViL model may not be fully adapted due to no robust target model available in prior. This limitation hinders effective knowledge adaptation at this stage. To address this issue, we propose the incorporation of a specialized memory-aware predictor to provide additional learning guidance – most-likely category encouragement, complementing the conventional predictive consistency constraint." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23713" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.227 + ], + "angle": 0, + "content": "Most-likely category encouragement. The rationale behind incorporating this learning constraint is to harness the collective knowledge of both the target model and the ViL model in order to enhance the discernment of probable category labels for each sample. Given the sluggish nature of this search process, it has been devised to function as a form of learning regularization. An illustration of this regularization process is presented in Fig. 3. Specifically, it is realized through two distinct steps as detailed below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.229, + 0.47, + 0.336 + ], + "angle": 0, + "content": "(I) Memory-aware predictor. We initiate the process by generating pseudo-labels that represent the most likely category distribution, utilizing historical information stored in a prediction bank. The prediction bank archives two types of historical data for all samples in the target domain: (1) predictions from the target model denoted by \\(\\{p_i\\}_{i = 1}^n\\) and (2) predictions from the ViL model denoted by \\(\\{p_i'\\}_{i = 1}^n\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.336, + 0.47, + 0.488 + ], + "angle": 0, + "content": "Throughout the adaptation process, the predictions from the target model are updated iteratively. At the end of each training iteration, the newly predicted labels for the training batch from the target model replace their counterparts in the prediction bank. In contrast, predictions from the ViL model are updated collectively in an epoch-wise manner, triggering updates every \\( M \\) iterations. This mixed-update strategy is designed to strike a balance between maintaining the stability of the customized ViL model's guidance and capturing the task-specific dynamics inherent in the adaptation process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.471, + 0.534 + ], + "angle": 0, + "content": "Based on the provided prediction bank, the creation of a pseudo-label for the most probable category involves a historical prediction fusion process as:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.551, + 0.47, + 0.568 + ], + "angle": 0, + "content": "\\[\n\\bar {\\boldsymbol {p}} _ {i} = \\omega \\boldsymbol {p} _ {i} + (1 - \\omega) \\boldsymbol {p} _ {i} ^ {\\prime}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.674 + ], + "angle": 0, + "content": "Here, the weight \\(\\omega\\), drawn from an Exponential distribution with parameter \\(\\lambda\\), is a crucial factor. This fusion introduces dynamic bias rectification (represented by \\(\\pmb{p}_i\\)) based on the guidance from the customized ViL model \\((\\pmb{p}_i')\\). The role of \\(\\pmb{p}_i\\) is to provide adjustments, leading us to adopt an asymmetric random weighting approach represented by \\(\\omega\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.471, + 0.812 + ], + "angle": 0, + "content": "(II) Category attention calibration. Subsequently, we formulate a regularization technique employing pseudo-labels acquired through category attention calibration. Specifically, we begin by identifying the top- \\(N\\) most probable categories using \\(\\bar{p}_i\\). The indices of these identified categories are denoted by \\(\\mathcal{M}_i = \\{m_k\\}_{k=1}^N\\). With \\(\\mathcal{M}_i\\), the target model's logit of a target domain sample \\(x_i\\), denoted as \\(l_i\\), is segregated into positive and negative category groups. We define this regularization as:" + }, + { + "type": "equation", + "bbox": [ + 0.099, + 0.826, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L _ {\\mathrm {M C E}} = \\min _ {\\theta t} \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\mathcal {X} _ {t}} \\log \\frac {\\exp \\left(a _ {i} / \\tau\\right)}{\\sum_ {j \\neq \\mathcal {M} _ {i}} \\exp \\left(b _ {i} \\cdot l _ {i , j} / \\tau\\right)} \\tag {5} \\\\ a _ {i} = \\prod_ {k = 1} ^ {N} \\boldsymbol {l} _ {i, m _ {k}}, \\quad b _ {i} = \\sum_ {k = 1} ^ {N} \\boldsymbol {l} _ {i, m _ {k}} \\\\ \\end{array}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.091, + 0.882, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.253, + 0.895, + 0.324 + ], + "angle": 0, + "content": "Figure 3. Illustration of most-likely category encouragement. In contrast to the conventional approach that assigns equal importance to all categories (depicted by the gray line), our approach (represented by the black line) introduces additional supervision by incorporating extra knowledge about the two most likely categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.894, + 0.369 + ], + "angle": 0, + "content": "where \\( l_{i,a} \\) denotes the \\( a \\)-th element of \\( l_{i} \\) and \\( \\tau \\) is the temperature parameter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.895, + 0.552 + ], + "angle": 0, + "content": "In Eq. (5), we note that the product operation with \\( a_{i} \\) in the numerator amplifies penalties for the probability decrease on the most likely categories compared to the sum form. Similarly, the sum with \\( b_{i} \\) in the denominator serves as an increasing weighting parameter to enhance suppression of values at other locations. Moreover, \\( a_{i} \\) is more sensitive to changes than \\( b_{i} \\) due to \\( \\frac{\\partial a_{i}}{\\partial m_{k}} \\propto O(n^{N - 1}) \\) and \\( \\frac{\\partial b_{i}}{\\partial m_{k}} \\propto O(1) \\). By combining the use of \\( a_{i} \\) and \\( b_{i} \\), we globally impose a calibration effect on the elements corresponding to the most likely categories within the logit \\( l_{i} \\). Essentially, attention is introduced to these potential categories, as illustrated in the box with a yellow background in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.555, + 0.894, + 0.598 + ], + "angle": 0, + "content": "Predictive Consistency. For the purpose of knowledge adaptation, we incorporate the conventional predictive consistency loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.609, + 0.892, + 0.63 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {P C}} = \\min _ {\\theta_ {t}} \\left[ - \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\mathcal {X} _ {t}} \\mathrm {I} \\left(\\theta_ {t} (\\boldsymbol {x} _ {i}), \\theta_ {v} (\\boldsymbol {x} _ {i}, \\boldsymbol {v} *)\\right) + \\alpha L _ {B} \\right], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.895, + 0.807 + ], + "angle": 0, + "content": "where \\(\\theta_t(\\pmb{x}_i)\\) represents the target prediction, \\(\\theta_v(\\pmb{x}_i, \\pmb{v})\\) denotes the ViL prediction, and \\(\\pmb{v}\\) is the prompt context learned during the initial phase of task-specific customization. The function \\(\\mathrm{I}(\\cdot, \\cdot)\\) corresponds to the mutual information function. The parameter \\(\\alpha\\) serves as a trade-off parameter, and the category balance term \\(L_{\\mathrm{B}} = \\mathrm{KL}(\\bar{\\pmb{q}} || \\frac{1}{C})\\) aligns with previous approaches [35, 42], preventing solution collapse by ensuring the empirical label distribution \\(\\bar{\\pmb{q}}\\) matches the uniform distribution \\(\\frac{1}{C}\\). For the reasons elaborated in Section 3.1, we employ mutual information for alignment." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.654, + 0.833 + ], + "angle": 0, + "content": "3.3. Model training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "To systematically distill and leverage task-specific knowledge from the ViL model, we adopt an epoch-wise training approach for DIFO. The training process is divided into \\( T \\) epochs, each comprising two stages aligned with the two" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23714" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.092, + 0.286, + 0.106 + ], + "angle": 0, + "content": "Algorithm 1 Training of DIFO" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.108, + 0.455, + 0.154 + ], + "angle": 0, + "content": "Input: Pre-trained source model \\(\\theta_{s}\\), target model \\(\\theta_{t}\\), ViL model \\(\\theta_{v}\\), unlabelled target domain \\(\\mathcal{X}_{t}\\), learnable prompt context \\(\\boldsymbol{v}\\), #epoch \\(T\\), #iteration per epoch \\(M\\)." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.155, + 0.33, + 0.169 + ], + "angle": 0, + "content": "Output: The adapted target model \\(\\theta_t\\)." + }, + { + "type": "title", + "bbox": [ + 0.08, + 0.17, + 0.158, + 0.182 + ], + "angle": 0, + "content": "Procedure:" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.186, + 0.465, + 0.202 + ], + "angle": 0, + "content": "1: Initialisation: Set \\(\\theta_{t} = \\theta_{s}\\) and \\(\\pmb{v} = a\\) photo of a [CLS]." + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.203, + 0.204, + 0.215 + ], + "angle": 0, + "content": "2: for \\( t = 1:T \\) do" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.217, + 0.429, + 0.232 + ], + "angle": 0, + "content": "3: Update ViL predictions in the prediction bank." + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.233, + 0.374, + 0.246 + ], + "angle": 0, + "content": "4: Step1" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.248, + 0.234, + 0.26 + ], + "angle": 0, + "content": "5: for \\(m = 1:M\\) do" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.262, + 0.304, + 0.276 + ], + "angle": 0, + "content": "6: Sample a batch from \\(\\mathcal{X}_t\\);" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.277, + 0.46, + 0.292 + ], + "angle": 0, + "content": "7: Forward prompt \\(\\pmb{v}\\) and this batch \\(\\mathcal{X}_t^b\\) through \\(\\theta_v\\);" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.293, + 0.373, + 0.307 + ], + "angle": 0, + "content": "8: Forward this batch data through \\(\\theta_t\\);" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.308, + 0.457, + 0.337 + ], + "angle": 0, + "content": "9: Customize \\(\\theta_v\\) by optimizing \\(L_{\\mathrm{TSC}}\\) (Eq. (1)) and obtain task-specific prompt context \\(\\pmb{v}^{*}\\)." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.339, + 0.176, + 0.35 + ], + "angle": 0, + "content": "10: end for" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.354, + 0.373, + 0.367 + ], + "angle": 0, + "content": "11: Step2" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.369, + 0.234, + 0.381 + ], + "angle": 0, + "content": "12: for \\(m = 1:M\\) do" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.383, + 0.304, + 0.397 + ], + "angle": 0, + "content": "13: Sample a batch from \\(\\mathcal{X}_t\\);" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.398, + 0.415, + 0.413 + ], + "angle": 0, + "content": "14: Forward the \\(\\pmb{v}^{*}\\) and this batch through \\(\\theta_{\\upsilon}\\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.414, + 0.372, + 0.428 + ], + "angle": 0, + "content": "15: Forward this batch data through \\(\\theta_{t}\\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.429, + 0.404, + 0.443 + ], + "angle": 0, + "content": "16: Discover most-likely category (Eq. (4));" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.444, + 0.452, + 0.458 + ], + "angle": 0, + "content": "17: Update model \\(\\theta_{t}\\) by optimizing \\(L_{\\mathrm{MKA}}\\) (Eq. (7))." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.46, + 0.456, + 0.473 + ], + "angle": 0, + "content": "18: Update target predictions in the prediction bank." + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.475, + 0.176, + 0.487 + ], + "angle": 0, + "content": "19: end for" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.489, + 0.203, + 0.502 + ], + "angle": 0, + "content": "20: Set \\(\\pmb{v} = \\pmb{v}^{*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.505, + 0.159, + 0.516 + ], + "angle": 0, + "content": "21: end for" + }, + { + "type": "text", + "bbox": [ + 0.087, + 0.519, + 0.278, + 0.533 + ], + "angle": 0, + "content": "22: return Adapted model \\(\\theta_{t}\\)" + }, + { + "type": "list", + "bbox": [ + 0.087, + 0.186, + 0.465, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.471, + 0.609 + ], + "angle": 0, + "content": "steps in the DIFO framework (Fig. 2). During the first stage, training is governed by the objective \\( L_{\\mathrm{TSC}} \\), and in the subsequent second stage, the objective function transitions to" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.62, + 0.47, + 0.636 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {M K A}} = L _ {\\mathrm {P C}} + \\beta L _ {\\mathrm {M C E}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.646, + 0.469, + 0.677 + ], + "angle": 0, + "content": "where \\(\\beta\\) is a trade-off parameter. We summarize the whole training procedure of DIFO in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.689, + 0.209, + 0.707 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.472, + 0.806 + ], + "angle": 0, + "content": "Datasets. We evaluate four standard benchmarks: Office-31 [29], Office-Home [39], VisDA [26] and DomainNet-126 [27]. Among them, Office-31 is a small-scaled dataset; Office-Home is a medium-scale dataset; VisDA and DomainNet-126 are both large-scale datasets. The details of the four datasets are provided in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Competitor. We compare DIFO with 18 existing top-performing methods into three groups. (1) The first group contains Source (the source model's results), CLIP [28] and Source+CLIP where Source+CLIP directly average the results of the source model and CLIP. (2) The second group includes three state-of-the-art UDA methods" + }, + { + "type": "table_caption", + "bbox": [ + 0.565, + 0.09, + 0.828, + 0.104 + ], + "angle": 0, + "content": "Table 1. Closed-set SFDA on Office-31 (%)" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.115, + 0.892, + 0.279 + ], + "angle": 0, + "content": "
MethodVenueA→DA→WD→AD→WW→AW→DAvg.
Source-79.176.659.995.561.498.878.6
SHOT [24]ICML2093.791.174.298.274.6100.88.6
NRC [42]NIPS2196.090.875.399.075.0100.89.4
GKD [32]IROS2194.691.675.198.775.1100.89.2
HCL [11]NIPS2194.792.575.998.277.7100.89.8
AaD [43]NIPS2296.492.175.099.176.5100.89.9
AdaCon [2]CVPR2287.783.173.791.377.672.881.0
CoWA [19]ICML2294.495.276.298.577.699.890.3
SCLM [34]NN2295.890.075.598.975.599.889.4
ELR [44]ICLR2393.893.376.298.076.9100.89.6
PLUE [25]CVPR2389.288.472.897.169.697.985.8
TPDS [35]IJCV2397.194.575.798.775.599.890.2
DIFO-C-RN-93.692.178.595.778.897.089.3
DIFO-C-B32-97.295.583.097.283.298.892.5
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.308, + 0.894, + 0.4 + ], + "angle": 0, + "content": "DAPL [8], PADCLIP [17] and ADCLIP [30] that are also multimodal guiding-based. (3) The third group comprises 13 current state-of-the-art SFDA models: SHOT [24], NRC [42], GKD [32], HCL [11], AaD [43], AdaCon [2], CoWA [19], SCLM [34], ELR [44], PLUE [25], TPDS [35] and CRS [45]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.894, + 0.521 + ], + "angle": 0, + "content": "For comprehensive comparisons, we implement DIFO in two variants: (1) DIFO-C-RN (weak version) and (2) DIFO-C-B32 (strong version). The key distinction lies in the backbone of the CLIP image-encoder. Specifically, for DIFO-C-RN, ResNet101 [10] is employed on the VisDA dataset, while ResNet50 [10] is used on the other three datasets. On the other hand, DIFO-C-B32 adopts ViT-B/32 [9] as the backbone across all datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.892, + 0.59 + ], + "angle": 0, + "content": "SFDA settings. We consider three distinct settings: the conventional closed-set SFDA setting, the partial-set and the open-set SFDA settings. The experiment implementation details are provided in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.605, + 0.692, + 0.62 + ], + "angle": 0, + "content": "4.1. Comparison Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Comparison on Closed-set SFDA setting. The comparisons of the four evaluation datasets are listed in Tab. 1~3. DIFO-C-B32 surpasses the previous best method CoWA (on Office-31), TPDS (on Office-Home) and PLUE (on VisDA) and GKD (on DomainNet-126) by \\(2.2\\%\\), \\(9.6\\%\\) \\(2.0\\%\\) and \\(11.3\\%\\) in average accuracy respectively. Specifically, DIFO-C-B32 obtains the best results on 4 out of 6 tasks on Office-31 while surpassing previous methods on all tasks of the other three datasets. As for DIFO-C-RN, besides Office-31, it obtains the second-best results and beat the previous best methods by \\(5.9\\%\\), \\(0.5\\%\\) and \\(8.0\\%\\) on Office-Home, VisDA and DomainNet-126 in average accuracy. The comparison of DIFO-C-RN shows that our method can still perform well despite using a weaker CLIP. Based on a strong CLIP (see results of DIFO-C-B32), our method's performance can improve further as we expected. All of the results indicate that the DIFO can boost the cross-domain performance in closed-set SFDA setting." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23715" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 2. Closed-set SFDA on Office-Home and VisDA (%). SF and M means source-free and multimodal, respectively; the full results on VisDA are in Supplementary." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.13, + 0.892, + 0.322 + ], + "angle": 0, + "content": "
MethodVenueSF MOffice-HomeVisDASy→Re
Ar→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg.
Source--43.767.073.949.960.162.551.740.972.664.246.378.159.249.2
DAPL-RN [8]TNNLS23X √54.184.384.874.483.785.074.554.684.875.254.783.874.586.9
PADCLIP-RN [17]ICCV23X √57.584.083.877.885.584.776.359.285.478.160.286.776.688.5
ADCLIP-RN [30]ICCVW23X √55.485.285.676.185.886.276.756.185.476.856.185.575.987.7
SHOT [24]ICML20√ X56.777.980.668.078.079.467.954.582.374.258.684.571.982.7
NRC [42]NIPS21√ X57.780.382.068.179.878.665.356.483.071.058.685.672.285.9
GKD [32]IROS21√ X56.578.281.868.778.979.167.654.882.674.458.584.872.283.0
AaD [43]NIPS22√ X59.379.382.168.979.879.567.257.483.172.158.585.472.788.0
AdaCon [2]CVPR22√ X47.275.175.560.773.373.260.245.276.665.648.379.165.086.8
CoWA [19]ICML22√ X56.978.481.069.180.079.967.757.282.472.860.584.572.586.9
SCLM [34]NN22√ X58.280.381.569.379.080.769.056.882.774.760.685.073.085.3
ELR [44]ICLR23√ X58.478.781.569.279.579.366.358.082.673.459.885.172.685.8
PLUE [25]CVPR23√ X49.173.578.262.973.574.562.248.378.668.651.881.566.988.3
TPDS [35]IJCV23√ X59.380.382.170.679.480.969.856.882.174.561.285.373.587.6
DIFO-C-RN-√ √62.687.587.179.587.987.478.363.488.180.063.387.779.488.8
DIFO-C-B32-√ √70.690.688.882.590.688.880.970.188.983.470.591.283.190.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.154, + 0.334, + 0.816, + 0.35 + ], + "angle": 0, + "content": "Table 3. Closed-set SFDA on DomainNet-126 (\\%). SF and M means source-free and multimodal, respectively." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.36, + 0.892, + 0.508 + ], + "angle": 0, + "content": "
MethodVenueSFMC→PC→RC→SP→CP→RP→SR→CR→PR→SS→CS→PS→RAvg.
Source---44.659.847.553.375.346.255.362.746.455.150.759.554.7
DAPL-RN [8]TNNLS23✗✓72.487.665.972.787.665.673.272.466.273.872.987.874.8
ADCLIP-RN [30]ICCVW23✗✓71.788.166.073.286.965.273.673.068.472.374.289.375.2
SHOT [24]ICML20✓✗63.578.259.567.981.361.767.767.657.870.264.078.068.1
GKD [32]IROS21✓✗61.477.460.369.681.463.268.368.459.571.565.277.668.7
NRC [42]NIPS21✓✗62.677.158.362.981.360.764.769.458.769.465.878.767.5
AdaCon [2]CVPR22✓✗60.874.855.962.278.358.263.168.155.667.166.075.465.4
CoWA [19]ICML22✓✗64.680.660.666.279.860.869.067.260.069.065.879.968.6
PLUE [25]CVPR23✓✗59.874.056.061.678.557.961.665.953.867.564.376.064.7
TPDS [35]IJCV23✓✗62.977.159.865.679.061.566.467.058.268.664.375.367.1
DIFO-C-RN-✓✓73.889.069.474.088.770.174.874.669.674.774.388.076.7
DIFO-C-B32-✓✓76.687.274.980.087.475.680.877.375.580.576.787.380.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.52, + 0.893, + 0.551 + ], + "angle": 0, + "content": "Table 4. Results (%) of CLIP and Source+CLIP on the four evaluation datasets. The backbone of CLIP image-encoder in CLP-C-RN and CLP-C-B32 are the same as DIFO-C-RN and DIFO-C-B32, respectively. The full results are provided in Supplementary." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.56, + 0.891, + 0.656 + ], + "angle": 0, + "content": "
MethodVenueOffice-31Office-HomeVisDASy→ReDomainNet-126
→A→D→W→Avg.→Ar→Cl→Pr→Rw→Avg.→C→P→R→S→Avg.
CLIP-RN [28]ICML2173.173.967.071.472.551.981.582.572.183.767.970.287.165.472.7
Source+CLIP-RN-76.390.484.083.675.457.484.485.775.782.071.871.487.366.574.3
DIFO-C-RN-78.695.393.989.379.363.187.787.579.488.874.574.288.569.776.7
CLIP-B32 [28]ICML2176.082.780.679.874.659.884.385.576.182.974.773.585.771.276.3
Source+CLIP-B32-78.593.089.687.078.962.586.187.778.882.076.873.786.070.876.8
DIFO-C-B32-83.198.096.492.582.370.490.888.883.190.380.476.987.375.380.0
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.472, + 0.773 + ], + "angle": 0, + "content": "Comparison to CLIP based prediction results. The original CLIP model can conduct general image classification. We carry out a quantitative comparison between DIFO's adaptation performance and CLIP's performance on the four datasets, averaging the adaptation results of DIFO grouped by the target domain name." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "As presented in the bottom of Tab. 4, DIFO-C-B32 outperforms CLIP-B32 on all tasks. On average accuracy, DIFO-C-B32 increases the performance by \\(12.7\\%\\), \\(7.0\\%\\), \\(7.4\\%\\) and \\(3.7\\%\\) in Office-31, Office-Home, VisDA and DomainNet-126, respectively. Regarding the weak version, as reported in the top, DIFO-C-RN maintains similar advantages with the increase of \\(17.9\\%\\), \\(7.3\\%\\), \\(5.1\\%\\) and \\(4.0\\%\\). The result shows that the domain generality of the original CLIP model" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.681, + 0.892, + 0.711 + ], + "angle": 0, + "content": "cannot fully excel to the target domain, and task-specific customization is needed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Interestingly, compared with CLIP-B32, except for VisDA with a tiny gap of \\(0.9\\%\\), Source+CLIP-B32 averagely improve by \\(7.2\\%\\) at most on the other datasets. Meanwhile, Source+CLIP-B32 is beaten by DIFO-C-B32 with an increase of \\(3.2\\%\\) at least. In the group of DIFO-C-RN, we have the same observation. These results imply that directly weighting the source model and CLIP is an intuitive knowledge adaptation scheme, but it is hard to perform adaptation deeply. Considering Source+CLIP is an average version, we conduct a comprehensive comparison with the weighting strategy where the weighting coefficient of CLIP prediction varies from 0.0 to 1.0. Here, we conduct this experiment" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23716" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.089, + 0.46, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.228, + 0.472, + 0.27 + ], + "angle": 0, + "content": "Figure 4. The performance of the scheme directly weighting the source model and CLIP-B32. All results are normalized by corresponding DIFO-C-B32 accuracies for a clear view." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.285, + 0.472, + 0.407 + ], + "angle": 0, + "content": "based on more challenging CLIP-B32 due to its large performance gap with Source (see the first row in Tab. \\(1 \\sim 3\\)). For a clear view, all weighted accuracies are normalized by the corresponding DIFO-C-B32 accuracies, respectively. As shown in Fig. 4, no result can exceed the value of 1.0. This indicates that weighting the source model and CLIP in a zero-shot manner cannot obtain desirable task-specific fusion, and a carefully designed distilling is necessary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.41, + 0.472, + 0.517 + ], + "angle": 0, + "content": "Comparison on Partial-set and Open-set SFDA settings. These are the variations of traditional Closed-set SFDA setting, following the same as SHOT [24] (the detailed setting introduction is provided in Supplementary). As reported in Tab. 5, compared with previous best method CoWA (Partial-set) and CRS (Open-set), our DIFO-C-B32 improves by \\(2.4\\%\\) and \\(2.7\\%\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.525, + 0.233, + 0.541 + ], + "angle": 0, + "content": "4.2. Model Analysis" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.548, + 0.472, + 0.729 + ], + "angle": 0, + "content": "Feature distribution visualization. Taking task \\(\\mathrm{Ar} \\rightarrow \\mathrm{Cl}\\) in Office-Home as a toy experiment, we visualize feature distribution using t-SNE tool. Meanwhile, we choose 5 comparisons, including the source model (termed Source), CLIP-B32's zero shot (termed CLIP), SHOT, TPDS and Oracle (trained on domain Cl with the real labels). As shown at the top of Fig. 5, from Souce to DIFO-C-B32, category aliasing gradually relieves. Compared with Oracle, DIFO-C-B32 has the most similar distribution shape. To verify this point, we also give the 3D Density chart results arranged at the bottom of Fig. 5. These results confirm the effectiveness of our DIFO-C-B32 in terms of Feature distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.795 + ], + "angle": 0, + "content": "Ablataion study. We evaluate the (1) effect of \\( L_{\\mathrm{TSC}} \\), \\( L_{\\mathrm{MCE}} \\) and \\( L_{\\mathrm{PC}} \\), (2) effect of optimization of mutual information, (3) effect of task-specific customization and (4) effect of historical prediction fusion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.472, + 0.902 + ], + "angle": 0, + "content": "For this first issue, we conduct a progressive experiment to isolate the loss's effects. The top four rows of Tab. 6 list the ablation study results. For convenience comparison, the baseline (the first row) is the source model results. When single \\( L_{\\mathrm{TSP}} \\) or \\( L_{\\mathrm{MCE}} \\) works, the accuracy largely increases on the three datasets with an improvement of about \\( 20\\% \\) in average accuracy compared with the baseline. As both of them" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.119 + ], + "angle": 0, + "content": "Table 5. Partial-set SFDA and Open-set SFDA on Office-Home \\((\\%)\\). The full results are provided in Supplementary." + }, + { + "type": "table", + "bbox": [ + 0.512, + 0.129, + 0.88, + 0.223 + ], + "angle": 0, + "content": "
Partial-set SFDAVenueAvg.Open-set SFDAVenueAvg.
Source-62.8Source-46.6
SHOT [24]ICML2079.3SHOT [24]ICML2072.8
HCL [11]NIPS2179.6HCL [11]NIPS2172.6
CoWA [19]ICML2283.2CoWA [19]ICML2273.2
AaD [43]NIPS2279.7AaD [43]NIPS2271.8
CRS [45]CVPR2380.6CRS [45]CVPR2373.2
DIFO-C-B32-85.6DIFO-C-B32-75.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.242, + 0.892, + 0.27 + ], + "angle": 0, + "content": "Table 6. Classification results of ablation study (%) on Office-31 Office-Home and VisDA." + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.282, + 0.875, + 0.396 + ], + "angle": 0, + "content": "
L TSCL MCEL PCOffice-31Office-HomeVisDAAvg.
XXX78.659.249.262.3
✓XX82.477.484.481.4
X✓X82.176.588.682.4
✓✓X87.080.088.385.1
✓✓✓92.583.190.388.6
DIFO-C-B32 w/ KL90.481.589.087.0
DIFO-C-B32 w/ CLIP90.781.188.886.8
DIFO-C-B32 w/o p i'89.873.587.083.4
DIFO-C-B32 w/o p i88.982.288.986.7
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.427, + 0.895, + 0.532 + ], + "angle": 0, + "content": "are adopted, the accuracy evident increase (3.7% in average, the fourth row) on the top of the case of only \\( L_{\\mathrm{TSC}} \\) and further enhanced by adopting of item \\( L_{\\mathrm{PC}} \\) (3.5% in average, the fifth row). The results indicate: (1) all objective components positively affect the final performance, (2) \\( L_{\\mathrm{MCE}} \\), \\( L_{\\mathrm{PC}} \\) is crucial due to providing a new soft supervision for coarse-to-fine adaptation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.896, + 0.775 + ], + "angle": 0, + "content": "For the second and third issues, we propose two variation methods of DIFO-C-B32 to evaluate the effect. One is DIFO-C-B32 w/ KL where the mutual information maximization loss in \\( L_{\\mathrm{TSC}} \\), \\( L_{\\mathrm{PC}} \\) are replaced by KL divergence loss. The other one is DIFO-C-B32 w/ CLIP where the prompt learning-based customization for CLIP is cancelled, and the inputted prompt is set to the fixed template of \"a photo of a [CLS].\" during the entire adaptation. As presented in the last two rows in Tab. 6, DIFO-C-B32 (the fifth row) beats DIFO-C-B32 w/ KL and DIFO-C-B32 w/ CLIP with average improvement of \\( 1.6\\% \\) at least, respectively confirming the effect of adopting mutual information optimization and task-specific customization. As for the fourth issue, its effect is verified by the performance decreases \\( (3.4\\% \\) in average at most) in the variation methods (the last two rows), which remove \\( p_i' \\) and \\( p_i \\) from the fusion respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.786, + 0.888, + 0.803 + ], + "angle": 0, + "content": "4.3. Task-Specific Knowledge Adaptation Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.87 + ], + "angle": 0, + "content": "In this part, we give a feature space shift analysis using the measure of MMD (maximum mean discrepancy) distance [47] to verify whether the proposed method ensures a task-specific knowledge adaptation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.894, + 0.9 + ], + "angle": 0, + "content": "In this experiment, we first train a domain-invariant Oracle model over all Office-Home data with real labels, and use" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23717" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.088, + 0.235, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.152, + 0.18, + 0.192, + 0.189 + ], + "angle": 0, + "content": "Source" + }, + { + "type": "image", + "bbox": [ + 0.238, + 0.089, + 0.359, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.18, + 0.31, + 0.189 + ], + "angle": 0, + "content": "CLIP" + }, + { + "type": "image", + "bbox": [ + 0.361, + 0.089, + 0.483, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.407, + 0.179, + 0.439, + 0.189 + ], + "angle": 0, + "content": "SHOT" + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.089, + 0.61, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.533, + 0.179, + 0.564, + 0.189 + ], + "angle": 0, + "content": "TPDS" + }, + { + "type": "image", + "bbox": [ + 0.613, + 0.089, + 0.735, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.179, + 0.706, + 0.189 + ], + "angle": 0, + "content": "DIFO-C-B32" + }, + { + "type": "image", + "bbox": [ + 0.737, + 0.089, + 0.86, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.78, + 0.179, + 0.818, + 0.189 + ], + "angle": 0, + "content": "Oracle" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.192, + 0.23, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.235, + 0.192, + 0.354, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.36, + 0.192, + 0.48, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.483, + 0.192, + 0.605, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.608, + 0.192, + 0.732, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.192, + 0.857, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.895, + 0.345 + ], + "angle": 0, + "content": "Figure 5. Feature distribution visualization comparison on transfer task \\(\\mathrm{Ar}\\rightarrow \\mathrm{Cl}\\) in Office-Home. Oracle is trained on target domain Cl using the ground-truth labels. Different colors stand for different categories. Top: t-SNE feature distribution over 65 categories. Bottom: The corresponding 3D density charts. For easy view, the first 10 categories were used in this plot." + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.366, + 0.273, + 0.51 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.366, + 0.468, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.521, + 0.471, + 0.565 + ], + "angle": 0, + "content": "Figure 6. The evolving dynamics of MMD distance during adaption of \\(\\mathrm{Ar} \\rightarrow \\mathrm{Cl}\\) in Office-Home. Left and Right present the varying curves of MMD distance and accuracy, respectively" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.47, + 0.76 + ], + "angle": 0, + "content": "the logits to express the ideal task-specific space \\(\\mathcal{O}\\). After that, an analysis is conducted on the transfer task \\(\\mathrm{Ar} \\to \\mathrm{Cl}\\). During this adaptation, there are \\(T\\) (epoch number) intermediate target models and customized CLIP models. We feedforward the target data through each intermediate model and take the logits as a space. Thus, we obtain \\(T\\) intermediate target feature spaces \\(\\{\\mathcal{U}_k\\}_{k=1}^T\\) and \\(T\\) intermediate customized CLIP feature spaces \\(\\{\\mathcal{V}\\}_{k=1}^T\\). Within this context, these intermediate spaces can depict the task-specific distillation to \\(\\mathcal{O}\\). In practice, the CLIP image encoder's backbone is set to ViT-B/32." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.471, + 0.869 + ], + "angle": 0, + "content": "In the left of Fig. 6, we give the MMD distance change curve of \\(\\{\\mathcal{U}_k\\}_{k=1}^T\\) (in red, termed TGT) and \\(\\{\\mathcal{V}\\}_{k=1}^T\\) (in blue, termed CUS-CLIP), taking \\(\\mathcal{O}\\) as the original space. It is seen that at early epochs (\\(1 \\sim 4\\)), TGT and CUS-CLIP sharply decrease and then maintain a gradual decrease in the following epochs. Meanwhile, this change is consistent with the accuracy varying shown in the right of Fig. 6." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "These results indicate that our DIFO encourages task-specific knowledge adaptation due to converging the ideal" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.37, + 0.895, + 0.507 + ], + "angle": 0, + "content": "task-specific space. Besides, we observe two details. First, after epoch 1, CUS-CLIP's distance reduces by 2.2, which is 58.6 time of TGT's decrease of 0.038. This is because CLIP represents a heterogeneous space of vision-language, much different from the vision space \\(\\mathcal{O}\\). Furthermore, the large distance decrease confirms the effect of customization. Second, the synchronized distance reductions of CUS-CLIP and TGT indicate the interaction between the target model and CLIP is a crucial design for task-specific distillation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.62, + 0.536 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.895, + 0.757 + ], + "angle": 0, + "content": "We present an innovative approach, referred to as DIFO, designed to tackle the SFDA problem. To the best of our knowledge, this marks the initial endeavor to address SFDA by leveraging a pretrained ViL foundation model, departing from previous approaches that predominantly concentrated on self-mining auxiliary information. DIFO is featured with alternating between customization of the ViL model and the transfer of task-specific knowledge from the customized ViL model. We introduce two pivotal designs: a mutual information-based alignment for ViL customization and a most-likely category encouragement for more precise adaptation of task-specific knowledge. Our method's effectiveness is validated by state-of-the-art experimental results across four challenging datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.77, + 0.661, + 0.788 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This work is supported by the German Research Foundation (DFG) and National Natural Science Foundation of China (NSFC) in project Crossmodal Learning under contract Sonderforschungsbereich Transregio 169, the Hamburg Landesforschungsforderungsprojekt Cross, NSFC (61773083); NSFC (62206168, 62276048). Shanghai SAST Funding (202410013)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23718" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.471, + 0.156 + ], + "angle": 0, + "content": "[1] Alex Andonian, Shixing Chen, and Raffay Hamid. Robust cross-modal representation learning with progressive self-distillation. In CVPR, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.16, + 0.472, + 0.2 + ], + "angle": 0, + "content": "[2] Dian Chen, Dequan Wang, Trevor Darrell, and Sayna Ebrahimi. Contrastive test-time adaptation. In CVPR, 2022. 5, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.204, + 0.472, + 0.258 + ], + "angle": 0, + "content": "[3] Weijie Chen, Luojun Lin, Shicai Yang, Di Xie, Shiliang Pu, and Yueting Zhuang. 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A pytorch implementation of maximum mean discrepancies (MMD) loss. https://github.com/ZongxianLee/MMD_Loss.Pytorch, 2019. 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.872 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "23720" + } + ] +] \ No newline at end of file diff --git a/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_origin.pdf b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c736672540474dcce3959df40077f468b5dac138 --- /dev/null +++ b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/031d437d-6302-4046-b01d-f59ceeac78db_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:51239d03ac2e7f7939dc347190de1e4ec7cce8e5d3a585cc516f9fc411495982 +size 2897316 diff --git a/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/full.md b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bb60ead90cd42ec084e595a028082102458d3b6f --- /dev/null +++ b/2024/Source-Free Domain Adaptation with Frozen Multimodal Foundation Model/full.md @@ -0,0 +1,354 @@ +# Source-Free Domain Adaptation with Frozen Multimodal Foundation Model + +Song Tang $^{1,2,3}$ , Wenxin Su $^{1}$ , Mao Ye $^{*4}$ , and Xiatian Zhu $^{*5}$ + +1University of Shanghai for Science and Technology 2Universität Hamburg 3ComOriginMat Inc. + +4University of Electronic Science and Technology of China 5University of Surrey + +tangs@usst.edu.cn, {suwenxin43, cvlab.uestc}@gmail.com, xiatian.zhu@surrey.ac.uk + +# Abstract + +Source-Free Domain Adaptation (SFDA) aims to adapt a source model for a target domain, with only access to unlabeled target training data and the source model pretrained on a supervised source domain. Relying on pseudo labeling and/or auxiliary supervision, conventional methods are inevitably error-prone. To mitigate this limitation, in this work we for the first time explore the potentials of off-the-shelf vision-language (ViL) multimodal models (e.g., CLIP) with rich whilst heterogeneous knowledge. We find that directly applying the ViL model to the target domain in a zero-shot fashion is unsatisfactory, as it is not specialized for this particular task but largely generic. To make it task specific, we propose a novel Distilling multiModal Foundation mOdel (DIFO) approach. Specifically, DIFO alternates between two steps during adaptation: (i) Customizing the ViL model by maximizing the mutual information with the target model in a prompt learning manner, (ii) Distilling the knowledge of this customized ViL model to the target model. For more fine-grained and reliable distillation, we further introduce two effective regularization terms, namely most-likely category encouragement and predictive consistency. Extensive experiments show that DIFO significantly outperforms the state-of-the-art alternatives. Code is here. + +# 1. Introduction + +Unsupervised Domain Adaptation (UDA) relies on both well-annotated source data and unannotated target data. However, due to heightened safety and privacy concerns, accessing source data freely has become difficult [18, 23]. In response, Source-Free Domain Adaptation (SFDA) has gained attention as a more practical solution, aiming to transfer a pretrained source model to the target domain using only unlabeled target data. + +![](images/33090923e17fc171744e1617cc9c005cfb6532ee449e37016a7c6c94710d50ab.jpg) +Figure 1. We expand beyond traditional SFDA methods that rely solely on a pretrained source model and unlabeled target data. Instead, we innovate by exploring off-the-shelf multimodal foundation models, such as CLIP, in an unsupervised manner (marked by the box with blue background). + +Due to the absence of source samples, traditional distribution matching approaches are no longer viable [7, 14]. The predominant alternative is self-supervised learning, which generates or mines auxiliary information to facilitate unsupervised adaptation. Two main approaches exist: constructing a pseudo source domain to leverage established UDA methods such as adversarial learning [16, 41] or domain shift minimization based on distribution measurement [5, 15, 37] and mining extra supervision from the source model [11, 18, 40] or target data [34, 42, 43]. In the presence of domain distribution shift, applying the source model to the target domain introduces inevitable errors in pseudo-labeling or auxiliary supervision, thereby limiting adaptation performance. + +To address identified limitations, we pioneer the exploration of off-the-shelf multimodal foundation models, such as the vision-language (ViL) model CLIP [24], transcending the constraints of both the source model and target data knowledge. However, direct application of the ViL model proves unsatisfactory, lacking specialization for specific tasks. To overcome this, we propose a novel task-specific distillation approach named Distilling multiModal + +Foundation mOdel (DIFO). Initially, we customize the ViL model through unsupervised prompt learning for imposing task-specific information. Subsequently, we distil the knowledge from this customized ViL model to the target model, with joint supervision through two designed regularization terms: (1) most-likely category encouragement for coarse-grained distillation and (2) predictive consistency for fine-grained distillation. + +Our contributions are summarized as follows. (1) Pioneering the use of generic but heterogeneous knowledge sources (e.g., the off-the-shelf ViL model) for the SFDA problem, transcending the limited knowledge boundary of a pretrained source model and unlabeled target data. (2) Development of the novel DIFO approach to effectively distill useful task-specific knowledge from the general-purpose ViL model. (3) Extensive evaluation on standard benchmarks, demonstrating the significant superiority of our DIFO over previous state-of-the-art alternatives under conventional closed-set settings, as well as more challenging partial-set and open-set settings. + +# 2. Related Work + +Source-free domain adaptation. Existing SFDA approaches fall into three distinct categories. The first explicitly aligns the pseudo source domain with the target domain, treating SFDA as a specialized case of unsupervised domain adaptation. This alignment is achieved by constructing the pseudo source domain through a generative model [21, 38] or by splitting the target domain based on prior source hypotheses [6]. + +The second group extracts cross-domain factors from the source domain and transfers them in successive model adaptation for aligning feature distributions across the two domains. For example, [31] establishes a mapping relationship from a sample and its exemplar Support Vector Machine (SVM) (an individual classifier) on the source domain to ensure individual classification on the target domain. Some approaches leverage pre-trained source models to generate auxiliary factors, such as multi-hypothesis [18], prototypes [36], source distribution estimation [5], or hard samples [20] to aid in feature alignment. + +The third group incorporates auxiliary information refined from the unlabeled target domain. In addition to widely used pseudo-labels [3, 24], geometry information, such as intrinsic neighborhood structure [33] and target data manifold [34], has also been exploited. + +Despite continual advancements, these methods are limited by the knowledge derived solely from the pretrained source model and unlabeled target data. We break this limitation by tapping into the rich knowledge encoded in off-the-shelf multimodal foundation models. + +Large multimodal model. Multimodal vision-language (ViL) models, such as CLIP [28] and ALIGN [13], have + +shown promise across various mono-modal and multimodal tasks by capturing modality-invariant features. Approaches in this domain can be broadly categorized into two lines. + +The first line focuses on enhancing ViL model performance. For instance, in [8, 46], prompt learning optimizes the text encoder through the use of tailored, learnable prompts designed for specific scenarios. Other efforts aim to improve data efficiency by repurposing noisy data [1]. + +The second line utilizes ViL models as external knowledge to enhance downstream tasks, as demonstrated in this paper. Previous work in knowledge transfer primarily falls into two frameworks. For the first scheme, where the ViL model is directly applied to the target task in a zero-shot fashion [22], domain generality is leveraged without task-specific refinement. The second scheme does not focus on source model adaptation. Instead, it fine-tunes the ViL model to the target domain through prompt or adaptor learning with an amount of manal labels [4]. + +A relevant method to our DIFO is the UDA method DAPL [8]. Although both adopt CLIP, they differ significantly in problem setting and methodology. DAPL employs CLIP to learn domain-specific prompts, aiming to disentangle domain and category information in CLIP's visual features. In contrast, DIFO aligns target features to a progressively customized vision-language latent space in a memory-aware fashion. Importantly, DAPL requires labeled source data, making it inapplicable in SFDA. + +# 3. Methodology + +Problem statement. In the context of two distinct yet interrelated domains—namely, the labeled source domain and the unlabeled target domain—both characterized by the same set of $C$ categories, the following notation is employed. The source samples and their corresponding labels are represented as $\mathcal{X}_s$ and $\mathcal{Y}_s$ respectively. Similarly, the target samples and their true labels are denoted as $\mathcal{X}_t = \{\pmb{x}_i\}_{i=1}^n$ and $\mathcal{Y}_t = \{y_i\}_{i=1}^n$ , where $n$ signifies the number of samples. + +We aim to learn a target model $\theta_t: \mathcal{X}_t \to \mathcal{Y}_t$ . This involves utilizing (1) a pre-trained source model $\theta_s: \mathcal{X}_s \to \mathcal{Y}_s$ , (2) unlabeled target data, and (3) a Visual-Language (ViL) model denoted as $\theta_v$ . + +Overview. As depicted in Fig. 2, the proposed DIFO framework alternates between two distinct steps to customize and distill the off-the-shelf ViL knowledge. + +In the first step, we engage in prompt learning on the ViL model for the purpose of task-specific customization. This serves to mitigate the guidance error within the ViL model. In particular, we adopt a mutual information-based alignment approach. This approach is characterized by its richness in context and interaction between the target model and the ViL model, as opposed to placing blind trust in either model alone as conventional methods. + +![](images/b9a880d506f08b86ecaf952ad0b735640344cbcc9c7c29ab5f95679bbae724ee.jpg) +Figure 2. Overview of our DIFO: The process involves two alternating steps. First, we perform (a) task-specific customization of a ViL model through task-specific prompt learning ( $L_{\mathrm{TSC}}$ ). This is achieved under soft predictive guidance using mutual information maximization. Second, we undertake (b) memory-aware knowledge adaptation, incorporating two regularizations: most-likely category encouragement ( $L_{\mathrm{MCE}}$ ) predicted by our dynamic memory-aware predictor, along with the typical predictive consistency ( $L_{\mathrm{PC}}$ ). These regularizations are designed to facilitate a coarse-to-fine adaptation. + +In the second step, knowledge adaptation takes place within a unique constraint that encourages the identification of the most probable category labels in the logit space, while concurrently maintaining the typical predictive consistency. The most likely category labels are determined by a carefully designed memory-aware predictor, which dynamically integrates knowledge from both the target model and the ViL model in a cumulative fashion. + +# 3.1. Task-Specific ViL Model Customization + +We adopt the prompt learning framework for ViL model customization, with all the parameters of the ViL model frozen throughout. The only learnable part in customization is the prompts each assigned for a specific class. To optimize these prompts, we need a useful supervision. In SFDA, however, it is challenging to customize such a domain-generic ViL model towards the target domain, at the absence of a well-trained target domain model. This is because, none of them can reasonably make predictions. That means there is no clearly good supervision signals available. + +To address this challenge, we propose to explore the wisdom of the crowd by leveraging their predictive interaction as the supervision. Formally, we denote the predictions by the target model and the ViL model as $\theta_t(\boldsymbol{x}_i)$ and $\theta_v(\boldsymbol{x}_i)$ , respectively, given an unlabeled target sample $\boldsymbol{x}_k$ . We conduct the customization by maximizing the mutual information of their predictions as: + +$$ +L _ {\mathrm {T S C}} = - \min _ {\boldsymbol {v}} \mathbb {E} _ {\boldsymbol {x} _ {i} \in \chi_ {t}} \mathrm {I} \left(\theta_ {t} \left(\boldsymbol {x} _ {i}\right), \theta_ {v} \left(\boldsymbol {x} _ {i}, \boldsymbol {v}\right)\right) \tag {1} +$$ + +where $\pmb{v}$ is the prompt context to be learned and the function $\mathrm{I}(\cdot ,\cdot)$ measures the mutual information [12]. + +This alignment design differs significantly from the conventional adoption of the Kullback-Leibler (KL) divergence. First of all, the mutual information is a lower optimization bound than KL divergence, facilitating deeper alignment (see Theorem 1 with the proof provided in Supplementary). + +Theorem 1 Given two random variables $X, Y$ . Their mutual information $I(X,Y)$ and KL divergence $D_{\mathrm{KL}}(X||Y)$ satisfy the unequal relationship as follows. + +$$ +- \mathrm {I} (X, Y) \leq D _ {\mathrm {K L}} (X, Y). \tag {2} +$$ + +Crucially, the KL divergence exhibits an inherent bias towards a specific prediction, making it less suitable for our context where none of the predictions holds a significant advantage. On the contrary, mutual information considers the joint distribution or correlation between the two predictions. This distinction arises from their respective definitions: $-\mathrm{I}(X,Y) = -H(X) + H(X|Y)$ and $D_{\mathrm{KL}}(X,Y) = -H(X) + H(X:Y)$ , where + +$$ +H (X \mid Y) = - \sum_ {\leftarrow} p (\boldsymbol {x}, \boldsymbol {y}) \log p (\boldsymbol {x} \mid \boldsymbol {y}) \tag {3} +$$ + +$$ +H \left(X: Y\right) = - \sum p (\boldsymbol {x}) \log p (\boldsymbol {y}). +$$ + +The conditional entropy component $H(X|Y)$ of mutual information explicitly captures the joint distributions, a feature absent in KL divergence. Empirically, we also confirm the significance of incorporating this joint distribution-based interaction between the two predictions during the customization of the ViL model (see ablation study in Tab. 6 and task-specific knowledge adaptation analysis in Section 4.3). + +# 3.2. Memory-Aware Knowledge Adaptation + +As previously mentioned, even with customization for the target domain, the ViL model may not be fully adapted due to no robust target model available in prior. This limitation hinders effective knowledge adaptation at this stage. To address this issue, we propose the incorporation of a specialized memory-aware predictor to provide additional learning guidance – most-likely category encouragement, complementing the conventional predictive consistency constraint. + +Most-likely category encouragement. The rationale behind incorporating this learning constraint is to harness the collective knowledge of both the target model and the ViL model in order to enhance the discernment of probable category labels for each sample. Given the sluggish nature of this search process, it has been devised to function as a form of learning regularization. An illustration of this regularization process is presented in Fig. 3. Specifically, it is realized through two distinct steps as detailed below. + +(I) Memory-aware predictor. We initiate the process by generating pseudo-labels that represent the most likely category distribution, utilizing historical information stored in a prediction bank. The prediction bank archives two types of historical data for all samples in the target domain: (1) predictions from the target model denoted by $\{p_i\}_{i = 1}^n$ and (2) predictions from the ViL model denoted by $\{p_i'\}_{i = 1}^n$ . + +Throughout the adaptation process, the predictions from the target model are updated iteratively. At the end of each training iteration, the newly predicted labels for the training batch from the target model replace their counterparts in the prediction bank. In contrast, predictions from the ViL model are updated collectively in an epoch-wise manner, triggering updates every $M$ iterations. This mixed-update strategy is designed to strike a balance between maintaining the stability of the customized ViL model's guidance and capturing the task-specific dynamics inherent in the adaptation process. + +Based on the provided prediction bank, the creation of a pseudo-label for the most probable category involves a historical prediction fusion process as: + +$$ +\bar {\boldsymbol {p}} _ {i} = \omega \boldsymbol {p} _ {i} + (1 - \omega) \boldsymbol {p} _ {i} ^ {\prime}. \tag {4} +$$ + +Here, the weight $\omega$ , drawn from an Exponential distribution with parameter $\lambda$ , is a crucial factor. This fusion introduces dynamic bias rectification (represented by $\pmb{p}_i$ ) based on the guidance from the customized ViL model $(\pmb{p}_i')$ . The role of $\pmb{p}_i$ is to provide adjustments, leading us to adopt an asymmetric random weighting approach represented by $\omega$ . + +(II) Category attention calibration. Subsequently, we formulate a regularization technique employing pseudo-labels acquired through category attention calibration. Specifically, we begin by identifying the top- $N$ most probable categories using $\bar{p}_i$ . The indices of these identified categories are denoted by $\mathcal{M}_i = \{m_k\}_{k=1}^N$ . With $\mathcal{M}_i$ , the target model's logit of a target domain sample $x_i$ , denoted as $l_i$ , is segregated into positive and negative category groups. We define this regularization as: + +$$ +\begin{array}{l} L _ {\mathrm {M C E}} = \min _ {\theta t} \mathbb {E} _ {\boldsymbol {x} _ {i} \in \mathcal {X} _ {t}} \log \frac {\exp \left(a _ {i} / \tau\right)}{\sum_ {j \neq \mathcal {M} _ {i}} \exp \left(b _ {i} \cdot l _ {i , j} / \tau\right)} \tag {5} \\ a _ {i} = \prod_ {k = 1} ^ {N} \boldsymbol {l} _ {i, m _ {k}}, \quad b _ {i} = \sum_ {k = 1} ^ {N} \boldsymbol {l} _ {i, m _ {k}} \\ \end{array} +$$ + +![](images/102c3302efd2d097288c9fa34db29e0e59f88101a106c60a01080c5074051551.jpg) +Figure 3. Illustration of most-likely category encouragement. In contrast to the conventional approach that assigns equal importance to all categories (depicted by the gray line), our approach (represented by the black line) introduces additional supervision by incorporating extra knowledge about the two most likely categories. + +where $l_{i,a}$ denotes the $a$ -th element of $l_{i}$ and $\tau$ is the temperature parameter. + +In Eq. (5), we note that the product operation with $a_{i}$ in the numerator amplifies penalties for the probability decrease on the most likely categories compared to the sum form. Similarly, the sum with $b_{i}$ in the denominator serves as an increasing weighting parameter to enhance suppression of values at other locations. Moreover, $a_{i}$ is more sensitive to changes than $b_{i}$ due to $\frac{\partial a_{i}}{\partial m_{k}} \propto O(n^{N - 1})$ and $\frac{\partial b_{i}}{\partial m_{k}} \propto O(1)$ . By combining the use of $a_{i}$ and $b_{i}$ , we globally impose a calibration effect on the elements corresponding to the most likely categories within the logit $l_{i}$ . Essentially, attention is introduced to these potential categories, as illustrated in the box with a yellow background in Fig. 3. + +Predictive Consistency. For the purpose of knowledge adaptation, we incorporate the conventional predictive consistency loss as: + +$$ +L _ {\mathrm {P C}} = \min _ {\theta_ {t}} \left[ - \mathbb {E} _ {\boldsymbol {x} _ {i} \in \mathcal {X} _ {t}} \mathrm {I} \left(\theta_ {t} (\boldsymbol {x} _ {i}), \theta_ {v} (\boldsymbol {x} _ {i}, \boldsymbol {v} *)\right) + \alpha L _ {B} \right], \tag {6} +$$ + +where $\theta_t(\pmb{x}_i)$ represents the target prediction, $\theta_v(\pmb{x}_i, \pmb{v})$ denotes the ViL prediction, and $\pmb{v}$ is the prompt context learned during the initial phase of task-specific customization. The function $\mathrm{I}(\cdot, \cdot)$ corresponds to the mutual information function. The parameter $\alpha$ serves as a trade-off parameter, and the category balance term $L_{\mathrm{B}} = \mathrm{KL}(\bar{\pmb{q}} || \frac{1}{C})$ aligns with previous approaches [35, 42], preventing solution collapse by ensuring the empirical label distribution $\bar{\pmb{q}}$ matches the uniform distribution $\frac{1}{C}$ . For the reasons elaborated in Section 3.1, we employ mutual information for alignment. + +# 3.3. Model training + +To systematically distill and leverage task-specific knowledge from the ViL model, we adopt an epoch-wise training approach for DIFO. The training process is divided into $T$ epochs, each comprising two stages aligned with the two + +# Algorithm 1 Training of DIFO + +Input: Pre-trained source model $\theta_{s}$ , target model $\theta_{t}$ , ViL model $\theta_{v}$ , unlabelled target domain $\mathcal{X}_{t}$ , learnable prompt context $\boldsymbol{v}$ , #epoch $T$ , #iteration per epoch $M$ . + +Output: The adapted target model $\theta_t$ . + +# Procedure: + +1: Initialisation: Set $\theta_{t} = \theta_{s}$ and $\pmb{v} = a$ photo of a [CLS]. +2: for $t = 1:T$ do +3: Update ViL predictions in the prediction bank. +4: Step1 +5: for $m = 1:M$ do +6: Sample a batch from $\mathcal{X}_t$ ; +7: Forward prompt $\pmb{v}$ and this batch $\mathcal{X}_t^b$ through $\theta_v$ ; +8: Forward this batch data through $\theta_t$ ; +9: Customize $\theta_v$ by optimizing $L_{\mathrm{TSC}}$ (Eq. (1)) and obtain task-specific prompt context $\pmb{v}^{*}$ . +10: end for +11: Step2 +12: for $m = 1:M$ do +13: Sample a batch from $\mathcal{X}_t$ ; +14: Forward the $\pmb{v}^{*}$ and this batch through $\theta_{\upsilon}$ +15: Forward this batch data through $\theta_{t}$ +16: Discover most-likely category (Eq. (4)); +17: Update model $\theta_{t}$ by optimizing $L_{\mathrm{MKA}}$ (Eq. (7)). +18: Update target predictions in the prediction bank. +19: end for +20: Set $\pmb{v} = \pmb{v}^{*}$ +21: end for +22: return Adapted model $\theta_{t}$ + +steps in the DIFO framework (Fig. 2). During the first stage, training is governed by the objective $L_{\mathrm{TSC}}$ , and in the subsequent second stage, the objective function transitions to + +$$ +L _ {\mathrm {M K A}} = L _ {\mathrm {P C}} + \beta L _ {\mathrm {M C E}}, \tag {7} +$$ + +where $\beta$ is a trade-off parameter. We summarize the whole training procedure of DIFO in Algorithm 1. + +# 4. Experiments + +Datasets. We evaluate four standard benchmarks: Office-31 [29], Office-Home [39], VisDA [26] and DomainNet-126 [27]. Among them, Office-31 is a small-scaled dataset; Office-Home is a medium-scale dataset; VisDA and DomainNet-126 are both large-scale datasets. The details of the four datasets are provided in Supplementary. + +Competitor. We compare DIFO with 18 existing top-performing methods into three groups. (1) The first group contains Source (the source model's results), CLIP [28] and Source+CLIP where Source+CLIP directly average the results of the source model and CLIP. (2) The second group includes three state-of-the-art UDA methods + +Table 1. Closed-set SFDA on Office-31 (%) + +
MethodVenueA→DA→WD→AD→WW→AW→DAvg.
Source-79.176.659.995.561.498.878.6
SHOT [24]ICML2093.791.174.298.274.6100.88.6
NRC [42]NIPS2196.090.875.399.075.0100.89.4
GKD [32]IROS2194.691.675.198.775.1100.89.2
HCL [11]NIPS2194.792.575.998.277.7100.89.8
AaD [43]NIPS2296.492.175.099.176.5100.89.9
AdaCon [2]CVPR2287.783.173.791.377.672.881.0
CoWA [19]ICML2294.495.276.298.577.699.890.3
SCLM [34]NN2295.890.075.598.975.599.889.4
ELR [44]ICLR2393.893.376.298.076.9100.89.6
PLUE [25]CVPR2389.288.472.897.169.697.985.8
TPDS [35]IJCV2397.194.575.798.775.599.890.2
DIFO-C-RN-93.692.178.595.778.897.089.3
DIFO-C-B32-97.295.583.097.283.298.892.5
+ +DAPL [8], PADCLIP [17] and ADCLIP [30] that are also multimodal guiding-based. (3) The third group comprises 13 current state-of-the-art SFDA models: SHOT [24], NRC [42], GKD [32], HCL [11], AaD [43], AdaCon [2], CoWA [19], SCLM [34], ELR [44], PLUE [25], TPDS [35] and CRS [45]. + +For comprehensive comparisons, we implement DIFO in two variants: (1) DIFO-C-RN (weak version) and (2) DIFO-C-B32 (strong version). The key distinction lies in the backbone of the CLIP image-encoder. Specifically, for DIFO-C-RN, ResNet101 [10] is employed on the VisDA dataset, while ResNet50 [10] is used on the other three datasets. On the other hand, DIFO-C-B32 adopts ViT-B/32 [9] as the backbone across all datasets. + +SFDA settings. We consider three distinct settings: the conventional closed-set SFDA setting, the partial-set and the open-set SFDA settings. The experiment implementation details are provided in Supplementary. + +# 4.1. Comparison Results + +Comparison on Closed-set SFDA setting. The comparisons of the four evaluation datasets are listed in Tab. 1~3. DIFO-C-B32 surpasses the previous best method CoWA (on Office-31), TPDS (on Office-Home) and PLUE (on VisDA) and GKD (on DomainNet-126) by $2.2\%$ , $9.6\%$ $2.0\%$ and $11.3\%$ in average accuracy respectively. Specifically, DIFO-C-B32 obtains the best results on 4 out of 6 tasks on Office-31 while surpassing previous methods on all tasks of the other three datasets. As for DIFO-C-RN, besides Office-31, it obtains the second-best results and beat the previous best methods by $5.9\%$ , $0.5\%$ and $8.0\%$ on Office-Home, VisDA and DomainNet-126 in average accuracy. The comparison of DIFO-C-RN shows that our method can still perform well despite using a weaker CLIP. Based on a strong CLIP (see results of DIFO-C-B32), our method's performance can improve further as we expected. All of the results indicate that the DIFO can boost the cross-domain performance in closed-set SFDA setting. + +Table 2. Closed-set SFDA on Office-Home and VisDA (%). SF and M means source-free and multimodal, respectively; the full results on VisDA are in Supplementary. + +
MethodVenueSF MOffice-HomeVisDASy→Re
Ar→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg.
Source--43.767.073.949.960.162.551.740.972.664.246.378.159.249.2
DAPL-RN [8]TNNLS23X √54.184.384.874.483.785.074.554.684.875.254.783.874.586.9
PADCLIP-RN [17]ICCV23X √57.584.083.877.885.584.776.359.285.478.160.286.776.688.5
ADCLIP-RN [30]ICCVW23X √55.485.285.676.185.886.276.756.185.476.856.185.575.987.7
SHOT [24]ICML20√ X56.777.980.668.078.079.467.954.582.374.258.684.571.982.7
NRC [42]NIPS21√ X57.780.382.068.179.878.665.356.483.071.058.685.672.285.9
GKD [32]IROS21√ X56.578.281.868.778.979.167.654.882.674.458.584.872.283.0
AaD [43]NIPS22√ X59.379.382.168.979.879.567.257.483.172.158.585.472.788.0
AdaCon [2]CVPR22√ X47.275.175.560.773.373.260.245.276.665.648.379.165.086.8
CoWA [19]ICML22√ X56.978.481.069.180.079.967.757.282.472.860.584.572.586.9
SCLM [34]NN22√ X58.280.381.569.379.080.769.056.882.774.760.685.073.085.3
ELR [44]ICLR23√ X58.478.781.569.279.579.366.358.082.673.459.885.172.685.8
PLUE [25]CVPR23√ X49.173.578.262.973.574.562.248.378.668.651.881.566.988.3
TPDS [35]IJCV23√ X59.380.382.170.679.480.969.856.882.174.561.285.373.587.6
DIFO-C-RN-√ √62.687.587.179.587.987.478.363.488.180.063.387.779.488.8
DIFO-C-B32-√ √70.690.688.882.590.688.880.970.188.983.470.591.283.190.3
+ +Table 3. Closed-set SFDA on DomainNet-126 (\%). SF and M means source-free and multimodal, respectively. + +
MethodVenueSFMC→PC→RC→SP→CP→RP→SR→CR→PR→SS→CS→PS→RAvg.
Source---44.659.847.553.375.346.255.362.746.455.150.759.554.7
DAPL-RN [8]TNNLS23✗✓72.487.665.972.787.665.673.272.466.273.872.987.874.8
ADCLIP-RN [30]ICCVW23✗✓71.788.166.073.286.965.273.673.068.472.374.289.375.2
SHOT [24]ICML20✓✗63.578.259.567.981.361.767.767.657.870.264.078.068.1
GKD [32]IROS21✓✗61.477.460.369.681.463.268.368.459.571.565.277.668.7
NRC [42]NIPS21✓✗62.677.158.362.981.360.764.769.458.769.465.878.767.5
AdaCon [2]CVPR22✓✗60.874.855.962.278.358.263.168.155.667.166.075.465.4
CoWA [19]ICML22✓✗64.680.660.666.279.860.869.067.260.069.065.879.968.6
PLUE [25]CVPR23✓✗59.874.056.061.678.557.961.665.953.867.564.376.064.7
TPDS [35]IJCV23✓✗62.977.159.865.679.061.566.467.058.268.664.375.367.1
DIFO-C-RN-✓✓73.889.069.474.088.770.174.874.669.674.774.388.076.7
DIFO-C-B32-✓✓76.687.274.980.087.475.680.877.375.580.576.787.380.0
+ +Table 4. Results (%) of CLIP and Source+CLIP on the four evaluation datasets. The backbone of CLIP image-encoder in CLP-C-RN and CLP-C-B32 are the same as DIFO-C-RN and DIFO-C-B32, respectively. The full results are provided in Supplementary. + +
MethodVenueOffice-31Office-HomeVisDASy→ReDomainNet-126
→A→D→W→Avg.→Ar→Cl→Pr→Rw→Avg.→C→P→R→S→Avg.
CLIP-RN [28]ICML2173.173.967.071.472.551.981.582.572.183.767.970.287.165.472.7
Source+CLIP-RN-76.390.484.083.675.457.484.485.775.782.071.871.487.366.574.3
DIFO-C-RN-78.695.393.989.379.363.187.787.579.488.874.574.288.569.776.7
CLIP-B32 [28]ICML2176.082.780.679.874.659.884.385.576.182.974.773.585.771.276.3
Source+CLIP-B32-78.593.089.687.078.962.586.187.778.882.076.873.786.070.876.8
DIFO-C-B32-83.198.096.492.582.370.490.888.883.190.380.476.987.375.380.0
+ +Comparison to CLIP based prediction results. The original CLIP model can conduct general image classification. We carry out a quantitative comparison between DIFO's adaptation performance and CLIP's performance on the four datasets, averaging the adaptation results of DIFO grouped by the target domain name. + +As presented in the bottom of Tab. 4, DIFO-C-B32 outperforms CLIP-B32 on all tasks. On average accuracy, DIFO-C-B32 increases the performance by $12.7\%$ , $7.0\%$ , $7.4\%$ and $3.7\%$ in Office-31, Office-Home, VisDA and DomainNet-126, respectively. Regarding the weak version, as reported in the top, DIFO-C-RN maintains similar advantages with the increase of $17.9\%$ , $7.3\%$ , $5.1\%$ and $4.0\%$ . The result shows that the domain generality of the original CLIP model + +cannot fully excel to the target domain, and task-specific customization is needed. + +Interestingly, compared with CLIP-B32, except for VisDA with a tiny gap of $0.9\%$ , Source+CLIP-B32 averagely improve by $7.2\%$ at most on the other datasets. Meanwhile, Source+CLIP-B32 is beaten by DIFO-C-B32 with an increase of $3.2\%$ at least. In the group of DIFO-C-RN, we have the same observation. These results imply that directly weighting the source model and CLIP is an intuitive knowledge adaptation scheme, but it is hard to perform adaptation deeply. Considering Source+CLIP is an average version, we conduct a comprehensive comparison with the weighting strategy where the weighting coefficient of CLIP prediction varies from 0.0 to 1.0. Here, we conduct this experiment + +![](images/3b26860047386a85e932091f20117cf811ba115c02bf5c3524b93519673a1edb.jpg) +Figure 4. The performance of the scheme directly weighting the source model and CLIP-B32. All results are normalized by corresponding DIFO-C-B32 accuracies for a clear view. + +based on more challenging CLIP-B32 due to its large performance gap with Source (see the first row in Tab. $1 \sim 3$ ). For a clear view, all weighted accuracies are normalized by the corresponding DIFO-C-B32 accuracies, respectively. As shown in Fig. 4, no result can exceed the value of 1.0. This indicates that weighting the source model and CLIP in a zero-shot manner cannot obtain desirable task-specific fusion, and a carefully designed distilling is necessary. + +Comparison on Partial-set and Open-set SFDA settings. These are the variations of traditional Closed-set SFDA setting, following the same as SHOT [24] (the detailed setting introduction is provided in Supplementary). As reported in Tab. 5, compared with previous best method CoWA (Partial-set) and CRS (Open-set), our DIFO-C-B32 improves by $2.4\%$ and $2.7\%$ , respectively. + +# 4.2. Model Analysis + +Feature distribution visualization. Taking task $\mathrm{Ar} \rightarrow \mathrm{Cl}$ in Office-Home as a toy experiment, we visualize feature distribution using t-SNE tool. Meanwhile, we choose 5 comparisons, including the source model (termed Source), CLIP-B32's zero shot (termed CLIP), SHOT, TPDS and Oracle (trained on domain Cl with the real labels). As shown at the top of Fig. 5, from Souce to DIFO-C-B32, category aliasing gradually relieves. Compared with Oracle, DIFO-C-B32 has the most similar distribution shape. To verify this point, we also give the 3D Density chart results arranged at the bottom of Fig. 5. These results confirm the effectiveness of our DIFO-C-B32 in terms of Feature distribution. + +Ablataion study. We evaluate the (1) effect of $L_{\mathrm{TSC}}$ , $L_{\mathrm{MCE}}$ and $L_{\mathrm{PC}}$ , (2) effect of optimization of mutual information, (3) effect of task-specific customization and (4) effect of historical prediction fusion. + +For this first issue, we conduct a progressive experiment to isolate the loss's effects. The top four rows of Tab. 6 list the ablation study results. For convenience comparison, the baseline (the first row) is the source model results. When single $L_{\mathrm{TSP}}$ or $L_{\mathrm{MCE}}$ works, the accuracy largely increases on the three datasets with an improvement of about $20\%$ in average accuracy compared with the baseline. As both of them + +Table 5. Partial-set SFDA and Open-set SFDA on Office-Home $(\%)$ . The full results are provided in Supplementary. + +
Partial-set SFDAVenueAvg.Open-set SFDAVenueAvg.
Source-62.8Source-46.6
SHOT [24]ICML2079.3SHOT [24]ICML2072.8
HCL [11]NIPS2179.6HCL [11]NIPS2172.6
CoWA [19]ICML2283.2CoWA [19]ICML2273.2
AaD [43]NIPS2279.7AaD [43]NIPS2271.8
CRS [45]CVPR2380.6CRS [45]CVPR2373.2
DIFO-C-B32-85.6DIFO-C-B32-75.9
+ +Table 6. Classification results of ablation study (%) on Office-31 Office-Home and VisDA. + +
L TSCL MCEL PCOffice-31Office-HomeVisDAAvg.
XXX78.659.249.262.3
✓XX82.477.484.481.4
X✓X82.176.588.682.4
✓✓X87.080.088.385.1
✓✓✓92.583.190.388.6
DIFO-C-B32 w/ KL90.481.589.087.0
DIFO-C-B32 w/ CLIP90.781.188.886.8
DIFO-C-B32 w/o p i'89.873.587.083.4
DIFO-C-B32 w/o p i88.982.288.986.7
+ +are adopted, the accuracy evident increase (3.7% in average, the fourth row) on the top of the case of only $L_{\mathrm{TSC}}$ and further enhanced by adopting of item $L_{\mathrm{PC}}$ (3.5% in average, the fifth row). The results indicate: (1) all objective components positively affect the final performance, (2) $L_{\mathrm{MCE}}$ , $L_{\mathrm{PC}}$ is crucial due to providing a new soft supervision for coarse-to-fine adaptation. + +For the second and third issues, we propose two variation methods of DIFO-C-B32 to evaluate the effect. One is DIFO-C-B32 w/ KL where the mutual information maximization loss in $L_{\mathrm{TSC}}$ , $L_{\mathrm{PC}}$ are replaced by KL divergence loss. The other one is DIFO-C-B32 w/ CLIP where the prompt learning-based customization for CLIP is cancelled, and the inputted prompt is set to the fixed template of "a photo of a [CLS]." during the entire adaptation. As presented in the last two rows in Tab. 6, DIFO-C-B32 (the fifth row) beats DIFO-C-B32 w/ KL and DIFO-C-B32 w/ CLIP with average improvement of $1.6\%$ at least, respectively confirming the effect of adopting mutual information optimization and task-specific customization. As for the fourth issue, its effect is verified by the performance decreases $(3.4\%$ in average at most) in the variation methods (the last two rows), which remove $p_i'$ and $p_i$ from the fusion respectively. + +# 4.3. Task-Specific Knowledge Adaptation Analysis + +In this part, we give a feature space shift analysis using the measure of MMD (maximum mean discrepancy) distance [47] to verify whether the proposed method ensures a task-specific knowledge adaptation. + +In this experiment, we first train a domain-invariant Oracle model over all Office-Home data with real labels, and use + +![](images/48a4d1c6bf2a835975c7ebb9ca66ef7ecc80b1cc9925114736e11ae7c184f4b3.jpg) +Source + +![](images/80bb58617f83c1e2f218badbda1f1316fe9012ceb00d70a371917ba91ed5f77f.jpg) +CLIP + +![](images/dd63f2cc23b49daa9938726837fbc62f7a4c03a47b55cef1e4f74dc53a17f267.jpg) +SHOT + +![](images/d2ad274d62cdddc32062fe802e18501fa327fcaa4171d78988d644e8476db72f.jpg) +TPDS + +![](images/54774a514d15f060b5a43eba493d2f7397d2efd44c030b3a89f06f5413ffba13.jpg) +DIFO-C-B32 + +![](images/4dcf522eb9519db170790167fd023ce1f48cef83ef6e98e1dc191ae44c763fd7.jpg) +Oracle + +![](images/b62710b1931928333c312cc66bcc8e12d60de47f024cfb883dc2a53202f3811b.jpg) +Figure 5. Feature distribution visualization comparison on transfer task $\mathrm{Ar}\rightarrow \mathrm{Cl}$ in Office-Home. Oracle is trained on target domain Cl using the ground-truth labels. Different colors stand for different categories. Top: t-SNE feature distribution over 65 categories. Bottom: The corresponding 3D density charts. For easy view, the first 10 categories were used in this plot. + +![](images/0326ec4ee1cb4e723da4874897b37c4ba2b2776a28bc5ec29512388bd0a81637.jpg) + +![](images/ea5c48a06ab0a1643857b0024221b51d96cfdf6b648895c2c2e7ef0bb40c3ae8.jpg) + +![](images/2ef10853082fa9699bbd21b2f10c627f83ea8163fb5541dce5820ee12427fcd3.jpg) + +![](images/00bb252782872160b32b1fa71cd361a53840792a8432ce8cc50853e66dbee666.jpg) + +![](images/532d1b5bc35f812ce1202298bdaf0abfe68e99b8cbd509bd7b902dcc336da1a4.jpg) + +![](images/c139258b696aaf76993dec4b07e0e7d1696ff1c094a31398b6fd5814118c49f3.jpg) +Figure 6. The evolving dynamics of MMD distance during adaption of $\mathrm{Ar} \rightarrow \mathrm{Cl}$ in Office-Home. Left and Right present the varying curves of MMD distance and accuracy, respectively + +![](images/3092ad539664b52a52d77b8af8750bba8d39eefc87c973bb67f83d85e7862982.jpg) + +the logits to express the ideal task-specific space $\mathcal{O}$ . After that, an analysis is conducted on the transfer task $\mathrm{Ar} \to \mathrm{Cl}$ . During this adaptation, there are $T$ (epoch number) intermediate target models and customized CLIP models. We feedforward the target data through each intermediate model and take the logits as a space. Thus, we obtain $T$ intermediate target feature spaces $\{\mathcal{U}_k\}_{k=1}^T$ and $T$ intermediate customized CLIP feature spaces $\{\mathcal{V}\}_{k=1}^T$ . Within this context, these intermediate spaces can depict the task-specific distillation to $\mathcal{O}$ . In practice, the CLIP image encoder's backbone is set to ViT-B/32. + +In the left of Fig. 6, we give the MMD distance change curve of $\{\mathcal{U}_k\}_{k=1}^T$ (in red, termed TGT) and $\{\mathcal{V}\}_{k=1}^T$ (in blue, termed CUS-CLIP), taking $\mathcal{O}$ as the original space. It is seen that at early epochs ( $1 \sim 4$ ), TGT and CUS-CLIP sharply decrease and then maintain a gradual decrease in the following epochs. Meanwhile, this change is consistent with the accuracy varying shown in the right of Fig. 6. + +These results indicate that our DIFO encourages task-specific knowledge adaptation due to converging the ideal + +task-specific space. Besides, we observe two details. First, after epoch 1, CUS-CLIP's distance reduces by 2.2, which is 58.6 time of TGT's decrease of 0.038. This is because CLIP represents a heterogeneous space of vision-language, much different from the vision space $\mathcal{O}$ . Furthermore, the large distance decrease confirms the effect of customization. Second, the synchronized distance reductions of CUS-CLIP and TGT indicate the interaction between the target model and CLIP is a crucial design for task-specific distillation. + +# 5. Conclusion + +We present an innovative approach, referred to as DIFO, designed to tackle the SFDA problem. To the best of our knowledge, this marks the initial endeavor to address SFDA by leveraging a pretrained ViL foundation model, departing from previous approaches that predominantly concentrated on self-mining auxiliary information. DIFO is featured with alternating between customization of the ViL model and the transfer of task-specific knowledge from the customized ViL model. We introduce two pivotal designs: a mutual information-based alignment for ViL customization and a most-likely category encouragement for more precise adaptation of task-specific knowledge. Our method's effectiveness is validated by state-of-the-art experimental results across four challenging datasets. + +# Acknowledgement + +This work is supported by the German Research Foundation (DFG) and National Natural Science Foundation of China (NSFC) in project Crossmodal Learning under contract Sonderforschungsbereich Transregio 169, the Hamburg Landesforschungsforderungsprojekt Cross, NSFC (61773083); NSFC (62206168, 62276048). Shanghai SAST Funding (202410013). + +# References + +[1] Alex Andonian, Shixing Chen, and Raffay Hamid. Robust cross-modal representation learning with progressive self-distillation. In CVPR, 2022. 2 +[2] Dian Chen, Dequan Wang, Trevor Darrell, and Sayna Ebrahimi. Contrastive test-time adaptation. In CVPR, 2022. 5, 6 +[3] Weijie Chen, Luojun Lin, Shicai Yang, Di Xie, Shiliang Pu, and Yueting Zhuang. Self-supervised noisy label learning for source-free unsupervised domain adaptation. 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However, due to heightened safety and privacy concerns, accessing source data freely has become difficult [18, 23]. In response, Source-Free Domain Adaptation (SFDA) has gained attention as a more practical solution, aiming to transfer a pretrained source model to the target domain using only unlabeled target data." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 320, + 244, + 531, + 371 + ], + "blocks": [ + { + "bbox": [ + 320, + 244, + 531, + 371 + ], + "lines": [ + { + "bbox": [ + 320, + 244, + 531, + 371 + ], + "spans": [ + { + "bbox": [ + 320, + 244, + 531, + 371 + ], + "type": "image", + "image_path": "33090923e17fc171744e1617cc9c005cfb6532ee449e37016a7c6c94710d50ab.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 378, + 547, + 434 + ], + "lines": [ + { + "bbox": [ + 305, + 378, + 547, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 378, + 547, + 434 + ], + "type": "text", + "content": "Figure 1. We expand beyond traditional SFDA methods that rely solely on a pretrained source model and unlabeled target data. Instead, we innovate by exploring off-the-shelf multimodal foundation models, such as CLIP, in an unsupervised manner (marked by the box with blue background)." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 450, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 547, + 617 + ], + "type": "text", + "content": "Due to the absence of source samples, traditional distribution matching approaches are no longer viable [7, 14]. The predominant alternative is self-supervised learning, which generates or mines auxiliary information to facilitate unsupervised adaptation. Two main approaches exist: constructing a pseudo source domain to leverage established UDA methods such as adversarial learning [16, 41] or domain shift minimization based on distribution measurement [5, 15, 37] and mining extra supervision from the source model [11, 18, 40] or target data [34, 42, 43]. In the presence of domain distribution shift, applying the source model to the target domain introduces inevitable errors in pseudo-labeling or auxiliary supervision, thereby limiting adaptation performance." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 714 + ], + "type": "text", + "content": "To address identified limitations, we pioneer the exploration of off-the-shelf multimodal foundation models, such as the vision-language (ViL) model CLIP [24], transcending the constraints of both the source model and target data knowledge. However, direct application of the ViL model proves unsatisfactory, lacking specialization for specific tasks. To overcome this, we propose a novel task-specific distillation approach named Distilling multiModal" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23711" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "Foundation mOdel (DIFO). Initially, we customize the ViL model through unsupervised prompt learning for imposing task-specific information. Subsequently, we distil the knowledge from this customized ViL model to the target model, with joint supervision through two designed regularization terms: (1) most-likely category encouragement for coarse-grained distillation and (2) predictive consistency for fine-grained distillation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 168, + 289, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 168, + 289, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 168, + 289, + 312 + ], + "type": "text", + "content": "Our contributions are summarized as follows. (1) Pioneering the use of generic but heterogeneous knowledge sources (e.g., the off-the-shelf ViL model) for the SFDA problem, transcending the limited knowledge boundary of a pretrained source model and unlabeled target data. (2) Development of the novel DIFO approach to effectively distill useful task-specific knowledge from the general-purpose ViL model. (3) Extensive evaluation on standard benchmarks, demonstrating the significant superiority of our DIFO over previous state-of-the-art alternatives under conventional closed-set settings, as well as more challenging partial-set and open-set settings." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 320, + 134, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 134, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 134, + 333 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 340, + 289, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 289, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 289, + 435 + ], + "type": "text", + "content": "Source-free domain adaptation. Existing SFDA approaches fall into three distinct categories. The first explicitly aligns the pseudo source domain with the target domain, treating SFDA as a specialized case of unsupervised domain adaptation. This alignment is achieved by constructing the pseudo source domain through a generative model [21, 38] or by splitting the target domain based on prior source hypotheses [6]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 437, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 289, + 567 + ], + "type": "text", + "content": "The second group extracts cross-domain factors from the source domain and transfers them in successive model adaptation for aligning feature distributions across the two domains. For example, [31] establishes a mapping relationship from a sample and its exemplar Support Vector Machine (SVM) (an individual classifier) on the source domain to ensure individual classification on the target domain. Some approaches leverage pre-trained source models to generate auxiliary factors, such as multi-hypothesis [18], prototypes [36], source distribution estimation [5], or hard samples [20] to aid in feature alignment." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 568, + 289, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 289, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 289, + 628 + ], + "type": "text", + "content": "The third group incorporates auxiliary information refined from the unlabeled target domain. In addition to widely used pseudo-labels [3, 24], geometry information, such as intrinsic neighborhood structure [33] and target data manifold [34], has also been exploited." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 628, + 289, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 289, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 289, + 687 + ], + "type": "text", + "content": "Despite continual advancements, these methods are limited by the knowledge derived solely from the pretrained source model and unlabeled target data. We break this limitation by tapping into the rich knowledge encoded in off-the-shelf multimodal foundation models." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "Large multimodal model. Multimodal vision-language (ViL) models, such as CLIP [28] and ALIGN [13], have" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "shown promise across various mono-modal and multimodal tasks by capturing modality-invariant features. Approaches in this domain can be broadly categorized into two lines." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 109, + 547, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 109, + 547, + 169 + ], + "spans": [ + { + "bbox": [ + 304, + 109, + 547, + 169 + ], + "type": "text", + "content": "The first line focuses on enhancing ViL model performance. For instance, in [8, 46], prompt learning optimizes the text encoder through the use of tailored, learnable prompts designed for specific scenarios. Other efforts aim to improve data efficiency by repurposing noisy data [1]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 170, + 547, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 170, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 547, + 289 + ], + "type": "text", + "content": "The second line utilizes ViL models as external knowledge to enhance downstream tasks, as demonstrated in this paper. Previous work in knowledge transfer primarily falls into two frameworks. For the first scheme, where the ViL model is directly applied to the target task in a zero-shot fashion [22], domain generality is leveraged without task-specific refinement. The second scheme does not focus on source model adaptation. Instead, it fine-tunes the ViL model to the target domain through prompt or adaptor learning with an amount of manal labels [4]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 291, + 548, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 548, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 548, + 399 + ], + "type": "text", + "content": "A relevant method to our DIFO is the UDA method DAPL [8]. Although both adopt CLIP, they differ significantly in problem setting and methodology. DAPL employs CLIP to learn domain-specific prompts, aiming to disentangle domain and category information in CLIP's visual features. In contrast, DIFO aligns target features to a progressively customized vision-language latent space in a memory-aware fashion. Importantly, DAPL requires labeled source data, making it inapplicable in SFDA." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 412, + 389, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 412, + 389, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 412, + 389, + 426 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": "Problem statement. In the context of two distinct yet interrelated domains—namely, the labeled source domain and the unlabeled target domain—both characterized by the same set of " + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": " categories, the following notation is employed. The source samples and their corresponding labels are represented as " + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_s" + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_s" + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": " respectively. Similarly, the target samples and their true labels are denoted as " + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{X}_t = \\{\\pmb{x}_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}_t = \\{y_i\\}_{i=1}^n" + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 433, + 547, + 529 + ], + "type": "text", + "content": " signifies the number of samples." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "text", + "content": "We aim to learn a target model " + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\theta_t: \\mathcal{X}_t \\to \\mathcal{Y}_t" + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "text", + "content": ". This involves utilizing (1) a pre-trained source model " + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\theta_s: \\mathcal{X}_s \\to \\mathcal{Y}_s" + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "text", + "content": ", (2) unlabeled target data, and (3) a Visual-Language (ViL) model denoted as " + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "inline_equation", + "content": "\\theta_v" + }, + { + "bbox": [ + 304, + 530, + 547, + 578 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 580, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 547, + 616 + ], + "type": "text", + "content": "Overview. As depicted in Fig. 2, the proposed DIFO framework alternates between two distinct steps to customize and distill the off-the-shelf ViL knowledge." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "content": "In the first step, we engage in prompt learning on the ViL model for the purpose of task-specific customization. This serves to mitigate the guidance error within the ViL model. In particular, we adopt a mutual information-based alignment approach. This approach is characterized by its richness in context and interaction between the target model and the ViL model, as opposed to placing blind trust in either model alone as conventional methods." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23712" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 75, + 72, + 520, + 200 + ], + "blocks": [ + { + "bbox": [ + 75, + 72, + 520, + 200 + ], + "lines": [ + { + "bbox": [ + 75, + 72, + 520, + 200 + ], + "spans": [ + { + "bbox": [ + 75, + 72, + 520, + 200 + ], + "type": "image", + "image_path": "b9a880d506f08b86ecaf952ad0b735640344cbcc9c7c29ab5f95679bbae724ee.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "text", + "content": "Figure 2. Overview of our DIFO: The process involves two alternating steps. First, we perform (a) task-specific customization of a ViL model through task-specific prompt learning (" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{TSC}}" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "text", + "content": "). This is achieved under soft predictive guidance using mutual information maximization. Second, we undertake (b) memory-aware knowledge adaptation, incorporating two regularizations: most-likely category encouragement (" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MCE}}" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "text", + "content": ") predicted by our dynamic memory-aware predictor, along with the typical predictive consistency (" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{PC}}" + }, + { + "bbox": [ + 46, + 209, + 548, + 266 + ], + "type": "text", + "content": "). These regularizations are designed to facilitate a coarse-to-fine adaptation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 281, + 290, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 290, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 290, + 376 + ], + "type": "text", + "content": "In the second step, knowledge adaptation takes place within a unique constraint that encourages the identification of the most probable category labels in the logit space, while concurrently maintaining the typical predictive consistency. The most likely category labels are determined by a carefully designed memory-aware predictor, which dynamically integrates knowledge from both the target model and the ViL model in a cumulative fashion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 381, + 257, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 381, + 257, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 381, + 257, + 395 + ], + "type": "text", + "content": "3.1. Task-Specific ViL Model Customization" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 400, + 288, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 288, + 519 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 288, + 519 + ], + "type": "text", + "content": "We adopt the prompt learning framework for ViL model customization, with all the parameters of the ViL model frozen throughout. The only learnable part in customization is the prompts each assigned for a specific class. To optimize these prompts, we need a useful supervision. In SFDA, however, it is challenging to customize such a domain-generic ViL model towards the target domain, at the absence of a well-trained target domain model. This is because, none of them can reasonably make predictions. That means there is no clearly good supervision signals available." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "text", + "content": "To address this challenge, we propose to explore the wisdom of the crowd by leveraging their predictive interaction as the supervision. Formally, we denote the predictions by the target model and the ViL model as " + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "inline_equation", + "content": "\\theta_t(\\boldsymbol{x}_i)" + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "inline_equation", + "content": "\\theta_v(\\boldsymbol{x}_i)" + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "text", + "content": ", respectively, given an unlabeled target sample " + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_k" + }, + { + "bbox": [ + 46, + 520, + 288, + 604 + ], + "type": "text", + "content": ". We conduct the customization by maximizing the mutual information of their predictions as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 75, + 609, + 287, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 609, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 75, + 609, + 287, + 625 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {T S C}} = - \\min _ {\\boldsymbol {v}} \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\chi_ {t}} \\mathrm {I} \\left(\\theta_ {t} \\left(\\boldsymbol {x} _ {i}\\right), \\theta_ {v} \\left(\\boldsymbol {x} _ {i}, \\boldsymbol {v}\\right)\\right) \\tag {1}", + "image_path": "a3912ff0db9ec4b55b8acbed7d82b9cdf65d6487ecc620720724e8d0f87a72af.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "type": "text", + "content": " is the prompt context to be learned and the function " + }, + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\mathrm{I}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 630, + 287, + 653 + ], + "type": "text", + "content": " measures the mutual information [12]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 714 + ], + "type": "text", + "content": "This alignment design differs significantly from the conventional adoption of the Kullback-Leibler (KL) divergence. First of all, the mutual information is a lower optimization bound than KL divergence, facilitating deeper alignment (see Theorem 1 with the proof provided in Supplementary)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "spans": [ + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "text", + "content": "Theorem 1 Given two random variables " + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "inline_equation", + "content": "X, Y" + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "text", + "content": ". Their mutual information " + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "inline_equation", + "content": "I(X,Y)" + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "text", + "content": " and KL divergence " + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(X||Y)" + }, + { + "bbox": [ + 305, + 281, + 548, + 317 + ], + "type": "text", + "content": " satisfy the unequal relationship as follows." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 369, + 326, + 546, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 326, + 546, + 340 + ], + "spans": [ + { + "bbox": [ + 369, + 326, + 546, + 340 + ], + "type": "interline_equation", + "content": "- \\mathrm {I} (X, Y) \\leq D _ {\\mathrm {K L}} (X, Y). \\tag {2}", + "image_path": "d59a0ef76865c598ff2690a23e6d91dfaeab7493adf78f04aaa0246b926e203a.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "spans": [ + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "type": "text", + "content": "Crucially, the KL divergence exhibits an inherent bias towards a specific prediction, making it less suitable for our context where none of the predictions holds a significant advantage. On the contrary, mutual information considers the joint distribution or correlation between the two predictions. This distinction arises from their respective definitions: " + }, + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "type": "inline_equation", + "content": "-\\mathrm{I}(X,Y) = -H(X) + H(X|Y)" + }, + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{KL}}(X,Y) = -H(X) + H(X:Y)" + }, + { + "bbox": [ + 305, + 354, + 547, + 452 + ], + "type": "text", + "content": ", where" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 345, + 460, + 547, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 460, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 345, + 460, + 547, + 484 + ], + "type": "interline_equation", + "content": "H (X \\mid Y) = - \\sum_ {\\leftarrow} p (\\boldsymbol {x}, \\boldsymbol {y}) \\log p (\\boldsymbol {x} \\mid \\boldsymbol {y}) \\tag {3}", + "image_path": "d1418993d993f6e085dc510ab844c5bc9dae0988831e26463d4cbc65240ac3dc.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 347, + 479, + 488, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 479, + 488, + 498 + ], + "spans": [ + { + "bbox": [ + 347, + 479, + 488, + 498 + ], + "type": "interline_equation", + "content": "H \\left(X: Y\\right) = - \\sum p (\\boldsymbol {x}) \\log p (\\boldsymbol {y}).", + "image_path": "548dcbdb6e3aac56811e9fd225e4b91dfb6b5ca8b38c8bada55c52adc5ce4b21.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 507, + 548, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 548, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 548, + 591 + ], + "type": "text", + "content": "The conditional entropy component " + }, + { + "bbox": [ + 304, + 507, + 548, + 591 + ], + "type": "inline_equation", + "content": "H(X|Y)" + }, + { + "bbox": [ + 304, + 507, + 548, + 591 + ], + "type": "text", + "content": " of mutual information explicitly captures the joint distributions, a feature absent in KL divergence. Empirically, we also confirm the significance of incorporating this joint distribution-based interaction between the two predictions during the customization of the ViL model (see ablation study in Tab. 6 and task-specific knowledge adaptation analysis in Section 4.3)." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 599, + 513, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 513, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 513, + 612 + ], + "type": "text", + "content": "3.2. Memory-Aware Knowledge Adaptation" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 713 + ], + "type": "text", + "content": "As previously mentioned, even with customization for the target domain, the ViL model may not be fully adapted due to no robust target model available in prior. This limitation hinders effective knowledge adaptation at this stage. To address this issue, we propose the incorporation of a specialized memory-aware predictor to provide additional learning guidance – most-likely category encouragement, complementing the conventional predictive consistency constraint." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23713" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 179 + ], + "type": "text", + "content": "Most-likely category encouragement. The rationale behind incorporating this learning constraint is to harness the collective knowledge of both the target model and the ViL model in order to enhance the discernment of probable category labels for each sample. Given the sluggish nature of this search process, it has been devised to function as a form of learning regularization. An illustration of this regularization process is presented in Fig. 3. Specifically, it is realized through two distinct steps as detailed below." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "type": "text", + "content": "(I) Memory-aware predictor. We initiate the process by generating pseudo-labels that represent the most likely category distribution, utilizing historical information stored in a prediction bank. The prediction bank archives two types of historical data for all samples in the target domain: (1) predictions from the target model denoted by " + }, + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\{p_i\\}_{i = 1}^n" + }, + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "type": "text", + "content": " and (2) predictions from the ViL model denoted by " + }, + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\{p_i'\\}_{i = 1}^n" + }, + { + "bbox": [ + 46, + 181, + 287, + 266 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 266, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 386 + ], + "type": "text", + "content": "Throughout the adaptation process, the predictions from the target model are updated iteratively. At the end of each training iteration, the newly predicted labels for the training batch from the target model replace their counterparts in the prediction bank. In contrast, predictions from the ViL model are updated collectively in an epoch-wise manner, triggering updates every " + }, + { + "bbox": [ + 46, + 266, + 287, + 386 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 266, + 287, + 386 + ], + "type": "text", + "content": " iterations. This mixed-update strategy is designed to strike a balance between maintaining the stability of the customized ViL model's guidance and capturing the task-specific dynamics inherent in the adaptation process." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 387, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 288, + 422 + ], + "type": "text", + "content": "Based on the provided prediction bank, the creation of a pseudo-label for the most probable category involves a historical prediction fusion process as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 436, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 436, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 115, + 436, + 287, + 449 + ], + "type": "interline_equation", + "content": "\\bar {\\boldsymbol {p}} _ {i} = \\omega \\boldsymbol {p} _ {i} + (1 - \\omega) \\boldsymbol {p} _ {i} ^ {\\prime}. \\tag {4}", + "image_path": "46f8fb757267334272a09d8a5000947b94fb89416bb66a23204a17760029ac4f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": "Here, the weight " + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": ", drawn from an Exponential distribution with parameter " + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": ", is a crucial factor. This fusion introduces dynamic bias rectification (represented by " + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i" + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": ") based on the guidance from the customized ViL model " + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "inline_equation", + "content": "(\\pmb{p}_i')" + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": ". The role of " + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\pmb{p}_i" + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": " is to provide adjustments, leading us to adopt an asymmetric random weighting approach represented by " + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 462, + 287, + 533 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": "(II) Category attention calibration. Subsequently, we formulate a regularization technique employing pseudo-labels acquired through category attention calibration. Specifically, we begin by identifying the top- " + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": " most probable categories using " + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\bar{p}_i" + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": ". The indices of these identified categories are denoted by " + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_i = \\{m_k\\}_{k=1}^N" + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": ". With " + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_i" + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": ", the target model's logit of a target domain sample " + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "inline_equation", + "content": "x_i" + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "inline_equation", + "content": "l_i" + }, + { + "bbox": [ + 46, + 535, + 288, + 643 + ], + "type": "text", + "content": ", is segregated into positive and negative category groups. We define this regularization as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 60, + 654, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 60, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 60, + 654, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L _ {\\mathrm {M C E}} = \\min _ {\\theta t} \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\mathcal {X} _ {t}} \\log \\frac {\\exp \\left(a _ {i} / \\tau\\right)}{\\sum_ {j \\neq \\mathcal {M} _ {i}} \\exp \\left(b _ {i} \\cdot l _ {i , j} / \\tau\\right)} \\tag {5} \\\\ a _ {i} = \\prod_ {k = 1} ^ {N} \\boldsymbol {l} _ {i, m _ {k}}, \\quad b _ {i} = \\sum_ {k = 1} ^ {N} \\boldsymbol {l} _ {i, m _ {k}} \\\\ \\end{array}", + "image_path": "43b882e21273f722e365f8a35d78304883444ce71459070f1f8c0fd156e71add.jpg" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 72, + 539, + 191 + ], + "blocks": [ + { + "bbox": [ + 315, + 72, + 539, + 191 + ], + "lines": [ + { + "bbox": [ + 315, + 72, + 539, + 191 + ], + "spans": [ + { + "bbox": [ + 315, + 72, + 539, + 191 + ], + "type": "image", + "image_path": "102c3302efd2d097288c9fa34db29e0e59f88101a106c60a01080c5074051551.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 200, + 547, + 256 + ], + "lines": [ + { + "bbox": [ + 304, + 200, + 547, + 256 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 547, + 256 + ], + "type": "text", + "content": "Figure 3. Illustration of most-likely category encouragement. In contrast to the conventional approach that assigns equal importance to all categories (depicted by the gray line), our approach (represented by the black line) introduces additional supervision by incorporating extra knowledge about the two most likely categories." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "inline_equation", + "content": "l_{i,a}" + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "text", + "content": "-th element of " + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 268, + 547, + 292 + ], + "type": "text", + "content": " is the temperature parameter." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": "In Eq. (5), we note that the product operation with " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": " in the numerator amplifies penalties for the probability decrease on the most likely categories compared to the sum form. Similarly, the sum with " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": " in the denominator serves as an increasing weighting parameter to enhance suppression of values at other locations. Moreover, " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": " is more sensitive to changes than " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": " due to " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\frac{\\partial a_{i}}{\\partial m_{k}} \\propto O(n^{N - 1})" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "\\frac{\\partial b_{i}}{\\partial m_{k}} \\propto O(1)" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": ". By combining the use of " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "a_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "b_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": ", we globally impose a calibration effect on the elements corresponding to the most likely categories within the logit " + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "inline_equation", + "content": "l_{i}" + }, + { + "bbox": [ + 304, + 293, + 547, + 437 + ], + "type": "text", + "content": ". Essentially, attention is introduced to these potential categories, as illustrated in the box with a yellow background in Fig. 3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 439, + 547, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 439, + 547, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 439, + 547, + 473 + ], + "type": "text", + "content": "Predictive Consistency. For the purpose of knowledge adaptation, we incorporate the conventional predictive consistency loss as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 317, + 482, + 545, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 482, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 317, + 482, + 545, + 498 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {P C}} = \\min _ {\\theta_ {t}} \\left[ - \\mathbb {E} _ {\\boldsymbol {x} _ {i} \\in \\mathcal {X} _ {t}} \\mathrm {I} \\left(\\theta_ {t} (\\boldsymbol {x} _ {i}), \\theta_ {v} (\\boldsymbol {x} _ {i}, \\boldsymbol {v} *)\\right) + \\alpha L _ {B} \\right], \\tag {6}", + "image_path": "4d151150ec43c7b56e0f44515e67e2e412b2c58e7f2167387fc63ab0af24eb50.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\theta_t(\\pmb{x}_i)" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " represents the target prediction, " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\theta_v(\\pmb{x}_i, \\pmb{v})" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " denotes the ViL prediction, and " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " is the prompt context learned during the initial phase of task-specific customization. The function " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\mathrm{I}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " corresponds to the mutual information function. The parameter " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " serves as a trade-off parameter, and the category balance term " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{B}} = \\mathrm{KL}(\\bar{\\pmb{q}} || \\frac{1}{C})" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " aligns with previous approaches [35, 42], preventing solution collapse by ensuring the empirical label distribution " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\bar{\\pmb{q}}" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": " matches the uniform distribution " + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "inline_equation", + "content": "\\frac{1}{C}" + }, + { + "bbox": [ + 304, + 506, + 547, + 639 + ], + "type": "text", + "content": ". For the reasons elaborated in Section 3.1, we employ mutual information for alignment." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 647, + 400, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 400, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 400, + 659 + ], + "type": "text", + "content": "3.3. Model training" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "To systematically distill and leverage task-specific knowledge from the ViL model, we adopt an epoch-wise training approach for DIFO. The training process is divided into " + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": " epochs, each comprising two stages aligned with the two" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23714" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 175, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 175, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 175, + 83 + ], + "type": "text", + "content": "Algorithm 1 Training of DIFO" + } + ] + } + ], + "index": 0 + 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During the first stage, training is governed by the objective " + }, + { + "bbox": [ + 46, + 445, + 288, + 482 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{TSC}}" + }, + { + "bbox": [ + 46, + 445, + 288, + 482 + ], + "type": "text", + "content": ", and in the subsequent second stage, the objective function transitions to" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 117, + 491, + 287, + 503 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 491, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 117, + 491, + 287, + 503 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {M K A}} = L _ {\\mathrm {P C}} + \\beta L _ {\\mathrm {M C E}}, \\tag {7}", + "image_path": "9162c1d124095119049975345877b99bd04495c104d862347777602c1ff2430d.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 511, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 511, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 511, + 287, + 536 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 511, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 511, + 287, + 536 + ], + "type": "text", + "content": " is a trade-off parameter. We summarize the whole training procedure of DIFO in Algorithm 1." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 47, + 545, + 127, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 545, + 127, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 545, + 127, + 559 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 46, + 566, + 288, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 288, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 288, + 638 + ], + "type": "text", + "content": "Datasets. We evaluate four standard benchmarks: Office-31 [29], Office-Home [39], VisDA [26] and DomainNet-126 [27]. Among them, Office-31 is a small-scaled dataset; Office-Home is a medium-scale dataset; VisDA and DomainNet-126 are both large-scale datasets. The details of the four datasets are provided in Supplementary." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 713 + ], + "type": "text", + "content": "Competitor. We compare DIFO with 18 existing top-performing methods into three groups. (1) The first group contains Source (the source model's results), CLIP [28] and Source+CLIP where Source+CLIP directly average the results of the source model and CLIP. (2) The second group includes three state-of-the-art UDA methods" + } + ] + } + ], + "index": 32 + }, + { + "type": "table", + "bbox": [ + 307, + 91, + 545, + 220 + ], + "blocks": [ + { + "bbox": [ + 345, + 71, + 506, + 82 + ], + "lines": [ + { + "bbox": [ + 345, + 71, + 506, + 82 + ], + "spans": [ + { + "bbox": [ + 345, + 71, + 506, + 82 + ], + "type": "text", + "content": "Table 1. Closed-set SFDA on Office-31 (%)" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 91, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 307, + 91, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 307, + 91, + 545, + 220 + ], + "type": "table", + "html": "
MethodVenueA→DA→WD→AD→WW→AW→DAvg.
Source-79.176.659.995.561.498.878.6
SHOT [24]ICML2093.791.174.298.274.6100.88.6
NRC [42]NIPS2196.090.875.399.075.0100.89.4
GKD [32]IROS2194.691.675.198.775.1100.89.2
HCL [11]NIPS2194.792.575.998.277.7100.89.8
AaD [43]NIPS2296.492.175.099.176.5100.89.9
AdaCon [2]CVPR2287.783.173.791.377.672.881.0
CoWA [19]ICML2294.495.276.298.577.699.890.3
SCLM [34]NN2295.890.075.598.975.599.889.4
ELR [44]ICLR2393.893.376.298.076.9100.89.6
PLUE [25]CVPR2389.288.472.897.169.697.985.8
TPDS [35]IJCV2397.194.575.798.775.599.890.2
DIFO-C-RN-93.692.178.595.778.897.089.3
DIFO-C-B32-97.295.583.097.283.298.892.5
", + "image_path": "8b47cc14db011ec6371fa7fbacdae87b5e03f71b5c8c5d8619e79b79411a21f4.jpg" + } + ] + } + ], + "index": 34, + "angle": 0, + "type": "table_body" + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 243, + 547, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 243, + 547, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 243, + 547, + 316 + ], + "type": "text", + "content": "DAPL [8], PADCLIP [17] and ADCLIP [30] that are also multimodal guiding-based. (3) The third group comprises 13 current state-of-the-art SFDA models: SHOT [24], NRC [42], GKD [32], HCL [11], AaD [43], AdaCon [2], CoWA [19], SCLM [34], ELR [44], PLUE [25], TPDS [35] and CRS [45]." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 317, + 547, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 547, + 412 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 547, + 412 + ], + "type": "text", + "content": "For comprehensive comparisons, we implement DIFO in two variants: (1) DIFO-C-RN (weak version) and (2) DIFO-C-B32 (strong version). The key distinction lies in the backbone of the CLIP image-encoder. Specifically, for DIFO-C-RN, ResNet101 [10] is employed on the VisDA dataset, while ResNet50 [10] is used on the other three datasets. On the other hand, DIFO-C-B32 adopts ViT-B/32 [9] as the backbone across all datasets." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 467 + ], + "type": "text", + "content": "SFDA settings. We consider three distinct settings: the conventional closed-set SFDA setting, the partial-set and the open-set SFDA settings. The experiment implementation details are provided in Supplementary." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 306, + 479, + 423, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 479, + 423, + 491 + ], + "spans": [ + { + "bbox": [ + 306, + 479, + 423, + 491 + ], + "type": "text", + "content": "4.1. Comparison Results" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "Comparison on Closed-set SFDA setting. The comparisons of the four evaluation datasets are listed in Tab. 1~3. DIFO-C-B32 surpasses the previous best method CoWA (on Office-31), TPDS (on Office-Home) and PLUE (on VisDA) and GKD (on DomainNet-126) by " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "9.6\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "2.0\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "11.3\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": " in average accuracy respectively. Specifically, DIFO-C-B32 obtains the best results on 4 out of 6 tasks on Office-31 while surpassing previous methods on all tasks of the other three datasets. As for DIFO-C-RN, besides Office-31, it obtains the second-best results and beat the previous best methods by " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "5.9\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "inline_equation", + "content": "8.0\\%" + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": " on Office-Home, VisDA and DomainNet-126 in average accuracy. The comparison of DIFO-C-RN shows that our method can still perform well despite using a weaker CLIP. Based on a strong CLIP (see results of DIFO-C-B32), our method's performance can improve further as we expected. All of the results indicate that the DIFO can boost the cross-domain performance in closed-set SFDA setting." + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23715" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 102, + 545, + 255 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 2. Closed-set SFDA on Office-Home and VisDA (%). SF and M means source-free and multimodal, respectively; the full results on VisDA are in Supplementary." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 102, + 545, + 255 + ], + "lines": [ + { + "bbox": [ + 48, + 102, + 545, + 255 + ], + "spans": [ + { + "bbox": [ + 48, + 102, + 545, + 255 + ], + "type": "table", + "html": "
MethodVenueSF MOffice-HomeVisDASy→Re
Ar→ClAr→PrAr→RwCl→ArCl→PrCl→RwPr→ArPr→ClPr→RwRw→ArRw→ClRw→PrAvg.
Source--43.767.073.949.960.162.551.740.972.664.246.378.159.249.2
DAPL-RN [8]TNNLS23X √54.184.384.874.483.785.074.554.684.875.254.783.874.586.9
PADCLIP-RN [17]ICCV23X √57.584.083.877.885.584.776.359.285.478.160.286.776.688.5
ADCLIP-RN [30]ICCVW23X √55.485.285.676.185.886.276.756.185.476.856.185.575.987.7
SHOT [24]ICML20√ X56.777.980.668.078.079.467.954.582.374.258.684.571.982.7
NRC [42]NIPS21√ X57.780.382.068.179.878.665.356.483.071.058.685.672.285.9
GKD [32]IROS21√ X56.578.281.868.778.979.167.654.882.674.458.584.872.283.0
AaD [43]NIPS22√ X59.379.382.168.979.879.567.257.483.172.158.585.472.788.0
AdaCon [2]CVPR22√ X47.275.175.560.773.373.260.245.276.665.648.379.165.086.8
CoWA [19]ICML22√ X56.978.481.069.180.079.967.757.282.472.860.584.572.586.9
SCLM [34]NN22√ X58.280.381.569.379.080.769.056.882.774.760.685.073.085.3
ELR [44]ICLR23√ X58.478.781.569.279.579.366.358.082.673.459.885.172.685.8
PLUE [25]CVPR23√ X49.173.578.262.973.574.562.248.378.668.651.881.566.988.3
TPDS [35]IJCV23√ X59.380.382.170.679.480.969.856.882.174.561.285.373.587.6
DIFO-C-RN-√ √62.687.587.179.587.987.478.363.488.180.063.387.779.488.8
DIFO-C-B32-√ √70.690.688.882.590.688.880.970.188.983.470.591.283.190.3
", + "image_path": "43537830b4bbe76f353d55ac4c2cd5cb01581102ce86a46159f6a18b4c389a48.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 285, + 545, + 402 + ], + "blocks": [ + { + "bbox": [ + 94, + 264, + 499, + 277 + ], + "lines": [ + { + "bbox": [ + 94, + 264, + 499, + 277 + ], + "spans": [ + { + "bbox": [ + 94, + 264, + 499, + 277 + ], + "type": "text", + "content": "Table 3. Closed-set SFDA on DomainNet-126 (\\%). SF and M means source-free and multimodal, respectively." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 285, + 545, + 402 + ], + "lines": [ + { + "bbox": [ + 48, + 285, + 545, + 402 + ], + "spans": [ + { + "bbox": [ + 48, + 285, + 545, + 402 + ], + "type": "table", + "html": "
MethodVenueSFMC→PC→RC→SP→CP→RP→SR→CR→PR→SS→CS→PS→RAvg.
Source---44.659.847.553.375.346.255.362.746.455.150.759.554.7
DAPL-RN [8]TNNLS23✗✓72.487.665.972.787.665.673.272.466.273.872.987.874.8
ADCLIP-RN [30]ICCVW23✗✓71.788.166.073.286.965.273.673.068.472.374.289.375.2
SHOT [24]ICML20✓✗63.578.259.567.981.361.767.767.657.870.264.078.068.1
GKD [32]IROS21✓✗61.477.460.369.681.463.268.368.459.571.565.277.668.7
NRC [42]NIPS21✓✗62.677.158.362.981.360.764.769.458.769.465.878.767.5
AdaCon [2]CVPR22✓✗60.874.855.962.278.358.263.168.155.667.166.075.465.4
CoWA [19]ICML22✓✗64.680.660.666.279.860.869.067.260.069.065.879.968.6
PLUE [25]CVPR23✓✗59.874.056.061.678.557.961.665.953.867.564.376.064.7
TPDS [35]IJCV23✓✗62.977.159.865.679.061.566.467.058.268.664.375.367.1
DIFO-C-RN-✓✓73.889.069.474.088.770.174.874.669.674.774.388.076.7
DIFO-C-B32-✓✓76.687.274.980.087.475.680.877.375.580.576.787.380.0
", + "image_path": "7ce10d786dd1534b64b228c8ba95118f362c46399df7dc69193bbdc8856f3452.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 443, + 545, + 519 + ], + "blocks": [ + { + "bbox": [ + 46, + 411, + 546, + 436 + ], + "lines": [ + { + "bbox": [ + 46, + 411, + 546, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 546, + 436 + ], + "type": "text", + "content": "Table 4. Results (%) of CLIP and Source+CLIP on the four evaluation datasets. The backbone of CLIP image-encoder in CLP-C-RN and CLP-C-B32 are the same as DIFO-C-RN and DIFO-C-B32, respectively. The full results are provided in Supplementary." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 443, + 545, + 519 + ], + "lines": [ + { + "bbox": [ + 50, + 443, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 50, + 443, + 545, + 519 + ], + "type": "table", + "html": "
MethodVenueOffice-31Office-HomeVisDASy→ReDomainNet-126
→A→D→W→Avg.→Ar→Cl→Pr→Rw→Avg.→C→P→R→S→Avg.
CLIP-RN [28]ICML2173.173.967.071.472.551.981.582.572.183.767.970.287.165.472.7
Source+CLIP-RN-76.390.484.083.675.457.484.485.775.782.071.871.487.366.574.3
DIFO-C-RN-78.695.393.989.379.363.187.787.579.488.874.574.288.569.776.7
CLIP-B32 [28]ICML2176.082.780.679.874.659.884.385.576.182.974.773.585.771.276.3
Source+CLIP-B32-78.593.089.687.078.962.586.187.778.882.076.873.786.070.876.8
DIFO-C-B32-83.198.096.492.582.370.490.888.883.190.380.476.987.375.380.0
", + "image_path": "80299e001c22f733dd14e620a86da90967f52c020d00a1c0ff17df600b691346.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 539, + 288, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 288, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 288, + 612 + ], + "type": "text", + "content": "Comparison to CLIP based prediction results. The original CLIP model can conduct general image classification. We carry out a quantitative comparison between DIFO's adaptation performance and CLIP's performance on the four datasets, averaging the adaptation results of DIFO grouped by the target domain name." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "As presented in the bottom of Tab. 4, DIFO-C-B32 outperforms CLIP-B32 on all tasks. On average accuracy, DIFO-C-B32 increases the performance by " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "12.7\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "7.0\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "7.4\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "3.7\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " in Office-31, Office-Home, VisDA and DomainNet-126, respectively. Regarding the weak version, as reported in the top, DIFO-C-RN maintains similar advantages with the increase of " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "17.9\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "7.3\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "inline_equation", + "content": "4.0\\%" + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": ". The result shows that the domain generality of the original CLIP model" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 539, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 539, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 305, + 539, + 545, + 563 + ], + "type": "text", + "content": "cannot fully excel to the target domain, and task-specific customization is needed." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Interestingly, compared with CLIP-B32, except for VisDA with a tiny gap of " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": ", Source+CLIP-B32 averagely improve by " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "7.2\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " at most on the other datasets. Meanwhile, Source+CLIP-B32 is beaten by DIFO-C-B32 with an increase of " + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": " at least. In the group of DIFO-C-RN, we have the same observation. These results imply that directly weighting the source model and CLIP is an intuitive knowledge adaptation scheme, but it is hard to perform adaptation deeply. Considering Source+CLIP is an average version, we conduct a comprehensive comparison with the weighting strategy where the weighting coefficient of CLIP prediction varies from 0.0 to 1.0. Here, we conduct this experiment" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23716" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 281, + 178 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 281, + 178 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 281, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 281, + 178 + ], + "type": "image", + "image_path": "3b26860047386a85e932091f20117cf811ba115c02bf5c3524b93519673a1edb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 180, + 288, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 180, + 288, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 180, + 288, + 213 + ], + "type": "text", + "content": "Figure 4. The performance of the scheme directly weighting the source model and CLIP-B32. All results are normalized by corresponding DIFO-C-B32 accuracies for a clear view." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 225, + 288, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 225, + 288, + 322 + ], + "spans": [ + { + "bbox": [ + 45, + 225, + 288, + 322 + ], + "type": "text", + "content": "based on more challenging CLIP-B32 due to its large performance gap with Source (see the first row in Tab. " + }, + { + "bbox": [ + 45, + 225, + 288, + 322 + ], + "type": "inline_equation", + "content": "1 \\sim 3" + }, + { + "bbox": [ + 45, + 225, + 288, + 322 + ], + "type": "text", + "content": "). For a clear view, all weighted accuracies are normalized by the corresponding DIFO-C-B32 accuracies, respectively. As shown in Fig. 4, no result can exceed the value of 1.0. This indicates that weighting the source model and CLIP in a zero-shot manner cannot obtain desirable task-specific fusion, and a carefully designed distilling is necessary." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "type": "text", + "content": "Comparison on Partial-set and Open-set SFDA settings. These are the variations of traditional Closed-set SFDA setting, following the same as SHOT [24] (the detailed setting introduction is provided in Supplementary). As reported in Tab. 5, compared with previous best method CoWA (Partial-set) and CRS (Open-set), our DIFO-C-B32 improves by " + }, + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 46, + 324, + 288, + 409 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 415, + 142, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 142, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 142, + 428 + ], + "type": "text", + "content": "4.2. Model Analysis" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 434, + 288, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 434, + 288, + 577 + ], + "spans": [ + { + "bbox": [ + 45, + 434, + 288, + 577 + ], + "type": "text", + "content": "Feature distribution visualization. Taking task " + }, + { + "bbox": [ + 45, + 434, + 288, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{Ar} \\rightarrow \\mathrm{Cl}" + }, + { + "bbox": [ + 45, + 434, + 288, + 577 + ], + "type": "text", + "content": " in Office-Home as a toy experiment, we visualize feature distribution using t-SNE tool. Meanwhile, we choose 5 comparisons, including the source model (termed Source), CLIP-B32's zero shot (termed CLIP), SHOT, TPDS and Oracle (trained on domain Cl with the real labels). As shown at the top of Fig. 5, from Souce to DIFO-C-B32, category aliasing gradually relieves. Compared with Oracle, DIFO-C-B32 has the most similar distribution shape. To verify this point, we also give the 3D Density chart results arranged at the bottom of Fig. 5. These results confirm the effectiveness of our DIFO-C-B32 in terms of Feature distribution." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "text", + "content": "Ablataion study. We evaluate the (1) effect of " + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{TSC}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MCE}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{PC}}" + }, + { + "bbox": [ + 46, + 582, + 288, + 629 + ], + "type": "text", + "content": ", (2) effect of optimization of mutual information, (3) effect of task-specific customization and (4) effect of historical prediction fusion." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "For this first issue, we conduct a progressive experiment to isolate the loss's effects. The top four rows of Tab. 6 list the ablation study results. For convenience comparison, the baseline (the first row) is the source model results. When single " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{TSP}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MCE}}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " works, the accuracy largely increases on the three datasets with an improvement of about " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " in average accuracy compared with the baseline. As both of them" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 313, + 102, + 538, + 176 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": "Table 5. Partial-set SFDA and Open-set SFDA on Office-Home " + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 305, + 70, + 545, + 94 + ], + "type": "text", + "content": ". The full results are provided in Supplementary." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 102, + 538, + 176 + ], + "lines": [ + { + "bbox": [ + 313, + 102, + 538, + 176 + ], + "spans": [ + { + "bbox": [ + 313, + 102, + 538, + 176 + ], + "type": "table", + "html": "
Partial-set SFDAVenueAvg.Open-set SFDAVenueAvg.
Source-62.8Source-46.6
SHOT [24]ICML2079.3SHOT [24]ICML2072.8
HCL [11]NIPS2179.6HCL [11]NIPS2172.6
CoWA [19]ICML2283.2CoWA [19]ICML2273.2
AaD [43]NIPS2279.7AaD [43]NIPS2271.8
CRS [45]CVPR2380.6CRS [45]CVPR2373.2
DIFO-C-B32-85.6DIFO-C-B32-75.9
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L TSCL MCEL PCOffice-31Office-HomeVisDAAvg.
XXX78.659.249.262.3
✓XX82.477.484.481.4
X✓X82.176.588.682.4
✓✓X87.080.088.385.1
✓✓✓92.583.190.388.6
DIFO-C-B32 w/ KL90.481.589.087.0
DIFO-C-B32 w/ CLIP90.781.188.886.8
DIFO-C-B32 w/o p i'89.873.587.083.4
DIFO-C-B32 w/o p i88.982.288.986.7
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The results indicate: (1) all objective components positively affect the final performance, (2) " + }, + { + "bbox": [ + 304, + 338, + 547, + 421 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{MCE}}" + }, + { + "bbox": [ + 304, + 338, + 547, + 421 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 338, + 547, + 421 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{PC}}" + }, + { + "bbox": [ + 304, + 338, + 547, + 421 + ], + "type": "text", + "content": " is crucial due to providing a new soft supervision for coarse-to-fine adaptation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": "For the second and third issues, we propose two variation methods of DIFO-C-B32 to evaluate the effect. One is DIFO-C-B32 w/ KL where the mutual information maximization loss in " + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{TSC}}" + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{PC}}" + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": " are replaced by KL divergence loss. The other one is DIFO-C-B32 w/ CLIP where the prompt learning-based customization for CLIP is cancelled, and the inputted prompt is set to the fixed template of \"a photo of a [CLS].\" during the entire adaptation. As presented in the last two rows in Tab. 6, DIFO-C-B32 (the fifth row) beats DIFO-C-B32 w/ KL and DIFO-C-B32 w/ CLIP with average improvement of " + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "inline_equation", + "content": "1.6\\%" + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": " at least, respectively confirming the effect of adopting mutual information optimization and task-specific customization. As for the fourth issue, its effect is verified by the performance decreases " + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "inline_equation", + "content": "(3.4\\%" + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": " in average at most) in the variation methods (the last two rows), which remove " + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "inline_equation", + "content": "p_i'" + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 304, + 422, + 548, + 613 + ], + "type": "text", + "content": " from the fusion respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 622, + 543, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 622, + 543, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 622, + 543, + 635 + ], + "type": "text", + "content": "4.3. Task-Specific Knowledge Adaptation Analysis" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 641, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 689 + ], + "type": "text", + "content": "In this part, we give a feature space shift analysis using the measure of MMD (maximum mean discrepancy) distance [47] to verify whether the proposed method ensures a task-specific knowledge adaptation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 712 + ], + "type": "text", + "content": "In this experiment, we first train a domain-invariant Oracle model over all Office-Home data with real labels, and use" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 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Feature distribution visualization comparison on transfer task " + }, + { + "bbox": [ + 46, + 239, + 547, + 273 + ], + "type": "inline_equation", + "content": "\\mathrm{Ar}\\rightarrow \\mathrm{Cl}" + }, + { + "bbox": [ + 46, + 239, + 547, + 273 + ], + "type": "text", + "content": " in Office-Home. Oracle is trained on target domain Cl using the ground-truth labels. Different colors stand for different categories. Top: t-SNE feature distribution over 65 categories. Bottom: The corresponding 3D density charts. For easy view, the first 10 categories were used in this plot." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 143, + 152, + 216, + 232 + ], + "blocks": [ + { + "bbox": [ + 143, + 152, + 216, + 232 + ], + "lines": [ + { + "bbox": [ + 143, + 152, + 216, + 232 + ], + "spans": [ + { + "bbox": [ + 143, + 152, + 216, + 232 + ], + "type": "image", + "image_path": "0326ec4ee1cb4e723da4874897b37c4ba2b2776a28bc5ec29512388bd0a81637.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 220, + 152, + 293, + 232 + ], + "blocks": [ + { + "bbox": [ + 220, + 152, + 293, + 232 + ], + "lines": [ + { + "bbox": [ + 220, + 152, + 293, + 232 + ], + "spans": [ + { + "bbox": [ + 220, + 152, + 293, + 232 + ], + "type": "image", + "image_path": "ea5c48a06ab0a1643857b0024221b51d96cfdf6b648895c2c2e7ef0bb40c3ae8.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 295, + 152, + 370, + 232 + ], + "blocks": [ + { + "bbox": [ + 295, + 152, + 370, + 232 + ], + "lines": [ + { + "bbox": [ + 295, + 152, + 370, + 232 + ], + "spans": [ + { + "bbox": [ + 295, + 152, + 370, + 232 + ], + "type": "image", + "image_path": "2ef10853082fa9699bbd21b2f10c627f83ea8163fb5541dce5820ee12427fcd3.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 372, + 152, + 447, + 232 + ], + "blocks": [ + { + "bbox": [ + 372, + 152, + 447, + 232 + ], + "lines": [ + { + "bbox": [ + 372, + 152, + 447, + 232 + ], + "spans": [ + { + "bbox": [ + 372, + 152, + 447, + 232 + ], + "type": "image", + "image_path": "00bb252782872160b32b1fa71cd361a53840792a8432ce8cc50853e66dbee666.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 449, + 152, + 524, + 232 + ], + "blocks": [ + { + "bbox": [ + 449, + 152, + 524, + 232 + ], + "lines": [ + { + "bbox": [ + 449, + 152, + 524, + 232 + ], + "spans": [ + { + "bbox": [ + 449, + 152, + 524, + 232 + ], + "type": "image", + "image_path": "532d1b5bc35f812ce1202298bdaf0abfe68e99b8cbd509bd7b902dcc336da1a4.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 48, + 289, + 167, + 403 + ], + "blocks": [ + { + "bbox": [ + 48, + 289, + 167, + 403 + ], + "lines": [ + { + "bbox": [ + 48, + 289, + 167, + 403 + ], + "spans": [ + { + "bbox": [ + 48, + 289, + 167, + 403 + ], + "type": "image", + "image_path": "c139258b696aaf76993dec4b07e0e7d1696ff1c094a31398b6fd5814118c49f3.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 412, + 288, + 447 + ], + "lines": [ + { + "bbox": [ + 46, + 412, + 288, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 288, + 447 + ], + "type": "text", + "content": "Figure 6. The evolving dynamics of MMD distance during adaption of " + }, + { + "bbox": [ + 46, + 412, + 288, + 447 + ], + "type": "inline_equation", + "content": "\\mathrm{Ar} \\rightarrow \\mathrm{Cl}" + }, + { + "bbox": [ + 46, + 412, + 288, + 447 + ], + "type": "text", + "content": " in Office-Home. Left and Right present the varying curves of MMD distance and accuracy, respectively" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 167, + 289, + 286, + 404 + ], + "blocks": [ + { + "bbox": [ + 167, + 289, + 286, + 404 + ], + "lines": [ + { + "bbox": [ + 167, + 289, + 286, + 404 + ], + "spans": [ + { + "bbox": [ + 167, + 289, + 286, + 404 + ], + "type": "image", + "image_path": "3092ad539664b52a52d77b8af8750bba8d39eefc87c973bb67f83d85e7862982.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": "the logits to express the ideal task-specific space " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": ". After that, an analysis is conducted on the transfer task " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathrm{Ar} \\to \\mathrm{Cl}" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": ". During this adaptation, there are " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": " (epoch number) intermediate target models and customized CLIP models. We feedforward the target data through each intermediate model and take the logits as a space. Thus, we obtain " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": " intermediate target feature spaces " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{U}_k\\}_{k=1}^T" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": " intermediate customized CLIP feature spaces " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}\\}_{k=1}^T" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": ". Within this context, these intermediate spaces can depict the task-specific distillation to " + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 470, + 287, + 601 + ], + "type": "text", + "content": ". In practice, the CLIP image encoder's backbone is set to ViT-B/32." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "text", + "content": "In the left of Fig. 6, we give the MMD distance change curve of " + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{U}_k\\}_{k=1}^T" + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "text", + "content": " (in red, termed TGT) and " + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}\\}_{k=1}^T" + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "text", + "content": " (in blue, termed CUS-CLIP), taking " + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "text", + "content": " as the original space. It is seen that at early epochs (" + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "inline_equation", + "content": "1 \\sim 4" + }, + { + "bbox": [ + 46, + 604, + 288, + 688 + ], + "type": "text", + "content": "), TGT and CUS-CLIP sharply decrease and then maintain a gradual decrease in the following epochs. Meanwhile, this change is consistent with the accuracy varying shown in the right of Fig. 6." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "type": "text", + "content": "These results indicate that our DIFO encourages task-specific knowledge adaptation due to converging the ideal" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 293, + 547, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 401 + ], + "type": "text", + "content": "task-specific space. Besides, we observe two details. First, after epoch 1, CUS-CLIP's distance reduces by 2.2, which is 58.6 time of TGT's decrease of 0.038. This is because CLIP represents a heterogeneous space of vision-language, much different from the vision space " + }, + { + "bbox": [ + 304, + 293, + 547, + 401 + ], + "type": "inline_equation", + "content": "\\mathcal{O}" + }, + { + "bbox": [ + 304, + 293, + 547, + 401 + ], + "type": "text", + "content": ". Furthermore, the large distance decrease confirms the effect of customization. Second, the synchronized distance reductions of CUS-CLIP and TGT indicate the interaction between the target model and CLIP is a crucial design for task-specific distillation." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 411, + 379, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 379, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 379, + 424 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 431, + 547, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 599 + ], + "type": "text", + "content": "We present an innovative approach, referred to as DIFO, designed to tackle the SFDA problem. To the best of our knowledge, this marks the initial endeavor to address SFDA by leveraging a pretrained ViL foundation model, departing from previous approaches that predominantly concentrated on self-mining auxiliary information. DIFO is featured with alternating between customization of the ViL model and the transfer of task-specific knowledge from the customized ViL model. We introduce two pivotal designs: a mutual information-based alignment for ViL customization and a most-likely category encouragement for more precise adaptation of task-specific knowledge. Our method's effectiveness is validated by state-of-the-art experimental results across four challenging datasets." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 609, + 404, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 404, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 404, + 624 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 713 + ], + "type": "text", + "content": "This work is supported by the German Research Foundation (DFG) and National Natural Science Foundation of China (NSFC) in project Crossmodal Learning under contract Sonderforschungsbereich Transregio 169, the Hamburg Landesforschungsforderungsprojekt Cross, NSFC (61773083); NSFC (62206168, 62276048). Shanghai SAST Funding (202410013)." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23718" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 123 + ], + "type": "text", + "content": "[1] Alex Andonian, Shixing Chen, and Raffay Hamid. 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"page_idx": 0 + }, + { + "type": "image", + "img_path": "images/216f64b0e4669da958f32dafc413407d3272237dbf82df9d6cc38426c1dd6d7c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 305, + 754, + 372 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/efdb77ff2c1be10662405eddb70009639c3130506ea6abdfb2ad94efe18a92ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 305, + 887, + 372 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"A train riding on rails, autumn view\"", + "bbox": [ + 163, + 377, + 442, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a1ddd08de8b9c2d62e4ca734a2e7bdc2f646a8e0529640729c2e33af70f0760b.jpg", + "image_caption": [ + "Figure 1. Given an input video and a text prompt describing the target objects and scene, our method generates a new video in which the overall motion and scene layout of the input video are preserved, while allowing for notable structural and appearance changes." + ], + "image_footnote": [], + "bbox": [ + 101, + 393, + 233, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/173e5c9ccbdfb40bdd4afbf88057d755de3cf398cd2a48d743687a9e48d45191.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 235, + 393, + 361, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fd13adb83e179b7844005827b82411942542f4ab9a04e90e387f05b27cd0d8e8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 362, + 393, + 491, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "\"A dolphin jumping into the ocean\"", + "bbox": [ + 573, + 377, + 828, + 392 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c74b071a4111ee2ad4f06128640aa5c3433cfcf4dea046612aebd01554968f2a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 495, + 393, + 625, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3d530a08591eebfdcfd0b80fd7b3f2caea177cd6dee78623882157f1199fa90f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 393, + 754, + 458 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/56700d80c784605a4e341536a8f80bd861b851040652fad14a6e3069153a4074.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 393, + 887, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 508, + 313, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present a new method for text-driven motion transfer – synthesizing a video that complies with an input text prompt describing the target objects and scene while maintaining an input video's motion and scene layout. Prior methods are confined to transferring motion across two subjects within the same or closely related object categories and are applicable for limited domains (e.g., humans). In this work, we consider a significantly more challenging setting in which the target and source objects differ drastically in shape and fine-grained motion characteristics (e.g., translating a jumping dog into a dolphin). To this end, we leverage a pre-trained and fixed text-to-video diffusion model, which provides us with generative and motion priors. The pillar of our method is a new space-time feature loss derived directly from the model. This loss guides the generation process to preserve the overall motion of the input video while complying with the target object in terms of shape and fine-grained motion traits. 1 Project page: https://diffusion-motion-transfer.github.io/", + "bbox": [ + 73, + 526, + 472, + 805 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 821, + 207, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Imagine transferring the car's motion shown in the video in Fig. 1 to a different object, such as a bicycle or a train. This task poses a crucial challenge - retaining key motion", + "bbox": [ + 75, + 835, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "characteristics of the input video, such as the car's direction of motion, speed, and pose, while substantially altering the dynamic object's structure to convey the target's unique visual attributes. Conceptually, solving this task requires prior knowledge about objects' appearance, pose, shape, and motion under deformations and different viewpoints, as well as an understanding of their interaction with the scene (e.g., turning the car into a bicycle requires revealing unseen background content and synthesizing plausible scene effects, such as shadows).", + "bbox": [ + 500, + 508, + 890, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous methods have been primarily focused on transferring motion across two similarly-looking videos depicting two subjects within the same object category. These methods are typically confined to object categories for which strong geometric priors exist, e.g., humans for which parametric models for robust shape and pose are available (e.g., [7, 11]). Other works attempt to learn such explicit mid-level representation in a self-supervised manner from the input videos (e.g., [38, 58])– an extremely challenging task by itself. In this work, we take the task of motion transfer to the realm of text-driven video editing, where the target object and scene are specified via a text prompt. We aim at addressing a significantly more general setting, which involves transferring motion across different object categories under significant variations in shape and deformations across time (Fig. 1). Here, we define motion as a sequence of semantic objects' parts' positions and strive to preserve the position of those parts across different object", + "bbox": [ + 496, + 648, + 892, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "Code will be made publicly available.", + "bbox": [ + 94, + 886, + 302, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8466", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "categories (e.g., legs, arms) while making the target object move realistically.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our approach diverges from traditional motion transfer works by avoiding explicit mid-level modeling of pose and shape. Instead, we harness the generative motion priors learned from broad video data by a pre-trained and fixed text-to-video model. Specifically, we delve into the intermediate space-time feature representation learned by the video model and introduce a new loss that guides the generation process of the target video towards the preservation of the original video's overall scene layout and motion. Importantly, our method allows flexibility and deviations from the exact structure and shape of the source objects. This contrasts with prior works in text-driven image and video editing that manipulate spatial features of a pre-trained text-to-image model. These methods inherently lack the ability to perform consistent structural edits across frames since they rely solely on spatial image priors. To the best of our knowledge, our work is the first to empirically analyze and harness space-time features of a text-to-video model.", + "bbox": [ + 75, + 119, + 467, + 368 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our lightweight framework works in a zero-shot fashion, requiring no training data or fine-tuning. We demonstrate results on many videos and edits, encompassing various objects and scenes. We further suggest a new metric to measure motion similarity under shape deviation and quantitatively evaluate our method w.r.t. existing text-to-video methods, demonstrating state-of-the-art performance in terms of motion preservation and edit fidelity.", + "bbox": [ + 75, + 369, + 467, + 479 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarize, our key contributions include:", + "bbox": [ + 94, + 481, + 395, + 494 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- An effective zero-shot framework that harnesses the generative motion prior of a pre-trained text-to-video model for the task of motion transfer.", + "- New insights about the space-time intermediate features learned by a pre-trained text-to-video diffusion model.", + "- A new metric for evaluating motion fidelity under structural deviations between two videos.", + "- State-of-the-art results compared to competing methods, achieving a significantly better balance between motion preservation and fidelity to the target prompt." + ], + "bbox": [ + 76, + 494, + 467, + 633 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 76, + 647, + 220, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Motion transfer. A related task to ours is motion transfer from a source to a target subject, where the subjects are of the same or closely related object categories (e.g., [1, 11, 29, 51, 52, 64, 65]). These methods take as input a driving video depicting the source motion, and an image or a video, depicting the target subject. A prevalent approach among these methods is to explicitly model the pose of the dynamic object via a parametric model (e.g. OpenPose [7]). Thus, these methods are largely restricted to domains for which robust parametric models exist (e.g., humans or faces) or to transferring motion across videos depicting similar motion and closely related object categories. In contrast, we are aimed at text-driven motion transfer across distinct object categories. That is, the target object and scene are specified through a text prompt, where the source and target objects can differ significantly in shape,", + "bbox": [ + 75, + 676, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "appearance, and their natural fine-grained motion traits.", + "bbox": [ + 500, + 90, + 864, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Text-to-video models. Early works on text-to-video generation utilized VAE or conditional GAN frameworks [31, 37, 42] trained on small-scale datasets of simple domains (e.g., moving digits). Recently, there have been substantial efforts in training large-scale text-to-video models on vast datasets with autoregressive Transformers (e.g., [24, 61, 66]) or Diffusion Models (e.g., [5, 22]). A recent trend extends pre-trained text-to-image (T2I) diffusion models to text-to-video (T2V) generation by adding temporal layers on top of an image architecture [4, 18, 45, 54]. Make-A-Video [54] add temporal Convs and attention layers to a pre-trained T2I pixel-space diffusion model. Other works extend T2I diffusion models that operate on a latent space (e.g., StableDiffusion [49]) to the temporal domain [4, 18].", + "bbox": [ + 496, + 112, + 890, + 306 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Several works [13, 17, 39, 63] train or fine-tune diffusion models for video-to-video translation tasks. Gen-1 [17] design a video architecture that is conditioned on structure/appearance representations, allowing text-driven appearance manipulation of a reference video. Control-A-Video [13] extends a conditional T2I to the temporal domain, allowing the generation of videos that preserve the per-frame layout of a reference video. Nevertheless, since these methods are conditioned on generic mid-level representations of the reference video, they do not allow the preservation of the motion of the reference video while significantly deviating from the per-frame structural layout. In this work, we utilize a pre-trained publicly available T2V diffusion model [8, 62] and show for the first time how it can be leveraged for motion transfer in a zero-shot manner.", + "bbox": [ + 496, + 308, + 890, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Image & video editing via feature manipulation. There has been unprecedented progress in text-to-image generation using diffusion models [14, 15, 21, 41]. Following this success, a surge of works empirically analyzed the internal feature representation of prominent T2I diffusion models, e.g., StableDiffusion [49], and showed how to perform various editing tasks using simple operations in the T2I feature space.[6, 12, 20, 23, 34, 44, 60]. Prompt-to-Prompt [20] analyzed the cross-attention maps and showed how to manipulate them for controlling the spatial composition in generated images. Plug-and-Play Diffusion (PnP) [60] showed that the spatial features capture semantic information at high spatial granularity and utilized them for imagedto-image translation.", + "bbox": [ + 496, + 523, + 890, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A prominent line of works adopt a pre-trained T2I diffusion model for video editing [9, 19, 28, 47, 67]. For example, Tune-A-Video [67] fine-tunes a T2I model on a single input video and uses the fine-tuned model for stylizing the video or replacing object categories. TokenFlow [19] performs consistent video editing in a zero-shot manner by enforcing consistency on the diffusion features across frames. Nevertheless, these methods do not have access to a T2V generative motion prior and are not designed for edits that require significant structural deviation from the original video. Unlike these works, we leverage the motion prior of a large-scale T2V model, which allows us to support edits that require shape deviation (e.g., car to bike in Fig. 1), uti", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8467", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/14f203c96fdc09e9eeb38c25fc84385da23e4b0da9ba9d230d92365d34c74275.jpg", + "image_caption": [ + "Figure 2. Diffusion feature inversion via guided feature reconstruction. We extract space-time features $\\pmb{f}$ from an input video (a) and steer the generation process of a random sample to produce the same feature $\\pmb{f}$ , using feature reconstruction as guidance (b); the synthesized videos closely resemble the original video content in terms of appearance, shape, and pose. Replacing the full space-time features with their spatial marginal mean feature $\\mathrm{SMM}[f]$ allows for more flexibility (c); the SMM feature inversion results capture the original object pose, general position, and scene layout yet are not restricted to the original content at the pixel-level. This is also demonstrated in the nearest neighbor frames retrieved from other videos depicting similar actions, according to similarly in $\\mathrm{SMM}[f]$ features (c)." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 436, + 381 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/460d7896f23ce7231600684bd9d40c5892e8f02fc20a7c621029ea97045f7c11.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 442, + 88, + 666, + 369 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1bb9114eda4981b7379f296c65b81e21a52fd1eb395d80a72b929e0597994c98.jpg", + "image_caption": [ + "(d)" + ], + "image_footnote": [], + "bbox": [ + 669, + 88, + 893, + 366 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "lizing a novel loss function that we derive from the model's feature space. To the best of our knowledge, our work is the first to investigate the internal feature representation of a T2V model and leverage it for an editing task.", + "bbox": [ + 75, + 474, + 470, + 532 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consistent video editing. Several recent methods have leveraged layered video representations for consistent text-driven video editing [2, 10, 25, 27, 30, 33, 68]. For example, Text2LIVE [2] proposed to use a pre-trained Layered Neural Atlases (NLA) [27] representation, which is edited using losses defined in CLIP text-image space [48]. However, since the structure and motion of the edited video are determined via the pre-trained NLA, such methods are restricted to only appearance changes. Recently, [30] generalized this approach to allow local structural changes in the edited videos. Nevertheless, NLA takes hours to train, and cannot faithfully represent complex videos due to the strong regularization of objects' motion. In addition, all these methods use a 2D generative prior, thus cannot support large structure deviation and adaption of motion.", + "bbox": [ + 75, + 537, + 472, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 758, + 204, + 776 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion models. Diffusion models [15, 21, 45, 55] are generative models that aim to approximate a data distribution $q$ by mapping an input noise $\\boldsymbol{x}_T \\sim \\mathcal{N}(0, I)$ to a clean sample $\\boldsymbol{x}_0 \\sim q$ , through an iterative denoising process. The DDIM sampler allows to denoise an initial noise $\\boldsymbol{x}_T$ in a deterministic manner [56]. By applying DDIM inversion, a clean sample $\\boldsymbol{x}_0$ can be mapped back to the sequence of noisy samples $\\{\\boldsymbol{x}_i\\}_{t=1}^T$ used to generate it.", + "bbox": [ + 75, + 787, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In latent text-to-image (T2I) diffusion models, e.g., StableDiffusion [49], a pre-trained encoder compresses an RGB image $\\pmb{I} \\in \\mathbb{R}^{H \\times W \\times 3}$ to a latent $\\pmb{x} \\in \\mathbb{R}^{H' \\times W' \\times 4}$ , which can be decoded back to the high-resolution space. These T2I models comprise a UNet architecture [50], which consists of Convolutions and Attention modules.", + "bbox": [ + 496, + 474, + 890, + 560 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Latent video diffusion models (e.g., [4, 62]) extend latent T2I models to text-to-video by inflating the 2D architecture to the temporal domain, i.e., adding temporal convolutions and temporal attention layers, and fine-tuning on video datasets. In this case, the T2V model generates a latent video $\\pmb{x} \\in \\mathbb{R}^{F \\times H' \\times W' \\times 4}$ , which is then decoded to the output RGB video $\\mathcal{V} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}$ . In this work, we utilize the publicly available ZeroScope T2V [8] model, which inflates StableDiffusion [49].", + "bbox": [ + 496, + 561, + 892, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 705, + 589, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an input video $\\mathcal{V}$ and a target text prompt $P$ , our goal is to generate a new video $\\mathcal{J}$ that preserves the overall motion and semantic layout of $\\mathcal{V}$ , while complying with $P$ . We utilize ZeroScope - a pre-trained latent T2V model [8, 62].", + "bbox": [ + 496, + 731, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The key component of our method, illustrated in Fig. 3, is a novel objective function that is used as guidance during the generation process of $\\mathcal{I}$ . We conceive this objective based on our empirical analysis that reveals new insights about space-time diffusion features extracted from the model. Specifically, we show that the first-order statistics of the features in the spatial dimensions, i.e., the spatial marginal mean of the features, can serve as a powerful per", + "bbox": [ + 496, + 787, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8468", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/41f4b5ac53b34528af3bc4e3b42521819b132492bcb0102e86a1c245b8c3de87.jpg", + "image_caption": [ + "(a) Spatial Marginal Mean (SMM) Feature" + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 540, + 263 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/787ae027084f48b6173e42136ab6c0d72bc62da205caf351ab2a7d90e2850d55.jpg", + "image_caption": [ + "(b) Motion-Guided Video Generation", + "Figure 3. Pipeline. (a) Given an input video, we apply DDIM inversion and extract space-time features $\\pmb{f} \\in \\mathbb{R}^{F \\times M \\times N \\times D}$ from intermediate layer activations. We obtain our Spatial Marginal Mean (SMM) feature $\\mathrm{SMM}[f] \\in \\mathbb{R}^{F \\times D}$ by computing the mean over the spatial dimensions, and compute the pairwise differences between each pair of SMM features. (b) For editing, we guide the generation at each denoising step with our Pairwise SMM differences objective (b). See Sec. 4 for more details." + ], + "image_footnote": [], + "bbox": [ + 540, + 88, + 885, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "frame global descriptor that (i) retains spatial information such as objects' position, pose, and the semantic layout of the scene, and (ii) robust to pixel-level variations in both appearance and shape.", + "bbox": [ + 75, + 359, + 470, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Space-time analysis of diffusion features", + "text_level": 1, + "bbox": [ + 76, + 428, + 421, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We focus our analysis on features extracted from the intermediate layer activations of the video model. Recall that the video model is initialized from a text-to-image model, for which the semantic DIFT features [57], were shown to encode localized semantic information shared across objects from different domains [57, 60]. Here, we examine the space-time properties of the corresponding features in the video model. See Supplementary Material (SM) for details about the video model architecture and feature selection.", + "bbox": [ + 75, + 450, + 468, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the input video $\\mathcal{V}$ , we apply DDIM inversion with an empty prompt [56], and obtain a sequence of latents $[\\pmb{x}_1,\\dots,\\pmb{x}_T]$ , where $\\pmb{x}_t$ is the video latent at generation step $t$ . We input the latent $\\pmb{x}_t$ to the network and extract the space-time features $\\pmb{f}(\\pmb{x}_t) \\in \\mathbb{R}^{F \\times M \\times N \\times D}$ , where $F, M, N$ are the number of frames, height and width of the $D$ dimensional feature activation, respectively.", + "bbox": [ + 75, + 577, + 468, + 676 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Diffusion feature inversion. To gain a better understanding of what the features $\\{\\pmb{f}(\\pmb{x}_t)\\}_{t=1}^T$ encode, we adopt the concept of \"feature inversion\" [35, 53, 59] (not to confuse with \"DDIM inversion\"). Our goal is to optimize for a video $\\mathcal{V}^*$ , randomly initialized, that would produce these features when fed into the network. Specifically, this is achieved using feature reconstruction guidance [16, 40] during the sampling process of $\\mathcal{V}^*$ . Formally,", + "bbox": [ + 75, + 681, + 470, + 794 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\boldsymbol {x}} _ {T} \\sim \\mathcal {N} (0, \\mathcal {I}) \\\\ \\hat {\\boldsymbol {x}} _ {t - 1} = \\Phi \\left(\\boldsymbol {x} _ {t} ^ {*}, P _ {s}\\right), \\text {w h e r e} \\boldsymbol {x} _ {t} ^ {*} = \\operatorname {a r g m i n} _ {\\hat {\\boldsymbol {x}}} \\| \\boldsymbol {f} (\\boldsymbol {x} _ {\\mathbf {t}}) - \\boldsymbol {f} (\\hat {\\boldsymbol {x}} _ {\\mathbf {t}}) \\| ^ {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 799, + 482, + 830 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $\\Phi$ is the diffusion model, and $P_{s}$ is a general text prompt describing the input video (e.g., \"a car\"). We minimize the feature reconstruction objective using gradient descent at each generation step. See SM for more details.", + "bbox": [ + 75, + 843, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 2 shows our inversion results for the space-time features extracted from an input video; we repeat the inversion process several times, each with different random initialization (i.e., different seeds). We observe that inverted videos nearly reconstruct the original frames (Fig. 2(b)).", + "bbox": [ + 496, + 359, + 890, + 430 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ultimately, we opt to find a feature descriptor that retains such information about objects' pose and the semantic layout of the scene yet is robust to variations in appearance and shape. To reduce the dependency on the pixel-level information, we introduce a new feature descriptor, dubbed Spatial Marginal Mean (SMM), obtained by reducing the spatial dimensions. Formally,", + "bbox": [ + 496, + 429, + 892, + 525 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S M M} [ \\boldsymbol {f} (\\boldsymbol {x} _ {t}) ] = \\frac {1}{M \\cdot N} \\sum_ {i = 1} ^ {M} \\sum_ {j = 1} ^ {N} \\boldsymbol {f} (\\boldsymbol {x} _ {t}) _ {i, j} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 523, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where $\\pmb {f}(\\pmb {x}_t)_{i,j}\\in \\mathbb{R}^D$ is the entry at spatial location $(i,j)$ in the space-time feature volume $\\pmb {f}(\\pmb {x}_t)$", + "bbox": [ + 496, + 564, + 890, + 592 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We repeat the inversion experiment (Eq. 1), with $\\{\\mathrm{SMM}[\\pmb {f}(\\pmb {x}_t)]\\}_{t = 1}^T$ as the target features to reconstruct. Figure 2(c) shows the inversion results for the SMM features for different initializations. Remarkably, although the spatial dimensions are collapsed in the SMM features, the inverted videos convey the correct pose and position of objects while depicting larger structural and appearance variations than using the full space-time features.", + "bbox": [ + 496, + 592, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We further demonstrate these properties by treating the spatial marginal mean associated with each frame as a global per-frame descriptor, and using it to retrieve nearest neighbor frames from other videos. As seen in Fig. 2(d), the retrieved nearest frames depict the same pose, under noticeable appearance and viewpoint changes.", + "bbox": [ + 496, + 703, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Motion-guided video generation", + "text_level": 1, + "bbox": [ + 500, + 794, + 782, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on our findings, we now turn to the task of generating a new video $\\mathcal{I}$ that complies with the input prompt $P$ and preserves the motion characteristics of the driving video $\\mathcal{V}$ . Our feature inversion analysis raises the question of whether the same approach can be used for editing by replacing the source prompt $P_{s}$ with an edit prompt $P$ in Eq. 1.", + "bbox": [ + 496, + 815, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8469", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1e2985a71677ff0f74be54d67fd535f565f0d1b999cdf8cc93d34c7af11f96d3.jpg", + "image_caption": [ + "Figure 4. Sample results of our method. See SM for full video results." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 890, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Figure 7 shows these results for a couple of videos, which demonstrate two issues: (i) depending on the initialization, the optimization may converge to a local minima in which the accurate position of objects and their orientation may differ from the input, (ii) the SMM features still retain appearance information, which reduces the fidelity to the text prompt. We propose the following two components to resolve these issues.", + "bbox": [ + 75, + 564, + 468, + 675 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Pairwise SMM differences. As seen in Fig. 7, directly optimizing for the SMM features often prevents us from deviating from the original appearance. To circumvent this, we propose an objective function to preserve the pairwise differences of the SMM features rather than their exact values. Formally, let $\\phi_i^t,\\tilde{\\phi}_i^t\\in \\mathbb{R}^d$ be the SMM features for frame $i$ and step $t$ for the driving video and the generated video, respectively. For a generation step $t$ , the pairwise SMM differences $\\Delta^t,\\tilde{\\Delta}^t\\in \\mathbb{R}^{F\\times F\\times d}$ are defined as follows:", + "bbox": [ + 75, + 680, + 468, + 806 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta_ {(i, j)} ^ {t} = \\phi_ {i} ^ {t} - \\phi_ {j} ^ {t} \\quad \\tilde {\\Delta} _ {(i, j)} ^ {t} = \\tilde {\\phi} _ {i} ^ {t} - \\tilde {\\phi} _ {j} ^ {t} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 808, + 468, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $i,j\\in \\{1,\\ldots ,F\\}$ . Our loss for time step $t$ is then:", + "bbox": [ + 76, + 833, + 431, + 849 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\operatorname {S M M} (\\boldsymbol {f} (\\boldsymbol {x} _ {t})), \\operatorname {S M M} (\\boldsymbol {f} (\\tilde {\\boldsymbol {x}} _ {t}))) = \\sum_ {i} \\sum_ {j} | | \\Delta_ {(i, j)} ^ {t} - \\tilde {\\Delta} _ {(i, j)} ^ {t} | | _ {2} ^ {2} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Motion-Guided Video Generation", + "text_level": 1, + "bbox": [ + 498, + 563, + 828, + 578 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e9945fb60e026b0e27918885993fc9c5b302e12bc42945c040066301670420c3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Input:
V, P▷ Input video and target text prompt
{x_t}T_{t=1}← DDIM-Inv[V] ∀t ∈ [T]
ε0 ~ N(0, I)
x̂T = LFξ(xT) + (ε0 - LFξ(ε0))▷ Filtered noise (Eq. 4.2)
For t = T, ..., 1 do
f(x_t), f(x̂_t) ← Extract space-time features
SMM(f(x_t)), SMM(f(x̂_t)) ← Spatial marginal mean (Eq. 1)
xt* = argminx̂_t L(SMM(f(x_t)), SMM(f(x̂_t)))
x̂_t-1 = Φ(x_t*, P)▷ Apply a denoising step
Output: J ← x0
", + "bbox": [ + 501, + 580, + 890, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Intuitively, this loss lets us preserve the relative changes in the features through time, while discarding the exact appearance information of the source video (Fig. 7).", + "bbox": [ + 496, + 766, + 890, + 809 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Initialization. It is well-known that the diffusion denoising process is performed in a coarse-to-fine manner, thus, the initialization plays an important role in defining the low frequencies of the generated content [3, 36]. Initialization from a random point may often converge to an undesired local minimum, in which object position is not well-", + "bbox": [ + 496, + 815, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8470", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "preserved. Note that the low-frequency information of the original video is readily available in the DDIM inverted noise $\\pmb{x}_T$ . However, we empirically found that this initialization often restricts edit-ability [43] (see SM for an example). We thus extract only the low frequencies from $\\pmb{x}_T$ . Specifically, let $\\pmb{x} \\in \\mathbb{R}^{F \\times M \\times N}$ be a tensor representing $F$ frames, with a spatial resolution of $M \\times N$ . We denote by $LF_{\\xi}(\\pmb{x})$ the operation of spatially downsampling and upsampling $\\pmb{x}$ by a factor of $\\xi$ . Then, our initial latent $\\tilde{\\pmb{x}}_T$ is given by:", + "bbox": [ + 76, + 90, + 472, + 231 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {x}} _ {T} = L F _ {\\xi} \\left(\\boldsymbol {x} _ {T}\\right) + \\left(\\epsilon_ {0} - L F _ {\\xi} \\left(\\epsilon_ {0}\\right)\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 234, + 468, + 251 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\epsilon_0\\sim \\mathcal{N}(0,I)$ is a random noise. Intuitively, $\\tilde{\\pmb{x}}_T$ preserves the low-frequencies of the DDIM noise where the higher frequencies are determined by $\\epsilon_0$", + "bbox": [ + 76, + 260, + 468, + 303 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To summarize, starting from the filtered latent $\\tilde{\\pmb{x}}_T$ , our method deploys the following guided generation process:", + "bbox": [ + 76, + 301, + 468, + 330 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {x} _ {t} ^ {*} = \\operatorname {a r g m i n} _ {\\tilde {\\boldsymbol {x}} _ {t}} \\mathcal {L} (\\operatorname {S M M} (\\boldsymbol {f} (\\boldsymbol {x} _ {t})), \\operatorname {S M M} (\\boldsymbol {f} (\\tilde {\\boldsymbol {x}} _ {t})))\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 340, + 426, + 358 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {x}} _ {t - 1} = \\Phi (\\boldsymbol {x} _ {t} ^ {*}, P)\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 358, + 240, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our full framework is summarized in Alg. 1.", + "bbox": [ + 76, + 381, + 372, + 397 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Results", + "text_level": 1, + "bbox": [ + 76, + 409, + 163, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on various scenes and object categories, most of which involve camera as well as object motion. The driving videos are taken from DAVIS dataset [46] and from the Web. Our video results and implementation details are available in the Supplementary Materials (SM).", + "bbox": [ + 76, + 431, + 468, + 503 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figures 1, 4 show sample results of our method. As seen, our method facilitates edits that involve notable changes to the shape and structure of deforming objects, while preserving camera and objects' motion. For instance, we preserve the 3D pose of the car when transferring its motion to a bike or a train (Fig. 1); and maintain the actions of non-rigidly moving objects, e.g., sitting dog or walking camel in Fig. 4.", + "bbox": [ + 75, + 503, + 468, + 601 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines We compare our method to the following text-driven video editing methods: (i) Shape-Aware Layered Neural Atlases (SA-NLA) [30] that utilizes a pre-trained layered video representation [27] and a pre-trained T2I model [49]. (ii) TokenFlow [19], a zero-shot method that works in the feature space of a pre-trained T2I model (iii) GEN-1 [17] and (iv) Control-A-Video [13], both are video-to-video diffusion models that condition the generation on input depth maps, (v) Tune-A-Video [67] that inflates a T2I model and finetunes it on a single test video, and (iv) SDEdit [36] applied to the same T2V model as our method.", + "bbox": [ + 75, + 604, + 470, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Qualitative evaluation", + "text_level": 1, + "bbox": [ + 76, + 766, + 284, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 5 shows a qualitative comparison to SA-NLA [30]. Note that SA-NLA utilizes a layered video representation [27], which requires foreground/background separation masks and takes $\\sim 10$ hours to train. Thus, we compare to their provided videos and edit prompts qualitatively. As seen in Fig. 5, both our method and SA-NLA exhibit high fidelity to the original motion. Nevertheless, our method allows for greater deviation in structure, (e.g., matching the", + "bbox": [ + 75, + 787, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a08664cc0ad5d572b9ee811eb1e97fc74f829bdedbc227a61a04849407a77ce5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 90, + 629, + 209 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2041cd08e27bd1ea26587e727a42b0ecd4aed968e338e8c00aea94db5760085b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 90, + 763, + 209 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/8b6b1ebcc3aceadf7fc301f97742ec00e1215d6e69a9917d9e1654bb05d41f6b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 98, + 890, + 209 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c984ee63b9a6443e08e2626aa76218a5ff981fced73ef22ddee7233ed7f1fe57.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 209, + 629, + 329 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4a1cc656b23f2cb088e7e7fd793f57efcb521b696b302d754836a6c8abe761da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 629, + 209, + 763, + 329 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6e364702eafd21dc40c9a2bb92527a0caabc9e6c84ddcb439129fcfc86fdd0b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 763, + 209, + 890, + 329 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/033bf5db62b9fc645bb0c3a3dde7d37744771f27cb2b565aa64c8a742dd07390.jpg", + "image_caption": [ + "Original Frames", + "Figure 5. Comparison to SA-NLA [30]. See SM for video results, structure of a duck in the swan example) and adaption of fine-grained motion traits, which are necessary for capturing the unique attributes of the target object. For example, adapting the shape and movement of a dog's tail to resemble a naturally-looking cat's tail." + ], + "image_footnote": [], + "bbox": [ + 501, + 329, + 629, + 448 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1ce9288a0ad2e337eb52357f1a89cc1d5cee0c36076740ac6a77270a1fa158b8.jpg", + "image_caption": [ + "SA-NLA" + ], + "image_footnote": [], + "bbox": [ + 629, + 329, + 763, + 448 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/10e9d8b526de98e48064ac29e08960a96cf2478e323fb4e814fb42d14800f4ea.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 763, + 329, + 890, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 6 provides comparisons to the additional baselines. As seen, none of these methods can both convey the original motion and adhere to the edit prompt. TokenFlow [19] is tailored to preserve structure of the input video. Gen-1 [17] and Control-A-Video [13] struggle to deviate from the input shapes as they condition the generation on the per-frame depth maps extracted from the input video. Tune-A-Video [67] manages to fulfill the target prompt, yet objects are not aligned in pose and motion (e.g., camel to bear). Our method significantly outperforms these baselines, by successfully matching the desired edits, which require significant structural changes and may involve synthesizing dynamic scene elements (e.g., smoke behind the motorbike). We refer the reader to the SM for full video results.", + "bbox": [ + 498, + 554, + 890, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative evaluation. We numerically evaluate the key aspects of our results using the following metrics:", + "bbox": [ + 498, + 753, + 890, + 782 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(i) Edit fidelity. Following previous works (e.g., [17, 19]), we use CLIP [48] to measure the similarity between each frame and the target text and report the average score.", + "(ii) Motion fidelity. We aim to assess the fidelity of our results in preserving the original motion. Given our task involves structural deviations, there is no alignment between pixels in the original and output videos. Consequently, traditional metrics such as comparing optical-flow fields are" + ], + "bbox": [ + 498, + 785, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8471", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/931566520dd45be01aad60e47a239a64308b4b98413a192b9ed6677ac3ff2c6b.jpg", + "image_caption": [ + "Input" + ], + "image_footnote": [], + "bbox": [ + 83, + 116, + 217, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c71a36c49de539f8bce25fd8707b64ff38da79a3810a0f1662621a73ffea7b1b.jpg", + "image_caption": [ + "TokenFlow" + ], + "image_footnote": [], + "bbox": [ + 220, + 116, + 351, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cbad7c2aa0bcaeecf85c7ddf6d5fbf2c704439d784a2acd001a4f7c63edde57d.jpg", + "image_caption": [ + "Gen-1", + "\"A motorbike driving in a scenic desert\"" + ], + "image_footnote": [], + "bbox": [ + 352, + 116, + 483, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7ba42143622dfccbd543a9002c34fe9131b928d1b2ce6806f3433187a9e25642.jpg", + "image_caption": [ + "Tune-A-Video" + ], + "image_footnote": [], + "bbox": [ + 486, + 116, + 619, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/496cd50623807c6553a20a3c8ed1782d70a739164bc0869e5973203f639ed3d4.jpg", + "image_caption": [ + "Control-A-Video" + ], + "image_footnote": [], + "bbox": [ + 620, + 116, + 751, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1e1c3161782f545f792358fd7eea845c9b16e536f3d6deb838b5ec51d82aab4b.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 753, + 116, + 883, + 172 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a9e490d452f90fb3d04187d3bbee86ced1fe13c2983ffd26e7cbe42e3c9258da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 172, + 217, + 231 + ], + "page_idx": 6 + }, + 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+ "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/38d83e34b61c82bee23ec72a37f96815925475f244736d91638fdc22c8f74341.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 380, + 217, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b3088ca3f8af11b25787b76212a2f4819c520272b3a232bbbb718ed715ac7f70.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 220, + 380, + 351, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/84c7cb57a41f4e5c4fcd50c5d427703247534e87b89f8ee5fdf3b58c0fbd95c5.jpg", + "image_caption": [ + "\"A giraffe walking in the zoo\"" + ], + "image_footnote": [], + "bbox": [ + 352, + 380, + 483, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9948772752ea2d9a8e9be6208551d8821478555064d1180fc59147433e5fd433.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 380, + 619, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c4c4f6432da53cc84ff57ebf7d05351a29795dd6943b332166e5a76262779ba.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 380, + 751, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c74711a7e5f6b0a865b126e908703597ff283a76fe822ff50805feb0cd67fe5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 380, + 883, + 438 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b5a2b664b70da830db6237051649bbb16828d978f78decb0df03c8b210bb7fc5.jpg", + "image_caption": [ + "Figure 6. Comparison. Sample results comparing our method to TokenFlow [19], Gen-1 [17], Tune-A-Video [67], and Control-A-Video [13]. See SM for full video comparisons." + ], + "image_footnote": [], + "bbox": [ + 83, + 438, + 217, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d4639c8d0a1baa261cc16c493a8eed8215f927b18e4ecdedfcd452137caaa659.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 220, + 438, + 351, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03536f3da6300a6faf6f392965092bb92439fb091a9580df26a68f86457e69f4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 438, + 483, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a89c25935c6870e00fcd5e9e27bdc304af1d1c17d0aae03608404911830aa2b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 438, + 619, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/787c051a02bc4fb9b3dae0e03ef643d818250b99eaa2411315a7febd0b83b6e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 620, + 438, + 751, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/020d62ad50d7dda3d3b8b9b038a01c570bcce1bd2e21779cd98d55a16c85a20b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 753, + 438, + 883, + 496 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8d051c6321060462c1f574bd9a283f6b0c57a3d9337516193af1e60f1ef7cdde.jpg", + "image_caption": [ + "(a) Original Frames", + "(b) Space-time feature loss" + ], + "image_footnote": [], + "bbox": [ + 80, + 550, + 210, + 608 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3623b126f154c60de7e0b0fb2212b6e16c47f700da42ba73e485d9cde083d58e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 212, + 550, + 344, + 607 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6670cb9317ec629b5780f6a86c594a4cec3f1b221be0f21c0c341845d012ea26.jpg", + "image_caption": [ + "(c) SMM feature loss", + "\"A car driving in a forest", + "\"A giraffe walking on the rocks\"" + ], + "image_footnote": [], + "bbox": [ + 346, + 550, + 478, + 607 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7a78ea8c1ba25fbad32fe83701fd187d52a57b67b7b07f5e4a79be5126350224.jpg", + "image_caption": [ + "(d) w/o guidance" + ], + "image_footnote": [], + "bbox": [ + 486, + 550, + 620, + 607 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26739f0da9149526debd207240185bbe3071848991757c9e563d727b1eaadf64.jpg", + "image_caption": [ + "(e) w/o low-freq. init" + ], + "image_footnote": [], + "bbox": [ + 624, + 550, + 756, + 607 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bb9bcb3bf26d2f62a7e929dc8643617772ef6cd342d9278e3f8201205e62e382.jpg", + "image_caption": [ + "(f) Full method" + ], + "image_footnote": [], + "bbox": [ + 759, + 550, + 890, + 607 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ce77066be6b7f4919fcfdee476d3e480507c0204ac392603da34a5d9b27260f6.jpg", + "image_caption": [ + "Figure 7. Ablation. (b-c) We compare alternative loss functions instead of our pairwise SMM differences loss (Eq. 4.2); (b) using full space-time features reconstruction prevents deviations in appearance and shape; (c) SMM feature reconstruction allows for more flexibility yet retains appearance information. (d-f) Ablation of our key components: (d) directly sampling from the initial latent w/o optimization preserves only the coarse layout. (e) Starting our optimization from randomly sampled noise (w/o low frequency filtering Eq. 4.2) results in lower motion fidelity compared to our full method (f)." + ], + "image_footnote": [], + "bbox": [ + 80, + 617, + 210, + 674 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5ec72eca7c02a257c7618dbef97030433cea6e768b824137449a805c2a71174d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 212, + 617, + 344, + 674 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/be0adee4dc24e32243f397aa569c455de1d84fa82405308c74425800f2f9b222.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 346, + 617, + 478, + 674 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ae464d7d3bc5dfeaa874bbb2d1eee8c9c07d8b8d392731f0025e28fbe190b119.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 617, + 620, + 674 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f24d510f2193a4a00623f99fd7f07434c98803f7b110336964998c0d25e5f7da.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 624, + 617, + 756, + 674 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/deea76b1b349cca1ed278c9a181844acda410147e185198b2b9571e5dbdd6d97.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 617, + 890, + 674 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "unsuitable for our use case. We thus introduce a new metric, based on similarity between unaligned long-trajectories. We expect that even under structural changes, the two sets of trajectories would exhibit shared characteristics.", + "bbox": [ + 75, + 753, + 467, + 810 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Specifically, we use off-the-shelf tracking method [26] to estimate $\\mathcal{T} = \\{\\tau_1,\\dots ,\\tau_n\\}$ , $\\tilde{\\mathcal{T}} = \\{\\tilde{\\tau}_1,\\dots ,\\tilde{\\tau}_m\\}$ , two sets of tracklets in the input and output videos, respectively.", + "bbox": [ + 75, + 811, + 467, + 856 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Inspired by the Chamfer distance, we define our Motion-Fidelity-Score as follows. For each tracklet $\\tau_{i}\\in \\mathcal{T}$ , we measure the similarity to its nearest neighbor in $\\tilde{\\tau}_i\\in \\mathcal{T}$", + "bbox": [ + 76, + 857, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and vice versa.", + "bbox": [ + 500, + 753, + 601, + 767 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {1}{m} \\sum_ {\\tilde {\\tau} \\in \\tilde {\\mathcal {T}}} \\max _ {\\tau \\in \\mathcal {T}} \\operatorname {c o r r} (\\tau , \\tilde {\\tau}) + \\frac {1}{n} \\sum_ {\\tau \\in \\mathcal {T}} \\max _ {\\tilde {\\tau} \\in \\tilde {\\mathcal {T}}} \\operatorname {c o r r} (\\tau , \\tilde {\\tau}) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 770, + 890, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "where the correlation between two tracklets $\\mathbf{corr}(\\tau, \\tilde{\\tau})$ is computed as follows, similarly to [32]:", + "bbox": [ + 498, + 818, + 890, + 847 + ], + "page_idx": 6 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c o r r} (\\tau , \\tilde {\\tau}) = \\frac {1}{F} \\sum_ {k = 1} ^ {F} \\frac {v _ {k} ^ {x} \\cdot \\tilde {v} _ {k} ^ {x} + v _ {k} ^ {y} \\cdot \\tilde {v} _ {k} ^ {y}}{\\sqrt {(v _ {k} ^ {x}) ^ {2} + (v _ {k} ^ {y}) ^ {2}} \\cdot \\sqrt {(\\tilde {v} _ {k} ^ {x}) ^ {2} + (\\tilde {v} _ {k} ^ {y}) ^ {2}}}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 856, + 880, + 897 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8472", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1744aad4a551a67842c04d27656fe764930de312ce2331d9743df6f369f9da66.jpg", + "image_caption": [ + "Figure 8. Quantitative evaluation. For each baseline, we measure CLIP text similarity and motion fidelity (Eq. 5). there is a trade-off between preserving fidelity to the original pixel-level motion and satisfying the desired edit. Our method exhibits a better balance between these two metrics." + ], + "image_footnote": [], + "bbox": [ + 84, + 88, + 460, + 285 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "where $(v_k^x, v_k^y), (\\tilde{v}_k^x, \\tilde{v}_k^y)$ are the $k^{th}$ frame displacement of tracklets $\\tau, \\tilde{\\tau}$ respectively.", + "bbox": [ + 75, + 364, + 468, + 393 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure. 8 reports the metrics above for a set of 54 video-edit text pairs containing 21 unique videos. Our method outperforms the baselines by achieving both high fidelity to the target text prompt and the original motion. Since TokenFlow [19] explicitly does not allow to deviate from original trajectories, their motion fidelity metric score is trivially high, while the edit fidelity score is low. Control-A-Video [13] exhibits a similar behavior since it utilizes depth maps as a guidance signal to edit the video. Tune-A-Video [67] shows an inverse trend, i.e., satisfying the desired edit at the cost of motion fidelity. We further consider SDEdit [36] with different noise levels, none of which can resolve the motion-edit tradeoff. Note that Gen1's API outputs a different number of frames, thus we could not quantitatively evaluate their performance.", + "bbox": [ + 75, + 393, + 468, + 602 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(iii) User study. We employ the Two-alternative Forced Choice (2AFC) protocol for text-driven video editing [2, 17, 19, 47]. Participants are presented with the input video, our results and a baseline, and are asked to determine which video better aligns with the text prompt while preserving the motion of the original video. We collected 7000 user judgments from 150 users. As seen in Table 1, our method is consistently preferred over all baselines.", + "bbox": [ + 75, + 604, + 468, + 717 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Ablations", + "text_level": 1, + "bbox": [ + 76, + 724, + 187, + 738 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Fig. 7, we ablate key design choices in our framework. First, we consider alternative loss functions by substituting the pairwise SMM differences in Eq.4.2 with: (i) full space-time features $\\pmb{f}$ and (ii) SMM features (Eq.1). Figure 7 (b) shows that space-time features restrict both shape and appearance variations; optimizing for SMM features (c) increases flexibility yet is insufficient for matching the edit.", + "bbox": [ + 75, + 746, + 468, + 844 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We next ablate our guided sampling and latent initialization strategy. Sampling from the initial latent without optimization (d) converges to unrelated objects' pose, while initializing the optimization from randomly sampled noise", + "bbox": [ + 75, + 844, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d918aa343a6ead676deec062184d403db06af0760339af4fbac2691cc64c52eb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 90, + 702, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f68ab6cb17994a121ccc307e0e8fa8c6e953c50a92a0afb096d27dfe3e7eb0af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 90, + 903, + 186 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/93d982a3db378f5e7d19899c3db748c483d22feee5e972ee06aff2885b3e4180.jpg", + "image_caption": [ + "Figure 9. Limitations. Our method struggles to preserve the original motion since the combination of the original motion and the edit prompt may be out of distribution for the T2V model." + ], + "image_footnote": [], + "bbox": [ + 504, + 186, + 704, + 272 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fa7e71c1fe64168ffe12cb8a219d3a43d002b4f5baa5a8567db094806d989354.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 186, + 903, + 272 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/70cbbee1cdd93b629c6aa0f7236c3e77bde7668c7ea7646627cc2c0fb78261f4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodJudgements in our favor (%)
TokenFlow72.57%
Control-A-Video84.50%
Tune-A-Video77.80%
", + "bbox": [ + 526, + 333, + 864, + 405 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. User Study. We report the percentage of judgments in our favor w.r.t. each baseline.", + "bbox": [ + 498, + 407, + 890, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(e) fails to retain the original motion characteristics.", + "bbox": [ + 500, + 450, + 841, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and conclusions", + "text_level": 1, + "bbox": [ + 500, + 486, + 750, + 502 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We tackled the task of text-driven motion transfer, focusing on scenarios where the source and target objects differ in shape and fine-grained motion traits. We introduced a zero-shot method that utilizes a pre-trained T2V diffusion model, through a simple optimization framework. Our work is the first to analyze and reveal new insights about spacetime T2V features, and the first to show how to harness their properties for text-driven motion transfer.", + "bbox": [ + 496, + 513, + 890, + 626 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As for limitations, our performance relies on the generative priors learned by the T2V model. Thus, in some cases, the combination of target object and input video motion may be out-of-distribution for the T2V model. In this case, the motion fidelity of our results would be degraded or suffer from visual artifacts (Fig. 9). Moreover, publicly available T2V models are still in infancy, in terms of quality, resolution, video length, and the scale of their training data compared to the vast distribution of natural videos. Despite the limitations of publicly available T2V models, our method significantly improves over prior methods, demonstrating the potential of leveraging the priors and space-time feature space learned by these models.", + "bbox": [ + 496, + 628, + 890, + 809 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 830, + 687, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This project received funding from the Israeli Science Foundation (grant 2303/20). We thank GEN-1 authors for their help in conducting comparisons.", + "bbox": [ + 498, + 857, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8473", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Guha Balakrishnan, Amy Zhao, Adrian V Dalca, Fredo Durand, and John Guttag. Synthesizing images of humans in unseen poses. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8340-8348, 2018. 2", + "[2] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. In European Conference on Computer Vision, pages 707-723. Springer, 2022. 3, 8", + "[3] Omer Bar-Tal, Lior Yariv, Yaron Lipman, and Tali Dekel. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.129, + 0.859, + 0.151 + ], + "angle": 0, + "content": "Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer" + }, + { + "type": "text", + "bbox": [ + 0.119, + 0.157, + 0.241, + 0.175 + ], + "angle": 0, + "content": "Danah Yatim\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.277, + 0.158, + 0.414, + 0.174 + ], + "angle": 0, + "content": "Rafail Fridman\\(^{1*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.451, + 0.159, + 0.567, + 0.174 + ], + "angle": 0, + "content": "Omer Bar-Tal" + }, + { + "type": "text", + "bbox": [ + 0.611, + 0.158, + 0.717, + 0.174 + ], + "angle": 0, + "content": "Yoni Kasten2" + }, + { + "type": "text", + "bbox": [ + 0.757, + 0.158, + 0.848, + 0.174 + ], + "angle": 0, + "content": "Tali Dekel" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.176, + 0.51, + 0.191 + ], + "angle": 0, + "content": "Weizmann Institute of Science" + }, + { + "type": "text", + "bbox": [ + 0.552, + 0.176, + 0.709, + 0.191 + ], + "angle": 0, + "content": "NVIDIA Research" + }, + { + "type": "text", + "bbox": [ + 0.396, + 0.195, + 0.574, + 0.209 + ], + "angle": 0, + "content": "*Indicates equal contribution." + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.24, + 0.098, + 0.272 + ], + "angle": 270, + "content": "Input" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.221, + 0.232, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.235, + 0.221, + 0.362, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.364, + 0.221, + 0.494, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.221, + 0.626, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.221, + 0.755, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.221, + 0.888, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.291, + 0.418, + 0.305 + ], + "angle": 0, + "content": "\"A bike driving in a snowy forest\"" + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.364, + 0.097, + 0.389 + ], + "angle": 270, + "content": "Edit" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.306, + 0.235, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.306, + 0.362, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.364, + 0.306, + 0.493, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.594, + 0.291, + 0.81, + 0.305 + ], + "angle": 0, + "content": "\"A horse jumping into a river\"" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.306, + 0.625, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.627, + 0.306, + 0.755, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.306, + 0.888, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.165, + 0.378, + 0.443, + 0.392 + ], + "angle": 0, + "content": "\"A train riding on rails, autumn view\"" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.394, + 0.235, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.394, + 0.362, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.364, + 0.394, + 0.493, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.574, + 0.378, + 0.829, + 0.393 + ], + "angle": 0, + "content": "\"A dolphin jumping into the ocean\"" + }, + { + "type": "image", + "bbox": [ + 0.496, + 0.394, + 0.626, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.628, + 0.394, + 0.755, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.394, + 0.888, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.469, + 0.893, + 0.497 + ], + "angle": 0, + "content": "Figure 1. Given an input video and a text prompt describing the target objects and scene, our method generates a new video in which the overall motion and scene layout of the input video are preserved, while allowing for notable structural and appearance changes." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.509, + 0.314, + 0.524 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.527, + 0.473, + 0.806 + ], + "angle": 0, + "content": "We present a new method for text-driven motion transfer – synthesizing a video that complies with an input text prompt describing the target objects and scene while maintaining an input video's motion and scene layout. Prior methods are confined to transferring motion across two subjects within the same or closely related object categories and are applicable for limited domains (e.g., humans). In this work, we consider a significantly more challenging setting in which the target and source objects differ drastically in shape and fine-grained motion characteristics (e.g., translating a jumping dog into a dolphin). To this end, we leverage a pre-trained and fixed text-to-video diffusion model, which provides us with generative and motion priors. The pillar of our method is a new space-time feature loss derived directly from the model. This loss guides the generation process to preserve the overall motion of the input video while complying with the target object in terms of shape and fine-grained motion traits. 1 Project page: https://diffusion-motion-transfer.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.822, + 0.209, + 0.836 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.837, + 0.469, + 0.88 + ], + "angle": 0, + "content": "Imagine transferring the car's motion shown in the video in Fig. 1 to a different object, such as a bicycle or a train. This task poses a crucial challenge - retaining key motion" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.51, + 0.892, + 0.649 + ], + "angle": 0, + "content": "characteristics of the input video, such as the car's direction of motion, speed, and pose, while substantially altering the dynamic object's structure to convey the target's unique visual attributes. Conceptually, solving this task requires prior knowledge about objects' appearance, pose, shape, and motion under deformations and different viewpoints, as well as an understanding of their interaction with the scene (e.g., turning the car into a bicycle requires revealing unseen background content and synthesizing plausible scene effects, such as shadows)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.65, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Previous methods have been primarily focused on transferring motion across two similarly-looking videos depicting two subjects within the same object category. These methods are typically confined to object categories for which strong geometric priors exist, e.g., humans for which parametric models for robust shape and pose are available (e.g., [7, 11]). Other works attempt to learn such explicit mid-level representation in a self-supervised manner from the input videos (e.g., [38, 58])– an extremely challenging task by itself. In this work, we take the task of motion transfer to the realm of text-driven video editing, where the target object and scene are specified via a text prompt. We aim at addressing a significantly more general setting, which involves transferring motion across different object categories under significant variations in shape and deformations across time (Fig. 1). Here, we define motion as a sequence of semantic objects' parts' positions and strive to preserve the position of those parts across different object" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.303, + 0.9 + ], + "angle": 0, + "content": "Code will be made publicly available." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8466" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.12 + ], + "angle": 0, + "content": "categories (e.g., legs, arms) while making the target object move realistically." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.12, + 0.468, + 0.369 + ], + "angle": 0, + "content": "Our approach diverges from traditional motion transfer works by avoiding explicit mid-level modeling of pose and shape. Instead, we harness the generative motion priors learned from broad video data by a pre-trained and fixed text-to-video model. Specifically, we delve into the intermediate space-time feature representation learned by the video model and introduce a new loss that guides the generation process of the target video towards the preservation of the original video's overall scene layout and motion. Importantly, our method allows flexibility and deviations from the exact structure and shape of the source objects. This contrasts with prior works in text-driven image and video editing that manipulate spatial features of a pre-trained text-to-image model. These methods inherently lack the ability to perform consistent structural edits across frames since they rely solely on spatial image priors. To the best of our knowledge, our work is the first to empirically analyze and harness space-time features of a text-to-video model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.468, + 0.481 + ], + "angle": 0, + "content": "Our lightweight framework works in a zero-shot fashion, requiring no training data or fine-tuning. We demonstrate results on many videos and edits, encompassing various objects and scenes. We further suggest a new metric to measure motion similarity under shape deviation and quantitatively evaluate our method w.r.t. existing text-to-video methods, demonstrating state-of-the-art performance in terms of motion preservation and edit fidelity." + }, + { + "type": "text", + "bbox": [ + 0.096, + 0.482, + 0.397, + 0.495 + ], + "angle": 0, + "content": "To summarize, our key contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.496, + 0.468, + 0.536 + ], + "angle": 0, + "content": "- An effective zero-shot framework that harnesses the generative motion prior of a pre-trained text-to-video model for the task of motion transfer." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.537, + 0.468, + 0.564 + ], + "angle": 0, + "content": "- New insights about the space-time intermediate features learned by a pre-trained text-to-video diffusion model." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.565, + 0.468, + 0.592 + ], + "angle": 0, + "content": "- A new metric for evaluating motion fidelity under structural deviations between two videos." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.593, + 0.468, + 0.635 + ], + "angle": 0, + "content": "- State-of-the-art results compared to competing methods, achieving a significantly better balance between motion preservation and fidelity to the target prompt." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.496, + 0.468, + 0.635 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.648, + 0.221, + 0.663 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.678, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Motion transfer. A related task to ours is motion transfer from a source to a target subject, where the subjects are of the same or closely related object categories (e.g., [1, 11, 29, 51, 52, 64, 65]). These methods take as input a driving video depicting the source motion, and an image or a video, depicting the target subject. A prevalent approach among these methods is to explicitly model the pose of the dynamic object via a parametric model (e.g. OpenPose [7]). Thus, these methods are largely restricted to domains for which robust parametric models exist (e.g., humans or faces) or to transferring motion across videos depicting similar motion and closely related object categories. In contrast, we are aimed at text-driven motion transfer across distinct object categories. That is, the target object and scene are specified through a text prompt, where the source and target objects can differ significantly in shape," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.866, + 0.107 + ], + "angle": 0, + "content": "appearance, and their natural fine-grained motion traits." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.113, + 0.892, + 0.307 + ], + "angle": 0, + "content": "Text-to-video models. Early works on text-to-video generation utilized VAE or conditional GAN frameworks [31, 37, 42] trained on small-scale datasets of simple domains (e.g., moving digits). Recently, there have been substantial efforts in training large-scale text-to-video models on vast datasets with autoregressive Transformers (e.g., [24, 61, 66]) or Diffusion Models (e.g., [5, 22]). A recent trend extends pre-trained text-to-image (T2I) diffusion models to text-to-video (T2V) generation by adding temporal layers on top of an image architecture [4, 18, 45, 54]. Make-A-Video [54] add temporal Convs and attention layers to a pre-trained T2I pixel-space diffusion model. Other works extend T2I diffusion models that operate on a latent space (e.g., StableDiffusion [49]) to the temporal domain [4, 18]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.309, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Several works [13, 17, 39, 63] train or fine-tune diffusion models for video-to-video translation tasks. Gen-1 [17] design a video architecture that is conditioned on structure/appearance representations, allowing text-driven appearance manipulation of a reference video. Control-A-Video [13] extends a conditional T2I to the temporal domain, allowing the generation of videos that preserve the per-frame layout of a reference video. Nevertheless, since these methods are conditioned on generic mid-level representations of the reference video, they do not allow the preservation of the motion of the reference video while significantly deviating from the per-frame structural layout. In this work, we utilize a pre-trained publicly available T2V diffusion model [8, 62] and show for the first time how it can be leveraged for motion transfer in a zero-shot manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Image & video editing via feature manipulation. There has been unprecedented progress in text-to-image generation using diffusion models [14, 15, 21, 41]. Following this success, a surge of works empirically analyzed the internal feature representation of prominent T2I diffusion models, e.g., StableDiffusion [49], and showed how to perform various editing tasks using simple operations in the T2I feature space.[6, 12, 20, 23, 34, 44, 60]. Prompt-to-Prompt [20] analyzed the cross-attention maps and showed how to manipulate them for controlling the spatial composition in generated images. Plug-and-Play Diffusion (PnP) [60] showed that the spatial features capture semantic information at high spatial granularity and utilized them for imagedto-image translation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "A prominent line of works adopt a pre-trained T2I diffusion model for video editing [9, 19, 28, 47, 67]. For example, Tune-A-Video [67] fine-tunes a T2I model on a single input video and uses the fine-tuned model for stylizing the video or replacing object categories. TokenFlow [19] performs consistent video editing in a zero-shot manner by enforcing consistency on the diffusion features across frames. Nevertheless, these methods do not have access to a T2V generative motion prior and are not designed for edits that require significant structural deviation from the original video. Unlike these works, we leverage the motion prior of a large-scale T2V model, which allows us to support edits that require shape deviation (e.g., car to bike in Fig. 1), uti" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8467" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.437, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.444, + 0.089, + 0.668, + 0.37 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.547, + 0.372, + 0.565, + 0.382 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image", + "bbox": [ + 0.671, + 0.089, + 0.895, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.774, + 0.371, + 0.794, + 0.382 + ], + "angle": 0, + "content": "(d)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.895, + 0.462 + ], + "angle": 0, + "content": "Figure 2. Diffusion feature inversion via guided feature reconstruction. We extract space-time features \\( \\pmb{f} \\) from an input video (a) and steer the generation process of a random sample to produce the same feature \\( \\pmb{f} \\), using feature reconstruction as guidance (b); the synthesized videos closely resemble the original video content in terms of appearance, shape, and pose. Replacing the full space-time features with their spatial marginal mean feature \\( \\mathrm{SMM}[f] \\) allows for more flexibility (c); the SMM feature inversion results capture the original object pose, general position, and scene layout yet are not restricted to the original content at the pixel-level. This is also demonstrated in the nearest neighbor frames retrieved from other videos depicting similar actions, according to similarly in \\( \\mathrm{SMM}[f] \\) features (c)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.476, + 0.471, + 0.534 + ], + "angle": 0, + "content": "lizing a novel loss function that we derive from the model's feature space. To the best of our knowledge, our work is the first to investigate the internal feature representation of a T2V model and leverage it for an editing task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.473, + 0.749 + ], + "angle": 0, + "content": "Consistent video editing. Several recent methods have leveraged layered video representations for consistent text-driven video editing [2, 10, 25, 27, 30, 33, 68]. For example, Text2LIVE [2] proposed to use a pre-trained Layered Neural Atlases (NLA) [27] representation, which is edited using losses defined in CLIP text-image space [48]. However, since the structure and motion of the edited video are determined via the pre-trained NLA, such methods are restricted to only appearance changes. Recently, [30] generalized this approach to allow local structural changes in the edited videos. Nevertheless, NLA takes hours to train, and cannot faithfully represent complex videos due to the strong regularization of objects' motion. In addition, all these methods use a 2D generative prior, thus cannot support large structure deviation and adaption of motion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.759, + 0.205, + 0.777 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Diffusion models. Diffusion models [15, 21, 45, 55] are generative models that aim to approximate a data distribution \\( q \\) by mapping an input noise \\( \\boldsymbol{x}_T \\sim \\mathcal{N}(0, I) \\) to a clean sample \\( \\boldsymbol{x}_0 \\sim q \\), through an iterative denoising process. The DDIM sampler allows to denoise an initial noise \\( \\boldsymbol{x}_T \\) in a deterministic manner [56]. By applying DDIM inversion, a clean sample \\( \\boldsymbol{x}_0 \\) can be mapped back to the sequence of noisy samples \\( \\{\\boldsymbol{x}_i\\}_{t=1}^T \\) used to generate it." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.561 + ], + "angle": 0, + "content": "In latent text-to-image (T2I) diffusion models, e.g., StableDiffusion [49], a pre-trained encoder compresses an RGB image \\( \\pmb{I} \\in \\mathbb{R}^{H \\times W \\times 3} \\) to a latent \\( \\pmb{x} \\in \\mathbb{R}^{H' \\times W' \\times 4} \\), which can be decoded back to the high-resolution space. These T2I models comprise a UNet architecture [50], which consists of Convolutions and Attention modules." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.893, + 0.691 + ], + "angle": 0, + "content": "Latent video diffusion models (e.g., [4, 62]) extend latent T2I models to text-to-video by inflating the 2D architecture to the temporal domain, i.e., adding temporal convolutions and temporal attention layers, and fine-tuning on video datasets. In this case, the T2V model generates a latent video \\(\\pmb{x} \\in \\mathbb{R}^{F \\times H' \\times W' \\times 4}\\), which is then decoded to the output RGB video \\(\\mathcal{V} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}\\). In this work, we utilize the publicly available ZeroScope T2V [8] model, which inflates StableDiffusion [49]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.707, + 0.591, + 0.722 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Given an input video \\(\\mathcal{V}\\) and a target text prompt \\(P\\), our goal is to generate a new video \\(\\mathcal{J}\\) that preserves the overall motion and semantic layout of \\(\\mathcal{V}\\), while complying with \\(P\\). We utilize ZeroScope - a pre-trained latent T2V model [8, 62]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.789, + 0.892, + 0.902 + ], + "angle": 0, + "content": "The key component of our method, illustrated in Fig. 3, is a novel objective function that is used as guidance during the generation process of \\(\\mathcal{I}\\). We conceive this objective based on our empirical analysis that reveals new insights about space-time diffusion features extracted from the model. Specifically, we show that the first-order statistics of the features in the spatial dimensions, i.e., the spatial marginal mean of the features, can serve as a powerful per" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8468" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.541, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.23, + 0.268, + 0.457, + 0.281 + ], + "angle": 0, + "content": "(a) Spatial Marginal Mean (SMM) Feature" + }, + { + "type": "image", + "bbox": [ + 0.542, + 0.089, + 0.887, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.59, + 0.268, + 0.783, + 0.28 + ], + "angle": 0, + "content": "(b) Motion-Guided Video Generation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.291, + 0.895, + 0.346 + ], + "angle": 0, + "content": "Figure 3. Pipeline. (a) Given an input video, we apply DDIM inversion and extract space-time features \\(\\pmb{f} \\in \\mathbb{R}^{F \\times M \\times N \\times D}\\) from intermediate layer activations. We obtain our Spatial Marginal Mean (SMM) feature \\(\\mathrm{SMM}[f] \\in \\mathbb{R}^{F \\times D}\\) by computing the mean over the spatial dimensions, and compute the pairwise differences between each pair of SMM features. (b) For editing, we guide the generation at each denoising step with our Pairwise SMM differences objective (b). See Sec. 4 for more details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.471, + 0.418 + ], + "angle": 0, + "content": "frame global descriptor that (i) retains spatial information such as objects' position, pose, and the semantic layout of the scene, and (ii) robust to pixel-level variations in both appearance and shape." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.429, + 0.422, + 0.445 + ], + "angle": 0, + "content": "4.1. Space-time analysis of diffusion features" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.577 + ], + "angle": 0, + "content": "We focus our analysis on features extracted from the intermediate layer activations of the video model. Recall that the video model is initialized from a text-to-image model, for which the semantic DIFT features [57], were shown to encode localized semantic information shared across objects from different domains [57, 60]. Here, we examine the space-time properties of the corresponding features in the video model. See Supplementary Material (SM) for details about the video model architecture and feature selection." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.678 + ], + "angle": 0, + "content": "Given the input video \\(\\mathcal{V}\\), we apply DDIM inversion with an empty prompt [56], and obtain a sequence of latents \\([\\pmb{x}_1,\\dots,\\pmb{x}_T]\\), where \\(\\pmb{x}_t\\) is the video latent at generation step \\(t\\). We input the latent \\(\\pmb{x}_t\\) to the network and extract the space-time features \\(\\pmb{f}(\\pmb{x}_t) \\in \\mathbb{R}^{F \\times M \\times N \\times D}\\), where \\(F, M, N\\) are the number of frames, height and width of the \\(D\\) dimensional feature activation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.471, + 0.795 + ], + "angle": 0, + "content": "Diffusion feature inversion. To gain a better understanding of what the features \\(\\{\\pmb{f}(\\pmb{x}_t)\\}_{t=1}^T\\) encode, we adopt the concept of \"feature inversion\" [35, 53, 59] (not to confuse with \"DDIM inversion\"). Our goal is to optimize for a video \\(\\mathcal{V}^*\\), randomly initialized, that would produce these features when fed into the network. Specifically, this is achieved using feature reconstruction guidance [16, 40] during the sampling process of \\(\\mathcal{V}^*\\). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.8, + 0.483, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\boldsymbol {x}} _ {T} \\sim \\mathcal {N} (0, \\mathcal {I}) \\\\ \\hat {\\boldsymbol {x}} _ {t - 1} = \\Phi \\left(\\boldsymbol {x} _ {t} ^ {*}, P _ {s}\\right), \\text {w h e r e} \\boldsymbol {x} _ {t} ^ {*} = \\operatorname {a r g m i n} _ {\\hat {\\boldsymbol {x}}} \\| \\boldsymbol {f} (\\boldsymbol {x} _ {\\mathbf {t}}) - \\boldsymbol {f} (\\hat {\\boldsymbol {x}} _ {\\mathbf {t}}) \\| ^ {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.844, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Here, \\(\\Phi\\) is the diffusion model, and \\(P_{s}\\) is a general text prompt describing the input video (e.g., \"a car\"). We minimize the feature reconstruction objective using gradient descent at each generation step. See SM for more details." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.431 + ], + "angle": 0, + "content": "Figure 2 shows our inversion results for the space-time features extracted from an input video; we repeat the inversion process several times, each with different random initialization (i.e., different seeds). We observe that inverted videos nearly reconstruct the original frames (Fig. 2(b))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.893, + 0.526 + ], + "angle": 0, + "content": "Ultimately, we opt to find a feature descriptor that retains such information about objects' pose and the semantic layout of the scene yet is robust to variations in appearance and shape. To reduce the dependency on the pixel-level information, we introduce a new feature descriptor, dubbed Spatial Marginal Mean (SMM), obtained by reducing the spatial dimensions. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.525, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S M M} [ \\boldsymbol {f} (\\boldsymbol {x} _ {t}) ] = \\frac {1}{M \\cdot N} \\sum_ {i = 1} ^ {M} \\sum_ {j = 1} ^ {N} \\boldsymbol {f} (\\boldsymbol {x} _ {t}) _ {i, j} \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.891, + 0.593 + ], + "angle": 0, + "content": "Where \\(\\pmb {f}(\\pmb {x}_t)_{i,j}\\in \\mathbb{R}^D\\) is the entry at spatial location \\((i,j)\\) in the space-time feature volume \\(\\pmb {f}(\\pmb {x}_t)\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.593, + 0.892, + 0.704 + ], + "angle": 0, + "content": "We repeat the inversion experiment (Eq. 1), with \\(\\{\\mathrm{SMM}[\\pmb {f}(\\pmb {x}_t)]\\}_{t = 1}^T\\) as the target features to reconstruct. Figure 2(c) shows the inversion results for the SMM features for different initializations. Remarkably, although the spatial dimensions are collapsed in the SMM features, the inverted videos convey the correct pose and position of objects while depicting larger structural and appearance variations than using the full space-time features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.789 + ], + "angle": 0, + "content": "We further demonstrate these properties by treating the spatial marginal mean associated with each frame as a global per-frame descriptor, and using it to retrieve nearest neighbor frames from other videos. As seen in Fig. 2(d), the retrieved nearest frames depict the same pose, under noticeable appearance and viewpoint changes." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.795, + 0.783, + 0.81 + ], + "angle": 0, + "content": "4.2. Motion-guided video generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.816, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Based on our findings, we now turn to the task of generating a new video \\(\\mathcal{I}\\) that complies with the input prompt \\(P\\) and preserves the motion characteristics of the driving video \\(\\mathcal{V}\\). Our feature inversion analysis raises the question of whether the same approach can be used for editing by replacing the source prompt \\(P_{s}\\) with an edit prompt \\(P\\) in Eq. 1." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8469" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.891, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.543, + 0.698, + 0.556 + ], + "angle": 0, + "content": "Figure 4. Sample results of our method. See SM for full video results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.565, + 0.47, + 0.676 + ], + "angle": 0, + "content": "Figure 7 shows these results for a couple of videos, which demonstrate two issues: (i) depending on the initialization, the optimization may converge to a local minima in which the accurate position of objects and their orientation may differ from the input, (ii) the SMM features still retain appearance information, which reduces the fidelity to the text prompt. We propose the following two components to resolve these issues." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.469, + 0.807 + ], + "angle": 0, + "content": "Pairwise SMM differences. As seen in Fig. 7, directly optimizing for the SMM features often prevents us from deviating from the original appearance. To circumvent this, we propose an objective function to preserve the pairwise differences of the SMM features rather than their exact values. Formally, let \\(\\phi_i^t,\\tilde{\\phi}_i^t\\in \\mathbb{R}^d\\) be the SMM features for frame \\(i\\) and step \\(t\\) for the driving video and the generated video, respectively. For a generation step \\(t\\), the pairwise SMM differences \\(\\Delta^t,\\tilde{\\Delta}^t\\in \\mathbb{R}^{F\\times F\\times d}\\) are defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.809, + 0.469, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\Delta_ {(i, j)} ^ {t} = \\phi_ {i} ^ {t} - \\phi_ {j} ^ {t} \\quad \\tilde {\\Delta} _ {(i, j)} ^ {t} = \\tilde {\\phi} _ {i} ^ {t} - \\tilde {\\phi} _ {j} ^ {t} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.834, + 0.433, + 0.85 + ], + "angle": 0, + "content": "for \\(i,j\\in \\{1,\\ldots ,F\\}\\) . Our loss for time step \\(t\\) is then:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.855, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\operatorname {S M M} (\\boldsymbol {f} (\\boldsymbol {x} _ {t})), \\operatorname {S M M} (\\boldsymbol {f} (\\tilde {\\boldsymbol {x}} _ {t}))) = \\sum_ {i} \\sum_ {j} | | \\Delta_ {(i, j)} ^ {t} - \\tilde {\\Delta} _ {(i, j)} ^ {t} | | _ {2} ^ {2} \\tag {3}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.564, + 0.829, + 0.579 + ], + "angle": 0, + "content": "Algorithm 1 Motion-Guided Video Generation" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.581, + 0.892, + 0.732 + ], + "angle": 0, + "content": "
Input:
V, P▷ Input video and target text prompt
{x_t}T_{t=1}← DDIM-Inv[V] ∀t ∈ [T]
ε0 ~ N(0, I)
x̂T = LFξ(xT) + (ε0 - LFξ(ε0))▷ Filtered noise (Eq. 4.2)
For t = T, ..., 1 do
f(x_t), f(x̂_t) ← Extract space-time features
SMM(f(x_t)), SMM(f(x̂_t)) ← Spatial marginal mean (Eq. 1)
xt* = argminx̂_t L(SMM(f(x_t)), SMM(f(x̂_t)))
x̂_t-1 = Φ(x_t*, P)▷ Apply a denoising step
Output: J ← x0
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.767, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Intuitively, this loss lets us preserve the relative changes in the features through time, while discarding the exact appearance information of the source video (Fig. 7)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.816, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Initialization. It is well-known that the diffusion denoising process is performed in a coarse-to-fine manner, thus, the initialization plays an important role in defining the low frequencies of the generated content [3, 36]. Initialization from a random point may often converge to an undesired local minimum, in which object position is not well-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8470" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.232 + ], + "angle": 0, + "content": "preserved. Note that the low-frequency information of the original video is readily available in the DDIM inverted noise \\( \\pmb{x}_T \\). However, we empirically found that this initialization often restricts edit-ability [43] (see SM for an example). We thus extract only the low frequencies from \\( \\pmb{x}_T \\). Specifically, let \\( \\pmb{x} \\in \\mathbb{R}^{F \\times M \\times N} \\) be a tensor representing \\( F \\) frames, with a spatial resolution of \\( M \\times N \\). We denote by \\( LF_{\\xi}(\\pmb{x}) \\) the operation of spatially downsampling and upsampling \\( \\pmb{x} \\) by a factor of \\( \\xi \\). Then, our initial latent \\( \\tilde{\\pmb{x}}_T \\) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.235, + 0.47, + 0.252 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {x}} _ {T} = L F _ {\\xi} \\left(\\boldsymbol {x} _ {T}\\right) + \\left(\\epsilon_ {0} - L F _ {\\xi} \\left(\\epsilon_ {0}\\right)\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.261, + 0.47, + 0.304 + ], + "angle": 0, + "content": "where \\(\\epsilon_0\\sim \\mathcal{N}(0,I)\\) is a random noise. Intuitively, \\(\\tilde{\\pmb{x}}_T\\) preserves the low-frequencies of the DDIM noise where the higher frequencies are determined by \\(\\epsilon_0\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.303, + 0.47, + 0.332 + ], + "angle": 0, + "content": "To summarize, starting from the filtered latent \\(\\tilde{\\pmb{x}}_T\\), our method deploys the following guided generation process:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.342, + 0.427, + 0.359 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {x} _ {t} ^ {*} = \\operatorname {a r g m i n} _ {\\tilde {\\boldsymbol {x}} _ {t}} \\mathcal {L} (\\operatorname {S M M} (\\boldsymbol {f} (\\boldsymbol {x} _ {t})), \\operatorname {S M M} (\\boldsymbol {f} (\\tilde {\\boldsymbol {x}} _ {t})))\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.121, + 0.359, + 0.241, + 0.372 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {x}} _ {t - 1} = \\Phi (\\boldsymbol {x} _ {t} ^ {*}, P)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.382, + 0.373, + 0.398 + ], + "angle": 0, + "content": "Our full framework is summarized in Alg. 1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.41, + 0.164, + 0.424 + ], + "angle": 0, + "content": "5. Results" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.433, + 0.469, + 0.504 + ], + "angle": 0, + "content": "We evaluate our method on various scenes and object categories, most of which involve camera as well as object motion. The driving videos are taken from DAVIS dataset [46] and from the Web. Our video results and implementation details are available in the Supplementary Materials (SM)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.47, + 0.602 + ], + "angle": 0, + "content": "Figures 1, 4 show sample results of our method. As seen, our method facilitates edits that involve notable changes to the shape and structure of deforming objects, while preserving camera and objects' motion. For instance, we preserve the 3D pose of the car when transferring its motion to a bike or a train (Fig. 1); and maintain the actions of non-rigidly moving objects, e.g., sitting dog or walking camel in Fig. 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.471, + 0.76 + ], + "angle": 0, + "content": "Baselines We compare our method to the following text-driven video editing methods: (i) Shape-Aware Layered Neural Atlases (SA-NLA) [30] that utilizes a pre-trained layered video representation [27] and a pre-trained T2I model [49]. (ii) TokenFlow [19], a zero-shot method that works in the feature space of a pre-trained T2I model (iii) GEN-1 [17] and (iv) Control-A-Video [13], both are video-to-video diffusion models that condition the generation on input depth maps, (v) Tune-A-Video [67] that inflates a T2I model and finetunes it on a single test video, and (iv) SDEdit [36] applied to the same T2V model as our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.767, + 0.285, + 0.782 + ], + "angle": 0, + "content": "5.1. Qualitative evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.788, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Figure 5 shows a qualitative comparison to SA-NLA [30]. Note that SA-NLA utilizes a layered video representation [27], which requires foreground/background separation masks and takes \\(\\sim 10\\) hours to train. Thus, we compare to their provided videos and edit prompts qualitatively. As seen in Fig. 5, both our method and SA-NLA exhibit high fidelity to the original motion. Nevertheless, our method allows for greater deviation in structure, (e.g., matching the" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.091, + 0.63, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.091, + 0.764, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.099, + 0.892, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.21, + 0.63, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.21, + 0.764, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.21, + 0.892, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.33, + 0.63, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.33, + 0.764, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.33, + 0.892, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.523, + 0.449, + 0.608, + 0.459 + ], + "angle": 0, + "content": "Original Frames" + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.449, + 0.72, + 0.458 + ], + "angle": 0, + "content": "SA-NLA" + }, + { + "type": "image_caption", + "bbox": [ + 0.814, + 0.449, + 0.842, + 0.457 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.555 + ], + "angle": 0, + "content": "Figure 5. Comparison to SA-NLA [30]. See SM for video results, structure of a duck in the swan example) and adaption of fine-grained motion traits, which are necessary for capturing the unique attributes of the target object. For example, adapting the shape and movement of a dog's tail to resemble a naturally-looking cat's tail." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.555, + 0.892, + 0.75 + ], + "angle": 0, + "content": "Figure 6 provides comparisons to the additional baselines. As seen, none of these methods can both convey the original motion and adhere to the edit prompt. TokenFlow [19] is tailored to preserve structure of the input video. Gen-1 [17] and Control-A-Video [13] struggle to deviate from the input shapes as they condition the generation on the per-frame depth maps extracted from the input video. Tune-A-Video [67] manages to fulfill the target prompt, yet objects are not aligned in pose and motion (e.g., camel to bear). Our method significantly outperforms these baselines, by successfully matching the desired edits, which require significant structural changes and may involve synthesizing dynamic scene elements (e.g., smoke behind the motorbike). We refer the reader to the SM for full video results." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.754, + 0.891, + 0.783 + ], + "angle": 0, + "content": "Quantitative evaluation. We numerically evaluate the key aspects of our results using the following metrics:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.786, + 0.892, + 0.828 + ], + "angle": 0, + "content": "(i) Edit fidelity. Following previous works (e.g., [17, 19]), we use CLIP [48] to measure the similarity between each frame and the target text and report the average score." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.83, + 0.892, + 0.901 + ], + "angle": 0, + "content": "(ii) Motion fidelity. We aim to assess the fidelity of our results in preserving the original motion. Given our task involves structural deviations, there is no alignment between pixels in the original and output videos. Consequently, traditional metrics such as comparing optical-flow fields are" + }, + { + "type": "list", + "bbox": [ + 0.499, + 0.786, + 0.892, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8471" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.092, + 0.168, + 0.103 + ], + "angle": 0, + "content": "Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.252, + 0.092, + 0.307, + 0.102 + ], + "angle": 0, + "content": "TokenFlow" + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.093, + 0.424, + 0.102 + ], + "angle": 0, + "content": "Gen-1" + }, + { + "type": "image_caption", + "bbox": [ + 0.514, + 0.093, + 0.581, + 0.102 + ], + "angle": 0, + "content": "Tune-A-Video" + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.093, + 0.717, + 0.102 + ], + "angle": 0, + "content": "Control-A-Video" + }, + { + "type": "image_caption", + "bbox": [ + 0.794, + 0.093, + 0.82, + 0.102 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.382, + 0.105, + 0.643, + 0.116 + ], + "angle": 0, + "content": "\"A motorbike driving in a scenic desert\"" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.117, + 0.218, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.117, + 0.352, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.117, + 0.485, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.117, + 0.62, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.117, + 0.752, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.117, + 0.885, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.174, + 0.218, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.174, + 0.352, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.174, + 0.485, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.174, + 0.62, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.174, + 0.752, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.174, + 0.885, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.433, + 0.236, + 0.592, + 0.248 + ], + "angle": 0, + "content": "\"A car driving in a city\"" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.249, + 0.218, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.249, + 0.352, + 0.307 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 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0.754, + 0.308, + 0.885, + 0.366 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.413, + 0.37, + 0.611, + 0.381 + ], + "angle": 0, + "content": "\"A giraffe walking in the zoo\"" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.381, + 0.218, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.381, + 0.352, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.381, + 0.485, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.381, + 0.62, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.381, + 0.752, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.381, + 0.885, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.439, + 0.218, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.221, + 0.439, + 0.352, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.439, + 0.485, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.439, + 0.62, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.439, + 0.752, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.754, + 0.439, + 0.885, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.499, + 0.891, + 0.525 + ], + "angle": 0, + "content": "Figure 6. Comparison. Sample results comparing our method to TokenFlow [19], Gen-1 [17], Tune-A-Video [67], and Control-A-Video [13]. See SM for full video comparisons." + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.529, + 0.199, + 0.541 + ], + "angle": 0, + "content": "(a) Original Frames" + }, + { + "type": "image_caption", + "bbox": [ + 0.212, + 0.529, + 0.352, + 0.541 + ], + "angle": 0, + "content": "(b) Space-time feature loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.362, + 0.529, + 0.474, + 0.54 + ], + "angle": 0, + "content": "(c) SMM feature loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.51, + 0.529, + 0.598, + 0.541 + ], + "angle": 0, + "content": "(d) w/o guidance" + }, + { + "type": "image_caption", + "bbox": [ + 0.636, + 0.529, + 0.744, + 0.541 + ], + "angle": 0, + "content": "(e) w/o low-freq. init" + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.529, + 0.866, + 0.54 + ], + "angle": 0, + "content": "(f) Full method" + }, + { + "type": "image_caption", + "bbox": [ + 0.413, + 0.542, + 0.558, + 0.551 + ], + "angle": 0, + "content": "\"A car driving in a forest" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.551, + 0.212, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.551, + 0.345, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.347, + 0.551, + 0.48, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.488, + 0.551, + 0.622, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.551, + 0.757, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.551, + 0.892, + 0.608 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.394, + 0.608, + 0.578, + 0.617 + ], + "angle": 0, + "content": "\"A giraffe walking on the rocks\"" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.618, + 0.212, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.214, + 0.618, + 0.345, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.347, + 0.618, + 0.48, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.618, + 0.622, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.618, + 0.757, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.618, + 0.891, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.675, + 0.891, + 0.738 + ], + "angle": 0, + "content": "Figure 7. Ablation. (b-c) We compare alternative loss functions instead of our pairwise SMM differences loss (Eq. 4.2); (b) using full space-time features reconstruction prevents deviations in appearance and shape; (c) SMM feature reconstruction allows for more flexibility yet retains appearance information. (d-f) Ablation of our key components: (d) directly sampling from the initial latent w/o optimization preserves only the coarse layout. (e) Starting our optimization from randomly sampled noise (w/o low frequency filtering Eq. 4.2) results in lower motion fidelity compared to our full method (f)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.755, + 0.468, + 0.811 + ], + "angle": 0, + "content": "unsuitable for our use case. We thus introduce a new metric, based on similarity between unaligned long-trajectories. We expect that even under structural changes, the two sets of trajectories would exhibit shared characteristics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.812, + 0.468, + 0.857 + ], + "angle": 0, + "content": "Specifically, we use off-the-shelf tracking method [26] to estimate \\(\\mathcal{T} = \\{\\tau_1,\\dots ,\\tau_n\\}\\), \\(\\tilde{\\mathcal{T}} = \\{\\tilde{\\tau}_1,\\dots ,\\tilde{\\tau}_m\\}\\), two sets of tracklets in the input and output videos, respectively." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.858, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Inspired by the Chamfer distance, we define our Motion-Fidelity-Score as follows. For each tracklet \\(\\tau_{i}\\in \\mathcal{T}\\), we measure the similarity to its nearest neighbor in \\(\\tilde{\\tau}_i\\in \\mathcal{T}\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.755, + 0.602, + 0.768 + ], + "angle": 0, + "content": "and vice versa." + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.771, + 0.892, + 0.81 + ], + "angle": 0, + "content": "\\[\n\\frac {1}{m} \\sum_ {\\tilde {\\tau} \\in \\tilde {\\mathcal {T}}} \\max _ {\\tau \\in \\mathcal {T}} \\operatorname {c o r r} (\\tau , \\tilde {\\tau}) + \\frac {1}{n} \\sum_ {\\tau \\in \\mathcal {T}} \\max _ {\\tilde {\\tau} \\in \\tilde {\\mathcal {T}}} \\operatorname {c o r r} (\\tau , \\tilde {\\tau}) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.819, + 0.891, + 0.848 + ], + "angle": 0, + "content": "where the correlation between two tracklets \\(\\mathbf{corr}(\\tau, \\tilde{\\tau})\\) is computed as follows, similarly to [32]:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.857, + 0.881, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c o r r} (\\tau , \\tilde {\\tau}) = \\frac {1}{F} \\sum_ {k = 1} ^ {F} \\frac {v _ {k} ^ {x} \\cdot \\tilde {v} _ {k} ^ {x} + v _ {k} ^ {y} \\cdot \\tilde {v} _ {k} ^ {y}}{\\sqrt {(v _ {k} ^ {x}) ^ {2} + (v _ {k} ^ {y}) ^ {2}} \\cdot \\sqrt {(\\tilde {v} _ {k} ^ {x}) ^ {2} + (\\tilde {v} _ {k} ^ {y}) ^ {2}}}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8472" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.089, + 0.462, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.47, + 0.351 + ], + "angle": 0, + "content": "Figure 8. Quantitative evaluation. For each baseline, we measure CLIP text similarity and motion fidelity (Eq. 5). there is a trade-off between preserving fidelity to the original pixel-level motion and satisfying the desired edit. Our method exhibits a better balance between these two metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.365, + 0.47, + 0.394 + ], + "angle": 0, + "content": "where \\((v_k^x, v_k^y), (\\tilde{v}_k^x, \\tilde{v}_k^y)\\) are the \\(k^{th}\\) frame displacement of tracklets \\(\\tau, \\tilde{\\tau}\\) respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.469, + 0.603 + ], + "angle": 0, + "content": "Figure. 8 reports the metrics above for a set of 54 video-edit text pairs containing 21 unique videos. Our method outperforms the baselines by achieving both high fidelity to the target text prompt and the original motion. Since TokenFlow [19] explicitly does not allow to deviate from original trajectories, their motion fidelity metric score is trivially high, while the edit fidelity score is low. Control-A-Video [13] exhibits a similar behavior since it utilizes depth maps as a guidance signal to edit the video. Tune-A-Video [67] shows an inverse trend, i.e., satisfying the desired edit at the cost of motion fidelity. We further consider SDEdit [36] with different noise levels, none of which can resolve the motion-edit tradeoff. Note that Gen1's API outputs a different number of frames, thus we could not quantitatively evaluate their performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.469, + 0.718 + ], + "angle": 0, + "content": "(iii) User study. We employ the Two-alternative Forced Choice (2AFC) protocol for text-driven video editing [2, 17, 19, 47]. Participants are presented with the input video, our results and a baseline, and are asked to determine which video better aligns with the text prompt while preserving the motion of the original video. We collected 7000 user judgments from 150 users. As seen in Table 1, our method is consistently preferred over all baselines." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.188, + 0.739 + ], + "angle": 0, + "content": "5.2. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.747, + 0.469, + 0.845 + ], + "angle": 0, + "content": "In Fig. 7, we ablate key design choices in our framework. First, we consider alternative loss functions by substituting the pairwise SMM differences in Eq.4.2 with: (i) full space-time features \\( \\pmb{f} \\) and (ii) SMM features (Eq.1). Figure 7 (b) shows that space-time features restrict both shape and appearance variations; optimizing for SMM features (c) increases flexibility yet is insufficient for matching the edit." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.845, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We next ablate our guided sampling and latent initialization strategy. Sampling from the initial latent without optimization (d) converges to unrelated objects' pose, while initializing the optimization from randomly sampled noise" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.091, + 0.704, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.091, + 0.905, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.187, + 0.705, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.708, + 0.187, + 0.905, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.275, + 0.892, + 0.315 + ], + "angle": 0, + "content": "Figure 9. Limitations. Our method struggles to preserve the original motion since the combination of the original motion and the edit prompt may be out of distribution for the T2V model." + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.334, + 0.866, + 0.406 + ], + "angle": 0, + "content": "
MethodJudgements in our favor (%)
TokenFlow72.57%
Control-A-Video84.50%
Tune-A-Video77.80%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.409, + 0.892, + 0.435 + ], + "angle": 0, + "content": "Table 1. User Study. We report the percentage of judgments in our favor w.r.t. each baseline." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.451, + 0.842, + 0.466 + ], + "angle": 0, + "content": "(e) fails to retain the original motion characteristics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.487, + 0.75, + 0.503 + ], + "angle": 0, + "content": "6. Discussion and conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.514, + 0.892, + 0.627 + ], + "angle": 0, + "content": "We tackled the task of text-driven motion transfer, focusing on scenarios where the source and target objects differ in shape and fine-grained motion traits. We introduced a zero-shot method that utilizes a pre-trained T2V diffusion model, through a simple optimization framework. Our work is the first to analyze and reveal new insights about spacetime T2V features, and the first to show how to harness their properties for text-driven motion transfer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.81 + ], + "angle": 0, + "content": "As for limitations, our performance relies on the generative priors learned by the T2V model. Thus, in some cases, the combination of target object and input video motion may be out-of-distribution for the T2V model. In this case, the motion fidelity of our results would be degraded or suffer from visual artifacts (Fig. 9). Moreover, publicly available T2V models are still in infancy, in terms of quality, resolution, video length, and the scale of their training data compared to the vast distribution of natural videos. Despite the limitations of publicly available T2V models, our method significantly improves over prior methods, demonstrating the potential of leveraging the priors and space-time feature space learned by these models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.688, + 0.848 + ], + "angle": 0, + "content": "7. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.858, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This project received funding from the Israeli Science Foundation (grant 2303/20). We thank GEN-1 authors for their help in conducting comparisons." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8473" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.178 + ], + "angle": 0, + "content": "[1] Guha Balakrishnan, Amy Zhao, Adrian V Dalca, Fredo Durand, and John Guttag. Synthesizing images of humans in unseen poses. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8340-8348, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.18, + 0.472, + 0.232 + ], + "angle": 0, + "content": "[2] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. In European Conference on Computer Vision, pages 707-723. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 2657-2666, 2022. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.471, + 0.662 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "8476" + } + ] +] \ No newline at end of file diff --git a/2024/Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer/2607e128-007d-45ee-9a2f-199fbf395f11_origin.pdf b/2024/Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer/2607e128-007d-45ee-9a2f-199fbf395f11_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..c62ef56ea9e12d2b3d3f3bfa049d5c57c7fa2b7a --- /dev/null +++ b/2024/Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer/2607e128-007d-45ee-9a2f-199fbf395f11_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f787a5cf55bc21289d05cc7c90d2c6943325ba038ade2f4ab8e4c401fedae9e3 +size 5064671 diff --git a/2024/Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer/full.md b/2024/Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer/full.md new file mode 100644 index 0000000000000000000000000000000000000000..04a7f7d903d29f55347feefa119fb2b9328f7879 --- /dev/null +++ b/2024/Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer/full.md @@ -0,0 +1,506 @@ +# Space-Time Diffusion Features for Zero-Shot Text-Driven Motion Transfer + +Danah Yatim $^{1*}$ + +Rafail Fridman $^{1*}$ + +Omer Bar-Tal + +Yoni Kasten2 + +Tali Dekel + +Weizmann Institute of Science + +NVIDIA Research + +*Indicates equal contribution. + +![](images/b99e24c43070d963266219e3b793e34cbd2859a4fd749330fac83651936a64ee.jpg) +Input + +![](images/c7ec9097663ed280f74287e8d2632e55d46937fe311e00febaaf89e3b2496b77.jpg) + +![](images/17a77059ae27e4339d8a58fc74c3b9f3f495f8426d44ddae9dc2cf9bce841cca.jpg) + +![](images/0734c6f5cbeb62dffd05ba86e88ba938f4b40fe25f300b33c0e2e2454630d826.jpg) + +![](images/6a8647c5e44f1958ea452d2233b421ed15a06219ee58132b60ae9ce89d2c21de.jpg) + +![](images/e57d3fa3b16b50184c5fc9f6ef3052050aafc7c4969f1e55fd175cfda29a97eb.jpg) + +"A bike driving in a snowy forest" + +![](images/b9389b4122920d836fd862e0a5383f15806b24360caafc2b4ff5f253bfb9018a.jpg) +Edit + +![](images/29f1408d89cf363674151ae54cecf784fb2a9361b7c275b28c592442777a24c2.jpg) + +![](images/51b32a6057110a2861b8fcd2eeaa3b2bde5e51d268b54dd794f418e54412075a.jpg) + +"A horse jumping into a river" + +![](images/342c7254d11e55c83851c7ca397ef1faa29c7cdc17e15a3531915ea0da811c5c.jpg) + +![](images/216f64b0e4669da958f32dafc413407d3272237dbf82df9d6cc38426c1dd6d7c.jpg) + +![](images/efdb77ff2c1be10662405eddb70009639c3130506ea6abdfb2ad94efe18a92ee.jpg) + +"A train riding on rails, autumn view" + +![](images/a1ddd08de8b9c2d62e4ca734a2e7bdc2f646a8e0529640729c2e33af70f0760b.jpg) +Figure 1. Given an input video and a text prompt describing the target objects and scene, our method generates a new video in which the overall motion and scene layout of the input video are preserved, while allowing for notable structural and appearance changes. + +![](images/173e5c9ccbdfb40bdd4afbf88057d755de3cf398cd2a48d743687a9e48d45191.jpg) + +![](images/fd13adb83e179b7844005827b82411942542f4ab9a04e90e387f05b27cd0d8e8.jpg) + +"A dolphin jumping into the ocean" + +![](images/c74b071a4111ee2ad4f06128640aa5c3433cfcf4dea046612aebd01554968f2a.jpg) + +![](images/3d530a08591eebfdcfd0b80fd7b3f2caea177cd6dee78623882157f1199fa90f.jpg) + +![](images/56700d80c784605a4e341536a8f80bd861b851040652fad14a6e3069153a4074.jpg) + +# Abstract + +We present a new method for text-driven motion transfer – synthesizing a video that complies with an input text prompt describing the target objects and scene while maintaining an input video's motion and scene layout. Prior methods are confined to transferring motion across two subjects within the same or closely related object categories and are applicable for limited domains (e.g., humans). In this work, we consider a significantly more challenging setting in which the target and source objects differ drastically in shape and fine-grained motion characteristics (e.g., translating a jumping dog into a dolphin). To this end, we leverage a pre-trained and fixed text-to-video diffusion model, which provides us with generative and motion priors. The pillar of our method is a new space-time feature loss derived directly from the model. This loss guides the generation process to preserve the overall motion of the input video while complying with the target object in terms of shape and fine-grained motion traits. 1 Project page: https://diffusion-motion-transfer.github.io/ + +# 1. Introduction + +Imagine transferring the car's motion shown in the video in Fig. 1 to a different object, such as a bicycle or a train. This task poses a crucial challenge - retaining key motion + +characteristics of the input video, such as the car's direction of motion, speed, and pose, while substantially altering the dynamic object's structure to convey the target's unique visual attributes. Conceptually, solving this task requires prior knowledge about objects' appearance, pose, shape, and motion under deformations and different viewpoints, as well as an understanding of their interaction with the scene (e.g., turning the car into a bicycle requires revealing unseen background content and synthesizing plausible scene effects, such as shadows). + +Previous methods have been primarily focused on transferring motion across two similarly-looking videos depicting two subjects within the same object category. These methods are typically confined to object categories for which strong geometric priors exist, e.g., humans for which parametric models for robust shape and pose are available (e.g., [7, 11]). Other works attempt to learn such explicit mid-level representation in a self-supervised manner from the input videos (e.g., [38, 58])– an extremely challenging task by itself. In this work, we take the task of motion transfer to the realm of text-driven video editing, where the target object and scene are specified via a text prompt. We aim at addressing a significantly more general setting, which involves transferring motion across different object categories under significant variations in shape and deformations across time (Fig. 1). Here, we define motion as a sequence of semantic objects' parts' positions and strive to preserve the position of those parts across different object + +categories (e.g., legs, arms) while making the target object move realistically. + +Our approach diverges from traditional motion transfer works by avoiding explicit mid-level modeling of pose and shape. Instead, we harness the generative motion priors learned from broad video data by a pre-trained and fixed text-to-video model. Specifically, we delve into the intermediate space-time feature representation learned by the video model and introduce a new loss that guides the generation process of the target video towards the preservation of the original video's overall scene layout and motion. Importantly, our method allows flexibility and deviations from the exact structure and shape of the source objects. This contrasts with prior works in text-driven image and video editing that manipulate spatial features of a pre-trained text-to-image model. These methods inherently lack the ability to perform consistent structural edits across frames since they rely solely on spatial image priors. To the best of our knowledge, our work is the first to empirically analyze and harness space-time features of a text-to-video model. + +Our lightweight framework works in a zero-shot fashion, requiring no training data or fine-tuning. We demonstrate results on many videos and edits, encompassing various objects and scenes. We further suggest a new metric to measure motion similarity under shape deviation and quantitatively evaluate our method w.r.t. existing text-to-video methods, demonstrating state-of-the-art performance in terms of motion preservation and edit fidelity. + +To summarize, our key contributions include: + +- An effective zero-shot framework that harnesses the generative motion prior of a pre-trained text-to-video model for the task of motion transfer. +- New insights about the space-time intermediate features learned by a pre-trained text-to-video diffusion model. +- A new metric for evaluating motion fidelity under structural deviations between two videos. +- State-of-the-art results compared to competing methods, achieving a significantly better balance between motion preservation and fidelity to the target prompt. + +# 2. Related works + +Motion transfer. A related task to ours is motion transfer from a source to a target subject, where the subjects are of the same or closely related object categories (e.g., [1, 11, 29, 51, 52, 64, 65]). These methods take as input a driving video depicting the source motion, and an image or a video, depicting the target subject. A prevalent approach among these methods is to explicitly model the pose of the dynamic object via a parametric model (e.g. OpenPose [7]). Thus, these methods are largely restricted to domains for which robust parametric models exist (e.g., humans or faces) or to transferring motion across videos depicting similar motion and closely related object categories. In contrast, we are aimed at text-driven motion transfer across distinct object categories. That is, the target object and scene are specified through a text prompt, where the source and target objects can differ significantly in shape, + +appearance, and their natural fine-grained motion traits. + +Text-to-video models. Early works on text-to-video generation utilized VAE or conditional GAN frameworks [31, 37, 42] trained on small-scale datasets of simple domains (e.g., moving digits). Recently, there have been substantial efforts in training large-scale text-to-video models on vast datasets with autoregressive Transformers (e.g., [24, 61, 66]) or Diffusion Models (e.g., [5, 22]). A recent trend extends pre-trained text-to-image (T2I) diffusion models to text-to-video (T2V) generation by adding temporal layers on top of an image architecture [4, 18, 45, 54]. Make-A-Video [54] add temporal Convs and attention layers to a pre-trained T2I pixel-space diffusion model. Other works extend T2I diffusion models that operate on a latent space (e.g., StableDiffusion [49]) to the temporal domain [4, 18]. + +Several works [13, 17, 39, 63] train or fine-tune diffusion models for video-to-video translation tasks. Gen-1 [17] design a video architecture that is conditioned on structure/appearance representations, allowing text-driven appearance manipulation of a reference video. Control-A-Video [13] extends a conditional T2I to the temporal domain, allowing the generation of videos that preserve the per-frame layout of a reference video. Nevertheless, since these methods are conditioned on generic mid-level representations of the reference video, they do not allow the preservation of the motion of the reference video while significantly deviating from the per-frame structural layout. In this work, we utilize a pre-trained publicly available T2V diffusion model [8, 62] and show for the first time how it can be leveraged for motion transfer in a zero-shot manner. + +Image & video editing via feature manipulation. There has been unprecedented progress in text-to-image generation using diffusion models [14, 15, 21, 41]. Following this success, a surge of works empirically analyzed the internal feature representation of prominent T2I diffusion models, e.g., StableDiffusion [49], and showed how to perform various editing tasks using simple operations in the T2I feature space.[6, 12, 20, 23, 34, 44, 60]. Prompt-to-Prompt [20] analyzed the cross-attention maps and showed how to manipulate them for controlling the spatial composition in generated images. Plug-and-Play Diffusion (PnP) [60] showed that the spatial features capture semantic information at high spatial granularity and utilized them for imagedto-image translation. + +A prominent line of works adopt a pre-trained T2I diffusion model for video editing [9, 19, 28, 47, 67]. For example, Tune-A-Video [67] fine-tunes a T2I model on a single input video and uses the fine-tuned model for stylizing the video or replacing object categories. TokenFlow [19] performs consistent video editing in a zero-shot manner by enforcing consistency on the diffusion features across frames. Nevertheless, these methods do not have access to a T2V generative motion prior and are not designed for edits that require significant structural deviation from the original video. Unlike these works, we leverage the motion prior of a large-scale T2V model, which allows us to support edits that require shape deviation (e.g., car to bike in Fig. 1), uti + +![](images/14f203c96fdc09e9eeb38c25fc84385da23e4b0da9ba9d230d92365d34c74275.jpg) +Figure 2. Diffusion feature inversion via guided feature reconstruction. We extract space-time features $\pmb{f}$ from an input video (a) and steer the generation process of a random sample to produce the same feature $\pmb{f}$ , using feature reconstruction as guidance (b); the synthesized videos closely resemble the original video content in terms of appearance, shape, and pose. Replacing the full space-time features with their spatial marginal mean feature $\mathrm{SMM}[f]$ allows for more flexibility (c); the SMM feature inversion results capture the original object pose, general position, and scene layout yet are not restricted to the original content at the pixel-level. This is also demonstrated in the nearest neighbor frames retrieved from other videos depicting similar actions, according to similarly in $\mathrm{SMM}[f]$ features (c). + +![](images/460d7896f23ce7231600684bd9d40c5892e8f02fc20a7c621029ea97045f7c11.jpg) +(c) + +![](images/1bb9114eda4981b7379f296c65b81e21a52fd1eb395d80a72b929e0597994c98.jpg) +(d) + +lizing a novel loss function that we derive from the model's feature space. To the best of our knowledge, our work is the first to investigate the internal feature representation of a T2V model and leverage it for an editing task. + +Consistent video editing. Several recent methods have leveraged layered video representations for consistent text-driven video editing [2, 10, 25, 27, 30, 33, 68]. For example, Text2LIVE [2] proposed to use a pre-trained Layered Neural Atlases (NLA) [27] representation, which is edited using losses defined in CLIP text-image space [48]. However, since the structure and motion of the edited video are determined via the pre-trained NLA, such methods are restricted to only appearance changes. Recently, [30] generalized this approach to allow local structural changes in the edited videos. Nevertheless, NLA takes hours to train, and cannot faithfully represent complex videos due to the strong regularization of objects' motion. In addition, all these methods use a 2D generative prior, thus cannot support large structure deviation and adaption of motion. + +# 3. Preliminary + +Diffusion models. Diffusion models [15, 21, 45, 55] are generative models that aim to approximate a data distribution $q$ by mapping an input noise $\boldsymbol{x}_T \sim \mathcal{N}(0, I)$ to a clean sample $\boldsymbol{x}_0 \sim q$ , through an iterative denoising process. The DDIM sampler allows to denoise an initial noise $\boldsymbol{x}_T$ in a deterministic manner [56]. By applying DDIM inversion, a clean sample $\boldsymbol{x}_0$ can be mapped back to the sequence of noisy samples $\{\boldsymbol{x}_i\}_{t=1}^T$ used to generate it. + +In latent text-to-image (T2I) diffusion models, e.g., StableDiffusion [49], a pre-trained encoder compresses an RGB image $\pmb{I} \in \mathbb{R}^{H \times W \times 3}$ to a latent $\pmb{x} \in \mathbb{R}^{H' \times W' \times 4}$ , which can be decoded back to the high-resolution space. These T2I models comprise a UNet architecture [50], which consists of Convolutions and Attention modules. + +Latent video diffusion models (e.g., [4, 62]) extend latent T2I models to text-to-video by inflating the 2D architecture to the temporal domain, i.e., adding temporal convolutions and temporal attention layers, and fine-tuning on video datasets. In this case, the T2V model generates a latent video $\pmb{x} \in \mathbb{R}^{F \times H' \times W' \times 4}$ , which is then decoded to the output RGB video $\mathcal{V} \in \mathbb{R}^{F \times H \times W \times 3}$ . In this work, we utilize the publicly available ZeroScope T2V [8] model, which inflates StableDiffusion [49]. + +# 4. Method + +Given an input video $\mathcal{V}$ and a target text prompt $P$ , our goal is to generate a new video $\mathcal{J}$ that preserves the overall motion and semantic layout of $\mathcal{V}$ , while complying with $P$ . We utilize ZeroScope - a pre-trained latent T2V model [8, 62]. + +The key component of our method, illustrated in Fig. 3, is a novel objective function that is used as guidance during the generation process of $\mathcal{I}$ . We conceive this objective based on our empirical analysis that reveals new insights about space-time diffusion features extracted from the model. Specifically, we show that the first-order statistics of the features in the spatial dimensions, i.e., the spatial marginal mean of the features, can serve as a powerful per + +![](images/41f4b5ac53b34528af3bc4e3b42521819b132492bcb0102e86a1c245b8c3de87.jpg) +(a) Spatial Marginal Mean (SMM) Feature + +![](images/787ae027084f48b6173e42136ab6c0d72bc62da205caf351ab2a7d90e2850d55.jpg) +(b) Motion-Guided Video Generation +Figure 3. Pipeline. (a) Given an input video, we apply DDIM inversion and extract space-time features $\pmb{f} \in \mathbb{R}^{F \times M \times N \times D}$ from intermediate layer activations. We obtain our Spatial Marginal Mean (SMM) feature $\mathrm{SMM}[f] \in \mathbb{R}^{F \times D}$ by computing the mean over the spatial dimensions, and compute the pairwise differences between each pair of SMM features. (b) For editing, we guide the generation at each denoising step with our Pairwise SMM differences objective (b). See Sec. 4 for more details. + +frame global descriptor that (i) retains spatial information such as objects' position, pose, and the semantic layout of the scene, and (ii) robust to pixel-level variations in both appearance and shape. + +# 4.1. Space-time analysis of diffusion features + +We focus our analysis on features extracted from the intermediate layer activations of the video model. Recall that the video model is initialized from a text-to-image model, for which the semantic DIFT features [57], were shown to encode localized semantic information shared across objects from different domains [57, 60]. Here, we examine the space-time properties of the corresponding features in the video model. See Supplementary Material (SM) for details about the video model architecture and feature selection. + +Given the input video $\mathcal{V}$ , we apply DDIM inversion with an empty prompt [56], and obtain a sequence of latents $[\pmb{x}_1,\dots,\pmb{x}_T]$ , where $\pmb{x}_t$ is the video latent at generation step $t$ . We input the latent $\pmb{x}_t$ to the network and extract the space-time features $\pmb{f}(\pmb{x}_t) \in \mathbb{R}^{F \times M \times N \times D}$ , where $F, M, N$ are the number of frames, height and width of the $D$ dimensional feature activation, respectively. + +Diffusion feature inversion. To gain a better understanding of what the features $\{\pmb{f}(\pmb{x}_t)\}_{t=1}^T$ encode, we adopt the concept of "feature inversion" [35, 53, 59] (not to confuse with "DDIM inversion"). Our goal is to optimize for a video $\mathcal{V}^*$ , randomly initialized, that would produce these features when fed into the network. Specifically, this is achieved using feature reconstruction guidance [16, 40] during the sampling process of $\mathcal{V}^*$ . Formally, + +$$ +\begin{array}{l} \hat {\boldsymbol {x}} _ {T} \sim \mathcal {N} (0, \mathcal {I}) \\ \hat {\boldsymbol {x}} _ {t - 1} = \Phi \left(\boldsymbol {x} _ {t} ^ {*}, P _ {s}\right), \text {w h e r e} \boldsymbol {x} _ {t} ^ {*} = \operatorname {a r g m i n} _ {\hat {\boldsymbol {x}}} \| \boldsymbol {f} (\boldsymbol {x} _ {\mathbf {t}}) - \boldsymbol {f} (\hat {\boldsymbol {x}} _ {\mathbf {t}}) \| ^ {2} \\ \end{array} +$$ + +Here, $\Phi$ is the diffusion model, and $P_{s}$ is a general text prompt describing the input video (e.g., "a car"). We minimize the feature reconstruction objective using gradient descent at each generation step. See SM for more details. + +Figure 2 shows our inversion results for the space-time features extracted from an input video; we repeat the inversion process several times, each with different random initialization (i.e., different seeds). We observe that inverted videos nearly reconstruct the original frames (Fig. 2(b)). + +Ultimately, we opt to find a feature descriptor that retains such information about objects' pose and the semantic layout of the scene yet is robust to variations in appearance and shape. To reduce the dependency on the pixel-level information, we introduce a new feature descriptor, dubbed Spatial Marginal Mean (SMM), obtained by reducing the spatial dimensions. Formally, + +$$ +\operatorname {S M M} [ \boldsymbol {f} (\boldsymbol {x} _ {t}) ] = \frac {1}{M \cdot N} \sum_ {i = 1} ^ {M} \sum_ {j = 1} ^ {N} \boldsymbol {f} (\boldsymbol {x} _ {t}) _ {i, j} \tag {1} +$$ + +Where $\pmb {f}(\pmb {x}_t)_{i,j}\in \mathbb{R}^D$ is the entry at spatial location $(i,j)$ in the space-time feature volume $\pmb {f}(\pmb {x}_t)$ + +We repeat the inversion experiment (Eq. 1), with $\{\mathrm{SMM}[\pmb {f}(\pmb {x}_t)]\}_{t = 1}^T$ as the target features to reconstruct. Figure 2(c) shows the inversion results for the SMM features for different initializations. Remarkably, although the spatial dimensions are collapsed in the SMM features, the inverted videos convey the correct pose and position of objects while depicting larger structural and appearance variations than using the full space-time features. + +We further demonstrate these properties by treating the spatial marginal mean associated with each frame as a global per-frame descriptor, and using it to retrieve nearest neighbor frames from other videos. As seen in Fig. 2(d), the retrieved nearest frames depict the same pose, under noticeable appearance and viewpoint changes. + +# 4.2. Motion-guided video generation + +Based on our findings, we now turn to the task of generating a new video $\mathcal{I}$ that complies with the input prompt $P$ and preserves the motion characteristics of the driving video $\mathcal{V}$ . Our feature inversion analysis raises the question of whether the same approach can be used for editing by replacing the source prompt $P_{s}$ with an edit prompt $P$ in Eq. 1. + +![](images/1e2985a71677ff0f74be54d67fd535f565f0d1b999cdf8cc93d34c7af11f96d3.jpg) +Figure 4. Sample results of our method. See SM for full video results. + +Figure 7 shows these results for a couple of videos, which demonstrate two issues: (i) depending on the initialization, the optimization may converge to a local minima in which the accurate position of objects and their orientation may differ from the input, (ii) the SMM features still retain appearance information, which reduces the fidelity to the text prompt. We propose the following two components to resolve these issues. + +Pairwise SMM differences. As seen in Fig. 7, directly optimizing for the SMM features often prevents us from deviating from the original appearance. To circumvent this, we propose an objective function to preserve the pairwise differences of the SMM features rather than their exact values. Formally, let $\phi_i^t,\tilde{\phi}_i^t\in \mathbb{R}^d$ be the SMM features for frame $i$ and step $t$ for the driving video and the generated video, respectively. For a generation step $t$ , the pairwise SMM differences $\Delta^t,\tilde{\Delta}^t\in \mathbb{R}^{F\times F\times d}$ are defined as follows: + +$$ +\Delta_ {(i, j)} ^ {t} = \phi_ {i} ^ {t} - \phi_ {j} ^ {t} \quad \tilde {\Delta} _ {(i, j)} ^ {t} = \tilde {\phi} _ {i} ^ {t} - \tilde {\phi} _ {j} ^ {t} \tag {2} +$$ + +for $i,j\in \{1,\ldots ,F\}$ . Our loss for time step $t$ is then: + +$$ +\mathcal {L} (\operatorname {S M M} (\boldsymbol {f} (\boldsymbol {x} _ {t})), \operatorname {S M M} (\boldsymbol {f} (\tilde {\boldsymbol {x}} _ {t}))) = \sum_ {i} \sum_ {j} | | \Delta_ {(i, j)} ^ {t} - \tilde {\Delta} _ {(i, j)} ^ {t} | | _ {2} ^ {2} \tag {3} +$$ + +# Algorithm 1 Motion-Guided Video Generation + +
Input:
V, P▷ Input video and target text prompt
{x_t}T_{t=1}← DDIM-Inv[V] ∀t ∈ [T]
ε0 ~ N(0, I)
x̂T = LFξ(xT) + (ε0 - LFξ(ε0))▷ Filtered noise (Eq. 4.2)
For t = T, ..., 1 do
f(x_t), f(x̂_t) ← Extract space-time features
SMM(f(x_t)), SMM(f(x̂_t)) ← Spatial marginal mean (Eq. 1)
xt* = argminx̂_t L(SMM(f(x_t)), SMM(f(x̂_t)))
x̂_t-1 = Φ(x_t*, P)▷ Apply a denoising step
Output: J ← x0
+ +Intuitively, this loss lets us preserve the relative changes in the features through time, while discarding the exact appearance information of the source video (Fig. 7). + +Initialization. It is well-known that the diffusion denoising process is performed in a coarse-to-fine manner, thus, the initialization plays an important role in defining the low frequencies of the generated content [3, 36]. Initialization from a random point may often converge to an undesired local minimum, in which object position is not well- + +preserved. Note that the low-frequency information of the original video is readily available in the DDIM inverted noise $\pmb{x}_T$ . However, we empirically found that this initialization often restricts edit-ability [43] (see SM for an example). We thus extract only the low frequencies from $\pmb{x}_T$ . Specifically, let $\pmb{x} \in \mathbb{R}^{F \times M \times N}$ be a tensor representing $F$ frames, with a spatial resolution of $M \times N$ . We denote by $LF_{\xi}(\pmb{x})$ the operation of spatially downsampling and upsampling $\pmb{x}$ by a factor of $\xi$ . Then, our initial latent $\tilde{\pmb{x}}_T$ is given by: + +$$ +\tilde {\boldsymbol {x}} _ {T} = L F _ {\xi} \left(\boldsymbol {x} _ {T}\right) + \left(\epsilon_ {0} - L F _ {\xi} \left(\epsilon_ {0}\right)\right) \tag {4} +$$ + +where $\epsilon_0\sim \mathcal{N}(0,I)$ is a random noise. Intuitively, $\tilde{\pmb{x}}_T$ preserves the low-frequencies of the DDIM noise where the higher frequencies are determined by $\epsilon_0$ + +To summarize, starting from the filtered latent $\tilde{\pmb{x}}_T$ , our method deploys the following guided generation process: + +$$ +\boldsymbol {x} _ {t} ^ {*} = \operatorname {a r g m i n} _ {\tilde {\boldsymbol {x}} _ {t}} \mathcal {L} (\operatorname {S M M} (\boldsymbol {f} (\boldsymbol {x} _ {t})), \operatorname {S M M} (\boldsymbol {f} (\tilde {\boldsymbol {x}} _ {t}))) +$$ + +$$ +\tilde {\boldsymbol {x}} _ {t - 1} = \Phi (\boldsymbol {x} _ {t} ^ {*}, P) +$$ + +Our full framework is summarized in Alg. 1. + +# 5. Results + +We evaluate our method on various scenes and object categories, most of which involve camera as well as object motion. The driving videos are taken from DAVIS dataset [46] and from the Web. Our video results and implementation details are available in the Supplementary Materials (SM). + +Figures 1, 4 show sample results of our method. As seen, our method facilitates edits that involve notable changes to the shape and structure of deforming objects, while preserving camera and objects' motion. For instance, we preserve the 3D pose of the car when transferring its motion to a bike or a train (Fig. 1); and maintain the actions of non-rigidly moving objects, e.g., sitting dog or walking camel in Fig. 4. + +Baselines We compare our method to the following text-driven video editing methods: (i) Shape-Aware Layered Neural Atlases (SA-NLA) [30] that utilizes a pre-trained layered video representation [27] and a pre-trained T2I model [49]. (ii) TokenFlow [19], a zero-shot method that works in the feature space of a pre-trained T2I model (iii) GEN-1 [17] and (iv) Control-A-Video [13], both are video-to-video diffusion models that condition the generation on input depth maps, (v) Tune-A-Video [67] that inflates a T2I model and finetunes it on a single test video, and (iv) SDEdit [36] applied to the same T2V model as our method. + +# 5.1. Qualitative evaluation + +Figure 5 shows a qualitative comparison to SA-NLA [30]. Note that SA-NLA utilizes a layered video representation [27], which requires foreground/background separation masks and takes $\sim 10$ hours to train. Thus, we compare to their provided videos and edit prompts qualitatively. As seen in Fig. 5, both our method and SA-NLA exhibit high fidelity to the original motion. Nevertheless, our method allows for greater deviation in structure, (e.g., matching the + +![](images/a08664cc0ad5d572b9ee811eb1e97fc74f829bdedbc227a61a04849407a77ce5.jpg) + +![](images/2041cd08e27bd1ea26587e727a42b0ecd4aed968e338e8c00aea94db5760085b.jpg) + +![](images/8b6b1ebcc3aceadf7fc301f97742ec00e1215d6e69a9917d9e1654bb05d41f6b.jpg) + +![](images/c984ee63b9a6443e08e2626aa76218a5ff981fced73ef22ddee7233ed7f1fe57.jpg) + +![](images/4a1cc656b23f2cb088e7e7fd793f57efcb521b696b302d754836a6c8abe761da.jpg) + +![](images/b6e364702eafd21dc40c9a2bb92527a0caabc9e6c84ddcb439129fcfc86fdd0b.jpg) + +![](images/033bf5db62b9fc645bb0c3a3dde7d37744771f27cb2b565aa64c8a742dd07390.jpg) +Original Frames +Figure 5. Comparison to SA-NLA [30]. See SM for video results, structure of a duck in the swan example) and adaption of fine-grained motion traits, which are necessary for capturing the unique attributes of the target object. For example, adapting the shape and movement of a dog's tail to resemble a naturally-looking cat's tail. + +![](images/1ce9288a0ad2e337eb52357f1a89cc1d5cee0c36076740ac6a77270a1fa158b8.jpg) +SA-NLA + +![](images/10e9d8b526de98e48064ac29e08960a96cf2478e323fb4e814fb42d14800f4ea.jpg) +Ours + +Figure 6 provides comparisons to the additional baselines. As seen, none of these methods can both convey the original motion and adhere to the edit prompt. TokenFlow [19] is tailored to preserve structure of the input video. Gen-1 [17] and Control-A-Video [13] struggle to deviate from the input shapes as they condition the generation on the per-frame depth maps extracted from the input video. Tune-A-Video [67] manages to fulfill the target prompt, yet objects are not aligned in pose and motion (e.g., camel to bear). Our method significantly outperforms these baselines, by successfully matching the desired edits, which require significant structural changes and may involve synthesizing dynamic scene elements (e.g., smoke behind the motorbike). We refer the reader to the SM for full video results. + +Quantitative evaluation. We numerically evaluate the key aspects of our results using the following metrics: + +(i) Edit fidelity. Following previous works (e.g., [17, 19]), we use CLIP [48] to measure the similarity between each frame and the target text and report the average score. +(ii) Motion fidelity. We aim to assess the fidelity of our results in preserving the original motion. Given our task involves structural deviations, there is no alignment between pixels in the original and output videos. Consequently, traditional metrics such as comparing optical-flow fields are + +![](images/931566520dd45be01aad60e47a239a64308b4b98413a192b9ed6677ac3ff2c6b.jpg) +Input + +![](images/c71a36c49de539f8bce25fd8707b64ff38da79a3810a0f1662621a73ffea7b1b.jpg) +TokenFlow + +![](images/cbad7c2aa0bcaeecf85c7ddf6d5fbf2c704439d784a2acd001a4f7c63edde57d.jpg) +Gen-1 +"A motorbike driving in a scenic desert" + +![](images/7ba42143622dfccbd543a9002c34fe9131b928d1b2ce6806f3433187a9e25642.jpg) +Tune-A-Video + +![](images/496cd50623807c6553a20a3c8ed1782d70a739164bc0869e5973203f639ed3d4.jpg) +Control-A-Video + +![](images/1e1c3161782f545f792358fd7eea845c9b16e536f3d6deb838b5ec51d82aab4b.jpg) +Ours + +![](images/a9e490d452f90fb3d04187d3bbee86ced1fe13c2983ffd26e7cbe42e3c9258da.jpg) + +![](images/a90807e9f97bbc934fbdfd2fbcbe88ff3a8ffbf909e00825c561c0dd4e286936.jpg) + +![](images/518f0d5499f47f92404cea3c24a2b4777ab299862a2419580172919c651dad7a.jpg) + +![](images/e0a15ab606c652e7bf75c6c56b62920e1fb73441df3f5c07d846425481cb914f.jpg) + +![](images/3d1585ba7826c1e1ec8f25093e9b2617e754c7d2b7ae1767d073c1fe271b405d.jpg) + +![](images/1742cf6fb8e31de3fdcf29c98c45d290c43e7ac0eac26e19e00429a9023c9870.jpg) + +![](images/b8ea615877aa84c4953079ec367015fa02395fb8efb94fb664789a557599c04f.jpg) + +![](images/e4c2e4ed64df08a75f102dd9a92b4a4b9cc14e9a6a5c80567d3b2997e3b7d375.jpg) + +![](images/4ce081b15eeb8c4d422bdb3be1bbc79b034ddb97e9f93f4e1f16d6e24677577d.jpg) +"A car driving in a city" + +![](images/4c36180a9853c7074820737c1a9eccdd14787fa5dcb04b16dc4df1c36e2492d9.jpg) + +![](images/6fb90546d1a8e905502d1d7acf3f9254afaedcefa5917e0cc1ad32936bf5b0b5.jpg) + +![](images/2e70ad8bc9bce7af3350994a1a090339303ce12c5122d77f56b3e69b6c97994e.jpg) + +![](images/3e9d64b5fcc55b9f94cf5637b4c17295aa33a917b942c7f54b2b02a934a5bc39.jpg) + +![](images/c77b2069682787093336edee518d1a4eb747fb82fe139bee619bef594e2669c6.jpg) + +![](images/166cd26503dc99b338b65294417906a7a84362d5c261e6c9f31bc56109c25480.jpg) + +![](images/44d3e3ca4895cccfee801d5e9abb49ce425669cc0112d8adba8c2576d5d5b7d5.jpg) + +![](images/9aabd5e55978ff6f4b302767e1dd6ee3464c0ba3d72e623c192cc7b365d2b053.jpg) + +![](images/8f6be0ce821843e5d49056aca4321007f60d1c2cd5378a0ada9405901beb29de.jpg) + +![](images/38d83e34b61c82bee23ec72a37f96815925475f244736d91638fdc22c8f74341.jpg) + +![](images/b3088ca3f8af11b25787b76212a2f4819c520272b3a232bbbb718ed715ac7f70.jpg) + +![](images/84c7cb57a41f4e5c4fcd50c5d427703247534e87b89f8ee5fdf3b58c0fbd95c5.jpg) +"A giraffe walking in the zoo" + +![](images/9948772752ea2d9a8e9be6208551d8821478555064d1180fc59147433e5fd433.jpg) + +![](images/8c4c4f6432da53cc84ff57ebf7d05351a29795dd6943b332166e5a76262779ba.jpg) + +![](images/9c74711a7e5f6b0a865b126e908703597ff283a76fe822ff50805feb0cd67fe5.jpg) + +![](images/b5a2b664b70da830db6237051649bbb16828d978f78decb0df03c8b210bb7fc5.jpg) +Figure 6. Comparison. Sample results comparing our method to TokenFlow [19], Gen-1 [17], Tune-A-Video [67], and Control-A-Video [13]. See SM for full video comparisons. + +![](images/d4639c8d0a1baa261cc16c493a8eed8215f927b18e4ecdedfcd452137caaa659.jpg) + +![](images/03536f3da6300a6faf6f392965092bb92439fb091a9580df26a68f86457e69f4.jpg) + +![](images/8a89c25935c6870e00fcd5e9e27bdc304af1d1c17d0aae03608404911830aa2b.jpg) + +![](images/787c051a02bc4fb9b3dae0e03ef643d818250b99eaa2411315a7febd0b83b6e7.jpg) + +![](images/020d62ad50d7dda3d3b8b9b038a01c570bcce1bd2e21779cd98d55a16c85a20b.jpg) + +![](images/8d051c6321060462c1f574bd9a283f6b0c57a3d9337516193af1e60f1ef7cdde.jpg) +(a) Original Frames +(b) Space-time feature loss + +![](images/3623b126f154c60de7e0b0fb2212b6e16c47f700da42ba73e485d9cde083d58e.jpg) + +![](images/6670cb9317ec629b5780f6a86c594a4cec3f1b221be0f21c0c341845d012ea26.jpg) +(c) SMM feature loss +"A car driving in a forest +"A giraffe walking on the rocks" + +![](images/7a78ea8c1ba25fbad32fe83701fd187d52a57b67b7b07f5e4a79be5126350224.jpg) +(d) w/o guidance + +![](images/26739f0da9149526debd207240185bbe3071848991757c9e563d727b1eaadf64.jpg) +(e) w/o low-freq. init + +![](images/bb9bcb3bf26d2f62a7e929dc8643617772ef6cd342d9278e3f8201205e62e382.jpg) +(f) Full method + +![](images/ce77066be6b7f4919fcfdee476d3e480507c0204ac392603da34a5d9b27260f6.jpg) +Figure 7. Ablation. (b-c) We compare alternative loss functions instead of our pairwise SMM differences loss (Eq. 4.2); (b) using full space-time features reconstruction prevents deviations in appearance and shape; (c) SMM feature reconstruction allows for more flexibility yet retains appearance information. (d-f) Ablation of our key components: (d) directly sampling from the initial latent w/o optimization preserves only the coarse layout. (e) Starting our optimization from randomly sampled noise (w/o low frequency filtering Eq. 4.2) results in lower motion fidelity compared to our full method (f). + +![](images/5ec72eca7c02a257c7618dbef97030433cea6e768b824137449a805c2a71174d.jpg) + +![](images/be0adee4dc24e32243f397aa569c455de1d84fa82405308c74425800f2f9b222.jpg) + +![](images/ae464d7d3bc5dfeaa874bbb2d1eee8c9c07d8b8d392731f0025e28fbe190b119.jpg) + +![](images/f24d510f2193a4a00623f99fd7f07434c98803f7b110336964998c0d25e5f7da.jpg) + +![](images/deea76b1b349cca1ed278c9a181844acda410147e185198b2b9571e5dbdd6d97.jpg) + +unsuitable for our use case. We thus introduce a new metric, based on similarity between unaligned long-trajectories. We expect that even under structural changes, the two sets of trajectories would exhibit shared characteristics. + +Specifically, we use off-the-shelf tracking method [26] to estimate $\mathcal{T} = \{\tau_1,\dots ,\tau_n\}$ , $\tilde{\mathcal{T}} = \{\tilde{\tau}_1,\dots ,\tilde{\tau}_m\}$ , two sets of tracklets in the input and output videos, respectively. + +Inspired by the Chamfer distance, we define our Motion-Fidelity-Score as follows. For each tracklet $\tau_{i}\in \mathcal{T}$ , we measure the similarity to its nearest neighbor in $\tilde{\tau}_i\in \mathcal{T}$ + +and vice versa. + +$$ +\frac {1}{m} \sum_ {\tilde {\tau} \in \tilde {\mathcal {T}}} \max _ {\tau \in \mathcal {T}} \operatorname {c o r r} (\tau , \tilde {\tau}) + \frac {1}{n} \sum_ {\tau \in \mathcal {T}} \max _ {\tilde {\tau} \in \tilde {\mathcal {T}}} \operatorname {c o r r} (\tau , \tilde {\tau}) \tag {5} +$$ + +where the correlation between two tracklets $\mathbf{corr}(\tau, \tilde{\tau})$ is computed as follows, similarly to [32]: + +$$ +\mathbf {c o r r} (\tau , \tilde {\tau}) = \frac {1}{F} \sum_ {k = 1} ^ {F} \frac {v _ {k} ^ {x} \cdot \tilde {v} _ {k} ^ {x} + v _ {k} ^ {y} \cdot \tilde {v} _ {k} ^ {y}}{\sqrt {(v _ {k} ^ {x}) ^ {2} + (v _ {k} ^ {y}) ^ {2}} \cdot \sqrt {(\tilde {v} _ {k} ^ {x}) ^ {2} + (\tilde {v} _ {k} ^ {y}) ^ {2}}} +$$ + +![](images/1744aad4a551a67842c04d27656fe764930de312ce2331d9743df6f369f9da66.jpg) +Figure 8. Quantitative evaluation. For each baseline, we measure CLIP text similarity and motion fidelity (Eq. 5). there is a trade-off between preserving fidelity to the original pixel-level motion and satisfying the desired edit. Our method exhibits a better balance between these two metrics. + +where $(v_k^x, v_k^y), (\tilde{v}_k^x, \tilde{v}_k^y)$ are the $k^{th}$ frame displacement of tracklets $\tau, \tilde{\tau}$ respectively. + +Figure. 8 reports the metrics above for a set of 54 video-edit text pairs containing 21 unique videos. Our method outperforms the baselines by achieving both high fidelity to the target text prompt and the original motion. Since TokenFlow [19] explicitly does not allow to deviate from original trajectories, their motion fidelity metric score is trivially high, while the edit fidelity score is low. Control-A-Video [13] exhibits a similar behavior since it utilizes depth maps as a guidance signal to edit the video. Tune-A-Video [67] shows an inverse trend, i.e., satisfying the desired edit at the cost of motion fidelity. We further consider SDEdit [36] with different noise levels, none of which can resolve the motion-edit tradeoff. Note that Gen1's API outputs a different number of frames, thus we could not quantitatively evaluate their performance. + +(iii) User study. We employ the Two-alternative Forced Choice (2AFC) protocol for text-driven video editing [2, 17, 19, 47]. Participants are presented with the input video, our results and a baseline, and are asked to determine which video better aligns with the text prompt while preserving the motion of the original video. We collected 7000 user judgments from 150 users. As seen in Table 1, our method is consistently preferred over all baselines. + +# 5.2. Ablations + +In Fig. 7, we ablate key design choices in our framework. First, we consider alternative loss functions by substituting the pairwise SMM differences in Eq.4.2 with: (i) full space-time features $\pmb{f}$ and (ii) SMM features (Eq.1). Figure 7 (b) shows that space-time features restrict both shape and appearance variations; optimizing for SMM features (c) increases flexibility yet is insufficient for matching the edit. + +We next ablate our guided sampling and latent initialization strategy. Sampling from the initial latent without optimization (d) converges to unrelated objects' pose, while initializing the optimization from randomly sampled noise + +![](images/d918aa343a6ead676deec062184d403db06af0760339af4fbac2691cc64c52eb.jpg) + +![](images/f68ab6cb17994a121ccc307e0e8fa8c6e953c50a92a0afb096d27dfe3e7eb0af.jpg) + +![](images/93d982a3db378f5e7d19899c3db748c483d22feee5e972ee06aff2885b3e4180.jpg) +Figure 9. Limitations. Our method struggles to preserve the original motion since the combination of the original motion and the edit prompt may be out of distribution for the T2V model. + +![](images/fa7e71c1fe64168ffe12cb8a219d3a43d002b4f5baa5a8567db094806d989354.jpg) + +
MethodJudgements in our favor (%)
TokenFlow72.57%
Control-A-Video84.50%
Tune-A-Video77.80%
+ +Table 1. User Study. We report the percentage of judgments in our favor w.r.t. each baseline. + +(e) fails to retain the original motion characteristics. + +# 6. Discussion and conclusions + +We tackled the task of text-driven motion transfer, focusing on scenarios where the source and target objects differ in shape and fine-grained motion traits. We introduced a zero-shot method that utilizes a pre-trained T2V diffusion model, through a simple optimization framework. Our work is the first to analyze and reveal new insights about spacetime T2V features, and the first to show how to harness their properties for text-driven motion transfer. + +As for limitations, our performance relies on the generative priors learned by the T2V model. Thus, in some cases, the combination of target object and input video motion may be out-of-distribution for the T2V model. In this case, the motion fidelity of our results would be degraded or suffer from visual artifacts (Fig. 9). Moreover, publicly available T2V models are still in infancy, in terms of quality, resolution, video length, and the scale of their training data compared to the vast distribution of natural videos. Despite the limitations of publicly available T2V models, our method significantly improves over prior methods, demonstrating the potential of leveraging the priors and space-time feature space learned by these models. + +# 7. Acknowledgements + +This project received funding from the Israeli Science Foundation (grant 2303/20). We thank GEN-1 authors for their help in conducting comparisons. + +# References + +[1] Guha Balakrishnan, Amy Zhao, Adrian V Dalca, Fredo Durand, and John Guttag. Synthesizing images of humans in unseen poses. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 8340-8348, 2018. 2 +[2] Omer Bar-Tal, Dolev Ofri-Amar, Rafail Fridman, Yoni Kasten, and Tali Dekel. Text2live: Text-driven layered image and video editing. 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Prior methods are confined to transferring motion across two subjects within the same or closely related object categories and are applicable for limited domains (e.g., humans). In this work, we consider a significantly more challenging setting in which the target and source objects differ drastically in shape and fine-grained motion characteristics (e.g., translating a jumping dog into a dolphin). To this end, we leverage a pre-trained and fixed text-to-video diffusion model, which provides us with generative and motion priors. The pillar of our method is a new space-time feature loss derived directly from the model. This loss guides the generation process to preserve the overall motion of the input video while complying with the target object in terms of shape and fine-grained motion traits. 1 Project page: https://diffusion-motion-transfer.github.io/" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 47, + 651, + 127, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 127, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 127, + 662 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 662, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 662, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 662, + 287, + 696 + ], + "type": "text", + "content": "Imagine transferring the car's motion shown in the video in Fig. 1 to a different object, such as a bicycle or a train. This task poses a crucial challenge - retaining key motion" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 306, + 403, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 545, + 514 + ], + "type": "text", + "content": "characteristics of the input video, such as the car's direction of motion, speed, and pose, while substantially altering the dynamic object's structure to convey the target's unique visual attributes. Conceptually, solving this task requires prior knowledge about objects' appearance, pose, shape, and motion under deformations and different viewpoints, as well as an understanding of their interaction with the scene (e.g., turning the car into a bicycle requires revealing unseen background content and synthesizing plausible scene effects, such as shadows)." + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 514, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 546, + 714 + ], + "type": "text", + "content": "Previous methods have been primarily focused on transferring motion across two similarly-looking videos depicting two subjects within the same object category. These methods are typically confined to object categories for which strong geometric priors exist, e.g., humans for which parametric models for robust shape and pose are available (e.g., [7, 11]). Other works attempt to learn such explicit mid-level representation in a self-supervised manner from the input videos (e.g., [38, 58])– an extremely challenging task by itself. In this work, we take the task of motion transfer to the realm of text-driven video editing, where the target object and scene are specified via a text prompt. We aim at addressing a significantly more general setting, which involves transferring motion across different object categories under significant variations in shape and deformations across time (Fig. 1). Here, we define motion as a sequence of semantic objects' parts' positions and strive to preserve the position of those parts across different object" + } + ] + } + ], + "index": 41 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 185, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 185, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 185, + 712 + ], + "type": "text", + "content": "Code will be made publicly available." + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8466" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "categories (e.g., legs, arms) while making the target object move realistically." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 95, + 286, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 95, + 286, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 95, + 286, + 292 + ], + "type": "text", + "content": "Our approach diverges from traditional motion transfer works by avoiding explicit mid-level modeling of pose and shape. Instead, we harness the generative motion priors learned from broad video data by a pre-trained and fixed text-to-video model. Specifically, we delve into the intermediate space-time feature representation learned by the video model and introduce a new loss that guides the generation process of the target video towards the preservation of the original video's overall scene layout and motion. Importantly, our method allows flexibility and deviations from the exact structure and shape of the source objects. This contrasts with prior works in text-driven image and video editing that manipulate spatial features of a pre-trained text-to-image model. These methods inherently lack the ability to perform consistent structural edits across frames since they rely solely on spatial image priors. To the best of our knowledge, our work is the first to empirically analyze and harness space-time features of a text-to-video model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 293, + 286, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 286, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 286, + 380 + ], + "type": "text", + "content": "Our lightweight framework works in a zero-shot fashion, requiring no training data or fine-tuning. We demonstrate results on many videos and edits, encompassing various objects and scenes. We further suggest a new metric to measure motion similarity under shape deviation and quantitatively evaluate our method w.r.t. existing text-to-video methods, demonstrating state-of-the-art performance in terms of motion preservation and edit fidelity." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 58, + 381, + 242, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 381, + 242, + 392 + ], + "spans": [ + { + "bbox": [ + 58, + 381, + 242, + 392 + ], + "type": "text", + "content": "To summarize, our key contributions include:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 392, + 286, + 502 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 392, + 286, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 286, + 424 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 286, + 424 + ], + "type": "text", + "content": "- An effective zero-shot framework that harnesses the generative motion prior of a pre-trained text-to-video model for the task of motion transfer." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 425, + 286, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 425, + 286, + 446 + ], + "spans": [ + { + "bbox": [ + 47, + 425, + 286, + 446 + ], + "type": "text", + "content": "- New insights about the space-time intermediate features learned by a pre-trained text-to-video diffusion model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 447, + 286, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 447, + 286, + 468 + ], + "spans": [ + { + "bbox": [ + 47, + 447, + 286, + 468 + ], + "type": "text", + "content": "- A new metric for evaluating motion fidelity under structural deviations between two videos." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 469, + 286, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 469, + 286, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 469, + 286, + 502 + ], + "type": "text", + "content": "- State-of-the-art results compared to competing methods, achieving a significantly better balance between motion preservation and fidelity to the target prompt." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 513, + 135, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 513, + 135, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 513, + 135, + 525 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 536, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 286, + 713 + ], + "type": "text", + "content": "Motion transfer. A related task to ours is motion transfer from a source to a target subject, where the subjects are of the same or closely related object categories (e.g., [1, 11, 29, 51, 52, 64, 65]). These methods take as input a driving video depicting the source motion, and an image or a video, depicting the target subject. A prevalent approach among these methods is to explicitly model the pose of the dynamic object via a parametric model (e.g. OpenPose [7]). Thus, these methods are largely restricted to domains for which robust parametric models exist (e.g., humans or faces) or to transferring motion across videos depicting similar motion and closely related object categories. In contrast, we are aimed at text-driven motion transfer across distinct object categories. That is, the target object and scene are specified through a text prompt, where the source and target objects can differ significantly in shape," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 529, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 529, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 529, + 84 + ], + "type": "text", + "content": "appearance, and their natural fine-grained motion traits." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 89, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 89, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 304, + 89, + 545, + 243 + ], + "type": "text", + "content": "Text-to-video models. Early works on text-to-video generation utilized VAE or conditional GAN frameworks [31, 37, 42] trained on small-scale datasets of simple domains (e.g., moving digits). Recently, there have been substantial efforts in training large-scale text-to-video models on vast datasets with autoregressive Transformers (e.g., [24, 61, 66]) or Diffusion Models (e.g., [5, 22]). A recent trend extends pre-trained text-to-image (T2I) diffusion models to text-to-video (T2V) generation by adding temporal layers on top of an image architecture [4, 18, 45, 54]. Make-A-Video [54] add temporal Convs and attention layers to a pre-trained T2I pixel-space diffusion model. Other works extend T2I diffusion models that operate on a latent space (e.g., StableDiffusion [49]) to the temporal domain [4, 18]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 244, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 244, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 244, + 545, + 410 + ], + "type": "text", + "content": "Several works [13, 17, 39, 63] train or fine-tune diffusion models for video-to-video translation tasks. Gen-1 [17] design a video architecture that is conditioned on structure/appearance representations, allowing text-driven appearance manipulation of a reference video. Control-A-Video [13] extends a conditional T2I to the temporal domain, allowing the generation of videos that preserve the per-frame layout of a reference video. Nevertheless, since these methods are conditioned on generic mid-level representations of the reference video, they do not allow the preservation of the motion of the reference video while significantly deviating from the per-frame structural layout. In this work, we utilize a pre-trained publicly available T2V diffusion model [8, 62] and show for the first time how it can be leveraged for motion transfer in a zero-shot manner." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 415, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 568 + ], + "type": "text", + "content": "Image & video editing via feature manipulation. There has been unprecedented progress in text-to-image generation using diffusion models [14, 15, 21, 41]. Following this success, a surge of works empirically analyzed the internal feature representation of prominent T2I diffusion models, e.g., StableDiffusion [49], and showed how to perform various editing tasks using simple operations in the T2I feature space.[6, 12, 20, 23, 34, 44, 60]. Prompt-to-Prompt [20] analyzed the cross-attention maps and showed how to manipulate them for controlling the spatial composition in generated images. Plug-and-Play Diffusion (PnP) [60] showed that the spatial features capture semantic information at high spatial granularity and utilized them for imagedto-image translation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "A prominent line of works adopt a pre-trained T2I diffusion model for video editing [9, 19, 28, 47, 67]. For example, Tune-A-Video [67] fine-tunes a T2I model on a single input video and uses the fine-tuned model for stylizing the video or replacing object categories. TokenFlow [19] performs consistent video editing in a zero-shot manner by enforcing consistency on the diffusion features across frames. Nevertheless, these methods do not have access to a T2V generative motion prior and are not designed for edits that require significant structural deviation from the original video. Unlike these works, we leverage the motion prior of a large-scale T2V model, which allows us to support edits that require shape deviation (e.g., car to bike in Fig. 1), uti" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8467" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 267, + 302 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 267, + 302 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 267, + 302 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 267, + 302 + ], + "type": "image", + "image_path": "14f203c96fdc09e9eeb38c25fc84385da23e4b0da9ba9d230d92365d34c74275.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "text", + "content": "Figure 2. Diffusion feature inversion via guided feature reconstruction. We extract space-time features " + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "text", + "content": " from an input video (a) and steer the generation process of a random sample to produce the same feature " + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "text", + "content": ", using feature reconstruction as guidance (b); the synthesized videos closely resemble the original video content in terms of appearance, shape, and pose. Replacing the full space-time features with their spatial marginal mean feature " + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "inline_equation", + "content": "\\mathrm{SMM}[f]" + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "text", + "content": " allows for more flexibility (c); the SMM feature inversion results capture the original object pose, general position, and scene layout yet are not restricted to the original content at the pixel-level. This is also demonstrated in the nearest neighbor frames retrieved from other videos depicting similar actions, according to similarly in " + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "inline_equation", + "content": "\\mathrm{SMM}[f]" + }, + { + "bbox": [ + 46, + 303, + 547, + 365 + ], + "type": "text", + "content": " features (c)." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 271, + 70, + 408, + 293 + ], + "blocks": [ + { + "bbox": [ + 271, + 70, + 408, + 293 + ], + "lines": [ + { + "bbox": [ + 271, + 70, + 408, + 293 + ], + "spans": [ + { + "bbox": [ + 271, + 70, + 408, + 293 + ], + "type": "image", + "image_path": "460d7896f23ce7231600684bd9d40c5892e8f02fc20a7c621029ea97045f7c11.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 334, + 294, + 345, + 302 + ], + "lines": [ + { + "bbox": [ + 334, + 294, + 345, + 302 + ], + "spans": [ + { + "bbox": [ + 334, + 294, + 345, + 302 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 410, + 70, + 547, + 290 + ], + "blocks": [ + { + "bbox": [ + 410, + 70, + 547, + 290 + ], + "lines": [ + { + "bbox": [ + 410, + 70, + 547, + 290 + ], + "spans": [ + { + "bbox": [ + 410, + 70, + 547, + 290 + ], + "type": "image", + "image_path": "1bb9114eda4981b7379f296c65b81e21a52fd1eb395d80a72b929e0597994c98.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 473, + 293, + 485, + 302 + ], + "lines": [ + { + "bbox": [ + 473, + 293, + 485, + 302 + ], + "spans": [ + { + "bbox": [ + 473, + 293, + 485, + 302 + ], + "type": "text", + "content": "(d)" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 376, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 422 + ], + "type": "text", + "content": "lizing a novel loss function that we derive from the model's feature space. To the best of our knowledge, our work is the first to investigate the internal feature representation of a T2V model and leverage it for an editing task." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 426, + 289, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 289, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 289, + 593 + ], + "type": "text", + "content": "Consistent video editing. Several recent methods have leveraged layered video representations for consistent text-driven video editing [2, 10, 25, 27, 30, 33, 68]. For example, Text2LIVE [2] proposed to use a pre-trained Layered Neural Atlases (NLA) [27] representation, which is edited using losses defined in CLIP text-image space [48]. However, since the structure and motion of the edited video are determined via the pre-trained NLA, such methods are restricted to only appearance changes. Recently, [30] generalized this approach to allow local structural changes in the edited videos. Nevertheless, NLA takes hours to train, and cannot faithfully represent complex videos due to the strong regularization of objects' motion. In addition, all these methods use a 2D generative prior, thus cannot support large structure deviation and adaption of motion." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 601, + 125, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 601, + 125, + 615 + ], + "spans": [ + { + "bbox": [ + 47, + 601, + 125, + 615 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": "Diffusion models. Diffusion models [15, 21, 45, 55] are generative models that aim to approximate a data distribution " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": " by mapping an input noise " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_T \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": " to a clean sample " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_0 \\sim q" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": ", through an iterative denoising process. The DDIM sampler allows to denoise an initial noise " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_T" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": " in a deterministic manner [56]. By applying DDIM inversion, a clean sample " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_0" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": " can be mapped back to the sequence of noisy samples " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\{\\boldsymbol{x}_i\\}_{t=1}^T" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": " used to generate it." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "type": "text", + "content": "In latent text-to-image (T2I) diffusion models, e.g., StableDiffusion [49], a pre-trained encoder compresses an RGB image " + }, + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "type": "inline_equation", + "content": "\\pmb{I} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "type": "text", + "content": " to a latent " + }, + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^{H' \\times W' \\times 4}" + }, + { + "bbox": [ + 304, + 376, + 545, + 444 + ], + "type": "text", + "content": ", which can be decoded back to the high-resolution space. These T2I models comprise a UNet architecture [50], which consists of Convolutions and Attention modules." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "type": "text", + "content": "Latent video diffusion models (e.g., [4, 62]) extend latent T2I models to text-to-video by inflating the 2D architecture to the temporal domain, i.e., adding temporal convolutions and temporal attention layers, and fine-tuning on video datasets. In this case, the T2V model generates a latent video " + }, + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^{F \\times H' \\times W' \\times 4}" + }, + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "type": "text", + "content": ", which is then decoded to the output RGB video " + }, + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "type": "inline_equation", + "content": "\\mathcal{V} \\in \\mathbb{R}^{F \\times H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 445, + 546, + 547 + ], + "type": "text", + "content": ". In this work, we utilize the publicly available ZeroScope T2V [8] model, which inflates StableDiffusion [49]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 559, + 361, + 571 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 559, + 361, + 571 + ], + "spans": [ + { + "bbox": [ + 306, + 559, + 361, + 571 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "content": "Given an input video " + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "content": " and a target text prompt " + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "content": ", our goal is to generate a new video " + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{J}" + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "content": " that preserves the overall motion and semantic layout of " + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "content": ", while complying with " + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 579, + 545, + 624 + ], + "type": "text", + "content": ". We utilize ZeroScope - a pre-trained latent T2V model [8, 62]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 624, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 624, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 624, + 545, + 714 + ], + "type": "text", + "content": "The key component of our method, illustrated in Fig. 3, is a novel objective function that is used as guidance during the generation process of " + }, + { + "bbox": [ + 304, + 624, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 624, + 545, + 714 + ], + "type": "text", + "content": ". We conceive this objective based on our empirical analysis that reveals new insights about space-time diffusion features extracted from the model. Specifically, we show that the first-order statistics of the features in the spatial dimensions, i.e., the spatial marginal mean of the features, can serve as a powerful per" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8468" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 331, + 209 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 331, + 209 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 331, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 331, + 209 + ], + "type": "image", + "image_path": "41f4b5ac53b34528af3bc4e3b42521819b132492bcb0102e86a1c245b8c3de87.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 140, + 212, + 279, + 222 + ], + "lines": [ + { + "bbox": [ + 140, + 212, + 279, + 222 + ], + "spans": [ + { + "bbox": [ + 140, + 212, + 279, + 222 + ], + "type": "text", + "content": "(a) Spatial Marginal Mean (SMM) Feature" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 331, + 70, + 542, + 208 + ], + "blocks": [ + { + "bbox": [ + 331, + 70, + 542, + 208 + ], + "lines": [ + { + "bbox": [ + 331, + 70, + 542, + 208 + ], + "spans": [ + { + "bbox": [ + 331, + 70, + 542, + 208 + ], + "type": "image", + "image_path": "787ae027084f48b6173e42136ab6c0d72bc62da205caf351ab2a7d90e2850d55.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 361, + 212, + 479, + 221 + ], + "lines": [ + { + "bbox": [ + 361, + 212, + 479, + 221 + ], + "spans": [ + { + "bbox": [ + 361, + 212, + 479, + 221 + ], + "type": "text", + "content": "(b) Motion-Guided Video Generation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "type": "text", + "content": "Figure 3. Pipeline. (a) Given an input video, we apply DDIM inversion and extract space-time features " + }, + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "type": "inline_equation", + "content": "\\pmb{f} \\in \\mathbb{R}^{F \\times M \\times N \\times D}" + }, + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "type": "text", + "content": " from intermediate layer activations. We obtain our Spatial Marginal Mean (SMM) feature " + }, + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "type": "inline_equation", + "content": "\\mathrm{SMM}[f] \\in \\mathbb{R}^{F \\times D}" + }, + { + "bbox": [ + 46, + 230, + 547, + 274 + ], + "type": "text", + "content": " by computing the mean over the spatial dimensions, and compute the pairwise differences between each pair of SMM features. (b) For editing, we guide the generation at each denoising step with our Pairwise SMM differences objective (b). See Sec. 4 for more details." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 288, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 288, + 331 + ], + "type": "text", + "content": "frame global descriptor that (i) retains spatial information such as objects' position, pose, and the semantic layout of the scene, and (ii) robust to pixel-level variations in both appearance and shape." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 339, + 258, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 258, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 258, + 352 + ], + "type": "text", + "content": "4.1. Space-time analysis of diffusion features" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 357, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 456 + ], + "type": "text", + "content": "We focus our analysis on features extracted from the intermediate layer activations of the video model. Recall that the video model is initialized from a text-to-image model, for which the semantic DIFT features [57], were shown to encode localized semantic information shared across objects from different domains [57, 60]. Here, we examine the space-time properties of the corresponding features in the video model. See Supplementary Material (SM) for details about the video model architecture and feature selection." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": "Given the input video " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": ", we apply DDIM inversion with an empty prompt [56], and obtain a sequence of latents " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "[\\pmb{x}_1,\\dots,\\pmb{x}_T]" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": " is the video latent at generation step " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": ". We input the latent " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\pmb{x}_t" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": " to the network and extract the space-time features " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "\\pmb{f}(\\pmb{x}_t) \\in \\mathbb{R}^{F \\times M \\times N \\times D}" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "F, M, N" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": " are the number of frames, height and width of the " + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 457, + 287, + 536 + ], + "type": "text", + "content": " dimensional feature activation, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "text", + "content": "Diffusion feature inversion. To gain a better understanding of what the features " + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "inline_equation", + "content": "\\{\\pmb{f}(\\pmb{x}_t)\\}_{t=1}^T" + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "text", + "content": " encode, we adopt the concept of \"feature inversion\" [35, 53, 59] (not to confuse with \"DDIM inversion\"). Our goal is to optimize for a video " + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^*" + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "text", + "content": ", randomly initialized, that would produce these features when fed into the network. Specifically, this is achieved using feature reconstruction guidance [16, 40] during the sampling process of " + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "inline_equation", + "content": "\\mathcal{V}^*" + }, + { + "bbox": [ + 46, + 540, + 288, + 629 + ], + "type": "text", + "content": ". Formally," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 51, + 633, + 295, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 633, + 295, + 658 + ], + "spans": [ + { + "bbox": [ + 51, + 633, + 295, + 658 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\boldsymbol {x}} _ {T} \\sim \\mathcal {N} (0, \\mathcal {I}) \\\\ \\hat {\\boldsymbol {x}} _ {t - 1} = \\Phi \\left(\\boldsymbol {x} _ {t} ^ {*}, P _ {s}\\right), \\text {w h e r e} \\boldsymbol {x} _ {t} ^ {*} = \\operatorname {a r g m i n} _ {\\hat {\\boldsymbol {x}}} \\| \\boldsymbol {f} (\\boldsymbol {x} _ {\\mathbf {t}}) - \\boldsymbol {f} (\\hat {\\boldsymbol {x}} _ {\\mathbf {t}}) \\| ^ {2} \\\\ \\end{array}", + "image_path": "a7ec7f3e0f7b47953a1ea5331859cb2b61c64dc2f9419c175420196f7d604682.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "type": "text", + "content": " is the diffusion model, and " + }, + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 46, + 668, + 288, + 714 + ], + "type": "text", + "content": " is a general text prompt describing the input video (e.g., \"a car\"). We minimize the feature reconstruction objective using gradient descent at each generation step. See SM for more details." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 285, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 341 + ], + "type": "text", + "content": "Figure 2 shows our inversion results for the space-time features extracted from an input video; we repeat the inversion process several times, each with different random initialization (i.e., different seeds). We observe that inverted videos nearly reconstruct the original frames (Fig. 2(b))." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 340, + 546, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 546, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 546, + 416 + ], + "type": "text", + "content": "Ultimately, we opt to find a feature descriptor that retains such information about objects' pose and the semantic layout of the scene yet is robust to variations in appearance and shape. To reduce the dependency on the pixel-level information, we introduce a new feature descriptor, dubbed Spatial Marginal Mean (SMM), obtained by reducing the spatial dimensions. Formally," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 344, + 415, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 415, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 344, + 415, + 545, + 449 + ], + "type": "interline_equation", + "content": "\\operatorname {S M M} [ \\boldsymbol {f} (\\boldsymbol {x} _ {t}) ] = \\frac {1}{M \\cdot N} \\sum_ {i = 1} ^ {M} \\sum_ {j = 1} ^ {N} \\boldsymbol {f} (\\boldsymbol {x} _ {t}) _ {i, j} \\tag {1}", + "image_path": "02c0d560769af02143c27bbebd7e31a93184b22dae5909d8f18f7f0942a9de1e.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\pmb {f}(\\pmb {x}_t)_{i,j}\\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "text", + "content": " is the entry at spatial location " + }, + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "text", + "content": " in the space-time feature volume " + }, + { + "bbox": [ + 304, + 447, + 545, + 469 + ], + "type": "inline_equation", + "content": "\\pmb {f}(\\pmb {x}_t)" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 469, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 469, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 469, + 545, + 557 + ], + "type": "text", + "content": "We repeat the inversion experiment (Eq. 1), with " + }, + { + "bbox": [ + 304, + 469, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\{\\mathrm{SMM}[\\pmb {f}(\\pmb {x}_t)]\\}_{t = 1}^T" + }, + { + "bbox": [ + 304, + 469, + 545, + 557 + ], + "type": "text", + "content": " as the target features to reconstruct. Figure 2(c) shows the inversion results for the SMM features for different initializations. Remarkably, although the spatial dimensions are collapsed in the SMM features, the inverted videos convey the correct pose and position of objects while depicting larger structural and appearance variations than using the full space-time features." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 557, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 624 + ], + "type": "text", + "content": "We further demonstrate these properties by treating the spatial marginal mean associated with each frame as a global per-frame descriptor, and using it to retrieve nearest neighbor frames from other videos. As seen in Fig. 2(d), the retrieved nearest frames depict the same pose, under noticeable appearance and viewpoint changes." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 629, + 479, + 641 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 629, + 479, + 641 + ], + "spans": [ + { + "bbox": [ + 306, + 629, + 479, + 641 + ], + "type": "text", + "content": "4.2. Motion-guided video generation" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "content": "Based on our findings, we now turn to the task of generating a new video " + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "content": " that complies with the input prompt " + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "content": " and preserves the motion characteristics of the driving video " + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "content": ". Our feature inversion analysis raises the question of whether the same approach can be used for editing by replacing the source prompt " + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "inline_equation", + "content": "P_{s}" + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "content": " with an edit prompt " + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 646, + 545, + 714 + ], + "type": "text", + "content": " in Eq. 1." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8469" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 545, + 427 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 545, + 427 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 545, + 427 + ], + "type": "image", + "image_path": "1e2985a71677ff0f74be54d67fd535f565f0d1b999cdf8cc93d34c7af11f96d3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 165, + 430, + 427, + 440 + ], + "lines": [ + { + "bbox": [ + 165, + 430, + 427, + 440 + ], + "spans": [ + { + "bbox": [ + 165, + 430, + 427, + 440 + ], + "type": "text", + "content": "Figure 4. Sample results of our method. See SM for full video results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 447, + 287, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 447, + 287, + 535 + ], + "spans": [ + { + "bbox": [ + 46, + 447, + 287, + 535 + ], + "type": "text", + "content": "Figure 7 shows these results for a couple of videos, which demonstrate two issues: (i) depending on the initialization, the optimization may converge to a local minima in which the accurate position of objects and their orientation may differ from the input, (ii) the SMM features still retain appearance information, which reduces the fidelity to the text prompt. We propose the following two components to resolve these issues." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "content": "Pairwise SMM differences. As seen in Fig. 7, directly optimizing for the SMM features often prevents us from deviating from the original appearance. To circumvent this, we propose an objective function to preserve the pairwise differences of the SMM features rather than their exact values. Formally, let " + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\phi_i^t,\\tilde{\\phi}_i^t\\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "content": " be the SMM features for frame " + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "content": " and step " + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "content": " for the driving video and the generated video, respectively. For a generation step " + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "content": ", the pairwise SMM differences " + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\Delta^t,\\tilde{\\Delta}^t\\in \\mathbb{R}^{F\\times F\\times d}" + }, + { + "bbox": [ + 46, + 539, + 287, + 639 + ], + "type": "text", + "content": " are defined as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 88, + 640, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 640, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 88, + 640, + 287, + 657 + ], + "type": "interline_equation", + "content": "\\Delta_ {(i, j)} ^ {t} = \\phi_ {i} ^ {t} - \\phi_ {j} ^ {t} \\quad \\tilde {\\Delta} _ {(i, j)} ^ {t} = \\tilde {\\phi} _ {i} ^ {t} - \\tilde {\\phi} _ {j} ^ {t} \\tag {2}", + "image_path": "38956f683297a410487392170a1908bf353926a710f13cd5ae28e2424b97b6a8.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "type": "inline_equation", + "content": "i,j\\in \\{1,\\ldots ,F\\}" + }, + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "type": "text", + "content": " . Our loss for time step " + }, + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 660, + 264, + 673 + ], + "type": "text", + "content": " is then:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\operatorname {S M M} (\\boldsymbol {f} (\\boldsymbol {x} _ {t})), \\operatorname {S M M} (\\boldsymbol {f} (\\tilde {\\boldsymbol {x}} _ {t}))) = \\sum_ {i} \\sum_ {j} | | \\Delta_ {(i, j)} ^ {t} - \\tilde {\\Delta} _ {(i, j)} ^ {t} | | _ {2} ^ {2} \\tag {3}", + "image_path": "598bcdaea61fd2c8e7a77be37be7aa01a917cfa02dd3374d1035b5a4da3a526b.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 446, + 507, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 446, + 507, + 458 + ], + "spans": [ + { + "bbox": [ + 305, + 446, + 507, + 458 + ], + "type": "text", + "content": "Algorithm 1 Motion-Guided Video Generation" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 460, + 545, + 579 + ], + "blocks": [ + { + "bbox": [ + 307, + 460, + 545, + 579 + ], + "lines": [ + { + "bbox": [ + 307, + 460, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 307, + 460, + 545, + 579 + ], + "type": "table", + "html": "
Input:
V, P▷ Input video and target text prompt
{x_t}T_{t=1}← DDIM-Inv[V] ∀t ∈ [T]
ε0 ~ N(0, I)
x̂T = LFξ(xT) + (ε0 - LFξ(ε0))▷ Filtered noise (Eq. 4.2)
For t = T, ..., 1 do
f(x_t), f(x̂_t) ← Extract space-time features
SMM(f(x_t)), SMM(f(x̂_t)) ← Spatial marginal mean (Eq. 1)
xt* = argminx̂_t L(SMM(f(x_t)), SMM(f(x̂_t)))
x̂_t-1 = Φ(x_t*, P)▷ Apply a denoising step
Output: J ← x0
", + "image_path": "e9945fb60e026b0e27918885993fc9c5b302e12bc42945c040066301670420c3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 607, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 607, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 607, + 545, + 641 + ], + "type": "text", + "content": "Intuitively, this loss lets us preserve the relative changes in the features through time, while discarding the exact appearance information of the source video (Fig. 7)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 646, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 646, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 646, + 545, + 713 + ], + "type": "text", + "content": "Initialization. It is well-known that the diffusion denoising process is performed in a coarse-to-fine manner, thus, the initialization plays an important role in defining the low frequencies of the generated content [3, 36]. Initialization from a random point may often converge to an undesired local minimum, in which object position is not well-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8470" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": "preserved. Note that the low-frequency information of the original video is readily available in the DDIM inverted noise " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": ". However, we empirically found that this initialization often restricts edit-ability [43] (see SM for an example). We thus extract only the low frequencies from " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{x}_T" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": ". Specifically, let " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^{F \\times M \\times N}" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": " be a tensor representing " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": " frames, with a spatial resolution of " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "M \\times N" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": ". We denote by " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "LF_{\\xi}(\\pmb{x})" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": " the operation of spatially downsampling and upsampling " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\pmb{x}" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": " by a factor of " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": ". Then, our initial latent " + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}}_T" + }, + { + "bbox": [ + 47, + 72, + 289, + 183 + ], + "type": "text", + "content": " is given by:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 96, + 186, + 287, + 199 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 186, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 96, + 186, + 287, + 199 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {x}} _ {T} = L F _ {\\xi} \\left(\\boldsymbol {x} _ {T}\\right) + \\left(\\epsilon_ {0} - L F _ {\\xi} \\left(\\epsilon_ {0}\\right)\\right) \\tag {4}", + "image_path": "f544c3ebbac5722dad4c2b684e3c20e609ee023c34fc53f6507024d7d49f8d1a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\epsilon_0\\sim \\mathcal{N}(0,I)" + }, + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "text", + "content": " is a random noise. Intuitively, " + }, + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}}_T" + }, + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "text", + "content": " preserves the low-frequencies of the DDIM noise where the higher frequencies are determined by " + }, + { + "bbox": [ + 47, + 206, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\epsilon_0" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 239, + 287, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 287, + 262 + ], + "type": "text", + "content": "To summarize, starting from the filtered latent " + }, + { + "bbox": [ + 47, + 239, + 287, + 262 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}}_T" + }, + { + "bbox": [ + 47, + 239, + 287, + 262 + ], + "type": "text", + "content": ", our method deploys the following guided generation process:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 71, + 270, + 261, + 284 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 270, + 261, + 284 + ], + "spans": [ + { + "bbox": [ + 71, + 270, + 261, + 284 + ], + "type": "interline_equation", + "content": "\\boldsymbol {x} _ {t} ^ {*} = \\operatorname {a r g m i n} _ {\\tilde {\\boldsymbol {x}} _ {t}} \\mathcal {L} (\\operatorname {S M M} (\\boldsymbol {f} (\\boldsymbol {x} _ {t})), \\operatorname {S M M} (\\boldsymbol {f} (\\tilde {\\boldsymbol {x}} _ {t})))", + "image_path": "f2a4f2724e65146951c8e5ef9e9d66b6c4a790e7e7b9f7ed9e5d18ca35088432.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 74, + 284, + 147, + 294 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 284, + 147, + 294 + ], + "spans": [ + { + "bbox": [ + 74, + 284, + 147, + 294 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {x}} _ {t - 1} = \\Phi (\\boldsymbol {x} _ {t} ^ {*}, P)", + "image_path": "699d23775763ef7bb4642859baf14b42add5b518db6a77e2671d27ad025dc3d9.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 302, + 228, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 302, + 228, + 315 + ], + "spans": [ + { + "bbox": [ + 47, + 302, + 228, + 315 + ], + "type": "text", + "content": "Our full framework is summarized in Alg. 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 324, + 100, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 100, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 100, + 335 + ], + "type": "text", + "content": "5. Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 342, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 287, + 399 + ], + "type": "text", + "content": "We evaluate our method on various scenes and object categories, most of which involve camera as well as object motion. The driving videos are taken from DAVIS dataset [46] and from the Web. Our video results and implementation details are available in the Supplementary Materials (SM)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 399, + 287, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 476 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 476 + ], + "type": "text", + "content": "Figures 1, 4 show sample results of our method. As seen, our method facilitates edits that involve notable changes to the shape and structure of deforming objects, while preserving camera and objects' motion. For instance, we preserve the 3D pose of the car when transferring its motion to a bike or a train (Fig. 1); and maintain the actions of non-rigidly moving objects, e.g., sitting dog or walking camel in Fig. 4." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 479, + 288, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 288, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 288, + 601 + ], + "type": "text", + "content": "Baselines We compare our method to the following text-driven video editing methods: (i) Shape-Aware Layered Neural Atlases (SA-NLA) [30] that utilizes a pre-trained layered video representation [27] and a pre-trained T2I model [49]. (ii) TokenFlow [19], a zero-shot method that works in the feature space of a pre-trained T2I model (iii) GEN-1 [17] and (iv) Control-A-Video [13], both are video-to-video diffusion models that condition the generation on input depth maps, (v) Tune-A-Video [67] that inflates a T2I model and finetunes it on a single test video, and (iv) SDEdit [36] applied to the same T2V model as our method." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 607, + 174, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 607, + 174, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 607, + 174, + 619 + ], + "type": "text", + "content": "5.1. Qualitative evaluation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": "Figure 5 shows a qualitative comparison to SA-NLA [30]. Note that SA-NLA utilizes a layered video representation [27], which requires foreground/background separation masks and takes " + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\sim 10" + }, + { + "bbox": [ + 46, + 624, + 288, + 715 + ], + "type": "text", + "content": " hours to train. Thus, we compare to their provided videos and edit prompts qualitatively. As seen in Fig. 5, both our method and SA-NLA exhibit high fidelity to the original motion. 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Comparison to SA-NLA [30]. See SM for video results, structure of a duck in the swan example) and adaption of fine-grained motion traits, which are necessary for capturing the unique attributes of the target object. For example, adapting the shape and movement of a dog's tail to resemble a naturally-looking cat's tail." + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 385, + 261, + 467, + 355 + ], + "blocks": [ + { + "bbox": [ + 385, + 261, + 467, + 355 + ], + "lines": [ + { + "bbox": [ + 385, + 261, + 467, + 355 + ], + "spans": [ + { + "bbox": [ + 385, + 261, + 467, + 355 + ], + "type": "image", + "image_path": "1ce9288a0ad2e337eb52357f1a89cc1d5cee0c36076740ac6a77270a1fa158b8.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 411, + 355, + 440, + 362 + ], + "lines": [ + { + "bbox": [ + 411, + 355, + 440, + 362 + ], + "spans": [ + { + "bbox": [ + 411, + 355, + 440, + 362 + ], + "type": "text", + "content": "SA-NLA" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 467, + 261, + 545, + 355 + ], + "blocks": [ + { + "bbox": [ + 467, + 261, + 545, + 355 + ], + "lines": [ + { + "bbox": [ + 467, + 261, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 467, + 261, + 545, + 355 + ], + "type": "image", + "image_path": "10e9d8b526de98e48064ac29e08960a96cf2478e323fb4e814fb42d14800f4ea.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 498, + 355, + 515, + 361 + ], + "lines": [ + { + "bbox": [ + 498, + 355, + 515, + 361 + ], + "spans": [ + { + "bbox": [ + 498, + 355, + 515, + 361 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 439, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 439, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 305, + 439, + 545, + 594 + ], + "type": "text", + "content": "Figure 6 provides comparisons to the additional baselines. As seen, none of these methods can both convey the original motion and adhere to the edit prompt. TokenFlow [19] is tailored to preserve structure of the input video. Gen-1 [17] and Control-A-Video [13] struggle to deviate from the input shapes as they condition the generation on the per-frame depth maps extracted from the input video. Tune-A-Video [67] manages to fulfill the target prompt, yet objects are not aligned in pose and motion (e.g., camel to bear). Our method significantly outperforms these baselines, by successfully matching the desired edits, which require significant structural changes and may involve synthesizing dynamic scene elements (e.g., smoke behind the motorbike). 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Ablation. (b-c) We compare alternative loss functions instead of our pairwise SMM differences loss (Eq. 4.2); (b) using full space-time features reconstruction prevents deviations in appearance and shape; (c) SMM feature reconstruction allows for more flexibility yet retains appearance information. (d-f) Ablation of our key components: (d) directly sampling from the initial latent w/o optimization preserves only the coarse layout. (e) Starting our optimization from randomly sampled noise (w/o low frequency filtering Eq. 4.2) results in lower motion fidelity compared to our full method (f)." + } + ] + } + ], + "index": 66, + "angle": 0, + "type": "image_caption" + } + ], + "index": 60 + }, + { + "type": "image", + "bbox": [ + 130, + 489, + 211, + 534 + ], + "blocks": [ + { + "bbox": [ + 130, + 489, + 211, + 534 + ], + "lines": [ + { + "bbox": [ + 130, + 489, + 211, + 534 + ], + "spans": [ + { + "bbox": [ + 130, + 489, + 211, + 534 + ], + "type": "image", + "image_path": "5ec72eca7c02a257c7618dbef97030433cea6e768b824137449a805c2a71174d.jpg" + } + ] + } + ], + "index": 61, + "angle": 0, + "type": "image_body" + } + ], + "index": 61 + }, + { + "type": "image", + "bbox": [ + 212, + 489, + 293, + 534 + ], + "blocks": [ + { + "bbox": [ + 212, + 489, + 293, + 534 + ], + "lines": [ + { + "bbox": [ + 212, + 489, + 293, + 534 + ], + "spans": [ + { + "bbox": [ + 212, + 489, + 293, + 534 + ], + "type": "image", + "image_path": "be0adee4dc24e32243f397aa569c455de1d84fa82405308c74425800f2f9b222.jpg" + } + ] + } + ], + "index": 62, + "angle": 0, + "type": "image_body" + } + ], + "index": 62 + }, + { + "type": "image", + "bbox": [ + 299, + 489, + 380, + 534 + ], + "blocks": [ + { + "bbox": [ + 299, + 489, + 380, + 534 + ], + "lines": [ + { + "bbox": [ + 299, + 489, + 380, + 534 + ], + "spans": [ + { + "bbox": [ + 299, + 489, + 380, + 534 + ], + "type": "image", + "image_path": "ae464d7d3bc5dfeaa874bbb2d1eee8c9c07d8b8d392731f0025e28fbe190b119.jpg" + } + ] + } + ], + "index": 63, + "angle": 0, + "type": "image_body" + } + ], + "index": 63 + }, + { + "type": "image", + "bbox": [ + 382, + 489, + 463, + 534 + ], + "blocks": [ + { + "bbox": [ + 382, + 489, + 463, + 534 + ], + "lines": [ + { + "bbox": [ + 382, + 489, + 463, + 534 + ], + "spans": [ + { + "bbox": [ + 382, + 489, + 463, + 534 + ], + "type": "image", + "image_path": "f24d510f2193a4a00623f99fd7f07434c98803f7b110336964998c0d25e5f7da.jpg" + } + ] + } + ], + "index": 64, + "angle": 0, + "type": "image_body" + } + ], + "index": 64 + }, + { + "type": "image", + "bbox": [ + 465, + 489, + 545, + 534 + ], + "blocks": [ + { + "bbox": [ + 465, + 489, + 545, + 534 + ], + "lines": [ + { + "bbox": [ + 465, + 489, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 465, + 489, + 545, + 534 + ], + "type": "image", + "image_path": "deea76b1b349cca1ed278c9a181844acda410147e185198b2b9571e5dbdd6d97.jpg" + } + ] + } + ], + "index": 65, + "angle": 0, + "type": "image_body" + } + ], + "index": 65 + }, + { + "bbox": [ + 46, + 597, + 286, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 286, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 286, + 642 + ], + "type": "text", + "content": "unsuitable for our use case. We thus introduce a new metric, based on similarity between unaligned long-trajectories. We expect that even under structural changes, the two sets of trajectories would exhibit shared characteristics." + } + ] + } + ], + "index": 67 + }, + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "spans": [ + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "type": "text", + "content": "Specifically, we use off-the-shelf tracking method [26] to estimate " + }, + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "type": "inline_equation", + "content": "\\mathcal{T} = \\{\\tau_1,\\dots ,\\tau_n\\}" + }, + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathcal{T}} = \\{\\tilde{\\tau}_1,\\dots ,\\tilde{\\tau}_m\\}" + }, + { + "bbox": [ + 46, + 643, + 286, + 678 + ], + "type": "text", + "content": ", two sets of tracklets in the input and output videos, respectively." + } + ] + } + ], + "index": 68 + }, + { + "bbox": [ + 47, + 679, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 679, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 679, + 287, + 713 + ], + "type": "text", + "content": "Inspired by the Chamfer distance, we define our Motion-Fidelity-Score as follows. For each tracklet " + }, + { + "bbox": [ + 47, + 679, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\tau_{i}\\in \\mathcal{T}" + }, + { + "bbox": [ + 47, + 679, + 287, + 713 + ], + "type": "text", + "content": ", we measure the similarity to its nearest neighbor in " + }, + { + "bbox": [ + 47, + 679, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{\\tau}_i\\in \\mathcal{T}" + } + ] + } + ], + "index": 69 + }, + { + "bbox": [ + 306, + 597, + 368, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 597, + 368, + 608 + ], + "spans": [ + { + "bbox": [ + 306, + 597, + 368, + 608 + ], + "type": "text", + "content": "and vice versa." + } + ] + } + ], + "index": 70 + }, + { + "bbox": [ + 323, + 610, + 545, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 610, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 323, + 610, + 545, + 641 + ], + "type": "interline_equation", + "content": "\\frac {1}{m} \\sum_ {\\tilde {\\tau} \\in \\tilde {\\mathcal {T}}} \\max _ {\\tau \\in \\mathcal {T}} \\operatorname {c o r r} (\\tau , \\tilde {\\tau}) + \\frac {1}{n} \\sum_ {\\tau \\in \\mathcal {T}} \\max _ {\\tilde {\\tau} \\in \\tilde {\\mathcal {T}}} \\operatorname {c o r r} (\\tau , \\tilde {\\tau}) \\tag {5}", + "image_path": "cc29101649d0f42de5f6013517c52d3e43896c88ae49100eefa3b3a85a195859.jpg" + } + ] + } + ], + "index": 71 + }, + { + "bbox": [ + 305, + 648, + 545, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 648, + 545, + 671 + ], + "spans": [ + { + "bbox": [ + 305, + 648, + 545, + 671 + ], + "type": "text", + "content": "where the correlation between two tracklets " + }, + { + "bbox": [ + 305, + 648, + 545, + 671 + ], + "type": "inline_equation", + "content": "\\mathbf{corr}(\\tau, \\tilde{\\tau})" + }, + { + "bbox": [ + 305, + 648, + 545, + 671 + ], + "type": "text", + "content": " is computed as follows, similarly to [32]:" + } + ] + } + ], + "index": 72 + }, + { + "bbox": [ + 310, + 678, + 539, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 678, + 539, + 711 + ], + "spans": [ + { + "bbox": [ + 310, + 678, + 539, + 711 + ], + "type": "interline_equation", + "content": "\\mathbf {c o r r} (\\tau , \\tilde {\\tau}) = \\frac {1}{F} \\sum_ {k = 1} ^ {F} \\frac {v _ {k} ^ {x} \\cdot \\tilde {v} _ {k} ^ {x} + v _ {k} ^ {y} \\cdot \\tilde {v} _ {k} ^ {y}}{\\sqrt {(v _ {k} ^ {x}) ^ {2} + (v _ {k} ^ {y}) ^ {2}} \\cdot \\sqrt {(\\tilde {v} _ {k} ^ {x}) ^ {2} + (\\tilde {v} _ {k} ^ {y}) ^ {2}}}", + "image_path": "526ba2aecf6bb50a71c17bcb0d7c446becd5341ab588e9c0045fafa22205a76b.jpg" + } + ] + } + ], + "index": 73 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8472" + } + ] + } + ], + "index": 74 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 70, + 282, + 226 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 282, + 226 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 282, + 226 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 282, + 226 + ], + "type": "image", + "image_path": "1744aad4a551a67842c04d27656fe764930de312ce2331d9743df6f369f9da66.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 287, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 287, + 277 + ], + "type": "text", + "content": "Figure 8. Quantitative evaluation. For each baseline, we measure CLIP text similarity and motion fidelity (Eq. 5). there is a trade-off between preserving fidelity to the original pixel-level motion and satisfying the desired edit. Our method exhibits a better balance between these two metrics." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "inline_equation", + "content": "(v_k^x, v_k^y), (\\tilde{v}_k^x, \\tilde{v}_k^y)" + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "text", + "content": " are the " + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "text", + "content": " frame displacement of tracklets " + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "inline_equation", + "content": "\\tau, \\tilde{\\tau}" + }, + { + "bbox": [ + 46, + 289, + 287, + 312 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": "Figure. 8 reports the metrics above for a set of 54 video-edit text pairs containing 21 unique videos. Our method outperforms the baselines by achieving both high fidelity to the target text prompt and the original motion. Since TokenFlow [19] explicitly does not allow to deviate from original trajectories, their motion fidelity metric score is trivially high, while the edit fidelity score is low. Control-A-Video [13] exhibits a similar behavior since it utilizes depth maps as a guidance signal to edit the video. Tune-A-Video [67] shows an inverse trend, i.e., satisfying the desired edit at the cost of motion fidelity. We further consider SDEdit [36] with different noise levels, none of which can resolve the motion-edit tradeoff. Note that Gen1's API outputs a different number of frames, thus we could not quantitatively evaluate their performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 479, + 287, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 568 + ], + "type": "text", + "content": "(iii) User study. We employ the Two-alternative Forced Choice (2AFC) protocol for text-driven video editing [2, 17, 19, 47]. Participants are presented with the input video, our results and a baseline, and are asked to determine which video better aligns with the text prompt while preserving the motion of the original video. We collected 7000 user judgments from 150 users. As seen in Table 1, our method is consistently preferred over all baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 574, + 115, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 115, + 585 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 115, + 585 + ], + "type": "text", + "content": "5.2. Ablations" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 591, + 287, + 669 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 591, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 46, + 591, + 287, + 669 + ], + "type": "text", + "content": "In Fig. 7, we ablate key design choices in our framework. First, we consider alternative loss functions by substituting the pairwise SMM differences in Eq.4.2 with: (i) full space-time features " + }, + { + "bbox": [ + 46, + 591, + 287, + 669 + ], + "type": "inline_equation", + "content": "\\pmb{f}" + }, + { + "bbox": [ + 46, + 591, + 287, + 669 + ], + "type": "text", + "content": " and (ii) SMM features (Eq.1). Figure 7 (b) shows that space-time features restrict both shape and appearance variations; optimizing for SMM features (c) increases flexibility yet is insufficient for matching the edit." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 669, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 669, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 669, + 287, + 713 + ], + "type": "text", + "content": "We next ablate our guided sampling and latent initialization strategy. Sampling from the initial latent without optimization (d) converges to unrelated objects' pose, while initializing the optimization from randomly sampled noise" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 72, + 430, + 147 + ], + "blocks": [ + { + "bbox": [ + 310, + 72, + 430, + 147 + ], + "lines": [ + { + "bbox": [ + 310, + 72, + 430, + 147 + ], + "spans": [ + { + "bbox": [ + 310, + 72, + 430, + 147 + ], + "type": "image", + "image_path": "d918aa343a6ead676deec062184d403db06af0760339af4fbac2691cc64c52eb.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 433, + 72, + 553, + 148 + ], + "blocks": [ + { + "bbox": [ + 433, + 72, + 553, + 148 + ], + "lines": [ + { + "bbox": [ + 433, + 72, + 553, + 148 + ], + "spans": [ + { + "bbox": [ + 433, + 72, + 553, + 148 + ], + "type": "image", + "image_path": "f68ab6cb17994a121ccc307e0e8fa8c6e953c50a92a0afb096d27dfe3e7eb0af.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 148, + 431, + 216 + ], + "blocks": [ + { + "bbox": [ + 309, + 148, + 431, + 216 + ], + "lines": [ + { + "bbox": [ + 309, + 148, + 431, + 216 + ], + "spans": [ + { + "bbox": [ + 309, + 148, + 431, + 216 + ], + "type": "image", + "image_path": "93d982a3db378f5e7d19899c3db748c483d22feee5e972ee06aff2885b3e4180.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 217, + 545, + 249 + ], + "lines": [ + { + "bbox": [ + 305, + 217, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 305, + 217, + 545, + 249 + ], + "type": "text", + "content": "Figure 9. Limitations. Our method struggles to preserve the original motion since the combination of the original motion and the edit prompt may be out of distribution for the T2V model." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 433, + 148, + 553, + 216 + ], + "blocks": [ + { + "bbox": [ + 433, + 148, + 553, + 216 + ], + "lines": [ + { + "bbox": [ + 433, + 148, + 553, + 216 + ], + "spans": [ + { + "bbox": [ + 433, + 148, + 553, + 216 + ], + "type": "image", + "image_path": "fa7e71c1fe64168ffe12cb8a219d3a43d002b4f5baa5a8567db094806d989354.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 322, + 264, + 529, + 321 + ], + "blocks": [ + { + "bbox": [ + 322, + 264, + 529, + 321 + ], + "lines": [ + { + "bbox": [ + 322, + 264, + 529, + 321 + ], + "spans": [ + { + "bbox": [ + 322, + 264, + 529, + 321 + ], + "type": "table", + "html": "
MethodJudgements in our favor (%)
TokenFlow72.57%
Control-A-Video84.50%
Tune-A-Video77.80%
", + "image_path": "70cbbee1cdd93b629c6aa0f7236c3e77bde7668c7ea7646627cc2c0fb78261f4.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 323, + 545, + 344 + ], + "lines": [ + { + "bbox": [ + 305, + 323, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 545, + 344 + ], + "type": "text", + "content": "Table 1. User Study. We report the percentage of judgments in our favor w.r.t. each baseline." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 357, + 515, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 515, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 515, + 369 + ], + "type": "text", + "content": "(e) fails to retain the original motion characteristics." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 385, + 459, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 459, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 459, + 398 + ], + "type": "text", + "content": "6. Discussion and conclusions" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 407, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 496 + ], + "type": "text", + "content": "We tackled the task of text-driven motion transfer, focusing on scenarios where the source and target objects differ in shape and fine-grained motion traits. We introduced a zero-shot method that utilizes a pre-trained T2V diffusion model, through a simple optimization framework. Our work is the first to analyze and reveal new insights about spacetime T2V features, and the first to show how to harness their properties for text-driven motion transfer." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 498, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 641 + ], + "type": "text", + "content": "As for limitations, our performance relies on the generative priors learned by the T2V model. Thus, in some cases, the combination of target object and input video motion may be out-of-distribution for the T2V model. In this case, the motion fidelity of our results would be degraded or suffer from visual artifacts (Fig. 9). Moreover, publicly available T2V models are still in infancy, in terms of quality, resolution, video length, and the scale of their training data compared to the vast distribution of natural videos. Despite the limitations of publicly available T2V models, our method significantly improves over prior methods, demonstrating the potential of leveraging the priors and space-time feature space learned by these models." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 658, + 421, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 421, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 421, + 671 + ], + "type": "text", + "content": "7. Acknowledgements" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 679, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 679, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 679, + 545, + 713 + ], + "type": "text", + "content": "This project received funding from the Israeli Science Foundation (grant 2303/20). We thank GEN-1 authors for their help in conducting comparisons." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8473" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 140 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 140 + ], + "type": "text", + "content": "[1] Guha Balakrishnan, Amy Zhao, Adrian V Dalca, Fredo Durand, and John Guttag. 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Our dynamic scene representation achieves photorealistic quality, real-time high-resolution rendering and compact model size. (a) Our lite-version model can render 8K 6-DoF video at 66 FPS on an Nvidia RTX 4090 GPU. (b) Example novel view rendering of a challenging scene. (c) Quantitative comparisons of rendering quality, speed and model size with prior arts on the Neural 3D Video Dataset." + ], + "image_footnote": [], + "bbox": [ + 366, + 287, + 488, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/df7227b74c56a46c42c7e1a16f79ff034fabb59035179aa0de672a9ad651b25e.jpg", + "image_caption": [ + "(b) High Quality Result" + ], + "image_footnote": [], + "bbox": [ + 490, + 287, + 612, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e3b9055d6a63d2d9aa3e96d2ebc3b4397b1996f45c64336a40b08b33e3079783.jpg", + "image_caption": [ + "(c) Comparison on Quality, Speed and Size" + ], + "image_footnote": [], + "bbox": [ + 616, + 287, + 888, + 446 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 550, + 312, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Novel view synthesis of dynamic scenes has been an intriguing yet challenging problem. Despite recent advancements, simultaneously achieving high-resolution photorealistic results, real-time rendering, and compact storage remains a formidable task. To address these challenges, we propose Spacetime Gaussian Feature Splating as a novel dynamic scene representation, composed of three pivotal components. First, we formulate expressive Spacetime Gaussians by enhancing 3D Gaussians with temporal opacity and parametric motion/rotation. This enables Spacetime Gaussians to capture static, dynamic, as well as transient content within a scene. Second, we introduce splatted feature rendering, which replaces spherical harmonics with neural features. These features facilitate the modeling of view- and time-dependent appearance while maintaining small size. Third, we leverage the guidance of training error and coarse depth to sample new Gaussians in areas that are challenging to converge with existing pipelines. Experiments on several established real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed, while retaining compact storage. At $8K$", + "bbox": [ + 75, + 583, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "resolution, our lite-version model can render at 60 FPS on an Nvidia RTX 4090 GPU.", + "bbox": [ + 500, + 551, + 890, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 612, + 630, + 628 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Photorealistic modeling of real-world dynamic scenes has been persistently pursued in computer vision and graphics. It allows users to freely explore dynamic scenes at novel viewpoints and timestamps, thus providing strong immersive experience, and can vastly benefit applications in VR/AR, broadcasting, education, etc.", + "bbox": [ + 496, + 637, + 890, + 727 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent advances in novel view synthesis, especially Neural Radiance Fields (NeRF) [66], have greatly improved the convenience and fidelity of static scene modeling from casual multi-view inputs in non-lab environments. Since then, large quantities of work [6-8, 15, 18, 27, 41, 67, 82] have emerged aiming to enhance rendering quality and speed. Particularly, [18, 41] propose to use anisotropic radial basis functions as 3D representations, which are highly adaptive to scene structures and boost the modeling of de", + "bbox": [ + 496, + 728, + 890, + 864 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 526, + 875, + 661, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Work done while Zhan was an intern at OPPO US Research Center.", + "bbox": [ + 527, + 887, + 890, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8508", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tails. 3D Gaussian Splatting (3DGS) [41] further presents an efficient rasterization-based scheme for differentiable volume rendering. Instead of shooting rays from camera to the scene and sampling points along each ray, 3DGS rasterizes 3D Gaussians onto image plane via splatting, which brings about notable rendering speedup.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the success on static scenes, directly applying the above methods per-frame to dynamic scenes is challenging, due to the overhead in model size and training time. State-of-the-art dynamic view synthesis methods [4, 12, 28, 48, 80, 87] adopt a holistic approach where multiple frames are represented in a single model. NeRFPlayer [80] and HyperReel [4] combine static spatial representations [15, 67] with temporal feature sharing/interpolation to improve model compactness. This strategy exploits the characteristic that adjacent frames in natural videos usually exhibit high similarity. In a similar vein, MixVoxels [87] uses time-variant latents and bridges them with spatial features by inner product. K-Planes [28] and HexPlane [12] factorize the 4D spacetime domain into multiple 2D planes for compact representation. One limitation of these methods is that their grid-like representations cannot fully adapt to the dynamics of scene structures, hindering the modeling of delicate details. Meanwhile, they struggle to produce real-time high-resolution rendering without sacrificing quality.", + "bbox": [ + 75, + 183, + 470, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we present a novel representation for dynamic view synthesis. Our approach simultaneously achieves photorealistic quality, real-time high-resolution rendering and compact model size (see Fig. 1 for example results and comparisons with state-of-the-arts). At the core of our approach is Spacetime Gaussian (STG), which extends 3D Gaussian to 4D spacetime domain. We propose to equip 3D Gaussian with time-dependent opacity along with polynomially parameterized motion and rotation. As a result, STGs are capable of faithfully modeling static, dynamic as well as transient (i.e., emerging or vanishing) content in a scene.", + "bbox": [ + 75, + 488, + 468, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To enhance model compactness and account for time-varying appearance, we propose splatted feature rendering. Specifically, for each Spacetime Gaussian, instead of storing spherical harmonic coefficients, we store features that encode base color, view-related information and time-related information. These features are rasterized to image space via differentiable splatting, and then go through a tiny multi-layer perceptrons (MLP) network to produce the final color. While smaller in size than spherical harmonics, these features exhibit strong expressiveness.", + "bbox": [ + 75, + 671, + 468, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Additionally, we introduce guided sampling of Gaussians to improve rendering quality of complex scenes. We observe that distant areas which are sparsely covered by Gaussians at initialization tend to have blurry rendering results. To tackle this problem, we propose to sample new", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gaussians in the 4D scene with the guidance of training error and coarse depth.", + "bbox": [ + 498, + 90, + 888, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, the contributions of our work are the following:", + "bbox": [ + 498, + 121, + 888, + 151 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We present a novel representation based on Spacetime Gaussian for high-fidelity and efficient dynamic view synthesis.", + "- We propose splatted feature rendering, which enhances model compactness and facilitates the modeling of time-varying appearance.", + "- We introduce a guided sampling approach for Gaussians to improve rendering quality at distant sparsely covered areas.", + "- Extensive experiments on various real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed while keeping small model size. Our lite-version model enables 8K rendering at 60 FPS." + ], + "bbox": [ + 500, + 152, + 888, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 359, + 640, + 375 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel View Synthesis. Early approaches leverage image-based rendering techniques with proxy geometry/depth to sample novel views from source images [11, 13, 20, 31, 34, 44, 46, 103]. Chaurasia et al. [14] estimate a depth map to blend pixels from source views and employ superpixels to compensate for missing depth data. Hedman et al. [32] utilize RGBD sensors to improve rendering quality and speed. Penner and Zhang [72] leverage volumetric voxels for continuity in synthesized views and robustness to depth uncertainty. Hedman et al. [33] learn the blending scheme with neural networks. Flynn et al. [26] combine multi-plane images with learned gradient descent. Wiles et al. [92] sput latent features from point cloud for novel view synthesis.", + "bbox": [ + 498, + 383, + 890, + 580 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Scene Representations. In recent years, neural scene representations have achieved great progress in novel view synthesis. These methods allocate neural features to structures such as volume [62, 78], texture [16, 84], or point cloud [1]. The seminal work of NeRF [66] proposes to leverage differentiable volume rendering. It does not require proxy geometry and instead uses MLPs to implicitly encode density and radiance in 3D space. Later on, numerous works emerge to boost the quality and efficiency of differentiable volume rendering. One group of methods focuses on improving the sampling strategy to reduce the number of point queries [4, 68, 73] or applies light field-based formulation [3, 25, 53, 54, 79, 81, 89]. Another group trades space for speed by incorporating explicit and localized neural representations [8, 15, 17, 27, 36, 60, 67, 75, 82, 83, 96, 101]. Among them, to improve model compactness, Instant-NGP [67] uses hash grid while TensoRF [15] utilizes tensor decomposition.", + "bbox": [ + 496, + 598, + 892, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, 3D Gaussian Splitting (3DGS) [41] proposes to use anisotropic 3D Gaussians as scene representation", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8509", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "and presents an efficient differentiable rasterizer to splat these Gaussians to the image plane. Their method enables fast high-resolution rendering, while preserving great rendering quality. Similar to 3DGS, NeuRBF [18] leverages anisotropic radial basis functions for neural representation and achieves high-fidelity rendering. However, the above methods focus on static scene representation.", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dynamic Novel View Synthesis. A widely adopted setting for dynamic free-viewpoint rendering is using multiview videos as input. Classic methods in this area include [19, 21, 39, 40, 49-51, 98, 104]. More recently, Broxton et al. [10] use multi-sphere image as bootstrap and then convert it to layered meshes. Bansal et al. [5] separate static and dynamic contents and manipulate video with deep network in screen space. Bemana et al. [9] learn a neural network to implicitly map view, time or light coordinates to 2D images. Attal et al. [2] use multi-sphere representations to handle the depth and occlusions in 360-degree videos. Lin et al. [57, 58] propose 3D mask volume to addresses the temporal inconsistency of disocclusions. Neural Volumes [62] uses an encoder-decoder network to encode images into a 3D volume and decode it with volume rendering. Lombardi et al. [63] enhance Neural Volumes by decoding a mixture of dynamic geometric primitives from latent code and skipping samples in empty space for efficient ray marching. Extending static NeRF-related representations to dynamic scenes are also being actively explored [4, 12, 28, 38, 42, 47, 48, 56, 71, 77, 80, 87, 88, 90, 91]. DyNeRF [48] combines NeRF with time-conditioned latent codes to compactly represent dynamic scenes. StreamRF [47] accelerates the training of dynamic scenes by modeling the differences of consecutive frames. NeRFPlayer [80] decomposes scene into static, new and deforming fields and proposes streaming of feature channels. MixVoxels [87] represents scene with a mixture of static and dynamic voxels to accelerate rendering. HyperReel [4] utilizes sampling prediction network to reduce sampling points and leverages keyframe-based representation. K-Planes [28], HexPlane [12] and Tensor4D [77] factorize 4D spacetime domain into 2D feature planes for compact model size.", + "bbox": [ + 75, + 218, + 472, + 717 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Another line of research tackles dynamic view synthesis from monocular videos [22, 23, 29, 30, 52, 55, 61, 69, 70, 74, 85, 86, 94]. Under this setting, a single camera moves around in the dynamic scene, providing only one observed viewpoint at each timestep. To address the sparsity of supervision, priors on motion, scene flow or depth are usually introduced. In this work, we focus on the dynamic representation itself and only consider the setting of multi-view input videos.", + "bbox": [ + 75, + 718, + 470, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recently, there are several work on this topic that are concurrent to ours [37, 45, 59, 64, 93, 95, 97, 99, 100]. 4K4D [97] combines 4D point clouds with K-Planes [28]", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and discrete image-based rendering, and uses differentiable depth peeling to train the model. Luiten et al. [64] models 4D scene with a set of moving 3D Gaussians, whose positions and rotations are discretely defined at each step. Their method demonstrates appealing results for 3D tracking, but its rendering quality is less favorable due to flickering artifacts. Yang et al. [100] leverage 4D Gaussians and 4D spherindrical harmonics for dynamic modelling. 4D Gaussians essentially represent motion with linear model. Comparatively, our polynomial motion model is more expressive, resulting in higher rendering quality. Our method also has higher rendering speed than their work. Yang et al. [99] and Wu et al. [93] prioritize on monocular dynamic view synthesis and employ deformation fields to deform a set of canonical 3D Gaussians. For multi-view videos setting, the performance of [99] is not extensively evaluated while [93] depicts inferior rendering quality and speed than ours.", + "bbox": [ + 496, + 90, + 893, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary: 3D Gaussian Splatting", + "text_level": 1, + "bbox": [ + 498, + 359, + 826, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given images at multiple viewpoints with known camera poses, 3D Gaussian Splatting [41] (3DGS) optimizes a set of anisotropic 3D Gaussians via differentiable rasterization to represent a static 3D scene. Owing to their efficient rasterization, the optimized model can render high-fidelity novel views in real-time.", + "bbox": [ + 496, + 383, + 893, + 473 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3DGS [41] associates a 3D Gaussian $i$ with a position $\\mu_{i}$ , covariance matrix $\\Sigma_{i}$ , opacity $\\sigma_{i}$ and spherical harmonics (SH) coefficients $\\mathbf{h}_i$ . The final opacity of a 3D Gaussian at any spatial point $\\mathbf{x}$ is", + "bbox": [ + 496, + 474, + 893, + 536 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} = \\sigma_ {i} \\exp \\left(- \\frac {1}{2} (\\mathbf {x} - \\mu_ {i}) ^ {T} \\Sigma_ {i} ^ {- 1} (\\mathbf {x} - \\mu_ {i})\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 541, + 890, + 574 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\Sigma_{i}$ is positive semi-definite and can be decomposed into scaling matrix $S_{i}$ and rotation matrix $R_{i}$ :", + "bbox": [ + 500, + 579, + 890, + 609 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma_ {i} = R _ {i} S _ {i} S _ {i} ^ {T} R _ {i} ^ {T}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 614, + 890, + 633 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $S_{i}$ is a diagonal matrix and is parameterized by a 3D vector $\\mathbf{s}_i$ , and $R_{i}$ is parameterized by a quaternion $q$ .", + "bbox": [ + 496, + 638, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To render an image, 3D Gaussians are first projected to 2D image space via an approximation of the perspective transformation [105]. Specifically, the projection of a 3D Gaussian is approximated as a 2D Gaussian with center $\\mu_i^{2D}$ and covariance $\\Sigma_i^{2D}$ . Let $W, K$ be the viewing transformation and projection matrix, $\\mu_i^{2D}$ and $\\Sigma_i^{2D}$ are computed as", + "bbox": [ + 496, + 669, + 893, + 760 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {i} ^ {2 D} = \\left(K \\left(\\left(W \\mu_ {i}\\right) / \\left(W \\mu_ {i}\\right) _ {z}\\right)\\right) _ {1: 2}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 763, + 890, + 782 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma_ {i} ^ {2 D} = \\left(J W \\Sigma_ {i} W ^ {T} J ^ {T}\\right) _ {1: 2, 1: 2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 785, + 890, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $J$ is the Jacobian of the projective transformation.", + "bbox": [ + 500, + 809, + 874, + 824 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "After sorting the Gaussians in depth order, the color at a pixel is obtained by volume rendering:", + "bbox": [ + 496, + 825, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} = \\sum_ {i \\in \\mathcal {N}} \\mathbf {c} _ {i} \\alpha_ {i} ^ {2 D} \\prod_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j} ^ {2 D}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 861, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8510", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/87b295ef671e5c08ccb0eba3bedc5680e619c6015b80b24416e57b9658a7d2a7.jpg", + "image_caption": [ + "(a) Spacetime Gaussians" + ], + "image_footnote": [], + "bbox": [ + 91, + 92, + 509, + 266 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f01319d0a8fc1201f970f5f0610e9c9164810c6f58d026addf02f010c1df07a8.jpg", + "image_caption": [ + "(b) Feature Splitting and Rendering", + "Figure 2. Overview of Spacetime Gaussians and splatted feature rendering. (a) Our method leverages a set of Spacetime Gaussians (STG) to represent the dynamic scenes. On top of 3D Gaussian, each STG is further equipped with temporal opacity, polynomial motion/rotation and time-dependent features. (b) We visualize the splatted features as maps, which are converted to color image via MLP." + ], + "image_footnote": [], + "bbox": [ + 526, + 98, + 890, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{i}^{2D}$ is a 2D version of Eq. (1), with $\\mu_{i}, \\Sigma_{i}, \\mathbf{x}$ replaced by $\\mu_{i}^{2D}, \\Sigma_{i}^{2D}, \\mathbf{x}^{2D}$ (pixel coordinate). $\\mathbf{c}_{i}$ is the RGB color after evaluating SH with view direction and coefficients $\\mathbf{h}_{i}$ .", + "bbox": [ + 75, + 369, + 468, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 75, + 443, + 168, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose a novel representation based on Spacetime Gaussians for modeling dynamic 3D scenes. Our approach takes multi-view videos as input and creates 6-DoF video that allows rendering at novel views. We first describe the formulation of our Spacetime Gaussian (STG) in Sec. 4.1. Then in Sec. 4.2, we present feature-based splatting for time-varying rendering. Sec. 4.3 details our optimization process and Sec. 4.4 introduces guided sampling of Gaussians.", + "bbox": [ + 75, + 468, + 468, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Spacetime Gaussians", + "text_level": 1, + "bbox": [ + 75, + 612, + 274, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To represent 4D dynamics, we propose Spacetime Gaussians (STG) that combine 3D Gaussians with temporal components to model emerging/vanishing content as well as motion/deformation, as shown in Fig. 2 (a). Specifically, we introduce temporal radial basis function to encode temporal opacity, which can effectively model scene content that emerges or vanishes within the duration of video. Meanwhile, we utilize time-conditioned parametric functions for the position and rotation of 3D Gaussians to model the motion and deformation in the scene. For a spacetime point $(\\mathbf{x},t)$ , the opacity of an STG is", + "bbox": [ + 75, + 635, + 468, + 801 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} (t) = \\sigma_ {i} (t) \\exp \\left(- \\frac {1}{2} (\\mathbf {x} - \\mu_ {i} (t)) ^ {T} \\Sigma_ {i} (t) ^ {- 1} (\\mathbf {x} - \\mu_ {i} (t))\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 809, + 473, + 854 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma_{i}(t)$ is temporal opacity, $\\mu_{i}(t),\\Sigma_{i}(t)$ are time-dependent position and covariance, and $i$ stands for the ith STG. We detail each of the components below.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal Radial Basis Function. We use a temporal radial basis function to represent the temporal opacity of an STG at any time $t$ . Inspired by [18, 41] that use radial basis functions for approximating spatial signals, we utilize 1D Gaussian for the temporal opacity $\\sigma_{i}(t)$ :", + "bbox": [ + 498, + 369, + 892, + 446 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma_ {i} (t) = \\sigma_ {i} ^ {s} \\exp \\left(- s _ {i} ^ {\\tau} | t - \\mu_ {i} ^ {\\tau} | ^ {2}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 465, + 890, + 483 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_i^\\tau$ is temporal center, $s_i^\\tau$ is temporal scaling factor, and $\\sigma_i^s$ is time-independent spatial opacity. $\\mu_i^\\tau$ represents the timestamp for the STG to be most visible while $s_i^\\tau$ determines its effective duration (i.e., the time duration where its temporal opacity is high). We include $\\sigma_i^s$ to allow spatial opacity variation across STGs.", + "bbox": [ + 496, + 493, + 890, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Polynomial Motion Trajectory. For each STG, we employ a time-conditioned function to model its motion. Motivated by [24, 35], we choose polynomial function:", + "bbox": [ + 496, + 609, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu_ {i} (t) = \\sum_ {k = 0} ^ {n _ {p}} b _ {i, k} \\left(t - \\mu_ {i} ^ {\\tau}\\right) ^ {k}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 669, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mu_{i}(t)$ denotes the spatial position of an STG at time $t$ . $\\{b_{i,k}\\}_{k=0}^{n_p}, b_{i,k} \\in \\mathbb{R}$ are the corresponding polynomial coefficients and are optimized during training. Combining Eq. (7) and Eq. (8), complex and long motion can be represented by multiple short segments with simpler motion. In our implementation, we use $n_p = 3$ as we find it a good balance between representation capacity and model size.", + "bbox": [ + 496, + 723, + 890, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Polynomial Rotation. Following [41], we use real-valued quaternion to parameterize the rotation matrix $R_{i}$ in Eq. (2). Similar to motion trajectory, we adopt a polynomial func", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8511", + "bbox": [ + 480, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/37b02f8d8245d811982e5d387c57e52df0791c9608e9c49b1e20148c9950785a.jpg", + "image_caption": [ + "Figure 3. Illustration of our guided sampling strategy for Gaussians. Our strategy samples new Gaussians along rays by leveraging the guidance of training error and coarse depth." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 888, + 392 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tion to represent quaternion:", + "bbox": [ + 76, + 434, + 266, + 448 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq _ {i} (t) = \\sum_ {k = 0} ^ {n _ {q}} c _ {i, k} \\left(t - \\mu_ {i} ^ {\\tau}\\right) ^ {k}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 460, + 468, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $q_{i}(t)$ is the rotation (in quaternion) of an STG at time $t$ , and $\\{c_{i,k}\\}_{k=0}^{n_q}, c_{i,k} \\in \\mathbb{R}$ are polynomial coefficients. After converting $q_{i}(t)$ to rotation matrix $R_{i}(t)$ , the covariance $\\Sigma_{i}(t)$ at time $t$ can be obtained via Eq. (2). We set $n_q = 1$ in our experiments.", + "bbox": [ + 76, + 515, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that we keep the scaling matrix $S_{i}$ in Eq. (2) to be time-independent, since we experimentally do not observe improvement in rendering quality when applying time-conditioned function on this parameter.", + "bbox": [ + 75, + 590, + 468, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Splatted Feature Rendering", + "text_level": 1, + "bbox": [ + 76, + 662, + 326, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To encode view- and time-dependent radiance both accurately and compactly, we store features instead of spherical harmonics coefficients (SH) in each STG. Specifically, the features $\\mathbf{f}_i(t)\\in \\mathbb{R}^9$ of each STG consist of three parts:", + "bbox": [ + 75, + 686, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f} _ {i} (t) = \\left[ \\mathbf {f} _ {i} ^ {\\text {b a s e}}, \\mathbf {f} _ {i} ^ {\\text {d i r}}, \\quad (t - \\mu_ {i} ^ {\\tau}) \\mathbf {f} _ {i} ^ {\\text {t i m e}} \\right] ^ {T}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 762, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{base}} \\in \\mathbb{R}^{3}$ contains base RGB color, and $\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{dir}}$ , $\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{time}} \\in \\mathbb{R}^{3}$ encode information related to view direction and time. The feature splatting process is similar to Gaussian Splatting [41], except that the RGB color $c_{i}$ in Eq. (5) is now replaced by features $\\mathbf{f}_{i}(t)$ . After splatting to image space, we split the splatted features at each pixel into $\\mathbf{F}^{\\mathrm{base}}$ , $\\mathbf{F}^{\\mathrm{dir}}$ , $\\mathbf{F}^{\\mathrm{time}}$ , whose channels correspond to the three parts in Eq. (10).", + "bbox": [ + 75, + 792, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The final RGB color at each pixel is obtained after going through a 2-layer MLP $\\Phi$ :", + "bbox": [ + 498, + 433, + 890, + 463 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} = \\mathbf {F} ^ {\\text {b a s e}} + \\Phi (\\mathbf {F} ^ {\\text {d i r}}, \\mathbf {F} ^ {\\text {t i m e}}, \\mathbf {r}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 473, + 890, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{r}$ is the view direction at the pixel and is additionally concatenated with the features as input. Fig. 2 (b) shows an illustration of the rendering process.", + "bbox": [ + 496, + 502, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared to SH encoding, our feature-based approach requires fewer parameters for each STG (9 vs. 48 for 3-degree SH). At the same time, since the MLP network $\\Phi$ is shallow and narrow, our method still achieves fast rendering speed.", + "bbox": [ + 496, + 547, + 890, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To maximize rendering speed, we can also optionally drop $\\Phi$ and only keep $\\mathbf{F}^{base}$ during training and rendering. We refer to this configuration as our lite-version model.", + "bbox": [ + 496, + 625, + 890, + 669 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Optimization", + "text_level": 1, + "bbox": [ + 500, + 678, + 637, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The parameters to be optimized include the MLP $\\Phi$ and the parameters of each STG $(\\sigma_i^s, s_i^\\tau, \\mu_i^\\tau, \\{b_{i,k}\\}_{k=0}^{n_p}, \\{c_{i,k}\\}_{k=0}^{n_q}, \\mathbf{s}_i, \\mathbf{f}_i^{\\mathrm{base}}, \\mathbf{f}_i^{\\mathrm{dir}}, \\mathbf{f}_i^{\\mathrm{time}})$ .", + "bbox": [ + 496, + 702, + 890, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Following [41], we optimize these parameters through differentiable splatting and gradient-based backpropagation, and interleave with density control of Gaussians. We use rendering loss that compares rendered images with groundtruth images. The rendering loss consists of a $\\mathcal{L}_1$ term and a D-SSIM term.", + "bbox": [ + 496, + 748, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Guided Sampling of Gaussians", + "text_level": 1, + "bbox": [ + 500, + 847, + 772, + 863 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We observe that areas which have sparse Gaussians at initialization are challenging to converge to high rendering", + "bbox": [ + 496, + 869, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8512", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "quality, especially if these areas are far away from the training cameras. Therefore, we further introduce a strategy to sample new Gaussians with the guidance of training error and coarse depth.", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We sample new Gaussians along the rays of pixels that have large errors during training, as illustrated in Fig. 3. To ensure sampling effectiveness, we conduct sampling after training loss is stable. Since error maps can be noisy during training, we patch-wise aggregate training errors to prioritize on areas with substantial errors rather than outlier pixels. Then we sample a ray from the center pixel of each selected patches that have large errors. To avoid sampling in an excessively large depth range, we exploit the coarse depth map of Gaussians' centers to determine a more specific depth range. The depth map is generated during feature splatting and incurs little computational overhead. New Gaussians are then uniformly sampled within the depth range along the rays. We additionally add small noises to the centers of the newly sampled Gaussians. Among the sampled Gaussians, the unnecessary ones will have low opacity after steps of training and be pruned. For the scenes in our experiments, the above sampling process only needs to be conducted no more than 3 times.", + "bbox": [ + 75, + 151, + 470, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our guided sampling strategy is complimentary to the density control techniques in [41]. While density control gradually grows Gaussians near existing ones by splitting, our approach can sample new Gaussians at regions that have sparse or no Gaussians.", + "bbox": [ + 75, + 439, + 468, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 527, + 299, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We initialize our STGs with the structure-from-motion sparse point clouds from all available timestamps. For density control, we conduct more aggressive pruning than [41] to reduce the number of Gaussians and keep model size to be relatively small. We use Adam optimizer [43]. The training time for a 50-frame sequence is 40-60 minutes on a single NVIDIA A6000 GPU. We adapt the splatting process to support different camera models in real world datasets. See supplementary material for more implementation details.", + "bbox": [ + 75, + 554, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 76, + 705, + 209, + 722 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on three real-world benchmarks: Neural 3D Video Dataset [48] (Sec. 6.1), Google Immersive Dataset [10] (Sec. 6.2), and Technicolor Dataset [76] (Sec. 6.3). We also conduct ablation studies on various aspects of our method (Sec. 6.4). Please refer to supplementary material and video for more results and real-time demo.", + "bbox": [ + 75, + 729, + 467, + 821 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Neural 3D Video Dataset", + "text_level": 1, + "bbox": [ + 76, + 830, + 303, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The Neural 3D Video Dataset [48] contains six indoor multi-view video sequences captured by 18 to 21 cameras at $2704 \\times 2028$ resolution. Following common practice, train-", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/c8212397cf819939f2c973f37d3153135c18d91aaa99e46d3955f363137fa7ee.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons on the Neural 3D Video Dataset. \"FPS\" is measured at $1352 \\times 1014$ resolution. \"Size\" is the total model size for 300 frames. Some methods only report part of the scenes. For fair comparison, we additionally report our results under their settings. $^1$ only includes the Flame Salmon scene. $^2$ excludes the Coffee Martini scene." + ], + "table_footnote": [], + "table_body": "
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size↓
Neural Volumes [62]122.80-0.0620.295--
LLFF [65]123.24-0.0760.235--
DyNeRF [48]129.58-0.0200.0830.01528 MB
Ours129.480.0380.0220.063103300 MB
HexPlane [12]231.71--0.075-200 MB
Ours232.740.0270.0120.039140190 MB
StreamRF [47]28.26---10.95310 MB
NeRFPlayer [80]30.690.034-0.1110.055130 MB
HyperReel [4]31.100.036-0.0962360 MB
K-Planes [28]31.63-0.018-0.3311 MB
MixVoxels-L [87]31.34-0.0170.09637.7500 MB
MixVoxels-X [87]31.73-0.0150.0644.6500 MB
Ours32.050.0260.0140.044140200 MB
", + "bbox": [ + 501, + 180, + 890, + 333 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/78ac38681fb3ffbf8cd80aefed6f0005bdb79789d30c56198c84d85a9fee0095.jpg", + "table_caption": [ + "Table 2. Quantitative comparisons on the Google Immersive Dataset. \"Size/Fr\" stands for model size per frame." + ], + "table_footnote": [], + "table_body": "
MethodPSNR↑DSSIM1↓LPIPS↓FPS↑Size/Fr↓
NeRFPlayer [80]25.80.0760.1960.1217.1 MB
HyperReel [4]28.80.0630.19341.2 MB
Ours29.20.0420.081991.2 MB
", + "bbox": [ + 500, + 382, + 890, + 448 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ing and evaluation are conducted at half resolution, and the first camera is held out for evaluation [48]. The number of frames is 300 for each scene.", + "bbox": [ + 496, + 473, + 890, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use PSNR, DSSIM and LPIPS [102] as evaluation metrics. As mentioned in [4, 28], there is an inconsistency in the DSSIM implementation across methods. For fair comparison, we do our best to group existing methods' DSSIM results into two categories $(\\mathrm{DSSIM}_1$ and $\\mathrm{DSSIM}_2)$ . Using the structural_similarity function from scikit-image library, $\\mathrm{DSSIM}_1$ sets data_range to 1.0 while $\\mathrm{DSSIM}_2$ sets data_range to 2.0. We use FPS as metric for rendering speed. Metrics are averaged over all six scenes except noted otherwise.", + "bbox": [ + 496, + 518, + 890, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Tab. 1, our method achieves 140 FPS and outperforms the others by a large margin. Our approach also has the best LPIPS in all comparisons and the best PSNR/DSSIM in most cases. Fig. 4 shows qualitative comparisons on a representative view that is widely used in other work. Compared to the other baselines, our result contains more vivid details (e.g., the textures on the salmon) and artifact-less rendering (e.g., the caustics on the cup). Please see supplementary material for comparisons with concurrent methods.", + "bbox": [ + 496, + 670, + 890, + 820 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2. Google Immersive Dataset", + "text_level": 1, + "bbox": [ + 500, + 830, + 740, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Google Immersive Dataset [10] contains indoor and outdoor scenes captured with a 46-camera rig. The cameras are in fish-eye mode and are mounted on an outward-facing hemi", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8513", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c3d8f4e3168797f7b7d30d975138012c87511b14fec1a9b8102d14dacec0bb33.jpg", + "image_caption": [ + "Figure 4. Qualitative comparisons on the Neural 3D Video Dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 890, + 428 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7c80f9b3bd67376423925775bb138a1fac751d50faf4707e06928ee3c4c127e4.jpg", + "image_caption": [ + "Figure 5. Qualitative comparisons on the Google Immersive Dataset." + ], + "image_footnote": [], + "bbox": [ + 81, + 470, + 887, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "sphere. Compared to outside-in setups, there is less overlap among views, hence posing additional challenges.", + "bbox": [ + 76, + 852, + 468, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following [4, 80], we evaluate on 7 selected scenes", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "(Welder, Flames, Truck, Exhibit, Face Paint 1, Face Paint 2, Cave) and hold out the center camera as test view. The numerical results of NeRFPlayer [80] and HyperReel [4] are", + "bbox": [ + 500, + 852, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8514", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8fe1463d0b8a6cc4b62452c17928b15f9bfe9c4d8a875bd2a00a47aecaab4f08.jpg", + "table_caption": [ + "Table 3. Quantitative comparisons on the Technicolor Dataset. \"Size/Fr\" stands for model size per frame." + ], + "table_footnote": [], + "table_body": "
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size/Fr↓
DyNeRF [48]31.8-0.0210.1400.020.6 MB
HyperReel [4]32.70.047-0.1094.001.2 MB
Ours33.60.0400.0190.08486.71.1 MB
", + "bbox": [ + 76, + 125, + 467, + 183 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/a1926271c1652592c1077d29eb859b491467a740e9bbb7ff797f3f3825904c9c.jpg", + "table_caption": [ + "Table 4. Ablation study of proposed components. Conducted on all the five scenes from the Technicolor Dataset." + ], + "table_footnote": [], + "table_body": "
MethodPSNR↑DSSIM1↓LPIPS↓
w/o Temporal Opacity31.00.0630.153
w/o Polynomial Motion32.60.0450.099
w/o Polynomial Rotation33.40.0420.085
w/o Feature Splitting33.00.0440.097
w/o Guided Sampling of Gaussians33.30.0410.085
Ours Full33.60.0400.084
", + "bbox": [ + 76, + 222, + 467, + 325 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0d41b83c6c49c39e7492f4e45a61df31deb1496b1c8706b0aea180032f44edae.jpg", + "table_caption": [ + "Table 5. Ablation study on the number of frames whose SfM point clouds are used in initialization. Conducted on the Theater scene from the Technicolor Dataset." + ], + "table_footnote": [], + "table_body": "
Every N FramesPSNR↑DSSIM1↓LPIPS↓Size↓
N = 131.580.0590.124110.2 MB
N = 431.510.0570.11746.7 MB
N = 1631.040.0600.13932.6 MB
", + "bbox": [ + 76, + 385, + 467, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "from their papers. The visual results of NeRFPlayer [80] are obtained from their authors while those of HyperReel [4] are produced by running their released codes.", + "bbox": [ + 75, + 470, + 467, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Tab. 2, our method outperforms NeRFPlayer and HyperReel in both speed and quality. Compared to HyperReel, our method is over 10 times faster in rendering speed. Although our PSNR is only $0.4\\mathrm{dB}$ higher, the improvements in DSSIM and LPIPS are significant. When compared to NeRFPlayer, the margin is larger for all metrics. Visual comparisons are shown in Fig. 5. Our method depicts sharper details and fewer artifacts than the others.", + "bbox": [ + 75, + 517, + 467, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. Technicolor Dataset", + "text_level": 1, + "bbox": [ + 76, + 648, + 264, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Technicolor Light Field Dataset [76] contains videos taken with a 4x4 camera array. Each camera is time-synchronized and the spatial resolution is $2048 \\times 1088$ . In alignment with HyperReel [4], we hold out the camera at second row second column and evaluate on five scenes (Birthday, Fabien, Painter, Theater, Trains) at full resolution.", + "bbox": [ + 75, + 671, + 467, + 760 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 3 shows the comparisons, where our method achieves noticeable gain in quality and speed. Please refer to supplementary material for visual comparisons.", + "bbox": [ + 75, + 761, + 467, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 816, + 228, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To evaluate the effectiveness of proposed components, we conduct an ablation study in Tab. 4 using all the five scenes from Technicolor Dataset. Below we describe the configuration and performance of each ablation baseline.", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Temporal Opacity. \"w/o Temporal Opacity\" fixes the center and scale of the temporal radial basis functions during training. This variant suffers from a significant performance drop, revealing the importance of temporal opacity.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Polynomial Motion and Rotation. \"w/o Polynomial Motion\" and \"w/o Polynomial Rotation\" fix the spatial position and rotation of STGs respectively. Both lead to a performance drop. Comparatively, motion is more important than rotation, which motivates us to use a lower-degree polynomial for rotation.", + "bbox": [ + 496, + 151, + 890, + 239 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feature Splatting. \"w/o Feature Splatting\" uses the base RGB color $\\mathbf{F}^{base}$ as the final color. It can be seen that there is a moderate drop in quality due to reduced ability to model view- and time-dependent appearance.", + "bbox": [ + 496, + 242, + 890, + 301 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Guided Sampling of Gaussians. \"w/o Guided Sampling of Gaussians\" does not encounter much performance drop in this dataset. The reason is that the scenes contain rich textures and can be well covered by SfM points. However, for other challenging scenes, guided sampling plays an important role (see Fig. 3 and supplementary material for examples).", + "bbox": [ + 496, + 301, + 890, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Number of Frames used for Initialization. We further analyzed the number of frames used for initialization in Tab. 5. Using fewer frames slightly downgrade quality, but also significantly reduces model size. It reveals that the compactness of our method can be further enhanced with a good selection of frames for initialization.", + "bbox": [ + 496, + 407, + 890, + 497 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.5. Limitations", + "text_level": 1, + "bbox": [ + 500, + 508, + 624, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Although our representation achieves fast rendering speed, it cannot be trained on-the-fly. The support for on-the-fly training could benefit numerous streaming applications. To achieve this, advanced initialization techniques could be explored to accelerate the training process or alleviate the requirement of per-scene training. On the other hand, our method currently focuses on multi-view video inputs. It is promising to adapt our approach to monocular setting by combining with regularization or generative priors.", + "bbox": [ + 496, + 531, + 890, + 667 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 681, + 617, + 696 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a novel representation based on Spacetime Gaussians for dynamic view synthesis. The proposed Spacetime Gaussians are enhanced with temporal opacity and parametric motion/rotation to model complex 4D content. To increase model compactness and encode view/time-dependent appearance, we introduce splatted feature rendering, which utilizes neural features and a lightweight MLP instead of spherical harmonics. Additionally, we leverage guided sampling of Gaussians to further improve the rendering quality of complex scenes. Experiments on real-world datasets show that our representation delivers state-of-the-art quality at high resolution and FPS, while maintaining a compact model size.", + "bbox": [ + 496, + 705, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8515", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics. In European Conference on Computer Vision, pages 696-712. Springer, 2020. 2", + "[2] Benjamin Attal, Selena Ling, Aaron Gokaslan, Christian Richardt, and James Tompkin. 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Parallax photography: creating 3d cinematic effects from stills. In Proceedings of Graphics Interface 2009, pages 111-118. Canadian Information Processing Society, 2009. 2", + "[104] C Lawrence Zitnick, Sing Bing Kang, Matthew Uytendaele, Simon Winder, and Richard Szeliski. High-quality video view interpolation using a layered representation. ACM transactions on graphics (TOG), 23(3):600-608, 2004. 3", + "[105] Matthias Zwicker, Hanspeter Pfister, Jeroen Van Baar, and Markus Gross. Ewa volume splatting. In Proceedings Visualization, 2001. VIS'01., pages 29-538. IEEE, 2001. 3" + ], + "bbox": [ + 78, + 90, + 468, + 585 + ], + "page_idx": 12 + }, + { + "type": "page_number", + "text": "8520", + "bbox": [ + 482, + 945, + 516, + 955 + ], + "page_idx": 12 + } +] \ No newline at end of file diff --git a/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/fc66fcb8-31e6-496e-8bf3-fedca92ba729_model.json b/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/fc66fcb8-31e6-496e-8bf3-fedca92ba729_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0a13bb50e93c4c9965bc916f150a3a64cccd070f --- /dev/null +++ b/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/fc66fcb8-31e6-496e-8bf3-fedca92ba729_model.json @@ -0,0 +1,3141 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.131, + 0.877, + 0.153 + ], + "angle": 0, + "content": "Spacetime Gaussian Feature Splating for Real-Time Dynamic View Synthesis" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.18, + 0.338, + 0.198 + ], + "angle": 0, + "content": "Zhan \\(\\mathbf{L}\\mathbf{i}^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.378, + 0.181, + 0.492, + 0.199 + ], + "angle": 0, + "content": "Zhang Chen\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.199, + 0.474, + 0.216 + ], + "angle": 0, + "content": "1 OPPO US Research Center" + }, + { + "type": "text", + "bbox": [ + 0.532, + 0.181, + 0.623, + 0.199 + ], + "angle": 0, + "content": "Zhong Li\\(^{1\\dagger}\\)" + }, + { + "type": "text", + "bbox": [ + 0.665, + 0.181, + 0.721, + 0.198 + ], + "angle": 0, + "content": "Yi \\(\\mathrm{Xu}^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.514, + 0.199, + 0.726, + 0.218 + ], + "angle": 0, + "content": "2Portland State University" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.22, + 0.271, + 0.234 + ], + "angle": 0, + "content": "lizhan@pdx.edu" + }, + { + "type": "text", + "bbox": [ + 0.307, + 0.221, + 0.476, + 0.234 + ], + "angle": 0, + "content": "zhang.chen@oppo.com" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.22, + 0.664, + 0.234 + ], + "angle": 0, + "content": "zhong.li@oppo.com" + }, + { + "type": "text", + "bbox": [ + 0.699, + 0.22, + 0.826, + 0.234 + ], + "angle": 0, + "content": "yi.xu@oppo.com" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.238, + 0.76, + 0.251 + ], + "angle": 0, + "content": "https://oppo-us-research.github.io/SpacetimeGaussians-website/" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.289, + 0.362, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.124, + 0.451, + 0.319, + 0.463 + ], + "angle": 0, + "content": "(a) Real-Time 8K Demo at 66 FPS" + }, + { + "type": "image", + "bbox": [ + 0.367, + 0.289, + 0.49, + 0.447 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.422, + 0.451, + 0.556, + 0.464 + ], + "angle": 0, + "content": "(b) High Quality Result" + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.289, + 0.614, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.289, + 0.89, + 0.448 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.641, + 0.451, + 0.882, + 0.464 + ], + "angle": 0, + "content": "(c) Comparison on Quality, Speed and Size" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.476, + 0.893, + 0.531 + ], + "angle": 0, + "content": "Figure 1. Our dynamic scene representation achieves photorealistic quality, real-time high-resolution rendering and compact model size. (a) Our lite-version model can render 8K 6-DoF video at 66 FPS on an Nvidia RTX 4090 GPU. (b) Example novel view rendering of a challenging scene. (c) Quantitative comparisons of rendering quality, speed and model size with prior arts on the Neural 3D Video Dataset." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.551, + 0.313, + 0.567 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Novel view synthesis of dynamic scenes has been an intriguing yet challenging problem. Despite recent advancements, simultaneously achieving high-resolution photorealistic results, real-time rendering, and compact storage remains a formidable task. To address these challenges, we propose Spacetime Gaussian Feature Splating as a novel dynamic scene representation, composed of three pivotal components. First, we formulate expressive Spacetime Gaussians by enhancing 3D Gaussians with temporal opacity and parametric motion/rotation. This enables Spacetime Gaussians to capture static, dynamic, as well as transient content within a scene. Second, we introduce splatted feature rendering, which replaces spherical harmonics with neural features. These features facilitate the modeling of view- and time-dependent appearance while maintaining small size. Third, we leverage the guidance of training error and coarse depth to sample new Gaussians in areas that are challenging to converge with existing pipelines. Experiments on several established real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed, while retaining compact storage. At \\(8K\\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.553, + 0.892, + 0.582 + ], + "angle": 0, + "content": "resolution, our lite-version model can render at 60 FPS on an Nvidia RTX 4090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.613, + 0.631, + 0.629 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Photorealistic modeling of real-world dynamic scenes has been persistently pursued in computer vision and graphics. It allows users to freely explore dynamic scenes at novel viewpoints and timestamps, thus providing strong immersive experience, and can vastly benefit applications in VR/AR, broadcasting, education, etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.892, + 0.865 + ], + "angle": 0, + "content": "Recent advances in novel view synthesis, especially Neural Radiance Fields (NeRF) [66], have greatly improved the convenience and fidelity of static scene modeling from casual multi-view inputs in non-lab environments. Since then, large quantities of work [6-8, 15, 18, 27, 41, 67, 82] have emerged aiming to enhance rendering quality and speed. Particularly, [18, 41] propose to use anisotropic radial basis functions as 3D representations, which are highly adaptive to scene structures and boost the modeling of de" + }, + { + "type": "page_footnote", + "bbox": [ + 0.527, + 0.875, + 0.663, + 0.888 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "page_footnote", + "bbox": [ + 0.529, + 0.888, + 0.891, + 0.899 + ], + "angle": 0, + "content": "* Work done while Zhan was an intern at OPPO US Research Center." + }, + { + "type": "list", + "bbox": [ + 0.527, + 0.875, + 0.891, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8508" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.183 + ], + "angle": 0, + "content": "tails. 3D Gaussian Splatting (3DGS) [41] further presents an efficient rasterization-based scheme for differentiable volume rendering. Instead of shooting rays from camera to the scene and sampling points along each ray, 3DGS rasterizes 3D Gaussians onto image plane via splatting, which brings about notable rendering speedup." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.184, + 0.471, + 0.488 + ], + "angle": 0, + "content": "Despite the success on static scenes, directly applying the above methods per-frame to dynamic scenes is challenging, due to the overhead in model size and training time. State-of-the-art dynamic view synthesis methods [4, 12, 28, 48, 80, 87] adopt a holistic approach where multiple frames are represented in a single model. NeRFPlayer [80] and HyperReel [4] combine static spatial representations [15, 67] with temporal feature sharing/interpolation to improve model compactness. This strategy exploits the characteristic that adjacent frames in natural videos usually exhibit high similarity. In a similar vein, MixVoxels [87] uses time-variant latents and bridges them with spatial features by inner product. K-Planes [28] and HexPlane [12] factorize the 4D spacetime domain into multiple 2D planes for compact representation. One limitation of these methods is that their grid-like representations cannot fully adapt to the dynamics of scene structures, hindering the modeling of delicate details. Meanwhile, they struggle to produce real-time high-resolution rendering without sacrificing quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.47, + 0.669 + ], + "angle": 0, + "content": "In this work, we present a novel representation for dynamic view synthesis. Our approach simultaneously achieves photorealistic quality, real-time high-resolution rendering and compact model size (see Fig. 1 for example results and comparisons with state-of-the-arts). At the core of our approach is Spacetime Gaussian (STG), which extends 3D Gaussian to 4D spacetime domain. We propose to equip 3D Gaussian with time-dependent opacity along with polynomially parameterized motion and rotation. As a result, STGs are capable of faithfully modeling static, dynamic as well as transient (i.e., emerging or vanishing) content in a scene." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.824 + ], + "angle": 0, + "content": "To enhance model compactness and account for time-varying appearance, we propose splatted feature rendering. Specifically, for each Spacetime Gaussian, instead of storing spherical harmonic coefficients, we store features that encode base color, view-related information and time-related information. These features are rasterized to image space via differentiable splatting, and then go through a tiny multi-layer perceptrons (MLP) network to produce the final color. While smaller in size than spherical harmonics, these features exhibit strong expressiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Additionally, we introduce guided sampling of Gaussians to improve rendering quality of complex scenes. We observe that distant areas which are sparsely covered by Gaussians at initialization tend to have blurry rendering results. To tackle this problem, we propose to sample new" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.89, + 0.122 + ], + "angle": 0, + "content": "Gaussians in the 4D scene with the guidance of training error and coarse depth." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.89, + 0.152 + ], + "angle": 0, + "content": "In summary, the contributions of our work are the following:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.153, + 0.89, + 0.197 + ], + "angle": 0, + "content": "- We present a novel representation based on Spacetime Gaussian for high-fidelity and efficient dynamic view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.198, + 0.89, + 0.242 + ], + "angle": 0, + "content": "- We propose splatted feature rendering, which enhances model compactness and facilitates the modeling of time-varying appearance." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.243, + 0.89, + 0.286 + ], + "angle": 0, + "content": "- We introduce a guided sampling approach for Gaussians to improve rendering quality at distant sparsely covered areas." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.288, + 0.89, + 0.348 + ], + "angle": 0, + "content": "- Extensive experiments on various real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed while keeping small model size. Our lite-version model enables 8K rendering at 60 FPS." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.153, + 0.89, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.36, + 0.642, + 0.375 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.582 + ], + "angle": 0, + "content": "Novel View Synthesis. Early approaches leverage image-based rendering techniques with proxy geometry/depth to sample novel views from source images [11, 13, 20, 31, 34, 44, 46, 103]. Chaurasia et al. [14] estimate a depth map to blend pixels from source views and employ superpixels to compensate for missing depth data. Hedman et al. [32] utilize RGBD sensors to improve rendering quality and speed. Penner and Zhang [72] leverage volumetric voxels for continuity in synthesized views and robustness to depth uncertainty. Hedman et al. [33] learn the blending scheme with neural networks. Flynn et al. [26] combine multi-plane images with learned gradient descent. Wiles et al. [92] sput latent features from point cloud for novel view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.893, + 0.87 + ], + "angle": 0, + "content": "Neural Scene Representations. In recent years, neural scene representations have achieved great progress in novel view synthesis. These methods allocate neural features to structures such as volume [62, 78], texture [16, 84], or point cloud [1]. The seminal work of NeRF [66] proposes to leverage differentiable volume rendering. It does not require proxy geometry and instead uses MLPs to implicitly encode density and radiance in 3D space. Later on, numerous works emerge to boost the quality and efficiency of differentiable volume rendering. One group of methods focuses on improving the sampling strategy to reduce the number of point queries [4, 68, 73] or applies light field-based formulation [3, 25, 53, 54, 79, 81, 89]. Another group trades space for speed by incorporating explicit and localized neural representations [8, 15, 17, 27, 36, 60, 67, 75, 82, 83, 96, 101]. Among them, to improve model compactness, Instant-NGP [67] uses hash grid while TensoRF [15] utilizes tensor decomposition." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recently, 3D Gaussian Splitting (3DGS) [41] proposes to use anisotropic 3D Gaussians as scene representation" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8509" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "and presents an efficient differentiable rasterizer to splat these Gaussians to the image plane. Their method enables fast high-resolution rendering, while preserving great rendering quality. Similar to 3DGS, NeuRBF [18] leverages anisotropic radial basis functions for neural representation and achieves high-fidelity rendering. However, the above methods focus on static scene representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.219, + 0.473, + 0.718 + ], + "angle": 0, + "content": "Dynamic Novel View Synthesis. A widely adopted setting for dynamic free-viewpoint rendering is using multiview videos as input. Classic methods in this area include [19, 21, 39, 40, 49-51, 98, 104]. More recently, Broxton et al. [10] use multi-sphere image as bootstrap and then convert it to layered meshes. Bansal et al. [5] separate static and dynamic contents and manipulate video with deep network in screen space. Bemana et al. [9] learn a neural network to implicitly map view, time or light coordinates to 2D images. Attal et al. [2] use multi-sphere representations to handle the depth and occlusions in 360-degree videos. Lin et al. [57, 58] propose 3D mask volume to addresses the temporal inconsistency of disocclusions. Neural Volumes [62] uses an encoder-decoder network to encode images into a 3D volume and decode it with volume rendering. Lombardi et al. [63] enhance Neural Volumes by decoding a mixture of dynamic geometric primitives from latent code and skipping samples in empty space for efficient ray marching. Extending static NeRF-related representations to dynamic scenes are also being actively explored [4, 12, 28, 38, 42, 47, 48, 56, 71, 77, 80, 87, 88, 90, 91]. DyNeRF [48] combines NeRF with time-conditioned latent codes to compactly represent dynamic scenes. StreamRF [47] accelerates the training of dynamic scenes by modeling the differences of consecutive frames. NeRFPlayer [80] decomposes scene into static, new and deforming fields and proposes streaming of feature channels. MixVoxels [87] represents scene with a mixture of static and dynamic voxels to accelerate rendering. HyperReel [4] utilizes sampling prediction network to reduce sampling points and leverages keyframe-based representation. K-Planes [28], HexPlane [12] and Tensor4D [77] factorize 4D spacetime domain into 2D feature planes for compact model size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.472, + 0.854 + ], + "angle": 0, + "content": "Another line of research tackles dynamic view synthesis from monocular videos [22, 23, 29, 30, 52, 55, 61, 69, 70, 74, 85, 86, 94]. Under this setting, a single camera moves around in the dynamic scene, providing only one observed viewpoint at each timestep. To address the sparsity of supervision, priors on motion, scene flow or depth are usually introduced. In this work, we focus on the dynamic representation itself and only consider the setting of multi-view input videos." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recently, there are several work on this topic that are concurrent to ours [37, 45, 59, 64, 93, 95, 97, 99, 100]. 4K4D [97] combines 4D point clouds with K-Planes [28]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.351 + ], + "angle": 0, + "content": "and discrete image-based rendering, and uses differentiable depth peeling to train the model. Luiten et al. [64] models 4D scene with a set of moving 3D Gaussians, whose positions and rotations are discretely defined at each step. Their method demonstrates appealing results for 3D tracking, but its rendering quality is less favorable due to flickering artifacts. Yang et al. [100] leverage 4D Gaussians and 4D spherindrical harmonics for dynamic modelling. 4D Gaussians essentially represent motion with linear model. Comparatively, our polynomial motion model is more expressive, resulting in higher rendering quality. Our method also has higher rendering speed than their work. Yang et al. [99] and Wu et al. [93] prioritize on monocular dynamic view synthesis and employ deformation fields to deform a set of canonical 3D Gaussians. For multi-view videos setting, the performance of [99] is not extensively evaluated while [93] depicts inferior rendering quality and speed than ours." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.36, + 0.828, + 0.379 + ], + "angle": 0, + "content": "3. Preliminary: 3D Gaussian Splatting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.385, + 0.895, + 0.474 + ], + "angle": 0, + "content": "Given images at multiple viewpoints with known camera poses, 3D Gaussian Splatting [41] (3DGS) optimizes a set of anisotropic 3D Gaussians via differentiable rasterization to represent a static 3D scene. Owing to their efficient rasterization, the optimized model can render high-fidelity novel views in real-time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.895, + 0.537 + ], + "angle": 0, + "content": "3DGS [41] associates a 3D Gaussian \\(i\\) with a position \\(\\mu_{i}\\), covariance matrix \\(\\Sigma_{i}\\), opacity \\(\\sigma_{i}\\) and spherical harmonics (SH) coefficients \\(\\mathbf{h}_i\\). The final opacity of a 3D Gaussian at any spatial point \\(\\mathbf{x}\\) is" + }, + { + "type": "equation", + "bbox": [ + 0.546, + 0.542, + 0.892, + 0.575 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} = \\sigma_ {i} \\exp \\left(- \\frac {1}{2} (\\mathbf {x} - \\mu_ {i}) ^ {T} \\Sigma_ {i} ^ {- 1} (\\mathbf {x} - \\mu_ {i})\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.58, + 0.892, + 0.61 + ], + "angle": 0, + "content": "\\(\\Sigma_{i}\\) is positive semi-definite and can be decomposed into scaling matrix \\(S_{i}\\) and rotation matrix \\(R_{i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.615, + 0.892, + 0.634 + ], + "angle": 0, + "content": "\\[\n\\Sigma_ {i} = R _ {i} S _ {i} S _ {i} ^ {T} R _ {i} ^ {T}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.669 + ], + "angle": 0, + "content": "where \\( S_{i} \\) is a diagonal matrix and is parameterized by a 3D vector \\( \\mathbf{s}_i \\), and \\( R_{i} \\) is parameterized by a quaternion \\( q \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.895, + 0.761 + ], + "angle": 0, + "content": "To render an image, 3D Gaussians are first projected to 2D image space via an approximation of the perspective transformation [105]. Specifically, the projection of a 3D Gaussian is approximated as a 2D Gaussian with center \\(\\mu_i^{2D}\\) and covariance \\(\\Sigma_i^{2D}\\). Let \\(W, K\\) be the viewing transformation and projection matrix, \\(\\mu_i^{2D}\\) and \\(\\Sigma_i^{2D}\\) are computed as" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.765, + 0.892, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\mu_ {i} ^ {2 D} = \\left(K \\left(\\left(W \\mu_ {i}\\right) / \\left(W \\mu_ {i}\\right) _ {z}\\right)\\right) _ {1: 2}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.786, + 0.892, + 0.805 + ], + "angle": 0, + "content": "\\[\n\\Sigma_ {i} ^ {2 D} = \\left(J W \\Sigma_ {i} W ^ {T} J ^ {T}\\right) _ {1: 2, 1: 2}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.81, + 0.875, + 0.825 + ], + "angle": 0, + "content": "where \\(J\\) is the Jacobian of the projective transformation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.856 + ], + "angle": 0, + "content": "After sorting the Gaussians in depth order, the color at a pixel is obtained by volume rendering:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.862, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} = \\sum_ {i \\in \\mathcal {N}} \\mathbf {c} _ {i} \\alpha_ {i} ^ {2 D} \\prod_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j} ^ {2 D}\\right), \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8510" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.093, + 0.51, + 0.267 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.277, + 0.366, + 0.291 + ], + "angle": 0, + "content": "(a) Spacetime Gaussians" + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.099, + 0.891, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.608, + 0.277, + 0.818, + 0.291 + ], + "angle": 0, + "content": "(b) Feature Splitting and Rendering" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.303, + 0.893, + 0.346 + ], + "angle": 0, + "content": "Figure 2. Overview of Spacetime Gaussians and splatted feature rendering. (a) Our method leverages a set of Spacetime Gaussians (STG) to represent the dynamic scenes. On top of 3D Gaussian, each STG is further equipped with temporal opacity, polynomial motion/rotation and time-dependent features. (b) We visualize the splatted features as maps, which are converted to color image via MLP." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.47, + 0.432 + ], + "angle": 0, + "content": "where \\(\\alpha_{i}^{2D}\\) is a 2D version of Eq. (1), with \\(\\mu_{i}, \\Sigma_{i}, \\mathbf{x}\\) replaced by \\(\\mu_{i}^{2D}, \\Sigma_{i}^{2D}, \\mathbf{x}^{2D}\\) (pixel coordinate). \\(\\mathbf{c}_{i}\\) is the RGB color after evaluating SH with view direction and coefficients \\(\\mathbf{h}_{i}\\)." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.444, + 0.169, + 0.459 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.469, + 0.47, + 0.604 + ], + "angle": 0, + "content": "We propose a novel representation based on Spacetime Gaussians for modeling dynamic 3D scenes. Our approach takes multi-view videos as input and creates 6-DoF video that allows rendering at novel views. We first describe the formulation of our Spacetime Gaussian (STG) in Sec. 4.1. Then in Sec. 4.2, we present feature-based splatting for time-varying rendering. Sec. 4.3 details our optimization process and Sec. 4.4 introduces guided sampling of Gaussians." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.613, + 0.276, + 0.629 + ], + "angle": 0, + "content": "4.1. Spacetime Gaussians" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.803 + ], + "angle": 0, + "content": "To represent 4D dynamics, we propose Spacetime Gaussians (STG) that combine 3D Gaussians with temporal components to model emerging/vanishing content as well as motion/deformation, as shown in Fig. 2 (a). Specifically, we introduce temporal radial basis function to encode temporal opacity, which can effectively model scene content that emerges or vanishes within the duration of video. Meanwhile, we utilize time-conditioned parametric functions for the position and rotation of 3D Gaussians to model the motion and deformation in the scene. For a spacetime point \\((\\mathbf{x},t)\\), the opacity of an STG is" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.81, + 0.474, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} (t) = \\sigma_ {i} (t) \\exp \\left(- \\frac {1}{2} (\\mathbf {x} - \\mu_ {i} (t)) ^ {T} \\Sigma_ {i} (t) ^ {- 1} (\\mathbf {x} - \\mu_ {i} (t))\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "where \\(\\sigma_{i}(t)\\) is temporal opacity, \\(\\mu_{i}(t),\\Sigma_{i}(t)\\) are time-dependent position and covariance, and \\(i\\) stands for the ith STG. We detail each of the components below." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.371, + 0.893, + 0.448 + ], + "angle": 0, + "content": "Temporal Radial Basis Function. We use a temporal radial basis function to represent the temporal opacity of an STG at any time \\( t \\). Inspired by [18, 41] that use radial basis functions for approximating spatial signals, we utilize 1D Gaussian for the temporal opacity \\( \\sigma_{i}(t) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.466, + 0.892, + 0.484 + ], + "angle": 0, + "content": "\\[\n\\sigma_ {i} (t) = \\sigma_ {i} ^ {s} \\exp \\left(- s _ {i} ^ {\\tau} | t - \\mu_ {i} ^ {\\tau} | ^ {2}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.585 + ], + "angle": 0, + "content": "where \\(\\mu_i^\\tau\\) is temporal center, \\(s_i^\\tau\\) is temporal scaling factor, and \\(\\sigma_i^s\\) is time-independent spatial opacity. \\(\\mu_i^\\tau\\) represents the timestamp for the STG to be most visible while \\(s_i^\\tau\\) determines its effective duration (i.e., the time duration where its temporal opacity is high). We include \\(\\sigma_i^s\\) to allow spatial opacity variation across STGs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Polynomial Motion Trajectory. For each STG, we employ a time-conditioned function to model its motion. Motivated by [24, 35], we choose polynomial function:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.67, + 0.892, + 0.711 + ], + "angle": 0, + "content": "\\[\n\\mu_ {i} (t) = \\sum_ {k = 0} ^ {n _ {p}} b _ {i, k} \\left(t - \\mu_ {i} ^ {\\tau}\\right) ^ {k}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.724, + 0.892, + 0.83 + ], + "angle": 0, + "content": "where \\(\\mu_{i}(t)\\) denotes the spatial position of an STG at time \\(t\\). \\(\\{b_{i,k}\\}_{k=0}^{n_p}, b_{i,k} \\in \\mathbb{R}\\) are the corresponding polynomial coefficients and are optimized during training. Combining Eq. (7) and Eq. (8), complex and long motion can be represented by multiple short segments with simpler motion. In our implementation, we use \\(n_p = 3\\) as we find it a good balance between representation capacity and model size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Polynomial Rotation. Following [41], we use real-valued quaternion to parameterize the rotation matrix \\( R_{i} \\) in Eq. (2). Similar to motion trajectory, we adopt a polynomial func" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8511" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.09, + 0.889, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.397, + 0.893, + 0.425 + ], + "angle": 0, + "content": "Figure 3. Illustration of our guided sampling strategy for Gaussians. Our strategy samples new Gaussians along rays by leveraging the guidance of training error and coarse depth." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.435, + 0.267, + 0.449 + ], + "angle": 0, + "content": "tion to represent quaternion:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.462, + 0.469, + 0.502 + ], + "angle": 0, + "content": "\\[\nq _ {i} (t) = \\sum_ {k = 0} ^ {n _ {q}} c _ {i, k} \\left(t - \\mu_ {i} ^ {\\tau}\\right) ^ {k}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.516, + 0.469, + 0.59 + ], + "angle": 0, + "content": "where \\( q_{i}(t) \\) is the rotation (in quaternion) of an STG at time \\( t \\), and \\( \\{c_{i,k}\\}_{k=0}^{n_q}, c_{i,k} \\in \\mathbb{R} \\) are polynomial coefficients. After converting \\( q_{i}(t) \\) to rotation matrix \\( R_{i}(t) \\), the covariance \\( \\Sigma_{i}(t) \\) at time \\( t \\) can be obtained via Eq. (2). We set \\( n_q = 1 \\) in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.653 + ], + "angle": 0, + "content": "Note that we keep the scaling matrix \\( S_{i} \\) in Eq. (2) to be time-independent, since we experimentally do not observe improvement in rendering quality when applying time-conditioned function on this parameter." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.327, + 0.681 + ], + "angle": 0, + "content": "4.2. Splatted Feature Rendering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.469, + 0.749 + ], + "angle": 0, + "content": "To encode view- and time-dependent radiance both accurately and compactly, we store features instead of spherical harmonics coefficients (SH) in each STG. Specifically, the features \\(\\mathbf{f}_i(t)\\in \\mathbb{R}^9\\) of each STG consist of three parts:" + }, + { + "type": "equation", + "bbox": [ + 0.147, + 0.763, + 0.469, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f} _ {i} (t) = \\left[ \\mathbf {f} _ {i} ^ {\\text {b a s e}}, \\mathbf {f} _ {i} ^ {\\text {d i r}}, \\quad (t - \\mu_ {i} ^ {\\tau}) \\mathbf {f} _ {i} ^ {\\text {t i m e}} \\right] ^ {T}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{base}} \\in \\mathbb{R}^{3}\\) contains base RGB color, and \\(\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{dir}}\\), \\(\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{time}} \\in \\mathbb{R}^{3}\\) encode information related to view direction and time. The feature splatting process is similar to Gaussian Splatting [41], except that the RGB color \\(c_{i}\\) in Eq. (5) is now replaced by features \\(\\mathbf{f}_{i}(t)\\). After splatting to image space, we split the splatted features at each pixel into \\(\\mathbf{F}^{\\mathrm{base}}\\), \\(\\mathbf{F}^{\\mathrm{dir}}\\), \\(\\mathbf{F}^{\\mathrm{time}}\\), whose channels correspond to the three parts in Eq. (10)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.434, + 0.892, + 0.464 + ], + "angle": 0, + "content": "The final RGB color at each pixel is obtained after going through a 2-layer MLP \\(\\Phi\\):" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.474, + 0.891, + 0.492 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} = \\mathbf {F} ^ {\\text {b a s e}} + \\Phi (\\mathbf {F} ^ {\\text {d i r}}, \\mathbf {F} ^ {\\text {t i m e}}, \\mathbf {r}), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.549 + ], + "angle": 0, + "content": "where \\(\\mathbf{r}\\) is the view direction at the pixel and is additionally concatenated with the features as input. Fig. 2 (b) shows an illustration of the rendering process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.624 + ], + "angle": 0, + "content": "Compared to SH encoding, our feature-based approach requires fewer parameters for each STG (9 vs. 48 for 3-degree SH). At the same time, since the MLP network \\(\\Phi\\) is shallow and narrow, our method still achieves fast rendering speed." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.892, + 0.67 + ], + "angle": 0, + "content": "To maximize rendering speed, we can also optionally drop \\(\\Phi\\) and only keep \\(\\mathbf{F}^{base}\\) during training and rendering. We refer to this configuration as our lite-version model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.679, + 0.638, + 0.695 + ], + "angle": 0, + "content": "4.3. Optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.749 + ], + "angle": 0, + "content": "The parameters to be optimized include the MLP \\(\\Phi\\) and the parameters of each STG \\((\\sigma_i^s, s_i^\\tau, \\mu_i^\\tau, \\{b_{i,k}\\}_{k=0}^{n_p}, \\{c_{i,k}\\}_{k=0}^{n_q}, \\mathbf{s}_i, \\mathbf{f}_i^{\\mathrm{base}}, \\mathbf{f}_i^{\\mathrm{dir}}, \\mathbf{f}_i^{\\mathrm{time}})\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.749, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Following [41], we optimize these parameters through differentiable splatting and gradient-based backpropagation, and interleave with density control of Gaussians. We use rendering loss that compares rendered images with groundtruth images. The rendering loss consists of a \\(\\mathcal{L}_1\\) term and a D-SSIM term." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.848, + 0.773, + 0.864 + ], + "angle": 0, + "content": "4.4. Guided Sampling of Gaussians" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We observe that areas which have sparse Gaussians at initialization are challenging to converge to high rendering" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8512" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "quality, especially if these areas are far away from the training cameras. Therefore, we further introduce a strategy to sample new Gaussians with the guidance of training error and coarse depth." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.152, + 0.471, + 0.438 + ], + "angle": 0, + "content": "We sample new Gaussians along the rays of pixels that have large errors during training, as illustrated in Fig. 3. To ensure sampling effectiveness, we conduct sampling after training loss is stable. Since error maps can be noisy during training, we patch-wise aggregate training errors to prioritize on areas with substantial errors rather than outlier pixels. Then we sample a ray from the center pixel of each selected patches that have large errors. To avoid sampling in an excessively large depth range, we exploit the coarse depth map of Gaussians' centers to determine a more specific depth range. The depth map is generated during feature splatting and incurs little computational overhead. New Gaussians are then uniformly sampled within the depth range along the rays. We additionally add small noises to the centers of the newly sampled Gaussians. Among the sampled Gaussians, the unnecessary ones will have low opacity after steps of training and be pruned. For the scenes in our experiments, the above sampling process only needs to be conducted no more than 3 times." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.44, + 0.47, + 0.515 + ], + "angle": 0, + "content": "Our guided sampling strategy is complimentary to the density control techniques in [41]. While density control gradually grows Gaussians near existing ones by splitting, our approach can sample new Gaussians at regions that have sparse or no Gaussians." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.529, + 0.3, + 0.547 + ], + "angle": 0, + "content": "5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.47, + 0.692 + ], + "angle": 0, + "content": "We initialize our STGs with the structure-from-motion sparse point clouds from all available timestamps. For density control, we conduct more aggressive pruning than [41] to reduce the number of Gaussians and keep model size to be relatively small. We use Adam optimizer [43]. The training time for a 50-frame sequence is 40-60 minutes on a single NVIDIA A6000 GPU. We adapt the splatting process to support different camera models in real world datasets. See supplementary material for more implementation details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.706, + 0.21, + 0.723 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.468, + 0.822 + ], + "angle": 0, + "content": "We evaluate our method on three real-world benchmarks: Neural 3D Video Dataset [48] (Sec. 6.1), Google Immersive Dataset [10] (Sec. 6.2), and Technicolor Dataset [76] (Sec. 6.3). We also conduct ablation studies on various aspects of our method (Sec. 6.4). Please refer to supplementary material and video for more results and real-time demo." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.305, + 0.848 + ], + "angle": 0, + "content": "6.1. Neural 3D Video Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The Neural 3D Video Dataset [48] contains six indoor multi-view video sequences captured by 18 to 21 cameras at \\(2704 \\times 2028\\) resolution. Following common practice, train-" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.089, + 0.894, + 0.174 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons on the Neural 3D Video Dataset. \"FPS\" is measured at \\(1352 \\times 1014\\) resolution. \"Size\" is the total model size for 300 frames. Some methods only report part of the scenes. For fair comparison, we additionally report our results under their settings. \\(^1\\) only includes the Flame Salmon scene. \\(^2\\) excludes the Coffee Martini scene." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.181, + 0.892, + 0.334 + ], + "angle": 0, + "content": "
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size↓
Neural Volumes [62]122.80-0.0620.295--
LLFF [65]123.24-0.0760.235--
DyNeRF [48]129.58-0.0200.0830.01528 MB
Ours129.480.0380.0220.063103300 MB
HexPlane [12]231.71--0.075-200 MB
Ours232.740.0270.0120.039140190 MB
StreamRF [47]28.26---10.95310 MB
NeRFPlayer [80]30.690.034-0.1110.055130 MB
HyperReel [4]31.100.036-0.0962360 MB
K-Planes [28]31.63-0.018-0.3311 MB
MixVoxels-L [87]31.34-0.0170.09637.7500 MB
MixVoxels-X [87]31.73-0.0150.0644.6500 MB
Ours32.050.0260.0140.044140200 MB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.347, + 0.892, + 0.375 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on the Google Immersive Dataset. \"Size/Fr\" stands for model size per frame." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.383, + 0.892, + 0.449 + ], + "angle": 0, + "content": "
MethodPSNR↑DSSIM1↓LPIPS↓FPS↑Size/Fr↓
NeRFPlayer [80]25.80.0760.1960.1217.1 MB
HyperReel [4]28.80.0630.19341.2 MB
Ours29.20.0420.081991.2 MB
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.519 + ], + "angle": 0, + "content": "ing and evaluation are conducted at half resolution, and the first camera is held out for evaluation [48]. The number of frames is 300 for each scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.67 + ], + "angle": 0, + "content": "We use PSNR, DSSIM and LPIPS [102] as evaluation metrics. As mentioned in [4, 28], there is an inconsistency in the DSSIM implementation across methods. For fair comparison, we do our best to group existing methods' DSSIM results into two categories \\((\\mathrm{DSSIM}_1\\) and \\(\\mathrm{DSSIM}_2)\\). Using the structural_similarity function from scikit-image library, \\(\\mathrm{DSSIM}_1\\) sets data_range to 1.0 while \\(\\mathrm{DSSIM}_2\\) sets data_range to 2.0. We use FPS as metric for rendering speed. Metrics are averaged over all six scenes except noted otherwise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.821 + ], + "angle": 0, + "content": "As shown in Tab. 1, our method achieves 140 FPS and outperforms the others by a large margin. Our approach also has the best LPIPS in all comparisons and the best PSNR/DSSIM in most cases. Fig. 4 shows qualitative comparisons on a representative view that is widely used in other work. Compared to the other baselines, our result contains more vivid details (e.g., the textures on the salmon) and artifact-less rendering (e.g., the caustics on the cup). Please see supplementary material for comparisons with concurrent methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.741, + 0.848 + ], + "angle": 0, + "content": "6.2. Google Immersive Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Google Immersive Dataset [10] contains indoor and outdoor scenes captured with a 46-camera rig. The cameras are in fish-eye mode and are mounted on an outward-facing hemi" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8513" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.891, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.275, + 0.441, + 0.695, + 0.456 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparisons on the Neural 3D Video Dataset." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.472, + 0.888, + 0.81 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.269, + 0.823, + 0.7, + 0.837 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparisons on the Google Immersive Dataset." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.853, + 0.469, + 0.884 + ], + "angle": 0, + "content": "sphere. Compared to outside-in setups, there is less overlap among views, hence posing additional challenges." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Following [4, 80], we evaluate on 7 selected scenes" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.853, + 0.892, + 0.899 + ], + "angle": 0, + "content": "(Welder, Flames, Truck, Exhibit, Face Paint 1, Face Paint 2, Cave) and hold out the center camera as test view. The numerical results of NeRFPlayer [80] and HyperReel [4] are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8514" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.09, + 0.468, + 0.118 + ], + "angle": 0, + "content": "Table 3. Quantitative comparisons on the Technicolor Dataset. \"Size/Fr\" stands for model size per frame." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.126, + 0.468, + 0.184 + ], + "angle": 0, + "content": "
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size/Fr↓
DyNeRF [48]31.8-0.0210.1400.020.6 MB
HyperReel [4]32.70.047-0.1094.001.2 MB
Ours33.60.0400.0190.08486.71.1 MB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.191, + 0.468, + 0.218 + ], + "angle": 0, + "content": "Table 4. Ablation study of proposed components. Conducted on all the five scenes from the Technicolor Dataset." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.223, + 0.468, + 0.326 + ], + "angle": 0, + "content": "
MethodPSNR↑DSSIM1↓LPIPS↓
w/o Temporal Opacity31.00.0630.153
w/o Polynomial Motion32.60.0450.099
w/o Polynomial Rotation33.40.0420.085
w/o Feature Splitting33.00.0440.097
w/o Guided Sampling of Gaussians33.30.0410.085
Ours Full33.60.0400.084
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.333, + 0.468, + 0.373 + ], + "angle": 0, + "content": "Table 5. Ablation study on the number of frames whose SfM point clouds are used in initialization. Conducted on the Theater scene from the Technicolor Dataset." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.386, + 0.468, + 0.456 + ], + "angle": 0, + "content": "
Every N FramesPSNR↑DSSIM1↓LPIPS↓Size↓
N = 131.580.0590.124110.2 MB
N = 431.510.0570.11746.7 MB
N = 1631.040.0600.13932.6 MB
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.468, + 0.517 + ], + "angle": 0, + "content": "from their papers. The visual results of NeRFPlayer [80] are obtained from their authors while those of HyperReel [4] are produced by running their released codes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.468, + 0.639 + ], + "angle": 0, + "content": "As shown in Tab. 2, our method outperforms NeRFPlayer and HyperReel in both speed and quality. Compared to HyperReel, our method is over 10 times faster in rendering speed. Although our PSNR is only \\(0.4\\mathrm{dB}\\) higher, the improvements in DSSIM and LPIPS are significant. When compared to NeRFPlayer, the margin is larger for all metrics. Visual comparisons are shown in Fig. 5. Our method depicts sharper details and fewer artifacts than the others." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.649, + 0.266, + 0.663 + ], + "angle": 0, + "content": "6.3. Technicolor Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.468, + 0.761 + ], + "angle": 0, + "content": "Technicolor Light Field Dataset [76] contains videos taken with a 4x4 camera array. Each camera is time-synchronized and the spatial resolution is \\(2048 \\times 1088\\). In alignment with HyperReel [4], we hold out the camera at second row second column and evaluate on five scenes (Birthday, Fabien, Painter, Theater, Trains) at full resolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.762, + 0.468, + 0.808 + ], + "angle": 0, + "content": "Tab. 3 shows the comparisons, where our method achieves noticeable gain in quality and speed. Please refer to supplementary material for visual comparisons." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.229, + 0.833 + ], + "angle": 0, + "content": "6.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To evaluate the effectiveness of proposed components, we conduct an ablation study in Tab. 4 using all the five scenes from Technicolor Dataset. Below we describe the configuration and performance of each ablation baseline." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "Temporal Opacity. \"w/o Temporal Opacity\" fixes the center and scale of the temporal radial basis functions during training. This variant suffers from a significant performance drop, revealing the importance of temporal opacity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.152, + 0.892, + 0.241 + ], + "angle": 0, + "content": "Polynomial Motion and Rotation. \"w/o Polynomial Motion\" and \"w/o Polynomial Rotation\" fix the spatial position and rotation of STGs respectively. Both lead to a performance drop. Comparatively, motion is more important than rotation, which motivates us to use a lower-degree polynomial for rotation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.303 + ], + "angle": 0, + "content": "Feature Splatting. \"w/o Feature Splatting\" uses the base RGB color \\(\\mathbf{F}^{base}\\) as the final color. It can be seen that there is a moderate drop in quality due to reduced ability to model view- and time-dependent appearance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.408 + ], + "angle": 0, + "content": "Guided Sampling of Gaussians. \"w/o Guided Sampling of Gaussians\" does not encounter much performance drop in this dataset. The reason is that the scenes contain rich textures and can be well covered by SfM points. However, for other challenging scenes, guided sampling plays an important role (see Fig. 3 and supplementary material for examples)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.892, + 0.498 + ], + "angle": 0, + "content": "Number of Frames used for Initialization. We further analyzed the number of frames used for initialization in Tab. 5. Using fewer frames slightly downgrade quality, but also significantly reduces model size. It reveals that the compactness of our method can be further enhanced with a good selection of frames for initialization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.509, + 0.625, + 0.524 + ], + "angle": 0, + "content": "6.5. Limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Although our representation achieves fast rendering speed, it cannot be trained on-the-fly. The support for on-the-fly training could benefit numerous streaming applications. To achieve this, advanced initialization techniques could be explored to accelerate the training process or alleviate the requirement of per-scene training. On the other hand, our method currently focuses on multi-view video inputs. It is promising to adapt our approach to monocular setting by combining with regularization or generative priors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.682, + 0.619, + 0.697 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.892, + 0.888 + ], + "angle": 0, + "content": "We present a novel representation based on Spacetime Gaussians for dynamic view synthesis. The proposed Spacetime Gaussians are enhanced with temporal opacity and parametric motion/rotation to model complex 4D content. To increase model compactness and encode view/time-dependent appearance, we introduce splatted feature rendering, which utilizes neural features and a lightweight MLP instead of spherical harmonics. Additionally, we leverage guided sampling of Gaussians to further improve the rendering quality of complex scenes. Experiments on real-world datasets show that our representation delivers state-of-the-art quality at high resolution and FPS, while maintaining a compact model size." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8515" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.469, + 0.171 + ], + "angle": 0, + "content": "[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics. In European Conference on Computer Vision, pages 696-712. 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IEEE, 2001. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.517, + 0.956 + ], + "angle": 0, + "content": "8520" + } + ] +] \ No newline at end of file diff --git a/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/fc66fcb8-31e6-496e-8bf3-fedca92ba729_origin.pdf b/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/fc66fcb8-31e6-496e-8bf3-fedca92ba729_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..82c1bc582b702f9a80cce67b6c96bae8c95ea2a5 --- /dev/null +++ b/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/fc66fcb8-31e6-496e-8bf3-fedca92ba729_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5e7e6b2315da928658e3495193b71a62a154da7c6f6ac007500da7a0651dd754 +size 4281000 diff --git a/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/full.md b/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/full.md new file mode 100644 index 0000000000000000000000000000000000000000..36a3ce693605f5802de73e46b4f4adb652831ad5 --- /dev/null +++ b/2024/Spacetime Gaussian Feature Splatting for Real-Time Dynamic View Synthesis/full.md @@ -0,0 +1,418 @@ +# Spacetime Gaussian Feature Splating for Real-Time Dynamic View Synthesis + +Zhan $\mathbf{L}\mathbf{i}^{1,2*}$ + +Zhang Chen $^{1\dagger}$ + +1 OPPO US Research Center + +Zhong Li $^{1\dagger}$ + +Yi $\mathrm{Xu}^{1}$ + +2Portland State University + +lizhan@pdx.edu + +zhang.chen@oppo.com + +zhong.li@oppo.com + +yi.xu@oppo.com + +https://oppo-us-research.github.io/SpacetimeGaussians-website/ + +![](images/dc434270418b603257811c79e29cef6b8a5514a7375fbec41d19da563caa4165.jpg) +(a) Real-Time 8K Demo at 66 FPS + +![](images/bd991f9a9030a855557b19622c7294c71ea5895a78d678bed4d432316337919d.jpg) +Figure 1. Our dynamic scene representation achieves photorealistic quality, real-time high-resolution rendering and compact model size. (a) Our lite-version model can render 8K 6-DoF video at 66 FPS on an Nvidia RTX 4090 GPU. (b) Example novel view rendering of a challenging scene. (c) Quantitative comparisons of rendering quality, speed and model size with prior arts on the Neural 3D Video Dataset. + +![](images/df7227b74c56a46c42c7e1a16f79ff034fabb59035179aa0de672a9ad651b25e.jpg) +(b) High Quality Result + +![](images/e3b9055d6a63d2d9aa3e96d2ebc3b4397b1996f45c64336a40b08b33e3079783.jpg) +(c) Comparison on Quality, Speed and Size + +# Abstract + +Novel view synthesis of dynamic scenes has been an intriguing yet challenging problem. Despite recent advancements, simultaneously achieving high-resolution photorealistic results, real-time rendering, and compact storage remains a formidable task. To address these challenges, we propose Spacetime Gaussian Feature Splating as a novel dynamic scene representation, composed of three pivotal components. First, we formulate expressive Spacetime Gaussians by enhancing 3D Gaussians with temporal opacity and parametric motion/rotation. This enables Spacetime Gaussians to capture static, dynamic, as well as transient content within a scene. Second, we introduce splatted feature rendering, which replaces spherical harmonics with neural features. These features facilitate the modeling of view- and time-dependent appearance while maintaining small size. Third, we leverage the guidance of training error and coarse depth to sample new Gaussians in areas that are challenging to converge with existing pipelines. Experiments on several established real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed, while retaining compact storage. At $8K$ + +resolution, our lite-version model can render at 60 FPS on an Nvidia RTX 4090 GPU. + +# 1. Introduction + +Photorealistic modeling of real-world dynamic scenes has been persistently pursued in computer vision and graphics. It allows users to freely explore dynamic scenes at novel viewpoints and timestamps, thus providing strong immersive experience, and can vastly benefit applications in VR/AR, broadcasting, education, etc. + +Recent advances in novel view synthesis, especially Neural Radiance Fields (NeRF) [66], have greatly improved the convenience and fidelity of static scene modeling from casual multi-view inputs in non-lab environments. Since then, large quantities of work [6-8, 15, 18, 27, 41, 67, 82] have emerged aiming to enhance rendering quality and speed. Particularly, [18, 41] propose to use anisotropic radial basis functions as 3D representations, which are highly adaptive to scene structures and boost the modeling of de + +tails. 3D Gaussian Splatting (3DGS) [41] further presents an efficient rasterization-based scheme for differentiable volume rendering. Instead of shooting rays from camera to the scene and sampling points along each ray, 3DGS rasterizes 3D Gaussians onto image plane via splatting, which brings about notable rendering speedup. + +Despite the success on static scenes, directly applying the above methods per-frame to dynamic scenes is challenging, due to the overhead in model size and training time. State-of-the-art dynamic view synthesis methods [4, 12, 28, 48, 80, 87] adopt a holistic approach where multiple frames are represented in a single model. NeRFPlayer [80] and HyperReel [4] combine static spatial representations [15, 67] with temporal feature sharing/interpolation to improve model compactness. This strategy exploits the characteristic that adjacent frames in natural videos usually exhibit high similarity. In a similar vein, MixVoxels [87] uses time-variant latents and bridges them with spatial features by inner product. K-Planes [28] and HexPlane [12] factorize the 4D spacetime domain into multiple 2D planes for compact representation. One limitation of these methods is that their grid-like representations cannot fully adapt to the dynamics of scene structures, hindering the modeling of delicate details. Meanwhile, they struggle to produce real-time high-resolution rendering without sacrificing quality. + +In this work, we present a novel representation for dynamic view synthesis. Our approach simultaneously achieves photorealistic quality, real-time high-resolution rendering and compact model size (see Fig. 1 for example results and comparisons with state-of-the-arts). At the core of our approach is Spacetime Gaussian (STG), which extends 3D Gaussian to 4D spacetime domain. We propose to equip 3D Gaussian with time-dependent opacity along with polynomially parameterized motion and rotation. As a result, STGs are capable of faithfully modeling static, dynamic as well as transient (i.e., emerging or vanishing) content in a scene. + +To enhance model compactness and account for time-varying appearance, we propose splatted feature rendering. Specifically, for each Spacetime Gaussian, instead of storing spherical harmonic coefficients, we store features that encode base color, view-related information and time-related information. These features are rasterized to image space via differentiable splatting, and then go through a tiny multi-layer perceptrons (MLP) network to produce the final color. While smaller in size than spherical harmonics, these features exhibit strong expressiveness. + +Additionally, we introduce guided sampling of Gaussians to improve rendering quality of complex scenes. We observe that distant areas which are sparsely covered by Gaussians at initialization tend to have blurry rendering results. To tackle this problem, we propose to sample new + +Gaussians in the 4D scene with the guidance of training error and coarse depth. + +In summary, the contributions of our work are the following: + +- We present a novel representation based on Spacetime Gaussian for high-fidelity and efficient dynamic view synthesis. +- We propose splatted feature rendering, which enhances model compactness and facilitates the modeling of time-varying appearance. +- We introduce a guided sampling approach for Gaussians to improve rendering quality at distant sparsely covered areas. +- Extensive experiments on various real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed while keeping small model size. Our lite-version model enables 8K rendering at 60 FPS. + +# 2. Related Work + +Novel View Synthesis. Early approaches leverage image-based rendering techniques with proxy geometry/depth to sample novel views from source images [11, 13, 20, 31, 34, 44, 46, 103]. Chaurasia et al. [14] estimate a depth map to blend pixels from source views and employ superpixels to compensate for missing depth data. Hedman et al. [32] utilize RGBD sensors to improve rendering quality and speed. Penner and Zhang [72] leverage volumetric voxels for continuity in synthesized views and robustness to depth uncertainty. Hedman et al. [33] learn the blending scheme with neural networks. Flynn et al. [26] combine multi-plane images with learned gradient descent. Wiles et al. [92] sput latent features from point cloud for novel view synthesis. + +Neural Scene Representations. In recent years, neural scene representations have achieved great progress in novel view synthesis. These methods allocate neural features to structures such as volume [62, 78], texture [16, 84], or point cloud [1]. The seminal work of NeRF [66] proposes to leverage differentiable volume rendering. It does not require proxy geometry and instead uses MLPs to implicitly encode density and radiance in 3D space. Later on, numerous works emerge to boost the quality and efficiency of differentiable volume rendering. One group of methods focuses on improving the sampling strategy to reduce the number of point queries [4, 68, 73] or applies light field-based formulation [3, 25, 53, 54, 79, 81, 89]. Another group trades space for speed by incorporating explicit and localized neural representations [8, 15, 17, 27, 36, 60, 67, 75, 82, 83, 96, 101]. Among them, to improve model compactness, Instant-NGP [67] uses hash grid while TensoRF [15] utilizes tensor decomposition. + +Recently, 3D Gaussian Splitting (3DGS) [41] proposes to use anisotropic 3D Gaussians as scene representation + +and presents an efficient differentiable rasterizer to splat these Gaussians to the image plane. Their method enables fast high-resolution rendering, while preserving great rendering quality. Similar to 3DGS, NeuRBF [18] leverages anisotropic radial basis functions for neural representation and achieves high-fidelity rendering. However, the above methods focus on static scene representation. + +Dynamic Novel View Synthesis. A widely adopted setting for dynamic free-viewpoint rendering is using multiview videos as input. Classic methods in this area include [19, 21, 39, 40, 49-51, 98, 104]. More recently, Broxton et al. [10] use multi-sphere image as bootstrap and then convert it to layered meshes. Bansal et al. [5] separate static and dynamic contents and manipulate video with deep network in screen space. Bemana et al. [9] learn a neural network to implicitly map view, time or light coordinates to 2D images. Attal et al. [2] use multi-sphere representations to handle the depth and occlusions in 360-degree videos. Lin et al. [57, 58] propose 3D mask volume to addresses the temporal inconsistency of disocclusions. Neural Volumes [62] uses an encoder-decoder network to encode images into a 3D volume and decode it with volume rendering. Lombardi et al. [63] enhance Neural Volumes by decoding a mixture of dynamic geometric primitives from latent code and skipping samples in empty space for efficient ray marching. Extending static NeRF-related representations to dynamic scenes are also being actively explored [4, 12, 28, 38, 42, 47, 48, 56, 71, 77, 80, 87, 88, 90, 91]. DyNeRF [48] combines NeRF with time-conditioned latent codes to compactly represent dynamic scenes. StreamRF [47] accelerates the training of dynamic scenes by modeling the differences of consecutive frames. NeRFPlayer [80] decomposes scene into static, new and deforming fields and proposes streaming of feature channels. MixVoxels [87] represents scene with a mixture of static and dynamic voxels to accelerate rendering. HyperReel [4] utilizes sampling prediction network to reduce sampling points and leverages keyframe-based representation. K-Planes [28], HexPlane [12] and Tensor4D [77] factorize 4D spacetime domain into 2D feature planes for compact model size. + +Another line of research tackles dynamic view synthesis from monocular videos [22, 23, 29, 30, 52, 55, 61, 69, 70, 74, 85, 86, 94]. Under this setting, a single camera moves around in the dynamic scene, providing only one observed viewpoint at each timestep. To address the sparsity of supervision, priors on motion, scene flow or depth are usually introduced. In this work, we focus on the dynamic representation itself and only consider the setting of multi-view input videos. + +Recently, there are several work on this topic that are concurrent to ours [37, 45, 59, 64, 93, 95, 97, 99, 100]. 4K4D [97] combines 4D point clouds with K-Planes [28] + +and discrete image-based rendering, and uses differentiable depth peeling to train the model. Luiten et al. [64] models 4D scene with a set of moving 3D Gaussians, whose positions and rotations are discretely defined at each step. Their method demonstrates appealing results for 3D tracking, but its rendering quality is less favorable due to flickering artifacts. Yang et al. [100] leverage 4D Gaussians and 4D spherindrical harmonics for dynamic modelling. 4D Gaussians essentially represent motion with linear model. Comparatively, our polynomial motion model is more expressive, resulting in higher rendering quality. Our method also has higher rendering speed than their work. Yang et al. [99] and Wu et al. [93] prioritize on monocular dynamic view synthesis and employ deformation fields to deform a set of canonical 3D Gaussians. For multi-view videos setting, the performance of [99] is not extensively evaluated while [93] depicts inferior rendering quality and speed than ours. + +# 3. Preliminary: 3D Gaussian Splatting + +Given images at multiple viewpoints with known camera poses, 3D Gaussian Splatting [41] (3DGS) optimizes a set of anisotropic 3D Gaussians via differentiable rasterization to represent a static 3D scene. Owing to their efficient rasterization, the optimized model can render high-fidelity novel views in real-time. + +3DGS [41] associates a 3D Gaussian $i$ with a position $\mu_{i}$ , covariance matrix $\Sigma_{i}$ , opacity $\sigma_{i}$ and spherical harmonics (SH) coefficients $\mathbf{h}_i$ . The final opacity of a 3D Gaussian at any spatial point $\mathbf{x}$ is + +$$ +\alpha_ {i} = \sigma_ {i} \exp \left(- \frac {1}{2} (\mathbf {x} - \mu_ {i}) ^ {T} \Sigma_ {i} ^ {- 1} (\mathbf {x} - \mu_ {i})\right). \tag {1} +$$ + +$\Sigma_{i}$ is positive semi-definite and can be decomposed into scaling matrix $S_{i}$ and rotation matrix $R_{i}$ : + +$$ +\Sigma_ {i} = R _ {i} S _ {i} S _ {i} ^ {T} R _ {i} ^ {T}, \tag {2} +$$ + +where $S_{i}$ is a diagonal matrix and is parameterized by a 3D vector $\mathbf{s}_i$ , and $R_{i}$ is parameterized by a quaternion $q$ . + +To render an image, 3D Gaussians are first projected to 2D image space via an approximation of the perspective transformation [105]. Specifically, the projection of a 3D Gaussian is approximated as a 2D Gaussian with center $\mu_i^{2D}$ and covariance $\Sigma_i^{2D}$ . Let $W, K$ be the viewing transformation and projection matrix, $\mu_i^{2D}$ and $\Sigma_i^{2D}$ are computed as + +$$ +\mu_ {i} ^ {2 D} = \left(K \left(\left(W \mu_ {i}\right) / \left(W \mu_ {i}\right) _ {z}\right)\right) _ {1: 2}, \tag {3} +$$ + +$$ +\Sigma_ {i} ^ {2 D} = \left(J W \Sigma_ {i} W ^ {T} J ^ {T}\right) _ {1: 2, 1: 2}, \tag {4} +$$ + +where $J$ is the Jacobian of the projective transformation. + +After sorting the Gaussians in depth order, the color at a pixel is obtained by volume rendering: + +$$ +\mathbf {I} = \sum_ {i \in \mathcal {N}} \mathbf {c} _ {i} \alpha_ {i} ^ {2 D} \prod_ {j = 1} ^ {i - 1} \left(1 - \alpha_ {j} ^ {2 D}\right), \tag {5} +$$ + +![](images/87b295ef671e5c08ccb0eba3bedc5680e619c6015b80b24416e57b9658a7d2a7.jpg) +(a) Spacetime Gaussians + +![](images/f01319d0a8fc1201f970f5f0610e9c9164810c6f58d026addf02f010c1df07a8.jpg) +(b) Feature Splitting and Rendering +Figure 2. Overview of Spacetime Gaussians and splatted feature rendering. (a) Our method leverages a set of Spacetime Gaussians (STG) to represent the dynamic scenes. On top of 3D Gaussian, each STG is further equipped with temporal opacity, polynomial motion/rotation and time-dependent features. (b) We visualize the splatted features as maps, which are converted to color image via MLP. + +where $\alpha_{i}^{2D}$ is a 2D version of Eq. (1), with $\mu_{i}, \Sigma_{i}, \mathbf{x}$ replaced by $\mu_{i}^{2D}, \Sigma_{i}^{2D}, \mathbf{x}^{2D}$ (pixel coordinate). $\mathbf{c}_{i}$ is the RGB color after evaluating SH with view direction and coefficients $\mathbf{h}_{i}$ . + +# 4. Method + +We propose a novel representation based on Spacetime Gaussians for modeling dynamic 3D scenes. Our approach takes multi-view videos as input and creates 6-DoF video that allows rendering at novel views. We first describe the formulation of our Spacetime Gaussian (STG) in Sec. 4.1. Then in Sec. 4.2, we present feature-based splatting for time-varying rendering. Sec. 4.3 details our optimization process and Sec. 4.4 introduces guided sampling of Gaussians. + +# 4.1. Spacetime Gaussians + +To represent 4D dynamics, we propose Spacetime Gaussians (STG) that combine 3D Gaussians with temporal components to model emerging/vanishing content as well as motion/deformation, as shown in Fig. 2 (a). Specifically, we introduce temporal radial basis function to encode temporal opacity, which can effectively model scene content that emerges or vanishes within the duration of video. Meanwhile, we utilize time-conditioned parametric functions for the position and rotation of 3D Gaussians to model the motion and deformation in the scene. For a spacetime point $(\mathbf{x},t)$ , the opacity of an STG is + +$$ +\alpha_ {i} (t) = \sigma_ {i} (t) \exp \left(- \frac {1}{2} (\mathbf {x} - \mu_ {i} (t)) ^ {T} \Sigma_ {i} (t) ^ {- 1} (\mathbf {x} - \mu_ {i} (t))\right), \tag {6} +$$ + +where $\sigma_{i}(t)$ is temporal opacity, $\mu_{i}(t),\Sigma_{i}(t)$ are time-dependent position and covariance, and $i$ stands for the ith STG. We detail each of the components below. + +Temporal Radial Basis Function. We use a temporal radial basis function to represent the temporal opacity of an STG at any time $t$ . Inspired by [18, 41] that use radial basis functions for approximating spatial signals, we utilize 1D Gaussian for the temporal opacity $\sigma_{i}(t)$ : + +$$ +\sigma_ {i} (t) = \sigma_ {i} ^ {s} \exp \left(- s _ {i} ^ {\tau} | t - \mu_ {i} ^ {\tau} | ^ {2}\right), \tag {7} +$$ + +where $\mu_i^\tau$ is temporal center, $s_i^\tau$ is temporal scaling factor, and $\sigma_i^s$ is time-independent spatial opacity. $\mu_i^\tau$ represents the timestamp for the STG to be most visible while $s_i^\tau$ determines its effective duration (i.e., the time duration where its temporal opacity is high). We include $\sigma_i^s$ to allow spatial opacity variation across STGs. + +Polynomial Motion Trajectory. For each STG, we employ a time-conditioned function to model its motion. Motivated by [24, 35], we choose polynomial function: + +$$ +\mu_ {i} (t) = \sum_ {k = 0} ^ {n _ {p}} b _ {i, k} \left(t - \mu_ {i} ^ {\tau}\right) ^ {k}, \tag {8} +$$ + +where $\mu_{i}(t)$ denotes the spatial position of an STG at time $t$ . $\{b_{i,k}\}_{k=0}^{n_p}, b_{i,k} \in \mathbb{R}$ are the corresponding polynomial coefficients and are optimized during training. Combining Eq. (7) and Eq. (8), complex and long motion can be represented by multiple short segments with simpler motion. In our implementation, we use $n_p = 3$ as we find it a good balance between representation capacity and model size. + +Polynomial Rotation. Following [41], we use real-valued quaternion to parameterize the rotation matrix $R_{i}$ in Eq. (2). Similar to motion trajectory, we adopt a polynomial func + +![](images/37b02f8d8245d811982e5d387c57e52df0791c9608e9c49b1e20148c9950785a.jpg) +Figure 3. Illustration of our guided sampling strategy for Gaussians. Our strategy samples new Gaussians along rays by leveraging the guidance of training error and coarse depth. + +tion to represent quaternion: + +$$ +q _ {i} (t) = \sum_ {k = 0} ^ {n _ {q}} c _ {i, k} \left(t - \mu_ {i} ^ {\tau}\right) ^ {k}, \tag {9} +$$ + +where $q_{i}(t)$ is the rotation (in quaternion) of an STG at time $t$ , and $\{c_{i,k}\}_{k=0}^{n_q}, c_{i,k} \in \mathbb{R}$ are polynomial coefficients. After converting $q_{i}(t)$ to rotation matrix $R_{i}(t)$ , the covariance $\Sigma_{i}(t)$ at time $t$ can be obtained via Eq. (2). We set $n_q = 1$ in our experiments. + +Note that we keep the scaling matrix $S_{i}$ in Eq. (2) to be time-independent, since we experimentally do not observe improvement in rendering quality when applying time-conditioned function on this parameter. + +# 4.2. Splatted Feature Rendering + +To encode view- and time-dependent radiance both accurately and compactly, we store features instead of spherical harmonics coefficients (SH) in each STG. Specifically, the features $\mathbf{f}_i(t)\in \mathbb{R}^9$ of each STG consist of three parts: + +$$ +\mathbf {f} _ {i} (t) = \left[ \mathbf {f} _ {i} ^ {\text {b a s e}}, \mathbf {f} _ {i} ^ {\text {d i r}}, \quad (t - \mu_ {i} ^ {\tau}) \mathbf {f} _ {i} ^ {\text {t i m e}} \right] ^ {T}, \tag {10} +$$ + +where $\mathbf{f}_{\mathbf{i}}^{\mathrm{base}} \in \mathbb{R}^{3}$ contains base RGB color, and $\mathbf{f}_{\mathbf{i}}^{\mathrm{dir}}$ , $\mathbf{f}_{\mathbf{i}}^{\mathrm{time}} \in \mathbb{R}^{3}$ encode information related to view direction and time. The feature splatting process is similar to Gaussian Splatting [41], except that the RGB color $c_{i}$ in Eq. (5) is now replaced by features $\mathbf{f}_{i}(t)$ . After splatting to image space, we split the splatted features at each pixel into $\mathbf{F}^{\mathrm{base}}$ , $\mathbf{F}^{\mathrm{dir}}$ , $\mathbf{F}^{\mathrm{time}}$ , whose channels correspond to the three parts in Eq. (10). + +The final RGB color at each pixel is obtained after going through a 2-layer MLP $\Phi$ : + +$$ +\mathbf {I} = \mathbf {F} ^ {\text {b a s e}} + \Phi (\mathbf {F} ^ {\text {d i r}}, \mathbf {F} ^ {\text {t i m e}}, \mathbf {r}), \tag {11} +$$ + +where $\mathbf{r}$ is the view direction at the pixel and is additionally concatenated with the features as input. Fig. 2 (b) shows an illustration of the rendering process. + +Compared to SH encoding, our feature-based approach requires fewer parameters for each STG (9 vs. 48 for 3-degree SH). At the same time, since the MLP network $\Phi$ is shallow and narrow, our method still achieves fast rendering speed. + +To maximize rendering speed, we can also optionally drop $\Phi$ and only keep $\mathbf{F}^{base}$ during training and rendering. We refer to this configuration as our lite-version model. + +# 4.3. Optimization + +The parameters to be optimized include the MLP $\Phi$ and the parameters of each STG $(\sigma_i^s, s_i^\tau, \mu_i^\tau, \{b_{i,k}\}_{k=0}^{n_p}, \{c_{i,k}\}_{k=0}^{n_q}, \mathbf{s}_i, \mathbf{f}_i^{\mathrm{base}}, \mathbf{f}_i^{\mathrm{dir}}, \mathbf{f}_i^{\mathrm{time}})$ . + +Following [41], we optimize these parameters through differentiable splatting and gradient-based backpropagation, and interleave with density control of Gaussians. We use rendering loss that compares rendered images with groundtruth images. The rendering loss consists of a $\mathcal{L}_1$ term and a D-SSIM term. + +# 4.4. Guided Sampling of Gaussians + +We observe that areas which have sparse Gaussians at initialization are challenging to converge to high rendering + +quality, especially if these areas are far away from the training cameras. Therefore, we further introduce a strategy to sample new Gaussians with the guidance of training error and coarse depth. + +We sample new Gaussians along the rays of pixels that have large errors during training, as illustrated in Fig. 3. To ensure sampling effectiveness, we conduct sampling after training loss is stable. Since error maps can be noisy during training, we patch-wise aggregate training errors to prioritize on areas with substantial errors rather than outlier pixels. Then we sample a ray from the center pixel of each selected patches that have large errors. To avoid sampling in an excessively large depth range, we exploit the coarse depth map of Gaussians' centers to determine a more specific depth range. The depth map is generated during feature splatting and incurs little computational overhead. New Gaussians are then uniformly sampled within the depth range along the rays. We additionally add small noises to the centers of the newly sampled Gaussians. Among the sampled Gaussians, the unnecessary ones will have low opacity after steps of training and be pruned. For the scenes in our experiments, the above sampling process only needs to be conducted no more than 3 times. + +Our guided sampling strategy is complimentary to the density control techniques in [41]. While density control gradually grows Gaussians near existing ones by splitting, our approach can sample new Gaussians at regions that have sparse or no Gaussians. + +# 5. Implementation Details + +We initialize our STGs with the structure-from-motion sparse point clouds from all available timestamps. For density control, we conduct more aggressive pruning than [41] to reduce the number of Gaussians and keep model size to be relatively small. We use Adam optimizer [43]. The training time for a 50-frame sequence is 40-60 minutes on a single NVIDIA A6000 GPU. We adapt the splatting process to support different camera models in real world datasets. See supplementary material for more implementation details. + +# 6. Experiments + +We evaluate our method on three real-world benchmarks: Neural 3D Video Dataset [48] (Sec. 6.1), Google Immersive Dataset [10] (Sec. 6.2), and Technicolor Dataset [76] (Sec. 6.3). We also conduct ablation studies on various aspects of our method (Sec. 6.4). Please refer to supplementary material and video for more results and real-time demo. + +# 6.1. Neural 3D Video Dataset + +The Neural 3D Video Dataset [48] contains six indoor multi-view video sequences captured by 18 to 21 cameras at $2704 \times 2028$ resolution. Following common practice, train- + +Table 1. Quantitative comparisons on the Neural 3D Video Dataset. "FPS" is measured at $1352 \times 1014$ resolution. "Size" is the total model size for 300 frames. Some methods only report part of the scenes. For fair comparison, we additionally report our results under their settings. $^1$ only includes the Flame Salmon scene. $^2$ excludes the Coffee Martini scene. + +
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size↓
Neural Volumes [62]122.80-0.0620.295--
LLFF [65]123.24-0.0760.235--
DyNeRF [48]129.58-0.0200.0830.01528 MB
Ours129.480.0380.0220.063103300 MB
HexPlane [12]231.71--0.075-200 MB
Ours232.740.0270.0120.039140190 MB
StreamRF [47]28.26---10.95310 MB
NeRFPlayer [80]30.690.034-0.1110.055130 MB
HyperReel [4]31.100.036-0.0962360 MB
K-Planes [28]31.63-0.018-0.3311 MB
MixVoxels-L [87]31.34-0.0170.09637.7500 MB
MixVoxels-X [87]31.73-0.0150.0644.6500 MB
Ours32.050.0260.0140.044140200 MB
+ +Table 2. Quantitative comparisons on the Google Immersive Dataset. "Size/Fr" stands for model size per frame. + +
MethodPSNR↑DSSIM1↓LPIPS↓FPS↑Size/Fr↓
NeRFPlayer [80]25.80.0760.1960.1217.1 MB
HyperReel [4]28.80.0630.19341.2 MB
Ours29.20.0420.081991.2 MB
+ +ing and evaluation are conducted at half resolution, and the first camera is held out for evaluation [48]. The number of frames is 300 for each scene. + +We use PSNR, DSSIM and LPIPS [102] as evaluation metrics. As mentioned in [4, 28], there is an inconsistency in the DSSIM implementation across methods. For fair comparison, we do our best to group existing methods' DSSIM results into two categories $(\mathrm{DSSIM}_1$ and $\mathrm{DSSIM}_2)$ . Using the structural_similarity function from scikit-image library, $\mathrm{DSSIM}_1$ sets data_range to 1.0 while $\mathrm{DSSIM}_2$ sets data_range to 2.0. We use FPS as metric for rendering speed. Metrics are averaged over all six scenes except noted otherwise. + +As shown in Tab. 1, our method achieves 140 FPS and outperforms the others by a large margin. Our approach also has the best LPIPS in all comparisons and the best PSNR/DSSIM in most cases. Fig. 4 shows qualitative comparisons on a representative view that is widely used in other work. Compared to the other baselines, our result contains more vivid details (e.g., the textures on the salmon) and artifact-less rendering (e.g., the caustics on the cup). Please see supplementary material for comparisons with concurrent methods. + +# 6.2. Google Immersive Dataset + +Google Immersive Dataset [10] contains indoor and outdoor scenes captured with a 46-camera rig. The cameras are in fish-eye mode and are mounted on an outward-facing hemi + +![](images/c3d8f4e3168797f7b7d30d975138012c87511b14fec1a9b8102d14dacec0bb33.jpg) +Figure 4. Qualitative comparisons on the Neural 3D Video Dataset. + +![](images/7c80f9b3bd67376423925775bb138a1fac751d50faf4707e06928ee3c4c127e4.jpg) +Figure 5. Qualitative comparisons on the Google Immersive Dataset. + +sphere. Compared to outside-in setups, there is less overlap among views, hence posing additional challenges. + +Following [4, 80], we evaluate on 7 selected scenes + +(Welder, Flames, Truck, Exhibit, Face Paint 1, Face Paint 2, Cave) and hold out the center camera as test view. The numerical results of NeRFPlayer [80] and HyperReel [4] are + +Table 3. Quantitative comparisons on the Technicolor Dataset. "Size/Fr" stands for model size per frame. + +
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size/Fr↓
DyNeRF [48]31.8-0.0210.1400.020.6 MB
HyperReel [4]32.70.047-0.1094.001.2 MB
Ours33.60.0400.0190.08486.71.1 MB
+ +Table 4. Ablation study of proposed components. Conducted on all the five scenes from the Technicolor Dataset. + +
MethodPSNR↑DSSIM1↓LPIPS↓
w/o Temporal Opacity31.00.0630.153
w/o Polynomial Motion32.60.0450.099
w/o Polynomial Rotation33.40.0420.085
w/o Feature Splitting33.00.0440.097
w/o Guided Sampling of Gaussians33.30.0410.085
Ours Full33.60.0400.084
+ +Table 5. Ablation study on the number of frames whose SfM point clouds are used in initialization. Conducted on the Theater scene from the Technicolor Dataset. + +
Every N FramesPSNR↑DSSIM1↓LPIPS↓Size↓
N = 131.580.0590.124110.2 MB
N = 431.510.0570.11746.7 MB
N = 1631.040.0600.13932.6 MB
+ +from their papers. The visual results of NeRFPlayer [80] are obtained from their authors while those of HyperReel [4] are produced by running their released codes. + +As shown in Tab. 2, our method outperforms NeRFPlayer and HyperReel in both speed and quality. Compared to HyperReel, our method is over 10 times faster in rendering speed. Although our PSNR is only $0.4\mathrm{dB}$ higher, the improvements in DSSIM and LPIPS are significant. When compared to NeRFPlayer, the margin is larger for all metrics. Visual comparisons are shown in Fig. 5. Our method depicts sharper details and fewer artifacts than the others. + +# 6.3. Technicolor Dataset + +Technicolor Light Field Dataset [76] contains videos taken with a 4x4 camera array. Each camera is time-synchronized and the spatial resolution is $2048 \times 1088$ . In alignment with HyperReel [4], we hold out the camera at second row second column and evaluate on five scenes (Birthday, Fabien, Painter, Theater, Trains) at full resolution. + +Tab. 3 shows the comparisons, where our method achieves noticeable gain in quality and speed. Please refer to supplementary material for visual comparisons. + +# 6.4. Ablation Study + +To evaluate the effectiveness of proposed components, we conduct an ablation study in Tab. 4 using all the five scenes from Technicolor Dataset. Below we describe the configuration and performance of each ablation baseline. + +Temporal Opacity. "w/o Temporal Opacity" fixes the center and scale of the temporal radial basis functions during training. This variant suffers from a significant performance drop, revealing the importance of temporal opacity. + +Polynomial Motion and Rotation. "w/o Polynomial Motion" and "w/o Polynomial Rotation" fix the spatial position and rotation of STGs respectively. Both lead to a performance drop. Comparatively, motion is more important than rotation, which motivates us to use a lower-degree polynomial for rotation. + +Feature Splatting. "w/o Feature Splatting" uses the base RGB color $\mathbf{F}^{base}$ as the final color. It can be seen that there is a moderate drop in quality due to reduced ability to model view- and time-dependent appearance. + +Guided Sampling of Gaussians. "w/o Guided Sampling of Gaussians" does not encounter much performance drop in this dataset. The reason is that the scenes contain rich textures and can be well covered by SfM points. However, for other challenging scenes, guided sampling plays an important role (see Fig. 3 and supplementary material for examples). + +Number of Frames used for Initialization. We further analyzed the number of frames used for initialization in Tab. 5. Using fewer frames slightly downgrade quality, but also significantly reduces model size. It reveals that the compactness of our method can be further enhanced with a good selection of frames for initialization. + +# 6.5. Limitations + +Although our representation achieves fast rendering speed, it cannot be trained on-the-fly. The support for on-the-fly training could benefit numerous streaming applications. To achieve this, advanced initialization techniques could be explored to accelerate the training process or alleviate the requirement of per-scene training. On the other hand, our method currently focuses on multi-view video inputs. It is promising to adapt our approach to monocular setting by combining with regularization or generative priors. + +# 7. Conclusion + +We present a novel representation based on Spacetime Gaussians for dynamic view synthesis. The proposed Spacetime Gaussians are enhanced with temporal opacity and parametric motion/rotation to model complex 4D content. 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Despite recent advancements, simultaneously achieving high-resolution photorealistic results, real-time rendering, and compact storage remains a formidable task. To address these challenges, we propose Spacetime Gaussian Feature Splating as a novel dynamic scene representation, composed of three pivotal components. First, we formulate expressive Spacetime Gaussians by enhancing 3D Gaussians with temporal opacity and parametric motion/rotation. This enables Spacetime Gaussians to capture static, dynamic, as well as transient content within a scene. Second, we introduce splatted feature rendering, which replaces spherical harmonics with neural features. These features facilitate the modeling of view- and time-dependent appearance while maintaining small size. Third, we leverage the guidance of training error and coarse depth to sample new Gaussians in areas that are challenging to converge with existing pipelines. Experiments on several established real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed, while retaining compact storage. At " + }, + { + "bbox": [ + 46, + 462, + 288, + 714 + ], + "type": "inline_equation", + "content": "8K" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 437, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 545, + 460 + ], + "type": "text", + "content": "resolution, our lite-version model can render at 60 FPS on an Nvidia RTX 4090 GPU." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 485, + 386, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 485, + 386, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 485, + 386, + 498 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 505, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 545, + 576 + ], + "type": "text", + "content": "Photorealistic modeling of real-world dynamic scenes has been persistently pursued in computer vision and graphics. It allows users to freely explore dynamic scenes at novel viewpoints and timestamps, thus providing strong immersive experience, and can vastly benefit applications in VR/AR, broadcasting, education, etc." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 577, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 545, + 685 + ], + "type": "text", + "content": "Recent advances in novel view synthesis, especially Neural Radiance Fields (NeRF) [66], have greatly improved the convenience and fidelity of static scene modeling from casual multi-view inputs in non-lab environments. Since then, large quantities of work [6-8, 15, 18, 27, 41, 67, 82] have emerged aiming to enhance rendering quality and speed. Particularly, [18, 41] propose to use anisotropic radial basis functions as 3D representations, which are highly adaptive to scene structures and boost the modeling of de" + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 322, + 693, + 405, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 693, + 405, + 703 + ], + "spans": [ + { + "bbox": [ + 322, + 693, + 405, + 703 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 323, + 703, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 703, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 323, + 703, + 545, + 712 + ], + "type": "text", + "content": "* Work done while Zhan was an intern at OPPO US Research Center." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8508" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "tails. 3D Gaussian Splatting (3DGS) [41] further presents an efficient rasterization-based scheme for differentiable volume rendering. Instead of shooting rays from camera to the scene and sampling points along each ray, 3DGS rasterizes 3D Gaussians onto image plane via splatting, which brings about notable rendering speedup." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 145, + 288, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 145, + 288, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 145, + 288, + 386 + ], + "type": "text", + "content": "Despite the success on static scenes, directly applying the above methods per-frame to dynamic scenes is challenging, due to the overhead in model size and training time. State-of-the-art dynamic view synthesis methods [4, 12, 28, 48, 80, 87] adopt a holistic approach where multiple frames are represented in a single model. NeRFPlayer [80] and HyperReel [4] combine static spatial representations [15, 67] with temporal feature sharing/interpolation to improve model compactness. This strategy exploits the characteristic that adjacent frames in natural videos usually exhibit high similarity. In a similar vein, MixVoxels [87] uses time-variant latents and bridges them with spatial features by inner product. K-Planes [28] and HexPlane [12] factorize the 4D spacetime domain into multiple 2D planes for compact representation. One limitation of these methods is that their grid-like representations cannot fully adapt to the dynamics of scene structures, hindering the modeling of delicate details. Meanwhile, they struggle to produce real-time high-resolution rendering without sacrificing quality." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 387, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 287, + 529 + ], + "type": "text", + "content": "In this work, we present a novel representation for dynamic view synthesis. Our approach simultaneously achieves photorealistic quality, real-time high-resolution rendering and compact model size (see Fig. 1 for example results and comparisons with state-of-the-arts). At the core of our approach is Spacetime Gaussian (STG), which extends 3D Gaussian to 4D spacetime domain. We propose to equip 3D Gaussian with time-dependent opacity along with polynomially parameterized motion and rotation. As a result, STGs are capable of faithfully modeling static, dynamic as well as transient (i.e., emerging or vanishing) content in a scene." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 532, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 652 + ], + "type": "text", + "content": "To enhance model compactness and account for time-varying appearance, we propose splatted feature rendering. Specifically, for each Spacetime Gaussian, instead of storing spherical harmonic coefficients, we store features that encode base color, view-related information and time-related information. These features are rasterized to image space via differentiable splatting, and then go through a tiny multi-layer perceptrons (MLP) network to produce the final color. While smaller in size than spherical harmonics, these features exhibit strong expressiveness." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Additionally, we introduce guided sampling of Gaussians to improve rendering quality of complex scenes. We observe that distant areas which are sparsely covered by Gaussians at initialization tend to have blurry rendering results. To tackle this problem, we propose to sample new" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 544, + 96 + ], + "type": "text", + "content": "Gaussians in the 4D scene with the guidance of training error and coarse depth." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 96, + 544, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 544, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 544, + 120 + ], + "type": "text", + "content": "In summary, the contributions of our work are the following:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 121, + 544, + 275 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 121, + 544, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 121, + 544, + 156 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 544, + 156 + ], + "type": "text", + "content": "- We present a novel representation based on Spacetime Gaussian for high-fidelity and efficient dynamic view synthesis." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 156, + 544, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 156, + 544, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 544, + 191 + ], + "type": "text", + "content": "- We propose splatted feature rendering, which enhances model compactness and facilitates the modeling of time-varying appearance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 192, + 544, + 226 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 192, + 544, + 226 + ], + "spans": [ + { + "bbox": [ + 306, + 192, + 544, + 226 + ], + "type": "text", + "content": "- We introduce a guided sampling approach for Gaussians to improve rendering quality at distant sparsely covered areas." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 228, + 544, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 544, + 275 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 544, + 275 + ], + "type": "text", + "content": "- Extensive experiments on various real-world datasets demonstrate that our method achieves state-of-the-art rendering quality and speed while keeping small model size. Our lite-version model enables 8K rendering at 60 FPS." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 285, + 392, + 297 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 285, + 392, + 297 + ], + "spans": [ + { + "bbox": [ + 306, + 285, + 392, + 297 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 460 + ], + "type": "text", + "content": "Novel View Synthesis. Early approaches leverage image-based rendering techniques with proxy geometry/depth to sample novel views from source images [11, 13, 20, 31, 34, 44, 46, 103]. Chaurasia et al. [14] estimate a depth map to blend pixels from source views and employ superpixels to compensate for missing depth data. Hedman et al. [32] utilize RGBD sensors to improve rendering quality and speed. Penner and Zhang [72] leverage volumetric voxels for continuity in synthesized views and robustness to depth uncertainty. Hedman et al. [33] learn the blending scheme with neural networks. Flynn et al. [26] combine multi-plane images with learned gradient descent. Wiles et al. [92] sput latent features from point cloud for novel view synthesis." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 474, + 546, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 546, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 546, + 689 + ], + "type": "text", + "content": "Neural Scene Representations. In recent years, neural scene representations have achieved great progress in novel view synthesis. These methods allocate neural features to structures such as volume [62, 78], texture [16, 84], or point cloud [1]. The seminal work of NeRF [66] proposes to leverage differentiable volume rendering. It does not require proxy geometry and instead uses MLPs to implicitly encode density and radiance in 3D space. Later on, numerous works emerge to boost the quality and efficiency of differentiable volume rendering. One group of methods focuses on improving the sampling strategy to reduce the number of point queries [4, 68, 73] or applies light field-based formulation [3, 25, 53, 54, 79, 81, 89]. Another group trades space for speed by incorporating explicit and localized neural representations [8, 15, 17, 27, 36, 60, 67, 75, 82, 83, 96, 101]. Among them, to improve model compactness, Instant-NGP [67] uses hash grid while TensoRF [15] utilizes tensor decomposition." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Recently, 3D Gaussian Splitting (3DGS) [41] proposes to use anisotropic 3D Gaussians as scene representation" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8509" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "and presents an efficient differentiable rasterizer to splat these Gaussians to the image plane. Their method enables fast high-resolution rendering, while preserving great rendering quality. Similar to 3DGS, NeuRBF [18] leverages anisotropic radial basis functions for neural representation and achieves high-fidelity rendering. However, the above methods focus on static scene representation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 173, + 289, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 173, + 289, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 289, + 568 + ], + "type": "text", + "content": "Dynamic Novel View Synthesis. A widely adopted setting for dynamic free-viewpoint rendering is using multiview videos as input. Classic methods in this area include [19, 21, 39, 40, 49-51, 98, 104]. More recently, Broxton et al. [10] use multi-sphere image as bootstrap and then convert it to layered meshes. Bansal et al. [5] separate static and dynamic contents and manipulate video with deep network in screen space. Bemana et al. [9] learn a neural network to implicitly map view, time or light coordinates to 2D images. Attal et al. [2] use multi-sphere representations to handle the depth and occlusions in 360-degree videos. Lin et al. [57, 58] propose 3D mask volume to addresses the temporal inconsistency of disocclusions. Neural Volumes [62] uses an encoder-decoder network to encode images into a 3D volume and decode it with volume rendering. Lombardi et al. [63] enhance Neural Volumes by decoding a mixture of dynamic geometric primitives from latent code and skipping samples in empty space for efficient ray marching. Extending static NeRF-related representations to dynamic scenes are also being actively explored [4, 12, 28, 38, 42, 47, 48, 56, 71, 77, 80, 87, 88, 90, 91]. DyNeRF [48] combines NeRF with time-conditioned latent codes to compactly represent dynamic scenes. StreamRF [47] accelerates the training of dynamic scenes by modeling the differences of consecutive frames. NeRFPlayer [80] decomposes scene into static, new and deforming fields and proposes streaming of feature channels. MixVoxels [87] represents scene with a mixture of static and dynamic voxels to accelerate rendering. HyperReel [4] utilizes sampling prediction network to reduce sampling points and leverages keyframe-based representation. K-Planes [28], HexPlane [12] and Tensor4D [77] factorize 4D spacetime domain into 2D feature planes for compact model size." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 569, + 288, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 288, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 288, + 676 + ], + "type": "text", + "content": "Another line of research tackles dynamic view synthesis from monocular videos [22, 23, 29, 30, 52, 55, 61, 69, 70, 74, 85, 86, 94]. Under this setting, a single camera moves around in the dynamic scene, providing only one observed viewpoint at each timestep. To address the sparsity of supervision, priors on motion, scene flow or depth are usually introduced. In this work, we focus on the dynamic representation itself and only consider the setting of multi-view input videos." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "Recently, there are several work on this topic that are concurrent to ours [37, 45, 59, 64, 93, 95, 97, 99, 100]. 4K4D [97] combines 4D point clouds with K-Planes [28]" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "and discrete image-based rendering, and uses differentiable depth peeling to train the model. Luiten et al. [64] models 4D scene with a set of moving 3D Gaussians, whose positions and rotations are discretely defined at each step. Their method demonstrates appealing results for 3D tracking, but its rendering quality is less favorable due to flickering artifacts. Yang et al. [100] leverage 4D Gaussians and 4D spherindrical harmonics for dynamic modelling. 4D Gaussians essentially represent motion with linear model. Comparatively, our polynomial motion model is more expressive, resulting in higher rendering quality. Our method also has higher rendering speed than their work. Yang et al. [99] and Wu et al. [93] prioritize on monocular dynamic view synthesis and employ deformation fields to deform a set of canonical 3D Gaussians. For multi-view videos setting, the performance of [99] is not extensively evaluated while [93] depicts inferior rendering quality and speed than ours." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 285, + 506, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 285, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 506, + 300 + ], + "type": "text", + "content": "3. Preliminary: 3D Gaussian Splatting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 547, + 375 + ], + "type": "text", + "content": "Given images at multiple viewpoints with known camera poses, 3D Gaussian Splatting [41] (3DGS) optimizes a set of anisotropic 3D Gaussians via differentiable rasterization to represent a static 3D scene. Owing to their efficient rasterization, the optimized model can render high-fidelity novel views in real-time." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": "3DGS [41] associates a 3D Gaussian " + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": " with a position " + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": ", covariance matrix " + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "inline_equation", + "content": "\\Sigma_{i}" + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": ", opacity " + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": " and spherical harmonics (SH) coefficients " + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_i" + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": ". The final opacity of a 3D Gaussian at any spatial point " + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 376, + 547, + 425 + ], + "type": "text", + "content": " is" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 334, + 429, + 545, + 455 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 429, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 334, + 429, + 545, + 455 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} = \\sigma_ {i} \\exp \\left(- \\frac {1}{2} (\\mathbf {x} - \\mu_ {i}) ^ {T} \\Sigma_ {i} ^ {- 1} (\\mathbf {x} - \\mu_ {i})\\right). \\tag {1}", + "image_path": "00f5b95ba1d9aadc01eb440cc0e51e36306b79d1d2d52d243c8518119f9b2704.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\Sigma_{i}" + }, + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "text", + "content": " is positive semi-definite and can be decomposed into scaling matrix " + }, + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "text", + "content": " and rotation matrix " + }, + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "inline_equation", + "content": "R_{i}" + }, + { + "bbox": [ + 306, + 459, + 545, + 483 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 387, + 487, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 487, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 387, + 487, + 545, + 502 + ], + "type": "interline_equation", + "content": "\\Sigma_ {i} = R _ {i} S _ {i} S _ {i} ^ {T} R _ {i} ^ {T}, \\tag {2}", + "image_path": "5c3970d7f62fee23c96aa61381fa112b287eb7e4b8d3eee8a462715f18286c3e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": " is a diagonal matrix and is parameterized by a 3D vector " + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_i" + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "inline_equation", + "content": "R_{i}" + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": " is parameterized by a quaternion " + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 506, + 545, + 529 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "content": "To render an image, 3D Gaussians are first projected to 2D image space via an approximation of the perspective transformation [105]. Specifically, the projection of a 3D Gaussian is approximated as a 2D Gaussian with center " + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\mu_i^{2D}" + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "content": " and covariance " + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\Sigma_i^{2D}" + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "inline_equation", + "content": "W, K" + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "content": " be the viewing transformation and projection matrix, " + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\mu_i^{2D}" + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "inline_equation", + "content": "\\Sigma_i^{2D}" + }, + { + "bbox": [ + 304, + 530, + 547, + 602 + ], + "type": "text", + "content": " are computed as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 357, + 605, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 605, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 357, + 605, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\mu_ {i} ^ {2 D} = \\left(K \\left(\\left(W \\mu_ {i}\\right) / \\left(W \\mu_ {i}\\right) _ {z}\\right)\\right) _ {1: 2}, \\tag {3}", + "image_path": "8883210352d94bb7abc7def76ff6a25fa2543d2e1fa0edb6f142d11501f048bb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 357, + 622, + 545, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 622, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 357, + 622, + 545, + 637 + ], + "type": "interline_equation", + "content": "\\Sigma_ {i} ^ {2 D} = \\left(J W \\Sigma_ {i} W ^ {T} J ^ {T}\\right) _ {1: 2, 1: 2}, \\tag {4}", + "image_path": "82accdef6cb38facfbb053c8975950d5aebb39a2e7bc5f4ae5443f97dff93f76.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 641, + 535, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 641, + 535, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 641, + 535, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 641, + 535, + 653 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 306, + 641, + 535, + 653 + ], + "type": "text", + "content": " is the Jacobian of the projective transformation." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "content": "After sorting the Gaussians in depth order, the color at a pixel is obtained by volume rendering:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 362, + 682, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 682, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 362, + 682, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {I} = \\sum_ {i \\in \\mathcal {N}} \\mathbf {c} _ {i} \\alpha_ {i} ^ {2 D} \\prod_ {j = 1} ^ {i - 1} \\left(1 - \\alpha_ {j} ^ {2 D}\\right), \\tag {5}", + "image_path": "77facdfb6ca028cfc0eee9bc9e6f2a91a74c1ca8392be385559e0bec09104d8a.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8510" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 73, + 312, + 211 + ], + "blocks": [ + { + "bbox": [ + 56, + 73, + 312, + 211 + ], + "lines": [ + { + "bbox": [ + 56, + 73, + 312, + 211 + ], + "spans": [ + { + "bbox": [ + 56, + 73, + 312, + 211 + ], + "type": "image", + "image_path": "87b295ef671e5c08ccb0eba3bedc5680e619c6015b80b24416e57b9658a7d2a7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 219, + 223, + 230 + ], + "lines": [ + { + "bbox": [ + 135, + 219, + 223, + 230 + ], + "spans": [ + { + "bbox": [ + 135, + 219, + 223, + 230 + ], + "type": "text", + "content": "(a) Spacetime Gaussians" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 322, + 78, + 545, + 208 + ], + "blocks": [ + { + "bbox": [ + 322, + 78, + 545, + 208 + ], + "lines": [ + { + "bbox": [ + 322, + 78, + 545, + 208 + ], + "spans": [ + { + "bbox": [ + 322, + 78, + 545, + 208 + ], + "type": "image", + "image_path": "f01319d0a8fc1201f970f5f0610e9c9164810c6f58d026addf02f010c1df07a8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 372, + 219, + 500, + 230 + ], + "lines": [ + { + "bbox": [ + 372, + 219, + 500, + 230 + ], + "spans": [ + { + "bbox": [ + 372, + 219, + 500, + 230 + ], + "type": "text", + "content": "(b) Feature Splitting and Rendering" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 239, + 546, + 274 + ], + "lines": [ + { + "bbox": [ + 45, + 239, + 546, + 274 + ], + "spans": [ + { + "bbox": [ + 45, + 239, + 546, + 274 + ], + "type": "text", + "content": "Figure 2. Overview of Spacetime Gaussians and splatted feature rendering. (a) Our method leverages a set of Spacetime Gaussians (STG) to represent the dynamic scenes. On top of 3D Gaussian, each STG is further equipped with temporal opacity, polynomial motion/rotation and time-dependent features. (b) We visualize the splatted features as maps, which are converted to color image via MLP." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{2D}" + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "content": " is a 2D version of Eq. (1), with " + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\mu_{i}, \\Sigma_{i}, \\mathbf{x}" + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "content": " replaced by " + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\mu_{i}^{2D}, \\Sigma_{i}^{2D}, \\mathbf{x}^{2D}" + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "content": " (pixel coordinate). " + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{i}" + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "content": " is the RGB color after evaluating SH with view direction and coefficients " + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{h}_{i}" + }, + { + "bbox": [ + 46, + 293, + 287, + 342 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 351, + 103, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 103, + 363 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 103, + 363 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 371, + 287, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 371, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 371, + 287, + 478 + ], + "type": "text", + "content": "We propose a novel representation based on Spacetime Gaussians for modeling dynamic 3D scenes. Our approach takes multi-view videos as input and creates 6-DoF video that allows rendering at novel views. We first describe the formulation of our Spacetime Gaussian (STG) in Sec. 4.1. Then in Sec. 4.2, we present feature-based splatting for time-varying rendering. Sec. 4.3 details our optimization process and Sec. 4.4 introduces guided sampling of Gaussians." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 485, + 168, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 168, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 168, + 498 + ], + "type": "text", + "content": "4.1. Spacetime Gaussians" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 503, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 635 + ], + "type": "text", + "content": "To represent 4D dynamics, we propose Spacetime Gaussians (STG) that combine 3D Gaussians with temporal components to model emerging/vanishing content as well as motion/deformation, as shown in Fig. 2 (a). Specifically, we introduce temporal radial basis function to encode temporal opacity, which can effectively model scene content that emerges or vanishes within the duration of video. Meanwhile, we utilize time-conditioned parametric functions for the position and rotation of 3D Gaussians to model the motion and deformation in the scene. For a spacetime point " + }, + { + "bbox": [ + 46, + 503, + 287, + 635 + ], + "type": "inline_equation", + "content": "(\\mathbf{x},t)" + }, + { + "bbox": [ + 46, + 503, + 287, + 635 + ], + "type": "text", + "content": ", the opacity of an STG is" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 641, + 290, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 641, + 290, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 641, + 290, + 677 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} (t) = \\sigma_ {i} (t) \\exp \\left(- \\frac {1}{2} (\\mathbf {x} - \\mu_ {i} (t)) ^ {T} \\Sigma_ {i} (t) ^ {- 1} (\\mathbf {x} - \\mu_ {i} (t))\\right), \\tag {6}", + "image_path": "ecaea91277c13b528acd8927c6f8d7b2a5dd966c47abb7f5c579603eaaa5b0a5.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\sigma_{i}(t)" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " is temporal opacity, " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mu_{i}(t),\\Sigma_{i}(t)" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " are time-dependent position and covariance, and " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " stands for the ith STG. We detail each of the components below." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "type": "text", + "content": "Temporal Radial Basis Function. We use a temporal radial basis function to represent the temporal opacity of an STG at any time " + }, + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "type": "text", + "content": ". Inspired by [18, 41] that use radial basis functions for approximating spatial signals, we utilize 1D Gaussian for the temporal opacity " + }, + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "type": "inline_equation", + "content": "\\sigma_{i}(t)" + }, + { + "bbox": [ + 305, + 293, + 546, + 354 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 358, + 369, + 545, + 383 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 369, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 358, + 369, + 545, + 383 + ], + "type": "interline_equation", + "content": "\\sigma_ {i} (t) = \\sigma_ {i} ^ {s} \\exp \\left(- s _ {i} ^ {\\tau} | t - \\mu_ {i} ^ {\\tau} | ^ {2}\\right), \\tag {7}", + "image_path": "716fe9b6451162ec8b692f09bfa950ac42172f57ccc5d768465d3dc7c6653e48.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "inline_equation", + "content": "\\mu_i^\\tau" + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": " is temporal center, " + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "inline_equation", + "content": "s_i^\\tau" + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": " is temporal scaling factor, and " + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "inline_equation", + "content": "\\sigma_i^s" + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": " is time-independent spatial opacity. " + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "inline_equation", + "content": "\\mu_i^\\tau" + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": " represents the timestamp for the STG to be most visible while " + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "inline_equation", + "content": "s_i^\\tau" + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": " determines its effective duration (i.e., the time duration where its temporal opacity is high). We include " + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "inline_equation", + "content": "\\sigma_i^s" + }, + { + "bbox": [ + 304, + 391, + 545, + 463 + ], + "type": "text", + "content": " to allow spatial opacity variation across STGs." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 483, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 519 + ], + "type": "text", + "content": "Polynomial Motion Trajectory. For each STG, we employ a time-conditioned function to model its motion. Motivated by [24, 35], we choose polynomial function:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 370, + 530, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 530, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 370, + 530, + 545, + 563 + ], + "type": "interline_equation", + "content": "\\mu_ {i} (t) = \\sum_ {k = 0} ^ {n _ {p}} b _ {i, k} \\left(t - \\mu_ {i} ^ {\\tau}\\right) ^ {k}, \\tag {8}", + "image_path": "b20573f1fb518ccda8968161491d7923e5fb4a8e017002eed106d5cbb0a91a4a.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "spans": [ + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\mu_{i}(t)" + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "text", + "content": " denotes the spatial position of an STG at time " + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "inline_equation", + "content": "\\{b_{i,k}\\}_{k=0}^{n_p}, b_{i,k} \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "text", + "content": " are the corresponding polynomial coefficients and are optimized during training. Combining Eq. (7) and Eq. (8), complex and long motion can be represented by multiple short segments with simpler motion. In our implementation, we use " + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "inline_equation", + "content": "n_p = 3" + }, + { + "bbox": [ + 304, + 573, + 545, + 657 + ], + "type": "text", + "content": " as we find it a good balance between representation capacity and model size." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "Polynomial Rotation. Following [41], we use real-valued quaternion to parameterize the rotation matrix " + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "R_{i}" + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": " in Eq. (2). Similar to motion trajectory, we adopt a polynomial func" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 314, + 757 + ], + "type": "text", + "content": "8511" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 544, + 311 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 544, + 311 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 544, + 311 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 544, + 311 + ], + "type": "image", + "image_path": "37b02f8d8245d811982e5d387c57e52df0791c9608e9c49b1e20148c9950785a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 314, + 546, + 336 + ], + "lines": [ + { + "bbox": [ + 46, + 314, + 546, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 546, + 336 + ], + "type": "text", + "content": "Figure 3. Illustration of our guided sampling strategy for Gaussians. Our strategy samples new Gaussians along rays by leveraging the guidance of training error and coarse depth." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 344, + 163, + 355 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 163, + 355 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 163, + 355 + ], + "type": "text", + "content": "tion to represent quaternion:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 365, + 287, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 365, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 112, + 365, + 287, + 397 + ], + "type": "interline_equation", + "content": "q _ {i} (t) = \\sum_ {k = 0} ^ {n _ {q}} c _ {i, k} \\left(t - \\mu_ {i} ^ {\\tau}\\right) ^ {k}, \\tag {9}", + "image_path": "ec399aca4b19893e612b5670e8b99fb853ea32f25582a00b702c618ed2030e5a.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "q_{i}(t)" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": " is the rotation (in quaternion) of an STG at time " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\{c_{i,k}\\}_{k=0}^{n_q}, c_{i,k} \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": " are polynomial coefficients. After converting " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "q_{i}(t)" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": " to rotation matrix " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "R_{i}(t)" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": ", the covariance " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "\\Sigma_{i}(t)" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": " can be obtained via Eq. (2). We set " + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "inline_equation", + "content": "n_q = 1" + }, + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": " in our experiments." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": "Note that we keep the scaling matrix " + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": " in Eq. (2) to be time-independent, since we experimentally do not observe improvement in rendering quality when applying time-conditioned function on this parameter." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 525, + 200, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 200, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 200, + 539 + ], + "type": "text", + "content": "4.2. Splatted Feature Rendering" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 544, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 287, + 593 + ], + "type": "text", + "content": "To encode view- and time-dependent radiance both accurately and compactly, we store features instead of spherical harmonics coefficients (SH) in each STG. Specifically, the features " + }, + { + "bbox": [ + 46, + 544, + 287, + 593 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i(t)\\in \\mathbb{R}^9" + }, + { + "bbox": [ + 46, + 544, + 287, + 593 + ], + "type": "text", + "content": " of each STG consist of three parts:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 89, + 604, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 604, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 89, + 604, + 287, + 620 + ], + "type": "interline_equation", + "content": "\\mathbf {f} _ {i} (t) = \\left[ \\mathbf {f} _ {i} ^ {\\text {b a s e}}, \\mathbf {f} _ {i} ^ {\\text {d i r}}, \\quad (t - \\mu_ {i} ^ {\\tau}) \\mathbf {f} _ {i} ^ {\\text {t i m e}} \\right] ^ {T}, \\tag {10}", + "image_path": "4efc13fc93dbeda327e17d676fed4b9f2e573d9f457d8956eddbcf762cd8385d.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{base}} \\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " contains base RGB color, and " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{dir}}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{\\mathbf{i}}^{\\mathrm{time}} \\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " encode information related to view direction and time. The feature splatting process is similar to Gaussian Splatting [41], except that the RGB color " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "c_{i}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": " in Eq. (5) is now replaced by features " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_{i}(t)" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ". After splatting to image space, we split the splatted features at each pixel into " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{\\mathrm{base}}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{\\mathrm{dir}}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{\\mathrm{time}}" + }, + { + "bbox": [ + 46, + 628, + 287, + 713 + ], + "type": "text", + "content": ", whose channels correspond to the three parts in Eq. (10)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 343, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 343, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 305, + 343, + 545, + 367 + ], + "type": "text", + "content": "The final RGB color at each pixel is obtained after going through a 2-layer MLP " + }, + { + "bbox": [ + 305, + 343, + 545, + 367 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 305, + 343, + 545, + 367 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 365, + 375, + 545, + 389 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 375, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 365, + 375, + 545, + 389 + ], + "type": "interline_equation", + "content": "\\mathbf {I} = \\mathbf {F} ^ {\\text {b a s e}} + \\Phi (\\mathbf {F} ^ {\\text {d i r}}, \\mathbf {F} ^ {\\text {t i m e}}, \\mathbf {r}), \\tag {11}", + "image_path": "f6ede4383b324ce9fe97a47e80b0c4e9911dd4599f7e83b4e33020a5ffca96ae.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 398, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 434 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 398, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{r}" + }, + { + "bbox": [ + 304, + 398, + 545, + 434 + ], + "type": "text", + "content": " is the view direction at the pixel and is additionally concatenated with the features as input. Fig. 2 (b) shows an illustration of the rendering process." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "content": "Compared to SH encoding, our feature-based approach requires fewer parameters for each STG (9 vs. 48 for 3-degree SH). At the same time, since the MLP network " + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "content": " is shallow and narrow, our method still achieves fast rendering speed." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "type": "text", + "content": "To maximize rendering speed, we can also optionally drop " + }, + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "type": "text", + "content": " and only keep " + }, + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{base}" + }, + { + "bbox": [ + 304, + 495, + 545, + 530 + ], + "type": "text", + "content": " during training and rendering. We refer to this configuration as our lite-version model." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 537, + 390, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 537, + 390, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 537, + 390, + 550 + ], + "type": "text", + "content": "4.3. Optimization" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "type": "text", + "content": "The parameters to be optimized include the MLP " + }, + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "type": "text", + "content": " and the parameters of each STG " + }, + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "type": "inline_equation", + "content": "(\\sigma_i^s, s_i^\\tau, \\mu_i^\\tau, \\{b_{i,k}\\}_{k=0}^{n_p}, \\{c_{i,k}\\}_{k=0}^{n_q}, \\mathbf{s}_i, \\mathbf{f}_i^{\\mathrm{base}}, \\mathbf{f}_i^{\\mathrm{dir}}, \\mathbf{f}_i^{\\mathrm{time}})" + }, + { + "bbox": [ + 304, + 556, + 545, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 593, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 593, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 593, + 545, + 662 + ], + "type": "text", + "content": "Following [41], we optimize these parameters through differentiable splatting and gradient-based backpropagation, and interleave with density control of Gaussians. We use rendering loss that compares rendered images with groundtruth images. The rendering loss consists of a " + }, + { + "bbox": [ + 304, + 593, + 545, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 304, + 593, + 545, + 662 + ], + "type": "text", + "content": " term and a D-SSIM term." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 671, + 473, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 671, + 473, + 684 + ], + "spans": [ + { + "bbox": [ + 306, + 671, + 473, + 684 + ], + "type": "text", + "content": "4.4. Guided Sampling of Gaussians" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 714 + ], + "type": "text", + "content": "We observe that areas which have sparse Gaussians at initialization are challenging to converge to high rendering" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8512" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "quality, especially if these areas are far away from the training cameras. Therefore, we further introduce a strategy to sample new Gaussians with the guidance of training error and coarse depth." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 120, + 288, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 120, + 288, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 120, + 288, + 346 + ], + "type": "text", + "content": "We sample new Gaussians along the rays of pixels that have large errors during training, as illustrated in Fig. 3. To ensure sampling effectiveness, we conduct sampling after training loss is stable. Since error maps can be noisy during training, we patch-wise aggregate training errors to prioritize on areas with substantial errors rather than outlier pixels. Then we sample a ray from the center pixel of each selected patches that have large errors. To avoid sampling in an excessively large depth range, we exploit the coarse depth map of Gaussians' centers to determine a more specific depth range. The depth map is generated during feature splatting and incurs little computational overhead. New Gaussians are then uniformly sampled within the depth range along the rays. We additionally add small noises to the centers of the newly sampled Gaussians. Among the sampled Gaussians, the unnecessary ones will have low opacity after steps of training and be pruned. For the scenes in our experiments, the above sampling process only needs to be conducted no more than 3 times." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 348, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 348, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 348, + 287, + 407 + ], + "type": "text", + "content": "Our guided sampling strategy is complimentary to the density control techniques in [41]. While density control gradually grows Gaussians near existing ones by splitting, our approach can sample new Gaussians at regions that have sparse or no Gaussians." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 418, + 183, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 418, + 183, + 433 + ], + "spans": [ + { + "bbox": [ + 47, + 418, + 183, + 433 + ], + "type": "text", + "content": "5. Implementation Details" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 439, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 287, + 548 + ], + "type": "text", + "content": "We initialize our STGs with the structure-from-motion sparse point clouds from all available timestamps. For density control, we conduct more aggressive pruning than [41] to reduce the number of Gaussians and keep model size to be relatively small. We use Adam optimizer [43]. The training time for a 50-frame sequence is 40-60 minutes on a single NVIDIA A6000 GPU. We adapt the splatting process to support different camera models in real world datasets. See supplementary material for more implementation details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 559, + 128, + 572 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 128, + 572 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 128, + 572 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 578, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 286, + 651 + ], + "type": "text", + "content": "We evaluate our method on three real-world benchmarks: Neural 3D Video Dataset [48] (Sec. 6.1), Google Immersive Dataset [10] (Sec. 6.2), and Technicolor Dataset [76] (Sec. 6.3). We also conduct ablation studies on various aspects of our method (Sec. 6.4). Please refer to supplementary material and video for more results and real-time demo." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 186, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 186, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 186, + 671 + ], + "type": "text", + "content": "6.1. Neural 3D Video Dataset" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "The Neural 3D Video Dataset [48] contains six indoor multi-view video sequences captured by 18 to 21 cameras at " + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "inline_equation", + "content": "2704 \\times 2028" + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": " resolution. Following common practice, train-" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 143, + 545, + 264 + ], + "blocks": [ + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "lines": [ + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons on the Neural 3D Video Dataset. \"FPS\" is measured at " + }, + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "inline_equation", + "content": "1352 \\times 1014" + }, + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "text", + "content": " resolution. \"Size\" is the total model size for 300 frames. Some methods only report part of the scenes. For fair comparison, we additionally report our results under their settings. " + }, + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "inline_equation", + "content": "^1" + }, + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "text", + "content": " only includes the Flame Salmon scene. " + }, + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 70, + 547, + 137 + ], + "type": "text", + "content": " excludes the Coffee Martini scene." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 143, + 545, + 264 + ], + "lines": [ + { + "bbox": [ + 307, + 143, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 307, + 143, + 545, + 264 + ], + "type": "table", + "html": "
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size↓
Neural Volumes [62]122.80-0.0620.295--
LLFF [65]123.24-0.0760.235--
DyNeRF [48]129.58-0.0200.0830.01528 MB
Ours129.480.0380.0220.063103300 MB
HexPlane [12]231.71--0.075-200 MB
Ours232.740.0270.0120.039140190 MB
StreamRF [47]28.26---10.95310 MB
NeRFPlayer [80]30.690.034-0.1110.055130 MB
HyperReel [4]31.100.036-0.0962360 MB
K-Planes [28]31.63-0.018-0.3311 MB
MixVoxels-L [87]31.34-0.0170.09637.7500 MB
MixVoxels-X [87]31.73-0.0150.0644.6500 MB
Ours32.050.0260.0140.044140200 MB
", + "image_path": "c8212397cf819939f2c973f37d3153135c18d91aaa99e46d3955f363137fa7ee.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 306, + 303, + 545, + 355 + ], + "blocks": [ + { + "bbox": [ + 305, + 274, + 545, + 297 + ], + "lines": [ + { + "bbox": [ + 305, + 274, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 305, + 274, + 545, + 297 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on the Google Immersive Dataset. \"Size/Fr\" stands for model size per frame." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 303, + 545, + 355 + ], + "lines": [ + { + "bbox": [ + 306, + 303, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 545, + 355 + ], + "type": "table", + "html": "
MethodPSNR↑DSSIM1↓LPIPS↓FPS↑Size/Fr↓
NeRFPlayer [80]25.80.0760.1960.1217.1 MB
HyperReel [4]28.80.0630.19341.2 MB
Ours29.20.0420.081991.2 MB
", + "image_path": "78ac38681fb3ffbf8cd80aefed6f0005bdb79789d30c56198c84d85a9fee0095.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 411 + ], + "type": "text", + "content": "ing and evaluation are conducted at half resolution, and the first camera is held out for evaluation [48]. The number of frames is 300 for each scene." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": "We use PSNR, DSSIM and LPIPS [102] as evaluation metrics. As mentioned in [4, 28], there is an inconsistency in the DSSIM implementation across methods. For fair comparison, we do our best to group existing methods' DSSIM results into two categories " + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "inline_equation", + "content": "(\\mathrm{DSSIM}_1" + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "inline_equation", + "content": "\\mathrm{DSSIM}_2)" + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": ". Using the structural_similarity function from scikit-image library, " + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "inline_equation", + "content": "\\mathrm{DSSIM}_1" + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": " sets data_range to 1.0 while " + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "inline_equation", + "content": "\\mathrm{DSSIM}_2" + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": " sets data_range to 2.0. We use FPS as metric for rendering speed. Metrics are averaged over all six scenes except noted otherwise." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 531, + 545, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 650 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 650 + ], + "type": "text", + "content": "As shown in Tab. 1, our method achieves 140 FPS and outperforms the others by a large margin. Our approach also has the best LPIPS in all comparisons and the best PSNR/DSSIM in most cases. Fig. 4 shows qualitative comparisons on a representative view that is widely used in other work. Compared to the other baselines, our result contains more vivid details (e.g., the textures on the salmon) and artifact-less rendering (e.g., the caustics on the cup). Please see supplementary material for comparisons with concurrent methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 658, + 453, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 453, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 453, + 671 + ], + "type": "text", + "content": "6.2. Google Immersive Dataset" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Google Immersive Dataset [10] contains indoor and outdoor scenes captured with a 46-camera rig. The cameras are in fish-eye mode and are mounted on an outward-facing hemi" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8513" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 545, + 339 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 545, + 339 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 545, + 339 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 545, + 339 + ], + "type": "image", + "image_path": "c3d8f4e3168797f7b7d30d975138012c87511b14fec1a9b8102d14dacec0bb33.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 168, + 349, + 425, + 361 + ], + "lines": [ + { + "bbox": [ + 168, + 349, + 425, + 361 + ], + "spans": [ + { + "bbox": [ + 168, + 349, + 425, + 361 + ], + "type": "text", + "content": "Figure 4. Qualitative comparisons on the Neural 3D Video Dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 50, + 373, + 543, + 641 + ], + "blocks": [ + { + "bbox": [ + 50, + 373, + 543, + 641 + ], + "lines": [ + { + "bbox": [ + 50, + 373, + 543, + 641 + ], + "spans": [ + { + "bbox": [ + 50, + 373, + 543, + 641 + ], + "type": "image", + "image_path": "7c80f9b3bd67376423925775bb138a1fac751d50faf4707e06928ee3c4c127e4.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 164, + 651, + 428, + 662 + ], + "lines": [ + { + "bbox": [ + 164, + 651, + 428, + 662 + ], + "spans": [ + { + "bbox": [ + 164, + 651, + 428, + 662 + ], + "type": "text", + "content": "Figure 5. Qualitative comparisons on the Google Immersive Dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 675, + 287, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 675, + 287, + 700 + ], + "spans": [ + { + "bbox": [ + 47, + 675, + 287, + 700 + ], + "type": "text", + "content": "sphere. Compared to outside-in setups, there is less overlap among views, hence posing additional challenges." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Following [4, 80], we evaluate on 7 selected scenes" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 675, + 545, + 712 + ], + "type": "text", + "content": "(Welder, Flames, Truck, Exhibit, Face Paint 1, Face Paint 2, Cave) and hold out the center camera as test view. The numerical results of NeRFPlayer [80] and HyperReel [4] are" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8514" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 99, + 286, + 145 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 286, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 286, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 286, + 93 + ], + "type": "text", + "content": "Table 3. Quantitative comparisons on the Technicolor Dataset. \"Size/Fr\" stands for model size per frame." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 99, + 286, + 145 + ], + "lines": [ + { + "bbox": [ + 47, + 99, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 47, + 99, + 286, + 145 + ], + "type": "table", + "html": "
MethodPSNR↑DSSIM1↓DSSIM2↓LPIPS↓FPS↑Size/Fr↓
DyNeRF [48]31.8-0.0210.1400.020.6 MB
HyperReel [4]32.70.047-0.1094.001.2 MB
Ours33.60.0400.0190.08486.71.1 MB
", + "image_path": "8fe1463d0b8a6cc4b62452c17928b15f9bfe9c4d8a875bd2a00a47aecaab4f08.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 47, + 176, + 286, + 258 + ], + "blocks": [ + { + "bbox": [ + 47, + 151, + 286, + 172 + ], + "lines": [ + { + "bbox": [ + 47, + 151, + 286, + 172 + ], + "spans": [ + { + "bbox": [ + 47, + 151, + 286, + 172 + ], + "type": "text", + "content": "Table 4. Ablation study of proposed components. Conducted on all the five scenes from the Technicolor Dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 176, + 286, + 258 + ], + "lines": [ + { + "bbox": [ + 47, + 176, + 286, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 176, + 286, + 258 + ], + "type": "table", + "html": "
MethodPSNR↑DSSIM1↓LPIPS↓
w/o Temporal Opacity31.00.0630.153
w/o Polynomial Motion32.60.0450.099
w/o Polynomial Rotation33.40.0420.085
w/o Feature Splitting33.00.0440.097
w/o Guided Sampling of Gaussians33.30.0410.085
Ours Full33.60.0400.084
", + "image_path": "a1926271c1652592c1077d29eb859b491467a740e9bbb7ff797f3f3825904c9c.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 47, + 305, + 286, + 361 + ], + "blocks": [ + { + "bbox": [ + 47, + 263, + 286, + 295 + ], + "lines": [ + { + "bbox": [ + 47, + 263, + 286, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 263, + 286, + 295 + ], + "type": "text", + "content": "Table 5. Ablation study on the number of frames whose SfM point clouds are used in initialization. Conducted on the Theater scene from the Technicolor Dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 305, + 286, + 361 + ], + "lines": [ + { + "bbox": [ + 47, + 305, + 286, + 361 + ], + "spans": [ + { + "bbox": [ + 47, + 305, + 286, + 361 + ], + "type": "table", + "html": "
Every N FramesPSNR↑DSSIM1↓LPIPS↓Size↓
N = 131.580.0590.124110.2 MB
N = 431.510.0570.11746.7 MB
N = 1631.040.0600.13932.6 MB
", + "image_path": "0d41b83c6c49c39e7492f4e45a61df31deb1496b1c8706b0aea180032f44edae.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 373, + 286, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 286, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 286, + 409 + ], + "type": "text", + "content": "from their papers. The visual results of NeRFPlayer [80] are obtained from their authors while those of HyperReel [4] are produced by running their released codes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 410, + 286, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 286, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 286, + 506 + ], + "type": "text", + "content": "As shown in Tab. 2, our method outperforms NeRFPlayer and HyperReel in both speed and quality. Compared to HyperReel, our method is over 10 times faster in rendering speed. Although our PSNR is only " + }, + { + "bbox": [ + 46, + 410, + 286, + 506 + ], + "type": "inline_equation", + "content": "0.4\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 410, + 286, + 506 + ], + "type": "text", + "content": " higher, the improvements in DSSIM and LPIPS are significant. When compared to NeRFPlayer, the margin is larger for all metrics. Visual comparisons are shown in Fig. 5. Our method depicts sharper details and fewer artifacts than the others." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 514, + 162, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 514, + 162, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 514, + 162, + 525 + ], + "type": "text", + "content": "6.3. Technicolor Dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 532, + 286, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 286, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 286, + 602 + ], + "type": "text", + "content": "Technicolor Light Field Dataset [76] contains videos taken with a 4x4 camera array. Each camera is time-synchronized and the spatial resolution is " + }, + { + "bbox": [ + 46, + 532, + 286, + 602 + ], + "type": "inline_equation", + "content": "2048 \\times 1088" + }, + { + "bbox": [ + 46, + 532, + 286, + 602 + ], + "type": "text", + "content": ". In alignment with HyperReel [4], we hold out the camera at second row second column and evaluate on five scenes (Birthday, Fabien, Painter, Theater, Trains) at full resolution." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 603, + 286, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 603, + 286, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 603, + 286, + 639 + ], + "type": "text", + "content": "Tab. 3 shows the comparisons, where our method achieves noticeable gain in quality and speed. Please refer to supplementary material for visual comparisons." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 647, + 140, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 140, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 140, + 659 + ], + "type": "text", + "content": "6.4. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "To evaluate the effectiveness of proposed components, we conduct an ablation study in Tab. 4 using all the five scenes from Technicolor Dataset. Below we describe the configuration and performance of each ablation baseline." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "Temporal Opacity. \"w/o Temporal Opacity\" fixes the center and scale of the temporal radial basis functions during training. This variant suffers from a significant performance drop, revealing the importance of temporal opacity." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 120, + 545, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 120, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 304, + 120, + 545, + 190 + ], + "type": "text", + "content": "Polynomial Motion and Rotation. \"w/o Polynomial Motion\" and \"w/o Polynomial Rotation\" fix the spatial position and rotation of STGs respectively. Both lead to a performance drop. Comparatively, motion is more important than rotation, which motivates us to use a lower-degree polynomial for rotation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": "Feature Splatting. \"w/o Feature Splatting\" uses the base RGB color " + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "inline_equation", + "content": "\\mathbf{F}^{base}" + }, + { + "bbox": [ + 304, + 192, + 545, + 239 + ], + "type": "text", + "content": " as the final color. It can be seen that there is a moderate drop in quality due to reduced ability to model view- and time-dependent appearance." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 323 + ], + "type": "text", + "content": "Guided Sampling of Gaussians. \"w/o Guided Sampling of Gaussians\" does not encounter much performance drop in this dataset. The reason is that the scenes contain rich textures and can be well covered by SfM points. However, for other challenging scenes, guided sampling plays an important role (see Fig. 3 and supplementary material for examples)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 323, + 545, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 394 + ], + "type": "text", + "content": "Number of Frames used for Initialization. We further analyzed the number of frames used for initialization in Tab. 5. Using fewer frames slightly downgrade quality, but also significantly reduces model size. It reveals that the compactness of our method can be further enhanced with a good selection of frames for initialization." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 403, + 382, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 382, + 415 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 382, + 415 + ], + "type": "text", + "content": "6.5. Limitations" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 545, + 529 + ], + "type": "text", + "content": "Although our representation achieves fast rendering speed, it cannot be trained on-the-fly. The support for on-the-fly training could benefit numerous streaming applications. To achieve this, advanced initialization techniques could be explored to accelerate the training process or alleviate the requirement of per-scene training. On the other hand, our method currently focuses on multi-view video inputs. It is promising to adapt our approach to monocular setting by combining with regularization or generative priors." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 540, + 378, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 540, + 378, + 552 + ], + "spans": [ + { + "bbox": [ + 306, + 540, + 378, + 552 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 559, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 703 + ], + "type": "text", + "content": "We present a novel representation based on Spacetime Gaussians for dynamic view synthesis. The proposed Spacetime Gaussians are enhanced with temporal opacity and parametric motion/rotation to model complex 4D content. To increase model compactness and encode view/time-dependent appearance, we introduce splatted feature rendering, which utilizes neural features and a lightweight MLP instead of spherical harmonics. Additionally, we leverage guided sampling of Gaussians to further improve the rendering quality of complex scenes. Experiments on real-world datasets show that our representation delivers state-of-the-art quality at high resolution and FPS, while maintaining a compact model size." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8515" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 58, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. 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IEEE, 2001. 3" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 316, + 757 + ], + "type": "text", + "content": "8520" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 12 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spanning Training Progress_ Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning/aa264c21-255c-4403-aadd-d1e518b57566_content_list.json b/2024/Spanning Training Progress_ Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning/aa264c21-255c-4403-aadd-d1e518b57566_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..623a02a3e291028d41109c95281d69921b10b83b --- /dev/null +++ b/2024/Spanning Training Progress_ Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning/aa264c21-255c-4403-aadd-d1e518b57566_content_list.json @@ -0,0 +1,1812 @@ +[ + { + "type": "text", + "text": "Spanning Training Progress: Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning", + "text_level": 1, + "bbox": [ + 122, + 128, + 846, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xin Zhang $^{1,2*}$ Jiawei Du $^{2,3\\dagger}$ Yunsong Li $^{1}$ Weiying Xie $^{1‡}$ Joel Tianyi Zhou $^{2,3‡}$", + "bbox": [ + 156, + 200, + 818, + 237 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research (A*STAR), Singapore \n $^{3}$ Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore \nxinzhang01@stu.xidian.edu.cn, {dujw, Joey_Zhou}@cfar.astar.edu.sg \n{ysli, wyxie}@mail.xidian.edu.cn", + "bbox": [ + 122, + 239, + 843, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 344, + 313, + 359 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dataset pruning aims to construct a coreset capable of achieving performance comparable to the original, full dataset. Most existing dataset pruning methods rely on snapshot-based criteria to identify representative samples, often resulting in poor generalization across various pruning and cross-architecture scenarios. Recent studies have addressed this issue by expanding the scope of training dynamics considered, including factors such as forgetting event and probability change, typically using an averaging approach. However, these works struggle to integrate a broader range of training dynamics without overlooking well-generalized samples, which may not be sufficiently highlighted in an averaging manner. In this study, we propose a novel dataset pruning method termed as Temporal Dual-Depth Scoring (TDDS), to tackle this problem. TDDS utilizes a dual-depth strategy to achieve a balance between incorporating extensive training dynamics and identifying representative samples for dataset pruning. In the first depth, we estimate the series of each sample's individual contributions spanning the training progress, ensuring comprehensive integration of training dynamics. In the second depth, we focus on the variability of the sample-wise contributions identified in the first depth to highlight well-generalized samples. Extensive experiments conducted on CIFAR and ImageNet datasets verify the superiority of TDDS over previous SOTA methods. Specifically on CIFAR100, our method achieves $54.51\\%$ accuracy with only $10\\%$ training data, surpassing baselines methods by more than $12.69\\%$ . Our codes are available at https://github.com/zhangxin-xd/Dataset-Pruning-TDDS.", + "bbox": [ + 76, + 378, + 473, + 832 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/082cb78abe905810a38b2fea4fa61bfe7c1604b8009c1cd5426c6e86204853b9.jpg", + "image_caption": [ + "Figure 1. (a) Coresetets constructed by snapshot-based dataset pruning tend to fluctuate depending on the epochs selected for data selection. The red and blue points represent the data samples of two coresets constructed with $90\\%$ pruning rate at Epoch 10 and 100 from the same training progress, respectively. (b) Snapshot-based coresets fail to generalize to pruning settings, especially pruning rates. The accuracy gap between coresets constructed at Epoch 10 and 100 is increasing as the pruning rate grows. Here, we measure importance using the error vector score, a classic snapshot-based criterion defined in [31]. These scores are obtained by training ResNet-18 on CIFAR-10." + ], + "image_footnote": [], + "bbox": [ + 513, + 340, + 885, + 462 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 659, + 632, + 674 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Explosively growing datasets [9, 20, 52, 53] have been crucial for the success of deep neural networks (DNNs) in various applications [7, 21, 35, 50]. However, learning from large-scale datasets is both time-consuming and financially prohibitive [5, 27, 39, 40, 44, 48]. Actually, a substantial portion of data samples are redundant [43, 46, 51], which means they can be excluded from training without compromising performance.", + "bbox": [ + 496, + 686, + 892, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Numerous dataset pruning works [12, 16, 17, 22, 25, 29, 32, 46, 49] have explored various criteria [13, 41] for identifying important data samples, including distribution distance [45, 46], uncertainty [8], loss [31, 43], and gradient [31]. Most of them evaluate sample importance using a snapshot of training progress. For example, Paul et al. [31]", + "bbox": [ + 496, + 809, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Equal contribution. \n $\\ddagger$ Corresponding authors. \n*Work completed during internship at A*STAR", + "bbox": [ + 94, + 862, + 346, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "26223", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "uses the error vector score generated by a few epochs $^{1}$ in early training; Xia et al. [46] calculates the distribution distances of features at the end of training.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, these snapshot-based pruning methods have two potential problems. Firstly, the importance scores of samples fluctuate with epochs during the progress of training. Consequently, the coresets constructed by the importance scores at different snapshots of training progress differ from each other significantly. As verified in Figure 1(a), the coresets constructed at Epoch 10 and 100 obviously contain different samples. Secondly, relying on importance scores from a snapshot can lead to overfitting in the construction of the coreset, as this approach may not generalize well across different scenarios, such as varying pruning rates. As shown in Figure 1(b), the accuracy gap of coresets from different snapshots becomes larger as the pruning rate increases.", + "bbox": [ + 75, + 137, + 468, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these two problems, a straightforward approach is to consider a broader range of training dynamics throughout the training process, with a focus on selecting well-generalized data samples. For example, Pleiss et al. [33] involves training dynamics by measuring the probability gap between the target class and the second largest class in each epoch; Toneva et al. [43] monitors the forgetting events throughout the entire training process. These forgetting events occur when samples, classified correctly in a prior epoch, are subsequently predicted incorrectly. Unfortunately, existing studies fall short of balancing the incorporation of training dynamics with the effective identification of well-generalized samples. The use of an averaging down-sampling operation aims to cover a broader range of training dynamics. However, this approach can inadvertently lead to the neglect of well-generalized samples during data selection, ultimately degrading overall performance.", + "bbox": [ + 75, + 333, + 468, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose Temporal Dual-Depth Scoring (TDDS) pruning method, designed to effectively balance and address the aforementioned problems. We employ a dual-depth temporal scoring metric that spans the training process for data selection. In the inner level (depth one), we approximate the actual contribution of each sample in every epoch. This approximation is achieved by projecting the sample-wise gradients onto the accumulated gradient in each epoch, following the approach suggested by Du et al. [11]. We then integrate these contributions over a specified window, typically spanning 10 epochs, to incorporate more training dynamics. In the outer level (depth two), we reduce reliance on the averaging down-sampling operation to prevent overlooking vital samples. Well-generalized samples are identified based on the variability of the projected gradients, calculated in each window from the inner level. This design of the outer level draws inspiration from He et al. [15], who tracked the variance of predicted target probabilities throughout training to enhance pruning effectiveness.", + "bbox": [ + 75, + 590, + 468, + 877 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The pipeline of our proposed TDDS is clearly illustrated in Figure 2. Extensive experiments demonstrate the superior generalization capability of the proposed TDDS, enabling it to outperform other comparison methods across different pruning settings on various datasets and networks. For example, on CIFAR-100, our method achieves $54.51\\%$ accuracy with only $10\\%$ training data, surpassing random selection by $7.83\\%$ and other SOTA methods by at least $12.69\\%$ .", + "bbox": [ + 500, + 90, + 890, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our main contributions are summarized as:", + "bbox": [ + 517, + 215, + 805, + 229 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We examine the poor generalization resulting from existing snapshot-based dataset pruning. Subsequently, we analyze the inefficacy of current solutions to this generalization issue, attributing it to the inability to balance the incorporation of training dynamics with the effective identification of well-generalized samples.", + "- We thereby propose a novel dataset pruning method called Temporal Dual-Depth Scoring (TDDS), resorting to two temporal depths/levels to take respective care of the contribution evaluation and generalization spanning training progress. Experiments on diverse datasets and networks demonstrate the effectiveness of TDDS, achieving SOTA performance." + ], + "bbox": [ + 500, + 233, + 890, + 429 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 453, + 648, + 469 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Dataset Pruning", + "text_level": 1, + "bbox": [ + 500, + 481, + 661, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dataset Pruning, also known as Coreset Selection aims to shrink the dataset scale by selecting important samples according to some predefined criteria. Herding [6, 45] and Moderate [46] calculate the distance in feature space. Entropy [8] and Cal [24] explore the uncertainty and decision boundary with the predicted outputs. GradND/EL2N [31] quantifies the importance of a sample with its gradient magnitude. Most of these methods are snapshot-based, that is they do not care about the training dynamics that actually distinguish the behaviors of samples in the overall optimization. There are some efficient training methods [10, 28, 42, 47], which focus more on training efficiency and execute online selection spanning training progress. For example, gradient matching-based methods GradMatch [18] and Craig [26] minimize the distance between gradients produced by the full dataset and coreset. ACS [17] selects samples with larger gradient magnitude to accelerate quantization-aware training. These methods can capture training dynamics but often necessitate repeated importance re-evaluating and can not be generalized to different networks. Some methods such as Forgetting [43] and AUM [33] also have proved training dynamics benefits samples importance assessment. However, the downsampling operation, which averages dynamics across training, disregards the variability crucial for evaluating sample generalization, ultimately resulting in suboptimal coresets.", + "bbox": [ + 496, + 507, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "Usually, the first 10 or 20 epochs.", + "bbox": [ + 94, + 886, + 281, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "26224", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Variance in Deep Learning", + "text_level": 1, + "bbox": [ + 76, + 90, + 318, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Variance, a standard second-order statistic, revealing the variability along a certain dimension, has been explored in numerous works [4, 30, 34]. For example, MVT [30] transfers the observed variance of one class to another to improve the robustness of the unseen examples and few-shot learning tasks. VICReg [4] maintains variance of embeddings to prevent the collapse in which two branches produce identical outputs regardless of inputs. For the gradient, its variance along the parameter dimension is an approximation of Hessian matrix indicating loss landscape. Based on that, Fishr [34] matches domain-level variances of gradients for out-of-distribution generalization. LCMat [37] induces a better adaptation of the pruned dataset on the perturbed parameter region than the exact point matching. Besides, calculating gradient variance along time dimension tracks dynamic optimization change. VoG [1] uses this to estimate sample importance and the visualization shows that high-variance samples are more worthwhile to learn. Dyn-Unc [15] calculates the time-dimension variance of predicted target class probability to evaluate sample importance. Differing from VoG and Dyn-Unc, our TDDS does not need pixel-wise gradient calculation while considering non-target probabilities, which enables a more precise evaluation with lower computational overhead.", + "bbox": [ + 75, + 113, + 473, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 489, + 202, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Throughout this paper, we denote the full training dataset as $\\mathbb{U} = \\{(x_n,y_n)\\}_{n = 1}^N$ , where $x_{n}\\in \\mathbb{R}^{D}$ and $y_{n}\\in \\mathbb{R}^{1\\times C}$ are drawn i.i.d. from a natural distribution $\\mathcal{D}$ . We denote a neural network parameterized with weight matrix $\\pmb{\\theta}$ as $f_{\\pmb{\\theta}}$ . Under these definitions, the optimization objective of $f_{\\pmb{\\theta}}$ on $\\mathbb{U}$ is to minimize empirical risk $\\mathcal{L}(\\mathbb{U};\\pmb {\\theta}) = \\frac{1}{N}\\sum_{n = 1}^{N}\\ell (f_{\\pmb{\\theta}}(\\pmb {x}_n),\\pmb {y}_n)$ , where $f_{\\pmb{\\theta}}(\\pmb {x}_n)\\in \\mathbb{R}^{1\\times C}$ outputs the predicted probabilities of each class. Typically, $\\pmb{\\theta}$ is updated as follow2,", + "bbox": [ + 75, + 515, + 468, + 652 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} _ {t + 1} = \\boldsymbol {\\theta} _ {t} - \\eta \\sum_ {n = 1, \\boldsymbol {x} _ {n} \\in \\mathbb {U}} ^ {N} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 661, + 468, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\eta$ is the learning rate and $\\pmb{g}_t(\\pmb{x}_n)$ is defined as the gradient calculated over the data pair $(\\pmb{x}_n, \\pmb{y}_n)$ in epoch $t$ .", + "bbox": [ + 75, + 715, + 468, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dataset pruning aims to enhance training efficiency by constructing a coreset $\\mathbb{S} = \\{(x_n,y_m)\\}_{m = 1}^M$ , $\\mathbb{S}\\subset \\mathbb{U}$ that can achieve comparable performance to $\\mathbb{U}$ . The objective of dataset pruning can be formulated as,", + "bbox": [ + 75, + 747, + 468, + 806 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\substack {(\\boldsymbol {x}, \\boldsymbol {y}) \\sim \\mathcal {D} \\\\ \\boldsymbol {\\theta} _ {0} \\sim \\mathcal {P} _ {\\boldsymbol {\\theta} _ {0}}}} {\\mathbb {E}} \\left[ \\ell \\left(f _ {(\\mathrm {U}, \\boldsymbol {\\theta} _ {0})} (\\boldsymbol {x}), \\boldsymbol {y}\\right) \\right] \\simeq \\underset {\\substack {(\\boldsymbol {x}, \\boldsymbol {y}) \\sim \\mathcal {D} \\\\ \\boldsymbol {\\theta} _ {0} \\sim \\mathcal {P} _ {\\boldsymbol {\\theta} _ {0}}}} {\\mathbb {E}} \\left[ \\ell \\left(f _ {(\\mathrm {S}, \\boldsymbol {\\theta} _ {0})} (\\boldsymbol {x}), \\boldsymbol {y}\\right) \\right], \\tag{2}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 816, + 467, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f_{(\\mathbb{U},\\pmb{\\theta}_0)}$ and $f_{(\\mathbb{S},\\pmb{\\theta}_0)}$ represent the networks trained on $\\mathbb{U}$ and $\\mathbb{S}$ with weight $\\pmb{\\theta}_0$ initialized from distribution $\\mathcal{P}_{\\pmb{\\theta}_0}$ .", + "bbox": [ + 500, + 90, + 890, + 122 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Methodology", + "text_level": 1, + "bbox": [ + 500, + 132, + 633, + 148 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As discussed earlier, despite that exploring long-range dynamics provides a more comprehensive sample evaluation, the averaging operation hinders the construction of a coreset with strong generalization. In this section, we present the proposed Temporal Dual-Depth Scoring (TDDS) strategy, which balances the incorporation of training dynamics and the identification of well-generalized samples. In the outer level, we identify samples with their variability during training which is encouraged theoretically by the optimization space matching between coreset and original dataset (refer to Section 4.1). In the inner level, the gradient in the outer level is replaced with the projected component on the accumulated direction to estimate valid contributions in every epoch (refer to Section 4.2). Finally, to enhance efficiency, we conduct TDDS with a moving window (refer to Section 4.3). The proposed TDDS is summarized in Algorithm 1.", + "bbox": [ + 496, + 157, + 890, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Outer Level: Enhance Coreset Generalization by Maximizing Variance", + "text_level": 1, + "bbox": [ + 498, + 406, + 890, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To construct the coreset $\\mathbb{S}$ satisfying Equation 2, gradient-based methods [3, 18, 26] propose to minimize the distance between full dataset and coreset gradient,", + "bbox": [ + 496, + 444, + 890, + 491 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\min } \\| \\boldsymbol {G} _ {t, \\mathrm {U}} - \\tilde {\\boldsymbol {G}} _ {t, \\mathbb {S}} \\|, \\quad \\text {w h e r e}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 494, + 859, + 520 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {G} _ {t, \\mathbb {U}} = \\sum_ {\\substack {n = 1, \\\\ \\boldsymbol {x} _ {n} \\in \\mathbb {U}}} ^ {| \\mathbb {U} |} \\boldsymbol {g} _ {t} (\\boldsymbol {x} _ {n}), \\quad \\tilde {\\boldsymbol {G}} _ {t, \\mathbb {S}} = \\sum_ {\\substack {m = 1, \\\\ \\boldsymbol {x} _ {m} \\in \\mathbb {S}}} ^ {| \\mathbb {S} |} \\boldsymbol {g} _ {t} (\\boldsymbol {x} _ {m}), \\tag{3}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 525, + 890, + 578 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\tilde{G}_{t,\\mathbb{S}}$ can be regarded as the gradient reconstruction in coreset space. To solve this minimization problem, Huang et al. [17] recommends pruning samples with smaller gradient magnitudes to minimize their potential impact on optimization.", + "bbox": [ + 498, + 584, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, whenever the distance is minimized, the obtained snapshot-based coreset fails to generalize across training progress. Here are the reasons: (1) the distinctive contributions of samples are temporal statistics. Evaluating them at a specific time point causes significant bias when considering dynamic optimization; (2) samples with larger individual gradients dominate the matching process. Without considering the current optimization context, these samples introduce a substantial error in approximating the accumulated gradient.", + "bbox": [ + 496, + 660, + 890, + 811 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To address the first issue, we proposed to extend Equation 3 to a continuous training duration to capture training dynamics,", + "bbox": [ + 496, + 811, + 890, + 856 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\min } \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\| \\boldsymbol {\\mathcal {G}} _ {t, \\mathbb {U}} - \\tilde {\\boldsymbol {\\mathcal {G}}} _ {t, \\mathbb {S}} \\| ^ {2}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 862, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2Here, $t$ indicates epoch and the batch-wise updates [2] in one epoch are omitted.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "26225", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/07bd123adda81a9ec948be85dac64ebcef742fcf69b43c051175704c110158fb.jpg", + "image_caption": [ + "Figure 2. The pipeline of our proposed TDDS. First, we record individual predicted probabilities of samples $f_{t_i}^{x_n} = f_{\\theta_{t_i}}(\\pmb{x}_n)$ during training. Then, we approximate the projected gradient, i.e. the component of gradient $g_{t_i}^{x_n} = g_{t_i}(\\pmb{x}_n)$ on accumulated gradient $G_{t_i}$ direction, with KL-based loss difference between two adjacent epochs. Next, the projected gradients are used to estimate individual contributions of samples. Finally, the important samples are identified with larger projected gradient variances over time." + ], + "image_footnote": [], + "bbox": [ + 140, + 85, + 831, + 329 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, the gradients generated by $\\mathbb{U}$ and $\\mathbb{S}$ at epoch $t$ are defined as $\\pmb{\\mathcal{G}}_{t,\\mathbb{U}} = [|\\pmb{g}_t(\\pmb{x}_n)|]_{n=1}^N$ and similarly $\\tilde{\\pmb{G}}_{t,\\mathbb{S}}$ is its reconstructed counterpart using $\\mathbb{S}$ . Here we use magnitude instead of gradient itself to balance the training dynamic integration and complexity. Experiments in Section 5.4 also shows that magnitude-based minimization performs better than gradient-based when considering continuous training.", + "bbox": [ + 75, + 421, + 468, + 527 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Directly solving Equation 4 is NP-hard. Thus, we turn to its equivalent, temporal gradient variance maximization,", + "bbox": [ + 75, + 527, + 468, + 558 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\max } \\mathcal {R} (\\mathbb {S}), \\quad \\mathcal {R} (\\mathbb {S}) = \\sum_ {t = 1} ^ {T} \\| \\boldsymbol {G} _ {t, \\mathbb {S}} - \\overline {{\\boldsymbol {G}}} _ {\\mathbb {S}} \\| ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 568, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{\\pmb{G}}_{\\mathbb{S}} = \\frac{1}{T}\\sum_{t = 1}^{T}\\pmb{G}_{t,\\mathbb{S}},\\pmb{G}_{t,\\mathbb{S}} = [|\\pmb{g}_t(\\pmb{x}_m)|]_{m = 1}^M$ is the mean gradient over training time. Detailed proof can be founded in Supplementary. Equation 5 measures the variability of samples and enhances the identification of wellgeneralized samples compared to previous average-based methods [33, 43].", + "bbox": [ + 75, + 619, + 468, + 713 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Inner Level: Estimate Actual Contribution with Projected Gradient", + "text_level": 1, + "bbox": [ + 76, + 722, + 468, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "According to Equation 5, sample importance can be evaluated with its gradient variance over time. For any sample $\\boldsymbol{x}_n$ , we have,", + "bbox": [ + 75, + 760, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} (\\boldsymbol {x} _ {n}) = \\sum_ {t = 1} ^ {T} \\left\\| \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| - \\overline {{\\left| \\boldsymbol {g} \\left(\\boldsymbol {x} _ {n}\\right) \\right|}} \\right\\| ^ {2}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 815, + 468, + 857 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{|\\pmb{g}(\\pmb{x}_n)|} = \\frac{1}{T}\\sum_{t=1}^{T}|\\pmb{g}_t(\\pmb{x}_n)|$ . Equation 6 treats sample-wise gradient independently, which may not pre", + "bbox": [ + 76, + 867, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/0407cbe5c8ad1019ed75f4a865863849988bb84e52da32f0d9aa6499f6581993.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 506, + 417, + 694, + 532 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/88b6cbdc6087fee669125ffd370904b292cf2dc052afe505308f365f25dc4c48.jpg", + "image_caption": [ + "(b)", + "Figure 3. Incorporating sample-wise gradient in the current optimization context. After projecting onto the current accumulated gradient, samples with similar gradients exhibit different behaviors." + ], + "image_footnote": [], + "bbox": [ + 702, + 434, + 890, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "cisely describe the valid contribution in the current optimization context. That is the second problem mentioned in Section 4.1. As illustrated in Figure 3(a), the gradient of sample $\\boldsymbol{x}_n$ remains constant between $t$ and $t + 1$ . However, when incorporating it into the current optimization context, its valid contribution undergoes a significant shift. Thus, we propose to calculate the gradient variance after projecting it on the accumulated direction, that is, $|\\boldsymbol{g}_t(\\boldsymbol{x}_n)|$ is reformulated as,", + "bbox": [ + 496, + 650, + 890, + 785 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| = \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\cdot \\sum_ {j = 1, \\boldsymbol {x} _ {j} \\in \\mathbb {U}} ^ {| \\mathbb {U} |} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {j}\\right) \\right|. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 797, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Calculating Equation 6 requires sample-wise gradients over a period of $T$ , which is not feasible due to time and memory constraints. According to Equation 1, the accumu", + "bbox": [ + 498, + 854, + 892, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "26226", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "lated gradient is equal to $\\frac{1}{\\eta} (\\pmb{\\theta}_t - \\pmb{\\theta}_{t + 1})$ , thus the projection in Equation 7 is reformed as loss difference,", + "bbox": [ + 75, + 90, + 468, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| = \\frac {1}{\\eta} \\left| \\left(\\boldsymbol {\\theta} _ {t} - \\boldsymbol {\\theta} _ {t + 1}\\right) \\nabla_ {\\boldsymbol {\\theta} _ {t}} \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right), \\boldsymbol {y} _ {n}\\right) \\right| \\tag {8} \\\\ \\approx \\frac {1}{\\eta} \\left| \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t + 1}} (\\boldsymbol {x} _ {n}), \\boldsymbol {y} _ {n}\\right) - \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t}} (\\boldsymbol {x} _ {n}), \\boldsymbol {y} _ {n}\\right) \\right|, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 132, + 468, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "which can be deduced from the first-order Taylor expansion.", + "bbox": [ + 76, + 207, + 467, + 222 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus, we can evaluate the per-sample contribution to the accumulated gradient direction with its loss change. In the context of classification, $\\ell$ is typically Cross Entropy (CE) loss,", + "bbox": [ + 75, + 222, + 467, + 280 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\ell_ {t} ^ {n} = \\boldsymbol {y} _ {n} ^ {\\top} \\cdot \\log \\frac {f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right)}{f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right)}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 281, + 468, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Delta \\ell_t^n = \\ell(f_{\\theta_{t+1}}(\\pmb{x}_n), \\pmb{y}_n) - \\ell(f_{\\pmb{\\theta}_t}(\\pmb{x}_n), \\pmb{y}_n)$ . Due to the one-hot $\\pmb{y}_n$ , non-target probabilities are unfortunately overlooked, obliterating a significant amount of distinctive information. This reminds us of the Kullback-Leibler (KL) divergence loss, which can be achieved by simply replacing $\\pmb{y}_n$ with $f_{\\pmb{\\theta}_{t+1}}(\\pmb{x}_n)$ ,", + "bbox": [ + 76, + 321, + 468, + 414 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\ell_ {t} ^ {n} = f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right) ^ {\\top} \\cdot \\log \\frac {f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right)}{f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right)}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 426, + 468, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering that $f_{\\pmb{\\theta}_t(\\pmb{x}_n)}$ follows a Bernoulli distribution $\\mathcal{B}(p_t)$ , where $p_t$ represents the probability of the target class at epoch $t$ . If $p_t$ equals $p_{t + 1}$ , Equation 9 fails to distinguish, but Equation 10 can still differentiate the contributions of samples with $q_{t}$ and $q_{t + 1}$ . Here, $q_{t}$ and $q_{t + 1}$ are the non-target probability distributions. This effectiveness has been proved in Section 5.4.", + "bbox": [ + 75, + 470, + 468, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Efficient Implementation of TDDS", + "text_level": 1, + "bbox": [ + 76, + 585, + 375, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When computing $\\mathcal{R}(\\pmb{x}_n)$ with Equation 6, Equation 8, and Equation 10, storing $T$ -epoch predicted outputs may lead to out-of-memory problems, especially with large datasets like ImageNet (containing 1, 281, 167 samples across 1,000 classes). As a solution, we suggest an efficient calculation using an exponential moving average (EMA) weighting strategy. For any training point $t \\geq K$ , the variance $\\mathcal{R}_t(\\pmb{x}_n)^3$ is computed over a $K$ -epoch window ranging from $t - K + 1$ to $t$ ,", + "bbox": [ + 75, + 609, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) = \\sum_ {t - K + 1} ^ {t} \\left\\| \\left| \\Delta \\ell_ {t} ^ {n} \\right| - \\overline {{\\left| \\Delta \\ell_ {t} ^ {n} \\right|}} \\right\\| ^ {2}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 757, + 468, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\overline{|\\Delta\\ell_t^n|}$ is the average of loss difference in a window. For $T$ -epoch trajectory, $T - K + 1$ windows are weighted as,", + "bbox": [ + 76, + 811, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} \\left(\\boldsymbol {x} _ {n}\\right) = \\beta \\mathcal {R} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) + (1 - \\beta) \\mathcal {R} \\left(\\boldsymbol {x} _ {n}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 858, + 468, + 875 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\beta$ is the decay coefficient of EMA whose setting is examined in Section 5.3. With this EMA, we only need to store predicted outputs for one window, significantly alleviating storage burden.", + "bbox": [ + 496, + 90, + 890, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After sorting $\\{\\mathcal{R}(\\pmb{x}_n)\\}_{n=1}^N$ , the top-M samples are selected to construct coreset denoted as $\\{\\mathbb{S}, r\\} = \\{(x_m, y_m), \\mathcal{R}(x_m)\\}_{m=1}^M$ . Since, the samples with larger $\\mathcal{R}(\\pmb{x}_m)$ contribute more in the original data training. We remark that this dominance should be maintained in coreset training, i.e.,", + "bbox": [ + 498, + 151, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\theta} _ {t + 1} = \\boldsymbol {\\theta} _ {t} - \\eta \\sum_ {m = 1} ^ {M} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {m}\\right) \\mathcal {R} \\left(\\boldsymbol {x} _ {m}\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 251, + 890, + 292 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This helps to transfer relative sample importance to coreset training. This effectiveness is proved in Section 5.4.", + "bbox": [ + 498, + 301, + 890, + 332 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 Temporal Dual-Depth Scoring (TDDS)", + "bbox": [ + 500, + 345, + 849, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Training dataset U; A network $f_{\\theta}$ with weight $\\theta$ ; Learning rate $\\eta$ ; Epochs $T$ ; Iterations $I$ per epoch; Window size $K$ ; Decay factor $\\beta$ .", + "bbox": [ + 498, + 362, + 888, + 422 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "1: for $t = 1$ to $T$ do", + "bbox": [ + 509, + 426, + 647, + 439 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2: for $i = 1$ to $I$ , Sample a mini-batch $\\mathbb{B}_i \\subset \\mathbb{U}$ do", + "bbox": [ + 509, + 441, + 854, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3: Record predicted probabilities $f_{\\pmb{\\theta}_t}(x_n)$ , $x_n \\in \\mathbb{B}_i$", + "bbox": [ + 509, + 455, + 880, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4: Calculate $\\Delta \\ell_t^n$ for each $\\pmb{x}_n\\in \\mathbb{B}_i$", + "bbox": [ + 509, + 470, + 774, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\triangleright$ Defined in Equation 10", + "bbox": [ + 715, + 487, + 883, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5: Update weight $\\pmb{\\theta}_{i + 1} = \\pmb{\\theta}_i - \\eta \\pmb{G}_{t,\\mathbb{B}_i}$", + "bbox": [ + 509, + 501, + 795, + 516 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6: end for", + "bbox": [ + 509, + 517, + 598, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "7: if $K \\leq t \\leq T$ then", + "bbox": [ + 509, + 531, + 673, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "8: Calculate $\\mathcal{R}_t(\\pmb{x}_n)$ in one window, $\\pmb{x}_n\\in \\mathbb{U}$", + "bbox": [ + 509, + 546, + 841, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\triangleright$ Defined in Equation 11", + "bbox": [ + 715, + 561, + 880, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "9: Update $\\mathcal{R}(\\pmb{x}_n)$ with EMA, $\\pmb{x}_n\\in \\mathbb{U}$", + "bbox": [ + 509, + 577, + 795, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\triangleright$ Defined in Equation 12", + "bbox": [ + 718, + 592, + 887, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "10: end if", + "bbox": [ + 504, + 607, + 589, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "11: end for", + "bbox": [ + 504, + 622, + 581, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "12: Select Top-M $\\{\\mathbb{S},r\\} \\leftarrow \\{(\\pmb {x}_m,\\pmb {y}_m),\\mathcal{R}(\\pmb {x}_m)\\}_{m = 1}^M$", + "bbox": [ + 504, + 636, + 859, + 652 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Selected subset $\\mathbb{S} = \\{(x_m, y_m)\\}_{m=1}^M$ ; associated sample-wise importance $r = \\{\\mathcal{R}(x_m)\\}_{m=1}^M$", + "bbox": [ + 504, + 652, + 890, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 714, + 630, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Experiment Settings", + "text_level": 1, + "bbox": [ + 500, + 739, + 692, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Networks. The effectiveness of the proposed TDDS is evaluated on three popular benchmarks, i.e., CIFAR-10, CIFAR-100 [19], and ImageNet-1K [9] with three networks, i.e., ResNet-18, ResNet-34 [14], and SwinT [21]. We also verify the cross-architecture performance on four networks including ResNet-50 [14], VGG-16 [38], MobileNet-v2 [36], and ShuffleNet [23].", + "bbox": [ + 496, + 762, + 890, + 868 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training Hyperparameters. Theoretically, if pruning rate $p = 1 - \\frac{|\\mathbb{S}|}{|\\mathbb{U}|}$ , where $0 < p \\leq 1$ , the training process", + "bbox": [ + 496, + 869, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "3The constant coefficient $\\eta$ has been omitted.", + "bbox": [ + 94, + 886, + 334, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "26227", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e0f3bed757ebb2ecd46d086ebdd305963e460f561b66fb3c13e2978ed6aa7b72.jpg", + "table_caption": [ + "Table 1. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-E. The model trained with the full dataset achieves $95.23\\%$ and $78.21\\%$ accuracy." + ], + "table_footnote": [], + "table_body": "
pCIFAR-10CIFAR-100
30%50%70%80%90%30%50%70%80%90%
Random94.58 ±0.0493.38 ±0.1790.61 ±0.4488.87 ±0.4783.77 ±0.2675.53 ±0.0471.95 ±0.1664.59 ±0.3257.79 ±0.2446.68 ±1.07
Entropy [8]94.45 ±0.0791.90 ±0.1686.24 ±0.2683.49 ±0.2172.06 ±0.8172.39 ±0.2064.44 ±0.3650.73 ±0.8642.86 ±0.2529.56 ±0.54
Forgetting [43]95.45 ±0.2495.05 ±0.0589.14 ±2.0476.18 ±3.1845.87 ±1.8777.38 ±0.0970.76 ±0.4049.92 ±0.2838.42 ±1.1325.82 ±0.52
EL2N [31]95.43 ±0.1095.06 ±0.0486.69 ±1.7168.64 ±3.7031.89 ±1.5176.89 ±0.3167.57 ±0.1536.45 ±1.3617.31 ±0.339.10 ±0.69
AUM [33]95.44 ±0.0995.19 ±0.0991.19 ±0.6369.60 ±3.1134.74 ±0.1177.35 ±0.1868.17 ±0.5231.69 ±0.3418.43 ±0.479.29 ±0.27
Moderate [46]93.96 ±0.0692.34 ±0.0989.71 ±0.1487.75 ±0.2783.61 ±0.2474.60 ±0.1070.29 ±0.3162.81 ±0.0856.52 ±0.3741.82 ±1.12
Dyn-Unc[15]95.08 ±0.0294.03 ±0.1489.40 ±0.1379.76 ±1.0937.12 ±1.1273.36 ±0.1065.90 ±0.2550.16 ±0.4739.19 ±0.2715.20 ±0.41
TDDS95.47 ±0.0695.21 ±0.0493.03 ±0.2591.30 ±0.2585.46 ±0.2177.56 ±0.0674.04 ±0.3467.78 ±0.4463.01 ±0.1254.51 ±0.22
", + "bbox": [ + 151, + 140, + 823, + 359 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/1723b7d0b0597c5726289285ce12c8c522eee57fc31b6b864b3c8f9bf5c20f6d.jpg", + "image_caption": [ + "Figure 4. Parameter analysis of range $T$ and window size $K$ on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.3, 0.5, 0.7, 0.8, and 0.9." + ], + "image_footnote": [], + "bbox": [ + 81, + 380, + 248, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0c507c469d36d67f48b1297ff526eab9bdbb2e3f4dc1c6427ec71c6404f45969.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 248, + 380, + 410, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/0a274433ea05945a7baecf5df7f098ecd5abcc31dc76b0efb9c20d4f8f7ef1c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 408, + 380, + 571, + 481 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/442b37b32aeb7ff5e9c63d481a917255eb2007cebe8834d2f6a37a6a6f41d019.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 570, + 380, + 732, + 479 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4fd9c50ad27359198197473b053c751b90eb456222ecd4c34adc42e6f051e29d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 730, + 380, + 890, + 479 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f888901dc867509530a218a2501b35998bd140b7905100033b0a985ce5517520.jpg", + "table_caption": [ + "Table 2. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-P. The model trained with the full dataset achieves $95.23\\%$ and $78.21\\%$ accuracy." + ], + "table_footnote": [], + "table_body": "
pCIFAR-10CIFAR-100
30%50%70%30%50%70%
Random94.33 ±0.1793.4 ±0.1790.94 ±0.3874.59 ±0.2771.07 ±0.465.3 ±0.21
Entropy [8]94.44 ±0.292.11 ±0.4785.67 ±0.7172.26 ±0.0863.26 ±0.2950.49 ±0.88
Forgetting [43]95.36 ±0.1395.29 ±0.1890.56 ±1.876.91 ±0.3268.6 ±1.0238.06 ±1.14
EL2N [31]95.44 ±0.1594.61 ±0.2087.48 ±1.3376.25 ±0.2465.90 ±1.0634.42 ±1.50
AUM [33]95.07 ±0.2495.26 ±0.1591.36 ±1.476.93 ±0.3267.42 ±0.4930.64 ±0.58
Moderate [46]93.86 ±0.1192.58 ±0.3090.56 ±0.2774.60 ±0.4171.10 ±0.2465.34 ±0.41
CCS [51]95.40 ±0.1295.04 ±0.3793.00 ±0.1677.14 ±0.3174.45 ±0.1668.92 ±0.12
TDDS95.50 ±0.0795.66 ±0.0893.92 ±0.0477.95 ±0.3074.98 ±0.1669.46 ±0.10
", + "bbox": [ + 81, + 627, + 468, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "speeds up by $\\frac{1}{1 - p}$ times. We consider two coreset training strategies: Strategy-E prioritizes efficiency with same-epoch training on both full dataset and coreset. Strategy-P", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/20fcab60609eab9ac55eb148f1744d81cc96d034d531aac9afcf5092cb90a2b0.jpg", + "table_caption": [ + "Table 3. Comparison of different dataset pruning methods on ImageNet-1K with ResNet-34 under Strategy-E. The model trained with the full dataset achieves $73.54\\%$ Top-1 accuracy." + ], + "table_footnote": [], + "table_body": "
pImageNet-1K
70%80%90%
Random64.1960.7652.63
Entropy[8]62.3456.8043.39
Forgetting [43]64.2962.0152.14
EL2N [31]46.9232.6815.90
AUM [33]39.3423.6411.70
Moderate [46]64.0461.3552.45
TDDS64.6962.5653.91
", + "bbox": [ + 504, + 614, + 906, + 767 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "prioritizes performance by training coreset for more epochs. If $\\frac{|\\mathbb{S}|}{|\\mathbb{U}|} = 1 - p$ , the training process is extended to $\\frac{1}{1 - p}$ times of the original one. For CIFAR-10 and -100, we train ResNet-18 for 200 epochs with a batch size of 128. For ImageNet, ResNet-34 and Swin-T are trained for 60 [51] and 300 epochs [15] with batch sizes of 256 and 1024, respec", + "bbox": [ + 498, + 806, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "26228", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cfa1bd938f063bb9d3ceeb4759c681b98a36ab658794a2aef47ba7740986cc63.jpg", + "image_caption": [ + "Figure 5. Parameter analysis of decay coefficient $\\beta$ on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.7, 0.8, and 0.9." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 472, + 165 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tively. SGD optimizer with momentum of 0.9 and weight decay of 0.0005 is used for update networks. The learning rate is initialized as 0.1 and decays with the cosine annealing scheduler. During experiments, we found that smaller batch size boosts performance at high pruning rates (shown in Supplementary). Thus, for $p = 0.8$ , we halved the batch size, and for $p = 0.9$ , we reduced it to one-fourth. All compared methods use the same settings. With Strategy-P, for example, training a CIFAR coreset with only $50\\%$ training samples takes 400 epochs, while keeping the other hyperparameters unchanged. Considering the time-consuming training, we only conduct Strategy-P experiments at pruning rates of 0.3, 0.5, 0.7.", + "bbox": [ + 75, + 246, + 468, + 441 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. Eight baselines are used for comparison, with the latter seven being SOTA methods: 1) Random; 2) Entropy [8]; 3) Forgetting [43]; 4) EL2N [31]; 5) AUM [33]; 6) Moderate [46]; 7) CCS [51]; 8) Dyn-Unc [15]. Due to the limited page, we provide the technical details of these baselines in Supplementary.", + "bbox": [ + 75, + 441, + 468, + 534 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Benchmark Evaluation Results", + "text_level": 1, + "bbox": [ + 76, + 544, + 352, + 559 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ResNet-18 on CIFAR-10 and 100. Table 1 and Table 2 report the performance of different dataset pruning methods under Strategy-E and P, respectively. Under both strategies, TDDS consistently outperforms other methods. For instance, under Strategy-E, none of the compared methods surpasses Random at aggressive pruning rates, while TDDS achieves $85.46\\%$ and $54.51\\%$ accuracy after pruning $90\\%$ samples of CIFAR-10 and 100 surpassing Random by $1.69\\%$ and $7.83\\%$ , respectively. By extending the training duration, Strategy-P enhances the performance of all methods to varying degrees. TDDS still maintains its superiority, for example, with only $30\\%$ training data, the accuracy on CIFAR-10 and -100 are $93.92\\%$ and $69.46\\%$ outperforming CCS by $0.92\\%$ and $0.54\\%$ , respectively. These results highlight TDDS as a promising choice for both efficiency and performance-oriented dataset pruning.", + "bbox": [ + 75, + 568, + 468, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ResNet on ImageNet-1K. For ImageNet-1K, we train ResNet-34 models on original dataset for 90 epochs to collect training dynamics and then train the model on coreset for 60 epochs as [51]. Experiment results are given in Table 3. The results show that the proposed TDDS has better performance on ImageNet-1K, especially under aggressive", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pruning rates. For example, when pruning $90\\%$ samples, TDDS still achieves $53.91\\%$ which is $1.77\\%$ and $1.46\\%$ higher than Forgetting and Moderate, respectively.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Swin-T on ImageNet-1k. We also evaluate Swin-T on ImageNet-1K. Like Dyn-Unc [15], Table 4 reports the results under four pruning rates. Notably, TDDS consistently outperforms other competitors, for example, after pruning $50\\%$ training data, TDDS achieves $78.33\\%$ accuracy, surpassing Forgetting, Moderate, and Dyn-Unc by $4.01\\%$ , $3.35\\%$ and $0.69\\%$ , respectively.", + "bbox": [ + 496, + 136, + 890, + 242 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6e4cd72a2caf97cfe219d9f9743a649a93a3be4783d62606ba5bcdcf27785016.jpg", + "table_caption": [ + "Table 4. Comparison of different dataset pruning methods on ImageNet-1K with Swin-T under Strategy-E. The model trained with the full dataset achieves $79.58\\%$ Top-1 accuracy." + ], + "table_footnote": [], + "table_body": "
pImageNet-1K
25%30%40%50%
Random77.8277.1875.9374.54
Forgetting [43]78.7078.2777.5574.32
Moderate [46]77.7477.0675.9474.98
Dyn-Unc [15]79.5479.1478.4977.64
TDDS79.7679.5779.0978.33
", + "bbox": [ + 504, + 309, + 906, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Parameter Analysis", + "text_level": 1, + "bbox": [ + 500, + 497, + 687, + 512 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Estimation Range $T$ and Window Size $K$ . Due to the random initialization, models adapt to prominent features (easy samples) during early training. As training progresses, models gradually acquire more abstract and complex features (hard samples) that are challenging to capture in early training. Thus, the importance of samples should be estimated in different training phases with respect to different pruning levels. As shown in Figure 4, we analyze the influence of range $T$ and window size $K$ on perfor", + "bbox": [ + 496, + 520, + 890, + 656 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5a702ebad6d68663f885a9c711b2aa9717836b00fa4fa0dc06e9f7f386c8b765.jpg", + "table_caption": [ + "Table 5. Ablation study for Dual-depth strategy. The numbers in square brackets indicate the improvement in accuracy of the method presented in the current column compared to the corresponding method in the previous column." + ], + "table_footnote": [], + "table_body": "
pCIFAR-100
EL2NEL2N+outerTDDS
30%76.8977.47[+ 0.58]77.56[+ 0.09]
50%67.5773.93[+ 6.36]74.04[+ 0.11]
70%36.4567.04[+30.59]67.78[+ 0.74]
80%17.3158.21[+40.90]63.01[+ 1.80]
90%9.1040.36[+31.26]54.51[+14.15]
outerX✓✓
innerXX✓
", + "bbox": [ + 522, + 747, + 867, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "26229", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61902f4c2dd2e389807233afe2ea6826aa4b6cc4bf1a52862d6bb44a5106631a.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 83, + 85, + 356, + 248 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/94b1ee73542c153601fe8bb8741e4ca6b2b418b8d906b2e55edbdbb16db47187.jpg", + "image_caption": [ + "(b)", + "Figure 6. Ablation studies for (a) Gradient Magnitude vs. Gradient, (b) KL-based Loss Difference, and (c) Importance-aware Coreset Training. In (a), GM and G represent estimating sample contribution with gradient magnitude and gradient, respectively. In (b), KL and CE represent calculating loss difference with KL and CE loss, respectively. In (c), Imp-aware and Imp-unaware represent training coreset with and without weighting samples with their importance scores, respectively." + ], + "image_footnote": [], + "bbox": [ + 356, + 87, + 620, + 248 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/754d2608562739bbf7406ef86c8bbd5498d0e92c40d16ba4b4386b1fec6ad94b.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 620, + 87, + 893, + 248 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mance. Apparently, for a larger pruning rate, we should select samples earlier in training. For CIFAR-100, the optimal $(p,T,K)$ setting is (0.3, 90, 10), (0.5, 70, 10), (0.7, 60, 20), (0.8, 20, 10), and (0.9, 10, 5). The parameter settings of CIFAR-10 and ImageNet are reported in Supplementary.", + "bbox": [ + 75, + 344, + 468, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Decay Coefficient $\\beta$ of EMA. In contrast to the simple average (SA), EMA employs exponential weighting, giving more weight to the most recent window. We examine four values of $\\beta$ , where $\\beta = 0$ represents SA. As illustrated in Figure 5, EMA outperforms SA regardless of the $\\beta$ value chosen. Among the considered pruning levels, $\\beta = 0.9$ yields the best performance, surpassing $\\beta = 0.95$ and $\\beta = 0.85$ .", + "bbox": [ + 75, + 419, + 472, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 558, + 240, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Gradient Magnitude vs Gradient. We use gradient magnitudes in Equation 4. Although gradients themselves appear capable of describing optimization, our experimental findings indicate that the use of gradient magnitudes yields superior performance, as depicted in Figure 6(a). We argue that gradients often prioritize samples with frequently reversing gradients, resulting in unstable training and slower convergence.", + "bbox": [ + 75, + 583, + 468, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "KL-based Loss Difference. As discussed in Section 4.3, the KL loss provides a more comprehensive assessment of loss difference and is expected to precisely characterize sample contribution. To evaluate its effectiveness, we replace KL loss with CE loss and conduct experiments across all considered pruning rates. As illustrated in Figure 6(b), although CE is slightly higher than KL when the pruning rate is $30\\%$ , KL exhibits an absolute advantage at all other pruning levels. For example, when pruning rate is $90\\%$ , KL outperforms CE by a substantial margin of $15.97\\%$ .", + "bbox": [ + 75, + 704, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Importance-aware Coreset Training. We formulate importance-aware subset training as Equation 13. The maintained relative importance provides optimization guid", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ance for subset training. As shown in Figure 6(c), the advantage becomes increasingly pronounced as the pruning rate rises. When pruning rate is $90\\%$ , the accuracy of importance-aware subset training outperforms its unaware counterpart by $6.55\\%$ .", + "bbox": [ + 496, + 344, + 893, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Dual-Depth Strategy. To investigate the effectiveness of the proposed Dual-Depth strategy, we replace the inner depth with EL2N, and Table 5 indicates that incorporating the outer depth boosts EL2N at all considered pruning rates. Nevertheless, this enhancement still falls short of our dual-depth design, particularly evident in aggressive pruning scenarios.", + "bbox": [ + 496, + 419, + 893, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 539, + 617, + 554 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we reveal that the snapshot-based data pruning results in poor generalization across various pruning scenarios. However, existing methods fail to identify well-generalized samples even with evaluation criteria considering the whole training progress. We attribute this to the averaging-based dynamics incorporation and imprecise sample contribution characterization. To address these problems, we propose a dataset pruning method called TDDS, which designs a Temporal Dual-Depth Scoring strategy to balance the incorporation of training dynamics and the identification of well-generalized samples. Extensive experiments on various datasets and networks, demonstrate the SOTA performance of our proposed method.", + "bbox": [ + 496, + 565, + 893, + 762 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 773, + 666, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research is supported in part by the National Natural Science Foundation of China under Grant 62121001, Grant 62322117, and Grant 62371365. This research is also supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research) and Jiawei Du's A*STAR Career Development Fund (CDF) C233312004.", + "bbox": [ + 496, + 799, + 893, + 891 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "26230", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Chirag Agarwal, Daniel D'souza, and Sara Hooker. Estimating example difficulty using variance of gradients. In IEEE Conf. Comput. Vis. Pattern Recog., pages 10368-10378, 2022. 3", + "[2] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. Neurocomputing, 5(4-5):185-196, 1993. 3", + "[3] Lukas Balles, Giovanni Zappella, and Cedric Archambeau. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 17205-17216, 2023. 1" + ], + "bbox": [ + 501, + 92, + 890, + 559 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "26232", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Spanning Training Progress_ Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning/aa264c21-255c-4403-aadd-d1e518b57566_model.json b/2024/Spanning Training Progress_ Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning/aa264c21-255c-4403-aadd-d1e518b57566_model.json new file mode 100644 index 0000000000000000000000000000000000000000..24f6368c77a5e740fb7c8e9777d630fca5f3b049 --- /dev/null +++ b/2024/Spanning Training Progress_ Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning/aa264c21-255c-4403-aadd-d1e518b57566_model.json @@ -0,0 +1,2464 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.124, + 0.13, + 0.848, + 0.177 + ], + "angle": 0, + "content": "Spanning Training Progress: Temporal Dual-Depth Scoring (TDDS) for Enhanced Dataset Pruning" + }, + { + "type": "text", + "bbox": [ + 0.157, + 0.202, + 0.819, + 0.238 + ], + "angle": 0, + "content": "Xin Zhang\\(^{1,2*}\\) Jiawei Du\\(^{2,3\\dagger}\\) Yunsong Li\\(^{1}\\) Weiying Xie\\(^{1‡}\\) Joel Tianyi Zhou\\(^{2,3‡}\\)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.24, + 0.844, + 0.31 + ], + "angle": 0, + "content": "\\(^{2}\\)Centre for Frontier AI Research (CFAR), Agency for Science, Technology and Research (A*STAR), Singapore \n\\(^{3}\\)Institute of High Performance Computing (IHPC), Agency for Science, Technology and Research (A*STAR), Singapore \nxinzhang01@stu.xidian.edu.cn, {dujw, Joey_Zhou}@cfar.astar.edu.sg \n{ysli, wyxie}@mail.xidian.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.345, + 0.314, + 0.361 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.474, + 0.833 + ], + "angle": 0, + "content": "Dataset pruning aims to construct a coreset capable of achieving performance comparable to the original, full dataset. Most existing dataset pruning methods rely on snapshot-based criteria to identify representative samples, often resulting in poor generalization across various pruning and cross-architecture scenarios. Recent studies have addressed this issue by expanding the scope of training dynamics considered, including factors such as forgetting event and probability change, typically using an averaging approach. However, these works struggle to integrate a broader range of training dynamics without overlooking well-generalized samples, which may not be sufficiently highlighted in an averaging manner. In this study, we propose a novel dataset pruning method termed as Temporal Dual-Depth Scoring (TDDS), to tackle this problem. TDDS utilizes a dual-depth strategy to achieve a balance between incorporating extensive training dynamics and identifying representative samples for dataset pruning. In the first depth, we estimate the series of each sample's individual contributions spanning the training progress, ensuring comprehensive integration of training dynamics. In the second depth, we focus on the variability of the sample-wise contributions identified in the first depth to highlight well-generalized samples. Extensive experiments conducted on CIFAR and ImageNet datasets verify the superiority of TDDS over previous SOTA methods. Specifically on CIFAR100, our method achieves \\(54.51\\%\\) accuracy with only \\(10\\%\\) training data, surpassing baselines methods by more than \\(12.69\\%\\). Our codes are available at https://github.com/zhangxin-xd/Dataset-Pruning-TDDS." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.342, + 0.887, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.477, + 0.895, + 0.629 + ], + "angle": 0, + "content": "Figure 1. (a) Coresetets constructed by snapshot-based dataset pruning tend to fluctuate depending on the epochs selected for data selection. The red and blue points represent the data samples of two coresets constructed with \\(90\\%\\) pruning rate at Epoch 10 and 100 from the same training progress, respectively. (b) Snapshot-based coresets fail to generalize to pruning settings, especially pruning rates. The accuracy gap between coresets constructed at Epoch 10 and 100 is increasing as the pruning rate grows. Here, we measure importance using the error vector score, a classic snapshot-based criterion defined in [31]. These scores are obtained by training ResNet-18 on CIFAR-10." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.66, + 0.633, + 0.675 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.893, + 0.808 + ], + "angle": 0, + "content": "Explosively growing datasets [9, 20, 52, 53] have been crucial for the success of deep neural networks (DNNs) in various applications [7, 21, 35, 50]. However, learning from large-scale datasets is both time-consuming and financially prohibitive [5, 27, 39, 40, 44, 48]. Actually, a substantial portion of data samples are redundant [43, 46, 51], which means they can be excluded from training without compromising performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Numerous dataset pruning works [12, 16, 17, 22, 25, 29, 32, 46, 49] have explored various criteria [13, 41] for identifying important data samples, including distribution distance [45, 46], uncertainty [8], loss [31, 43], and gradient [31]. Most of them evaluate sample importance using a snapshot of training progress. For example, Paul et al. [31]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.863, + 0.348, + 0.901 + ], + "angle": 0, + "content": "\\(\\dagger\\) Equal contribution. \n\\(\\ddagger\\) Corresponding authors. \n*Work completed during internship at A*STAR" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26223" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.137 + ], + "angle": 0, + "content": "uses the error vector score generated by a few epochs\\(^{1}\\) in early training; Xia et al. [46] calculates the distribution distances of features at the end of training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.47, + 0.333 + ], + "angle": 0, + "content": "However, these snapshot-based pruning methods have two potential problems. Firstly, the importance scores of samples fluctuate with epochs during the progress of training. Consequently, the coresets constructed by the importance scores at different snapshots of training progress differ from each other significantly. As verified in Figure 1(a), the coresets constructed at Epoch 10 and 100 obviously contain different samples. Secondly, relying on importance scores from a snapshot can lead to overfitting in the construction of the coreset, as this approach may not generalize well across different scenarios, such as varying pruning rates. As shown in Figure 1(b), the accuracy gap of coresets from different snapshots becomes larger as the pruning rate increases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.47, + 0.59 + ], + "angle": 0, + "content": "To address these two problems, a straightforward approach is to consider a broader range of training dynamics throughout the training process, with a focus on selecting well-generalized data samples. For example, Pleiss et al. [33] involves training dynamics by measuring the probability gap between the target class and the second largest class in each epoch; Toneva et al. [43] monitors the forgetting events throughout the entire training process. These forgetting events occur when samples, classified correctly in a prior epoch, are subsequently predicted incorrectly. Unfortunately, existing studies fall short of balancing the incorporation of training dynamics with the effective identification of well-generalized samples. The use of an averaging down-sampling operation aims to cover a broader range of training dynamics. However, this approach can inadvertently lead to the neglect of well-generalized samples during data selection, ultimately degrading overall performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.47, + 0.878 + ], + "angle": 0, + "content": "In this paper, we propose Temporal Dual-Depth Scoring (TDDS) pruning method, designed to effectively balance and address the aforementioned problems. We employ a dual-depth temporal scoring metric that spans the training process for data selection. In the inner level (depth one), we approximate the actual contribution of each sample in every epoch. This approximation is achieved by projecting the sample-wise gradients onto the accumulated gradient in each epoch, following the approach suggested by Du et al. [11]. We then integrate these contributions over a specified window, typically spanning 10 epochs, to incorporate more training dynamics. In the outer level (depth two), we reduce reliance on the averaging down-sampling operation to prevent overlooking vital samples. Well-generalized samples are identified based on the variability of the projected gradients, calculated in each window from the inner level. This design of the outer level draws inspiration from He et al. [15], who tracked the variance of predicted target probabilities throughout training to enhance pruning effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "The pipeline of our proposed TDDS is clearly illustrated in Figure 2. Extensive experiments demonstrate the superior generalization capability of the proposed TDDS, enabling it to outperform other comparison methods across different pruning settings on various datasets and networks. For example, on CIFAR-100, our method achieves \\(54.51\\%\\) accuracy with only \\(10\\%\\) training data, surpassing random selection by \\(7.83\\%\\) and other SOTA methods by at least \\(12.69\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.216, + 0.807, + 0.23 + ], + "angle": 0, + "content": "Our main contributions are summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.234, + 0.892, + 0.324 + ], + "angle": 0, + "content": "- We examine the poor generalization resulting from existing snapshot-based dataset pruning. Subsequently, we analyze the inefficacy of current solutions to this generalization issue, attributing it to the inability to balance the incorporation of training dynamics with the effective identification of well-generalized samples." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.325, + 0.892, + 0.43 + ], + "angle": 0, + "content": "- We thereby propose a novel dataset pruning method called Temporal Dual-Depth Scoring (TDDS), resorting to two temporal depths/levels to take respective care of the contribution evaluation and generalization spanning training progress. Experiments on diverse datasets and networks demonstrate the effectiveness of TDDS, achieving SOTA performance." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.234, + 0.892, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.454, + 0.65, + 0.47 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.482, + 0.663, + 0.499 + ], + "angle": 0, + "content": "2.1. Dataset Pruning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Dataset Pruning, also known as Coreset Selection aims to shrink the dataset scale by selecting important samples according to some predefined criteria. Herding [6, 45] and Moderate [46] calculate the distance in feature space. Entropy [8] and Cal [24] explore the uncertainty and decision boundary with the predicted outputs. GradND/EL2N [31] quantifies the importance of a sample with its gradient magnitude. Most of these methods are snapshot-based, that is they do not care about the training dynamics that actually distinguish the behaviors of samples in the overall optimization. There are some efficient training methods [10, 28, 42, 47], which focus more on training efficiency and execute online selection spanning training progress. For example, gradient matching-based methods GradMatch [18] and Craig [26] minimize the distance between gradients produced by the full dataset and coreset. ACS [17] selects samples with larger gradient magnitude to accelerate quantization-aware training. These methods can capture training dynamics but often necessitate repeated importance re-evaluating and can not be generalized to different networks. Some methods such as Forgetting [43] and AUM [33] also have proved training dynamics benefits samples importance assessment. However, the downsampling operation, which averages dynamics across training, disregards the variability crucial for evaluating sample generalization, ultimately resulting in suboptimal coresets." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.282, + 0.9 + ], + "angle": 0, + "content": "Usually, the first 10 or 20 epochs." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26224" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.32, + 0.108 + ], + "angle": 0, + "content": "2.2. Variance in Deep Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.474, + 0.478 + ], + "angle": 0, + "content": "Variance, a standard second-order statistic, revealing the variability along a certain dimension, has been explored in numerous works [4, 30, 34]. For example, MVT [30] transfers the observed variance of one class to another to improve the robustness of the unseen examples and few-shot learning tasks. VICReg [4] maintains variance of embeddings to prevent the collapse in which two branches produce identical outputs regardless of inputs. For the gradient, its variance along the parameter dimension is an approximation of Hessian matrix indicating loss landscape. Based on that, Fishr [34] matches domain-level variances of gradients for out-of-distribution generalization. LCMat [37] induces a better adaptation of the pruned dataset on the perturbed parameter region than the exact point matching. Besides, calculating gradient variance along time dimension tracks dynamic optimization change. VoG [1] uses this to estimate sample importance and the visualization shows that high-variance samples are more worthwhile to learn. Dyn-Unc [15] calculates the time-dimension variance of predicted target class probability to evaluate sample importance. Differing from VoG and Dyn-Unc, our TDDS does not need pixel-wise gradient calculation while considering non-target probabilities, which enables a more precise evaluation with lower computational overhead." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.49, + 0.204, + 0.508 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.653 + ], + "angle": 0, + "content": "Throughout this paper, we denote the full training dataset as \\(\\mathbb{U} = \\{(x_n,y_n)\\}_{n = 1}^N\\), where \\(x_{n}\\in \\mathbb{R}^{D}\\) and \\(y_{n}\\in \\mathbb{R}^{1\\times C}\\) are drawn i.i.d. from a natural distribution \\(\\mathcal{D}\\). We denote a neural network parameterized with weight matrix \\(\\pmb{\\theta}\\) as \\(f_{\\pmb{\\theta}}\\). Under these definitions, the optimization objective of \\(f_{\\pmb{\\theta}}\\) on \\(\\mathbb{U}\\) is to minimize empirical risk \\(\\mathcal{L}(\\mathbb{U};\\pmb {\\theta}) = \\frac{1}{N}\\sum_{n = 1}^{N}\\ell (f_{\\pmb{\\theta}}(\\pmb {x}_n),\\pmb {y}_n)\\), where \\(f_{\\pmb{\\theta}}(\\pmb {x}_n)\\in \\mathbb{R}^{1\\times C}\\) outputs the predicted probabilities of each class. Typically, \\(\\pmb{\\theta}\\) is updated as follow2," + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.662, + 0.47, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} _ {t + 1} = \\boldsymbol {\\theta} _ {t} - \\eta \\sum_ {n = 1, \\boldsymbol {x} _ {n} \\in \\mathbb {U}} ^ {N} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.469, + 0.747 + ], + "angle": 0, + "content": "where \\(\\eta\\) is the learning rate and \\(\\pmb{g}_t(\\pmb{x}_n)\\) is defined as the gradient calculated over the data pair \\((\\pmb{x}_n, \\pmb{y}_n)\\) in epoch \\(t\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.748, + 0.47, + 0.808 + ], + "angle": 0, + "content": "Dataset pruning aims to enhance training efficiency by constructing a coreset \\(\\mathbb{S} = \\{(x_n,y_m)\\}_{m = 1}^M\\), \\(\\mathbb{S}\\subset \\mathbb{U}\\) that can achieve comparable performance to \\(\\mathbb{U}\\). The objective of dataset pruning can be formulated as," + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.817, + 0.468, + 0.866 + ], + "angle": 0, + "content": "\\[\n\\underset {\\substack {(\\boldsymbol {x}, \\boldsymbol {y}) \\sim \\mathcal {D} \\\\ \\boldsymbol {\\theta} _ {0} \\sim \\mathcal {P} _ {\\boldsymbol {\\theta} _ {0}}}} {\\mathbb {E}} \\left[ \\ell \\left(f _ {(\\mathrm {U}, \\boldsymbol {\\theta} _ {0})} (\\boldsymbol {x}), \\boldsymbol {y}\\right) \\right] \\simeq \\underset {\\substack {(\\boldsymbol {x}, \\boldsymbol {y}) \\sim \\mathcal {D} \\\\ \\boldsymbol {\\theta} _ {0} \\sim \\mathcal {P} _ {\\boldsymbol {\\theta} _ {0}}}} {\\mathbb {E}} \\left[ \\ell \\left(f _ {(\\mathrm {S}, \\boldsymbol {\\theta} _ {0})} (\\boldsymbol {x}), \\boldsymbol {y}\\right) \\right], \\tag{2}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.47, + 0.9 + ], + "angle": 0, + "content": "2Here, \\( t \\) indicates epoch and the batch-wise updates [2] in one epoch are omitted." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.123 + ], + "angle": 0, + "content": "where \\(f_{(\\mathbb{U},\\pmb{\\theta}_0)}\\) and \\(f_{(\\mathbb{S},\\pmb{\\theta}_0)}\\) represent the networks trained on \\(\\mathbb{U}\\) and \\(\\mathbb{S}\\) with weight \\(\\pmb{\\theta}_0\\) initialized from distribution \\(\\mathcal{P}_{\\pmb{\\theta}_0}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.133, + 0.635, + 0.15 + ], + "angle": 0, + "content": "4. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.158, + 0.892, + 0.4 + ], + "angle": 0, + "content": "As discussed earlier, despite that exploring long-range dynamics provides a more comprehensive sample evaluation, the averaging operation hinders the construction of a coreset with strong generalization. In this section, we present the proposed Temporal Dual-Depth Scoring (TDDS) strategy, which balances the incorporation of training dynamics and the identification of well-generalized samples. In the outer level, we identify samples with their variability during training which is encouraged theoretically by the optimization space matching between coreset and original dataset (refer to Section 4.1). In the inner level, the gradient in the outer level is replaced with the projected component on the accumulated direction to estimate valid contributions in every epoch (refer to Section 4.2). Finally, to enhance efficiency, we conduct TDDS with a moving window (refer to Section 4.3). The proposed TDDS is summarized in Algorithm 1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.407, + 0.892, + 0.438 + ], + "angle": 0, + "content": "4.1. Outer Level: Enhance Coreset Generalization by Maximizing Variance" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.892, + 0.492 + ], + "angle": 0, + "content": "To construct the coreset \\(\\mathbb{S}\\) satisfying Equation 2, gradient-based methods [3, 18, 26] propose to minimize the distance between full dataset and coreset gradient," + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.496, + 0.86, + 0.521 + ], + "angle": 0, + "content": "\\[\n\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\min } \\| \\boldsymbol {G} _ {t, \\mathrm {U}} - \\tilde {\\boldsymbol {G}} _ {t, \\mathbb {S}} \\|, \\quad \\text {w h e r e}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.526, + 0.892, + 0.579 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {G} _ {t, \\mathbb {U}} = \\sum_ {\\substack {n = 1, \\\\ \\boldsymbol {x} _ {n} \\in \\mathbb {U}}} ^ {| \\mathbb {U} |} \\boldsymbol {g} _ {t} (\\boldsymbol {x} _ {n}), \\quad \\tilde {\\boldsymbol {G}} _ {t, \\mathbb {S}} = \\sum_ {\\substack {m = 1, \\\\ \\boldsymbol {x} _ {m} \\in \\mathbb {S}}} ^ {| \\mathbb {S} |} \\boldsymbol {g} _ {t} (\\boldsymbol {x} _ {m}), \\tag{3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.585, + 0.892, + 0.659 + ], + "angle": 0, + "content": "\\(\\tilde{G}_{t,\\mathbb{S}}\\) can be regarded as the gradient reconstruction in coreset space. To solve this minimization problem, Huang et al. [17] recommends pruning samples with smaller gradient magnitudes to minimize their potential impact on optimization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.812 + ], + "angle": 0, + "content": "However, whenever the distance is minimized, the obtained snapshot-based coreset fails to generalize across training progress. Here are the reasons: (1) the distinctive contributions of samples are temporal statistics. Evaluating them at a specific time point causes significant bias when considering dynamic optimization; (2) samples with larger individual gradients dominate the matching process. Without considering the current optimization context, these samples introduce a substantial error in approximating the accumulated gradient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.857 + ], + "angle": 0, + "content": "To address the first issue, we proposed to extend Equation 3 to a continuous training duration to capture training dynamics," + }, + { + "type": "equation", + "bbox": [ + 0.561, + 0.863, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\min } \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\| \\boldsymbol {\\mathcal {G}} _ {t, \\mathbb {U}} - \\tilde {\\boldsymbol {\\mathcal {G}}} _ {t, \\mathbb {S}} \\| ^ {2}, \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26225" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.087, + 0.832, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.34, + 0.895, + 0.397 + ], + "angle": 0, + "content": "Figure 2. The pipeline of our proposed TDDS. First, we record individual predicted probabilities of samples \\( f_{t_i}^{x_n} = f_{\\theta_{t_i}}(\\pmb{x}_n) \\) during training. Then, we approximate the projected gradient, i.e. the component of gradient \\( g_{t_i}^{x_n} = g_{t_i}(\\pmb{x}_n) \\) on accumulated gradient \\( G_{t_i} \\) direction, with KL-based loss difference between two adjacent epochs. Next, the projected gradients are used to estimate individual contributions of samples. Finally, the important samples are identified with larger projected gradient variances over time." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.47, + 0.528 + ], + "angle": 0, + "content": "Here, the gradients generated by \\(\\mathbb{U}\\) and \\(\\mathbb{S}\\) at epoch \\(t\\) are defined as \\(\\pmb{\\mathcal{G}}_{t,\\mathbb{U}} = [|\\pmb{g}_t(\\pmb{x}_n)|]_{n=1}^N\\) and similarly \\(\\tilde{\\pmb{G}}_{t,\\mathbb{S}}\\) is its reconstructed counterpart using \\(\\mathbb{S}\\). Here we use magnitude instead of gradient itself to balance the training dynamic integration and complexity. Experiments in Section 5.4 also shows that magnitude-based minimization performs better than gradient-based when considering continuous training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.47, + 0.559 + ], + "angle": 0, + "content": "Directly solving Equation 4 is NP-hard. Thus, we turn to its equivalent, temporal gradient variance maximization," + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.569, + 0.47, + 0.61 + ], + "angle": 0, + "content": "\\[\n\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\max } \\mathcal {R} (\\mathbb {S}), \\quad \\mathcal {R} (\\mathbb {S}) = \\sum_ {t = 1} ^ {T} \\| \\boldsymbol {G} _ {t, \\mathbb {S}} - \\overline {{\\boldsymbol {G}}} _ {\\mathbb {S}} \\| ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.47, + 0.714 + ], + "angle": 0, + "content": "where \\(\\overline{\\pmb{G}}_{\\mathbb{S}} = \\frac{1}{T}\\sum_{t = 1}^{T}\\pmb{G}_{t,\\mathbb{S}},\\pmb{G}_{t,\\mathbb{S}} = [|\\pmb{g}_t(\\pmb{x}_m)|]_{m = 1}^M\\) is the mean gradient over training time. Detailed proof can be founded in Supplementary. Equation 5 measures the variability of samples and enhances the identification of wellgeneralized samples compared to previous average-based methods [33, 43]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.47, + 0.755 + ], + "angle": 0, + "content": "4.2. Inner Level: Estimate Actual Contribution with Projected Gradient" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.761, + 0.47, + 0.807 + ], + "angle": 0, + "content": "According to Equation 5, sample importance can be evaluated with its gradient variance over time. For any sample \\( \\boldsymbol{x}_n \\), we have," + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.816, + 0.47, + 0.858 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} (\\boldsymbol {x} _ {n}) = \\sum_ {t = 1} ^ {T} \\left\\| \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| - \\overline {{\\left| \\boldsymbol {g} \\left(\\boldsymbol {x} _ {n}\\right) \\right|}} \\right\\| ^ {2}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.868, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\overline{|\\pmb{g}(\\pmb{x}_n)|} = \\frac{1}{T}\\sum_{t=1}^{T}|\\pmb{g}_t(\\pmb{x}_n)|\\). Equation 6 treats sample-wise gradient independently, which may not pre" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.419, + 0.695, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.539, + 0.613, + 0.551 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.703, + 0.435, + 0.892, + 0.533 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.79, + 0.538, + 0.81, + 0.551 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.567, + 0.894, + 0.621 + ], + "angle": 0, + "content": "Figure 3. Incorporating sample-wise gradient in the current optimization context. After projecting onto the current accumulated gradient, samples with similar gradients exhibit different behaviors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.786 + ], + "angle": 0, + "content": "cisely describe the valid contribution in the current optimization context. That is the second problem mentioned in Section 4.1. As illustrated in Figure 3(a), the gradient of sample \\( \\boldsymbol{x}_n \\) remains constant between \\( t \\) and \\( t + 1 \\). However, when incorporating it into the current optimization context, its valid contribution undergoes a significant shift. Thus, we propose to calculate the gradient variance after projecting it on the accumulated direction, that is, \\( |\\boldsymbol{g}_t(\\boldsymbol{x}_n)| \\) is reformulated as," + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.798, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| = \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\cdot \\sum_ {j = 1, \\boldsymbol {x} _ {j} \\in \\mathbb {U}} ^ {| \\mathbb {U} |} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {j}\\right) \\right|. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Calculating Equation 6 requires sample-wise gradients over a period of \\( T \\), which is not feasible due to time and memory constraints. According to Equation 1, the accumu" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26226" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.47, + 0.122 + ], + "angle": 0, + "content": "lated gradient is equal to \\(\\frac{1}{\\eta} (\\pmb{\\theta}_t - \\pmb{\\theta}_{t + 1})\\), thus the projection in Equation 7 is reformed as loss difference," + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.133, + 0.47, + 0.197 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| = \\frac {1}{\\eta} \\left| \\left(\\boldsymbol {\\theta} _ {t} - \\boldsymbol {\\theta} _ {t + 1}\\right) \\nabla_ {\\boldsymbol {\\theta} _ {t}} \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right), \\boldsymbol {y} _ {n}\\right) \\right| \\tag {8} \\\\ \\approx \\frac {1}{\\eta} \\left| \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t + 1}} (\\boldsymbol {x} _ {n}), \\boldsymbol {y} _ {n}\\right) - \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t}} (\\boldsymbol {x} _ {n}), \\boldsymbol {y} _ {n}\\right) \\right|, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.208, + 0.468, + 0.223 + ], + "angle": 0, + "content": "which can be deduced from the first-order Taylor expansion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.223, + 0.468, + 0.281 + ], + "angle": 0, + "content": "Thus, we can evaluate the per-sample contribution to the accumulated gradient direction with its loss change. In the context of classification, \\(\\ell\\) is typically Cross Entropy (CE) loss," + }, + { + "type": "equation", + "bbox": [ + 0.18, + 0.282, + 0.469, + 0.316 + ], + "angle": 0, + "content": "\\[\n\\Delta \\ell_ {t} ^ {n} = \\boldsymbol {y} _ {n} ^ {\\top} \\cdot \\log \\frac {f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right)}{f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right)}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.322, + 0.469, + 0.415 + ], + "angle": 0, + "content": "where \\(\\Delta \\ell_t^n = \\ell(f_{\\theta_{t+1}}(\\pmb{x}_n), \\pmb{y}_n) - \\ell(f_{\\pmb{\\theta}_t}(\\pmb{x}_n), \\pmb{y}_n)\\). Due to the one-hot \\(\\pmb{y}_n\\), non-target probabilities are unfortunately overlooked, obliterating a significant amount of distinctive information. This reminds us of the Kullback-Leibler (KL) divergence loss, which can be achieved by simply replacing \\(\\pmb{y}_n\\) with \\(f_{\\pmb{\\theta}_{t+1}}(\\pmb{x}_n)\\)," + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.427, + 0.469, + 0.461 + ], + "angle": 0, + "content": "\\[\n\\Delta \\ell_ {t} ^ {n} = f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right) ^ {\\top} \\cdot \\log \\frac {f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right)}{f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right)}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.47, + 0.576 + ], + "angle": 0, + "content": "Considering that \\( f_{\\pmb{\\theta}_t(\\pmb{x}_n)} \\) follows a Bernoulli distribution \\( \\mathcal{B}(p_t) \\), where \\( p_t \\) represents the probability of the target class at epoch \\( t \\). If \\( p_t \\) equals \\( p_{t + 1} \\), Equation 9 fails to distinguish, but Equation 10 can still differentiate the contributions of samples with \\( q_{t} \\) and \\( q_{t + 1} \\). Here, \\( q_{t} \\) and \\( q_{t + 1} \\) are the non-target probability distributions. This effectiveness has been proved in Section 5.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.377, + 0.603 + ], + "angle": 0, + "content": "4.3. Efficient Implementation of TDDS" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.61, + 0.469, + 0.746 + ], + "angle": 0, + "content": "When computing \\(\\mathcal{R}(\\pmb{x}_n)\\) with Equation 6, Equation 8, and Equation 10, storing \\(T\\)-epoch predicted outputs may lead to out-of-memory problems, especially with large datasets like ImageNet (containing 1, 281, 167 samples across 1,000 classes). As a solution, we suggest an efficient calculation using an exponential moving average (EMA) weighting strategy. For any training point \\(t \\geq K\\), the variance \\(\\mathcal{R}_t(\\pmb{x}_n)^3\\) is computed over a \\(K\\)-epoch window ranging from \\(t - K + 1\\) to \\(t\\)," + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.758, + 0.469, + 0.8 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) = \\sum_ {t - K + 1} ^ {t} \\left\\| \\left| \\Delta \\ell_ {t} ^ {n} \\right| - \\overline {{\\left| \\Delta \\ell_ {t} ^ {n} \\right|}} \\right\\| ^ {2}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.812, + 0.469, + 0.857 + ], + "angle": 0, + "content": "where \\( \\overline{|\\Delta\\ell_t^n|} \\) is the average of loss difference in a window. For \\( T \\)-epoch trajectory, \\( T - K + 1 \\) windows are weighted as," + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.859, + 0.469, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} \\left(\\boldsymbol {x} _ {n}\\right) = \\beta \\mathcal {R} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) + (1 - \\beta) \\mathcal {R} \\left(\\boldsymbol {x} _ {n}\\right), \\tag {12}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.887, + 0.336, + 0.9 + ], + "angle": 0, + "content": "3The constant coefficient \\(\\eta\\) has been omitted." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.152 + ], + "angle": 0, + "content": "where \\(\\beta\\) is the decay coefficient of EMA whose setting is examined in Section 5.3. With this EMA, we only need to store predicted outputs for one window, significantly alleviating storage burden." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.152, + 0.892, + 0.243 + ], + "angle": 0, + "content": "After sorting \\(\\{\\mathcal{R}(\\pmb{x}_n)\\}_{n=1}^N\\), the top-M samples are selected to construct coreset denoted as \\(\\{\\mathbb{S}, r\\} = \\{(x_m, y_m), \\mathcal{R}(x_m)\\}_{m=1}^M\\). Since, the samples with larger \\(\\mathcal{R}(\\pmb{x}_m)\\) contribute more in the original data training. We remark that this dominance should be maintained in coreset training, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.252, + 0.892, + 0.293 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\theta} _ {t + 1} = \\boldsymbol {\\theta} _ {t} - \\eta \\sum_ {m = 1} ^ {M} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {m}\\right) \\mathcal {R} \\left(\\boldsymbol {x} _ {m}\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.302, + 0.892, + 0.333 + ], + "angle": 0, + "content": "This helps to transfer relative sample importance to coreset training. This effectiveness is proved in Section 5.4." + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.346, + 0.85, + 0.361 + ], + "angle": 0, + "content": "Algorithm 1 Temporal Dual-Depth Scoring (TDDS)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.363, + 0.889, + 0.424 + ], + "angle": 0, + "content": "Input: Training dataset U; A network \\(f_{\\theta}\\) with weight \\(\\theta\\); Learning rate \\(\\eta\\); Epochs \\(T\\); Iterations \\(I\\) per epoch; Window size \\(K\\); Decay factor \\(\\beta\\)." + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.427, + 0.648, + 0.44 + ], + "angle": 0, + "content": "1: for \\( t = 1 \\) to \\( T \\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.442, + 0.856, + 0.456 + ], + "angle": 0, + "content": "2: for \\(i = 1\\) to \\(I\\), Sample a mini-batch \\(\\mathbb{B}_i \\subset \\mathbb{U}\\) do" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.457, + 0.882, + 0.472 + ], + "angle": 0, + "content": "3: Record predicted probabilities \\( f_{\\pmb{\\theta}_t}(x_n) \\), \\( x_n \\in \\mathbb{B}_i \\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.472, + 0.776, + 0.487 + ], + "angle": 0, + "content": "4: Calculate \\(\\Delta \\ell_t^n\\) for each \\(\\pmb{x}_n\\in \\mathbb{B}_i\\)" + }, + { + "type": "text", + "bbox": [ + 0.717, + 0.488, + 0.884, + 0.501 + ], + "angle": 0, + "content": "\\(\\triangleright\\) Defined in Equation 10" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.502, + 0.796, + 0.517 + ], + "angle": 0, + "content": "5: Update weight \\(\\pmb{\\theta}_{i + 1} = \\pmb{\\theta}_i - \\eta \\pmb{G}_{t,\\mathbb{B}_i}\\)" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.518, + 0.599, + 0.53 + ], + "angle": 0, + "content": "6: end for" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.532, + 0.674, + 0.546 + ], + "angle": 0, + "content": "7: if \\( K \\leq t \\leq T \\) then" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.547, + 0.842, + 0.562 + ], + "angle": 0, + "content": "8: Calculate \\(\\mathcal{R}_t(\\pmb{x}_n)\\) in one window, \\(\\pmb{x}_n\\in \\mathbb{U}\\)" + }, + { + "type": "text", + "bbox": [ + 0.717, + 0.563, + 0.882, + 0.577 + ], + "angle": 0, + "content": "\\(\\triangleright\\) Defined in Equation 11" + }, + { + "type": "text", + "bbox": [ + 0.511, + 0.578, + 0.796, + 0.592 + ], + "angle": 0, + "content": "9: Update \\(\\mathcal{R}(\\pmb{x}_n)\\) with EMA, \\(\\pmb{x}_n\\in \\mathbb{U}\\)" + }, + { + "type": "text", + "bbox": [ + 0.72, + 0.593, + 0.888, + 0.607 + ], + "angle": 0, + "content": "\\(\\triangleright\\) Defined in Equation 12" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.608, + 0.59, + 0.62 + ], + "angle": 0, + "content": "10: end if" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.623, + 0.583, + 0.635 + ], + "angle": 0, + "content": "11: end for" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.637, + 0.86, + 0.654 + ], + "angle": 0, + "content": "12: Select Top-M \\(\\{\\mathbb{S},r\\} \\leftarrow \\{(\\pmb {x}_m,\\pmb {y}_m),\\mathcal{R}(\\pmb {x}_m)\\}_{m = 1}^M\\)" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.654, + 0.892, + 0.685 + ], + "angle": 0, + "content": "Output: Selected subset \\(\\mathbb{S} = \\{(x_m, y_m)\\}_{m=1}^M\\); associated sample-wise importance \\(r = \\{\\mathcal{R}(x_m)\\}_{m=1}^M\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.715, + 0.632, + 0.732 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.693, + 0.756 + ], + "angle": 0, + "content": "5.1. Experiment Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Datasets and Networks. The effectiveness of the proposed TDDS is evaluated on three popular benchmarks, i.e., CIFAR-10, CIFAR-100 [19], and ImageNet-1K [9] with three networks, i.e., ResNet-18, ResNet-34 [14], and SwinT [21]. We also verify the cross-architecture performance on four networks including ResNet-50 [14], VGG-16 [38], MobileNet-v2 [36], and ShuffleNet [23]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.87, + 0.892, + 0.904 + ], + "angle": 0, + "content": "Training Hyperparameters. Theoretically, if pruning rate \\( p = 1 - \\frac{|\\mathbb{S}|}{|\\mathbb{U}|} \\), where \\( 0 < p \\leq 1 \\), the training process" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "26227" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.119 + ], + "angle": 0, + "content": "Table 1. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-E. The model trained with the full dataset achieves \\(95.23\\%\\) and \\(78.21\\%\\) accuracy." + }, + { + "type": "table", + "bbox": [ + 0.153, + 0.141, + 0.825, + 0.361 + ], + "angle": 0, + "content": "
pCIFAR-10CIFAR-100
30%50%70%80%90%30%50%70%80%90%
Random94.58 ±0.0493.38 ±0.1790.61 ±0.4488.87 ±0.4783.77 ±0.2675.53 ±0.0471.95 ±0.1664.59 ±0.3257.79 ±0.2446.68 ±1.07
Entropy [8]94.45 ±0.0791.90 ±0.1686.24 ±0.2683.49 ±0.2172.06 ±0.8172.39 ±0.2064.44 ±0.3650.73 ±0.8642.86 ±0.2529.56 ±0.54
Forgetting [43]95.45 ±0.2495.05 ±0.0589.14 ±2.0476.18 ±3.1845.87 ±1.8777.38 ±0.0970.76 ±0.4049.92 ±0.2838.42 ±1.1325.82 ±0.52
EL2N [31]95.43 ±0.1095.06 ±0.0486.69 ±1.7168.64 ±3.7031.89 ±1.5176.89 ±0.3167.57 ±0.1536.45 ±1.3617.31 ±0.339.10 ±0.69
AUM [33]95.44 ±0.0995.19 ±0.0991.19 ±0.6369.60 ±3.1134.74 ±0.1177.35 ±0.1868.17 ±0.5231.69 ±0.3418.43 ±0.479.29 ±0.27
Moderate [46]93.96 ±0.0692.34 ±0.0989.71 ±0.1487.75 ±0.2783.61 ±0.2474.60 ±0.1070.29 ±0.3162.81 ±0.0856.52 ±0.3741.82 ±1.12
Dyn-Unc[15]95.08 ±0.0294.03 ±0.1489.40 ±0.1379.76 ±1.0937.12 ±1.1273.36 ±0.1065.90 ±0.2550.16 ±0.4739.19 ±0.2715.20 ±0.41
TDDS95.47 ±0.0695.21 ±0.0493.03 ±0.2591.30 ±0.2585.46 ±0.2177.56 ±0.0674.04 ±0.3467.78 ±0.4463.01 ±0.1254.51 ±0.22
" + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.381, + 0.249, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.249, + 0.381, + 0.411, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.41, + 0.381, + 0.572, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.571, + 0.381, + 0.733, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.731, + 0.381, + 0.892, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.495, + 0.893, + 0.523 + ], + "angle": 0, + "content": "Figure 4. Parameter analysis of range \\( T \\) and window size \\( K \\) on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.3, 0.5, 0.7, 0.8, and 0.9." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.547, + 0.472, + 0.604 + ], + "angle": 0, + "content": "Table 2. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-P. The model trained with the full dataset achieves \\(95.23\\%\\) and \\(78.21\\%\\) accuracy." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.628, + 0.469, + 0.817 + ], + "angle": 0, + "content": "
pCIFAR-10CIFAR-100
30%50%70%30%50%70%
Random94.33 ±0.1793.4 ±0.1790.94 ±0.3874.59 ±0.2771.07 ±0.465.3 ±0.21
Entropy [8]94.44 ±0.292.11 ±0.4785.67 ±0.7172.26 ±0.0863.26 ±0.2950.49 ±0.88
Forgetting [43]95.36 ±0.1395.29 ±0.1890.56 ±1.876.91 ±0.3268.6 ±1.0238.06 ±1.14
EL2N [31]95.44 ±0.1594.61 ±0.2087.48 ±1.3376.25 ±0.2465.90 ±1.0634.42 ±1.50
AUM [33]95.07 ±0.2495.26 ±0.1591.36 ±1.476.93 ±0.3267.42 ±0.4930.64 ±0.58
Moderate [46]93.86 ±0.1192.58 ±0.3090.56 ±0.2774.60 ±0.4171.10 ±0.2465.34 ±0.41
CCS [51]95.40 ±0.1295.04 ±0.3793.00 ±0.1677.14 ±0.3174.45 ±0.1668.92 ±0.12
TDDS95.50 ±0.0795.66 ±0.0893.92 ±0.0477.95 ±0.3074.98 ±0.1669.46 ±0.10
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.472, + 0.903 + ], + "angle": 0, + "content": "speeds up by \\(\\frac{1}{1 - p}\\) times. We consider two coreset training strategies: Strategy-E prioritizes efficiency with same-epoch training on both full dataset and coreset. Strategy-P" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.547, + 0.895, + 0.591 + ], + "angle": 0, + "content": "Table 3. Comparison of different dataset pruning methods on ImageNet-1K with ResNet-34 under Strategy-E. The model trained with the full dataset achieves \\(73.54\\%\\) Top-1 accuracy." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.615, + 0.907, + 0.768 + ], + "angle": 0, + "content": "
pImageNet-1K
70%80%90%
Random64.1960.7652.63
Entropy[8]62.3456.8043.39
Forgetting [43]64.2962.0152.14
EL2N [31]46.9232.6815.90
AUM [33]39.3423.6411.70
Moderate [46]64.0461.3552.45
TDDS64.6962.5653.91
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.808, + 0.895, + 0.903 + ], + "angle": 0, + "content": "prioritizes performance by training coreset for more epochs. If \\( \\frac{|\\mathbb{S}|}{|\\mathbb{U}|} = 1 - p \\), the training process is extended to \\( \\frac{1}{1 - p} \\) times of the original one. For CIFAR-10 and -100, we train ResNet-18 for 200 epochs with a batch size of 128. For ImageNet, ResNet-34 and Swin-T are trained for 60 [51] and 300 epochs [15] with batch sizes of 256 and 1024, respec" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "26228" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.087, + 0.473, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.177, + 0.47, + 0.219 + ], + "angle": 0, + "content": "Figure 5. Parameter analysis of decay coefficient \\(\\beta\\) on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.7, 0.8, and 0.9." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.47, + 0.442 + ], + "angle": 0, + "content": "tively. SGD optimizer with momentum of 0.9 and weight decay of 0.0005 is used for update networks. The learning rate is initialized as 0.1 and decays with the cosine annealing scheduler. During experiments, we found that smaller batch size boosts performance at high pruning rates (shown in Supplementary). Thus, for \\( p = 0.8 \\), we halved the batch size, and for \\( p = 0.9 \\), we reduced it to one-fourth. All compared methods use the same settings. With Strategy-P, for example, training a CIFAR coreset with only \\( 50\\% \\) training samples takes 400 epochs, while keeping the other hyperparameters unchanged. Considering the time-consuming training, we only conduct Strategy-P experiments at pruning rates of 0.3, 0.5, 0.7." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.443, + 0.47, + 0.535 + ], + "angle": 0, + "content": "Baselines. Eight baselines are used for comparison, with the latter seven being SOTA methods: 1) Random; 2) Entropy [8]; 3) Forgetting [43]; 4) EL2N [31]; 5) AUM [33]; 6) Moderate [46]; 7) CCS [51]; 8) Dyn-Unc [15]. Due to the limited page, we provide the technical details of these baselines in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.353, + 0.56 + ], + "angle": 0, + "content": "5.2. Benchmark Evaluation Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.81 + ], + "angle": 0, + "content": "ResNet-18 on CIFAR-10 and 100. Table 1 and Table 2 report the performance of different dataset pruning methods under Strategy-E and P, respectively. Under both strategies, TDDS consistently outperforms other methods. For instance, under Strategy-E, none of the compared methods surpasses Random at aggressive pruning rates, while TDDS achieves \\(85.46\\%\\) and \\(54.51\\%\\) accuracy after pruning \\(90\\%\\) samples of CIFAR-10 and 100 surpassing Random by \\(1.69\\%\\) and \\(7.83\\%\\), respectively. By extending the training duration, Strategy-P enhances the performance of all methods to varying degrees. TDDS still maintains its superiority, for example, with only \\(30\\%\\) training data, the accuracy on CIFAR-10 and -100 are \\(93.92\\%\\) and \\(69.46\\%\\) outperforming CCS by \\(0.92\\%\\) and \\(0.54\\%\\), respectively. These results highlight TDDS as a promising choice for both efficiency and performance-oriented dataset pruning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.47, + 0.902 + ], + "angle": 0, + "content": "ResNet on ImageNet-1K. For ImageNet-1K, we train ResNet-34 models on original dataset for 90 epochs to collect training dynamics and then train the model on coreset for 60 epochs as [51]. Experiment results are given in Table 3. The results show that the proposed TDDS has better performance on ImageNet-1K, especially under aggressive" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "pruning rates. For example, when pruning \\(90\\%\\) samples, TDDS still achieves \\(53.91\\%\\) which is \\(1.77\\%\\) and \\(1.46\\%\\) higher than Forgetting and Moderate, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Swin-T on ImageNet-1k. We also evaluate Swin-T on ImageNet-1K. Like Dyn-Unc [15], Table 4 reports the results under four pruning rates. Notably, TDDS consistently outperforms other competitors, for example, after pruning \\(50\\%\\) training data, TDDS achieves \\(78.33\\%\\) accuracy, surpassing Forgetting, Moderate, and Dyn-Unc by \\(4.01\\%\\), \\(3.35\\%\\) and \\(0.69\\%\\), respectively." + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.256, + 0.892, + 0.299 + ], + "angle": 0, + "content": "Table 4. Comparison of different dataset pruning methods on ImageNet-1K with Swin-T under Strategy-E. The model trained with the full dataset achieves \\(79.58\\%\\) Top-1 accuracy." + }, + { + "type": "table", + "bbox": [ + 0.506, + 0.31, + 0.907, + 0.461 + ], + "angle": 0, + "content": "
pImageNet-1K
25%30%40%50%
Random77.8277.1875.9374.54
Forgetting [43]78.7078.2777.5574.32
Moderate [46]77.7477.0675.9474.98
Dyn-Unc [15]79.5479.1478.4977.64
TDDS79.7679.5779.0978.33
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.498, + 0.688, + 0.513 + ], + "angle": 0, + "content": "5.3. Parameter Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Estimation Range \\( T \\) and Window Size \\( K \\). Due to the random initialization, models adapt to prominent features (easy samples) during early training. As training progresses, models gradually acquire more abstract and complex features (hard samples) that are challenging to capture in early training. Thus, the importance of samples should be estimated in different training phases with respect to different pruning levels. As shown in Figure 4, we analyze the influence of range \\( T \\) and window size \\( K \\) on perfor" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.68, + 0.892, + 0.737 + ], + "angle": 0, + "content": "Table 5. Ablation study for Dual-depth strategy. The numbers in square brackets indicate the improvement in accuracy of the method presented in the current column compared to the corresponding method in the previous column." + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.748, + 0.868, + 0.9 + ], + "angle": 0, + "content": "
pCIFAR-100
EL2NEL2N+outerTDDS
30%76.8977.47[+ 0.58]77.56[+ 0.09]
50%67.5773.93[+ 6.36]74.04[+ 0.11]
70%36.4567.04[+30.59]67.78[+ 0.74]
80%17.3158.21[+40.90]63.01[+ 1.80]
90%9.1040.36[+31.26]54.51[+14.15]
outerX✓✓
innerXX✓
" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "26229" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.087, + 0.357, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.231, + 0.25, + 0.246, + 0.26 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.357, + 0.088, + 0.621, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.25, + 0.515, + 0.26 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.621, + 0.088, + 0.895, + 0.249 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.767, + 0.25, + 0.782, + 0.26 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.275, + 0.895, + 0.332 + ], + "angle": 0, + "content": "Figure 6. Ablation studies for (a) Gradient Magnitude vs. Gradient, (b) KL-based Loss Difference, and (c) Importance-aware Coreset Training. In (a), GM and G represent estimating sample contribution with gradient magnitude and gradient, respectively. In (b), KL and CE represent calculating loss difference with KL and CE loss, respectively. In (c), Imp-aware and Imp-unaware represent training coreset with and without weighting samples with their importance scores, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.42 + ], + "angle": 0, + "content": "mance. Apparently, for a larger pruning rate, we should select samples earlier in training. For CIFAR-100, the optimal \\((p,T,K)\\) setting is (0.3, 90, 10), (0.5, 70, 10), (0.7, 60, 20), (0.8, 20, 10), and (0.9, 10, 5). The parameter settings of CIFAR-10 and ImageNet are reported in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.473, + 0.542 + ], + "angle": 0, + "content": "Decay Coefficient \\(\\beta\\) of EMA. In contrast to the simple average (SA), EMA employs exponential weighting, giving more weight to the most recent window. We examine four values of \\(\\beta\\), where \\(\\beta = 0\\) represents SA. As illustrated in Figure 5, EMA outperforms SA regardless of the \\(\\beta\\) value chosen. Among the considered pruning levels, \\(\\beta = 0.9\\) yields the best performance, surpassing \\(\\beta = 0.95\\) and \\(\\beta = 0.85\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.559, + 0.241, + 0.573 + ], + "angle": 0, + "content": "5.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.584, + 0.47, + 0.704 + ], + "angle": 0, + "content": "Gradient Magnitude vs Gradient. We use gradient magnitudes in Equation 4. Although gradients themselves appear capable of describing optimization, our experimental findings indicate that the use of gradient magnitudes yields superior performance, as depicted in Figure 6(a). We argue that gradients often prioritize samples with frequently reversing gradients, resulting in unstable training and slower convergence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.856 + ], + "angle": 0, + "content": "KL-based Loss Difference. As discussed in Section 4.3, the KL loss provides a more comprehensive assessment of loss difference and is expected to precisely characterize sample contribution. To evaluate its effectiveness, we replace KL loss with CE loss and conduct experiments across all considered pruning rates. As illustrated in Figure 6(b), although CE is slightly higher than KL when the pruning rate is \\(30\\%\\), KL exhibits an absolute advantage at all other pruning levels. For example, when pruning rate is \\(90\\%\\), KL outperforms CE by a substantial margin of \\(15.97\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Importance-aware Coreset Training. We formulate importance-aware subset training as Equation 13. The maintained relative importance provides optimization guid" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.895, + 0.42 + ], + "angle": 0, + "content": "ance for subset training. As shown in Figure 6(c), the advantage becomes increasingly pronounced as the pruning rate rises. When pruning rate is \\(90\\%\\), the accuracy of importance-aware subset training outperforms its unaware counterpart by \\(6.55\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.895, + 0.526 + ], + "angle": 0, + "content": "Dual-Depth Strategy. To investigate the effectiveness of the proposed Dual-Depth strategy, we replace the inner depth with EL2N, and Table 5 indicates that incorporating the outer depth boosts EL2N at all considered pruning rates. Nevertheless, this enhancement still falls short of our dual-depth design, particularly evident in aggressive pruning scenarios." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.54, + 0.619, + 0.555 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.894, + 0.763 + ], + "angle": 0, + "content": "In this study, we reveal that the snapshot-based data pruning results in poor generalization across various pruning scenarios. However, existing methods fail to identify well-generalized samples even with evaluation criteria considering the whole training progress. We attribute this to the averaging-based dynamics incorporation and imprecise sample contribution characterization. To address these problems, we propose a dataset pruning method called TDDS, which designs a Temporal Dual-Depth Scoring strategy to balance the incorporation of training dynamics and the identification of well-generalized samples. Extensive experiments on various datasets and networks, demonstrate the SOTA performance of our proposed method." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.775, + 0.667, + 0.792 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.894, + 0.892 + ], + "angle": 0, + "content": "This research is supported in part by the National Natural Science Foundation of China under Grant 62121001, Grant 62322117, and Grant 62371365. This research is also supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research) and Jiawei Du's A*STAR Career Development Fund (CDF) C233312004." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "26230" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Chirag Agarwal, Daniel D'souza, and Sara Hooker. Estimating example difficulty using variance of gradients. In IEEE Conf. Comput. Vis. Pattern Recog., pages 10368-10378, 2022. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.468, + 0.198 + ], + "angle": 0, + "content": "[2] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. 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Most existing dataset pruning methods rely on snapshot-based criteria to identify representative samples, often resulting in poor generalization across various pruning and cross-architecture scenarios. Recent studies have addressed this issue by expanding the scope of training dynamics considered, including factors such as forgetting event and probability change, typically using an averaging approach. However, these works struggle to integrate a broader range of training dynamics without overlooking well-generalized samples, which may not be sufficiently highlighted in an averaging manner. In this study, we propose a novel dataset pruning method termed as Temporal Dual-Depth Scoring (TDDS), to tackle this problem. TDDS utilizes a dual-depth strategy to achieve a balance between incorporating extensive training dynamics and identifying representative samples for dataset pruning. In the first depth, we estimate the series of each sample's individual contributions spanning the training progress, ensuring comprehensive integration of training dynamics. In the second depth, we focus on the variability of the sample-wise contributions identified in the first depth to highlight well-generalized samples. Extensive experiments conducted on CIFAR and ImageNet datasets verify the superiority of TDDS over previous SOTA methods. Specifically on CIFAR100, our method achieves $54.51\%$ accuracy with only $10\%$ training data, surpassing baselines methods by more than $12.69\%$ . Our codes are available at https://github.com/zhangxin-xd/Dataset-Pruning-TDDS. + +![](images/082cb78abe905810a38b2fea4fa61bfe7c1604b8009c1cd5426c6e86204853b9.jpg) +Figure 1. (a) Coresetets constructed by snapshot-based dataset pruning tend to fluctuate depending on the epochs selected for data selection. The red and blue points represent the data samples of two coresets constructed with $90\%$ pruning rate at Epoch 10 and 100 from the same training progress, respectively. (b) Snapshot-based coresets fail to generalize to pruning settings, especially pruning rates. The accuracy gap between coresets constructed at Epoch 10 and 100 is increasing as the pruning rate grows. Here, we measure importance using the error vector score, a classic snapshot-based criterion defined in [31]. These scores are obtained by training ResNet-18 on CIFAR-10. + +# 1. Introduction + +Explosively growing datasets [9, 20, 52, 53] have been crucial for the success of deep neural networks (DNNs) in various applications [7, 21, 35, 50]. However, learning from large-scale datasets is both time-consuming and financially prohibitive [5, 27, 39, 40, 44, 48]. Actually, a substantial portion of data samples are redundant [43, 46, 51], which means they can be excluded from training without compromising performance. + +Numerous dataset pruning works [12, 16, 17, 22, 25, 29, 32, 46, 49] have explored various criteria [13, 41] for identifying important data samples, including distribution distance [45, 46], uncertainty [8], loss [31, 43], and gradient [31]. Most of them evaluate sample importance using a snapshot of training progress. For example, Paul et al. [31] + +uses the error vector score generated by a few epochs $^{1}$ in early training; Xia et al. [46] calculates the distribution distances of features at the end of training. + +However, these snapshot-based pruning methods have two potential problems. Firstly, the importance scores of samples fluctuate with epochs during the progress of training. Consequently, the coresets constructed by the importance scores at different snapshots of training progress differ from each other significantly. As verified in Figure 1(a), the coresets constructed at Epoch 10 and 100 obviously contain different samples. Secondly, relying on importance scores from a snapshot can lead to overfitting in the construction of the coreset, as this approach may not generalize well across different scenarios, such as varying pruning rates. As shown in Figure 1(b), the accuracy gap of coresets from different snapshots becomes larger as the pruning rate increases. + +To address these two problems, a straightforward approach is to consider a broader range of training dynamics throughout the training process, with a focus on selecting well-generalized data samples. For example, Pleiss et al. [33] involves training dynamics by measuring the probability gap between the target class and the second largest class in each epoch; Toneva et al. [43] monitors the forgetting events throughout the entire training process. These forgetting events occur when samples, classified correctly in a prior epoch, are subsequently predicted incorrectly. Unfortunately, existing studies fall short of balancing the incorporation of training dynamics with the effective identification of well-generalized samples. The use of an averaging down-sampling operation aims to cover a broader range of training dynamics. However, this approach can inadvertently lead to the neglect of well-generalized samples during data selection, ultimately degrading overall performance. + +In this paper, we propose Temporal Dual-Depth Scoring (TDDS) pruning method, designed to effectively balance and address the aforementioned problems. We employ a dual-depth temporal scoring metric that spans the training process for data selection. In the inner level (depth one), we approximate the actual contribution of each sample in every epoch. This approximation is achieved by projecting the sample-wise gradients onto the accumulated gradient in each epoch, following the approach suggested by Du et al. [11]. We then integrate these contributions over a specified window, typically spanning 10 epochs, to incorporate more training dynamics. In the outer level (depth two), we reduce reliance on the averaging down-sampling operation to prevent overlooking vital samples. Well-generalized samples are identified based on the variability of the projected gradients, calculated in each window from the inner level. This design of the outer level draws inspiration from He et al. [15], who tracked the variance of predicted target probabilities throughout training to enhance pruning effectiveness. + +The pipeline of our proposed TDDS is clearly illustrated in Figure 2. Extensive experiments demonstrate the superior generalization capability of the proposed TDDS, enabling it to outperform other comparison methods across different pruning settings on various datasets and networks. For example, on CIFAR-100, our method achieves $54.51\%$ accuracy with only $10\%$ training data, surpassing random selection by $7.83\%$ and other SOTA methods by at least $12.69\%$ . + +Our main contributions are summarized as: + +- We examine the poor generalization resulting from existing snapshot-based dataset pruning. Subsequently, we analyze the inefficacy of current solutions to this generalization issue, attributing it to the inability to balance the incorporation of training dynamics with the effective identification of well-generalized samples. +- We thereby propose a novel dataset pruning method called Temporal Dual-Depth Scoring (TDDS), resorting to two temporal depths/levels to take respective care of the contribution evaluation and generalization spanning training progress. Experiments on diverse datasets and networks demonstrate the effectiveness of TDDS, achieving SOTA performance. + +# 2. Related Works + +# 2.1. Dataset Pruning + +Dataset Pruning, also known as Coreset Selection aims to shrink the dataset scale by selecting important samples according to some predefined criteria. Herding [6, 45] and Moderate [46] calculate the distance in feature space. Entropy [8] and Cal [24] explore the uncertainty and decision boundary with the predicted outputs. GradND/EL2N [31] quantifies the importance of a sample with its gradient magnitude. Most of these methods are snapshot-based, that is they do not care about the training dynamics that actually distinguish the behaviors of samples in the overall optimization. There are some efficient training methods [10, 28, 42, 47], which focus more on training efficiency and execute online selection spanning training progress. For example, gradient matching-based methods GradMatch [18] and Craig [26] minimize the distance between gradients produced by the full dataset and coreset. ACS [17] selects samples with larger gradient magnitude to accelerate quantization-aware training. These methods can capture training dynamics but often necessitate repeated importance re-evaluating and can not be generalized to different networks. Some methods such as Forgetting [43] and AUM [33] also have proved training dynamics benefits samples importance assessment. However, the downsampling operation, which averages dynamics across training, disregards the variability crucial for evaluating sample generalization, ultimately resulting in suboptimal coresets. + +# 2.2. Variance in Deep Learning + +Variance, a standard second-order statistic, revealing the variability along a certain dimension, has been explored in numerous works [4, 30, 34]. For example, MVT [30] transfers the observed variance of one class to another to improve the robustness of the unseen examples and few-shot learning tasks. VICReg [4] maintains variance of embeddings to prevent the collapse in which two branches produce identical outputs regardless of inputs. For the gradient, its variance along the parameter dimension is an approximation of Hessian matrix indicating loss landscape. Based on that, Fishr [34] matches domain-level variances of gradients for out-of-distribution generalization. LCMat [37] induces a better adaptation of the pruned dataset on the perturbed parameter region than the exact point matching. Besides, calculating gradient variance along time dimension tracks dynamic optimization change. VoG [1] uses this to estimate sample importance and the visualization shows that high-variance samples are more worthwhile to learn. Dyn-Unc [15] calculates the time-dimension variance of predicted target class probability to evaluate sample importance. Differing from VoG and Dyn-Unc, our TDDS does not need pixel-wise gradient calculation while considering non-target probabilities, which enables a more precise evaluation with lower computational overhead. + +# 3. Preliminary + +Throughout this paper, we denote the full training dataset as $\mathbb{U} = \{(x_n,y_n)\}_{n = 1}^N$ , where $x_{n}\in \mathbb{R}^{D}$ and $y_{n}\in \mathbb{R}^{1\times C}$ are drawn i.i.d. from a natural distribution $\mathcal{D}$ . We denote a neural network parameterized with weight matrix $\pmb{\theta}$ as $f_{\pmb{\theta}}$ . Under these definitions, the optimization objective of $f_{\pmb{\theta}}$ on $\mathbb{U}$ is to minimize empirical risk $\mathcal{L}(\mathbb{U};\pmb {\theta}) = \frac{1}{N}\sum_{n = 1}^{N}\ell (f_{\pmb{\theta}}(\pmb {x}_n),\pmb {y}_n)$ , where $f_{\pmb{\theta}}(\pmb {x}_n)\in \mathbb{R}^{1\times C}$ outputs the predicted probabilities of each class. Typically, $\pmb{\theta}$ is updated as follow2, + +$$ +\boldsymbol {\theta} _ {t + 1} = \boldsymbol {\theta} _ {t} - \eta \sum_ {n = 1, \boldsymbol {x} _ {n} \in \mathbb {U}} ^ {N} \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {n}\right), \tag {1} +$$ + +where $\eta$ is the learning rate and $\pmb{g}_t(\pmb{x}_n)$ is defined as the gradient calculated over the data pair $(\pmb{x}_n, \pmb{y}_n)$ in epoch $t$ . + +Dataset pruning aims to enhance training efficiency by constructing a coreset $\mathbb{S} = \{(x_n,y_m)\}_{m = 1}^M$ , $\mathbb{S}\subset \mathbb{U}$ that can achieve comparable performance to $\mathbb{U}$ . The objective of dataset pruning can be formulated as, + +$$ +\underset {\substack {(\boldsymbol {x}, \boldsymbol {y}) \sim \mathcal {D} \\ \boldsymbol {\theta} _ {0} \sim \mathcal {P} _ {\boldsymbol {\theta} _ {0}}}} {\mathbb {E}} \left[ \ell \left(f _ {(\mathrm {U}, \boldsymbol {\theta} _ {0})} (\boldsymbol {x}), \boldsymbol {y}\right) \right] \simeq \underset {\substack {(\boldsymbol {x}, \boldsymbol {y}) \sim \mathcal {D} \\ \boldsymbol {\theta} _ {0} \sim \mathcal {P} _ {\boldsymbol {\theta} _ {0}}}} {\mathbb {E}} \left[ \ell \left(f _ {(\mathrm {S}, \boldsymbol {\theta} _ {0})} (\boldsymbol {x}), \boldsymbol {y}\right) \right], \tag{2} +$$ + +where $f_{(\mathbb{U},\pmb{\theta}_0)}$ and $f_{(\mathbb{S},\pmb{\theta}_0)}$ represent the networks trained on $\mathbb{U}$ and $\mathbb{S}$ with weight $\pmb{\theta}_0$ initialized from distribution $\mathcal{P}_{\pmb{\theta}_0}$ . + +# 4. Methodology + +As discussed earlier, despite that exploring long-range dynamics provides a more comprehensive sample evaluation, the averaging operation hinders the construction of a coreset with strong generalization. In this section, we present the proposed Temporal Dual-Depth Scoring (TDDS) strategy, which balances the incorporation of training dynamics and the identification of well-generalized samples. In the outer level, we identify samples with their variability during training which is encouraged theoretically by the optimization space matching between coreset and original dataset (refer to Section 4.1). In the inner level, the gradient in the outer level is replaced with the projected component on the accumulated direction to estimate valid contributions in every epoch (refer to Section 4.2). Finally, to enhance efficiency, we conduct TDDS with a moving window (refer to Section 4.3). The proposed TDDS is summarized in Algorithm 1. + +# 4.1. Outer Level: Enhance Coreset Generalization by Maximizing Variance + +To construct the coreset $\mathbb{S}$ satisfying Equation 2, gradient-based methods [3, 18, 26] propose to minimize the distance between full dataset and coreset gradient, + +$$ +\mathbb {S} ^ {*} = \underset {\mathbb {S} \subset \mathbb {U}} {\arg \min } \| \boldsymbol {G} _ {t, \mathrm {U}} - \tilde {\boldsymbol {G}} _ {t, \mathbb {S}} \|, \quad \text {w h e r e} +$$ + +$$ +\boldsymbol {G} _ {t, \mathbb {U}} = \sum_ {\substack {n = 1, \\ \boldsymbol {x} _ {n} \in \mathbb {U}}} ^ {| \mathbb {U} |} \boldsymbol {g} _ {t} (\boldsymbol {x} _ {n}), \quad \tilde {\boldsymbol {G}} _ {t, \mathbb {S}} = \sum_ {\substack {m = 1, \\ \boldsymbol {x} _ {m} \in \mathbb {S}}} ^ {| \mathbb {S} |} \boldsymbol {g} _ {t} (\boldsymbol {x} _ {m}), \tag{3} +$$ + +$\tilde{G}_{t,\mathbb{S}}$ can be regarded as the gradient reconstruction in coreset space. To solve this minimization problem, Huang et al. [17] recommends pruning samples with smaller gradient magnitudes to minimize their potential impact on optimization. + +However, whenever the distance is minimized, the obtained snapshot-based coreset fails to generalize across training progress. Here are the reasons: (1) the distinctive contributions of samples are temporal statistics. Evaluating them at a specific time point causes significant bias when considering dynamic optimization; (2) samples with larger individual gradients dominate the matching process. Without considering the current optimization context, these samples introduce a substantial error in approximating the accumulated gradient. + +To address the first issue, we proposed to extend Equation 3 to a continuous training duration to capture training dynamics, + +$$ +\mathbb {S} ^ {*} = \underset {\mathbb {S} \subset \mathbb {U}} {\arg \min } \frac {1}{T} \sum_ {t = 1} ^ {T} \| \boldsymbol {\mathcal {G}} _ {t, \mathbb {U}} - \tilde {\boldsymbol {\mathcal {G}}} _ {t, \mathbb {S}} \| ^ {2}, \tag {4} +$$ + +![](images/07bd123adda81a9ec948be85dac64ebcef742fcf69b43c051175704c110158fb.jpg) +Figure 2. The pipeline of our proposed TDDS. First, we record individual predicted probabilities of samples $f_{t_i}^{x_n} = f_{\theta_{t_i}}(\pmb{x}_n)$ during training. Then, we approximate the projected gradient, i.e. the component of gradient $g_{t_i}^{x_n} = g_{t_i}(\pmb{x}_n)$ on accumulated gradient $G_{t_i}$ direction, with KL-based loss difference between two adjacent epochs. Next, the projected gradients are used to estimate individual contributions of samples. Finally, the important samples are identified with larger projected gradient variances over time. + +Here, the gradients generated by $\mathbb{U}$ and $\mathbb{S}$ at epoch $t$ are defined as $\pmb{\mathcal{G}}_{t,\mathbb{U}} = [|\pmb{g}_t(\pmb{x}_n)|]_{n=1}^N$ and similarly $\tilde{\pmb{G}}_{t,\mathbb{S}}$ is its reconstructed counterpart using $\mathbb{S}$ . Here we use magnitude instead of gradient itself to balance the training dynamic integration and complexity. Experiments in Section 5.4 also shows that magnitude-based minimization performs better than gradient-based when considering continuous training. + +Directly solving Equation 4 is NP-hard. Thus, we turn to its equivalent, temporal gradient variance maximization, + +$$ +\mathbb {S} ^ {*} = \underset {\mathbb {S} \subset \mathbb {U}} {\arg \max } \mathcal {R} (\mathbb {S}), \quad \mathcal {R} (\mathbb {S}) = \sum_ {t = 1} ^ {T} \| \boldsymbol {G} _ {t, \mathbb {S}} - \overline {{\boldsymbol {G}}} _ {\mathbb {S}} \| ^ {2}, \tag {5} +$$ + +where $\overline{\pmb{G}}_{\mathbb{S}} = \frac{1}{T}\sum_{t = 1}^{T}\pmb{G}_{t,\mathbb{S}},\pmb{G}_{t,\mathbb{S}} = [|\pmb{g}_t(\pmb{x}_m)|]_{m = 1}^M$ is the mean gradient over training time. Detailed proof can be founded in Supplementary. Equation 5 measures the variability of samples and enhances the identification of wellgeneralized samples compared to previous average-based methods [33, 43]. + +# 4.2. Inner Level: Estimate Actual Contribution with Projected Gradient + +According to Equation 5, sample importance can be evaluated with its gradient variance over time. For any sample $\boldsymbol{x}_n$ , we have, + +$$ +\mathcal {R} (\boldsymbol {x} _ {n}) = \sum_ {t = 1} ^ {T} \left\| \left| \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {n}\right) \right| - \overline {{\left| \boldsymbol {g} \left(\boldsymbol {x} _ {n}\right) \right|}} \right\| ^ {2}, \tag {6} +$$ + +where $\overline{|\pmb{g}(\pmb{x}_n)|} = \frac{1}{T}\sum_{t=1}^{T}|\pmb{g}_t(\pmb{x}_n)|$ . Equation 6 treats sample-wise gradient independently, which may not pre + +![](images/0407cbe5c8ad1019ed75f4a865863849988bb84e52da32f0d9aa6499f6581993.jpg) +(a) + +![](images/88b6cbdc6087fee669125ffd370904b292cf2dc052afe505308f365f25dc4c48.jpg) +(b) +Figure 3. Incorporating sample-wise gradient in the current optimization context. After projecting onto the current accumulated gradient, samples with similar gradients exhibit different behaviors. + +cisely describe the valid contribution in the current optimization context. That is the second problem mentioned in Section 4.1. As illustrated in Figure 3(a), the gradient of sample $\boldsymbol{x}_n$ remains constant between $t$ and $t + 1$ . However, when incorporating it into the current optimization context, its valid contribution undergoes a significant shift. Thus, we propose to calculate the gradient variance after projecting it on the accumulated direction, that is, $|\boldsymbol{g}_t(\boldsymbol{x}_n)|$ is reformulated as, + +$$ +\left| \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {n}\right) \right| = \left| \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {n}\right) \cdot \sum_ {j = 1, \boldsymbol {x} _ {j} \in \mathbb {U}} ^ {| \mathbb {U} |} \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {j}\right) \right|. \tag {7} +$$ + +Calculating Equation 6 requires sample-wise gradients over a period of $T$ , which is not feasible due to time and memory constraints. According to Equation 1, the accumu + +lated gradient is equal to $\frac{1}{\eta} (\pmb{\theta}_t - \pmb{\theta}_{t + 1})$ , thus the projection in Equation 7 is reformed as loss difference, + +$$ +\begin{array}{l} \left| \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {n}\right) \right| = \frac {1}{\eta} \left| \left(\boldsymbol {\theta} _ {t} - \boldsymbol {\theta} _ {t + 1}\right) \nabla_ {\boldsymbol {\theta} _ {t}} \ell \left(f _ {\boldsymbol {\theta} _ {t}} \left(\boldsymbol {x} _ {n}\right), \boldsymbol {y} _ {n}\right) \right| \tag {8} \\ \approx \frac {1}{\eta} \left| \ell \left(f _ {\boldsymbol {\theta} _ {t + 1}} (\boldsymbol {x} _ {n}), \boldsymbol {y} _ {n}\right) - \ell \left(f _ {\boldsymbol {\theta} _ {t}} (\boldsymbol {x} _ {n}), \boldsymbol {y} _ {n}\right) \right|, \\ \end{array} +$$ + +which can be deduced from the first-order Taylor expansion. + +Thus, we can evaluate the per-sample contribution to the accumulated gradient direction with its loss change. In the context of classification, $\ell$ is typically Cross Entropy (CE) loss, + +$$ +\Delta \ell_ {t} ^ {n} = \boldsymbol {y} _ {n} ^ {\top} \cdot \log \frac {f _ {\boldsymbol {\theta} _ {t + 1}} \left(\boldsymbol {x} _ {n}\right)}{f _ {\boldsymbol {\theta} _ {t}} \left(\boldsymbol {x} _ {n}\right)}, \tag {9} +$$ + +where $\Delta \ell_t^n = \ell(f_{\theta_{t+1}}(\pmb{x}_n), \pmb{y}_n) - \ell(f_{\pmb{\theta}_t}(\pmb{x}_n), \pmb{y}_n)$ . Due to the one-hot $\pmb{y}_n$ , non-target probabilities are unfortunately overlooked, obliterating a significant amount of distinctive information. This reminds us of the Kullback-Leibler (KL) divergence loss, which can be achieved by simply replacing $\pmb{y}_n$ with $f_{\pmb{\theta}_{t+1}}(\pmb{x}_n)$ , + +$$ +\Delta \ell_ {t} ^ {n} = f _ {\boldsymbol {\theta} _ {t + 1}} \left(\boldsymbol {x} _ {n}\right) ^ {\top} \cdot \log \frac {f _ {\boldsymbol {\theta} _ {t + 1}} \left(\boldsymbol {x} _ {n}\right)}{f _ {\boldsymbol {\theta} _ {t}} \left(\boldsymbol {x} _ {n}\right)}. \tag {10} +$$ + +Considering that $f_{\pmb{\theta}_t(\pmb{x}_n)}$ follows a Bernoulli distribution $\mathcal{B}(p_t)$ , where $p_t$ represents the probability of the target class at epoch $t$ . If $p_t$ equals $p_{t + 1}$ , Equation 9 fails to distinguish, but Equation 10 can still differentiate the contributions of samples with $q_{t}$ and $q_{t + 1}$ . Here, $q_{t}$ and $q_{t + 1}$ are the non-target probability distributions. This effectiveness has been proved in Section 5.4. + +# 4.3. Efficient Implementation of TDDS + +When computing $\mathcal{R}(\pmb{x}_n)$ with Equation 6, Equation 8, and Equation 10, storing $T$ -epoch predicted outputs may lead to out-of-memory problems, especially with large datasets like ImageNet (containing 1, 281, 167 samples across 1,000 classes). As a solution, we suggest an efficient calculation using an exponential moving average (EMA) weighting strategy. For any training point $t \geq K$ , the variance $\mathcal{R}_t(\pmb{x}_n)^3$ is computed over a $K$ -epoch window ranging from $t - K + 1$ to $t$ , + +$$ +\mathcal {R} _ {t} \left(\boldsymbol {x} _ {n}\right) = \sum_ {t - K + 1} ^ {t} \left\| \left| \Delta \ell_ {t} ^ {n} \right| - \overline {{\left| \Delta \ell_ {t} ^ {n} \right|}} \right\| ^ {2}, \tag {11} +$$ + +where $\overline{|\Delta\ell_t^n|}$ is the average of loss difference in a window. For $T$ -epoch trajectory, $T - K + 1$ windows are weighted as, + +$$ +\mathcal {R} \left(\boldsymbol {x} _ {n}\right) = \beta \mathcal {R} _ {t} \left(\boldsymbol {x} _ {n}\right) + (1 - \beta) \mathcal {R} \left(\boldsymbol {x} _ {n}\right), \tag {12} +$$ + +where $\beta$ is the decay coefficient of EMA whose setting is examined in Section 5.3. With this EMA, we only need to store predicted outputs for one window, significantly alleviating storage burden. + +After sorting $\{\mathcal{R}(\pmb{x}_n)\}_{n=1}^N$ , the top-M samples are selected to construct coreset denoted as $\{\mathbb{S}, r\} = \{(x_m, y_m), \mathcal{R}(x_m)\}_{m=1}^M$ . Since, the samples with larger $\mathcal{R}(\pmb{x}_m)$ contribute more in the original data training. We remark that this dominance should be maintained in coreset training, i.e., + +$$ +\boldsymbol {\theta} _ {t + 1} = \boldsymbol {\theta} _ {t} - \eta \sum_ {m = 1} ^ {M} \boldsymbol {g} _ {t} \left(\boldsymbol {x} _ {m}\right) \mathcal {R} \left(\boldsymbol {x} _ {m}\right). \tag {13} +$$ + +This helps to transfer relative sample importance to coreset training. This effectiveness is proved in Section 5.4. + +Algorithm 1 Temporal Dual-Depth Scoring (TDDS) + +Input: Training dataset U; A network $f_{\theta}$ with weight $\theta$ ; Learning rate $\eta$ ; Epochs $T$ ; Iterations $I$ per epoch; Window size $K$ ; Decay factor $\beta$ . + +1: for $t = 1$ to $T$ do + +2: for $i = 1$ to $I$ , Sample a mini-batch $\mathbb{B}_i \subset \mathbb{U}$ do + +3: Record predicted probabilities $f_{\pmb{\theta}_t}(x_n)$ , $x_n \in \mathbb{B}_i$ + +4: Calculate $\Delta \ell_t^n$ for each $\pmb{x}_n\in \mathbb{B}_i$ + +$\triangleright$ Defined in Equation 10 + +5: Update weight $\pmb{\theta}_{i + 1} = \pmb{\theta}_i - \eta \pmb{G}_{t,\mathbb{B}_i}$ + +6: end for + +7: if $K \leq t \leq T$ then + +8: Calculate $\mathcal{R}_t(\pmb{x}_n)$ in one window, $\pmb{x}_n\in \mathbb{U}$ + +$\triangleright$ Defined in Equation 11 + +9: Update $\mathcal{R}(\pmb{x}_n)$ with EMA, $\pmb{x}_n\in \mathbb{U}$ + +$\triangleright$ Defined in Equation 12 + +10: end if + +11: end for + +12: Select Top-M $\{\mathbb{S},r\} \leftarrow \{(\pmb {x}_m,\pmb {y}_m),\mathcal{R}(\pmb {x}_m)\}_{m = 1}^M$ + +Output: Selected subset $\mathbb{S} = \{(x_m, y_m)\}_{m=1}^M$ ; associated sample-wise importance $r = \{\mathcal{R}(x_m)\}_{m=1}^M$ + +# 5. Experiments + +# 5.1. Experiment Settings + +Datasets and Networks. The effectiveness of the proposed TDDS is evaluated on three popular benchmarks, i.e., CIFAR-10, CIFAR-100 [19], and ImageNet-1K [9] with three networks, i.e., ResNet-18, ResNet-34 [14], and SwinT [21]. We also verify the cross-architecture performance on four networks including ResNet-50 [14], VGG-16 [38], MobileNet-v2 [36], and ShuffleNet [23]. + +Training Hyperparameters. Theoretically, if pruning rate $p = 1 - \frac{|\mathbb{S}|}{|\mathbb{U}|}$ , where $0 < p \leq 1$ , the training process + +Table 1. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-E. The model trained with the full dataset achieves $95.23\%$ and $78.21\%$ accuracy. + +
pCIFAR-10CIFAR-100
30%50%70%80%90%30%50%70%80%90%
Random94.58 ±0.0493.38 ±0.1790.61 ±0.4488.87 ±0.4783.77 ±0.2675.53 ±0.0471.95 ±0.1664.59 ±0.3257.79 ±0.2446.68 ±1.07
Entropy [8]94.45 ±0.0791.90 ±0.1686.24 ±0.2683.49 ±0.2172.06 ±0.8172.39 ±0.2064.44 ±0.3650.73 ±0.8642.86 ±0.2529.56 ±0.54
Forgetting [43]95.45 ±0.2495.05 ±0.0589.14 ±2.0476.18 ±3.1845.87 ±1.8777.38 ±0.0970.76 ±0.4049.92 ±0.2838.42 ±1.1325.82 ±0.52
EL2N [31]95.43 ±0.1095.06 ±0.0486.69 ±1.7168.64 ±3.7031.89 ±1.5176.89 ±0.3167.57 ±0.1536.45 ±1.3617.31 ±0.339.10 ±0.69
AUM [33]95.44 ±0.0995.19 ±0.0991.19 ±0.6369.60 ±3.1134.74 ±0.1177.35 ±0.1868.17 ±0.5231.69 ±0.3418.43 ±0.479.29 ±0.27
Moderate [46]93.96 ±0.0692.34 ±0.0989.71 ±0.1487.75 ±0.2783.61 ±0.2474.60 ±0.1070.29 ±0.3162.81 ±0.0856.52 ±0.3741.82 ±1.12
Dyn-Unc[15]95.08 ±0.0294.03 ±0.1489.40 ±0.1379.76 ±1.0937.12 ±1.1273.36 ±0.1065.90 ±0.2550.16 ±0.4739.19 ±0.2715.20 ±0.41
TDDS95.47 ±0.0695.21 ±0.0493.03 ±0.2591.30 ±0.2585.46 ±0.2177.56 ±0.0674.04 ±0.3467.78 ±0.4463.01 ±0.1254.51 ±0.22
+ +![](images/1723b7d0b0597c5726289285ce12c8c522eee57fc31b6b864b3c8f9bf5c20f6d.jpg) +Figure 4. Parameter analysis of range $T$ and window size $K$ on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.3, 0.5, 0.7, 0.8, and 0.9. + +![](images/0c507c469d36d67f48b1297ff526eab9bdbb2e3f4dc1c6427ec71c6404f45969.jpg) + +![](images/0a274433ea05945a7baecf5df7f098ecd5abcc31dc76b0efb9c20d4f8f7ef1c8.jpg) + +![](images/442b37b32aeb7ff5e9c63d481a917255eb2007cebe8834d2f6a37a6a6f41d019.jpg) + +![](images/4fd9c50ad27359198197473b053c751b90eb456222ecd4c34adc42e6f051e29d.jpg) + +Table 2. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-P. The model trained with the full dataset achieves $95.23\%$ and $78.21\%$ accuracy. + +
pCIFAR-10CIFAR-100
30%50%70%30%50%70%
Random94.33 ±0.1793.4 ±0.1790.94 ±0.3874.59 ±0.2771.07 ±0.465.3 ±0.21
Entropy [8]94.44 ±0.292.11 ±0.4785.67 ±0.7172.26 ±0.0863.26 ±0.2950.49 ±0.88
Forgetting [43]95.36 ±0.1395.29 ±0.1890.56 ±1.876.91 ±0.3268.6 ±1.0238.06 ±1.14
EL2N [31]95.44 ±0.1594.61 ±0.2087.48 ±1.3376.25 ±0.2465.90 ±1.0634.42 ±1.50
AUM [33]95.07 ±0.2495.26 ±0.1591.36 ±1.476.93 ±0.3267.42 ±0.4930.64 ±0.58
Moderate [46]93.86 ±0.1192.58 ±0.3090.56 ±0.2774.60 ±0.4171.10 ±0.2465.34 ±0.41
CCS [51]95.40 ±0.1295.04 ±0.3793.00 ±0.1677.14 ±0.3174.45 ±0.1668.92 ±0.12
TDDS95.50 ±0.0795.66 ±0.0893.92 ±0.0477.95 ±0.3074.98 ±0.1669.46 ±0.10
+ +speeds up by $\frac{1}{1 - p}$ times. We consider two coreset training strategies: Strategy-E prioritizes efficiency with same-epoch training on both full dataset and coreset. Strategy-P + +Table 3. Comparison of different dataset pruning methods on ImageNet-1K with ResNet-34 under Strategy-E. The model trained with the full dataset achieves $73.54\%$ Top-1 accuracy. + +
pImageNet-1K
70%80%90%
Random64.1960.7652.63
Entropy[8]62.3456.8043.39
Forgetting [43]64.2962.0152.14
EL2N [31]46.9232.6815.90
AUM [33]39.3423.6411.70
Moderate [46]64.0461.3552.45
TDDS64.6962.5653.91
+ +prioritizes performance by training coreset for more epochs. If $\frac{|\mathbb{S}|}{|\mathbb{U}|} = 1 - p$ , the training process is extended to $\frac{1}{1 - p}$ times of the original one. For CIFAR-10 and -100, we train ResNet-18 for 200 epochs with a batch size of 128. For ImageNet, ResNet-34 and Swin-T are trained for 60 [51] and 300 epochs [15] with batch sizes of 256 and 1024, respec + +![](images/cfa1bd938f063bb9d3ceeb4759c681b98a36ab658794a2aef47ba7740986cc63.jpg) +Figure 5. Parameter analysis of decay coefficient $\beta$ on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.7, 0.8, and 0.9. + +tively. SGD optimizer with momentum of 0.9 and weight decay of 0.0005 is used for update networks. The learning rate is initialized as 0.1 and decays with the cosine annealing scheduler. During experiments, we found that smaller batch size boosts performance at high pruning rates (shown in Supplementary). Thus, for $p = 0.8$ , we halved the batch size, and for $p = 0.9$ , we reduced it to one-fourth. All compared methods use the same settings. With Strategy-P, for example, training a CIFAR coreset with only $50\%$ training samples takes 400 epochs, while keeping the other hyperparameters unchanged. Considering the time-consuming training, we only conduct Strategy-P experiments at pruning rates of 0.3, 0.5, 0.7. + +Baselines. Eight baselines are used for comparison, with the latter seven being SOTA methods: 1) Random; 2) Entropy [8]; 3) Forgetting [43]; 4) EL2N [31]; 5) AUM [33]; 6) Moderate [46]; 7) CCS [51]; 8) Dyn-Unc [15]. Due to the limited page, we provide the technical details of these baselines in Supplementary. + +# 5.2. Benchmark Evaluation Results + +ResNet-18 on CIFAR-10 and 100. Table 1 and Table 2 report the performance of different dataset pruning methods under Strategy-E and P, respectively. Under both strategies, TDDS consistently outperforms other methods. For instance, under Strategy-E, none of the compared methods surpasses Random at aggressive pruning rates, while TDDS achieves $85.46\%$ and $54.51\%$ accuracy after pruning $90\%$ samples of CIFAR-10 and 100 surpassing Random by $1.69\%$ and $7.83\%$ , respectively. By extending the training duration, Strategy-P enhances the performance of all methods to varying degrees. TDDS still maintains its superiority, for example, with only $30\%$ training data, the accuracy on CIFAR-10 and -100 are $93.92\%$ and $69.46\%$ outperforming CCS by $0.92\%$ and $0.54\%$ , respectively. These results highlight TDDS as a promising choice for both efficiency and performance-oriented dataset pruning. + +ResNet on ImageNet-1K. For ImageNet-1K, we train ResNet-34 models on original dataset for 90 epochs to collect training dynamics and then train the model on coreset for 60 epochs as [51]. Experiment results are given in Table 3. The results show that the proposed TDDS has better performance on ImageNet-1K, especially under aggressive + +pruning rates. For example, when pruning $90\%$ samples, TDDS still achieves $53.91\%$ which is $1.77\%$ and $1.46\%$ higher than Forgetting and Moderate, respectively. + +Swin-T on ImageNet-1k. We also evaluate Swin-T on ImageNet-1K. Like Dyn-Unc [15], Table 4 reports the results under four pruning rates. Notably, TDDS consistently outperforms other competitors, for example, after pruning $50\%$ training data, TDDS achieves $78.33\%$ accuracy, surpassing Forgetting, Moderate, and Dyn-Unc by $4.01\%$ , $3.35\%$ and $0.69\%$ , respectively. + +Table 4. Comparison of different dataset pruning methods on ImageNet-1K with Swin-T under Strategy-E. The model trained with the full dataset achieves $79.58\%$ Top-1 accuracy. + +
pImageNet-1K
25%30%40%50%
Random77.8277.1875.9374.54
Forgetting [43]78.7078.2777.5574.32
Moderate [46]77.7477.0675.9474.98
Dyn-Unc [15]79.5479.1478.4977.64
TDDS79.7679.5779.0978.33
+ +# 5.3. Parameter Analysis + +Estimation Range $T$ and Window Size $K$ . Due to the random initialization, models adapt to prominent features (easy samples) during early training. As training progresses, models gradually acquire more abstract and complex features (hard samples) that are challenging to capture in early training. Thus, the importance of samples should be estimated in different training phases with respect to different pruning levels. As shown in Figure 4, we analyze the influence of range $T$ and window size $K$ on perfor + +Table 5. Ablation study for Dual-depth strategy. The numbers in square brackets indicate the improvement in accuracy of the method presented in the current column compared to the corresponding method in the previous column. + +
pCIFAR-100
EL2NEL2N+outerTDDS
30%76.8977.47[+ 0.58]77.56[+ 0.09]
50%67.5773.93[+ 6.36]74.04[+ 0.11]
70%36.4567.04[+30.59]67.78[+ 0.74]
80%17.3158.21[+40.90]63.01[+ 1.80]
90%9.1040.36[+31.26]54.51[+14.15]
outerX✓✓
innerXX✓
+ +![](images/61902f4c2dd2e389807233afe2ea6826aa4b6cc4bf1a52862d6bb44a5106631a.jpg) +(a) + +![](images/94b1ee73542c153601fe8bb8741e4ca6b2b418b8d906b2e55edbdbb16db47187.jpg) +(b) +Figure 6. Ablation studies for (a) Gradient Magnitude vs. Gradient, (b) KL-based Loss Difference, and (c) Importance-aware Coreset Training. In (a), GM and G represent estimating sample contribution with gradient magnitude and gradient, respectively. In (b), KL and CE represent calculating loss difference with KL and CE loss, respectively. In (c), Imp-aware and Imp-unaware represent training coreset with and without weighting samples with their importance scores, respectively. + +![](images/754d2608562739bbf7406ef86c8bbd5498d0e92c40d16ba4b4386b1fec6ad94b.jpg) +(c) + +mance. Apparently, for a larger pruning rate, we should select samples earlier in training. For CIFAR-100, the optimal $(p,T,K)$ setting is (0.3, 90, 10), (0.5, 70, 10), (0.7, 60, 20), (0.8, 20, 10), and (0.9, 10, 5). The parameter settings of CIFAR-10 and ImageNet are reported in Supplementary. + +Decay Coefficient $\beta$ of EMA. In contrast to the simple average (SA), EMA employs exponential weighting, giving more weight to the most recent window. We examine four values of $\beta$ , where $\beta = 0$ represents SA. As illustrated in Figure 5, EMA outperforms SA regardless of the $\beta$ value chosen. Among the considered pruning levels, $\beta = 0.9$ yields the best performance, surpassing $\beta = 0.95$ and $\beta = 0.85$ . + +# 5.4. Ablation Studies + +Gradient Magnitude vs Gradient. We use gradient magnitudes in Equation 4. Although gradients themselves appear capable of describing optimization, our experimental findings indicate that the use of gradient magnitudes yields superior performance, as depicted in Figure 6(a). We argue that gradients often prioritize samples with frequently reversing gradients, resulting in unstable training and slower convergence. + +KL-based Loss Difference. As discussed in Section 4.3, the KL loss provides a more comprehensive assessment of loss difference and is expected to precisely characterize sample contribution. To evaluate its effectiveness, we replace KL loss with CE loss and conduct experiments across all considered pruning rates. As illustrated in Figure 6(b), although CE is slightly higher than KL when the pruning rate is $30\%$ , KL exhibits an absolute advantage at all other pruning levels. For example, when pruning rate is $90\%$ , KL outperforms CE by a substantial margin of $15.97\%$ . + +Importance-aware Coreset Training. We formulate importance-aware subset training as Equation 13. The maintained relative importance provides optimization guid + +ance for subset training. As shown in Figure 6(c), the advantage becomes increasingly pronounced as the pruning rate rises. When pruning rate is $90\%$ , the accuracy of importance-aware subset training outperforms its unaware counterpart by $6.55\%$ . + +Dual-Depth Strategy. To investigate the effectiveness of the proposed Dual-Depth strategy, we replace the inner depth with EL2N, and Table 5 indicates that incorporating the outer depth boosts EL2N at all considered pruning rates. Nevertheless, this enhancement still falls short of our dual-depth design, particularly evident in aggressive pruning scenarios. + +# 6. Conclusion + +In this study, we reveal that the snapshot-based data pruning results in poor generalization across various pruning scenarios. However, existing methods fail to identify well-generalized samples even with evaluation criteria considering the whole training progress. We attribute this to the averaging-based dynamics incorporation and imprecise sample contribution characterization. To address these problems, we propose a dataset pruning method called TDDS, which designs a Temporal Dual-Depth Scoring strategy to balance the incorporation of training dynamics and the identification of well-generalized samples. Extensive experiments on various datasets and networks, demonstrate the SOTA performance of our proposed method. + +# Acknowledgements + +This research is supported in part by the National Natural Science Foundation of China under Grant 62121001, Grant 62322117, and Grant 62371365. This research is also supported by Joey Tianyi Zhou's A*STAR SERC Central Research Fund (Use-inspired Basic Research) and Jiawei Du's A*STAR Career Development Fund (CDF) C233312004. + +# References + +[1] Chirag Agarwal, Daniel D'souza, and Sara Hooker. Estimating example difficulty using variance of gradients. In IEEE Conf. Comput. Vis. Pattern Recog., pages 10368-10378, 2022. 3 +[2] Shun-ichi Amari. Backpropagation and stochastic gradient descent method. Neurocomputing, 5(4-5):185-196, 1993. 3 +[3] Lukas Balles, Giovanni Zappella, and Cedric Archambeau. 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The red and blue points represent the data samples of two coresets constructed with " + }, + { + "bbox": [ + 305, + 377, + 547, + 498 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 305, + 377, + 547, + 498 + ], + "type": "text", + "content": " pruning rate at Epoch 10 and 100 from the same training progress, respectively. (b) Snapshot-based coresets fail to generalize to pruning settings, especially pruning rates. The accuracy gap between coresets constructed at Epoch 10 and 100 is increasing as the pruning rate grows. Here, we measure importance using the error vector score, a classic snapshot-based criterion defined in [31]. 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Actually, a substantial portion of data samples are redundant [43, 46, 51], which means they can be excluded from training without compromising performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 714 + ], + "type": "text", + "content": "Numerous dataset pruning works [12, 16, 17, 22, 25, 29, 32, 46, 49] have explored various criteria [13, 41] for identifying important data samples, including distribution distance [45, 46], uncertainty [8], loss [31, 43], and gradient [31]. Most of them evaluate sample importance using a snapshot of training progress. For example, Paul et al. [31]" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 683, + 212, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 212, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 212, + 713 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 58, + 683, + 212, + 713 + ], + "type": "text", + "content": " Equal contribution. \n" + }, + { + "bbox": [ + 58, + 683, + 212, + 713 + ], + "type": "inline_equation", + "content": "\\ddagger" + }, + { + "bbox": [ + 58, + 683, + 212, + 713 + ], + "type": "text", + "content": " Corresponding authors. \n*Work completed during internship at A*STAR" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26223" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "uses the error vector score generated by a few epochs" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " in early training; Xia et al. [46] calculates the distribution distances of features at the end of training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 287, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 287, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 287, + 263 + ], + "type": "text", + "content": "However, these snapshot-based pruning methods have two potential problems. Firstly, the importance scores of samples fluctuate with epochs during the progress of training. Consequently, the coresets constructed by the importance scores at different snapshots of training progress differ from each other significantly. As verified in Figure 1(a), the coresets constructed at Epoch 10 and 100 obviously contain different samples. Secondly, relying on importance scores from a snapshot can lead to overfitting in the construction of the coreset, as this approach may not generalize well across different scenarios, such as varying pruning rates. As shown in Figure 1(b), the accuracy gap of coresets from different snapshots becomes larger as the pruning rate increases." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 264, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 287, + 467 + ], + "type": "text", + "content": "To address these two problems, a straightforward approach is to consider a broader range of training dynamics throughout the training process, with a focus on selecting well-generalized data samples. For example, Pleiss et al. [33] involves training dynamics by measuring the probability gap between the target class and the second largest class in each epoch; Toneva et al. [43] monitors the forgetting events throughout the entire training process. These forgetting events occur when samples, classified correctly in a prior epoch, are subsequently predicted incorrectly. Unfortunately, existing studies fall short of balancing the incorporation of training dynamics with the effective identification of well-generalized samples. The use of an averaging down-sampling operation aims to cover a broader range of training dynamics. However, this approach can inadvertently lead to the neglect of well-generalized samples during data selection, ultimately degrading overall performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 468, + 287, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 695 + ], + "type": "text", + "content": "In this paper, we propose Temporal Dual-Depth Scoring (TDDS) pruning method, designed to effectively balance and address the aforementioned problems. We employ a dual-depth temporal scoring metric that spans the training process for data selection. In the inner level (depth one), we approximate the actual contribution of each sample in every epoch. This approximation is achieved by projecting the sample-wise gradients onto the accumulated gradient in each epoch, following the approach suggested by Du et al. [11]. We then integrate these contributions over a specified window, typically spanning 10 epochs, to incorporate more training dynamics. In the outer level (depth two), we reduce reliance on the averaging down-sampling operation to prevent overlooking vital samples. Well-generalized samples are identified based on the variability of the projected gradients, calculated in each window from the inner level. This design of the outer level draws inspiration from He et al. [15], who tracked the variance of predicted target probabilities throughout training to enhance pruning effectiveness." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": "The pipeline of our proposed TDDS is clearly illustrated in Figure 2. Extensive experiments demonstrate the superior generalization capability of the proposed TDDS, enabling it to outperform other comparison methods across different pruning settings on various datasets and networks. For example, on CIFAR-100, our method achieves " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "54.51\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " accuracy with only " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " training data, surpassing random selection by " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "7.83\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " and other SOTA methods by at least " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "12.69\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 317, + 171, + 493, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 171, + 493, + 182 + ], + "spans": [ + { + "bbox": [ + 317, + 171, + 493, + 182 + ], + "type": "text", + "content": "Our main contributions are summarized as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 185, + 545, + 340 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 185, + 545, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 185, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 306, + 185, + 545, + 256 + ], + "type": "text", + "content": "- We examine the poor generalization resulting from existing snapshot-based dataset pruning. Subsequently, we analyze the inefficacy of current solutions to this generalization issue, attributing it to the inability to balance the incorporation of training dynamics with the effective identification of well-generalized samples." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 257, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 257, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 257, + 545, + 340 + ], + "type": "text", + "content": "- We thereby propose a novel dataset pruning method called Temporal Dual-Depth Scoring (TDDS), resorting to two temporal depths/levels to take respective care of the contribution evaluation and generalization spanning training progress. Experiments on diverse datasets and networks demonstrate the effectiveness of TDDS, achieving SOTA performance." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 359, + 397, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 359, + 397, + 372 + ], + "spans": [ + { + "bbox": [ + 306, + 359, + 397, + 372 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 381, + 405, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 405, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 405, + 395 + ], + "type": "text", + "content": "2.1. Dataset Pruning" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 402, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 713 + ], + "type": "text", + "content": "Dataset Pruning, also known as Coreset Selection aims to shrink the dataset scale by selecting important samples according to some predefined criteria. Herding [6, 45] and Moderate [46] calculate the distance in feature space. Entropy [8] and Cal [24] explore the uncertainty and decision boundary with the predicted outputs. GradND/EL2N [31] quantifies the importance of a sample with its gradient magnitude. Most of these methods are snapshot-based, that is they do not care about the training dynamics that actually distinguish the behaviors of samples in the overall optimization. There are some efficient training methods [10, 28, 42, 47], which focus more on training efficiency and execute online selection spanning training progress. For example, gradient matching-based methods GradMatch [18] and Craig [26] minimize the distance between gradients produced by the full dataset and coreset. ACS [17] selects samples with larger gradient magnitude to accelerate quantization-aware training. These methods can capture training dynamics but often necessitate repeated importance re-evaluating and can not be generalized to different networks. Some methods such as Forgetting [43] and AUM [33] also have proved training dynamics benefits samples importance assessment. However, the downsampling operation, which averages dynamics across training, disregards the variability crucial for evaluating sample generalization, ultimately resulting in suboptimal coresets." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 172, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 172, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 172, + 712 + ], + "type": "text", + "content": "Usually, the first 10 or 20 epochs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26224" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 195, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 195, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 195, + 85 + ], + "type": "text", + "content": "2.2. Variance in Deep Learning" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 290, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 290, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 290, + 378 + ], + "type": "text", + "content": "Variance, a standard second-order statistic, revealing the variability along a certain dimension, has been explored in numerous works [4, 30, 34]. For example, MVT [30] transfers the observed variance of one class to another to improve the robustness of the unseen examples and few-shot learning tasks. VICReg [4] maintains variance of embeddings to prevent the collapse in which two branches produce identical outputs regardless of inputs. For the gradient, its variance along the parameter dimension is an approximation of Hessian matrix indicating loss landscape. Based on that, Fishr [34] matches domain-level variances of gradients for out-of-distribution generalization. LCMat [37] induces a better adaptation of the pruned dataset on the perturbed parameter region than the exact point matching. Besides, calculating gradient variance along time dimension tracks dynamic optimization change. VoG [1] uses this to estimate sample importance and the visualization shows that high-variance samples are more worthwhile to learn. Dyn-Unc [15] calculates the time-dimension variance of predicted target class probability to evaluate sample importance. Differing from VoG and Dyn-Unc, our TDDS does not need pixel-wise gradient calculation while considering non-target probabilities, which enables a more precise evaluation with lower computational overhead." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 388, + 124, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 124, + 402 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 124, + 402 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": "Throughout this paper, we denote the full training dataset as " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbb{U} = \\{(x_n,y_n)\\}_{n = 1}^N" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "x_{n}\\in \\mathbb{R}^{D}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "y_{n}\\in \\mathbb{R}^{1\\times C}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " are drawn i.i.d. from a natural distribution " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": ". We denote a neural network parameterized with weight matrix " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "f_{\\pmb{\\theta}}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": ". Under these definitions, the optimization objective of " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "f_{\\pmb{\\theta}}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathbb{U}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " is to minimize empirical risk " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\mathbb{U};\\pmb {\\theta}) = \\frac{1}{N}\\sum_{n = 1}^{N}\\ell (f_{\\pmb{\\theta}}(\\pmb {x}_n),\\pmb {y}_n)" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "f_{\\pmb{\\theta}}(\\pmb {x}_n)\\in \\mathbb{R}^{1\\times C}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " outputs the predicted probabilities of each class. Typically, " + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 46, + 408, + 287, + 517 + ], + "type": "text", + "content": " is updated as follow2," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 99, + 524, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, + 524, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 99, + 524, + 287, + 559 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} _ {t + 1} = \\boldsymbol {\\theta} _ {t} - \\eta \\sum_ {n = 1, \\boldsymbol {x} _ {n} \\in \\mathbb {U}} ^ {N} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right), \\tag {1}", + "image_path": "75d68cf861838f5e3d08bcccd16b383bc9b805d2113937960a57a4daa82e646d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "text", + "content": " is the learning rate and " + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\pmb{g}_t(\\pmb{x}_n)" + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "text", + "content": " is defined as the gradient calculated over the data pair " + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "inline_equation", + "content": "(\\pmb{x}_n, \\pmb{y}_n)" + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "text", + "content": " in epoch " + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 567, + 287, + 591 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "text", + "content": "Dataset pruning aims to enhance training efficiency by constructing a coreset " + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathbb{S} = \\{(x_n,y_m)\\}_{m = 1}^M" + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathbb{S}\\subset \\mathbb{U}" + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "text", + "content": " that can achieve comparable performance to " + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\mathbb{U}" + }, + { + "bbox": [ + 46, + 592, + 287, + 639 + ], + "type": "text", + "content": ". The objective of dataset pruning can be formulated as," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 647, + 286, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 647, + 286, + 685 + ], + "spans": [ + { + "bbox": [ + 48, + 647, + 286, + 685 + ], + "type": "interline_equation", + "content": "\\underset {\\substack {(\\boldsymbol {x}, \\boldsymbol {y}) \\sim \\mathcal {D} \\\\ \\boldsymbol {\\theta} _ {0} \\sim \\mathcal {P} _ {\\boldsymbol {\\theta} _ {0}}}} {\\mathbb {E}} \\left[ \\ell \\left(f _ {(\\mathrm {U}, \\boldsymbol {\\theta} _ {0})} (\\boldsymbol {x}), \\boldsymbol {y}\\right) \\right] \\simeq \\underset {\\substack {(\\boldsymbol {x}, \\boldsymbol {y}) \\sim \\mathcal {D} \\\\ \\boldsymbol {\\theta} _ {0} \\sim \\mathcal {P} _ {\\boldsymbol {\\theta} _ {0}}}} {\\mathbb {E}} \\left[ \\ell \\left(f _ {(\\mathrm {S}, \\boldsymbol {\\theta} _ {0})} (\\boldsymbol {x}), \\boldsymbol {y}\\right) \\right], \\tag{2}", + "image_path": "239dec09905e76638af294747b5740b878e6d52fcd446e3e55e76d4d81f37796.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "f_{(\\mathbb{U},\\pmb{\\theta}_0)}" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "f_{(\\mathbb{S},\\pmb{\\theta}_0)}" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " represent the networks trained on " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathbb{U}" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathbb{S}" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " with weight " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}_0" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": " initialized from distribution " + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_{\\pmb{\\theta}_0}" + }, + { + "bbox": [ + 306, + 72, + 545, + 97 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 105, + 388, + 118 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 105, + 388, + 118 + ], + "spans": [ + { + "bbox": [ + 306, + 105, + 388, + 118 + ], + "type": "text", + "content": "4. Methodology" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 125, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 125, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 125, + 545, + 316 + ], + "type": "text", + "content": "As discussed earlier, despite that exploring long-range dynamics provides a more comprehensive sample evaluation, the averaging operation hinders the construction of a coreset with strong generalization. In this section, we present the proposed Temporal Dual-Depth Scoring (TDDS) strategy, which balances the incorporation of training dynamics and the identification of well-generalized samples. In the outer level, we identify samples with their variability during training which is encouraged theoretically by the optimization space matching between coreset and original dataset (refer to Section 4.1). In the inner level, the gradient in the outer level is replaced with the projected component on the accumulated direction to estimate valid contributions in every epoch (refer to Section 4.2). Finally, to enhance efficiency, we conduct TDDS with a moving window (refer to Section 4.3). The proposed TDDS is summarized in Algorithm 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 322, + 545, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 322, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 322, + 545, + 346 + ], + "type": "text", + "content": "4.1. Outer Level: Enhance Coreset Generalization by Maximizing Variance" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 352, + 545, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 545, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 545, + 389 + ], + "type": "text", + "content": "To construct the coreset " + }, + { + "bbox": [ + 304, + 352, + 545, + 389 + ], + "type": "inline_equation", + "content": "\\mathbb{S}" + }, + { + "bbox": [ + 304, + 352, + 545, + 389 + ], + "type": "text", + "content": " satisfying Equation 2, gradient-based methods [3, 18, 26] propose to minimize the distance between full dataset and coreset gradient," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 365, + 392, + 526, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 392, + 526, + 412 + ], + "spans": [ + { + "bbox": [ + 365, + 392, + 526, + 412 + ], + "type": "interline_equation", + "content": "\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\min } \\| \\boldsymbol {G} _ {t, \\mathrm {U}} - \\tilde {\\boldsymbol {G}} _ {t, \\mathbb {S}} \\|, \\quad \\text {w h e r e}", + "image_path": "4332d43a006c8c036d20626a62ec713e9341dda00edc39c81a3635ee5b741546.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 326, + 416, + 545, + 458 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 416, + 545, + 458 + ], + "spans": [ + { + "bbox": [ + 326, + 416, + 545, + 458 + ], + "type": "interline_equation", + "content": "\\boldsymbol {G} _ {t, \\mathbb {U}} = \\sum_ {\\substack {n = 1, \\\\ \\boldsymbol {x} _ {n} \\in \\mathbb {U}}} ^ {| \\mathbb {U} |} \\boldsymbol {g} _ {t} (\\boldsymbol {x} _ {n}), \\quad \\tilde {\\boldsymbol {G}} _ {t, \\mathbb {S}} = \\sum_ {\\substack {m = 1, \\\\ \\boldsymbol {x} _ {m} \\in \\mathbb {S}}} ^ {| \\mathbb {S} |} \\boldsymbol {g} _ {t} (\\boldsymbol {x} _ {m}), \\tag{3}", + "image_path": "c79072ae9a7452833c97bb8716b76ac90860d49006e4a4a7fb49dd887dd72c43.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 463, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 463, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 463, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{G}_{t,\\mathbb{S}}" + }, + { + "bbox": [ + 305, + 463, + 545, + 521 + ], + "type": "text", + "content": " can be regarded as the gradient reconstruction in coreset space. To solve this minimization problem, Huang et al. [17] recommends pruning samples with smaller gradient magnitudes to minimize their potential impact on optimization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 523, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 643 + ], + "type": "text", + "content": "However, whenever the distance is minimized, the obtained snapshot-based coreset fails to generalize across training progress. Here are the reasons: (1) the distinctive contributions of samples are temporal statistics. Evaluating them at a specific time point causes significant bias when considering dynamic optimization; (2) samples with larger individual gradients dominate the matching process. Without considering the current optimization context, these samples introduce a substantial error in approximating the accumulated gradient." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 678 + ], + "type": "text", + "content": "To address the first issue, we proposed to extend Equation 3 to a continuous training duration to capture training dynamics," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 343, + 683, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 683, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 343, + 683, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\min } \\frac {1}{T} \\sum_ {t = 1} ^ {T} \\| \\boldsymbol {\\mathcal {G}} _ {t, \\mathbb {U}} - \\tilde {\\boldsymbol {\\mathcal {G}}} _ {t, \\mathbb {S}} \\| ^ {2}, \\tag {4}", + "image_path": "e733ea1c0db4a15f994385338134cebd4bbfe0e8193efb4f865bf13080876c5b.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "2Here, " + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": " indicates epoch and the batch-wise updates [2] in one epoch are omitted." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26225" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 68, + 509, + 261 + ], + "blocks": [ + { + "bbox": [ + 86, + 68, + 509, + 261 + ], + "lines": [ + { + "bbox": [ + 86, + 68, + 509, + 261 + ], + "spans": [ + { + "bbox": [ + 86, + 68, + 509, + 261 + ], + "type": "image", + "image_path": "07bd123adda81a9ec948be85dac64ebcef742fcf69b43c051175704c110158fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "lines": [ + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "spans": [ + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "text", + "content": "Figure 2. The pipeline of our proposed TDDS. First, we record individual predicted probabilities of samples " + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "inline_equation", + "content": "f_{t_i}^{x_n} = f_{\\theta_{t_i}}(\\pmb{x}_n)" + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "text", + "content": " during training. Then, we approximate the projected gradient, i.e. the component of gradient " + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "inline_equation", + "content": "g_{t_i}^{x_n} = g_{t_i}(\\pmb{x}_n)" + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "text", + "content": " on accumulated gradient " + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "inline_equation", + "content": "G_{t_i}" + }, + { + "bbox": [ + 45, + 269, + 547, + 314 + ], + "type": "text", + "content": " direction, with KL-based loss difference between two adjacent epochs. Next, the projected gradients are used to estimate individual contributions of samples. Finally, the important samples are identified with larger projected gradient variances over time." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": "Here, the gradients generated by " + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathbb{U}" + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathbb{S}" + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": " at epoch " + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": " are defined as " + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\pmb{\\mathcal{G}}_{t,\\mathbb{U}} = [|\\pmb{g}_t(\\pmb{x}_n)|]_{n=1}^N" + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": " and similarly " + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{G}}_{t,\\mathbb{S}}" + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": " is its reconstructed counterpart using " + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathbb{S}" + }, + { + "bbox": [ + 46, + 334, + 287, + 418 + ], + "type": "text", + "content": ". Here we use magnitude instead of gradient itself to balance the training dynamic integration and complexity. Experiments in Section 5.4 also shows that magnitude-based minimization performs better than gradient-based when considering continuous training." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 442 + ], + "type": "text", + "content": "Directly solving Equation 4 is NP-hard. Thus, we turn to its equivalent, temporal gradient variance maximization," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 56, + 450, + 287, + 483 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 450, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 56, + 450, + 287, + 483 + ], + "type": "interline_equation", + "content": "\\mathbb {S} ^ {*} = \\underset {\\mathbb {S} \\subset \\mathbb {U}} {\\arg \\max } \\mathcal {R} (\\mathbb {S}), \\quad \\mathcal {R} (\\mathbb {S}) = \\sum_ {t = 1} ^ {T} \\| \\boldsymbol {G} _ {t, \\mathbb {S}} - \\overline {{\\boldsymbol {G}}} _ {\\mathbb {S}} \\| ^ {2}, \\tag {5}", + "image_path": "571b49d262844ccb579015e39907e880d5e680d3fb6314bdb04c57ed2922b538.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 491, + 287, + 565 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 565 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 565 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 491, + 287, + 565 + ], + "type": "inline_equation", + "content": "\\overline{\\pmb{G}}_{\\mathbb{S}} = \\frac{1}{T}\\sum_{t = 1}^{T}\\pmb{G}_{t,\\mathbb{S}},\\pmb{G}_{t,\\mathbb{S}} = [|\\pmb{g}_t(\\pmb{x}_m)|]_{m = 1}^M" + }, + { + "bbox": [ + 46, + 491, + 287, + 565 + ], + "type": "text", + "content": " is the mean gradient over training time. Detailed proof can be founded in Supplementary. Equation 5 measures the variability of samples and enhances the identification of wellgeneralized samples compared to previous average-based methods [33, 43]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 572, + 287, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 287, + 597 + ], + "type": "text", + "content": "4.2. Inner Level: Estimate Actual Contribution with Projected Gradient" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 602, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 602, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 602, + 287, + 639 + ], + "type": "text", + "content": "According to Equation 5, sample importance can be evaluated with its gradient variance over time. For any sample " + }, + { + "bbox": [ + 46, + 602, + 287, + 639 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_n" + }, + { + "bbox": [ + 46, + 602, + 287, + 639 + ], + "type": "text", + "content": ", we have," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 88, + 646, + 287, + 679 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 646, + 287, + 679 + ], + "spans": [ + { + "bbox": [ + 88, + 646, + 287, + 679 + ], + "type": "interline_equation", + "content": "\\mathcal {R} (\\boldsymbol {x} _ {n}) = \\sum_ {t = 1} ^ {T} \\left\\| \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| - \\overline {{\\left| \\boldsymbol {g} \\left(\\boldsymbol {x} _ {n}\\right) \\right|}} \\right\\| ^ {2}, \\tag {6}", + "image_path": "68d0a296e1595d112dcbcef57fc85f6e7effe7ecb9333096b40ef7ee74f77754.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 687, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 687, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 687, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 687, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\overline{|\\pmb{g}(\\pmb{x}_n)|} = \\frac{1}{T}\\sum_{t=1}^{T}|\\pmb{g}_t(\\pmb{x}_n)|" + }, + { + "bbox": [ + 47, + 687, + 287, + 714 + ], + "type": "text", + "content": ". 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Incorporating sample-wise gradient in the current optimization context. After projecting onto the current accumulated gradient, samples with similar gradients exhibit different behaviors." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "text", + "content": "cisely describe the valid contribution in the current optimization context. That is the second problem mentioned in Section 4.1. As illustrated in Figure 3(a), the gradient of sample " + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}_n" + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "text", + "content": " remains constant between " + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "text", + "content": ". However, when incorporating it into the current optimization context, its valid contribution undergoes a significant shift. Thus, we propose to calculate the gradient variance after projecting it on the accumulated direction, that is, " + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "inline_equation", + "content": "|\\boldsymbol{g}_t(\\boldsymbol{x}_n)|" + }, + { + "bbox": [ + 304, + 515, + 545, + 622 + ], + "type": "text", + "content": " is reformulated as," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 341, + 632, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 632, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 341, + 632, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| = \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\cdot \\sum_ {j = 1, \\boldsymbol {x} _ {j} \\in \\mathbb {U}} ^ {| \\mathbb {U} |} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {j}\\right) \\right|. \\tag {7}", + "image_path": "173ac0058277affca1015dcad91f2adb146f65bd29aa5a5bffc45179dcf4ab1e.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "content": "Calculating Equation 6 requires sample-wise gradients over a period of " + }, + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 677, + 546, + 714 + ], + "type": "text", + "content": ", which is not feasible due to time and memory constraints. According to Equation 1, the accumu" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26226" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": "lated gradient is equal to " + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "\\frac{1}{\\eta} (\\pmb{\\theta}_t - \\pmb{\\theta}_{t + 1})" + }, + { + "bbox": [ + 46, + 72, + 287, + 96 + ], + "type": "text", + "content": ", thus the projection in Equation 7 is reformed as loss difference," + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 105, + 287, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 105, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 55, + 105, + 287, + 156 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left| \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) \\right| = \\frac {1}{\\eta} \\left| \\left(\\boldsymbol {\\theta} _ {t} - \\boldsymbol {\\theta} _ {t + 1}\\right) \\nabla_ {\\boldsymbol {\\theta} _ {t}} \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right), \\boldsymbol {y} _ {n}\\right) \\right| \\tag {8} \\\\ \\approx \\frac {1}{\\eta} \\left| \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t + 1}} (\\boldsymbol {x} _ {n}), \\boldsymbol {y} _ {n}\\right) - \\ell \\left(f _ {\\boldsymbol {\\theta} _ {t}} (\\boldsymbol {x} _ {n}), \\boldsymbol {y} _ {n}\\right) \\right|, \\\\ \\end{array}", + "image_path": "a14451eea0a484d05fc2cf7611574e05bc5181a6c219cae72a35f1f5e8e9467c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 164, + 286, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 164, + 286, + 176 + ], + "spans": [ + { + "bbox": [ + 47, + 164, + 286, + 176 + ], + "type": "text", + "content": "which can be deduced from the first-order Taylor expansion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 176, + 286, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 176, + 286, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 176, + 286, + 222 + ], + "type": "text", + "content": "Thus, we can evaluate the per-sample contribution to the accumulated gradient direction with its loss change. In the context of classification, " + }, + { + "bbox": [ + 46, + 176, + 286, + 222 + ], + "type": "inline_equation", + "content": "\\ell" + }, + { + "bbox": [ + 46, + 176, + 286, + 222 + ], + "type": "text", + "content": " is typically Cross Entropy (CE) loss," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 223, + 287, + 250 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 223, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 110, + 223, + 287, + 250 + ], + "type": "interline_equation", + "content": "\\Delta \\ell_ {t} ^ {n} = \\boldsymbol {y} _ {n} ^ {\\top} \\cdot \\log \\frac {f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right)}{f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right)}, \\tag {9}", + "image_path": "9d8e5c12a5d56d1427a28e9ef38c8a3c0b8d8927f69a809d71e0d0a9f0b19626.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "inline_equation", + "content": "\\Delta \\ell_t^n = \\ell(f_{\\theta_{t+1}}(\\pmb{x}_n), \\pmb{y}_n) - \\ell(f_{\\pmb{\\theta}_t}(\\pmb{x}_n), \\pmb{y}_n)" + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "text", + "content": ". Due to the one-hot " + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "inline_equation", + "content": "\\pmb{y}_n" + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "text", + "content": ", non-target probabilities are unfortunately overlooked, obliterating a significant amount of distinctive information. This reminds us of the Kullback-Leibler (KL) divergence loss, which can be achieved by simply replacing " + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "inline_equation", + "content": "\\pmb{y}_n" + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "inline_equation", + "content": "f_{\\pmb{\\theta}_{t+1}}(\\pmb{x}_n)" + }, + { + "bbox": [ + 47, + 255, + 287, + 328 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 92, + 338, + 287, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 338, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 92, + 338, + 287, + 365 + ], + "type": "interline_equation", + "content": "\\Delta \\ell_ {t} ^ {n} = f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right) ^ {\\top} \\cdot \\log \\frac {f _ {\\boldsymbol {\\theta} _ {t + 1}} \\left(\\boldsymbol {x} _ {n}\\right)}{f _ {\\boldsymbol {\\theta} _ {t}} \\left(\\boldsymbol {x} _ {n}\\right)}. \\tag {10}", + "image_path": "bd91eb05641c106e8d60df8cfce4f6a8096a8e99b28abc4ece43eef3783b99a6.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": "Considering that " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "f_{\\pmb{\\theta}_t(\\pmb{x}_n)}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " follows a Bernoulli distribution " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{B}(p_t)" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " represents the probability of the target class at epoch " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " equals " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "p_{t + 1}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": ", Equation 9 fails to distinguish, but Equation 10 can still differentiate the contributions of samples with " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "q_{t + 1}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "inline_equation", + "content": "q_{t + 1}" + }, + { + "bbox": [ + 46, + 373, + 287, + 456 + ], + "type": "text", + "content": " are the non-target probability distributions. This effectiveness has been proved in Section 5.4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 464, + 230, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 230, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 230, + 477 + ], + "type": "text", + "content": "4.3. Efficient Implementation of TDDS" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": "When computing " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\pmb{x}_n)" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": " with Equation 6, Equation 8, and Equation 10, storing " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": "-epoch predicted outputs may lead to out-of-memory problems, especially with large datasets like ImageNet (containing 1, 281, 167 samples across 1,000 classes). As a solution, we suggest an efficient calculation using an exponential moving average (EMA) weighting strategy. For any training point " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "t \\geq K" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": ", the variance " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_t(\\pmb{x}_n)^3" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": " is computed over a " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": "-epoch window ranging from " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "t - K + 1" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 483, + 287, + 590 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 85, + 600, + 287, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 600, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 85, + 600, + 287, + 633 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) = \\sum_ {t - K + 1} ^ {t} \\left\\| \\left| \\Delta \\ell_ {t} ^ {n} \\right| - \\overline {{\\left| \\Delta \\ell_ {t} ^ {n} \\right|}} \\right\\| ^ {2}, \\tag {11}", + "image_path": "8ab7f9671d9f0f2123fbf31903a5f786dcc15692a98c242fb0c5e2b7fb9bdc51.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\overline{|\\Delta\\ell_t^n|}" + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "text", + "content": " is the average of loss difference in a window. For " + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "text", + "content": "-epoch trajectory, " + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "inline_equation", + "content": "T - K + 1" + }, + { + "bbox": [ + 47, + 643, + 287, + 678 + ], + "type": "text", + "content": " windows are weighted as," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 83, + 680, + 287, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 680, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 83, + 680, + 287, + 693 + ], + "type": "interline_equation", + "content": "\\mathcal {R} \\left(\\boldsymbol {x} _ {n}\\right) = \\beta \\mathcal {R} _ {t} \\left(\\boldsymbol {x} _ {n}\\right) + (1 - \\beta) \\mathcal {R} \\left(\\boldsymbol {x} _ {n}\\right), \\tag {12}", + "image_path": "beb87cba3c0382d00d1b84ff12fd890a715bfd4c696db04230f9067f1f75da5f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 72, + 545, + 120 + ], + "type": "text", + "content": " is the decay coefficient of EMA whose setting is examined in Section 5.3. With this EMA, we only need to store predicted outputs for one window, significantly alleviating storage burden." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "text", + "content": "After sorting " + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{R}(\\pmb{x}_n)\\}_{n=1}^N" + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "text", + "content": ", the top-M samples are selected to construct coreset denoted as " + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\{\\mathbb{S}, r\\} = \\{(x_m, y_m), \\mathcal{R}(x_m)\\}_{m=1}^M" + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "text", + "content": ". Since, the samples with larger " + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\pmb{x}_m)" + }, + { + "bbox": [ + 305, + 120, + 545, + 192 + ], + "type": "text", + "content": " contribute more in the original data training. We remark that this dominance should be maintained in coreset training, i.e.," + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 351, + 199, + 545, + 232 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 199, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 351, + 199, + 545, + 232 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\theta} _ {t + 1} = \\boldsymbol {\\theta} _ {t} - \\eta \\sum_ {m = 1} ^ {M} \\boldsymbol {g} _ {t} \\left(\\boldsymbol {x} _ {m}\\right) \\mathcal {R} \\left(\\boldsymbol {x} _ {m}\\right). \\tag {13}", + "image_path": "2290c7f362fa4312f70acd71f8d8abd3a33a600fe83443467d4d1af015a4404d.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 239, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 545, + 263 + ], + "type": "text", + "content": "This helps to transfer relative sample importance to coreset training. This effectiveness is proved in Section 5.4." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 274, + 520, + 285 + ], + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 520, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 520, + 285 + ], + "type": "text", + "content": "Algorithm 1 Temporal Dual-Depth Scoring (TDDS)" + } + ] + } + ], + "index": 18, + "type": "text" + }, + { + "bbox": [ + 305, + 287, + 544, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 287, + 544, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 287, + 544, + 335 + ], + "type": "text", + "content": "Input: Training dataset U; A network " + }, + { + "bbox": [ + 305, + 287, + 544, + 335 + ], + "type": "inline_equation", + "content": "f_{\\theta}" + }, + { + "bbox": [ + 305, + 287, + 544, + 335 + ], + "type": "text", + "content": " with weight " + }, + { + "bbox": [ + 305, + 287, + 544, + 335 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + 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subset " + }, + { + "bbox": [ + 309, + 517, + 545, + 542 + ], + "type": "inline_equation", + "content": "\\mathbb{S} = \\{(x_m, y_m)\\}_{m=1}^M" + }, + { + "bbox": [ + 309, + 517, + 545, + 542 + ], + "type": "text", + "content": "; associated sample-wise importance " + }, + { + "bbox": [ + 309, + 517, + 545, + 542 + ], + "type": "inline_equation", + "content": "r = \\{\\mathcal{R}(x_m)\\}_{m=1}^M" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 306, + 566, + 386, + 579 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 566, + 386, + 579 + ], + "spans": [ + { + "bbox": [ + 306, + 566, + 386, + 579 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 306, + 586, + 424, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 424, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 424, + 598 + ], + "type": "text", + "content": "5.1. Experiment Settings" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 688 + ], + "type": "text", + "content": "Datasets and Networks. The effectiveness of the proposed TDDS is evaluated on three popular benchmarks, i.e., CIFAR-10, CIFAR-100 [19], and ImageNet-1K [9] with three networks, i.e., ResNet-18, ResNet-34 [14], and SwinT [21]. We also verify the cross-architecture performance on four networks including ResNet-50 [14], VGG-16 [38], MobileNet-v2 [36], and ShuffleNet [23]." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "type": "text", + "content": "Training Hyperparameters. Theoretically, if pruning rate " + }, + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "type": "inline_equation", + "content": "p = 1 - \\frac{|\\mathbb{S}|}{|\\mathbb{U}|}" + }, + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "type": "inline_equation", + "content": "0 < p \\leq 1" + }, + { + "bbox": [ + 304, + 689, + 545, + 715 + ], + "type": "text", + "content": ", the training process" + } + ] + } + ], + "index": 39 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 205, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 205, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 205, + 712 + ], + "type": "text", + "content": "3The constant coefficient " + }, + { + "bbox": [ + 58, + 702, + 205, + 712 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 58, + 702, + 205, + 712 + ], + "type": "text", + "content": " has been omitted." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "26227" + } + ] + } + ], + "index": 40 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 93, + 111, + 504, + 285 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": "Table 1. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-E. The model trained with the full dataset achieves " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "95.23\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "inline_equation", + "content": "78.21\\%" + }, + { + "bbox": [ + 46, + 70, + 547, + 94 + ], + "type": "text", + "content": " accuracy." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 93, + 111, + 504, + 285 + ], + "lines": [ + { + "bbox": [ + 93, + 111, + 504, + 285 + ], + "spans": [ + { + "bbox": [ + 93, + 111, + 504, + 285 + ], + "type": "table", + "html": "
pCIFAR-10CIFAR-100
30%50%70%80%90%30%50%70%80%90%
Random94.58 ±0.0493.38 ±0.1790.61 ±0.4488.87 ±0.4783.77 ±0.2675.53 ±0.0471.95 ±0.1664.59 ±0.3257.79 ±0.2446.68 ±1.07
Entropy [8]94.45 ±0.0791.90 ±0.1686.24 ±0.2683.49 ±0.2172.06 ±0.8172.39 ±0.2064.44 ±0.3650.73 ±0.8642.86 ±0.2529.56 ±0.54
Forgetting [43]95.45 ±0.2495.05 ±0.0589.14 ±2.0476.18 ±3.1845.87 ±1.8777.38 ±0.0970.76 ±0.4049.92 ±0.2838.42 ±1.1325.82 ±0.52
EL2N [31]95.43 ±0.1095.06 ±0.0486.69 ±1.7168.64 ±3.7031.89 ±1.5176.89 ±0.3167.57 ±0.1536.45 ±1.3617.31 ±0.339.10 ±0.69
AUM [33]95.44 ±0.0995.19 ±0.0991.19 ±0.6369.60 ±3.1134.74 ±0.1177.35 ±0.1868.17 ±0.5231.69 ±0.3418.43 ±0.479.29 ±0.27
Moderate [46]93.96 ±0.0692.34 ±0.0989.71 ±0.1487.75 ±0.2783.61 ±0.2474.60 ±0.1070.29 ±0.3162.81 ±0.0856.52 ±0.3741.82 ±1.12
Dyn-Unc[15]95.08 ±0.0294.03 ±0.1489.40 ±0.1379.76 ±1.0937.12 ±1.1273.36 ±0.1065.90 ±0.2550.16 ±0.4739.19 ±0.2715.20 ±0.41
TDDS95.47 ±0.0695.21 ±0.0493.03 ±0.2591.30 ±0.2585.46 ±0.2177.56 ±0.0674.04 ±0.3467.78 ±0.4463.01 ±0.1254.51 ±0.22
", + "image_path": "e0f3bed757ebb2ecd46d086ebdd305963e460f561b66fb3c13e2978ed6aa7b72.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 301, + 152, + 381 + ], + "blocks": [ + { + "bbox": [ + 50, + 301, + 152, + 381 + ], + "lines": [ + { + "bbox": [ + 50, + 301, + 152, + 381 + ], + "spans": [ + { + "bbox": [ + 50, + 301, + 152, + 381 + ], + "type": "image", + "image_path": "1723b7d0b0597c5726289285ce12c8c522eee57fc31b6b864b3c8f9bf5c20f6d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "lines": [ + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "type": "text", + "content": "Figure 4. Parameter analysis of range " + }, + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "type": "text", + "content": " and window size " + }, + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 392, + 546, + 414 + ], + "type": "text", + "content": " on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.3, 0.5, 0.7, 0.8, and 0.9." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 152, + 301, + 251, + 381 + ], + "blocks": [ + { + "bbox": [ + 152, + 301, + 251, + 381 + ], + "lines": [ + { + "bbox": [ + 152, + 301, + 251, + 381 + ], + "spans": [ + { + "bbox": [ + 152, + 301, + 251, + 381 + ], + "type": "image", + "image_path": "0c507c469d36d67f48b1297ff526eab9bdbb2e3f4dc1c6427ec71c6404f45969.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 250, + 301, + 350, + 381 + ], + "blocks": [ + { + "bbox": [ + 250, + 301, + 350, + 381 + ], + "lines": [ + { + "bbox": [ + 250, + 301, + 350, + 381 + ], + "spans": [ + { + "bbox": [ + 250, + 301, + 350, + 381 + ], + "type": "image", + "image_path": "0a274433ea05945a7baecf5df7f098ecd5abcc31dc76b0efb9c20d4f8f7ef1c8.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 349, + 301, + 448, + 380 + ], + "blocks": [ + { + "bbox": [ + 349, + 301, + 448, + 380 + ], + "lines": [ + { + "bbox": [ + 349, + 301, + 448, + 380 + ], + "spans": [ + { + "bbox": [ + 349, + 301, + 448, + 380 + ], + "type": "image", + "image_path": "442b37b32aeb7ff5e9c63d481a917255eb2007cebe8834d2f6a37a6a6f41d019.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 447, + 301, + 545, + 380 + ], + "blocks": [ + { + "bbox": [ + 447, + 301, + 545, + 380 + ], + "lines": [ + { + "bbox": [ + 447, + 301, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 447, + 301, + 545, + 380 + ], + "type": "image", + "image_path": "4fd9c50ad27359198197473b053c751b90eb456222ecd4c34adc42e6f051e29d.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 50, + 497, + 287, + 647 + ], + "blocks": [ + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "lines": [ + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "type": "text", + "content": "Table 2. Comparison of different dataset pruning methods on CIFAR-10 and 100 with ResNet-18 under Strategy-P. The model trained with the full dataset achieves " + }, + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "type": "inline_equation", + "content": "95.23\\%" + }, + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "type": "inline_equation", + "content": "78.21\\%" + }, + { + "bbox": [ + 46, + 433, + 288, + 478 + ], + "type": "text", + "content": " accuracy." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 497, + 287, + 647 + ], + "lines": [ + { + "bbox": [ + 50, + 497, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 50, + 497, + 287, + 647 + ], + "type": "table", + "html": "
pCIFAR-10CIFAR-100
30%50%70%30%50%70%
Random94.33 ±0.1793.4 ±0.1790.94 ±0.3874.59 ±0.2771.07 ±0.465.3 ±0.21
Entropy [8]94.44 ±0.292.11 ±0.4785.67 ±0.7172.26 ±0.0863.26 ±0.2950.49 ±0.88
Forgetting [43]95.36 ±0.1395.29 ±0.1890.56 ±1.876.91 ±0.3268.6 ±1.0238.06 ±1.14
EL2N [31]95.44 ±0.1594.61 ±0.2087.48 ±1.3376.25 ±0.2465.90 ±1.0634.42 ±1.50
AUM [33]95.07 ±0.2495.26 ±0.1591.36 ±1.476.93 ±0.3267.42 ±0.4930.64 ±0.58
Moderate [46]93.86 ±0.1192.58 ±0.3090.56 ±0.2774.60 ±0.4171.10 ±0.2465.34 ±0.41
CCS [51]95.40 ±0.1295.04 ±0.3793.00 ±0.1677.14 ±0.3174.45 ±0.1668.92 ±0.12
TDDS95.50 ±0.0795.66 ±0.0893.92 ±0.0477.95 ±0.3074.98 ±0.1669.46 ±0.10
", + "image_path": "f888901dc867509530a218a2501b35998bd140b7905100033b0a985ce5517520.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "speeds up by " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\frac{1}{1 - p}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " times. We consider two coreset training strategies: Strategy-E prioritizes efficiency with same-epoch training on both full dataset and coreset. Strategy-P" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 309, + 487, + 555, + 608 + ], + "blocks": [ + { + "bbox": [ + 305, + 433, + 547, + 468 + ], + "lines": [ + { + "bbox": [ + 305, + 433, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 433, + 547, + 468 + ], + "type": "text", + "content": "Table 3. Comparison of different dataset pruning methods on ImageNet-1K with ResNet-34 under Strategy-E. The model trained with the full dataset achieves " + }, + { + "bbox": [ + 305, + 433, + 547, + 468 + ], + "type": "inline_equation", + "content": "73.54\\%" + }, + { + "bbox": [ + 305, + 433, + 547, + 468 + ], + "type": "text", + "content": " Top-1 accuracy." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 487, + 555, + 608 + ], + "lines": [ + { + "bbox": [ + 309, + 487, + 555, + 608 + ], + "spans": [ + { + "bbox": [ + 309, + 487, + 555, + 608 + ], + "type": "table", + "html": "
pImageNet-1K
70%80%90%
Random64.1960.7652.63
Entropy[8]62.3456.8043.39
Forgetting [43]64.2962.0152.14
EL2N [31]46.9232.6815.90
AUM [33]39.3423.6411.70
Moderate [46]64.0461.3552.45
TDDS64.6962.5653.91
", + "image_path": "20fcab60609eab9ac55eb148f1744d81cc96d034d531aac9afcf5092cb90a2b0.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "type": "text", + "content": "prioritizes performance by training coreset for more epochs. If " + }, + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\frac{|\\mathbb{S}|}{|\\mathbb{U}|} = 1 - p" + }, + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "type": "text", + "content": ", the training process is extended to " + }, + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\frac{1}{1 - p}" + }, + { + "bbox": [ + 305, + 639, + 547, + 715 + ], + "type": "text", + "content": " times of the original one. For CIFAR-10 and -100, we train ResNet-18 for 200 epochs with a batch size of 128. For ImageNet, ResNet-34 and Swin-T are trained for 60 [51] and 300 epochs [15] with batch sizes of 256 and 1024, respec" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "26228" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 289, + 131 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 289, + 131 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 289, + 131 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 289, + 131 + ], + "type": "image", + "image_path": "cfa1bd938f063bb9d3ceeb4759c681b98a36ab658794a2aef47ba7740986cc63.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "lines": [ + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "spans": [ + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "type": "text", + "content": "Figure 5. Parameter analysis of decay coefficient " + }, + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 140, + 287, + 173 + ], + "type": "text", + "content": " on CIFAR-100 with ResNet-18. From left to right, the corresponding pruning rates are 0.7, 0.8, and 0.9." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "text", + "content": "tively. SGD optimizer with momentum of 0.9 and weight decay of 0.0005 is used for update networks. The learning rate is initialized as 0.1 and decays with the cosine annealing scheduler. During experiments, we found that smaller batch size boosts performance at high pruning rates (shown in Supplementary). Thus, for " + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "inline_equation", + "content": "p = 0.8" + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "text", + "content": ", we halved the batch size, and for " + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "inline_equation", + "content": "p = 0.9" + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "text", + "content": ", we reduced it to one-fourth. All compared methods use the same settings. With Strategy-P, for example, training a CIFAR coreset with only " + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 195, + 287, + 350 + ], + "type": "text", + "content": " training samples takes 400 epochs, while keeping the other hyperparameters unchanged. Considering the time-consuming training, we only conduct Strategy-P experiments at pruning rates of 0.3, 0.5, 0.7." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 350, + 287, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 423 + ], + "type": "text", + "content": "Baselines. Eight baselines are used for comparison, with the latter seven being SOTA methods: 1) Random; 2) Entropy [8]; 3) Forgetting [43]; 4) EL2N [31]; 5) AUM [33]; 6) Moderate [46]; 7) CCS [51]; 8) Dyn-Unc [15]. Due to the limited page, we provide the technical details of these baselines in Supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 431, + 216, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 216, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 216, + 443 + ], + "type": "text", + "content": "5.2. Benchmark Evaluation Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": "ResNet-18 on CIFAR-10 and 100. Table 1 and Table 2 report the performance of different dataset pruning methods under Strategy-E and P, respectively. Under both strategies, TDDS consistently outperforms other methods. For instance, under Strategy-E, none of the compared methods surpasses Random at aggressive pruning rates, while TDDS achieves " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "85.46\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "54.51\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " accuracy after pruning " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " samples of CIFAR-10 and 100 surpassing Random by " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "1.69\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "7.83\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": ", respectively. By extending the training duration, Strategy-P enhances the performance of all methods to varying degrees. TDDS still maintains its superiority, for example, with only " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " training data, the accuracy on CIFAR-10 and -100 are " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "93.92\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "69.46\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " outperforming CCS by " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "0.92\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "inline_equation", + "content": "0.54\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 641 + ], + "type": "text", + "content": ", respectively. These results highlight TDDS as a promising choice for both efficiency and performance-oriented dataset pruning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "ResNet on ImageNet-1K. For ImageNet-1K, we train ResNet-34 models on original dataset for 90 epochs to collect training dynamics and then train the model on coreset for 60 epochs as [51]. Experiment results are given in Table 3. The results show that the proposed TDDS has better performance on ImageNet-1K, especially under aggressive" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "pruning rates. For example, when pruning " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " samples, TDDS still achieves " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "53.91\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " which is " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "1.77\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "1.46\\%" + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": " higher than Forgetting and Moderate, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": "Swin-T on ImageNet-1k. We also evaluate Swin-T on ImageNet-1K. Like Dyn-Unc [15], Table 4 reports the results under four pruning rates. Notably, TDDS consistently outperforms other competitors, for example, after pruning " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": " training data, TDDS achieves " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "78.33\\%" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": " accuracy, surpassing Forgetting, Moderate, and Dyn-Unc by " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "4.01\\%" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "3.35\\%" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "inline_equation", + "content": "0.69\\%" + }, + { + "bbox": [ + 304, + 108, + 545, + 192 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 245, + 555, + 365 + ], + "blocks": [ + { + "bbox": [ + 304, + 202, + 545, + 236 + ], + "lines": [ + { + "bbox": [ + 304, + 202, + 545, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 545, + 236 + ], + "type": "text", + "content": "Table 4. Comparison of different dataset pruning methods on ImageNet-1K with Swin-T under Strategy-E. The model trained with the full dataset achieves " + }, + { + "bbox": [ + 304, + 202, + 545, + 236 + ], + "type": "inline_equation", + "content": "79.58\\%" + }, + { + "bbox": [ + 304, + 202, + 545, + 236 + ], + "type": "text", + "content": " Top-1 accuracy." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 245, + 555, + 365 + ], + "lines": [ + { + "bbox": [ + 309, + 245, + 555, + 365 + ], + "spans": [ + { + "bbox": [ + 309, + 245, + 555, + 365 + ], + "type": "table", + "html": "
pImageNet-1K
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Random77.8277.1875.9374.54
Forgetting [43]78.7078.2777.5574.32
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Dyn-Unc [15]79.5479.1478.4977.64
TDDS79.7679.5779.0978.33
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pCIFAR-100
EL2NEL2N+outerTDDS
30%76.8977.47[+ 0.58]77.56[+ 0.09]
50%67.5773.93[+ 6.36]74.04[+ 0.11]
70%36.4567.04[+30.59]67.78[+ 0.74]
80%17.3158.21[+40.90]63.01[+ 1.80]
90%9.1040.36[+31.26]54.51[+14.15]
outerX✓✓
innerXX✓
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Ablation studies for (a) Gradient Magnitude vs. Gradient, (b) KL-based Loss Difference, and (c) Importance-aware Coreset Training. In (a), GM and G represent estimating sample contribution with gradient magnitude and gradient, respectively. In (b), KL and CE represent calculating loss difference with KL and CE loss, respectively. In (c), Imp-aware and Imp-unaware represent training coreset with and without weighting samples with their importance scores, respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 380, + 69, + 547, + 197 + ], + "blocks": [ + { + "bbox": [ + 380, + 69, + 547, + 197 + ], + "lines": [ + { + "bbox": [ + 380, + 69, + 547, + 197 + ], + "spans": [ + { + "bbox": [ + 380, + 69, + 547, + 197 + ], + "type": "image", + "image_path": "754d2608562739bbf7406ef86c8bbd5498d0e92c40d16ba4b4386b1fec6ad94b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 469, + 198, + 478, + 205 + ], + "lines": [ + { + "bbox": [ + 469, + 198, + 478, + 205 + ], + "spans": [ + { + "bbox": [ + 469, + 198, + 478, + 205 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 273, + 287, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 332 + ], + "type": "text", + "content": "mance. Apparently, for a larger pruning rate, we should select samples earlier in training. For CIFAR-100, the optimal " + }, + { + "bbox": [ + 46, + 273, + 287, + 332 + ], + "type": "inline_equation", + "content": "(p,T,K)" + }, + { + "bbox": [ + 46, + 273, + 287, + 332 + ], + "type": "text", + "content": " setting is (0.3, 90, 10), (0.5, 70, 10), (0.7, 60, 20), (0.8, 20, 10), and (0.9, 10, 5). The parameter settings of CIFAR-10 and ImageNet are reported in Supplementary." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": "Decay Coefficient " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": " of EMA. In contrast to the simple average (SA), EMA employs exponential weighting, giving more weight to the most recent window. We examine four values of " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta = 0" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": " represents SA. As illustrated in Figure 5, EMA outperforms SA regardless of the " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": " value chosen. Among the considered pruning levels, " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta = 0.9" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": " yields the best performance, surpassing " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta = 0.95" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\beta = 0.85" + }, + { + "bbox": [ + 46, + 332, + 289, + 429 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 442, + 147, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 442, + 147, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 442, + 147, + 453 + ], + "type": "text", + "content": "5.4. Ablation Studies" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 462, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 462, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 287, + 557 + ], + "type": "text", + "content": "Gradient Magnitude vs Gradient. We use gradient magnitudes in Equation 4. Although gradients themselves appear capable of describing optimization, our experimental findings indicate that the use of gradient magnitudes yields superior performance, as depicted in Figure 6(a). We argue that gradients often prioritize samples with frequently reversing gradients, resulting in unstable training and slower convergence." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": "KL-based Loss Difference. As discussed in Section 4.3, the KL loss provides a more comprehensive assessment of loss difference and is expected to precisely characterize sample contribution. To evaluate its effectiveness, we replace KL loss with CE loss and conduct experiments across all considered pruning rates. As illustrated in Figure 6(b), although CE is slightly higher than KL when the pruning rate is " + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": ", KL exhibits an absolute advantage at all other pruning levels. For example, when pruning rate is " + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": ", KL outperforms CE by a substantial margin of " + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "inline_equation", + "content": "15.97\\%" + }, + { + "bbox": [ + 46, + 558, + 287, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Importance-aware Coreset Training. We formulate importance-aware subset training as Equation 13. The maintained relative importance provides optimization guid" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "type": "text", + "content": "ance for subset training. As shown in Figure 6(c), the advantage becomes increasingly pronounced as the pruning rate rises. When pruning rate is " + }, + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "type": "text", + "content": ", the accuracy of importance-aware subset training outperforms its unaware counterpart by " + }, + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "type": "inline_equation", + "content": "6.55\\%" + }, + { + "bbox": [ + 304, + 273, + 547, + 332 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 332, + 547, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 547, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 547, + 416 + ], + "type": "text", + "content": "Dual-Depth Strategy. To investigate the effectiveness of the proposed Dual-Depth strategy, we replace the inner depth with EL2N, and Table 5 indicates that incorporating the outer depth boosts EL2N at all considered pruning rates. Nevertheless, this enhancement still falls short of our dual-depth design, particularly evident in aggressive pruning scenarios." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 427, + 378, + 439 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 427, + 378, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 427, + 378, + 439 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "content": "In this study, we reveal that the snapshot-based data pruning results in poor generalization across various pruning scenarios. However, existing methods fail to identify well-generalized samples even with evaluation criteria considering the whole training progress. We attribute this to the averaging-based dynamics incorporation and imprecise sample contribution characterization. To address these problems, we propose a dataset pruning method called TDDS, which designs a Temporal Dual-Depth Scoring strategy to balance the incorporation of training dynamics and the identification of well-generalized samples. Extensive experiments on various datasets and networks, demonstrate the SOTA performance of our proposed method." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 613, + 408, + 627 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 613, + 408, + 627 + ], + "spans": [ + { + "bbox": [ + 306, + 613, + 408, + 627 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 633, + 547, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 633, + 547, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 547, + 706 + ], + "type": "text", + "content": "This research is supported in part by the National Natural Science Foundation of China under Grant 62121001, Grant 62322117, and Grant 62371365. 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Existing methods are often constrained by limited receptive fields, resulting in sub-optimal performance when handling scenarios with large motion. In this paper, we introduce a new pipeline for VFI, which can effectively integrate global-level information to alleviate issues associated with large motion. Specifically, we first estimate a pair of initial intermediate flows using a high-resolution feature map for extracting local details. Then, we incorporate a sparse global matching branch to compensate for flow estimation, which consists of identifying flaws in initial flows and generating sparse flow compensation with a global receptive field. Finally, we adaptively merge the initial flow estimation with global flow compensation, yielding a more accurate intermediate flow. To evaluate the effectiveness of our method in handling large motion, we carefully curate a more challenging subset from commonly used benchmarks. Our method demonstrates the state-of-the-art performance on these VFI subsets with large motion.", + "bbox": [ + 75, + 318, + 473, + 606 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 650, + 209, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video Frame Interpolation (VFI) seeks to generate the intermediate frame from a given pair of inference frames, which has received increasing attention. It has various real-life applications, such as creating slow motion videos [3, 10, 13], video compression [12, 33] and novel view synthesis [1, 7, 38]. Currently, flow-based algorithms occupy a prominent position [9, 17, 18, 26, 28, 30, 37] in VFI task, where the flow from the target frame to the input frames, namely, intermediate flow, is explicitly estimated for warping input frames to the target frame.", + "bbox": [ + 75, + 676, + 468, + 827 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nevertheless, existing optical flow [11, 32, 34] algorithms cannot be directly applied to estimate intermediate flows due to the absence of the target frame. To", + "bbox": [ + 75, + 828, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/762fff4f144f87de028c0558e1edbc81f8344b1f4109d3d6e867acc44d30ade6.jpg", + "image_caption": [ + "(a)" + ], + "image_footnote": [], + "bbox": [ + 563, + 286, + 645, + 428 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e4a8d41f549106f9d307b2ff8edbf7a661592b1231164a428fd0e5d011689036.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 681, + 287, + 864, + 428 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8b67fbd6851c08eb3751032a4f273d66455d158735c91098210ab3afa3820273.jpg", + "image_caption": [ + "Overlay of $I_0,I_1$ Motion Magnitude Range (92.0,393.9)" + ], + "image_footnote": [], + "bbox": [ + 514, + 449, + 629, + 500 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bc6c08707956cfa85a17bb64f98245f34e6711af2f3ac07708c3b94d8df864ee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 449, + 756, + 500 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb48eabcff9846e4d9bb371ac53adb30e69fb1be2edca32edbb04320e52e884e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 764, + 450, + 882, + 500 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/32e885d71687fa354583fd8391f4f8fa6e88662f11dcf8f12525782797d4886c.jpg", + "image_caption": [ + "After Sparse Global Matching: Shifted Flow Fix $f_{t\\rightarrow 0}$" + ], + "image_footnote": [], + "bbox": [ + 509, + 527, + 630, + 580 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0f74ed9e956a9e01f2e26bda823ff0c285c1d46d3a3e44886ab28f85beba36d2.jpg", + "image_caption": [ + "Initial Intermediate Flow Estimation $\\tilde{F}_{t\\rightarrow 0},\\tilde{F}_{t\\rightarrow 1}$", + "Merged Flow $F_{t\\rightarrow 0}$", + "(c)" + ], + "image_footnote": [], + "bbox": [ + 637, + 527, + 754, + 580 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2379e816dbbdbfc131cc2b1d81bf2e89eba935dfe45e35866c69f83c71c8ba67.jpg", + "image_caption": [ + "Difference Map $D_0$", + "Synthesized $I_{t}$ with (right) and without (left) Sparse Global Matching Block", + "Figure 1. (a) Our framework without sparse global matching, pretrained on small motion dataset, for capturing local details. (b) Our framework with sparse global matching, fine-tuned on large motion dataset, for capturing global large motion. (c) Key components in our algorithm, illustrating the effect of our sparse global matching branch. (Using Ours-1/4-Points, from Table 1.)" + ], + "image_footnote": [], + "bbox": [ + 763, + 527, + 885, + 582 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "address this, many algorithms first estimate the bidirectional flow between two input frames and then generate intermediate optical flows using various flow reversal techniques [13, 15, 19, 24, 29, 35, 39]. Alternatively, recent algorithms directly estimate the intermediate flow with proper supervision [9, 17, 37] and achieve improved performance on datasets where small-to-medium motions are prevalent [27].", + "bbox": [ + 496, + 734, + 890, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, real-world video frame interpolation encounters various complex challenges, with the problem of handling large motion being particularly prominent. In scenar", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*: Equal Contribution. ☑ Corresponding author (lmwang@nju.edu.cn).", + "bbox": [ + 76, + 886, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "19125", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ios characterized by large motion, the correspondence of objects between frames is hard to locate due to the large pixel shifting. Many works have been proposed to alleviate this problem. For example, XVFI [29] addressed this by creating an extreme 4K training dataset and a scalable framework. However, its performance improvement is limited when applied to small motion scenarios [25]. FILM [27] introduced scale-agnostic features and a weight-sharing approach to improve model generalization across different motion scales. In fact, due to its limited receptive field, the model's depth can become excessively deep when dealing with large motion. This increases computational complexity and falls short in handling fast-moving small objects.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we introduce a sparse global matching pipeline to specifically handle the challenges posed by large motion in the VFI task, by effectively integrating global-level information into intermediate flow estimation. Our VFI method establishes sparse global correspondences between input frames using a global receptive field and takes a two-step strategy to compensate for the intermediate flow estimation. Specifically, as shown in Figure 1 (a - b), our method begins with an initial estimation of a pair of intermediate flows using a relatively high-resolution feature map. Following this initial estimation, our approach incorporates a sparse global matching branch to locate potential error in the flow estimation results, and then produce flow residual to provide an effective remedy for capturing large motion.", + "bbox": [ + 75, + 305, + 472, + 532 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To be specific, in our sparse global matching branch, we build a difference map to pinpoint the flaws in initial intermediate flow estimations. Concentrating on these defective areas, our approach employs sparse global matching to establish global correspondences between two adjacent input frames, specifically at these sparsely targeted locations. Subsequently, we convert this bidirectional sparse flow correspondence into intermediate flow compensation. Finally, we employ a flow merging block to adaptively merge the initial intermediate flows and flow compensation, thereby effectively combining the local details with the global correlation. As shown in Figure 1 (c), our sparse global matching branch can effectively locate the error regions and rectify the flaws in the initial intermediate flow estimation, yielding a significantly enhanced synthesized intermediate frame.", + "bbox": [ + 75, + 535, + 472, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In order to benchmark the effectiveness of our sparse global matching module on handling large motion, we carefully analyze motion magnitude and sufficiency within existing benchmarks, X-Test [29], Xiph [22] and SNUFILM [4]. In our analysis, we utilize the motion sufficiency filtering method described in [1], emphasizing the minimum of the top $5\\%$ of each pixel's flow magnitude' as the key indicator of large motion sufficiency. In the end, we carefully curate the most challenging subsets for large mo", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tion frame interpolation evaluation. In the most challenging testing conditions, our proposed method demonstrates a substantial improvement in terms of PSNR, enhancing it by $0.66\\mathrm{dB}$ while correcting half of the points in initial flow estimation. Furthermore, even with the correction of just 1/8 points, we still observe a notable increase of 0.48 dB. Notably, our approach establishes a new state-of-the-art performance benchmark in these exceptionally challenging scenarios. In summary, our main contributions include:", + "bbox": [ + 496, + 90, + 893, + 227 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a sparse global matching algorithm tailored to effectively capture large motion.", + "- We designed an effective two-step framework for capturing large motion. First, by estimating initial intermediate flows to extract the local details, then targets and corrects the detected flaws through sparse global matching at sparsely targeted defective points.", + "- Our models demonstrate state-of-the-art performance on the most challenging subset of the commonly used large motion benchmark, namely, X-Test-L, Xiph-L, SNU-FILM-L hard and extreme." + ], + "bbox": [ + 500, + 228, + 890, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 410, + 640, + 426 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Flow-Based Video Frame Interpolation", + "text_level": 1, + "bbox": [ + 500, + 435, + 834, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Flow-based algorithms for video frame interpolation focus on estimating intermediate flows. These flows enable the model to either forward warp or backward warp the input frames to the target frame. Some algorithms first compute bidirectional flows between two input frames and apply different flow reversal techniques to obtain intermediate flows [24, 29, 35], while the others directly estimate intermediate flows [9, 17, 37].", + "bbox": [ + 496, + 459, + 890, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "However, flow reversal techniques may introduce artifacts to intermediate flows, which can harm the details of the intermediate flows, causing misalignment [13] or holes [35]. Direct estimation of intermediate flows is also restricted by the model design, usually has a limited perceptive field [9, 37], and lacks robustness on large motion.", + "bbox": [ + 496, + 582, + 890, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Addressing the issue of large motion in video frame interpolation, FILM [27] adopts a coarse-to-fine approach and shares weights between layers. It also trains on data with varied motion magnitudes, enabling it to learn to handle large motions. AMT [18] uses the RAFT-like structure to construct an all-pair correlation map and locally refines the intermediate flow afterward. BiFormer [26] employs a global feature extractor to extract global features and build local bilateral correlation maps. However, due to the high resolution of the VFI task, giving the model a genuine global receptive field is challenging.", + "bbox": [ + 496, + 672, + 890, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, our work uses local features to estimate the intermediate flows and global features to sparsely generate bidirectional flow compensation by global matching. We then adaptively merge the flows and flow compensation to", + "bbox": [ + 496, + 840, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "19126", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5393eea0876f5f773fe050b09b20e799135be84bd01c8cab312815f533069b79.jpg", + "image_caption": [ + "Figure 2. Overview of our proposed structure. First, local features are extracted by a local feature extractor for flow estimation $\\widetilde{F}_{t\\rightarrow 0},\\widetilde{F}_{t\\rightarrow 1}$ . Then, our sparse global matching branch locates the flaws by constructing difference maps $D_0,D_1$ . Next, we perform sparse global matching using global features extracted by a global feature extractor. Finally, after shifting global correspondences $f_{0\\to 1},f_{1\\to 0}$ to intermediate flow compensation $f_{t\\to 1},f_{t\\to 0}$ , we adaptively merge $\\widetilde{F}_{t\\rightarrow 0},\\widetilde{F}_{t\\rightarrow 1}$ with $f_{t\\to 1},f_{t\\to 0}$ and adopts a flow refine in a residual manner for interpolating the intermediate frame." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 890, + 275 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "obtain the final intermediate flow with both global information and local details.", + "bbox": [ + 75, + 367, + 470, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Transformer", + "text_level": 1, + "bbox": [ + 76, + 407, + 210, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformers have gained widespread popularity across various computer vision tasks [2, 6, 20, 40], demonstrating impressive feature extraction capabilities. Recently, Transformer-based backbone has already been introduced to solve VFI task [16, 22, 28, 37]. VFIFormer [21] uses cross-scale window-based attention. EMA-VFI [37] uses Inter-frame Attention to extract appearance and motion features using the same similarity matrix. BiFormer [26] adopts pretrained Twins architecture [5] for global feature extraction and builds local bilateral correlation cost volume. However, when handling large motion, these methods are more or less restricted by their local receptive field. Therefore, we propose a two-step strategy: employing a hybrid Transformer and CNN-based backbone for initial flow estimation, followed by a sparse global matching block utilizing a global receptive field.", + "bbox": [ + 75, + 430, + 468, + 672 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Global Matching", + "text_level": 1, + "bbox": [ + 76, + 681, + 243, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Global matching is extensively studied in local feature matching tasks. LoFTR [31] replaces the traditional dense matching method, using cost volume to search for correspondence, with self and cross attention layers in Transformer. COTR [14] takes a different approach by formulating the correspondence problem as a functional mapping and utilizing a Transformer as the function to query the points of interest. For dense matching, GMFlow [34] adopted Transformer block to extract strong discriminative features to build a global matching map. In VFI tasks, not every part of the image requires dense global matching. Our sparse global matching strategy, on the other hand, specifically targets and corrects the defective areas of the flows.", + "bbox": [ + 75, + 703, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 366, + 589, + 382 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a pair of RGB frames $I_0, I_1$ , and a timestep $t$ , we need to synthesize an intermediate frame $I_t$ . We illustrate our overall model pipeline in Figure 2.", + "bbox": [ + 496, + 392, + 890, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method consists of a local feature branch and a sparse global matching branch. The local feature branch is responsible for estimating the initial intermediate flows, namely $\\widetilde{F}_{t\\rightarrow 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ . In the sparse global matching branch, we focus on the defective areas of $\\widetilde{F}_{t\\rightarrow 0}$ , $\\widetilde{F}_{t\\rightarrow 1}$ , and perform sparse global matching to obtain flow compensation, $f_{t\\rightarrow 0}$ and $f_{t\\rightarrow 1}$ . Then we adaptively merge $\\widetilde{F}_{t\\rightarrow 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ with $f_{t\\rightarrow 0}$ and $f_{t\\rightarrow 1}$ by our flow merge block, to obtain more accurate intermediate flows, $F_{t\\rightarrow 0}$ , $F_{t\\rightarrow 1}$ . Finally, after a few flow refine blocks, we use this pair of intermediate flows to synthesize the intermediate frame $\\widehat{I}_t$ .", + "bbox": [ + 496, + 439, + 892, + 604 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, we first introduce each component in our local feature branch briefly in Section 3.1. From Section 3.2 and onward, we delve into a detailed discussion of our sparse global matching branch.", + "bbox": [ + 496, + 606, + 890, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Local Feature Branch", + "text_level": 1, + "bbox": [ + 500, + 679, + 702, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Figure 2, our local feature branch consists of three parts, namely, the local feature extractor, the flow estimation block, and the RefineNet [9]. We draw inspiration from RIFE [9] and EMA-VFI [37], while retaining certain distinctive aspects. We now introduce them sequentially.", + "bbox": [ + 496, + 703, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Local Feature Extractor. EMA-VFI [37] has already verified the effectiveness of CNN and Transformer hybrid structure. We follow its design and keep our deepest feature resolution stays at $H / 8 \\times W / 8$ scale, instead of $H / 16 \\times W / 16$ in EMA-VFI. Furthermore, we simplified the specially designed Transformer structure in EMA-VFI to simple cross attention to extract inter-frame appearance features at a lower computation cost.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "19127", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Flow Estimation. We use the extracted appearance feature and input frames $I_0, I_1 \\in \\mathbb{R}^{3 \\times H \\times W}$ to directly estimate intermediate flows $F_{t \\to 0}, F_{t \\to 1}$ , along with a fusion map $O$ , in a coarse-to-fine manner. This is achieved by several layers of CNN block, inspired by the intuitive design of RIFE [9] and EMA-VFI [37]. Then, the target frame can be generated by:", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {I} _ {t} = O \\odot \\overleftarrow {\\mathcal {W}} \\left(I _ {0}, F _ {t \\rightarrow 0}\\right) + (1 - O) \\odot \\overleftarrow {\\mathcal {W}} \\left(I _ {1}, F _ {t \\rightarrow 1}\\right) \\quad (1)\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 204, + 468, + 226 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{\\mathcal{W}}$ is image backward warping operation, $\\odot$ is Hadamard product operator.", + "bbox": [ + 75, + 236, + 468, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Flow Refine. We share the same U-net-shaped network with RIFE to refine the synthesized frame $\\widehat{I}_t$ . More details can be found in Appendix A.", + "bbox": [ + 75, + 268, + 468, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Locate Flaws in Flows: Difference Map", + "text_level": 1, + "bbox": [ + 76, + 321, + 415, + 338 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the limited receptive field of local feature branch, the estimated initial bidirectional flows, $\\widetilde{F}_{t\\rightarrow 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ , may be relatively coarse. Consequently, it is necessary to identify the flaws in $\\widetilde{F}_{t\\rightarrow 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ . Therefore, we construct the difference map $D_0$ and $D_{1}$ to check the correctness of $\\widetilde{F}_{t\\rightarrow 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ , by using both of the input frames $I_{0}$ and $I_{1}$ as ground truth reference. The values in the difference maps $D_0$ and $D_{1}$ serve as indicators of the likelihood of error in flow estimation, with higher values suggesting a greater probability of inaccuracies.", + "bbox": [ + 75, + 344, + 468, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In particular, we first use $\\widetilde{F}_{t\\rightarrow 0}$ to backward warp $I_0$ to $\\widetilde{I}_t$ , then use $\\widetilde{F}_{t\\rightarrow 1}$ to forward warp $\\widetilde{I}_t$ to $\\widetilde{I}_1$ . And we compare the $\\widetilde{I}_1$ and input frame $I_{1}$ by doing summation over RGB channels after subtraction to obtain difference map $\\widetilde{D}_{0\\rightarrow 1}$ .", + "bbox": [ + 75, + 494, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {I} _ {1} = \\overrightarrow {\\mathcal {W}} \\left(\\overleftarrow {\\mathcal {W}} \\left(I _ {0}, \\widetilde {F} _ {t \\rightarrow 0}\\right), \\widetilde {F} _ {t \\rightarrow 1}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 569, + 468, + 595 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {D} _ {0 \\rightarrow 1} = \\sum_ {R G B} | I _ {1} - \\widetilde {I} _ {1} | \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 598, + 468, + 630 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overleftarrow{\\mathcal{W}}$ is backward warp, $\\overrightarrow{\\mathcal{W}}$ is forward warp.", + "bbox": [ + 76, + 637, + 398, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Through the combination of backward warp and forward warp, we get an initial difference map $\\widetilde{D}_{0\\rightarrow 1}$ . Currently, the flaws in $\\widetilde{D}_{0\\rightarrow 1}$ are caused by two reasons, the first reason is due to the flaws in our coarse flow estimation, $\\widetilde{F}_{t\\rightarrow 0}$ , $\\widetilde{F}_{t\\rightarrow 1}$ . The second reason is that even if $\\widetilde{F}_{t\\rightarrow 0}$ , $\\widetilde{F}_{t\\rightarrow 1}$ were perfectly accurate, occlusions and cropping would still occur inevitably, i.e. some existing pixels in $I_0$ disappearing in $I_{1}$ , creating incorrect pixel mappings and holes in the warped image.", + "bbox": [ + 75, + 657, + 468, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To filter out the second cause of flaws, we create a map full of ones, and repeat the above warping process to obtain a $0/1$ mask, $M_{0\\to 1}^{holes}$ . The positions in mask $M_{0\\to 1}^{holes}$ where the element becomes 0 correspond to the potential hole areas in the warped image $\\widetilde{I}_1$ .", + "bbox": [ + 75, + 792, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then, we can multiply this map $M_{0\\to 1}^{holes}$ with our initial difference map $\\widetilde{D}_{0\\rightarrow 1}$ to filter out the potential holes caused", + "bbox": [ + 75, + 868, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1dccc7dba248de1a7e9f3cb7d99fd396666462f7139856c80c2f056dbd6e9f84.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 498, + 90, + 692, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/59ede7f5775da0f450605e8be250c951319c35dbe37157335689881a33788151.jpg", + "image_caption": [ + "(a) Mean Motion Magnitude" + ], + "image_footnote": [], + "bbox": [ + 501, + 172, + 692, + 255 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/94d38bb51bc24497032358075cf0602121f298c7bfe454128094a98c139352e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 97, + 888, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/422b796dfef124864fd7f399d8de9c27b4c44311e3f22c28f8d2cf9f5b294c48.jpg", + "image_caption": [ + "(b) Motion Sufficiency Ranking", + "Figure 3. Large motion dataset benchmark analysis. Top: Whole dataset. Below: Keeping the most challenging half of Xiph and SNU-FILM. Four charts share the same legend." + ], + "image_footnote": [], + "bbox": [ + 697, + 180, + 888, + 255 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "by occlusion and cropping, and obtain $D_{0\\to 1}$ , focusing on the flaws caused by inaccurate intermediate flow estimation.", + "bbox": [ + 498, + 335, + 890, + 364 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {0 \\rightarrow 1} = M _ {0 \\rightarrow 1} ^ {\\text {h o l e s}} \\odot \\widetilde {D} _ {0 \\rightarrow 1} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 371, + 890, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As a result, $D_{0 \\to 1}$ enables us to identify the misaligned regions in $\\widetilde{I}_1$ that are caused solely by the flaws in the estimated flows $\\widetilde{F}_{t \\to 0}, \\widetilde{F}_{t \\to 1}$ . Furthermore, we reverse the previous warping combination to find the underlying source points responsible for these misalignments in $\\widetilde{I}_1$ .", + "bbox": [ + 496, + 398, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD _ {0} = \\overrightarrow {\\mathcal {W}} \\left(\\overleftarrow {\\mathcal {W}} \\left(D _ {0 \\rightarrow 1}, \\widetilde {F} _ {t \\rightarrow 1}\\right), \\widetilde {F} _ {t \\rightarrow 0}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 478, + 890, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Difference map $D_0$ illustrates the extent to which each point in $I_0$ leads to the misalignment in $\\widetilde{I}_1$ . To address this, it is essential to prioritize the regions with higher values in $D_0$ . These regions indicate the points that exacerbate significant misalignment. Difference map $D_1$ can be produced symmetrically.", + "bbox": [ + 496, + 512, + 890, + 603 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Sparse Global Matching", + "text_level": 1, + "bbox": [ + 500, + 611, + 723, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To emphasize the region with higher values in $D_0$ and $D_{1}$ we can select the top- $k$ points out of $D_0$ , $D_{1}$ and do global matching for those points to provide more accurate matching flow $f_{0\\rightarrow 1}$ and $f_{1\\rightarrow 0}$ , for preparing the flow compensation $f_{t\\rightarrow 1}$ and $f_{t\\rightarrow 1}$ .", + "bbox": [ + 496, + 633, + 890, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sparse global matching allows the selected points in $I_0$ to have a global receptive field on $I_{1}$ . We adopt the pretrained global feature extractor from GMFlow [34] to generate discriminative global features $A_0^i, A_1^i \\in \\mathbb{R}^{\\left(\\frac{H}{2^i}, \\frac{W}{2^i}\\right) \\times C}$ , where $C$ is the number of feature channels. We construct a sparse feature map $a_0^i \\in \\mathbb{R}^{K \\times C}$ according to top- $k$ indices selected from $D_0$ . The corresponding area of $A_0^i, A_1^i$ should have higher similarity, and the same intuition also applies to $a_0^i$ and $A_1^i$ . Therefore, we can construct a similarity matrix $S_{0 \\to 1} \\in K \\times \\left(\\frac{H}{2^i} \\cdot \\frac{W}{2^i}\\right)$ :", + "bbox": [ + 496, + 710, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS _ {0 \\rightarrow 1} = S o f t m a x \\left(\\frac {a _ {0} ^ {i} A _ {1} ^ {i}}{\\sqrt {C}}\\right) \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 864, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "19128", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Then we create a coordinate map $B \\in \\mathbb{R}^{\\left(\\frac{H}{2^i} \\cdot \\frac{W}{2^i}\\right) \\times 2}$ . Using top- $k$ indices selected from $D_0$ , we extract the corresponding points from the coordinate map $B$ to form a sparse coordinate map $b_0 \\in \\mathbb{R}^{K \\times 2}$ . We use the product between similarity matrix $S_{0 \\to 1}$ and $b_0$ to represent the estimated position in $I_1$ for selected $k$ points. Therefore, the subtraction between the previous product $S_{0 \\to 1}b_0$ and $b_0$ can represent the flow for those points, namely $f_{0 \\to 1}$ :", + "bbox": [ + 75, + 88, + 472, + 214 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widetilde {f} _ {0 \\rightarrow 1} = S _ {0 \\rightarrow 1} b _ {0} - b _ {0} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 224, + 468, + 244 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus, $\\widetilde{f}_{0\\rightarrow 1}$ is obtained in a global matching manner, making it more capable of capturing large motions. Finally, we reuse the top- $k$ indices from $D_0$ to fill $\\widetilde{f}_{0\\rightarrow 1} \\in \\mathbb{R}^{K\\times 2}$ to $f_{0\\rightarrow 1} \\in \\mathbb{R}^{\\frac{H}{2^i} \\times \\frac{W}{2^i} \\times 2}$ with zero. $f_{1\\rightarrow 0}$ can be obtained symmetrically.", + "bbox": [ + 76, + 257, + 468, + 338 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Flow Shifting", + "text_level": 1, + "bbox": [ + 76, + 347, + 217, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The goal of our sparse global matching branch is to acquire sparse flow compensation $f_{t\\to 0}$ and $\\underline{f}_{t\\to 1}$ to improve the estimated intermediate flows, $\\widetilde{F}_{t\\to 0}$ , $F_{t\\to 1}$ , with large motion capturing ability. Next, we shift $f_{0\\to 1}$ , $f_{1\\to 0}$ to $f_{t\\to 1}$ , $f_{t\\to 0}$ by flow shifting, which can help mitigate the coordinate system mismatch.", + "bbox": [ + 76, + 369, + 468, + 459 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We intercept a $(1 - t)$ proportion of $f_{0\\rightarrow 1}$ and shift this $(1 - t)$ proportion along the remaining $t$ proportion of the flow $f_{0\\rightarrow 1}$ . Through this shifting operation, we can obtain $f_{t\\rightarrow 1}$ , and the shifting operation is performed by forward warping:", + "bbox": [ + 76, + 460, + 468, + 536 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {t \\rightarrow 1} = \\overrightarrow {\\mathcal {W}} ((1 - t) f _ {0 \\rightarrow 1}, t f _ {0 \\rightarrow 1}) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 539, + 468, + 560 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {t \\rightarrow 0} = \\overrightarrow {\\mathcal {W}} (t f _ {1 \\rightarrow 0}, (1 - t) f _ {1 \\rightarrow 0}) \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 563, + 468, + 582 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that $f_{t \\to 1}$ is flow shifted by $f_{0 \\to 1}$ and $f_{t \\to 0}$ is flow shifted by $f_{1 \\to 0}$ , we also list the $f_{t \\to 0}$ in Equation (9) for clarity.", + "bbox": [ + 75, + 594, + 468, + 638 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the forward warping process, the number of sparsely chosen points will potentially change, and we will again choose the top- $k$ points with the least occlusion possibility.", + "bbox": [ + 75, + 640, + 468, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Instead of using the estimated target frame $\\widetilde{I}_t$ and input frames $I_0, I_1$ to perform global matching and obtain intermediate flow compensation $f_{t\\to 0}$ and $f_{t\\rightarrow 1}$ , we use global matching between $I_0, I_1$ only and perform flow shift. The reason is that $\\widetilde{I}_t$ synthesized by $\\widetilde{F}_{t\\to 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ is not reliable. Since we aim to minimize accumulated propagation errors, we endeavor to minimize the usage of intermediate results wherever possible.", + "bbox": [ + 75, + 699, + 468, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Flow Merge Block", + "text_level": 1, + "bbox": [ + 76, + 830, + 254, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "If we directly replace $\\widetilde{F}_{t\\to 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ with the flow compensation $f_{t\\to 0}$ and $f_{t\\to 1}$ , the resulting flow may lack smoothness. In addition, the flow compensation $f_{t\\to 0}$ and", + "bbox": [ + 75, + 853, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$f_{t\\to 1}$ can also make mistakes. Therefore, we designed a flow merge block $\\mathcal{M}$ to adaptively merge $\\widetilde{F}_{t\\rightarrow 0}$ and $f_{t\\rightarrow 0}$ as well as $\\widetilde{F}_{t\\rightarrow 1}$ and $f_{t\\rightarrow 1}$ :", + "bbox": [ + 498, + 90, + 890, + 137 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {F} _ {t \\rightarrow 0} = \\mathcal {M} \\left(\\widetilde {F} _ {t \\rightarrow 0}, f _ {t \\rightarrow 0}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 148, + 890, + 169 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {F} _ {t \\rightarrow 1} = \\mathcal {M} \\left(\\widetilde {F} _ {t \\rightarrow 1}, f _ {t \\rightarrow 1}\\right) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 611, + 172, + 890, + 191 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by the convex sampling in RAFT [32], we take the $\\widehat{F}_{t\\rightarrow 0}$ at each pixel to be the convex combination of $R\\times R$ neighbors of $\\widetilde{F}_{t\\rightarrow 0}$ and $R\\times R$ neighbors of $f_{t\\rightarrow 0}$ where $\\mathbf{R}$ is the neighborhood range. We use two convolutional layers to predict a $2\\times R^2\\times \\frac{H}{2^i}\\times \\frac{W}{2^i}$ weight assignment, and apply softmax of the $2\\times R^2$ neighborhood to obtain masks $[W_{main},W_{sgm}]$ , where $W_{main},W_{sgm}\\in \\mathbb{R}^{R^2\\times \\frac{H}{2^i}\\times \\frac{W}{2^i}}$ . $W_{main}$ stands for the weight for the local feature branch flow estimations, and $W_{sgm}$ stands for the weight for sparse global matching block flow compensation. Finally, the flow merge block outputs the $\\widehat{F}_{t\\rightarrow 0}$ , obtained by taking weighted sum over the $\\widetilde{F}_{t\\rightarrow 0}$ and $f_{t\\rightarrow 0}$ neighborhood.", + "bbox": [ + 498, + 208, + 892, + 409 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Large Motion VFI Benchmark", + "text_level": 1, + "bbox": [ + 498, + 428, + 781, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To better illustrate our algorithm's effectiveness in handling large motions, we analyzed several widely used large motion datasets, namely, SNU-FILM extreme and hard [4], Xiph [22], and X-Test [29]. We utilized RAFT [32] to estimate optical flow between input frames as evidence, allowing for a detailed assessment of motion magnitudes.", + "bbox": [ + 496, + 455, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "According to Figure 3a, SNU-FILM and Xiph's mean motion magnitude is much lower than X-Test's. For example, we can see that about $60\\%$ of SNU-FILM test cases' mean motion magnitude is below 15, while Xiph has about $40\\%$ test cases below 30.", + "bbox": [ + 496, + 547, + 890, + 623 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we also refer to the criterion in [1] for assessing motion sufficiency, requiring at least $10\\%$ of each pixel's flow to have a magnitude of at least 8 pixels within a $270 \\times 270$ resolution. We adjusted this criterion by lowering the percentage threshold to $5\\%$ while simultaneously increasing the required magnitude to account for the larger resolution of our input frames. This adjusted criterion, representing the minimum magnitude of the top $5\\%$ pixel flows, forms the basis for our proportion ranking of the benchmark datasets in Figure 3b.", + "bbox": [ + 496, + 626, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As depicted in the cumulative distribution chart Figure 3b, we found that over $50\\%$ of X-Test have at least $5\\%$ of each pixel's flow with a magnitude of at least 150 pixels. In contrast, Xiph [22] and SNU-FILM [4] contain fewer large motion pixels. Consequently, we focused our evaluation on the most challenging half of these benchmarks to assess our algorithm's performance improvements in handling genuinely large motion data, with details in Section 5.2.", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "19129", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c75b4fe70168273d82aa6e9fb97c917da343e0e27dbb4f24eef5f413c1c88a21.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation (PSNR/SSIM) among different challenging benchmarks (see Section 4). The best results and the second best results in each column are marked in red and blue respectively. Ours-1/N Points means that we sparsely select 1/N points of the initial intermediate flows estimation to perform global matching by the evidence provided by difference map $D_0$ , $D_1$ . \"OOM\" denotes the out-of-memory issue when evaluating on an NVIDIA V100-32G GPU." + ], + "table_footnote": [], + "table_body": "
X-Test-LSNU-FILM-LXiph-L
2K4Khardextreme2K4K
XVFI [29]29.82/0.895129.02/0.886627.58/0.909522.99/0.826029.17/0.844928.09/0.7889
FILM [27]30.08/0.8941OOM28.35/0.915623.06/0.824729.89/0.853327.11/0.7699
BiFormer [26]30.32/0.906730.11/0.907028.18/0.915423.55/0.838329.61/0.854128.89/0.8133
RIFE [9]29.87/0.880528.98/0.875628.19/0.917222.84/0.823030.18/0.863328.07/0.7982
EMA-VFI-small [37]29.51/0.877528.60/0.873328.57/0.918923.18/0.829230.54/0.871828.40/0.8109
Ours-local-branch30.39/0.894629.25/0.886128.73/0.920723.19/0.830130.89/0.874528.59/0.8115
Ours-1/8-Points30.83/0.902229.73/0.892828.82/0.920823.54/0.835530.88/0.874928.90/0.8151
Ours-1/4-Points30.88/0.904329.78/0.894828.86/0.921223.58/0.836830.89/0.875129.15/0.8169
Ours-1/2-Points30.99/0.907229.91/0.897228.88/0.921623.62/0.837730.93/0.875529.25/0.8180
", + "bbox": [ + 93, + 146, + 877, + 340 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 364, + 209, + 382 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Implementation Detail", + "text_level": 1, + "bbox": [ + 76, + 390, + 287, + 406 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training Datasets. We use two training datasets, Vimeo90K [36] for pretraining on small-to-medium motion and X4K1000FPS (X-Train) [29] for finetuning on large motion. Vimeo90K contains 51,312 triplets with a resolution of $448 \\times 256$ for training. It has an average motion magnitude between 1 to 8 pixels [36]. X4K1000FPS (X-Train) contains 4,408 clips with a resolution of $768 \\times 768$ , each clip has 65 consecutive frames.", + "bbox": [ + 75, + 414, + 470, + 535 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Local Feature Branch Training. We first train our model framework without the sparse global matching branch on Vimeo90K. We crop each training instance to 256x256 patches and perform random flip, time reversal, and random rotation augmentation, following [9, 37]. The training batch size is set to 32. We use AdamW as our optimizer with $\\beta_{1} = 0.9$ , $\\beta_{2} = 0.999$ and weight decay $1e^{-4}$ . After 2,000 warmup steps, we gradually increase the learning rate to $2e^{-4}$ , then use cosine annealing for 480k steps (300 epochs) to reduce the learning rate from $2e^{-4}$ to $2e^{-5}$ . We follow the training loss design of [9, 37] for both training and finetuning, which is included in Appendix B.", + "bbox": [ + 75, + 536, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sparse Global Branch Finetuning. We load our pretrained framework, and a global feature extractor from GM-Flow [34], operating on $i = 3$ in Equation (6). Then we integrate our sparse global matching branch into the framework, setting the sparsity ratio, i.e. $1/8$ , $1/4$ , $1/2$ , and finetuning the sparse global matching block on X-Train. When fine-tuning, we freeze the pretrained framework and the global feature extractor. We crop $512 \\times 512$ patches from the original training image, and random resize the input images with $50\\%$ probability to remain the $512 \\times 512$ size, $25\\%$ probability to downscale to $256 \\times 256$ size and $25\\%$ probability to $128 \\times 128$ size. We apply random flipping", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "augmentation, following [29]. The batch size, learning rate and optimizer are the same as our local feature branch, except that warmup steps are set to 1k steps, and the total steps are set to 13.7k (100 epochs). The parameter freezing and random rescaling are for preserving the model's ability to capture small motion details to the greatest extent possible.", + "bbox": [ + 496, + 364, + 890, + 458 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Test Dataset", + "text_level": 1, + "bbox": [ + 500, + 467, + 632, + 482 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The proposed algorithm is designed for capturing large motions. Therefore, we test our model's performance on the most challenging subset of the commonly used large motion benchmark, described in Section 4. We used PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index) as evaluation metric.", + "bbox": [ + 496, + 491, + 890, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "X4K1000FPS (X-Test) [29] is a 4K resolution benchmark, with 1000fps high frame rate. X-Test contains 15 clips of 33 successive 4K frames extracted from videos with 1000fps. We have selected X-Test, specifically with the largest temporal gap, naming X-Test-L, as our primary benchmark for evaluating large motion scenarios. We choose the $0_{th}$ and $32_{nd}$ frames as input and evaluate the quality of the synthesized $16_{th}$ output frame. Our testing procedure follows [8] to provide both 4K and downsampled 2K resolution results. SNU-FILM [4] is a widely-used VFI benchmark, with $1280 \\times 720$ resolution. It has four different difficulty settings according to the temporal gap between two input frames, each with 310 triplets for evaluation. The larger the temporal gap, the more challenging this benchmark becomes. We test our model on the most challenging half of the SNU-FILM hard and extreme, naming SNU-FILM-L, with 155 triplets each. In the meantime, we also provide the performance on the 'easy' and 'medium' settings on the whole dataset in Table 2 to show our model's capability in handling small-to-medium motions.", + "bbox": [ + 496, + 580, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Xiph [22] is a 4K dataset with 8 scenes, each with 100 con", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "19130", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "secutive frames, extracted from 60fps videos. While it is often denoted as a benchmark for evaluating large motion, it does not match the level of difficulty exhibited by the X-Test. Therefore, we build this benchmark by doubling the input temporal gap and keeping the most challenging half of the dataset, naming Xiph-L, resulting in 192 test instances. By downsampling and center-cropping, we obtain 'Xiph-L-2K' and 'Xiph-L-4K' results, following [23].", + "bbox": [ + 75, + 90, + 472, + 213 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Comparison with Previous Methods", + "text_level": 1, + "bbox": [ + 76, + 223, + 390, + 239 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To fully inspect our model's capacity on large motion, we evaluate our model on the aforementioned large motion datasets benchmarks and give our analysis compared results with recent VFI approaches, including ones designed for large motion, such as XVFI [29], FILM [27], BiFormer [26], and ones that performed well on commonly used datasets but not designed for large motion, namely, RIFE [9], EMA-VFI [37].", + "bbox": [ + 75, + 248, + 468, + 368 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Table 1, the performance of our local feature branch, without finetuned on X-Train, has already surpassed most methods. We attribute this to the capacity of CNN and Transformer hybrid framework and high feature resolution $(H / 8\\times W / 8)$ . But without the sparse global matching block, our results are not comparable to BiFormer in SNUFILM-L extreme, Xiph-L-4K and XVFI in X-Test-L-4K.", + "bbox": [ + 75, + 369, + 468, + 474 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "After we incorporate the sparse global matching branch and finetuned on X-Train, our performance on large motion benchmarks are boosted. When we only sparsely select 1/8 of the points in initial flow estimation by the guidance of difference map $D_0$ , $D_1$ , our performance improved 0.44dB on X-Test-L-2K and 0.48dB on X-Test-L-4K in terms of PSNR. With more points introduced to be compensated, the performance can be potentially improved by 0.6dB and 0.66dB on X-Test-L-2K and X-Test-L-4K respectively.", + "bbox": [ + 75, + 476, + 470, + 611 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Small-to-medium Motion Benchmark Performance. From the data presented in Table 2, we observe that our results remain consistent with those in small-to-medium scenarios, and they are comparable to a SOTA algorithm, VFI-Former [21], on these benchmarks. This suggests that our local feature branch already achieves satisfactory results, and introducing our sparse global matching branch has a limited negative impact on the overall performance.", + "bbox": [ + 75, + 612, + 468, + 733 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For qualitative results, we also give the visual comparisons between our method and previous VFI methods in Figure 4. Four variants of our method lie inside the red frame. For fair comparison, 'Local Branch (ft.)' is also finetuned on X-Test, with Flow Refine Block in Figure 2, but without sparse global matching modules. In blue frames, our global compensation branch can fix the unmatched areas with large motion, yielding better visual effect than the 'Local Branch (ft.)' model. And with more points added into the sparse global matching block, the visual effect becomes better. When compared to other methods, our model", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ffcbea99a5ae57e58a3bc58d9ef025bdfcae87660768a953cb353b0f31b4f7f5.jpg", + "table_caption": [ + "Table 2. Performance on small-to-medium benchmarks, SNU-FILM easy and medium." + ], + "table_footnote": [], + "table_body": "
SNU-FILM
easymedium
PSNRSSIMPSNRSSIM
VFIFormer [21]40.130.990736.090.9799
Local Branch (ft.)40.150.990736.070.9795
1/8 Points40.150.990736.070.9795
1/4 Points40.140.990636.050.9795
1/2 Points40.150.990736.050.9795
", + "bbox": [ + 509, + 128, + 883, + 277 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/55def036f866856d470d3b6420e75eddc2905599bc518959eeb504901dd438bd.jpg", + "table_caption": [ + "Table 3. Comparison of finetuning with different settings. Local Branch (ft.) contains no global matching." + ], + "table_footnote": [], + "table_body": "
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)30.580.897729.440.8895
1/8 Points30.830.902229.730.8928
1/4 Points30.880.904329.780.8948
1/2 Points30.990.907229.910.8972
Full Global Matching31.030.907429.950.8974
", + "bbox": [ + 501, + 321, + 895, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "can preserve both the small details and large motion well.", + "bbox": [ + 500, + 476, + 879, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 500, + 653, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we ablate the effect of our key component, sparse global matching pipeline fintuning, difference map generation in Section 3.2, and merge block in Section 3.5.", + "bbox": [ + 496, + 523, + 890, + 568 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sparse Global Matching. To demonstrate that the primary source of our performance improvements comes from the sparse global matching branch rather than the finetuning process alone, we constructed a Local Branch (ft.) model, incorporating the learnable Flow Refine module (as depicted in Figure 2), to finetune on the X-Train dataset. Our results indicate that while fine-tuning on a large motion dataset can enhance model performance in challenging scenarios with large motion, global matching consistently outperforms it. Furthermore, we present a comprehensive overview of the global matching performance in Table 3. It is evident that as more points are selected, performance reaches saturation, because not every point needs a global receptive field.", + "bbox": [ + 496, + 568, + 890, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Difference Map. Our sparse global matching algorithm is guided by difference map, $D_0$ and $D_{1}$ , which can help us identify flaws in the initial estimation of intermediate flows. We then select the top- $k$ defective points to correct them. To evaluate the effectiveness of the difference map guidance, we conducted a random sampling strategy to replace the map generation and top- $k$ sampling. The results presented in Table 4 demonstrate that selecting random positions for", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "19131", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/609da1df0b284b1abebb53843f86895465da6e7e0105710ac73b281bc039a065.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 147, + 74, + 305, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d43f6b127c92b1817a44021b844b0007d0e9186d4ab332c3728f0dc79cdd8a0b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 147, + 138, + 303, + 199 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4c4b58095049713542b8b7725b5dc2c3fda5153030c56a6bc456e95382587ca3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 147, + 203, + 303, + 263 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/90161b74e945262d104b7010486e07da452f15ceab57020e7fca188bb0265517.jpg", + "image_caption": [ + "Overlay" + ], + "image_footnote": [], + "bbox": [ + 147, + 268, + 303, + 328 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b2ec69f7f169ac8916cfe9406b5bbf092bf508074118594e6cd560eb0782b641.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 74, + 581, + 136 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1f35af479f3313d200bc64e53ff4eb729c197f4a2e94477b51ba68867898ffc9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 138, + 581, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/57d02cef95f91433e0f7d9e7f4f8de3466d42796a7f01f1ab83fbfa6c9f35e6f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 169, + 581, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0e1941ab151ecddb31bea07f8b55e8a92a7d28d475fd5eeb370158a636ceb637.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 202, + 581, + 233 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47cfe6b59aca1911f80710b0e89553b6086803d3464d0b0dbe3941021a137f09.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 233, + 581, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15cc3774abd93e843ac3bb0e7a57f1f33bbe70f782100c41b4d60444875c10cf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 310, + 268, + 581, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/751a6b3eb4876e769cdf3f6f4f45b789589fb173a0a9a264795ff6763cb539ed.jpg", + "image_caption": [ + "Overlay(crop) XVFI FILM BiFormer RIFE", + "Local Branch (ft.) 1/8 Points 1/4 Points 1/2 Points GT", + "Figure 4. Visual comparison with different methods, instances selected from X-Test-L [29]. We provide the optical flow magnitude on the left, measured by RAFT [32]. Four sparsity setting of our methods lies in the red frame. Blue frames place a greater emphasis on demonstrating large motion, while green frames is more inclined to demonstrate the effect on local details. Best viewed in zoom." + ], + "image_footnote": [], + "bbox": [ + 310, + 299, + 581, + 330 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3f2c856143181e65ca35dc7bc46a1ab6f1c66606b5f0d6f1a4e2521aff11c738.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 73, + 849, + 136 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/308b843dc54b23fe32f083212905a70aac4831b8e5fde4627696e320b40250ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 138, + 848, + 169 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a7a6957b22fed9c21088adf5c8aaf570d0960180680240c80d057ad667ea89f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 169, + 848, + 200 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/882ec14e7f9ff791f1b684d277c582681814ce9a99ff2ac70b251dc84dcd93ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 202, + 848, + 233 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/83a428dddf5d501531d9b260a65025a12777e67d0e62a693fb5eabf011ad47a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 233, + 848, + 265 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0a1bbc12162bcae8b84500da5ef3601a1f52913b450bdce8cb0ccd7e727e2ff6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 268, + 848, + 297 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3b5de2f550d1dc8d3bb2d955fecbdcfd6fae6929c34e6ec67e50e016cca20341.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 581, + 297, + 848, + 330 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/77e9116def7cfdd497495332fcf21305db5fb93a9ca281a877f96bd0b52cce22.jpg", + "table_caption": [ + "Table 4. Comparison on random sampling $k$ points between generating difference map and sampling top- $k$ points." + ], + "table_footnote": [], + "table_body": "
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Ours-1/2-top-k30.990.907229.910.8972
Ours-1/4-top-k30.880.904329.780.8948
Ours-1/8-top-k30.830.902229.730.8928
Local Branch (ft.)30.580.897729.440.8895
Ours-1/2-random30.890.905729.860.8967
Ours-1/4-random30.670.901429.550.8923
Ours-1/8-random30.550.899229.470.8893
", + "bbox": [ + 86, + 439, + 460, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "correction is not as effective as choosing the top- $k$ defective points from the difference map. When dealing with sparse points, random sampling can even decrease accuracy by replacing correct flow with an inaccurate flow compensation. As the number of points increases, this gap narrows. Nevertheless, it is still evident that selecting top- $k$ on the difference map outperforms random sampling.", + "bbox": [ + 75, + 641, + 468, + 747 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Flow Merge. To show the effectiveness of our flow merge block, we remove the merge block and directly apply the sparse flow compensation patches $f_{t\\rightarrow 0}$ and $f_{t\\rightarrow 1}$ on $\\widetilde{F}_{t\\rightarrow 0}$ and $\\widetilde{F}_{t\\rightarrow 1}$ , respectively. From Table 5, we can see that after removing the merge block, the obtained results still exhibit slightly higher performance than the fine-tuned local branch model, indicating the effectiveness of our flow compensation patches $f_{t\\rightarrow 0}$ and $f_{t\\rightarrow 1}$ . However, it is noteworthy that as we involve more points in the flow compensation, the improvement in results becomes negligible and even falls", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/dfdad782dd25a01979931e448699fc8642425d9be6f62bc71dea103cf97ee42c.jpg", + "table_caption": [ + "Table 5. Results of our structure with or w/o merge block." + ], + "table_footnote": [], + "table_body": "
Merge BlockX-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)×30.580.897729.440.8895
Local Branch (ft.)√30.550.897129.440.8889
1/8 Points√30.830.902229.730.8995
1/2 Points×30.750.902529.690.8936
1/4 Points×30.770.901429.700.8924
1/8 Points×30.750.899229.640.8910
", + "bbox": [ + 500, + 424, + 890, + 551 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "short of only using 1/8 points, highlighting the necessity of our merge block.", + "bbox": [ + 498, + 565, + 892, + 595 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 599, + 619, + 614 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper we have presented a sparse global matching algorithm designed to effectively address the challenges posed by large motion in video frame interpolation. We establish a framework that extracts local features for intermediate flow estimation. Then we target the flaws in the initial flow estimation and perform sparse global matching to produce sparse flow compensation across a global receptive field. By adaptively merging initial intermediate flow estimation with sparse global matching flow compensation, we achieve state-of-the-art performance on the most challenging subset of commonly used large motion datasets while keeping the performance on small-to-medium motion benchmark.", + "bbox": [ + 496, + 626, + 892, + 821 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by the National Key R&D Program of China (No. 2022ZD0160900), the National Natural Science Foundation of China (No. 62076119, No. 61921006), and Collaborative Innovation Center of Novel Software Technology and Industrialization.", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "19132", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Tim Brooks and Jonathan T Barron. Learning to synthesize motion blur. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 6840-6848, 2019. 1, 2, 5", + "[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. End-to-end object detection with transformers. 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In International Conference on Learning Representations, 2021. 3" + ], + "bbox": [ + 501, + 92, + 892, + 372 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "19134", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/e8af234c-bd88-478c-b3ba-46c221c02a9f_model.json b/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/e8af234c-bd88-478c-b3ba-46c221c02a9f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..923ad775644aec61f228c05fa2bbadda2bbf0231 --- /dev/null +++ b/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/e8af234c-bd88-478c-b3ba-46c221c02a9f_model.json @@ -0,0 +1,2541 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.131, + 0.862, + 0.154 + ], + "angle": 0, + "content": "Sparse Global Matching for Video Frame Interpolation with Large Motion" + }, + { + "type": "text", + "bbox": [ + 0.21, + 0.18, + 0.761, + 0.2 + ], + "angle": 0, + "content": "Chunxu Liu\\(^{1,*}\\) Guozhen Zhang\\(^{1,*}\\) Rui Zhao\\(^{2}\\) Limin Wang\\(^{1,3,\\boxtimes}\\)" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.2, + 0.778, + 0.234 + ], + "angle": 0, + "content": "\\(^{1}\\)State Key Laboratory for Novel Software Technology, Nanjing University \\(^{2}\\) SenseTime Research Shanghai AI Lab" + }, + { + "type": "text", + "bbox": [ + 0.358, + 0.236, + 0.608, + 0.252 + ], + "angle": 0, + "content": "https://sgm-vfi.github.io" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.607 + ], + "angle": 0, + "content": "Large motion poses a critical challenge in Video Frame Interpolation (VFI) task. Existing methods are often constrained by limited receptive fields, resulting in sub-optimal performance when handling scenarios with large motion. In this paper, we introduce a new pipeline for VFI, which can effectively integrate global-level information to alleviate issues associated with large motion. Specifically, we first estimate a pair of initial intermediate flows using a high-resolution feature map for extracting local details. Then, we incorporate a sparse global matching branch to compensate for flow estimation, which consists of identifying flaws in initial flows and generating sparse flow compensation with a global receptive field. Finally, we adaptively merge the initial flow estimation with global flow compensation, yielding a more accurate intermediate flow. To evaluate the effectiveness of our method in handling large motion, we carefully curate a more challenging subset from commonly used benchmarks. Our method demonstrates the state-of-the-art performance on these VFI subsets with large motion." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.651, + 0.21, + 0.667 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.47, + 0.828 + ], + "angle": 0, + "content": "Video Frame Interpolation (VFI) seeks to generate the intermediate frame from a given pair of inference frames, which has received increasing attention. It has various real-life applications, such as creating slow motion videos [3, 10, 13], video compression [12, 33] and novel view synthesis [1, 7, 38]. Currently, flow-based algorithms occupy a prominent position [9, 17, 18, 26, 28, 30, 37] in VFI task, where the flow from the target frame to the input frames, namely, intermediate flow, is explicitly estimated for warping input frames to the target frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.829, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Nevertheless, existing optical flow [11, 32, 34] algorithms cannot be directly applied to estimate intermediate flows due to the absence of the target frame. To" + }, + { + "type": "image", + "bbox": [ + 0.564, + 0.287, + 0.646, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.596, + 0.432, + 0.613, + 0.442 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.682, + 0.288, + 0.866, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.775, + 0.431, + 0.794, + 0.442 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.45, + 0.63, + 0.5 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.5, + 0.631, + 0.531 + ], + "angle": 0, + "content": "Overlay of \\(I_0,I_1\\) Motion Magnitude Range (92.0,393.9)" + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.45, + 0.758, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.635, + 0.504, + 0.764, + 0.528 + ], + "angle": 0, + "content": "Initial Intermediate Flow Estimation \\(\\tilde{F}_{t\\rightarrow 0},\\tilde{F}_{t\\rightarrow 1}\\)" + }, + { + "type": "image", + "bbox": [ + 0.766, + 0.451, + 0.883, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.504, + 0.858, + 0.527 + ], + "angle": 0, + "content": "Difference Map \\(D_0\\)" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.528, + 0.631, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.586, + 0.641, + 0.609 + ], + "angle": 0, + "content": "After Sparse Global Matching: Shifted Flow Fix \\( f_{t\\rightarrow 0} \\)" + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.529, + 0.756, + 0.581 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.585, + 0.728, + 0.609 + ], + "angle": 0, + "content": "Merged Flow \\(F_{t\\rightarrow 0}\\)" + }, + { + "type": "image", + "bbox": [ + 0.764, + 0.528, + 0.886, + 0.583 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.75, + 0.584, + 0.889, + 0.615 + ], + "angle": 0, + "content": "Synthesized \\(I_{t}\\) with (right) and without (left) Sparse Global Matching Block" + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.617, + 0.706, + 0.628 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.639, + 0.894, + 0.724 + ], + "angle": 0, + "content": "Figure 1. (a) Our framework without sparse global matching, pretrained on small motion dataset, for capturing local details. (b) Our framework with sparse global matching, fine-tuned on large motion dataset, for capturing global large motion. (c) Key components in our algorithm, illustrating the effect of our sparse global matching branch. (Using Ours-1/4-Points, from Table 1.)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.854 + ], + "angle": 0, + "content": "address this, many algorithms first estimate the bidirectional flow between two input frames and then generate intermediate optical flows using various flow reversal techniques [13, 15, 19, 24, 29, 35, 39]. Alternatively, recent algorithms directly estimate the intermediate flow with proper supervision [9, 17, 37] and achieve improved performance on datasets where small-to-medium motions are prevalent [27]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "However, real-world video frame interpolation encounters various complex challenges, with the problem of handling large motion being particularly prominent. In scenar" + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.887, + 0.468, + 0.901 + ], + "angle": 0, + "content": "*: Equal Contribution. ☑ Corresponding author (lmwang@nju.edu.cn)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19125" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "ios characterized by large motion, the correspondence of objects between frames is hard to locate due to the large pixel shifting. Many works have been proposed to alleviate this problem. For example, XVFI [29] addressed this by creating an extreme 4K training dataset and a scalable framework. However, its performance improvement is limited when applied to small motion scenarios [25]. FILM [27] introduced scale-agnostic features and a weight-sharing approach to improve model generalization across different motion scales. In fact, due to its limited receptive field, the model's depth can become excessively deep when dealing with large motion. This increases computational complexity and falls short in handling fast-moving small objects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.473, + 0.533 + ], + "angle": 0, + "content": "In this paper, we introduce a sparse global matching pipeline to specifically handle the challenges posed by large motion in the VFI task, by effectively integrating global-level information into intermediate flow estimation. Our VFI method establishes sparse global correspondences between input frames using a global receptive field and takes a two-step strategy to compensate for the intermediate flow estimation. Specifically, as shown in Figure 1 (a - b), our method begins with an initial estimation of a pair of intermediate flows using a relatively high-resolution feature map. Following this initial estimation, our approach incorporates a sparse global matching branch to locate potential error in the flow estimation results, and then produce flow residual to provide an effective remedy for capturing large motion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.536, + 0.473, + 0.765 + ], + "angle": 0, + "content": "To be specific, in our sparse global matching branch, we build a difference map to pinpoint the flaws in initial intermediate flow estimations. Concentrating on these defective areas, our approach employs sparse global matching to establish global correspondences between two adjacent input frames, specifically at these sparsely targeted locations. Subsequently, we convert this bidirectional sparse flow correspondence into intermediate flow compensation. Finally, we employ a flow merging block to adaptively merge the initial intermediate flows and flow compensation, thereby effectively combining the local details with the global correlation. As shown in Figure 1 (c), our sparse global matching branch can effectively locate the error regions and rectify the flaws in the initial intermediate flow estimation, yielding a significantly enhanced synthesized intermediate frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.904 + ], + "angle": 0, + "content": "In order to benchmark the effectiveness of our sparse global matching module on handling large motion, we carefully analyze motion magnitude and sufficiency within existing benchmarks, X-Test [29], Xiph [22] and SNUFILM [4]. In our analysis, we utilize the motion sufficiency filtering method described in [1], emphasizing the minimum of the top \\(5\\%\\) of each pixel's flow magnitude' as the key indicator of large motion sufficiency. In the end, we carefully curate the most challenging subsets for large mo" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.092, + 0.895, + 0.228 + ], + "angle": 0, + "content": "tion frame interpolation evaluation. In the most challenging testing conditions, our proposed method demonstrates a substantial improvement in terms of PSNR, enhancing it by \\(0.66\\mathrm{dB}\\) while correcting half of the points in initial flow estimation. Furthermore, even with the correction of just 1/8 points, we still observe a notable increase of 0.48 dB. Notably, our approach establishes a new state-of-the-art performance benchmark in these exceptionally challenging scenarios. In summary, our main contributions include:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.229, + 0.892, + 0.259 + ], + "angle": 0, + "content": "- We introduce a sparse global matching algorithm tailored to effectively capture large motion." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.259, + 0.892, + 0.334 + ], + "angle": 0, + "content": "- We designed an effective two-step framework for capturing large motion. First, by estimating initial intermediate flows to extract the local details, then targets and corrects the detected flaws through sparse global matching at sparsely targeted defective points." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.334, + 0.892, + 0.395 + ], + "angle": 0, + "content": "- Our models demonstrate state-of-the-art performance on the most challenging subset of the commonly used large motion benchmark, namely, X-Test-L, Xiph-L, SNU-FILM-L hard and extreme." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.229, + 0.892, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.411, + 0.642, + 0.427 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.436, + 0.836, + 0.453 + ], + "angle": 0, + "content": "2.1. Flow-Based Video Frame Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.46, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Flow-based algorithms for video frame interpolation focus on estimating intermediate flows. These flows enable the model to either forward warp or backward warp the input frames to the target frame. Some algorithms first compute bidirectional flows between two input frames and apply different flow reversal techniques to obtain intermediate flows [24, 29, 35], while the others directly estimate intermediate flows [9, 17, 37]." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.583, + 0.892, + 0.674 + ], + "angle": 0, + "content": "However, flow reversal techniques may introduce artifacts to intermediate flows, which can harm the details of the intermediate flows, causing misalignment [13] or holes [35]. Direct estimation of intermediate flows is also restricted by the model design, usually has a limited perceptive field [9, 37], and lacks robustness on large motion." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.674, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Addressing the issue of large motion in video frame interpolation, FILM [27] adopts a coarse-to-fine approach and shares weights between layers. It also trains on data with varied motion magnitudes, enabling it to learn to handle large motions. AMT [18] uses the RAFT-like structure to construct an all-pair correlation map and locally refines the intermediate flow afterward. BiFormer [26] employs a global feature extractor to extract global features and build local bilateral correlation maps. However, due to the high resolution of the VFI task, giving the model a genuine global receptive field is challenging." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.841, + 0.892, + 0.903 + ], + "angle": 0, + "content": "In contrast, our work uses local features to estimate the intermediate flows and global features to sparsely generate bidirectional flow compensation by global matching. We then adaptively merge the flows and flow compensation to" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "19126" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.089, + 0.892, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.287, + 0.893, + 0.357 + ], + "angle": 0, + "content": "Figure 2. Overview of our proposed structure. First, local features are extracted by a local feature extractor for flow estimation \\(\\widetilde{F}_{t\\rightarrow 0},\\widetilde{F}_{t\\rightarrow 1}\\). Then, our sparse global matching branch locates the flaws by constructing difference maps \\(D_0,D_1\\). Next, we perform sparse global matching using global features extracted by a global feature extractor. Finally, after shifting global correspondences \\(f_{0\\to 1},f_{1\\to 0}\\) to intermediate flow compensation \\(f_{t\\to 1},f_{t\\to 0}\\), we adaptively merge \\(\\widetilde{F}_{t\\rightarrow 0},\\widetilde{F}_{t\\rightarrow 1}\\) with \\(f_{t\\to 1},f_{t\\to 0}\\) and adopts a flow refine in a residual manner for interpolating the intermediate frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.399 + ], + "angle": 0, + "content": "obtain the final intermediate flow with both global information and local details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.408, + 0.212, + 0.423 + ], + "angle": 0, + "content": "2.2. Transformer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.673 + ], + "angle": 0, + "content": "Transformers have gained widespread popularity across various computer vision tasks [2, 6, 20, 40], demonstrating impressive feature extraction capabilities. Recently, Transformer-based backbone has already been introduced to solve VFI task [16, 22, 28, 37]. VFIFormer [21] uses cross-scale window-based attention. EMA-VFI [37] uses Inter-frame Attention to extract appearance and motion features using the same similarity matrix. BiFormer [26] adopts pretrained Twins architecture [5] for global feature extraction and builds local bilateral correlation cost volume. However, when handling large motion, these methods are more or less restricted by their local receptive field. Therefore, we propose a two-step strategy: employing a hybrid Transformer and CNN-based backbone for initial flow estimation, followed by a sparse global matching block utilizing a global receptive field." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.245, + 0.698 + ], + "angle": 0, + "content": "2.3. Global Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Global matching is extensively studied in local feature matching tasks. LoFTR [31] replaces the traditional dense matching method, using cost volume to search for correspondence, with self and cross attention layers in Transformer. COTR [14] takes a different approach by formulating the correspondence problem as a functional mapping and utilizing a Transformer as the function to query the points of interest. For dense matching, GMFlow [34] adopted Transformer block to extract strong discriminative features to build a global matching map. In VFI tasks, not every part of the image requires dense global matching. Our sparse global matching strategy, on the other hand, specifically targets and corrects the defective areas of the flows." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.367, + 0.591, + 0.383 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Given a pair of RGB frames \\( I_0, I_1 \\), and a timestep \\( t \\), we need to synthesize an intermediate frame \\( I_t \\). We illustrate our overall model pipeline in Figure 2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.44, + 0.893, + 0.606 + ], + "angle": 0, + "content": "Our method consists of a local feature branch and a sparse global matching branch. The local feature branch is responsible for estimating the initial intermediate flows, namely \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\). In the sparse global matching branch, we focus on the defective areas of \\(\\widetilde{F}_{t\\rightarrow 0}\\), \\(\\widetilde{F}_{t\\rightarrow 1}\\), and perform sparse global matching to obtain flow compensation, \\(f_{t\\rightarrow 0}\\) and \\(f_{t\\rightarrow 1}\\). Then we adaptively merge \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\) with \\(f_{t\\rightarrow 0}\\) and \\(f_{t\\rightarrow 1}\\) by our flow merge block, to obtain more accurate intermediate flows, \\(F_{t\\rightarrow 0}\\), \\(F_{t\\rightarrow 1}\\). Finally, after a few flow refine blocks, we use this pair of intermediate flows to synthesize the intermediate frame \\(\\widehat{I}_t\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.892, + 0.669 + ], + "angle": 0, + "content": "In the following, we first introduce each component in our local feature branch briefly in Section 3.1. From Section 3.2 and onward, we delve into a detailed discussion of our sparse global matching branch." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.704, + 0.695 + ], + "angle": 0, + "content": "3.1. Local Feature Branch" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.78 + ], + "angle": 0, + "content": "As shown in Figure 2, our local feature branch consists of three parts, namely, the local feature extractor, the flow estimation block, and the RefineNet [9]. We draw inspiration from RIFE [9] and EMA-VFI [37], while retaining certain distinctive aspects. We now introduce them sequentially." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Local Feature Extractor. EMA-VFI [37] has already verified the effectiveness of CNN and Transformer hybrid structure. We follow its design and keep our deepest feature resolution stays at \\( H / 8 \\times W / 8 \\) scale, instead of \\( H / 16 \\times W / 16 \\) in EMA-VFI. Furthermore, we simplified the specially designed Transformer structure in EMA-VFI to simple cross attention to extract inter-frame appearance features at a lower computation cost." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19127" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "Flow Estimation. We use the extracted appearance feature and input frames \\( I_0, I_1 \\in \\mathbb{R}^{3 \\times H \\times W} \\) to directly estimate intermediate flows \\( F_{t \\to 0}, F_{t \\to 1} \\), along with a fusion map \\( O \\), in a coarse-to-fine manner. This is achieved by several layers of CNN block, inspired by the intuitive design of RIFE [9] and EMA-VFI [37]. Then, the target frame can be generated by:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.205, + 0.47, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\widehat {I} _ {t} = O \\odot \\overleftarrow {\\mathcal {W}} \\left(I _ {0}, F _ {t \\rightarrow 0}\\right) + (1 - O) \\odot \\overleftarrow {\\mathcal {W}} \\left(I _ {1}, F _ {t \\rightarrow 1}\\right) \\quad (1)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.237, + 0.47, + 0.269 + ], + "angle": 0, + "content": "where \\(\\overline{\\mathcal{W}}\\) is image backward warping operation, \\(\\odot\\) is Hadamard product operator." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.269, + 0.469, + 0.315 + ], + "angle": 0, + "content": "Flow Refine. We share the same U-net-shaped network with RIFE to refine the synthesized frame \\(\\widehat{I}_t\\). More details can be found in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.322, + 0.416, + 0.339 + ], + "angle": 0, + "content": "3.2. Locate Flaws in Flows: Difference Map" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.345, + 0.47, + 0.496 + ], + "angle": 0, + "content": "Due to the limited receptive field of local feature branch, the estimated initial bidirectional flows, \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\), may be relatively coarse. Consequently, it is necessary to identify the flaws in \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\). Therefore, we construct the difference map \\(D_0\\) and \\(D_{1}\\) to check the correctness of \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\), by using both of the input frames \\(I_{0}\\) and \\(I_{1}\\) as ground truth reference. The values in the difference maps \\(D_0\\) and \\(D_{1}\\) serve as indicators of the likelihood of error in flow estimation, with higher values suggesting a greater probability of inaccuracies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.496, + 0.469, + 0.558 + ], + "angle": 0, + "content": "In particular, we first use \\(\\widetilde{F}_{t\\rightarrow 0}\\) to backward warp \\(I_0\\) to \\(\\widetilde{I}_t\\), then use \\(\\widetilde{F}_{t\\rightarrow 1}\\) to forward warp \\(\\widetilde{I}_t\\) to \\(\\widetilde{I}_1\\). And we compare the \\(\\widetilde{I}_1\\) and input frame \\(I_{1}\\) by doing summation over RGB channels after subtraction to obtain difference map \\(\\widetilde{D}_{0\\rightarrow 1}\\)." + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.57, + 0.469, + 0.596 + ], + "angle": 0, + "content": "\\[\n\\widetilde {I} _ {1} = \\overrightarrow {\\mathcal {W}} \\left(\\overleftarrow {\\mathcal {W}} \\left(I _ {0}, \\widetilde {F} _ {t \\rightarrow 0}\\right), \\widetilde {F} _ {t \\rightarrow 1}\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.599, + 0.469, + 0.631 + ], + "angle": 0, + "content": "\\[\n\\widetilde {D} _ {0 \\rightarrow 1} = \\sum_ {R G B} | I _ {1} - \\widetilde {I} _ {1} | \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.638, + 0.4, + 0.658 + ], + "angle": 0, + "content": "where \\(\\overleftarrow{\\mathcal{W}}\\) is backward warp, \\(\\overrightarrow{\\mathcal{W}}\\) is forward warp." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.469, + 0.793 + ], + "angle": 0, + "content": "Through the combination of backward warp and forward warp, we get an initial difference map \\(\\widetilde{D}_{0\\rightarrow 1}\\). Currently, the flaws in \\(\\widetilde{D}_{0\\rightarrow 1}\\) are caused by two reasons, the first reason is due to the flaws in our coarse flow estimation, \\(\\widetilde{F}_{t\\rightarrow 0}\\), \\(\\widetilde{F}_{t\\rightarrow 1}\\). The second reason is that even if \\(\\widetilde{F}_{t\\rightarrow 0}\\), \\(\\widetilde{F}_{t\\rightarrow 1}\\) were perfectly accurate, occlusions and cropping would still occur inevitably, i.e. some existing pixels in \\(I_0\\) disappearing in \\(I_{1}\\), creating incorrect pixel mappings and holes in the warped image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.794, + 0.469, + 0.869 + ], + "angle": 0, + "content": "To filter out the second cause of flaws, we create a map full of ones, and repeat the above warping process to obtain a \\(0/1\\) mask, \\(M_{0\\to 1}^{holes}\\). The positions in mask \\(M_{0\\to 1}^{holes}\\) where the element becomes 0 correspond to the potential hole areas in the warped image \\(\\widetilde{I}_1\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.869, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Then, we can multiply this map \\(M_{0\\to 1}^{holes}\\) with our initial difference map \\(\\widetilde{D}_{0\\rightarrow 1}\\) to filter out the potential holes caused" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.092, + 0.693, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.174, + 0.693, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.259, + 0.675, + 0.272 + ], + "angle": 0, + "content": "(a) Mean Motion Magnitude" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.098, + 0.89, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.181, + 0.89, + 0.256 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.259, + 0.88, + 0.272 + ], + "angle": 0, + "content": "(b) Motion Sufficiency Ranking" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.326 + ], + "angle": 0, + "content": "Figure 3. Large motion dataset benchmark analysis. Top: Whole dataset. Below: Keeping the most challenging half of Xiph and SNU-FILM. Four charts share the same legend." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.336, + 0.892, + 0.366 + ], + "angle": 0, + "content": "by occlusion and cropping, and obtain \\(D_{0\\to 1}\\), focusing on the flaws caused by inaccurate intermediate flow estimation." + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.372, + 0.891, + 0.39 + ], + "angle": 0, + "content": "\\[\nD _ {0 \\rightarrow 1} = M _ {0 \\rightarrow 1} ^ {\\text {h o l e s}} \\odot \\widetilde {D} _ {0 \\rightarrow 1} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.475 + ], + "angle": 0, + "content": "As a result, \\( D_{0 \\to 1} \\) enables us to identify the misaligned regions in \\( \\widetilde{I}_1 \\) that are caused solely by the flaws in the estimated flows \\( \\widetilde{F}_{t \\to 0}, \\widetilde{F}_{t \\to 1} \\). Furthermore, we reverse the previous warping combination to find the underlying source points responsible for these misalignments in \\( \\widetilde{I}_1 \\)." + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.479, + 0.891, + 0.506 + ], + "angle": 0, + "content": "\\[\nD _ {0} = \\overrightarrow {\\mathcal {W}} \\left(\\overleftarrow {\\mathcal {W}} \\left(D _ {0 \\rightarrow 1}, \\widetilde {F} _ {t \\rightarrow 1}\\right), \\widetilde {F} _ {t \\rightarrow 0}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.513, + 0.892, + 0.604 + ], + "angle": 0, + "content": "Difference map \\( D_0 \\) illustrates the extent to which each point in \\( I_0 \\) leads to the misalignment in \\( \\widetilde{I}_1 \\). To address this, it is essential to prioritize the regions with higher values in \\( D_0 \\). These regions indicate the points that exacerbate significant misalignment. Difference map \\( D_1 \\) can be produced symmetrically." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.612, + 0.724, + 0.629 + ], + "angle": 0, + "content": "3.3. Sparse Global Matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.892, + 0.711 + ], + "angle": 0, + "content": "To emphasize the region with higher values in \\(D_0\\) and \\(D_{1}\\) we can select the top- \\(k\\) points out of \\(D_0\\), \\(D_{1}\\) and do global matching for those points to provide more accurate matching flow \\(f_{0\\rightarrow 1}\\) and \\(f_{1\\rightarrow 0}\\), for preparing the flow compensation \\(f_{t\\rightarrow 1}\\) and \\(f_{t\\rightarrow 1}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.711, + 0.892, + 0.866 + ], + "angle": 0, + "content": "Sparse global matching allows the selected points in \\(I_0\\) to have a global receptive field on \\(I_{1}\\). We adopt the pretrained global feature extractor from GMFlow [34] to generate discriminative global features \\(A_0^i, A_1^i \\in \\mathbb{R}^{\\left(\\frac{H}{2^i}, \\frac{W}{2^i}\\right) \\times C}\\), where \\(C\\) is the number of feature channels. We construct a sparse feature map \\(a_0^i \\in \\mathbb{R}^{K \\times C}\\) according to top-\\(k\\) indices selected from \\(D_0\\). The corresponding area of \\(A_0^i, A_1^i\\) should have higher similarity, and the same intuition also applies to \\(a_0^i\\) and \\(A_1^i\\). Therefore, we can construct a similarity matrix \\(S_{0 \\to 1} \\in K \\times \\left(\\frac{H}{2^i} \\cdot \\frac{W}{2^i}\\right)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.865, + 0.891, + 0.9 + ], + "angle": 0, + "content": "\\[\nS _ {0 \\rightarrow 1} = S o f t m a x \\left(\\frac {a _ {0} ^ {i} A _ {1} ^ {i}}{\\sqrt {C}}\\right) \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19128" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.089, + 0.473, + 0.215 + ], + "angle": 0, + "content": "Then we create a coordinate map \\( B \\in \\mathbb{R}^{\\left(\\frac{H}{2^i} \\cdot \\frac{W}{2^i}\\right) \\times 2} \\). Using top-\\( k \\) indices selected from \\( D_0 \\), we extract the corresponding points from the coordinate map \\( B \\) to form a sparse coordinate map \\( b_0 \\in \\mathbb{R}^{K \\times 2} \\). We use the product between similarity matrix \\( S_{0 \\to 1} \\) and \\( b_0 \\) to represent the estimated position in \\( I_1 \\) for selected \\( k \\) points. Therefore, the subtraction between the previous product \\( S_{0 \\to 1}b_0 \\) and \\( b_0 \\) can represent the flow for those points, namely \\( f_{0 \\to 1} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.225, + 0.47, + 0.246 + ], + "angle": 0, + "content": "\\[\n\\widetilde {f} _ {0 \\rightarrow 1} = S _ {0 \\rightarrow 1} b _ {0} - b _ {0} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.258, + 0.47, + 0.339 + ], + "angle": 0, + "content": "Thus, \\(\\widetilde{f}_{0\\rightarrow 1}\\) is obtained in a global matching manner, making it more capable of capturing large motions. Finally, we reuse the top-\\(k\\) indices from \\(D_0\\) to fill \\(\\widetilde{f}_{0\\rightarrow 1} \\in \\mathbb{R}^{K\\times 2}\\) to \\(f_{0\\rightarrow 1} \\in \\mathbb{R}^{\\frac{H}{2^i} \\times \\frac{W}{2^i} \\times 2}\\) with zero. \\(f_{1\\rightarrow 0}\\) can be obtained symmetrically." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.348, + 0.218, + 0.364 + ], + "angle": 0, + "content": "3.4. Flow Shifting" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.371, + 0.469, + 0.46 + ], + "angle": 0, + "content": "The goal of our sparse global matching branch is to acquire sparse flow compensation \\( f_{t\\to 0} \\) and \\( \\underline{f}_{t\\to 1} \\) to improve the estimated intermediate flows, \\( \\widetilde{F}_{t\\to 0} \\), \\( F_{t\\to 1} \\), with large motion capturing ability. Next, we shift \\( f_{0\\to 1} \\), \\( f_{1\\to 0} \\) to \\( f_{t\\to 1} \\), \\( f_{t\\to 0} \\) by flow shifting, which can help mitigate the coordinate system mismatch." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.461, + 0.47, + 0.537 + ], + "angle": 0, + "content": "We intercept a \\((1 - t)\\) proportion of \\(f_{0\\rightarrow 1}\\) and shift this \\((1 - t)\\) proportion along the remaining \\(t\\) proportion of the flow \\(f_{0\\rightarrow 1}\\). Through this shifting operation, we can obtain \\(f_{t\\rightarrow 1}\\), and the shifting operation is performed by forward warping:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.54, + 0.469, + 0.561 + ], + "angle": 0, + "content": "\\[\nf _ {t \\rightarrow 1} = \\overrightarrow {\\mathcal {W}} ((1 - t) f _ {0 \\rightarrow 1}, t f _ {0 \\rightarrow 1}) \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.564, + 0.469, + 0.583 + ], + "angle": 0, + "content": "\\[\nf _ {t \\rightarrow 0} = \\overrightarrow {\\mathcal {W}} (t f _ {1 \\rightarrow 0}, (1 - t) f _ {1 \\rightarrow 0}) \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.469, + 0.64 + ], + "angle": 0, + "content": "Note that \\( f_{t \\to 1} \\) is flow shifted by \\( f_{0 \\to 1} \\) and \\( f_{t \\to 0} \\) is flow shifted by \\( f_{1 \\to 0} \\), we also list the \\( f_{t \\to 0} \\) in Equation (9) for clarity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.469, + 0.7 + ], + "angle": 0, + "content": "After the forward warping process, the number of sparsely chosen points will potentially change, and we will again choose the top-\\(k\\) points with the least occlusion possibility." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.7, + 0.469, + 0.822 + ], + "angle": 0, + "content": "Instead of using the estimated target frame \\(\\widetilde{I}_t\\) and input frames \\(I_0, I_1\\) to perform global matching and obtain intermediate flow compensation \\(f_{t\\to 0}\\) and \\(f_{t\\rightarrow 1}\\), we use global matching between \\(I_0, I_1\\) only and perform flow shift. The reason is that \\(\\widetilde{I}_t\\) synthesized by \\(\\widetilde{F}_{t\\to 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\) is not reliable. Since we aim to minimize accumulated propagation errors, we endeavor to minimize the usage of intermediate results wherever possible." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.255, + 0.847 + ], + "angle": 0, + "content": "3.5. Flow Merge Block" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.854, + 0.469, + 0.902 + ], + "angle": 0, + "content": "If we directly replace \\(\\widetilde{F}_{t\\to 0}\\) and \\(\\widetilde{F}_{t\\rightarrow 1}\\) with the flow compensation \\(f_{t\\to 0}\\) and \\(f_{t\\to 1}\\), the resulting flow may lack smoothness. In addition, the flow compensation \\(f_{t\\to 0}\\) and" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "\\(f_{t\\to 1}\\) can also make mistakes. Therefore, we designed a flow merge block \\(\\mathcal{M}\\) to adaptively merge \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(f_{t\\rightarrow 0}\\) as well as \\(\\widetilde{F}_{t\\rightarrow 1}\\) and \\(f_{t\\rightarrow 1}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.15, + 0.892, + 0.17 + ], + "angle": 0, + "content": "\\[\n\\widehat {F} _ {t \\rightarrow 0} = \\mathcal {M} \\left(\\widetilde {F} _ {t \\rightarrow 0}, f _ {t \\rightarrow 0}\\right) \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.612, + 0.173, + 0.892, + 0.192 + ], + "angle": 0, + "content": "\\[\n\\widehat {F} _ {t \\rightarrow 1} = \\mathcal {M} \\left(\\widetilde {F} _ {t \\rightarrow 1}, f _ {t \\rightarrow 1}\\right) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.209, + 0.893, + 0.41 + ], + "angle": 0, + "content": "Inspired by the convex sampling in RAFT [32], we take the \\(\\widehat{F}_{t\\rightarrow 0}\\) at each pixel to be the convex combination of \\(R\\times R\\) neighbors of \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(R\\times R\\) neighbors of \\(f_{t\\rightarrow 0}\\) where \\(\\mathbf{R}\\) is the neighborhood range. We use two convolutional layers to predict a \\(2\\times R^2\\times \\frac{H}{2^i}\\times \\frac{W}{2^i}\\) weight assignment, and apply softmax of the \\(2\\times R^2\\) neighborhood to obtain masks \\([W_{main},W_{sgm}]\\), where \\(W_{main},W_{sgm}\\in \\mathbb{R}^{R^2\\times \\frac{H}{2^i}\\times \\frac{W}{2^i}}\\). \\(W_{main}\\) stands for the weight for the local feature branch flow estimations, and \\(W_{sgm}\\) stands for the weight for sparse global matching block flow compensation. Finally, the flow merge block outputs the \\(\\widehat{F}_{t\\rightarrow 0}\\), obtained by taking weighted sum over the \\(\\widetilde{F}_{t\\rightarrow 0}\\) and \\(f_{t\\rightarrow 0}\\) neighborhood." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.429, + 0.782, + 0.447 + ], + "angle": 0, + "content": "4. Large Motion VFI Benchmark" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.547 + ], + "angle": 0, + "content": "To better illustrate our algorithm's effectiveness in handling large motions, we analyzed several widely used large motion datasets, namely, SNU-FILM extreme and hard [4], Xiph [22], and X-Test [29]. We utilized RAFT [32] to estimate optical flow between input frames as evidence, allowing for a detailed assessment of motion magnitudes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.549, + 0.892, + 0.624 + ], + "angle": 0, + "content": "According to Figure 3a, SNU-FILM and Xiph's mean motion magnitude is much lower than X-Test's. For example, we can see that about \\(60\\%\\) of SNU-FILM test cases' mean motion magnitude is below 15, while Xiph has about \\(40\\%\\) test cases below 30." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.892, + 0.779 + ], + "angle": 0, + "content": "In addition, we also refer to the criterion in [1] for assessing motion sufficiency, requiring at least \\(10\\%\\) of each pixel's flow to have a magnitude of at least 8 pixels within a \\(270 \\times 270\\) resolution. We adjusted this criterion by lowering the percentage threshold to \\(5\\%\\) while simultaneously increasing the required magnitude to account for the larger resolution of our input frames. This adjusted criterion, representing the minimum magnitude of the top \\(5\\%\\) pixel flows, forms the basis for our proportion ranking of the benchmark datasets in Figure 3b." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As depicted in the cumulative distribution chart Figure 3b, we found that over \\(50\\%\\) of X-Test have at least \\(5\\%\\) of each pixel's flow with a magnitude of at least 150 pixels. In contrast, Xiph [22] and SNU-FILM [4] contain fewer large motion pixels. Consequently, we focused our evaluation on the most challenging half of these benchmarks to assess our algorithm's performance improvements in handling genuinely large motion data, with details in Section 5.2." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "19129" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.146 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation (PSNR/SSIM) among different challenging benchmarks (see Section 4). The best results and the second best results in each column are marked in red and blue respectively. Ours-1/N Points means that we sparsely select 1/N points of the initial intermediate flows estimation to perform global matching by the evidence provided by difference map \\(D_0\\), \\(D_1\\). \"OOM\" denotes the out-of-memory issue when evaluating on an NVIDIA V100-32G GPU." + }, + { + "type": "table", + "bbox": [ + 0.094, + 0.147, + 0.878, + 0.342 + ], + "angle": 0, + "content": "
X-Test-LSNU-FILM-LXiph-L
2K4Khardextreme2K4K
XVFI [29]29.82/0.895129.02/0.886627.58/0.909522.99/0.826029.17/0.844928.09/0.7889
FILM [27]30.08/0.8941OOM28.35/0.915623.06/0.824729.89/0.853327.11/0.7699
BiFormer [26]30.32/0.906730.11/0.907028.18/0.915423.55/0.838329.61/0.854128.89/0.8133
RIFE [9]29.87/0.880528.98/0.875628.19/0.917222.84/0.823030.18/0.863328.07/0.7982
EMA-VFI-small [37]29.51/0.877528.60/0.873328.57/0.918923.18/0.829230.54/0.871828.40/0.8109
Ours-local-branch30.39/0.894629.25/0.886128.73/0.920723.19/0.830130.89/0.874528.59/0.8115
Ours-1/8-Points30.83/0.902229.73/0.892828.82/0.920823.54/0.835530.88/0.874928.90/0.8151
Ours-1/4-Points30.88/0.904329.78/0.894828.86/0.921223.58/0.836830.89/0.875129.15/0.8169
Ours-1/2-Points30.99/0.907229.91/0.897228.88/0.921623.62/0.837730.93/0.875529.25/0.8180
" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.365, + 0.21, + 0.383 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.391, + 0.288, + 0.407 + ], + "angle": 0, + "content": "5.1. Implementation Detail" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.415, + 0.471, + 0.536 + ], + "angle": 0, + "content": "Training Datasets. We use two training datasets, Vimeo90K [36] for pretraining on small-to-medium motion and X4K1000FPS (X-Train) [29] for finetuning on large motion. Vimeo90K contains 51,312 triplets with a resolution of \\(448 \\times 256\\) for training. It has an average motion magnitude between 1 to 8 pixels [36]. X4K1000FPS (X-Train) contains 4,408 clips with a resolution of \\(768 \\times 768\\), each clip has 65 consecutive frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.47, + 0.719 + ], + "angle": 0, + "content": "Local Feature Branch Training. We first train our model framework without the sparse global matching branch on Vimeo90K. We crop each training instance to 256x256 patches and perform random flip, time reversal, and random rotation augmentation, following [9, 37]. The training batch size is set to 32. We use AdamW as our optimizer with \\(\\beta_{1} = 0.9\\), \\(\\beta_{2} = 0.999\\) and weight decay \\(1e^{-4}\\). After 2,000 warmup steps, we gradually increase the learning rate to \\(2e^{-4}\\), then use cosine annealing for 480k steps (300 epochs) to reduce the learning rate from \\(2e^{-4}\\) to \\(2e^{-5}\\). We follow the training loss design of [9, 37] for both training and finetuning, which is included in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Sparse Global Branch Finetuning. We load our pretrained framework, and a global feature extractor from GM-Flow [34], operating on \\( i = 3 \\) in Equation (6). Then we integrate our sparse global matching branch into the framework, setting the sparsity ratio, i.e. \\( 1/8 \\), \\( 1/4 \\), \\( 1/2 \\), and finetuning the sparse global matching block on X-Train. When fine-tuning, we freeze the pretrained framework and the global feature extractor. We crop \\( 512 \\times 512 \\) patches from the original training image, and random resize the input images with \\( 50\\% \\) probability to remain the \\( 512 \\times 512 \\) size, \\( 25\\% \\) probability to downscale to \\( 256 \\times 256 \\) size and \\( 25\\% \\) probability to \\( 128 \\times 128 \\) size. We apply random flipping" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.459 + ], + "angle": 0, + "content": "augmentation, following [29]. The batch size, learning rate and optimizer are the same as our local feature branch, except that warmup steps are set to 1k steps, and the total steps are set to 13.7k (100 epochs). The parameter freezing and random rescaling are for preserving the model's ability to capture small motion details to the greatest extent possible." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.633, + 0.483 + ], + "angle": 0, + "content": "5.2. Test Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.581 + ], + "angle": 0, + "content": "The proposed algorithm is designed for capturing large motions. Therefore, we test our model's performance on the most challenging subset of the commonly used large motion benchmark, described in Section 4. We used PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index) as evaluation metric." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.884 + ], + "angle": 0, + "content": "X4K1000FPS (X-Test) [29] is a 4K resolution benchmark, with 1000fps high frame rate. X-Test contains 15 clips of 33 successive 4K frames extracted from videos with 1000fps. We have selected X-Test, specifically with the largest temporal gap, naming X-Test-L, as our primary benchmark for evaluating large motion scenarios. We choose the \\(0_{th}\\) and \\(32_{nd}\\) frames as input and evaluate the quality of the synthesized \\(16_{th}\\) output frame. Our testing procedure follows [8] to provide both 4K and downsampled 2K resolution results. SNU-FILM [4] is a widely-used VFI benchmark, with \\(1280 \\times 720\\) resolution. It has four different difficulty settings according to the temporal gap between two input frames, each with 310 triplets for evaluation. The larger the temporal gap, the more challenging this benchmark becomes. We test our model on the most challenging half of the SNU-FILM hard and extreme, naming SNU-FILM-L, with 155 triplets each. In the meantime, we also provide the performance on the 'easy' and 'medium' settings on the whole dataset in Table 2 to show our model's capability in handling small-to-medium motions." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Xiph [22] is a 4K dataset with 8 scenes, each with 100 con" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19130" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.214 + ], + "angle": 0, + "content": "secutive frames, extracted from 60fps videos. While it is often denoted as a benchmark for evaluating large motion, it does not match the level of difficulty exhibited by the X-Test. Therefore, we build this benchmark by doubling the input temporal gap and keeping the most challenging half of the dataset, naming Xiph-L, resulting in 192 test instances. By downsampling and center-cropping, we obtain 'Xiph-L-2K' and 'Xiph-L-4K' results, following [23]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.224, + 0.391, + 0.24 + ], + "angle": 0, + "content": "5.3. Comparison with Previous Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.47, + 0.369 + ], + "angle": 0, + "content": "To fully inspect our model's capacity on large motion, we evaluate our model on the aforementioned large motion datasets benchmarks and give our analysis compared results with recent VFI approaches, including ones designed for large motion, such as XVFI [29], FILM [27], BiFormer [26], and ones that performed well on commonly used datasets but not designed for large motion, namely, RIFE [9], EMA-VFI [37]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.476 + ], + "angle": 0, + "content": "As shown in Table 1, the performance of our local feature branch, without finetuned on X-Train, has already surpassed most methods. We attribute this to the capacity of CNN and Transformer hybrid framework and high feature resolution \\((H / 8\\times W / 8)\\). But without the sparse global matching block, our results are not comparable to BiFormer in SNUFILM-L extreme, Xiph-L-4K and XVFI in X-Test-L-4K." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.472, + 0.612 + ], + "angle": 0, + "content": "After we incorporate the sparse global matching branch and finetuned on X-Train, our performance on large motion benchmarks are boosted. When we only sparsely select 1/8 of the points in initial flow estimation by the guidance of difference map \\(D_0\\), \\(D_1\\), our performance improved 0.44dB on X-Test-L-2K and 0.48dB on X-Test-L-4K in terms of PSNR. With more points introduced to be compensated, the performance can be potentially improved by 0.6dB and 0.66dB on X-Test-L-2K and X-Test-L-4K respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Small-to-medium Motion Benchmark Performance. From the data presented in Table 2, we observe that our results remain consistent with those in small-to-medium scenarios, and they are comparable to a SOTA algorithm, VFI-Former [21], on these benchmarks. This suggests that our local feature branch already achieves satisfactory results, and introducing our sparse global matching branch has a limited negative impact on the overall performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "For qualitative results, we also give the visual comparisons between our method and previous VFI methods in Figure 4. Four variants of our method lie inside the red frame. For fair comparison, 'Local Branch (ft.)' is also finetuned on X-Test, with Flow Refine Block in Figure 2, but without sparse global matching modules. In blue frames, our global compensation branch can fix the unmatched areas with large motion, yielding better visual effect than the 'Local Branch (ft.)' model. And with more points added into the sparse global matching block, the visual effect becomes better. When compared to other methods, our model" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.892, + 0.118 + ], + "angle": 0, + "content": "Table 2. Performance on small-to-medium benchmarks, SNU-FILM easy and medium." + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.129, + 0.885, + 0.279 + ], + "angle": 0, + "content": "
SNU-FILM
easymedium
PSNRSSIMPSNRSSIM
VFIFormer [21]40.130.990736.090.9799
Local Branch (ft.)40.150.990736.070.9795
1/8 Points40.150.990736.070.9795
1/4 Points40.140.990636.050.9795
1/2 Points40.150.990736.050.9795
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.284, + 0.892, + 0.313 + ], + "angle": 0, + "content": "Table 3. Comparison of finetuning with different settings. Local Branch (ft.) contains no global matching." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.323, + 0.897, + 0.453 + ], + "angle": 0, + "content": "
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)30.580.897729.440.8895
1/8 Points30.830.902229.730.8928
1/4 Points30.880.904329.780.8948
1/2 Points30.990.907229.910.8972
Full Global Matching31.030.907429.950.8974
" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.477, + 0.88, + 0.492 + ], + "angle": 0, + "content": "can preserve both the small details and large motion well." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.5, + 0.655, + 0.517 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.569 + ], + "angle": 0, + "content": "In this section, we ablate the effect of our key component, sparse global matching pipeline fintuning, difference map generation in Section 3.2, and merge block in Section 3.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Sparse Global Matching. To demonstrate that the primary source of our performance improvements comes from the sparse global matching branch rather than the finetuning process alone, we constructed a Local Branch (ft.) model, incorporating the learnable Flow Refine module (as depicted in Figure 2), to finetune on the X-Train dataset. Our results indicate that while fine-tuning on a large motion dataset can enhance model performance in challenging scenarios with large motion, global matching consistently outperforms it. Furthermore, we present a comprehensive overview of the global matching performance in Table 3. It is evident that as more points are selected, performance reaches saturation, because not every point needs a global receptive field." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Difference Map. Our sparse global matching algorithm is guided by difference map, \\(D_0\\) and \\(D_{1}\\), which can help us identify flaws in the initial estimation of intermediate flows. We then select the top-\\(k\\) defective points to correct them. To evaluate the effectiveness of the difference map guidance, we conducted a random sampling strategy to replace the map generation and top-\\(k\\) sampling. The results presented in Table 4 demonstrate that selecting random positions for" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "19131" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.148, + 0.075, + 0.306, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.148, + 0.14, + 0.305, + 0.2 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.148, + 0.204, + 0.305, + 0.265 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.148, + 0.269, + 0.305, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.331, + 0.259, + 0.343 + ], + "angle": 0, + "content": "Overlay" + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.075, + 0.582, + 0.137 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.139, + 0.582, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.17, + 0.582, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.203, + 0.582, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.234, + 0.582, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.269, + 0.582, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.312, + 0.3, + 0.582, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.306, + 0.332, + 0.572, + 0.345 + ], + "angle": 0, + "content": "Overlay(crop) XVFI FILM BiFormer RIFE" + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.074, + 0.85, + 0.137 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.139, + 0.849, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.17, + 0.849, + 0.201 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.203, + 0.849, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.234, + 0.849, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.269, + 0.849, + 0.299 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.582, + 0.299, + 0.849, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.582, + 0.332, + 0.849, + 0.345 + ], + "angle": 0, + "content": "Local Branch (ft.) 1/8 Points 1/4 Points 1/2 Points GT" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.351, + 0.895, + 0.394 + ], + "angle": 0, + "content": "Figure 4. Visual comparison with different methods, instances selected from X-Test-L [29]. We provide the optical flow magnitude on the left, measured by RAFT [32]. Four sparsity setting of our methods lies in the red frame. Blue frames place a greater emphasis on demonstrating large motion, while green frames is more inclined to demonstrate the effect on local details. Best viewed in zoom." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.407, + 0.47, + 0.437 + ], + "angle": 0, + "content": "Table 4. Comparison on random sampling \\( k \\) points between generating difference map and sampling top- \\( k \\) points." + }, + { + "type": "table", + "bbox": [ + 0.087, + 0.44, + 0.462, + 0.611 + ], + "angle": 0, + "content": "
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Ours-1/2-top-k30.990.907229.910.8972
Ours-1/4-top-k30.880.904329.780.8948
Ours-1/8-top-k30.830.902229.730.8928
Local Branch (ft.)30.580.897729.440.8895
Ours-1/2-random30.890.905729.860.8967
Ours-1/4-random30.670.901429.550.8923
Ours-1/8-random30.550.899229.470.8893
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.748 + ], + "angle": 0, + "content": "correction is not as effective as choosing the top-\\(k\\) defective points from the difference map. When dealing with sparse points, random sampling can even decrease accuracy by replacing correct flow with an inaccurate flow compensation. As the number of points increases, this gap narrows. Nevertheless, it is still evident that selecting top-\\(k\\) on the difference map outperforms random sampling." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Flow Merge. To show the effectiveness of our flow merge block, we remove the merge block and directly apply the sparse flow compensation patches \\( f_{t\\rightarrow 0} \\) and \\( f_{t\\rightarrow 1} \\) on \\( \\widetilde{F}_{t\\rightarrow 0} \\) and \\( \\widetilde{F}_{t\\rightarrow 1} \\), respectively. From Table 5, we can see that after removing the merge block, the obtained results still exhibit slightly higher performance than the fine-tuned local branch model, indicating the effectiveness of our flow compensation patches \\( f_{t\\rightarrow 0} \\) and \\( f_{t\\rightarrow 1} \\). However, it is noteworthy that as we involve more points in the flow compensation, the improvement in results becomes negligible and even falls" + }, + { + "type": "table_caption", + "bbox": [ + 0.514, + 0.408, + 0.878, + 0.422 + ], + "angle": 0, + "content": "Table 5. Results of our structure with or w/o merge block." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.425, + 0.892, + 0.553 + ], + "angle": 0, + "content": "
Merge BlockX-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)×30.580.897729.440.8895
Local Branch (ft.)√30.550.897129.440.8889
1/8 Points√30.830.902229.730.8995
1/2 Points×30.750.902529.690.8936
1/4 Points×30.770.901429.700.8924
1/8 Points×30.750.899229.640.8910
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.566, + 0.893, + 0.597 + ], + "angle": 0, + "content": "short of only using 1/8 points, highlighting the necessity of our merge block." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.601, + 0.62, + 0.616 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.893, + 0.822 + ], + "angle": 0, + "content": "In this paper we have presented a sparse global matching algorithm designed to effectively address the challenges posed by large motion in video frame interpolation. We establish a framework that extracts local features for intermediate flow estimation. Then we target the flaws in the initial flow estimation and perform sparse global matching to produce sparse flow compensation across a global receptive field. By adaptively merging initial intermediate flow estimation with sparse global matching flow compensation, we achieve state-of-the-art performance on the most challenging subset of commonly used large motion datasets while keeping the performance on small-to-medium motion benchmark." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by the National Key R&D Program of China (No. 2022ZD0160900), the National Natural Science Foundation of China (No. 62076119, No. 61921006), and Collaborative Innovation Center of Novel Software Technology and Industrialization." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "19132" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Tim Brooks and Jonathan T Barron. Learning to synthesize motion blur. 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In International Conference on Learning Representations, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.893, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "19134" + } + ] +] \ No newline at end of file diff --git a/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/e8af234c-bd88-478c-b3ba-46c221c02a9f_origin.pdf b/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/e8af234c-bd88-478c-b3ba-46c221c02a9f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..47f5054d19ac291128c9de07064464d3a249a918 --- /dev/null +++ b/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/e8af234c-bd88-478c-b3ba-46c221c02a9f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b4a9e9ae04fdb74051fa63cd461dada683b605d2b4db11a1b5baddcd09b14559 +size 9503206 diff --git a/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/full.md b/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ba3846153ebe0500741dc0410c4fe1455b7fc6f1 --- /dev/null +++ b/2024/Sparse Global Matching for Video Frame Interpolation with Large Motion/full.md @@ -0,0 +1,385 @@ +# Sparse Global Matching for Video Frame Interpolation with Large Motion + +Chunxu Liu $^{1,*}$ Guozhen Zhang $^{1,*}$ Rui Zhao $^{2}$ Limin Wang $^{1,3,\boxtimes}$ + +$^{1}$ State Key Laboratory for Novel Software Technology, Nanjing University $^{2}$ SenseTime Research Shanghai AI Lab + +https://sgm-vfi.github.io + +# Abstract + +Large motion poses a critical challenge in Video Frame Interpolation (VFI) task. Existing methods are often constrained by limited receptive fields, resulting in sub-optimal performance when handling scenarios with large motion. In this paper, we introduce a new pipeline for VFI, which can effectively integrate global-level information to alleviate issues associated with large motion. Specifically, we first estimate a pair of initial intermediate flows using a high-resolution feature map for extracting local details. Then, we incorporate a sparse global matching branch to compensate for flow estimation, which consists of identifying flaws in initial flows and generating sparse flow compensation with a global receptive field. Finally, we adaptively merge the initial flow estimation with global flow compensation, yielding a more accurate intermediate flow. To evaluate the effectiveness of our method in handling large motion, we carefully curate a more challenging subset from commonly used benchmarks. Our method demonstrates the state-of-the-art performance on these VFI subsets with large motion. + +# 1. Introduction + +Video Frame Interpolation (VFI) seeks to generate the intermediate frame from a given pair of inference frames, which has received increasing attention. It has various real-life applications, such as creating slow motion videos [3, 10, 13], video compression [12, 33] and novel view synthesis [1, 7, 38]. Currently, flow-based algorithms occupy a prominent position [9, 17, 18, 26, 28, 30, 37] in VFI task, where the flow from the target frame to the input frames, namely, intermediate flow, is explicitly estimated for warping input frames to the target frame. + +Nevertheless, existing optical flow [11, 32, 34] algorithms cannot be directly applied to estimate intermediate flows due to the absence of the target frame. To + +![](images/762fff4f144f87de028c0558e1edbc81f8344b1f4109d3d6e867acc44d30ade6.jpg) +(a) + +![](images/e4a8d41f549106f9d307b2ff8edbf7a661592b1231164a428fd0e5d011689036.jpg) +(b) + +![](images/8b67fbd6851c08eb3751032a4f273d66455d158735c91098210ab3afa3820273.jpg) +Overlay of $I_0,I_1$ Motion Magnitude Range (92.0,393.9) + +![](images/bc6c08707956cfa85a17bb64f98245f34e6711af2f3ac07708c3b94d8df864ee.jpg) + +![](images/bb48eabcff9846e4d9bb371ac53adb30e69fb1be2edca32edbb04320e52e884e.jpg) + +![](images/32e885d71687fa354583fd8391f4f8fa6e88662f11dcf8f12525782797d4886c.jpg) +After Sparse Global Matching: Shifted Flow Fix $f_{t\rightarrow 0}$ + +![](images/0f74ed9e956a9e01f2e26bda823ff0c285c1d46d3a3e44886ab28f85beba36d2.jpg) +Initial Intermediate Flow Estimation $\tilde{F}_{t\rightarrow 0},\tilde{F}_{t\rightarrow 1}$ +Merged Flow $F_{t\rightarrow 0}$ +(c) + +![](images/2379e816dbbdbfc131cc2b1d81bf2e89eba935dfe45e35866c69f83c71c8ba67.jpg) +Difference Map $D_0$ +Synthesized $I_{t}$ with (right) and without (left) Sparse Global Matching Block +Figure 1. (a) Our framework without sparse global matching, pretrained on small motion dataset, for capturing local details. (b) Our framework with sparse global matching, fine-tuned on large motion dataset, for capturing global large motion. (c) Key components in our algorithm, illustrating the effect of our sparse global matching branch. (Using Ours-1/4-Points, from Table 1.) + +address this, many algorithms first estimate the bidirectional flow between two input frames and then generate intermediate optical flows using various flow reversal techniques [13, 15, 19, 24, 29, 35, 39]. Alternatively, recent algorithms directly estimate the intermediate flow with proper supervision [9, 17, 37] and achieve improved performance on datasets where small-to-medium motions are prevalent [27]. + +However, real-world video frame interpolation encounters various complex challenges, with the problem of handling large motion being particularly prominent. In scenar + +ios characterized by large motion, the correspondence of objects between frames is hard to locate due to the large pixel shifting. Many works have been proposed to alleviate this problem. For example, XVFI [29] addressed this by creating an extreme 4K training dataset and a scalable framework. However, its performance improvement is limited when applied to small motion scenarios [25]. FILM [27] introduced scale-agnostic features and a weight-sharing approach to improve model generalization across different motion scales. In fact, due to its limited receptive field, the model's depth can become excessively deep when dealing with large motion. This increases computational complexity and falls short in handling fast-moving small objects. + +In this paper, we introduce a sparse global matching pipeline to specifically handle the challenges posed by large motion in the VFI task, by effectively integrating global-level information into intermediate flow estimation. Our VFI method establishes sparse global correspondences between input frames using a global receptive field and takes a two-step strategy to compensate for the intermediate flow estimation. Specifically, as shown in Figure 1 (a - b), our method begins with an initial estimation of a pair of intermediate flows using a relatively high-resolution feature map. Following this initial estimation, our approach incorporates a sparse global matching branch to locate potential error in the flow estimation results, and then produce flow residual to provide an effective remedy for capturing large motion. + +To be specific, in our sparse global matching branch, we build a difference map to pinpoint the flaws in initial intermediate flow estimations. Concentrating on these defective areas, our approach employs sparse global matching to establish global correspondences between two adjacent input frames, specifically at these sparsely targeted locations. Subsequently, we convert this bidirectional sparse flow correspondence into intermediate flow compensation. Finally, we employ a flow merging block to adaptively merge the initial intermediate flows and flow compensation, thereby effectively combining the local details with the global correlation. As shown in Figure 1 (c), our sparse global matching branch can effectively locate the error regions and rectify the flaws in the initial intermediate flow estimation, yielding a significantly enhanced synthesized intermediate frame. + +In order to benchmark the effectiveness of our sparse global matching module on handling large motion, we carefully analyze motion magnitude and sufficiency within existing benchmarks, X-Test [29], Xiph [22] and SNUFILM [4]. In our analysis, we utilize the motion sufficiency filtering method described in [1], emphasizing the minimum of the top $5\%$ of each pixel's flow magnitude' as the key indicator of large motion sufficiency. In the end, we carefully curate the most challenging subsets for large mo + +tion frame interpolation evaluation. In the most challenging testing conditions, our proposed method demonstrates a substantial improvement in terms of PSNR, enhancing it by $0.66\mathrm{dB}$ while correcting half of the points in initial flow estimation. Furthermore, even with the correction of just 1/8 points, we still observe a notable increase of 0.48 dB. Notably, our approach establishes a new state-of-the-art performance benchmark in these exceptionally challenging scenarios. In summary, our main contributions include: + +- We introduce a sparse global matching algorithm tailored to effectively capture large motion. +- We designed an effective two-step framework for capturing large motion. First, by estimating initial intermediate flows to extract the local details, then targets and corrects the detected flaws through sparse global matching at sparsely targeted defective points. +- Our models demonstrate state-of-the-art performance on the most challenging subset of the commonly used large motion benchmark, namely, X-Test-L, Xiph-L, SNU-FILM-L hard and extreme. + +# 2. Related Work + +# 2.1. Flow-Based Video Frame Interpolation + +Flow-based algorithms for video frame interpolation focus on estimating intermediate flows. These flows enable the model to either forward warp or backward warp the input frames to the target frame. Some algorithms first compute bidirectional flows between two input frames and apply different flow reversal techniques to obtain intermediate flows [24, 29, 35], while the others directly estimate intermediate flows [9, 17, 37]. + +However, flow reversal techniques may introduce artifacts to intermediate flows, which can harm the details of the intermediate flows, causing misalignment [13] or holes [35]. Direct estimation of intermediate flows is also restricted by the model design, usually has a limited perceptive field [9, 37], and lacks robustness on large motion. + +Addressing the issue of large motion in video frame interpolation, FILM [27] adopts a coarse-to-fine approach and shares weights between layers. It also trains on data with varied motion magnitudes, enabling it to learn to handle large motions. AMT [18] uses the RAFT-like structure to construct an all-pair correlation map and locally refines the intermediate flow afterward. BiFormer [26] employs a global feature extractor to extract global features and build local bilateral correlation maps. However, due to the high resolution of the VFI task, giving the model a genuine global receptive field is challenging. + +In contrast, our work uses local features to estimate the intermediate flows and global features to sparsely generate bidirectional flow compensation by global matching. We then adaptively merge the flows and flow compensation to + +![](images/5393eea0876f5f773fe050b09b20e799135be84bd01c8cab312815f533069b79.jpg) +Figure 2. Overview of our proposed structure. First, local features are extracted by a local feature extractor for flow estimation $\widetilde{F}_{t\rightarrow 0},\widetilde{F}_{t\rightarrow 1}$ . Then, our sparse global matching branch locates the flaws by constructing difference maps $D_0,D_1$ . Next, we perform sparse global matching using global features extracted by a global feature extractor. Finally, after shifting global correspondences $f_{0\to 1},f_{1\to 0}$ to intermediate flow compensation $f_{t\to 1},f_{t\to 0}$ , we adaptively merge $\widetilde{F}_{t\rightarrow 0},\widetilde{F}_{t\rightarrow 1}$ with $f_{t\to 1},f_{t\to 0}$ and adopts a flow refine in a residual manner for interpolating the intermediate frame. + +obtain the final intermediate flow with both global information and local details. + +# 2.2. Transformer + +Transformers have gained widespread popularity across various computer vision tasks [2, 6, 20, 40], demonstrating impressive feature extraction capabilities. Recently, Transformer-based backbone has already been introduced to solve VFI task [16, 22, 28, 37]. VFIFormer [21] uses cross-scale window-based attention. EMA-VFI [37] uses Inter-frame Attention to extract appearance and motion features using the same similarity matrix. BiFormer [26] adopts pretrained Twins architecture [5] for global feature extraction and builds local bilateral correlation cost volume. However, when handling large motion, these methods are more or less restricted by their local receptive field. Therefore, we propose a two-step strategy: employing a hybrid Transformer and CNN-based backbone for initial flow estimation, followed by a sparse global matching block utilizing a global receptive field. + +# 2.3. Global Matching + +Global matching is extensively studied in local feature matching tasks. LoFTR [31] replaces the traditional dense matching method, using cost volume to search for correspondence, with self and cross attention layers in Transformer. COTR [14] takes a different approach by formulating the correspondence problem as a functional mapping and utilizing a Transformer as the function to query the points of interest. For dense matching, GMFlow [34] adopted Transformer block to extract strong discriminative features to build a global matching map. In VFI tasks, not every part of the image requires dense global matching. Our sparse global matching strategy, on the other hand, specifically targets and corrects the defective areas of the flows. + +# 3. Method + +Given a pair of RGB frames $I_0, I_1$ , and a timestep $t$ , we need to synthesize an intermediate frame $I_t$ . We illustrate our overall model pipeline in Figure 2. + +Our method consists of a local feature branch and a sparse global matching branch. The local feature branch is responsible for estimating the initial intermediate flows, namely $\widetilde{F}_{t\rightarrow 0}$ and $\widetilde{F}_{t\rightarrow 1}$ . In the sparse global matching branch, we focus on the defective areas of $\widetilde{F}_{t\rightarrow 0}$ , $\widetilde{F}_{t\rightarrow 1}$ , and perform sparse global matching to obtain flow compensation, $f_{t\rightarrow 0}$ and $f_{t\rightarrow 1}$ . Then we adaptively merge $\widetilde{F}_{t\rightarrow 0}$ and $\widetilde{F}_{t\rightarrow 1}$ with $f_{t\rightarrow 0}$ and $f_{t\rightarrow 1}$ by our flow merge block, to obtain more accurate intermediate flows, $F_{t\rightarrow 0}$ , $F_{t\rightarrow 1}$ . Finally, after a few flow refine blocks, we use this pair of intermediate flows to synthesize the intermediate frame $\widehat{I}_t$ . + +In the following, we first introduce each component in our local feature branch briefly in Section 3.1. From Section 3.2 and onward, we delve into a detailed discussion of our sparse global matching branch. + +# 3.1. Local Feature Branch + +As shown in Figure 2, our local feature branch consists of three parts, namely, the local feature extractor, the flow estimation block, and the RefineNet [9]. We draw inspiration from RIFE [9] and EMA-VFI [37], while retaining certain distinctive aspects. We now introduce them sequentially. + +Local Feature Extractor. EMA-VFI [37] has already verified the effectiveness of CNN and Transformer hybrid structure. We follow its design and keep our deepest feature resolution stays at $H / 8 \times W / 8$ scale, instead of $H / 16 \times W / 16$ in EMA-VFI. Furthermore, we simplified the specially designed Transformer structure in EMA-VFI to simple cross attention to extract inter-frame appearance features at a lower computation cost. + +Flow Estimation. We use the extracted appearance feature and input frames $I_0, I_1 \in \mathbb{R}^{3 \times H \times W}$ to directly estimate intermediate flows $F_{t \to 0}, F_{t \to 1}$ , along with a fusion map $O$ , in a coarse-to-fine manner. This is achieved by several layers of CNN block, inspired by the intuitive design of RIFE [9] and EMA-VFI [37]. Then, the target frame can be generated by: + +$$ +\widehat {I} _ {t} = O \odot \overleftarrow {\mathcal {W}} \left(I _ {0}, F _ {t \rightarrow 0}\right) + (1 - O) \odot \overleftarrow {\mathcal {W}} \left(I _ {1}, F _ {t \rightarrow 1}\right) \quad (1) +$$ + +where $\overline{\mathcal{W}}$ is image backward warping operation, $\odot$ is Hadamard product operator. + +Flow Refine. We share the same U-net-shaped network with RIFE to refine the synthesized frame $\widehat{I}_t$ . More details can be found in Appendix A. + +# 3.2. Locate Flaws in Flows: Difference Map + +Due to the limited receptive field of local feature branch, the estimated initial bidirectional flows, $\widetilde{F}_{t\rightarrow 0}$ and $\widetilde{F}_{t\rightarrow 1}$ , may be relatively coarse. Consequently, it is necessary to identify the flaws in $\widetilde{F}_{t\rightarrow 0}$ and $\widetilde{F}_{t\rightarrow 1}$ . Therefore, we construct the difference map $D_0$ and $D_{1}$ to check the correctness of $\widetilde{F}_{t\rightarrow 0}$ and $\widetilde{F}_{t\rightarrow 1}$ , by using both of the input frames $I_{0}$ and $I_{1}$ as ground truth reference. The values in the difference maps $D_0$ and $D_{1}$ serve as indicators of the likelihood of error in flow estimation, with higher values suggesting a greater probability of inaccuracies. + +In particular, we first use $\widetilde{F}_{t\rightarrow 0}$ to backward warp $I_0$ to $\widetilde{I}_t$ , then use $\widetilde{F}_{t\rightarrow 1}$ to forward warp $\widetilde{I}_t$ to $\widetilde{I}_1$ . And we compare the $\widetilde{I}_1$ and input frame $I_{1}$ by doing summation over RGB channels after subtraction to obtain difference map $\widetilde{D}_{0\rightarrow 1}$ . + +$$ +\widetilde {I} _ {1} = \overrightarrow {\mathcal {W}} \left(\overleftarrow {\mathcal {W}} \left(I _ {0}, \widetilde {F} _ {t \rightarrow 0}\right), \widetilde {F} _ {t \rightarrow 1}\right) \tag {2} +$$ + +$$ +\widetilde {D} _ {0 \rightarrow 1} = \sum_ {R G B} | I _ {1} - \widetilde {I} _ {1} | \tag {3} +$$ + +where $\overleftarrow{\mathcal{W}}$ is backward warp, $\overrightarrow{\mathcal{W}}$ is forward warp. + +Through the combination of backward warp and forward warp, we get an initial difference map $\widetilde{D}_{0\rightarrow 1}$ . Currently, the flaws in $\widetilde{D}_{0\rightarrow 1}$ are caused by two reasons, the first reason is due to the flaws in our coarse flow estimation, $\widetilde{F}_{t\rightarrow 0}$ , $\widetilde{F}_{t\rightarrow 1}$ . The second reason is that even if $\widetilde{F}_{t\rightarrow 0}$ , $\widetilde{F}_{t\rightarrow 1}$ were perfectly accurate, occlusions and cropping would still occur inevitably, i.e. some existing pixels in $I_0$ disappearing in $I_{1}$ , creating incorrect pixel mappings and holes in the warped image. + +To filter out the second cause of flaws, we create a map full of ones, and repeat the above warping process to obtain a $0/1$ mask, $M_{0\to 1}^{holes}$ . The positions in mask $M_{0\to 1}^{holes}$ where the element becomes 0 correspond to the potential hole areas in the warped image $\widetilde{I}_1$ . + +Then, we can multiply this map $M_{0\to 1}^{holes}$ with our initial difference map $\widetilde{D}_{0\rightarrow 1}$ to filter out the potential holes caused + +![](images/1dccc7dba248de1a7e9f3cb7d99fd396666462f7139856c80c2f056dbd6e9f84.jpg) + +![](images/59ede7f5775da0f450605e8be250c951319c35dbe37157335689881a33788151.jpg) +(a) Mean Motion Magnitude + +![](images/94d38bb51bc24497032358075cf0602121f298c7bfe454128094a98c139352e7.jpg) + +![](images/422b796dfef124864fd7f399d8de9c27b4c44311e3f22c28f8d2cf9f5b294c48.jpg) +(b) Motion Sufficiency Ranking +Figure 3. Large motion dataset benchmark analysis. Top: Whole dataset. Below: Keeping the most challenging half of Xiph and SNU-FILM. Four charts share the same legend. + +by occlusion and cropping, and obtain $D_{0\to 1}$ , focusing on the flaws caused by inaccurate intermediate flow estimation. + +$$ +D _ {0 \rightarrow 1} = M _ {0 \rightarrow 1} ^ {\text {h o l e s}} \odot \widetilde {D} _ {0 \rightarrow 1} \tag {4} +$$ + +As a result, $D_{0 \to 1}$ enables us to identify the misaligned regions in $\widetilde{I}_1$ that are caused solely by the flaws in the estimated flows $\widetilde{F}_{t \to 0}, \widetilde{F}_{t \to 1}$ . Furthermore, we reverse the previous warping combination to find the underlying source points responsible for these misalignments in $\widetilde{I}_1$ . + +$$ +D _ {0} = \overrightarrow {\mathcal {W}} \left(\overleftarrow {\mathcal {W}} \left(D _ {0 \rightarrow 1}, \widetilde {F} _ {t \rightarrow 1}\right), \widetilde {F} _ {t \rightarrow 0}\right) \tag {5} +$$ + +Difference map $D_0$ illustrates the extent to which each point in $I_0$ leads to the misalignment in $\widetilde{I}_1$ . To address this, it is essential to prioritize the regions with higher values in $D_0$ . These regions indicate the points that exacerbate significant misalignment. Difference map $D_1$ can be produced symmetrically. + +# 3.3. Sparse Global Matching + +To emphasize the region with higher values in $D_0$ and $D_{1}$ we can select the top- $k$ points out of $D_0$ , $D_{1}$ and do global matching for those points to provide more accurate matching flow $f_{0\rightarrow 1}$ and $f_{1\rightarrow 0}$ , for preparing the flow compensation $f_{t\rightarrow 1}$ and $f_{t\rightarrow 1}$ . + +Sparse global matching allows the selected points in $I_0$ to have a global receptive field on $I_{1}$ . We adopt the pretrained global feature extractor from GMFlow [34] to generate discriminative global features $A_0^i, A_1^i \in \mathbb{R}^{\left(\frac{H}{2^i}, \frac{W}{2^i}\right) \times C}$ , where $C$ is the number of feature channels. We construct a sparse feature map $a_0^i \in \mathbb{R}^{K \times C}$ according to top- $k$ indices selected from $D_0$ . The corresponding area of $A_0^i, A_1^i$ should have higher similarity, and the same intuition also applies to $a_0^i$ and $A_1^i$ . Therefore, we can construct a similarity matrix $S_{0 \to 1} \in K \times \left(\frac{H}{2^i} \cdot \frac{W}{2^i}\right)$ : + +$$ +S _ {0 \rightarrow 1} = S o f t m a x \left(\frac {a _ {0} ^ {i} A _ {1} ^ {i}}{\sqrt {C}}\right) \tag {6} +$$ + +Then we create a coordinate map $B \in \mathbb{R}^{\left(\frac{H}{2^i} \cdot \frac{W}{2^i}\right) \times 2}$ . Using top- $k$ indices selected from $D_0$ , we extract the corresponding points from the coordinate map $B$ to form a sparse coordinate map $b_0 \in \mathbb{R}^{K \times 2}$ . We use the product between similarity matrix $S_{0 \to 1}$ and $b_0$ to represent the estimated position in $I_1$ for selected $k$ points. Therefore, the subtraction between the previous product $S_{0 \to 1}b_0$ and $b_0$ can represent the flow for those points, namely $f_{0 \to 1}$ : + +$$ +\widetilde {f} _ {0 \rightarrow 1} = S _ {0 \rightarrow 1} b _ {0} - b _ {0} \tag {7} +$$ + +Thus, $\widetilde{f}_{0\rightarrow 1}$ is obtained in a global matching manner, making it more capable of capturing large motions. Finally, we reuse the top- $k$ indices from $D_0$ to fill $\widetilde{f}_{0\rightarrow 1} \in \mathbb{R}^{K\times 2}$ to $f_{0\rightarrow 1} \in \mathbb{R}^{\frac{H}{2^i} \times \frac{W}{2^i} \times 2}$ with zero. $f_{1\rightarrow 0}$ can be obtained symmetrically. + +# 3.4. Flow Shifting + +The goal of our sparse global matching branch is to acquire sparse flow compensation $f_{t\to 0}$ and $\underline{f}_{t\to 1}$ to improve the estimated intermediate flows, $\widetilde{F}_{t\to 0}$ , $F_{t\to 1}$ , with large motion capturing ability. Next, we shift $f_{0\to 1}$ , $f_{1\to 0}$ to $f_{t\to 1}$ , $f_{t\to 0}$ by flow shifting, which can help mitigate the coordinate system mismatch. + +We intercept a $(1 - t)$ proportion of $f_{0\rightarrow 1}$ and shift this $(1 - t)$ proportion along the remaining $t$ proportion of the flow $f_{0\rightarrow 1}$ . Through this shifting operation, we can obtain $f_{t\rightarrow 1}$ , and the shifting operation is performed by forward warping: + +$$ +f _ {t \rightarrow 1} = \overrightarrow {\mathcal {W}} ((1 - t) f _ {0 \rightarrow 1}, t f _ {0 \rightarrow 1}) \tag {8} +$$ + +$$ +f _ {t \rightarrow 0} = \overrightarrow {\mathcal {W}} (t f _ {1 \rightarrow 0}, (1 - t) f _ {1 \rightarrow 0}) \tag {9} +$$ + +Note that $f_{t \to 1}$ is flow shifted by $f_{0 \to 1}$ and $f_{t \to 0}$ is flow shifted by $f_{1 \to 0}$ , we also list the $f_{t \to 0}$ in Equation (9) for clarity. + +After the forward warping process, the number of sparsely chosen points will potentially change, and we will again choose the top- $k$ points with the least occlusion possibility. + +Instead of using the estimated target frame $\widetilde{I}_t$ and input frames $I_0, I_1$ to perform global matching and obtain intermediate flow compensation $f_{t\to 0}$ and $f_{t\rightarrow 1}$ , we use global matching between $I_0, I_1$ only and perform flow shift. The reason is that $\widetilde{I}_t$ synthesized by $\widetilde{F}_{t\to 0}$ and $\widetilde{F}_{t\rightarrow 1}$ is not reliable. Since we aim to minimize accumulated propagation errors, we endeavor to minimize the usage of intermediate results wherever possible. + +# 3.5. Flow Merge Block + +If we directly replace $\widetilde{F}_{t\to 0}$ and $\widetilde{F}_{t\rightarrow 1}$ with the flow compensation $f_{t\to 0}$ and $f_{t\to 1}$ , the resulting flow may lack smoothness. In addition, the flow compensation $f_{t\to 0}$ and + +$f_{t\to 1}$ can also make mistakes. Therefore, we designed a flow merge block $\mathcal{M}$ to adaptively merge $\widetilde{F}_{t\rightarrow 0}$ and $f_{t\rightarrow 0}$ as well as $\widetilde{F}_{t\rightarrow 1}$ and $f_{t\rightarrow 1}$ : + +$$ +\widehat {F} _ {t \rightarrow 0} = \mathcal {M} \left(\widetilde {F} _ {t \rightarrow 0}, f _ {t \rightarrow 0}\right) \tag {10} +$$ + +$$ +\widehat {F} _ {t \rightarrow 1} = \mathcal {M} \left(\widetilde {F} _ {t \rightarrow 1}, f _ {t \rightarrow 1}\right) \tag {11} +$$ + +Inspired by the convex sampling in RAFT [32], we take the $\widehat{F}_{t\rightarrow 0}$ at each pixel to be the convex combination of $R\times R$ neighbors of $\widetilde{F}_{t\rightarrow 0}$ and $R\times R$ neighbors of $f_{t\rightarrow 0}$ where $\mathbf{R}$ is the neighborhood range. We use two convolutional layers to predict a $2\times R^2\times \frac{H}{2^i}\times \frac{W}{2^i}$ weight assignment, and apply softmax of the $2\times R^2$ neighborhood to obtain masks $[W_{main},W_{sgm}]$ , where $W_{main},W_{sgm}\in \mathbb{R}^{R^2\times \frac{H}{2^i}\times \frac{W}{2^i}}$ . $W_{main}$ stands for the weight for the local feature branch flow estimations, and $W_{sgm}$ stands for the weight for sparse global matching block flow compensation. Finally, the flow merge block outputs the $\widehat{F}_{t\rightarrow 0}$ , obtained by taking weighted sum over the $\widetilde{F}_{t\rightarrow 0}$ and $f_{t\rightarrow 0}$ neighborhood. + +# 4. Large Motion VFI Benchmark + +To better illustrate our algorithm's effectiveness in handling large motions, we analyzed several widely used large motion datasets, namely, SNU-FILM extreme and hard [4], Xiph [22], and X-Test [29]. We utilized RAFT [32] to estimate optical flow between input frames as evidence, allowing for a detailed assessment of motion magnitudes. + +According to Figure 3a, SNU-FILM and Xiph's mean motion magnitude is much lower than X-Test's. For example, we can see that about $60\%$ of SNU-FILM test cases' mean motion magnitude is below 15, while Xiph has about $40\%$ test cases below 30. + +In addition, we also refer to the criterion in [1] for assessing motion sufficiency, requiring at least $10\%$ of each pixel's flow to have a magnitude of at least 8 pixels within a $270 \times 270$ resolution. We adjusted this criterion by lowering the percentage threshold to $5\%$ while simultaneously increasing the required magnitude to account for the larger resolution of our input frames. This adjusted criterion, representing the minimum magnitude of the top $5\%$ pixel flows, forms the basis for our proportion ranking of the benchmark datasets in Figure 3b. + +As depicted in the cumulative distribution chart Figure 3b, we found that over $50\%$ of X-Test have at least $5\%$ of each pixel's flow with a magnitude of at least 150 pixels. In contrast, Xiph [22] and SNU-FILM [4] contain fewer large motion pixels. Consequently, we focused our evaluation on the most challenging half of these benchmarks to assess our algorithm's performance improvements in handling genuinely large motion data, with details in Section 5.2. + +Table 1. Quantitative evaluation (PSNR/SSIM) among different challenging benchmarks (see Section 4). The best results and the second best results in each column are marked in red and blue respectively. Ours-1/N Points means that we sparsely select 1/N points of the initial intermediate flows estimation to perform global matching by the evidence provided by difference map $D_0$ , $D_1$ . "OOM" denotes the out-of-memory issue when evaluating on an NVIDIA V100-32G GPU. + +
X-Test-LSNU-FILM-LXiph-L
2K4Khardextreme2K4K
XVFI [29]29.82/0.895129.02/0.886627.58/0.909522.99/0.826029.17/0.844928.09/0.7889
FILM [27]30.08/0.8941OOM28.35/0.915623.06/0.824729.89/0.853327.11/0.7699
BiFormer [26]30.32/0.906730.11/0.907028.18/0.915423.55/0.838329.61/0.854128.89/0.8133
RIFE [9]29.87/0.880528.98/0.875628.19/0.917222.84/0.823030.18/0.863328.07/0.7982
EMA-VFI-small [37]29.51/0.877528.60/0.873328.57/0.918923.18/0.829230.54/0.871828.40/0.8109
Ours-local-branch30.39/0.894629.25/0.886128.73/0.920723.19/0.830130.89/0.874528.59/0.8115
Ours-1/8-Points30.83/0.902229.73/0.892828.82/0.920823.54/0.835530.88/0.874928.90/0.8151
Ours-1/4-Points30.88/0.904329.78/0.894828.86/0.921223.58/0.836830.89/0.875129.15/0.8169
Ours-1/2-Points30.99/0.907229.91/0.897228.88/0.921623.62/0.837730.93/0.875529.25/0.8180
+ +# 5. Experiments + +# 5.1. Implementation Detail + +Training Datasets. We use two training datasets, Vimeo90K [36] for pretraining on small-to-medium motion and X4K1000FPS (X-Train) [29] for finetuning on large motion. Vimeo90K contains 51,312 triplets with a resolution of $448 \times 256$ for training. It has an average motion magnitude between 1 to 8 pixels [36]. X4K1000FPS (X-Train) contains 4,408 clips with a resolution of $768 \times 768$ , each clip has 65 consecutive frames. + +Local Feature Branch Training. We first train our model framework without the sparse global matching branch on Vimeo90K. We crop each training instance to 256x256 patches and perform random flip, time reversal, and random rotation augmentation, following [9, 37]. The training batch size is set to 32. We use AdamW as our optimizer with $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ and weight decay $1e^{-4}$ . After 2,000 warmup steps, we gradually increase the learning rate to $2e^{-4}$ , then use cosine annealing for 480k steps (300 epochs) to reduce the learning rate from $2e^{-4}$ to $2e^{-5}$ . We follow the training loss design of [9, 37] for both training and finetuning, which is included in Appendix B. + +Sparse Global Branch Finetuning. We load our pretrained framework, and a global feature extractor from GM-Flow [34], operating on $i = 3$ in Equation (6). Then we integrate our sparse global matching branch into the framework, setting the sparsity ratio, i.e. $1/8$ , $1/4$ , $1/2$ , and finetuning the sparse global matching block on X-Train. When fine-tuning, we freeze the pretrained framework and the global feature extractor. We crop $512 \times 512$ patches from the original training image, and random resize the input images with $50\%$ probability to remain the $512 \times 512$ size, $25\%$ probability to downscale to $256 \times 256$ size and $25\%$ probability to $128 \times 128$ size. We apply random flipping + +augmentation, following [29]. The batch size, learning rate and optimizer are the same as our local feature branch, except that warmup steps are set to 1k steps, and the total steps are set to 13.7k (100 epochs). The parameter freezing and random rescaling are for preserving the model's ability to capture small motion details to the greatest extent possible. + +# 5.2. Test Dataset + +The proposed algorithm is designed for capturing large motions. Therefore, we test our model's performance on the most challenging subset of the commonly used large motion benchmark, described in Section 4. We used PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index) as evaluation metric. + +X4K1000FPS (X-Test) [29] is a 4K resolution benchmark, with 1000fps high frame rate. X-Test contains 15 clips of 33 successive 4K frames extracted from videos with 1000fps. We have selected X-Test, specifically with the largest temporal gap, naming X-Test-L, as our primary benchmark for evaluating large motion scenarios. We choose the $0_{th}$ and $32_{nd}$ frames as input and evaluate the quality of the synthesized $16_{th}$ output frame. Our testing procedure follows [8] to provide both 4K and downsampled 2K resolution results. SNU-FILM [4] is a widely-used VFI benchmark, with $1280 \times 720$ resolution. It has four different difficulty settings according to the temporal gap between two input frames, each with 310 triplets for evaluation. The larger the temporal gap, the more challenging this benchmark becomes. We test our model on the most challenging half of the SNU-FILM hard and extreme, naming SNU-FILM-L, with 155 triplets each. In the meantime, we also provide the performance on the 'easy' and 'medium' settings on the whole dataset in Table 2 to show our model's capability in handling small-to-medium motions. + +Xiph [22] is a 4K dataset with 8 scenes, each with 100 con + +secutive frames, extracted from 60fps videos. While it is often denoted as a benchmark for evaluating large motion, it does not match the level of difficulty exhibited by the X-Test. Therefore, we build this benchmark by doubling the input temporal gap and keeping the most challenging half of the dataset, naming Xiph-L, resulting in 192 test instances. By downsampling and center-cropping, we obtain 'Xiph-L-2K' and 'Xiph-L-4K' results, following [23]. + +# 5.3. Comparison with Previous Methods + +To fully inspect our model's capacity on large motion, we evaluate our model on the aforementioned large motion datasets benchmarks and give our analysis compared results with recent VFI approaches, including ones designed for large motion, such as XVFI [29], FILM [27], BiFormer [26], and ones that performed well on commonly used datasets but not designed for large motion, namely, RIFE [9], EMA-VFI [37]. + +As shown in Table 1, the performance of our local feature branch, without finetuned on X-Train, has already surpassed most methods. We attribute this to the capacity of CNN and Transformer hybrid framework and high feature resolution $(H / 8\times W / 8)$ . But without the sparse global matching block, our results are not comparable to BiFormer in SNUFILM-L extreme, Xiph-L-4K and XVFI in X-Test-L-4K. + +After we incorporate the sparse global matching branch and finetuned on X-Train, our performance on large motion benchmarks are boosted. When we only sparsely select 1/8 of the points in initial flow estimation by the guidance of difference map $D_0$ , $D_1$ , our performance improved 0.44dB on X-Test-L-2K and 0.48dB on X-Test-L-4K in terms of PSNR. With more points introduced to be compensated, the performance can be potentially improved by 0.6dB and 0.66dB on X-Test-L-2K and X-Test-L-4K respectively. + +Small-to-medium Motion Benchmark Performance. From the data presented in Table 2, we observe that our results remain consistent with those in small-to-medium scenarios, and they are comparable to a SOTA algorithm, VFI-Former [21], on these benchmarks. This suggests that our local feature branch already achieves satisfactory results, and introducing our sparse global matching branch has a limited negative impact on the overall performance. + +For qualitative results, we also give the visual comparisons between our method and previous VFI methods in Figure 4. Four variants of our method lie inside the red frame. For fair comparison, 'Local Branch (ft.)' is also finetuned on X-Test, with Flow Refine Block in Figure 2, but without sparse global matching modules. In blue frames, our global compensation branch can fix the unmatched areas with large motion, yielding better visual effect than the 'Local Branch (ft.)' model. And with more points added into the sparse global matching block, the visual effect becomes better. When compared to other methods, our model + +Table 2. Performance on small-to-medium benchmarks, SNU-FILM easy and medium. + +
SNU-FILM
easymedium
PSNRSSIMPSNRSSIM
VFIFormer [21]40.130.990736.090.9799
Local Branch (ft.)40.150.990736.070.9795
1/8 Points40.150.990736.070.9795
1/4 Points40.140.990636.050.9795
1/2 Points40.150.990736.050.9795
+ +Table 3. Comparison of finetuning with different settings. Local Branch (ft.) contains no global matching. + +
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)30.580.897729.440.8895
1/8 Points30.830.902229.730.8928
1/4 Points30.880.904329.780.8948
1/2 Points30.990.907229.910.8972
Full Global Matching31.030.907429.950.8974
+ +can preserve both the small details and large motion well. + +# 5.4. Ablation Study + +In this section, we ablate the effect of our key component, sparse global matching pipeline fintuning, difference map generation in Section 3.2, and merge block in Section 3.5. + +Sparse Global Matching. To demonstrate that the primary source of our performance improvements comes from the sparse global matching branch rather than the finetuning process alone, we constructed a Local Branch (ft.) model, incorporating the learnable Flow Refine module (as depicted in Figure 2), to finetune on the X-Train dataset. Our results indicate that while fine-tuning on a large motion dataset can enhance model performance in challenging scenarios with large motion, global matching consistently outperforms it. Furthermore, we present a comprehensive overview of the global matching performance in Table 3. It is evident that as more points are selected, performance reaches saturation, because not every point needs a global receptive field. + +Difference Map. Our sparse global matching algorithm is guided by difference map, $D_0$ and $D_{1}$ , which can help us identify flaws in the initial estimation of intermediate flows. We then select the top- $k$ defective points to correct them. To evaluate the effectiveness of the difference map guidance, we conducted a random sampling strategy to replace the map generation and top- $k$ sampling. The results presented in Table 4 demonstrate that selecting random positions for + +![](images/609da1df0b284b1abebb53843f86895465da6e7e0105710ac73b281bc039a065.jpg) + +![](images/d43f6b127c92b1817a44021b844b0007d0e9186d4ab332c3728f0dc79cdd8a0b.jpg) + +![](images/4c4b58095049713542b8b7725b5dc2c3fda5153030c56a6bc456e95382587ca3.jpg) + +![](images/90161b74e945262d104b7010486e07da452f15ceab57020e7fca188bb0265517.jpg) +Overlay + +![](images/b2ec69f7f169ac8916cfe9406b5bbf092bf508074118594e6cd560eb0782b641.jpg) + +![](images/1f35af479f3313d200bc64e53ff4eb729c197f4a2e94477b51ba68867898ffc9.jpg) + +![](images/57d02cef95f91433e0f7d9e7f4f8de3466d42796a7f01f1ab83fbfa6c9f35e6f.jpg) + +![](images/0e1941ab151ecddb31bea07f8b55e8a92a7d28d475fd5eeb370158a636ceb637.jpg) + +![](images/47cfe6b59aca1911f80710b0e89553b6086803d3464d0b0dbe3941021a137f09.jpg) + +![](images/15cc3774abd93e843ac3bb0e7a57f1f33bbe70f782100c41b4d60444875c10cf.jpg) + +![](images/751a6b3eb4876e769cdf3f6f4f45b789589fb173a0a9a264795ff6763cb539ed.jpg) +Overlay(crop) XVFI FILM BiFormer RIFE +Local Branch (ft.) 1/8 Points 1/4 Points 1/2 Points GT +Figure 4. Visual comparison with different methods, instances selected from X-Test-L [29]. We provide the optical flow magnitude on the left, measured by RAFT [32]. Four sparsity setting of our methods lies in the red frame. Blue frames place a greater emphasis on demonstrating large motion, while green frames is more inclined to demonstrate the effect on local details. Best viewed in zoom. + +![](images/3f2c856143181e65ca35dc7bc46a1ab6f1c66606b5f0d6f1a4e2521aff11c738.jpg) + +![](images/308b843dc54b23fe32f083212905a70aac4831b8e5fde4627696e320b40250ff.jpg) + +![](images/a7a6957b22fed9c21088adf5c8aaf570d0960180680240c80d057ad667ea89f0.jpg) + +![](images/882ec14e7f9ff791f1b684d277c582681814ce9a99ff2ac70b251dc84dcd93ed.jpg) + +![](images/83a428dddf5d501531d9b260a65025a12777e67d0e62a693fb5eabf011ad47a0.jpg) + +![](images/0a1bbc12162bcae8b84500da5ef3601a1f52913b450bdce8cb0ccd7e727e2ff6.jpg) + +![](images/3b5de2f550d1dc8d3bb2d955fecbdcfd6fae6929c34e6ec67e50e016cca20341.jpg) + +Table 4. Comparison on random sampling $k$ points between generating difference map and sampling top- $k$ points. + +
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Ours-1/2-top-k30.990.907229.910.8972
Ours-1/4-top-k30.880.904329.780.8948
Ours-1/8-top-k30.830.902229.730.8928
Local Branch (ft.)30.580.897729.440.8895
Ours-1/2-random30.890.905729.860.8967
Ours-1/4-random30.670.901429.550.8923
Ours-1/8-random30.550.899229.470.8893
+ +correction is not as effective as choosing the top- $k$ defective points from the difference map. When dealing with sparse points, random sampling can even decrease accuracy by replacing correct flow with an inaccurate flow compensation. As the number of points increases, this gap narrows. Nevertheless, it is still evident that selecting top- $k$ on the difference map outperforms random sampling. + +Flow Merge. To show the effectiveness of our flow merge block, we remove the merge block and directly apply the sparse flow compensation patches $f_{t\rightarrow 0}$ and $f_{t\rightarrow 1}$ on $\widetilde{F}_{t\rightarrow 0}$ and $\widetilde{F}_{t\rightarrow 1}$ , respectively. From Table 5, we can see that after removing the merge block, the obtained results still exhibit slightly higher performance than the fine-tuned local branch model, indicating the effectiveness of our flow compensation patches $f_{t\rightarrow 0}$ and $f_{t\rightarrow 1}$ . However, it is noteworthy that as we involve more points in the flow compensation, the improvement in results becomes negligible and even falls + +Table 5. Results of our structure with or w/o merge block. + +
Merge BlockX-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)×30.580.897729.440.8895
Local Branch (ft.)√30.550.897129.440.8889
1/8 Points√30.830.902229.730.8995
1/2 Points×30.750.902529.690.8936
1/4 Points×30.770.901429.700.8924
1/8 Points×30.750.899229.640.8910
+ +short of only using 1/8 points, highlighting the necessity of our merge block. + +# 6. Conclusion + +In this paper we have presented a sparse global matching algorithm designed to effectively address the challenges posed by large motion in video frame interpolation. We establish a framework that extracts local features for intermediate flow estimation. Then we target the flaws in the initial flow estimation and perform sparse global matching to produce sparse flow compensation across a global receptive field. By adaptively merging initial intermediate flow estimation with sparse global matching flow compensation, we achieve state-of-the-art performance on the most challenging subset of commonly used large motion datasets while keeping the performance on small-to-medium motion benchmark. + +Acknowledgements. 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+ 544, + 487 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 459, + 462, + 544, + 487 + ], + "type": "text", + "content": " with (right) and without (left) Sparse Global Matching Block" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 506, + 547, + 573 + ], + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 573 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 573 + ], + "type": "text", + "content": "Figure 1. (a) Our framework without sparse global matching, pretrained on small motion dataset, for capturing local details. (b) Our framework with sparse global matching, fine-tuned on large motion dataset, for capturing global large motion. (c) Key components in our algorithm, illustrating the effect of our sparse global matching branch. (Using Ours-1/4-Points, from Table 1.)" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 582, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 676 + ], + "type": "text", + "content": "address this, many algorithms first estimate the bidirectional flow between two input frames and then generate intermediate optical flows using various flow reversal techniques [13, 15, 19, 24, 29, 35, 39]. Alternatively, recent algorithms directly estimate the intermediate flow with proper supervision [9, 17, 37] and achieve improved performance on datasets where small-to-medium motions are prevalent [27]." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "However, real-world video frame interpolation encounters various complex challenges, with the problem of handling large motion being particularly prominent. In scenar" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 702, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 702, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 702, + 286, + 713 + ], + "type": "text", + "content": "*: Equal Contribution. ☑ Corresponding author (lmwang@nju.edu.cn)." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19125" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "ios characterized by large motion, the correspondence of objects between frames is hard to locate due to the large pixel shifting. Many works have been proposed to alleviate this problem. For example, XVFI [29] addressed this by creating an extreme 4K training dataset and a scalable framework. However, its performance improvement is limited when applied to small motion scenarios [25]. FILM [27] introduced scale-agnostic features and a weight-sharing approach to improve model generalization across different motion scales. In fact, due to its limited receptive field, the model's depth can become excessively deep when dealing with large motion. This increases computational complexity and falls short in handling fast-moving small objects." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 242, + 289, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 289, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 289, + 422 + ], + "type": "text", + "content": "In this paper, we introduce a sparse global matching pipeline to specifically handle the challenges posed by large motion in the VFI task, by effectively integrating global-level information into intermediate flow estimation. Our VFI method establishes sparse global correspondences between input frames using a global receptive field and takes a two-step strategy to compensate for the intermediate flow estimation. Specifically, as shown in Figure 1 (a - b), our method begins with an initial estimation of a pair of intermediate flows using a relatively high-resolution feature map. Following this initial estimation, our approach incorporates a sparse global matching branch to locate potential error in the flow estimation results, and then produce flow residual to provide an effective remedy for capturing large motion." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 424, + 289, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 424, + 289, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 424, + 289, + 605 + ], + "type": "text", + "content": "To be specific, in our sparse global matching branch, we build a difference map to pinpoint the flaws in initial intermediate flow estimations. Concentrating on these defective areas, our approach employs sparse global matching to establish global correspondences between two adjacent input frames, specifically at these sparsely targeted locations. Subsequently, we convert this bidirectional sparse flow correspondence into intermediate flow compensation. Finally, we employ a flow merging block to adaptively merge the initial intermediate flows and flow compensation, thereby effectively combining the local details with the global correlation. As shown in Figure 1 (c), our sparse global matching branch can effectively locate the error regions and rectify the flaws in the initial intermediate flow estimation, yielding a significantly enhanced synthesized intermediate frame." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "In order to benchmark the effectiveness of our sparse global matching module on handling large motion, we carefully analyze motion magnitude and sufficiency within existing benchmarks, X-Test [29], Xiph [22] and SNUFILM [4]. In our analysis, we utilize the motion sufficiency filtering method described in [1], emphasizing the minimum of the top " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": " of each pixel's flow magnitude' as the key indicator of large motion sufficiency. In the end, we carefully curate the most challenging subsets for large mo" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": "tion frame interpolation evaluation. In the most challenging testing conditions, our proposed method demonstrates a substantial improvement in terms of PSNR, enhancing it by " + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "inline_equation", + "content": "0.66\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 72, + 547, + 180 + ], + "type": "text", + "content": " while correcting half of the points in initial flow estimation. Furthermore, even with the correction of just 1/8 points, we still observe a notable increase of 0.48 dB. Notably, our approach establishes a new state-of-the-art performance benchmark in these exceptionally challenging scenarios. In summary, our main contributions include:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 181, + 545, + 312 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 306, + 181, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 181, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 181, + 545, + 205 + ], + "type": "text", + "content": "- We introduce a sparse global matching algorithm tailored to effectively capture large motion." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 205, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 545, + 264 + ], + "type": "text", + "content": "- We designed an effective two-step framework for capturing large motion. First, by estimating initial intermediate flows to extract the local details, then targets and corrects the detected flaws through sparse global matching at sparsely targeted defective points." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 264, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 264, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 264, + 545, + 312 + ], + "type": "text", + "content": "- Our models demonstrate state-of-the-art performance on the most challenging subset of the commonly used large motion benchmark, namely, X-Test-L, Xiph-L, SNU-FILM-L hard and extreme." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 325, + 392, + 338 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 325, + 392, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 325, + 392, + 338 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 345, + 511, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 345, + 511, + 358 + ], + "spans": [ + { + "bbox": [ + 306, + 345, + 511, + 358 + ], + "type": "text", + "content": "2.1. Flow-Based Video Frame Interpolation" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 364, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 545, + 461 + ], + "type": "text", + "content": "Flow-based algorithms for video frame interpolation focus on estimating intermediate flows. These flows enable the model to either forward warp or backward warp the input frames to the target frame. Some algorithms first compute bidirectional flows between two input frames and apply different flow reversal techniques to obtain intermediate flows [24, 29, 35], while the others directly estimate intermediate flows [9, 17, 37]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 461, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 533 + ], + "type": "text", + "content": "However, flow reversal techniques may introduce artifacts to intermediate flows, which can harm the details of the intermediate flows, causing misalignment [13] or holes [35]. Direct estimation of intermediate flows is also restricted by the model design, usually has a limited perceptive field [9, 37], and lacks robustness on large motion." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 665 + ], + "type": "text", + "content": "Addressing the issue of large motion in video frame interpolation, FILM [27] adopts a coarse-to-fine approach and shares weights between layers. It also trains on data with varied motion magnitudes, enabling it to learn to handle large motions. AMT [18] uses the RAFT-like structure to construct an all-pair correlation map and locally refines the intermediate flow afterward. BiFormer [26] employs a global feature extractor to extract global features and build local bilateral correlation maps. However, due to the high resolution of the VFI task, giving the model a genuine global receptive field is challenging." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 666, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 715 + ], + "type": "text", + "content": "In contrast, our work uses local features to estimate the intermediate flows and global features to sparsely generate bidirectional flow compensation by global matching. We then adaptively merge the flows and flow compensation to" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19126" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 545, + 218 + ], + "type": "image", + "image_path": "5393eea0876f5f773fe050b09b20e799135be84bd01c8cab312815f533069b79.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "lines": [ + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": "Figure 2. Overview of our proposed structure. First, local features are extracted by a local feature extractor for flow estimation " + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0},\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": ". Then, our sparse global matching branch locates the flaws by constructing difference maps " + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "inline_equation", + "content": "D_0,D_1" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": ". Next, we perform sparse global matching using global features extracted by a global feature extractor. Finally, after shifting global correspondences " + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "inline_equation", + "content": "f_{0\\to 1},f_{1\\to 0}" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": " to intermediate flow compensation " + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "inline_equation", + "content": "f_{t\\to 1},f_{t\\to 0}" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": ", we adaptively merge " + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0},\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "inline_equation", + "content": "f_{t\\to 1},f_{t\\to 0}" + }, + { + "bbox": [ + 46, + 227, + 546, + 282 + ], + "type": "text", + "content": " and adopts a flow refine in a residual manner for interpolating the intermediate frame." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 291, + 288, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 316 + ], + "type": "text", + "content": "obtain the final intermediate flow with both global information and local details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 323, + 129, + 335 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 129, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 129, + 335 + ], + "type": "text", + "content": "2.2. Transformer" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 341, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 533 + ], + "type": "text", + "content": "Transformers have gained widespread popularity across various computer vision tasks [2, 6, 20, 40], demonstrating impressive feature extraction capabilities. Recently, Transformer-based backbone has already been introduced to solve VFI task [16, 22, 28, 37]. VFIFormer [21] uses cross-scale window-based attention. EMA-VFI [37] uses Inter-frame Attention to extract appearance and motion features using the same similarity matrix. BiFormer [26] adopts pretrained Twins architecture [5] for global feature extraction and builds local bilateral correlation cost volume. However, when handling large motion, these methods are more or less restricted by their local receptive field. Therefore, we propose a two-step strategy: employing a hybrid Transformer and CNN-based backbone for initial flow estimation, followed by a sparse global matching block utilizing a global receptive field." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 540, + 149, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 149, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 149, + 552 + ], + "type": "text", + "content": "2.3. Global Matching" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 713 + ], + "type": "text", + "content": "Global matching is extensively studied in local feature matching tasks. LoFTR [31] replaces the traditional dense matching method, using cost volume to search for correspondence, with self and cross attention layers in Transformer. COTR [14] takes a different approach by formulating the correspondence problem as a functional mapping and utilizing a Transformer as the function to query the points of interest. For dense matching, GMFlow [34] adopted Transformer block to extract strong discriminative features to build a global matching map. In VFI tasks, not every part of the image requires dense global matching. Our sparse global matching strategy, on the other hand, specifically targets and corrects the defective areas of the flows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 290, + 361, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 290, + 361, + 303 + ], + "spans": [ + { + "bbox": [ + 306, + 290, + 361, + 303 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "text", + "content": "Given a pair of RGB frames " + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "inline_equation", + "content": "I_0, I_1" + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "text", + "content": ", and a timestep " + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "text", + "content": ", we need to synthesize an intermediate frame " + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "inline_equation", + "content": "I_t" + }, + { + "bbox": [ + 304, + 311, + 545, + 347 + ], + "type": "text", + "content": ". We illustrate our overall model pipeline in Figure 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": "Our method consists of a local feature branch and a sparse global matching branch. The local feature branch is responsible for estimating the initial intermediate flows, namely " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ". In the sparse global matching branch, we focus on the defective areas of " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", and perform sparse global matching to obtain flow compensation, " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ". Then we adaptively merge " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": " by our flow merge block, to obtain more accurate intermediate flows, " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "F_{t\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "F_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": ". Finally, after a few flow refine blocks, we use this pair of intermediate flows to synthesize the intermediate frame " + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "inline_equation", + "content": "\\widehat{I}_t" + }, + { + "bbox": [ + 304, + 348, + 546, + 479 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 480, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 545, + 529 + ], + "type": "text", + "content": "In the following, we first introduce each component in our local feature branch briefly in Section 3.1. From Section 3.2 and onward, we delve into a detailed discussion of our sparse global matching branch." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 538, + 430, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 430, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 430, + 550 + ], + "type": "text", + "content": "3.1. Local Feature Branch" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 557, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 617 + ], + "type": "text", + "content": "As shown in Figure 2, our local feature branch consists of three parts, namely, the local feature extractor, the flow estimation block, and the RefineNet [9]. We draw inspiration from RIFE [9] and EMA-VFI [37], while retaining certain distinctive aspects. We now introduce them sequentially." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Local Feature Extractor. EMA-VFI [37] has already verified the effectiveness of CNN and Transformer hybrid structure. We follow its design and keep our deepest feature resolution stays at " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "H / 8 \\times W / 8" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " scale, instead of " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "H / 16 \\times W / 16" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " in EMA-VFI. Furthermore, we simplified the specially designed Transformer structure in EMA-VFI to simple cross attention to extract inter-frame appearance features at a lower computation cost." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19127" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "Flow Estimation. We use the extracted appearance feature and input frames " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "I_0, I_1 \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " to directly estimate intermediate flows " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "F_{t \\to 0}, F_{t \\to 1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": ", along with a fusion map " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": ", in a coarse-to-fine manner. This is achieved by several layers of CNN block, inspired by the intuitive design of RIFE [9] and EMA-VFI [37]. Then, the target frame can be generated by:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 162, + 287, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 162, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 55, + 162, + 287, + 179 + ], + "type": "interline_equation", + "content": "\\widehat {I} _ {t} = O \\odot \\overleftarrow {\\mathcal {W}} \\left(I _ {0}, F _ {t \\rightarrow 0}\\right) + (1 - O) \\odot \\overleftarrow {\\mathcal {W}} \\left(I _ {1}, F _ {t \\rightarrow 1}\\right) \\quad (1)", + "image_path": "668b133ff2db8e42325b575f47b8a96e48d8f3651fce73f8878bff1999cb65be.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "type": "inline_equation", + "content": "\\overline{\\mathcal{W}}" + }, + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "type": "text", + "content": " is image backward warping operation, " + }, + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 187, + 287, + 213 + ], + "type": "text", + "content": " is Hadamard product operator." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 213, + 287, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 287, + 249 + ], + "type": "text", + "content": "Flow Refine. We share the same U-net-shaped network with RIFE to refine the synthesized frame " + }, + { + "bbox": [ + 46, + 213, + 287, + 249 + ], + "type": "inline_equation", + "content": "\\widehat{I}_t" + }, + { + "bbox": [ + 46, + 213, + 287, + 249 + ], + "type": "text", + "content": ". More details can be found in Appendix A." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 255, + 254, + 268 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 254, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 254, + 268 + ], + "type": "text", + "content": "3.2. Locate Flaws in Flows: Difference Map" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": "Due to the limited receptive field of local feature branch, the estimated initial bidirectional flows, " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": ", may be relatively coarse. Consequently, it is necessary to identify the flaws in " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": ". Therefore, we construct the difference map " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " to check the correctness of " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": ", by using both of the input frames " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "I_{0}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " as ground truth reference. The values in the difference maps " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 46, + 273, + 287, + 392 + ], + "type": "text", + "content": " serve as indicators of the likelihood of error in flow estimation, with higher values suggesting a greater probability of inaccuracies." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": "In particular, we first use " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " to backward warp " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_t" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": ", then use " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " to forward warp " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_t" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_1" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": ". And we compare the " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_1" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " and input frame " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": " by doing summation over RGB channels after subtraction to obtain difference map " + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_{0\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 392, + 287, + 441 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 451, + 287, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 451, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 287, + 472 + ], + "type": "interline_equation", + "content": "\\widetilde {I} _ {1} = \\overrightarrow {\\mathcal {W}} \\left(\\overleftarrow {\\mathcal {W}} \\left(I _ {0}, \\widetilde {F} _ {t \\rightarrow 0}\\right), \\widetilde {F} _ {t \\rightarrow 1}\\right) \\tag {2}", + "image_path": "ed3a7dd670bff66df8dd4e5c5fddfa00c8c60044b63e4d60333b42726a5514f9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 91, + 474, + 287, + 499 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 474, + 287, + 499 + ], + "spans": [ + { + "bbox": [ + 91, + 474, + 287, + 499 + ], + "type": "interline_equation", + "content": "\\widetilde {D} _ {0 \\rightarrow 1} = \\sum_ {R G B} | I _ {1} - \\widetilde {I} _ {1} | \\tag {3}", + "image_path": "e6d1585285b40a1cce0f253450ef808a739b70ab9d3d9d66535a981f63352998.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "type": "inline_equation", + "content": "\\overleftarrow{\\mathcal{W}}" + }, + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "type": "text", + "content": " is backward warp, " + }, + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "type": "inline_equation", + "content": "\\overrightarrow{\\mathcal{W}}" + }, + { + "bbox": [ + 47, + 505, + 244, + 521 + ], + "type": "text", + "content": " is forward warp." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": "Through the combination of backward warp and forward warp, we get an initial difference map " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_{0\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": ". Currently, the flaws in " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_{0\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " are caused by two reasons, the first reason is due to the flaws in our coarse flow estimation, " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": ". The second reason is that even if " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " were perfectly accurate, occlusions and cropping would still occur inevitably, i.e. some existing pixels in " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": " disappearing in " + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 46, + 521, + 287, + 628 + ], + "type": "text", + "content": ", creating incorrect pixel mappings and holes in the warped image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "content": "To filter out the second cause of flaws, we create a map full of ones, and repeat the above warping process to obtain a " + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "inline_equation", + "content": "0/1" + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "content": " mask, " + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "inline_equation", + "content": "M_{0\\to 1}^{holes}" + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "content": ". The positions in mask " + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "inline_equation", + "content": "M_{0\\to 1}^{holes}" + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "content": " where the element becomes 0 correspond to the potential hole areas in the warped image " + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_1" + }, + { + "bbox": [ + 46, + 628, + 287, + 688 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "type": "text", + "content": "Then, we can multiply this map " + }, + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "type": "inline_equation", + "content": "M_{0\\to 1}^{holes}" + }, + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "type": "text", + "content": " with our initial difference map " + }, + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\widetilde{D}_{0\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 688, + 287, + 713 + ], + "type": "text", + "content": " to filter out the potential holes caused" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 305, + 72, + 424, + 137 + ], + "blocks": [ + { + "bbox": [ + 305, + 72, + 424, + 137 + ], + "lines": [ + { + "bbox": [ + 305, + 72, + 424, + 137 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 424, + 137 + ], + "type": "image", + "image_path": "1dccc7dba248de1a7e9f3cb7d99fd396666462f7139856c80c2f056dbd6e9f84.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 307, + 137, + 424, + 202 + ], + "blocks": [ + { + "bbox": [ + 307, + 137, + 424, + 202 + ], + "lines": [ + { + "bbox": [ + 307, + 137, + 424, + 202 + ], + "spans": [ + { + "bbox": [ + 307, + 137, + 424, + 202 + ], + "type": "image", + "image_path": "59ede7f5775da0f450605e8be250c951319c35dbe37157335689881a33788151.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 319, + 205, + 413, + 215 + ], + "lines": [ + { + "bbox": [ + 319, + 205, + 413, + 215 + ], + "spans": [ + { + "bbox": [ + 319, + 205, + 413, + 215 + ], + "type": "text", + "content": "(a) Mean Motion Magnitude" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 427, + 77, + 544, + 137 + ], + "blocks": [ + { + "bbox": [ + 427, + 77, + 544, + 137 + ], + "lines": [ + { + "bbox": [ + 427, + 77, + 544, + 137 + ], + "spans": [ + { + "bbox": [ + 427, + 77, + 544, + 137 + ], + "type": "image", + "image_path": "94d38bb51bc24497032358075cf0602121f298c7bfe454128094a98c139352e7.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 427, + 143, + 544, + 202 + ], + "blocks": [ + { + "bbox": [ + 427, + 143, + 544, + 202 + ], + "lines": [ + { + "bbox": [ + 427, + 143, + 544, + 202 + ], + "spans": [ + { + "bbox": [ + 427, + 143, + 544, + 202 + ], + "type": "image", + "image_path": "422b796dfef124864fd7f399d8de9c27b4c44311e3f22c28f8d2cf9f5b294c48.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 205, + 538, + 215 + ], + "lines": [ + { + "bbox": [ + 435, + 205, + 538, + 215 + ], + "spans": [ + { + "bbox": [ + 435, + 205, + 538, + 215 + ], + "type": "text", + "content": "(b) Motion Sufficiency Ranking" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 224, + 545, + 258 + ], + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 258 + ], + "type": "text", + "content": "Figure 3. Large motion dataset benchmark analysis. Top: Whole dataset. Below: Keeping the most challenging half of Xiph and SNU-FILM. Four charts share the same legend." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 266, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 289 + ], + "type": "text", + "content": "by occlusion and cropping, and obtain " + }, + { + "bbox": [ + 305, + 266, + 545, + 289 + ], + "type": "inline_equation", + "content": "D_{0\\to 1}" + }, + { + "bbox": [ + 305, + 266, + 545, + 289 + ], + "type": "text", + "content": ", focusing on the flaws caused by inaccurate intermediate flow estimation." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 372, + 294, + 545, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 294, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 372, + 294, + 545, + 308 + ], + "type": "interline_equation", + "content": "D _ {0 \\rightarrow 1} = M _ {0 \\rightarrow 1} ^ {\\text {h o l e s}} \\odot \\widetilde {D} _ {0 \\rightarrow 1} \\tag {4}", + "image_path": "f8e2e5bcbc44e0ce114a03ac0e9ebd2dbcf3db2c391eb091e15b98f5e076adb4.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": "As a result, " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "D_{0 \\to 1}" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " enables us to identify the misaligned regions in " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_1" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": " that are caused solely by the flaws in the estimated flows " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t \\to 0}, \\widetilde{F}_{t \\to 1}" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": ". Furthermore, we reverse the previous warping combination to find the underlying source points responsible for these misalignments in " + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_1" + }, + { + "bbox": [ + 304, + 316, + 545, + 376 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 347, + 379, + 545, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 379, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 347, + 379, + 545, + 400 + ], + "type": "interline_equation", + "content": "D _ {0} = \\overrightarrow {\\mathcal {W}} \\left(\\overleftarrow {\\mathcal {W}} \\left(D _ {0 \\rightarrow 1}, \\widetilde {F} _ {t \\rightarrow 1}\\right), \\widetilde {F} _ {t \\rightarrow 0}\\right) \\tag {5}", + "image_path": "1319becd8243d474f4ed598fe051f35f2fcb2b62056bcd1daeb96c1114d6f9c5.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "content": "Difference map " + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "content": " illustrates the extent to which each point in " + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "content": " leads to the misalignment in " + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_1" + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "content": ". To address this, it is essential to prioritize the regions with higher values in " + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "content": ". These regions indicate the points that exacerbate significant misalignment. Difference map " + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "inline_equation", + "content": "D_1" + }, + { + "bbox": [ + 304, + 406, + 545, + 478 + ], + "type": "text", + "content": " can be produced symmetrically." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 484, + 443, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 484, + 443, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 484, + 443, + 498 + ], + "type": "text", + "content": "3.3. Sparse Global Matching" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": "To emphasize the region with higher values in " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": " we can select the top- " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": " points out of " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": " and do global matching for those points to provide more accurate matching flow " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "f_{0\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "f_{1\\rightarrow 0}" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": ", for preparing the flow compensation " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 304, + 502, + 545, + 563 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": "Sparse global matching allows the selected points in " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": " to have a global receptive field on " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": ". We adopt the pretrained global feature extractor from GMFlow [34] to generate discriminative global features " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "A_0^i, A_1^i \\in \\mathbb{R}^{\\left(\\frac{H}{2^i}, \\frac{W}{2^i}\\right) \\times C}" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": " is the number of feature channels. We construct a sparse feature map " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "a_0^i \\in \\mathbb{R}^{K \\times C}" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": " according to top-" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": " indices selected from " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": ". The corresponding area of " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "A_0^i, A_1^i" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": " should have higher similarity, and the same intuition also applies to " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "a_0^i" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "A_1^i" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": ". Therefore, we can construct a similarity matrix " + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "inline_equation", + "content": "S_{0 \\to 1} \\in K \\times \\left(\\frac{H}{2^i} \\cdot \\frac{W}{2^i}\\right)" + }, + { + "bbox": [ + 304, + 563, + 545, + 685 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 366, + 685, + 545, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 685, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 366, + 685, + 545, + 712 + ], + "type": "interline_equation", + "content": "S _ {0 \\rightarrow 1} = S o f t m a x \\left(\\frac {a _ {0} ^ {i} A _ {1} ^ {i}}{\\sqrt {C}}\\right) \\tag {6}", + "image_path": "33d42efdd3552540d0b5dd38424b97a6be87d0f0b698de2f94b8594b76fd696e.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19128" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": "Then we create a coordinate map " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "B \\in \\mathbb{R}^{\\left(\\frac{H}{2^i} \\cdot \\frac{W}{2^i}\\right) \\times 2}" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": ". Using top-" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " indices selected from " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": ", we extract the corresponding points from the coordinate map " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " to form a sparse coordinate map " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "b_0 \\in \\mathbb{R}^{K \\times 2}" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": ". We use the product between similarity matrix " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "S_{0 \\to 1}" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "b_0" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " to represent the estimated position in " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "I_1" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " for selected " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " points. Therefore, the subtraction between the previous product " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "S_{0 \\to 1}b_0" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "b_0" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": " can represent the flow for those points, namely " + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "inline_equation", + "content": "f_{0 \\to 1}" + }, + { + "bbox": [ + 46, + 70, + 289, + 170 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 121, + 178, + 287, + 194 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 178, + 287, + 194 + ], + "spans": [ + { + "bbox": [ + 121, + 178, + 287, + 194 + ], + "type": "interline_equation", + "content": "\\widetilde {f} _ {0 \\rightarrow 1} = S _ {0 \\rightarrow 1} b _ {0} - b _ {0} \\tag {7}", + "image_path": "97bdd2c65e3beafe67dbdcec854a846a4029429e5f9ad1093aceaa85baab205c.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": "Thus, " + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "inline_equation", + "content": "\\widetilde{f}_{0\\rightarrow 1}" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": " is obtained in a global matching manner, making it more capable of capturing large motions. Finally, we reuse the top-" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": " indices from " + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": " to fill " + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "inline_equation", + "content": "\\widetilde{f}_{0\\rightarrow 1} \\in \\mathbb{R}^{K\\times 2}" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "inline_equation", + "content": "f_{0\\rightarrow 1} \\in \\mathbb{R}^{\\frac{H}{2^i} \\times \\frac{W}{2^i} \\times 2}" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": " with zero. " + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "inline_equation", + "content": "f_{1\\rightarrow 0}" + }, + { + "bbox": [ + 47, + 204, + 287, + 268 + ], + "type": "text", + "content": " can be obtained symmetrically." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 275, + 133, + 288 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 133, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 133, + 288 + ], + "type": "text", + "content": "3.4. Flow Shifting" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": "The goal of our sparse global matching branch is to acquire sparse flow compensation " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "f_{t\\to 0}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\underline{f}_{t\\to 1}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": " to improve the estimated intermediate flows, " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\to 0}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "F_{t\\to 1}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": ", with large motion capturing ability. Next, we shift " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "f_{0\\to 1}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "f_{1\\to 0}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "f_{t\\to 1}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "inline_equation", + "content": "f_{t\\to 0}" + }, + { + "bbox": [ + 47, + 293, + 287, + 364 + ], + "type": "text", + "content": " by flow shifting, which can help mitigate the coordinate system mismatch." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": "We intercept a " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "(1 - t)" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " proportion of " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "f_{0\\rightarrow 1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " and shift this " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "(1 - t)" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " proportion along the remaining " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": " proportion of the flow " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "f_{0\\rightarrow 1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": ". Through this shifting operation, we can obtain " + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 47, + 365, + 287, + 425 + ], + "type": "text", + "content": ", and the shifting operation is performed by forward warping:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 98, + 427, + 287, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 427, + 287, + 444 + ], + "spans": [ + { + "bbox": [ + 98, + 427, + 287, + 444 + ], + "type": "interline_equation", + "content": "f _ {t \\rightarrow 1} = \\overrightarrow {\\mathcal {W}} ((1 - t) f _ {0 \\rightarrow 1}, t f _ {0 \\rightarrow 1}) \\tag {8}", + "image_path": "cf106c6e2de1180aac48f028d48cddd62b7873cf5e7e937307a82821d40134f8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 100, + 446, + 287, + 461 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 446, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 100, + 446, + 287, + 461 + ], + "type": "interline_equation", + "content": "f _ {t \\rightarrow 0} = \\overrightarrow {\\mathcal {W}} (t f _ {1 \\rightarrow 0}, (1 - t) f _ {1 \\rightarrow 0}) \\tag {9}", + "image_path": "18e7f8920f439d0659a3c6f3cbe569400048a62e4587499b60eb9804b397e2b5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "content": "Note that " + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "inline_equation", + "content": "f_{t \\to 1}" + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "content": " is flow shifted by " + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "inline_equation", + "content": "f_{0 \\to 1}" + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "inline_equation", + "content": "f_{t \\to 0}" + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "content": " is flow shifted by " + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "inline_equation", + "content": "f_{1 \\to 0}" + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "content": ", we also list the " + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "inline_equation", + "content": "f_{t \\to 0}" + }, + { + "bbox": [ + 46, + 471, + 287, + 506 + ], + "type": "text", + "content": " in Equation (9) for clarity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 507, + 287, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 554 + ], + "type": "text", + "content": "After the forward warping process, the number of sparsely chosen points will potentially change, and we will again choose the top-" + }, + { + "bbox": [ + 46, + 507, + 287, + 554 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 507, + 287, + 554 + ], + "type": "text", + "content": " points with the least occlusion possibility." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": "Instead of using the estimated target frame " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_t" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " and input frames " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "I_0, I_1" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " to perform global matching and obtain intermediate flow compensation " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "f_{t\\to 0}" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": ", we use global matching between " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "I_0, I_1" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " only and perform flow shift. The reason is that " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\widetilde{I}_t" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " synthesized by " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\to 0}" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 554, + 287, + 651 + ], + "type": "text", + "content": " is not reliable. Since we aim to minimize accumulated propagation errors, we endeavor to minimize the usage of intermediate results wherever possible." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 658, + 156, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 156, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 156, + 670 + ], + "type": "text", + "content": "3.5. Flow Merge Block" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "content": "If we directly replace " + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\to 0}" + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "content": " with the flow compensation " + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\to 0}" + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\to 1}" + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "content": ", the resulting flow may lack smoothness. In addition, the flow compensation " + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\to 0}" + }, + { + "bbox": [ + 46, + 676, + 287, + 714 + ], + "type": "text", + "content": " and" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "f_{t\\to 1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " can also make mistakes. Therefore, we designed a flow merge block " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " to adaptively merge " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " as well as " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 305, + 72, + 545, + 109 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 373, + 118, + 545, + 134 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 118, + 545, + 134 + ], + "spans": [ + { + "bbox": [ + 373, + 118, + 545, + 134 + ], + "type": "interline_equation", + "content": "\\widehat {F} _ {t \\rightarrow 0} = \\mathcal {M} \\left(\\widetilde {F} _ {t \\rightarrow 0}, f _ {t \\rightarrow 0}\\right) \\tag {10}", + "image_path": "21f2d7f66e40ce9be3bb66bc34e9e826adae91cfcaa3be2907ed078d7abe963c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 374, + 137, + 545, + 152 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 374, + 137, + 545, + 152 + ], + "spans": [ + { + "bbox": [ + 374, + 137, + 545, + 152 + ], + "type": "interline_equation", + "content": "\\widehat {F} _ {t \\rightarrow 1} = \\mathcal {M} \\left(\\widetilde {F} _ {t \\rightarrow 1}, f _ {t \\rightarrow 1}\\right) \\tag {11}", + "image_path": "9823d69636ceb1de53649473c892758222f3e1970a1bcf21d272f611dea30587.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": "Inspired by the convex sampling in RAFT [32], we take the " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "\\widehat{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " at each pixel to be the convex combination of " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "R\\times R" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " neighbors of " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "R\\times R" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " neighbors of " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " is the neighborhood range. We use two convolutional layers to predict a " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "2\\times R^2\\times \\frac{H}{2^i}\\times \\frac{W}{2^i}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " weight assignment, and apply softmax of the " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "2\\times R^2" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " neighborhood to obtain masks " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "[W_{main},W_{sgm}]" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "W_{main},W_{sgm}\\in \\mathbb{R}^{R^2\\times \\frac{H}{2^i}\\times \\frac{W}{2^i}}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "W_{main}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " stands for the weight for the local feature branch flow estimations, and " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "W_{sgm}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " stands for the weight for sparse global matching block flow compensation. Finally, the flow merge block outputs the " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "\\widehat{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": ", obtained by taking weighted sum over the " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 305, + 165, + 546, + 324 + ], + "type": "text", + "content": " neighborhood." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 339, + 478, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 339, + 478, + 354 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 478, + 354 + ], + "type": "text", + "content": "4. Large Motion VFI Benchmark" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 433 + ], + "type": "text", + "content": "To better illustrate our algorithm's effectiveness in handling large motions, we analyzed several widely used large motion datasets, namely, SNU-FILM extreme and hard [4], Xiph [22], and X-Test [29]. We utilized RAFT [32] to estimate optical flow between input frames as evidence, allowing for a detailed assessment of motion magnitudes." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "content": "According to Figure 3a, SNU-FILM and Xiph's mean motion magnitude is much lower than X-Test's. For example, we can see that about " + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "content": " of SNU-FILM test cases' mean motion magnitude is below 15, while Xiph has about " + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 304, + 434, + 545, + 494 + ], + "type": "text", + "content": " test cases below 30." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "text", + "content": "In addition, we also refer to the criterion in [1] for assessing motion sufficiency, requiring at least " + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "text", + "content": " of each pixel's flow to have a magnitude of at least 8 pixels within a " + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "inline_equation", + "content": "270 \\times 270" + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "text", + "content": " resolution. We adjusted this criterion by lowering the percentage threshold to " + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "text", + "content": " while simultaneously increasing the required magnitude to account for the larger resolution of our input frames. This adjusted criterion, representing the minimum magnitude of the top " + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 496, + 545, + 616 + ], + "type": "text", + "content": " pixel flows, forms the basis for our proportion ranking of the benchmark datasets in Figure 3b." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "As depicted in the cumulative distribution chart Figure 3b, we found that over " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " of X-Test have at least " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " of each pixel's flow with a magnitude of at least 150 pixels. In contrast, Xiph [22] and SNU-FILM [4] contain fewer large motion pixels. Consequently, we focused our evaluation on the most challenging half of these benchmarks to assess our algorithm's performance improvements in handling genuinely large motion data, with details in Section 5.2." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "19129" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 57, + 116, + 537, + 270 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation (PSNR/SSIM) among different challenging benchmarks (see Section 4). The best results and the second best results in each column are marked in red and blue respectively. Ours-1/N Points means that we sparsely select 1/N points of the initial intermediate flows estimation to perform global matching by the evidence provided by difference map " + }, + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "inline_equation", + "content": "D_1" + }, + { + "bbox": [ + 46, + 70, + 547, + 115 + ], + "type": "text", + "content": ". \"OOM\" denotes the out-of-memory issue when evaluating on an NVIDIA V100-32G GPU." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 57, + 116, + 537, + 270 + ], + "lines": [ + { + "bbox": [ + 57, + 116, + 537, + 270 + ], + "spans": [ + { + "bbox": [ + 57, + 116, + 537, + 270 + ], + "type": "table", + "html": "
X-Test-LSNU-FILM-LXiph-L
2K4Khardextreme2K4K
XVFI [29]29.82/0.895129.02/0.886627.58/0.909522.99/0.826029.17/0.844928.09/0.7889
FILM [27]30.08/0.8941OOM28.35/0.915623.06/0.824729.89/0.853327.11/0.7699
BiFormer [26]30.32/0.906730.11/0.907028.18/0.915423.55/0.838329.61/0.854128.89/0.8133
RIFE [9]29.87/0.880528.98/0.875628.19/0.917222.84/0.823030.18/0.863328.07/0.7982
EMA-VFI-small [37]29.51/0.877528.60/0.873328.57/0.918923.18/0.829230.54/0.871828.40/0.8109
Ours-local-branch30.39/0.894629.25/0.886128.73/0.920723.19/0.830130.89/0.874528.59/0.8115
Ours-1/8-Points30.83/0.902229.73/0.892828.82/0.920823.54/0.835530.88/0.874928.90/0.8151
Ours-1/4-Points30.88/0.904329.78/0.894828.86/0.921223.58/0.836830.89/0.875129.15/0.8169
Ours-1/2-Points30.99/0.907229.91/0.897228.88/0.921623.62/0.837730.93/0.875529.25/0.8180
", + "image_path": "c75b4fe70168273d82aa6e9fb97c917da343e0e27dbb4f24eef5f413c1c88a21.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 289, + 128, + 303 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 128, + 303 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 128, + 303 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 309, + 176, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 309, + 176, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 309, + 176, + 322 + ], + "type": "text", + "content": "5.1. Implementation Detail" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "type": "text", + "content": "Training Datasets. We use two training datasets, Vimeo90K [36] for pretraining on small-to-medium motion and X4K1000FPS (X-Train) [29] for finetuning on large motion. Vimeo90K contains 51,312 triplets with a resolution of " + }, + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "type": "inline_equation", + "content": "448 \\times 256" + }, + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "type": "text", + "content": " for training. It has an average motion magnitude between 1 to 8 pixels [36]. X4K1000FPS (X-Train) contains 4,408 clips with a resolution of " + }, + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "type": "inline_equation", + "content": "768 \\times 768" + }, + { + "bbox": [ + 46, + 328, + 288, + 424 + ], + "type": "text", + "content": ", each clip has 65 consecutive frames." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": "Local Feature Branch Training. We first train our model framework without the sparse global matching branch on Vimeo90K. We crop each training instance to 256x256 patches and perform random flip, time reversal, and random rotation augmentation, following [9, 37]. The training batch size is set to 32. We use AdamW as our optimizer with " + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999" + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": " and weight decay " + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "inline_equation", + "content": "1e^{-4}" + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": ". After 2,000 warmup steps, we gradually increase the learning rate to " + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "inline_equation", + "content": "2e^{-4}" + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": ", then use cosine annealing for 480k steps (300 epochs) to reduce the learning rate from " + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "inline_equation", + "content": "2e^{-4}" + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "inline_equation", + "content": "2e^{-5}" + }, + { + "bbox": [ + 46, + 425, + 287, + 569 + ], + "type": "text", + "content": ". We follow the training loss design of [9, 37] for both training and finetuning, which is included in Appendix B." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Sparse Global Branch Finetuning. We load our pretrained framework, and a global feature extractor from GM-Flow [34], operating on " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "i = 3" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " in Equation (6). Then we integrate our sparse global matching branch into the framework, setting the sparsity ratio, i.e. " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "1/8" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "1/4" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "1/2" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ", and finetuning the sparse global matching block on X-Train. When fine-tuning, we freeze the pretrained framework and the global feature extractor. We crop " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " patches from the original training image, and random resize the input images with " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " probability to remain the " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " size, " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " probability to downscale to " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " size and " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " probability to " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " size. We apply random flipping" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 289, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 363 + ], + "type": "text", + "content": "augmentation, following [29]. The batch size, learning rate and optimizer are the same as our local feature branch, except that warmup steps are set to 1k steps, and the total steps are set to 13.7k (100 epochs). The parameter freezing and random rescaling are for preserving the model's ability to capture small motion details to the greatest extent possible." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 370, + 387, + 382 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 387, + 382 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 387, + 382 + ], + "type": "text", + "content": "5.2. Test Dataset" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 389, + 545, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 460 + ], + "type": "text", + "content": "The proposed algorithm is designed for capturing large motions. Therefore, we test our model's performance on the most challenging subset of the commonly used large motion benchmark, described in Section 4. We used PSNR (Peak Signal-to-Noise Ratio) and SSIM (Structural Similarity Index) as evaluation metric." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "text", + "content": "X4K1000FPS (X-Test) [29] is a 4K resolution benchmark, with 1000fps high frame rate. X-Test contains 15 clips of 33 successive 4K frames extracted from videos with 1000fps. We have selected X-Test, specifically with the largest temporal gap, naming X-Test-L, as our primary benchmark for evaluating large motion scenarios. We choose the " + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "inline_equation", + "content": "0_{th}" + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "inline_equation", + "content": "32_{nd}" + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "text", + "content": " frames as input and evaluate the quality of the synthesized " + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "inline_equation", + "content": "16_{th}" + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "text", + "content": " output frame. Our testing procedure follows [8] to provide both 4K and downsampled 2K resolution results. SNU-FILM [4] is a widely-used VFI benchmark, with " + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "inline_equation", + "content": "1280 \\times 720" + }, + { + "bbox": [ + 304, + 460, + 545, + 700 + ], + "type": "text", + "content": " resolution. It has four different difficulty settings according to the temporal gap between two input frames, each with 310 triplets for evaluation. The larger the temporal gap, the more challenging this benchmark becomes. We test our model on the most challenging half of the SNU-FILM hard and extreme, naming SNU-FILM-L, with 155 triplets each. In the meantime, we also provide the performance on the 'easy' and 'medium' settings on the whole dataset in Table 2 to show our model's capability in handling small-to-medium motions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Xiph [22] is a 4K dataset with 8 scenes, each with 100 con" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19130" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 169 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 169 + ], + "type": "text", + "content": "secutive frames, extracted from 60fps videos. While it is often denoted as a benchmark for evaluating large motion, it does not match the level of difficulty exhibited by the X-Test. Therefore, we build this benchmark by doubling the input temporal gap and keeping the most challenging half of the dataset, naming Xiph-L, resulting in 192 test instances. By downsampling and center-cropping, we obtain 'Xiph-L-2K' and 'Xiph-L-4K' results, following [23]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 177, + 239, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 177, + 239, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 177, + 239, + 190 + ], + "type": "text", + "content": "5.3. Comparison with Previous Methods" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 197, + 287, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 287, + 292 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 287, + 292 + ], + "type": "text", + "content": "To fully inspect our model's capacity on large motion, we evaluate our model on the aforementioned large motion datasets benchmarks and give our analysis compared results with recent VFI approaches, including ones designed for large motion, such as XVFI [29], FILM [27], BiFormer [26], and ones that performed well on commonly used datasets but not designed for large motion, namely, RIFE [9], EMA-VFI [37]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "text", + "content": "As shown in Table 1, the performance of our local feature branch, without finetuned on X-Train, has already surpassed most methods. We attribute this to the capacity of CNN and Transformer hybrid framework and high feature resolution " + }, + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "inline_equation", + "content": "(H / 8\\times W / 8)" + }, + { + "bbox": [ + 46, + 293, + 287, + 376 + ], + "type": "text", + "content": ". But without the sparse global matching block, our results are not comparable to BiFormer in SNUFILM-L extreme, Xiph-L-4K and XVFI in X-Test-L-4K." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "type": "text", + "content": "After we incorporate the sparse global matching branch and finetuned on X-Train, our performance on large motion benchmarks are boosted. When we only sparsely select 1/8 of the points in initial flow estimation by the guidance of difference map " + }, + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "type": "inline_equation", + "content": "D_1" + }, + { + "bbox": [ + 46, + 377, + 288, + 484 + ], + "type": "text", + "content": ", our performance improved 0.44dB on X-Test-L-2K and 0.48dB on X-Test-L-4K in terms of PSNR. With more points introduced to be compensated, the performance can be potentially improved by 0.6dB and 0.66dB on X-Test-L-2K and X-Test-L-4K respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 581 + ], + "type": "text", + "content": "Small-to-medium Motion Benchmark Performance. From the data presented in Table 2, we observe that our results remain consistent with those in small-to-medium scenarios, and they are comparable to a SOTA algorithm, VFI-Former [21], on these benchmarks. This suggests that our local feature branch already achieves satisfactory results, and introducing our sparse global matching branch has a limited negative impact on the overall performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "For qualitative results, we also give the visual comparisons between our method and previous VFI methods in Figure 4. Four variants of our method lie inside the red frame. For fair comparison, 'Local Branch (ft.)' is also finetuned on X-Test, with Flow Refine Block in Figure 2, but without sparse global matching modules. In blue frames, our global compensation branch can fix the unmatched areas with large motion, yielding better visual effect than the 'Local Branch (ft.)' model. And with more points added into the sparse global matching block, the visual effect becomes better. When compared to other methods, our model" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 312, + 102, + 541, + 220 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 545, + 93 + ], + "type": "text", + "content": "Table 2. Performance on small-to-medium benchmarks, SNU-FILM easy and medium." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 312, + 102, + 541, + 220 + ], + "lines": [ + { + "bbox": [ + 312, + 102, + 541, + 220 + ], + "spans": [ + { + "bbox": [ + 312, + 102, + 541, + 220 + ], + "type": "table", + "html": "
SNU-FILM
easymedium
PSNRSSIMPSNRSSIM
VFIFormer [21]40.130.990736.090.9799
Local Branch (ft.)40.150.990736.070.9795
1/8 Points40.150.990736.070.9795
1/4 Points40.140.990636.050.9795
1/2 Points40.150.990736.050.9795
", + "image_path": "ffcbea99a5ae57e58a3bc58d9ef025bdfcae87660768a953cb353b0f31b4f7f5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 255, + 548, + 358 + ], + "blocks": [ + { + "bbox": [ + 306, + 224, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 306, + 224, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 545, + 247 + ], + "type": "text", + "content": "Table 3. Comparison of finetuning with different settings. Local Branch (ft.) contains no global matching." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 255, + 548, + 358 + ], + "lines": [ + { + "bbox": [ + 307, + 255, + 548, + 358 + ], + "spans": [ + { + "bbox": [ + 307, + 255, + 548, + 358 + ], + "type": "table", + "html": "
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)30.580.897729.440.8895
1/8 Points30.830.902229.730.8928
1/4 Points30.880.904329.780.8948
1/2 Points30.990.907229.910.8972
Full Global Matching31.030.907429.950.8974
", + "image_path": "55def036f866856d470d3b6420e75eddc2905599bc518959eeb504901dd438bd.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 377, + 538, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 377, + 538, + 389 + ], + "spans": [ + { + "bbox": [ + 306, + 377, + 538, + 389 + ], + "type": "text", + "content": "can preserve both the small details and large motion well." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 396, + 400, + 409 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 400, + 409 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 400, + 409 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 415, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 450 + ], + "type": "text", + "content": "In this section, we ablate the effect of our key component, sparse global matching pipeline fintuning, difference map generation in Section 3.2, and merge block in Section 3.5." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 450, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 545, + 617 + ], + "type": "text", + "content": "Sparse Global Matching. To demonstrate that the primary source of our performance improvements comes from the sparse global matching branch rather than the finetuning process alone, we constructed a Local Branch (ft.) model, incorporating the learnable Flow Refine module (as depicted in Figure 2), to finetune on the X-Train dataset. Our results indicate that while fine-tuning on a large motion dataset can enhance model performance in challenging scenarios with large motion, global matching consistently outperforms it. Furthermore, we present a comprehensive overview of the global matching performance in Table 3. It is evident that as more points are selected, performance reaches saturation, because not every point needs a global receptive field." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Difference Map. Our sparse global matching algorithm is guided by difference map, " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "D_0" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "D_{1}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": ", which can help us identify flaws in the initial estimation of intermediate flows. We then select the top-" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " defective points to correct them. To evaluate the effectiveness of the difference map guidance, we conducted a random sampling strategy to replace the map generation and top-" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " sampling. 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Visual comparison with different methods, instances selected from X-Test-L [29]. We provide the optical flow magnitude on the left, measured by RAFT [32]. Four sparsity setting of our methods lies in the red frame. Blue frames place a greater emphasis on demonstrating large motion, while green frames is more inclined to demonstrate the effect on local details. 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Comparison on random sampling " + }, + { + "bbox": [ + 47, + 322, + 287, + 346 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 322, + 287, + 346 + ], + "type": "text", + "content": " points between generating difference map and sampling top- " + }, + { + "bbox": [ + 47, + 322, + 287, + 346 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 322, + 287, + 346 + ], + "type": "text", + "content": " points." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 348, + 282, + 483 + ], + "lines": [ + { + "bbox": [ + 53, + 348, + 282, + 483 + ], + "spans": [ + { + "bbox": [ + 53, + 348, + 282, + 483 + ], + "type": "table", + "html": "
X-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Ours-1/2-top-k30.990.907229.910.8972
Ours-1/4-top-k30.880.904329.780.8948
Ours-1/8-top-k30.830.902229.730.8928
Local Branch (ft.)30.580.897729.440.8895
Ours-1/2-random30.890.905729.860.8967
Ours-1/4-random30.670.901429.550.8923
Ours-1/8-random30.550.899229.470.8893
", + "image_path": "77e9116def7cfdd497495332fcf21305db5fb93a9ca281a877f96bd0b52cce22.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "table_body" + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "type": "text", + "content": "correction is not as effective as choosing the top-" + }, + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "type": "text", + "content": " defective points from the difference map. When dealing with sparse points, random sampling can even decrease accuracy by replacing correct flow with an inaccurate flow compensation. As the number of points increases, this gap narrows. Nevertheless, it is still evident that selecting top-" + }, + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 508, + 287, + 592 + ], + "type": "text", + "content": " on the difference map outperforms random sampling." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "Flow Merge. To show the effectiveness of our flow merge block, we remove the merge block and directly apply the sparse flow compensation patches " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\widetilde{F}_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ", respectively. From Table 5, we can see that after removing the merge block, the obtained results still exhibit slightly higher performance than the fine-tuned local branch model, indicating the effectiveness of our flow compensation patches " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 0}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "f_{t\\rightarrow 1}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": ". However, it is noteworthy that as we involve more points in the flow compensation, the improvement in results becomes negligible and even falls" + } + ] + } + ], + "index": 25 + }, + { + "type": "table", + "bbox": [ + 306, + 336, + 545, + 437 + ], + "blocks": [ + { + "bbox": [ + 314, + 323, + 537, + 334 + ], + "lines": [ + { + "bbox": [ + 314, + 323, + 537, + 334 + ], + "spans": [ + { + "bbox": [ + 314, + 323, + 537, + 334 + ], + "type": "text", + "content": "Table 5. Results of our structure with or w/o merge block." + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 336, + 545, + 437 + ], + "lines": [ + { + "bbox": [ + 306, + 336, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 336, + 545, + 437 + ], + "type": "table", + "html": "
Merge BlockX-Test-L-2KX-Test-L-4K
PSNRSSIMPSNRSSIM
Local Branch (ft.)×30.580.897729.440.8895
Local Branch (ft.)√30.550.897129.440.8889
1/8 Points√30.830.902229.730.8995
1/2 Points×30.750.902529.690.8936
1/4 Points×30.770.901429.700.8924
1/8 Points×30.750.899229.640.8910
", + "image_path": "dfdad782dd25a01979931e448699fc8642425d9be6f62bc71dea103cf97ee42c.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "table_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 448, + 546, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 448, + 546, + 472 + ], + "spans": [ + { + "bbox": [ + 305, + 448, + 546, + 472 + ], + "type": "text", + "content": "short of only using 1/8 points, highlighting the necessity of our merge block." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 475, + 379, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 379, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 379, + 487 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 496, + 546, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 546, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 546, + 651 + ], + "type": "text", + "content": "In this paper we have presented a sparse global matching algorithm designed to effectively address the challenges posed by large motion in video frame interpolation. We establish a framework that extracts local features for intermediate flow estimation. Then we target the flaws in the initial flow estimation and perform sparse global matching to produce sparse flow compensation across a global receptive field. By adaptively merging initial intermediate flow estimation with sparse global matching flow compensation, we achieve state-of-the-art performance on the most challenging subset of commonly used large motion datasets while keeping the performance on small-to-medium motion benchmark." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by the National Key R&D Program of China (No. 2022ZD0160900), the National Natural Science Foundation of China (No. 62076119, No. 61921006), and Collaborative Innovation Center of Novel Software Technology and Industrialization." + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "19132" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Tim Brooks and Jonathan T Barron. 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In International Conference on Learning Representations, 2021. 3" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "19134" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_content_list.json b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..a90147075eaa5ebf1ff8d0b302772a5ea52b3749 --- /dev/null +++ b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_content_list.json @@ -0,0 +1,1489 @@ +[ + { + "type": "text", + "text": "Sparse Semi-DETR: Sparse Learnable Queries for Semi-Supervised Object Detection", + "text_level": 1, + "bbox": [ + 228, + 130, + 743, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tahira Shehzadi $^{1,2,3}$ , Khurram Azeem Hashmi $^{1,2,3}$ , Didier Stricker $^{1,2,3}$ , Muhammad Zeshan Afzal $^{1,2,3}$ , $^{1}$ DFKI, $^{2}$ RPTU Kaiserslautern-Landau, $^{3}$ MindGarage-RPTU", + "bbox": [ + 88, + 202, + 880, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1b364a3d1886a39ededbdd60a4ea4ef356f66cba671910f0a481b6fdf703a8d7.jpg", + "image_caption": [ + "(a) Semi-DETR" + ], + "image_footnote": [], + "bbox": [ + 76, + 273, + 607, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0476da3b7ee057933a49cf2f953fe71130ef9848e40dffb45ae3a7058232f753.jpg", + "image_caption": [ + "(c) Comparison of SSOD Methods", + "Figure 1. (a)-(b) Comparative Overview of SSOD advancements: Sparse Semi-DETR's major improvement lies in its Query Refinement Module and Reliable Pseudo-label Filtering Module, significantly enhancing detection of small or obscured objects and reliability in complex scenarios, surpassing all other methods as shown in the graph in (c)." + ], + "image_footnote": [], + "bbox": [ + 611, + 271, + 890, + 434 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 520, + 313, + 535 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we address the limitations of the DETR-based semi-supervised object detection (SSOD) framework, particularly focusing on the challenges posed by the quality of object queries. In DETR-based SSOD, the one-to-one assignment strategy provides inaccurate pseudo-labels, while the one-to-many assignments strategy leads to overlapping predictions. These issues compromise training efficiency and degrade model performance, especially in detecting small or occluded objects. We introduce Sparse Semi-DETR, a novel transformer-based, end-to-end semi-supervised object detection solution to overcome these challenges. Sparse Semi-DETR incorporates a Query Refinement Module to enhance the quality of object queries, significantly improving detection capabilities for small and partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy and consistency. On the MS-COCO and Pascal VOC object detection benchmarks, Sparse Semi-DETR achieves a significant improvement over current state-of-the-art methods that highlight Sparse Semi-DETR's effectiveness in semi-supervised object detection, particularly in challenging scenarios involving small or par", + "bbox": [ + 75, + 568, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tially obscured objects.", + "bbox": [ + 500, + 521, + 655, + 537 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 570, + 632, + 585 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Semi-Supervised Object Detection (SSOD) aims to improve the effectiveness of fully supervised object detection through the integration of abundant unlabeled data [3, 12, 15, 19, 28, 39, 49-52, 58]. It has applications in diverse fields, ranging from autonomous vehicles [14, 20] to healthcare [31, 44], where obtaining extensive labeled datasets is often impractical or cost-prohibitive [1].", + "bbox": [ + 496, + 597, + 893, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several SSOD methods [3, 12, 15, 19, 28, 39, 49-52, 58] have been proposed. Two prevalent approaches in this domain are pseudo-labeling [27, 30, 39, 45, 50-52, 58] and consistency-based regularization [3, 12, 15, 19, 28, 49]. STAC [39] introduced a simple multi-stage SSOD training method with pseudo-labeling and consistency training, later simplified by a Teacher-Student framework for generating pseudo-labels [27]. Based on this framework, considerable research efforts have been directed towards enhancing the quality of pseudo-labels [51, 58]. These traditional SSOD methods are built upon conventional detectors like one-stage [33, 42] and two-stage [9, 35], which involve various manually designed components such as an", + "bbox": [ + 496, + 703, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5840", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "chor boxes and non-maximum suppression (NMS). Employing object detection methods in SSOD poses several potential challenges that must be carefully dealt with to obtain reasonable performance. These factors include overfitting of the labeled data [37], pseudo-label noise [10], bias induced through label imbalance [17, 32], and poor detection performance on small objects [56]. Recently, DETR-based [2, 16, 18, 25, 38, 55, 59] SSOD methods [46, 56] remove the need for traditional components like NMS.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Even though DETR-based SSOD [46, 56] has progressed remarkably, state-of-the-art methods possess some limitations. (1) DETR-based SSOD methods perform poorly in the detection of small objects, as shown in Figure 4. This is because these methods don't use multi-scale features [36] like Feature Pyramid Networks (FPN) [22], which play an important role in identifying smaller objects as in CNN-based SSOD methods [3, 12, 15, 19, 28, 49, 51, 52, 58]. Although recent advancements in DETR-based object detection [2, 16, 18, 25, 38, 55, 59] have improved the detection of small objects, their SSOD adaptation is still unable to cater this challenge effectively [56]. (2) SSOD approaches [51, 52, 56, 58] rely on handcrafted post-processing methods such as NMS [35]. This problem specifically appears in DETR-based SSOD when we use a large number of object queries and the one-to-many assignment strategy [56]. In DETR-based SSOD methods, this problem is partially solved using the one-to-one or hybrid (combination of one-to-one and one-to-many) assignment strategy. However, the hybrid assignment strategy is preferred because the one-to-one assignment strategy produces inaccurate pseudo-labels [46], thus resulting in inefficient learning. Although the number of duplicate bounding boxes is less in the hybrid strategy [56], the amount is high enough to impact object detection performance adversely, as depicted in Figure 5. (3) The pseudolabel generation produces both high and low-quality labels. The DETR-based SSOD methods lack an effective refinement strategy for one-to-many assignments, which is crucial for filtering out low-quality proposals.", + "bbox": [ + 75, + 231, + 472, + 670 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above mentioned issues, we propose enhancing the state-of-the-art DETR-based SSOD approach, namely 'Sparse Semi-DETR', presented in Figure 1 (b). Our approach involves expanding its architecture by integrating a couple of novel modules designed to mitigate the identified shortcomings. The key module among these is the Query-Refinement module, as depicted in Figure 2 and explained in Figure 3. This module significantly improves the quality of the queries and reduces their numbers. The proposed module uses the low-level features from the backbone and high-level features extracted directly from weakly augmented images using ROI alignment [13]. Fusing these features results in overcoming the first shortcoming, i.e., detecting small and obscured objects, as shown in Figure 4. The attention mechanism drives the aggregation of the features,", + "bbox": [ + 75, + 674, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "resulting in refined, high-quality features to carry forward. To ensure the quality of the query features, the attention mechanism is accompanied by a query-matching strategy for filtering irrelevant queries. Thus, the Query Refinement Module not only improves the quality of the queries but also reduces their numbers, giving rise to efficient processing. This module results in significantly fewer overlapping proposals, improving the performance overall, thereby solving the second limitation. Besides, we introduce a Reliable Pseudo-Label Filtering Module, as illustrated in Figure 2, inspired by Hybrid-DETR [16] to address the third limitation. Employing this module significantly reduces the low-quality pseudo-labels. Therefore, it further reduces the amount of duplicate predictions that may still occur after the second stage of the hybrid assignment strategy. Our approach provides better results than previous SSOD methods, as shown in Figure 1 (c).", + "bbox": [ + 496, + 90, + 893, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The key contributions of this work can be outlined as follows:", + "bbox": [ + 498, + 349, + 893, + 378 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We present Sparse Semi-DETR, a novel approach in semi-supervised object detection, introducing two novel contributions. To our knowledge, we are the first to examine and propose query refinement and low-quality proposal filtering for the one-to-many query assignment strategy.", + "2. We introduce a novel query refinement module designed to improve object query features, particularly in complex detection scenarios such as identifying small or partially obscured objects. This enhancement not only boosts performance but also aids in learning semantic feature invariance among object queries.", + "3. We introduce a Reliable Pseudo-Label Filtering Module specifically designed to reduce the effect of noisy pseudolabels. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths, enhancing the consistency of the learning process.", + "4. Sparse Semi-DETR outperforms current state-of-the-art methods on MS-COCO and Pascal VOC benchmarks. With only $10\\%$ labeled data from MS-COCO using ResNet-50 backbone, it achieves a 44.3 mAP, exceeding prior baselines by 0.8 mAP. Additionally, when trained on the complete COCO set with extra unlabeled data, it further improves, rising from 49.2 to 51.3 mAP." + ], + "bbox": [ + 500, + 380, + 893, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 758, + 640, + 776 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Object Detection", + "text_level": 1, + "bbox": [ + 500, + 785, + 666, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Object detection identifies and locates objects in images or videos. Deep learning-based object detection approaches are typically categorized into two primary groups: two-stage detectors [9, 35] and one-stage detectors [23, 26, 34, 42]. These methods depend on numerous heuristics, such as generating anchors and NMS. Recently, DEetection TRans", + "bbox": [ + 496, + 809, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5841", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "former (DETR) [2] considers object detection as a set prediction problem, using transformer [43] to adeptly transform sparse object candidates [40] into precise target objects. Our Sparse Semi-DETR detects small or partially obscured objects in the DETR-based SSOD setting. Notably, our framework is compatible with various DETR-based detectors [4, 5, 7, 8, 24, 29, 47, 48, 59], offering flexibility in integration.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Semi-Supervised Object Detection", + "text_level": 1, + "bbox": [ + 76, + 224, + 375, + 239 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Most research in SSOD employs detectors categorized into three types: one-stage, two-stage, and DETR-based systems. One-stage STAC [39], an early SSOD, introduced a simple training strategy combining pseudo-labeling and consistency training, later streamlined by a student-teacher framework for easier pseudo-label generation [27]. DSL [3] introduced novel techniques including Adaptive Filtering, Aggregated Teacher, and uncertainty-consistency-regularization for improved generalization. Dense Teacher [57] introduced Dense Pseudo-Labels (DPL) for richer information and a region selection method to reduce noise.", + "bbox": [ + 75, + 248, + 472, + 414 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Two-stage. Humble Teacher [41] uses soft labels and a teacher ensemble to boost pseudo-label reliability, matching other results. Instant-Teaching [58] creates pseudo annotations from weak augmentations, treating them as ground truth under strong augmentations with Mixup [54]. Unbiased Teacher [27] tackles class imbalance in pseudo-labeling with focal loss, focusing on underrepresented classes. Soft Teacher [51] minimizes incorrect foreground proposal classification by applying teacher-provided confidence scores to reduce classification loss. PseCo [19] enhances detector performance by combining pseudo-labeling with label and feature consistency methods, also using focal loss to address class imbalance.", + "bbox": [ + 75, + 416, + 472, + 611 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DETR-based. Omni-DETR [46] is designed for omnisupervised detection and adapts to SSOD with a basic pseudo-label filtering method. It employs the one-to-one assignment strategy proposed in DETR [2], and encounters challenges when dealing with inaccurate pseudo-bounding boxes produced by the teacher network. These inaccuracies result in reduced performance, highlighting its limitations. Semi-DETR [56] adopts a stage-wise strategy, employing a one-to-many matching strategy in the first stage and switching to a one-to-one matching strategy in the second stage. This approach provides NMS-free end-to-end detection benefits but reduces performance compared to a one-to-many assignment strategy. Moreover, Omni-DETR and Semi-DETR struggle to detect small or occluded objects. Our work introduces an advanced query refinement module that significantly refines object queries, enhancing training efficiency and performance and leading to the detection of small or densely packed objects in the DETR-based SSOD framework.", + "bbox": [ + 75, + 613, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 89, + 627, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In DETR-based SSOD, one-to-one assignment strategy, denoted by $\\hat{\\sigma}_{one2one}$ , is achieved by applying Hungarian algorithm between the predictions made by the student model and the pseudo-labels provided by the teacher model as follows:", + "bbox": [ + 498, + 116, + 893, + 178 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {o n e 2 o n e} = \\underset {\\sigma \\in \\xi_ {N}} {\\arg \\min } \\sum_ {j} ^ {N} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {y} _ {\\sigma (j)} ^ {s}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 552, + 191, + 893, + 234 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{\\mathrm{match}}\\left(\\hat{y}_j^t,\\hat{y}_{\\sigma (j)}^s\\right)$ is the matching cost between the pseudo-labels $\\hat{y}_j^t$ generated by the teacher network and the predictions of the student network with index $\\sigma (j)$ and $\\xi_{N}$ is the permutation of $N$ elements. Semi-DETR [56] addresses the issue of imprecise initial pseudo-labels by shifting from a one-to-one to a one-to-many assignment strategy, increasing the number of positive object queries to improve detection accuracy:", + "bbox": [ + 496, + 251, + 893, + 380 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {o n e 2 m a n y} = \\left\\{\\underset {\\sigma_ {j} \\in C _ {M} ^ {N}} {\\arg \\min } \\sum_ {k} ^ {M} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {y} _ {\\sigma_ {j} (k)} ^ {s}\\right) \\right\\} _ {j} ^ {| \\hat {y} ^ {t} |} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 393, + 892, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $C_N^M$ represents the combination of $M$ and $N$ , denoting that a subset of $M$ proposals is associated with each pseudo box $\\hat{y}_j^t$ . Semi-DETR initially adopts a one-to-many assignment to improve label quality, then shifts to one-to-one assignment for an NMS-free model. This approach adopts a one-to-many assignment strategy aimed at boosting performance, but it's less effective with small or occluded objects.", + "bbox": [ + 496, + 458, + 893, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Sparse Semi-DETR", + "text_level": 1, + "bbox": [ + 500, + 598, + 689, + 616 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In semi-supervised learning, a collection of labeled data denoted as $D_{l}$ , where $D_{l} = \\{x_{i}^{l},y_{i}^{l}\\}_{i = 1}^{N_{l}}$ is given, along with a set of unlabeled data represented as $D_{u}$ , where $D_{u} = \\{x_{i}^{u}\\}_{i = 1}^{N_{u}}$ . Here, $N_{l}$ and $N_{u}$ correspond to the number of labeled and unlabeled data. The annotations $y_{i}^{l}$ for the label data $x^{l}$ contain object labels and bounding box information. The pipeline of the Sparse Semi-DETR framework is depicted in Figure 2. It introduces a Query Refinement Module for processing query features to enhance semantic representation for complex detection scenarios, such as identifying small or partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy. For comparison purposes, we employ DINO [55] with a ResNet-50 backbone. This section gives a detailed overview of the modules of Sparse Semi-DETR. We explain briefly our semi-supervised approach in Appendix A1.1.", + "bbox": [ + 496, + 626, + 895, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5842", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/943cb47550f52d7b91751c4b5b0f63e437d3d12c5498de46c727e6797d5479a1.jpg", + "image_caption": [ + "Figure 2. An overview of the Sparse Semi-DETR framework. It contains two networks: the student network and the teacher network. Labeled data is used for student network training, employing a supervised loss. Unlabeled data is fed to the teacher network with weak augmentation and the student network with strong augmentation. The teacher network takes unlabeled data to generate pseudo-labels. Here, the query refinement module provides refined queries to avoid incorrect bipartite matching with teacher-generated pseudo-labels. For a detailed overview of the query refinement module, see Figure 3. Furthermore, a Reliable Pseudo-label Filtering strategy is employed to filter low-quality pseudo-labels progressively during training." + ], + "image_footnote": [], + "bbox": [ + 117, + 89, + 851, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Query Refinement", + "text_level": 1, + "bbox": [ + 76, + 429, + 254, + 445 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by recent advancements in vision-based networks [11, 53], we introduce an innovative approach to enhance object query features. For each unlabeled image $I \\in \\mathbb{R}^{H \\times W \\times C}$ , we extract query features $F_{s1} \\in \\mathbb{R}^{b \\times W_1 \\times 256}$ from strongly augmented image $I$ . Similarly, we extract query features $F_{t1}$ from weakly augmented image $I$ , also in the same dimension. Subsequently, feature extraction from the image backbones occurs. This results in the generation of features $F_{s2}$ for the student and $F_{t2}$ for the teacher network as $\\mathbb{R}^{b \\times W_2 \\times 256}$ . These features, encompassing both label and bounding box details, vary with the batch size, as indicated by $b$ . The feature sets $W_1$ and $W_2$ differ in size, with $W_2$ being substantially larger than $W_1$ . We provide a brief overview of each component of Query Refinement Module as illustrated in Figure 3.", + "bbox": [ + 75, + 458, + 468, + 684 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Query Refinement Module. In our approach, we handle multi-scale features $F_{t1}$ and $F_{t2}$ with a focus on effective aggregation. The finer details are encapsulated within the features $F_{t1}$ , while the features $F_{t2}$ encapsulate more abstract elements such as shapes and patterns. Simple aggregation of these features has been shown to degrade performance, as indicated in Table 5e). To solve this issue, we implement dual strategies to extract local and global information from high and low-resolution features. High-resolution features are crucial for detecting small objects. However, processing them with attentional operations is computationally demanding. To address this, we firstly convert the query label features $F_{t2} \\in (\\mathbb{R}^{b \\times W_2 \\times 256})$ into $F_{t2}' \\in (\\mathbb{R}^{b \\times W_2 \\times 16})$ by decreasing the channel dimension, and retaining the original resolution", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$b \\times W_{2}$ . Then, we apply attentional mechanism on $F_{t2}^{\\prime}$ to calculate the attentional weights $W_{k + q}$ in attention block as follows:", + "bbox": [ + 498, + 429, + 890, + 473 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nW _ {k + q} = F _ {k} ^ {\\prime} \\cdot F _ {q} ^ {\\prime}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 635, + 474, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\mathbf {W}} _ {k + q} = \\frac {\\exp \\left(W _ {k + q}\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(W _ {k + q}\\right)}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 500, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_{k + q}$ is the attentional weights of $F_{k}^{\\prime}$ and $F_{q}^{\\prime}$ , and $\\bar{\\mathbf{W}}_{k + q}$ is the normalized form of $W_{k + q}$ . Using normalized attention weights, we compute the enhanced queries representation $Q$ as follows:", + "bbox": [ + 498, + 542, + 893, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nQ = \\bar {\\mathbf {W}} _ {k + q} \\cdot F _ {v} ^ {\\prime} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 638, + 617, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "now we find the similarity between the attentional $F_{t2}$ features and $F_{t1}$ features to obtain $F_{cs}^{\\prime} \\in \\mathbb{R}^{b \\times W_1 \\times 16}$ from $Q \\in \\mathbb{R}^{b \\times W_2 \\times 16}$ as follows:", + "bbox": [ + 498, + 646, + 890, + 691 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {c s} ^ {\\prime} = \\frac {\\sum_ {i = l} ^ {n} P _ {l} Q _ {l}}{\\sqrt {\\sum_ {l = 1} ^ {n} P _ {l} ^ {2}} \\sqrt {\\sum_ {l = 1} ^ {n} Q _ {l} ^ {2}}} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 702, + 890, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $P$ and $Q$ are $F_{t1}$ and attentional $F_{t2}$ features, respectively. Then, we concatenate $F_{cs}'$ with $P$ to obtain refined query features. Interestingly, we observe a performance drop when our feature refinement strategy is applied to strongly augmented image features for the teacher network, as detailed in Table 5b. However, we achieve optimal results by concatenating strongly augmented image features and applying our refinement strategy to weakly augmented image features. Consequently, we proceed by concatenating the features $F_{s1}$ with $F_{s2}$ , thereby obtaining the query features", + "bbox": [ + 496, + 750, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5843", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/14b2567cf53534b6dfee193e26585068654d372ab70c8e1febb7542d8ce17c21.jpg", + "image_caption": [ + "Figure 3. Overview of the Query Refinement Module. The query features from strong and weak augmented unlabeled images are refined through the Query Refinement Module. It amplifies the semantic representation of object queries and improves performance for small objects. For the best view, zoom in." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 467, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$r_s$ . Note that $r_t$ , despite having a dimensional size equivalent to $F_{cs}^{\\prime} + P$ , encapsulates substantially more intricate representations. This improved performance is due to the integration of high-resolution and low-resolution features.", + "bbox": [ + 75, + 405, + 470, + 467 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, we form the decoder queries in the student-teacher network by merging the teacher's original queries $q_{t}$ with refined queries $r_{s}$ , and the student's original queries $q_{s}$ with refined queries $r_{t}$ , respectively. This integration forms the inputs for the decoder as follows:", + "bbox": [ + 75, + 470, + 470, + 546 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {o} _ {t}, o _ {t} = \\operatorname {D e c} _ {t} \\left(\\left[ r _ {s}, q _ {t} \\right], E _ {t} [ A ]\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 566, + 468, + 583 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {o} _ {s}, o _ {s} = \\operatorname {D e c} _ {s} \\left(\\left[ r _ {t}, q _ {s} \\right], E _ {s} [ A ]\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 173, + 585, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where $E_{s}$ and $E_{t}$ refer to the encoded image features. $\\hat{o}_{s}$ and $\\hat{o}_{t}$ indicate the decoded features of refined queries, while $o_{s}$ and $o_{t}$ represent the decoded features of original object queries. Here, $t$ is for teacher and $s$ for student network. Following DN-DETR [18], we use the attention mask $A$ to protect information leakage, ensuring the learning process's integrity.", + "bbox": [ + 75, + 622, + 468, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Reliable Pseudo-Label Filtering Module", + "text_level": 1, + "bbox": [ + 76, + 751, + 419, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The one-to-many training strategy, while effective, causes duplication prediction in the first stage. We introduce a pseudo-label filtering module to address this and improve the filtering of pseudo boxes rich in semantic content for refined query learning. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths. We employ m groups of ground truths $\\hat{g} = \\{\\hat{g}_1,\\hat{g}_2,\\dots ,\\hat{g}_m\\}$ for one-to-many as", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "signment strategy and select the top-k predictions as follows:", + "bbox": [ + 500, + 90, + 893, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\sigma} _ {o n e 2 m a n y} = \\left\\{\\underset {\\sigma_ {j} \\in C _ {M} ^ {N}} {\\arg \\min } \\sum_ {k} ^ {M} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {g} _ {\\sigma_ {j} (k)} ^ {s}\\right) \\right\\} _ {j} ^ {| \\hat {y} ^ {t} |} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 117, + 893, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $C_N^M$ represents the combination of $M$ and $N$ , denoting that a subset of $M$ proposals is associated with each pseudo box $\\hat{y}_j^t$ . Here, $m$ is set to 6. Furthermore, we use the remaining predictions to filter out duplicates in the top-k predictions in the one-to-one matching branch. Through this improved selection scheme, we achieve a performance improvement of 0.4 mAP when $m$ is set to 6, as shown in Table 5a. However, we observe no significant benefits when increasing $m$ greater than 6, as detailed in Table 6a.", + "bbox": [ + 496, + 176, + 893, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 328, + 630, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 352, + 601, + 366 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our approach on the MS-COCO [21] and Pascal VOC [6] datasets, benchmarking it against current SOTA SSOD methods. Following [51, 56], Sparse Semi-DETR is evaluated in three scenarios: COCO-Partial. We use $1\\%$ , $5\\%$ , $10\\%$ of train2017 as label data and rest as unlabeled data. COCO-Full. We take train2017 as label data and unlabel2017 as unlabel data. VOC. We take VOC2007 as label data and VOC2012 as unlabel data. Evaluation metrics include $AP_{50:95}$ , $AP_{50}$ , and $AP_{75}$ [51, 56].", + "bbox": [ + 496, + 375, + 893, + 512 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 521, + 718, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We set the quantity of DINO original object queries to 900. For the setting hyperparameters, following [56] : (1) In the COCO-Partial setting, we set the training iterations to 120k with a labeled to unlabeled data ratio of 1:4. The first 60k iterations adopt a one-to-many assignment strategy. (2) In the COCO-Full setting, Sparse Semi-DETR is trained for 240k iterations with labeled to unlabeled data ratio of 1:1. The first 120k iterations adopt a one-to-many assignment strategy. (3) In the VOC setting, we train the network for 60k iterations with a labeled to unlabeled data ratio of 1:4. The first 40k iterations adopt a one-to-many assignment strategy. For all experiments, the filtering threshold $\\sigma$ value is 0.4. We set the value of m to 6 and the value of k to 4. We provide complete implementation details for each experiment in Appendix A1.2.", + "bbox": [ + 496, + 544, + 893, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6. Results and Comparisons", + "text_level": 1, + "bbox": [ + 500, + 784, + 738, + 801 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate Sparse Semi-DETR and compare it against current SOTA SSOD methods. Our results demonstrate the superior performance of Sparse Semi-DETR in these aspects: (1) its effectiveness compared to both one-stage and two-stage detectors, (2) its comparison with traditional DETR-based detectors, and (3) its exceptional proficiency in accurately", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5844", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/86aaba2dcbb76d319856d0d243962a44a7e965ca5c65fb7860c25008f1bfb4ed.jpg", + "image_caption": [ + "Figure 4. Visual comparison of Sparse Semi-DETR with the two previous approaches on the COCO $10\\%$ label dataset. These results highlight Sparse Semi-DETR's capabilities, particularly in identifying small objects and those obscured by obstacles (as indicated by white arrows) in the third-row images. For optimal clarity and detail, please zoom in." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 893, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "detecting small and partially occluded objects. We provide more results details in Appendix A1.3.", + "bbox": [ + 75, + 419, + 470, + 450 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "COCO-Partial benchmark. Sparse Semi-DETR outperforms the current SSOD methods in COCO-Partial across all experiment settings, as demonstrated in Table 1. (1) We compare our method to both one-stage and two-stage SSOD. Sparse Semi-DETR surpasses Dense Teacher by 8.52, 7.79, 7.17 mAP on $1\\%$ , $5\\%$ , and $10\\%$ label data. It also outperforms PseCo by 8.47, 8.30, 8.24 mAP on $1\\%$ , $5\\%$ , and $10\\%$ label data. Sparse Semi-DETR's superior performance as a semi-supervised object detector is achieved without needing hand-crafted components commonly used in two-stage and one-stage detectors. (2) When compared to DETR-based detectors, Sparse Semi-DETR outperforms omni-DETR by 3.30, 3.10, and 3.00 mAP and beats Semi-DETR by 0.40, 0.70, 0.80 mAP on $1\\%$ , $5\\%$ , and $10\\%$ label data. (3) Sparse Semi-DETR's exceptional proficiency in precisely detecting small and partially obscured objects is a standout feature. In Figure 4, we visually compare Sparse Semi-DETR with the two preceding approaches using the COCO $10\\%$ labeled dataset. These results demonstrate the impressive capabilities of Sparse Semi-DETR, particularly in its ability to identify small objects and objects concealed by obstacles, as highlighted in the third-row images by the white arrows. Table 2 exhibits a remarkable performance boost of Sparse Semi-DETR on small objects. It surpasses the Semi-DETR by 1.20, 0.90 and 1.70 mAP on small objects using $1\\%$ , $5\\%$ , and $10\\%$ label data, respectively. It highlights the superior efficiency and accuracy of Sparse Semi-DETR in detecting smaller objects.", + "bbox": [ + 75, + 455, + 472, + 878 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "COCO-Full benchmark. In Table 4, when incorporating", + "bbox": [ + 76, + 885, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "additional unlabeled2017 data, Sparse Semi-DETR demonstrates a substantial improvement, achieving an impressive $2.1\\mathrm{mAP}$ gain and reaching a total of $51.3\\mathrm{mAP}$ . It surpasses the performance of Dense Teacher, PseCo, and Semi-DETR by 5.2, 5.2, and $0.9\\mathrm{mAP}$ , respectively, highlighting the effectiveness of Sparse Semi-DETR.", + "bbox": [ + 496, + 419, + 893, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pascal VOC benchmark. Sparse Semi-DETR exhibits a remarkable performance boost on the Pascal VOC benchmark, as shown in Table 3. It surpasses the supervised baseline by 5.1 improvement on $AP_{50}$ and by 5.91 impressive increase on $AP_{50:95}$ . Furthermore, it outperforms all previously single-stage, two-stage, and DETR-based SSOD methods by a significant margin.", + "bbox": [ + 496, + 511, + 893, + 618 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 631, + 663, + 645 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This section ablates the key design choices of Sparse Semi-DETR. The experiments detailed in this section are executed on the MS COCO dataset with $10\\%$ label data, employing DINO as the primary detector.", + "bbox": [ + 496, + 655, + 893, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Individual Component. We conduct three experiments to assess the efficacy of each module of Sparse Semi-DETR, as detailed in Table 5a. We employ Semi-DETR as our baseline model. Notably, integrating each component into Sparse Semi-DETR leads to consistent performance improvements. Specifically, adding the Query Refinement and Pseudo-Label Filtering modules yields a significant increase of $0.8\\mathrm{mAP}$ . These results confirm that each component of Sparse Semi-DETR enhances our model's performance.", + "bbox": [ + 496, + 718, + 893, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effect of Query Refinement Module. We examine the impact of the Query Refinement (QR) Module. In Table 5b, we explore various QR combinations to determine the most", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5845", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/edd5ea9e09389a5bb7323332ac8a1e207b2f01b08ae8d02f704f2d8eed45a0cd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsReferenceCOCO-Partial
1%5%10%
FCOS [42] (Supervised)-8.43 ± 0.0317.01 ± 0.0120.98 ± 0.01
DSL [3]CVPR2222.03 ± 0.28 (+13.98)30.87 ± 0.24 (+13.86)36.22 ± 0.18 (+15.24)
Unbiased Teacher v2 [28]CVPR2222.71 ± 0.42 (+14.28)30.08 ± 0.04 (+13.07)32.61 ± 0.03 (+11.63)
Dense Teacher [57]ECCV2222.38 ± 0.31 (+13.95)33.01 ± 0.14 (+16.00)37.13 ± 0.12 (+16.15)
Faster RCNN [35] (Supervised)-9.05 ± 0.1618.47 ± 0.2223.86 ± 0.81
Humble Teacher [41]CVPR2216.96 ± 0.38 (+7.91)27.70 ± 0.15 (+9.23)31.61 ± 0.28 (+7.75)
Instant-Teaching [58]CVPR2118.05 ± 0.15 (+9.00)26.75 ± 0.05 (+8.28)30.40 ± 0.05 (+6.54)
Soft Teacher [51]ICCV2120.46 ± 0.39 (+11.41)30.74 ± 0.08 (+12.27)34.04 ± 0.14 (+10.18)
PseCo [19]ECCV2222.43 ± 0.36 (+13.38)32.50 ± 0.08 (+14.03)36.06 ± 0.24 (+12.2)
DINO [55] (Supervised)-18.00 ± 0.2129.50 ± 0.1635.00 ± 0.12
Omni-DETR [46] (DINO)CVPR2227.60 (+9.60)37.70(+8.20)41.30 (+6.30)
Semi-DETR [56] (DINO)CVPR2330.5 ± 0.30 (+12.50)40.10 ± 0.15 (+10.6)43.5 ± 0.10 (+8.5)
Sparse Semi-DETR-30.9 ± 0.23 (+12.90)40.8 ± 0.12 (+11.30)44.3 ± 0.01 (+9.30)
", + "bbox": [ + 125, + 88, + 844, + 315 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f79cf1fc39e3b102bb83e99dbf4fe0b2c9f1a8aa08775ee344c74f9b455d2715.jpg", + "table_caption": [ + "Table 1. Comparing Sparse Semi-DETR with other approaches on COCO-Partial setting. The results are the average across all five folds. Under the COCO-partial setting, FCOS serves as the baseline for one-stage detectors, Faster RCNN for two-stage detectors, and DINO for transformer-based end-to-end detectors." + ], + "table_footnote": [], + "table_body": "
MethodsLabelsCOCO-Partial
APSAPMAPL
Semi-DETR [56]1%13.631.240.8
5%23.043.153.7
10%25.246.858.0
Sparse Semi-DETR1%14.832.541.4
5%23.944.254.2
10%26.948.059.6
", + "bbox": [ + 91, + 395, + 354, + 498 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8f73f7d132b5fa86d8d75683dd5ef6f90c6e23ef841c85b2a2b82de83c9b00ae.jpg", + "table_caption": [ + "Table 2. Experimental results on COCO-partial settings for small, medium, and large objects. The results shown are the average across all five folds. We reproduce Semi-DETR results using their source code." + ], + "table_footnote": [], + "table_body": "
MethodsVOC12
AP50AP50:95
FCOS [42] (Supervised)71.3645.52
DSL [3]80.7056.80
Dense Teacher [57]79.8955.87
Faster RCNN [35] (Supervised)72.7542.04
STAC [39]77.4544.64
HumbleTeacher [41]80.9453.04
Instant-Teaching [58]79.2050.00
DINO [55] (Supervised)81.2059.60
Semi-DETR [56] (DINO)86.1065.20
Sparse Semi-DETR86.3065.51
", + "bbox": [ + 367, + 380, + 614, + 526 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c3e5b6929b87f1b4be7f7a7eb531c8aa74b0ecfe33bd601fb5ea9ec1d9feb5ea.jpg", + "table_caption": [ + "Table 3. Experimental results on Pascal VOC protocol. Here, FCOS, Faster RCNN, and DINO are the supervised baselines." + ], + "table_footnote": [], + "table_body": "
MethodCOCO-Full (100%)
STAC [39] (18×)39.5 →0.3 39.2
Unbiased Teacher (9×)40.2 →1.1 41.3
SoftTeacher [51] (24×)40.9 →3.6 44.5
DSL [3] (12×)40.2 →3.6 43.8
Dense Teacher [57] (18×)41.2 →3.6 46.1
PseCo (24×)41.0 →5.1 46.1
Instant-Teaching [58] (24×)37.6 →0.27 40.2
Semi-DETR [56] (8×)48.6 →1.8 50.4
Sparse Semi-DETR (8×)49.2 →2.1 51.3
", + "bbox": [ + 627, + 380, + 888, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparing Sparse Semi-DETR with other approaches on COCO-Full. Note that 1 denotes 30k training iterations, while an $\\mathbf{N}\\times$ signifies N times 30k iterations.", + "bbox": [ + 625, + 537, + 893, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "effective design. Applying QR selectively to the student, teacher, or both networks, we find that employing QR on weak augmented image features $F_{t1}$ and $F_{t2}$ , and integrating them into the student network with the original decoder queries yields the best results. Table 5c shows that processing $F_{t1}$ features without MLP (in [56]) improves results. Table 5d presents our study on the impact of different query variants, where we observe that QR consistently outperforms other methods. Finally, Table 5e shows that using an attentional block in the QR module is more effective than simple concatenation or cosine similarity. We provide more analysis of the Query Refinement Module supplementary document. Figure 5 compares Sparse Semi-DETR and Semi-DETR. Sparse Semi-DETR, processing fewer but refined queries, demonstrates lower duplication rates in this training approach.", + "bbox": [ + 75, + 619, + 472, + 861 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of Reliable Pseudo-Label Filtering Module. In our analysis of the Pseudo-Label Filtering Module, we examine", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "the impact of various parameters. Table 6a shows that a smaller m results in lower performance due to the inclusion of poor-quality labels. Performance improves with a moderately larger m due to enhanced auxiliary loss. However, excessively large m values trigger NMS, negatively impacting performance. Additionally, in Table 6b, we analyze the selection of the k value and find that setting k to 4 yields the best performance. In Table 6c, the optimal performance for $\\sigma$ is achieved at 0.4; values lower than this may lead to the generation of noisy pseudo-labels, whereas higher values can decrease the number of effective pseudo-labels.", + "bbox": [ + 496, + 619, + 893, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Limitation. We still have duplications when we apply the one-to-many training strategy in both stages. Table 7 illustrates that a one-to-many strategy for $120\\mathrm{k}$ iterations with Sparse Semi-DETR achieves a $44.6\\mathrm{mAP}$ using NMS. In comparison, $60\\mathrm{k}$ iterations in the first stage attain a comparable $44.3\\mathrm{mAP}$ without NMS. Future works can explore this aspect.", + "bbox": [ + 496, + 794, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5846", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/0458c875e7b9d16c45747be9b82f46ec9033a0e3ddc43950c9a53d1920fce785.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Query RefinementPseudo-Label FilteringmAP\\( AP_{50} \\)\\( AP_{75} \\)
XX43.558.946.0
✓X43.861.147.3
X✓43.960.546.3
✓✓44.361.747.6
", + "bbox": [ + 145, + 88, + 553, + 166 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "(a) Effect of Individual Component.", + "bbox": [ + 248, + 169, + 449, + 181 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b5fcbac70fce3add6c3b45020cb9610ac66dd33be30965797d3d6633be3de370.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TeacherStudentmAP\\( AP_{50} \\)\\( AP_{75} \\)
XX43.558.946.0
✓X43.861.247.2
X✓44.361.747.6
✓✓42.859.745.8
", + "bbox": [ + 558, + 89, + 820, + 162 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/2a3a9045b836de791206e3c011e3584473b7486723c1f8fa496205583c7ead7c.jpg", + "table_caption": [ + "(b) Effect of QR on Student and Teacher module." + ], + "table_footnote": [], + "table_body": "
MLPmAPAP50AP75
✓43.760.946.9
X44.361.747.6
", + "bbox": [ + 99, + 186, + 295, + 241 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/4b6aab90f7adb39c0898dbfdde8e1836194775af2d2fa3cd45da2b3fc8365270.jpg", + "table_caption": [ + "(c) Effect of MLP." + ], + "table_footnote": [], + "table_body": "
MethodmAPAP50AP75
Single-view Queries43.059.346.3
Cross-view Queries43.558.946.0
Query Refinement44.361.747.6
", + "bbox": [ + 303, + 183, + 576, + 246 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b848c18b6f25b9fc5325c49e76c9d5b1f8738e11b8128c9ac3cd2b2db00b6272.jpg", + "table_caption": [ + "(d) Effect of different variants of queries." + ], + "table_footnote": [], + "table_body": "
MethodmAPAP50AP75
Simple Concat43.458.846.1
Cosine Similarity43.760.346.1
Attention Module44.361.747.6
", + "bbox": [ + 594, + 181, + 859, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cfdd17fb3d41945b962b35978fa46710dd387c43db79a3918948a8c9cfaca4e5.jpg", + "image_caption": [ + "Figure 5. The top-row figures display Semi-DETR's detection results, and the bottom-row shows Sparse Semi-DETR's outcomes. Both networks were trained for 120k iterations using one-to-many and one-to-one strategies. Sparse Semi-DETR eliminates redundant bounding boxes in the bottom-left image and detects small objects, like knives, in the top-right image, as indicated by white arrows." + ], + "image_footnote": [], + "bbox": [ + 81, + 383, + 468, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 720, + 194, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, we successfully address the inherent limitations of DETR-based semi-supervised object detection frameworks by introducing Sparse Semi-DETR. This novel solution effectively tackles overlapping predictions and the detection of small objects. Sparse Semi-DETR incorporates a Query Refinement Module to enhance object query quality, mainly benefiting the detection of small and partially obscured objects. Besides, it also introduces a Reliable PseudoLabel Filtering Module to filter out low-quality pseudolabels selectively, thereby enhancing overall detection accu", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f4be649e12b5e2c216529bff6d01ca1578ce44e884527c1e8d58ec9c02a9991c.jpg", + "table_caption": [ + "(e) Effectiveness of Attentional module in QR.", + "Table 5. Ablations for the proposed Sparse Semi-DETR on COCO $10\\%$ Label dataset. (a) We analyze the effectiveness of each module of Sparse Semi-DETR. (b) We experiment with different QR combinations to identify the optimal design, applying QR selectively on the student, the teacher, or both. (c) We analyze the effect of using MLP layers for $F_{t1}$ and $F_{s1}$ . Empirical observation reveals that we do not require MLP as in [56]. (d) We observe the effect of the attentional block in the Query Refinement module by replacing it with simple concatenation or cosine similarity. (e) We vary the type of object queries fed to the decoder with the decoder's original queries. The best results are highlighted." + ], + "table_footnote": [], + "table_body": "
m (k=4)mAP
244.0
444.1
644.3
844.2
", + "bbox": [ + 524, + 383, + 643, + 469 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e754791c19c7f0ca2670baaa00aedfd6a23908efd364e326c72b248d66ee7aa2.jpg", + "table_caption": [ + "(a) Effect of m." + ], + "table_footnote": [], + "table_body": "
k (m=6)mAP
243.8
444.3
644.1
843.9
", + "bbox": [ + 650, + 385, + 771, + 469 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5adcb88ea0ab5bcb0a70c3818a2c46dadb7fe6c51f2fb097b014ddd0c2f75f77.jpg", + "table_caption": [ + "(b) Effect of k." + ], + "table_footnote": [], + "table_body": "
σmAP
0.243.2
0.343.8
0.444.3
0.544.0
", + "bbox": [ + 777, + 383, + 867, + 469 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6f25d3af713f8f37d6ad0d8d892f1c48a8426d9ccdf4a69ad1dfcd7a16bc3ddd.jpg", + "table_caption": [ + "(c) Effect of $\\sigma$", + "Table 6. Ablations for the Reliable Pseudo-Label Filtering Module on COCO $10\\%$ Label dataset. We study the impact of various parameters as augmented ground truth (m), top pseudolabels selection (k) and filtering threshold $(\\sigma)$ ." + ], + "table_footnote": [], + "table_body": "
Iterations40k60k80k100k120k
mAP43.544.344.043.844.6
without-NMSYYYYN
", + "bbox": [ + 549, + 571, + 844, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Evaluating One-to-Many Assignment Strategy.", + "bbox": [ + 527, + 633, + 861, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "racy and consistency with the remaining high-quality labels. Our method outperforms existing SSOD approaches, with extensive experiments demonstrating its effectiveness.", + "bbox": [ + 496, + 680, + 893, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethical considerations. We study semi-supervised models, and agree that standard ethical considerations for visual recognition are applicable to our work.", + "bbox": [ + 496, + 728, + 893, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 796, + 666, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was in parts supported by the EU Horizon Europe Framework under grant agreements 101135724 (LUMINOUS) and 101092312 (AIRISE) and by the Federal Ministry of Education and Research of Germany (BMBF) under grant 01QE2227C (HERON).", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5847", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Ting Cai and Kirthevasan Kandasamy. 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In International Conference on Learning Representations, 2021. 2, 3" + ], + "bbox": [ + 78, + 90, + 470, + 556 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "5850", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_model.json b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_model.json new file mode 100644 index 0000000000000000000000000000000000000000..bdec89d0d7110e667c6760bfdbbc93c7a834ab44 --- /dev/null +++ b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_model.json @@ -0,0 +1,2235 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.23, + 0.131, + 0.744, + 0.177 + ], + "angle": 0, + "content": "Sparse Semi-DETR: Sparse Learnable Queries for Semi-Supervised Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.203, + 0.882, + 0.24 + ], + "angle": 0, + "content": "Tahira Shehzadi\\(^{1,2,3}\\), Khurram Azeem Hashmi\\(^{1,2,3}\\), Didier Stricker\\(^{1,2,3}\\), Muhammad Zeshan Afzal\\(^{1,2,3}\\), \\(^{1}\\)DFKI, \\(^{2}\\)RPTU Kaiserslautern-Landau, \\(^{3}\\)MindGarage-RPTU" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.274, + 0.608, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.177, + 0.44, + 0.245, + 0.45 + ], + "angle": 0, + "content": "(a) Semi-DETR" + }, + { + "type": "image", + "bbox": [ + 0.612, + 0.272, + 0.891, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.685, + 0.436, + 0.835, + 0.446 + ], + "angle": 0, + "content": "(c) Comparison of SSOD Methods" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.466, + 0.895, + 0.509 + ], + "angle": 0, + "content": "Figure 1. (a)-(b) Comparative Overview of SSOD advancements: Sparse Semi-DETR's major improvement lies in its Query Refinement Module and Reliable Pseudo-label Filtering Module, significantly enhancing detection of small or obscured objects and reliability in complex scenarios, surpassing all other methods as shown in the graph in (c)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.521, + 0.314, + 0.536 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.474, + 0.903 + ], + "angle": 0, + "content": "In this paper, we address the limitations of the DETR-based semi-supervised object detection (SSOD) framework, particularly focusing on the challenges posed by the quality of object queries. In DETR-based SSOD, the one-to-one assignment strategy provides inaccurate pseudo-labels, while the one-to-many assignments strategy leads to overlapping predictions. These issues compromise training efficiency and degrade model performance, especially in detecting small or occluded objects. We introduce Sparse Semi-DETR, a novel transformer-based, end-to-end semi-supervised object detection solution to overcome these challenges. Sparse Semi-DETR incorporates a Query Refinement Module to enhance the quality of object queries, significantly improving detection capabilities for small and partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy and consistency. On the MS-COCO and Pascal VOC object detection benchmarks, Sparse Semi-DETR achieves a significant improvement over current state-of-the-art methods that highlight Sparse Semi-DETR's effectiveness in semi-supervised object detection, particularly in challenging scenarios involving small or par" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.522, + 0.656, + 0.538 + ], + "angle": 0, + "content": "tially obscured objects." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.571, + 0.633, + 0.587 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.703 + ], + "angle": 0, + "content": "Semi-Supervised Object Detection (SSOD) aims to improve the effectiveness of fully supervised object detection through the integration of abundant unlabeled data [3, 12, 15, 19, 28, 39, 49-52, 58]. It has applications in diverse fields, ranging from autonomous vehicles [14, 20] to healthcare [31, 44], where obtaining extensive labeled datasets is often impractical or cost-prohibitive [1]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Several SSOD methods [3, 12, 15, 19, 28, 39, 49-52, 58] have been proposed. Two prevalent approaches in this domain are pseudo-labeling [27, 30, 39, 45, 50-52, 58] and consistency-based regularization [3, 12, 15, 19, 28, 49]. STAC [39] introduced a simple multi-stage SSOD training method with pseudo-labeling and consistency training, later simplified by a Teacher-Student framework for generating pseudo-labels [27]. Based on this framework, considerable research efforts have been directed towards enhancing the quality of pseudo-labels [51, 58]. These traditional SSOD methods are built upon conventional detectors like one-stage [33, 42] and two-stage [9, 35], which involve various manually designed components such as an" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5840" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "chor boxes and non-maximum suppression (NMS). Employing object detection methods in SSOD poses several potential challenges that must be carefully dealt with to obtain reasonable performance. These factors include overfitting of the labeled data [37], pseudo-label noise [10], bias induced through label imbalance [17, 32], and poor detection performance on small objects [56]. Recently, DETR-based [2, 16, 18, 25, 38, 55, 59] SSOD methods [46, 56] remove the need for traditional components like NMS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.232, + 0.473, + 0.671 + ], + "angle": 0, + "content": "Even though DETR-based SSOD [46, 56] has progressed remarkably, state-of-the-art methods possess some limitations. (1) DETR-based SSOD methods perform poorly in the detection of small objects, as shown in Figure 4. This is because these methods don't use multi-scale features [36] like Feature Pyramid Networks (FPN) [22], which play an important role in identifying smaller objects as in CNN-based SSOD methods [3, 12, 15, 19, 28, 49, 51, 52, 58]. Although recent advancements in DETR-based object detection [2, 16, 18, 25, 38, 55, 59] have improved the detection of small objects, their SSOD adaptation is still unable to cater this challenge effectively [56]. (2) SSOD approaches [51, 52, 56, 58] rely on handcrafted post-processing methods such as NMS [35]. This problem specifically appears in DETR-based SSOD when we use a large number of object queries and the one-to-many assignment strategy [56]. In DETR-based SSOD methods, this problem is partially solved using the one-to-one or hybrid (combination of one-to-one and one-to-many) assignment strategy. However, the hybrid assignment strategy is preferred because the one-to-one assignment strategy produces inaccurate pseudo-labels [46], thus resulting in inefficient learning. Although the number of duplicate bounding boxes is less in the hybrid strategy [56], the amount is high enough to impact object detection performance adversely, as depicted in Figure 5. (3) The pseudolabel generation produces both high and low-quality labels. The DETR-based SSOD methods lack an effective refinement strategy for one-to-many assignments, which is crucial for filtering out low-quality proposals." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To address the above mentioned issues, we propose enhancing the state-of-the-art DETR-based SSOD approach, namely 'Sparse Semi-DETR', presented in Figure 1 (b). Our approach involves expanding its architecture by integrating a couple of novel modules designed to mitigate the identified shortcomings. The key module among these is the Query-Refinement module, as depicted in Figure 2 and explained in Figure 3. This module significantly improves the quality of the queries and reduces their numbers. The proposed module uses the low-level features from the backbone and high-level features extracted directly from weakly augmented images using ROI alignment [13]. Fusing these features results in overcoming the first shortcoming, i.e., detecting small and obscured objects, as shown in Figure 4. The attention mechanism drives the aggregation of the features," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.349 + ], + "angle": 0, + "content": "resulting in refined, high-quality features to carry forward. To ensure the quality of the query features, the attention mechanism is accompanied by a query-matching strategy for filtering irrelevant queries. Thus, the Query Refinement Module not only improves the quality of the queries but also reduces their numbers, giving rise to efficient processing. This module results in significantly fewer overlapping proposals, improving the performance overall, thereby solving the second limitation. Besides, we introduce a Reliable Pseudo-Label Filtering Module, as illustrated in Figure 2, inspired by Hybrid-DETR [16] to address the third limitation. Employing this module significantly reduces the low-quality pseudo-labels. Therefore, it further reduces the amount of duplicate predictions that may still occur after the second stage of the hybrid assignment strategy. Our approach provides better results than previous SSOD methods, as shown in Figure 1 (c)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.35, + 0.894, + 0.379 + ], + "angle": 0, + "content": "The key contributions of this work can be outlined as follows:" + }, + { + "type": "text", + "bbox": [ + 0.502, + 0.381, + 0.895, + 0.456 + ], + "angle": 0, + "content": "1. We present Sparse Semi-DETR, a novel approach in semi-supervised object detection, introducing two novel contributions. To our knowledge, we are the first to examine and propose query refinement and low-quality proposal filtering for the one-to-many query assignment strategy." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.457, + 0.894, + 0.547 + ], + "angle": 0, + "content": "2. We introduce a novel query refinement module designed to improve object query features, particularly in complex detection scenarios such as identifying small or partially obscured objects. This enhancement not only boosts performance but also aids in learning semantic feature invariance among object queries." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.547, + 0.895, + 0.638 + ], + "angle": 0, + "content": "3. We introduce a Reliable Pseudo-Label Filtering Module specifically designed to reduce the effect of noisy pseudolabels. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths, enhancing the consistency of the learning process." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.638, + 0.895, + 0.743 + ], + "angle": 0, + "content": "4. Sparse Semi-DETR outperforms current state-of-the-art methods on MS-COCO and Pascal VOC benchmarks. With only \\(10\\%\\) labeled data from MS-COCO using ResNet-50 backbone, it achieves a 44.3 mAP, exceeding prior baselines by 0.8 mAP. Additionally, when trained on the complete COCO set with extra unlabeled data, it further improves, rising from 49.2 to 51.3 mAP." + }, + { + "type": "list", + "bbox": [ + 0.501, + 0.381, + 0.895, + 0.743 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.76, + 0.642, + 0.777 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.667, + 0.803 + ], + "angle": 0, + "content": "2.1. Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Object detection identifies and locates objects in images or videos. Deep learning-based object detection approaches are typically categorized into two primary groups: two-stage detectors [9, 35] and one-stage detectors [23, 26, 34, 42]. These methods depend on numerous heuristics, such as generating anchors and NMS. Recently, DEetection TRans" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5841" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "former (DETR) [2] considers object detection as a set prediction problem, using transformer [43] to adeptly transform sparse object candidates [40] into precise target objects. Our Sparse Semi-DETR detects small or partially obscured objects in the DETR-based SSOD setting. Notably, our framework is compatible with various DETR-based detectors [4, 5, 7, 8, 24, 29, 47, 48, 59], offering flexibility in integration." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.225, + 0.377, + 0.24 + ], + "angle": 0, + "content": "2.2. Semi-Supervised Object Detection" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.249, + 0.473, + 0.415 + ], + "angle": 0, + "content": "Most research in SSOD employs detectors categorized into three types: one-stage, two-stage, and DETR-based systems. One-stage STAC [39], an early SSOD, introduced a simple training strategy combining pseudo-labeling and consistency training, later streamlined by a student-teacher framework for easier pseudo-label generation [27]. DSL [3] introduced novel techniques including Adaptive Filtering, Aggregated Teacher, and uncertainty-consistency-regularization for improved generalization. Dense Teacher [57] introduced Dense Pseudo-Labels (DPL) for richer information and a region selection method to reduce noise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.417, + 0.473, + 0.612 + ], + "angle": 0, + "content": "Two-stage. Humble Teacher [41] uses soft labels and a teacher ensemble to boost pseudo-label reliability, matching other results. Instant-Teaching [58] creates pseudo annotations from weak augmentations, treating them as ground truth under strong augmentations with Mixup [54]. Unbiased Teacher [27] tackles class imbalance in pseudo-labeling with focal loss, focusing on underrepresented classes. Soft Teacher [51] minimizes incorrect foreground proposal classification by applying teacher-provided confidence scores to reduce classification loss. PseCo [19] enhances detector performance by combining pseudo-labeling with label and feature consistency methods, also using focal loss to address class imbalance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.473, + 0.901 + ], + "angle": 0, + "content": "DETR-based. Omni-DETR [46] is designed for omnisupervised detection and adapts to SSOD with a basic pseudo-label filtering method. It employs the one-to-one assignment strategy proposed in DETR [2], and encounters challenges when dealing with inaccurate pseudo-bounding boxes produced by the teacher network. These inaccuracies result in reduced performance, highlighting its limitations. Semi-DETR [56] adopts a stage-wise strategy, employing a one-to-many matching strategy in the first stage and switching to a one-to-one matching strategy in the second stage. This approach provides NMS-free end-to-end detection benefits but reduces performance compared to a one-to-many assignment strategy. Moreover, Omni-DETR and Semi-DETR struggle to detect small or occluded objects. Our work introduces an advanced query refinement module that significantly refines object queries, enhancing training efficiency and performance and leading to the detection of small or densely packed objects in the DETR-based SSOD framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.09, + 0.628, + 0.108 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.117, + 0.895, + 0.179 + ], + "angle": 0, + "content": "In DETR-based SSOD, one-to-one assignment strategy, denoted by \\(\\hat{\\sigma}_{one2one}\\), is achieved by applying Hungarian algorithm between the predictions made by the student model and the pseudo-labels provided by the teacher model as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.553, + 0.192, + 0.894, + 0.235 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {o n e 2 o n e} = \\underset {\\sigma \\in \\xi_ {N}} {\\arg \\min } \\sum_ {j} ^ {N} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {y} _ {\\sigma (j)} ^ {s}\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.252, + 0.895, + 0.381 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{\\mathrm{match}}\\left(\\hat{y}_j^t,\\hat{y}_{\\sigma (j)}^s\\right)\\) is the matching cost between the pseudo-labels \\(\\hat{y}_j^t\\) generated by the teacher network and the predictions of the student network with index \\(\\sigma (j)\\) and \\(\\xi_{N}\\) is the permutation of \\(N\\) elements. Semi-DETR [56] addresses the issue of imprecise initial pseudo-labels by shifting from a one-to-one to a one-to-many assignment strategy, increasing the number of positive object queries to improve detection accuracy:" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.395, + 0.893, + 0.445 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {o n e 2 m a n y} = \\left\\{\\underset {\\sigma_ {j} \\in C _ {M} ^ {N}} {\\arg \\min } \\sum_ {k} ^ {M} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {y} _ {\\sigma_ {j} (k)} ^ {s}\\right) \\right\\} _ {j} ^ {| \\hat {y} ^ {t} |} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.895, + 0.581 + ], + "angle": 0, + "content": "where \\( C_N^M \\) represents the combination of \\( M \\) and \\( N \\), denoting that a subset of \\( M \\) proposals is associated with each pseudo box \\( \\hat{y}_j^t \\). Semi-DETR initially adopts a one-to-many assignment to improve label quality, then shifts to one-to-one assignment for an NMS-free model. This approach adopts a one-to-many assignment strategy aimed at boosting performance, but it's less effective with small or occluded objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.599, + 0.69, + 0.617 + ], + "angle": 0, + "content": "4. Sparse Semi-DETR" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.897, + 0.902 + ], + "angle": 0, + "content": "In semi-supervised learning, a collection of labeled data denoted as \\( D_{l} \\), where \\( D_{l} = \\{x_{i}^{l},y_{i}^{l}\\}_{i = 1}^{N_{l}} \\) is given, along with a set of unlabeled data represented as \\( D_{u} \\), where \\( D_{u} = \\{x_{i}^{u}\\}_{i = 1}^{N_{u}} \\). Here, \\( N_{l} \\) and \\( N_{u} \\) correspond to the number of labeled and unlabeled data. The annotations \\( y_{i}^{l} \\) for the label data \\( x^{l} \\) contain object labels and bounding box information. The pipeline of the Sparse Semi-DETR framework is depicted in Figure 2. It introduces a Query Refinement Module for processing query features to enhance semantic representation for complex detection scenarios, such as identifying small or partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy. For comparison purposes, we employ DINO [55] with a ResNet-50 backbone. This section gives a detailed overview of the modules of Sparse Semi-DETR. We explain briefly our semi-supervised approach in Appendix A1.1." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5842" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.09, + 0.852, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.333, + 0.892, + 0.417 + ], + "angle": 0, + "content": "Figure 2. An overview of the Sparse Semi-DETR framework. It contains two networks: the student network and the teacher network. Labeled data is used for student network training, employing a supervised loss. Unlabeled data is fed to the teacher network with weak augmentation and the student network with strong augmentation. The teacher network takes unlabeled data to generate pseudo-labels. Here, the query refinement module provides refined queries to avoid incorrect bipartite matching with teacher-generated pseudo-labels. For a detailed overview of the query refinement module, see Figure 3. Furthermore, a Reliable Pseudo-label Filtering strategy is employed to filter low-quality pseudo-labels progressively during training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.43, + 0.255, + 0.446 + ], + "angle": 0, + "content": "4.1. Query Refinement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.685 + ], + "angle": 0, + "content": "Inspired by recent advancements in vision-based networks [11, 53], we introduce an innovative approach to enhance object query features. For each unlabeled image \\(I \\in \\mathbb{R}^{H \\times W \\times C}\\), we extract query features \\(F_{s1} \\in \\mathbb{R}^{b \\times W_1 \\times 256}\\) from strongly augmented image \\(I\\). Similarly, we extract query features \\(F_{t1}\\) from weakly augmented image \\(I\\), also in the same dimension. Subsequently, feature extraction from the image backbones occurs. This results in the generation of features \\(F_{s2}\\) for the student and \\(F_{t2}\\) for the teacher network as \\(\\mathbb{R}^{b \\times W_2 \\times 256}\\). These features, encompassing both label and bounding box details, vary with the batch size, as indicated by \\(b\\). The feature sets \\(W_1\\) and \\(W_2\\) differ in size, with \\(W_2\\) being substantially larger than \\(W_1\\). We provide a brief overview of each component of Query Refinement Module as illustrated in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Query Refinement Module. In our approach, we handle multi-scale features \\( F_{t1} \\) and \\( F_{t2} \\) with a focus on effective aggregation. The finer details are encapsulated within the features \\( F_{t1} \\), while the features \\( F_{t2} \\) encapsulate more abstract elements such as shapes and patterns. Simple aggregation of these features has been shown to degrade performance, as indicated in Table 5e). To solve this issue, we implement dual strategies to extract local and global information from high and low-resolution features. High-resolution features are crucial for detecting small objects. However, processing them with attentional operations is computationally demanding. To address this, we firstly convert the query label features \\( F_{t2} \\in (\\mathbb{R}^{b \\times W_2 \\times 256}) \\) into \\( F_{t2}' \\in (\\mathbb{R}^{b \\times W_2 \\times 16}) \\) by decreasing the channel dimension, and retaining the original resolution" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.891, + 0.474 + ], + "angle": 0, + "content": "\\(b \\times W_{2}\\). Then, we apply attentional mechanism on \\(F_{t2}^{\\prime}\\) to calculate the attentional weights \\(W_{k + q}\\) in attention block as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.637, + 0.476, + 0.892, + 0.495 + ], + "angle": 0, + "content": "\\[\nW _ {k + q} = F _ {k} ^ {\\prime} \\cdot F _ {q} ^ {\\prime}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.501, + 0.892, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\bar {\\mathbf {W}} _ {k + q} = \\frac {\\exp \\left(W _ {k + q}\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(W _ {k + q}\\right)}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.543, + 0.894, + 0.605 + ], + "angle": 0, + "content": "where \\( W_{k + q} \\) is the attentional weights of \\( F_{k}^{\\prime} \\) and \\( F_{q}^{\\prime} \\), and \\( \\bar{\\mathbf{W}}_{k + q} \\) is the normalized form of \\( W_{k + q} \\). Using normalized attention weights, we compute the enhanced queries representation \\( Q \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.639, + 0.618, + 0.892, + 0.635 + ], + "angle": 0, + "content": "\\[\nQ = \\bar {\\mathbf {W}} _ {k + q} \\cdot F _ {v} ^ {\\prime} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.647, + 0.892, + 0.692 + ], + "angle": 0, + "content": "now we find the similarity between the attentional \\(F_{t2}\\) features and \\(F_{t1}\\) features to obtain \\(F_{cs}^{\\prime} \\in \\mathbb{R}^{b \\times W_1 \\times 16}\\) from \\(Q \\in \\mathbb{R}^{b \\times W_2 \\times 16}\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.591, + 0.703, + 0.892, + 0.741 + ], + "angle": 0, + "content": "\\[\nF _ {c s} ^ {\\prime} = \\frac {\\sum_ {i = l} ^ {n} P _ {l} Q _ {l}}{\\sqrt {\\sum_ {l = 1} ^ {n} P _ {l} ^ {2}} \\sqrt {\\sum_ {l = 1} ^ {n} Q _ {l} ^ {2}}} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.901 + ], + "angle": 0, + "content": "where \\( P \\) and \\( Q \\) are \\( F_{t1} \\) and attentional \\( F_{t2} \\) features, respectively. Then, we concatenate \\( F_{cs}' \\) with \\( P \\) to obtain refined query features. Interestingly, we observe a performance drop when our feature refinement strategy is applied to strongly augmented image features for the teacher network, as detailed in Table 5b. However, we achieve optimal results by concatenating strongly augmented image features and applying our refinement strategy to weakly augmented image features. Consequently, we proceed by concatenating the features \\( F_{s1} \\) with \\( F_{s2} \\), thereby obtaining the query features" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "5843" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.468, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.313, + 0.473, + 0.385 + ], + "angle": 0, + "content": "Figure 3. Overview of the Query Refinement Module. The query features from strong and weak augmented unlabeled images are refined through the Query Refinement Module. It amplifies the semantic representation of object queries and improves performance for small objects. For the best view, zoom in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.471, + 0.468 + ], + "angle": 0, + "content": "\\(r_s\\). Note that \\(r_t\\), despite having a dimensional size equivalent to \\(F_{cs}^{\\prime} + P\\), encapsulates substantially more intricate representations. This improved performance is due to the integration of high-resolution and low-resolution features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.471, + 0.471, + 0.547 + ], + "angle": 0, + "content": "Then, we form the decoder queries in the student-teacher network by merging the teacher's original queries \\( q_{t} \\) with refined queries \\( r_{s} \\), and the student's original queries \\( q_{s} \\) with refined queries \\( r_{t} \\), respectively. This integration forms the inputs for the decoder as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.568, + 0.47, + 0.584 + ], + "angle": 0, + "content": "\\[\n\\hat {o} _ {t}, o _ {t} = \\operatorname {D e c} _ {t} \\left(\\left[ r _ {s}, q _ {t} \\right], E _ {t} [ A ]\\right) \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.174, + 0.587, + 0.47, + 0.603 + ], + "angle": 0, + "content": "\\[\n\\hat {o} _ {s}, o _ {s} = \\operatorname {D e c} _ {s} \\left(\\left[ r _ {t}, q _ {s} \\right], E _ {s} [ A ]\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.623, + 0.47, + 0.73 + ], + "angle": 0, + "content": "Where \\( E_{s} \\) and \\( E_{t} \\) refer to the encoded image features. \\( \\hat{o}_{s} \\) and \\( \\hat{o}_{t} \\) indicate the decoded features of refined queries, while \\( o_{s} \\) and \\( o_{t} \\) represent the decoded features of original object queries. Here, \\( t \\) is for teacher and \\( s \\) for student network. Following DN-DETR [18], we use the attention mask \\( A \\) to protect information leakage, ensuring the learning process's integrity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.752, + 0.421, + 0.769 + ], + "angle": 0, + "content": "4.2. Reliable Pseudo-Label Filtering Module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The one-to-many training strategy, while effective, causes duplication prediction in the first stage. We introduce a pseudo-label filtering module to address this and improve the filtering of pseudo boxes rich in semantic content for refined query learning. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths. We employ m groups of ground truths \\(\\hat{g} = \\{\\hat{g}_1,\\hat{g}_2,\\dots ,\\hat{g}_m\\}\\) for one-to-many as" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.894, + 0.107 + ], + "angle": 0, + "content": "signment strategy and select the top-k predictions as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.118, + 0.894, + 0.168 + ], + "angle": 0, + "content": "\\[\n\\hat {\\sigma} _ {o n e 2 m a n y} = \\left\\{\\underset {\\sigma_ {j} \\in C _ {M} ^ {N}} {\\arg \\min } \\sum_ {k} ^ {M} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {g} _ {\\sigma_ {j} (k)} ^ {s}\\right) \\right\\} _ {j} ^ {| \\hat {y} ^ {t} |} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.178, + 0.895, + 0.316 + ], + "angle": 0, + "content": "where \\( C_N^M \\) represents the combination of \\( M \\) and \\( N \\), denoting that a subset of \\( M \\) proposals is associated with each pseudo box \\( \\hat{y}_j^t \\). Here, \\( m \\) is set to 6. Furthermore, we use the remaining predictions to filter out duplicates in the top-k predictions in the one-to-one matching branch. Through this improved selection scheme, we achieve a performance improvement of 0.4 mAP when \\( m \\) is set to 6, as shown in Table 5a. However, we observe no significant benefits when increasing \\( m \\) greater than 6, as detailed in Table 6a." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.329, + 0.632, + 0.345 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.353, + 0.602, + 0.367 + ], + "angle": 0, + "content": "5.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.376, + 0.894, + 0.513 + ], + "angle": 0, + "content": "We evaluate our approach on the MS-COCO [21] and Pascal VOC [6] datasets, benchmarking it against current SOTA SSOD methods. Following [51, 56], Sparse Semi-DETR is evaluated in three scenarios: COCO-Partial. We use \\(1\\%\\), \\(5\\%\\), \\(10\\%\\) of train2017 as label data and rest as unlabeled data. COCO-Full. We take train2017 as label data and unlabel2017 as unlabel data. VOC. We take VOC2007 as label data and VOC2012 as unlabel data. Evaluation metrics include \\(AP_{50:95}\\), \\(AP_{50}\\), and \\(AP_{75}\\) [51, 56]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.522, + 0.719, + 0.538 + ], + "angle": 0, + "content": "5.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.895, + 0.773 + ], + "angle": 0, + "content": "We set the quantity of DINO original object queries to 900. For the setting hyperparameters, following [56] : (1) In the COCO-Partial setting, we set the training iterations to 120k with a labeled to unlabeled data ratio of 1:4. The first 60k iterations adopt a one-to-many assignment strategy. (2) In the COCO-Full setting, Sparse Semi-DETR is trained for 240k iterations with labeled to unlabeled data ratio of 1:1. The first 120k iterations adopt a one-to-many assignment strategy. (3) In the VOC setting, we train the network for 60k iterations with a labeled to unlabeled data ratio of 1:4. The first 40k iterations adopt a one-to-many assignment strategy. For all experiments, the filtering threshold \\(\\sigma\\) value is 0.4. We set the value of m to 6 and the value of k to 4. We provide complete implementation details for each experiment in Appendix A1.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.785, + 0.74, + 0.803 + ], + "angle": 0, + "content": "6. Results and Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We evaluate Sparse Semi-DETR and compare it against current SOTA SSOD methods. Our results demonstrate the superior performance of Sparse Semi-DETR in these aspects: (1) its effectiveness compared to both one-stage and two-stage detectors, (2) its comparison with traditional DETR-based detectors, and (3) its exceptional proficiency in accurately" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5844" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.088, + 0.895, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.364, + 0.895, + 0.407 + ], + "angle": 0, + "content": "Figure 4. Visual comparison of Sparse Semi-DETR with the two previous approaches on the COCO \\(10\\%\\) label dataset. These results highlight Sparse Semi-DETR's capabilities, particularly in identifying small objects and those obscured by obstacles (as indicated by white arrows) in the third-row images. For optimal clarity and detail, please zoom in." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.471, + 0.451 + ], + "angle": 0, + "content": "detecting small and partially occluded objects. We provide more results details in Appendix A1.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.457, + 0.473, + 0.88 + ], + "angle": 0, + "content": "COCO-Partial benchmark. Sparse Semi-DETR outperforms the current SSOD methods in COCO-Partial across all experiment settings, as demonstrated in Table 1. (1) We compare our method to both one-stage and two-stage SSOD. Sparse Semi-DETR surpasses Dense Teacher by 8.52, 7.79, 7.17 mAP on \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) label data. It also outperforms PseCo by 8.47, 8.30, 8.24 mAP on \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) label data. Sparse Semi-DETR's superior performance as a semi-supervised object detector is achieved without needing hand-crafted components commonly used in two-stage and one-stage detectors. (2) When compared to DETR-based detectors, Sparse Semi-DETR outperforms omni-DETR by 3.30, 3.10, and 3.00 mAP and beats Semi-DETR by 0.40, 0.70, 0.80 mAP on \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) label data. (3) Sparse Semi-DETR's exceptional proficiency in precisely detecting small and partially obscured objects is a standout feature. In Figure 4, we visually compare Sparse Semi-DETR with the two preceding approaches using the COCO \\(10\\%\\) labeled dataset. These results demonstrate the impressive capabilities of Sparse Semi-DETR, particularly in its ability to identify small objects and objects concealed by obstacles, as highlighted in the third-row images by the white arrows. Table 2 exhibits a remarkable performance boost of Sparse Semi-DETR on small objects. It surpasses the Semi-DETR by 1.20, 0.90 and 1.70 mAP on small objects using \\(1\\%\\), \\(5\\%\\), and \\(10\\%\\) label data, respectively. It highlights the superior efficiency and accuracy of Sparse Semi-DETR in detecting smaller objects." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.886, + 0.471, + 0.902 + ], + "angle": 0, + "content": "COCO-Full benchmark. In Table 4, when incorporating" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.895, + 0.51 + ], + "angle": 0, + "content": "additional unlabeled2017 data, Sparse Semi-DETR demonstrates a substantial improvement, achieving an impressive \\(2.1\\mathrm{mAP}\\) gain and reaching a total of \\(51.3\\mathrm{mAP}\\). It surpasses the performance of Dense Teacher, PseCo, and Semi-DETR by 5.2, 5.2, and \\(0.9\\mathrm{mAP}\\), respectively, highlighting the effectiveness of Sparse Semi-DETR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.895, + 0.619 + ], + "angle": 0, + "content": "Pascal VOC benchmark. Sparse Semi-DETR exhibits a remarkable performance boost on the Pascal VOC benchmark, as shown in Table 3. It surpasses the supervised baseline by 5.1 improvement on \\(AP_{50}\\) and by 5.91 impressive increase on \\(AP_{50:95}\\). Furthermore, it outperforms all previously single-stage, two-stage, and DETR-based SSOD methods by a significant margin." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.632, + 0.665, + 0.646 + ], + "angle": 0, + "content": "6.1. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.895, + 0.717 + ], + "angle": 0, + "content": "This section ablates the key design choices of Sparse Semi-DETR. The experiments detailed in this section are executed on the MS COCO dataset with \\(10\\%\\) label data, employing DINO as the primary detector." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.895, + 0.854 + ], + "angle": 0, + "content": "Effect of Individual Component. We conduct three experiments to assess the efficacy of each module of Sparse Semi-DETR, as detailed in Table 5a. We employ Semi-DETR as our baseline model. Notably, integrating each component into Sparse Semi-DETR leads to consistent performance improvements. Specifically, adding the Query Refinement and Pseudo-Label Filtering modules yields a significant increase of \\(0.8\\mathrm{mAP}\\). These results confirm that each component of Sparse Semi-DETR enhances our model's performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Effect of Query Refinement Module. We examine the impact of the Query Refinement (QR) Module. In Table 5b, we explore various QR combinations to determine the most" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5845" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.127, + 0.089, + 0.846, + 0.316 + ], + "angle": 0, + "content": "
MethodsReferenceCOCO-Partial
1%5%10%
FCOS [42] (Supervised)-8.43 ± 0.0317.01 ± 0.0120.98 ± 0.01
DSL [3]CVPR2222.03 ± 0.28 (+13.98)30.87 ± 0.24 (+13.86)36.22 ± 0.18 (+15.24)
Unbiased Teacher v2 [28]CVPR2222.71 ± 0.42 (+14.28)30.08 ± 0.04 (+13.07)32.61 ± 0.03 (+11.63)
Dense Teacher [57]ECCV2222.38 ± 0.31 (+13.95)33.01 ± 0.14 (+16.00)37.13 ± 0.12 (+16.15)
Faster RCNN [35] (Supervised)-9.05 ± 0.1618.47 ± 0.2223.86 ± 0.81
Humble Teacher [41]CVPR2216.96 ± 0.38 (+7.91)27.70 ± 0.15 (+9.23)31.61 ± 0.28 (+7.75)
Instant-Teaching [58]CVPR2118.05 ± 0.15 (+9.00)26.75 ± 0.05 (+8.28)30.40 ± 0.05 (+6.54)
Soft Teacher [51]ICCV2120.46 ± 0.39 (+11.41)30.74 ± 0.08 (+12.27)34.04 ± 0.14 (+10.18)
PseCo [19]ECCV2222.43 ± 0.36 (+13.38)32.50 ± 0.08 (+14.03)36.06 ± 0.24 (+12.2)
DINO [55] (Supervised)-18.00 ± 0.2129.50 ± 0.1635.00 ± 0.12
Omni-DETR [46] (DINO)CVPR2227.60 (+9.60)37.70(+8.20)41.30 (+6.30)
Semi-DETR [56] (DINO)CVPR2330.5 ± 0.30 (+12.50)40.10 ± 0.15 (+10.6)43.5 ± 0.10 (+8.5)
Sparse Semi-DETR-30.9 ± 0.23 (+12.90)40.8 ± 0.12 (+11.30)44.3 ± 0.01 (+9.30)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.325, + 0.895, + 0.368 + ], + "angle": 0, + "content": "Table 1. Comparing Sparse Semi-DETR with other approaches on COCO-Partial setting. The results are the average across all five folds. Under the COCO-partial setting, FCOS serves as the baseline for one-stage detectors, Faster RCNN for two-stage detectors, and DINO for transformer-based end-to-end detectors." + }, + { + "type": "table", + "bbox": [ + 0.093, + 0.396, + 0.356, + 0.499 + ], + "angle": 0, + "content": "
MethodsLabelsCOCO-Partial
APSAPMAPL
Semi-DETR [56]1%13.631.240.8
5%23.043.153.7
10%25.246.858.0
Sparse Semi-DETR1%14.832.541.4
5%23.944.254.2
10%26.948.059.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.09, + 0.509, + 0.358, + 0.581 + ], + "angle": 0, + "content": "Table 2. Experimental results on COCO-partial settings for small, medium, and large objects. The results shown are the average across all five folds. We reproduce Semi-DETR results using their source code." + }, + { + "type": "table", + "bbox": [ + 0.369, + 0.381, + 0.616, + 0.527 + ], + "angle": 0, + "content": "
MethodsVOC12
AP50AP50:95
FCOS [42] (Supervised)71.3645.52
DSL [3]80.7056.80
Dense Teacher [57]79.8955.87
Faster RCNN [35] (Supervised)72.7542.04
STAC [39]77.4544.64
HumbleTeacher [41]80.9453.04
Instant-Teaching [58]79.2050.00
DINO [55] (Supervised)81.2059.60
Semi-DETR [56] (DINO)86.1065.20
Sparse Semi-DETR86.3065.51
" + }, + { + "type": "table_caption", + "bbox": [ + 0.366, + 0.537, + 0.618, + 0.592 + ], + "angle": 0, + "content": "Table 3. Experimental results on Pascal VOC protocol. Here, FCOS, Faster RCNN, and DINO are the supervised baselines." + }, + { + "type": "table", + "bbox": [ + 0.629, + 0.381, + 0.889, + 0.527 + ], + "angle": 0, + "content": "
MethodCOCO-Full (100%)
STAC [39] (18×)39.5 →0.3 39.2
Unbiased Teacher (9×)40.2 →1.1 41.3
SoftTeacher [51] (24×)40.9 →3.6 44.5
DSL [3] (12×)40.2 →3.6 43.8
Dense Teacher [57] (18×)41.2 →3.6 46.1
PseCo (24×)41.0 →5.1 46.1
Instant-Teaching [58] (24×)37.6 →0.27 40.2
Semi-DETR [56] (8×)48.6 →1.8 50.4
Sparse Semi-DETR (8×)49.2 →2.1 51.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.627, + 0.538, + 0.895, + 0.594 + ], + "angle": 0, + "content": "Table 4. Comparing Sparse Semi-DETR with other approaches on COCO-Full. Note that 1 denotes 30k training iterations, while an \\(\\mathbf{N}\\times\\) signifies N times 30k iterations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.473, + 0.862 + ], + "angle": 0, + "content": "effective design. Applying QR selectively to the student, teacher, or both networks, we find that employing QR on weak augmented image features \\( F_{t1} \\) and \\( F_{t2} \\), and integrating them into the student network with the original decoder queries yields the best results. Table 5c shows that processing \\( F_{t1} \\) features without MLP (in [56]) improves results. Table 5d presents our study on the impact of different query variants, where we observe that QR consistently outperforms other methods. Finally, Table 5e shows that using an attentional block in the QR module is more effective than simple concatenation or cosine similarity. We provide more analysis of the Query Refinement Module supplementary document. Figure 5 compares Sparse Semi-DETR and Semi-DETR. Sparse Semi-DETR, processing fewer but refined queries, demonstrates lower duplication rates in this training approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Effect of Reliable Pseudo-Label Filtering Module. In our analysis of the Pseudo-Label Filtering Module, we examine" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.895, + 0.788 + ], + "angle": 0, + "content": "the impact of various parameters. Table 6a shows that a smaller m results in lower performance due to the inclusion of poor-quality labels. Performance improves with a moderately larger m due to enhanced auxiliary loss. However, excessively large m values trigger NMS, negatively impacting performance. Additionally, in Table 6b, we analyze the selection of the k value and find that setting k to 4 yields the best performance. In Table 6c, the optimal performance for \\(\\sigma\\) is achieved at 0.4; values lower than this may lead to the generation of noisy pseudo-labels, whereas higher values can decrease the number of effective pseudo-labels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Limitation. We still have duplications when we apply the one-to-many training strategy in both stages. Table 7 illustrates that a one-to-many strategy for \\(120\\mathrm{k}\\) iterations with Sparse Semi-DETR achieves a \\(44.6\\mathrm{mAP}\\) using NMS. In comparison, \\(60\\mathrm{k}\\) iterations in the first stage attain a comparable \\(44.3\\mathrm{mAP}\\) without NMS. Future works can explore this aspect." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5846" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.146, + 0.089, + 0.554, + 0.167 + ], + "angle": 0, + "content": "
Query RefinementPseudo-Label FilteringmAP\\( AP_{50} \\)\\( AP_{75} \\)
XX43.558.946.0
✓X43.861.147.3
X✓43.960.546.3
✓✓44.361.747.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.249, + 0.17, + 0.45, + 0.182 + ], + "angle": 0, + "content": "(a) Effect of Individual Component." + }, + { + "type": "table", + "bbox": [ + 0.56, + 0.09, + 0.821, + 0.164 + ], + "angle": 0, + "content": "
TeacherStudentmAP\\( AP_{50} \\)\\( AP_{75} \\)
XX43.558.946.0
✓X43.861.247.2
X✓44.361.747.6
✓✓42.859.745.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.555, + 0.168, + 0.824, + 0.18 + ], + "angle": 0, + "content": "(b) Effect of QR on Student and Teacher module." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.187, + 0.296, + 0.242 + ], + "angle": 0, + "content": "
MLPmAPAP50AP75
✓43.760.946.9
X44.361.747.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.147, + 0.244, + 0.25, + 0.255 + ], + "angle": 0, + "content": "(c) Effect of MLP." + }, + { + "type": "table", + "bbox": [ + 0.304, + 0.184, + 0.578, + 0.247 + ], + "angle": 0, + "content": "
MethodmAPAP50AP75
Single-view Queries43.059.346.3
Cross-view Queries43.558.946.0
Query Refinement44.361.747.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.326, + 0.25, + 0.556, + 0.262 + ], + "angle": 0, + "content": "(d) Effect of different variants of queries." + }, + { + "type": "table", + "bbox": [ + 0.596, + 0.183, + 0.86, + 0.248 + ], + "angle": 0, + "content": "
MethodmAPAP50AP75
Simple Concat43.458.846.1
Cosine Similarity43.760.346.1
Attention Module44.361.747.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.599, + 0.25, + 0.857, + 0.262 + ], + "angle": 0, + "content": "(e) Effectiveness of Attentional module in QR." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.275, + 0.894, + 0.36 + ], + "angle": 0, + "content": "Table 5. Ablations for the proposed Sparse Semi-DETR on COCO \\(10\\%\\) Label dataset. (a) We analyze the effectiveness of each module of Sparse Semi-DETR. (b) We experiment with different QR combinations to identify the optimal design, applying QR selectively on the student, the teacher, or both. (c) We analyze the effect of using MLP layers for \\(F_{t1}\\) and \\(F_{s1}\\). Empirical observation reveals that we do not require MLP as in [56]. (d) We observe the effect of the attentional block in the Query Refinement module by replacing it with simple concatenation or cosine similarity. (e) We vary the type of object queries fed to the decoder with the decoder's original queries. The best results are highlighted." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.384, + 0.47, + 0.598 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.608, + 0.471, + 0.692 + ], + "angle": 0, + "content": "Figure 5. The top-row figures display Semi-DETR's detection results, and the bottom-row shows Sparse Semi-DETR's outcomes. Both networks were trained for 120k iterations using one-to-many and one-to-one strategies. Sparse Semi-DETR eliminates redundant bounding boxes in the bottom-left image and detects small objects, like knives, in the top-right image, as indicated by white arrows." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.196, + 0.737 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "In conclusion, we successfully address the inherent limitations of DETR-based semi-supervised object detection frameworks by introducing Sparse Semi-DETR. This novel solution effectively tackles overlapping predictions and the detection of small objects. Sparse Semi-DETR incorporates a Query Refinement Module to enhance object query quality, mainly benefiting the detection of small and partially obscured objects. Besides, it also introduces a Reliable PseudoLabel Filtering Module to filter out low-quality pseudolabels selectively, thereby enhancing overall detection accu" + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.385, + 0.644, + 0.47 + ], + "angle": 0, + "content": "
m (k=4)mAP
244.0
444.1
644.3
844.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.541, + 0.472, + 0.628, + 0.484 + ], + "angle": 0, + "content": "(a) Effect of m." + }, + { + "type": "table", + "bbox": [ + 0.651, + 0.386, + 0.772, + 0.47 + ], + "angle": 0, + "content": "
k (m=6)mAP
243.8
444.3
644.1
843.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.669, + 0.472, + 0.752, + 0.484 + ], + "angle": 0, + "content": "(b) Effect of k." + }, + { + "type": "table", + "bbox": [ + 0.778, + 0.385, + 0.869, + 0.47 + ], + "angle": 0, + "content": "
σmAP
0.243.2
0.343.8
0.444.3
0.544.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.781, + 0.472, + 0.864, + 0.484 + ], + "angle": 0, + "content": "(c) Effect of \\(\\sigma\\)" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.497, + 0.894, + 0.553 + ], + "angle": 0, + "content": "Table 6. Ablations for the Reliable Pseudo-Label Filtering Module on COCO \\(10\\%\\) Label dataset. We study the impact of various parameters as augmented ground truth (m), top pseudolabels selection (k) and filtering threshold \\((\\sigma)\\)." + }, + { + "type": "table", + "bbox": [ + 0.55, + 0.573, + 0.845, + 0.623 + ], + "angle": 0, + "content": "
Iterations40k60k80k100k120k
mAP43.544.344.043.844.6
without-NMSYYYYN
" + }, + { + "type": "table_caption", + "bbox": [ + 0.529, + 0.634, + 0.862, + 0.649 + ], + "angle": 0, + "content": "Table 7. Evaluating One-to-Many Assignment Strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.894, + 0.726 + ], + "angle": 0, + "content": "racy and consistency with the remaining high-quality labels. Our method outperforms existing SSOD approaches, with extensive experiments demonstrating its effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.894, + 0.775 + ], + "angle": 0, + "content": "Ethical considerations. We study semi-supervised models, and agree that standard ethical considerations for visual recognition are applicable to our work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.797, + 0.667, + 0.814 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.901 + ], + "angle": 0, + "content": "This work was in parts supported by the EU Horizon Europe Framework under grant agreements 101135724 (LUMINOUS) and 101092312 (AIRISE) and by the Federal Ministry of Education and Research of Germany (BMBF) under grant 01QE2227C (HERON)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5847" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Ting Cai and Kirthevasan Kandasamy. 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In International Conference on Learning Representations, 2021. 2, 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.956 + ], + "angle": 0, + "content": "5850" + } + ] +] \ No newline at end of file diff --git a/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_origin.pdf b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f577d1ae1c50aafc025ff24e18a3a07b99be8c84 --- /dev/null +++ b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/b3fec2a6-daae-4072-a5bd-8911b9d30c68_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4e8e6cbcc4bfcc0930eaf88c7aca278512a778ace724c83a0ca51527172a4e56 +size 9134035 diff --git a/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/full.md b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/full.md new file mode 100644 index 0000000000000000000000000000000000000000..3a151d5e18ff9bad9455c6bfb38ce29598bf1a7e --- /dev/null +++ b/2024/Sparse Semi-DETR_ Sparse Learnable Queries for Semi-Supervised Object Detection/full.md @@ -0,0 +1,314 @@ +# Sparse Semi-DETR: Sparse Learnable Queries for Semi-Supervised Object Detection + +Tahira Shehzadi $^{1,2,3}$ , Khurram Azeem Hashmi $^{1,2,3}$ , Didier Stricker $^{1,2,3}$ , Muhammad Zeshan Afzal $^{1,2,3}$ , $^{1}$ DFKI, $^{2}$ RPTU Kaiserslautern-Landau, $^{3}$ MindGarage-RPTU + +![](images/1b364a3d1886a39ededbdd60a4ea4ef356f66cba671910f0a481b6fdf703a8d7.jpg) +(a) Semi-DETR + +![](images/0476da3b7ee057933a49cf2f953fe71130ef9848e40dffb45ae3a7058232f753.jpg) +(c) Comparison of SSOD Methods +Figure 1. (a)-(b) Comparative Overview of SSOD advancements: Sparse Semi-DETR's major improvement lies in its Query Refinement Module and Reliable Pseudo-label Filtering Module, significantly enhancing detection of small or obscured objects and reliability in complex scenarios, surpassing all other methods as shown in the graph in (c). + +# Abstract + +In this paper, we address the limitations of the DETR-based semi-supervised object detection (SSOD) framework, particularly focusing on the challenges posed by the quality of object queries. In DETR-based SSOD, the one-to-one assignment strategy provides inaccurate pseudo-labels, while the one-to-many assignments strategy leads to overlapping predictions. These issues compromise training efficiency and degrade model performance, especially in detecting small or occluded objects. We introduce Sparse Semi-DETR, a novel transformer-based, end-to-end semi-supervised object detection solution to overcome these challenges. Sparse Semi-DETR incorporates a Query Refinement Module to enhance the quality of object queries, significantly improving detection capabilities for small and partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy and consistency. On the MS-COCO and Pascal VOC object detection benchmarks, Sparse Semi-DETR achieves a significant improvement over current state-of-the-art methods that highlight Sparse Semi-DETR's effectiveness in semi-supervised object detection, particularly in challenging scenarios involving small or par + +tially obscured objects. + +# 1. Introduction + +Semi-Supervised Object Detection (SSOD) aims to improve the effectiveness of fully supervised object detection through the integration of abundant unlabeled data [3, 12, 15, 19, 28, 39, 49-52, 58]. It has applications in diverse fields, ranging from autonomous vehicles [14, 20] to healthcare [31, 44], where obtaining extensive labeled datasets is often impractical or cost-prohibitive [1]. + +Several SSOD methods [3, 12, 15, 19, 28, 39, 49-52, 58] have been proposed. Two prevalent approaches in this domain are pseudo-labeling [27, 30, 39, 45, 50-52, 58] and consistency-based regularization [3, 12, 15, 19, 28, 49]. STAC [39] introduced a simple multi-stage SSOD training method with pseudo-labeling and consistency training, later simplified by a Teacher-Student framework for generating pseudo-labels [27]. Based on this framework, considerable research efforts have been directed towards enhancing the quality of pseudo-labels [51, 58]. These traditional SSOD methods are built upon conventional detectors like one-stage [33, 42] and two-stage [9, 35], which involve various manually designed components such as an + +chor boxes and non-maximum suppression (NMS). Employing object detection methods in SSOD poses several potential challenges that must be carefully dealt with to obtain reasonable performance. These factors include overfitting of the labeled data [37], pseudo-label noise [10], bias induced through label imbalance [17, 32], and poor detection performance on small objects [56]. Recently, DETR-based [2, 16, 18, 25, 38, 55, 59] SSOD methods [46, 56] remove the need for traditional components like NMS. + +Even though DETR-based SSOD [46, 56] has progressed remarkably, state-of-the-art methods possess some limitations. (1) DETR-based SSOD methods perform poorly in the detection of small objects, as shown in Figure 4. This is because these methods don't use multi-scale features [36] like Feature Pyramid Networks (FPN) [22], which play an important role in identifying smaller objects as in CNN-based SSOD methods [3, 12, 15, 19, 28, 49, 51, 52, 58]. Although recent advancements in DETR-based object detection [2, 16, 18, 25, 38, 55, 59] have improved the detection of small objects, their SSOD adaptation is still unable to cater this challenge effectively [56]. (2) SSOD approaches [51, 52, 56, 58] rely on handcrafted post-processing methods such as NMS [35]. This problem specifically appears in DETR-based SSOD when we use a large number of object queries and the one-to-many assignment strategy [56]. In DETR-based SSOD methods, this problem is partially solved using the one-to-one or hybrid (combination of one-to-one and one-to-many) assignment strategy. However, the hybrid assignment strategy is preferred because the one-to-one assignment strategy produces inaccurate pseudo-labels [46], thus resulting in inefficient learning. Although the number of duplicate bounding boxes is less in the hybrid strategy [56], the amount is high enough to impact object detection performance adversely, as depicted in Figure 5. (3) The pseudolabel generation produces both high and low-quality labels. The DETR-based SSOD methods lack an effective refinement strategy for one-to-many assignments, which is crucial for filtering out low-quality proposals. + +To address the above mentioned issues, we propose enhancing the state-of-the-art DETR-based SSOD approach, namely 'Sparse Semi-DETR', presented in Figure 1 (b). Our approach involves expanding its architecture by integrating a couple of novel modules designed to mitigate the identified shortcomings. The key module among these is the Query-Refinement module, as depicted in Figure 2 and explained in Figure 3. This module significantly improves the quality of the queries and reduces their numbers. The proposed module uses the low-level features from the backbone and high-level features extracted directly from weakly augmented images using ROI alignment [13]. Fusing these features results in overcoming the first shortcoming, i.e., detecting small and obscured objects, as shown in Figure 4. The attention mechanism drives the aggregation of the features, + +resulting in refined, high-quality features to carry forward. To ensure the quality of the query features, the attention mechanism is accompanied by a query-matching strategy for filtering irrelevant queries. Thus, the Query Refinement Module not only improves the quality of the queries but also reduces their numbers, giving rise to efficient processing. This module results in significantly fewer overlapping proposals, improving the performance overall, thereby solving the second limitation. Besides, we introduce a Reliable Pseudo-Label Filtering Module, as illustrated in Figure 2, inspired by Hybrid-DETR [16] to address the third limitation. Employing this module significantly reduces the low-quality pseudo-labels. Therefore, it further reduces the amount of duplicate predictions that may still occur after the second stage of the hybrid assignment strategy. Our approach provides better results than previous SSOD methods, as shown in Figure 1 (c). + +The key contributions of this work can be outlined as follows: + +1. We present Sparse Semi-DETR, a novel approach in semi-supervised object detection, introducing two novel contributions. To our knowledge, we are the first to examine and propose query refinement and low-quality proposal filtering for the one-to-many query assignment strategy. +2. We introduce a novel query refinement module designed to improve object query features, particularly in complex detection scenarios such as identifying small or partially obscured objects. This enhancement not only boosts performance but also aids in learning semantic feature invariance among object queries. +3. We introduce a Reliable Pseudo-Label Filtering Module specifically designed to reduce the effect of noisy pseudolabels. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths, enhancing the consistency of the learning process. +4. Sparse Semi-DETR outperforms current state-of-the-art methods on MS-COCO and Pascal VOC benchmarks. With only $10\%$ labeled data from MS-COCO using ResNet-50 backbone, it achieves a 44.3 mAP, exceeding prior baselines by 0.8 mAP. Additionally, when trained on the complete COCO set with extra unlabeled data, it further improves, rising from 49.2 to 51.3 mAP. + +# 2. Related Work + +# 2.1. Object Detection + +Object detection identifies and locates objects in images or videos. Deep learning-based object detection approaches are typically categorized into two primary groups: two-stage detectors [9, 35] and one-stage detectors [23, 26, 34, 42]. These methods depend on numerous heuristics, such as generating anchors and NMS. Recently, DEetection TRans + +former (DETR) [2] considers object detection as a set prediction problem, using transformer [43] to adeptly transform sparse object candidates [40] into precise target objects. Our Sparse Semi-DETR detects small or partially obscured objects in the DETR-based SSOD setting. Notably, our framework is compatible with various DETR-based detectors [4, 5, 7, 8, 24, 29, 47, 48, 59], offering flexibility in integration. + +# 2.2. Semi-Supervised Object Detection + +Most research in SSOD employs detectors categorized into three types: one-stage, two-stage, and DETR-based systems. One-stage STAC [39], an early SSOD, introduced a simple training strategy combining pseudo-labeling and consistency training, later streamlined by a student-teacher framework for easier pseudo-label generation [27]. DSL [3] introduced novel techniques including Adaptive Filtering, Aggregated Teacher, and uncertainty-consistency-regularization for improved generalization. Dense Teacher [57] introduced Dense Pseudo-Labels (DPL) for richer information and a region selection method to reduce noise. + +Two-stage. Humble Teacher [41] uses soft labels and a teacher ensemble to boost pseudo-label reliability, matching other results. Instant-Teaching [58] creates pseudo annotations from weak augmentations, treating them as ground truth under strong augmentations with Mixup [54]. Unbiased Teacher [27] tackles class imbalance in pseudo-labeling with focal loss, focusing on underrepresented classes. Soft Teacher [51] minimizes incorrect foreground proposal classification by applying teacher-provided confidence scores to reduce classification loss. PseCo [19] enhances detector performance by combining pseudo-labeling with label and feature consistency methods, also using focal loss to address class imbalance. + +DETR-based. Omni-DETR [46] is designed for omnisupervised detection and adapts to SSOD with a basic pseudo-label filtering method. It employs the one-to-one assignment strategy proposed in DETR [2], and encounters challenges when dealing with inaccurate pseudo-bounding boxes produced by the teacher network. These inaccuracies result in reduced performance, highlighting its limitations. Semi-DETR [56] adopts a stage-wise strategy, employing a one-to-many matching strategy in the first stage and switching to a one-to-one matching strategy in the second stage. This approach provides NMS-free end-to-end detection benefits but reduces performance compared to a one-to-many assignment strategy. Moreover, Omni-DETR and Semi-DETR struggle to detect small or occluded objects. Our work introduces an advanced query refinement module that significantly refines object queries, enhancing training efficiency and performance and leading to the detection of small or densely packed objects in the DETR-based SSOD framework. + +# 3. Preliminary + +In DETR-based SSOD, one-to-one assignment strategy, denoted by $\hat{\sigma}_{one2one}$ , is achieved by applying Hungarian algorithm between the predictions made by the student model and the pseudo-labels provided by the teacher model as follows: + +$$ +\hat {\sigma} _ {o n e 2 o n e} = \underset {\sigma \in \xi_ {N}} {\arg \min } \sum_ {j} ^ {N} \mathcal {L} _ {\text {m a t c h}} \left(\hat {y} _ {j} ^ {t}, \hat {y} _ {\sigma (j)} ^ {s}\right) \tag {1} +$$ + +where $\mathcal{L}_{\mathrm{match}}\left(\hat{y}_j^t,\hat{y}_{\sigma (j)}^s\right)$ is the matching cost between the pseudo-labels $\hat{y}_j^t$ generated by the teacher network and the predictions of the student network with index $\sigma (j)$ and $\xi_{N}$ is the permutation of $N$ elements. Semi-DETR [56] addresses the issue of imprecise initial pseudo-labels by shifting from a one-to-one to a one-to-many assignment strategy, increasing the number of positive object queries to improve detection accuracy: + +$$ +\hat {\sigma} _ {o n e 2 m a n y} = \left\{\underset {\sigma_ {j} \in C _ {M} ^ {N}} {\arg \min } \sum_ {k} ^ {M} \mathcal {L} _ {\text {m a t c h}} \left(\hat {y} _ {j} ^ {t}, \hat {y} _ {\sigma_ {j} (k)} ^ {s}\right) \right\} _ {j} ^ {| \hat {y} ^ {t} |} \tag {2} +$$ + +where $C_N^M$ represents the combination of $M$ and $N$ , denoting that a subset of $M$ proposals is associated with each pseudo box $\hat{y}_j^t$ . Semi-DETR initially adopts a one-to-many assignment to improve label quality, then shifts to one-to-one assignment for an NMS-free model. This approach adopts a one-to-many assignment strategy aimed at boosting performance, but it's less effective with small or occluded objects. + +# 4. Sparse Semi-DETR + +In semi-supervised learning, a collection of labeled data denoted as $D_{l}$ , where $D_{l} = \{x_{i}^{l},y_{i}^{l}\}_{i = 1}^{N_{l}}$ is given, along with a set of unlabeled data represented as $D_{u}$ , where $D_{u} = \{x_{i}^{u}\}_{i = 1}^{N_{u}}$ . Here, $N_{l}$ and $N_{u}$ correspond to the number of labeled and unlabeled data. The annotations $y_{i}^{l}$ for the label data $x^{l}$ contain object labels and bounding box information. The pipeline of the Sparse Semi-DETR framework is depicted in Figure 2. It introduces a Query Refinement Module for processing query features to enhance semantic representation for complex detection scenarios, such as identifying small or partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy. For comparison purposes, we employ DINO [55] with a ResNet-50 backbone. This section gives a detailed overview of the modules of Sparse Semi-DETR. We explain briefly our semi-supervised approach in Appendix A1.1. + +![](images/943cb47550f52d7b91751c4b5b0f63e437d3d12c5498de46c727e6797d5479a1.jpg) +Figure 2. An overview of the Sparse Semi-DETR framework. It contains two networks: the student network and the teacher network. Labeled data is used for student network training, employing a supervised loss. Unlabeled data is fed to the teacher network with weak augmentation and the student network with strong augmentation. The teacher network takes unlabeled data to generate pseudo-labels. Here, the query refinement module provides refined queries to avoid incorrect bipartite matching with teacher-generated pseudo-labels. For a detailed overview of the query refinement module, see Figure 3. Furthermore, a Reliable Pseudo-label Filtering strategy is employed to filter low-quality pseudo-labels progressively during training. + +# 4.1. Query Refinement + +Inspired by recent advancements in vision-based networks [11, 53], we introduce an innovative approach to enhance object query features. For each unlabeled image $I \in \mathbb{R}^{H \times W \times C}$ , we extract query features $F_{s1} \in \mathbb{R}^{b \times W_1 \times 256}$ from strongly augmented image $I$ . Similarly, we extract query features $F_{t1}$ from weakly augmented image $I$ , also in the same dimension. Subsequently, feature extraction from the image backbones occurs. This results in the generation of features $F_{s2}$ for the student and $F_{t2}$ for the teacher network as $\mathbb{R}^{b \times W_2 \times 256}$ . These features, encompassing both label and bounding box details, vary with the batch size, as indicated by $b$ . The feature sets $W_1$ and $W_2$ differ in size, with $W_2$ being substantially larger than $W_1$ . We provide a brief overview of each component of Query Refinement Module as illustrated in Figure 3. + +Query Refinement Module. In our approach, we handle multi-scale features $F_{t1}$ and $F_{t2}$ with a focus on effective aggregation. The finer details are encapsulated within the features $F_{t1}$ , while the features $F_{t2}$ encapsulate more abstract elements such as shapes and patterns. Simple aggregation of these features has been shown to degrade performance, as indicated in Table 5e). To solve this issue, we implement dual strategies to extract local and global information from high and low-resolution features. High-resolution features are crucial for detecting small objects. However, processing them with attentional operations is computationally demanding. To address this, we firstly convert the query label features $F_{t2} \in (\mathbb{R}^{b \times W_2 \times 256})$ into $F_{t2}' \in (\mathbb{R}^{b \times W_2 \times 16})$ by decreasing the channel dimension, and retaining the original resolution + +$b \times W_{2}$ . Then, we apply attentional mechanism on $F_{t2}^{\prime}$ to calculate the attentional weights $W_{k + q}$ in attention block as follows: + +$$ +W _ {k + q} = F _ {k} ^ {\prime} \cdot F _ {q} ^ {\prime}, \tag {3} +$$ + +$$ +\bar {\mathbf {W}} _ {k + q} = \frac {\exp \left(W _ {k + q}\right)}{\sum_ {l = 1} ^ {L} \exp \left(W _ {k + q}\right)}, \tag {4} +$$ + +where $W_{k + q}$ is the attentional weights of $F_{k}^{\prime}$ and $F_{q}^{\prime}$ , and $\bar{\mathbf{W}}_{k + q}$ is the normalized form of $W_{k + q}$ . Using normalized attention weights, we compute the enhanced queries representation $Q$ as follows: + +$$ +Q = \bar {\mathbf {W}} _ {k + q} \cdot F _ {v} ^ {\prime} \tag {5} +$$ + +now we find the similarity between the attentional $F_{t2}$ features and $F_{t1}$ features to obtain $F_{cs}^{\prime} \in \mathbb{R}^{b \times W_1 \times 16}$ from $Q \in \mathbb{R}^{b \times W_2 \times 16}$ as follows: + +$$ +F _ {c s} ^ {\prime} = \frac {\sum_ {i = l} ^ {n} P _ {l} Q _ {l}}{\sqrt {\sum_ {l = 1} ^ {n} P _ {l} ^ {2}} \sqrt {\sum_ {l = 1} ^ {n} Q _ {l} ^ {2}}} \tag {6} +$$ + +where $P$ and $Q$ are $F_{t1}$ and attentional $F_{t2}$ features, respectively. Then, we concatenate $F_{cs}'$ with $P$ to obtain refined query features. Interestingly, we observe a performance drop when our feature refinement strategy is applied to strongly augmented image features for the teacher network, as detailed in Table 5b. However, we achieve optimal results by concatenating strongly augmented image features and applying our refinement strategy to weakly augmented image features. Consequently, we proceed by concatenating the features $F_{s1}$ with $F_{s2}$ , thereby obtaining the query features + +![](images/14b2567cf53534b6dfee193e26585068654d372ab70c8e1febb7542d8ce17c21.jpg) +Figure 3. Overview of the Query Refinement Module. The query features from strong and weak augmented unlabeled images are refined through the Query Refinement Module. It amplifies the semantic representation of object queries and improves performance for small objects. For the best view, zoom in. + +$r_s$ . Note that $r_t$ , despite having a dimensional size equivalent to $F_{cs}^{\prime} + P$ , encapsulates substantially more intricate representations. This improved performance is due to the integration of high-resolution and low-resolution features. + +Then, we form the decoder queries in the student-teacher network by merging the teacher's original queries $q_{t}$ with refined queries $r_{s}$ , and the student's original queries $q_{s}$ with refined queries $r_{t}$ , respectively. This integration forms the inputs for the decoder as follows: + +$$ +\hat {o} _ {t}, o _ {t} = \operatorname {D e c} _ {t} \left(\left[ r _ {s}, q _ {t} \right], E _ {t} [ A ]\right) \tag {7} +$$ + +$$ +\hat {o} _ {s}, o _ {s} = \operatorname {D e c} _ {s} \left(\left[ r _ {t}, q _ {s} \right], E _ {s} [ A ]\right) \tag {8} +$$ + +Where $E_{s}$ and $E_{t}$ refer to the encoded image features. $\hat{o}_{s}$ and $\hat{o}_{t}$ indicate the decoded features of refined queries, while $o_{s}$ and $o_{t}$ represent the decoded features of original object queries. Here, $t$ is for teacher and $s$ for student network. Following DN-DETR [18], we use the attention mask $A$ to protect information leakage, ensuring the learning process's integrity. + +# 4.2. Reliable Pseudo-Label Filtering Module + +The one-to-many training strategy, while effective, causes duplication prediction in the first stage. We introduce a pseudo-label filtering module to address this and improve the filtering of pseudo boxes rich in semantic content for refined query learning. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths. We employ m groups of ground truths $\hat{g} = \{\hat{g}_1,\hat{g}_2,\dots ,\hat{g}_m\}$ for one-to-many as + +signment strategy and select the top-k predictions as follows: + +$$ +\hat {\sigma} _ {o n e 2 m a n y} = \left\{\underset {\sigma_ {j} \in C _ {M} ^ {N}} {\arg \min } \sum_ {k} ^ {M} \mathcal {L} _ {\text {m a t c h}} \left(\hat {y} _ {j} ^ {t}, \hat {g} _ {\sigma_ {j} (k)} ^ {s}\right) \right\} _ {j} ^ {| \hat {y} ^ {t} |} \tag {9} +$$ + +where $C_N^M$ represents the combination of $M$ and $N$ , denoting that a subset of $M$ proposals is associated with each pseudo box $\hat{y}_j^t$ . Here, $m$ is set to 6. Furthermore, we use the remaining predictions to filter out duplicates in the top-k predictions in the one-to-one matching branch. Through this improved selection scheme, we achieve a performance improvement of 0.4 mAP when $m$ is set to 6, as shown in Table 5a. However, we observe no significant benefits when increasing $m$ greater than 6, as detailed in Table 6a. + +# 5. Experiments + +# 5.1. Datasets + +We evaluate our approach on the MS-COCO [21] and Pascal VOC [6] datasets, benchmarking it against current SOTA SSOD methods. Following [51, 56], Sparse Semi-DETR is evaluated in three scenarios: COCO-Partial. We use $1\%$ , $5\%$ , $10\%$ of train2017 as label data and rest as unlabeled data. COCO-Full. We take train2017 as label data and unlabel2017 as unlabel data. VOC. We take VOC2007 as label data and VOC2012 as unlabel data. Evaluation metrics include $AP_{50:95}$ , $AP_{50}$ , and $AP_{75}$ [51, 56]. + +# 5.2. Implementation Details + +We set the quantity of DINO original object queries to 900. For the setting hyperparameters, following [56] : (1) In the COCO-Partial setting, we set the training iterations to 120k with a labeled to unlabeled data ratio of 1:4. The first 60k iterations adopt a one-to-many assignment strategy. (2) In the COCO-Full setting, Sparse Semi-DETR is trained for 240k iterations with labeled to unlabeled data ratio of 1:1. The first 120k iterations adopt a one-to-many assignment strategy. (3) In the VOC setting, we train the network for 60k iterations with a labeled to unlabeled data ratio of 1:4. The first 40k iterations adopt a one-to-many assignment strategy. For all experiments, the filtering threshold $\sigma$ value is 0.4. We set the value of m to 6 and the value of k to 4. We provide complete implementation details for each experiment in Appendix A1.2. + +# 6. Results and Comparisons + +We evaluate Sparse Semi-DETR and compare it against current SOTA SSOD methods. Our results demonstrate the superior performance of Sparse Semi-DETR in these aspects: (1) its effectiveness compared to both one-stage and two-stage detectors, (2) its comparison with traditional DETR-based detectors, and (3) its exceptional proficiency in accurately + +![](images/86aaba2dcbb76d319856d0d243962a44a7e965ca5c65fb7860c25008f1bfb4ed.jpg) +Figure 4. Visual comparison of Sparse Semi-DETR with the two previous approaches on the COCO $10\%$ label dataset. These results highlight Sparse Semi-DETR's capabilities, particularly in identifying small objects and those obscured by obstacles (as indicated by white arrows) in the third-row images. For optimal clarity and detail, please zoom in. + +detecting small and partially occluded objects. We provide more results details in Appendix A1.3. + +COCO-Partial benchmark. Sparse Semi-DETR outperforms the current SSOD methods in COCO-Partial across all experiment settings, as demonstrated in Table 1. (1) We compare our method to both one-stage and two-stage SSOD. Sparse Semi-DETR surpasses Dense Teacher by 8.52, 7.79, 7.17 mAP on $1\%$ , $5\%$ , and $10\%$ label data. It also outperforms PseCo by 8.47, 8.30, 8.24 mAP on $1\%$ , $5\%$ , and $10\%$ label data. Sparse Semi-DETR's superior performance as a semi-supervised object detector is achieved without needing hand-crafted components commonly used in two-stage and one-stage detectors. (2) When compared to DETR-based detectors, Sparse Semi-DETR outperforms omni-DETR by 3.30, 3.10, and 3.00 mAP and beats Semi-DETR by 0.40, 0.70, 0.80 mAP on $1\%$ , $5\%$ , and $10\%$ label data. (3) Sparse Semi-DETR's exceptional proficiency in precisely detecting small and partially obscured objects is a standout feature. In Figure 4, we visually compare Sparse Semi-DETR with the two preceding approaches using the COCO $10\%$ labeled dataset. These results demonstrate the impressive capabilities of Sparse Semi-DETR, particularly in its ability to identify small objects and objects concealed by obstacles, as highlighted in the third-row images by the white arrows. Table 2 exhibits a remarkable performance boost of Sparse Semi-DETR on small objects. It surpasses the Semi-DETR by 1.20, 0.90 and 1.70 mAP on small objects using $1\%$ , $5\%$ , and $10\%$ label data, respectively. It highlights the superior efficiency and accuracy of Sparse Semi-DETR in detecting smaller objects. + +COCO-Full benchmark. In Table 4, when incorporating + +additional unlabeled2017 data, Sparse Semi-DETR demonstrates a substantial improvement, achieving an impressive $2.1\mathrm{mAP}$ gain and reaching a total of $51.3\mathrm{mAP}$ . It surpasses the performance of Dense Teacher, PseCo, and Semi-DETR by 5.2, 5.2, and $0.9\mathrm{mAP}$ , respectively, highlighting the effectiveness of Sparse Semi-DETR. + +Pascal VOC benchmark. Sparse Semi-DETR exhibits a remarkable performance boost on the Pascal VOC benchmark, as shown in Table 3. It surpasses the supervised baseline by 5.1 improvement on $AP_{50}$ and by 5.91 impressive increase on $AP_{50:95}$ . Furthermore, it outperforms all previously single-stage, two-stage, and DETR-based SSOD methods by a significant margin. + +# 6.1. Ablation Studies + +This section ablates the key design choices of Sparse Semi-DETR. The experiments detailed in this section are executed on the MS COCO dataset with $10\%$ label data, employing DINO as the primary detector. + +Effect of Individual Component. We conduct three experiments to assess the efficacy of each module of Sparse Semi-DETR, as detailed in Table 5a. We employ Semi-DETR as our baseline model. Notably, integrating each component into Sparse Semi-DETR leads to consistent performance improvements. Specifically, adding the Query Refinement and Pseudo-Label Filtering modules yields a significant increase of $0.8\mathrm{mAP}$ . These results confirm that each component of Sparse Semi-DETR enhances our model's performance. + +Effect of Query Refinement Module. We examine the impact of the Query Refinement (QR) Module. In Table 5b, we explore various QR combinations to determine the most + +
MethodsReferenceCOCO-Partial
1%5%10%
FCOS [42] (Supervised)-8.43 ± 0.0317.01 ± 0.0120.98 ± 0.01
DSL [3]CVPR2222.03 ± 0.28 (+13.98)30.87 ± 0.24 (+13.86)36.22 ± 0.18 (+15.24)
Unbiased Teacher v2 [28]CVPR2222.71 ± 0.42 (+14.28)30.08 ± 0.04 (+13.07)32.61 ± 0.03 (+11.63)
Dense Teacher [57]ECCV2222.38 ± 0.31 (+13.95)33.01 ± 0.14 (+16.00)37.13 ± 0.12 (+16.15)
Faster RCNN [35] (Supervised)-9.05 ± 0.1618.47 ± 0.2223.86 ± 0.81
Humble Teacher [41]CVPR2216.96 ± 0.38 (+7.91)27.70 ± 0.15 (+9.23)31.61 ± 0.28 (+7.75)
Instant-Teaching [58]CVPR2118.05 ± 0.15 (+9.00)26.75 ± 0.05 (+8.28)30.40 ± 0.05 (+6.54)
Soft Teacher [51]ICCV2120.46 ± 0.39 (+11.41)30.74 ± 0.08 (+12.27)34.04 ± 0.14 (+10.18)
PseCo [19]ECCV2222.43 ± 0.36 (+13.38)32.50 ± 0.08 (+14.03)36.06 ± 0.24 (+12.2)
DINO [55] (Supervised)-18.00 ± 0.2129.50 ± 0.1635.00 ± 0.12
Omni-DETR [46] (DINO)CVPR2227.60 (+9.60)37.70(+8.20)41.30 (+6.30)
Semi-DETR [56] (DINO)CVPR2330.5 ± 0.30 (+12.50)40.10 ± 0.15 (+10.6)43.5 ± 0.10 (+8.5)
Sparse Semi-DETR-30.9 ± 0.23 (+12.90)40.8 ± 0.12 (+11.30)44.3 ± 0.01 (+9.30)
+ +Table 1. Comparing Sparse Semi-DETR with other approaches on COCO-Partial setting. The results are the average across all five folds. Under the COCO-partial setting, FCOS serves as the baseline for one-stage detectors, Faster RCNN for two-stage detectors, and DINO for transformer-based end-to-end detectors. + +
MethodsLabelsCOCO-Partial
APSAPMAPL
Semi-DETR [56]1%13.631.240.8
5%23.043.153.7
10%25.246.858.0
Sparse Semi-DETR1%14.832.541.4
5%23.944.254.2
10%26.948.059.6
+ +Table 2. Experimental results on COCO-partial settings for small, medium, and large objects. The results shown are the average across all five folds. We reproduce Semi-DETR results using their source code. + +
MethodsVOC12
AP50AP50:95
FCOS [42] (Supervised)71.3645.52
DSL [3]80.7056.80
Dense Teacher [57]79.8955.87
Faster RCNN [35] (Supervised)72.7542.04
STAC [39]77.4544.64
HumbleTeacher [41]80.9453.04
Instant-Teaching [58]79.2050.00
DINO [55] (Supervised)81.2059.60
Semi-DETR [56] (DINO)86.1065.20
Sparse Semi-DETR86.3065.51
+ +Table 3. Experimental results on Pascal VOC protocol. Here, FCOS, Faster RCNN, and DINO are the supervised baselines. + +
MethodCOCO-Full (100%)
STAC [39] (18×)39.5 →0.3 39.2
Unbiased Teacher (9×)40.2 →1.1 41.3
SoftTeacher [51] (24×)40.9 →3.6 44.5
DSL [3] (12×)40.2 →3.6 43.8
Dense Teacher [57] (18×)41.2 →3.6 46.1
PseCo (24×)41.0 →5.1 46.1
Instant-Teaching [58] (24×)37.6 →0.27 40.2
Semi-DETR [56] (8×)48.6 →1.8 50.4
Sparse Semi-DETR (8×)49.2 →2.1 51.3
+ +Table 4. Comparing Sparse Semi-DETR with other approaches on COCO-Full. Note that 1 denotes 30k training iterations, while an $\mathbf{N}\times$ signifies N times 30k iterations. + +effective design. Applying QR selectively to the student, teacher, or both networks, we find that employing QR on weak augmented image features $F_{t1}$ and $F_{t2}$ , and integrating them into the student network with the original decoder queries yields the best results. Table 5c shows that processing $F_{t1}$ features without MLP (in [56]) improves results. Table 5d presents our study on the impact of different query variants, where we observe that QR consistently outperforms other methods. Finally, Table 5e shows that using an attentional block in the QR module is more effective than simple concatenation or cosine similarity. We provide more analysis of the Query Refinement Module supplementary document. Figure 5 compares Sparse Semi-DETR and Semi-DETR. Sparse Semi-DETR, processing fewer but refined queries, demonstrates lower duplication rates in this training approach. + +Effect of Reliable Pseudo-Label Filtering Module. In our analysis of the Pseudo-Label Filtering Module, we examine + +the impact of various parameters. Table 6a shows that a smaller m results in lower performance due to the inclusion of poor-quality labels. Performance improves with a moderately larger m due to enhanced auxiliary loss. However, excessively large m values trigger NMS, negatively impacting performance. Additionally, in Table 6b, we analyze the selection of the k value and find that setting k to 4 yields the best performance. In Table 6c, the optimal performance for $\sigma$ is achieved at 0.4; values lower than this may lead to the generation of noisy pseudo-labels, whereas higher values can decrease the number of effective pseudo-labels. + +Limitation. We still have duplications when we apply the one-to-many training strategy in both stages. Table 7 illustrates that a one-to-many strategy for $120\mathrm{k}$ iterations with Sparse Semi-DETR achieves a $44.6\mathrm{mAP}$ using NMS. In comparison, $60\mathrm{k}$ iterations in the first stage attain a comparable $44.3\mathrm{mAP}$ without NMS. Future works can explore this aspect. + +
Query RefinementPseudo-Label FilteringmAP\( AP_{50} \)\( AP_{75} \)
XX43.558.946.0
✓X43.861.147.3
X✓43.960.546.3
✓✓44.361.747.6
+ +(a) Effect of Individual Component. + +
TeacherStudentmAP\( AP_{50} \)\( AP_{75} \)
XX43.558.946.0
✓X43.861.247.2
X✓44.361.747.6
✓✓42.859.745.8
+ +(b) Effect of QR on Student and Teacher module. + +
MLPmAPAP50AP75
✓43.760.946.9
X44.361.747.6
+ +(c) Effect of MLP. + +
MethodmAPAP50AP75
Single-view Queries43.059.346.3
Cross-view Queries43.558.946.0
Query Refinement44.361.747.6
+ +(d) Effect of different variants of queries. + +
MethodmAPAP50AP75
Simple Concat43.458.846.1
Cosine Similarity43.760.346.1
Attention Module44.361.747.6
+ +![](images/cfdd17fb3d41945b962b35978fa46710dd387c43db79a3918948a8c9cfaca4e5.jpg) +Figure 5. The top-row figures display Semi-DETR's detection results, and the bottom-row shows Sparse Semi-DETR's outcomes. Both networks were trained for 120k iterations using one-to-many and one-to-one strategies. Sparse Semi-DETR eliminates redundant bounding boxes in the bottom-left image and detects small objects, like knives, in the top-right image, as indicated by white arrows. + +# 7. Conclusion + +In conclusion, we successfully address the inherent limitations of DETR-based semi-supervised object detection frameworks by introducing Sparse Semi-DETR. This novel solution effectively tackles overlapping predictions and the detection of small objects. Sparse Semi-DETR incorporates a Query Refinement Module to enhance object query quality, mainly benefiting the detection of small and partially obscured objects. Besides, it also introduces a Reliable PseudoLabel Filtering Module to filter out low-quality pseudolabels selectively, thereby enhancing overall detection accu + +(e) Effectiveness of Attentional module in QR. +Table 5. Ablations for the proposed Sparse Semi-DETR on COCO $10\%$ Label dataset. (a) We analyze the effectiveness of each module of Sparse Semi-DETR. (b) We experiment with different QR combinations to identify the optimal design, applying QR selectively on the student, the teacher, or both. (c) We analyze the effect of using MLP layers for $F_{t1}$ and $F_{s1}$ . Empirical observation reveals that we do not require MLP as in [56]. (d) We observe the effect of the attentional block in the Query Refinement module by replacing it with simple concatenation or cosine similarity. (e) We vary the type of object queries fed to the decoder with the decoder's original queries. The best results are highlighted. + +
m (k=4)mAP
244.0
444.1
644.3
844.2
+ +(a) Effect of m. + +
k (m=6)mAP
243.8
444.3
644.1
843.9
+ +(b) Effect of k. + +
σmAP
0.243.2
0.343.8
0.444.3
0.544.0
+ +(c) Effect of $\sigma$ +Table 6. Ablations for the Reliable Pseudo-Label Filtering Module on COCO $10\%$ Label dataset. We study the impact of various parameters as augmented ground truth (m), top pseudolabels selection (k) and filtering threshold $(\sigma)$ . + +
Iterations40k60k80k100k120k
mAP43.544.344.043.844.6
without-NMSYYYYN
+ +Table 7. Evaluating One-to-Many Assignment Strategy. + +racy and consistency with the remaining high-quality labels. Our method outperforms existing SSOD approaches, with extensive experiments demonstrating its effectiveness. + +Ethical considerations. We study semi-supervised models, and agree that standard ethical considerations for visual recognition are applicable to our work. + +# Acknowledgements + +This work was in parts supported by the EU Horizon Europe Framework under grant agreements 101135724 (LUMINOUS) and 101092312 (AIRISE) and by the Federal Ministry of Education and Research of Germany (BMBF) under grant 01QE2227C (HERON). + +# References + +[1] Ting Cai and Kirthevasan Kandasamy. Active cost-aware labeling of streaming data. In International Conference on Artificial Intelligence and Statistics, pages 9117-9136. PMLR, 2023. 1 +[2] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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CoRR, abs/2106.09018, 2021. 1, 2, 3, 5, 7 + +[52] Qize Yang, Xihan Wei, Biao Wang, Xian-Sheng Hua, and Lei Zhang. Interactive self-training with mean teachers for semi-supervised object detection. In 2021 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5937-5946, 2021. 1, 2 +[53] Xin Yu, Peng Dai, Wenbo Li, Lan Ma, Jiajun Shen, Jia Li, and Xiaojuan Qi. Towards efficient and scale-robust ultrahigh-definition image demoiring. In European Conference on Computer Vision, pages 646–662. Springer, 2022. 4 +[54] Hongyi Zhang, Moustapha Cisse, Yann Dauphin, and David Lopez-Paz. mixup: Beyond empirical risk minimization. ArXiv, abs/1710.09412, 2017. 3 +[55] Hao Zhang, Feng Li, Shilong Liu, Lei Zhang, Hang Su, Jun Zhu, Lionel Ni, and Heung-Yeung Shum. DINO: DETR with improved denoising anchor boxes for end-to-end object detection. 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(a)-(b) Comparative Overview of SSOD advancements: Sparse Semi-DETR's major improvement lies in its Query Refinement Module and Reliable Pseudo-label Filtering Module, significantly enhancing detection of small or obscured objects and reliability in complex scenarios, surpassing all other methods as shown in the graph in (c)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 412, + 192, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 412, + 192, + 424 + ], + "spans": [ + { + "bbox": [ + 143, + 412, + 192, + 424 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 450, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 290, + 715 + ], + "type": "text", + "content": "In this paper, we address the limitations of the DETR-based semi-supervised object detection (SSOD) framework, particularly focusing on the challenges posed by the quality of object queries. In DETR-based SSOD, the one-to-one assignment strategy provides inaccurate pseudo-labels, while the one-to-many assignments strategy leads to overlapping predictions. These issues compromise training efficiency and degrade model performance, especially in detecting small or occluded objects. We introduce Sparse Semi-DETR, a novel transformer-based, end-to-end semi-supervised object detection solution to overcome these challenges. Sparse Semi-DETR incorporates a Query Refinement Module to enhance the quality of object queries, significantly improving detection capabilities for small and partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy and consistency. On the MS-COCO and Pascal VOC object detection benchmarks, Sparse Semi-DETR achieves a significant improvement over current state-of-the-art methods that highlight Sparse Semi-DETR's effectiveness in semi-supervised object detection, particularly in challenging scenarios involving small or par" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 413, + 401, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 401, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 401, + 426 + ], + "type": "text", + "content": "tially obscured objects." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 452, + 387, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 387, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 387, + 464 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 473, + 547, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 556 + ], + "type": "text", + "content": "Semi-Supervised Object Detection (SSOD) aims to improve the effectiveness of fully supervised object detection through the integration of abundant unlabeled data [3, 12, 15, 19, 28, 39, 49-52, 58]. It has applications in diverse fields, ranging from autonomous vehicles [14, 20] to healthcare [31, 44], where obtaining extensive labeled datasets is often impractical or cost-prohibitive [1]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 548, + 714 + ], + "type": "text", + "content": "Several SSOD methods [3, 12, 15, 19, 28, 39, 49-52, 58] have been proposed. Two prevalent approaches in this domain are pseudo-labeling [27, 30, 39, 45, 50-52, 58] and consistency-based regularization [3, 12, 15, 19, 28, 49]. STAC [39] introduced a simple multi-stage SSOD training method with pseudo-labeling and consistency training, later simplified by a Teacher-Student framework for generating pseudo-labels [27]. Based on this framework, considerable research efforts have been directed towards enhancing the quality of pseudo-labels [51, 58]. These traditional SSOD methods are built upon conventional detectors like one-stage [33, 42] and two-stage [9, 35], which involve various manually designed components such as an" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5840" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "chor boxes and non-maximum suppression (NMS). Employing object detection methods in SSOD poses several potential challenges that must be carefully dealt with to obtain reasonable performance. These factors include overfitting of the labeled data [37], pseudo-label noise [10], bias induced through label imbalance [17, 32], and poor detection performance on small objects [56]. Recently, DETR-based [2, 16, 18, 25, 38, 55, 59] SSOD methods [46, 56] remove the need for traditional components like NMS." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 183, + 289, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 183, + 289, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 183, + 289, + 531 + ], + "type": "text", + "content": "Even though DETR-based SSOD [46, 56] has progressed remarkably, state-of-the-art methods possess some limitations. (1) DETR-based SSOD methods perform poorly in the detection of small objects, as shown in Figure 4. This is because these methods don't use multi-scale features [36] like Feature Pyramid Networks (FPN) [22], which play an important role in identifying smaller objects as in CNN-based SSOD methods [3, 12, 15, 19, 28, 49, 51, 52, 58]. Although recent advancements in DETR-based object detection [2, 16, 18, 25, 38, 55, 59] have improved the detection of small objects, their SSOD adaptation is still unable to cater this challenge effectively [56]. (2) SSOD approaches [51, 52, 56, 58] rely on handcrafted post-processing methods such as NMS [35]. This problem specifically appears in DETR-based SSOD when we use a large number of object queries and the one-to-many assignment strategy [56]. In DETR-based SSOD methods, this problem is partially solved using the one-to-one or hybrid (combination of one-to-one and one-to-many) assignment strategy. However, the hybrid assignment strategy is preferred because the one-to-one assignment strategy produces inaccurate pseudo-labels [46], thus resulting in inefficient learning. Although the number of duplicate bounding boxes is less in the hybrid strategy [56], the amount is high enough to impact object detection performance adversely, as depicted in Figure 5. (3) The pseudolabel generation produces both high and low-quality labels. The DETR-based SSOD methods lack an effective refinement strategy for one-to-many assignments, which is crucial for filtering out low-quality proposals." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 714 + ], + "type": "text", + "content": "To address the above mentioned issues, we propose enhancing the state-of-the-art DETR-based SSOD approach, namely 'Sparse Semi-DETR', presented in Figure 1 (b). Our approach involves expanding its architecture by integrating a couple of novel modules designed to mitigate the identified shortcomings. The key module among these is the Query-Refinement module, as depicted in Figure 2 and explained in Figure 3. This module significantly improves the quality of the queries and reduces their numbers. The proposed module uses the low-level features from the backbone and high-level features extracted directly from weakly augmented images using ROI alignment [13]. Fusing these features results in overcoming the first shortcoming, i.e., detecting small and obscured objects, as shown in Figure 4. The attention mechanism drives the aggregation of the features," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 276 + ], + "type": "text", + "content": "resulting in refined, high-quality features to carry forward. To ensure the quality of the query features, the attention mechanism is accompanied by a query-matching strategy for filtering irrelevant queries. Thus, the Query Refinement Module not only improves the quality of the queries but also reduces their numbers, giving rise to efficient processing. This module results in significantly fewer overlapping proposals, improving the performance overall, thereby solving the second limitation. Besides, we introduce a Reliable Pseudo-Label Filtering Module, as illustrated in Figure 2, inspired by Hybrid-DETR [16] to address the third limitation. Employing this module significantly reduces the low-quality pseudo-labels. Therefore, it further reduces the amount of duplicate predictions that may still occur after the second stage of the hybrid assignment strategy. Our approach provides better results than previous SSOD methods, as shown in Figure 1 (c)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 277, + 547, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 277, + 547, + 300 + ], + "spans": [ + { + "bbox": [ + 305, + 277, + 547, + 300 + ], + "type": "text", + "content": "The key contributions of this work can be outlined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 301, + 547, + 588 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 307, + 301, + 547, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 301, + 547, + 361 + ], + "spans": [ + { + "bbox": [ + 307, + 301, + 547, + 361 + ], + "type": "text", + "content": "1. We present Sparse Semi-DETR, a novel approach in semi-supervised object detection, introducing two novel contributions. To our knowledge, we are the first to examine and propose query refinement and low-quality proposal filtering for the one-to-many query assignment strategy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 361, + 547, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 547, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 547, + 433 + ], + "type": "text", + "content": "2. We introduce a novel query refinement module designed to improve object query features, particularly in complex detection scenarios such as identifying small or partially obscured objects. This enhancement not only boosts performance but also aids in learning semantic feature invariance among object queries." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 433, + 547, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 547, + 505 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 547, + 505 + ], + "type": "text", + "content": "3. We introduce a Reliable Pseudo-Label Filtering Module specifically designed to reduce the effect of noisy pseudolabels. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths, enhancing the consistency of the learning process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 505, + 547, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 505, + 547, + 588 + ], + "spans": [ + { + "bbox": [ + 306, + 505, + 547, + 588 + ], + "type": "text", + "content": "4. Sparse Semi-DETR outperforms current state-of-the-art methods on MS-COCO and Pascal VOC benchmarks. With only " + }, + { + "bbox": [ + 306, + 505, + 547, + 588 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 306, + 505, + 547, + 588 + ], + "type": "text", + "content": " labeled data from MS-COCO using ResNet-50 backbone, it achieves a 44.3 mAP, exceeding prior baselines by 0.8 mAP. Additionally, when trained on the complete COCO set with extra unlabeled data, it further improves, rising from 49.2 to 51.3 mAP." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 601, + 392, + 615 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 601, + 392, + 615 + ], + "spans": [ + { + "bbox": [ + 306, + 601, + 392, + 615 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 622, + 408, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 408, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 408, + 635 + ], + "type": "text", + "content": "2.1. Object Detection" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "content": "Object detection identifies and locates objects in images or videos. Deep learning-based object detection approaches are typically categorized into two primary groups: two-stage detectors [9, 35] and one-stage detectors [23, 26, 34, 42]. These methods depend on numerous heuristics, such as generating anchors and NMS. Recently, DEetection TRans" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5841" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "former (DETR) [2] considers object detection as a set prediction problem, using transformer [43] to adeptly transform sparse object candidates [40] into precise target objects. Our Sparse Semi-DETR detects small or partially obscured objects in the DETR-based SSOD setting. Notably, our framework is compatible with various DETR-based detectors [4, 5, 7, 8, 24, 29, 47, 48, 59], offering flexibility in integration." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 178, + 230, + 190 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 230, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 230, + 190 + ], + "type": "text", + "content": "2.2. Semi-Supervised Object Detection" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 197, + 289, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 197, + 289, + 328 + ], + "spans": [ + { + "bbox": [ + 46, + 197, + 289, + 328 + ], + "type": "text", + "content": "Most research in SSOD employs detectors categorized into three types: one-stage, two-stage, and DETR-based systems. One-stage STAC [39], an early SSOD, introduced a simple training strategy combining pseudo-labeling and consistency training, later streamlined by a student-teacher framework for easier pseudo-label generation [27]. DSL [3] introduced novel techniques including Adaptive Filtering, Aggregated Teacher, and uncertainty-consistency-regularization for improved generalization. Dense Teacher [57] introduced Dense Pseudo-Labels (DPL) for richer information and a region selection method to reduce noise." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 330, + 289, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 330, + 289, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 330, + 289, + 484 + ], + "type": "text", + "content": "Two-stage. Humble Teacher [41] uses soft labels and a teacher ensemble to boost pseudo-label reliability, matching other results. Instant-Teaching [58] creates pseudo annotations from weak augmentations, treating them as ground truth under strong augmentations with Mixup [54]. Unbiased Teacher [27] tackles class imbalance in pseudo-labeling with focal loss, focusing on underrepresented classes. Soft Teacher [51] minimizes incorrect foreground proposal classification by applying teacher-provided confidence scores to reduce classification loss. PseCo [19] enhances detector performance by combining pseudo-labeling with label and feature consistency methods, also using focal loss to address class imbalance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 289, + 713 + ], + "type": "text", + "content": "DETR-based. Omni-DETR [46] is designed for omnisupervised detection and adapts to SSOD with a basic pseudo-label filtering method. It employs the one-to-one assignment strategy proposed in DETR [2], and encounters challenges when dealing with inaccurate pseudo-bounding boxes produced by the teacher network. These inaccuracies result in reduced performance, highlighting its limitations. Semi-DETR [56] adopts a stage-wise strategy, employing a one-to-many matching strategy in the first stage and switching to a one-to-one matching strategy in the second stage. This approach provides NMS-free end-to-end detection benefits but reduces performance compared to a one-to-many assignment strategy. Moreover, Omni-DETR and Semi-DETR struggle to detect small or occluded objects. Our work introduces an advanced query refinement module that significantly refines object queries, enhancing training efficiency and performance and leading to the detection of small or densely packed objects in the DETR-based SSOD framework." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 71, + 384, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 384, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 384, + 85 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 92, + 547, + 141 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 92, + 547, + 141 + ], + "spans": [ + { + "bbox": [ + 305, + 92, + 547, + 141 + ], + "type": "text", + "content": "In DETR-based SSOD, one-to-one assignment strategy, denoted by " + }, + { + "bbox": [ + 305, + 92, + 547, + 141 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}_{one2one}" + }, + { + "bbox": [ + 305, + 92, + 547, + 141 + ], + "type": "text", + "content": ", is achieved by applying Hungarian algorithm between the predictions made by the student model and the pseudo-labels provided by the teacher model as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 338, + 152, + 547, + 186 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 338, + 152, + 547, + 186 + ], + "spans": [ + { + "bbox": [ + 338, + 152, + 547, + 186 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {o n e 2 o n e} = \\underset {\\sigma \\in \\xi_ {N}} {\\arg \\min } \\sum_ {j} ^ {N} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {y} _ {\\sigma (j)} ^ {s}\\right) \\tag {1}", + "image_path": "2d2b1e7325de89ba05dacf282588169cd8030faf3a760ab5070f790787c124ea.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{match}}\\left(\\hat{y}_j^t,\\hat{y}_{\\sigma (j)}^s\\right)" + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "content": " is the matching cost between the pseudo-labels " + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "inline_equation", + "content": "\\hat{y}_j^t" + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "content": " generated by the teacher network and the predictions of the student network with index " + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "inline_equation", + "content": "\\sigma (j)" + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "inline_equation", + "content": "\\xi_{N}" + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "content": " is the permutation of " + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 199, + 547, + 301 + ], + "type": "text", + "content": " elements. Semi-DETR [56] addresses the issue of imprecise initial pseudo-labels by shifting from a one-to-one to a one-to-many assignment strategy, increasing the number of positive object queries to improve detection accuracy:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 312, + 546, + 352 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 312, + 546, + 352 + ], + "spans": [ + { + "bbox": [ + 312, + 312, + 546, + 352 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {o n e 2 m a n y} = \\left\\{\\underset {\\sigma_ {j} \\in C _ {M} ^ {N}} {\\arg \\min } \\sum_ {k} ^ {M} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {y} _ {\\sigma_ {j} (k)} ^ {s}\\right) \\right\\} _ {j} ^ {| \\hat {y} ^ {t} |} \\tag {2}", + "image_path": "1eef331999eba478bb7966ee7ac07341dda9bf684398f9ae0a049c7bc0b1791b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "inline_equation", + "content": "C_N^M" + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "content": " represents the combination of " + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "content": ", denoting that a subset of " + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "content": " proposals is associated with each pseudo box " + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "inline_equation", + "content": "\\hat{y}_j^t" + }, + { + "bbox": [ + 304, + 363, + 547, + 460 + ], + "type": "text", + "content": ". Semi-DETR initially adopts a one-to-many assignment to improve label quality, then shifts to one-to-one assignment for an NMS-free model. This approach adopts a one-to-many assignment strategy aimed at boosting performance, but it's less effective with small or occluded objects." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 474, + 422, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 474, + 422, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 474, + 422, + 488 + ], + "type": "text", + "content": "4. Sparse Semi-DETR" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": "In semi-supervised learning, a collection of labeled data denoted as " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "D_{l}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "D_{l} = \\{x_{i}^{l},y_{i}^{l}\\}_{i = 1}^{N_{l}}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": " is given, along with a set of unlabeled data represented as " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "D_{u}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "D_{u} = \\{x_{i}^{u}\\}_{i = 1}^{N_{u}}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "N_{u}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": " correspond to the number of labeled and unlabeled data. The annotations " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "y_{i}^{l}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": " for the label data " + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "inline_equation", + "content": "x^{l}" + }, + { + "bbox": [ + 304, + 496, + 548, + 714 + ], + "type": "text", + "content": " contain object labels and bounding box information. The pipeline of the Sparse Semi-DETR framework is depicted in Figure 2. It introduces a Query Refinement Module for processing query features to enhance semantic representation for complex detection scenarios, such as identifying small or partially obscured objects. Additionally, we integrate a Reliable Pseudo-Label Filtering Module that selectively filters high-quality pseudo-labels, thereby enhancing detection accuracy. For comparison purposes, we employ DINO [55] with a ResNet-50 backbone. This section gives a detailed overview of the modules of Sparse Semi-DETR. We explain briefly our semi-supervised approach in Appendix A1.1." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5842" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 71, + 521, + 249 + ], + "blocks": [ + { + "bbox": [ + 72, + 71, + 521, + 249 + ], + "lines": [ + { + "bbox": [ + 72, + 71, + 521, + 249 + ], + "spans": [ + { + "bbox": [ + 72, + 71, + 521, + 249 + ], + "type": "image", + "image_path": "943cb47550f52d7b91751c4b5b0f63e437d3d12c5498de46c727e6797d5479a1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 263, + 545, + 330 + ], + "lines": [ + { + "bbox": [ + 46, + 263, + 545, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 545, + 330 + ], + "type": "text", + "content": "Figure 2. An overview of the Sparse Semi-DETR framework. It contains two networks: the student network and the teacher network. Labeled data is used for student network training, employing a supervised loss. Unlabeled data is fed to the teacher network with weak augmentation and the student network with strong augmentation. The teacher network takes unlabeled data to generate pseudo-labels. Here, the query refinement module provides refined queries to avoid incorrect bipartite matching with teacher-generated pseudo-labels. For a detailed overview of the query refinement module, see Figure 3. Furthermore, a Reliable Pseudo-label Filtering strategy is employed to filter low-quality pseudo-labels progressively during training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 340, + 156, + 353 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 156, + 353 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 156, + 353 + ], + "type": "text", + "content": "4.1. Query Refinement" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": "Inspired by recent advancements in vision-based networks [11, 53], we introduce an innovative approach to enhance object query features. For each unlabeled image " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": ", we extract query features " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "F_{s1} \\in \\mathbb{R}^{b \\times W_1 \\times 256}" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " from strongly augmented image " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": ". Similarly, we extract query features " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " from weakly augmented image " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": ", also in the same dimension. Subsequently, feature extraction from the image backbones occurs. This results in the generation of features " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "F_{s2}" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " for the student and " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "F_{t2}" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " for the teacher network as " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{b \\times W_2 \\times 256}" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": ". These features, encompassing both label and bounding box details, vary with the batch size, as indicated by " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "b" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": ". The feature sets " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "W_1" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "W_2" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " differ in size, with " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "W_2" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": " being substantially larger than " + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "inline_equation", + "content": "W_1" + }, + { + "bbox": [ + 46, + 363, + 287, + 542 + ], + "type": "text", + "content": ". We provide a brief overview of each component of Query Refinement Module as illustrated in Figure 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Query Refinement Module. In our approach, we handle multi-scale features " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{t2}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " with a focus on effective aggregation. The finer details are encapsulated within the features " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": ", while the features " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{t2}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " encapsulate more abstract elements such as shapes and patterns. Simple aggregation of these features has been shown to degrade performance, as indicated in Table 5e). To solve this issue, we implement dual strategies to extract local and global information from high and low-resolution features. High-resolution features are crucial for detecting small objects. However, processing them with attentional operations is computationally demanding. To address this, we firstly convert the query label features " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{t2} \\in (\\mathbb{R}^{b \\times W_2 \\times 256})" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "F_{t2}' \\in (\\mathbb{R}^{b \\times W_2 \\times 16})" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " by decreasing the channel dimension, and retaining the original resolution" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "inline_equation", + "content": "b \\times W_{2}" + }, + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "text", + "content": ". Then, we apply attentional mechanism on " + }, + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "inline_equation", + "content": "F_{t2}^{\\prime}" + }, + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "text", + "content": " to calculate the attentional weights " + }, + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "inline_equation", + "content": "W_{k + q}" + }, + { + "bbox": [ + 305, + 340, + 545, + 375 + ], + "type": "text", + "content": " in attention block as follows:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 389, + 376, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 389, + 376, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 389, + 376, + 545, + 392 + ], + "type": "interline_equation", + "content": "W _ {k + q} = F _ {k} ^ {\\prime} \\cdot F _ {q} ^ {\\prime}, \\tag {3}", + "image_path": "478835df5acb584c96e401013d783fd90ac0b7d797c346e258d5f6f923678bec.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 365, + 396, + 545, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 396, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 365, + 396, + 545, + 426 + ], + "type": "interline_equation", + "content": "\\bar {\\mathbf {W}} _ {k + q} = \\frac {\\exp \\left(W _ {k + q}\\right)}{\\sum_ {l = 1} ^ {L} \\exp \\left(W _ {k + q}\\right)}, \\tag {4}", + "image_path": "611ef61f3d4e329ae462d55d84c04edcba9fddf094130fc5582e254700d4609f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "inline_equation", + "content": "W_{k + q}" + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": " is the attentional weights of " + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "inline_equation", + "content": "F_{k}^{\\prime}" + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "inline_equation", + "content": "F_{q}^{\\prime}" + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{W}}_{k + q}" + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": " is the normalized form of " + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "inline_equation", + "content": "W_{k + q}" + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": ". Using normalized attention weights, we compute the enhanced queries representation " + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 430, + 547, + 479 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 391, + 489, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 489, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 391, + 489, + 545, + 502 + ], + "type": "interline_equation", + "content": "Q = \\bar {\\mathbf {W}} _ {k + q} \\cdot F _ {v} ^ {\\prime} \\tag {5}", + "image_path": "2d2fafebb169346acf835da7b8aac63b542dd04859a612bd96ffb3f9f406489c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "spans": [ + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "text", + "content": "now we find the similarity between the attentional " + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "inline_equation", + "content": "F_{t2}" + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "text", + "content": " features and " + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "text", + "content": " features to obtain " + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "inline_equation", + "content": "F_{cs}^{\\prime} \\in \\mathbb{R}^{b \\times W_1 \\times 16}" + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{b \\times W_2 \\times 16}" + }, + { + "bbox": [ + 305, + 512, + 545, + 548 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 361, + 556, + 545, + 586 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 556, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 361, + 556, + 545, + 586 + ], + "type": "interline_equation", + "content": "F _ {c s} ^ {\\prime} = \\frac {\\sum_ {i = l} ^ {n} P _ {l} Q _ {l}}{\\sqrt {\\sum_ {l = 1} ^ {n} P _ {l} ^ {2}} \\sqrt {\\sum_ {l = 1} ^ {n} Q _ {l} ^ {2}}} \\tag {6}", + "image_path": "ec07cd4f786c445bea599c50349b714e14f79a53f1f874c7bde87e0dab81ca14.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " and attentional " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "F_{t2}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " features, respectively. Then, we concatenate " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "F_{cs}'" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " to obtain refined query features. Interestingly, we observe a performance drop when our feature refinement strategy is applied to strongly augmented image features for the teacher network, as detailed in Table 5b. However, we achieve optimal results by concatenating strongly augmented image features and applying our refinement strategy to weakly augmented image features. Consequently, we proceed by concatenating the features " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "F_{s1}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "inline_equation", + "content": "F_{s2}" + }, + { + "bbox": [ + 304, + 594, + 547, + 713 + ], + "type": "text", + "content": ", thereby obtaining the query features" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5843" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 286, + 240 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 286, + 240 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 286, + 240 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 286, + 240 + ], + "type": "image", + "image_path": "14b2567cf53534b6dfee193e26585068654d372ab70c8e1febb7542d8ce17c21.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 247, + 289, + 304 + ], + "lines": [ + { + "bbox": [ + 46, + 247, + 289, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 289, + 304 + ], + "type": "text", + "content": "Figure 3. Overview of the Query Refinement Module. The query features from strong and weak augmented unlabeled images are refined through the Query Refinement Module. It amplifies the semantic representation of object queries and improves performance for small objects. For the best view, zoom in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "inline_equation", + "content": "r_s" + }, + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "text", + "content": ". Note that " + }, + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "text", + "content": ", despite having a dimensional size equivalent to " + }, + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "inline_equation", + "content": "F_{cs}^{\\prime} + P" + }, + { + "bbox": [ + 46, + 321, + 288, + 370 + ], + "type": "text", + "content": ", encapsulates substantially more intricate representations. This improved performance is due to the integration of high-resolution and low-resolution features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "text", + "content": "Then, we form the decoder queries in the student-teacher network by merging the teacher's original queries " + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "inline_equation", + "content": "q_{t}" + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "text", + "content": " with refined queries " + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "inline_equation", + "content": "r_{s}" + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "text", + "content": ", and the student's original queries " + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "inline_equation", + "content": "q_{s}" + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "text", + "content": " with refined queries " + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "inline_equation", + "content": "r_{t}" + }, + { + "bbox": [ + 46, + 373, + 288, + 433 + ], + "type": "text", + "content": ", respectively. This integration forms the inputs for the decoder as follows:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 449, + 287, + 462 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 449, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 287, + 462 + ], + "type": "interline_equation", + "content": "\\hat {o} _ {t}, o _ {t} = \\operatorname {D e c} _ {t} \\left(\\left[ r _ {s}, q _ {t} \\right], E _ {t} [ A ]\\right) \\tag {7}", + "image_path": "e0576ac6eea23bce57f4b73200f4497e350ba14f025cdcdc929d7ceb298c6751.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 464, + 287, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 106, + 464, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 106, + 464, + 287, + 477 + ], + "type": "interline_equation", + "content": "\\hat {o} _ {s}, o _ {s} = \\operatorname {D e c} _ {s} \\left(\\left[ r _ {t}, q _ {s} \\right], E _ {s} [ A ]\\right) \\tag {8}", + "image_path": "c3a8ad074dfc0db86b6ea74e0753c3186677be623c7883f43628c0037d5fe1be.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "E_{s}" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "E_{t}" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " refer to the encoded image features. " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\hat{o}_{s}" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "\\hat{o}_{t}" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " indicate the decoded features of refined queries, while " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "o_{s}" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "o_{t}" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " represent the decoded features of original object queries. Here, " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " is for teacher and " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " for student network. Following DN-DETR [18], we use the attention mask " + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 493, + 287, + 578 + ], + "type": "text", + "content": " to protect information leakage, ensuring the learning process's integrity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 595, + 257, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 257, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 257, + 609 + ], + "type": "text", + "content": "4.2. Reliable Pseudo-Label Filtering Module" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "The one-to-many training strategy, while effective, causes duplication prediction in the first stage. We introduce a pseudo-label filtering module to address this and improve the filtering of pseudo boxes rich in semantic content for refined query learning. This module is designed to efficiently identify and extract reliable pseudo boxes from unlabeled data using augmented ground truths. We employ m groups of ground truths " + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{g} = \\{\\hat{g}_1,\\hat{g}_2,\\dots ,\\hat{g}_m\\}" + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": " for one-to-many as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 547, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 547, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 547, + 84 + ], + "type": "text", + "content": "signment strategy and select the top-k predictions as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 312, + 93, + 547, + 133 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 93, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 312, + 93, + 547, + 133 + ], + "type": "interline_equation", + "content": "\\hat {\\sigma} _ {o n e 2 m a n y} = \\left\\{\\underset {\\sigma_ {j} \\in C _ {M} ^ {N}} {\\arg \\min } \\sum_ {k} ^ {M} \\mathcal {L} _ {\\text {m a t c h}} \\left(\\hat {y} _ {j} ^ {t}, \\hat {g} _ {\\sigma_ {j} (k)} ^ {s}\\right) \\right\\} _ {j} ^ {| \\hat {y} ^ {t} |} \\tag {9}", + "image_path": "e5b3527ae14bd072d63dfaf39bbcfb84d7657a593680defd8593e04d4e8b8cb7.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "C_N^M" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": " represents the combination of " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": ", denoting that a subset of " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": " proposals is associated with each pseudo box " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "\\hat{y}_j^t" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": " is set to 6. Furthermore, we use the remaining predictions to filter out duplicates in the top-k predictions in the one-to-one matching branch. Through this improved selection scheme, we achieve a performance improvement of 0.4 mAP when " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": " is set to 6, as shown in Table 5a. However, we observe no significant benefits when increasing " + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 140, + 547, + 250 + ], + "type": "text", + "content": " greater than 6, as detailed in Table 6a." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 260, + 386, + 273 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 260, + 386, + 273 + ], + "spans": [ + { + "bbox": [ + 306, + 260, + 386, + 273 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 279, + 368, + 290 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 279, + 368, + 290 + ], + "spans": [ + { + "bbox": [ + 306, + 279, + 368, + 290 + ], + "type": "text", + "content": "5.1. Datasets" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": "We evaluate our approach on the MS-COCO [21] and Pascal VOC [6] datasets, benchmarking it against current SOTA SSOD methods. Following [51, 56], Sparse Semi-DETR is evaluated in three scenarios: COCO-Partial. We use " + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": " of train2017 as label data and rest as unlabeled data. COCO-Full. We take train2017 as label data and unlabel2017 as unlabel data. VOC. We take VOC2007 as label data and VOC2012 as unlabel data. Evaluation metrics include " + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "inline_equation", + "content": "AP_{50:95}" + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "inline_equation", + "content": "AP_{50}" + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "inline_equation", + "content": "AP_{75}" + }, + { + "bbox": [ + 304, + 297, + 547, + 406 + ], + "type": "text", + "content": " [51, 56]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 413, + 440, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 440, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 440, + 426 + ], + "type": "text", + "content": "5.2. Implementation Details" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 431, + 547, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 547, + 612 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 547, + 612 + ], + "type": "text", + "content": "We set the quantity of DINO original object queries to 900. For the setting hyperparameters, following [56] : (1) In the COCO-Partial setting, we set the training iterations to 120k with a labeled to unlabeled data ratio of 1:4. The first 60k iterations adopt a one-to-many assignment strategy. (2) In the COCO-Full setting, Sparse Semi-DETR is trained for 240k iterations with labeled to unlabeled data ratio of 1:1. The first 120k iterations adopt a one-to-many assignment strategy. (3) In the VOC setting, we train the network for 60k iterations with a labeled to unlabeled data ratio of 1:4. The first 40k iterations adopt a one-to-many assignment strategy. For all experiments, the filtering threshold " + }, + { + "bbox": [ + 304, + 431, + 547, + 612 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 431, + 547, + 612 + ], + "type": "text", + "content": " value is 0.4. We set the value of m to 6 and the value of k to 4. We provide complete implementation details for each experiment in Appendix A1.2." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 621, + 452, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 452, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 452, + 635 + ], + "type": "text", + "content": "6. Results and Comparisons" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "We evaluate Sparse Semi-DETR and compare it against current SOTA SSOD methods. Our results demonstrate the superior performance of Sparse Semi-DETR in these aspects: (1) its effectiveness compared to both one-stage and two-stage detectors, (2) its comparison with traditional DETR-based detectors, and (3) its exceptional proficiency in accurately" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5844" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 547, + 281 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 547, + 281 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 547, + 281 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 547, + 281 + ], + "type": "image", + "image_path": "86aaba2dcbb76d319856d0d243962a44a7e965ca5c65fb7860c25008f1bfb4ed.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 288, + 547, + 322 + ], + "lines": [ + { + "bbox": [ + 46, + 288, + 547, + 322 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 547, + 322 + ], + "type": "text", + "content": "Figure 4. Visual comparison of Sparse Semi-DETR with the two previous approaches on the COCO " + }, + { + "bbox": [ + 46, + 288, + 547, + 322 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 288, + 547, + 322 + ], + "type": "text", + "content": " label dataset. These results highlight Sparse Semi-DETR's capabilities, particularly in identifying small objects and those obscured by obstacles (as indicated by white arrows) in the third-row images. For optimal clarity and detail, please zoom in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 332, + 288, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 288, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 288, + 357 + ], + "type": "text", + "content": "detecting small and partially occluded objects. We provide more results details in Appendix A1.3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": "COCO-Partial benchmark. Sparse Semi-DETR outperforms the current SSOD methods in COCO-Partial across all experiment settings, as demonstrated in Table 1. (1) We compare our method to both one-stage and two-stage SSOD. Sparse Semi-DETR surpasses Dense Teacher by 8.52, 7.79, 7.17 mAP on " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": " label data. It also outperforms PseCo by 8.47, 8.30, 8.24 mAP on " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": " label data. Sparse Semi-DETR's superior performance as a semi-supervised object detector is achieved without needing hand-crafted components commonly used in two-stage and one-stage detectors. (2) When compared to DETR-based detectors, Sparse Semi-DETR outperforms omni-DETR by 3.30, 3.10, and 3.00 mAP and beats Semi-DETR by 0.40, 0.70, 0.80 mAP on " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": " label data. (3) Sparse Semi-DETR's exceptional proficiency in precisely detecting small and partially obscured objects is a standout feature. In Figure 4, we visually compare Sparse Semi-DETR with the two preceding approaches using the COCO " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": " labeled dataset. These results demonstrate the impressive capabilities of Sparse Semi-DETR, particularly in its ability to identify small objects and objects concealed by obstacles, as highlighted in the third-row images by the white arrows. Table 2 exhibits a remarkable performance boost of Sparse Semi-DETR on small objects. It surpasses the Semi-DETR by 1.20, 0.90 and 1.70 mAP on small objects using " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 361, + 289, + 696 + ], + "type": "text", + "content": " label data, respectively. It highlights the superior efficiency and accuracy of Sparse Semi-DETR in detecting smaller objects." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 288, + 714 + ], + "type": "text", + "content": "COCO-Full benchmark. In Table 4, when incorporating" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "text", + "content": "additional unlabeled2017 data, Sparse Semi-DETR demonstrates a substantial improvement, achieving an impressive " + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "inline_equation", + "content": "2.1\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "text", + "content": " gain and reaching a total of " + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "inline_equation", + "content": "51.3\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "text", + "content": ". It surpasses the performance of Dense Teacher, PseCo, and Semi-DETR by 5.2, 5.2, and " + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "inline_equation", + "content": "0.9\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 332, + 547, + 403 + ], + "type": "text", + "content": ", respectively, highlighting the effectiveness of Sparse Semi-DETR." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "type": "text", + "content": "Pascal VOC benchmark. Sparse Semi-DETR exhibits a remarkable performance boost on the Pascal VOC benchmark, as shown in Table 3. It surpasses the supervised baseline by 5.1 improvement on " + }, + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "type": "inline_equation", + "content": "AP_{50}" + }, + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "type": "text", + "content": " and by 5.91 impressive increase on " + }, + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "type": "inline_equation", + "content": "AP_{50:95}" + }, + { + "bbox": [ + 304, + 405, + 547, + 490 + ], + "type": "text", + "content": ". Furthermore, it outperforms all previously single-stage, two-stage, and DETR-based SSOD methods by a significant margin." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 500, + 406, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 500, + 406, + 511 + ], + "spans": [ + { + "bbox": [ + 306, + 500, + 406, + 511 + ], + "type": "text", + "content": "6.1. Ablation Studies" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 519, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 547, + 567 + ], + "type": "text", + "content": "This section ablates the key design choices of Sparse Semi-DETR. The experiments detailed in this section are executed on the MS COCO dataset with " + }, + { + "bbox": [ + 304, + 519, + 547, + 567 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 519, + 547, + 567 + ], + "type": "text", + "content": " label data, employing DINO as the primary detector." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": "Effect of Individual Component. We conduct three experiments to assess the efficacy of each module of Sparse Semi-DETR, as detailed in Table 5a. We employ Semi-DETR as our baseline model. Notably, integrating each component into Sparse Semi-DETR leads to consistent performance improvements. Specifically, adding the Query Refinement and Pseudo-Label Filtering modules yields a significant increase of " + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "inline_equation", + "content": "0.8\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 569, + 547, + 676 + ], + "type": "text", + "content": ". These results confirm that each component of Sparse Semi-DETR enhances our model's performance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Effect of Query Refinement Module. We examine the impact of the Query Refinement (QR) Module. In Table 5b, we explore various QR combinations to determine the most" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5845" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 70, + 517, + 250 + ], + "blocks": [ + { + "bbox": [ + 77, + 70, + 517, + 250 + ], + "lines": [ + { + "bbox": [ + 77, + 70, + 517, + 250 + ], + "spans": [ + { + "bbox": [ + 77, + 70, + 517, + 250 + ], + "type": "table", + "html": "
MethodsReferenceCOCO-Partial
1%5%10%
FCOS [42] (Supervised)-8.43 ± 0.0317.01 ± 0.0120.98 ± 0.01
DSL [3]CVPR2222.03 ± 0.28 (+13.98)30.87 ± 0.24 (+13.86)36.22 ± 0.18 (+15.24)
Unbiased Teacher v2 [28]CVPR2222.71 ± 0.42 (+14.28)30.08 ± 0.04 (+13.07)32.61 ± 0.03 (+11.63)
Dense Teacher [57]ECCV2222.38 ± 0.31 (+13.95)33.01 ± 0.14 (+16.00)37.13 ± 0.12 (+16.15)
Faster RCNN [35] (Supervised)-9.05 ± 0.1618.47 ± 0.2223.86 ± 0.81
Humble Teacher [41]CVPR2216.96 ± 0.38 (+7.91)27.70 ± 0.15 (+9.23)31.61 ± 0.28 (+7.75)
Instant-Teaching [58]CVPR2118.05 ± 0.15 (+9.00)26.75 ± 0.05 (+8.28)30.40 ± 0.05 (+6.54)
Soft Teacher [51]ICCV2120.46 ± 0.39 (+11.41)30.74 ± 0.08 (+12.27)34.04 ± 0.14 (+10.18)
PseCo [19]ECCV2222.43 ± 0.36 (+13.38)32.50 ± 0.08 (+14.03)36.06 ± 0.24 (+12.2)
DINO [55] (Supervised)-18.00 ± 0.2129.50 ± 0.1635.00 ± 0.12
Omni-DETR [46] (DINO)CVPR2227.60 (+9.60)37.70(+8.20)41.30 (+6.30)
Semi-DETR [56] (DINO)CVPR2330.5 ± 0.30 (+12.50)40.10 ± 0.15 (+10.6)43.5 ± 0.10 (+8.5)
Sparse Semi-DETR-30.9 ± 0.23 (+12.90)40.8 ± 0.12 (+11.30)44.3 ± 0.01 (+9.30)
", + "image_path": "edd5ea9e09389a5bb7323332ac8a1e207b2f01b08ae8d02f704f2d8eed45a0cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 313, + 217, + 395 + ], + "blocks": [ + { + "bbox": [ + 46, + 257, + 547, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 547, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 547, + 291 + ], + "type": "text", + "content": "Table 1. Comparing Sparse Semi-DETR with other approaches on COCO-Partial setting. The results are the average across all five folds. Under the COCO-partial setting, FCOS serves as the baseline for one-stage detectors, Faster RCNN for two-stage detectors, and DINO for transformer-based end-to-end detectors." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 313, + 217, + 395 + ], + "lines": [ + { + "bbox": [ + 56, + 313, + 217, + 395 + ], + "spans": [ + { + "bbox": [ + 56, + 313, + 217, + 395 + ], + "type": "table", + "html": "
MethodsLabelsCOCO-Partial
APSAPMAPL
Semi-DETR [56]1%13.631.240.8
5%23.043.153.7
10%25.246.858.0
Sparse Semi-DETR1%14.832.541.4
5%23.944.254.2
10%26.948.059.6
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MethodsVOC12
AP50AP50:95
FCOS [42] (Supervised)71.3645.52
DSL [3]80.7056.80
Dense Teacher [57]79.8955.87
Faster RCNN [35] (Supervised)72.7542.04
STAC [39]77.4544.64
HumbleTeacher [41]80.9453.04
Instant-Teaching [58]79.2050.00
DINO [55] (Supervised)81.2059.60
Semi-DETR [56] (DINO)86.1065.20
Sparse Semi-DETR86.3065.51
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MethodCOCO-Full (100%)
STAC [39] (18×)39.5 →0.3 39.2
Unbiased Teacher (9×)40.2 →1.1 41.3
SoftTeacher [51] (24×)40.9 →3.6 44.5
DSL [3] (12×)40.2 →3.6 43.8
Dense Teacher [57] (18×)41.2 →3.6 46.1
PseCo (24×)41.0 →5.1 46.1
Instant-Teaching [58] (24×)37.6 →0.27 40.2
Semi-DETR [56] (8×)48.6 →1.8 50.4
Sparse Semi-DETR (8×)49.2 →2.1 51.3
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Note that 1 denotes 30k training iterations, while an " + }, + { + "bbox": [ + 383, + 426, + 547, + 470 + ], + "type": "inline_equation", + "content": "\\mathbf{N}\\times" + }, + { + "bbox": [ + 383, + 426, + 547, + 470 + ], + "type": "text", + "content": " signifies N times 30k iterations." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "text", + "content": "effective design. Applying QR selectively to the student, teacher, or both networks, we find that employing QR on weak augmented image features " + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "inline_equation", + "content": "F_{t2}" + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "text", + "content": ", and integrating them into the student network with the original decoder queries yields the best results. Table 5c shows that processing " + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "inline_equation", + "content": "F_{t1}" + }, + { + "bbox": [ + 46, + 491, + 289, + 682 + ], + "type": "text", + "content": " features without MLP (in [56]) improves results. Table 5d presents our study on the impact of different query variants, where we observe that QR consistently outperforms other methods. Finally, Table 5e shows that using an attentional block in the QR module is more effective than simple concatenation or cosine similarity. We provide more analysis of the Query Refinement Module supplementary document. Figure 5 compares Sparse Semi-DETR and Semi-DETR. Sparse Semi-DETR, processing fewer but refined queries, demonstrates lower duplication rates in this training approach." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Effect of Reliable Pseudo-Label Filtering Module. In our analysis of the Pseudo-Label Filtering Module, we examine" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 491, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 624 + ], + "type": "text", + "content": "the impact of various parameters. Table 6a shows that a smaller m results in lower performance due to the inclusion of poor-quality labels. Performance improves with a moderately larger m due to enhanced auxiliary loss. However, excessively large m values trigger NMS, negatively impacting performance. Additionally, in Table 6b, we analyze the selection of the k value and find that setting k to 4 yields the best performance. In Table 6c, the optimal performance for " + }, + { + "bbox": [ + 304, + 491, + 547, + 624 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 491, + 547, + 624 + ], + "type": "text", + "content": " is achieved at 0.4; values lower than this may lead to the generation of noisy pseudo-labels, whereas higher values can decrease the number of effective pseudo-labels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": "Limitation. We still have duplications when we apply the one-to-many training strategy in both stages. Table 7 illustrates that a one-to-many strategy for " + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "inline_equation", + "content": "120\\mathrm{k}" + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": " iterations with Sparse Semi-DETR achieves a " + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "inline_equation", + "content": "44.6\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": " using NMS. In comparison, " + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "inline_equation", + "content": "60\\mathrm{k}" + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": " iterations in the first stage attain a comparable " + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "inline_equation", + "content": "44.3\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": " without NMS. Future works can explore this aspect." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5846" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 89, + 70, + 339, + 132 + ], + "blocks": [ + { + "bbox": [ + 89, + 70, + 339, + 132 + ], + "lines": [ + { + "bbox": [ + 89, + 70, + 339, + 132 + ], + "spans": [ + { + "bbox": [ + 89, + 70, + 339, + 132 + ], + "type": "table", + "html": "
Query RefinementPseudo-Label FilteringmAP\\( AP_{50} \\)\\( AP_{75} \\)
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✓X43.861.147.3
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TeacherStudentmAP\\( AP_{50} \\)\\( AP_{75} \\)
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MLPmAPAP50AP75
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MethodmAPAP50AP75
Single-view Queries43.059.346.3
Cross-view Queries43.558.946.0
Query Refinement44.361.747.6
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MethodmAPAP50AP75
Simple Concat43.458.846.1
Cosine Similarity43.760.346.1
Attention Module44.361.747.6
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m (k=4)mAP
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k (m=6)mAP
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σmAP
0.243.2
0.343.8
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Our method outperforms existing SSOD approaches, with extensive experiments demonstrating its effectiveness." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 577, + 547, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 547, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 547, + 613 + ], + "type": "text", + "content": "Ethical considerations. We study semi-supervised models, and agree that standard ethical considerations for visual recognition are applicable to our work." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 631, + 408, + 644 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 631, + 408, + 644 + ], + "spans": [ + { + "bbox": [ + 306, + 631, + 408, + 644 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "This work was in parts supported by the EU Horizon Europe Framework under grant agreements 101135724 (LUMINOUS) and 101092312 (AIRISE) and by the Federal Ministry of Education and Research of Germany (BMBF) under grant 01QE2227C (HERON)." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5847" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Ting Cai and Kirthevasan Kandasamy. 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But they require either a fairly dense sampling of the viewing sphere, or pre-training on an existing dataset, thereby limiting their generalizability. In contrast, photometric stereo (PS) approaches have shown great potential for achieving high-quality reconstruction under sparse viewpoints. Yet, they are impractical because they typically require tedious laboratory conditions, are restricted to dark rooms, and often multi-staged, making them subject to accumulated errors. To address these shortcomings, we propose an end-to-end uncalibrated multi-view PS framework for reconstructing high-resolution shapes acquired from sparse viewpoints in a real-world environment. We relax the dark room assumption, and allow a combination of static ambient lighting and dynamic near LED lighting, thereby enabling easy data capture outside the lab. Experimental validation confirms that it outperforms existing baseline approaches in the regime of sparse viewpoints by a large margin. This allows to bring high-accuracy 3D reconstruction from the dark room to the real world, while maintaining a reasonable data capture complexity.", + "bbox": [ + 75, + 333, + 472, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 675, + 209, + 690 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The challenge of 3D reconstruction stands as a cornerstone in both computer vision and computer graphics. Despite notable progress in recovering an object's shape from dense image viewpoints, predicting consistent geometry from sparse viewpoints remains a difficult task. Contemporary approaches employing neural data structures depend heavily on extensive training data to achieve generalization in the context of sparse views. Additionally, the presence of a wide baseline or textureless objects form significant obstacles. In contrast, photometric methodologies like photometric stereo (PS) excel in reconstructing geometry, even in textureless regions. This capability is attributed to the abun", + "bbox": [ + 75, + 696, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e484abd1f8da38cadfee03b24958334199b2ee1f1fa1736a7f6b77f9e96dec2c.jpg", + "image_caption": [ + "Multi-illumination data at viewpoint 1" + ], + "image_footnote": [], + "bbox": [ + 504, + 311, + 598, + 419 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f859c10146c0912ffe63f6911819ecffb008ea50c15a1fc9f58b9c26d64c03e9.jpg", + "image_caption": [ + "Multi-illumination data at viewpoint 2" + ], + "image_footnote": [], + "bbox": [ + 601, + 311, + 694, + 419 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb8c0d3f923ef4502153f92ad0bd298eaee58ba3e8c67722ffd595fe5f5eb59a.jpg", + "image_caption": [ + "PS-NeRF [60]" + ], + "image_footnote": [], + "bbox": [ + 696, + 311, + 792, + 419 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fc34dde2b27b7fe4660f050e43b34c54be2a6358091780fef6fb8789c686db55.jpg", + "image_caption": [ + "Ours", + "Figure 1. We introduce the first framework for multi-view uncalibrated point-light photometric stereo. Given a set of PS images captured from different viewpoints (left), our method recovers high-fidelity 3D reconstruction (right). The acquisition of uncalibrated point-light PS imagery captured under ambient lighting in a sparse multi-view setup does not only allow for easy data capture, but also leads to 3D reconstructions of unprecedented detail. Here, with as few as two views we are able to reconstruct the squirrel's 3D geometry at higher precision than the state-of-the-art." + ], + "image_footnote": [], + "bbox": [ + 794, + 311, + 888, + 419 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "dance of shading information derived from images acquired under diverse illumination. Yet, such approaches typically require a controlled laboratory setup to fulfill the necessary dark room and directional light assumptions. As a consequence, PS approaches become impractical beyond the confines of a laboratory.", + "bbox": [ + 496, + 617, + 890, + 708 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address these shortcomings we combine state-of-the-art volume rendering formulations with a sparse multi-view photometric stereo model. In particular, we advocate a physically realistic lighting model that combines ambient light and uncalibrated point-light illumination. Our approach facilitates simplified data acquisition, and we introduce a novel pipeline capable of reconstructing an object's geometry from a sparse set of viewpoints, even if the object is completely textureless. Furthermore, since we assume a point-light model instead of distant directional lighting, we can infer absolute depth from a single viewpoint, allowing us to address the challenge of wide camera baselines.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The contribution was done while at TUM.", + "bbox": [ + 99, + 886, + 331, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11862", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In detail, our contributions are as follows:", + "bbox": [ + 76, + 90, + 354, + 104 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering formulation with a physically realistic model of ambient light and point lights.", + "- We eliminate the need for a dark room environment, dense capturing process, and distant lighting. Thereby we enhance the accessibility and simplify data acquisition for setups beyond traditional laboratory settings.", + "- We validate that it can be successfully used for accurate shape reconstruction of textureless objects in highly sparse scenarios with wide baselines.", + "- Despite the absence of pre-processing or vast training data, we outperform cutting-edge approaches that either rely only on static ambient illumination or PS imagery." + ], + "bbox": [ + 76, + 107, + 467, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 325, + 217, + 340 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we categorize pertinent works into two distinct groups. The first category focuses on neural 3D reconstruction, emphasizing the use of images captured under static ambient illumination. Subsequently, the second category delves into photometric stereo (PS) approaches, which specifically involve methods assuming images captured under varying illumination conditions.", + "bbox": [ + 75, + 347, + 467, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Neural 3D reconstruction", + "text_level": 1, + "bbox": [ + 76, + 460, + 308, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our context, the domain of neural 3D reconstruction under static ambient light can be bifurcated into two distinct subcategories. The first comprises methodologies that presume a dense sampling of the viewing sphere [5, 11, 12, 14, 36, 38, 39, 52, 63, 64, 68]. Conversely, the second subcategory encompasses techniques adept at handling sparse camera viewpoints [7, 9, 13, 16, 22, 33, 43, 47, 51, 53, 56-59, 61, 62, 65-67].", + "bbox": [ + 75, + 477, + 467, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given our emphasis on a sparse set of camera viewpoints, our focus will be directed toward the latter set of methodologies. The majority of sparse reconstruction approaches within this category hinge on training with a specific dataset [9, 13, 16, 47, 53, 57-59, 61, 62, 65, 67]. The reliance on extensive training data renders these techniques susceptible to errors when confronted with objects not represented in the training dataset, thereby introducing sensitivity to the domain gap between training and test data.", + "bbox": [ + 75, + 598, + 467, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efforts have been undertaken to mitigate the challenges associated with the domain gap. One approach involves fine-tuning pre-trained architectures during test time with sparse input data [22, 33, 43]. However, while fine-tuning enables fine-scale refinement of the predicted reconstruction, the broader issue of generalization to entirely different datasets persists as a challenge. Furthermore, it is crucial to note that all the previously mentioned sparse approaches presume small camera baselines and textured objects. To achieve a full reconstruction of an object from sparse views, it becomes imperative to develop texture-", + "bbox": [ + 75, + 734, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "agnostic approaches capable of handling wide baselines.", + "bbox": [ + 498, + 90, + 870, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another set of approaches involves the utilization of pretraining to establish a geometric prior [51, 56, 66]. Yu et al. [66] leverages this geometric prior to predict a depth and normal map, albeit with a limitation in fine-scale details due to its coarse resolution. Notably, [51, 56] address this limitation. Wu et al. [56] relax the assumption on small baselines, although a reasonable overlap of sparse views remains necessary for consistent 3D reconstruction. Vora et al. [51] demonstrate promising results with much less overlap, employing only three viewpoints. However, the use of template shapes as a prior term introduces the risk of the reconstruction quality being affected by the domain gap curse.", + "bbox": [ + 496, + 107, + 890, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, our approach eliminates the requirement for training data and operates effectively in wide baseline scenarios, independent of the object's texture. This accomplishment can be attributed to the integration of PS principles, which we will elucidate in the subsequent discussion.", + "bbox": [ + 496, + 287, + 890, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Photometric Stereo", + "text_level": 1, + "bbox": [ + 500, + 378, + 684, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The principle of PS [54] has a long and established history, renowned for yielding high-quality and finely detailed geometric estimates, due to its capturing process: multiple images under different illumination of a static object are captured from a single camera viewpoint.", + "bbox": [ + 496, + 400, + 890, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our case, PS approaches can thus be categorized into two main types. The first category pertains to single-view methods [17, 23, 29, 30, 32, 35, 40, 45, 46, 50], wherein data is acquired as described above. The second category involves multi-view methods [1, 10, 21, 26-28, 31, 41, 55, 60, 72], where the capturing process is repeated at multiple camera viewpoints.", + "bbox": [ + 496, + 476, + 890, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Within the context of our task, we concentrate on the multi-view scenario. Many existing approaches in this domain assume knowledge of the light source for each image, earning them the designation of calibrated PS (CPS). In this case, frequently the light is parameterized as directional [1, 10, 28, 72], while approaches employing point-light illumination are more sparsely represented [10, 28, 31], owing to the intricate model and the much more complex calibration process [46]. In a broader context, the calibration of each image's light source is impractical and tedious, underscoring the advantage of the uncalibrated case, which inherently facilitates a more straightforward and streamlined capturing process.", + "bbox": [ + 496, + 583, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Efforts have been dedicated to exploring the uncalibrated PS (UPS) scenario, where there is no prior knowledge of the light source [21, 26, 27, 41, 55, 60]. Nevertheless, all these uncalibrated methods typically assume a distant and directional light model or permit a lighting model based on spherical harmonics [2, 4, 18, 19, 44, 48, 49], albeit at the expense of being restricted to Lambertian objects [55]. Consequently, the exploration of the uncalibrated point", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11863", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "light case remains uncharted territory, particularly in the multi-view scenario.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite the impractical assumption of calibrated light or the constraint of uncalibrated directional lighting, the aforementioned multi-view photometric stereo approaches demand a dark room and lack accommodation for ambient light [1, 10, 21, 26-28, 31, 41, 60, 72]. Additionally, they comprise multiple stages, rendering them prone to initialization and accumulation errors [21, 26-28, 31, 41, 55, 60]. Furthermore, these methods assume Lambertian objects [31, 55] and crucially rely on a dense sampling of camera viewpoints around the object [21, 28, 31, 41, 55].", + "bbox": [ + 75, + 121, + 467, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The approach most closely related to ours is the sparse method PS-NeRF [60], which assumes uncalibrated directional lighting with imagery captured in a dark room. This method comprises multiple stages, where initially, a pretrained network [8] is utilized to estimate the initial light, along with normal information for each image and camera view. Subsequently, this acquired information is employed to estimate the object's mesh through the optimization of an occupancy field [39]. The outputs of both stages are then combined to derive a consistent normal map of the object. Although PS-NeRF demonstrates impressive results in a sparse scenario with five viewpoints, its susceptibility to error accumulation is a potential limitation, given the involvement of multiple stages.", + "bbox": [ + 75, + 273, + 467, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our proposed model addresses the aforementioned limitations comprehensively. Notably, we excel in handling sparse yet wide baseline scenarios, where existing state-of-the-art methods encounter challenges. Our investigation tackles the open challenge of multi-view uncalibrated pointlight PS within an end-to-end framework, liberating us from the constraints associated with Lambertian objects. Furthermore, our approach facilitates easy data capture in the presence of ambient light, eliminating the need for a dark room.", + "bbox": [ + 75, + 484, + 467, + 621 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Setting and image formation model", + "text_level": 1, + "bbox": [ + 76, + 633, + 395, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider an object under static illumination photographed from several different viewpoints. For every viewpoint, we are given a set of $N + 1$ images $(I^l)_{l = 0,\\dots ,N}$ . Image $I^0$ is captured only under static ambient illumination and called the ambient image. For images $I^{1}$ to $I^{N}$ , the object is in addition to the ambient illumination also illuminated by a single achromatic point-light source with scalar light intensity $L_0\\in \\mathbb{R}^+$ , placed at a different location $\\mathbf{p}^l\\in \\mathbb{R}^3$ for each image and viewpoint. We use the common assumption in volume rendering [36, 52, 56, 64] that the image brightness $I^l$ is the same as the accumulated radiance of the volume rendering, see Eq. (4). Note that we do not add an index for the viewpoint to the image to not clutter notation, whenever we later evaluate an image at a pixel location, we assume it implicitly means a pixel at a specific viewpoint. In particular, a sum over all pixels is the", + "bbox": [ + 75, + 659, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sum over all pixels at every viewpoint location.", + "bbox": [ + 500, + 90, + 812, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "According to the linearity of the radiance, the total radiance for the image $l$ is given by a sum $\\mathcal{L}^l = \\mathcal{L}_{\\mathrm{amb}} + \\mathcal{L}_{\\mathrm{pt}}^l$ , where $\\mathcal{L}_{\\mathrm{amb}}$ is the radiance due to the static illumination, the same for each image, and $\\mathcal{L}_{\\mathrm{pt}}^l$ is the radiance due to the point-light source used for that particular image. We will first express the radiance due to the point-light source with respect to the material and lighting parameters, which allows to take into account the different illuminations of the images. Subsequently, we elaborate on how we deal with the ambient component.", + "bbox": [ + 496, + 106, + 890, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Point-light illumination and material", + "text_level": 1, + "bbox": [ + 498, + 266, + 818, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The field $L(\\mathbf{x},\\mathbf{n},\\mathbf{v})$ maps points $\\mathbf{x}\\in \\mathbb{R}^3$ , normal direction $\\mathbf{n}(\\mathbf{x})\\in \\mathbb{S}^2$ and viewing direction $\\mathbf{v}\\in \\mathbb{S}^2$ to its radiance. It can be expressed in terms of geometry, material and lighting with the classical rendering equation [24]. Since for now we only consider a single achromatic point-light source with intensity $L_{0}$ at position $\\mathbf{p}$ , this equation simplifies to", + "bbox": [ + 496, + 287, + 890, + 380 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}) = \\frac {L _ {0}}{\\| \\mathbf {p} - \\mathbf {x} \\| ^ {2}} f _ {\\mathrm {r}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}) \\max (0, \\mathbf {n} \\cdot \\mathbf {l}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 387, + 890, + 421 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{l} = \\frac{\\mathbf{p} - \\mathbf{x}}{\\|\\mathbf{p} - \\mathbf{x}\\|}$", + "bbox": [ + 500, + 430, + 622, + 449 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As a model for the spatially varying reflectance $f_{\\mathrm{r}}$ , we use the simplified Disney BRDF [25]. It is relatively simple yet expressive enough to resemble a wide variety of materials. It has already been successfully used in several other prior works [5, 34, 69]. The Disney BRDF requires three parameters to be available at every point $\\mathbf{x} \\in \\mathbb{R}^3$ : An RGB diffuse albedo $\\rho \\in \\mathbb{R}_{\\geq 0}^{3}$ , a roughness $\\alpha_{\\mathrm{r}} > 0$ and a specular albedo $\\alpha_{\\mathrm{s}} \\in [0,1]$ .", + "bbox": [ + 496, + 449, + 890, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As in [5], all three BRDF parameters can be represented with MLPs. One MLP with network parameters $\\gamma_{1}$ computes the diffuse parameter $\\rho$ , a second MLP with network parameters $\\gamma_{2}$ computes the specular parameters $(\\alpha_{\\mathrm{r}},\\alpha_{\\mathrm{s}})$ . To encompass all point-light and BRDF parameters, we concatenate them into the vectors $\\phi = (\\mathbf{p}^{1},\\dots,\\mathbf{p}^{M})$ , which includes all light source positions (where $M$ is the product of $N$ with the number of viewpoints), and $\\gamma = (\\gamma_{1},\\gamma_{2})$ , representing the BRDF parameters. Both $\\phi$ and $\\gamma$ serve as the network parameters to be learned during optimization. However, note that one of our contributions is a novel strategy to deal with the diffuse albedo later on in Sec. 5.2, which dramatically improves performance in extremely sparse scenarios.", + "bbox": [ + 496, + 569, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We assume that the intensity $L_{0}$ remains constant across all images and views. This assumption is reasonable, e.g., when using a smartphone's flashlight or a sole LED, as shown in our experiments. A constant intensity introduces a scale ambiguity between the $f_{\\mathrm{r}}$ and $L_{0}$ . We set $L_{0} \\equiv 1$ and subsequently estimate a scaled version of the BRDF, i.e., the intensity is absorbed into the BRDF. This is feasible, since we can scale the Disney BRDF arbitrarily.", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11864", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Ambient light", + "text_level": 1, + "bbox": [ + 76, + 90, + 220, + 107 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given the provided ambient image, we adopt the approach from [71], which involves subtracting the ambient image from all other images. This process effectively eliminates ambient radiance from our considerations, simulating a traditional dark room scenario. A drawback is that in practice, the captured images contain additive noise, hence such a subtraction will double the variance of the noise distribution, resulting in noisier input images. Nevertheless, as can be seen in the results, our approach works successfully with this strategy even if we use a simple smartphone camera for the data capture.", + "bbox": [ + 75, + 114, + 468, + 280 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, this simplification is enabled by the fact that the point-light sources are near the object, making it easy to obtain a well exposed contribution from the point-light source. In methods assuming directional lighting, the practical simulation often involves using a point-light source placed far from the object, ensuring that the object's diameter is significantly smaller than the distance between the point-light and the object. For example, for the DiLiGenTMV dataset [28], the light sources are roughly $1\\mathrm{m}$ from the object, whereas for our setup, the distance is approximately $25\\mathrm{cm}$ . As a consequence, for a given static ambient illumination, the distant point-light will need to be $16\\times$ brighter in the Diligent setup to obtain a similar signal to noise ratio. This increased brightness requirement escalates the hardware demands, especially if the highest quality is sought.", + "bbox": [ + 75, + 280, + 470, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Other illumination effects", + "text_level": 1, + "bbox": [ + 76, + 518, + 310, + 534 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We do not model indirect lighting and cast-shadows explicitly. However, multiple previous works [3, 20, 34, 37, 70] and PS frameworks [10, 17, 28, 46] have demonstrated that satisfactory results can be achieved without taking these into account. In addition, we use the robust $L^1$ -norm in our data term (7) to further increase robustness. Furthermore, we will expose a simple strategy in Sec. 5 to reduce the impact of cast-shadows, which inevitably occur when capturing a nonconvex object under changing illumination.", + "bbox": [ + 75, + 541, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Volume rendering of the surface", + "text_level": 1, + "bbox": [ + 76, + 693, + 370, + 710 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For differentiable rendering we build upon VolSDF [64] because in contrast to NeRF [36] it allows us to decouple geometric representation and appearance. As discussed in [47, 56, 65], VolSDF exhibits poor reconstruction quality in the sparse viewpoint scenario due to the shape-radiance ambiguity. We eliminate this ambiguity thanks to photometric stereo, providing shading cues from different illuminations for each viewpoint. To this end, we employ the radiance field in Eq. (1) and apply it to the multi-view uncalibrated point-light PS setting. The integration of differentiable volume rendering with a physically realistic lighting model provides an efficient solution to the multi-view", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "photometric stereo problem, enabling high-quality reconstruction even with sparse viewpoints, as demonstrated in the subsequent results.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Geometry model and associated density. The geometry of the scene is modeled with a signed distance function (SDF) $d: \\Omega \\to \\mathbb{R}$ within the volume $\\Omega \\subset \\mathbb{R}^3$ . We follow [42, 52, 63, 64] and represent the SDF with an MLP $d(\\mathbf{x}; \\theta)$ parametrized by $\\theta$ . Note that we assume positive values of the SDF $d$ inside the object, thus the normal vector is given by $\\mathbf{n} = \\nabla d / \\| \\nabla d\\|$ on $\\Omega$ . To render the scene, we follow [64] and transform the SDF into a density $\\sigma: \\Omega \\to \\mathbb{R}_{\\geq 0}$ by means of the transformation", + "bbox": [ + 496, + 136, + 890, + 272 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma (\\mathbf {x}) = \\beta^ {- 1} \\Psi_ {\\beta} (- d (\\mathbf {x})), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 276, + 890, + 295 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Psi_{\\beta}$ denotes the cumulative distribution function of the Laplace distribution with zero mean. The positive scale parameter $\\beta$ is learned during optimization. For simplicity, we assume it is included in the set of SDF parameters $\\theta$ .", + "bbox": [ + 496, + 300, + 890, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Volume Rendering. Using the density (2), we can now set up a distribution of weights $w(t)$ along each ray $\\mathbf{x}(t) = \\mathbf{c} + t\\mathbf{v}, t \\geq 0$ defined by the center of projection $\\mathbf{c}$ of the camera and viewing direction $\\mathbf{v}$ ,", + "bbox": [ + 496, + 359, + 890, + 421 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw (t) = \\sigma (\\mathbf {x} (t)) \\exp \\left(- \\int_ {0} ^ {t} \\sigma (\\mathbf {x} (s)) \\mathrm {d} s\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 425, + 890, + 460 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is the derivative of the opacity function, which is monotonically increasing from zero to one, and thus $w$ is indeed a probability distribution [64]. In particular, the integral", + "bbox": [ + 496, + 463, + 890, + 523 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p} = \\int_ {0} ^ {\\infty} w (t) L (\\mathbf {x} (t), \\mathbf {n} (t), \\mathbf {v}) \\mathrm {d} t, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 522, + 890, + 554 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to compute radiance $\\mathcal{L}_p$ in the pixel $p\\in \\mathbb{R}^2$ corresponding to the ray $\\mathbf{x}(t)$ is well-defined. Intuitively, we accumulate the radiance field (1) of the point-light source at locations where opacity increases, i.e. where we move towards the inside of the object. For an ideal sharp boundary, $w$ would be a Dirac distribution with its peak placed at the boundary.", + "bbox": [ + 496, + 556, + 890, + 647 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As was done in [64] we approximate the integral (4) using the quadrature rule", + "bbox": [ + 496, + 647, + 890, + 678 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {p} \\approx \\sum_ {i = 1} ^ {m - 1} \\left(t _ {i + 1} - t _ {i}\\right) w \\left(t _ {i}\\right) L \\left(\\mathbf {x} \\left(t _ {i}\\right), \\mathbf {n} \\left(t _ {i}\\right), \\mathbf {v}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 683, + 890, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for numerical integration with a discrete set of samples $t_1 < t_2 < \\dots < t_m$ . Note that the integral (3) required for $w(t_i)$ in (5) can be numerically computed using an analogous formula while iteratively accumulating the sum (5).", + "bbox": [ + 496, + 728, + 890, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Training objective and optimization", + "text_level": 1, + "bbox": [ + 496, + 800, + 823, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to reconstruct the scene by inverse rendering, we train our neural networks from the available input images. We optimize for the geometry parameters $\\theta$ of the SDF network and point-light and BRDF parameters $\\phi$ and $\\gamma$ of the appearance network, respectively.", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11865", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5.1. Vanilla loss function with MLP for albedo", + "text_level": 1, + "bbox": [ + 76, + 90, + 433, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall loss consists of the sum of an inverse rendering loss $E_{\\mathrm{RGB}}(\\theta, \\phi, \\gamma)$ , an Eikonal loss $E_{\\mathrm{eik}}(\\theta)$ and a mask loss $E_{\\mathrm{mask}}(\\theta)$ for the SDF,", + "bbox": [ + 76, + 113, + 468, + 159 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE (\\theta , \\phi , \\gamma) = E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma) + \\lambda_ {1} E _ {\\mathrm {e i k}} (\\theta) + \\lambda_ {2} E _ {\\text {m a s k}} (\\theta), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 167, + 468, + 185 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with respective weighting parameters $\\lambda_1, \\lambda_2 \\geq 0$ given as hyperparameters. We will describe the different terms in detail in the following.", + "bbox": [ + 76, + 193, + 468, + 238 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The rendering loss", + "bbox": [ + 96, + 239, + 230, + 253 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma) = \\sum_ {p} \\sum_ {l \\in B _ {\\tau} (p)} \\left\\| I _ {p} ^ {l} - \\mathcal {L} _ {p} ^ {l} (\\theta , \\phi , \\gamma) \\right\\| _ {1} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 261, + 468, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "encourages that the rendered images resemble the input images. As a strategy to deal with cast-shadows, for each pixel $p$ , we use only the $\\tau$ brightest views $B_{\\tau}(p) \\subset \\{1 \\dots N\\}$ , where $\\tau > 0$ is a hyper-parameter. This reduces the impact of cast-shadows, as a pixel will have the smallest possible brightness when it lies in shadow. Such a strategy is necessary since despite the use of an $L^1$ -norm to improve robustness against outliers, some regions with frequent cast-shadows would still exhibit small artefacts, as can be seen in Fig. 2. In order to avoid wasting meaningful information due to this heuristic, we set $\\tau = N$ for the first half of the iterations, and then set it to $\\tau = \\lceil \\frac{3}{4} N \\rceil$ for the second half for improved handling of cast-shadows.", + "bbox": [ + 76, + 304, + 470, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Eikonal term", + "bbox": [ + 96, + 501, + 223, + 513 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE _ {\\mathrm {e i k}} (\\theta) = \\sum_ {\\mathbf {x}} \\left(\\left\\| \\nabla_ {\\mathbf {x}} d (\\mathbf {x}; \\theta) \\right\\| - 1\\right) ^ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 521, + 468, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "encourages $d(\\mathbf{x};\\theta)$ to approximate an SDF, as it penalizes deviations from the respective partial differential equation which every SDF satisfies, see e.g. [15].", + "bbox": [ + 76, + 561, + 468, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we follow [5, 52] and employ the mask loss", + "bbox": [ + 96, + 607, + 442, + 622 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE _ {\\text {m a s k}} (\\theta) = \\sum_ {p} \\operatorname {B C E} \\left(M _ {p}, W _ {p} (\\theta)\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 155, + 630, + 468, + 664 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "to impose silhouette consistency by means of the binary cross entropy (BCE) between the given binary mask $M_{p}$ at the pixel $p$ and the sum $W_{p}(\\theta) = \\sum_{i=1}^{m-1} w(t_{i};\\theta)$ of the weights at the sampling locations $t_{i}$ used in (5).", + "bbox": [ + 76, + 671, + 468, + 734 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Using the optimal diffuse albedo", + "text_level": 1, + "bbox": [ + 76, + 741, + 362, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we introduce a strategy to handle the diffuse albedo. This is inspired by [17], however in their single-view approach they are only able to handle the least-squares case, i.e. $L^2$ , while we extend their formulation to objective functions of the form of an $L^p$ -norm, with $p = 1$ in our case, see Eq. (7). In lieu of employing an MLP for modeling the diffuse albedo, we opt for approximating an optimal solution considering the remaining parameters. This allows us to exclude the diffuse albedo from the optimization", + "bbox": [ + 76, + 763, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/316363b2f55a0466a63ae7b294c37ae992c3a0e5b0bdb43690891ab93c5dfd0d.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 630, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0bf9fb90e483bce5c5f2883db97bd18c6ae44833fd3939cc9b60fee473ed7c16.jpg", + "image_caption": [ + "w/o truncation" + ], + "image_footnote": [], + "bbox": [ + 632, + 89, + 759, + 213 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/cbb80f3db5953b1ad83a183d45ab76f6812e32cb43d29721c8227b9d1fa2b74b.jpg", + "image_caption": [ + "w/ truncation", + "Figure 2. Effect of cast-shadows on the result. The region behind the ear exhibits frequent cast-shadows in the input images (left), which induce artefacts in the estimated mesh (middle). Our truncation strategy (Sec. 5.1) successfully eliminates these (right)." + ], + "image_footnote": [], + "bbox": [ + 761, + 89, + 888, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "process. Our subsequent demonstration will underscore the significant benefits of this approach in the context of sparse views, leading to markedly improved final geometry. A key technical change is the domain of the diffuse parameter $\\rho$ . So far, it has been a vector field defined in world space $\\Omega$ , implemented with a neural network. However, in the following we only try to recover the projection of $\\rho$ on the image planes. Thus, the input to $\\rho$ will be a pixel, and the output is the diffuse albedo at the intersection between the pixel's ray and the object surface. In particular, the set of BRDF parameters is reduced to $\\gamma = \\gamma_{2}$ and now only includes specular parameters.", + "bbox": [ + 496, + 309, + 890, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Reformulation of the data term. We will now derive an expression for the data term which allows to solve for diffuse albedo $\\rho$ when given all of the other parameters. Note that the SVBRDF can be decomposed into a diffuse part and a specular part [25],", + "bbox": [ + 498, + 489, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\mathrm {r}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}) = \\frac {\\rho (\\mathbf {x})}{\\pi} + f _ {\\mathrm {s}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 575, + 890, + 606 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the specular part $f_{s}$ depends on both the roughness and specular albedo. If we denote the BRDF-independent factor of the radiance field (1) by", + "bbox": [ + 498, + 614, + 890, + 660 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS ^ {l} (\\mathbf {x}, \\mathbf {n}) = \\frac {L _ {0}}{\\| \\mathbf {x} - \\mathbf {p} ^ {l} \\| ^ {2}} \\max (0, \\mathbf {n} \\cdot \\mathbf {l}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 570, + 669, + 890, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "this implies that the total radiance field is the sum of diffuse radiance $\\frac{\\rho}{\\pi} S^l$ and specular radiance $L_{s}^{l} = f_{s}S^{l}$", + "bbox": [ + 498, + 713, + 890, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inserting this into the volume rendering equation (4), we can thus re-arrange the data term (7) as", + "bbox": [ + 498, + 744, + 890, + 773 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nE _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma , \\rho) = \\sum_ {p} \\sum_ {l \\in S _ {\\tau} (p)} \\left\\| b _ {p} ^ {l} (\\theta , \\phi , \\gamma) - \\rho_ {p} a _ {p} ^ {l} (\\theta , \\phi) \\right\\| _ {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 784, + 888, + 818 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w i t h} a _ {p} ^ {l} (\\theta , \\phi) = \\frac {1}{\\pi} \\int_ {0} ^ {\\infty} w _ {\\theta} (t) S ^ {l} (\\mathbf {x} (t), \\mathbf {n} _ {\\theta} (t)) d t,\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 821, + 844, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nb _ {p} ^ {l} (\\theta , \\phi , \\gamma) = I _ {p} ^ {l} - \\int_ {0} ^ {\\infty} w _ {\\theta} (t) L _ {s} ^ {l} (\\mathbf {x} (t), \\mathbf {n} _ {\\theta} (t), \\mathbf {v}) \\mathrm {d} t. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 856, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11866", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/0b76a767f9d3525b7438e9e18b49888abd502c0b6831cbdd18f86d375b9acee2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 215, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/791d8c0f7e5146136557ad427c246eb1ad81ab40c15bd6389e471774330cc9ca.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 88, + 351, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2c2e940475ec275a1c2c0d64f06eec9ce6fa9dcbebab2d2ff4f198bd7cffd50a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 88, + 488, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f2fbe2104cfe1789464e0853cacdd8d8e15eb2d4dd19caaa986f9488f73410b7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 88, + 622, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e456e9d05f99b90088e706a1f5b88babccf1c59250dc6434d3ebbbc11e1af47a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 624, + 89, + 759, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/ba893907ebfff2653b8c38745cf168117102f312648526dd28e113cd727afe31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 89, + 895, + 223 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ba982d3ada94a2896ee42e54608462ae345495f02fbf4b14cb6a5c349457139.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 224, + 215, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b0b33248077d422b0d23a6913e0929a84a37a148c8bf671cecb47e9be4d76c83.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 217, + 224, + 351, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/aed9e7d0952a545024a556a33368b326706eb5119d239002829462c6e059eb31.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 224, + 488, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/7ef6cf2a649ba72dcccc387c6375ee1368a2cb6cfee7937cfdbd642eff29733b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 224, + 622, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/13bf65b592b2e14e7f9b24701204da4fb4923261ff0539f573390c61c419264b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 624, + 224, + 759, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e0b924f1df27f590b66ba8fe1bce8b7509c0ff47dd31bbcccea4076489c7985d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 224, + 895, + 358 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b6c53ea157d0df8df4d61112b8b02568bd13d6a30ba4c12b6763d20cf600f521.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 80, + 361, + 215, + 477 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/36510e363a7e5c2cf286c03728d8d382026d9e0edb3b0f1b8c3bf8eaa7be1f31.jpg", + "image_caption": [ + "[56]" + ], + "image_footnote": [], + "bbox": [ + 217, + 361, + 351, + 477 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/13ae59f6c1170596fd92e61646471230a81af8f7337c9b8b903d6bebcd22937a.jpg", + "image_caption": [ + "[10] (directional light)" + ], + "image_footnote": [], + "bbox": [ + 352, + 361, + 488, + 477 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a7486fee1223a73299d6438275b08ab8a6d842cad8dbd582e61eb277c4c3a80d.jpg", + "image_caption": [ + "[10] (point-light)", + "Figure 3. Full 3D reconstruction of one synthetic and two real objects from 6 viewpoints. While some of the baseline reconstructions (with directional or point-light models) exhibit texture-induced patterns, distortions or other artefacts, the proposed framework consistently yields artefact- and distortion-free reconstructions with finer geometric details. Additional results are shown in the supplementary." + ], + "image_footnote": [], + "bbox": [ + 488, + 361, + 622, + 477 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/373f6e21228766d7239ef4a72df1b9fd6e8b0a59606372617413126a5497e65e.jpg", + "image_caption": [ + "[60]" + ], + "image_footnote": [], + "bbox": [ + 624, + 361, + 758, + 477 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/51d80fd74f2fe355ea5fbbb3db82b28038de9d8c8a79b393a810f0d25130e28f.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 759, + 361, + 895, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When keeping $\\theta, \\phi$ , and $\\gamma$ fixed, this expression can be minimized pixel-wise for $\\rho$ as a linear least absolute deviation problem, as we show next.", + "bbox": [ + 75, + 558, + 468, + 603 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Alternate treatment of the diffuse albedo. It is now possible to completely exclude the diffuse albedo $\\rho$ from the optimization and simply replace it by the optimal value", + "bbox": [ + 75, + 606, + 468, + 652 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\rho_ {\\theta , \\gamma} ^ {*} = \\underset {\\rho} {\\arg \\min } E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma , \\rho) \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 667, + 468, + 694 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with respect to the other parameters. In our case, we are facing a linear least absolute deviation problem which can be solved individually for each pixel.", + "bbox": [ + 75, + 708, + 468, + 753 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We thus approximate the solution using a few iterations of iterative reweighted least squares [6], as it efficiently solves the problem while providing a differentiable expression. In order to simplify notation, we omit the dependency w.r.t. the parameters and denote only the channel-wise operations, where we iteratively compute", + "bbox": [ + 75, + 756, + 468, + 847 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\rho_ {p} ^ {*} \\approx \\rho_ {p} ^ {(k)} = \\frac {b _ {p} ^ {\\top} W _ {p} ^ {(k)} a _ {p}}{a _ {p} ^ {\\top} W _ {p} ^ {(k)} a _ {p}} \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 861, + 468, + 905 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with diagonal matrices", + "bbox": [ + 500, + 558, + 653, + 574 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nW _ {p} ^ {(k)} = \\left\\{ \\begin{array}{l l} \\operatorname {d i a g} \\left(\\max \\left(\\epsilon , \\left| b _ {p} - \\rho_ {p} ^ {(k - 1)} a _ {p} \\right|\\right) ^ {- 1}\\right) & \\text {i f} k \\geq 1, \\\\ I & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 616, + 890, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Above, $k$ is the index of iteration, and $a_{p}$ and $b_{p}$ are the vectors whose components are given in Eq. (12). The small constant $\\epsilon > 0$ avoids numerical issues, and $I$ is an identity matrix of matching size. The gradient of $\\rho_{p}^{(k)}$ with respect to $\\theta$ and $\\gamma$ is computed using automatic differentiation, however the gradient of $W_{p}^{(k)}$ is not back-propagated, as it makes the optimization much more difficult and degrades the quality of the results.", + "bbox": [ + 496, + 670, + 890, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In the forthcoming evaluation section, we demonstrate that this formulation delivers exceptional performance in 3D reconstruction from sparse viewpoints. Notably, it proves particularly advantageous in the most sparse scenarios, where only two viewpoints are available, showcasing its superiority over the previous MLP-based formulation.", + "bbox": [ + 496, + 810, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11867", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/70a24bcbb12fe780e39005cf3dfebf887e3da9215852413fbf5631950d31fdff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 133, + 87, + 320, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/920f25e6d99a32a5ae18821105301ea345d71b7ba17bd689d85536338c78c7e7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 88, + 483, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6a0593c76481bc33443b74c305aff214b569979995a84566b0eda50d29e08c2b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 485, + 88, + 647, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1be26b5ca4a982bd51bc005fee66364078be79d1b7814d04eaa375cd587e5fb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 88, + 810, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bab47f412ab7cd68c5212c1efad3bf4c110ab986fd4e0a73da30aeda099c8288.jpg", + "image_caption": [ + "Input image" + ], + "image_footnote": [], + "bbox": [ + 135, + 246, + 320, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/03238a92605ddcc980df71311f777faa2699e9c1087faeef95fd89d0dd2ec741.jpg", + "image_caption": [ + "[56]" + ], + "image_footnote": [], + "bbox": [ + 321, + 246, + 483, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/46d1f360e2f33a7b0f3d7808712feaf2242077d790ef8d85539458266e6cc259.jpg", + "image_caption": [ + "[60]", + "Figure 4. Results for both dog1 and dog2 obtained with 5 viewpoints reveal a notable performance degradation in [56] and [60] when confronted with complex textures. This deterioration is attributed to a generalization failure of their learned priors. In contrast, our approach, which does not rely on any prior, provides a superior reconstruction that is unaffected by the complex texture." + ], + "image_footnote": [], + "bbox": [ + 485, + 246, + 647, + 402 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fc24ce5b476f4ce55e8b740c384ebbfb67bb00aa305222948c54c0f2201e8095.jpg", + "image_caption": [ + "Ours" + ], + "image_footnote": [], + "bbox": [ + 648, + 246, + 810, + 402 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5e08bcac449a14046a8bec4e3dad845f0d485c2d506f0c20fb4d690cae71d95f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
↓RMSE×100↓MAE
[56][10]D[10]P[60]Ours[56][10]D[10]P[60]Ours
dog12.18.913.92.10.422.039.939.218.84.6
dog22.28.413.42.10.423.229.640.319.54.8
girl10.96.12.31.50.317.241.846.523.89.6
girl21.55.24.81.50.323.940.047.323.410.2
", + "bbox": [ + 78, + 472, + 465, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. RMSE and MAE for full 3D reconstructions. RMSE is computed based on the vertex to mesh distance, and the MAE is computed using the angular error between the normals of a vertex and its closest point in the ground truth mesh. OurAlbedoNet leads to highly similar results as our main framework in this scenario.", + "bbox": [ + 75, + 561, + 468, + 631 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. Results", + "text_level": 1, + "bbox": [ + 76, + 638, + 163, + 652 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To substantiate the efficacy of our framework, we conduct evaluations on both synthetic and real-world datasets. We generate four synthetic scans by combining two distinct geometries with two different materials. The first material is white, rendering it textureless, while the second material exhibits a high degree of texture. This design enables us to quantify the influence of texture on the obtained results. The four synthetic scans are denoted as dog1, dog2, girl1, and girl2. Additionally, we acquire real-world data for six objects, namely, bird, squirrel, hawk, rooster, flamingo and pumpkin. We also consider the DiLiGenT-MV dataset [28].", + "bbox": [ + 75, + 666, + 468, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Evaluation. We first evaluate full 3D reconstruction using only six viewpoints in total, except for $dog1$ and $dog2$ where five viewpoints are considered. We evaluate against both state-of-the-art sparse viewpoint reconstruction approaches", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "assuming static illumination [33, 47, 56, 65] and photometric stereo approaches [10, 60]. Since [10] allows for directional and point-light illumination, we consider both cases in our evaluation. [10]D and [10]P refers to the directional and point-light version, respectively. Given the calibrated nature of their framework, we furnish the estimated lighting parameters using our approach. Additionally, we explore a more challenging scenario wherein only two viewpoints with a wide baseline are available. We therefore introduce an ablated version of our framework, wherein the diffuse albedo is modeled with an MLP. This adaptation allows to highlight the advantages of employing the optimal diffuse albedo introduced in Sec. 5.2.", + "bbox": [ + 496, + 474, + 890, + 671 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Full 3D reconstruction. As anticipated, [33, 47, 65] produce degenerate meshes in our wide baseline setup. Results in the supplementary demonstrate that they perform adequately when the distance between cameras is sufficiently small, although our framework consistently outperforms them. Conversely, Tab. 1 and Fig. 3 illustrate that our approach surpasses relevant baselines [10, 56, 60] both quantitatively and qualitatively. Our method yields sharper details without visible artifacts. Furthermore, error maps (shown in the supplementary material) reveal that the geometry obtained with [60] exhibits global distortions. Additionally, Fig. 4 demonstrates that both [56, 60] perform poorly when confronted with complex textures, while our results remain unaffected. This suggests that their pre-trained priors failed", + "bbox": [ + 496, + 679, + 892, + 891 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11868", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d27da7d9bae56e7a823bfe9716e96702ed7917bf25c31c0e7d821c1ffbeed44c.jpg", + "image_caption": [ + "Figure 5. Re constructions from two distant viewpoints. Severe artefacts can be noticed for both [60] and OurAlbedoNet, and more particularly [60] introduce significant distortions in the shapes, as a result of using normal maps which do not provide strong enough constraints on the absolute position of the points." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 831, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to generalize for the given texture, possibly misassigning it as geometric patterns. This shows the advantage of approaches without relying on learned priors. The results for the DiLiGenT-MV dataset [28] are shown in the supplementary, demonstrating a high accuracy in the classical scenario of a dark room and distant light sources.", + "bbox": [ + 75, + 590, + 470, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Two viewpoints. We denote our ablated framework, which uses a diffuse albedo network, as OurAlbedoNet. We exclude [56] from consideration as they require at least three viewpoints. Fig. 5 vividly illustrates the advantage of our framework in this challenging scenario, especially with the use of the optimal diffuse albedo. Notably, [60] and OurAlbedoNet exhibit pronounced artifacts and inaccuracies in geometric details in certain regions. Moreover, [60] results in severe distortions of the shape. We attribute this to their heavy reliance on per-view normal maps for reconstruction, which lacks absolute depth information about the shape. In contrast, our method directly estimates the shape from various point-light illuminations, coupled with a suitable model (Eq. (1)). This approach provides relevant cues", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "about the absolute position of the points, contributing to more accurate and high-quality reconstructions.", + "bbox": [ + 498, + 590, + 890, + 621 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. A dedicated section is available in the supplementary.", + "bbox": [ + 498, + 625, + 890, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 661, + 619, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We introduced the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering approach with a physically realistic illumination model consisting of an ambient component and uncalibrated point-lights. As demonstrated in a variety of experiments, the proposed approach offers a practical paradigm to create highly accurate 3D reconstructions from sparse and distant viewpoints, even outside a controlled dark room environment.", + "bbox": [ + 496, + 681, + 890, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment This work was supported by the ERC Advanced Grant SIMULACRON, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2117 - 422037984.", + "bbox": [ + 496, + 818, + 893, + 892 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11869", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Meghna Asthana, William Smith, and Patrik Huber. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12525-12536, 2023. 2, 3" + ], + "bbox": [ + 501, + 92, + 890, + 571 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "11872", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Sparse Views Near Light_ A Practical Paradigm for Uncalibrated Point-light Photometric Stereo/631ca577-50bf-4627-9720-eaa20e92dcf3_model.json b/2024/Sparse Views Near Light_ A Practical Paradigm for Uncalibrated Point-light Photometric Stereo/631ca577-50bf-4627-9720-eaa20e92dcf3_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ac5399e861542e587228f005ce710fb4436d1995 --- /dev/null +++ b/2024/Sparse Views Near Light_ A Practical Paradigm for Uncalibrated Point-light Photometric Stereo/631ca577-50bf-4627-9720-eaa20e92dcf3_model.json @@ -0,0 +1,2950 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.351, + 0.131, + 0.619, + 0.153 + ], + "angle": 0, + "content": "Sparse Views, Near Light:" + }, + { + "type": "title", + "bbox": [ + 0.132, + 0.16, + 0.838, + 0.182 + ], + "angle": 0, + "content": "A Practical Paradigm for Uncalibrated Point-light Photometric Stereo" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.206, + 0.934, + 0.244 + ], + "angle": 0, + "content": "Mohammed Brahimi\\(^{1,2}\\) Bjoern Haefner\\(^{1,2,4^*}\\) Zhenzhang Ye\\(^{1,2}\\) Bastian Goldluecke\\(^{3}\\) Daniel Cremers\\(^{1,2}\\) TU Munich,\\(^{2}\\) Munich Center for Machine Learning,\\(^{3}\\) University of Konstanz,\\(^{4}\\) NVIDIA" + }, + { + "type": "text", + "bbox": [ + 0.257, + 0.246, + 0.741, + 0.261 + ], + "angle": 0, + "content": "{mohammed.brahimi, bjoern.haefner, yez, cremers}@tum.de" + }, + { + "type": "text", + "bbox": [ + 0.357, + 0.264, + 0.659, + 0.277 + ], + "angle": 0, + "content": "bastian.goldluecke@uni-konstanz.de" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.313, + 0.313, + 0.329 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.473, + 0.668 + ], + "angle": 0, + "content": "Neural approaches have shown a significant progress on camera-based reconstruction. But they require either a fairly dense sampling of the viewing sphere, or pre-training on an existing dataset, thereby limiting their generalizability. In contrast, photometric stereo (PS) approaches have shown great potential for achieving high-quality reconstruction under sparse viewpoints. Yet, they are impractical because they typically require tedious laboratory conditions, are restricted to dark rooms, and often multi-staged, making them subject to accumulated errors. To address these shortcomings, we propose an end-to-end uncalibrated multi-view PS framework for reconstructing high-resolution shapes acquired from sparse viewpoints in a real-world environment. We relax the dark room assumption, and allow a combination of static ambient lighting and dynamic near LED lighting, thereby enabling easy data capture outside the lab. Experimental validation confirms that it outperforms existing baseline approaches in the regime of sparse viewpoints by a large margin. This allows to bring high-accuracy 3D reconstruction from the dark room to the real world, while maintaining a reasonable data capture complexity." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.676, + 0.21, + 0.691 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.47, + 0.879 + ], + "angle": 0, + "content": "The challenge of 3D reconstruction stands as a cornerstone in both computer vision and computer graphics. Despite notable progress in recovering an object's shape from dense image viewpoints, predicting consistent geometry from sparse viewpoints remains a difficult task. Contemporary approaches employing neural data structures depend heavily on extensive training data to achieve generalization in the context of sparse views. Additionally, the presence of a wide baseline or textureless objects form significant obstacles. In contrast, photometric methodologies like photometric stereo (PS) excel in reconstructing geometry, even in textureless regions. This capability is attributed to the abun" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.312, + 0.599, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.423, + 0.591, + 0.478 + ], + "angle": 0, + "content": "Multi-illumination data at viewpoint 1" + }, + { + "type": "image", + "bbox": [ + 0.602, + 0.312, + 0.695, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.61, + 0.423, + 0.686, + 0.478 + ], + "angle": 0, + "content": "Multi-illumination data at viewpoint 2" + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.312, + 0.793, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.443, + 0.788, + 0.457 + ], + "angle": 0, + "content": "PS-NeRF [60]" + }, + { + "type": "image", + "bbox": [ + 0.795, + 0.312, + 0.889, + 0.42 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.826, + 0.444, + 0.857, + 0.457 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.607 + ], + "angle": 0, + "content": "Figure 1. We introduce the first framework for multi-view uncalibrated point-light photometric stereo. Given a set of PS images captured from different viewpoints (left), our method recovers high-fidelity 3D reconstruction (right). The acquisition of uncalibrated point-light PS imagery captured under ambient lighting in a sparse multi-view setup does not only allow for easy data capture, but also leads to 3D reconstructions of unprecedented detail. Here, with as few as two views we are able to reconstruct the squirrel's 3D geometry at higher precision than the state-of-the-art." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.709 + ], + "angle": 0, + "content": "dance of shading information derived from images acquired under diverse illumination. Yet, such approaches typically require a controlled laboratory setup to fulfill the necessary dark room and directional light assumptions. As a consequence, PS approaches become impractical beyond the confines of a laboratory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To address these shortcomings we combine state-of-the-art volume rendering formulations with a sparse multi-view photometric stereo model. In particular, we advocate a physically realistic lighting model that combines ambient light and uncalibrated point-light illumination. Our approach facilitates simplified data acquisition, and we introduce a novel pipeline capable of reconstructing an object's geometry from a sparse set of viewpoints, even if the object is completely textureless. Furthermore, since we assume a point-light model instead of distant directional lighting, we can infer absolute depth from a single viewpoint, allowing us to address the challenge of wide camera baselines." + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.332, + 0.9 + ], + "angle": 0, + "content": "*The contribution was done while at TUM." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11862" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.356, + 0.106 + ], + "angle": 0, + "content": "In detail, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.108, + 0.468, + 0.167 + ], + "angle": 0, + "content": "- We introduce the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering formulation with a physically realistic model of ambient light and point lights." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.168, + 0.468, + 0.227 + ], + "angle": 0, + "content": "- We eliminate the need for a dark room environment, dense capturing process, and distant lighting. Thereby we enhance the accessibility and simplify data acquisition for setups beyond traditional laboratory settings." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.228, + 0.468, + 0.272 + ], + "angle": 0, + "content": "- We validate that it can be successfully used for accurate shape reconstruction of textureless objects in highly sparse scenarios with wide baselines." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.274, + 0.468, + 0.318 + ], + "angle": 0, + "content": "- Despite the absence of pre-processing or vast training data, we outperform cutting-edge approaches that either rely only on static ambient illumination or PS imagery." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.108, + 0.468, + 0.318 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.326, + 0.218, + 0.342 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.468, + 0.453 + ], + "angle": 0, + "content": "In this section, we categorize pertinent works into two distinct groups. The first category focuses on neural 3D reconstruction, emphasizing the use of images captured under static ambient illumination. Subsequently, the second category delves into photometric stereo (PS) approaches, which specifically involve methods assuming images captured under varying illumination conditions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.461, + 0.31, + 0.476 + ], + "angle": 0, + "content": "2.1. Neural 3D reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.468, + 0.597 + ], + "angle": 0, + "content": "In our context, the domain of neural 3D reconstruction under static ambient light can be bifurcated into two distinct subcategories. The first comprises methodologies that presume a dense sampling of the viewing sphere [5, 11, 12, 14, 36, 38, 39, 52, 63, 64, 68]. Conversely, the second subcategory encompasses techniques adept at handling sparse camera viewpoints [7, 9, 13, 16, 22, 33, 43, 47, 51, 53, 56-59, 61, 62, 65-67]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.468, + 0.734 + ], + "angle": 0, + "content": "Given our emphasis on a sparse set of camera viewpoints, our focus will be directed toward the latter set of methodologies. The majority of sparse reconstruction approaches within this category hinge on training with a specific dataset [9, 13, 16, 47, 53, 57-59, 61, 62, 65, 67]. The reliance on extensive training data renders these techniques susceptible to errors when confronted with objects not represented in the training dataset, thereby introducing sensitivity to the domain gap between training and test data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Efforts have been undertaken to mitigate the challenges associated with the domain gap. One approach involves fine-tuning pre-trained architectures during test time with sparse input data [22, 33, 43]. However, while fine-tuning enables fine-scale refinement of the predicted reconstruction, the broader issue of generalization to entirely different datasets persists as a challenge. Furthermore, it is crucial to note that all the previously mentioned sparse approaches presume small camera baselines and textured objects. To achieve a full reconstruction of an object from sparse views, it becomes imperative to develop texture-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.872, + 0.107 + ], + "angle": 0, + "content": "agnostic approaches capable of handling wide baselines." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.108, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Another set of approaches involves the utilization of pretraining to establish a geometric prior [51, 56, 66]. Yu et al. [66] leverages this geometric prior to predict a depth and normal map, albeit with a limitation in fine-scale details due to its coarse resolution. Notably, [51, 56] address this limitation. Wu et al. [56] relax the assumption on small baselines, although a reasonable overlap of sparse views remains necessary for consistent 3D reconstruction. Vora et al. [51] demonstrate promising results with much less overlap, employing only three viewpoints. However, the use of template shapes as a prior term introduces the risk of the reconstruction quality being affected by the domain gap curse." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.365 + ], + "angle": 0, + "content": "In contrast, our approach eliminates the requirement for training data and operates effectively in wide baseline scenarios, independent of the object's texture. This accomplishment can be attributed to the integration of PS principles, which we will elucidate in the subsequent discussion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.38, + 0.685, + 0.395 + ], + "angle": 0, + "content": "2.2. Photometric Stereo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.891, + 0.476 + ], + "angle": 0, + "content": "The principle of PS [54] has a long and established history, renowned for yielding high-quality and finely detailed geometric estimates, due to its capturing process: multiple images under different illumination of a static object are captured from a single camera viewpoint." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.583 + ], + "angle": 0, + "content": "In our case, PS approaches can thus be categorized into two main types. The first category pertains to single-view methods [17, 23, 29, 30, 32, 35, 40, 45, 46, 50], wherein data is acquired as described above. The second category involves multi-view methods [1, 10, 21, 26-28, 31, 41, 55, 60, 72], where the capturing process is repeated at multiple camera viewpoints." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Within the context of our task, we concentrate on the multi-view scenario. Many existing approaches in this domain assume knowledge of the light source for each image, earning them the designation of calibrated PS (CPS). In this case, frequently the light is parameterized as directional [1, 10, 28, 72], while approaches employing point-light illumination are more sparsely represented [10, 28, 31], owing to the intricate model and the much more complex calibration process [46]. In a broader context, the calibration of each image's light source is impractical and tedious, underscoring the advantage of the uncalibrated case, which inherently facilitates a more straightforward and streamlined capturing process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Efforts have been dedicated to exploring the uncalibrated PS (UPS) scenario, where there is no prior knowledge of the light source [21, 26, 27, 41, 55, 60]. Nevertheless, all these uncalibrated methods typically assume a distant and directional light model or permit a lighting model based on spherical harmonics [2, 4, 18, 19, 44, 48, 49], albeit at the expense of being restricted to Lambertian objects [55]. Consequently, the exploration of the uncalibrated point" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11863" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "light case remains uncharted territory, particularly in the multi-view scenario." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.468, + 0.273 + ], + "angle": 0, + "content": "Despite the impractical assumption of calibrated light or the constraint of uncalibrated directional lighting, the aforementioned multi-view photometric stereo approaches demand a dark room and lack accommodation for ambient light [1, 10, 21, 26-28, 31, 41, 60, 72]. Additionally, they comprise multiple stages, rendering them prone to initialization and accumulation errors [21, 26-28, 31, 41, 55, 60]. Furthermore, these methods assume Lambertian objects [31, 55] and crucially rely on a dense sampling of camera viewpoints around the object [21, 28, 31, 41, 55]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.468, + 0.485 + ], + "angle": 0, + "content": "The approach most closely related to ours is the sparse method PS-NeRF [60], which assumes uncalibrated directional lighting with imagery captured in a dark room. This method comprises multiple stages, where initially, a pretrained network [8] is utilized to estimate the initial light, along with normal information for each image and camera view. Subsequently, this acquired information is employed to estimate the object's mesh through the optimization of an occupancy field [39]. The outputs of both stages are then combined to derive a consistent normal map of the object. Although PS-NeRF demonstrates impressive results in a sparse scenario with five viewpoints, its susceptibility to error accumulation is a potential limitation, given the involvement of multiple stages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.468, + 0.622 + ], + "angle": 0, + "content": "Our proposed model addresses the aforementioned limitations comprehensively. Notably, we excel in handling sparse yet wide baseline scenarios, where existing state-of-the-art methods encounter challenges. Our investigation tackles the open challenge of multi-view uncalibrated pointlight PS within an end-to-end framework, liberating us from the constraints associated with Lambertian objects. Furthermore, our approach facilitates easy data capture in the presence of ambient light, eliminating the need for a dark room." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.634, + 0.396, + 0.65 + ], + "angle": 0, + "content": "3. Setting and image formation model" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.468, + 0.901 + ], + "angle": 0, + "content": "We consider an object under static illumination photographed from several different viewpoints. For every viewpoint, we are given a set of \\(N + 1\\) images \\((I^l)_{l = 0,\\dots ,N}\\). Image \\(I^0\\) is captured only under static ambient illumination and called the ambient image. For images \\(I^{1}\\) to \\(I^{N}\\), the object is in addition to the ambient illumination also illuminated by a single achromatic point-light source with scalar light intensity \\(L_0\\in \\mathbb{R}^+\\), placed at a different location \\(\\mathbf{p}^l\\in \\mathbb{R}^3\\) for each image and viewpoint. We use the common assumption in volume rendering [36, 52, 56, 64] that the image brightness \\(I^l\\) is the same as the accumulated radiance of the volume rendering, see Eq. (4). Note that we do not add an index for the viewpoint to the image to not clutter notation, whenever we later evaluate an image at a pixel location, we assume it implicitly means a pixel at a specific viewpoint. In particular, a sum over all pixels is the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.813, + 0.106 + ], + "angle": 0, + "content": "sum over all pixels at every viewpoint location." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.258 + ], + "angle": 0, + "content": "According to the linearity of the radiance, the total radiance for the image \\(l\\) is given by a sum \\(\\mathcal{L}^l = \\mathcal{L}_{\\mathrm{amb}} + \\mathcal{L}_{\\mathrm{pt}}^l\\), where \\(\\mathcal{L}_{\\mathrm{amb}}\\) is the radiance due to the static illumination, the same for each image, and \\(\\mathcal{L}_{\\mathrm{pt}}^l\\) is the radiance due to the point-light source used for that particular image. We will first express the radiance due to the point-light source with respect to the material and lighting parameters, which allows to take into account the different illuminations of the images. Subsequently, we elaborate on how we deal with the ambient component." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.267, + 0.819, + 0.282 + ], + "angle": 0, + "content": "3.1. Point-light illumination and material" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.381 + ], + "angle": 0, + "content": "The field \\(L(\\mathbf{x},\\mathbf{n},\\mathbf{v})\\) maps points \\(\\mathbf{x}\\in \\mathbb{R}^3\\), normal direction \\(\\mathbf{n}(\\mathbf{x})\\in \\mathbb{S}^2\\) and viewing direction \\(\\mathbf{v}\\in \\mathbb{S}^2\\) to its radiance. It can be expressed in terms of geometry, material and lighting with the classical rendering equation [24]. Since for now we only consider a single achromatic point-light source with intensity \\(L_{0}\\) at position \\(\\mathbf{p}\\), this equation simplifies to" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.388, + 0.892, + 0.422 + ], + "angle": 0, + "content": "\\[\nL (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}) = \\frac {L _ {0}}{\\| \\mathbf {p} - \\mathbf {x} \\| ^ {2}} f _ {\\mathrm {r}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}) \\max (0, \\mathbf {n} \\cdot \\mathbf {l}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.431, + 0.623, + 0.45 + ], + "angle": 0, + "content": "where \\(\\mathbf{l} = \\frac{\\mathbf{p} - \\mathbf{x}}{\\|\\mathbf{p} - \\mathbf{x}\\|}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.892, + 0.569 + ], + "angle": 0, + "content": "As a model for the spatially varying reflectance \\( f_{\\mathrm{r}} \\), we use the simplified Disney BRDF [25]. It is relatively simple yet expressive enough to resemble a wide variety of materials. It has already been successfully used in several other prior works [5, 34, 69]. The Disney BRDF requires three parameters to be available at every point \\( \\mathbf{x} \\in \\mathbb{R}^3 \\): An RGB diffuse albedo \\( \\rho \\in \\mathbb{R}_{\\geq 0}^{3} \\), a roughness \\( \\alpha_{\\mathrm{r}} > 0 \\) and a specular albedo \\( \\alpha_{\\mathrm{s}} \\in [0,1] \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.57, + 0.892, + 0.78 + ], + "angle": 0, + "content": "As in [5], all three BRDF parameters can be represented with MLPs. One MLP with network parameters \\(\\gamma_{1}\\) computes the diffuse parameter \\(\\rho\\), a second MLP with network parameters \\(\\gamma_{2}\\) computes the specular parameters \\((\\alpha_{\\mathrm{r}},\\alpha_{\\mathrm{s}})\\). To encompass all point-light and BRDF parameters, we concatenate them into the vectors \\(\\phi = (\\mathbf{p}^{1},\\dots,\\mathbf{p}^{M})\\), which includes all light source positions (where \\(M\\) is the product of \\(N\\) with the number of viewpoints), and \\(\\gamma = (\\gamma_{1},\\gamma_{2})\\), representing the BRDF parameters. Both \\(\\phi\\) and \\(\\gamma\\) serve as the network parameters to be learned during optimization. However, note that one of our contributions is a novel strategy to deal with the diffuse albedo later on in Sec. 5.2, which dramatically improves performance in extremely sparse scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We assume that the intensity \\( L_{0} \\) remains constant across all images and views. This assumption is reasonable, e.g., when using a smartphone's flashlight or a sole LED, as shown in our experiments. A constant intensity introduces a scale ambiguity between the \\( f_{\\mathrm{r}} \\) and \\( L_{0} \\). We set \\( L_{0} \\equiv 1 \\) and subsequently estimate a scaled version of the BRDF, i.e., the intensity is absorbed into the BRDF. This is feasible, since we can scale the Disney BRDF arbitrarily." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11864" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.221, + 0.108 + ], + "angle": 0, + "content": "3.2. Ambient light" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.281 + ], + "angle": 0, + "content": "Given the provided ambient image, we adopt the approach from [71], which involves subtracting the ambient image from all other images. This process effectively eliminates ambient radiance from our considerations, simulating a traditional dark room scenario. A drawback is that in practice, the captured images contain additive noise, hence such a subtraction will double the variance of the noise distribution, resulting in noisier input images. Nevertheless, as can be seen in the results, our approach works successfully with this strategy even if we use a simple smartphone camera for the data capture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.281, + 0.471, + 0.509 + ], + "angle": 0, + "content": "However, this simplification is enabled by the fact that the point-light sources are near the object, making it easy to obtain a well exposed contribution from the point-light source. In methods assuming directional lighting, the practical simulation often involves using a point-light source placed far from the object, ensuring that the object's diameter is significantly smaller than the distance between the point-light and the object. For example, for the DiLiGenTMV dataset [28], the light sources are roughly \\(1\\mathrm{m}\\) from the object, whereas for our setup, the distance is approximately \\(25\\mathrm{cm}\\). As a consequence, for a given static ambient illumination, the distant point-light will need to be \\(16\\times\\) brighter in the Diligent setup to obtain a similar signal to noise ratio. This increased brightness requirement escalates the hardware demands, especially if the highest quality is sought." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.519, + 0.312, + 0.535 + ], + "angle": 0, + "content": "3.3. Other illumination effects" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.469, + 0.68 + ], + "angle": 0, + "content": "We do not model indirect lighting and cast-shadows explicitly. However, multiple previous works [3, 20, 34, 37, 70] and PS frameworks [10, 17, 28, 46] have demonstrated that satisfactory results can be achieved without taking these into account. In addition, we use the robust \\( L^1 \\)-norm in our data term (7) to further increase robustness. Furthermore, we will expose a simple strategy in Sec. 5 to reduce the impact of cast-shadows, which inevitably occur when capturing a nonconvex object under changing illumination." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.694, + 0.371, + 0.712 + ], + "angle": 0, + "content": "4. Volume rendering of the surface" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "For differentiable rendering we build upon VolSDF [64] because in contrast to NeRF [36] it allows us to decouple geometric representation and appearance. As discussed in [47, 56, 65], VolSDF exhibits poor reconstruction quality in the sparse viewpoint scenario due to the shape-radiance ambiguity. We eliminate this ambiguity thanks to photometric stereo, providing shading cues from different illuminations for each viewpoint. To this end, we employ the radiance field in Eq. (1) and apply it to the multi-view uncalibrated point-light PS setting. The integration of differentiable volume rendering with a physically realistic lighting model provides an efficient solution to the multi-view" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "photometric stereo problem, enabling high-quality reconstruction even with sparse viewpoints, as demonstrated in the subsequent results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.137, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Geometry model and associated density. The geometry of the scene is modeled with a signed distance function (SDF) \\(d: \\Omega \\to \\mathbb{R}\\) within the volume \\(\\Omega \\subset \\mathbb{R}^3\\). We follow [42, 52, 63, 64] and represent the SDF with an MLP \\(d(\\mathbf{x}; \\theta)\\) parametrized by \\(\\theta\\). Note that we assume positive values of the SDF \\(d\\) inside the object, thus the normal vector is given by \\(\\mathbf{n} = \\nabla d / \\| \\nabla d\\|\\) on \\(\\Omega\\). To render the scene, we follow [64] and transform the SDF into a density \\(\\sigma: \\Omega \\to \\mathbb{R}_{\\geq 0}\\) by means of the transformation" + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.277, + 0.892, + 0.296 + ], + "angle": 0, + "content": "\\[\n\\sigma (\\mathbf {x}) = \\beta^ {- 1} \\Psi_ {\\beta} (- d (\\mathbf {x})), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.301, + 0.892, + 0.36 + ], + "angle": 0, + "content": "where \\(\\Psi_{\\beta}\\) denotes the cumulative distribution function of the Laplace distribution with zero mean. The positive scale parameter \\(\\beta\\) is learned during optimization. For simplicity, we assume it is included in the set of SDF parameters \\(\\theta\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.892, + 0.422 + ], + "angle": 0, + "content": "Volume Rendering. Using the density (2), we can now set up a distribution of weights \\( w(t) \\) along each ray \\( \\mathbf{x}(t) = \\mathbf{c} + t\\mathbf{v}, t \\geq 0 \\) defined by the center of projection \\( \\mathbf{c} \\) of the camera and viewing direction \\( \\mathbf{v} \\)," + }, + { + "type": "equation", + "bbox": [ + 0.552, + 0.426, + 0.892, + 0.462 + ], + "angle": 0, + "content": "\\[\nw (t) = \\sigma (\\mathbf {x} (t)) \\exp \\left(- \\int_ {0} ^ {t} \\sigma (\\mathbf {x} (s)) \\mathrm {d} s\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.892, + 0.524 + ], + "angle": 0, + "content": "This is the derivative of the opacity function, which is monotonically increasing from zero to one, and thus \\( w \\) is indeed a probability distribution [64]. In particular, the integral" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.523, + 0.892, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p} = \\int_ {0} ^ {\\infty} w (t) L (\\mathbf {x} (t), \\mathbf {n} (t), \\mathbf {v}) \\mathrm {d} t, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.648 + ], + "angle": 0, + "content": "to compute radiance \\(\\mathcal{L}_p\\) in the pixel \\(p\\in \\mathbb{R}^2\\) corresponding to the ray \\(\\mathbf{x}(t)\\) is well-defined. Intuitively, we accumulate the radiance field (1) of the point-light source at locations where opacity increases, i.e. where we move towards the inside of the object. For an ideal sharp boundary, \\(w\\) would be a Dirac distribution with its peak placed at the boundary." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.648, + 0.892, + 0.679 + ], + "angle": 0, + "content": "As was done in [64] we approximate the integral (4) using the quadrature rule" + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.684, + 0.892, + 0.725 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {p} \\approx \\sum_ {i = 1} ^ {m - 1} \\left(t _ {i + 1} - t _ {i}\\right) w \\left(t _ {i}\\right) L \\left(\\mathbf {x} \\left(t _ {i}\\right), \\mathbf {n} \\left(t _ {i}\\right), \\mathbf {v}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.892, + 0.79 + ], + "angle": 0, + "content": "for numerical integration with a discrete set of samples \\( t_1 < t_2 < \\dots < t_m \\). Note that the integral (3) required for \\( w(t_i) \\) in (5) can be numerically computed using an analogous formula while iteratively accumulating the sum (5)." + }, + { + "type": "title", + "bbox": [ + 0.498, + 0.801, + 0.824, + 0.818 + ], + "angle": 0, + "content": "5. Training objective and optimization" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In order to reconstruct the scene by inverse rendering, we train our neural networks from the available input images. We optimize for the geometry parameters \\(\\theta\\) of the SDF network and point-light and BRDF parameters \\(\\phi\\) and \\(\\gamma\\) of the appearance network, respectively." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11865" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.434, + 0.106 + ], + "angle": 0, + "content": "5.1. Vanilla loss function with MLP for albedo" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.114, + 0.47, + 0.16 + ], + "angle": 0, + "content": "The overall loss consists of the sum of an inverse rendering loss \\( E_{\\mathrm{RGB}}(\\theta, \\phi, \\gamma) \\), an Eikonal loss \\( E_{\\mathrm{eik}}(\\theta) \\) and a mask loss \\( E_{\\mathrm{mask}}(\\theta) \\) for the SDF," + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.169, + 0.469, + 0.186 + ], + "angle": 0, + "content": "\\[\nE (\\theta , \\phi , \\gamma) = E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma) + \\lambda_ {1} E _ {\\mathrm {e i k}} (\\theta) + \\lambda_ {2} E _ {\\text {m a s k}} (\\theta), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.194, + 0.47, + 0.239 + ], + "angle": 0, + "content": "with respective weighting parameters \\(\\lambda_1, \\lambda_2 \\geq 0\\) given as hyperparameters. We will describe the different terms in detail in the following." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.24, + 0.232, + 0.255 + ], + "angle": 0, + "content": "The rendering loss" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.262, + 0.47, + 0.297 + ], + "angle": 0, + "content": "\\[\nE _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma) = \\sum_ {p} \\sum_ {l \\in B _ {\\tau} (p)} \\left\\| I _ {p} ^ {l} - \\mathcal {L} _ {p} ^ {l} (\\theta , \\phi , \\gamma) \\right\\| _ {1} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.305, + 0.471, + 0.501 + ], + "angle": 0, + "content": "encourages that the rendered images resemble the input images. As a strategy to deal with cast-shadows, for each pixel \\( p \\), we use only the \\( \\tau \\) brightest views \\( B_{\\tau}(p) \\subset \\{1 \\dots N\\} \\), where \\( \\tau > 0 \\) is a hyper-parameter. This reduces the impact of cast-shadows, as a pixel will have the smallest possible brightness when it lies in shadow. Such a strategy is necessary since despite the use of an \\( L^1 \\)-norm to improve robustness against outliers, some regions with frequent cast-shadows would still exhibit small artefacts, as can be seen in Fig. 2. In order to avoid wasting meaningful information due to this heuristic, we set \\( \\tau = N \\) for the first half of the iterations, and then set it to \\( \\tau = \\lceil \\frac{3}{4} N \\rceil \\) for the second half for improved handling of cast-shadows." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.502, + 0.224, + 0.515 + ], + "angle": 0, + "content": "The Eikonal term" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.522, + 0.469, + 0.555 + ], + "angle": 0, + "content": "\\[\nE _ {\\mathrm {e i k}} (\\theta) = \\sum_ {\\mathbf {x}} \\left(\\left\\| \\nabla_ {\\mathbf {x}} d (\\mathbf {x}; \\theta) \\right\\| - 1\\right) ^ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.563, + 0.469, + 0.607 + ], + "angle": 0, + "content": "encourages \\(d(\\mathbf{x};\\theta)\\) to approximate an SDF, as it penalizes deviations from the respective partial differential equation which every SDF satisfies, see e.g. [15]." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.608, + 0.444, + 0.623 + ], + "angle": 0, + "content": "Finally, we follow [5, 52] and employ the mask loss" + }, + { + "type": "equation", + "bbox": [ + 0.156, + 0.631, + 0.469, + 0.665 + ], + "angle": 0, + "content": "\\[\nE _ {\\text {m a s k}} (\\theta) = \\sum_ {p} \\operatorname {B C E} \\left(M _ {p}, W _ {p} (\\theta)\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.672, + 0.469, + 0.735 + ], + "angle": 0, + "content": "to impose silhouette consistency by means of the binary cross entropy (BCE) between the given binary mask \\( M_{p} \\) at the pixel \\( p \\) and the sum \\( W_{p}(\\theta) = \\sum_{i=1}^{m-1} w(t_{i};\\theta) \\) of the weights at the sampling locations \\( t_{i} \\) used in (5)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.363, + 0.759 + ], + "angle": 0, + "content": "5.2. Using the optimal diffuse albedo" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this section, we introduce a strategy to handle the diffuse albedo. This is inspired by [17], however in their single-view approach they are only able to handle the least-squares case, i.e. \\( L^2 \\), while we extend their formulation to objective functions of the form of an \\( L^p \\)-norm, with \\( p = 1 \\) in our case, see Eq. (7). In lieu of employing an MLP for modeling the diffuse albedo, we opt for approximating an optimal solution considering the remaining parameters. This allows us to exclude the diffuse albedo from the optimization" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.632, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.532, + 0.218, + 0.605, + 0.232 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.09, + 0.761, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.653, + 0.218, + 0.741, + 0.23 + ], + "angle": 0, + "content": "w/o truncation" + }, + { + "type": "image", + "bbox": [ + 0.763, + 0.09, + 0.89, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.785, + 0.218, + 0.866, + 0.23 + ], + "angle": 0, + "content": "w/ truncation" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.238, + 0.892, + 0.294 + ], + "angle": 0, + "content": "Figure 2. Effect of cast-shadows on the result. The region behind the ear exhibits frequent cast-shadows in the input images (left), which induce artefacts in the estimated mesh (middle). Our truncation strategy (Sec. 5.1) successfully eliminates these (right)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.49 + ], + "angle": 0, + "content": "process. Our subsequent demonstration will underscore the significant benefits of this approach in the context of sparse views, leading to markedly improved final geometry. A key technical change is the domain of the diffuse parameter \\(\\rho\\). So far, it has been a vector field defined in world space \\(\\Omega\\), implemented with a neural network. However, in the following we only try to recover the projection of \\(\\rho\\) on the image planes. Thus, the input to \\(\\rho\\) will be a pixel, and the output is the diffuse albedo at the intersection between the pixel's ray and the object surface. In particular, the set of BRDF parameters is reduced to \\(\\gamma = \\gamma_{2}\\) and now only includes specular parameters." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.491, + 0.892, + 0.567 + ], + "angle": 0, + "content": "Reformulation of the data term. We will now derive an expression for the data term which allows to solve for diffuse albedo \\(\\rho\\) when given all of the other parameters. Note that the SVBRDF can be decomposed into a diffuse part and a specular part [25]," + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.577, + 0.891, + 0.607 + ], + "angle": 0, + "content": "\\[\nf _ {\\mathrm {r}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}) = \\frac {\\rho (\\mathbf {x})}{\\pi} + f _ {\\mathrm {s}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.615, + 0.892, + 0.661 + ], + "angle": 0, + "content": "where the specular part \\( f_{s} \\) depends on both the roughness and specular albedo. If we denote the BRDF-independent factor of the radiance field (1) by" + }, + { + "type": "equation", + "bbox": [ + 0.571, + 0.67, + 0.891, + 0.706 + ], + "angle": 0, + "content": "\\[\nS ^ {l} (\\mathbf {x}, \\mathbf {n}) = \\frac {L _ {0}}{\\| \\mathbf {x} - \\mathbf {p} ^ {l} \\| ^ {2}} \\max (0, \\mathbf {n} \\cdot \\mathbf {l}), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.714, + 0.891, + 0.744 + ], + "angle": 0, + "content": "this implies that the total radiance field is the sum of diffuse radiance \\(\\frac{\\rho}{\\pi} S^l\\) and specular radiance \\(L_{s}^{l} = f_{s}S^{l}\\)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.745, + 0.891, + 0.775 + ], + "angle": 0, + "content": "Inserting this into the volume rendering equation (4), we can thus re-arrange the data term (7) as" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.785, + 0.89, + 0.819 + ], + "angle": 0, + "content": "\\[\nE _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma , \\rho) = \\sum_ {p} \\sum_ {l \\in S _ {\\tau} (p)} \\left\\| b _ {p} ^ {l} (\\theta , \\phi , \\gamma) - \\rho_ {p} a _ {p} ^ {l} (\\theta , \\phi) \\right\\| _ {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.822, + 0.845, + 0.855 + ], + "angle": 0, + "content": "\\[\n\\text {w i t h} a _ {p} ^ {l} (\\theta , \\phi) = \\frac {1}{\\pi} \\int_ {0} ^ {\\infty} w _ {\\theta} (t) S ^ {l} (\\mathbf {x} (t), \\mathbf {n} _ {\\theta} (t)) d t,\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.538, + 0.857, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\nb _ {p} ^ {l} (\\theta , \\phi , \\gamma) = I _ {p} ^ {l} - \\int_ {0} ^ {\\infty} w _ {\\theta} (t) L _ {s} ^ {l} (\\mathbf {x} (t), \\mathbf {n} _ {\\theta} (t), \\mathbf {v}) \\mathrm {d} t. \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11866" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.216, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.089, + 0.352, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.089, + 0.489, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.089, + 0.624, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.09, + 0.76, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.09, + 0.897, + 0.224 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.226, + 0.216, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.226, + 0.352, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.226, + 0.489, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.226, + 0.624, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.226, + 0.76, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.226, + 0.897, + 0.359 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.362, + 0.216, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.481, + 0.185, + 0.495 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.218, + 0.362, + 0.352, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.271, + 0.481, + 0.299, + 0.495 + ], + "angle": 0, + "content": "[56]" + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.362, + 0.489, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.354, + 0.481, + 0.487, + 0.495 + ], + "angle": 0, + "content": "[10] (directional light)" + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.362, + 0.624, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.506, + 0.481, + 0.608, + 0.495 + ], + "angle": 0, + "content": "[10] (point-light)" + }, + { + "type": "image", + "bbox": [ + 0.625, + 0.362, + 0.759, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.679, + 0.481, + 0.706, + 0.495 + ], + "angle": 0, + "content": "[60]" + }, + { + "type": "image", + "bbox": [ + 0.761, + 0.362, + 0.897, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.813, + 0.481, + 0.845, + 0.494 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.501, + 0.894, + 0.545 + ], + "angle": 0, + "content": "Figure 3. Full 3D reconstruction of one synthetic and two real objects from 6 viewpoints. While some of the baseline reconstructions (with directional or point-light models) exhibit texture-induced patterns, distortions or other artefacts, the proposed framework consistently yields artefact- and distortion-free reconstructions with finer geometric details. Additional results are shown in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.47, + 0.604 + ], + "angle": 0, + "content": "When keeping \\(\\theta, \\phi\\), and \\(\\gamma\\) fixed, this expression can be minimized pixel-wise for \\(\\rho\\) as a linear least absolute deviation problem, as we show next." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.47, + 0.653 + ], + "angle": 0, + "content": "Alternate treatment of the diffuse albedo. It is now possible to completely exclude the diffuse albedo \\(\\rho\\) from the optimization and simply replace it by the optimal value" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.669, + 0.47, + 0.695 + ], + "angle": 0, + "content": "\\[\n\\rho_ {\\theta , \\gamma} ^ {*} = \\underset {\\rho} {\\arg \\min } E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma , \\rho) \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.755 + ], + "angle": 0, + "content": "with respect to the other parameters. In our case, we are facing a linear least absolute deviation problem which can be solved individually for each pixel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.757, + 0.469, + 0.848 + ], + "angle": 0, + "content": "We thus approximate the solution using a few iterations of iterative reweighted least squares [6], as it efficiently solves the problem while providing a differentiable expression. In order to simplify notation, we omit the dependency w.r.t. the parameters and denote only the channel-wise operations, where we iteratively compute" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.862, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\rho_ {p} ^ {*} \\approx \\rho_ {p} ^ {(k)} = \\frac {b _ {p} ^ {\\top} W _ {p} ^ {(k)} a _ {p}}{a _ {p} ^ {\\top} W _ {p} ^ {(k)} a _ {p}} \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.559, + 0.655, + 0.575 + ], + "angle": 0, + "content": "with diagonal matrices" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.617, + 0.892, + 0.671 + ], + "angle": 0, + "content": "\\[\nW _ {p} ^ {(k)} = \\left\\{ \\begin{array}{l l} \\operatorname {d i a g} \\left(\\max \\left(\\epsilon , \\left| b _ {p} - \\rho_ {p} ^ {(k - 1)} a _ {p} \\right|\\right) ^ {- 1}\\right) & \\text {i f} k \\geq 1, \\\\ I & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Above, \\( k \\) is the index of iteration, and \\( a_{p} \\) and \\( b_{p} \\) are the vectors whose components are given in Eq. (12). The small constant \\( \\epsilon > 0 \\) avoids numerical issues, and \\( I \\) is an identity matrix of matching size. The gradient of \\( \\rho_{p}^{(k)} \\) with respect to \\( \\theta \\) and \\( \\gamma \\) is computed using automatic differentiation, however the gradient of \\( W_{p}^{(k)} \\) is not back-propagated, as it makes the optimization much more difficult and degrades the quality of the results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In the forthcoming evaluation section, we demonstrate that this formulation delivers exceptional performance in 3D reconstruction from sparse viewpoints. Notably, it proves particularly advantageous in the most sparse scenarios, where only two viewpoints are available, showcasing its superiority over the previous MLP-based formulation." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11867" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.135, + 0.088, + 0.321, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.089, + 0.484, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.089, + 0.648, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.089, + 0.812, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.136, + 0.247, + 0.321, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.197, + 0.408, + 0.286, + 0.423 + ], + "angle": 0, + "content": "Input image" + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.247, + 0.484, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.388, + 0.408, + 0.42, + 0.423 + ], + "angle": 0, + "content": "[56]" + }, + { + "type": "image", + "bbox": [ + 0.486, + 0.247, + 0.648, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.551, + 0.408, + 0.583, + 0.423 + ], + "angle": 0, + "content": "[60]" + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.247, + 0.811, + 0.403 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.711, + 0.408, + 0.749, + 0.422 + ], + "angle": 0, + "content": "Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.426, + 0.895, + 0.468 + ], + "angle": 0, + "content": "Figure 4. Results for both dog1 and dog2 obtained with 5 viewpoints reveal a notable performance degradation in [56] and [60] when confronted with complex textures. This deterioration is attributed to a generalization failure of their learned priors. In contrast, our approach, which does not rely on any prior, provides a superior reconstruction that is unaffected by the complex texture." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.473, + 0.466, + 0.557 + ], + "angle": 0, + "content": "
↓RMSE×100↓MAE
[56][10]D[10]P[60]Ours[56][10]D[10]P[60]Ours
dog12.18.913.92.10.422.039.939.218.84.6
dog22.28.413.42.10.423.229.640.319.54.8
girl10.96.12.31.50.317.241.846.523.89.6
girl21.55.24.81.50.323.940.047.323.410.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.632 + ], + "angle": 0, + "content": "Table 1. RMSE and MAE for full 3D reconstructions. RMSE is computed based on the vertex to mesh distance, and the MAE is computed using the angular error between the normals of a vertex and its closest point in the ground truth mesh. OurAlbedoNet leads to highly similar results as our main framework in this scenario." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.64, + 0.164, + 0.654 + ], + "angle": 0, + "content": "6. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.667, + 0.47, + 0.834 + ], + "angle": 0, + "content": "To substantiate the efficacy of our framework, we conduct evaluations on both synthetic and real-world datasets. We generate four synthetic scans by combining two distinct geometries with two different materials. The first material is white, rendering it textureless, while the second material exhibits a high degree of texture. This design enables us to quantify the influence of texture on the obtained results. The four synthetic scans are denoted as dog1, dog2, girl1, and girl2. Additionally, we acquire real-world data for six objects, namely, bird, squirrel, hawk, rooster, flamingo and pumpkin. We also consider the DiLiGenT-MV dataset [28]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Evaluation. We first evaluate full 3D reconstruction using only six viewpoints in total, except for \\( dog1 \\) and \\( dog2 \\) where five viewpoints are considered. We evaluate against both state-of-the-art sparse viewpoint reconstruction approaches" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.672 + ], + "angle": 0, + "content": "assuming static illumination [33, 47, 56, 65] and photometric stereo approaches [10, 60]. Since [10] allows for directional and point-light illumination, we consider both cases in our evaluation. [10]D and [10]P refers to the directional and point-light version, respectively. Given the calibrated nature of their framework, we furnish the estimated lighting parameters using our approach. Additionally, we explore a more challenging scenario wherein only two viewpoints with a wide baseline are available. We therefore introduce an ablated version of our framework, wherein the diffuse albedo is modeled with an MLP. This adaptation allows to highlight the advantages of employing the optimal diffuse albedo introduced in Sec. 5.2." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.893, + 0.892 + ], + "angle": 0, + "content": "Full 3D reconstruction. As anticipated, [33, 47, 65] produce degenerate meshes in our wide baseline setup. Results in the supplementary demonstrate that they perform adequately when the distance between cameras is sufficiently small, although our framework consistently outperforms them. Conversely, Tab. 1 and Fig. 3 illustrate that our approach surpasses relevant baselines [10, 56, 60] both quantitatively and qualitatively. Our method yields sharper details without visible artifacts. Furthermore, error maps (shown in the supplementary material) reveal that the geometry obtained with [60] exhibits global distortions. Additionally, Fig. 4 demonstrates that both [56, 60] perform poorly when confronted with complex textures, while our results remain unaffected. This suggests that their pre-trained priors failed" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11868" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.833, + 0.539 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.541, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Figure 5. Re constructions from two distant viewpoints. Severe artefacts can be noticed for both [60] and OurAlbedoNet, and more particularly [60] introduce significant distortions in the shapes, as a result of using normal maps which do not provide strong enough constraints on the absolute position of the points." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.471, + 0.682 + ], + "angle": 0, + "content": "to generalize for the given texture, possibly misassigning it as geometric patterns. This shows the advantage of approaches without relying on learned priors. The results for the DiLiGenT-MV dataset [28] are shown in the supplementary, demonstrating a high accuracy in the classical scenario of a dark room and distant light sources." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Two viewpoints. We denote our ablated framework, which uses a diffuse albedo network, as OurAlbedoNet. We exclude [56] from consideration as they require at least three viewpoints. Fig. 5 vividly illustrates the advantage of our framework in this challenging scenario, especially with the use of the optimal diffuse albedo. Notably, [60] and OurAlbedoNet exhibit pronounced artifacts and inaccuracies in geometric details in certain regions. Moreover, [60] results in severe distortions of the shape. We attribute this to their heavy reliance on per-view normal maps for reconstruction, which lacks absolute depth information about the shape. In contrast, our method directly estimates the shape from various point-light illuminations, coupled with a suitable model (Eq. (1)). This approach provides relevant cues" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.592, + 0.892, + 0.622 + ], + "angle": 0, + "content": "about the absolute position of the points, contributing to more accurate and high-quality reconstructions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.625, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Limitations and future work. A dedicated section is available in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.662, + 0.62, + 0.677 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.816 + ], + "angle": 0, + "content": "We introduced the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering approach with a physically realistic illumination model consisting of an ambient component and uncalibrated point-lights. As demonstrated in a variety of experiments, the proposed approach offers a practical paradigm to create highly accurate 3D reconstructions from sparse and distant viewpoints, even outside a controlled dark room environment." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.819, + 0.894, + 0.893 + ], + "angle": 0, + "content": "Acknowledgment This work was supported by the ERC Advanced Grant SIMULACRON, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2117 - 422037984." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11869" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.183 + ], + "angle": 0, + "content": "[1] Meghna Asthana, William Smith, and Patrik Huber. 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But they require either a fairly dense sampling of the viewing sphere, or pre-training on an existing dataset, thereby limiting their generalizability. In contrast, photometric stereo (PS) approaches have shown great potential for achieving high-quality reconstruction under sparse viewpoints. Yet, they are impractical because they typically require tedious laboratory conditions, are restricted to dark rooms, and often multi-staged, making them subject to accumulated errors. To address these shortcomings, we propose an end-to-end uncalibrated multi-view PS framework for reconstructing high-resolution shapes acquired from sparse viewpoints in a real-world environment. We relax the dark room assumption, and allow a combination of static ambient lighting and dynamic near LED lighting, thereby enabling easy data capture outside the lab. Experimental validation confirms that it outperforms existing baseline approaches in the regime of sparse viewpoints by a large margin. This allows to bring high-accuracy 3D reconstruction from the dark room to the real world, while maintaining a reasonable data capture complexity. + +# 1. Introduction + +The challenge of 3D reconstruction stands as a cornerstone in both computer vision and computer graphics. Despite notable progress in recovering an object's shape from dense image viewpoints, predicting consistent geometry from sparse viewpoints remains a difficult task. Contemporary approaches employing neural data structures depend heavily on extensive training data to achieve generalization in the context of sparse views. Additionally, the presence of a wide baseline or textureless objects form significant obstacles. In contrast, photometric methodologies like photometric stereo (PS) excel in reconstructing geometry, even in textureless regions. This capability is attributed to the abun + +![](images/e484abd1f8da38cadfee03b24958334199b2ee1f1fa1736a7f6b77f9e96dec2c.jpg) +Multi-illumination data at viewpoint 1 + +![](images/f859c10146c0912ffe63f6911819ecffb008ea50c15a1fc9f58b9c26d64c03e9.jpg) +Multi-illumination data at viewpoint 2 + +![](images/bb8c0d3f923ef4502153f92ad0bd298eaee58ba3e8c67722ffd595fe5f5eb59a.jpg) +PS-NeRF [60] + +![](images/fc34dde2b27b7fe4660f050e43b34c54be2a6358091780fef6fb8789c686db55.jpg) +Ours +Figure 1. We introduce the first framework for multi-view uncalibrated point-light photometric stereo. Given a set of PS images captured from different viewpoints (left), our method recovers high-fidelity 3D reconstruction (right). The acquisition of uncalibrated point-light PS imagery captured under ambient lighting in a sparse multi-view setup does not only allow for easy data capture, but also leads to 3D reconstructions of unprecedented detail. Here, with as few as two views we are able to reconstruct the squirrel's 3D geometry at higher precision than the state-of-the-art. + +dance of shading information derived from images acquired under diverse illumination. Yet, such approaches typically require a controlled laboratory setup to fulfill the necessary dark room and directional light assumptions. As a consequence, PS approaches become impractical beyond the confines of a laboratory. + +To address these shortcomings we combine state-of-the-art volume rendering formulations with a sparse multi-view photometric stereo model. In particular, we advocate a physically realistic lighting model that combines ambient light and uncalibrated point-light illumination. Our approach facilitates simplified data acquisition, and we introduce a novel pipeline capable of reconstructing an object's geometry from a sparse set of viewpoints, even if the object is completely textureless. Furthermore, since we assume a point-light model instead of distant directional lighting, we can infer absolute depth from a single viewpoint, allowing us to address the challenge of wide camera baselines. + +In detail, our contributions are as follows: + +- We introduce the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering formulation with a physically realistic model of ambient light and point lights. +- We eliminate the need for a dark room environment, dense capturing process, and distant lighting. Thereby we enhance the accessibility and simplify data acquisition for setups beyond traditional laboratory settings. +- We validate that it can be successfully used for accurate shape reconstruction of textureless objects in highly sparse scenarios with wide baselines. +- Despite the absence of pre-processing or vast training data, we outperform cutting-edge approaches that either rely only on static ambient illumination or PS imagery. + +# 2. Related Work + +In this section, we categorize pertinent works into two distinct groups. The first category focuses on neural 3D reconstruction, emphasizing the use of images captured under static ambient illumination. Subsequently, the second category delves into photometric stereo (PS) approaches, which specifically involve methods assuming images captured under varying illumination conditions. + +# 2.1. Neural 3D reconstruction + +In our context, the domain of neural 3D reconstruction under static ambient light can be bifurcated into two distinct subcategories. The first comprises methodologies that presume a dense sampling of the viewing sphere [5, 11, 12, 14, 36, 38, 39, 52, 63, 64, 68]. Conversely, the second subcategory encompasses techniques adept at handling sparse camera viewpoints [7, 9, 13, 16, 22, 33, 43, 47, 51, 53, 56-59, 61, 62, 65-67]. + +Given our emphasis on a sparse set of camera viewpoints, our focus will be directed toward the latter set of methodologies. The majority of sparse reconstruction approaches within this category hinge on training with a specific dataset [9, 13, 16, 47, 53, 57-59, 61, 62, 65, 67]. The reliance on extensive training data renders these techniques susceptible to errors when confronted with objects not represented in the training dataset, thereby introducing sensitivity to the domain gap between training and test data. + +Efforts have been undertaken to mitigate the challenges associated with the domain gap. One approach involves fine-tuning pre-trained architectures during test time with sparse input data [22, 33, 43]. However, while fine-tuning enables fine-scale refinement of the predicted reconstruction, the broader issue of generalization to entirely different datasets persists as a challenge. Furthermore, it is crucial to note that all the previously mentioned sparse approaches presume small camera baselines and textured objects. To achieve a full reconstruction of an object from sparse views, it becomes imperative to develop texture- + +agnostic approaches capable of handling wide baselines. + +Another set of approaches involves the utilization of pretraining to establish a geometric prior [51, 56, 66]. Yu et al. [66] leverages this geometric prior to predict a depth and normal map, albeit with a limitation in fine-scale details due to its coarse resolution. Notably, [51, 56] address this limitation. Wu et al. [56] relax the assumption on small baselines, although a reasonable overlap of sparse views remains necessary for consistent 3D reconstruction. Vora et al. [51] demonstrate promising results with much less overlap, employing only three viewpoints. However, the use of template shapes as a prior term introduces the risk of the reconstruction quality being affected by the domain gap curse. + +In contrast, our approach eliminates the requirement for training data and operates effectively in wide baseline scenarios, independent of the object's texture. This accomplishment can be attributed to the integration of PS principles, which we will elucidate in the subsequent discussion. + +# 2.2. Photometric Stereo + +The principle of PS [54] has a long and established history, renowned for yielding high-quality and finely detailed geometric estimates, due to its capturing process: multiple images under different illumination of a static object are captured from a single camera viewpoint. + +In our case, PS approaches can thus be categorized into two main types. The first category pertains to single-view methods [17, 23, 29, 30, 32, 35, 40, 45, 46, 50], wherein data is acquired as described above. The second category involves multi-view methods [1, 10, 21, 26-28, 31, 41, 55, 60, 72], where the capturing process is repeated at multiple camera viewpoints. + +Within the context of our task, we concentrate on the multi-view scenario. Many existing approaches in this domain assume knowledge of the light source for each image, earning them the designation of calibrated PS (CPS). In this case, frequently the light is parameterized as directional [1, 10, 28, 72], while approaches employing point-light illumination are more sparsely represented [10, 28, 31], owing to the intricate model and the much more complex calibration process [46]. In a broader context, the calibration of each image's light source is impractical and tedious, underscoring the advantage of the uncalibrated case, which inherently facilitates a more straightforward and streamlined capturing process. + +Efforts have been dedicated to exploring the uncalibrated PS (UPS) scenario, where there is no prior knowledge of the light source [21, 26, 27, 41, 55, 60]. Nevertheless, all these uncalibrated methods typically assume a distant and directional light model or permit a lighting model based on spherical harmonics [2, 4, 18, 19, 44, 48, 49], albeit at the expense of being restricted to Lambertian objects [55]. Consequently, the exploration of the uncalibrated point + +light case remains uncharted territory, particularly in the multi-view scenario. + +Despite the impractical assumption of calibrated light or the constraint of uncalibrated directional lighting, the aforementioned multi-view photometric stereo approaches demand a dark room and lack accommodation for ambient light [1, 10, 21, 26-28, 31, 41, 60, 72]. Additionally, they comprise multiple stages, rendering them prone to initialization and accumulation errors [21, 26-28, 31, 41, 55, 60]. Furthermore, these methods assume Lambertian objects [31, 55] and crucially rely on a dense sampling of camera viewpoints around the object [21, 28, 31, 41, 55]. + +The approach most closely related to ours is the sparse method PS-NeRF [60], which assumes uncalibrated directional lighting with imagery captured in a dark room. This method comprises multiple stages, where initially, a pretrained network [8] is utilized to estimate the initial light, along with normal information for each image and camera view. Subsequently, this acquired information is employed to estimate the object's mesh through the optimization of an occupancy field [39]. The outputs of both stages are then combined to derive a consistent normal map of the object. Although PS-NeRF demonstrates impressive results in a sparse scenario with five viewpoints, its susceptibility to error accumulation is a potential limitation, given the involvement of multiple stages. + +Our proposed model addresses the aforementioned limitations comprehensively. Notably, we excel in handling sparse yet wide baseline scenarios, where existing state-of-the-art methods encounter challenges. Our investigation tackles the open challenge of multi-view uncalibrated pointlight PS within an end-to-end framework, liberating us from the constraints associated with Lambertian objects. Furthermore, our approach facilitates easy data capture in the presence of ambient light, eliminating the need for a dark room. + +# 3. Setting and image formation model + +We consider an object under static illumination photographed from several different viewpoints. For every viewpoint, we are given a set of $N + 1$ images $(I^l)_{l = 0,\dots ,N}$ . Image $I^0$ is captured only under static ambient illumination and called the ambient image. For images $I^{1}$ to $I^{N}$ , the object is in addition to the ambient illumination also illuminated by a single achromatic point-light source with scalar light intensity $L_0\in \mathbb{R}^+$ , placed at a different location $\mathbf{p}^l\in \mathbb{R}^3$ for each image and viewpoint. We use the common assumption in volume rendering [36, 52, 56, 64] that the image brightness $I^l$ is the same as the accumulated radiance of the volume rendering, see Eq. (4). Note that we do not add an index for the viewpoint to the image to not clutter notation, whenever we later evaluate an image at a pixel location, we assume it implicitly means a pixel at a specific viewpoint. In particular, a sum over all pixels is the + +sum over all pixels at every viewpoint location. + +According to the linearity of the radiance, the total radiance for the image $l$ is given by a sum $\mathcal{L}^l = \mathcal{L}_{\mathrm{amb}} + \mathcal{L}_{\mathrm{pt}}^l$ , where $\mathcal{L}_{\mathrm{amb}}$ is the radiance due to the static illumination, the same for each image, and $\mathcal{L}_{\mathrm{pt}}^l$ is the radiance due to the point-light source used for that particular image. We will first express the radiance due to the point-light source with respect to the material and lighting parameters, which allows to take into account the different illuminations of the images. Subsequently, we elaborate on how we deal with the ambient component. + +# 3.1. Point-light illumination and material + +The field $L(\mathbf{x},\mathbf{n},\mathbf{v})$ maps points $\mathbf{x}\in \mathbb{R}^3$ , normal direction $\mathbf{n}(\mathbf{x})\in \mathbb{S}^2$ and viewing direction $\mathbf{v}\in \mathbb{S}^2$ to its radiance. It can be expressed in terms of geometry, material and lighting with the classical rendering equation [24]. Since for now we only consider a single achromatic point-light source with intensity $L_{0}$ at position $\mathbf{p}$ , this equation simplifies to + +$$ +L (\mathbf {x}, \mathbf {n}, \mathbf {v}) = \frac {L _ {0}}{\| \mathbf {p} - \mathbf {x} \| ^ {2}} f _ {\mathrm {r}} (\mathbf {x}, \mathbf {n}, \mathbf {v}, \mathbf {l}) \max (0, \mathbf {n} \cdot \mathbf {l}), \tag {1} +$$ + +where $\mathbf{l} = \frac{\mathbf{p} - \mathbf{x}}{\|\mathbf{p} - \mathbf{x}\|}$ + +As a model for the spatially varying reflectance $f_{\mathrm{r}}$ , we use the simplified Disney BRDF [25]. It is relatively simple yet expressive enough to resemble a wide variety of materials. It has already been successfully used in several other prior works [5, 34, 69]. The Disney BRDF requires three parameters to be available at every point $\mathbf{x} \in \mathbb{R}^3$ : An RGB diffuse albedo $\rho \in \mathbb{R}_{\geq 0}^{3}$ , a roughness $\alpha_{\mathrm{r}} > 0$ and a specular albedo $\alpha_{\mathrm{s}} \in [0,1]$ . + +As in [5], all three BRDF parameters can be represented with MLPs. One MLP with network parameters $\gamma_{1}$ computes the diffuse parameter $\rho$ , a second MLP with network parameters $\gamma_{2}$ computes the specular parameters $(\alpha_{\mathrm{r}},\alpha_{\mathrm{s}})$ . To encompass all point-light and BRDF parameters, we concatenate them into the vectors $\phi = (\mathbf{p}^{1},\dots,\mathbf{p}^{M})$ , which includes all light source positions (where $M$ is the product of $N$ with the number of viewpoints), and $\gamma = (\gamma_{1},\gamma_{2})$ , representing the BRDF parameters. Both $\phi$ and $\gamma$ serve as the network parameters to be learned during optimization. However, note that one of our contributions is a novel strategy to deal with the diffuse albedo later on in Sec. 5.2, which dramatically improves performance in extremely sparse scenarios. + +We assume that the intensity $L_{0}$ remains constant across all images and views. This assumption is reasonable, e.g., when using a smartphone's flashlight or a sole LED, as shown in our experiments. A constant intensity introduces a scale ambiguity between the $f_{\mathrm{r}}$ and $L_{0}$ . We set $L_{0} \equiv 1$ and subsequently estimate a scaled version of the BRDF, i.e., the intensity is absorbed into the BRDF. This is feasible, since we can scale the Disney BRDF arbitrarily. + +# 3.2. Ambient light + +Given the provided ambient image, we adopt the approach from [71], which involves subtracting the ambient image from all other images. This process effectively eliminates ambient radiance from our considerations, simulating a traditional dark room scenario. A drawback is that in practice, the captured images contain additive noise, hence such a subtraction will double the variance of the noise distribution, resulting in noisier input images. Nevertheless, as can be seen in the results, our approach works successfully with this strategy even if we use a simple smartphone camera for the data capture. + +However, this simplification is enabled by the fact that the point-light sources are near the object, making it easy to obtain a well exposed contribution from the point-light source. In methods assuming directional lighting, the practical simulation often involves using a point-light source placed far from the object, ensuring that the object's diameter is significantly smaller than the distance between the point-light and the object. For example, for the DiLiGenTMV dataset [28], the light sources are roughly $1\mathrm{m}$ from the object, whereas for our setup, the distance is approximately $25\mathrm{cm}$ . As a consequence, for a given static ambient illumination, the distant point-light will need to be $16\times$ brighter in the Diligent setup to obtain a similar signal to noise ratio. This increased brightness requirement escalates the hardware demands, especially if the highest quality is sought. + +# 3.3. Other illumination effects + +We do not model indirect lighting and cast-shadows explicitly. However, multiple previous works [3, 20, 34, 37, 70] and PS frameworks [10, 17, 28, 46] have demonstrated that satisfactory results can be achieved without taking these into account. In addition, we use the robust $L^1$ -norm in our data term (7) to further increase robustness. Furthermore, we will expose a simple strategy in Sec. 5 to reduce the impact of cast-shadows, which inevitably occur when capturing a nonconvex object under changing illumination. + +# 4. Volume rendering of the surface + +For differentiable rendering we build upon VolSDF [64] because in contrast to NeRF [36] it allows us to decouple geometric representation and appearance. As discussed in [47, 56, 65], VolSDF exhibits poor reconstruction quality in the sparse viewpoint scenario due to the shape-radiance ambiguity. We eliminate this ambiguity thanks to photometric stereo, providing shading cues from different illuminations for each viewpoint. To this end, we employ the radiance field in Eq. (1) and apply it to the multi-view uncalibrated point-light PS setting. The integration of differentiable volume rendering with a physically realistic lighting model provides an efficient solution to the multi-view + +photometric stereo problem, enabling high-quality reconstruction even with sparse viewpoints, as demonstrated in the subsequent results. + +Geometry model and associated density. The geometry of the scene is modeled with a signed distance function (SDF) $d: \Omega \to \mathbb{R}$ within the volume $\Omega \subset \mathbb{R}^3$ . We follow [42, 52, 63, 64] and represent the SDF with an MLP $d(\mathbf{x}; \theta)$ parametrized by $\theta$ . Note that we assume positive values of the SDF $d$ inside the object, thus the normal vector is given by $\mathbf{n} = \nabla d / \| \nabla d\|$ on $\Omega$ . To render the scene, we follow [64] and transform the SDF into a density $\sigma: \Omega \to \mathbb{R}_{\geq 0}$ by means of the transformation + +$$ +\sigma (\mathbf {x}) = \beta^ {- 1} \Psi_ {\beta} (- d (\mathbf {x})), \tag {2} +$$ + +where $\Psi_{\beta}$ denotes the cumulative distribution function of the Laplace distribution with zero mean. The positive scale parameter $\beta$ is learned during optimization. For simplicity, we assume it is included in the set of SDF parameters $\theta$ . + +Volume Rendering. Using the density (2), we can now set up a distribution of weights $w(t)$ along each ray $\mathbf{x}(t) = \mathbf{c} + t\mathbf{v}, t \geq 0$ defined by the center of projection $\mathbf{c}$ of the camera and viewing direction $\mathbf{v}$ , + +$$ +w (t) = \sigma (\mathbf {x} (t)) \exp \left(- \int_ {0} ^ {t} \sigma (\mathbf {x} (s)) \mathrm {d} s\right). \tag {3} +$$ + +This is the derivative of the opacity function, which is monotonically increasing from zero to one, and thus $w$ is indeed a probability distribution [64]. In particular, the integral + +$$ +\mathcal {L} _ {p} = \int_ {0} ^ {\infty} w (t) L (\mathbf {x} (t), \mathbf {n} (t), \mathbf {v}) \mathrm {d} t, \tag {4} +$$ + +to compute radiance $\mathcal{L}_p$ in the pixel $p\in \mathbb{R}^2$ corresponding to the ray $\mathbf{x}(t)$ is well-defined. Intuitively, we accumulate the radiance field (1) of the point-light source at locations where opacity increases, i.e. where we move towards the inside of the object. For an ideal sharp boundary, $w$ would be a Dirac distribution with its peak placed at the boundary. + +As was done in [64] we approximate the integral (4) using the quadrature rule + +$$ +\mathcal {L} _ {p} \approx \sum_ {i = 1} ^ {m - 1} \left(t _ {i + 1} - t _ {i}\right) w \left(t _ {i}\right) L \left(\mathbf {x} \left(t _ {i}\right), \mathbf {n} \left(t _ {i}\right), \mathbf {v}\right). \tag {5} +$$ + +for numerical integration with a discrete set of samples $t_1 < t_2 < \dots < t_m$ . Note that the integral (3) required for $w(t_i)$ in (5) can be numerically computed using an analogous formula while iteratively accumulating the sum (5). + +# 5. Training objective and optimization + +In order to reconstruct the scene by inverse rendering, we train our neural networks from the available input images. We optimize for the geometry parameters $\theta$ of the SDF network and point-light and BRDF parameters $\phi$ and $\gamma$ of the appearance network, respectively. + +# 5.1. Vanilla loss function with MLP for albedo + +The overall loss consists of the sum of an inverse rendering loss $E_{\mathrm{RGB}}(\theta, \phi, \gamma)$ , an Eikonal loss $E_{\mathrm{eik}}(\theta)$ and a mask loss $E_{\mathrm{mask}}(\theta)$ for the SDF, + +$$ +E (\theta , \phi , \gamma) = E _ {\mathrm {R G B}} (\theta , \phi , \gamma) + \lambda_ {1} E _ {\mathrm {e i k}} (\theta) + \lambda_ {2} E _ {\text {m a s k}} (\theta), \tag {6} +$$ + +with respective weighting parameters $\lambda_1, \lambda_2 \geq 0$ given as hyperparameters. We will describe the different terms in detail in the following. + +The rendering loss + +$$ +E _ {\mathrm {R G B}} (\theta , \phi , \gamma) = \sum_ {p} \sum_ {l \in B _ {\tau} (p)} \left\| I _ {p} ^ {l} - \mathcal {L} _ {p} ^ {l} (\theta , \phi , \gamma) \right\| _ {1} \tag {7} +$$ + +encourages that the rendered images resemble the input images. As a strategy to deal with cast-shadows, for each pixel $p$ , we use only the $\tau$ brightest views $B_{\tau}(p) \subset \{1 \dots N\}$ , where $\tau > 0$ is a hyper-parameter. This reduces the impact of cast-shadows, as a pixel will have the smallest possible brightness when it lies in shadow. Such a strategy is necessary since despite the use of an $L^1$ -norm to improve robustness against outliers, some regions with frequent cast-shadows would still exhibit small artefacts, as can be seen in Fig. 2. In order to avoid wasting meaningful information due to this heuristic, we set $\tau = N$ for the first half of the iterations, and then set it to $\tau = \lceil \frac{3}{4} N \rceil$ for the second half for improved handling of cast-shadows. + +The Eikonal term + +$$ +E _ {\mathrm {e i k}} (\theta) = \sum_ {\mathbf {x}} \left(\left\| \nabla_ {\mathbf {x}} d (\mathbf {x}; \theta) \right\| - 1\right) ^ {2} \tag {8} +$$ + +encourages $d(\mathbf{x};\theta)$ to approximate an SDF, as it penalizes deviations from the respective partial differential equation which every SDF satisfies, see e.g. [15]. + +Finally, we follow [5, 52] and employ the mask loss + +$$ +E _ {\text {m a s k}} (\theta) = \sum_ {p} \operatorname {B C E} \left(M _ {p}, W _ {p} (\theta)\right), \tag {9} +$$ + +to impose silhouette consistency by means of the binary cross entropy (BCE) between the given binary mask $M_{p}$ at the pixel $p$ and the sum $W_{p}(\theta) = \sum_{i=1}^{m-1} w(t_{i};\theta)$ of the weights at the sampling locations $t_{i}$ used in (5). + +# 5.2. Using the optimal diffuse albedo + +In this section, we introduce a strategy to handle the diffuse albedo. This is inspired by [17], however in their single-view approach they are only able to handle the least-squares case, i.e. $L^2$ , while we extend their formulation to objective functions of the form of an $L^p$ -norm, with $p = 1$ in our case, see Eq. (7). In lieu of employing an MLP for modeling the diffuse albedo, we opt for approximating an optimal solution considering the remaining parameters. This allows us to exclude the diffuse albedo from the optimization + +![](images/316363b2f55a0466a63ae7b294c37ae992c3a0e5b0bdb43690891ab93c5dfd0d.jpg) +Input image + +![](images/0bf9fb90e483bce5c5f2883db97bd18c6ae44833fd3939cc9b60fee473ed7c16.jpg) +w/o truncation + +![](images/cbb80f3db5953b1ad83a183d45ab76f6812e32cb43d29721c8227b9d1fa2b74b.jpg) +w/ truncation +Figure 2. Effect of cast-shadows on the result. The region behind the ear exhibits frequent cast-shadows in the input images (left), which induce artefacts in the estimated mesh (middle). Our truncation strategy (Sec. 5.1) successfully eliminates these (right). + +process. Our subsequent demonstration will underscore the significant benefits of this approach in the context of sparse views, leading to markedly improved final geometry. A key technical change is the domain of the diffuse parameter $\rho$ . So far, it has been a vector field defined in world space $\Omega$ , implemented with a neural network. However, in the following we only try to recover the projection of $\rho$ on the image planes. Thus, the input to $\rho$ will be a pixel, and the output is the diffuse albedo at the intersection between the pixel's ray and the object surface. In particular, the set of BRDF parameters is reduced to $\gamma = \gamma_{2}$ and now only includes specular parameters. + +Reformulation of the data term. We will now derive an expression for the data term which allows to solve for diffuse albedo $\rho$ when given all of the other parameters. Note that the SVBRDF can be decomposed into a diffuse part and a specular part [25], + +$$ +f _ {\mathrm {r}} (\mathbf {x}, \mathbf {n}, \mathbf {v}, \mathbf {l}) = \frac {\rho (\mathbf {x})}{\pi} + f _ {\mathrm {s}} (\mathbf {x}, \mathbf {n}, \mathbf {v}, \mathbf {l}), \tag {10} +$$ + +where the specular part $f_{s}$ depends on both the roughness and specular albedo. If we denote the BRDF-independent factor of the radiance field (1) by + +$$ +S ^ {l} (\mathbf {x}, \mathbf {n}) = \frac {L _ {0}}{\| \mathbf {x} - \mathbf {p} ^ {l} \| ^ {2}} \max (0, \mathbf {n} \cdot \mathbf {l}), \tag {11} +$$ + +this implies that the total radiance field is the sum of diffuse radiance $\frac{\rho}{\pi} S^l$ and specular radiance $L_{s}^{l} = f_{s}S^{l}$ + +Inserting this into the volume rendering equation (4), we can thus re-arrange the data term (7) as + +$$ +E _ {\mathrm {R G B}} (\theta , \phi , \gamma , \rho) = \sum_ {p} \sum_ {l \in S _ {\tau} (p)} \left\| b _ {p} ^ {l} (\theta , \phi , \gamma) - \rho_ {p} a _ {p} ^ {l} (\theta , \phi) \right\| _ {1} +$$ + +$$ +\text {w i t h} a _ {p} ^ {l} (\theta , \phi) = \frac {1}{\pi} \int_ {0} ^ {\infty} w _ {\theta} (t) S ^ {l} (\mathbf {x} (t), \mathbf {n} _ {\theta} (t)) d t, +$$ + +$$ +b _ {p} ^ {l} (\theta , \phi , \gamma) = I _ {p} ^ {l} - \int_ {0} ^ {\infty} w _ {\theta} (t) L _ {s} ^ {l} (\mathbf {x} (t), \mathbf {n} _ {\theta} (t), \mathbf {v}) \mathrm {d} t. \tag {12} +$$ + +![](images/0b76a767f9d3525b7438e9e18b49888abd502c0b6831cbdd18f86d375b9acee2.jpg) + +![](images/791d8c0f7e5146136557ad427c246eb1ad81ab40c15bd6389e471774330cc9ca.jpg) + +![](images/2c2e940475ec275a1c2c0d64f06eec9ce6fa9dcbebab2d2ff4f198bd7cffd50a.jpg) + +![](images/f2fbe2104cfe1789464e0853cacdd8d8e15eb2d4dd19caaa986f9488f73410b7.jpg) + +![](images/e456e9d05f99b90088e706a1f5b88babccf1c59250dc6434d3ebbbc11e1af47a.jpg) + +![](images/ba893907ebfff2653b8c38745cf168117102f312648526dd28e113cd727afe31.jpg) + +![](images/7ba982d3ada94a2896ee42e54608462ae345495f02fbf4b14cb6a5c349457139.jpg) + +![](images/b0b33248077d422b0d23a6913e0929a84a37a148c8bf671cecb47e9be4d76c83.jpg) + +![](images/aed9e7d0952a545024a556a33368b326706eb5119d239002829462c6e059eb31.jpg) + +![](images/7ef6cf2a649ba72dcccc387c6375ee1368a2cb6cfee7937cfdbd642eff29733b.jpg) + +![](images/13bf65b592b2e14e7f9b24701204da4fb4923261ff0539f573390c61c419264b.jpg) + +![](images/e0b924f1df27f590b66ba8fe1bce8b7509c0ff47dd31bbcccea4076489c7985d.jpg) + +![](images/b6c53ea157d0df8df4d61112b8b02568bd13d6a30ba4c12b6763d20cf600f521.jpg) +Input image + +![](images/36510e363a7e5c2cf286c03728d8d382026d9e0edb3b0f1b8c3bf8eaa7be1f31.jpg) +[56] + +![](images/13ae59f6c1170596fd92e61646471230a81af8f7337c9b8b903d6bebcd22937a.jpg) +[10] (directional light) + +![](images/a7486fee1223a73299d6438275b08ab8a6d842cad8dbd582e61eb277c4c3a80d.jpg) +[10] (point-light) +Figure 3. Full 3D reconstruction of one synthetic and two real objects from 6 viewpoints. While some of the baseline reconstructions (with directional or point-light models) exhibit texture-induced patterns, distortions or other artefacts, the proposed framework consistently yields artefact- and distortion-free reconstructions with finer geometric details. Additional results are shown in the supplementary. + +![](images/373f6e21228766d7239ef4a72df1b9fd6e8b0a59606372617413126a5497e65e.jpg) +[60] + +![](images/51d80fd74f2fe355ea5fbbb3db82b28038de9d8c8a79b393a810f0d25130e28f.jpg) +Ours + +When keeping $\theta, \phi$ , and $\gamma$ fixed, this expression can be minimized pixel-wise for $\rho$ as a linear least absolute deviation problem, as we show next. + +Alternate treatment of the diffuse albedo. It is now possible to completely exclude the diffuse albedo $\rho$ from the optimization and simply replace it by the optimal value + +$$ +\rho_ {\theta , \gamma} ^ {*} = \underset {\rho} {\arg \min } E _ {\mathrm {R G B}} (\theta , \phi , \gamma , \rho) \tag {13} +$$ + +with respect to the other parameters. In our case, we are facing a linear least absolute deviation problem which can be solved individually for each pixel. + +We thus approximate the solution using a few iterations of iterative reweighted least squares [6], as it efficiently solves the problem while providing a differentiable expression. In order to simplify notation, we omit the dependency w.r.t. the parameters and denote only the channel-wise operations, where we iteratively compute + +$$ +\rho_ {p} ^ {*} \approx \rho_ {p} ^ {(k)} = \frac {b _ {p} ^ {\top} W _ {p} ^ {(k)} a _ {p}}{a _ {p} ^ {\top} W _ {p} ^ {(k)} a _ {p}} \tag {14} +$$ + +with diagonal matrices + +$$ +W _ {p} ^ {(k)} = \left\{ \begin{array}{l l} \operatorname {d i a g} \left(\max \left(\epsilon , \left| b _ {p} - \rho_ {p} ^ {(k - 1)} a _ {p} \right|\right) ^ {- 1}\right) & \text {i f} k \geq 1, \\ I & \text {o t h e r w i s e .} \end{array} \right. \tag {15} +$$ + +Above, $k$ is the index of iteration, and $a_{p}$ and $b_{p}$ are the vectors whose components are given in Eq. (12). The small constant $\epsilon > 0$ avoids numerical issues, and $I$ is an identity matrix of matching size. The gradient of $\rho_{p}^{(k)}$ with respect to $\theta$ and $\gamma$ is computed using automatic differentiation, however the gradient of $W_{p}^{(k)}$ is not back-propagated, as it makes the optimization much more difficult and degrades the quality of the results. + +In the forthcoming evaluation section, we demonstrate that this formulation delivers exceptional performance in 3D reconstruction from sparse viewpoints. Notably, it proves particularly advantageous in the most sparse scenarios, where only two viewpoints are available, showcasing its superiority over the previous MLP-based formulation. + +![](images/70a24bcbb12fe780e39005cf3dfebf887e3da9215852413fbf5631950d31fdff.jpg) + +![](images/920f25e6d99a32a5ae18821105301ea345d71b7ba17bd689d85536338c78c7e7.jpg) + +![](images/6a0593c76481bc33443b74c305aff214b569979995a84566b0eda50d29e08c2b.jpg) + +![](images/1be26b5ca4a982bd51bc005fee66364078be79d1b7814d04eaa375cd587e5fb3.jpg) + +![](images/bab47f412ab7cd68c5212c1efad3bf4c110ab986fd4e0a73da30aeda099c8288.jpg) +Input image + +![](images/03238a92605ddcc980df71311f777faa2699e9c1087faeef95fd89d0dd2ec741.jpg) +[56] + +![](images/46d1f360e2f33a7b0f3d7808712feaf2242077d790ef8d85539458266e6cc259.jpg) +[60] +Figure 4. Results for both dog1 and dog2 obtained with 5 viewpoints reveal a notable performance degradation in [56] and [60] when confronted with complex textures. This deterioration is attributed to a generalization failure of their learned priors. In contrast, our approach, which does not rely on any prior, provides a superior reconstruction that is unaffected by the complex texture. + +![](images/fc24ce5b476f4ce55e8b740c384ebbfb67bb00aa305222948c54c0f2201e8095.jpg) +Ours + +
↓RMSE×100↓MAE
[56][10]D[10]P[60]Ours[56][10]D[10]P[60]Ours
dog12.18.913.92.10.422.039.939.218.84.6
dog22.28.413.42.10.423.229.640.319.54.8
girl10.96.12.31.50.317.241.846.523.89.6
girl21.55.24.81.50.323.940.047.323.410.2
+ +Table 1. RMSE and MAE for full 3D reconstructions. RMSE is computed based on the vertex to mesh distance, and the MAE is computed using the angular error between the normals of a vertex and its closest point in the ground truth mesh. OurAlbedoNet leads to highly similar results as our main framework in this scenario. + +# 6. Results + +To substantiate the efficacy of our framework, we conduct evaluations on both synthetic and real-world datasets. We generate four synthetic scans by combining two distinct geometries with two different materials. The first material is white, rendering it textureless, while the second material exhibits a high degree of texture. This design enables us to quantify the influence of texture on the obtained results. The four synthetic scans are denoted as dog1, dog2, girl1, and girl2. Additionally, we acquire real-world data for six objects, namely, bird, squirrel, hawk, rooster, flamingo and pumpkin. We also consider the DiLiGenT-MV dataset [28]. + +Evaluation. We first evaluate full 3D reconstruction using only six viewpoints in total, except for $dog1$ and $dog2$ where five viewpoints are considered. We evaluate against both state-of-the-art sparse viewpoint reconstruction approaches + +assuming static illumination [33, 47, 56, 65] and photometric stereo approaches [10, 60]. Since [10] allows for directional and point-light illumination, we consider both cases in our evaluation. [10]D and [10]P refers to the directional and point-light version, respectively. Given the calibrated nature of their framework, we furnish the estimated lighting parameters using our approach. Additionally, we explore a more challenging scenario wherein only two viewpoints with a wide baseline are available. We therefore introduce an ablated version of our framework, wherein the diffuse albedo is modeled with an MLP. This adaptation allows to highlight the advantages of employing the optimal diffuse albedo introduced in Sec. 5.2. + +Full 3D reconstruction. As anticipated, [33, 47, 65] produce degenerate meshes in our wide baseline setup. Results in the supplementary demonstrate that they perform adequately when the distance between cameras is sufficiently small, although our framework consistently outperforms them. Conversely, Tab. 1 and Fig. 3 illustrate that our approach surpasses relevant baselines [10, 56, 60] both quantitatively and qualitatively. Our method yields sharper details without visible artifacts. Furthermore, error maps (shown in the supplementary material) reveal that the geometry obtained with [60] exhibits global distortions. Additionally, Fig. 4 demonstrates that both [56, 60] perform poorly when confronted with complex textures, while our results remain unaffected. This suggests that their pre-trained priors failed + +![](images/d27da7d9bae56e7a823bfe9716e96702ed7917bf25c31c0e7d821c1ffbeed44c.jpg) +Figure 5. Re constructions from two distant viewpoints. Severe artefacts can be noticed for both [60] and OurAlbedoNet, and more particularly [60] introduce significant distortions in the shapes, as a result of using normal maps which do not provide strong enough constraints on the absolute position of the points. + +to generalize for the given texture, possibly misassigning it as geometric patterns. This shows the advantage of approaches without relying on learned priors. The results for the DiLiGenT-MV dataset [28] are shown in the supplementary, demonstrating a high accuracy in the classical scenario of a dark room and distant light sources. + +Two viewpoints. We denote our ablated framework, which uses a diffuse albedo network, as OurAlbedoNet. We exclude [56] from consideration as they require at least three viewpoints. Fig. 5 vividly illustrates the advantage of our framework in this challenging scenario, especially with the use of the optimal diffuse albedo. Notably, [60] and OurAlbedoNet exhibit pronounced artifacts and inaccuracies in geometric details in certain regions. Moreover, [60] results in severe distortions of the shape. We attribute this to their heavy reliance on per-view normal maps for reconstruction, which lacks absolute depth information about the shape. In contrast, our method directly estimates the shape from various point-light illuminations, coupled with a suitable model (Eq. (1)). This approach provides relevant cues + +about the absolute position of the points, contributing to more accurate and high-quality reconstructions. + +Limitations and future work. A dedicated section is available in the supplementary. + +# 7. Conclusion + +We introduced the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering approach with a physically realistic illumination model consisting of an ambient component and uncalibrated point-lights. As demonstrated in a variety of experiments, the proposed approach offers a practical paradigm to create highly accurate 3D reconstructions from sparse and distant viewpoints, even outside a controlled dark room environment. + +Acknowledgment This work was supported by the ERC Advanced Grant SIMULACRON, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2117 - 422037984. + +# References + +[1] Meghna Asthana, William Smith, and Patrik Huber. Neural apparent brdf fields for multiview photometric stereo. In Proceedings of the 19th ACM SIGGRAPH European Conference on Visual Media Production, pages 1-10, 2022. 2, 3 +[2] Ronen Basri and David W Jacobs. Lambertian reflectance and linear subspaces. 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But they require either a fairly dense sampling of the viewing sphere, or pre-training on an existing dataset, thereby limiting their generalizability. In contrast, photometric stereo (PS) approaches have shown great potential for achieving high-quality reconstruction under sparse viewpoints. Yet, they are impractical because they typically require tedious laboratory conditions, are restricted to dark rooms, and often multi-staged, making them subject to accumulated errors. To address these shortcomings, we propose an end-to-end uncalibrated multi-view PS framework for reconstructing high-resolution shapes acquired from sparse viewpoints in a real-world environment. We relax the dark room assumption, and allow a combination of static ambient lighting and dynamic near LED lighting, thereby enabling easy data capture outside the lab. Experimental validation confirms that it outperforms existing baseline approaches in the regime of sparse viewpoints by a large margin. This allows to bring high-accuracy 3D reconstruction from the dark room to the real world, while maintaining a reasonable data capture complexity." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 535, + 128, + 547 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 552, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 287, + 696 + ], + "type": "text", + "content": "The challenge of 3D reconstruction stands as a cornerstone in both computer vision and computer graphics. Despite notable progress in recovering an object's shape from dense image viewpoints, predicting consistent geometry from sparse viewpoints remains a difficult task. Contemporary approaches employing neural data structures depend heavily on extensive training data to achieve generalization in the context of sparse views. Additionally, the presence of a wide baseline or textureless objects form significant obstacles. In contrast, photometric methodologies like photometric stereo (PS) excel in reconstructing geometry, even in textureless regions. This capability is attributed to the abun" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 247, + 366, + 332 + ], + "blocks": [ + { + "bbox": [ + 309, + 247, + 366, + 332 + ], + "lines": [ + { + "bbox": [ + 309, + 247, + 366, + 332 + ], + "spans": [ + { + "bbox": [ + 309, + 247, + 366, + 332 + ], + "type": "image", + "image_path": "e484abd1f8da38cadfee03b24958334199b2ee1f1fa1736a7f6b77f9e96dec2c.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 335, + 361, + 378 + ], + "lines": [ + { + "bbox": [ + 313, + 335, + 361, + 378 + ], + "spans": [ + { + "bbox": [ + 313, + 335, + 361, + 378 + ], + "type": "text", + "content": "Multi-illumination data at viewpoint 1" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 368, + 247, + 425, + 332 + ], + "blocks": [ + { + "bbox": [ + 368, + 247, + 425, + 332 + ], + "lines": [ + { + "bbox": [ + 368, + 247, + 425, + 332 + ], + "spans": [ + { + "bbox": [ + 368, + 247, + 425, + 332 + ], + "type": "image", + "image_path": "f859c10146c0912ffe63f6911819ecffb008ea50c15a1fc9f58b9c26d64c03e9.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 373, + 335, + 419, + 378 + ], + "lines": [ + { + "bbox": [ + 373, + 335, + 419, + 378 + ], + "spans": [ + { + "bbox": [ + 373, + 335, + 419, + 378 + ], + "type": "text", + "content": "Multi-illumination data at viewpoint 2" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 426, + 247, + 485, + 332 + ], + "blocks": [ + { + "bbox": [ + 426, + 247, + 485, + 332 + ], + "lines": [ + { + "bbox": [ + 426, + 247, + 485, + 332 + ], + "spans": [ + { + "bbox": [ + 426, + 247, + 485, + 332 + ], + "type": "image", + "image_path": "bb8c0d3f923ef4502153f92ad0bd298eaee58ba3e8c67722ffd595fe5f5eb59a.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 350, + 482, + 361 + ], + "lines": [ + { + "bbox": [ + 429, + 350, + 482, + 361 + ], + "spans": [ + { + "bbox": [ + 429, + 350, + 482, + 361 + ], + "type": "text", + "content": "PS-NeRF [60]" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 486, + 247, + 544, + 332 + ], + "blocks": [ + { + "bbox": [ + 486, + 247, + 544, + 332 + ], + "lines": [ + { + "bbox": [ + 486, + 247, + 544, + 332 + ], + "spans": [ + { + "bbox": [ + 486, + 247, + 544, + 332 + ], + "type": "image", + "image_path": "fc34dde2b27b7fe4660f050e43b34c54be2a6358091780fef6fb8789c686db55.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 505, + 351, + 524, + 361 + ], + "lines": [ + { + "bbox": [ + 505, + 351, + 524, + 361 + ], + "spans": [ + { + "bbox": [ + 505, + 351, + 524, + 361 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 380, + 545, + 480 + ], + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 480 + ], + "type": "text", + "content": "Figure 1. We introduce the first framework for multi-view uncalibrated point-light photometric stereo. Given a set of PS images captured from different viewpoints (left), our method recovers high-fidelity 3D reconstruction (right). The acquisition of uncalibrated point-light PS imagery captured under ambient lighting in a sparse multi-view setup does not only allow for easy data capture, but also leads to 3D reconstructions of unprecedented detail. Here, with as few as two views we are able to reconstruct the squirrel's 3D geometry at higher precision than the state-of-the-art." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 489, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 545, + 561 + ], + "type": "text", + "content": "dance of shading information derived from images acquired under diverse illumination. Yet, such approaches typically require a controlled laboratory setup to fulfill the necessary dark room and directional light assumptions. As a consequence, PS approaches become impractical beyond the confines of a laboratory." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "To address these shortcomings we combine state-of-the-art volume rendering formulations with a sparse multi-view photometric stereo model. In particular, we advocate a physically realistic lighting model that combines ambient light and uncalibrated point-light illumination. Our approach facilitates simplified data acquisition, and we introduce a novel pipeline capable of reconstructing an object's geometry from a sparse set of viewpoints, even if the object is completely textureless. Furthermore, since we assume a point-light model instead of distant directional lighting, we can infer absolute depth from a single viewpoint, allowing us to address the challenge of wide camera baselines." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 203, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 203, + 712 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 203, + 712 + ], + "type": "text", + "content": "*The contribution was done while at TUM." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11862" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 217, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 217, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 217, + 83 + ], + "type": "text", + "content": "In detail, our contributions are as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 85, + 286, + 251 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 85, + 286, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 85, + 286, + 132 + ], + "spans": [ + { + "bbox": [ + 47, + 85, + 286, + 132 + ], + "type": "text", + "content": "- We introduce the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering formulation with a physically realistic model of ambient light and point lights." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 133, + 286, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 286, + 179 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 286, + 179 + ], + "type": "text", + "content": "- We eliminate the need for a dark room environment, dense capturing process, and distant lighting. Thereby we enhance the accessibility and simplify data acquisition for setups beyond traditional laboratory settings." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 180, + 286, + 215 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 180, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 47, + 180, + 286, + 215 + ], + "type": "text", + "content": "- We validate that it can be successfully used for accurate shape reconstruction of textureless objects in highly sparse scenarios with wide baselines." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 217, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 286, + 251 + ], + "type": "text", + "content": "- Despite the absence of pre-processing or vast training data, we outperform cutting-edge approaches that either rely only on static ambient illumination or PS imagery." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 258, + 133, + 270 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 258, + 133, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 258, + 133, + 270 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 275, + 286, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 286, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 286, + 358 + ], + "type": "text", + "content": "In this section, we categorize pertinent works into two distinct groups. The first category focuses on neural 3D reconstruction, emphasizing the use of images captured under static ambient illumination. Subsequently, the second category delves into photometric stereo (PS) approaches, which specifically involve methods assuming images captured under varying illumination conditions." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 365, + 189, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 365, + 189, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 189, + 376 + ], + "type": "text", + "content": "2.1. Neural 3D reconstruction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 378, + 286, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 286, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 286, + 472 + ], + "type": "text", + "content": "In our context, the domain of neural 3D reconstruction under static ambient light can be bifurcated into two distinct subcategories. The first comprises methodologies that presume a dense sampling of the viewing sphere [5, 11, 12, 14, 36, 38, 39, 52, 63, 64, 68]. Conversely, the second subcategory encompasses techniques adept at handling sparse camera viewpoints [7, 9, 13, 16, 22, 33, 43, 47, 51, 53, 56-59, 61, 62, 65-67]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 474, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 286, + 581 + ], + "type": "text", + "content": "Given our emphasis on a sparse set of camera viewpoints, our focus will be directed toward the latter set of methodologies. The majority of sparse reconstruction approaches within this category hinge on training with a specific dataset [9, 13, 16, 47, 53, 57-59, 61, 62, 65, 67]. The reliance on extensive training data renders these techniques susceptible to errors when confronted with objects not represented in the training dataset, thereby introducing sensitivity to the domain gap between training and test data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 713 + ], + "type": "text", + "content": "Efforts have been undertaken to mitigate the challenges associated with the domain gap. One approach involves fine-tuning pre-trained architectures during test time with sparse input data [22, 33, 43]. However, while fine-tuning enables fine-scale refinement of the predicted reconstruction, the broader issue of generalization to entirely different datasets persists as a challenge. Furthermore, it is crucial to note that all the previously mentioned sparse approaches presume small camera baselines and textured objects. To achieve a full reconstruction of an object from sparse views, it becomes imperative to develop texture-" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 72, + 533, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 533, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 533, + 84 + ], + "type": "text", + "content": "agnostic approaches capable of handling wide baselines." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 85, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 85, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 85, + 545, + 228 + ], + "type": "text", + "content": "Another set of approaches involves the utilization of pretraining to establish a geometric prior [51, 56, 66]. Yu et al. [66] leverages this geometric prior to predict a depth and normal map, albeit with a limitation in fine-scale details due to its coarse resolution. Notably, [51, 56] address this limitation. Wu et al. [56] relax the assumption on small baselines, although a reasonable overlap of sparse views remains necessary for consistent 3D reconstruction. Vora et al. [51] demonstrate promising results with much less overlap, employing only three viewpoints. However, the use of template shapes as a prior term introduces the risk of the reconstruction quality being affected by the domain gap curse." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 228, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 289 + ], + "type": "text", + "content": "In contrast, our approach eliminates the requirement for training data and operates effectively in wide baseline scenarios, independent of the object's texture. This accomplishment can be attributed to the integration of PS principles, which we will elucidate in the subsequent discussion." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 300, + 419, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 300, + 419, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 300, + 419, + 312 + ], + "type": "text", + "content": "2.2. Photometric Stereo" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 317, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 376 + ], + "type": "text", + "content": "The principle of PS [54] has a long and established history, renowned for yielding high-quality and finely detailed geometric estimates, due to its capturing process: multiple images under different illumination of a static object are captured from a single camera viewpoint." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 377, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 461 + ], + "type": "text", + "content": "In our case, PS approaches can thus be categorized into two main types. The first category pertains to single-view methods [17, 23, 29, 30, 32, 35, 40, 45, 46, 50], wherein data is acquired as described above. The second category involves multi-view methods [1, 10, 21, 26-28, 31, 41, 55, 60, 72], where the capturing process is repeated at multiple camera viewpoints." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 617 + ], + "type": "text", + "content": "Within the context of our task, we concentrate on the multi-view scenario. Many existing approaches in this domain assume knowledge of the light source for each image, earning them the designation of calibrated PS (CPS). In this case, frequently the light is parameterized as directional [1, 10, 28, 72], while approaches employing point-light illumination are more sparsely represented [10, 28, 31], owing to the intricate model and the much more complex calibration process [46]. In a broader context, the calibration of each image's light source is impractical and tedious, underscoring the advantage of the uncalibrated case, which inherently facilitates a more straightforward and streamlined capturing process." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "Efforts have been dedicated to exploring the uncalibrated PS (UPS) scenario, where there is no prior knowledge of the light source [21, 26, 27, 41, 55, 60]. Nevertheless, all these uncalibrated methods typically assume a distant and directional light model or permit a lighting model based on spherical harmonics [2, 4, 18, 19, 44, 48, 49], albeit at the expense of being restricted to Lambertian objects [55]. Consequently, the exploration of the uncalibrated point" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11863" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "light case remains uncharted territory, particularly in the multi-view scenario." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 286, + 216 + ], + "type": "text", + "content": "Despite the impractical assumption of calibrated light or the constraint of uncalibrated directional lighting, the aforementioned multi-view photometric stereo approaches demand a dark room and lack accommodation for ambient light [1, 10, 21, 26-28, 31, 41, 60, 72]. Additionally, they comprise multiple stages, rendering them prone to initialization and accumulation errors [21, 26-28, 31, 41, 55, 60]. Furthermore, these methods assume Lambertian objects [31, 55] and crucially rely on a dense sampling of camera viewpoints around the object [21, 28, 31, 41, 55]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 217, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 286, + 384 + ], + "type": "text", + "content": "The approach most closely related to ours is the sparse method PS-NeRF [60], which assumes uncalibrated directional lighting with imagery captured in a dark room. This method comprises multiple stages, where initially, a pretrained network [8] is utilized to estimate the initial light, along with normal information for each image and camera view. Subsequently, this acquired information is employed to estimate the object's mesh through the optimization of an occupancy field [39]. The outputs of both stages are then combined to derive a consistent normal map of the object. Although PS-NeRF demonstrates impressive results in a sparse scenario with five viewpoints, its susceptibility to error accumulation is a potential limitation, given the involvement of multiple stages." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 286, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 286, + 492 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 286, + 492 + ], + "type": "text", + "content": "Our proposed model addresses the aforementioned limitations comprehensively. Notably, we excel in handling sparse yet wide baseline scenarios, where existing state-of-the-art methods encounter challenges. Our investigation tackles the open challenge of multi-view uncalibrated pointlight PS within an end-to-end framework, liberating us from the constraints associated with Lambertian objects. Furthermore, our approach facilitates easy data capture in the presence of ambient light, eliminating the need for a dark room." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 242, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 242, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 242, + 514 + ], + "type": "text", + "content": "3. Setting and image formation model" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": "We consider an object under static illumination photographed from several different viewpoints. For every viewpoint, we are given a set of " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "N + 1" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "(I^l)_{l = 0,\\dots ,N}" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": ". Image " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "I^0" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " is captured only under static ambient illumination and called the ambient image. For images " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "I^{1}" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "I^{N}" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": ", the object is in addition to the ambient illumination also illuminated by a single achromatic point-light source with scalar light intensity " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "L_0\\in \\mathbb{R}^+" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": ", placed at a different location " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}^l\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " for each image and viewpoint. We use the common assumption in volume rendering [36, 52, 56, 64] that the image brightness " + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "inline_equation", + "content": "I^l" + }, + { + "bbox": [ + 46, + 522, + 286, + 713 + ], + "type": "text", + "content": " is the same as the accumulated radiance of the volume rendering, see Eq. (4). Note that we do not add an index for the viewpoint to the image to not clutter notation, whenever we later evaluate an image at a pixel location, we assume it implicitly means a pixel at a specific viewpoint. In particular, a sum over all pixels is the" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 497, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 497, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 497, + 83 + ], + "type": "text", + "content": "sum over all pixels at every viewpoint location." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "text", + "content": "According to the linearity of the radiance, the total radiance for the image " + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "text", + "content": " is given by a sum " + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}^l = \\mathcal{L}_{\\mathrm{amb}} + \\mathcal{L}_{\\mathrm{pt}}^l" + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{amb}}" + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "text", + "content": " is the radiance due to the static illumination, the same for each image, and " + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{pt}}^l" + }, + { + "bbox": [ + 304, + 84, + 545, + 204 + ], + "type": "text", + "content": " is the radiance due to the point-light source used for that particular image. We will first express the radiance due to the point-light source with respect to the material and lighting parameters, which allows to take into account the different illuminations of the images. Subsequently, we elaborate on how we deal with the ambient component." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 211, + 501, + 223 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 211, + 501, + 223 + ], + "spans": [ + { + "bbox": [ + 305, + 211, + 501, + 223 + ], + "type": "text", + "content": "3.1. Point-light illumination and material" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": "The field " + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "inline_equation", + "content": "L(\\mathbf{x},\\mathbf{n},\\mathbf{v})" + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": " maps points " + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{x}\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": ", normal direction " + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{n}(\\mathbf{x})\\in \\mathbb{S}^2" + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": " and viewing direction " + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{v}\\in \\mathbb{S}^2" + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": " to its radiance. It can be expressed in terms of geometry, material and lighting with the classical rendering equation [24]. Since for now we only consider a single achromatic point-light source with intensity " + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "inline_equation", + "content": "L_{0}" + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": " at position " + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 228, + 545, + 301 + ], + "type": "text", + "content": ", this equation simplifies to" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 315, + 307, + 545, + 334 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 307, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 315, + 307, + 545, + 334 + ], + "type": "interline_equation", + "content": "L (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}) = \\frac {L _ {0}}{\\| \\mathbf {p} - \\mathbf {x} \\| ^ {2}} f _ {\\mathrm {r}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}) \\max (0, \\mathbf {n} \\cdot \\mathbf {l}), \\tag {1}", + "image_path": "299296118624766ae38033464496a018fb8ec4caf78787736a1d32a972b2ca51.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 341, + 381, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 341, + 381, + 356 + ], + "spans": [ + { + "bbox": [ + 306, + 341, + 381, + 356 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 341, + 381, + 356 + ], + "type": "inline_equation", + "content": "\\mathbf{l} = \\frac{\\mathbf{p} - \\mathbf{x}}{\\|\\mathbf{p} - \\mathbf{x}\\|}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "content": "As a model for the spatially varying reflectance " + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "content": ", we use the simplified Disney BRDF [25]. It is relatively simple yet expressive enough to resemble a wide variety of materials. It has already been successfully used in several other prior works [5, 34, 69]. The Disney BRDF requires three parameters to be available at every point " + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "content": ": An RGB diffuse albedo " + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\rho \\in \\mathbb{R}_{\\geq 0}^{3}" + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "content": ", a roughness " + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\alpha_{\\mathrm{r}} > 0" + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "content": " and a specular albedo " + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\alpha_{\\mathrm{s}} \\in [0,1]" + }, + { + "bbox": [ + 304, + 356, + 545, + 450 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": "As in [5], all three BRDF parameters can be represented with MLPs. One MLP with network parameters " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\gamma_{1}" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": " computes the diffuse parameter " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": ", a second MLP with network parameters " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\gamma_{2}" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": " computes the specular parameters " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "(\\alpha_{\\mathrm{r}},\\alpha_{\\mathrm{s}})" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": ". To encompass all point-light and BRDF parameters, we concatenate them into the vectors " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\phi = (\\mathbf{p}^{1},\\dots,\\mathbf{p}^{M})" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": ", which includes all light source positions (where " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": " is the product of " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": " with the number of viewpoints), and " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\gamma = (\\gamma_{1},\\gamma_{2})" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": ", representing the BRDF parameters. Both " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 451, + 545, + 617 + ], + "type": "text", + "content": " serve as the network parameters to be learned during optimization. However, note that one of our contributions is a novel strategy to deal with the diffuse albedo later on in Sec. 5.2, which dramatically improves performance in extremely sparse scenarios." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "We assume that the intensity " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{0}" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " remains constant across all images and views. This assumption is reasonable, e.g., when using a smartphone's flashlight or a sole LED, as shown in our experiments. A constant intensity introduces a scale ambiguity between the " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{0}" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": ". We set " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "L_{0} \\equiv 1" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " and subsequently estimate a scaled version of the BRDF, i.e., the intensity is absorbed into the BRDF. This is feasible, since we can scale the Disney BRDF arbitrarily." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11864" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 135, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 135, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 135, + 85 + ], + "type": "text", + "content": "3.2. Ambient light" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 222 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 222 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 222 + ], + "type": "text", + "content": "Given the provided ambient image, we adopt the approach from [71], which involves subtracting the ambient image from all other images. This process effectively eliminates ambient radiance from our considerations, simulating a traditional dark room scenario. A drawback is that in practice, the captured images contain additive noise, hence such a subtraction will double the variance of the noise distribution, resulting in noisier input images. Nevertheless, as can be seen in the results, our approach works successfully with this strategy even if we use a simple smartphone camera for the data capture." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "spans": [ + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "text", + "content": "However, this simplification is enabled by the fact that the point-light sources are near the object, making it easy to obtain a well exposed contribution from the point-light source. In methods assuming directional lighting, the practical simulation often involves using a point-light source placed far from the object, ensuring that the object's diameter is significantly smaller than the distance between the point-light and the object. For example, for the DiLiGenTMV dataset [28], the light sources are roughly " + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "inline_equation", + "content": "1\\mathrm{m}" + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "text", + "content": " from the object, whereas for our setup, the distance is approximately " + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "inline_equation", + "content": "25\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "text", + "content": ". As a consequence, for a given static ambient illumination, the distant point-light will need to be " + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "inline_equation", + "content": "16\\times" + }, + { + "bbox": [ + 46, + 222, + 288, + 403 + ], + "type": "text", + "content": " brighter in the Diligent setup to obtain a similar signal to noise ratio. This increased brightness requirement escalates the hardware demands, especially if the highest quality is sought." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 411, + 190, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 411, + 190, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 411, + 190, + 423 + ], + "type": "text", + "content": "3.3. Other illumination effects" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 429, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 538 + ], + "type": "text", + "content": "We do not model indirect lighting and cast-shadows explicitly. However, multiple previous works [3, 20, 34, 37, 70] and PS frameworks [10, 17, 28, 46] have demonstrated that satisfactory results can be achieved without taking these into account. In addition, we use the robust " + }, + { + "bbox": [ + 46, + 429, + 287, + 538 + ], + "type": "inline_equation", + "content": "L^1" + }, + { + "bbox": [ + 46, + 429, + 287, + 538 + ], + "type": "text", + "content": "-norm in our data term (7) to further increase robustness. Furthermore, we will expose a simple strategy in Sec. 5 to reduce the impact of cast-shadows, which inevitably occur when capturing a nonconvex object under changing illumination." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 549, + 227, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 227, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 227, + 563 + ], + "type": "text", + "content": "4. Volume rendering of the surface" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "For differentiable rendering we build upon VolSDF [64] because in contrast to NeRF [36] it allows us to decouple geometric representation and appearance. As discussed in [47, 56, 65], VolSDF exhibits poor reconstruction quality in the sparse viewpoint scenario due to the shape-radiance ambiguity. We eliminate this ambiguity thanks to photometric stereo, providing shading cues from different illuminations for each viewpoint. To this end, we employ the radiance field in Eq. (1) and apply it to the multi-view uncalibrated point-light PS setting. The integration of differentiable volume rendering with a physically realistic lighting model provides an efficient solution to the multi-view" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "photometric stereo problem, enabling high-quality reconstruction even with sparse viewpoints, as demonstrated in the subsequent results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": "Geometry model and associated density. The geometry of the scene is modeled with a signed distance function (SDF) " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "d: \\Omega \\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": " within the volume " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\Omega \\subset \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": ". We follow [42, 52, 63, 64] and represent the SDF with an MLP " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "d(\\mathbf{x}; \\theta)" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": " parametrized by " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": ". Note that we assume positive values of the SDF " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": " inside the object, thus the normal vector is given by " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{n} = \\nabla d / \\| \\nabla d\\|" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": ". To render the scene, we follow [64] and transform the SDF into a density " + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "inline_equation", + "content": "\\sigma: \\Omega \\to \\mathbb{R}_{\\geq 0}" + }, + { + "bbox": [ + 304, + 108, + 545, + 216 + ], + "type": "text", + "content": " by means of the transformation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 373, + 219, + 545, + 234 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 219, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 373, + 219, + 545, + 234 + ], + "type": "interline_equation", + "content": "\\sigma (\\mathbf {x}) = \\beta^ {- 1} \\Psi_ {\\beta} (- d (\\mathbf {x})), \\tag {2}", + "image_path": "62dd341dcbece3fcc9b3484636a793a45d0f60917ca6eae34d65824c1ed54c57.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\Psi_{\\beta}" + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "content": " denotes the cumulative distribution function of the Laplace distribution with zero mean. The positive scale parameter " + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "content": " is learned during optimization. For simplicity, we assume it is included in the set of SDF parameters " + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 238, + 545, + 285 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "text", + "content": "Volume Rendering. Using the density (2), we can now set up a distribution of weights " + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "inline_equation", + "content": "w(t)" + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "text", + "content": " along each ray " + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{x}(t) = \\mathbf{c} + t\\mathbf{v}, t \\geq 0" + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "text", + "content": " defined by the center of projection " + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "text", + "content": " of the camera and viewing direction " + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 304, + 285, + 545, + 334 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 337, + 337, + 545, + 365 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 337, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 337, + 337, + 545, + 365 + ], + "type": "interline_equation", + "content": "w (t) = \\sigma (\\mathbf {x} (t)) \\exp \\left(- \\int_ {0} ^ {t} \\sigma (\\mathbf {x} (s)) \\mathrm {d} s\\right). \\tag {3}", + "image_path": "d4691680ecc8d19e0add881f74c4c60dc711a4b3db041f4d54195f95881f1492.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 367, + 545, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 545, + 415 + ], + "type": "text", + "content": "This is the derivative of the opacity function, which is monotonically increasing from zero to one, and thus " + }, + { + "bbox": [ + 304, + 367, + 545, + 415 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 367, + 545, + 415 + ], + "type": "text", + "content": " is indeed a probability distribution [64]. In particular, the integral" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 352, + 414, + 545, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 414, + 545, + 439 + ], + "spans": [ + { + "bbox": [ + 352, + 414, + 545, + 439 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p} = \\int_ {0} ^ {\\infty} w (t) L (\\mathbf {x} (t), \\mathbf {n} (t), \\mathbf {v}) \\mathrm {d} t, \\tag {4}", + "image_path": "d2468b7e9f95c488e3cb8f2c21c2f0d05643b95c2bfd7200084d7bc3fe26eb35.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "text", + "content": "to compute radiance " + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_p" + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "text", + "content": " in the pixel " + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "inline_equation", + "content": "p\\in \\mathbb{R}^2" + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "text", + "content": " corresponding to the ray " + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "inline_equation", + "content": "\\mathbf{x}(t)" + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "text", + "content": " is well-defined. Intuitively, we accumulate the radiance field (1) of the point-light source at locations where opacity increases, i.e. where we move towards the inside of the object. For an ideal sharp boundary, " + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 441, + 545, + 513 + ], + "type": "text", + "content": " would be a Dirac distribution with its peak placed at the boundary." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 513, + 545, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 513, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 513, + 545, + 537 + ], + "type": "text", + "content": "As was done in [64] we approximate the integral (4) using the quadrature rule" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 541, + 545, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 541, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 332, + 541, + 545, + 574 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {p} \\approx \\sum_ {i = 1} ^ {m - 1} \\left(t _ {i + 1} - t _ {i}\\right) w \\left(t _ {i}\\right) L \\left(\\mathbf {x} \\left(t _ {i}\\right), \\mathbf {n} \\left(t _ {i}\\right), \\mathbf {v}\\right). \\tag {5}", + "image_path": "ef78bd2c355019b818110d2ef5c2885081637a8cc66d28890fc9c2544a087437.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "type": "text", + "content": "for numerical integration with a discrete set of samples " + }, + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "type": "inline_equation", + "content": "t_1 < t_2 < \\dots < t_m" + }, + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "type": "text", + "content": ". Note that the integral (3) required for " + }, + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "type": "inline_equation", + "content": "w(t_i)" + }, + { + "bbox": [ + 304, + 577, + 545, + 625 + ], + "type": "text", + "content": " in (5) can be numerically computed using an analogous formula while iteratively accumulating the sum (5)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 634, + 504, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 634, + 504, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 634, + 504, + 647 + ], + "type": "text", + "content": "5. Training objective and optimization" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "In order to reconstruct the scene by inverse rendering, we train our neural networks from the available input images. We optimize for the geometry parameters " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " of the SDF network and point-light and BRDF parameters " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": " of the appearance network, respectively." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11865" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 265, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 265, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 265, + 83 + ], + "type": "text", + "content": "5.1. Vanilla loss function with MLP for albedo" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "spans": [ + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "text", + "content": "The overall loss consists of the sum of an inverse rendering loss " + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{RGB}}(\\theta, \\phi, \\gamma)" + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "text", + "content": ", an Eikonal loss " + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{eik}}(\\theta)" + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "text", + "content": " and a mask loss " + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{mask}}(\\theta)" + }, + { + "bbox": [ + 47, + 90, + 287, + 126 + ], + "type": "text", + "content": " for the SDF," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 133, + 287, + 147 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 133, + 287, + 147 + ], + "spans": [ + { + "bbox": [ + 52, + 133, + 287, + 147 + ], + "type": "interline_equation", + "content": "E (\\theta , \\phi , \\gamma) = E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma) + \\lambda_ {1} E _ {\\mathrm {e i k}} (\\theta) + \\lambda_ {2} E _ {\\text {m a s k}} (\\theta), \\tag {6}", + "image_path": "9187f8754492709d107f166e7904422ed5e4ec62ed4c73e75602baf57414d918.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 153, + 287, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 153, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 47, + 153, + 287, + 189 + ], + "type": "text", + "content": "with respective weighting parameters " + }, + { + "bbox": [ + 47, + 153, + 287, + 189 + ], + "type": "inline_equation", + "content": "\\lambda_1, \\lambda_2 \\geq 0" + }, + { + "bbox": [ + 47, + 153, + 287, + 189 + ], + "type": "text", + "content": " given as hyperparameters. We will describe the different terms in detail in the following." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 190, + 141, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 190, + 141, + 201 + ], + "spans": [ + { + "bbox": [ + 59, + 190, + 141, + 201 + ], + "type": "text", + "content": "The rendering loss" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 207, + 287, + 235 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 207, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 61, + 207, + 287, + 235 + ], + "type": "interline_equation", + "content": "E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma) = \\sum_ {p} \\sum_ {l \\in B _ {\\tau} (p)} \\left\\| I _ {p} ^ {l} - \\mathcal {L} _ {p} ^ {l} (\\theta , \\phi , \\gamma) \\right\\| _ {1} \\tag {7}", + "image_path": "3cb9598efdf589dded0c19b5bd008620b85439a6bd4f29878c5de7fd20a1097d.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": "encourages that the rendered images resemble the input images. As a strategy to deal with cast-shadows, for each pixel " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": ", we use only the " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": " brightest views " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "B_{\\tau}(p) \\subset \\{1 \\dots N\\}" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "\\tau > 0" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": " is a hyper-parameter. This reduces the impact of cast-shadows, as a pixel will have the smallest possible brightness when it lies in shadow. Such a strategy is necessary since despite the use of an " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "L^1" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": "-norm to improve robustness against outliers, some regions with frequent cast-shadows would still exhibit small artefacts, as can be seen in Fig. 2. In order to avoid wasting meaningful information due to this heuristic, we set " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "\\tau = N" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": " for the first half of the iterations, and then set it to " + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "inline_equation", + "content": "\\tau = \\lceil \\frac{3}{4} N \\rceil" + }, + { + "bbox": [ + 47, + 241, + 288, + 396 + ], + "type": "text", + "content": " for the second half for improved handling of cast-shadows." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 397, + 137, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 397, + 137, + 407 + ], + "spans": [ + { + "bbox": [ + 59, + 397, + 137, + 407 + ], + "type": "text", + "content": "The Eikonal term" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 96, + 413, + 287, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 413, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 96, + 413, + 287, + 439 + ], + "type": "interline_equation", + "content": "E _ {\\mathrm {e i k}} (\\theta) = \\sum_ {\\mathbf {x}} \\left(\\left\\| \\nabla_ {\\mathbf {x}} d (\\mathbf {x}; \\theta) \\right\\| - 1\\right) ^ {2} \\tag {8}", + "image_path": "3720d88060c065f68e65f2463cb9a64fc6d8c38222af7a782d248f49d9ef6c30.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": "encourages " + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "inline_equation", + "content": "d(\\mathbf{x};\\theta)" + }, + { + "bbox": [ + 47, + 445, + 287, + 480 + ], + "type": "text", + "content": " to approximate an SDF, as it penalizes deviations from the respective partial differential equation which every SDF satisfies, see e.g. [15]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 481, + 271, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 481, + 271, + 493 + ], + "spans": [ + { + "bbox": [ + 59, + 481, + 271, + 493 + ], + "type": "text", + "content": "Finally, we follow [5, 52] and employ the mask loss" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 95, + 499, + 287, + 526 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 95, + 499, + 287, + 526 + ], + "spans": [ + { + "bbox": [ + 95, + 499, + 287, + 526 + ], + "type": "interline_equation", + "content": "E _ {\\text {m a s k}} (\\theta) = \\sum_ {p} \\operatorname {B C E} \\left(M _ {p}, W _ {p} (\\theta)\\right), \\tag {9}", + "image_path": "d85a332d299d506448f734ac2509277881ae7811de8637c24f3ddb0ef6dc530c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "text", + "content": "to impose silhouette consistency by means of the binary cross entropy (BCE) between the given binary mask " + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "inline_equation", + "content": "M_{p}" + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "text", + "content": " at the pixel " + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "text", + "content": " and the sum " + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "inline_equation", + "content": "W_{p}(\\theta) = \\sum_{i=1}^{m-1} w(t_{i};\\theta)" + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "text", + "content": " of the weights at the sampling locations " + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "inline_equation", + "content": "t_{i}" + }, + { + "bbox": [ + 47, + 532, + 287, + 582 + ], + "type": "text", + "content": " used in (5)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 587, + 222, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 222, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 222, + 601 + ], + "type": "text", + "content": "5.2. Using the optimal diffuse albedo" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "content": "In this section, we introduce a strategy to handle the diffuse albedo. This is inspired by [17], however in their single-view approach they are only able to handle the least-squares case, i.e. " + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "L^2" + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "content": ", while we extend their formulation to objective functions of the form of an " + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "L^p" + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "content": "-norm, with " + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "inline_equation", + "content": "p = 1" + }, + { + "bbox": [ + 47, + 605, + 287, + 713 + ], + "type": "text", + "content": " in our case, see Eq. (7). In lieu of employing an MLP for modeling the diffuse albedo, we opt for approximating an optimal solution considering the remaining parameters. This allows us to exclude the diffuse albedo from the optimization" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 386, + 169 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 386, + 169 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 386, + 169 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 386, + 169 + ], + "type": "image", + "image_path": "316363b2f55a0466a63ae7b294c37ae992c3a0e5b0bdb43690891ab93c5dfd0d.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 325, + 172, + 370, + 183 + ], + "lines": [ + { + "bbox": [ + 325, + 172, + 370, + 183 + ], + "spans": [ + { + "bbox": [ + 325, + 172, + 370, + 183 + ], + "type": "text", + "content": "Input image" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 387, + 71, + 465, + 169 + ], + "blocks": [ + { + "bbox": [ + 387, + 71, + 465, + 169 + ], + "lines": [ + { + "bbox": [ + 387, + 71, + 465, + 169 + ], + "spans": [ + { + "bbox": [ + 387, + 71, + 465, + 169 + ], + "type": "image", + "image_path": "0bf9fb90e483bce5c5f2883db97bd18c6ae44833fd3939cc9b60fee473ed7c16.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 399, + 172, + 453, + 182 + ], + "lines": [ + { + "bbox": [ + 399, + 172, + 453, + 182 + ], + "spans": [ + { + "bbox": [ + 399, + 172, + 453, + 182 + ], + "type": "text", + "content": "w/o truncation" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 466, + 71, + 544, + 169 + ], + "blocks": [ + { + "bbox": [ + 466, + 71, + 544, + 169 + ], + "lines": [ + { + "bbox": [ + 466, + 71, + 544, + 169 + ], + "spans": [ + { + "bbox": [ + 466, + 71, + 544, + 169 + ], + "type": "image", + "image_path": "cbb80f3db5953b1ad83a183d45ab76f6812e32cb43d29721c8227b9d1fa2b74b.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 480, + 172, + 529, + 182 + ], + "lines": [ + { + "bbox": [ + 480, + 172, + 529, + 182 + ], + "spans": [ + { + "bbox": [ + 480, + 172, + 529, + 182 + ], + "type": "text", + "content": "w/ truncation" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 305, + 188, + 545, + 232 + ], + "type": "text", + "content": "Figure 2. Effect of cast-shadows on the result. The region behind the ear exhibits frequent cast-shadows in the input images (left), which induce artefacts in the estimated mesh (middle). Our truncation strategy (Sec. 5.1) successfully eliminates these (right)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "content": "process. Our subsequent demonstration will underscore the significant benefits of this approach in the context of sparse views, leading to markedly improved final geometry. A key technical change is the domain of the diffuse parameter " + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "content": ". So far, it has been a vector field defined in world space " + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "content": ", implemented with a neural network. However, in the following we only try to recover the projection of " + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "content": " on the image planes. Thus, the input to " + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "content": " will be a pixel, and the output is the diffuse albedo at the intersection between the pixel's ray and the object surface. In particular, the set of BRDF parameters is reduced to " + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "inline_equation", + "content": "\\gamma = \\gamma_{2}" + }, + { + "bbox": [ + 304, + 245, + 545, + 388 + ], + "type": "text", + "content": " and now only includes specular parameters." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": "Reformulation of the data term. We will now derive an expression for the data term which allows to solve for diffuse albedo " + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 305, + 388, + 545, + 449 + ], + "type": "text", + "content": " when given all of the other parameters. Note that the SVBRDF can be decomposed into a diffuse part and a specular part [25]," + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 348, + 456, + 545, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 456, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 348, + 456, + 545, + 480 + ], + "type": "interline_equation", + "content": "f _ {\\mathrm {r}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}) = \\frac {\\rho (\\mathbf {x})}{\\pi} + f _ {\\mathrm {s}} (\\mathbf {x}, \\mathbf {n}, \\mathbf {v}, \\mathbf {l}), \\tag {10}", + "image_path": "7431ea9973ad1b6d76646f4ed74f03562e73a8b674e228a885e6c9220c1cc54b.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 487, + 545, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 487, + 545, + 523 + ], + "spans": [ + { + "bbox": [ + 305, + 487, + 545, + 523 + ], + "type": "text", + "content": "where the specular part " + }, + { + "bbox": [ + 305, + 487, + 545, + 523 + ], + "type": "inline_equation", + "content": "f_{s}" + }, + { + "bbox": [ + 305, + 487, + 545, + 523 + ], + "type": "text", + "content": " depends on both the roughness and specular albedo. If we denote the BRDF-independent factor of the radiance field (1) by" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 349, + 530, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 349, + 530, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 349, + 530, + 545, + 559 + ], + "type": "interline_equation", + "content": "S ^ {l} (\\mathbf {x}, \\mathbf {n}) = \\frac {L _ {0}}{\\| \\mathbf {x} - \\mathbf {p} ^ {l} \\| ^ {2}} \\max (0, \\mathbf {n} \\cdot \\mathbf {l}), \\tag {11}", + "image_path": "243c6157ad3ad0564fe934e1c66c21c3e412668de1a18d57628ac8ad13edd8b8.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 565, + 545, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 565, + 545, + 589 + ], + "spans": [ + { + "bbox": [ + 305, + 565, + 545, + 589 + ], + "type": "text", + "content": "this implies that the total radiance field is the sum of diffuse radiance " + }, + { + "bbox": [ + 305, + 565, + 545, + 589 + ], + "type": "inline_equation", + "content": "\\frac{\\rho}{\\pi} S^l" + }, + { + "bbox": [ + 305, + 565, + 545, + 589 + ], + "type": "text", + "content": " and specular radiance " + }, + { + "bbox": [ + 305, + 565, + 545, + 589 + ], + "type": "inline_equation", + "content": "L_{s}^{l} = f_{s}S^{l}" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 590, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 590, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 590, + 545, + 613 + ], + "type": "text", + "content": "Inserting this into the volume rendering equation (4), we can thus re-arrange the data term (7) as" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 621, + 544, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 544, + 648 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 544, + 648 + ], + "type": "interline_equation", + "content": "E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma , \\rho) = \\sum_ {p} \\sum_ {l \\in S _ {\\tau} (p)} \\left\\| b _ {p} ^ {l} (\\theta , \\phi , \\gamma) - \\rho_ {p} a _ {p} ^ {l} (\\theta , \\phi) \\right\\| _ {1}", + "image_path": "04e36a666d029c12a660eca202e5bd4b6c17e672d0f4c9b9268546a031fbbdc3.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 318, + 651, + 517, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 651, + 517, + 677 + ], + "spans": [ + { + "bbox": [ + 318, + 651, + 517, + 677 + ], + "type": "interline_equation", + "content": "\\text {w i t h} a _ {p} ^ {l} (\\theta , \\phi) = \\frac {1}{\\pi} \\int_ {0} ^ {\\infty} w _ {\\theta} (t) S ^ {l} (\\mathbf {x} (t), \\mathbf {n} _ {\\theta} (t)) d t,", + "image_path": "4f1a79a825c7b2925f7a013c7e4e5d752aa599a479d3f3a7b370f1f1bcce0d56.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 329, + 678, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + 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Full 3D reconstruction of one synthetic and two real objects from 6 viewpoints. While some of the baseline reconstructions (with directional or point-light models) exhibit texture-induced patterns, distortions or other artefacts, the proposed framework consistently yields artefact- and distortion-free reconstructions with finer geometric details. Additional results are shown in the supplementary." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 382, + 286, + 464, + 378 + ], + "blocks": [ + { + "bbox": [ + 382, + 286, + 464, + 378 + ], + "lines": [ + { + "bbox": [ + 382, + 286, + 464, + 378 + ], + "spans": [ + { + "bbox": [ + 382, + 286, + 464, + 378 + ], + "type": "image", + "image_path": "373f6e21228766d7239ef4a72df1b9fd6e8b0a59606372617413126a5497e65e.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 415, + 380, + 432, + 392 + ], + "lines": [ + { + "bbox": [ + 415, + 380, + 432, + 392 + ], + "spans": [ + { + "bbox": [ + 415, + 380, + 432, + 392 + ], + "type": "text", + "content": "[60]" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 465, + 286, + 548, + 378 + ], + "blocks": [ + { + "bbox": [ + 465, + 286, + 548, + 378 + ], + "lines": [ + { + "bbox": [ + 465, + 286, + 548, + 378 + ], + "spans": [ + { + "bbox": [ + 465, + 286, + 548, + 378 + ], + "type": "image", + "image_path": "51d80fd74f2fe355ea5fbbb3db82b28038de9d8c8a79b393a810f0d25130e28f.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 497, + 380, + 517, + 391 + ], + "lines": [ + { + "bbox": [ + 497, + 380, + 517, + 391 + ], + "spans": [ + { + "bbox": [ + 497, + 380, + 517, + 391 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "text", + "content": "When keeping " + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "inline_equation", + "content": "\\theta, \\phi" + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "text", + "content": " fixed, this expression can be minimized pixel-wise for " + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 442, + 287, + 478 + ], + "type": "text", + "content": " as a linear least absolute deviation problem, as we show next." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 480, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 287, + 517 + ], + "type": "text", + "content": "Alternate treatment of the diffuse albedo. It is now possible to completely exclude the diffuse albedo " + }, + { + "bbox": [ + 46, + 480, + 287, + 517 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 480, + 287, + 517 + ], + "type": "text", + "content": " from the optimization and simply replace it by the optimal value" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 100, + 529, + 287, + 550 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 529, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 100, + 529, + 287, + 550 + ], + "type": "interline_equation", + "content": "\\rho_ {\\theta , \\gamma} ^ {*} = \\underset {\\rho} {\\arg \\min } E _ {\\mathrm {R G B}} (\\theta , \\phi , \\gamma , \\rho) \\tag {13}", + "image_path": "7a0f199e0c3901d483255befbd1cbb766e38130c912a1490508891849b54bd23.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 46, + 561, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 597 + ], + "type": "text", + "content": "with respect to the other parameters. In our case, we are facing a linear least absolute deviation problem which can be solved individually for each pixel." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 599, + 287, + 671 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 599, + 287, + 671 + ], + "spans": [ + { + "bbox": [ + 46, + 599, + 287, + 671 + ], + "type": "text", + "content": "We thus approximate the solution using a few iterations of iterative reweighted least squares [6], as it efficiently solves the problem while providing a differentiable expression. In order to simplify notation, we omit the dependency w.r.t. the parameters and denote only the channel-wise operations, where we iteratively compute" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 115, + 682, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 682, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 115, + 682, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\rho_ {p} ^ {*} \\approx \\rho_ {p} ^ {(k)} = \\frac {b _ {p} ^ {\\top} W _ {p} ^ {(k)} a _ {p}}{a _ {p} ^ {\\top} W _ {p} ^ {(k)} a _ {p}} \\tag {14}", + "image_path": "4a4151b6b7841e36d5785ddbf7673638d70bb59678be89689889cc1cc09227ad.jpg" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 442, + 400, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 400, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 400, + 455 + ], + "type": "text", + "content": "with diagonal matrices" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 309, + 488, + 545, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 488, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 309, + 488, + 545, + 531 + ], + "type": "interline_equation", + "content": "W _ {p} ^ {(k)} = \\left\\{ \\begin{array}{l l} \\operatorname {d i a g} \\left(\\max \\left(\\epsilon , \\left| b _ {p} - \\rho_ {p} ^ {(k - 1)} a _ {p} \\right|\\right) ^ {- 1}\\right) & \\text {i f} k \\geq 1, \\\\ I & \\text {o t h e r w i s e .} \\end{array} \\right. \\tag {15}", + "image_path": "f1c761742f5a8a05065868866d8f4db7756915311fa3576c8af547c53a49e81b.jpg" + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": "Above, " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " is the index of iteration, and " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "a_{p}" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "b_{p}" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " are the vectors whose components are given in Eq. (12). The small constant " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\epsilon > 0" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " avoids numerical issues, and " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " is an identity matrix of matching size. The gradient of " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\rho_{p}^{(k)}" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " with respect to " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " is computed using automatic differentiation, however the gradient of " + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "inline_equation", + "content": "W_{p}^{(k)}" + }, + { + "bbox": [ + 304, + 531, + 545, + 629 + ], + "type": "text", + "content": " is not back-propagated, as it makes the optimization much more difficult and degrades the quality of the results." + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 714 + ], + "type": "text", + "content": "In the forthcoming evaluation section, we demonstrate that this formulation delivers exceptional performance in 3D reconstruction from sparse viewpoints. Notably, it proves particularly advantageous in the most sparse scenarios, where only two viewpoints are available, showcasing its superiority over the previous MLP-based formulation." + } + ] + } + ], + "index": 34 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11867" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 82, + 69, + 196, + 194 + ], + "blocks": [ + { + "bbox": [ + 82, + 69, + 196, + 194 + ], + "lines": [ + { + "bbox": [ + 82, + 69, + 196, + 194 + ], + "spans": [ + { + "bbox": [ + 82, + 69, + 196, + 194 + ], + "type": "image", + "image_path": "70a24bcbb12fe780e39005cf3dfebf887e3da9215852413fbf5631950d31fdff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 197, + 70, + 296, + 194 + ], + "blocks": [ + { + "bbox": [ + 197, + 70, + 296, + 194 + ], + "lines": [ + { + "bbox": [ + 197, + 70, + 296, + 194 + ], + "spans": [ + { + "bbox": [ + 197, + 70, + 296, + 194 + ], + "type": "image", + "image_path": "920f25e6d99a32a5ae18821105301ea345d71b7ba17bd689d85536338c78c7e7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 297, + 70, + 396, + 194 + ], + "blocks": [ + { + "bbox": [ + 297, + 70, + 396, + 194 + ], + "lines": [ + { + "bbox": [ + 297, + 70, + 396, + 194 + ], + "spans": [ + { + "bbox": [ + 297, + 70, + 396, + 194 + ], + "type": "image", + "image_path": "6a0593c76481bc33443b74c305aff214b569979995a84566b0eda50d29e08c2b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 397, + 70, + 496, + 194 + ], + "blocks": [ + { + "bbox": [ + 397, + 70, + 496, + 194 + ], + "lines": [ + { + "bbox": [ + 397, + 70, + 496, + 194 + ], + "spans": [ + { + "bbox": [ + 397, + 70, + 496, + 194 + ], + "type": "image", + "image_path": "1be26b5ca4a982bd51bc005fee66364078be79d1b7814d04eaa375cd587e5fb3.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 83, + 195, + 196, + 319 + ], + "blocks": [ + { + "bbox": [ + 83, + 195, + 196, + 319 + ], + "lines": [ + { + "bbox": [ + 83, + 195, + 196, + 319 + ], + "spans": [ + { + "bbox": [ + 83, + 195, + 196, + 319 + ], + "type": "image", + "image_path": "bab47f412ab7cd68c5212c1efad3bf4c110ab986fd4e0a73da30aeda099c8288.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 120, + 323, + 175, + 335 + ], + "lines": [ + { + "bbox": [ + 120, + 323, + 175, + 335 + ], + "spans": [ + { + "bbox": [ + 120, + 323, + 175, + 335 + ], + "type": "text", + "content": "Input image" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 197, + 195, + 296, + 319 + ], + "blocks": [ + { + "bbox": [ + 197, + 195, + 296, + 319 + ], + "lines": [ + { + "bbox": [ + 197, + 195, + 296, + 319 + ], + "spans": [ + { + "bbox": [ + 197, + 195, + 296, + 319 + ], + "type": "image", + "image_path": "03238a92605ddcc980df71311f777faa2699e9c1087faeef95fd89d0dd2ec741.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 237, + 323, + 257, + 335 + ], + "lines": [ + { + "bbox": [ + 237, + 323, + 257, + 335 + ], + "spans": [ + { + "bbox": [ + 237, + 323, + 257, + 335 + ], + "type": "text", + "content": "[56]" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 297, + 195, + 396, + 319 + ], + "blocks": [ + { + "bbox": [ + 297, + 195, + 396, + 319 + ], + "lines": [ + { + "bbox": [ + 297, + 195, + 396, + 319 + ], + "spans": [ + { + "bbox": [ + 297, + 195, + 396, + 319 + ], + "type": "image", + "image_path": "46d1f360e2f33a7b0f3d7808712feaf2242077d790ef8d85539458266e6cc259.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 337, + 323, + 356, + 335 + ], + "lines": [ + { + "bbox": [ + 337, + 323, + 356, + 335 + ], + "spans": [ + { + "bbox": [ + 337, + 323, + 356, + 335 + ], + "type": "text", + "content": "[60]" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 337, + 547, + 370 + ], + "lines": [ + { + "bbox": [ + 46, + 337, + 547, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 547, + 370 + ], + "type": "text", + "content": "Figure 4. Results for both dog1 and dog2 obtained with 5 viewpoints reveal a notable performance degradation in [56] and [60] when confronted with complex textures. This deterioration is attributed to a generalization failure of their learned priors. In contrast, our approach, which does not rely on any prior, provides a superior reconstruction that is unaffected by the complex texture." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 397, + 195, + 496, + 319 + ], + "blocks": [ + { + "bbox": [ + 397, + 195, + 496, + 319 + ], + "lines": [ + { + "bbox": [ + 397, + 195, + 496, + 319 + ], + "spans": [ + { + "bbox": [ + 397, + 195, + 496, + 319 + ], + "type": "image", + "image_path": "fc24ce5b476f4ce55e8b740c384ebbfb67bb00aa305222948c54c0f2201e8095.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 435, + 323, + 458, + 334 + ], + "lines": [ + { + "bbox": [ + 435, + 323, + 458, + 334 + ], + "spans": [ + { + "bbox": [ + 435, + 323, + 458, + 334 + ], + "type": "text", + "content": "Ours" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 48, + 374, + 285, + 441 + ], + "blocks": [ + { + "bbox": [ + 48, + 374, + 285, + 441 + ], + "lines": [ + { + "bbox": [ + 48, + 374, + 285, + 441 + ], + "spans": [ + { + "bbox": [ + 48, + 374, + 285, + 441 + ], + "type": "table", + "html": "
↓RMSE×100↓MAE
[56][10]D[10]P[60]Ours[56][10]D[10]P[60]Ours
dog12.18.913.92.10.422.039.939.218.84.6
dog22.28.413.42.10.423.229.640.319.54.8
girl10.96.12.31.50.317.241.846.523.89.6
girl21.55.24.81.50.323.940.047.323.410.2
", + "image_path": "5e08bcac449a14046a8bec4e3dad845f0d485c2d506f0c20fb4d690cae71d95f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 445, + 287, + 500 + ], + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 500 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 500 + ], + "type": "text", + "content": "Table 1. RMSE and MAE for full 3D reconstructions. RMSE is computed based on the vertex to mesh distance, and the MAE is computed using the angular error between the normals of a vertex and its closest point in the ground truth mesh. OurAlbedoNet leads to highly similar results as our main framework in this scenario." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 506, + 100, + 517 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 506, + 100, + 517 + ], + "spans": [ + { + "bbox": [ + 47, + 506, + 100, + 517 + ], + "type": "text", + "content": "6. Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 528, + 287, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 528, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 528, + 287, + 660 + ], + "type": "text", + "content": "To substantiate the efficacy of our framework, we conduct evaluations on both synthetic and real-world datasets. We generate four synthetic scans by combining two distinct geometries with two different materials. The first material is white, rendering it textureless, while the second material exhibits a high degree of texture. This design enables us to quantify the influence of texture on the obtained results. The four synthetic scans are denoted as dog1, dog2, girl1, and girl2. Additionally, we acquire real-world data for six objects, namely, bird, squirrel, hawk, rooster, flamingo and pumpkin. We also consider the DiLiGenT-MV dataset [28]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Evaluation. We first evaluate full 3D reconstruction using only six viewpoints in total, except for " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "dog1" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "inline_equation", + "content": "dog2" + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": " where five viewpoints are considered. We evaluate against both state-of-the-art sparse viewpoint reconstruction approaches" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 376, + 545, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 532 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 532 + ], + "type": "text", + "content": "assuming static illumination [33, 47, 56, 65] and photometric stereo approaches [10, 60]. Since [10] allows for directional and point-light illumination, we consider both cases in our evaluation. [10]D and [10]P refers to the directional and point-light version, respectively. Given the calibrated nature of their framework, we furnish the estimated lighting parameters using our approach. Additionally, we explore a more challenging scenario wherein only two viewpoints with a wide baseline are available. We therefore introduce an ablated version of our framework, wherein the diffuse albedo is modeled with an MLP. This adaptation allows to highlight the advantages of employing the optimal diffuse albedo introduced in Sec. 5.2." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 538, + 546, + 706 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 546, + 706 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 546, + 706 + ], + "type": "text", + "content": "Full 3D reconstruction. As anticipated, [33, 47, 65] produce degenerate meshes in our wide baseline setup. Results in the supplementary demonstrate that they perform adequately when the distance between cameras is sufficiently small, although our framework consistently outperforms them. Conversely, Tab. 1 and Fig. 3 illustrate that our approach surpasses relevant baselines [10, 56, 60] both quantitatively and qualitatively. Our method yields sharper details without visible artifacts. Furthermore, error maps (shown in the supplementary material) reveal that the geometry obtained with [60] exhibits global distortions. Additionally, Fig. 4 demonstrates that both [56, 60] perform poorly when confronted with complex textures, while our results remain unaffected. This suggests that their pre-trained priors failed" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11868" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 509, + 426 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 509, + 426 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 509, + 426 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 509, + 426 + ], + "type": "image", + "image_path": "d27da7d9bae56e7a823bfe9716e96702ed7917bf25c31c0e7d821c1ffbeed44c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 428, + 547, + 462 + ], + "lines": [ + { + "bbox": [ + 46, + 428, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 547, + 462 + ], + "type": "text", + "content": "Figure 5. Re constructions from two distant viewpoints. Severe artefacts can be noticed for both [60] and OurAlbedoNet, and more particularly [60] introduce significant distortions in the shapes, as a result of using normal maps which do not provide strong enough constraints on the absolute position of the points." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 468, + 288, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 288, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 288, + 540 + ], + "type": "text", + "content": "to generalize for the given texture, possibly misassigning it as geometric patterns. This shows the advantage of approaches without relying on learned priors. The results for the DiLiGenT-MV dataset [28] are shown in the supplementary, demonstrating a high accuracy in the classical scenario of a dark room and distant light sources." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Two viewpoints. We denote our ablated framework, which uses a diffuse albedo network, as OurAlbedoNet. We exclude [56] from consideration as they require at least three viewpoints. Fig. 5 vividly illustrates the advantage of our framework in this challenging scenario, especially with the use of the optimal diffuse albedo. Notably, [60] and OurAlbedoNet exhibit pronounced artifacts and inaccuracies in geometric details in certain regions. Moreover, [60] results in severe distortions of the shape. We attribute this to their heavy reliance on per-view normal maps for reconstruction, which lacks absolute depth information about the shape. In contrast, our method directly estimates the shape from various point-light illuminations, coupled with a suitable model (Eq. (1)). This approach provides relevant cues" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 468, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 468, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 305, + 468, + 545, + 492 + ], + "type": "text", + "content": "about the absolute position of the points, contributing to more accurate and high-quality reconstructions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 495, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 545, + 519 + ], + "type": "text", + "content": "Limitations and future work. A dedicated section is available in the supplementary." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 524, + 379, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 524, + 379, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 524, + 379, + 536 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 540, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 646 + ], + "type": "text", + "content": "We introduced the first framework for multi-view uncalibrated point-light photometric stereo. It combines a state-of-the-art volume rendering approach with a physically realistic illumination model consisting of an ambient component and uncalibrated point-lights. As demonstrated in a variety of experiments, the proposed approach offers a practical paradigm to create highly accurate 3D reconstructions from sparse and distant viewpoints, even outside a controlled dark room environment." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 648, + 547, + 707 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 648, + 547, + 707 + ], + "spans": [ + { + "bbox": [ + 304, + 648, + 547, + 707 + ], + "type": "text", + "content": "Acknowledgment This work was supported by the ERC Advanced Grant SIMULACRON, and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany's Excellence Strategy - EXC 2117 - 422037984." + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11869" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 144 + ], + "type": "text", + "content": "[1] Meghna Asthana, William Smith, and Patrik Huber. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12525-12536, 2023. 2, 3" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "11872" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_content_list.json b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..89126cd22979fbc815bc513c0de1012997760b4d --- /dev/null +++ b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_content_list.json @@ -0,0 +1,1449 @@ +[ + { + "type": "text", + "text": "SparseOcc: Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction", + "text_level": 1, + "bbox": [ + 196, + 130, + 776, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Pin Tang1 Zhongdao Wang2 Guoqing Wang1 Jilai Zheng1", + "bbox": [ + 225, + 202, + 740, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xiangxuan Ren1 Bailan Feng2 Chao Ma1*", + "bbox": [ + 310, + 220, + 683, + 238 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University \n2 Huawei Noah's Ark Lab", + "bbox": [ + 148, + 239, + 818, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{pin.tang,guoqing.wang,zhengjilai,bunny.renxiangxuan,chaoma}@sjtu.edu.cn", + "bbox": [ + 168, + 276, + 800, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{wangzhongdao,fengbailan}@huawei.com", + "bbox": [ + 325, + 295, + 645, + 309 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Project page: https://pintang1999.github.io/sparseocc.html", + "bbox": [ + 243, + 311, + 718, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 361, + 313, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision-based perception for autonomous driving requires an explicit modeling of a 3D space, where 2D latent representations are mapped and subsequent 3D operators are applied. However, operating on dense latent spaces introduces a cubic time and space complexity, which limits scalability in terms of perception range or spatial resolution. Existing approaches compress the dense representation using projections like Bird's Eye View (BEV) or Tri-Perspective View (TPV). Although efficient, these projections result in information loss, especially for tasks like semantic occupancy prediction. To address this, we propose SparseOcc, an efficient occupancy network inspired by sparse point cloud processing. It utilizes a lossless sparse latent representation with three key innovations. Firstly, a 3D sparse diffuser performs latent completion using spatially decomposed 3D sparse convolutional kernels. Secondly, a feature pyramid and sparse interpolation enhance scales with information from others. Finally, the transformer head is redesigned as a sparse variant. SparseOcc achieves a remarkable $74.9\\%$ reduction on FLOPs over the dense baseline. Interestingly, it also improves accuracy, from $12.8\\%$ to $14.1\\%$ mIOU, which in part can be attributed to the sparse representation's ability to avoid hallucinations on empty voxels.", + "bbox": [ + 75, + 393, + 473, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 787, + 209, + 803 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Accurate perception of the surrounding environment is crucial for autonomous driving systems [11, 14]. In recent years, vision-based 3D perception algorithms have gained significant attention and advancement due to their cost-", + "bbox": [ + 75, + 814, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6525e2461113870efa7c96a98324e7a9fdbecb7c5298e575cbe086217d0e3f32.jpg", + "image_caption": [ + "Figure 1. (a) Vision-based perception methods for autonomous driving typically first extract image features by a 2D latent encoder and then map them to 3D using view transformation. (b) For the 3D latent space, existing methods mostly employ the dense, BEV, or TPV representation, while we rethink the possibility of using sparse representation to achieve superior efficiency and accuracy." + ], + "image_footnote": [], + "bbox": [ + 501, + 359, + 890, + 559 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "effectiveness. The typical workflow involves employing a 2D encoder to extract latent representations from images. A view transformation method, such as lift-splat-shoot (LSS) [25], is then applied to lift the perspective 2D latent features to a 3D voxel space, utilizing predicted depth information. This 3D scene representation serves as the foundation for deriving geometry and semantic information to describe the driving environment, supporting various 3D perception tasks including object detection [15, 17, 40, 43], semantic segmentation [11, 30, 36], and semantic occupancy prediction [13, 33, 34]. In this study, we specifically focus on the challenging task of semantic occupancy prediction [31-34], which entails predicting both static and dynamic elements within the scene.", + "bbox": [ + 496, + 671, + 893, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Several alternatives are available for representing 3D", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Corresponding author.", + "bbox": [ + 94, + 886, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "15035", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "spatial latent information. The dense representation [33] is the most straightforward approach, storing features in continuous memory and enabling direct application of dense 3D operations like convolutions. However, this representation is redundant and inefficient, as approximately $67\\%$ of the considered 3D space is empty1. Bird Eye's View (BEV) [12, 19, 22] has gained popularity as a recent prevalent representation. It involves projecting the 3D space onto a BEV plane, significantly reducing computational costs by leveraging efficient 2D building blocks in a BEV encoder. However, this projection introduces the loss of geometry information, thereby limiting the fine-grained capacity of the BEV representation to comprehend the 3D scene structure. A Tri-Perspective View (TPV) [13] representation is proposed to mitigate the information loss, but it still suffers from degraded perception accuracy.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we seek a latent representation that encodes the 3D scene structure in a lossless manner while minimizing computational costs. Drawing inspiration from the similarities between sparse 3D vision features and point clouds, we rethink the feasibility of employing a pure sparse representation for the 3D latent space, a common practice in point cloud processing [7]. Specifically, we utilize the coordinate (COO) format to store sparse tensors and introduce a series of sparse building blocks tailored for the sparse representation. Our proposed method, SparseOcc, is an occupancy network where all 3D layers operate on sparse tensors. The key designs of SparseOcc are as follows:", + "bbox": [ + 75, + 333, + 472, + 513 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Sparse Latent Diffuser: This component enables the propagation of non-empty features to adjacent empty regions, facilitating scene completion. To ensure efficiency, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels.", + "- Sparse Feature Pyramid: We build a feature pyramid that incorporates sparse interpolation operations to enhance scales with information from other scales. This pyramid design expands the reception fields, reducing the need for excessive diffusers within each scale, which helps preserve sparsity.", + "- Sparse Transformer Head: The final component of SparseOcc is a 3D sparse transformer head responsible for generating semantic occupancy predictions. By segmenting only occupied voxels rather than the entire 3D volume, we achieve a remarkable reduction in computational costs." + ], + "bbox": [ + 76, + 515, + 468, + 770 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Based on the sparse latent representation, SparseOcc achieves a significant reduction in computation overhead. In the nuScenes-Occupancy benchmark [33], it reduces the FLOPs of existing approaches using dense or TPV representations by $59.8\\%$ to $74.9\\%$ , and memory usage by $31.6\\%$ to $40.9\\%$ . Remarkably, the semantic occupancy", + "bbox": [ + 75, + 772, + 468, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "accuracy not only remains intact but improves, surpassing the state-of-the-art C-CONet. Specifically, the semantic occupancy accuracy increases from $12.8\\%$ to $14.1\\%$ mIoU. This improvement highlights the superiority of the sparse representation over the dense one in terms of accuracy, as it naturally avoids hallucinations on empty voxels. Considering the effectiveness and efficiency demonstrated by SparseOcc, we propose that it can serve as a new baseline for occupancy networks.", + "bbox": [ + 500, + 90, + 890, + 227 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 243, + 640, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. 3D Scene Representation", + "text_level": 1, + "bbox": [ + 500, + 268, + 728, + 285 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Dense Representation. Representing the surrounding environment with spatial latent information is an indispensable procedure for autonomous driving perception algorithms. A straightforward solution is to split the scene into voxels and describe the scene with 3D volume representation where 3D operators are applied [4, 28, 33, 34, 41]. For example, OpenOccupancy [33] first uses a 2D encoder to extract image features and further uses LSS to lift the features to 3D space. Then, ResNet3D [9] and FPN3D [20] are used to diffuse non-empty features to adjacent empty areas. SurroudOcc [34] uses successive deformable cross attention layers [45] to transform the multi-scale image features to multi-scale 3D dense volume. However, these 3D operators are often in cubic time and spatial time complexity, which is not affordable in practice.", + "bbox": [ + 498, + 292, + 890, + 520 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "BEV Representation. The past several years have witnessed the prosperous development of BEV representation in tasks such as 3D object detection [8, 17, 19, 22], BEV semantic segmentation [24, 26, 42], and instance prediction [10]. They either forward project the image features to 3D spaces with estimated depth, then compress the 3D feature volume to BEV map, or update the BEV queries via backward deformable attention. Despite efficiency, the geometry lossy projection results in the relatively coarse representation of the 3D scene, hindering its generalization to the fine-grained semantic occupancy prediction task.", + "bbox": [ + 498, + 521, + 890, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "TPV Representation. To make a trade-off between efficacy and efficiency, TPV representation is proposed [13, 47]. It first constructs three cross-planes perpendicular to each other to represent the 3D scene. Then, sets of queries are initialized on these planes to aggregate features from images and exchange features across views via the attention mechanism. Then, they efficiently reconstruct each voxel in the 3D space by summing its projected features on the three planes for downstream tasks. Although the loss of geometry is mitigated, it is still hard to capture the complex driving scene, leading to degraded performance.", + "bbox": [ + 498, + 688, + 890, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we rethink the 3D scene representation from a sparse view and seek an effective but also efficient method for semantic occupancy prediction.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1We conduct statics using the ground-truth occupancy labels of the first 10 sequences in the SemanticKITTI dataset.", + "bbox": [ + 76, + 875, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "15036", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Scene Completion in Occupancy Prediction", + "text_level": 1, + "bbox": [ + 76, + 90, + 444, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Both LiDAR points and lifted 3D representation only cover the initial intersection surface between the ray from the sensor and objects. Hence, a few methods have been proposed to diffuse non-empty features to surrounding empty regions [18, 35]. These methods essentially are the same as the 3D dense representation based ones since they also stack 3D dense operators to diffuse features. In contrast, we explore the potential of using a pure sparse representation and propose a sparse latent diffuser for scene completion. This approach rethinks the conventional method of feature diffusion in 3D space, offering a more efficient way to fill in the gaps in the scene representation.", + "bbox": [ + 75, + 113, + 472, + 297 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Approach", + "text_level": 1, + "bbox": [ + 76, + 309, + 267, + 327 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminary: Sparse Representation", + "text_level": 1, + "bbox": [ + 76, + 334, + 390, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a monocular image or a set of images $\\mathbf{I} = \\{I_i\\}_{i=1}^{N_{\\mathrm{view}}}$ captured by surrounding cameras, the goal of vision-based 3D semantic occupancy prediction is to predict a semantic label for every voxel in a predefined 3D volume $\\{0,1,2,\\dots,C\\}^{H\\times W\\times D}$ , where $H, W, D$ denotes the spatial resolution, the class label 0 indicates empty voxel, $C$ is the number of semantic classes for non-empty voxels.", + "bbox": [ + 75, + 354, + 468, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the initial stage of our model, we follow the Lift-Spat-Shoot (LSS) [25] framework. The images are first passed through an image encoder, such as ResNet [9] augmented with FPN [20]. This encoder generates latent features on the 2D perspective plane. Subsequently, the 2D latent features are lifted to the 3D space using predicted depth maps, resulting in dense cubic features denoted as $\\mathbf{V} \\in \\mathbb{R}^{H \\times W \\times D \\times C}$ . Notably, we observe that approximately $80\\%$ of the voxels in $\\mathbf{V}$ are empty. This sparsity arises due to the nature of LSS, where 2D features are cast through ray casting and become sparser in distant regions.", + "bbox": [ + 75, + 463, + 468, + 628 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We then convert the dense feature $\\mathbf{V}$ to a sparse representation by gathering non-empty voxels. The sparse tensor is stored in a commonly used coordinate (COO) format:", + "bbox": [ + 75, + 628, + 468, + 675 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {V} = \\left\\{(\\mathbf {p} _ {i} = [ x _ {i}, y _ {i}, z _ {i} ] \\in \\mathbb {R} ^ {3}, \\mathbf {f} _ {i} \\in \\mathbb {R} ^ {C}) | i = 1, 2, \\dots N \\right\\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 686, + 454, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the above equation, $N$ represents the number of nonempty voxels, while $\\mathbf{p}_i$ and $\\mathbf{f}_i$ denote the coordinates and features of the $i$ -th voxel, respectively. All subsequent operations are performed on this sparse representation, eliminating redundant computations on empty voxels. The following sections elaborate on the proposed sparse building blocks, namely the sparse latent diffuser, feature pyramid, and transformer head. An overview is shown in Fig. 2.", + "bbox": [ + 75, + 715, + 468, + 838 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Sparse Latent Diffuser", + "text_level": 1, + "bbox": [ + 76, + 847, + 287, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The sparse representation $\\mathbb{V}$ is derived through a ray casting manner, resulting in a predominantly sparse depiction", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "limited to the initial intersection face between a ray and an object. Consequently, the majority of observations are inherently incomplete. Contrarily, the objective of an occupancy network is to predict complete occupancy rather than solely the visible parts. Traditional approaches address this by incorporating 3D dense convolutions (such as 3D ResNet and 3D FPN) or attention layers (such as deformable self-attention) to diffuse non-empty features to adjacent empty regions, thereby completing the scene. In this work, we aim to design a sparse variant of the latent diffuser. However, a notable challenge arises as the objective of the diffuser appears to conflict with the sparse design: By stacking more completion blocks, the scene is better completed, but the spatial sparsity also decreases, hindering efficiency. To strike a balance between scene completion and sparsity, we build our sparse latent diffuser with two key components: A sparse completion block, which executes only necessary latent diffusion; and a contextual aggregation block, which aggregates valid features without engaging in completion.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sparse Completion Block. We opt for the 3D sparse convolution implemented by [7] to build the sparse completion block. A sparse convolution performs the computation in a local window in which at least one non-empty voxel resides, allowing the diffusion of features from non-empty voxels to their neighbors. The range of diffusion can be expanded by stacking multiple layers of sparse convolution. To maintain the spatial sparsity, we only use one 3D convolution layer in a sparse completion block.", + "bbox": [ + 496, + 380, + 890, + 517 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Contextual Aggregation Block. After completion, we introduce the contextual aggregation block to effectively utilize geometry and semantic features from the local context. For constructing this block, we choose sparse submanifold convolution [7] over regular sparse convolution. Submanifold convolution ensures that an output location is active only if the corresponding input location is active, thereby maintaining sparsity even when stacking multiple layers.", + "bbox": [ + 496, + 518, + 890, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Kernel Decomposition. Foreground objects and background elements in driving scenes often exhibit specific shape distributions. For instance, roadways and sidewalks typically have a thin, flat shape located at the bottom of the 3D volume, making them amenable to completion through convolutions in the horizontal direction. Conversely, structures like buildings or car-like objects have a rectangular shape, necessitating feature diffusion in the vertical direction. To fully leverage these distinct shape distributions, we decompose a conventional $k \\times k \\times k$ kernel into orthogonal kernels [46]. Specifically, for the sparse completion block, we replace the sparse convolution with three consecutive layers with $k \\times k \\times 1$ , $k \\times 1 \\times k$ , and $1 \\times k \\times k$ kernels, respectively. For the contextual aggregation block, we follow Cylinder3D [46] and replace a $k \\times k \\times k$ submanifold convolution with two parallel but asymmetrical branches of decomposed layers. One branch consists of two consecu", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "15037", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8ba99954ae3e19186d73265cc3b97af43f24ce1c275d40fb6e2276b758db018b.jpg", + "image_caption": [ + "Figure 2. Overview of the proposed approach. (a) Images captured by monocular or surrounding cameras are first passed to a 2D encoder, yielding 2D latent features. Then the latent features are mapped to 3D using the predicted depth map following the LSS [25]. (b) SparseOcc adopts a sparse representation for the latent space. Upon this representation, we introduce three key building blocks: a latent diffuser that performs completion, a feature pyramid that enhances receptive filed, and a transformer head that predicts semantic occupancy." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 421, + 303 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7770f3f7109e66bb42dbfa87af614dcd411bf30abbf0ff6385267a88f091c72f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 421, + 88, + 893, + 304 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7267879d51d74138094acd266af86fd6db9226983d217686361dce2ed8011197.jpg", + "image_caption": [ + "(a) Sparse Completion Block", + "(b) Contextual Aggregation Block", + "Figure 3. Two building blocks of the sparse latent diffuser. (a) The sparse completion block diffuses non-empty features to empty neighbors, and (b) The contextual aggregation block aggregates geometry and semantic features without engaging in completion." + ], + "image_footnote": [], + "bbox": [ + 106, + 392, + 429, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tive layers with $1 \\times k \\times k$ ad $k \\times 1 \\times k$ kernels, and the other branch with $k \\times 1 \\times k$ ad $1 \\times k \\times k$ kernels. Note that the complexity is reduced from $\\mathcal{O}(k^3)$ to $\\mathcal{O}(3k^2)$ or $\\mathcal{O}(4k^2)$ after the decomposition. Though the actual cost is not reduced when we use a small kernel with $k = 3$ , the expressive capacity of decomposed kernels outperforms a single full kernel, thus we can still achieve efficiency improvements by stacking fewer layers.", + "bbox": [ + 75, + 714, + 468, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Sparse Feature Pyramid", + "text_level": 1, + "bbox": [ + 76, + 845, + 302, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "A straightforward approach to complete the scene is to stack the proposed sparse diffuser multiple times, akin to SCP-", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Net [35]. However, this necessitates a substantial number of sparse diffusers to ensure an adequately large receptive field, which is particularly important for recognizing large objects like \"truck\" or static elements such as \"road\". The computation cost is obviously expensive. To address this issue, we note that down-sample layers, implemented with sparse convolution with a stride greater than one, not only reduce the spatial resolution but also increase the relative sparsity in the new scale. By building a multi-scale sparse feature pyramid with down-sample layers, we are readily able to obtain a coarse-to-fine representation of the scene. This ensures that querying any spatial location can be addressed by at least one feature scale, simultaneously reducing computation costs. Formally, we stack the sparse diffuser for $L$ times, each is followed by a down-sample layer, and the feature pyramid is collected as $\\{\\mathbb{V}_l\\}_{l=1}^L$ . Additionally, the spatial size along the height dimension of the last two scales is too small, so we simply omit the $D$ dimension. For the completion blocks, the 3D convolution is replaced with a 2D version with $3 \\times 3$ kernel. For the contextual aggregation block, we replace the asymmetrical branches with two parallel 2D submanifold convolutions with $5 \\times 5$ kernels.", + "bbox": [ + 496, + 398, + 890, + 729 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Sparse Voxel Decoder. Former methods [6, 41] uses multi-scale deformable attention transformer (MSDeformAttn) [44] in the pixel/voxel decoder responsible for aggregating intra-scale and inter-scale features. Targeting for saving GPU memory and time, we simplify this process by using interpolation to fuse multi-scale sparse features output by the 3D sparse encoder. Specifically, for a given scale $\\mathbb{V}_l$ from the feature pyramid, we augment it by fusing all the other scales,", + "bbox": [ + 496, + 731, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbb {V}} _ {l} = \\sum_ {j \\neq l} W _ {j} \\cdot \\operatorname {I n t e r p} \\left(\\mathbb {V} _ {j}, \\mathbb {V} _ {l}\\right), 2 \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 869, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "15038", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $W_{j}$ is a learned weight for the $j$ -th scale, and $\\mathrm{Interp}(\\mathbb{X},\\mathbb{Y})$ indicates linear interpolation from a sparse tensor $\\mathbb{X}$ to another $\\mathbb{Y}$ .", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Leveraging this lightweight feature fusion approach, the feature pyramid is enriched with semantic information from different scales. Moreover, the high-resolution features benefit from additional completion provided by the low-resolution features, as the denser low-resolution features resist dilution by interpolation operators.", + "bbox": [ + 76, + 138, + 467, + 229 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Sparse Transformer Head", + "text_level": 1, + "bbox": [ + 76, + 246, + 313, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We frame the semantic occupancy prediction as a 3D segmentation problem and employ a transformer head, inspired by the design of Mask2Former [6]. This head iteratively updates a set of learnable queries through masked attention and subsequently decodes these queries into 3D masks for all semantic classes. However, a challenge arises due to the need for dense binary masks to represent semantic classes. Additionally, as we perform predictions in a 3D space [41], the computational and memory costs associated with applying successive transformer decoder layers to dense masks become impractical.", + "bbox": [ + 75, + 272, + 467, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To overcome this challenge, we adapt the dense transformer head to a sparse variant. Specifically, we assert that accurate segmentation is crucial for occupied voxels, while non-occupied voxels need not be considered during this phase. In the ensuing discussion, we outline several steps to delineate the sparse transformer decoder.", + "bbox": [ + 75, + 441, + 467, + 530 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Preprocessing and Notations. Given the sparse feature pyramid $\\hat{\\mathbb{V}}_l$ , we first employ a linear binary classifier for coarse segmentation. The binary classifier is trained to label a voxel as empty if the semantic ground truth is 0 and nonempty otherwise. We only preserve voxels that are classified as non-empty, resulting in a filtered, sparser tensor $\\hat{\\mathbb{V}}_l = \\{(\\mathbf{p}_i,\\mathbf{f}_i)|i = 1,\\dots,N_l\\}$ , where we use $N_{l}$ to denote the number of remaining voxels for the $l$ -th scale. Storing variant features for the empty voxels is unnecessary, and instead, we find it suffices to use only a single learnable token $\\mathbf{p}_{\\phi}$ to represent all the empty voxels.", + "bbox": [ + 75, + 534, + 467, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Query Decoding. The former method [41] performs outer product between queries $Q \\in \\mathbb{R}^{N_q \\times C}$ and 3D dense features $F \\in \\mathbb{R}^{C \\times H \\times W \\times D}$ to decode the queries to 3D mask with shape $(N_q, H, W, D)$ , which has a time complexity of $\\mathcal{O}(N_q HWDC)$ . To facilitate inference speed, we only perform outer product between $Q$ and $\\mathbf{p}_{\\phi} \\cup \\{\\mathbf{f}_i | (\\mathbf{p}_i, \\mathbf{f}_i) \\in \\hat{\\mathbb{V}}_l\\}$ to obtain a series of occupied masks $M^{\\mathrm{occ}} \\in \\mathbb{R}^{N_q \\times N_l}$ and a single mask $M^{\\phi} \\in \\mathbb{R}^{N_q \\times 1}$ that represents empty voxels. With the saved coordinates $\\mathbf{p}$ of occupied voxels, we can easily reconstruct the dense 3D mask $M \\in \\mathbb{R}^{Q \\times H \\times W \\times Z}$ from the predicted sparse tensor, using a scatter operation that does not break the gradient flow. This way, the complexity is reduced to $\\mathcal{O}(N_l N_q C + HWZ)$ for mask predic", + "bbox": [ + 75, + 702, + 467, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "tion and reconstruction. Note that", + "bbox": [ + 500, + 90, + 723, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {O} \\left(N _ {l} N _ {q} C + H W Z\\right) \\\\ = \\mathcal {O} \\left(H W Z N _ {q} C \\left(\\frac {N _ {l}}{H W Z} + \\frac {1}{N _ {q} C}\\right)\\right) \\tag {2} \\\\ < \\mathcal {O} (H W Z N _ {q} C), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 116, + 890, + 189 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "because $N_{l} / HWZ$ is rather smaller than 1 in our sparse case. Moreover, the $N_{q}$ queries are also input to a $C$ -way linear classifier to classify the corresponding 3D mask into predefined $C$ semantic categories.", + "bbox": [ + 496, + 198, + 890, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Query Updating. Given the input $L$ layers of multi-scale sparse features, we iteratively alternate between query decoding and query updating in each transformer layer. With the predicted 3D masks $M_{l-1}$ in the $(l-1)$ -th transformer layer, we update the queries via", + "bbox": [ + 496, + 258, + 890, + 334 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {l} = \\operatorname {s o f t m a x} \\left[ \\mathcal {M} _ {l - 1} + W _ {q} Q _ {l - 1} \\left(W _ {k} \\hat {\\mathbf {V}} _ {l}\\right) ^ {T} \\right] W _ {v} \\hat {\\mathbf {V}} _ {l} + Q _ {l - 1}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 343, + 897, + 380 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{q}, W_{k}, W_{v}$ are linear layers, $\\hat{\\mathbf{V}}_{l}$ is the dense version reconstructed from $\\hat{\\mathbb{V}}_{l}$ , and the attention mask $\\mathcal{M}_{l-1}$ at location $(x,y,z)$ is obtained by", + "bbox": [ + 496, + 381, + 890, + 429 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {M} _ {l - 1} (x, y, z) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} \\sigma \\left(M _ {l - 1} ^ {\\prime} (x, y, z)\\right) \\geq 0. 5 \\\\ - \\infty & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 504, + 439, + 890, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\sigma$ is the sigmoid function, $M_{l-1}^{\\prime} = \\max\\text{pooling}(M_{l-1})$ which resizes the 3D mask to the same resolution of $\\hat{\\mathbf{V}}_l$ , similar to implementation in [41].", + "bbox": [ + 496, + 507, + 890, + 555 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Objective Function", + "text_level": 1, + "bbox": [ + 500, + 563, + 683, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Considering the sparse transformer head formulates semantic occupancy as a mask set prediction task [6, 41], bipartite matching with Hungarian solver is used to assign binary mask labels and corresponding semantic class labels to the predicted masks. Based on the assignment, we calculate the mask loss $\\mathcal{L}_{\\mathrm{mask}}$ and classification loss $\\mathcal{L}_{\\mathrm{cls}}$ . Additionally, $\\mathcal{L}_{\\mathrm{depth}}$ is calculated between the predicted depth map and ground-truth projected by point clouds, for supervision of the LSS component. Moreover, the coarse binary classification on non-empty voxels is also supervised by a segmentation loss $\\mathcal{L}_{\\mathrm{seg}}$ . Finally, the overall objective function is a simple summation of these loss terms", + "bbox": [ + 496, + 587, + 890, + 767 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {d e p t h}} + \\mathcal {L} _ {\\text {s e g}}. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 779, + 890, + 796 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 806, + 630, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 500, + 832, + 689, + 848 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. We evaluate our proposed SparseOcc on nuScenes-Occupancy [33] and SemanticKITTI [2]. nuScenes-Occupancy [33] extends the famous large-scale", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "15039", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/f522214de494c83a903bc9d0b5ed5aad832527fb6e072fe1f2d7e0e6999e5666.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInputIoUmIoUbarrierbicyclebuscarconst. veh.motorcyclepedestriantraffic conetrailertruckdrive. surf.other flatsidewalkterrainmannadevegetationFLOPsMemory3D/Overall Latency
MonoScene [4]C18.46.97.13.99.37.25.63.05.94.44.94.214.96.37.97.410.07.6---
TPVFormer [13]C15.37.89.34.111.310.15.24.35.95.36.86.513.69.08.38.09.28.21132G20G0.57/0.73s
OpenOccupancy [33]C19.310.39.96.811.211.56.38.48.64.34.29.922.015.814.113.57.310.21716G19G0.84/1.22s
C-CONet [33]C20.112.813.28.115.417.26.311.210.08.34.712.131.418.818.716.34.88.21810G21G2.18/2.58s
SparseOcc (ours)C21.814.116.19.315.118.67.39.411.29.47.213.031.821.720.718.86.110.6455G13G0.19/0.25s
", + "bbox": [ + 80, + 88, + 893, + 215 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/43a909d5e937bdf121471562ad8fd1915bede431995e2496f1b1eb2f94226f24.jpg", + "table_caption": [ + "Table 1. Semantic occupancy prediction results on nuScenes-Occupancy [33] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs, training GPU memory, and 3D/overall inference latency. The C denotes camera and the bold numbers indicate the best results." + ], + "table_footnote": [], + "table_body": "
MethodInputIoUmIoUroad (15.30%)sidewalk (11.13%)parking (1.12%)other-ground (0.56%)building (14.1%)car (3.92%)truck (0.16%)bicycle (0.03%)motorcycle (0.03%)other-vehicle (0.20%)vegetation (39.3%)trunk (0.51%)terrain (9.17%)person (0.07%)bicyclist (0.07%)motorcyclist (0.05%)fence (3.90%)pole (0.29%)traffic-sign (0.08%)FLOPs
LMSCNet* [27]C28.616.7040.6818.224.380.0010.3118.330.000.000.000.000.000.000.000.000.000.0013.660.0220.540.000.000.000.001.210.000.00
3DSketch* [5]C33.307.5041.3221.630.000.0014.8118.590.000.000.000.000.000.000.000.0019.090.0026.400.000.000.000.000.730.000.00
AICNet* [16]C29.598.3143.5520.5511.970.0712.9414.714.530.000.000.000.000.0015.372.9028.710.000.000.000.002.520.060.00
JS3C-Net* [37]C38.9810.3150.4923.7411.940.0715.0324.654.410.000.006.1518.114.3326.860.670.270.000.003.943.771.45
MonoScene† [4]C36.8611.0856.5226.7214.270.4614.0923.266.980.610.451.4817.892.8129.641.861.200.005.844.142.25
TPVFormer [13]C35.6111.3656.5025.8720.600.8513.8823.818.080.360.054.3516.922.2630.380.510.890.005.943.141.52
OccFormer [41]C36.5013.4658.8526.8819.610.3114.4025.0925.530.811.198.5219.633.9332.622.782.820.005.614.262.86
SparseOccC36.4813.1259.5929.6820.440.4715.4124.0318.070.780.898.9418.893.4631.063.680.620.006.733.892.60
", + "bbox": [ + 80, + 267, + 890, + 445 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Semantic scene completion results on SemanticKITTI [1] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs. The C denotes camera and the bold numbers indicate the best results. The methods with “*” are RGB-input variants reported by [4] for fair comparison.", + "bbox": [ + 76, + 446, + 892, + 488 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "autonomous driving datasets nuScenes [3] with 3D dense semantic occupancy annotations on key frames for 1 \"empty\" class and 16 semantic classes using Augmenting And Purifying pipeline. It covers 700 and 150 driving scenes in the training and validation set of nuScenes. The multi-view images and corresponding LiDAR points are provided by the original nuScenes dataset. SemanticKITTI [2] contains 22 sequences including monocular images, LiDAR points, point cloud segmentation labels and semantic scene completion annotations. The sequence 08 is officially split for validation, sequences 00-10 (excluding 08) are used for training, and sequences 11-21 are the test set. It annotates each 3D voxel with 1 \"empty\" class or 19 semantic classes.", + "bbox": [ + 75, + 502, + 468, + 714 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metric. We follow the common practice and report the intersection over union (IoU) of occupied voxels regardless of their semantic labels to evaluate the reconstructed geometry shape. The semantic mIoU of all semantic classes is also reported to evaluate the semantic-aware perception ability. For efficiency analysis, FLOPs is also evaluated using the analysis tool provided by [22].", + "bbox": [ + 75, + 715, + 468, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details. For image encoder, we follow the previous work [33, 41] for fair comparison and use EfficientNetB7 [29] and SecondFPN [39] on SemanticKITTI and ResNet-50 [9] on nuScenes-Occupancy. The 2D to 3D view transformation is implemented as the same as [33, 41].", + "bbox": [ + 75, + 824, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "And it generates a 3D feature volume of size $128 \\times 128 \\times 16$ and $128 \\times 128 \\times 10$ with 128 channels for SemanticKITTI and nuScenes-Occupancy, which is converted to sparse representation. We stack the sparse diffuser for $L = 4$ times, each followed by a sparse convolution with stride 2 for downsampling. The kernel size $k$ of the orthogonal convolutions in sparse completion block and contextual aggregation block is set to 3. The sparse voxel decoder projects the multi-scale features to 192 channels and enhances them via interpolation and summation. The sparse transformer head consists of 9 layers for query updating and decoding and the number of queries $N_{q}$ is 100. Following [6, 41], we sample 50176 points for supervision according to the class frequency for fast training speed. During inference, the predicted masks are upsampled $2 \\times$ and $4 \\times$ to the size of ground-truth via trilinear interpolation for evaluation on SemanticKITTI and nuScenes-Occupancy, respectively.", + "bbox": [ + 496, + 502, + 890, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Optimization. AdamW [23] optimizer with an initial learning rate of 1e-4 and a weight decay of 0.01 is leveraged during training. We train the model for 30 epochs on SemanticKITTI and 24 epochs on nuScenes-Occupancy with a batch size of 8 on 8 v100 GPUs.", + "bbox": [ + 496, + 758, + 890, + 834 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Benchmark Performance", + "text_level": 1, + "bbox": [ + 500, + 845, + 728, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this part, we compare our SparseOcc with the published state-of-the-art methods on nuScenes-Occupancy and Se", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "15040", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "manticKITTI. The results of the former methods are directly derived from their papers or code with their configurations. NuScenes-Occupancy. As shown in Tab. 1, our SparseOcc successfully outperforms the 3D dense representation based C-CONet [33] by $1.7\\%$ geometry IoU and $1.3\\%$ semantic mIoU. This accomplishment highlights SparseOcc's effectiveness. Besides, we can observe that the model FLOPs are reduced by $74.9\\%$ relatively, which further justifies the efficiency of our SparseOcc. More surprisingly, SparseOcc not only produces a remarkable $80.8\\%$ improvement in mIoU over TPVFormer [13] which uses efficient TPV view as 3D scene representation, but also reduces the FLOPs by $59.8\\%$ . We find that TPVFormer uses a relatively large image backbone ResNet-101 [9], and the multi-layer image cross-attention as well as cross-view attention between dense TPV maps also impose lots of computational burden. In contrast, our SparseOcc uses sparse operators in the 3D space, helping us achieve superior performance with a lightweight implementation. Besides, SparseOcc exhibits a noteworthy reduction in 3D inference latency, i.e., the time for 3D feature processing.", + "bbox": [ + 76, + 90, + 468, + 409 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SemanticKITTI. We quantitatively compare the proposed SparseOcc with several previous works in Tab. 2. we can see that SparseOcc achieves comparable performance with OccFormer [41] and significantly better than other methods in terms of semantic mIoU. Please note that different from OccFormer which builds long-range and dynamic dependency in the 3D space using Swin Transformer [21], the 3D encoder of SparseOcc is built with spconv [7] only. Consequently, the model FLOPs of SparseOcc is just $44.2\\%$ of OccFormer [41] approximately.", + "bbox": [ + 76, + 409, + 470, + 560 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Qualitative Evaluation", + "text_level": 1, + "bbox": [ + 76, + 570, + 287, + 585 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We visualize the 3D semantic occupancy prediction results of several challenging scenes in nuScenes-Occupancy validation set in Fig. 4. As can be seen, compared with the 3D dense counterpart C-CONet [33], our SparseOcc can better complete the large area flat-like road (first row), capture the complicated structure of vegetation (second row) and reconstruct car in the distance (third row). We can conclude that benefiting from the proposed sparse latent diffuser and learned sparse feature pyramid, our sparse occupancy transformer head can generate relatively accurate scene-level descriptions in an efficient way.", + "bbox": [ + 75, + 594, + 468, + 760 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 770, + 240, + 786 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sparse Completion Blok. As illustrated in Sec. 3.2, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels in the sparse completion block. Tab. 3 ablates the type and number of diffusion kernels. Surprisingly, we find that SparseOcc can perform satisfactorily even if no sparse completion block is applied. We think that it is because the decoder which", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c0447f955be1f7d72201e61a1527b9e84df840521488f77bcd0f61a4065436bc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Conv TypeConv NumKernel SizeIoUmIoU
-0-35.512.1
Regular13×3×335.812.2
236.412.3
336.212.6
Decomposed13×3×136.513.1
23×1×336.612.8
31×3×136.412.7
", + "bbox": [ + 526, + 88, + 867, + 199 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b5817c099151bc2169e33766cf62c50bc7491b295c2961d44371ce7b4c4026c8.jpg", + "table_caption": [ + "Table 3. Ablation on different designs of Sparse Completion Block on SemanticKITTI val set." + ], + "table_footnote": [], + "table_body": "
TypeIoUmIoUMemoryFLOPs
FPN3D[20]34.49.813.2G307G
MSDeformAttn3D36.713.319.8G379G
Sparse Decoder36.513.113.3G279G
", + "bbox": [ + 524, + 237, + 867, + 296 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b6b3274ddce3a2dd8b4416de93e7f51129a570695ec892ba7bb7e9ced85cc5f7.jpg", + "table_caption": [ + "Table 4. Ablation on voxel decoder on SemanticKITTI val set." + ], + "table_footnote": [], + "table_body": "
TypeIoUmIoUMemoryFLOPs
Linear Head36.811.89.8G5.4G
Trans. Head36.213.219.9G19.0G
Sparse Trans. Head36.513.113.3G13.5G
", + "bbox": [ + 524, + 320, + 867, + 378 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Ablation on segmentation head on SemanticKITTI val set.", + "bbox": [ + 500, + 381, + 890, + 407 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "fuses sparse feature pyramid can also complete the scene to some extent. Compared with regular $3 \\times 3 \\times 3$ kernel, the decomposed orthogonal achieves better scene completion and segmentation results. Besides, stacking more convolution blocks does not improve performance. Hence, we build our sparse completion block with only a group of decomposed orthogonal.", + "bbox": [ + 496, + 429, + 890, + 535 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sparse Feature Pyramid. As shown in Tab. 4, we observe that when the SparseOcc equipped with 6 layers of multi-scale deformable attention (MSDeformAttn), it performs better than the proposed sparse decoder. However, when the layer number of MSDeformAttn decreases, the IoU and mIoU both drop and lag behind the proposed simple sparse decoder. Moreover, the training GPU memory and FLOPs of the MSDeformAttn3D are much higher than the proposed interpolation and summation method. Compared with FPN3D [20], our sparse voxel decoder is $2.1\\%$ IoU and $3.3\\%$ mIoU higher with slightly more memory.", + "bbox": [ + 496, + 536, + 890, + 703 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Sparse Transformer Head. We compare several different prediction heads, including simple linear head, transformer head proposed in [41], and our sparse transformer head in Tab. 5. As can be seen, the linear head achieves the best geometry IoU of 36.8. We postulate it may be because the output of the linear head is supervised by an explicit geometry loss, i.e., a cross-entropy loss on occupied and non-occupied voxels. On the contrary, the transformer decoder formulates occupancy prediction as mask generation for each semantic class exclusively. Consequently, no explicit supervision is or can be imposed on the occupied voxels. SparseOcc uses a linear layer for coarse segmentation to filter out the non-occupied voxels and then proposes", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "15041", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05fa9a7a1d81eb91714f39b4507e363194f4eb6d532abc99d28b7143c63e1931.jpg", + "image_caption": [ + "Figure 4. Qualitative results of 3D semantic occupancy on nuScenes-Occupancy validation set. The input multi-view images are shown on the leftmost and the occupancy predictions of C-CONet [33], our SparseOcc, and the ground-truth are then visualized sequentially. Compared to 3D dense representation based C-CONet [38], our SparseOcc achieves better completion and segmentation as highlighted by the red circles." + ], + "image_footnote": [], + "bbox": [ + 138, + 95, + 826, + 429 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b1bda890ca7ccb17b4f8cff9305b32ef684c9acc91489ae236ce42abe41c5b1d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Method2D BackboneInput SizeIoUmIoU
C-CONet [33]R-50704 × 25616.68.6
R-501600 × 90019.310.3
R-1011600 × 90020.211.4
SparseOccR-50704 × 25621.814.1
R-501600 × 90020.414.6
", + "bbox": [ + 89, + 498, + 455, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Ablation on input size and 2D backbone on nuScenes-Occupancy.", + "bbox": [ + 76, + 585, + 470, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "a sparse transformer head for mask prediction. Therefore, it makes an appropriate trade-off between these two kinds of occupancy heads and achieves satisfactory performance with low training memory.", + "bbox": [ + 75, + 628, + 468, + 689 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Input Image Size. A larger input image size has a larger resolution of image features, thus having a larger feature density in the 3D space, which further influences the performance. From Tab. 6, we can observe that SparseOcc still performs better than C-CONet, even though it is trained using a smaller input size $(704 \\times 256)$ and image backbone (R-50), which further demonstrates the effectiveness of our SparseOcc. Additionally, using a larger input image size $(1600 \\times 900)$ can improve mIoU for both C-CONet and the proposed SparseOcc, thanks to the density increase of semantic features. However, the IoU of SparseOcc drops when using higher image resolution. We blame it on the wrong hallucination on spatially empty voxels caused by over-dense 3D sparse features. When inactivating the sparse", + "bbox": [ + 75, + 689, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "completion block in the last sparse latent diffuser layer, this hallucination can be relieved.", + "bbox": [ + 498, + 501, + 890, + 532 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 549, + 619, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we explore the possibility of using pure sparse representation for 3D scene description and present SpaseOcc for 3D semantic occupancy prediction. Specifically, a sparse latent diffuser with decomposed orthogonal kernels is proposed to propagate the non-empty features to their adjacent empty area. To efficiently complete the scene, we stack layers of diffusers and downsampling layers to generate a coarse-to-fine sparse feature pyramid, which is further fused via simple interpolation and summation. In this way, the feature pyramid is enhanced by multi-scale semantic information. Finally, we use a sparse transformer head to query multi-scale sparse features and generate semantic occupancy predictions. Without bells and whistles, SparseOcc achieves state-of-the-art results on nuScenes-Occupancy and comparable performance on SemanticKITTI, fully demonstrating its superior effectiveness and efficiency.", + "bbox": [ + 496, + 575, + 890, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work was supported by NSFC (62322113, 62376156), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities.", + "bbox": [ + 498, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "15042", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. In ICCV, 2019. 6", + "[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. 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Pointocc: Cylindrical tri-perspective view for point-based 3d semantic occupancy prediction. arXiv:2308.16896, 2023. 2" + ], + "bbox": [ + 78, + 90, + 468, + 828 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "15044", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_model.json b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2de4e49b31a7d53f8387869b8c2dd0a781f26c49 --- /dev/null +++ b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_model.json @@ -0,0 +1,1991 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.197, + 0.131, + 0.777, + 0.177 + ], + "angle": 0, + "content": "SparseOcc: Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.203, + 0.741, + 0.222 + ], + "angle": 0, + "content": "Pin Tang1 Zhongdao Wang2 Guoqing Wang1 Jilai Zheng1" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.222, + 0.684, + 0.239 + ], + "angle": 0, + "content": "Xiangxuan Ren1 Bailan Feng2 Chao Ma1*" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.24, + 0.82, + 0.274 + ], + "angle": 0, + "content": "1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University \n2 Huawei Noah's Ark Lab" + }, + { + "type": "text", + "bbox": [ + 0.169, + 0.277, + 0.801, + 0.293 + ], + "angle": 0, + "content": "{pin.tang,guoqing.wang,zhengjilai,bunny.renxiangxuan,chaoma}@sjtu.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.326, + 0.296, + 0.646, + 0.31 + ], + "angle": 0, + "content": "{wangzhongdao,fengbailan}@huawei.com" + }, + { + "type": "text", + "bbox": [ + 0.245, + 0.313, + 0.719, + 0.327 + ], + "angle": 0, + "content": "Project page: https://pintang1999.github.io/sparseocc.html" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.362, + 0.314, + 0.379 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.395, + 0.474, + 0.759 + ], + "angle": 0, + "content": "Vision-based perception for autonomous driving requires an explicit modeling of a 3D space, where 2D latent representations are mapped and subsequent 3D operators are applied. However, operating on dense latent spaces introduces a cubic time and space complexity, which limits scalability in terms of perception range or spatial resolution. Existing approaches compress the dense representation using projections like Bird's Eye View (BEV) or Tri-Perspective View (TPV). Although efficient, these projections result in information loss, especially for tasks like semantic occupancy prediction. To address this, we propose SparseOcc, an efficient occupancy network inspired by sparse point cloud processing. It utilizes a lossless sparse latent representation with three key innovations. Firstly, a 3D sparse diffuser performs latent completion using spatially decomposed 3D sparse convolutional kernels. Secondly, a feature pyramid and sparse interpolation enhance scales with information from others. Finally, the transformer head is redesigned as a sparse variant. SparseOcc achieves a remarkable \\(74.9\\%\\) reduction on FLOPs over the dense baseline. Interestingly, it also improves accuracy, from \\(12.8\\%\\) to \\(14.1\\%\\) mIOU, which in part can be attributed to the sparse representation's ability to avoid hallucinations on empty voxels." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.788, + 0.21, + 0.804 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.815, + 0.471, + 0.876 + ], + "angle": 0, + "content": "Accurate perception of the surrounding environment is crucial for autonomous driving systems [11, 14]. In recent years, vision-based 3D perception algorithms have gained significant attention and advancement due to their cost-" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.361, + 0.892, + 0.56 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.569, + 0.895, + 0.655 + ], + "angle": 0, + "content": "Figure 1. (a) Vision-based perception methods for autonomous driving typically first extract image features by a 2D latent encoder and then map them to 3D using view transformation. (b) For the 3D latent space, existing methods mostly employ the dense, BEV, or TPV representation, while we rethink the possibility of using sparse representation to achieve superior efficiency and accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.895, + 0.883 + ], + "angle": 0, + "content": "effectiveness. The typical workflow involves employing a 2D encoder to extract latent representations from images. A view transformation method, such as lift-splat-shoot (LSS) [25], is then applied to lift the perspective 2D latent features to a 3D voxel space, utilizing predicted depth information. This 3D scene representation serves as the foundation for deriving geometry and semantic information to describe the driving environment, supporting various 3D perception tasks including object detection [15, 17, 40, 43], semantic segmentation [11, 30, 36], and semantic occupancy prediction [13, 33, 34]. In this study, we specifically focus on the challenging task of semantic occupancy prediction [31-34], which entails predicting both static and dynamic elements within the scene." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Several alternatives are available for representing 3D" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.227, + 0.9 + ], + "angle": 0, + "content": "* Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15035" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "spatial latent information. The dense representation [33] is the most straightforward approach, storing features in continuous memory and enabling direct application of dense 3D operations like convolutions. However, this representation is redundant and inefficient, as approximately \\(67\\%\\) of the considered 3D space is empty1. Bird Eye's View (BEV) [12, 19, 22] has gained popularity as a recent prevalent representation. It involves projecting the 3D space onto a BEV plane, significantly reducing computational costs by leveraging efficient 2D building blocks in a BEV encoder. However, this projection introduces the loss of geometry information, thereby limiting the fine-grained capacity of the BEV representation to comprehend the 3D scene structure. A Tri-Perspective View (TPV) [13] representation is proposed to mitigate the information loss, but it still suffers from degraded perception accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.473, + 0.515 + ], + "angle": 0, + "content": "In this paper, we seek a latent representation that encodes the 3D scene structure in a lossless manner while minimizing computational costs. Drawing inspiration from the similarities between sparse 3D vision features and point clouds, we rethink the feasibility of employing a pure sparse representation for the 3D latent space, a common practice in point cloud processing [7]. Specifically, we utilize the coordinate (COO) format to store sparse tensors and introduce a series of sparse building blocks tailored for the sparse representation. Our proposed method, SparseOcc, is an occupancy network where all 3D layers operate on sparse tensors. The key designs of SparseOcc are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.516, + 0.47, + 0.59 + ], + "angle": 0, + "content": "- Sparse Latent Diffuser: This component enables the propagation of non-empty features to adjacent empty regions, facilitating scene completion. To ensure efficiency, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.591, + 0.47, + 0.682 + ], + "angle": 0, + "content": "- Sparse Feature Pyramid: We build a feature pyramid that incorporates sparse interpolation operations to enhance scales with information from other scales. This pyramid design expands the reception fields, reducing the need for excessive diffusers within each scale, which helps preserve sparsity." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.682, + 0.47, + 0.771 + ], + "angle": 0, + "content": "- Sparse Transformer Head: The final component of SparseOcc is a 3D sparse transformer head responsible for generating semantic occupancy predictions. By segmenting only occupied voxels rather than the entire 3D volume, we achieve a remarkable reduction in computational costs." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.516, + 0.47, + 0.771 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.773, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Based on the sparse latent representation, SparseOcc achieves a significant reduction in computation overhead. In the nuScenes-Occupancy benchmark [33], it reduces the FLOPs of existing approaches using dense or TPV representations by \\(59.8\\%\\) to \\(74.9\\%\\), and memory usage by \\(31.6\\%\\) to \\(40.9\\%\\). Remarkably, the semantic occupancy" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "accuracy not only remains intact but improves, surpassing the state-of-the-art C-CONet. Specifically, the semantic occupancy accuracy increases from \\(12.8\\%\\) to \\(14.1\\%\\) mIoU. This improvement highlights the superiority of the sparse representation over the dense one in terms of accuracy, as it naturally avoids hallucinations on empty voxels. Considering the effectiveness and efficiency demonstrated by SparseOcc, we propose that it can serve as a new baseline for occupancy networks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.244, + 0.642, + 0.26 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.269, + 0.729, + 0.286 + ], + "angle": 0, + "content": "2.1. 3D Scene Representation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.294, + 0.892, + 0.521 + ], + "angle": 0, + "content": "3D Dense Representation. Representing the surrounding environment with spatial latent information is an indispensable procedure for autonomous driving perception algorithms. A straightforward solution is to split the scene into voxels and describe the scene with 3D volume representation where 3D operators are applied [4, 28, 33, 34, 41]. For example, OpenOccupancy [33] first uses a 2D encoder to extract image features and further uses LSS to lift the features to 3D space. Then, ResNet3D [9] and FPN3D [20] are used to diffuse non-empty features to adjacent empty areas. SurroudOcc [34] uses successive deformable cross attention layers [45] to transform the multi-scale image features to multi-scale 3D dense volume. However, these 3D operators are often in cubic time and spatial time complexity, which is not affordable in practice." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.522, + 0.892, + 0.688 + ], + "angle": 0, + "content": "BEV Representation. The past several years have witnessed the prosperous development of BEV representation in tasks such as 3D object detection [8, 17, 19, 22], BEV semantic segmentation [24, 26, 42], and instance prediction [10]. They either forward project the image features to 3D spaces with estimated depth, then compress the 3D feature volume to BEV map, or update the BEV queries via backward deformable attention. Despite efficiency, the geometry lossy projection results in the relatively coarse representation of the 3D scene, hindering its generalization to the fine-grained semantic occupancy prediction task." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.689, + 0.892, + 0.855 + ], + "angle": 0, + "content": "TPV Representation. To make a trade-off between efficacy and efficiency, TPV representation is proposed [13, 47]. It first constructs three cross-planes perpendicular to each other to represent the 3D scene. Then, sets of queries are initialized on these planes to aggregate features from images and exchange features across views via the attention mechanism. Then, they efficiently reconstruct each voxel in the 3D space by summing its projected features on the three planes for downstream tasks. Although the loss of geometry is mitigated, it is still hard to capture the complex driving scene, leading to degraded performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we rethink the 3D scene representation from a sparse view and seek an effective but also efficient method for semantic occupancy prediction." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "1We conduct statics using the ground-truth occupancy labels of the first 10 sequences in the SemanticKITTI dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "15036" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.445, + 0.108 + ], + "angle": 0, + "content": "2.2. Scene Completion in Occupancy Prediction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.473, + 0.298 + ], + "angle": 0, + "content": "Both LiDAR points and lifted 3D representation only cover the initial intersection surface between the ray from the sensor and objects. Hence, a few methods have been proposed to diffuse non-empty features to surrounding empty regions [18, 35]. These methods essentially are the same as the 3D dense representation based ones since they also stack 3D dense operators to diffuse features. In contrast, we explore the potential of using a pure sparse representation and propose a sparse latent diffuser for scene completion. This approach rethinks the conventional method of feature diffusion in 3D space, offering a more efficient way to fill in the gaps in the scene representation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.31, + 0.269, + 0.328 + ], + "angle": 0, + "content": "3. Proposed Approach" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.335, + 0.392, + 0.351 + ], + "angle": 0, + "content": "3.1. Preliminary: Sparse Representation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.469, + 0.463 + ], + "angle": 0, + "content": "Given a monocular image or a set of images \\(\\mathbf{I} = \\{I_i\\}_{i=1}^{N_{\\mathrm{view}}}\\) captured by surrounding cameras, the goal of vision-based 3D semantic occupancy prediction is to predict a semantic label for every voxel in a predefined 3D volume \\(\\{0,1,2,\\dots,C\\}^{H\\times W\\times D}\\), where \\(H, W, D\\) denotes the spatial resolution, the class label 0 indicates empty voxel, \\(C\\) is the number of semantic classes for non-empty voxels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.464, + 0.469, + 0.629 + ], + "angle": 0, + "content": "In the initial stage of our model, we follow the Lift-Spat-Shoot (LSS) [25] framework. The images are first passed through an image encoder, such as ResNet [9] augmented with FPN [20]. This encoder generates latent features on the 2D perspective plane. Subsequently, the 2D latent features are lifted to the 3D space using predicted depth maps, resulting in dense cubic features denoted as \\(\\mathbf{V} \\in \\mathbb{R}^{H \\times W \\times D \\times C}\\). Notably, we observe that approximately \\(80\\%\\) of the voxels in \\(\\mathbf{V}\\) are empty. This sparsity arises due to the nature of LSS, where 2D features are cast through ray casting and become sparser in distant regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.676 + ], + "angle": 0, + "content": "We then convert the dense feature \\(\\mathbf{V}\\) to a sparse representation by gathering non-empty voxels. The sparse tensor is stored in a commonly used coordinate (COO) format:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.687, + 0.455, + 0.706 + ], + "angle": 0, + "content": "\\[\n\\mathbb {V} = \\left\\{(\\mathbf {p} _ {i} = [ x _ {i}, y _ {i}, z _ {i} ] \\in \\mathbb {R} ^ {3}, \\mathbf {f} _ {i} \\in \\mathbb {R} ^ {C}) | i = 1, 2, \\dots N \\right\\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.469, + 0.839 + ], + "angle": 0, + "content": "In the above equation, \\(N\\) represents the number of nonempty voxels, while \\(\\mathbf{p}_i\\) and \\(\\mathbf{f}_i\\) denote the coordinates and features of the \\(i\\)-th voxel, respectively. All subsequent operations are performed on this sparse representation, eliminating redundant computations on empty voxels. The following sections elaborate on the proposed sparse building blocks, namely the sparse latent diffuser, feature pyramid, and transformer head. An overview is shown in Fig. 2." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.289, + 0.864 + ], + "angle": 0, + "content": "3.2. Sparse Latent Diffuser" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "The sparse representation \\(\\mathbb{V}\\) is derived through a ray casting manner, resulting in a predominantly sparse depiction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.379 + ], + "angle": 0, + "content": "limited to the initial intersection face between a ray and an object. Consequently, the majority of observations are inherently incomplete. Contrarily, the objective of an occupancy network is to predict complete occupancy rather than solely the visible parts. Traditional approaches address this by incorporating 3D dense convolutions (such as 3D ResNet and 3D FPN) or attention layers (such as deformable self-attention) to diffuse non-empty features to adjacent empty regions, thereby completing the scene. In this work, we aim to design a sparse variant of the latent diffuser. However, a notable challenge arises as the objective of the diffuser appears to conflict with the sparse design: By stacking more completion blocks, the scene is better completed, but the spatial sparsity also decreases, hindering efficiency. To strike a balance between scene completion and sparsity, we build our sparse latent diffuser with two key components: A sparse completion block, which executes only necessary latent diffusion; and a contextual aggregation block, which aggregates valid features without engaging in completion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.381, + 0.892, + 0.518 + ], + "angle": 0, + "content": "Sparse Completion Block. We opt for the 3D sparse convolution implemented by [7] to build the sparse completion block. A sparse convolution performs the computation in a local window in which at least one non-empty voxel resides, allowing the diffusion of features from non-empty voxels to their neighbors. The range of diffusion can be expanded by stacking multiple layers of sparse convolution. To maintain the spatial sparsity, we only use one 3D convolution layer in a sparse completion block." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Contextual Aggregation Block. After completion, we introduce the contextual aggregation block to effectively utilize geometry and semantic features from the local context. For constructing this block, we choose sparse submanifold convolution [7] over regular sparse convolution. Submanifold convolution ensures that an output location is active only if the corresponding input location is active, thereby maintaining sparsity even when stacking multiple layers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Kernel Decomposition. Foreground objects and background elements in driving scenes often exhibit specific shape distributions. For instance, roadways and sidewalks typically have a thin, flat shape located at the bottom of the 3D volume, making them amenable to completion through convolutions in the horizontal direction. Conversely, structures like buildings or car-like objects have a rectangular shape, necessitating feature diffusion in the vertical direction. To fully leverage these distinct shape distributions, we decompose a conventional \\(k \\times k \\times k\\) kernel into orthogonal kernels [46]. Specifically, for the sparse completion block, we replace the sparse convolution with three consecutive layers with \\(k \\times k \\times 1\\), \\(k \\times 1 \\times k\\), and \\(1 \\times k \\times k\\) kernels, respectively. For the contextual aggregation block, we follow Cylinder3D [46] and replace a \\(k \\times k \\times k\\) submanifold convolution with two parallel but asymmetrical branches of decomposed layers. One branch consists of two consecu" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15037" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.422, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.423, + 0.089, + 0.895, + 0.305 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.317, + 0.895, + 0.377 + ], + "angle": 0, + "content": "Figure 2. Overview of the proposed approach. (a) Images captured by monocular or surrounding cameras are first passed to a 2D encoder, yielding 2D latent features. Then the latent features are mapped to 3D using the predicted depth map following the LSS [25]. (b) SparseOcc adopts a sparse representation for the latent space. Upon this representation, we introduce three key building blocks: a latent diffuser that performs completion, a feature pyramid that enhances receptive filed, and a transformer head that predicts semantic occupancy." + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.393, + 0.431, + 0.609 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.614, + 0.253, + 0.626 + ], + "angle": 0, + "content": "(a) Sparse Completion Block" + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.614, + 0.45, + 0.626 + ], + "angle": 0, + "content": "(b) Contextual Aggregation Block" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.638, + 0.47, + 0.695 + ], + "angle": 0, + "content": "Figure 3. Two building blocks of the sparse latent diffuser. (a) The sparse completion block diffuses non-empty features to empty neighbors, and (b) The contextual aggregation block aggregates geometry and semantic features without engaging in completion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.47, + 0.837 + ], + "angle": 0, + "content": "tive layers with \\(1 \\times k \\times k\\) ad \\(k \\times 1 \\times k\\) kernels, and the other branch with \\(k \\times 1 \\times k\\) ad \\(1 \\times k \\times k\\) kernels. Note that the complexity is reduced from \\(\\mathcal{O}(k^3)\\) to \\(\\mathcal{O}(3k^2)\\) or \\(\\mathcal{O}(4k^2)\\) after the decomposition. Though the actual cost is not reduced when we use a small kernel with \\(k = 3\\), the expressive capacity of decomposed kernels outperforms a single full kernel, thus we can still achieve efficiency improvements by stacking fewer layers." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.847, + 0.303, + 0.864 + ], + "angle": 0, + "content": "3.3. Sparse Feature Pyramid" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "A straightforward approach to complete the scene is to stack the proposed sparse diffuser multiple times, akin to SCP-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.892, + 0.731 + ], + "angle": 0, + "content": "Net [35]. However, this necessitates a substantial number of sparse diffusers to ensure an adequately large receptive field, which is particularly important for recognizing large objects like \"truck\" or static elements such as \"road\". The computation cost is obviously expensive. To address this issue, we note that down-sample layers, implemented with sparse convolution with a stride greater than one, not only reduce the spatial resolution but also increase the relative sparsity in the new scale. By building a multi-scale sparse feature pyramid with down-sample layers, we are readily able to obtain a coarse-to-fine representation of the scene. This ensures that querying any spatial location can be addressed by at least one feature scale, simultaneously reducing computation costs. Formally, we stack the sparse diffuser for \\( L \\) times, each is followed by a down-sample layer, and the feature pyramid is collected as \\( \\{\\mathbb{V}_l\\}_{l=1}^L \\). Additionally, the spatial size along the height dimension of the last two scales is too small, so we simply omit the \\( D \\) dimension. For the completion blocks, the 3D convolution is replaced with a 2D version with \\( 3 \\times 3 \\) kernel. For the contextual aggregation block, we replace the asymmetrical branches with two parallel 2D submanifold convolutions with \\( 5 \\times 5 \\) kernels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.732, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Sparse Voxel Decoder. Former methods [6, 41] uses multi-scale deformable attention transformer (MSDeformAttn) [44] in the pixel/voxel decoder responsible for aggregating intra-scale and inter-scale features. Targeting for saving GPU memory and time, we simplify this process by using interpolation to fuse multi-scale sparse features output by the 3D sparse encoder. Specifically, for a given scale \\(\\mathbb{V}_l\\) from the feature pyramid, we augment it by fusing all the other scales," + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.871, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbb {V}} _ {l} = \\sum_ {j \\neq l} W _ {j} \\cdot \\operatorname {I n t e r p} \\left(\\mathbb {V} _ {j}, \\mathbb {V} _ {l}\\right), 2 \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15038" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "where \\( W_{j} \\) is a learned weight for the \\( j \\)-th scale, and \\( \\mathrm{Interp}(\\mathbb{X},\\mathbb{Y}) \\) indicates linear interpolation from a sparse tensor \\( \\mathbb{X} \\) to another \\( \\mathbb{Y} \\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.14, + 0.468, + 0.231 + ], + "angle": 0, + "content": "Leveraging this lightweight feature fusion approach, the feature pyramid is enriched with semantic information from different scales. Moreover, the high-resolution features benefit from additional completion provided by the low-resolution features, as the denser low-resolution features resist dilution by interpolation operators." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.247, + 0.314, + 0.263 + ], + "angle": 0, + "content": "3.4. Sparse Transformer Head" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.468, + 0.438 + ], + "angle": 0, + "content": "We frame the semantic occupancy prediction as a 3D segmentation problem and employ a transformer head, inspired by the design of Mask2Former [6]. This head iteratively updates a set of learnable queries through masked attention and subsequently decodes these queries into 3D masks for all semantic classes. However, a challenge arises due to the need for dense binary masks to represent semantic classes. Additionally, as we perform predictions in a 3D space [41], the computational and memory costs associated with applying successive transformer decoder layers to dense masks become impractical." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.468, + 0.531 + ], + "angle": 0, + "content": "To overcome this challenge, we adapt the dense transformer head to a sparse variant. Specifically, we assert that accurate segmentation is crucial for occupied voxels, while non-occupied voxels need not be considered during this phase. In the ensuing discussion, we outline several steps to delineate the sparse transformer decoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.468, + 0.7 + ], + "angle": 0, + "content": "Preprocessing and Notations. Given the sparse feature pyramid \\(\\hat{\\mathbb{V}}_l\\), we first employ a linear binary classifier for coarse segmentation. The binary classifier is trained to label a voxel as empty if the semantic ground truth is 0 and nonempty otherwise. We only preserve voxels that are classified as non-empty, resulting in a filtered, sparser tensor \\(\\hat{\\mathbb{V}}_l = \\{(\\mathbf{p}_i,\\mathbf{f}_i)|i = 1,\\dots,N_l\\}\\), where we use \\(N_{l}\\) to denote the number of remaining voxels for the \\(l\\)-th scale. Storing variant features for the empty voxels is unnecessary, and instead, we find it suffices to use only a single learnable token \\(\\mathbf{p}_{\\phi}\\) to represent all the empty voxels." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Query Decoding. The former method [41] performs outer product between queries \\(Q \\in \\mathbb{R}^{N_q \\times C}\\) and 3D dense features \\(F \\in \\mathbb{R}^{C \\times H \\times W \\times D}\\) to decode the queries to 3D mask with shape \\((N_q, H, W, D)\\), which has a time complexity of \\(\\mathcal{O}(N_q HWDC)\\). To facilitate inference speed, we only perform outer product between \\(Q\\) and \\(\\mathbf{p}_{\\phi} \\cup \\{\\mathbf{f}_i | (\\mathbf{p}_i, \\mathbf{f}_i) \\in \\hat{\\mathbb{V}}_l\\}\\) to obtain a series of occupied masks \\(M^{\\mathrm{occ}} \\in \\mathbb{R}^{N_q \\times N_l}\\) and a single mask \\(M^{\\phi} \\in \\mathbb{R}^{N_q \\times 1}\\) that represents empty voxels. With the saved coordinates \\(\\mathbf{p}\\) of occupied voxels, we can easily reconstruct the dense 3D mask \\(M \\in \\mathbb{R}^{Q \\times H \\times W \\times Z}\\) from the predicted sparse tensor, using a scatter operation that does not break the gradient flow. This way, the complexity is reduced to \\(\\mathcal{O}(N_l N_q C + HWZ)\\) for mask predic" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.725, + 0.105 + ], + "angle": 0, + "content": "tion and reconstruction. Note that" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.117, + 0.892, + 0.19 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {O} \\left(N _ {l} N _ {q} C + H W Z\\right) \\\\ = \\mathcal {O} \\left(H W Z N _ {q} C \\left(\\frac {N _ {l}}{H W Z} + \\frac {1}{N _ {q} C}\\right)\\right) \\tag {2} \\\\ < \\mathcal {O} (H W Z N _ {q} C), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.259 + ], + "angle": 0, + "content": "because \\( N_{l} / HWZ \\) is rather smaller than 1 in our sparse case. Moreover, the \\( N_{q} \\) queries are also input to a \\( C \\)-way linear classifier to classify the corresponding 3D mask into predefined \\( C \\) semantic categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.26, + 0.892, + 0.335 + ], + "angle": 0, + "content": "Query Updating. Given the input \\( L \\) layers of multi-scale sparse features, we iteratively alternate between query decoding and query updating in each transformer layer. With the predicted 3D masks \\( M_{l-1} \\) in the \\( (l-1) \\)-th transformer layer, we update the queries via" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.344, + 0.898, + 0.381 + ], + "angle": 0, + "content": "\\[\nQ _ {l} = \\operatorname {s o f t m a x} \\left[ \\mathcal {M} _ {l - 1} + W _ {q} Q _ {l - 1} \\left(W _ {k} \\hat {\\mathbf {V}} _ {l}\\right) ^ {T} \\right] W _ {v} \\hat {\\mathbf {V}} _ {l} + Q _ {l - 1}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.892, + 0.43 + ], + "angle": 0, + "content": "where \\(W_{q}, W_{k}, W_{v}\\) are linear layers, \\(\\hat{\\mathbf{V}}_{l}\\) is the dense version reconstructed from \\(\\hat{\\mathbb{V}}_{l}\\), and the attention mask \\(\\mathcal{M}_{l-1}\\) at location \\((x,y,z)\\) is obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.506, + 0.44, + 0.891, + 0.495 + ], + "angle": 0, + "content": "\\[\n\\mathcal {M} _ {l - 1} (x, y, z) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} \\sigma \\left(M _ {l - 1} ^ {\\prime} (x, y, z)\\right) \\geq 0. 5 \\\\ - \\infty & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.556 + ], + "angle": 0, + "content": "where \\(\\sigma\\) is the sigmoid function, \\(M_{l-1}^{\\prime} = \\max\\text{pooling}(M_{l-1})\\) which resizes the 3D mask to the same resolution of \\(\\hat{\\mathbf{V}}_l\\), similar to implementation in [41]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.564, + 0.684, + 0.58 + ], + "angle": 0, + "content": "3.5. Objective Function" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.892, + 0.768 + ], + "angle": 0, + "content": "Considering the sparse transformer head formulates semantic occupancy as a mask set prediction task [6, 41], bipartite matching with Hungarian solver is used to assign binary mask labels and corresponding semantic class labels to the predicted masks. Based on the assignment, we calculate the mask loss \\(\\mathcal{L}_{\\mathrm{mask}}\\) and classification loss \\(\\mathcal{L}_{\\mathrm{cls}}\\). Additionally, \\(\\mathcal{L}_{\\mathrm{depth}}\\) is calculated between the predicted depth map and ground-truth projected by point clouds, for supervision of the LSS component. Moreover, the coarse binary classification on non-empty voxels is also supervised by a segmentation loss \\(\\mathcal{L}_{\\mathrm{seg}}\\). Finally, the overall objective function is a simple summation of these loss terms" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.78, + 0.891, + 0.797 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {d e p t h}} + \\mathcal {L} _ {\\text {s e g}}. \\tag {5}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.808, + 0.632, + 0.825 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.691, + 0.849 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Datasets. We evaluate our proposed SparseOcc on nuScenes-Occupancy [33] and SemanticKITTI [2]. nuScenes-Occupancy [33] extends the famous large-scale" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15039" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.894, + 0.217 + ], + "angle": 0, + "content": "
MethodInputIoUmIoUbarrierbicyclebuscarconst. veh.motorcyclepedestriantraffic conetrailertruckdrive. surf.other flatsidewalkterrainmannadevegetationFLOPsMemory3D/Overall Latency
MonoScene [4]C18.46.97.13.99.37.25.63.05.94.44.94.214.96.37.97.410.07.6---
TPVFormer [13]C15.37.89.34.111.310.15.24.35.95.36.86.513.69.08.38.09.28.21132G20G0.57/0.73s
OpenOccupancy [33]C19.310.39.96.811.211.56.38.48.64.34.29.922.015.814.113.57.310.21716G19G0.84/1.22s
C-CONet [33]C20.112.813.28.115.417.26.311.210.08.34.712.131.418.818.716.34.88.21810G21G2.18/2.58s
SparseOcc (ours)C21.814.116.19.315.118.67.39.411.29.47.213.031.821.720.718.86.110.6455G13G0.19/0.25s
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.219, + 0.893, + 0.26 + ], + "angle": 0, + "content": "Table 1. Semantic occupancy prediction results on nuScenes-Occupancy [33] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs, training GPU memory, and 3D/overall inference latency. The C denotes camera and the bold numbers indicate the best results." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.268, + 0.892, + 0.446 + ], + "angle": 0, + "content": "
MethodInputIoUmIoUroad (15.30%)sidewalk (11.13%)parking (1.12%)other-ground (0.56%)building (14.1%)car (3.92%)truck (0.16%)bicycle (0.03%)motorcycle (0.03%)other-vehicle (0.20%)vegetation (39.3%)trunk (0.51%)terrain (9.17%)person (0.07%)bicyclist (0.07%)motorcyclist (0.05%)fence (3.90%)pole (0.29%)traffic-sign (0.08%)FLOPs
LMSCNet* [27]C28.616.7040.6818.224.380.0010.3118.330.000.000.000.000.000.000.000.000.000.0013.660.0220.540.000.000.000.001.210.000.00
3DSketch* [5]C33.307.5041.3221.630.000.0014.8118.590.000.000.000.000.000.000.000.0019.090.0026.400.000.000.000.000.730.000.00
AICNet* [16]C29.598.3143.5520.5511.970.0712.9414.714.530.000.000.000.000.0015.372.9028.710.000.000.000.002.520.060.00
JS3C-Net* [37]C38.9810.3150.4923.7411.940.0715.0324.654.410.000.006.1518.114.3326.860.670.270.000.003.943.771.45
MonoScene† [4]C36.8611.0856.5226.7214.270.4614.0923.266.980.610.451.4817.892.8129.641.861.200.005.844.142.25
TPVFormer [13]C35.6111.3656.5025.8720.600.8513.8823.818.080.360.054.3516.922.2630.380.510.890.005.943.141.52
OccFormer [41]C36.5013.4658.8526.8819.610.3114.4025.0925.530.811.198.5219.633.9332.622.782.820.005.614.262.86
SparseOccC36.4813.1259.5929.6820.440.4715.4124.0318.070.780.898.9418.893.4631.063.680.620.006.733.892.60
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.447, + 0.893, + 0.489 + ], + "angle": 0, + "content": "Table 2. Semantic scene completion results on SemanticKITTI [1] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs. The C denotes camera and the bold numbers indicate the best results. The methods with “*” are RGB-input variants reported by [4] for fair comparison." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.503, + 0.47, + 0.715 + ], + "angle": 0, + "content": "autonomous driving datasets nuScenes [3] with 3D dense semantic occupancy annotations on key frames for 1 \"empty\" class and 16 semantic classes using Augmenting And Purifying pipeline. It covers 700 and 150 driving scenes in the training and validation set of nuScenes. The multi-view images and corresponding LiDAR points are provided by the original nuScenes dataset. SemanticKITTI [2] contains 22 sequences including monocular images, LiDAR points, point cloud segmentation labels and semantic scene completion annotations. The sequence 08 is officially split for validation, sequences 00-10 (excluding 08) are used for training, and sequences 11-21 are the test set. It annotates each 3D voxel with 1 \"empty\" class or 19 semantic classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.824 + ], + "angle": 0, + "content": "Evaluation Metric. We follow the common practice and report the intersection over union (IoU) of occupied voxels regardless of their semantic labels to evaluate the reconstructed geometry shape. The semantic mIoU of all semantic classes is also reported to evaluate the semantic-aware perception ability. For efficiency analysis, FLOPs is also evaluated using the analysis tool provided by [22]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Implementation Details. For image encoder, we follow the previous work [33, 41] for fair comparison and use EfficientNetB7 [29] and SecondFPN [39] on SemanticKITTI and ResNet-50 [9] on nuScenes-Occupancy. The 2D to 3D view transformation is implemented as the same as [33, 41]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.76 + ], + "angle": 0, + "content": "And it generates a 3D feature volume of size \\(128 \\times 128 \\times 16\\) and \\(128 \\times 128 \\times 10\\) with 128 channels for SemanticKITTI and nuScenes-Occupancy, which is converted to sparse representation. We stack the sparse diffuser for \\(L = 4\\) times, each followed by a sparse convolution with stride 2 for downsampling. The kernel size \\(k\\) of the orthogonal convolutions in sparse completion block and contextual aggregation block is set to 3. The sparse voxel decoder projects the multi-scale features to 192 channels and enhances them via interpolation and summation. The sparse transformer head consists of 9 layers for query updating and decoding and the number of queries \\(N_{q}\\) is 100. Following [6, 41], we sample 50176 points for supervision according to the class frequency for fast training speed. During inference, the predicted masks are upsampled \\(2 \\times\\) and \\(4 \\times\\) to the size of ground-truth via trilinear interpolation for evaluation on SemanticKITTI and nuScenes-Occupancy, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.892, + 0.835 + ], + "angle": 0, + "content": "Optimization. AdamW [23] optimizer with an initial learning rate of 1e-4 and a weight decay of 0.01 is leveraged during training. We train the model for 30 epochs on SemanticKITTI and 24 epochs on nuScenes-Occupancy with a batch size of 8 on 8 v100 GPUs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.73, + 0.862 + ], + "angle": 0, + "content": "4.2. Benchmark Performance" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In this part, we compare our SparseOcc with the published state-of-the-art methods on nuScenes-Occupancy and Se" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "15040" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.41 + ], + "angle": 0, + "content": "manticKITTI. The results of the former methods are directly derived from their papers or code with their configurations. NuScenes-Occupancy. As shown in Tab. 1, our SparseOcc successfully outperforms the 3D dense representation based C-CONet [33] by \\(1.7\\%\\) geometry IoU and \\(1.3\\%\\) semantic mIoU. This accomplishment highlights SparseOcc's effectiveness. Besides, we can observe that the model FLOPs are reduced by \\(74.9\\%\\) relatively, which further justifies the efficiency of our SparseOcc. More surprisingly, SparseOcc not only produces a remarkable \\(80.8\\%\\) improvement in mIoU over TPVFormer [13] which uses efficient TPV view as 3D scene representation, but also reduces the FLOPs by \\(59.8\\%\\). We find that TPVFormer uses a relatively large image backbone ResNet-101 [9], and the multi-layer image cross-attention as well as cross-view attention between dense TPV maps also impose lots of computational burden. In contrast, our SparseOcc uses sparse operators in the 3D space, helping us achieve superior performance with a lightweight implementation. Besides, SparseOcc exhibits a noteworthy reduction in 3D inference latency, i.e., the time for 3D feature processing." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.41, + 0.471, + 0.561 + ], + "angle": 0, + "content": "SemanticKITTI. We quantitatively compare the proposed SparseOcc with several previous works in Tab. 2. we can see that SparseOcc achieves comparable performance with OccFormer [41] and significantly better than other methods in terms of semantic mIoU. Please note that different from OccFormer which builds long-range and dynamic dependency in the 3D space using Swin Transformer [21], the 3D encoder of SparseOcc is built with spconv [7] only. Consequently, the model FLOPs of SparseOcc is just \\(44.2\\%\\) of OccFormer [41] approximately." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.571, + 0.288, + 0.587 + ], + "angle": 0, + "content": "4.3. Qualitative Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.761 + ], + "angle": 0, + "content": "We visualize the 3D semantic occupancy prediction results of several challenging scenes in nuScenes-Occupancy validation set in Fig. 4. As can be seen, compared with the 3D dense counterpart C-CONet [33], our SparseOcc can better complete the large area flat-like road (first row), capture the complicated structure of vegetation (second row) and reconstruct car in the distance (third row). We can conclude that benefiting from the proposed sparse latent diffuser and learned sparse feature pyramid, our sparse occupancy transformer head can generate relatively accurate scene-level descriptions in an efficient way." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.771, + 0.241, + 0.787 + ], + "angle": 0, + "content": "4.4. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Sparse Completion Blok. As illustrated in Sec. 3.2, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels in the sparse completion block. Tab. 3 ablates the type and number of diffusion kernels. Surprisingly, we find that SparseOcc can perform satisfactorily even if no sparse completion block is applied. We think that it is because the decoder which" + }, + { + "type": "table", + "bbox": [ + 0.527, + 0.089, + 0.868, + 0.2 + ], + "angle": 0, + "content": "
Conv TypeConv NumKernel SizeIoUmIoU
-0-35.512.1
Regular13×3×335.812.2
236.412.3
336.212.6
Decomposed13×3×136.513.1
23×1×336.612.8
31×3×136.412.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.203, + 0.892, + 0.23 + ], + "angle": 0, + "content": "Table 3. Ablation on different designs of Sparse Completion Block on SemanticKITTI val set." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.238, + 0.868, + 0.297 + ], + "angle": 0, + "content": "
TypeIoUmIoUMemoryFLOPs
FPN3D[20]34.49.813.2G307G
MSDeformAttn3D36.713.319.8G379G
Sparse Decoder36.513.113.3G279G
" + }, + { + "type": "table_caption", + "bbox": [ + 0.51, + 0.3, + 0.881, + 0.313 + ], + "angle": 0, + "content": "Table 4. Ablation on voxel decoder on SemanticKITTI val set." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.321, + 0.868, + 0.379 + ], + "angle": 0, + "content": "
TypeIoUmIoUMemoryFLOPs
Linear Head36.811.89.8G5.4G
Trans. Head36.213.219.9G19.0G
Sparse Trans. Head36.513.113.3G13.5G
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.382, + 0.892, + 0.409 + ], + "angle": 0, + "content": "Table 5. Ablation on segmentation head on SemanticKITTI val set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.43, + 0.892, + 0.536 + ], + "angle": 0, + "content": "fuses sparse feature pyramid can also complete the scene to some extent. Compared with regular \\(3 \\times 3 \\times 3\\) kernel, the decomposed orthogonal achieves better scene completion and segmentation results. Besides, stacking more convolution blocks does not improve performance. Hence, we build our sparse completion block with only a group of decomposed orthogonal." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.537, + 0.892, + 0.704 + ], + "angle": 0, + "content": "Sparse Feature Pyramid. As shown in Tab. 4, we observe that when the SparseOcc equipped with 6 layers of multi-scale deformable attention (MSDeformAttn), it performs better than the proposed sparse decoder. However, when the layer number of MSDeformAttn decreases, the IoU and mIoU both drop and lag behind the proposed simple sparse decoder. Moreover, the training GPU memory and FLOPs of the MSDeformAttn3D are much higher than the proposed interpolation and summation method. Compared with FPN3D [20], our sparse voxel decoder is \\(2.1\\%\\) IoU and \\(3.3\\%\\) mIoU higher with slightly more memory." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Sparse Transformer Head. We compare several different prediction heads, including simple linear head, transformer head proposed in [41], and our sparse transformer head in Tab. 5. As can be seen, the linear head achieves the best geometry IoU of 36.8. We postulate it may be because the output of the linear head is supervised by an explicit geometry loss, i.e., a cross-entropy loss on occupied and non-occupied voxels. On the contrary, the transformer decoder formulates occupancy prediction as mask generation for each semantic class exclusively. Consequently, no explicit supervision is or can be imposed on the occupied voxels. SparseOcc uses a linear layer for coarse segmentation to filter out the non-occupied voxels and then proposes" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "15041" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.096, + 0.827, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.432, + 0.895, + 0.488 + ], + "angle": 0, + "content": "Figure 4. Qualitative results of 3D semantic occupancy on nuScenes-Occupancy validation set. The input multi-view images are shown on the leftmost and the occupancy predictions of C-CONet [33], our SparseOcc, and the ground-truth are then visualized sequentially. Compared to 3D dense representation based C-CONet [38], our SparseOcc achieves better completion and segmentation as highlighted by the red circles." + }, + { + "type": "table", + "bbox": [ + 0.091, + 0.499, + 0.457, + 0.585 + ], + "angle": 0, + "content": "
Method2D BackboneInput SizeIoUmIoU
C-CONet [33]R-50704 × 25616.68.6
R-501600 × 90019.310.3
R-1011600 × 90020.211.4
SparseOccR-50704 × 25621.814.1
R-501600 × 90020.414.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.587, + 0.471, + 0.618 + ], + "angle": 0, + "content": "Table 6. Ablation on input size and 2D backbone on nuScenes-Occupancy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.69 + ], + "angle": 0, + "content": "a sparse transformer head for mask prediction. Therefore, it makes an appropriate trade-off between these two kinds of occupancy heads and achieves satisfactory performance with low training memory." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.69, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Input Image Size. A larger input image size has a larger resolution of image features, thus having a larger feature density in the 3D space, which further influences the performance. From Tab. 6, we can observe that SparseOcc still performs better than C-CONet, even though it is trained using a smaller input size \\((704 \\times 256)\\) and image backbone (R-50), which further demonstrates the effectiveness of our SparseOcc. Additionally, using a larger input image size \\((1600 \\times 900)\\) can improve mIoU for both C-CONet and the proposed SparseOcc, thanks to the density increase of semantic features. However, the IoU of SparseOcc drops when using higher image resolution. We blame it on the wrong hallucination on spatially empty voxels caused by over-dense 3D sparse features. When inactivating the sparse" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.533 + ], + "angle": 0, + "content": "completion block in the last sparse latent diffuser layer, this hallucination can be relieved." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.62, + 0.567 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.835 + ], + "angle": 0, + "content": "In this paper, we explore the possibility of using pure sparse representation for 3D scene description and present SpaseOcc for 3D semantic occupancy prediction. Specifically, a sparse latent diffuser with decomposed orthogonal kernels is proposed to propagate the non-empty features to their adjacent empty area. To efficiently complete the scene, we stack layers of diffusers and downsampling layers to generate a coarse-to-fine sparse feature pyramid, which is further fused via simple interpolation and summation. In this way, the feature pyramid is enhanced by multi-scale semantic information. Finally, we use a sparse transformer head to query multi-scale sparse features and generate semantic occupancy predictions. Without bells and whistles, SparseOcc achieves state-of-the-art results on nuScenes-Occupancy and comparable performance on SemanticKITTI, fully demonstrating its superior effectiveness and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. This work was supported by NSFC (62322113, 62376156), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "15042" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. 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Pointocc: Cylindrical tri-perspective view for point-based 3d semantic occupancy prediction. arXiv:2308.16896, 2023. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.829 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "15044" + } + ] +] \ No newline at end of file diff --git a/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_origin.pdf b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8176dd7030bc8d6b730dbb4a8049751fd8f25a97 --- /dev/null +++ b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/6bce05c4-f8ee-4452-886d-3f99d4f2a003_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:91ec7b69d38967cd884b07ef88c283cc5905fde9d5c2a75a29fdec50b8905e04 +size 1422168 diff --git a/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/full.md b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a84e906b1fd97dcea020a2a59fbd53ac678ff2dd --- /dev/null +++ b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/full.md @@ -0,0 +1,282 @@ +# SparseOcc: Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction + +Pin Tang1 Zhongdao Wang2 Guoqing Wang1 Jilai Zheng1 + +Xiangxuan Ren1 Bailan Feng2 Chao Ma1* + +1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University +2 Huawei Noah's Ark Lab + +{pin.tang,guoqing.wang,zhengjilai,bunny.renxiangxuan,chaoma}@sjtu.edu.cn + +{wangzhongdao,fengbailan}@huawei.com + +Project page: https://pintang1999.github.io/sparseocc.html + +# Abstract + +Vision-based perception for autonomous driving requires an explicit modeling of a 3D space, where 2D latent representations are mapped and subsequent 3D operators are applied. However, operating on dense latent spaces introduces a cubic time and space complexity, which limits scalability in terms of perception range or spatial resolution. Existing approaches compress the dense representation using projections like Bird's Eye View (BEV) or Tri-Perspective View (TPV). Although efficient, these projections result in information loss, especially for tasks like semantic occupancy prediction. To address this, we propose SparseOcc, an efficient occupancy network inspired by sparse point cloud processing. It utilizes a lossless sparse latent representation with three key innovations. Firstly, a 3D sparse diffuser performs latent completion using spatially decomposed 3D sparse convolutional kernels. Secondly, a feature pyramid and sparse interpolation enhance scales with information from others. Finally, the transformer head is redesigned as a sparse variant. SparseOcc achieves a remarkable $74.9\%$ reduction on FLOPs over the dense baseline. Interestingly, it also improves accuracy, from $12.8\%$ to $14.1\%$ mIOU, which in part can be attributed to the sparse representation's ability to avoid hallucinations on empty voxels. + +# 1. Introduction + +Accurate perception of the surrounding environment is crucial for autonomous driving systems [11, 14]. In recent years, vision-based 3D perception algorithms have gained significant attention and advancement due to their cost- + +![](images/6525e2461113870efa7c96a98324e7a9fdbecb7c5298e575cbe086217d0e3f32.jpg) +Figure 1. (a) Vision-based perception methods for autonomous driving typically first extract image features by a 2D latent encoder and then map them to 3D using view transformation. (b) For the 3D latent space, existing methods mostly employ the dense, BEV, or TPV representation, while we rethink the possibility of using sparse representation to achieve superior efficiency and accuracy. + +effectiveness. The typical workflow involves employing a 2D encoder to extract latent representations from images. A view transformation method, such as lift-splat-shoot (LSS) [25], is then applied to lift the perspective 2D latent features to a 3D voxel space, utilizing predicted depth information. This 3D scene representation serves as the foundation for deriving geometry and semantic information to describe the driving environment, supporting various 3D perception tasks including object detection [15, 17, 40, 43], semantic segmentation [11, 30, 36], and semantic occupancy prediction [13, 33, 34]. In this study, we specifically focus on the challenging task of semantic occupancy prediction [31-34], which entails predicting both static and dynamic elements within the scene. + +Several alternatives are available for representing 3D + +spatial latent information. The dense representation [33] is the most straightforward approach, storing features in continuous memory and enabling direct application of dense 3D operations like convolutions. However, this representation is redundant and inefficient, as approximately $67\%$ of the considered 3D space is empty1. Bird Eye's View (BEV) [12, 19, 22] has gained popularity as a recent prevalent representation. It involves projecting the 3D space onto a BEV plane, significantly reducing computational costs by leveraging efficient 2D building blocks in a BEV encoder. However, this projection introduces the loss of geometry information, thereby limiting the fine-grained capacity of the BEV representation to comprehend the 3D scene structure. A Tri-Perspective View (TPV) [13] representation is proposed to mitigate the information loss, but it still suffers from degraded perception accuracy. + +In this paper, we seek a latent representation that encodes the 3D scene structure in a lossless manner while minimizing computational costs. Drawing inspiration from the similarities between sparse 3D vision features and point clouds, we rethink the feasibility of employing a pure sparse representation for the 3D latent space, a common practice in point cloud processing [7]. Specifically, we utilize the coordinate (COO) format to store sparse tensors and introduce a series of sparse building blocks tailored for the sparse representation. Our proposed method, SparseOcc, is an occupancy network where all 3D layers operate on sparse tensors. The key designs of SparseOcc are as follows: + +- Sparse Latent Diffuser: This component enables the propagation of non-empty features to adjacent empty regions, facilitating scene completion. To ensure efficiency, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels. +- Sparse Feature Pyramid: We build a feature pyramid that incorporates sparse interpolation operations to enhance scales with information from other scales. This pyramid design expands the reception fields, reducing the need for excessive diffusers within each scale, which helps preserve sparsity. +- Sparse Transformer Head: The final component of SparseOcc is a 3D sparse transformer head responsible for generating semantic occupancy predictions. By segmenting only occupied voxels rather than the entire 3D volume, we achieve a remarkable reduction in computational costs. + +Based on the sparse latent representation, SparseOcc achieves a significant reduction in computation overhead. In the nuScenes-Occupancy benchmark [33], it reduces the FLOPs of existing approaches using dense or TPV representations by $59.8\%$ to $74.9\%$ , and memory usage by $31.6\%$ to $40.9\%$ . Remarkably, the semantic occupancy + +accuracy not only remains intact but improves, surpassing the state-of-the-art C-CONet. Specifically, the semantic occupancy accuracy increases from $12.8\%$ to $14.1\%$ mIoU. This improvement highlights the superiority of the sparse representation over the dense one in terms of accuracy, as it naturally avoids hallucinations on empty voxels. Considering the effectiveness and efficiency demonstrated by SparseOcc, we propose that it can serve as a new baseline for occupancy networks. + +# 2. Related Work + +# 2.1. 3D Scene Representation + +3D Dense Representation. Representing the surrounding environment with spatial latent information is an indispensable procedure for autonomous driving perception algorithms. A straightforward solution is to split the scene into voxels and describe the scene with 3D volume representation where 3D operators are applied [4, 28, 33, 34, 41]. For example, OpenOccupancy [33] first uses a 2D encoder to extract image features and further uses LSS to lift the features to 3D space. Then, ResNet3D [9] and FPN3D [20] are used to diffuse non-empty features to adjacent empty areas. SurroudOcc [34] uses successive deformable cross attention layers [45] to transform the multi-scale image features to multi-scale 3D dense volume. However, these 3D operators are often in cubic time and spatial time complexity, which is not affordable in practice. + +BEV Representation. The past several years have witnessed the prosperous development of BEV representation in tasks such as 3D object detection [8, 17, 19, 22], BEV semantic segmentation [24, 26, 42], and instance prediction [10]. They either forward project the image features to 3D spaces with estimated depth, then compress the 3D feature volume to BEV map, or update the BEV queries via backward deformable attention. Despite efficiency, the geometry lossy projection results in the relatively coarse representation of the 3D scene, hindering its generalization to the fine-grained semantic occupancy prediction task. + +TPV Representation. To make a trade-off between efficacy and efficiency, TPV representation is proposed [13, 47]. It first constructs three cross-planes perpendicular to each other to represent the 3D scene. Then, sets of queries are initialized on these planes to aggregate features from images and exchange features across views via the attention mechanism. Then, they efficiently reconstruct each voxel in the 3D space by summing its projected features on the three planes for downstream tasks. Although the loss of geometry is mitigated, it is still hard to capture the complex driving scene, leading to degraded performance. + +In this paper, we rethink the 3D scene representation from a sparse view and seek an effective but also efficient method for semantic occupancy prediction. + +# 2.2. Scene Completion in Occupancy Prediction + +Both LiDAR points and lifted 3D representation only cover the initial intersection surface between the ray from the sensor and objects. Hence, a few methods have been proposed to diffuse non-empty features to surrounding empty regions [18, 35]. These methods essentially are the same as the 3D dense representation based ones since they also stack 3D dense operators to diffuse features. In contrast, we explore the potential of using a pure sparse representation and propose a sparse latent diffuser for scene completion. This approach rethinks the conventional method of feature diffusion in 3D space, offering a more efficient way to fill in the gaps in the scene representation. + +# 3. Proposed Approach + +# 3.1. Preliminary: Sparse Representation + +Given a monocular image or a set of images $\mathbf{I} = \{I_i\}_{i=1}^{N_{\mathrm{view}}}$ captured by surrounding cameras, the goal of vision-based 3D semantic occupancy prediction is to predict a semantic label for every voxel in a predefined 3D volume $\{0,1,2,\dots,C\}^{H\times W\times D}$ , where $H, W, D$ denotes the spatial resolution, the class label 0 indicates empty voxel, $C$ is the number of semantic classes for non-empty voxels. + +In the initial stage of our model, we follow the Lift-Spat-Shoot (LSS) [25] framework. The images are first passed through an image encoder, such as ResNet [9] augmented with FPN [20]. This encoder generates latent features on the 2D perspective plane. Subsequently, the 2D latent features are lifted to the 3D space using predicted depth maps, resulting in dense cubic features denoted as $\mathbf{V} \in \mathbb{R}^{H \times W \times D \times C}$ . Notably, we observe that approximately $80\%$ of the voxels in $\mathbf{V}$ are empty. This sparsity arises due to the nature of LSS, where 2D features are cast through ray casting and become sparser in distant regions. + +We then convert the dense feature $\mathbf{V}$ to a sparse representation by gathering non-empty voxels. The sparse tensor is stored in a commonly used coordinate (COO) format: + +$$ +\mathbb {V} = \left\{(\mathbf {p} _ {i} = [ x _ {i}, y _ {i}, z _ {i} ] \in \mathbb {R} ^ {3}, \mathbf {f} _ {i} \in \mathbb {R} ^ {C}) | i = 1, 2, \dots N \right\}. +$$ + +In the above equation, $N$ represents the number of nonempty voxels, while $\mathbf{p}_i$ and $\mathbf{f}_i$ denote the coordinates and features of the $i$ -th voxel, respectively. All subsequent operations are performed on this sparse representation, eliminating redundant computations on empty voxels. The following sections elaborate on the proposed sparse building blocks, namely the sparse latent diffuser, feature pyramid, and transformer head. An overview is shown in Fig. 2. + +# 3.2. Sparse Latent Diffuser + +The sparse representation $\mathbb{V}$ is derived through a ray casting manner, resulting in a predominantly sparse depiction + +limited to the initial intersection face between a ray and an object. Consequently, the majority of observations are inherently incomplete. Contrarily, the objective of an occupancy network is to predict complete occupancy rather than solely the visible parts. Traditional approaches address this by incorporating 3D dense convolutions (such as 3D ResNet and 3D FPN) or attention layers (such as deformable self-attention) to diffuse non-empty features to adjacent empty regions, thereby completing the scene. In this work, we aim to design a sparse variant of the latent diffuser. However, a notable challenge arises as the objective of the diffuser appears to conflict with the sparse design: By stacking more completion blocks, the scene is better completed, but the spatial sparsity also decreases, hindering efficiency. To strike a balance between scene completion and sparsity, we build our sparse latent diffuser with two key components: A sparse completion block, which executes only necessary latent diffusion; and a contextual aggregation block, which aggregates valid features without engaging in completion. + +Sparse Completion Block. We opt for the 3D sparse convolution implemented by [7] to build the sparse completion block. A sparse convolution performs the computation in a local window in which at least one non-empty voxel resides, allowing the diffusion of features from non-empty voxels to their neighbors. The range of diffusion can be expanded by stacking multiple layers of sparse convolution. To maintain the spatial sparsity, we only use one 3D convolution layer in a sparse completion block. + +Contextual Aggregation Block. After completion, we introduce the contextual aggregation block to effectively utilize geometry and semantic features from the local context. For constructing this block, we choose sparse submanifold convolution [7] over regular sparse convolution. Submanifold convolution ensures that an output location is active only if the corresponding input location is active, thereby maintaining sparsity even when stacking multiple layers. + +Kernel Decomposition. Foreground objects and background elements in driving scenes often exhibit specific shape distributions. For instance, roadways and sidewalks typically have a thin, flat shape located at the bottom of the 3D volume, making them amenable to completion through convolutions in the horizontal direction. Conversely, structures like buildings or car-like objects have a rectangular shape, necessitating feature diffusion in the vertical direction. To fully leverage these distinct shape distributions, we decompose a conventional $k \times k \times k$ kernel into orthogonal kernels [46]. Specifically, for the sparse completion block, we replace the sparse convolution with three consecutive layers with $k \times k \times 1$ , $k \times 1 \times k$ , and $1 \times k \times k$ kernels, respectively. For the contextual aggregation block, we follow Cylinder3D [46] and replace a $k \times k \times k$ submanifold convolution with two parallel but asymmetrical branches of decomposed layers. One branch consists of two consecu + +![](images/8ba99954ae3e19186d73265cc3b97af43f24ce1c275d40fb6e2276b758db018b.jpg) +Figure 2. Overview of the proposed approach. (a) Images captured by monocular or surrounding cameras are first passed to a 2D encoder, yielding 2D latent features. Then the latent features are mapped to 3D using the predicted depth map following the LSS [25]. (b) SparseOcc adopts a sparse representation for the latent space. Upon this representation, we introduce three key building blocks: a latent diffuser that performs completion, a feature pyramid that enhances receptive filed, and a transformer head that predicts semantic occupancy. + +![](images/7770f3f7109e66bb42dbfa87af614dcd411bf30abbf0ff6385267a88f091c72f.jpg) + +![](images/7267879d51d74138094acd266af86fd6db9226983d217686361dce2ed8011197.jpg) +(a) Sparse Completion Block +(b) Contextual Aggregation Block +Figure 3. Two building blocks of the sparse latent diffuser. (a) The sparse completion block diffuses non-empty features to empty neighbors, and (b) The contextual aggregation block aggregates geometry and semantic features without engaging in completion. + +tive layers with $1 \times k \times k$ ad $k \times 1 \times k$ kernels, and the other branch with $k \times 1 \times k$ ad $1 \times k \times k$ kernels. Note that the complexity is reduced from $\mathcal{O}(k^3)$ to $\mathcal{O}(3k^2)$ or $\mathcal{O}(4k^2)$ after the decomposition. Though the actual cost is not reduced when we use a small kernel with $k = 3$ , the expressive capacity of decomposed kernels outperforms a single full kernel, thus we can still achieve efficiency improvements by stacking fewer layers. + +# 3.3. Sparse Feature Pyramid + +A straightforward approach to complete the scene is to stack the proposed sparse diffuser multiple times, akin to SCP- + +Net [35]. However, this necessitates a substantial number of sparse diffusers to ensure an adequately large receptive field, which is particularly important for recognizing large objects like "truck" or static elements such as "road". The computation cost is obviously expensive. To address this issue, we note that down-sample layers, implemented with sparse convolution with a stride greater than one, not only reduce the spatial resolution but also increase the relative sparsity in the new scale. By building a multi-scale sparse feature pyramid with down-sample layers, we are readily able to obtain a coarse-to-fine representation of the scene. This ensures that querying any spatial location can be addressed by at least one feature scale, simultaneously reducing computation costs. Formally, we stack the sparse diffuser for $L$ times, each is followed by a down-sample layer, and the feature pyramid is collected as $\{\mathbb{V}_l\}_{l=1}^L$ . Additionally, the spatial size along the height dimension of the last two scales is too small, so we simply omit the $D$ dimension. For the completion blocks, the 3D convolution is replaced with a 2D version with $3 \times 3$ kernel. For the contextual aggregation block, we replace the asymmetrical branches with two parallel 2D submanifold convolutions with $5 \times 5$ kernels. + +Sparse Voxel Decoder. Former methods [6, 41] uses multi-scale deformable attention transformer (MSDeformAttn) [44] in the pixel/voxel decoder responsible for aggregating intra-scale and inter-scale features. Targeting for saving GPU memory and time, we simplify this process by using interpolation to fuse multi-scale sparse features output by the 3D sparse encoder. Specifically, for a given scale $\mathbb{V}_l$ from the feature pyramid, we augment it by fusing all the other scales, + +$$ +\hat {\mathbb {V}} _ {l} = \sum_ {j \neq l} W _ {j} \cdot \operatorname {I n t e r p} \left(\mathbb {V} _ {j}, \mathbb {V} _ {l}\right), 2 \tag {1} +$$ + +where $W_{j}$ is a learned weight for the $j$ -th scale, and $\mathrm{Interp}(\mathbb{X},\mathbb{Y})$ indicates linear interpolation from a sparse tensor $\mathbb{X}$ to another $\mathbb{Y}$ . + +Leveraging this lightweight feature fusion approach, the feature pyramid is enriched with semantic information from different scales. Moreover, the high-resolution features benefit from additional completion provided by the low-resolution features, as the denser low-resolution features resist dilution by interpolation operators. + +# 3.4. Sparse Transformer Head + +We frame the semantic occupancy prediction as a 3D segmentation problem and employ a transformer head, inspired by the design of Mask2Former [6]. This head iteratively updates a set of learnable queries through masked attention and subsequently decodes these queries into 3D masks for all semantic classes. However, a challenge arises due to the need for dense binary masks to represent semantic classes. Additionally, as we perform predictions in a 3D space [41], the computational and memory costs associated with applying successive transformer decoder layers to dense masks become impractical. + +To overcome this challenge, we adapt the dense transformer head to a sparse variant. Specifically, we assert that accurate segmentation is crucial for occupied voxels, while non-occupied voxels need not be considered during this phase. In the ensuing discussion, we outline several steps to delineate the sparse transformer decoder. + +Preprocessing and Notations. Given the sparse feature pyramid $\hat{\mathbb{V}}_l$ , we first employ a linear binary classifier for coarse segmentation. The binary classifier is trained to label a voxel as empty if the semantic ground truth is 0 and nonempty otherwise. We only preserve voxels that are classified as non-empty, resulting in a filtered, sparser tensor $\hat{\mathbb{V}}_l = \{(\mathbf{p}_i,\mathbf{f}_i)|i = 1,\dots,N_l\}$ , where we use $N_{l}$ to denote the number of remaining voxels for the $l$ -th scale. Storing variant features for the empty voxels is unnecessary, and instead, we find it suffices to use only a single learnable token $\mathbf{p}_{\phi}$ to represent all the empty voxels. + +Query Decoding. The former method [41] performs outer product between queries $Q \in \mathbb{R}^{N_q \times C}$ and 3D dense features $F \in \mathbb{R}^{C \times H \times W \times D}$ to decode the queries to 3D mask with shape $(N_q, H, W, D)$ , which has a time complexity of $\mathcal{O}(N_q HWDC)$ . To facilitate inference speed, we only perform outer product between $Q$ and $\mathbf{p}_{\phi} \cup \{\mathbf{f}_i | (\mathbf{p}_i, \mathbf{f}_i) \in \hat{\mathbb{V}}_l\}$ to obtain a series of occupied masks $M^{\mathrm{occ}} \in \mathbb{R}^{N_q \times N_l}$ and a single mask $M^{\phi} \in \mathbb{R}^{N_q \times 1}$ that represents empty voxels. With the saved coordinates $\mathbf{p}$ of occupied voxels, we can easily reconstruct the dense 3D mask $M \in \mathbb{R}^{Q \times H \times W \times Z}$ from the predicted sparse tensor, using a scatter operation that does not break the gradient flow. This way, the complexity is reduced to $\mathcal{O}(N_l N_q C + HWZ)$ for mask predic + +tion and reconstruction. Note that + +$$ +\begin{array}{l} \mathcal {O} \left(N _ {l} N _ {q} C + H W Z\right) \\ = \mathcal {O} \left(H W Z N _ {q} C \left(\frac {N _ {l}}{H W Z} + \frac {1}{N _ {q} C}\right)\right) \tag {2} \\ < \mathcal {O} (H W Z N _ {q} C), \\ \end{array} +$$ + +because $N_{l} / HWZ$ is rather smaller than 1 in our sparse case. Moreover, the $N_{q}$ queries are also input to a $C$ -way linear classifier to classify the corresponding 3D mask into predefined $C$ semantic categories. + +Query Updating. Given the input $L$ layers of multi-scale sparse features, we iteratively alternate between query decoding and query updating in each transformer layer. With the predicted 3D masks $M_{l-1}$ in the $(l-1)$ -th transformer layer, we update the queries via + +$$ +Q _ {l} = \operatorname {s o f t m a x} \left[ \mathcal {M} _ {l - 1} + W _ {q} Q _ {l - 1} \left(W _ {k} \hat {\mathbf {V}} _ {l}\right) ^ {T} \right] W _ {v} \hat {\mathbf {V}} _ {l} + Q _ {l - 1}, \tag {3} +$$ + +where $W_{q}, W_{k}, W_{v}$ are linear layers, $\hat{\mathbf{V}}_{l}$ is the dense version reconstructed from $\hat{\mathbb{V}}_{l}$ , and the attention mask $\mathcal{M}_{l-1}$ at location $(x,y,z)$ is obtained by + +$$ +\mathcal {M} _ {l - 1} (x, y, z) = \left\{ \begin{array}{l l} 0 & \text {i f} \sigma \left(M _ {l - 1} ^ {\prime} (x, y, z)\right) \geq 0. 5 \\ - \infty & \text {o t h e r w i s e} \end{array} \right. \tag {4} +$$ + +where $\sigma$ is the sigmoid function, $M_{l-1}^{\prime} = \max\text{pooling}(M_{l-1})$ which resizes the 3D mask to the same resolution of $\hat{\mathbf{V}}_l$ , similar to implementation in [41]. + +# 3.5. Objective Function + +Considering the sparse transformer head formulates semantic occupancy as a mask set prediction task [6, 41], bipartite matching with Hungarian solver is used to assign binary mask labels and corresponding semantic class labels to the predicted masks. Based on the assignment, we calculate the mask loss $\mathcal{L}_{\mathrm{mask}}$ and classification loss $\mathcal{L}_{\mathrm{cls}}$ . Additionally, $\mathcal{L}_{\mathrm{depth}}$ is calculated between the predicted depth map and ground-truth projected by point clouds, for supervision of the LSS component. Moreover, the coarse binary classification on non-empty voxels is also supervised by a segmentation loss $\mathcal{L}_{\mathrm{seg}}$ . Finally, the overall objective function is a simple summation of these loss terms + +$$ +\mathcal {L} = \mathcal {L} _ {\text {m a s k}} + \mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {d e p t h}} + \mathcal {L} _ {\text {s e g}}. \tag {5} +$$ + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. We evaluate our proposed SparseOcc on nuScenes-Occupancy [33] and SemanticKITTI [2]. nuScenes-Occupancy [33] extends the famous large-scale + +
MethodInputIoUmIoUbarrierbicyclebuscarconst. veh.motorcyclepedestriantraffic conetrailertruckdrive. surf.other flatsidewalkterrainmannadevegetationFLOPsMemory3D/Overall Latency
MonoScene [4]C18.46.97.13.99.37.25.63.05.94.44.94.214.96.37.97.410.07.6---
TPVFormer [13]C15.37.89.34.111.310.15.24.35.95.36.86.513.69.08.38.09.28.21132G20G0.57/0.73s
OpenOccupancy [33]C19.310.39.96.811.211.56.38.48.64.34.29.922.015.814.113.57.310.21716G19G0.84/1.22s
C-CONet [33]C20.112.813.28.115.417.26.311.210.08.34.712.131.418.818.716.34.88.21810G21G2.18/2.58s
SparseOcc (ours)C21.814.116.19.315.118.67.39.411.29.47.213.031.821.720.718.86.110.6455G13G0.19/0.25s
+ +Table 1. Semantic occupancy prediction results on nuScenes-Occupancy [33] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs, training GPU memory, and 3D/overall inference latency. The C denotes camera and the bold numbers indicate the best results. + +
MethodInputIoUmIoUroad (15.30%)sidewalk (11.13%)parking (1.12%)other-ground (0.56%)building (14.1%)car (3.92%)truck (0.16%)bicycle (0.03%)motorcycle (0.03%)other-vehicle (0.20%)vegetation (39.3%)trunk (0.51%)terrain (9.17%)person (0.07%)bicyclist (0.07%)motorcyclist (0.05%)fence (3.90%)pole (0.29%)traffic-sign (0.08%)FLOPs
LMSCNet* [27]C28.616.7040.6818.224.380.0010.3118.330.000.000.000.000.000.000.000.000.000.0013.660.0220.540.000.000.000.001.210.000.00
3DSketch* [5]C33.307.5041.3221.630.000.0014.8118.590.000.000.000.000.000.000.000.0019.090.0026.400.000.000.000.000.730.000.00
AICNet* [16]C29.598.3143.5520.5511.970.0712.9414.714.530.000.000.000.000.0015.372.9028.710.000.000.000.002.520.060.00
JS3C-Net* [37]C38.9810.3150.4923.7411.940.0715.0324.654.410.000.006.1518.114.3326.860.670.270.000.003.943.771.45
MonoScene† [4]C36.8611.0856.5226.7214.270.4614.0923.266.980.610.451.4817.892.8129.641.861.200.005.844.142.25
TPVFormer [13]C35.6111.3656.5025.8720.600.8513.8823.818.080.360.054.3516.922.2630.380.510.890.005.943.141.52
OccFormer [41]C36.5013.4658.8526.8819.610.3114.4025.0925.530.811.198.5219.633.9332.622.782.820.005.614.262.86
SparseOccC36.4813.1259.5929.6820.440.4715.4124.0318.070.780.898.9418.893.4631.063.680.620.006.733.892.60
+ +Table 2. Semantic scene completion results on SemanticKITTI [1] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs. The C denotes camera and the bold numbers indicate the best results. The methods with “*” are RGB-input variants reported by [4] for fair comparison. + +autonomous driving datasets nuScenes [3] with 3D dense semantic occupancy annotations on key frames for 1 "empty" class and 16 semantic classes using Augmenting And Purifying pipeline. It covers 700 and 150 driving scenes in the training and validation set of nuScenes. The multi-view images and corresponding LiDAR points are provided by the original nuScenes dataset. SemanticKITTI [2] contains 22 sequences including monocular images, LiDAR points, point cloud segmentation labels and semantic scene completion annotations. The sequence 08 is officially split for validation, sequences 00-10 (excluding 08) are used for training, and sequences 11-21 are the test set. It annotates each 3D voxel with 1 "empty" class or 19 semantic classes. + +Evaluation Metric. We follow the common practice and report the intersection over union (IoU) of occupied voxels regardless of their semantic labels to evaluate the reconstructed geometry shape. The semantic mIoU of all semantic classes is also reported to evaluate the semantic-aware perception ability. For efficiency analysis, FLOPs is also evaluated using the analysis tool provided by [22]. + +Implementation Details. For image encoder, we follow the previous work [33, 41] for fair comparison and use EfficientNetB7 [29] and SecondFPN [39] on SemanticKITTI and ResNet-50 [9] on nuScenes-Occupancy. The 2D to 3D view transformation is implemented as the same as [33, 41]. + +And it generates a 3D feature volume of size $128 \times 128 \times 16$ and $128 \times 128 \times 10$ with 128 channels for SemanticKITTI and nuScenes-Occupancy, which is converted to sparse representation. We stack the sparse diffuser for $L = 4$ times, each followed by a sparse convolution with stride 2 for downsampling. The kernel size $k$ of the orthogonal convolutions in sparse completion block and contextual aggregation block is set to 3. The sparse voxel decoder projects the multi-scale features to 192 channels and enhances them via interpolation and summation. The sparse transformer head consists of 9 layers for query updating and decoding and the number of queries $N_{q}$ is 100. Following [6, 41], we sample 50176 points for supervision according to the class frequency for fast training speed. During inference, the predicted masks are upsampled $2 \times$ and $4 \times$ to the size of ground-truth via trilinear interpolation for evaluation on SemanticKITTI and nuScenes-Occupancy, respectively. + +Optimization. AdamW [23] optimizer with an initial learning rate of 1e-4 and a weight decay of 0.01 is leveraged during training. We train the model for 30 epochs on SemanticKITTI and 24 epochs on nuScenes-Occupancy with a batch size of 8 on 8 v100 GPUs. + +# 4.2. Benchmark Performance + +In this part, we compare our SparseOcc with the published state-of-the-art methods on nuScenes-Occupancy and Se + +manticKITTI. The results of the former methods are directly derived from their papers or code with their configurations. NuScenes-Occupancy. As shown in Tab. 1, our SparseOcc successfully outperforms the 3D dense representation based C-CONet [33] by $1.7\%$ geometry IoU and $1.3\%$ semantic mIoU. This accomplishment highlights SparseOcc's effectiveness. Besides, we can observe that the model FLOPs are reduced by $74.9\%$ relatively, which further justifies the efficiency of our SparseOcc. More surprisingly, SparseOcc not only produces a remarkable $80.8\%$ improvement in mIoU over TPVFormer [13] which uses efficient TPV view as 3D scene representation, but also reduces the FLOPs by $59.8\%$ . We find that TPVFormer uses a relatively large image backbone ResNet-101 [9], and the multi-layer image cross-attention as well as cross-view attention between dense TPV maps also impose lots of computational burden. In contrast, our SparseOcc uses sparse operators in the 3D space, helping us achieve superior performance with a lightweight implementation. Besides, SparseOcc exhibits a noteworthy reduction in 3D inference latency, i.e., the time for 3D feature processing. + +SemanticKITTI. We quantitatively compare the proposed SparseOcc with several previous works in Tab. 2. we can see that SparseOcc achieves comparable performance with OccFormer [41] and significantly better than other methods in terms of semantic mIoU. Please note that different from OccFormer which builds long-range and dynamic dependency in the 3D space using Swin Transformer [21], the 3D encoder of SparseOcc is built with spconv [7] only. Consequently, the model FLOPs of SparseOcc is just $44.2\%$ of OccFormer [41] approximately. + +# 4.3. Qualitative Evaluation + +We visualize the 3D semantic occupancy prediction results of several challenging scenes in nuScenes-Occupancy validation set in Fig. 4. As can be seen, compared with the 3D dense counterpart C-CONet [33], our SparseOcc can better complete the large area flat-like road (first row), capture the complicated structure of vegetation (second row) and reconstruct car in the distance (third row). We can conclude that benefiting from the proposed sparse latent diffuser and learned sparse feature pyramid, our sparse occupancy transformer head can generate relatively accurate scene-level descriptions in an efficient way. + +# 4.4. Ablation Studies + +Sparse Completion Blok. As illustrated in Sec. 3.2, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels in the sparse completion block. Tab. 3 ablates the type and number of diffusion kernels. Surprisingly, we find that SparseOcc can perform satisfactorily even if no sparse completion block is applied. We think that it is because the decoder which + +
Conv TypeConv NumKernel SizeIoUmIoU
-0-35.512.1
Regular13×3×335.812.2
236.412.3
336.212.6
Decomposed13×3×136.513.1
23×1×336.612.8
31×3×136.412.7
+ +Table 3. Ablation on different designs of Sparse Completion Block on SemanticKITTI val set. + +
TypeIoUmIoUMemoryFLOPs
FPN3D[20]34.49.813.2G307G
MSDeformAttn3D36.713.319.8G379G
Sparse Decoder36.513.113.3G279G
+ +Table 4. Ablation on voxel decoder on SemanticKITTI val set. + +
TypeIoUmIoUMemoryFLOPs
Linear Head36.811.89.8G5.4G
Trans. Head36.213.219.9G19.0G
Sparse Trans. Head36.513.113.3G13.5G
+ +Table 5. Ablation on segmentation head on SemanticKITTI val set. + +fuses sparse feature pyramid can also complete the scene to some extent. Compared with regular $3 \times 3 \times 3$ kernel, the decomposed orthogonal achieves better scene completion and segmentation results. Besides, stacking more convolution blocks does not improve performance. Hence, we build our sparse completion block with only a group of decomposed orthogonal. + +Sparse Feature Pyramid. As shown in Tab. 4, we observe that when the SparseOcc equipped with 6 layers of multi-scale deformable attention (MSDeformAttn), it performs better than the proposed sparse decoder. However, when the layer number of MSDeformAttn decreases, the IoU and mIoU both drop and lag behind the proposed simple sparse decoder. Moreover, the training GPU memory and FLOPs of the MSDeformAttn3D are much higher than the proposed interpolation and summation method. Compared with FPN3D [20], our sparse voxel decoder is $2.1\%$ IoU and $3.3\%$ mIoU higher with slightly more memory. + +Sparse Transformer Head. We compare several different prediction heads, including simple linear head, transformer head proposed in [41], and our sparse transformer head in Tab. 5. As can be seen, the linear head achieves the best geometry IoU of 36.8. We postulate it may be because the output of the linear head is supervised by an explicit geometry loss, i.e., a cross-entropy loss on occupied and non-occupied voxels. On the contrary, the transformer decoder formulates occupancy prediction as mask generation for each semantic class exclusively. Consequently, no explicit supervision is or can be imposed on the occupied voxels. SparseOcc uses a linear layer for coarse segmentation to filter out the non-occupied voxels and then proposes + +![](images/05fa9a7a1d81eb91714f39b4507e363194f4eb6d532abc99d28b7143c63e1931.jpg) +Figure 4. Qualitative results of 3D semantic occupancy on nuScenes-Occupancy validation set. The input multi-view images are shown on the leftmost and the occupancy predictions of C-CONet [33], our SparseOcc, and the ground-truth are then visualized sequentially. Compared to 3D dense representation based C-CONet [38], our SparseOcc achieves better completion and segmentation as highlighted by the red circles. + +
Method2D BackboneInput SizeIoUmIoU
C-CONet [33]R-50704 × 25616.68.6
R-501600 × 90019.310.3
R-1011600 × 90020.211.4
SparseOccR-50704 × 25621.814.1
R-501600 × 90020.414.6
+ +Table 6. Ablation on input size and 2D backbone on nuScenes-Occupancy. + +a sparse transformer head for mask prediction. Therefore, it makes an appropriate trade-off between these two kinds of occupancy heads and achieves satisfactory performance with low training memory. + +Input Image Size. A larger input image size has a larger resolution of image features, thus having a larger feature density in the 3D space, which further influences the performance. From Tab. 6, we can observe that SparseOcc still performs better than C-CONet, even though it is trained using a smaller input size $(704 \times 256)$ and image backbone (R-50), which further demonstrates the effectiveness of our SparseOcc. Additionally, using a larger input image size $(1600 \times 900)$ can improve mIoU for both C-CONet and the proposed SparseOcc, thanks to the density increase of semantic features. However, the IoU of SparseOcc drops when using higher image resolution. We blame it on the wrong hallucination on spatially empty voxels caused by over-dense 3D sparse features. When inactivating the sparse + +completion block in the last sparse latent diffuser layer, this hallucination can be relieved. + +# 5. Conclusion + +In this paper, we explore the possibility of using pure sparse representation for 3D scene description and present SpaseOcc for 3D semantic occupancy prediction. Specifically, a sparse latent diffuser with decomposed orthogonal kernels is proposed to propagate the non-empty features to their adjacent empty area. To efficiently complete the scene, we stack layers of diffusers and downsampling layers to generate a coarse-to-fine sparse feature pyramid, which is further fused via simple interpolation and summation. In this way, the feature pyramid is enhanced by multi-scale semantic information. Finally, we use a sparse transformer head to query multi-scale sparse features and generate semantic occupancy predictions. Without bells and whistles, SparseOcc achieves state-of-the-art results on nuScenes-Occupancy and comparable performance on SemanticKITTI, fully demonstrating its superior effectiveness and efficiency. + +Acknowledgements. This work was supported by NSFC (62322113, 62376156), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities. + +# References + +[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. In ICCV, 2019. 6 +[2] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. Semantickitti: A dataset for semantic scene understanding of lidar sequences. In ICCV, 2019. 5, 6 +[3] Holger Caesar, Varun Bankiti, Alex H Lang, Sourabh Vora, Venice Erin Liong, Qiang Xu, Anush Krishnan, Yu Pan, Giancarlo Baldan, and Oscar Beijbom. 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Pointocc: Cylindrical tri-perspective view for point-based 3d semantic occupancy prediction. arXiv:2308.16896, 2023. 2 \ No newline at end of file diff --git a/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/images.zip b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e4fbfba495b1646f8f2d832b6c0ecc1417a3f256 --- /dev/null +++ b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a7a9d639d6637da06dc4603c620dd2a83f230e997c4a7ea2f898a9bf048a4d0e +size 563960 diff --git a/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/layout.json b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..858f469f3f2294725e32ae0b19ea8b6144f80736 --- /dev/null +++ b/2024/SparseOcc_ Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction/layout.json @@ -0,0 +1,8091 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 120, + 103, + 475, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 120, + 103, + 475, + 140 + ], + "spans": [ + { + "bbox": [ + 120, + 103, + 475, + 140 + ], + "type": "text", + "content": "SparseOcc: Rethinking Sparse Latent Representation for Vision-Based Semantic Occupancy Prediction" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 138, + 160, + 453, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 160, + 453, + 175 + ], + "spans": [ + { + "bbox": [ + 138, + 160, + 453, + 175 + ], + "type": "text", + "content": "Pin Tang1 Zhongdao Wang2 Guoqing Wang1 Jilai Zheng1" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 190, + 175, + 418, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 190, + 175, + 418, + 189 + ], + "spans": [ + { + "bbox": [ + 190, + 175, + 418, + 189 + ], + "type": "text", + "content": "Xiangxuan Ren1 Bailan Feng2 Chao Ma1*" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 91, + 190, + 501, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 190, + 501, + 217 + ], + "spans": [ + { + "bbox": [ + 91, + 190, + 501, + 217 + ], + "type": "text", + "content": "1 MoE Key Lab of Artificial Intelligence, AI Institute, Shanghai Jiao Tong University \n2 Huawei Noah's Ark Lab" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 103, + 219, + 490, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 103, + 219, + 490, + 232 + ], + "spans": [ + { + "bbox": [ + 103, + 219, + 490, + 232 + ], + "type": "text", + "content": "{pin.tang,guoqing.wang,zhengjilai,bunny.renxiangxuan,chaoma}@sjtu.edu.cn" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 199, + 234, + 395, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 199, + 234, + 395, + 245 + ], + "spans": [ + { + "bbox": [ + 199, + 234, + 395, + 245 + ], + "type": "text", + "content": "{wangzhongdao,fengbailan}@huawei.com" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 149, + 247, + 440, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 149, + 247, + 440, + 258 + ], + "spans": [ + { + "bbox": [ + 149, + 247, + 440, + 258 + ], + "type": "text", + "content": "Project page: https://pintang1999.github.io/sparseocc.html" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "spans": [ + { + "bbox": [ + 143, + 286, + 192, + 300 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "text", + "content": "Vision-based perception for autonomous driving requires an explicit modeling of a 3D space, where 2D latent representations are mapped and subsequent 3D operators are applied. However, operating on dense latent spaces introduces a cubic time and space complexity, which limits scalability in terms of perception range or spatial resolution. Existing approaches compress the dense representation using projections like Bird's Eye View (BEV) or Tri-Perspective View (TPV). Although efficient, these projections result in information loss, especially for tasks like semantic occupancy prediction. To address this, we propose SparseOcc, an efficient occupancy network inspired by sparse point cloud processing. It utilizes a lossless sparse latent representation with three key innovations. Firstly, a 3D sparse diffuser performs latent completion using spatially decomposed 3D sparse convolutional kernels. Secondly, a feature pyramid and sparse interpolation enhance scales with information from others. Finally, the transformer head is redesigned as a sparse variant. 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Interestingly, it also improves accuracy, from " + }, + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "inline_equation", + "content": "12.8\\%" + }, + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "inline_equation", + "content": "14.1\\%" + }, + { + "bbox": [ + 46, + 312, + 290, + 601 + ], + "type": "text", + "content": " mIOU, which in part can be attributed to the sparse representation's ability to avoid hallucinations on empty voxels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 624, + 128, + 636 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 645, + 288, + 693 + ], + "type": "text", + "content": "Accurate perception of the surrounding environment is crucial for autonomous driving systems [11, 14]. In recent years, vision-based 3D perception algorithms have gained significant attention and advancement due to their cost-" + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 285, + 545, + 443 + ], + "blocks": [ + { + "bbox": [ + 307, + 285, + 545, + 443 + ], + "lines": [ + { + "bbox": [ + 307, + 285, + 545, + 443 + ], + "spans": [ + { + "bbox": [ + 307, + 285, + 545, + 443 + ], + "type": "image", + "image_path": "6525e2461113870efa7c96a98324e7a9fdbecb7c5298e575cbe086217d0e3f32.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 450, + 547, + 518 + ], + "lines": [ + { + "bbox": [ + 305, + 450, + 547, + 518 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 547, + 518 + ], + "type": "text", + "content": "Figure 1. (a) Vision-based perception methods for autonomous driving typically first extract image features by a 2D latent encoder and then map them to 3D using view transformation. (b) For the 3D latent space, existing methods mostly employ the dense, BEV, or TPV representation, while we rethink the possibility of using sparse representation to achieve superior efficiency and accuracy." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 532, + 547, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 547, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 547, + 699 + ], + "type": "text", + "content": "effectiveness. The typical workflow involves employing a 2D encoder to extract latent representations from images. A view transformation method, such as lift-splat-shoot (LSS) [25], is then applied to lift the perspective 2D latent features to a 3D voxel space, utilizing predicted depth information. This 3D scene representation serves as the foundation for deriving geometry and semantic information to describe the driving environment, supporting various 3D perception tasks including object detection [15, 17, 40, 43], semantic segmentation [11, 30, 36], and semantic occupancy prediction [13, 33, 34]. In this study, we specifically focus on the challenging task of semantic occupancy prediction [31-34], which entails predicting both static and dynamic elements within the scene." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Several alternatives are available for representing 3D" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 138, + 712 + ], + "type": "text", + "content": "* Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15035" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "spatial latent information. The dense representation [33] is the most straightforward approach, storing features in continuous memory and enabling direct application of dense 3D operations like convolutions. However, this representation is redundant and inefficient, as approximately " + }, + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "inline_equation", + "content": "67\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": " of the considered 3D space is empty1. Bird Eye's View (BEV) [12, 19, 22] has gained popularity as a recent prevalent representation. It involves projecting the 3D space onto a BEV plane, significantly reducing computational costs by leveraging efficient 2D building blocks in a BEV encoder. However, this projection introduces the loss of geometry information, thereby limiting the fine-grained capacity of the BEV representation to comprehend the 3D scene structure. A Tri-Perspective View (TPV) [13] representation is proposed to mitigate the information loss, but it still suffers from degraded perception accuracy." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 289, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 289, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 289, + 407 + ], + "type": "text", + "content": "In this paper, we seek a latent representation that encodes the 3D scene structure in a lossless manner while minimizing computational costs. Drawing inspiration from the similarities between sparse 3D vision features and point clouds, we rethink the feasibility of employing a pure sparse representation for the 3D latent space, a common practice in point cloud processing [7]. Specifically, we utilize the coordinate (COO) format to store sparse tensors and introduce a series of sparse building blocks tailored for the sparse representation. Our proposed method, SparseOcc, is an occupancy network where all 3D layers operate on sparse tensors. The key designs of SparseOcc are as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 408, + 287, + 610 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 287, + 467 + ], + "type": "text", + "content": "- Sparse Latent Diffuser: This component enables the propagation of non-empty features to adjacent empty regions, facilitating scene completion. To ensure efficiency, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 468, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 468, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 287, + 540 + ], + "type": "text", + "content": "- Sparse Feature Pyramid: We build a feature pyramid that incorporates sparse interpolation operations to enhance scales with information from other scales. This pyramid design expands the reception fields, reducing the need for excessive diffusers within each scale, which helps preserve sparsity." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 540, + 287, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 287, + 610 + ], + "type": "text", + "content": "- Sparse Transformer Head: The final component of SparseOcc is a 3D sparse transformer head responsible for generating semantic occupancy predictions. By segmenting only occupied voxels rather than the entire 3D volume, we achieve a remarkable reduction in computational costs." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "text", + "content": "Based on the sparse latent representation, SparseOcc achieves a significant reduction in computation overhead. In the nuScenes-Occupancy benchmark [33], it reduces the FLOPs of existing approaches using dense or TPV representations by " + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "inline_equation", + "content": "59.8\\%" + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "inline_equation", + "content": "74.9\\%" + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "text", + "content": ", and memory usage by " + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "inline_equation", + "content": "31.6\\%" + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "inline_equation", + "content": "40.9\\%" + }, + { + "bbox": [ + 46, + 612, + 287, + 684 + ], + "type": "text", + "content": ". Remarkably, the semantic occupancy" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "type": "text", + "content": "accuracy not only remains intact but improves, surpassing the state-of-the-art C-CONet. Specifically, the semantic occupancy accuracy increases from " + }, + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "12.8\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "14.1\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 180 + ], + "type": "text", + "content": " mIoU. This improvement highlights the superiority of the sparse representation over the dense one in terms of accuracy, as it naturally avoids hallucinations on empty voxels. Considering the effectiveness and efficiency demonstrated by SparseOcc, we propose that it can serve as a new baseline for occupancy networks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 193, + 392, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 193, + 392, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 193, + 392, + 205 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 213, + 446, + 226 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 213, + 446, + 226 + ], + "spans": [ + { + "bbox": [ + 306, + 213, + 446, + 226 + ], + "type": "text", + "content": "2.1. 3D Scene Representation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 232, + 545, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 412 + ], + "type": "text", + "content": "3D Dense Representation. Representing the surrounding environment with spatial latent information is an indispensable procedure for autonomous driving perception algorithms. A straightforward solution is to split the scene into voxels and describe the scene with 3D volume representation where 3D operators are applied [4, 28, 33, 34, 41]. For example, OpenOccupancy [33] first uses a 2D encoder to extract image features and further uses LSS to lift the features to 3D space. Then, ResNet3D [9] and FPN3D [20] are used to diffuse non-empty features to adjacent empty areas. SurroudOcc [34] uses successive deformable cross attention layers [45] to transform the multi-scale image features to multi-scale 3D dense volume. However, these 3D operators are often in cubic time and spatial time complexity, which is not affordable in practice." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 413, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 413, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 545, + 544 + ], + "type": "text", + "content": "BEV Representation. The past several years have witnessed the prosperous development of BEV representation in tasks such as 3D object detection [8, 17, 19, 22], BEV semantic segmentation [24, 26, 42], and instance prediction [10]. They either forward project the image features to 3D spaces with estimated depth, then compress the 3D feature volume to BEV map, or update the BEV queries via backward deformable attention. Despite efficiency, the geometry lossy projection results in the relatively coarse representation of the 3D scene, hindering its generalization to the fine-grained semantic occupancy prediction task." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 545, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 545, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 305, + 545, + 545, + 677 + ], + "type": "text", + "content": "TPV Representation. To make a trade-off between efficacy and efficiency, TPV representation is proposed [13, 47]. It first constructs three cross-planes perpendicular to each other to represent the 3D scene. Then, sets of queries are initialized on these planes to aggregate features from images and exchange features across views via the attention mechanism. Then, they efficiently reconstruct each voxel in the 3D space by summing its projected features on the three planes for downstream tasks. Although the loss of geometry is mitigated, it is still hard to capture the complex driving scene, leading to degraded performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we rethink the 3D scene representation from a sparse view and seek an effective but also efficient method for semantic occupancy prediction." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 713 + ], + "type": "text", + "content": "1We conduct statics using the ground-truth occupancy labels of the first 10 sequences in the SemanticKITTI dataset." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "15036" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 272, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 272, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 272, + 85 + ], + "type": "text", + "content": "2.2. Scene Completion in Occupancy Prediction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 289, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 289, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 289, + 236 + ], + "type": "text", + "content": "Both LiDAR points and lifted 3D representation only cover the initial intersection surface between the ray from the sensor and objects. Hence, a few methods have been proposed to diffuse non-empty features to surrounding empty regions [18, 35]. These methods essentially are the same as the 3D dense representation based ones since they also stack 3D dense operators to diffuse features. In contrast, we explore the potential of using a pure sparse representation and propose a sparse latent diffuser for scene completion. This approach rethinks the conventional method of feature diffusion in 3D space, offering a more efficient way to fill in the gaps in the scene representation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 245, + 164, + 259 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 245, + 164, + 259 + ], + "spans": [ + { + "bbox": [ + 47, + 245, + 164, + 259 + ], + "type": "text", + "content": "3. Proposed Approach" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 265, + 239, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 239, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 239, + 277 + ], + "type": "text", + "content": "3.1. Preliminary: Sparse Representation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "text", + "content": "Given a monocular image or a set of images " + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\mathbf{I} = \\{I_i\\}_{i=1}^{N_{\\mathrm{view}}}" + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "text", + "content": " captured by surrounding cameras, the goal of vision-based 3D semantic occupancy prediction is to predict a semantic label for every voxel in a predefined 3D volume " + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\{0,1,2,\\dots,C\\}^{H\\times W\\times D}" + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "inline_equation", + "content": "H, W, D" + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "text", + "content": " denotes the spatial resolution, the class label 0 indicates empty voxel, " + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 281, + 287, + 366 + ], + "type": "text", + "content": " is the number of semantic classes for non-empty voxels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "text", + "content": "In the initial stage of our model, we follow the Lift-Spat-Shoot (LSS) [25] framework. The images are first passed through an image encoder, such as ResNet [9] augmented with FPN [20]. This encoder generates latent features on the 2D perspective plane. Subsequently, the 2D latent features are lifted to the 3D space using predicted depth maps, resulting in dense cubic features denoted as " + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{H \\times W \\times D \\times C}" + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "text", + "content": ". Notably, we observe that approximately " + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "text", + "content": " of the voxels in " + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 367, + 287, + 498 + ], + "type": "text", + "content": " are empty. This sparsity arises due to the nature of LSS, where 2D features are cast through ray casting and become sparser in distant regions." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 535 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 535 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 535 + ], + "type": "text", + "content": "We then convert the dense feature " + }, + { + "bbox": [ + 46, + 498, + 287, + 535 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 498, + 287, + 535 + ], + "type": "text", + "content": " to a sparse representation by gathering non-empty voxels. The sparse tensor is stored in a commonly used coordinate (COO) format:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 544, + 278, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 544, + 278, + 559 + ], + "spans": [ + { + "bbox": [ + 55, + 544, + 278, + 559 + ], + "type": "interline_equation", + "content": "\\mathbb {V} = \\left\\{(\\mathbf {p} _ {i} = [ x _ {i}, y _ {i}, z _ {i} ] \\in \\mathbb {R} ^ {3}, \\mathbf {f} _ {i} \\in \\mathbb {R} ^ {C}) | i = 1, 2, \\dots N \\right\\}.", + "image_path": "ffb9dc459ff13d4e1b6fa6f775bc641ca27976b245abaf9e669006f5873979f5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "text", + "content": "In the above equation, " + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "text", + "content": " represents the number of nonempty voxels, while " + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_i" + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "text", + "content": " denote the coordinates and features of the " + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 567, + 287, + 664 + ], + "type": "text", + "content": "-th voxel, respectively. All subsequent operations are performed on this sparse representation, eliminating redundant computations on empty voxels. The following sections elaborate on the proposed sparse building blocks, namely the sparse latent diffuser, feature pyramid, and transformer head. An overview is shown in Fig. 2." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 671, + 176, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 176, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 176, + 684 + ], + "type": "text", + "content": "3.2. Sparse Latent Diffuser" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "The sparse representation " + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbb{V}" + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": " is derived through a ray casting manner, resulting in a predominantly sparse depiction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "limited to the initial intersection face between a ray and an object. Consequently, the majority of observations are inherently incomplete. Contrarily, the objective of an occupancy network is to predict complete occupancy rather than solely the visible parts. Traditional approaches address this by incorporating 3D dense convolutions (such as 3D ResNet and 3D FPN) or attention layers (such as deformable self-attention) to diffuse non-empty features to adjacent empty regions, thereby completing the scene. In this work, we aim to design a sparse variant of the latent diffuser. However, a notable challenge arises as the objective of the diffuser appears to conflict with the sparse design: By stacking more completion blocks, the scene is better completed, but the spatial sparsity also decreases, hindering efficiency. To strike a balance between scene completion and sparsity, we build our sparse latent diffuser with two key components: A sparse completion block, which executes only necessary latent diffusion; and a contextual aggregation block, which aggregates valid features without engaging in completion." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 301, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 301, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 304, + 301, + 545, + 410 + ], + "type": "text", + "content": "Sparse Completion Block. We opt for the 3D sparse convolution implemented by [7] to build the sparse completion block. A sparse convolution performs the computation in a local window in which at least one non-empty voxel resides, allowing the diffusion of features from non-empty voxels to their neighbors. The range of diffusion can be expanded by stacking multiple layers of sparse convolution. To maintain the spatial sparsity, we only use one 3D convolution layer in a sparse completion block." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 411, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 509 + ], + "type": "text", + "content": "Contextual Aggregation Block. After completion, we introduce the contextual aggregation block to effectively utilize geometry and semantic features from the local context. For constructing this block, we choose sparse submanifold convolution [7] over regular sparse convolution. Submanifold convolution ensures that an output location is active only if the corresponding input location is active, thereby maintaining sparsity even when stacking multiple layers." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Kernel Decomposition. Foreground objects and background elements in driving scenes often exhibit specific shape distributions. For instance, roadways and sidewalks typically have a thin, flat shape located at the bottom of the 3D volume, making them amenable to completion through convolutions in the horizontal direction. Conversely, structures like buildings or car-like objects have a rectangular shape, necessitating feature diffusion in the vertical direction. To fully leverage these distinct shape distributions, we decompose a conventional " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "k \\times k \\times k" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " kernel into orthogonal kernels [46]. Specifically, for the sparse completion block, we replace the sparse convolution with three consecutive layers with " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "k \\times k \\times 1" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "k \\times 1 \\times k" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "1 \\times k \\times k" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " kernels, respectively. For the contextual aggregation block, we follow Cylinder3D [46] and replace a " + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "inline_equation", + "content": "k \\times k \\times k" + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": " submanifold convolution with two parallel but asymmetrical branches of decomposed layers. One branch consists of two consecu" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15037" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 258, + 240 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 258, + 240 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 258, + 240 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 258, + 240 + ], + "type": "image", + "image_path": "8ba99954ae3e19186d73265cc3b97af43f24ce1c275d40fb6e2276b758db018b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 251, + 547, + 298 + ], + "lines": [ + { + "bbox": [ + 46, + 251, + 547, + 298 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 547, + 298 + ], + "type": "text", + "content": "Figure 2. Overview of the proposed approach. (a) Images captured by monocular or surrounding cameras are first passed to a 2D encoder, yielding 2D latent features. Then the latent features are mapped to 3D using the predicted depth map following the LSS [25]. (b) SparseOcc adopts a sparse representation for the latent space. Upon this representation, we introduce three key building blocks: a latent diffuser that performs completion, a feature pyramid that enhances receptive filed, and a transformer head that predicts semantic occupancy." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 258, + 70, + 547, + 241 + ], + "blocks": [ + { + "bbox": [ + 258, + 70, + 547, + 241 + ], + "lines": [ + { + "bbox": [ + 258, + 70, + 547, + 241 + ], + "spans": [ + { + "bbox": [ + 258, + 70, + 547, + 241 + ], + "type": "image", + "image_path": "7770f3f7109e66bb42dbfa87af614dcd411bf30abbf0ff6385267a88f091c72f.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 65, + 311, + 263, + 482 + ], + "blocks": [ + { + "bbox": [ + 65, + 311, + 263, + 482 + ], + "lines": [ + { + "bbox": [ + 65, + 311, + 263, + 482 + ], + "spans": [ + { + "bbox": [ + 65, + 311, + 263, + 482 + ], + "type": "image", + "image_path": "7267879d51d74138094acd266af86fd6db9226983d217686361dce2ed8011197.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 486, + 154, + 495 + ], + "lines": [ + { + "bbox": [ + 59, + 486, + 154, + 495 + ], + "spans": [ + { + "bbox": [ + 59, + 486, + 154, + 495 + ], + "type": "text", + "content": "(a) Sparse Completion Block" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 162, + 486, + 275, + 495 + ], + "lines": [ + { + "bbox": [ + 162, + 486, + 275, + 495 + ], + "spans": [ + { + "bbox": [ + 162, + 486, + 275, + 495 + ], + "type": "text", + "content": "(b) Contextual Aggregation Block" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 505, + 287, + 550 + ], + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 550 + ], + "type": "text", + "content": "Figure 3. Two building blocks of the sparse latent diffuser. (a) The sparse completion block diffuses non-empty features to empty neighbors, and (b) The contextual aggregation block aggregates geometry and semantic features without engaging in completion." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": "tive layers with " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "1 \\times k \\times k" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " ad " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "k \\times 1 \\times k" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " kernels, and the other branch with " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "k \\times 1 \\times k" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " ad " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "1 \\times k \\times k" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " kernels. Note that the complexity is reduced from " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(k^3)" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(3k^2)" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(4k^2)" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": " after the decomposition. Though the actual cost is not reduced when we use a small kernel with " + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 46, + 566, + 287, + 662 + ], + "type": "text", + "content": ", the expressive capacity of decomposed kernels outperforms a single full kernel, thus we can still achieve efficiency improvements by stacking fewer layers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 670, + 185, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 185, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 185, + 684 + ], + "type": "text", + "content": "3.3. Sparse Feature Pyramid" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "A straightforward approach to complete the scene is to stack the proposed sparse diffuser multiple times, akin to SCP-" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "content": "Net [35]. However, this necessitates a substantial number of sparse diffusers to ensure an adequately large receptive field, which is particularly important for recognizing large objects like \"truck\" or static elements such as \"road\". The computation cost is obviously expensive. To address this issue, we note that down-sample layers, implemented with sparse convolution with a stride greater than one, not only reduce the spatial resolution but also increase the relative sparsity in the new scale. By building a multi-scale sparse feature pyramid with down-sample layers, we are readily able to obtain a coarse-to-fine representation of the scene. This ensures that querying any spatial location can be addressed by at least one feature scale, simultaneously reducing computation costs. Formally, we stack the sparse diffuser for " + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "content": " times, each is followed by a down-sample layer, and the feature pyramid is collected as " + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\{\\mathbb{V}_l\\}_{l=1}^L" + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "content": ". Additionally, the spatial size along the height dimension of the last two scales is too small, so we simply omit the " + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "content": " dimension. For the completion blocks, the 3D convolution is replaced with a 2D version with " + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "content": " kernel. For the contextual aggregation block, we replace the asymmetrical branches with two parallel 2D submanifold convolutions with " + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "inline_equation", + "content": "5 \\times 5" + }, + { + "bbox": [ + 304, + 316, + 545, + 578 + ], + "type": "text", + "content": " kernels." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "type": "text", + "content": "Sparse Voxel Decoder. Former methods [6, 41] uses multi-scale deformable attention transformer (MSDeformAttn) [44] in the pixel/voxel decoder responsible for aggregating intra-scale and inter-scale features. Targeting for saving GPU memory and time, we simplify this process by using interpolation to fuse multi-scale sparse features output by the 3D sparse encoder. Specifically, for a given scale " + }, + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\mathbb{V}_l" + }, + { + "bbox": [ + 304, + 579, + 545, + 686 + ], + "type": "text", + "content": " from the feature pyramid, we augment it by fusing all the other scales," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 358, + 689, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 689, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 358, + 689, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbb {V}} _ {l} = \\sum_ {j \\neq l} W _ {j} \\cdot \\operatorname {I n t e r p} \\left(\\mathbb {V} _ {j}, \\mathbb {V} _ {l}\\right), 2 \\tag {1}", + "image_path": "e0999f30af20d2c1623ba49b42c23c91c78af53871d552b23591f3566988f13f.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15038" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "W_{j}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " is a learned weight for the " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "-th scale, and " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathrm{Interp}(\\mathbb{X},\\mathbb{Y})" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " indicates linear interpolation from a sparse tensor " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathbb{X}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": " to another " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\mathbb{Y}" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 110, + 286, + 182 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 110, + 286, + 182 + ], + "spans": [ + { + "bbox": [ + 47, + 110, + 286, + 182 + ], + "type": "text", + "content": "Leveraging this lightweight feature fusion approach, the feature pyramid is enriched with semantic information from different scales. Moreover, the high-resolution features benefit from additional completion provided by the low-resolution features, as the denser low-resolution features resist dilution by interpolation operators." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 195, + 192, + 208 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 195, + 192, + 208 + ], + "spans": [ + { + "bbox": [ + 47, + 195, + 192, + 208 + ], + "type": "text", + "content": "3.4. Sparse Transformer Head" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 216, + 286, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 286, + 346 + ], + "type": "text", + "content": "We frame the semantic occupancy prediction as a 3D segmentation problem and employ a transformer head, inspired by the design of Mask2Former [6]. This head iteratively updates a set of learnable queries through masked attention and subsequently decodes these queries into 3D masks for all semantic classes. However, a challenge arises due to the need for dense binary masks to represent semantic classes. Additionally, as we perform predictions in a 3D space [41], the computational and memory costs associated with applying successive transformer decoder layers to dense masks become impractical." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 350, + 286, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 286, + 420 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 286, + 420 + ], + "type": "text", + "content": "To overcome this challenge, we adapt the dense transformer head to a sparse variant. Specifically, we assert that accurate segmentation is crucial for occupied voxels, while non-occupied voxels need not be considered during this phase. In the ensuing discussion, we outline several steps to delineate the sparse transformer decoder." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "content": "Preprocessing and Notations. Given the sparse feature pyramid " + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbb{V}}_l" + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "content": ", we first employ a linear binary classifier for coarse segmentation. The binary classifier is trained to label a voxel as empty if the semantic ground truth is 0 and nonempty otherwise. We only preserve voxels that are classified as non-empty, resulting in a filtered, sparser tensor " + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbb{V}}_l = \\{(\\mathbf{p}_i,\\mathbf{f}_i)|i = 1,\\dots,N_l\\}" + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "content": ", where we use " + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "content": " to denote the number of remaining voxels for the " + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "content": "-th scale. Storing variant features for the empty voxels is unnecessary, and instead, we find it suffices to use only a single learnable token " + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\phi}" + }, + { + "bbox": [ + 46, + 423, + 286, + 554 + ], + "type": "text", + "content": " to represent all the empty voxels." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": "Query Decoding. The former method [41] performs outer product between queries " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "Q \\in \\mathbb{R}^{N_q \\times C}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " and 3D dense features " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{C \\times H \\times W \\times D}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " to decode the queries to 3D mask with shape " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "(N_q, H, W, D)" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": ", which has a time complexity of " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N_q HWDC)" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": ". To facilitate inference speed, we only perform outer product between " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_{\\phi} \\cup \\{\\mathbf{f}_i | (\\mathbf{p}_i, \\mathbf{f}_i) \\in \\hat{\\mathbb{V}}_l\\}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " to obtain a series of occupied masks " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "M^{\\mathrm{occ}} \\in \\mathbb{R}^{N_q \\times N_l}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " and a single mask " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "M^{\\phi} \\in \\mathbb{R}^{N_q \\times 1}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " that represents empty voxels. With the saved coordinates " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " of occupied voxels, we can easily reconstruct the dense 3D mask " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "M \\in \\mathbb{R}^{Q \\times H \\times W \\times Z}" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " from the predicted sparse tensor, using a scatter operation that does not break the gradient flow. This way, the complexity is reduced to " + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(N_l N_q C + HWZ)" + }, + { + "bbox": [ + 46, + 556, + 286, + 713 + ], + "type": "text", + "content": " for mask predic" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 443, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 443, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 443, + 83 + ], + "type": "text", + "content": "tion and reconstruction. Note that" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 348, + 92, + 545, + 150 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 92, + 545, + 150 + ], + "spans": [ + { + "bbox": [ + 348, + 92, + 545, + 150 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {O} \\left(N _ {l} N _ {q} C + H W Z\\right) \\\\ = \\mathcal {O} \\left(H W Z N _ {q} C \\left(\\frac {N _ {l}}{H W Z} + \\frac {1}{N _ {q} C}\\right)\\right) \\tag {2} \\\\ < \\mathcal {O} (H W Z N _ {q} C), \\\\ \\end{array}", + "image_path": "d7599a73b858862016c8466f9407564fe8ceca9772ef6686bdfbbe742d620e60.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "text", + "content": "because " + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "inline_equation", + "content": "N_{l} / HWZ" + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "text", + "content": " is rather smaller than 1 in our sparse case. Moreover, the " + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "inline_equation", + "content": "N_{q}" + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "text", + "content": " queries are also input to a " + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "text", + "content": "-way linear classifier to classify the corresponding 3D mask into predefined " + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 157, + 545, + 205 + ], + "type": "text", + "content": " semantic categories." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "text", + "content": "Query Updating. Given the input " + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "text", + "content": " layers of multi-scale sparse features, we iteratively alternate between query decoding and query updating in each transformer layer. With the predicted 3D masks " + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "inline_equation", + "content": "M_{l-1}" + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "inline_equation", + "content": "(l-1)" + }, + { + "bbox": [ + 304, + 205, + 545, + 265 + ], + "type": "text", + "content": "-th transformer layer, we update the queries via" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 272, + 549, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 272, + 549, + 301 + ], + "spans": [ + { + "bbox": [ + 306, + 272, + 549, + 301 + ], + "type": "interline_equation", + "content": "Q _ {l} = \\operatorname {s o f t m a x} \\left[ \\mathcal {M} _ {l - 1} + W _ {q} Q _ {l - 1} \\left(W _ {k} \\hat {\\mathbf {V}} _ {l}\\right) ^ {T} \\right] W _ {v} \\hat {\\mathbf {V}} _ {l} + Q _ {l - 1}, \\tag {3}", + "image_path": "cceb31713f49a986896d81cc40a93c1c154381257b2f7ac705de96662c352cfa.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "inline_equation", + "content": "W_{q}, W_{k}, W_{v}" + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "content": " are linear layers, " + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{V}}_{l}" + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "content": " is the dense version reconstructed from " + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbb{V}}_{l}" + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "content": ", and the attention mask " + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{l-1}" + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "content": " at location " + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "inline_equation", + "content": "(x,y,z)" + }, + { + "bbox": [ + 304, + 302, + 545, + 340 + ], + "type": "text", + "content": " is obtained by" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 309, + 348, + 545, + 392 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 348, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 309, + 348, + 545, + 392 + ], + "type": "interline_equation", + "content": "\\mathcal {M} _ {l - 1} (x, y, z) = \\left\\{ \\begin{array}{l l} 0 & \\text {i f} \\sigma \\left(M _ {l - 1} ^ {\\prime} (x, y, z)\\right) \\geq 0. 5 \\\\ - \\infty & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {4}", + "image_path": "3709931dc7d9e2c74c86bfa0fa804fbdd52b9062c5605216be50a48f624ce215.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "text", + "content": " is the sigmoid function, " + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "inline_equation", + "content": "M_{l-1}^{\\prime} = \\max\\text{pooling}(M_{l-1})" + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "text", + "content": " which resizes the 3D mask to the same resolution of " + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{V}}_l" + }, + { + "bbox": [ + 304, + 402, + 545, + 440 + ], + "type": "text", + "content": ", similar to implementation in [41]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 446, + 418, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 446, + 418, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 446, + 418, + 459 + ], + "type": "text", + "content": "3.5. Objective Function" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "text", + "content": "Considering the sparse transformer head formulates semantic occupancy as a mask set prediction task [6, 41], bipartite matching with Hungarian solver is used to assign binary mask labels and corresponding semantic class labels to the predicted masks. Based on the assignment, we calculate the mask loss " + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mask}}" + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "text", + "content": " and classification loss " + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "text", + "content": ". Additionally, " + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{depth}}" + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "text", + "content": " is calculated between the predicted depth map and ground-truth projected by point clouds, for supervision of the LSS component. Moreover, the coarse binary classification on non-empty voxels is also supervised by a segmentation loss " + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{seg}}" + }, + { + "bbox": [ + 304, + 465, + 545, + 608 + ], + "type": "text", + "content": ". Finally, the overall objective function is a simple summation of these loss terms" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 350, + 617, + 545, + 631 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 617, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 350, + 617, + 545, + 631 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {m a s k}} + \\mathcal {L} _ {\\text {c l s}} + \\mathcal {L} _ {\\text {d e p t h}} + \\mathcal {L} _ {\\text {s e g}}. \\tag {5}", + "image_path": "dc77ab50eb40fe45c561893eb3bdd8d02bea00ef098d068d82cd703ff0189339.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 639, + 386, + 653 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 639, + 386, + 653 + ], + "spans": [ + { + "bbox": [ + 306, + 639, + 386, + 653 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 659, + 422, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 422, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 422, + 672 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Datasets. We evaluate our proposed SparseOcc on nuScenes-Occupancy [33] and SemanticKITTI [2]. nuScenes-Occupancy [33] extends the famous large-scale" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15039" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 547, + 171 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 547, + 171 + ], + "type": "table", + "html": "
MethodInputIoUmIoUbarrierbicyclebuscarconst. veh.motorcyclepedestriantraffic conetrailertruckdrive. surf.other flatsidewalkterrainmannadevegetationFLOPsMemory3D/Overall Latency
MonoScene [4]C18.46.97.13.99.37.25.63.05.94.44.94.214.96.37.97.410.07.6---
TPVFormer [13]C15.37.89.34.111.310.15.24.35.95.36.86.513.69.08.38.09.28.21132G20G0.57/0.73s
OpenOccupancy [33]C19.310.39.96.811.211.56.38.48.64.34.29.922.015.814.113.57.310.21716G19G0.84/1.22s
C-CONet [33]C20.112.813.28.115.417.26.311.210.08.34.712.131.418.818.716.34.88.21810G21G2.18/2.58s
SparseOcc (ours)C21.814.116.19.315.118.67.39.411.29.47.213.031.821.720.718.86.110.6455G13G0.19/0.25s
", + "image_path": "f522214de494c83a903bc9d0b5ed5aad832527fb6e072fe1f2d7e0e6999e5666.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 49, + 212, + 545, + 353 + ], + "blocks": [ + { + "bbox": [ + 47, + 173, + 546, + 205 + ], + "lines": [ + { + "bbox": [ + 47, + 173, + 546, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 173, + 546, + 205 + ], + "type": "text", + "content": "Table 1. Semantic occupancy prediction results on nuScenes-Occupancy [33] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs, training GPU memory, and 3D/overall inference latency. The C denotes camera and the bold numbers indicate the best results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 212, + 545, + 353 + ], + "lines": [ + { + "bbox": [ + 49, + 212, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 49, + 212, + 545, + 353 + ], + "type": "table", + "html": "
MethodInputIoUmIoUroad (15.30%)sidewalk (11.13%)parking (1.12%)other-ground (0.56%)building (14.1%)car (3.92%)truck (0.16%)bicycle (0.03%)motorcycle (0.03%)other-vehicle (0.20%)vegetation (39.3%)trunk (0.51%)terrain (9.17%)person (0.07%)bicyclist (0.07%)motorcyclist (0.05%)fence (3.90%)pole (0.29%)traffic-sign (0.08%)FLOPs
LMSCNet* [27]C28.616.7040.6818.224.380.0010.3118.330.000.000.000.000.000.000.000.000.000.0013.660.0220.540.000.000.000.001.210.000.00
3DSketch* [5]C33.307.5041.3221.630.000.0014.8118.590.000.000.000.000.000.000.000.0019.090.0026.400.000.000.000.000.730.000.00
AICNet* [16]C29.598.3143.5520.5511.970.0712.9414.714.530.000.000.000.000.0015.372.9028.710.000.000.000.002.520.060.00
JS3C-Net* [37]C38.9810.3150.4923.7411.940.0715.0324.654.410.000.006.1518.114.3326.860.670.270.000.003.943.771.45
MonoScene† [4]C36.8611.0856.5226.7214.270.4614.0923.266.980.610.451.4817.892.8129.641.861.200.005.844.142.25
TPVFormer [13]C35.6111.3656.5025.8720.600.8513.8823.818.080.360.054.3516.922.2630.380.510.890.005.943.141.52
OccFormer [41]C36.5013.4658.8526.8819.610.3114.4025.0925.530.811.198.5219.633.9332.622.782.820.005.614.262.86
SparseOccC36.4813.1259.5929.6820.440.4715.4124.0318.070.780.898.9418.893.4631.063.680.620.006.733.892.60
", + "image_path": "43a909d5e937bdf121471562ad8fd1915bede431995e2496f1b1eb2f94226f24.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 354, + 546, + 387 + ], + "lines": [ + { + "bbox": [ + 47, + 354, + 546, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 354, + 546, + 387 + ], + "type": "text", + "content": "Table 2. Semantic scene completion results on SemanticKITTI [1] validation set. For accuracy evaluation, We report the geometric metric IoU, semantic metric mIoU, and the IoU for each semantic class. For efficiency evaluation, we report the FLOPs. The C denotes camera and the bold numbers indicate the best results. The methods with “*” are RGB-input variants reported by [4] for fair comparison." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 398, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 398, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 398, + 287, + 566 + ], + "type": "text", + "content": "autonomous driving datasets nuScenes [3] with 3D dense semantic occupancy annotations on key frames for 1 \"empty\" class and 16 semantic classes using Augmenting And Purifying pipeline. It covers 700 and 150 driving scenes in the training and validation set of nuScenes. The multi-view images and corresponding LiDAR points are provided by the original nuScenes dataset. SemanticKITTI [2] contains 22 sequences including monocular images, LiDAR points, point cloud segmentation labels and semantic scene completion annotations. The sequence 08 is officially split for validation, sequences 00-10 (excluding 08) are used for training, and sequences 11-21 are the test set. It annotates each 3D voxel with 1 \"empty\" class or 19 semantic classes." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 567, + 287, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 652 + ], + "type": "text", + "content": "Evaluation Metric. We follow the common practice and report the intersection over union (IoU) of occupied voxels regardless of their semantic labels to evaluate the reconstructed geometry shape. The semantic mIoU of all semantic classes is also reported to evaluate the semantic-aware perception ability. For efficiency analysis, FLOPs is also evaluated using the analysis tool provided by [22]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 715 + ], + "type": "text", + "content": "Implementation Details. For image encoder, we follow the previous work [33, 41] for fair comparison and use EfficientNetB7 [29] and SecondFPN [39] on SemanticKITTI and ResNet-50 [9] on nuScenes-Occupancy. The 2D to 3D view transformation is implemented as the same as [33, 41]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": "And it generates a 3D feature volume of size " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "128 \\times 128 \\times 16" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "128 \\times 128 \\times 10" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " with 128 channels for SemanticKITTI and nuScenes-Occupancy, which is converted to sparse representation. We stack the sparse diffuser for " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "L = 4" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " times, each followed by a sparse convolution with stride 2 for downsampling. The kernel size " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " of the orthogonal convolutions in sparse completion block and contextual aggregation block is set to 3. The sparse voxel decoder projects the multi-scale features to 192 channels and enhances them via interpolation and summation. The sparse transformer head consists of 9 layers for query updating and decoding and the number of queries " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "N_{q}" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " is 100. Following [6, 41], we sample 50176 points for supervision according to the class frequency for fast training speed. During inference, the predicted masks are upsampled " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "inline_equation", + "content": "4 \\times" + }, + { + "bbox": [ + 304, + 398, + 545, + 601 + ], + "type": "text", + "content": " to the size of ground-truth via trilinear interpolation for evaluation on SemanticKITTI and nuScenes-Occupancy, respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 601, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 661 + ], + "type": "text", + "content": "Optimization. AdamW [23] optimizer with an initial learning rate of 1e-4 and a weight decay of 0.01 is leveraged during training. We train the model for 30 epochs on SemanticKITTI and 24 epochs on nuScenes-Occupancy with a batch size of 8 on 8 v100 GPUs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 670, + 446, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 446, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 446, + 682 + ], + "type": "text", + "content": "4.2. Benchmark Performance" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "In this part, we compare our SparseOcc with the published state-of-the-art methods on nuScenes-Occupancy and Se" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15040" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "content": "manticKITTI. The results of the former methods are directly derived from their papers or code with their configurations. NuScenes-Occupancy. As shown in Tab. 1, our SparseOcc successfully outperforms the 3D dense representation based C-CONet [33] by " + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "content": " geometry IoU and " + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "inline_equation", + "content": "1.3\\%" + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "content": " semantic mIoU. This accomplishment highlights SparseOcc's effectiveness. Besides, we can observe that the model FLOPs are reduced by " + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "inline_equation", + "content": "74.9\\%" + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "content": " relatively, which further justifies the efficiency of our SparseOcc. More surprisingly, SparseOcc not only produces a remarkable " + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "inline_equation", + "content": "80.8\\%" + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "content": " improvement in mIoU over TPVFormer [13] which uses efficient TPV view as 3D scene representation, but also reduces the FLOPs by " + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "inline_equation", + "content": "59.8\\%" + }, + { + "bbox": [ + 47, + 72, + 287, + 324 + ], + "type": "text", + "content": ". We find that TPVFormer uses a relatively large image backbone ResNet-101 [9], and the multi-layer image cross-attention as well as cross-view attention between dense TPV maps also impose lots of computational burden. In contrast, our SparseOcc uses sparse operators in the 3D space, helping us achieve superior performance with a lightweight implementation. Besides, SparseOcc exhibits a noteworthy reduction in 3D inference latency, i.e., the time for 3D feature processing." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 324, + 288, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 324, + 288, + 444 + ], + "spans": [ + { + "bbox": [ + 47, + 324, + 288, + 444 + ], + "type": "text", + "content": "SemanticKITTI. We quantitatively compare the proposed SparseOcc with several previous works in Tab. 2. we can see that SparseOcc achieves comparable performance with OccFormer [41] and significantly better than other methods in terms of semantic mIoU. Please note that different from OccFormer which builds long-range and dynamic dependency in the 3D space using Swin Transformer [21], the 3D encoder of SparseOcc is built with spconv [7] only. Consequently, the model FLOPs of SparseOcc is just " + }, + { + "bbox": [ + 47, + 324, + 288, + 444 + ], + "type": "inline_equation", + "content": "44.2\\%" + }, + { + "bbox": [ + 47, + 324, + 288, + 444 + ], + "type": "text", + "content": " of OccFormer [41] approximately." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 452, + 176, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 452, + 176, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 176, + 464 + ], + "type": "text", + "content": "4.3. Qualitative Evaluation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 471, + 287, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 602 + ], + "type": "text", + "content": "We visualize the 3D semantic occupancy prediction results of several challenging scenes in nuScenes-Occupancy validation set in Fig. 4. As can be seen, compared with the 3D dense counterpart C-CONet [33], our SparseOcc can better complete the large area flat-like road (first row), capture the complicated structure of vegetation (second row) and reconstruct car in the distance (third row). We can conclude that benefiting from the proposed sparse latent diffuser and learned sparse feature pyramid, our sparse occupancy transformer head can generate relatively accurate scene-level descriptions in an efficient way." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 610, + 147, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 610, + 147, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 610, + 147, + 623 + ], + "type": "text", + "content": "4.4. Ablation Studies" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Sparse Completion Blok. As illustrated in Sec. 3.2, a 3D diffusion kernel is spatially decomposed into a combination of three orthogonal convolutional kernels in the sparse completion block. Tab. 3 ablates the type and number of diffusion kernels. Surprisingly, we find that SparseOcc can perform satisfactorily even if no sparse completion block is applied. We think that it is because the decoder which" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 322, + 70, + 531, + 158 + ], + "blocks": [ + { + "bbox": [ + 322, + 70, + 531, + 158 + ], + "lines": [ + { + "bbox": [ + 322, + 70, + 531, + 158 + ], + "spans": [ + { + "bbox": [ + 322, + 70, + 531, + 158 + ], + "type": "table", + "html": "
Conv TypeConv NumKernel SizeIoUmIoU
-0-35.512.1
Regular13×3×335.812.2
236.412.3
336.212.6
Decomposed13×3×136.513.1
23×1×336.612.8
31×3×136.412.7
", + "image_path": "c0447f955be1f7d72201e61a1527b9e84df840521488f77bcd0f61a4065436bc.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 321, + 188, + 531, + 235 + ], + "blocks": [ + { + "bbox": [ + 306, + 160, + 545, + 182 + ], + "lines": [ + { + "bbox": [ + 306, + 160, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 306, + 160, + 545, + 182 + ], + "type": "text", + "content": "Table 3. Ablation on different designs of Sparse Completion Block on SemanticKITTI val set." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 188, + 531, + 235 + ], + "lines": [ + { + "bbox": [ + 321, + 188, + 531, + 235 + ], + "spans": [ + { + "bbox": [ + 321, + 188, + 531, + 235 + ], + "type": "table", + "html": "
TypeIoUmIoUMemoryFLOPs
FPN3D[20]34.49.813.2G307G
MSDeformAttn3D36.713.319.8G379G
Sparse Decoder36.513.113.3G279G
", + "image_path": "b5817c099151bc2169e33766cf62c50bc7491b295c2961d44371ce7b4c4026c8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 321, + 254, + 531, + 300 + ], + "blocks": [ + { + "bbox": [ + 312, + 237, + 539, + 247 + ], + "lines": [ + { + "bbox": [ + 312, + 237, + 539, + 247 + ], + "spans": [ + { + "bbox": [ + 312, + 237, + 539, + 247 + ], + "type": "text", + "content": "Table 4. Ablation on voxel decoder on SemanticKITTI val set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 254, + 531, + 300 + ], + "lines": [ + { + "bbox": [ + 321, + 254, + 531, + 300 + ], + "spans": [ + { + "bbox": [ + 321, + 254, + 531, + 300 + ], + "type": "table", + "html": "
TypeIoUmIoUMemoryFLOPs
Linear Head36.811.89.8G5.4G
Trans. Head36.213.219.9G19.0G
Sparse Trans. Head36.513.113.3G13.5G
", + "image_path": "b6b3274ddce3a2dd8b4416de93e7f51129a570695ec892ba7bb7e9ced85cc5f7.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 302, + 545, + 323 + ], + "lines": [ + { + "bbox": [ + 306, + 302, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 302, + 545, + 323 + ], + "type": "text", + "content": "Table 5. Ablation on segmentation head on SemanticKITTI val set." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 340, + 545, + 424 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 340, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 304, + 340, + 545, + 424 + ], + "type": "text", + "content": "fuses sparse feature pyramid can also complete the scene to some extent. Compared with regular " + }, + { + "bbox": [ + 304, + 340, + 545, + 424 + ], + "type": "inline_equation", + "content": "3 \\times 3 \\times 3" + }, + { + "bbox": [ + 304, + 340, + 545, + 424 + ], + "type": "text", + "content": " kernel, the decomposed orthogonal achieves better scene completion and segmentation results. Besides, stacking more convolution blocks does not improve performance. Hence, we build our sparse completion block with only a group of decomposed orthogonal." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": "Sparse Feature Pyramid. As shown in Tab. 4, we observe that when the SparseOcc equipped with 6 layers of multi-scale deformable attention (MSDeformAttn), it performs better than the proposed sparse decoder. However, when the layer number of MSDeformAttn decreases, the IoU and mIoU both drop and lag behind the proposed simple sparse decoder. Moreover, the training GPU memory and FLOPs of the MSDeformAttn3D are much higher than the proposed interpolation and summation method. Compared with FPN3D [20], our sparse voxel decoder is " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "2.1\\%" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "inline_equation", + "content": "3.3\\%" + }, + { + "bbox": [ + 304, + 425, + 545, + 557 + ], + "type": "text", + "content": " mIoU higher with slightly more memory." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Sparse Transformer Head. We compare several different prediction heads, including simple linear head, transformer head proposed in [41], and our sparse transformer head in Tab. 5. As can be seen, the linear head achieves the best geometry IoU of 36.8. We postulate it may be because the output of the linear head is supervised by an explicit geometry loss, i.e., a cross-entropy loss on occupied and non-occupied voxels. On the contrary, the transformer decoder formulates occupancy prediction as mask generation for each semantic class exclusively. Consequently, no explicit supervision is or can be imposed on the occupied voxels. SparseOcc uses a linear layer for coarse segmentation to filter out the non-occupied voxels and then proposes" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "15041" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 76, + 506, + 340 + ], + "blocks": [ + { + "bbox": [ + 85, + 76, + 506, + 340 + ], + "lines": [ + { + "bbox": [ + 85, + 76, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 85, + 76, + 506, + 340 + ], + "type": "image", + "image_path": "05fa9a7a1d81eb91714f39b4507e363194f4eb6d532abc99d28b7143c63e1931.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 342, + 547, + 386 + ], + "lines": [ + { + "bbox": [ + 46, + 342, + 547, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 547, + 386 + ], + "type": "text", + "content": "Figure 4. Qualitative results of 3D semantic occupancy on nuScenes-Occupancy validation set. The input multi-view images are shown on the leftmost and the occupancy predictions of C-CONet [33], our SparseOcc, and the ground-truth are then visualized sequentially. Compared to 3D dense representation based C-CONet [38], our SparseOcc achieves better completion and segmentation as highlighted by the red circles." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 55, + 395, + 279, + 463 + ], + "blocks": [ + { + "bbox": [ + 55, + 395, + 279, + 463 + ], + "lines": [ + { + "bbox": [ + 55, + 395, + 279, + 463 + ], + "spans": [ + { + "bbox": [ + 55, + 395, + 279, + 463 + ], + "type": "table", + "html": "
Method2D BackboneInput SizeIoUmIoU
C-CONet [33]R-50704 × 25616.68.6
R-501600 × 90019.310.3
R-1011600 × 90020.211.4
SparseOccR-50704 × 25621.814.1
R-501600 × 90020.414.6
", + "image_path": "b1bda890ca7ccb17b4f8cff9305b32ef684c9acc91489ae236ce42abe41c5b1d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 464, + 288, + 489 + ], + "lines": [ + { + "bbox": [ + 47, + 464, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 288, + 489 + ], + "type": "text", + "content": "Table 6. Ablation on input size and 2D backbone on nuScenes-Occupancy." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 498, + 287, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 546 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 546 + ], + "type": "text", + "content": "a sparse transformer head for mask prediction. Therefore, it makes an appropriate trade-off between these two kinds of occupancy heads and achieves satisfactory performance with low training memory." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": "Input Image Size. A larger input image size has a larger resolution of image features, thus having a larger feature density in the 3D space, which further influences the performance. From Tab. 6, we can observe that SparseOcc still performs better than C-CONet, even though it is trained using a smaller input size " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "(704 \\times 256)" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " and image backbone (R-50), which further demonstrates the effectiveness of our SparseOcc. Additionally, using a larger input image size " + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "inline_equation", + "content": "(1600 \\times 900)" + }, + { + "bbox": [ + 46, + 546, + 288, + 714 + ], + "type": "text", + "content": " can improve mIoU for both C-CONet and the proposed SparseOcc, thanks to the density increase of semantic features. However, the IoU of SparseOcc drops when using higher image resolution. We blame it on the wrong hallucination on spatially empty voxels caused by over-dense 3D sparse features. When inactivating the sparse" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 397, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 422 + ], + "type": "text", + "content": "completion block in the last sparse latent diffuser layer, this hallucination can be relieved." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 435, + 379, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 379, + 449 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 379, + 449 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 456, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 661 + ], + "type": "text", + "content": "In this paper, we explore the possibility of using pure sparse representation for 3D scene description and present SpaseOcc for 3D semantic occupancy prediction. Specifically, a sparse latent diffuser with decomposed orthogonal kernels is proposed to propagate the non-empty features to their adjacent empty area. To efficiently complete the scene, we stack layers of diffusers and downsampling layers to generate a coarse-to-fine sparse feature pyramid, which is further fused via simple interpolation and summation. In this way, the feature pyramid is enhanced by multi-scale semantic information. Finally, we use a sparse transformer head to query multi-scale sparse features and generate semantic occupancy predictions. Without bells and whistles, SparseOcc achieves state-of-the-art results on nuScenes-Occupancy and comparable performance on SemanticKITTI, fully demonstrating its superior effectiveness and efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements. This work was supported by NSFC (62322113, 62376156), Shanghai Municipal Science and Technology Major Project (2021SHZDZX0102), and the Fundamental Research Funds for the Central Universities." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "15042" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Jens Behley, Martin Garbade, Andres Milioto, Jan Quenzel, Sven Behnke, Cyril Stachniss, and Jurgen Gall. 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However, existing regression-based methods discard the spatial location prior in input image with a global pooling, leading to inferior accuracy and are limited to single instance localization tasks. We study the regression-based keypoint localization from a new perspective by leveraging the spatial location prior. Instead of regressing on the pooled feature, the proposed Spatial-Aware Regression (SAR) maintains the spatial location map and outputs spatial coordinates and confidence score for each grid, which are optimized with a unified objective. Benefited by the location prior, these spatial-aware outputs can be efficiently optimized, resulting in better localization performance. Moreover, incorporating spatial prior makes SAR more general and can be applied into various keypoint localization tasks. We test the proposed method in 4 keypoint localization tasks including single/multi-person 2D/3D pose estimation, and the whole-body pose estimation. Extensive experiments demonstrate its promising performance, e.g., consistently outperforming recent regressions-based methods $^{\\dagger}$ .", + "bbox": [ + 75, + 318, + 473, + 650 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 681, + 209, + 698 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Keypoint localization aims to locate target keypoints from an input image and is a fundamental task in the field of computer vision. It has a wide range of applications in human pose estimation [21, 26-28] and facial landmark detection [19], et al. Existing methods for keypoint localization can be summarized into two categories: heatmap-based [21, 29, 31] and regression-based [10, 23, 25], respectively. Regression-based method directly adopts neural network to learn the mapping from input RGB image to keypoint coordinates. Heatmap-based method uses a probability map (also referred as heatmap) to encode the likelihood", + "bbox": [ + 75, + 708, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c8ae01dca51e5dab07fbc1a94ba2bcea04b867c7de1290155def847673b3f5e3.jpg", + "image_caption": [ + "Figure 1. Illustration of (Top) regression-based method, (Middle) standard heatmap-based method, and (Bottom) the proposed SAR for keypoint localization." + ], + "image_footnote": [], + "bbox": [ + 501, + 285, + 893, + 417 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of the target location and retrieves it by selecting location with the highest probability.", + "bbox": [ + 498, + 489, + 890, + 518 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As illustrated in Fig. 1, heatmap-based method selects pre-defined points on heatmaps as localization results, which are easy to optimize. However, low-resolution heatmap leads to high quantization error and high-resolution heatmap enlarges the computation and storage cost. Regression-based method is more efficient and robust to quantization error, but is hard to optimize and commonly achieve inferior performance. One reason is that conventional regression destroys the spatial location information of the feature map by a global pooling, thus cannot provide a good initialization for the following regression. This design also limits the application of regression to differentiate and locate multiple keypoints of the same type, e.g., multi-person pose estimation.", + "bbox": [ + 496, + 521, + 892, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This work is motivated to facilitate the regression-based localization by embedding spatial location prior into regression. Grids in the extracted feature map provide different starting points for regression, making them fitted to locate different keypoints. Regressing from different starting points also introduces duplicate predictions, and we do not know which grids produce the best localization results. Prior works [5, 18] assume the results of grids near the target location are accurate and select them via a separate classification branch. We argue that this heuristic design is not optimal in all cases, e.g., for occluded or truncated", + "bbox": [ + 496, + 734, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "†Project page: https://github.com/kenethwdk/SAR", + "bbox": [ + 94, + 886, + 436, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "624", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "keypoints. Moreover, this multi-task learning pipeline introduces optimization inconsistency between classification and regression [2] and is sensitive to many hyperparameters.", + "bbox": [ + 75, + 90, + 467, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This work presents the Spatial-Aware Regression (SAR), a novel regression method that effectively utilizes the spatial location prior in input image to generate spatial-aware outputs and automatically select the best prediction. As shown in Fig. 1, SAR regresses coordinates on each grid to utilize its spatial location cues. Benefited by the prior, SAR is able to leverage better starting points. Selecting different starting points also helps to differentiate similar keypoints, making SAR applicable to more challenging tasks like multi-person pose estimation.", + "bbox": [ + 75, + 136, + 467, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SAR performs localization on a set of grids, which can be extracted by deep neural networks like CNN [4] or Vision Transformer [31]. To utilize the spatial location prior, SAR introduces a spatial-aware regressor to locate target locations based on spatial location of each grid. To handle duplicate predictions, we propose a spatial-aware selector to evaluate the quality of each regression as confidence score, and select the best prediction. The selector is jointly optimized with the regressor with a unified objective, leading to automatic regression and selection without heuristic design and complex hyperparameters. The introduced selector also depresses the influence of inaccurate predictions. SAR can work well on a low-resolution feature map, thus introduces marginal computational overheads and maintains similar efficiency with existing regression-based methods.", + "bbox": [ + 75, + 287, + 467, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "SAR shares all merits of conventional regression and surpasses it in many aspects. We test its effectiveness on various keypoint localization tasks including single/multiperson 2D/3D pose estimation and whole-body pose estimation. Extensive experiments on 7 keypoint localization benchmarks demonstrate its superior performance in keypoint localization. For example, SAR obtains $72.5\\%$ AP on COCO Keypoint dataset [14], which is higher than conventional regression and heatmap by $16.5\\%$ and $1.8\\%$ . SAR is robust to various input size and output stride, making it more general to deal with complex scenarios. SAR can also generalize well to detect various types of keypoints, arbitrary number of keypoints, as well as 2D/3D keypoints.", + "bbox": [ + 75, + 513, + 467, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 723, + 218, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Heatmap-based Keypoint Localization encodes keypoint location with a probability map, which is introduced by [24]. This type of methods estimates heatmaps and retrieves keypoint coordinates with a post-processing operation. Heatmap-based methods dominate the field of keypoint localization because heatmap is easy to learn with CNN. Pioneer works [16, 21, 29] design powerful CNN models to estimate high resolution heatmaps for human pose estimation and facial landmark detection, then the target keypoint can be simply obtained by a post-processing", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "shifting [16, 33]. Due to the limitation of feature map size, some works [18] combine regression and add an offset branch to avoid quantization error. These methods improve the performance of heatmap. However, they rely on high resolution heatmap to locate keypoints, which results in high computation and storage cost.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Regression-based Keypoint Localization directly learns the mapping from input image to output coordinates via a neural network, which is adopted by several classical methods [1, 25]. Researchers have proposed many methods to improve the performance of direct regression. The first kind of methods changes the way of regression. Integral pose regression [23] leverages the soft-argmax operation to regress keypoint locations by integrating a latent heatmap, which is proved to be superior to direct regression. Sampling-argmax [11] further improves soft-argmax by minimizing the error between samples drawing from a distribution with groundtruth, avoiding unconstrained probability map in previous method. Some work improves regression by proposing new loss functions. RLE [10] changes the predefined Gaussian or Laplace distribution in commonly used regression loss with a learned distribution via normalizing flow. Recently, researchers also try to improve direct regression by proposing more powerful backbones in Transformer architecture [31, 32], such as TokenPose [12] and PETR [20].", + "bbox": [ + 496, + 181, + 890, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although many regression-based works have been proposed, they ignore the spatial location prior, leading to inferior performance and cannot be applied to multiple keypoints localization tasks. This work shows that embedding the spatial prior into regression significantly improves its performance and generalization capability on various human keypoint localization tasks. A more detailed comparison with heatmap-based and existing regression-based methods is presented in the Sec. 3.3.", + "bbox": [ + 496, + 484, + 890, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 633, + 589, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 500, + 657, + 609, + 672 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The goal of keypoint localization is to estimate the coordinates of target keypoints from input images, which can be denoted as,", + "bbox": [ + 496, + 681, + 890, + 724 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\mathcal {K} _ {s} \\right\\} _ {s = 1} ^ {m} = \\operatorname {l o c a t e} (\\mathcal {I}), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 727, + 890, + 744 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\kappa_{s}$ denotes the $s$ -th keypoint coordinates and $m$ is the number of keypoints in this image, which is equal to 1 for single-keypoint localization and larger than 1 for multi-keypoint localization.", + "bbox": [ + 496, + 751, + 890, + 811 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given an input image $\\mathcal{I} \\in \\mathbb{R}^{3 \\times H \\times W}$ , existing methods first adopt a backbone $\\Phi(\\cdot)$ , e.g., CNN-based [21] or Transformer-based [31] network to extract feature map $\\mathbf{F} \\in \\mathbb{R}^{c \\times h \\times w}$ , i.e.,", + "bbox": [ + 496, + 811, + 890, + 871 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} = \\left\\{\\mathcal {F} _ {i, j}, \\mathcal {P} _ {i, j} \\right\\} _ {i = 1 \\dots h} ^ {j = 1 \\dots w} = \\Phi (\\mathcal {I}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 883, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "625", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/415297b848754acbacaffc5f1a3a3cf9e3b5b18de72fb958aa04ccafd97562ca.jpg", + "image_caption": [ + "Figure 2. The pipeline of the proposed Spatial-Aware Regression (SAR) for keypoint localization. SAR first adopts a backbone to extract a set of features, which are passed to spatial-aware regressor and selector to generate corresponding keypoint coordinates and confidence scores. During training, SAR applies Laplacian kernel function and normalization to convert the outputs into corresponding score and calculate the unified objective to train the whole model. During inference, SAR selects regressed outputs with large confidence score." + ], + "image_footnote": [], + "bbox": [ + 99, + 87, + 872, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f = \\mathcal{F}_{i,j}$ is a visual feature on the feature map $\\mathbf{F}$ , $p = \\mathcal{P}_{i,j}$ is the spatial location of this grid, $h, w$ denotes the spatial size of $\\mathbf{F}$ . $\\mathcal{P} = \\{(i,j)\\}_{i=1\\dots h}^{j=1\\dots w}$ is named as the spatial location prior, which is crucial for keypoint localization.", + "bbox": [ + 75, + 392, + 470, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Conventional regression will apply a pooling on $\\mathbf{F}$ to get a global feature $f^g$ , then adopt a regressor to obtain final localization results,", + "bbox": [ + 75, + 455, + 470, + 500 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} = \\mathcal {R} (f ^ {g}). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 228, + 512, + 468, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A $\\ell_1$ or $\\ell_2$ loss is applied on the regressed output to train model, e.g., $\\mathcal{L} = \\ell_1(\\mathcal{K},\\mathcal{K}^*)$ .", + "bbox": [ + 75, + 541, + 468, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The above paradigm has several drawbacks. First, pooling only preserves visual information $f^g$ and discards the spatial location prior $\\mathcal{P}$ , making Eq. (3) hard to optimize. This pooling operation also makes regression sensitive to instance scale. Second, it is difficult to differentiate multiple keypoints of the same category only with $f^g$ , because those keypoints present similar visual appearances and different locations. Although extra operation such as box cropping can remedy this issue, it involves extra object detection process and can be sensitive to detection error.", + "bbox": [ + 75, + 571, + 468, + 720 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We present the Spatial-Aware Regression (SAR) method to integrate the spatial location prior $\\mathcal{P}$ into regression to pursue better localization performance. SAR adopts both spatial location prior $\\mathcal{P}$ and visual feature $f^g$ or $\\mathcal{F}$ to perform localization, which can be denoted as,", + "bbox": [ + 75, + 723, + 468, + 799 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} = \\operatorname {S A R} (\\mathcal {P}, f ^ {g} | \\mathcal {F}). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 199, + 811, + 468, + 829 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SAR shares all the merits of regression-based methods, which are efficient and robust to quantization error. Benefited by the spatial location prior, SAR is easier to optimize and achieves superior keypoint localization performance. It", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "also works well in multi-keypoints localization tasks to detect arbitrary number of keypoints from an input image. All these make SAR a better and robust keypoint localization method. In the following we will present the detailed implementation of SAR.", + "bbox": [ + 496, + 392, + 893, + 468 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Spatial-Aware Regression", + "text_level": 1, + "bbox": [ + 500, + 481, + 733, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given the spatial location prior $\\mathcal{P}$ and visual feature $\\mathcal{F}$ or $f^g$ , SAR aims to locate the target location $\\kappa^{*}$ . We first consider the single keypoint localization that only one target exists in $\\mathcal{I}$ . Multiple keypoints localizations can be estimated by repeating the same process for each target in the input image. The core components of SAR are spatial-aware regressor to generate multiple outputs and spatial-aware selector to select the optimal output, respectively. Both components are jointly optimized by a unified training objective.", + "bbox": [ + 496, + 505, + 890, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spatial-aware regressor aims to get the target location by regressing the coordinates from each grid in $\\mathcal{P}$ . To relieve the difficulty of direct regression, we introduce the spatial location prior in original $\\mathbf{F}$ into regression process, which can be denoted as,", + "bbox": [ + 496, + 643, + 890, + 717 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {K} _ {t} = \\mathcal {R} \\left(f _ {t}\\right) + p _ {t}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 632, + 732, + 890, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $f_{t}$ denotes the visual feature of $t$ -th grid and $p_t$ is its location prior. $\\mathcal{K}_t$ is the regressed output by $t$ -th grid. $f_{t}$ can be obtained by directly taking the feature at corresponding location of $\\mathcal{F}_t$ . It can also be generated from the pooled feature $f^g$ with a grid-wise FC layer, which produces a comparable performance as shown in our experiments.", + "bbox": [ + 496, + 763, + 890, + 853 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compared with Eq. (3), Eq. (5) involves more detailed feature grids and each grid has different spatial location prior $p_t$ to regress the target. Intuitively, for some grids", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "626", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "near the target $\\kappa^{*}$ , they will produce more reliable predictions, thus relieving the difficulty of direct regression in Eq. (3). As each grid generates a prediction, we further propose spatial-aware selector to handle duplicate predictions and select the accurate one.", + "bbox": [ + 75, + 90, + 468, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spatial-aware selector. It is not reasonable to optimize every $\\{\\mathcal{K}_t\\}$ w.r.t. the target, because not all grids are suited to predict a specific keypoint. Equally optimizing all $\\{\\mathcal{K}_t\\}$ will cause the learning degenerate to conventional regression as the model tends to focus on learning hard samples for localization. To reduce the influence of inaccurate predictions and improve the training efficiency, we introduce a spatial-aware selector $S(\\cdot)$ to automatically evaluate the importance of each grid in locating target $\\mathcal{K}^*$ . We predict a confidence score for each regressed output based on the feature $f_t$ , i.e.,", + "bbox": [ + 75, + 167, + 470, + 335 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ns _ {t} = \\mathcal {S} \\left(f _ {t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 338, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $s_t$ denotes the score of selecting the $t$ -th output as the final result. Adopting a heuristic predefined strategy, e.g., selecting grids near the target, is unreasonable to optimize $S(\\cdot)$ and may introduce optimization conflict with regressor. Instead, we jointly optimize the selector with regressor under a unified objective, letting model to select proper points by itself.", + "bbox": [ + 75, + 364, + 468, + 470 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unified objective. The goal of SAR is to optimize $\\{\\mathcal{K}_t, s_t\\}$ to accurately locate target $\\mathcal{K}^*$ . We propose a unified objective to jointly optimize the regressor and selector to avoid optimization contradiction in naive multi-task learning pipeline. We rely on regression to achieve the goal of localization and regard selection as an auxiliary task to reduce the difficulty of regression. This intuition leads to a unified objective function that aims to maximize the overall regression quality score weighted by the regression confidence, i.e.,", + "bbox": [ + 75, + 472, + 468, + 622 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = - \\log \\sum w _ {t} \\cdot r _ {t}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 625, + 468, + 646 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $r_t \\in [0,1]$ denotes the regression quality score of the $t$ -th output and $w_t$ denotes the corresponding regression weight. During training, we measure the regression quality score of each grid with the groundtruth $\\mathcal{K}^*$ by a Laplacian kernel to convert the estimated location $\\mathcal{K}_t$ into a score $r_t$ , that is", + "bbox": [ + 75, + 656, + 468, + 746 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr _ {t} = e ^ {- \\lambda \\cdot \\left| \\mathcal {K} _ {t} - \\mathcal {K} ^ {*} \\right|}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 748, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $r_t \\in [0,1]$ indicates the accuracy of the regressed output and $\\lambda$ is the only hyperparameter of SAR. We set $\\lambda$ to 16 for all experiments and normalize the coordinates by the feature map size.", + "bbox": [ + 75, + 777, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The weight $w_{t}$ generated by the $t$ -th grid should be correlated with other grids. In other words, once some outputs are selected, the remaining should be suppressed. To achieve this goal, we adopt a two-step normalization opera", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "tion on the confidence score $\\{s_t\\}$ to generate $w_{t}$ , i.e.,", + "bbox": [ + 498, + 90, + 851, + 107 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nc _ {t} = \\sigma \\left(s _ {t}\\right), w _ {t} = \\frac {c _ {t}}{\\sum c _ {t}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 116, + 890, + 147 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\sigma(\\cdot)$ denotes the sigmoid function to convert score into $c_{t} \\in [0,1]$ . Eq. (9) first normalizes each score into $[0,1]$ individually then utilizes element-sum to correlate them. Therefore, optimizing a high score $s_{t}$ will decrease others. One advantage of the two-step normalization is the introduced extra score $c_{t}$ , which is not influenced by the target number and can be used to select outputs by a fixed threshold during inference. Another way to generate weight $w_{t}$ is to apply softmax on $s_{t}$ . However, this one-step normalization cannot generate reliable high confidence score in multiple keypoints localization task during inference, because the value of generated $w_{t}$ depends on the number of targets in the image. Therefore, it is hard to select final outputs by a fixed threshold $\\gamma$ .", + "bbox": [ + 496, + 156, + 890, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The unified objective weights each output by the confidence score and is adopted to maximize the overall regression quality. We then give a detailed analysis on Eq. (7) and show how it optimizes both coordinates and confidence scores with a unified loss function. Specifically, the goal of SAR is to minimize the following objective,", + "bbox": [ + 496, + 367, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {w _ {t}, r _ {t}} {\\arg \\min } - \\log \\sum w _ {t} \\cdot r _ {t}, \\text {s . t .} \\sum w _ {t} = 1. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 469, + 890, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Due to the monotonic increase property of $\\log (\\cdot)$ function, the optimal $w_{t},r_{t}$ satisfy that $\\sum w_{i}\\cdot r_{t} = 1$ .With the normalization in selection process, we also can get $\\sum w_{t} = 1$ Therefore, optimizing Eq. (10) is equal to maximizing the regression score $r_t$ and will result in two cases:", + "bbox": [ + 496, + 508, + 890, + 582 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- $\\forall t \\in [1, n], r_t \\to 1$ . This means that all grids can accurately regress the target, i.e., $\\mathcal{K}_t = \\mathcal{K}^*$ . In this case, $w_t$ is not important because we can select any output as final result. However, this case rarely happens, especially for multi-keypoints localization task where the same regressed output $\\mathcal{K}_t$ will be used to compute $r_t$ for different groundtruth $\\mathcal{K}^*$ .", + "- $\\exists t \\in [1, n], r_t \\to 1, \\forall s \\in [1, n] \\setminus t, w_s \\to 0$ . This means that some grids can accurately regress the target location $(r_t \\to 1)$ . Meanwhile, the model tends to output low confidence scores $w_s \\to 0$ to relieve the influence of inaccurate regression outputs. This case effectively leverages spatial location priors at some grids to generate accurate predictions, which are hence selected by the selector as final results." + ], + "bbox": [ + 500, + 583, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above analysis shows that, our proposed training objective trains regressor and selector to boost the accuracy of keypoint localization. It also relieves need of careful multi-task design and hyperparameter tuning in different tasks.", + "bbox": [ + 496, + 810, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inference. Similar to regression-based methods, SAR only needs a simple decoding process for inference. It first", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "627", + "bbox": [ + 485, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9994d01257f3bd3104c48b174907e6b817cf56e500d0db3edb5839aa8082121b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 89, + 181, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/51cb001ac1ca8b824f2951dbca7d2b0eff7c61452ecd88d3151d1324a1f30ef6.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 183, + 90, + 282, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4b5e7de966348bc244f4f95d4fb8fa74b5f3f31fe871f99d9623abbd06edba64.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 90, + 382, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5b7a0879d2e78c53e0f265e80d54a3ce2f9471d8c2ab476cfd22b87cec835b0c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 383, + 90, + 488, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/396544b20cceef324d1a639a331c7b1489e1ef7c4d56d6f75a87960a8b06f4ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 90, + 589, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/8552e8d266fe0245c59dd46d911b29e901a40a9a40eda49bb660a3a7defef610.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 591, + 90, + 687, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/131f0aa9d4cee514722136cae1d72c452441a95f1707d7ceaca4eb6cb9d20e17.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 691, + 90, + 787, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/62bdaf4aac43cbdbee4b44c97c6b8f90ca466308a04f015614d29186b85c02c7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 789, + 90, + 888, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2b5b1b88d6d06e92b8707cf82666eb5b10823f1e97902eeb898e68baa7767976.jpg", + "image_caption": [ + "target", + "Figure 3. Visualization of heatmap [29] and confidence score map predicted by SAR in single/multi-keypoint localization. Target keypoints are denoted by star. SAR can locate keypoints that are out of range of the image and effectively avoids missed detection in crowded scenes." + ], + "image_footnote": [], + "bbox": [ + 80, + 191, + 181, + 290 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/952b3dc64b268473fb707af78c36c4ae46a62358362a85cb0ad8f0086bdbd710.jpg", + "image_caption": [ + "heatmap" + ], + "image_footnote": [], + "bbox": [ + 183, + 191, + 281, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a9d45ee07ec6e908883d85d0c77ff546bb8b9ead70243cdbee6be912df4eb3fb.jpg", + "image_caption": [ + "confidence map" + ], + "image_footnote": [], + "bbox": [ + 282, + 191, + 382, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f3fa620eeaa79bcacf654d24c04eb44abc5ce7384522500d50266024646614f8.jpg", + "image_caption": [ + "SAR" + ], + "image_footnote": [], + "bbox": [ + 383, + 191, + 486, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/03554f1ff15e737839f5158d2318888cbf36c3d47c3a147967127041db6f453f.jpg", + "image_caption": [ + "target" + ], + "image_footnote": [], + "bbox": [ + 488, + 191, + 589, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/de3c41fdb3ba97acf45c81ff749f49937d64ceb584c34d36d67542dc6b28baa6.jpg", + "image_caption": [ + "heatmap" + ], + "image_footnote": [], + "bbox": [ + 591, + 191, + 687, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/102a14291289ecd2389013b868fb3e70c36086dec7bef8f0e92fd9c9917fe23c.jpg", + "image_caption": [ + "confidence map" + ], + "image_footnote": [], + "bbox": [ + 691, + 191, + 785, + 289 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/705593307b50f46fcaa415167fd216e70135630502c65b5df953cb78ff98d6f7.jpg", + "image_caption": [ + "SAR" + ], + "image_footnote": [], + "bbox": [ + 787, + 191, + 888, + 289 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "forwards input to get the regressed output $\\{\\mathcal{K}_t\\}$ and confidence score $\\{c_t\\}$ . It then selects the top $m$ predictions with scores larger than $\\gamma$ as the final result,", + "bbox": [ + 75, + 358, + 468, + 405 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\{\\mathcal {K} \\} = \\left\\{\\mathcal {K} _ {t} \\right\\} _ {t \\in \\Delta}, \\Delta = \\underset {t} {\\operatorname {t o p}} (m, \\{c _ {t} \\geq \\gamma \\}). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 416, + 468, + 440 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The value $m$ is decided by different tasks, e.g., in top-down task we set $m = 1$ and in bottom-up task we set $m = 30$ . Compared with previous heatmap-based methods, SAR does not require complex post-processing operation like shifting [29] or DARK [33] and can be implemented on GPU parallelly. It also works well on low-resolution feature maps, thus is more efficient. SAR is also faster than previous detection-based methods that adopt a Hough voting [18] or accumulation operation [8].", + "bbox": [ + 75, + 452, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Discussions", + "text_level": 1, + "bbox": [ + 76, + 599, + 202, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison to regression. SAR can be regarded as a generalized regression to process feature map. It degenerates to conventional regression when the size of feature map is $1 \\times 1$ . SAR extends the regression-based method by enhancing its performance and capability in handling multiple keypoint localization by exploring the spatial prior. SAR shares all merits of regression, e.g., low computation and storage complexity and produces a continuous output to relieve the quantization error.", + "bbox": [ + 75, + 628, + 468, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Comparison to heatmap. SAR does not suffer from the quantization error in heatmap and removes the necessity of complex post-processing operation. SAR also differs from methods that combines heatmap with offset regression in both motivation and implementation. Those methods treat heatmap generation and offset regression with equal importance, and their performance is limited by the quality of heatmap. SAR does not assume fixed anchor point (e.g., person center) for regression, thus is general and robust to", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "occlusion and truncation. This property enables SAR to locate keypoints out of input image as shown in Fig. 3.", + "bbox": [ + 496, + 358, + 890, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visualization. In Fig. 3, we visualize the confidence score map predicted by SAR and heatmap generated by [29]. Compared with heatmap, SAR is more effective in locating multiple keypoints and is more robust to crowded scenes, e.g., keypoints missed by the heatmap can be reliably detected by SAR. More extensive experiment and visualization results will be presented in following section.", + "bbox": [ + 496, + 388, + 892, + 494 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 508, + 632, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section we validate the effectiveness of the proposed SAR on various keypoint localization tasks. We first test SAR on the widely studied 2D human pose estimation task to demonstrate its basic keypoint localization ability. Moreover, we further verify SAR is more general than conventional regression in three aspects, i.e., generalization to various type of keypoints on whole-body pose estimation task, generalization to arbitrary number of keypoints on multi-person pose estimation task and generalization to 3D keypoint localization on 3D human pose estimation task. Descriptions of datasets, evaluation metrics, detailed implementation of experiments and qualitative results are provided in supplemental material.", + "bbox": [ + 496, + 534, + 890, + 731 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2D Human Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 741, + 748, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2D human pose estimation is a classical localization task that aims to locate the human body keypoints such as knee or shoulder and researchers have proposed many methods to boost its performance. We first conduct experiments on this task to verify the effectiveness of the proposed method, including commonly used large-scale in-the-wild benchmarks COCO Keypoint [14] and MPII [25]. Following previous works, we report the OKS-based AP and PCKh@0.5/0.1 for COCO Keypoint and MPII evaluation respectively. Ex", + "bbox": [ + 496, + 763, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "628", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/1e7fb2da6dac276c918dbc47e17575b9124b45b23d686772caa07e0ed682c2c7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodGFLOPsDeconvsAP\\( AP^{50} \\)\\( AP^{75} \\)Kpt.Error(px)
Regression4.053.882.457.78.5
RLE4.069.689.376.07.8
Heatmap9.7✓70.791.277.67.6
Heatmap+Offset9.7✓70.991.377.87.6
SAR4.071.391.579.17.3
SAR9.7✓72.592.379.97.1
SAR (\\( f^g+FC \\))5.371.191.478.67.3
", + "bbox": [ + 78, + 88, + 468, + 220 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/2d1d6b3c021f5f787d584c5772382c50defa534907a056e482ab075bc254fe22.jpg", + "image_caption": [ + "Figure 4. Comparison with baselines under different output stride." + ], + "image_footnote": [], + "bbox": [ + 78, + 261, + 468, + 390 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "periments on MPII are shown in supplemental material.", + "bbox": [ + 75, + 431, + 444, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with baselines. We first evaluate the proposed SAR with two types of commonly used baselines under the same setting. Experiments are conducted based on SimplePose [29], ResNet-50 [4] is adopted as the backbone. The results are summarized in Table 1. Compared with conventional regression that adopts pooled feature to regress target, SAR obtains superior performance without carefully designed loss or modules. It improves the regression baseline from 53.8 to 72.5. SAR is also better than heatmap-based methods that also utilize the spatial location prior to locate target. We also compare a simple multi-task method that also combine heatmap and regression, which is denoted as heatmap+offset. It can be observed that simply combining two tasks cannot get better performance because it introduces contradiction and more hyperparameters into training, and their performance is also limited by heatmap. We also show that the improvement of SAR mainly comes from the spatial location prior $\\mathcal{P}$ , rather than the visual feature $\\mathcal{F}$ . We keep the same input $f^g$ of SAR and conventional regression, thus the only difference is the introduced location prior $\\mathcal{P}$ , which is denoted as $f^g +\\mathrm{FC}$ . $f^g +\\mathrm{FC}$ explicitly compensates the missed spatial information in $f^g$ and obtains 71.1 AP, which is higher than most baselines.", + "bbox": [ + 75, + 446, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Analysis on spatial size. SAR shares the merits of regression that is free of quantization error, we conduct experiments on various network output strides and input sizes to demonstrate the superior merits of the proposed SAR. In Fig. 4 we investigate the effect of different output stride to localization performance. We can observe that heatmap-based methods are affected by the output stride greatly due", + "bbox": [ + 75, + 795, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/00f7e241db6e64004af5ad8ae60643cda753dce3223240b29c9e066cca78dbae.jpg", + "table_caption": [ + "Table 1. Comparison with baselines on COCO Keypoint val set based on SimplePose [29]. Input size is $256 \\times 192$ ." + ], + "table_footnote": [], + "table_body": "
MethodInput sizeAP\\( AP^{50} \\)\\( AP^{75} \\)AR
Regression64×6422.755.014.637.5
Heatmap64×6433.270.626.840.2
SimCC [13]64×6437.571.934.743.1
SAR64×6439.274.936.345.6
Regression128×12843.175.245.257.9
Heatmap128×12860.087.868.165.0
SimCC [13]128×12861.987.868.766.3
SAR128×12862.587.870.467.4
Regression256×19253.882.457.767.6
Heatmap256×19270.791.277.674.3
SimCC [13]256×19271.291.278.774.9
SAR256×19272.592.379.976.1
", + "bbox": [ + 501, + 88, + 883, + 272 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison with baselines under different input size.", + "bbox": [ + 509, + 276, + 879, + 290 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a46291a5a21d8d71f33e966d890323cc563d7374cf9c9dd82fe73302a4d00ee2.jpg", + "image_caption": [ + "Figure 5. Illustration of sampled keypoint localization results of (Top) 2D human pose estimation, (Middle) whole-body pose estimation, and (Bottom) 3D human pose estimation." + ], + "image_footnote": [], + "bbox": [ + 513, + 292, + 879, + 510 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to the quantization error in low resolution heatmap. However, SAR obtains stable performance on various output strides and is constantly superior to heatmap-based methods. Therefore, SAR can be integrated to different backbone without any modification. We also test SAR with other methods on different input size to show its robustness to different input resolution. The results are shown in Table 2. SAR can handle different input size well and achieves superior performance, e.g., higher than previous SimCC [13] under the same setting.", + "bbox": [ + 496, + 577, + 890, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparison with other methods. Finally, we give a comprehensive comparison with other methods on COCO Keypoint test-dev set. Results are shown in Table 3. Equipped with different backbones, SAR outperforms previous methods and achieves superior performance.", + "bbox": [ + 496, + 729, + 890, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Whole-Body Pose Estimation", + "text_level": 1, + "bbox": [ + 500, + 816, + 759, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We further verify the generalization of the proposed SAR to other type of keypoints on whole-body pose estimation task, which aims to locate keypoints of human body, foot, face and hand. Compared with previous task that only focuses", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "629", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/242d918751c69c961cb08e811fedca882525cf466362b8b994a8cc748b17af6d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneInput sizeAP\\( AP^{50} \\)\\( AP^{75} \\)\\( AP^M \\)\\( AP^L \\)AR
Heatmap-based
SimplePose [29]ResNet-50384×28871.591.178.767.878.076.9
HRNet [21]HRNet-W48384×28875.592.583.371.981.580.5
SimCC [13]HRNet-W48384×28876.092.483.572.581.981.1
Regression-based
DeepPose [25]ResNet-152256×19259.387.666.756.864.9-
Integral Pose [23]ResNet-101256×25667.888.274.863.974.0-
RLE [10]HRNet-W48384×28875.792.382.972.381.3-
Ours (SAR)ResNet-50384×28873.591.980.969.679.778.8
Ours (SAR)HRNet-W48384×28876.392.583.672.682.481.2
", + "bbox": [ + 80, + 88, + 888, + 262 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/26cfdfa18855ec7b8e94cd25b5b296194ba238be12f973df163ce14faf336f47.jpg", + "table_caption": [ + "Table 3. Comparison with other methods on COCO Keypoint test-dev set." + ], + "table_footnote": [], + "table_body": "
MethodInput sizeBackbonebodyfootfacehandwhole-body
APARAPARAPARAPARAPAR
Baselines
Heatmap [29]256×192ResNet-5065.273.861.574.960.671.546.058.452.163.3
Heatmap [29]256×192HRNet-W4870.177.667.578.765.674.353.563.957.968.1
SAR256×192ResNet-5067.374.961.575.283.288.748.360.859.168.0
SAR256×192HRNet-W4871.078.969.181.888.192.358.469.265.174.0
SoTA methods
DeepPose [25]384×288ResNet-10144.456.836.853.749.366.323.541.033.548.4
SimplePose [29]384×288ResNet-5066.674.763.576.373.281.253.764.757.367.1
HRNet [21]384×288HRNet-W4872.279.169.680.177.683.458.767.863.271.7
ZoomNet [7]384×288HR32+HR1874.581.060.970.888.092.457.973.463.074.2
ZoomNAS [30]384×288-74.080.761.771.888.993.062.574.065.474.4
Ours (SAR)384×288HRNet-W4871.279.669.382.690.393.361.372.166.675.6
", + "bbox": [ + 78, + 287, + 890, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparison with other methods on COCO Whole-Body benchmark.", + "bbox": [ + 253, + 508, + 712, + 522 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "on human body, whole-body pose estimation is more challenging due to the large scale variance of different type of keypoints. Therefore, this task can be used to test the ability of localization method on handling scale variance. Following previous works, we conduct experiments on large-scale in-the-wild benchmark COCO Whole-Body [7] and report the OKS-based AP on each subset.", + "bbox": [ + 75, + 534, + 468, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4 shows results. We first compare SAR with heatmap baseline using ResNet-50 and HRNet-W48 as backbone. SAR outperforms heatmap by a large margin, especially on small scale keypoints of face and hand. This demonstrates the benefit of continuous output of SAR, which is free of quantization error in heatmap. We also compare SAR with top-down based methods SimplePose, HRNet, ZoomNet and ZoomNAS. We implement SAR with top-down HRNet under the same setting, and Table 4 shows that our method achieves the best performance on most subsets, without carefully designed multi-branch model in ZoomNet and ZoomNAS. It demonstrates that SAR can generalize to locate various types of keypoints.", + "bbox": [ + 75, + 641, + 470, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Multi-Person Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 849, + 341, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "One advantage of SAR is that it can be applied to multiple keypoints localization tasks, while most of previous meth", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ods, e.g., regression-based methods and SimCC [13] cannot be used to locate multiple keypoints of the same type simultaneously. Multiple keypoints localization task such as multi-person pose estimation (MPPE) is common because it eliminates the assumption that only one instance exists in the input image in single-keypoint localization. Benefited by embedding spatial prior, the proposed method can be applied to MPPE tasks such as bottom-up MPPE and single-stage MPPE. Following previous works, we conduct experiments on COCO [14], OCHuman [34] and CrowdPose [9] and report OKS-based AP metrics.", + "bbox": [ + 496, + 534, + 890, + 700 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For bottom-up MPPE, we adapt SAR with AE [17] to locate multiple keypoints simultaneously because it separately implements localization and grouping. For single-stage MPPE, we conduct experiments on two widely used methods, i.e., CenterNet [35] and DEKR [3], to locate multiple person center points.", + "bbox": [ + 496, + 702, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "All experiments are conducted under the same setting. As shown in Table 5, SAR can successfully detect arbitrary number of keypoints and produce more reliable results than heatmap on all benchmarks. From Fig. 3 we can observe that SAR outputs higher confidence score for detected keypoints, which is important in MPPE because it avoids missed localization.", + "bbox": [ + 496, + 795, + 890, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "630", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e58abe8208e08339c7ed322009bc25fc5b68ecbc75fc8fe76ad4ead16f0a7b15.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodCOCOOCHumanCrowdPose
APAPMAPLARAPAPMAPLARAPAPEAPMAPL
Bottom-up MPPE based on AE [17]
Heatmap48.444.154.854.1----46.759.946.636.7
SAR50.045.056.956.2----48.261.148.038.9
Single-stage Regression MPPE
CenterNet [35]57.650.568.463.134.115.236.269.360.968.961.751.7
+SAR60.352.671.164.739.615.540.571.562.269.863.053.7
DEKR [3]61.854.772.867.535.69.637.571.365.273.066.055.9
+SAR64.556.875.569.140.917.241.973.866.373.767.057.6
", + "bbox": [ + 78, + 88, + 893, + 250 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fbf85c647cfaaa19757494de199d0138657ebd85bdb9db0a92fa18c4de34b72b.jpg", + "table_caption": [ + "Table 5. Comparison with other methods on multi-person pose estimation benchmarks." + ], + "table_footnote": [], + "table_body": "
MethodsDir.Dis.EatGre.Phon.PosePur.SitSitD.Smo.Phot.WaitWalkWalkD.WalkP.Avg
Baselines
Regression46.553.547.946.953.346.448.964.364.653.154.247.540.953.445.251.7
RLE47.151.350.448.053.045.847.465.069.053.752.046.740.951.244.751.6
Integral Pose45.351.547.545.553.242.647.163.963.853.053.846.140.051.343.250.6
SAR-3D46.551.146.945.349.745.146.958.763.250.051.146.140.551.344.149.4
SAR-decouple42.249.546.844.852.242.543.860.765.150.752.644.737.850.041.648.9
SoTA methods
Sun [22]52.854.854.254.361.853.153.671.786.761.567.253.447.161.663.459.1
PoseNet [15]50.555.750.151.753.946.850.061.968.052.555.949.941.856.146.953.3
Sun [23]47.547.749.550.251.443.846.458.965.749.455.847.838.949.043.849.6
RLE [10]43.351.044.544.551.743.146.059.263.749.652.544.137.550.541.248.6
Ours (SAR)40.947.844.843.450.341.042.658.261.248.950.042.936.248.340.247.1
", + "bbox": [ + 78, + 275, + 895, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Comparison with other methods on Human3.6M benchmark.", + "bbox": [ + 276, + 477, + 691, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Monocular 3D Human Pose Estimation", + "text_level": 1, + "bbox": [ + 76, + 507, + 415, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section we show that SAR can also generalize to perform 3D keypoint localization. We conduct experiments on Human3.6M [6], a large-scale indoor benchmark for 3D human pose estimation. For evaluation, MPJPE is reported to measure the error of the predicted keypoints and groundtruth in 3D space. Following [10], we use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation.", + "bbox": [ + 75, + 532, + 468, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SAR for 3D keypoint. We propose two variants of SAR to locate 3D keypoint. The first is SAR-3D that generates 3D feature map $\\mathbf{F}_{3D} \\in \\mathbb{R}^{c \\times d \\times h \\times w}$ from $\\mathbf{F}$ to provide 3D spatial location prior to locate target, which is similar to Integral Pose [23] that also generates 3D heatmap. Benefited by the continuous output of SAR, a small sized $\\mathbf{F}_{3D}$ can already produce promising results, e.g., $d = h = w = 16$ . For the second variant, we decouple the depth dimension from spatial dimension and estimate it with a separate localization branch, which is denoted as SAR-decouple. For $x, y$ coordinates, we directly adopt 2D estimation pipeline. For $z$ dimension, we convert the feature map $\\mathbf{F}$ to a 1D feature map $\\mathbf{F}_z \\in \\mathbb{R}^{c \\times d}$ to locate $z$ -dim of keypoint, $d = 64$ .", + "bbox": [ + 75, + 641, + 470, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Baselines. We first compare SAR with several 3D keypoint localization methods, including regression, RLE [10] and Integral Pose [29]. All experiments are conducted under the same setting. As shown in Table 6, both two variants", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of SAR achieve superior 3D keypoint localization accuracy, which is lower than Integral Pose by 1.2 and 1.7 MPJPE. SAR-decouple achieves better performance than SAR-3D. We think that it is because SAR-decouple with large spatial size can generate more accurate localization results, which is consistent with experiments in Sec. 4.1.", + "bbox": [ + 496, + 507, + 890, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison with other methods. In Table 6 we also compare SAR with recent methods under the same setting, e.g., with flip test. We can observe that SAR reduces the MPJPE from 48.6 to 47.1, which is better than most image-based 3D human pose estimation methods.", + "bbox": [ + 496, + 599, + 890, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 690, + 619, + 705 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work proposes a novel and effective regression method by integrating spatial location prior to relieve the difficulty of direct regression. We introduce spatial-aware regressor and selector with a unified objective to achieve spatial-aware regression. Comprehensive experiments on four different keypoint localization tasks and seven benchmarks demonstrate the promising effectiveness and generalization capability of the proposed method.", + "bbox": [ + 496, + 717, + 890, + 839 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work is supported in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award.", + "bbox": [ + 496, + 839, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "631", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Joao Carreira, Pulkit Agrawal, Katerina Fragkiadaki, and Jitendra Malik. Human pose estimation with iterative error feedback. 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Objects as points. arXiv preprint arXiv:1904.07850, 2019. 7, 8", + "bbox": [ + 78, + 90, + 470, + 132 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "633", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Spatial-Aware Regression for Keypoint Localization/fbd66afd-f4f6-451c-8993-88b8e434975c_model.json b/2024/Spatial-Aware Regression for Keypoint Localization/fbd66afd-f4f6-451c-8993-88b8e434975c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5bcd7f6376353cb9bdfb354faa68dbd284b22cd8 --- /dev/null +++ b/2024/Spatial-Aware Regression for Keypoint Localization/fbd66afd-f4f6-451c-8993-88b8e434975c_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.223, + 0.131, + 0.748, + 0.153 + ], + "angle": 0, + "content": "Spatial-Aware Regression for Keypoint Localization" + }, + { + "type": "text", + "bbox": [ + 0.227, + 0.182, + 0.744, + 0.253 + ], + "angle": 0, + "content": "Dongkai Wang Shiliang Zhang National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University {dongkai.wang, slzhang.jdl}@pku.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.319, + 0.474, + 0.651 + ], + "angle": 0, + "content": "Regression-based keypoint localization shows advantages of high efficiency and better robustness to quantization errors than heatmap-based methods. However, existing regression-based methods discard the spatial location prior in input image with a global pooling, leading to inferior accuracy and are limited to single instance localization tasks. We study the regression-based keypoint localization from a new perspective by leveraging the spatial location prior. Instead of regressing on the pooled feature, the proposed Spatial-Aware Regression (SAR) maintains the spatial location map and outputs spatial coordinates and confidence score for each grid, which are optimized with a unified objective. Benefited by the location prior, these spatial-aware outputs can be efficiently optimized, resulting in better localization performance. Moreover, incorporating spatial prior makes SAR more general and can be applied into various keypoint localization tasks. We test the proposed method in 4 keypoint localization tasks including single/multi-person 2D/3D pose estimation, and the whole-body pose estimation. Extensive experiments demonstrate its promising performance, e.g., consistently outperforming recent regressions-based methods\\(^{\\dagger}\\)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.682, + 0.21, + 0.699 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.709, + 0.47, + 0.875 + ], + "angle": 0, + "content": "Keypoint localization aims to locate target keypoints from an input image and is a fundamental task in the field of computer vision. It has a wide range of applications in human pose estimation [21, 26-28] and facial landmark detection [19], et al. Existing methods for keypoint localization can be summarized into two categories: heatmap-based [21, 29, 31] and regression-based [10, 23, 25], respectively. Regression-based method directly adopts neural network to learn the mapping from input RGB image to keypoint coordinates. Heatmap-based method uses a probability map (also referred as heatmap) to encode the likelihood" + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.286, + 0.895, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.429, + 0.895, + 0.47 + ], + "angle": 0, + "content": "Figure 1. Illustration of (Top) regression-based method, (Middle) standard heatmap-based method, and (Bottom) the proposed SAR for keypoint localization." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.52 + ], + "angle": 0, + "content": "of the target location and retrieves it by selecting location with the highest probability." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.522, + 0.893, + 0.734 + ], + "angle": 0, + "content": "As illustrated in Fig. 1, heatmap-based method selects pre-defined points on heatmaps as localization results, which are easy to optimize. However, low-resolution heatmap leads to high quantization error and high-resolution heatmap enlarges the computation and storage cost. Regression-based method is more efficient and robust to quantization error, but is hard to optimize and commonly achieve inferior performance. One reason is that conventional regression destroys the spatial location information of the feature map by a global pooling, thus cannot provide a good initialization for the following regression. This design also limits the application of regression to differentiate and locate multiple keypoints of the same type, e.g., multi-person pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.902 + ], + "angle": 0, + "content": "This work is motivated to facilitate the regression-based localization by embedding spatial location prior into regression. Grids in the extracted feature map provide different starting points for regression, making them fitted to locate different keypoints. Regressing from different starting points also introduces duplicate predictions, and we do not know which grids produce the best localization results. Prior works [5, 18] assume the results of grids near the target location are accurate and select them via a separate classification branch. We argue that this heuristic design is not optimal in all cases, e.g., for occluded or truncated" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.437, + 0.902 + ], + "angle": 0, + "content": "†Project page: https://github.com/kenethwdk/SAR" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "624" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.137 + ], + "angle": 0, + "content": "keypoints. Moreover, this multi-task learning pipeline introduces optimization inconsistency between classification and regression [2] and is sensitive to many hyperparameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.468, + 0.287 + ], + "angle": 0, + "content": "This work presents the Spatial-Aware Regression (SAR), a novel regression method that effectively utilizes the spatial location prior in input image to generate spatial-aware outputs and automatically select the best prediction. As shown in Fig. 1, SAR regresses coordinates on each grid to utilize its spatial location cues. Benefited by the prior, SAR is able to leverage better starting points. Selecting different starting points also helps to differentiate similar keypoints, making SAR applicable to more challenging tasks like multi-person pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.468, + 0.514 + ], + "angle": 0, + "content": "SAR performs localization on a set of grids, which can be extracted by deep neural networks like CNN [4] or Vision Transformer [31]. To utilize the spatial location prior, SAR introduces a spatial-aware regressor to locate target locations based on spatial location of each grid. To handle duplicate predictions, we propose a spatial-aware selector to evaluate the quality of each regression as confidence score, and select the best prediction. The selector is jointly optimized with the regressor with a unified objective, leading to automatic regression and selection without heuristic design and complex hyperparameters. The introduced selector also depresses the influence of inaccurate predictions. SAR can work well on a low-resolution feature map, thus introduces marginal computational overheads and maintains similar efficiency with existing regression-based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.515, + 0.468, + 0.71 + ], + "angle": 0, + "content": "SAR shares all merits of conventional regression and surpasses it in many aspects. We test its effectiveness on various keypoint localization tasks including single/multiperson 2D/3D pose estimation and whole-body pose estimation. Extensive experiments on 7 keypoint localization benchmarks demonstrate its superior performance in keypoint localization. For example, SAR obtains \\(72.5\\%\\) AP on COCO Keypoint dataset [14], which is higher than conventional regression and heatmap by \\(16.5\\%\\) and \\(1.8\\%\\). SAR is robust to various input size and output stride, making it more general to deal with complex scenarios. SAR can also generalize well to detect various types of keypoints, arbitrary number of keypoints, as well as 2D/3D keypoints." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.219, + 0.74 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Heatmap-based Keypoint Localization encodes keypoint location with a probability map, which is introduced by [24]. This type of methods estimates heatmaps and retrieves keypoint coordinates with a post-processing operation. Heatmap-based methods dominate the field of keypoint localization because heatmap is easy to learn with CNN. Pioneer works [16, 21, 29] design powerful CNN models to estimate high resolution heatmaps for human pose estimation and facial landmark detection, then the target keypoint can be simply obtained by a post-processing" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "shifting [16, 33]. Due to the limitation of feature map size, some works [18] combine regression and add an offset branch to avoid quantization error. These methods improve the performance of heatmap. However, they rely on high resolution heatmap to locate keypoints, which results in high computation and storage cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.484 + ], + "angle": 0, + "content": "Regression-based Keypoint Localization directly learns the mapping from input image to output coordinates via a neural network, which is adopted by several classical methods [1, 25]. Researchers have proposed many methods to improve the performance of direct regression. The first kind of methods changes the way of regression. Integral pose regression [23] leverages the soft-argmax operation to regress keypoint locations by integrating a latent heatmap, which is proved to be superior to direct regression. Sampling-argmax [11] further improves soft-argmax by minimizing the error between samples drawing from a distribution with groundtruth, avoiding unconstrained probability map in previous method. Some work improves regression by proposing new loss functions. RLE [10] changes the predefined Gaussian or Laplace distribution in commonly used regression loss with a learned distribution via normalizing flow. Recently, researchers also try to improve direct regression by proposing more powerful backbones in Transformer architecture [31, 32], such as TokenPose [12] and PETR [20]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.62 + ], + "angle": 0, + "content": "Although many regression-based works have been proposed, they ignore the spatial location prior, leading to inferior performance and cannot be applied to multiple keypoints localization tasks. This work shows that embedding the spatial prior into regression significantly improves its performance and generalization capability on various human keypoint localization tasks. A more detailed comparison with heatmap-based and existing regression-based methods is presented in the Sec. 3.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.591, + 0.649 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.659, + 0.61, + 0.674 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.683, + 0.891, + 0.726 + ], + "angle": 0, + "content": "The goal of keypoint localization is to estimate the coordinates of target keypoints from input images, which can be denoted as," + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.728, + 0.891, + 0.745 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\mathcal {K} _ {s} \\right\\} _ {s = 1} ^ {m} = \\operatorname {l o c a t e} (\\mathcal {I}), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.752, + 0.891, + 0.812 + ], + "angle": 0, + "content": "where \\(\\kappa_{s}\\) denotes the \\(s\\)-th keypoint coordinates and \\(m\\) is the number of keypoints in this image, which is equal to 1 for single-keypoint localization and larger than 1 for multi-keypoint localization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.872 + ], + "angle": 0, + "content": "Given an input image \\(\\mathcal{I} \\in \\mathbb{R}^{3 \\times H \\times W}\\), existing methods first adopt a backbone \\(\\Phi(\\cdot)\\), e.g., CNN-based [21] or Transformer-based [31] network to extract feature map \\(\\mathbf{F} \\in \\mathbb{R}^{c \\times h \\times w}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.585, + 0.884, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} = \\left\\{\\mathcal {F} _ {i, j}, \\mathcal {P} _ {i, j} \\right\\} _ {i = 1 \\dots h} ^ {j = 1 \\dots w} = \\Phi (\\mathcal {I}), \\tag {2}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "625" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.088, + 0.873, + 0.309 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.321, + 0.895, + 0.381 + ], + "angle": 0, + "content": "Figure 2. The pipeline of the proposed Spatial-Aware Regression (SAR) for keypoint localization. SAR first adopts a backbone to extract a set of features, which are passed to spatial-aware regressor and selector to generate corresponding keypoint coordinates and confidence scores. During training, SAR applies Laplacian kernel function and normalization to convert the outputs into corresponding score and calculate the unified objective to train the whole model. During inference, SAR selects regressed outputs with large confidence score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.471, + 0.456 + ], + "angle": 0, + "content": "where \\( f = \\mathcal{F}_{i,j} \\) is a visual feature on the feature map \\( \\mathbf{F} \\), \\( p = \\mathcal{P}_{i,j} \\) is the spatial location of this grid, \\( h, w \\) denotes the spatial size of \\( \\mathbf{F} \\). \\( \\mathcal{P} = \\{(i,j)\\}_{i=1\\dots h}^{j=1\\dots w} \\) is named as the spatial location prior, which is crucial for keypoint localization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.456, + 0.472, + 0.501 + ], + "angle": 0, + "content": "Conventional regression will apply a pooling on \\(\\mathbf{F}\\) to get a global feature \\(f^g\\), then adopt a regressor to obtain final localization results," + }, + { + "type": "equation", + "bbox": [ + 0.229, + 0.513, + 0.47, + 0.531 + ], + "angle": 0, + "content": "\\[\n\\mathcal {K} = \\mathcal {R} (f ^ {g}). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.47, + 0.572 + ], + "angle": 0, + "content": "A \\(\\ell_1\\) or \\(\\ell_2\\) loss is applied on the regressed output to train model, e.g., \\(\\mathcal{L} = \\ell_1(\\mathcal{K},\\mathcal{K}^*)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.573, + 0.47, + 0.722 + ], + "angle": 0, + "content": "The above paradigm has several drawbacks. First, pooling only preserves visual information \\( f^g \\) and discards the spatial location prior \\( \\mathcal{P} \\), making Eq. (3) hard to optimize. This pooling operation also makes regression sensitive to instance scale. Second, it is difficult to differentiate multiple keypoints of the same category only with \\( f^g \\), because those keypoints present similar visual appearances and different locations. Although extra operation such as box cropping can remedy this issue, it involves extra object detection process and can be sensitive to detection error." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.724, + 0.47, + 0.8 + ], + "angle": 0, + "content": "We present the Spatial-Aware Regression (SAR) method to integrate the spatial location prior \\(\\mathcal{P}\\) into regression to pursue better localization performance. SAR adopts both spatial location prior \\(\\mathcal{P}\\) and visual feature \\(f^g\\) or \\(\\mathcal{F}\\) to perform localization, which can be denoted as," + }, + { + "type": "equation", + "bbox": [ + 0.2, + 0.812, + 0.47, + 0.83 + ], + "angle": 0, + "content": "\\[\n\\mathcal {K} = \\operatorname {S A R} (\\mathcal {P}, f ^ {g} | \\mathcal {F}). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "SAR shares all the merits of regression-based methods, which are efficient and robust to quantization error. Benefited by the spatial location prior, SAR is easier to optimize and achieves superior keypoint localization performance. It" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.393, + 0.895, + 0.469 + ], + "angle": 0, + "content": "also works well in multi-keypoints localization tasks to detect arbitrary number of keypoints from an input image. All these make SAR a better and robust keypoint localization method. In the following we will present the detailed implementation of SAR." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.482, + 0.734, + 0.499 + ], + "angle": 0, + "content": "3.2. Spatial-Aware Regression" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.892, + 0.643 + ], + "angle": 0, + "content": "Given the spatial location prior \\(\\mathcal{P}\\) and visual feature \\(\\mathcal{F}\\) or \\(f^g\\), SAR aims to locate the target location \\(\\kappa^{*}\\). We first consider the single keypoint localization that only one target exists in \\(\\mathcal{I}\\). Multiple keypoints localizations can be estimated by repeating the same process for each target in the input image. The core components of SAR are spatial-aware regressor to generate multiple outputs and spatial-aware selector to select the optimal output, respectively. Both components are jointly optimized by a unified training objective." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.718 + ], + "angle": 0, + "content": "Spatial-aware regressor aims to get the target location by regressing the coordinates from each grid in \\(\\mathcal{P}\\). To relieve the difficulty of direct regression, we introduce the spatial location prior in original \\(\\mathbf{F}\\) into regression process, which can be denoted as," + }, + { + "type": "equation", + "bbox": [ + 0.633, + 0.733, + 0.892, + 0.751 + ], + "angle": 0, + "content": "\\[\n\\mathcal {K} _ {t} = \\mathcal {R} \\left(f _ {t}\\right) + p _ {t}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.892, + 0.854 + ], + "angle": 0, + "content": "where \\( f_{t} \\) denotes the visual feature of \\( t \\)-th grid and \\( p_t \\) is its location prior. \\( \\mathcal{K}_t \\) is the regressed output by \\( t \\)-th grid. \\( f_{t} \\) can be obtained by directly taking the feature at corresponding location of \\( \\mathcal{F}_t \\). It can also be generated from the pooled feature \\( f^g \\) with a grid-wise FC layer, which produces a comparable performance as shown in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Compared with Eq. (3), Eq. (5) involves more detailed feature grids and each grid has different spatial location prior \\( p_t \\) to regress the target. Intuitively, for some grids" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "626" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.166 + ], + "angle": 0, + "content": "near the target \\(\\kappa^{*}\\), they will produce more reliable predictions, thus relieving the difficulty of direct regression in Eq. (3). As each grid generates a prediction, we further propose spatial-aware selector to handle duplicate predictions and select the accurate one." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.169, + 0.471, + 0.336 + ], + "angle": 0, + "content": "Spatial-aware selector. It is not reasonable to optimize every \\(\\{\\mathcal{K}_t\\}\\) w.r.t. the target, because not all grids are suited to predict a specific keypoint. Equally optimizing all \\(\\{\\mathcal{K}_t\\}\\) will cause the learning degenerate to conventional regression as the model tends to focus on learning hard samples for localization. To reduce the influence of inaccurate predictions and improve the training efficiency, we introduce a spatial-aware selector \\(S(\\cdot)\\) to automatically evaluate the importance of each grid in locating target \\(\\mathcal{K}^*\\). We predict a confidence score for each regressed output based on the feature \\(f_t\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.232, + 0.339, + 0.47, + 0.356 + ], + "angle": 0, + "content": "\\[\ns _ {t} = \\mathcal {S} \\left(f _ {t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.472 + ], + "angle": 0, + "content": "where \\( s_t \\) denotes the score of selecting the \\( t \\)-th output as the final result. Adopting a heuristic predefined strategy, e.g., selecting grids near the target, is unreasonable to optimize \\( S(\\cdot) \\) and may introduce optimization conflict with regressor. Instead, we jointly optimize the selector with regressor under a unified objective, letting model to select proper points by itself." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.623 + ], + "angle": 0, + "content": "Unified objective. The goal of SAR is to optimize \\(\\{\\mathcal{K}_t, s_t\\}\\) to accurately locate target \\(\\mathcal{K}^*\\). We propose a unified objective to jointly optimize the regressor and selector to avoid optimization contradiction in naive multi-task learning pipeline. We rely on regression to achieve the goal of localization and regard selection as an auxiliary task to reduce the difficulty of regression. This intuition leads to a unified objective function that aims to maximize the overall regression quality score weighted by the regression confidence, i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.198, + 0.625, + 0.469, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = - \\log \\sum w _ {t} \\cdot r _ {t}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.747 + ], + "angle": 0, + "content": "where \\(r_t \\in [0,1]\\) denotes the regression quality score of the \\(t\\)-th output and \\(w_t\\) denotes the corresponding regression weight. During training, we measure the regression quality score of each grid with the groundtruth \\(\\mathcal{K}^*\\) by a Laplacian kernel to convert the estimated location \\(\\mathcal{K}_t\\) into a score \\(r_t\\), that is" + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.749, + 0.469, + 0.768 + ], + "angle": 0, + "content": "\\[\nr _ {t} = e ^ {- \\lambda \\cdot \\left| \\mathcal {K} _ {t} - \\mathcal {K} ^ {*} \\right|}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.469, + 0.84 + ], + "angle": 0, + "content": "where \\(r_t \\in [0,1]\\) indicates the accuracy of the regressed output and \\(\\lambda\\) is the only hyperparameter of SAR. We set \\(\\lambda\\) to 16 for all experiments and normalize the coordinates by the feature map size." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The weight \\( w_{t} \\) generated by the \\( t \\)-th grid should be correlated with other grids. In other words, once some outputs are selected, the remaining should be suppressed. To achieve this goal, we adopt a two-step normalization opera" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.852, + 0.108 + ], + "angle": 0, + "content": "tion on the confidence score \\(\\{s_t\\}\\) to generate \\(w_{t}\\), i.e.," + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.117, + 0.892, + 0.148 + ], + "angle": 0, + "content": "\\[\nc _ {t} = \\sigma \\left(s _ {t}\\right), w _ {t} = \\frac {c _ {t}}{\\sum c _ {t}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.157, + 0.892, + 0.368 + ], + "angle": 0, + "content": "where \\(\\sigma(\\cdot)\\) denotes the sigmoid function to convert score into \\(c_{t} \\in [0,1]\\). Eq. (9) first normalizes each score into \\([0,1]\\) individually then utilizes element-sum to correlate them. Therefore, optimizing a high score \\(s_{t}\\) will decrease others. One advantage of the two-step normalization is the introduced extra score \\(c_{t}\\), which is not influenced by the target number and can be used to select outputs by a fixed threshold during inference. Another way to generate weight \\(w_{t}\\) is to apply softmax on \\(s_{t}\\). However, this one-step normalization cannot generate reliable high confidence score in multiple keypoints localization task during inference, because the value of generated \\(w_{t}\\) depends on the number of targets in the image. Therefore, it is hard to select final outputs by a fixed threshold \\(\\gamma\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.892, + 0.459 + ], + "angle": 0, + "content": "The unified objective weights each output by the confidence score and is adopted to maximize the overall regression quality. We then give a detailed analysis on Eq. (7) and show how it optimizes both coordinates and confidence scores with a unified loss function. Specifically, the goal of SAR is to minimize the following objective," + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.47, + 0.892, + 0.499 + ], + "angle": 0, + "content": "\\[\n\\underset {w _ {t}, r _ {t}} {\\arg \\min } - \\log \\sum w _ {t} \\cdot r _ {t}, \\text {s . t .} \\sum w _ {t} = 1. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.583 + ], + "angle": 0, + "content": "Due to the monotonic increase property of \\(\\log (\\cdot)\\) function, the optimal \\(w_{t},r_{t}\\) satisfy that \\(\\sum w_{i}\\cdot r_{t} = 1\\) .With the normalization in selection process, we also can get \\(\\sum w_{t} = 1\\) Therefore, optimizing Eq. (10) is equal to maximizing the regression score \\(r_t\\) and will result in two cases:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.584, + 0.892, + 0.688 + ], + "angle": 0, + "content": "- \\(\\forall t \\in [1, n], r_t \\to 1\\). This means that all grids can accurately regress the target, i.e., \\(\\mathcal{K}_t = \\mathcal{K}^*\\). In this case, \\(w_t\\) is not important because we can select any output as final result. However, this case rarely happens, especially for multi-keypoints localization task where the same regressed output \\(\\mathcal{K}_t\\) will be used to compute \\(r_t\\) for different groundtruth \\(\\mathcal{K}^*\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.689, + 0.892, + 0.809 + ], + "angle": 0, + "content": "- \\(\\exists t \\in [1, n], r_t \\to 1, \\forall s \\in [1, n] \\setminus t, w_s \\to 0\\). This means that some grids can accurately regress the target location \\((r_t \\to 1)\\). Meanwhile, the model tends to output low confidence scores \\(w_s \\to 0\\) to relieve the influence of inaccurate regression outputs. This case effectively leverages spatial location priors at some grids to generate accurate predictions, which are hence selected by the selector as final results." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.584, + 0.892, + 0.809 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.871 + ], + "angle": 0, + "content": "The above analysis shows that, our proposed training objective trains regressor and selector to boost the accuracy of keypoint localization. It also relieves need of careful multi-task design and hyperparameter tuning in different tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Inference. Similar to regression-based methods, SAR only needs a simple decoding process for inference. It first" + }, + { + "type": "page_number", + "bbox": [ + 0.486, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "627" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.182, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.091, + 0.283, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.091, + 0.383, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.091, + 0.489, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.49, + 0.091, + 0.591, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.091, + 0.689, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.091, + 0.788, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.79, + 0.091, + 0.89, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.193, + 0.182, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.113, + 0.291, + 0.151, + 0.304 + ], + "angle": 0, + "content": "target" + }, + { + "type": "image", + "bbox": [ + 0.184, + 0.193, + 0.282, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.291, + 0.262, + 0.304 + ], + "angle": 0, + "content": "heatmap" + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.193, + 0.383, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.284, + 0.291, + 0.385, + 0.304 + ], + "angle": 0, + "content": "confidence map" + }, + { + "type": "image", + "bbox": [ + 0.385, + 0.193, + 0.488, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.419, + 0.291, + 0.453, + 0.304 + ], + "angle": 0, + "content": "SAR" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.193, + 0.591, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.517, + 0.291, + 0.557, + 0.304 + ], + "angle": 0, + "content": "target" + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.193, + 0.688, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.61, + 0.291, + 0.666, + 0.304 + ], + "angle": 0, + "content": "heatmap" + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.193, + 0.787, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.291, + 0.792, + 0.304 + ], + "angle": 0, + "content": "confidence map" + }, + { + "type": "image", + "bbox": [ + 0.789, + 0.193, + 0.89, + 0.29 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.824, + 0.291, + 0.858, + 0.304 + ], + "angle": 0, + "content": "SAR" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.315, + 0.894, + 0.345 + ], + "angle": 0, + "content": "Figure 3. Visualization of heatmap [29] and confidence score map predicted by SAR in single/multi-keypoint localization. Target keypoints are denoted by star. SAR can locate keypoints that are out of range of the image and effectively avoids missed detection in crowded scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.47, + 0.406 + ], + "angle": 0, + "content": "forwards input to get the regressed output \\(\\{\\mathcal{K}_t\\}\\) and confidence score \\(\\{c_t\\}\\). It then selects the top \\(m\\) predictions with scores larger than \\(\\gamma\\) as the final result," + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.417, + 0.469, + 0.441 + ], + "angle": 0, + "content": "\\[\n\\{\\mathcal {K} \\} = \\left\\{\\mathcal {K} _ {t} \\right\\} _ {t \\in \\Delta}, \\Delta = \\underset {t} {\\operatorname {t o p}} (m, \\{c _ {t} \\geq \\gamma \\}). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.47, + 0.59 + ], + "angle": 0, + "content": "The value \\( m \\) is decided by different tasks, e.g., in top-down task we set \\( m = 1 \\) and in bottom-up task we set \\( m = 30 \\). Compared with previous heatmap-based methods, SAR does not require complex post-processing operation like shifting [29] or DARK [33] and can be implemented on GPU parallelly. It also works well on low-resolution feature maps, thus is more efficient. SAR is also faster than previous detection-based methods that adopt a Hough voting [18] or accumulation operation [8]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.6, + 0.203, + 0.615 + ], + "angle": 0, + "content": "3.3. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.47, + 0.764 + ], + "angle": 0, + "content": "Comparison to regression. SAR can be regarded as a generalized regression to process feature map. It degenerates to conventional regression when the size of feature map is \\( 1 \\times 1 \\). SAR extends the regression-based method by enhancing its performance and capability in handling multiple keypoint localization by exploring the spatial prior. SAR shares all merits of regression, e.g., low computation and storage complexity and produces a continuous output to relieve the quantization error." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Comparison to heatmap. SAR does not suffer from the quantization error in heatmap and removes the necessity of complex post-processing operation. SAR also differs from methods that combines heatmap with offset regression in both motivation and implementation. Those methods treat heatmap generation and offset regression with equal importance, and their performance is limited by the quality of heatmap. SAR does not assume fixed anchor point (e.g., person center) for regression, thus is general and robust to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.359, + 0.892, + 0.389 + ], + "angle": 0, + "content": "occlusion and truncation. This property enables SAR to locate keypoints out of input image as shown in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.39, + 0.893, + 0.496 + ], + "angle": 0, + "content": "Visualization. In Fig. 3, we visualize the confidence score map predicted by SAR and heatmap generated by [29]. Compared with heatmap, SAR is more effective in locating multiple keypoints and is more robust to crowded scenes, e.g., keypoints missed by the heatmap can be reliably detected by SAR. More extensive experiment and visualization results will be presented in following section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.51, + 0.633, + 0.527 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.732 + ], + "angle": 0, + "content": "In this section we validate the effectiveness of the proposed SAR on various keypoint localization tasks. We first test SAR on the widely studied 2D human pose estimation task to demonstrate its basic keypoint localization ability. Moreover, we further verify SAR is more general than conventional regression in three aspects, i.e., generalization to various type of keypoints on whole-body pose estimation task, generalization to arbitrary number of keypoints on multi-person pose estimation task and generalization to 3D keypoint localization on 3D human pose estimation task. Descriptions of datasets, evaluation metrics, detailed implementation of experiments and qualitative results are provided in supplemental material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.742, + 0.749, + 0.756 + ], + "angle": 0, + "content": "4.1.2D Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.903 + ], + "angle": 0, + "content": "2D human pose estimation is a classical localization task that aims to locate the human body keypoints such as knee or shoulder and researchers have proposed many methods to boost its performance. We first conduct experiments on this task to verify the effectiveness of the proposed method, including commonly used large-scale in-the-wild benchmarks COCO Keypoint [14] and MPII [25]. Following previous works, we report the OKS-based AP and PCKh@0.5/0.1 for COCO Keypoint and MPII evaluation respectively. Ex" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "628" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.47, + 0.221 + ], + "angle": 0, + "content": "
MethodGFLOPsDeconvsAP\\( AP^{50} \\)\\( AP^{75} \\)Kpt.Error(px)
Regression4.053.882.457.78.5
RLE4.069.689.376.07.8
Heatmap9.7✓70.791.277.67.6
Heatmap+Offset9.7✓70.991.377.87.6
SAR4.071.391.579.17.3
SAR9.7✓72.592.379.97.1
SAR (\\( f^g+FC \\))5.371.191.478.67.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.225, + 0.47, + 0.253 + ], + "angle": 0, + "content": "Table 1. Comparison with baselines on COCO Keypoint val set based on SimplePose [29]. Input size is \\(256 \\times 192\\)." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.262, + 0.47, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.4, + 0.468, + 0.415 + ], + "angle": 0, + "content": "Figure 4. Comparison with baselines under different output stride." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.445, + 0.447 + ], + "angle": 0, + "content": "periments on MPII are shown in supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Comparison with baselines. We first evaluate the proposed SAR with two types of commonly used baselines under the same setting. Experiments are conducted based on SimplePose [29], ResNet-50 [4] is adopted as the backbone. The results are summarized in Table 1. Compared with conventional regression that adopts pooled feature to regress target, SAR obtains superior performance without carefully designed loss or modules. It improves the regression baseline from 53.8 to 72.5. SAR is also better than heatmap-based methods that also utilize the spatial location prior to locate target. We also compare a simple multi-task method that also combine heatmap and regression, which is denoted as heatmap+offset. It can be observed that simply combining two tasks cannot get better performance because it introduces contradiction and more hyperparameters into training, and their performance is also limited by heatmap. We also show that the improvement of SAR mainly comes from the spatial location prior \\(\\mathcal{P}\\), rather than the visual feature \\(\\mathcal{F}\\). We keep the same input \\(f^g\\) of SAR and conventional regression, thus the only difference is the introduced location prior \\(\\mathcal{P}\\), which is denoted as \\(f^g +\\mathrm{FC}\\). \\(f^g +\\mathrm{FC}\\) explicitly compensates the missed spatial information in \\(f^g\\) and obtains 71.1 AP, which is higher than most baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Analysis on spatial size. SAR shares the merits of regression that is free of quantization error, we conduct experiments on various network output strides and input sizes to demonstrate the superior merits of the proposed SAR. In Fig. 4 we investigate the effect of different output stride to localization performance. We can observe that heatmap-based methods are affected by the output stride greatly due" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.089, + 0.885, + 0.273 + ], + "angle": 0, + "content": "
MethodInput sizeAP\\( AP^{50} \\)\\( AP^{75} \\)AR
Regression64×6422.755.014.637.5
Heatmap64×6433.270.626.840.2
SimCC [13]64×6437.571.934.743.1
SAR64×6439.274.936.345.6
Regression128×12843.175.245.257.9
Heatmap128×12860.087.868.165.0
SimCC [13]128×12861.987.868.766.3
SAR128×12862.587.870.467.4
Regression256×19253.882.457.767.6
Heatmap256×19270.791.277.674.3
SimCC [13]256×19271.291.278.774.9
SAR256×19272.592.379.976.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.511, + 0.277, + 0.88, + 0.291 + ], + "angle": 0, + "content": "Table 2. Comparison with baselines under different input size." + }, + { + "type": "image", + "bbox": [ + 0.514, + 0.294, + 0.88, + 0.511 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.522, + 0.894, + 0.565 + ], + "angle": 0, + "content": "Figure 5. Illustration of sampled keypoint localization results of (Top) 2D human pose estimation, (Middle) whole-body pose estimation, and (Bottom) 3D human pose estimation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.578, + 0.892, + 0.729 + ], + "angle": 0, + "content": "to the quantization error in low resolution heatmap. However, SAR obtains stable performance on various output strides and is constantly superior to heatmap-based methods. Therefore, SAR can be integrated to different backbone without any modification. We also test SAR with other methods on different input size to show its robustness to different input resolution. The results are shown in Table 2. SAR can handle different input size well and achieves superior performance, e.g., higher than previous SimCC [13] under the same setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.892, + 0.806 + ], + "angle": 0, + "content": "Comparison with other methods. Finally, we give a comprehensive comparison with other methods on COCO Keypoint test-dev set. Results are shown in Table 3. Equipped with different backbones, SAR outperforms previous methods and achieves superior performance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.76, + 0.832 + ], + "angle": 0, + "content": "4.2. Whole-Body Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We further verify the generalization of the proposed SAR to other type of keypoints on whole-body pose estimation task, which aims to locate keypoints of human body, foot, face and hand. Compared with previous task that only focuses" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "629" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.89, + 0.263 + ], + "angle": 0, + "content": "
MethodBackboneInput sizeAP\\( AP^{50} \\)\\( AP^{75} \\)\\( AP^M \\)\\( AP^L \\)AR
Heatmap-based
SimplePose [29]ResNet-50384×28871.591.178.767.878.076.9
HRNet [21]HRNet-W48384×28875.592.583.371.981.580.5
SimCC [13]HRNet-W48384×28876.092.483.572.581.981.1
Regression-based
DeepPose [25]ResNet-152256×19259.387.666.756.864.9-
Integral Pose [23]ResNet-101256×25667.888.274.863.974.0-
RLE [10]HRNet-W48384×28875.792.382.972.381.3-
Ours (SAR)ResNet-50384×28873.591.980.969.679.778.8
Ours (SAR)HRNet-W48384×28876.392.583.672.682.481.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.253, + 0.267, + 0.715, + 0.281 + ], + "angle": 0, + "content": "Table 3. Comparison with other methods on COCO Keypoint test-dev set." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.288, + 0.891, + 0.504 + ], + "angle": 0, + "content": "
MethodInput sizeBackbonebodyfootfacehandwhole-body
APARAPARAPARAPARAPAR
Baselines
Heatmap [29]256×192ResNet-5065.273.861.574.960.671.546.058.452.163.3
Heatmap [29]256×192HRNet-W4870.177.667.578.765.674.353.563.957.968.1
SAR256×192ResNet-5067.374.961.575.283.288.748.360.859.168.0
SAR256×192HRNet-W4871.078.969.181.888.192.358.469.265.174.0
SoTA methods
DeepPose [25]384×288ResNet-10144.456.836.853.749.366.323.541.033.548.4
SimplePose [29]384×288ResNet-5066.674.763.576.373.281.253.764.757.367.1
HRNet [21]384×288HRNet-W4872.279.169.680.177.683.458.767.863.271.7
ZoomNet [7]384×288HR32+HR1874.581.060.970.888.092.457.973.463.074.2
ZoomNAS [30]384×288-74.080.761.771.888.993.062.574.065.474.4
Ours (SAR)384×288HRNet-W4871.279.669.382.690.393.361.372.166.675.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.254, + 0.509, + 0.713, + 0.523 + ], + "angle": 0, + "content": "Table 4. Comparison with other methods on COCO Whole-Body benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.64 + ], + "angle": 0, + "content": "on human body, whole-body pose estimation is more challenging due to the large scale variance of different type of keypoints. Therefore, this task can be used to test the ability of localization method on handling scale variance. Following previous works, we conduct experiments on large-scale in-the-wild benchmark COCO Whole-Body [7] and report the OKS-based AP on each subset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.471, + 0.839 + ], + "angle": 0, + "content": "Table 4 shows results. We first compare SAR with heatmap baseline using ResNet-50 and HRNet-W48 as backbone. SAR outperforms heatmap by a large margin, especially on small scale keypoints of face and hand. This demonstrates the benefit of continuous output of SAR, which is free of quantization error in heatmap. We also compare SAR with top-down based methods SimplePose, HRNet, ZoomNet and ZoomNAS. We implement SAR with top-down HRNet under the same setting, and Table 4 shows that our method achieves the best performance on most subsets, without carefully designed multi-branch model in ZoomNet and ZoomNAS. It demonstrates that SAR can generalize to locate various types of keypoints." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.85, + 0.342, + 0.865 + ], + "angle": 0, + "content": "4.3. Multi-Person Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "One advantage of SAR is that it can be applied to multiple keypoints localization tasks, while most of previous meth" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.701 + ], + "angle": 0, + "content": "ods, e.g., regression-based methods and SimCC [13] cannot be used to locate multiple keypoints of the same type simultaneously. Multiple keypoints localization task such as multi-person pose estimation (MPPE) is common because it eliminates the assumption that only one instance exists in the input image in single-keypoint localization. Benefited by embedding spatial prior, the proposed method can be applied to MPPE tasks such as bottom-up MPPE and single-stage MPPE. Following previous works, we conduct experiments on COCO [14], OCHuman [34] and CrowdPose [9] and report OKS-based AP metrics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.703, + 0.892, + 0.794 + ], + "angle": 0, + "content": "For bottom-up MPPE, we adapt SAR with AE [17] to locate multiple keypoints simultaneously because it separately implements localization and grouping. For single-stage MPPE, we conduct experiments on two widely used methods, i.e., CenterNet [35] and DEKR [3], to locate multiple person center points." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.9 + ], + "angle": 0, + "content": "All experiments are conducted under the same setting. As shown in Table 5, SAR can successfully detect arbitrary number of keypoints and produce more reliable results than heatmap on all benchmarks. From Fig. 3 we can observe that SAR outputs higher confidence score for detected keypoints, which is important in MPPE because it avoids missed localization." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "630" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.894, + 0.251 + ], + "angle": 0, + "content": "
MethodCOCOOCHumanCrowdPose
APAPMAPLARAPAPMAPLARAPAPEAPMAPL
Bottom-up MPPE based on AE [17]
Heatmap48.444.154.854.1----46.759.946.636.7
SAR50.045.056.956.2----48.261.148.038.9
Single-stage Regression MPPE
CenterNet [35]57.650.568.463.134.115.236.269.360.968.961.751.7
+SAR60.352.671.164.739.615.540.571.562.269.863.053.7
DEKR [3]61.854.772.867.535.69.637.571.365.273.066.055.9
+SAR64.556.875.569.140.917.241.973.866.373.767.057.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.226, + 0.255, + 0.743, + 0.27 + ], + "angle": 0, + "content": "Table 5. Comparison with other methods on multi-person pose estimation benchmarks." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.276, + 0.896, + 0.475 + ], + "angle": 0, + "content": "
MethodsDir.Dis.EatGre.Phon.PosePur.SitSitD.Smo.Phot.WaitWalkWalkD.WalkP.Avg
Baselines
Regression46.553.547.946.953.346.448.964.364.653.154.247.540.953.445.251.7
RLE47.151.350.448.053.045.847.465.069.053.752.046.740.951.244.751.6
Integral Pose45.351.547.545.553.242.647.163.963.853.053.846.140.051.343.250.6
SAR-3D46.551.146.945.349.745.146.958.763.250.051.146.140.551.344.149.4
SAR-decouple42.249.546.844.852.242.543.860.765.150.752.644.737.850.041.648.9
SoTA methods
Sun [22]52.854.854.254.361.853.153.671.786.761.567.253.447.161.663.459.1
PoseNet [15]50.555.750.151.753.946.850.061.968.052.555.949.941.856.146.953.3
Sun [23]47.547.749.550.251.443.846.458.965.749.455.847.838.949.043.849.6
RLE [10]43.351.044.544.551.743.146.059.263.749.652.544.137.550.541.248.6
Ours (SAR)40.947.844.843.450.341.042.658.261.248.950.042.936.248.340.247.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.277, + 0.478, + 0.692, + 0.492 + ], + "angle": 0, + "content": "Table 6. Comparison with other methods on Human3.6M benchmark." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.508, + 0.416, + 0.523 + ], + "angle": 0, + "content": "4.4. Monocular 3D Human Pose Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.64 + ], + "angle": 0, + "content": "In this section we show that SAR can also generalize to perform 3D keypoint localization. We conduct experiments on Human3.6M [6], a large-scale indoor benchmark for 3D human pose estimation. For evaluation, MPJPE is reported to measure the error of the predicted keypoints and groundtruth in 3D space. Following [10], we use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.471, + 0.839 + ], + "angle": 0, + "content": "SAR for 3D keypoint. We propose two variants of SAR to locate 3D keypoint. The first is SAR-3D that generates 3D feature map \\(\\mathbf{F}_{3D} \\in \\mathbb{R}^{c \\times d \\times h \\times w}\\) from \\(\\mathbf{F}\\) to provide 3D spatial location prior to locate target, which is similar to Integral Pose [23] that also generates 3D heatmap. Benefited by the continuous output of SAR, a small sized \\(\\mathbf{F}_{3D}\\) can already produce promising results, e.g., \\(d = h = w = 16\\). For the second variant, we decouple the depth dimension from spatial dimension and estimate it with a separate localization branch, which is denoted as SAR-decouple. For \\(x, y\\) coordinates, we directly adopt 2D estimation pipeline. For \\(z\\) dimension, we convert the feature map \\(\\mathbf{F}\\) to a 1D feature map \\(\\mathbf{F}_z \\in \\mathbb{R}^{c \\times d}\\) to locate \\(z\\)-dim of keypoint, \\(d = 64\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Baselines. We first compare SAR with several 3D keypoint localization methods, including regression, RLE [10] and Integral Pose [29]. All experiments are conducted under the same setting. As shown in Table 6, both two variants" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.599 + ], + "angle": 0, + "content": "of SAR achieve superior 3D keypoint localization accuracy, which is lower than Integral Pose by 1.2 and 1.7 MPJPE. SAR-decouple achieves better performance than SAR-3D. We think that it is because SAR-decouple with large spatial size can generate more accurate localization results, which is consistent with experiments in Sec. 4.1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.892, + 0.677 + ], + "angle": 0, + "content": "Comparison with other methods. In Table 6 we also compare SAR with recent methods under the same setting, e.g., with flip test. We can observe that SAR reduces the MPJPE from 48.6 to 47.1, which is better than most image-based 3D human pose estimation methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.691, + 0.62, + 0.707 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.84 + ], + "angle": 0, + "content": "This work proposes a novel and effective regression method by integrating spatial location prior to relieve the difficulty of direct regression. We introduce spatial-aware regressor and selector with a unified objective to achieve spatial-aware regression. Comprehensive experiments on four different keypoint localization tasks and seven benchmarks demonstrate the promising effectiveness and generalization capability of the proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgement This work is supported in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award." + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.51, + 0.957 + ], + "angle": 0, + "content": "631" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Joao Carreira, Pulkit Agrawal, Katerina Fragkiadaki, and Jitendra Malik. Human pose estimation with iterative error feedback. 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Objects as points. arXiv preprint arXiv:1904.07850, 2019. 7, 8" + }, + { + "type": "page_number", + "bbox": [ + 0.487, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "633" + } + ] +] \ No newline at end of file diff --git a/2024/Spatial-Aware Regression for Keypoint Localization/fbd66afd-f4f6-451c-8993-88b8e434975c_origin.pdf b/2024/Spatial-Aware Regression for Keypoint Localization/fbd66afd-f4f6-451c-8993-88b8e434975c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..40a4df454adfe5e35fb2728de70db61c6d8bb843 --- /dev/null +++ b/2024/Spatial-Aware Regression for Keypoint Localization/fbd66afd-f4f6-451c-8993-88b8e434975c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:040834d49ba9a3e4b4b976ecd36607fa1304227979e668d45c5a24ddb0123f69 +size 1852024 diff --git a/2024/Spatial-Aware Regression for Keypoint Localization/full.md b/2024/Spatial-Aware Regression for Keypoint Localization/full.md new file mode 100644 index 0000000000000000000000000000000000000000..bb4bc66296dc84504fe4088529a7088e01b006ed --- /dev/null +++ b/2024/Spatial-Aware Regression for Keypoint Localization/full.md @@ -0,0 +1,327 @@ +# Spatial-Aware Regression for Keypoint Localization + +Dongkai Wang Shiliang Zhang National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University {dongkai.wang, slzhang.jdl}@pku.edu.cn + +# Abstract + +Regression-based keypoint localization shows advantages of high efficiency and better robustness to quantization errors than heatmap-based methods. However, existing regression-based methods discard the spatial location prior in input image with a global pooling, leading to inferior accuracy and are limited to single instance localization tasks. We study the regression-based keypoint localization from a new perspective by leveraging the spatial location prior. Instead of regressing on the pooled feature, the proposed Spatial-Aware Regression (SAR) maintains the spatial location map and outputs spatial coordinates and confidence score for each grid, which are optimized with a unified objective. Benefited by the location prior, these spatial-aware outputs can be efficiently optimized, resulting in better localization performance. Moreover, incorporating spatial prior makes SAR more general and can be applied into various keypoint localization tasks. We test the proposed method in 4 keypoint localization tasks including single/multi-person 2D/3D pose estimation, and the whole-body pose estimation. Extensive experiments demonstrate its promising performance, e.g., consistently outperforming recent regressions-based methods $^{\dagger}$ . + +# 1. Introduction + +Keypoint localization aims to locate target keypoints from an input image and is a fundamental task in the field of computer vision. It has a wide range of applications in human pose estimation [21, 26-28] and facial landmark detection [19], et al. Existing methods for keypoint localization can be summarized into two categories: heatmap-based [21, 29, 31] and regression-based [10, 23, 25], respectively. Regression-based method directly adopts neural network to learn the mapping from input RGB image to keypoint coordinates. Heatmap-based method uses a probability map (also referred as heatmap) to encode the likelihood + +![](images/c8ae01dca51e5dab07fbc1a94ba2bcea04b867c7de1290155def847673b3f5e3.jpg) +Figure 1. Illustration of (Top) regression-based method, (Middle) standard heatmap-based method, and (Bottom) the proposed SAR for keypoint localization. + +of the target location and retrieves it by selecting location with the highest probability. + +As illustrated in Fig. 1, heatmap-based method selects pre-defined points on heatmaps as localization results, which are easy to optimize. However, low-resolution heatmap leads to high quantization error and high-resolution heatmap enlarges the computation and storage cost. Regression-based method is more efficient and robust to quantization error, but is hard to optimize and commonly achieve inferior performance. One reason is that conventional regression destroys the spatial location information of the feature map by a global pooling, thus cannot provide a good initialization for the following regression. This design also limits the application of regression to differentiate and locate multiple keypoints of the same type, e.g., multi-person pose estimation. + +This work is motivated to facilitate the regression-based localization by embedding spatial location prior into regression. Grids in the extracted feature map provide different starting points for regression, making them fitted to locate different keypoints. Regressing from different starting points also introduces duplicate predictions, and we do not know which grids produce the best localization results. Prior works [5, 18] assume the results of grids near the target location are accurate and select them via a separate classification branch. We argue that this heuristic design is not optimal in all cases, e.g., for occluded or truncated + +keypoints. Moreover, this multi-task learning pipeline introduces optimization inconsistency between classification and regression [2] and is sensitive to many hyperparameters. + +This work presents the Spatial-Aware Regression (SAR), a novel regression method that effectively utilizes the spatial location prior in input image to generate spatial-aware outputs and automatically select the best prediction. As shown in Fig. 1, SAR regresses coordinates on each grid to utilize its spatial location cues. Benefited by the prior, SAR is able to leverage better starting points. Selecting different starting points also helps to differentiate similar keypoints, making SAR applicable to more challenging tasks like multi-person pose estimation. + +SAR performs localization on a set of grids, which can be extracted by deep neural networks like CNN [4] or Vision Transformer [31]. To utilize the spatial location prior, SAR introduces a spatial-aware regressor to locate target locations based on spatial location of each grid. To handle duplicate predictions, we propose a spatial-aware selector to evaluate the quality of each regression as confidence score, and select the best prediction. The selector is jointly optimized with the regressor with a unified objective, leading to automatic regression and selection without heuristic design and complex hyperparameters. The introduced selector also depresses the influence of inaccurate predictions. SAR can work well on a low-resolution feature map, thus introduces marginal computational overheads and maintains similar efficiency with existing regression-based methods. + +SAR shares all merits of conventional regression and surpasses it in many aspects. We test its effectiveness on various keypoint localization tasks including single/multiperson 2D/3D pose estimation and whole-body pose estimation. Extensive experiments on 7 keypoint localization benchmarks demonstrate its superior performance in keypoint localization. For example, SAR obtains $72.5\%$ AP on COCO Keypoint dataset [14], which is higher than conventional regression and heatmap by $16.5\%$ and $1.8\%$ . SAR is robust to various input size and output stride, making it more general to deal with complex scenarios. SAR can also generalize well to detect various types of keypoints, arbitrary number of keypoints, as well as 2D/3D keypoints. + +# 2. Related Work + +Heatmap-based Keypoint Localization encodes keypoint location with a probability map, which is introduced by [24]. This type of methods estimates heatmaps and retrieves keypoint coordinates with a post-processing operation. Heatmap-based methods dominate the field of keypoint localization because heatmap is easy to learn with CNN. Pioneer works [16, 21, 29] design powerful CNN models to estimate high resolution heatmaps for human pose estimation and facial landmark detection, then the target keypoint can be simply obtained by a post-processing + +shifting [16, 33]. Due to the limitation of feature map size, some works [18] combine regression and add an offset branch to avoid quantization error. These methods improve the performance of heatmap. However, they rely on high resolution heatmap to locate keypoints, which results in high computation and storage cost. + +Regression-based Keypoint Localization directly learns the mapping from input image to output coordinates via a neural network, which is adopted by several classical methods [1, 25]. Researchers have proposed many methods to improve the performance of direct regression. The first kind of methods changes the way of regression. Integral pose regression [23] leverages the soft-argmax operation to regress keypoint locations by integrating a latent heatmap, which is proved to be superior to direct regression. Sampling-argmax [11] further improves soft-argmax by minimizing the error between samples drawing from a distribution with groundtruth, avoiding unconstrained probability map in previous method. Some work improves regression by proposing new loss functions. RLE [10] changes the predefined Gaussian or Laplace distribution in commonly used regression loss with a learned distribution via normalizing flow. Recently, researchers also try to improve direct regression by proposing more powerful backbones in Transformer architecture [31, 32], such as TokenPose [12] and PETR [20]. + +Although many regression-based works have been proposed, they ignore the spatial location prior, leading to inferior performance and cannot be applied to multiple keypoints localization tasks. This work shows that embedding the spatial prior into regression significantly improves its performance and generalization capability on various human keypoint localization tasks. A more detailed comparison with heatmap-based and existing regression-based methods is presented in the Sec. 3.3. + +# 3. Method + +# 3.1. Overview + +The goal of keypoint localization is to estimate the coordinates of target keypoints from input images, which can be denoted as, + +$$ +\left\{\mathcal {K} _ {s} \right\} _ {s = 1} ^ {m} = \operatorname {l o c a t e} (\mathcal {I}), \tag {1} +$$ + +where $\kappa_{s}$ denotes the $s$ -th keypoint coordinates and $m$ is the number of keypoints in this image, which is equal to 1 for single-keypoint localization and larger than 1 for multi-keypoint localization. + +Given an input image $\mathcal{I} \in \mathbb{R}^{3 \times H \times W}$ , existing methods first adopt a backbone $\Phi(\cdot)$ , e.g., CNN-based [21] or Transformer-based [31] network to extract feature map $\mathbf{F} \in \mathbb{R}^{c \times h \times w}$ , i.e., + +$$ +\mathbf {F} = \left\{\mathcal {F} _ {i, j}, \mathcal {P} _ {i, j} \right\} _ {i = 1 \dots h} ^ {j = 1 \dots w} = \Phi (\mathcal {I}), \tag {2} +$$ + +![](images/415297b848754acbacaffc5f1a3a3cf9e3b5b18de72fb958aa04ccafd97562ca.jpg) +Figure 2. The pipeline of the proposed Spatial-Aware Regression (SAR) for keypoint localization. SAR first adopts a backbone to extract a set of features, which are passed to spatial-aware regressor and selector to generate corresponding keypoint coordinates and confidence scores. During training, SAR applies Laplacian kernel function and normalization to convert the outputs into corresponding score and calculate the unified objective to train the whole model. During inference, SAR selects regressed outputs with large confidence score. + +where $f = \mathcal{F}_{i,j}$ is a visual feature on the feature map $\mathbf{F}$ , $p = \mathcal{P}_{i,j}$ is the spatial location of this grid, $h, w$ denotes the spatial size of $\mathbf{F}$ . $\mathcal{P} = \{(i,j)\}_{i=1\dots h}^{j=1\dots w}$ is named as the spatial location prior, which is crucial for keypoint localization. + +Conventional regression will apply a pooling on $\mathbf{F}$ to get a global feature $f^g$ , then adopt a regressor to obtain final localization results, + +$$ +\mathcal {K} = \mathcal {R} (f ^ {g}). \tag {3} +$$ + +A $\ell_1$ or $\ell_2$ loss is applied on the regressed output to train model, e.g., $\mathcal{L} = \ell_1(\mathcal{K},\mathcal{K}^*)$ . + +The above paradigm has several drawbacks. First, pooling only preserves visual information $f^g$ and discards the spatial location prior $\mathcal{P}$ , making Eq. (3) hard to optimize. This pooling operation also makes regression sensitive to instance scale. Second, it is difficult to differentiate multiple keypoints of the same category only with $f^g$ , because those keypoints present similar visual appearances and different locations. Although extra operation such as box cropping can remedy this issue, it involves extra object detection process and can be sensitive to detection error. + +We present the Spatial-Aware Regression (SAR) method to integrate the spatial location prior $\mathcal{P}$ into regression to pursue better localization performance. SAR adopts both spatial location prior $\mathcal{P}$ and visual feature $f^g$ or $\mathcal{F}$ to perform localization, which can be denoted as, + +$$ +\mathcal {K} = \operatorname {S A R} (\mathcal {P}, f ^ {g} | \mathcal {F}). \tag {4} +$$ + +SAR shares all the merits of regression-based methods, which are efficient and robust to quantization error. Benefited by the spatial location prior, SAR is easier to optimize and achieves superior keypoint localization performance. It + +also works well in multi-keypoints localization tasks to detect arbitrary number of keypoints from an input image. All these make SAR a better and robust keypoint localization method. In the following we will present the detailed implementation of SAR. + +# 3.2. Spatial-Aware Regression + +Given the spatial location prior $\mathcal{P}$ and visual feature $\mathcal{F}$ or $f^g$ , SAR aims to locate the target location $\kappa^{*}$ . We first consider the single keypoint localization that only one target exists in $\mathcal{I}$ . Multiple keypoints localizations can be estimated by repeating the same process for each target in the input image. The core components of SAR are spatial-aware regressor to generate multiple outputs and spatial-aware selector to select the optimal output, respectively. Both components are jointly optimized by a unified training objective. + +Spatial-aware regressor aims to get the target location by regressing the coordinates from each grid in $\mathcal{P}$ . To relieve the difficulty of direct regression, we introduce the spatial location prior in original $\mathbf{F}$ into regression process, which can be denoted as, + +$$ +\mathcal {K} _ {t} = \mathcal {R} \left(f _ {t}\right) + p _ {t}, \tag {5} +$$ + +where $f_{t}$ denotes the visual feature of $t$ -th grid and $p_t$ is its location prior. $\mathcal{K}_t$ is the regressed output by $t$ -th grid. $f_{t}$ can be obtained by directly taking the feature at corresponding location of $\mathcal{F}_t$ . It can also be generated from the pooled feature $f^g$ with a grid-wise FC layer, which produces a comparable performance as shown in our experiments. + +Compared with Eq. (3), Eq. (5) involves more detailed feature grids and each grid has different spatial location prior $p_t$ to regress the target. Intuitively, for some grids + +near the target $\kappa^{*}$ , they will produce more reliable predictions, thus relieving the difficulty of direct regression in Eq. (3). As each grid generates a prediction, we further propose spatial-aware selector to handle duplicate predictions and select the accurate one. + +Spatial-aware selector. It is not reasonable to optimize every $\{\mathcal{K}_t\}$ w.r.t. the target, because not all grids are suited to predict a specific keypoint. Equally optimizing all $\{\mathcal{K}_t\}$ will cause the learning degenerate to conventional regression as the model tends to focus on learning hard samples for localization. To reduce the influence of inaccurate predictions and improve the training efficiency, we introduce a spatial-aware selector $S(\cdot)$ to automatically evaluate the importance of each grid in locating target $\mathcal{K}^*$ . We predict a confidence score for each regressed output based on the feature $f_t$ , i.e., + +$$ +s _ {t} = \mathcal {S} \left(f _ {t}\right), \tag {6} +$$ + +where $s_t$ denotes the score of selecting the $t$ -th output as the final result. Adopting a heuristic predefined strategy, e.g., selecting grids near the target, is unreasonable to optimize $S(\cdot)$ and may introduce optimization conflict with regressor. Instead, we jointly optimize the selector with regressor under a unified objective, letting model to select proper points by itself. + +Unified objective. The goal of SAR is to optimize $\{\mathcal{K}_t, s_t\}$ to accurately locate target $\mathcal{K}^*$ . We propose a unified objective to jointly optimize the regressor and selector to avoid optimization contradiction in naive multi-task learning pipeline. We rely on regression to achieve the goal of localization and regard selection as an auxiliary task to reduce the difficulty of regression. This intuition leads to a unified objective function that aims to maximize the overall regression quality score weighted by the regression confidence, i.e., + +$$ +\mathcal {L} = - \log \sum w _ {t} \cdot r _ {t}, \tag {7} +$$ + +where $r_t \in [0,1]$ denotes the regression quality score of the $t$ -th output and $w_t$ denotes the corresponding regression weight. During training, we measure the regression quality score of each grid with the groundtruth $\mathcal{K}^*$ by a Laplacian kernel to convert the estimated location $\mathcal{K}_t$ into a score $r_t$ , that is + +$$ +r _ {t} = e ^ {- \lambda \cdot \left| \mathcal {K} _ {t} - \mathcal {K} ^ {*} \right|}, \tag {8} +$$ + +where $r_t \in [0,1]$ indicates the accuracy of the regressed output and $\lambda$ is the only hyperparameter of SAR. We set $\lambda$ to 16 for all experiments and normalize the coordinates by the feature map size. + +The weight $w_{t}$ generated by the $t$ -th grid should be correlated with other grids. In other words, once some outputs are selected, the remaining should be suppressed. To achieve this goal, we adopt a two-step normalization opera + +tion on the confidence score $\{s_t\}$ to generate $w_{t}$ , i.e., + +$$ +c _ {t} = \sigma \left(s _ {t}\right), w _ {t} = \frac {c _ {t}}{\sum c _ {t}}, \tag {9} +$$ + +where $\sigma(\cdot)$ denotes the sigmoid function to convert score into $c_{t} \in [0,1]$ . Eq. (9) first normalizes each score into $[0,1]$ individually then utilizes element-sum to correlate them. Therefore, optimizing a high score $s_{t}$ will decrease others. One advantage of the two-step normalization is the introduced extra score $c_{t}$ , which is not influenced by the target number and can be used to select outputs by a fixed threshold during inference. Another way to generate weight $w_{t}$ is to apply softmax on $s_{t}$ . However, this one-step normalization cannot generate reliable high confidence score in multiple keypoints localization task during inference, because the value of generated $w_{t}$ depends on the number of targets in the image. Therefore, it is hard to select final outputs by a fixed threshold $\gamma$ . + +The unified objective weights each output by the confidence score and is adopted to maximize the overall regression quality. We then give a detailed analysis on Eq. (7) and show how it optimizes both coordinates and confidence scores with a unified loss function. Specifically, the goal of SAR is to minimize the following objective, + +$$ +\underset {w _ {t}, r _ {t}} {\arg \min } - \log \sum w _ {t} \cdot r _ {t}, \text {s . t .} \sum w _ {t} = 1. \tag {10} +$$ + +Due to the monotonic increase property of $\log (\cdot)$ function, the optimal $w_{t},r_{t}$ satisfy that $\sum w_{i}\cdot r_{t} = 1$ .With the normalization in selection process, we also can get $\sum w_{t} = 1$ Therefore, optimizing Eq. (10) is equal to maximizing the regression score $r_t$ and will result in two cases: + +- $\forall t \in [1, n], r_t \to 1$ . This means that all grids can accurately regress the target, i.e., $\mathcal{K}_t = \mathcal{K}^*$ . In this case, $w_t$ is not important because we can select any output as final result. However, this case rarely happens, especially for multi-keypoints localization task where the same regressed output $\mathcal{K}_t$ will be used to compute $r_t$ for different groundtruth $\mathcal{K}^*$ . +- $\exists t \in [1, n], r_t \to 1, \forall s \in [1, n] \setminus t, w_s \to 0$ . This means that some grids can accurately regress the target location $(r_t \to 1)$ . Meanwhile, the model tends to output low confidence scores $w_s \to 0$ to relieve the influence of inaccurate regression outputs. This case effectively leverages spatial location priors at some grids to generate accurate predictions, which are hence selected by the selector as final results. + +The above analysis shows that, our proposed training objective trains regressor and selector to boost the accuracy of keypoint localization. It also relieves need of careful multi-task design and hyperparameter tuning in different tasks. + +Inference. Similar to regression-based methods, SAR only needs a simple decoding process for inference. It first + +![](images/9994d01257f3bd3104c48b174907e6b817cf56e500d0db3edb5839aa8082121b.jpg) + +![](images/51cb001ac1ca8b824f2951dbca7d2b0eff7c61452ecd88d3151d1324a1f30ef6.jpg) + +![](images/4b5e7de966348bc244f4f95d4fb8fa74b5f3f31fe871f99d9623abbd06edba64.jpg) + +![](images/5b7a0879d2e78c53e0f265e80d54a3ce2f9471d8c2ab476cfd22b87cec835b0c.jpg) + +![](images/396544b20cceef324d1a639a331c7b1489e1ef7c4d56d6f75a87960a8b06f4ab.jpg) + +![](images/8552e8d266fe0245c59dd46d911b29e901a40a9a40eda49bb660a3a7defef610.jpg) + +![](images/131f0aa9d4cee514722136cae1d72c452441a95f1707d7ceaca4eb6cb9d20e17.jpg) + +![](images/62bdaf4aac43cbdbee4b44c97c6b8f90ca466308a04f015614d29186b85c02c7.jpg) + +![](images/2b5b1b88d6d06e92b8707cf82666eb5b10823f1e97902eeb898e68baa7767976.jpg) +target +Figure 3. Visualization of heatmap [29] and confidence score map predicted by SAR in single/multi-keypoint localization. Target keypoints are denoted by star. SAR can locate keypoints that are out of range of the image and effectively avoids missed detection in crowded scenes. + +![](images/952b3dc64b268473fb707af78c36c4ae46a62358362a85cb0ad8f0086bdbd710.jpg) +heatmap + +![](images/a9d45ee07ec6e908883d85d0c77ff546bb8b9ead70243cdbee6be912df4eb3fb.jpg) +confidence map + +![](images/f3fa620eeaa79bcacf654d24c04eb44abc5ce7384522500d50266024646614f8.jpg) +SAR + +![](images/03554f1ff15e737839f5158d2318888cbf36c3d47c3a147967127041db6f453f.jpg) +target + +![](images/de3c41fdb3ba97acf45c81ff749f49937d64ceb584c34d36d67542dc6b28baa6.jpg) +heatmap + +![](images/102a14291289ecd2389013b868fb3e70c36086dec7bef8f0e92fd9c9917fe23c.jpg) +confidence map + +![](images/705593307b50f46fcaa415167fd216e70135630502c65b5df953cb78ff98d6f7.jpg) +SAR + +forwards input to get the regressed output $\{\mathcal{K}_t\}$ and confidence score $\{c_t\}$ . It then selects the top $m$ predictions with scores larger than $\gamma$ as the final result, + +$$ +\{\mathcal {K} \} = \left\{\mathcal {K} _ {t} \right\} _ {t \in \Delta}, \Delta = \underset {t} {\operatorname {t o p}} (m, \{c _ {t} \geq \gamma \}). \tag {11} +$$ + +The value $m$ is decided by different tasks, e.g., in top-down task we set $m = 1$ and in bottom-up task we set $m = 30$ . Compared with previous heatmap-based methods, SAR does not require complex post-processing operation like shifting [29] or DARK [33] and can be implemented on GPU parallelly. It also works well on low-resolution feature maps, thus is more efficient. SAR is also faster than previous detection-based methods that adopt a Hough voting [18] or accumulation operation [8]. + +# 3.3. Discussions + +Comparison to regression. SAR can be regarded as a generalized regression to process feature map. It degenerates to conventional regression when the size of feature map is $1 \times 1$ . SAR extends the regression-based method by enhancing its performance and capability in handling multiple keypoint localization by exploring the spatial prior. SAR shares all merits of regression, e.g., low computation and storage complexity and produces a continuous output to relieve the quantization error. + +Comparison to heatmap. SAR does not suffer from the quantization error in heatmap and removes the necessity of complex post-processing operation. SAR also differs from methods that combines heatmap with offset regression in both motivation and implementation. Those methods treat heatmap generation and offset regression with equal importance, and their performance is limited by the quality of heatmap. SAR does not assume fixed anchor point (e.g., person center) for regression, thus is general and robust to + +occlusion and truncation. This property enables SAR to locate keypoints out of input image as shown in Fig. 3. + +Visualization. In Fig. 3, we visualize the confidence score map predicted by SAR and heatmap generated by [29]. Compared with heatmap, SAR is more effective in locating multiple keypoints and is more robust to crowded scenes, e.g., keypoints missed by the heatmap can be reliably detected by SAR. More extensive experiment and visualization results will be presented in following section. + +# 4. Experiments + +In this section we validate the effectiveness of the proposed SAR on various keypoint localization tasks. We first test SAR on the widely studied 2D human pose estimation task to demonstrate its basic keypoint localization ability. Moreover, we further verify SAR is more general than conventional regression in three aspects, i.e., generalization to various type of keypoints on whole-body pose estimation task, generalization to arbitrary number of keypoints on multi-person pose estimation task and generalization to 3D keypoint localization on 3D human pose estimation task. Descriptions of datasets, evaluation metrics, detailed implementation of experiments and qualitative results are provided in supplemental material. + +# 4.1.2D Human Pose Estimation + +2D human pose estimation is a classical localization task that aims to locate the human body keypoints such as knee or shoulder and researchers have proposed many methods to boost its performance. We first conduct experiments on this task to verify the effectiveness of the proposed method, including commonly used large-scale in-the-wild benchmarks COCO Keypoint [14] and MPII [25]. Following previous works, we report the OKS-based AP and PCKh@0.5/0.1 for COCO Keypoint and MPII evaluation respectively. Ex + +
MethodGFLOPsDeconvsAP\( AP^{50} \)\( AP^{75} \)Kpt.Error(px)
Regression4.053.882.457.78.5
RLE4.069.689.376.07.8
Heatmap9.7✓70.791.277.67.6
Heatmap+Offset9.7✓70.991.377.87.6
SAR4.071.391.579.17.3
SAR9.7✓72.592.379.97.1
SAR (\( f^g+FC \))5.371.191.478.67.3
+ +![](images/2d1d6b3c021f5f787d584c5772382c50defa534907a056e482ab075bc254fe22.jpg) +Figure 4. Comparison with baselines under different output stride. + +periments on MPII are shown in supplemental material. + +Comparison with baselines. We first evaluate the proposed SAR with two types of commonly used baselines under the same setting. Experiments are conducted based on SimplePose [29], ResNet-50 [4] is adopted as the backbone. The results are summarized in Table 1. Compared with conventional regression that adopts pooled feature to regress target, SAR obtains superior performance without carefully designed loss or modules. It improves the regression baseline from 53.8 to 72.5. SAR is also better than heatmap-based methods that also utilize the spatial location prior to locate target. We also compare a simple multi-task method that also combine heatmap and regression, which is denoted as heatmap+offset. It can be observed that simply combining two tasks cannot get better performance because it introduces contradiction and more hyperparameters into training, and their performance is also limited by heatmap. We also show that the improvement of SAR mainly comes from the spatial location prior $\mathcal{P}$ , rather than the visual feature $\mathcal{F}$ . We keep the same input $f^g$ of SAR and conventional regression, thus the only difference is the introduced location prior $\mathcal{P}$ , which is denoted as $f^g +\mathrm{FC}$ . $f^g +\mathrm{FC}$ explicitly compensates the missed spatial information in $f^g$ and obtains 71.1 AP, which is higher than most baselines. + +Analysis on spatial size. SAR shares the merits of regression that is free of quantization error, we conduct experiments on various network output strides and input sizes to demonstrate the superior merits of the proposed SAR. In Fig. 4 we investigate the effect of different output stride to localization performance. We can observe that heatmap-based methods are affected by the output stride greatly due + +Table 1. Comparison with baselines on COCO Keypoint val set based on SimplePose [29]. Input size is $256 \times 192$ . + +
MethodInput sizeAP\( AP^{50} \)\( AP^{75} \)AR
Regression64×6422.755.014.637.5
Heatmap64×6433.270.626.840.2
SimCC [13]64×6437.571.934.743.1
SAR64×6439.274.936.345.6
Regression128×12843.175.245.257.9
Heatmap128×12860.087.868.165.0
SimCC [13]128×12861.987.868.766.3
SAR128×12862.587.870.467.4
Regression256×19253.882.457.767.6
Heatmap256×19270.791.277.674.3
SimCC [13]256×19271.291.278.774.9
SAR256×19272.592.379.976.1
+ +Table 2. Comparison with baselines under different input size. + +![](images/a46291a5a21d8d71f33e966d890323cc563d7374cf9c9dd82fe73302a4d00ee2.jpg) +Figure 5. Illustration of sampled keypoint localization results of (Top) 2D human pose estimation, (Middle) whole-body pose estimation, and (Bottom) 3D human pose estimation. + +to the quantization error in low resolution heatmap. However, SAR obtains stable performance on various output strides and is constantly superior to heatmap-based methods. Therefore, SAR can be integrated to different backbone without any modification. We also test SAR with other methods on different input size to show its robustness to different input resolution. The results are shown in Table 2. SAR can handle different input size well and achieves superior performance, e.g., higher than previous SimCC [13] under the same setting. + +Comparison with other methods. Finally, we give a comprehensive comparison with other methods on COCO Keypoint test-dev set. Results are shown in Table 3. Equipped with different backbones, SAR outperforms previous methods and achieves superior performance. + +# 4.2. Whole-Body Pose Estimation + +We further verify the generalization of the proposed SAR to other type of keypoints on whole-body pose estimation task, which aims to locate keypoints of human body, foot, face and hand. Compared with previous task that only focuses + +
MethodBackboneInput sizeAP\( AP^{50} \)\( AP^{75} \)\( AP^M \)\( AP^L \)AR
Heatmap-based
SimplePose [29]ResNet-50384×28871.591.178.767.878.076.9
HRNet [21]HRNet-W48384×28875.592.583.371.981.580.5
SimCC [13]HRNet-W48384×28876.092.483.572.581.981.1
Regression-based
DeepPose [25]ResNet-152256×19259.387.666.756.864.9-
Integral Pose [23]ResNet-101256×25667.888.274.863.974.0-
RLE [10]HRNet-W48384×28875.792.382.972.381.3-
Ours (SAR)ResNet-50384×28873.591.980.969.679.778.8
Ours (SAR)HRNet-W48384×28876.392.583.672.682.481.2
+ +Table 3. Comparison with other methods on COCO Keypoint test-dev set. + +
MethodInput sizeBackbonebodyfootfacehandwhole-body
APARAPARAPARAPARAPAR
Baselines
Heatmap [29]256×192ResNet-5065.273.861.574.960.671.546.058.452.163.3
Heatmap [29]256×192HRNet-W4870.177.667.578.765.674.353.563.957.968.1
SAR256×192ResNet-5067.374.961.575.283.288.748.360.859.168.0
SAR256×192HRNet-W4871.078.969.181.888.192.358.469.265.174.0
SoTA methods
DeepPose [25]384×288ResNet-10144.456.836.853.749.366.323.541.033.548.4
SimplePose [29]384×288ResNet-5066.674.763.576.373.281.253.764.757.367.1
HRNet [21]384×288HRNet-W4872.279.169.680.177.683.458.767.863.271.7
ZoomNet [7]384×288HR32+HR1874.581.060.970.888.092.457.973.463.074.2
ZoomNAS [30]384×288-74.080.761.771.888.993.062.574.065.474.4
Ours (SAR)384×288HRNet-W4871.279.669.382.690.393.361.372.166.675.6
+ +Table 4. Comparison with other methods on COCO Whole-Body benchmark. + +on human body, whole-body pose estimation is more challenging due to the large scale variance of different type of keypoints. Therefore, this task can be used to test the ability of localization method on handling scale variance. Following previous works, we conduct experiments on large-scale in-the-wild benchmark COCO Whole-Body [7] and report the OKS-based AP on each subset. + +Table 4 shows results. We first compare SAR with heatmap baseline using ResNet-50 and HRNet-W48 as backbone. SAR outperforms heatmap by a large margin, especially on small scale keypoints of face and hand. This demonstrates the benefit of continuous output of SAR, which is free of quantization error in heatmap. We also compare SAR with top-down based methods SimplePose, HRNet, ZoomNet and ZoomNAS. We implement SAR with top-down HRNet under the same setting, and Table 4 shows that our method achieves the best performance on most subsets, without carefully designed multi-branch model in ZoomNet and ZoomNAS. It demonstrates that SAR can generalize to locate various types of keypoints. + +# 4.3. Multi-Person Pose Estimation + +One advantage of SAR is that it can be applied to multiple keypoints localization tasks, while most of previous meth + +ods, e.g., regression-based methods and SimCC [13] cannot be used to locate multiple keypoints of the same type simultaneously. Multiple keypoints localization task such as multi-person pose estimation (MPPE) is common because it eliminates the assumption that only one instance exists in the input image in single-keypoint localization. Benefited by embedding spatial prior, the proposed method can be applied to MPPE tasks such as bottom-up MPPE and single-stage MPPE. Following previous works, we conduct experiments on COCO [14], OCHuman [34] and CrowdPose [9] and report OKS-based AP metrics. + +For bottom-up MPPE, we adapt SAR with AE [17] to locate multiple keypoints simultaneously because it separately implements localization and grouping. For single-stage MPPE, we conduct experiments on two widely used methods, i.e., CenterNet [35] and DEKR [3], to locate multiple person center points. + +All experiments are conducted under the same setting. As shown in Table 5, SAR can successfully detect arbitrary number of keypoints and produce more reliable results than heatmap on all benchmarks. From Fig. 3 we can observe that SAR outputs higher confidence score for detected keypoints, which is important in MPPE because it avoids missed localization. + +
MethodCOCOOCHumanCrowdPose
APAPMAPLARAPAPMAPLARAPAPEAPMAPL
Bottom-up MPPE based on AE [17]
Heatmap48.444.154.854.1----46.759.946.636.7
SAR50.045.056.956.2----48.261.148.038.9
Single-stage Regression MPPE
CenterNet [35]57.650.568.463.134.115.236.269.360.968.961.751.7
+SAR60.352.671.164.739.615.540.571.562.269.863.053.7
DEKR [3]61.854.772.867.535.69.637.571.365.273.066.055.9
+SAR64.556.875.569.140.917.241.973.866.373.767.057.6
+ +Table 5. Comparison with other methods on multi-person pose estimation benchmarks. + +
MethodsDir.Dis.EatGre.Phon.PosePur.SitSitD.Smo.Phot.WaitWalkWalkD.WalkP.Avg
Baselines
Regression46.553.547.946.953.346.448.964.364.653.154.247.540.953.445.251.7
RLE47.151.350.448.053.045.847.465.069.053.752.046.740.951.244.751.6
Integral Pose45.351.547.545.553.242.647.163.963.853.053.846.140.051.343.250.6
SAR-3D46.551.146.945.349.745.146.958.763.250.051.146.140.551.344.149.4
SAR-decouple42.249.546.844.852.242.543.860.765.150.752.644.737.850.041.648.9
SoTA methods
Sun [22]52.854.854.254.361.853.153.671.786.761.567.253.447.161.663.459.1
PoseNet [15]50.555.750.151.753.946.850.061.968.052.555.949.941.856.146.953.3
Sun [23]47.547.749.550.251.443.846.458.965.749.455.847.838.949.043.849.6
RLE [10]43.351.044.544.551.743.146.059.263.749.652.544.137.550.541.248.6
Ours (SAR)40.947.844.843.450.341.042.658.261.248.950.042.936.248.340.247.1
+ +Table 6. Comparison with other methods on Human3.6M benchmark. + +# 4.4. Monocular 3D Human Pose Estimation + +In this section we show that SAR can also generalize to perform 3D keypoint localization. We conduct experiments on Human3.6M [6], a large-scale indoor benchmark for 3D human pose estimation. For evaluation, MPJPE is reported to measure the error of the predicted keypoints and groundtruth in 3D space. Following [10], we use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation. + +SAR for 3D keypoint. We propose two variants of SAR to locate 3D keypoint. The first is SAR-3D that generates 3D feature map $\mathbf{F}_{3D} \in \mathbb{R}^{c \times d \times h \times w}$ from $\mathbf{F}$ to provide 3D spatial location prior to locate target, which is similar to Integral Pose [23] that also generates 3D heatmap. Benefited by the continuous output of SAR, a small sized $\mathbf{F}_{3D}$ can already produce promising results, e.g., $d = h = w = 16$ . For the second variant, we decouple the depth dimension from spatial dimension and estimate it with a separate localization branch, which is denoted as SAR-decouple. For $x, y$ coordinates, we directly adopt 2D estimation pipeline. For $z$ dimension, we convert the feature map $\mathbf{F}$ to a 1D feature map $\mathbf{F}_z \in \mathbb{R}^{c \times d}$ to locate $z$ -dim of keypoint, $d = 64$ . + +Baselines. We first compare SAR with several 3D keypoint localization methods, including regression, RLE [10] and Integral Pose [29]. All experiments are conducted under the same setting. As shown in Table 6, both two variants + +of SAR achieve superior 3D keypoint localization accuracy, which is lower than Integral Pose by 1.2 and 1.7 MPJPE. SAR-decouple achieves better performance than SAR-3D. We think that it is because SAR-decouple with large spatial size can generate more accurate localization results, which is consistent with experiments in Sec. 4.1. + +Comparison with other methods. In Table 6 we also compare SAR with recent methods under the same setting, e.g., with flip test. We can observe that SAR reduces the MPJPE from 48.6 to 47.1, which is better than most image-based 3D human pose estimation methods. + +# 5. Conclusion + +This work proposes a novel and effective regression method by integrating spatial location prior to relieve the difficulty of direct regression. We introduce spatial-aware regressor and selector with a unified objective to achieve spatial-aware regression. Comprehensive experiments on four different keypoint localization tasks and seven benchmarks demonstrate the promising effectiveness and generalization capability of the proposed method. + +Acknowledgement This work is supported in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award. + +# References + +[1] Joao Carreira, Pulkit Agrawal, Katerina Fragkiadaki, and Jitendra Malik. 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In ECCV, 2022. 6, 7 +[14] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dálár, and C Lawrence Zitnick. Microsoft coco: Common objects in context. In ECCV, 2014. 2, 5, 7 +[15] Gyeongsik Moon, Ju Yong Chang, and Kyoung Mu Lee. Camera distance-aware top-down approach for 3d multiperson pose estimation from a single rgb image. In ICCV, 2019. 8 +[16] Alejandro Newell, Kaiyu Yang, and Jia Deng. Stacked hourglass networks for human pose estimation. In ECCV, 2016. 2 +[17] Alejandro Newell, Zhiao Huang, and Jia Deng. Associative embedding: End-to-end learning for joint detection and grouping. In NeurIPS, 2017. 7, 8 + +[18] George Papandreou, Tyler Zhu, Nori Kanazawa, Alexander Toshev, Jonathan Tompson, Chris Bregler, and Kevin Murphy. Towards accurate multi-person pose estimation in the wild. In CVPR, 2017. 1, 2, 5 +[19] Christos Sagonas, Georgios Tzimiropoulos, Stefanos Zafeiriou, and Maja Pantic. 300 faces in-the-wild challenge: The first facial landmark localization challenge. In ICCVW, 2013. 1 +[20] Dahu Shi, Xing Wei, Liangqi Li, Ye Ren, and Wenming Tan. End-to-end multi-person pose estimation with transformers. In CVPR, 2022. 2 +[21] Ke Sun, Bin Xiao, Dong Liu, and Jingdong Wang. Deep high-resolution representation learning for human pose estimation. In CVPR, 2019. 1, 2, 7 +[22] Xiao Sun, Jiaxiang Shang, Shuang Liang, and Yichen Wei. Compositional human pose regression. In ICCV, 2017. 8 +[23] Xiao Sun, Bin Xiao, Fangyin Wei, Shuang Liang, and Yichen Wei. Integral human pose regression. In ECCV, 2018. 1, 2, 7, 8 +[24] Jonathan J. Tompson, Arjun Jain, Yann LeCun, and Christoph Bregler. Joint training of a convolutional network and a graphical model for human pose estimation. NeurIPS, 2014. 2 +[25] Alexander Toshev and Christian Szegedy. Deeppose: Human pose estimation via deep neural networks. In CVPR, 2014, 1, 2, 5, 7 +[26] Dongkai Wang and Shiliang Zhang. 3d human mesh recovery with sequentially global rotation estimation. In CVPR, 2023. 1 +[27] Dongkai Wang and Shiliang Zhang. Contextual instance decoupling for instance-level human analysis. IEEE TPAMI, 2023. +[28] Dongkai Wang, Shiliang Zhang, Yaowei Wang, Yonghong Tian, Tiejun Huang, and Wen Gao. Humvis: Human-centric visual analysis system. In ACM MM, 2023. 1 +[29] Bin Xiao, Haiping Wu, and Yichen Wei. Simple baselines for human pose estimation and tracking. In ECCV, 2018. 1, 2, 5, 6, 7, 8 +[30] Lumin Xu, Sheng Jin, Wentao Liu, Chen Qian, Wanli Ouyang, Ping Luo, and Xiaogang Wang. Zoomnas: searching for whole-body human pose estimation in the wild. IEEE TPAMI, 2022. 7 +[31] Yufei Xu, Jing Zhang, Qiming Zhang, and Dacheng Tao. Vitpose: Simple vision transformer baselines for human pose estimation. arXiv preprint arXiv:2204.12484, 2022. 1, 2 +[32] Shiyu Xuan, Qingpei Guo, Ming Yang, and Shiliang Zhang. Pink: Unveiling the power of referential comprehension for multi-modal llms. arXiv preprint arXiv:2310.00582, 2023. 2 +[33] Feng Zhang, Xiatian Zhu, Hanbin Dai, Mao Ye, and Ce Zhu. Distribution-aware coordinate representation for human pose estimation. In CVPR, 2020. 2, 5 +[34] Song-Hai Zhang, Ruilong Li, Xin Dong, Paul Rosin, Zixi Cai, Xi Han, Dingcheng Yang, Haozhi Huang, and Shi-Min Hu. Pose2seg: Detection free human instance segmentation. In CVPR, 2019. 7 + +[35] Xingyi Zhou, Dequan Wang, and Philipp Kähenbuhl. Objects as points. arXiv preprint arXiv:1904.07850, 2019. 7, 8 \ No newline at end of file diff --git a/2024/Spatial-Aware Regression for Keypoint Localization/images.zip b/2024/Spatial-Aware Regression for Keypoint Localization/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..a10d172d49bf2044773311bc35eaab0fed81da2b --- /dev/null +++ b/2024/Spatial-Aware Regression for Keypoint Localization/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e5ecc8b8273cf5b8768e80b6d2e4f05200009278f4f33770ed5e4219bece535f +size 683951 diff --git a/2024/Spatial-Aware Regression for Keypoint Localization/layout.json b/2024/Spatial-Aware Regression for Keypoint Localization/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..fc8e4eda0fd405766de4a2fafd9d13c11e8d563d --- /dev/null +++ b/2024/Spatial-Aware Regression for Keypoint Localization/layout.json @@ -0,0 +1,9064 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 136, + 103, + 457, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 103, + 457, + 121 + ], + "spans": [ + { + "bbox": [ + 136, + 103, + 457, + 121 + ], + "type": "text", + "content": "Spatial-Aware Regression for Keypoint Localization" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 138, + 144, + 455, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 138, + 144, + 455, + 200 + ], + "spans": [ + { + "bbox": [ + 138, + 144, + 455, + 200 + ], + "type": "text", + "content": "Dongkai Wang Shiliang Zhang National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University {dongkai.wang, slzhang.jdl}@pku.edu.cn" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "type": "text", + "content": "Regression-based keypoint localization shows advantages of high efficiency and better robustness to quantization errors than heatmap-based methods. However, existing regression-based methods discard the spatial location prior in input image with a global pooling, leading to inferior accuracy and are limited to single instance localization tasks. We study the regression-based keypoint localization from a new perspective by leveraging the spatial location prior. Instead of regressing on the pooled feature, the proposed Spatial-Aware Regression (SAR) maintains the spatial location map and outputs spatial coordinates and confidence score for each grid, which are optimized with a unified objective. Benefited by the location prior, these spatial-aware outputs can be efficiently optimized, resulting in better localization performance. Moreover, incorporating spatial prior makes SAR more general and can be applied into various keypoint localization tasks. We test the proposed method in 4 keypoint localization tasks including single/multi-person 2D/3D pose estimation, and the whole-body pose estimation. Extensive experiments demonstrate its promising performance, e.g., consistently outperforming recent regressions-based methods" + }, + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "type": "inline_equation", + "content": "^{\\dagger}" + }, + { + "bbox": [ + 46, + 252, + 290, + 515 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 540, + 128, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 128, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 128, + 553 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 561, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 561, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 561, + 287, + 693 + ], + "type": "text", + "content": "Keypoint localization aims to locate target keypoints from an input image and is a fundamental task in the field of computer vision. It has a wide range of applications in human pose estimation [21, 26-28] and facial landmark detection [19], et al. Existing methods for keypoint localization can be summarized into two categories: heatmap-based [21, 29, 31] and regression-based [10, 23, 25], respectively. Regression-based method directly adopts neural network to learn the mapping from input RGB image to keypoint coordinates. Heatmap-based method uses a probability map (also referred as heatmap) to encode the likelihood" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 307, + 226, + 547, + 331 + ], + "blocks": [ + { + "bbox": [ + 307, + 226, + 547, + 331 + ], + "lines": [ + { + "bbox": [ + 307, + 226, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 307, + 226, + 547, + 331 + ], + "type": "image", + "image_path": "c8ae01dca51e5dab07fbc1a94ba2bcea04b867c7de1290155def847673b3f5e3.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 339, + 547, + 372 + ], + "lines": [ + { + "bbox": [ + 305, + 339, + 547, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 339, + 547, + 372 + ], + "type": "text", + "content": "Figure 1. Illustration of (Top) regression-based method, (Middle) standard heatmap-based method, and (Bottom) the proposed SAR for keypoint localization." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 388, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 411 + ], + "type": "text", + "content": "of the target location and retrieves it by selecting location with the highest probability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 413, + 546, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 413, + 546, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 413, + 546, + 581 + ], + "type": "text", + "content": "As illustrated in Fig. 1, heatmap-based method selects pre-defined points on heatmaps as localization results, which are easy to optimize. However, low-resolution heatmap leads to high quantization error and high-resolution heatmap enlarges the computation and storage cost. Regression-based method is more efficient and robust to quantization error, but is hard to optimize and commonly achieve inferior performance. One reason is that conventional regression destroys the spatial location information of the feature map by a global pooling, thus cannot provide a good initialization for the following regression. This design also limits the application of regression to differentiate and locate multiple keypoints of the same type, e.g., multi-person pose estimation." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 714 + ], + "type": "text", + "content": "This work is motivated to facilitate the regression-based localization by embedding spatial location prior into regression. Grids in the extracted feature map provide different starting points for regression, making them fitted to locate different keypoints. Regressing from different starting points also introduces duplicate predictions, and we do not know which grids produce the best localization results. Prior works [5, 18] assume the results of grids near the target location are accurate and select them via a separate classification branch. We argue that this heuristic design is not optimal in all cases, e.g., for occluded or truncated" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 267, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 267, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 267, + 714 + ], + "type": "text", + "content": "†Project page: https://github.com/kenethwdk/SAR" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "624" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 108 + ], + "type": "text", + "content": "keypoints. Moreover, this multi-task learning pipeline introduces optimization inconsistency between classification and regression [2] and is sensitive to many hyperparameters." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 286, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 286, + 227 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 286, + 227 + ], + "type": "text", + "content": "This work presents the Spatial-Aware Regression (SAR), a novel regression method that effectively utilizes the spatial location prior in input image to generate spatial-aware outputs and automatically select the best prediction. As shown in Fig. 1, SAR regresses coordinates on each grid to utilize its spatial location cues. Benefited by the prior, SAR is able to leverage better starting points. Selecting different starting points also helps to differentiate similar keypoints, making SAR applicable to more challenging tasks like multi-person pose estimation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 228, + 286, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 286, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 286, + 407 + ], + "type": "text", + "content": "SAR performs localization on a set of grids, which can be extracted by deep neural networks like CNN [4] or Vision Transformer [31]. To utilize the spatial location prior, SAR introduces a spatial-aware regressor to locate target locations based on spatial location of each grid. To handle duplicate predictions, we propose a spatial-aware selector to evaluate the quality of each regression as confidence score, and select the best prediction. The selector is jointly optimized with the regressor with a unified objective, leading to automatic regression and selection without heuristic design and complex hyperparameters. The introduced selector also depresses the influence of inaccurate predictions. SAR can work well on a low-resolution feature map, thus introduces marginal computational overheads and maintains similar efficiency with existing regression-based methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "text", + "content": "SAR shares all merits of conventional regression and surpasses it in many aspects. We test its effectiveness on various keypoint localization tasks including single/multiperson 2D/3D pose estimation and whole-body pose estimation. Extensive experiments on 7 keypoint localization benchmarks demonstrate its superior performance in keypoint localization. For example, SAR obtains " + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "inline_equation", + "content": "72.5\\%" + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "text", + "content": " AP on COCO Keypoint dataset [14], which is higher than conventional regression and heatmap by " + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "inline_equation", + "content": "16.5\\%" + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "inline_equation", + "content": "1.8\\%" + }, + { + "bbox": [ + 46, + 407, + 286, + 562 + ], + "type": "text", + "content": ". SAR is robust to various input size and output stride, making it more general to deal with complex scenarios. SAR can also generalize well to detect various types of keypoints, arbitrary number of keypoints, as well as 2D/3D keypoints." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Heatmap-based Keypoint Localization encodes keypoint location with a probability map, which is introduced by [24]. This type of methods estimates heatmaps and retrieves keypoint coordinates with a post-processing operation. Heatmap-based methods dominate the field of keypoint localization because heatmap is easy to learn with CNN. Pioneer works [16, 21, 29] design powerful CNN models to estimate high resolution heatmaps for human pose estimation and facial landmark detection, then the target keypoint can be simply obtained by a post-processing" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "shifting [16, 33]. Due to the limitation of feature map size, some works [18] combine regression and add an offset branch to avoid quantization error. These methods improve the performance of heatmap. However, they rely on high resolution heatmap to locate keypoints, which results in high computation and storage cost." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 144, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 383 + ], + "type": "text", + "content": "Regression-based Keypoint Localization directly learns the mapping from input image to output coordinates via a neural network, which is adopted by several classical methods [1, 25]. Researchers have proposed many methods to improve the performance of direct regression. The first kind of methods changes the way of regression. Integral pose regression [23] leverages the soft-argmax operation to regress keypoint locations by integrating a latent heatmap, which is proved to be superior to direct regression. Sampling-argmax [11] further improves soft-argmax by minimizing the error between samples drawing from a distribution with groundtruth, avoiding unconstrained probability map in previous method. Some work improves regression by proposing new loss functions. RLE [10] changes the predefined Gaussian or Laplace distribution in commonly used regression loss with a learned distribution via normalizing flow. Recently, researchers also try to improve direct regression by proposing more powerful backbones in Transformer architecture [31, 32], such as TokenPose [12] and PETR [20]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 491 + ], + "type": "text", + "content": "Although many regression-based works have been proposed, they ignore the spatial location prior, leading to inferior performance and cannot be applied to multiple keypoints localization tasks. This work shows that embedding the spatial prior into regression significantly improves its performance and generalization capability on various human keypoint localization tasks. A more detailed comparison with heatmap-based and existing regression-based methods is presented in the Sec. 3.3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 502, + 361, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 361, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 361, + 514 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 521, + 373, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 373, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 373, + 533 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 540, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 574 + ], + "type": "text", + "content": "The goal of keypoint localization is to estimate the coordinates of target keypoints from input images, which can be denoted as," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 378, + 576, + 545, + 590 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 576, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 378, + 576, + 545, + 590 + ], + "type": "interline_equation", + "content": "\\left\\{\\mathcal {K} _ {s} \\right\\} _ {s = 1} ^ {m} = \\operatorname {l o c a t e} (\\mathcal {I}), \\tag {1}", + "image_path": "f264545f4fec5f4f064c787314e4d122423561333724a8364a923e434ca50513.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\kappa_{s}" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": "-th keypoint coordinates and " + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 595, + 545, + 643 + ], + "type": "text", + "content": " is the number of keypoints in this image, which is equal to 1 for single-keypoint localization and larger than 1 for multi-keypoint localization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "content": "Given an input image " + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "inline_equation", + "content": "\\mathcal{I} \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "content": ", existing methods first adopt a backbone " + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot)" + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "content": ", e.g., CNN-based [21] or Transformer-based [31] network to extract feature map " + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{c \\times h \\times w}" + }, + { + "bbox": [ + 304, + 643, + 545, + 690 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 358, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 358, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {F} = \\left\\{\\mathcal {F} _ {i, j}, \\mathcal {P} _ {i, j} \\right\\} _ {i = 1 \\dots h} ^ {j = 1 \\dots w} = \\Phi (\\mathcal {I}), \\tag {2}", + "image_path": "ff2ce694d4e2b3af87e721bfb05d543a45a1b90f897c9d170c4a4445df6d9265.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 297, + 749, + 312, + 757 + ], + "type": "text", + "content": "625" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 69, + 534, + 244 + ], + "blocks": [ + { + "bbox": [ + 61, + 69, + 534, + 244 + ], + "lines": [ + { + "bbox": [ + 61, + 69, + 534, + 244 + ], + "spans": [ + { + "bbox": [ + 61, + 69, + 534, + 244 + ], + "type": "image", + "image_path": "415297b848754acbacaffc5f1a3a3cf9e3b5b18de72fb958aa04ccafd97562ca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 254, + 547, + 301 + ], + "lines": [ + { + "bbox": [ + 46, + 254, + 547, + 301 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 547, + 301 + ], + "type": "text", + "content": "Figure 2. The pipeline of the proposed Spatial-Aware Regression (SAR) for keypoint localization. SAR first adopts a backbone to extract a set of features, which are passed to spatial-aware regressor and selector to generate corresponding keypoint coordinates and confidence scores. During training, SAR applies Laplacian kernel function and normalization to convert the outputs into corresponding score and calculate the unified objective to train the whole model. During inference, SAR selects regressed outputs with large confidence score." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "f = \\mathcal{F}_{i,j}" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": " is a visual feature on the feature map " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "p = \\mathcal{P}_{i,j}" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": " is the spatial location of this grid, " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "h, w" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": " denotes the spatial size of " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "inline_equation", + "content": "\\mathcal{P} = \\{(i,j)\\}_{i=1\\dots h}^{j=1\\dots w}" + }, + { + "bbox": [ + 46, + 311, + 288, + 361 + ], + "type": "text", + "content": " is named as the spatial location prior, which is crucial for keypoint localization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "type": "text", + "content": "Conventional regression will apply a pooling on " + }, + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "type": "text", + "content": " to get a global feature " + }, + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 46, + 361, + 288, + 396 + ], + "type": "text", + "content": ", then adopt a regressor to obtain final localization results," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 140, + 406, + 287, + 420 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 140, + 406, + 287, + 420 + ], + "spans": [ + { + "bbox": [ + 140, + 406, + 287, + 420 + ], + "type": "interline_equation", + "content": "\\mathcal {K} = \\mathcal {R} (f ^ {g}). \\tag {3}", + "image_path": "5b04805da0331e5e85bd5a43dcc2d806beaadd218e493d855625e11cf2517169.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "text", + "content": "A " + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "text", + "content": " loss is applied on the regressed output to train model, e.g., " + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{L} = \\ell_1(\\mathcal{K},\\mathcal{K}^*)" + }, + { + "bbox": [ + 46, + 429, + 287, + 453 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "text", + "content": "The above paradigm has several drawbacks. First, pooling only preserves visual information " + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "text", + "content": " and discards the spatial location prior " + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "text", + "content": ", making Eq. (3) hard to optimize. This pooling operation also makes regression sensitive to instance scale. Second, it is difficult to differentiate multiple keypoints of the same category only with " + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 46, + 453, + 287, + 571 + ], + "type": "text", + "content": ", because those keypoints present similar visual appearances and different locations. Although extra operation such as box cropping can remedy this issue, it involves extra object detection process and can be sensitive to detection error." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "text", + "content": "We present the Spatial-Aware Regression (SAR) method to integrate the spatial location prior " + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "text", + "content": " into regression to pursue better localization performance. SAR adopts both spatial location prior " + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "text", + "content": " and visual feature " + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 573, + 287, + 633 + ], + "type": "text", + "content": " to perform localization, which can be denoted as," + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 122, + 643, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 643, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 122, + 643, + 287, + 657 + ], + "type": "interline_equation", + "content": "\\mathcal {K} = \\operatorname {S A R} (\\mathcal {P}, f ^ {g} | \\mathcal {F}). \\tag {4}", + "image_path": "5a7dd0ff83b75c4901388c7255903b9eb36d3a12b2386839b2f8c434dc518474.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "SAR shares all the merits of regression-based methods, which are efficient and robust to quantization error. Benefited by the spatial location prior, SAR is easier to optimize and achieves superior keypoint localization performance. It" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 311, + 547, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 311, + 547, + 371 + ], + "spans": [ + { + "bbox": [ + 304, + 311, + 547, + 371 + ], + "type": "text", + "content": "also works well in multi-keypoints localization tasks to detect arbitrary number of keypoints from an input image. All these make SAR a better and robust keypoint localization method. In the following we will present the detailed implementation of SAR." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 381, + 449, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 381, + 449, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 381, + 449, + 395 + ], + "type": "text", + "content": "3.2. Spatial-Aware Regression" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "content": "Given the spatial location prior " + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "content": " and visual feature " + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "content": ", SAR aims to locate the target location " + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\kappa^{*}" + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "content": ". We first consider the single keypoint localization that only one target exists in " + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 304, + 400, + 545, + 509 + ], + "type": "text", + "content": ". Multiple keypoints localizations can be estimated by repeating the same process for each target in the input image. The core components of SAR are spatial-aware regressor to generate multiple outputs and spatial-aware selector to select the optimal output, respectively. Both components are jointly optimized by a unified training objective." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "type": "text", + "content": "Spatial-aware regressor aims to get the target location by regressing the coordinates from each grid in " + }, + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "type": "text", + "content": ". To relieve the difficulty of direct regression, we introduce the spatial location prior in original " + }, + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 304, + 510, + 545, + 568 + ], + "type": "text", + "content": " into regression process, which can be denoted as," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 387, + 580, + 545, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 387, + 580, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 387, + 580, + 545, + 594 + ], + "type": "interline_equation", + "content": "\\mathcal {K} _ {t} = \\mathcal {R} \\left(f _ {t}\\right) + p _ {t}, \\tag {5}", + "image_path": "1983153a852473d870adb70d0ece35692cd15b29087692b3dab6b9692eaf7cd6.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": " denotes the visual feature of " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "-th grid and " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": " is its location prior. " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_t" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": " is the regressed output by " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": "-th grid. " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": " can be obtained by directly taking the feature at corresponding location of " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_t" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": ". It can also be generated from the pooled feature " + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 304, + 605, + 545, + 676 + ], + "type": "text", + "content": " with a grid-wise FC layer, which produces a comparable performance as shown in our experiments." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "Compared with Eq. (3), Eq. (5) involves more detailed feature grids and each grid has different spatial location prior " + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "inline_equation", + "content": "p_t" + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": " to regress the target. Intuitively, for some grids" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "626" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": "near the target " + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "inline_equation", + "content": "\\kappa^{*}" + }, + { + "bbox": [ + 46, + 72, + 287, + 131 + ], + "type": "text", + "content": ", they will produce more reliable predictions, thus relieving the difficulty of direct regression in Eq. (3). As each grid generates a prediction, we further propose spatial-aware selector to handle duplicate predictions and select the accurate one." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "content": "Spatial-aware selector. It is not reasonable to optimize every " + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{K}_t\\}" + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "content": " w.r.t. the target, because not all grids are suited to predict a specific keypoint. Equally optimizing all " + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{K}_t\\}" + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "content": " will cause the learning degenerate to conventional regression as the model tends to focus on learning hard samples for localization. To reduce the influence of inaccurate predictions and improve the training efficiency, we introduce a spatial-aware selector " + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "content": " to automatically evaluate the importance of each grid in locating target " + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "inline_equation", + "content": "\\mathcal{K}^*" + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "content": ". We predict a confidence score for each regressed output based on the feature " + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "inline_equation", + "content": "f_t" + }, + { + "bbox": [ + 46, + 133, + 288, + 266 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 268, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 268, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 141, + 268, + 287, + 281 + ], + "type": "interline_equation", + "content": "s _ {t} = \\mathcal {S} \\left(f _ {t}\\right), \\tag {6}", + "image_path": "710e419711c744bf43c37c78ce84dc5c9475675cf3801a5f37d9d3fe6fd42482.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "inline_equation", + "content": "s_t" + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": " denotes the score of selecting the " + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": "-th output as the final result. Adopting a heuristic predefined strategy, e.g., selecting grids near the target, is unreasonable to optimize " + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "inline_equation", + "content": "S(\\cdot)" + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": " and may introduce optimization conflict with regressor. Instead, we jointly optimize the selector with regressor under a unified objective, letting model to select proper points by itself." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "type": "text", + "content": "Unified objective. The goal of SAR is to optimize " + }, + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{K}_t, s_t\\}" + }, + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "type": "text", + "content": " to accurately locate target " + }, + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{K}^*" + }, + { + "bbox": [ + 46, + 374, + 287, + 493 + ], + "type": "text", + "content": ". We propose a unified objective to jointly optimize the regressor and selector to avoid optimization contradiction in naive multi-task learning pipeline. We rely on regression to achieve the goal of localization and regard selection as an auxiliary task to reduce the difficulty of regression. This intuition leads to a unified objective function that aims to maximize the overall regression quality score weighted by the regression confidence, i.e.," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 121, + 495, + 287, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 495, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 121, + 495, + 287, + 512 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = - \\log \\sum w _ {t} \\cdot r _ {t}, \\tag {7}", + "image_path": "ef8c208dfe7525415e2d72e30c1bfc81ea385355cdd43149fad0e8fa90eb50d1.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "r_t \\in [0,1]" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": " denotes the regression quality score of the " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": "-th output and " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "w_t" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": " denotes the corresponding regression weight. During training, we measure the regression quality score of each grid with the groundtruth " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{K}^*" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": " by a Laplacian kernel to convert the estimated location " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_t" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": " into a score " + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 46, + 520, + 287, + 591 + ], + "type": "text", + "content": ", that is" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 593, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 593, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 129, + 593, + 287, + 608 + ], + "type": "interline_equation", + "content": "r _ {t} = e ^ {- \\lambda \\cdot \\left| \\mathcal {K} _ {t} - \\mathcal {K} ^ {*} \\right|}, \\tag {8}", + "image_path": "169a8d35db519018e5ec0da501fd99dcac2beea1db963834d1e697a1c9e74a31.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "inline_equation", + "content": "r_t \\in [0,1]" + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "text", + "content": " indicates the accuracy of the regressed output and " + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "text", + "content": " is the only hyperparameter of SAR. We set " + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 616, + 287, + 665 + ], + "type": "text", + "content": " to 16 for all experiments and normalize the coordinates by the feature map size." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "The weight " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " generated by the " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "-th grid should be correlated with other grids. In other words, once some outputs are selected, the remaining should be suppressed. To achieve this goal, we adopt a two-step normalization opera" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "type": "text", + "content": "tion on the confidence score " + }, + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "type": "inline_equation", + "content": "\\{s_t\\}" + }, + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "type": "text", + "content": " to generate " + }, + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 305, + 72, + 521, + 85 + ], + "type": "text", + "content": ", i.e.," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 375, + 92, + 545, + 117 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 92, + 545, + 117 + ], + "spans": [ + { + "bbox": [ + 375, + 92, + 545, + 117 + ], + "type": "interline_equation", + "content": "c _ {t} = \\sigma \\left(s _ {t}\\right), w _ {t} = \\frac {c _ {t}}{\\sum c _ {t}}, \\tag {9}", + "image_path": "39205612f0b099dc7d338cea1df8a9c21d8130c867ac3d86b24bd92d600dee6c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "spans": [ + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\sigma(\\cdot)" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": " denotes the sigmoid function to convert score into " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "c_{t} \\in [0,1]" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": ". Eq. (9) first normalizes each score into " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": " individually then utilizes element-sum to correlate them. Therefore, optimizing a high score " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "s_{t}" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": " will decrease others. One advantage of the two-step normalization is the introduced extra score " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "c_{t}" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": ", which is not influenced by the target number and can be used to select outputs by a fixed threshold during inference. Another way to generate weight " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": " is to apply softmax on " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "s_{t}" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": ". However, this one-step normalization cannot generate reliable high confidence score in multiple keypoints localization task during inference, because the value of generated " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "w_{t}" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": " depends on the number of targets in the image. Therefore, it is hard to select final outputs by a fixed threshold " + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 124, + 545, + 291 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 291, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 545, + 363 + ], + "type": "text", + "content": "The unified objective weights each output by the confidence score and is adopted to maximize the overall regression quality. We then give a detailed analysis on Eq. (7) and show how it optimizes both coordinates and confidence scores with a unified loss function. Specifically, the goal of SAR is to minimize the following objective," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 330, + 372, + 545, + 395 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 372, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 330, + 372, + 545, + 395 + ], + "type": "interline_equation", + "content": "\\underset {w _ {t}, r _ {t}} {\\arg \\min } - \\log \\sum w _ {t} \\cdot r _ {t}, \\text {s . t .} \\sum w _ {t} = 1. \\tag {10}", + "image_path": "04afd0d138f5e0a991e99cc19ed1342dde724a907d010001fed3b1752ad27c49.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "content": "Due to the monotonic increase property of " + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\log (\\cdot)" + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "content": " function, the optimal " + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "inline_equation", + "content": "w_{t},r_{t}" + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "content": " satisfy that " + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\sum w_{i}\\cdot r_{t} = 1" + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "content": " .With the normalization in selection process, we also can get " + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "inline_equation", + "content": "\\sum w_{t} = 1" + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "content": " Therefore, optimizing Eq. (10) is equal to maximizing the regression score " + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 304, + 403, + 545, + 461 + ], + "type": "text", + "content": " and will result in two cases:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 462, + 545, + 640 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\forall t \\in [1, n], r_t \\to 1" + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": ". This means that all grids can accurately regress the target, i.e., " + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_t = \\mathcal{K}^*" + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": ". In this case, " + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "inline_equation", + "content": "w_t" + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": " is not important because we can select any output as final result. However, this case rarely happens, especially for multi-keypoints localization task where the same regressed output " + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_t" + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": " will be used to compute " + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "inline_equation", + "content": "r_t" + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": " for different groundtruth " + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{K}^*" + }, + { + "bbox": [ + 306, + 462, + 545, + 544 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "text", + "content": "- " + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\exists t \\in [1, n], r_t \\to 1, \\forall s \\in [1, n] \\setminus t, w_s \\to 0" + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "text", + "content": ". This means that some grids can accurately regress the target location " + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "inline_equation", + "content": "(r_t \\to 1)" + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "text", + "content": ". Meanwhile, the model tends to output low confidence scores " + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "inline_equation", + "content": "w_s \\to 0" + }, + { + "bbox": [ + 306, + 545, + 545, + 640 + ], + "type": "text", + "content": " to relieve the influence of inaccurate regression outputs. This case effectively leverages spatial location priors at some grids to generate accurate predictions, which are hence selected by the selector as final results." + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 689 + ], + "type": "text", + "content": "The above analysis shows that, our proposed training objective trains regressor and selector to boost the accuracy of keypoint localization. It also relieves need of careful multi-task design and hyperparameter tuning in different tasks." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Inference. Similar to regression-based methods, SAR only needs a simple decoding process for inference. 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It then selects the top " + }, + { + "bbox": [ + 46, + 284, + 287, + 321 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 284, + 287, + 321 + ], + "type": "text", + "content": " predictions with scores larger than " + }, + { + "bbox": [ + 46, + 284, + 287, + 321 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 284, + 287, + 321 + ], + "type": "text", + "content": " as the final result," + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 81, + 330, + 287, + 349 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 330, + 287, + 349 + ], + "spans": [ + { + "bbox": [ + 81, + 330, + 287, + 349 + ], + "type": "interline_equation", + "content": "\\{\\mathcal {K} \\} = \\left\\{\\mathcal {K} _ {t} \\right\\} _ {t \\in \\Delta}, \\Delta = \\underset {t} {\\operatorname {t o p}} (m, \\{c _ {t} \\geq \\gamma \\}). \\tag {11}", + "image_path": "e09bfc74729fe952f398291469d86d100729b0a4fd575f8f96e492e8be042dda.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "text", + "content": "The value " + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "text", + "content": " is decided by different tasks, e.g., in top-down task we set " + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "inline_equation", + "content": "m = 1" + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "text", + "content": " and in bottom-up task we set " + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "inline_equation", + "content": "m = 30" + }, + { + "bbox": [ + 46, + 358, + 287, + 467 + ], + "type": "text", + "content": ". Compared with previous heatmap-based methods, SAR does not require complex post-processing operation like shifting [29] or DARK [33] and can be implemented on GPU parallelly. It also works well on low-resolution feature maps, thus is more efficient. SAR is also faster than previous detection-based methods that adopt a Hough voting [18] or accumulation operation [8]." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 47, + 475, + 124, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 475, + 124, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 475, + 124, + 487 + ], + "type": "text", + "content": "3.3. Discussions" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "content": "Comparison to regression. SAR can be regarded as a generalized regression to process feature map. It degenerates to conventional regression when the size of feature map is " + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 498, + 287, + 605 + ], + "type": "text", + "content": ". SAR extends the regression-based method by enhancing its performance and capability in handling multiple keypoint localization by exploring the spatial prior. SAR shares all merits of regression, e.g., low computation and storage complexity and produces a continuous output to relieve the quantization error." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Comparison to heatmap. SAR does not suffer from the quantization error in heatmap and removes the necessity of complex post-processing operation. SAR also differs from methods that combines heatmap with offset regression in both motivation and implementation. Those methods treat heatmap generation and offset regression with equal importance, and their performance is limited by the quality of heatmap. SAR does not assume fixed anchor point (e.g., person center) for regression, thus is general and robust to" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 284, + 545, + 308 + ], + "type": "text", + "content": "occlusion and truncation. This property enables SAR to locate keypoints out of input image as shown in Fig. 3." + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 308, + 546, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 308, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 546, + 392 + ], + "type": "text", + "content": "Visualization. In Fig. 3, we visualize the confidence score map predicted by SAR and heatmap generated by [29]. Compared with heatmap, SAR is more effective in locating multiple keypoints and is more robust to crowded scenes, e.g., keypoints missed by the heatmap can be reliably detected by SAR. More extensive experiment and visualization results will be presented in following section." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 306, + 403, + 387, + 417 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 387, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 387, + 417 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 304, + 423, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 579 + ], + "type": "text", + "content": "In this section we validate the effectiveness of the proposed SAR on various keypoint localization tasks. We first test SAR on the widely studied 2D human pose estimation task to demonstrate its basic keypoint localization ability. Moreover, we further verify SAR is more general than conventional regression in three aspects, i.e., generalization to various type of keypoints on whole-body pose estimation task, generalization to arbitrary number of keypoints on multi-person pose estimation task and generalization to 3D keypoint localization on 3D human pose estimation task. Descriptions of datasets, evaluation metrics, detailed implementation of experiments and qualitative results are provided in supplemental material." + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 306, + 587, + 458, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 587, + 458, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 587, + 458, + 598 + ], + "type": "text", + "content": "4.1.2D Human Pose Estimation" + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 715 + ], + "type": "text", + "content": "2D human pose estimation is a classical localization task that aims to locate the human body keypoints such as knee or shoulder and researchers have proposed many methods to boost its performance. We first conduct experiments on this task to verify the effectiveness of the proposed method, including commonly used large-scale in-the-wild benchmarks COCO Keypoint [14] and MPII [25]. Following previous works, we report the OKS-based AP and PCKh@0.5/0.1 for COCO Keypoint and MPII evaluation respectively. Ex" + } + ] + } + ], + "index": 36 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "628" + } + ] + } + ], + "index": 37 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 287, + 175 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 287, + 175 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 287, + 175 + ], + "type": "table", + "html": "
MethodGFLOPsDeconvsAP\\( AP^{50} \\)\\( AP^{75} \\)Kpt.Error(px)
Regression4.053.882.457.78.5
RLE4.069.689.376.07.8
Heatmap9.7✓70.791.277.67.6
Heatmap+Offset9.7✓70.991.377.87.6
SAR4.071.391.579.17.3
SAR9.7✓72.592.379.97.1
SAR (\\( f^g+FC \\))5.371.191.478.67.3
", + "image_path": "1e7fb2da6dac276c918dbc47e17575b9124b45b23d686772caa07e0ed682c2c7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 48, + 207, + 287, + 309 + ], + "blocks": [ + { + "bbox": [ + 48, + 207, + 287, + 309 + ], + "lines": [ + { + "bbox": [ + 48, + 207, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 48, + 207, + 287, + 309 + ], + "type": "image", + "image_path": "2d1d6b3c021f5f787d584c5772382c50defa534907a056e482ab075bc254fe22.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 316, + 286, + 328 + ], + "lines": [ + { + "bbox": [ + 47, + 316, + 286, + 328 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 286, + 328 + ], + "type": "text", + "content": "Figure 4. Comparison with baselines under different output stride." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 272, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 272, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 272, + 354 + ], + "type": "text", + "content": "periments on MPII are shown in supplemental material." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": "Comparison with baselines. We first evaluate the proposed SAR with two types of commonly used baselines under the same setting. Experiments are conducted based on SimplePose [29], ResNet-50 [4] is adopted as the backbone. The results are summarized in Table 1. Compared with conventional regression that adopts pooled feature to regress target, SAR obtains superior performance without carefully designed loss or modules. It improves the regression baseline from 53.8 to 72.5. SAR is also better than heatmap-based methods that also utilize the spatial location prior to locate target. We also compare a simple multi-task method that also combine heatmap and regression, which is denoted as heatmap+offset. It can be observed that simply combining two tasks cannot get better performance because it introduces contradiction and more hyperparameters into training, and their performance is also limited by heatmap. We also show that the improvement of SAR mainly comes from the spatial location prior " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": ", rather than the visual feature " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": ". We keep the same input " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": " of SAR and conventional regression, thus the only difference is the introduced location prior " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": ", which is denoted as " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "f^g +\\mathrm{FC}" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "f^g +\\mathrm{FC}" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": " explicitly compensates the missed spatial information in " + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "inline_equation", + "content": "f^g" + }, + { + "bbox": [ + 46, + 354, + 287, + 628 + ], + "type": "text", + "content": " and obtains 71.1 AP, which is higher than most baselines." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 714 + ], + "type": "text", + "content": "Analysis on spatial size. SAR shares the merits of regression that is free of quantization error, we conduct experiments on various network output strides and input sizes to demonstrate the superior merits of the proposed SAR. In Fig. 4 we investigate the effect of different output stride to localization performance. We can observe that heatmap-based methods are affected by the output stride greatly due" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 70, + 541, + 216 + ], + "blocks": [ + { + "bbox": [ + 47, + 178, + 287, + 200 + ], + "lines": [ + { + "bbox": [ + 47, + 178, + 287, + 200 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 287, + 200 + ], + "type": "text", + "content": "Table 1. Comparison with baselines on COCO Keypoint val set based on SimplePose [29]. Input size is " + }, + { + "bbox": [ + 47, + 178, + 287, + 200 + ], + "type": "inline_equation", + "content": "256 \\times 192" + }, + { + "bbox": [ + 47, + 178, + 287, + 200 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 70, + 541, + 216 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 541, + 216 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 541, + 216 + ], + "type": "table", + "html": "
MethodInput sizeAP\\( AP^{50} \\)\\( AP^{75} \\)AR
Regression64×6422.755.014.637.5
Heatmap64×6433.270.626.840.2
SimCC [13]64×6437.571.934.743.1
SAR64×6439.274.936.345.6
Regression128×12843.175.245.257.9
Heatmap128×12860.087.868.165.0
SimCC [13]128×12861.987.868.766.3
SAR128×12862.587.870.467.4
Regression256×19253.882.457.767.6
Heatmap256×19270.791.277.674.3
SimCC [13]256×19271.291.278.774.9
SAR256×19272.592.379.976.1
", + "image_path": "00f7e241db6e64004af5ad8ae60643cda753dce3223240b29c9e066cca78dbae.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 312, + 219, + 538, + 230 + ], + "lines": [ + { + "bbox": [ + 312, + 219, + 538, + 230 + ], + "spans": [ + { + "bbox": [ + 312, + 219, + 538, + 230 + ], + "type": "text", + "content": "Table 2. Comparison with baselines under different input size." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 314, + 232, + 538, + 404 + ], + "blocks": [ + { + "bbox": [ + 314, + 232, + 538, + 404 + ], + "lines": [ + { + "bbox": [ + 314, + 232, + 538, + 404 + ], + "spans": [ + { + "bbox": [ + 314, + 232, + 538, + 404 + ], + "type": "image", + "image_path": "a46291a5a21d8d71f33e966d890323cc563d7374cf9c9dd82fe73302a4d00ee2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 413, + 547, + 447 + ], + "lines": [ + { + "bbox": [ + 305, + 413, + 547, + 447 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 547, + 447 + ], + "type": "text", + "content": "Figure 5. Illustration of sampled keypoint localization results of (Top) 2D human pose estimation, (Middle) whole-body pose estimation, and (Bottom) 3D human pose estimation." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 457, + 545, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 457, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 545, + 577 + ], + "type": "text", + "content": "to the quantization error in low resolution heatmap. However, SAR obtains stable performance on various output strides and is constantly superior to heatmap-based methods. Therefore, SAR can be integrated to different backbone without any modification. We also test SAR with other methods on different input size to show its robustness to different input resolution. The results are shown in Table 2. SAR can handle different input size well and achieves superior performance, e.g., higher than previous SimCC [13] under the same setting." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 578, + 545, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 638 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 638 + ], + "type": "text", + "content": "Comparison with other methods. Finally, we give a comprehensive comparison with other methods on COCO Keypoint test-dev set. Results are shown in Table 3. Equipped with different backbones, SAR outperforms previous methods and achieves superior performance." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 647, + 465, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 465, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 465, + 658 + ], + "type": "text", + "content": "4.2. Whole-Body Pose Estimation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We further verify the generalization of the proposed SAR to other type of keypoints on whole-body pose estimation task, which aims to locate keypoints of human body, foot, face and hand. Compared with previous task that only focuses" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "629" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 70, + 544, + 208 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 544, + 208 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 544, + 208 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 544, + 208 + ], + "type": "table", + "html": "
MethodBackboneInput sizeAP\\( AP^{50} \\)\\( AP^{75} \\)\\( AP^M \\)\\( AP^L \\)AR
Heatmap-based
SimplePose [29]ResNet-50384×28871.591.178.767.878.076.9
HRNet [21]HRNet-W48384×28875.592.583.371.981.580.5
SimCC [13]HRNet-W48384×28876.092.483.572.581.981.1
Regression-based
DeepPose [25]ResNet-152256×19259.387.666.756.864.9-
Integral Pose [23]ResNet-101256×25667.888.274.863.974.0-
RLE [10]HRNet-W48384×28875.792.382.972.381.3-
Ours (SAR)ResNet-50384×28873.591.980.969.679.778.8
Ours (SAR)HRNet-W48384×28876.392.583.672.682.481.2
", + "image_path": "242d918751c69c961cb08e811fedca882525cf466362b8b994a8cc748b17af6d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 228, + 545, + 399 + ], + "blocks": [ + { + "bbox": [ + 154, + 211, + 437, + 222 + ], + "lines": [ + { + "bbox": [ + 154, + 211, + 437, + 222 + ], + "spans": [ + { + "bbox": [ + 154, + 211, + 437, + 222 + ], + "type": "text", + "content": "Table 3. Comparison with other methods on COCO Keypoint test-dev set." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 228, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 48, + 228, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 48, + 228, + 545, + 399 + ], + "type": "table", + "html": "
MethodInput sizeBackbonebodyfootfacehandwhole-body
APARAPARAPARAPARAPAR
Baselines
Heatmap [29]256×192ResNet-5065.273.861.574.960.671.546.058.452.163.3
Heatmap [29]256×192HRNet-W4870.177.667.578.765.674.353.563.957.968.1
SAR256×192ResNet-5067.374.961.575.283.288.748.360.859.168.0
SAR256×192HRNet-W4871.078.969.181.888.192.358.469.265.174.0
SoTA methods
DeepPose [25]384×288ResNet-10144.456.836.853.749.366.323.541.033.548.4
SimplePose [29]384×288ResNet-5066.674.763.576.373.281.253.764.757.367.1
HRNet [21]384×288HRNet-W4872.279.169.680.177.683.458.767.863.271.7
ZoomNet [7]384×288HR32+HR1874.581.060.970.888.092.457.973.463.074.2
ZoomNAS [30]384×288-74.080.761.771.888.993.062.574.065.474.4
Ours (SAR)384×288HRNet-W4871.279.669.382.690.393.361.372.166.675.6
", + "image_path": "26cfdfa18855ec7b8e94cd25b5b296194ba238be12f973df163ce14faf336f47.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 155, + 403, + 436, + 414 + ], + "lines": [ + { + "bbox": [ + 155, + 403, + 436, + 414 + ], + "spans": [ + { + "bbox": [ + 155, + 403, + 436, + 414 + ], + "type": "text", + "content": "Table 4. Comparison with other methods on COCO Whole-Body benchmark." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 423, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 506 + ], + "type": "text", + "content": "on human body, whole-body pose estimation is more challenging due to the large scale variance of different type of keypoints. Therefore, this task can be used to test the ability of localization method on handling scale variance. Following previous works, we conduct experiments on large-scale in-the-wild benchmark COCO Whole-Body [7] and report the OKS-based AP on each subset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": "Table 4 shows results. We first compare SAR with heatmap baseline using ResNet-50 and HRNet-W48 as backbone. SAR outperforms heatmap by a large margin, especially on small scale keypoints of face and hand. This demonstrates the benefit of continuous output of SAR, which is free of quantization error in heatmap. We also compare SAR with top-down based methods SimplePose, HRNet, ZoomNet and ZoomNAS. We implement SAR with top-down HRNet under the same setting, and Table 4 shows that our method achieves the best performance on most subsets, without carefully designed multi-branch model in ZoomNet and ZoomNAS. It demonstrates that SAR can generalize to locate various types of keypoints." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 673, + 209, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 673, + 209, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 673, + 209, + 685 + ], + "type": "text", + "content": "4.3. Multi-Person Pose Estimation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "One advantage of SAR is that it can be applied to multiple keypoints localization tasks, while most of previous meth" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 423, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 555 + ], + "type": "text", + "content": "ods, e.g., regression-based methods and SimCC [13] cannot be used to locate multiple keypoints of the same type simultaneously. Multiple keypoints localization task such as multi-person pose estimation (MPPE) is common because it eliminates the assumption that only one instance exists in the input image in single-keypoint localization. Benefited by embedding spatial prior, the proposed method can be applied to MPPE tasks such as bottom-up MPPE and single-stage MPPE. Following previous works, we conduct experiments on COCO [14], OCHuman [34] and CrowdPose [9] and report OKS-based AP metrics." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 545, + 628 + ], + "type": "text", + "content": "For bottom-up MPPE, we adapt SAR with AE [17] to locate multiple keypoints simultaneously because it separately implements localization and grouping. For single-stage MPPE, we conduct experiments on two widely used methods, i.e., CenterNet [35] and DEKR [3], to locate multiple person center points." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 712 + ], + "type": "text", + "content": "All experiments are conducted under the same setting. As shown in Table 5, SAR can successfully detect arbitrary number of keypoints and produce more reliable results than heatmap on all benchmarks. From Fig. 3 we can observe that SAR outputs higher confidence score for detected keypoints, which is important in MPPE because it avoids missed localization." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "630" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 198 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 198 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 198 + ], + "type": "table", + "html": "
MethodCOCOOCHumanCrowdPose
APAPMAPLARAPAPMAPLARAPAPEAPMAPL
Bottom-up MPPE based on AE [17]
Heatmap48.444.154.854.1----46.759.946.636.7
SAR50.045.056.956.2----48.261.148.038.9
Single-stage Regression MPPE
CenterNet [35]57.650.568.463.134.115.236.269.360.968.961.751.7
+SAR60.352.671.164.739.615.540.571.562.269.863.053.7
DEKR [3]61.854.772.867.535.69.637.571.365.273.066.055.9
+SAR64.556.875.569.140.917.241.973.866.373.767.057.6
", + "image_path": "e58abe8208e08339c7ed322009bc25fc5b68ecbc75fc8fe76ad4ead16f0a7b15.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 218, + 548, + 376 + ], + "blocks": [ + { + "bbox": [ + 138, + 201, + 454, + 213 + ], + "lines": [ + { + "bbox": [ + 138, + 201, + 454, + 213 + ], + "spans": [ + { + "bbox": [ + 138, + 201, + 454, + 213 + ], + "type": "text", + "content": "Table 5. Comparison with other methods on multi-person pose estimation benchmarks." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 218, + 548, + 376 + ], + "lines": [ + { + "bbox": [ + 48, + 218, + 548, + 376 + ], + "spans": [ + { + "bbox": [ + 48, + 218, + 548, + 376 + ], + "type": "table", + "html": "
MethodsDir.Dis.EatGre.Phon.PosePur.SitSitD.Smo.Phot.WaitWalkWalkD.WalkP.Avg
Baselines
Regression46.553.547.946.953.346.448.964.364.653.154.247.540.953.445.251.7
RLE47.151.350.448.053.045.847.465.069.053.752.046.740.951.244.751.6
Integral Pose45.351.547.545.553.242.647.163.963.853.053.846.140.051.343.250.6
SAR-3D46.551.146.945.349.745.146.958.763.250.051.146.140.551.344.149.4
SAR-decouple42.249.546.844.852.242.543.860.765.150.752.644.737.850.041.648.9
SoTA methods
Sun [22]52.854.854.254.361.853.153.671.786.761.567.253.447.161.663.459.1
PoseNet [15]50.555.750.151.753.946.850.061.968.052.555.949.941.856.146.953.3
Sun [23]47.547.749.550.251.443.846.458.965.749.455.847.838.949.043.849.6
RLE [10]43.351.044.544.551.743.146.059.263.749.652.544.137.550.541.248.6
Ours (SAR)40.947.844.843.450.341.042.658.261.248.950.042.936.248.340.247.1
", + "image_path": "fbf85c647cfaaa19757494de199d0138657ebd85bdb9db0a92fa18c4de34b72b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 169, + 378, + 423, + 389 + ], + "lines": [ + { + "bbox": [ + 169, + 378, + 423, + 389 + ], + "spans": [ + { + "bbox": [ + 169, + 378, + 423, + 389 + ], + "type": "text", + "content": "Table 6. Comparison with other methods on Human3.6M benchmark." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 402, + 254, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 402, + 254, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 402, + 254, + 414 + ], + "type": "text", + "content": "4.4. Monocular 3D Human Pose Estimation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 422, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 506 + ], + "type": "text", + "content": "In this section we show that SAR can also generalize to perform 3D keypoint localization. We conduct experiments on Human3.6M [6], a large-scale indoor benchmark for 3D human pose estimation. For evaluation, MPJPE is reported to measure the error of the predicted keypoints and groundtruth in 3D space. Following [10], we use (S1, S5, S6, S7, S8) for training and (S9, S11) for evaluation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": "SAR for 3D keypoint. We propose two variants of SAR to locate 3D keypoint. The first is SAR-3D that generates 3D feature map " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{3D} \\in \\mathbb{R}^{c \\times d \\times h \\times w}" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " to provide 3D spatial location prior to locate target, which is similar to Integral Pose [23] that also generates 3D heatmap. Benefited by the continuous output of SAR, a small sized " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{3D}" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " can already produce promising results, e.g., " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "d = h = w = 16" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": ". For the second variant, we decouple the depth dimension from spatial dimension and estimate it with a separate localization branch, which is denoted as SAR-decouple. For " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "x, y" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " coordinates, we directly adopt 2D estimation pipeline. For " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " dimension, we convert the feature map " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " to a 1D feature map " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_z \\in \\mathbb{R}^{c \\times d}" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": " to locate " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": "-dim of keypoint, " + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "inline_equation", + "content": "d = 64" + }, + { + "bbox": [ + 46, + 508, + 288, + 664 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Baselines. We first compare SAR with several 3D keypoint localization methods, including regression, RLE [10] and Integral Pose [29]. All experiments are conducted under the same setting. As shown in Table 6, both two variants" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 402, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 474 + ], + "type": "text", + "content": "of SAR achieve superior 3D keypoint localization accuracy, which is lower than Integral Pose by 1.2 and 1.7 MPJPE. SAR-decouple achieves better performance than SAR-3D. We think that it is because SAR-decouple with large spatial size can generate more accurate localization results, which is consistent with experiments in Sec. 4.1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 475, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 536 + ], + "type": "text", + "content": "Comparison with other methods. In Table 6 we also compare SAR with recent methods under the same setting, e.g., with flip test. We can observe that SAR reduces the MPJPE from 48.6 to 47.1, which is better than most image-based 3D human pose estimation methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 547, + 379, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 379, + 559 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 379, + 559 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 568, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 665 + ], + "type": "text", + "content": "This work proposes a novel and effective regression method by integrating spatial location prior to relieve the difficulty of direct regression. We introduce spatial-aware regressor and selector with a unified objective to achieve spatial-aware regression. Comprehensive experiments on four different keypoint localization tasks and seven benchmarks demonstrate the promising effectiveness and generalization capability of the proposed method." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgement This work is supported in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, in part by the Okawa Foundation Research Award." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "631" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Joao Carreira, Pulkit Agrawal, Katerina Fragkiadaki, and Jitendra Malik. 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Tracking 2D pixels in 3D space. To estimate 2D motion under the occlusion and complex 3D motion, we lift 2D pixels into 3D and perform tracking in the 3D space. Two cases of the estimated 3D and 2D trajectories of a waving butterfly (top) and a group of swimming dolphins (bottom) are illustrated." + ], + "image_footnote": [], + "bbox": [ + 98, + 267, + 254, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/857801b5e8163c74e892311e7f09dd7c5fab7aa3bf078c9c3f4daf35ffa8ac19.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 256, + 267, + 413, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d56ccbadd4865ee99a0ebd62fcc19ee2c496257bc294299e8c2fb057e75cbcee.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 416, + 267, + 573, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/445b0804c7687c1cba791d1952eeb92716f3e19d6c4371e75b5e8ec40a10668a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 576, + 267, + 732, + 544 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1755a45e3c81f33f4c05e2da9cc05b76273089838801322aa2b0e53bb02fb4af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 735, + 267, + 890, + 544 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 623, + 313, + 638 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as", + "bbox": [ + 73, + 650, + 473, + 848 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation. And our project page is available at https://henry123-boy.github.io/SpaTracker/.", + "bbox": [ + 496, + 609, + 893, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 750, + 632, + 766 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Motion estimation has historically been approached through two main paradigms: feature tracking [37, 38, 58, 64] and optical flow [1, 19, 62]. While each type of method enables numerous applications, neither of them fully captures the motion in a video: optical flow only produces motion for adjacent frames, whereas feature tracking only tracks sparse pixels.", + "bbox": [ + 496, + 777, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An ideal solution would involve the ability to estimate", + "bbox": [ + 517, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "aside_text", + "text": "2D Trajectories 3D Trajectories 2D Trajectories 3D Trajectories", + "bbox": [ + 76, + 268, + 94, + 545 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*The first two authors contributed equally. The authors from Zhejiang University are affiliated with the State Key Lab of CAD&CG. †Corresponding author: Xiaowei Zhou.", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20406", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "both dense and long-range pixel trajectories in a video sequence [55, 56]. Seminal work like Particle Video [56] has bridged the gap by representing video motion using a set of semi-dense and long-range particles. More recently, several efforts [11, 12, 17, 29] have revisited this problem, formulating it as tracking any point and addressing it through supervised learning frameworks. While trained solely on synthetic datasets [14, 81], these methods consistently demonstrate strong generalization abilities to real-world videos, pushing the boundaries of long-range pixel tracking through occlusions.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While great progress has been achieved, current solutions still struggle in challenging scenarios, particularly in cases of complex deformation accompanied by frequent self-occlusions. We argue that one potential cause for this difficulty stems from tracking only in the 2D image space, thereby disregarding the inherent 3D nature of motion. As motion takes place in 3D space, certain properties can only be adequately expressed through 3D representations. For example, rotation can be succinctly explained by three parameters in 3D, and occlusion can be simply expressed with z-buffering, but they are much more complicated to express within a 2D representation. In addition, the key component of these methods — using $2D$ feature correlation to predict motion updates — can be insufficient. Image projection can bring spatially distant regions into proximity within the 2D space, which can cause the local 2D neighborhood for correlation to potentially contain irrelevant context (especially near occlusion boundaries), thereby leading to difficulties in reasoning.", + "bbox": [ + 75, + 260, + 472, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle these challenges, we propose to leverage geometric priors from state-of-the-art monocular depth estimators [2] to lift 2D pixels into 3D, and perform tracking in the 3D space. This involves conducting feature correlation in 3D, which provides more meaningful 3D context for tracking especially in cases of complex motion. Tracking in 3D also allows for enforcing 3D motion priors [52, 63] such as ARAP constraint. Encouraging the model to learn which points move rigidly together can help track ambiguous or occluded pixels, as their motion can then be inferred using neighboring unambiguous and visible regions within the same rigid group.", + "bbox": [ + 75, + 550, + 472, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we propose to represent the 3D scene of each frame with triplane feature maps [10], which are obtained by first lifting image features to 3D featured point clouds and then splatting them onto three orthogonal planes. The triplane representation is compact and regular, suitable for our learning framework. Moreover, it covers the 3D space densely, enabling us to extract the feature vectors of any 3D point for tracking. We then compute 3D trajectories for query pixels through iterative updates predicted by a transformer using features from our triplane representation. To regularize the estimated 3D trajectories", + "bbox": [ + 75, + 734, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "with 3D motion prior, our model additionally predicts a rigidity embedding for each trajectory, which allows us to softly group pixels exhibiting the same rigid body motion and enforce an ARAP regularization for each rigid cluster. We demonstrate that the rigidity embedding can be learned self-supervisedly and produce reasonable segmentation of different rigid parts.", + "bbox": [ + 496, + 90, + 893, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our model achieves state-of-the-art performance on various public tracking benchmarks including TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Qualitative results on challenging Internet videos also demonstrate the superior capability of our model to handle fast complex motion and extended occlusion.", + "bbox": [ + 496, + 198, + 893, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 498, + 301, + 640, + 316 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Optical flow. Optical flow is the task of estimating dense 2D pixel-level motion between a pair of frames. While traditional methods [1, 6, 8, 19, 74, 78] formulate it as an energy minimization problem, recent approaches [13, 23, 24, 61, 76] have demonstrated the ability to predict optical flow directly using deep neural networks. Notably, RAFT [62] employs a 4D correlation volume and estimates optical flow through iteratively updates with a recurrent operator. More recently, transformer-based flow estimators [21, 26, 59, 80] achieved superior performance, showing the strong capacity of the transformer architecture. However, pairwise optical flow methods are not suitable for long-term tracking, as they are not designed to handle long temporal contexts [8, 74]. Multi-frame optical flow methods [25, 28, 32, 54, 69] extend pairwise flow by incorporating multi-frame contexts (typically 3-5 frames), but this remains insufficient for tracking through long occlusions in videos spanning tens or hundreds of frames.", + "bbox": [ + 496, + 327, + 893, + 599 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Tracking any point. Recognizing the limitations of optical flow, seminal work Particle Video [56] proposes to represent video motion as a set of long-range particles that move through time, which are optimized by enforcing long-range appearance consistency and motion coherence with variational techniques. However, Particle Video only generates semi-dense tracks and cannot recover from occlusion events [55]. Recently, PIPs [17] revisited this idea by introducing a feedforward network that takes RGB frames of a fixed temporal window (8 frames) as input and predicts the motion for any given query point through iterative updates. However, PIPs tracks points independently, neglecting spatial context information, and will lose the target if they stay occluded beyond the temporal window. Several recent advancements [3, 11, 12, 42, 71, 81] in point tracking have surfaced, addressing some of PIPs' limitations. TAPIR [12] relaxes the fixed-length window constraint by using a temporal depthwise convolutional network capable of accommodating variable lengths. Co", + "bbox": [ + 496, + 613, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20407", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bf0b5e255c67d23149282eda10cb0a1774b4fc861a4fcbed2b4d60e4748dda06.jpg", + "image_caption": [ + "Figure 2. Overview of Our Pipeline. We first encode each frame into a triplane representation (a) using a triplane encoder (b). We then initialize and iteratively update point trajectories in the 3D space using a transformer with features extracted from these triplanes as input (c). The 3D trajectories are trained with ground truth annotations and are regularized by an as-rigid-as-possible (ARAP) constraint with learned rigidity embedding (d). The ARAP constraint enforces that 3D distances between points with similar rigidity embeddings remain constant over time. Here $d_{ij}$ represents the distance between points $i$ and $j$ , while $s_{ij}$ denotes the rigid similarity. Our method produces accurate long-range motion tracks even under fast movements and severe occlusion (e)." + ], + "image_footnote": [], + "bbox": [ + 101, + 87, + 470, + 342 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1388707f573cd97128dd6d0266af7b4812b435973b95a8684e07c969c0fe59af.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 477, + 88, + 856, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Tracker [29] proposed to jointly track multiple points and leverage spatial correlation between them, leading to state-of-the-art performance.", + "bbox": [ + 75, + 450, + 468, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Though significant progress has been made, these works all compute feature correlation in the 2D image space, losing important information about the 3D scene where the motion actually takes place. In contrast, we lift 2D points into 3D and perform tracking in the 3D space. The more meaningful 3D contexts (as opposed to 2D), along with an as-rigid-as-possible regularization, facilitate improved handling of occlusions and enhance tracking accuracy. Previous studies have also explored computing 2D motion with a touch of 3D, e.g., through depth-separated layers [30, 57, 60, 77] or quasi-3D space [71]. However, distinct from their optimization-based pipelines, we perform long-range 3D tracking in a more efficient, feedforward manner.", + "bbox": [ + 75, + 496, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Scene flow. Scene flow defines a dense 3D motion field of points in a scene. Early work estimates scene flow in multi-view stereo settings [49, 66, 79] through variational optimization [22]. The introduction of depth sensors enabled more effective scene flow estimation from pairs or sequences of RGB-D frames [16, 18, 20, 27, 52, 63, 72]. A considerable number of recent scene flow methods rely on stereo inputs [39, 41], but many of them are tailored specifically for self-driving scenes, lacking generalizability to diverse non-automotive contexts. Another line of research [7, 15, 34, 36, 45, 75] estimates 3D motion from a pair or a sequence of point clouds. An important prior that is often used for scene flow estimation is local", + "bbox": [ + 75, + 703, + 470, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "rigidity [67, 68], where pixels are grouped into rigidly moving clusters (object or part-level), in either a soft or hard manner. For example, RAFT-3D [63] learns rigid-motion embeddings to softly group pixels into rigid objects. Scene flow estimation is also often solved as a sub-task in non-rigid reconstruction pipelines [31, 35, 43]. For example, DynamicFusion [44] takes depth maps as input and computes dense volumetric warp functions by interpolating a sparse set of transformations as bases. In contrast to prior works, we learn to predict long-range 3D trajectories through supervised learning, providing generalization capabilities for handling complex real-world motion.", + "bbox": [ + 496, + 450, + 890, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 647, + 589, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a monocular video as input, our method tracks any given query pixels across the entire video. Different from prior methods that establish correspondences solely in the 2D space, we lift pixels to 3D using an off-the-shelf monocular depth estimator and perform tracking in a 3D space with richer and more spatially meaningful 3D contextual information, thereby enhancing the overall tracking performance.", + "bbox": [ + 496, + 672, + 890, + 794 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 2 presents the overview of our proposed pipeline. We first encode the appearance and geometry information of each frame into a triplane representation (Sec. 3.1). Then we perform iterative prediction of trajectories in the 3D space using these triplanes in a sliding window fashion (Sec. 3.2). We leverage the as-rigid-as-possible (ARAP) 3D motion prior during training to facilitate track", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20408", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ing especially in challenging scenarios of occlusion and large motion (Sec. 3.3). Finally, we describe our training strategy in Sec. 3.4.", + "bbox": [ + 75, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Triplane Encoding of Input Video Frames", + "text_level": 1, + "bbox": [ + 76, + 146, + 434, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To perform tracking in the 3D space, we need to lift 2D pixels into 3D and construct a 3D representation that encodes the feature for each 3D location. To this end, we propose to use triplane features as the 3D scene representation for each frame detailed below.", + "bbox": [ + 75, + 169, + 467, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To start with, for each frame, we obtain its monocular depth map using a pretrained monocular depth estimator, alongside multi-scale feature maps generated by a convolutional neural network (CNN). Subsequently, 2D pixels are unprojected into a set of 3D point clouds, where each 3D point is associated with a feature vector. This feature vector is a concatenation of the corresponding image feature and a positional embedding [65] of its 3D location.", + "bbox": [ + 75, + 246, + 467, + 366 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While this featured point cloud captures both geometry and appearance information, it is incomplete and only covers visible regions (2.5D). Additionally, its irregular and unordered nature poses challenges for effective learning. One simple solution involves voxelizing the point cloud into a 3D feature volume and completing it with 3D convolutions. Yet, this approach is memory and computationally intensive. To obtain 3D features densely and efficiently, we propose to use triplane feature maps, which are obtained by orthographically projecting and average splatting [46] the featured point cloud onto three orthogonal 2D planes, as illustrated in Fig. 2(b). Finally, additional convolutional layers are applied to process and complete each feature map. This triplane feature encoding process is applied to each video frame. Since we do not assume access to camera poses, each triplane is defined within the camera coordinate frame of its respective frame.", + "bbox": [ + 75, + 367, + 467, + 623 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This triplane representation is compact and enables us to efficiently represent the 3D feature for any given 3D point within the field of view. This process involves projecting the point onto three feature planes, extracting its corresponding feature vectors through bilinear interpolation, and fusing them via simple addition.", + "bbox": [ + 75, + 625, + 467, + 714 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that while similar concepts of triplanes are explored in related fields [10, 48, 73], our focus here is distinct. Rather than learning a triplane to represent the 3D scene from scratch, we directly leverage monocular depth priors to obtain a triplane where the primary objective is to facilitate tracking in the 3D space, introducing a novel perspective to the field of pixel tracking.", + "bbox": [ + 75, + 715, + 467, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Iterative Trajectory Prediction", + "text_level": 1, + "bbox": [ + 76, + 830, + 349, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a set of query pixels in the query frame, Sec. 3.1 allows us to obtain their 3D locations and their corresponding triplane features. We now describe the process to estimate", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "their 3D trajectories across the entire video.", + "bbox": [ + 498, + 90, + 787, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following CoTracker [29], we partition the video into overlapping windows of length $T_{s}$ . In each window, we iteratively estimate 3D trajectories for query points over $M$ steps using a transformer. The final 3D trajectories are then propagated to the next window and updated, and this process continues until the end of the video.", + "bbox": [ + 496, + 106, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Iterative prediction. We now focus on the iterative prediction of 3D trajectories within the first temporal window. Given the 3D location $\\mathbf{X}_1 \\in \\mathbb{R}^3$ of a query pixel in the first frame, our goal is to predict its 3D corresponding locations (or in other words, its 3D trajectory) in subsequent frames $\\{\\mathbf{X}_t\\}_{t=2}^{T_s}$ , where $t$ is the frame index.", + "bbox": [ + 496, + 200, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Because we adopt an iterative updating strategy to estimate the 3D trajectories, we further denote the prediction at the $m$ -th step as $\\{X_t^m\\}_{t=2}^{T_s}$ . To start with, we initialize $\\{X_t^0\\}_{t=2}^{T_s}$ to be all equal to $X_1$ , and then we iteratively update the 3D trajectory using a transformer $\\Psi$ .", + "bbox": [ + 496, + 292, + 890, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, for the point $\\mathbf{X}_t^m$ at the $m$ -th iteration, we define its input feature $\\mathbf{G}_t^m$ to the transformer as:", + "bbox": [ + 496, + 368, + 890, + 398 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {G} _ {t} ^ {m} = \\left[ \\gamma \\left(\\boldsymbol {X} _ {t} ^ {m}\\right), \\boldsymbol {F} _ {t} ^ {m}, \\boldsymbol {C} _ {t} ^ {m}, \\gamma \\left(\\boldsymbol {X} _ {t} ^ {m} - \\boldsymbol {X} _ {1}\\right) \\right] \\in \\mathbb {R} ^ {D}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 407, + 890, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma$ is the positional encoding function and $F_{t}^{m}$ is the feature of point $X_{t}^{m}$ . At the first iteration, $F_{t}^{0}$ is extracted from the triplane of frame $t$ at $X_{t}^{0}$ . For later iterations, $F_{t}^{m}$ is a direct output of the transformer from the previous iteration. $C_{t}^{m}$ denotes correlation features, which are computed by comparing $F_{t}^{m}$ and local triplane features around $X_{t}^{m}$ at frame $t$ . More details of correlation features can be found in the supplementary material.", + "bbox": [ + 496, + 436, + 890, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For each update, the transformer takes as input the features for the trajectories of all query points across the entire window. We denote this set of features at the $m$ -th iteration as $\\mathcal{G}^m \\in \\mathbb{R}^{N \\times T_s \\times D} = \\{\\pmb{G}_{i,t}^m \\mid i = 1, \\dots, N; t = 1, \\dots, T_s\\}$ , where $i$ is the query point index and $N$ is the number of query points. $\\Psi$ then takes $\\mathcal{G}^m$ as input and predicts the new set of point positions and features:", + "bbox": [ + 496, + 556, + 890, + 662 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {X} ^ {m + 1}, \\mathcal {F} ^ {m + 1} = \\Psi (\\mathcal {G} ^ {m}), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 672, + 890, + 690 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{X}^{m + 1}$ denotes the set of updated point positions, and $\\mathcal{F}^{m + 1}$ denotes the set of updated point features. New $\\mathcal{G}^{m + 1}$ can then be defined according to Eq. 1, and the same process is repeated $M$ times to obtain the final 3D trajectories for all query points $\\mathcal{X}^M = \\{\\pmb {X}_{i,t}^M\\}$ . The 2D correspondence predictions can be computed by simply projecting $\\{\\pmb {X}_{i,t}^M\\}$ back onto the 2D image plane.", + "bbox": [ + 496, + 700, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As query pixels may not have corresponding pixels at some frames due to occlusions, we additionally predict the visibility for each point of the 3D trajectories at the final iteration $M$ . Specifically, for each point $\\mathbf{X}_{i,t}^{M}$ , we employ an MLP network that takes the feature $\\mathbf{F}_{i,t}^{M}$ as input and predicts a visibility score $v_{i,t}$ .", + "bbox": [ + 496, + 808, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "footer", + "text": "20409", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Handling long videos. To track points across a long video, we utilize overlapping sliding windows where each pair of adjacent windows has half of their frames overlapped. Given the results from the previous window, we initialize trajectories of the first $\\frac{T_s}{2}$ frames of the current window by copying the results of the last $\\frac{T_s}{2}$ frames from the previous window. The trajectories of the last $\\frac{T_s}{2}$ frames in the current window are initialized by copying the result of the frame $\\frac{T_s}{2}$ .", + "bbox": [ + 75, + 90, + 472, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. As Rigid As Possible Constraint", + "text_level": 1, + "bbox": [ + 76, + 243, + 359, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "An advantage of tracking points in 3D is that we can enforce an as-rigid-as-possible (ARAP) constraint, which enhances spatial consistency and facilitates the prediction of motion especially during occlusions.", + "bbox": [ + 75, + 267, + 468, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Enforcing proper ARAP constraints requires identifying if two points belong to the same rigid part. To this end, at each iteration $m$ , we additionally compute a rigidity embedding $\\pmb{E}_i^m$ for each trajectory by aggregating its features $\\{\\pmb{G}_{i,t}^{m}\\}_{t = 1}^{T_s}$ across time. Then, the rigidity affinity $s_{ij}^{m}$ between any two trajectories $i$ and $j$ can be calculated as:", + "bbox": [ + 75, + 329, + 468, + 420 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i j} ^ {m} = \\operatorname {s i m} \\left(\\boldsymbol {E} _ {i} ^ {m}, \\boldsymbol {E} _ {j} ^ {m}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 197, + 433, + 468, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{sim}(\\cdot ,\\cdot)$ is the cosine similarity measure.", + "bbox": [ + 76, + 464, + 393, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By the definition of rigidity, the distances between points that are rigidly moving together should be preserved over time. Therefore, we formulate our ARAP loss as follows, encouraging the distances between pairs of points exhibiting high rigidity to remain constant over time:", + "bbox": [ + 75, + 479, + 468, + 556 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {a r a p}} = \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T _ {s}} \\sum_ {\\Omega_ {i j}} w ^ {m} s _ {i j} ^ {m} | | d \\left(\\boldsymbol {X} _ {i, t} ^ {m}, \\boldsymbol {X} _ {j, t} ^ {m}\\right) - d \\left(\\boldsymbol {X} _ {i, 1}, \\boldsymbol {X} _ {j, 1}\\right) | | _ {1}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 569, + 468, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\Omega_{ij}$ is the set of all pairwise indices and $d(\\cdot, \\cdot)$ is the Euclidean distance function, and $w^{m} = 0.8^{M - m}$ is the weight for the $m$ -th step. This ARAP loss provides gradients for learning both the 3D trajectories and the rigidity embeddings.", + "bbox": [ + 75, + 614, + 468, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Based on the affinity score between any two points, we can perform spectral clustering [47, 70] to obtain the segmentation of query pixels. Experiments in Sec. 4 show that our method can generate meaningful segmentation of rigid parts.", + "bbox": [ + 75, + 691, + 468, + 767 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training", + "text_level": 1, + "bbox": [ + 76, + 779, + 181, + 795 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition to the ARAP loss, we supervise the predicted trajectories using ground truth 3D trajectories at each iteration, which is defined as:", + "bbox": [ + 75, + 804, + 468, + 848 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t r a j}} = \\sum_ {m = 1} ^ {M} \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {T _ {s}} w ^ {m} | | \\boldsymbol {X} _ {i, t} ^ {m} - \\hat {\\boldsymbol {X}} _ {i, t} ^ {m} | | _ {1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 861, + 468, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $X_{i,t}^{m}$ and $\\hat{X}_{i,t}^{m}$ are the predicted and ground-truth 3D corresponding locations, respectively, and $w^{m}$ is the weight for the $m$ -th step, identical to that in Eq. 4.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The predicted visibilities are supervised using:", + "bbox": [ + 517, + 136, + 826, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {v i s}} = \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {T _ {s}} \\mathrm {C E} \\left(v _ {i, t}, \\hat {v} _ {i, t}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 598, + 156, + 890, + 198 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $v_{i,t}$ and $\\hat{v}_{i,t}$ denote the predicted and ground-truth visibility, respectively. CE represents the cross entropy loss.", + "bbox": [ + 498, + 202, + 890, + 232 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss function for training is defined as:", + "bbox": [ + 517, + 233, + 836, + 247 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {t r a j}} + \\alpha \\mathcal {L} _ {\\text {v i s}} + \\beta \\mathcal {L} _ {\\text {a r a p}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 253, + 890, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\alpha$ and $\\beta$ are weighting coefficients. In practice, they are set as 10 and 0.1, respectively.", + "bbox": [ + 498, + 275, + 890, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 311, + 718, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our model on the TAP-Vid-Kubric dataset [11, 14]. Our training data contains 11,000 24-frame RGBD sequences with full-length 3D trajectory annotations. During training, we use ground truth depth maps and camera intrinsics to unproject pixels into 3D space. In cases where the depth map and intrinsics are unavailable at inference, we use ZoeDepth [2] to predict the metric depth map for each video frame, and simply set the focal length to be the same as the image width. To generate triplane feature maps, we discretize the depth values into $d = 256$ bins. The resolutions of the triplane feature maps are $h \\times w$ , $w \\times d$ , $h \\times d$ for XY, XZ, and YZ planes, respectively, where $h$ , $w$ are the image height and width. The number of channels of the triplane features is 128.", + "bbox": [ + 498, + 335, + 890, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our model with eight 80GB A100 GPUs for 200k iterations. The total training time is around 6 days. The iteration steps $M$ and sliding window length $T_{s}$ are set to 6 and 8 respectively. In each training batch, we sample $N = 256$ query points. The transformer $\\Psi$ consists of six blocks, each comprising both spatial and temporal attention layers. For more details, please refer to the supplementary material.", + "bbox": [ + 498, + 547, + 890, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 679, + 632, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At inference, our method can operate in two different modalities. The first modality (and the primary focus of this paper) is long-range 2D pixel tracking. In this modality, the input is an RGB video without known depth or camera intrinsics, and we rely on ZoeDepth [2] to estimate the depth maps. Due to the lack of precise depth and intrinsics information, we only evaluate the 2D projection of the 3D trajectories onto the image plane, i.e., 2D pixel trajectories. When RGBD videos and camera intrinsics are available, our method can be used in the second modality to predict long-range 3D trajectories. We evaluate our method for both 2D and 3D tracking performance in Sec 4.1 and Sec 4.2, respectively, and then conduct ablation studies in Sec. 4.3.", + "bbox": [ + 498, + 704, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20410", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/c016e759874c9d57690f23355268ea259afdabf85397053a8bca60303a1caa9d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsKinetics [9]DAVIS [50]RGB-Stacking [33]Average
AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑
TAP-Net [11]38.554.480.633.048.678.854.668.387.742.057.182.4
PIPs [17]31.753.772.942.264.877.715.728.477.129.950.075.9
OmniMotion [71]--46.462.785.369.582.590.3---
TAPIR [12]49.664.285.056.270.086.554.269.884.453.368.085.3
CoTracker [29]48.764.386.560.675.489.363.177.087.857.472.287.8
Ours50.165.986.961.176.389.563.577.688.258.273.388.2
", + "bbox": [ + 78, + 78, + 893, + 215 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. 2D Tracking Evaluation", + "text_level": 1, + "bbox": [ + 76, + 267, + 297, + 282 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct our evaluation on three long-range 2D tracking benchmarks: TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Our method is compared with baseline 2D tracking methods, namely TAP-Net [11], PIPs [17], OmniMotion [71], TAPIR [12] and CoTracker [29]. The evaluation protocols and comparison results on each of the benchmarks are represented below.", + "bbox": [ + 75, + 292, + 470, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "TAP-Vid Benchmark [11] contains a few datasets: TAP-Vid-DAVIS [50] (30 real videos of about 34-104 frames), TAP-Vid-Kinetics [9] (1144 real videos of 250 frames) and RGB-Stacking [33] (50 synthetic videos of 250 frames). Each video in the benchmark is annotated with ground truth 2D trajectories and occlusions spanning the entire video duration for well-distributed points. We evaluate performance using the same metrics as the TAP-Vid benchmark [11]: average position accuracy $(< \\delta_{\\mathrm{avg}}^x)$ , Average Jaccard (AJ), and Occlusion Accuracy (OA). Please refer to the supplement for more details. We follow the \"queried first\" evaluation protocol in CoTracker [29]. Specifically, we use the first frame as the query frame and predict the 2D locations of query pixels from this frame in all subsequent frames. The quantitative comparisons are reported in Tab. 1, which shows our method consistently outperforms all baselines except Omnimotion across all three datasets, demonstrating the benefits of tracking in the 3D space. Omnimotion also performs tracking in 3D and obtains the best results on RGB-Stacking by optimizing all frames at once, but it requires very costly test-time optimization.", + "bbox": [ + 75, + 407, + 470, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "BADJA [4] is a benchmark containing seven videos of moving animals with annotated keypoints. The metrics used in this benchmark include segment-based accuracy (segA) and 3px accuracy ( $\\delta^{3\\mathrm{px}}$ ). The predicted keypoint positions are deemed accurate when its distance from the ground truth keypoint is less than $0.2\\sqrt{A}$ , where $A$ is the summation of the area of the segmentation mask. $\\delta^{3\\mathrm{px}}$ depicts the percentage of the correct keypoints whose distances from their ground truth are within three pixels. As shown in Tab. 2, our method demonstrates competitive performance in terms of $\\delta^{3\\mathrm{px}}$ and surpasses all baseline methods by a", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0bca97ef27c1bfb2290e40170590939f767422c102f0539112e02e7a647befac.jpg", + "table_caption": [ + "Table 1. 2D Tracking Results on the TAP-Vid Benchmark. We report the average jaccard (AJ), average position accuracy $(<\\delta_{\\mathrm{avg}}^x)$ , and occlusion accuracy (OA) on Kinetics [9], DAVIS [50] and RGB-Stacking [33] datasets." + ], + "table_footnote": [], + "table_body": "
MethodssegA ↓δ3px ↑
TAP-Net [11]54.46.3
PIPs [17]61.913.5
TAPIR [12]66.915.2
OmniMotion [71]57.213.2
CoTracker [29]63.618.0
Ours69.217.1
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MethodsMTE↓<δxavg↑Survival↑
TAP-Net [11]37.829.252.8
PIPs [81]41.030.467.0
CoTracker [29]30.556.276.1
Ours w/ ZoeDepth [2]28.358.478.6
Ours w/ GT depth26.664.178.0
", + "bbox": [ + 501, + 441, + 888, + 542 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. 2D Tracking Results on the PointOdyssey Dataset [81]. The Median Trajectory Error (MTE), average position accuracy $(<\\delta_{avg}^{x})$ , and survival rate (Survival) are reported.", + "bbox": [ + 500, + 546, + 890, + 589 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "large margin in segment-based accuracy.", + "bbox": [ + 500, + 618, + 769, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PointOdyssey [81] is a large-scale synthetic dataset featuring diverse animated characters ranging from humans to animals, placed within diverse 3D environments. We evaluate our method on PointOdyssey's test set which contains 12 videos with complex motion, each spanning approximately 2000 frames. We adopt the evaluation metrics proposed in PointOdyssey [81] which are designed for evaluating very long trajectories. These metrics include the Median Trajectory Error (MTE), $< \\delta_{\\mathrm{avg}}^x$ (consistent with TAP-Vid), and the survival rate. The survival rate is defined as the average number of frames until tracking failure over the video length. Tracking failure is identified when the L2 error exceeds 50 pixels at a resolution of $256 \\times 256$ . In Tab. 3, we report results for baseline methods as well as our method using depths from ZoeDepth [2] (default) and GT depth annotations. Our method consistently outperforms", + "bbox": [ + 496, + 657, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20411", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/aa5e95d2a7077af8c74cd9ff8e0f8c555ef77247493bbdda1908ee531ecd5225.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 109, + 88, + 261, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2fd40a5e3a73c468047cce9a13129517effebd606d741684a3dbfe61eaad96ef.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 111, + 156, + 261, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5f7d9c45889c67d22b28727c547836885c0f9500eded1665cb32dd1685f60d94.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 111, + 222, + 261, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/15a0fcad60671ddb97c9b8d5424ff88b7f836b7baf8a87294f2f392614d1a475.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 111, + 286, + 261, + 352 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6d312ec6ea4dfbb83c9ab2a2339e81501eeb2d1bd6b4811e1e5ef67391cc5cb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 111, + 353, + 261, + 417 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3109a81678974553943ee72e18e4ee67266b38f65a3e0944fb98212d6312a0d7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 111, + 417, + 261, + 486 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f6b91df3205dc6c99263b53252ff0be46ccbdc2a76978f7106191809287761ed.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 111, + 486, + 261, + 551 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6736ec9cb0deafaec8de24c84dc14cc18842a5f019a3ffd6f3329288e2a15f8e.jpg", + "image_caption": [ + "Figure 3. Qualitative Comparison. For each sequence we show tracking results of CoTracker [29] and our method SpatialTracker." + ], + "image_footnote": [], + "bbox": [ + 111, + 551, + 261, + 617 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8bebb2f55f9eeae13d002eadc47a97c352a9f38c99f5e656b837e68beb7901c1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 88, + 415, + 155 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d754b05c5397949921e4cd7ed58dcedd173b2b05525e4b7a3e9d672cf356a703.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 156, + 415, + 220 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c4a80b152d29e679c1d625d9e6b0c883a670cf7d9d7c973a4479bfead5069b38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 264, + 222, + 415, + 285 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/928231d0f84f47d6dc059b35bd666f054529ea3b0a84048b093a628dd4adcf72.jpg", + 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In particular, we demonstrate that with access to more accurate ground truth depth, our performance can be further enhanced. This suggests the potential of our method to continue improving alongside advancements in monocular depth estimation.", + "bbox": [ + 75, + 662, + 468, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. We present qualitative comparisons with CoTracker [29] on challenging videos from DAVIS [50] and Internet footage in Fig. 3. Our method outperforms CoTracker in handling complex human motion with self-occlusions, achieves a better understanding of rigid groups, and can effectively track small, rapidly moving objects even in the presence of occlusions. Please refer to the supplementary video for more results and better visualizations.", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.3D Tracking Evaluation", + "text_level": 1, + "bbox": [ + 498, + 661, + 720, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given an RGBD video (with known depth and intrinsics) as input, our method can estimate true 3D trajectories. Since no baseline method can directly be used for long-range 3D tracking, we construct our baselines by composing existing methods. Our first baseline is chained RAFT-3D [63]. RAFT-3D is designed for pairwise scene flow estimation, so to obtain long-range scene flow, we chain its scene flow prediction of consecutive frames. Our second baseline is to directly lift the predicted 2D trajectories from CoTracker [29] using the input depth maps.", + "bbox": [ + 496, + 686, + 890, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our method and baselines on the PointOdyssey [81] dataset. We create 231 testing sequences from the test set, each consisting of 24 frames and with a reduced frame rate set at one-fifth of the original. We", + "bbox": [ + 498, + 840, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "aside_text", + "text": "Ours CoTracker [29] Ours CoTracker [29] Ours CoTracker [29] Ours CoTracker [29]", + "bbox": [ + 76, + 93, + 91, + 595 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20412", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/97869bc3d12374850b8a544ef7bf589eb03ca8aed909717a282557d772da3ce7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsATE3D ↓δ0.1 ↑δ0.2 ↑
Chained RAFT3D [63]0.700.120.25
Lifted CoTracker [29]0.770.510.64
Ours0.220.590.76
", + "bbox": [ + 78, + 88, + 470, + 160 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/8460f4bc6c31e580d96f4b169aa7a6ecc94ec6d34b891f7e65f32da7c6988022.jpg", + "table_caption": [ + "Table 4. 3D Tracking Results on the PointOdyssey Dataset. $\\mathrm{ATE}_{3D}$ is the average trajectory error in 3D space and $\\delta_t$ measures the percentage of points whose distances are within $t$ (in meter) from the ground truth." + ], + "table_footnote": [], + "table_body": "
MethodsAJ↑<δxavg↑OA↑
Ours w/o ARAP55.171.687.4
Ours w/ DPT [53]51.470.783.3
Ours w/ MiDaS [5]56.373.986.6
Ours w/ ZoeDepth [2] (default)61.176.389.5
", + "bbox": [ + 78, + 234, + 473, + 328 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation Study on the DAVIS Dataset. The Average Jaccard (AJ), average position accuracy $(<\\delta_{\\mathrm{avg}}^x)$ , and Occlusion Accuracy (OA) are reported. We evaluate the effectiveness of the ARAP constraint and the influence of different monocular depth estimators (ZoeDepth [2], MiDaS [5] and DPT [53]). \"Ours w/ZoeDepth\" is the default model we use in our experiments.", + "bbox": [ + 75, + 333, + 470, + 417 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "use three evaluation metrics, namely $\\mathrm{ATE}_{3\\mathrm{D}}$ , $\\delta_{0.1}$ , and $\\delta_{0.2}$ . $\\mathrm{ATE}_{3\\mathrm{D}}$ is the average trajectory error in 3D space. $\\delta_{0.1}$ and $\\delta_{0.2}$ measure the percentage of points whose distances are within $0.1\\mathrm{m}$ and $0.2\\mathrm{m}$ from the ground truth, respectively.", + "bbox": [ + 75, + 430, + 468, + 491 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results are shown in Tab. 4. Our method outperforms both \"Chained RAFT-3D\" and \"Lifted CoTracker\" consistently on all three metrics by a large margin. We found that RAFT-3D, trained on FlyingThings [40], generalizes poorly on PointOdyssey, possibly due to the fact that its dense-SE3 module is sensitive to domain gaps. In contrast, also trained on a different dataset (Kubric), our method exhibits strong generalization to PointOdyssey, affirming the efficacy of our design for 3D trajectory prediction. In addition, both baselines cannot handle occlusion and will lose track of points once they become occluded, hurting the performance significantly.", + "bbox": [ + 75, + 491, + 470, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation and Analysis", + "text_level": 1, + "bbox": [ + 76, + 681, + 284, + 698 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effectiveness of ARAP loss and rigidity embedding. We ablate the ARAP loss and report the result \"Ours w/o ARAP\" on the TAP-Vid-DAVIS [11, 51] dataset in Tab. 5. Without the ARAP loss, the performance drops substantially, verifying the effectiveness of the ARAP constraint. We additionally showcase qualitative results of the rigid part segmentation, utilizing our learned rigidity embeddings in Fig. 4, demonstrating their effectiveness.", + "bbox": [ + 75, + 705, + 468, + 828 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Analysis on monocular depth estimators. To study the influence of different monocular depth estimation methods on our model, we evaluate our method with three monocular depth models: ZoeDepth [2] (default), MiDaS [5],", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9c3fe704c16d51627ca1cc0cd04c0a1edb1789be10a9d7164df903314720e473.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 517, + 88, + 635, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8be9438c4c8a36816b5441bdfc3d1a8193c69be9fecfa25cb39f2e5e1abfa8ee.jpg", + "image_caption": [ + "Figure 4. Rigid Part Segmentation. We utilize spectral clustering on the rigidity embedding to determine rigid groups. Each color represents a distinct rigid group." + ], + "image_footnote": [], + "bbox": [ + 517, + 157, + 635, + 226 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a0e86ee688ffca98207ba134e268ef426aebeadd87a0a6a11156a17c0c73aae2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 88, + 754, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6947fb33ca87259dc93c60d4b2086abc5edef6366c2916c9e1f4b9fb472870e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 637, + 157, + 754, + 226 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/11c48fdb5bf74ae88f491205269c2ef52cf2016de908a384d61f9960f728feb0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 88, + 875, + 157 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/bcda10462d663e2b809b8c5adbb8504da5fb47a14d56a6632a87d4f3fac6100b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 157, + 875, + 226 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "and DPT [53]. We report the results on the TAP-ViddAVIS [11, 51] dataset in Tab. 5. \"Ours w/ ZoeDepth\" achieves the best results, probably due to the fact that ZoeDepth [2] is a metric depth estimator and exhibits less temporal inconsistency across frames compared to relative depth estimators MiDaS [5] and DPT [53]. Furthermore, it is noteworthy that the efficacy of our model has a positive correlation with the advancements in the underlying monocular depth models. Please refer to the supplementary material for additional analysis and ablations.", + "bbox": [ + 496, + 292, + 892, + 445 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Discussion", + "text_level": 1, + "bbox": [ + 500, + 470, + 748, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we show that a properly designed 3D representation is crucial for solving the long-standing challenge of dense and long-range motion estimation in videos. Motion naturally occurs in 3D and tracking motion in 3D allows us to better leverage its regularity in 3D, e.g., the ARAP constraint. We proposed a novel framework that estimates 3D trajectories using triplane representations with a learnable ARAP constraint that identifies the rigid groups in the scene and enforces rigidity within each group. Experiments demonstrated the superior performance of our method compared to existing baselines and its applicability to challenging real-world scenarios.", + "bbox": [ + 496, + 500, + 892, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Our current model relies on off-the-shelf monocular depth estimators whose accuracy may affect the final tracking performance as shown in Tab. 5. However, we anticipate that advancements in monocular reconstruction will enhance the performance of motion estimation. We expect a closer interplay between these two problems, benefiting each other in the near future.", + "bbox": [ + 496, + 685, + 890, + 791 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 800, + 660, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by National Key Research and Development Program of China (No. 2020AAA0108900), Ant Group, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University.", + "bbox": [ + 496, + 824, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20413", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Steven S. Beauchemin and John L. Barron. The computation of optical flow. 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Pointodyssey: A large-scale synthetic dataset for long-term point tracking. In Int. Conf. Comput. Vis., pages 19855-19865, 2023. 2, 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 247 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "20417", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/SpatialTracker_ Tracking Any 2D Pixels in 3D Space/fee0371c-0071-4b47-bb08-5807dbb57d30_model.json b/2024/SpatialTracker_ Tracking Any 2D Pixels in 3D Space/fee0371c-0071-4b47-bb08-5807dbb57d30_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e2ebf081f650271754cf4a323944b23744d71c26 --- /dev/null +++ b/2024/SpatialTracker_ Tracking Any 2D Pixels in 3D Space/fee0371c-0071-4b47-bb08-5807dbb57d30_model.json @@ -0,0 +1,2930 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.218, + 0.131, + 0.753, + 0.154 + ], + "angle": 0, + "content": "SpatialTracker: Tracking Any 2D Pixels in 3D Space" + }, + { + "type": "text", + "bbox": [ + 0.209, + 0.179, + 0.761, + 0.245 + ], + "angle": 0, + "content": "Yuxi Xiao\\(^{1,3*}\\) Qianqian Wang\\(^{2*}\\) Shangzhan Zhang\\(^{1,3}\\) Nan Xue\\(^{3}\\) Sida Peng\\(^{1}\\) Yujun Shen\\(^{3}\\) Xiaowei Zhou\\(^{1\\dagger}\\) \\(^{1}\\)Zhejiang University \\(^{2}\\)UC Berkeley \\(^{3}\\)Ant Group" + }, + { + "type": "aside_text", + "bbox": [ + 0.078, + 0.269, + 0.095, + 0.546 + ], + "angle": 270, + "content": "2D Trajectories 3D Trajectories 2D Trajectories 3D Trajectories" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.268, + 0.255, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.258, + 0.268, + 0.414, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.417, + 0.268, + 0.574, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.577, + 0.268, + 0.733, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.736, + 0.268, + 0.892, + 0.545 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.568, + 0.895, + 0.61 + ], + "angle": 0, + "content": "Figure 1. Tracking 2D pixels in 3D space. To estimate 2D motion under the occlusion and complex 3D motion, we lift 2D pixels into 3D and perform tracking in the 3D space. Two cases of the estimated 3D and 2D trajectories of a waving butterfly (top) and a group of swimming dolphins (bottom) are illustrated." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.624, + 0.314, + 0.64 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.651, + 0.474, + 0.849 + ], + "angle": 0, + "content": "Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "*The first two authors contributed equally. The authors from Zhejiang University are affiliated with the State Key Lab of CAD&CG. †Corresponding author: Xiaowei Zhou." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.895, + 0.732 + ], + "angle": 0, + "content": "rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation. And our project page is available at https://henry123-boy.github.io/SpaTracker/." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.751, + 0.633, + 0.767 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.778, + 0.894, + 0.884 + ], + "angle": 0, + "content": "Motion estimation has historically been approached through two main paradigms: feature tracking [37, 38, 58, 64] and optical flow [1, 19, 62]. While each type of method enables numerous applications, neither of them fully captures the motion in a video: optical flow only produces motion for adjacent frames, whereas feature tracking only tracks sparse pixels." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "An ideal solution would involve the ability to estimate" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20406" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "both dense and long-range pixel trajectories in a video sequence [55, 56]. Seminal work like Particle Video [56] has bridged the gap by representing video motion using a set of semi-dense and long-range particles. More recently, several efforts [11, 12, 17, 29] have revisited this problem, formulating it as tracking any point and addressing it through supervised learning frameworks. While trained solely on synthetic datasets [14, 81], these methods consistently demonstrate strong generalization abilities to real-world videos, pushing the boundaries of long-range pixel tracking through occlusions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.548 + ], + "angle": 0, + "content": "While great progress has been achieved, current solutions still struggle in challenging scenarios, particularly in cases of complex deformation accompanied by frequent self-occlusions. We argue that one potential cause for this difficulty stems from tracking only in the 2D image space, thereby disregarding the inherent 3D nature of motion. As motion takes place in 3D space, certain properties can only be adequately expressed through 3D representations. For example, rotation can be succinctly explained by three parameters in 3D, and occlusion can be simply expressed with z-buffering, but they are much more complicated to express within a 2D representation. In addition, the key component of these methods — using \\(2D\\) feature correlation to predict motion updates — can be insufficient. Image projection can bring spatially distant regions into proximity within the 2D space, which can cause the local 2D neighborhood for correlation to potentially contain irrelevant context (especially near occlusion boundaries), thereby leading to difficulties in reasoning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.473, + 0.734 + ], + "angle": 0, + "content": "To tackle these challenges, we propose to leverage geometric priors from state-of-the-art monocular depth estimators [2] to lift 2D pixels into 3D, and perform tracking in the 3D space. This involves conducting feature correlation in 3D, which provides more meaningful 3D context for tracking especially in cases of complex motion. Tracking in 3D also allows for enforcing 3D motion priors [52, 63] such as ARAP constraint. Encouraging the model to learn which points move rigidly together can help track ambiguous or occluded pixels, as their motion can then be inferred using neighboring unambiguous and visible regions within the same rigid group." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Specifically, we propose to represent the 3D scene of each frame with triplane feature maps [10], which are obtained by first lifting image features to 3D featured point clouds and then splatting them onto three orthogonal planes. The triplane representation is compact and regular, suitable for our learning framework. Moreover, it covers the 3D space densely, enabling us to extract the feature vectors of any 3D point for tracking. We then compute 3D trajectories for query pixels through iterative updates predicted by a transformer using features from our triplane representation. To regularize the estimated 3D trajectories" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.198 + ], + "angle": 0, + "content": "with 3D motion prior, our model additionally predicts a rigidity embedding for each trajectory, which allows us to softly group pixels exhibiting the same rigid body motion and enforce an ARAP regularization for each rigid cluster. We demonstrate that the rigidity embedding can be learned self-supervisedly and produce reasonable segmentation of different rigid parts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.895, + 0.288 + ], + "angle": 0, + "content": "Our model achieves state-of-the-art performance on various public tracking benchmarks including TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Qualitative results on challenging Internet videos also demonstrate the superior capability of our model to handle fast complex motion and extended occlusion." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.303, + 0.642, + 0.318 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.328, + 0.895, + 0.6 + ], + "angle": 0, + "content": "Optical flow. Optical flow is the task of estimating dense 2D pixel-level motion between a pair of frames. While traditional methods [1, 6, 8, 19, 74, 78] formulate it as an energy minimization problem, recent approaches [13, 23, 24, 61, 76] have demonstrated the ability to predict optical flow directly using deep neural networks. Notably, RAFT [62] employs a 4D correlation volume and estimates optical flow through iteratively updates with a recurrent operator. More recently, transformer-based flow estimators [21, 26, 59, 80] achieved superior performance, showing the strong capacity of the transformer architecture. However, pairwise optical flow methods are not suitable for long-term tracking, as they are not designed to handle long temporal contexts [8, 74]. Multi-frame optical flow methods [25, 28, 32, 54, 69] extend pairwise flow by incorporating multi-frame contexts (typically 3-5 frames), but this remains insufficient for tracking through long occlusions in videos spanning tens or hundreds of frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Tracking any point. Recognizing the limitations of optical flow, seminal work Particle Video [56] proposes to represent video motion as a set of long-range particles that move through time, which are optimized by enforcing long-range appearance consistency and motion coherence with variational techniques. However, Particle Video only generates semi-dense tracks and cannot recover from occlusion events [55]. Recently, PIPs [17] revisited this idea by introducing a feedforward network that takes RGB frames of a fixed temporal window (8 frames) as input and predicts the motion for any given query point through iterative updates. However, PIPs tracks points independently, neglecting spatial context information, and will lose the target if they stay occluded beyond the temporal window. Several recent advancements [3, 11, 12, 42, 71, 81] in point tracking have surfaced, addressing some of PIPs' limitations. TAPIR [12] relaxes the fixed-length window constraint by using a temporal depthwise convolutional network capable of accommodating variable lengths. Co" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20407" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.088, + 0.472, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.478, + 0.089, + 0.857, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.355, + 0.892, + 0.439 + ], + "angle": 0, + "content": "Figure 2. Overview of Our Pipeline. We first encode each frame into a triplane representation (a) using a triplane encoder (b). We then initialize and iteratively update point trajectories in the 3D space using a transformer with features extracted from these triplanes as input (c). The 3D trajectories are trained with ground truth annotations and are regularized by an as-rigid-as-possible (ARAP) constraint with learned rigidity embedding (d). The ARAP constraint enforces that 3D distances between points with similar rigidity embeddings remain constant over time. Here \\( d_{ij} \\) represents the distance between points \\( i \\) and \\( j \\), while \\( s_{ij} \\) denotes the rigid similarity. Our method produces accurate long-range motion tracks even under fast movements and severe occlusion (e)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.47, + 0.496 + ], + "angle": 0, + "content": "Tracker [29] proposed to jointly track multiple points and leverage spatial correlation between them, leading to state-of-the-art performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.47, + 0.692 + ], + "angle": 0, + "content": "Though significant progress has been made, these works all compute feature correlation in the 2D image space, losing important information about the 3D scene where the motion actually takes place. In contrast, we lift 2D points into 3D and perform tracking in the 3D space. The more meaningful 3D contexts (as opposed to 2D), along with an as-rigid-as-possible regularization, facilitate improved handling of occlusions and enhance tracking accuracy. Previous studies have also explored computing 2D motion with a touch of 3D, e.g., through depth-separated layers [30, 57, 60, 77] or quasi-3D space [71]. However, distinct from their optimization-based pipelines, we perform long-range 3D tracking in a more efficient, feedforward manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Scene flow. Scene flow defines a dense 3D motion field of points in a scene. Early work estimates scene flow in multi-view stereo settings [49, 66, 79] through variational optimization [22]. The introduction of depth sensors enabled more effective scene flow estimation from pairs or sequences of RGB-D frames [16, 18, 20, 27, 52, 63, 72]. A considerable number of recent scene flow methods rely on stereo inputs [39, 41], but many of them are tailored specifically for self-driving scenes, lacking generalizability to diverse non-automotive contexts. Another line of research [7, 15, 34, 36, 45, 75] estimates 3D motion from a pair or a sequence of point clouds. An important prior that is often used for scene flow estimation is local" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.451, + 0.892, + 0.633 + ], + "angle": 0, + "content": "rigidity [67, 68], where pixels are grouped into rigidly moving clusters (object or part-level), in either a soft or hard manner. For example, RAFT-3D [63] learns rigid-motion embeddings to softly group pixels into rigid objects. Scene flow estimation is also often solved as a sub-task in non-rigid reconstruction pipelines [31, 35, 43]. For example, DynamicFusion [44] takes depth maps as input and computes dense volumetric warp functions by interpolating a sparse set of transformations as bases. In contrast to prior works, we learn to predict long-range 3D trajectories through supervised learning, providing generalization capabilities for handling complex real-world motion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.648, + 0.591, + 0.663 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.795 + ], + "angle": 0, + "content": "Given a monocular video as input, our method tracks any given query pixels across the entire video. Different from prior methods that establish correspondences solely in the 2D space, we lift pixels to 3D using an off-the-shelf monocular depth estimator and perform tracking in a 3D space with richer and more spatially meaningful 3D contextual information, thereby enhancing the overall tracking performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Fig. 2 presents the overview of our proposed pipeline. We first encode the appearance and geometry information of each frame into a triplane representation (Sec. 3.1). Then we perform iterative prediction of trajectories in the 3D space using these triplanes in a sliding window fashion (Sec. 3.2). We leverage the as-rigid-as-possible (ARAP) 3D motion prior during training to facilitate track" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20408" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "ing especially in challenging scenarios of occlusion and large motion (Sec. 3.3). Finally, we describe our training strategy in Sec. 3.4." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.147, + 0.436, + 0.164 + ], + "angle": 0, + "content": "3.1. Triplane Encoding of Input Video Frames" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.468, + 0.246 + ], + "angle": 0, + "content": "To perform tracking in the 3D space, we need to lift 2D pixels into 3D and construct a 3D representation that encodes the feature for each 3D location. To this end, we propose to use triplane features as the 3D scene representation for each frame detailed below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.468, + 0.367 + ], + "angle": 0, + "content": "To start with, for each frame, we obtain its monocular depth map using a pretrained monocular depth estimator, alongside multi-scale feature maps generated by a convolutional neural network (CNN). Subsequently, 2D pixels are unprojected into a set of 3D point clouds, where each 3D point is associated with a feature vector. This feature vector is a concatenation of the corresponding image feature and a positional embedding [65] of its 3D location." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.468, + 0.624 + ], + "angle": 0, + "content": "While this featured point cloud captures both geometry and appearance information, it is incomplete and only covers visible regions (2.5D). Additionally, its irregular and unordered nature poses challenges for effective learning. One simple solution involves voxelizing the point cloud into a 3D feature volume and completing it with 3D convolutions. Yet, this approach is memory and computationally intensive. To obtain 3D features densely and efficiently, we propose to use triplane feature maps, which are obtained by orthographically projecting and average splatting [46] the featured point cloud onto three orthogonal 2D planes, as illustrated in Fig. 2(b). Finally, additional convolutional layers are applied to process and complete each feature map. This triplane feature encoding process is applied to each video frame. Since we do not assume access to camera poses, each triplane is defined within the camera coordinate frame of its respective frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.468, + 0.715 + ], + "angle": 0, + "content": "This triplane representation is compact and enables us to efficiently represent the 3D feature for any given 3D point within the field of view. This process involves projecting the point onto three feature planes, extracting its corresponding feature vectors through bilinear interpolation, and fusing them via simple addition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.468, + 0.822 + ], + "angle": 0, + "content": "Note that while similar concepts of triplanes are explored in related fields [10, 48, 73], our focus here is distinct. Rather than learning a triplane to represent the 3D scene from scratch, we directly leverage monocular depth priors to obtain a triplane where the primary objective is to facilitate tracking in the 3D space, introducing a novel perspective to the field of pixel tracking." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.35, + 0.849 + ], + "angle": 0, + "content": "3.2. Iterative Trajectory Prediction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Given a set of query pixels in the query frame, Sec. 3.1 allows us to obtain their 3D locations and their corresponding triplane features. We now describe the process to estimate" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.789, + 0.106 + ], + "angle": 0, + "content": "their 3D trajectories across the entire video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.197 + ], + "angle": 0, + "content": "Following CoTracker [29], we partition the video into overlapping windows of length \\( T_{s} \\). In each window, we iteratively estimate 3D trajectories for query points over \\( M \\) steps using a transformer. The final 3D trajectories are then propagated to the next window and updated, and this process continues until the end of the video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.294 + ], + "angle": 0, + "content": "Iterative prediction. We now focus on the iterative prediction of 3D trajectories within the first temporal window. Given the 3D location \\( \\mathbf{X}_1 \\in \\mathbb{R}^3 \\) of a query pixel in the first frame, our goal is to predict its 3D corresponding locations (or in other words, its 3D trajectory) in subsequent frames \\( \\{\\mathbf{X}_t\\}_{t=2}^{T_s} \\), where \\( t \\) is the frame index." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.892, + 0.369 + ], + "angle": 0, + "content": "Because we adopt an iterative updating strategy to estimate the 3D trajectories, we further denote the prediction at the \\(m\\)-th step as \\(\\{X_t^m\\}_{t=2}^{T_s}\\). To start with, we initialize \\(\\{X_t^0\\}_{t=2}^{T_s}\\) to be all equal to \\(X_1\\), and then we iteratively update the 3D trajectory using a transformer \\(\\Psi\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.4 + ], + "angle": 0, + "content": "Specifically, for the point \\( \\mathbf{X}_t^m \\) at the \\( m \\)-th iteration, we define its input feature \\( \\mathbf{G}_t^m \\) to the transformer as:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.409, + 0.892, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {G} _ {t} ^ {m} = \\left[ \\gamma \\left(\\boldsymbol {X} _ {t} ^ {m}\\right), \\boldsymbol {F} _ {t} ^ {m}, \\boldsymbol {C} _ {t} ^ {m}, \\gamma \\left(\\boldsymbol {X} _ {t} ^ {m} - \\boldsymbol {X} _ {1}\\right) \\right] \\in \\mathbb {R} ^ {D}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.892, + 0.558 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the positional encoding function and \\(F_{t}^{m}\\) is the feature of point \\(X_{t}^{m}\\). At the first iteration, \\(F_{t}^{0}\\) is extracted from the triplane of frame \\(t\\) at \\(X_{t}^{0}\\). For later iterations, \\(F_{t}^{m}\\) is a direct output of the transformer from the previous iteration. \\(C_{t}^{m}\\) denotes correlation features, which are computed by comparing \\(F_{t}^{m}\\) and local triplane features around \\(X_{t}^{m}\\) at frame \\(t\\). More details of correlation features can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.664 + ], + "angle": 0, + "content": "For each update, the transformer takes as input the features for the trajectories of all query points across the entire window. We denote this set of features at the \\(m\\)-th iteration as \\(\\mathcal{G}^m \\in \\mathbb{R}^{N \\times T_s \\times D} = \\{\\pmb{G}_{i,t}^m \\mid i = 1, \\dots, N; t = 1, \\dots, T_s\\}\\), where \\(i\\) is the query point index and \\(N\\) is the number of query points. \\(\\Psi\\) then takes \\(\\mathcal{G}^m\\) as input and predicts the new set of point positions and features:" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.673, + 0.891, + 0.691 + ], + "angle": 0, + "content": "\\[\n\\mathcal {X} ^ {m + 1}, \\mathcal {F} ^ {m + 1} = \\Psi (\\mathcal {G} ^ {m}), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.701, + 0.892, + 0.809 + ], + "angle": 0, + "content": "where \\(\\mathcal{X}^{m + 1}\\) denotes the set of updated point positions, and \\(\\mathcal{F}^{m + 1}\\) denotes the set of updated point features. New \\(\\mathcal{G}^{m + 1}\\) can then be defined according to Eq. 1, and the same process is repeated \\(M\\) times to obtain the final 3D trajectories for all query points \\(\\mathcal{X}^M = \\{\\pmb {X}_{i,t}^M\\}\\). The 2D correspondence predictions can be computed by simply projecting \\(\\{\\pmb {X}_{i,t}^M\\}\\) back onto the 2D image plane." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As query pixels may not have corresponding pixels at some frames due to occlusions, we additionally predict the visibility for each point of the 3D trajectories at the final iteration \\(M\\). Specifically, for each point \\(\\mathbf{X}_{i,t}^{M}\\), we employ an MLP network that takes the feature \\(\\mathbf{F}_{i,t}^{M}\\) as input and predicts a visibility score \\(v_{i,t}\\)." + }, + { + "type": "footer", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20409" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.233 + ], + "angle": 0, + "content": "Handling long videos. To track points across a long video, we utilize overlapping sliding windows where each pair of adjacent windows has half of their frames overlapped. Given the results from the previous window, we initialize trajectories of the first \\(\\frac{T_s}{2}\\) frames of the current window by copying the results of the last \\(\\frac{T_s}{2}\\) frames from the previous window. The trajectories of the last \\(\\frac{T_s}{2}\\) frames in the current window are initialized by copying the result of the frame \\(\\frac{T_s}{2}\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.244, + 0.36, + 0.26 + ], + "angle": 0, + "content": "3.3. As Rigid As Possible Constraint" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.268, + 0.47, + 0.329 + ], + "angle": 0, + "content": "An advantage of tracking points in 3D is that we can enforce an as-rigid-as-possible (ARAP) constraint, which enhances spatial consistency and facilitates the prediction of motion especially during occlusions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.469, + 0.421 + ], + "angle": 0, + "content": "Enforcing proper ARAP constraints requires identifying if two points belong to the same rigid part. To this end, at each iteration \\(m\\), we additionally compute a rigidity embedding \\(\\pmb{E}_i^m\\) for each trajectory by aggregating its features \\(\\{\\pmb{G}_{i,t}^{m}\\}_{t = 1}^{T_s}\\) across time. Then, the rigidity affinity \\(s_{ij}^{m}\\) between any two trajectories \\(i\\) and \\(j\\) can be calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.199, + 0.434, + 0.47, + 0.454 + ], + "angle": 0, + "content": "\\[\ns _ {i j} ^ {m} = \\operatorname {s i m} \\left(\\boldsymbol {E} _ {i} ^ {m}, \\boldsymbol {E} _ {j} ^ {m}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.465, + 0.394, + 0.48 + ], + "angle": 0, + "content": "where \\(\\mathrm{sim}(\\cdot ,\\cdot)\\) is the cosine similarity measure." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.481, + 0.47, + 0.557 + ], + "angle": 0, + "content": "By the definition of rigidity, the distances between points that are rigidly moving together should be preserved over time. Therefore, we formulate our ARAP loss as follows, encouraging the distances between pairs of points exhibiting high rigidity to remain constant over time:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.57, + 0.469, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {a r a p}} = \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T _ {s}} \\sum_ {\\Omega_ {i j}} w ^ {m} s _ {i j} ^ {m} | | d \\left(\\boldsymbol {X} _ {i, t} ^ {m}, \\boldsymbol {X} _ {j, t} ^ {m}\\right) - d \\left(\\boldsymbol {X} _ {i, 1}, \\boldsymbol {X} _ {j, 1}\\right) | | _ {1}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.616, + 0.47, + 0.691 + ], + "angle": 0, + "content": "where \\(\\Omega_{ij}\\) is the set of all pairwise indices and \\(d(\\cdot, \\cdot)\\) is the Euclidean distance function, and \\(w^{m} = 0.8^{M - m}\\) is the weight for the \\(m\\)-th step. This ARAP loss provides gradients for learning both the 3D trajectories and the rigidity embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.693, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Based on the affinity score between any two points, we can perform spectral clustering [47, 70] to obtain the segmentation of query pixels. Experiments in Sec. 4 show that our method can generate meaningful segmentation of rigid parts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.78, + 0.182, + 0.796 + ], + "angle": 0, + "content": "3.4. Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.805, + 0.469, + 0.849 + ], + "angle": 0, + "content": "In addition to the ARAP loss, we supervise the predicted trajectories using ground truth 3D trajectories at each iteration, which is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.862, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t r a j}} = \\sum_ {m = 1} ^ {M} \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {T _ {s}} w ^ {m} | | \\boldsymbol {X} _ {i, t} ^ {m} - \\hat {\\boldsymbol {X}} _ {i, t} ^ {m} | | _ {1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.137 + ], + "angle": 0, + "content": "where \\( X_{i,t}^{m} \\) and \\( \\hat{X}_{i,t}^{m} \\) are the predicted and ground-truth 3D corresponding locations, respectively, and \\( w^{m} \\) is the weight for the \\( m \\)-th step, identical to that in Eq. 4." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.137, + 0.828, + 0.152 + ], + "angle": 0, + "content": "The predicted visibilities are supervised using:" + }, + { + "type": "equation", + "bbox": [ + 0.599, + 0.157, + 0.892, + 0.199 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {v i s}} = \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {T _ {s}} \\mathrm {C E} \\left(v _ {i, t}, \\hat {v} _ {i, t}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.203, + 0.892, + 0.233 + ], + "angle": 0, + "content": "where \\( v_{i,t} \\) and \\( \\hat{v}_{i,t} \\) denote the predicted and ground-truth visibility, respectively. CE represents the cross entropy loss." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.234, + 0.838, + 0.248 + ], + "angle": 0, + "content": "The total loss function for training is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.255, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {t r a j}} + \\alpha \\mathcal {L} _ {\\text {v i s}} + \\beta \\mathcal {L} _ {\\text {a r a p}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.276, + 0.892, + 0.307 + ], + "angle": 0, + "content": "where \\(\\alpha\\) and \\(\\beta\\) are weighting coefficients. In practice, they are set as 10 and 0.1, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.313, + 0.719, + 0.329 + ], + "angle": 0, + "content": "3.5. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.336, + 0.892, + 0.547 + ], + "angle": 0, + "content": "We train our model on the TAP-Vid-Kubric dataset [11, 14]. Our training data contains 11,000 24-frame RGBD sequences with full-length 3D trajectory annotations. During training, we use ground truth depth maps and camera intrinsics to unproject pixels into 3D space. In cases where the depth map and intrinsics are unavailable at inference, we use ZoeDepth [2] to predict the metric depth map for each video frame, and simply set the focal length to be the same as the image width. To generate triplane feature maps, we discretize the depth values into \\( d = 256 \\) bins. The resolutions of the triplane feature maps are \\( h \\times w \\), \\( w \\times d \\), \\( h \\times d \\) for XY, XZ, and YZ planes, respectively, where \\( h \\), \\( w \\) are the image height and width. The number of channels of the triplane features is 128." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.548, + 0.892, + 0.668 + ], + "angle": 0, + "content": "We train our model with eight 80GB A100 GPUs for 200k iterations. The total training time is around 6 days. The iteration steps \\( M \\) and sliding window length \\( T_{s} \\) are set to 6 and 8 respectively. In each training batch, we sample \\( N = 256 \\) query points. The transformer \\( \\Psi \\) consists of six blocks, each comprising both spatial and temporal attention layers. For more details, please refer to the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.633, + 0.696 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "At inference, our method can operate in two different modalities. The first modality (and the primary focus of this paper) is long-range 2D pixel tracking. In this modality, the input is an RGB video without known depth or camera intrinsics, and we rely on ZoeDepth [2] to estimate the depth maps. Due to the lack of precise depth and intrinsics information, we only evaluate the 2D projection of the 3D trajectories onto the image plane, i.e., 2D pixel trajectories. When RGBD videos and camera intrinsics are available, our method can be used in the second modality to predict long-range 3D trajectories. We evaluate our method for both 2D and 3D tracking performance in Sec 4.1 and Sec 4.2, respectively, and then conduct ablation studies in Sec. 4.3." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "20410" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.079, + 0.895, + 0.216 + ], + "angle": 0, + "content": "
MethodsKinetics [9]DAVIS [50]RGB-Stacking [33]Average
AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑
TAP-Net [11]38.554.480.633.048.678.854.668.387.742.057.182.4
PIPs [17]31.753.772.942.264.877.715.728.477.129.950.075.9
OmniMotion [71]--46.462.785.369.582.590.3---
TAPIR [12]49.664.285.056.270.086.554.269.884.453.368.085.3
CoTracker [29]48.764.386.560.675.489.363.177.087.857.472.287.8
Ours50.165.986.961.176.389.563.577.688.258.273.388.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.221, + 0.893, + 0.251 + ], + "angle": 0, + "content": "Table 1. 2D Tracking Results on the TAP-Vid Benchmark. We report the average jaccard (AJ), average position accuracy \\((<\\delta_{\\mathrm{avg}}^x)\\), and occlusion accuracy (OA) on Kinetics [9], DAVIS [50] and RGB-Stacking [33] datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.268, + 0.298, + 0.284 + ], + "angle": 0, + "content": "4.1. 2D Tracking Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.471, + 0.399 + ], + "angle": 0, + "content": "We conduct our evaluation on three long-range 2D tracking benchmarks: TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Our method is compared with baseline 2D tracking methods, namely TAP-Net [11], PIPs [17], OmniMotion [71], TAPIR [12] and CoTracker [29]. The evaluation protocols and comparison results on each of the benchmarks are represented below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.408, + 0.471, + 0.726 + ], + "angle": 0, + "content": "TAP-Vid Benchmark [11] contains a few datasets: TAP-Vid-DAVIS [50] (30 real videos of about 34-104 frames), TAP-Vid-Kinetics [9] (1144 real videos of 250 frames) and RGB-Stacking [33] (50 synthetic videos of 250 frames). Each video in the benchmark is annotated with ground truth 2D trajectories and occlusions spanning the entire video duration for well-distributed points. We evaluate performance using the same metrics as the TAP-Vid benchmark [11]: average position accuracy \\((< \\delta_{\\mathrm{avg}}^x)\\), Average Jaccard (AJ), and Occlusion Accuracy (OA). Please refer to the supplement for more details. We follow the \"queried first\" evaluation protocol in CoTracker [29]. Specifically, we use the first frame as the query frame and predict the 2D locations of query pixels from this frame in all subsequent frames. The quantitative comparisons are reported in Tab. 1, which shows our method consistently outperforms all baselines except Omnimotion across all three datasets, demonstrating the benefits of tracking in the 3D space. Omnimotion also performs tracking in 3D and obtains the best results on RGB-Stacking by optimizing all frames at once, but it requires very costly test-time optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "BADJA [4] is a benchmark containing seven videos of moving animals with annotated keypoints. The metrics used in this benchmark include segment-based accuracy (segA) and 3px accuracy (\\(\\delta^{3\\mathrm{px}}\\)). The predicted keypoint positions are deemed accurate when its distance from the ground truth keypoint is less than \\(0.2\\sqrt{A}\\), where \\(A\\) is the summation of the area of the segmentation mask. \\(\\delta^{3\\mathrm{px}}\\) depicts the percentage of the correct keypoints whose distances from their ground truth are within three pixels. As shown in Tab. 2, our method demonstrates competitive performance in terms of \\(\\delta^{3\\mathrm{px}}\\) and surpasses all baseline methods by a" + }, + { + "type": "table", + "bbox": [ + 0.528, + 0.266, + 0.864, + 0.38 + ], + "angle": 0, + "content": "
MethodssegA ↓δ3px ↑
TAP-Net [11]54.46.3
PIPs [17]61.913.5
TAPIR [12]66.915.2
OmniMotion [71]57.213.2
CoTracker [29]63.618.0
Ours69.217.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.384, + 0.892, + 0.426 + ], + "angle": 0, + "content": "Table 2. 2D Tracking Results on the BADJA Dataset [4]. The segment-based accuracy (segA) and 3px accuracy \\((\\delta^{3\\mathrm{px}})\\) are reported." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.442, + 0.889, + 0.543 + ], + "angle": 0, + "content": "
MethodsMTE↓<δxavg↑Survival↑
TAP-Net [11]37.829.252.8
PIPs [81]41.030.467.0
CoTracker [29]30.556.276.1
Ours w/ ZoeDepth [2]28.358.478.6
Ours w/ GT depth26.664.178.0
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.547, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Table 3. 2D Tracking Results on the PointOdyssey Dataset [81]. The Median Trajectory Error (MTE), average position accuracy \\((<\\delta_{avg}^{x})\\), and survival rate (Survival) are reported." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.619, + 0.771, + 0.634 + ], + "angle": 0, + "content": "large margin in segment-based accuracy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.903 + ], + "angle": 0, + "content": "PointOdyssey [81] is a large-scale synthetic dataset featuring diverse animated characters ranging from humans to animals, placed within diverse 3D environments. We evaluate our method on PointOdyssey's test set which contains 12 videos with complex motion, each spanning approximately 2000 frames. We adopt the evaluation metrics proposed in PointOdyssey [81] which are designed for evaluating very long trajectories. These metrics include the Median Trajectory Error (MTE), \\(< \\delta_{\\mathrm{avg}}^x\\) (consistent with TAP-Vid), and the survival rate. The survival rate is defined as the average number of frames until tracking failure over the video length. Tracking failure is identified when the L2 error exceeds 50 pixels at a resolution of \\(256 \\times 256\\). In Tab. 3, we report results for baseline methods as well as our method using depths from ZoeDepth [2] (default) and GT depth annotations. Our method consistently outperforms" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20411" + } + ], + [ + { + "type": "aside_text", + "bbox": [ + 0.078, + 0.094, + 0.093, + 0.596 + ], + "angle": 270, + "content": "Ours CoTracker [29] Ours CoTracker [29] Ours CoTracker [29] Ours CoTracker [29]" + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.089, + 0.263, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.157, + 0.263, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.223, + 0.263, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.287, + 0.263, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.354, + 0.263, + 0.419 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.419, + 0.263, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.487, + 0.263, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.112, + 0.553, + 0.263, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.089, + 0.416, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.157, + 0.416, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.223, + 0.416, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.287, + 0.416, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.353, + 0.416, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.487, + 0.416, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.265, + 0.553, + 0.416, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.089, + 0.57, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.157, + 0.569, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.223, + 0.57, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.287, + 0.569, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.353, + 0.57, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.487, + 0.569, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.418, + 0.553, + 0.57, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.089, + 0.723, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.157, + 0.722, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.223, + 0.722, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.287, + 0.722, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.353, + 0.722, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.487, + 0.722, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.572, + 0.553, + 0.722, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.089, + 0.876, + 0.156 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.156, + 0.876, + 0.222 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.223, + 0.876, + 0.286 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.287, + 0.876, + 0.353 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.353, + 0.876, + 0.486 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.487, + 0.876, + 0.552 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.724, + 0.553, + 0.876, + 0.618 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.629, + 0.872, + 0.644 + ], + "angle": 0, + "content": "Figure 3. Qualitative Comparison. For each sequence we show tracking results of CoTracker [29] and our method SpatialTracker." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.47, + 0.754 + ], + "angle": 0, + "content": "the baselines across all metrics by a noticeable margin. In particular, we demonstrate that with access to more accurate ground truth depth, our performance can be further enhanced. This suggests the potential of our method to continue improving alongside advancements in monocular depth estimation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Qualitative Results. We present qualitative comparisons with CoTracker [29] on challenging videos from DAVIS [50] and Internet footage in Fig. 3. Our method outperforms CoTracker in handling complex human motion with self-occlusions, achieves a better understanding of rigid groups, and can effectively track small, rapidly moving objects even in the presence of occlusions. Please refer to the supplementary video for more results and better visualizations." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.662, + 0.722, + 0.679 + ], + "angle": 0, + "content": "4.2.3D Tracking Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Given an RGBD video (with known depth and intrinsics) as input, our method can estimate true 3D trajectories. Since no baseline method can directly be used for long-range 3D tracking, we construct our baselines by composing existing methods. Our first baseline is chained RAFT-3D [63]. RAFT-3D is designed for pairwise scene flow estimation, so to obtain long-range scene flow, we chain its scene flow prediction of consecutive frames. Our second baseline is to directly lift the predicted 2D trajectories from CoTracker [29] using the input depth maps." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We evaluate our method and baselines on the PointOdyssey [81] dataset. We create 231 testing sequences from the test set, each consisting of 24 frames and with a reduced frame rate set at one-fifth of the original. We" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20412" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.472, + 0.161 + ], + "angle": 0, + "content": "
MethodsATE3D ↓δ0.1 ↑δ0.2 ↑
Chained RAFT3D [63]0.700.120.25
Lifted CoTracker [29]0.770.510.64
Ours0.220.590.76
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.167, + 0.47, + 0.223 + ], + "angle": 0, + "content": "Table 4. 3D Tracking Results on the PointOdyssey Dataset. \\(\\mathrm{ATE}_{3D}\\) is the average trajectory error in 3D space and \\(\\delta_t\\) measures the percentage of points whose distances are within \\(t\\) (in meter) from the ground truth." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.236, + 0.474, + 0.329 + ], + "angle": 0, + "content": "
MethodsAJ↑<δxavg↑OA↑
Ours w/o ARAP55.171.687.4
Ours w/ DPT [53]51.470.783.3
Ours w/ MiDaS [5]56.373.986.6
Ours w/ ZoeDepth [2] (default)61.176.389.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.334, + 0.472, + 0.419 + ], + "angle": 0, + "content": "Table 5. Ablation Study on the DAVIS Dataset. The Average Jaccard (AJ), average position accuracy \\((<\\delta_{\\mathrm{avg}}^x)\\), and Occlusion Accuracy (OA) are reported. We evaluate the effectiveness of the ARAP constraint and the influence of different monocular depth estimators (ZoeDepth [2], MiDaS [5] and DPT [53]). \"Ours w/ZoeDepth\" is the default model we use in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.47, + 0.492 + ], + "angle": 0, + "content": "use three evaluation metrics, namely \\(\\mathrm{ATE}_{3\\mathrm{D}}\\), \\(\\delta_{0.1}\\), and \\(\\delta_{0.2}\\). \\(\\mathrm{ATE}_{3\\mathrm{D}}\\) is the average trajectory error in 3D space. \\(\\delta_{0.1}\\) and \\(\\delta_{0.2}\\) measure the percentage of points whose distances are within \\(0.1\\mathrm{m}\\) and \\(0.2\\mathrm{m}\\) from the ground truth, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.471, + 0.675 + ], + "angle": 0, + "content": "The results are shown in Tab. 4. Our method outperforms both \"Chained RAFT-3D\" and \"Lifted CoTracker\" consistently on all three metrics by a large margin. We found that RAFT-3D, trained on FlyingThings [40], generalizes poorly on PointOdyssey, possibly due to the fact that its dense-SE3 module is sensitive to domain gaps. In contrast, also trained on a different dataset (Kubric), our method exhibits strong generalization to PointOdyssey, affirming the efficacy of our design for 3D trajectory prediction. In addition, both baselines cannot handle occlusion and will lose track of points once they become occluded, hurting the performance significantly." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.683, + 0.285, + 0.699 + ], + "angle": 0, + "content": "4.3. Ablation and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.706, + 0.47, + 0.829 + ], + "angle": 0, + "content": "Effectiveness of ARAP loss and rigidity embedding. We ablate the ARAP loss and report the result \"Ours w/o ARAP\" on the TAP-Vid-DAVIS [11, 51] dataset in Tab. 5. Without the ARAP loss, the performance drops substantially, verifying the effectiveness of the ARAP constraint. We additionally showcase qualitative results of the rigid part segmentation, utilizing our learned rigidity embeddings in Fig. 4, demonstrating their effectiveness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Analysis on monocular depth estimators. To study the influence of different monocular depth estimation methods on our model, we evaluate our method with three monocular depth models: ZoeDepth [2] (default), MiDaS [5]," + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.089, + 0.637, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.518, + 0.159, + 0.637, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.089, + 0.755, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.638, + 0.159, + 0.755, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.089, + 0.877, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.757, + 0.159, + 0.877, + 0.227 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.231, + 0.894, + 0.275 + ], + "angle": 0, + "content": "Figure 4. Rigid Part Segmentation. We utilize spectral clustering on the rigidity embedding to determine rigid groups. Each color represents a distinct rigid group." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.294, + 0.893, + 0.446 + ], + "angle": 0, + "content": "and DPT [53]. We report the results on the TAP-ViddAVIS [11, 51] dataset in Tab. 5. \"Ours w/ ZoeDepth\" achieves the best results, probably due to the fact that ZoeDepth [2] is a metric depth estimator and exhibits less temporal inconsistency across frames compared to relative depth estimators MiDaS [5] and DPT [53]. Furthermore, it is noteworthy that the efficacy of our model has a positive correlation with the advancements in the underlying monocular depth models. Please refer to the supplementary material for additional analysis and ablations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.471, + 0.749, + 0.487 + ], + "angle": 0, + "content": "5. Conclusion and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.893, + 0.682 + ], + "angle": 0, + "content": "In this work, we show that a properly designed 3D representation is crucial for solving the long-standing challenge of dense and long-range motion estimation in videos. Motion naturally occurs in 3D and tracking motion in 3D allows us to better leverage its regularity in 3D, e.g., the ARAP constraint. We proposed a novel framework that estimates 3D trajectories using triplane representations with a learnable ARAP constraint that identifies the rigid groups in the scene and enforces rigidity within each group. Experiments demonstrated the superior performance of our method compared to existing baselines and its applicability to challenging real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.892, + 0.792 + ], + "angle": 0, + "content": "Our current model relies on off-the-shelf monocular depth estimators whose accuracy may affect the final tracking performance as shown in Tab. 5. However, we anticipate that advancements in monocular reconstruction will enhance the performance of motion estimation. We expect a closer interplay between these two problems, benefiting each other in the near future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.801, + 0.661, + 0.818 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.902 + ], + "angle": 0, + "content": "This work was partially supported by National Key Research and Development Program of China (No. 2020AAA0108900), Ant Group, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20413" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Steven S. Beauchemin and John L. Barron. The computation of optical flow. 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Tracking 2D pixels in 3D space. To estimate 2D motion under the occlusion and complex 3D motion, we lift 2D pixels into 3D and perform tracking in the 3D space. Two cases of the estimated 3D and 2D trajectories of a waving butterfly (top) and a group of swimming dolphins (bottom) are illustrated. + +![](images/857801b5e8163c74e892311e7f09dd7c5fab7aa3bf078c9c3f4daf35ffa8ac19.jpg) + +![](images/d56ccbadd4865ee99a0ebd62fcc19ee2c496257bc294299e8c2fb057e75cbcee.jpg) + +![](images/445b0804c7687c1cba791d1952eeb92716f3e19d6c4371e75b5e8ec40a10668a.jpg) + +![](images/1755a45e3c81f33f4c05e2da9cc05b76273089838801322aa2b0e53bb02fb4af.jpg) + +# Abstract + +Recovering dense and long-range pixel motion in videos is a challenging problem. Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as + +rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation. And our project page is available at https://henry123-boy.github.io/SpaTracker/. + +# 1. Introduction + +Motion estimation has historically been approached through two main paradigms: feature tracking [37, 38, 58, 64] and optical flow [1, 19, 62]. While each type of method enables numerous applications, neither of them fully captures the motion in a video: optical flow only produces motion for adjacent frames, whereas feature tracking only tracks sparse pixels. + +An ideal solution would involve the ability to estimate + +both dense and long-range pixel trajectories in a video sequence [55, 56]. Seminal work like Particle Video [56] has bridged the gap by representing video motion using a set of semi-dense and long-range particles. More recently, several efforts [11, 12, 17, 29] have revisited this problem, formulating it as tracking any point and addressing it through supervised learning frameworks. While trained solely on synthetic datasets [14, 81], these methods consistently demonstrate strong generalization abilities to real-world videos, pushing the boundaries of long-range pixel tracking through occlusions. + +While great progress has been achieved, current solutions still struggle in challenging scenarios, particularly in cases of complex deformation accompanied by frequent self-occlusions. We argue that one potential cause for this difficulty stems from tracking only in the 2D image space, thereby disregarding the inherent 3D nature of motion. As motion takes place in 3D space, certain properties can only be adequately expressed through 3D representations. For example, rotation can be succinctly explained by three parameters in 3D, and occlusion can be simply expressed with z-buffering, but they are much more complicated to express within a 2D representation. In addition, the key component of these methods — using $2D$ feature correlation to predict motion updates — can be insufficient. Image projection can bring spatially distant regions into proximity within the 2D space, which can cause the local 2D neighborhood for correlation to potentially contain irrelevant context (especially near occlusion boundaries), thereby leading to difficulties in reasoning. + +To tackle these challenges, we propose to leverage geometric priors from state-of-the-art monocular depth estimators [2] to lift 2D pixels into 3D, and perform tracking in the 3D space. This involves conducting feature correlation in 3D, which provides more meaningful 3D context for tracking especially in cases of complex motion. Tracking in 3D also allows for enforcing 3D motion priors [52, 63] such as ARAP constraint. Encouraging the model to learn which points move rigidly together can help track ambiguous or occluded pixels, as their motion can then be inferred using neighboring unambiguous and visible regions within the same rigid group. + +Specifically, we propose to represent the 3D scene of each frame with triplane feature maps [10], which are obtained by first lifting image features to 3D featured point clouds and then splatting them onto three orthogonal planes. The triplane representation is compact and regular, suitable for our learning framework. Moreover, it covers the 3D space densely, enabling us to extract the feature vectors of any 3D point for tracking. We then compute 3D trajectories for query pixels through iterative updates predicted by a transformer using features from our triplane representation. To regularize the estimated 3D trajectories + +with 3D motion prior, our model additionally predicts a rigidity embedding for each trajectory, which allows us to softly group pixels exhibiting the same rigid body motion and enforce an ARAP regularization for each rigid cluster. We demonstrate that the rigidity embedding can be learned self-supervisedly and produce reasonable segmentation of different rigid parts. + +Our model achieves state-of-the-art performance on various public tracking benchmarks including TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Qualitative results on challenging Internet videos also demonstrate the superior capability of our model to handle fast complex motion and extended occlusion. + +# 2. Related Work + +Optical flow. Optical flow is the task of estimating dense 2D pixel-level motion between a pair of frames. While traditional methods [1, 6, 8, 19, 74, 78] formulate it as an energy minimization problem, recent approaches [13, 23, 24, 61, 76] have demonstrated the ability to predict optical flow directly using deep neural networks. Notably, RAFT [62] employs a 4D correlation volume and estimates optical flow through iteratively updates with a recurrent operator. More recently, transformer-based flow estimators [21, 26, 59, 80] achieved superior performance, showing the strong capacity of the transformer architecture. However, pairwise optical flow methods are not suitable for long-term tracking, as they are not designed to handle long temporal contexts [8, 74]. Multi-frame optical flow methods [25, 28, 32, 54, 69] extend pairwise flow by incorporating multi-frame contexts (typically 3-5 frames), but this remains insufficient for tracking through long occlusions in videos spanning tens or hundreds of frames. + +Tracking any point. Recognizing the limitations of optical flow, seminal work Particle Video [56] proposes to represent video motion as a set of long-range particles that move through time, which are optimized by enforcing long-range appearance consistency and motion coherence with variational techniques. However, Particle Video only generates semi-dense tracks and cannot recover from occlusion events [55]. Recently, PIPs [17] revisited this idea by introducing a feedforward network that takes RGB frames of a fixed temporal window (8 frames) as input and predicts the motion for any given query point through iterative updates. However, PIPs tracks points independently, neglecting spatial context information, and will lose the target if they stay occluded beyond the temporal window. Several recent advancements [3, 11, 12, 42, 71, 81] in point tracking have surfaced, addressing some of PIPs' limitations. TAPIR [12] relaxes the fixed-length window constraint by using a temporal depthwise convolutional network capable of accommodating variable lengths. Co + +![](images/bf0b5e255c67d23149282eda10cb0a1774b4fc861a4fcbed2b4d60e4748dda06.jpg) +Figure 2. Overview of Our Pipeline. We first encode each frame into a triplane representation (a) using a triplane encoder (b). We then initialize and iteratively update point trajectories in the 3D space using a transformer with features extracted from these triplanes as input (c). The 3D trajectories are trained with ground truth annotations and are regularized by an as-rigid-as-possible (ARAP) constraint with learned rigidity embedding (d). The ARAP constraint enforces that 3D distances between points with similar rigidity embeddings remain constant over time. Here $d_{ij}$ represents the distance between points $i$ and $j$ , while $s_{ij}$ denotes the rigid similarity. Our method produces accurate long-range motion tracks even under fast movements and severe occlusion (e). + +![](images/1388707f573cd97128dd6d0266af7b4812b435973b95a8684e07c969c0fe59af.jpg) + +Tracker [29] proposed to jointly track multiple points and leverage spatial correlation between them, leading to state-of-the-art performance. + +Though significant progress has been made, these works all compute feature correlation in the 2D image space, losing important information about the 3D scene where the motion actually takes place. In contrast, we lift 2D points into 3D and perform tracking in the 3D space. The more meaningful 3D contexts (as opposed to 2D), along with an as-rigid-as-possible regularization, facilitate improved handling of occlusions and enhance tracking accuracy. Previous studies have also explored computing 2D motion with a touch of 3D, e.g., through depth-separated layers [30, 57, 60, 77] or quasi-3D space [71]. However, distinct from their optimization-based pipelines, we perform long-range 3D tracking in a more efficient, feedforward manner. + +Scene flow. Scene flow defines a dense 3D motion field of points in a scene. Early work estimates scene flow in multi-view stereo settings [49, 66, 79] through variational optimization [22]. The introduction of depth sensors enabled more effective scene flow estimation from pairs or sequences of RGB-D frames [16, 18, 20, 27, 52, 63, 72]. A considerable number of recent scene flow methods rely on stereo inputs [39, 41], but many of them are tailored specifically for self-driving scenes, lacking generalizability to diverse non-automotive contexts. Another line of research [7, 15, 34, 36, 45, 75] estimates 3D motion from a pair or a sequence of point clouds. An important prior that is often used for scene flow estimation is local + +rigidity [67, 68], where pixels are grouped into rigidly moving clusters (object or part-level), in either a soft or hard manner. For example, RAFT-3D [63] learns rigid-motion embeddings to softly group pixels into rigid objects. Scene flow estimation is also often solved as a sub-task in non-rigid reconstruction pipelines [31, 35, 43]. For example, DynamicFusion [44] takes depth maps as input and computes dense volumetric warp functions by interpolating a sparse set of transformations as bases. In contrast to prior works, we learn to predict long-range 3D trajectories through supervised learning, providing generalization capabilities for handling complex real-world motion. + +# 3. Method + +Given a monocular video as input, our method tracks any given query pixels across the entire video. Different from prior methods that establish correspondences solely in the 2D space, we lift pixels to 3D using an off-the-shelf monocular depth estimator and perform tracking in a 3D space with richer and more spatially meaningful 3D contextual information, thereby enhancing the overall tracking performance. + +Fig. 2 presents the overview of our proposed pipeline. We first encode the appearance and geometry information of each frame into a triplane representation (Sec. 3.1). Then we perform iterative prediction of trajectories in the 3D space using these triplanes in a sliding window fashion (Sec. 3.2). We leverage the as-rigid-as-possible (ARAP) 3D motion prior during training to facilitate track + +ing especially in challenging scenarios of occlusion and large motion (Sec. 3.3). Finally, we describe our training strategy in Sec. 3.4. + +# 3.1. Triplane Encoding of Input Video Frames + +To perform tracking in the 3D space, we need to lift 2D pixels into 3D and construct a 3D representation that encodes the feature for each 3D location. To this end, we propose to use triplane features as the 3D scene representation for each frame detailed below. + +To start with, for each frame, we obtain its monocular depth map using a pretrained monocular depth estimator, alongside multi-scale feature maps generated by a convolutional neural network (CNN). Subsequently, 2D pixels are unprojected into a set of 3D point clouds, where each 3D point is associated with a feature vector. This feature vector is a concatenation of the corresponding image feature and a positional embedding [65] of its 3D location. + +While this featured point cloud captures both geometry and appearance information, it is incomplete and only covers visible regions (2.5D). Additionally, its irregular and unordered nature poses challenges for effective learning. One simple solution involves voxelizing the point cloud into a 3D feature volume and completing it with 3D convolutions. Yet, this approach is memory and computationally intensive. To obtain 3D features densely and efficiently, we propose to use triplane feature maps, which are obtained by orthographically projecting and average splatting [46] the featured point cloud onto three orthogonal 2D planes, as illustrated in Fig. 2(b). Finally, additional convolutional layers are applied to process and complete each feature map. This triplane feature encoding process is applied to each video frame. Since we do not assume access to camera poses, each triplane is defined within the camera coordinate frame of its respective frame. + +This triplane representation is compact and enables us to efficiently represent the 3D feature for any given 3D point within the field of view. This process involves projecting the point onto three feature planes, extracting its corresponding feature vectors through bilinear interpolation, and fusing them via simple addition. + +Note that while similar concepts of triplanes are explored in related fields [10, 48, 73], our focus here is distinct. Rather than learning a triplane to represent the 3D scene from scratch, we directly leverage monocular depth priors to obtain a triplane where the primary objective is to facilitate tracking in the 3D space, introducing a novel perspective to the field of pixel tracking. + +# 3.2. Iterative Trajectory Prediction + +Given a set of query pixels in the query frame, Sec. 3.1 allows us to obtain their 3D locations and their corresponding triplane features. We now describe the process to estimate + +their 3D trajectories across the entire video. + +Following CoTracker [29], we partition the video into overlapping windows of length $T_{s}$ . In each window, we iteratively estimate 3D trajectories for query points over $M$ steps using a transformer. The final 3D trajectories are then propagated to the next window and updated, and this process continues until the end of the video. + +Iterative prediction. We now focus on the iterative prediction of 3D trajectories within the first temporal window. Given the 3D location $\mathbf{X}_1 \in \mathbb{R}^3$ of a query pixel in the first frame, our goal is to predict its 3D corresponding locations (or in other words, its 3D trajectory) in subsequent frames $\{\mathbf{X}_t\}_{t=2}^{T_s}$ , where $t$ is the frame index. + +Because we adopt an iterative updating strategy to estimate the 3D trajectories, we further denote the prediction at the $m$ -th step as $\{X_t^m\}_{t=2}^{T_s}$ . To start with, we initialize $\{X_t^0\}_{t=2}^{T_s}$ to be all equal to $X_1$ , and then we iteratively update the 3D trajectory using a transformer $\Psi$ . + +Specifically, for the point $\mathbf{X}_t^m$ at the $m$ -th iteration, we define its input feature $\mathbf{G}_t^m$ to the transformer as: + +$$ +\boldsymbol {G} _ {t} ^ {m} = \left[ \gamma \left(\boldsymbol {X} _ {t} ^ {m}\right), \boldsymbol {F} _ {t} ^ {m}, \boldsymbol {C} _ {t} ^ {m}, \gamma \left(\boldsymbol {X} _ {t} ^ {m} - \boldsymbol {X} _ {1}\right) \right] \in \mathbb {R} ^ {D}, \tag {1} +$$ + +where $\gamma$ is the positional encoding function and $F_{t}^{m}$ is the feature of point $X_{t}^{m}$ . At the first iteration, $F_{t}^{0}$ is extracted from the triplane of frame $t$ at $X_{t}^{0}$ . For later iterations, $F_{t}^{m}$ is a direct output of the transformer from the previous iteration. $C_{t}^{m}$ denotes correlation features, which are computed by comparing $F_{t}^{m}$ and local triplane features around $X_{t}^{m}$ at frame $t$ . More details of correlation features can be found in the supplementary material. + +For each update, the transformer takes as input the features for the trajectories of all query points across the entire window. We denote this set of features at the $m$ -th iteration as $\mathcal{G}^m \in \mathbb{R}^{N \times T_s \times D} = \{\pmb{G}_{i,t}^m \mid i = 1, \dots, N; t = 1, \dots, T_s\}$ , where $i$ is the query point index and $N$ is the number of query points. $\Psi$ then takes $\mathcal{G}^m$ as input and predicts the new set of point positions and features: + +$$ +\mathcal {X} ^ {m + 1}, \mathcal {F} ^ {m + 1} = \Psi (\mathcal {G} ^ {m}), \tag {2} +$$ + +where $\mathcal{X}^{m + 1}$ denotes the set of updated point positions, and $\mathcal{F}^{m + 1}$ denotes the set of updated point features. New $\mathcal{G}^{m + 1}$ can then be defined according to Eq. 1, and the same process is repeated $M$ times to obtain the final 3D trajectories for all query points $\mathcal{X}^M = \{\pmb {X}_{i,t}^M\}$ . The 2D correspondence predictions can be computed by simply projecting $\{\pmb {X}_{i,t}^M\}$ back onto the 2D image plane. + +As query pixels may not have corresponding pixels at some frames due to occlusions, we additionally predict the visibility for each point of the 3D trajectories at the final iteration $M$ . Specifically, for each point $\mathbf{X}_{i,t}^{M}$ , we employ an MLP network that takes the feature $\mathbf{F}_{i,t}^{M}$ as input and predicts a visibility score $v_{i,t}$ . + +Handling long videos. To track points across a long video, we utilize overlapping sliding windows where each pair of adjacent windows has half of their frames overlapped. Given the results from the previous window, we initialize trajectories of the first $\frac{T_s}{2}$ frames of the current window by copying the results of the last $\frac{T_s}{2}$ frames from the previous window. The trajectories of the last $\frac{T_s}{2}$ frames in the current window are initialized by copying the result of the frame $\frac{T_s}{2}$ . + +# 3.3. As Rigid As Possible Constraint + +An advantage of tracking points in 3D is that we can enforce an as-rigid-as-possible (ARAP) constraint, which enhances spatial consistency and facilitates the prediction of motion especially during occlusions. + +Enforcing proper ARAP constraints requires identifying if two points belong to the same rigid part. To this end, at each iteration $m$ , we additionally compute a rigidity embedding $\pmb{E}_i^m$ for each trajectory by aggregating its features $\{\pmb{G}_{i,t}^{m}\}_{t = 1}^{T_s}$ across time. Then, the rigidity affinity $s_{ij}^{m}$ between any two trajectories $i$ and $j$ can be calculated as: + +$$ +s _ {i j} ^ {m} = \operatorname {s i m} \left(\boldsymbol {E} _ {i} ^ {m}, \boldsymbol {E} _ {j} ^ {m}\right), \tag {3} +$$ + +where $\mathrm{sim}(\cdot ,\cdot)$ is the cosine similarity measure. + +By the definition of rigidity, the distances between points that are rigidly moving together should be preserved over time. Therefore, we formulate our ARAP loss as follows, encouraging the distances between pairs of points exhibiting high rigidity to remain constant over time: + +$$ +\mathcal {L} _ {\text {a r a p}} = \sum_ {m = 1} ^ {M} \sum_ {t = 1} ^ {T _ {s}} \sum_ {\Omega_ {i j}} w ^ {m} s _ {i j} ^ {m} | | d \left(\boldsymbol {X} _ {i, t} ^ {m}, \boldsymbol {X} _ {j, t} ^ {m}\right) - d \left(\boldsymbol {X} _ {i, 1}, \boldsymbol {X} _ {j, 1}\right) | | _ {1}, \tag {4} +$$ + +where $\Omega_{ij}$ is the set of all pairwise indices and $d(\cdot, \cdot)$ is the Euclidean distance function, and $w^{m} = 0.8^{M - m}$ is the weight for the $m$ -th step. This ARAP loss provides gradients for learning both the 3D trajectories and the rigidity embeddings. + +Based on the affinity score between any two points, we can perform spectral clustering [47, 70] to obtain the segmentation of query pixels. Experiments in Sec. 4 show that our method can generate meaningful segmentation of rigid parts. + +# 3.4. Training + +In addition to the ARAP loss, we supervise the predicted trajectories using ground truth 3D trajectories at each iteration, which is defined as: + +$$ +\mathcal {L} _ {\text {t r a j}} = \sum_ {m = 1} ^ {M} \sum_ {i = 1} ^ {N} \sum_ {t = 1} ^ {T _ {s}} w ^ {m} | | \boldsymbol {X} _ {i, t} ^ {m} - \hat {\boldsymbol {X}} _ {i, t} ^ {m} | | _ {1}, \tag {5} +$$ + +where $X_{i,t}^{m}$ and $\hat{X}_{i,t}^{m}$ are the predicted and ground-truth 3D corresponding locations, respectively, and $w^{m}$ is the weight for the $m$ -th step, identical to that in Eq. 4. + +The predicted visibilities are supervised using: + +$$ +\mathcal {L} _ {\mathrm {v i s}} = \sum_ {i = 1} ^ {N} \sum_ {t = 1} ^ {T _ {s}} \mathrm {C E} \left(v _ {i, t}, \hat {v} _ {i, t}\right), \tag {6} +$$ + +where $v_{i,t}$ and $\hat{v}_{i,t}$ denote the predicted and ground-truth visibility, respectively. CE represents the cross entropy loss. + +The total loss function for training is defined as: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \mathcal {L} _ {\text {t r a j}} + \alpha \mathcal {L} _ {\text {v i s}} + \beta \mathcal {L} _ {\text {a r a p}}, \tag {7} +$$ + +where $\alpha$ and $\beta$ are weighting coefficients. In practice, they are set as 10 and 0.1, respectively. + +# 3.5. Implementation Details + +We train our model on the TAP-Vid-Kubric dataset [11, 14]. Our training data contains 11,000 24-frame RGBD sequences with full-length 3D trajectory annotations. During training, we use ground truth depth maps and camera intrinsics to unproject pixels into 3D space. In cases where the depth map and intrinsics are unavailable at inference, we use ZoeDepth [2] to predict the metric depth map for each video frame, and simply set the focal length to be the same as the image width. To generate triplane feature maps, we discretize the depth values into $d = 256$ bins. The resolutions of the triplane feature maps are $h \times w$ , $w \times d$ , $h \times d$ for XY, XZ, and YZ planes, respectively, where $h$ , $w$ are the image height and width. The number of channels of the triplane features is 128. + +We train our model with eight 80GB A100 GPUs for 200k iterations. The total training time is around 6 days. The iteration steps $M$ and sliding window length $T_{s}$ are set to 6 and 8 respectively. In each training batch, we sample $N = 256$ query points. The transformer $\Psi$ consists of six blocks, each comprising both spatial and temporal attention layers. For more details, please refer to the supplementary material. + +# 4. Experiments + +At inference, our method can operate in two different modalities. The first modality (and the primary focus of this paper) is long-range 2D pixel tracking. In this modality, the input is an RGB video without known depth or camera intrinsics, and we rely on ZoeDepth [2] to estimate the depth maps. Due to the lack of precise depth and intrinsics information, we only evaluate the 2D projection of the 3D trajectories onto the image plane, i.e., 2D pixel trajectories. When RGBD videos and camera intrinsics are available, our method can be used in the second modality to predict long-range 3D trajectories. We evaluate our method for both 2D and 3D tracking performance in Sec 4.1 and Sec 4.2, respectively, and then conduct ablation studies in Sec. 4.3. + +
MethodsKinetics [9]DAVIS [50]RGB-Stacking [33]Average
AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑
TAP-Net [11]38.554.480.633.048.678.854.668.387.742.057.182.4
PIPs [17]31.753.772.942.264.877.715.728.477.129.950.075.9
OmniMotion [71]--46.462.785.369.582.590.3---
TAPIR [12]49.664.285.056.270.086.554.269.884.453.368.085.3
CoTracker [29]48.764.386.560.675.489.363.177.087.857.472.287.8
Ours50.165.986.961.176.389.563.577.688.258.273.388.2
+ +# 4.1. 2D Tracking Evaluation + +We conduct our evaluation on three long-range 2D tracking benchmarks: TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Our method is compared with baseline 2D tracking methods, namely TAP-Net [11], PIPs [17], OmniMotion [71], TAPIR [12] and CoTracker [29]. The evaluation protocols and comparison results on each of the benchmarks are represented below. + +TAP-Vid Benchmark [11] contains a few datasets: TAP-Vid-DAVIS [50] (30 real videos of about 34-104 frames), TAP-Vid-Kinetics [9] (1144 real videos of 250 frames) and RGB-Stacking [33] (50 synthetic videos of 250 frames). Each video in the benchmark is annotated with ground truth 2D trajectories and occlusions spanning the entire video duration for well-distributed points. We evaluate performance using the same metrics as the TAP-Vid benchmark [11]: average position accuracy $(< \delta_{\mathrm{avg}}^x)$ , Average Jaccard (AJ), and Occlusion Accuracy (OA). Please refer to the supplement for more details. We follow the "queried first" evaluation protocol in CoTracker [29]. Specifically, we use the first frame as the query frame and predict the 2D locations of query pixels from this frame in all subsequent frames. The quantitative comparisons are reported in Tab. 1, which shows our method consistently outperforms all baselines except Omnimotion across all three datasets, demonstrating the benefits of tracking in the 3D space. Omnimotion also performs tracking in 3D and obtains the best results on RGB-Stacking by optimizing all frames at once, but it requires very costly test-time optimization. + +BADJA [4] is a benchmark containing seven videos of moving animals with annotated keypoints. The metrics used in this benchmark include segment-based accuracy (segA) and 3px accuracy ( $\delta^{3\mathrm{px}}$ ). The predicted keypoint positions are deemed accurate when its distance from the ground truth keypoint is less than $0.2\sqrt{A}$ , where $A$ is the summation of the area of the segmentation mask. $\delta^{3\mathrm{px}}$ depicts the percentage of the correct keypoints whose distances from their ground truth are within three pixels. As shown in Tab. 2, our method demonstrates competitive performance in terms of $\delta^{3\mathrm{px}}$ and surpasses all baseline methods by a + +Table 1. 2D Tracking Results on the TAP-Vid Benchmark. We report the average jaccard (AJ), average position accuracy $(<\delta_{\mathrm{avg}}^x)$ , and occlusion accuracy (OA) on Kinetics [9], DAVIS [50] and RGB-Stacking [33] datasets. + +
MethodssegA ↓δ3px ↑
TAP-Net [11]54.46.3
PIPs [17]61.913.5
TAPIR [12]66.915.2
OmniMotion [71]57.213.2
CoTracker [29]63.618.0
Ours69.217.1
+ +Table 2. 2D Tracking Results on the BADJA Dataset [4]. The segment-based accuracy (segA) and 3px accuracy $(\delta^{3\mathrm{px}})$ are reported. + +
MethodsMTE↓<δxavg↑Survival↑
TAP-Net [11]37.829.252.8
PIPs [81]41.030.467.0
CoTracker [29]30.556.276.1
Ours w/ ZoeDepth [2]28.358.478.6
Ours w/ GT depth26.664.178.0
+ +Table 3. 2D Tracking Results on the PointOdyssey Dataset [81]. The Median Trajectory Error (MTE), average position accuracy $(<\delta_{avg}^{x})$ , and survival rate (Survival) are reported. + +large margin in segment-based accuracy. + +PointOdyssey [81] is a large-scale synthetic dataset featuring diverse animated characters ranging from humans to animals, placed within diverse 3D environments. We evaluate our method on PointOdyssey's test set which contains 12 videos with complex motion, each spanning approximately 2000 frames. We adopt the evaluation metrics proposed in PointOdyssey [81] which are designed for evaluating very long trajectories. These metrics include the Median Trajectory Error (MTE), $< \delta_{\mathrm{avg}}^x$ (consistent with TAP-Vid), and the survival rate. The survival rate is defined as the average number of frames until tracking failure over the video length. Tracking failure is identified when the L2 error exceeds 50 pixels at a resolution of $256 \times 256$ . In Tab. 3, we report results for baseline methods as well as our method using depths from ZoeDepth [2] (default) and GT depth annotations. Our method consistently outperforms + +![](images/aa5e95d2a7077af8c74cd9ff8e0f8c555ef77247493bbdda1908ee531ecd5225.jpg) + +![](images/2fd40a5e3a73c468047cce9a13129517effebd606d741684a3dbfe61eaad96ef.jpg) + +![](images/5f7d9c45889c67d22b28727c547836885c0f9500eded1665cb32dd1685f60d94.jpg) + +![](images/15a0fcad60671ddb97c9b8d5424ff88b7f836b7baf8a87294f2f392614d1a475.jpg) + +![](images/b6d312ec6ea4dfbb83c9ab2a2339e81501eeb2d1bd6b4811e1e5ef67391cc5cb.jpg) + +![](images/3109a81678974553943ee72e18e4ee67266b38f65a3e0944fb98212d6312a0d7.jpg) + +![](images/f6b91df3205dc6c99263b53252ff0be46ccbdc2a76978f7106191809287761ed.jpg) + +![](images/6736ec9cb0deafaec8de24c84dc14cc18842a5f019a3ffd6f3329288e2a15f8e.jpg) +Figure 3. Qualitative Comparison. For each sequence we show tracking results of CoTracker [29] and our method SpatialTracker. + +![](images/8bebb2f55f9eeae13d002eadc47a97c352a9f38c99f5e656b837e68beb7901c1.jpg) + +![](images/d754b05c5397949921e4cd7ed58dcedd173b2b05525e4b7a3e9d672cf356a703.jpg) + +![](images/c4a80b152d29e679c1d625d9e6b0c883a670cf7d9d7c973a4479bfead5069b38.jpg) + +![](images/928231d0f84f47d6dc059b35bd666f054529ea3b0a84048b093a628dd4adcf72.jpg) + +![](images/2854a1963fd5eacde340652b6f8f72971d168a5c1b675ab660120c0f007808e4.jpg) + +![](images/057b6078a25e39f9eca17782d9f850c2b999e8e3df8161c38cdbbe453686000d.jpg) + +![](images/24320d2d2b081da4a5d757048d91fe72c6c6a12dfdbe26875c45dc863d5bb179.jpg) + +![](images/e385c2fb5732e5317fb8004a065be9c2b2b459f9b036a582234472b78f1d582d.jpg) + +![](images/4ece94c306b61b799e68f26e77db3018ce4971cf1c7ba71f3cbcd513ccd96ee6.jpg) + +![](images/fc9545ecc05aa0d60ca4a8095df9d315df36f18de2bbde9523ec170a5592fe3e.jpg) + +![](images/e437fc4e1810bd2ce447e722cae693f81661797014a01d3486ef63868cf97105.jpg) + +![](images/fd4fb8d4bc1c7894bbea01ab1d67bd6469a557b260ca96915755d3e7fdc3121b.jpg) + +![](images/e0e7b1283d259fdd65a10d096b4db8f1a82d692e54f19cbeb4ca3759026cf0e7.jpg) + +![](images/a48218b2e31e6bbeac83da1fba6df7d4ad9364afc04021b4f26b947c5a3be9b2.jpg) + +![](images/2aabd9238fd0c791e03c0de37e7bcb85e4c16da9e7e4d5c4f15ac8776dbba7e6.jpg) + +![](images/16db41b1b36617c4073a5b04f54306b8aee90776df1516a31d2327143552be4e.jpg) + +![](images/4ca63b019d73898cb6668adbb13e6e68036dcf83d8e4086a5cddeefec96ed073.jpg) + +![](images/e9d87d0e12f579111e87d2f7877064d6178b431fb8da2510f7f3068cdb78c09f.jpg) + +![](images/cd856abccf0a8fe39f5158fb7a2bd427e100cdc34f2869538ea979d90fdfe97c.jpg) + +![](images/b0f73424fea9124f0760a8982d8a86ee01d7cb8298a71543d803868ee9f1baef.jpg) + +![](images/4c407ea5d127940a3ef060287e0d239b8c20205621d2e280626103ad323f2ca3.jpg) + +![](images/80855319443cbba848e6d7974f5c8923661b136f1ecf476881ffdf4825b7503f.jpg) + +![](images/8878c45c7a5b9ac0a796fddc34c2cd872f5a9a0cc373e120a06e1450f72ed90a.jpg) + +![](images/bb9629dbfbef2c27a5e32afc48a5e7a25d1fb29f855749bc7da17cb8867c5db9.jpg) + +![](images/75a2469b313b43bbb1af9e3e88fa95d0698e9625504d815611d827a8fe21c35a.jpg) + +![](images/b47ee5f02ffa6436c37e7048fddf38b5e3f9d706d01c66953407fd2216586a9e.jpg) + +![](images/38475f3b7ceb67820ec7f395a879c8f76b3f19e31a3d6ba7a2c1de7185f5dc69.jpg) + +![](images/300ea2479ca1e8516107289f5efe4fb2fa06ff326f1d481a28acb4c38d478839.jpg) + +the baselines across all metrics by a noticeable margin. In particular, we demonstrate that with access to more accurate ground truth depth, our performance can be further enhanced. This suggests the potential of our method to continue improving alongside advancements in monocular depth estimation. + +Qualitative Results. We present qualitative comparisons with CoTracker [29] on challenging videos from DAVIS [50] and Internet footage in Fig. 3. Our method outperforms CoTracker in handling complex human motion with self-occlusions, achieves a better understanding of rigid groups, and can effectively track small, rapidly moving objects even in the presence of occlusions. Please refer to the supplementary video for more results and better visualizations. + +# 4.2.3D Tracking Evaluation + +Given an RGBD video (with known depth and intrinsics) as input, our method can estimate true 3D trajectories. Since no baseline method can directly be used for long-range 3D tracking, we construct our baselines by composing existing methods. Our first baseline is chained RAFT-3D [63]. RAFT-3D is designed for pairwise scene flow estimation, so to obtain long-range scene flow, we chain its scene flow prediction of consecutive frames. Our second baseline is to directly lift the predicted 2D trajectories from CoTracker [29] using the input depth maps. + +We evaluate our method and baselines on the PointOdyssey [81] dataset. We create 231 testing sequences from the test set, each consisting of 24 frames and with a reduced frame rate set at one-fifth of the original. We + +
MethodsATE3D ↓δ0.1 ↑δ0.2 ↑
Chained RAFT3D [63]0.700.120.25
Lifted CoTracker [29]0.770.510.64
Ours0.220.590.76
+ +Table 4. 3D Tracking Results on the PointOdyssey Dataset. $\mathrm{ATE}_{3D}$ is the average trajectory error in 3D space and $\delta_t$ measures the percentage of points whose distances are within $t$ (in meter) from the ground truth. + +
MethodsAJ↑<δxavg↑OA↑
Ours w/o ARAP55.171.687.4
Ours w/ DPT [53]51.470.783.3
Ours w/ MiDaS [5]56.373.986.6
Ours w/ ZoeDepth [2] (default)61.176.389.5
+ +Table 5. Ablation Study on the DAVIS Dataset. The Average Jaccard (AJ), average position accuracy $(<\delta_{\mathrm{avg}}^x)$ , and Occlusion Accuracy (OA) are reported. We evaluate the effectiveness of the ARAP constraint and the influence of different monocular depth estimators (ZoeDepth [2], MiDaS [5] and DPT [53]). "Ours w/ZoeDepth" is the default model we use in our experiments. + +use three evaluation metrics, namely $\mathrm{ATE}_{3\mathrm{D}}$ , $\delta_{0.1}$ , and $\delta_{0.2}$ . $\mathrm{ATE}_{3\mathrm{D}}$ is the average trajectory error in 3D space. $\delta_{0.1}$ and $\delta_{0.2}$ measure the percentage of points whose distances are within $0.1\mathrm{m}$ and $0.2\mathrm{m}$ from the ground truth, respectively. + +The results are shown in Tab. 4. Our method outperforms both "Chained RAFT-3D" and "Lifted CoTracker" consistently on all three metrics by a large margin. We found that RAFT-3D, trained on FlyingThings [40], generalizes poorly on PointOdyssey, possibly due to the fact that its dense-SE3 module is sensitive to domain gaps. In contrast, also trained on a different dataset (Kubric), our method exhibits strong generalization to PointOdyssey, affirming the efficacy of our design for 3D trajectory prediction. In addition, both baselines cannot handle occlusion and will lose track of points once they become occluded, hurting the performance significantly. + +# 4.3. Ablation and Analysis + +Effectiveness of ARAP loss and rigidity embedding. We ablate the ARAP loss and report the result "Ours w/o ARAP" on the TAP-Vid-DAVIS [11, 51] dataset in Tab. 5. Without the ARAP loss, the performance drops substantially, verifying the effectiveness of the ARAP constraint. We additionally showcase qualitative results of the rigid part segmentation, utilizing our learned rigidity embeddings in Fig. 4, demonstrating their effectiveness. + +Analysis on monocular depth estimators. To study the influence of different monocular depth estimation methods on our model, we evaluate our method with three monocular depth models: ZoeDepth [2] (default), MiDaS [5], + +![](images/9c3fe704c16d51627ca1cc0cd04c0a1edb1789be10a9d7164df903314720e473.jpg) + +![](images/8be9438c4c8a36816b5441bdfc3d1a8193c69be9fecfa25cb39f2e5e1abfa8ee.jpg) +Figure 4. Rigid Part Segmentation. We utilize spectral clustering on the rigidity embedding to determine rigid groups. Each color represents a distinct rigid group. + +![](images/a0e86ee688ffca98207ba134e268ef426aebeadd87a0a6a11156a17c0c73aae2.jpg) + +![](images/6947fb33ca87259dc93c60d4b2086abc5edef6366c2916c9e1f4b9fb472870e1.jpg) + +![](images/11c48fdb5bf74ae88f491205269c2ef52cf2016de908a384d61f9960f728feb0.jpg) + +![](images/bcda10462d663e2b809b8c5adbb8504da5fb47a14d56a6632a87d4f3fac6100b.jpg) + +and DPT [53]. We report the results on the TAP-ViddAVIS [11, 51] dataset in Tab. 5. "Ours w/ ZoeDepth" achieves the best results, probably due to the fact that ZoeDepth [2] is a metric depth estimator and exhibits less temporal inconsistency across frames compared to relative depth estimators MiDaS [5] and DPT [53]. Furthermore, it is noteworthy that the efficacy of our model has a positive correlation with the advancements in the underlying monocular depth models. Please refer to the supplementary material for additional analysis and ablations. + +# 5. Conclusion and Discussion + +In this work, we show that a properly designed 3D representation is crucial for solving the long-standing challenge of dense and long-range motion estimation in videos. Motion naturally occurs in 3D and tracking motion in 3D allows us to better leverage its regularity in 3D, e.g., the ARAP constraint. We proposed a novel framework that estimates 3D trajectories using triplane representations with a learnable ARAP constraint that identifies the rigid groups in the scene and enforces rigidity within each group. Experiments demonstrated the superior performance of our method compared to existing baselines and its applicability to challenging real-world scenarios. + +Our current model relies on off-the-shelf monocular depth estimators whose accuracy may affect the final tracking performance as shown in Tab. 5. However, we anticipate that advancements in monocular reconstruction will enhance the performance of motion estimation. We expect a closer interplay between these two problems, benefiting each other in the near future. + +# Acknowledgement + +This work was partially supported by National Key Research and Development Program of China (No. 2020AAA0108900), Ant Group, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University. + +# References + +[1] Steven S. Beauchemin and John L. Barron. The computation of optical flow. ACM computing surveys (CSUR), 27(3):433-466, 1995. 1, 2 +[2] Shariq Farooq Bhat, Reiner Birkl, Diana Wofk, Peter Wonka, and Matthias Müller. Zoedepth: Zero-shot transfer by combining relative and metric depth. CoRR, abs/2302.12288, 2023. 2, 5, 6, 8 +[3] Weikang Bian, Zhaoyang Huang, Xiaoyu Shi, Yitong Dong, Yijin Li, and Hongsheng Li. Context-tap: Tracking any point demands spatial context features. arXiv preprint arXiv:2306.02000, 2023. 2 +[4] Benjamin Biggs, Thomas Roddick, Andrew W. Fitzgibbon, and Roberto Cipolla. 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Tracking 2D pixels in 3D space. To estimate 2D motion under the occlusion and complex 3D motion, we lift 2D pixels into 3D and perform tracking in the 3D space. 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Part of the difficulty arises from the 3D-to-2D projection process, leading to occlusions and discontinuities in the 2D motion domain. While 2D motion can be intricate, we posit that the underlying 3D motion can often be simple and low-dimensional. In this work, we propose to estimate point trajectories in 3D space to mitigate the issues caused by image projection. Our method, named SpatialTracker, lifts 2D pixels to 3D using monocular depth estimators, represents the 3D content of each frame efficiently using a triplane representation, and performs iterative updates using a transformer to estimate 3D trajectories. Tracking in 3D allows us to leverage as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 483, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 547, + 579 + ], + "type": "text", + "content": "rigid-as-possible (ARAP) constraints while simultaneously learning a rigidity embedding that clusters pixels into different rigid parts. Extensive evaluation shows that our approach achieves state-of-the-art tracking performance both qualitatively and quantitatively, particularly in challenging scenarios such as out-of-plane rotation. And our project page is available at https://henry123-boy.github.io/SpaTracker/." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 594, + 387, + 607 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 594, + 387, + 607 + ], + "spans": [ + { + "bbox": [ + 306, + 594, + 387, + 607 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "type": "text", + "content": "Motion estimation has historically been approached through two main paradigms: feature tracking [37, 38, 58, 64] and optical flow [1, 19, 62]. While each type of method enables numerous applications, neither of them fully captures the motion in a video: optical flow only produces motion for adjacent frames, whereas feature tracking only tracks sparse pixels." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 713 + ], + "type": "text", + "content": "An ideal solution would involve the ability to estimate" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 213, + 58, + 432 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 47, + 213, + 58, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 58, + 432 + ], + "type": "text", + "content": "2D Trajectories 3D Trajectories 2D Trajectories 3D Trajectories" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "*The first two authors contributed equally. The authors from Zhejiang University are affiliated with the State Key Lab of CAD&CG. †Corresponding author: Xiaowei Zhou." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20406" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "both dense and long-range pixel trajectories in a video sequence [55, 56]. Seminal work like Particle Video [56] has bridged the gap by representing video motion using a set of semi-dense and long-range particles. More recently, several efforts [11, 12, 17, 29] have revisited this problem, formulating it as tracking any point and addressing it through supervised learning frameworks. While trained solely on synthetic datasets [14, 81], these methods consistently demonstrate strong generalization abilities to real-world videos, pushing the boundaries of long-range pixel tracking through occlusions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "type": "text", + "content": "While great progress has been achieved, current solutions still struggle in challenging scenarios, particularly in cases of complex deformation accompanied by frequent self-occlusions. We argue that one potential cause for this difficulty stems from tracking only in the 2D image space, thereby disregarding the inherent 3D nature of motion. As motion takes place in 3D space, certain properties can only be adequately expressed through 3D representations. For example, rotation can be succinctly explained by three parameters in 3D, and occlusion can be simply expressed with z-buffering, but they are much more complicated to express within a 2D representation. In addition, the key component of these methods — using " + }, + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "type": "inline_equation", + "content": "2D" + }, + { + "bbox": [ + 46, + 206, + 289, + 434 + ], + "type": "text", + "content": " feature correlation to predict motion updates — can be insufficient. Image projection can bring spatially distant regions into proximity within the 2D space, which can cause the local 2D neighborhood for correlation to potentially contain irrelevant context (especially near occlusion boundaries), thereby leading to difficulties in reasoning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 436, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 289, + 581 + ], + "type": "text", + "content": "To tackle these challenges, we propose to leverage geometric priors from state-of-the-art monocular depth estimators [2] to lift 2D pixels into 3D, and perform tracking in the 3D space. This involves conducting feature correlation in 3D, which provides more meaningful 3D context for tracking especially in cases of complex motion. Tracking in 3D also allows for enforcing 3D motion priors [52, 63] such as ARAP constraint. Encouraging the model to learn which points move rigidly together can help track ambiguous or occluded pixels, as their motion can then be inferred using neighboring unambiguous and visible regions within the same rigid group." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 289, + 715 + ], + "type": "text", + "content": "Specifically, we propose to represent the 3D scene of each frame with triplane feature maps [10], which are obtained by first lifting image features to 3D featured point clouds and then splatting them onto three orthogonal planes. The triplane representation is compact and regular, suitable for our learning framework. Moreover, it covers the 3D space densely, enabling us to extract the feature vectors of any 3D point for tracking. We then compute 3D trajectories for query pixels through iterative updates predicted by a transformer using features from our triplane representation. To regularize the estimated 3D trajectories" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 156 + ], + "type": "text", + "content": "with 3D motion prior, our model additionally predicts a rigidity embedding for each trajectory, which allows us to softly group pixels exhibiting the same rigid body motion and enforce an ARAP regularization for each rigid cluster. We demonstrate that the rigidity embedding can be learned self-supervisedly and produce reasonable segmentation of different rigid parts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 157, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 547, + 228 + ], + "type": "text", + "content": "Our model achieves state-of-the-art performance on various public tracking benchmarks including TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Qualitative results on challenging Internet videos also demonstrate the superior capability of our model to handle fast complex motion and extended occlusion." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 239, + 392, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 239, + 392, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 239, + 392, + 251 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 259, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 259, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 259, + 547, + 475 + ], + "type": "text", + "content": "Optical flow. Optical flow is the task of estimating dense 2D pixel-level motion between a pair of frames. While traditional methods [1, 6, 8, 19, 74, 78] formulate it as an energy minimization problem, recent approaches [13, 23, 24, 61, 76] have demonstrated the ability to predict optical flow directly using deep neural networks. Notably, RAFT [62] employs a 4D correlation volume and estimates optical flow through iteratively updates with a recurrent operator. More recently, transformer-based flow estimators [21, 26, 59, 80] achieved superior performance, showing the strong capacity of the transformer architecture. However, pairwise optical flow methods are not suitable for long-term tracking, as they are not designed to handle long temporal contexts [8, 74]. Multi-frame optical flow methods [25, 28, 32, 54, 69] extend pairwise flow by incorporating multi-frame contexts (typically 3-5 frames), but this remains insufficient for tracking through long occlusions in videos spanning tens or hundreds of frames." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 486, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 715 + ], + "type": "text", + "content": "Tracking any point. Recognizing the limitations of optical flow, seminal work Particle Video [56] proposes to represent video motion as a set of long-range particles that move through time, which are optimized by enforcing long-range appearance consistency and motion coherence with variational techniques. However, Particle Video only generates semi-dense tracks and cannot recover from occlusion events [55]. Recently, PIPs [17] revisited this idea by introducing a feedforward network that takes RGB frames of a fixed temporal window (8 frames) as input and predicts the motion for any given query point through iterative updates. However, PIPs tracks points independently, neglecting spatial context information, and will lose the target if they stay occluded beyond the temporal window. Several recent advancements [3, 11, 12, 42, 71, 81] in point tracking have surfaced, addressing some of PIPs' limitations. TAPIR [12] relaxes the fixed-length window constraint by using a temporal depthwise convolutional network capable of accommodating variable lengths. Co" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20407" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 69, + 288, + 271 + ], + "blocks": [ + { + "bbox": [ + 62, + 69, + 288, + 271 + ], + "lines": [ + { + "bbox": [ + 62, + 69, + 288, + 271 + ], + "spans": [ + { + "bbox": [ + 62, + 69, + 288, + 271 + ], + "type": "image", + "image_path": "bf0b5e255c67d23149282eda10cb0a1774b4fc861a4fcbed2b4d60e4748dda06.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "lines": [ + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "text", + "content": "Figure 2. Overview of Our Pipeline. We first encode each frame into a triplane representation (a) using a triplane encoder (b). We then initialize and iteratively update point trajectories in the 3D space using a transformer with features extracted from these triplanes as input (c). The 3D trajectories are trained with ground truth annotations and are regularized by an as-rigid-as-possible (ARAP) constraint with learned rigidity embedding (d). The ARAP constraint enforces that 3D distances between points with similar rigidity embeddings remain constant over time. Here " + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "inline_equation", + "content": "d_{ij}" + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "text", + "content": " represents the distance between points " + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "inline_equation", + "content": "s_{ij}" + }, + { + "bbox": [ + 46, + 281, + 545, + 347 + ], + "type": "text", + "content": " denotes the rigid similarity. Our method produces accurate long-range motion tracks even under fast movements and severe occlusion (e)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 292, + 70, + 524, + 271 + ], + "blocks": [ + { + "bbox": [ + 292, + 70, + 524, + 271 + ], + "lines": [ + { + "bbox": [ + 292, + 70, + 524, + 271 + ], + "spans": [ + { + "bbox": [ + 292, + 70, + 524, + 271 + ], + "type": "image", + "image_path": "1388707f573cd97128dd6d0266af7b4812b435973b95a8684e07c969c0fe59af.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 357, + 287, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 392 + ], + "type": "text", + "content": "Tracker [29] proposed to jointly track multiple points and leverage spatial correlation between them, leading to state-of-the-art performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 393, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 287, + 548 + ], + "type": "text", + "content": "Though significant progress has been made, these works all compute feature correlation in the 2D image space, losing important information about the 3D scene where the motion actually takes place. In contrast, we lift 2D points into 3D and perform tracking in the 3D space. The more meaningful 3D contexts (as opposed to 2D), along with an as-rigid-as-possible regularization, facilitate improved handling of occlusions and enhance tracking accuracy. Previous studies have also explored computing 2D motion with a touch of 3D, e.g., through depth-separated layers [30, 57, 60, 77] or quasi-3D space [71]. However, distinct from their optimization-based pipelines, we perform long-range 3D tracking in a more efficient, feedforward manner." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 288, + 713 + ], + "type": "text", + "content": "Scene flow. Scene flow defines a dense 3D motion field of points in a scene. Early work estimates scene flow in multi-view stereo settings [49, 66, 79] through variational optimization [22]. The introduction of depth sensors enabled more effective scene flow estimation from pairs or sequences of RGB-D frames [16, 18, 20, 27, 52, 63, 72]. A considerable number of recent scene flow methods rely on stereo inputs [39, 41], but many of them are tailored specifically for self-driving scenes, lacking generalizability to diverse non-automotive contexts. Another line of research [7, 15, 34, 36, 45, 75] estimates 3D motion from a pair or a sequence of point clouds. An important prior that is often used for scene flow estimation is local" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 357, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 501 + ], + "type": "text", + "content": "rigidity [67, 68], where pixels are grouped into rigidly moving clusters (object or part-level), in either a soft or hard manner. For example, RAFT-3D [63] learns rigid-motion embeddings to softly group pixels into rigid objects. Scene flow estimation is also often solved as a sub-task in non-rigid reconstruction pipelines [31, 35, 43]. For example, DynamicFusion [44] takes depth maps as input and computes dense volumetric warp functions by interpolating a sparse set of transformations as bases. In contrast to prior works, we learn to predict long-range 3D trajectories through supervised learning, providing generalization capabilities for handling complex real-world motion." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 513, + 361, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 513, + 361, + 525 + ], + "spans": [ + { + "bbox": [ + 306, + 513, + 361, + 525 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "content": "Given a monocular video as input, our method tracks any given query pixels across the entire video. Different from prior methods that establish correspondences solely in the 2D space, we lift pixels to 3D using an off-the-shelf monocular depth estimator and perform tracking in a 3D space with richer and more spatially meaningful 3D contextual information, thereby enhancing the overall tracking performance." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Fig. 2 presents the overview of our proposed pipeline. We first encode the appearance and geometry information of each frame into a triplane representation (Sec. 3.1). Then we perform iterative prediction of trajectories in the 3D space using these triplanes in a sliding window fashion (Sec. 3.2). We leverage the as-rigid-as-possible (ARAP) 3D motion prior during training to facilitate track" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20408" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 109 + ], + "type": "text", + "content": "ing especially in challenging scenarios of occlusion and large motion (Sec. 3.3). Finally, we describe our training strategy in Sec. 3.4." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 116, + 266, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 116, + 266, + 129 + ], + "spans": [ + { + "bbox": [ + 47, + 116, + 266, + 129 + ], + "type": "text", + "content": "3.1. Triplane Encoding of Input Video Frames" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 134, + 286, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 286, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 286, + 194 + ], + "type": "text", + "content": "To perform tracking in the 3D space, we need to lift 2D pixels into 3D and construct a 3D representation that encodes the feature for each 3D location. To this end, we propose to use triplane features as the 3D scene representation for each frame detailed below." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 195, + 286, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 286, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 286, + 290 + ], + "type": "text", + "content": "To start with, for each frame, we obtain its monocular depth map using a pretrained monocular depth estimator, alongside multi-scale feature maps generated by a convolutional neural network (CNN). Subsequently, 2D pixels are unprojected into a set of 3D point clouds, where each 3D point is associated with a feature vector. This feature vector is a concatenation of the corresponding image feature and a positional embedding [65] of its 3D location." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 291, + 286, + 494 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 286, + 494 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 286, + 494 + ], + "type": "text", + "content": "While this featured point cloud captures both geometry and appearance information, it is incomplete and only covers visible regions (2.5D). Additionally, its irregular and unordered nature poses challenges for effective learning. One simple solution involves voxelizing the point cloud into a 3D feature volume and completing it with 3D convolutions. Yet, this approach is memory and computationally intensive. To obtain 3D features densely and efficiently, we propose to use triplane feature maps, which are obtained by orthographically projecting and average splatting [46] the featured point cloud onto three orthogonal 2D planes, as illustrated in Fig. 2(b). Finally, additional convolutional layers are applied to process and complete each feature map. This triplane feature encoding process is applied to each video frame. Since we do not assume access to camera poses, each triplane is defined within the camera coordinate frame of its respective frame." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 495, + 286, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 286, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 286, + 566 + ], + "type": "text", + "content": "This triplane representation is compact and enables us to efficiently represent the 3D feature for any given 3D point within the field of view. This process involves projecting the point onto three feature planes, extracting its corresponding feature vectors through bilinear interpolation, and fusing them via simple addition." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 567, + 286, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 286, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 286, + 651 + ], + "type": "text", + "content": "Note that while similar concepts of triplanes are explored in related fields [10, 48, 73], our focus here is distinct. Rather than learning a triplane to represent the 3D scene from scratch, we directly leverage monocular depth priors to obtain a triplane where the primary objective is to facilitate tracking in the 3D space, introducing a novel perspective to the field of pixel tracking." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 658, + 214, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 214, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 214, + 672 + ], + "type": "text", + "content": "3.2. Iterative Trajectory Prediction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Given a set of query pixels in the query frame, Sec. 3.1 allows us to obtain their 3D locations and their corresponding triplane features. We now describe the process to estimate" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 482, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 482, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 482, + 83 + ], + "type": "text", + "content": "their 3D trajectories across the entire video." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "type": "text", + "content": "Following CoTracker [29], we partition the video into overlapping windows of length " + }, + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "type": "text", + "content": ". In each window, we iteratively estimate 3D trajectories for query points over " + }, + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 84, + 545, + 156 + ], + "type": "text", + "content": " steps using a transformer. The final 3D trajectories are then propagated to the next window and updated, and this process continues until the end of the video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "content": "Iterative prediction. We now focus on the iterative prediction of 3D trajectories within the first temporal window. Given the 3D location " + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1 \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "content": " of a query pixel in the first frame, our goal is to predict its 3D corresponding locations (or in other words, its 3D trajectory) in subsequent frames " + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{X}_t\\}_{t=2}^{T_s}" + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 159, + 545, + 232 + ], + "type": "text", + "content": " is the frame index." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": "Because we adopt an iterative updating strategy to estimate the 3D trajectories, we further denote the prediction at the " + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": "-th step as " + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\{X_t^m\\}_{t=2}^{T_s}" + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": ". To start with, we initialize " + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\{X_t^0\\}_{t=2}^{T_s}" + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": " to be all equal to " + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "inline_equation", + "content": "X_1" + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": ", and then we iteratively update the 3D trajectory using a transformer " + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 232, + 545, + 292 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "text", + "content": "Specifically, for the point " + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t^m" + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "text", + "content": " at the " + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "text", + "content": "-th iteration, we define its input feature " + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "inline_equation", + "content": "\\mathbf{G}_t^m" + }, + { + "bbox": [ + 304, + 292, + 545, + 316 + ], + "type": "text", + "content": " to the transformer as:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 323, + 545, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 323, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 318, + 323, + 545, + 338 + ], + "type": "interline_equation", + "content": "\\boldsymbol {G} _ {t} ^ {m} = \\left[ \\gamma \\left(\\boldsymbol {X} _ {t} ^ {m}\\right), \\boldsymbol {F} _ {t} ^ {m}, \\boldsymbol {C} _ {t} ^ {m}, \\gamma \\left(\\boldsymbol {X} _ {t} ^ {m} - \\boldsymbol {X} _ {1}\\right) \\right] \\in \\mathbb {R} ^ {D}, \\tag {1}", + "image_path": "97a20b2e8645ee9a4486cc60d3582a5b46561eedad1b199cb9630f7318ecb267.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " is the positional encoding function and " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "F_{t}^{m}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " is the feature of point " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "X_{t}^{m}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": ". At the first iteration, " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "F_{t}^{0}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " is extracted from the triplane of frame " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "X_{t}^{0}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": ". For later iterations, " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "F_{t}^{m}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " is a direct output of the transformer from the previous iteration. " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "C_{t}^{m}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " denotes correlation features, which are computed by comparing " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "F_{t}^{m}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " and local triplane features around " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "X_{t}^{m}" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": " at frame " + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 346, + 545, + 441 + ], + "type": "text", + "content": ". More details of correlation features can be found in the supplementary material." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": "For each update, the transformer takes as input the features for the trajectories of all query points across the entire window. We denote this set of features at the " + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": "-th iteration as " + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^m \\in \\mathbb{R}^{N \\times T_s \\times D} = \\{\\pmb{G}_{i,t}^m \\mid i = 1, \\dots, N; t = 1, \\dots, T_s\\}" + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": " is the query point index and " + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": " is the number of query points. " + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": " then takes " + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^m" + }, + { + "bbox": [ + 304, + 441, + 545, + 525 + ], + "type": "text", + "content": " as input and predicts the new set of point positions and features:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 372, + 533, + 545, + 547 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 533, + 545, + 547 + ], + "spans": [ + { + "bbox": [ + 372, + 533, + 545, + 547 + ], + "type": "interline_equation", + "content": "\\mathcal {X} ^ {m + 1}, \\mathcal {F} ^ {m + 1} = \\Psi (\\mathcal {G} ^ {m}), \\tag {2}", + "image_path": "a73e25954897985ac5017716b990a73f7af689d128a3fefd2e01135f66926b87.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^{m + 1}" + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": " denotes the set of updated point positions, and " + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{m + 1}" + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": " denotes the set of updated point features. New " + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{G}^{m + 1}" + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": " can then be defined according to Eq. 1, and the same process is repeated " + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": " times to obtain the final 3D trajectories for all query points " + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\mathcal{X}^M = \\{\\pmb {X}_{i,t}^M\\}" + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": ". The 2D correspondence predictions can be computed by simply projecting " + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "inline_equation", + "content": "\\{\\pmb {X}_{i,t}^M\\}" + }, + { + "bbox": [ + 304, + 555, + 545, + 640 + ], + "type": "text", + "content": " back onto the 2D image plane." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "text", + "content": "As query pixels may not have corresponding pixels at some frames due to occlusions, we additionally predict the visibility for each point of the 3D trajectories at the final iteration " + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "text", + "content": ". Specifically, for each point " + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{i,t}^{M}" + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "text", + "content": ", we employ an MLP network that takes the feature " + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{i,t}^{M}" + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "text", + "content": " as input and predicts a visibility score " + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "inline_equation", + "content": "v_{i,t}" + }, + { + "bbox": [ + 304, + 640, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "footer", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20409" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "text", + "content": "Handling long videos. To track points across a long video, we utilize overlapping sliding windows where each pair of adjacent windows has half of their frames overlapped. Given the results from the previous window, we initialize trajectories of the first " + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "inline_equation", + "content": "\\frac{T_s}{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "text", + "content": " frames of the current window by copying the results of the last " + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "inline_equation", + "content": "\\frac{T_s}{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "text", + "content": " frames from the previous window. The trajectories of the last " + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "inline_equation", + "content": "\\frac{T_s}{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "text", + "content": " frames in the current window are initialized by copying the result of the frame " + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "inline_equation", + "content": "\\frac{T_s}{2}" + }, + { + "bbox": [ + 46, + 72, + 289, + 184 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 193, + 220, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 193, + 220, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 193, + 220, + 205 + ], + "type": "text", + "content": "3.3. As Rigid As Possible Constraint" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 212, + 287, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 212, + 287, + 260 + ], + "spans": [ + { + "bbox": [ + 46, + 212, + 287, + 260 + ], + "type": "text", + "content": "An advantage of tracking points in 3D is that we can enforce an as-rigid-as-possible (ARAP) constraint, which enhances spatial consistency and facilitates the prediction of motion especially during occlusions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": "Enforcing proper ARAP constraints requires identifying if two points belong to the same rigid part. To this end, at each iteration " + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": ", we additionally compute a rigidity embedding " + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "inline_equation", + "content": "\\pmb{E}_i^m" + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": " for each trajectory by aggregating its features " + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "inline_equation", + "content": "\\{\\pmb{G}_{i,t}^{m}\\}_{t = 1}^{T_s}" + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": " across time. Then, the rigidity affinity " + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "inline_equation", + "content": "s_{ij}^{m}" + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": " between any two trajectories " + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 261, + 287, + 333 + ], + "type": "text", + "content": " can be calculated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 121, + 343, + 287, + 359 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 121, + 343, + 287, + 359 + ], + "spans": [ + { + "bbox": [ + 121, + 343, + 287, + 359 + ], + "type": "interline_equation", + "content": "s _ {i j} ^ {m} = \\operatorname {s i m} \\left(\\boldsymbol {E} _ {i} ^ {m}, \\boldsymbol {E} _ {j} ^ {m}\\right), \\tag {3}", + "image_path": "5458f39d937add0020a003d4f78e51f5b346e2f2ccc97959be0f8336f27dafb6.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 368, + 241, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 368, + 241, + 380 + ], + "spans": [ + { + "bbox": [ + 47, + 368, + 241, + 380 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 368, + 241, + 380 + ], + "type": "inline_equation", + "content": "\\mathrm{sim}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 368, + 241, + 380 + ], + "type": "text", + "content": " is the cosine similarity measure." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 380, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 287, + 441 + ], + "type": "text", + "content": "By the definition of rigidity, the distances between points that are rigidly moving together should be preserved over time. Therefore, we formulate our ARAP loss as follows, encouraging the distances between pairs of points exhibiting high rigidity to remain constant over time:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 451, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 451, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 55, + 451, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {a r a p}} = \\sum_ {m = 1} ^ {M} \\sum_ {t = 1} ^ {T _ {s}} \\sum_ {\\Omega_ {i j}} w ^ {m} s _ {i j} ^ {m} | | d \\left(\\boldsymbol {X} _ {i, t} ^ {m}, \\boldsymbol {X} _ {j, t} ^ {m}\\right) - d \\left(\\boldsymbol {X} _ {i, 1}, \\boldsymbol {X} _ {j, 1}\\right) | | _ {1}, \\tag {4}", + "image_path": "d4875d9e45a00b95c9920ad1b427be91da8d0c122b88c75ebe5137125ad1ae0a.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\Omega_{ij}" + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "text", + "content": " is the set of all pairwise indices and " + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "inline_equation", + "content": "d(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "text", + "content": " is the Euclidean distance function, and " + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "inline_equation", + "content": "w^{m} = 0.8^{M - m}" + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "text", + "content": " is the weight for the " + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 487, + 287, + 547 + ], + "type": "text", + "content": "-th step. This ARAP loss provides gradients for learning both the 3D trajectories and the rigidity embeddings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 548, + 287, + 608 + ], + "type": "text", + "content": "Based on the affinity score between any two points, we can perform spectral clustering [47, 70] to obtain the segmentation of query pixels. Experiments in Sec. 4 show that our method can generate meaningful segmentation of rigid parts." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 617, + 111, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 111, + 630 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 111, + 630 + ], + "type": "text", + "content": "3.4. Training" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 637, + 287, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 637, + 287, + 672 + ], + "spans": [ + { + "bbox": [ + 46, + 637, + 287, + 672 + ], + "type": "text", + "content": "In addition to the ARAP loss, we supervise the predicted trajectories using ground truth 3D trajectories at each iteration, which is defined as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 83, + 682, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 682, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 83, + 682, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t r a j}} = \\sum_ {m = 1} ^ {M} \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {T _ {s}} w ^ {m} | | \\boldsymbol {X} _ {i, t} ^ {m} - \\hat {\\boldsymbol {X}} _ {i, t} ^ {m} | | _ {1}, \\tag {5}", + "image_path": "c0e7d7f7b9192fed364c040a16e9219bebbb4be32d19e324aedafcc5fe9098d6.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "X_{i,t}^{m}" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\hat{X}_{i,t}^{m}" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " are the predicted and ground-truth 3D corresponding locations, respectively, and " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "w^{m}" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " is the weight for the " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "-th step, identical to that in Eq. 4." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 317, + 108, + 506, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 108, + 506, + 120 + ], + "spans": [ + { + "bbox": [ + 317, + 108, + 506, + 120 + ], + "type": "text", + "content": "The predicted visibilities are supervised using:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 366, + 124, + 545, + 157 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 124, + 545, + 157 + ], + "spans": [ + { + "bbox": [ + 366, + 124, + 545, + 157 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {v i s}} = \\sum_ {i = 1} ^ {N} \\sum_ {t = 1} ^ {T _ {s}} \\mathrm {C E} \\left(v _ {i, t}, \\hat {v} _ {i, t}\\right), \\tag {6}", + "image_path": "bce63ef6523db04ac170f6ad5739f9031347f6031221ade9a6971f897a0cfee7.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "spans": [ + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "type": "inline_equation", + "content": "v_{i,t}" + }, + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "type": "inline_equation", + "content": "\\hat{v}_{i,t}" + }, + { + "bbox": [ + 305, + 160, + 545, + 184 + ], + "type": "text", + "content": " denote the predicted and ground-truth visibility, respectively. CE represents the cross entropy loss." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 185, + 512, + 196 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 185, + 512, + 196 + ], + "spans": [ + { + "bbox": [ + 317, + 185, + 512, + 196 + ], + "type": "text", + "content": "The total loss function for training is defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 362, + 201, + 545, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 201, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 362, + 201, + 545, + 214 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t o t a l}} = \\mathcal {L} _ {\\text {t r a j}} + \\alpha \\mathcal {L} _ {\\text {v i s}} + \\beta \\mathcal {L} _ {\\text {a r a p}}, \\tag {7}", + "image_path": "a1a4b6d4604249f2b217920379dc1f99530c57480a542ad798e2162fd486661d.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 305, + 218, + 545, + 243 + ], + "type": "text", + "content": " are weighting coefficients. In practice, they are set as 10 and 0.1, respectively." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 247, + 440, + 260 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 440, + 260 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 440, + 260 + ], + "type": "text", + "content": "3.5. Implementation Details" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": "We train our model on the TAP-Vid-Kubric dataset [11, 14]. Our training data contains 11,000 24-frame RGBD sequences with full-length 3D trajectory annotations. During training, we use ground truth depth maps and camera intrinsics to unproject pixels into 3D space. In cases where the depth map and intrinsics are unavailable at inference, we use ZoeDepth [2] to predict the metric depth map for each video frame, and simply set the focal length to be the same as the image width. To generate triplane feature maps, we discretize the depth values into " + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "inline_equation", + "content": "d = 256" + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": " bins. The resolutions of the triplane feature maps are " + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "inline_equation", + "content": "h \\times w" + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "inline_equation", + "content": "w \\times d" + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "inline_equation", + "content": "h \\times d" + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": " for XY, XZ, and YZ planes, respectively, where " + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 305, + 266, + 545, + 433 + ], + "type": "text", + "content": " are the image height and width. The number of channels of the triplane features is 128." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "text", + "content": "We train our model with eight 80GB A100 GPUs for 200k iterations. The total training time is around 6 days. The iteration steps " + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "text", + "content": " and sliding window length " + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "T_{s}" + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "text", + "content": " are set to 6 and 8 respectively. In each training batch, we sample " + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "N = 256" + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "text", + "content": " query points. The transformer " + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "\\Psi" + }, + { + "bbox": [ + 305, + 434, + 545, + 529 + ], + "type": "text", + "content": " consists of six blocks, each comprising both spatial and temporal attention layers. For more details, please refer to the supplementary material." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 538, + 387, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 387, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 387, + 551 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 558, + 545, + 713 + ], + "type": "text", + "content": "At inference, our method can operate in two different modalities. The first modality (and the primary focus of this paper) is long-range 2D pixel tracking. In this modality, the input is an RGB video without known depth or camera intrinsics, and we rely on ZoeDepth [2] to estimate the depth maps. Due to the lack of precise depth and intrinsics information, we only evaluate the 2D projection of the 3D trajectories onto the image plane, i.e., 2D pixel trajectories. When RGBD videos and camera intrinsics are available, our method can be used in the second modality to predict long-range 3D trajectories. We evaluate our method for both 2D and 3D tracking performance in Sec 4.1 and Sec 4.2, respectively, and then conduct ablation studies in Sec. 4.3." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20410" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 62, + 547, + 171 + ], + "blocks": [ + { + "bbox": [ + 48, + 62, + 547, + 171 + ], + "lines": [ + { + "bbox": [ + 48, + 62, + 547, + 171 + ], + "spans": [ + { + "bbox": [ + 48, + 62, + 547, + 171 + ], + "type": "table", + "html": "
MethodsKinetics [9]DAVIS [50]RGB-Stacking [33]Average
AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑AJ ↑<δavg↑OA ↑
TAP-Net [11]38.554.480.633.048.678.854.668.387.742.057.182.4
PIPs [17]31.753.772.942.264.877.715.728.477.129.950.075.9
OmniMotion [71]--46.462.785.369.582.590.3---
TAPIR [12]49.664.285.056.270.086.554.269.884.453.368.085.3
CoTracker [29]48.764.386.560.675.489.363.177.087.857.472.287.8
Ours50.165.986.961.176.389.563.577.688.258.273.388.2
", + "image_path": "c016e759874c9d57690f23355268ea259afdabf85397053a8bca60303a1caa9d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 212, + 182, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 212, + 182, + 224 + ], + "spans": [ + { + "bbox": [ + 47, + 212, + 182, + 224 + ], + "type": "text", + "content": "4.1. 2D Tracking Evaluation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 232, + 288, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 288, + 316 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 288, + 316 + ], + "type": "text", + "content": "We conduct our evaluation on three long-range 2D tracking benchmarks: TAP-Vid [11], BADJA [4] and PointOdyssey [81]. Our method is compared with baseline 2D tracking methods, namely TAP-Net [11], PIPs [17], OmniMotion [71], TAPIR [12] and CoTracker [29]. The evaluation protocols and comparison results on each of the benchmarks are represented below." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 323, + 288, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 288, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 288, + 574 + ], + "type": "text", + "content": "TAP-Vid Benchmark [11] contains a few datasets: TAP-Vid-DAVIS [50] (30 real videos of about 34-104 frames), TAP-Vid-Kinetics [9] (1144 real videos of 250 frames) and RGB-Stacking [33] (50 synthetic videos of 250 frames). Each video in the benchmark is annotated with ground truth 2D trajectories and occlusions spanning the entire video duration for well-distributed points. We evaluate performance using the same metrics as the TAP-Vid benchmark [11]: average position accuracy " + }, + { + "bbox": [ + 46, + 323, + 288, + 574 + ], + "type": "inline_equation", + "content": "(< \\delta_{\\mathrm{avg}}^x)" + }, + { + "bbox": [ + 46, + 323, + 288, + 574 + ], + "type": "text", + "content": ", Average Jaccard (AJ), and Occlusion Accuracy (OA). Please refer to the supplement for more details. We follow the \"queried first\" evaluation protocol in CoTracker [29]. Specifically, we use the first frame as the query frame and predict the 2D locations of query pixels from this frame in all subsequent frames. The quantitative comparisons are reported in Tab. 1, which shows our method consistently outperforms all baselines except Omnimotion across all three datasets, demonstrating the benefits of tracking in the 3D space. Omnimotion also performs tracking in 3D and obtains the best results on RGB-Stacking by optimizing all frames at once, but it requires very costly test-time optimization." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "BADJA [4] is a benchmark containing seven videos of moving animals with annotated keypoints. The metrics used in this benchmark include segment-based accuracy (segA) and 3px accuracy (" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta^{3\\mathrm{px}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "). The predicted keypoint positions are deemed accurate when its distance from the ground truth keypoint is less than " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "0.2\\sqrt{A}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " is the summation of the area of the segmentation mask. " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta^{3\\mathrm{px}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " depicts the percentage of the correct keypoints whose distances from their ground truth are within three pixels. As shown in Tab. 2, our method demonstrates competitive performance in terms of " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\delta^{3\\mathrm{px}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " and surpasses all baseline methods by a" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 323, + 210, + 528, + 300 + ], + "blocks": [ + { + "bbox": [ + 46, + 175, + 546, + 198 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 546, + 198 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 546, + 198 + ], + "type": "text", + "content": "Table 1. 2D Tracking Results on the TAP-Vid Benchmark. We report the average jaccard (AJ), average position accuracy " + }, + { + "bbox": [ + 46, + 175, + 546, + 198 + ], + "type": "inline_equation", + "content": "(<\\delta_{\\mathrm{avg}}^x)" + }, + { + "bbox": [ + 46, + 175, + 546, + 198 + ], + "type": "text", + "content": ", and occlusion accuracy (OA) on Kinetics [9], DAVIS [50] and RGB-Stacking [33] datasets." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 323, + 210, + 528, + 300 + ], + "lines": [ + { + "bbox": [ + 323, + 210, + 528, + 300 + ], + "spans": [ + { + "bbox": [ + 323, + 210, + 528, + 300 + ], + "type": "table", + "html": "
MethodssegA ↓δ3px ↑
TAP-Net [11]54.46.3
PIPs [17]61.913.5
TAPIR [12]66.915.2
OmniMotion [71]57.213.2
CoTracker [29]63.618.0
Ours69.217.1
", + "image_path": "0bca97ef27c1bfb2290e40170590939f767422c102f0539112e02e7a647befac.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 350, + 544, + 430 + ], + "blocks": [ + { + "bbox": [ + 305, + 304, + 545, + 337 + ], + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 337 + ], + "type": "text", + "content": "Table 2. 2D Tracking Results on the BADJA Dataset [4]. The segment-based accuracy (segA) and 3px accuracy " + }, + { + "bbox": [ + 305, + 304, + 545, + 337 + ], + "type": "inline_equation", + "content": "(\\delta^{3\\mathrm{px}})" + }, + { + "bbox": [ + 305, + 304, + 545, + 337 + ], + "type": "text", + "content": " are reported." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 350, + 544, + 430 + ], + "lines": [ + { + "bbox": [ + 307, + 350, + 544, + 430 + ], + "spans": [ + { + "bbox": [ + 307, + 350, + 544, + 430 + ], + "type": "table", + "html": "
MethodsMTE↓<δxavg↑Survival↑
TAP-Net [11]37.829.252.8
PIPs [81]41.030.467.0
CoTracker [29]30.556.276.1
Ours w/ ZoeDepth [2]28.358.478.6
Ours w/ GT depth26.664.178.0
", + "image_path": "2a3b8d16088d178518fc330d33d609c4d8c9ef7e781f1e3d4229e0e5ad06f672.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 433, + 545, + 467 + ], + "lines": [ + { + "bbox": [ + 306, + 433, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 545, + 467 + ], + "type": "text", + "content": "Table 3. 2D Tracking Results on the PointOdyssey Dataset [81]. The Median Trajectory Error (MTE), average position accuracy " + }, + { + "bbox": [ + 306, + 433, + 545, + 467 + ], + "type": "inline_equation", + "content": "(<\\delta_{avg}^{x})" + }, + { + "bbox": [ + 306, + 433, + 545, + 467 + ], + "type": "text", + "content": ", and survival rate (Survival) are reported." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 490, + 471, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 471, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 471, + 502 + ], + "type": "text", + "content": "large margin in segment-based accuracy." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": "PointOdyssey [81] is a large-scale synthetic dataset featuring diverse animated characters ranging from humans to animals, placed within diverse 3D environments. We evaluate our method on PointOdyssey's test set which contains 12 videos with complex motion, each spanning approximately 2000 frames. We adopt the evaluation metrics proposed in PointOdyssey [81] which are designed for evaluating very long trajectories. These metrics include the Median Trajectory Error (MTE), " + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "inline_equation", + "content": "< \\delta_{\\mathrm{avg}}^x" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": " (consistent with TAP-Vid), and the survival rate. The survival rate is defined as the average number of frames until tracking failure over the video length. Tracking failure is identified when the L2 error exceeds 50 pixels at a resolution of " + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 521, + 547, + 715 + ], + "type": "text", + "content": ". In Tab. 3, we report results for baseline methods as well as our method using depths from ZoeDepth [2] (default) and GT depth annotations. Our method consistently outperforms" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20411" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 67, + 70, + 160, + 123 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 160, + 123 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 160, + 123 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 160, + 123 + ], + "type": "image", + "image_path": "aa5e95d2a7077af8c74cd9ff8e0f8c555ef77247493bbdda1908ee531ecd5225.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 68, + 124, + 160, + 175 + ], + "blocks": [ + { + "bbox": [ + 68, + 124, + 160, + 175 + ], + "lines": [ + { + "bbox": [ + 68, + 124, + 160, + 175 + ], + "spans": [ + { + "bbox": [ + 68, + 124, + 160, + 175 + ], + "type": "image", + "image_path": "2fd40a5e3a73c468047cce9a13129517effebd606d741684a3dbfe61eaad96ef.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 68, + 176, + 160, + 226 + ], + "blocks": [ + { + "bbox": [ + 68, + 176, + 160, + 226 + ], + "lines": [ + { + "bbox": [ + 68, + 176, + 160, + 226 + ], + "spans": [ + { + "bbox": [ + 68, + 176, + 160, + 226 + ], + "type": "image", + "image_path": "5f7d9c45889c67d22b28727c547836885c0f9500eded1665cb32dd1685f60d94.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 68, + 227, + 160, + 279 + ], + "blocks": [ + { + "bbox": [ + 68, + 227, + 160, + 279 + ], + "lines": [ + { + "bbox": [ + 68, + 227, + 160, + 279 + ], + "spans": [ + { + "bbox": [ + 68, + 227, + 160, + 279 + ], + "type": "image", + "image_path": "15a0fcad60671ddb97c9b8d5424ff88b7f836b7baf8a87294f2f392614d1a475.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 68, + 280, + 160, + 331 + ], + "blocks": [ + { + "bbox": [ + 68, + 280, + 160, + 331 + ], + "lines": [ + { + "bbox": [ + 68, + 280, + 160, + 331 + ], + "spans": [ + { + "bbox": [ + 68, + 280, + 160, + 331 + ], + "type": "image", + "image_path": "b6d312ec6ea4dfbb83c9ab2a2339e81501eeb2d1bd6b4811e1e5ef67391cc5cb.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 68, + 331, + 160, + 385 + ], + "blocks": [ + { + "bbox": [ + 68, + 331, + 160, + 385 + ], + "lines": [ + { + "bbox": [ + 68, + 331, + 160, + 385 + ], + "spans": [ + { + "bbox": [ + 68, + 331, + 160, + 385 + ], + "type": "image", + "image_path": "3109a81678974553943ee72e18e4ee67266b38f65a3e0944fb98212d6312a0d7.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 68, + 385, + 160, + 437 + ], + "blocks": [ + { + "bbox": [ + 68, + 385, + 160, + 437 + ], + "lines": [ + { + "bbox": [ + 68, + 385, + 160, + 437 + ], + "spans": [ + { + "bbox": [ + 68, + 385, + 160, + 437 + ], + "type": "image", + "image_path": "f6b91df3205dc6c99263b53252ff0be46ccbdc2a76978f7106191809287761ed.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 68, + 437, + 160, + 489 + ], + "blocks": [ + { + "bbox": [ + 68, + 437, + 160, + 489 + ], + "lines": [ + { + "bbox": [ + 68, + 437, + 160, + 489 + ], + "spans": [ + { + "bbox": [ + 68, + 437, + 160, + 489 + ], + "type": "image", + "image_path": "6736ec9cb0deafaec8de24c84dc14cc18842a5f019a3ffd6f3329288e2a15f8e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 498, + 533, + 510 + ], + "lines": [ + { + "bbox": [ + 58, + 498, + 533, + 510 + ], + "spans": [ + { + "bbox": [ + 58, + 498, + 533, + 510 + ], + "type": "text", + "content": "Figure 3. Qualitative Comparison. 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In particular, we demonstrate that with access to more accurate ground truth depth, our performance can be further enhanced. This suggests the potential of our method to continue improving alongside advancements in monocular depth estimation." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "Qualitative Results. We present qualitative comparisons with CoTracker [29] on challenging videos from DAVIS [50] and Internet footage in Fig. 3. Our method outperforms CoTracker in handling complex human motion with self-occlusions, achieves a better understanding of rigid groups, and can effectively track small, rapidly moving objects even in the presence of occlusions. Please refer to the supplementary video for more results and better visualizations." + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 305, + 524, + 441, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 524, + 441, + 537 + ], + "spans": [ + { + "bbox": [ + 305, + 524, + 441, + 537 + ], + "type": "text", + "content": "4.2.3D Tracking Evaluation" + } + ] + } + ], + "index": 40 + }, + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 664 + ], + "type": "text", + "content": "Given an RGBD video (with known depth and intrinsics) as input, our method can estimate true 3D trajectories. Since no baseline method can directly be used for long-range 3D tracking, we construct our baselines by composing existing methods. Our first baseline is chained RAFT-3D [63]. RAFT-3D is designed for pairwise scene flow estimation, so to obtain long-range scene flow, we chain its scene flow prediction of consecutive frames. Our second baseline is to directly lift the predicted 2D trajectories from CoTracker [29] using the input depth maps." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 545, + 713 + ], + "type": "text", + "content": "We evaluate our method and baselines on the PointOdyssey [81] dataset. We create 231 testing sequences from the test set, each consisting of 24 frames and with a reduced frame rate set at one-fifth of the original. We" + } + ] + } + ], + "index": 42 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 74, + 56, + 472 + ], + "type": "aside_text", + "angle": 270, + "lines": [ + { + "bbox": [ + 47, + 74, + 56, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 74, + 56, + 472 + ], + "type": "text", + "content": "Ours CoTracker [29] Ours CoTracker [29] Ours CoTracker [29] Ours CoTracker [29]" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20412" + } + ] + } + ], + "index": 43 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 288, + 127 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 288, + 127 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 288, + 127 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 288, + 127 + ], + "type": "table", + "html": "
MethodsATE3D ↓δ0.1 ↑δ0.2 ↑
Chained RAFT3D [63]0.700.120.25
Lifted CoTracker [29]0.770.510.64
Ours0.220.590.76
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MethodsAJ↑<δxavg↑OA↑
Ours w/o ARAP55.171.687.4
Ours w/ DPT [53]51.470.783.3
Ours w/ MiDaS [5]56.373.986.6
Ours w/ ZoeDepth [2] (default)61.176.389.5
", + "image_path": "8460f4bc6c31e580d96f4b169aa7a6ecc94ec6d34b891f7e65f32da7c6988022.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 264, + 288, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 264, + 288, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 288, + 331 + ], + "type": "text", + "content": "Table 5. Ablation Study on the DAVIS Dataset. The Average Jaccard (AJ), average position accuracy " + }, + { + "bbox": [ + 46, + 264, + 288, + 331 + ], + "type": "inline_equation", + "content": "(<\\delta_{\\mathrm{avg}}^x)" + }, + { + "bbox": [ + 46, + 264, + 288, + 331 + ], + "type": "text", + "content": ", and Occlusion Accuracy (OA) are reported. We evaluate the effectiveness of the ARAP constraint and the influence of different monocular depth estimators (ZoeDepth [2], MiDaS [5] and DPT [53]). \"Ours w/ZoeDepth\" is the default model we use in our experiments." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": "use three evaluation metrics, namely " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{ATE}_{3\\mathrm{D}}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\delta_{0.1}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\delta_{0.2}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\mathrm{ATE}_{3\\mathrm{D}}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": " is the average trajectory error in 3D space. " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\delta_{0.1}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "\\delta_{0.2}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": " measure the percentage of points whose distances are within " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{m}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "inline_equation", + "content": "0.2\\mathrm{m}" + }, + { + "bbox": [ + 46, + 341, + 287, + 389 + ], + "type": "text", + "content": " from the ground truth, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 389, + 288, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 288, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 288, + 534 + ], + "type": "text", + "content": "The results are shown in Tab. 4. Our method outperforms both \"Chained RAFT-3D\" and \"Lifted CoTracker\" consistently on all three metrics by a large margin. We found that RAFT-3D, trained on FlyingThings [40], generalizes poorly on PointOdyssey, possibly due to the fact that its dense-SE3 module is sensitive to domain gaps. In contrast, also trained on a different dataset (Kubric), our method exhibits strong generalization to PointOdyssey, affirming the efficacy of our design for 3D trajectory prediction. In addition, both baselines cannot handle occlusion and will lose track of points once they become occluded, hurting the performance significantly." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 540, + 174, + 553 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 174, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 174, + 553 + ], + "type": "text", + "content": "4.3. Ablation and Analysis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 559, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 559, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 559, + 287, + 656 + ], + "type": "text", + "content": "Effectiveness of ARAP loss and rigidity embedding. We ablate the ARAP loss and report the result \"Ours w/o ARAP\" on the TAP-Vid-DAVIS [11, 51] dataset in Tab. 5. Without the ARAP loss, the performance drops substantially, verifying the effectiveness of the ARAP constraint. We additionally showcase qualitative results of the rigid part segmentation, utilizing our learned rigidity embeddings in Fig. 4, demonstrating their effectiveness." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "Analysis on monocular depth estimators. To study the influence of different monocular depth estimation methods on our model, we evaluate our method with three monocular depth models: ZoeDepth [2] (default), MiDaS [5]," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 317, + 70, + 389, + 125 + ], + "blocks": [ + { + "bbox": [ + 317, + 70, + 389, + 125 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 389, + 125 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 389, + 125 + ], + "type": "image", + "image_path": "9c3fe704c16d51627ca1cc0cd04c0a1edb1789be10a9d7164df903314720e473.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 317, + 125, + 389, + 179 + ], + "blocks": [ + { + "bbox": [ + 317, + 125, + 389, + 179 + ], + "lines": [ + { + "bbox": [ + 317, + 125, + 389, + 179 + ], + "spans": [ + { + "bbox": [ + 317, + 125, + 389, + 179 + ], + "type": "image", + "image_path": "8be9438c4c8a36816b5441bdfc3d1a8193c69be9fecfa25cb39f2e5e1abfa8ee.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 182, + 547, + 217 + ], + "lines": [ + { + "bbox": [ + 304, + 182, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 547, + 217 + ], + "type": "text", + "content": "Figure 4. Rigid Part Segmentation. We utilize spectral clustering on the rigidity embedding to determine rigid groups. Each color represents a distinct rigid group." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 390, + 70, + 462, + 125 + ], + "blocks": [ + { + "bbox": [ + 390, + 70, + 462, + 125 + ], + "lines": [ + { + "bbox": [ + 390, + 70, + 462, + 125 + ], + "spans": [ + { + "bbox": [ + 390, + 70, + 462, + 125 + ], + "type": "image", + "image_path": "a0e86ee688ffca98207ba134e268ef426aebeadd87a0a6a11156a17c0c73aae2.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 390, + 125, + 462, + 179 + ], + "blocks": [ + { + "bbox": [ + 390, + 125, + 462, + 179 + ], + "lines": [ + { + "bbox": [ + 390, + 125, + 462, + 179 + ], + "spans": [ + { + "bbox": [ + 390, + 125, + 462, + 179 + ], + "type": "image", + "image_path": "6947fb33ca87259dc93c60d4b2086abc5edef6366c2916c9e1f4b9fb472870e1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 463, + 70, + 536, + 125 + ], + "blocks": [ + { + "bbox": [ + 463, + 70, + 536, + 125 + ], + "lines": [ + { + "bbox": [ + 463, + 70, + 536, + 125 + ], + "spans": [ + { + "bbox": [ + 463, + 70, + 536, + 125 + ], + "type": "image", + "image_path": "11c48fdb5bf74ae88f491205269c2ef52cf2016de908a384d61f9960f728feb0.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 463, + 125, + 536, + 179 + ], + "blocks": [ + { + "bbox": [ + 463, + 125, + 536, + 179 + ], + "lines": [ + { + "bbox": [ + 463, + 125, + 536, + 179 + ], + "spans": [ + { + "bbox": [ + 463, + 125, + 536, + 179 + ], + "type": "image", + "image_path": "bcda10462d663e2b809b8c5adbb8504da5fb47a14d56a6632a87d4f3fac6100b.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "spans": [ + { + "bbox": [ + 304, + 232, + 546, + 353 + ], + "type": "text", + "content": "and DPT [53]. We report the results on the TAP-ViddAVIS [11, 51] dataset in Tab. 5. \"Ours w/ ZoeDepth\" achieves the best results, probably due to the fact that ZoeDepth [2] is a metric depth estimator and exhibits less temporal inconsistency across frames compared to relative depth estimators MiDaS [5] and DPT [53]. Furthermore, it is noteworthy that the efficacy of our model has a positive correlation with the advancements in the underlying monocular depth models. Please refer to the supplementary material for additional analysis and ablations." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 373, + 458, + 385 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 373, + 458, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 373, + 458, + 385 + ], + "type": "text", + "content": "5. Conclusion and Discussion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 396, + 546, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 546, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 546, + 540 + ], + "type": "text", + "content": "In this work, we show that a properly designed 3D representation is crucial for solving the long-standing challenge of dense and long-range motion estimation in videos. Motion naturally occurs in 3D and tracking motion in 3D allows us to better leverage its regularity in 3D, e.g., the ARAP constraint. We proposed a novel framework that estimates 3D trajectories using triplane representations with a learnable ARAP constraint that identifies the rigid groups in the scene and enforces rigidity within each group. Experiments demonstrated the superior performance of our method compared to existing baselines and its applicability to challenging real-world scenarios." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 543, + 545, + 627 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 545, + 627 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 545, + 627 + ], + "type": "text", + "content": "Our current model relies on off-the-shelf monocular depth estimators whose accuracy may affect the final tracking performance as shown in Tab. 5. However, we anticipate that advancements in monocular reconstruction will enhance the performance of motion estimation. We expect a closer interplay between these two problems, benefiting each other in the near future." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 634, + 404, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 634, + 404, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 634, + 404, + 647 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 714 + ], + "type": "text", + "content": "This work was partially supported by National Key Research and Development Program of China (No. 2020AAA0108900), Ant Group, and Information Technology Center and State Key Lab of CAD&CG, Zhejiang University." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20413" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Steven S. 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Vis., pages 19855-19865, 2023. 2, 6, 7" + } + ] + } + ], + "index": 2 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20417" + } + ] + } + ], + "index": 4 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SpatialVLM_ Endowing Vision-Language Models with Spatial Reasoning Capabilities/dc5db9cb-fcf5-4067-8b85-ffb92320aba8_content_list.json b/2024/SpatialVLM_ Endowing Vision-Language Models with Spatial Reasoning Capabilities/dc5db9cb-fcf5-4067-8b85-ffb92320aba8_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..66e4f8e5b4e74ff3a3db35fd483bf9e7bc09d53d --- /dev/null +++ b/2024/SpatialVLM_ Endowing Vision-Language Models with Spatial Reasoning Capabilities/dc5db9cb-fcf5-4067-8b85-ffb92320aba8_content_list.json @@ -0,0 +1,2118 @@ +[ + { + "type": "text", + "text": "SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities", + "text_level": 1, + "bbox": [ + 76, + 130, + 893, + 155 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Boyuan Chen $^{1,3,\\ast,\\dagger}$ , Zhuo Xu $^{1,\\ast}$ , Sean Kirmani $^{1}$ , Brian Ichter $^{1}$ , Dorsa Sadigh $^{1}$ , Leonidas Guibas $^{2}$ , Fei Xia $^{1}$", + "bbox": [ + 251, + 179, + 718, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Google DeepMind, $^{2}$ Google Research, $^{3}$ MIT", + "bbox": [ + 310, + 232, + 658, + 252 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c8fd07e2642424ad484442d81c68a36daa2da33cea6b7f01c139cfd0fb65e35.jpg", + "image_caption": [ + "User" + ], + "image_footnote": [], + "bbox": [ + 86, + 289, + 116, + 311 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "You are a cleaning robot that is 1 meter wide, now you are standing in a living room and see the image, you want to move from here to the door that leads to the backyard, do you think I can go through the path between the sofa and the table and chairs.", + "bbox": [ + 120, + 287, + 272, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9f6a2b0ef073549d1fa2cae988b0ecd791acf9e27f5f067b8837755694aa56ad.jpg", + "image_caption": [ + "GPT-4V*" + ], + "image_footnote": [], + "bbox": [ + 276, + 268, + 457, + 381 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "As an AI, I'm unable to physically interact with environments, but I can provide some insights based on the image provided. ... From the image, we can make some visual estimations. Judging from the image, it appears that the sofa and the table are quite close to each other, and there may not be enough space to accommodate a 1-meter wide robot....", + "bbox": [ + 464, + 275, + 877, + 330 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Spatial-VLM", + "text_level": 1, + "bbox": [ + 460, + 334, + 511, + 343 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/fa5e67e24ddb7dd510845a396d7b739ad8af8f46bb6582d0fb19c454dd05fa54.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 345, + 488, + 364 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[VLM Reasoning] How wide is the path between the sofa and the table and chairs? [VLM Answer] 1.56m [Answer] Yes, the robot can go through the path between the sofa and the table and chairs since it is wider than the robot's width.", + "bbox": [ + 493, + 345, + 867, + 375 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/53e593d4497b17f6d9c90806eb43598b9880a99657d0fefa7a43cb9d65cce458.jpg", + "image_caption": [ + "User" + ], + "image_footnote": [], + "bbox": [ + 86, + 417, + 116, + 439 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Which can is the closest to the yellow finger that is on the right most side of the picture, the blue, orange or the silver one?", + "bbox": [ + 120, + 417, + 264, + 457 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9e7fb0efab206bb03aba5e6c7e8abb8fa9108ccc4fbf2c53bc7371ce99f1c625.jpg", + "image_caption": [ + "GPT-4V" + ], + "image_footnote": [], + "bbox": [ + 276, + 398, + 457, + 512 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "After estimating the distances by measuring the Euclidean distances between the yellow finger and each of the cans, it is clear that the silver can is the closest to the yellow finger with an approximate distance of 110 units. In comparison, the blue can is about 262 units away, and the orange can is approximately 233 units away from the yellow finger.", + "bbox": [ + 462, + 402, + 883, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Spatial-VLM", + "text_level": 1, + "bbox": [ + 460, + 460, + 514, + 470 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dbf485eec537c85e5a7b022d6069ab33e0853fa2ddea697ebbdab72eabcad57b.jpg", + "image_caption": [ + "Figure 1. We present SpatialVLM, a data synthesis and pre-training mechanism to enhance VLMs' spatial reasoning capabilities. We demonstrate that VLMs trained on our synthetic data exhibit strong spatial reasoning capabilities, and can generate metric distance estimation from 2D input images, addressing blind spots of current state-of-the-art VLMs like GPT-4V. (* GPT-4V accessed Nov. 2023)." + ], + "image_footnote": [], + "bbox": [ + 462, + 472, + 488, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[VLM Reasoning] How far is the yellow finger from the blue can? [VLM Answer] 0.5m [VLM Reasoning] How far is the yellow finger from the orange can? [VLM Anser] 0.59m [VLM Reasoning] How far is the yellow finger from the silver can? [VLM Answer] 0.21m [Answer] The silver can is the closest to the yellow finger that is on the right most side of the picture.", + "bbox": [ + 495, + 470, + 870, + 525 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 236, + 604, + 310, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size difference. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in training recipe including data quality, training pipeline and", + "bbox": [ + 73, + 636, + 473, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "VLM architecture. Our work features the first Internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Website: https://spatial-vlm.github.io/", + "bbox": [ + 496, + 604, + 893, + 712 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 723, + 624, + 739 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Vision language models (VLMs) have made significant progress in recent years across a variety of tasks including image captioning, visual question answering (VQA), embodied planning, action recognition, and more [2, 18, 24, 31]. While VLMs are powerful general-purpose models for a wide range of tasks, most state-of-the-art VLMs still struggle with spatial reasoning, i.e. tasks that require understanding the position of objects in 3D space, or spatial relationships between them. Spatial reasoning capabilities are useful in their own right, but also for downstream applications such as in robotics or AR. For example, a spatial", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Equal Contribution;† Work done during internship at Google DeepMind; Correspond to boyuanc@mit.edu; zhuoxu, xiafei@google.com", + "bbox": [ + 75, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14455", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "reasoning-imbued VLM can be used as a better general-purpose reward annotator [51] and success detector [19].", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The exploration of foundation models like VLMs is often inspired by human capabilities. Humans, through embodied experiences and evolutionary development, possess innate spatial reasoning skills. We effortlessly determine spatial relationships, such as the positioning of objects relative to each other or estimating distances and sizes, without complex chain-of-thoughts or mental computations. This natural proficiency in direct spatial reasoning tasks contrasts with the current limitations of VLMs and thus prevents them from accomplishing real-world tasks that requires multiple steps of spatial reasoning. This gap leads us to a compelling research question: can we imbue VLMs with spatial reasoning abilities akin to those of humans?", + "bbox": [ + 75, + 122, + 470, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Therefore, we hypothesize that the limited the spatial reasoning abilities of current VLMs is not due to a fundamental limitation of their architecture, but rather is a limitation in common datasets available at scale on which such models are trained. For example, many VLMs [13, 18, 42] are trained on internet-scale datasets characterized by image-caption pairs [12], which contain limited spatial information. This is partially due to the difficulties of obtaining spatial-information-rich embodied data or high-quality human annotations for 3D-aware queries.", + "bbox": [ + 75, + 305, + 468, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Automatic data generation and augmentation techniques are one approach to deal with the data limitation problem [36, 50, 53, 63]. However, most previous data generation efforts focus on rendering photorealistic images with ground truth semantic annotation but overlook the richness of objects and 3D relationships. In contrast, we focus on extracting spatial information directly from real world data in order to capture the diversity and complexity of the true 3D world.", + "bbox": [ + 75, + 444, + 468, + 564 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our key insight is that recent advancement in off-the-shelf vision models can automatically generate rich 3D spatial annotations from 2D images. To this end, we propose a system called SpatialVLM that enables data generation and training of VLMs to enhance their spatial reasoning capabilities. Concretely, by combining 1) open-vocabulary detection, 2) metric depth estimation, 3) semantic segmentation and 4) object-centric captioning models, we can densely annotate real world data at scale. SpatialVLM converts the data generated by vision models into a format can be used to train VLMs on a mixture of captioning, VQA and spatial reasoning data. Training on such data gives SpatialVLM the perceptual foundations of the 3D world which allows spatial reasoning through an LLM.", + "bbox": [ + 75, + 566, + 470, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through experiments, we find our trained VLM exhibit many desirable capabilities. First, its ability to answer qualitative spatial questions is greatly enhanced. Secondly, it can perform quantitative estimation reliably despite noisy training data. Such capability not only gives it common sense knowledge about object sizes but also makes it useful as a open-vocabulary reward annotator for rearrangement tasks. Thirdly, we find this spatial Vision Language Model, benefiting from its natural language interface, can perform", + "bbox": [ + 75, + 763, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "spatial chain-of-thought to solve complex spatial reasoning tasks when combined with a powerful Large Language Model. Our main contributions are:", + "bbox": [ + 498, + 90, + 890, + 135 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We endow VLMs quantitative spatial reasoning capability, which is a fundamental capability of humans.", + "- We design a framework to automatically label 3D spatial reasoning VQA data based on real world images at the Internet scale.", + "- We study various training recipes: data quality, training pipeline, freeze/unfreeze visual encoder, etc, and investigate how they affect the learning quality.", + "- We show examples of new capabilities in complex reasoning and robotics unlocked by the introduced task and method." + ], + "bbox": [ + 500, + 136, + 893, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 297, + 635, + 314 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Learning Spatial Reasoning. Spatial distance estimation has been traditionally addressed as a part of broader tasks, such as SLAM [8, 21] or depth estimation [23]. When applying these spatial concepts to reasoning, prior works often focus on explicit spatial scene memories [26, 27] or spatial scene graphs [29, 30, 59, 60]. Scene graphs allow interpretable, structured, statistical relation learning based on the spatial structures they encode. To answer spatial problems in VQA formats, they must handle it explicitly as a pathfinding problem on said scene graph. VLMs, on the other hand, are pretrained on large amounts of loosely structured information from vision-language datasets. Unlike scene graphs, the spatial understanding is encoded implicitly. We can infuse the depth and 3D structure into the weights with an auxiliary task [34, 45], capturing the relational information. In our work, we address the spatial relationship problem directly in the VLM, without an explicit underlying scene graph. In addition to understanding relative relationships in qualitative terms, we also explore estimating explicit metric distance relationships between objects in a scene.", + "bbox": [ + 496, + 324, + 893, + 611 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Grounding Vision-Language Models. Large language models (LLMs) are trained on internet-scale data, making them effective commonsense reasoners. However, LLMs (and by extension VLMs) may lack the necessary grounding to perform well at social reasoning [40], physical reasoning [25], physics reasoning [44], embodied tasks [1, 32, 55], and spatial reasoning tasks [42, 52]. Though language model with interactive world experience show grounding improvements [64, 67], the introduction of large vision models, such as Flamingo [2], PaLI [13], or PaLM-E [18], has enabled a leap in performance. These visually-grounded models have been used for several downstream tasks, such as in robotic success detection [18, 20, 54, 65], action prediction [7, 56], and reward prediction [16, 22, 46, 48]. In this work we approach the problem of spatial reasoning through finetuning a VLM on a generated VQA dataset. By directly finetuning a VLM on this task, we inherit the generality and reasoning capabilities of the underlying VLM as well as show how this approach is capable of tasks like reward generation.", + "bbox": [ + 496, + 628, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14456", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/b5c8077a33e7cc726a821684899936291c740b9686845dae697debe1d3f3efe3.jpg", + "image_caption": [ + "Figure 2. An overview of our data synthesis pipeline. (a) We use CLIP to filter noisy internet images and only keep scene-level photos. (b) We apply pre-trained expert models on internet-scale images so that we get object-centric segmentation, depth and caption. (c) We lift the 2D image into 3D point clouds, which can be parsed by shape analysis rules to extract useful properties like 3D bounding box. (d) We avoid asking ambiguous questions by clustering object captions using CLIP similarity score (e) We synthesize millions of spatial question and answers from object captions and extracted properties." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 872, + 385 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Spatial Information in Vision-Language Datasets. Many prior works have focused on benchmarking VLMs [58, 66], considering tasks like VQA (e.g. VQAv2 [28], OK-VQA [47], COCO [41], or Visual Genome [37]). Others have focused on fine-grained scene understanding, such as semantic segmentation [5, 35], object detection [11], or object identification [15, 57]. Others have focused specifically on spatial reasoning as a task, answering questions about object spatial relations (e.g., above, below, left, right) in real [42, 52] or simulated [33] scenes. Real data in this domain can be limited by the amount generated by human labelers, while synthetic data has inherently bounded expressivity. In this work we consider how to automatically generate real data, and focus on the problem of not just spatial relations, but metric spatial distances, which can be directly applied to many downstream tasks.", + "bbox": [ + 75, + 479, + 472, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. SpatialVLM", + "text_level": 1, + "bbox": [ + 76, + 722, + 200, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To equip VLMs with both qualitatively and quantitatively spatial reasoning capabilities, we propose to generate a large-scale spatial VQA dataset, which is used to train VLMs. Concretely, we design a comprehensive data generation framework which first leverages off-the-shelf computer vision models including open-vocabulary detection, metric depth estimation, semantic segmentation and object-centric captioning models to extract object-centric contexts, and then adopts template-based approach to generate massive spatial VQA data of reasonable quality. We train our SpatialVLM using the generated dataset", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to learn direct spatial reasoning capabilities, which we can then combine with the high-level commonsense reasoning embedded in LLMs to unlock chain-of-thoughts spatial reasoning.", + "bbox": [ + 496, + 479, + 892, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Spatial Grounding from 2D Images", + "text_level": 1, + "bbox": [ + 498, + 532, + 807, + 549 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We hypothesize that the reason for the lack of spatial reasoning capabilities of today's VLMs is not their architecture, but the lack of spatial reasoning training data. Following this insight, we design a pipeline that generates VQA data containing spatial reasoning questions. The pipeline is summarized in in Figure 2 and described in detail as follows.", + "bbox": [ + 496, + 555, + 893, + 645 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Semantic Filtering While internet-scale image captioning datasets have been widely used in VLM training [13], many images in these datasets are not suitable for synthesizing spatial reasoning QA, due to the fact that they either consist of a single object or don't have a scene background (e.g. product pictures on shopping websites or screenshots of computer screen). Therefore, as the first step in our data synthesis pipeline, we adopt a CLIP-based open-vocabulary classification model to classify all images and rule out those that are not suitable.", + "bbox": [ + 496, + 651, + 893, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Object-centric Contexts Extraction from 2D Images In order to extract object-centric spatial contexts from 2D images, we leverage a series of off-the-shelf expert models, including region proposal, region captioning [4], and semantic segmentation [39] modules to extract object-centric information. With this step, we obtain object-centric entities consisting of pixel clusters as well as open-vocabulary caption descriptions.", + "bbox": [ + 496, + 794, + 895, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14457", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1d1d743a234fef952b95955d33d3e605426ab8035870b9afedb5e8c8ac8cef87.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 119, + 241, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8f6ee9c7441d012d7da5451177fc8ca60c9203609aba58cc81052eb067ebe8e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 193, + 241, + 272 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5700998de35071c6d733d6cc0328b5ebcc389270138bc40ed6937456745bed5a.jpg", + "image_caption": [ + "Figure 3. Example data entries from the synthetic dataset. Given the output of vision expert models, we follow a set of question generation template to generate both quantitative and qualitative question-answer pairs to highlight the diversity of the dataset. The spatial concepts are highlighted in blue. Such visual question-answer pairs can be easily mixed together with other captioning or question answering datasets and use the same training objectives." + ], + "image_footnote": [], + "bbox": [ + 99, + 272, + 241, + 354 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Qualitative Q & A", + "text_level": 1, + "bbox": [ + 325, + 97, + 470, + 113 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Find out if the girl", + "bbox": [ + 259, + 125, + 356, + 138 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "wearing a purple shirt is", + "bbox": [ + 259, + 140, + 390, + 151 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "situated behind or in", + "bbox": [ + 259, + 152, + 370, + 164 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "front of the girl wearing a", + "bbox": [ + 259, + 165, + 395, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "blue sweatshirt.", + "bbox": [ + 259, + 178, + 346, + 188 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It's the woman", + "bbox": [ + 406, + 138, + 493, + 150 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "wearing white shirt.", + "bbox": [ + 406, + 152, + 519, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Does the stool lie in front", + "bbox": [ + 259, + 220, + 395, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of the microwave oven?", + "bbox": [ + 259, + 233, + 390, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Yes, the stool is in front", + "bbox": [ + 406, + 220, + 532, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of the microwave oven.", + "bbox": [ + 406, + 233, + 532, + 244 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Is the plate positioned", + "bbox": [ + 259, + 286, + 380, + 297 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on the left or right side of", + "bbox": [ + 259, + 299, + 395, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "the green and yellow", + "bbox": [ + 259, + 311, + 374, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "napkin?", + "bbox": [ + 259, + 324, + 305, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The plate is to the", + "bbox": [ + 406, + 299, + 504, + 311 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "right.", + "bbox": [ + 406, + 311, + 434, + 323 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Quantitative Q & A", + "text_level": 1, + "bbox": [ + 638, + 97, + 792, + 113 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Measure the distance", + "bbox": [ + 573, + 132, + 691, + 143 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from the cake shaped like", + "bbox": [ + 573, + 145, + 712, + 156 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a house to the girl", + "bbox": [ + 573, + 157, + 671, + 169 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "wearing a purple shirt?", + "bbox": [ + 573, + 171, + 697, + 183 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Around half a meter", + "bbox": [ + 725, + 151, + 834, + 162 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Can you provide the", + "bbox": [ + 573, + 200, + 683, + 213 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "distance measurement", + "bbox": [ + 573, + 214, + 697, + 224 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "between the microwave", + "bbox": [ + 573, + 226, + 702, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "oven and the kitchen", + "bbox": [ + 573, + 238, + 687, + 250 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "counter?", + "bbox": [ + 573, + 251, + 622, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "They are 1 meter apart.", + "bbox": [ + 725, + 226, + 852, + 238 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "How wide is the plate?", + "bbox": [ + 573, + 305, + 696, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "20 centimeters", + "bbox": [ + 725, + 305, + 807, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lifting 2D Contexts to 3D Contexts Traditional spatial VQA datasets generated using object detection and bounding box positioning [38] are limited to the 2D image plane (lack of depth or altitude contexts) and pixel-level reasoning (lack of metric-scale size and distance contexts). We perform depth estimation [6] to lift monocular 2D pixels to metric-scale 3D point clouds. We further canonicalize the camera coordinate system of the point cloud into a geodetic coordinate system, which is done by horizontal surface (e.g. \"floor\", \"table top\") segmentation [10] and frame transfer. To the best of our knowledge, we are the first to lift internet-scale images to object-centric 3D point clouds and use it to synthesize VQA data embedded with 3D spatial reasoning supervision.", + "bbox": [ + 75, + 436, + 472, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Ambiguity Resolution Sometimes there are multiple objects of similar categories in one image, leading to ambiguities of their caption labels. For example, one same caption label \"cake\" can refer to multiple different cakes in a same image. Therefore, before we can ask questions about these objects, we need to make sure the reference expressions are not ambiguous. We made two key design choices that have been validated empirically to be effective in tackling this challenge:", + "bbox": [ + 75, + 641, + 470, + 762 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We deliberately choose to avoid common object detectors, which tend to produce fixed and coarse categories such as \"cake\", and adopt FlexCap [4], a user-configurable object-centric captioning approach. In practice, for each object we can sample a random caption of a variable length between 1 - 6 words. As a result, our object annotations are fine-grained, such as \"cake shaped like a house\" and \"cup cake in plastic container\".", + "- We design a semantic-oriented post-processing algorithm that" + ], + "bbox": [ + 76, + 763, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "further remove ambiguities by augmenting or rejecting object captions. Details of this algorithm are shown in Appendix ?? .", + "bbox": [ + 514, + 436, + 893, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Large-Scale Spatial Reasoning VQA Dataset", + "text_level": 1, + "bbox": [ + 500, + 479, + 877, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As motivated in Section 3, we focus our study on infusing \"straightforward\" spatial reasoning capabilities into VLMs by pretraining with synthetic data. Therefore, we synthesize spatial-reasoning QA pairs that involve no more than two objects (denoted \"A\" and \"B\") in the image and consider the two following categories of questions.", + "bbox": [ + 496, + 503, + 890, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Qualitative questions: those that ask for judgement of some spatial relations. Examples are \"Given two objects A and B, which is more towards the left?\", \"Is object A more elevated than object B?\" and \"Among A and B, which is bigger in width?\".", + "bbox": [ + 496, + 603, + 893, + 664 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Quantitative questions: those that ask for more fine-grained answers that include numbers and units. Examples include \"how much to the left is object A compared to object B?\", \"How far is object A from the B?\", \"Find out how far A is positioned behind B relative to the camera\". Similar to the aforementioned examples, such questions can be synthesized using a main question template, and one can fill the object name entries using the object captions after disambiguation. This property allows us to do template-based generation, an approach commonly adopted by instruction tuning works [61]. The answers to the questions are obtained through appropriate functions that we develop, which take as input the segmented point clouds and 3D bounding boxes of the relevant objects.", + "bbox": [ + 496, + 672, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We designate 38 different types of qualitative and quantitative spatial reasoning questions, each featuring around 20", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14458", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "User:", + "text_level": 1, + "bbox": [ + 140, + 95, + 174, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Does the blue coke can, the orange can, and the silver seven up can on the table roughly form an isosceles triangle? Roughly means the difference between the longest and shortest triangle edges is smaller than $0.1\\mathrm{m}$", + "bbox": [ + 140, + 109, + 808, + 135 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/bd4f5a25707fd8d83071a4d195d849ef51d4b6eae57fee366f4d8606d86e082d.jpg", + "image_caption": [ + "Figure 4. Chain-of-thought spatial reasoning. We illustrate that we can perform Chain-of-Thought Spatial reasoning with SpatialVLM. In this example, with the help of an LLM orchestrating SpatialVLM, the system is able to answer questions like \"Does the blue coke can, the red coke can, and the green sponge on the table roughly form an equilateral triangle\"." + ], + "image_footnote": [], + "bbox": [ + 133, + 142, + 326, + 261 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LLM: What is the distance between the blue coke can and the orange can?", + "bbox": [ + 341, + 143, + 776, + 156 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VLM: 0.4m", + "bbox": [ + 341, + 157, + 408, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LLM: What is the distance between the orange can and the silver seven up can?", + "bbox": [ + 341, + 170, + 805, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VLM: 0.48m", + "bbox": [ + 341, + 183, + 415, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LLM: What is the distance between the blue coke can and the silver seven up can?", + "bbox": [ + 341, + 196, + 821, + 208 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VLM: 0.41m", + "bbox": [ + 341, + 210, + 416, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "LLM: Since the difference between the longest and shortest triangle edges (0.48m - 0.4m = 0.08m) is smaller than 0.1 m, the blue coke can, the orange can, and the silver seven up can roughly form an isosceles triangle.", + "bbox": [ + 341, + 223, + 838, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "question templates and 10 answer templates (we show examples in Appendix. ??). We also add bias the sampling to encourage concise answers. Finally we introduce a human-aligned rounding mechanism in Appendix ?? to make number roundings in a human-like way. Using such an approach, we are able to generate ample question answering data pairs for the monocular camera images in webli and vqa datasets. Fig 3 shows several example synthetic question answering pairs we obtained. In total, we create a massive dataset with 10 million images and 2 billion direct spatial reasoning QA pairs, featuring $50\\%$ qualitative questions and $50\\%$ quantitative questions. Thanks to the diversity of object captions and distance units, our synthetic dataset features significant diversity in terms of object description, question type and phrasing.", + "bbox": [ + 75, + 335, + 472, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Learning Spatial Reasoning", + "text_level": 1, + "bbox": [ + 76, + 556, + 328, + 573 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Direct Spatial Reasoning is defined as following, a Vision-Language Model takes as input an image $\\mathcal{I}$ and a query $\\mathcal{Q}$ of a spatial task, and output an answer $\\mathcal{A}$ , in the format of a text string, without using external tools or interacting with other large models. We adopt the same architecture and training procedure of PaLM-E [18] except replacing PaLM [14] backbone with PaLM 2-S [3], a smaller variant. We then train our model using a mixture of the original PaLM-E dataset and our dataset, with $5\\%$ of tokens dedicated to spatial reasoning tasks. Similar to PaLM-E, our method has the ability to perform VQA as well as basic embodied planning when combined. The key difference is that it can answer spatial reasoning questions about both binary predicates and quantitative estimations.", + "bbox": [ + 75, + 580, + 468, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Chain-of-Thought Spatial Reasoning Many real-world tasks require multiple steps of spatial reasoning. For example, to determine if object A can fit into object B, one would need to reason about sizes and constraints. Sometimes one would need to reason over grounded spatial concept (e.g. the counter in the image is 1 meter high) and common sense knowledge (so that a toddler cannot reach it). SpatialVLM provides a natural language", + "bbox": [ + 75, + 794, + 472, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "interface to query with grounded concepts, when combined with a powerful LLM, we can perform complex spatial reasoning.", + "bbox": [ + 498, + 335, + 890, + 366 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We call this method \"Chain-of-Thought Spatial Reasoning\". While our synthesized data only contains direct spatial reasoning questions, it's easy for a VLM to compose them together to solve complex questions that require multi-hop chain-of-thought reasoning. Similar to the method in Socratic Models [68] and LLM as coordinator [9], we utilize an LLM (text-davinci-003) to coordinate and communicate with our SpatialVLM to solve complex problems with Chain-of-Thought prompting [62] as shown in Fig. 4. The LLM can break down complex questions into simple questions, query the VLM, and put the reasoning together to derive the result.", + "bbox": [ + 496, + 367, + 892, + 532 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 547, + 625, + 565 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct experiments to answer the following questions:", + "bbox": [ + 500, + 573, + 870, + 588 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Q1 Does our spatial VQA data generation and training pipeline improve VLM's general spatial reasoning capabilities? And how well does it perform?", + "Q2 How does the noisy synthetic spatial VQA data and different training strategies affect the learning performance?", + "Q3 Does the VLM equipped with \"direct\" spatial reasoning capabilities unlock new capabilities such as chain-of-thought reasoning and embodied planning?" + ], + "bbox": [ + 506, + 589, + 890, + 709 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our model using a mixture of PaLM-E training set and our spatial VQA dataset. To verify whether VLM's limitation in spatial reasoning is a data problem, we choose the following state-of-the-art VLMs as baselines, all trained on mixtures in which semantic-captioning tasks occupy a heavy weight, and without our spatial VQA dataset.", + "bbox": [ + 496, + 710, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GPT-4V $^{1}$ GPT-4V is a version of GPT-4 [49] that supports multimodal input, it achieves state-of-the-art performance in many vision-language tasks.", + "bbox": [ + 496, + 800, + 890, + 845 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PaLI [13]. An encoder-decoder VLM trained on multi-lingual corpora, it shows state-of-the-art performance on captioning", + "bbox": [ + 496, + 845, + 890, + 877 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1Accessed Nov 2023 via OpenAI API.", + "bbox": [ + 517, + 886, + 715, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14459", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/95ad01a8f4785b3e6b2743e4591805171abe16d4ab3dbb8e704098d5dc2481fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
GPT-4VLLaVA-1.5InstructBLIPPaLIPaLM-EPaLM 2-EOurs
Binary PredicateAccuracy68.0%71.3%60.4%60.7%50.2%50.4%75.2%
QuantitativeOutput numbers %1.0%20.9%26.0%52.0%83.2%88.8%99.0%
In range [50, 200]%0.0%13.0%7.9%5.3%23.7%33.9%37.2%
", + "bbox": [ + 119, + 88, + 848, + 162 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Accuracy of different VLMs on binary predicate tasks and quantitative questions about spatial relationship. As can be seen from this table, our proposed method outperforms baselines on binary predicate prediction tasks by a large margin owing to the addition of synthetic data. For quantitative estimation tasks, our method outputs valid format more often (99.0% of the time) than baseline methods. In addition, our method outputs quantitative distance estimation that is closer to ground truth annotated by human more often than baseline methods.", + "bbox": [ + 75, + 172, + 893, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "and visual-question answering tasks. We used PaLI-X 55B variant in our experiments.", + "bbox": [ + 75, + 246, + 467, + 275 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PaLM-E [18]. A VLM trained on internet-scale vision, language, and vision-language data, as well as robotics data. It shows state-of-the-art performance in OKVQA benchmark, as well as being capable of robot planning tasks. We used PaLM-E 12B across our experiments.", + "bbox": [ + 75, + 276, + 468, + 351 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PaLM 2-E The vanilla PaLM 2-E is an updated version of PaLM-E[18] with exact same training procedure but a more recent LLM backbone. Due to the shared network architecture and training procedure with SpatialVLM, vanilla PaLM 2-E naturally serves as the baseline to study the effect of generated data. In the rest of the paper, unless specifically noted, PaLM 2-E corresponds to PaLM 2-S in terms of parameter count following the naming convention in PaLM 2 technical report [3]. Finally, we consider open source models like LLaVA-1.5 [43] and InstructBLIP [17].", + "bbox": [ + 75, + 353, + 470, + 505 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Spatial VQA performance", + "text_level": 1, + "bbox": [ + 76, + 517, + 313, + 534 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To stress-test the VLM's spatial reasoning capabilities, a spatial reasoning VQA benchmark with guaranteed performance grounding is required. However, there is not such a proper benchmark available in the literature. Therefore, we created a benchmark by having human annotators label a diverse set of \"direct\" qualitative and quantitative VQAs on a subset of WebLI images [13], which are unseen to all VLMs during the training phase. The benchmark questions and answers are diverse and freeform, following the synthetic data generation pattern described in Section 3.2 (details in Appendix.??). We annotated 331 qualitative spatial reasoning VQA pairs and 215 quantitative spatial reasoning VQA pairs.", + "bbox": [ + 75, + 540, + 468, + 723 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Qualitative Spatial VQA For such questions, both the human annotated answers and VLM outputs are freeform natural language. Therefore, to evaluate the performance of the VLMs, we use human raters to determine if an answer is correct, and show the success rates of the VLMs in Table. 1. It is shown that SpatialVLM is able to achieve significantly higher accuracy compared to all baselines that are not trained using the synthetic spatial VQA data, surpassing other vision-language models including GPT-4V. Among the baselines, the second best model is LLaVA-1.5, which might be caused by their use of bounding boxes and corresponding captions in visual instruction tuning.", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Anecdotally, we found LLaVA-1.5 performs well in 2D spatial relationship inference, but inferior to our models in 3D spatial reasoning. This experiment suggests that large and high-quality spatial reasoning data is key to spatial reasoning capabilities, which are not present in pretraining datasets of state-of-the-art VLMs.", + "bbox": [ + 496, + 246, + 893, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Quantitative Spatial VQA For these questions, both human annotator answers and the VLM outputs are natural language descriptions of distance, height, elevation, etc, using their preferred units. We design two metrics for evaluating the performance of the VLM. First, we use the success rate of the VLM to produce a number to reflect if the VLM is able to understand the quantitative spatial reasoning question. Second, since the answer can range widely from centimeters to kilometers, we use percentages of the VLM answers that fall into half to twice of the ground truth value to represent how accurate the VLM's estimates are. The results are shown in Table. 1, and it is shown that our model performs better on both metrics than baselines with large margins. We observed that baseline VLMs are reluctant to give answers consisting of numbers. For example, replying \"No.\" to questions like \"Can you tell me the distance between ...\" This is likely due the the distribution of the training data. Additionally, we find that state-of-the-art VLM GPT-4V often refrain from generating answers about distance in SI units with a disclaimer text \"I'm sorry, but I cannot provide an exact distance as the image does not offer precise references for measurement...\" Our approach SpatialVLM achieves significantly higher success rate than all baselines, achieving in-range results on almost half of the questions. This performance is remarkable given that the human annotations are noisy, and agreement among annotators are not often guaranteed (Appendix. ??). To better understand our model's performance and limitations, we visualized the relative error against the ground truth value in Fig. ?? in the Appendix. We found that SpatialVLM does well on medium range scenes like those with objects 1-10 meters from the camera. This coincides with the range where our monocular depth estimator [6] reliably outputs metric accurate depth estimations, which indicates that our method inherits the biases and limitations from expert vision models in the data synthesis pipeline. We therefore hypothesize that the quality of monocular depth estimator has an significant influence on quantitative distance estimation.", + "bbox": [ + 496, + 356, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14460", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3cf7cf38fee98a148a1396a7b5fd4733c42f463487a0b82da1678d002e98e466.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 88, + 223, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d8b47dc602a6fb0d4df6502ab7addf8e9d9b7571dc2680644b96fb3941d08b90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 88, + 352, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/26e7ffb0d6a1160502841329b20ec8802a527cd2b45ecfadbe6e7b21736a0804.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 88, + 478, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/56cf31e87a674b75af596df69077aaddcb25c523584d20bbe9706947d60ee9ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 88, + 602, + 167 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/78c8abb054d5a579fe4fabedec4e75ce4ac99ca9edf40cea300916149c5243fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 604, + 89, + 870, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/de7da4f24386339539fa368684dce1910225125b7ecf6eddadc8dcfec9716489.jpg", + "image_caption": [ + "Figure 5. Given a sequence of images where the robot gripper is approaching the coke can, we ask SpatialVLM \"What is the distance between the yellow gripper and the coke can\". We are able to get accurate and monotonically decreasing distance estimations." + ], + "image_footnote": [], + "bbox": [ + 99, + 167, + 223, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4b6af85518f0838ab20332ff33d719085d7e552a7ea6b3537c2021615481538f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 225, + 167, + 352, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ad0a60ed6df988dabf931c82e13af1bc79b0f629852c0239878bca7ef4062357.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 354, + 167, + 478, + 244 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ec6bfbc0a80d28e5efedf5d0a777e6b505afbaf5fa4f48b201bd3eeb24f6cb8e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 167, + 602, + 244 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dbb89d13ea868ef49da5872f00ce1946ff2365467d364d219090c78372542004.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
General VQA benchmarksOKVQAVQA v2
PaLM 2-E w/o co-training61.4%76.6%
Ours61.0(-0.4)%79.0(+2.4)%
", + "bbox": [ + 89, + 308, + 455, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Effect of Spatial VQA Data to General VQA", + "text_level": 1, + "bbox": [ + 76, + 488, + 450, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The second question we want to answer is: since we co-train with a considerable amount of spatial VQA data, whether the performance of VLM in other tasks will degrade as a result. We compared our model with the vanilla PaLM 2-E trained without the spatial VQA dataset on general VQA benchmarks, and as summarized in Table. 2, our model achieves comparable performance as PaLM 2-E on the OKVQA benchmark, in which limited spatial reasoning questions are included, and performs slightly better on VQA-v2 test-dev benchmark, which includes spatial reasoning questions. This seem to suggest that VLMs are generally underfitting in the distribution of tasks close to spatial reasoning, and can benefit from spatial VQA supervisions without hurting their general VQA capabilities.", + "bbox": [ + 75, + 513, + 468, + 710 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Effect of Visual Transformer (ViT) Encoder in Spatial Reasoning", + "text_level": 1, + "bbox": [ + 76, + 723, + 468, + 755 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Does a frozen ViT (trained on contrastive objective) encode enough information to perform spatial reasoning? To study this, we start at the 110k training step and branch into two training runs, one with the ViT frozen, the other with ViT unfrozen. We train both models for 70k steps, and evaluate percentages of answers from both models that fall into various ranges of the ground truth value in Table 3.", + "bbox": [ + 75, + 762, + 468, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "It is shown that for larger scale and less fine-grained distance estimation, such as making a rough estimation with in the", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/fa24c5ced262d4a02ecd329cafa10c8855fb7e63119c60a49d805c958229f039.jpg", + "table_caption": [ + "Table 2. VQA performance. Co-training on SpatialVLM training mix and finetuning on VQA datasets (VQA v2) improves VQA performance. A PaLM 2-E model trained with SpatialVLM data improves VQA v2 performance by $2.4\\%$ compared to a model with the same number of parameters, but without the data. However, we don't find OKVQA task to benefit from SpatialVLM training." + ], + "table_footnote": [], + "table_body": "
[50, 200)%[66.7, 150)%[90, 110)%
Frozen ViT34.9%9.3%5.6%
Unfrozen ViT37.2(+2.3)%10.7(+1.4)%8.4(+2.8)%
", + "bbox": [ + 511, + 308, + 877, + 362 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e42095a7739e9b98b39a4a2a5404e9438397c85a9827bbda886241aa02a4e314.jpg", + "table_caption": [ + "Table 3. Comparison on finetuning with frozen or unfrozen ViT. We find it is beneficial to unfreeze the pretrained ViT for distance estimation tasks." + ], + "table_footnote": [], + "table_body": "
Gaussian std00.10.20.3
MSE(m)0.0460.0530.0390.048
[50, 200]%59.0%55.8%61.1%61.1%
", + "bbox": [ + 524, + 428, + 864, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparison on different data noise levels, controlled using standard deviation (STD) of Gaussian noise. We find that our model can learn despite moderate amount of random noise.", + "bbox": [ + 498, + 496, + 890, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "half-to-twice range of the ground truth, training without freezing ViT performs slightly worse but comparable with unfrozen ViT. However, for more fine-grained distance estimation like estimating accurate quantitative values, the model with unfrozen ViT performed considerably better. We hypothesize that the pretrained ViT (with contrastive or classification loss) is lossy in its fine-grained spatial information. Our model achieves $8.4\\%$ accuracy for predicting a value $0.9 \\times$ to $1.1 \\times$ range of human annotation. This is remarkable since humans annotations are noisy. In fact, human sometimes tend to give noisy estimations, as they prefer to round an estimation of 0.8 meter to 1 meter. It remains challenging to evaluate quantitative spatial reasoning capabilities of vision-language models in broad domains.", + "bbox": [ + 496, + 565, + 893, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Effect of Noisy Quantitative Spatial Answers", + "text_level": 1, + "bbox": [ + 498, + 771, + 879, + 787 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since the quantitative answers of the spatial VQA dataset are noisy, we study if VLMs can learn generalizable quantitative estimations from a large amount of noisy training data. To do so, we first come up with a domain where we are able to generate high quality quantitative answers. As discussed in Section 4.1 the monocular depth estimation is one of the steps in the data generation pipeline that induce the most noises. Therefore, we", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14461", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5db67c602c7ccb99f6b59882fa1492df0a3e5b8ad0c364684d8d4e3e24a44818.jpg", + "image_caption": [ + "Figure 6. SpatialVLM as reward generator for robotics tasks. SpatialVLM provides a \"natural-language queriable\" distance estimation tool, and can be used for robotics tasks. For example, for the task \"pick orange tea bottle\", the reward/cost function can be the a function of the response of \"What is the distance between the yellow gripper fingers and the orange tea bottle\". And for the task \"put the apple into the bowl\", the reward/cost function can be a function of the response of \"what is the distance between the apple and bowl\". We sample different gripper positions and show the cost function in the above scatter plots." + ], + "image_footnote": [], + "bbox": [ + 117, + 106, + 281, + 209 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6dac6e3dca80bb027ad22e9c9df3a7e82f536f4d908f5195b07964041abb111b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 292, + 88, + 455, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/804405a92e6c48c5edf94883e049559aee9981cfa66880a2952f45d87d03f208.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 464, + 88, + 630, + 217 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/720f465c442827522840e04ea45a298c9dfc00d90f2e8561cef800c3cf3ca561.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 635, + 88, + 800, + 215 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/56e2584a08e33c31e8d095ded7bfadac6438d7ac397da770b81ce04536db456c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 812, + 90, + 844, + 200 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "leverage our robotic manipulation dataset, which provides near-ground-truth depth information captured using a depth camera. As a result, the generated quantitative answers are more accurate. We train VLM using this dataset, and find the model able to perform fine-grained distance estimation in the manipulation domain (Fig. 5), which further demonstrates the data accuracy.", + "bbox": [ + 75, + 329, + 470, + 419 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To study how noisy data affects VLM training, we add Gaussian noises upon the quantitative answers of the accurate manipulation spatial VQA dataset, and obtain a series of noisy datasets of different noise level. We train VLMs using the noisy datasets and evaluate them using a human annotated quantitative spatial VQA benchmark for manipulation. Table. 4 compares how different Gaussian noise standard deviations affect the overall VLM performance on quantitative spatial VQA. Since the objects in the manipulation VQA datasets are within 1 meter range, we added the mean squared error (MSE) as a metric to evaluate the VLM performance, as well as the half-to-twice percentage which is defined in Section 4.1. It is shown that VLMs trained on datasets of different noise levels achieve similar spatial reasoning accuracy. We speculate this is due to the noisy nature of the training data and the manually annotated evaluation benchmark, and that VLM can learn a spatial reasoning common-sense despite noisy data. We observed this interesting phenomenon in robotics experiments as well. In Fig. 6, the distance estimation is exhibit a bias towards the mean since the model is heavily regularized.", + "bbox": [ + 75, + 421, + 473, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Spatial Reasoning Unlocks Novel Applications", + "text_level": 1, + "bbox": [ + 76, + 723, + 467, + 739 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "VLM as a Dense Reward Annotator One important application of VLM is robotics. Recently, works have shown that VLMs and LLMs can serve as universal open-vocabulary reward annotators and success detector [20] for robotics tasks, which can be used to derive useful control policies. However, the reward annotation ability of VLMs are often limited by lack of spatial awareness. Since SpatialVLM is able to quantitatively estimate distances or sizes from image, it's uniquely suited as a dense reward annotator. We conduct a real robot experiment where we specify a task in nature language and ask SpatialVLM", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to annotate a reward for each frame in a trajectory. In Figure 6, each dot illustrates an object location and their color indicates the annotated reward. As the robot makes progress towards the specified goal, we can see the reward increase monotonically, indicating the ability of SpatialVLM to serve as a dense reward annotator. While our example is not an in-depth benchmark of such capability, we hope our demonstration can inspire future research that involves quantitative metric estimation by VLMs, an area that was previously overlooked.", + "bbox": [ + 496, + 328, + 893, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Chain-of-Thought Spatial Reasoning In this section, we investigate whether SpatialVLM can be used to do tasks requiring multi-step reasoning, given its enhanced ability to answer elemental spatial questions. We demonstrate a few examples in Figure 1 and Figure 4. A large language model, in this case GPT-4, when equipped with SpatialVLM as a spatial reasoning submodule, can perform complex spatial reasoning tasks, such as answering if 3 objects in the environment can form a \"isosceles triangle\".", + "bbox": [ + 496, + 500, + 893, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 660, + 612, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In conclusion, our research addresses the challenge of infusing spatial reasoning to VLMs, and approach it by constructing a framework for automatic generation of 3D spatial reasoning VQA data based on Internet-scale real-world images. We ablate different design choices in the recipes for training VLMs, such as training with large amount of noisy data and unfreezing ViT. While our direct spatial queries are built on a finite set of templates, we show SpatialVLM can be extended to tackle more complicated chain-of-thought reasoning that requires spatial reasoning components. SpatialVLM is also demonstrated to be useful for robotics tasks, where we show that a 3D spatial-aware VLM could be used as a reward annotator for robotics tasks. Additional study of more nuanced geometric primitives can also help fully ground spatial reasoning in 3D geometry.", + "bbox": [ + 496, + 688, + 893, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14462", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 169, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael Ahn, Anthony Brohan, Noah Brown, Yevgen Chebotar, Omar Cortes, Byron David, Chelsea Finn, Chuyuan Fu, Keerthana Gopalakrishnan, Karol Hausman, et al. 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Socratic models: Composing zero-shot multimodal reasoning with language. arXiv preprint arXiv:2204.00598, 2022. 5", + "bbox": [ + 531, + 90, + 893, + 133 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14465", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SpatialVLM_ Endowing Vision-Language Models with Spatial Reasoning Capabilities/dc5db9cb-fcf5-4067-8b85-ffb92320aba8_model.json b/2024/SpatialVLM_ Endowing Vision-Language Models with Spatial Reasoning Capabilities/dc5db9cb-fcf5-4067-8b85-ffb92320aba8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..988c3aea8e3a93dd157922eccd3d0037df3892da --- /dev/null +++ b/2024/SpatialVLM_ Endowing Vision-Language Models with Spatial Reasoning Capabilities/dc5db9cb-fcf5-4067-8b85-ffb92320aba8_model.json @@ -0,0 +1,2939 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.131, + 0.895, + 0.156 + ], + "angle": 0, + "content": "SpatialVLM: Endowing Vision-Language Models with Spatial Reasoning Capabilities" + }, + { + "type": "text", + "bbox": [ + 0.252, + 0.18, + 0.72, + 0.218 + ], + "angle": 0, + "content": "Boyuan Chen\\(^{1,3,\\ast,\\dagger}\\), Zhuo Xu\\(^{1,\\ast}\\), Sean Kirmani\\(^{1}\\), Brian Ichter\\(^{1}\\), Dorsa Sadigh\\(^{1}\\), Leonidas Guibas\\(^{2}\\), Fei Xia\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.312, + 0.233, + 0.66, + 0.253 + ], + "angle": 0, + "content": "\\(^{1}\\)Google DeepMind, \\(^{2}\\)Google Research, \\(^{3}\\)MIT" + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.277, + 0.113, + 0.286 + ], + "angle": 0, + "content": "User" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.29, + 0.117, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.289, + 0.274, + 0.376 + ], + "angle": 0, + "content": "You are a cleaning robot that is 1 meter wide, now you are standing in a living room and see the image, you want to move from here to the door that leads to the backyard, do you think I can go through the path between the sofa and the table and chairs." + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.269, + 0.458, + 0.382 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.461, + 0.265, + 0.498, + 0.274 + ], + "angle": 0, + "content": "GPT-4V*" + }, + { + "type": "text", + "bbox": [ + 0.465, + 0.276, + 0.879, + 0.331 + ], + "angle": 0, + "content": "As an AI, I'm unable to physically interact with environments, but I can provide some insights based on the image provided. ... From the image, we can make some visual estimations. Judging from the image, it appears that the sofa and the table are quite close to each other, and there may not be enough space to accommodate a 1-meter wide robot...." + }, + { + "type": "title", + "bbox": [ + 0.462, + 0.335, + 0.513, + 0.344 + ], + "angle": 0, + "content": "Spatial-VLM" + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.346, + 0.489, + 0.365 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.495, + 0.346, + 0.868, + 0.376 + ], + "angle": 0, + "content": "[VLM Reasoning] How wide is the path between the sofa and the table and chairs? [VLM Answer] 1.56m [Answer] Yes, the robot can go through the path between the sofa and the table and chairs since it is wider than the robot's width." + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.406, + 0.112, + 0.414 + ], + "angle": 0, + "content": "User" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.419, + 0.117, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.419, + 0.266, + 0.458 + ], + "angle": 0, + "content": "Which can is the closest to the yellow finger that is on the right most side of the picture, the blue, orange or the silver one?" + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.4, + 0.458, + 0.513 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.461, + 0.391, + 0.495, + 0.4 + ], + "angle": 0, + "content": "GPT-4V" + }, + { + "type": "text", + "bbox": [ + 0.464, + 0.403, + 0.885, + 0.459 + ], + "angle": 0, + "content": "After estimating the distances by measuring the Euclidean distances between the yellow finger and each of the cans, it is clear that the silver can is the closest to the yellow finger with an approximate distance of 110 units. In comparison, the blue can is about 262 units away, and the orange can is approximately 233 units away from the yellow finger." + }, + { + "type": "title", + "bbox": [ + 0.462, + 0.462, + 0.515, + 0.471 + ], + "angle": 0, + "content": "Spatial-VLM" + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.473, + 0.489, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.496, + 0.472, + 0.872, + 0.526 + ], + "angle": 0, + "content": "[VLM Reasoning] How far is the yellow finger from the blue can? [VLM Answer] 0.5m [VLM Reasoning] How far is the yellow finger from the orange can? [VLM Anser] 0.59m [VLM Reasoning] How far is the yellow finger from the silver can? [VLM Answer] 0.21m [Answer] The silver can is the closest to the yellow finger that is on the right most side of the picture." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.537, + 0.895, + 0.58 + ], + "angle": 0, + "content": "Figure 1. We present SpatialVLM, a data synthesis and pre-training mechanism to enhance VLMs' spatial reasoning capabilities. We demonstrate that VLMs trained on our synthetic data exhibit strong spatial reasoning capabilities, and can generate metric distance estimation from 2D input images, addressing blind spots of current state-of-the-art VLMs like GPT-4V. (* GPT-4V accessed Nov. 2023)." + }, + { + "type": "title", + "bbox": [ + 0.237, + 0.605, + 0.312, + 0.621 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.637, + 0.474, + 0.865 + ], + "angle": 0, + "content": "Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size difference. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in training recipe including data quality, training pipeline and" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.875, + 0.47, + 0.901 + ], + "angle": 0, + "content": "* Equal Contribution;† Work done during internship at Google DeepMind; Correspond to boyuanc@mit.edu; zhuoxu, xiafei@google.com" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.895, + 0.713 + ], + "angle": 0, + "content": "VLM architecture. Our work features the first Internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Website: https://spatial-vlm.github.io/" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.724, + 0.625, + 0.74 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Vision language models (VLMs) have made significant progress in recent years across a variety of tasks including image captioning, visual question answering (VQA), embodied planning, action recognition, and more [2, 18, 24, 31]. While VLMs are powerful general-purpose models for a wide range of tasks, most state-of-the-art VLMs still struggle with spatial reasoning, i.e. tasks that require understanding the position of objects in 3D space, or spatial relationships between them. Spatial reasoning capabilities are useful in their own right, but also for downstream applications such as in robotics or AR. For example, a spatial" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14455" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "reasoning-imbued VLM can be used as a better general-purpose reward annotator [51] and success detector [19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.123, + 0.471, + 0.304 + ], + "angle": 0, + "content": "The exploration of foundation models like VLMs is often inspired by human capabilities. Humans, through embodied experiences and evolutionary development, possess innate spatial reasoning skills. We effortlessly determine spatial relationships, such as the positioning of objects relative to each other or estimating distances and sizes, without complex chain-of-thoughts or mental computations. This natural proficiency in direct spatial reasoning tasks contrasts with the current limitations of VLMs and thus prevents them from accomplishing real-world tasks that requires multiple steps of spatial reasoning. This gap leads us to a compelling research question: can we imbue VLMs with spatial reasoning abilities akin to those of humans?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.47, + 0.442 + ], + "angle": 0, + "content": "Therefore, we hypothesize that the limited the spatial reasoning abilities of current VLMs is not due to a fundamental limitation of their architecture, but rather is a limitation in common datasets available at scale on which such models are trained. For example, many VLMs [13, 18, 42] are trained on internet-scale datasets characterized by image-caption pairs [12], which contain limited spatial information. This is partially due to the difficulties of obtaining spatial-information-rich embodied data or high-quality human annotations for 3D-aware queries." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.565 + ], + "angle": 0, + "content": "Automatic data generation and augmentation techniques are one approach to deal with the data limitation problem [36, 50, 53, 63]. However, most previous data generation efforts focus on rendering photorealistic images with ground truth semantic annotation but overlook the richness of objects and 3D relationships. In contrast, we focus on extracting spatial information directly from real world data in order to capture the diversity and complexity of the true 3D world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.471, + 0.763 + ], + "angle": 0, + "content": "Our key insight is that recent advancement in off-the-shelf vision models can automatically generate rich 3D spatial annotations from 2D images. To this end, we propose a system called SpatialVLM that enables data generation and training of VLMs to enhance their spatial reasoning capabilities. Concretely, by combining 1) open-vocabulary detection, 2) metric depth estimation, 3) semantic segmentation and 4) object-centric captioning models, we can densely annotate real world data at scale. SpatialVLM converts the data generated by vision models into a format can be used to train VLMs on a mixture of captioning, VQA and spatial reasoning data. Training on such data gives SpatialVLM the perceptual foundations of the 3D world which allows spatial reasoning through an LLM." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Through experiments, we find our trained VLM exhibit many desirable capabilities. First, its ability to answer qualitative spatial questions is greatly enhanced. Secondly, it can perform quantitative estimation reliably despite noisy training data. Such capability not only gives it common sense knowledge about object sizes but also makes it useful as a open-vocabulary reward annotator for rearrangement tasks. Thirdly, we find this spatial Vision Language Model, benefiting from its natural language interface, can perform" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "spatial chain-of-thought to solve complex spatial reasoning tasks when combined with a powerful Large Language Model. Our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.137, + 0.894, + 0.166 + ], + "angle": 0, + "content": "- We endow VLMs quantitative spatial reasoning capability, which is a fundamental capability of humans." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.168, + 0.894, + 0.21 + ], + "angle": 0, + "content": "- We design a framework to automatically label 3D spatial reasoning VQA data based on real world images at the Internet scale." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.213, + 0.892, + 0.258 + ], + "angle": 0, + "content": "- We study various training recipes: data quality, training pipeline, freeze/unfreeze visual encoder, etc, and investigate how they affect the learning quality." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.258, + 0.892, + 0.287 + ], + "angle": 0, + "content": "- We show examples of new capabilities in complex reasoning and robotics unlocked by the introduced task and method." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.137, + 0.894, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.299, + 0.636, + 0.315 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.325, + 0.895, + 0.612 + ], + "angle": 0, + "content": "Learning Spatial Reasoning. Spatial distance estimation has been traditionally addressed as a part of broader tasks, such as SLAM [8, 21] or depth estimation [23]. When applying these spatial concepts to reasoning, prior works often focus on explicit spatial scene memories [26, 27] or spatial scene graphs [29, 30, 59, 60]. Scene graphs allow interpretable, structured, statistical relation learning based on the spatial structures they encode. To answer spatial problems in VQA formats, they must handle it explicitly as a pathfinding problem on said scene graph. VLMs, on the other hand, are pretrained on large amounts of loosely structured information from vision-language datasets. Unlike scene graphs, the spatial understanding is encoded implicitly. We can infuse the depth and 3D structure into the weights with an auxiliary task [34, 45], capturing the relational information. In our work, we address the spatial relationship problem directly in the VLM, without an explicit underlying scene graph. In addition to understanding relative relationships in qualitative terms, we also explore estimating explicit metric distance relationships between objects in a scene." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Grounding Vision-Language Models. Large language models (LLMs) are trained on internet-scale data, making them effective commonsense reasoners. However, LLMs (and by extension VLMs) may lack the necessary grounding to perform well at social reasoning [40], physical reasoning [25], physics reasoning [44], embodied tasks [1, 32, 55], and spatial reasoning tasks [42, 52]. Though language model with interactive world experience show grounding improvements [64, 67], the introduction of large vision models, such as Flamingo [2], PaLI [13], or PaLM-E [18], has enabled a leap in performance. These visually-grounded models have been used for several downstream tasks, such as in robotic success detection [18, 20, 54, 65], action prediction [7, 56], and reward prediction [16, 22, 46, 48]. In this work we approach the problem of spatial reasoning through finetuning a VLM on a generated VQA dataset. By directly finetuning a VLM on this task, we inherit the generality and reasoning capabilities of the underlying VLM as well as show how this approach is capable of tasks like reward generation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14456" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.873, + 0.386 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.396, + 0.896, + 0.466 + ], + "angle": 0, + "content": "Figure 2. An overview of our data synthesis pipeline. (a) We use CLIP to filter noisy internet images and only keep scene-level photos. (b) We apply pre-trained expert models on internet-scale images so that we get object-centric segmentation, depth and caption. (c) We lift the 2D image into 3D point clouds, which can be parsed by shape analysis rules to extract useful properties like 3D bounding box. (d) We avoid asking ambiguous questions by clustering object captions using CLIP similarity score (e) We synthesize millions of spatial question and answers from object captions and extracted properties." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.48, + 0.473, + 0.707 + ], + "angle": 0, + "content": "Spatial Information in Vision-Language Datasets. Many prior works have focused on benchmarking VLMs [58, 66], considering tasks like VQA (e.g. VQAv2 [28], OK-VQA [47], COCO [41], or Visual Genome [37]). Others have focused on fine-grained scene understanding, such as semantic segmentation [5, 35], object detection [11], or object identification [15, 57]. Others have focused specifically on spatial reasoning as a task, answering questions about object spatial relations (e.g., above, below, left, right) in real [42, 52] or simulated [33] scenes. Real data in this domain can be limited by the amount generated by human labelers, while synthetic data has inherently bounded expressivity. In this work we consider how to automatically generate real data, and focus on the problem of not just spatial relations, but metric spatial distances, which can be directly applied to many downstream tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.723, + 0.202, + 0.74 + ], + "angle": 0, + "content": "3. SpatialVLM" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To equip VLMs with both qualitatively and quantitatively spatial reasoning capabilities, we propose to generate a large-scale spatial VQA dataset, which is used to train VLMs. Concretely, we design a comprehensive data generation framework which first leverages off-the-shelf computer vision models including open-vocabulary detection, metric depth estimation, semantic segmentation and object-centric captioning models to extract object-centric contexts, and then adopts template-based approach to generate massive spatial VQA data of reasonable quality. We train our SpatialVLM using the generated dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.48, + 0.893, + 0.526 + ], + "angle": 0, + "content": "to learn direct spatial reasoning capabilities, which we can then combine with the high-level commonsense reasoning embedded in LLMs to unlock chain-of-thoughts spatial reasoning." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.533, + 0.808, + 0.55 + ], + "angle": 0, + "content": "3.1. Spatial Grounding from 2D Images" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.894, + 0.646 + ], + "angle": 0, + "content": "We hypothesize that the reason for the lack of spatial reasoning capabilities of today's VLMs is not their architecture, but the lack of spatial reasoning training data. Following this insight, we design a pipeline that generates VQA data containing spatial reasoning questions. The pipeline is summarized in in Figure 2 and described in detail as follows." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.895, + 0.789 + ], + "angle": 0, + "content": "Semantic Filtering While internet-scale image captioning datasets have been widely used in VLM training [13], many images in these datasets are not suitable for synthesizing spatial reasoning QA, due to the fact that they either consist of a single object or don't have a scene background (e.g. product pictures on shopping websites or screenshots of computer screen). Therefore, as the first step in our data synthesis pipeline, we adopt a CLIP-based open-vocabulary classification model to classify all images and rule out those that are not suitable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Object-centric Contexts Extraction from 2D Images In order to extract object-centric spatial contexts from 2D images, we leverage a series of off-the-shelf expert models, including region proposal, region captioning [4], and semantic segmentation [39] modules to extract object-centric information. With this step, we obtain object-centric entities consisting of pixel clusters as well as open-vocabulary caption descriptions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14457" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.121, + 0.242, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.194, + 0.242, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.273, + 0.242, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.326, + 0.098, + 0.471, + 0.114 + ], + "angle": 0, + "content": "Qualitative Q & A" + }, + { + "type": "text", + "bbox": [ + 0.26, + 0.126, + 0.357, + 0.139 + ], + "angle": 0, + "content": "Find out if the girl" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.141, + 0.391, + 0.152 + ], + "angle": 0, + "content": "wearing a purple shirt is" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.153, + 0.372, + 0.165 + ], + "angle": 0, + "content": "situated behind or in" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.166, + 0.396, + 0.178 + ], + "angle": 0, + "content": "front of the girl wearing a" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.179, + 0.347, + 0.189 + ], + "angle": 0, + "content": "blue sweatshirt." + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.14, + 0.494, + 0.151 + ], + "angle": 0, + "content": "It's the woman" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.153, + 0.521, + 0.166 + ], + "angle": 0, + "content": "wearing white shirt." + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.221, + 0.397, + 0.232 + ], + "angle": 0, + "content": "Does the stool lie in front" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.234, + 0.391, + 0.245 + ], + "angle": 0, + "content": "of the microwave oven?" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.221, + 0.534, + 0.232 + ], + "angle": 0, + "content": "Yes, the stool is in front" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.234, + 0.534, + 0.245 + ], + "angle": 0, + "content": "of the microwave oven." + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.287, + 0.381, + 0.299 + ], + "angle": 0, + "content": "Is the plate positioned" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.3, + 0.397, + 0.312 + ], + "angle": 0, + "content": "on the left or right side of" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.313, + 0.375, + 0.324 + ], + "angle": 0, + "content": "the green and yellow" + }, + { + "type": "text", + "bbox": [ + 0.261, + 0.325, + 0.307, + 0.337 + ], + "angle": 0, + "content": "napkin?" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.3, + 0.505, + 0.312 + ], + "angle": 0, + "content": "The plate is to the" + }, + { + "type": "text", + "bbox": [ + 0.408, + 0.313, + 0.436, + 0.324 + ], + "angle": 0, + "content": "right." + }, + { + "type": "title", + "bbox": [ + 0.639, + 0.098, + 0.794, + 0.114 + ], + "angle": 0, + "content": "Quantitative Q & A" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.133, + 0.692, + 0.144 + ], + "angle": 0, + "content": "Measure the distance" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.146, + 0.714, + 0.157 + ], + "angle": 0, + "content": "from the cake shaped like" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.158, + 0.672, + 0.17 + ], + "angle": 0, + "content": "a house to the girl" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.172, + 0.699, + 0.184 + ], + "angle": 0, + "content": "wearing a purple shirt?" + }, + { + "type": "text", + "bbox": [ + 0.727, + 0.152, + 0.836, + 0.164 + ], + "angle": 0, + "content": "Around half a meter" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.202, + 0.684, + 0.214 + ], + "angle": 0, + "content": "Can you provide the" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.215, + 0.699, + 0.226 + ], + "angle": 0, + "content": "distance measurement" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.227, + 0.703, + 0.238 + ], + "angle": 0, + "content": "between the microwave" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.239, + 0.688, + 0.25 + ], + "angle": 0, + "content": "oven and the kitchen" + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.252, + 0.624, + 0.263 + ], + "angle": 0, + "content": "counter?" + }, + { + "type": "text", + "bbox": [ + 0.727, + 0.227, + 0.854, + 0.239 + ], + "angle": 0, + "content": "They are 1 meter apart." + }, + { + "type": "text", + "bbox": [ + 0.575, + 0.306, + 0.697, + 0.318 + ], + "angle": 0, + "content": "How wide is the plate?" + }, + { + "type": "text", + "bbox": [ + 0.727, + 0.306, + 0.808, + 0.317 + ], + "angle": 0, + "content": "20 centimeters" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.367, + 0.895, + 0.424 + ], + "angle": 0, + "content": "Figure 3. Example data entries from the synthetic dataset. Given the output of vision expert models, we follow a set of question generation template to generate both quantitative and qualitative question-answer pairs to highlight the diversity of the dataset. The spatial concepts are highlighted in blue. Such visual question-answer pairs can be easily mixed together with other captioning or question answering datasets and use the same training objectives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.473, + 0.634 + ], + "angle": 0, + "content": "Lifting 2D Contexts to 3D Contexts Traditional spatial VQA datasets generated using object detection and bounding box positioning [38] are limited to the 2D image plane (lack of depth or altitude contexts) and pixel-level reasoning (lack of metric-scale size and distance contexts). We perform depth estimation [6] to lift monocular 2D pixels to metric-scale 3D point clouds. We further canonicalize the camera coordinate system of the point cloud into a geodetic coordinate system, which is done by horizontal surface (e.g. \"floor\", \"table top\") segmentation [10] and frame transfer. To the best of our knowledge, we are the first to lift internet-scale images to object-centric 3D point clouds and use it to synthesize VQA data embedded with 3D spatial reasoning supervision." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.472, + 0.763 + ], + "angle": 0, + "content": "Ambiguity Resolution Sometimes there are multiple objects of similar categories in one image, leading to ambiguities of their caption labels. For example, one same caption label \"cake\" can refer to multiple different cakes in a same image. Therefore, before we can ask questions about these objects, we need to make sure the reference expressions are not ambiguous. We made two key design choices that have been validated empirically to be effective in tackling this challenge:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.765, + 0.47, + 0.886 + ], + "angle": 0, + "content": "- We deliberately choose to avoid common object detectors, which tend to produce fixed and coarse categories such as \"cake\", and adopt FlexCap [4], a user-configurable object-centric captioning approach. In practice, for each object we can sample a random caption of a variable length between 1 - 6 words. As a result, our object annotations are fine-grained, such as \"cake shaped like a house\" and \"cup cake in plastic container\"." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.887, + 0.47, + 0.902 + ], + "angle": 0, + "content": "- We design a semantic-oriented post-processing algorithm that" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.765, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.515, + 0.437, + 0.894, + 0.468 + ], + "angle": 0, + "content": "further remove ambiguities by augmenting or rejecting object captions. Details of this algorithm are shown in Appendix ?? ." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.48, + 0.878, + 0.496 + ], + "angle": 0, + "content": "3.2. Large-Scale Spatial Reasoning VQA Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.504, + 0.892, + 0.595 + ], + "angle": 0, + "content": "As motivated in Section 3, we focus our study on infusing \"straightforward\" spatial reasoning capabilities into VLMs by pretraining with synthetic data. Therefore, we synthesize spatial-reasoning QA pairs that involve no more than two objects (denoted \"A\" and \"B\") in the image and consider the two following categories of questions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.604, + 0.894, + 0.665 + ], + "angle": 0, + "content": "Qualitative questions: those that ask for judgement of some spatial relations. Examples are \"Given two objects A and B, which is more towards the left?\", \"Is object A more elevated than object B?\" and \"Among A and B, which is bigger in width?\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Quantitative questions: those that ask for more fine-grained answers that include numbers and units. Examples include \"how much to the left is object A compared to object B?\", \"How far is object A from the B?\", \"Find out how far A is positioned behind B relative to the camera\". Similar to the aforementioned examples, such questions can be synthesized using a main question template, and one can fill the object name entries using the object captions after disambiguation. This property allows us to do template-based generation, an approach commonly adopted by instruction tuning works [61]. The answers to the questions are obtained through appropriate functions that we develop, which take as input the segmented point clouds and 3D bounding boxes of the relevant objects." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "We designate 38 different types of qualitative and quantitative spatial reasoning questions, each featuring around 20" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14458" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.141, + 0.097, + 0.175, + 0.107 + ], + "angle": 0, + "content": "User:" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.111, + 0.81, + 0.136 + ], + "angle": 0, + "content": "Does the blue coke can, the orange can, and the silver seven up can on the table roughly form an isosceles triangle? Roughly means the difference between the longest and shortest triangle edges is smaller than \\(0.1\\mathrm{m}\\)" + }, + { + "type": "image", + "bbox": [ + 0.134, + 0.143, + 0.327, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.342, + 0.144, + 0.777, + 0.157 + ], + "angle": 0, + "content": "LLM: What is the distance between the blue coke can and the orange can?" + }, + { + "type": "text", + "bbox": [ + 0.343, + 0.158, + 0.41, + 0.169 + ], + "angle": 0, + "content": "VLM: 0.4m" + }, + { + "type": "text", + "bbox": [ + 0.343, + 0.171, + 0.807, + 0.183 + ], + "angle": 0, + "content": "LLM: What is the distance between the orange can and the silver seven up can?" + }, + { + "type": "text", + "bbox": [ + 0.343, + 0.184, + 0.416, + 0.196 + ], + "angle": 0, + "content": "VLM: 0.48m" + }, + { + "type": "text", + "bbox": [ + 0.343, + 0.197, + 0.822, + 0.209 + ], + "angle": 0, + "content": "LLM: What is the distance between the blue coke can and the silver seven up can?" + }, + { + "type": "text", + "bbox": [ + 0.343, + 0.211, + 0.417, + 0.222 + ], + "angle": 0, + "content": "VLM: 0.41m" + }, + { + "type": "text", + "bbox": [ + 0.343, + 0.224, + 0.839, + 0.264 + ], + "angle": 0, + "content": "LLM: Since the difference between the longest and shortest triangle edges (0.48m - 0.4m = 0.08m) is smaller than 0.1 m, the blue coke can, the orange can, and the silver seven up can roughly form an isosceles triangle." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.278, + 0.895, + 0.321 + ], + "angle": 0, + "content": "Figure 4. Chain-of-thought spatial reasoning. We illustrate that we can perform Chain-of-Thought Spatial reasoning with SpatialVLM. In this example, with the help of an LLM orchestrating SpatialVLM, the system is able to answer questions like \"Does the blue coke can, the red coke can, and the green sponge on the table roughly form an equilateral triangle\"." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.549 + ], + "angle": 0, + "content": "question templates and 10 answer templates (we show examples in Appendix. ??). We also add bias the sampling to encourage concise answers. Finally we introduce a human-aligned rounding mechanism in Appendix ?? to make number roundings in a human-like way. Using such an approach, we are able to generate ample question answering data pairs for the monocular camera images in webli and vqa datasets. Fig 3 shows several example synthetic question answering pairs we obtained. In total, we create a massive dataset with 10 million images and 2 billion direct spatial reasoning QA pairs, featuring \\(50\\%\\) qualitative questions and \\(50\\%\\) quantitative questions. Thanks to the diversity of object captions and distance units, our synthetic dataset features significant diversity in terms of object description, question type and phrasing." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.329, + 0.574 + ], + "angle": 0, + "content": "3.3. Learning Spatial Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Direct Spatial Reasoning is defined as following, a Vision-Language Model takes as input an image \\(\\mathcal{I}\\) and a query \\(\\mathcal{Q}\\) of a spatial task, and output an answer \\(\\mathcal{A}\\), in the format of a text string, without using external tools or interacting with other large models. We adopt the same architecture and training procedure of PaLM-E [18] except replacing PaLM [14] backbone with PaLM 2-S [3], a smaller variant. We then train our model using a mixture of the original PaLM-E dataset and our dataset, with \\(5\\%\\) of tokens dedicated to spatial reasoning tasks. Similar to PaLM-E, our method has the ability to perform VQA as well as basic embodied planning when combined. The key difference is that it can answer spatial reasoning questions about both binary predicates and quantitative estimations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Chain-of-Thought Spatial Reasoning Many real-world tasks require multiple steps of spatial reasoning. For example, to determine if object A can fit into object B, one would need to reason about sizes and constraints. Sometimes one would need to reason over grounded spatial concept (e.g. the counter in the image is 1 meter high) and common sense knowledge (so that a toddler cannot reach it). SpatialVLM provides a natural language" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.337, + 0.892, + 0.367 + ], + "angle": 0, + "content": "interface to query with grounded concepts, when combined with a powerful LLM, we can perform complex spatial reasoning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.893, + 0.534 + ], + "angle": 0, + "content": "We call this method \"Chain-of-Thought Spatial Reasoning\". While our synthesized data only contains direct spatial reasoning questions, it's easy for a VLM to compose them together to solve complex questions that require multi-hop chain-of-thought reasoning. Similar to the method in Socratic Models [68] and LLM as coordinator [9], we utilize an LLM (text-davinci-003) to coordinate and communicate with our SpatialVLM to solve complex problems with Chain-of-Thought prompting [62] as shown in Fig. 4. The LLM can break down complex questions into simple questions, query the VLM, and put the reasoning together to derive the result." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.627, + 0.566 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.574, + 0.872, + 0.589 + ], + "angle": 0, + "content": "We conduct experiments to answer the following questions:" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.59, + 0.892, + 0.634 + ], + "angle": 0, + "content": "Q1 Does our spatial VQA data generation and training pipeline improve VLM's general spatial reasoning capabilities? And how well does it perform?" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.635, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Q2 How does the noisy synthetic spatial VQA data and different training strategies affect the learning performance?" + }, + { + "type": "text", + "bbox": [ + 0.508, + 0.665, + 0.892, + 0.71 + ], + "angle": 0, + "content": "Q3 Does the VLM equipped with \"direct\" spatial reasoning capabilities unlock new capabilities such as chain-of-thought reasoning and embodied planning?" + }, + { + "type": "list", + "bbox": [ + 0.507, + 0.59, + 0.892, + 0.71 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.711, + 0.892, + 0.8 + ], + "angle": 0, + "content": "We train our model using a mixture of PaLM-E training set and our spatial VQA dataset. To verify whether VLM's limitation in spatial reasoning is a data problem, we choose the following state-of-the-art VLMs as baselines, all trained on mixtures in which semantic-captioning tasks occupy a heavy weight, and without our spatial VQA dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.801, + 0.892, + 0.847 + ], + "angle": 0, + "content": "GPT-4V\\(^{1}\\) GPT-4V is a version of GPT-4 [49] that supports multimodal input, it achieves state-of-the-art performance in many vision-language tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.847, + 0.892, + 0.878 + ], + "angle": 0, + "content": "PaLI [13]. An encoder-decoder VLM trained on multi-lingual corpora, it shows state-of-the-art performance on captioning" + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.887, + 0.716, + 0.901 + ], + "angle": 0, + "content": "1Accessed Nov 2023 via OpenAI API." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14459" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.12, + 0.089, + 0.849, + 0.164 + ], + "angle": 0, + "content": "
GPT-4VLLaVA-1.5InstructBLIPPaLIPaLM-EPaLM 2-EOurs
Binary PredicateAccuracy68.0%71.3%60.4%60.7%50.2%50.4%75.2%
QuantitativeOutput numbers %1.0%20.9%26.0%52.0%83.2%88.8%99.0%
In range [50, 200]%0.0%13.0%7.9%5.3%23.7%33.9%37.2%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.174, + 0.895, + 0.232 + ], + "angle": 0, + "content": "Table 1. Accuracy of different VLMs on binary predicate tasks and quantitative questions about spatial relationship. As can be seen from this table, our proposed method outperforms baselines on binary predicate prediction tasks by a large margin owing to the addition of synthetic data. For quantitative estimation tasks, our method outputs valid format more often (99.0% of the time) than baseline methods. In addition, our method outputs quantitative distance estimation that is closer to ground truth annotated by human more often than baseline methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.247, + 0.468, + 0.276 + ], + "angle": 0, + "content": "and visual-question answering tasks. We used PaLI-X 55B variant in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.47, + 0.352 + ], + "angle": 0, + "content": "PaLM-E [18]. A VLM trained on internet-scale vision, language, and vision-language data, as well as robotics data. It shows state-of-the-art performance in OKVQA benchmark, as well as being capable of robot planning tasks. We used PaLM-E 12B across our experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.354, + 0.471, + 0.506 + ], + "angle": 0, + "content": "PaLM 2-E The vanilla PaLM 2-E is an updated version of PaLM-E[18] with exact same training procedure but a more recent LLM backbone. Due to the shared network architecture and training procedure with SpatialVLM, vanilla PaLM 2-E naturally serves as the baseline to study the effect of generated data. In the rest of the paper, unless specifically noted, PaLM 2-E corresponds to PaLM 2-S in terms of parameter count following the naming convention in PaLM 2 technical report [3]. Finally, we consider open source models like LLaVA-1.5 [43] and InstructBLIP [17]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.518, + 0.315, + 0.535 + ], + "angle": 0, + "content": "4.1. Spatial VQA performance" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.541, + 0.47, + 0.724 + ], + "angle": 0, + "content": "To stress-test the VLM's spatial reasoning capabilities, a spatial reasoning VQA benchmark with guaranteed performance grounding is required. However, there is not such a proper benchmark available in the literature. Therefore, we created a benchmark by having human annotators label a diverse set of \"direct\" qualitative and quantitative VQAs on a subset of WebLI images [13], which are unseen to all VLMs during the training phase. The benchmark questions and answers are diverse and freeform, following the synthetic data generation pattern described in Section 3.2 (details in Appendix.??). We annotated 331 qualitative spatial reasoning VQA pairs and 215 quantitative spatial reasoning VQA pairs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Qualitative Spatial VQA For such questions, both the human annotated answers and VLM outputs are freeform natural language. Therefore, to evaluate the performance of the VLMs, we use human raters to determine if an answer is correct, and show the success rates of the VLMs in Table. 1. It is shown that SpatialVLM is able to achieve significantly higher accuracy compared to all baselines that are not trained using the synthetic spatial VQA data, surpassing other vision-language models including GPT-4V. Among the baselines, the second best model is LLaVA-1.5, which might be caused by their use of bounding boxes and corresponding captions in visual instruction tuning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.895, + 0.337 + ], + "angle": 0, + "content": "Anecdotally, we found LLaVA-1.5 performs well in 2D spatial relationship inference, but inferior to our models in 3D spatial reasoning. This experiment suggests that large and high-quality spatial reasoning data is key to spatial reasoning capabilities, which are not present in pretraining datasets of state-of-the-art VLMs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Quantitative Spatial VQA For these questions, both human annotator answers and the VLM outputs are natural language descriptions of distance, height, elevation, etc, using their preferred units. We design two metrics for evaluating the performance of the VLM. First, we use the success rate of the VLM to produce a number to reflect if the VLM is able to understand the quantitative spatial reasoning question. Second, since the answer can range widely from centimeters to kilometers, we use percentages of the VLM answers that fall into half to twice of the ground truth value to represent how accurate the VLM's estimates are. The results are shown in Table. 1, and it is shown that our model performs better on both metrics than baselines with large margins. We observed that baseline VLMs are reluctant to give answers consisting of numbers. For example, replying \"No.\" to questions like \"Can you tell me the distance between ...\" This is likely due the the distribution of the training data. Additionally, we find that state-of-the-art VLM GPT-4V often refrain from generating answers about distance in SI units with a disclaimer text \"I'm sorry, but I cannot provide an exact distance as the image does not offer precise references for measurement...\" Our approach SpatialVLM achieves significantly higher success rate than all baselines, achieving in-range results on almost half of the questions. This performance is remarkable given that the human annotations are noisy, and agreement among annotators are not often guaranteed (Appendix. ??). To better understand our model's performance and limitations, we visualized the relative error against the ground truth value in Fig. ?? in the Appendix. We found that SpatialVLM does well on medium range scenes like those with objects 1-10 meters from the camera. This coincides with the range where our monocular depth estimator [6] reliably outputs metric accurate depth estimations, which indicates that our method inherits the biases and limitations from expert vision models in the data synthesis pipeline. We therefore hypothesize that the quality of monocular depth estimator has an significant influence on quantitative distance estimation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "14460" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.225, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.089, + 0.353, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.089, + 0.479, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.481, + 0.089, + 0.603, + 0.168 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.605, + 0.09, + 0.871, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.168, + 0.225, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.227, + 0.168, + 0.353, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.355, + 0.168, + 0.479, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.481, + 0.168, + 0.603, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.257, + 0.892, + 0.286 + ], + "angle": 0, + "content": "Figure 5. Given a sequence of images where the robot gripper is approaching the coke can, we ask SpatialVLM \"What is the distance between the yellow gripper and the coke can\". We are able to get accurate and monotonically decreasing distance estimations." + }, + { + "type": "table", + "bbox": [ + 0.09, + 0.309, + 0.456, + 0.366 + ], + "angle": 0, + "content": "
General VQA benchmarksOKVQAVQA v2
PaLM 2-E w/o co-training61.4%76.6%
Ours61.0(-0.4)%79.0(+2.4)%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.46 + ], + "angle": 0, + "content": "Table 2. VQA performance. Co-training on SpatialVLM training mix and finetuning on VQA datasets (VQA v2) improves VQA performance. A PaLM 2-E model trained with SpatialVLM data improves VQA v2 performance by \\(2.4\\%\\) compared to a model with the same number of parameters, but without the data. However, we don't find OKVQA task to benefit from SpatialVLM training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.489, + 0.452, + 0.505 + ], + "angle": 0, + "content": "4.2. Effect of Spatial VQA Data to General VQA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.514, + 0.47, + 0.711 + ], + "angle": 0, + "content": "The second question we want to answer is: since we co-train with a considerable amount of spatial VQA data, whether the performance of VLM in other tasks will degrade as a result. We compared our model with the vanilla PaLM 2-E trained without the spatial VQA dataset on general VQA benchmarks, and as summarized in Table. 2, our model achieves comparable performance as PaLM 2-E on the OKVQA benchmark, in which limited spatial reasoning questions are included, and performs slightly better on VQA-v2 test-dev benchmark, which includes spatial reasoning questions. This seem to suggest that VLMs are generally underfitting in the distribution of tasks close to spatial reasoning, and can benefit from spatial VQA supervisions without hurting their general VQA capabilities." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.47, + 0.756 + ], + "angle": 0, + "content": "4.3. Effect of Visual Transformer (ViT) Encoder in Spatial Reasoning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Does a frozen ViT (trained on contrastive objective) encode enough information to perform spatial reasoning? To study this, we start at the 110k training step and branch into two training runs, one with the ViT frozen, the other with ViT unfrozen. We train both models for 70k steps, and evaluate percentages of answers from both models that fall into various ranges of the ground truth value in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "It is shown that for larger scale and less fine-grained distance estimation, such as making a rough estimation with in the" + }, + { + "type": "table", + "bbox": [ + 0.513, + 0.309, + 0.879, + 0.363 + ], + "angle": 0, + "content": "
[50, 200)%[66.7, 150)%[90, 110)%
Frozen ViT34.9%9.3%5.6%
Unfrozen ViT37.2(+2.3)%10.7(+1.4)%8.4(+2.8)%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.373, + 0.894, + 0.414 + ], + "angle": 0, + "content": "Table 3. Comparison on finetuning with frozen or unfrozen ViT. We find it is beneficial to unfreeze the pretrained ViT for distance estimation tasks." + }, + { + "type": "table", + "bbox": [ + 0.525, + 0.429, + 0.866, + 0.486 + ], + "angle": 0, + "content": "
Gaussian std00.10.20.3
MSE(m)0.0460.0530.0390.048
[50, 200]%59.0%55.8%61.1%61.1%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.497, + 0.892, + 0.539 + ], + "angle": 0, + "content": "Table 4. Comparison on different data noise levels, controlled using standard deviation (STD) of Gaussian noise. We find that our model can learn despite moderate amount of random noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.566, + 0.895, + 0.763 + ], + "angle": 0, + "content": "half-to-twice range of the ground truth, training without freezing ViT performs slightly worse but comparable with unfrozen ViT. However, for more fine-grained distance estimation like estimating accurate quantitative values, the model with unfrozen ViT performed considerably better. We hypothesize that the pretrained ViT (with contrastive or classification loss) is lossy in its fine-grained spatial information. Our model achieves \\(8.4\\%\\) accuracy for predicting a value \\(0.9 \\times\\) to \\(1.1 \\times\\) range of human annotation. This is remarkable since humans annotations are noisy. In fact, human sometimes tend to give noisy estimations, as they prefer to round an estimation of 0.8 meter to 1 meter. It remains challenging to evaluate quantitative spatial reasoning capabilities of vision-language models in broad domains." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.772, + 0.88, + 0.789 + ], + "angle": 0, + "content": "4.4. Effect of Noisy Quantitative Spatial Answers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Since the quantitative answers of the spatial VQA dataset are noisy, we study if VLMs can learn generalizable quantitative estimations from a large amount of noisy training data. To do so, we first come up with a domain where we are able to generate high quality quantitative answers. As discussed in Section 4.1 the monocular depth estimation is one of the steps in the data generation pipeline that induce the most noises. Therefore, we" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "14461" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.107, + 0.282, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.293, + 0.089, + 0.457, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.465, + 0.089, + 0.631, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.636, + 0.089, + 0.801, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.813, + 0.091, + 0.845, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.233, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Figure 6. SpatialVLM as reward generator for robotics tasks. SpatialVLM provides a \"natural-language queriable\" distance estimation tool, and can be used for robotics tasks. For example, for the task \"pick orange tea bottle\", the reward/cost function can be the a function of the response of \"What is the distance between the yellow gripper fingers and the orange tea bottle\". And for the task \"put the apple into the bowl\", the reward/cost function can be a function of the response of \"what is the distance between the apple and bowl\". We sample different gripper positions and show the cost function in the above scatter plots." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.471, + 0.42 + ], + "angle": 0, + "content": "leverage our robotic manipulation dataset, which provides near-ground-truth depth information captured using a depth camera. As a result, the generated quantitative answers are more accurate. We train VLM using this dataset, and find the model able to perform fine-grained distance estimation in the manipulation domain (Fig. 5), which further demonstrates the data accuracy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.474, + 0.71 + ], + "angle": 0, + "content": "To study how noisy data affects VLM training, we add Gaussian noises upon the quantitative answers of the accurate manipulation spatial VQA dataset, and obtain a series of noisy datasets of different noise level. We train VLMs using the noisy datasets and evaluate them using a human annotated quantitative spatial VQA benchmark for manipulation. Table. 4 compares how different Gaussian noise standard deviations affect the overall VLM performance on quantitative spatial VQA. Since the objects in the manipulation VQA datasets are within 1 meter range, we added the mean squared error (MSE) as a metric to evaluate the VLM performance, as well as the half-to-twice percentage which is defined in Section 4.1. It is shown that VLMs trained on datasets of different noise levels achieve similar spatial reasoning accuracy. We speculate this is due to the noisy nature of the training data and the manually annotated evaluation benchmark, and that VLM can learn a spatial reasoning common-sense despite noisy data. We observed this interesting phenomenon in robotics experiments as well. In Fig. 6, the distance estimation is exhibit a bias towards the mean since the model is heavily regularized." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.724, + 0.468, + 0.741 + ], + "angle": 0, + "content": "4.5. Spatial Reasoning Unlocks Novel Applications" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.472, + 0.903 + ], + "angle": 0, + "content": "VLM as a Dense Reward Annotator One important application of VLM is robotics. Recently, works have shown that VLMs and LLMs can serve as universal open-vocabulary reward annotators and success detector [20] for robotics tasks, which can be used to derive useful control policies. However, the reward annotation ability of VLMs are often limited by lack of spatial awareness. Since SpatialVLM is able to quantitatively estimate distances or sizes from image, it's uniquely suited as a dense reward annotator. We conduct a real robot experiment where we specify a task in nature language and ask SpatialVLM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.895, + 0.466 + ], + "angle": 0, + "content": "to annotate a reward for each frame in a trajectory. In Figure 6, each dot illustrates an object location and their color indicates the annotated reward. As the robot makes progress towards the specified goal, we can see the reward increase monotonically, indicating the ability of SpatialVLM to serve as a dense reward annotator. While our example is not an in-depth benchmark of such capability, we hope our demonstration can inspire future research that involves quantitative metric estimation by VLMs, an area that was previously overlooked." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.501, + 0.895, + 0.639 + ], + "angle": 0, + "content": "Chain-of-Thought Spatial Reasoning In this section, we investigate whether SpatialVLM can be used to do tasks requiring multi-step reasoning, given its enhanced ability to answer elemental spatial questions. We demonstrate a few examples in Figure 1 and Figure 4. A large language model, in this case GPT-4, when equipped with SpatialVLM as a spatial reasoning submodule, can perform complex spatial reasoning tasks, such as answering if 3 objects in the environment can form a \"isosceles triangle\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.661, + 0.613, + 0.677 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In conclusion, our research addresses the challenge of infusing spatial reasoning to VLMs, and approach it by constructing a framework for automatic generation of 3D spatial reasoning VQA data based on Internet-scale real-world images. We ablate different design choices in the recipes for training VLMs, such as training with large amount of noisy data and unfreezing ViT. While our direct spatial queries are built on a finite set of templates, we show SpatialVLM can be extended to tackle more complicated chain-of-thought reasoning that requires spatial reasoning components. SpatialVLM is also demonstrated to be useful for robotics tasks, where we show that a 3D spatial-aware VLM could be used as a reward annotator for robotics tasks. Additional study of more nuanced geometric primitives can also help fully ground spatial reasoning in 3D geometry." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14462" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.17, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.472, + 0.185 + ], + "angle": 0, + "content": "[1] Michael Ahn, Anthony Brohan, Noah Brown, Yevgen Chebotar, Omar Cortes, Byron David, Chelsea Finn, Chuyuan Fu, Keerthana Gopalakrishnan, Karol Hausman, et al. 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From the image, we can make some visual estimations. Judging from the image, it appears that the sofa and the table are quite close to each other, and there may not be enough space to accommodate a 1-meter wide robot.... + +# Spatial-VLM + +![](images/fa5e67e24ddb7dd510845a396d7b739ad8af8f46bb6582d0fb19c454dd05fa54.jpg) + +[VLM Reasoning] How wide is the path between the sofa and the table and chairs? [VLM Answer] 1.56m [Answer] Yes, the robot can go through the path between the sofa and the table and chairs since it is wider than the robot's width. + +![](images/53e593d4497b17f6d9c90806eb43598b9880a99657d0fefa7a43cb9d65cce458.jpg) +User + +Which can is the closest to the yellow finger that is on the right most side of the picture, the blue, orange or the silver one? + +![](images/9e7fb0efab206bb03aba5e6c7e8abb8fa9108ccc4fbf2c53bc7371ce99f1c625.jpg) +GPT-4V + +After estimating the distances by measuring the Euclidean distances between the yellow finger and each of the cans, it is clear that the silver can is the closest to the yellow finger with an approximate distance of 110 units. In comparison, the blue can is about 262 units away, and the orange can is approximately 233 units away from the yellow finger. + +# Spatial-VLM + +![](images/dbf485eec537c85e5a7b022d6069ab33e0853fa2ddea697ebbdab72eabcad57b.jpg) +Figure 1. We present SpatialVLM, a data synthesis and pre-training mechanism to enhance VLMs' spatial reasoning capabilities. We demonstrate that VLMs trained on our synthetic data exhibit strong spatial reasoning capabilities, and can generate metric distance estimation from 2D input images, addressing blind spots of current state-of-the-art VLMs like GPT-4V. (* GPT-4V accessed Nov. 2023). + +[VLM Reasoning] How far is the yellow finger from the blue can? [VLM Answer] 0.5m [VLM Reasoning] How far is the yellow finger from the orange can? [VLM Anser] 0.59m [VLM Reasoning] How far is the yellow finger from the silver can? [VLM Answer] 0.21m [Answer] The silver can is the closest to the yellow finger that is on the right most side of the picture. + +# Abstract + +Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size difference. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in training recipe including data quality, training pipeline and + +VLM architecture. Our work features the first Internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Website: https://spatial-vlm.github.io/ + +# 1. Introduction + +Vision language models (VLMs) have made significant progress in recent years across a variety of tasks including image captioning, visual question answering (VQA), embodied planning, action recognition, and more [2, 18, 24, 31]. While VLMs are powerful general-purpose models for a wide range of tasks, most state-of-the-art VLMs still struggle with spatial reasoning, i.e. tasks that require understanding the position of objects in 3D space, or spatial relationships between them. Spatial reasoning capabilities are useful in their own right, but also for downstream applications such as in robotics or AR. For example, a spatial + +reasoning-imbued VLM can be used as a better general-purpose reward annotator [51] and success detector [19]. + +The exploration of foundation models like VLMs is often inspired by human capabilities. Humans, through embodied experiences and evolutionary development, possess innate spatial reasoning skills. We effortlessly determine spatial relationships, such as the positioning of objects relative to each other or estimating distances and sizes, without complex chain-of-thoughts or mental computations. This natural proficiency in direct spatial reasoning tasks contrasts with the current limitations of VLMs and thus prevents them from accomplishing real-world tasks that requires multiple steps of spatial reasoning. This gap leads us to a compelling research question: can we imbue VLMs with spatial reasoning abilities akin to those of humans? + +Therefore, we hypothesize that the limited the spatial reasoning abilities of current VLMs is not due to a fundamental limitation of their architecture, but rather is a limitation in common datasets available at scale on which such models are trained. For example, many VLMs [13, 18, 42] are trained on internet-scale datasets characterized by image-caption pairs [12], which contain limited spatial information. This is partially due to the difficulties of obtaining spatial-information-rich embodied data or high-quality human annotations for 3D-aware queries. + +Automatic data generation and augmentation techniques are one approach to deal with the data limitation problem [36, 50, 53, 63]. However, most previous data generation efforts focus on rendering photorealistic images with ground truth semantic annotation but overlook the richness of objects and 3D relationships. In contrast, we focus on extracting spatial information directly from real world data in order to capture the diversity and complexity of the true 3D world. + +Our key insight is that recent advancement in off-the-shelf vision models can automatically generate rich 3D spatial annotations from 2D images. To this end, we propose a system called SpatialVLM that enables data generation and training of VLMs to enhance their spatial reasoning capabilities. Concretely, by combining 1) open-vocabulary detection, 2) metric depth estimation, 3) semantic segmentation and 4) object-centric captioning models, we can densely annotate real world data at scale. SpatialVLM converts the data generated by vision models into a format can be used to train VLMs on a mixture of captioning, VQA and spatial reasoning data. Training on such data gives SpatialVLM the perceptual foundations of the 3D world which allows spatial reasoning through an LLM. + +Through experiments, we find our trained VLM exhibit many desirable capabilities. First, its ability to answer qualitative spatial questions is greatly enhanced. Secondly, it can perform quantitative estimation reliably despite noisy training data. Such capability not only gives it common sense knowledge about object sizes but also makes it useful as a open-vocabulary reward annotator for rearrangement tasks. Thirdly, we find this spatial Vision Language Model, benefiting from its natural language interface, can perform + +spatial chain-of-thought to solve complex spatial reasoning tasks when combined with a powerful Large Language Model. Our main contributions are: + +- We endow VLMs quantitative spatial reasoning capability, which is a fundamental capability of humans. +- We design a framework to automatically label 3D spatial reasoning VQA data based on real world images at the Internet scale. +- We study various training recipes: data quality, training pipeline, freeze/unfreeze visual encoder, etc, and investigate how they affect the learning quality. +- We show examples of new capabilities in complex reasoning and robotics unlocked by the introduced task and method. + +# 2. Related Work + +Learning Spatial Reasoning. Spatial distance estimation has been traditionally addressed as a part of broader tasks, such as SLAM [8, 21] or depth estimation [23]. When applying these spatial concepts to reasoning, prior works often focus on explicit spatial scene memories [26, 27] or spatial scene graphs [29, 30, 59, 60]. Scene graphs allow interpretable, structured, statistical relation learning based on the spatial structures they encode. To answer spatial problems in VQA formats, they must handle it explicitly as a pathfinding problem on said scene graph. VLMs, on the other hand, are pretrained on large amounts of loosely structured information from vision-language datasets. Unlike scene graphs, the spatial understanding is encoded implicitly. We can infuse the depth and 3D structure into the weights with an auxiliary task [34, 45], capturing the relational information. In our work, we address the spatial relationship problem directly in the VLM, without an explicit underlying scene graph. In addition to understanding relative relationships in qualitative terms, we also explore estimating explicit metric distance relationships between objects in a scene. + +Grounding Vision-Language Models. Large language models (LLMs) are trained on internet-scale data, making them effective commonsense reasoners. However, LLMs (and by extension VLMs) may lack the necessary grounding to perform well at social reasoning [40], physical reasoning [25], physics reasoning [44], embodied tasks [1, 32, 55], and spatial reasoning tasks [42, 52]. Though language model with interactive world experience show grounding improvements [64, 67], the introduction of large vision models, such as Flamingo [2], PaLI [13], or PaLM-E [18], has enabled a leap in performance. These visually-grounded models have been used for several downstream tasks, such as in robotic success detection [18, 20, 54, 65], action prediction [7, 56], and reward prediction [16, 22, 46, 48]. In this work we approach the problem of spatial reasoning through finetuning a VLM on a generated VQA dataset. By directly finetuning a VLM on this task, we inherit the generality and reasoning capabilities of the underlying VLM as well as show how this approach is capable of tasks like reward generation. + +![](images/b5c8077a33e7cc726a821684899936291c740b9686845dae697debe1d3f3efe3.jpg) +Figure 2. An overview of our data synthesis pipeline. (a) We use CLIP to filter noisy internet images and only keep scene-level photos. (b) We apply pre-trained expert models on internet-scale images so that we get object-centric segmentation, depth and caption. (c) We lift the 2D image into 3D point clouds, which can be parsed by shape analysis rules to extract useful properties like 3D bounding box. (d) We avoid asking ambiguous questions by clustering object captions using CLIP similarity score (e) We synthesize millions of spatial question and answers from object captions and extracted properties. + +Spatial Information in Vision-Language Datasets. Many prior works have focused on benchmarking VLMs [58, 66], considering tasks like VQA (e.g. VQAv2 [28], OK-VQA [47], COCO [41], or Visual Genome [37]). Others have focused on fine-grained scene understanding, such as semantic segmentation [5, 35], object detection [11], or object identification [15, 57]. Others have focused specifically on spatial reasoning as a task, answering questions about object spatial relations (e.g., above, below, left, right) in real [42, 52] or simulated [33] scenes. Real data in this domain can be limited by the amount generated by human labelers, while synthetic data has inherently bounded expressivity. In this work we consider how to automatically generate real data, and focus on the problem of not just spatial relations, but metric spatial distances, which can be directly applied to many downstream tasks. + +# 3. SpatialVLM + +To equip VLMs with both qualitatively and quantitatively spatial reasoning capabilities, we propose to generate a large-scale spatial VQA dataset, which is used to train VLMs. Concretely, we design a comprehensive data generation framework which first leverages off-the-shelf computer vision models including open-vocabulary detection, metric depth estimation, semantic segmentation and object-centric captioning models to extract object-centric contexts, and then adopts template-based approach to generate massive spatial VQA data of reasonable quality. We train our SpatialVLM using the generated dataset + +to learn direct spatial reasoning capabilities, which we can then combine with the high-level commonsense reasoning embedded in LLMs to unlock chain-of-thoughts spatial reasoning. + +# 3.1. Spatial Grounding from 2D Images + +We hypothesize that the reason for the lack of spatial reasoning capabilities of today's VLMs is not their architecture, but the lack of spatial reasoning training data. Following this insight, we design a pipeline that generates VQA data containing spatial reasoning questions. The pipeline is summarized in in Figure 2 and described in detail as follows. + +Semantic Filtering While internet-scale image captioning datasets have been widely used in VLM training [13], many images in these datasets are not suitable for synthesizing spatial reasoning QA, due to the fact that they either consist of a single object or don't have a scene background (e.g. product pictures on shopping websites or screenshots of computer screen). Therefore, as the first step in our data synthesis pipeline, we adopt a CLIP-based open-vocabulary classification model to classify all images and rule out those that are not suitable. + +Object-centric Contexts Extraction from 2D Images In order to extract object-centric spatial contexts from 2D images, we leverage a series of off-the-shelf expert models, including region proposal, region captioning [4], and semantic segmentation [39] modules to extract object-centric information. With this step, we obtain object-centric entities consisting of pixel clusters as well as open-vocabulary caption descriptions. + +![](images/1d1d743a234fef952b95955d33d3e605426ab8035870b9afedb5e8c8ac8cef87.jpg) + +![](images/8f6ee9c7441d012d7da5451177fc8ca60c9203609aba58cc81052eb067ebe8e1.jpg) + +![](images/5700998de35071c6d733d6cc0328b5ebcc389270138bc40ed6937456745bed5a.jpg) +Figure 3. Example data entries from the synthetic dataset. Given the output of vision expert models, we follow a set of question generation template to generate both quantitative and qualitative question-answer pairs to highlight the diversity of the dataset. The spatial concepts are highlighted in blue. Such visual question-answer pairs can be easily mixed together with other captioning or question answering datasets and use the same training objectives. + +# Qualitative Q & A + +Find out if the girl + +wearing a purple shirt is + +situated behind or in + +front of the girl wearing a + +blue sweatshirt. + +It's the woman + +wearing white shirt. + +Does the stool lie in front + +of the microwave oven? + +Yes, the stool is in front + +of the microwave oven. + +Is the plate positioned + +on the left or right side of + +the green and yellow + +napkin? + +The plate is to the + +right. + +# Quantitative Q & A + +Measure the distance + +from the cake shaped like + +a house to the girl + +wearing a purple shirt? + +Around half a meter + +Can you provide the + +distance measurement + +between the microwave + +oven and the kitchen + +counter? + +They are 1 meter apart. + +How wide is the plate? + +20 centimeters + +Lifting 2D Contexts to 3D Contexts Traditional spatial VQA datasets generated using object detection and bounding box positioning [38] are limited to the 2D image plane (lack of depth or altitude contexts) and pixel-level reasoning (lack of metric-scale size and distance contexts). We perform depth estimation [6] to lift monocular 2D pixels to metric-scale 3D point clouds. We further canonicalize the camera coordinate system of the point cloud into a geodetic coordinate system, which is done by horizontal surface (e.g. "floor", "table top") segmentation [10] and frame transfer. To the best of our knowledge, we are the first to lift internet-scale images to object-centric 3D point clouds and use it to synthesize VQA data embedded with 3D spatial reasoning supervision. + +Ambiguity Resolution Sometimes there are multiple objects of similar categories in one image, leading to ambiguities of their caption labels. For example, one same caption label "cake" can refer to multiple different cakes in a same image. Therefore, before we can ask questions about these objects, we need to make sure the reference expressions are not ambiguous. We made two key design choices that have been validated empirically to be effective in tackling this challenge: + +- We deliberately choose to avoid common object detectors, which tend to produce fixed and coarse categories such as "cake", and adopt FlexCap [4], a user-configurable object-centric captioning approach. In practice, for each object we can sample a random caption of a variable length between 1 - 6 words. As a result, our object annotations are fine-grained, such as "cake shaped like a house" and "cup cake in plastic container". +- We design a semantic-oriented post-processing algorithm that + +further remove ambiguities by augmenting or rejecting object captions. Details of this algorithm are shown in Appendix ?? . + +# 3.2. Large-Scale Spatial Reasoning VQA Dataset + +As motivated in Section 3, we focus our study on infusing "straightforward" spatial reasoning capabilities into VLMs by pretraining with synthetic data. Therefore, we synthesize spatial-reasoning QA pairs that involve no more than two objects (denoted "A" and "B") in the image and consider the two following categories of questions. + +Qualitative questions: those that ask for judgement of some spatial relations. Examples are "Given two objects A and B, which is more towards the left?", "Is object A more elevated than object B?" and "Among A and B, which is bigger in width?". + +Quantitative questions: those that ask for more fine-grained answers that include numbers and units. Examples include "how much to the left is object A compared to object B?", "How far is object A from the B?", "Find out how far A is positioned behind B relative to the camera". Similar to the aforementioned examples, such questions can be synthesized using a main question template, and one can fill the object name entries using the object captions after disambiguation. This property allows us to do template-based generation, an approach commonly adopted by instruction tuning works [61]. The answers to the questions are obtained through appropriate functions that we develop, which take as input the segmented point clouds and 3D bounding boxes of the relevant objects. + +We designate 38 different types of qualitative and quantitative spatial reasoning questions, each featuring around 20 + +# User: + +Does the blue coke can, the orange can, and the silver seven up can on the table roughly form an isosceles triangle? Roughly means the difference between the longest and shortest triangle edges is smaller than $0.1\mathrm{m}$ + +![](images/bd4f5a25707fd8d83071a4d195d849ef51d4b6eae57fee366f4d8606d86e082d.jpg) +Figure 4. Chain-of-thought spatial reasoning. We illustrate that we can perform Chain-of-Thought Spatial reasoning with SpatialVLM. In this example, with the help of an LLM orchestrating SpatialVLM, the system is able to answer questions like "Does the blue coke can, the red coke can, and the green sponge on the table roughly form an equilateral triangle". + +LLM: What is the distance between the blue coke can and the orange can? + +VLM: 0.4m + +LLM: What is the distance between the orange can and the silver seven up can? + +VLM: 0.48m + +LLM: What is the distance between the blue coke can and the silver seven up can? + +VLM: 0.41m + +LLM: Since the difference between the longest and shortest triangle edges (0.48m - 0.4m = 0.08m) is smaller than 0.1 m, the blue coke can, the orange can, and the silver seven up can roughly form an isosceles triangle. + +question templates and 10 answer templates (we show examples in Appendix. ??). We also add bias the sampling to encourage concise answers. Finally we introduce a human-aligned rounding mechanism in Appendix ?? to make number roundings in a human-like way. Using such an approach, we are able to generate ample question answering data pairs for the monocular camera images in webli and vqa datasets. Fig 3 shows several example synthetic question answering pairs we obtained. In total, we create a massive dataset with 10 million images and 2 billion direct spatial reasoning QA pairs, featuring $50\%$ qualitative questions and $50\%$ quantitative questions. Thanks to the diversity of object captions and distance units, our synthetic dataset features significant diversity in terms of object description, question type and phrasing. + +# 3.3. Learning Spatial Reasoning + +Direct Spatial Reasoning is defined as following, a Vision-Language Model takes as input an image $\mathcal{I}$ and a query $\mathcal{Q}$ of a spatial task, and output an answer $\mathcal{A}$ , in the format of a text string, without using external tools or interacting with other large models. We adopt the same architecture and training procedure of PaLM-E [18] except replacing PaLM [14] backbone with PaLM 2-S [3], a smaller variant. We then train our model using a mixture of the original PaLM-E dataset and our dataset, with $5\%$ of tokens dedicated to spatial reasoning tasks. Similar to PaLM-E, our method has the ability to perform VQA as well as basic embodied planning when combined. The key difference is that it can answer spatial reasoning questions about both binary predicates and quantitative estimations. + +Chain-of-Thought Spatial Reasoning Many real-world tasks require multiple steps of spatial reasoning. For example, to determine if object A can fit into object B, one would need to reason about sizes and constraints. Sometimes one would need to reason over grounded spatial concept (e.g. the counter in the image is 1 meter high) and common sense knowledge (so that a toddler cannot reach it). SpatialVLM provides a natural language + +interface to query with grounded concepts, when combined with a powerful LLM, we can perform complex spatial reasoning. + +We call this method "Chain-of-Thought Spatial Reasoning". While our synthesized data only contains direct spatial reasoning questions, it's easy for a VLM to compose them together to solve complex questions that require multi-hop chain-of-thought reasoning. Similar to the method in Socratic Models [68] and LLM as coordinator [9], we utilize an LLM (text-davinci-003) to coordinate and communicate with our SpatialVLM to solve complex problems with Chain-of-Thought prompting [62] as shown in Fig. 4. The LLM can break down complex questions into simple questions, query the VLM, and put the reasoning together to derive the result. + +# 4. Experiments + +We conduct experiments to answer the following questions: + +Q1 Does our spatial VQA data generation and training pipeline improve VLM's general spatial reasoning capabilities? And how well does it perform? +Q2 How does the noisy synthetic spatial VQA data and different training strategies affect the learning performance? +Q3 Does the VLM equipped with "direct" spatial reasoning capabilities unlock new capabilities such as chain-of-thought reasoning and embodied planning? + +We train our model using a mixture of PaLM-E training set and our spatial VQA dataset. To verify whether VLM's limitation in spatial reasoning is a data problem, we choose the following state-of-the-art VLMs as baselines, all trained on mixtures in which semantic-captioning tasks occupy a heavy weight, and without our spatial VQA dataset. + +GPT-4V $^{1}$ GPT-4V is a version of GPT-4 [49] that supports multimodal input, it achieves state-of-the-art performance in many vision-language tasks. + +PaLI [13]. An encoder-decoder VLM trained on multi-lingual corpora, it shows state-of-the-art performance on captioning + +
GPT-4VLLaVA-1.5InstructBLIPPaLIPaLM-EPaLM 2-EOurs
Binary PredicateAccuracy68.0%71.3%60.4%60.7%50.2%50.4%75.2%
QuantitativeOutput numbers %1.0%20.9%26.0%52.0%83.2%88.8%99.0%
In range [50, 200]%0.0%13.0%7.9%5.3%23.7%33.9%37.2%
+ +Table 1. Accuracy of different VLMs on binary predicate tasks and quantitative questions about spatial relationship. As can be seen from this table, our proposed method outperforms baselines on binary predicate prediction tasks by a large margin owing to the addition of synthetic data. For quantitative estimation tasks, our method outputs valid format more often (99.0% of the time) than baseline methods. In addition, our method outputs quantitative distance estimation that is closer to ground truth annotated by human more often than baseline methods. + +and visual-question answering tasks. We used PaLI-X 55B variant in our experiments. + +PaLM-E [18]. A VLM trained on internet-scale vision, language, and vision-language data, as well as robotics data. It shows state-of-the-art performance in OKVQA benchmark, as well as being capable of robot planning tasks. We used PaLM-E 12B across our experiments. + +PaLM 2-E The vanilla PaLM 2-E is an updated version of PaLM-E[18] with exact same training procedure but a more recent LLM backbone. Due to the shared network architecture and training procedure with SpatialVLM, vanilla PaLM 2-E naturally serves as the baseline to study the effect of generated data. In the rest of the paper, unless specifically noted, PaLM 2-E corresponds to PaLM 2-S in terms of parameter count following the naming convention in PaLM 2 technical report [3]. Finally, we consider open source models like LLaVA-1.5 [43] and InstructBLIP [17]. + +# 4.1. Spatial VQA performance + +To stress-test the VLM's spatial reasoning capabilities, a spatial reasoning VQA benchmark with guaranteed performance grounding is required. However, there is not such a proper benchmark available in the literature. Therefore, we created a benchmark by having human annotators label a diverse set of "direct" qualitative and quantitative VQAs on a subset of WebLI images [13], which are unseen to all VLMs during the training phase. The benchmark questions and answers are diverse and freeform, following the synthetic data generation pattern described in Section 3.2 (details in Appendix.??). We annotated 331 qualitative spatial reasoning VQA pairs and 215 quantitative spatial reasoning VQA pairs. + +Qualitative Spatial VQA For such questions, both the human annotated answers and VLM outputs are freeform natural language. Therefore, to evaluate the performance of the VLMs, we use human raters to determine if an answer is correct, and show the success rates of the VLMs in Table. 1. It is shown that SpatialVLM is able to achieve significantly higher accuracy compared to all baselines that are not trained using the synthetic spatial VQA data, surpassing other vision-language models including GPT-4V. Among the baselines, the second best model is LLaVA-1.5, which might be caused by their use of bounding boxes and corresponding captions in visual instruction tuning. + +Anecdotally, we found LLaVA-1.5 performs well in 2D spatial relationship inference, but inferior to our models in 3D spatial reasoning. This experiment suggests that large and high-quality spatial reasoning data is key to spatial reasoning capabilities, which are not present in pretraining datasets of state-of-the-art VLMs. + +Quantitative Spatial VQA For these questions, both human annotator answers and the VLM outputs are natural language descriptions of distance, height, elevation, etc, using their preferred units. We design two metrics for evaluating the performance of the VLM. First, we use the success rate of the VLM to produce a number to reflect if the VLM is able to understand the quantitative spatial reasoning question. Second, since the answer can range widely from centimeters to kilometers, we use percentages of the VLM answers that fall into half to twice of the ground truth value to represent how accurate the VLM's estimates are. The results are shown in Table. 1, and it is shown that our model performs better on both metrics than baselines with large margins. We observed that baseline VLMs are reluctant to give answers consisting of numbers. For example, replying "No." to questions like "Can you tell me the distance between ..." This is likely due the the distribution of the training data. Additionally, we find that state-of-the-art VLM GPT-4V often refrain from generating answers about distance in SI units with a disclaimer text "I'm sorry, but I cannot provide an exact distance as the image does not offer precise references for measurement..." Our approach SpatialVLM achieves significantly higher success rate than all baselines, achieving in-range results on almost half of the questions. This performance is remarkable given that the human annotations are noisy, and agreement among annotators are not often guaranteed (Appendix. ??). To better understand our model's performance and limitations, we visualized the relative error against the ground truth value in Fig. ?? in the Appendix. We found that SpatialVLM does well on medium range scenes like those with objects 1-10 meters from the camera. This coincides with the range where our monocular depth estimator [6] reliably outputs metric accurate depth estimations, which indicates that our method inherits the biases and limitations from expert vision models in the data synthesis pipeline. We therefore hypothesize that the quality of monocular depth estimator has an significant influence on quantitative distance estimation. + +![](images/3cf7cf38fee98a148a1396a7b5fd4733c42f463487a0b82da1678d002e98e466.jpg) + +![](images/d8b47dc602a6fb0d4df6502ab7addf8e9d9b7571dc2680644b96fb3941d08b90.jpg) + +![](images/26e7ffb0d6a1160502841329b20ec8802a527cd2b45ecfadbe6e7b21736a0804.jpg) + +![](images/56cf31e87a674b75af596df69077aaddcb25c523584d20bbe9706947d60ee9ce.jpg) + +![](images/78c8abb054d5a579fe4fabedec4e75ce4ac99ca9edf40cea300916149c5243fe.jpg) + +![](images/de7da4f24386339539fa368684dce1910225125b7ecf6eddadc8dcfec9716489.jpg) +Figure 5. Given a sequence of images where the robot gripper is approaching the coke can, we ask SpatialVLM "What is the distance between the yellow gripper and the coke can". We are able to get accurate and monotonically decreasing distance estimations. + +![](images/4b6af85518f0838ab20332ff33d719085d7e552a7ea6b3537c2021615481538f.jpg) + +![](images/ad0a60ed6df988dabf931c82e13af1bc79b0f629852c0239878bca7ef4062357.jpg) + +![](images/ec6bfbc0a80d28e5efedf5d0a777e6b505afbaf5fa4f48b201bd3eeb24f6cb8e.jpg) + +
General VQA benchmarksOKVQAVQA v2
PaLM 2-E w/o co-training61.4%76.6%
Ours61.0(-0.4)%79.0(+2.4)%
+ +# 4.2. Effect of Spatial VQA Data to General VQA + +The second question we want to answer is: since we co-train with a considerable amount of spatial VQA data, whether the performance of VLM in other tasks will degrade as a result. We compared our model with the vanilla PaLM 2-E trained without the spatial VQA dataset on general VQA benchmarks, and as summarized in Table. 2, our model achieves comparable performance as PaLM 2-E on the OKVQA benchmark, in which limited spatial reasoning questions are included, and performs slightly better on VQA-v2 test-dev benchmark, which includes spatial reasoning questions. This seem to suggest that VLMs are generally underfitting in the distribution of tasks close to spatial reasoning, and can benefit from spatial VQA supervisions without hurting their general VQA capabilities. + +# 4.3. Effect of Visual Transformer (ViT) Encoder in Spatial Reasoning + +Does a frozen ViT (trained on contrastive objective) encode enough information to perform spatial reasoning? To study this, we start at the 110k training step and branch into two training runs, one with the ViT frozen, the other with ViT unfrozen. We train both models for 70k steps, and evaluate percentages of answers from both models that fall into various ranges of the ground truth value in Table 3. + +It is shown that for larger scale and less fine-grained distance estimation, such as making a rough estimation with in the + +Table 2. VQA performance. Co-training on SpatialVLM training mix and finetuning on VQA datasets (VQA v2) improves VQA performance. A PaLM 2-E model trained with SpatialVLM data improves VQA v2 performance by $2.4\%$ compared to a model with the same number of parameters, but without the data. However, we don't find OKVQA task to benefit from SpatialVLM training. + +
[50, 200)%[66.7, 150)%[90, 110)%
Frozen ViT34.9%9.3%5.6%
Unfrozen ViT37.2(+2.3)%10.7(+1.4)%8.4(+2.8)%
+ +Table 3. Comparison on finetuning with frozen or unfrozen ViT. We find it is beneficial to unfreeze the pretrained ViT for distance estimation tasks. + +
Gaussian std00.10.20.3
MSE(m)0.0460.0530.0390.048
[50, 200]%59.0%55.8%61.1%61.1%
+ +Table 4. Comparison on different data noise levels, controlled using standard deviation (STD) of Gaussian noise. We find that our model can learn despite moderate amount of random noise. + +half-to-twice range of the ground truth, training without freezing ViT performs slightly worse but comparable with unfrozen ViT. However, for more fine-grained distance estimation like estimating accurate quantitative values, the model with unfrozen ViT performed considerably better. We hypothesize that the pretrained ViT (with contrastive or classification loss) is lossy in its fine-grained spatial information. Our model achieves $8.4\%$ accuracy for predicting a value $0.9 \times$ to $1.1 \times$ range of human annotation. This is remarkable since humans annotations are noisy. In fact, human sometimes tend to give noisy estimations, as they prefer to round an estimation of 0.8 meter to 1 meter. It remains challenging to evaluate quantitative spatial reasoning capabilities of vision-language models in broad domains. + +# 4.4. Effect of Noisy Quantitative Spatial Answers + +Since the quantitative answers of the spatial VQA dataset are noisy, we study if VLMs can learn generalizable quantitative estimations from a large amount of noisy training data. To do so, we first come up with a domain where we are able to generate high quality quantitative answers. As discussed in Section 4.1 the monocular depth estimation is one of the steps in the data generation pipeline that induce the most noises. Therefore, we + +![](images/5db67c602c7ccb99f6b59882fa1492df0a3e5b8ad0c364684d8d4e3e24a44818.jpg) +Figure 6. SpatialVLM as reward generator for robotics tasks. SpatialVLM provides a "natural-language queriable" distance estimation tool, and can be used for robotics tasks. For example, for the task "pick orange tea bottle", the reward/cost function can be the a function of the response of "What is the distance between the yellow gripper fingers and the orange tea bottle". And for the task "put the apple into the bowl", the reward/cost function can be a function of the response of "what is the distance between the apple and bowl". We sample different gripper positions and show the cost function in the above scatter plots. + +![](images/6dac6e3dca80bb027ad22e9c9df3a7e82f536f4d908f5195b07964041abb111b.jpg) + +![](images/804405a92e6c48c5edf94883e049559aee9981cfa66880a2952f45d87d03f208.jpg) + +![](images/720f465c442827522840e04ea45a298c9dfc00d90f2e8561cef800c3cf3ca561.jpg) + +![](images/56e2584a08e33c31e8d095ded7bfadac6438d7ac397da770b81ce04536db456c.jpg) + +leverage our robotic manipulation dataset, which provides near-ground-truth depth information captured using a depth camera. As a result, the generated quantitative answers are more accurate. We train VLM using this dataset, and find the model able to perform fine-grained distance estimation in the manipulation domain (Fig. 5), which further demonstrates the data accuracy. + +To study how noisy data affects VLM training, we add Gaussian noises upon the quantitative answers of the accurate manipulation spatial VQA dataset, and obtain a series of noisy datasets of different noise level. We train VLMs using the noisy datasets and evaluate them using a human annotated quantitative spatial VQA benchmark for manipulation. Table. 4 compares how different Gaussian noise standard deviations affect the overall VLM performance on quantitative spatial VQA. Since the objects in the manipulation VQA datasets are within 1 meter range, we added the mean squared error (MSE) as a metric to evaluate the VLM performance, as well as the half-to-twice percentage which is defined in Section 4.1. It is shown that VLMs trained on datasets of different noise levels achieve similar spatial reasoning accuracy. We speculate this is due to the noisy nature of the training data and the manually annotated evaluation benchmark, and that VLM can learn a spatial reasoning common-sense despite noisy data. We observed this interesting phenomenon in robotics experiments as well. In Fig. 6, the distance estimation is exhibit a bias towards the mean since the model is heavily regularized. + +# 4.5. Spatial Reasoning Unlocks Novel Applications + +VLM as a Dense Reward Annotator One important application of VLM is robotics. Recently, works have shown that VLMs and LLMs can serve as universal open-vocabulary reward annotators and success detector [20] for robotics tasks, which can be used to derive useful control policies. However, the reward annotation ability of VLMs are often limited by lack of spatial awareness. Since SpatialVLM is able to quantitatively estimate distances or sizes from image, it's uniquely suited as a dense reward annotator. We conduct a real robot experiment where we specify a task in nature language and ask SpatialVLM + +to annotate a reward for each frame in a trajectory. In Figure 6, each dot illustrates an object location and their color indicates the annotated reward. As the robot makes progress towards the specified goal, we can see the reward increase monotonically, indicating the ability of SpatialVLM to serve as a dense reward annotator. While our example is not an in-depth benchmark of such capability, we hope our demonstration can inspire future research that involves quantitative metric estimation by VLMs, an area that was previously overlooked. + +Chain-of-Thought Spatial Reasoning In this section, we investigate whether SpatialVLM can be used to do tasks requiring multi-step reasoning, given its enhanced ability to answer elemental spatial questions. We demonstrate a few examples in Figure 1 and Figure 4. A large language model, in this case GPT-4, when equipped with SpatialVLM as a spatial reasoning submodule, can perform complex spatial reasoning tasks, such as answering if 3 objects in the environment can form a "isosceles triangle". + +# 5. Conclusion + +In conclusion, our research addresses the challenge of infusing spatial reasoning to VLMs, and approach it by constructing a framework for automatic generation of 3D spatial reasoning VQA data based on Internet-scale real-world images. We ablate different design choices in the recipes for training VLMs, such as training with large amount of noisy data and unfreezing ViT. While our direct spatial queries are built on a finite set of templates, we show SpatialVLM can be extended to tackle more complicated chain-of-thought reasoning that requires spatial reasoning components. SpatialVLM is also demonstrated to be useful for robotics tasks, where we show that a 3D spatial-aware VLM could be used as a reward annotator for robotics tasks. Additional study of more nuanced geometric primitives can also help fully ground spatial reasoning in 3D geometry. + +# References + +[1] Michael Ahn, Anthony Brohan, Noah Brown, Yevgen Chebotar, Omar Cortes, Byron David, Chelsea Finn, Chuyuan Fu, Keerthana Gopalakrishnan, Karol Hausman, et al. 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Judging from the image, it appears that the sofa and the table are quite close to each other, and there may not be enough space to accommodate a 1-meter wide robot...." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 282, + 265, + 313, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 282, + 265, + 313, + 272 + ], + "spans": [ + { + "bbox": [ + 282, + 265, + 313, + 272 + ], + "type": "text", + "content": "Spatial-VLM" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 283, + 274, + 299, + 289 + ], + "blocks": [ + { + "bbox": [ + 283, + 274, + 299, + 289 + ], + "lines": [ + { + "bbox": [ + 283, + 274, + 299, + 289 + ], + "spans": [ + { + "bbox": [ + 283, + 274, + 299, + 289 + ], + "type": "image", + "image_path": "fa5e67e24ddb7dd510845a396d7b739ad8af8f46bb6582d0fb19c454dd05fa54.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 302, + 274, + 531, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 274, + 531, + 297 + ], + "spans": [ + { + "bbox": [ + 302, + 274, + 531, + 297 + ], + "type": "text", + "content": "[VLM Reasoning] How wide is the path between the sofa and the table and chairs? [VLM Answer] 1.56m [Answer] Yes, the robot can go through the path between the sofa and the table and chairs since it is wider than the robot's width." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 53, + 331, + 71, + 348 + ], + "blocks": [ + { + "bbox": [ + 54, + 321, + 68, + 327 + ], + "lines": [ + { + "bbox": [ + 54, + 321, + 68, + 327 + ], + "spans": [ + { + "bbox": [ + 54, + 321, + 68, + 327 + ], + "type": "text", + "content": "User" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 53, + 331, + 71, + 348 + ], + "lines": [ + { + "bbox": [ + 53, + 331, + 71, + 348 + ], + "spans": [ + { + "bbox": [ + 53, + 331, + 71, + 348 + ], + "type": "image", + "image_path": "53e593d4497b17f6d9c90806eb43598b9880a99657d0fefa7a43cb9d65cce458.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 74, + 331, + 162, + 362 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 331, + 162, + 362 + ], + "spans": [ + { + "bbox": [ + 74, + 331, + 162, + 362 + ], + "type": "text", + "content": "Which can is the closest to the yellow finger that is on the right most side of the picture, the blue, orange or the silver one?" + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 169, + 316, + 280, + 406 + ], + "blocks": [ + { + "bbox": [ + 169, + 316, + 280, + 406 + ], + "lines": [ + { + "bbox": [ + 169, + 316, + 280, + 406 + ], + "spans": [ + { + "bbox": [ + 169, + 316, + 280, + 406 + ], + "type": "image", + "image_path": "9e7fb0efab206bb03aba5e6c7e8abb8fa9108ccc4fbf2c53bc7371ce99f1c625.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 282, + 309, + 302, + 316 + ], + "lines": [ + { + "bbox": [ + 282, + 309, + 302, + 316 + ], + "spans": [ + { + "bbox": [ + 282, + 309, + 302, + 316 + ], + "type": "text", + "content": "GPT-4V" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 283, + 319, + 541, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 283, + 319, + 541, + 363 + ], + "spans": [ + { + "bbox": [ + 283, + 319, + 541, + 363 + ], + "type": "text", + "content": "After estimating the distances by measuring the Euclidean distances between the yellow finger and each of the cans, it is clear that the silver can is the closest to the yellow finger with an approximate distance of 110 units. In comparison, the blue can is about 262 units away, and the orange can is approximately 233 units away from the yellow finger." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 282, + 365, + 315, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 282, + 365, + 315, + 373 + ], + "spans": [ + { + "bbox": [ + 282, + 365, + 315, + 373 + ], + "type": "text", + "content": "Spatial-VLM" + } + ] + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 283, + 374, + 299, + 388 + ], + "blocks": [ + { + "bbox": [ + 283, + 374, + 299, + 388 + ], + "lines": [ + { + "bbox": [ + 283, + 374, + 299, + 388 + ], + "spans": [ + { + "bbox": [ + 283, + 374, + 299, + 388 + ], + "type": "image", + "image_path": "dbf485eec537c85e5a7b022d6069ab33e0853fa2ddea697ebbdab72eabcad57b.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 425, + 547, + 459 + ], + "lines": [ + { + "bbox": [ + 46, + 425, + 547, + 459 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 547, + 459 + ], + "type": "text", + "content": "Figure 1. We present SpatialVLM, a data synthesis and pre-training mechanism to enhance VLMs' spatial reasoning capabilities. We demonstrate that VLMs trained on our synthetic data exhibit strong spatial reasoning capabilities, and can generate metric distance estimation from 2D input images, addressing blind spots of current state-of-the-art VLMs like GPT-4V. (* GPT-4V accessed Nov. 2023)." + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 21 + }, + { + "bbox": [ + 303, + 373, + 533, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 303, + 373, + 533, + 416 + ], + "spans": [ + { + "bbox": [ + 303, + 373, + 533, + 416 + ], + "type": "text", + "content": "[VLM Reasoning] How far is the yellow finger from the blue can? [VLM Answer] 0.5m [VLM Reasoning] How far is the yellow finger from the orange can? [VLM Anser] 0.59m [VLM Reasoning] How far is the yellow finger from the silver can? [VLM Answer] 0.21m [Answer] The silver can is the closest to the yellow finger that is on the right most side of the picture." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 145, + 479, + 190, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 479, + 190, + 491 + ], + "spans": [ + { + "bbox": [ + 145, + 479, + 190, + 491 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 45, + 504, + 290, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 504, + 290, + 685 + ], + "spans": [ + { + "bbox": [ + 45, + 504, + 290, + 685 + ], + "type": "text", + "content": "Understanding and reasoning about spatial relationships is a fundamental capability for Visual Question Answering (VQA) and robotics. While Vision Language Models (VLM) have demonstrated remarkable performance in certain VQA benchmarks, they still lack capabilities in 3D spatial reasoning, such as recognizing quantitative relationships of physical objects like distances or size difference. We hypothesize that VLMs' limited spatial reasoning capability is due to the lack of 3D spatial knowledge in training data and aim to solve this problem by training VLMs with Internet-scale spatial reasoning data. To this end, we present a system to facilitate this approach. We first develop an automatic 3D spatial VQA data generation framework that scales up to 2 billion VQA examples on 10 million real-world images. We then investigate various factors in training recipe including data quality, training pipeline and" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 479, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 564 + ], + "type": "text", + "content": "VLM architecture. Our work features the first Internet-scale 3D spatial reasoning dataset in metric space. By training a VLM on such data, we significantly enhance its ability on both qualitative and quantitative spatial VQA. Finally, we demonstrate that this VLM unlocks novel downstream applications in chain-of-thought spatial reasoning and robotics due to its quantitative estimation capability. Website: https://spatial-vlm.github.io/" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 573, + 382, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 573, + 382, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 573, + 382, + 586 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Vision language models (VLMs) have made significant progress in recent years across a variety of tasks including image captioning, visual question answering (VQA), embodied planning, action recognition, and more [2, 18, 24, 31]. While VLMs are powerful general-purpose models for a wide range of tasks, most state-of-the-art VLMs still struggle with spatial reasoning, i.e. tasks that require understanding the position of objects in 3D space, or spatial relationships between them. Spatial reasoning capabilities are useful in their own right, but also for downstream applications such as in robotics or AR. For example, a spatial" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 693, + 287, + 713 + ], + "type": "text", + "content": "* Equal Contribution;† Work done during internship at Google DeepMind; Correspond to boyuanc@mit.edu; zhuoxu, xiafei@google.com" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14455" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "reasoning-imbued VLM can be used as a better general-purpose reward annotator [51] and success detector [19]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 97, + 288, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 97, + 288, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 97, + 288, + 240 + ], + "type": "text", + "content": "The exploration of foundation models like VLMs is often inspired by human capabilities. Humans, through embodied experiences and evolutionary development, possess innate spatial reasoning skills. We effortlessly determine spatial relationships, such as the positioning of objects relative to each other or estimating distances and sizes, without complex chain-of-thoughts or mental computations. This natural proficiency in direct spatial reasoning tasks contrasts with the current limitations of VLMs and thus prevents them from accomplishing real-world tasks that requires multiple steps of spatial reasoning. This gap leads us to a compelling research question: can we imbue VLMs with spatial reasoning abilities akin to those of humans?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 242, + 287, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 350 + ], + "type": "text", + "content": "Therefore, we hypothesize that the limited the spatial reasoning abilities of current VLMs is not due to a fundamental limitation of their architecture, but rather is a limitation in common datasets available at scale on which such models are trained. For example, many VLMs [13, 18, 42] are trained on internet-scale datasets characterized by image-caption pairs [12], which contain limited spatial information. This is partially due to the difficulties of obtaining spatial-information-rich embodied data or high-quality human annotations for 3D-aware queries." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 352, + 287, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 447 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 447 + ], + "type": "text", + "content": "Automatic data generation and augmentation techniques are one approach to deal with the data limitation problem [36, 50, 53, 63]. However, most previous data generation efforts focus on rendering photorealistic images with ground truth semantic annotation but overlook the richness of objects and 3D relationships. In contrast, we focus on extracting spatial information directly from real world data in order to capture the diversity and complexity of the true 3D world." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 288, + 604 + ], + "type": "text", + "content": "Our key insight is that recent advancement in off-the-shelf vision models can automatically generate rich 3D spatial annotations from 2D images. To this end, we propose a system called SpatialVLM that enables data generation and training of VLMs to enhance their spatial reasoning capabilities. Concretely, by combining 1) open-vocabulary detection, 2) metric depth estimation, 3) semantic segmentation and 4) object-centric captioning models, we can densely annotate real world data at scale. SpatialVLM converts the data generated by vision models into a format can be used to train VLMs on a mixture of captioning, VQA and spatial reasoning data. Training on such data gives SpatialVLM the perceptual foundations of the 3D world which allows spatial reasoning through an LLM." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 714 + ], + "type": "text", + "content": "Through experiments, we find our trained VLM exhibit many desirable capabilities. First, its ability to answer qualitative spatial questions is greatly enhanced. Secondly, it can perform quantitative estimation reliably despite noisy training data. Such capability not only gives it common sense knowledge about object sizes but also makes it useful as a open-vocabulary reward annotator for rearrangement tasks. Thirdly, we find this spatial Vision Language Model, benefiting from its natural language interface, can perform" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 107 + ], + "type": "text", + "content": "spatial chain-of-thought to solve complex spatial reasoning tasks when combined with a powerful Large Language Model. Our main contributions are:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 108, + 547, + 227 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 108, + 547, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 108, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 306, + 108, + 547, + 131 + ], + "type": "text", + "content": "- We endow VLMs quantitative spatial reasoning capability, which is a fundamental capability of humans." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 133, + 547, + 166 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 547, + 166 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 547, + 166 + ], + "type": "text", + "content": "- We design a framework to automatically label 3D spatial reasoning VQA data based on real world images at the Internet scale." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 168, + 545, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 168, + 545, + 204 + ], + "spans": [ + { + "bbox": [ + 306, + 168, + 545, + 204 + ], + "type": "text", + "content": "- We study various training recipes: data quality, training pipeline, freeze/unfreeze visual encoder, etc, and investigate how they affect the learning quality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 204, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 204, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 306, + 204, + 545, + 227 + ], + "type": "text", + "content": "- We show examples of new capabilities in complex reasoning and robotics unlocked by the introduced task and method." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 236, + 389, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 236, + 389, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 236, + 389, + 249 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 257, + 547, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 257, + 547, + 484 + ], + "spans": [ + { + "bbox": [ + 304, + 257, + 547, + 484 + ], + "type": "text", + "content": "Learning Spatial Reasoning. Spatial distance estimation has been traditionally addressed as a part of broader tasks, such as SLAM [8, 21] or depth estimation [23]. When applying these spatial concepts to reasoning, prior works often focus on explicit spatial scene memories [26, 27] or spatial scene graphs [29, 30, 59, 60]. Scene graphs allow interpretable, structured, statistical relation learning based on the spatial structures they encode. To answer spatial problems in VQA formats, they must handle it explicitly as a pathfinding problem on said scene graph. VLMs, on the other hand, are pretrained on large amounts of loosely structured information from vision-language datasets. Unlike scene graphs, the spatial understanding is encoded implicitly. We can infuse the depth and 3D structure into the weights with an auxiliary task [34, 45], capturing the relational information. In our work, we address the spatial relationship problem directly in the VLM, without an explicit underlying scene graph. In addition to understanding relative relationships in qualitative terms, we also explore estimating explicit metric distance relationships between objects in a scene." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 547, + 713 + ], + "type": "text", + "content": "Grounding Vision-Language Models. Large language models (LLMs) are trained on internet-scale data, making them effective commonsense reasoners. However, LLMs (and by extension VLMs) may lack the necessary grounding to perform well at social reasoning [40], physical reasoning [25], physics reasoning [44], embodied tasks [1, 32, 55], and spatial reasoning tasks [42, 52]. Though language model with interactive world experience show grounding improvements [64, 67], the introduction of large vision models, such as Flamingo [2], PaLI [13], or PaLM-E [18], has enabled a leap in performance. These visually-grounded models have been used for several downstream tasks, such as in robotic success detection [18, 20, 54, 65], action prediction [7, 56], and reward prediction [16, 22, 46, 48]. In this work we approach the problem of spatial reasoning through finetuning a VLM on a generated VQA dataset. By directly finetuning a VLM on this task, we inherit the generality and reasoning capabilities of the underlying VLM as well as show how this approach is capable of tasks like reward generation." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14456" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 534, + 305 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 534, + 305 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 534, + 305 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 534, + 305 + ], + "type": "image", + "image_path": "b5c8077a33e7cc726a821684899936291c740b9686845dae697debe1d3f3efe3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 313, + 548, + 369 + ], + "lines": [ + { + "bbox": [ + 46, + 313, + 548, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 548, + 369 + ], + "type": "text", + "content": "Figure 2. An overview of our data synthesis pipeline. (a) We use CLIP to filter noisy internet images and only keep scene-level photos. (b) We apply pre-trained expert models on internet-scale images so that we get object-centric segmentation, depth and caption. (c) We lift the 2D image into 3D point clouds, which can be parsed by shape analysis rules to extract useful properties like 3D bounding box. (d) We avoid asking ambiguous questions by clustering object captions using CLIP similarity score (e) We synthesize millions of spatial question and answers from object captions and extracted properties." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 380, + 289, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 380, + 289, + 559 + ], + "spans": [ + { + "bbox": [ + 46, + 380, + 289, + 559 + ], + "type": "text", + "content": "Spatial Information in Vision-Language Datasets. Many prior works have focused on benchmarking VLMs [58, 66], considering tasks like VQA (e.g. VQAv2 [28], OK-VQA [47], COCO [41], or Visual Genome [37]). Others have focused on fine-grained scene understanding, such as semantic segmentation [5, 35], object detection [11], or object identification [15, 57]. Others have focused specifically on spatial reasoning as a task, answering questions about object spatial relations (e.g., above, below, left, right) in real [42, 52] or simulated [33] scenes. Real data in this domain can be limited by the amount generated by human labelers, while synthetic data has inherently bounded expressivity. In this work we consider how to automatically generate real data, and focus on the problem of not just spatial relations, but metric spatial distances, which can be directly applied to many downstream tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 572, + 123, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 572, + 123, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 572, + 123, + 586 + ], + "type": "text", + "content": "3. SpatialVLM" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "To equip VLMs with both qualitatively and quantitatively spatial reasoning capabilities, we propose to generate a large-scale spatial VQA dataset, which is used to train VLMs. Concretely, we design a comprehensive data generation framework which first leverages off-the-shelf computer vision models including open-vocabulary detection, metric depth estimation, semantic segmentation and object-centric captioning models to extract object-centric contexts, and then adopts template-based approach to generate massive spatial VQA data of reasonable quality. We train our SpatialVLM using the generated dataset" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 380, + 546, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 546, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 546, + 416 + ], + "type": "text", + "content": "to learn direct spatial reasoning capabilities, which we can then combine with the high-level commonsense reasoning embedded in LLMs to unlock chain-of-thoughts spatial reasoning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 422, + 494, + 435 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 422, + 494, + 435 + ], + "spans": [ + { + "bbox": [ + 305, + 422, + 494, + 435 + ], + "type": "text", + "content": "3.1. Spatial Grounding from 2D Images" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 440, + 547, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 547, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 547, + 511 + ], + "type": "text", + "content": "We hypothesize that the reason for the lack of spatial reasoning capabilities of today's VLMs is not their architecture, but the lack of spatial reasoning training data. Following this insight, we design a pipeline that generates VQA data containing spatial reasoning questions. The pipeline is summarized in in Figure 2 and described in detail as follows." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 516, + 547, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 547, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 547, + 624 + ], + "type": "text", + "content": "Semantic Filtering While internet-scale image captioning datasets have been widely used in VLM training [13], many images in these datasets are not suitable for synthesizing spatial reasoning QA, due to the fact that they either consist of a single object or don't have a scene background (e.g. product pictures on shopping websites or screenshots of computer screen). Therefore, as the first step in our data synthesis pipeline, we adopt a CLIP-based open-vocabulary classification model to classify all images and rule out those that are not suitable." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 548, + 715 + ], + "type": "text", + "content": "Object-centric Contexts Extraction from 2D Images In order to extract object-centric spatial contexts from 2D images, we leverage a series of off-the-shelf expert models, including region proposal, region captioning [4], and semantic segmentation [39] modules to extract object-centric information. With this step, we obtain object-centric entities consisting of pixel clusters as well as open-vocabulary caption descriptions." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14457" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 95, + 148, + 152 + ], + "blocks": [ + { + "bbox": [ + 61, + 95, + 148, + 152 + ], + "lines": [ + { + "bbox": [ + 61, + 95, + 148, + 152 + ], + "spans": [ + { + "bbox": [ + 61, + 95, + 148, + 152 + ], + "type": "image", + "image_path": "1d1d743a234fef952b95955d33d3e605426ab8035870b9afedb5e8c8ac8cef87.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 153, + 148, + 216 + ], + "blocks": [ + { + "bbox": [ + 61, + 153, + 148, + 216 + ], + "lines": [ + { + "bbox": [ + 61, + 153, + 148, + 216 + ], + "spans": [ + { + "bbox": [ + 61, + 153, + 148, + 216 + ], + "type": "image", + "image_path": "8f6ee9c7441d012d7da5451177fc8ca60c9203609aba58cc81052eb067ebe8e1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 61, + 216, + 148, + 281 + ], + "blocks": [ + { + "bbox": [ + 61, + 216, + 148, + 281 + ], + "lines": [ + { + "bbox": [ + 61, + 216, + 148, + 281 + ], + "spans": [ + { + "bbox": [ + 61, + 216, + 148, + 281 + ], + "type": "image", + "image_path": "5700998de35071c6d733d6cc0328b5ebcc389270138bc40ed6937456745bed5a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 290, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 290, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 547, + 335 + ], + "type": "text", + "content": "Figure 3. Example data entries from the synthetic dataset. Given the output of vision expert models, we follow a set of question generation template to generate both quantitative and qualitative question-answer pairs to highlight the diversity of the dataset. The spatial concepts are highlighted in blue. Such visual question-answer pairs can be easily mixed together with other captioning or question answering datasets and use the same training objectives." + } + ] + } + ], + "index": 35, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 199, + 77, + 288, + 90 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 199, + 77, + 288, + 90 + ], + "spans": [ + { + "bbox": [ + 199, + 77, + 288, + 90 + ], + "type": "text", + "content": "Qualitative Q & A" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 159, + 99, + 218, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 99, + 218, + 110 + ], + "spans": [ + { + "bbox": [ + 159, + 99, + 218, + 110 + ], + "type": "text", + "content": "Find out if the girl" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 159, + 111, + 239, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 111, + 239, + 120 + ], + "spans": [ + { + "bbox": [ + 159, + 111, + 239, + 120 + ], + "type": "text", + "content": "wearing a purple shirt is" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 159, + 121, + 227, + 130 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 121, + 227, + 130 + ], + "spans": [ + { + "bbox": [ + 159, + 121, + 227, + 130 + ], + "type": "text", + "content": "situated behind or in" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 159, + 131, + 242, + 140 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 131, + 242, + 140 + ], + "spans": [ + { + "bbox": [ + 159, + 131, + 242, + 140 + ], + "type": "text", + "content": "front of the girl wearing a" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 159, + 141, + 212, + 149 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 141, + 212, + 149 + ], + "spans": [ + { + "bbox": [ + 159, + 141, + 212, + 149 + ], + "type": "text", + "content": "blue sweatshirt." + } + ] + } + ], + "index": 8 + }, 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the plate positioned" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 159, + 237, + 242, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 237, + 242, + 247 + ], + "spans": [ + { + "bbox": [ + 159, + 237, + 242, + 247 + ], + "type": "text", + "content": "on the left or right side of" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 159, + 247, + 229, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 247, + 229, + 256 + ], + "spans": [ + { + "bbox": [ + 159, + 247, + 229, + 256 + ], + "type": "text", + "content": "the green and yellow" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 159, + 257, + 187, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 257, + 187, + 266 + ], + "spans": [ + { + "bbox": [ + 159, + 257, + 187, + 266 + ], + "type": "text", + "content": "napkin?" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 249, + 237, + 309, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 249, + 237, + 309, + 247 + ], + "spans": [ + { + "bbox": [ + 249, + 237, + 309, + 247 + ], + "type": "text", + "content": "The plate is to the" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 249, + 247, + 266, + 256 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 249, + 247, + 266, + 256 + ], + "spans": [ + { + "bbox": [ + 249, + 247, + 266, + 256 + ], + "type": "text", + "content": "right." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 391, + 77, + 485, + 90 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 391, + 77, + 485, + 90 + ], + "spans": [ + { + "bbox": [ + 391, + 77, + 485, + 90 + ], + "type": "text", + "content": "Quantitative Q & A" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 351, + 105, + 423, + 114 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 105, + 423, + 114 + ], + "spans": [ + { + "bbox": [ + 351, + 105, + 423, + 114 + ], + "type": "text", + "content": "Measure the distance" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 351, + 115, + 436, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 115, + 436, + 124 + ], + "spans": [ + { + "bbox": [ + 351, + 115, + 436, + 124 + ], + "type": "text", + "content": "from the cake shaped like" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 351, + 125, + 411, + 134 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 125, + 411, + 134 + ], + "spans": [ + { + "bbox": [ + 351, + 125, + 411, + 134 + ], + "type": "text", + "content": "a house to the girl" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 351, + 136, + 427, + 145 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 136, + 427, + 145 + ], + "spans": [ + { + "bbox": [ + 351, + 136, + 427, + 145 + ], + "type": "text", + "content": "wearing a purple shirt?" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 444, + 120, + 511, + 129 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 444, + 120, + 511, + 129 + ], + "spans": [ + { + "bbox": [ + 444, + 120, + 511, + 129 + ], + "type": "text", + "content": "Around half a meter" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 351, + 159, + 418, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 159, + 418, + 169 + ], + "spans": [ + { + "bbox": [ + 351, + 159, + 418, + 169 + ], + "type": "text", + "content": "Can you provide the" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 351, + 170, + 427, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 170, + 427, + 178 + ], + "spans": [ + { + "bbox": [ + 351, + 170, + 427, + 178 + ], + "type": "text", + "content": "distance measurement" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 351, + 179, + 430, + 188 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 179, + 430, + 188 + ], + "spans": [ + { + "bbox": [ + 351, + 179, + 430, + 188 + ], + "type": "text", + "content": "between the microwave" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 351, + 189, + 421, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 189, + 421, + 198 + ], + "spans": [ + { + "bbox": [ + 351, + 189, + 421, + 198 + ], + "type": "text", + "content": "oven and the kitchen" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 351, + 199, + 381, + 208 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 199, + 381, + 208 + ], + "spans": [ + { + "bbox": [ + 351, + 199, + 381, + 208 + ], + "type": "text", + "content": "counter?" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 444, + 179, + 522, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 444, + 179, + 522, + 189 + ], + "spans": [ + { + "bbox": [ + 444, + 179, + 522, + 189 + ], + "type": "text", + "content": "They are 1 meter apart." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 351, + 242, + 426, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 242, + 426, + 251 + ], + "spans": [ + { + "bbox": [ + 351, + 242, + 426, + 251 + ], + "type": "text", + "content": "How wide is the plate?" + } + ] + } + ], + "index": 33 + }, + { + "bbox": [ + 444, + 242, + 494, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 444, + 242, + 494, + 251 + ], + "spans": [ + { + "bbox": [ + 444, + 242, + 494, + 251 + ], + "type": "text", + "content": "20 centimeters" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 46, + 346, + 289, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 502 + ], + "type": "text", + "content": "Lifting 2D Contexts to 3D Contexts Traditional spatial VQA datasets generated using object detection and bounding box positioning [38] are limited to the 2D image plane (lack of depth or altitude contexts) and pixel-level reasoning (lack of metric-scale size and distance contexts). We perform depth estimation [6] to lift monocular 2D pixels to metric-scale 3D point clouds. We further canonicalize the camera coordinate system of the point cloud into a geodetic coordinate system, which is done by horizontal surface (e.g. \"floor\", \"table top\") segmentation [10] and frame transfer. To the best of our knowledge, we are the first to lift internet-scale images to object-centric 3D point clouds and use it to synthesize VQA data embedded with 3D spatial reasoning supervision." + } + ] + } + ], + "index": 36 + }, + { + "bbox": [ + 46, + 508, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 288, + 604 + ], + "type": "text", + "content": "Ambiguity Resolution Sometimes there are multiple objects of similar categories in one image, leading to ambiguities of their caption labels. For example, one same caption label \"cake\" can refer to multiple different cakes in a same image. Therefore, before we can ask questions about these objects, we need to make sure the reference expressions are not ambiguous. We made two key design choices that have been validated empirically to be effective in tackling this challenge:" + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 47, + 605, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 40, + "blocks": [ + { + "bbox": [ + 47, + 605, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 701 + ], + "type": "text", + "content": "- We deliberately choose to avoid common object detectors, which tend to produce fixed and coarse categories such as \"cake\", and adopt FlexCap [4], a user-configurable object-centric captioning approach. In practice, for each object we can sample a random caption of a variable length between 1 - 6 words. As a result, our object annotations are fine-grained, such as \"cake shaped like a house\" and \"cup cake in plastic container\"." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 47, + 702, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 702, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 702, + 287, + 714 + ], + "type": "text", + "content": "- We design a semantic-oriented post-processing algorithm that" + } + ] + } + ], + "index": 39 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 315, + 346, + 547, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 346, + 547, + 370 + ], + "spans": [ + { + "bbox": [ + 315, + 346, + 547, + 370 + ], + "type": "text", + "content": "further remove ambiguities by augmenting or rejecting object captions. Details of this algorithm are shown in Appendix ?? ." + } + ] + } + ], + "index": 41 + }, + { + "bbox": [ + 306, + 380, + 537, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 537, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 537, + 392 + ], + "type": "text", + "content": "3.2. Large-Scale Spatial Reasoning VQA Dataset" + } + ] + } + ], + "index": 42 + }, + { + "bbox": [ + 304, + 399, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 399, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 399, + 545, + 471 + ], + "type": "text", + "content": "As motivated in Section 3, we focus our study on infusing \"straightforward\" spatial reasoning capabilities into VLMs by pretraining with synthetic data. Therefore, we synthesize spatial-reasoning QA pairs that involve no more than two objects (denoted \"A\" and \"B\") in the image and consider the two following categories of questions." + } + ] + } + ], + "index": 43 + }, + { + "bbox": [ + 304, + 478, + 547, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 478, + 547, + 526 + ], + "spans": [ + { + "bbox": [ + 304, + 478, + 547, + 526 + ], + "type": "text", + "content": "Qualitative questions: those that ask for judgement of some spatial relations. Examples are \"Given two objects A and B, which is more towards the left?\", \"Is object A more elevated than object B?\" and \"Among A and B, which is bigger in width?\"." + } + ] + } + ], + "index": 44 + }, + { + "bbox": [ + 304, + 533, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 689 + ], + "type": "text", + "content": "Quantitative questions: those that ask for more fine-grained answers that include numbers and units. Examples include \"how much to the left is object A compared to object B?\", \"How far is object A from the B?\", \"Find out how far A is positioned behind B relative to the camera\". Similar to the aforementioned examples, such questions can be synthesized using a main question template, and one can fill the object name entries using the object captions after disambiguation. This property allows us to do template-based generation, an approach commonly adopted by instruction tuning works [61]. The answers to the questions are obtained through appropriate functions that we develop, which take as input the segmented point clouds and 3D bounding boxes of the relevant objects." + } + ] + } + ], + "index": 45 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "We designate 38 different types of qualitative and quantitative spatial reasoning questions, each featuring around 20" + } + ] + } + ], + "index": 46 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14458" + } + ] + } + ], + "index": 47 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 86, + 76, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 76, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 86, + 76, + 107, + 84 + ], + "type": "text", + "content": "User:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 86, + 87, + 495, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 87, + 495, + 107 + ], + "spans": [ + { + "bbox": [ + 86, + 87, + 495, + 107 + ], + "type": "text", + "content": "Does the blue coke can, the orange can, and the silver seven up can on the table roughly form an isosceles triangle? Roughly means the difference between the longest and shortest triangle edges is smaller than " + }, + { + "bbox": [ + 86, + 87, + 495, + 107 + ], + "type": "inline_equation", + "content": "0.1\\mathrm{m}" + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 82, + 113, + 200, + 207 + ], + "blocks": [ + { + "bbox": [ + 82, + 113, + 200, + 207 + ], + "lines": [ + { + "bbox": [ + 82, + 113, + 200, + 207 + ], + "spans": [ + { + "bbox": [ + 82, + 113, + 200, + 207 + ], + "type": "image", + "image_path": "bd4f5a25707fd8d83071a4d195d849ef51d4b6eae57fee366f4d8606d86e082d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 547, + 254 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 547, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 547, + 254 + ], + "type": "text", + "content": "Figure 4. Chain-of-thought spatial reasoning. We illustrate that we can perform Chain-of-Thought Spatial reasoning with SpatialVLM. In this example, with the help of an LLM orchestrating SpatialVLM, the system is able to answer questions like \"Does the blue coke can, the red coke can, and the green sponge on the table roughly form an equilateral triangle\"." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 209, + 114, + 475, + 124 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 114, + 475, + 124 + ], + "spans": [ + { + "bbox": [ + 209, + 114, + 475, + 124 + ], + "type": "text", + "content": "LLM: What is the distance between the blue coke can and the orange can?" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 209, + 125, + 250, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 125, + 250, + 133 + ], + "spans": [ + { + "bbox": [ + 209, + 125, + 250, + 133 + ], + "type": "text", + "content": "VLM: 0.4m" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 209, + 135, + 493, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 135, + 493, + 144 + ], + "spans": [ + { + "bbox": [ + 209, + 135, + 493, + 144 + ], + "type": "text", + "content": "LLM: What is the distance between the orange can and the silver seven up can?" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 209, + 145, + 254, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 145, + 254, + 155 + ], + "spans": [ + { + "bbox": [ + 209, + 145, + 254, + 155 + ], + "type": "text", + "content": "VLM: 0.48m" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 209, + 156, + 503, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 156, + 503, + 165 + ], + "spans": [ + { + "bbox": [ + 209, + 156, + 503, + 165 + ], + "type": "text", + "content": "LLM: What is the distance between the blue coke can and the silver seven up can?" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 209, + 167, + 255, + 175 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 167, + 255, + 175 + ], + "spans": [ + { + "bbox": [ + 209, + 167, + 255, + 175 + ], + "type": "text", + "content": "VLM: 0.41m" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 209, + 177, + 513, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 209, + 177, + 513, + 209 + ], + "spans": [ + { + "bbox": [ + 209, + 177, + 513, + 209 + ], + "type": "text", + "content": "LLM: Since the difference between the longest and shortest triangle edges (0.48m - 0.4m = 0.08m) is smaller than 0.1 m, the blue coke can, the orange can, and the silver seven up can roughly form an isosceles triangle." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "type": "text", + "content": "question templates and 10 answer templates (we show examples in Appendix. ??). We also add bias the sampling to encourage concise answers. Finally we introduce a human-aligned rounding mechanism in Appendix ?? to make number roundings in a human-like way. Using such an approach, we are able to generate ample question answering data pairs for the monocular camera images in webli and vqa datasets. Fig 3 shows several example synthetic question answering pairs we obtained. In total, we create a massive dataset with 10 million images and 2 billion direct spatial reasoning QA pairs, featuring " + }, + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "type": "text", + "content": " qualitative questions and " + }, + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 266, + 289, + 434 + ], + "type": "text", + "content": " quantitative questions. Thanks to the diversity of object captions and distance units, our synthetic dataset features significant diversity in terms of object description, question type and phrasing." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 441, + 201, + 454 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 201, + 454 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 201, + 454 + ], + "type": "text", + "content": "3.3. Learning Spatial Reasoning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": "Direct Spatial Reasoning is defined as following, a Vision-Language Model takes as input an image " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{I}" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " and a query " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " of a spatial task, and output an answer " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{A}" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": ", in the format of a text string, without using external tools or interacting with other large models. We adopt the same architecture and training procedure of PaLM-E [18] except replacing PaLM [14] backbone with PaLM 2-S [3], a smaller variant. We then train our model using a mixture of the original PaLM-E dataset and our dataset, with " + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 460, + 287, + 616 + ], + "type": "text", + "content": " of tokens dedicated to spatial reasoning tasks. Similar to PaLM-E, our method has the ability to perform VQA as well as basic embodied planning when combined. The key difference is that it can answer spatial reasoning questions about both binary predicates and quantitative estimations." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 289, + 715 + ], + "type": "text", + "content": "Chain-of-Thought Spatial Reasoning Many real-world tasks require multiple steps of spatial reasoning. For example, to determine if object A can fit into object B, one would need to reason about sizes and constraints. Sometimes one would need to reason over grounded spatial concept (e.g. the counter in the image is 1 meter high) and common sense knowledge (so that a toddler cannot reach it). SpatialVLM provides a natural language" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 266, + 545, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 266, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 305, + 266, + 545, + 290 + ], + "type": "text", + "content": "interface to query with grounded concepts, when combined with a powerful LLM, we can perform complex spatial reasoning." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 291, + 546, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 546, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 546, + 422 + ], + "type": "text", + "content": "We call this method \"Chain-of-Thought Spatial Reasoning\". While our synthesized data only contains direct spatial reasoning questions, it's easy for a VLM to compose them together to solve complex questions that require multi-hop chain-of-thought reasoning. Similar to the method in Socratic Models [68] and LLM as coordinator [9], we utilize an LLM (text-davinci-003) to coordinate and communicate with our SpatialVLM to solve complex problems with Chain-of-Thought prompting [62] as shown in Fig. 4. The LLM can break down complex questions into simple questions, query the VLM, and put the reasoning together to derive the result." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 434, + 383, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 383, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 383, + 448 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 454, + 533, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 533, + 466 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 533, + 466 + ], + "type": "text", + "content": "We conduct experiments to answer the following questions:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 310, + 467, + 545, + 562 + ], + "type": "list", + "angle": 0, + "index": 22, + "blocks": [ + { + "bbox": [ + 310, + 467, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 467, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 310, + 467, + 545, + 502 + ], + "type": "text", + "content": "Q1 Does our spatial VQA data generation and training pipeline improve VLM's general spatial reasoning capabilities? And how well does it perform?" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 310, + 502, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 502, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 310, + 502, + 545, + 526 + ], + "type": "text", + "content": "Q2 How does the noisy synthetic spatial VQA data and different training strategies affect the learning performance?" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 310, + 526, + 545, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 526, + 545, + 562 + ], + "spans": [ + { + "bbox": [ + 310, + 526, + 545, + 562 + ], + "type": "text", + "content": "Q3 Does the VLM equipped with \"direct\" spatial reasoning capabilities unlock new capabilities such as chain-of-thought reasoning and embodied planning?" + } + ] + } + ], + "index": 21 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 563, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 563, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 563, + 545, + 633 + ], + "type": "text", + "content": "We train our model using a mixture of PaLM-E training set and our spatial VQA dataset. To verify whether VLM's limitation in spatial reasoning is a data problem, we choose the following state-of-the-art VLMs as baselines, all trained on mixtures in which semantic-captioning tasks occupy a heavy weight, and without our spatial VQA dataset." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 634, + 545, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 634, + 545, + 670 + ], + "spans": [ + { + "bbox": [ + 304, + 634, + 545, + 670 + ], + "type": "text", + "content": "GPT-4V" + }, + { + "bbox": [ + 304, + 634, + 545, + 670 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 304, + 634, + 545, + 670 + ], + "type": "text", + "content": " GPT-4V is a version of GPT-4 [49] that supports multimodal input, it achieves state-of-the-art performance in many vision-language tasks." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 670, + 545, + 695 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 670, + 545, + 695 + ], + "spans": [ + { + "bbox": [ + 304, + 670, + 545, + 695 + ], + "type": "text", + "content": "PaLI [13]. An encoder-decoder VLM trained on multi-lingual corpora, it shows state-of-the-art performance on captioning" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 317, + 702, + 438, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 702, + 438, + 713 + ], + "spans": [ + { + "bbox": [ + 317, + 702, + 438, + 713 + ], + "type": "text", + "content": "1Accessed Nov 2023 via OpenAI API." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14459" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 73, + 70, + 519, + 129 + ], + "blocks": [ + { + "bbox": [ + 73, + 70, + 519, + 129 + ], + "lines": [ + { + "bbox": [ + 73, + 70, + 519, + 129 + ], + "spans": [ + { + "bbox": [ + 73, + 70, + 519, + 129 + ], + "type": "table", + "html": "
GPT-4VLLaVA-1.5InstructBLIPPaLIPaLM-EPaLM 2-EOurs
Binary PredicateAccuracy68.0%71.3%60.4%60.7%50.2%50.4%75.2%
QuantitativeOutput numbers %1.0%20.9%26.0%52.0%83.2%88.8%99.0%
In range [50, 200]%0.0%13.0%7.9%5.3%23.7%33.9%37.2%
", + "image_path": "95ad01a8f4785b3e6b2743e4591805171abe16d4ab3dbb8e704098d5dc2481fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 137, + 547, + 183 + ], + "lines": [ + { + "bbox": [ + 46, + 137, + 547, + 183 + ], + "spans": [ + { + "bbox": [ + 46, + 137, + 547, + 183 + ], + "type": "text", + "content": "Table 1. Accuracy of different VLMs on binary predicate tasks and quantitative questions about spatial relationship. As can be seen from this table, our proposed method outperforms baselines on binary predicate prediction tasks by a large margin owing to the addition of synthetic data. For quantitative estimation tasks, our method outputs valid format more often (99.0% of the time) than baseline methods. In addition, our method outputs quantitative distance estimation that is closer to ground truth annotated by human more often than baseline methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 195, + 286, + 218 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 195, + 286, + 218 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 286, + 218 + ], + "type": "text", + "content": "and visual-question answering tasks. We used PaLI-X 55B variant in our experiments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 219, + 287, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 287, + 278 + ], + "type": "text", + "content": "PaLM-E [18]. A VLM trained on internet-scale vision, language, and vision-language data, as well as robotics data. It shows state-of-the-art performance in OKVQA benchmark, as well as being capable of robot planning tasks. We used PaLM-E 12B across our experiments." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 280, + 288, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 280, + 288, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 280, + 288, + 400 + ], + "type": "text", + "content": "PaLM 2-E The vanilla PaLM 2-E is an updated version of PaLM-E[18] with exact same training procedure but a more recent LLM backbone. Due to the shared network architecture and training procedure with SpatialVLM, vanilla PaLM 2-E naturally serves as the baseline to study the effect of generated data. In the rest of the paper, unless specifically noted, PaLM 2-E corresponds to PaLM 2-S in terms of parameter count following the naming convention in PaLM 2 technical report [3]. Finally, we consider open source models like LLaVA-1.5 [43] and InstructBLIP [17]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 410, + 192, + 423 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 410, + 192, + 423 + ], + "spans": [ + { + "bbox": [ + 47, + 410, + 192, + 423 + ], + "type": "text", + "content": "4.1. Spatial VQA performance" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 428, + 287, + 573 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 428, + 287, + 573 + ], + "spans": [ + { + "bbox": [ + 46, + 428, + 287, + 573 + ], + "type": "text", + "content": "To stress-test the VLM's spatial reasoning capabilities, a spatial reasoning VQA benchmark with guaranteed performance grounding is required. However, there is not such a proper benchmark available in the literature. Therefore, we created a benchmark by having human annotators label a diverse set of \"direct\" qualitative and quantitative VQAs on a subset of WebLI images [13], which are unseen to all VLMs during the training phase. The benchmark questions and answers are diverse and freeform, following the synthetic data generation pattern described in Section 3.2 (details in Appendix.??). We annotated 331 qualitative spatial reasoning VQA pairs and 215 quantitative spatial reasoning VQA pairs." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "Qualitative Spatial VQA For such questions, both the human annotated answers and VLM outputs are freeform natural language. Therefore, to evaluate the performance of the VLMs, we use human raters to determine if an answer is correct, and show the success rates of the VLMs in Table. 1. It is shown that SpatialVLM is able to achieve significantly higher accuracy compared to all baselines that are not trained using the synthetic spatial VQA data, surpassing other vision-language models including GPT-4V. Among the baselines, the second best model is LLaVA-1.5, which might be caused by their use of bounding boxes and corresponding captions in visual instruction tuning." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 195, + 547, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 547, + 266 + ], + "type": "text", + "content": "Anecdotally, we found LLaVA-1.5 performs well in 2D spatial relationship inference, but inferior to our models in 3D spatial reasoning. This experiment suggests that large and high-quality spatial reasoning data is key to spatial reasoning capabilities, which are not present in pretraining datasets of state-of-the-art VLMs." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 715 + ], + "type": "text", + "content": "Quantitative Spatial VQA For these questions, both human annotator answers and the VLM outputs are natural language descriptions of distance, height, elevation, etc, using their preferred units. We design two metrics for evaluating the performance of the VLM. First, we use the success rate of the VLM to produce a number to reflect if the VLM is able to understand the quantitative spatial reasoning question. Second, since the answer can range widely from centimeters to kilometers, we use percentages of the VLM answers that fall into half to twice of the ground truth value to represent how accurate the VLM's estimates are. The results are shown in Table. 1, and it is shown that our model performs better on both metrics than baselines with large margins. We observed that baseline VLMs are reluctant to give answers consisting of numbers. For example, replying \"No.\" to questions like \"Can you tell me the distance between ...\" This is likely due the the distribution of the training data. Additionally, we find that state-of-the-art VLM GPT-4V often refrain from generating answers about distance in SI units with a disclaimer text \"I'm sorry, but I cannot provide an exact distance as the image does not offer precise references for measurement...\" Our approach SpatialVLM achieves significantly higher success rate than all baselines, achieving in-range results on almost half of the questions. This performance is remarkable given that the human annotations are noisy, and agreement among annotators are not often guaranteed (Appendix. ??). To better understand our model's performance and limitations, we visualized the relative error against the ground truth value in Fig. ?? in the Appendix. We found that SpatialVLM does well on medium range scenes like those with objects 1-10 meters from the camera. This coincides with the range where our monocular depth estimator [6] reliably outputs metric accurate depth estimations, which indicates that our method inherits the biases and limitations from expert vision models in the data synthesis pipeline. We therefore hypothesize that the quality of monocular depth estimator has an significant influence on quantitative distance estimation." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14460" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 137, + 132 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 137, + 132 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 137, + 132 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 137, + 132 + ], + "type": "image", + "image_path": "3cf7cf38fee98a148a1396a7b5fd4733c42f463487a0b82da1678d002e98e466.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 138, + 70, + 216, + 132 + ], + "blocks": [ + { + "bbox": [ + 138, + 70, + 216, + 132 + ], + "lines": [ + { + "bbox": [ + 138, + 70, + 216, + 132 + ], + "spans": [ + { + "bbox": [ + 138, + 70, + 216, + 132 + ], + "type": "image", + "image_path": "d8b47dc602a6fb0d4df6502ab7addf8e9d9b7571dc2680644b96fb3941d08b90.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 217, + 70, + 293, + 133 + ], + "blocks": [ + { + "bbox": [ + 217, + 70, + 293, + 133 + ], + "lines": [ + { + "bbox": [ + 217, + 70, + 293, + 133 + ], + "spans": [ + { + "bbox": [ + 217, + 70, + 293, + 133 + ], + "type": "image", + "image_path": "26e7ffb0d6a1160502841329b20ec8802a527cd2b45ecfadbe6e7b21736a0804.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 294, + 70, + 369, + 133 + ], + "blocks": [ + { + "bbox": [ + 294, + 70, + 369, + 133 + ], + "lines": [ + { + "bbox": [ + 294, + 70, + 369, + 133 + ], + "spans": [ + { + "bbox": [ + 294, + 70, + 369, + 133 + ], + "type": "image", + "image_path": "56cf31e87a674b75af596df69077aaddcb25c523584d20bbe9706947d60ee9ce.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 370, + 71, + 533, + 194 + ], + "blocks": [ + { + "bbox": [ + 370, + 71, + 533, + 194 + ], + "lines": [ + { + "bbox": [ + 370, + 71, + 533, + 194 + ], + "spans": [ + { + "bbox": [ + 370, + 71, + 533, + 194 + ], + "type": "image", + "image_path": "78c8abb054d5a579fe4fabedec4e75ce4ac99ca9edf40cea300916149c5243fe.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 61, + 133, + 137, + 194 + ], + "blocks": [ + { + "bbox": [ + 61, + 133, + 137, + 194 + ], + "lines": [ + { + "bbox": [ + 61, + 133, + 137, + 194 + ], + "spans": [ + { + "bbox": [ + 61, + 133, + 137, + 194 + ], + "type": "image", + "image_path": "de7da4f24386339539fa368684dce1910225125b7ecf6eddadc8dcfec9716489.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 203, + 545, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 203, + 545, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 545, + 226 + ], + "type": "text", + "content": "Figure 5. Given a sequence of images where the robot gripper is approaching the coke can, we ask SpatialVLM \"What is the distance between the yellow gripper and the coke can\". We are able to get accurate and monotonically decreasing distance estimations." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 138, + 133, + 216, + 194 + ], + "blocks": [ + { + "bbox": [ + 138, + 133, + 216, + 194 + ], + "lines": [ + { + "bbox": [ + 138, + 133, + 216, + 194 + ], + "spans": [ + { + "bbox": [ + 138, + 133, + 216, + 194 + ], + "type": "image", + "image_path": "4b6af85518f0838ab20332ff33d719085d7e552a7ea6b3537c2021615481538f.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 217, + 133, + 293, + 194 + ], + "blocks": [ + { + "bbox": [ + 217, + 133, + 293, + 194 + ], + "lines": [ + { + "bbox": [ + 217, + 133, + 293, + 194 + ], + "spans": [ + { + "bbox": [ + 217, + 133, + 293, + 194 + ], + "type": "image", + "image_path": "ad0a60ed6df988dabf931c82e13af1bc79b0f629852c0239878bca7ef4062357.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 294, + 133, + 369, + 194 + ], + "blocks": [ + { + "bbox": [ + 294, + 133, + 369, + 194 + ], + "lines": [ + { + "bbox": [ + 294, + 133, + 369, + 194 + ], + "spans": [ + { + "bbox": [ + 294, + 133, + 369, + 194 + ], + "type": "image", + "image_path": "ec6bfbc0a80d28e5efedf5d0a777e6b505afbaf5fa4f48b201bd3eeb24f6cb8e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 55, + 244, + 279, + 289 + ], + "blocks": [ + { + "bbox": [ + 55, + 244, + 279, + 289 + ], + "lines": [ + { + "bbox": [ + 55, + 244, + 279, + 289 + ], + "spans": [ + { + "bbox": [ + 55, + 244, + 279, + 289 + ], + "type": "table", + "html": "
General VQA benchmarksOKVQAVQA v2
PaLM 2-E w/o co-training61.4%76.6%
Ours61.0(-0.4)%79.0(+2.4)%
", + "image_path": "dbb89d13ea868ef49da5872f00ce1946ff2365467d364d219090c78372542004.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 387, + 276, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 276, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 276, + 399 + ], + "type": "text", + "content": "4.2. Effect of Spatial VQA Data to General VQA" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 407, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 407, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 407, + 287, + 563 + ], + "type": "text", + "content": "The second question we want to answer is: since we co-train with a considerable amount of spatial VQA data, whether the performance of VLM in other tasks will degrade as a result. We compared our model with the vanilla PaLM 2-E trained without the spatial VQA dataset on general VQA benchmarks, and as summarized in Table. 2, our model achieves comparable performance as PaLM 2-E on the OKVQA benchmark, in which limited spatial reasoning questions are included, and performs slightly better on VQA-v2 test-dev benchmark, which includes spatial reasoning questions. This seem to suggest that VLMs are generally underfitting in the distribution of tasks close to spatial reasoning, and can benefit from spatial VQA supervisions without hurting their general VQA capabilities." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 573, + 287, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 287, + 598 + ], + "type": "text", + "content": "4.3. Effect of Visual Transformer (ViT) Encoder in Spatial Reasoning" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 604, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 287, + 688 + ], + "type": "text", + "content": "Does a frozen ViT (trained on contrastive objective) encode enough information to perform spatial reasoning? To study this, we start at the 110k training step and branch into two training runs, one with the ViT frozen, the other with ViT unfrozen. We train both models for 70k steps, and evaluate percentages of answers from both models that fall into various ranges of the ground truth value in Table 3." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "It is shown that for larger scale and less fine-grained distance estimation, such as making a rough estimation with in the" + } + ] + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 313, + 244, + 537, + 287 + ], + "blocks": [ + { + "bbox": [ + 46, + 297, + 287, + 364 + ], + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 364 + ], + "type": "text", + "content": "Table 2. VQA performance. Co-training on SpatialVLM training mix and finetuning on VQA datasets (VQA v2) improves VQA performance. A PaLM 2-E model trained with SpatialVLM data improves VQA v2 performance by " + }, + { + "bbox": [ + 46, + 297, + 287, + 364 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 46, + 297, + 287, + 364 + ], + "type": "text", + "content": " compared to a model with the same number of parameters, but without the data. However, we don't find OKVQA task to benefit from SpatialVLM training." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 313, + 244, + 537, + 287 + ], + "lines": [ + { + "bbox": [ + 313, + 244, + 537, + 287 + ], + "spans": [ + { + "bbox": [ + 313, + 244, + 537, + 287 + ], + "type": "table", + "html": "
[50, 200)%[66.7, 150)%[90, 110)%
Frozen ViT34.9%9.3%5.6%
Unfrozen ViT37.2(+2.3)%10.7(+1.4)%8.4(+2.8)%
", + "image_path": "fa24c5ced262d4a02ecd329cafa10c8855fb7e63119c60a49d805c958229f039.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 321, + 339, + 529, + 384 + ], + "blocks": [ + { + "bbox": [ + 305, + 295, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 305, + 295, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 295, + 547, + 327 + ], + "type": "text", + "content": "Table 3. Comparison on finetuning with frozen or unfrozen ViT. We find it is beneficial to unfreeze the pretrained ViT for distance estimation tasks." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 339, + 529, + 384 + ], + "lines": [ + { + "bbox": [ + 321, + 339, + 529, + 384 + ], + "spans": [ + { + "bbox": [ + 321, + 339, + 529, + 384 + ], + "type": "table", + "html": "
Gaussian std00.10.20.3
MSE(m)0.0460.0530.0390.048
[50, 200]%59.0%55.8%61.1%61.1%
", + "image_path": "e42095a7739e9b98b39a4a2a5404e9438397c85a9827bbda886241aa02a4e314.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "table_body" + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 393, + 545, + 426 + ], + "lines": [ + { + "bbox": [ + 305, + 393, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 305, + 393, + 545, + 426 + ], + "type": "text", + "content": "Table 4. Comparison on different data noise levels, controlled using standard deviation (STD) of Gaussian noise. We find that our model can learn despite moderate amount of random noise." + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "content": "half-to-twice range of the ground truth, training without freezing ViT performs slightly worse but comparable with unfrozen ViT. However, for more fine-grained distance estimation like estimating accurate quantitative values, the model with unfrozen ViT performed considerably better. We hypothesize that the pretrained ViT (with contrastive or classification loss) is lossy in its fine-grained spatial information. Our model achieves " + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "inline_equation", + "content": "8.4\\%" + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "content": " accuracy for predicting a value " + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "inline_equation", + "content": "0.9 \\times" + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "inline_equation", + "content": "1.1 \\times" + }, + { + "bbox": [ + 304, + 448, + 547, + 604 + ], + "type": "text", + "content": " range of human annotation. This is remarkable since humans annotations are noisy. In fact, human sometimes tend to give noisy estimations, as they prefer to round an estimation of 0.8 meter to 1 meter. It remains challenging to evaluate quantitative spatial reasoning capabilities of vision-language models in broad domains." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 611, + 538, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 538, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 538, + 624 + ], + "type": "text", + "content": "4.4. Effect of Noisy Quantitative Spatial Answers" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Since the quantitative answers of the spatial VQA dataset are noisy, we study if VLMs can learn generalizable quantitative estimations from a large amount of noisy training data. To do so, we first come up with a domain where we are able to generate high quality quantitative answers. As discussed in Section 4.1 the monocular depth estimation is one of the steps in the data generation pipeline that induce the most noises. Therefore, we" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14461" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 84, + 172, + 166 + ], + "blocks": [ + { + "bbox": [ + 72, + 84, + 172, + 166 + ], + "lines": [ + { + "bbox": [ + 72, + 84, + 172, + 166 + ], + "spans": [ + { + "bbox": [ + 72, + 84, + 172, + 166 + ], + "type": "image", + "image_path": "5db67c602c7ccb99f6b59882fa1492df0a3e5b8ad0c364684d8d4e3e24a44818.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 184, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 45, + 184, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 45, + 184, + 547, + 240 + ], + "type": "text", + "content": "Figure 6. SpatialVLM as reward generator for robotics tasks. SpatialVLM provides a \"natural-language queriable\" distance estimation tool, and can be used for robotics tasks. For example, for the task \"pick orange tea bottle\", the reward/cost function can be the a function of the response of \"What is the distance between the yellow gripper fingers and the orange tea bottle\". And for the task \"put the apple into the bowl\", the reward/cost function can be a function of the response of \"what is the distance between the apple and bowl\". We sample different gripper positions and show the cost function in the above scatter plots." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 179, + 70, + 279, + 171 + ], + "blocks": [ + { + "bbox": [ + 179, + 70, + 279, + 171 + ], + "lines": [ + { + "bbox": [ + 179, + 70, + 279, + 171 + ], + "spans": [ + { + "bbox": [ + 179, + 70, + 279, + 171 + ], + "type": "image", + "image_path": "6dac6e3dca80bb027ad22e9c9df3a7e82f536f4d908f5195b07964041abb111b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 284, + 70, + 386, + 172 + ], + "blocks": [ + { + "bbox": [ + 284, + 70, + 386, + 172 + ], + "lines": [ + { + "bbox": [ + 284, + 70, + 386, + 172 + ], + "spans": [ + { + "bbox": [ + 284, + 70, + 386, + 172 + ], + "type": "image", + "image_path": "804405a92e6c48c5edf94883e049559aee9981cfa66880a2952f45d87d03f208.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 389, + 70, + 490, + 171 + ], + "blocks": [ + { + "bbox": [ + 389, + 70, + 490, + 171 + ], + "lines": [ + { + "bbox": [ + 389, + 70, + 490, + 171 + ], + "spans": [ + { + "bbox": [ + 389, + 70, + 490, + 171 + ], + "type": "image", + "image_path": "720f465c442827522840e04ea45a298c9dfc00d90f2e8561cef800c3cf3ca561.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 497, + 72, + 517, + 159 + ], + "blocks": [ + { + "bbox": [ + 497, + 72, + 517, + 159 + ], + "lines": [ + { + "bbox": [ + 497, + 72, + 517, + 159 + ], + "spans": [ + { + "bbox": [ + 497, + 72, + 517, + 159 + ], + "type": "image", + "image_path": "56e2584a08e33c31e8d095ded7bfadac6438d7ac397da770b81ce04536db456c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 261, + 288, + 332 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 288, + 332 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 288, + 332 + ], + "type": "text", + "content": "leverage our robotic manipulation dataset, which provides near-ground-truth depth information captured using a depth camera. As a result, the generated quantitative answers are more accurate. We train VLM using this dataset, and find the model able to perform fine-grained distance estimation in the manipulation domain (Fig. 5), which further demonstrates the data accuracy." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 334, + 290, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 290, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 290, + 562 + ], + "type": "text", + "content": "To study how noisy data affects VLM training, we add Gaussian noises upon the quantitative answers of the accurate manipulation spatial VQA dataset, and obtain a series of noisy datasets of different noise level. We train VLMs using the noisy datasets and evaluate them using a human annotated quantitative spatial VQA benchmark for manipulation. Table. 4 compares how different Gaussian noise standard deviations affect the overall VLM performance on quantitative spatial VQA. Since the objects in the manipulation VQA datasets are within 1 meter range, we added the mean squared error (MSE) as a metric to evaluate the VLM performance, as well as the half-to-twice percentage which is defined in Section 4.1. It is shown that VLMs trained on datasets of different noise levels achieve similar spatial reasoning accuracy. We speculate this is due to the noisy nature of the training data and the manually annotated evaluation benchmark, and that VLM can learn a spatial reasoning common-sense despite noisy data. We observed this interesting phenomenon in robotics experiments as well. In Fig. 6, the distance estimation is exhibit a bias towards the mean since the model is heavily regularized." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 573, + 286, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 286, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 286, + 586 + ], + "type": "text", + "content": "4.5. Spatial Reasoning Unlocks Novel Applications" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "VLM as a Dense Reward Annotator One important application of VLM is robotics. Recently, works have shown that VLMs and LLMs can serve as universal open-vocabulary reward annotators and success detector [20] for robotics tasks, which can be used to derive useful control policies. However, the reward annotation ability of VLMs are often limited by lack of spatial awareness. Since SpatialVLM is able to quantitatively estimate distances or sizes from image, it's uniquely suited as a dense reward annotator. We conduct a real robot experiment where we specify a task in nature language and ask SpatialVLM" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 260, + 547, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 547, + 369 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 547, + 369 + ], + "type": "text", + "content": "to annotate a reward for each frame in a trajectory. In Figure 6, each dot illustrates an object location and their color indicates the annotated reward. As the robot makes progress towards the specified goal, we can see the reward increase monotonically, indicating the ability of SpatialVLM to serve as a dense reward annotator. While our example is not an in-depth benchmark of such capability, we hope our demonstration can inspire future research that involves quantitative metric estimation by VLMs, an area that was previously overlooked." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 396, + 547, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 547, + 506 + ], + "type": "text", + "content": "Chain-of-Thought Spatial Reasoning In this section, we investigate whether SpatialVLM can be used to do tasks requiring multi-step reasoning, given its enhanced ability to answer elemental spatial questions. We demonstrate a few examples in Figure 1 and Figure 4. A large language model, in this case GPT-4, when equipped with SpatialVLM as a spatial reasoning submodule, can perform complex spatial reasoning tasks, such as answering if 3 objects in the environment can form a \"isosceles triangle\"." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 523, + 375, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 523, + 375, + 536 + ], + "spans": [ + { + "bbox": [ + 306, + 523, + 375, + 536 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 715 + ], + "type": "text", + "content": "In conclusion, our research addresses the challenge of infusing spatial reasoning to VLMs, and approach it by constructing a framework for automatic generation of 3D spatial reasoning VQA data based on Internet-scale real-world images. We ablate different design choices in the recipes for training VLMs, such as training with large amount of noisy data and unfreezing ViT. While our direct spatial queries are built on a finite set of templates, we show SpatialVLM can be extended to tackle more complicated chain-of-thought reasoning that requires spatial reasoning components. SpatialVLM is also demonstrated to be useful for robotics tasks, where we show that a 3D spatial-aware VLM could be used as a reward annotator for robotics tasks. Additional study of more nuanced geometric primitives can also help fully ground spatial reasoning in 3D geometry." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14462" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 104, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 104, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 104, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 289, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 146 + ], + "type": "text", + "content": "[1] Michael Ahn, Anthony Brohan, Noah Brown, Yevgen Chebotar, Omar Cortes, Byron David, Chelsea Finn, Chuyuan Fu, Keerthana Gopalakrishnan, Karol Hausman, et al. 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Socratic models: Composing zero-shot multimodal reasoning with language. arXiv preprint arXiv:2204.00598, 2022. 5" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14465" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spatio-Temporal Turbulence Mitigation_ A Translational Perspective/eefae261-74a4-4bbc-a466-69dbac77972f_content_list.json b/2024/Spatio-Temporal Turbulence Mitigation_ A Translational Perspective/eefae261-74a4-4bbc-a466-69dbac77972f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e69dd55c5bf312c8e2db676907c30db9ceedce9f --- /dev/null +++ b/2024/Spatio-Temporal Turbulence Mitigation_ A Translational Perspective/eefae261-74a4-4bbc-a466-69dbac77972f_content_list.json @@ -0,0 +1,1925 @@ +[ + { + "type": "text", + "text": "Spatio-Temporal Turbulence Mitigation: A Translational Perspective", + "text_level": 1, + "bbox": [ + 135, + 130, + 833, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xingguang Zhang1 Nicholas Chimitt1 Yiheng Chi1 Zhiyuan Mao2 Stanley H. Chan1 \n1School of Electrical and Computer Engineering, Purdue University 2Samsung Research America \n{zhan3275, nchimitt, chi14, stanch}@purdue.edu, m940421@gmail.com", + "bbox": [ + 99, + 179, + 869, + 234 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and generalization to real-world dynamic scenarios remain severely limited. Building upon the intuitions of classical TM algorithms, we present the Deep Atmospheric Turbulence Mitigation network (DATUM). DATUM aims to overcome major challenges when transitioning from classical to deep learning approaches. By carefully integrating the merits of classical multi-frame TM methods into a deep network structure, we demonstrate that DATUM can efficiently perform long-range temporal aggregation using a recurrent fashion, while deformable attention and temporal-channel attention seamlessly facilitate pixel registration and lucky imaging. With additional supervision, tilt and blur degradation can be jointly mitigated. These inductive biases empower DATUM to significantly outperform existing methods while delivering a tenfold increase in processing speed. A large-scale training dataset, ATSyn, is presented as a co-invention to enable the generalization to real turbulence. Our code and datasets are available at https://xg416.github.io/DATUM", + "bbox": [ + 75, + 300, + 473, + 648 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 676, + 209, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Atmospheric turbulence is a dominant image degradation for long-range imaging systems. Reconstructing images distorted by atmospheric turbulence is an important task for many civilian and military applications. The degradation process can be considered a combination of content-invariant random pixel displacement (i.e., tilt) and random blur. Until recently, reconstruction algorithms have often been in the form of model-based solutions, often relying on modalities such as pixel registration and deblurring. Although there have been many important insights into the problem, e.g., lucky imaging, they are primarily limited to static scenes with slow processing speed.", + "bbox": [ + 75, + 703, + 468, + 885 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the development of physics-grounded data synthe", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/be9fff2833f96f1f2477b4403a99306723ce3f539185e977878f70db4732cb2d.jpg", + "image_caption": [ + "Figure 1. Benchmarking video restoration models for turbulence mitigation on our ATSyn-dynamic dataset. The circles in orange are other video-based TM networks, and the circles in blue are representative video deblurring and general restoration networks. The proposed Deep Atmospheric TURbulence Mitigation network (DATUM) is state-of-the-art while highly efficient." + ], + "image_footnote": [], + "bbox": [ + 514, + 290, + 857, + 489 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sis methods [7, 17, 18, 33, 65, 77], data-driven algorithms have been developed in the past two years. Most existing deep learning methods focus on single-frame problems [24, 32, 34, 44, 45, 48, 49, 53, 71]. Since the degradation is highly ill-posed, the performance of these algorithms is naturally limited, especially when attempting to generalize to real data. On the other hand, multi-frame turbulence mitigation networks [1, 26, 72] have shown greater potential for generalization across a broader spectrum of real-world test scenarios. However, these networks are adapted from generic video restoration methods and do not reflect the insights developed by traditional methods; few turbulence-specific properties are incorporated as inductive biases into their methods.", + "bbox": [ + 496, + 623, + 893, + 835 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "For deep learning methods to work on real-world scenarios, two common factors hinder the application of current turbulence mitigation methods: (1) the complexity of current data-driven methods is usually high, which impedes the", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "2889", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "practical deployment of these algorithms, and (2) the data synthesis models are suboptimal, either too slow to produce large-scale and diverse datasets or not accurate enough to represent the real-world turbulence profiles, restricting the generalization capability of the model trained on the data.", + "bbox": [ + 75, + 90, + 467, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome these pressing issues, we propose the Deep Atmospheric Turbulence Mitigation (DATUM) network and the ATSyn dataset. We offer three contributions:", + "bbox": [ + 76, + 167, + 467, + 212 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- DATUM is the first deep-learning video restoration method customized for turbulence mitigation based on classical insights. By carefully integrating the merits of classical multi-frame TM methods, we propose feature-reference registration, temporal fusion, and the decoupling of pixel rectification and deblurring as effective inductive biases in the multi-frame TM challenge.", + "- DATUM is the first recurrent model for turbulence restoration. It is significantly more lightweight and efficient than the prior multi-frame TM methods. On both synthetic and real data, DATUM consistently surpasses the SOTA methods while being $10 \\times$ faster.", + "- Through the integration of numerous theoretical and practical improvements in physics modeling over the Zernike-based simulators, we further propose an extensive, real-world inspired dataset ATSyn. Experiments on real-world data show that models trained on ATSyn significantly generalize better than those trained on alternative ones." + ], + "bbox": [ + 76, + 213, + 467, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related works", + "text_level": 1, + "bbox": [ + 76, + 500, + 220, + 513 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Turbulence modeling", + "text_level": 1, + "bbox": [ + 76, + 525, + 274, + 540 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Atmospheric turbulence simulation spans from computational optics to computer vision-oriented approaches. Optical simulations use split-step methods, which numerically propagate waves through phase screens that represent the atmosphere's spatially varying index of refraction [6, 21, 55, 60]. Despite the existence of moderately faster optical simulations, including brightness function-based simulations [30, 31, 66] or learning-based alternatives [46, 47], the relatively slow speed limits their application in deep learning training [43]. In computer vision simulations, pixels are first displaced according to heuristic correlation functions followed by invariant Gaussian blur [7, 33, 77], offering speed but arguably lacking physical foundations. Recent Zernike-based methods [9, 12, 13, 43] can match the statistics of optics-based simulation, achieving realistic visual quality while maintaining a fast data synthesis speed. It has been applied to turbulence mitigation [24, 25, 44, 72] to facilitate the generalization capability of those models.", + "bbox": [ + 75, + 547, + 467, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Conventional turbulence mitigation", + "text_level": 1, + "bbox": [ + 76, + 830, + 383, + 847 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conventional TM algorithms, since [17, 18, 65], mostly treat the TM challenge as a many-to-one restoration problem. Considering that turbulence primarily induces random", + "bbox": [ + 75, + 854, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tilt and blur, the common procedure in conventional algorithms is as follows. They first align the input frames to account for pixel displacements, followed by temporal fusion to combine the information from the aligned frames. Subsequently, the residual blur is often considered to be spatially invariant, allowing a blind deconvolution to be applied to produce a visually satisfactory image.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The tilt rectification is typically achieved in a two-step fashion: construct a tilt-free reference frame, then register every frame with respect to the reference. Since the pixel displacement is assumed to be zero-mean over time [17, 36], the temporal average can be assumed tilt-free [22, 40, 41, 63, 77] and hence be the reference frame. Besides that, low-rank components from all input frames are frequently used [33, 35, 69] as the reference. The registration step can be done by B-spline or optical flow based warping [40, 41, 63, 69, 77] in the spatial domain or phase correction [2, 22, 70] in the phase domain. Because of the \"lucky effect\" phenomenon [20] in the short-exposure turbulence, the goal of temporal aggregation is to identify and fuse the randomly emerging sharp regions, a technique known as lucky fusion [4]. [33, 42, 77] design spatial descriptors to select and score lucky regions. [2] identify and fuse sharp components in the wavelet space, and [23, 33] apply a similar principle to the sparse components derived through robust PCA. While several methods have been proposed for moving object scenarios [3, 42, 50, 52, 57], they are restricted by their assumption that the dynamic regions are rigid and can be isolated, leaving the remaining static regions to be restored using the conventional pipelines.", + "bbox": [ + 496, + 198, + 890, + 546 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Learning-based turbulence mitigation", + "text_level": 1, + "bbox": [ + 500, + 559, + 826, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the rapid advancements in machine learning, numerous recent learning-based methods have demonstrated superior turbulence mitigation results. The majority of them are single-frame TM methods. [32, 45, 49, 53] demonstrate promising performance using generative models with simplified turbulence properties as prior. [34, 48, 71] focus on restoring long-range face images through turbulence. [24, 44] show physics-grounded synthetic data facilitates certain degrees of generalization capability. These single-frame methods do not account for the temporal dimension and can fall short in multi-frame TM scenarios. In contrast, video-based TM algorithms [26, 72] exhibit superior adaptability by leveraging the temporal information, but their designs lack the integration of specific turbulence properties, making their model less efficient. Moreover, [26] only simulated mild turbulence effect, which restricts the generalization capability of their model. Although [72] has achieved better generalization, the point spread function (PSF) implementation is less precise, and the parameter sets are not physics-oriented. Hence, the representative of their turbulence modalities is restricted.", + "bbox": [ + 496, + 583, + 890, + 898 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2890", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/db30be6a1962f72241a954041d7f8e174bc833ab184d739a775fe3ad8c6c15ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 89, + 869, + 191 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4f6bfae93df77c0cf7c64b9ed2979d61cfbd2f66efbb6810d87079e7bd88399e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 193, + 869, + 349 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c6eac9e66a532bc48642a5c85500e73322b8a255e16f61721f7be9ea3609cbb0.jpg", + "image_caption": [ + "Figure 2. The proposed DATUM network. In this figure, block (a) shows the three common stages proposed by classical TM methods. The corresponding stages in DATUM are shown in block (b), which illustrates the forward time process of the $t$ -th frame. The dashed line means the information passing from other temporal directions and frames. Block (c), (d), and (e) demonstrate the DAAB, GRUM, and MTCSA modules, respectively, where the input features are marked by green, and the output features are marked by red." + ], + "image_footnote": [], + "bbox": [ + 101, + 349, + 867, + 452 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed method", + "text_level": 1, + "bbox": [ + 76, + 544, + 246, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Insights from Classical Methods", + "text_level": 1, + "bbox": [ + 76, + 571, + 359, + 585 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Image degradation by atmospheric turbulence can be roughly described by a compositional operation of the blur $\\mathcal{B}$ and the tilt $\\mathcal{T}$ via the relationship $\\mathbf{I} = [\\mathcal{B} \\circ \\mathcal{T}](\\mathbf{J}) + \\mathbf{n}$ , where $\\mathbf{J}$ is the clean image, $\\mathbf{I}$ is the distorted image, and $\\mathbf{n}$ is the noise term. Traditional algorithms handle turbulence in three steps, as illustrated in Fig. 2:", + "bbox": [ + 75, + 595, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Frame-to-reference registration [77], where a reference frame is constructed from the observed images and all images are registered with respect to the reference using optical flow. In strong turbulence or dynamic scenes, constructing a reference is often difficult.", + "- Lucky image fusion [2, 27], where a \"lucky\" image is constructed by collecting the sharpest and most consistent patches from the inputs. However, if turbulence is strong, identifying lucky patches can be difficult.", + "- Blind deconvolution [42], where a final blind deconvolution algorithm is employed to sharpen the lucky image. The success and failure of this step depend heavily on how spatially uniform the blur in the lucky image is. Oftentimes, since the blur is spatially varying, the perfor" + ], + "bbox": [ + 76, + 689, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mance of blind deconvolution is limited.", + "bbox": [ + 511, + 545, + 781, + 559 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "While each step is important each has its limitations, motivating us to develop end-to-end trained networks to approximate these functions. Empowered by training on our physical-grounded dataset, our network enjoys the inductive biases of those insights while avoiding their limitations.", + "bbox": [ + 498, + 561, + 890, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. DATUM network", + "text_level": 1, + "bbox": [ + 500, + 650, + 669, + 664 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2.1 Overview", + "text_level": 1, + "bbox": [ + 500, + 674, + 620, + 688 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The block diagram of the DATUM network is depicted in Fig. 2. We first summarize these three components and describe them in detail in the next subsections.", + "bbox": [ + 498, + 699, + 890, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Feature-to-reference registration. This component is analogous to the classical frame-to-reference registration. For each input frame $I_{t}$ at time $t$ , we first extract three levels of features $f_{t}^{\\{1,2,3\\}}$ . We propose the Deformable Attention Alignment Block (DAAB) to register the high-level feature $f_{t}^{3}$ to a previously hidden reference map $r_{t-1}^{\\prime}$ . We also propose the Gated Reference Update Module (GRUM) updates this reference feature recurrently, which is inspired by the gated recurrent unit [5, 15] and illustrated in Fig. 2.", + "bbox": [ + 496, + 746, + 890, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Temporal fusion. This component is analogous to the", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "2891", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "classical lucky fusion step. The registered feature $f_{t}$ , together with $r_{t-1}'$ and $f_{t}^{3}$ , are fused by a new Deep Integration Module (DIM). DIM consists of a series of Residual Dense Blocks (RDB) [73] and is used to produce the forward embedding $e_{t}^{fw}$ . Since $e_{t}^{fw}$ is a deep feature, it is presumed to be free of tilt and is thus utilized for updating the reference feature for the subsequent frame. After the bidirectional recurrent process, we perform a temporal fusion of $e_{t}^{fw}$ by augmenting it with the backward embedding $e_{t}^{bw}$ and bidirectional embeddings from neighboring frames. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA) module for this purpose.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Post processing. In the final stage, the temporally fused features are decoded to form the turbulence-free image. This decoding involves a twin of decoders. The first predicts a reverse tilt map that rectifies the shallow features, and the second subsequently reconstructs the clean image.", + "bbox": [ + 75, + 273, + 470, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2.2 components", + "text_level": 1, + "bbox": [ + 76, + 375, + 215, + 388 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Feature registration via Deformable Attention Alignment Block (DAAB). In classical methods, a crucial stage for turbulence mitigation is registering the input frames to the tilt-free reference frame. This reference frame is usually obtained by temporal averaging or using variants of principle component analysis. However, these methods may not be applicable to dynamic videos. Since learning-based video TM is possible [26, 72], the deep feature of a video TM network can be considered tilt-mitigated to work as the reference feature for the next input feature. This section explains our method to use deformable attention to facilitate feature registration in our DATUM network.", + "bbox": [ + 75, + 398, + 468, + 580 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The computations in the DDAB are summarized in Algorithm 1, where $(A;B)$ denotes warping $A$ by deformation field $B$ , $\\phi (A;p)$ denotes sampling $A$ by positions $p$ . $W_{K}$ , $W_{V}$ , $W_{Q}$ , and $W$ are linear projections on the channel dimension, and $\\sigma$ denotes the SoftMax. The optical flow at line 3 is estimated with the SPyNet [54], and lines 6-11 are inspired by the guided deformation attention (GDA) [38].", + "bbox": [ + 75, + 582, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Temporal fusion via Multi-head Temporal Channel Self-Attention (MTCSA). After feature registration and deep integration, we propose to augment the embedding with contra-directional information, which is essential to ensure consistent restoration quality across various frames. In addition, like classical methods, a spatially adaptive fusion with adjacent frames is advantageous. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA), as illustrated in Fig. 2. The MTCSA begins by concatenating channels from multiple frames, followed by a $1 \\times 1$ convolution to shrink the channel dimension. Separable convolution is used to construct the spatially varying query, key, and value on the temporal and channel dimensions, and the dynamic fusion is facilitated by self-attention. Finally, a", + "bbox": [ + 75, + 688, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Deformation Attention Alignment Block" + ], + "code_body": "1: Input: Current frame feature $f_{t}^{3}$ , reference feature $r_{t-1}^{\\prime}$ and alignment flow from last frame $O_{t-1}^{f\\rightarrow r}$ , two downsampled frames $I_{t}$ and $I_{t-1}$ \n2: Output: Updated feature $f_{t}$ and flow $O_{t}^{f\\rightarrow r}$ $\\triangleright$ Estimate rough deformation field $\\hat{O}_{t}^{f\\rightarrow r}$ that register feature $f_{t}^{3}$ to reference $r_{t-1}^{\\prime}$ \n3: Estimate the optical flow $O_{t\\rightarrow t-1}^{f}$ from $I_{t}$ and $I_{t-1}$ . \n4: $\\hat{O}_{t}^{f\\rightarrow r} \\gets O_{t-1}^{f\\rightarrow r} + (O_{t\\rightarrow t-1}^{f}\\hat{O}_{t-1}^{f\\rightarrow r})$ \n5: Pre-align $\\hat{f}_{t} \\gets (\\hat{O}_{t}^{f\\rightarrow r}, f_{t}^{3})$ $\\triangleright$ Register input feature to reference frame using multi-group multi-head deformation attention \n6: for all group $g$ do \n $\\triangleright$ Predict offsets $o_{t}^{(g)}$ \n7: $\\Delta o_{t}^{(g)} \\gets \\text{RDB}(\\text{Concat}(\\hat{f}_{t}, r_{t-1}', \\hat{O}_{t}^{f\\rightarrow r}))$ \n8: $o_{t}^{(g)} \\gets \\hat{O}_{t}^{f\\rightarrow r} + \\Delta o_{t}^{(g)}$ $\\triangleright$ Compute the $g$ -th aligned feature $\\hat{f}_{t}^{(g)}$ : \n9: $K^{(g)} \\gets \\phi(f_{t}^{3}W_{K}; o_{t}^{(g)})$ , $V^{(g)} \\gets \\phi(f_{t}^{3}W_{V}; o_{t}^{(g)})$ \n10: $Q \\gets r_{t-1}'W_{Q}, \\hat{f}_{t}^{(g)} \\gets \\sigma(QK^{(g)T}/\\sqrt{C})V^{(g)}$ \n11: end for \n12: Fuse all groups $f_{t} \\gets \\text{Concat}(\\{\\hat{f}_{t}^{(g)}\\})W$ \n13: Update final alignment flow $O_{t}^{f\\rightarrow r}$ by mean of $\\{o_{t}^{(g)}\\}$ \n14: Output $f_{t} \\gets f_{t} + \\text{FeedForward}(f_{t})$", + "bbox": [ + 508, + 109, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "residual connection is used to stabilize training. Considering the quadratic complexity of MTCSA relative to window size, this size is kept moderate. Additionally, we integrate a hard-coded positional embedding wherein features from the focal frame are positioned at the end. This strategy is essential for boundary frames with disproportionate neighboring frames on either side.", + "bbox": [ + 496, + 502, + 890, + 607 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Twin decoder and loss function Given the refined feature embedding from the MTCSA, we also developed a twin decoder to progressively remove the tilt and blur, as shown in Fig. 2. The decoder uses transposed convolution for upsampling and channel attention blocks (CAB) [68] for decoding. Before decoding in higher levels, the deep features are concatenated with the shallow features to facilitate the residual connection like a typical UNet [56]. Since the deep and shallow features are misaligned by the random tilt $\\mathcal{L}$ , we propose to first rectify the shallow features by the estimated inverse tilt field $\\hat{\\mathcal{T}}^{-1}$ estimated in the first stage. The tilt-rectification is optimized by reducing the loss:", + "bbox": [ + 496, + 608, + 892, + 790 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {t i l t}} = \\mathcal {L} _ {\\text {c h a r}} \\left(\\boldsymbol {I} _ {\\mathrm {G T}}, \\left(\\boldsymbol {I} _ {\\text {t i l t}}; \\tilde {\\mathcal {T}} ^ {- 1}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 797, + 890, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Where $\\mathcal{L}_{\\mathrm{char}}$ denotes the Charbonnier loss [10], $I_{\\mathrm{GT}}$ is the input frame and $I_{\\mathrm{tilt}}$ is the tilt-only frame that can be produced without additional cost by our data synthesis method. In the second stage, the rectified shallow features are jointly decoded with the deep features to generate the final recon", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "2892", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/8d03611d2c083b0db28c75ed87c410e3b385f2854394b2318c89e1ed1c00098e.jpg", + "image_caption": [ + "Figure 3. Scheme of our data synthesis method." + ], + "image_footnote": [], + "bbox": [ + 96, + 88, + 444, + 234 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "struction $\\hat{\\pmb{I}}$ . The overall loss function is computed by:", + "bbox": [ + 76, + 276, + 431, + 292 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\alpha_ {1} \\mathcal {L} _ {\\text {t i l t}} + \\alpha_ {2} \\mathcal {L} _ {\\text {c h a r}} (\\boldsymbol {I} _ {\\mathrm {G T}}, \\hat {\\boldsymbol {I}}) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 299, + 468, + 316 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where weights $\\alpha_{1}$ and $\\alpha_{2}$ are empirically set to 0.2 and 0.8.", + "bbox": [ + 76, + 324, + 467, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. ATSyn dataset", + "text_level": 1, + "bbox": [ + 76, + 345, + 225, + 361 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.1 Physics-based data synthesis", + "text_level": 1, + "bbox": [ + 76, + 369, + 328, + 383 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As introduced previously, the ground truth image $J$ is first geometrically distorted and then blurred to produce the degraded image $I$ in our synthesis method. Data synthesis for the turbulence effect essentially requires a physics-grounded representation of and. We adopted the Zernike-based turbulence simulator [12, 13] and improved it with non-trivial modifications. Fig. 3 presents the scheme of our implementation. The and is generated from the phase distortion represented by Zernike polynomials $\\{\\mathbf{Z}_i\\}$ [51] as the basis, with corresponding coefficients $\\mathbf{a}_i$ where $i$ ranging from 1 to 36. Among all 36 coefficients, $i = 1$ denotes the current component, $i = 2, 3$ controls the by a constant scale, and the rest high order Zernike coefficients contribute to the blur effect.", + "bbox": [ + 75, + 393, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The phase distortion can be assumed as a wide sense stationary (WSS) random field [13]. Hence, it can be sampled with Fast Fourier Transform (FFT) from white Gaussian noise and the autocorrelation map. Transforming the phase distortion to the spatial domain point spread functions (PSF) can be achieved by the Phase-to-Space (P2S) transform, which transforms the sampled Zernike coefficients to spatial coefficients $\\beta$ , assuming the PSFs can be represented by a low-rank approximation of 100 basis $\\psi$ and corresponding $\\beta$ . The overall degradation in the spatial domain is implemented by", + "bbox": [ + 75, + 604, + 467, + 771 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {I} = \\sum_ {k = 1} ^ {1 0 0} \\psi_ {k} * (\\boldsymbol {\\beta} _ {k} \\cdot (\\boldsymbol {J};)) + \\boldsymbol {n}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 777, + 468, + 818 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\circ$ denotes the depth-wise convolution. Although subtle, this fundamentally generates more reliable degradation than the simulator in [72], as elaborated in [14]. Except for this, our correlation kernels are more precise by incorporating the continuous $C_n^2$ path technique [11].", + "bbox": [ + 76, + 825, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Guideline of implementation", + "text_level": 1, + "bbox": [ + 500, + 90, + 751, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the proposed simulator, we created the ATSyn dataset to match various real-world turbulence conditions and benchmark deep neural networks for turbulence mitigation. This dataset is segmented into two distinct subsets based on scene type: the ATSyn-dynamic and ATSyn-static. The dynamic sequences contain camera or object motion, whereas the static sequences are each associated with only one underlying clean image. We adopted parameters including focal length, F-number, distance, wavelength, scene size, and sensor resolution to control the simulation. In comparison with the synthetic dataset introduced in [72], which utilized the $D / r_0$ [19] and empirically chosen blur kernel size, our dataset's parameter space more closely aligns with actual camera settings, making it more representative.", + "bbox": [ + 496, + 114, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ATSyn-dynamic contains 4,350 training and 1,097 validation instances synthesized from [26, 58], and ATSyn-static contains 2,000 and 1,000 instances synthesized from the Places dataset [75] for training and validation, respectively. Those instances have varying numbers of frames, each with a distinct turbulence parameter set. Besides ground truth and fully degraded videos, ATSyn further provides associated $\\mathcal{T}$ -only videos to facilitate the training of $\\mathcal{L}_{\\mathrm{tilt}}$ in Eq. 1. We categorize the turbulence parameters by three levels: weak, medium, and strong. The range of turbulence parameters is determined by matching with a largescale, long-range video dataset [16] and other real-world videos, with more details in the supplementary document.", + "bbox": [ + 496, + 325, + 890, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 535, + 633, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Training setting", + "text_level": 1, + "bbox": [ + 500, + 560, + 658, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section describes how we trained our DATUM and other models. Except for turbulence mitigation networks [26, 44, 72], we also benchmarked several representative video restoration [37, 38] and deblurring networks [74, 76] for a more thorough comparison.", + "bbox": [ + 496, + 583, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To train the proposed model, we used the Adam optimizer [29] with the Cosine Annealing learning rate schedule [39]. The initial learning rate is $2 \\times 10^{-4}$ , and batch size is 8. All dynamic scene TM networks in this experiment are trained end-to-end from scratch for 800K iterations. To get their static-scene variant, we fine-tuned them on the static-scene modality with half the initial learning rate and 400K iterations. We clip the gradient if the L2 norm exceeds 20 to prevent gradient explosion during inference.", + "bbox": [ + 496, + 659, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We trained the ESTRNN [74], RNN-MBP [76], and RVRT [74] with the same configuration as DATUM. The number of input frames of DATUM and ESTRNN during training is set to 30 for ATSyn-dynamic and 36 for ATSyn-static. Since RNN-MBP and RVRT require much more resources to train, the number of input frames is set to 16. Because TSRWGAN [26], TMT [72], and TurbNet [44] are", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "2893", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/85816fc0a893f9a02a3381ac0ec47d1557ef4acb8f457ed00b8a1cd685bbb9fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsTurbNet [44]TSRWGAN [26]VRT [37]TMT [72]RNN-MBP [76]ESTRNN [74]RVRT [38]DATUM [ours]
PSNR24.222926.326227.611427.741927.715227.346927.851228.5875
SSIMcw0.82300.85960.86910.87410.87300.86170.87880.8803
", + "bbox": [ + 86, + 88, + 877, + 130 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a19289f1e4a5dd0276c16e53f5dfdfc21b9db1e5f0facb17c9ba4a4279a9e7db.jpg", + "table_caption": [ + "Table 1. Preliminary study: evaluate on TMT's synthetic dynamic scene data [72]. ${\\mathrm{{SSIM}}}_{\\mathrm{{CW}}}$ denotes Complex Wavelet SSIM." + ], + "table_footnote": [], + "table_body": "
Turbulence LevelWeakMediumStrongOverallCost
MethodsPSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)SizeFPS
TSRWGAN [26]27.08440.857526.70460.851425.42300.837226.45410.849346.280.87
TMT [72]29.11830.883628.50500.879126.97440.855228.26650.873426.040.80
VRT [37]28.84530.879728.26280.876926.74920.850628.01790.869918.320.17
RNN-MBP [76]27.92430.869927.47420.864226.08120.849527.21610.861814.161.14
ESTRNN [74]28.98050.875028.33380.869726.88970.846328.13470.86452.46827.65
RVRT [38]29.60800.884528.96050.880627.53440.859528.76720.875613.502.43
DATUM [ours]30.20580.885729.62030.882928.25500.864029.42220.87815.7549.17
", + "bbox": [ + 86, + 161, + 877, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "all designed for turbulence mitigation, we trained them following the original paper and public code.", + "bbox": [ + 75, + 354, + 468, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison on dynamic scene modality", + "text_level": 1, + "bbox": [ + 76, + 392, + 419, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first trained and evaluated all networks for comparison on a previous Zernike-based synthetic dataset [72] for preliminary study. We choose PSNR and Complex Wavelet Structure Similarity [59] (CW-SSIM) as the criterion in this paper, and the reason for selecting CW-SSIM rather than SSIM is provided in the supplementary document. The result in Table 1 shows our DATUM outperforms the previous state-of-the-art TMT [72] with $5 \\times$ fewer parameters and over $10 \\times$ faster inference speed. We also benchmark a representative single-frame TM network [44] to demonstrate the superiority of multi-frame TM methods. Next, we present extensive results from the ATSyn-dynamic dataset in Table 2. Our model outperforms all other networks by a significant margin, while it is the second smallest network among all models and the most efficient network among all existing turbulence mitigation networks.", + "bbox": [ + 75, + 415, + 468, + 657 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison on static scene modality", + "text_level": 1, + "bbox": [ + 76, + 665, + 393, + 681 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When training on the ATSyn-static, the loss is computed between the single ground truth and all output frames. For testing, we instead calculate the average score of the central four frames in the entire output sequence (for single-directional models, we use the last 4). We evaluated the performance on the ATSyn-static and the turbulence text dataset [64], and the result is shown in Table 3. The turbulence text dataset contains 100 sequences of text images, each a static scene of degraded text pattern captured at 300 meters or farther. Real-world turbulence videos do not have ground truth, while [64] uses the accuracy score of pretrained text recognition models CRNN [61], DAN [67], and ASTER [62] as metrics, where a better turbulence mitigation offers better recognition performances. Our model is", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9c13459224199be1ae964307b1821c8905b7f382e006ca8b611bd72189a1bddf.jpg", + "table_caption": [ + "Table 2. Performance comparison on the ATSyn-dynamic set, we list the image quality scores on different turbulence levels and frame-wise resource consumption (measured with $960\\times 540$ frame sequences on RTX 2080 Ti)." + ], + "table_footnote": [], + "table_body": "
BenchmarkATSyn-staticTurb-Text (%)
MethodsPSNRSSIMCWCRNN/DAN/ASTER
TSRWGAN [26]23.160.840760.30 / 73.90 / 74.40
TMT [72]24.510.871680.90 / 87.25 / 88.55
VRT [37]24.270.864176.30 / 84.45 / 83.60
RNN-MBP [76]24.640.877551.35 / 65.00 / 64.30
ESTRNN [74]26.230.901787.10 / 97.80 / 96.95
RVRT [38]25.710.887686.40 / 89.00 / 89.20
DATUM [ours]26.760.910293.55 / 97.95 / 97.25
", + "bbox": [ + 506, + 351, + 883, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Static scene modality. CRNN/DAN/ASTER are the text recognition rates of these three models from the restored images.", + "bbox": [ + 498, + 481, + 890, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "trained on a wide range of turbulence conditions and generic data, without specific augmentation tricks, yet performs on par with the best systems in the $\\mathrm{UG2 + }$ turbulence challenge [64]. Our model outperforms other networks trained on the ATSyn-static dataset by an even larger margin.", + "bbox": [ + 498, + 531, + 890, + 608 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 618, + 648, + 633 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our ablation study examines key elements that introduce effective inductive biases of our model, including the use of additional frames, recurrent reference updating, feature-reference registration, and multi-frame embedding fusion.", + "bbox": [ + 496, + 642, + 890, + 702 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Influence of the number of input frames. The number of input frames for both training and inference matters for recurrent-based networks, especially in turbulence mitigation. Since turbulence degradation is caused by zero-mean stochastic phase distortion, the more frames the network can perceive, the better the non-distortion state it can evaluate. This is particularly valid for static scene sequences, where the pixel-level turbulence statistics are much easier to track and analyze through time.", + "bbox": [ + 496, + 703, + 890, + 839 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We trained two models with 12-frame and 24-frame inputs and presented their respective performance during inference in Fig. 4. This figure shows in the temporal range of our experimental setting, a positive correlation between the", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "2894", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/24f4efb1ce1802add5e88cf059afc6a01f759f19e96826082b1bc99e128a5a5e.jpg", + "image_caption": [ + "(a) On ATSyn-dynamic", + "Figure 4. Influence of the number of input frames." + ], + "image_footnote": [], + "bbox": [ + 91, + 89, + 267, + 191 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b136392c75f597b2ffde52b0ca9b4a773b577b11e927f9b35fad94a1b3b42a63.jpg", + "image_caption": [ + "(b) On ATSyn-static" + ], + "image_footnote": [], + "bbox": [ + 285, + 90, + 455, + 191 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "performance and the number of input frames always exists, especially on the static scene modality where an over 1 dB boost can be obtained with more frames. This phenomenon suggests one of the success factors for turbulence mitigation is the capability of fusing more frames, similar to the video super-resolution problem [8].", + "bbox": [ + 75, + 250, + 467, + 339 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Influence of DAAB, MTCSA, GRUM, and twin decoder. The design of DAAB and MTCSA are inspired by pixel registration and lucky fusion in the conventional TM methods. Although our spatial registration and temporal fusion are implemented at the feature level, they are still effective in turbulence mitigation, as shown in Table 4.", + "bbox": [ + 75, + 339, + 467, + 429 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "While the MTCSA fuses embeddings from multiple frames in a sliding window manner, determining the optimal window size is crucial. If the window size is too small, the temporal fusion only relies on the implicit temporal propagation by the recurrent unit, limiting the performance; if the window size is too large, because of the quadratic complexity along the temporal dimension, the MTCSA becomes very resource-demanded, and the network becomes less flexible to deal with a small number of input frames. We investigated the temporal window size of the MTCSA module, as shown in Fig. 4, where we found that five frames meet the trade-off between performance and efficiency.", + "bbox": [ + 75, + 430, + 467, + 609 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The GRUM utilizes a gating mechanism in the recurrent network to facilitate more extended temporal dependency [5, 15]. It fuses the reference feature with deeper embeddings in a more adaptive manner, which also turns out to be effective. Finally, in the post-processing stage, we compared the two-stage twin decoder with the one-stage plain decoder. We found that by incorporating additional supervision and rectifying shallow features in the decoding stage, better performance can be obtained.", + "bbox": [ + 75, + 611, + 467, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Comparison on real-world data", + "text_level": 1, + "bbox": [ + 76, + 756, + 354, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we demonstrate our data's generalization capability qualitatively and quantitatively on real-world data.", + "bbox": [ + 75, + 780, + 467, + 810 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the impracticality of directly obtaining ground truth images for real-world turbulence scenarios, quantitative performance evaluation typically involves applying restored images to downstream tasks, as noted in [24, 44, 49]. Adopting this approach, we evaluated various restoration methods using the turbulence text dataset. The results are", + "bbox": [ + 75, + 810, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/439a88d59eb1570378ee17417f1b7f79148b69674ae677a2747a9551188021a3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ComponentsPSNR / SSIMSizeGMACs
Base (MTCSA-1f)28.62 / 0.84653.912261.5
Base (MTCSA-3f)28.79 / 0.84974.131272.7
* Base (MTCSA-5f)28.87 / 0.85224.768304.2
Base (MTCSA-7f)28.92 / 0.85325.808358.1
+ GRUM29.06 / 0.85764.894317.7
+ DAAB29.33 / 0.86385.241351.8
+ Twin Decoder29.42 / 0.86475.754372.7
", + "bbox": [ + 514, + 88, + 883, + 204 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Ablation study. We conducted experiments on the ATSdynamic set by adding each proposed component progressively and observed a constant performance improvement.", + "bbox": [ + 498, + 208, + 890, + 250 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/44f184a9f854d372e63247ee9fc3415837a7bc2fd5a4cf0ce0a7423ab5ae499d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 526, + 272, + 864, + 441 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d63c52b2027a35416ad28d7643907639bde6d6470e652b3206930b52bf4be9ba.jpg", + "table_caption": [ + "Figure 5. Comparison on the real-world turbulence-text dataset. The metric is the average text recognition accuracy of CRNN, DAN, and ASTER tested on the restored images." + ], + "table_footnote": [], + "table_body": "
Face RetrievalDegradedSimulator in [72]Our simulator
Rank 537.75%38.83%39.18%
Rank 1040.59%41.83%42.18%
Rank 2045.29%46.40%46.70%
", + "bbox": [ + 509, + 507, + 883, + 564 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Face recognition results on a subset of the BRIAR dataset.", + "bbox": [ + 500, + 566, + 888, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "presented in Fig. 5, revealing two key insights: 1) our proposed ATSyn-static dataset enhances the generalization capabilities of other TM methods. 2) on both synthetic and real-world sequences, DATUM consistently outperforms other models trained on our dataset. To further validate the effectiveness of our modifications to the Zernike-based simulator, we extensively compared DATUM trained on our ATSyn-dynamic dataset and TMT's dataset [72]. We first enhance the long-range subset in the BRIAR dataset [16] by those two versions, run the same pre-trained face recognition model [28] on the enhanced images, and it yields the result provided in Table 5. We can observe the ATSyndynamic dataset improved network performance on realworld videos compared to the [72] dataset. These comparisons demonstrate our method facilitates better generalization of both scene types than other existing datasets.", + "bbox": [ + 496, + 597, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also provide a qualitative comparison in Fig. 6 and 7 to demonstrate the advance of our network and dataset. By comparing the same networks trained by our data and their original checkpoints, our data enhances their general", + "bbox": [ + 498, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "2895", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/11f50f6364043a22b219a8a790013a057b1a203022b111ae07affc0420bde299.jpg", + "image_caption": [ + "(a) Input frame" + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 194, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b02934d5566d9c1a0450c64ce0038bc80fdf1df1d2ac66beb3e3c3d7047fba43.jpg", + "image_caption": [ + "(b)TSRWGAN [26]" + ], + "image_footnote": [], + "bbox": [ + 196, + 90, + 310, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7945235633030d621b396547ab52f3d8de409187955e7182f0f9fbacdde8927f.jpg", + "image_caption": [ + "(c) TMT [72]" + ], + "image_footnote": [], + "bbox": [ + 313, + 90, + 426, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8b956273d4c1e2c7a197e36f370680736cf7e7a56fb7c24c9f047822a16d2b98.jpg", + "image_caption": [ + "(d) NDIR [36]" + ], + "image_footnote": [], + "bbox": [ + 426, + 90, + 542, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fde5272a0329cdc6b2ae33399cb930b695cd3f8b60211c45cf06f0d1177a1d29.jpg", + "image_caption": [ + "(e) TurbNet [44]" + ], + "image_footnote": [], + "bbox": [ + 544, + 90, + 658, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f84d080e599deb5f2aa616fd4346f1b39b0d142a271c2176884bdce92c479cd0.jpg", + "image_caption": [ + "(f) AT-DDPM [49]" + ], + "image_footnote": [], + "bbox": [ + 658, + 90, + 774, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1d1ae5f63c29e0cbf0994f9635a6846e4c84beadef76eb890fbe974226e631ea.jpg", + "image_caption": [ + "(g) PiRN [24]" + ], + "image_footnote": [], + "bbox": [ + 776, + 90, + 890, + 189 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8ae5beda7947d956ce5561610cd366af1654cc9d096fc734300474cb4ec46d8f.jpg", + "image_caption": [ + "(h) DATUM [Ours]" + ], + "image_footnote": [], + "bbox": [ + 80, + 204, + 194, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ef83ec53b5a4451c52280d7703d8a0d6c87394f99c9f1a74c1944ac2500dd35a.jpg", + "image_caption": [ + "(i) TSRWGAN* [26]" + ], + "image_footnote": [], + "bbox": [ + 196, + 204, + 310, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/307334fd638fdbf97a50d6f42efb48e15a5a126953cc44c4e13e2e35b95b2330.jpg", + "image_caption": [ + "(j) TMT* [72]" + ], + "image_footnote": [], + "bbox": [ + 312, + 204, + 426, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eb79700b3cf043568bd601797c2b451df94c989b0728eca25a3f1550530112c4.jpg", + "image_caption": [ + "(k) RNN-MBP* [44]" + ], + "image_footnote": [], + "bbox": [ + 426, + 204, + 542, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c7e1ccdab8c6fb9a437b26b0c0e6849fee81717c824b7fd4d674cd096240ed07.jpg", + "image_caption": [ + "(1) RVRT* [38]" + ], + "image_footnote": [], + "bbox": [ + 542, + 204, + 658, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7ee45eb75f46078dce61b2d563e3cd928c002746d407b5086e2e969a99bd513b.jpg", + "image_caption": [ + "(m) VRT* [26]" + ], + "image_footnote": [], + "bbox": [ + 658, + 204, + 774, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/68406b069eda7815eb60651effa10e427407a6736dc3a9237f6c0d55a781d633.jpg", + "image_caption": [ + "(n) ESTRNN* [74]" + ], + "image_footnote": [], + "bbox": [ + 776, + 204, + 890, + 303 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/102b92634325f2fa68e838f4990b3d7478ddb0045fc43d81eedab33f62a809f7.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison on the turbulence-text dataset [64]. The input frame (a) is the 49th frame of the 94th sequence in [64]. Figures on the top row are restoration results of corresponding TM methods using their original model and checkpoints. Figures on the bottom row are TM or general restoration models (marked by *) trained on our ATSyn-static dataset.", + "(a) Input frame" + ], + "image_footnote": [], + "bbox": [ + 78, + 383, + 194, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0ae8fde4b4da2e4f24782b8ee3ed891216bb3adffd9a3cb0be9ce9ad35ee0606.jpg", + "image_caption": [ + "(b) TSRWGAN [26]" + ], + "image_footnote": [], + "bbox": [ + 196, + 383, + 310, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cb68a2199c3d841b1cad6d1d99ebe08d52a761816b426a0e6263eb694d7bc1a6.jpg", + "image_caption": [ + "(c) TMT [72]" + ], + "image_footnote": [], + "bbox": [ + 312, + 383, + 426, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca20368a06c1d433ea9b3cd9aa7156dc017c89689f4c1eade3590dc88573b9eb.jpg", + "image_caption": [ + "(d) TurbNet [44]" + ], + "image_footnote": [], + "bbox": [ + 426, + 383, + 542, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/112abf924aa029cd26f85e9cfccfb3716b1e094199fbf71f3bb8bd1f65a3f446.jpg", + "image_caption": [ + "(e) ATNet [48]" + ], + "image_footnote": [], + "bbox": [ + 542, + 383, + 658, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/dc555926ea603da5866dfe430ee97783b51c9531cd2c740831a71fab2ecb18a6.jpg", + "image_caption": [ + "(f) AT-DDPM [49]" + ], + "image_footnote": [], + "bbox": [ + 658, + 383, + 774, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4acc2c856ab26a7bee5ab331c0a7c7dbf179e632e2e286486bc65cc9d2af0ed8.jpg", + "image_caption": [ + "(g) PiRN-SR [24]" + ], + "image_footnote": [], + "bbox": [ + 776, + 383, + 890, + 474 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fbda63c23816f95cfe3927c6036e1f69270834413f3d73966fac624e47d6db58.jpg", + "image_caption": [ + "(h) DATUM* [Ours]" + ], + "image_footnote": [], + "bbox": [ + 78, + 487, + 194, + 575 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e74ff30d6e82b14fdfc08fda84ad523635b8be86847e505f658aa6e1b6876bb1.jpg", + "image_caption": [ + "(i) TSRWGAN* [26]", + "Figure 7. Qualitative comparison on a dynamic scene sample from the BRIAR dataset [16]. Figures on the top row are the original restoration results of corresponding TM methods. Figures on the bottom row are models (marked by *) trained on ATSyn-dynamic dataset." + ], + "image_footnote": [], + "bbox": [ + 196, + 487, + 310, + 577 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cad4144615c5dd9026084de3040e02ef46569c6436e3c8d7bc0aa97283707289.jpg", + "image_caption": [ + "(j) $\\mathrm{TMT^{*}}$ [72]" + ], + "image_footnote": [], + "bbox": [ + 312, + 487, + 426, + 577 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/fb95c094045329d984e7412454e0a2059ec989af97f749628338cf3227712902.jpg", + "image_caption": [ + "(k) RNN-MBP* [44]" + ], + "image_footnote": [], + "bbox": [ + 426, + 487, + 542, + 577 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/175c97c7f225b47dfdfd2f0e5bafd856efced2dcc7611be9dd256840e7c18d35.jpg", + "image_caption": [ + "(1) RVRT* [38]" + ], + "image_footnote": [], + "bbox": [ + 542, + 487, + 658, + 577 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/15b04559f0959afd180fcc6a860a5366bb7da60107f3ff8711b7fd88e0941140.jpg", + "image_caption": [ + "(m) VRT* [26]" + ], + "image_footnote": [], + "bbox": [ + 658, + 487, + 774, + 577 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a8e0738d49e7f78275f2c1b2a374a7d05d25c64cc422124d23fd3d953311eca0.jpg", + "image_caption": [ + "(n) ESTRNN* [74]" + ], + "image_footnote": [], + "bbox": [ + 776, + 487, + 890, + 577 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ization capability. On the other hand, by comparison among all networks trained on our dataset, our model significantly outperforms other networks.", + "bbox": [ + 75, + 655, + 468, + 700 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 720, + 194, + 736 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this research, we introduced a novel approach leveraging deep learning to address the enduring challenge of atmospheric turbulence mitigation. Taking a translational perspective, our method integrated the strengths of traditional turbulence mitigation (TM) techniques into a neural network architecture. This fusion elevated our network to state-of-the-art performance while ensuring significantly enhanced efficiency and speed compared to prior TM models. Additionally, we developed a physics-based synthesis method that accurately models the degradation process.", + "bbox": [ + 75, + 750, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This led to the creation of an extensive synthetic dataset covering a diverse spectrum of turbulence effects. Utilizing this dataset, we facilitated a stronger generalization capability for data-driven models than other existing datasets.", + "bbox": [ + 496, + 656, + 890, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments and Disclosure of Funding The research is based upon work supported in part by the Intelligence Advanced Research Projects Activity (IARPA) under Contract No. 2022-21102100004, and in part by the National Science Foundation under the grants CCSS-2030570 and IIS-2133032. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein.", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "2896", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nantheera Anantrasirichai. Atmospheric turbulence removal with complex-valued convolutional neural network. Pattern Recognition Letters, 171:69-75, 2023. 1", + "[2] Nantheera Anantrasirichai, Alin Achim, Nick G. Kingsbury, and David R. Bull. 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IEEE Transactions on Pattern Analysis and Machine Intelligence, 35(1):157-170, 2013. 1, 2, 3" + ], + "bbox": [ + 501, + 92, + 890, + 656 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "2899", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Spatio-Temporal Turbulence Mitigation_ A Translational Perspective/eefae261-74a4-4bbc-a466-69dbac77972f_model.json b/2024/Spatio-Temporal Turbulence Mitigation_ A Translational Perspective/eefae261-74a4-4bbc-a466-69dbac77972f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8ca760ab65fefb0a37284a0fd0ddb2f4ca6f9c8f --- /dev/null +++ b/2024/Spatio-Temporal Turbulence Mitigation_ A Translational Perspective/eefae261-74a4-4bbc-a466-69dbac77972f_model.json @@ -0,0 +1,3049 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.137, + 0.131, + 0.834, + 0.154 + ], + "angle": 0, + "content": "Spatio-Temporal Turbulence Mitigation: A Translational Perspective" + }, + { + "type": "text", + "bbox": [ + 0.1, + 0.18, + 0.87, + 0.235 + ], + "angle": 0, + "content": "Xingguang Zhang1 Nicholas Chimitt1 Yiheng Chi1 Zhiyuan Mao2 Stanley H. Chan1 \n1School of Electrical and Computer Engineering, Purdue University 2Samsung Research America \n{zhan3275, nchimitt, chi14, stanch}@purdue.edu, m940421@gmail.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.301, + 0.474, + 0.649 + ], + "angle": 0, + "content": "Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and generalization to real-world dynamic scenarios remain severely limited. Building upon the intuitions of classical TM algorithms, we present the Deep Atmospheric Turbulence Mitigation network (DATUM). DATUM aims to overcome major challenges when transitioning from classical to deep learning approaches. By carefully integrating the merits of classical multi-frame TM methods into a deep network structure, we demonstrate that DATUM can efficiently perform long-range temporal aggregation using a recurrent fashion, while deformable attention and temporal-channel attention seamlessly facilitate pixel registration and lucky imaging. With additional supervision, tilt and blur degradation can be jointly mitigated. These inductive biases empower DATUM to significantly outperform existing methods while delivering a tenfold increase in processing speed. A large-scale training dataset, ATSyn, is presented as a co-invention to enable the generalization to real turbulence. Our code and datasets are available at https://xg416.github.io/DATUM" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.678, + 0.21, + 0.695 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.886 + ], + "angle": 0, + "content": "Atmospheric turbulence is a dominant image degradation for long-range imaging systems. Reconstructing images distorted by atmospheric turbulence is an important task for many civilian and military applications. The degradation process can be considered a combination of content-invariant random pixel displacement (i.e., tilt) and random blur. Until recently, reconstruction algorithms have often been in the form of model-based solutions, often relying on modalities such as pixel registration and deblurring. Although there have been many important insights into the problem, e.g., lucky imaging, they are primarily limited to static scenes with slow processing speed." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "With the development of physics-grounded data synthe" + }, + { + "type": "image", + "bbox": [ + 0.516, + 0.291, + 0.858, + 0.49 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.505, + 0.895, + 0.59 + ], + "angle": 0, + "content": "Figure 1. Benchmarking video restoration models for turbulence mitigation on our ATSyn-dynamic dataset. The circles in orange are other video-based TM networks, and the circles in blue are representative video deblurring and general restoration networks. The proposed Deep Atmospheric TURbulence Mitigation network (DATUM) is state-of-the-art while highly efficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.895, + 0.836 + ], + "angle": 0, + "content": "sis methods [7, 17, 18, 33, 65, 77], data-driven algorithms have been developed in the past two years. Most existing deep learning methods focus on single-frame problems [24, 32, 34, 44, 45, 48, 49, 53, 71]. Since the degradation is highly ill-posed, the performance of these algorithms is naturally limited, especially when attempting to generalize to real data. On the other hand, multi-frame turbulence mitigation networks [1, 26, 72] have shown greater potential for generalization across a broader spectrum of real-world test scenarios. However, these networks are adapted from generic video restoration methods and do not reflect the insights developed by traditional methods; few turbulence-specific properties are incorporated as inductive biases into their methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "For deep learning methods to work on real-world scenarios, two common factors hinder the application of current turbulence mitigation methods: (1) the complexity of current data-driven methods is usually high, which impedes the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2889" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.168 + ], + "angle": 0, + "content": "practical deployment of these algorithms, and (2) the data synthesis models are suboptimal, either too slow to produce large-scale and diverse datasets or not accurate enough to represent the real-world turbulence profiles, restricting the generalization capability of the model trained on the data." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.168, + 0.468, + 0.213 + ], + "angle": 0, + "content": "To overcome these pressing issues, we propose the Deep Atmospheric Turbulence Mitigation (DATUM) network and the ATSyn dataset. We offer three contributions:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.214, + 0.468, + 0.318 + ], + "angle": 0, + "content": "- DATUM is the first deep-learning video restoration method customized for turbulence mitigation based on classical insights. By carefully integrating the merits of classical multi-frame TM methods, we propose feature-reference registration, temporal fusion, and the decoupling of pixel rectification and deblurring as effective inductive biases in the multi-frame TM challenge." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.319, + 0.468, + 0.394 + ], + "angle": 0, + "content": "- DATUM is the first recurrent model for turbulence restoration. It is significantly more lightweight and efficient than the prior multi-frame TM methods. On both synthetic and real data, DATUM consistently surpasses the SOTA methods while being \\(10 \\times\\) faster." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.395, + 0.468, + 0.485 + ], + "angle": 0, + "content": "- Through the integration of numerous theoretical and practical improvements in physics modeling over the Zernike-based simulators, we further propose an extensive, real-world inspired dataset ATSyn. Experiments on real-world data show that models trained on ATSyn significantly generalize better than those trained on alternative ones." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.214, + 0.468, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.501, + 0.222, + 0.515 + ], + "angle": 0, + "content": "2. Related works" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.526, + 0.276, + 0.541 + ], + "angle": 0, + "content": "2.1. Turbulence modeling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.549, + 0.468, + 0.82 + ], + "angle": 0, + "content": "Atmospheric turbulence simulation spans from computational optics to computer vision-oriented approaches. Optical simulations use split-step methods, which numerically propagate waves through phase screens that represent the atmosphere's spatially varying index of refraction [6, 21, 55, 60]. Despite the existence of moderately faster optical simulations, including brightness function-based simulations [30, 31, 66] or learning-based alternatives [46, 47], the relatively slow speed limits their application in deep learning training [43]. In computer vision simulations, pixels are first displaced according to heuristic correlation functions followed by invariant Gaussian blur [7, 33, 77], offering speed but arguably lacking physical foundations. Recent Zernike-based methods [9, 12, 13, 43] can match the statistics of optics-based simulation, achieving realistic visual quality while maintaining a fast data synthesis speed. It has been applied to turbulence mitigation [24, 25, 44, 72] to facilitate the generalization capability of those models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.385, + 0.848 + ], + "angle": 0, + "content": "2.2. Conventional turbulence mitigation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Conventional TM algorithms, since [17, 18, 65], mostly treat the TM challenge as a many-to-one restoration problem. Considering that turbulence primarily induces random" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.891, + 0.198 + ], + "angle": 0, + "content": "tilt and blur, the common procedure in conventional algorithms is as follows. They first align the input frames to account for pixel displacements, followed by temporal fusion to combine the information from the aligned frames. Subsequently, the residual blur is often considered to be spatially invariant, allowing a blind deconvolution to be applied to produce a visually satisfactory image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.547 + ], + "angle": 0, + "content": "The tilt rectification is typically achieved in a two-step fashion: construct a tilt-free reference frame, then register every frame with respect to the reference. Since the pixel displacement is assumed to be zero-mean over time [17, 36], the temporal average can be assumed tilt-free [22, 40, 41, 63, 77] and hence be the reference frame. Besides that, low-rank components from all input frames are frequently used [33, 35, 69] as the reference. The registration step can be done by B-spline or optical flow based warping [40, 41, 63, 69, 77] in the spatial domain or phase correction [2, 22, 70] in the phase domain. Because of the \"lucky effect\" phenomenon [20] in the short-exposure turbulence, the goal of temporal aggregation is to identify and fuse the randomly emerging sharp regions, a technique known as lucky fusion [4]. [33, 42, 77] design spatial descriptors to select and score lucky regions. [2] identify and fuse sharp components in the wavelet space, and [23, 33] apply a similar principle to the sparse components derived through robust PCA. While several methods have been proposed for moving object scenarios [3, 42, 50, 52, 57], they are restricted by their assumption that the dynamic regions are rigid and can be isolated, leaving the remaining static regions to be restored using the conventional pipelines." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.56, + 0.827, + 0.575 + ], + "angle": 0, + "content": "2.3. Learning-based turbulence mitigation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.9 + ], + "angle": 0, + "content": "With the rapid advancements in machine learning, numerous recent learning-based methods have demonstrated superior turbulence mitigation results. The majority of them are single-frame TM methods. [32, 45, 49, 53] demonstrate promising performance using generative models with simplified turbulence properties as prior. [34, 48, 71] focus on restoring long-range face images through turbulence. [24, 44] show physics-grounded synthetic data facilitates certain degrees of generalization capability. These single-frame methods do not account for the temporal dimension and can fall short in multi-frame TM scenarios. In contrast, video-based TM algorithms [26, 72] exhibit superior adaptability by leveraging the temporal information, but their designs lack the integration of specific turbulence properties, making their model less efficient. Moreover, [26] only simulated mild turbulence effect, which restricts the generalization capability of their model. Although [72] has achieved better generalization, the point spread function (PSF) implementation is less precise, and the parameter sets are not physics-oriented. Hence, the representative of their turbulence modalities is restricted." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2890" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.09, + 0.87, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.194, + 0.87, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.35, + 0.869, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.464, + 0.893, + 0.52 + ], + "angle": 0, + "content": "Figure 2. The proposed DATUM network. In this figure, block (a) shows the three common stages proposed by classical TM methods. The corresponding stages in DATUM are shown in block (b), which illustrates the forward time process of the \\( t \\)-th frame. The dashed line means the information passing from other temporal directions and frames. Block (c), (d), and (e) demonstrate the DAAB, GRUM, and MTCSA modules, respectively, where the input features are marked by green, and the output features are marked by red." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.545, + 0.248, + 0.56 + ], + "angle": 0, + "content": "3. Proposed method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.572, + 0.36, + 0.587 + ], + "angle": 0, + "content": "3.1. Insights from Classical Methods" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.687 + ], + "angle": 0, + "content": "Image degradation by atmospheric turbulence can be roughly described by a compositional operation of the blur \\(\\mathcal{B}\\) and the tilt \\(\\mathcal{T}\\) via the relationship \\(\\mathbf{I} = [\\mathcal{B} \\circ \\mathcal{T}](\\mathbf{J}) + \\mathbf{n}\\), where \\(\\mathbf{J}\\) is the clean image, \\(\\mathbf{I}\\) is the distorted image, and \\(\\mathbf{n}\\) is the noise term. Traditional algorithms handle turbulence in three steps, as illustrated in Fig. 2:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.763 + ], + "angle": 0, + "content": "- Frame-to-reference registration [77], where a reference frame is constructed from the observed images and all images are registered with respect to the reference using optical flow. In strong turbulence or dynamic scenes, constructing a reference is often difficult." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.765, + 0.469, + 0.825 + ], + "angle": 0, + "content": "- Lucky image fusion [2, 27], where a \"lucky\" image is constructed by collecting the sharpest and most consistent patches from the inputs. However, if turbulence is strong, identifying lucky patches can be difficult." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.826, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- Blind deconvolution [42], where a final blind deconvolution algorithm is employed to sharpen the lucky image. The success and failure of this step depend heavily on how spatially uniform the blur in the lucky image is. Oftentimes, since the blur is spatially varying, the perfor" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.69, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.546, + 0.782, + 0.56 + ], + "angle": 0, + "content": "mance of blind deconvolution is limited." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.562, + 0.892, + 0.638 + ], + "angle": 0, + "content": "While each step is important each has its limitations, motivating us to develop end-to-end trained networks to approximate these functions. Empowered by training on our physical-grounded dataset, our network enjoys the inductive biases of those insights while avoiding their limitations." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.67, + 0.665 + ], + "angle": 0, + "content": "3.2. DATUM network" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.675, + 0.621, + 0.689 + ], + "angle": 0, + "content": "3.2.1 Overview" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.7, + 0.892, + 0.745 + ], + "angle": 0, + "content": "The block diagram of the DATUM network is depicted in Fig. 2. We first summarize these three components and describe them in detail in the next subsections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.747, + 0.892, + 0.884 + ], + "angle": 0, + "content": "Feature-to-reference registration. This component is analogous to the classical frame-to-reference registration. For each input frame \\(I_{t}\\) at time \\(t\\), we first extract three levels of features \\(f_{t}^{\\{1,2,3\\}}\\). We propose the Deformable Attention Alignment Block (DAAB) to register the high-level feature \\(f_{t}^{3}\\) to a previously hidden reference map \\(r_{t-1}^{\\prime}\\). We also propose the Gated Reference Update Module (GRUM) updates this reference feature recurrently, which is inspired by the gated recurrent unit [5, 15] and illustrated in Fig. 2." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Temporal fusion. This component is analogous to the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "2891" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.273 + ], + "angle": 0, + "content": "classical lucky fusion step. The registered feature \\( f_{t} \\), together with \\( r_{t-1}' \\) and \\( f_{t}^{3} \\), are fused by a new Deep Integration Module (DIM). DIM consists of a series of Residual Dense Blocks (RDB) [73] and is used to produce the forward embedding \\( e_{t}^{fw} \\). Since \\( e_{t}^{fw} \\) is a deep feature, it is presumed to be free of tilt and is thus utilized for updating the reference feature for the subsequent frame. After the bidirectional recurrent process, we perform a temporal fusion of \\( e_{t}^{fw} \\) by augmenting it with the backward embedding \\( e_{t}^{bw} \\) and bidirectional embeddings from neighboring frames. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA) module for this purpose." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.472, + 0.351 + ], + "angle": 0, + "content": "Post processing. In the final stage, the temporally fused features are decoded to form the turbulence-free image. This decoding involves a twin of decoders. The first predicts a reverse tilt map that rectifies the shallow features, and the second subsequently reconstructs the clean image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.375, + 0.216, + 0.39 + ], + "angle": 0, + "content": "3.2.2 components" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.4, + 0.47, + 0.581 + ], + "angle": 0, + "content": "Feature registration via Deformable Attention Alignment Block (DAAB). In classical methods, a crucial stage for turbulence mitigation is registering the input frames to the tilt-free reference frame. This reference frame is usually obtained by temporal averaging or using variants of principle component analysis. However, these methods may not be applicable to dynamic videos. Since learning-based video TM is possible [26, 72], the deep feature of a video TM network can be considered tilt-mitigated to work as the reference feature for the next input feature. This section explains our method to use deformable attention to facilitate feature registration in our DATUM network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.47, + 0.688 + ], + "angle": 0, + "content": "The computations in the DDAB are summarized in Algorithm 1, where \\((A;B)\\) denotes warping \\(A\\) by deformation field \\(B\\), \\(\\phi (A;p)\\) denotes sampling \\(A\\) by positions \\(p\\). \\(W_{K}\\), \\(W_{V}\\), \\(W_{Q}\\), and \\(W\\) are linear projections on the channel dimension, and \\(\\sigma\\) denotes the SoftMax. The optical flow at line 3 is estimated with the SPyNet [54], and lines 6-11 are inspired by the guided deformation attention (GDA) [38]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Temporal fusion via Multi-head Temporal Channel Self-Attention (MTCSA). After feature registration and deep integration, we propose to augment the embedding with contra-directional information, which is essential to ensure consistent restoration quality across various frames. In addition, like classical methods, a spatially adaptive fusion with adjacent frames is advantageous. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA), as illustrated in Fig. 2. The MTCSA begins by concatenating channels from multiple frames, followed by a \\(1 \\times 1\\) convolution to shrink the channel dimension. Separable convolution is used to construct the spatially varying query, key, and value on the temporal and channel dimensions, and the dynamic fusion is facilitated by self-attention. Finally, a" + }, + { + "type": "code_caption", + "bbox": [ + 0.503, + 0.091, + 0.86, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 Deformation Attention Alignment Block" + }, + { + "type": "algorithm", + "bbox": [ + 0.509, + 0.111, + 0.892, + 0.478 + ], + "angle": 0, + "content": "1: Input: Current frame feature \\( f_{t}^{3} \\), reference feature \\( r_{t-1}^{\\prime} \\) and alignment flow from last frame \\( O_{t-1}^{f\\rightarrow r} \\), two downsampled frames \\( I_{t} \\) and \\( I_{t-1} \\) \n2: Output: Updated feature \\( f_{t} \\) and flow \\( O_{t}^{f\\rightarrow r} \\) \n\\( \\triangleright \\) Estimate rough deformation field \\( \\hat{O}_{t}^{f\\rightarrow r} \\) that register feature \\( f_{t}^{3} \\) to reference \\( r_{t-1}^{\\prime} \\) \n3: Estimate the optical flow \\( O_{t\\rightarrow t-1}^{f} \\) from \\( I_{t} \\) and \\( I_{t-1} \\). \n4: \\( \\hat{O}_{t}^{f\\rightarrow r} \\gets O_{t-1}^{f\\rightarrow r} + (O_{t\\rightarrow t-1}^{f}\\hat{O}_{t-1}^{f\\rightarrow r}) \\) \n5: Pre-align \\( \\hat{f}_{t} \\gets (\\hat{O}_{t}^{f\\rightarrow r}, f_{t}^{3}) \\) \n\\( \\triangleright \\) Register input feature to reference frame using multi-group multi-head deformation attention \n6: for all group \\( g \\) do \n\\( \\triangleright \\) Predict offsets \\( o_{t}^{(g)} \\) \n7: \\( \\Delta o_{t}^{(g)} \\gets \\text{RDB}(\\text{Concat}(\\hat{f}_{t}, r_{t-1}', \\hat{O}_{t}^{f\\rightarrow r})) \\) \n8: \\( o_{t}^{(g)} \\gets \\hat{O}_{t}^{f\\rightarrow r} + \\Delta o_{t}^{(g)} \\) \n\\( \\triangleright \\) Compute the \\( g \\)-th aligned feature \\( \\hat{f}_{t}^{(g)} \\): \n9: \\( K^{(g)} \\gets \\phi(f_{t}^{3}W_{K}; o_{t}^{(g)}) \\), \\( V^{(g)} \\gets \\phi(f_{t}^{3}W_{V}; o_{t}^{(g)}) \\) \n10: \\( Q \\gets r_{t-1}'W_{Q}, \\hat{f}_{t}^{(g)} \\gets \\sigma(QK^{(g)T}/\\sqrt{C})V^{(g)} \\) \n11: end for \n12: Fuse all groups \\( f_{t} \\gets \\text{Concat}(\\{\\hat{f}_{t}^{(g)}\\})W \\) \n13: Update final alignment flow \\( O_{t}^{f\\rightarrow r} \\) by mean of \\( \\{o_{t}^{(g)}\\} \\) \n14: Output \\( f_{t} \\gets f_{t} + \\text{FeedForward}(f_{t}) \\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.503, + 0.892, + 0.608 + ], + "angle": 0, + "content": "residual connection is used to stabilize training. Considering the quadratic complexity of MTCSA relative to window size, this size is kept moderate. Additionally, we integrate a hard-coded positional embedding wherein features from the focal frame are positioned at the end. This strategy is essential for boundary frames with disproportionate neighboring frames on either side." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.893, + 0.791 + ], + "angle": 0, + "content": "Twin decoder and loss function Given the refined feature embedding from the MTCSA, we also developed a twin decoder to progressively remove the tilt and blur, as shown in Fig. 2. The decoder uses transposed convolution for upsampling and channel attention blocks (CAB) [68] for decoding. Before decoding in higher levels, the deep features are concatenated with the shallow features to facilitate the residual connection like a typical UNet [56]. Since the deep and shallow features are misaligned by the random tilt \\(\\mathcal{L}\\), we propose to first rectify the shallow features by the estimated inverse tilt field \\(\\hat{\\mathcal{T}}^{-1}\\) estimated in the first stage. The tilt-rectification is optimized by reducing the loss:" + }, + { + "type": "equation", + "bbox": [ + 0.595, + 0.799, + 0.891, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {t i l t}} = \\mathcal {L} _ {\\text {c h a r}} \\left(\\boldsymbol {I} _ {\\mathrm {G T}}, \\left(\\boldsymbol {I} _ {\\text {t i l t}}; \\tilde {\\mathcal {T}} ^ {- 1}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Where \\(\\mathcal{L}_{\\mathrm{char}}\\) denotes the Charbonnier loss [10], \\(I_{\\mathrm{GT}}\\) is the input frame and \\(I_{\\mathrm{tilt}}\\) is the tilt-only frame that can be produced without additional cost by our data synthesis method. In the second stage, the rectified shallow features are jointly decoded with the deep features to generate the final recon" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2892" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.098, + 0.089, + 0.445, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.24, + 0.414, + 0.254 + ], + "angle": 0, + "content": "Figure 3. Scheme of our data synthesis method." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.277, + 0.432, + 0.293 + ], + "angle": 0, + "content": "struction \\(\\hat{\\pmb{I}}\\). The overall loss function is computed by:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.3, + 0.469, + 0.317 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\alpha_ {1} \\mathcal {L} _ {\\text {t i l t}} + \\alpha_ {2} \\mathcal {L} _ {\\text {c h a r}} (\\boldsymbol {I} _ {\\mathrm {G T}}, \\hat {\\boldsymbol {I}}) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.325, + 0.468, + 0.34 + ], + "angle": 0, + "content": "where weights \\(\\alpha_{1}\\) and \\(\\alpha_{2}\\) are empirically set to 0.2 and 0.8." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.347, + 0.226, + 0.362 + ], + "angle": 0, + "content": "3.3. ATSyn dataset" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.371, + 0.33, + 0.385 + ], + "angle": 0, + "content": "3.3.1 Physics-based data synthesis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.469, + 0.603 + ], + "angle": 0, + "content": "As introduced previously, the ground truth image \\( J \\) is first geometrically distorted and then blurred to produce the degraded image \\( I \\) in our synthesis method. Data synthesis for the turbulence effect essentially requires a physics-grounded representation of and. We adopted the Zernike-based turbulence simulator [12, 13] and improved it with non-trivial modifications. Fig. 3 presents the scheme of our implementation. The and is generated from the phase distortion represented by Zernike polynomials \\( \\{\\mathbf{Z}_i\\} \\) [51] as the basis, with corresponding coefficients \\( \\mathbf{a}_i \\) where \\( i \\) ranging from 1 to 36. Among all 36 coefficients, \\( i = 1 \\) denotes the current component, \\( i = 2, 3 \\) controls the by a constant scale, and the rest high order Zernike coefficients contribute to the blur effect." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.468, + 0.772 + ], + "angle": 0, + "content": "The phase distortion can be assumed as a wide sense stationary (WSS) random field [13]. Hence, it can be sampled with Fast Fourier Transform (FFT) from white Gaussian noise and the autocorrelation map. Transforming the phase distortion to the spatial domain point spread functions (PSF) can be achieved by the Phase-to-Space (P2S) transform, which transforms the sampled Zernike coefficients to spatial coefficients \\(\\beta\\), assuming the PSFs can be represented by a low-rank approximation of 100 basis \\(\\psi\\) and corresponding \\(\\beta\\). The overall degradation in the spatial domain is implemented by" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.778, + 0.469, + 0.819 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {I} = \\sum_ {k = 1} ^ {1 0 0} \\psi_ {k} * (\\boldsymbol {\\beta} _ {k} \\cdot (\\boldsymbol {J};)) + \\boldsymbol {n}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.826, + 0.468, + 0.902 + ], + "angle": 0, + "content": "where \\(\\circ\\) denotes the depth-wise convolution. Although subtle, this fundamentally generates more reliable degradation than the simulator in [72], as elaborated in [14]. Except for this, our correlation kernels are more precise by incorporating the continuous \\(C_n^2\\) path technique [11]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.753, + 0.107 + ], + "angle": 0, + "content": "3.3.2 Guideline of implementation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.892, + 0.326 + ], + "angle": 0, + "content": "With the proposed simulator, we created the ATSyn dataset to match various real-world turbulence conditions and benchmark deep neural networks for turbulence mitigation. This dataset is segmented into two distinct subsets based on scene type: the ATSyn-dynamic and ATSyn-static. The dynamic sequences contain camera or object motion, whereas the static sequences are each associated with only one underlying clean image. We adopted parameters including focal length, F-number, distance, wavelength, scene size, and sensor resolution to control the simulation. In comparison with the synthetic dataset introduced in [72], which utilized the \\( D / r_0 \\) [19] and empirically chosen blur kernel size, our dataset's parameter space more closely aligns with actual camera settings, making it more representative." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.892, + 0.523 + ], + "angle": 0, + "content": "ATSyn-dynamic contains 4,350 training and 1,097 validation instances synthesized from [26, 58], and ATSyn-static contains 2,000 and 1,000 instances synthesized from the Places dataset [75] for training and validation, respectively. Those instances have varying numbers of frames, each with a distinct turbulence parameter set. Besides ground truth and fully degraded videos, ATSyn further provides associated \\(\\mathcal{T}\\)-only videos to facilitate the training of \\(\\mathcal{L}_{\\mathrm{tilt}}\\) in Eq. 1. We categorize the turbulence parameters by three levels: weak, medium, and strong. The range of turbulence parameters is determined by matching with a largescale, long-range video dataset [16] and other real-world videos, with more details in the supplementary document." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.536, + 0.634, + 0.553 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.561, + 0.66, + 0.577 + ], + "angle": 0, + "content": "4.1. Training setting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.891, + 0.659 + ], + "angle": 0, + "content": "This section describes how we trained our DATUM and other models. Except for turbulence mitigation networks [26, 44, 72], we also benchmarked several representative video restoration [37, 38] and deblurring networks [74, 76] for a more thorough comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.795 + ], + "angle": 0, + "content": "To train the proposed model, we used the Adam optimizer [29] with the Cosine Annealing learning rate schedule [39]. The initial learning rate is \\( 2 \\times 10^{-4} \\), and batch size is 8. All dynamic scene TM networks in this experiment are trained end-to-end from scratch for 800K iterations. To get their static-scene variant, we fine-tuned them on the static-scene modality with half the initial learning rate and 400K iterations. We clip the gradient if the L2 norm exceeds 20 to prevent gradient explosion during inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We trained the ESTRNN [74], RNN-MBP [76], and RVRT [74] with the same configuration as DATUM. The number of input frames of DATUM and ESTRNN during training is set to 30 for ATSyn-dynamic and 36 for ATSyn-static. Since RNN-MBP and RVRT require much more resources to train, the number of input frames is set to 16. Because TSRWGAN [26], TMT [72], and TurbNet [44] are" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2893" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.878, + 0.131 + ], + "angle": 0, + "content": "
MethodsTurbNet [44]TSRWGAN [26]VRT [37]TMT [72]RNN-MBP [76]ESTRNN [74]RVRT [38]DATUM [ours]
PSNR24.222926.326227.611427.741927.715227.346927.851228.5875
SSIMcw0.82300.85960.86910.87410.87300.86170.87880.8803
" + }, + { + "type": "table_caption", + "bbox": [ + 0.113, + 0.135, + 0.855, + 0.15 + ], + "angle": 0, + "content": "Table 1. Preliminary study: evaluate on TMT's synthetic dynamic scene data [72]. \\( {\\mathrm{{SSIM}}}_{\\mathrm{{CW}}} \\) denotes Complex Wavelet SSIM." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.162, + 0.878, + 0.294 + ], + "angle": 0, + "content": "
Turbulence LevelWeakMediumStrongOverallCost
MethodsPSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)SizeFPS
TSRWGAN [26]27.08440.857526.70460.851425.42300.837226.45410.849346.280.87
TMT [72]29.11830.883628.50500.879126.97440.855228.26650.873426.040.80
VRT [37]28.84530.879728.26280.876926.74920.850628.01790.869918.320.17
RNN-MBP [76]27.92430.869927.47420.864226.08120.849527.21610.861814.161.14
ESTRNN [74]28.98050.875028.33380.869726.88970.846328.13470.86452.46827.65
RVRT [38]29.60800.884528.96050.880627.53440.859528.76720.875613.502.43
DATUM [ours]30.20580.885729.62030.882928.25500.864029.42220.87815.7549.17
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.3, + 0.893, + 0.328 + ], + "angle": 0, + "content": "Table 2. Performance comparison on the ATSyn-dynamic set, we list the image quality scores on different turbulence levels and frame-wise resource consumption (measured with \\(960\\times 540\\) frame sequences on RTX 2080 Ti)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.355, + 0.47, + 0.387 + ], + "angle": 0, + "content": "all designed for turbulence mitigation, we trained them following the original paper and public code." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.393, + 0.421, + 0.41 + ], + "angle": 0, + "content": "4.2. Comparison on dynamic scene modality" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.47, + 0.658 + ], + "angle": 0, + "content": "We first trained and evaluated all networks for comparison on a previous Zernike-based synthetic dataset [72] for preliminary study. We choose PSNR and Complex Wavelet Structure Similarity [59] (CW-SSIM) as the criterion in this paper, and the reason for selecting CW-SSIM rather than SSIM is provided in the supplementary document. The result in Table 1 shows our DATUM outperforms the previous state-of-the-art TMT [72] with \\(5 \\times\\) fewer parameters and over \\(10 \\times\\) faster inference speed. We also benchmark a representative single-frame TM network [44] to demonstrate the superiority of multi-frame TM methods. Next, we present extensive results from the ATSyn-dynamic dataset in Table 2. Our model outperforms all other networks by a significant margin, while it is the second smallest network among all models and the most efficient network among all existing turbulence mitigation networks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.666, + 0.395, + 0.683 + ], + "angle": 0, + "content": "4.3. Comparison on static scene modality" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "When training on the ATSyn-static, the loss is computed between the single ground truth and all output frames. For testing, we instead calculate the average score of the central four frames in the entire output sequence (for single-directional models, we use the last 4). We evaluated the performance on the ATSyn-static and the turbulence text dataset [64], and the result is shown in Table 3. The turbulence text dataset contains 100 sequences of text images, each a static scene of degraded text pattern captured at 300 meters or farther. Real-world turbulence videos do not have ground truth, while [64] uses the accuracy score of pretrained text recognition models CRNN [61], DAN [67], and ASTER [62] as metrics, where a better turbulence mitigation offers better recognition performances. Our model is" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.352, + 0.885, + 0.476 + ], + "angle": 0, + "content": "
BenchmarkATSyn-staticTurb-Text (%)
MethodsPSNRSSIMCWCRNN/DAN/ASTER
TSRWGAN [26]23.160.840760.30 / 73.90 / 74.40
TMT [72]24.510.871680.90 / 87.25 / 88.55
VRT [37]24.270.864176.30 / 84.45 / 83.60
RNN-MBP [76]24.640.877551.35 / 65.00 / 64.30
ESTRNN [74]26.230.901787.10 / 97.80 / 96.95
RVRT [38]25.710.887686.40 / 89.00 / 89.20
DATUM [ours]26.760.910293.55 / 97.95 / 97.25
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.482, + 0.892, + 0.51 + ], + "angle": 0, + "content": "Table 3. Static scene modality. CRNN/DAN/ASTER are the text recognition rates of these three models from the restored images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.532, + 0.892, + 0.609 + ], + "angle": 0, + "content": "trained on a wide range of turbulence conditions and generic data, without specific augmentation tricks, yet performs on par with the best systems in the \\(\\mathrm{UG2 + }\\) turbulence challenge [64]. Our model outperforms other networks trained on the ATSyn-static dataset by an even larger margin." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.619, + 0.65, + 0.635 + ], + "angle": 0, + "content": "4.4. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.703 + ], + "angle": 0, + "content": "Our ablation study examines key elements that introduce effective inductive biases of our model, including the use of additional frames, recurrent reference updating, feature-reference registration, and multi-frame embedding fusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.84 + ], + "angle": 0, + "content": "Influence of the number of input frames. The number of input frames for both training and inference matters for recurrent-based networks, especially in turbulence mitigation. Since turbulence degradation is caused by zero-mean stochastic phase distortion, the more frames the network can perceive, the better the non-distortion state it can evaluate. This is particularly valid for static scene sequences, where the pixel-level turbulence statistics are much easier to track and analyze through time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We trained two models with 12-frame and 24-frame inputs and presented their respective performance during inference in Fig. 4. This figure shows in the temporal range of our experimental setting, a positive correlation between the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2894" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.093, + 0.09, + 0.268, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.197, + 0.241, + 0.21 + ], + "angle": 0, + "content": "(a) On ATSyn-dynamic" + }, + { + "type": "image", + "bbox": [ + 0.286, + 0.091, + 0.457, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.317, + 0.197, + 0.425, + 0.21 + ], + "angle": 0, + "content": "(b) On ATSyn-static" + }, + { + "type": "image_caption", + "bbox": [ + 0.122, + 0.219, + 0.423, + 0.233 + ], + "angle": 0, + "content": "Figure 4. Influence of the number of input frames." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.468, + 0.34 + ], + "angle": 0, + "content": "performance and the number of input frames always exists, especially on the static scene modality where an over 1 dB boost can be obtained with more frames. This phenomenon suggests one of the success factors for turbulence mitigation is the capability of fusing more frames, similar to the video super-resolution problem [8]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.468, + 0.43 + ], + "angle": 0, + "content": "Influence of DAAB, MTCSA, GRUM, and twin decoder. The design of DAAB and MTCSA are inspired by pixel registration and lucky fusion in the conventional TM methods. Although our spatial registration and temporal fusion are implemented at the feature level, they are still effective in turbulence mitigation, as shown in Table 4." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.431, + 0.468, + 0.611 + ], + "angle": 0, + "content": "While the MTCSA fuses embeddings from multiple frames in a sliding window manner, determining the optimal window size is crucial. If the window size is too small, the temporal fusion only relies on the implicit temporal propagation by the recurrent unit, limiting the performance; if the window size is too large, because of the quadratic complexity along the temporal dimension, the MTCSA becomes very resource-demanded, and the network becomes less flexible to deal with a small number of input frames. We investigated the temporal window size of the MTCSA module, as shown in Fig. 4, where we found that five frames meet the trade-off between performance and efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.468, + 0.747 + ], + "angle": 0, + "content": "The GRUM utilizes a gating mechanism in the recurrent network to facilitate more extended temporal dependency [5, 15]. It fuses the reference feature with deeper embeddings in a more adaptive manner, which also turns out to be effective. Finally, in the post-processing stage, we compared the two-stage twin decoder with the one-stage plain decoder. We found that by incorporating additional supervision and rectifying shallow features in the decoding stage, better performance can be obtained." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.355, + 0.773 + ], + "angle": 0, + "content": "4.5. Comparison on real-world data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.468, + 0.811 + ], + "angle": 0, + "content": "In this section, we demonstrate our data's generalization capability qualitatively and quantitatively on real-world data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Given the impracticality of directly obtaining ground truth images for real-world turbulence scenarios, quantitative performance evaluation typically involves applying restored images to downstream tasks, as noted in [24, 44, 49]. Adopting this approach, we evaluated various restoration methods using the turbulence text dataset. The results are" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.089, + 0.885, + 0.205 + ], + "angle": 0, + "content": "
ComponentsPSNR / SSIMSizeGMACs
Base (MTCSA-1f)28.62 / 0.84653.912261.5
Base (MTCSA-3f)28.79 / 0.84974.131272.7
* Base (MTCSA-5f)28.87 / 0.85224.768304.2
Base (MTCSA-7f)28.92 / 0.85325.808358.1
+ GRUM29.06 / 0.85764.894317.7
+ DAAB29.33 / 0.86385.241351.8
+ Twin Decoder29.42 / 0.86475.754372.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.209, + 0.892, + 0.251 + ], + "angle": 0, + "content": "Table 4. Ablation study. We conducted experiments on the ATSdynamic set by adding each proposed component progressively and observed a constant performance improvement." + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.273, + 0.865, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.452, + 0.892, + 0.494 + ], + "angle": 0, + "content": "Figure 5. Comparison on the real-world turbulence-text dataset. The metric is the average text recognition accuracy of CRNN, DAN, and ASTER tested on the restored images." + }, + { + "type": "table", + "bbox": [ + 0.51, + 0.508, + 0.884, + 0.565 + ], + "angle": 0, + "content": "
Face RetrievalDegradedSimulator in [72]Our simulator
Rank 537.75%38.83%39.18%
Rank 1040.59%41.83%42.18%
Rank 2045.29%46.40%46.70%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.568, + 0.89, + 0.582 + ], + "angle": 0, + "content": "Table 5. Face recognition results on a subset of the BRIAR dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.84 + ], + "angle": 0, + "content": "presented in Fig. 5, revealing two key insights: 1) our proposed ATSyn-static dataset enhances the generalization capabilities of other TM methods. 2) on both synthetic and real-world sequences, DATUM consistently outperforms other models trained on our dataset. To further validate the effectiveness of our modifications to the Zernike-based simulator, we extensively compared DATUM trained on our ATSyn-dynamic dataset and TMT's dataset [72]. We first enhance the long-range subset in the BRIAR dataset [16] by those two versions, run the same pre-trained face recognition model [28] on the enhanced images, and it yields the result provided in Table 5. We can observe the ATSyndynamic dataset improved network performance on realworld videos compared to the [72] dataset. These comparisons demonstrate our method facilitates better generalization of both scene types than other existing datasets." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We also provide a qualitative comparison in Fig. 6 and 7 to demonstrate the advance of our network and dataset. By comparing the same networks trained by our data and their original checkpoints, our data enhances their general" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "2895" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.091, + 0.195, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.192, + 0.173, + 0.203 + ], + "angle": 0, + "content": "(a) Input frame" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.091, + 0.312, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.192, + 0.302, + 0.203 + ], + "angle": 0, + "content": "(b)TSRWGAN [26]" + }, + { + "type": "image", + "bbox": [ + 0.314, + 0.091, + 0.427, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.338, + 0.192, + 0.402, + 0.203 + ], + "angle": 0, + "content": "(c) TMT [72]" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.091, + 0.544, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.452, + 0.192, + 0.519, + 0.203 + ], + "angle": 0, + "content": "(d) NDIR [36]" + }, + { + "type": "image", + "bbox": [ + 0.545, + 0.091, + 0.659, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.192, + 0.64, + 0.203 + ], + "angle": 0, + "content": "(e) TurbNet [44]" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.091, + 0.775, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.674, + 0.192, + 0.761, + 0.203 + ], + "angle": 0, + "content": "(f) AT-DDPM [49]" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.091, + 0.892, + 0.19 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.801, + 0.192, + 0.865, + 0.203 + ], + "angle": 0, + "content": "(g) PiRN [24]" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.205, + 0.195, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.305, + 0.186, + 0.317 + ], + "angle": 0, + "content": "(h) DATUM [Ours]" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.205, + 0.311, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.305, + 0.303, + 0.317 + ], + "angle": 0, + "content": "(i) TSRWGAN* [26]" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.205, + 0.427, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.305, + 0.404, + 0.317 + ], + "angle": 0, + "content": "(j) TMT* [72]" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.205, + 0.543, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.437, + 0.305, + 0.534, + 0.317 + ], + "angle": 0, + "content": "(k) RNN-MBP* [44]" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.205, + 0.659, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.305, + 0.638, + 0.317 + ], + "angle": 0, + "content": "(1) RVRT* [38]" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.205, + 0.775, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.682, + 0.305, + 0.753, + 0.317 + ], + "angle": 0, + "content": "(m) VRT* [26]" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.205, + 0.892, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.305, + 0.879, + 0.317 + ], + "angle": 0, + "content": "(n) ESTRNN* [74]" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.328, + 0.892, + 0.371 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison on the turbulence-text dataset [64]. The input frame (a) is the 49th frame of the 94th sequence in [64]. Figures on the top row are restoration results of corresponding TM methods using their original model and checkpoints. Figures on the bottom row are TM or general restoration models (marked by *) trained on our ATSyn-static dataset." + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.385, + 0.195, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.476, + 0.173, + 0.487 + ], + "angle": 0, + "content": "(a) Input frame" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.385, + 0.311, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.476, + 0.302, + 0.487 + ], + "angle": 0, + "content": "(b) TSRWGAN [26]" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.385, + 0.427, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.338, + 0.476, + 0.402, + 0.487 + ], + "angle": 0, + "content": "(c) TMT [72]" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.385, + 0.543, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.446, + 0.476, + 0.524, + 0.487 + ], + "angle": 0, + "content": "(d) TurbNet [44]" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.385, + 0.659, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.476, + 0.636, + 0.487 + ], + "angle": 0, + "content": "(e) ATNet [48]" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.385, + 0.775, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.673, + 0.476, + 0.761, + 0.487 + ], + "angle": 0, + "content": "(f) AT-DDPM [49]" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.385, + 0.892, + 0.475 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.792, + 0.476, + 0.875, + 0.487 + ], + "angle": 0, + "content": "(g) PiRN-SR [24]" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.488, + 0.195, + 0.577 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.087, + 0.579, + 0.189, + 0.59 + ], + "angle": 0, + "content": "(h) DATUM* [Ours]" + }, + { + "type": "image", + "bbox": [ + 0.197, + 0.488, + 0.311, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.205, + 0.579, + 0.303, + 0.59 + ], + "angle": 0, + "content": "(i) TSRWGAN* [26]" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.488, + 0.427, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.336, + 0.579, + 0.404, + 0.59 + ], + "angle": 0, + "content": "(j) \\(\\mathrm{TMT^{*}}\\) [72]" + }, + { + "type": "image", + "bbox": [ + 0.428, + 0.488, + 0.543, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.436, + 0.579, + 0.534, + 0.59 + ], + "angle": 0, + "content": "(k) RNN-MBP* [44]" + }, + { + "type": "image", + "bbox": [ + 0.544, + 0.488, + 0.659, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.566, + 0.579, + 0.637, + 0.59 + ], + "angle": 0, + "content": "(1) RVRT* [38]" + }, + { + "type": "image", + "bbox": [ + 0.66, + 0.488, + 0.775, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.682, + 0.579, + 0.753, + 0.59 + ], + "angle": 0, + "content": "(m) VRT* [26]" + }, + { + "type": "image", + "bbox": [ + 0.777, + 0.488, + 0.892, + 0.578 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.579, + 0.879, + 0.59 + ], + "angle": 0, + "content": "(n) ESTRNN* [74]" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.602, + 0.892, + 0.631 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison on a dynamic scene sample from the BRIAR dataset [16]. Figures on the top row are the original restoration results of corresponding TM methods. Figures on the bottom row are models (marked by *) trained on ATSyn-dynamic dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.47, + 0.702 + ], + "angle": 0, + "content": "ization capability. On the other hand, by comparison among all networks trained on our dataset, our model significantly outperforms other networks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.722, + 0.196, + 0.737 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In this research, we introduced a novel approach leveraging deep learning to address the enduring challenge of atmospheric turbulence mitigation. Taking a translational perspective, our method integrated the strengths of traditional turbulence mitigation (TM) techniques into a neural network architecture. This fusion elevated our network to state-of-the-art performance while ensuring significantly enhanced efficiency and speed compared to prior TM models. Additionally, we developed a physics-based synthesis method that accurately models the degradation process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.892, + 0.717 + ], + "angle": 0, + "content": "This led to the creation of an extensive synthetic dataset covering a diverse spectrum of turbulence effects. Utilizing this dataset, we facilitated a stronger generalization capability for data-driven models than other existing datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments and Disclosure of Funding The research is based upon work supported in part by the Intelligence Advanced Research Projects Activity (IARPA) under Contract No. 2022-21102100004, and in part by the National Science Foundation under the grants CCSS-2030570 and IIS-2133032. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of IARPA, or the U.S. Government. 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Chan1 +1School of Electrical and Computer Engineering, Purdue University 2Samsung Research America +{zhan3275, nchimitt, chi14, stanch}@purdue.edu, m940421@gmail.com + +# Abstract + +Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and generalization to real-world dynamic scenarios remain severely limited. Building upon the intuitions of classical TM algorithms, we present the Deep Atmospheric Turbulence Mitigation network (DATUM). DATUM aims to overcome major challenges when transitioning from classical to deep learning approaches. By carefully integrating the merits of classical multi-frame TM methods into a deep network structure, we demonstrate that DATUM can efficiently perform long-range temporal aggregation using a recurrent fashion, while deformable attention and temporal-channel attention seamlessly facilitate pixel registration and lucky imaging. With additional supervision, tilt and blur degradation can be jointly mitigated. These inductive biases empower DATUM to significantly outperform existing methods while delivering a tenfold increase in processing speed. A large-scale training dataset, ATSyn, is presented as a co-invention to enable the generalization to real turbulence. Our code and datasets are available at https://xg416.github.io/DATUM + +# 1. Introduction + +Atmospheric turbulence is a dominant image degradation for long-range imaging systems. Reconstructing images distorted by atmospheric turbulence is an important task for many civilian and military applications. The degradation process can be considered a combination of content-invariant random pixel displacement (i.e., tilt) and random blur. Until recently, reconstruction algorithms have often been in the form of model-based solutions, often relying on modalities such as pixel registration and deblurring. Although there have been many important insights into the problem, e.g., lucky imaging, they are primarily limited to static scenes with slow processing speed. + +With the development of physics-grounded data synthe + +![](images/be9fff2833f96f1f2477b4403a99306723ce3f539185e977878f70db4732cb2d.jpg) +Figure 1. Benchmarking video restoration models for turbulence mitigation on our ATSyn-dynamic dataset. The circles in orange are other video-based TM networks, and the circles in blue are representative video deblurring and general restoration networks. The proposed Deep Atmospheric TURbulence Mitigation network (DATUM) is state-of-the-art while highly efficient. + +sis methods [7, 17, 18, 33, 65, 77], data-driven algorithms have been developed in the past two years. Most existing deep learning methods focus on single-frame problems [24, 32, 34, 44, 45, 48, 49, 53, 71]. Since the degradation is highly ill-posed, the performance of these algorithms is naturally limited, especially when attempting to generalize to real data. On the other hand, multi-frame turbulence mitigation networks [1, 26, 72] have shown greater potential for generalization across a broader spectrum of real-world test scenarios. However, these networks are adapted from generic video restoration methods and do not reflect the insights developed by traditional methods; few turbulence-specific properties are incorporated as inductive biases into their methods. + +For deep learning methods to work on real-world scenarios, two common factors hinder the application of current turbulence mitigation methods: (1) the complexity of current data-driven methods is usually high, which impedes the + +practical deployment of these algorithms, and (2) the data synthesis models are suboptimal, either too slow to produce large-scale and diverse datasets or not accurate enough to represent the real-world turbulence profiles, restricting the generalization capability of the model trained on the data. + +To overcome these pressing issues, we propose the Deep Atmospheric Turbulence Mitigation (DATUM) network and the ATSyn dataset. We offer three contributions: + +- DATUM is the first deep-learning video restoration method customized for turbulence mitigation based on classical insights. By carefully integrating the merits of classical multi-frame TM methods, we propose feature-reference registration, temporal fusion, and the decoupling of pixel rectification and deblurring as effective inductive biases in the multi-frame TM challenge. +- DATUM is the first recurrent model for turbulence restoration. It is significantly more lightweight and efficient than the prior multi-frame TM methods. On both synthetic and real data, DATUM consistently surpasses the SOTA methods while being $10 \times$ faster. +- Through the integration of numerous theoretical and practical improvements in physics modeling over the Zernike-based simulators, we further propose an extensive, real-world inspired dataset ATSyn. Experiments on real-world data show that models trained on ATSyn significantly generalize better than those trained on alternative ones. + +# 2. Related works + +# 2.1. Turbulence modeling + +Atmospheric turbulence simulation spans from computational optics to computer vision-oriented approaches. Optical simulations use split-step methods, which numerically propagate waves through phase screens that represent the atmosphere's spatially varying index of refraction [6, 21, 55, 60]. Despite the existence of moderately faster optical simulations, including brightness function-based simulations [30, 31, 66] or learning-based alternatives [46, 47], the relatively slow speed limits their application in deep learning training [43]. In computer vision simulations, pixels are first displaced according to heuristic correlation functions followed by invariant Gaussian blur [7, 33, 77], offering speed but arguably lacking physical foundations. Recent Zernike-based methods [9, 12, 13, 43] can match the statistics of optics-based simulation, achieving realistic visual quality while maintaining a fast data synthesis speed. It has been applied to turbulence mitigation [24, 25, 44, 72] to facilitate the generalization capability of those models. + +# 2.2. Conventional turbulence mitigation + +Conventional TM algorithms, since [17, 18, 65], mostly treat the TM challenge as a many-to-one restoration problem. Considering that turbulence primarily induces random + +tilt and blur, the common procedure in conventional algorithms is as follows. They first align the input frames to account for pixel displacements, followed by temporal fusion to combine the information from the aligned frames. Subsequently, the residual blur is often considered to be spatially invariant, allowing a blind deconvolution to be applied to produce a visually satisfactory image. + +The tilt rectification is typically achieved in a two-step fashion: construct a tilt-free reference frame, then register every frame with respect to the reference. Since the pixel displacement is assumed to be zero-mean over time [17, 36], the temporal average can be assumed tilt-free [22, 40, 41, 63, 77] and hence be the reference frame. Besides that, low-rank components from all input frames are frequently used [33, 35, 69] as the reference. The registration step can be done by B-spline or optical flow based warping [40, 41, 63, 69, 77] in the spatial domain or phase correction [2, 22, 70] in the phase domain. Because of the "lucky effect" phenomenon [20] in the short-exposure turbulence, the goal of temporal aggregation is to identify and fuse the randomly emerging sharp regions, a technique known as lucky fusion [4]. [33, 42, 77] design spatial descriptors to select and score lucky regions. [2] identify and fuse sharp components in the wavelet space, and [23, 33] apply a similar principle to the sparse components derived through robust PCA. While several methods have been proposed for moving object scenarios [3, 42, 50, 52, 57], they are restricted by their assumption that the dynamic regions are rigid and can be isolated, leaving the remaining static regions to be restored using the conventional pipelines. + +# 2.3. Learning-based turbulence mitigation + +With the rapid advancements in machine learning, numerous recent learning-based methods have demonstrated superior turbulence mitigation results. The majority of them are single-frame TM methods. [32, 45, 49, 53] demonstrate promising performance using generative models with simplified turbulence properties as prior. [34, 48, 71] focus on restoring long-range face images through turbulence. [24, 44] show physics-grounded synthetic data facilitates certain degrees of generalization capability. These single-frame methods do not account for the temporal dimension and can fall short in multi-frame TM scenarios. In contrast, video-based TM algorithms [26, 72] exhibit superior adaptability by leveraging the temporal information, but their designs lack the integration of specific turbulence properties, making their model less efficient. Moreover, [26] only simulated mild turbulence effect, which restricts the generalization capability of their model. Although [72] has achieved better generalization, the point spread function (PSF) implementation is less precise, and the parameter sets are not physics-oriented. Hence, the representative of their turbulence modalities is restricted. + +![](images/db30be6a1962f72241a954041d7f8e174bc833ab184d739a775fe3ad8c6c15ab.jpg) + +![](images/4f6bfae93df77c0cf7c64b9ed2979d61cfbd2f66efbb6810d87079e7bd88399e.jpg) + +![](images/c6eac9e66a532bc48642a5c85500e73322b8a255e16f61721f7be9ea3609cbb0.jpg) +Figure 2. The proposed DATUM network. In this figure, block (a) shows the three common stages proposed by classical TM methods. The corresponding stages in DATUM are shown in block (b), which illustrates the forward time process of the $t$ -th frame. The dashed line means the information passing from other temporal directions and frames. Block (c), (d), and (e) demonstrate the DAAB, GRUM, and MTCSA modules, respectively, where the input features are marked by green, and the output features are marked by red. + +# 3. Proposed method + +# 3.1. Insights from Classical Methods + +Image degradation by atmospheric turbulence can be roughly described by a compositional operation of the blur $\mathcal{B}$ and the tilt $\mathcal{T}$ via the relationship $\mathbf{I} = [\mathcal{B} \circ \mathcal{T}](\mathbf{J}) + \mathbf{n}$ , where $\mathbf{J}$ is the clean image, $\mathbf{I}$ is the distorted image, and $\mathbf{n}$ is the noise term. Traditional algorithms handle turbulence in three steps, as illustrated in Fig. 2: + +- Frame-to-reference registration [77], where a reference frame is constructed from the observed images and all images are registered with respect to the reference using optical flow. In strong turbulence or dynamic scenes, constructing a reference is often difficult. +- Lucky image fusion [2, 27], where a "lucky" image is constructed by collecting the sharpest and most consistent patches from the inputs. However, if turbulence is strong, identifying lucky patches can be difficult. +- Blind deconvolution [42], where a final blind deconvolution algorithm is employed to sharpen the lucky image. The success and failure of this step depend heavily on how spatially uniform the blur in the lucky image is. Oftentimes, since the blur is spatially varying, the perfor + +mance of blind deconvolution is limited. + +While each step is important each has its limitations, motivating us to develop end-to-end trained networks to approximate these functions. Empowered by training on our physical-grounded dataset, our network enjoys the inductive biases of those insights while avoiding their limitations. + +# 3.2. DATUM network + +# 3.2.1 Overview + +The block diagram of the DATUM network is depicted in Fig. 2. We first summarize these three components and describe them in detail in the next subsections. + +Feature-to-reference registration. This component is analogous to the classical frame-to-reference registration. For each input frame $I_{t}$ at time $t$ , we first extract three levels of features $f_{t}^{\{1,2,3\}}$ . We propose the Deformable Attention Alignment Block (DAAB) to register the high-level feature $f_{t}^{3}$ to a previously hidden reference map $r_{t-1}^{\prime}$ . We also propose the Gated Reference Update Module (GRUM) updates this reference feature recurrently, which is inspired by the gated recurrent unit [5, 15] and illustrated in Fig. 2. + +Temporal fusion. This component is analogous to the + +classical lucky fusion step. The registered feature $f_{t}$ , together with $r_{t-1}'$ and $f_{t}^{3}$ , are fused by a new Deep Integration Module (DIM). DIM consists of a series of Residual Dense Blocks (RDB) [73] and is used to produce the forward embedding $e_{t}^{fw}$ . Since $e_{t}^{fw}$ is a deep feature, it is presumed to be free of tilt and is thus utilized for updating the reference feature for the subsequent frame. After the bidirectional recurrent process, we perform a temporal fusion of $e_{t}^{fw}$ by augmenting it with the backward embedding $e_{t}^{bw}$ and bidirectional embeddings from neighboring frames. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA) module for this purpose. + +Post processing. In the final stage, the temporally fused features are decoded to form the turbulence-free image. This decoding involves a twin of decoders. The first predicts a reverse tilt map that rectifies the shallow features, and the second subsequently reconstructs the clean image. + +# 3.2.2 components + +Feature registration via Deformable Attention Alignment Block (DAAB). In classical methods, a crucial stage for turbulence mitigation is registering the input frames to the tilt-free reference frame. This reference frame is usually obtained by temporal averaging or using variants of principle component analysis. However, these methods may not be applicable to dynamic videos. Since learning-based video TM is possible [26, 72], the deep feature of a video TM network can be considered tilt-mitigated to work as the reference feature for the next input feature. This section explains our method to use deformable attention to facilitate feature registration in our DATUM network. + +The computations in the DDAB are summarized in Algorithm 1, where $(A;B)$ denotes warping $A$ by deformation field $B$ , $\phi (A;p)$ denotes sampling $A$ by positions $p$ . $W_{K}$ , $W_{V}$ , $W_{Q}$ , and $W$ are linear projections on the channel dimension, and $\sigma$ denotes the SoftMax. The optical flow at line 3 is estimated with the SPyNet [54], and lines 6-11 are inspired by the guided deformation attention (GDA) [38]. + +Temporal fusion via Multi-head Temporal Channel Self-Attention (MTCSA). After feature registration and deep integration, we propose to augment the embedding with contra-directional information, which is essential to ensure consistent restoration quality across various frames. In addition, like classical methods, a spatially adaptive fusion with adjacent frames is advantageous. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA), as illustrated in Fig. 2. The MTCSA begins by concatenating channels from multiple frames, followed by a $1 \times 1$ convolution to shrink the channel dimension. Separable convolution is used to construct the spatially varying query, key, and value on the temporal and channel dimensions, and the dynamic fusion is facilitated by self-attention. Finally, a + +Algorithm 1 Deformation Attention Alignment Block +1: Input: Current frame feature $f_{t}^{3}$ , reference feature $r_{t-1}^{\prime}$ and alignment flow from last frame $O_{t-1}^{f\rightarrow r}$ , two downsampled frames $I_{t}$ and $I_{t-1}$ +2: Output: Updated feature $f_{t}$ and flow $O_{t}^{f\rightarrow r}$ $\triangleright$ Estimate rough deformation field $\hat{O}_{t}^{f\rightarrow r}$ that register feature $f_{t}^{3}$ to reference $r_{t-1}^{\prime}$ +3: Estimate the optical flow $O_{t\rightarrow t-1}^{f}$ from $I_{t}$ and $I_{t-1}$ . +4: $\hat{O}_{t}^{f\rightarrow r} \gets O_{t-1}^{f\rightarrow r} + (O_{t\rightarrow t-1}^{f}\hat{O}_{t-1}^{f\rightarrow r})$ +5: Pre-align $\hat{f}_{t} \gets (\hat{O}_{t}^{f\rightarrow r}, f_{t}^{3})$ $\triangleright$ Register input feature to reference frame using multi-group multi-head deformation attention +6: for all group $g$ do + $\triangleright$ Predict offsets $o_{t}^{(g)}$ +7: $\Delta o_{t}^{(g)} \gets \text{RDB}(\text{Concat}(\hat{f}_{t}, r_{t-1}', \hat{O}_{t}^{f\rightarrow r}))$ +8: $o_{t}^{(g)} \gets \hat{O}_{t}^{f\rightarrow r} + \Delta o_{t}^{(g)}$ $\triangleright$ Compute the $g$ -th aligned feature $\hat{f}_{t}^{(g)}$ : +9: $K^{(g)} \gets \phi(f_{t}^{3}W_{K}; o_{t}^{(g)})$ , $V^{(g)} \gets \phi(f_{t}^{3}W_{V}; o_{t}^{(g)})$ +10: $Q \gets r_{t-1}'W_{Q}, \hat{f}_{t}^{(g)} \gets \sigma(QK^{(g)T}/\sqrt{C})V^{(g)}$ +11: end for +12: Fuse all groups $f_{t} \gets \text{Concat}(\{\hat{f}_{t}^{(g)}\})W$ +13: Update final alignment flow $O_{t}^{f\rightarrow r}$ by mean of $\{o_{t}^{(g)}\}$ +14: Output $f_{t} \gets f_{t} + \text{FeedForward}(f_{t})$ + +residual connection is used to stabilize training. Considering the quadratic complexity of MTCSA relative to window size, this size is kept moderate. Additionally, we integrate a hard-coded positional embedding wherein features from the focal frame are positioned at the end. This strategy is essential for boundary frames with disproportionate neighboring frames on either side. + +Twin decoder and loss function Given the refined feature embedding from the MTCSA, we also developed a twin decoder to progressively remove the tilt and blur, as shown in Fig. 2. The decoder uses transposed convolution for upsampling and channel attention blocks (CAB) [68] for decoding. Before decoding in higher levels, the deep features are concatenated with the shallow features to facilitate the residual connection like a typical UNet [56]. Since the deep and shallow features are misaligned by the random tilt $\mathcal{L}$ , we propose to first rectify the shallow features by the estimated inverse tilt field $\hat{\mathcal{T}}^{-1}$ estimated in the first stage. The tilt-rectification is optimized by reducing the loss: + +$$ +\mathcal {L} _ {\text {t i l t}} = \mathcal {L} _ {\text {c h a r}} \left(\boldsymbol {I} _ {\mathrm {G T}}, \left(\boldsymbol {I} _ {\text {t i l t}}; \tilde {\mathcal {T}} ^ {- 1}\right)\right) \tag {1} +$$ + +Where $\mathcal{L}_{\mathrm{char}}$ denotes the Charbonnier loss [10], $I_{\mathrm{GT}}$ is the input frame and $I_{\mathrm{tilt}}$ is the tilt-only frame that can be produced without additional cost by our data synthesis method. In the second stage, the rectified shallow features are jointly decoded with the deep features to generate the final recon + +![](images/8d03611d2c083b0db28c75ed87c410e3b385f2854394b2318c89e1ed1c00098e.jpg) +Figure 3. Scheme of our data synthesis method. + +struction $\hat{\pmb{I}}$ . The overall loss function is computed by: + +$$ +\mathcal {L} = \alpha_ {1} \mathcal {L} _ {\text {t i l t}} + \alpha_ {2} \mathcal {L} _ {\text {c h a r}} (\boldsymbol {I} _ {\mathrm {G T}}, \hat {\boldsymbol {I}}) \tag {2} +$$ + +where weights $\alpha_{1}$ and $\alpha_{2}$ are empirically set to 0.2 and 0.8. + +# 3.3. ATSyn dataset + +# 3.3.1 Physics-based data synthesis + +As introduced previously, the ground truth image $J$ is first geometrically distorted and then blurred to produce the degraded image $I$ in our synthesis method. Data synthesis for the turbulence effect essentially requires a physics-grounded representation of and. We adopted the Zernike-based turbulence simulator [12, 13] and improved it with non-trivial modifications. Fig. 3 presents the scheme of our implementation. The and is generated from the phase distortion represented by Zernike polynomials $\{\mathbf{Z}_i\}$ [51] as the basis, with corresponding coefficients $\mathbf{a}_i$ where $i$ ranging from 1 to 36. Among all 36 coefficients, $i = 1$ denotes the current component, $i = 2, 3$ controls the by a constant scale, and the rest high order Zernike coefficients contribute to the blur effect. + +The phase distortion can be assumed as a wide sense stationary (WSS) random field [13]. Hence, it can be sampled with Fast Fourier Transform (FFT) from white Gaussian noise and the autocorrelation map. Transforming the phase distortion to the spatial domain point spread functions (PSF) can be achieved by the Phase-to-Space (P2S) transform, which transforms the sampled Zernike coefficients to spatial coefficients $\beta$ , assuming the PSFs can be represented by a low-rank approximation of 100 basis $\psi$ and corresponding $\beta$ . The overall degradation in the spatial domain is implemented by + +$$ +\boldsymbol {I} = \sum_ {k = 1} ^ {1 0 0} \psi_ {k} * (\boldsymbol {\beta} _ {k} \cdot (\boldsymbol {J};)) + \boldsymbol {n}, \tag {3} +$$ + +where $\circ$ denotes the depth-wise convolution. Although subtle, this fundamentally generates more reliable degradation than the simulator in [72], as elaborated in [14]. Except for this, our correlation kernels are more precise by incorporating the continuous $C_n^2$ path technique [11]. + +# 3.3.2 Guideline of implementation + +With the proposed simulator, we created the ATSyn dataset to match various real-world turbulence conditions and benchmark deep neural networks for turbulence mitigation. This dataset is segmented into two distinct subsets based on scene type: the ATSyn-dynamic and ATSyn-static. The dynamic sequences contain camera or object motion, whereas the static sequences are each associated with only one underlying clean image. We adopted parameters including focal length, F-number, distance, wavelength, scene size, and sensor resolution to control the simulation. In comparison with the synthetic dataset introduced in [72], which utilized the $D / r_0$ [19] and empirically chosen blur kernel size, our dataset's parameter space more closely aligns with actual camera settings, making it more representative. + +ATSyn-dynamic contains 4,350 training and 1,097 validation instances synthesized from [26, 58], and ATSyn-static contains 2,000 and 1,000 instances synthesized from the Places dataset [75] for training and validation, respectively. Those instances have varying numbers of frames, each with a distinct turbulence parameter set. Besides ground truth and fully degraded videos, ATSyn further provides associated $\mathcal{T}$ -only videos to facilitate the training of $\mathcal{L}_{\mathrm{tilt}}$ in Eq. 1. We categorize the turbulence parameters by three levels: weak, medium, and strong. The range of turbulence parameters is determined by matching with a largescale, long-range video dataset [16] and other real-world videos, with more details in the supplementary document. + +# 4. Experiments + +# 4.1. Training setting + +This section describes how we trained our DATUM and other models. Except for turbulence mitigation networks [26, 44, 72], we also benchmarked several representative video restoration [37, 38] and deblurring networks [74, 76] for a more thorough comparison. + +To train the proposed model, we used the Adam optimizer [29] with the Cosine Annealing learning rate schedule [39]. The initial learning rate is $2 \times 10^{-4}$ , and batch size is 8. All dynamic scene TM networks in this experiment are trained end-to-end from scratch for 800K iterations. To get their static-scene variant, we fine-tuned them on the static-scene modality with half the initial learning rate and 400K iterations. We clip the gradient if the L2 norm exceeds 20 to prevent gradient explosion during inference. + +We trained the ESTRNN [74], RNN-MBP [76], and RVRT [74] with the same configuration as DATUM. The number of input frames of DATUM and ESTRNN during training is set to 30 for ATSyn-dynamic and 36 for ATSyn-static. Since RNN-MBP and RVRT require much more resources to train, the number of input frames is set to 16. Because TSRWGAN [26], TMT [72], and TurbNet [44] are + +
MethodsTurbNet [44]TSRWGAN [26]VRT [37]TMT [72]RNN-MBP [76]ESTRNN [74]RVRT [38]DATUM [ours]
PSNR24.222926.326227.611427.741927.715227.346927.851228.5875
SSIMcw0.82300.85960.86910.87410.87300.86170.87880.8803
+ +Table 1. Preliminary study: evaluate on TMT's synthetic dynamic scene data [72]. ${\mathrm{{SSIM}}}_{\mathrm{{CW}}}$ denotes Complex Wavelet SSIM. + +
Turbulence LevelWeakMediumStrongOverallCost
MethodsPSNR\( SSIM_{CW} \)PSNR\( SSIM_{CW} \)PSNR\( SSIM_{CW} \)PSNR\( SSIM_{CW} \)SizeFPS
TSRWGAN [26]27.08440.857526.70460.851425.42300.837226.45410.849346.280.87
TMT [72]29.11830.883628.50500.879126.97440.855228.26650.873426.040.80
VRT [37]28.84530.879728.26280.876926.74920.850628.01790.869918.320.17
RNN-MBP [76]27.92430.869927.47420.864226.08120.849527.21610.861814.161.14
ESTRNN [74]28.98050.875028.33380.869726.88970.846328.13470.86452.46827.65
RVRT [38]29.60800.884528.96050.880627.53440.859528.76720.875613.502.43
DATUM [ours]30.20580.885729.62030.882928.25500.864029.42220.87815.7549.17
+ +all designed for turbulence mitigation, we trained them following the original paper and public code. + +# 4.2. Comparison on dynamic scene modality + +We first trained and evaluated all networks for comparison on a previous Zernike-based synthetic dataset [72] for preliminary study. We choose PSNR and Complex Wavelet Structure Similarity [59] (CW-SSIM) as the criterion in this paper, and the reason for selecting CW-SSIM rather than SSIM is provided in the supplementary document. The result in Table 1 shows our DATUM outperforms the previous state-of-the-art TMT [72] with $5 \times$ fewer parameters and over $10 \times$ faster inference speed. We also benchmark a representative single-frame TM network [44] to demonstrate the superiority of multi-frame TM methods. Next, we present extensive results from the ATSyn-dynamic dataset in Table 2. Our model outperforms all other networks by a significant margin, while it is the second smallest network among all models and the most efficient network among all existing turbulence mitigation networks. + +# 4.3. Comparison on static scene modality + +When training on the ATSyn-static, the loss is computed between the single ground truth and all output frames. For testing, we instead calculate the average score of the central four frames in the entire output sequence (for single-directional models, we use the last 4). We evaluated the performance on the ATSyn-static and the turbulence text dataset [64], and the result is shown in Table 3. The turbulence text dataset contains 100 sequences of text images, each a static scene of degraded text pattern captured at 300 meters or farther. Real-world turbulence videos do not have ground truth, while [64] uses the accuracy score of pretrained text recognition models CRNN [61], DAN [67], and ASTER [62] as metrics, where a better turbulence mitigation offers better recognition performances. Our model is + +Table 2. Performance comparison on the ATSyn-dynamic set, we list the image quality scores on different turbulence levels and frame-wise resource consumption (measured with $960\times 540$ frame sequences on RTX 2080 Ti). + +
BenchmarkATSyn-staticTurb-Text (%)
MethodsPSNRSSIMCWCRNN/DAN/ASTER
TSRWGAN [26]23.160.840760.30 / 73.90 / 74.40
TMT [72]24.510.871680.90 / 87.25 / 88.55
VRT [37]24.270.864176.30 / 84.45 / 83.60
RNN-MBP [76]24.640.877551.35 / 65.00 / 64.30
ESTRNN [74]26.230.901787.10 / 97.80 / 96.95
RVRT [38]25.710.887686.40 / 89.00 / 89.20
DATUM [ours]26.760.910293.55 / 97.95 / 97.25
+ +Table 3. Static scene modality. CRNN/DAN/ASTER are the text recognition rates of these three models from the restored images. + +trained on a wide range of turbulence conditions and generic data, without specific augmentation tricks, yet performs on par with the best systems in the $\mathrm{UG2 + }$ turbulence challenge [64]. Our model outperforms other networks trained on the ATSyn-static dataset by an even larger margin. + +# 4.4. Ablation study + +Our ablation study examines key elements that introduce effective inductive biases of our model, including the use of additional frames, recurrent reference updating, feature-reference registration, and multi-frame embedding fusion. + +Influence of the number of input frames. The number of input frames for both training and inference matters for recurrent-based networks, especially in turbulence mitigation. Since turbulence degradation is caused by zero-mean stochastic phase distortion, the more frames the network can perceive, the better the non-distortion state it can evaluate. This is particularly valid for static scene sequences, where the pixel-level turbulence statistics are much easier to track and analyze through time. + +We trained two models with 12-frame and 24-frame inputs and presented their respective performance during inference in Fig. 4. This figure shows in the temporal range of our experimental setting, a positive correlation between the + +![](images/24f4efb1ce1802add5e88cf059afc6a01f759f19e96826082b1bc99e128a5a5e.jpg) +(a) On ATSyn-dynamic +Figure 4. Influence of the number of input frames. + +![](images/b136392c75f597b2ffde52b0ca9b4a773b577b11e927f9b35fad94a1b3b42a63.jpg) +(b) On ATSyn-static + +performance and the number of input frames always exists, especially on the static scene modality where an over 1 dB boost can be obtained with more frames. This phenomenon suggests one of the success factors for turbulence mitigation is the capability of fusing more frames, similar to the video super-resolution problem [8]. + +Influence of DAAB, MTCSA, GRUM, and twin decoder. The design of DAAB and MTCSA are inspired by pixel registration and lucky fusion in the conventional TM methods. Although our spatial registration and temporal fusion are implemented at the feature level, they are still effective in turbulence mitigation, as shown in Table 4. + +While the MTCSA fuses embeddings from multiple frames in a sliding window manner, determining the optimal window size is crucial. If the window size is too small, the temporal fusion only relies on the implicit temporal propagation by the recurrent unit, limiting the performance; if the window size is too large, because of the quadratic complexity along the temporal dimension, the MTCSA becomes very resource-demanded, and the network becomes less flexible to deal with a small number of input frames. We investigated the temporal window size of the MTCSA module, as shown in Fig. 4, where we found that five frames meet the trade-off between performance and efficiency. + +The GRUM utilizes a gating mechanism in the recurrent network to facilitate more extended temporal dependency [5, 15]. It fuses the reference feature with deeper embeddings in a more adaptive manner, which also turns out to be effective. Finally, in the post-processing stage, we compared the two-stage twin decoder with the one-stage plain decoder. We found that by incorporating additional supervision and rectifying shallow features in the decoding stage, better performance can be obtained. + +# 4.5. Comparison on real-world data + +In this section, we demonstrate our data's generalization capability qualitatively and quantitatively on real-world data. + +Given the impracticality of directly obtaining ground truth images for real-world turbulence scenarios, quantitative performance evaluation typically involves applying restored images to downstream tasks, as noted in [24, 44, 49]. Adopting this approach, we evaluated various restoration methods using the turbulence text dataset. The results are + +
ComponentsPSNR / SSIMSizeGMACs
Base (MTCSA-1f)28.62 / 0.84653.912261.5
Base (MTCSA-3f)28.79 / 0.84974.131272.7
* Base (MTCSA-5f)28.87 / 0.85224.768304.2
Base (MTCSA-7f)28.92 / 0.85325.808358.1
+ GRUM29.06 / 0.85764.894317.7
+ DAAB29.33 / 0.86385.241351.8
+ Twin Decoder29.42 / 0.86475.754372.7
+ +Table 4. Ablation study. We conducted experiments on the ATSdynamic set by adding each proposed component progressively and observed a constant performance improvement. + +![](images/44f184a9f854d372e63247ee9fc3415837a7bc2fd5a4cf0ce0a7423ab5ae499d.jpg) + +Figure 5. Comparison on the real-world turbulence-text dataset. The metric is the average text recognition accuracy of CRNN, DAN, and ASTER tested on the restored images. + +
Face RetrievalDegradedSimulator in [72]Our simulator
Rank 537.75%38.83%39.18%
Rank 1040.59%41.83%42.18%
Rank 2045.29%46.40%46.70%
+ +Table 5. Face recognition results on a subset of the BRIAR dataset. + +presented in Fig. 5, revealing two key insights: 1) our proposed ATSyn-static dataset enhances the generalization capabilities of other TM methods. 2) on both synthetic and real-world sequences, DATUM consistently outperforms other models trained on our dataset. To further validate the effectiveness of our modifications to the Zernike-based simulator, we extensively compared DATUM trained on our ATSyn-dynamic dataset and TMT's dataset [72]. We first enhance the long-range subset in the BRIAR dataset [16] by those two versions, run the same pre-trained face recognition model [28] on the enhanced images, and it yields the result provided in Table 5. We can observe the ATSyndynamic dataset improved network performance on realworld videos compared to the [72] dataset. These comparisons demonstrate our method facilitates better generalization of both scene types than other existing datasets. + +We also provide a qualitative comparison in Fig. 6 and 7 to demonstrate the advance of our network and dataset. By comparing the same networks trained by our data and their original checkpoints, our data enhances their general + +![](images/11f50f6364043a22b219a8a790013a057b1a203022b111ae07affc0420bde299.jpg) +(a) Input frame + +![](images/b02934d5566d9c1a0450c64ce0038bc80fdf1df1d2ac66beb3e3c3d7047fba43.jpg) +(b)TSRWGAN [26] + +![](images/7945235633030d621b396547ab52f3d8de409187955e7182f0f9fbacdde8927f.jpg) +(c) TMT [72] + +![](images/8b956273d4c1e2c7a197e36f370680736cf7e7a56fb7c24c9f047822a16d2b98.jpg) +(d) NDIR [36] + +![](images/fde5272a0329cdc6b2ae33399cb930b695cd3f8b60211c45cf06f0d1177a1d29.jpg) +(e) TurbNet [44] + +![](images/f84d080e599deb5f2aa616fd4346f1b39b0d142a271c2176884bdce92c479cd0.jpg) +(f) AT-DDPM [49] + +![](images/1d1ae5f63c29e0cbf0994f9635a6846e4c84beadef76eb890fbe974226e631ea.jpg) +(g) PiRN [24] + +![](images/8ae5beda7947d956ce5561610cd366af1654cc9d096fc734300474cb4ec46d8f.jpg) +(h) DATUM [Ours] + +![](images/ef83ec53b5a4451c52280d7703d8a0d6c87394f99c9f1a74c1944ac2500dd35a.jpg) +(i) TSRWGAN* [26] + +![](images/307334fd638fdbf97a50d6f42efb48e15a5a126953cc44c4e13e2e35b95b2330.jpg) +(j) TMT* [72] + +![](images/eb79700b3cf043568bd601797c2b451df94c989b0728eca25a3f1550530112c4.jpg) +(k) RNN-MBP* [44] + +![](images/c7e1ccdab8c6fb9a437b26b0c0e6849fee81717c824b7fd4d674cd096240ed07.jpg) +(1) RVRT* [38] + +![](images/7ee45eb75f46078dce61b2d563e3cd928c002746d407b5086e2e969a99bd513b.jpg) +(m) VRT* [26] + +![](images/68406b069eda7815eb60651effa10e427407a6736dc3a9237f6c0d55a781d633.jpg) +(n) ESTRNN* [74] + +![](images/102b92634325f2fa68e838f4990b3d7478ddb0045fc43d81eedab33f62a809f7.jpg) +Figure 6. Qualitative comparison on the turbulence-text dataset [64]. The input frame (a) is the 49th frame of the 94th sequence in [64]. Figures on the top row are restoration results of corresponding TM methods using their original model and checkpoints. Figures on the bottom row are TM or general restoration models (marked by *) trained on our ATSyn-static dataset. +(a) Input frame + +![](images/0ae8fde4b4da2e4f24782b8ee3ed891216bb3adffd9a3cb0be9ce9ad35ee0606.jpg) +(b) TSRWGAN [26] + +![](images/cb68a2199c3d841b1cad6d1d99ebe08d52a761816b426a0e6263eb694d7bc1a6.jpg) +(c) TMT [72] + +![](images/ca20368a06c1d433ea9b3cd9aa7156dc017c89689f4c1eade3590dc88573b9eb.jpg) +(d) TurbNet [44] + +![](images/112abf924aa029cd26f85e9cfccfb3716b1e094199fbf71f3bb8bd1f65a3f446.jpg) +(e) ATNet [48] + +![](images/dc555926ea603da5866dfe430ee97783b51c9531cd2c740831a71fab2ecb18a6.jpg) +(f) AT-DDPM [49] + +![](images/4acc2c856ab26a7bee5ab331c0a7c7dbf179e632e2e286486bc65cc9d2af0ed8.jpg) +(g) PiRN-SR [24] + +![](images/fbda63c23816f95cfe3927c6036e1f69270834413f3d73966fac624e47d6db58.jpg) +(h) DATUM* [Ours] + +![](images/e74ff30d6e82b14fdfc08fda84ad523635b8be86847e505f658aa6e1b6876bb1.jpg) +(i) TSRWGAN* [26] +Figure 7. Qualitative comparison on a dynamic scene sample from the BRIAR dataset [16]. Figures on the top row are the original restoration results of corresponding TM methods. Figures on the bottom row are models (marked by *) trained on ATSyn-dynamic dataset. + +![](images/cad4144615c5dd9026084de3040e02ef46569c6436e3c8d7bc0aa97283707289.jpg) +(j) $\mathrm{TMT^{*}}$ [72] + +![](images/fb95c094045329d984e7412454e0a2059ec989af97f749628338cf3227712902.jpg) +(k) RNN-MBP* [44] + +![](images/175c97c7f225b47dfdfd2f0e5bafd856efced2dcc7611be9dd256840e7c18d35.jpg) +(1) RVRT* [38] + +![](images/15b04559f0959afd180fcc6a860a5366bb7da60107f3ff8711b7fd88e0941140.jpg) +(m) VRT* [26] + +![](images/a8e0738d49e7f78275f2c1b2a374a7d05d25c64cc422124d23fd3d953311eca0.jpg) +(n) ESTRNN* [74] + +ization capability. On the other hand, by comparison among all networks trained on our dataset, our model significantly outperforms other networks. + +# 5. Conclusion + +In this research, we introduced a novel approach leveraging deep learning to address the enduring challenge of atmospheric turbulence mitigation. Taking a translational perspective, our method integrated the strengths of traditional turbulence mitigation (TM) techniques into a neural network architecture. This fusion elevated our network to state-of-the-art performance while ensuring significantly enhanced efficiency and speed compared to prior TM models. Additionally, we developed a physics-based synthesis method that accurately models the degradation process. + +This led to the creation of an extensive synthetic dataset covering a diverse spectrum of turbulence effects. Utilizing this dataset, we facilitated a stronger generalization capability for data-driven models than other existing datasets. + +Acknowledgments and Disclosure of Funding The research is based upon work supported in part by the Intelligence Advanced Research Projects Activity (IARPA) under Contract No. 2022-21102100004, and in part by the National Science Foundation under the grants CCSS-2030570 and IIS-2133032. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of IARPA, or the U.S. Government. The U.S. Government is authorized to reproduce and distribute reprints for governmental purposes notwithstanding any copyright annotation therein. + +# References + +[1] Nantheera Anantrasirichai. Atmospheric turbulence removal with complex-valued convolutional neural network. 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Chan1 \n1School of Electrical and Computer Engineering, Purdue University 2Samsung Research America \n{zhan3275, nchimitt, chi14, stanch}@purdue.edu, m940421@gmail.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "spans": [ + { + "bbox": [ + 143, + 213, + 192, + 225 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 290, + 514 + ], + "type": "text", + "content": "Recovering images distorted by atmospheric turbulence is a challenging inverse problem due to the stochastic nature of turbulence. Although numerous turbulence mitigation (TM) algorithms have been proposed, their efficiency and generalization to real-world dynamic scenarios remain severely limited. Building upon the intuitions of classical TM algorithms, we present the Deep Atmospheric Turbulence Mitigation network (DATUM). DATUM aims to overcome major challenges when transitioning from classical to deep learning approaches. By carefully integrating the merits of classical multi-frame TM methods into a deep network structure, we demonstrate that DATUM can efficiently perform long-range temporal aggregation using a recurrent fashion, while deformable attention and temporal-channel attention seamlessly facilitate pixel registration and lucky imaging. With additional supervision, tilt and blur degradation can be jointly mitigated. These inductive biases empower DATUM to significantly outperform existing methods while delivering a tenfold increase in processing speed. A large-scale training dataset, ATSyn, is presented as a co-invention to enable the generalization to real turbulence. Our code and datasets are available at https://xg416.github.io/DATUM" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 536, + 128, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 128, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 128, + 550 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 701 + ], + "type": "text", + "content": "Atmospheric turbulence is a dominant image degradation for long-range imaging systems. Reconstructing images distorted by atmospheric turbulence is an important task for many civilian and military applications. The degradation process can be considered a combination of content-invariant random pixel displacement (i.e., tilt) and random blur. Until recently, reconstruction algorithms have often been in the form of model-based solutions, often relying on modalities such as pixel registration and deblurring. Although there have been many important insights into the problem, e.g., lucky imaging, they are primarily limited to static scenes with slow processing speed." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "With the development of physics-grounded data synthe" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 315, + 230, + 525, + 388 + ], + "blocks": [ + { + "bbox": [ + 315, + 230, + 525, + 388 + ], + "lines": [ + { + "bbox": [ + 315, + 230, + 525, + 388 + ], + "spans": [ + { + "bbox": [ + 315, + 230, + 525, + 388 + ], + "type": "image", + "image_path": "be9fff2833f96f1f2477b4403a99306723ce3f539185e977878f70db4732cb2d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 399, + 547, + 467 + ], + "lines": [ + { + "bbox": [ + 305, + 399, + 547, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 399, + 547, + 467 + ], + "type": "text", + "content": "Figure 1. Benchmarking video restoration models for turbulence mitigation on our ATSyn-dynamic dataset. The circles in orange are other video-based TM networks, and the circles in blue are representative video deblurring and general restoration networks. The proposed Deep Atmospheric TURbulence Mitigation network (DATUM) is state-of-the-art while highly efficient." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 494, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 547, + 662 + ], + "type": "text", + "content": "sis methods [7, 17, 18, 33, 65, 77], data-driven algorithms have been developed in the past two years. Most existing deep learning methods focus on single-frame problems [24, 32, 34, 44, 45, 48, 49, 53, 71]. Since the degradation is highly ill-posed, the performance of these algorithms is naturally limited, especially when attempting to generalize to real data. On the other hand, multi-frame turbulence mitigation networks [1, 26, 72] have shown greater potential for generalization across a broader spectrum of real-world test scenarios. However, these networks are adapted from generic video restoration methods and do not reflect the insights developed by traditional methods; few turbulence-specific properties are incorporated as inductive biases into their methods." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "For deep learning methods to work on real-world scenarios, two common factors hinder the application of current turbulence mitigation methods: (1) the complexity of current data-driven methods is usually high, which impedes the" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2889" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "content": "practical deployment of these algorithms, and (2) the data synthesis models are suboptimal, either too slow to produce large-scale and diverse datasets or not accurate enough to represent the real-world turbulence profiles, restricting the generalization capability of the model trained on the data." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 133, + 286, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 133, + 286, + 168 + ], + "spans": [ + { + "bbox": [ + 47, + 133, + 286, + 168 + ], + "type": "text", + "content": "To overcome these pressing issues, we propose the Deep Atmospheric Turbulence Mitigation (DATUM) network and the ATSyn dataset. We offer three contributions:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 169, + 286, + 384 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 169, + 286, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 169, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 47, + 169, + 286, + 251 + ], + "type": "text", + "content": "- DATUM is the first deep-learning video restoration method customized for turbulence mitigation based on classical insights. By carefully integrating the merits of classical multi-frame TM methods, we propose feature-reference registration, temporal fusion, and the decoupling of pixel rectification and deblurring as effective inductive biases in the multi-frame TM challenge." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 252, + 286, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 286, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 286, + 312 + ], + "type": "text", + "content": "- DATUM is the first recurrent model for turbulence restoration. It is significantly more lightweight and efficient than the prior multi-frame TM methods. On both synthetic and real data, DATUM consistently surpasses the SOTA methods while being " + }, + { + "bbox": [ + 47, + 252, + 286, + 312 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 47, + 252, + 286, + 312 + ], + "type": "text", + "content": " faster." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 312, + 286, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 286, + 384 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 286, + 384 + ], + "type": "text", + "content": "- Through the integration of numerous theoretical and practical improvements in physics modeling over the Zernike-based simulators, we further propose an extensive, real-world inspired dataset ATSyn. Experiments on real-world data show that models trained on ATSyn significantly generalize better than those trained on alternative ones." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 396, + 135, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 135, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 135, + 407 + ], + "type": "text", + "content": "2. Related works" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 416, + 168, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 168, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 168, + 428 + ], + "type": "text", + "content": "2.1. Turbulence modeling" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 434, + 286, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 286, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 286, + 649 + ], + "type": "text", + "content": "Atmospheric turbulence simulation spans from computational optics to computer vision-oriented approaches. Optical simulations use split-step methods, which numerically propagate waves through phase screens that represent the atmosphere's spatially varying index of refraction [6, 21, 55, 60]. Despite the existence of moderately faster optical simulations, including brightness function-based simulations [30, 31, 66] or learning-based alternatives [46, 47], the relatively slow speed limits their application in deep learning training [43]. In computer vision simulations, pixels are first displaced according to heuristic correlation functions followed by invariant Gaussian blur [7, 33, 77], offering speed but arguably lacking physical foundations. Recent Zernike-based methods [9, 12, 13, 43] can match the statistics of optics-based simulation, achieving realistic visual quality while maintaining a fast data synthesis speed. It has been applied to turbulence mitigation [24, 25, 44, 72] to facilitate the generalization capability of those models." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 235, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 235, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 235, + 671 + ], + "type": "text", + "content": "2.2. Conventional turbulence mitigation" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 286, + 713 + ], + "type": "text", + "content": "Conventional TM algorithms, since [17, 18, 65], mostly treat the TM challenge as a many-to-one restoration problem. Considering that turbulence primarily induces random" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "tilt and blur, the common procedure in conventional algorithms is as follows. They first align the input frames to account for pixel displacements, followed by temporal fusion to combine the information from the aligned frames. Subsequently, the residual blur is often considered to be spatially invariant, allowing a blind deconvolution to be applied to produce a visually satisfactory image." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 157, + 545, + 433 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 433 + ], + "type": "text", + "content": "The tilt rectification is typically achieved in a two-step fashion: construct a tilt-free reference frame, then register every frame with respect to the reference. Since the pixel displacement is assumed to be zero-mean over time [17, 36], the temporal average can be assumed tilt-free [22, 40, 41, 63, 77] and hence be the reference frame. Besides that, low-rank components from all input frames are frequently used [33, 35, 69] as the reference. The registration step can be done by B-spline or optical flow based warping [40, 41, 63, 69, 77] in the spatial domain or phase correction [2, 22, 70] in the phase domain. Because of the \"lucky effect\" phenomenon [20] in the short-exposure turbulence, the goal of temporal aggregation is to identify and fuse the randomly emerging sharp regions, a technique known as lucky fusion [4]. [33, 42, 77] design spatial descriptors to select and score lucky regions. [2] identify and fuse sharp components in the wavelet space, and [23, 33] apply a similar principle to the sparse components derived through robust PCA. While several methods have been proposed for moving object scenarios [3, 42, 50, 52, 57], they are restricted by their assumption that the dynamic regions are rigid and can be isolated, leaving the remaining static regions to be restored using the conventional pipelines." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 443, + 506, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 443, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 306, + 443, + 506, + 455 + ], + "type": "text", + "content": "2.3. Learning-based turbulence mitigation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 712 + ], + "type": "text", + "content": "With the rapid advancements in machine learning, numerous recent learning-based methods have demonstrated superior turbulence mitigation results. The majority of them are single-frame TM methods. [32, 45, 49, 53] demonstrate promising performance using generative models with simplified turbulence properties as prior. [34, 48, 71] focus on restoring long-range face images through turbulence. [24, 44] show physics-grounded synthetic data facilitates certain degrees of generalization capability. These single-frame methods do not account for the temporal dimension and can fall short in multi-frame TM scenarios. In contrast, video-based TM algorithms [26, 72] exhibit superior adaptability by leveraging the temporal information, but their designs lack the integration of specific turbulence properties, making their model less efficient. Moreover, [26] only simulated mild turbulence effect, which restricts the generalization capability of their model. Although [72] has achieved better generalization, the point spread function (PSF) implementation is less precise, and the parameter sets are not physics-oriented. Hence, the representative of their turbulence modalities is restricted." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2890" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 71, + 532, + 152 + ], + "blocks": [ + { + "bbox": [ + 61, + 71, + 532, + 152 + ], + "lines": [ + { + "bbox": [ + 61, + 71, + 532, + 152 + ], + "spans": [ + { + "bbox": [ + 61, + 71, + 532, + 152 + ], + "type": "image", + "image_path": "db30be6a1962f72241a954041d7f8e174bc833ab184d739a775fe3ad8c6c15ab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 153, + 532, + 277 + ], + "blocks": [ + { + "bbox": [ + 61, + 153, + 532, + 277 + ], + "lines": [ + { + "bbox": [ + 61, + 153, + 532, + 277 + ], + "spans": [ + { + "bbox": [ + 61, + 153, + 532, + 277 + ], + "type": "image", + "image_path": "4f6bfae93df77c0cf7c64b9ed2979d61cfbd2f66efbb6810d87079e7bd88399e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 62, + 277, + 531, + 358 + ], + "blocks": [ + { + "bbox": [ + 62, + 277, + 531, + 358 + ], + "lines": [ + { + "bbox": [ + 62, + 277, + 531, + 358 + ], + "spans": [ + { + "bbox": [ + 62, + 277, + 531, + 358 + ], + "type": "image", + "image_path": "c6eac9e66a532bc48642a5c85500e73322b8a255e16f61721f7be9ea3609cbb0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 367, + 546, + 411 + ], + "lines": [ + { + "bbox": [ + 46, + 367, + 546, + 411 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 546, + 411 + ], + "type": "text", + "content": "Figure 2. The proposed DATUM network. In this figure, block (a) shows the three common stages proposed by classical TM methods. The corresponding stages in DATUM are shown in block (b), which illustrates the forward time process of the " + }, + { + "bbox": [ + 46, + 367, + 546, + 411 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 367, + 546, + 411 + ], + "type": "text", + "content": "-th frame. The dashed line means the information passing from other temporal directions and frames. Block (c), (d), and (e) demonstrate the DAAB, GRUM, and MTCSA modules, respectively, where the input features are marked by green, and the output features are marked by red." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 431, + 151, + 443 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 151, + 443 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 151, + 443 + ], + "type": "text", + "content": "3. Proposed method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 453, + 220, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 453, + 220, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 453, + 220, + 464 + ], + "type": "text", + "content": "3.1. Insights from Classical Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": "Image degradation by atmospheric turbulence can be roughly described by a compositional operation of the blur " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{B}" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " and the tilt " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " via the relationship " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{I} = [\\mathcal{B} \\circ \\mathcal{T}](\\mathbf{J}) + \\mathbf{n}" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{J}" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " is the clean image, " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " is the distorted image, and " + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": " is the noise term. Traditional algorithms handle turbulence in three steps, as illustrated in Fig. 2:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 546, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 546, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 546, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 546, + 287, + 604 + ], + "type": "text", + "content": "- Frame-to-reference registration [77], where a reference frame is constructed from the observed images and all images are registered with respect to the reference using optical flow. In strong turbulence or dynamic scenes, constructing a reference is often difficult." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 653 + ], + "type": "text", + "content": "- Lucky image fusion [2, 27], where a \"lucky\" image is constructed by collecting the sharpest and most consistent patches from the inputs. However, if turbulence is strong, identifying lucky patches can be difficult." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "text", + "content": "- Blind deconvolution [42], where a final blind deconvolution algorithm is employed to sharpen the lucky image. The success and failure of this step depend heavily on how spatially uniform the blur in the lucky image is. Oftentimes, since the blur is spatially varying, the perfor" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 432, + 478, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 432, + 478, + 443 + ], + "spans": [ + { + "bbox": [ + 313, + 432, + 478, + 443 + ], + "type": "text", + "content": "mance of blind deconvolution is limited." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 445, + 545, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 445, + 545, + 505 + ], + "spans": [ + { + "bbox": [ + 305, + 445, + 545, + 505 + ], + "type": "text", + "content": "While each step is important each has its limitations, motivating us to develop end-to-end trained networks to approximate these functions. Empowered by training on our physical-grounded dataset, our network enjoys the inductive biases of those insights while avoiding their limitations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 515, + 410, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 410, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 410, + 526 + ], + "type": "text", + "content": "3.2. DATUM network" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 534, + 380, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 380, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 380, + 545 + ], + "type": "text", + "content": "3.2.1 Overview" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 554, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 554, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 554, + 545, + 590 + ], + "type": "text", + "content": "The block diagram of the DATUM network is depicted in Fig. 2. We first summarize these three components and describe them in detail in the next subsections." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "content": "Feature-to-reference registration. This component is analogous to the classical frame-to-reference registration. For each input frame " + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "content": ", we first extract three levels of features " + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "inline_equation", + "content": "f_{t}^{\\{1,2,3\\}}" + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "content": ". We propose the Deformable Attention Alignment Block (DAAB) to register the high-level feature " + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "inline_equation", + "content": "f_{t}^{3}" + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "content": " to a previously hidden reference map " + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "inline_equation", + "content": "r_{t-1}^{\\prime}" + }, + { + "bbox": [ + 304, + 591, + 545, + 700 + ], + "type": "text", + "content": ". We also propose the Gated Reference Update Module (GRUM) updates this reference feature recurrently, which is inspired by the gated recurrent unit [5, 15] and illustrated in Fig. 2." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "Temporal fusion. This component is analogous to the" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "2891" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "classical lucky fusion step. The registered feature " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": ", together with " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "r_{t-1}'" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "f_{t}^{3}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": ", are fused by a new Deep Integration Module (DIM). DIM consists of a series of Residual Dense Blocks (RDB) [73] and is used to produce the forward embedding " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "e_{t}^{fw}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "e_{t}^{fw}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " is a deep feature, it is presumed to be free of tilt and is thus utilized for updating the reference feature for the subsequent frame. After the bidirectional recurrent process, we perform a temporal fusion of " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "e_{t}^{fw}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " by augmenting it with the backward embedding " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "e_{t}^{bw}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " and bidirectional embeddings from neighboring frames. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA) module for this purpose." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 288, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 288, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 288, + 277 + ], + "type": "text", + "content": "Post processing. In the final stage, the temporally fused features are decoded to form the turbulence-free image. This decoding involves a twin of decoders. The first predicts a reverse tilt map that rectifies the shallow features, and the second subsequently reconstructs the clean image." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 297, + 132, + 308 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 132, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 132, + 308 + ], + "type": "text", + "content": "3.2.2 components" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 460 + ], + "type": "text", + "content": "Feature registration via Deformable Attention Alignment Block (DAAB). In classical methods, a crucial stage for turbulence mitigation is registering the input frames to the tilt-free reference frame. This reference frame is usually obtained by temporal averaging or using variants of principle component analysis. However, these methods may not be applicable to dynamic videos. Since learning-based video TM is possible [26, 72], the deep feature of a video TM network can be considered tilt-mitigated to work as the reference feature for the next input feature. This section explains our method to use deformable attention to facilitate feature registration in our DATUM network." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": "The computations in the DDAB are summarized in Algorithm 1, where " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "(A;B)" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": " denotes warping " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": " by deformation field " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\phi (A;p)" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": " denotes sampling " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": " by positions " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "W_{K}" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "W_{V}" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "W_{Q}" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": " are linear projections on the channel dimension, and " + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 461, + 287, + 544 + ], + "type": "text", + "content": " denotes the SoftMax. The optical flow at line 3 is estimated with the SPyNet [54], and lines 6-11 are inspired by the guided deformation attention (GDA) [38]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": "Temporal fusion via Multi-head Temporal Channel Self-Attention (MTCSA). After feature registration and deep integration, we propose to augment the embedding with contra-directional information, which is essential to ensure consistent restoration quality across various frames. In addition, like classical methods, a spatially adaptive fusion with adjacent frames is advantageous. We propose the Multi-head Temporal-Channel Self-Attention (MTCSA), as illustrated in Fig. 2. The MTCSA begins by concatenating channels from multiple frames, followed by a " + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 545, + 288, + 714 + ], + "type": "text", + "content": " convolution to shrink the channel dimension. Separable convolution is used to construct the spatially varying query, key, and value on the temporal and channel dimensions, and the dynamic fusion is facilitated by self-attention. Finally, a" + } + ] + } + ], + "index": 5 + }, + { + "type": "code", + "bbox": [ + 311, + 87, + 545, + 378 + ], + "blocks": [ + { + "bbox": [ + 307, + 72, + 526, + 84 + ], + "lines": [ + { + "bbox": [ + 307, + 72, + 526, + 84 + ], + "spans": [ + { + "bbox": [ + 307, + 72, + 526, + 84 + ], + "type": "text", + "content": "Algorithm 1 Deformation Attention Alignment Block" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "lines": [ + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": "1: Input: Current frame feature " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "f_{t}^{3}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": ", reference feature " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "r_{t-1}^{\\prime}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " and alignment flow from last frame " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "O_{t-1}^{f\\rightarrow r}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": ", two downsampled frames " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "I_{t-1}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n2: Output: Updated feature " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "f_{t}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " and flow " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "O_{t}^{f\\rightarrow r}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " Estimate rough deformation field " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\hat{O}_{t}^{f\\rightarrow r}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " that register feature " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "f_{t}^{3}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " to reference " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "r_{t-1}^{\\prime}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n3: Estimate the optical flow " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "O_{t\\rightarrow t-1}^{f}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "I_{t}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "I_{t-1}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": ". \n4: " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\hat{O}_{t}^{f\\rightarrow r} \\gets O_{t-1}^{f\\rightarrow r} + (O_{t\\rightarrow t-1}^{f}\\hat{O}_{t-1}^{f\\rightarrow r})" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n5: Pre-align " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\hat{f}_{t} \\gets (\\hat{O}_{t}^{f\\rightarrow r}, f_{t}^{3})" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " Register input feature to reference frame using multi-group multi-head deformation attention \n6: for all group " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " do \n" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " Predict offsets " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "o_{t}^{(g)}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n7: " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\Delta o_{t}^{(g)} \\gets \\text{RDB}(\\text{Concat}(\\hat{f}_{t}, r_{t-1}', \\hat{O}_{t}^{f\\rightarrow r}))" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n8: " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "o_{t}^{(g)} \\gets \\hat{O}_{t}^{f\\rightarrow r} + \\Delta o_{t}^{(g)}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " Compute the " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": "-th aligned feature " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\hat{f}_{t}^{(g)}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": ": \n9: " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "K^{(g)} \\gets \\phi(f_{t}^{3}W_{K}; o_{t}^{(g)})" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "V^{(g)} \\gets \\phi(f_{t}^{3}W_{V}; o_{t}^{(g)})" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n10: " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "Q \\gets r_{t-1}'W_{Q}, \\hat{f}_{t}^{(g)} \\gets \\sigma(QK^{(g)T}/\\sqrt{C})V^{(g)}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n11: end for \n12: Fuse all groups " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "f_{t} \\gets \\text{Concat}(\\{\\hat{f}_{t}^{(g)}\\})W" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n13: Update final alignment flow " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "O_{t}^{f\\rightarrow r}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " by mean of " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\{o_{t}^{(g)}\\}" + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "text", + "content": " \n14: Output " + }, + { + "bbox": [ + 311, + 87, + 545, + 378 + ], + "type": "inline_equation", + "content": "f_{t} \\gets f_{t} + \\text{FeedForward}(f_{t})" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "code_body" + } + ], + "index": 7, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 398, + 545, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 398, + 545, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 398, + 545, + 481 + ], + "type": "text", + "content": "residual connection is used to stabilize training. Considering the quadratic complexity of MTCSA relative to window size, this size is kept moderate. Additionally, we integrate a hard-coded positional embedding wherein features from the focal frame are positioned at the end. This strategy is essential for boundary frames with disproportionate neighboring frames on either side." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "type": "text", + "content": "Twin decoder and loss function Given the refined feature embedding from the MTCSA, we also developed a twin decoder to progressively remove the tilt and blur, as shown in Fig. 2. The decoder uses transposed convolution for upsampling and channel attention blocks (CAB) [68] for decoding. Before decoding in higher levels, the deep features are concatenated with the shallow features to facilitate the residual connection like a typical UNet [56]. Since the deep and shallow features are misaligned by the random tilt " + }, + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "type": "text", + "content": ", we propose to first rectify the shallow features by the estimated inverse tilt field " + }, + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "type": "inline_equation", + "content": "\\hat{\\mathcal{T}}^{-1}" + }, + { + "bbox": [ + 304, + 482, + 546, + 626 + ], + "type": "text", + "content": " estimated in the first stage. The tilt-rectification is optimized by reducing the loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 364, + 632, + 545, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 632, + 545, + 647 + ], + "spans": [ + { + "bbox": [ + 364, + 632, + 545, + 647 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {t i l t}} = \\mathcal {L} _ {\\text {c h a r}} \\left(\\boldsymbol {I} _ {\\mathrm {G T}}, \\left(\\boldsymbol {I} _ {\\text {t i l t}}; \\tilde {\\mathcal {T}} ^ {- 1}\\right)\\right) \\tag {1}", + "image_path": "954e7cb26309801be54d1bce37e1528e42b0616c1b99ef164d75d2d09adb89c8.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Where " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{char}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " denotes the Charbonnier loss [10], " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{GT}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " is the input frame and " + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{\\mathrm{tilt}}" + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": " is the tilt-only frame that can be produced without additional cost by our data synthesis method. In the second stage, the rectified shallow features are jointly decoded with the deep features to generate the final recon" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2892" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 70, + 272, + 186 + ], + "blocks": [ + { + "bbox": [ + 59, + 70, + 272, + 186 + ], + "lines": [ + { + "bbox": [ + 59, + 70, + 272, + 186 + ], + "spans": [ + { + "bbox": [ + 59, + 70, + 272, + 186 + ], + "type": "image", + "image_path": "8d03611d2c083b0db28c75ed87c410e3b385f2854394b2318c89e1ed1c00098e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 80, + 190, + 253, + 201 + ], + "lines": [ + { + "bbox": [ + 80, + 190, + 253, + 201 + ], + "spans": [ + { + "bbox": [ + 80, + 190, + 253, + 201 + ], + "type": "text", + "content": "Figure 3. Scheme of our data synthesis method." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 219, + 264, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 219, + 264, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 219, + 264, + 232 + ], + "type": "text", + "content": "struction " + }, + { + "bbox": [ + 47, + 219, + 264, + 232 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{I}}" + }, + { + "bbox": [ + 47, + 219, + 264, + 232 + ], + "type": "text", + "content": ". The overall loss function is computed by:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 237, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 237, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 104, + 237, + 287, + 251 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\alpha_ {1} \\mathcal {L} _ {\\text {t i l t}} + \\alpha_ {2} \\mathcal {L} _ {\\text {c h a r}} (\\boldsymbol {I} _ {\\mathrm {G T}}, \\hat {\\boldsymbol {I}}) \\tag {2}", + "image_path": "9430e11cf13d983975772557db81f7874edde2e36c0ba5f09e60019bcc50a80e.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "type": "text", + "content": "where weights " + }, + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "type": "inline_equation", + "content": "\\alpha_{1}" + }, + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "type": "inline_equation", + "content": "\\alpha_{2}" + }, + { + "bbox": [ + 47, + 257, + 286, + 269 + ], + "type": "text", + "content": " are empirically set to 0.2 and 0.8." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 274, + 138, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 138, + 286 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 138, + 286 + ], + "type": "text", + "content": "3.3. ATSyn dataset" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 293, + 201, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 201, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 201, + 304 + ], + "type": "text", + "content": "3.3.1 Physics-based data synthesis" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": "As introduced previously, the ground truth image " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " is first geometrically distorted and then blurred to produce the degraded image " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " in our synthesis method. Data synthesis for the turbulence effect essentially requires a physics-grounded representation of and. We adopted the Zernike-based turbulence simulator [12, 13] and improved it with non-trivial modifications. Fig. 3 presents the scheme of our implementation. The and is generated from the phase distortion represented by Zernike polynomials " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{Z}_i\\}" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " [51] as the basis, with corresponding coefficients " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{a}_i" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " ranging from 1 to 36. Among all 36 coefficients, " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "i = 1" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " denotes the current component, " + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "inline_equation", + "content": "i = 2, 3" + }, + { + "bbox": [ + 46, + 312, + 287, + 477 + ], + "type": "text", + "content": " controls the by a constant scale, and the rest high order Zernike coefficients contribute to the blur effect." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "text", + "content": "The phase distortion can be assumed as a wide sense stationary (WSS) random field [13]. Hence, it can be sampled with Fast Fourier Transform (FFT) from white Gaussian noise and the autocorrelation map. Transforming the phase distortion to the spatial domain point spread functions (PSF) can be achieved by the Phase-to-Space (P2S) transform, which transforms the sampled Zernike coefficients to spatial coefficients " + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "text", + "content": ", assuming the PSFs can be represented by a low-rank approximation of 100 basis " + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "text", + "content": " and corresponding " + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 479, + 286, + 611 + ], + "type": "text", + "content": ". The overall degradation in the spatial domain is implemented by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 100, + 616, + 287, + 648 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 616, + 287, + 648 + ], + "spans": [ + { + "bbox": [ + 100, + 616, + 287, + 648 + ], + "type": "interline_equation", + "content": "\\boldsymbol {I} = \\sum_ {k = 1} ^ {1 0 0} \\psi_ {k} * (\\boldsymbol {\\beta} _ {k} \\cdot (\\boldsymbol {J};)) + \\boldsymbol {n}, \\tag {3}", + "image_path": "ab87ab00c3f45019009df6c8da3468f6214125ecb62f2104c2b315f61f4421d4.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\circ" + }, + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "type": "text", + "content": " denotes the depth-wise convolution. Although subtle, this fundamentally generates more reliable degradation than the simulator in [72], as elaborated in [14]. Except for this, our correlation kernels are more precise by incorporating the continuous " + }, + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "type": "inline_equation", + "content": "C_n^2" + }, + { + "bbox": [ + 47, + 654, + 286, + 714 + ], + "type": "text", + "content": " path technique [11]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 460, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 460, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 460, + 84 + ], + "type": "text", + "content": "3.3.2 Guideline of implementation" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "content": "With the proposed simulator, we created the ATSyn dataset to match various real-world turbulence conditions and benchmark deep neural networks for turbulence mitigation. This dataset is segmented into two distinct subsets based on scene type: the ATSyn-dynamic and ATSyn-static. The dynamic sequences contain camera or object motion, whereas the static sequences are each associated with only one underlying clean image. We adopted parameters including focal length, F-number, distance, wavelength, scene size, and sensor resolution to control the simulation. In comparison with the synthetic dataset introduced in [72], which utilized the " + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "inline_equation", + "content": "D / r_0" + }, + { + "bbox": [ + 304, + 91, + 545, + 258 + ], + "type": "text", + "content": " [19] and empirically chosen blur kernel size, our dataset's parameter space more closely aligns with actual camera settings, making it more representative." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "type": "text", + "content": "ATSyn-dynamic contains 4,350 training and 1,097 validation instances synthesized from [26, 58], and ATSyn-static contains 2,000 and 1,000 instances synthesized from the Places dataset [75] for training and validation, respectively. Those instances have varying numbers of frames, each with a distinct turbulence parameter set. Besides ground truth and fully degraded videos, ATSyn further provides associated " + }, + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "type": "text", + "content": "-only videos to facilitate the training of " + }, + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{tilt}}" + }, + { + "bbox": [ + 304, + 258, + 545, + 414 + ], + "type": "text", + "content": " in Eq. 1. We categorize the turbulence parameters by three levels: weak, medium, and strong. The range of turbulence parameters is determined by matching with a largescale, long-range video dataset [16] and other real-world videos, with more details in the supplementary document." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 424, + 388, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 424, + 388, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 424, + 388, + 437 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 444, + 403, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 444, + 403, + 456 + ], + "spans": [ + { + "bbox": [ + 306, + 444, + 403, + 456 + ], + "type": "text", + "content": "4.1. Training setting" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "content": "This section describes how we trained our DATUM and other models. Except for turbulence mitigation networks [26, 44, 72], we also benchmarked several representative video restoration [37, 38] and deblurring networks [74, 76] for a more thorough comparison." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "content": "To train the proposed model, we used the Adam optimizer [29] with the Cosine Annealing learning rate schedule [39]. The initial learning rate is " + }, + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "inline_equation", + "content": "2 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 522, + 545, + 629 + ], + "type": "text", + "content": ", and batch size is 8. All dynamic scene TM networks in this experiment are trained end-to-end from scratch for 800K iterations. To get their static-scene variant, we fine-tuned them on the static-scene modality with half the initial learning rate and 400K iterations. We clip the gradient if the L2 norm exceeds 20 to prevent gradient explosion during inference." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "We trained the ESTRNN [74], RNN-MBP [76], and RVRT [74] with the same configuration as DATUM. The number of input frames of DATUM and ESTRNN during training is set to 30 for ATSyn-dynamic and 36 for ATSyn-static. Since RNN-MBP and RVRT require much more resources to train, the number of input frames is set to 16. Because TSRWGAN [26], TMT [72], and TurbNet [44] are" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2893" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 537, + 103 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 537, + 103 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 537, + 103 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 537, + 103 + ], + "type": "table", + "html": "
MethodsTurbNet [44]TSRWGAN [26]VRT [37]TMT [72]RNN-MBP [76]ESTRNN [74]RVRT [38]DATUM [ours]
PSNR24.222926.326227.611427.741927.715227.346927.851228.5875
SSIMcw0.82300.85960.86910.87410.87300.86170.87880.8803
", + "image_path": "85816fc0a893f9a02a3381ac0ec47d1557ef4acb8f457ed00b8a1cd685bbb9fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 128, + 537, + 232 + ], + "blocks": [ + { + "bbox": [ + 69, + 106, + 523, + 118 + ], + "lines": [ + { + "bbox": [ + 69, + 106, + 523, + 118 + ], + "spans": [ + { + "bbox": [ + 69, + 106, + 523, + 118 + ], + "type": "text", + "content": "Table 1. Preliminary study: evaluate on TMT's synthetic dynamic scene data [72]. " + }, + { + "bbox": [ + 69, + 106, + 523, + 118 + ], + "type": "inline_equation", + "content": "{\\mathrm{{SSIM}}}_{\\mathrm{{CW}}}" + }, + { + "bbox": [ + 69, + 106, + 523, + 118 + ], + "type": "text", + "content": " denotes Complex Wavelet SSIM." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 128, + 537, + 232 + ], + "lines": [ + { + "bbox": [ + 53, + 128, + 537, + 232 + ], + "spans": [ + { + "bbox": [ + 53, + 128, + 537, + 232 + ], + "type": "table", + "html": "
Turbulence LevelWeakMediumStrongOverallCost
MethodsPSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)PSNR\\( SSIM_{CW} \\)SizeFPS
TSRWGAN [26]27.08440.857526.70460.851425.42300.837226.45410.849346.280.87
TMT [72]29.11830.883628.50500.879126.97440.855228.26650.873426.040.80
VRT [37]28.84530.879728.26280.876926.74920.850628.01790.869918.320.17
RNN-MBP [76]27.92430.869927.47420.864226.08120.849527.21610.861814.161.14
ESTRNN [74]28.98050.875028.33380.869726.88970.846328.13470.86452.46827.65
RVRT [38]29.60800.884528.96050.880627.53440.859528.76720.875613.502.43
DATUM [ours]30.20580.885729.62030.882928.25500.864029.42220.87815.7549.17
", + "image_path": "a19289f1e4a5dd0276c16e53f5dfdfc21b9db1e5f0facb17c9ba4a4279a9e7db.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 287, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 287, + 306 + ], + "type": "text", + "content": "all designed for turbulence mitigation, we trained them following the original paper and public code." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 311, + 257, + 324 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 311, + 257, + 324 + ], + "spans": [ + { + "bbox": [ + 47, + 311, + 257, + 324 + ], + "type": "text", + "content": "4.2. Comparison on dynamic scene modality" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "type": "text", + "content": "We first trained and evaluated all networks for comparison on a previous Zernike-based synthetic dataset [72] for preliminary study. We choose PSNR and Complex Wavelet Structure Similarity [59] (CW-SSIM) as the criterion in this paper, and the reason for selecting CW-SSIM rather than SSIM is provided in the supplementary document. The result in Table 1 shows our DATUM outperforms the previous state-of-the-art TMT [72] with " + }, + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "type": "inline_equation", + "content": "5 \\times" + }, + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "type": "text", + "content": " fewer parameters and over " + }, + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "type": "inline_equation", + "content": "10 \\times" + }, + { + "bbox": [ + 46, + 329, + 287, + 521 + ], + "type": "text", + "content": " faster inference speed. We also benchmark a representative single-frame TM network [44] to demonstrate the superiority of multi-frame TM methods. Next, we present extensive results from the ATSyn-dynamic dataset in Table 2. Our model outperforms all other networks by a significant margin, while it is the second smallest network among all models and the most efficient network among all existing turbulence mitigation networks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 527, + 241, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 527, + 241, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 527, + 241, + 540 + ], + "type": "text", + "content": "4.3. Comparison on static scene modality" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "When training on the ATSyn-static, the loss is computed between the single ground truth and all output frames. For testing, we instead calculate the average score of the central four frames in the entire output sequence (for single-directional models, we use the last 4). We evaluated the performance on the ATSyn-static and the turbulence text dataset [64], and the result is shown in Table 3. The turbulence text dataset contains 100 sequences of text images, each a static scene of degraded text pattern captured at 300 meters or farther. Real-world turbulence videos do not have ground truth, while [64] uses the accuracy score of pretrained text recognition models CRNN [61], DAN [67], and ASTER [62] as metrics, where a better turbulence mitigation offers better recognition performances. Our model is" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 310, + 278, + 541, + 376 + ], + "blocks": [ + { + "bbox": [ + 46, + 237, + 546, + 259 + ], + "lines": [ + { + "bbox": [ + 46, + 237, + 546, + 259 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 546, + 259 + ], + "type": "text", + "content": "Table 2. Performance comparison on the ATSyn-dynamic set, we list the image quality scores on different turbulence levels and frame-wise resource consumption (measured with " + }, + { + "bbox": [ + 46, + 237, + 546, + 259 + ], + "type": "inline_equation", + "content": "960\\times 540" + }, + { + "bbox": [ + 46, + 237, + 546, + 259 + ], + "type": "text", + "content": " frame sequences on RTX 2080 Ti)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 278, + 541, + 376 + ], + "lines": [ + { + "bbox": [ + 310, + 278, + 541, + 376 + ], + "spans": [ + { + "bbox": [ + 310, + 278, + 541, + 376 + ], + "type": "table", + "html": "
BenchmarkATSyn-staticTurb-Text (%)
MethodsPSNRSSIMCWCRNN/DAN/ASTER
TSRWGAN [26]23.160.840760.30 / 73.90 / 74.40
TMT [72]24.510.871680.90 / 87.25 / 88.55
VRT [37]24.270.864176.30 / 84.45 / 83.60
RNN-MBP [76]24.640.877551.35 / 65.00 / 64.30
ESTRNN [74]26.230.901787.10 / 97.80 / 96.95
RVRT [38]25.710.887686.40 / 89.00 / 89.20
DATUM [ours]26.760.910293.55 / 97.95 / 97.25
", + "image_path": "9c13459224199be1ae964307b1821c8905b7f382e006ca8b611bd72189a1bddf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 381, + 545, + 403 + ], + "lines": [ + { + "bbox": [ + 305, + 381, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 305, + 381, + 545, + 403 + ], + "type": "text", + "content": "Table 3. Static scene modality. CRNN/DAN/ASTER are the text recognition rates of these three models from the restored images." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 421, + 545, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 421, + 545, + 482 + ], + "spans": [ + { + "bbox": [ + 305, + 421, + 545, + 482 + ], + "type": "text", + "content": "trained on a wide range of turbulence conditions and generic data, without specific augmentation tricks, yet performs on par with the best systems in the " + }, + { + "bbox": [ + 305, + 421, + 545, + 482 + ], + "type": "inline_equation", + "content": "\\mathrm{UG2 + }" + }, + { + "bbox": [ + 305, + 421, + 545, + 482 + ], + "type": "text", + "content": " turbulence challenge [64]. Our model outperforms other networks trained on the ATSyn-static dataset by an even larger margin." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 490, + 397, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 490, + 397, + 502 + ], + "spans": [ + { + "bbox": [ + 306, + 490, + 397, + 502 + ], + "type": "text", + "content": "4.4. Ablation study" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 556 + ], + "type": "text", + "content": "Our ablation study examines key elements that introduce effective inductive biases of our model, including the use of additional frames, recurrent reference updating, feature-reference registration, and multi-frame embedding fusion." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 665 + ], + "type": "text", + "content": "Influence of the number of input frames. The number of input frames for both training and inference matters for recurrent-based networks, especially in turbulence mitigation. Since turbulence degradation is caused by zero-mean stochastic phase distortion, the more frames the network can perceive, the better the non-distortion state it can evaluate. This is particularly valid for static scene sequences, where the pixel-level turbulence statistics are much easier to track and analyze through time." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "We trained two models with 12-frame and 24-frame inputs and presented their respective performance during inference in Fig. 4. This figure shows in the temporal range of our experimental setting, a positive correlation between the" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "2894" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 71, + 164, + 152 + ], + "blocks": [ + { + "bbox": [ + 56, + 71, + 164, + 152 + ], + "lines": [ + { + "bbox": [ + 56, + 71, + 164, + 152 + ], + "spans": [ + { + "bbox": [ + 56, + 71, + 164, + 152 + ], + "type": "image", + "image_path": "24f4efb1ce1802add5e88cf059afc6a01f759f19e96826082b1bc99e128a5a5e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 156, + 147, + 166 + ], + "lines": [ + { + "bbox": [ + 70, + 156, + 147, + 166 + ], + "spans": [ + { + "bbox": [ + 70, + 156, + 147, + 166 + ], + "type": "text", + "content": "(a) On ATSyn-dynamic" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 74, + 173, + 258, + 184 + ], + "lines": [ + { + "bbox": [ + 74, + 173, + 258, + 184 + ], + "spans": [ + { + "bbox": [ + 74, + 173, + 258, + 184 + ], + "type": "text", + "content": "Figure 4. Influence of the number of input frames." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 175, + 72, + 279, + 152 + ], + "blocks": [ + { + "bbox": [ + 175, + 72, + 279, + 152 + ], + "lines": [ + { + "bbox": [ + 175, + 72, + 279, + 152 + ], + "spans": [ + { + "bbox": [ + 175, + 72, + 279, + 152 + ], + "type": "image", + "image_path": "b136392c75f597b2ffde52b0ca9b4a773b577b11e927f9b35fad94a1b3b42a63.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 194, + 156, + 260, + 166 + ], + "lines": [ + { + "bbox": [ + 194, + 156, + 260, + 166 + ], + "spans": [ + { + "bbox": [ + 194, + 156, + 260, + 166 + ], + "type": "text", + "content": "(b) On ATSyn-static" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 198, + 286, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 286, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 286, + 269 + ], + "type": "text", + "content": "performance and the number of input frames always exists, especially on the static scene modality where an over 1 dB boost can be obtained with more frames. This phenomenon suggests one of the success factors for turbulence mitigation is the capability of fusing more frames, similar to the video super-resolution problem [8]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 269, + 286, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 286, + 340 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 286, + 340 + ], + "type": "text", + "content": "Influence of DAAB, MTCSA, GRUM, and twin decoder. The design of DAAB and MTCSA are inspired by pixel registration and lucky fusion in the conventional TM methods. Although our spatial registration and temporal fusion are implemented at the feature level, they are still effective in turbulence mitigation, as shown in Table 4." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 341, + 286, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 341, + 286, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 341, + 286, + 483 + ], + "type": "text", + "content": "While the MTCSA fuses embeddings from multiple frames in a sliding window manner, determining the optimal window size is crucial. If the window size is too small, the temporal fusion only relies on the implicit temporal propagation by the recurrent unit, limiting the performance; if the window size is too large, because of the quadratic complexity along the temporal dimension, the MTCSA becomes very resource-demanded, and the network becomes less flexible to deal with a small number of input frames. We investigated the temporal window size of the MTCSA module, as shown in Fig. 4, where we found that five frames meet the trade-off between performance and efficiency." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 484, + 286, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 286, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 286, + 591 + ], + "type": "text", + "content": "The GRUM utilizes a gating mechanism in the recurrent network to facilitate more extended temporal dependency [5, 15]. It fuses the reference feature with deeper embeddings in a more adaptive manner, which also turns out to be effective. Finally, in the post-processing stage, we compared the two-stage twin decoder with the one-stage plain decoder. We found that by incorporating additional supervision and rectifying shallow features in the decoding stage, better performance can be obtained." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 599, + 217, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 217, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 217, + 612 + ], + "type": "text", + "content": "4.5. Comparison on real-world data" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 618, + 286, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 286, + 642 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 286, + 642 + ], + "type": "text", + "content": "In this section, we demonstrate our data's generalization capability qualitatively and quantitatively on real-world data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 713 + ], + "type": "text", + "content": "Given the impracticality of directly obtaining ground truth images for real-world turbulence scenarios, quantitative performance evaluation typically involves applying restored images to downstream tasks, as noted in [24, 44, 49]. Adopting this approach, we evaluated various restoration methods using the turbulence text dataset. The results are" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 70, + 541, + 162 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 541, + 162 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 541, + 162 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 541, + 162 + ], + "type": "table", + "html": "
ComponentsPSNR / SSIMSizeGMACs
Base (MTCSA-1f)28.62 / 0.84653.912261.5
Base (MTCSA-3f)28.79 / 0.84974.131272.7
* Base (MTCSA-5f)28.87 / 0.85224.768304.2
Base (MTCSA-7f)28.92 / 0.85325.808358.1
+ GRUM29.06 / 0.85764.894317.7
+ DAAB29.33 / 0.86385.241351.8
+ Twin Decoder29.42 / 0.86475.754372.7
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Face RetrievalDegradedSimulator in [72]Our simulator
Rank 537.75%38.83%39.18%
Rank 1040.59%41.83%42.18%
Rank 2045.29%46.40%46.70%
", + "image_path": "d63c52b2027a35416ad28d7643907639bde6d6470e652b3206930b52bf4be9ba.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 449, + 544, + 460 + ], + "lines": [ + { + "bbox": [ + 306, + 449, + 544, + 460 + ], + "spans": [ + { + "bbox": [ + 306, + 449, + 544, + 460 + ], + "type": "text", + "content": "Table 5. Face recognition results on a subset of the BRIAR dataset." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 473, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 665 + ], + "type": "text", + "content": "presented in Fig. 5, revealing two key insights: 1) our proposed ATSyn-static dataset enhances the generalization capabilities of other TM methods. 2) on both synthetic and real-world sequences, DATUM consistently outperforms other models trained on our dataset. To further validate the effectiveness of our modifications to the Zernike-based simulator, we extensively compared DATUM trained on our ATSyn-dynamic dataset and TMT's dataset [72]. We first enhance the long-range subset in the BRIAR dataset [16] by those two versions, run the same pre-trained face recognition model [28] on the enhanced images, and it yields the result provided in Table 5. We can observe the ATSyndynamic dataset improved network performance on realworld videos compared to the [72] dataset. These comparisons demonstrate our method facilitates better generalization of both scene types than other existing datasets." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 545, + 713 + ], + "type": "text", + "content": "We also provide a qualitative comparison in Fig. 6 and 7 to demonstrate the advance of our network and dataset. 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Qualitative comparison on the turbulence-text dataset [64]. The input frame (a) is the 49th frame of the 94th sequence in [64]. Figures on the top row are restoration results of corresponding TM methods using their original model and checkpoints. 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Qualitative comparison on a dynamic scene sample from the BRIAR dataset [16]. Figures on the top row are the original restoration results of corresponding TM methods. Figures on the bottom row are models (marked by *) trained on ATSyn-dynamic dataset." + } + ] + } + ], + "index": 57, + "angle": 0, + "type": "image_caption" + } + ], + "index": 45 + }, + { + "type": "image", + "bbox": [ + 191, + 386, + 261, + 457 + ], + "blocks": [ + { + "bbox": [ + 191, + 386, + 261, + 457 + ], + "lines": [ + { + "bbox": [ + 191, + 386, + 261, + 457 + ], + "spans": [ + { + "bbox": [ + 191, + 386, + 261, + 457 + ], + "type": "image", + "image_path": "cad4144615c5dd9026084de3040e02ef46569c6436e3c8d7bc0aa97283707289.jpg" + } + ] + } + ], + "index": 47, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 205, + 458, + 247, + 467 + ], + "lines": [ + { + "bbox": [ + 205, + 458, + 247, + 467 + ], + "spans": [ + { + "bbox": [ + 205, + 458, + 247, + 467 + ], + "type": "text", + "content": "(j) " + }, + { + "bbox": [ + 205, + 458, + 247, + 467 + ], + "type": "inline_equation", + "content": "\\mathrm{TMT^{*}}" + }, + { + "bbox": [ + 205, + 458, + 247, + 467 + ], + "type": "text", + "content": " [72]" + } + ] + } + ], + "index": 48, + "angle": 0, + "type": "image_caption" + } + ], + "index": 47 + }, + { + "type": "image", + "bbox": [ + 261, + 386, + 332, + 457 + ], + "blocks": [ + { + "bbox": [ + 261, + 386, + 332, + 457 + ], + "lines": [ + { + "bbox": [ + 261, + 386, + 332, + 457 + ], + "spans": [ + { + "bbox": [ + 261, + 386, + 332, + 457 + ], + "type": "image", + "image_path": "fb95c094045329d984e7412454e0a2059ec989af97f749628338cf3227712902.jpg" + } + ] + } + ], + "index": 49, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 266, + 458, + 326, + 467 + ], + "lines": [ + { + "bbox": [ + 266, + 458, + 326, + 467 + ], + "spans": [ + { + "bbox": [ + 266, + 458, + 326, + 467 + ], + "type": "text", + "content": "(k) RNN-MBP* [44]" + } + ] + } + ], + "index": 50, + "angle": 0, + "type": "image_caption" + } + ], + "index": 49 + }, + { + "type": "image", + "bbox": [ + 332, + 386, + 403, + 457 + ], + "blocks": [ + { + "bbox": [ + 332, + 386, + 403, + 457 + ], + "lines": [ + { + "bbox": [ + 332, + 386, + 403, + 457 + ], + "spans": [ + { + "bbox": [ + 332, + 386, + 403, + 457 + ], + "type": "image", + "image_path": "175c97c7f225b47dfdfd2f0e5bafd856efced2dcc7611be9dd256840e7c18d35.jpg" + } + ] + } + ], + "index": 51, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 346, + 458, + 389, + 467 + ], + "lines": [ + { + "bbox": [ + 346, + 458, + 389, + 467 + ], + "spans": [ + { + "bbox": [ + 346, + 458, + 389, + 467 + ], + "type": "text", + "content": "(1) RVRT* [38]" + } + ] + } + ], + "index": 52, + "angle": 0, + "type": "image_caption" + } + ], + "index": 51 + }, + { + "type": "image", + "bbox": [ + 403, + 386, + 474, + 457 + ], + "blocks": [ + { + "bbox": [ + 403, + 386, + 474, + 457 + ], + "lines": [ + { + "bbox": [ + 403, + 386, + 474, + 457 + ], + "spans": [ + { + "bbox": [ + 403, + 386, + 474, + 457 + ], + "type": "image", + "image_path": "15b04559f0959afd180fcc6a860a5366bb7da60107f3ff8711b7fd88e0941140.jpg" + } + ] + } + ], + "index": 53, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 417, + 458, + 460, + 467 + ], + "lines": [ + { + "bbox": [ + 417, + 458, + 460, + 467 + ], + "spans": [ + { + "bbox": [ + 417, + 458, + 460, + 467 + ], + "type": "text", + "content": "(m) VRT* [26]" + } + ] + } + ], + "index": 54, + "angle": 0, + "type": "image_caption" + } + ], + "index": 53 + }, + { + "type": "image", + "bbox": [ + 475, + 386, + 545, + 457 + ], + "blocks": [ + { + "bbox": [ + 475, + 386, + 545, + 457 + ], + "lines": [ + { + "bbox": [ + 475, + 386, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 475, + 386, + 545, + 457 + ], + "type": "image", + "image_path": "a8e0738d49e7f78275f2c1b2a374a7d05d25c64cc422124d23fd3d953311eca0.jpg" + } + ] + } + ], + "index": 55, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 482, + 458, + 537, + 467 + ], + "lines": [ + { + "bbox": [ + 482, + 458, + 537, + 467 + ], + "spans": [ + { + "bbox": [ + 482, + 458, + 537, + 467 + ], + "type": "text", + "content": "(n) ESTRNN* [74]" + } + ] + } + ], + "index": 56, + "angle": 0, + "type": "image_caption" + } + ], + "index": 55 + }, + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 555 + ], + "type": "text", + "content": "ization capability. On the other hand, by comparison among all networks trained on our dataset, our model significantly outperforms other networks." + } + ] + } + ], + "index": 58 + }, + { + "bbox": [ + 47, + 571, + 119, + 583 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 571, + 119, + 583 + ], + "spans": [ + { + "bbox": [ + 47, + 571, + 119, + 583 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 59 + }, + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 713 + ], + "type": "text", + "content": "In this research, we introduced a novel approach leveraging deep learning to address the enduring challenge of atmospheric turbulence mitigation. Taking a translational perspective, our method integrated the strengths of traditional turbulence mitigation (TM) techniques into a neural network architecture. This fusion elevated our network to state-of-the-art performance while ensuring significantly enhanced efficiency and speed compared to prior TM models. Additionally, we developed a physics-based synthesis method that accurately models the degradation process." + } + ] + } + ], + "index": 60 + }, + { + "bbox": [ + 304, + 520, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 545, + 567 + ], + "type": "text", + "content": "This led to the creation of an extensive synthetic dataset covering a diverse spectrum of turbulence effects. Utilizing this dataset, we facilitated a stronger generalization capability for data-driven models than other existing datasets." + } + ] + } + ], + "index": 61 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Acknowledgments and Disclosure of Funding The research is based upon work supported in part by the Intelligence Advanced Research Projects Activity (IARPA) under Contract No. 2022-21102100004, and in part by the National Science Foundation under the grants CCSS-2030570 and IIS-2133032. The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies, either expressed or implied, of IARPA, or the U.S. Government. 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Removing atmospheric turbulence via space-invariant deconvolution. 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However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of indoor environments. Unlike existing methods, which typically assume distant lighting like an environment map, we propose a learnable Gaussian directional encoding to better model the view-dependent effects under near-field lighting conditions. Importantly, our new directional encoding captures the spatially-varying nature of near-field lighting and emulates the behavior of prefiltered environment maps. As a result, it enables the efficient evaluation of preconvolved specular color at any 3D location with varying roughness coefficients. We further introduce a data-driven geometry prior that helps alleviate the shape radiance ambiguity in reflection modeling. We show that our Gaussian directional encoding and geometry prior significantly improve the modeling of challenging specular reflections in neural radiance fields, which helps decompose appearance into more physically meaningful components.", + "bbox": [ + 75, + 309, + 473, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 646, + 209, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Neural radiance fields (NeRFs) have emerged as a popular scene representation for novel-view synthesis [34, 45, 51]. By training a neural network based on sparse observations of a 3D scene, NeRF-like representations are able to synthesize novel views with photorealistic visual quality. In particular, with a scalable model design, such as InstantNGP [36], NeRFs are able to model room-scale 3D scenes with extraordinary detail [53]. However, existing approaches typically only manage to model mild view-dependent effects like those seen on nearly diffuse surfaces. When encountering highly view-dependent glossy surfaces, NeRFs struggle to model the high-frequency changes when the viewpoint changes. Instead, they tend to \"fake\" specular reflections by placing them behind surfaces, which may result in poor view interpolation and \"foggy\" geometry [47]. Moreover, fake", + "bbox": [ + 75, + 672, + 472, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a0614387486ba2fd7115a6e176f287445f7e247bfed693c892db967d34e247db.jpg", + "image_caption": [ + "Figure 1. We propose a Gaussian directional encoding that leads to better modeling of specular reflections under near-field lighting conditions. In contrast, the integrated directional encoding utilized in Ref-NeRF [47] and Fourier directional encoding in NeRF [34] exhibit suboptimal performance under similar conditions." + ], + "image_footnote": [], + "bbox": [ + 503, + 277, + 893, + 439 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "reflections are not viable if one can look behind the surface, as NeRF can no longer hide the reflections there.", + "bbox": [ + 498, + 534, + 893, + 565 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Accurately modeling and reconstructing specular reflections presents notable challenges, especially for room-scale scenes. Physically correct reflection modeling involves pathtracing many rays for every single pixel, which is impractical for NeRF-like volumetric scene representations, primarily due to the large computational requirements to shade a single pixel. Consequently, an efficient approximation of the reflection shading is needed for a feasible modeling of reflections. Existing works [14, 47] address this challenge by incorporating heuristic modules inspired by real-time image-based lighting (IBL) [35] techniques, such as explicit ray bounce computations to enhance NeRF's capability to simulate reflections, and integrated directional encoding to simulate appearance change under varying surface roughness.", + "bbox": [ + 496, + 566, + 895, + 779 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "While these improvements have shown to be effective in modeling specular reflections for NeRFs, they are limited to object-level reconstruction under distant lighting, which assumes the object is lit by a 2D environment map. They work poorly for modeling near-field lighting, where the corresponding environment map varies spatially. The issue is that existing methods rely on directional encodings to embed ray directions for generating view-dependent reflections.", + "bbox": [ + 496, + 779, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21188", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "These encodings, such as Fourier encoding or spherical harmonics, are spatially invariant. Figure 1 demonstrates one example of NeRF [34] and Ref-NeRF [47] reconstructions of an indoor scene with spatially-varying lighting. NeRF produces extremely noisy geometry, resulting in artifacts in the rendering result. Ref-NeRF offers a slight improvement, but still struggles with noisy geometry and view interpolation. This illustrates that the spatial invariance in the directional encodings of existing methods presents challenges under spatially-varying lighting conditions.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a novel Gaussian directional encoding that is tailored for spatially varying lighting conditions. Instead of only encoding a 2D ray direction, we use a set of learnable 3D Gaussians as the basis to embed a 5D ray space including both ray origin and ray direction. We show that, with appropriately optimized Gaussian parameters, this encoding introduces an important inductive bias towards near-field lighting, which enhances the model's ability to capture the characteristics of specular surfaces, leading to photorealistic reconstructions of shiny reflections. We further demonstrate that by changing the scale of the 3D Gaussians, we can edit the apparent roughness of a surface.", + "bbox": [ + 75, + 242, + 472, + 422 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While our proposed Gaussian directional encoding improves the reflection modeling of NeRF, high-quality reflection reconstruction also requires an accurate surface geometry and normal in order to compute accurate reflection rays. However, the geometry within NeRFs is often noisy in the early phases of training, which presents challenges in simultaneously optimizing for good geometry and reflections. To better address this challenge, we introduce a data-driven prior to direct the NeRF model towards the desired solution. We deploy a monocular normal estimation network to supervise the normal of the geometry at the beginning of the training stage, and show that this bootstrapping strategy improves the reconstruction of normals, and further leads to successful modeling of specular reflections. We conduct experiments on several public datasets and show that the proposed method outperforms existing methods, achieving higher-quality photorealistic rendering of reflective scenes while also providing more meaningful and accurate color component decomposition. Our contributions can be summarized as follows:", + "bbox": [ + 75, + 422, + 472, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel Gaussian directional encoding that is more effective in modeling view-dependent effects under near-field lighting conditions.", + "- We propose to use monocular normal estimation to resolve shape-radiance ambiguity in the early training stages.", + "- Our full NeRF pipeline achieves state-of-the-art novel-view synthesis performance for specular reflections." + ], + "bbox": [ + 76, + 724, + 468, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 844, + 218, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Reflection-aware NeRFs. Successfully modeling view-dependent effects, such as specular reflections, can greatly", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "enhance the photorealism of the reconstructed NeRF. NeRF models view-dependency by conditioning the radiance on the positional encoding [43] of the input ray direction, which is only capable of mild view-dependent effects. Ref-NeRF [47] improves NeRF's capability for modeling reflections by conditioning the view-dependent appearance on the reflection ray direction instead of incident ray direction, and by modulating the directional encoding based on surface roughness. This reparameterization of outgoing radiance makes the underlying scene function simpler, leading to a better geometry and view interpolation quality for glossy objects. Ref-NeuS [14] further extends these concepts to a surface-based representation. However, these are primarily designed for object-level reconstruction under environment map lighting conditions. Modeling large-scale scenes with near-field lighting remains a problem. Clean-NeRF [30] decomposes the radiance into diffuse and specular colors, and supervises the two components by least-square estimations of multiple input rays. This alleviates the ambiguity of highly specular regions; yet, it does not change the view-dependent structure of the NeRF model, thus limiting its ability to model reflections. NeRF-DS [54] models peculiarities in dynamic scenes and considers the variations in reflections caused by dynamic geometry through the use of a dynamic normal field, but requires additional object masks for accurate specular reconstruction.", + "bbox": [ + 496, + 90, + 893, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NeRF-based Inverse Rendering. Inverse rendering goes beyond simple reflection modeling and aims to jointly recover one or more of scene geometry, material appearance and the lighting condition. In practice, the material appearance is typically modeled using physically-based rendering assets such as albedo, roughness and glossiness. Mesh-based inverse rendering methods [2, 38, 49, 68] try to recover materials using differentiable path tracing [25]. However, they typically assume a given geometry, since optimizing mesh geometry is challenging. On the contrary, NeRF-based inverse rendering approaches [5, 42, 65, 66] make it easier to optimize geometry jointly by modeling material properties and density continuously in a volumetric 3D space. The lighting is usually represented as point or directional lights [5, 23, 60], an environment texture map [31-33, 42, 65], or an implicit texture map modeled by spherical Gaussians [6, 11, 18, 63, 66, 66, 67] or MLPs [7, 29]. Most methods are limited to object-level reconstruction and assume the lighting is spatially invariant (i.e. distant). Several light estimation techniques [13, 26, 27, 41] explore using 3D light primitives or spatially-varying spherical Gaussians to model spatially varying lighting. However, these methods focus on data-driven approaches to estimate lighting for image editing. NeILF [56] and NeILF++ [62] model lighting as a 5D light field using another MLP, but still focus mainly on small-scale reconstruction. Several works apply inverse rendering for relighting outdoor scenes [24, 40, 48, 58]. However, they fo", + "bbox": [ + 496, + 493, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21189", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/f4418cee136b1d66e9b2ffd94268584dc8d55974c80094f3e2047b19ad456556.jpg", + "image_caption": [ + "Figure 2. An overview of our model. The key enabler for specular reflections is our novel 3D Gaussian directional encoding module that converts the reflected ray into a spatially-varying embedding, which is further decoded into specular color." + ], + "image_footnote": [], + "bbox": [ + 81, + 89, + 893, + 186 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "cus more on diffuse materials with correct shadow modeling instead of reflections. In this work, we have a different goal compared to inverse rendering, focusing only on correctly modeling reflections for better novel-view synthesis, rather than trying to discern material properties for standalone use.", + "bbox": [ + 75, + 233, + 468, + 309 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "NeRF with mirror reflections. One special case of reflection is mirror reflection. One approach represents the reflected scene as a separate NeRF [15], and composites the two NeRF results in image space. This is also deployed in image-based rendering [52] and large-scale NeRF reconstruction [50]. Given a multi-mirror scene, the idea can be further extended to multi-space NeRFs [57]. An alternate approach is to explicitly model the mirror geometry, and to render the mirrored scene by path tracing [16, 61]. However, since estimating the mirror geometry is highly ill-posed, manual annotation is usually needed. Curved reflectors need even more careful handling [22, 46].", + "bbox": [ + 75, + 311, + 473, + 494 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 506, + 215, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first review Ref-NeRF [47] for decomposing view-dependent appearance. Similar to NeRF, Ref-NeRF models the scene as a function that maps the position $\\mathbf{x}$ and view direction $\\mathbf{d}$ to the final color $\\mathbf{c}$ and density $\\tau$ . The difference is that Ref-NeRF predicts the color as a combination of diffuse color $\\mathbf{c}_{\\mathrm{d}}$ and specular color $\\mathbf{c}_{\\mathrm{s}}$ :", + "bbox": [ + 75, + 531, + 470, + 622 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} = \\gamma \\left(\\mathbf {c} _ {\\mathrm {d}} + \\mathbf {c} _ {\\mathrm {s}} \\odot \\mathbf {s}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 202, + 631, + 468, + 646 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{s}$ is the specular tint, $\\odot$ the element-wise product, and $\\gamma (\\cdot)$ a tone-mapping function. To predict the specular color $\\mathbf{c}_{\\mathrm{s}}$ , Ref-NeRF first predicts the surface normal $\\mathbf{n}$ , roughness $\\rho$ , and features $\\varphi$ at location $\\mathbf{x}$ using an MLP. Then, the specular color $\\mathbf{c}_{\\mathrm{s}}$ is parameterized as a function of the reflection direction $\\mathbf{d}_{\\mathrm{r}}$ :", + "bbox": [ + 75, + 654, + 468, + 744 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {c} _ {\\mathrm {s}} = F _ {\\boldsymbol {\\theta}} \\left(\\lambda_ {\\mathrm {I D E}} \\left(\\mathbf {d} _ {\\mathrm {r}}, \\rho\\right), \\varphi\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 753, + 468, + 770 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\lambda_{\\mathrm{IDE}}(\\cdot)$ is the integrated directional encoding introduced by Ref-NeRF, $F_{\\theta}(\\cdot)$ represents an MLP with parameters $\\theta$ , and the reflection direction $\\mathbf{d}_{\\mathrm{r}}$ is the input direction $\\mathbf{d}$ reflected at the predicted surface normal $\\mathbf{n}$ :", + "bbox": [ + 75, + 777, + 470, + 838 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {\\mathrm {r}} = \\mathbf {d} - 2 (\\mathbf {d} \\cdot \\mathbf {n}) \\mathbf {n}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 845, + 468, + 862 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By conditioning the specular color on reflection direction and roughness, the function $F_{\\theta}$ needs to fit is much simpler.", + "bbox": [ + 75, + 869, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 498, + 232, + 589, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our goal is to enhance NeRF's capabilities for modeling specular reflections under near-field lighting conditions. Figure 2 presents an overview of our pipeline. A key contribution is the 3D Gaussian directional encoding that maps a ray and surface roughness to a ray embedding.", + "bbox": [ + 496, + 258, + 893, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To render a pixel, we sample points along an input ray $\\mathbf{o} + t\\mathbf{d}$ , and predict volume density $\\tau'$ , diffuse color $\\mathbf{c}_{\\mathrm{d}}'$ , tint $\\mathbf{s}'$ , roughness $\\rho'$ , and normal direction $\\mathbf{n}'$ at each sample point (we denote per-sample properties using a prime). Given that reflections occur only at the surface, we evaluate the specular component once per ray on the surface obtained from the NeRF depth. This also results in less computation than per-sample-point specular shading. Consequently, we calculate volumetric depth $t_0$ by rendering the ray marching distance at each sample point. We also volumetrically render all attributes to synthesize screen-space attributes ( $\\mathbf{c}_{\\mathrm{d}}, \\mathbf{s}, \\rho, \\mathbf{n}$ ). Note that the rendered normal must be normalized to yield the final screen-space normal $\\mathbf{n}$ . We then evaluate the specular component by first computing the reflected ray using origin $\\mathbf{o}_{\\mathrm{r}} = \\mathbf{o} + t_0\\mathbf{d}$ , and the reflection direction $\\mathbf{d}_{\\mathrm{r}}$ derived using Equation 3. The reflected ray $\\mathbf{o}_{\\mathrm{r}} + t\\mathbf{d}_{\\mathrm{r}}$ and surface roughness $\\rho$ are then encoded using our novel 3D Gaussian directional encoding. After a tiny MLP, we compute the specular color $\\mathbf{c}_{\\mathrm{s}}$ , and the final rendering result using Equation 1.", + "bbox": [ + 496, + 335, + 893, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "From a physically based rendering perspective, Equation 1 is analogous to the Cook-Torrance approximation [10] of the rendering equation [19]. The term $\\mathbf{c}_{\\mathrm{s}} \\odot \\mathbf{s}$ can be interpreted as the split-sum approximation of the specular part of the Cook-Torrance model, with the specular color $\\mathbf{c}_{\\mathrm{s}}$ corresponding to the preconvolved incident light, and the tint s to the pre-integrated bidirectional reflectance distribution function (BRDF).", + "bbox": [ + 496, + 638, + 893, + 758 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Gaussian Directional Encoding", + "text_level": 1, + "bbox": [ + 498, + 770, + 774, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Existing works parameterize view-dependent appearance by first encoding view or reflection direction into Fourier or spherical harmonics (SH) features, which results in a spatially invariant encoding of the view direction. Therefore, it becomes challenging for the NeRF to model spatially varying view-dependent effects, such as near-field lighting. We illustrate this via a toy example in Figure 3, where we place", + "bbox": [ + 496, + 795, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21190", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f988da75a78a0b338d0e41633d4a01183b148ec7552a9ee652c841a08378d4b3.jpg", + "image_caption": [ + "Figure 3. Toy example of 3D Gaussian encoding. Left: A hemisphere probe translates underneath 4 lights along positions numbered 1 to 4. Note that we dilate the lights for better visualization. Right: Representation of the probe's specular components using spherical harmonics and our 3D Gaussian directional encoding. The SH encoding shows a more complex pattern under position change, while ours has spatially largely invariant coefficients. This suggests a simpler function for the specular prediction MLP to fit using Gaussian directional encoding." + ], + "image_footnote": [], + "bbox": [ + 80, + 95, + 455, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a hemispherical specular probe in a simple scene with four lights of different shapes and colors. Then, we represent the specular component of the toy example by linearly combining the directional encoding features. We find the optimal coefficients for each encoding type that best fit the ground-truth specular component using stochastic gradient descent, and visualize them in Figure 3. We can see that even for this simple toy setup, the SH-based encoding requires complex, spatially varying coefficients, which complicates the underlying function for the NeRF to fit and interpolate.", + "bbox": [ + 75, + 332, + 470, + 484 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose to spatially vary the encoding function by defining the basis functions via several learnable 3D Gaussians. Specifically, we parameterize 3D Gaussians using their position $\\pmb{\\mu}_i\\in \\mathbb{R}^3$ , scale $\\sigma_{i}\\in \\mathbb{R}^{3}$ , and quaternion rotation $\\mathbf{q}_i\\in \\mathbb{H}$ :", + "bbox": [ + 75, + 484, + 470, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {G} _ {i} (\\mathbf {x}) = \\exp \\left(- \\left\\| \\mathcal {Q} \\left(\\mathbf {x} - \\boldsymbol {\\mu} _ {i}; \\mathbf {q} _ {i}\\right) \\odot \\boldsymbol {\\sigma} _ {i} ^ {- 1} \\right\\| _ {2} ^ {2}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 565, + 468, + 590 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{Q}(\\mathbf{v};\\mathbf{q}_i)$ represents applying quaternion rotation $\\mathbf{q}_i$ to the vector $\\mathbf{v}$ . To compute the $i$ -th dimension of the encoding for a ray $\\mathbf{o} + t\\mathbf{d}$ , we need to define a basis function $\\mathcal{P}_i(\\mathbf{o},\\mathbf{d}) \\in \\mathbb{R}$ that maps the ray to a scalar value given the Gaussian parameters. While there are many ways to define the mapping, we find one that is efficient and has a closed-form solution by defining the projection as the maximum value of the Gaussian along the ray:", + "bbox": [ + 75, + 595, + 470, + 717 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {i} (\\mathbf {o}, \\mathbf {d}) = \\max _ {t \\geq 0} \\mathcal {G} _ {i} (\\mathbf {o} + t \\mathbf {d}). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 724, + 468, + 747 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the supplement, we derive the closed-form solution:", + "bbox": [ + 76, + 753, + 437, + 768 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} _ {i} (\\mathbf {o}, \\mathbf {d}) = \\left\\{ \\begin{array}{l l} \\exp \\left(\\frac {\\left(\\mathbf {o} _ {i} ^ {\\top} \\mathbf {d} _ {i}\\right) ^ {2}}{\\mathbf {d} _ {i} ^ {\\top} \\mathbf {d} _ {i}} - \\mathbf {o} _ {i} ^ {\\top} \\mathbf {o} _ {i}\\right) & \\mathbf {o} _ {i} ^ {\\top} \\mathbf {d} _ {i} < 0 \\\\ \\mathcal {G} _ {i} (\\mathbf {o}) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 773, + 468, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{o}_i$ and $\\mathbf{d}_i$ are the ray origin and direction transformed into Gaussian-local space:", + "bbox": [ + 75, + 821, + 468, + 853 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {o} _ {i} = \\mathcal {Q} (\\mathbf {o} - \\boldsymbol {\\mu} _ {i}; \\mathbf {q} _ {i}) \\odot \\sigma_ {i} ^ {- 1}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 858, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {d} _ {i} = \\mathcal {Q} (\\mathbf {d}; \\mathbf {q} _ {i}) \\odot \\sigma_ {i} ^ {- 1}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 878, + 468, + 897 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/78692e67d272236fb8e4537dbf343b413a1ff16b58a78783890e3b45abfcfa1f.jpg", + "image_caption": [ + "Figure 4. Stereographic projections of the specular fitting results for the toy example in Figure 3. Both encodings produce 25 coefficients for each color channel, which are then summed to produce the final color. Note that the GT shows soft boundaries because it is preconvolved. The 3D Gaussian-based encoding demonstrates superior performance in representing the specular change with positional changes, and is also capable of smoothly varying roughness." + ], + "image_footnote": [], + "bbox": [ + 506, + 93, + 888, + 367 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By applying Equation 6 for every 3D Gaussian, we obtain a vector of projected values $\\{\\mathcal{P}_i\\}$ , which forms our final encoding features. Similar to existing NeRF-based representations [9, 34, 36], we rely on a small MLP to convert the encoding to a specular color $\\mathbf{c}_{\\mathrm{s}}$ .", + "bbox": [ + 496, + 483, + 893, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As illustrated by the toy example in Figure 3, our Gaussian directional encoding exhibits more constant coefficients in response to the position changes, suggesting a smoother mapping from the embedding features to the specular color. This smoothness is due to the Gaussian basis function producing spatially varying features that mimic the behavior of how the specular component would change under near-field lighting conditions. As a result, the underlying functions that model the specular reflections are easier to learn.", + "bbox": [ + 496, + 561, + 893, + 698 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also visualize the fitted specular color of both approaches in Figure 4. Our 3D Gaussian directional encoding more accurately captures the spatial variations of the specular components.", + "bbox": [ + 496, + 700, + 893, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Similar to Ref-NeRF, we use an additional \"roughness\" value $\\rho$ to control the maximum frequency of the specular color. We achieve this in our Gaussian embedding by multiplying each Gaussian's scale $\\sigma_{i}$ with the roughness $\\rho$ . Intuitively, a larger Gaussian results in a smoother function with varying direction $\\mathbf{d}$ . Substituting the $\\sigma_{i}$ with $\\rho \\sigma_{i}$ in Equation 6 leads to the complete equation of our 3D Gaussian encoding. Figure 4 demonstrates the ability of our 3D Gaussian-based encoding to modify roughness on the fly.", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21191", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Optimizing the Gaussian Directional Encoding", + "text_level": 1, + "bbox": [ + 76, + 90, + 470, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "It is worth noting that our proposed Gaussian encoding correctly models spatially varying specular reflections only when the Gaussians are positioned properly in 3D space. We thus jointly optimize the Gaussian parameters together with the NeRF during training, to ensure the Gaussians are in the optimal state for modeling reflections. However, there is no direct supervision for the Gaussian parameters.", + "bbox": [ + 75, + 113, + 468, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our experiments show that without proper initial Gaussian parameters, the optimization may lead to suboptimal local minima, resulting in inconsistent quality of specular reconstruction. To address this, we propose an initialization stage for the Gaussian parameters and to bootstrap the specular color prediction. As mentioned earlier, the specular color is essentially the preconvolved incident light, which can be directly deduced from input images.", + "bbox": [ + 75, + 219, + 470, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motivated by this observation, we train the 3D Gaussians and the specular decoder $(\\mathrm{MLP}_3$ in Figure 2) in the initialization stage using the input images. We train an incident light field that accommodates a diversity of rays and roughness values. Therefore, we apply a range of Gaussian blurs to all input images using a series of standard deviations, generating Gaussian pyramids. These pyramids of input images provide a pseudo target for incident light under different degrees of surface roughness. In each iteration of the training, we sample pixels from the pyramids and trace rays to these pixels. The traced rays are also associated with a roughness value that is equivalent to the blur's standard deviation. We encode each ray with roughness using our Gaussian directional encoding, and predict the specular color $\\mathbf{c}_{\\mathrm{s}}$ using the decoder. By minimizing the errors between $\\mathbf{c}_{\\mathrm{s}}$ and the pseudo ground truth, we refine the Gaussian parameters and the specular decoder, which then serve as initialization for the subsequent joint optimization stage.", + "bbox": [ + 75, + 340, + 472, + 613 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Resolving the Shape-Radiance Ambiguity", + "text_level": 1, + "bbox": [ + 76, + 619, + 434, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Regardless of any view-dependent parameterization, there remains a fundamental ambiguity between shape and radiance in NeRFs. For example, consider a perfect mirror reflection. Without any prior knowledge, it is nearly impossible for the NeRF model to tell whether the mirror is a flat surface with perfect reflection, or a window to a (virtual) scene behind the surface. Therefore, prior information is needed to guide the model to learn the correct geometry. Inspired by recent progress in monocular geometry estimation [4, 12, 39, 59], we propose to supervise the predicted normal $\\mathbf{n}$ using monocular normal estimation $\\mathbf{n}_{\\mathrm{mono}}$ [12]:", + "bbox": [ + 75, + 642, + 470, + 808 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {m o n o}} = \\sum_ {j} \\left\\| \\mathbf {n} ^ {j} - \\mathbf {R} ^ {j} \\mathbf {n} _ {\\mathrm {m o n o}} ^ {j} \\right\\| _ {2} ^ {2}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 814, + 470, + 847 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the superscript $j$ is a ray index, and $\\mathbf{R}^j$ is the corresponding camera rotation matrix that converts normals from view space to world space.", + "bbox": [ + 75, + 854, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/5075a3ac83240cc5c87f268ef2df01f6ecde4fd12a8771ce1279f47e84daa1e1.jpg", + "image_caption": [ + "Target", + "Full", + "w/o $\\mathcal{L}_{\\mathrm{mono}}$", + "w/o early stop", + "Figure 5. The specular component reconstruction (first row, except the first image), novel-view synthesis results (second row) and normal visualizations (third row) under varying monocular normal supervision. The target normal visualizes the monocular normal prediction. Without $\\mathcal{L}_{\\mathrm{mono}}$ , the predicted normal exhibits enormous error, leading to poor specular reconstruction. Without early stopping $\\mathcal{L}_{\\mathrm{mono}}$ , minor errors in the predicted normals lead to a slight degradation in the reflection quality compared to our full model." + ], + "image_footnote": [], + "bbox": [ + 504, + 101, + 888, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "However, monocular normals are prone to error. We therefore use them primarily as initialization and apply $\\mathcal{L}_{\\mathrm{mono}}$ only at the beginning of the training, so that the errors in the normals do not overwhelm the geometry of the NeRF. Figure 5 and Table 2 show results with different configurations of $\\mathcal{L}_{\\mathrm{mono}}$ . We can see that without monocular normal as supervision ('w/o $\\mathcal{L}_{\\mathrm{mono}}$ ), the predicted normals have catastrophic errors, such as those pointing inwards (orange) or lying parallel (violet) to the surface. Consequently, the learned specular component is less accurate due to the incorrect normals. Despite this, a somewhat plausible specular reflection can still be learned as the Gaussian encoding can \"cheat\" the reflections even with erroneous normals. On the other hand, without early stopping of the loss ('w/o early stop'), minor inaccuracies from the monocular normals permeate into predicted normals, leading to a degradation of the reflection quality.", + "bbox": [ + 496, + 376, + 893, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Losses", + "text_level": 1, + "bbox": [ + 500, + 642, + 586, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To jointly optimize all parameters within our proposed pipeline, we use a combination of loss terms:", + "bbox": [ + 496, + 665, + 890, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c}} + \\mathcal {L} _ {\\text {p r o p}} + \\lambda_ {\\text {d i s t}} \\mathcal {L} _ {\\text {d i s t}} + \\lambda_ {\\text {m o n o}} \\mathcal {L} _ {\\text {m o n o}} + \\lambda_ {\\text {n o r m}} \\mathcal {L} _ {\\text {n o r m}}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 707, + 890, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this equation, $\\mathcal{L}_{\\mathrm{c}}$ is the L1 reconstruction loss between the predicted and ground-truth colors. The terms $\\mathcal{L}_{\\mathrm{prop}}$ and $\\mathcal{L}_{\\mathrm{dist}}$ are adopted from mip-NeRF 360 [3], where $\\mathcal{L}_{\\mathrm{prop}}$ supervises the density proposal networks, and $\\mathcal{L}_{\\mathrm{dist}}$ is the distortion loss encouraging density sparsity. To tie predicted normals to the density field, we use Ref-NeRF's normal prediction loss $\\mathcal{L}_{\\mathrm{norm}}$ [47], which guides the predicted normal $\\mathbf{n}$ with the density gradient direction. Further elaboration on these loss components can be found in the supplementary material.", + "bbox": [ + 496, + 734, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In our experiments, we set $\\lambda_{\\mathrm{dist}} = 0.002$ , aligning with the settings of the \"nerfacto\" model in Nerfstudio [44]. For", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21192", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/6e27975e7ed58c96d7cba0dc351d996ca8cf4f9c1f9e36f718a8b0f565f5cfe7.jpg", + "table_caption": [ + "Table 1. Quantitative comparisons of novel-view synthesis on three datasets. We highlight the best numbers in bold." + ], + "table_footnote": [], + "table_body": "
MethodsEyeful Tower dataset [53]NISR [50] + Inria [38] datasetShiny dataset [47]
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Ours32.5830.93280.144530.7710.89090.165526.5640.72770.2776
NeRF [34]31.8540.92540.162630.7480.88730.172826.4690.72350.2852
Ref-NeRF [47]31.6520.92580.157030.6540.89030.166926.5020.72420.2827
MS-NeRF [57]31.7150.93110.156130.2240.88400.181626.4660.70700.3225
GT Test ImageGT & SfM NormalOursRef-NeRF [47]MS-NeRF [57]NeRF [34]
Eyeful Workshop
NISR LivingRoom2
Eyeful Office2
", + "bbox": [ + 76, + 107, + 893, + 579 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 6. Comparisons of novel-view synthesis quality and normal map visualizations. Our method consistently reconstructs reflections while other methods either produce 'faked' reflections, resulting in incorrect normals, or fail to model reflections entirely.", + "bbox": [ + 75, + 583, + 892, + 612 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$\\lambda_{\\mathrm{mono}}$ , we choose a value of 1 in the first 4K iterations, and reduce to 0 thereafter to cease its effect, as described earlier. We find that our method is robust to the value of $\\lambda_{\\mathrm{mono}}$ as it only serves as initialization. We also assign $\\lambda_{\\mathrm{norm}} = 10^{-3}$ , which is slightly higher than the weight in Ref-NeRF [47], as we find that this produces slightly smoother normals without substantially compromising the rendering quality.", + "bbox": [ + 75, + 619, + 473, + 728 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 739, + 209, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. To model room-scale scenes, we employ a network architecture similar to the \"nerfacto\" model presented in Nerfstudio [44]. We use two small density networks as proposal networks, supervised via $\\mathcal{L}_{\\mathrm{prop}}$ . We sample 256 and 96 points for each proposal network, and 48 points for the final NeRF model. These three networks all use hash-based positional encodings. When querying the hash features in the final NeRF model, we incorporate the LOD-aware scheme proposed in VR-NeRF [53]. We train our model", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "for 100,000 iterations and randomly sample 12,800 rays in each iteration. This process takes around 8 GB of GPU memory and approximately 3.5 hours to train a model using an NVIDIA A100 GPU. Further details regarding the model's structure can be found in the supplementary materials.", + "bbox": [ + 496, + 619, + 893, + 696 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate our method on several datasets with a focus on indoor scenes characterized by near-field lighting conditions. First, we evaluate on the Eyeful Tower dataset [53], which provides high-quality HDR captures of 11 indoor scenes. Each scene is coupled with calibrated camera parameters and a mesh reconstructed via Agisoft Metashape [1]. We select 9 scenes that feature notable reflective properties. We downsample the images of each scene to a resolution of $854 \\times 1280$ pixels. We curated around 50-70 views per scene that contain glossy surfaces for evaluation, leaving the remaining views for training. We also evaluate our approach on public indoor datasets NISR [50] and Inria [38] (NISR+Inria). Moreover, to assess the performance under", + "bbox": [ + 496, + 703, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21193", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/191aa998a13f1e839c5084aa64f6ce4f3b1e106d14f26bed69b9682eb61d08db.jpg", + "image_caption": [ + "Figure 7. Intermediate components of our approach compared to Ref-NeRF [47]. Our approach produces a more meaningful decomposition under room-scale lighting settings." + ], + "image_footnote": [], + "bbox": [ + 80, + 90, + 890, + 340 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "far-field lighting, we evaluate the real shiny dataset in Ref-NeRF [47]. We report the average PSNR, SSIM, and LPIPS [64] metrics for evaluating rendering quality.", + "bbox": [ + 75, + 378, + 470, + 425 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 436, + 215, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our method with several baselines: NeRF [34], Ref-NeRF [47], and MS-NeRF [57], which specializes in mirror-like reflections by decomposing NeRF into multiple spaces. For a fair comparison, we re-implement these baselines, such that we share the same NeRF backbone and rendering configurations, with the only difference being the way different methods decompose and parameterize the output color. We report the numerical results across three datasets in Table 1. Our method demonstrates superior performance on the Eyeful Tower dataset, indicating the effectiveness of our method. On the NISR+Inria datasets, our method marginally outperforms the baselines, likely due to the dataset containing few reflection surfaces. Notably, while our method is tailored for near-field lighting conditions, it also shows promising results on the Shiny dataset, which comprises far-field lighting scenarios. This is because our Gaussian directional encoding can simulate a spatially invariant encoding by positioning Gaussians at a significant distance.", + "bbox": [ + 75, + 460, + 470, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative results on the Eyeful Tower and NISR+Inria datasets are provided in Figure 6. We can see that while other baselines occasionally synthesize plausible reflections, they resort to approximations that fake the reflections by placing emitters underneath the surface. As a result, they either produce incorrect geometry, or fail to model the reflections. Our method, in contrast, successfully models specular highlights on the surface. We provide additional video results in the supplementary material.", + "bbox": [ + 75, + 733, + 468, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also visualize and compare the decomposition produced by our method and Ref-NeRF in Figure 7. We can see", + "bbox": [ + 75, + 869, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c496a1f8ae23690a55311735cbad98741f8113fdc5b5fe5d12f92891dfbd496d.jpg", + "image_caption": [ + "Figure 8. We evaluate the novel-view synthesis quality with respect to the number of Gaussians across five scenes. The green dashed line is the setting we use in our experiments." + ], + "image_footnote": [], + "bbox": [ + 498, + 375, + 893, + 486 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "that Ref-NeRF fails to obtain a meaningful decomposition under near-field lighting, and produces holes in the geometry, whereas our method consistently achieves a realistic separation of specular and diffuse components.", + "bbox": [ + 498, + 544, + 893, + 604 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Ablation Studies", + "text_level": 1, + "bbox": [ + 500, + 614, + 663, + 628 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Number of Gaussians. One important hyperparameter in the Gaussian directional encoding is the number of Gaussians, as it directly influences the model's capacity to represent specular colors. We conduct experiments to evaluate the impact of varying the number of Gaussians on five scenes from the Eyeful Tower dataset, and show the relationship between the number of Gaussians and the rendering quality in Figure 8. The rendering quality improves when using more Gaussians, but the improvement saturates as the number increases beyond 400. Note that using a larger number of Gaussians also entails greater computation costs and GPU memory requirements for every rendered pixel. Therefore, we use 256 Gaussians for all experiments, to strike a balance between rendering quality and computational efficiency.", + "bbox": [ + 496, + 638, + 893, + 849 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Optimizing Gaussians. To optimize the Gaussian directional encoding effectively, we first initialize them by training an incident light field, and then jointly finetune the Gaus", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21194", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a069467b947f55e597579c3a74106d77518aca77f0fe32f3f0495164f451280b.jpg", + "table_caption": [ + "Table 2. Ablations of our method on the Eyeful Tower dataset [53]. The \"e.s.\" indicates early stopping the $\\mathcal{L}_{\\mathrm{mono}}$ after 4K iterations." + ], + "table_footnote": [], + "table_body": "
MethodGaussians Init.Mono. Opt.E. S. Prior\\( {\\mathcal{L}}_{\\text{mono }} \\)PSNR↑SSIM↑LPIPS↓
Full✓✓✓✓32.580.93280.1445
w/o init✘✓✓✓32.520.93040.1429
w/o opt.✓✘✓✓32.060.92650.1581
w/o \\( {\\mathcal{L}}_{\\text{mono }} \\)✓✓✘-32.310.92880.1503
w/o e.s.✓✓✓✘32.460.92920.1502
", + "bbox": [ + 81, + 121, + 460, + 234 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d4ac95ee386b74c84014376c9e7da2e5a3f4c919155b041861f19d2bc92f820.jpg", + "image_caption": [ + "Figure 9. Example results under different Gaussian optimization settings. Without initializing the Gaussian parameters ('w/o init') or optimizing Gaussians jointly with the NeRF ('w/o opt.'), the Gaussian embedding struggles to model specularities accurately." + ], + "image_footnote": [], + "bbox": [ + 80, + 236, + 465, + 462 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sian encoding together with the NeRF model. We demonstrate the significance of initialization ('w/o init') and fine-tuning ('w/o opt.') by omitting each process individually. We show quantitative results in Table 2 and a qualitative example in Figure 9. Without initialization, the model can still reconstruct reflections to some extent, resulting in a slightly better average LPIPS score, yet it fails to model some specular details, such as the light blobs. Neglecting the joint optimization of Gaussians leads to complete failure in modeling specular reflections. As illustrated in Figure 9, with the inaccurate specular modeling, the tints suppress the specular reflections, which ultimately leads to the inability to represent reflections in the final rendered image.", + "bbox": [ + 75, + 529, + 472, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and Conclusion", + "text_level": 1, + "bbox": [ + 76, + 739, + 323, + 755 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Applications. Our primary goal was to improve the quality of novel-view synthesis with specular reflective surfaces. We achieve this via our proposed Gaussian directional encoding that enables a meaningful decomposition of specular and diffuse components in a scene. Moreover, this also enables applications other than novel-view synthesis, such as reflection removal, and surface roughness editing. For instance, Figure 7 shows that we can easily remove reflections using the diffuse component. Furthermore, Figure 10 demonstrates", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/c0149805caa2359d9f2f152c9704756e08c95f1fce0c7662b04bd3f7e73c35ba.jpg", + "image_caption": [ + "Figure 10. We can control the roughness of the scene by adding an offset to the input roughness." + ], + "image_footnote": [], + "bbox": [ + 506, + 87, + 893, + 246 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1614d5b18f25ef28f8660954b5ff6ce5c887d1154516b1345f58ef0a8289aa16.jpg", + "image_caption": [ + "Figure 11. Our method cannot reconstruct mirror-like perfect reflections due to the limited capacity of the 3D Gaussian encoding." + ], + "image_footnote": [], + "bbox": [ + 500, + 287, + 887, + 373 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "an example of editing roughness. By adding an offset to the predicted roughness during rendering, we can effectively manipulate the glossiness of the real surface.", + "bbox": [ + 498, + 417, + 890, + 462 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. While our method improves on existing baselines, it has some limitations. As we parameterize the specular color via only several hundreds of Gaussians, the encoding is limited to relatively low frequency compared with perfect mirror-like reflections. We show such a failure case in Figure 11. We can see that our method is only able to learn a blurry version of the reflection. This could be alleviated by using many more Gaussians, as demonstrated in 3D Gaussian splatting [20]. However, the computational cost of traversing all Gaussians for every pixel quickly becomes prohibitive in our implementation. More efficient traversal, such as by rasterization, could be interesting future work.", + "bbox": [ + 496, + 467, + 893, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conclusion. In this paper, we proposed a pipeline to improve the existing approach in modeling and reconstructing view-dependent effects in a NeRF representation. Central to our approach is a new Gaussian directional encoding to enhance the capability of neural radiance fields to model specular reflections under near-field lighting. We also utilize monocular normal supervision to help resolve shape-radiance ambiguity. Experiments have demonstrated the effectiveness of each of our contributions. We believe this work proposes a practical and effective solution for reconstructing NeRFs in room-scale scenes, specifically addressing the challenges of accurately capturing specular reflections.", + "bbox": [ + 496, + 654, + 895, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. The authors from HKUST were partly supported by the Hong Kong Research Grants Council (RGC). We would like to thank Linning Xu and Zhao Dong for helpful discussions.", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21195", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Agisoft LLC. Agisoft Metashape Professional. 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In AAAI, 2024. 2" + ], + "bbox": [ + 78, + 90, + 470, + 501 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "21198", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/3d459af2-f520-428c-a01a-361ee7f87043_model.json b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/3d459af2-f520-428c-a01a-361ee7f87043_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b7ec69f8b41ade54fb6702794b55bef26c1f912d --- /dev/null +++ b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/3d459af2-f520-428c-a01a-361ee7f87043_model.json @@ -0,0 +1,2268 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.141, + 0.131, + 0.823, + 0.154 + ], + "angle": 0, + "content": "SpecNeRF: Gaussian Directional Encoding for Specular Reflections" + }, + { + "type": "text", + "bbox": [ + 0.202, + 0.173, + 0.768, + 0.209 + ], + "angle": 0, + "content": "Li Ma\\(^{1,2}\\) Vasu Agrawal\\(^{2}\\) Haithem Turki\\(^{2,3}\\) Changil Kim\\(^{2}\\) Chen Gao\\(^{2}\\) Pedro Sander\\(^{1}\\) Michael Zollhöfer\\(^{2}\\) Christian Richardt\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.216, + 0.706, + 0.253 + ], + "angle": 0, + "content": "1The Hong Kong University of Science and Technology 2Meta Reality Labs 3Carnegie Mellon University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.277, + 0.314, + 0.293 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.31, + 0.474, + 0.613 + ], + "angle": 0, + "content": "Neural radiance fields have achieved remarkable performance in modeling the appearance of 3D scenes. However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of indoor environments. Unlike existing methods, which typically assume distant lighting like an environment map, we propose a learnable Gaussian directional encoding to better model the view-dependent effects under near-field lighting conditions. Importantly, our new directional encoding captures the spatially-varying nature of near-field lighting and emulates the behavior of prefiltered environment maps. As a result, it enables the efficient evaluation of preconvolved specular color at any 3D location with varying roughness coefficients. We further introduce a data-driven geometry prior that helps alleviate the shape radiance ambiguity in reflection modeling. We show that our Gaussian directional encoding and geometry prior significantly improve the modeling of challenging specular reflections in neural radiance fields, which helps decompose appearance into more physically meaningful components." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.647, + 0.21, + 0.663 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Neural radiance fields (NeRFs) have emerged as a popular scene representation for novel-view synthesis [34, 45, 51]. By training a neural network based on sparse observations of a 3D scene, NeRF-like representations are able to synthesize novel views with photorealistic visual quality. In particular, with a scalable model design, such as InstantNGP [36], NeRFs are able to model room-scale 3D scenes with extraordinary detail [53]. However, existing approaches typically only manage to model mild view-dependent effects like those seen on nearly diffuse surfaces. When encountering highly view-dependent glossy surfaces, NeRFs struggle to model the high-frequency changes when the viewpoint changes. Instead, they tend to \"fake\" specular reflections by placing them behind surfaces, which may result in poor view interpolation and \"foggy\" geometry [47]. Moreover, fake" + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.279, + 0.895, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.45, + 0.895, + 0.52 + ], + "angle": 0, + "content": "Figure 1. We propose a Gaussian directional encoding that leads to better modeling of specular reflections under near-field lighting conditions. In contrast, the integrated directional encoding utilized in Ref-NeRF [47] and Fourier directional encoding in NeRF [34] exhibit suboptimal performance under similar conditions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.535, + 0.895, + 0.566 + ], + "angle": 0, + "content": "reflections are not viable if one can look behind the surface, as NeRF can no longer hide the reflections there." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.567, + 0.896, + 0.78 + ], + "angle": 0, + "content": "Accurately modeling and reconstructing specular reflections presents notable challenges, especially for room-scale scenes. Physically correct reflection modeling involves pathtracing many rays for every single pixel, which is impractical for NeRF-like volumetric scene representations, primarily due to the large computational requirements to shade a single pixel. Consequently, an efficient approximation of the reflection shading is needed for a feasible modeling of reflections. Existing works [14, 47] address this challenge by incorporating heuristic modules inspired by real-time image-based lighting (IBL) [35] techniques, such as explicit ray bounce computations to enhance NeRF's capability to simulate reflections, and integrated directional encoding to simulate appearance change under varying surface roughness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.897, + 0.903 + ], + "angle": 0, + "content": "While these improvements have shown to be effective in modeling specular reflections for NeRFs, they are limited to object-level reconstruction under distant lighting, which assumes the object is lit by a 2D environment map. They work poorly for modeling near-field lighting, where the corresponding environment map varies spatially. The issue is that existing methods rely on directional encodings to embed ray directions for generating view-dependent reflections." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21188" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "These encodings, such as Fourier encoding or spherical harmonics, are spatially invariant. Figure 1 demonstrates one example of NeRF [34] and Ref-NeRF [47] reconstructions of an indoor scene with spatially-varying lighting. NeRF produces extremely noisy geometry, resulting in artifacts in the rendering result. Ref-NeRF offers a slight improvement, but still struggles with noisy geometry and view interpolation. This illustrates that the spatial invariance in the directional encodings of existing methods presents challenges under spatially-varying lighting conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.424 + ], + "angle": 0, + "content": "In this work, we propose a novel Gaussian directional encoding that is tailored for spatially varying lighting conditions. Instead of only encoding a 2D ray direction, we use a set of learnable 3D Gaussians as the basis to embed a 5D ray space including both ray origin and ray direction. We show that, with appropriately optimized Gaussian parameters, this encoding introduces an important inductive bias towards near-field lighting, which enhances the model's ability to capture the characteristics of specular surfaces, leading to photorealistic reconstructions of shiny reflections. We further demonstrate that by changing the scale of the 3D Gaussians, we can edit the apparent roughness of a surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.424, + 0.473, + 0.725 + ], + "angle": 0, + "content": "While our proposed Gaussian directional encoding improves the reflection modeling of NeRF, high-quality reflection reconstruction also requires an accurate surface geometry and normal in order to compute accurate reflection rays. However, the geometry within NeRFs is often noisy in the early phases of training, which presents challenges in simultaneously optimizing for good geometry and reflections. To better address this challenge, we introduce a data-driven prior to direct the NeRF model towards the desired solution. We deploy a monocular normal estimation network to supervise the normal of the geometry at the beginning of the training stage, and show that this bootstrapping strategy improves the reconstruction of normals, and further leads to successful modeling of specular reflections. We conduct experiments on several public datasets and show that the proposed method outperforms existing methods, achieving higher-quality photorealistic rendering of reflective scenes while also providing more meaningful and accurate color component decomposition. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.726, + 0.47, + 0.771 + ], + "angle": 0, + "content": "- We propose a novel Gaussian directional encoding that is more effective in modeling view-dependent effects under near-field lighting conditions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.772, + 0.469, + 0.801 + ], + "angle": 0, + "content": "- We propose to use monocular normal estimation to resolve shape-radiance ambiguity in the early training stages." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.802, + 0.47, + 0.831 + ], + "angle": 0, + "content": "- Our full NeRF pipeline achieves state-of-the-art novel-view synthesis performance for specular reflections." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.726, + 0.47, + 0.831 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.845, + 0.219, + 0.86 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Reflection-aware NeRFs. Successfully modeling view-dependent effects, such as specular reflections, can greatly" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.485 + ], + "angle": 0, + "content": "enhance the photorealism of the reconstructed NeRF. NeRF models view-dependency by conditioning the radiance on the positional encoding [43] of the input ray direction, which is only capable of mild view-dependent effects. Ref-NeRF [47] improves NeRF's capability for modeling reflections by conditioning the view-dependent appearance on the reflection ray direction instead of incident ray direction, and by modulating the directional encoding based on surface roughness. This reparameterization of outgoing radiance makes the underlying scene function simpler, leading to a better geometry and view interpolation quality for glossy objects. Ref-NeuS [14] further extends these concepts to a surface-based representation. However, these are primarily designed for object-level reconstruction under environment map lighting conditions. Modeling large-scale scenes with near-field lighting remains a problem. Clean-NeRF [30] decomposes the radiance into diffuse and specular colors, and supervises the two components by least-square estimations of multiple input rays. This alleviates the ambiguity of highly specular regions; yet, it does not change the view-dependent structure of the NeRF model, thus limiting its ability to model reflections. NeRF-DS [54] models peculiarities in dynamic scenes and considers the variations in reflections caused by dynamic geometry through the use of a dynamic normal field, but requires additional object masks for accurate specular reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.897, + 0.903 + ], + "angle": 0, + "content": "NeRF-based Inverse Rendering. Inverse rendering goes beyond simple reflection modeling and aims to jointly recover one or more of scene geometry, material appearance and the lighting condition. In practice, the material appearance is typically modeled using physically-based rendering assets such as albedo, roughness and glossiness. Mesh-based inverse rendering methods [2, 38, 49, 68] try to recover materials using differentiable path tracing [25]. However, they typically assume a given geometry, since optimizing mesh geometry is challenging. On the contrary, NeRF-based inverse rendering approaches [5, 42, 65, 66] make it easier to optimize geometry jointly by modeling material properties and density continuously in a volumetric 3D space. The lighting is usually represented as point or directional lights [5, 23, 60], an environment texture map [31-33, 42, 65], or an implicit texture map modeled by spherical Gaussians [6, 11, 18, 63, 66, 66, 67] or MLPs [7, 29]. Most methods are limited to object-level reconstruction and assume the lighting is spatially invariant (i.e. distant). Several light estimation techniques [13, 26, 27, 41] explore using 3D light primitives or spatially-varying spherical Gaussians to model spatially varying lighting. However, these methods focus on data-driven approaches to estimate lighting for image editing. NeILF [56] and NeILF++ [62] model lighting as a 5D light field using another MLP, but still focus mainly on small-scale reconstruction. Several works apply inverse rendering for relighting outdoor scenes [24, 40, 48, 58]. However, they fo" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21189" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.09, + 0.895, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.197, + 0.895, + 0.226 + ], + "angle": 0, + "content": "Figure 2. An overview of our model. The key enabler for specular reflections is our novel 3D Gaussian directional encoding module that converts the reflected ray into a spatially-varying embedding, which is further decoded into specular color." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.234, + 0.47, + 0.31 + ], + "angle": 0, + "content": "cus more on diffuse materials with correct shadow modeling instead of reflections. In this work, we have a different goal compared to inverse rendering, focusing only on correctly modeling reflections for better novel-view synthesis, rather than trying to discern material properties for standalone use." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.313, + 0.474, + 0.495 + ], + "angle": 0, + "content": "NeRF with mirror reflections. One special case of reflection is mirror reflection. One approach represents the reflected scene as a separate NeRF [15], and composites the two NeRF results in image space. This is also deployed in image-based rendering [52] and large-scale NeRF reconstruction [50]. Given a multi-mirror scene, the idea can be further extended to multi-space NeRFs [57]. An alternate approach is to explicitly model the mirror geometry, and to render the mirrored scene by path tracing [16, 61]. However, since estimating the mirror geometry is highly ill-posed, manual annotation is usually needed. Curved reflectors need even more careful handling [22, 46]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.507, + 0.216, + 0.523 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.532, + 0.471, + 0.623 + ], + "angle": 0, + "content": "We first review Ref-NeRF [47] for decomposing view-dependent appearance. Similar to NeRF, Ref-NeRF models the scene as a function that maps the position \\(\\mathbf{x}\\) and view direction \\(\\mathbf{d}\\) to the final color \\(\\mathbf{c}\\) and density \\(\\tau\\). The difference is that Ref-NeRF predicts the color as a combination of diffuse color \\(\\mathbf{c}_{\\mathrm{d}}\\) and specular color \\(\\mathbf{c}_{\\mathrm{s}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.204, + 0.632, + 0.47, + 0.647 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} = \\gamma \\left(\\mathbf {c} _ {\\mathrm {d}} + \\mathbf {c} _ {\\mathrm {s}} \\odot \\mathbf {s}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.745 + ], + "angle": 0, + "content": "where \\(\\mathbf{s}\\) is the specular tint, \\(\\odot\\) the element-wise product, and \\(\\gamma (\\cdot)\\) a tone-mapping function. To predict the specular color \\(\\mathbf{c}_{\\mathrm{s}}\\), Ref-NeRF first predicts the surface normal \\(\\mathbf{n}\\), roughness \\(\\rho\\), and features \\(\\varphi\\) at location \\(\\mathbf{x}\\) using an MLP. Then, the specular color \\(\\mathbf{c}_{\\mathrm{s}}\\) is parameterized as a function of the reflection direction \\(\\mathbf{d}_{\\mathrm{r}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.754, + 0.47, + 0.771 + ], + "angle": 0, + "content": "\\[\n\\mathbf {c} _ {\\mathrm {s}} = F _ {\\boldsymbol {\\theta}} \\left(\\lambda_ {\\mathrm {I D E}} \\left(\\mathbf {d} _ {\\mathrm {r}}, \\rho\\right), \\varphi\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.471, + 0.839 + ], + "angle": 0, + "content": "where \\(\\lambda_{\\mathrm{IDE}}(\\cdot)\\) is the integrated directional encoding introduced by Ref-NeRF, \\(F_{\\theta}(\\cdot)\\) represents an MLP with parameters \\(\\theta\\), and the reflection direction \\(\\mathbf{d}_{\\mathrm{r}}\\) is the input direction \\(\\mathbf{d}\\) reflected at the predicted surface normal \\(\\mathbf{n}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.847, + 0.47, + 0.863 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {\\mathrm {r}} = \\mathbf {d} - 2 (\\mathbf {d} \\cdot \\mathbf {n}) \\mathbf {n}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "By conditioning the specular color on reflection direction and roughness, the function \\(F_{\\theta}\\) needs to fit is much simpler." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.233, + 0.591, + 0.248 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.894, + 0.335 + ], + "angle": 0, + "content": "Our goal is to enhance NeRF's capabilities for modeling specular reflections under near-field lighting conditions. Figure 2 presents an overview of our pipeline. A key contribution is the 3D Gaussian directional encoding that maps a ray and surface roughness to a ray embedding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.336, + 0.895, + 0.636 + ], + "angle": 0, + "content": "To render a pixel, we sample points along an input ray \\(\\mathbf{o} + t\\mathbf{d}\\), and predict volume density \\(\\tau'\\), diffuse color \\(\\mathbf{c}_{\\mathrm{d}}'\\), tint \\(\\mathbf{s}'\\), roughness \\(\\rho'\\), and normal direction \\(\\mathbf{n}'\\) at each sample point (we denote per-sample properties using a prime). Given that reflections occur only at the surface, we evaluate the specular component once per ray on the surface obtained from the NeRF depth. This also results in less computation than per-sample-point specular shading. Consequently, we calculate volumetric depth \\(t_0\\) by rendering the ray marching distance at each sample point. We also volumetrically render all attributes to synthesize screen-space attributes (\\(\\mathbf{c}_{\\mathrm{d}}, \\mathbf{s}, \\rho, \\mathbf{n}\\)). Note that the rendered normal must be normalized to yield the final screen-space normal \\(\\mathbf{n}\\). We then evaluate the specular component by first computing the reflected ray using origin \\(\\mathbf{o}_{\\mathrm{r}} = \\mathbf{o} + t_0\\mathbf{d}\\), and the reflection direction \\(\\mathbf{d}_{\\mathrm{r}}\\) derived using Equation 3. The reflected ray \\(\\mathbf{o}_{\\mathrm{r}} + t\\mathbf{d}_{\\mathrm{r}}\\) and surface roughness \\(\\rho\\) are then encoded using our novel 3D Gaussian directional encoding. After a tiny MLP, we compute the specular color \\(\\mathbf{c}_{\\mathrm{s}}\\), and the final rendering result using Equation 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.894, + 0.759 + ], + "angle": 0, + "content": "From a physically based rendering perspective, Equation 1 is analogous to the Cook-Torrance approximation [10] of the rendering equation [19]. The term \\( \\mathbf{c}_{\\mathrm{s}} \\odot \\mathbf{s} \\) can be interpreted as the split-sum approximation of the specular part of the Cook-Torrance model, with the specular color \\( \\mathbf{c}_{\\mathrm{s}} \\) corresponding to the preconvolved incident light, and the tint s to the pre-integrated bidirectional reflectance distribution function (BRDF)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.771, + 0.776, + 0.788 + ], + "angle": 0, + "content": "4.1. Gaussian Directional Encoding" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Existing works parameterize view-dependent appearance by first encoding view or reflection direction into Fourier or spherical harmonics (SH) features, which results in a spatially invariant encoding of the view direction. Therefore, it becomes challenging for the NeRF to model spatially varying view-dependent effects, such as near-field lighting. We illustrate this via a toy example in Figure 3, where we place" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21190" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.096, + 0.457, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.2, + 0.473, + 0.326 + ], + "angle": 0, + "content": "Figure 3. Toy example of 3D Gaussian encoding. Left: A hemisphere probe translates underneath 4 lights along positions numbered 1 to 4. Note that we dilate the lights for better visualization. Right: Representation of the probe's specular components using spherical harmonics and our 3D Gaussian directional encoding. The SH encoding shows a more complex pattern under position change, while ours has spatially largely invariant coefficients. This suggests a simpler function for the specular prediction MLP to fit using Gaussian directional encoding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.333, + 0.471, + 0.485 + ], + "angle": 0, + "content": "a hemispherical specular probe in a simple scene with four lights of different shapes and colors. Then, we represent the specular component of the toy example by linearly combining the directional encoding features. We find the optimal coefficients for each encoding type that best fit the ground-truth specular component using stochastic gradient descent, and visualize them in Figure 3. We can see that even for this simple toy setup, the SH-based encoding requires complex, spatially varying coefficients, which complicates the underlying function for the NeRF to fit and interpolate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.471, + 0.56 + ], + "angle": 0, + "content": "We propose to spatially vary the encoding function by defining the basis functions via several learnable 3D Gaussians. Specifically, we parameterize 3D Gaussians using their position \\(\\pmb{\\mu}_i\\in \\mathbb{R}^3\\), scale \\(\\sigma_{i}\\in \\mathbb{R}^{3}\\), and quaternion rotation \\(\\mathbf{q}_i\\in \\mathbb{H}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.566, + 0.47, + 0.592 + ], + "angle": 0, + "content": "\\[\n\\mathcal {G} _ {i} (\\mathbf {x}) = \\exp \\left(- \\left\\| \\mathcal {Q} \\left(\\mathbf {x} - \\boldsymbol {\\mu} _ {i}; \\mathbf {q} _ {i}\\right) \\odot \\boldsymbol {\\sigma} _ {i} ^ {- 1} \\right\\| _ {2} ^ {2}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.471, + 0.718 + ], + "angle": 0, + "content": "where \\(\\mathcal{Q}(\\mathbf{v};\\mathbf{q}_i)\\) represents applying quaternion rotation \\(\\mathbf{q}_i\\) to the vector \\(\\mathbf{v}\\). To compute the \\(i\\)-th dimension of the encoding for a ray \\(\\mathbf{o} + t\\mathbf{d}\\), we need to define a basis function \\(\\mathcal{P}_i(\\mathbf{o},\\mathbf{d}) \\in \\mathbb{R}\\) that maps the ray to a scalar value given the Gaussian parameters. While there are many ways to define the mapping, we find one that is efficient and has a closed-form solution by defining the projection as the maximum value of the Gaussian along the ray:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.725, + 0.47, + 0.748 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {i} (\\mathbf {o}, \\mathbf {d}) = \\max _ {t \\geq 0} \\mathcal {G} _ {i} (\\mathbf {o} + t \\mathbf {d}). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.754, + 0.438, + 0.769 + ], + "angle": 0, + "content": "In the supplement, we derive the closed-form solution:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.774, + 0.47, + 0.817 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} _ {i} (\\mathbf {o}, \\mathbf {d}) = \\left\\{ \\begin{array}{l l} \\exp \\left(\\frac {\\left(\\mathbf {o} _ {i} ^ {\\top} \\mathbf {d} _ {i}\\right) ^ {2}}{\\mathbf {d} _ {i} ^ {\\top} \\mathbf {d} _ {i}} - \\mathbf {o} _ {i} ^ {\\top} \\mathbf {o} _ {i}\\right) & \\mathbf {o} _ {i} ^ {\\top} \\mathbf {d} _ {i} < 0 \\\\ \\mathcal {G} _ {i} (\\mathbf {o}) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.823, + 0.469, + 0.854 + ], + "angle": 0, + "content": "where \\(\\mathbf{o}_i\\) and \\(\\mathbf{d}_i\\) are the ray origin and direction transformed into Gaussian-local space:" + }, + { + "type": "equation", + "bbox": [ + 0.177, + 0.859, + 0.47, + 0.877 + ], + "angle": 0, + "content": "\\[\n\\mathbf {o} _ {i} = \\mathcal {Q} (\\mathbf {o} - \\boldsymbol {\\mu} _ {i}; \\mathbf {q} _ {i}) \\odot \\sigma_ {i} ^ {- 1}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.879, + 0.47, + 0.898 + ], + "angle": 0, + "content": "\\[\n\\mathbf {d} _ {i} = \\mathcal {Q} (\\mathbf {d}; \\mathbf {q} _ {i}) \\odot \\sigma_ {i} ^ {- 1}. \\tag {8}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.094, + 0.889, + 0.368 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.375, + 0.895, + 0.473 + ], + "angle": 0, + "content": "Figure 4. Stereographic projections of the specular fitting results for the toy example in Figure 3. Both encodings produce 25 coefficients for each color channel, which are then summed to produce the final color. Note that the GT shows soft boundaries because it is preconvolved. The 3D Gaussian-based encoding demonstrates superior performance in representing the specular change with positional changes, and is also capable of smoothly varying roughness." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.484, + 0.894, + 0.56 + ], + "angle": 0, + "content": "By applying Equation 6 for every 3D Gaussian, we obtain a vector of projected values \\(\\{\\mathcal{P}_i\\}\\), which forms our final encoding features. Similar to existing NeRF-based representations [9, 34, 36], we rely on a small MLP to convert the encoding to a specular color \\(\\mathbf{c}_{\\mathrm{s}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.895, + 0.699 + ], + "angle": 0, + "content": "As illustrated by the toy example in Figure 3, our Gaussian directional encoding exhibits more constant coefficients in response to the position changes, suggesting a smoother mapping from the embedding features to the specular color. This smoothness is due to the Gaussian basis function producing spatially varying features that mimic the behavior of how the specular component would change under near-field lighting conditions. As a result, the underlying functions that model the specular reflections are easier to learn." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.895, + 0.763 + ], + "angle": 0, + "content": "We also visualize the fitted specular color of both approaches in Figure 4. Our 3D Gaussian directional encoding more accurately captures the spatial variations of the specular components." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Similar to Ref-NeRF, we use an additional \"roughness\" value \\(\\rho\\) to control the maximum frequency of the specular color. We achieve this in our Gaussian embedding by multiplying each Gaussian's scale \\(\\sigma_{i}\\) with the roughness \\(\\rho\\). Intuitively, a larger Gaussian results in a smoother function with varying direction \\(\\mathbf{d}\\). Substituting the \\(\\sigma_{i}\\) with \\(\\rho \\sigma_{i}\\) in Equation 6 leads to the complete equation of our 3D Gaussian encoding. Figure 4 demonstrates the ability of our 3D Gaussian-based encoding to modify roughness on the fly." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21191" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.471, + 0.108 + ], + "angle": 0, + "content": "4.2. Optimizing the Gaussian Directional Encoding" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.22 + ], + "angle": 0, + "content": "It is worth noting that our proposed Gaussian encoding correctly models spatially varying specular reflections only when the Gaussians are positioned properly in 3D space. We thus jointly optimize the Gaussian parameters together with the NeRF during training, to ensure the Gaussians are in the optimal state for modeling reflections. However, there is no direct supervision for the Gaussian parameters." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.22, + 0.471, + 0.34 + ], + "angle": 0, + "content": "Our experiments show that without proper initial Gaussian parameters, the optimization may lead to suboptimal local minima, resulting in inconsistent quality of specular reconstruction. To address this, we propose an initialization stage for the Gaussian parameters and to bootstrap the specular color prediction. As mentioned earlier, the specular color is essentially the preconvolved incident light, which can be directly deduced from input images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.473, + 0.614 + ], + "angle": 0, + "content": "Motivated by this observation, we train the 3D Gaussians and the specular decoder \\((\\mathrm{MLP}_3\\) in Figure 2) in the initialization stage using the input images. We train an incident light field that accommodates a diversity of rays and roughness values. Therefore, we apply a range of Gaussian blurs to all input images using a series of standard deviations, generating Gaussian pyramids. These pyramids of input images provide a pseudo target for incident light under different degrees of surface roughness. In each iteration of the training, we sample pixels from the pyramids and trace rays to these pixels. The traced rays are also associated with a roughness value that is equivalent to the blur's standard deviation. We encode each ray with roughness using our Gaussian directional encoding, and predict the specular color \\(\\mathbf{c}_{\\mathrm{s}}\\) using the decoder. By minimizing the errors between \\(\\mathbf{c}_{\\mathrm{s}}\\) and the pseudo ground truth, we refine the Gaussian parameters and the specular decoder, which then serve as initialization for the subsequent joint optimization stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.62, + 0.436, + 0.637 + ], + "angle": 0, + "content": "4.3. Resolving the Shape-Radiance Ambiguity" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.472, + 0.809 + ], + "angle": 0, + "content": "Regardless of any view-dependent parameterization, there remains a fundamental ambiguity between shape and radiance in NeRFs. For example, consider a perfect mirror reflection. Without any prior knowledge, it is nearly impossible for the NeRF model to tell whether the mirror is a flat surface with perfect reflection, or a window to a (virtual) scene behind the surface. Therefore, prior information is needed to guide the model to learn the correct geometry. Inspired by recent progress in monocular geometry estimation [4, 12, 39, 59], we propose to supervise the predicted normal \\(\\mathbf{n}\\) using monocular normal estimation \\(\\mathbf{n}_{\\mathrm{mono}}\\) [12]:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.815, + 0.471, + 0.848 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {m o n o}} = \\sum_ {j} \\left\\| \\mathbf {n} ^ {j} - \\mathbf {R} ^ {j} \\mathbf {n} _ {\\mathrm {m o n o}} ^ {j} \\right\\| _ {2} ^ {2}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.855, + 0.473, + 0.902 + ], + "angle": 0, + "content": "where the superscript \\(j\\) is a ray index, and \\(\\mathbf{R}^j\\) is the corresponding camera rotation matrix that converts normals from view space to world space." + }, + { + "type": "image_caption", + "bbox": [ + 0.534, + 0.09, + 0.57, + 0.101 + ], + "angle": 0, + "content": "Target" + }, + { + "type": "image_caption", + "bbox": [ + 0.637, + 0.09, + 0.66, + 0.1 + ], + "angle": 0, + "content": "Full" + }, + { + "type": "image_caption", + "bbox": [ + 0.716, + 0.09, + 0.773, + 0.101 + ], + "angle": 0, + "content": "w/o \\(\\mathcal{L}_{\\mathrm{mono}}\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.804, + 0.09, + 0.88, + 0.101 + ], + "angle": 0, + "content": "w/o early stop" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.102, + 0.89, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.255, + 0.894, + 0.366 + ], + "angle": 0, + "content": "Figure 5. The specular component reconstruction (first row, except the first image), novel-view synthesis results (second row) and normal visualizations (third row) under varying monocular normal supervision. The target normal visualizes the monocular normal prediction. Without \\(\\mathcal{L}_{\\mathrm{mono}}\\), the predicted normal exhibits enormous error, leading to poor specular reconstruction. Without early stopping \\(\\mathcal{L}_{\\mathrm{mono}}\\), minor errors in the predicted normals lead to a slight degradation in the reflection quality compared to our full model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.377, + 0.895, + 0.635 + ], + "angle": 0, + "content": "However, monocular normals are prone to error. We therefore use them primarily as initialization and apply \\(\\mathcal{L}_{\\mathrm{mono}}\\) only at the beginning of the training, so that the errors in the normals do not overwhelm the geometry of the NeRF. Figure 5 and Table 2 show results with different configurations of \\(\\mathcal{L}_{\\mathrm{mono}}\\). We can see that without monocular normal as supervision ('w/o \\(\\mathcal{L}_{\\mathrm{mono}}\\)), the predicted normals have catastrophic errors, such as those pointing inwards (orange) or lying parallel (violet) to the surface. Consequently, the learned specular component is less accurate due to the incorrect normals. Despite this, a somewhat plausible specular reflection can still be learned as the Gaussian encoding can \"cheat\" the reflections even with erroneous normals. On the other hand, without early stopping of the loss ('w/o early stop'), minor inaccuracies from the monocular normals permeate into predicted normals, leading to a degradation of the reflection quality." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.643, + 0.587, + 0.658 + ], + "angle": 0, + "content": "4.4. Losses" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.666, + 0.892, + 0.697 + ], + "angle": 0, + "content": "To jointly optimize all parameters within our proposed pipeline, we use a combination of loss terms:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.708, + 0.892, + 0.724 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c}} + \\mathcal {L} _ {\\text {p r o p}} + \\lambda_ {\\text {d i s t}} \\mathcal {L} _ {\\text {d i s t}} + \\lambda_ {\\text {m o n o}} \\mathcal {L} _ {\\text {m o n o}} + \\lambda_ {\\text {n o r m}} \\mathcal {L} _ {\\text {n o r m}}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.871 + ], + "angle": 0, + "content": "In this equation, \\(\\mathcal{L}_{\\mathrm{c}}\\) is the L1 reconstruction loss between the predicted and ground-truth colors. The terms \\(\\mathcal{L}_{\\mathrm{prop}}\\) and \\(\\mathcal{L}_{\\mathrm{dist}}\\) are adopted from mip-NeRF 360 [3], where \\(\\mathcal{L}_{\\mathrm{prop}}\\) supervises the density proposal networks, and \\(\\mathcal{L}_{\\mathrm{dist}}\\) is the distortion loss encouraging density sparsity. To tie predicted normals to the density field, we use Ref-NeRF's normal prediction loss \\(\\mathcal{L}_{\\mathrm{norm}}\\) [47], which guides the predicted normal \\(\\mathbf{n}\\) with the density gradient direction. Further elaboration on these loss components can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In our experiments, we set \\(\\lambda_{\\mathrm{dist}} = 0.002\\), aligning with the settings of the \"nerfacto\" model in Nerfstudio [44]. For" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21192" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.142, + 0.089, + 0.826, + 0.104 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons of novel-view synthesis on three datasets. We highlight the best numbers in bold." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.108, + 0.895, + 0.58 + ], + "angle": 0, + "content": "
MethodsEyeful Tower dataset [53]NISR [50] + Inria [38] datasetShiny dataset [47]
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Ours32.5830.93280.144530.7710.89090.165526.5640.72770.2776
NeRF [34]31.8540.92540.162630.7480.88730.172826.4690.72350.2852
Ref-NeRF [47]31.6520.92580.157030.6540.89030.166926.5020.72420.2827
MS-NeRF [57]31.7150.93110.156130.2240.88400.181626.4660.70700.3225
GT Test ImageGT & SfM NormalOursRef-NeRF [47]MS-NeRF [57]NeRF [34]
Eyeful Workshop
NISR LivingRoom2
Eyeful Office2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.584, + 0.893, + 0.613 + ], + "angle": 0, + "content": "Figure 6. Comparisons of novel-view synthesis quality and normal map visualizations. Our method consistently reconstructs reflections while other methods either produce 'faked' reflections, resulting in incorrect normals, or fail to model reflections entirely." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.62, + 0.475, + 0.729 + ], + "angle": 0, + "content": "\\(\\lambda_{\\mathrm{mono}}\\), we choose a value of 1 in the first 4K iterations, and reduce to 0 thereafter to cease its effect, as described earlier. We find that our method is robust to the value of \\(\\lambda_{\\mathrm{mono}}\\) as it only serves as initialization. We also assign \\(\\lambda_{\\mathrm{norm}} = 10^{-3}\\), which is slightly higher than the weight in Ref-NeRF [47], as we find that this produces slightly smoother normals without substantially compromising the rendering quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.21, + 0.758 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Implementation. To model room-scale scenes, we employ a network architecture similar to the \"nerfacto\" model presented in Nerfstudio [44]. We use two small density networks as proposal networks, supervised via \\(\\mathcal{L}_{\\mathrm{prop}}\\). We sample 256 and 96 points for each proposal network, and 48 points for the final NeRF model. These three networks all use hash-based positional encodings. When querying the hash features in the final NeRF model, we incorporate the LOD-aware scheme proposed in VR-NeRF [53]. We train our model" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.895, + 0.698 + ], + "angle": 0, + "content": "for 100,000 iterations and randomly sample 12,800 rays in each iteration. This process takes around 8 GB of GPU memory and approximately 3.5 hours to train a model using an NVIDIA A100 GPU. Further details regarding the model's structure can be found in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Datasets. We evaluate our method on several datasets with a focus on indoor scenes characterized by near-field lighting conditions. First, we evaluate on the Eyeful Tower dataset [53], which provides high-quality HDR captures of 11 indoor scenes. Each scene is coupled with calibrated camera parameters and a mesh reconstructed via Agisoft Metashape [1]. We select 9 scenes that feature notable reflective properties. We downsample the images of each scene to a resolution of \\(854 \\times 1280\\) pixels. We curated around 50-70 views per scene that contain glossy surfaces for evaluation, leaving the remaining views for training. We also evaluate our approach on public indoor datasets NISR [50] and Inria [38] (NISR+Inria). Moreover, to assess the performance under" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21193" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.092, + 0.892, + 0.342 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.342, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Figure 7. Intermediate components of our approach compared to Ref-NeRF [47]. Our approach produces a more meaningful decomposition under room-scale lighting settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.471, + 0.426 + ], + "angle": 0, + "content": "far-field lighting, we evaluate the real shiny dataset in Ref-NeRF [47]. We report the average PSNR, SSIM, and LPIPS [64] metrics for evaluating rendering quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.437, + 0.216, + 0.453 + ], + "angle": 0, + "content": "5.1. Comparisons" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.471, + 0.733 + ], + "angle": 0, + "content": "We compare our method with several baselines: NeRF [34], Ref-NeRF [47], and MS-NeRF [57], which specializes in mirror-like reflections by decomposing NeRF into multiple spaces. For a fair comparison, we re-implement these baselines, such that we share the same NeRF backbone and rendering configurations, with the only difference being the way different methods decompose and parameterize the output color. We report the numerical results across three datasets in Table 1. Our method demonstrates superior performance on the Eyeful Tower dataset, indicating the effectiveness of our method. On the NISR+Inria datasets, our method marginally outperforms the baselines, likely due to the dataset containing few reflection surfaces. Notably, while our method is tailored for near-field lighting conditions, it also shows promising results on the Shiny dataset, which comprises far-field lighting scenarios. This is because our Gaussian directional encoding can simulate a spatially invariant encoding by positioning Gaussians at a significant distance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.47, + 0.87 + ], + "angle": 0, + "content": "Qualitative results on the Eyeful Tower and NISR+Inria datasets are provided in Figure 6. We can see that while other baselines occasionally synthesize plausible reflections, they resort to approximations that fake the reflections by placing emitters underneath the surface. As a result, they either produce incorrect geometry, or fail to model the reflections. Our method, in contrast, successfully models specular highlights on the surface. We provide additional video results in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We also visualize and compare the decomposition produced by our method and Ref-NeRF in Figure 7. We can see" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.375, + 0.895, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.49, + 0.892, + 0.532 + ], + "angle": 0, + "content": "Figure 8. We evaluate the novel-view synthesis quality with respect to the number of Gaussians across five scenes. The green dashed line is the setting we use in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.545, + 0.894, + 0.606 + ], + "angle": 0, + "content": "that Ref-NeRF fails to obtain a meaningful decomposition under near-field lighting, and produces holes in the geometry, whereas our method consistently achieves a realistic separation of specular and diffuse components." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.665, + 0.63 + ], + "angle": 0, + "content": "5.2. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.895, + 0.851 + ], + "angle": 0, + "content": "Number of Gaussians. One important hyperparameter in the Gaussian directional encoding is the number of Gaussians, as it directly influences the model's capacity to represent specular colors. We conduct experiments to evaluate the impact of varying the number of Gaussians on five scenes from the Eyeful Tower dataset, and show the relationship between the number of Gaussians and the rendering quality in Figure 8. The rendering quality improves when using more Gaussians, but the improvement saturates as the number increases beyond 400. Note that using a larger number of Gaussians also entails greater computation costs and GPU memory requirements for every rendered pixel. Therefore, we use 256 Gaussians for all experiments, to strike a balance between rendering quality and computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Optimizing Gaussians. To optimize the Gaussian directional encoding effectively, we first initialize them by training an incident light field, and then jointly finetune the Gaus" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21194" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.09, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 2. Ablations of our method on the Eyeful Tower dataset [53]. The \"e.s.\" indicates early stopping the \\(\\mathcal{L}_{\\mathrm{mono}}\\) after 4K iterations." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.122, + 0.462, + 0.235 + ], + "angle": 0, + "content": "
MethodGaussians Init.Mono. Opt.E. S. Prior\\( {\\mathcal{L}}_{\\text{mono }} \\)PSNR↑SSIM↑LPIPS↓
Full✓✓✓✓32.580.93280.1445
w/o init✘✓✓✓32.520.93040.1429
w/o opt.✓✘✓✓32.060.92650.1581
w/o \\( {\\mathcal{L}}_{\\text{mono }} \\)✓✓✘-32.310.92880.1503
w/o e.s.✓✓✓✘32.460.92920.1502
" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.237, + 0.467, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.465, + 0.47, + 0.522 + ], + "angle": 0, + "content": "Figure 9. Example results under different Gaussian optimization settings. Without initializing the Gaussian parameters ('w/o init') or optimizing Gaussians jointly with the NeRF ('w/o opt.'), the Gaussian embedding struggles to model specularities accurately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.473, + 0.727 + ], + "angle": 0, + "content": "sian encoding together with the NeRF model. We demonstrate the significance of initialization ('w/o init') and fine-tuning ('w/o opt.') by omitting each process individually. We show quantitative results in Table 2 and a qualitative example in Figure 9. Without initialization, the model can still reconstruct reflections to some extent, resulting in a slightly better average LPIPS score, yet it fails to model some specular details, such as the light blobs. Neglecting the joint optimization of Gaussians leads to complete failure in modeling specular reflections. As illustrated in Figure 9, with the inaccurate specular modeling, the tints suppress the specular reflections, which ultimately leads to the inability to represent reflections in the final rendered image." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.74, + 0.325, + 0.756 + ], + "angle": 0, + "content": "6. Discussion and Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Applications. Our primary goal was to improve the quality of novel-view synthesis with specular reflective surfaces. We achieve this via our proposed Gaussian directional encoding that enables a meaningful decomposition of specular and diffuse components in a scene. Moreover, this also enables applications other than novel-view synthesis, such as reflection removal, and surface roughness editing. For instance, Figure 7 shows that we can easily remove reflections using the diffuse component. Furthermore, Figure 10 demonstrates" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.088, + 0.895, + 0.247 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.25, + 0.892, + 0.278 + ], + "angle": 0, + "content": "Figure 10. We can control the roughness of the scene by adding an offset to the input roughness." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.289, + 0.888, + 0.374 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.377, + 0.894, + 0.406 + ], + "angle": 0, + "content": "Figure 11. Our method cannot reconstruct mirror-like perfect reflections due to the limited capacity of the 3D Gaussian encoding." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.418, + 0.892, + 0.463 + ], + "angle": 0, + "content": "an example of editing roughness. By adding an offset to the predicted roughness during rendering, we can effectively manipulate the glossiness of the real surface." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.895, + 0.651 + ], + "angle": 0, + "content": "Limitations. While our method improves on existing baselines, it has some limitations. As we parameterize the specular color via only several hundreds of Gaussians, the encoding is limited to relatively low frequency compared with perfect mirror-like reflections. We show such a failure case in Figure 11. We can see that our method is only able to learn a blurry version of the reflection. This could be alleviated by using many more Gaussians, as demonstrated in 3D Gaussian splatting [20]. However, the computational cost of traversing all Gaussians for every pixel quickly becomes prohibitive in our implementation. More efficient traversal, such as by rasterization, could be interesting future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.897, + 0.837 + ], + "angle": 0, + "content": "Conclusion. In this paper, we proposed a pipeline to improve the existing approach in modeling and reconstructing view-dependent effects in a NeRF representation. Central to our approach is a new Gaussian directional encoding to enhance the capability of neural radiance fields to model specular reflections under near-field lighting. We also utilize monocular normal supervision to help resolve shape-radiance ambiguity. Experiments have demonstrated the effectiveness of each of our contributions. We believe this work proposes a practical and effective solution for reconstructing NeRFs in room-scale scenes, specifically addressing the challenges of accurately capturing specular reflections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. The authors from HKUST were partly supported by the Hong Kong Research Grants Council (RGC). We would like to thank Linning Xu and Zhao Dong for helpful discussions." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "21195" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.142 + ], + "angle": 0, + "content": "[1] Agisoft LLC. Agisoft Metashape Professional. 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In AAAI, 2024. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.502 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "21198" + } + ] +] \ No newline at end of file diff --git a/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/3d459af2-f520-428c-a01a-361ee7f87043_origin.pdf b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/3d459af2-f520-428c-a01a-361ee7f87043_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9ce8cfce9ff9027438cc4bc0d2a6841b7f6c07a8 --- /dev/null +++ b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/3d459af2-f520-428c-a01a-361ee7f87043_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:53d733c65c12d1d6a528c9bada55e009407e4ac17c411ea74b54d8e14333ac78 +size 10262579 diff --git a/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/full.md b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/full.md new file mode 100644 index 0000000000000000000000000000000000000000..d17335f9739dd2e4ed882b97dfcce426f5656674 --- /dev/null +++ b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/full.md @@ -0,0 +1,308 @@ +# SpecNeRF: Gaussian Directional Encoding for Specular Reflections + +Li Ma $^{1,2}$ Vasu Agrawal $^{2}$ Haithem Turki $^{2,3}$ Changil Kim $^{2}$ Chen Gao $^{2}$ Pedro Sander $^{1}$ Michael Zollhöfer $^{2}$ Christian Richardt $^{2}$ + +1The Hong Kong University of Science and Technology 2Meta Reality Labs 3Carnegie Mellon University + +# Abstract + +Neural radiance fields have achieved remarkable performance in modeling the appearance of 3D scenes. However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of indoor environments. Unlike existing methods, which typically assume distant lighting like an environment map, we propose a learnable Gaussian directional encoding to better model the view-dependent effects under near-field lighting conditions. Importantly, our new directional encoding captures the spatially-varying nature of near-field lighting and emulates the behavior of prefiltered environment maps. As a result, it enables the efficient evaluation of preconvolved specular color at any 3D location with varying roughness coefficients. We further introduce a data-driven geometry prior that helps alleviate the shape radiance ambiguity in reflection modeling. We show that our Gaussian directional encoding and geometry prior significantly improve the modeling of challenging specular reflections in neural radiance fields, which helps decompose appearance into more physically meaningful components. + +# 1. Introduction + +Neural radiance fields (NeRFs) have emerged as a popular scene representation for novel-view synthesis [34, 45, 51]. By training a neural network based on sparse observations of a 3D scene, NeRF-like representations are able to synthesize novel views with photorealistic visual quality. In particular, with a scalable model design, such as InstantNGP [36], NeRFs are able to model room-scale 3D scenes with extraordinary detail [53]. However, existing approaches typically only manage to model mild view-dependent effects like those seen on nearly diffuse surfaces. When encountering highly view-dependent glossy surfaces, NeRFs struggle to model the high-frequency changes when the viewpoint changes. Instead, they tend to "fake" specular reflections by placing them behind surfaces, which may result in poor view interpolation and "foggy" geometry [47]. Moreover, fake + +![](images/a0614387486ba2fd7115a6e176f287445f7e247bfed693c892db967d34e247db.jpg) +Figure 1. We propose a Gaussian directional encoding that leads to better modeling of specular reflections under near-field lighting conditions. In contrast, the integrated directional encoding utilized in Ref-NeRF [47] and Fourier directional encoding in NeRF [34] exhibit suboptimal performance under similar conditions. + +reflections are not viable if one can look behind the surface, as NeRF can no longer hide the reflections there. + +Accurately modeling and reconstructing specular reflections presents notable challenges, especially for room-scale scenes. Physically correct reflection modeling involves pathtracing many rays for every single pixel, which is impractical for NeRF-like volumetric scene representations, primarily due to the large computational requirements to shade a single pixel. Consequently, an efficient approximation of the reflection shading is needed for a feasible modeling of reflections. Existing works [14, 47] address this challenge by incorporating heuristic modules inspired by real-time image-based lighting (IBL) [35] techniques, such as explicit ray bounce computations to enhance NeRF's capability to simulate reflections, and integrated directional encoding to simulate appearance change under varying surface roughness. + +While these improvements have shown to be effective in modeling specular reflections for NeRFs, they are limited to object-level reconstruction under distant lighting, which assumes the object is lit by a 2D environment map. They work poorly for modeling near-field lighting, where the corresponding environment map varies spatially. The issue is that existing methods rely on directional encodings to embed ray directions for generating view-dependent reflections. + +These encodings, such as Fourier encoding or spherical harmonics, are spatially invariant. Figure 1 demonstrates one example of NeRF [34] and Ref-NeRF [47] reconstructions of an indoor scene with spatially-varying lighting. NeRF produces extremely noisy geometry, resulting in artifacts in the rendering result. Ref-NeRF offers a slight improvement, but still struggles with noisy geometry and view interpolation. This illustrates that the spatial invariance in the directional encodings of existing methods presents challenges under spatially-varying lighting conditions. + +In this work, we propose a novel Gaussian directional encoding that is tailored for spatially varying lighting conditions. Instead of only encoding a 2D ray direction, we use a set of learnable 3D Gaussians as the basis to embed a 5D ray space including both ray origin and ray direction. We show that, with appropriately optimized Gaussian parameters, this encoding introduces an important inductive bias towards near-field lighting, which enhances the model's ability to capture the characteristics of specular surfaces, leading to photorealistic reconstructions of shiny reflections. We further demonstrate that by changing the scale of the 3D Gaussians, we can edit the apparent roughness of a surface. + +While our proposed Gaussian directional encoding improves the reflection modeling of NeRF, high-quality reflection reconstruction also requires an accurate surface geometry and normal in order to compute accurate reflection rays. However, the geometry within NeRFs is often noisy in the early phases of training, which presents challenges in simultaneously optimizing for good geometry and reflections. To better address this challenge, we introduce a data-driven prior to direct the NeRF model towards the desired solution. We deploy a monocular normal estimation network to supervise the normal of the geometry at the beginning of the training stage, and show that this bootstrapping strategy improves the reconstruction of normals, and further leads to successful modeling of specular reflections. We conduct experiments on several public datasets and show that the proposed method outperforms existing methods, achieving higher-quality photorealistic rendering of reflective scenes while also providing more meaningful and accurate color component decomposition. Our contributions can be summarized as follows: + +- We propose a novel Gaussian directional encoding that is more effective in modeling view-dependent effects under near-field lighting conditions. +- We propose to use monocular normal estimation to resolve shape-radiance ambiguity in the early training stages. +- Our full NeRF pipeline achieves state-of-the-art novel-view synthesis performance for specular reflections. + +# 2. Related Work + +Reflection-aware NeRFs. Successfully modeling view-dependent effects, such as specular reflections, can greatly + +enhance the photorealism of the reconstructed NeRF. NeRF models view-dependency by conditioning the radiance on the positional encoding [43] of the input ray direction, which is only capable of mild view-dependent effects. Ref-NeRF [47] improves NeRF's capability for modeling reflections by conditioning the view-dependent appearance on the reflection ray direction instead of incident ray direction, and by modulating the directional encoding based on surface roughness. This reparameterization of outgoing radiance makes the underlying scene function simpler, leading to a better geometry and view interpolation quality for glossy objects. Ref-NeuS [14] further extends these concepts to a surface-based representation. However, these are primarily designed for object-level reconstruction under environment map lighting conditions. Modeling large-scale scenes with near-field lighting remains a problem. Clean-NeRF [30] decomposes the radiance into diffuse and specular colors, and supervises the two components by least-square estimations of multiple input rays. This alleviates the ambiguity of highly specular regions; yet, it does not change the view-dependent structure of the NeRF model, thus limiting its ability to model reflections. NeRF-DS [54] models peculiarities in dynamic scenes and considers the variations in reflections caused by dynamic geometry through the use of a dynamic normal field, but requires additional object masks for accurate specular reconstruction. + +NeRF-based Inverse Rendering. Inverse rendering goes beyond simple reflection modeling and aims to jointly recover one or more of scene geometry, material appearance and the lighting condition. In practice, the material appearance is typically modeled using physically-based rendering assets such as albedo, roughness and glossiness. Mesh-based inverse rendering methods [2, 38, 49, 68] try to recover materials using differentiable path tracing [25]. However, they typically assume a given geometry, since optimizing mesh geometry is challenging. On the contrary, NeRF-based inverse rendering approaches [5, 42, 65, 66] make it easier to optimize geometry jointly by modeling material properties and density continuously in a volumetric 3D space. The lighting is usually represented as point or directional lights [5, 23, 60], an environment texture map [31-33, 42, 65], or an implicit texture map modeled by spherical Gaussians [6, 11, 18, 63, 66, 66, 67] or MLPs [7, 29]. Most methods are limited to object-level reconstruction and assume the lighting is spatially invariant (i.e. distant). Several light estimation techniques [13, 26, 27, 41] explore using 3D light primitives or spatially-varying spherical Gaussians to model spatially varying lighting. However, these methods focus on data-driven approaches to estimate lighting for image editing. NeILF [56] and NeILF++ [62] model lighting as a 5D light field using another MLP, but still focus mainly on small-scale reconstruction. Several works apply inverse rendering for relighting outdoor scenes [24, 40, 48, 58]. However, they fo + +![](images/f4418cee136b1d66e9b2ffd94268584dc8d55974c80094f3e2047b19ad456556.jpg) +Figure 2. An overview of our model. The key enabler for specular reflections is our novel 3D Gaussian directional encoding module that converts the reflected ray into a spatially-varying embedding, which is further decoded into specular color. + +cus more on diffuse materials with correct shadow modeling instead of reflections. In this work, we have a different goal compared to inverse rendering, focusing only on correctly modeling reflections for better novel-view synthesis, rather than trying to discern material properties for standalone use. + +NeRF with mirror reflections. One special case of reflection is mirror reflection. One approach represents the reflected scene as a separate NeRF [15], and composites the two NeRF results in image space. This is also deployed in image-based rendering [52] and large-scale NeRF reconstruction [50]. Given a multi-mirror scene, the idea can be further extended to multi-space NeRFs [57]. An alternate approach is to explicitly model the mirror geometry, and to render the mirrored scene by path tracing [16, 61]. However, since estimating the mirror geometry is highly ill-posed, manual annotation is usually needed. Curved reflectors need even more careful handling [22, 46]. + +# 3. Preliminaries + +We first review Ref-NeRF [47] for decomposing view-dependent appearance. Similar to NeRF, Ref-NeRF models the scene as a function that maps the position $\mathbf{x}$ and view direction $\mathbf{d}$ to the final color $\mathbf{c}$ and density $\tau$ . The difference is that Ref-NeRF predicts the color as a combination of diffuse color $\mathbf{c}_{\mathrm{d}}$ and specular color $\mathbf{c}_{\mathrm{s}}$ : + +$$ +\mathbf {c} = \gamma \left(\mathbf {c} _ {\mathrm {d}} + \mathbf {c} _ {\mathrm {s}} \odot \mathbf {s}\right), \tag {1} +$$ + +where $\mathbf{s}$ is the specular tint, $\odot$ the element-wise product, and $\gamma (\cdot)$ a tone-mapping function. To predict the specular color $\mathbf{c}_{\mathrm{s}}$ , Ref-NeRF first predicts the surface normal $\mathbf{n}$ , roughness $\rho$ , and features $\varphi$ at location $\mathbf{x}$ using an MLP. Then, the specular color $\mathbf{c}_{\mathrm{s}}$ is parameterized as a function of the reflection direction $\mathbf{d}_{\mathrm{r}}$ : + +$$ +\mathbf {c} _ {\mathrm {s}} = F _ {\boldsymbol {\theta}} \left(\lambda_ {\mathrm {I D E}} \left(\mathbf {d} _ {\mathrm {r}}, \rho\right), \varphi\right), \tag {2} +$$ + +where $\lambda_{\mathrm{IDE}}(\cdot)$ is the integrated directional encoding introduced by Ref-NeRF, $F_{\theta}(\cdot)$ represents an MLP with parameters $\theta$ , and the reflection direction $\mathbf{d}_{\mathrm{r}}$ is the input direction $\mathbf{d}$ reflected at the predicted surface normal $\mathbf{n}$ : + +$$ +\mathbf {d} _ {\mathrm {r}} = \mathbf {d} - 2 (\mathbf {d} \cdot \mathbf {n}) \mathbf {n}. \tag {3} +$$ + +By conditioning the specular color on reflection direction and roughness, the function $F_{\theta}$ needs to fit is much simpler. + +# 4. Method + +Our goal is to enhance NeRF's capabilities for modeling specular reflections under near-field lighting conditions. Figure 2 presents an overview of our pipeline. A key contribution is the 3D Gaussian directional encoding that maps a ray and surface roughness to a ray embedding. + +To render a pixel, we sample points along an input ray $\mathbf{o} + t\mathbf{d}$ , and predict volume density $\tau'$ , diffuse color $\mathbf{c}_{\mathrm{d}}'$ , tint $\mathbf{s}'$ , roughness $\rho'$ , and normal direction $\mathbf{n}'$ at each sample point (we denote per-sample properties using a prime). Given that reflections occur only at the surface, we evaluate the specular component once per ray on the surface obtained from the NeRF depth. This also results in less computation than per-sample-point specular shading. Consequently, we calculate volumetric depth $t_0$ by rendering the ray marching distance at each sample point. We also volumetrically render all attributes to synthesize screen-space attributes ( $\mathbf{c}_{\mathrm{d}}, \mathbf{s}, \rho, \mathbf{n}$ ). Note that the rendered normal must be normalized to yield the final screen-space normal $\mathbf{n}$ . We then evaluate the specular component by first computing the reflected ray using origin $\mathbf{o}_{\mathrm{r}} = \mathbf{o} + t_0\mathbf{d}$ , and the reflection direction $\mathbf{d}_{\mathrm{r}}$ derived using Equation 3. The reflected ray $\mathbf{o}_{\mathrm{r}} + t\mathbf{d}_{\mathrm{r}}$ and surface roughness $\rho$ are then encoded using our novel 3D Gaussian directional encoding. After a tiny MLP, we compute the specular color $\mathbf{c}_{\mathrm{s}}$ , and the final rendering result using Equation 1. + +From a physically based rendering perspective, Equation 1 is analogous to the Cook-Torrance approximation [10] of the rendering equation [19]. The term $\mathbf{c}_{\mathrm{s}} \odot \mathbf{s}$ can be interpreted as the split-sum approximation of the specular part of the Cook-Torrance model, with the specular color $\mathbf{c}_{\mathrm{s}}$ corresponding to the preconvolved incident light, and the tint s to the pre-integrated bidirectional reflectance distribution function (BRDF). + +# 4.1. Gaussian Directional Encoding + +Existing works parameterize view-dependent appearance by first encoding view or reflection direction into Fourier or spherical harmonics (SH) features, which results in a spatially invariant encoding of the view direction. Therefore, it becomes challenging for the NeRF to model spatially varying view-dependent effects, such as near-field lighting. We illustrate this via a toy example in Figure 3, where we place + +![](images/f988da75a78a0b338d0e41633d4a01183b148ec7552a9ee652c841a08378d4b3.jpg) +Figure 3. Toy example of 3D Gaussian encoding. Left: A hemisphere probe translates underneath 4 lights along positions numbered 1 to 4. Note that we dilate the lights for better visualization. Right: Representation of the probe's specular components using spherical harmonics and our 3D Gaussian directional encoding. The SH encoding shows a more complex pattern under position change, while ours has spatially largely invariant coefficients. This suggests a simpler function for the specular prediction MLP to fit using Gaussian directional encoding. + +a hemispherical specular probe in a simple scene with four lights of different shapes and colors. Then, we represent the specular component of the toy example by linearly combining the directional encoding features. We find the optimal coefficients for each encoding type that best fit the ground-truth specular component using stochastic gradient descent, and visualize them in Figure 3. We can see that even for this simple toy setup, the SH-based encoding requires complex, spatially varying coefficients, which complicates the underlying function for the NeRF to fit and interpolate. + +We propose to spatially vary the encoding function by defining the basis functions via several learnable 3D Gaussians. Specifically, we parameterize 3D Gaussians using their position $\pmb{\mu}_i\in \mathbb{R}^3$ , scale $\sigma_{i}\in \mathbb{R}^{3}$ , and quaternion rotation $\mathbf{q}_i\in \mathbb{H}$ : + +$$ +\mathcal {G} _ {i} (\mathbf {x}) = \exp \left(- \left\| \mathcal {Q} \left(\mathbf {x} - \boldsymbol {\mu} _ {i}; \mathbf {q} _ {i}\right) \odot \boldsymbol {\sigma} _ {i} ^ {- 1} \right\| _ {2} ^ {2}\right), \tag {4} +$$ + +where $\mathcal{Q}(\mathbf{v};\mathbf{q}_i)$ represents applying quaternion rotation $\mathbf{q}_i$ to the vector $\mathbf{v}$ . To compute the $i$ -th dimension of the encoding for a ray $\mathbf{o} + t\mathbf{d}$ , we need to define a basis function $\mathcal{P}_i(\mathbf{o},\mathbf{d}) \in \mathbb{R}$ that maps the ray to a scalar value given the Gaussian parameters. While there are many ways to define the mapping, we find one that is efficient and has a closed-form solution by defining the projection as the maximum value of the Gaussian along the ray: + +$$ +\mathcal {P} _ {i} (\mathbf {o}, \mathbf {d}) = \max _ {t \geq 0} \mathcal {G} _ {i} (\mathbf {o} + t \mathbf {d}). \tag {5} +$$ + +In the supplement, we derive the closed-form solution: + +$$ +\mathcal {P} _ {i} (\mathbf {o}, \mathbf {d}) = \left\{ \begin{array}{l l} \exp \left(\frac {\left(\mathbf {o} _ {i} ^ {\top} \mathbf {d} _ {i}\right) ^ {2}}{\mathbf {d} _ {i} ^ {\top} \mathbf {d} _ {i}} - \mathbf {o} _ {i} ^ {\top} \mathbf {o} _ {i}\right) & \mathbf {o} _ {i} ^ {\top} \mathbf {d} _ {i} < 0 \\ \mathcal {G} _ {i} (\mathbf {o}) & \text {o t h e r w i s e ,} \end{array} \right. \tag {6} +$$ + +where $\mathbf{o}_i$ and $\mathbf{d}_i$ are the ray origin and direction transformed into Gaussian-local space: + +$$ +\mathbf {o} _ {i} = \mathcal {Q} (\mathbf {o} - \boldsymbol {\mu} _ {i}; \mathbf {q} _ {i}) \odot \sigma_ {i} ^ {- 1}, \tag {7} +$$ + +$$ +\mathbf {d} _ {i} = \mathcal {Q} (\mathbf {d}; \mathbf {q} _ {i}) \odot \sigma_ {i} ^ {- 1}. \tag {8} +$$ + +![](images/78692e67d272236fb8e4537dbf343b413a1ff16b58a78783890e3b45abfcfa1f.jpg) +Figure 4. Stereographic projections of the specular fitting results for the toy example in Figure 3. Both encodings produce 25 coefficients for each color channel, which are then summed to produce the final color. Note that the GT shows soft boundaries because it is preconvolved. The 3D Gaussian-based encoding demonstrates superior performance in representing the specular change with positional changes, and is also capable of smoothly varying roughness. + +By applying Equation 6 for every 3D Gaussian, we obtain a vector of projected values $\{\mathcal{P}_i\}$ , which forms our final encoding features. Similar to existing NeRF-based representations [9, 34, 36], we rely on a small MLP to convert the encoding to a specular color $\mathbf{c}_{\mathrm{s}}$ . + +As illustrated by the toy example in Figure 3, our Gaussian directional encoding exhibits more constant coefficients in response to the position changes, suggesting a smoother mapping from the embedding features to the specular color. This smoothness is due to the Gaussian basis function producing spatially varying features that mimic the behavior of how the specular component would change under near-field lighting conditions. As a result, the underlying functions that model the specular reflections are easier to learn. + +We also visualize the fitted specular color of both approaches in Figure 4. Our 3D Gaussian directional encoding more accurately captures the spatial variations of the specular components. + +Similar to Ref-NeRF, we use an additional "roughness" value $\rho$ to control the maximum frequency of the specular color. We achieve this in our Gaussian embedding by multiplying each Gaussian's scale $\sigma_{i}$ with the roughness $\rho$ . Intuitively, a larger Gaussian results in a smoother function with varying direction $\mathbf{d}$ . Substituting the $\sigma_{i}$ with $\rho \sigma_{i}$ in Equation 6 leads to the complete equation of our 3D Gaussian encoding. Figure 4 demonstrates the ability of our 3D Gaussian-based encoding to modify roughness on the fly. + +# 4.2. Optimizing the Gaussian Directional Encoding + +It is worth noting that our proposed Gaussian encoding correctly models spatially varying specular reflections only when the Gaussians are positioned properly in 3D space. We thus jointly optimize the Gaussian parameters together with the NeRF during training, to ensure the Gaussians are in the optimal state for modeling reflections. However, there is no direct supervision for the Gaussian parameters. + +Our experiments show that without proper initial Gaussian parameters, the optimization may lead to suboptimal local minima, resulting in inconsistent quality of specular reconstruction. To address this, we propose an initialization stage for the Gaussian parameters and to bootstrap the specular color prediction. As mentioned earlier, the specular color is essentially the preconvolved incident light, which can be directly deduced from input images. + +Motivated by this observation, we train the 3D Gaussians and the specular decoder $(\mathrm{MLP}_3$ in Figure 2) in the initialization stage using the input images. We train an incident light field that accommodates a diversity of rays and roughness values. Therefore, we apply a range of Gaussian blurs to all input images using a series of standard deviations, generating Gaussian pyramids. These pyramids of input images provide a pseudo target for incident light under different degrees of surface roughness. In each iteration of the training, we sample pixels from the pyramids and trace rays to these pixels. The traced rays are also associated with a roughness value that is equivalent to the blur's standard deviation. We encode each ray with roughness using our Gaussian directional encoding, and predict the specular color $\mathbf{c}_{\mathrm{s}}$ using the decoder. By minimizing the errors between $\mathbf{c}_{\mathrm{s}}$ and the pseudo ground truth, we refine the Gaussian parameters and the specular decoder, which then serve as initialization for the subsequent joint optimization stage. + +# 4.3. Resolving the Shape-Radiance Ambiguity + +Regardless of any view-dependent parameterization, there remains a fundamental ambiguity between shape and radiance in NeRFs. For example, consider a perfect mirror reflection. Without any prior knowledge, it is nearly impossible for the NeRF model to tell whether the mirror is a flat surface with perfect reflection, or a window to a (virtual) scene behind the surface. Therefore, prior information is needed to guide the model to learn the correct geometry. Inspired by recent progress in monocular geometry estimation [4, 12, 39, 59], we propose to supervise the predicted normal $\mathbf{n}$ using monocular normal estimation $\mathbf{n}_{\mathrm{mono}}$ [12]: + +$$ +\mathcal {L} _ {\mathrm {m o n o}} = \sum_ {j} \left\| \mathbf {n} ^ {j} - \mathbf {R} ^ {j} \mathbf {n} _ {\mathrm {m o n o}} ^ {j} \right\| _ {2} ^ {2}, \tag {9} +$$ + +where the superscript $j$ is a ray index, and $\mathbf{R}^j$ is the corresponding camera rotation matrix that converts normals from view space to world space. + +![](images/5075a3ac83240cc5c87f268ef2df01f6ecde4fd12a8771ce1279f47e84daa1e1.jpg) +Target +Full +w/o $\mathcal{L}_{\mathrm{mono}}$ +w/o early stop +Figure 5. The specular component reconstruction (first row, except the first image), novel-view synthesis results (second row) and normal visualizations (third row) under varying monocular normal supervision. The target normal visualizes the monocular normal prediction. Without $\mathcal{L}_{\mathrm{mono}}$ , the predicted normal exhibits enormous error, leading to poor specular reconstruction. Without early stopping $\mathcal{L}_{\mathrm{mono}}$ , minor errors in the predicted normals lead to a slight degradation in the reflection quality compared to our full model. + +However, monocular normals are prone to error. We therefore use them primarily as initialization and apply $\mathcal{L}_{\mathrm{mono}}$ only at the beginning of the training, so that the errors in the normals do not overwhelm the geometry of the NeRF. Figure 5 and Table 2 show results with different configurations of $\mathcal{L}_{\mathrm{mono}}$ . We can see that without monocular normal as supervision ('w/o $\mathcal{L}_{\mathrm{mono}}$ ), the predicted normals have catastrophic errors, such as those pointing inwards (orange) or lying parallel (violet) to the surface. Consequently, the learned specular component is less accurate due to the incorrect normals. Despite this, a somewhat plausible specular reflection can still be learned as the Gaussian encoding can "cheat" the reflections even with erroneous normals. On the other hand, without early stopping of the loss ('w/o early stop'), minor inaccuracies from the monocular normals permeate into predicted normals, leading to a degradation of the reflection quality. + +# 4.4. Losses + +To jointly optimize all parameters within our proposed pipeline, we use a combination of loss terms: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {c}} + \mathcal {L} _ {\text {p r o p}} + \lambda_ {\text {d i s t}} \mathcal {L} _ {\text {d i s t}} + \lambda_ {\text {m o n o}} \mathcal {L} _ {\text {m o n o}} + \lambda_ {\text {n o r m}} \mathcal {L} _ {\text {n o r m}}. \tag {10} +$$ + +In this equation, $\mathcal{L}_{\mathrm{c}}$ is the L1 reconstruction loss between the predicted and ground-truth colors. The terms $\mathcal{L}_{\mathrm{prop}}$ and $\mathcal{L}_{\mathrm{dist}}$ are adopted from mip-NeRF 360 [3], where $\mathcal{L}_{\mathrm{prop}}$ supervises the density proposal networks, and $\mathcal{L}_{\mathrm{dist}}$ is the distortion loss encouraging density sparsity. To tie predicted normals to the density field, we use Ref-NeRF's normal prediction loss $\mathcal{L}_{\mathrm{norm}}$ [47], which guides the predicted normal $\mathbf{n}$ with the density gradient direction. Further elaboration on these loss components can be found in the supplementary material. + +In our experiments, we set $\lambda_{\mathrm{dist}} = 0.002$ , aligning with the settings of the "nerfacto" model in Nerfstudio [44]. For + +Table 1. Quantitative comparisons of novel-view synthesis on three datasets. We highlight the best numbers in bold. + +
MethodsEyeful Tower dataset [53]NISR [50] + Inria [38] datasetShiny dataset [47]
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Ours32.5830.93280.144530.7710.89090.165526.5640.72770.2776
NeRF [34]31.8540.92540.162630.7480.88730.172826.4690.72350.2852
Ref-NeRF [47]31.6520.92580.157030.6540.89030.166926.5020.72420.2827
MS-NeRF [57]31.7150.93110.156130.2240.88400.181626.4660.70700.3225
GT Test ImageGT & SfM NormalOursRef-NeRF [47]MS-NeRF [57]NeRF [34]
Eyeful Workshop
NISR LivingRoom2
Eyeful Office2
+ +Figure 6. Comparisons of novel-view synthesis quality and normal map visualizations. Our method consistently reconstructs reflections while other methods either produce 'faked' reflections, resulting in incorrect normals, or fail to model reflections entirely. + +$\lambda_{\mathrm{mono}}$ , we choose a value of 1 in the first 4K iterations, and reduce to 0 thereafter to cease its effect, as described earlier. We find that our method is robust to the value of $\lambda_{\mathrm{mono}}$ as it only serves as initialization. We also assign $\lambda_{\mathrm{norm}} = 10^{-3}$ , which is slightly higher than the weight in Ref-NeRF [47], as we find that this produces slightly smoother normals without substantially compromising the rendering quality. + +# 5. Experiments + +Implementation. To model room-scale scenes, we employ a network architecture similar to the "nerfacto" model presented in Nerfstudio [44]. We use two small density networks as proposal networks, supervised via $\mathcal{L}_{\mathrm{prop}}$ . We sample 256 and 96 points for each proposal network, and 48 points for the final NeRF model. These three networks all use hash-based positional encodings. When querying the hash features in the final NeRF model, we incorporate the LOD-aware scheme proposed in VR-NeRF [53]. We train our model + +for 100,000 iterations and randomly sample 12,800 rays in each iteration. This process takes around 8 GB of GPU memory and approximately 3.5 hours to train a model using an NVIDIA A100 GPU. Further details regarding the model's structure can be found in the supplementary materials. + +Datasets. We evaluate our method on several datasets with a focus on indoor scenes characterized by near-field lighting conditions. First, we evaluate on the Eyeful Tower dataset [53], which provides high-quality HDR captures of 11 indoor scenes. Each scene is coupled with calibrated camera parameters and a mesh reconstructed via Agisoft Metashape [1]. We select 9 scenes that feature notable reflective properties. We downsample the images of each scene to a resolution of $854 \times 1280$ pixels. We curated around 50-70 views per scene that contain glossy surfaces for evaluation, leaving the remaining views for training. We also evaluate our approach on public indoor datasets NISR [50] and Inria [38] (NISR+Inria). Moreover, to assess the performance under + +![](images/191aa998a13f1e839c5084aa64f6ce4f3b1e106d14f26bed69b9682eb61d08db.jpg) +Figure 7. Intermediate components of our approach compared to Ref-NeRF [47]. Our approach produces a more meaningful decomposition under room-scale lighting settings. + +far-field lighting, we evaluate the real shiny dataset in Ref-NeRF [47]. We report the average PSNR, SSIM, and LPIPS [64] metrics for evaluating rendering quality. + +# 5.1. Comparisons + +We compare our method with several baselines: NeRF [34], Ref-NeRF [47], and MS-NeRF [57], which specializes in mirror-like reflections by decomposing NeRF into multiple spaces. For a fair comparison, we re-implement these baselines, such that we share the same NeRF backbone and rendering configurations, with the only difference being the way different methods decompose and parameterize the output color. We report the numerical results across three datasets in Table 1. Our method demonstrates superior performance on the Eyeful Tower dataset, indicating the effectiveness of our method. On the NISR+Inria datasets, our method marginally outperforms the baselines, likely due to the dataset containing few reflection surfaces. Notably, while our method is tailored for near-field lighting conditions, it also shows promising results on the Shiny dataset, which comprises far-field lighting scenarios. This is because our Gaussian directional encoding can simulate a spatially invariant encoding by positioning Gaussians at a significant distance. + +Qualitative results on the Eyeful Tower and NISR+Inria datasets are provided in Figure 6. We can see that while other baselines occasionally synthesize plausible reflections, they resort to approximations that fake the reflections by placing emitters underneath the surface. As a result, they either produce incorrect geometry, or fail to model the reflections. Our method, in contrast, successfully models specular highlights on the surface. We provide additional video results in the supplementary material. + +We also visualize and compare the decomposition produced by our method and Ref-NeRF in Figure 7. We can see + +![](images/c496a1f8ae23690a55311735cbad98741f8113fdc5b5fe5d12f92891dfbd496d.jpg) +Figure 8. We evaluate the novel-view synthesis quality with respect to the number of Gaussians across five scenes. The green dashed line is the setting we use in our experiments. + +that Ref-NeRF fails to obtain a meaningful decomposition under near-field lighting, and produces holes in the geometry, whereas our method consistently achieves a realistic separation of specular and diffuse components. + +# 5.2. Ablation Studies + +Number of Gaussians. One important hyperparameter in the Gaussian directional encoding is the number of Gaussians, as it directly influences the model's capacity to represent specular colors. We conduct experiments to evaluate the impact of varying the number of Gaussians on five scenes from the Eyeful Tower dataset, and show the relationship between the number of Gaussians and the rendering quality in Figure 8. The rendering quality improves when using more Gaussians, but the improvement saturates as the number increases beyond 400. Note that using a larger number of Gaussians also entails greater computation costs and GPU memory requirements for every rendered pixel. Therefore, we use 256 Gaussians for all experiments, to strike a balance between rendering quality and computational efficiency. + +Optimizing Gaussians. To optimize the Gaussian directional encoding effectively, we first initialize them by training an incident light field, and then jointly finetune the Gaus + +Table 2. Ablations of our method on the Eyeful Tower dataset [53]. The "e.s." indicates early stopping the $\mathcal{L}_{\mathrm{mono}}$ after 4K iterations. + +
MethodGaussians Init.Mono. Opt.E. S. Prior\( {\mathcal{L}}_{\text{mono }} \)PSNR↑SSIM↑LPIPS↓
Full✓✓✓✓32.580.93280.1445
w/o init✘✓✓✓32.520.93040.1429
w/o opt.✓✘✓✓32.060.92650.1581
w/o \( {\mathcal{L}}_{\text{mono }} \)✓✓✘-32.310.92880.1503
w/o e.s.✓✓✓✘32.460.92920.1502
+ +![](images/3d4ac95ee386b74c84014376c9e7da2e5a3f4c919155b041861f19d2bc92f820.jpg) +Figure 9. Example results under different Gaussian optimization settings. Without initializing the Gaussian parameters ('w/o init') or optimizing Gaussians jointly with the NeRF ('w/o opt.'), the Gaussian embedding struggles to model specularities accurately. + +sian encoding together with the NeRF model. We demonstrate the significance of initialization ('w/o init') and fine-tuning ('w/o opt.') by omitting each process individually. We show quantitative results in Table 2 and a qualitative example in Figure 9. Without initialization, the model can still reconstruct reflections to some extent, resulting in a slightly better average LPIPS score, yet it fails to model some specular details, such as the light blobs. Neglecting the joint optimization of Gaussians leads to complete failure in modeling specular reflections. As illustrated in Figure 9, with the inaccurate specular modeling, the tints suppress the specular reflections, which ultimately leads to the inability to represent reflections in the final rendered image. + +# 6. Discussion and Conclusion + +Applications. Our primary goal was to improve the quality of novel-view synthesis with specular reflective surfaces. We achieve this via our proposed Gaussian directional encoding that enables a meaningful decomposition of specular and diffuse components in a scene. Moreover, this also enables applications other than novel-view synthesis, such as reflection removal, and surface roughness editing. For instance, Figure 7 shows that we can easily remove reflections using the diffuse component. Furthermore, Figure 10 demonstrates + +![](images/c0149805caa2359d9f2f152c9704756e08c95f1fce0c7662b04bd3f7e73c35ba.jpg) +Figure 10. We can control the roughness of the scene by adding an offset to the input roughness. + +![](images/1614d5b18f25ef28f8660954b5ff6ce5c887d1154516b1345f58ef0a8289aa16.jpg) +Figure 11. Our method cannot reconstruct mirror-like perfect reflections due to the limited capacity of the 3D Gaussian encoding. + +an example of editing roughness. By adding an offset to the predicted roughness during rendering, we can effectively manipulate the glossiness of the real surface. + +Limitations. While our method improves on existing baselines, it has some limitations. As we parameterize the specular color via only several hundreds of Gaussians, the encoding is limited to relatively low frequency compared with perfect mirror-like reflections. We show such a failure case in Figure 11. We can see that our method is only able to learn a blurry version of the reflection. This could be alleviated by using many more Gaussians, as demonstrated in 3D Gaussian splatting [20]. However, the computational cost of traversing all Gaussians for every pixel quickly becomes prohibitive in our implementation. More efficient traversal, such as by rasterization, could be interesting future work. + +Conclusion. In this paper, we proposed a pipeline to improve the existing approach in modeling and reconstructing view-dependent effects in a NeRF representation. Central to our approach is a new Gaussian directional encoding to enhance the capability of neural radiance fields to model specular reflections under near-field lighting. We also utilize monocular normal supervision to help resolve shape-radiance ambiguity. Experiments have demonstrated the effectiveness of each of our contributions. We believe this work proposes a practical and effective solution for reconstructing NeRFs in room-scale scenes, specifically addressing the challenges of accurately capturing specular reflections. + +Acknowledgments. 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In CVPR, 2018. 7 +[65] Xiuming Zhang, Pratul P. Srinivasan, Boyang Deng, Paul Debevec, William T. Freeman, and Jonathan T. Barron. NeR-Factor: Neural factorization of shape and reflectance under an unknown illumination. ACM Trans. Graph., 40(6):237:1-18, 2021. 2 +[66] Yuanqing Zhang, Jiaming Sun, Xingyi He, Huan Fu, Rongfei Jia, and Xiaowei Zhou. Modeling indirect illumination for inverse rendering. In CVPR, 2022. 2 +[67] Youjia Zhang, Teng Xu, Junqing Yu, Yuteng Ye, Junle Wang, Yanqing Jing, Jingyi Yu, and Wei Yang. NeMF: Inverse volume rendering with neural microflake field. In ICCV, 2023. 2 +[68] Yiyu Zhuang, Qi Zhang, Xuan Wang, Hao Zhu, Ying Feng, Xiaoyu Li, Ying Shan, and Xun Cao. NeAI: A pre-convoluted representation for plug-and-play neural ambient illumination. In AAAI, 2024. 2 \ No newline at end of file diff --git a/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/images.zip b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1bd565d40d25d1b9613cf38032b1ca256edb7957 --- /dev/null +++ b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9f108c67d8d318119614aa632a36aee41cb7fb4d591edc20adb3807578c62c27 +size 727803 diff --git a/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/layout.json b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ff22dfd1ce69d41e9655b62495075c165d072300 --- /dev/null +++ b/2024/SpecNeRF_ Gaussian Directional Encoding for Specular Reflections/layout.json @@ -0,0 +1,8731 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 86, + 103, + 503, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 103, + 503, + 121 + ], + "spans": [ + { + "bbox": [ + 86, + 103, + 503, + 121 + ], + "type": "text", + "content": "SpecNeRF: Gaussian Directional Encoding for Specular Reflections" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "spans": [ + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": "Li Ma" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Vasu Agrawal" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Haithem Turki" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{2,3}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Changil Kim" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Chen Gao" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Pedro Sander" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Michael Zollhöfer" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "text", + "content": " Christian Richardt" + }, + { + "bbox": [ + 123, + 137, + 470, + 165 + ], + "type": "inline_equation", + "content": "^{2}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 161, + 171, + 432, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 161, + 171, + 432, + 200 + ], + "spans": [ + { + "bbox": [ + 161, + 171, + 432, + 200 + ], + "type": "text", + "content": "1The Hong Kong University of Science and Technology 2Meta Reality Labs 3Carnegie Mellon University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 219, + 192, + 232 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 219, + 192, + 232 + ], + "spans": [ + { + "bbox": [ + 143, + 219, + 192, + 232 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 245, + 290, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 245, + 290, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 245, + 290, + 485 + ], + "type": "text", + "content": "Neural radiance fields have achieved remarkable performance in modeling the appearance of 3D scenes. However, existing approaches still struggle with the view-dependent appearance of glossy surfaces, especially under complex lighting of indoor environments. Unlike existing methods, which typically assume distant lighting like an environment map, we propose a learnable Gaussian directional encoding to better model the view-dependent effects under near-field lighting conditions. Importantly, our new directional encoding captures the spatially-varying nature of near-field lighting and emulates the behavior of prefiltered environment maps. As a result, it enables the efficient evaluation of preconvolved specular color at any 3D location with varying roughness coefficients. We further introduce a data-driven geometry prior that helps alleviate the shape radiance ambiguity in reflection modeling. We show that our Gaussian directional encoding and geometry prior significantly improve the modeling of challenging specular reflections in neural radiance fields, which helps decompose appearance into more physically meaningful components." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 512, + 128, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 128, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 128, + 525 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 533, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 289, + 715 + ], + "type": "text", + "content": "Neural radiance fields (NeRFs) have emerged as a popular scene representation for novel-view synthesis [34, 45, 51]. By training a neural network based on sparse observations of a 3D scene, NeRF-like representations are able to synthesize novel views with photorealistic visual quality. In particular, with a scalable model design, such as InstantNGP [36], NeRFs are able to model room-scale 3D scenes with extraordinary detail [53]. However, existing approaches typically only manage to model mild view-dependent effects like those seen on nearly diffuse surfaces. When encountering highly view-dependent glossy surfaces, NeRFs struggle to model the high-frequency changes when the viewpoint changes. Instead, they tend to \"fake\" specular reflections by placing them behind surfaces, which may result in poor view interpolation and \"foggy\" geometry [47]. Moreover, fake" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 220, + 547, + 348 + ], + "blocks": [ + { + "bbox": [ + 308, + 220, + 547, + 348 + ], + "lines": [ + { + "bbox": [ + 308, + 220, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 308, + 220, + 547, + 348 + ], + "type": "image", + "image_path": "a0614387486ba2fd7115a6e176f287445f7e247bfed693c892db967d34e247db.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 356, + 547, + 411 + ], + "lines": [ + { + "bbox": [ + 305, + 356, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 305, + 356, + 547, + 411 + ], + "type": "text", + "content": "Figure 1. We propose a Gaussian directional encoding that leads to better modeling of specular reflections under near-field lighting conditions. In contrast, the integrated directional encoding utilized in Ref-NeRF [47] and Fourier directional encoding in NeRF [34] exhibit suboptimal performance under similar conditions." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 423, + 547, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 423, + 547, + 448 + ], + "spans": [ + { + "bbox": [ + 305, + 423, + 547, + 448 + ], + "type": "text", + "content": "reflections are not viable if one can look behind the surface, as NeRF can no longer hide the reflections there." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 449, + 548, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 548, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 548, + 617 + ], + "type": "text", + "content": "Accurately modeling and reconstructing specular reflections presents notable challenges, especially for room-scale scenes. Physically correct reflection modeling involves pathtracing many rays for every single pixel, which is impractical for NeRF-like volumetric scene representations, primarily due to the large computational requirements to shade a single pixel. Consequently, an efficient approximation of the reflection shading is needed for a feasible modeling of reflections. Existing works [14, 47] address this challenge by incorporating heuristic modules inspired by real-time image-based lighting (IBL) [35] techniques, such as explicit ray bounce computations to enhance NeRF's capability to simulate reflections, and integrated directional encoding to simulate appearance change under varying surface roughness." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 548, + 715 + ], + "type": "text", + "content": "While these improvements have shown to be effective in modeling specular reflections for NeRFs, they are limited to object-level reconstruction under distant lighting, which assumes the object is lit by a 2D environment map. They work poorly for modeling near-field lighting, where the corresponding environment map varies spatially. The issue is that existing methods rely on directional encodings to embed ray directions for generating view-dependent reflections." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21188" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "These encodings, such as Fourier encoding or spherical harmonics, are spatially invariant. Figure 1 demonstrates one example of NeRF [34] and Ref-NeRF [47] reconstructions of an indoor scene with spatially-varying lighting. NeRF produces extremely noisy geometry, resulting in artifacts in the rendering result. Ref-NeRF offers a slight improvement, but still struggles with noisy geometry and view interpolation. This illustrates that the spatial invariance in the directional encodings of existing methods presents challenges under spatially-varying lighting conditions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 335 + ], + "type": "text", + "content": "In this work, we propose a novel Gaussian directional encoding that is tailored for spatially varying lighting conditions. Instead of only encoding a 2D ray direction, we use a set of learnable 3D Gaussians as the basis to embed a 5D ray space including both ray origin and ray direction. We show that, with appropriately optimized Gaussian parameters, this encoding introduces an important inductive bias towards near-field lighting, which enhances the model's ability to capture the characteristics of specular surfaces, leading to photorealistic reconstructions of shiny reflections. We further demonstrate that by changing the scale of the 3D Gaussians, we can edit the apparent roughness of a surface." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 335, + 289, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 335, + 289, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 335, + 289, + 574 + ], + "type": "text", + "content": "While our proposed Gaussian directional encoding improves the reflection modeling of NeRF, high-quality reflection reconstruction also requires an accurate surface geometry and normal in order to compute accurate reflection rays. However, the geometry within NeRFs is often noisy in the early phases of training, which presents challenges in simultaneously optimizing for good geometry and reflections. To better address this challenge, we introduce a data-driven prior to direct the NeRF model towards the desired solution. We deploy a monocular normal estimation network to supervise the normal of the geometry at the beginning of the training stage, and show that this bootstrapping strategy improves the reconstruction of normals, and further leads to successful modeling of specular reflections. We conduct experiments on several public datasets and show that the proposed method outperforms existing methods, achieving higher-quality photorealistic rendering of reflective scenes while also providing more meaningful and accurate color component decomposition. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 574, + 287, + 658 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 574, + 287, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 287, + 610 + ], + "type": "text", + "content": "- We propose a novel Gaussian directional encoding that is more effective in modeling view-dependent effects under near-field lighting conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 611, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 611, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 611, + 287, + 634 + ], + "type": "text", + "content": "- We propose to use monocular normal estimation to resolve shape-radiance ambiguity in the early training stages." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 635, + 287, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 287, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 287, + 658 + ], + "type": "text", + "content": "- Our full NeRF pipeline achieves state-of-the-art novel-view synthesis performance for specular reflections." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Reflection-aware NeRFs. Successfully modeling view-dependent effects, such as specular reflections, can greatly" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 384 + ], + "type": "text", + "content": "enhance the photorealism of the reconstructed NeRF. NeRF models view-dependency by conditioning the radiance on the positional encoding [43] of the input ray direction, which is only capable of mild view-dependent effects. Ref-NeRF [47] improves NeRF's capability for modeling reflections by conditioning the view-dependent appearance on the reflection ray direction instead of incident ray direction, and by modulating the directional encoding based on surface roughness. This reparameterization of outgoing radiance makes the underlying scene function simpler, leading to a better geometry and view interpolation quality for glossy objects. Ref-NeuS [14] further extends these concepts to a surface-based representation. However, these are primarily designed for object-level reconstruction under environment map lighting conditions. Modeling large-scale scenes with near-field lighting remains a problem. Clean-NeRF [30] decomposes the radiance into diffuse and specular colors, and supervises the two components by least-square estimations of multiple input rays. This alleviates the ambiguity of highly specular regions; yet, it does not change the view-dependent structure of the NeRF model, thus limiting its ability to model reflections. NeRF-DS [54] models peculiarities in dynamic scenes and considers the variations in reflections caused by dynamic geometry through the use of a dynamic normal field, but requires additional object masks for accurate specular reconstruction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 391, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 548, + 715 + ], + "type": "text", + "content": "NeRF-based Inverse Rendering. Inverse rendering goes beyond simple reflection modeling and aims to jointly recover one or more of scene geometry, material appearance and the lighting condition. In practice, the material appearance is typically modeled using physically-based rendering assets such as albedo, roughness and glossiness. Mesh-based inverse rendering methods [2, 38, 49, 68] try to recover materials using differentiable path tracing [25]. However, they typically assume a given geometry, since optimizing mesh geometry is challenging. On the contrary, NeRF-based inverse rendering approaches [5, 42, 65, 66] make it easier to optimize geometry jointly by modeling material properties and density continuously in a volumetric 3D space. The lighting is usually represented as point or directional lights [5, 23, 60], an environment texture map [31-33, 42, 65], or an implicit texture map modeled by spherical Gaussians [6, 11, 18, 63, 66, 66, 67] or MLPs [7, 29]. Most methods are limited to object-level reconstruction and assume the lighting is spatially invariant (i.e. distant). Several light estimation techniques [13, 26, 27, 41] explore using 3D light primitives or spatially-varying spherical Gaussians to model spatially varying lighting. However, these methods focus on data-driven approaches to estimate lighting for image editing. NeILF [56] and NeILF++ [62] model lighting as a 5D light field using another MLP, but still focus mainly on small-scale reconstruction. Several works apply inverse rendering for relighting outdoor scenes [24, 40, 48, 58]. However, they fo" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21189" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 71, + 547, + 148 + ], + "blocks": [ + { + "bbox": [ + 50, + 71, + 547, + 148 + ], + "lines": [ + { + "bbox": [ + 50, + 71, + 547, + 148 + ], + "spans": [ + { + "bbox": [ + 50, + 71, + 547, + 148 + ], + "type": "image", + "image_path": "f4418cee136b1d66e9b2ffd94268584dc8d55974c80094f3e2047b19ad456556.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 156, + 547, + 178 + ], + "lines": [ + { + "bbox": [ + 46, + 156, + 547, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 156, + 547, + 178 + ], + "type": "text", + "content": "Figure 2. An overview of our model. The key enabler for specular reflections is our novel 3D Gaussian directional encoding module that converts the reflected ray into a spatially-varying embedding, which is further decoded into specular color." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 185, + 287, + 245 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 185, + 287, + 245 + ], + "spans": [ + { + "bbox": [ + 46, + 185, + 287, + 245 + ], + "type": "text", + "content": "cus more on diffuse materials with correct shadow modeling instead of reflections. In this work, we have a different goal compared to inverse rendering, focusing only on correctly modeling reflections for better novel-view synthesis, rather than trying to discern material properties for standalone use." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 247, + 290, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 290, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 290, + 392 + ], + "type": "text", + "content": "NeRF with mirror reflections. One special case of reflection is mirror reflection. One approach represents the reflected scene as a separate NeRF [15], and composites the two NeRF results in image space. This is also deployed in image-based rendering [52] and large-scale NeRF reconstruction [50]. Given a multi-mirror scene, the idea can be further extended to multi-space NeRFs [57]. An alternate approach is to explicitly model the mirror geometry, and to render the mirrored scene by path tracing [16, 61]. However, since estimating the mirror geometry is highly ill-posed, manual annotation is usually needed. Curved reflectors need even more careful handling [22, 46]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 401, + 132, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 132, + 414 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 132, + 414 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": "We first review Ref-NeRF [47] for decomposing view-dependent appearance. Similar to NeRF, Ref-NeRF models the scene as a function that maps the position " + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": " and view direction " + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": " to the final color " + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": " and density " + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": ". The difference is that Ref-NeRF predicts the color as a combination of diffuse color " + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{d}}" + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": " and specular color " + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 421, + 288, + 493 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 124, + 500, + 287, + 512 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 500, + 287, + 512 + ], + "spans": [ + { + "bbox": [ + 124, + 500, + 287, + 512 + ], + "type": "interline_equation", + "content": "\\mathbf {c} = \\gamma \\left(\\mathbf {c} _ {\\mathrm {d}} + \\mathbf {c} _ {\\mathrm {s}} \\odot \\mathbf {s}\\right), \\tag {1}", + "image_path": "704e3d76582c1cb02563df5acd8b1606adacfc8c51fefb4991337e83eb69ffa4.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{s}" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": " is the specular tint, " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": " the element-wise product, and " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\gamma (\\cdot)" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": " a tone-mapping function. To predict the specular color " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": ", Ref-NeRF first predicts the surface normal " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": ", roughness " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": ", and features " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": " at location " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": " using an MLP. Then, the specular color " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": " is parameterized as a function of the reflection direction " + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 518, + 287, + 590 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 115, + 597, + 287, + 610 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 597, + 287, + 610 + ], + "spans": [ + { + "bbox": [ + 115, + 597, + 287, + 610 + ], + "type": "interline_equation", + "content": "\\mathbf {c} _ {\\mathrm {s}} = F _ {\\boldsymbol {\\theta}} \\left(\\lambda_ {\\mathrm {I D E}} \\left(\\mathbf {d} _ {\\mathrm {r}}, \\rho\\right), \\varphi\\right), \\tag {2}", + "image_path": "6a616fff62560df7791372f902ca8436e9e3684bde245b48b0f99150df50ff4f.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{IDE}}(\\cdot)" + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": " is the integrated directional encoding introduced by Ref-NeRF, " + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "inline_equation", + "content": "F_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": " represents an MLP with parameters " + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": ", and the reflection direction " + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_{\\mathrm{r}}" + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": " is the input direction " + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": " reflected at the predicted surface normal " + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 46, + 616, + 288, + 664 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 123, + 670, + 287, + 683 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 670, + 287, + 683 + ], + "spans": [ + { + "bbox": [ + 123, + 670, + 287, + 683 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {\\mathrm {r}} = \\mathbf {d} - 2 (\\mathbf {d} \\cdot \\mathbf {n}) \\mathbf {n}. \\tag {3}", + "image_path": "0712e53080c854f4267da163cc80e6829475743a1a6f24dcb7236f44ee57933c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "content": "By conditioning the specular color on reflection direction and roughness, the function " + }, + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 46, + 689, + 289, + 714 + ], + "type": "text", + "content": " needs to fit is much simpler." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 184, + 361, + 196 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 184, + 361, + 196 + ], + "spans": [ + { + "bbox": [ + 305, + 184, + 361, + 196 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 205, + 547, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 547, + 265 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 547, + 265 + ], + "type": "text", + "content": "Our goal is to enhance NeRF's capabilities for modeling specular reflections under near-field lighting conditions. Figure 2 presents an overview of our pipeline. A key contribution is the 3D Gaussian directional encoding that maps a ray and surface roughness to a ray embedding." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": "To render a pixel, we sample points along an input ray " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", and predict volume density " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\tau'" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", diffuse color " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{d}}'" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", tint " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{s}'" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", roughness " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\rho'" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", and normal direction " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{n}'" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": " at each sample point (we denote per-sample properties using a prime). Given that reflections occur only at the surface, we evaluate the specular component once per ray on the surface obtained from the NeRF depth. This also results in less computation than per-sample-point specular shading. Consequently, we calculate volumetric depth " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "t_0" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": " by rendering the ray marching distance at each sample point. We also volumetrically render all attributes to synthesize screen-space attributes (" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{d}}, \\mathbf{s}, \\rho, \\mathbf{n}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": "). Note that the rendered normal must be normalized to yield the final screen-space normal " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ". We then evaluate the specular component by first computing the reflected ray using origin " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_{\\mathrm{r}} = \\mathbf{o} + t_0\\mathbf{d}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", and the reflection direction " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": " derived using Equation 3. The reflected ray " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_{\\mathrm{r}} + t\\mathbf{d}_{\\mathrm{r}}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": " and surface roughness " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": " are then encoded using our novel 3D Gaussian directional encoding. After a tiny MLP, we compute the specular color " + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 304, + 266, + 547, + 503 + ], + "type": "text", + "content": ", and the final rendering result using Equation 1." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "content": "From a physically based rendering perspective, Equation 1 is analogous to the Cook-Torrance approximation [10] of the rendering equation [19]. The term " + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}} \\odot \\mathbf{s}" + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "content": " can be interpreted as the split-sum approximation of the specular part of the Cook-Torrance model, with the specular color " + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 304, + 506, + 547, + 601 + ], + "type": "text", + "content": " corresponding to the preconvolved incident light, and the tint s to the pre-integrated bidirectional reflectance distribution function (BRDF)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 610, + 474, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 610, + 474, + 624 + ], + "spans": [ + { + "bbox": [ + 305, + 610, + 474, + 624 + ], + "type": "text", + "content": "4.1. Gaussian Directional Encoding" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 713 + ], + "type": "text", + "content": "Existing works parameterize view-dependent appearance by first encoding view or reflection direction into Fourier or spherical harmonics (SH) features, which results in a spatially invariant encoding of the view direction. Therefore, it becomes challenging for the NeRF to model spatially varying view-dependent effects, such as near-field lighting. We illustrate this via a toy example in Figure 3, where we place" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21190" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 76, + 279, + 148 + ], + "blocks": [ + { + "bbox": [ + 49, + 76, + 279, + 148 + ], + "lines": [ + { + "bbox": [ + 49, + 76, + 279, + 148 + ], + "spans": [ + { + "bbox": [ + 49, + 76, + 279, + 148 + ], + "type": "image", + "image_path": "f988da75a78a0b338d0e41633d4a01183b148ec7552a9ee652c841a08378d4b3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 158, + 289, + 258 + ], + "lines": [ + { + "bbox": [ + 46, + 158, + 289, + 258 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 289, + 258 + ], + "type": "text", + "content": "Figure 3. Toy example of 3D Gaussian encoding. Left: A hemisphere probe translates underneath 4 lights along positions numbered 1 to 4. Note that we dilate the lights for better visualization. Right: Representation of the probe's specular components using spherical harmonics and our 3D Gaussian directional encoding. The SH encoding shows a more complex pattern under position change, while ours has spatially largely invariant coefficients. This suggests a simpler function for the specular prediction MLP to fit using Gaussian directional encoding." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 263, + 288, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 263, + 288, + 384 + ], + "spans": [ + { + "bbox": [ + 46, + 263, + 288, + 384 + ], + "type": "text", + "content": "a hemispherical specular probe in a simple scene with four lights of different shapes and colors. Then, we represent the specular component of the toy example by linearly combining the directional encoding features. We find the optimal coefficients for each encoding type that best fit the ground-truth specular component using stochastic gradient descent, and visualize them in Figure 3. We can see that even for this simple toy setup, the SH-based encoding requires complex, spatially varying coefficients, which complicates the underlying function for the NeRF to fit and interpolate." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "content": "We propose to spatially vary the encoding function by defining the basis functions via several learnable 3D Gaussians. Specifically, we parameterize 3D Gaussians using their position " + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_i\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "content": ", scale " + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "inline_equation", + "content": "\\sigma_{i}\\in \\mathbb{R}^{3}" + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "content": ", and quaternion rotation " + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i\\in \\mathbb{H}" + }, + { + "bbox": [ + 46, + 384, + 288, + 443 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 74, + 448, + 287, + 468 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 448, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 74, + 448, + 287, + 468 + ], + "type": "interline_equation", + "content": "\\mathcal {G} _ {i} (\\mathbf {x}) = \\exp \\left(- \\left\\| \\mathcal {Q} \\left(\\mathbf {x} - \\boldsymbol {\\mu} _ {i}; \\mathbf {q} _ {i}\\right) \\odot \\boldsymbol {\\sigma} _ {i} ^ {- 1} \\right\\| _ {2} ^ {2}\\right), \\tag {4}", + "image_path": "9b9bf293b473dcc7ea3c934b2d36e76114b36ba21bbc59cf1353da208a61127b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}(\\mathbf{v};\\mathbf{q}_i)" + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": " represents applying quaternion rotation " + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{q}_i" + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": " to the vector " + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{v}" + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": ". To compute the " + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": "-th dimension of the encoding for a ray " + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathbf{o} + t\\mathbf{d}" + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": ", we need to define a basis function " + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_i(\\mathbf{o},\\mathbf{d}) \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 472, + 288, + 568 + ], + "type": "text", + "content": " that maps the ray to a scalar value given the Gaussian parameters. While there are many ways to define the mapping, we find one that is efficient and has a closed-form solution by defining the projection as the maximum value of the Gaussian along the ray:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 574, + 287, + 592 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 574, + 287, + 592 + ], + "spans": [ + { + "bbox": [ + 107, + 574, + 287, + 592 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {i} (\\mathbf {o}, \\mathbf {d}) = \\max _ {t \\geq 0} \\mathcal {G} _ {i} (\\mathbf {o} + t \\mathbf {d}). \\tag {5}", + "image_path": "abb61db6f94a4b8d3552dc0a2fd887b7d38d5eadd589239e6a10c0b09ef8264a.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 597, + 268, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 268, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 268, + 609 + ], + "type": "text", + "content": "In the supplement, we derive the closed-form solution:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 613, + 287, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 613, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 59, + 613, + 287, + 647 + ], + "type": "interline_equation", + "content": "\\mathcal {P} _ {i} (\\mathbf {o}, \\mathbf {d}) = \\left\\{ \\begin{array}{l l} \\exp \\left(\\frac {\\left(\\mathbf {o} _ {i} ^ {\\top} \\mathbf {d} _ {i}\\right) ^ {2}}{\\mathbf {d} _ {i} ^ {\\top} \\mathbf {d} _ {i}} - \\mathbf {o} _ {i} ^ {\\top} \\mathbf {o} _ {i}\\right) & \\mathbf {o} _ {i} ^ {\\top} \\mathbf {d} _ {i} < 0 \\\\ \\mathcal {G} _ {i} (\\mathbf {o}) & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {6}", + "image_path": "dc3fa96eeaa76da59664f68d7928a0b9645745e2cdfc7c97bfccc10a31e8a30b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{o}_i" + }, + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\mathbf{d}_i" + }, + { + "bbox": [ + 46, + 651, + 287, + 676 + ], + "type": "text", + "content": " are the ray origin and direction transformed into Gaussian-local space:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 108, + 680, + 287, + 694 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 680, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 108, + 680, + 287, + 694 + ], + "type": "interline_equation", + "content": "\\mathbf {o} _ {i} = \\mathcal {Q} (\\mathbf {o} - \\boldsymbol {\\mu} _ {i}; \\mathbf {q} _ {i}) \\odot \\sigma_ {i} ^ {- 1}, \\tag {7}", + "image_path": "f515b234dc446d0ded129a453ed55bdc65f8911432d20f9bfb449faf4859edf3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 108, + 696, + 287, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 696, + 287, + 711 + ], + "spans": [ + { + "bbox": [ + 108, + 696, + 287, + 711 + ], + "type": "interline_equation", + "content": "\\mathbf {d} _ {i} = \\mathcal {Q} (\\mathbf {d}; \\mathbf {q} _ {i}) \\odot \\sigma_ {i} ^ {- 1}. \\tag {8}", + "image_path": "fc012eed3b100d287855d9bb7e5cb0bc7722f31e361238cbfbcb3b11f159c0fb.jpg" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 310, + 74, + 544, + 291 + ], + "blocks": [ + { + "bbox": [ + 310, + 74, + 544, + 291 + ], + "lines": [ + { + "bbox": [ + 310, + 74, + 544, + 291 + ], + "spans": [ + { + "bbox": [ + 310, + 74, + 544, + 291 + ], + "type": "image", + "image_path": "78692e67d272236fb8e4537dbf343b413a1ff16b58a78783890e3b45abfcfa1f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 297, + 547, + 374 + ], + "lines": [ + { + "bbox": [ + 304, + 297, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 297, + 547, + 374 + ], + "type": "text", + "content": "Figure 4. Stereographic projections of the specular fitting results for the toy example in Figure 3. Both encodings produce 25 coefficients for each color channel, which are then summed to produce the final color. Note that the GT shows soft boundaries because it is preconvolved. The 3D Gaussian-based encoding demonstrates superior performance in representing the specular change with positional changes, and is also capable of smoothly varying roughness." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "spans": [ + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "type": "text", + "content": "By applying Equation 6 for every 3D Gaussian, we obtain a vector of projected values " + }, + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{P}_i\\}" + }, + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "type": "text", + "content": ", which forms our final encoding features. Similar to existing NeRF-based representations [9, 34, 36], we rely on a small MLP to convert the encoding to a specular color " + }, + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 304, + 383, + 547, + 443 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 445, + 547, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 553 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 553 + ], + "type": "text", + "content": "As illustrated by the toy example in Figure 3, our Gaussian directional encoding exhibits more constant coefficients in response to the position changes, suggesting a smoother mapping from the embedding features to the specular color. This smoothness is due to the Gaussian basis function producing spatially varying features that mimic the behavior of how the specular component would change under near-field lighting conditions. As a result, the underlying functions that model the specular reflections are easier to learn." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 555, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 604 + ], + "type": "text", + "content": "We also visualize the fitted specular color of both approaches in Figure 4. Our 3D Gaussian directional encoding more accurately captures the spatial variations of the specular components." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "Similar to Ref-NeRF, we use an additional \"roughness\" value " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " to control the maximum frequency of the specular color. We achieve this in our Gaussian embedding by multiplying each Gaussian's scale " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " with the roughness " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ". Intuitively, a larger Gaussian results in a smoother function with varying direction " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ". Substituting the " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{i}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\rho \\sigma_{i}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " in Equation 6 leads to the complete equation of our 3D Gaussian encoding. Figure 4 demonstrates the ability of our 3D Gaussian-based encoding to modify roughness on the fly." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21191" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 288, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 288, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 288, + 85 + ], + "type": "text", + "content": "4.2. Optimizing the Gaussian Directional Encoding" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 174 + ], + "type": "text", + "content": "It is worth noting that our proposed Gaussian encoding correctly models spatially varying specular reflections only when the Gaussians are positioned properly in 3D space. We thus jointly optimize the Gaussian parameters together with the NeRF during training, to ensure the Gaussians are in the optimal state for modeling reflections. However, there is no direct supervision for the Gaussian parameters." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 174, + 288, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 174, + 288, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 174, + 288, + 269 + ], + "type": "text", + "content": "Our experiments show that without proper initial Gaussian parameters, the optimization may lead to suboptimal local minima, resulting in inconsistent quality of specular reconstruction. To address this, we propose an initialization stage for the Gaussian parameters and to bootstrap the specular color prediction. As mentioned earlier, the specular color is essentially the preconvolved incident light, which can be directly deduced from input images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "text", + "content": "Motivated by this observation, we train the 3D Gaussians and the specular decoder " + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "inline_equation", + "content": "(\\mathrm{MLP}_3" + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "text", + "content": " in Figure 2) in the initialization stage using the input images. We train an incident light field that accommodates a diversity of rays and roughness values. Therefore, we apply a range of Gaussian blurs to all input images using a series of standard deviations, generating Gaussian pyramids. These pyramids of input images provide a pseudo target for incident light under different degrees of surface roughness. In each iteration of the training, we sample pixels from the pyramids and trace rays to these pixels. The traced rays are also associated with a roughness value that is equivalent to the blur's standard deviation. We encode each ray with roughness using our Gaussian directional encoding, and predict the specular color " + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "text", + "content": " using the decoder. By minimizing the errors between " + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_{\\mathrm{s}}" + }, + { + "bbox": [ + 46, + 270, + 289, + 486 + ], + "type": "text", + "content": " and the pseudo ground truth, we refine the Gaussian parameters and the specular decoder, which then serve as initialization for the subsequent joint optimization stage." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 491, + 266, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 266, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 266, + 504 + ], + "type": "text", + "content": "4.3. Resolving the Shape-Radiance Ambiguity" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "type": "text", + "content": "Regardless of any view-dependent parameterization, there remains a fundamental ambiguity between shape and radiance in NeRFs. For example, consider a perfect mirror reflection. Without any prior knowledge, it is nearly impossible for the NeRF model to tell whether the mirror is a flat surface with perfect reflection, or a window to a (virtual) scene behind the surface. Therefore, prior information is needed to guide the model to learn the correct geometry. Inspired by recent progress in monocular geometry estimation [4, 12, 39, 59], we propose to supervise the predicted normal " + }, + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "type": "text", + "content": " using monocular normal estimation " + }, + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 46, + 509, + 288, + 640 + ], + "type": "text", + "content": " [12]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 98, + 645, + 288, + 671 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 645, + 288, + 671 + ], + "spans": [ + { + "bbox": [ + 98, + 645, + 288, + 671 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {m o n o}} = \\sum_ {j} \\left\\| \\mathbf {n} ^ {j} - \\mathbf {R} ^ {j} \\mathbf {n} _ {\\mathrm {m o n o}} ^ {j} \\right\\| _ {2} ^ {2}, \\tag {9}", + "image_path": "6842a0049407960e0aa238fcc15aca7c8f3959021fff28cf91b4ccf4bf0d4482.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": "where the superscript " + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": " is a ray index, and " + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{R}^j" + }, + { + "bbox": [ + 46, + 677, + 289, + 714 + ], + "type": "text", + "content": " is the corresponding camera rotation matrix that converts normals from view space to world space." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 80, + 544, + 200 + ], + "blocks": [ + { + "bbox": [ + 326, + 71, + 348, + 79 + ], + "lines": [ + { + "bbox": [ + 326, + 71, + 348, + 79 + ], + "spans": [ + { + "bbox": [ + 326, + 71, + 348, + 79 + ], + "type": "text", + "content": "Target" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 389, + 71, + 403, + 79 + ], + "lines": [ + { + "bbox": [ + 389, + 71, + 403, + 79 + ], + "spans": [ + { + "bbox": [ + 389, + 71, + 403, + 79 + ], + "type": "text", + "content": "Full" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 438, + 71, + 473, + 79 + ], + "lines": [ + { + "bbox": [ + 438, + 71, + 473, + 79 + ], + "spans": [ + { + "bbox": [ + 438, + 71, + 473, + 79 + ], + "type": "text", + "content": "w/o " + }, + { + "bbox": [ + 438, + 71, + 473, + 79 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 492, + 71, + 538, + 79 + ], + "lines": [ + { + "bbox": [ + 492, + 71, + 538, + 79 + ], + "spans": [ + { + "bbox": [ + 492, + 71, + 538, + 79 + ], + "type": "text", + "content": "w/o early stop" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 80, + 544, + 200 + ], + "lines": [ + { + "bbox": [ + 309, + 80, + 544, + 200 + ], + "spans": [ + { + "bbox": [ + 309, + 80, + 544, + 200 + ], + "type": "image", + "image_path": "5075a3ac83240cc5c87f268ef2df01f6ecde4fd12a8771ce1279f47e84daa1e1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "type": "text", + "content": "Figure 5. The specular component reconstruction (first row, except the first image), novel-view synthesis results (second row) and normal visualizations (third row) under varying monocular normal supervision. The target normal visualizes the monocular normal prediction. Without " + }, + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "type": "text", + "content": ", the predicted normal exhibits enormous error, leading to poor specular reconstruction. Without early stopping " + }, + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 304, + 201, + 547, + 289 + ], + "type": "text", + "content": ", minor errors in the predicted normals lead to a slight degradation in the reflection quality compared to our full model." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "text", + "content": "However, monocular normals are prone to error. We therefore use them primarily as initialization and apply " + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "text", + "content": " only at the beginning of the training, so that the errors in the normals do not overwhelm the geometry of the NeRF. Figure 5 and Table 2 show results with different configurations of " + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "text", + "content": ". We can see that without monocular normal as supervision ('w/o " + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 304, + 298, + 547, + 502 + ], + "type": "text", + "content": "), the predicted normals have catastrophic errors, such as those pointing inwards (orange) or lying parallel (violet) to the surface. Consequently, the learned specular component is less accurate due to the incorrect normals. Despite this, a somewhat plausible specular reflection can still be learned as the Gaussian encoding can \"cheat\" the reflections even with erroneous normals. On the other hand, without early stopping of the loss ('w/o early stop'), minor inaccuracies from the monocular normals permeate into predicted normals, leading to a degradation of the reflection quality." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 509, + 359, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 359, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 359, + 521 + ], + "type": "text", + "content": "4.4. Losses" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 527, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 527, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 527, + 545, + 552 + ], + "type": "text", + "content": "To jointly optimize all parameters within our proposed pipeline, we use a combination of loss terms:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 310, + 560, + 545, + 573 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 560, + 545, + 573 + ], + "spans": [ + { + "bbox": [ + 310, + 560, + 545, + 573 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c}} + \\mathcal {L} _ {\\text {p r o p}} + \\lambda_ {\\text {d i s t}} \\mathcal {L} _ {\\text {d i s t}} + \\lambda_ {\\text {m o n o}} \\mathcal {L} _ {\\text {m o n o}} + \\lambda_ {\\text {n o r m}} \\mathcal {L} _ {\\text {n o r m}}. \\tag {10}", + "image_path": "6b1f85771d73f1fb2479f8e0baacbd175c7fe51d25a5e51549e232b50e68a797.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": "In this equation, " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{c}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " is the L1 reconstruction loss between the predicted and ground-truth colors. The terms " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prop}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " are adopted from mip-NeRF 360 [3], where " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prop}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " supervises the density proposal networks, and " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{dist}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " is the distortion loss encouraging density sparsity. To tie predicted normals to the density field, we use Ref-NeRF's normal prediction loss " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{norm}}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " [47], which guides the predicted normal " + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 304, + 582, + 545, + 689 + ], + "type": "text", + "content": " with the density gradient direction. Further elaboration on these loss components can be found in the supplementary material." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "In our experiments, we set " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{dist}} = 0.002" + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": ", aligning with the settings of the \"nerfacto\" model in Nerfstudio [44]. For" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21192" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 85, + 547, + 459 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 505, + 82 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 505, + 82 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 505, + 82 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons of novel-view synthesis on three datasets. We highlight the best numbers in bold." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 85, + 547, + 459 + ], + "lines": [ + { + "bbox": [ + 47, + 85, + 547, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 85, + 547, + 459 + ], + "type": "table", + "html": "
MethodsEyeful Tower dataset [53]NISR [50] + Inria [38] datasetShiny dataset [47]
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
Ours32.5830.93280.144530.7710.89090.165526.5640.72770.2776
NeRF [34]31.8540.92540.162630.7480.88730.172826.4690.72350.2852
Ref-NeRF [47]31.6520.92580.157030.6540.89030.166926.5020.72420.2827
MS-NeRF [57]31.7150.93110.156130.2240.88400.181626.4660.70700.3225
GT Test ImageGT & SfM NormalOursRef-NeRF [47]MS-NeRF [57]NeRF [34]
Eyeful Workshop
NISR LivingRoom2
Eyeful Office2
", + "image_path": "6e27975e7ed58c96d7cba0dc351d996ca8cf4f9c1f9e36f718a8b0f565f5cfe7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 462, + 546, + 485 + ], + "lines": [ + { + "bbox": [ + 46, + 462, + 546, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 462, + 546, + 485 + ], + "type": "text", + "content": "Figure 6. Comparisons of novel-view synthesis quality and normal map visualizations. Our method consistently reconstructs reflections while other methods either produce 'faked' reflections, resulting in incorrect normals, or fail to model reflections entirely." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mono}}" + }, + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "text", + "content": ", we choose a value of 1 in the first 4K iterations, and reduce to 0 thereafter to cease its effect, as described earlier. We find that our method is robust to the value of " + }, + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{mono}}" + }, + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "text", + "content": " as it only serves as initialization. We also assign " + }, + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{norm}} = 10^{-3}" + }, + { + "bbox": [ + 46, + 491, + 290, + 577 + ], + "type": "text", + "content": ", which is slightly higher than the weight in Ref-NeRF [47], as we find that this produces slightly smoother normals without substantially compromising the rendering quality." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 586, + 128, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 128, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 128, + 600 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Implementation. To model room-scale scenes, we employ a network architecture similar to the \"nerfacto\" model presented in Nerfstudio [44]. We use two small density networks as proposal networks, supervised via " + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{prop}}" + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": ". We sample 256 and 96 points for each proposal network, and 48 points for the final NeRF model. These three networks all use hash-based positional encodings. When querying the hash features in the final NeRF model, we incorporate the LOD-aware scheme proposed in VR-NeRF [53]. We train our model" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 491, + 547, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 547, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 547, + 552 + ], + "type": "text", + "content": "for 100,000 iterations and randomly sample 12,800 rays in each iteration. This process takes around 8 GB of GPU memory and approximately 3.5 hours to train a model using an NVIDIA A100 GPU. Further details regarding the model's structure can be found in the supplementary materials." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "content": "Datasets. We evaluate our method on several datasets with a focus on indoor scenes characterized by near-field lighting conditions. First, we evaluate on the Eyeful Tower dataset [53], which provides high-quality HDR captures of 11 indoor scenes. Each scene is coupled with calibrated camera parameters and a mesh reconstructed via Agisoft Metashape [1]. We select 9 scenes that feature notable reflective properties. We downsample the images of each scene to a resolution of " + }, + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "inline_equation", + "content": "854 \\times 1280" + }, + { + "bbox": [ + 304, + 557, + 548, + 715 + ], + "type": "text", + "content": " pixels. We curated around 50-70 views per scene that contain glossy surfaces for evaluation, leaving the remaining views for training. We also evaluate our approach on public indoor datasets NISR [50] and Inria [38] (NISR+Inria). Moreover, to assess the performance under" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21193" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 72, + 545, + 270 + ], + "blocks": [ + { + "bbox": [ + 49, + 72, + 545, + 270 + ], + "lines": [ + { + "bbox": [ + 49, + 72, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 49, + 72, + 545, + 270 + ], + "type": "image", + "image_path": "191aa998a13f1e839c5084aa64f6ce4f3b1e106d14f26bed69b9682eb61d08db.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 270, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 547, + 293 + ], + "type": "text", + "content": "Figure 7. Intermediate components of our approach compared to Ref-NeRF [47]. Our approach produces a more meaningful decomposition under room-scale lighting settings." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 288, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 288, + 337 + ], + "type": "text", + "content": "far-field lighting, we evaluate the real shiny dataset in Ref-NeRF [47]. We report the average PSNR, SSIM, and LPIPS [64] metrics for evaluating rendering quality." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 346, + 132, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 132, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 132, + 358 + ], + "type": "text", + "content": "5.1. Comparisons" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 365, + 288, + 580 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 288, + 580 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 288, + 580 + ], + "type": "text", + "content": "We compare our method with several baselines: NeRF [34], Ref-NeRF [47], and MS-NeRF [57], which specializes in mirror-like reflections by decomposing NeRF into multiple spaces. For a fair comparison, we re-implement these baselines, such that we share the same NeRF backbone and rendering configurations, with the only difference being the way different methods decompose and parameterize the output color. We report the numerical results across three datasets in Table 1. Our method demonstrates superior performance on the Eyeful Tower dataset, indicating the effectiveness of our method. On the NISR+Inria datasets, our method marginally outperforms the baselines, likely due to the dataset containing few reflection surfaces. Notably, while our method is tailored for near-field lighting conditions, it also shows promising results on the Shiny dataset, which comprises far-field lighting scenarios. This is because our Gaussian directional encoding can simulate a spatially invariant encoding by positioning Gaussians at a significant distance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 287, + 689 + ], + "type": "text", + "content": "Qualitative results on the Eyeful Tower and NISR+Inria datasets are provided in Figure 6. We can see that while other baselines occasionally synthesize plausible reflections, they resort to approximations that fake the reflections by placing emitters underneath the surface. As a result, they either produce incorrect geometry, or fail to model the reflections. Our method, in contrast, successfully models specular highlights on the surface. We provide additional video results in the supplementary material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 713 + ], + "type": "text", + "content": "We also visualize and compare the decomposition produced by our method and Ref-NeRF in Figure 7. We can see" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 305, + 297, + 547, + 385 + ], + "blocks": [ + { + "bbox": [ + 305, + 297, + 547, + 385 + ], + "lines": [ + { + "bbox": [ + 305, + 297, + 547, + 385 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 547, + 385 + ], + "type": "image", + "image_path": "c496a1f8ae23690a55311735cbad98741f8113fdc5b5fe5d12f92891dfbd496d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 388, + 545, + 421 + ], + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 421 + ], + "type": "text", + "content": "Figure 8. We evaluate the novel-view synthesis quality with respect to the number of Gaussians across five scenes. The green dashed line is the setting we use in our experiments." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 431, + 547, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 431, + 547, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 547, + 479 + ], + "type": "text", + "content": "that Ref-NeRF fails to obtain a meaningful decomposition under near-field lighting, and produces holes in the geometry, whereas our method consistently achieves a realistic separation of specular and diffuse components." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 487, + 406, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 406, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 406, + 498 + ], + "type": "text", + "content": "5.2. Ablation Studies" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 506, + 547, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 673 + ], + "type": "text", + "content": "Number of Gaussians. One important hyperparameter in the Gaussian directional encoding is the number of Gaussians, as it directly influences the model's capacity to represent specular colors. We conduct experiments to evaluate the impact of varying the number of Gaussians on five scenes from the Eyeful Tower dataset, and show the relationship between the number of Gaussians and the rendering quality in Figure 8. The rendering quality improves when using more Gaussians, but the improvement saturates as the number increases beyond 400. Note that using a larger number of Gaussians also entails greater computation costs and GPU memory requirements for every rendered pixel. Therefore, we use 256 Gaussians for all experiments, to strike a balance between rendering quality and computational efficiency." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "Optimizing Gaussians. To optimize the Gaussian directional encoding effectively, we first initialize them by training an incident light field, and then jointly finetune the Gaus" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21194" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 96, + 282, + 186 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "type": "text", + "content": "Table 2. Ablations of our method on the Eyeful Tower dataset [53]. The \"e.s.\" indicates early stopping the " + }, + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{mono}}" + }, + { + "bbox": [ + 47, + 71, + 287, + 93 + ], + "type": "text", + "content": " after 4K iterations." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 96, + 282, + 186 + ], + "lines": [ + { + "bbox": [ + 50, + 96, + 282, + 186 + ], + "spans": [ + { + "bbox": [ + 50, + 96, + 282, + 186 + ], + "type": "table", + "html": "
MethodGaussians Init.Mono. Opt.E. S. Prior\\( {\\mathcal{L}}_{\\text{mono }} \\)PSNR↑SSIM↑LPIPS↓
Full✓✓✓✓32.580.93280.1445
w/o init✘✓✓✓32.520.93040.1429
w/o opt.✓✘✓✓32.060.92650.1581
w/o \\( {\\mathcal{L}}_{\\text{mono }} \\)✓✓✘-32.310.92880.1503
w/o e.s.✓✓✓✘32.460.92920.1502
", + "image_path": "a069467b947f55e597579c3a74106d77518aca77f0fe32f3f0495164f451280b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 49, + 187, + 285, + 366 + ], + "blocks": [ + { + "bbox": [ + 49, + 187, + 285, + 366 + ], + "lines": [ + { + "bbox": [ + 49, + 187, + 285, + 366 + ], + "spans": [ + { + "bbox": [ + 49, + 187, + 285, + 366 + ], + "type": "image", + "image_path": "3d4ac95ee386b74c84014376c9e7da2e5a3f4c919155b041861f19d2bc92f820.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 368, + 287, + 413 + ], + "lines": [ + { + "bbox": [ + 46, + 368, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 287, + 413 + ], + "type": "text", + "content": "Figure 9. Example results under different Gaussian optimization settings. Without initializing the Gaussian parameters ('w/o init') or optimizing Gaussians jointly with the NeRF ('w/o opt.'), the Gaussian embedding struggles to model specularities accurately." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 419, + 289, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 289, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 289, + 575 + ], + "type": "text", + "content": "sian encoding together with the NeRF model. We demonstrate the significance of initialization ('w/o init') and fine-tuning ('w/o opt.') by omitting each process individually. We show quantitative results in Table 2 and a qualitative example in Figure 9. Without initialization, the model can still reconstruct reflections to some extent, resulting in a slightly better average LPIPS score, yet it fails to model some specular details, such as the light blobs. Neglecting the joint optimization of Gaussians leads to complete failure in modeling specular reflections. As illustrated in Figure 9, with the inaccurate specular modeling, the tints suppress the specular reflections, which ultimately leads to the inability to represent reflections in the final rendered image." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 586, + 198, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 198, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 198, + 598 + ], + "type": "text", + "content": "6. Discussion and Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Applications. Our primary goal was to improve the quality of novel-view synthesis with specular reflective surfaces. We achieve this via our proposed Gaussian directional encoding that enables a meaningful decomposition of specular and diffuse components in a scene. Moreover, this also enables applications other than novel-view synthesis, such as reflection removal, and surface roughness editing. For instance, Figure 7 shows that we can easily remove reflections using the diffuse component. Furthermore, Figure 10 demonstrates" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 69, + 547, + 195 + ], + "blocks": [ + { + "bbox": [ + 310, + 69, + 547, + 195 + ], + "lines": [ + { + "bbox": [ + 310, + 69, + 547, + 195 + ], + "spans": [ + { + "bbox": [ + 310, + 69, + 547, + 195 + ], + "type": "image", + "image_path": "c0149805caa2359d9f2f152c9704756e08c95f1fce0c7662b04bd3f7e73c35ba.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 198, + 545, + 220 + ], + "lines": [ + { + "bbox": [ + 305, + 198, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 198, + 545, + 220 + ], + "type": "text", + "content": "Figure 10. We can control the roughness of the scene by adding an offset to the input roughness." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 228, + 543, + 296 + ], + "blocks": [ + { + "bbox": [ + 306, + 228, + 543, + 296 + ], + "lines": [ + { + "bbox": [ + 306, + 228, + 543, + 296 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 543, + 296 + ], + "type": "image", + "image_path": "1614d5b18f25ef28f8660954b5ff6ce5c887d1154516b1345f58ef0a8289aa16.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 298, + 547, + 321 + ], + "lines": [ + { + "bbox": [ + 306, + 298, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 306, + 298, + 547, + 321 + ], + "type": "text", + "content": "Figure 11. Our method cannot reconstruct mirror-like perfect reflections due to the limited capacity of the 3D Gaussian encoding." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 366 + ], + "type": "text", + "content": "an example of editing roughness. By adding an offset to the predicted roughness during rendering, we can effectively manipulate the glossiness of the real surface." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 370, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 547, + 515 + ], + "type": "text", + "content": "Limitations. While our method improves on existing baselines, it has some limitations. As we parameterize the specular color via only several hundreds of Gaussians, the encoding is limited to relatively low frequency compared with perfect mirror-like reflections. We show such a failure case in Figure 11. We can see that our method is only able to learn a blurry version of the reflection. This could be alleviated by using many more Gaussians, as demonstrated in 3D Gaussian splatting [20]. However, the computational cost of traversing all Gaussians for every pixel quickly becomes prohibitive in our implementation. More efficient traversal, such as by rasterization, could be interesting future work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 518, + 548, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 548, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 548, + 662 + ], + "type": "text", + "content": "Conclusion. In this paper, we proposed a pipeline to improve the existing approach in modeling and reconstructing view-dependent effects in a NeRF representation. Central to our approach is a new Gaussian directional encoding to enhance the capability of neural radiance fields to model specular reflections under near-field lighting. We also utilize monocular normal supervision to help resolve shape-radiance ambiguity. Experiments have demonstrated the effectiveness of each of our contributions. We believe this work proposes a practical and effective solution for reconstructing NeRFs in room-scale scenes, specifically addressing the challenges of accurately capturing specular reflections." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgments. The authors from HKUST were partly supported by the Hong Kong Research Grants Council (RGC). We would like to thank Linning Xu and Zhao Dong for helpful discussions." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "21195" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 18, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 112 + ], + "type": "text", + "content": "[1] Agisoft LLC. 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In AAAI, 2024. 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21198" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/2d618972-8924-4059-ac0c-1df6a06ff55a_content_list.json b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/2d618972-8924-4059-ac0c-1df6a06ff55a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..30ac37e23ed47115d8fd5bce86e31aa0dbfa7805 --- /dev/null +++ b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/2d618972-8924-4059-ac0c-1df6a06ff55a_content_list.json @@ -0,0 +1,1902 @@ +[ + { + "type": "text", + "text": "Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation", + "text_level": 1, + "bbox": [ + 101, + 130, + 867, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dongliang Cao", + "bbox": [ + 88, + 179, + 218, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Marvin Eisenberger2", + "bbox": [ + 240, + 179, + 406, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nafie El Amrani", + "bbox": [ + 428, + 179, + 566, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Daniel Cremers", + "bbox": [ + 588, + 180, + 723, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Florian Bernard1", + "bbox": [ + 743, + 180, + 877, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 University of Bonn", + "bbox": [ + 248, + 204, + 415, + 223 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Technical University of Munich", + "bbox": [ + 454, + 204, + 720, + 223 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c37dddab6b9cdf987f809b30b70b3672d54c09143d25886fccb0d54911207ab5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 276, + 870, + 424 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/dcd5fc76dd4bb103422f6c9bb183dac5eec7c45450eb7cf334186fefaffda996.jpg", + "image_caption": [ + "Figure 1. Top: 3D shape interpolation. Compared to the SOTA shape interpolation method NeuroMorph [27], our method obtains more reliable interpolation even under large non-isometry. Bottom left: 3D shape matching. The point-wise correspondences found by the SOTA shape matching method URSSM [12] contains local mismatches. In contrast, our method enables smooth shape matching. Bottom right: 3D shape matching and interpolation. Our method is the first unsupervised method that obtains both accurate correspondences (shown as texture transfer) and realistic interpolation that capture both the pose-dominant and shape-dominant deformations." + ], + "image_footnote": [], + "bbox": [ + 84, + 426, + 480, + 585 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/171455d236821728eb21fb224abd5eda81170b93170004827727d6d87928fe06.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 490, + 426, + 887, + 589 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 672, + 313, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid", + "bbox": [ + 73, + 705, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches.", + "bbox": [ + 496, + 674, + 893, + 796 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 816, + 632, + 830 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Computing maps between 3D shapes is a fundamental problem in computer vision and computer graphics, since it opens the door to understanding different object categories and enables both shape analysis [50] and shape genera", + "bbox": [ + 496, + 840, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "3658", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tion [22]. One specific class of approaches builds shape relationships is statistical shape models (e.g. SMPL [51]). To do so, these methods require dense point-wise correspondences between large collections of 3D shapes. Even though shape matching has been studied extensively in the literature [75, 77], finding accurate point-wise correspondences between non-rigidly deformed 3D shapes remains challenging due to different discretisation, non-isometry and partiality. Once shapes are in correspondence, shape interpolation methods can be applied to increase the shape diversity for shape generation [27, 57] and for different applications (e.g. animation [42], interactive shape editing [39]).", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the interrelation between shape matching and interpolation, prior works mainly consider them as two separate problems. In the context of shape matching, the functional map framework [58] is one of the most dominant pipelines and has been extended by many follow-up works [19, 61, 63, 64]. However, functional map methods only map shapes in the spectral domain and thus lead to local unsmooth point-wise correspondences (see URSSM in Fig. 1 bottom left), which is undesirable for many downstream tasks (e.g. shape interpolation [23], or statistical shape analysis [45, 51]). Meanwhile, shape matching methods based on non-rigid registration (i.e. spatial maps) typically rely on time-consuming iterative optimisation schemes [40, 43] and careful initialisation [6, 54], and thus often achieve worse performance due to the optimisation complexity [17]. To overcome the above limitations, our method takes the best of both worlds by combining spectral and spatial maps. For shape interpolation, most works assume that the shapes are already in correspondence and aim to design more efficient and realistic deformation energies [9, 35, 81]. As a consequence, wrong correspondences often lead to undesirable interpolation trajectories. Only few approaches [24, 27] explicitly consider shape matching and interpolation together, but mostly under overly strict assumptions (e.g. volume preservation). Tab. 1 summarises the comparison between different learning-based shape matching approaches. Unlike prior methods, we propose the first unsupervised framework that harmonises spectral and spatial maps for both shape matching and interpolation. We summarise our main contributions as follows:", + "bbox": [ + 75, + 275, + 472, + 743 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- For the first time we fuse spectral and spatial maps to enable the joint unsupervised learning of both non-rigid 3D shape matching and interpolation.", + "- Our method predicts both pose-dominant and shape-dominant deformations, in contrast to prior interpolation methods that mainly focus on pose-dominant ones due to local deformation priors.", + "- We set the new state-of-the-art shape matching and interpolation performance on numerous challenging benchmarks, even compared to supervised methods." + ], + "bbox": [ + 76, + 746, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/92661f242dbab33c774d31d8f8dbccdbe0c84c72534c35780b98eb20e76c6cfd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsUnsup.SpectralSpatialInterp.
FMNet [48]X✓XX
3D-CODED [32]XX✓X
GeomFMaps [18]X✓XX
TransMatch [76]XX✓X
UnsupFMNet [33]✓✓XX
SURFMNet [68]✓✓XX
Deep Shells [26]✓✓✓X
CorrNet3D [82]✓X✓X
NeuroMorph [27]✓X✓✓
AttnFMaps [44]✓✓XX
URSSM [12]✓✓XX
Ours✓✓✓✓
", + "bbox": [ + 509, + 89, + 883, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Learning-based shape matching method comparison. Our method is the first unsupervised learning approach that operates in both spectral and spatial domains to enable accurate shape matching and realistic shape interpolation.", + "bbox": [ + 498, + 295, + 890, + 351 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 383, + 635, + 398 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Shape matching", + "text_level": 1, + "bbox": [ + 500, + 417, + 660, + 434 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Shape matching aims to find point-wise correspondences between shapes. Classical shape matching approaches [37, 65, 80] establish correspondences by explicitly considering geometric relations. Other methods [6, 24, 30, 40] solve the problem based on non-rigid shape registration. However, directly finding point-wise correspondences often leads to complex optimisation problems that typically require time-consuming iterative optimisation strategies and are thus only applicable for low-resolution shapes [65, 66, 80], which limits their applications in real-world settings.", + "bbox": [ + 496, + 452, + 890, + 603 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast, the functional map framework finds correspondences in the spectral domain [58], where the correspondence relationship can be encoded into a small matrix, namely the functional map. Due to its simple yet efficient formulation, the functional map framework has been extended by many follow-up works, e.g. improving the matching accuracy [29, 62], extending it to more challenging scenarios (e.g. non-isometry [25, 53, 61, 63], partiality [49, 64]). Together with the development of deep learning, many learning-based approaches are proposed [33, 48, 68] and lead to state-of-the-art performance [3, 10-12]. Nevertheless, the map in the spectral domain does not guarantee smooth point-wise correspondences. Therefore, the conversion of functional map into smooth and accurate point-wise correspondences is still an open-problem that is extensively studied [31, 56, 59, 78]. Unlike most functional map methods, our method harmonises the spectral and spatial maps together and thus leads to more accurate and smooth pointwise correspondences.", + "bbox": [ + 496, + 613, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "3659", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Shape interpolation", + "text_level": 1, + "bbox": [ + 76, + 90, + 266, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Shape interpolation is a well-studied problem in computer graphics that aims to continuously deform a source shape to a target shape. The most common strategy is to define an interpolation path in some higher dimensional space [9, 35, 36, 81]. To this end, various deformation measurements (e.g. as-rigid-as-possible (ARAP) [72], PriMo [8], etc.) are proposed to optimise the interpolation path so that the local distortion between any consecutive shapes is minimised. Another direction is to interpolate intrinsic quantities like dihedral angles before reconstructing the 3D shape [1, 4]. Other methods formulate shape interpolation as a time-dependent gradient flow [13, 21] by incorporating certain constraints (e.g. volume preservation [23, 24]). Nevertheless, most of them assume known correspondences between two shapes, which is unrealistic for real-world 3D shapes. The most relevant approach to our work is NeuroMorph [27], which is an unsupervised framework for both shape matching and interpolation. However, it has several limitations: In the context of shape matching, it is based on the geodesic distance preservation that is computationally expensive and only valid for near-isometric shape deformation. In the context of shape interpolation, it solely utilises the as-rigid-as-possible [72] to deform the source shape into the target shape, which can only model the low-frequency pose-dominant deformations (see Fig. 1 in [27]). In contrast, we utilise more efficient spectral regularisation and thus lead to more accurate shape matching even under large non-isometry. Furthermore, our method is able to capture both pose-dominant and shape-dominant deformations based on our novel test-time adaptation.", + "bbox": [ + 76, + 114, + 473, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Deep functional map in a nutshell", + "text_level": 1, + "bbox": [ + 76, + 585, + 385, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section we provide a summary of the popular deep functional map framework [68]. We consider a pair of 3D shapes $\\mathcal{X}$ and $\\mathcal{Y}$ represented as triangle meshes with $n_{\\mathcal{X}}$ and $n_{\\mathcal{Y}}$ (w.l.o.g. $n_{\\mathcal{X}} \\leq n_{\\mathcal{Y}}$ ) vertices, respectively. Here we summarise the main steps of its pipeline:", + "bbox": [ + 76, + 611, + 468, + 686 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Compute the Laplacian matrices $\\mathbf{L}_{\\mathcal{X}},\\mathbf{L}_{\\mathcal{Y}}$ [60] and the corresponding first $k$ eigenfunctions $\\Phi_{\\mathcal{X}},\\Phi_{\\mathcal{Y}}$ and eigenvalues $\\Lambda_{\\mathcal{X}},\\Lambda_{\\mathcal{Y}}$ in matrix notation, respectively.", + "2. Compute feature vectors $\\mathbf{F}_{\\mathcal{X}},\\mathbf{F}_{\\mathcal{Y}}$ defined on each shape via a learnable feature extractor $\\mathcal{F}_{\\theta}$", + "3. Compute the functional maps $\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}},\\mathbf{C}_{\\mathcal{Y}\\mathcal{X}}$ associated with the Laplacian eigenfunctions by solving the optimisation problem" + ], + "bbox": [ + 76, + 686, + 468, + 809 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {C} _ {\\mathcal {X Y}} = \\arg \\min _ {\\mathbf {C}} E _ {\\text {d a t a}} (\\mathbf {C}) + \\lambda E _ {\\text {r e g}} (\\mathbf {C}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 823, + 468, + 844 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, minimising $E_{\\mathrm{data}}(\\mathbf{C}) = \\left\\| \\mathbf{C}\\boldsymbol{\\Phi}_{\\mathcal{X}}^{\\dagger}\\mathbf{F}_{\\mathcal{X}} - \\boldsymbol{\\Phi}_{\\mathcal{Y}}^{\\dagger}\\mathbf{F}_{\\mathcal{Y}}\\right\\|_{F}^{2}$ enforces descriptor preservation, while minimising the", + "bbox": [ + 96, + 859, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "regularisation term $E_{\\mathrm{reg}}$ imposes certain structural properties (e.g. Laplacian commutativity [58]).", + "bbox": [ + 517, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. During training, structural regularisation (e.g. orthogonality, bijectivity [68]) is imposed on the functional maps, i.e.", + "bbox": [ + 500, + 121, + 890, + 167 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s t r u c t}} = \\lambda_ {\\mathrm {b i j}} L _ {\\mathrm {b i j}} + \\lambda_ {\\mathrm {o r t h}} L _ {\\mathrm {o r t h}}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 176, + 890, + 193 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "5. During inference, the point-wise map $\\Pi_{\\mathcal{Y}\\mathcal{X}}$ is obtained based on the map relationship $\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}} = \\Phi_{\\mathcal{Y}}^{\\dagger}\\Pi_{\\mathcal{Y}\\mathcal{X}}\\Phi_{\\mathcal{X}}$ , e.g. either by nearest neighbour search in the spectral domain or by other post-processing techniques [25, 31, 56, 78].", + "bbox": [ + 500, + 200, + 893, + 276 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Our method", + "text_level": 1, + "bbox": [ + 500, + 290, + 627, + 306 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The framework of our method is depicted in Fig. 2. Our method aims to predict both accurate point-wise correspondences and realistic shape interpolation paths in an unsupervised manner. Therefore, our framework can be divided into two sub-modules, namely the shape matching module (Sec. 4.1) and the shape interpolation module (Sec. 4.2). Our unsupervised loss and test-time adaptation are introduced in Sec. 4.3 and Sec. 4.4, respectively.", + "bbox": [ + 498, + 314, + 893, + 436 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Shape matching module", + "text_level": 1, + "bbox": [ + 500, + 444, + 723, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Point-wise map computation. Point-wise map computation aims to find dense correspondences between two shapes. In theory, the point-wise map $\\Pi_{\\mathcal{X}\\mathcal{Y}}$ should be a (partial) permutation matrix, i.e.", + "bbox": [ + 498, + 467, + 890, + 527 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{\\boldsymbol {\\Pi} \\in \\{0, 1 \\} ^ {n _ {\\mathcal {X}} \\times n _ {\\mathcal {Y}}}: \\boldsymbol {\\Pi} \\mathbf {1} _ {n _ {\\mathcal {Y}}} = \\mathbf {1} _ {n _ {\\mathcal {X}}}, \\mathbf {1} _ {n _ {\\mathcal {X}}} ^ {\\top} \\boldsymbol {\\Pi} \\leq \\mathbf {1} _ {n _ {\\mathcal {Y}}} ^ {\\top} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 535, + 890, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Pi (i,j)$ indicates whether the vertex $\\mathbf{X}^i$ in shape $\\mathcal{X}$ corresponds to the vertex $\\mathbf{Y}^j$ in shape $\\mathcal{V}$ . In our work the point-wise correspondences $\\Pi_{\\mathcal{XY}}$ between shapes $\\mathcal{X}$ and $\\mathcal{V}$ are obtained based on similarity measurement of the extracted features. To this end, the Siamese feature extractor $\\mathcal{F}_{\\theta}$ (i.e. DiffusionNet [71]) is used to extract features $\\mathbf{F}_{\\mathcal{X}},\\mathbf{F}_{\\mathcal{Y}}$ from input shapes, respectively. Following prior works [12, 27], we use the softmax operator to produce a soft correspondence matrix to make the computation differentiable, i.e. $\\Pi_{\\mathcal{XY}} = \\mathrm{Softmax}\\left(\\mathbf{F}_{\\mathcal{X}}\\mathbf{F}_{\\mathcal{Y}}^{T}\\right)$ . The softmax operator is applied in each row to ensure that elements are non-negative and $\\Pi_{\\mathcal{XY}}\\mathbf{1}_{n_{\\mathcal{Y}}} = \\mathbf{1}_{n_{\\mathcal{X}}}$ . In this way, $\\Pi_{\\mathcal{XY}}$ can be interpreted as a soft assignment of vertices $\\mathbf{Y}$ in shape $\\mathcal{V}$ to vertices $\\mathbf{X}$ in shape $\\mathcal{X}$ .", + "bbox": [ + 498, + 568, + 892, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Functional map computation. The goal of the functional map computation is to impose spectral regularisation on the obtained point-wise maps based on the coupling relationship $\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}} = \\boldsymbol{\\Phi}_{\\mathcal{Y}}^{\\dagger}\\boldsymbol{\\Pi}_{\\mathcal{Y}\\mathcal{X}}\\boldsymbol{\\Phi}_{\\mathcal{X}}$ . Therefore, the functional map computation is only used for training as part of the spectral loss computation. The computation pipeline of functional maps is explained in Sec. 3 and the details of the spectral loss can be found in Sec. 4.3.", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3660", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8e4fc02a41b45265c3544f980c7dfaf3062924addac75091d1623e55113edec1.jpg", + "image_caption": [ + "Figure 2. Method overview. First, the Siamese feature extractor $\\mathcal{F}_{\\theta}$ is used to extract features $\\mathbf{F}_{\\mathcal{X}}, \\mathbf{F}_{\\mathcal{Y}}$ from input shapes $\\mathcal{X}, \\mathcal{Y}$ , respectively. The extracted features are then used to compute both bidirectional functional maps $\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}}$ , $\\mathbf{C}_{\\mathcal{Y}\\mathcal{X}}$ and point-wise maps $\\Pi_{\\mathcal{X}\\mathcal{Y}}, \\Pi_{\\mathcal{Y}\\mathcal{X}}$ . Afterwards, the computed point-wise maps are used to bring the shape into correspondences. In the context of shape interpolation, a series of time steps $t$ is sampled and fed into the interpolator $\\Omega_{\\gamma}$ together with shape information to predict a series of interpolated shapes $X(t), Y(t)$ . During training the spectral loss $L_{\\mathrm{spectral}}$ is used to regularise the predicted functional maps and point maps, while the spatial loss $L_{\\mathrm{spatial}}$ is used to regularise the interpolation trajectories of both shapes." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 893, + 303 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Shape interpolation module", + "text_level": 1, + "bbox": [ + 76, + 428, + 326, + 444 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The goal of the shape interpolation module $\\Omega_{\\gamma}$ is to predict the deformation field $\\Delta(t) \\in \\mathbb{R}^{n \\times 3}$ , where $t \\in [0,1]$ , that continuously deforms the shape $\\mathcal{X}$ into the shape $\\mathcal{Y}$ , and vice versa. The deformation field of shape $\\mathcal{X}$ forms the interpolation trajectory", + "bbox": [ + 75, + 450, + 468, + 527 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} (t) = \\mathbf {X} + \\Delta_ {\\mathcal {X}} (t). \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 539, + 468, + 556 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The interpolation trajectory shifts shape $\\mathcal{X}$ from its original locations $\\mathbf{X}(0) = \\mathbf{X}$ into new locations $\\mathbf{X}(1)\\approx \\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y}$ , which are close to the corresponding vertices in shape $\\mathcal{V}$ . Following NeuroMorph [27], we use EdgeConv [79] blocks with residual connections [34] to build our interpolator $\\Omega_{\\gamma}$ . Similarly, the input feature of shape $\\mathcal{X}$ in the interpolator is the 7-dimensional feature vector $\\mathbf{Z}_{\\mathcal{X}}\\in \\mathbb{R}^{n_{\\mathcal{X}}\\times 7}$ that can be expressed in the form", + "bbox": [ + 75, + 566, + 468, + 688 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Z} _ {\\mathcal {X}} (t) = \\left(\\mathbf {X}, \\boldsymbol {\\Pi} _ {\\mathcal {X} \\mathcal {Y}} \\mathbf {Y} - \\mathbf {X}, t \\mathbf {1} _ {n _ {\\mathcal {X}}}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 700, + 468, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X}$ is the vertices of the shape $\\mathcal{X}$ , $\\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y} - \\mathbf{X}$ is the vertex offsets between shape $\\mathcal{X}$ and $\\mathcal{Y}$ , $t\\mathbf{1}_{n_{\\mathcal{X}}}$ is the sampled time that broadcasts to all vertices. The deformation fields are given by the output of the interpolator multiplied by time, i.e. $\\Delta_{\\mathcal{X}}(t) = t\\cdot \\Omega_{\\gamma}(\\mathbf{Z}_{\\mathcal{X}}(t))$ . To this end, the interpolator can immediately predict a trivial solution (i.e. linear interpolation) by setting $\\Omega_{\\gamma}(\\mathbf{Z}_{\\mathcal{X}}(t)) = \\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y} - \\mathbf{X}$ , since it satisfies the boundary conditions of the interpolation [27]:", + "bbox": [ + 75, + 728, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} (0) = \\mathbf {X} + 0 \\cdot \\left(\\Pi_ {\\mathcal {X Y}} \\mathbf {Y} - \\mathbf {X}\\right) = \\mathbf {X}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 861, + 468, + 877 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} (1) = \\mathbf {X} + 1 \\cdot \\left(\\Pi_ {\\mathcal {X Y}} \\mathbf {Y} - \\mathbf {X}\\right) = \\Pi_ {\\mathcal {X Y}} \\mathbf {Y}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 880, + 468, + 896 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the linear interpolation is a degenerate solution, since our goal is to obtain geometrically realistic shape interpolation. To prevent the interpolator prediction from falling into the trivial solution, spatial regularisation needs to be imposed, including a deformation energy [72] and additional regularisation, which will be introduced in Sec. 4.3.", + "bbox": [ + 500, + 428, + 890, + 518 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Unsupervised loss", + "text_level": 1, + "bbox": [ + 500, + 530, + 671, + 545 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section we introduce the spectral and spatial regularisation that enable unsupervised training of our method. Spectral regularisation. To obtain accurate point-wise correspondences for shape matching and shape interpolation, we utilise a spectral regularisation based on the functional map framework. Unlike prior works [15, 27] relying on geodesic distance preservation that is computationally expensive and only valid for near-isometric deformation [33], the spectral regularisation imposed on the functional maps is more efficient and works well also for non-isometric deformations [12, 20, 44]. Unlike most previous deep functional map methods [18, 26, 68] relying on off-the-shelf post-processing techniques [25, 56] to obtain point-wise maps (see Sec. 3), we aim to directly obtain point-wise map based on deep feature similarity. To this end, we combine structural regularisation in Eq. (2) with the coupling loss [12, 63, 73] to build our spectral regularisation", + "bbox": [ + 496, + 551, + 890, + 811 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s p e c t r a l}} = \\lambda_ {\\text {s t r u c t}} L _ {\\text {s t r u c t}} + \\lambda_ {\\text {c o u p l e}} L _ {\\text {c o u p l e}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 823, + 890, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 500, + 852, + 544, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {c o u p l e}} = \\left\\| \\mathbf {C} _ {\\mathcal {X Y}} - \\boldsymbol {\\Phi} _ {\\mathcal {Y}} ^ {\\dagger} \\boldsymbol {\\Pi} _ {\\mathcal {Y X}} \\boldsymbol {\\Phi} _ {\\mathcal {X}} \\right\\| _ {F} ^ {2}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 875, + 890, + 905 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "3661", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spatial regularisation. Finding point-wise correspondences solely based on spectral regularisation leads to local mismatches, which is undesirable for many downstream tasks including shape interpolation. To compensate for this, one of our spatial regularisation terms aims to directly align two shapes in the spatial domain, i.e.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {a l i g n}} = \\left\\| \\mathbf {X} (1) - \\boldsymbol {\\Pi} _ {\\mathcal {X Y}} \\mathbf {Y} \\right\\| _ {F} ^ {2} + \\left\\| \\mathbf {Y} (1) - \\boldsymbol {\\Pi} _ {\\mathcal {Y X}} \\mathbf {X} \\right\\| _ {F} ^ {2}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 186, + 468, + 219 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As mentioned in Sec. 4.2, additional spatial regularisation for shape deformation is needed to avoid trivial degenerated solutions. To this end, similar to [27, 83], the ARAP deformation energy [72] is used to regularise the interpolation trajectory. ARAP is a low-frequency preserving deformation energy that encourages locally rigid transformations. During training, we sample $T + 1$ discrete timesteps uniformly $\\mathbf{X}_k \\coloneqq \\mathbf{X}(k / T)$ for $k \\in \\{0, \\dots, T\\}$ to compute the ARAP energy as", + "bbox": [ + 75, + 220, + 468, + 356 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} E _ {\\mathrm {a r a p}} \\left(\\mathbf {X} _ {k}, \\mathbf {X} _ {k + 1}\\right) = \\\\ \\min _ {\\mathbf {R} _ {i} \\in S O (3)} \\sum_ {i = 1} ^ {n _ {\\mathcal {X}}} \\sum_ {j \\in \\mathcal {N} _ {i}} \\left\\| \\mathbf {R} _ {i} \\mathbf {E} _ {k} ^ {i j} - \\mathbf {E} _ {k + 1} ^ {i j} \\right\\| _ {F} ^ {2}, \\tag {11} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 368, + 468, + 429 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{E}_k^{ij} = \\mathbf{X}_k^i -\\mathbf{X}_k^j\\in \\mathbb{R}^3$ is the triangle edge between mesh vertices $\\mathbf{X}_k^j$ and $\\mathbf{X}_k^i$ . The rotation matrices $\\mathbf{R}_i$ can be computed in closed form for an efficient deformation (see [72] for details). Finally, our ARAP regularisation term can be expressed in the form", + "bbox": [ + 75, + 438, + 468, + 517 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {a r a p}} = \\sum_ {k = 0} ^ {T - 1} E _ {\\text {a r a p}} \\left(\\mathbf {X} _ {k}, \\mathbf {X} _ {k + 1}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 525, + 468, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Analogously, the loss in Eq. (12) is also applied to the reverse sequence for shape $\\mathcal{V}$ . However, the ARAP deformation energy only enables low-frequency pose-dominant deformation. To capture the shape-dominant deformation, we propose a test-time adaptation described in Sec. 4.4. Apart from the ARAP regularisation, we propose two additional regularisation terms to encourage smooth and symmetric deformation trajectories from shape $\\mathcal{X}$ to shape $\\mathcal{Y}$ , and vice versa. The symmetry loss encourages symmetric deformation trajectories from both directions, i.e.", + "bbox": [ + 75, + 574, + 468, + 724 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\mathrm {s y m}} = \\sum_ {k = 1} ^ {T - 1} \\| \\mathbf {X} _ {k} - \\boldsymbol {\\Pi} _ {\\mathcal {X Y}} \\mathbf {Y} _ {T - k} \\| _ {F} ^ {2}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 732, + 468, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This loss is also applied with the roles of $\\mathbf{X}$ and $\\mathbf{Y}$ swapped. Since we would like to also model the shape-dominant deformation, we only want $\\mathbf{X}_k\\approx \\Pi_{\\mathcal{XY}}\\mathbf{Y}_{T - k}$ allowing for shape-based variations. To this end, we introduce a temporal shape variance loss defined as", + "bbox": [ + 75, + 781, + 468, + 856 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {v a r}} = \\sum_ {i = 1} ^ {n \\chi} \\operatorname {V a r} \\left(\\left\\| \\mathbf {X} _ {k} - \\Pi_ {\\mathcal {X Y}} \\mathbf {Y} _ {T - k} \\right\\| ^ {i}\\right), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 864, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\operatorname{Var}(\\mathbf{X}^i) = \\frac{1}{T - 1}\\sum_{k = 1}^{T}(\\mathbf{X}_k^i -\\bar{\\mathbf{X}}^i)^2$ is the alignment error variance of the $i$ -th vertex during the interpolation sequence and $\\bar{\\mathbf{X}}^i = \\frac{1}{T}\\sum_{k = 1}^{T}\\mathbf{X}_k^i$ is the mean. In this manner, we assume that shape variations are nearly constant throughout the interpolation sequence. Similar to Eq. (13), the loss is also applied for the reverse direction $\\mathbf{Y}$ . The spatial loss is the linear combination of the above losses, i.e.", + "bbox": [ + 496, + 88, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {s p a t i a l}} = \\lambda_ {\\text {a l i g n}} L _ {\\text {a l i g n}} + \\lambda_ {\\text {a r a p}} L _ {\\text {a r a p}} + \\lambda_ {\\text {s y m}} L _ {\\text {s y m}} + \\lambda_ {\\text {v a r}} L _ {\\text {v a r}}. \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 205, + 893, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The total loss is the sum of the spectral loss and spatial loss.", + "bbox": [ + 500, + 237, + 888, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.4. Test-time adaptation", + "text_level": 1, + "bbox": [ + 500, + 261, + 694, + 276 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The spatial loss defined in Eq. (15) encourages low-frequency pose-dominant deformations, while the shape-based deformations are not well-modelled. To this end, we propose a novel test-time adaptation to obtain more accurate correspondences and better capture the shape-dominant deformation. Specifically, we optimise for an additional shape-dominant deformation field $\\Delta_s(t) \\in \\mathbb{R}^{n_x \\times 3}$ (with $t \\in [0,1]$ ) between $\\mathbf{X}(t)$ and $\\mathbf{Y}(1 - t)$ :", + "bbox": [ + 496, + 282, + 890, + 405 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Delta} _ {s} (t) = \\underset {\\boldsymbol {\\Delta}} {\\arg \\min } \\operatorname {C D} (\\mathbf {X} (t) + \\boldsymbol {\\Delta}, \\mathbf {Y} (1 - t)) + \\lambda_ {\\mathrm {D}} L _ {\\mathrm {D}} (\\boldsymbol {\\Delta}), \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 412, + 890, + 448 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we consider the standard Chamfer distance", + "bbox": [ + 500, + 449, + 828, + 462 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {C D} \\left(\\mathbf {S} _ {1}, \\mathbf {S} _ {2}\\right) = \\frac {1}{| \\mathbf {S} _ {1} |} \\sum_ {\\mathbf {x} \\in \\mathbf {S} _ {1}} \\min _ {\\mathbf {y} \\in \\mathbf {S} _ {2}} \\| \\mathbf {x} - \\mathbf {y} \\| _ {2} ^ {2} \\\\ + \\frac {1}{| \\mathbf {S} _ {2} |} \\sum_ {\\mathbf {y} \\in \\mathbf {S} _ {2}} \\min _ {\\mathbf {x} \\in \\mathbf {S} _ {1}} \\| \\mathbf {x} - \\mathbf {y} \\| _ {2} ^ {2}, \\tag {17} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 473, + 890, + 549 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and $L_{\\mathrm{D}}(\\cdot)$ is the Dirichlet energy [53] which promotes smooth deformations. The VectorAdam [47] optimiser is used to optimise the additional shape-based deformation field. Once we obtain the optimal $\\Delta_s(t)$ , we use linear interpolation to obtain the shape-dominant deformation trajectory, i.e.", + "bbox": [ + 496, + 558, + 890, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} \\left(t, t _ {s}\\right) = \\left(1 - t _ {s}\\right) \\cdot \\left(\\mathbf {X} (t) + \\boldsymbol {\\Delta} _ {s} (t)\\right) + t _ {s} \\cdot \\mathbf {Y} (1 - t), \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 657, + 890, + 675 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $t_s \\in [0,1]$ is the sampled time for shape-dominant deformation. Fig. 3 demonstrates an example of our test-time adaptation for $t = \\{0,0.5,1\\}$ and $t_s = \\{0,0.5,1\\}$ .", + "bbox": [ + 496, + 684, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the optimisation of the shape-dominant deformation field $\\Delta_s(t)$ , we obtain the final point-wise correspondences based on the spatial map using", + "bbox": [ + 496, + 729, + 890, + 773 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\Pi} _ {\\mathcal {X Y}} = \\mathrm {N N} (\\mathbf {Y}, \\mathbf {X} (1, 1)), \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 784, + 890, + 800 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where NN denotes nearest neighbour search in $\\mathbf{Y}$ for each entry in $\\mathbf{X}(1,1)$ . Optimisation based on the Chamfer distance is highly non-convex and prone to local minima for non-rigid shape registration [32, 74, 82]. However, for the optimisation in Eq. (16), the two shapes are already in the same pose with only minor shape variations.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "3662", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7503fea7f300ce9717e3d51567d61b34a6afcef9fec64b39c6a6a0c9805f29fb.jpg", + "image_caption": [ + "Figure 3. Visualisation of our test-time adaptation. Starting from pose-dominant deformation based on ARAP, we obtain $\\mathbf{X}(t,t_s = 0)$ (i.e. the last row). Afterwards, we optimise the shape-dominant deformation field $\\Delta_{s}(t)$ for each sampled time point. Finally, the linear interpolation is performed to obtain the shape-dominant interpolation trajectories (shown by arrows)." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 467, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experimental results", + "text_level": 1, + "bbox": [ + 76, + 364, + 276, + 383 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section we demonstrate the advantages of our method in the context of 3D shape matching and interpolation.", + "bbox": [ + 75, + 392, + 470, + 422 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Shape matching", + "text_level": 1, + "bbox": [ + 76, + 435, + 238, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Near-isometric shape matching. We evaluate the matching accuracy of our method on three near-isometric benchmarks: FAUST [7], SCAPE [2] and SHREC'19 [55]. Instead of the original meshes, we consider the more challenging remeshed versions from [18, 61]. The FAUST dataset consists of 10 humans with 10 different poses each, where the training and testing split is 80/20. The SCAPE dataset contains 71 different poses of the same person, split into 51 and 20 shapes for training and testing. The SHREC'19 dataset is subject to particular challenges with significant variance in the mesh connectivity and shape geometry. It has a total of 430 pairs for evaluation.", + "bbox": [ + 75, + 460, + 468, + 641 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. The mean geodesic error [41] is used as evaluation metric. We compare our method with state-of-the-art axiomatic, supervised and unsupervised methods. The results are summarised in Tab. 2. Our method outperforms the previous state-of-the-art methods (see the PCK curves in Fig. 4). Meanwhile, our method achieves substantially better cross-dataset generalisation ability than existing learning-based methods.", + "bbox": [ + 75, + 642, + 468, + 762 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Non-isometric shape matching. Regarding non-isometric shape matching, we consider the SMAL dataset [84] and DT4D-H dataset [53]. The SMAL dataset contains 49 four-legged animal shapes of 8 species [28]. Following Donati et al. [20], we use the last 20 shapes for testing, resulting in a 29/20 split of the dataset. DT4D-H dataset is based on the large-scale animation dataset DeformingThings4D [46]. Nine classes of humanoid shapes are used for evaluation, resulting in 198/95 shapes for training/testing.", + "bbox": [ + 75, + 763, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/42a5e63bc5058f35e345238397e4d05f84b4d4fb0d4d1941f205e21b96e843a6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TrainFAUSTSCAPEFAUST + SCAPE
TestFAUSTSCAPESHREC'19
Axiomatic Methods
BCICP [61]6.111.0-
ZoomOut [56]6.17.5-
Smooth Shells [25]2.54.7-
DiscreteOp [63]5.613.1-
Supervised Methods
FMNet [48]11.017.0-
GeomFMaps [18]2.63.07.9
Unsupervised Methods
WSupFMNet [70]3.84.4-
Deep Shells [26]1.72.521.1
NeuroMorph [27]2.35.68.5
DUO-FMNet [20]2.52.66.4
AttnFMaps [44]1.92.25.8
URSSM [12]1.61.94.6
Ours1.41.83.2
", + "bbox": [ + 522, + 88, + 870, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Near-isometric shape matching and cross-dataset generalisation on FAUST, SCAPE and SHREC'19. Our method outperforms prior axiomatic, supervised and unsupervised methods and demonstrates superior cross-dataset generalisation ability.", + "bbox": [ + 498, + 380, + 892, + 436 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/9d3f539bbc8b4cf9eafdcb9695bf23e6a90c1e69e9842fdbfbfc58d945f68c7f.jpg", + "image_caption": [ + "Figure 4. Near-isometric shape matching on FAUST, SCAPE. Proportion of correct keypoints (PCK) curves and corresponding area under curve (scores in the legend) of our method in comparison to existing state-of-the-art methods." + ], + "image_footnote": [], + "bbox": [ + 506, + 440, + 687, + 555 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/cec5060a24945139a5554dca7420cb64e30e75bc6eb815833832e7eb3e66a279.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 439, + 893, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. The results are summarised in Tab. 3. Our method substantially outperforms the previous state-of-the-art in the context of non-isometric shape matching, even compared to recent supervised methods. In Fig. 5, we summarise the PCK curves of our method compared to state-of-the-art methods on both non-isometric datasets. Fig. 6 provides qualitative results of our method compared to them.", + "bbox": [ + 496, + 641, + 893, + 750 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Shape interpolation", + "text_level": 1, + "bbox": [ + 500, + 756, + 687, + 772 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. Following NeuroMorph [27], we evaluate our method on the FAUST [7] and MANO [67] datasets. The MANO dataset contains synthetic hands in various poses with a train/test split of 100/20.", + "bbox": [ + 496, + 779, + 892, + 840 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Two metrics are applied to evaluate the performance of the shape interpolation. The first conformal distortion metric [38] measures how much individual triangles of a mesh distort throughout the interpolation se", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "3663", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8ee02e9672666be99ed1b08c6341f7ebae2633b36fa3b0875a51ebcc61b9785d.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Geo. error (×100)SMALDT4D-H
intra-classinter-class
Axiomatic Methods
ZoomOut [56]38.44.029.0
Smooth Shells [25]36.11.16.3
DiscreteOp [63]38.13.627.6
Supervised Methods
FMNet [48]42.09.638.0
GeomFMaps [18]8.42.14.1
Unsupervised Methods
WSupFMNet [70]7.63.322.6
Deep Shells [26]29.33.431.1
NeuroMorph [27]5.914.425.3
DUO-FMNet [20]6.72.615.8
AttnFMaps [44]5.41.711.6
URSSM [12]3.90.94.1
Ours1.90.93.3
", + "bbox": [ + 89, + 88, + 459, + 356 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Non-isometric matching on SMAL and DT4D-H. Our method substantially outperforms previous state-of-the-art methods even in comparison to supervised methods, especially for nonisometric shape matching (i.e. SMAL and DT4D-H inter-class).", + "bbox": [ + 76, + 366, + 470, + 422 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7e2b62efe9ce17b06a4eaf72fcad33e4d737905b92a4500ef8a4f94f29a41bb3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 81, + 430, + 267, + 546 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f38a5fb637490f0b3c5162b1129ca5cd07a03c189d06e5a17b74982f8d9056b4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 287, + 430, + 470, + 545 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5001a8e227f48ad85879cf129813a425fd0fc1eef5482b4140fc41ae0d9652f9.jpg", + "image_caption": [ + "Figure 5. Non-isometric matching on SMAL, DT4D-H inter-class datasets. Our method sets to new state of the art by a large margin based on the combination of spectral and spatial maps.", + "Figure 6. Non-isometric matching on SMAL and DT4D-H. Our method obtains more accurate matching results even in the presence of large non-isometric shape deformations." + ], + "image_footnote": [], + "bbox": [ + 91, + 609, + 460, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "quence, compared to the original shape. The second metric is the Chamfer distance between the target and the final deformed shapes. Besides NeuroMorph, we further evaluate our method against other two baselines (i.e. LIMP [15]", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and Hamiltonian [23]) that require ground-truth correspondences for interpolation. Fig. 7 summarises the performance of our method against other baselines. Our method achieves state-of-the-art performance on both datasets, even compared to methods relying on ground-truth correspondences. Fig. 8 shows the interpolation results of our method on the MANO dataset.", + "bbox": [ + 496, + 90, + 892, + 196 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/0e651eea8d2aa595bde3125445b42caca6b394adee98601ca4413df17d5037c2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 208, + 687, + 325 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c94e65cd9257a801dba64f9f515cae352ddd006b64fd58da7b3dbe7cc88c2c50.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 707, + 208, + 888, + 327 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/796da33d6dec908490a6858138084aa0090e0b8f2cb5a675c64971ecafce9640.jpg", + "image_caption": [ + "Figure 7. Interpolation on FAUST and MANO datasets. Our method achieves state-of-the-art performance on both datasets, even in comparison to methods that requires ground-truth correspondences (shown as dashed lines)." + ], + "image_footnote": [], + "bbox": [ + 504, + 330, + 687, + 449 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8149713b754a59e95d282fbfe667183fadf742b89fa62f8b57ecb4f774ef7b6b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 709, + 330, + 888, + 449 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/de77817329ac89ae9204fef3f7b319cd17fd0c1fd672c944f51d4edbfc34e53f.jpg", + "image_caption": [ + "Figure 8. Shape interpolation on MANO. Our method obtains a smooth interpolation trajectory between hands in different poses." + ], + "image_footnote": [], + "bbox": [ + 506, + 535, + 890, + 595 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Statistical shape analysis on medical data", + "text_level": 1, + "bbox": [ + 500, + 650, + 852, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To better demonstrate the potential of our method for real-world applications, we conduct statistical shape analysis using medical data. To this end, we use the real-world LUNA16 dataset [69] that contains chest CT scans with corresponding lung segmentation masks. Based on the provided segmentation masks, we reconstruct 3D lung shapes represented as triangle meshes using Marching Cubes [52]. In this way, we get a total of 22 shapes from manual selection. Starting from 22 shapes, our method obtains both accurate point-wise correspondences and smooth interpolation trajectories between them (see Fig. 9). Using our obtained correspondences, we build a statistical shape model (SSM) based on a point distribution model (PDM) [14]. The modes of variation of the SSM are summarised in Fig. 10. We evaluate the quality of the SSM w.r.t. the two standard", + "bbox": [ + 496, + 672, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "3664", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "metrics: generalisation and specificity [16] based on the Chamfer distance. We compare our method to the most recent method (i.e. S3M [5]). Tab. 4 summarises the results. Compared to S3M, our method obtains better generalisation and specificity.", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5f6fec154a563d99a646a4162e45dba24d1ffd4953ee428759f3b22b9d192fd1.jpg", + "image_caption": [ + "Figure 9. Matching and interpolation on LUNA16 dataset. Our method obtains accurate correspondences and realistic interpolations between each two lungs despite of large non-isometry." + ], + "image_footnote": [], + "bbox": [ + 91, + 178, + 145, + 231 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ba64a28eb9176b51d9ffe127839d380b49c54895cf489a4a6e795480103af38b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 153, + 179, + 207, + 227 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2709c8439ae32dbd497413033b155d4c1cbb6742f4ab5785cddc97d2e41b6c5e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 214, + 180, + 269, + 227 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/67a9fc6546a187b16c365ba667dbf49c8c64af5fa4c530039966622bcd84f3fb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 180, + 334, + 224 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/879d748c375f4421548b8c3b8e0454fb22ab4db7c13de39a13902d9e2b5543b3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 338, + 181, + 398, + 224 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1181880ca0b99e4b4f7ed392af720a3096eddb8593eb5e2aff552789c3e03b5c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 400, + 183, + 467, + 219 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/94a6ab7666a0e3d0c19230be7b91f92749a0c2604ee3a00d868c99d43b9a79a2.jpg", + "image_caption": [ + "Figure 10. Statistical shape analysis on LUNA16 dataset. The first row visualises the mean shape. While the second row and third row demonstrate the mean shape plus and minus $(\\times 2)$ the corresponding principal components, respectively." + ], + "image_footnote": [], + "bbox": [ + 98, + 309, + 444, + 479 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9660c4f9f434040a2d92b989a9cbe245da934780b946426f90da05b2d8cafb89.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Error [mm]Generalisation ↓Specificity ↓
S3M [5]2.926.23
Ours2.445.03
", + "bbox": [ + 114, + 566, + 431, + 623 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 678, + 223, + 695 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this section we conduct ablative experiments to analyse individual components of our approach. To this end, we consider only using the spectral loss $L_{\\mathrm{spectral}}$ in Eq. (8) for shape matching or use the feature similarity to obtain the final point-wise correspondences instead of test-time adaptation. For the experiment, we consider the challenging nonisometric SMAL and DT4D-H dataset.", + "bbox": [ + 75, + 704, + 467, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Results. Tab. 5 summarises the quantitative results. By comparing the first and the second rows, we can conclude that the spatial regularisation (i.e. $L_{\\mathrm{spatial}}$ in Eq. (15)) plays an important role in obtaining more accurate point-wise correspondences. By comparing the second and the third rows, we notice that the test-time adaptation can further boost the", + "bbox": [ + 75, + 810, + 467, + 898 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "matching performance. Together with both of them, our method achieves the most accurate shape matching results.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b53e76a5a1e2e0b1677e7d9a7f38c75bee578c0b6ab5ab91a2f9eca094ff3031.jpg", + "table_caption": [ + "Table 4. SSM evaluation. Our method substantially outperforms the state-of-the-art w.r.t. generalisation and specificity." + ], + "table_footnote": [], + "table_body": "
Geo. error (×100)SMALDT4D-H inter
Spectral only3.94.1
w.o. Test-time adaptation2.63.4
Ours1.93.3
", + "bbox": [ + 524, + 138, + 867, + 207 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Ablation study on the SMAL and DT4D-H datasets. The best result in each column is highlighted.", + "bbox": [ + 498, + 218, + 890, + 246 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Discussion and limitations", + "text_level": 1, + "bbox": [ + 500, + 272, + 743, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "For the first time we combine spectral and spatial maps to enable unsupervised learning for joint 3d shape matching and interpolation and thereby set the new state of the art in both tasks simultaneously. Yet, some limitations still give rise to future investigations. Compared to prior works [23, 24], our method captures pose and shape-dominant deformations without any prior knowledge. On the other hand, this separation between pose and shape is not always perfect: in practice, the interpolation module slightly alters the shape in some cases. In future work, we plan to investigate whether a clearer separation can be achieved by including additional assumptions about the input shape classes [83]. Another interesting direction is to integrate end-to-end statistical shape analysis into our framework for improved shape analysis and generation.", + "bbox": [ + 496, + 299, + 890, + 526 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "8. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 546, + 617, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work we propose the first unsupervised learning framework that harmonises spectral and spatial maps to enable joint 3D shape matching and interpolation. Our method allows to compute accurate shape correspondences and realistic interpolation trajectories between different 3D shapes without relying on any shape-specific prior knowledge. We experimentally demonstrate that our method sets the new state of the art in both shape matching and interpolation on numerous benchmarks. Moreover, we showcase the application of our method to real-world statistical shape models of medical data. Overall, we believe that our method will be a valuable contribution for bringing shape matching to practical applications in challenging real-world settings.", + "bbox": [ + 496, + 573, + 890, + 771 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "9. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 789, + 679, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 458610525, by the ERC Advanced Grant 'SIMULACRON' and by the Collaborative Research Center 'Discretization in Geometry and Dynamics' of the German Research Foundation.", + "bbox": [ + 496, + 816, + 890, + 886 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "3665", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Marc Alexa, Daniel Cohen-Or, and David Levin. Asrigid-as-possible shape interpolation. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, page 157-164, USA, 2000. 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In CVPR, 2017. 6" + ], + "bbox": [ + 503, + 92, + 890, + 431 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "3668", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/2d618972-8924-4059-ac0c-1df6a06ff55a_model.json b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/2d618972-8924-4059-ac0c-1df6a06ff55a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4451b55779f8a417f8d547d2c1609e5eb5b4fbf4 --- /dev/null +++ b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/2d618972-8924-4059-ac0c-1df6a06ff55a_model.json @@ -0,0 +1,2829 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.102, + 0.131, + 0.868, + 0.154 + ], + "angle": 0, + "content": "Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.18, + 0.22, + 0.201 + ], + "angle": 0, + "content": "Dongliang Cao" + }, + { + "type": "text", + "bbox": [ + 0.241, + 0.18, + 0.408, + 0.2 + ], + "angle": 0, + "content": "Marvin Eisenberger2" + }, + { + "type": "text", + "bbox": [ + 0.429, + 0.18, + 0.567, + 0.198 + ], + "angle": 0, + "content": "Nafie El Amrani" + }, + { + "type": "text", + "bbox": [ + 0.589, + 0.181, + 0.724, + 0.198 + ], + "angle": 0, + "content": "Daniel Cremers" + }, + { + "type": "text", + "bbox": [ + 0.744, + 0.181, + 0.879, + 0.198 + ], + "angle": 0, + "content": "Florian Bernard1" + }, + { + "type": "text", + "bbox": [ + 0.249, + 0.205, + 0.416, + 0.224 + ], + "angle": 0, + "content": "1 University of Bonn" + }, + { + "type": "text", + "bbox": [ + 0.455, + 0.205, + 0.721, + 0.224 + ], + "angle": 0, + "content": "\\(^{2}\\) Technical University of Munich" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.277, + 0.871, + 0.425 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.427, + 0.481, + 0.587 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.491, + 0.427, + 0.888, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.594, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Figure 1. Top: 3D shape interpolation. Compared to the SOTA shape interpolation method NeuroMorph [27], our method obtains more reliable interpolation even under large non-isometry. Bottom left: 3D shape matching. The point-wise correspondences found by the SOTA shape matching method URSSM [12] contains local mismatches. In contrast, our method enables smooth shape matching. Bottom right: 3D shape matching and interpolation. Our method is the first unsupervised method that obtains both accurate correspondences (shown as texture transfer) and realistic interpolation that capture both the pose-dominant and shape-dominant deformations." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.674, + 0.314, + 0.689 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.706, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.797 + ], + "angle": 0, + "content": "of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.817, + 0.633, + 0.832 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Computing maps between 3D shapes is a fundamental problem in computer vision and computer graphics, since it opens the door to understanding different object categories and enables both shape analysis [50] and shape genera" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3658" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "tion [22]. One specific class of approaches builds shape relationships is statistical shape models (e.g. SMPL [51]). To do so, these methods require dense point-wise correspondences between large collections of 3D shapes. Even though shape matching has been studied extensively in the literature [75, 77], finding accurate point-wise correspondences between non-rigidly deformed 3D shapes remains challenging due to different discretisation, non-isometry and partiality. Once shapes are in correspondence, shape interpolation methods can be applied to increase the shape diversity for shape generation [27, 57] and for different applications (e.g. animation [42], interactive shape editing [39])." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.276, + 0.473, + 0.744 + ], + "angle": 0, + "content": "Despite the interrelation between shape matching and interpolation, prior works mainly consider them as two separate problems. In the context of shape matching, the functional map framework [58] is one of the most dominant pipelines and has been extended by many follow-up works [19, 61, 63, 64]. However, functional map methods only map shapes in the spectral domain and thus lead to local unsmooth point-wise correspondences (see URSSM in Fig. 1 bottom left), which is undesirable for many downstream tasks (e.g. shape interpolation [23], or statistical shape analysis [45, 51]). Meanwhile, shape matching methods based on non-rigid registration (i.e. spatial maps) typically rely on time-consuming iterative optimisation schemes [40, 43] and careful initialisation [6, 54], and thus often achieve worse performance due to the optimisation complexity [17]. To overcome the above limitations, our method takes the best of both worlds by combining spectral and spatial maps. For shape interpolation, most works assume that the shapes are already in correspondence and aim to design more efficient and realistic deformation energies [9, 35, 81]. As a consequence, wrong correspondences often lead to undesirable interpolation trajectories. Only few approaches [24, 27] explicitly consider shape matching and interpolation together, but mostly under overly strict assumptions (e.g. volume preservation). Tab. 1 summarises the comparison between different learning-based shape matching approaches. Unlike prior methods, we propose the first unsupervised framework that harmonises spectral and spatial maps for both shape matching and interpolation. We summarise our main contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.747, + 0.47, + 0.793 + ], + "angle": 0, + "content": "- For the first time we fuse spectral and spatial maps to enable the joint unsupervised learning of both non-rigid 3D shape matching and interpolation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.794, + 0.47, + 0.853 + ], + "angle": 0, + "content": "- Our method predicts both pose-dominant and shape-dominant deformations, in contrast to prior interpolation methods that mainly focus on pose-dominant ones due to local deformation priors." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.853, + 0.47, + 0.899 + ], + "angle": 0, + "content": "- We set the new state-of-the-art shape matching and interpolation performance on numerous challenging benchmarks, even compared to supervised methods." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.747, + 0.47, + 0.899 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.511, + 0.09, + 0.885, + 0.287 + ], + "angle": 0, + "content": "
MethodsUnsup.SpectralSpatialInterp.
FMNet [48]X✓XX
3D-CODED [32]XX✓X
GeomFMaps [18]X✓XX
TransMatch [76]XX✓X
UnsupFMNet [33]✓✓XX
SURFMNet [68]✓✓XX
Deep Shells [26]✓✓✓X
CorrNet3D [82]✓X✓X
NeuroMorph [27]✓X✓✓
AttnFMaps [44]✓✓XX
URSSM [12]✓✓XX
Ours✓✓✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.296, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Table 1. Learning-based shape matching method comparison. Our method is the first unsupervised learning approach that operates in both spectral and spatial domains to enable accurate shape matching and realistic shape interpolation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.384, + 0.637, + 0.4 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.419, + 0.661, + 0.435 + ], + "angle": 0, + "content": "2.1. Shape matching" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.892, + 0.604 + ], + "angle": 0, + "content": "Shape matching aims to find point-wise correspondences between shapes. Classical shape matching approaches [37, 65, 80] establish correspondences by explicitly considering geometric relations. Other methods [6, 24, 30, 40] solve the problem based on non-rigid shape registration. However, directly finding point-wise correspondences often leads to complex optimisation problems that typically require time-consuming iterative optimisation strategies and are thus only applicable for low-resolution shapes [65, 66, 80], which limits their applications in real-world settings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.893, + 0.901 + ], + "angle": 0, + "content": "In contrast, the functional map framework finds correspondences in the spectral domain [58], where the correspondence relationship can be encoded into a small matrix, namely the functional map. Due to its simple yet efficient formulation, the functional map framework has been extended by many follow-up works, e.g. improving the matching accuracy [29, 62], extending it to more challenging scenarios (e.g. non-isometry [25, 53, 61, 63], partiality [49, 64]). Together with the development of deep learning, many learning-based approaches are proposed [33, 48, 68] and lead to state-of-the-art performance [3, 10-12]. Nevertheless, the map in the spectral domain does not guarantee smooth point-wise correspondences. Therefore, the conversion of functional map into smooth and accurate point-wise correspondences is still an open-problem that is extensively studied [31, 56, 59, 78]. Unlike most functional map methods, our method harmonises the spectral and spatial maps together and thus leads to more accurate and smooth pointwise correspondences." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3659" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.267, + 0.108 + ], + "angle": 0, + "content": "2.2. Shape interpolation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.115, + 0.474, + 0.569 + ], + "angle": 0, + "content": "Shape interpolation is a well-studied problem in computer graphics that aims to continuously deform a source shape to a target shape. The most common strategy is to define an interpolation path in some higher dimensional space [9, 35, 36, 81]. To this end, various deformation measurements (e.g. as-rigid-as-possible (ARAP) [72], PriMo [8], etc.) are proposed to optimise the interpolation path so that the local distortion between any consecutive shapes is minimised. Another direction is to interpolate intrinsic quantities like dihedral angles before reconstructing the 3D shape [1, 4]. Other methods formulate shape interpolation as a time-dependent gradient flow [13, 21] by incorporating certain constraints (e.g. volume preservation [23, 24]). Nevertheless, most of them assume known correspondences between two shapes, which is unrealistic for real-world 3D shapes. The most relevant approach to our work is NeuroMorph [27], which is an unsupervised framework for both shape matching and interpolation. However, it has several limitations: In the context of shape matching, it is based on the geodesic distance preservation that is computationally expensive and only valid for near-isometric shape deformation. In the context of shape interpolation, it solely utilises the as-rigid-as-possible [72] to deform the source shape into the target shape, which can only model the low-frequency pose-dominant deformations (see Fig. 1 in [27]). In contrast, we utilise more efficient spectral regularisation and thus lead to more accurate shape matching even under large non-isometry. Furthermore, our method is able to capture both pose-dominant and shape-dominant deformations based on our novel test-time adaptation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.586, + 0.387, + 0.604 + ], + "angle": 0, + "content": "3. Deep functional map in a nutshell" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.612, + 0.47, + 0.688 + ], + "angle": 0, + "content": "In this section we provide a summary of the popular deep functional map framework [68]. We consider a pair of 3D shapes \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) represented as triangle meshes with \\(n_{\\mathcal{X}}\\) and \\(n_{\\mathcal{Y}}\\) (w.l.o.g. \\(n_{\\mathcal{X}} \\leq n_{\\mathcal{Y}}\\)) vertices, respectively. Here we summarise the main steps of its pipeline:" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.688, + 0.47, + 0.734 + ], + "angle": 0, + "content": "1. Compute the Laplacian matrices \\(\\mathbf{L}_{\\mathcal{X}},\\mathbf{L}_{\\mathcal{Y}}\\) [60] and the corresponding first \\(k\\) eigenfunctions \\(\\Phi_{\\mathcal{X}},\\Phi_{\\mathcal{Y}}\\) and eigenvalues \\(\\Lambda_{\\mathcal{X}},\\Lambda_{\\mathcal{Y}}\\) in matrix notation, respectively." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.735, + 0.47, + 0.763 + ], + "angle": 0, + "content": "2. Compute feature vectors \\(\\mathbf{F}_{\\mathcal{X}},\\mathbf{F}_{\\mathcal{Y}}\\) defined on each shape via a learnable feature extractor \\(\\mathcal{F}_{\\theta}\\)" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.764, + 0.47, + 0.81 + ], + "angle": 0, + "content": "3. Compute the functional maps \\(\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}},\\mathbf{C}_{\\mathcal{Y}\\mathcal{X}}\\) associated with the Laplacian eigenfunctions by solving the optimisation problem" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.688, + 0.47, + 0.81 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.824, + 0.47, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathbf {C} _ {\\mathcal {X Y}} = \\arg \\min _ {\\mathbf {C}} E _ {\\text {d a t a}} (\\mathbf {C}) + \\lambda E _ {\\text {r e g}} (\\mathbf {C}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.86, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Here, minimising \\( E_{\\mathrm{data}}(\\mathbf{C}) = \\left\\| \\mathbf{C}\\boldsymbol{\\Phi}_{\\mathcal{X}}^{\\dagger}\\mathbf{F}_{\\mathcal{X}} - \\boldsymbol{\\Phi}_{\\mathcal{Y}}^{\\dagger}\\mathbf{F}_{\\mathcal{Y}}\\right\\|_{F}^{2} \\) enforces descriptor preservation, while minimising the" + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "regularisation term \\( E_{\\mathrm{reg}} \\) imposes certain structural properties (e.g. Laplacian commutativity [58])." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.122, + 0.892, + 0.168 + ], + "angle": 0, + "content": "4. During training, structural regularisation (e.g. orthogonality, bijectivity [68]) is imposed on the functional maps, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.178, + 0.892, + 0.194 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s t r u c t}} = \\lambda_ {\\mathrm {b i j}} L _ {\\mathrm {b i j}} + \\lambda_ {\\mathrm {o r t h}} L _ {\\mathrm {o r t h}}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.202, + 0.894, + 0.277 + ], + "angle": 0, + "content": "5. During inference, the point-wise map \\(\\Pi_{\\mathcal{Y}\\mathcal{X}}\\) is obtained based on the map relationship \\(\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}} = \\Phi_{\\mathcal{Y}}^{\\dagger}\\Pi_{\\mathcal{Y}\\mathcal{X}}\\Phi_{\\mathcal{X}}\\), e.g. either by nearest neighbour search in the spectral domain or by other post-processing techniques [25, 31, 56, 78]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.291, + 0.628, + 0.307 + ], + "angle": 0, + "content": "4. Our method" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.315, + 0.894, + 0.437 + ], + "angle": 0, + "content": "The framework of our method is depicted in Fig. 2. Our method aims to predict both accurate point-wise correspondences and realistic shape interpolation paths in an unsupervised manner. Therefore, our framework can be divided into two sub-modules, namely the shape matching module (Sec. 4.1) and the shape interpolation module (Sec. 4.2). Our unsupervised loss and test-time adaptation are introduced in Sec. 4.3 and Sec. 4.4, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.445, + 0.724, + 0.461 + ], + "angle": 0, + "content": "4.1. Shape matching module" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.468, + 0.892, + 0.529 + ], + "angle": 0, + "content": "Point-wise map computation. Point-wise map computation aims to find dense correspondences between two shapes. In theory, the point-wise map \\(\\Pi_{\\mathcal{X}\\mathcal{Y}}\\) should be a (partial) permutation matrix, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.536, + 0.892, + 0.569 + ], + "angle": 0, + "content": "\\[\n\\left\\{\\boldsymbol {\\Pi} \\in \\{0, 1 \\} ^ {n _ {\\mathcal {X}} \\times n _ {\\mathcal {Y}}}: \\boldsymbol {\\Pi} \\mathbf {1} _ {n _ {\\mathcal {Y}}} = \\mathbf {1} _ {n _ {\\mathcal {X}}}, \\mathbf {1} _ {n _ {\\mathcal {X}}} ^ {\\top} \\boldsymbol {\\Pi} \\leq \\mathbf {1} _ {n _ {\\mathcal {Y}}} ^ {\\top} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.569, + 0.893, + 0.78 + ], + "angle": 0, + "content": "where \\(\\Pi (i,j)\\) indicates whether the vertex \\(\\mathbf{X}^i\\) in shape \\(\\mathcal{X}\\) corresponds to the vertex \\(\\mathbf{Y}^j\\) in shape \\(\\mathcal{V}\\). In our work the point-wise correspondences \\(\\Pi_{\\mathcal{XY}}\\) between shapes \\(\\mathcal{X}\\) and \\(\\mathcal{V}\\) are obtained based on similarity measurement of the extracted features. To this end, the Siamese feature extractor \\(\\mathcal{F}_{\\theta}\\) (i.e. DiffusionNet [71]) is used to extract features \\(\\mathbf{F}_{\\mathcal{X}},\\mathbf{F}_{\\mathcal{Y}}\\) from input shapes, respectively. Following prior works [12, 27], we use the softmax operator to produce a soft correspondence matrix to make the computation differentiable, i.e. \\(\\Pi_{\\mathcal{XY}} = \\mathrm{Softmax}\\left(\\mathbf{F}_{\\mathcal{X}}\\mathbf{F}_{\\mathcal{Y}}^{T}\\right)\\). The softmax operator is applied in each row to ensure that elements are non-negative and \\(\\Pi_{\\mathcal{XY}}\\mathbf{1}_{n_{\\mathcal{Y}}} = \\mathbf{1}_{n_{\\mathcal{X}}}\\). In this way, \\(\\Pi_{\\mathcal{XY}}\\) can be interpreted as a soft assignment of vertices \\(\\mathbf{Y}\\) in shape \\(\\mathcal{V}\\) to vertices \\(\\mathbf{X}\\) in shape \\(\\mathcal{X}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Functional map computation. The goal of the functional map computation is to impose spectral regularisation on the obtained point-wise maps based on the coupling relationship \\(\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}} = \\boldsymbol{\\Phi}_{\\mathcal{Y}}^{\\dagger}\\boldsymbol{\\Pi}_{\\mathcal{Y}\\mathcal{X}}\\boldsymbol{\\Phi}_{\\mathcal{X}}\\). Therefore, the functional map computation is only used for training as part of the spectral loss computation. The computation pipeline of functional maps is explained in Sec. 3 and the details of the spectral loss can be found in Sec. 4.3." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3660" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.319, + 0.895, + 0.404 + ], + "angle": 0, + "content": "Figure 2. Method overview. First, the Siamese feature extractor \\(\\mathcal{F}_{\\theta}\\) is used to extract features \\(\\mathbf{F}_{\\mathcal{X}}, \\mathbf{F}_{\\mathcal{Y}}\\) from input shapes \\(\\mathcal{X}, \\mathcal{Y}\\), respectively. The extracted features are then used to compute both bidirectional functional maps \\(\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}}\\), \\(\\mathbf{C}_{\\mathcal{Y}\\mathcal{X}}\\) and point-wise maps \\(\\Pi_{\\mathcal{X}\\mathcal{Y}}, \\Pi_{\\mathcal{Y}\\mathcal{X}}\\). Afterwards, the computed point-wise maps are used to bring the shape into correspondences. In the context of shape interpolation, a series of time steps \\(t\\) is sampled and fed into the interpolator \\(\\Omega_{\\gamma}\\) together with shape information to predict a series of interpolated shapes \\(X(t), Y(t)\\). During training the spectral loss \\(L_{\\mathrm{spectral}}\\) is used to regularise the predicted functional maps and point maps, while the spatial loss \\(L_{\\mathrm{spatial}}\\) is used to regularise the interpolation trajectories of both shapes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.429, + 0.327, + 0.445 + ], + "angle": 0, + "content": "4.2. Shape interpolation module" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.452, + 0.47, + 0.528 + ], + "angle": 0, + "content": "The goal of the shape interpolation module \\(\\Omega_{\\gamma}\\) is to predict the deformation field \\(\\Delta(t) \\in \\mathbb{R}^{n \\times 3}\\), where \\(t \\in [0,1]\\), that continuously deforms the shape \\(\\mathcal{X}\\) into the shape \\(\\mathcal{Y}\\), and vice versa. The deformation field of shape \\(\\mathcal{X}\\) forms the interpolation trajectory" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.54, + 0.469, + 0.557 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} (t) = \\mathbf {X} + \\Delta_ {\\mathcal {X}} (t). \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.47, + 0.689 + ], + "angle": 0, + "content": "The interpolation trajectory shifts shape \\(\\mathcal{X}\\) from its original locations \\(\\mathbf{X}(0) = \\mathbf{X}\\) into new locations \\(\\mathbf{X}(1)\\approx \\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y}\\), which are close to the corresponding vertices in shape \\(\\mathcal{V}\\). Following NeuroMorph [27], we use EdgeConv [79] blocks with residual connections [34] to build our interpolator \\(\\Omega_{\\gamma}\\). Similarly, the input feature of shape \\(\\mathcal{X}\\) in the interpolator is the 7-dimensional feature vector \\(\\mathbf{Z}_{\\mathcal{X}}\\in \\mathbb{R}^{n_{\\mathcal{X}}\\times 7}\\) that can be expressed in the form" + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.701, + 0.469, + 0.718 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Z} _ {\\mathcal {X}} (t) = \\left(\\mathbf {X}, \\boldsymbol {\\Pi} _ {\\mathcal {X} \\mathcal {Y}} \\mathbf {Y} - \\mathbf {X}, t \\mathbf {1} _ {n _ {\\mathcal {X}}}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.851 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}\\) is the vertices of the shape \\(\\mathcal{X}\\), \\(\\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y} - \\mathbf{X}\\) is the vertex offsets between shape \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\), \\(t\\mathbf{1}_{n_{\\mathcal{X}}}\\) is the sampled time that broadcasts to all vertices. The deformation fields are given by the output of the interpolator multiplied by time, i.e. \\(\\Delta_{\\mathcal{X}}(t) = t\\cdot \\Omega_{\\gamma}(\\mathbf{Z}_{\\mathcal{X}}(t))\\). To this end, the interpolator can immediately predict a trivial solution (i.e. linear interpolation) by setting \\(\\Omega_{\\gamma}(\\mathbf{Z}_{\\mathcal{X}}(t)) = \\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y} - \\mathbf{X}\\), since it satisfies the boundary conditions of the interpolation [27]:" + }, + { + "type": "equation", + "bbox": [ + 0.128, + 0.862, + 0.469, + 0.878 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} (0) = \\mathbf {X} + 0 \\cdot \\left(\\Pi_ {\\mathcal {X Y}} \\mathbf {Y} - \\mathbf {X}\\right) = \\mathbf {X}, \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.881, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} (1) = \\mathbf {X} + 1 \\cdot \\left(\\Pi_ {\\mathcal {X Y}} \\mathbf {Y} - \\mathbf {X}\\right) = \\Pi_ {\\mathcal {X Y}} \\mathbf {Y}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.429, + 0.892, + 0.52 + ], + "angle": 0, + "content": "However, the linear interpolation is a degenerate solution, since our goal is to obtain geometrically realistic shape interpolation. To prevent the interpolator prediction from falling into the trivial solution, spatial regularisation needs to be imposed, including a deformation energy [72] and additional regularisation, which will be introduced in Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.673, + 0.546 + ], + "angle": 0, + "content": "4.3. Unsupervised loss" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.812 + ], + "angle": 0, + "content": "In this section we introduce the spectral and spatial regularisation that enable unsupervised training of our method. Spectral regularisation. To obtain accurate point-wise correspondences for shape matching and shape interpolation, we utilise a spectral regularisation based on the functional map framework. Unlike prior works [15, 27] relying on geodesic distance preservation that is computationally expensive and only valid for near-isometric deformation [33], the spectral regularisation imposed on the functional maps is more efficient and works well also for non-isometric deformations [12, 20, 44]. Unlike most previous deep functional map methods [18, 26, 68] relying on off-the-shelf post-processing techniques [25, 56] to obtain point-wise maps (see Sec. 3), we aim to directly obtain point-wise map based on deep feature similarity. To this end, we combine structural regularisation in Eq. (2) with the coupling loss [12, 63, 73] to build our spectral regularisation" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.824, + 0.891, + 0.841 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s p e c t r a l}} = \\lambda_ {\\text {s t r u c t}} L _ {\\text {s t r u c t}} + \\lambda_ {\\text {c o u p l e}} L _ {\\text {c o u p l e}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.853, + 0.545, + 0.865 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.875, + 0.891, + 0.906 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {c o u p l e}} = \\left\\| \\mathbf {C} _ {\\mathcal {X Y}} - \\boldsymbol {\\Phi} _ {\\mathcal {Y}} ^ {\\dagger} \\boldsymbol {\\Pi} _ {\\mathcal {Y X}} \\boldsymbol {\\Phi} _ {\\mathcal {X}} \\right\\| _ {F} ^ {2}. \\tag {9}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "3661" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "Spatial regularisation. Finding point-wise correspondences solely based on spectral regularisation leads to local mismatches, which is undesirable for many downstream tasks including shape interpolation. To compensate for this, one of our spatial regularisation terms aims to directly align two shapes in the spatial domain, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.188, + 0.469, + 0.22 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {a l i g n}} = \\left\\| \\mathbf {X} (1) - \\boldsymbol {\\Pi} _ {\\mathcal {X Y}} \\mathbf {Y} \\right\\| _ {F} ^ {2} + \\left\\| \\mathbf {Y} (1) - \\boldsymbol {\\Pi} _ {\\mathcal {Y X}} \\mathbf {X} \\right\\| _ {F} ^ {2}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.222, + 0.47, + 0.357 + ], + "angle": 0, + "content": "As mentioned in Sec. 4.2, additional spatial regularisation for shape deformation is needed to avoid trivial degenerated solutions. To this end, similar to [27, 83], the ARAP deformation energy [72] is used to regularise the interpolation trajectory. ARAP is a low-frequency preserving deformation energy that encourages locally rigid transformations. During training, we sample \\( T + 1 \\) discrete timesteps uniformly \\( \\mathbf{X}_k \\coloneqq \\mathbf{X}(k / T) \\) for \\( k \\in \\{0, \\dots, T\\} \\) to compute the ARAP energy as" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.369, + 0.469, + 0.43 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} E _ {\\mathrm {a r a p}} \\left(\\mathbf {X} _ {k}, \\mathbf {X} _ {k + 1}\\right) = \\\\ \\min _ {\\mathbf {R} _ {i} \\in S O (3)} \\sum_ {i = 1} ^ {n _ {\\mathcal {X}}} \\sum_ {j \\in \\mathcal {N} _ {i}} \\left\\| \\mathbf {R} _ {i} \\mathbf {E} _ {k} ^ {i j} - \\mathbf {E} _ {k + 1} ^ {i j} \\right\\| _ {F} ^ {2}, \\tag {11} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.469, + 0.518 + ], + "angle": 0, + "content": "where \\(\\mathbf{E}_k^{ij} = \\mathbf{X}_k^i -\\mathbf{X}_k^j\\in \\mathbb{R}^3\\) is the triangle edge between mesh vertices \\(\\mathbf{X}_k^j\\) and \\(\\mathbf{X}_k^i\\). The rotation matrices \\(\\mathbf{R}_i\\) can be computed in closed form for an efficient deformation (see [72] for details). Finally, our ARAP regularisation term can be expressed in the form" + }, + { + "type": "equation", + "bbox": [ + 0.165, + 0.526, + 0.469, + 0.567 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {a r a p}} = \\sum_ {k = 0} ^ {T - 1} E _ {\\text {a r a p}} \\left(\\mathbf {X} _ {k}, \\mathbf {X} _ {k + 1}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.575, + 0.469, + 0.726 + ], + "angle": 0, + "content": "Analogously, the loss in Eq. (12) is also applied to the reverse sequence for shape \\(\\mathcal{V}\\). However, the ARAP deformation energy only enables low-frequency pose-dominant deformation. To capture the shape-dominant deformation, we propose a test-time adaptation described in Sec. 4.4. Apart from the ARAP regularisation, we propose two additional regularisation terms to encourage smooth and symmetric deformation trajectories from shape \\(\\mathcal{X}\\) to shape \\(\\mathcal{Y}\\), and vice versa. The symmetry loss encourages symmetric deformation trajectories from both directions, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.733, + 0.469, + 0.775 + ], + "angle": 0, + "content": "\\[\nL _ {\\mathrm {s y m}} = \\sum_ {k = 1} ^ {T - 1} \\| \\mathbf {X} _ {k} - \\boldsymbol {\\Pi} _ {\\mathcal {X Y}} \\mathbf {Y} _ {T - k} \\| _ {F} ^ {2}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.469, + 0.857 + ], + "angle": 0, + "content": "This loss is also applied with the roles of \\(\\mathbf{X}\\) and \\(\\mathbf{Y}\\) swapped. Since we would like to also model the shape-dominant deformation, we only want \\(\\mathbf{X}_k\\approx \\Pi_{\\mathcal{XY}}\\mathbf{Y}_{T - k}\\) allowing for shape-based variations. To this end, we introduce a temporal shape variance loss defined as" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.865, + 0.469, + 0.904 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {v a r}} = \\sum_ {i = 1} ^ {n \\chi} \\operatorname {V a r} \\left(\\left\\| \\mathbf {X} _ {k} - \\Pi_ {\\mathcal {X Y}} \\mathbf {Y} _ {T - k} \\right\\| ^ {i}\\right), \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.089, + 0.892, + 0.197 + ], + "angle": 0, + "content": "where \\(\\operatorname{Var}(\\mathbf{X}^i) = \\frac{1}{T - 1}\\sum_{k = 1}^{T}(\\mathbf{X}_k^i -\\bar{\\mathbf{X}}^i)^2\\) is the alignment error variance of the \\(i\\)-th vertex during the interpolation sequence and \\(\\bar{\\mathbf{X}}^i = \\frac{1}{T}\\sum_{k = 1}^{T}\\mathbf{X}_k^i\\) is the mean. In this manner, we assume that shape variations are nearly constant throughout the interpolation sequence. Similar to Eq. (13), the loss is also applied for the reverse direction \\(\\mathbf{Y}\\). The spatial loss is the linear combination of the above losses, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.207, + 0.894, + 0.237 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {s p a t i a l}} = \\lambda_ {\\text {a l i g n}} L _ {\\text {a l i g n}} + \\lambda_ {\\text {a r a p}} L _ {\\text {a r a p}} + \\lambda_ {\\text {s y m}} L _ {\\text {s y m}} + \\lambda_ {\\text {v a r}} L _ {\\text {v a r}}. \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.238, + 0.89, + 0.253 + ], + "angle": 0, + "content": "The total loss is the sum of the spectral loss and spatial loss." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.262, + 0.695, + 0.277 + ], + "angle": 0, + "content": "4.4. Test-time adaptation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.284, + 0.892, + 0.406 + ], + "angle": 0, + "content": "The spatial loss defined in Eq. (15) encourages low-frequency pose-dominant deformations, while the shape-based deformations are not well-modelled. To this end, we propose a novel test-time adaptation to obtain more accurate correspondences and better capture the shape-dominant deformation. Specifically, we optimise for an additional shape-dominant deformation field \\(\\Delta_s(t) \\in \\mathbb{R}^{n_x \\times 3}\\) (with \\(t \\in [0,1]\\)) between \\(\\mathbf{X}(t)\\) and \\(\\mathbf{Y}(1 - t)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.414, + 0.891, + 0.449 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Delta} _ {s} (t) = \\underset {\\boldsymbol {\\Delta}} {\\arg \\min } \\operatorname {C D} (\\mathbf {X} (t) + \\boldsymbol {\\Delta}, \\mathbf {Y} (1 - t)) + \\lambda_ {\\mathrm {D}} L _ {\\mathrm {D}} (\\boldsymbol {\\Delta}), \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.45, + 0.829, + 0.463 + ], + "angle": 0, + "content": "where we consider the standard Chamfer distance" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.474, + 0.891, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {C D} \\left(\\mathbf {S} _ {1}, \\mathbf {S} _ {2}\\right) = \\frac {1}{| \\mathbf {S} _ {1} |} \\sum_ {\\mathbf {x} \\in \\mathbf {S} _ {1}} \\min _ {\\mathbf {y} \\in \\mathbf {S} _ {2}} \\| \\mathbf {x} - \\mathbf {y} \\| _ {2} ^ {2} \\\\ + \\frac {1}{| \\mathbf {S} _ {2} |} \\sum_ {\\mathbf {y} \\in \\mathbf {S} _ {2}} \\min _ {\\mathbf {x} \\in \\mathbf {S} _ {1}} \\| \\mathbf {x} - \\mathbf {y} \\| _ {2} ^ {2}, \\tag {17} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.559, + 0.892, + 0.65 + ], + "angle": 0, + "content": "and \\(L_{\\mathrm{D}}(\\cdot)\\) is the Dirichlet energy [53] which promotes smooth deformations. The VectorAdam [47] optimiser is used to optimise the additional shape-based deformation field. Once we obtain the optimal \\(\\Delta_s(t)\\), we use linear interpolation to obtain the shape-dominant deformation trajectory, i.e." + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.659, + 0.891, + 0.676 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} \\left(t, t _ {s}\\right) = \\left(1 - t _ {s}\\right) \\cdot \\left(\\mathbf {X} (t) + \\boldsymbol {\\Delta} _ {s} (t)\\right) + t _ {s} \\cdot \\mathbf {Y} (1 - t), \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.891, + 0.731 + ], + "angle": 0, + "content": "where \\( t_s \\in [0,1] \\) is the sampled time for shape-dominant deformation. Fig. 3 demonstrates an example of our test-time adaptation for \\( t = \\{0,0.5,1\\} \\) and \\( t_s = \\{0,0.5,1\\} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.891, + 0.775 + ], + "angle": 0, + "content": "After the optimisation of the shape-dominant deformation field \\(\\Delta_s(t)\\), we obtain the final point-wise correspondences based on the spatial map using" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.785, + 0.891, + 0.801 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\Pi} _ {\\mathcal {X Y}} = \\mathrm {N N} (\\mathbf {Y}, \\mathbf {X} (1, 1)), \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where NN denotes nearest neighbour search in \\(\\mathbf{Y}\\) for each entry in \\(\\mathbf{X}(1,1)\\). Optimisation based on the Chamfer distance is highly non-convex and prone to local minima for non-rigid shape registration [32, 74, 82]. However, for the optimisation in Eq. (16), the two shapes are already in the same pose with only minor shape variations." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3662" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.468, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.257, + 0.473, + 0.342 + ], + "angle": 0, + "content": "Figure 3. Visualisation of our test-time adaptation. Starting from pose-dominant deformation based on ARAP, we obtain \\(\\mathbf{X}(t,t_s = 0)\\) (i.e. the last row). Afterwards, we optimise the shape-dominant deformation field \\(\\Delta_{s}(t)\\) for each sampled time point. Finally, the linear interpolation is performed to obtain the shape-dominant interpolation trajectories (shown by arrows)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.366, + 0.277, + 0.384 + ], + "angle": 0, + "content": "5. Experimental results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.393, + 0.471, + 0.424 + ], + "angle": 0, + "content": "In this section we demonstrate the advantages of our method in the context of 3D shape matching and interpolation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.24, + 0.453 + ], + "angle": 0, + "content": "5.1. Shape matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.461, + 0.47, + 0.642 + ], + "angle": 0, + "content": "Near-isometric shape matching. We evaluate the matching accuracy of our method on three near-isometric benchmarks: FAUST [7], SCAPE [2] and SHREC'19 [55]. Instead of the original meshes, we consider the more challenging remeshed versions from [18, 61]. The FAUST dataset consists of 10 humans with 10 different poses each, where the training and testing split is 80/20. The SCAPE dataset contains 71 different poses of the same person, split into 51 and 20 shapes for training and testing. The SHREC'19 dataset is subject to particular challenges with significant variance in the mesh connectivity and shape geometry. It has a total of 430 pairs for evaluation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.763 + ], + "angle": 0, + "content": "Results. The mean geodesic error [41] is used as evaluation metric. We compare our method with state-of-the-art axiomatic, supervised and unsupervised methods. The results are summarised in Tab. 2. Our method outperforms the previous state-of-the-art methods (see the PCK curves in Fig. 4). Meanwhile, our method achieves substantially better cross-dataset generalisation ability than existing learning-based methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Non-isometric shape matching. Regarding non-isometric shape matching, we consider the SMAL dataset [84] and DT4D-H dataset [53]. The SMAL dataset contains 49 four-legged animal shapes of 8 species [28]. Following Donati et al. [20], we use the last 20 shapes for testing, resulting in a 29/20 split of the dataset. DT4D-H dataset is based on the large-scale animation dataset DeformingThings4D [46]. Nine classes of humanoid shapes are used for evaluation, resulting in 198/95 shapes for training/testing." + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.089, + 0.872, + 0.372 + ], + "angle": 0, + "content": "
TrainFAUSTSCAPEFAUST + SCAPE
TestFAUSTSCAPESHREC'19
Axiomatic Methods
BCICP [61]6.111.0-
ZoomOut [56]6.17.5-
Smooth Shells [25]2.54.7-
DiscreteOp [63]5.613.1-
Supervised Methods
FMNet [48]11.017.0-
GeomFMaps [18]2.63.07.9
Unsupervised Methods
WSupFMNet [70]3.84.4-
Deep Shells [26]1.72.521.1
NeuroMorph [27]2.35.68.5
DUO-FMNet [20]2.52.66.4
AttnFMaps [44]1.92.25.8
URSSM [12]1.61.94.6
Ours1.41.83.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.381, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Table 2. Near-isometric shape matching and cross-dataset generalisation on FAUST, SCAPE and SHREC'19. Our method outperforms prior axiomatic, supervised and unsupervised methods and demonstrates superior cross-dataset generalisation ability." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.441, + 0.688, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.44, + 0.895, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.572, + 0.893, + 0.627 + ], + "angle": 0, + "content": "Figure 4. Near-isometric shape matching on FAUST, SCAPE. Proportion of correct keypoints (PCK) curves and corresponding area under curve (scores in the legend) of our method in comparison to existing state-of-the-art methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.642, + 0.894, + 0.75 + ], + "angle": 0, + "content": "Results. The results are summarised in Tab. 3. Our method substantially outperforms the previous state-of-the-art in the context of non-isometric shape matching, even compared to recent supervised methods. In Fig. 5, we summarise the PCK curves of our method compared to state-of-the-art methods on both non-isometric datasets. Fig. 6 provides qualitative results of our method compared to them." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.688, + 0.773 + ], + "angle": 0, + "content": "5.2. Shape interpolation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.841 + ], + "angle": 0, + "content": "Datasets. Following NeuroMorph [27], we evaluate our method on the FAUST [7] and MANO [67] datasets. The MANO dataset contains synthetic hands in various poses with a train/test split of 100/20." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Results. Two metrics are applied to evaluate the performance of the shape interpolation. The first conformal distortion metric [38] measures how much individual triangles of a mesh distort throughout the interpolation se" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3663" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.09, + 0.089, + 0.46, + 0.357 + ], + "angle": 0, + "content": "
Geo. error (×100)SMALDT4D-H
intra-classinter-class
Axiomatic Methods
ZoomOut [56]38.44.029.0
Smooth Shells [25]36.11.16.3
DiscreteOp [63]38.13.627.6
Supervised Methods
FMNet [48]42.09.638.0
GeomFMaps [18]8.42.14.1
Unsupervised Methods
WSupFMNet [70]7.63.322.6
Deep Shells [26]29.33.431.1
NeuroMorph [27]5.914.425.3
DUO-FMNet [20]6.72.615.8
AttnFMaps [44]5.41.711.6
URSSM [12]3.90.94.1
Ours1.90.93.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.367, + 0.472, + 0.424 + ], + "angle": 0, + "content": "Table 3. Non-isometric matching on SMAL and DT4D-H. Our method substantially outperforms previous state-of-the-art methods even in comparison to supervised methods, especially for nonisometric shape matching (i.e. SMAL and DT4D-H inter-class)." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.431, + 0.268, + 0.547 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.289, + 0.431, + 0.472, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.562, + 0.47, + 0.605 + ], + "angle": 0, + "content": "Figure 5. Non-isometric matching on SMAL, DT4D-H inter-class datasets. Our method sets to new state of the art by a large margin based on the combination of spectral and spatial maps." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.61, + 0.462, + 0.771 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.782, + 0.471, + 0.825 + ], + "angle": 0, + "content": "Figure 6. Non-isometric matching on SMAL and DT4D-H. Our method obtains more accurate matching results even in the presence of large non-isometric shape deformations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "quence, compared to the original shape. The second metric is the Chamfer distance between the target and the final deformed shapes. Besides NeuroMorph, we further evaluate our method against other two baselines (i.e. LIMP [15]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.893, + 0.198 + ], + "angle": 0, + "content": "and Hamiltonian [23]) that require ground-truth correspondences for interpolation. Fig. 7 summarises the performance of our method against other baselines. Our method achieves state-of-the-art performance on both datasets, even compared to methods relying on ground-truth correspondences. Fig. 8 shows the interpolation results of our method on the MANO dataset." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.209, + 0.688, + 0.327 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.709, + 0.209, + 0.89, + 0.328 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.506, + 0.331, + 0.688, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.71, + 0.331, + 0.89, + 0.45 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.465, + 0.893, + 0.522 + ], + "angle": 0, + "content": "Figure 7. Interpolation on FAUST and MANO datasets. Our method achieves state-of-the-art performance on both datasets, even in comparison to methods that requires ground-truth correspondences (shown as dashed lines)." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.536, + 0.892, + 0.596 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.608, + 0.892, + 0.636 + ], + "angle": 0, + "content": "Figure 8. Shape interpolation on MANO. Our method obtains a smooth interpolation trajectory between hands in different poses." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.651, + 0.853, + 0.668 + ], + "angle": 0, + "content": "5.3. Statistical shape analysis on medical data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To better demonstrate the potential of our method for real-world applications, we conduct statistical shape analysis using medical data. To this end, we use the real-world LUNA16 dataset [69] that contains chest CT scans with corresponding lung segmentation masks. Based on the provided segmentation masks, we reconstruct 3D lung shapes represented as triangle meshes using Marching Cubes [52]. In this way, we get a total of 22 shapes from manual selection. Starting from 22 shapes, our method obtains both accurate point-wise correspondences and smooth interpolation trajectories between them (see Fig. 9). Using our obtained correspondences, we build a statistical shape model (SSM) based on a point distribution model (PDM) [14]. The modes of variation of the SSM are summarised in Fig. 10. We evaluate the quality of the SSM w.r.t. the two standard" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3664" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "metrics: generalisation and specificity [16] based on the Chamfer distance. We compare our method to the most recent method (i.e. S3M [5]). Tab. 4 summarises the results. Compared to S3M, our method obtains better generalisation and specificity." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.179, + 0.147, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.154, + 0.18, + 0.209, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.181, + 0.271, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.181, + 0.336, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.182, + 0.399, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.401, + 0.184, + 0.468, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.25, + 0.47, + 0.293 + ], + "angle": 0, + "content": "Figure 9. Matching and interpolation on LUNA16 dataset. Our method obtains accurate correspondences and realistic interpolations between each two lungs despite of large non-isometry." + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.31, + 0.446, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.493, + 0.47, + 0.549 + ], + "angle": 0, + "content": "Figure 10. Statistical shape analysis on LUNA16 dataset. The first row visualises the mean shape. While the second row and third row demonstrate the mean shape plus and minus \\((\\times 2)\\) the corresponding principal components, respectively." + }, + { + "type": "table", + "bbox": [ + 0.116, + 0.567, + 0.432, + 0.624 + ], + "angle": 0, + "content": "
Error [mm]Generalisation ↓Specificity ↓
S3M [5]2.926.23
Ours2.445.03
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.634, + 0.468, + 0.661 + ], + "angle": 0, + "content": "Table 4. SSM evaluation. Our method substantially outperforms the state-of-the-art w.r.t. generalisation and specificity." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.679, + 0.225, + 0.696 + ], + "angle": 0, + "content": "6. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.468, + 0.809 + ], + "angle": 0, + "content": "In this section we conduct ablative experiments to analyse individual components of our approach. To this end, we consider only using the spectral loss \\( L_{\\mathrm{spectral}} \\) in Eq. (8) for shape matching or use the feature similarity to obtain the final point-wise correspondences instead of test-time adaptation. For the experiment, we consider the challenging nonisometric SMAL and DT4D-H dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Results. Tab. 5 summarises the quantitative results. By comparing the first and the second rows, we can conclude that the spatial regularisation (i.e. \\(L_{\\mathrm{spatial}}\\) in Eq. (15)) plays an important role in obtaining more accurate point-wise correspondences. By comparing the second and the third rows, we notice that the test-time adaptation can further boost the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "matching performance. Together with both of them, our method achieves the most accurate shape matching results." + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.139, + 0.868, + 0.208 + ], + "angle": 0, + "content": "
Geo. error (×100)SMALDT4D-H inter
Spectral only3.94.1
w.o. Test-time adaptation2.63.4
Ours1.93.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.219, + 0.892, + 0.247 + ], + "angle": 0, + "content": "Table 5. Ablation study on the SMAL and DT4D-H datasets. The best result in each column is highlighted." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.273, + 0.744, + 0.289 + ], + "angle": 0, + "content": "7. Discussion and limitations" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.3, + 0.892, + 0.527 + ], + "angle": 0, + "content": "For the first time we combine spectral and spatial maps to enable unsupervised learning for joint 3d shape matching and interpolation and thereby set the new state of the art in both tasks simultaneously. Yet, some limitations still give rise to future investigations. Compared to prior works [23, 24], our method captures pose and shape-dominant deformations without any prior knowledge. On the other hand, this separation between pose and shape is not always perfect: in practice, the interpolation module slightly alters the shape in some cases. In future work, we plan to investigate whether a clearer separation can be achieved by including additional assumptions about the input shape classes [83]. Another interesting direction is to integrate end-to-end statistical shape analysis into our framework for improved shape analysis and generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.547, + 0.619, + 0.562 + ], + "angle": 0, + "content": "8. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.772 + ], + "angle": 0, + "content": "In this work we propose the first unsupervised learning framework that harmonises spectral and spatial maps to enable joint 3D shape matching and interpolation. Our method allows to compute accurate shape correspondences and realistic interpolation trajectories between different 3D shapes without relying on any shape-specific prior knowledge. We experimentally demonstrate that our method sets the new state of the art in both shape matching and interpolation on numerous benchmarks. Moreover, we showcase the application of our method to real-world statistical shape models of medical data. Overall, we believe that our method will be a valuable contribution for bringing shape matching to practical applications in challenging real-world settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.79, + 0.68, + 0.807 + ], + "angle": 0, + "content": "9. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.892, + 0.887 + ], + "angle": 0, + "content": "This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 458610525, by the ERC Advanced Grant 'SIMULACRON' and by the Collaborative Research Center 'Discretization in Geometry and Dynamics' of the German Research Foundation." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "3665" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Marc Alexa, Daniel Cohen-Or, and David Levin. Asrigid-as-possible shape interpolation. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, page 157-164, USA, 2000. 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Top: 3D shape interpolation. Compared to the SOTA shape interpolation method NeuroMorph [27], our method obtains more reliable interpolation even under large non-isometry. Bottom left: 3D shape matching. The point-wise correspondences found by the SOTA shape matching method URSSM [12] contains local mismatches. In contrast, our method enables smooth shape matching. Bottom right: 3D shape matching and interpolation. Our method is the first unsupervised method that obtains both accurate correspondences (shown as texture transfer) and realistic interpolation that capture both the pose-dominant and shape-dominant deformations. + +![](images/171455d236821728eb21fb224abd5eda81170b93170004827727d6d87928fe06.jpg) + +# Abstract + +Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid + +of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches. + +# 1. Introduction + +Computing maps between 3D shapes is a fundamental problem in computer vision and computer graphics, since it opens the door to understanding different object categories and enables both shape analysis [50] and shape genera + +tion [22]. One specific class of approaches builds shape relationships is statistical shape models (e.g. SMPL [51]). To do so, these methods require dense point-wise correspondences between large collections of 3D shapes. Even though shape matching has been studied extensively in the literature [75, 77], finding accurate point-wise correspondences between non-rigidly deformed 3D shapes remains challenging due to different discretisation, non-isometry and partiality. Once shapes are in correspondence, shape interpolation methods can be applied to increase the shape diversity for shape generation [27, 57] and for different applications (e.g. animation [42], interactive shape editing [39]). + +Despite the interrelation between shape matching and interpolation, prior works mainly consider them as two separate problems. In the context of shape matching, the functional map framework [58] is one of the most dominant pipelines and has been extended by many follow-up works [19, 61, 63, 64]. However, functional map methods only map shapes in the spectral domain and thus lead to local unsmooth point-wise correspondences (see URSSM in Fig. 1 bottom left), which is undesirable for many downstream tasks (e.g. shape interpolation [23], or statistical shape analysis [45, 51]). Meanwhile, shape matching methods based on non-rigid registration (i.e. spatial maps) typically rely on time-consuming iterative optimisation schemes [40, 43] and careful initialisation [6, 54], and thus often achieve worse performance due to the optimisation complexity [17]. To overcome the above limitations, our method takes the best of both worlds by combining spectral and spatial maps. For shape interpolation, most works assume that the shapes are already in correspondence and aim to design more efficient and realistic deformation energies [9, 35, 81]. As a consequence, wrong correspondences often lead to undesirable interpolation trajectories. Only few approaches [24, 27] explicitly consider shape matching and interpolation together, but mostly under overly strict assumptions (e.g. volume preservation). Tab. 1 summarises the comparison between different learning-based shape matching approaches. Unlike prior methods, we propose the first unsupervised framework that harmonises spectral and spatial maps for both shape matching and interpolation. We summarise our main contributions as follows: + +- For the first time we fuse spectral and spatial maps to enable the joint unsupervised learning of both non-rigid 3D shape matching and interpolation. +- Our method predicts both pose-dominant and shape-dominant deformations, in contrast to prior interpolation methods that mainly focus on pose-dominant ones due to local deformation priors. +- We set the new state-of-the-art shape matching and interpolation performance on numerous challenging benchmarks, even compared to supervised methods. + +
MethodsUnsup.SpectralSpatialInterp.
FMNet [48]X✓XX
3D-CODED [32]XX✓X
GeomFMaps [18]X✓XX
TransMatch [76]XX✓X
UnsupFMNet [33]✓✓XX
SURFMNet [68]✓✓XX
Deep Shells [26]✓✓✓X
CorrNet3D [82]✓X✓X
NeuroMorph [27]✓X✓✓
AttnFMaps [44]✓✓XX
URSSM [12]✓✓XX
Ours✓✓✓✓
+ +Table 1. Learning-based shape matching method comparison. Our method is the first unsupervised learning approach that operates in both spectral and spatial domains to enable accurate shape matching and realistic shape interpolation. + +# 2. Related work + +# 2.1. Shape matching + +Shape matching aims to find point-wise correspondences between shapes. Classical shape matching approaches [37, 65, 80] establish correspondences by explicitly considering geometric relations. Other methods [6, 24, 30, 40] solve the problem based on non-rigid shape registration. However, directly finding point-wise correspondences often leads to complex optimisation problems that typically require time-consuming iterative optimisation strategies and are thus only applicable for low-resolution shapes [65, 66, 80], which limits their applications in real-world settings. + +In contrast, the functional map framework finds correspondences in the spectral domain [58], where the correspondence relationship can be encoded into a small matrix, namely the functional map. Due to its simple yet efficient formulation, the functional map framework has been extended by many follow-up works, e.g. improving the matching accuracy [29, 62], extending it to more challenging scenarios (e.g. non-isometry [25, 53, 61, 63], partiality [49, 64]). Together with the development of deep learning, many learning-based approaches are proposed [33, 48, 68] and lead to state-of-the-art performance [3, 10-12]. Nevertheless, the map in the spectral domain does not guarantee smooth point-wise correspondences. Therefore, the conversion of functional map into smooth and accurate point-wise correspondences is still an open-problem that is extensively studied [31, 56, 59, 78]. Unlike most functional map methods, our method harmonises the spectral and spatial maps together and thus leads to more accurate and smooth pointwise correspondences. + +# 2.2. Shape interpolation + +Shape interpolation is a well-studied problem in computer graphics that aims to continuously deform a source shape to a target shape. The most common strategy is to define an interpolation path in some higher dimensional space [9, 35, 36, 81]. To this end, various deformation measurements (e.g. as-rigid-as-possible (ARAP) [72], PriMo [8], etc.) are proposed to optimise the interpolation path so that the local distortion between any consecutive shapes is minimised. Another direction is to interpolate intrinsic quantities like dihedral angles before reconstructing the 3D shape [1, 4]. Other methods formulate shape interpolation as a time-dependent gradient flow [13, 21] by incorporating certain constraints (e.g. volume preservation [23, 24]). Nevertheless, most of them assume known correspondences between two shapes, which is unrealistic for real-world 3D shapes. The most relevant approach to our work is NeuroMorph [27], which is an unsupervised framework for both shape matching and interpolation. However, it has several limitations: In the context of shape matching, it is based on the geodesic distance preservation that is computationally expensive and only valid for near-isometric shape deformation. In the context of shape interpolation, it solely utilises the as-rigid-as-possible [72] to deform the source shape into the target shape, which can only model the low-frequency pose-dominant deformations (see Fig. 1 in [27]). In contrast, we utilise more efficient spectral regularisation and thus lead to more accurate shape matching even under large non-isometry. Furthermore, our method is able to capture both pose-dominant and shape-dominant deformations based on our novel test-time adaptation. + +# 3. Deep functional map in a nutshell + +In this section we provide a summary of the popular deep functional map framework [68]. We consider a pair of 3D shapes $\mathcal{X}$ and $\mathcal{Y}$ represented as triangle meshes with $n_{\mathcal{X}}$ and $n_{\mathcal{Y}}$ (w.l.o.g. $n_{\mathcal{X}} \leq n_{\mathcal{Y}}$ ) vertices, respectively. Here we summarise the main steps of its pipeline: + +1. Compute the Laplacian matrices $\mathbf{L}_{\mathcal{X}},\mathbf{L}_{\mathcal{Y}}$ [60] and the corresponding first $k$ eigenfunctions $\Phi_{\mathcal{X}},\Phi_{\mathcal{Y}}$ and eigenvalues $\Lambda_{\mathcal{X}},\Lambda_{\mathcal{Y}}$ in matrix notation, respectively. +2. Compute feature vectors $\mathbf{F}_{\mathcal{X}},\mathbf{F}_{\mathcal{Y}}$ defined on each shape via a learnable feature extractor $\mathcal{F}_{\theta}$ +3. Compute the functional maps $\mathbf{C}_{\mathcal{X}\mathcal{Y}},\mathbf{C}_{\mathcal{Y}\mathcal{X}}$ associated with the Laplacian eigenfunctions by solving the optimisation problem + +$$ +\mathbf {C} _ {\mathcal {X Y}} = \arg \min _ {\mathbf {C}} E _ {\text {d a t a}} (\mathbf {C}) + \lambda E _ {\text {r e g}} (\mathbf {C}). \tag {1} +$$ + +Here, minimising $E_{\mathrm{data}}(\mathbf{C}) = \left\| \mathbf{C}\boldsymbol{\Phi}_{\mathcal{X}}^{\dagger}\mathbf{F}_{\mathcal{X}} - \boldsymbol{\Phi}_{\mathcal{Y}}^{\dagger}\mathbf{F}_{\mathcal{Y}}\right\|_{F}^{2}$ enforces descriptor preservation, while minimising the + +regularisation term $E_{\mathrm{reg}}$ imposes certain structural properties (e.g. Laplacian commutativity [58]). + +4. During training, structural regularisation (e.g. orthogonality, bijectivity [68]) is imposed on the functional maps, i.e. + +$$ +L _ {\text {s t r u c t}} = \lambda_ {\mathrm {b i j}} L _ {\mathrm {b i j}} + \lambda_ {\mathrm {o r t h}} L _ {\mathrm {o r t h}}. \tag {2} +$$ + +5. During inference, the point-wise map $\Pi_{\mathcal{Y}\mathcal{X}}$ is obtained based on the map relationship $\mathbf{C}_{\mathcal{X}\mathcal{Y}} = \Phi_{\mathcal{Y}}^{\dagger}\Pi_{\mathcal{Y}\mathcal{X}}\Phi_{\mathcal{X}}$ , e.g. either by nearest neighbour search in the spectral domain or by other post-processing techniques [25, 31, 56, 78]. + +# 4. Our method + +The framework of our method is depicted in Fig. 2. Our method aims to predict both accurate point-wise correspondences and realistic shape interpolation paths in an unsupervised manner. Therefore, our framework can be divided into two sub-modules, namely the shape matching module (Sec. 4.1) and the shape interpolation module (Sec. 4.2). Our unsupervised loss and test-time adaptation are introduced in Sec. 4.3 and Sec. 4.4, respectively. + +# 4.1. Shape matching module + +Point-wise map computation. Point-wise map computation aims to find dense correspondences between two shapes. In theory, the point-wise map $\Pi_{\mathcal{X}\mathcal{Y}}$ should be a (partial) permutation matrix, i.e. + +$$ +\left\{\boldsymbol {\Pi} \in \{0, 1 \} ^ {n _ {\mathcal {X}} \times n _ {\mathcal {Y}}}: \boldsymbol {\Pi} \mathbf {1} _ {n _ {\mathcal {Y}}} = \mathbf {1} _ {n _ {\mathcal {X}}}, \mathbf {1} _ {n _ {\mathcal {X}}} ^ {\top} \boldsymbol {\Pi} \leq \mathbf {1} _ {n _ {\mathcal {Y}}} ^ {\top} \right\}, \tag {3} +$$ + +where $\Pi (i,j)$ indicates whether the vertex $\mathbf{X}^i$ in shape $\mathcal{X}$ corresponds to the vertex $\mathbf{Y}^j$ in shape $\mathcal{V}$ . In our work the point-wise correspondences $\Pi_{\mathcal{XY}}$ between shapes $\mathcal{X}$ and $\mathcal{V}$ are obtained based on similarity measurement of the extracted features. To this end, the Siamese feature extractor $\mathcal{F}_{\theta}$ (i.e. DiffusionNet [71]) is used to extract features $\mathbf{F}_{\mathcal{X}},\mathbf{F}_{\mathcal{Y}}$ from input shapes, respectively. Following prior works [12, 27], we use the softmax operator to produce a soft correspondence matrix to make the computation differentiable, i.e. $\Pi_{\mathcal{XY}} = \mathrm{Softmax}\left(\mathbf{F}_{\mathcal{X}}\mathbf{F}_{\mathcal{Y}}^{T}\right)$ . The softmax operator is applied in each row to ensure that elements are non-negative and $\Pi_{\mathcal{XY}}\mathbf{1}_{n_{\mathcal{Y}}} = \mathbf{1}_{n_{\mathcal{X}}}$ . In this way, $\Pi_{\mathcal{XY}}$ can be interpreted as a soft assignment of vertices $\mathbf{Y}$ in shape $\mathcal{V}$ to vertices $\mathbf{X}$ in shape $\mathcal{X}$ . + +Functional map computation. The goal of the functional map computation is to impose spectral regularisation on the obtained point-wise maps based on the coupling relationship $\mathbf{C}_{\mathcal{X}\mathcal{Y}} = \boldsymbol{\Phi}_{\mathcal{Y}}^{\dagger}\boldsymbol{\Pi}_{\mathcal{Y}\mathcal{X}}\boldsymbol{\Phi}_{\mathcal{X}}$ . Therefore, the functional map computation is only used for training as part of the spectral loss computation. The computation pipeline of functional maps is explained in Sec. 3 and the details of the spectral loss can be found in Sec. 4.3. + +![](images/8e4fc02a41b45265c3544f980c7dfaf3062924addac75091d1623e55113edec1.jpg) +Figure 2. Method overview. First, the Siamese feature extractor $\mathcal{F}_{\theta}$ is used to extract features $\mathbf{F}_{\mathcal{X}}, \mathbf{F}_{\mathcal{Y}}$ from input shapes $\mathcal{X}, \mathcal{Y}$ , respectively. The extracted features are then used to compute both bidirectional functional maps $\mathbf{C}_{\mathcal{X}\mathcal{Y}}$ , $\mathbf{C}_{\mathcal{Y}\mathcal{X}}$ and point-wise maps $\Pi_{\mathcal{X}\mathcal{Y}}, \Pi_{\mathcal{Y}\mathcal{X}}$ . Afterwards, the computed point-wise maps are used to bring the shape into correspondences. In the context of shape interpolation, a series of time steps $t$ is sampled and fed into the interpolator $\Omega_{\gamma}$ together with shape information to predict a series of interpolated shapes $X(t), Y(t)$ . During training the spectral loss $L_{\mathrm{spectral}}$ is used to regularise the predicted functional maps and point maps, while the spatial loss $L_{\mathrm{spatial}}$ is used to regularise the interpolation trajectories of both shapes. + +# 4.2. Shape interpolation module + +The goal of the shape interpolation module $\Omega_{\gamma}$ is to predict the deformation field $\Delta(t) \in \mathbb{R}^{n \times 3}$ , where $t \in [0,1]$ , that continuously deforms the shape $\mathcal{X}$ into the shape $\mathcal{Y}$ , and vice versa. The deformation field of shape $\mathcal{X}$ forms the interpolation trajectory + +$$ +\mathbf {X} (t) = \mathbf {X} + \Delta_ {\mathcal {X}} (t). \tag {4} +$$ + +The interpolation trajectory shifts shape $\mathcal{X}$ from its original locations $\mathbf{X}(0) = \mathbf{X}$ into new locations $\mathbf{X}(1)\approx \Pi_{\mathcal{X}\mathcal{Y}}\mathbf{Y}$ , which are close to the corresponding vertices in shape $\mathcal{V}$ . Following NeuroMorph [27], we use EdgeConv [79] blocks with residual connections [34] to build our interpolator $\Omega_{\gamma}$ . Similarly, the input feature of shape $\mathcal{X}$ in the interpolator is the 7-dimensional feature vector $\mathbf{Z}_{\mathcal{X}}\in \mathbb{R}^{n_{\mathcal{X}}\times 7}$ that can be expressed in the form + +$$ +\mathbf {Z} _ {\mathcal {X}} (t) = \left(\mathbf {X}, \boldsymbol {\Pi} _ {\mathcal {X} \mathcal {Y}} \mathbf {Y} - \mathbf {X}, t \mathbf {1} _ {n _ {\mathcal {X}}}\right), \tag {5} +$$ + +where $\mathbf{X}$ is the vertices of the shape $\mathcal{X}$ , $\Pi_{\mathcal{X}\mathcal{Y}}\mathbf{Y} - \mathbf{X}$ is the vertex offsets between shape $\mathcal{X}$ and $\mathcal{Y}$ , $t\mathbf{1}_{n_{\mathcal{X}}}$ is the sampled time that broadcasts to all vertices. The deformation fields are given by the output of the interpolator multiplied by time, i.e. $\Delta_{\mathcal{X}}(t) = t\cdot \Omega_{\gamma}(\mathbf{Z}_{\mathcal{X}}(t))$ . To this end, the interpolator can immediately predict a trivial solution (i.e. linear interpolation) by setting $\Omega_{\gamma}(\mathbf{Z}_{\mathcal{X}}(t)) = \Pi_{\mathcal{X}\mathcal{Y}}\mathbf{Y} - \mathbf{X}$ , since it satisfies the boundary conditions of the interpolation [27]: + +$$ +\mathbf {X} (0) = \mathbf {X} + 0 \cdot \left(\Pi_ {\mathcal {X Y}} \mathbf {Y} - \mathbf {X}\right) = \mathbf {X}, \tag {6} +$$ + +$$ +\mathbf {X} (1) = \mathbf {X} + 1 \cdot \left(\Pi_ {\mathcal {X Y}} \mathbf {Y} - \mathbf {X}\right) = \Pi_ {\mathcal {X Y}} \mathbf {Y}. \tag {7} +$$ + +However, the linear interpolation is a degenerate solution, since our goal is to obtain geometrically realistic shape interpolation. To prevent the interpolator prediction from falling into the trivial solution, spatial regularisation needs to be imposed, including a deformation energy [72] and additional regularisation, which will be introduced in Sec. 4.3. + +# 4.3. Unsupervised loss + +In this section we introduce the spectral and spatial regularisation that enable unsupervised training of our method. Spectral regularisation. To obtain accurate point-wise correspondences for shape matching and shape interpolation, we utilise a spectral regularisation based on the functional map framework. Unlike prior works [15, 27] relying on geodesic distance preservation that is computationally expensive and only valid for near-isometric deformation [33], the spectral regularisation imposed on the functional maps is more efficient and works well also for non-isometric deformations [12, 20, 44]. Unlike most previous deep functional map methods [18, 26, 68] relying on off-the-shelf post-processing techniques [25, 56] to obtain point-wise maps (see Sec. 3), we aim to directly obtain point-wise map based on deep feature similarity. To this end, we combine structural regularisation in Eq. (2) with the coupling loss [12, 63, 73] to build our spectral regularisation + +$$ +L _ {\text {s p e c t r a l}} = \lambda_ {\text {s t r u c t}} L _ {\text {s t r u c t}} + \lambda_ {\text {c o u p l e}} L _ {\text {c o u p l e}}, \tag {8} +$$ + +where + +$$ +L _ {\text {c o u p l e}} = \left\| \mathbf {C} _ {\mathcal {X Y}} - \boldsymbol {\Phi} _ {\mathcal {Y}} ^ {\dagger} \boldsymbol {\Pi} _ {\mathcal {Y X}} \boldsymbol {\Phi} _ {\mathcal {X}} \right\| _ {F} ^ {2}. \tag {9} +$$ + +Spatial regularisation. Finding point-wise correspondences solely based on spectral regularisation leads to local mismatches, which is undesirable for many downstream tasks including shape interpolation. To compensate for this, one of our spatial regularisation terms aims to directly align two shapes in the spatial domain, i.e. + +$$ +L _ {\text {a l i g n}} = \left\| \mathbf {X} (1) - \boldsymbol {\Pi} _ {\mathcal {X Y}} \mathbf {Y} \right\| _ {F} ^ {2} + \left\| \mathbf {Y} (1) - \boldsymbol {\Pi} _ {\mathcal {Y X}} \mathbf {X} \right\| _ {F} ^ {2}. \tag {10} +$$ + +As mentioned in Sec. 4.2, additional spatial regularisation for shape deformation is needed to avoid trivial degenerated solutions. To this end, similar to [27, 83], the ARAP deformation energy [72] is used to regularise the interpolation trajectory. ARAP is a low-frequency preserving deformation energy that encourages locally rigid transformations. During training, we sample $T + 1$ discrete timesteps uniformly $\mathbf{X}_k \coloneqq \mathbf{X}(k / T)$ for $k \in \{0, \dots, T\}$ to compute the ARAP energy as + +$$ +\begin{array}{l} E _ {\mathrm {a r a p}} \left(\mathbf {X} _ {k}, \mathbf {X} _ {k + 1}\right) = \\ \min _ {\mathbf {R} _ {i} \in S O (3)} \sum_ {i = 1} ^ {n _ {\mathcal {X}}} \sum_ {j \in \mathcal {N} _ {i}} \left\| \mathbf {R} _ {i} \mathbf {E} _ {k} ^ {i j} - \mathbf {E} _ {k + 1} ^ {i j} \right\| _ {F} ^ {2}, \tag {11} \\ \end{array} +$$ + +where $\mathbf{E}_k^{ij} = \mathbf{X}_k^i -\mathbf{X}_k^j\in \mathbb{R}^3$ is the triangle edge between mesh vertices $\mathbf{X}_k^j$ and $\mathbf{X}_k^i$ . The rotation matrices $\mathbf{R}_i$ can be computed in closed form for an efficient deformation (see [72] for details). Finally, our ARAP regularisation term can be expressed in the form + +$$ +L _ {\text {a r a p}} = \sum_ {k = 0} ^ {T - 1} E _ {\text {a r a p}} \left(\mathbf {X} _ {k}, \mathbf {X} _ {k + 1}\right). \tag {12} +$$ + +Analogously, the loss in Eq. (12) is also applied to the reverse sequence for shape $\mathcal{V}$ . However, the ARAP deformation energy only enables low-frequency pose-dominant deformation. To capture the shape-dominant deformation, we propose a test-time adaptation described in Sec. 4.4. Apart from the ARAP regularisation, we propose two additional regularisation terms to encourage smooth and symmetric deformation trajectories from shape $\mathcal{X}$ to shape $\mathcal{Y}$ , and vice versa. The symmetry loss encourages symmetric deformation trajectories from both directions, i.e. + +$$ +L _ {\mathrm {s y m}} = \sum_ {k = 1} ^ {T - 1} \| \mathbf {X} _ {k} - \boldsymbol {\Pi} _ {\mathcal {X Y}} \mathbf {Y} _ {T - k} \| _ {F} ^ {2}. \tag {13} +$$ + +This loss is also applied with the roles of $\mathbf{X}$ and $\mathbf{Y}$ swapped. Since we would like to also model the shape-dominant deformation, we only want $\mathbf{X}_k\approx \Pi_{\mathcal{XY}}\mathbf{Y}_{T - k}$ allowing for shape-based variations. To this end, we introduce a temporal shape variance loss defined as + +$$ +L _ {\text {v a r}} = \sum_ {i = 1} ^ {n \chi} \operatorname {V a r} \left(\left\| \mathbf {X} _ {k} - \Pi_ {\mathcal {X Y}} \mathbf {Y} _ {T - k} \right\| ^ {i}\right), \tag {14} +$$ + +where $\operatorname{Var}(\mathbf{X}^i) = \frac{1}{T - 1}\sum_{k = 1}^{T}(\mathbf{X}_k^i -\bar{\mathbf{X}}^i)^2$ is the alignment error variance of the $i$ -th vertex during the interpolation sequence and $\bar{\mathbf{X}}^i = \frac{1}{T}\sum_{k = 1}^{T}\mathbf{X}_k^i$ is the mean. In this manner, we assume that shape variations are nearly constant throughout the interpolation sequence. Similar to Eq. (13), the loss is also applied for the reverse direction $\mathbf{Y}$ . The spatial loss is the linear combination of the above losses, i.e. + +$$ +L _ {\text {s p a t i a l}} = \lambda_ {\text {a l i g n}} L _ {\text {a l i g n}} + \lambda_ {\text {a r a p}} L _ {\text {a r a p}} + \lambda_ {\text {s y m}} L _ {\text {s y m}} + \lambda_ {\text {v a r}} L _ {\text {v a r}}. \tag {15} +$$ + +The total loss is the sum of the spectral loss and spatial loss. + +# 4.4. Test-time adaptation + +The spatial loss defined in Eq. (15) encourages low-frequency pose-dominant deformations, while the shape-based deformations are not well-modelled. To this end, we propose a novel test-time adaptation to obtain more accurate correspondences and better capture the shape-dominant deformation. Specifically, we optimise for an additional shape-dominant deformation field $\Delta_s(t) \in \mathbb{R}^{n_x \times 3}$ (with $t \in [0,1]$ ) between $\mathbf{X}(t)$ and $\mathbf{Y}(1 - t)$ : + +$$ +\boldsymbol {\Delta} _ {s} (t) = \underset {\boldsymbol {\Delta}} {\arg \min } \operatorname {C D} (\mathbf {X} (t) + \boldsymbol {\Delta}, \mathbf {Y} (1 - t)) + \lambda_ {\mathrm {D}} L _ {\mathrm {D}} (\boldsymbol {\Delta}), \tag {16} +$$ + +where we consider the standard Chamfer distance + +$$ +\begin{array}{l} \operatorname {C D} \left(\mathbf {S} _ {1}, \mathbf {S} _ {2}\right) = \frac {1}{| \mathbf {S} _ {1} |} \sum_ {\mathbf {x} \in \mathbf {S} _ {1}} \min _ {\mathbf {y} \in \mathbf {S} _ {2}} \| \mathbf {x} - \mathbf {y} \| _ {2} ^ {2} \\ + \frac {1}{| \mathbf {S} _ {2} |} \sum_ {\mathbf {y} \in \mathbf {S} _ {2}} \min _ {\mathbf {x} \in \mathbf {S} _ {1}} \| \mathbf {x} - \mathbf {y} \| _ {2} ^ {2}, \tag {17} \\ \end{array} +$$ + +and $L_{\mathrm{D}}(\cdot)$ is the Dirichlet energy [53] which promotes smooth deformations. The VectorAdam [47] optimiser is used to optimise the additional shape-based deformation field. Once we obtain the optimal $\Delta_s(t)$ , we use linear interpolation to obtain the shape-dominant deformation trajectory, i.e. + +$$ +\mathbf {X} \left(t, t _ {s}\right) = \left(1 - t _ {s}\right) \cdot \left(\mathbf {X} (t) + \boldsymbol {\Delta} _ {s} (t)\right) + t _ {s} \cdot \mathbf {Y} (1 - t), \tag {18} +$$ + +where $t_s \in [0,1]$ is the sampled time for shape-dominant deformation. Fig. 3 demonstrates an example of our test-time adaptation for $t = \{0,0.5,1\}$ and $t_s = \{0,0.5,1\}$ . + +After the optimisation of the shape-dominant deformation field $\Delta_s(t)$ , we obtain the final point-wise correspondences based on the spatial map using + +$$ +\boldsymbol {\Pi} _ {\mathcal {X Y}} = \mathrm {N N} (\mathbf {Y}, \mathbf {X} (1, 1)), \tag {19} +$$ + +where NN denotes nearest neighbour search in $\mathbf{Y}$ for each entry in $\mathbf{X}(1,1)$ . Optimisation based on the Chamfer distance is highly non-convex and prone to local minima for non-rigid shape registration [32, 74, 82]. However, for the optimisation in Eq. (16), the two shapes are already in the same pose with only minor shape variations. + +![](images/7503fea7f300ce9717e3d51567d61b34a6afcef9fec64b39c6a6a0c9805f29fb.jpg) +Figure 3. Visualisation of our test-time adaptation. Starting from pose-dominant deformation based on ARAP, we obtain $\mathbf{X}(t,t_s = 0)$ (i.e. the last row). Afterwards, we optimise the shape-dominant deformation field $\Delta_{s}(t)$ for each sampled time point. Finally, the linear interpolation is performed to obtain the shape-dominant interpolation trajectories (shown by arrows). + +# 5. Experimental results + +In this section we demonstrate the advantages of our method in the context of 3D shape matching and interpolation. + +# 5.1. Shape matching + +Near-isometric shape matching. We evaluate the matching accuracy of our method on three near-isometric benchmarks: FAUST [7], SCAPE [2] and SHREC'19 [55]. Instead of the original meshes, we consider the more challenging remeshed versions from [18, 61]. The FAUST dataset consists of 10 humans with 10 different poses each, where the training and testing split is 80/20. The SCAPE dataset contains 71 different poses of the same person, split into 51 and 20 shapes for training and testing. The SHREC'19 dataset is subject to particular challenges with significant variance in the mesh connectivity and shape geometry. It has a total of 430 pairs for evaluation. + +Results. The mean geodesic error [41] is used as evaluation metric. We compare our method with state-of-the-art axiomatic, supervised and unsupervised methods. The results are summarised in Tab. 2. Our method outperforms the previous state-of-the-art methods (see the PCK curves in Fig. 4). Meanwhile, our method achieves substantially better cross-dataset generalisation ability than existing learning-based methods. + +Non-isometric shape matching. Regarding non-isometric shape matching, we consider the SMAL dataset [84] and DT4D-H dataset [53]. The SMAL dataset contains 49 four-legged animal shapes of 8 species [28]. Following Donati et al. [20], we use the last 20 shapes for testing, resulting in a 29/20 split of the dataset. DT4D-H dataset is based on the large-scale animation dataset DeformingThings4D [46]. Nine classes of humanoid shapes are used for evaluation, resulting in 198/95 shapes for training/testing. + +
TrainFAUSTSCAPEFAUST + SCAPE
TestFAUSTSCAPESHREC'19
Axiomatic Methods
BCICP [61]6.111.0-
ZoomOut [56]6.17.5-
Smooth Shells [25]2.54.7-
DiscreteOp [63]5.613.1-
Supervised Methods
FMNet [48]11.017.0-
GeomFMaps [18]2.63.07.9
Unsupervised Methods
WSupFMNet [70]3.84.4-
Deep Shells [26]1.72.521.1
NeuroMorph [27]2.35.68.5
DUO-FMNet [20]2.52.66.4
AttnFMaps [44]1.92.25.8
URSSM [12]1.61.94.6
Ours1.41.83.2
+ +Table 2. Near-isometric shape matching and cross-dataset generalisation on FAUST, SCAPE and SHREC'19. Our method outperforms prior axiomatic, supervised and unsupervised methods and demonstrates superior cross-dataset generalisation ability. + +![](images/9d3f539bbc8b4cf9eafdcb9695bf23e6a90c1e69e9842fdbfbfc58d945f68c7f.jpg) +Figure 4. Near-isometric shape matching on FAUST, SCAPE. Proportion of correct keypoints (PCK) curves and corresponding area under curve (scores in the legend) of our method in comparison to existing state-of-the-art methods. + +![](images/cec5060a24945139a5554dca7420cb64e30e75bc6eb815833832e7eb3e66a279.jpg) + +Results. The results are summarised in Tab. 3. Our method substantially outperforms the previous state-of-the-art in the context of non-isometric shape matching, even compared to recent supervised methods. In Fig. 5, we summarise the PCK curves of our method compared to state-of-the-art methods on both non-isometric datasets. Fig. 6 provides qualitative results of our method compared to them. + +# 5.2. Shape interpolation + +Datasets. Following NeuroMorph [27], we evaluate our method on the FAUST [7] and MANO [67] datasets. The MANO dataset contains synthetic hands in various poses with a train/test split of 100/20. + +Results. Two metrics are applied to evaluate the performance of the shape interpolation. The first conformal distortion metric [38] measures how much individual triangles of a mesh distort throughout the interpolation se + +
Geo. error (×100)SMALDT4D-H
intra-classinter-class
Axiomatic Methods
ZoomOut [56]38.44.029.0
Smooth Shells [25]36.11.16.3
DiscreteOp [63]38.13.627.6
Supervised Methods
FMNet [48]42.09.638.0
GeomFMaps [18]8.42.14.1
Unsupervised Methods
WSupFMNet [70]7.63.322.6
Deep Shells [26]29.33.431.1
NeuroMorph [27]5.914.425.3
DUO-FMNet [20]6.72.615.8
AttnFMaps [44]5.41.711.6
URSSM [12]3.90.94.1
Ours1.90.93.3
+ +Table 3. Non-isometric matching on SMAL and DT4D-H. Our method substantially outperforms previous state-of-the-art methods even in comparison to supervised methods, especially for nonisometric shape matching (i.e. SMAL and DT4D-H inter-class). + +![](images/7e2b62efe9ce17b06a4eaf72fcad33e4d737905b92a4500ef8a4f94f29a41bb3.jpg) + +![](images/f38a5fb637490f0b3c5162b1129ca5cd07a03c189d06e5a17b74982f8d9056b4.jpg) + +![](images/5001a8e227f48ad85879cf129813a425fd0fc1eef5482b4140fc41ae0d9652f9.jpg) +Figure 5. Non-isometric matching on SMAL, DT4D-H inter-class datasets. Our method sets to new state of the art by a large margin based on the combination of spectral and spatial maps. +Figure 6. Non-isometric matching on SMAL and DT4D-H. Our method obtains more accurate matching results even in the presence of large non-isometric shape deformations. + +quence, compared to the original shape. The second metric is the Chamfer distance between the target and the final deformed shapes. Besides NeuroMorph, we further evaluate our method against other two baselines (i.e. LIMP [15] + +and Hamiltonian [23]) that require ground-truth correspondences for interpolation. Fig. 7 summarises the performance of our method against other baselines. Our method achieves state-of-the-art performance on both datasets, even compared to methods relying on ground-truth correspondences. Fig. 8 shows the interpolation results of our method on the MANO dataset. + +![](images/0e651eea8d2aa595bde3125445b42caca6b394adee98601ca4413df17d5037c2.jpg) + +![](images/c94e65cd9257a801dba64f9f515cae352ddd006b64fd58da7b3dbe7cc88c2c50.jpg) + +![](images/796da33d6dec908490a6858138084aa0090e0b8f2cb5a675c64971ecafce9640.jpg) +Figure 7. Interpolation on FAUST and MANO datasets. Our method achieves state-of-the-art performance on both datasets, even in comparison to methods that requires ground-truth correspondences (shown as dashed lines). + +![](images/8149713b754a59e95d282fbfe667183fadf742b89fa62f8b57ecb4f774ef7b6b.jpg) + +![](images/de77817329ac89ae9204fef3f7b319cd17fd0c1fd672c944f51d4edbfc34e53f.jpg) +Figure 8. Shape interpolation on MANO. Our method obtains a smooth interpolation trajectory between hands in different poses. + +# 5.3. Statistical shape analysis on medical data + +To better demonstrate the potential of our method for real-world applications, we conduct statistical shape analysis using medical data. To this end, we use the real-world LUNA16 dataset [69] that contains chest CT scans with corresponding lung segmentation masks. Based on the provided segmentation masks, we reconstruct 3D lung shapes represented as triangle meshes using Marching Cubes [52]. In this way, we get a total of 22 shapes from manual selection. Starting from 22 shapes, our method obtains both accurate point-wise correspondences and smooth interpolation trajectories between them (see Fig. 9). Using our obtained correspondences, we build a statistical shape model (SSM) based on a point distribution model (PDM) [14]. The modes of variation of the SSM are summarised in Fig. 10. We evaluate the quality of the SSM w.r.t. the two standard + +metrics: generalisation and specificity [16] based on the Chamfer distance. We compare our method to the most recent method (i.e. S3M [5]). Tab. 4 summarises the results. Compared to S3M, our method obtains better generalisation and specificity. + +![](images/5f6fec154a563d99a646a4162e45dba24d1ffd4953ee428759f3b22b9d192fd1.jpg) +Figure 9. Matching and interpolation on LUNA16 dataset. Our method obtains accurate correspondences and realistic interpolations between each two lungs despite of large non-isometry. + +![](images/ba64a28eb9176b51d9ffe127839d380b49c54895cf489a4a6e795480103af38b.jpg) + +![](images/2709c8439ae32dbd497413033b155d4c1cbb6742f4ab5785cddc97d2e41b6c5e.jpg) + +![](images/67a9fc6546a187b16c365ba667dbf49c8c64af5fa4c530039966622bcd84f3fb.jpg) + +![](images/879d748c375f4421548b8c3b8e0454fb22ab4db7c13de39a13902d9e2b5543b3.jpg) + +![](images/1181880ca0b99e4b4f7ed392af720a3096eddb8593eb5e2aff552789c3e03b5c.jpg) + +![](images/94a6ab7666a0e3d0c19230be7b91f92749a0c2604ee3a00d868c99d43b9a79a2.jpg) +Figure 10. Statistical shape analysis on LUNA16 dataset. The first row visualises the mean shape. While the second row and third row demonstrate the mean shape plus and minus $(\times 2)$ the corresponding principal components, respectively. + +
Error [mm]Generalisation ↓Specificity ↓
S3M [5]2.926.23
Ours2.445.03
+ +# 6. Ablation study + +In this section we conduct ablative experiments to analyse individual components of our approach. To this end, we consider only using the spectral loss $L_{\mathrm{spectral}}$ in Eq. (8) for shape matching or use the feature similarity to obtain the final point-wise correspondences instead of test-time adaptation. For the experiment, we consider the challenging nonisometric SMAL and DT4D-H dataset. + +Results. Tab. 5 summarises the quantitative results. By comparing the first and the second rows, we can conclude that the spatial regularisation (i.e. $L_{\mathrm{spatial}}$ in Eq. (15)) plays an important role in obtaining more accurate point-wise correspondences. By comparing the second and the third rows, we notice that the test-time adaptation can further boost the + +matching performance. Together with both of them, our method achieves the most accurate shape matching results. + +Table 4. SSM evaluation. Our method substantially outperforms the state-of-the-art w.r.t. generalisation and specificity. + +
Geo. error (×100)SMALDT4D-H inter
Spectral only3.94.1
w.o. Test-time adaptation2.63.4
Ours1.93.3
+ +Table 5. Ablation study on the SMAL and DT4D-H datasets. The best result in each column is highlighted. + +# 7. Discussion and limitations + +For the first time we combine spectral and spatial maps to enable unsupervised learning for joint 3d shape matching and interpolation and thereby set the new state of the art in both tasks simultaneously. Yet, some limitations still give rise to future investigations. Compared to prior works [23, 24], our method captures pose and shape-dominant deformations without any prior knowledge. On the other hand, this separation between pose and shape is not always perfect: in practice, the interpolation module slightly alters the shape in some cases. In future work, we plan to investigate whether a clearer separation can be achieved by including additional assumptions about the input shape classes [83]. Another interesting direction is to integrate end-to-end statistical shape analysis into our framework for improved shape analysis and generation. + +# 8. Conclusion + +In this work we propose the first unsupervised learning framework that harmonises spectral and spatial maps to enable joint 3D shape matching and interpolation. Our method allows to compute accurate shape correspondences and realistic interpolation trajectories between different 3D shapes without relying on any shape-specific prior knowledge. We experimentally demonstrate that our method sets the new state of the art in both shape matching and interpolation on numerous benchmarks. Moreover, we showcase the application of our method to real-world statistical shape models of medical data. Overall, we believe that our method will be a valuable contribution for bringing shape matching to practical applications in challenging real-world settings. + +# 9. Acknowledgement + +This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 458610525, by the ERC Advanced Grant 'SIMULACRON' and by the Collaborative Research Center 'Discretization in Geometry and Dynamics' of the German Research Foundation. + +# References + +[1] Marc Alexa, Daniel Cohen-Or, and David Levin. Asrigid-as-possible shape interpolation. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques, page 157-164, USA, 2000. ACM Press/Addison-Wesley Publishing Co. 3 +[2] Dragomir Anguelov, Praveen Srinivasan, Daphne Koller, Sebastian Thrun, Jim Rodgers, and James Davis. Scape: shape completion and animation of people. In ACM SIGGRAPH. 2005. 6 +[3] Souhaib Attaiki, Gautam Pai, and Maks Ovsjanikov. Dpfm: Deep partial functional maps. In International Conference on 3D Vision (3DV), 2021. 2 +[4] Seung-Yeob Baek, Jeonghun Lim, and Kunwoo Lee. Isometric shape interpolation. 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In CVPR, 2017. 6 \ No newline at end of file diff --git a/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/images.zip b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e1c3bdbedb385911ffa09df0dd2d934ce660bddf --- /dev/null +++ b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5086011cb8b4d2e2419017fb0452a65f3960cfa9a4ce56aba640946ee099b381 +size 685509 diff --git a/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/layout.json b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d597002f0153c4b8039616ab57ff48bdd0f42d80 --- /dev/null +++ b/2024/Spectral Meets Spatial_ Harmonising 3D Shape Matching and Interpolation/layout.json @@ -0,0 +1,10758 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "spans": [ + { + "bbox": [ + 62, + 103, + 531, + 121 + ], + "type": "text", + "content": "Spectral Meets Spatial: Harmonising 3D Shape Matching and Interpolation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 142, + 134, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 142, + 134, + 159 + ], + "spans": [ + { + "bbox": [ + 54, + 142, + 134, + 159 + ], + "type": "text", + "content": "Dongliang Cao" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 147, + 142, + 249, + 158 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 147, + 142, + 249, + 158 + ], + "spans": [ + { + "bbox": [ + 147, + 142, + 249, + 158 + ], + "type": "text", + "content": "Marvin Eisenberger2" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 262, + 142, + 347, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 262, + 142, + 347, + 156 + ], + "spans": [ + { + "bbox": [ + 262, + 142, + 347, + 156 + ], + "type": "text", + "content": "Nafie El Amrani" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 360, + 143, + 443, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 143, + 443, + 156 + ], + "spans": [ + { + "bbox": [ + 360, + 143, + 443, + 156 + ], + "type": "text", + "content": "Daniel Cremers" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 455, + 143, + 537, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 455, + 143, + 537, + 156 + ], + "spans": [ + { + "bbox": [ + 455, + 143, + 537, + 156 + ], + "type": "text", + "content": "Florian Bernard1" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 152, + 162, + 254, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 152, + 162, + 254, + 177 + ], + "spans": [ + { + "bbox": [ + 152, + 162, + 254, + 177 + ], + "type": "text", + "content": "1 University of Bonn" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 278, + 162, + 441, + 177 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 278, + 162, + 441, + 177 + ], + "spans": [ + { + "bbox": [ + 278, + 162, + 441, + 177 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 278, + 162, + 441, + 177 + ], + "type": "text", + "content": " Technical University of Munich" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 50, + 219, + 533, + 336 + ], + "blocks": [ + { + "bbox": [ + 50, + 219, + 533, + 336 + ], + "lines": [ + { + "bbox": [ + 50, + 219, + 533, + 336 + ], + "spans": [ + { + "bbox": [ + 50, + 219, + 533, + 336 + ], + "type": "image", + "image_path": "c37dddab6b9cdf987f809b30b70b3672d54c09143d25886fccb0d54911207ab5.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 52, + 338, + 294, + 464 + ], + "blocks": [ + { + "bbox": [ + 52, + 338, + 294, + 464 + ], + "lines": [ + { + "bbox": [ + 52, + 338, + 294, + 464 + ], + "spans": [ + { + "bbox": [ + 52, + 338, + 294, + 464 + ], + "type": "image", + "image_path": "dcd5fc76dd4bb103422f6c9bb183dac5eec7c45450eb7cf334186fefaffda996.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 470, + 545, + 526 + ], + "lines": [ + { + "bbox": [ + 45, + 470, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 45, + 470, + 545, + 526 + ], + "type": "text", + "content": "Figure 1. Top: 3D shape interpolation. Compared to the SOTA shape interpolation method NeuroMorph [27], our method obtains more reliable interpolation even under large non-isometry. Bottom left: 3D shape matching. The point-wise correspondences found by the SOTA shape matching method URSSM [12] contains local mismatches. In contrast, our method enables smooth shape matching. Bottom right: 3D shape matching and interpolation. Our method is the first unsupervised method that obtains both accurate correspondences (shown as texture transfer) and realistic interpolation that capture both the pose-dominant and shape-dominant deformations." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 300, + 338, + 543, + 467 + ], + "blocks": [ + { + "bbox": [ + 300, + 338, + 543, + 467 + ], + "lines": [ + { + "bbox": [ + 300, + 338, + 543, + 467 + ], + "spans": [ + { + "bbox": [ + 300, + 338, + 543, + 467 + ], + "type": "image", + "image_path": "171455d236821728eb21fb224abd5eda81170b93170004827727d6d87928fe06.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 143, + 533, + 192, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 533, + 192, + 545 + ], + "spans": [ + { + "bbox": [ + 143, + 533, + 192, + 545 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 45, + 559, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 559, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 559, + 288, + 715 + ], + "type": "text", + "content": "Although 3D shape matching and interpolation are highly interrelated, they are often studied separately and applied sequentially to relate different 3D shapes, thus resulting in sub-optimal performance. In this work we present a unified framework to predict both point-wise correspondences and shape interpolation between 3D shapes. To this end, we combine the deep functional map framework with classical surface deformation models to map shapes in both spectral and spatial domains. On the one hand, by incorporating spatial maps, our method obtains more accurate and smooth point-wise correspondences compared to previous functional map methods for shape matching. On the other hand, by introducing spectral maps, our method gets rid" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 534, + 547, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 631 + ], + "type": "text", + "content": "of commonly used but computationally expensive geodesic distance constraints that are only valid for near-isometric shape deformations. Furthermore, we propose a novel test-time adaptation scheme to capture both pose-dominant and shape-dominant deformations. Using different challenging datasets, we demonstrate that our method outperforms previous state-of-the-art methods for both shape matching and interpolation, even compared to supervised approaches." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 647, + 387, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 387, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 387, + 658 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 715 + ], + "type": "text", + "content": "Computing maps between 3D shapes is a fundamental problem in computer vision and computer graphics, since it opens the door to understanding different object categories and enables both shape analysis [50] and shape genera" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3658" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "tion [22]. One specific class of approaches builds shape relationships is statistical shape models (e.g. SMPL [51]). To do so, these methods require dense point-wise correspondences between large collections of 3D shapes. Even though shape matching has been studied extensively in the literature [75, 77], finding accurate point-wise correspondences between non-rigidly deformed 3D shapes remains challenging due to different discretisation, non-isometry and partiality. Once shapes are in correspondence, shape interpolation methods can be applied to increase the shape diversity for shape generation [27, 57] and for different applications (e.g. animation [42], interactive shape editing [39])." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 218, + 289, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 218, + 289, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 218, + 289, + 589 + ], + "type": "text", + "content": "Despite the interrelation between shape matching and interpolation, prior works mainly consider them as two separate problems. In the context of shape matching, the functional map framework [58] is one of the most dominant pipelines and has been extended by many follow-up works [19, 61, 63, 64]. However, functional map methods only map shapes in the spectral domain and thus lead to local unsmooth point-wise correspondences (see URSSM in Fig. 1 bottom left), which is undesirable for many downstream tasks (e.g. shape interpolation [23], or statistical shape analysis [45, 51]). Meanwhile, shape matching methods based on non-rigid registration (i.e. spatial maps) typically rely on time-consuming iterative optimisation schemes [40, 43] and careful initialisation [6, 54], and thus often achieve worse performance due to the optimisation complexity [17]. To overcome the above limitations, our method takes the best of both worlds by combining spectral and spatial maps. For shape interpolation, most works assume that the shapes are already in correspondence and aim to design more efficient and realistic deformation energies [9, 35, 81]. As a consequence, wrong correspondences often lead to undesirable interpolation trajectories. Only few approaches [24, 27] explicitly consider shape matching and interpolation together, but mostly under overly strict assumptions (e.g. volume preservation). Tab. 1 summarises the comparison between different learning-based shape matching approaches. Unlike prior methods, we propose the first unsupervised framework that harmonises spectral and spatial maps for both shape matching and interpolation. We summarise our main contributions as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 591, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 591, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 591, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 591, + 287, + 628 + ], + "type": "text", + "content": "- For the first time we fuse spectral and spatial maps to enable the joint unsupervised learning of both non-rigid 3D shape matching and interpolation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 628, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 287, + 675 + ], + "type": "text", + "content": "- Our method predicts both pose-dominant and shape-dominant deformations, in contrast to prior interpolation methods that mainly focus on pose-dominant ones due to local deformation priors." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 675, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 675, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 675, + 287, + 712 + ], + "type": "text", + "content": "- We set the new state-of-the-art shape matching and interpolation performance on numerous challenging benchmarks, even compared to supervised methods." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 312, + 71, + 541, + 227 + ], + "blocks": [ + { + "bbox": [ + 312, + 71, + 541, + 227 + ], + "lines": [ + { + "bbox": [ + 312, + 71, + 541, + 227 + ], + "spans": [ + { + "bbox": [ + 312, + 71, + 541, + 227 + ], + "type": "table", + "html": "
MethodsUnsup.SpectralSpatialInterp.
FMNet [48]X✓XX
3D-CODED [32]XX✓X
GeomFMaps [18]X✓XX
TransMatch [76]XX✓X
UnsupFMNet [33]✓✓XX
SURFMNet [68]✓✓XX
Deep Shells [26]✓✓✓X
CorrNet3D [82]✓X✓X
NeuroMorph [27]✓X✓✓
AttnFMaps [44]✓✓XX
URSSM [12]✓✓XX
Ours✓✓✓✓
", + "image_path": "92661f242dbab33c774d31d8f8dbccdbe0c84c72534c35780b98eb20e76c6cfd.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 234, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 305, + 234, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 305, + 234, + 545, + 278 + ], + "type": "text", + "content": "Table 1. Learning-based shape matching method comparison. Our method is the first unsupervised learning approach that operates in both spectral and spatial domains to enable accurate shape matching and realistic shape interpolation." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 304, + 389, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 304, + 389, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 304, + 389, + 316 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 331, + 404, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 404, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 404, + 344 + ], + "type": "text", + "content": "2.1. Shape matching" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 358, + 545, + 478 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 545, + 478 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 545, + 478 + ], + "type": "text", + "content": "Shape matching aims to find point-wise correspondences between shapes. Classical shape matching approaches [37, 65, 80] establish correspondences by explicitly considering geometric relations. Other methods [6, 24, 30, 40] solve the problem based on non-rigid shape registration. However, directly finding point-wise correspondences often leads to complex optimisation problems that typically require time-consuming iterative optimisation strategies and are thus only applicable for low-resolution shapes [65, 66, 80], which limits their applications in real-world settings." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 546, + 713 + ], + "type": "text", + "content": "In contrast, the functional map framework finds correspondences in the spectral domain [58], where the correspondence relationship can be encoded into a small matrix, namely the functional map. Due to its simple yet efficient formulation, the functional map framework has been extended by many follow-up works, e.g. improving the matching accuracy [29, 62], extending it to more challenging scenarios (e.g. non-isometry [25, 53, 61, 63], partiality [49, 64]). Together with the development of deep learning, many learning-based approaches are proposed [33, 48, 68] and lead to state-of-the-art performance [3, 10-12]. Nevertheless, the map in the spectral domain does not guarantee smooth point-wise correspondences. Therefore, the conversion of functional map into smooth and accurate point-wise correspondences is still an open-problem that is extensively studied [31, 56, 59, 78]. Unlike most functional map methods, our method harmonises the spectral and spatial maps together and thus leads to more accurate and smooth pointwise correspondences." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3659" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 163, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 163, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 163, + 85 + ], + "type": "text", + "content": "2.2. Shape interpolation" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 290, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 290, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 290, + 450 + ], + "type": "text", + "content": "Shape interpolation is a well-studied problem in computer graphics that aims to continuously deform a source shape to a target shape. The most common strategy is to define an interpolation path in some higher dimensional space [9, 35, 36, 81]. To this end, various deformation measurements (e.g. as-rigid-as-possible (ARAP) [72], PriMo [8], etc.) are proposed to optimise the interpolation path so that the local distortion between any consecutive shapes is minimised. Another direction is to interpolate intrinsic quantities like dihedral angles before reconstructing the 3D shape [1, 4]. Other methods formulate shape interpolation as a time-dependent gradient flow [13, 21] by incorporating certain constraints (e.g. volume preservation [23, 24]). Nevertheless, most of them assume known correspondences between two shapes, which is unrealistic for real-world 3D shapes. The most relevant approach to our work is NeuroMorph [27], which is an unsupervised framework for both shape matching and interpolation. However, it has several limitations: In the context of shape matching, it is based on the geodesic distance preservation that is computationally expensive and only valid for near-isometric shape deformation. In the context of shape interpolation, it solely utilises the as-rigid-as-possible [72] to deform the source shape into the target shape, which can only model the low-frequency pose-dominant deformations (see Fig. 1 in [27]). In contrast, we utilise more efficient spectral regularisation and thus lead to more accurate shape matching even under large non-isometry. Furthermore, our method is able to capture both pose-dominant and shape-dominant deformations based on our novel test-time adaptation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 464, + 236, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 236, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 236, + 478 + ], + "type": "text", + "content": "3. Deep functional map in a nutshell" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": "In this section we provide a summary of the popular deep functional map framework [68]. We consider a pair of 3D shapes " + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": " represented as triangle meshes with " + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "n_{\\mathcal{X}}" + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "n_{\\mathcal{Y}}" + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": " (w.l.o.g. " + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "inline_equation", + "content": "n_{\\mathcal{X}} \\leq n_{\\mathcal{Y}}" + }, + { + "bbox": [ + 47, + 484, + 287, + 544 + ], + "type": "text", + "content": ") vertices, respectively. Here we summarise the main steps of its pipeline:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 544, + 287, + 641 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "text", + "content": "1. Compute the Laplacian matrices " + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_{\\mathcal{X}},\\mathbf{L}_{\\mathcal{Y}}" + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "text", + "content": " [60] and the corresponding first " + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "text", + "content": " eigenfunctions " + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\Phi_{\\mathcal{X}},\\Phi_{\\mathcal{Y}}" + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "text", + "content": " and eigenvalues " + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\Lambda_{\\mathcal{X}},\\Lambda_{\\mathcal{Y}}" + }, + { + "bbox": [ + 48, + 544, + 287, + 581 + ], + "type": "text", + "content": " in matrix notation, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 582, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 604 + ], + "type": "text", + "content": "2. Compute feature vectors " + }, + { + "bbox": [ + 47, + 582, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathcal{X}},\\mathbf{F}_{\\mathcal{Y}}" + }, + { + "bbox": [ + 47, + 582, + 287, + 604 + ], + "type": "text", + "content": " defined on each shape via a learnable feature extractor " + }, + { + "bbox": [ + 47, + 582, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta}" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "type": "text", + "content": "3. Compute the functional maps " + }, + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}},\\mathbf{C}_{\\mathcal{Y}\\mathcal{X}}" + }, + { + "bbox": [ + 47, + 605, + 287, + 641 + ], + "type": "text", + "content": " associated with the Laplacian eigenfunctions by solving the optimisation problem" + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 86, + 652, + 287, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 652, + 287, + 669 + ], + "spans": [ + { + "bbox": [ + 86, + 652, + 287, + 669 + ], + "type": "interline_equation", + "content": "\\mathbf {C} _ {\\mathcal {X Y}} = \\arg \\min _ {\\mathbf {C}} E _ {\\text {d a t a}} (\\mathbf {C}) + \\lambda E _ {\\text {r e g}} (\\mathbf {C}). \\tag {1}", + "image_path": "f6da9921785fabb15efd85cec51e2fc935d952716c2c96c2647b2a1faaadbf7c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 59, + 681, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 681, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 681, + 287, + 714 + ], + "type": "text", + "content": "Here, minimising " + }, + { + "bbox": [ + 59, + 681, + 287, + 714 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{data}}(\\mathbf{C}) = \\left\\| \\mathbf{C}\\boldsymbol{\\Phi}_{\\mathcal{X}}^{\\dagger}\\mathbf{F}_{\\mathcal{X}} - \\boldsymbol{\\Phi}_{\\mathcal{Y}}^{\\dagger}\\mathbf{F}_{\\mathcal{Y}}\\right\\|_{F}^{2}" + }, + { + "bbox": [ + 59, + 681, + 287, + 714 + ], + "type": "text", + "content": " enforces descriptor preservation, while minimising the" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 317, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 317, + 72, + 545, + 96 + ], + "type": "text", + "content": "regularisation term " + }, + { + "bbox": [ + 317, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "E_{\\mathrm{reg}}" + }, + { + "bbox": [ + 317, + 72, + 545, + 96 + ], + "type": "text", + "content": " imposes certain structural properties (e.g. Laplacian commutativity [58])." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 96, + 545, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 96, + 545, + 133 + ], + "spans": [ + { + "bbox": [ + 306, + 96, + 545, + 133 + ], + "type": "text", + "content": "4. During training, structural regularisation (e.g. orthogonality, bijectivity [68]) is imposed on the functional maps, i.e." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 365, + 140, + 545, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 140, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 365, + 140, + 545, + 153 + ], + "type": "interline_equation", + "content": "L _ {\\text {s t r u c t}} = \\lambda_ {\\mathrm {b i j}} L _ {\\mathrm {b i j}} + \\lambda_ {\\mathrm {o r t h}} L _ {\\mathrm {o r t h}}. \\tag {2}", + "image_path": "aa30bdaac6b1044ee8b83014fe20bc197345601953e8a7ae815657f830fe6661.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "spans": [ + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "type": "text", + "content": "5. During inference, the point-wise map " + }, + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{Y}\\mathcal{X}}" + }, + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "type": "text", + "content": " is obtained based on the map relationship " + }, + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}} = \\Phi_{\\mathcal{Y}}^{\\dagger}\\Pi_{\\mathcal{Y}\\mathcal{X}}\\Phi_{\\mathcal{X}}" + }, + { + "bbox": [ + 306, + 159, + 547, + 219 + ], + "type": "text", + "content": ", e.g. either by nearest neighbour search in the spectral domain or by other post-processing techniques [25, 31, 56, 78]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 230, + 384, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 230, + 384, + 243 + ], + "spans": [ + { + "bbox": [ + 306, + 230, + 384, + 243 + ], + "type": "text", + "content": "4. Our method" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 249, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 249, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 249, + 547, + 346 + ], + "type": "text", + "content": "The framework of our method is depicted in Fig. 2. Our method aims to predict both accurate point-wise correspondences and realistic shape interpolation paths in an unsupervised manner. Therefore, our framework can be divided into two sub-modules, namely the shape matching module (Sec. 4.1) and the shape interpolation module (Sec. 4.2). Our unsupervised loss and test-time adaptation are introduced in Sec. 4.3 and Sec. 4.4, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 352, + 443, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 443, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 443, + 365 + ], + "type": "text", + "content": "4.1. Shape matching module" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 370, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 545, + 418 + ], + "type": "text", + "content": "Point-wise map computation. Point-wise map computation aims to find dense correspondences between two shapes. In theory, the point-wise map " + }, + { + "bbox": [ + 305, + 370, + 545, + 418 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{X}\\mathcal{Y}}" + }, + { + "bbox": [ + 305, + 370, + 545, + 418 + ], + "type": "text", + "content": " should be a (partial) permutation matrix, i.e." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 317, + 424, + 545, + 450 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 424, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 317, + 424, + 545, + 450 + ], + "type": "interline_equation", + "content": "\\left\\{\\boldsymbol {\\Pi} \\in \\{0, 1 \\} ^ {n _ {\\mathcal {X}} \\times n _ {\\mathcal {Y}}}: \\boldsymbol {\\Pi} \\mathbf {1} _ {n _ {\\mathcal {Y}}} = \\mathbf {1} _ {n _ {\\mathcal {X}}}, \\mathbf {1} _ {n _ {\\mathcal {X}}} ^ {\\top} \\boldsymbol {\\Pi} \\leq \\mathbf {1} _ {n _ {\\mathcal {Y}}} ^ {\\top} \\right\\}, \\tag {3}", + "image_path": "75d4d938f0404f136c2a06f636d34df0f457b59da8e1f80759aed3ce015b280f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\Pi (i,j)" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " indicates whether the vertex " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^i" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " in shape " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " corresponds to the vertex " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}^j" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " in shape " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": ". In our work the point-wise correspondences " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{XY}}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " between shapes " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " are obtained based on similarity measurement of the extracted features. To this end, the Siamese feature extractor " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " (i.e. DiffusionNet [71]) is used to extract features " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathcal{X}},\\mathbf{F}_{\\mathcal{Y}}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " from input shapes, respectively. Following prior works [12, 27], we use the softmax operator to produce a soft correspondence matrix to make the computation differentiable, i.e. " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{XY}} = \\mathrm{Softmax}\\left(\\mathbf{F}_{\\mathcal{X}}\\mathbf{F}_{\\mathcal{Y}}^{T}\\right)" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": ". The softmax operator is applied in each row to ensure that elements are non-negative and " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{XY}}\\mathbf{1}_{n_{\\mathcal{Y}}} = \\mathbf{1}_{n_{\\mathcal{X}}}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": ". In this way, " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{XY}}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " can be interpreted as a soft assignment of vertices " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " in shape " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " to vertices " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": " in shape " + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 450, + 546, + 617 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "Functional map computation. The goal of the functional map computation is to impose spectral regularisation on the obtained point-wise maps based on the coupling relationship " + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}} = \\boldsymbol{\\Phi}_{\\mathcal{Y}}^{\\dagger}\\boldsymbol{\\Pi}_{\\mathcal{Y}\\mathcal{X}}\\boldsymbol{\\Phi}_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": ". Therefore, the functional map computation is only used for training as part of the spectral loss computation. The computation pipeline of functional maps is explained in Sec. 3 and the details of the spectral loss can be found in Sec. 4.3." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3660" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 547, + 240 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 547, + 240 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 547, + 240 + ], + "type": "image", + "image_path": "8e4fc02a41b45265c3544f980c7dfaf3062924addac75091d1623e55113edec1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": "Figure 2. Method overview. First, the Siamese feature extractor " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\theta}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " is used to extract features " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\mathcal{X}}, \\mathbf{F}_{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " from input shapes " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{X}, \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": ", respectively. The extracted features are then used to compute both bidirectional functional maps " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathcal{X}\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_{\\mathcal{Y}\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " and point-wise maps " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{X}\\mathcal{Y}}, \\Pi_{\\mathcal{Y}\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": ". Afterwards, the computed point-wise maps are used to bring the shape into correspondences. In the context of shape interpolation, a series of time steps " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " is sampled and fed into the interpolator " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "\\Omega_{\\gamma}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " together with shape information to predict a series of interpolated shapes " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "X(t), Y(t)" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": ". During training the spectral loss " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{spectral}}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " is used to regularise the predicted functional maps and point maps, while the spatial loss " + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{spatial}}" + }, + { + "bbox": [ + 46, + 252, + 547, + 319 + ], + "type": "text", + "content": " is used to regularise the interpolation trajectories of both shapes." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 339, + 200, + 352 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 339, + 200, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 339, + 200, + 352 + ], + "type": "text", + "content": "4.2. Shape interpolation module" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": "The goal of the shape interpolation module " + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\Omega_{\\gamma}" + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": " is to predict the deformation field " + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\Delta(t) \\in \\mathbb{R}^{n \\times 3}" + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": ", that continuously deforms the shape " + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": " into the shape " + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": ", and vice versa. The deformation field of shape " + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 357, + 287, + 418 + ], + "type": "text", + "content": " forms the interpolation trajectory" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 123, + 427, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 427, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 123, + 427, + 287, + 441 + ], + "type": "interline_equation", + "content": "\\mathbf {X} (t) = \\mathbf {X} + \\Delta_ {\\mathcal {X}} (t). \\tag {4}", + "image_path": "6bbf8b4efa6b7204b46e84022dfbb2f975533fa5ed1fb94c3b294f89af957428.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": "The interpolation trajectory shifts shape " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": " from its original locations " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{X}(0) = \\mathbf{X}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": " into new locations " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{X}(1)\\approx \\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": ", which are close to the corresponding vertices in shape " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": ". Following NeuroMorph [27], we use EdgeConv [79] blocks with residual connections [34] to build our interpolator " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\Omega_{\\gamma}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": ". Similarly, the input feature of shape " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": " in the interpolator is the 7-dimensional feature vector " + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\mathbf{Z}_{\\mathcal{X}}\\in \\mathbb{R}^{n_{\\mathcal{X}}\\times 7}" + }, + { + "bbox": [ + 46, + 449, + 287, + 545 + ], + "type": "text", + "content": " that can be expressed in the form" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 94, + 555, + 287, + 568 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 555, + 287, + 568 + ], + "spans": [ + { + "bbox": [ + 94, + 555, + 287, + 568 + ], + "type": "interline_equation", + "content": "\\mathbf {Z} _ {\\mathcal {X}} (t) = \\left(\\mathbf {X}, \\boldsymbol {\\Pi} _ {\\mathcal {X} \\mathcal {Y}} \\mathbf {Y} - \\mathbf {X}, t \\mathbf {1} _ {n _ {\\mathcal {X}}}\\right), \\tag {5}", + "image_path": "a0180d14a4978bb8aaab5892175b3e857cbf213838cae27f52f3ce9a9f4acb4d.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": " is the vertices of the shape " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y} - \\mathbf{X}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": " is the vertex offsets between shape " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "t\\mathbf{1}_{n_{\\mathcal{X}}}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": " is the sampled time that broadcasts to all vertices. The deformation fields are given by the output of the interpolator multiplied by time, i.e. " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathcal{X}}(t) = t\\cdot \\Omega_{\\gamma}(\\mathbf{Z}_{\\mathcal{X}}(t))" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": ". To this end, the interpolator can immediately predict a trivial solution (i.e. linear interpolation) by setting " + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\Omega_{\\gamma}(\\mathbf{Z}_{\\mathcal{X}}(t)) = \\Pi_{\\mathcal{X}\\mathcal{Y}}\\mathbf{Y} - \\mathbf{X}" + }, + { + "bbox": [ + 46, + 577, + 287, + 673 + ], + "type": "text", + "content": ", since it satisfies the boundary conditions of the interpolation [27]:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 682, + 287, + 695 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 682, + 287, + 695 + ], + "spans": [ + { + "bbox": [ + 78, + 682, + 287, + 695 + ], + "type": "interline_equation", + "content": "\\mathbf {X} (0) = \\mathbf {X} + 0 \\cdot \\left(\\Pi_ {\\mathcal {X Y}} \\mathbf {Y} - \\mathbf {X}\\right) = \\mathbf {X}, \\tag {6}", + "image_path": "93118afe70b676aa0379b2d84746fbc9ad761cb237b8951546fd83ffed53774b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 78, + 697, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 697, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 78, + 697, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\mathbf {X} (1) = \\mathbf {X} + 1 \\cdot \\left(\\Pi_ {\\mathcal {X Y}} \\mathbf {Y} - \\mathbf {X}\\right) = \\Pi_ {\\mathcal {X Y}} \\mathbf {Y}. \\tag {7}", + "image_path": "6def5a2092412cef1330af2dde1971afc79ce80db4d0f552972c5937ba5af4bd.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 339, + 545, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 339, + 545, + 411 + ], + "spans": [ + { + "bbox": [ + 306, + 339, + 545, + 411 + ], + "type": "text", + "content": "However, the linear interpolation is a degenerate solution, since our goal is to obtain geometrically realistic shape interpolation. To prevent the interpolator prediction from falling into the trivial solution, spatial regularisation needs to be imposed, including a deformation energy [72] and additional regularisation, which will be introduced in Sec. 4.3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 420, + 411, + 432 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 411, + 432 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 411, + 432 + ], + "type": "text", + "content": "4.3. Unsupervised loss" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 437, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 643 + ], + "type": "text", + "content": "In this section we introduce the spectral and spatial regularisation that enable unsupervised training of our method. Spectral regularisation. To obtain accurate point-wise correspondences for shape matching and shape interpolation, we utilise a spectral regularisation based on the functional map framework. Unlike prior works [15, 27] relying on geodesic distance preservation that is computationally expensive and only valid for near-isometric deformation [33], the spectral regularisation imposed on the functional maps is more efficient and works well also for non-isometric deformations [12, 20, 44]. Unlike most previous deep functional map methods [18, 26, 68] relying on off-the-shelf post-processing techniques [25, 56] to obtain point-wise maps (see Sec. 3), we aim to directly obtain point-wise map based on deep feature similarity. To this end, we combine structural regularisation in Eq. (2) with the coupling loss [12, 63, 73] to build our spectral regularisation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 336, + 652, + 545, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 652, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 336, + 652, + 545, + 666 + ], + "type": "interline_equation", + "content": "L _ {\\text {s p e c t r a l}} = \\lambda_ {\\text {s t r u c t}} L _ {\\text {s t r u c t}} + \\lambda_ {\\text {c o u p l e}} L _ {\\text {c o u p l e}}, \\tag {8}", + "image_path": "5ab9799cb146dde2d3298edea1a225c2e5052c70e7658dc52ea540839137505c.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 675, + 333, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 675, + 333, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 675, + 333, + 685 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 348, + 693, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 693, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 348, + 693, + 545, + 717 + ], + "type": "interline_equation", + "content": "L _ {\\text {c o u p l e}} = \\left\\| \\mathbf {C} _ {\\mathcal {X Y}} - \\boldsymbol {\\Phi} _ {\\mathcal {Y}} ^ {\\dagger} \\boldsymbol {\\Pi} _ {\\mathcal {Y X}} \\boldsymbol {\\Phi} _ {\\mathcal {X}} \\right\\| _ {F} ^ {2}. \\tag {9}", + "image_path": "61e3ab95290fed11e8f8fe5fb4ca9b2bc28766479cc6b17fbf87e1eb596324a0.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "3661" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "Spatial regularisation. Finding point-wise correspondences solely based on spectral regularisation leads to local mismatches, which is undesirable for many downstream tasks including shape interpolation. To compensate for this, one of our spatial regularisation terms aims to directly align two shapes in the spatial domain, i.e." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 148, + 287, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 148, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 56, + 148, + 287, + 174 + ], + "type": "interline_equation", + "content": "L _ {\\text {a l i g n}} = \\left\\| \\mathbf {X} (1) - \\boldsymbol {\\Pi} _ {\\mathcal {X Y}} \\mathbf {Y} \\right\\| _ {F} ^ {2} + \\left\\| \\mathbf {Y} (1) - \\boldsymbol {\\Pi} _ {\\mathcal {Y X}} \\mathbf {X} \\right\\| _ {F} ^ {2}. \\tag {10}", + "image_path": "ef77152f226fd652d8ab07bcf61cc808bc7d299d9d1b422a4f80de2e94b50f7f.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "text", + "content": "As mentioned in Sec. 4.2, additional spatial regularisation for shape deformation is needed to avoid trivial degenerated solutions. To this end, similar to [27, 83], the ARAP deformation energy [72] is used to regularise the interpolation trajectory. ARAP is a low-frequency preserving deformation energy that encourages locally rigid transformations. During training, we sample " + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "inline_equation", + "content": "T + 1" + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "text", + "content": " discrete timesteps uniformly " + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_k \\coloneqq \\mathbf{X}(k / T)" + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "inline_equation", + "content": "k \\in \\{0, \\dots, T\\}" + }, + { + "bbox": [ + 46, + 175, + 287, + 282 + ], + "type": "text", + "content": " to compute the ARAP energy as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 292, + 287, + 340 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 292, + 287, + 340 + ], + "spans": [ + { + "bbox": [ + 56, + 292, + 287, + 340 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} E _ {\\mathrm {a r a p}} \\left(\\mathbf {X} _ {k}, \\mathbf {X} _ {k + 1}\\right) = \\\\ \\min _ {\\mathbf {R} _ {i} \\in S O (3)} \\sum_ {i = 1} ^ {n _ {\\mathcal {X}}} \\sum_ {j \\in \\mathcal {N} _ {i}} \\left\\| \\mathbf {R} _ {i} \\mathbf {E} _ {k} ^ {i j} - \\mathbf {E} _ {k + 1} ^ {i j} \\right\\| _ {F} ^ {2}, \\tag {11} \\\\ \\end{array}", + "image_path": "d402b47d09f75168bbe90fb113b5948ea9cd7f3b4ac91f51022f815e6bce4596.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_k^{ij} = \\mathbf{X}_k^i -\\mathbf{X}_k^j\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "text", + "content": " is the triangle edge between mesh vertices " + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_k^j" + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_k^i" + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "text", + "content": ". The rotation matrices " + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\mathbf{R}_i" + }, + { + "bbox": [ + 46, + 347, + 287, + 410 + ], + "type": "text", + "content": " can be computed in closed form for an efficient deformation (see [72] for details). Finally, our ARAP regularisation term can be expressed in the form" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 100, + 416, + 287, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 416, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 100, + 416, + 287, + 449 + ], + "type": "interline_equation", + "content": "L _ {\\text {a r a p}} = \\sum_ {k = 0} ^ {T - 1} E _ {\\text {a r a p}} \\left(\\mathbf {X} _ {k}, \\mathbf {X} _ {k + 1}\\right). \\tag {12}", + "image_path": "afa83d0aeb36fe0e78be9e693813835d463cc91a8d636468d9a13e9ed908eae2.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "text", + "content": "Analogously, the loss in Eq. (12) is also applied to the reverse sequence for shape " + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "text", + "content": ". However, the ARAP deformation energy only enables low-frequency pose-dominant deformation. To capture the shape-dominant deformation, we propose a test-time adaptation described in Sec. 4.4. Apart from the ARAP regularisation, we propose two additional regularisation terms to encourage smooth and symmetric deformation trajectories from shape " + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "text", + "content": " to shape " + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 455, + 287, + 574 + ], + "type": "text", + "content": ", and vice versa. The symmetry loss encourages symmetric deformation trajectories from both directions, i.e." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 92, + 580, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 580, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 92, + 580, + 287, + 613 + ], + "type": "interline_equation", + "content": "L _ {\\mathrm {s y m}} = \\sum_ {k = 1} ^ {T - 1} \\| \\mathbf {X} _ {k} - \\boldsymbol {\\Pi} _ {\\mathcal {X Y}} \\mathbf {Y} _ {T - k} \\| _ {F} ^ {2}. \\tag {13}", + "image_path": "783e3f6beaf5b615fcbcc0cbe771fd86f31cade3db2be871ff19d81920aa1d26.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": "This loss is also applied with the roles of " + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": " swapped. Since we would like to also model the shape-dominant deformation, we only want " + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_k\\approx \\Pi_{\\mathcal{XY}}\\mathbf{Y}_{T - k}" + }, + { + "bbox": [ + 46, + 619, + 287, + 678 + ], + "type": "text", + "content": " allowing for shape-based variations. To this end, we introduce a temporal shape variance loss defined as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 81, + 685, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 685, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 81, + 685, + 287, + 715 + ], + "type": "interline_equation", + "content": "L _ {\\text {v a r}} = \\sum_ {i = 1} ^ {n \\chi} \\operatorname {V a r} \\left(\\left\\| \\mathbf {X} _ {k} - \\Pi_ {\\mathcal {X Y}} \\mathbf {Y} _ {T - k} \\right\\| ^ {i}\\right), \\tag {14}", + "image_path": "e9e4decdfcefde1c801690db722a34cd3b3735505c53e2aac031c477caab84e3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\operatorname{Var}(\\mathbf{X}^i) = \\frac{1}{T - 1}\\sum_{k = 1}^{T}(\\mathbf{X}_k^i -\\bar{\\mathbf{X}}^i)^2" + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "text", + "content": " is the alignment error variance of the " + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "text", + "content": "-th vertex during the interpolation sequence and " + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\bar{\\mathbf{X}}^i = \\frac{1}{T}\\sum_{k = 1}^{T}\\mathbf{X}_k^i" + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "text", + "content": " is the mean. In this manner, we assume that shape variations are nearly constant throughout the interpolation sequence. Similar to Eq. (13), the loss is also applied for the reverse direction " + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 70, + 545, + 156 + ], + "type": "text", + "content": ". The spatial loss is the linear combination of the above losses, i.e." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 163, + 547, + 187 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 163, + 547, + 187 + ], + "spans": [ + { + "bbox": [ + 306, + 163, + 547, + 187 + ], + "type": "interline_equation", + "content": "L _ {\\text {s p a t i a l}} = \\lambda_ {\\text {a l i g n}} L _ {\\text {a l i g n}} + \\lambda_ {\\text {a r a p}} L _ {\\text {a r a p}} + \\lambda_ {\\text {s y m}} L _ {\\text {s y m}} + \\lambda_ {\\text {v a r}} L _ {\\text {v a r}}. \\tag {15}", + "image_path": "6db8945fc3bc9c0f32c316da9397bfcb92fdb277f15cda82ad04d08a895ae2d1.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 188, + 544, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 188, + 544, + 200 + ], + "spans": [ + { + "bbox": [ + 306, + 188, + 544, + 200 + ], + "type": "text", + "content": "The total loss is the sum of the spectral loss and spatial loss." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 207, + 425, + 219 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 207, + 425, + 219 + ], + "spans": [ + { + "bbox": [ + 306, + 207, + 425, + 219 + ], + "type": "text", + "content": "4.4. Test-time adaptation" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "text", + "content": "The spatial loss defined in Eq. (15) encourages low-frequency pose-dominant deformations, while the shape-based deformations are not well-modelled. To this end, we propose a novel test-time adaptation to obtain more accurate correspondences and better capture the shape-dominant deformation. Specifically, we optimise for an additional shape-dominant deformation field " + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\Delta_s(t) \\in \\mathbb{R}^{n_x \\times 3}" + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "text", + "content": " (with " + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "text", + "content": ") between " + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\mathbf{X}(t)" + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}(1 - t)" + }, + { + "bbox": [ + 304, + 224, + 545, + 321 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 327, + 545, + 355 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 545, + 355 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 545, + 355 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Delta} _ {s} (t) = \\underset {\\boldsymbol {\\Delta}} {\\arg \\min } \\operatorname {C D} (\\mathbf {X} (t) + \\boldsymbol {\\Delta}, \\mathbf {Y} (1 - t)) + \\lambda_ {\\mathrm {D}} L _ {\\mathrm {D}} (\\boldsymbol {\\Delta}), \\tag {16}", + "image_path": "2dd76da1d81d4173ed229e8d056f7f69fbd2ff08a1f812a9d71887bd7fb3834c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 356, + 507, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 356, + 507, + 366 + ], + "spans": [ + { + "bbox": [ + 306, + 356, + 507, + 366 + ], + "type": "text", + "content": "where we consider the standard Chamfer distance" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 315, + 375, + 545, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 375, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 315, + 375, + 545, + 435 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {C D} \\left(\\mathbf {S} _ {1}, \\mathbf {S} _ {2}\\right) = \\frac {1}{| \\mathbf {S} _ {1} |} \\sum_ {\\mathbf {x} \\in \\mathbf {S} _ {1}} \\min _ {\\mathbf {y} \\in \\mathbf {S} _ {2}} \\| \\mathbf {x} - \\mathbf {y} \\| _ {2} ^ {2} \\\\ + \\frac {1}{| \\mathbf {S} _ {2} |} \\sum_ {\\mathbf {y} \\in \\mathbf {S} _ {2}} \\min _ {\\mathbf {x} \\in \\mathbf {S} _ {1}} \\| \\mathbf {x} - \\mathbf {y} \\| _ {2} ^ {2}, \\tag {17} \\\\ \\end{array}", + "image_path": "66d0c0abcb674abc8cec8bab1df1ca44bd3e3863141eefa6af7f2087787e7ab1.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": "and " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{D}}(\\cdot)" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": " is the Dirichlet energy [53] which promotes smooth deformations. The VectorAdam [47] optimiser is used to optimise the additional shape-based deformation field. Once we obtain the optimal " + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\Delta_s(t)" + }, + { + "bbox": [ + 304, + 442, + 545, + 514 + ], + "type": "text", + "content": ", we use linear interpolation to obtain the shape-dominant deformation trajectory, i.e." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 310, + 521, + 545, + 535 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 521, + 545, + 535 + ], + "spans": [ + { + "bbox": [ + 310, + 521, + 545, + 535 + ], + "type": "interline_equation", + "content": "\\mathbf {X} \\left(t, t _ {s}\\right) = \\left(1 - t _ {s}\\right) \\cdot \\left(\\mathbf {X} (t) + \\boldsymbol {\\Delta} _ {s} (t)\\right) + t _ {s} \\cdot \\mathbf {Y} (1 - t), \\tag {18}", + "image_path": "5cb4ea01f002d013308ffaf37348e67c26ce94275882d03219bedc1848726a05.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "inline_equation", + "content": "t_s \\in [0,1]" + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": " is the sampled time for shape-dominant deformation. Fig. 3 demonstrates an example of our test-time adaptation for " + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "inline_equation", + "content": "t = \\{0,0.5,1\\}" + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "inline_equation", + "content": "t_s = \\{0,0.5,1\\}" + }, + { + "bbox": [ + 304, + 542, + 545, + 578 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 578, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 613 + ], + "type": "text", + "content": "After the optimisation of the shape-dominant deformation field " + }, + { + "bbox": [ + 304, + 578, + 545, + 613 + ], + "type": "inline_equation", + "content": "\\Delta_s(t)" + }, + { + "bbox": [ + 304, + 578, + 545, + 613 + ], + "type": "text", + "content": ", we obtain the final point-wise correspondences based on the spatial map using" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 369, + 621, + 545, + 634 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 621, + 545, + 634 + ], + "spans": [ + { + "bbox": [ + 369, + 621, + 545, + 634 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\Pi} _ {\\mathcal {X Y}} = \\mathrm {N N} (\\mathbf {Y}, \\mathbf {X} (1, 1)), \\tag {19}", + "image_path": "b98244422409ecce10b3491d314119a1763e52d3ef538b817254e85046a454fb.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "where NN denotes nearest neighbour search in " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " for each entry in " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}(1,1)" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": ". Optimisation based on the Chamfer distance is highly non-convex and prone to local minima for non-rigid shape registration [32, 74, 82]. However, for the optimisation in Eq. (16), the two shapes are already in the same pose with only minor shape variations." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3662" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 286, + 194 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 286, + 194 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 286, + 194 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 286, + 194 + ], + "type": "image", + "image_path": "7503fea7f300ce9717e3d51567d61b34a6afcef9fec64b39c6a6a0c9805f29fb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "type": "text", + "content": "Figure 3. Visualisation of our test-time adaptation. Starting from pose-dominant deformation based on ARAP, we obtain " + }, + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "type": "inline_equation", + "content": "\\mathbf{X}(t,t_s = 0)" + }, + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "type": "text", + "content": " (i.e. the last row). Afterwards, we optimise the shape-dominant deformation field " + }, + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "type": "inline_equation", + "content": "\\Delta_{s}(t)" + }, + { + "bbox": [ + 46, + 203, + 289, + 270 + ], + "type": "text", + "content": " for each sampled time point. Finally, the linear interpolation is performed to obtain the shape-dominant interpolation trajectories (shown by arrows)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 289, + 169, + 304 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 169, + 304 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 169, + 304 + ], + "type": "text", + "content": "5. Experimental results" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 311, + 288, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 311, + 288, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 311, + 288, + 335 + ], + "type": "text", + "content": "In this section we demonstrate the advantages of our method in the context of 3D shape matching and interpolation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 345, + 146, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 146, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 146, + 358 + ], + "type": "text", + "content": "5.1. Shape matching" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 508 + ], + "type": "text", + "content": "Near-isometric shape matching. We evaluate the matching accuracy of our method on three near-isometric benchmarks: FAUST [7], SCAPE [2] and SHREC'19 [55]. Instead of the original meshes, we consider the more challenging remeshed versions from [18, 61]. The FAUST dataset consists of 10 humans with 10 different poses each, where the training and testing split is 80/20. The SCAPE dataset contains 71 different poses of the same person, split into 51 and 20 shapes for training and testing. The SHREC'19 dataset is subject to particular challenges with significant variance in the mesh connectivity and shape geometry. It has a total of 430 pairs for evaluation." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 604 + ], + "type": "text", + "content": "Results. The mean geodesic error [41] is used as evaluation metric. We compare our method with state-of-the-art axiomatic, supervised and unsupervised methods. The results are summarised in Tab. 2. Our method outperforms the previous state-of-the-art methods (see the PCK curves in Fig. 4). Meanwhile, our method achieves substantially better cross-dataset generalisation ability than existing learning-based methods." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 288, + 715 + ], + "type": "text", + "content": "Non-isometric shape matching. Regarding non-isometric shape matching, we consider the SMAL dataset [84] and DT4D-H dataset [53]. The SMAL dataset contains 49 four-legged animal shapes of 8 species [28]. Following Donati et al. [20], we use the last 20 shapes for testing, resulting in a 29/20 split of the dataset. DT4D-H dataset is based on the large-scale animation dataset DeformingThings4D [46]. Nine classes of humanoid shapes are used for evaluation, resulting in 198/95 shapes for training/testing." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 320, + 70, + 533, + 294 + ], + "blocks": [ + { + "bbox": [ + 320, + 70, + 533, + 294 + ], + "lines": [ + { + "bbox": [ + 320, + 70, + 533, + 294 + ], + "spans": [ + { + "bbox": [ + 320, + 70, + 533, + 294 + ], + "type": "table", + "html": "
TrainFAUSTSCAPEFAUST + SCAPE
TestFAUSTSCAPESHREC'19
Axiomatic Methods
BCICP [61]6.111.0-
ZoomOut [56]6.17.5-
Smooth Shells [25]2.54.7-
DiscreteOp [63]5.613.1-
Supervised Methods
FMNet [48]11.017.0-
GeomFMaps [18]2.63.07.9
Unsupervised Methods
WSupFMNet [70]3.84.4-
Deep Shells [26]1.72.521.1
NeuroMorph [27]2.35.68.5
DUO-FMNet [20]2.52.66.4
AttnFMaps [44]1.92.25.8
URSSM [12]1.61.94.6
Ours1.41.83.2
", + "image_path": "42a5e63bc5058f35e345238397e4d05f84b4d4fb0d4d1941f205e21b96e843a6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 301, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 305, + 301, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 301, + 546, + 346 + ], + "type": "text", + "content": "Table 2. Near-isometric shape matching and cross-dataset generalisation on FAUST, SCAPE and SHREC'19. Our method outperforms prior axiomatic, supervised and unsupervised methods and demonstrates superior cross-dataset generalisation ability." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 310, + 349, + 421, + 440 + ], + "blocks": [ + { + "bbox": [ + 310, + 349, + 421, + 440 + ], + "lines": [ + { + "bbox": [ + 310, + 349, + 421, + 440 + ], + "spans": [ + { + "bbox": [ + 310, + 349, + 421, + 440 + ], + "type": "image", + "image_path": "9d3f539bbc8b4cf9eafdcb9695bf23e6a90c1e69e9842fdbfbfc58d945f68c7f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 453, + 546, + 496 + ], + "lines": [ + { + "bbox": [ + 305, + 453, + 546, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 453, + 546, + 496 + ], + "type": "text", + "content": "Figure 4. Near-isometric shape matching on FAUST, SCAPE. Proportion of correct keypoints (PCK) curves and corresponding area under curve (scores in the legend) of our method in comparison to existing state-of-the-art methods." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 433, + 348, + 547, + 440 + ], + "blocks": [ + { + "bbox": [ + 433, + 348, + 547, + 440 + ], + "lines": [ + { + "bbox": [ + 433, + 348, + 547, + 440 + ], + "spans": [ + { + "bbox": [ + 433, + 348, + 547, + 440 + ], + "type": "image", + "image_path": "cec5060a24945139a5554dca7420cb64e30e75bc6eb815833832e7eb3e66a279.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 508, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 508, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 508, + 547, + 594 + ], + "type": "text", + "content": "Results. The results are summarised in Tab. 3. Our method substantially outperforms the previous state-of-the-art in the context of non-isometric shape matching, even compared to recent supervised methods. In Fig. 5, we summarise the PCK curves of our method compared to state-of-the-art methods on both non-isometric datasets. Fig. 6 provides qualitative results of our method compared to them." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 421, + 612 + ], + "type": "text", + "content": "5.2. Shape interpolation" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 546, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 666 + ], + "type": "text", + "content": "Datasets. Following NeuroMorph [27], we evaluate our method on the FAUST [7] and MANO [67] datasets. The MANO dataset contains synthetic hands in various poses with a train/test split of 100/20." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Results. Two metrics are applied to evaluate the performance of the shape interpolation. The first conformal distortion metric [38] measures how much individual triangles of a mesh distort throughout the interpolation se" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3663" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 55, + 70, + 281, + 282 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 281, + 282 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 281, + 282 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 281, + 282 + ], + "type": "table", + "html": "
Geo. error (×100)SMALDT4D-H
intra-classinter-class
Axiomatic Methods
ZoomOut [56]38.44.029.0
Smooth Shells [25]36.11.16.3
DiscreteOp [63]38.13.627.6
Supervised Methods
FMNet [48]42.09.638.0
GeomFMaps [18]8.42.14.1
Unsupervised Methods
WSupFMNet [70]7.63.322.6
Deep Shells [26]29.33.431.1
NeuroMorph [27]5.914.425.3
DUO-FMNet [20]6.72.615.8
AttnFMaps [44]5.41.711.6
URSSM [12]3.90.94.1
Ours1.90.93.3
", + "image_path": "8ee02e9672666be99ed1b08c6341f7ebae2633b36fa3b0875a51ebcc61b9785d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 290, + 288, + 335 + ], + "lines": [ + { + "bbox": [ + 47, + 290, + 288, + 335 + ], + "spans": [ + { + "bbox": [ + 47, + 290, + 288, + 335 + ], + "type": "text", + "content": "Table 3. Non-isometric matching on SMAL and DT4D-H. Our method substantially outperforms previous state-of-the-art methods even in comparison to supervised methods, especially for nonisometric shape matching (i.e. SMAL and DT4D-H inter-class)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 341, + 164, + 433 + ], + "blocks": [ + { + "bbox": [ + 50, + 341, + 164, + 433 + ], + "lines": [ + { + "bbox": [ + 50, + 341, + 164, + 433 + ], + "spans": [ + { + "bbox": [ + 50, + 341, + 164, + 433 + ], + "type": "image", + "image_path": "7e2b62efe9ce17b06a4eaf72fcad33e4d737905b92a4500ef8a4f94f29a41bb3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 176, + 341, + 288, + 432 + ], + "blocks": [ + { + "bbox": [ + 176, + 341, + 288, + 432 + ], + "lines": [ + { + "bbox": [ + 176, + 341, + 288, + 432 + ], + "spans": [ + { + "bbox": [ + 176, + 341, + 288, + 432 + ], + "type": "image", + "image_path": "f38a5fb637490f0b3c5162b1129ca5cd07a03c189d06e5a17b74982f8d9056b4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 56, + 483, + 282, + 610 + ], + "blocks": [ + { + "bbox": [ + 46, + 445, + 287, + 479 + ], + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 479 + ], + "type": "text", + "content": "Figure 5. Non-isometric matching on SMAL, DT4D-H inter-class datasets. Our method sets to new state of the art by a large margin based on the combination of spectral and spatial maps." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 56, + 483, + 282, + 610 + ], + "lines": [ + { + "bbox": [ + 56, + 483, + 282, + 610 + ], + "spans": [ + { + "bbox": [ + 56, + 483, + 282, + 610 + ], + "type": "image", + "image_path": "5001a8e227f48ad85879cf129813a425fd0fc1eef5482b4140fc41ae0d9652f9.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 619, + 288, + 653 + ], + "lines": [ + { + "bbox": [ + 46, + 619, + 288, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 288, + 653 + ], + "type": "text", + "content": "Figure 6. Non-isometric matching on SMAL and DT4D-H. Our method obtains more accurate matching results even in the presence of large non-isometric shape deformations." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "quence, compared to the original shape. The second metric is the Chamfer distance between the target and the final deformed shapes. Besides NeuroMorph, we further evaluate our method against other two baselines (i.e. LIMP [15]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 546, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 546, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 546, + 156 + ], + "type": "text", + "content": "and Hamiltonian [23]) that require ground-truth correspondences for interpolation. Fig. 7 summarises the performance of our method against other baselines. Our method achieves state-of-the-art performance on both datasets, even compared to methods relying on ground-truth correspondences. Fig. 8 shows the interpolation results of our method on the MANO dataset." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 165, + 421, + 258 + ], + "blocks": [ + { + "bbox": [ + 310, + 165, + 421, + 258 + ], + "lines": [ + { + "bbox": [ + 310, + 165, + 421, + 258 + ], + "spans": [ + { + "bbox": [ + 310, + 165, + 421, + 258 + ], + "type": "image", + "image_path": "0e651eea8d2aa595bde3125445b42caca6b394adee98601ca4413df17d5037c2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 433, + 165, + 544, + 259 + ], + "blocks": [ + { + "bbox": [ + 433, + 165, + 544, + 259 + ], + "lines": [ + { + "bbox": [ + 433, + 165, + 544, + 259 + ], + "spans": [ + { + "bbox": [ + 433, + 165, + 544, + 259 + ], + "type": "image", + "image_path": "c94e65cd9257a801dba64f9f515cae352ddd006b64fd58da7b3dbe7cc88c2c50.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 262, + 421, + 356 + ], + "blocks": [ + { + "bbox": [ + 309, + 262, + 421, + 356 + ], + "lines": [ + { + "bbox": [ + 309, + 262, + 421, + 356 + ], + "spans": [ + { + "bbox": [ + 309, + 262, + 421, + 356 + ], + "type": "image", + "image_path": "796da33d6dec908490a6858138084aa0090e0b8f2cb5a675c64971ecafce9640.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 368, + 546, + 413 + ], + "lines": [ + { + "bbox": [ + 304, + 368, + 546, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 546, + 413 + ], + "type": "text", + "content": "Figure 7. Interpolation on FAUST and MANO datasets. Our method achieves state-of-the-art performance on both datasets, even in comparison to methods that requires ground-truth correspondences (shown as dashed lines)." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 434, + 262, + 544, + 356 + ], + "blocks": [ + { + "bbox": [ + 434, + 262, + 544, + 356 + ], + "lines": [ + { + "bbox": [ + 434, + 262, + 544, + 356 + ], + "spans": [ + { + "bbox": [ + 434, + 262, + 544, + 356 + ], + "type": "image", + "image_path": "8149713b754a59e95d282fbfe667183fadf742b89fa62f8b57ecb4f774ef7b6b.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 310, + 424, + 545, + 472 + ], + "blocks": [ + { + "bbox": [ + 310, + 424, + 545, + 472 + ], + "lines": [ + { + "bbox": [ + 310, + 424, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 310, + 424, + 545, + 472 + ], + "type": "image", + "image_path": "de77817329ac89ae9204fef3f7b319cd17fd0c1fd672c944f51d4edbfc34e53f.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 481, + 545, + 503 + ], + "lines": [ + { + "bbox": [ + 305, + 481, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 481, + 545, + 503 + ], + "type": "text", + "content": "Figure 8. Shape interpolation on MANO. Our method obtains a smooth interpolation trajectory between hands in different poses." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 515, + 522, + 529 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 515, + 522, + 529 + ], + "spans": [ + { + "bbox": [ + 306, + 515, + 522, + 529 + ], + "type": "text", + "content": "5.3. Statistical shape analysis on medical data" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 713 + ], + "type": "text", + "content": "To better demonstrate the potential of our method for real-world applications, we conduct statistical shape analysis using medical data. To this end, we use the real-world LUNA16 dataset [69] that contains chest CT scans with corresponding lung segmentation masks. Based on the provided segmentation masks, we reconstruct 3D lung shapes represented as triangle meshes using Marching Cubes [52]. In this way, we get a total of 22 shapes from manual selection. Starting from 22 shapes, our method obtains both accurate point-wise correspondences and smooth interpolation trajectories between them (see Fig. 9). Using our obtained correspondences, we build a statistical shape model (SSM) based on a point distribution model (PDM) [14]. The modes of variation of the SSM are summarised in Fig. 10. We evaluate the quality of the SSM w.r.t. the two standard" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3664" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "metrics: generalisation and specificity [16] based on the Chamfer distance. We compare our method to the most recent method (i.e. S3M [5]). Tab. 4 summarises the results. Compared to S3M, our method obtains better generalisation and specificity." + } + ] + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 56, + 141, + 89, + 183 + ], + "blocks": [ + { + "bbox": [ + 56, + 141, + 89, + 183 + ], + "lines": [ + { + "bbox": [ + 56, + 141, + 89, + 183 + ], + "spans": [ + { + "bbox": [ + 56, + 141, + 89, + 183 + ], + "type": "image", + "image_path": "5f6fec154a563d99a646a4162e45dba24d1ffd4953ee428759f3b22b9d192fd1.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 198, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 47, + 198, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 287, + 232 + ], + "type": "text", + "content": "Figure 9. Matching and interpolation on LUNA16 dataset. Our method obtains accurate correspondences and realistic interpolations between each two lungs despite of large non-isometry." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 94, + 142, + 127, + 180 + ], + "blocks": [ + { + "bbox": [ + 94, + 142, + 127, + 180 + ], + "lines": [ + { + "bbox": [ + 94, + 142, + 127, + 180 + ], + "spans": [ + { + "bbox": [ + 94, + 142, + 127, + 180 + ], + "type": "image", + "image_path": "ba64a28eb9176b51d9ffe127839d380b49c54895cf489a4a6e795480103af38b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 131, + 143, + 165, + 180 + ], + "blocks": [ + { + "bbox": [ + 131, + 143, + 165, + 180 + ], + "lines": [ + { + "bbox": [ + 131, + 143, + 165, + 180 + ], + "spans": [ + { + "bbox": [ + 131, + 143, + 165, + 180 + ], + "type": "image", + "image_path": "2709c8439ae32dbd497413033b155d4c1cbb6742f4ab5785cddc97d2e41b6c5e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 169, + 143, + 205, + 178 + ], + "blocks": [ + { + "bbox": [ + 169, + 143, + 205, + 178 + ], + "lines": [ + { + "bbox": [ + 169, + 143, + 205, + 178 + ], + "spans": [ + { + "bbox": [ + 169, + 143, + 205, + 178 + ], + "type": "image", + "image_path": "67a9fc6546a187b16c365ba667dbf49c8c64af5fa4c530039966622bcd84f3fb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 207, + 144, + 244, + 178 + ], + "blocks": [ + { + "bbox": [ + 207, + 144, + 244, + 178 + ], + "lines": [ + { + "bbox": [ + 207, + 144, + 244, + 178 + ], + "spans": [ + { + "bbox": [ + 207, + 144, + 244, + 178 + ], + "type": "image", + "image_path": "879d748c375f4421548b8c3b8e0454fb22ab4db7c13de39a13902d9e2b5543b3.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 245, + 145, + 286, + 174 + ], + "blocks": [ + { + "bbox": [ + 245, + 145, + 286, + 174 + ], + "lines": [ + { + "bbox": [ + 245, + 145, + 286, + 174 + ], + "spans": [ + { + "bbox": [ + 245, + 145, + 286, + 174 + ], + "type": "image", + "image_path": "1181880ca0b99e4b4f7ed392af720a3096eddb8593eb5e2aff552789c3e03b5c.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 60, + 245, + 272, + 380 + ], + "blocks": [ + { + "bbox": [ + 60, + 245, + 272, + 380 + ], + "lines": [ + { + "bbox": [ + 60, + 245, + 272, + 380 + ], + "spans": [ + { + "bbox": [ + 60, + 245, + 272, + 380 + ], + "type": "image", + "image_path": "94a6ab7666a0e3d0c19230be7b91f92749a0c2604ee3a00d868c99d43b9a79a2.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "lines": [ + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "type": "text", + "content": "Figure 10. Statistical shape analysis on LUNA16 dataset. The first row visualises the mean shape. While the second row and third row demonstrate the mean shape plus and minus " + }, + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "type": "inline_equation", + "content": "(\\times 2)" + }, + { + "bbox": [ + 46, + 390, + 287, + 434 + ], + "type": "text", + "content": " the corresponding principal components, respectively." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 70, + 449, + 264, + 494 + ], + "blocks": [ + { + "bbox": [ + 70, + 449, + 264, + 494 + ], + "lines": [ + { + "bbox": [ + 70, + 449, + 264, + 494 + ], + "spans": [ + { + "bbox": [ + 70, + 449, + 264, + 494 + ], + "type": "table", + "html": "
Error [mm]Generalisation ↓Specificity ↓
S3M [5]2.926.23
Ours2.445.03
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Geo. error (×100)SMALDT4D-H inter
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", + "image_path": "b53e76a5a1e2e0b1677e7d9a7f38c75bee578c0b6ab5ab91a2f9eca094ff3031.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "lines": [ + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "spans": [ + { + "bbox": [ + 305, + 173, + 545, + 195 + ], + "type": "text", + "content": "Table 5. Ablation study on the SMAL and DT4D-H datasets. The best result in each column is highlighted." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 216, + 455, + 228 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 216, + 455, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 216, + 455, + 228 + ], + "type": "text", + "content": "7. Discussion and limitations" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 237, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 237, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 237, + 545, + 417 + ], + "type": "text", + "content": "For the first time we combine spectral and spatial maps to enable unsupervised learning for joint 3d shape matching and interpolation and thereby set the new state of the art in both tasks simultaneously. Yet, some limitations still give rise to future investigations. Compared to prior works [23, 24], our method captures pose and shape-dominant deformations without any prior knowledge. On the other hand, this separation between pose and shape is not always perfect: in practice, the interpolation module slightly alters the shape in some cases. In future work, we plan to investigate whether a clearer separation can be achieved by including additional assumptions about the input shape classes [83]. Another interesting direction is to integrate end-to-end statistical shape analysis into our framework for improved shape analysis and generation." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 433, + 378, + 445 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 433, + 378, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 433, + 378, + 445 + ], + "type": "text", + "content": "8. Conclusion" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 454, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 611 + ], + "type": "text", + "content": "In this work we propose the first unsupervised learning framework that harmonises spectral and spatial maps to enable joint 3D shape matching and interpolation. Our method allows to compute accurate shape correspondences and realistic interpolation trajectories between different 3D shapes without relying on any shape-specific prior knowledge. We experimentally demonstrate that our method sets the new state of the art in both shape matching and interpolation on numerous benchmarks. Moreover, we showcase the application of our method to real-world statistical shape models of medical data. Overall, we believe that our method will be a valuable contribution for bringing shape matching to practical applications in challenging real-world settings." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 625, + 416, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 625, + 416, + 639 + ], + "spans": [ + { + "bbox": [ + 306, + 625, + 416, + 639 + ], + "type": "text", + "content": "9. Acknowledgement" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 647, + 545, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 702 + ], + "type": "text", + "content": "This work is supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - 458610525, by the ERC Advanced Grant 'SIMULACRON' and by the Collaborative Research Center 'Discretization in Geometry and Dynamics' of the German Research Foundation." + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3665" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Marc Alexa, Daniel Cohen-Or, and David Levin. 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In CVPR, 2017. 6" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "3668" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_content_list.json b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..8e4152982b45d1719bca329d4e75587985885a00 --- /dev/null +++ b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_content_list.json @@ -0,0 +1,1756 @@ +[ + { + "type": "text", + "text": "Spectral and Polarization Vision: Spectro-polarimetric Real-world Dataset", + "text_level": 1, + "bbox": [ + 277, + 130, + 692, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yujin Jeon $^{1,*}$ Eunsue Choi $^{1,*}$ Youngchan Kim $^{1}$ Yunseong Moon $^{1}$ Khalid Omer $^{2}$ Felix Heide $^{3}$ Seung-Hwan Baek $^{1}$", + "bbox": [ + 171, + 202, + 767, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ POSTECH $^{2}$ Meta $^{3}$ Princeton University", + "bbox": [ + 284, + 248, + 684, + 268 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 301, + 313, + 316 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Many image datasets exist, consisting of trichromatic intensity images taken with RGB cameras, which are designed to replicate human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although there are previous spectro-polarimetric datasets, they have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets, consisting of trichromatic Stokes images and hyperspectral Stokes images. These datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research.", + "bbox": [ + 75, + 334, + 473, + 681 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 712, + 209, + 728 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent progress in computer vision can be largely attributed to comprehensive studies of real-world image datasets, such as ImageNet [14]. Foundation models [1, 35, 53, 64] further underscore data significance. Most of these datasets comprise trichromatic intensity images, inspired by human visual perception, enabling machines to emulate human vision with trichromatic RGB cameras. As such, the datasets have facilitated the development of low-cost, camera-based autonomous agents capable of perceiving and interacting", + "bbox": [ + 75, + 738, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "with our world, as we do. However, the reliance on trichromatic intensity in existing image datasets also comes with inherent limitations for analyzing objects in depth. Examples include textureless surface, low-albedo objects, and transparent materials.", + "bbox": [ + 500, + 303, + 890, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Light possesses wave properties, including polarization and spectrum [9], which are not faithfully captured by trichromatic intensity imaging. While these properties are invisible to human, animals like honeybees and ants leverage the polarization and spectrum for navigation and other tasks. Horvath and Varju [25] provide diverse examples and mechanisms of spectral and polarimetric vision in animals. Partly drawing inspiration from nature, researchers have extended the analysis of spectrum and polarization to a variety of fields, including computer vision, robotics, and astronomy. This has spurred interest in polarimetric [7, 8, 38, 49] and hyperspectral imaging [2, 10, 28], and more recently, their integration into spectro-polarimetric imaging [3, 17, 18, 23, 26, 45, 47, 50, 54, 67]. Prior work using spectro-polarimetric images has shown potential for skin analysis [67], vegetation classification [63], shape reconstruction [27], object recognition [13], and segmentation [30, 55].", + "bbox": [ + 496, + 382, + 892, + 655 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "There are existing spectro-polarimetric datasets, summarized in Figure 2, that have been invaluable for these analysis [19, 38, 39, 52] and training neural networks [4, 11, 22, 36, 40-42, 46, 48]. However, these datasets unfortunately do not capture the diversity of real-world spectropolarimetric images as effectively as their trichromatic intensity counterparts do. They typically suffer from limited object, scene, and illumination diversity, contain primarily linear polarization information, and offer a small number of images. To advance the field, we propose a comprehensive spectro-polarimetric dataset that encompasses: (1) Full Stokes polarimetric data, including both linear and circular polarization states, represented by Stokes vectors [9] for each pixel and wavelength. (2) A diverse range of spectral channels, facilitating in-depth exploration of the interplay between spectrum and polarization. (3) A broad array of", + "bbox": [ + 496, + 657, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*These authors contributed equally to this work.", + "bbox": [ + 94, + 886, + 351, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "22098", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "real-world scenes, crucial for extracting meaningful statistics and relationships within spectro-polarimetric images.", + "bbox": [ + 75, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we introduce two spectro-polarimetric datasets designed to cover real-world spectro-polarimetric scenes: a trichromatic Stokes dataset consisting of 2,022 images, and a hyperspectral Stokes dataset containing 311 images across 21 spectral channels. The trichromatic Stokes dataset covers a wider range of scenes thanks to its convenient capture setup and process. The hyperspectral Stokes dataset provides richer spectral-polarimetric information than the trichromatic Stokes dataset. Both datasets cover a variety of natural indoor and outdoor scenes. Each image in these datasets is annotated with four specific parameters: the type of environment (indoor or outdoor), the illumination conditions (clear/cloudy sunlight or white/yellow office light), the timestamp of capture, and the scene categorization (either object- or scene-oriented).", + "bbox": [ + 75, + 121, + 468, + 347 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Utilizing these datasets, we systematically analyze the statistics of real-world spectro-polarimetric images. We focus on examining statistics of Stokes vectors, in addition to the gradients and polarimetric attributes associated with them. We also conduct an analysis of unpolarized and polarized images derived through polarimetric decomposition. We then develop two efficient spatio-spectral-polarimetric representations using principal component analysis (PCA) and implicit neural representation (INR). These representations exhibit effective denoising capabilities and low memory footprints by exploiting the compressible structure of spectro-polarimetric images. We also analyze the impact of intensity denoising for spectro-polarimetric images, spectral dependency of shape-from-polarization methods, and environment dependency on the statistics of spectropolarimetric images.", + "bbox": [ + 75, + 348, + 470, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, we make the following contributions.", + "bbox": [ + 96, + 589, + 429, + 604 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a trichromatic Stokes dataset and a hyperspectral Stokes dataset, featuring 2,333 diverse annotated indoor and outdoor scenes under various illumination conditions, which encompasses full-Stokes polarization data for linear and circular states.", + "- We develop efficient spatio-spectral-polarimetric representations and analyze real-world spectro-polarimetric images, encompassing Stokes vectors and their gradients, unpolarized and polarized images, shape from polarization, denoising, and environment dependency." + ], + "bbox": [ + 76, + 604, + 468, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 768, + 218, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spectro-polarimetric Image Dataset Several datasets have been introduced for analyzing polarization and spectral information. With the advent of trichromatic linear-polarization cameras, a line of work has attempted to acquire trichromatic linear-polarization images, ranging from a few objects and scenes [5, 11, 42, 52] to a large number of scenes for specific target applications such as reflection", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/52b8d9f67846fe527fa9ece3499e68b548dfedb7fb5477b0afee7295f3678d4e.jpg", + "image_caption": [ + "(a) Polarization ellipse", + "Figure 1. Polarization visualizations. (a) Polarization ellipse depicts the electric-field oscillation projected onto a plane tangent to the light propagation. (b) Poincaré sphere visualizes the polarization state of light on the normalized Stokes-vector axes $s_1', s_2', s_3'$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 689, + 243 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0457c3835359878177b937afd0c6fd7fdfb06f2eb2141d31f28c771e6afbf448.jpg", + "image_caption": [ + "(b) Poincaré sphere" + ], + "image_footnote": [], + "bbox": [ + 691, + 88, + 890, + 243 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "separation [40, 46] and glass segmentation [48]. Lapray et al. [39] acquire linear-polarization images for the near-infrared spectral band, albeit only on 10 objects. Fan et al. [19] acquire the first multi-spectral full-Stokes polarimetric dataset covering linear and circular states, while it only contains 64 flat objects captured in a lab environment. Our proposed datasets enables analyzing the statistics of real-world spectro-polarimetric images, which cannot be achieved by prior datasets. See Figure 2 for a comprehensive comparison.", + "bbox": [ + 496, + 330, + 890, + 481 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Applications of Spectro-polarimetric Imaging Spectropolarimetric information has been investigated for diverse vision and imaging tasks. Using linear-polarization images has found applications in shape reconstruction [4, 5, 7, 16, 21, 31, 41, 70], appearance acquisition [15, 36], removing reflections [37, 40, 46, 51, 59, 62], transparent-object segmentation [33, 48], seeing through scattering [20, 43, 68], and image enhancement [69]. Trichromatic Stokes images have been used for tone-mapping [12] and seeing through scattering [6]. Expanding into multi-spectral domain, spectral-polarimetric analysis has been applied to object recognition [13], skin analysis [67], dehazing [61], specular reflection inpainting [29], background segmentation [30] and tensor representation [65]. In addition to vision tasks, spectro-polarimetric imaging has been used for various biological applications, such as marsh vegetation classification [63], coastal wetland classification [55] and leaf nitrogen determination [44]. While the aforementioned studies demonstrate the benefits of using spectropolarimetric data, we believe that the full potential of spectro-polarimetric images is still locked by the absence of real-world spectro-polarimetric datasets.", + "bbox": [ + 496, + 500, + 890, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Background on Polarization", + "text_level": 1, + "bbox": [ + 500, + 844, + 759, + 861 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Polarization, the oscillation pattern of the electric field, can be represented using a Stokes vector, $\\mathbf{s} = [s_0,s_1,s_2,s_3]^\\intercal$", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "22099", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/13e1635d12e9d7a0ab526daad43f562a225d759bbb2b2efd7e4b0c3b19996a00.jpg", + "image_caption": [ + "Trichromatic Stokes dataset" + ], + "image_footnote": [], + "bbox": [ + 81, + 99, + 264, + 227 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/edbc326de1768d5be483da537c77cd563eccceec48977acfe1fa013262dfbaa7.jpg", + "image_caption": [ + "Hyperspectral Stokes dataset", + "(a) Dataset thumbnails visualized in sRGB" + ], + "image_footnote": [], + "bbox": [ + 267, + 99, + 468, + 228 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/26c811316f829440e74ae5d111e5657ae6b96943ab092d703b17f55f6db5d3cf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 250, + 263, + 330 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/032e0654b117d158e03bbc14625f5279e3edd9f367b03037dd01e6977a35ce16.jpg", + "image_caption": [ + "■ Scene-oriented" + ], + "image_footnote": [], + "bbox": [ + 282, + 247, + 366, + 320 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b1e646f6904aaf113902dabf68f5d29e69c6090a0f8a8afecd857a21d9338792.jpg", + "image_caption": [ + "Object-oriented" + ], + "image_footnote": [], + "bbox": [ + 382, + 248, + 460, + 319 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/19ebf8999cde6a346e5c3cdc972d9e6931b00989a9e9b00e1cbfcedf2d4fbca2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 340, + 263, + 436 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3d9ba8fa0953e01eef79e98487764757c16f3b55ff49e48d1455b9d7e41f2b54.jpg", + "image_caption": [ + "(b) Dataset Statistics", + "Figure 2. Spectro-polarimetric image datasets. We present trichromatic and hyperspectral Stokes datasets of which thumbnails are shown in (a) and label statistics in (b). The table shown on the right compares our datasets with existing spectro-polarimetric datasets. Ours are the only datasets that encompass both linear (LP) and circular (CP) polarization over multiple of spectral bands for diverse real scenes." + ], + "image_footnote": [], + "bbox": [ + 282, + 340, + 366, + 438 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/23477c263c2f4299234d9d3aaea71ab21b6650bb1c5dcc3f8bcdb26d81b1a147.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 379, + 340, + 462, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$s_0$ denotes the total intensity, $s_1$ and $s_2$ describe the differences in the intensity of linearly-polarized components at orientations of $0^{\\circ} / 90^{\\circ}$ and $45^{\\circ} / -45^{\\circ}$ , respectively. $s_3$ is the difference in intensity between right- and left-circularly polarized components. Figure 1 shows two visualization methods for polarization, the polarization ellipse and Poincaré sphere. Polarization ellipse can be described in terms of the orientation angle $\\psi$ and ellipticity $\\chi$ with respect to the projected Stokes vector $\\mathbf{x}$ and $\\mathbf{y}$ axes [9]. The Poincaré sphere visualizes polarization in a three-dimensional space, using the normalized Stokes-vector elements relative to the total intensity: $s_1' = s_1 / s_0$ , $s_2' = s_2 / s_0$ , $s_3' = s_3 / s_0$ . To effectively analyze a Stokes vector, one can compute the degree of polarization (DoP) denoted as $\\rho$ , the angle of linear polarization (AoLP) represented by $\\psi$ , and the ellipticity angle given by $\\chi$ , that is", + "bbox": [ + 75, + 500, + 468, + 742 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\rho = \\frac {P}{s _ {0}}, \\psi = \\frac {1}{2} \\arctan \\left(\\frac {s _ {2}}{s _ {1}}\\right), \\chi = \\frac {1}{2} \\arctan \\left(\\frac {s _ {3}}{L}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 750, + 468, + 782 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $P = \\sqrt{s_1^2 + s_2^2 + s_3^2}$ and $L = \\sqrt{s_1^2 + s_2^2}$ . We also use the polarimetric visualization method proposed by Wilkie et al. [60] using DoP, AoLP, and chirality of polarization (CoP). CoP describes the left- or right-handedness of the circularly polarized component, which is related to $\\chi$ . Finally, the Mueller matrix $\\mathbf{M} \\in \\mathbb{R}^{4 \\times 4}$ describes the change of a Stokes vector: $\\mathbf{s}_{\\mathrm{out}} = \\mathbf{M}\\mathbf{s}_{\\mathrm{in}}$ , where $\\mathbf{s}_{\\mathrm{in}}$ and $\\mathbf{s}_{\\mathrm{out}}$", + "bbox": [ + 75, + 792, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/7596b707040f160d0cbb317ea37b76856477c49a4a70639ea615865919ac5c86.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DatasetPolar.# of bandsScene countScene diversity
[41]LP1522Outdoor scenes
[5]LP1300Indoor objects
[39]LP610Indoor objects
[52]LP340Indoor objects
[11]LP33Indoor multiview
[11]LP32Synthetic multiview
[22]LP36Indoor multiview
[40]LP3807Reflective objects
[42]LP3500Outdoor scenes
[36]LP344,300Synthetic
[46]LP33,200Reflective objects
[48]LP34,500Transparent objects
[38]LP32,000Indoor/outdoor scenes
[19]LP, CP1867Flat objects
[34]LP, CP214Synthetic multiview
[34]LP, CP214Indoor/outdoor multiview
Ours (RGB)LP, CP32,022Indoor/outdoor scenes
Ours (HS)LP, CP21311Indoor/outdoor scenes
", + "bbox": [ + 478, + 101, + 885, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "are the input/output Stokes vectors. For more details on polarization, we refer to the book by Collett [9].", + "bbox": [ + 498, + 500, + 890, + 530 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Spectro-polarimetric Dataset", + "text_level": 1, + "bbox": [ + 500, + 547, + 766, + 565 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce a trichromatic Stokes dataset comprising 2,022 Stokes images and a hyperspectral Stokes dataset with 311 Stokes images at 21 spectral channels. Both datasets cover natural real-world indoor and outdoor scenes. Each Stokes image is accompanied by four labels: (1) the environment (indoor or outdoor), (2) the illumination condition, including clear or cloudy sunlight and white or incandescent light, (3) the time of image capture, (4) the scene type, distinguishing between object-oriented and scene-oriented. Figure 2 shows thumbnails, statistics, and comparison of our datasets to existing ones. Prior datasets suffer from a narrow range of scenes, restricted illumination conditions, linear polarization only, and fewer images.", + "bbox": [ + 496, + 573, + 890, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Acquisition We acquire the datasets using two imaging systems depicted in Figure 3(a), proposed and developed by previous studies [34, 56]. First, the trichromatic Stokes camera by Tu et al. [56] incorporates on-sensor quarterwave plates (QWPs) and linear polarizers (LPs) [9]. This allows for single-shot capture of trichromatic Stokes images, enabling convenient data collection on diverse scenes. The", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "22100", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/19b199622aad5f1f0286ed59e52e074e01b05ee7e5bb4d2d2a796dda8d053be9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 76, + 85, + 251, + 180 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ff600c947f52f981e2e8cabc40296abca33c09127f2d2b879a087f925480e509.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 254, + 87, + 455, + 194 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/113732ddce3ed700a5d87709eca0dab7d6e5a3c4c4ce7dca9f730212485946d7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 462, + 85, + 892, + 191 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/51c1daca8ee27d0408ea3929a31b8ab3b783c93ac0b754f1a8eb077c64df81eb.jpg", + "image_caption": [ + "(a) Stokes imaging system" + ], + "image_footnote": [], + "bbox": [ + 76, + 180, + 251, + 311 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/72d0427d17dddaf003cfc2ca4220ce06beae2140ca6224695369adbb84a09795.jpg", + "image_caption": [ + "(b) Camera response function" + ], + "image_footnote": [], + "bbox": [ + 251, + 205, + 454, + 311 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/be0c6e15c037540c96629bd1986b5bc3349efa8b2c3731e885ee8671eca99f4f.jpg", + "image_caption": [ + "(c) Multi-channel polarimetric images", + "Figure 3. Acquisition of spectro-polarimetric images. We capture spectro-polarimetric images using (a) trichromatic and hyperspectral Stokes cameras [34, 57]. (b) Camera response functions. (c) Reconstructed raw Stokes images per each spectral channel." + ], + "image_footnote": [], + "bbox": [ + 454, + 199, + 892, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "resolution of a trichromatic Stokes image is 1900 (height) $\\times$ 2100 (width) $\\times$ 4 (Stokes elements) $\\times$ 3 (RGB). Second, the hyperspectral Stokes camera from Kim et al. [34] captures images by sequentially scanning 21 spectral channels from $450\\mathrm{nm}$ to $650\\mathrm{nm}$ in $10\\mathrm{nm}$ increments with a LCTF which functions as a LP. For each spectral channel, we capture images by rotating a QWP. The resolution of a hyperspectral Stokes image is 512 (height) $\\times$ 612 (width) $\\times$ 4 (Stokes elements) $\\times$ 21 (wavelengths).", + "bbox": [ + 75, + 362, + 468, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spectro-polarimetric Image Formation Using the two imaging systems, we capture raw images from which a per-pixel Stokes vector for each spectral channel is reconstructed. We introduce an unified image formation model that can be applied to both cameras. Suppose a light ray with a Stokes vector $\\mathbf{s}_{\\lambda}$ at wavelength $\\lambda$ impinges on a Stokes camera. As the light passes through polarization filters modeled by the Mueller matrix $\\mathbf{M}(\\Theta)$ , its Stokes vector transforms. $\\Theta$ denotes the polarization-filter configuration. The camera sensor then captures light intensity, represented by the first element of the Stokes vector. The recorded intensity, $I_{c}(\\Theta)$ , at a spectral channel $c$ and polarimetric filter configuration $\\Theta$ , is described by", + "bbox": [ + 75, + 517, + 468, + 715 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} I _ {c} (\\Theta) = \\left[ \\int \\Omega_ {c, \\lambda} \\mathbf {M} _ {c} (\\Theta) \\mathbf {s} _ {\\lambda} d \\lambda \\right] _ {0} \\\\ = \\left[ \\mathbf {M} _ {c} (\\Theta) \\int \\Omega_ {c, \\lambda} \\mathbf {s} _ {\\lambda} d \\lambda \\right] _ {0} \\\\ = \\left[ \\mathbf {M} _ {c} (\\Theta) \\mathbf {s} _ {c} \\right] _ {0}, \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 723, + 468, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Omega_{c,\\lambda}$ is the spectral transmission per channel at wavelength $\\lambda$ shown in Figure 3(b). $[x]_0$ denotes the first-element of the Stokes vector $x$ , which is the total intensity. For a spectral channel $c$ , $\\mathbf{M}_c$ is the Mueller matrix of the polarization-modulating optics, and $\\mathbf{s}_c$ is the Stokes vector.", + "bbox": [ + 75, + 825, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For polarization modulation, both cameras utilize a QWP and a LP, yielding the Mueller matrix", + "bbox": [ + 500, + 362, + 890, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {M} _ {c} (\\Theta) = \\mathbf {C} _ {c} \\mathbf {Q} _ {c} \\left(\\theta_ {1}\\right) \\mathbf {P} _ {c} \\left(\\theta_ {2}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 405, + 890, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{C}_c$ is the error-compensating calibration matrix [34, 57]. $\\mathbf{Q}_c$ and $\\mathbf{P}_c$ are the QWP and LP Mueller matrices [9], respectively. The set $\\Theta = \\{\\theta_1,\\theta_2\\}$ denotes the corresponding angles of the QWP fast axis and the LP polarization axis, which is set for accurate Stokes vector reconstruction [34, 57]. Lastly, we determine the per-channel Stokes vector $\\mathbf{s}_c$ by solving the least-squares problem", + "bbox": [ + 496, + 433, + 892, + 540 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {s} _ {c}} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {| \\Theta |} \\left(I _ {c} (\\Theta_ {i}) - \\left[ \\mathbf {M} (\\Theta_ {i}) \\mathbf {s} _ {c} \\right] _ {0}\\right) ^ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 551, + 890, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For the hyperspectral Stokes camera, we use four configurations with the rotating QWP. For the trichromatic Stokes camera, the fixed micro-filter setup shown in Figure 3(a) gives four/eight configurations for the (red, blue) channels and the green channel, respectively.", + "bbox": [ + 496, + 604, + 890, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Figure 3(c) shows the reconstructed Stokes images. A Stokes vector is physically-valid if DoP meets the following inequality: $0 \\leq \\rho \\leq 1$ . $99\\%$ of the reconstructed Stokes vectors in our datasets satisfy this condition. For the following analysis, we filter out Stokes vectors violating the DoP condition and the unstable Stokes vectors reconstructed from saturated/underexposed pixel intensity.", + "bbox": [ + 496, + 680, + 890, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "5. Dataset Analysis", + "text_level": 1, + "bbox": [ + 500, + 799, + 663, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Noise and Intensity Denoising Spectro-polarimetric images are susceptible to noise due to the low-light throughput of spectral and polarimetric filters. Our datasets are not exempt from these issues. To assess noise in Stokes images, we capture and average 100 images of a scene shown", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "22101", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/08a2bf439be10d2d975b8ee93016b8c016d5ea5f7d4913204f91a2f303597e8f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 98, + 87, + 279, + 202 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/80f030427ce07d818d617b0da1cf757c7cc1e75f9edc54324cf06a32d2a43b33.jpg", + "image_caption": [ + "(a) Top 40 PCA bases of hyperspectral Stokes vector components" + ], + "image_footnote": [], + "bbox": [ + 282, + 88, + 464, + 204 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/34b839a8c8e3e3ec7e213bf82c2938b6b1a89004b2d1c75fd615cbd341d0c16c.jpg", + "image_caption": [ + "(c) Proportion of variance (log scale)" + ], + "image_footnote": [], + "bbox": [ + 475, + 89, + 658, + 229 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/6beafc6405626c62bf4ed5c888bdf8ffcda60596283bb6a3fea90671190fe0eb.jpg", + "image_caption": [ + "(d) BPP and MSE of PCA" + ], + "image_footnote": [], + "bbox": [ + 663, + 88, + 870, + 227 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3d7bc3013b168d2a9b0d2f675ddde8a6163fc7b1ded1c495c8fdefe7447e86b1.jpg", + "image_caption": [ + "(b) Qualitative results (DoP/AoLP)" + ], + "image_footnote": [], + "bbox": [ + 96, + 217, + 464, + 392 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3bb3146713a1a4ba90e0800fe26a29ddcdc414aef0b2c8badba6fab5b7517dd4.jpg", + "image_caption": [ + "(e) Training PSNR value" + ], + "image_footnote": [], + "bbox": [ + 475, + 257, + 663, + 388 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d7c04bd6be08d52be784f8cec484e93bd3bb43e18ca20c5b43fc0b2e3e06df62.jpg", + "image_caption": [ + "(f) BPP and MSE of INR" + ], + "image_footnote": [], + "bbox": [ + 666, + 253, + 870, + 388 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4f172d653e4cea0ced0a23beace1adcba303ca82368310ed409a59faa406b7ef.jpg", + "image_caption": [ + "Figure 4. Efficient spatio-spectral-polarimetric representations. (a) PCA basis of the hyperspectral Stokes dataset in sRGB. (b) Qualitative results of PCA and INR compared to single-shot denoising [66] at $550\\mathrm{nm}$ . (c) Proportion of variance with respect to each PCA basis in order, $\\log (\\sigma_i^2 / \\sum_n \\sigma_n^2)$ , where $\\sigma_i$ denotes standard deviation of the $i$ -th basis. (d) BPP and MSE analysis of PCA with respect to the number of PCA bases. (e) Training PSNR curve of INR. (f) BPP and MSE value of INR with respect to the number of MLP layers." + ], + "image_footnote": [], + "bbox": [ + 76, + 468, + 468, + 589 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/545135a5cc91a4ad03c0432b1fdb5965dc5229932718c1f143c2cf662300e0ed.jpg", + "image_caption": [ + "Figure 5. Noise in Stokes images and intensity denoising. (a) Stokes vector $s_1$ reconstructed from a single-shot, single-shot with a learned intensity denoiser [66], and burst imaging (Pseudo GT) averaged over 100 shots. (b) Reconstruction accuracy of a Stokes image with varying number of averaged images. (c) Reconstruction accuracy of normalized Stokes elements with and without intensity denoising." + ], + "image_footnote": [], + "bbox": [ + 76, + 590, + 468, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "in Figure 3(c) for each polarization configuration $\\Theta$ . From these averaged images, we reconstruct pseudo ground-truth Stokes image, shown in Figure 5(a). Figure 5(b) reports the MSE and PSNR of reconstructed Stokes images with respect to the number of averaged images. To achieve a", + "bbox": [ + 75, + 824, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PSNR exceeding $35\\mathrm{dB}$ , we need to average over 4/25 shots for the trichromatic/hyperspectral Stokes cameras, indicating lower SNR of the hyperspectral Stokes dataset. We find that state-of-the-art learning-based intensity denoising methods, such as KBNet [66], can effectively reduce noise for each polarization configuration, leading to accurate Stokes-vector reconstruction, despite lack of polarization images during training. For the denoised single-shot capture, we achieve a PSNR of $34.5\\mathrm{dB}$ , demonstrating the potential of using pretrained intensity restoration networks for Stokes imaging. Figure 5(c) shows PSNRs of reconstructed Stokes images per each spectral channel and normalized Stokes element. With the intensity denoising, we find that the PSNR significantly increases for $s_1$ , $s_2$ , and $s_3$ .", + "bbox": [ + 496, + 472, + 892, + 684 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Efficient Spatio-spectral-polarimetric Representations Each pixel in a hyperspectral Stokes image contains a Stokes vector for every spectral channel, leading to a total of $21 \\times 4 \\times 32$ bits using single-precision floating format. This results in a bit-per-pixel (BPP) value of 2,688, equating to $100\\mathrm{MB}$ for storing a single hyperspectral Stokes image of $512 \\times 612$ pixels. Given the substantial memory required to store a spectro-polarimetric image, we investigate efficient representations of real-world spatio-spectral-polarimetric data, for which we explore two methods: a PCA-based model and an implicit neural model.", + "bbox": [ + 496, + 704, + 890, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we apply PCA on non-overlapping hyperspectral Stokes patches. Figure 4(a) shows the 40 most significant", + "bbox": [ + 498, + 869, + 892, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "22102", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "PCA bases, revealing varied spatial and spectral features for each Stokes element: $s_0$ , $s_1$ , $s_2$ , $s_3$ . Notably, spatial structures are more evident in $s_0$ , while $s_1$ , $s_2$ , $s_3$ shows spectral features, suggesting a stronger correlation between spectrum and polarization than spatial features. To visualize hyperspectral intensity, we convert it to sRGB, which means that the same sRGB color may originate from different spectra. Figure 4(c) shows the variance of the coefficients for the top 200 PCA bases, indicating that spati-spectral-polarimetric data can indeed be compressed. This is further evidenced by Figure 4(d), which shows the reconstruction error and BPP when varying number of PCA bases used to recreate a hyperspectral Stokes image. Using $2.22\\mathrm{MB}$ coefficients adequately represents a $100\\mathrm{MB}$ hyperspectral Stokes image as shown in Figure 4(b), exhibiting a high compression rate with the reconstruction error of $2.69\\times 10^{-5}$ . See the Supplemental Document for further details on PCA analysis.", + "bbox": [ + 75, + 90, + 472, + 362 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Second, we devise an INR for hyperspectral Stokes images by modifying NeSpoF [34]. The original NeSpoF architecture models a volumetric hyperspectral Stokes field. Here, instead, we aim to represent a hyperspectral Stokes image. Specifically, our INR, modeled by an MLP $F_{\\gamma}$ , outputs the Stokes vector $s$ for a given pixel position $p_x, p_y$ and spectral channel index $c$ , that is", + "bbox": [ + 75, + 363, + 472, + 468 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {s} = F _ {\\gamma} \\left(p _ {x}, p _ {y}, c\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 479, + 468, + 496 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\gamma$ is the network parameters. We fit the MLP to a hyperspectral Stokes image by minimizing the reconstruction loss between the network output and the hyperspectral Stokes image. The training curve is shown in Figure 4(e). Figure 4(f) shows the reconstruction error and BPP of our INR with respect to varying number of the MLP layers. With just 8 layers corresponding to a BPP of 60, we achieve a converged reconstruction error of $1.90 \\times 10^{-5}$ , resulting in just $2.22\\mathrm{MB}$ of network parameters to represent a $100\\mathrm{MB}$ hyperspectral Stokes image. See Supplemental Document for architecture details.", + "bbox": [ + 75, + 503, + 472, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Both PCA and INR experiments validate that a natural spectro-polarimetric image is compressible. PCA provides PCA basis vectors that can be applied to any instance, however with a lower reconstruction accuracy than INR. INR is overfitted to a single instance, while higher reconstruction accuracy can be achieved. These representations are also beneficial for denoising spectral-polarimetric images, as shown in Figure 4(b), which even outperforms the learning-based intensity denoiser [66].", + "bbox": [ + 75, + 671, + 472, + 808 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Polarized and Unpolarized Intensity We decompose hyperspectral Stokes images into the polarized images $P = \\sqrt{s_1^2 + s_2^2 + s_3^2}$ and unpolarized images $U = s_0 - P$ per each spectral channel. Figure 6(a) shows specular reflections such as the glow of leather sofa separated into po", + "bbox": [ + 76, + 824, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dad01d455c5f223d5a00ea97a0dacbfdbcc6d1166bcdf03964ce71b26454c12e.jpg", + "image_caption": [ + "(a) Separation into polarized and unpolarized light" + ], + "image_footnote": [], + "bbox": [ + 522, + 87, + 870, + 257 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/991865a28e7ee694ca58927b5f1f4dc8c32ade4541d9ad95ddfe5e6c0caeac4d.jpg", + "image_caption": [ + "(b) Intensity distribution by polarization", + "Figure 6. Polarized and unpolarized light distributions. (a) Separation into polarized and unpolarized light. (b) Intensity distributions for polarized and unpolarized components. (c) Variance of PCA basis of polarized and unpolarized intensity across spectral channel." + ], + "image_footnote": [], + "bbox": [ + 504, + 268, + 697, + 380 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4530fbd91038d32a60e6d4744cc920029ae875b58edc4504380f3e22cdea193a.jpg", + "image_caption": [ + "(c) Variance of basis by polarization" + ], + "image_footnote": [], + "bbox": [ + 700, + 268, + 890, + 378 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "larized light. Note that the polarized image typically encodes the illumination colors for dielectric surfaces. Figure 6(b) reveals that the intensity distributions of polarized light, obtained from the entire hyperspectral Stokes dataset, is skewed towards low and high-intensity values compared to the unpolarized light. This is because polarized images mostly contain specular reflections, which is sparsely distributed and has high intensity values. We then compute the variance of the PCA bases for polarized intensity along the spectral channel. Figure 6(c) highlights that the spectral variance for polarized intensity is lower than that of unpolarized intensity. We speculate that the color of polarized light lies in a lower dimensional space than that of unpolarized light, since diffuse reflection with diverse spectral variations is mostly captured by unpolarized light, making the spectral variation of unpolarized light more pronounced.", + "bbox": [ + 496, + 482, + 893, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Stokes Vector Distributions in Natural Stokes Images Next, we analyze the distribution of all Stokes vectors in our Stokes dataset. Figure 7 shows the histograms of Stokes elements $s_0$ , $s_1$ , $s_2$ , $s_3$ across all spectral channel. We find that the distributions of Stokes elements $(s_1, s_2, s_3)$ have symmetric shapes of positive and negative sides. Stokes elements of $s_1$ and $s_2$ have similar shapes meaning that the directions of linearly-polarized light are equally distributed in natural images. The circular component $s_3$ is more condensed near zero than the linear elements, resulting in a", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "22103", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a01b8caf2b4dd5300486647aa5478efe9cb28c0187fcaa651b893262529f03d9.jpg", + "image_caption": [ + "(a) Visualization of Stokes vector" + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 468, + 179 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1b62e1ba99aa86b84970a188f2bccebcf98ef6f76f7eed7bf9b0b7d711a59ea9.jpg", + "image_caption": [ + "(b) Stokes vector distribution", + "Figure 7. Stokes-vector distributions. (a) Stokes images of $s_1$ , $s_2$ , and $s_3$ at the green channel. (b) Stokes-vector distributions of $s_0$ , $s_1$ , $s_2$ and $s_3$ for trichromatic and hyperspectral datasets." + ], + "image_footnote": [], + "bbox": [ + 76, + 194, + 459, + 321 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "higher peak both in trichromatic and hyperspectral datasets. This indicates that pixels are often more linearly polarized than circularly polarized. Refer to the Supplemental Document for further analysis.", + "bbox": [ + 75, + 398, + 468, + 460 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Gradient Analysis of Stokes Images Gradient distribution of images has been often used as priors for image-based applications including image restoration, understanding, and editing. Here, we perform gradient analysis of Stokes and polarization-feature images. Figure 8(b) shows that the gradient of Stokes and normalized Stokes vectors exhibits a similarity to Hyper-Laplacian priors, commonly used to describe the gradient of natural intensity-images. An interesting finding is that total intensity $s_0$ has more high-gradient values than the linear components of $s_1$ and $s_2$ , and the circular component $s_3$ has the lowest-value distribution.", + "bbox": [ + 75, + 477, + 468, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We analyze the gradient distributions of polarization features, including AoLP, degree of linear polarization (DoLP), degree of circular polarization (DoCP), and CoP. DoLP and DoCP are computed as $\\mathrm{DoLP} = \\sqrt{s_1^2 + s_2^2} / s_0$ and $\\mathrm{DoCP} = |s_3| / s_0$ respectively. To compute the gradient of AoLP images, we consider the angular wrapping property. That is, AoLP has a range from $-\\frac{\\pi}{2}$ to $\\frac{\\pi}{2}$ and the AoLPs of $-\\frac{\\pi}{2}$ and $\\frac{\\pi}{2}$ are identical. Thus, if the gradient exceeds $\\frac{\\pi}{2}$ , we estimate the gradient as $\\nabla \\mathrm{AoLP} - \\pi \\times \\mathrm{sign}(\\nabla \\mathrm{AoLP})$ , where $\\nabla$ is the gradient operator and $\\mathrm{sign}$ is the sign operator that returns 1 if positive, otherwise $-1$ . Figure 8(c) shows that the gradients of AoLP are generally higher than DoLP and DoCP. This implies that sparsity in the measurement gradient is milder for AoLP than DoLP and DoCP. DoLP and DoCP have shapes similar to HyperLaplacian priors while DoCP is sharper than DoLP. The", + "bbox": [ + 75, + 659, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/61e5db7117b492ef3307d3561460bb1b5ca2f541635034ad169d92736f6b5da9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 87, + 890, + 166 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/29dc883bbc282b415441de40ea5ff281a4bbcf3562cd2fc154da5dbcf1643f4d.jpg", + "image_caption": [ + "(a) Visualization of polarization features and gradients" + ], + "image_footnote": [], + "bbox": [ + 500, + 166, + 890, + 250 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d54bb3e031ed7d9baf9ed315dd7fad00c38c72bc55c26acd0ed1883b4bdd850d.jpg", + "image_caption": [ + "(b) Gradient distributions of Stokes vector" + ], + "image_footnote": [], + "bbox": [ + 500, + 263, + 890, + 377 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/58ecf995f2c55d4b12b3915f358de49bde2b5274f8f1632542dd64ce5c5fe6f0.jpg", + "image_caption": [ + "(c) Gradient distributions of polarization features", + "Figure 8. Gradient analysis of Stokes images. (a) Visualization of AoLP, DoLP, DoCP and CoP values and their gradients. Examining the log probability of the gradient for (b) Stokes vectors $s_0$ , $s_1$ , $s_2$ , $s_3$ and normalized Stokes vectors $s_1'$ , $s_2'$ , and $s_3'$ , and (c) polarization features including DoLP, DoCP, AoLP and CoP." + ], + "image_footnote": [], + "bbox": [ + 500, + 391, + 890, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "gradient of CoP shows symmetric distributions for right-circular and left-circular directions. Unlike AoLP, the probability decreases as the gradient approaches extreme values. The difference in tendency between linear-polarization and circular-polarization features, as well as their distributions, means that we need distinct priors for each polarization feature, emphasizing the importance of a full Stokes dataset that measure not only linear but also circular polarization.", + "bbox": [ + 496, + 609, + 890, + 731 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Shape from Polarization and Spectral Channels Methods that recover shape from polarization, SfP, have made rapid progress in the last decade. SfP aims to extract normals by analyzing the normal-dependent polarization change of reflected light. Specifically, SfP analyzes the DoP and AoLP based on Fresnel theory [9], which describes the polarization change of light upon reflection and transmission at a smooth surface [32, 41]. Here, we analyze an overlooked problem in SfP: the spectral dependency of estimated normals. Surface normals, as a geometric sur", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "22104", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5657ad2421673cac8001aaf59c93ff875ca873b6224563bdbd132049f26a25a4.jpg", + "image_caption": [ + "(a) Denoised Trichromatic" + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 189, + 152 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f22eb145d0a294366f5655e9d0af20f39212c25da859fdecab1bade01696da6d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 192, + 88, + 282, + 151 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0fbe3298a70bc7186f32306b70c80c2c42fbc1cbb597cd9d2fec78b676b45013.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 284, + 88, + 374, + 151 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3218d759c7241c157d030108f59e89d8e9e4ce6cdc64d678b564676928f9308c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 377, + 88, + 467, + 151 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/308710d00d5f81abf6bb5c4ae00b80a74bceaef40f5086a241fa4a35c5950877.jpg", + "image_caption": [ + "(b) Normal map from", + "denoised R channel", + "(c) Normal map from", + "(e) Denoised Trichromatic dataset", + "Figure 9. Spectral dependency of conventional SFP method. (a) Trichromatic Stokes image and estimated surface normals [41] for each red, green, and blue spectral channels shown in (b), (c), and (d). Graphs (e) and (f) show the probability distributions of standard deviation of normal component $x$ , $y$ , and $z$ along the spectral channels for both datasets." + ], + "image_footnote": [], + "bbox": [ + 91, + 161, + 287, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9452f3243c68fd8999f89e358f29566e0c7aab49b262ca84910c1d1a97b7254a.jpg", + "image_caption": [ + "(d) Normal map from", + "(f) Denoised Hyperspectral dataset" + ], + "image_footnote": [], + "bbox": [ + 287, + 161, + 467, + 271 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "face property, should be consistent regardless of the input spectral channels used for SfP. In Figure 9, we test the state-of-the-art SfP method by Lei et al. [41], designed for in-the-wild scenes. The evaluation results on our normalized Stokes dataset clearly reveal that normal maps reconstructed from different spectral channels exhibit variations. We compute the standard deviations of spectral variations for each $x$ , $y$ , and $z$ component of the estimated normals. Figures 9(e) and (f) show the probability distributions of the standard deviation, highlighting the large variations in the estimated normals for both hyperspectral and trichromatic datasets. Interestingly, the $x$ and $y$ components of normals show larger standard deviations than the $z$ component. This implies that the spectral variation of DoP, which determines the $z$ component, has less impact on the distribution than that of AoLP, which governs the $x$ and $y$ components.", + "bbox": [ + 75, + 390, + 468, + 632 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Environment Dependency Figure 10 shows the Poincaré spheres projected onto the $s_1' - s_2'$ and $s_1' - s_3'$ planes for the three data labels: Indoor, Sunlight and Cloudy. Sunlight is known to contain more circularly polarized light compared to other artificial lighting [25]. As shown in Figure 10(a), Stokes vectors are distributed more widely across $s_3'$ axis under sunlight compared with Indoor scene. In addition, we find that DoCP is distributed at higher values for the sunlight compared to the indoor: pixels with DoCP over 0.5 are rarely observed in indoor scenes. This is also confirmed in the example $s_3$ images for indoor and sunlight scenes.", + "bbox": [ + 75, + 657, + 467, + 823 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Another interesting finding is that cloudy or sunny illumination result in different polarization statistics. Figure 10(a) shows that Stokes vectors of cloudy scenes are more concentrated near the origin, meaning that light is more depolarized compared to light under clear sunlight.", + "bbox": [ + 75, + 824, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/63b612cd0e0f15640d6407d849c395089991ff56167d21b449243f5ff6446d42.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 509, + 88, + 630, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/82591d67cdd8a1f66b69f5f2e444fe0de06c800ba38f2ca2670db0805e437b49.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 88, + 743, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0d7dcc985cac6896475fdffbf4b35fe4671f9c4518e362bd33aa4b2c5787b0ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 88, + 883, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2bb0bb8175d4206daddfe686d7d56d98912f8dd2bc2429dda1cd9390db2246fa.jpg", + "image_caption": [ + "(a) Poincaré sphere projections" + ], + "image_footnote": [], + "bbox": [ + 509, + 185, + 630, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/7cd2fe00c56bd23f57614e679f928bbd9d335711e497468de83d7ccd173cfe87.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 632, + 186, + 743, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6056ddedb9a42638f1001f0103a1a295b14877b510310235de00fb6a82588ca9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 746, + 186, + 883, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0f91a0870b5311cb4aac073d6c8db13c1f1d2009869b5f8a7c4c4fcdf98f8cb6.jpg", + "image_caption": [ + "(b) DoCP distribution", + "Figure 10. Environment dependency. (a) Projected Poincaré spheres onto the $s_1' - s_2'$ and $s_1' - s_3'$ planes with respect to dataset labels. Colorbar is based on the normalized pixel count. (b) DoCP distributions for indoor and sunlight categories. (c) Example $s_3$ images." + ], + "image_footnote": [], + "bbox": [ + 500, + 282, + 638, + 372 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/390e8b16dc03c769dd2ac833f8e3b863298cd9ab2d80b9bf861c2ab76b23cb51.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 640, + 282, + 750, + 369 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4b32580a78ab7b975e3cb4c2e23a6ac873342e82120b5bf2c005cd6a41f042cc.jpg", + "image_caption": [ + "(c) $S_{3}$ visualization" + ], + "image_footnote": [], + "bbox": [ + 751, + 281, + 890, + 371 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This is aligned with previous studies [24, 58] that report the impact of cloud-particle scatterings on light depolarization.", + "bbox": [ + 498, + 479, + 890, + 510 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 529, + 617, + 544 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we have introduced a trichromatic and hyperspectral Stokes image dataset that encompasses diverse natural scenes and various illumination conditions, totaling more than 2,333 scenes. We analyze the empirical distribution of the Stokes vectors of natural spectropolarimetric images. To efficiently represent spati-spectral-polarimetric data, we devise a PCA-based model and an implicit neural representation. We further provide detailed analysis on Stokes gradient distributions, denoising characteristics, spectral dependency of SfP, and environment dependency. As such, our work provides a foundation for future research on spectral-polarimetric imaging and vision.", + "bbox": [ + 496, + 555, + 890, + 751 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements We thank Onur Akkaya for helpful discussion. Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, 2022R1A6A1A03052954). Felix Heide was supported by an NSF CAREER Award (2047359), a Packard Foundation Fellowship, a Sloan Research Fellowship, a Sony Young Faculty Award, a Project X Innovation Award, and an Amazon Science Research Award.", + "bbox": [ + 496, + 779, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "22105", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Springer, 2020. 2" + ], + "bbox": [ + 78, + 90, + 468, + 823 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "22108", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_model.json b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..118914fef151280e5e011d10683659d8b9efcfb1 --- /dev/null +++ b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_model.json @@ -0,0 +1,2829 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.279, + 0.131, + 0.693, + 0.177 + ], + "angle": 0, + "content": "Spectral and Polarization Vision: Spectro-polarimetric Real-world Dataset" + }, + { + "type": "text", + "bbox": [ + 0.173, + 0.203, + 0.768, + 0.24 + ], + "angle": 0, + "content": "Yujin Jeon\\(^{1,*}\\) Eunsue Choi\\(^{1,*}\\) Youngchan Kim\\(^{1}\\) Yunseong Moon\\(^{1}\\) Khalid Omer\\(^{2}\\) Felix Heide\\(^{3}\\) Seung-Hwan Baek\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.285, + 0.249, + 0.686, + 0.269 + ], + "angle": 0, + "content": "\\(^{1}\\) POSTECH \\(^{2}\\) Meta \\(^{3}\\) Princeton University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.303, + 0.314, + 0.318 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.335, + 0.474, + 0.683 + ], + "angle": 0, + "content": "Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Many image datasets exist, consisting of trichromatic intensity images taken with RGB cameras, which are designed to replicate human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although there are previous spectro-polarimetric datasets, they have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets, consisting of trichromatic Stokes images and hyperspectral Stokes images. These datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.713, + 0.21, + 0.729 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.739, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Recent progress in computer vision can be largely attributed to comprehensive studies of real-world image datasets, such as ImageNet [14]. Foundation models [1, 35, 53, 64] further underscore data significance. Most of these datasets comprise trichromatic intensity images, inspired by human visual perception, enabling machines to emulate human vision with trichromatic RGB cameras. As such, the datasets have facilitated the development of low-cost, camera-based autonomous agents capable of perceiving and interacting" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.304, + 0.892, + 0.38 + ], + "angle": 0, + "content": "with our world, as we do. However, the reliance on trichromatic intensity in existing image datasets also comes with inherent limitations for analyzing objects in depth. Examples include textureless surface, low-albedo objects, and transparent materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.383, + 0.893, + 0.656 + ], + "angle": 0, + "content": "Light possesses wave properties, including polarization and spectrum [9], which are not faithfully captured by trichromatic intensity imaging. While these properties are invisible to human, animals like honeybees and ants leverage the polarization and spectrum for navigation and other tasks. Horvath and Varju [25] provide diverse examples and mechanisms of spectral and polarimetric vision in animals. Partly drawing inspiration from nature, researchers have extended the analysis of spectrum and polarization to a variety of fields, including computer vision, robotics, and astronomy. This has spurred interest in polarimetric [7, 8, 38, 49] and hyperspectral imaging [2, 10, 28], and more recently, their integration into spectro-polarimetric imaging [3, 17, 18, 23, 26, 45, 47, 50, 54, 67]. Prior work using spectro-polarimetric images has shown potential for skin analysis [67], vegetation classification [63], shape reconstruction [27], object recognition [13], and segmentation [30, 55]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.902 + ], + "angle": 0, + "content": "There are existing spectro-polarimetric datasets, summarized in Figure 2, that have been invaluable for these analysis [19, 38, 39, 52] and training neural networks [4, 11, 22, 36, 40-42, 46, 48]. However, these datasets unfortunately do not capture the diversity of real-world spectropolarimetric images as effectively as their trichromatic intensity counterparts do. They typically suffer from limited object, scene, and illumination diversity, contain primarily linear polarization information, and offer a small number of images. To advance the field, we propose a comprehensive spectro-polarimetric dataset that encompasses: (1) Full Stokes polarimetric data, including both linear and circular polarization states, represented by Stokes vectors [9] for each pixel and wavelength. (2) A diverse range of spectral channels, facilitating in-depth exploration of the interplay between spectrum and polarization. (3) A broad array of" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.352, + 0.901 + ], + "angle": 0, + "content": "*These authors contributed equally to this work." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22098" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "real-world scenes, crucial for extracting meaningful statistics and relationships within spectro-polarimetric images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.122, + 0.47, + 0.348 + ], + "angle": 0, + "content": "To this end, we introduce two spectro-polarimetric datasets designed to cover real-world spectro-polarimetric scenes: a trichromatic Stokes dataset consisting of 2,022 images, and a hyperspectral Stokes dataset containing 311 images across 21 spectral channels. The trichromatic Stokes dataset covers a wider range of scenes thanks to its convenient capture setup and process. The hyperspectral Stokes dataset provides richer spectral-polarimetric information than the trichromatic Stokes dataset. Both datasets cover a variety of natural indoor and outdoor scenes. Each image in these datasets is annotated with four specific parameters: the type of environment (indoor or outdoor), the illumination conditions (clear/cloudy sunlight or white/yellow office light), the timestamp of capture, and the scene categorization (either object- or scene-oriented)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.471, + 0.59 + ], + "angle": 0, + "content": "Utilizing these datasets, we systematically analyze the statistics of real-world spectro-polarimetric images. We focus on examining statistics of Stokes vectors, in addition to the gradients and polarimetric attributes associated with them. We also conduct an analysis of unpolarized and polarized images derived through polarimetric decomposition. We then develop two efficient spatio-spectral-polarimetric representations using principal component analysis (PCA) and implicit neural representation (INR). These representations exhibit effective denoising capabilities and low memory footprints by exploiting the compressible structure of spectro-polarimetric images. We also analyze the impact of intensity denoising for spectro-polarimetric images, spectral dependency of shape-from-polarization methods, and environment dependency on the statistics of spectropolarimetric images." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.59, + 0.43, + 0.605 + ], + "angle": 0, + "content": "In summary, we make the following contributions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.605, + 0.469, + 0.679 + ], + "angle": 0, + "content": "- We introduce a trichromatic Stokes dataset and a hyperspectral Stokes dataset, featuring 2,333 diverse annotated indoor and outdoor scenes under various illumination conditions, which encompasses full-Stokes polarization data for linear and circular states." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.681, + 0.469, + 0.756 + ], + "angle": 0, + "content": "- We develop efficient spatio-spectral-polarimetric representations and analyze real-world spectro-polarimetric images, encompassing Stokes vectors and their gradients, unpolarized and polarized images, shape from polarization, denoising, and environment dependency." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.605, + 0.469, + 0.756 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.77, + 0.219, + 0.785 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Spectro-polarimetric Image Dataset Several datasets have been introduced for analyzing polarization and spectral information. With the advent of trichromatic linear-polarization cameras, a line of work has attempted to acquire trichromatic linear-polarization images, ranging from a few objects and scenes [5, 11, 42, 52] to a large number of scenes for specific target applications such as reflection" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.691, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.536, + 0.247, + 0.655, + 0.26 + ], + "angle": 0, + "content": "(a) Polarization ellipse" + }, + { + "type": "image", + "bbox": [ + 0.692, + 0.089, + 0.892, + 0.244 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.731, + 0.247, + 0.838, + 0.259 + ], + "angle": 0, + "content": "(b) Poincaré sphere" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.324 + ], + "angle": 0, + "content": "Figure 1. Polarization visualizations. (a) Polarization ellipse depicts the electric-field oscillation projected onto a plane tangent to the light propagation. (b) Poincaré sphere visualizes the polarization state of light on the normalized Stokes-vector axes \\( s_1', s_2', s_3' \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.331, + 0.892, + 0.482 + ], + "angle": 0, + "content": "separation [40, 46] and glass segmentation [48]. Lapray et al. [39] acquire linear-polarization images for the near-infrared spectral band, albeit only on 10 objects. Fan et al. [19] acquire the first multi-spectral full-Stokes polarimetric dataset covering linear and circular states, while it only contains 64 flat objects captured in a lab environment. Our proposed datasets enables analyzing the statistics of real-world spectro-polarimetric images, which cannot be achieved by prior datasets. See Figure 2 for a comprehensive comparison." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Applications of Spectro-polarimetric Imaging Spectropolarimetric information has been investigated for diverse vision and imaging tasks. Using linear-polarization images has found applications in shape reconstruction [4, 5, 7, 16, 21, 31, 41, 70], appearance acquisition [15, 36], removing reflections [37, 40, 46, 51, 59, 62], transparent-object segmentation [33, 48], seeing through scattering [20, 43, 68], and image enhancement [69]. Trichromatic Stokes images have been used for tone-mapping [12] and seeing through scattering [6]. Expanding into multi-spectral domain, spectral-polarimetric analysis has been applied to object recognition [13], skin analysis [67], dehazing [61], specular reflection inpainting [29], background segmentation [30] and tensor representation [65]. In addition to vision tasks, spectro-polarimetric imaging has been used for various biological applications, such as marsh vegetation classification [63], coastal wetland classification [55] and leaf nitrogen determination [44]. While the aforementioned studies demonstrate the benefits of using spectropolarimetric data, we believe that the full potential of spectro-polarimetric images is still locked by the absence of real-world spectro-polarimetric datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.845, + 0.76, + 0.862 + ], + "angle": 0, + "content": "3. Background on Polarization" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Polarization, the oscillation pattern of the electric field, can be represented using a Stokes vector, \\(\\mathbf{s} = [s_0,s_1,s_2,s_3]^\\intercal\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22099" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.09, + 0.242, + 0.099 + ], + "angle": 0, + "content": "Trichromatic Stokes dataset" + }, + { + "type": "image_caption", + "bbox": [ + 0.294, + 0.09, + 0.441, + 0.099 + ], + "angle": 0, + "content": "Hyperspectral Stokes dataset" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.1, + 0.266, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.166, + 0.229, + 0.376, + 0.239 + ], + "angle": 0, + "content": "(a) Dataset thumbnails visualized in sRGB" + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.1, + 0.47, + 0.229 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.25, + 0.264, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.248, + 0.367, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.383, + 0.249, + 0.461, + 0.32 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.322, + 0.368, + 0.332 + ], + "angle": 0, + "content": "■ Scene-oriented" + }, + { + "type": "image_caption", + "bbox": [ + 0.379, + 0.322, + 0.465, + 0.332 + ], + "angle": 0, + "content": "Object-oriented" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.341, + 0.264, + 0.438 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.341, + 0.367, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.38, + 0.341, + 0.464, + 0.439 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.214, + 0.44, + 0.32, + 0.45 + ], + "angle": 0, + "content": "(b) Dataset Statistics" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.453, + 0.892, + 0.496 + ], + "angle": 0, + "content": "Figure 2. Spectro-polarimetric image datasets. We present trichromatic and hyperspectral Stokes datasets of which thumbnails are shown in (a) and label statistics in (b). The table shown on the right compares our datasets with existing spectro-polarimetric datasets. Ours are the only datasets that encompass both linear (LP) and circular (CP) polarization over multiple of spectral bands for diverse real scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.47, + 0.743 + ], + "angle": 0, + "content": "\\(s_0\\) denotes the total intensity, \\(s_1\\) and \\(s_2\\) describe the differences in the intensity of linearly-polarized components at orientations of \\(0^{\\circ} / 90^{\\circ}\\) and \\(45^{\\circ} / -45^{\\circ}\\), respectively. \\(s_3\\) is the difference in intensity between right- and left-circularly polarized components. Figure 1 shows two visualization methods for polarization, the polarization ellipse and Poincaré sphere. Polarization ellipse can be described in terms of the orientation angle \\(\\psi\\) and ellipticity \\(\\chi\\) with respect to the projected Stokes vector \\(\\mathbf{x}\\) and \\(\\mathbf{y}\\) axes [9]. The Poincaré sphere visualizes polarization in a three-dimensional space, using the normalized Stokes-vector elements relative to the total intensity: \\(s_1' = s_1 / s_0\\), \\(s_2' = s_2 / s_0\\), \\(s_3' = s_3 / s_0\\). To effectively analyze a Stokes vector, one can compute the degree of polarization (DoP) denoted as \\(\\rho\\), the angle of linear polarization (AoLP) represented by \\(\\psi\\), and the ellipticity angle given by \\(\\chi\\), that is" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.751, + 0.469, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\rho = \\frac {P}{s _ {0}}, \\psi = \\frac {1}{2} \\arctan \\left(\\frac {s _ {2}}{s _ {1}}\\right), \\chi = \\frac {1}{2} \\arctan \\left(\\frac {s _ {3}}{L}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.793, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(P = \\sqrt{s_1^2 + s_2^2 + s_3^2}\\) and \\(L = \\sqrt{s_1^2 + s_2^2}\\). We also use the polarimetric visualization method proposed by Wilkie et al. [60] using DoP, AoLP, and chirality of polarization (CoP). CoP describes the left- or right-handedness of the circularly polarized component, which is related to \\(\\chi\\). Finally, the Mueller matrix \\(\\mathbf{M} \\in \\mathbb{R}^{4 \\times 4}\\) describes the change of a Stokes vector: \\(\\mathbf{s}_{\\mathrm{out}} = \\mathbf{M}\\mathbf{s}_{\\mathrm{in}}\\), where \\(\\mathbf{s}_{\\mathrm{in}}\\) and \\(\\mathbf{s}_{\\mathrm{out}}\\)" + }, + { + "type": "table", + "bbox": [ + 0.479, + 0.102, + 0.887, + 0.439 + ], + "angle": 0, + "content": "
DatasetPolar.# of bandsScene countScene diversity
[41]LP1522Outdoor scenes
[5]LP1300Indoor objects
[39]LP610Indoor objects
[52]LP340Indoor objects
[11]LP33Indoor multiview
[11]LP32Synthetic multiview
[22]LP36Indoor multiview
[40]LP3807Reflective objects
[42]LP3500Outdoor scenes
[36]LP344,300Synthetic
[46]LP33,200Reflective objects
[48]LP34,500Transparent objects
[38]LP32,000Indoor/outdoor scenes
[19]LP, CP1867Flat objects
[34]LP, CP214Synthetic multiview
[34]LP, CP214Indoor/outdoor multiview
Ours (RGB)LP, CP32,022Indoor/outdoor scenes
Ours (HS)LP, CP21311Indoor/outdoor scenes
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.501, + 0.892, + 0.531 + ], + "angle": 0, + "content": "are the input/output Stokes vectors. For more details on polarization, we refer to the book by Collett [9]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.767, + 0.566 + ], + "angle": 0, + "content": "4. Spectro-polarimetric Dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.772 + ], + "angle": 0, + "content": "We introduce a trichromatic Stokes dataset comprising 2,022 Stokes images and a hyperspectral Stokes dataset with 311 Stokes images at 21 spectral channels. Both datasets cover natural real-world indoor and outdoor scenes. Each Stokes image is accompanied by four labels: (1) the environment (indoor or outdoor), (2) the illumination condition, including clear or cloudy sunlight and white or incandescent light, (3) the time of image capture, (4) the scene type, distinguishing between object-oriented and scene-oriented. Figure 2 shows thumbnails, statistics, and comparison of our datasets to existing ones. Prior datasets suffer from a narrow range of scenes, restricted illumination conditions, linear polarization only, and fewer images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acquisition We acquire the datasets using two imaging systems depicted in Figure 3(a), proposed and developed by previous studies [34, 56]. First, the trichromatic Stokes camera by Tu et al. [56] incorporates on-sensor quarterwave plates (QWPs) and linear polarizers (LPs) [9]. This allows for single-shot capture of trichromatic Stokes images, enabling convenient data collection on diverse scenes. The" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22100" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.087, + 0.253, + 0.181 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.088, + 0.457, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.464, + 0.087, + 0.893, + 0.192 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.077, + 0.181, + 0.252, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.105, + 0.315, + 0.242, + 0.326 + ], + "angle": 0, + "content": "(a) Stokes imaging system" + }, + { + "type": "image", + "bbox": [ + 0.253, + 0.207, + 0.455, + 0.313 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.315, + 0.434, + 0.325 + ], + "angle": 0, + "content": "(b) Camera response function" + }, + { + "type": "image", + "bbox": [ + 0.455, + 0.2, + 0.893, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.315, + 0.753, + 0.326 + ], + "angle": 0, + "content": "(c) Multi-channel polarimetric images" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.33, + 0.893, + 0.358 + ], + "angle": 0, + "content": "Figure 3. Acquisition of spectro-polarimetric images. We capture spectro-polarimetric images using (a) trichromatic and hyperspectral Stokes cameras [34, 57]. (b) Camera response functions. (c) Reconstructed raw Stokes images per each spectral channel." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.363, + 0.47, + 0.501 + ], + "angle": 0, + "content": "resolution of a trichromatic Stokes image is 1900 (height) \\(\\times\\) 2100 (width) \\(\\times\\) 4 (Stokes elements) \\(\\times\\) 3 (RGB). Second, the hyperspectral Stokes camera from Kim et al. [34] captures images by sequentially scanning 21 spectral channels from \\(450\\mathrm{nm}\\) to \\(650\\mathrm{nm}\\) in \\(10\\mathrm{nm}\\) increments with a LCTF which functions as a LP. For each spectral channel, we capture images by rotating a QWP. The resolution of a hyperspectral Stokes image is 512 (height) \\(\\times\\) 612 (width) \\(\\times\\) 4 (Stokes elements) \\(\\times\\) 21 (wavelengths)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Spectro-polarimetric Image Formation Using the two imaging systems, we capture raw images from which a per-pixel Stokes vector for each spectral channel is reconstructed. We introduce an unified image formation model that can be applied to both cameras. Suppose a light ray with a Stokes vector \\(\\mathbf{s}_{\\lambda}\\) at wavelength \\(\\lambda\\) impinges on a Stokes camera. As the light passes through polarization filters modeled by the Mueller matrix \\(\\mathbf{M}(\\Theta)\\), its Stokes vector transforms. \\(\\Theta\\) denotes the polarization-filter configuration. The camera sensor then captures light intensity, represented by the first element of the Stokes vector. The recorded intensity, \\(I_{c}(\\Theta)\\), at a spectral channel \\(c\\) and polarimetric filter configuration \\(\\Theta\\), is described by" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.724, + 0.469, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} I _ {c} (\\Theta) = \\left[ \\int \\Omega_ {c, \\lambda} \\mathbf {M} _ {c} (\\Theta) \\mathbf {s} _ {\\lambda} d \\lambda \\right] _ {0} \\\\ = \\left[ \\mathbf {M} _ {c} (\\Theta) \\int \\Omega_ {c, \\lambda} \\mathbf {s} _ {\\lambda} d \\lambda \\right] _ {0} \\\\ = \\left[ \\mathbf {M} _ {c} (\\Theta) \\mathbf {s} _ {c} \\right] _ {0}, \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.902 + ], + "angle": 0, + "content": "where \\(\\Omega_{c,\\lambda}\\) is the spectral transmission per channel at wavelength \\(\\lambda\\) shown in Figure 3(b). \\([x]_0\\) denotes the first-element of the Stokes vector \\(x\\), which is the total intensity. For a spectral channel \\(c\\), \\(\\mathbf{M}_c\\) is the Mueller matrix of the polarization-modulating optics, and \\(\\mathbf{s}_c\\) is the Stokes vector." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.363, + 0.892, + 0.394 + ], + "angle": 0, + "content": "For polarization modulation, both cameras utilize a QWP and a LP, yielding the Mueller matrix" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.406, + 0.892, + 0.423 + ], + "angle": 0, + "content": "\\[\n\\mathbf {M} _ {c} (\\Theta) = \\mathbf {C} _ {c} \\mathbf {Q} _ {c} \\left(\\theta_ {1}\\right) \\mathbf {P} _ {c} \\left(\\theta_ {2}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.893, + 0.541 + ], + "angle": 0, + "content": "where \\(\\mathbf{C}_c\\) is the error-compensating calibration matrix [34, 57]. \\(\\mathbf{Q}_c\\) and \\(\\mathbf{P}_c\\) are the QWP and LP Mueller matrices [9], respectively. The set \\(\\Theta = \\{\\theta_1,\\theta_2\\}\\) denotes the corresponding angles of the QWP fast axis and the LP polarization axis, which is set for accurate Stokes vector reconstruction [34, 57]. Lastly, we determine the per-channel Stokes vector \\(\\mathbf{s}_c\\) by solving the least-squares problem" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.552, + 0.892, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {s} _ {c}} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {| \\Theta |} \\left(I _ {c} (\\Theta_ {i}) - \\left[ \\mathbf {M} (\\Theta_ {i}) \\mathbf {s} _ {c} \\right] _ {0}\\right) ^ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.892, + 0.68 + ], + "angle": 0, + "content": "For the hyperspectral Stokes camera, we use four configurations with the rotating QWP. For the trichromatic Stokes camera, the fixed micro-filter setup shown in Figure 3(a) gives four/eight configurations for the (red, blue) channels and the green channel, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.681, + 0.892, + 0.787 + ], + "angle": 0, + "content": "Figure 3(c) shows the reconstructed Stokes images. A Stokes vector is physically-valid if DoP meets the following inequality: \\(0 \\leq \\rho \\leq 1\\). \\(99\\%\\) of the reconstructed Stokes vectors in our datasets satisfy this condition. For the following analysis, we filter out Stokes vectors violating the DoP condition and the unstable Stokes vectors reconstructed from saturated/underexposed pixel intensity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.664, + 0.817 + ], + "angle": 0, + "content": "5. Dataset Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Noise and Intensity Denoising Spectro-polarimetric images are susceptible to noise due to the low-light throughput of spectral and polarimetric filters. Our datasets are not exempt from these issues. To assess noise in Stokes images, we capture and average 100 images of a scene shown" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22101" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.088, + 0.28, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.205, + 0.458, + 0.216 + ], + "angle": 0, + "content": "(a) Top 40 PCA bases of hyperspectral Stokes vector components" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.089, + 0.465, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.477, + 0.09, + 0.659, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.478, + 0.232, + 0.675, + 0.245 + ], + "angle": 0, + "content": "(c) Proportion of variance (log scale)" + }, + { + "type": "image", + "bbox": [ + 0.665, + 0.089, + 0.871, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.702, + 0.232, + 0.842, + 0.244 + ], + "angle": 0, + "content": "(d) BPP and MSE of PCA" + }, + { + "type": "image", + "bbox": [ + 0.098, + 0.218, + 0.465, + 0.393 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.188, + 0.394, + 0.373, + 0.405 + ], + "angle": 0, + "content": "(b) Qualitative results (DoP/AoLP)" + }, + { + "type": "image", + "bbox": [ + 0.477, + 0.258, + 0.665, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.393, + 0.643, + 0.405 + ], + "angle": 0, + "content": "(e) Training PSNR value" + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.254, + 0.871, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.702, + 0.393, + 0.835, + 0.405 + ], + "angle": 0, + "content": "(f) BPP and MSE of INR" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.409, + 0.894, + 0.465 + ], + "angle": 0, + "content": "Figure 4. Efficient spatio-spectral-polarimetric representations. (a) PCA basis of the hyperspectral Stokes dataset in sRGB. (b) Qualitative results of PCA and INR compared to single-shot denoising [66] at \\(550\\mathrm{nm}\\). (c) Proportion of variance with respect to each PCA basis in order, \\(\\log (\\sigma_i^2 / \\sum_n \\sigma_n^2)\\), where \\(\\sigma_i\\) denotes standard deviation of the \\(i\\)-th basis. (d) BPP and MSE analysis of PCA with respect to the number of PCA bases. (e) Training PSNR curve of INR. (f) BPP and MSE value of INR with respect to the number of MLP layers." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.469, + 0.47, + 0.59 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.591, + 0.47, + 0.695 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.71, + 0.47, + 0.807 + ], + "angle": 0, + "content": "Figure 5. Noise in Stokes images and intensity denoising. (a) Stokes vector \\( s_1 \\) reconstructed from a single-shot, single-shot with a learned intensity denoiser [66], and burst imaging (Pseudo GT) averaged over 100 shots. (b) Reconstruction accuracy of a Stokes image with varying number of averaged images. (c) Reconstruction accuracy of normalized Stokes elements with and without intensity denoising." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.902 + ], + "angle": 0, + "content": "in Figure 3(c) for each polarization configuration \\(\\Theta\\). From these averaged images, we reconstruct pseudo ground-truth Stokes image, shown in Figure 5(a). Figure 5(b) reports the MSE and PSNR of reconstructed Stokes images with respect to the number of averaged images. To achieve a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.893, + 0.685 + ], + "angle": 0, + "content": "PSNR exceeding \\(35\\mathrm{dB}\\), we need to average over 4/25 shots for the trichromatic/hyperspectral Stokes cameras, indicating lower SNR of the hyperspectral Stokes dataset. We find that state-of-the-art learning-based intensity denoising methods, such as KBNet [66], can effectively reduce noise for each polarization configuration, leading to accurate Stokes-vector reconstruction, despite lack of polarization images during training. For the denoised single-shot capture, we achieve a PSNR of \\(34.5\\mathrm{dB}\\), demonstrating the potential of using pretrained intensity restoration networks for Stokes imaging. Figure 5(c) shows PSNRs of reconstructed Stokes images per each spectral channel and normalized Stokes element. With the intensity denoising, we find that the PSNR significantly increases for \\(s_1\\), \\(s_2\\), and \\(s_3\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Efficient Spatio-spectral-polarimetric Representations Each pixel in a hyperspectral Stokes image contains a Stokes vector for every spectral channel, leading to a total of \\(21 \\times 4 \\times 32\\) bits using single-precision floating format. This results in a bit-per-pixel (BPP) value of 2,688, equating to \\(100\\mathrm{MB}\\) for storing a single hyperspectral Stokes image of \\(512 \\times 612\\) pixels. Given the substantial memory required to store a spectro-polarimetric image, we investigate efficient representations of real-world spatio-spectral-polarimetric data, for which we explore two methods: a PCA-based model and an implicit neural model." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.893, + 0.901 + ], + "angle": 0, + "content": "First, we apply PCA on non-overlapping hyperspectral Stokes patches. Figure 4(a) shows the 40 most significant" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22102" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.363 + ], + "angle": 0, + "content": "PCA bases, revealing varied spatial and spectral features for each Stokes element: \\( s_0 \\), \\( s_1 \\), \\( s_2 \\), \\( s_3 \\). Notably, spatial structures are more evident in \\( s_0 \\), while \\( s_1 \\), \\( s_2 \\), \\( s_3 \\) shows spectral features, suggesting a stronger correlation between spectrum and polarization than spatial features. To visualize hyperspectral intensity, we convert it to sRGB, which means that the same sRGB color may originate from different spectra. Figure 4(c) shows the variance of the coefficients for the top 200 PCA bases, indicating that spati-spectral-polarimetric data can indeed be compressed. This is further evidenced by Figure 4(d), which shows the reconstruction error and BPP when varying number of PCA bases used to recreate a hyperspectral Stokes image. Using \\( 2.22\\mathrm{MB} \\) coefficients adequately represents a \\( 100\\mathrm{MB} \\) hyperspectral Stokes image as shown in Figure 4(b), exhibiting a high compression rate with the reconstruction error of \\( 2.69\\times 10^{-5} \\). See the Supplemental Document for further details on PCA analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.473, + 0.469 + ], + "angle": 0, + "content": "Second, we devise an INR for hyperspectral Stokes images by modifying NeSpoF [34]. The original NeSpoF architecture models a volumetric hyperspectral Stokes field. Here, instead, we aim to represent a hyperspectral Stokes image. Specifically, our INR, modeled by an MLP \\( F_{\\gamma} \\), outputs the Stokes vector \\( s \\) for a given pixel position \\( p_x, p_y \\) and spectral channel index \\( c \\), that is" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.48, + 0.47, + 0.497 + ], + "angle": 0, + "content": "\\[\n\\mathbf {s} = F _ {\\gamma} \\left(p _ {x}, p _ {y}, c\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.473, + 0.67 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is the network parameters. We fit the MLP to a hyperspectral Stokes image by minimizing the reconstruction loss between the network output and the hyperspectral Stokes image. The training curve is shown in Figure 4(e). Figure 4(f) shows the reconstruction error and BPP of our INR with respect to varying number of the MLP layers. With just 8 layers corresponding to a BPP of 60, we achieve a converged reconstruction error of \\(1.90 \\times 10^{-5}\\), resulting in just \\(2.22\\mathrm{MB}\\) of network parameters to represent a \\(100\\mathrm{MB}\\) hyperspectral Stokes image. See Supplemental Document for architecture details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.473, + 0.809 + ], + "angle": 0, + "content": "Both PCA and INR experiments validate that a natural spectro-polarimetric image is compressible. PCA provides PCA basis vectors that can be applied to any instance, however with a lower reconstruction accuracy than INR. INR is overfitted to a single instance, while higher reconstruction accuracy can be achieved. These representations are also beneficial for denoising spectral-polarimetric images, as shown in Figure 4(b), which even outperforms the learning-based intensity denoiser [66]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Polarized and Unpolarized Intensity We decompose hyperspectral Stokes images into the polarized images \\( P = \\sqrt{s_1^2 + s_2^2 + s_3^2} \\) and unpolarized images \\( U = s_0 - P \\) per each spectral channel. Figure 6(a) shows specular reflections such as the glow of leather sofa separated into po" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.088, + 0.872, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.582, + 0.257, + 0.812, + 0.267 + ], + "angle": 0, + "content": "(a) Separation into polarized and unpolarized light" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.269, + 0.699, + 0.381 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.522, + 0.381, + 0.7, + 0.391 + ], + "angle": 0, + "content": "(b) Intensity distribution by polarization" + }, + { + "type": "image", + "bbox": [ + 0.701, + 0.269, + 0.892, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.719, + 0.381, + 0.883, + 0.391 + ], + "angle": 0, + "content": "(c) Variance of basis by polarization" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.402, + 0.895, + 0.472 + ], + "angle": 0, + "content": "Figure 6. Polarized and unpolarized light distributions. (a) Separation into polarized and unpolarized light. (b) Intensity distributions for polarized and unpolarized components. (c) Variance of PCA basis of polarized and unpolarized intensity across spectral channel." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.895, + 0.726 + ], + "angle": 0, + "content": "larized light. Note that the polarized image typically encodes the illumination colors for dielectric surfaces. Figure 6(b) reveals that the intensity distributions of polarized light, obtained from the entire hyperspectral Stokes dataset, is skewed towards low and high-intensity values compared to the unpolarized light. This is because polarized images mostly contain specular reflections, which is sparsely distributed and has high intensity values. We then compute the variance of the PCA bases for polarized intensity along the spectral channel. Figure 6(c) highlights that the spectral variance for polarized intensity is lower than that of unpolarized intensity. We speculate that the color of polarized light lies in a lower dimensional space than that of unpolarized light, since diffuse reflection with diverse spectral variations is mostly captured by unpolarized light, making the spectral variation of unpolarized light more pronounced." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Stokes Vector Distributions in Natural Stokes Images Next, we analyze the distribution of all Stokes vectors in our Stokes dataset. Figure 7 shows the histograms of Stokes elements \\( s_0 \\), \\( s_1 \\), \\( s_2 \\), \\( s_3 \\) across all spectral channel. We find that the distributions of Stokes elements \\( (s_1, s_2, s_3) \\) have symmetric shapes of positive and negative sides. Stokes elements of \\( s_1 \\) and \\( s_2 \\) have similar shapes meaning that the directions of linearly-polarized light are equally distributed in natural images. The circular component \\( s_3 \\) is more condensed near zero than the linear elements, resulting in a" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "22103" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.083, + 0.088, + 0.47, + 0.18 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.18, + 0.376, + 0.19 + ], + "angle": 0, + "content": "(a) Visualization of Stokes vector" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.195, + 0.46, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.198, + 0.323, + 0.353, + 0.334 + ], + "angle": 0, + "content": "(b) Stokes vector distribution" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.345, + 0.47, + 0.388 + ], + "angle": 0, + "content": "Figure 7. Stokes-vector distributions. (a) Stokes images of \\( s_1 \\), \\( s_2 \\), and \\( s_3 \\) at the green channel. (b) Stokes-vector distributions of \\( s_0 \\), \\( s_1 \\), \\( s_2 \\) and \\( s_3 \\) for trichromatic and hyperspectral datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.469, + 0.461 + ], + "angle": 0, + "content": "higher peak both in trichromatic and hyperspectral datasets. This indicates that pixels are often more linearly polarized than circularly polarized. Refer to the Supplemental Document for further analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.469, + 0.658 + ], + "angle": 0, + "content": "Gradient Analysis of Stokes Images Gradient distribution of images has been often used as priors for image-based applications including image restoration, understanding, and editing. Here, we perform gradient analysis of Stokes and polarization-feature images. Figure 8(b) shows that the gradient of Stokes and normalized Stokes vectors exhibits a similarity to Hyper-Laplacian priors, commonly used to describe the gradient of natural intensity-images. An interesting finding is that total intensity \\(s_0\\) has more high-gradient values than the linear components of \\(s_1\\) and \\(s_2\\), and the circular component \\(s_3\\) has the lowest-value distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.66, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We analyze the gradient distributions of polarization features, including AoLP, degree of linear polarization (DoLP), degree of circular polarization (DoCP), and CoP. DoLP and DoCP are computed as \\(\\mathrm{DoLP} = \\sqrt{s_1^2 + s_2^2} / s_0\\) and \\(\\mathrm{DoCP} = |s_3| / s_0\\) respectively. To compute the gradient of AoLP images, we consider the angular wrapping property. That is, AoLP has a range from \\(-\\frac{\\pi}{2}\\) to \\(\\frac{\\pi}{2}\\) and the AoLPs of \\(-\\frac{\\pi}{2}\\) and \\(\\frac{\\pi}{2}\\) are identical. Thus, if the gradient exceeds \\(\\frac{\\pi}{2}\\), we estimate the gradient as \\(\\nabla \\mathrm{AoLP} - \\pi \\times \\mathrm{sign}(\\nabla \\mathrm{AoLP})\\), where \\(\\nabla\\) is the gradient operator and \\(\\mathrm{sign}\\) is the sign operator that returns 1 if positive, otherwise \\(-1\\). Figure 8(c) shows that the gradients of AoLP are generally higher than DoLP and DoCP. This implies that sparsity in the measurement gradient is milder for AoLP than DoLP and DoCP. DoLP and DoCP have shapes similar to HyperLaplacian priors while DoCP is sharper than DoLP. The" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.088, + 0.891, + 0.167 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.167, + 0.891, + 0.251 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.252, + 0.85, + 0.263 + ], + "angle": 0, + "content": "(a) Visualization of polarization features and gradients" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.264, + 0.892, + 0.378 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.6, + 0.378, + 0.821, + 0.389 + ], + "angle": 0, + "content": "(b) Gradient distributions of Stokes vector" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.392, + 0.892, + 0.506 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.58, + 0.506, + 0.835, + 0.517 + ], + "angle": 0, + "content": "(c) Gradient distributions of polarization features" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.598 + ], + "angle": 0, + "content": "Figure 8. Gradient analysis of Stokes images. (a) Visualization of AoLP, DoLP, DoCP and CoP values and their gradients. Examining the log probability of the gradient for (b) Stokes vectors \\( s_0 \\), \\( s_1 \\), \\( s_2 \\), \\( s_3 \\) and normalized Stokes vectors \\( s_1' \\), \\( s_2' \\), and \\( s_3' \\), and (c) polarization features including DoLP, DoCP, AoLP and CoP." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.61, + 0.892, + 0.732 + ], + "angle": 0, + "content": "gradient of CoP shows symmetric distributions for right-circular and left-circular directions. Unlike AoLP, the probability decreases as the gradient approaches extreme values. The difference in tendency between linear-polarization and circular-polarization features, as well as their distributions, means that we need distinct priors for each polarization feature, emphasizing the importance of a full Stokes dataset that measure not only linear but also circular polarization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Shape from Polarization and Spectral Channels Methods that recover shape from polarization, SfP, have made rapid progress in the last decade. SfP aims to extract normals by analyzing the normal-dependent polarization change of reflected light. Specifically, SfP analyzes the DoP and AoLP based on Fresnel theory [9], which describes the polarization change of light upon reflection and transmission at a smooth surface [32, 41]. Here, we analyze an overlooked problem in SfP: the spectral dependency of estimated normals. Surface normals, as a geometric sur" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22104" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.19, + 0.153 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.193, + 0.089, + 0.283, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.089, + 0.375, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.378, + 0.089, + 0.468, + 0.152 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.081, + 0.153, + 0.19, + 0.162 + ], + "angle": 0, + "content": "(a) Denoised Trichromatic" + }, + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.153, + 0.283, + 0.162 + ], + "angle": 0, + "content": "(b) Normal map from" + }, + { + "type": "image_caption", + "bbox": [ + 0.194, + 0.162, + 0.281, + 0.169 + ], + "angle": 0, + "content": "denoised R channel" + }, + { + "type": "image_caption", + "bbox": [ + 0.285, + 0.153, + 0.374, + 0.162 + ], + "angle": 0, + "content": "(c) Normal map from" + }, + { + "type": "image_caption", + "bbox": [ + 0.378, + 0.153, + 0.468, + 0.162 + ], + "angle": 0, + "content": "(d) Normal map from" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.162, + 0.288, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.131, + 0.272, + 0.277, + 0.281 + ], + "angle": 0, + "content": "(e) Denoised Trichromatic dataset" + }, + { + "type": "image", + "bbox": [ + 0.288, + 0.162, + 0.468, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.305, + 0.272, + 0.455, + 0.281 + ], + "angle": 0, + "content": "(f) Denoised Hyperspectral dataset" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.292, + 0.47, + 0.376 + ], + "angle": 0, + "content": "Figure 9. Spectral dependency of conventional SFP method. (a) Trichromatic Stokes image and estimated surface normals [41] for each red, green, and blue spectral channels shown in (b), (c), and (d). Graphs (e) and (f) show the probability distributions of standard deviation of normal component \\( x \\), \\( y \\), and \\( z \\) along the spectral channels for both datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.391, + 0.47, + 0.633 + ], + "angle": 0, + "content": "face property, should be consistent regardless of the input spectral channels used for SfP. In Figure 9, we test the state-of-the-art SfP method by Lei et al. [41], designed for in-the-wild scenes. The evaluation results on our normalized Stokes dataset clearly reveal that normal maps reconstructed from different spectral channels exhibit variations. We compute the standard deviations of spectral variations for each \\( x \\), \\( y \\), and \\( z \\) component of the estimated normals. Figures 9(e) and (f) show the probability distributions of the standard deviation, highlighting the large variations in the estimated normals for both hyperspectral and trichromatic datasets. Interestingly, the \\( x \\) and \\( y \\) components of normals show larger standard deviations than the \\( z \\) component. This implies that the spectral variation of DoP, which determines the \\( z \\) component, has less impact on the distribution than that of AoLP, which governs the \\( x \\) and \\( y \\) components." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Environment Dependency Figure 10 shows the Poincaré spheres projected onto the \\( s_1' - s_2' \\) and \\( s_1' - s_3' \\) planes for the three data labels: Indoor, Sunlight and Cloudy. Sunlight is known to contain more circularly polarized light compared to other artificial lighting [25]. As shown in Figure 10(a), Stokes vectors are distributed more widely across \\( s_3' \\) axis under sunlight compared with Indoor scene. In addition, we find that DoCP is distributed at higher values for the sunlight compared to the indoor: pixels with DoCP over 0.5 are rarely observed in indoor scenes. This is also confirmed in the example \\( s_3 \\) images for indoor and sunlight scenes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Another interesting finding is that cloudy or sunny illumination result in different polarization statistics. Figure 10(a) shows that Stokes vectors of cloudy scenes are more concentrated near the origin, meaning that light is more depolarized compared to light under clear sunlight." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.089, + 0.631, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.089, + 0.744, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.089, + 0.885, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.186, + 0.631, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.633, + 0.187, + 0.744, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.747, + 0.187, + 0.884, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.621, + 0.272, + 0.793, + 0.282 + ], + "angle": 0, + "content": "(a) Poincaré sphere projections" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.283, + 0.639, + 0.373 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.373, + 0.63, + 0.384 + ], + "angle": 0, + "content": "(b) DoCP distribution" + }, + { + "type": "image", + "bbox": [ + 0.642, + 0.283, + 0.75, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.752, + 0.282, + 0.892, + 0.372 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.707, + 0.373, + 0.813, + 0.384 + ], + "angle": 0, + "content": "(c) \\(S_{3}\\) visualization" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.395, + 0.892, + 0.465 + ], + "angle": 0, + "content": "Figure 10. Environment dependency. (a) Projected Poincaré spheres onto the \\( s_1' - s_2' \\) and \\( s_1' - s_3' \\) planes with respect to dataset labels. Colorbar is based on the normalized pixel count. (b) DoCP distributions for indoor and sunlight categories. (c) Example \\( s_3 \\) images." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.481, + 0.891, + 0.511 + ], + "angle": 0, + "content": "This is aligned with previous studies [24, 58] that report the impact of cloud-particle scatterings on light depolarization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.53, + 0.619, + 0.545 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.556, + 0.892, + 0.752 + ], + "angle": 0, + "content": "In this work, we have introduced a trichromatic and hyperspectral Stokes image dataset that encompasses diverse natural scenes and various illumination conditions, totaling more than 2,333 scenes. We analyze the empirical distribution of the Stokes vectors of natural spectropolarimetric images. To efficiently represent spati-spectral-polarimetric data, we devise a PCA-based model and an implicit neural representation. We further provide detailed analysis on Stokes gradient distributions, denoising characteristics, spectral dependency of SfP, and environment dependency. As such, our work provides a foundation for future research on spectral-polarimetric imaging and vision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements We thank Onur Akkaya for helpful discussion. Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, 2022R1A6A1A03052954). Felix Heide was supported by an NSF CAREER Award (2047359), a Packard Foundation Fellowship, a Sloan Research Fellowship, a Sony Young Faculty Award, a Project X Innovation Award, and an Amazon Science Research Award." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "22105" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.252 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Springer, 2020. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.469, + 0.824 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "22108" + } + ] +] \ No newline at end of file diff --git a/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_origin.pdf b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..efbc6e8e70983b0bf0b9b16898bbe95ae0e1aac3 --- /dev/null +++ b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/af12fa50-9d20-41ff-af46-6bfc69201b2f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:50e06dd251ffbabbad3a7e9bf3a9434100e14ae99c5108351b51ff349022eba2 +size 3617419 diff --git a/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/full.md b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a544853df6772d84f95458ed86ae5df70e7a2536 --- /dev/null +++ b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/full.md @@ -0,0 +1,364 @@ +# Spectral and Polarization Vision: Spectro-polarimetric Real-world Dataset + +Yujin Jeon $^{1,*}$ Eunsue Choi $^{1,*}$ Youngchan Kim $^{1}$ Yunseong Moon $^{1}$ Khalid Omer $^{2}$ Felix Heide $^{3}$ Seung-Hwan Baek $^{1}$ + +$^{1}$ POSTECH $^{2}$ Meta $^{3}$ Princeton University + +# Abstract + +Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Many image datasets exist, consisting of trichromatic intensity images taken with RGB cameras, which are designed to replicate human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although there are previous spectro-polarimetric datasets, they have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets, consisting of trichromatic Stokes images and hyperspectral Stokes images. These datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research. + +# 1. Introduction + +Recent progress in computer vision can be largely attributed to comprehensive studies of real-world image datasets, such as ImageNet [14]. Foundation models [1, 35, 53, 64] further underscore data significance. Most of these datasets comprise trichromatic intensity images, inspired by human visual perception, enabling machines to emulate human vision with trichromatic RGB cameras. As such, the datasets have facilitated the development of low-cost, camera-based autonomous agents capable of perceiving and interacting + +with our world, as we do. However, the reliance on trichromatic intensity in existing image datasets also comes with inherent limitations for analyzing objects in depth. Examples include textureless surface, low-albedo objects, and transparent materials. + +Light possesses wave properties, including polarization and spectrum [9], which are not faithfully captured by trichromatic intensity imaging. While these properties are invisible to human, animals like honeybees and ants leverage the polarization and spectrum for navigation and other tasks. Horvath and Varju [25] provide diverse examples and mechanisms of spectral and polarimetric vision in animals. Partly drawing inspiration from nature, researchers have extended the analysis of spectrum and polarization to a variety of fields, including computer vision, robotics, and astronomy. This has spurred interest in polarimetric [7, 8, 38, 49] and hyperspectral imaging [2, 10, 28], and more recently, their integration into spectro-polarimetric imaging [3, 17, 18, 23, 26, 45, 47, 50, 54, 67]. Prior work using spectro-polarimetric images has shown potential for skin analysis [67], vegetation classification [63], shape reconstruction [27], object recognition [13], and segmentation [30, 55]. + +There are existing spectro-polarimetric datasets, summarized in Figure 2, that have been invaluable for these analysis [19, 38, 39, 52] and training neural networks [4, 11, 22, 36, 40-42, 46, 48]. However, these datasets unfortunately do not capture the diversity of real-world spectropolarimetric images as effectively as their trichromatic intensity counterparts do. They typically suffer from limited object, scene, and illumination diversity, contain primarily linear polarization information, and offer a small number of images. To advance the field, we propose a comprehensive spectro-polarimetric dataset that encompasses: (1) Full Stokes polarimetric data, including both linear and circular polarization states, represented by Stokes vectors [9] for each pixel and wavelength. (2) A diverse range of spectral channels, facilitating in-depth exploration of the interplay between spectrum and polarization. (3) A broad array of + +real-world scenes, crucial for extracting meaningful statistics and relationships within spectro-polarimetric images. + +To this end, we introduce two spectro-polarimetric datasets designed to cover real-world spectro-polarimetric scenes: a trichromatic Stokes dataset consisting of 2,022 images, and a hyperspectral Stokes dataset containing 311 images across 21 spectral channels. The trichromatic Stokes dataset covers a wider range of scenes thanks to its convenient capture setup and process. The hyperspectral Stokes dataset provides richer spectral-polarimetric information than the trichromatic Stokes dataset. Both datasets cover a variety of natural indoor and outdoor scenes. Each image in these datasets is annotated with four specific parameters: the type of environment (indoor or outdoor), the illumination conditions (clear/cloudy sunlight or white/yellow office light), the timestamp of capture, and the scene categorization (either object- or scene-oriented). + +Utilizing these datasets, we systematically analyze the statistics of real-world spectro-polarimetric images. We focus on examining statistics of Stokes vectors, in addition to the gradients and polarimetric attributes associated with them. We also conduct an analysis of unpolarized and polarized images derived through polarimetric decomposition. We then develop two efficient spatio-spectral-polarimetric representations using principal component analysis (PCA) and implicit neural representation (INR). These representations exhibit effective denoising capabilities and low memory footprints by exploiting the compressible structure of spectro-polarimetric images. We also analyze the impact of intensity denoising for spectro-polarimetric images, spectral dependency of shape-from-polarization methods, and environment dependency on the statistics of spectropolarimetric images. + +In summary, we make the following contributions. + +- We introduce a trichromatic Stokes dataset and a hyperspectral Stokes dataset, featuring 2,333 diverse annotated indoor and outdoor scenes under various illumination conditions, which encompasses full-Stokes polarization data for linear and circular states. +- We develop efficient spatio-spectral-polarimetric representations and analyze real-world spectro-polarimetric images, encompassing Stokes vectors and their gradients, unpolarized and polarized images, shape from polarization, denoising, and environment dependency. + +# 2. Related Work + +Spectro-polarimetric Image Dataset Several datasets have been introduced for analyzing polarization and spectral information. With the advent of trichromatic linear-polarization cameras, a line of work has attempted to acquire trichromatic linear-polarization images, ranging from a few objects and scenes [5, 11, 42, 52] to a large number of scenes for specific target applications such as reflection + +![](images/52b8d9f67846fe527fa9ece3499e68b548dfedb7fb5477b0afee7295f3678d4e.jpg) +(a) Polarization ellipse +Figure 1. Polarization visualizations. (a) Polarization ellipse depicts the electric-field oscillation projected onto a plane tangent to the light propagation. (b) Poincaré sphere visualizes the polarization state of light on the normalized Stokes-vector axes $s_1', s_2', s_3'$ . + +![](images/0457c3835359878177b937afd0c6fd7fdfb06f2eb2141d31f28c771e6afbf448.jpg) +(b) Poincaré sphere + +separation [40, 46] and glass segmentation [48]. Lapray et al. [39] acquire linear-polarization images for the near-infrared spectral band, albeit only on 10 objects. Fan et al. [19] acquire the first multi-spectral full-Stokes polarimetric dataset covering linear and circular states, while it only contains 64 flat objects captured in a lab environment. Our proposed datasets enables analyzing the statistics of real-world spectro-polarimetric images, which cannot be achieved by prior datasets. See Figure 2 for a comprehensive comparison. + +Applications of Spectro-polarimetric Imaging Spectropolarimetric information has been investigated for diverse vision and imaging tasks. Using linear-polarization images has found applications in shape reconstruction [4, 5, 7, 16, 21, 31, 41, 70], appearance acquisition [15, 36], removing reflections [37, 40, 46, 51, 59, 62], transparent-object segmentation [33, 48], seeing through scattering [20, 43, 68], and image enhancement [69]. Trichromatic Stokes images have been used for tone-mapping [12] and seeing through scattering [6]. Expanding into multi-spectral domain, spectral-polarimetric analysis has been applied to object recognition [13], skin analysis [67], dehazing [61], specular reflection inpainting [29], background segmentation [30] and tensor representation [65]. In addition to vision tasks, spectro-polarimetric imaging has been used for various biological applications, such as marsh vegetation classification [63], coastal wetland classification [55] and leaf nitrogen determination [44]. While the aforementioned studies demonstrate the benefits of using spectropolarimetric data, we believe that the full potential of spectro-polarimetric images is still locked by the absence of real-world spectro-polarimetric datasets. + +# 3. Background on Polarization + +Polarization, the oscillation pattern of the electric field, can be represented using a Stokes vector, $\mathbf{s} = [s_0,s_1,s_2,s_3]^\intercal$ + +![](images/13e1635d12e9d7a0ab526daad43f562a225d759bbb2b2efd7e4b0c3b19996a00.jpg) +Trichromatic Stokes dataset + +![](images/edbc326de1768d5be483da537c77cd563eccceec48977acfe1fa013262dfbaa7.jpg) +Hyperspectral Stokes dataset +(a) Dataset thumbnails visualized in sRGB + +![](images/26c811316f829440e74ae5d111e5657ae6b96943ab092d703b17f55f6db5d3cf.jpg) + +![](images/032e0654b117d158e03bbc14625f5279e3edd9f367b03037dd01e6977a35ce16.jpg) +■ Scene-oriented + +![](images/b1e646f6904aaf113902dabf68f5d29e69c6090a0f8a8afecd857a21d9338792.jpg) +Object-oriented + +![](images/19ebf8999cde6a346e5c3cdc972d9e6931b00989a9e9b00e1cbfcedf2d4fbca2.jpg) + +![](images/3d9ba8fa0953e01eef79e98487764757c16f3b55ff49e48d1455b9d7e41f2b54.jpg) +(b) Dataset Statistics +Figure 2. Spectro-polarimetric image datasets. We present trichromatic and hyperspectral Stokes datasets of which thumbnails are shown in (a) and label statistics in (b). The table shown on the right compares our datasets with existing spectro-polarimetric datasets. Ours are the only datasets that encompass both linear (LP) and circular (CP) polarization over multiple of spectral bands for diverse real scenes. + +![](images/23477c263c2f4299234d9d3aaea71ab21b6650bb1c5dcc3f8bcdb26d81b1a147.jpg) + +$s_0$ denotes the total intensity, $s_1$ and $s_2$ describe the differences in the intensity of linearly-polarized components at orientations of $0^{\circ} / 90^{\circ}$ and $45^{\circ} / -45^{\circ}$ , respectively. $s_3$ is the difference in intensity between right- and left-circularly polarized components. Figure 1 shows two visualization methods for polarization, the polarization ellipse and Poincaré sphere. Polarization ellipse can be described in terms of the orientation angle $\psi$ and ellipticity $\chi$ with respect to the projected Stokes vector $\mathbf{x}$ and $\mathbf{y}$ axes [9]. The Poincaré sphere visualizes polarization in a three-dimensional space, using the normalized Stokes-vector elements relative to the total intensity: $s_1' = s_1 / s_0$ , $s_2' = s_2 / s_0$ , $s_3' = s_3 / s_0$ . To effectively analyze a Stokes vector, one can compute the degree of polarization (DoP) denoted as $\rho$ , the angle of linear polarization (AoLP) represented by $\psi$ , and the ellipticity angle given by $\chi$ , that is + +$$ +\rho = \frac {P}{s _ {0}}, \psi = \frac {1}{2} \arctan \left(\frac {s _ {2}}{s _ {1}}\right), \chi = \frac {1}{2} \arctan \left(\frac {s _ {3}}{L}\right), \tag {1} +$$ + +where $P = \sqrt{s_1^2 + s_2^2 + s_3^2}$ and $L = \sqrt{s_1^2 + s_2^2}$ . We also use the polarimetric visualization method proposed by Wilkie et al. [60] using DoP, AoLP, and chirality of polarization (CoP). CoP describes the left- or right-handedness of the circularly polarized component, which is related to $\chi$ . Finally, the Mueller matrix $\mathbf{M} \in \mathbb{R}^{4 \times 4}$ describes the change of a Stokes vector: $\mathbf{s}_{\mathrm{out}} = \mathbf{M}\mathbf{s}_{\mathrm{in}}$ , where $\mathbf{s}_{\mathrm{in}}$ and $\mathbf{s}_{\mathrm{out}}$ + +
DatasetPolar.# of bandsScene countScene diversity
[41]LP1522Outdoor scenes
[5]LP1300Indoor objects
[39]LP610Indoor objects
[52]LP340Indoor objects
[11]LP33Indoor multiview
[11]LP32Synthetic multiview
[22]LP36Indoor multiview
[40]LP3807Reflective objects
[42]LP3500Outdoor scenes
[36]LP344,300Synthetic
[46]LP33,200Reflective objects
[48]LP34,500Transparent objects
[38]LP32,000Indoor/outdoor scenes
[19]LP, CP1867Flat objects
[34]LP, CP214Synthetic multiview
[34]LP, CP214Indoor/outdoor multiview
Ours (RGB)LP, CP32,022Indoor/outdoor scenes
Ours (HS)LP, CP21311Indoor/outdoor scenes
+ +are the input/output Stokes vectors. For more details on polarization, we refer to the book by Collett [9]. + +# 4. Spectro-polarimetric Dataset + +We introduce a trichromatic Stokes dataset comprising 2,022 Stokes images and a hyperspectral Stokes dataset with 311 Stokes images at 21 spectral channels. Both datasets cover natural real-world indoor and outdoor scenes. Each Stokes image is accompanied by four labels: (1) the environment (indoor or outdoor), (2) the illumination condition, including clear or cloudy sunlight and white or incandescent light, (3) the time of image capture, (4) the scene type, distinguishing between object-oriented and scene-oriented. Figure 2 shows thumbnails, statistics, and comparison of our datasets to existing ones. Prior datasets suffer from a narrow range of scenes, restricted illumination conditions, linear polarization only, and fewer images. + +Acquisition We acquire the datasets using two imaging systems depicted in Figure 3(a), proposed and developed by previous studies [34, 56]. First, the trichromatic Stokes camera by Tu et al. [56] incorporates on-sensor quarterwave plates (QWPs) and linear polarizers (LPs) [9]. This allows for single-shot capture of trichromatic Stokes images, enabling convenient data collection on diverse scenes. The + +![](images/19b199622aad5f1f0286ed59e52e074e01b05ee7e5bb4d2d2a796dda8d053be9.jpg) + +![](images/ff600c947f52f981e2e8cabc40296abca33c09127f2d2b879a087f925480e509.jpg) + +![](images/113732ddce3ed700a5d87709eca0dab7d6e5a3c4c4ce7dca9f730212485946d7.jpg) + +![](images/51c1daca8ee27d0408ea3929a31b8ab3b783c93ac0b754f1a8eb077c64df81eb.jpg) +(a) Stokes imaging system + +![](images/72d0427d17dddaf003cfc2ca4220ce06beae2140ca6224695369adbb84a09795.jpg) +(b) Camera response function + +![](images/be0c6e15c037540c96629bd1986b5bc3349efa8b2c3731e885ee8671eca99f4f.jpg) +(c) Multi-channel polarimetric images +Figure 3. Acquisition of spectro-polarimetric images. We capture spectro-polarimetric images using (a) trichromatic and hyperspectral Stokes cameras [34, 57]. (b) Camera response functions. (c) Reconstructed raw Stokes images per each spectral channel. + +resolution of a trichromatic Stokes image is 1900 (height) $\times$ 2100 (width) $\times$ 4 (Stokes elements) $\times$ 3 (RGB). Second, the hyperspectral Stokes camera from Kim et al. [34] captures images by sequentially scanning 21 spectral channels from $450\mathrm{nm}$ to $650\mathrm{nm}$ in $10\mathrm{nm}$ increments with a LCTF which functions as a LP. For each spectral channel, we capture images by rotating a QWP. The resolution of a hyperspectral Stokes image is 512 (height) $\times$ 612 (width) $\times$ 4 (Stokes elements) $\times$ 21 (wavelengths). + +Spectro-polarimetric Image Formation Using the two imaging systems, we capture raw images from which a per-pixel Stokes vector for each spectral channel is reconstructed. We introduce an unified image formation model that can be applied to both cameras. Suppose a light ray with a Stokes vector $\mathbf{s}_{\lambda}$ at wavelength $\lambda$ impinges on a Stokes camera. As the light passes through polarization filters modeled by the Mueller matrix $\mathbf{M}(\Theta)$ , its Stokes vector transforms. $\Theta$ denotes the polarization-filter configuration. The camera sensor then captures light intensity, represented by the first element of the Stokes vector. The recorded intensity, $I_{c}(\Theta)$ , at a spectral channel $c$ and polarimetric filter configuration $\Theta$ , is described by + +$$ +\begin{array}{l} I _ {c} (\Theta) = \left[ \int \Omega_ {c, \lambda} \mathbf {M} _ {c} (\Theta) \mathbf {s} _ {\lambda} d \lambda \right] _ {0} \\ = \left[ \mathbf {M} _ {c} (\Theta) \int \Omega_ {c, \lambda} \mathbf {s} _ {\lambda} d \lambda \right] _ {0} \\ = \left[ \mathbf {M} _ {c} (\Theta) \mathbf {s} _ {c} \right] _ {0}, \tag {2} \\ \end{array} +$$ + +where $\Omega_{c,\lambda}$ is the spectral transmission per channel at wavelength $\lambda$ shown in Figure 3(b). $[x]_0$ denotes the first-element of the Stokes vector $x$ , which is the total intensity. For a spectral channel $c$ , $\mathbf{M}_c$ is the Mueller matrix of the polarization-modulating optics, and $\mathbf{s}_c$ is the Stokes vector. + +For polarization modulation, both cameras utilize a QWP and a LP, yielding the Mueller matrix + +$$ +\mathbf {M} _ {c} (\Theta) = \mathbf {C} _ {c} \mathbf {Q} _ {c} \left(\theta_ {1}\right) \mathbf {P} _ {c} \left(\theta_ {2}\right), \tag {3} +$$ + +where $\mathbf{C}_c$ is the error-compensating calibration matrix [34, 57]. $\mathbf{Q}_c$ and $\mathbf{P}_c$ are the QWP and LP Mueller matrices [9], respectively. The set $\Theta = \{\theta_1,\theta_2\}$ denotes the corresponding angles of the QWP fast axis and the LP polarization axis, which is set for accurate Stokes vector reconstruction [34, 57]. Lastly, we determine the per-channel Stokes vector $\mathbf{s}_c$ by solving the least-squares problem + +$$ +\underset {\mathbf {s} _ {c}} {\operatorname {a r g m i n}} \sum_ {i = 1} ^ {| \Theta |} \left(I _ {c} (\Theta_ {i}) - \left[ \mathbf {M} (\Theta_ {i}) \mathbf {s} _ {c} \right] _ {0}\right) ^ {2}. \tag {4} +$$ + +For the hyperspectral Stokes camera, we use four configurations with the rotating QWP. For the trichromatic Stokes camera, the fixed micro-filter setup shown in Figure 3(a) gives four/eight configurations for the (red, blue) channels and the green channel, respectively. + +Figure 3(c) shows the reconstructed Stokes images. A Stokes vector is physically-valid if DoP meets the following inequality: $0 \leq \rho \leq 1$ . $99\%$ of the reconstructed Stokes vectors in our datasets satisfy this condition. For the following analysis, we filter out Stokes vectors violating the DoP condition and the unstable Stokes vectors reconstructed from saturated/underexposed pixel intensity. + +# 5. Dataset Analysis + +Noise and Intensity Denoising Spectro-polarimetric images are susceptible to noise due to the low-light throughput of spectral and polarimetric filters. Our datasets are not exempt from these issues. To assess noise in Stokes images, we capture and average 100 images of a scene shown + +![](images/08a2bf439be10d2d975b8ee93016b8c016d5ea5f7d4913204f91a2f303597e8f.jpg) + +![](images/80f030427ce07d818d617b0da1cf757c7cc1e75f9edc54324cf06a32d2a43b33.jpg) +(a) Top 40 PCA bases of hyperspectral Stokes vector components + +![](images/34b839a8c8e3e3ec7e213bf82c2938b6b1a89004b2d1c75fd615cbd341d0c16c.jpg) +(c) Proportion of variance (log scale) + +![](images/6beafc6405626c62bf4ed5c888bdf8ffcda60596283bb6a3fea90671190fe0eb.jpg) +(d) BPP and MSE of PCA + +![](images/3d7bc3013b168d2a9b0d2f675ddde8a6163fc7b1ded1c495c8fdefe7447e86b1.jpg) +(b) Qualitative results (DoP/AoLP) + +![](images/3bb3146713a1a4ba90e0800fe26a29ddcdc414aef0b2c8badba6fab5b7517dd4.jpg) +(e) Training PSNR value + +![](images/d7c04bd6be08d52be784f8cec484e93bd3bb43e18ca20c5b43fc0b2e3e06df62.jpg) +(f) BPP and MSE of INR + +![](images/4f172d653e4cea0ced0a23beace1adcba303ca82368310ed409a59faa406b7ef.jpg) +Figure 4. Efficient spatio-spectral-polarimetric representations. (a) PCA basis of the hyperspectral Stokes dataset in sRGB. (b) Qualitative results of PCA and INR compared to single-shot denoising [66] at $550\mathrm{nm}$ . (c) Proportion of variance with respect to each PCA basis in order, $\log (\sigma_i^2 / \sum_n \sigma_n^2)$ , where $\sigma_i$ denotes standard deviation of the $i$ -th basis. (d) BPP and MSE analysis of PCA with respect to the number of PCA bases. (e) Training PSNR curve of INR. (f) BPP and MSE value of INR with respect to the number of MLP layers. + +![](images/545135a5cc91a4ad03c0432b1fdb5965dc5229932718c1f143c2cf662300e0ed.jpg) +Figure 5. Noise in Stokes images and intensity denoising. (a) Stokes vector $s_1$ reconstructed from a single-shot, single-shot with a learned intensity denoiser [66], and burst imaging (Pseudo GT) averaged over 100 shots. (b) Reconstruction accuracy of a Stokes image with varying number of averaged images. (c) Reconstruction accuracy of normalized Stokes elements with and without intensity denoising. + +in Figure 3(c) for each polarization configuration $\Theta$ . From these averaged images, we reconstruct pseudo ground-truth Stokes image, shown in Figure 5(a). Figure 5(b) reports the MSE and PSNR of reconstructed Stokes images with respect to the number of averaged images. To achieve a + +PSNR exceeding $35\mathrm{dB}$ , we need to average over 4/25 shots for the trichromatic/hyperspectral Stokes cameras, indicating lower SNR of the hyperspectral Stokes dataset. We find that state-of-the-art learning-based intensity denoising methods, such as KBNet [66], can effectively reduce noise for each polarization configuration, leading to accurate Stokes-vector reconstruction, despite lack of polarization images during training. For the denoised single-shot capture, we achieve a PSNR of $34.5\mathrm{dB}$ , demonstrating the potential of using pretrained intensity restoration networks for Stokes imaging. Figure 5(c) shows PSNRs of reconstructed Stokes images per each spectral channel and normalized Stokes element. With the intensity denoising, we find that the PSNR significantly increases for $s_1$ , $s_2$ , and $s_3$ . + +Efficient Spatio-spectral-polarimetric Representations Each pixel in a hyperspectral Stokes image contains a Stokes vector for every spectral channel, leading to a total of $21 \times 4 \times 32$ bits using single-precision floating format. This results in a bit-per-pixel (BPP) value of 2,688, equating to $100\mathrm{MB}$ for storing a single hyperspectral Stokes image of $512 \times 612$ pixels. Given the substantial memory required to store a spectro-polarimetric image, we investigate efficient representations of real-world spatio-spectral-polarimetric data, for which we explore two methods: a PCA-based model and an implicit neural model. + +First, we apply PCA on non-overlapping hyperspectral Stokes patches. Figure 4(a) shows the 40 most significant + +PCA bases, revealing varied spatial and spectral features for each Stokes element: $s_0$ , $s_1$ , $s_2$ , $s_3$ . Notably, spatial structures are more evident in $s_0$ , while $s_1$ , $s_2$ , $s_3$ shows spectral features, suggesting a stronger correlation between spectrum and polarization than spatial features. To visualize hyperspectral intensity, we convert it to sRGB, which means that the same sRGB color may originate from different spectra. Figure 4(c) shows the variance of the coefficients for the top 200 PCA bases, indicating that spati-spectral-polarimetric data can indeed be compressed. This is further evidenced by Figure 4(d), which shows the reconstruction error and BPP when varying number of PCA bases used to recreate a hyperspectral Stokes image. Using $2.22\mathrm{MB}$ coefficients adequately represents a $100\mathrm{MB}$ hyperspectral Stokes image as shown in Figure 4(b), exhibiting a high compression rate with the reconstruction error of $2.69\times 10^{-5}$ . See the Supplemental Document for further details on PCA analysis. + +Second, we devise an INR for hyperspectral Stokes images by modifying NeSpoF [34]. The original NeSpoF architecture models a volumetric hyperspectral Stokes field. Here, instead, we aim to represent a hyperspectral Stokes image. Specifically, our INR, modeled by an MLP $F_{\gamma}$ , outputs the Stokes vector $s$ for a given pixel position $p_x, p_y$ and spectral channel index $c$ , that is + +$$ +\mathbf {s} = F _ {\gamma} \left(p _ {x}, p _ {y}, c\right), \tag {5} +$$ + +where $\gamma$ is the network parameters. We fit the MLP to a hyperspectral Stokes image by minimizing the reconstruction loss between the network output and the hyperspectral Stokes image. The training curve is shown in Figure 4(e). Figure 4(f) shows the reconstruction error and BPP of our INR with respect to varying number of the MLP layers. With just 8 layers corresponding to a BPP of 60, we achieve a converged reconstruction error of $1.90 \times 10^{-5}$ , resulting in just $2.22\mathrm{MB}$ of network parameters to represent a $100\mathrm{MB}$ hyperspectral Stokes image. See Supplemental Document for architecture details. + +Both PCA and INR experiments validate that a natural spectro-polarimetric image is compressible. PCA provides PCA basis vectors that can be applied to any instance, however with a lower reconstruction accuracy than INR. INR is overfitted to a single instance, while higher reconstruction accuracy can be achieved. These representations are also beneficial for denoising spectral-polarimetric images, as shown in Figure 4(b), which even outperforms the learning-based intensity denoiser [66]. + +Polarized and Unpolarized Intensity We decompose hyperspectral Stokes images into the polarized images $P = \sqrt{s_1^2 + s_2^2 + s_3^2}$ and unpolarized images $U = s_0 - P$ per each spectral channel. Figure 6(a) shows specular reflections such as the glow of leather sofa separated into po + +![](images/dad01d455c5f223d5a00ea97a0dacbfdbcc6d1166bcdf03964ce71b26454c12e.jpg) +(a) Separation into polarized and unpolarized light + +![](images/991865a28e7ee694ca58927b5f1f4dc8c32ade4541d9ad95ddfe5e6c0caeac4d.jpg) +(b) Intensity distribution by polarization +Figure 6. Polarized and unpolarized light distributions. (a) Separation into polarized and unpolarized light. (b) Intensity distributions for polarized and unpolarized components. (c) Variance of PCA basis of polarized and unpolarized intensity across spectral channel. + +![](images/4530fbd91038d32a60e6d4744cc920029ae875b58edc4504380f3e22cdea193a.jpg) +(c) Variance of basis by polarization + +larized light. Note that the polarized image typically encodes the illumination colors for dielectric surfaces. Figure 6(b) reveals that the intensity distributions of polarized light, obtained from the entire hyperspectral Stokes dataset, is skewed towards low and high-intensity values compared to the unpolarized light. This is because polarized images mostly contain specular reflections, which is sparsely distributed and has high intensity values. We then compute the variance of the PCA bases for polarized intensity along the spectral channel. Figure 6(c) highlights that the spectral variance for polarized intensity is lower than that of unpolarized intensity. We speculate that the color of polarized light lies in a lower dimensional space than that of unpolarized light, since diffuse reflection with diverse spectral variations is mostly captured by unpolarized light, making the spectral variation of unpolarized light more pronounced. + +Stokes Vector Distributions in Natural Stokes Images Next, we analyze the distribution of all Stokes vectors in our Stokes dataset. Figure 7 shows the histograms of Stokes elements $s_0$ , $s_1$ , $s_2$ , $s_3$ across all spectral channel. We find that the distributions of Stokes elements $(s_1, s_2, s_3)$ have symmetric shapes of positive and negative sides. Stokes elements of $s_1$ and $s_2$ have similar shapes meaning that the directions of linearly-polarized light are equally distributed in natural images. The circular component $s_3$ is more condensed near zero than the linear elements, resulting in a + +![](images/a01b8caf2b4dd5300486647aa5478efe9cb28c0187fcaa651b893262529f03d9.jpg) +(a) Visualization of Stokes vector + +![](images/1b62e1ba99aa86b84970a188f2bccebcf98ef6f76f7eed7bf9b0b7d711a59ea9.jpg) +(b) Stokes vector distribution +Figure 7. Stokes-vector distributions. (a) Stokes images of $s_1$ , $s_2$ , and $s_3$ at the green channel. (b) Stokes-vector distributions of $s_0$ , $s_1$ , $s_2$ and $s_3$ for trichromatic and hyperspectral datasets. + +higher peak both in trichromatic and hyperspectral datasets. This indicates that pixels are often more linearly polarized than circularly polarized. Refer to the Supplemental Document for further analysis. + +Gradient Analysis of Stokes Images Gradient distribution of images has been often used as priors for image-based applications including image restoration, understanding, and editing. Here, we perform gradient analysis of Stokes and polarization-feature images. Figure 8(b) shows that the gradient of Stokes and normalized Stokes vectors exhibits a similarity to Hyper-Laplacian priors, commonly used to describe the gradient of natural intensity-images. An interesting finding is that total intensity $s_0$ has more high-gradient values than the linear components of $s_1$ and $s_2$ , and the circular component $s_3$ has the lowest-value distribution. + +We analyze the gradient distributions of polarization features, including AoLP, degree of linear polarization (DoLP), degree of circular polarization (DoCP), and CoP. DoLP and DoCP are computed as $\mathrm{DoLP} = \sqrt{s_1^2 + s_2^2} / s_0$ and $\mathrm{DoCP} = |s_3| / s_0$ respectively. To compute the gradient of AoLP images, we consider the angular wrapping property. That is, AoLP has a range from $-\frac{\pi}{2}$ to $\frac{\pi}{2}$ and the AoLPs of $-\frac{\pi}{2}$ and $\frac{\pi}{2}$ are identical. Thus, if the gradient exceeds $\frac{\pi}{2}$ , we estimate the gradient as $\nabla \mathrm{AoLP} - \pi \times \mathrm{sign}(\nabla \mathrm{AoLP})$ , where $\nabla$ is the gradient operator and $\mathrm{sign}$ is the sign operator that returns 1 if positive, otherwise $-1$ . Figure 8(c) shows that the gradients of AoLP are generally higher than DoLP and DoCP. This implies that sparsity in the measurement gradient is milder for AoLP than DoLP and DoCP. DoLP and DoCP have shapes similar to HyperLaplacian priors while DoCP is sharper than DoLP. The + +![](images/61e5db7117b492ef3307d3561460bb1b5ca2f541635034ad169d92736f6b5da9.jpg) + +![](images/29dc883bbc282b415441de40ea5ff281a4bbcf3562cd2fc154da5dbcf1643f4d.jpg) +(a) Visualization of polarization features and gradients + +![](images/d54bb3e031ed7d9baf9ed315dd7fad00c38c72bc55c26acd0ed1883b4bdd850d.jpg) +(b) Gradient distributions of Stokes vector + +![](images/58ecf995f2c55d4b12b3915f358de49bde2b5274f8f1632542dd64ce5c5fe6f0.jpg) +(c) Gradient distributions of polarization features +Figure 8. Gradient analysis of Stokes images. (a) Visualization of AoLP, DoLP, DoCP and CoP values and their gradients. Examining the log probability of the gradient for (b) Stokes vectors $s_0$ , $s_1$ , $s_2$ , $s_3$ and normalized Stokes vectors $s_1'$ , $s_2'$ , and $s_3'$ , and (c) polarization features including DoLP, DoCP, AoLP and CoP. + +gradient of CoP shows symmetric distributions for right-circular and left-circular directions. Unlike AoLP, the probability decreases as the gradient approaches extreme values. The difference in tendency between linear-polarization and circular-polarization features, as well as their distributions, means that we need distinct priors for each polarization feature, emphasizing the importance of a full Stokes dataset that measure not only linear but also circular polarization. + +Shape from Polarization and Spectral Channels Methods that recover shape from polarization, SfP, have made rapid progress in the last decade. SfP aims to extract normals by analyzing the normal-dependent polarization change of reflected light. Specifically, SfP analyzes the DoP and AoLP based on Fresnel theory [9], which describes the polarization change of light upon reflection and transmission at a smooth surface [32, 41]. Here, we analyze an overlooked problem in SfP: the spectral dependency of estimated normals. Surface normals, as a geometric sur + +![](images/5657ad2421673cac8001aaf59c93ff875ca873b6224563bdbd132049f26a25a4.jpg) +(a) Denoised Trichromatic + +![](images/f22eb145d0a294366f5655e9d0af20f39212c25da859fdecab1bade01696da6d.jpg) + +![](images/0fbe3298a70bc7186f32306b70c80c2c42fbc1cbb597cd9d2fec78b676b45013.jpg) + +![](images/3218d759c7241c157d030108f59e89d8e9e4ce6cdc64d678b564676928f9308c.jpg) + +![](images/308710d00d5f81abf6bb5c4ae00b80a74bceaef40f5086a241fa4a35c5950877.jpg) +(b) Normal map from +denoised R channel +(c) Normal map from +(e) Denoised Trichromatic dataset +Figure 9. Spectral dependency of conventional SFP method. (a) Trichromatic Stokes image and estimated surface normals [41] for each red, green, and blue spectral channels shown in (b), (c), and (d). Graphs (e) and (f) show the probability distributions of standard deviation of normal component $x$ , $y$ , and $z$ along the spectral channels for both datasets. + +![](images/9452f3243c68fd8999f89e358f29566e0c7aab49b262ca84910c1d1a97b7254a.jpg) +(d) Normal map from +(f) Denoised Hyperspectral dataset + +face property, should be consistent regardless of the input spectral channels used for SfP. In Figure 9, we test the state-of-the-art SfP method by Lei et al. [41], designed for in-the-wild scenes. The evaluation results on our normalized Stokes dataset clearly reveal that normal maps reconstructed from different spectral channels exhibit variations. We compute the standard deviations of spectral variations for each $x$ , $y$ , and $z$ component of the estimated normals. Figures 9(e) and (f) show the probability distributions of the standard deviation, highlighting the large variations in the estimated normals for both hyperspectral and trichromatic datasets. Interestingly, the $x$ and $y$ components of normals show larger standard deviations than the $z$ component. This implies that the spectral variation of DoP, which determines the $z$ component, has less impact on the distribution than that of AoLP, which governs the $x$ and $y$ components. + +Environment Dependency Figure 10 shows the Poincaré spheres projected onto the $s_1' - s_2'$ and $s_1' - s_3'$ planes for the three data labels: Indoor, Sunlight and Cloudy. Sunlight is known to contain more circularly polarized light compared to other artificial lighting [25]. As shown in Figure 10(a), Stokes vectors are distributed more widely across $s_3'$ axis under sunlight compared with Indoor scene. In addition, we find that DoCP is distributed at higher values for the sunlight compared to the indoor: pixels with DoCP over 0.5 are rarely observed in indoor scenes. This is also confirmed in the example $s_3$ images for indoor and sunlight scenes. + +Another interesting finding is that cloudy or sunny illumination result in different polarization statistics. Figure 10(a) shows that Stokes vectors of cloudy scenes are more concentrated near the origin, meaning that light is more depolarized compared to light under clear sunlight. + +![](images/63b612cd0e0f15640d6407d849c395089991ff56167d21b449243f5ff6446d42.jpg) + +![](images/82591d67cdd8a1f66b69f5f2e444fe0de06c800ba38f2ca2670db0805e437b49.jpg) + +![](images/0d7dcc985cac6896475fdffbf4b35fe4671f9c4518e362bd33aa4b2c5787b0ce.jpg) + +![](images/2bb0bb8175d4206daddfe686d7d56d98912f8dd2bc2429dda1cd9390db2246fa.jpg) +(a) Poincaré sphere projections + +![](images/7cd2fe00c56bd23f57614e679f928bbd9d335711e497468de83d7ccd173cfe87.jpg) + +![](images/6056ddedb9a42638f1001f0103a1a295b14877b510310235de00fb6a82588ca9.jpg) + +![](images/0f91a0870b5311cb4aac073d6c8db13c1f1d2009869b5f8a7c4c4fcdf98f8cb6.jpg) +(b) DoCP distribution +Figure 10. Environment dependency. (a) Projected Poincaré spheres onto the $s_1' - s_2'$ and $s_1' - s_3'$ planes with respect to dataset labels. Colorbar is based on the normalized pixel count. (b) DoCP distributions for indoor and sunlight categories. (c) Example $s_3$ images. + +![](images/390e8b16dc03c769dd2ac833f8e3b863298cd9ab2d80b9bf861c2ab76b23cb51.jpg) + +![](images/4b32580a78ab7b975e3cb4c2e23a6ac873342e82120b5bf2c005cd6a41f042cc.jpg) +(c) $S_{3}$ visualization + +This is aligned with previous studies [24, 58] that report the impact of cloud-particle scatterings on light depolarization. + +# 6. Conclusion + +In this work, we have introduced a trichromatic and hyperspectral Stokes image dataset that encompasses diverse natural scenes and various illumination conditions, totaling more than 2,333 scenes. We analyze the empirical distribution of the Stokes vectors of natural spectropolarimetric images. To efficiently represent spati-spectral-polarimetric data, we devise a PCA-based model and an implicit neural representation. We further provide detailed analysis on Stokes gradient distributions, denoising characteristics, spectral dependency of SfP, and environment dependency. As such, our work provides a foundation for future research on spectral-polarimetric imaging and vision. + +Acknowledgements We thank Onur Akkaya for helpful discussion. Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, 2022R1A6A1A03052954). 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Springer, 2020. 2 \ No newline at end of file diff --git a/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/images.zip b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f573c99b2ba89bcff00909be4757df671b774c1d --- /dev/null +++ b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a2da92b3dfcd890261332e2fc1d965b7bfd80580a133811e70eabdc1f538348e +size 807054 diff --git a/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/layout.json b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4c3186d10e13eb441e92193860a99e9a73df6956 --- /dev/null +++ b/2024/Spectral and Polarization Vision_ Spectro-polarimetric Real-world Dataset/layout.json @@ -0,0 +1,12124 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 170, + 103, + 424, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 170, + 103, + 424, + 140 + ], + "spans": [ + { + "bbox": [ + 170, + 103, + 424, + 140 + ], + "type": "text", + "content": "Spectral and Polarization Vision: Spectro-polarimetric Real-world Dataset" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": "Yujin Jeon" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": " Eunsue Choi" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": " Youngchan Kim" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": " Yunseong Moon" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": " Khalid Omer" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": " Felix Heide" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "text", + "content": " Seung-Hwan Baek" + }, + { + "bbox": [ + 105, + 160, + 470, + 190 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "spans": [ + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "text", + "content": " POSTECH " + }, + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "text", + "content": " Meta " + }, + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 174, + 197, + 419, + 213 + ], + "type": "text", + "content": " Princeton University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 239, + 192, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 239, + 192, + 251 + ], + "spans": [ + { + "bbox": [ + 143, + 239, + 192, + 251 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 265, + 290, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 265, + 290, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 265, + 290, + 540 + ], + "type": "text", + "content": "Image datasets are essential not only in validating existing methods in computer vision but also in developing new methods. Many image datasets exist, consisting of trichromatic intensity images taken with RGB cameras, which are designed to replicate human vision. However, polarization and spectrum, the wave properties of light that animals in harsh environments and with limited brain capacity often rely on, remain underrepresented in existing datasets. Although there are previous spectro-polarimetric datasets, they have insufficient object diversity, limited illumination conditions, linear-only polarization data, and inadequate image count. Here, we introduce two spectro-polarimetric datasets, consisting of trichromatic Stokes images and hyperspectral Stokes images. These datasets encompass both linear and circular polarization; they introduce multiple spectral channels; and they feature a broad selection of real-world scenes. With our dataset in hand, we analyze the spectro-polarimetric image statistics, develop efficient representations of such high-dimensional data, and evaluate spectral dependency of shape-from-polarization methods. As such, the proposed dataset promises a foundation for data-driven spectro-polarimetric imaging and vision research." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 564, + 128, + 577 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 564, + 128, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 564, + 128, + 577 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 585, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 585, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 585, + 287, + 693 + ], + "type": "text", + "content": "Recent progress in computer vision can be largely attributed to comprehensive studies of real-world image datasets, such as ImageNet [14]. Foundation models [1, 35, 53, 64] further underscore data significance. Most of these datasets comprise trichromatic intensity images, inspired by human visual perception, enabling machines to emulate human vision with trichromatic RGB cameras. As such, the datasets have facilitated the development of low-cost, camera-based autonomous agents capable of perceiving and interacting" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 240, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 240, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 240, + 545, + 300 + ], + "type": "text", + "content": "with our world, as we do. However, the reliance on trichromatic intensity in existing image datasets also comes with inherent limitations for analyzing objects in depth. Examples include textureless surface, low-albedo objects, and transparent materials." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 303, + 546, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 303, + 546, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 303, + 546, + 519 + ], + "type": "text", + "content": "Light possesses wave properties, including polarization and spectrum [9], which are not faithfully captured by trichromatic intensity imaging. While these properties are invisible to human, animals like honeybees and ants leverage the polarization and spectrum for navigation and other tasks. Horvath and Varju [25] provide diverse examples and mechanisms of spectral and polarimetric vision in animals. Partly drawing inspiration from nature, researchers have extended the analysis of spectrum and polarization to a variety of fields, including computer vision, robotics, and astronomy. This has spurred interest in polarimetric [7, 8, 38, 49] and hyperspectral imaging [2, 10, 28], and more recently, their integration into spectro-polarimetric imaging [3, 17, 18, 23, 26, 45, 47, 50, 54, 67]. Prior work using spectro-polarimetric images has shown potential for skin analysis [67], vegetation classification [63], shape reconstruction [27], object recognition [13], and segmentation [30, 55]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 714 + ], + "type": "text", + "content": "There are existing spectro-polarimetric datasets, summarized in Figure 2, that have been invaluable for these analysis [19, 38, 39, 52] and training neural networks [4, 11, 22, 36, 40-42, 46, 48]. However, these datasets unfortunately do not capture the diversity of real-world spectropolarimetric images as effectively as their trichromatic intensity counterparts do. They typically suffer from limited object, scene, and illumination diversity, contain primarily linear polarization information, and offer a small number of images. To advance the field, we propose a comprehensive spectro-polarimetric dataset that encompasses: (1) Full Stokes polarimetric data, including both linear and circular polarization states, represented by Stokes vectors [9] for each pixel and wavelength. (2) A diverse range of spectral channels, facilitating in-depth exploration of the interplay between spectrum and polarization. (3) A broad array of" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 215, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 215, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 215, + 713 + ], + "type": "text", + "content": "*These authors contributed equally to this work." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22098" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 95 + ], + "type": "text", + "content": "real-world scenes, crucial for extracting meaningful statistics and relationships within spectro-polarimetric images." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 96, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 96, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 96, + 287, + 275 + ], + "type": "text", + "content": "To this end, we introduce two spectro-polarimetric datasets designed to cover real-world spectro-polarimetric scenes: a trichromatic Stokes dataset consisting of 2,022 images, and a hyperspectral Stokes dataset containing 311 images across 21 spectral channels. The trichromatic Stokes dataset covers a wider range of scenes thanks to its convenient capture setup and process. The hyperspectral Stokes dataset provides richer spectral-polarimetric information than the trichromatic Stokes dataset. Both datasets cover a variety of natural indoor and outdoor scenes. Each image in these datasets is annotated with four specific parameters: the type of environment (indoor or outdoor), the illumination conditions (clear/cloudy sunlight or white/yellow office light), the timestamp of capture, and the scene categorization (either object- or scene-oriented)." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 276, + 288, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 288, + 467 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 288, + 467 + ], + "type": "text", + "content": "Utilizing these datasets, we systematically analyze the statistics of real-world spectro-polarimetric images. We focus on examining statistics of Stokes vectors, in addition to the gradients and polarimetric attributes associated with them. We also conduct an analysis of unpolarized and polarized images derived through polarimetric decomposition. We then develop two efficient spatio-spectral-polarimetric representations using principal component analysis (PCA) and implicit neural representation (INR). These representations exhibit effective denoising capabilities and low memory footprints by exploiting the compressible structure of spectro-polarimetric images. We also analyze the impact of intensity denoising for spectro-polarimetric images, spectral dependency of shape-from-polarization methods, and environment dependency on the statistics of spectropolarimetric images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 467, + 263, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 467, + 263, + 479 + ], + "spans": [ + { + "bbox": [ + 59, + 467, + 263, + 479 + ], + "type": "text", + "content": "In summary, we make the following contributions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 479, + 287, + 598 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 479, + 287, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 287, + 537 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 287, + 537 + ], + "type": "text", + "content": "- We introduce a trichromatic Stokes dataset and a hyperspectral Stokes dataset, featuring 2,333 diverse annotated indoor and outdoor scenes under various illumination conditions, which encompasses full-Stokes polarization data for linear and circular states." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 539, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 539, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 539, + 287, + 598 + ], + "type": "text", + "content": "- We develop efficient spatio-spectral-polarimetric representations and analyze real-world spectro-polarimetric images, encompassing Stokes vectors and their gradients, unpolarized and polarized images, shape from polarization, denoising, and environment dependency." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 609, + 134, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 134, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 134, + 621 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Spectro-polarimetric Image Dataset Several datasets have been introduced for analyzing polarization and spectral information. With the advent of trichromatic linear-polarization cameras, a line of work has attempted to acquire trichromatic linear-polarization images, ranging from a few objects and scenes [5, 11, 42, 52] to a large number of scenes for specific target applications such as reflection" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 422, + 193 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 422, + 193 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 422, + 193 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 422, + 193 + ], + "type": "image", + "image_path": "52b8d9f67846fe527fa9ece3499e68b548dfedb7fb5477b0afee7295f3678d4e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 328, + 195, + 400, + 205 + ], + "lines": [ + { + "bbox": [ + 328, + 195, + 400, + 205 + ], + "spans": [ + { + "bbox": [ + 328, + 195, + 400, + 205 + ], + "type": "text", + "content": "(a) Polarization ellipse" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 211, + 545, + 256 + ], + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 256 + ], + "type": "text", + "content": "Figure 1. Polarization visualizations. (a) Polarization ellipse depicts the electric-field oscillation projected onto a plane tangent to the light propagation. (b) Poincaré sphere visualizes the polarization state of light on the normalized Stokes-vector axes " + }, + { + "bbox": [ + 304, + 211, + 545, + 256 + ], + "type": "inline_equation", + "content": "s_1', s_2', s_3'" + }, + { + "bbox": [ + 304, + 211, + 545, + 256 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 423, + 70, + 545, + 193 + ], + "blocks": [ + { + "bbox": [ + 423, + 70, + 545, + 193 + ], + "lines": [ + { + "bbox": [ + 423, + 70, + 545, + 193 + ], + "spans": [ + { + "bbox": [ + 423, + 70, + 545, + 193 + ], + "type": "image", + "image_path": "0457c3835359878177b937afd0c6fd7fdfb06f2eb2141d31f28c771e6afbf448.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 447, + 195, + 512, + 205 + ], + "lines": [ + { + "bbox": [ + 447, + 195, + 512, + 205 + ], + "spans": [ + { + "bbox": [ + 447, + 195, + 512, + 205 + ], + "type": "text", + "content": "(b) Poincaré sphere" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 262, + 545, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 545, + 381 + ], + "type": "text", + "content": "separation [40, 46] and glass segmentation [48]. Lapray et al. [39] acquire linear-polarization images for the near-infrared spectral band, albeit only on 10 objects. Fan et al. [19] acquire the first multi-spectral full-Stokes polarimetric dataset covering linear and circular states, while it only contains 64 flat objects captured in a lab environment. Our proposed datasets enables analyzing the statistics of real-world spectro-polarimetric images, which cannot be achieved by prior datasets. See Figure 2 for a comprehensive comparison." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 396, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 659 + ], + "type": "text", + "content": "Applications of Spectro-polarimetric Imaging Spectropolarimetric information has been investigated for diverse vision and imaging tasks. Using linear-polarization images has found applications in shape reconstruction [4, 5, 7, 16, 21, 31, 41, 70], appearance acquisition [15, 36], removing reflections [37, 40, 46, 51, 59, 62], transparent-object segmentation [33, 48], seeing through scattering [20, 43, 68], and image enhancement [69]. Trichromatic Stokes images have been used for tone-mapping [12] and seeing through scattering [6]. Expanding into multi-spectral domain, spectral-polarimetric analysis has been applied to object recognition [13], skin analysis [67], dehazing [61], specular reflection inpainting [29], background segmentation [30] and tensor representation [65]. In addition to vision tasks, spectro-polarimetric imaging has been used for various biological applications, such as marsh vegetation classification [63], coastal wetland classification [55] and leaf nitrogen determination [44]. While the aforementioned studies demonstrate the benefits of using spectropolarimetric data, we believe that the full potential of spectro-polarimetric images is still locked by the absence of real-world spectro-polarimetric datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 669, + 465, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 669, + 465, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 669, + 465, + 682 + ], + "type": "text", + "content": "3. 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"Hyperspectral Stokes dataset" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 101, + 181, + 230, + 189 + ], + "lines": [ + { + "bbox": [ + 101, + 181, + 230, + 189 + ], + "spans": [ + { + "bbox": [ + 101, + 181, + 230, + 189 + ], + "type": "text", + "content": "(a) Dataset thumbnails visualized in sRGB" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 164, + 79, + 287, + 181 + ], + "lines": [ + { + "bbox": [ + 164, + 79, + 287, + 181 + ], + "spans": [ + { + "bbox": [ + 164, + 79, + 287, + 181 + ], + "type": "image", + "image_path": "edbc326de1768d5be483da537c77cd563eccceec48977acfe1fa013262dfbaa7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 51, + 198, + 161, + 262 + ], + "blocks": [ + { + "bbox": [ + 51, + 198, + 161, + 262 + ], + "lines": [ + { + "bbox": [ + 51, + 198, + 161, + 262 + ], + "spans": [ + { 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[ + 46, + 358, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 545, + 392 + ], + "type": "text", + "content": "Figure 2. Spectro-polarimetric image datasets. We present trichromatic and hyperspectral Stokes datasets of which thumbnails are shown in (a) and label statistics in (b). The table shown on the right compares our datasets with existing spectro-polarimetric datasets. Ours are the only datasets that encompass both linear (LP) and circular (CP) polarization over multiple of spectral bands for diverse real scenes." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 232, + 270, + 283, + 347 + ], + "blocks": [ + { + "bbox": [ + 232, + 270, + 283, + 347 + ], + "lines": [ + { + "bbox": [ + 232, + 270, + 283, + 347 + ], + "spans": [ + { + "bbox": [ + 232, + 270, + 283, + 347 + ], + "type": "image", + "image_path": "23477c263c2f4299234d9d3aaea71ab21b6650bb1c5dcc3f8bcdb26d81b1a147.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " denotes the total intensity, " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " describe the differences in the intensity of linearly-polarized components at orientations of " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "0^{\\circ} / 90^{\\circ}" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "45^{\\circ} / -45^{\\circ}" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " is the difference in intensity between right- and left-circularly polarized components. Figure 1 shows two visualization methods for polarization, the polarization ellipse and Poincaré sphere. Polarization ellipse can be described in terms of the orientation angle " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " and ellipticity " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " with respect to the projected Stokes vector " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": " axes [9]. The Poincaré sphere visualizes polarization in a three-dimensional space, using the normalized Stokes-vector elements relative to the total intensity: " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_1' = s_1 / s_0" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_2' = s_2 / s_0" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "s_3' = s_3 / s_0" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ". To effectively analyze a Stokes vector, one can compute the degree of polarization (DoP) denoted as " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ", the angle of linear polarization (AoLP) represented by " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\psi" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ", and the ellipticity angle given by " + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 396, + 287, + 588 + ], + "type": "text", + "content": ", that is" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 52, + 594, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 594, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 52, + 594, + 287, + 620 + ], + "type": "interline_equation", + "content": "\\rho = \\frac {P}{s _ {0}}, \\psi = \\frac {1}{2} \\arctan \\left(\\frac {s _ {2}}{s _ {1}}\\right), \\chi = \\frac {1}{2} \\arctan \\left(\\frac {s _ {3}}{L}\\right), \\tag {1}", + "image_path": "e3173260433269990e88f214779048190fae7aaba807d464e6f40efa27b1f88f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "P = \\sqrt{s_1^2 + s_2^2 + s_3^2}" + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "L = \\sqrt{s_1^2 + s_2^2}" + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": ". We also use the polarimetric visualization method proposed by Wilkie et al. [60] using DoP, AoLP, and chirality of polarization (CoP). CoP describes the left- or right-handedness of the circularly polarized component, which is related to " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\chi" + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": ". Finally, the Mueller matrix " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{4 \\times 4}" + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": " describes the change of a Stokes vector: " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{\\mathrm{out}} = \\mathbf{M}\\mathbf{s}_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 628, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{\\mathrm{out}}" + } + ] + } + ], + "index": 17 + }, + { + "type": "table", + "bbox": [ + 293, + 80, + 542, + 347 + ], + "blocks": [ + { + "bbox": [ + 293, + 80, + 542, + 347 + ], + "lines": [ + { + "bbox": [ + 293, + 80, + 542, + 347 + ], + "spans": [ + { + "bbox": [ + 293, + 80, + 542, + 347 + ], + "type": "table", + "html": "
DatasetPolar.# of bandsScene countScene diversity
[41]LP1522Outdoor scenes
[5]LP1300Indoor objects
[39]LP610Indoor objects
[52]LP340Indoor objects
[11]LP33Indoor multiview
[11]LP32Synthetic multiview
[22]LP36Indoor multiview
[40]LP3807Reflective objects
[42]LP3500Outdoor scenes
[36]LP344,300Synthetic
[46]LP33,200Reflective objects
[48]LP34,500Transparent objects
[38]LP32,000Indoor/outdoor scenes
[19]LP, CP1867Flat objects
[34]LP, CP214Synthetic multiview
[34]LP, CP214Indoor/outdoor multiview
Ours (RGB)LP, CP32,022Indoor/outdoor scenes
Ours (HS)LP, CP21311Indoor/outdoor scenes
", + "image_path": "7596b707040f160d0cbb317ea37b76856477c49a4a70639ea615865919ac5c86.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 396, + 545, + 420 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 545, + 420 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 545, + 420 + ], + "type": "text", + "content": "are the input/output Stokes vectors. For more details on polarization, we refer to the book by Collett [9]." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 434, + 469, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 469, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 469, + 448 + ], + "type": "text", + "content": "4. Spectro-polarimetric Dataset" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 454, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 611 + ], + "type": "text", + "content": "We introduce a trichromatic Stokes dataset comprising 2,022 Stokes images and a hyperspectral Stokes dataset with 311 Stokes images at 21 spectral channels. Both datasets cover natural real-world indoor and outdoor scenes. Each Stokes image is accompanied by four labels: (1) the environment (indoor or outdoor), (2) the illumination condition, including clear or cloudy sunlight and white or incandescent light, (3) the time of image capture, (4) the scene type, distinguishing between object-oriented and scene-oriented. Figure 2 shows thumbnails, statistics, and comparison of our datasets to existing ones. Prior datasets suffer from a narrow range of scenes, restricted illumination conditions, linear polarization only, and fewer images." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Acquisition We acquire the datasets using two imaging systems depicted in Figure 3(a), proposed and developed by previous studies [34, 56]. First, the trichromatic Stokes camera by Tu et al. [56] incorporates on-sensor quarterwave plates (QWPs) and linear polarizers (LPs) [9]. This allows for single-shot capture of trichromatic Stokes images, enabling convenient data collection on diverse scenes. The" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22100" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 154, + 143 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 154, + 143 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 154, + 143 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 154, + 143 + ], + "type": "image", + "image_path": "19b199622aad5f1f0286ed59e52e074e01b05ee7e5bb4d2d2a796dda8d053be9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 156, + 69, + 279, + 154 + ], + "blocks": [ + { + "bbox": [ + 156, + 69, + 279, + 154 + ], + "lines": [ + { + "bbox": [ + 156, + 69, + 279, + 154 + ], + "spans": [ + { + "bbox": [ + 156, + 69, + 279, + 154 + ], + "type": "image", + "image_path": "ff600c947f52f981e2e8cabc40296abca33c09127f2d2b879a087f925480e509.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 283, + 68, + 546, + 152 + ], + "blocks": [ + { + "bbox": [ + 283, + 68, + 546, + 152 + ], + "lines": [ + { + "bbox": [ + 283, + 68, + 546, + 152 + ], + "spans": [ + { + "bbox": [ + 283, + 68, + 546, + 152 + ], + "type": "image", + "image_path": "113732ddce3ed700a5d87709eca0dab7d6e5a3c4c4ce7dca9f730212485946d7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 47, + 143, + 154, + 247 + ], + "blocks": [ + { + "bbox": [ + 47, + 143, + 154, + 247 + ], + "lines": [ + { + "bbox": [ + 47, + 143, + 154, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 143, + 154, + 247 + ], + "type": "image", + "image_path": "51c1daca8ee27d0408ea3929a31b8ab3b783c93ac0b754f1a8eb077c64df81eb.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 64, + 249, + 148, + 258 + ], + "lines": [ + { + "bbox": [ + 64, + 249, + 148, + 258 + ], + "spans": [ + { + "bbox": [ + 64, + 249, + 148, + 258 + ], + "type": "text", + "content": "(a) Stokes imaging system" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 154, + 163, + 278, + 247 + ], + "blocks": [ + { + "bbox": [ + 154, + 163, + 278, + 247 + ], + "lines": [ + { + "bbox": [ + 154, + 163, + 278, + 247 + ], + "spans": [ + { + "bbox": [ + 154, + 163, + 278, + 247 + ], + "type": "image", + "image_path": "72d0427d17dddaf003cfc2ca4220ce06beae2140ca6224695369adbb84a09795.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 172, + 249, + 265, + 257 + ], + "lines": [ + { + "bbox": [ + 172, + 249, + 265, + 257 + ], + "spans": [ + { + "bbox": [ + 172, + 249, + 265, + 257 + ], + "type": "text", + "content": "(b) Camera response function" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 278, + 158, + 546, + 249 + ], + "blocks": [ + { + "bbox": [ + 278, + 158, + 546, + 249 + ], + "lines": [ + { + "bbox": [ + 278, + 158, + 546, + 249 + ], + "spans": [ + { + "bbox": [ + 278, + 158, + 546, + 249 + ], + "type": "image", + "image_path": "be0c6e15c037540c96629bd1986b5bc3349efa8b2c3731e885ee8671eca99f4f.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 249, + 460, + 258 + ], + "lines": [ + { + "bbox": [ + 345, + 249, + 460, + 258 + ], + "spans": [ + { + "bbox": [ + 345, + 249, + 460, + 258 + ], + "type": "text", + "content": "(c) Multi-channel polarimetric images" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 261, + 546, + 283 + ], + "lines": [ + { + "bbox": [ + 46, + 261, + 546, + 283 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 546, + 283 + ], + "type": "text", + "content": "Figure 3. Acquisition of spectro-polarimetric images. We capture spectro-polarimetric images using (a) trichromatic and hyperspectral Stokes cameras [34, 57]. (b) Camera response functions. (c) Reconstructed raw Stokes images per each spectral channel." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": "resolution of a trichromatic Stokes image is 1900 (height) " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " 2100 (width) " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " 4 (Stokes elements) " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " 3 (RGB). Second, the hyperspectral Stokes camera from Kim et al. [34] captures images by sequentially scanning 21 spectral channels from " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "450\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "650\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "10\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " increments with a LCTF which functions as a LP. For each spectral channel, we capture images by rotating a QWP. The resolution of a hyperspectral Stokes image is 512 (height) " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " 612 (width) " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " 4 (Stokes elements) " + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "inline_equation", + "content": "\\times" + }, + { + "bbox": [ + 46, + 287, + 287, + 396 + ], + "type": "text", + "content": " 21 (wavelengths)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": "Spectro-polarimetric Image Formation Using the two imaging systems, we capture raw images from which a per-pixel Stokes vector for each spectral channel is reconstructed. We introduce an unified image formation model that can be applied to both cameras. Suppose a light ray with a Stokes vector " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_{\\lambda}" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": " at wavelength " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": " impinges on a Stokes camera. As the light passes through polarization filters modeled by the Mueller matrix " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\mathbf{M}(\\Theta)" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": ", its Stokes vector transforms. " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": " denotes the polarization-filter configuration. The camera sensor then captures light intensity, represented by the first element of the Stokes vector. The recorded intensity, " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "I_{c}(\\Theta)" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": ", at a spectral channel " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": " and polarimetric filter configuration " + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 410, + 287, + 567 + ], + "type": "text", + "content": ", is described by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 97, + 573, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 573, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 97, + 573, + 287, + 645 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} I _ {c} (\\Theta) = \\left[ \\int \\Omega_ {c, \\lambda} \\mathbf {M} _ {c} (\\Theta) \\mathbf {s} _ {\\lambda} d \\lambda \\right] _ {0} \\\\ = \\left[ \\mathbf {M} _ {c} (\\Theta) \\int \\Omega_ {c, \\lambda} \\mathbf {s} _ {\\lambda} d \\lambda \\right] _ {0} \\\\ = \\left[ \\mathbf {M} _ {c} (\\Theta) \\mathbf {s} _ {c} \\right] _ {0}, \\tag {2} \\\\ \\end{array}", + "image_path": "c62d69fe05e520d93f51654d7a8376e5143f81c2ff88d9527df06f176e3436d8.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\Omega_{c,\\lambda}" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " is the spectral transmission per channel at wavelength " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " shown in Figure 3(b). " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "[x]_0" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " denotes the first-element of the Stokes vector " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": ", which is the total intensity. For a spectral channel " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_c" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " is the Mueller matrix of the polarization-modulating optics, and " + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_c" + }, + { + "bbox": [ + 46, + 654, + 287, + 714 + ], + "type": "text", + "content": " is the Stokes vector." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 545, + 312 + ], + "type": "text", + "content": "For polarization modulation, both cameras utilize a QWP and a LP, yielding the Mueller matrix" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 365, + 321, + 545, + 335 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 321, + 545, + 335 + ], + "spans": [ + { + "bbox": [ + 365, + 321, + 545, + 335 + ], + "type": "interline_equation", + "content": "\\mathbf {M} _ {c} (\\Theta) = \\mathbf {C} _ {c} \\mathbf {Q} _ {c} \\left(\\theta_ {1}\\right) \\mathbf {P} _ {c} \\left(\\theta_ {2}\\right), \\tag {3}", + "image_path": "526cf89437d427f41501fb4c202efcfc5cc8b91c67f859cd4c38522ea064d998.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{C}_c" + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "content": " is the error-compensating calibration matrix [34, 57]. " + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_c" + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{P}_c" + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "content": " are the QWP and LP Mueller matrices [9], respectively. The set " + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "inline_equation", + "content": "\\Theta = \\{\\theta_1,\\theta_2\\}" + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "content": " denotes the corresponding angles of the QWP fast axis and the LP polarization axis, which is set for accurate Stokes vector reconstruction [34, 57]. Lastly, we determine the per-channel Stokes vector " + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "inline_equation", + "content": "\\mathbf{s}_c" + }, + { + "bbox": [ + 304, + 343, + 546, + 428 + ], + "type": "text", + "content": " by solving the least-squares problem" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 348, + 437, + 545, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 437, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 348, + 437, + 545, + 471 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {s} _ {c}} {\\operatorname {a r g m i n}} \\sum_ {i = 1} ^ {| \\Theta |} \\left(I _ {c} (\\Theta_ {i}) - \\left[ \\mathbf {M} (\\Theta_ {i}) \\mathbf {s} _ {c} \\right] _ {0}\\right) ^ {2}. \\tag {4}", + "image_path": "e94d7bfa25af78e5d8162473c6d56e4b31a33a93886c61ddce44131467415265.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 479, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 538 + ], + "type": "text", + "content": "For the hyperspectral Stokes camera, we use four configurations with the rotating QWP. For the trichromatic Stokes camera, the fixed micro-filter setup shown in Figure 3(a) gives four/eight configurations for the (red, blue) channels and the green channel, respectively." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "type": "text", + "content": "Figure 3(c) shows the reconstructed Stokes images. A Stokes vector is physically-valid if DoP meets the following inequality: " + }, + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "type": "inline_equation", + "content": "0 \\leq \\rho \\leq 1" + }, + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "type": "inline_equation", + "content": "99\\%" + }, + { + "bbox": [ + 304, + 539, + 545, + 623 + ], + "type": "text", + "content": " of the reconstructed Stokes vectors in our datasets satisfy this condition. For the following analysis, we filter out Stokes vectors violating the DoP condition and the unstable Stokes vectors reconstructed from saturated/underexposed pixel intensity." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 633, + 406, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 406, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 406, + 647 + ], + "type": "text", + "content": "5. Dataset Analysis" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Noise and Intensity Denoising Spectro-polarimetric images are susceptible to noise due to the low-light throughput of spectral and polarimetric filters. Our datasets are not exempt from these issues. To assess noise in Stokes images, we capture and average 100 images of a scene shown" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22101" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 69, + 171, + 160 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 171, + 160 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 171, + 160 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 171, + 160 + ], + "type": "image", + "image_path": "08a2bf439be10d2d975b8ee93016b8c016d5ea5f7d4913204f91a2f303597e8f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 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[ + { + "bbox": [ + 408, + 201, + 533, + 308 + ], + "type": "image", + "image_path": "d7c04bd6be08d52be784f8cec484e93bd3bb43e18ca20c5b43fc0b2e3e06df62.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 429, + 311, + 511, + 320 + ], + "lines": [ + { + "bbox": [ + 429, + 311, + 511, + 320 + ], + "spans": [ + { + "bbox": [ + 429, + 311, + 511, + 320 + ], + "type": "text", + "content": "(f) BPP and MSE of INR" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 47, + 371, + 287, + 467 + ], + "blocks": [ + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "lines": [ + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "text", + "content": "Figure 4. Efficient spatio-spectral-polarimetric representations. (a) PCA basis of the hyperspectral Stokes dataset in sRGB. (b) Qualitative results of PCA and INR compared to single-shot denoising [66] at " + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "inline_equation", + "content": "550\\mathrm{nm}" + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "text", + "content": ". (c) Proportion of variance with respect to each PCA basis in order, " + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "inline_equation", + "content": "\\log (\\sigma_i^2 / \\sum_n \\sigma_n^2)" + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "inline_equation", + "content": "\\sigma_i" + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "text", + "content": " denotes standard deviation of the " + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 323, + 547, + 368 + ], + "type": "text", + "content": "-th basis. (d) BPP and MSE analysis of PCA with respect to the number of PCA bases. (e) Training PSNR curve of INR. (f) BPP and MSE value of INR with respect to the number of MLP layers." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 371, + 287, + 467 + ], + "lines": [ + { + "bbox": [ + 47, + 371, + 287, + 467 + ], + "spans": [ + { + "bbox": [ + 47, + 371, + 287, + 467 + ], + "type": "image", + "image_path": "4f172d653e4cea0ced0a23beace1adcba303ca82368310ed409a59faa406b7ef.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 47, + 468, + 287, + 550 + ], + "blocks": [ + { + "bbox": [ + 47, + 468, + 287, + 550 + ], + "lines": [ + { + "bbox": [ + 47, + 468, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 468, + 287, + 550 + ], + "type": "image", + "image_path": "545135a5cc91a4ad03c0432b1fdb5965dc5229932718c1f143c2cf662300e0ed.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 562, + 287, + 639 + ], + "lines": [ + { + "bbox": [ + 46, + 562, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 562, + 287, + 639 + ], + "type": "text", + "content": "Figure 5. Noise in Stokes images and intensity denoising. (a) Stokes vector " + }, + { + "bbox": [ + 46, + 562, + 287, + 639 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 46, + 562, + 287, + 639 + ], + "type": "text", + "content": " reconstructed from a single-shot, single-shot with a learned intensity denoiser [66], and burst imaging (Pseudo GT) averaged over 100 shots. (b) Reconstruction accuracy of a Stokes image with varying number of averaged images. (c) Reconstruction accuracy of normalized Stokes elements with and without intensity denoising." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": "in Figure 3(c) for each polarization configuration " + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 653, + 288, + 714 + ], + "type": "text", + "content": ". From these averaged images, we reconstruct pseudo ground-truth Stokes image, shown in Figure 5(a). Figure 5(b) reports the MSE and PSNR of reconstructed Stokes images with respect to the number of averaged images. To achieve a" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": "PSNR exceeding " + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "inline_equation", + "content": "35\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": ", we need to average over 4/25 shots for the trichromatic/hyperspectral Stokes cameras, indicating lower SNR of the hyperspectral Stokes dataset. We find that state-of-the-art learning-based intensity denoising methods, such as KBNet [66], can effectively reduce noise for each polarization configuration, leading to accurate Stokes-vector reconstruction, despite lack of polarization images during training. For the denoised single-shot capture, we achieve a PSNR of " + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "inline_equation", + "content": "34.5\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": ", demonstrating the potential of using pretrained intensity restoration networks for Stokes imaging. Figure 5(c) shows PSNRs of reconstructed Stokes images per each spectral channel and normalized Stokes element. With the intensity denoising, we find that the PSNR significantly increases for " + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 304, + 374, + 546, + 542 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": "Efficient Spatio-spectral-polarimetric Representations Each pixel in a hyperspectral Stokes image contains a Stokes vector for every spectral channel, leading to a total of " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "21 \\times 4 \\times 32" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": " bits using single-precision floating format. This results in a bit-per-pixel (BPP) value of 2,688, equating to " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "100\\mathrm{MB}" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": " for storing a single hyperspectral Stokes image of " + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "inline_equation", + "content": "512 \\times 612" + }, + { + "bbox": [ + 304, + 558, + 545, + 689 + ], + "type": "text", + "content": " pixels. Given the substantial memory required to store a spectro-polarimetric image, we investigate efficient representations of real-world spatio-spectral-polarimetric data, for which we explore two methods: a PCA-based model and an implicit neural model." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 546, + 713 + ], + "type": "text", + "content": "First, we apply PCA on non-overlapping hyperspectral Stokes patches. Figure 4(a) shows the 40 most significant" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22102" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": "PCA bases, revealing varied spatial and spectral features for each Stokes element: " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ". Notably, spatial structures are more evident in " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ", while " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": " shows spectral features, suggesting a stronger correlation between spectrum and polarization than spatial features. To visualize hyperspectral intensity, we convert it to sRGB, which means that the same sRGB color may originate from different spectra. Figure 4(c) shows the variance of the coefficients for the top 200 PCA bases, indicating that spati-spectral-polarimetric data can indeed be compressed. This is further evidenced by Figure 4(d), which shows the reconstruction error and BPP when varying number of PCA bases used to recreate a hyperspectral Stokes image. Using " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "2.22\\mathrm{MB}" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": " coefficients adequately represents a " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "100\\mathrm{MB}" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": " hyperspectral Stokes image as shown in Figure 4(b), exhibiting a high compression rate with the reconstruction error of " + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "inline_equation", + "content": "2.69\\times 10^{-5}" + }, + { + "bbox": [ + 46, + 72, + 289, + 287 + ], + "type": "text", + "content": ". See the Supplemental Document for further details on PCA analysis." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "text", + "content": "Second, we devise an INR for hyperspectral Stokes images by modifying NeSpoF [34]. The original NeSpoF architecture models a volumetric hyperspectral Stokes field. Here, instead, we aim to represent a hyperspectral Stokes image. Specifically, our INR, modeled by an MLP " + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "inline_equation", + "content": "F_{\\gamma}" + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "text", + "content": ", outputs the Stokes vector " + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "text", + "content": " for a given pixel position " + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "inline_equation", + "content": "p_x, p_y" + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "text", + "content": " and spectral channel index " + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 288, + 289, + 371 + ], + "type": "text", + "content": ", that is" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 128, + 380, + 287, + 393 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 380, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 128, + 380, + 287, + 393 + ], + "type": "interline_equation", + "content": "\\mathbf {s} = F _ {\\gamma} \\left(p _ {x}, p _ {y}, c\\right), \\tag {5}", + "image_path": "27e444cf2e862ee61839c0b793986afa53f09512c24216bfaa17664b4a1605ea.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "text", + "content": " is the network parameters. We fit the MLP to a hyperspectral Stokes image by minimizing the reconstruction loss between the network output and the hyperspectral Stokes image. The training curve is shown in Figure 4(e). Figure 4(f) shows the reconstruction error and BPP of our INR with respect to varying number of the MLP layers. With just 8 layers corresponding to a BPP of 60, we achieve a converged reconstruction error of " + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "inline_equation", + "content": "1.90 \\times 10^{-5}" + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "text", + "content": ", resulting in just " + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "inline_equation", + "content": "2.22\\mathrm{MB}" + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "text", + "content": " of network parameters to represent a " + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "inline_equation", + "content": "100\\mathrm{MB}" + }, + { + "bbox": [ + 46, + 399, + 289, + 530 + ], + "type": "text", + "content": " hyperspectral Stokes image. See Supplemental Document for architecture details." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 532, + 289, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 289, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 289, + 640 + ], + "type": "text", + "content": "Both PCA and INR experiments validate that a natural spectro-polarimetric image is compressible. PCA provides PCA basis vectors that can be applied to any instance, however with a lower reconstruction accuracy than INR. INR is overfitted to a single instance, while higher reconstruction accuracy can be achieved. These representations are also beneficial for denoising spectral-polarimetric images, as shown in Figure 4(b), which even outperforms the learning-based intensity denoiser [66]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "content": "Polarized and Unpolarized Intensity We decompose hyperspectral Stokes images into the polarized images " + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "inline_equation", + "content": "P = \\sqrt{s_1^2 + s_2^2 + s_3^2}" + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "content": " and unpolarized images " + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "inline_equation", + "content": "U = s_0 - P" + }, + { + "bbox": [ + 47, + 653, + 289, + 715 + ], + "type": "text", + "content": " per each spectral channel. Figure 6(a) shows specular reflections such as the glow of leather sofa separated into po" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 320, + 69, + 533, + 204 + ], + "blocks": [ + { + "bbox": [ + 320, + 69, + 533, + 204 + ], + "lines": [ + { + "bbox": [ + 320, + 69, + 533, + 204 + ], + "spans": [ + { + "bbox": [ + 320, + 69, + 533, + 204 + ], + "type": "image", + "image_path": "dad01d455c5f223d5a00ea97a0dacbfdbcc6d1166bcdf03964ce71b26454c12e.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 356, + 203, + 496, + 211 + ], + "lines": [ + { + "bbox": [ + 356, + 203, + 496, + 211 + ], + "spans": [ + { + "bbox": [ + 356, + 203, + 496, + 211 + ], + "type": "text", + "content": "(a) Separation into polarized and unpolarized light" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 213, + 427, + 301 + ], + "blocks": [ + { + "bbox": [ + 309, + 213, + 427, + 301 + ], + "lines": [ + { + "bbox": [ + 309, + 213, + 427, + 301 + ], + "spans": [ + { + "bbox": [ + 309, + 213, + 427, + 301 + ], + "type": "image", + "image_path": "991865a28e7ee694ca58927b5f1f4dc8c32ade4541d9ad95ddfe5e6c0caeac4d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 319, + 301, + 428, + 309 + ], + "lines": [ + { + "bbox": [ + 319, + 301, + 428, + 309 + ], + "spans": [ + { + "bbox": [ + 319, + 301, + 428, + 309 + ], + "type": "text", + "content": "(b) Intensity distribution by polarization" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 318, + 547, + 373 + ], + "lines": [ + { + "bbox": [ + 304, + 318, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 547, + 373 + ], + "type": "text", + "content": "Figure 6. Polarized and unpolarized light distributions. (a) Separation into polarized and unpolarized light. (b) Intensity distributions for polarized and unpolarized components. (c) Variance of PCA basis of polarized and unpolarized intensity across spectral channel." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 429, + 213, + 545, + 300 + ], + "blocks": [ + { + "bbox": [ + 429, + 213, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 429, + 213, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 429, + 213, + 545, + 300 + ], + "type": "image", + "image_path": "4530fbd91038d32a60e6d4744cc920029ae875b58edc4504380f3e22cdea193a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 440, + 301, + 540, + 309 + ], + "lines": [ + { + "bbox": [ + 440, + 301, + 540, + 309 + ], + "spans": [ + { + "bbox": [ + 440, + 301, + 540, + 309 + ], + "type": "text", + "content": "(c) Variance of basis by polarization" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 547, + 574 + ], + "type": "text", + "content": "larized light. Note that the polarized image typically encodes the illumination colors for dielectric surfaces. Figure 6(b) reveals that the intensity distributions of polarized light, obtained from the entire hyperspectral Stokes dataset, is skewed towards low and high-intensity values compared to the unpolarized light. This is because polarized images mostly contain specular reflections, which is sparsely distributed and has high intensity values. We then compute the variance of the PCA bases for polarized intensity along the spectral channel. Figure 6(c) highlights that the spectral variance for polarized intensity is lower than that of unpolarized intensity. We speculate that the color of polarized light lies in a lower dimensional space than that of unpolarized light, since diffuse reflection with diverse spectral variations is mostly captured by unpolarized light, making the spectral variation of unpolarized light more pronounced." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "Stokes Vector Distributions in Natural Stokes Images Next, we analyze the distribution of all Stokes vectors in our Stokes dataset. Figure 7 shows the histograms of Stokes elements " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": " across all spectral channel. We find that the distributions of Stokes elements " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "(s_1, s_2, s_3)" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": " have symmetric shapes of positive and negative sides. Stokes elements of " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": " have similar shapes meaning that the directions of linearly-polarized light are equally distributed in natural images. The circular component " + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": " is more condensed near zero than the linear elements, resulting in a" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "22103" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 287, + 142 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 287, + 142 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 287, + 142 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 287, + 142 + ], + "type": "image", + "image_path": "a01b8caf2b4dd5300486647aa5478efe9cb28c0187fcaa651b893262529f03d9.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 142, + 230, + 150 + ], + "lines": [ + { + "bbox": [ + 121, + 142, + 230, + 150 + ], + "spans": [ + { + "bbox": [ + 121, + 142, + 230, + 150 + ], + "type": "text", + "content": "(a) Visualization of Stokes vector" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 47, + 154, + 281, + 255 + ], + "blocks": [ + { + "bbox": [ + 47, + 154, + 281, + 255 + ], + "lines": [ + { + "bbox": [ + 47, + 154, + 281, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 154, + 281, + 255 + ], + "type": "image", + "image_path": "1b62e1ba99aa86b84970a188f2bccebcf98ef6f76f7eed7bf9b0b7d711a59ea9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 255, + 216, + 264 + ], + "lines": [ + { + "bbox": [ + 121, + 255, + 216, + 264 + ], + "spans": [ + { + "bbox": [ + 121, + 255, + 216, + 264 + ], + "type": "text", + "content": "(b) Stokes vector distribution" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "lines": [ + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": "Figure 7. Stokes-vector distributions. (a) Stokes images of " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": " at the green channel. (b) Stokes-vector distributions of " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 47, + 273, + 287, + 307 + ], + "type": "text", + "content": " for trichromatic and hyperspectral datasets." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 316, + 287, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 365 + ], + "type": "text", + "content": "higher peak both in trichromatic and hyperspectral datasets. This indicates that pixels are often more linearly polarized than circularly polarized. Refer to the Supplemental Document for further analysis." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "text", + "content": "Gradient Analysis of Stokes Images Gradient distribution of images has been often used as priors for image-based applications including image restoration, understanding, and editing. Here, we perform gradient analysis of Stokes and polarization-feature images. Figure 8(b) shows that the gradient of Stokes and normalized Stokes vectors exhibits a similarity to Hyper-Laplacian priors, commonly used to describe the gradient of natural intensity-images. An interesting finding is that total intensity " + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "text", + "content": " has more high-gradient values than the linear components of " + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "text", + "content": ", and the circular component " + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 46, + 378, + 287, + 521 + ], + "type": "text", + "content": " has the lowest-value distribution." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": "We analyze the gradient distributions of polarization features, including AoLP, degree of linear polarization (DoLP), degree of circular polarization (DoCP), and CoP. DoLP and DoCP are computed as " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DoLP} = \\sqrt{s_1^2 + s_2^2} / s_0" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{DoCP} = |s_3| / s_0" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " respectively. To compute the gradient of AoLP images, we consider the angular wrapping property. That is, AoLP has a range from " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "-\\frac{\\pi}{2}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\frac{\\pi}{2}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and the AoLPs of " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "-\\frac{\\pi}{2}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\frac{\\pi}{2}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " are identical. Thus, if the gradient exceeds " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\frac{\\pi}{2}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ", we estimate the gradient as " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\nabla \\mathrm{AoLP} - \\pi \\times \\mathrm{sign}(\\nabla \\mathrm{AoLP})" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\nabla" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " is the gradient operator and " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": " is the sign operator that returns 1 if positive, otherwise " + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "inline_equation", + "content": "-1" + }, + { + "bbox": [ + 46, + 522, + 287, + 713 + ], + "type": "text", + "content": ". Figure 8(c) shows that the gradients of AoLP are generally higher than DoLP and DoCP. This implies that sparsity in the measurement gradient is milder for AoLP than DoLP and DoCP. DoLP and DoCP have shapes similar to HyperLaplacian priors while DoCP is sharper than DoLP. The" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 69, + 545, + 132 + ], + "blocks": [ + { + "bbox": [ + 306, + 69, + 545, + 132 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 545, + 132 + ], + "type": "image", + "image_path": "61e5db7117b492ef3307d3561460bb1b5ca2f541635034ad169d92736f6b5da9.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 306, + 132, + 545, + 198 + ], + "blocks": [ + { + "bbox": [ + 306, + 132, + 545, + 198 + ], + "lines": [ + { + "bbox": [ + 306, + 132, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 306, + 132, + 545, + 198 + ], + "type": "image", + "image_path": "29dc883bbc282b415441de40ea5ff281a4bbcf3562cd2fc154da5dbcf1643f4d.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 199, + 520, + 208 + ], + "lines": [ + { + "bbox": [ + 345, + 199, + 520, + 208 + ], + "spans": [ + { + "bbox": [ + 345, + 199, + 520, + 208 + ], + "type": "text", + "content": "(a) Visualization of polarization features and gradients" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 306, + 209, + 545, + 299 + ], + "blocks": [ + { + "bbox": [ + 306, + 209, + 545, + 299 + ], + "lines": [ + { + "bbox": [ + 306, + 209, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 545, + 299 + ], + "type": "image", + "image_path": "d54bb3e031ed7d9baf9ed315dd7fad00c38c72bc55c26acd0ed1883b4bdd850d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 367, + 299, + 502, + 308 + ], + "lines": [ + { + "bbox": [ + 367, + 299, + 502, + 308 + ], + "spans": [ + { + "bbox": [ + 367, + 299, + 502, + 308 + ], + "type": "text", + "content": "(b) Gradient distributions of Stokes vector" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 306, + 310, + 545, + 400 + ], + "blocks": [ + { + "bbox": [ + 306, + 310, + 545, + 400 + ], + "lines": [ + { + "bbox": [ + 306, + 310, + 545, + 400 + ], + "spans": [ + { + "bbox": [ + 306, + 310, + 545, + 400 + ], + "type": "image", + "image_path": "58ecf995f2c55d4b12b3915f358de49bde2b5274f8f1632542dd64ce5c5fe6f0.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 354, + 400, + 511, + 409 + ], + "lines": [ + { + "bbox": [ + 354, + 400, + 511, + 409 + ], + "spans": [ + { + "bbox": [ + 354, + 400, + 511, + 409 + ], + "type": "text", + "content": "(c) Gradient distributions of polarization features" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": "Figure 8. Gradient analysis of Stokes images. (a) Visualization of AoLP, DoLP, DoCP and CoP values and their gradients. Examining the log probability of the gradient for (b) Stokes vectors " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_0" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_1" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_2" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": " and normalized Stokes vectors " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_1'" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_2'" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "inline_equation", + "content": "s_3'" + }, + { + "bbox": [ + 304, + 418, + 545, + 473 + ], + "type": "text", + "content": ", and (c) polarization features including DoLP, DoCP, AoLP and CoP." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 579 + ], + "type": "text", + "content": "gradient of CoP shows symmetric distributions for right-circular and left-circular directions. Unlike AoLP, the probability decreases as the gradient approaches extreme values. The difference in tendency between linear-polarization and circular-polarization features, as well as their distributions, means that we need distinct priors for each polarization feature, emphasizing the importance of a full Stokes dataset that measure not only linear but also circular polarization." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Shape from Polarization and Spectral Channels Methods that recover shape from polarization, SfP, have made rapid progress in the last decade. SfP aims to extract normals by analyzing the normal-dependent polarization change of reflected light. Specifically, SfP analyzes the DoP and AoLP based on Fresnel theory [9], which describes the polarization change of light upon reflection and transmission at a smooth surface [32, 41]. Here, we analyze an overlooked problem in SfP: the spectral dependency of estimated normals. 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Spectral dependency of conventional SFP method. (a) Trichromatic Stokes image and estimated surface normals [41] for each red, green, and blue spectral channels shown in (b), (c), and (d). Graphs (e) and (f) show the probability distributions of standard deviation of normal component " + }, + { + "bbox": [ + 46, + 231, + 287, + 297 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 231, + 287, + 297 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 231, + 287, + 297 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 231, + 287, + 297 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 231, + 287, + 297 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 231, + 287, + 297 + ], + "type": "text", + "content": " along the spectral channels for both datasets." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 176, + 128, + 286, + 215 + ], + "blocks": [ + { + "bbox": [ + 231, + 121, + 286, + 128 + ], + "lines": [ + { + "bbox": [ + 231, + 121, + 286, + 128 + ], + "spans": [ + { + "bbox": [ + 231, + 121, + 286, + 128 + ], + "type": "text", + "content": "(d) Normal map from" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 176, + 128, + 286, + 215 + ], + "lines": [ + { + "bbox": [ + 176, + 128, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 176, + 128, + 286, + 215 + ], + "type": "image", + "image_path": "9452f3243c68fd8999f89e358f29566e0c7aab49b262ca84910c1d1a97b7254a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 186, + 215, + 278, + 222 + ], + "lines": [ + { + "bbox": [ + 186, + 215, + 278, + 222 + ], + "spans": [ + { + "bbox": [ + 186, + 215, + 278, + 222 + ], + "type": "text", + "content": "(f) Denoised Hyperspectral dataset" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": "face property, should be consistent regardless of the input spectral channels used for SfP. In Figure 9, we test the state-of-the-art SfP method by Lei et al. [41], designed for in-the-wild scenes. The evaluation results on our normalized Stokes dataset clearly reveal that normal maps reconstructed from different spectral channels exhibit variations. We compute the standard deviations of spectral variations for each " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " component of the estimated normals. Figures 9(e) and (f) show the probability distributions of the standard deviation, highlighting the large variations in the estimated normals for both hyperspectral and trichromatic datasets. Interestingly, the " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " components of normals show larger standard deviations than the " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " component. This implies that the spectral variation of DoP, which determines the " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " component, has less impact on the distribution than that of AoLP, which governs the " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 309, + 287, + 501 + ], + "type": "text", + "content": " components." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "text", + "content": "Environment Dependency Figure 10 shows the Poincaré spheres projected onto the " + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "inline_equation", + "content": "s_1' - s_2'" + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "inline_equation", + "content": "s_1' - s_3'" + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "text", + "content": " planes for the three data labels: Indoor, Sunlight and Cloudy. Sunlight is known to contain more circularly polarized light compared to other artificial lighting [25]. As shown in Figure 10(a), Stokes vectors are distributed more widely across " + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "inline_equation", + "content": "s_3'" + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "text", + "content": " axis under sunlight compared with Indoor scene. In addition, we find that DoCP is distributed at higher values for the sunlight compared to the indoor: pixels with DoCP over 0.5 are rarely observed in indoor scenes. This is also confirmed in the example " + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 46, + 521, + 286, + 652 + ], + "type": "text", + "content": " images for indoor and sunlight scenes." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 713 + ], + "type": "text", + "content": "Another interesting finding is that cloudy or sunny illumination result in different polarization statistics. Figure 10(a) shows that Stokes vectors of cloudy scenes are more concentrated near the origin, meaning that light is more depolarized compared to light under clear sunlight." + } + ] + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 312, + 70, + 386, + 147 + ], + "blocks": [ + { + "bbox": [ + 312, + 70, + 386, + 147 + ], + "lines": [ + { + "bbox": [ + 312, + 70, + 386, + 147 + ], + "spans": [ + { + "bbox": [ + 312, + 70, + 386, + 147 + ], + "type": "image", + "image_path": "63b612cd0e0f15640d6407d849c395089991ff56167d21b449243f5ff6446d42.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 387, + 70, + 455, + 147 + ], + "blocks": [ + { + "bbox": [ + 387, + 70, + 455, + 147 + ], + "lines": [ + { + "bbox": [ + 387, + 70, + 455, + 147 + ], + "spans": [ + { + "bbox": [ + 387, + 70, + 455, + 147 + ], + "type": "image", + "image_path": "82591d67cdd8a1f66b69f5f2e444fe0de06c800ba38f2ca2670db0805e437b49.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 457, + 70, + 541, + 147 + ], + "blocks": [ + { + "bbox": [ + 457, + 70, + 541, + 147 + ], + "lines": [ + { + "bbox": [ + 457, + 70, + 541, + 147 + ], + "spans": [ + { + "bbox": [ + 457, + 70, + 541, + 147 + ], + "type": "image", + "image_path": "0d7dcc985cac6896475fdffbf4b35fe4671f9c4518e362bd33aa4b2c5787b0ce.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 312, + 147, + 386, + 215 + ], + "blocks": [ + { + "bbox": [ + 312, + 147, + 386, + 215 + ], + "lines": [ + { + "bbox": [ + 312, + 147, + 386, + 215 + ], + "spans": [ + { + "bbox": [ + 312, + 147, + 386, + 215 + ], + "type": "image", + "image_path": "2bb0bb8175d4206daddfe686d7d56d98912f8dd2bc2429dda1cd9390db2246fa.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 380, + 215, + 485, + 223 + ], + "lines": [ + { + "bbox": [ + 380, + 215, + 485, + 223 + ], + "spans": [ + { + "bbox": [ + 380, + 215, + 485, + 223 + ], + "type": "text", + "content": "(a) Poincaré sphere projections" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 387, + 148, + 455, + 215 + ], + "blocks": [ + { + "bbox": [ + 387, + 148, + 455, + 215 + ], + "lines": [ + { + "bbox": [ + 387, + 148, + 455, + 215 + ], + "spans": [ + { + "bbox": [ + 387, + 148, + 455, + 215 + ], + "type": "image", + "image_path": "7cd2fe00c56bd23f57614e679f928bbd9d335711e497468de83d7ccd173cfe87.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 457, + 148, + 541, + 215 + ], + "blocks": [ + { + "bbox": [ + 457, + 148, + 541, + 215 + ], + "lines": [ + { + "bbox": [ + 457, + 148, + 541, + 215 + ], + "spans": [ + { + "bbox": [ + 457, + 148, + 541, + 215 + ], + "type": "image", + "image_path": "6056ddedb9a42638f1001f0103a1a295b14877b510310235de00fb6a82588ca9.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 306, + 224, + 391, + 295 + ], + "blocks": [ + { + "bbox": [ + 306, + 224, + 391, + 295 + ], + "lines": [ + { + "bbox": [ + 306, + 224, + 391, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 391, + 295 + ], + "type": "image", + "image_path": "0f91a0870b5311cb4aac073d6c8db13c1f1d2009869b5f8a7c4c4fcdf98f8cb6.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 315, + 295, + 385, + 304 + ], + "lines": [ + { + "bbox": [ + 315, + 295, + 385, + 304 + ], + "spans": [ + { + "bbox": [ + 315, + 295, + 385, + 304 + ], + "type": "text", + "content": "(b) DoCP distribution" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "text", + "content": "Figure 10. Environment dependency. (a) Projected Poincaré spheres onto the " + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "inline_equation", + "content": "s_1' - s_2'" + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "inline_equation", + "content": "s_1' - s_3'" + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "text", + "content": " planes with respect to dataset labels. Colorbar is based on the normalized pixel count. (b) DoCP distributions for indoor and sunlight categories. (c) Example " + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "inline_equation", + "content": "s_3" + }, + { + "bbox": [ + 305, + 312, + 545, + 368 + ], + "type": "text", + "content": " images." + } + ] + } + ], + "index": 29, + "angle": 0, + "type": "image_caption" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 392, + 224, + 459, + 293 + ], + "blocks": [ + { + "bbox": [ + 392, + 224, + 459, + 293 + ], + "lines": [ + { + "bbox": [ + 392, + 224, + 459, + 293 + ], + "spans": [ + { + "bbox": [ + 392, + 224, + 459, + 293 + ], + "type": "image", + "image_path": "390e8b16dc03c769dd2ac833f8e3b863298cd9ab2d80b9bf861c2ab76b23cb51.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 460, + 223, + 545, + 294 + ], + "blocks": [ + { + "bbox": [ + 460, + 223, + 545, + 294 + ], + "lines": [ + { + "bbox": [ + 460, + 223, + 545, + 294 + ], + "spans": [ + { + "bbox": [ + 460, + 223, + 545, + 294 + ], + "type": "image", + "image_path": "4b32580a78ab7b975e3cb4c2e23a6ac873342e82120b5bf2c005cd6a41f042cc.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 432, + 295, + 497, + 304 + ], + "lines": [ + { + "bbox": [ + 432, + 295, + 497, + 304 + ], + "spans": [ + { + "bbox": [ + 432, + 295, + 497, + 304 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 432, + 295, + 497, + 304 + ], + "type": "inline_equation", + "content": "S_{3}" + }, + { + "bbox": [ + 432, + 295, + 497, + 304 + ], + "type": "text", + "content": " visualization" + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 380, + 545, + 404 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 380, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 305, + 380, + 545, + 404 + ], + "type": "text", + "content": "This is aligned with previous studies [24, 58] that report the impact of cloud-particle scatterings on light depolarization." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 419, + 378, + 431 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 419, + 378, + 431 + ], + "spans": [ + { + "bbox": [ + 306, + 419, + 378, + 431 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 440, + 545, + 595 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 440, + 545, + 595 + ], + "spans": [ + { + "bbox": [ + 304, + 440, + 545, + 595 + ], + "type": "text", + "content": "In this work, we have introduced a trichromatic and hyperspectral Stokes image dataset that encompasses diverse natural scenes and various illumination conditions, totaling more than 2,333 scenes. We analyze the empirical distribution of the Stokes vectors of natural spectropolarimetric images. To efficiently represent spati-spectral-polarimetric data, we devise a PCA-based model and an implicit neural representation. We further provide detailed analysis on Stokes gradient distributions, denoising characteristics, spectral dependency of SfP, and environment dependency. As such, our work provides a foundation for future research on spectral-polarimetric imaging and vision." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements We thank Onur Akkaya for helpful discussion. Seung-Hwan Baek was supported by Korea NRF (RS-2023-00211658, 2022R1A6A1A03052954). Felix Heide was supported by an NSF CAREER Award (2047359), a Packard Foundation Fellowship, a Sloan Research Fellowship, a Sony Young Faculty Award, a Project X Innovation Award, and an Amazon Science Research Award." + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "22105" + } + ] + } + ], + "index": 34 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 199 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 199 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katie Millican, Malcolm Reynolds, Roman Ring, Eliza Rutherford, Serkan Cabi, Tengda Han, Zhitao Gong, Sina Samangooei, Marianne Monteiro, Jacob Menick, Sebastian Borgeaud, Andrew Brock, Aida Nematzadeh, Sahand Sharifzadeh, Mikolaj Binkowski, Ricardo Barreira, Oriol Vinyals, Andrew Zisserman, and Karen Simonyan. 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Springer, 2020. 2" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "22108" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_content_list.json b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..be023698c78c4c621410e0c3d94fd9beb65ca543 --- /dev/null +++ b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_content_list.json @@ -0,0 +1,1614 @@ +[ + { + "type": "text", + "text": "Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation", + "text_level": 1, + "bbox": [ + 106, + 130, + 864, + 154 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tianyu Luan $^{1,2*}$ Zhong Li $^{2}$ Lele Chen $^{2}$ Xuan Gong $^{3,2,1}$ \nLichang Chen $^{2,4}$ Yi Xu $^{2}$ Junsong Yuan $^{1}$ $^{1}$ State University of New York at Buffalo $^{2}$ OPPO US Research Center \n $^{3}$ Harvard Medical School $^{4}$ University of Maryland, College Park", + "bbox": [ + 186, + 178, + 781, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 296, + 313, + 313 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing 3D mesh shape evaluation metrics mainly focus on the overall shape but are usually less sensitive to local details. This makes them inconsistent with human evaluation, as human perception cares about both overall and detailed shape. In this paper, we propose an analytic metric named Spectrum Area Under the Curve Difference (SAUCD) that demonstrates better consistency with human evaluation. To compare the difference between two shapes, we first transform the 3D mesh to the spectrum domain using the discrete Laplace-Beltrami operator and Fourier transform. Then, we calculate the Area Under the Curve (AUC) difference between the two spectrums, so that each frequency band that captures either the overall or detailed shape is equitably considered. Taking human sensitivity across frequency bands into account, we further extend our metric by learning suitable weights for each frequency band which better aligns with human perception. To measure the performance of SAUCD, we build a 3D mesh evaluation dataset called Shape Grading, along with manual annotations from more than 800 subjects. By measuring the correlation between our metric and human evaluation, we demonstrate that SAUCD is well aligned with human evaluation, and outperforms previous 3D mesh metrics. Our project page: https://bit.ly/saucd.", + "bbox": [ + 75, + 328, + 473, + 691 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 718, + 209, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "With the recent progress of 3D reconstruction and processing techniques, 3D mesh shapes have increasing applications in fields such as video games, industrial design, 3D printing, etc. In these applications, assessing the visual quality of the 3D mesh shape is a crucial task. To meet the requirements of various applications, a promising evaluation metric should not only reflect the geometry measurement but also align with human visual perception. Considering that human beings perceive 3D meshes in both overall shape and local", + "bbox": [ + 75, + 743, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/68ad887ef6a4884fef3176a2252d2c6feebc30633a221d328c848bb4b26a2591.jpg", + "image_caption": [ + "Figure 1. An example of how previous spatial domain 3D shape metrics (Chamfer Distance [6] and UHD [47]) deviate from human evaluation. we create Mesh $A$ by adding a small pose error to the ground truth mesh, and by applying a large smoothing kernel to ground truth, we create Mesh $B$ . Contrary to human perception, previous spatial domain metrics evaluate Mesh $B$ better than Mesh $A$ . This indicates that while they are sensitive to general shape differences, they tend to overlook high-frequency details. Note that different metrics use different units of measurement." + ], + "image_footnote": [], + "bbox": [ + 537, + 292, + 854, + 503 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "details, it is a challenging task to find an evaluation metric that can align well with humans.", + "bbox": [ + 498, + 670, + 890, + 700 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous metrics have the following disadvantages in this scenario. Traditional spatial domain measurements such as Chamfer Distance [6] which calculates the mean distance between a vertex on one mesh and its nearest vertex on the other mesh, can accurately measure the spatial distance. However, it does not guarantee capturing all shape details. In fact, such measurements in the spatial domain often overlook finer shape details, as the details tend to get overwhelmed by the overall shape. Fig. 1 illustrates the discrepancy between spatial measurements and human evaluation as mesh details change. Specifically, When we remove the wrinkles from the ground truth mesh (resulting in Mesh $B$ ), the errors detected by previous metrics are not as significant as when we slightly", + "bbox": [ + 496, + 704, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done while Tianyu was an intern at OPPO US Research Center.", + "bbox": [ + 94, + 886, + 467, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20155", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "change the pose of the hand (Mesh $A$ ). However, humans tend to sense a significant difference between ground truth and Mesh $B$ , but barely recognize the difference between ground truth and Mesh $A$ . To mitigate this problem, previous works propose learning-based approaches, such as Single Shape Fréchet Inception Distance (SSFID) [46] based on learnable features from 3D shape. They compare the difference between the test mesh and the ground truth mesh in the latent feature space, and the design is expected to better align human perception. However, such learning-based methods would require a large amount of data to train the network. Their accuracy and generalizability are limited by the size of the dataset, data distribution, and annotation quality, not to mention the potential bias in collecting human perception feedback, which could mislead the learned metrics. An analytic metric that can better explain the shape difference is thus preferred.", + "bbox": [ + 75, + 90, + 472, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the above limitations, we design an analytic-based 3D shape evaluation metric named Spectrum Area Under the Curve Difference (SAUCD). Our metric measures mesh shape differences with a balanced consideration of both overall and detailed shape, making it better aligned with human evaluation. To allow our metric to capture detail variations, we leverage the 3D shape spectrum to decompose different levels of shape details from the overall shape, with details corresponding to higher-frequency components. The advantage of transforming the shape signal into the spectrum domain is that the high-frequency details are explicitly separated from the low-frequency overall shape. Therefore, it provides appropriate consideration to the information in different frequency bands, not just the low-frequency information of the overall shape in the dominant place. Thus, the details that human perception cares about will be better represented. Besides, the frequency analysis method allows the metric to be mostly analytic and better explained.", + "bbox": [ + 75, + 352, + 472, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We design SAUCD following the above inspiration. To begin with, both the test mesh and the ground truth mesh are transformed from the spatial to the spectrum domain using the discrete Laplace-Beltrami operator (DLBO), which encodes the mesh geometry information into a semidefinite Laplacian matrix. Once in the spectrum domain, we compare the regions under the two spectrums. Our Spectrum Area Under the Curve Difference metric is defined as the area of the non-overlapping region under the two spectrums - a larger area indicates a greater difference. Moreover, to better align with human evaluation, we further extend our design by learning a spectrum weight for SAUCD. However, different from previous learning-based approaches that use deep networks, large datasets, and extensive learning processes, our learning-based method requires the training of a weight vector. This vector measures the sensitivity of human perception across frequency bands, making the learned metric better aligned with human perception. We then evaluated the", + "bbox": [ + 75, + 628, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "effectiveness of SAUCD on our provided user study benchmark dataset named Shape Grading. Using Shape Grading, we compare our metrics with previous metrics by calculating the correlation between each metric and human scoring. In summary, our contributions are listed as follows.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We design an analytic-based 3D mesh shape metric named Spectrum AUC Difference (SAUCD), which evaluates the difference between a 3D mesh and its ground truth mesh. Our metric considers both the overall shape and intricate details, to align more closely with human perception.", + "- We further extend our design to a learnable metric. The extended metric explores the human perception sensitivity in different frequency bands, which further improves this metric.", + "- We build a user study benchmark dataset named Shape Grading which is annotated by more than 800 subjects. The provided dataset verifies that both versions of our metrics are consistent with human evaluation and outperform previous methods. This dataset can also facilitate 3D mesh metric evaluation in future research." + ], + "bbox": [ + 500, + 167, + 893, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our experiments show that both SAUCD and its extended version outperform previous methods with good generalizability to different types of objects.", + "bbox": [ + 496, + 395, + 893, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 452, + 650, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Metrics in 3D mesh reconstruction. Chamfer Distance [6] is a popular metric used in 3D mesh reconstruction tasks such as those in [21, 24, 32, 35, 45, 48-50]. Other spatial domain metrics, such as 3D Intersection over Union (IoU) in [10, 16, 17, 27, 33, 39]. F-score in [4, 15, 40, 43], and Unidirectional Hausdorff distance (UHD) in [47] are commonly focused on the geometry accuracy of mesh shapes. These metrics can provide accurate geometry measurements, but they are not designed to align with human evaluation. Deep-learning-based methods such as Single Shape Fréchet Inception Distance [46] are also used in 3D reconstruction. While these metrics have the capacity to adapt from human evaluation, they are more like black boxes, with performances subject to dataset size and annotation bias. Moreover, most previous works miss out on user study validation to verify if their metrics align with human evaluation.", + "bbox": [ + 496, + 477, + 893, + 718 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D shape generation metrics. Multiple metrics have been used in 3D shape generation, such as Minimal Matching Distance (MMD) [3], Jensen-Shannon Divergence (JSD) [22], Total Mutual Difference (TMD) [47], Fréchet Pointcloud Distance (FPD) [36], etc.. These metrics are designed to measure the differences between the generated distributions, while our task is to build a metric to compare the shape of two meshes.", + "bbox": [ + 496, + 719, + 893, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D mesh compression and watermarking metrics. Previous works [8, 12, 23, 41] focused on evaluating mesh errors in mesh compression and watermarking. Since compression and watermarking pursue mesh errors that cannot", + "bbox": [ + 496, + 840, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20156", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5cfa967ceea5defea1109f67661240f9273b4a66848aafdb6f2ea90584467277.jpg", + "image_caption": [ + "Figure 2. Our SAUCD metric is designed as follows: A. We use mesh Fourier Transform to analyze the spectrums of test and ground truth mesh. B. We compare the difference between two spectrum curves by calculating the Area Under the Curve (AUC) difference. C. We further extend our metric by multiplying the AUC difference with a learnable weight to capture human sensitivity in each frequency band." + ], + "image_footnote": [], + "bbox": [ + 151, + 89, + 820, + 268 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "be detected by humans, they mainly focus on barely noticed errors. However, our task is to build a metric that can handle generally occurring errors that happen in 3D reconstruction tasks and applications.", + "bbox": [ + 75, + 349, + 470, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 422, + 250, + 439 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our task is to design a metric aligned with human evaluation to measure the shape difference between a test triangle mesh and its corresponding ground truth triangle mesh. Specifically, given a test mesh $\\hat{M}$ and its ground truth mesh $M_{gt}$ , Spectrum AUC Difference (SAUCD) can be abstracted as", + "bbox": [ + 75, + 448, + 470, + 523 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nd = D (\\hat {M}, M _ {g t}). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 532, + 468, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$d$ is the distance between the test and the ground truth mesh. In this section, we will elaborate on how the distance function $D(\\cdot)$ is designed.", + "bbox": [ + 75, + 563, + 472, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 618, + 187, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, our metric is calculated via the following steps: First, we use mesh Fourier transform to analyze the spectrums of the test and ground truth mesh (in Sec. 3.2). Then we leverage each frequency band by calculating the Area Under the Curve (AUC) difference of the spectrum curves (in Sec. 3.3). Moreover, we further extended our metric by multiplying the AUC difference with a learnable weight to capture the human sensitivity on each frequency band (in Sec. 3.4). We will discuss each step in detail.", + "bbox": [ + 75, + 641, + 468, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Mesh spectrum analysis", + "text_level": 1, + "bbox": [ + 76, + 786, + 297, + 803 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In order to capture the overall shape as well as shape details, we choose to decompose the mesh signal into a spectrum. Considering the mesh as a function on a discretized manifold space, we can calculate the spectrum using the manifold space Fourier transform. In Hilbert space, the Fourier operator is defined as the eigenfunctions of the", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Laplacian operator [14]. The same definition and similar theories are extended to continuous and discrete manifold space by [5, 9]. The Laplacian operator on discrete manifold spaces, i.e. mesh space in our task, is named the Discrete Laplace-Beltrami operator (DLBO). Similar to the Laplacian operator in image space that encodes the pixel information by capturing the local pixel differences [20, 28, 30, 34, 38, 44], DLBO encodes the mesh shape information by capturing the local shape fluctuation. The \"Cotan formula\" defined in [25] is the most widely used discretization, which can be represented in matrix form as", + "bbox": [ + 496, + 348, + 893, + 515 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i j} = \\left\\{ \\begin{array}{c c} \\sum_ {j \\in N (i)} \\frac {1}{2 A _ {i}} \\left(\\cot \\alpha_ {i j} + \\cot \\beta_ {i j}\\right), & i = j \\\\ - \\frac {1}{2 A _ {i}} \\left(\\cot \\alpha_ {i j} + \\cot \\beta_ {i j}\\right), & i \\neq j \\wedge j \\in N (i) \\\\ 0, & i \\neq j \\wedge j \\notin N (i), \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 521, + 893, + 579 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L \\in \\mathbb{R}^{N \\times N}$ is the DLBO matrix, with $N$ the vertex number of the mesh. $L_{ij}$ indicates its entry in $i$ th row and $j$ th column, which represents the edge weight between vertex $v_i$ and $v_j$ . $A_i$ is the mixed Voronoi area of vertex $v_i$ on the mesh. As shown in Fig. 3, the $v_i$ 's mixed Voronoi area is defined as the area of the polygon in which the vertices are the circumcenters of $v_i$ 's surrounding faces. $N(i)$ is the index set of $v_i$ 's adjacent vertices. If $v_i$ and $v_j$ are adjacent, $\\alpha_{ij}$ and $\\beta_{ij}$ are the opposite angles of edge $(v_i, v_j)$ in each of the edge's two neighbor triangle faces, respectively (shown in Fig. 3). If not, $\\alpha_{ij}$ and $\\beta_{ij}$ are not defined and $L_{ij}$ is 0. As shown in Fig. 2, the DLBO matrix is used for mesh Fourier transform to get mesh spectrum. We calculate the Fourier operator $U^\\top$ , which is the eigenfunction of $L$ as", + "bbox": [ + 496, + 579, + 893, + 792 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL = U \\Lambda U ^ {\\top}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 650, + 797, + 892, + 816 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Lambda$ is a diagonal matrix whose diagonal elements are Fourier mesh frequencies.", + "bbox": [ + 496, + 825, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To ensure the mesh frequencies are non-negative, we need the DLBO matrix $L$ to be positive semidefinite. Our experiment in Fig. 7 gives an example of the counterintuitive", + "bbox": [ + 496, + 854, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20157", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/5631dbe3d5d881f53924c782e07ebc1fa5cf54758f8438bfb33b4160a774da77.jpg", + "image_caption": [ + "Figure 3. Variables defined in our discrete Laplace-Beltrami operator design." + ], + "image_footnote": [], + "bbox": [ + 102, + 88, + 222, + 186 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f6a09be4db54e5255572d657d3586f7f74dfe8c4904a35bdb265449ca477cb71.jpg", + "image_caption": [ + "Figure 4. Spectrum Area Under the Curve Difference. We design our metric using the AUC difference of the spectrums. The blue curve and red curve are the test and ground truth mesh spectrum, respectively. The purple area in the last graph is the Spectrum AUC Difference. Please find details in Sec. 3.3." + ], + "image_footnote": [], + "bbox": [ + 312, + 88, + 846, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "results when there are negative frequencies. However, the Coton formula in Eq. (2) does not guarantee to be positive semidefinite. We provide a simple example in Supplementary Materials Sec. 3 in which $L$ is not positive semidefinite when the mesh is not Delaunay triangulated and the mixed Voronoi areas are not all equal to each other. In our metric design, we made two small changes to the original Coton formula to make it positive semidefinite. a) Inspired by the symmetric normalization of the topology Laplacian matrix in [11], we make $L$ symmetric by changing the normalization parameter $A_{i}$ into a symmetric normalized manner $A_{i}^{\\frac{1}{2}}A_{j}^{\\frac{1}{2}}$ . b) We replace $\\cot \\alpha_{ij} + \\cot \\beta_{ij}$ with $|\\cot \\alpha_{ij} + \\cot \\beta_{ij}|$ . This ensures all the edge weights in the Laplacian matrix to be non-negative. Thus, our revision of DLBO is defined as", + "bbox": [ + 75, + 266, + 472, + 481 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i j} = \\left\\{ \\begin{array}{c c} \\frac {1}{2} \\sum_ {j \\in N (i)} A _ {i} ^ {- \\frac {1}{2}} A _ {j} ^ {- \\frac {1}{2}} | \\cot \\alpha_ {i j} + \\cot \\beta_ {i j} |, & i = j \\\\ - \\frac {1}{2} A _ {i} ^ {- \\frac {1}{2}} A _ {j} ^ {- \\frac {1}{2}} | \\cot \\alpha_ {i j} + \\cot \\beta_ {i j} |, & i \\neq j \\wedge j \\in N (i) \\\\ 0, & i \\neq j \\wedge j \\notin N (i). \\end{array} \\right. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 484, + 495, + 547 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We prove that our revision of the Cotan formula is positive semidefinite in Supplementary Materials Sec. 2. In Tab. 5, our experiments show that our DLBO matrix design outperforms the origin Cotan formula in [25], and the topology Laplacian matrix defined in [11].", + "bbox": [ + 75, + 549, + 470, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we obtain the mesh spectrum by acting Fourier operator on the mesh vertices", + "bbox": [ + 76, + 625, + 468, + 655 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nF _ {i} = \\sqrt {G _ {i , x} ^ {2} + G _ {i , y} ^ {2} + G _ {i , z} ^ {2}}, G = U ^ {\\top} v, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 665, + 468, + 691 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $v \\in \\mathbb{R}^{N \\times 3}$ indicates the 3D coordinates of $N$ mesh vertices. The result spectrum $F \\in \\mathbb{R}^N$ . Fig. 5 shows an example of the mesh spectrum (left side) and how the meshes look in different frequency bands (right side). This provides an illustration of the information contained in different frequency bands of the mesh spectrum.", + "bbox": [ + 75, + 700, + 470, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Spectrum AUC Difference", + "text_level": 1, + "bbox": [ + 76, + 801, + 316, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To reduce the noise and normalize the mesh scale, we also design noise pruning and AUC normalization procedures before calculating the Spectrum AUC Difference.", + "bbox": [ + 75, + 825, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Noise pruning. As shown in Fig. 4 process $(a)$ , we prune a small portion of the highest frequency information", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "to reduce the interference of noise. From the observation of the first two meshes (A and B) in Fig. 5, we can see that humans can barely notice the shape differences when the highest frequency parts are removed. Thus, if we try to evaluate the mesh shape that aligns with human perception, it is reasonable to remove high-frequency noise without losing much information that humans care about. Empirically, we choose to prune the highest $0.1\\%$ frequency information as noise. Our experiments in Tab. 4 show that this portion is more consistent with human perception while preserving good mesh quality.", + "bbox": [ + 496, + 266, + 890, + 431 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "AUC normalization. Given a spectrum $F(\\lambda)$ , its Area Under the Curve (AUC) can be defined as $\\int_{\\infty} F(\\lambda) d\\lambda$ . AUC normalization means using spectrum AUC to normalize the mesh scale. If the mesh scale increases by $s$ times in length, the mixed Voronoi area, i.e. $A_i$ in Eq. (4), will decrease by $s^2$ times. Thus, each element in the DLBO matrix $L$ will also decrease by $s^2$ times. Then, according to Eq. (3), the frequency $\\lambda$ will decrease $s^2$ times to $\\lambda / s^2$ , and according to Eq. (5), the spectrum amplitude $F$ will change to $sF$ because $v$ is increased by $s$ time and $U^\\top$ is still orthonormal. Then the area under the spectrum curve (the area boxed with red or blue lines in Fig. 4) changes as $A' = \\int sF(\\lambda) d\\lambda / s^2 = \\frac{1}{s} A$ .", + "bbox": [ + 496, + 433, + 892, + 616 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our approach, we normalize the area under the spectrum curve $A$ to 1 to resolve the scale difference, which means $s = A$ , $\\lambda$ decreases by $A^2$ times, and spectrum amplitude $F$ increases by $A$ times (Fig. 4 process (b)). AUC normalization fairly normalizes the scale of objects in different shapes by only changing the scale, not shape details. It normalizes the spectrum AUC of all mesh to 1, making the mesh spectrums differ only in distributions. Our experiments in Tab. 5 demonstrate this design can bring a fairer comparison of the spectrums and improve the human consistency of the metric. The experiment also demonstrates that this design outperforms the spatial domain scale normalization.", + "bbox": [ + 496, + 616, + 893, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Spectrum AUC Difference. In order to capture the difference between two mesh shapes in the spectrum domain, we design Spectrum AUC Difference (SAUCD) on the spectrum analysis results after noise pruning and AUC normalization:", + "bbox": [ + 496, + 797, + 893, + 859 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nd = D (\\hat {M}, M _ {g t}) = \\int_ {\\lambda} | \\hat {F} (\\lambda) - F _ {g t} (\\lambda) | d \\lambda , \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 872, + 892, + 905 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20158", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/309382284e5b35bdd9f56497042401fdf103b5cc4622cb0f44ab7ab118a7aaab.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
datasetRaww/ IQR removal
number of valid scores2430423775
Scoring range[0, 6][0, 6]
95% confidence interval0.3180.303
Relative 95% confidence interval5.33%5.04%
", + "bbox": [ + 101, + 88, + 446, + 154 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. Dataset statistics and error analysis.", + "bbox": [ + 138, + 166, + 403, + 179 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\hat{F}$ and $F_{gt}$ are the test and groundtruth mesh spectrum. As shown in Fig. 4 process $(c)$ , our metric is defined as the AUC difference of the two spectrum curves (the purple area). In Tab. 5, we compare our design with an alternative design which changes the amplitude difference $|\\hat{F} (\\lambda) - F_{gt}(\\lambda)|$ to energy difference $|\\hat{F} (\\lambda)^2 -F_{gt}(\\lambda)^2 |$ . The result shows our design is more consistent with human evaluation. Besides, experiments in Tab. 2 show our SAUCD metric aligns well with human evaluation, and outperforms SOTA metrics under multiple evaluation methods. Experiments in Fig. 8 show SAUCD has the capability to improve mesh detail qualities in 3D reconstruction when adapted into training loss.", + "bbox": [ + 75, + 207, + 470, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Human-adjusted Spectrum AUC Difference", + "text_level": 1, + "bbox": [ + 76, + 400, + 447, + 416 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also provide an extended metric version, in which we design a learnable weight parameter along the frequency bands. The weight parameter indicates the adjustment of human sensitivity to each frequency band. Specifically, we design the extended metric as", + "bbox": [ + 75, + 424, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd _ {w} = D _ {w} (\\hat {M}, M _ {g t}) = \\int_ {\\lambda} w (\\lambda) | \\hat {F} (\\lambda) - F _ {g t} (\\lambda) | d \\lambda . \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 511, + 468, + 542 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$w(\\lambda)$ is weight parameters indicating human sensitivity along frequency bands. Our training loss is defined as", + "bbox": [ + 76, + 554, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\lambda_ {p} \\mathcal {L} _ {p l c c} + \\lambda_ {s r} \\mathcal {L} _ {s r o c c} + \\lambda_ {r} \\mathcal {L} _ {r e g u}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 597, + 468, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{L}_{plcc}$ and $\\mathcal{L}_{srocc}$ are Pearson correlation loss and Spearman rank order loss. They are defined the same as Pearson's linear correlation [29] and Spearman's rank order correlation [37]. $\\mathcal{L}_{regu} = 1 / N\\sum_{i}(w_{i} - 1)^{2}$ is the regularization loss, which regularizes weight $w_{i}$ close to 1. $\\lambda_p$ , $\\lambda_{sr}$ , and $\\lambda_r$ are the loss weights of $\\mathcal{L}_{plcc}$ , $\\mathcal{L}_{srocc}$ , and $\\mathcal{L}_{regu}$ . More details of the loss functions can be found in Supplementary Materials Sec. 1. Our experiments in Sec. 4.3 show that after adjustment, the consistency between our metric output and human-annotated ground truth is improved.", + "bbox": [ + 75, + 626, + 470, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 791, + 207, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 816, + 171, + 830 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We build a user study benchmark dataset Shape Grading to evaluate whether our metric is aligned with human evaluation. The dataset contains the human evaluation scores for a variety of distorted meshes. Using this dataset, we can", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "calculate the correlation between metric outputs and human evaluation scores to see how aligned the test metrics are to human evaluation.", + "bbox": [ + 496, + 90, + 890, + 135 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset design. We choose 12 objects as ground truth 3D triangle mesh from public object/scene/human mesh datasets such as [18, 26, 42] and commercial datasets such as [1, 2]. These objects are picked from different categories including humans, animals, buildings, plants, etc.. For each object, we synthesize 7 different types of distortions which commonly occur in 3D reconstruction. For each distortion type we synthesize 4 distortion levels, which gives us $7 \\times 4 = 28$ distorted objects for every ground truth object. We rotate and render each distorted object into 3 videos using different materials for the mesh. In total, we generate $12 \\times 28 \\times 3 = 1,008$ distorted mesh videos. Supplementary Materials Sec. 4 shows the meshes and distortion types we use in our dataset.", + "bbox": [ + 496, + 138, + 892, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Human scoring procedure. We use a pairwise comparison scoring process similar to [31]. Each subject will evaluate all 28 distorted objects of one ground truth object with a certain material. The scoring follows a Swiss system tournament principle used in [31], in which each subject takes 6 rounds of pairwise comparison to score the distorted meshes. After 6 rounds of scoring, the meshes are scored from 0 to 6. 0 means the object loses in every round and 6 means it wins in every round. This process will largely reduce the biases among subjects, since the subjects are compelled to distribute an equal amount of points to the 28 distorted objects. The process will take about 15 minutes for each subject, avoiding the fatigue problem in [7]. For every object rendered with every material, we have 24 to 25 subjects scoring it. In total, we have 868 subjects (536 males, 316 females, and 16 others) who give us $868 \\times 28 = 24304$ scores. More details of the scoring procedure can be found in Supplementary Materials Sec. 5.", + "bbox": [ + 496, + 352, + 893, + 625 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Outlier detection. We use the interquartile range (IQR) method [13] which is widely used in statistics to detect and remove outliers. For each distorted mesh, we first find the 25 percentile and the 75 percentile of the scores. The score range in between is called the IQR range. We remove the scores that are 1.5IQR smaller than the 25 percentile or 1.5IQR larger than the 75 percentile. Our dataset error analysis in Tab. 1 shows, that by removing $2.2\\%$ of the scores using IQR, we can decrease the uncertainty of the final scoring result by nearly $6\\%$ .", + "bbox": [ + 496, + 626, + 893, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset error analysis. We analysis the average $95\\%$ confidence interval of our dataset scores in Tab. 1. The confidence interval of score $x$ can be calculated as $\\sigma_{\\bar{x}} = z_{0.95} \\times \\sigma / \\sqrt{N}$ where $\\sigma$ is the standard derivation of $x$ , $N$ is the number of valid scores, and $z_{0.95} \\approx 1.96$ . We report the average $95\\%$ confidence interval and the relative $95\\%$ confidence interval (which is the confidence interval divided by the scoring range). The result shows that dataset scoring", + "bbox": [ + 496, + 779, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20159", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/deebab21531514f681b68b443f7da111b48512814e5176e7f9a4f653bd361bf7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.540.15-0.100.57-0.06-0.12-0.200.070.040.30-0.200.170.097
Point-to-Surface0.450.19-0.040.66-0.08-0.25-0.32-0.200.010.13-0.21-0.120.017
Normal Difference0.460.110.060.280.110.210.290.470.270.390.110.270.253
IoU [16]0.600.630.010.510.300.02-0.070.200.140.47-0.09-0.010.225
F-score [43]0.580.090.050.330.030.060.160.340.270.250.010.340.208
SSFID [46]0.710.74-0.040.740.390.240.130.320.250.640.25-0.020.363
UHD [47]0.290.220.110.15-0.040.180.410.550.130.180.250.330.231
SAUCD (Ours)0.730.210.600.630.310.510.830.650.770.800.690.080.567
Adjusted SAUCD (Ours)0.790.190.560.640.360.540.790.760.750.770.670.360.598
", + "bbox": [ + 155, + 88, + 823, + 220 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/dd39e5ee34a39a311968774e30c93e0fcdba28559bd3aa5d1753d31584f7158e.jpg", + "table_caption": [ + "a. Pearson's linear correlation coefficient." + ], + "table_footnote": [], + "table_body": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.330.14-0.090.43-0.08-0.06-0.150.17-0.040.24-0.160.220.079
Point-to-Surface0.420.390.140.590.110.05-0.100.200.180.40-0.110.180.205
Normal Difference0.440.220.330.420.190.290.330.560.330.320.210.340.331
IoU [16]0.570.610.280.500.360.210.120.310.2620.560.030.300.342
F-score [43]0.470.250.200.520.210.110.070.360.300.42-0.010.350.27
SSFID [46]0.630.810.280.700.330.230.100.330.320.650.160.340.407
UHD [47]0.380.200.110.320.130.350.410.600.060.270.370.350.296
SAUCD (Ours)0.790.250.570.590.360.560.830.790.690.690.830.240.598
Adjusted SAUCD (Ours)0.830.210.550.590.380.600.820.800.690.680.750.420.611
", + "bbox": [ + 155, + 237, + 823, + 369 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d54ac75ec8cdb5914d073b0c1d2c60c67e45c54c36b62760761263014237a2fb.jpg", + "table_caption": [ + "b. Spearman's rank order correlation coefficient." + ], + "table_footnote": [], + "table_body": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.250.14-0.080.31-0.04-0.02-0.090.150.0130.19-0.070.220.080
Point-to-Surface0.330.300.070.450.100.08-0.030.170.130.30-0.010.160.171
Normal Difference0.340.160.170.310.180.220.260.440.250.230.160.270.250
IoU [16]0.420.440.240.370.280.220.140.260.200.410.100.230.275
F-score [43]0.370.170.140.420.150.110.090.280.230.340.010.300.216
SSFID [46]0.480.620.240.510.250.240.120.290.260.480.170.230.322
UHD [47]0.270.130.070.220.090.260.290.420.0480.190.280.240.209
SAUCD (Ours)0.600.160.420.410.270.450.650.570.550.470.600.190.445
Adjusted SAUCD (Ours)0.640.140.400.410.290.480.630.590.550.450.570.290.453
", + "bbox": [ + 155, + 388, + 823, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "c. Kendall's rank order correlation coefficient.", + "bbox": [ + 344, + 523, + 620, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Correlations between different metrics and human annotation. \"SAUCD\" is our basic version metric. \"Adjusted SAUCD\" is the human-adjusted version of our metric. The ranges of all three correlation coefficients are $[-1, 1]$ , and the higher the better.", + "bbox": [ + 75, + 549, + 892, + 578 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is accurate with a $5\\%$ error range with IQR outlier removal.", + "bbox": [ + 75, + 604, + 468, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation methods. We use 3 different evaluation methods to evaluate the correlation between our metrics and the human scoring (ground truth) on our Shape Grading benchmark dataset. Pearson's linear correlation coefficient (PLCC) [29] is used to evaluate the linear alignment between our metric and human perception. We also used Spearman's rank order correlation coefficient (SROCC) [37] and Kendall's rank order correlation coefficient (KROCC) [19] to evaluate the ranking order correlation between our metric and human perception. The possible ranges of 3 metrics are all $[-1, 1]$ . Higher numbers mean stronger correlations. More details of the three evaluation methods can be found in Supplementary Materials Sec. 1.", + "bbox": [ + 75, + 621, + 472, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Implementation details", + "text_level": 1, + "bbox": [ + 76, + 830, + 290, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We implement our basic version metric following Eq. (6). $\\hat{F} (\\lambda)$ and $F_{gt}(\\lambda)$ in Eq. (6) are both piece-wise functions, so we implement the integration by simply adding every piece", + "bbox": [ + 76, + 854, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "area together. We implement our human-adjusted version following Eq. (7). We use a 20-dimensional weight $w(\\lambda)$ to avoid overfitting. We interpolate $w$ to all frequencies of the ground truth and test meshes and element-wisely multiply them to the spectrums. In spectrum weight training, SROCC and PLCC are used as part of the loss function as Eq. (8). KROCC is not used in training but only for testing. We use a k-fold strategy for training the human-adjusted weight. Each time we choose 1 object for testing and the rest 11 objects for training, which means $k = 12$ . More implementation details can be found in Supplementary Materials Sec. 1.", + "bbox": [ + 496, + 604, + 893, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Quantitative and qualitative results", + "text_level": 1, + "bbox": [ + 498, + 784, + 792, + 801 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SOTA comparison. Tab. 2 shows our results compared to previous 3D mesh shape metrics. We evaluated the correlation between each metric and the human scoring via three different evaluation methods. We observe that a) without any learning-based design, our metric outperforms the SOTA learning-based (SSFID) and non-learning-based met", + "bbox": [ + 496, + 809, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20160", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/764d32b014fa0d52b399c11f8dc6b3bbd71e4da910c20d2b2a7308040c73399c.jpg", + "image_caption": [ + "Figure 5. An example of mesh spectrum curve: We do mesh Fourier transform on the \"Origin\" mesh and show the spectrum in the left graph. The $\\lambda$ -axis is the eigenvalues of the DLBO matrix, the larger the higher frequency. We also show how mesh changes when gradually removing high-frequency information (mesh A to G). The frequency bands of the meshes are shown as the colored arrows in the left graph." + ], + "image_footnote": [], + "bbox": [ + 140, + 89, + 392, + 258 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b28f9dc2d58842566417e939a2392debcc025e9afdd4b6a7e78b3ab3883285be.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 392, + 88, + 504, + 178 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ffdfc17c85a9aa9222a29a8078f8c66e61811739dbeac41d8d4f2ed990d09d2e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 504, + 89, + 616, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/069dc0d830bfde1a0fdae3dbcdee1d2deb3699aee80ccefae9c8ef2eafffbd96.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 616, + 89, + 728, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1fe77269e3a7ae08a08b41ab667a8b20b37ec18a76dee309216883011b2c24fb.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 728, + 89, + 831, + 176 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/be8c066fde23839299ad8b9d5336547fef19adf39135b3b736d510fef446f708.jpg", + "image_caption": [ + "D" + ], + "image_footnote": [], + "bbox": [ + 395, + 191, + 500, + 260 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8846b173a2faee5d3c7e7c7e131dbd6a9c7d87a18a475a0df31cd945c2a37d90.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 181, + 612, + 258 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e69893ab1afe64a8b7fe398432ff0f32fd413461409ac7b5e6c25d5b72103497.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 614, + 181, + 727, + 257 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/949eee0e4f94a2ff0469e702e5f40a35b17f59805c76eac90a5b3bb3364a8969.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 727, + 181, + 831, + 250 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "rics (Chamfer Distance, IoU, F-score, and UHD), b) our extended version metric with learned weights has better linearity and slightly better ranking order correction with human evaluation, and c) our results on different objects show that our metrics have good generalizability.", + "bbox": [ + 75, + 338, + 470, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spectrum example. We first show an example of mesh spectrum in Fig. 5. We decompose the \"origin\" mesh using the Fourier Transform and get the resulting spectrum (top-left graph). The meshes on the right (from mesh A to G) are generated by gradually removing high-frequency information. The frequency bands of the meshes are shown as colored arrows in and under the graph. As we see, the details gradually disappear as we remove high-frequency information.", + "bbox": [ + 75, + 415, + 468, + 549 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Frequency band separation. We explored the consistency between human perception and the information obtained from every frequency band. Specifically, we separate the frequency band exponentially and build metrics only using information from that frequency band. The results are shown in Tab. 3, we find the frequency bands [0, 0.001] and [0.01, 0.03] have the best consistency with human perception. Moreover, it shows that if we put all frequencies together, they can achieve better results.", + "bbox": [ + 75, + 551, + 470, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Trained weight. We show our trained weights in Human-adjusted metric in Fig. 6. Different lines represent different folds, and the bold purple line is the average weight. We can see the weights trained on each fold have similar patterns. We also observe that the weight curves have a small peak in the range A and two much larger peaks between A and B, which means our extended metric relies more on the information between A and B. We show an example of mesh shapes in the range A, B, and C at the bottom of Fig. 6. Mesh A obviously has fewer details than Mesh B, and the weight curve shows that this difference is what the learning process tries to emphasize.", + "bbox": [ + 75, + 688, + 470, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Negative frequencies. In Fig. 7 we illustrate how our revised Cotan formula DLBO in Eq. (4) improves fre", + "bbox": [ + 76, + 869, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1d05bd60080fb3c240c1e5a09eacb96e6e1840e48e4bb994effa4cc0f84c42c8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 531, + 335, + 754, + 465 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/efcc494b3d5fa2fa4731f88581ec2698e33c2f2aaaf947c5d4bfdb4584223ad9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 754, + 335, + 859, + 462 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/81c964bc79cb4c885bb6d9490d3a408b54de2aec34c25c88b999950f4f56ebc1.jpg", + "image_caption": [ + "Figure 6. Learned spectrum weights on all 12 folds. The name of colorful thin lines means the test object name of that fold. The bold purple line is the average weights of all folds. We also show some examples of mesh shape information in different frequency bands. Frequency band A is [0, 0.0075), B is [0, 0.03), and C is [0, 0.05)." + ], + "image_footnote": [], + "bbox": [ + 532, + 465, + 643, + 558 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/950f9ac4a3519d2644f9e0acb368bc1105d00b7801ad1d34f258ade94baaa04f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 465, + 751, + 556 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e24b6e02206c10ef8f949247a95ea27d87aee0b845ddd4a5359c3c806071289e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 751, + 464, + 859, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "quency analysis compared to the original Coton formula in Eq. (2) [25]. The first and second rows are the results of the original Coton formula DLBO and our revised Coton formula DLBO, respectively. The original Coton formula can yield negative frequencies due to its lack of positive semidefiniteness, whereas our revision ensures all frequencies are non-negative. For both objects in the figure, we remove different portions of high-frequency information and show the remaining low-frequency parts (resulting in “Filtered mesh 1” and “Filtered mesh 2”). For the left object, notice the counterintuitive sharp shapes in the red circle when using the Coton formula. The right object is a much more severe case. Sharp shapes in low-frequency parts show improper decomposition and high-frequency aliasing with low-frequency shapes, making the Coton formula unsuitable for spectral", + "bbox": [ + 496, + 672, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20161", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9ea0e2af7986dfe9f9da879e63a9da1c4bb3e821ba35ed7f298c61596fd3906a.jpg", + "image_caption": [ + "Figure 7. Counterintuitive low-frequencies information if some of the mesh frequencies are negative. We can see if we remove the high-frequency part of the mesh (resulting in \"Filtered mesh 1\" and \"Filtered mesh 2\") using the original Coton formula, the mesh's low-frequency parts show artifacts (sharp shapes). The red circles show the artifacts in the left object. The right object shows a case when these artifacts occur much more often. These artifacts do not occur using our revised Coton formula DLBO." + ], + "image_footnote": [], + "bbox": [ + 106, + 85, + 867, + 209 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f1164bb6ca22a653232857bec77621587f1f6f32d9bec7c7810538182e64d6fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Frequency bandPLCC ↑SROCC ↑KROCC ↑
[0, 0.001)0.4340.5150.376
[0.001, 0.003)0.2400.4090.281
[0.003, 0.01)0.2550.4550.340
[0.01, 0.03)0.4210.5280.391
[0.03, 0.1)0.2870.3510.250
[0.1,∞)0.3180.1920.155
(0,∞)0.5670.5980.445
", + "bbox": [ + 78, + 286, + 326, + 373 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/67f2af19e7b55a778dcc1f2471ff386086481ff5cf170d5ec96139dc2ff58661.jpg", + "table_caption": [ + "Table 3. Results when building metrics using each frequency band separately. The bottom row is our proposed metric." + ], + "table_footnote": [], + "table_body": "
Pruning PortionPLCC ↑SROCC ↑KROCC ↑
0%0.5130.5490.393
0.1%0.5670.5980.445
1%0.5540.6020.462
10%0.5170.5810.442
20%0.5030.5870.445
", + "bbox": [ + 331, + 287, + 588, + 354 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/af379534d24203931fd62f1918ca418f84307bd4df67327d6a861ee17accb833.jpg", + "table_caption": [ + "Table 4. Results with different pruning portions. The metric achieves better results with pruning portion to be $0.1\\%$ or $1\\%$ . We use pruning portion as $0.1\\%$ in our design." + ], + "table_footnote": [], + "table_body": "
ModulesPLCC ↑SROCC ↑KROCC ↑
Topology Laplacian [11]0.2980.3270.235
Cotan formula [25]0.4170.4700.340
Energy difference0.2680.3150.215
w/o normalization0.2570.5070.353
Spatial normalization0.2690.5420.392
Ours0.5670.5980.445
", + "bbox": [ + 594, + 289, + 890, + 368 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Module replacement. We replace each module of our metric with alternative designs to verify the design of each module.", + "bbox": [ + 594, + 378, + 892, + 421 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8c0e1e1821ca17bc722cd5a69ba37fd3fd3646a8f76fe2e4d9cb56548f171769.jpg", + "image_caption": [ + "Figure 8. We Adapt SAUCD into a loss function and use it in monocular-image-based 3D hand reconstruction. From left to right: input images, reconstruction result w/o SAUCD loss, reconstruction result w/ SAUCD loss, and ground truth mesh. We can see that the enhancement of SAUCD loss in mesh details is clearly noticeable." + ], + "image_footnote": [], + "bbox": [ + 109, + 448, + 441, + 566 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mesh comparison. In contrast, our revised formula yields smooth low-frequency components without these artifacts.", + "bbox": [ + 75, + 672, + 468, + 703 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Noise pruning portion. Tab. 4 shows our SAUCD metric performance by changing the noise pruning portion (Sec. 3.3). The metric achieves better results when the pruning portion is $0.1\\%$ or $1\\%$ . In our proposed metric, we choose the pruning portion to be $0.1\\%$ to best avoid possible high-frequency information loss.", + "bbox": [ + 75, + 704, + 470, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Module replacement. Tab. 5 shows our SAUCD metric performance by replacing some modules with alternative designs. First, we replace our revision of the discrete Laplace-Beltrami operator in Eq. (4) with topology Laplacian matrix in [11] and \"Cotan formula\" in [25]. Second, we change the AUC difference defined in Eq. (6) into the energy difference, which means changing $|\\hat{F}(\\lambda) - F_{gt}(\\lambda)|$ in Eq. (6) into", + "bbox": [ + 75, + 795, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$|\\hat{F}(\\lambda)^2 - F_{gt}(\\lambda)^2|$ . In the third experiment, we replace AUC normalization (in Sec. 3.3) with spatial normalization, where we normalize the meshes by their maximum range along all 3 spatial axes. We also removed the AUC normalization module for another comparison. Our experiments show SAUCD has better performance than alternative designs.", + "bbox": [ + 496, + 449, + 893, + 541 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Adapting SAUCD to loss function. We adapted our metric into a loss function to enhance the visual quality of 3D mesh reconstructions, as evident from the hand reconstruction results in Fig. 8. Details on the experiment's implementation are available in Supplementary Materials Sec. 7. From this experiment, we can see that the enhancement of SAUCD loss in mesh details is clearly noticeable.", + "bbox": [ + 496, + 542, + 893, + 647 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualized examples. We visualize examples in our dataset and their evaluation result using different metrics in Supplementary Materials Sec. 6.", + "bbox": [ + 496, + 648, + 893, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 708, + 627, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In order to propose a 3D shape evaluation that better aligns with human perception, we design an analytic metric named Spectrum AUC Difference (SAUCD). Our proposed SAUCD leverages mesh spectrum analysis to evaluate 3D shape that aligns with human evaluation, and its extended version Human-adjusted SAUCD further explores the sensitivity of human perception of each frequency band. To evaluate our new metrics, we build a user study dataset to compare our metrics with existing metrics. The results validate that both our new metrics are well aligned with human perceptions and outperform previous methods.", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20162", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Gobotree - photos, cut-outs, 3d people. https://www.gobotree.com/.", + "[2] Sketchfab - the best 3d viewer on the web. https://sketchfab.com/.", + "[3] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. Learning representations and generative models for 3d point clouds. 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Unsupervised 3d human mesh recovery from noisy point clouds. arXiv preprint arXiv:2107.07539, 2021." + ], + "bbox": [ + 78, + 90, + 470, + 731 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20164", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_model.json b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_model.json new file mode 100644 index 0000000000000000000000000000000000000000..b9c4acf3c4d97690d231ea3b25cdbecaf349b429 --- /dev/null +++ b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.107, + 0.131, + 0.865, + 0.155 + ], + "angle": 0, + "content": "Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation" + }, + { + "type": "text", + "bbox": [ + 0.187, + 0.179, + 0.782, + 0.265 + ], + "angle": 0, + "content": "Tianyu Luan\\(^{1,2*}\\) Zhong Li\\(^{2}\\) Lele Chen\\(^{2}\\) Xuan Gong\\(^{3,2,1}\\) \nLichang Chen\\(^{2,4}\\) Yi Xu\\(^{2}\\) Junsong Yuan\\(^{1}\\) \n\\(^{1}\\)State University of New York at Buffalo \\(^{2}\\)OPPO US Research Center \n\\(^{3}\\)Harvard Medical School \\(^{4}\\)University of Maryland, College Park" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.297, + 0.314, + 0.314 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.474, + 0.692 + ], + "angle": 0, + "content": "Existing 3D mesh shape evaluation metrics mainly focus on the overall shape but are usually less sensitive to local details. This makes them inconsistent with human evaluation, as human perception cares about both overall and detailed shape. In this paper, we propose an analytic metric named Spectrum Area Under the Curve Difference (SAUCD) that demonstrates better consistency with human evaluation. To compare the difference between two shapes, we first transform the 3D mesh to the spectrum domain using the discrete Laplace-Beltrami operator and Fourier transform. Then, we calculate the Area Under the Curve (AUC) difference between the two spectrums, so that each frequency band that captures either the overall or detailed shape is equitably considered. Taking human sensitivity across frequency bands into account, we further extend our metric by learning suitable weights for each frequency band which better aligns with human perception. To measure the performance of SAUCD, we build a 3D mesh evaluation dataset called Shape Grading, along with manual annotations from more than 800 subjects. By measuring the correlation between our metric and human evaluation, we demonstrate that SAUCD is well aligned with human evaluation, and outperforms previous 3D mesh metrics. Our project page: https://bit.ly/saucd." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.719, + 0.21, + 0.735 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.88 + ], + "angle": 0, + "content": "With the recent progress of 3D reconstruction and processing techniques, 3D mesh shapes have increasing applications in fields such as video games, industrial design, 3D printing, etc. In these applications, assessing the visual quality of the 3D mesh shape is a crucial task. To meet the requirements of various applications, a promising evaluation metric should not only reflect the geometry measurement but also align with human visual perception. Considering that human beings perceive 3D meshes in both overall shape and local" + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.294, + 0.856, + 0.504 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.514, + 0.895, + 0.639 + ], + "angle": 0, + "content": "Figure 1. An example of how previous spatial domain 3D shape metrics (Chamfer Distance [6] and UHD [47]) deviate from human evaluation. we create Mesh \\(A\\) by adding a small pose error to the ground truth mesh, and by applying a large smoothing kernel to ground truth, we create Mesh \\(B\\). Contrary to human perception, previous spatial domain metrics evaluate Mesh \\(B\\) better than Mesh \\(A\\). This indicates that while they are sensitive to general shape differences, they tend to overlook high-frequency details. Note that different metrics use different units of measurement." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.671, + 0.892, + 0.701 + ], + "angle": 0, + "content": "details, it is a challenging task to find an evaluation metric that can align well with humans." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Previous metrics have the following disadvantages in this scenario. Traditional spatial domain measurements such as Chamfer Distance [6] which calculates the mean distance between a vertex on one mesh and its nearest vertex on the other mesh, can accurately measure the spatial distance. However, it does not guarantee capturing all shape details. In fact, such measurements in the spatial domain often overlook finer shape details, as the details tend to get overwhelmed by the overall shape. Fig. 1 illustrates the discrepancy between spatial measurements and human evaluation as mesh details change. Specifically, When we remove the wrinkles from the ground truth mesh (resulting in Mesh \\( B \\)), the errors detected by previous metrics are not as significant as when we slightly" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.9 + ], + "angle": 0, + "content": "*Work done while Tianyu was an intern at OPPO US Research Center." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "20155" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.349 + ], + "angle": 0, + "content": "change the pose of the hand (Mesh \\(A\\)). However, humans tend to sense a significant difference between ground truth and Mesh \\(B\\), but barely recognize the difference between ground truth and Mesh \\(A\\). To mitigate this problem, previous works propose learning-based approaches, such as Single Shape Fréchet Inception Distance (SSFID) [46] based on learnable features from 3D shape. They compare the difference between the test mesh and the ground truth mesh in the latent feature space, and the design is expected to better align human perception. However, such learning-based methods would require a large amount of data to train the network. Their accuracy and generalizability are limited by the size of the dataset, data distribution, and annotation quality, not to mention the potential bias in collecting human perception feedback, which could mislead the learned metrics. An analytic metric that can better explain the shape difference is thus preferred." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.626 + ], + "angle": 0, + "content": "To address the above limitations, we design an analytic-based 3D shape evaluation metric named Spectrum Area Under the Curve Difference (SAUCD). Our metric measures mesh shape differences with a balanced consideration of both overall and detailed shape, making it better aligned with human evaluation. To allow our metric to capture detail variations, we leverage the 3D shape spectrum to decompose different levels of shape details from the overall shape, with details corresponding to higher-frequency components. The advantage of transforming the shape signal into the spectrum domain is that the high-frequency details are explicitly separated from the low-frequency overall shape. Therefore, it provides appropriate consideration to the information in different frequency bands, not just the low-frequency information of the overall shape in the dominant place. Thus, the details that human perception cares about will be better represented. Besides, the frequency analysis method allows the metric to be mostly analytic and better explained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.902 + ], + "angle": 0, + "content": "We design SAUCD following the above inspiration. To begin with, both the test mesh and the ground truth mesh are transformed from the spatial to the spectrum domain using the discrete Laplace-Beltrami operator (DLBO), which encodes the mesh geometry information into a semidefinite Laplacian matrix. Once in the spectrum domain, we compare the regions under the two spectrums. Our Spectrum Area Under the Curve Difference metric is defined as the area of the non-overlapping region under the two spectrums - a larger area indicates a greater difference. Moreover, to better align with human evaluation, we further extend our design by learning a spectrum weight for SAUCD. However, different from previous learning-based approaches that use deep networks, large datasets, and extensive learning processes, our learning-based method requires the training of a weight vector. This vector measures the sensitivity of human perception across frequency bands, making the learned metric better aligned with human perception. We then evaluated the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "effectiveness of SAUCD on our provided user study benchmark dataset named Shape Grading. Using Shape Grading, we compare our metrics with previous metrics by calculating the correlation between each metric and human scoring. In summary, our contributions are listed as follows." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.169, + 0.895, + 0.244 + ], + "angle": 0, + "content": "- We design an analytic-based 3D mesh shape metric named Spectrum AUC Difference (SAUCD), which evaluates the difference between a 3D mesh and its ground truth mesh. Our metric considers both the overall shape and intricate details, to align more closely with human perception." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.244, + 0.895, + 0.303 + ], + "angle": 0, + "content": "- We further extend our design to a learnable metric. The extended metric explores the human perception sensitivity in different frequency bands, which further improves this metric." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.305, + 0.895, + 0.395 + ], + "angle": 0, + "content": "- We build a user study benchmark dataset named Shape Grading which is annotated by more than 800 subjects. The provided dataset verifies that both versions of our metrics are consistent with human evaluation and outperform previous methods. This dataset can also facilitate 3D mesh metric evaluation in future research." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.169, + 0.895, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.895, + 0.443 + ], + "angle": 0, + "content": "Our experiments show that both SAUCD and its extended version outperform previous methods with good generalizability to different types of objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.453, + 0.651, + 0.469 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.895, + 0.719 + ], + "angle": 0, + "content": "Metrics in 3D mesh reconstruction. Chamfer Distance [6] is a popular metric used in 3D mesh reconstruction tasks such as those in [21, 24, 32, 35, 45, 48-50]. Other spatial domain metrics, such as 3D Intersection over Union (IoU) in [10, 16, 17, 27, 33, 39]. F-score in [4, 15, 40, 43], and Unidirectional Hausdorff distance (UHD) in [47] are commonly focused on the geometry accuracy of mesh shapes. These metrics can provide accurate geometry measurements, but they are not designed to align with human evaluation. Deep-learning-based methods such as Single Shape Fréchet Inception Distance [46] are also used in 3D reconstruction. While these metrics have the capacity to adapt from human evaluation, they are more like black boxes, with performances subject to dataset size and annotation bias. Moreover, most previous works miss out on user study validation to verify if their metrics align with human evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.84 + ], + "angle": 0, + "content": "3D shape generation metrics. Multiple metrics have been used in 3D shape generation, such as Minimal Matching Distance (MMD) [3], Jensen-Shannon Divergence (JSD) [22], Total Mutual Difference (TMD) [47], Fréchet Pointcloud Distance (FPD) [36], etc.. These metrics are designed to measure the differences between the generated distributions, while our task is to build a metric to compare the shape of two meshes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.895, + 0.902 + ], + "angle": 0, + "content": "3D mesh compression and watermarking metrics. Previous works [8, 12, 23, 41] focused on evaluating mesh errors in mesh compression and watermarking. Since compression and watermarking pursue mesh errors that cannot" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20156" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.153, + 0.09, + 0.821, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.28, + 0.895, + 0.325 + ], + "angle": 0, + "content": "Figure 2. Our SAUCD metric is designed as follows: A. We use mesh Fourier Transform to analyze the spectrums of test and ground truth mesh. B. We compare the difference between two spectrum curves by calculating the Area Under the Curve (AUC) difference. C. We further extend our metric by multiplying the AUC difference with a learnable weight to capture human sensitivity in each frequency band." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.471, + 0.412 + ], + "angle": 0, + "content": "be detected by humans, they mainly focus on barely noticed errors. However, our task is to build a metric that can handle generally occurring errors that happen in 3D reconstruction tasks and applications." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.423, + 0.251, + 0.44 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.471, + 0.525 + ], + "angle": 0, + "content": "Our task is to design a metric aligned with human evaluation to measure the shape difference between a test triangle mesh and its corresponding ground truth triangle mesh. Specifically, given a test mesh \\(\\hat{M}\\) and its ground truth mesh \\(M_{gt}\\), Spectrum AUC Difference (SAUCD) can be abstracted as" + }, + { + "type": "equation", + "bbox": [ + 0.213, + 0.534, + 0.47, + 0.553 + ], + "angle": 0, + "content": "\\[\nd = D (\\hat {M}, M _ {g t}). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.473, + 0.61 + ], + "angle": 0, + "content": "\\(d\\) is the distance between the test and the ground truth mesh. In this section, we will elaborate on how the distance function \\(D(\\cdot)\\) is designed." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.619, + 0.188, + 0.633 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.779 + ], + "angle": 0, + "content": "As shown in Fig. 2, our metric is calculated via the following steps: First, we use mesh Fourier transform to analyze the spectrums of the test and ground truth mesh (in Sec. 3.2). Then we leverage each frequency band by calculating the Area Under the Curve (AUC) difference of the spectrum curves (in Sec. 3.3). Moreover, we further extended our metric by multiplying the AUC difference with a learnable weight to capture the human sensitivity on each frequency band (in Sec. 3.4). We will discuss each step in detail." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.299, + 0.804 + ], + "angle": 0, + "content": "3.2. Mesh spectrum analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In order to capture the overall shape as well as shape details, we choose to decompose the mesh signal into a spectrum. Considering the mesh as a function on a discretized manifold space, we can calculate the spectrum using the manifold space Fourier transform. In Hilbert space, the Fourier operator is defined as the eigenfunctions of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.895, + 0.516 + ], + "angle": 0, + "content": "Laplacian operator [14]. The same definition and similar theories are extended to continuous and discrete manifold space by [5, 9]. The Laplacian operator on discrete manifold spaces, i.e. mesh space in our task, is named the Discrete Laplace-Beltrami operator (DLBO). Similar to the Laplacian operator in image space that encodes the pixel information by capturing the local pixel differences [20, 28, 30, 34, 38, 44], DLBO encodes the mesh shape information by capturing the local shape fluctuation. The \"Cotan formula\" defined in [25] is the most widely used discretization, which can be represented in matrix form as" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.522, + 0.894, + 0.58 + ], + "angle": 0, + "content": "\\[\nL _ {i j} = \\left\\{ \\begin{array}{c c} \\sum_ {j \\in N (i)} \\frac {1}{2 A _ {i}} \\left(\\cot \\alpha_ {i j} + \\cot \\beta_ {i j}\\right), & i = j \\\\ - \\frac {1}{2 A _ {i}} \\left(\\cot \\alpha_ {i j} + \\cot \\beta_ {i j}\\right), & i \\neq j \\wedge j \\in N (i) \\\\ 0, & i \\neq j \\wedge j \\notin N (i), \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.895, + 0.793 + ], + "angle": 0, + "content": "where \\(L \\in \\mathbb{R}^{N \\times N}\\) is the DLBO matrix, with \\(N\\) the vertex number of the mesh. \\(L_{ij}\\) indicates its entry in \\(i\\)th row and \\(j\\)th column, which represents the edge weight between vertex \\(v_i\\) and \\(v_j\\). \\(A_i\\) is the mixed Voronoi area of vertex \\(v_i\\) on the mesh. As shown in Fig. 3, the \\(v_i\\)'s mixed Voronoi area is defined as the area of the polygon in which the vertices are the circumcenters of \\(v_i\\)'s surrounding faces. \\(N(i)\\) is the index set of \\(v_i\\)'s adjacent vertices. If \\(v_i\\) and \\(v_j\\) are adjacent, \\(\\alpha_{ij}\\) and \\(\\beta_{ij}\\) are the opposite angles of edge \\((v_i, v_j)\\) in each of the edge's two neighbor triangle faces, respectively (shown in Fig. 3). If not, \\(\\alpha_{ij}\\) and \\(\\beta_{ij}\\) are not defined and \\(L_{ij}\\) is 0. As shown in Fig. 2, the DLBO matrix is used for mesh Fourier transform to get mesh spectrum. We calculate the Fourier operator \\(U^\\top\\), which is the eigenfunction of \\(L\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.651, + 0.799, + 0.893, + 0.817 + ], + "angle": 0, + "content": "\\[\nL = U \\Lambda U ^ {\\top}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.856 + ], + "angle": 0, + "content": "where \\(\\Lambda\\) is a diagonal matrix whose diagonal elements are Fourier mesh frequencies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To ensure the mesh frequencies are non-negative, we need the DLBO matrix \\(L\\) to be positive semidefinite. Our experiment in Fig. 7 gives an example of the counterintuitive" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20157" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.089, + 0.223, + 0.188 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.197, + 0.248, + 0.24 + ], + "angle": 0, + "content": "Figure 3. Variables defined in our discrete Laplace-Beltrami operator design." + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.089, + 0.848, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.262, + 0.197, + 0.894, + 0.24 + ], + "angle": 0, + "content": "Figure 4. Spectrum Area Under the Curve Difference. We design our metric using the AUC difference of the spectrums. The blue curve and red curve are the test and ground truth mesh spectrum, respectively. The purple area in the last graph is the Spectrum AUC Difference. Please find details in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.267, + 0.473, + 0.482 + ], + "angle": 0, + "content": "results when there are negative frequencies. However, the Coton formula in Eq. (2) does not guarantee to be positive semidefinite. We provide a simple example in Supplementary Materials Sec. 3 in which \\( L \\) is not positive semidefinite when the mesh is not Delaunay triangulated and the mixed Voronoi areas are not all equal to each other. In our metric design, we made two small changes to the original Coton formula to make it positive semidefinite. a) Inspired by the symmetric normalization of the topology Laplacian matrix in [11], we make \\( L \\) symmetric by changing the normalization parameter \\( A_{i} \\) into a symmetric normalized manner \\( A_{i}^{\\frac{1}{2}}A_{j}^{\\frac{1}{2}} \\). b) We replace \\( \\cot \\alpha_{ij} + \\cot \\beta_{ij} \\) with \\( |\\cot \\alpha_{ij} + \\cot \\beta_{ij}| \\). This ensures all the edge weights in the Laplacian matrix to be non-negative. Thus, our revision of DLBO is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.486, + 0.496, + 0.549 + ], + "angle": 0, + "content": "\\[\nL _ {i j} = \\left\\{ \\begin{array}{c c} \\frac {1}{2} \\sum_ {j \\in N (i)} A _ {i} ^ {- \\frac {1}{2}} A _ {j} ^ {- \\frac {1}{2}} | \\cot \\alpha_ {i j} + \\cot \\beta_ {i j} |, & i = j \\\\ - \\frac {1}{2} A _ {i} ^ {- \\frac {1}{2}} A _ {j} ^ {- \\frac {1}{2}} | \\cot \\alpha_ {i j} + \\cot \\beta_ {i j} |, & i \\neq j \\wedge j \\in N (i) \\\\ 0, & i \\neq j \\wedge j \\notin N (i). \\end{array} \\right. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.472, + 0.625 + ], + "angle": 0, + "content": "We prove that our revision of the Cotan formula is positive semidefinite in Supplementary Materials Sec. 2. In Tab. 5, our experiments show that our DLBO matrix design outperforms the origin Cotan formula in [25], and the topology Laplacian matrix defined in [11]." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.625, + 0.47, + 0.656 + ], + "angle": 0, + "content": "Finally, we obtain the mesh spectrum by acting Fourier operator on the mesh vertices" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.666, + 0.47, + 0.693 + ], + "angle": 0, + "content": "\\[\nF _ {i} = \\sqrt {G _ {i , x} ^ {2} + G _ {i , y} ^ {2} + G _ {i , z} ^ {2}}, G = U ^ {\\top} v, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.702, + 0.472, + 0.794 + ], + "angle": 0, + "content": "where \\( v \\in \\mathbb{R}^{N \\times 3} \\) indicates the 3D coordinates of \\( N \\) mesh vertices. The result spectrum \\( F \\in \\mathbb{R}^N \\). Fig. 5 shows an example of the mesh spectrum (left side) and how the meshes look in different frequency bands (right side). This provides an illustration of the information contained in different frequency bands of the mesh spectrum." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.317, + 0.818 + ], + "angle": 0, + "content": "3.3. Spectrum AUC Difference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.87 + ], + "angle": 0, + "content": "To reduce the noise and normalize the mesh scale, we also design noise pruning and AUC normalization procedures before calculating the Spectrum AUC Difference." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Noise pruning. As shown in Fig. 4 process \\((a)\\), we prune a small portion of the highest frequency information" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.267, + 0.892, + 0.433 + ], + "angle": 0, + "content": "to reduce the interference of noise. From the observation of the first two meshes (A and B) in Fig. 5, we can see that humans can barely notice the shape differences when the highest frequency parts are removed. Thus, if we try to evaluate the mesh shape that aligns with human perception, it is reasonable to remove high-frequency noise without losing much information that humans care about. Empirically, we choose to prune the highest \\(0.1\\%\\) frequency information as noise. Our experiments in Tab. 4 show that this portion is more consistent with human perception while preserving good mesh quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.893, + 0.617 + ], + "angle": 0, + "content": "AUC normalization. Given a spectrum \\( F(\\lambda) \\), its Area Under the Curve (AUC) can be defined as \\( \\int_{\\infty} F(\\lambda) d\\lambda \\). AUC normalization means using spectrum AUC to normalize the mesh scale. If the mesh scale increases by \\( s \\) times in length, the mixed Voronoi area, i.e. \\( A_i \\) in Eq. (4), will decrease by \\( s^2 \\) times. Thus, each element in the DLBO matrix \\( L \\) will also decrease by \\( s^2 \\) times. Then, according to Eq. (3), the frequency \\( \\lambda \\) will decrease \\( s^2 \\) times to \\( \\lambda / s^2 \\), and according to Eq. (5), the spectrum amplitude \\( F \\) will change to \\( sF \\) because \\( v \\) is increased by \\( s \\) time and \\( U^\\top \\) is still orthonormal. Then the area under the spectrum curve (the area boxed with red or blue lines in Fig. 4) changes as \\( A' = \\int sF(\\lambda) d\\lambda / s^2 = \\frac{1}{s} A \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.895, + 0.798 + ], + "angle": 0, + "content": "In our approach, we normalize the area under the spectrum curve \\( A \\) to 1 to resolve the scale difference, which means \\( s = A \\), \\( \\lambda \\) decreases by \\( A^2 \\) times, and spectrum amplitude \\( F \\) increases by \\( A \\) times (Fig. 4 process (b)). AUC normalization fairly normalizes the scale of objects in different shapes by only changing the scale, not shape details. It normalizes the spectrum AUC of all mesh to 1, making the mesh spectrums differ only in distributions. Our experiments in Tab. 5 demonstrate this design can bring a fairer comparison of the spectrums and improve the human consistency of the metric. The experiment also demonstrates that this design outperforms the spatial domain scale normalization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.799, + 0.894, + 0.86 + ], + "angle": 0, + "content": "Spectrum AUC Difference. In order to capture the difference between two mesh shapes in the spectrum domain, we design Spectrum AUC Difference (SAUCD) on the spectrum analysis results after noise pruning and AUC normalization:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.873, + 0.893, + 0.906 + ], + "angle": 0, + "content": "\\[\nd = D (\\hat {M}, M _ {g t}) = \\int_ {\\lambda} | \\hat {F} (\\lambda) - F _ {g t} (\\lambda) | d \\lambda , \\tag {6}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20158" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.102, + 0.089, + 0.447, + 0.155 + ], + "angle": 0, + "content": "
datasetRaww/ IQR removal
number of valid scores2430423775
Scoring range[0, 6][0, 6]
95% confidence interval0.3180.303
Relative 95% confidence interval5.33%5.04%
" + }, + { + "type": "table_caption", + "bbox": [ + 0.14, + 0.167, + 0.405, + 0.18 + ], + "angle": 0, + "content": "Table 1. Dataset statistics and error analysis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.208, + 0.471, + 0.391 + ], + "angle": 0, + "content": "where \\(\\hat{F}\\) and \\(F_{gt}\\) are the test and groundtruth mesh spectrum. As shown in Fig. 4 process \\((c)\\), our metric is defined as the AUC difference of the two spectrum curves (the purple area). In Tab. 5, we compare our design with an alternative design which changes the amplitude difference \\(|\\hat{F} (\\lambda) - F_{gt}(\\lambda)|\\) to energy difference \\(|\\hat{F} (\\lambda)^2 -F_{gt}(\\lambda)^2 |\\). The result shows our design is more consistent with human evaluation. Besides, experiments in Tab. 2 show our SAUCD metric aligns well with human evaluation, and outperforms SOTA metrics under multiple evaluation methods. Experiments in Fig. 8 show SAUCD has the capability to improve mesh detail qualities in 3D reconstruction when adapted into training loss." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.401, + 0.449, + 0.417 + ], + "angle": 0, + "content": "3.4. Human-adjusted Spectrum AUC Difference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.47, + 0.501 + ], + "angle": 0, + "content": "We also provide an extended metric version, in which we design a learnable weight parameter along the frequency bands. The weight parameter indicates the adjustment of human sensitivity to each frequency band. Specifically, we design the extended metric as" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.512, + 0.47, + 0.543 + ], + "angle": 0, + "content": "\\[\nd _ {w} = D _ {w} (\\hat {M}, M _ {g t}) = \\int_ {\\lambda} w (\\lambda) | \\hat {F} (\\lambda) - F _ {g t} (\\lambda) | d \\lambda . \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.555, + 0.469, + 0.586 + ], + "angle": 0, + "content": "\\(w(\\lambda)\\) is weight parameters indicating human sensitivity along frequency bands. Our training loss is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.598, + 0.47, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\lambda_ {p} \\mathcal {L} _ {p l c c} + \\lambda_ {s r} \\mathcal {L} _ {s r o c c} + \\lambda_ {r} \\mathcal {L} _ {r e g u}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.471, + 0.779 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}_{plcc}\\) and \\(\\mathcal{L}_{srocc}\\) are Pearson correlation loss and Spearman rank order loss. They are defined the same as Pearson's linear correlation [29] and Spearman's rank order correlation [37]. \\(\\mathcal{L}_{regu} = 1 / N\\sum_{i}(w_{i} - 1)^{2}\\) is the regularization loss, which regularizes weight \\(w_{i}\\) close to 1. \\(\\lambda_p\\), \\(\\lambda_{sr}\\), and \\(\\lambda_r\\) are the loss weights of \\(\\mathcal{L}_{plcc}\\), \\(\\mathcal{L}_{srocc}\\), and \\(\\mathcal{L}_{regu}\\). More details of the loss functions can be found in Supplementary Materials Sec. 1. Our experiments in Sec. 4.3 show that after adjustment, the consistency between our metric output and human-annotated ground truth is improved." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.792, + 0.209, + 0.809 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.173, + 0.831 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "We build a user study benchmark dataset Shape Grading to evaluate whether our metric is aligned with human evaluation. The dataset contains the human evaluation scores for a variety of distorted meshes. Using this dataset, we can" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.136 + ], + "angle": 0, + "content": "calculate the correlation between metric outputs and human evaluation scores to see how aligned the test metrics are to human evaluation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.893, + 0.349 + ], + "angle": 0, + "content": "Dataset design. We choose 12 objects as ground truth 3D triangle mesh from public object/scene/human mesh datasets such as [18, 26, 42] and commercial datasets such as [1, 2]. These objects are picked from different categories including humans, animals, buildings, plants, etc.. For each object, we synthesize 7 different types of distortions which commonly occur in 3D reconstruction. For each distortion type we synthesize 4 distortion levels, which gives us \\(7 \\times 4 = 28\\) distorted objects for every ground truth object. We rotate and render each distorted object into 3 videos using different materials for the mesh. In total, we generate \\(12 \\times 28 \\times 3 = 1,008\\) distorted mesh videos. Supplementary Materials Sec. 4 shows the meshes and distortion types we use in our dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.353, + 0.895, + 0.625 + ], + "angle": 0, + "content": "Human scoring procedure. We use a pairwise comparison scoring process similar to [31]. Each subject will evaluate all 28 distorted objects of one ground truth object with a certain material. The scoring follows a Swiss system tournament principle used in [31], in which each subject takes 6 rounds of pairwise comparison to score the distorted meshes. After 6 rounds of scoring, the meshes are scored from 0 to 6. 0 means the object loses in every round and 6 means it wins in every round. This process will largely reduce the biases among subjects, since the subjects are compelled to distribute an equal amount of points to the 28 distorted objects. The process will take about 15 minutes for each subject, avoiding the fatigue problem in [7]. For every object rendered with every material, we have 24 to 25 subjects scoring it. In total, we have 868 subjects (536 males, 316 females, and 16 others) who give us \\(868 \\times 28 = 24304\\) scores. More details of the scoring procedure can be found in Supplementary Materials Sec. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.627, + 0.894, + 0.779 + ], + "angle": 0, + "content": "Outlier detection. We use the interquartile range (IQR) method [13] which is widely used in statistics to detect and remove outliers. For each distorted mesh, we first find the 25 percentile and the 75 percentile of the scores. The score range in between is called the IQR range. We remove the scores that are 1.5IQR smaller than the 25 percentile or 1.5IQR larger than the 75 percentile. Our dataset error analysis in Tab. 1 shows, that by removing \\(2.2\\%\\) of the scores using IQR, we can decrease the uncertainty of the final scoring result by nearly \\(6\\%\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Dataset error analysis. We analysis the average \\(95\\%\\) confidence interval of our dataset scores in Tab. 1. The confidence interval of score \\(x\\) can be calculated as \\(\\sigma_{\\bar{x}} = z_{0.95} \\times \\sigma / \\sqrt{N}\\) where \\(\\sigma\\) is the standard derivation of \\(x\\), \\(N\\) is the number of valid scores, and \\(z_{0.95} \\approx 1.96\\). We report the average \\(95\\%\\) confidence interval and the relative \\(95\\%\\) confidence interval (which is the confidence interval divided by the scoring range). The result shows that dataset scoring" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20159" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.156, + 0.089, + 0.825, + 0.222 + ], + "angle": 0, + "content": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.540.15-0.100.57-0.06-0.12-0.200.070.040.30-0.200.170.097
Point-to-Surface0.450.19-0.040.66-0.08-0.25-0.32-0.200.010.13-0.21-0.120.017
Normal Difference0.460.110.060.280.110.210.290.470.270.390.110.270.253
IoU [16]0.600.630.010.510.300.02-0.070.200.140.47-0.09-0.010.225
F-score [43]0.580.090.050.330.030.060.160.340.270.250.010.340.208
SSFID [46]0.710.74-0.040.740.390.240.130.320.250.640.25-0.020.363
UHD [47]0.290.220.110.15-0.040.180.410.550.130.180.250.330.231
SAUCD (Ours)0.730.210.600.630.310.510.830.650.770.800.690.080.567
Adjusted SAUCD (Ours)0.790.190.560.640.360.540.790.760.750.770.670.360.598
" + }, + { + "type": "table_caption", + "bbox": [ + 0.361, + 0.225, + 0.608, + 0.237 + ], + "angle": 0, + "content": "a. Pearson's linear correlation coefficient." + }, + { + "type": "table", + "bbox": [ + 0.156, + 0.238, + 0.825, + 0.37 + ], + "angle": 0, + "content": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.330.14-0.090.43-0.08-0.06-0.150.17-0.040.24-0.160.220.079
Point-to-Surface0.420.390.140.590.110.05-0.100.200.180.40-0.110.180.205
Normal Difference0.440.220.330.420.190.290.330.560.330.320.210.340.331
IoU [16]0.570.610.280.500.360.210.120.310.2620.560.030.300.342
F-score [43]0.470.250.200.520.210.110.070.360.300.42-0.010.350.27
SSFID [46]0.630.810.280.700.330.230.100.330.320.650.160.340.407
UHD [47]0.380.200.110.320.130.350.410.600.060.270.370.350.296
SAUCD (Ours)0.790.250.570.590.360.560.830.790.690.690.830.240.598
Adjusted SAUCD (Ours)0.830.210.550.590.380.600.820.800.690.680.750.420.611
" + }, + { + "type": "table_caption", + "bbox": [ + 0.341, + 0.374, + 0.627, + 0.387 + ], + "angle": 0, + "content": "b. Spearman's rank order correlation coefficient." + }, + { + "type": "table", + "bbox": [ + 0.156, + 0.389, + 0.825, + 0.522 + ], + "angle": 0, + "content": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.250.14-0.080.31-0.04-0.02-0.090.150.0130.19-0.070.220.080
Point-to-Surface0.330.300.070.450.100.08-0.030.170.130.30-0.010.160.171
Normal Difference0.340.160.170.310.180.220.260.440.250.230.160.270.250
IoU [16]0.420.440.240.370.280.220.140.260.200.410.100.230.275
F-score [43]0.370.170.140.420.150.110.090.280.230.340.010.300.216
SSFID [46]0.480.620.240.510.250.240.120.290.260.480.170.230.322
UHD [47]0.270.130.070.220.090.260.290.420.0480.190.280.240.209
SAUCD (Ours)0.600.160.420.410.270.450.650.570.550.470.600.190.445
Adjusted SAUCD (Ours)0.640.140.400.410.290.480.630.590.550.450.570.290.453
" + }, + { + "type": "table_caption", + "bbox": [ + 0.346, + 0.525, + 0.621, + 0.538 + ], + "angle": 0, + "content": "c. Kendall's rank order correlation coefficient." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.55, + 0.893, + 0.579 + ], + "angle": 0, + "content": "Table 2. Correlations between different metrics and human annotation. \"SAUCD\" is our basic version metric. \"Adjusted SAUCD\" is the human-adjusted version of our metric. The ranges of all three correlation coefficients are \\([-1, 1]\\), and the higher the better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.47, + 0.62 + ], + "angle": 0, + "content": "is accurate with a \\(5\\%\\) error range with IQR outlier removal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.473, + 0.818 + ], + "angle": 0, + "content": "Evaluation methods. We use 3 different evaluation methods to evaluate the correlation between our metrics and the human scoring (ground truth) on our Shape Grading benchmark dataset. Pearson's linear correlation coefficient (PLCC) [29] is used to evaluate the linear alignment between our metric and human perception. We also used Spearman's rank order correlation coefficient (SROCC) [37] and Kendall's rank order correlation coefficient (KROCC) [19] to evaluate the ranking order correlation between our metric and human perception. The possible ranges of 3 metrics are all \\([-1, 1]\\). Higher numbers mean stronger correlations. More details of the three evaluation methods can be found in Supplementary Materials Sec. 1." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.292, + 0.848 + ], + "angle": 0, + "content": "4.2. Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "We implement our basic version metric following Eq. (6). \\(\\hat{F} (\\lambda)\\) and \\(F_{gt}(\\lambda)\\) in Eq. (6) are both piece-wise functions, so we implement the integration by simply adding every piece" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.895, + 0.772 + ], + "angle": 0, + "content": "area together. We implement our human-adjusted version following Eq. (7). We use a 20-dimensional weight \\( w(\\lambda) \\) to avoid overfitting. We interpolate \\( w \\) to all frequencies of the ground truth and test meshes and element-wisely multiply them to the spectrums. In spectrum weight training, SROCC and PLCC are used as part of the loss function as Eq. (8). KROCC is not used in training but only for testing. We use a k-fold strategy for training the human-adjusted weight. Each time we choose 1 object for testing and the rest 11 objects for training, which means \\( k = 12 \\). More implementation details can be found in Supplementary Materials Sec. 1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.785, + 0.794, + 0.802 + ], + "angle": 0, + "content": "4.3. Quantitative and qualitative results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.896, + 0.903 + ], + "angle": 0, + "content": "SOTA comparison. Tab. 2 shows our results compared to previous 3D mesh shape metrics. We evaluated the correlation between each metric and the human scoring via three different evaluation methods. We observe that a) without any learning-based design, our metric outperforms the SOTA learning-based (SSFID) and non-learning-based met" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20160" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.09, + 0.393, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.393, + 0.089, + 0.505, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.617, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.617, + 0.09, + 0.73, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.73, + 0.09, + 0.833, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.438, + 0.182, + 0.451, + 0.192 + ], + "angle": 0, + "content": "D" + }, + { + "type": "image", + "bbox": [ + 0.396, + 0.192, + 0.5, + 0.261 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.182, + 0.614, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.615, + 0.182, + 0.728, + 0.258 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.728, + 0.182, + 0.833, + 0.25 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.271, + 0.895, + 0.314 + ], + "angle": 0, + "content": "Figure 5. An example of mesh spectrum curve: We do mesh Fourier transform on the \"Origin\" mesh and show the spectrum in the left graph. The \\(\\lambda\\)-axis is the eigenvalues of the DLBO matrix, the larger the higher frequency. We also show how mesh changes when gradually removing high-frequency information (mesh A to G). The frequency bands of the meshes are shown as the colored arrows in the left graph." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.339, + 0.471, + 0.415 + ], + "angle": 0, + "content": "rics (Chamfer Distance, IoU, F-score, and UHD), b) our extended version metric with learned weights has better linearity and slightly better ranking order correction with human evaluation, and c) our results on different objects show that our metrics have good generalizability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.416, + 0.47, + 0.55 + ], + "angle": 0, + "content": "Spectrum example. We first show an example of mesh spectrum in Fig. 5. We decompose the \"origin\" mesh using the Fourier Transform and get the resulting spectrum (top-left graph). The meshes on the right (from mesh A to G) are generated by gradually removing high-frequency information. The frequency bands of the meshes are shown as colored arrows in and under the graph. As we see, the details gradually disappear as we remove high-frequency information." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.552, + 0.471, + 0.688 + ], + "angle": 0, + "content": "Frequency band separation. We explored the consistency between human perception and the information obtained from every frequency band. Specifically, we separate the frequency band exponentially and build metrics only using information from that frequency band. The results are shown in Tab. 3, we find the frequency bands [0, 0.001] and [0.01, 0.03] have the best consistency with human perception. Moreover, it shows that if we put all frequencies together, they can achieve better results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.869 + ], + "angle": 0, + "content": "Trained weight. We show our trained weights in Human-adjusted metric in Fig. 6. Different lines represent different folds, and the bold purple line is the average weight. We can see the weights trained on each fold have similar patterns. We also observe that the weight curves have a small peak in the range A and two much larger peaks between A and B, which means our extended metric relies more on the information between A and B. We show an example of mesh shapes in the range A, B, and C at the bottom of Fig. 6. Mesh A obviously has fewer details than Mesh B, and the weight curve shows that this difference is what the learning process tries to emphasize." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Negative frequencies. In Fig. 7 we illustrate how our revised Cotan formula DLBO in Eq. (4) improves fre" + }, + { + "type": "image", + "bbox": [ + 0.532, + 0.336, + 0.755, + 0.467 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.755, + 0.336, + 0.861, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.467, + 0.645, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.467, + 0.753, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.753, + 0.465, + 0.861, + 0.558 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.569, + 0.895, + 0.641 + ], + "angle": 0, + "content": "Figure 6. Learned spectrum weights on all 12 folds. The name of colorful thin lines means the test object name of that fold. The bold purple line is the average weights of all folds. We also show some examples of mesh shape information in different frequency bands. Frequency band A is [0, 0.0075), B is [0, 0.03), and C is [0, 0.05)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.895, + 0.902 + ], + "angle": 0, + "content": "quency analysis compared to the original Coton formula in Eq. (2) [25]. The first and second rows are the results of the original Coton formula DLBO and our revised Coton formula DLBO, respectively. The original Coton formula can yield negative frequencies due to its lack of positive semidefiniteness, whereas our revision ensures all frequencies are non-negative. For both objects in the figure, we remove different portions of high-frequency information and show the remaining low-frequency parts (resulting in “Filtered mesh 1” and “Filtered mesh 2”). For the left object, notice the counterintuitive sharp shapes in the red circle when using the Coton formula. The right object is a much more severe case. Sharp shapes in low-frequency parts show improper decomposition and high-frequency aliasing with low-frequency shapes, making the Coton formula unsuitable for spectral" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20161" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.087, + 0.868, + 0.21 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.218, + 0.895, + 0.275 + ], + "angle": 0, + "content": "Figure 7. Counterintuitive low-frequencies information if some of the mesh frequencies are negative. We can see if we remove the high-frequency part of the mesh (resulting in \"Filtered mesh 1\" and \"Filtered mesh 2\") using the original Coton formula, the mesh's low-frequency parts show artifacts (sharp shapes). The red circles show the artifacts in the left object. The right object shows a case when these artifacts occur much more often. These artifacts do not occur using our revised Coton formula DLBO." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.287, + 0.328, + 0.374 + ], + "angle": 0, + "content": "
Frequency bandPLCC ↑SROCC ↑KROCC ↑
[0, 0.001)0.4340.5150.376
[0.001, 0.003)0.2400.4090.281
[0.003, 0.01)0.2550.4550.340
[0.01, 0.03)0.4210.5280.391
[0.03, 0.1)0.2870.3510.250
[0.1,∞)0.3180.1920.155
(0,∞)0.5670.5980.445
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.383, + 0.328, + 0.426 + ], + "angle": 0, + "content": "Table 3. Results when building metrics using each frequency band separately. The bottom row is our proposed metric." + }, + { + "type": "table", + "bbox": [ + 0.332, + 0.288, + 0.589, + 0.356 + ], + "angle": 0, + "content": "
Pruning PortionPLCC ↑SROCC ↑KROCC ↑
0%0.5130.5490.393
0.1%0.5670.5980.445
1%0.5540.6020.462
10%0.5170.5810.442
20%0.5030.5870.445
" + }, + { + "type": "table_caption", + "bbox": [ + 0.332, + 0.367, + 0.591, + 0.424 + ], + "angle": 0, + "content": "Table 4. Results with different pruning portions. The metric achieves better results with pruning portion to be \\(0.1\\%\\) or \\(1\\%\\). We use pruning portion as \\(0.1\\%\\) in our design." + }, + { + "type": "table", + "bbox": [ + 0.596, + 0.29, + 0.892, + 0.369 + ], + "angle": 0, + "content": "
ModulesPLCC ↑SROCC ↑KROCC ↑
Topology Laplacian [11]0.2980.3270.235
Cotan formula [25]0.4170.4700.340
Energy difference0.2680.3150.215
w/o normalization0.2570.5070.353
Spatial normalization0.2690.5420.392
Ours0.5670.5980.445
" + }, + { + "type": "table_caption", + "bbox": [ + 0.595, + 0.38, + 0.893, + 0.422 + ], + "angle": 0, + "content": "Table 5. Module replacement. We replace each module of our metric with alternative designs to verify the design of each module." + }, + { + "type": "image", + "bbox": [ + 0.111, + 0.449, + 0.442, + 0.567 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.578, + 0.471, + 0.648 + ], + "angle": 0, + "content": "Figure 8. We Adapt SAUCD into a loss function and use it in monocular-image-based 3D hand reconstruction. From left to right: input images, reconstruction result w/o SAUCD loss, reconstruction result w/ SAUCD loss, and ground truth mesh. We can see that the enhancement of SAUCD loss in mesh details is clearly noticeable." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.704 + ], + "angle": 0, + "content": "mesh comparison. In contrast, our revised formula yields smooth low-frequency components without these artifacts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.795 + ], + "angle": 0, + "content": "Noise pruning portion. Tab. 4 shows our SAUCD metric performance by changing the noise pruning portion (Sec. 3.3). The metric achieves better results when the pruning portion is \\(0.1\\%\\) or \\(1\\%\\). In our proposed metric, we choose the pruning portion to be \\(0.1\\%\\) to best avoid possible high-frequency information loss." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Module replacement. Tab. 5 shows our SAUCD metric performance by replacing some modules with alternative designs. First, we replace our revision of the discrete Laplace-Beltrami operator in Eq. (4) with topology Laplacian matrix in [11] and \"Cotan formula\" in [25]. Second, we change the AUC difference defined in Eq. (6) into the energy difference, which means changing \\( |\\hat{F}(\\lambda) - F_{gt}(\\lambda)| \\) in Eq. (6) into" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.45, + 0.895, + 0.542 + ], + "angle": 0, + "content": "\\(|\\hat{F}(\\lambda)^2 - F_{gt}(\\lambda)^2|\\). In the third experiment, we replace AUC normalization (in Sec. 3.3) with spatial normalization, where we normalize the meshes by their maximum range along all 3 spatial axes. We also removed the AUC normalization module for another comparison. Our experiments show SAUCD has better performance than alternative designs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.543, + 0.895, + 0.648 + ], + "angle": 0, + "content": "Adapting SAUCD to loss function. We adapted our metric into a loss function to enhance the visual quality of 3D mesh reconstructions, as evident from the hand reconstruction results in Fig. 8. Details on the experiment's implementation are available in Supplementary Materials Sec. 7. From this experiment, we can see that the enhancement of SAUCD loss in mesh details is clearly noticeable." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.649, + 0.895, + 0.695 + ], + "angle": 0, + "content": "Visualized examples. We visualize examples in our dataset and their evaluation result using different metrics in Supplementary Materials Sec. 6." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.709, + 0.628, + 0.725 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In order to propose a 3D shape evaluation that better aligns with human perception, we design an analytic metric named Spectrum AUC Difference (SAUCD). Our proposed SAUCD leverages mesh spectrum analysis to evaluate 3D shape that aligns with human evaluation, and its extended version Human-adjusted SAUCD further explores the sensitivity of human perception of each frequency band. To evaluate our new metrics, we build a user study dataset to compare our metrics with existing metrics. 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Unsupervised 3d human mesh recovery from noisy point clouds. arXiv preprint arXiv:2107.07539, 2021." + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.732 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20164" + } + ] +] \ No newline at end of file diff --git a/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_origin.pdf b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..136d8c945e2ec076dc001facae55c3321815a579 --- /dev/null +++ b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/dc4ca58e-2733-4afc-93ce-8d6ac2242638_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:76d6d857e071bb9527e6e476e6bb2c50c633f95a0405e75e39ab92977e27253d +size 2344605 diff --git a/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/full.md b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b4e96ca9e7915590501bff90e78b45658c9eb929 --- /dev/null +++ b/2024/Spectrum AUC Difference (SAUCD)_ Human-aligned 3D Shape Evaluation/full.md @@ -0,0 +1,319 @@ +# Spectrum AUC Difference (SAUCD): Human-aligned 3D Shape Evaluation + +Tianyu Luan $^{1,2*}$ Zhong Li $^{2}$ Lele Chen $^{2}$ Xuan Gong $^{3,2,1}$ +Lichang Chen $^{2,4}$ Yi Xu $^{2}$ Junsong Yuan $^{1}$ $^{1}$ State University of New York at Buffalo $^{2}$ OPPO US Research Center + $^{3}$ Harvard Medical School $^{4}$ University of Maryland, College Park + +# Abstract + +Existing 3D mesh shape evaluation metrics mainly focus on the overall shape but are usually less sensitive to local details. This makes them inconsistent with human evaluation, as human perception cares about both overall and detailed shape. In this paper, we propose an analytic metric named Spectrum Area Under the Curve Difference (SAUCD) that demonstrates better consistency with human evaluation. To compare the difference between two shapes, we first transform the 3D mesh to the spectrum domain using the discrete Laplace-Beltrami operator and Fourier transform. Then, we calculate the Area Under the Curve (AUC) difference between the two spectrums, so that each frequency band that captures either the overall or detailed shape is equitably considered. Taking human sensitivity across frequency bands into account, we further extend our metric by learning suitable weights for each frequency band which better aligns with human perception. To measure the performance of SAUCD, we build a 3D mesh evaluation dataset called Shape Grading, along with manual annotations from more than 800 subjects. By measuring the correlation between our metric and human evaluation, we demonstrate that SAUCD is well aligned with human evaluation, and outperforms previous 3D mesh metrics. Our project page: https://bit.ly/saucd. + +# 1. Introduction + +With the recent progress of 3D reconstruction and processing techniques, 3D mesh shapes have increasing applications in fields such as video games, industrial design, 3D printing, etc. In these applications, assessing the visual quality of the 3D mesh shape is a crucial task. To meet the requirements of various applications, a promising evaluation metric should not only reflect the geometry measurement but also align with human visual perception. Considering that human beings perceive 3D meshes in both overall shape and local + +![](images/68ad887ef6a4884fef3176a2252d2c6feebc30633a221d328c848bb4b26a2591.jpg) +Figure 1. An example of how previous spatial domain 3D shape metrics (Chamfer Distance [6] and UHD [47]) deviate from human evaluation. we create Mesh $A$ by adding a small pose error to the ground truth mesh, and by applying a large smoothing kernel to ground truth, we create Mesh $B$ . Contrary to human perception, previous spatial domain metrics evaluate Mesh $B$ better than Mesh $A$ . This indicates that while they are sensitive to general shape differences, they tend to overlook high-frequency details. Note that different metrics use different units of measurement. + +details, it is a challenging task to find an evaluation metric that can align well with humans. + +Previous metrics have the following disadvantages in this scenario. Traditional spatial domain measurements such as Chamfer Distance [6] which calculates the mean distance between a vertex on one mesh and its nearest vertex on the other mesh, can accurately measure the spatial distance. However, it does not guarantee capturing all shape details. In fact, such measurements in the spatial domain often overlook finer shape details, as the details tend to get overwhelmed by the overall shape. Fig. 1 illustrates the discrepancy between spatial measurements and human evaluation as mesh details change. Specifically, When we remove the wrinkles from the ground truth mesh (resulting in Mesh $B$ ), the errors detected by previous metrics are not as significant as when we slightly + +change the pose of the hand (Mesh $A$ ). However, humans tend to sense a significant difference between ground truth and Mesh $B$ , but barely recognize the difference between ground truth and Mesh $A$ . To mitigate this problem, previous works propose learning-based approaches, such as Single Shape Fréchet Inception Distance (SSFID) [46] based on learnable features from 3D shape. They compare the difference between the test mesh and the ground truth mesh in the latent feature space, and the design is expected to better align human perception. However, such learning-based methods would require a large amount of data to train the network. Their accuracy and generalizability are limited by the size of the dataset, data distribution, and annotation quality, not to mention the potential bias in collecting human perception feedback, which could mislead the learned metrics. An analytic metric that can better explain the shape difference is thus preferred. + +To address the above limitations, we design an analytic-based 3D shape evaluation metric named Spectrum Area Under the Curve Difference (SAUCD). Our metric measures mesh shape differences with a balanced consideration of both overall and detailed shape, making it better aligned with human evaluation. To allow our metric to capture detail variations, we leverage the 3D shape spectrum to decompose different levels of shape details from the overall shape, with details corresponding to higher-frequency components. The advantage of transforming the shape signal into the spectrum domain is that the high-frequency details are explicitly separated from the low-frequency overall shape. Therefore, it provides appropriate consideration to the information in different frequency bands, not just the low-frequency information of the overall shape in the dominant place. Thus, the details that human perception cares about will be better represented. Besides, the frequency analysis method allows the metric to be mostly analytic and better explained. + +We design SAUCD following the above inspiration. To begin with, both the test mesh and the ground truth mesh are transformed from the spatial to the spectrum domain using the discrete Laplace-Beltrami operator (DLBO), which encodes the mesh geometry information into a semidefinite Laplacian matrix. Once in the spectrum domain, we compare the regions under the two spectrums. Our Spectrum Area Under the Curve Difference metric is defined as the area of the non-overlapping region under the two spectrums - a larger area indicates a greater difference. Moreover, to better align with human evaluation, we further extend our design by learning a spectrum weight for SAUCD. However, different from previous learning-based approaches that use deep networks, large datasets, and extensive learning processes, our learning-based method requires the training of a weight vector. This vector measures the sensitivity of human perception across frequency bands, making the learned metric better aligned with human perception. We then evaluated the + +effectiveness of SAUCD on our provided user study benchmark dataset named Shape Grading. Using Shape Grading, we compare our metrics with previous metrics by calculating the correlation between each metric and human scoring. In summary, our contributions are listed as follows. + +- We design an analytic-based 3D mesh shape metric named Spectrum AUC Difference (SAUCD), which evaluates the difference between a 3D mesh and its ground truth mesh. Our metric considers both the overall shape and intricate details, to align more closely with human perception. +- We further extend our design to a learnable metric. The extended metric explores the human perception sensitivity in different frequency bands, which further improves this metric. +- We build a user study benchmark dataset named Shape Grading which is annotated by more than 800 subjects. The provided dataset verifies that both versions of our metrics are consistent with human evaluation and outperform previous methods. This dataset can also facilitate 3D mesh metric evaluation in future research. + +Our experiments show that both SAUCD and its extended version outperform previous methods with good generalizability to different types of objects. + +# 2. Related Works + +Metrics in 3D mesh reconstruction. Chamfer Distance [6] is a popular metric used in 3D mesh reconstruction tasks such as those in [21, 24, 32, 35, 45, 48-50]. Other spatial domain metrics, such as 3D Intersection over Union (IoU) in [10, 16, 17, 27, 33, 39]. F-score in [4, 15, 40, 43], and Unidirectional Hausdorff distance (UHD) in [47] are commonly focused on the geometry accuracy of mesh shapes. These metrics can provide accurate geometry measurements, but they are not designed to align with human evaluation. Deep-learning-based methods such as Single Shape Fréchet Inception Distance [46] are also used in 3D reconstruction. While these metrics have the capacity to adapt from human evaluation, they are more like black boxes, with performances subject to dataset size and annotation bias. Moreover, most previous works miss out on user study validation to verify if their metrics align with human evaluation. + +3D shape generation metrics. Multiple metrics have been used in 3D shape generation, such as Minimal Matching Distance (MMD) [3], Jensen-Shannon Divergence (JSD) [22], Total Mutual Difference (TMD) [47], Fréchet Pointcloud Distance (FPD) [36], etc.. These metrics are designed to measure the differences between the generated distributions, while our task is to build a metric to compare the shape of two meshes. + +3D mesh compression and watermarking metrics. Previous works [8, 12, 23, 41] focused on evaluating mesh errors in mesh compression and watermarking. Since compression and watermarking pursue mesh errors that cannot + +![](images/5cfa967ceea5defea1109f67661240f9273b4a66848aafdb6f2ea90584467277.jpg) +Figure 2. Our SAUCD metric is designed as follows: A. We use mesh Fourier Transform to analyze the spectrums of test and ground truth mesh. B. We compare the difference between two spectrum curves by calculating the Area Under the Curve (AUC) difference. C. We further extend our metric by multiplying the AUC difference with a learnable weight to capture human sensitivity in each frequency band. + +be detected by humans, they mainly focus on barely noticed errors. However, our task is to build a metric that can handle generally occurring errors that happen in 3D reconstruction tasks and applications. + +# 3. Proposed Method + +Our task is to design a metric aligned with human evaluation to measure the shape difference between a test triangle mesh and its corresponding ground truth triangle mesh. Specifically, given a test mesh $\hat{M}$ and its ground truth mesh $M_{gt}$ , Spectrum AUC Difference (SAUCD) can be abstracted as + +$$ +d = D (\hat {M}, M _ {g t}). \tag {1} +$$ + +$d$ is the distance between the test and the ground truth mesh. In this section, we will elaborate on how the distance function $D(\cdot)$ is designed. + +# 3.1. Overview + +As shown in Fig. 2, our metric is calculated via the following steps: First, we use mesh Fourier transform to analyze the spectrums of the test and ground truth mesh (in Sec. 3.2). Then we leverage each frequency band by calculating the Area Under the Curve (AUC) difference of the spectrum curves (in Sec. 3.3). Moreover, we further extended our metric by multiplying the AUC difference with a learnable weight to capture the human sensitivity on each frequency band (in Sec. 3.4). We will discuss each step in detail. + +# 3.2. Mesh spectrum analysis + +In order to capture the overall shape as well as shape details, we choose to decompose the mesh signal into a spectrum. Considering the mesh as a function on a discretized manifold space, we can calculate the spectrum using the manifold space Fourier transform. In Hilbert space, the Fourier operator is defined as the eigenfunctions of the + +Laplacian operator [14]. The same definition and similar theories are extended to continuous and discrete manifold space by [5, 9]. The Laplacian operator on discrete manifold spaces, i.e. mesh space in our task, is named the Discrete Laplace-Beltrami operator (DLBO). Similar to the Laplacian operator in image space that encodes the pixel information by capturing the local pixel differences [20, 28, 30, 34, 38, 44], DLBO encodes the mesh shape information by capturing the local shape fluctuation. The "Cotan formula" defined in [25] is the most widely used discretization, which can be represented in matrix form as + +$$ +L _ {i j} = \left\{ \begin{array}{c c} \sum_ {j \in N (i)} \frac {1}{2 A _ {i}} \left(\cot \alpha_ {i j} + \cot \beta_ {i j}\right), & i = j \\ - \frac {1}{2 A _ {i}} \left(\cot \alpha_ {i j} + \cot \beta_ {i j}\right), & i \neq j \wedge j \in N (i) \\ 0, & i \neq j \wedge j \notin N (i), \end{array} \right. \tag {2} +$$ + +where $L \in \mathbb{R}^{N \times N}$ is the DLBO matrix, with $N$ the vertex number of the mesh. $L_{ij}$ indicates its entry in $i$ th row and $j$ th column, which represents the edge weight between vertex $v_i$ and $v_j$ . $A_i$ is the mixed Voronoi area of vertex $v_i$ on the mesh. As shown in Fig. 3, the $v_i$ 's mixed Voronoi area is defined as the area of the polygon in which the vertices are the circumcenters of $v_i$ 's surrounding faces. $N(i)$ is the index set of $v_i$ 's adjacent vertices. If $v_i$ and $v_j$ are adjacent, $\alpha_{ij}$ and $\beta_{ij}$ are the opposite angles of edge $(v_i, v_j)$ in each of the edge's two neighbor triangle faces, respectively (shown in Fig. 3). If not, $\alpha_{ij}$ and $\beta_{ij}$ are not defined and $L_{ij}$ is 0. As shown in Fig. 2, the DLBO matrix is used for mesh Fourier transform to get mesh spectrum. We calculate the Fourier operator $U^\top$ , which is the eigenfunction of $L$ as + +$$ +L = U \Lambda U ^ {\top}, \tag {3} +$$ + +where $\Lambda$ is a diagonal matrix whose diagonal elements are Fourier mesh frequencies. + +To ensure the mesh frequencies are non-negative, we need the DLBO matrix $L$ to be positive semidefinite. Our experiment in Fig. 7 gives an example of the counterintuitive + +![](images/5631dbe3d5d881f53924c782e07ebc1fa5cf54758f8438bfb33b4160a774da77.jpg) +Figure 3. Variables defined in our discrete Laplace-Beltrami operator design. + +![](images/f6a09be4db54e5255572d657d3586f7f74dfe8c4904a35bdb265449ca477cb71.jpg) +Figure 4. Spectrum Area Under the Curve Difference. We design our metric using the AUC difference of the spectrums. The blue curve and red curve are the test and ground truth mesh spectrum, respectively. The purple area in the last graph is the Spectrum AUC Difference. Please find details in Sec. 3.3. + +results when there are negative frequencies. However, the Coton formula in Eq. (2) does not guarantee to be positive semidefinite. We provide a simple example in Supplementary Materials Sec. 3 in which $L$ is not positive semidefinite when the mesh is not Delaunay triangulated and the mixed Voronoi areas are not all equal to each other. In our metric design, we made two small changes to the original Coton formula to make it positive semidefinite. a) Inspired by the symmetric normalization of the topology Laplacian matrix in [11], we make $L$ symmetric by changing the normalization parameter $A_{i}$ into a symmetric normalized manner $A_{i}^{\frac{1}{2}}A_{j}^{\frac{1}{2}}$ . b) We replace $\cot \alpha_{ij} + \cot \beta_{ij}$ with $|\cot \alpha_{ij} + \cot \beta_{ij}|$ . This ensures all the edge weights in the Laplacian matrix to be non-negative. Thus, our revision of DLBO is defined as + +$$ +L _ {i j} = \left\{ \begin{array}{c c} \frac {1}{2} \sum_ {j \in N (i)} A _ {i} ^ {- \frac {1}{2}} A _ {j} ^ {- \frac {1}{2}} | \cot \alpha_ {i j} + \cot \beta_ {i j} |, & i = j \\ - \frac {1}{2} A _ {i} ^ {- \frac {1}{2}} A _ {j} ^ {- \frac {1}{2}} | \cot \alpha_ {i j} + \cot \beta_ {i j} |, & i \neq j \wedge j \in N (i) \\ 0, & i \neq j \wedge j \notin N (i). \end{array} \right. \tag {4} +$$ + +We prove that our revision of the Cotan formula is positive semidefinite in Supplementary Materials Sec. 2. In Tab. 5, our experiments show that our DLBO matrix design outperforms the origin Cotan formula in [25], and the topology Laplacian matrix defined in [11]. + +Finally, we obtain the mesh spectrum by acting Fourier operator on the mesh vertices + +$$ +F _ {i} = \sqrt {G _ {i , x} ^ {2} + G _ {i , y} ^ {2} + G _ {i , z} ^ {2}}, G = U ^ {\top} v, \tag {5} +$$ + +where $v \in \mathbb{R}^{N \times 3}$ indicates the 3D coordinates of $N$ mesh vertices. The result spectrum $F \in \mathbb{R}^N$ . Fig. 5 shows an example of the mesh spectrum (left side) and how the meshes look in different frequency bands (right side). This provides an illustration of the information contained in different frequency bands of the mesh spectrum. + +# 3.3. Spectrum AUC Difference + +To reduce the noise and normalize the mesh scale, we also design noise pruning and AUC normalization procedures before calculating the Spectrum AUC Difference. + +Noise pruning. As shown in Fig. 4 process $(a)$ , we prune a small portion of the highest frequency information + +to reduce the interference of noise. From the observation of the first two meshes (A and B) in Fig. 5, we can see that humans can barely notice the shape differences when the highest frequency parts are removed. Thus, if we try to evaluate the mesh shape that aligns with human perception, it is reasonable to remove high-frequency noise without losing much information that humans care about. Empirically, we choose to prune the highest $0.1\%$ frequency information as noise. Our experiments in Tab. 4 show that this portion is more consistent with human perception while preserving good mesh quality. + +AUC normalization. Given a spectrum $F(\lambda)$ , its Area Under the Curve (AUC) can be defined as $\int_{\infty} F(\lambda) d\lambda$ . AUC normalization means using spectrum AUC to normalize the mesh scale. If the mesh scale increases by $s$ times in length, the mixed Voronoi area, i.e. $A_i$ in Eq. (4), will decrease by $s^2$ times. Thus, each element in the DLBO matrix $L$ will also decrease by $s^2$ times. Then, according to Eq. (3), the frequency $\lambda$ will decrease $s^2$ times to $\lambda / s^2$ , and according to Eq. (5), the spectrum amplitude $F$ will change to $sF$ because $v$ is increased by $s$ time and $U^\top$ is still orthonormal. Then the area under the spectrum curve (the area boxed with red or blue lines in Fig. 4) changes as $A' = \int sF(\lambda) d\lambda / s^2 = \frac{1}{s} A$ . + +In our approach, we normalize the area under the spectrum curve $A$ to 1 to resolve the scale difference, which means $s = A$ , $\lambda$ decreases by $A^2$ times, and spectrum amplitude $F$ increases by $A$ times (Fig. 4 process (b)). AUC normalization fairly normalizes the scale of objects in different shapes by only changing the scale, not shape details. It normalizes the spectrum AUC of all mesh to 1, making the mesh spectrums differ only in distributions. Our experiments in Tab. 5 demonstrate this design can bring a fairer comparison of the spectrums and improve the human consistency of the metric. The experiment also demonstrates that this design outperforms the spatial domain scale normalization. + +Spectrum AUC Difference. In order to capture the difference between two mesh shapes in the spectrum domain, we design Spectrum AUC Difference (SAUCD) on the spectrum analysis results after noise pruning and AUC normalization: + +$$ +d = D (\hat {M}, M _ {g t}) = \int_ {\lambda} | \hat {F} (\lambda) - F _ {g t} (\lambda) | d \lambda , \tag {6} +$$ + +
datasetRaww/ IQR removal
number of valid scores2430423775
Scoring range[0, 6][0, 6]
95% confidence interval0.3180.303
Relative 95% confidence interval5.33%5.04%
+ +Table 1. Dataset statistics and error analysis. + +where $\hat{F}$ and $F_{gt}$ are the test and groundtruth mesh spectrum. As shown in Fig. 4 process $(c)$ , our metric is defined as the AUC difference of the two spectrum curves (the purple area). In Tab. 5, we compare our design with an alternative design which changes the amplitude difference $|\hat{F} (\lambda) - F_{gt}(\lambda)|$ to energy difference $|\hat{F} (\lambda)^2 -F_{gt}(\lambda)^2 |$ . The result shows our design is more consistent with human evaluation. Besides, experiments in Tab. 2 show our SAUCD metric aligns well with human evaluation, and outperforms SOTA metrics under multiple evaluation methods. Experiments in Fig. 8 show SAUCD has the capability to improve mesh detail qualities in 3D reconstruction when adapted into training loss. + +# 3.4. Human-adjusted Spectrum AUC Difference + +We also provide an extended metric version, in which we design a learnable weight parameter along the frequency bands. The weight parameter indicates the adjustment of human sensitivity to each frequency band. Specifically, we design the extended metric as + +$$ +d _ {w} = D _ {w} (\hat {M}, M _ {g t}) = \int_ {\lambda} w (\lambda) | \hat {F} (\lambda) - F _ {g t} (\lambda) | d \lambda . \tag {7} +$$ + +$w(\lambda)$ is weight parameters indicating human sensitivity along frequency bands. Our training loss is defined as + +$$ +\mathcal {L} = \lambda_ {p} \mathcal {L} _ {p l c c} + \lambda_ {s r} \mathcal {L} _ {s r o c c} + \lambda_ {r} \mathcal {L} _ {r e g u}, \tag {8} +$$ + +where $\mathcal{L}_{plcc}$ and $\mathcal{L}_{srocc}$ are Pearson correlation loss and Spearman rank order loss. They are defined the same as Pearson's linear correlation [29] and Spearman's rank order correlation [37]. $\mathcal{L}_{regu} = 1 / N\sum_{i}(w_{i} - 1)^{2}$ is the regularization loss, which regularizes weight $w_{i}$ close to 1. $\lambda_p$ , $\lambda_{sr}$ , and $\lambda_r$ are the loss weights of $\mathcal{L}_{plcc}$ , $\mathcal{L}_{srocc}$ , and $\mathcal{L}_{regu}$ . More details of the loss functions can be found in Supplementary Materials Sec. 1. Our experiments in Sec. 4.3 show that after adjustment, the consistency between our metric output and human-annotated ground truth is improved. + +# 4. Experiments + +# 4.1. Dataset + +We build a user study benchmark dataset Shape Grading to evaluate whether our metric is aligned with human evaluation. The dataset contains the human evaluation scores for a variety of distorted meshes. Using this dataset, we can + +calculate the correlation between metric outputs and human evaluation scores to see how aligned the test metrics are to human evaluation. + +Dataset design. We choose 12 objects as ground truth 3D triangle mesh from public object/scene/human mesh datasets such as [18, 26, 42] and commercial datasets such as [1, 2]. These objects are picked from different categories including humans, animals, buildings, plants, etc.. For each object, we synthesize 7 different types of distortions which commonly occur in 3D reconstruction. For each distortion type we synthesize 4 distortion levels, which gives us $7 \times 4 = 28$ distorted objects for every ground truth object. We rotate and render each distorted object into 3 videos using different materials for the mesh. In total, we generate $12 \times 28 \times 3 = 1,008$ distorted mesh videos. Supplementary Materials Sec. 4 shows the meshes and distortion types we use in our dataset. + +Human scoring procedure. We use a pairwise comparison scoring process similar to [31]. Each subject will evaluate all 28 distorted objects of one ground truth object with a certain material. The scoring follows a Swiss system tournament principle used in [31], in which each subject takes 6 rounds of pairwise comparison to score the distorted meshes. After 6 rounds of scoring, the meshes are scored from 0 to 6. 0 means the object loses in every round and 6 means it wins in every round. This process will largely reduce the biases among subjects, since the subjects are compelled to distribute an equal amount of points to the 28 distorted objects. The process will take about 15 minutes for each subject, avoiding the fatigue problem in [7]. For every object rendered with every material, we have 24 to 25 subjects scoring it. In total, we have 868 subjects (536 males, 316 females, and 16 others) who give us $868 \times 28 = 24304$ scores. More details of the scoring procedure can be found in Supplementary Materials Sec. 5. + +Outlier detection. We use the interquartile range (IQR) method [13] which is widely used in statistics to detect and remove outliers. For each distorted mesh, we first find the 25 percentile and the 75 percentile of the scores. The score range in between is called the IQR range. We remove the scores that are 1.5IQR smaller than the 25 percentile or 1.5IQR larger than the 75 percentile. Our dataset error analysis in Tab. 1 shows, that by removing $2.2\%$ of the scores using IQR, we can decrease the uncertainty of the final scoring result by nearly $6\%$ . + +Dataset error analysis. We analysis the average $95\%$ confidence interval of our dataset scores in Tab. 1. The confidence interval of score $x$ can be calculated as $\sigma_{\bar{x}} = z_{0.95} \times \sigma / \sqrt{N}$ where $\sigma$ is the standard derivation of $x$ , $N$ is the number of valid scores, and $z_{0.95} \approx 1.96$ . We report the average $95\%$ confidence interval and the relative $95\%$ confidence interval (which is the confidence interval divided by the scoring range). The result shows that dataset scoring + +
Metrics\Object No.123456789101112Overall
Chamfer Distance [6]0.540.15-0.100.57-0.06-0.12-0.200.070.040.30-0.200.170.097
Point-to-Surface0.450.19-0.040.66-0.08-0.25-0.32-0.200.010.13-0.21-0.120.017
Normal Difference0.460.110.060.280.110.210.290.470.270.390.110.270.253
IoU [16]0.600.630.010.510.300.02-0.070.200.140.47-0.09-0.010.225
F-score [43]0.580.090.050.330.030.060.160.340.270.250.010.340.208
SSFID [46]0.710.74-0.040.740.390.240.130.320.250.640.25-0.020.363
UHD [47]0.290.220.110.15-0.040.180.410.550.130.180.250.330.231
SAUCD (Ours)0.730.210.600.630.310.510.830.650.770.800.690.080.567
Adjusted SAUCD (Ours)0.790.190.560.640.360.540.790.760.750.770.670.360.598
+ +a. Pearson's linear correlation coefficient. + +
Metrics\Object No.123456789101112Overall
Chamfer Distance [6]0.330.14-0.090.43-0.08-0.06-0.150.17-0.040.24-0.160.220.079
Point-to-Surface0.420.390.140.590.110.05-0.100.200.180.40-0.110.180.205
Normal Difference0.440.220.330.420.190.290.330.560.330.320.210.340.331
IoU [16]0.570.610.280.500.360.210.120.310.2620.560.030.300.342
F-score [43]0.470.250.200.520.210.110.070.360.300.42-0.010.350.27
SSFID [46]0.630.810.280.700.330.230.100.330.320.650.160.340.407
UHD [47]0.380.200.110.320.130.350.410.600.060.270.370.350.296
SAUCD (Ours)0.790.250.570.590.360.560.830.790.690.690.830.240.598
Adjusted SAUCD (Ours)0.830.210.550.590.380.600.820.800.690.680.750.420.611
+ +b. Spearman's rank order correlation coefficient. + +
Metrics\Object No.123456789101112Overall
Chamfer Distance [6]0.250.14-0.080.31-0.04-0.02-0.090.150.0130.19-0.070.220.080
Point-to-Surface0.330.300.070.450.100.08-0.030.170.130.30-0.010.160.171
Normal Difference0.340.160.170.310.180.220.260.440.250.230.160.270.250
IoU [16]0.420.440.240.370.280.220.140.260.200.410.100.230.275
F-score [43]0.370.170.140.420.150.110.090.280.230.340.010.300.216
SSFID [46]0.480.620.240.510.250.240.120.290.260.480.170.230.322
UHD [47]0.270.130.070.220.090.260.290.420.0480.190.280.240.209
SAUCD (Ours)0.600.160.420.410.270.450.650.570.550.470.600.190.445
Adjusted SAUCD (Ours)0.640.140.400.410.290.480.630.590.550.450.570.290.453
+ +c. Kendall's rank order correlation coefficient. + +Table 2. Correlations between different metrics and human annotation. "SAUCD" is our basic version metric. "Adjusted SAUCD" is the human-adjusted version of our metric. The ranges of all three correlation coefficients are $[-1, 1]$ , and the higher the better. + +is accurate with a $5\%$ error range with IQR outlier removal. + +Evaluation methods. We use 3 different evaluation methods to evaluate the correlation between our metrics and the human scoring (ground truth) on our Shape Grading benchmark dataset. Pearson's linear correlation coefficient (PLCC) [29] is used to evaluate the linear alignment between our metric and human perception. We also used Spearman's rank order correlation coefficient (SROCC) [37] and Kendall's rank order correlation coefficient (KROCC) [19] to evaluate the ranking order correlation between our metric and human perception. The possible ranges of 3 metrics are all $[-1, 1]$ . Higher numbers mean stronger correlations. More details of the three evaluation methods can be found in Supplementary Materials Sec. 1. + +# 4.2. Implementation details + +We implement our basic version metric following Eq. (6). $\hat{F} (\lambda)$ and $F_{gt}(\lambda)$ in Eq. (6) are both piece-wise functions, so we implement the integration by simply adding every piece + +area together. We implement our human-adjusted version following Eq. (7). We use a 20-dimensional weight $w(\lambda)$ to avoid overfitting. We interpolate $w$ to all frequencies of the ground truth and test meshes and element-wisely multiply them to the spectrums. In spectrum weight training, SROCC and PLCC are used as part of the loss function as Eq. (8). KROCC is not used in training but only for testing. We use a k-fold strategy for training the human-adjusted weight. Each time we choose 1 object for testing and the rest 11 objects for training, which means $k = 12$ . More implementation details can be found in Supplementary Materials Sec. 1. + +# 4.3. Quantitative and qualitative results + +SOTA comparison. Tab. 2 shows our results compared to previous 3D mesh shape metrics. We evaluated the correlation between each metric and the human scoring via three different evaluation methods. We observe that a) without any learning-based design, our metric outperforms the SOTA learning-based (SSFID) and non-learning-based met + +![](images/764d32b014fa0d52b399c11f8dc6b3bbd71e4da910c20d2b2a7308040c73399c.jpg) +Figure 5. An example of mesh spectrum curve: We do mesh Fourier transform on the "Origin" mesh and show the spectrum in the left graph. The $\lambda$ -axis is the eigenvalues of the DLBO matrix, the larger the higher frequency. We also show how mesh changes when gradually removing high-frequency information (mesh A to G). The frequency bands of the meshes are shown as the colored arrows in the left graph. + +![](images/b28f9dc2d58842566417e939a2392debcc025e9afdd4b6a7e78b3ab3883285be.jpg) + +![](images/ffdfc17c85a9aa9222a29a8078f8c66e61811739dbeac41d8d4f2ed990d09d2e.jpg) + +![](images/069dc0d830bfde1a0fdae3dbcdee1d2deb3699aee80ccefae9c8ef2eafffbd96.jpg) + +![](images/1fe77269e3a7ae08a08b41ab667a8b20b37ec18a76dee309216883011b2c24fb.jpg) + +![](images/be8c066fde23839299ad8b9d5336547fef19adf39135b3b736d510fef446f708.jpg) +D + +![](images/8846b173a2faee5d3c7e7c7e131dbd6a9c7d87a18a475a0df31cd945c2a37d90.jpg) + +![](images/e69893ab1afe64a8b7fe398432ff0f32fd413461409ac7b5e6c25d5b72103497.jpg) + +![](images/949eee0e4f94a2ff0469e702e5f40a35b17f59805c76eac90a5b3bb3364a8969.jpg) + +rics (Chamfer Distance, IoU, F-score, and UHD), b) our extended version metric with learned weights has better linearity and slightly better ranking order correction with human evaluation, and c) our results on different objects show that our metrics have good generalizability. + +Spectrum example. We first show an example of mesh spectrum in Fig. 5. We decompose the "origin" mesh using the Fourier Transform and get the resulting spectrum (top-left graph). The meshes on the right (from mesh A to G) are generated by gradually removing high-frequency information. The frequency bands of the meshes are shown as colored arrows in and under the graph. As we see, the details gradually disappear as we remove high-frequency information. + +Frequency band separation. We explored the consistency between human perception and the information obtained from every frequency band. Specifically, we separate the frequency band exponentially and build metrics only using information from that frequency band. The results are shown in Tab. 3, we find the frequency bands [0, 0.001] and [0.01, 0.03] have the best consistency with human perception. Moreover, it shows that if we put all frequencies together, they can achieve better results. + +Trained weight. We show our trained weights in Human-adjusted metric in Fig. 6. Different lines represent different folds, and the bold purple line is the average weight. We can see the weights trained on each fold have similar patterns. We also observe that the weight curves have a small peak in the range A and two much larger peaks between A and B, which means our extended metric relies more on the information between A and B. We show an example of mesh shapes in the range A, B, and C at the bottom of Fig. 6. Mesh A obviously has fewer details than Mesh B, and the weight curve shows that this difference is what the learning process tries to emphasize. + +Negative frequencies. In Fig. 7 we illustrate how our revised Cotan formula DLBO in Eq. (4) improves fre + +![](images/1d05bd60080fb3c240c1e5a09eacb96e6e1840e48e4bb994effa4cc0f84c42c8.jpg) + +![](images/efcc494b3d5fa2fa4731f88581ec2698e33c2f2aaaf947c5d4bfdb4584223ad9.jpg) + +![](images/81c964bc79cb4c885bb6d9490d3a408b54de2aec34c25c88b999950f4f56ebc1.jpg) +Figure 6. Learned spectrum weights on all 12 folds. The name of colorful thin lines means the test object name of that fold. The bold purple line is the average weights of all folds. We also show some examples of mesh shape information in different frequency bands. Frequency band A is [0, 0.0075), B is [0, 0.03), and C is [0, 0.05). + +![](images/950f9ac4a3519d2644f9e0acb368bc1105d00b7801ad1d34f258ade94baaa04f.jpg) + +![](images/e24b6e02206c10ef8f949247a95ea27d87aee0b845ddd4a5359c3c806071289e.jpg) + +quency analysis compared to the original Coton formula in Eq. (2) [25]. The first and second rows are the results of the original Coton formula DLBO and our revised Coton formula DLBO, respectively. The original Coton formula can yield negative frequencies due to its lack of positive semidefiniteness, whereas our revision ensures all frequencies are non-negative. For both objects in the figure, we remove different portions of high-frequency information and show the remaining low-frequency parts (resulting in “Filtered mesh 1” and “Filtered mesh 2”). For the left object, notice the counterintuitive sharp shapes in the red circle when using the Coton formula. The right object is a much more severe case. Sharp shapes in low-frequency parts show improper decomposition and high-frequency aliasing with low-frequency shapes, making the Coton formula unsuitable for spectral + +![](images/9ea0e2af7986dfe9f9da879e63a9da1c4bb3e821ba35ed7f298c61596fd3906a.jpg) +Figure 7. Counterintuitive low-frequencies information if some of the mesh frequencies are negative. We can see if we remove the high-frequency part of the mesh (resulting in "Filtered mesh 1" and "Filtered mesh 2") using the original Coton formula, the mesh's low-frequency parts show artifacts (sharp shapes). The red circles show the artifacts in the left object. The right object shows a case when these artifacts occur much more often. These artifacts do not occur using our revised Coton formula DLBO. + +
Frequency bandPLCC ↑SROCC ↑KROCC ↑
[0, 0.001)0.4340.5150.376
[0.001, 0.003)0.2400.4090.281
[0.003, 0.01)0.2550.4550.340
[0.01, 0.03)0.4210.5280.391
[0.03, 0.1)0.2870.3510.250
[0.1,∞)0.3180.1920.155
(0,∞)0.5670.5980.445
+ +Table 3. Results when building metrics using each frequency band separately. The bottom row is our proposed metric. + +
Pruning PortionPLCC ↑SROCC ↑KROCC ↑
0%0.5130.5490.393
0.1%0.5670.5980.445
1%0.5540.6020.462
10%0.5170.5810.442
20%0.5030.5870.445
+ +Table 4. Results with different pruning portions. The metric achieves better results with pruning portion to be $0.1\%$ or $1\%$ . We use pruning portion as $0.1\%$ in our design. + +
ModulesPLCC ↑SROCC ↑KROCC ↑
Topology Laplacian [11]0.2980.3270.235
Cotan formula [25]0.4170.4700.340
Energy difference0.2680.3150.215
w/o normalization0.2570.5070.353
Spatial normalization0.2690.5420.392
Ours0.5670.5980.445
+ +Table 5. Module replacement. We replace each module of our metric with alternative designs to verify the design of each module. + +![](images/8c0e1e1821ca17bc722cd5a69ba37fd3fd3646a8f76fe2e4d9cb56548f171769.jpg) +Figure 8. We Adapt SAUCD into a loss function and use it in monocular-image-based 3D hand reconstruction. From left to right: input images, reconstruction result w/o SAUCD loss, reconstruction result w/ SAUCD loss, and ground truth mesh. We can see that the enhancement of SAUCD loss in mesh details is clearly noticeable. + +mesh comparison. In contrast, our revised formula yields smooth low-frequency components without these artifacts. + +Noise pruning portion. Tab. 4 shows our SAUCD metric performance by changing the noise pruning portion (Sec. 3.3). The metric achieves better results when the pruning portion is $0.1\%$ or $1\%$ . In our proposed metric, we choose the pruning portion to be $0.1\%$ to best avoid possible high-frequency information loss. + +Module replacement. Tab. 5 shows our SAUCD metric performance by replacing some modules with alternative designs. First, we replace our revision of the discrete Laplace-Beltrami operator in Eq. (4) with topology Laplacian matrix in [11] and "Cotan formula" in [25]. Second, we change the AUC difference defined in Eq. (6) into the energy difference, which means changing $|\hat{F}(\lambda) - F_{gt}(\lambda)|$ in Eq. (6) into + +$|\hat{F}(\lambda)^2 - F_{gt}(\lambda)^2|$ . In the third experiment, we replace AUC normalization (in Sec. 3.3) with spatial normalization, where we normalize the meshes by their maximum range along all 3 spatial axes. We also removed the AUC normalization module for another comparison. Our experiments show SAUCD has better performance than alternative designs. + +Adapting SAUCD to loss function. We adapted our metric into a loss function to enhance the visual quality of 3D mesh reconstructions, as evident from the hand reconstruction results in Fig. 8. Details on the experiment's implementation are available in Supplementary Materials Sec. 7. From this experiment, we can see that the enhancement of SAUCD loss in mesh details is clearly noticeable. + +Visualized examples. We visualize examples in our dataset and their evaluation result using different metrics in Supplementary Materials Sec. 6. + +# 5. Conclusions + +In order to propose a 3D shape evaluation that better aligns with human perception, we design an analytic metric named Spectrum AUC Difference (SAUCD). Our proposed SAUCD leverages mesh spectrum analysis to evaluate 3D shape that aligns with human evaluation, and its extended version Human-adjusted SAUCD further explores the sensitivity of human perception of each frequency band. 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By measuring the correlation between our metric and human evaluation, we demonstrate that SAUCD is well aligned with human evaluation, and outperforms previous 3D mesh metrics. Our project page: https://bit.ly/saucd." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 569, + 128, + 582 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 569, + 128, + 582 + ], + "spans": [ + { + "bbox": [ + 47, + 569, + 128, + 582 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 589, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 696 + ], + "type": "text", + "content": "With the recent progress of 3D reconstruction and processing techniques, 3D mesh shapes have increasing applications in fields such as video games, industrial design, 3D printing, etc. In these applications, assessing the visual quality of the 3D mesh shape is a crucial task. To meet the requirements of various applications, a promising evaluation metric should not only reflect the geometry measurement but also align with human visual perception. Considering that human beings perceive 3D meshes in both overall shape and local" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 329, + 232, + 523, + 399 + ], + "blocks": [ + { + "bbox": [ + 329, + 232, + 523, + 399 + ], + "lines": [ + { + "bbox": [ + 329, + 232, + 523, + 399 + ], + "spans": [ + { + "bbox": [ + 329, + 232, + 523, + 399 + ], + "type": "image", + "image_path": "68ad887ef6a4884fef3176a2252d2c6feebc30633a221d328c848bb4b26a2591.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "lines": [ + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "text", + "content": "Figure 1. An example of how previous spatial domain 3D shape metrics (Chamfer Distance [6] and UHD [47]) deviate from human evaluation. we create Mesh " + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "text", + "content": " by adding a small pose error to the ground truth mesh, and by applying a large smoothing kernel to ground truth, we create Mesh " + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "text", + "content": ". Contrary to human perception, previous spatial domain metrics evaluate Mesh " + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "text", + "content": " better than Mesh " + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 305, + 407, + 547, + 506 + ], + "type": "text", + "content": ". This indicates that while they are sensitive to general shape differences, they tend to overlook high-frequency details. Note that different metrics use different units of measurement." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 531, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 531, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 305, + 531, + 545, + 555 + ], + "type": "text", + "content": "details, it is a challenging task to find an evaluation metric that can align well with humans." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "Previous metrics have the following disadvantages in this scenario. Traditional spatial domain measurements such as Chamfer Distance [6] which calculates the mean distance between a vertex on one mesh and its nearest vertex on the other mesh, can accurately measure the spatial distance. However, it does not guarantee capturing all shape details. In fact, such measurements in the spatial domain often overlook finer shape details, as the details tend to get overwhelmed by the overall shape. Fig. 1 illustrates the discrepancy between spatial measurements and human evaluation as mesh details change. Specifically, When we remove the wrinkles from the ground truth mesh (resulting in Mesh " + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 558, + 547, + 715 + ], + "type": "text", + "content": "), the errors detected by previous metrics are not as significant as when we slightly" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 712 + ], + "type": "text", + "content": "*Work done while Tianyu was an intern at OPPO US Research Center." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20155" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": "change the pose of the hand (Mesh " + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": "). However, humans tend to sense a significant difference between ground truth and Mesh " + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": ", but barely recognize the difference between ground truth and Mesh " + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": ". To mitigate this problem, previous works propose learning-based approaches, such as Single Shape Fréchet Inception Distance (SSFID) [46] based on learnable features from 3D shape. They compare the difference between the test mesh and the ground truth mesh in the latent feature space, and the design is expected to better align human perception. However, such learning-based methods would require a large amount of data to train the network. Their accuracy and generalizability are limited by the size of the dataset, data distribution, and annotation quality, not to mention the potential bias in collecting human perception feedback, which could mislead the learned metrics. An analytic metric that can better explain the shape difference is thus preferred." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 279, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 495 + ], + "type": "text", + "content": "To address the above limitations, we design an analytic-based 3D shape evaluation metric named Spectrum Area Under the Curve Difference (SAUCD). Our metric measures mesh shape differences with a balanced consideration of both overall and detailed shape, making it better aligned with human evaluation. To allow our metric to capture detail variations, we leverage the 3D shape spectrum to decompose different levels of shape details from the overall shape, with details corresponding to higher-frequency components. The advantage of transforming the shape signal into the spectrum domain is that the high-frequency details are explicitly separated from the low-frequency overall shape. Therefore, it provides appropriate consideration to the information in different frequency bands, not just the low-frequency information of the overall shape in the dominant place. Thus, the details that human perception cares about will be better represented. Besides, the frequency analysis method allows the metric to be mostly analytic and better explained." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": "We design SAUCD following the above inspiration. To begin with, both the test mesh and the ground truth mesh are transformed from the spatial to the spectrum domain using the discrete Laplace-Beltrami operator (DLBO), which encodes the mesh geometry information into a semidefinite Laplacian matrix. Once in the spectrum domain, we compare the regions under the two spectrums. Our Spectrum Area Under the Curve Difference metric is defined as the area of the non-overlapping region under the two spectrums - a larger area indicates a greater difference. Moreover, to better align with human evaluation, we further extend our design by learning a spectrum weight for SAUCD. However, different from previous learning-based approaches that use deep networks, large datasets, and extensive learning processes, our learning-based method requires the training of a weight vector. This vector measures the sensitivity of human perception across frequency bands, making the learned metric better aligned with human perception. We then evaluated the" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "effectiveness of SAUCD on our provided user study benchmark dataset named Shape Grading. Using Shape Grading, we compare our metrics with previous metrics by calculating the correlation between each metric and human scoring. In summary, our contributions are listed as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 133, + 547, + 312 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 306, + 133, + 547, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 547, + 193 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 547, + 193 + ], + "type": "text", + "content": "- We design an analytic-based 3D mesh shape metric named Spectrum AUC Difference (SAUCD), which evaluates the difference between a 3D mesh and its ground truth mesh. Our metric considers both the overall shape and intricate details, to align more closely with human perception." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 193, + 547, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 193, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 193, + 547, + 239 + ], + "type": "text", + "content": "- We further extend our design to a learnable metric. The extended metric explores the human perception sensitivity in different frequency bands, which further improves this metric." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 241, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 241, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 241, + 547, + 312 + ], + "type": "text", + "content": "- We build a user study benchmark dataset named Shape Grading which is annotated by more than 800 subjects. The provided dataset verifies that both versions of our metrics are consistent with human evaluation and outperform previous methods. This dataset can also facilitate 3D mesh metric evaluation in future research." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 313, + 547, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 547, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 547, + 350 + ], + "type": "text", + "content": "Our experiments show that both SAUCD and its extended version outperform previous methods with good generalizability to different types of objects." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 358, + 398, + 371 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 358, + 398, + 371 + ], + "spans": [ + { + "bbox": [ + 306, + 358, + 398, + 371 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 378, + 547, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 547, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 547, + 569 + ], + "type": "text", + "content": "Metrics in 3D mesh reconstruction. Chamfer Distance [6] is a popular metric used in 3D mesh reconstruction tasks such as those in [21, 24, 32, 35, 45, 48-50]. Other spatial domain metrics, such as 3D Intersection over Union (IoU) in [10, 16, 17, 27, 33, 39]. F-score in [4, 15, 40, 43], and Unidirectional Hausdorff distance (UHD) in [47] are commonly focused on the geometry accuracy of mesh shapes. These metrics can provide accurate geometry measurements, but they are not designed to align with human evaluation. Deep-learning-based methods such as Single Shape Fréchet Inception Distance [46] are also used in 3D reconstruction. While these metrics have the capacity to adapt from human evaluation, they are more like black boxes, with performances subject to dataset size and annotation bias. Moreover, most previous works miss out on user study validation to verify if their metrics align with human evaluation." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 665 + ], + "type": "text", + "content": "3D shape generation metrics. Multiple metrics have been used in 3D shape generation, such as Minimal Matching Distance (MMD) [3], Jensen-Shannon Divergence (JSD) [22], Total Mutual Difference (TMD) [47], Fréchet Pointcloud Distance (FPD) [36], etc.. These metrics are designed to measure the differences between the generated distributions, while our task is to build a metric to compare the shape of two meshes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 714 + ], + "type": "text", + "content": "3D mesh compression and watermarking metrics. Previous works [8, 12, 23, 41] focused on evaluating mesh errors in mesh compression and watermarking. Since compression and watermarking pursue mesh errors that cannot" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20156" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 93, + 71, + 502, + 213 + ], + "blocks": [ + { + "bbox": [ + 93, + 71, + 502, + 213 + ], + "lines": [ + { + "bbox": [ + 93, + 71, + 502, + 213 + ], + "spans": [ + { + "bbox": [ + 93, + 71, + 502, + 213 + ], + "type": "image", + "image_path": "5cfa967ceea5defea1109f67661240f9273b4a66848aafdb6f2ea90584467277.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 221, + 547, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 221, + 547, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 221, + 547, + 257 + ], + "type": "text", + "content": "Figure 2. Our SAUCD metric is designed as follows: A. We use mesh Fourier Transform to analyze the spectrums of test and ground truth mesh. B. We compare the difference between two spectrum curves by calculating the Area Under the Curve (AUC) difference. C. We further extend our metric by multiplying the AUC difference with a learnable weight to capture human sensitivity in each frequency band." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 288, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 288, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 288, + 326 + ], + "type": "text", + "content": "be detected by humans, they mainly focus on barely noticed errors. However, our task is to build a metric that can handle generally occurring errors that happen in 3D reconstruction tasks and applications." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 335, + 153, + 348 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 335, + 153, + 348 + ], + "spans": [ + { + "bbox": [ + 47, + 335, + 153, + 348 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "type": "text", + "content": "Our task is to design a metric aligned with human evaluation to measure the shape difference between a test triangle mesh and its corresponding ground truth triangle mesh. Specifically, given a test mesh " + }, + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "type": "text", + "content": " and its ground truth mesh " + }, + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "type": "inline_equation", + "content": "M_{gt}" + }, + { + "bbox": [ + 46, + 355, + 288, + 415 + ], + "type": "text", + "content": ", Spectrum AUC Difference (SAUCD) can be abstracted as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 130, + 422, + 287, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 422, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 130, + 422, + 287, + 437 + ], + "type": "interline_equation", + "content": "d = D (\\hat {M}, M _ {g t}). \\tag {1}", + "image_path": "da07348d14a1a278c482ff024c172ddb75ce3f6d893e23b440e67ee78c11f813.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 446, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 289, + 483 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 446, + 289, + 483 + ], + "type": "text", + "content": " is the distance between the test and the ground truth mesh. In this section, we will elaborate on how the distance function " + }, + { + "bbox": [ + 46, + 446, + 289, + 483 + ], + "type": "inline_equation", + "content": "D(\\cdot)" + }, + { + "bbox": [ + 46, + 446, + 289, + 483 + ], + "type": "text", + "content": " is designed." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 490, + 115, + 501 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 490, + 115, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 490, + 115, + 501 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 616 + ], + "type": "text", + "content": "As shown in Fig. 2, our metric is calculated via the following steps: First, we use mesh Fourier transform to analyze the spectrums of the test and ground truth mesh (in Sec. 3.2). Then we leverage each frequency band by calculating the Area Under the Curve (AUC) difference of the spectrum curves (in Sec. 3.3). Moreover, we further extended our metric by multiplying the AUC difference with a learnable weight to capture the human sensitivity on each frequency band (in Sec. 3.4). We will discuss each step in detail." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 623, + 182, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 182, + 636 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 182, + 636 + ], + "type": "text", + "content": "3.2. Mesh spectrum analysis" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "In order to capture the overall shape as well as shape details, we choose to decompose the mesh signal into a spectrum. Considering the mesh as a function on a discretized manifold space, we can calculate the spectrum using the manifold space Fourier transform. In Hilbert space, the Fourier operator is defined as the eigenfunctions of the" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 276, + 547, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 547, + 408 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 547, + 408 + ], + "type": "text", + "content": "Laplacian operator [14]. The same definition and similar theories are extended to continuous and discrete manifold space by [5, 9]. The Laplacian operator on discrete manifold spaces, i.e. mesh space in our task, is named the Discrete Laplace-Beltrami operator (DLBO). Similar to the Laplacian operator in image space that encodes the pixel information by capturing the local pixel differences [20, 28, 30, 34, 38, 44], DLBO encodes the mesh shape information by capturing the local shape fluctuation. The \"Cotan formula\" defined in [25] is the most widely used discretization, which can be represented in matrix form as" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 413, + 547, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 413, + 547, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 413, + 547, + 459 + ], + "type": "interline_equation", + "content": "L _ {i j} = \\left\\{ \\begin{array}{c c} \\sum_ {j \\in N (i)} \\frac {1}{2 A _ {i}} \\left(\\cot \\alpha_ {i j} + \\cot \\beta_ {i j}\\right), & i = j \\\\ - \\frac {1}{2 A _ {i}} \\left(\\cot \\alpha_ {i j} + \\cot \\beta_ {i j}\\right), & i \\neq j \\wedge j \\in N (i) \\\\ 0, & i \\neq j \\wedge j \\notin N (i), \\end{array} \\right. \\tag {2}", + "image_path": "9c2dfa9cf1374d143f4b3d489d7e29295f0ba6cf0125a5f62138a0e3c8613f6a.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "L \\in \\mathbb{R}^{N \\times N}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " is the DLBO matrix, with " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " the vertex number of the mesh. " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "L_{ij}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " indicates its entry in " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "th row and " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "th column, which represents the edge weight between vertex " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "A_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " is the mixed Voronoi area of vertex " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " on the mesh. As shown in Fig. 3, the " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "'s mixed Voronoi area is defined as the area of the polygon in which the vertices are the circumcenters of " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "'s surrounding faces. " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "N(i)" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " is the index set of " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": "'s adjacent vertices. If " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_i" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "v_j" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " are adjacent, " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\alpha_{ij}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\beta_{ij}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " are the opposite angles of edge " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "(v_i, v_j)" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " in each of the edge's two neighbor triangle faces, respectively (shown in Fig. 3). If not, " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\alpha_{ij}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "\\beta_{ij}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " are not defined and " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "L_{ij}" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " is 0. As shown in Fig. 2, the DLBO matrix is used for mesh Fourier transform to get mesh spectrum. We calculate the Fourier operator " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "U^\\top" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": ", which is the eigenfunction of " + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 459, + 547, + 628 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 398, + 632, + 546, + 647 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 398, + 632, + 546, + 647 + ], + "spans": [ + { + "bbox": [ + 398, + 632, + 546, + 647 + ], + "type": "interline_equation", + "content": "L = U \\Lambda U ^ {\\top}, \\tag {3}", + "image_path": "9f1a160bd143cb730dae344464a477ec820619c94d077757e8a0d4f93e0a06c2.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\Lambda" + }, + { + "bbox": [ + 304, + 654, + 545, + 677 + ], + "type": "text", + "content": " is a diagonal matrix whose diagonal elements are Fourier mesh frequencies." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": "To ensure the mesh frequencies are non-negative, we need the DLBO matrix " + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 677, + 546, + 713 + ], + "type": "text", + "content": " to be positive semidefinite. Our experiment in Fig. 7 gives an example of the counterintuitive" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20157" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 70, + 136, + 148 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 136, + 148 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 136, + 148 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 136, + 148 + ], + "type": "image", + "image_path": "5631dbe3d5d881f53924c782e07ebc1fa5cf54758f8438bfb33b4160a774da77.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 156, + 151, + 190 + ], + "lines": [ + { + "bbox": [ + 47, + 156, + 151, + 190 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 151, + 190 + ], + "type": "text", + "content": "Figure 3. Variables defined in our discrete Laplace-Beltrami operator design." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 191, + 70, + 518, + 148 + ], + "blocks": [ + { + "bbox": [ + 191, + 70, + 518, + 148 + ], + "lines": [ + { + "bbox": [ + 191, + 70, + 518, + 148 + ], + "spans": [ + { + "bbox": [ + 191, + 70, + 518, + 148 + ], + "type": "image", + "image_path": "f6a09be4db54e5255572d657d3586f7f74dfe8c4904a35bdb265449ca477cb71.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 160, + 156, + 547, + 190 + ], + "lines": [ + { + "bbox": [ + 160, + 156, + 547, + 190 + ], + "spans": [ + { + "bbox": [ + 160, + 156, + 547, + 190 + ], + "type": "text", + "content": "Figure 4. Spectrum Area Under the Curve Difference. We design our metric using the AUC difference of the spectrums. The blue curve and red curve are the test and ground truth mesh spectrum, respectively. The purple area in the last graph is the Spectrum AUC Difference. Please find details in Sec. 3.3." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "spans": [ + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": "results when there are negative frequencies. However, the Coton formula in Eq. (2) does not guarantee to be positive semidefinite. We provide a simple example in Supplementary Materials Sec. 3 in which " + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": " is not positive semidefinite when the mesh is not Delaunay triangulated and the mixed Voronoi areas are not all equal to each other. In our metric design, we made two small changes to the original Coton formula to make it positive semidefinite. a) Inspired by the symmetric normalization of the topology Laplacian matrix in [11], we make " + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": " symmetric by changing the normalization parameter " + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "inline_equation", + "content": "A_{i}" + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": " into a symmetric normalized manner " + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "inline_equation", + "content": "A_{i}^{\\frac{1}{2}}A_{j}^{\\frac{1}{2}}" + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": ". b) We replace " + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "inline_equation", + "content": "\\cot \\alpha_{ij} + \\cot \\beta_{ij}" + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "inline_equation", + "content": "|\\cot \\alpha_{ij} + \\cot \\beta_{ij}|" + }, + { + "bbox": [ + 46, + 211, + 289, + 381 + ], + "type": "text", + "content": ". This ensures all the edge weights in the Laplacian matrix to be non-negative. Thus, our revision of DLBO is defined as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 384, + 303, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 303, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 303, + 434 + ], + "type": "interline_equation", + "content": "L _ {i j} = \\left\\{ \\begin{array}{c c} \\frac {1}{2} \\sum_ {j \\in N (i)} A _ {i} ^ {- \\frac {1}{2}} A _ {j} ^ {- \\frac {1}{2}} | \\cot \\alpha_ {i j} + \\cot \\beta_ {i j} |, & i = j \\\\ - \\frac {1}{2} A _ {i} ^ {- \\frac {1}{2}} A _ {j} ^ {- \\frac {1}{2}} | \\cot \\alpha_ {i j} + \\cot \\beta_ {i j} |, & i \\neq j \\wedge j \\in N (i) \\\\ 0, & i \\neq j \\wedge j \\notin N (i). \\end{array} \\right. \\tag {4}", + "image_path": "811d389419ddc6f43cc861d48c520077409ec9704c700c01d652d986dadd1e22.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 435, + 288, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 288, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 288, + 495 + ], + "type": "text", + "content": "We prove that our revision of the Cotan formula is positive semidefinite in Supplementary Materials Sec. 2. In Tab. 5, our experiments show that our DLBO matrix design outperforms the origin Cotan formula in [25], and the topology Laplacian matrix defined in [11]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "text", + "content": "Finally, we obtain the mesh spectrum by acting Fourier operator on the mesh vertices" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 85, + 527, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 527, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 85, + 527, + 287, + 548 + ], + "type": "interline_equation", + "content": "F _ {i} = \\sqrt {G _ {i , x} ^ {2} + G _ {i , y} ^ {2} + G _ {i , z} ^ {2}}, G = U ^ {\\top} v, \\tag {5}", + "image_path": "50e2c5eb544cbd72d3d90001b77c5508216a461297356a923f210d52334a1e8c.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "inline_equation", + "content": "v \\in \\mathbb{R}^{N \\times 3}" + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "text", + "content": " indicates the 3D coordinates of " + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "text", + "content": " mesh vertices. The result spectrum " + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^N" + }, + { + "bbox": [ + 46, + 555, + 288, + 628 + ], + "type": "text", + "content": ". Fig. 5 shows an example of the mesh spectrum (left side) and how the meshes look in different frequency bands (right side). This provides an illustration of the information contained in different frequency bands of the mesh spectrum." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 635, + 194, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 194, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 194, + 647 + ], + "type": "text", + "content": "3.3. Spectrum AUC Difference" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 689 + ], + "type": "text", + "content": "To reduce the noise and normalize the mesh scale, we also design noise pruning and AUC normalization procedures before calculating the Spectrum AUC Difference." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Noise pruning. As shown in Fig. 4 process " + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "(a)" + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": ", we prune a small portion of the highest frequency information" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "content": "to reduce the interference of noise. From the observation of the first two meshes (A and B) in Fig. 5, we can see that humans can barely notice the shape differences when the highest frequency parts are removed. Thus, if we try to evaluate the mesh shape that aligns with human perception, it is reasonable to remove high-frequency noise without losing much information that humans care about. Empirically, we choose to prune the highest " + }, + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 304, + 211, + 545, + 342 + ], + "type": "text", + "content": " frequency information as noise. Our experiments in Tab. 4 show that this portion is more consistent with human perception while preserving good mesh quality." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": "AUC normalization. Given a spectrum " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "F(\\lambda)" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": ", its Area Under the Curve (AUC) can be defined as " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\int_{\\infty} F(\\lambda) d\\lambda" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": ". AUC normalization means using spectrum AUC to normalize the mesh scale. If the mesh scale increases by " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " times in length, the mixed Voronoi area, i.e. " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "A_i" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " in Eq. (4), will decrease by " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " times. Thus, each element in the DLBO matrix " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " will also decrease by " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " times. Then, according to Eq. (3), the frequency " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " will decrease " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "s^2" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " times to " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "\\lambda / s^2" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": ", and according to Eq. (5), the spectrum amplitude " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " will change to " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "sF" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " because " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "v" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " is increased by " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " time and " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "U^\\top" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": " is still orthonormal. Then the area under the spectrum curve (the area boxed with red or blue lines in Fig. 4) changes as " + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "inline_equation", + "content": "A' = \\int sF(\\lambda) d\\lambda / s^2 = \\frac{1}{s} A" + }, + { + "bbox": [ + 304, + 343, + 546, + 488 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": "In our approach, we normalize the area under the spectrum curve " + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": " to 1 to resolve the scale difference, which means " + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "inline_equation", + "content": "s = A" + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": " decreases by " + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "inline_equation", + "content": "A^2" + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": " times, and spectrum amplitude " + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "inline_equation", + "content": "F" + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": " increases by " + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 304, + 488, + 547, + 632 + ], + "type": "text", + "content": " times (Fig. 4 process (b)). AUC normalization fairly normalizes the scale of objects in different shapes by only changing the scale, not shape details. It normalizes the spectrum AUC of all mesh to 1, making the mesh spectrums differ only in distributions. Our experiments in Tab. 5 demonstrate this design can bring a fairer comparison of the spectrums and improve the human consistency of the metric. The experiment also demonstrates that this design outperforms the spatial domain scale normalization." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 632, + 547, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 547, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 547, + 681 + ], + "type": "text", + "content": "Spectrum AUC Difference. In order to capture the difference between two mesh shapes in the spectrum domain, we design Spectrum AUC Difference (SAUCD) on the spectrum analysis results after noise pruning and AUC normalization:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 336, + 691, + 546, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 691, + 546, + 717 + ], + "spans": [ + { + "bbox": [ + 336, + 691, + 546, + 717 + ], + "type": "interline_equation", + "content": "d = D (\\hat {M}, M _ {g t}) = \\int_ {\\lambda} | \\hat {F} (\\lambda) - F _ {g t} (\\lambda) | d \\lambda , \\tag {6}", + "image_path": "2b6be1b7f980a103ffca8d951327b70ee42e504103601c1546672dfce5b45c62.jpg" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20158" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 62, + 70, + 273, + 122 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 273, + 122 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 273, + 122 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 273, + 122 + ], + "type": "table", + "html": "
datasetRaww/ IQR removal
number of valid scores2430423775
Scoring range[0, 6][0, 6]
95% confidence interval0.3180.303
Relative 95% confidence interval5.33%5.04%
", + "image_path": "309382284e5b35bdd9f56497042401fdf103b5cc4622cb0f44ab7ab118a7aaab.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 132, + 247, + 142 + ], + "lines": [ + { + "bbox": [ + 85, + 132, + 247, + 142 + ], + "spans": [ + { + "bbox": [ + 85, + 132, + 247, + 142 + ], + "type": "text", + "content": "Table 1. Dataset statistics and error analysis." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "inline_equation", + "content": "\\hat{F}" + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "inline_equation", + "content": "F_{gt}" + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "content": " are the test and groundtruth mesh spectrum. As shown in Fig. 4 process " + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "inline_equation", + "content": "(c)" + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "content": ", our metric is defined as the AUC difference of the two spectrum curves (the purple area). In Tab. 5, we compare our design with an alternative design which changes the amplitude difference " + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "inline_equation", + "content": "|\\hat{F} (\\lambda) - F_{gt}(\\lambda)|" + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "content": " to energy difference " + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "inline_equation", + "content": "|\\hat{F} (\\lambda)^2 -F_{gt}(\\lambda)^2 |" + }, + { + "bbox": [ + 46, + 164, + 288, + 309 + ], + "type": "text", + "content": ". The result shows our design is more consistent with human evaluation. Besides, experiments in Tab. 2 show our SAUCD metric aligns well with human evaluation, and outperforms SOTA metrics under multiple evaluation methods. Experiments in Fig. 8 show SAUCD has the capability to improve mesh detail qualities in 3D reconstruction when adapted into training loss." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 317, + 274, + 330 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 274, + 330 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 274, + 330 + ], + "type": "text", + "content": "3.4. Human-adjusted Spectrum AUC Difference" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 336, + 287, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 287, + 396 + ], + "type": "text", + "content": "We also provide an extended metric version, in which we design a learnable weight parameter along the frequency bands. The weight parameter indicates the adjustment of human sensitivity to each frequency band. Specifically, we design the extended metric as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 55, + 405, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 405, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 55, + 405, + 287, + 430 + ], + "type": "interline_equation", + "content": "d _ {w} = D _ {w} (\\hat {M}, M _ {g t}) = \\int_ {\\lambda} w (\\lambda) | \\hat {F} (\\lambda) - F _ {g t} (\\lambda) | d \\lambda . \\tag {7}", + "image_path": "b060c44250878369e1105dd5ef3f58d7f7a37a916d6e6a3cb8f43fb33f53faaf.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 439, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 439, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 47, + 439, + 287, + 464 + ], + "type": "inline_equation", + "content": "w(\\lambda)" + }, + { + "bbox": [ + 47, + 439, + 287, + 464 + ], + "type": "text", + "content": " is weight parameters indicating human sensitivity along frequency bands. Our training loss is defined as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 88, + 473, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 473, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 88, + 473, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\lambda_ {p} \\mathcal {L} _ {p l c c} + \\lambda_ {s r} \\mathcal {L} _ {s r o c c} + \\lambda_ {r} \\mathcal {L} _ {r e g u}, \\tag {8}", + "image_path": "577d97beb01950fa7342eec06f3016aab61cc178c363c4d5d4da880fc7c4c9e8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{plcc}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{srocc}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": " are Pearson correlation loss and Spearman rank order loss. They are defined the same as Pearson's linear correlation [29] and Spearman's rank order correlation [37]. " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{regu} = 1 / N\\sum_{i}(w_{i} - 1)^{2}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": " is the regularization loss, which regularizes weight " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": " close to 1. " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_p" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_{sr}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\lambda_r" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": " are the loss weights of " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{plcc}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{srocc}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{regu}" + }, + { + "bbox": [ + 46, + 496, + 288, + 616 + ], + "type": "text", + "content": ". More details of the loss functions can be found in Supplementary Materials Sec. 1. Our experiments in Sec. 4.3 show that after adjustment, the consistency between our metric output and human-annotated ground truth is improved." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 627, + 127, + 640 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 627, + 127, + 640 + ], + "spans": [ + { + "bbox": [ + 47, + 627, + 127, + 640 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 105, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 105, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 105, + 658 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "We build a user study benchmark dataset Shape Grading to evaluate whether our metric is aligned with human evaluation. The dataset contains the human evaluation scores for a variety of distorted meshes. Using this dataset, we can" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 107 + ], + "type": "text", + "content": "calculate the correlation between metric outputs and human evaluation scores to see how aligned the test metrics are to human evaluation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "type": "text", + "content": "Dataset design. We choose 12 objects as ground truth 3D triangle mesh from public object/scene/human mesh datasets such as [18, 26, 42] and commercial datasets such as [1, 2]. These objects are picked from different categories including humans, animals, buildings, plants, etc.. For each object, we synthesize 7 different types of distortions which commonly occur in 3D reconstruction. For each distortion type we synthesize 4 distortion levels, which gives us " + }, + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "type": "inline_equation", + "content": "7 \\times 4 = 28" + }, + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "type": "text", + "content": " distorted objects for every ground truth object. We rotate and render each distorted object into 3 videos using different materials for the mesh. In total, we generate " + }, + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "type": "inline_equation", + "content": "12 \\times 28 \\times 3 = 1,008" + }, + { + "bbox": [ + 304, + 110, + 546, + 276 + ], + "type": "text", + "content": " distorted mesh videos. Supplementary Materials Sec. 4 shows the meshes and distortion types we use in our dataset." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 279, + 547, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 279, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 279, + 547, + 495 + ], + "type": "text", + "content": "Human scoring procedure. We use a pairwise comparison scoring process similar to [31]. Each subject will evaluate all 28 distorted objects of one ground truth object with a certain material. The scoring follows a Swiss system tournament principle used in [31], in which each subject takes 6 rounds of pairwise comparison to score the distorted meshes. After 6 rounds of scoring, the meshes are scored from 0 to 6. 0 means the object loses in every round and 6 means it wins in every round. This process will largely reduce the biases among subjects, since the subjects are compelled to distribute an equal amount of points to the 28 distorted objects. The process will take about 15 minutes for each subject, avoiding the fatigue problem in [7]. For every object rendered with every material, we have 24 to 25 subjects scoring it. In total, we have 868 subjects (536 males, 316 females, and 16 others) who give us " + }, + { + "bbox": [ + 304, + 279, + 547, + 495 + ], + "type": "inline_equation", + "content": "868 \\times 28 = 24304" + }, + { + "bbox": [ + 304, + 279, + 547, + 495 + ], + "type": "text", + "content": " scores. More details of the scoring procedure can be found in Supplementary Materials Sec. 5." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "type": "text", + "content": "Outlier detection. We use the interquartile range (IQR) method [13] which is widely used in statistics to detect and remove outliers. For each distorted mesh, we first find the 25 percentile and the 75 percentile of the scores. The score range in between is called the IQR range. We remove the scores that are 1.5IQR smaller than the 25 percentile or 1.5IQR larger than the 75 percentile. Our dataset error analysis in Tab. 1 shows, that by removing " + }, + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "type": "inline_equation", + "content": "2.2\\%" + }, + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "type": "text", + "content": " of the scores using IQR, we can decrease the uncertainty of the final scoring result by nearly " + }, + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 304, + 496, + 547, + 616 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": "Dataset error analysis. We analysis the average " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " confidence interval of our dataset scores in Tab. 1. The confidence interval of score " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " can be calculated as " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma_{\\bar{x}} = z_{0.95} \\times \\sigma / \\sqrt{N}" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " is the standard derivation of " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " is the number of valid scores, and " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "z_{0.95} \\approx 1.96" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": ". We report the average " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " confidence interval and the relative " + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 304, + 617, + 547, + 714 + ], + "type": "text", + "content": " confidence interval (which is the confidence interval divided by the scoring range). The result shows that dataset scoring" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20159" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 95, + 70, + 504, + 175 + ], + "blocks": [ + { + "bbox": [ + 95, + 70, + 504, + 175 + ], + "lines": [ + { + "bbox": [ + 95, + 70, + 504, + 175 + ], + "spans": [ + { + "bbox": [ + 95, + 70, + 504, + 175 + ], + "type": "table", + "html": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.540.15-0.100.57-0.06-0.12-0.200.070.040.30-0.200.170.097
Point-to-Surface0.450.19-0.040.66-0.08-0.25-0.32-0.200.010.13-0.21-0.120.017
Normal Difference0.460.110.060.280.110.210.290.470.270.390.110.270.253
IoU [16]0.600.630.010.510.300.02-0.070.200.140.47-0.09-0.010.225
F-score [43]0.580.090.050.330.030.060.160.340.270.250.010.340.208
SSFID [46]0.710.74-0.040.740.390.240.130.320.250.640.25-0.020.363
UHD [47]0.290.220.110.15-0.040.180.410.550.130.180.250.330.231
SAUCD (Ours)0.730.210.600.630.310.510.830.650.770.800.690.080.567
Adjusted SAUCD (Ours)0.790.190.560.640.360.540.790.760.750.770.670.360.598
", + "image_path": "deebab21531514f681b68b443f7da111b48512814e5176e7f9a4f653bd361bf7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 95, + 188, + 504, + 293 + ], + "blocks": [ + { + "bbox": [ + 220, + 178, + 372, + 187 + ], + "lines": [ + { + "bbox": [ + 220, + 178, + 372, + 187 + ], + "spans": [ + { + "bbox": [ + 220, + 178, + 372, + 187 + ], + "type": "text", + "content": "a. Pearson's linear correlation coefficient." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 95, + 188, + 504, + 293 + ], + "lines": [ + { + "bbox": [ + 95, + 188, + 504, + 293 + ], + "spans": [ + { + "bbox": [ + 95, + 188, + 504, + 293 + ], + "type": "table", + "html": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.330.14-0.090.43-0.08-0.06-0.150.17-0.040.24-0.160.220.079
Point-to-Surface0.420.390.140.590.110.05-0.100.200.180.40-0.110.180.205
Normal Difference0.440.220.330.420.190.290.330.560.330.320.210.340.331
IoU [16]0.570.610.280.500.360.210.120.310.2620.560.030.300.342
F-score [43]0.470.250.200.520.210.110.070.360.300.42-0.010.350.27
SSFID [46]0.630.810.280.700.330.230.100.330.320.650.160.340.407
UHD [47]0.380.200.110.320.130.350.410.600.060.270.370.350.296
SAUCD (Ours)0.790.250.570.590.360.560.830.790.690.690.830.240.598
Adjusted SAUCD (Ours)0.830.210.550.590.380.600.820.800.690.680.750.420.611
", + "image_path": "dd39e5ee34a39a311968774e30c93e0fcdba28559bd3aa5d1753d31584f7158e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 95, + 308, + 504, + 413 + ], + "blocks": [ + { + "bbox": [ + 208, + 296, + 383, + 306 + ], + "lines": [ + { + "bbox": [ + 208, + 296, + 383, + 306 + ], + "spans": [ + { + "bbox": [ + 208, + 296, + 383, + 306 + ], + "type": "text", + "content": "b. Spearman's rank order correlation coefficient." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 95, + 308, + 504, + 413 + ], + "lines": [ + { + "bbox": [ + 95, + 308, + 504, + 413 + ], + "spans": [ + { + "bbox": [ + 95, + 308, + 504, + 413 + ], + "type": "table", + "html": "
Metrics\\Object No.123456789101112Overall
Chamfer Distance [6]0.250.14-0.080.31-0.04-0.02-0.090.150.0130.19-0.070.220.080
Point-to-Surface0.330.300.070.450.100.08-0.030.170.130.30-0.010.160.171
Normal Difference0.340.160.170.310.180.220.260.440.250.230.160.270.250
IoU [16]0.420.440.240.370.280.220.140.260.200.410.100.230.275
F-score [43]0.370.170.140.420.150.110.090.280.230.340.010.300.216
SSFID [46]0.480.620.240.510.250.240.120.290.260.480.170.230.322
UHD [47]0.270.130.070.220.090.260.290.420.0480.190.280.240.209
SAUCD (Ours)0.600.160.420.410.270.450.650.570.550.470.600.190.445
Adjusted SAUCD (Ours)0.640.140.400.410.290.480.630.590.550.450.570.290.453
", + "image_path": "d54ac75ec8cdb5914d073b0c1d2c60c67e45c54c36b62760761263014237a2fb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 211, + 415, + 380, + 426 + ], + "lines": [ + { + "bbox": [ + 211, + 415, + 380, + 426 + ], + "spans": [ + { + "bbox": [ + 211, + 415, + 380, + 426 + ], + "type": "text", + "content": "c. Kendall's rank order correlation coefficient." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 435, + 546, + 458 + ], + "lines": [ + { + "bbox": [ + 46, + 435, + 546, + 458 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 546, + 458 + ], + "type": "text", + "content": "Table 2. Correlations between different metrics and human annotation. \"SAUCD\" is our basic version metric. \"Adjusted SAUCD\" is the human-adjusted version of our metric. The ranges of all three correlation coefficients are " + }, + { + "bbox": [ + 46, + 435, + 546, + 458 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 46, + 435, + 546, + 458 + ], + "type": "text", + "content": ", and the higher the better." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 479, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 491 + ], + "type": "text", + "content": "is accurate with a " + }, + { + "bbox": [ + 46, + 479, + 287, + 491 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 479, + 287, + 491 + ], + "type": "text", + "content": " error range with IQR outlier removal." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 492, + 289, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 289, + 647 + ], + "type": "text", + "content": "Evaluation methods. We use 3 different evaluation methods to evaluate the correlation between our metrics and the human scoring (ground truth) on our Shape Grading benchmark dataset. Pearson's linear correlation coefficient (PLCC) [29] is used to evaluate the linear alignment between our metric and human perception. We also used Spearman's rank order correlation coefficient (SROCC) [37] and Kendall's rank order correlation coefficient (KROCC) [19] to evaluate the ranking order correlation between our metric and human perception. The possible ranges of 3 metrics are all " + }, + { + "bbox": [ + 46, + 492, + 289, + 647 + ], + "type": "inline_equation", + "content": "[-1, 1]" + }, + { + "bbox": [ + 46, + 492, + 289, + 647 + ], + "type": "text", + "content": ". Higher numbers mean stronger correlations. More details of the three evaluation methods can be found in Supplementary Materials Sec. 1." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 178, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 178, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 178, + 671 + ], + "type": "text", + "content": "4.2. Implementation details" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": "We implement our basic version metric following Eq. (6). " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\hat{F} (\\lambda)" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "F_{gt}(\\lambda)" + }, + { + "bbox": [ + 47, + 677, + 288, + 715 + ], + "type": "text", + "content": " in Eq. (6) are both piece-wise functions, so we implement the integration by simply adding every piece" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "text", + "content": "area together. We implement our human-adjusted version following Eq. (7). We use a 20-dimensional weight " + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "inline_equation", + "content": "w(\\lambda)" + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "text", + "content": " to avoid overfitting. We interpolate " + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "text", + "content": " to all frequencies of the ground truth and test meshes and element-wisely multiply them to the spectrums. In spectrum weight training, SROCC and PLCC are used as part of the loss function as Eq. (8). KROCC is not used in training but only for testing. We use a k-fold strategy for training the human-adjusted weight. Each time we choose 1 object for testing and the rest 11 objects for training, which means " + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "inline_equation", + "content": "k = 12" + }, + { + "bbox": [ + 304, + 479, + 547, + 611 + ], + "type": "text", + "content": ". More implementation details can be found in Supplementary Materials Sec. 1." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 621, + 485, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 621, + 485, + 635 + ], + "spans": [ + { + "bbox": [ + 305, + 621, + 485, + 635 + ], + "type": "text", + "content": "4.3. Quantitative and qualitative results" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 548, + 715 + ], + "type": "text", + "content": "SOTA comparison. Tab. 2 shows our results compared to previous 3D mesh shape metrics. We evaluated the correlation between each metric and the human scoring via three different evaluation methods. We observe that a) without any learning-based design, our metric outperforms the SOTA learning-based (SSFID) and non-learning-based met" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20160" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 71, + 240, + 205 + ], + "blocks": [ + { + "bbox": [ + 86, + 71, + 240, + 205 + ], + "lines": [ + { + "bbox": [ + 86, + 71, + 240, + 205 + ], + "spans": [ + { + "bbox": [ + 86, + 71, + 240, + 205 + ], + "type": "image", + "image_path": "764d32b014fa0d52b399c11f8dc6b3bbd71e4da910c20d2b2a7308040c73399c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "lines": [ + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "type": "text", + "content": "Figure 5. An example of mesh spectrum curve: We do mesh Fourier transform on the \"Origin\" mesh and show the spectrum in the left graph. The " + }, + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 214, + 547, + 248 + ], + "type": "text", + "content": "-axis is the eigenvalues of the DLBO matrix, the larger the higher frequency. We also show how mesh changes when gradually removing high-frequency information (mesh A to G). The frequency bands of the meshes are shown as the colored arrows in the left graph." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 240, + 70, + 309, + 141 + ], + "blocks": [ + { + "bbox": [ + 240, + 70, + 309, + 141 + ], + "lines": [ + { + "bbox": [ + 240, + 70, + 309, + 141 + ], + "spans": [ + { + "bbox": [ + 240, + 70, + 309, + 141 + ], + "type": "image", + "image_path": "b28f9dc2d58842566417e939a2392debcc025e9afdd4b6a7e78b3ab3883285be.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 377, + 140 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 377, + 140 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 377, + 140 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 377, + 140 + ], + "type": "image", + "image_path": "ffdfc17c85a9aa9222a29a8078f8c66e61811739dbeac41d8d4f2ed990d09d2e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 377, + 71, + 446, + 140 + ], + "blocks": [ + { + "bbox": [ + 377, + 71, + 446, + 140 + ], + "lines": [ + { + "bbox": [ + 377, + 71, + 446, + 140 + ], + "spans": [ + { + "bbox": [ + 377, + 71, + 446, + 140 + ], + "type": "image", + "image_path": "069dc0d830bfde1a0fdae3dbcdee1d2deb3699aee80ccefae9c8ef2eafffbd96.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 446, + 71, + 509, + 140 + ], + "blocks": [ + { + "bbox": [ + 446, + 71, + 509, + 140 + ], + "lines": [ + { + "bbox": [ + 446, + 71, + 509, + 140 + ], + "spans": [ + { + "bbox": [ + 446, + 71, + 509, + 140 + ], + "type": "image", + "image_path": "1fe77269e3a7ae08a08b41ab667a8b20b37ec18a76dee309216883011b2c24fb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 242, + 152, + 306, + 206 + ], + "blocks": [ + { + "bbox": [ + 268, + 144, + 276, + 152 + ], + "lines": [ + { + "bbox": [ + 268, + 144, + 276, + 152 + ], + "spans": [ + { + "bbox": [ + 268, + 144, + 276, + 152 + ], + "type": "text", + "content": "D" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 242, + 152, + 306, + 206 + ], + "lines": [ + { + "bbox": [ + 242, + 152, + 306, + 206 + ], + "spans": [ + { + "bbox": [ + 242, + 152, + 306, + 206 + ], + "type": "image", + "image_path": "be8c066fde23839299ad8b9d5336547fef19adf39135b3b736d510fef446f708.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 306, + 144, + 375, + 205 + ], + "blocks": [ + { + "bbox": [ + 306, + 144, + 375, + 205 + ], + "lines": [ + { + "bbox": [ + 306, + 144, + 375, + 205 + ], + "spans": [ + { + "bbox": [ + 306, + 144, + 375, + 205 + ], + "type": "image", + "image_path": "8846b173a2faee5d3c7e7c7e131dbd6a9c7d87a18a475a0df31cd945c2a37d90.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 376, + 144, + 445, + 204 + ], + "blocks": [ + { + "bbox": [ + 376, + 144, + 445, + 204 + ], + "lines": [ + { + "bbox": [ + 376, + 144, + 445, + 204 + ], + "spans": [ + { + "bbox": [ + 376, + 144, + 445, + 204 + ], + "type": "image", + "image_path": "e69893ab1afe64a8b7fe398432ff0f32fd413461409ac7b5e6c25d5b72103497.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 445, + 144, + 509, + 198 + ], + "blocks": [ + { + "bbox": [ + 445, + 144, + 509, + 198 + ], + "lines": [ + { + "bbox": [ + 445, + 144, + 509, + 198 + ], + "spans": [ + { + "bbox": [ + 445, + 144, + 509, + 198 + ], + "type": "image", + "image_path": "949eee0e4f94a2ff0469e702e5f40a35b17f59805c76eac90a5b3bb3364a8969.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 268, + 288, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 268, + 288, + 328 + ], + "spans": [ + { + "bbox": [ + 46, + 268, + 288, + 328 + ], + "type": "text", + "content": "rics (Chamfer Distance, IoU, F-score, and UHD), b) our extended version metric with learned weights has better linearity and slightly better ranking order correction with human evaluation, and c) our results on different objects show that our metrics have good generalizability." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 329, + 287, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 329, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 46, + 329, + 287, + 435 + ], + "type": "text", + "content": "Spectrum example. We first show an example of mesh spectrum in Fig. 5. We decompose the \"origin\" mesh using the Fourier Transform and get the resulting spectrum (top-left graph). The meshes on the right (from mesh A to G) are generated by gradually removing high-frequency information. The frequency bands of the meshes are shown as colored arrows in and under the graph. As we see, the details gradually disappear as we remove high-frequency information." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 437, + 288, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 288, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 288, + 544 + ], + "type": "text", + "content": "Frequency band separation. We explored the consistency between human perception and the information obtained from every frequency band. Specifically, we separate the frequency band exponentially and build metrics only using information from that frequency band. The results are shown in Tab. 3, we find the frequency bands [0, 0.001] and [0.01, 0.03] have the best consistency with human perception. Moreover, it shows that if we put all frequencies together, they can achieve better results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 545, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 688 + ], + "type": "text", + "content": "Trained weight. We show our trained weights in Human-adjusted metric in Fig. 6. Different lines represent different folds, and the bold purple line is the average weight. We can see the weights trained on each fold have similar patterns. We also observe that the weight curves have a small peak in the range A and two much larger peaks between A and B, which means our extended metric relies more on the information between A and B. We show an example of mesh shapes in the range A, B, and C at the bottom of Fig. 6. Mesh A obviously has fewer details than Mesh B, and the weight curve shows that this difference is what the learning process tries to emphasize." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 289, + 714 + ], + "type": "text", + "content": "Negative frequencies. In Fig. 7 we illustrate how our revised Cotan formula DLBO in Eq. (4) improves fre" + } + ] + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 325, + 266, + 462, + 369 + ], + "blocks": [ + { + "bbox": [ + 325, + 266, + 462, + 369 + ], + "lines": [ + { + "bbox": [ + 325, + 266, + 462, + 369 + ], + "spans": [ + { + "bbox": [ + 325, + 266, + 462, + 369 + ], + "type": "image", + "image_path": "1d05bd60080fb3c240c1e5a09eacb96e6e1840e48e4bb994effa4cc0f84c42c8.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 462, + 266, + 526, + 366 + ], + "blocks": [ + { + "bbox": [ + 462, + 266, + 526, + 366 + ], + "lines": [ + { + "bbox": [ + 462, + 266, + 526, + 366 + ], + "spans": [ + { + "bbox": [ + 462, + 266, + 526, + 366 + ], + "type": "image", + "image_path": "efcc494b3d5fa2fa4731f88581ec2698e33c2f2aaaf947c5d4bfdb4584223ad9.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 326, + 369, + 394, + 442 + ], + "blocks": [ + { + "bbox": [ + 326, + 369, + 394, + 442 + ], + "lines": [ + { + "bbox": [ + 326, + 369, + 394, + 442 + ], + "spans": [ + { + "bbox": [ + 326, + 369, + 394, + 442 + ], + "type": "image", + "image_path": "81c964bc79cb4c885bb6d9490d3a408b54de2aec34c25c88b999950f4f56ebc1.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 450, + 547, + 507 + ], + "lines": [ + { + "bbox": [ + 305, + 450, + 547, + 507 + ], + "spans": [ + { + "bbox": [ + 305, + 450, + 547, + 507 + ], + "type": "text", + "content": "Figure 6. Learned spectrum weights on all 12 folds. The name of colorful thin lines means the test object name of that fold. The bold purple line is the average weights of all folds. We also show some examples of mesh shape information in different frequency bands. Frequency band A is [0, 0.0075), B is [0, 0.03), and C is [0, 0.05)." + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 395, + 369, + 460, + 441 + ], + "blocks": [ + { + "bbox": [ + 395, + 369, + 460, + 441 + ], + "lines": [ + { + "bbox": [ + 395, + 369, + 460, + 441 + ], + "spans": [ + { + "bbox": [ + 395, + 369, + 460, + 441 + ], + "type": "image", + "image_path": "950f9ac4a3519d2644f9e0acb368bc1105d00b7801ad1d34f258ade94baaa04f.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 460, + 368, + 526, + 441 + ], + "blocks": [ + { + "bbox": [ + 460, + 368, + 526, + 441 + ], + "lines": [ + { + "bbox": [ + 460, + 368, + 526, + 441 + ], + "spans": [ + { + "bbox": [ + 460, + 368, + 526, + 441 + ], + "type": "image", + "image_path": "e24b6e02206c10ef8f949247a95ea27d87aee0b845ddd4a5359c3c806071289e.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 533, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 714 + ], + "type": "text", + "content": "quency analysis compared to the original Coton formula in Eq. (2) [25]. The first and second rows are the results of the original Coton formula DLBO and our revised Coton formula DLBO, respectively. The original Coton formula can yield negative frequencies due to its lack of positive semidefiniteness, whereas our revision ensures all frequencies are non-negative. For both objects in the figure, we remove different portions of high-frequency information and show the remaining low-frequency parts (resulting in “Filtered mesh 1” and “Filtered mesh 2”). For the left object, notice the counterintuitive sharp shapes in the red circle when using the Coton formula. The right object is a much more severe case. Sharp shapes in low-frequency parts show improper decomposition and high-frequency aliasing with low-frequency shapes, making the Coton formula unsuitable for spectral" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20161" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 68, + 531, + 166 + ], + "blocks": [ + { + "bbox": [ + 65, + 68, + 531, + 166 + ], + "lines": [ + { + "bbox": [ + 65, + 68, + 531, + 166 + ], + "spans": [ + { + "bbox": [ + 65, + 68, + 531, + 166 + ], + "type": "image", + "image_path": "9ea0e2af7986dfe9f9da879e63a9da1c4bb3e821ba35ed7f298c61596fd3906a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 172, + 547, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 172, + 547, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 547, + 217 + ], + "type": "text", + "content": "Figure 7. Counterintuitive low-frequencies information if some of the mesh frequencies are negative. We can see if we remove the high-frequency part of the mesh (resulting in \"Filtered mesh 1\" and \"Filtered mesh 2\") using the original Coton formula, the mesh's low-frequency parts show artifacts (sharp shapes). The red circles show the artifacts in the left object. The right object shows a case when these artifacts occur much more often. These artifacts do not occur using our revised Coton formula DLBO." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 227, + 200, + 296 + ], + "blocks": [ + { + "bbox": [ + 48, + 227, + 200, + 296 + ], + "lines": [ + { + "bbox": [ + 48, + 227, + 200, + 296 + ], + "spans": [ + { + "bbox": [ + 48, + 227, + 200, + 296 + ], + "type": "table", + "html": "
Frequency bandPLCC ↑SROCC ↑KROCC ↑
[0, 0.001)0.4340.5150.376
[0.001, 0.003)0.2400.4090.281
[0.003, 0.01)0.2550.4550.340
[0.01, 0.03)0.4210.5280.391
[0.03, 0.1)0.2870.3510.250
[0.1,∞)0.3180.1920.155
(0,∞)0.5670.5980.445
", + "image_path": "f1164bb6ca22a653232857bec77621587f1f6f32d9bec7c7810538182e64d6fb.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 203, + 228, + 360, + 281 + ], + "blocks": [ + { + "bbox": [ + 46, + 303, + 200, + 337 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 200, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 200, + 337 + ], + "type": "text", + "content": "Table 3. Results when building metrics using each frequency band separately. The bottom row is our proposed metric." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 203, + 228, + 360, + 281 + ], + "lines": [ + { + "bbox": [ + 203, + 228, + 360, + 281 + ], + "spans": [ + { + "bbox": [ + 203, + 228, + 360, + 281 + ], + "type": "table", + "html": "
Pruning PortionPLCC ↑SROCC ↑KROCC ↑
0%0.5130.5490.393
0.1%0.5670.5980.445
1%0.5540.6020.462
10%0.5170.5810.442
20%0.5030.5870.445
", + "image_path": "67f2af19e7b55a778dcc1f2471ff386086481ff5cf170d5ec96139dc2ff58661.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 364, + 229, + 545, + 292 + ], + "blocks": [ + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "lines": [ + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "spans": [ + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "text", + "content": "Table 4. Results with different pruning portions. The metric achieves better results with pruning portion to be " + }, + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "text", + "content": ". We use pruning portion as " + }, + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 203, + 290, + 361, + 335 + ], + "type": "text", + "content": " in our design." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 364, + 229, + 545, + 292 + ], + "lines": [ + { + "bbox": [ + 364, + 229, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 364, + 229, + 545, + 292 + ], + "type": "table", + "html": "
ModulesPLCC ↑SROCC ↑KROCC ↑
Topology Laplacian [11]0.2980.3270.235
Cotan formula [25]0.4170.4700.340
Energy difference0.2680.3150.215
w/o normalization0.2570.5070.353
Spatial normalization0.2690.5420.392
Ours0.5670.5980.445
", + "image_path": "af379534d24203931fd62f1918ca418f84307bd4df67327d6a861ee17accb833.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 364, + 300, + 546, + 334 + ], + "lines": [ + { + "bbox": [ + 364, + 300, + 546, + 334 + ], + "spans": [ + { + "bbox": [ + 364, + 300, + 546, + 334 + ], + "type": "text", + "content": "Table 5. Module replacement. We replace each module of our metric with alternative designs to verify the design of each module." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 67, + 355, + 270, + 449 + ], + "blocks": [ + { + "bbox": [ + 67, + 355, + 270, + 449 + ], + "lines": [ + { + "bbox": [ + 67, + 355, + 270, + 449 + ], + "spans": [ + { + "bbox": [ + 67, + 355, + 270, + 449 + ], + "type": "image", + "image_path": "8c0e1e1821ca17bc722cd5a69ba37fd3fd3646a8f76fe2e4d9cb56548f171769.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 457, + 288, + 513 + ], + "lines": [ + { + "bbox": [ + 46, + 457, + 288, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 288, + 513 + ], + "type": "text", + "content": "Figure 8. We Adapt SAUCD into a loss function and use it in monocular-image-based 3D hand reconstruction. From left to right: input images, reconstruction result w/o SAUCD loss, reconstruction result w/ SAUCD loss, and ground truth mesh. We can see that the enhancement of SAUCD loss in mesh details is clearly noticeable." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 533, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 557 + ], + "type": "text", + "content": "mesh comparison. In contrast, our revised formula yields smooth low-frequency components without these artifacts." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "text", + "content": "Noise pruning portion. Tab. 4 shows our SAUCD metric performance by changing the noise pruning portion (Sec. 3.3). The metric achieves better results when the pruning portion is " + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "text", + "content": ". In our proposed metric, we choose the pruning portion to be " + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "inline_equation", + "content": "0.1\\%" + }, + { + "bbox": [ + 46, + 558, + 288, + 629 + ], + "type": "text", + "content": " to best avoid possible high-frequency information loss." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": "Module replacement. Tab. 5 shows our SAUCD metric performance by replacing some modules with alternative designs. First, we replace our revision of the discrete Laplace-Beltrami operator in Eq. (4) with topology Laplacian matrix in [11] and \"Cotan formula\" in [25]. Second, we change the AUC difference defined in Eq. (6) into the energy difference, which means changing " + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "inline_equation", + "content": "|\\hat{F}(\\lambda) - F_{gt}(\\lambda)|" + }, + { + "bbox": [ + 46, + 630, + 288, + 715 + ], + "type": "text", + "content": " in Eq. (6) into" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 356, + 547, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 356, + 547, + 429 + ], + "spans": [ + { + "bbox": [ + 304, + 356, + 547, + 429 + ], + "type": "inline_equation", + "content": "|\\hat{F}(\\lambda)^2 - F_{gt}(\\lambda)^2|" + }, + { + "bbox": [ + 304, + 356, + 547, + 429 + ], + "type": "text", + "content": ". In the third experiment, we replace AUC normalization (in Sec. 3.3) with spatial normalization, where we normalize the meshes by their maximum range along all 3 spatial axes. We also removed the AUC normalization module for another comparison. Our experiments show SAUCD has better performance than alternative designs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 430, + 547, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 547, + 513 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 547, + 513 + ], + "type": "text", + "content": "Adapting SAUCD to loss function. We adapted our metric into a loss function to enhance the visual quality of 3D mesh reconstructions, as evident from the hand reconstruction results in Fig. 8. Details on the experiment's implementation are available in Supplementary Materials Sec. 7. From this experiment, we can see that the enhancement of SAUCD loss in mesh details is clearly noticeable." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 514, + 547, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 514, + 547, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 514, + 547, + 550 + ], + "type": "text", + "content": "Visualized examples. We visualize examples in our dataset and their evaluation result using different metrics in Supplementary Materials Sec. 6." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 561, + 384, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 384, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 384, + 574 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "In order to propose a 3D shape evaluation that better aligns with human perception, we design an analytic metric named Spectrum AUC Difference (SAUCD). Our proposed SAUCD leverages mesh spectrum analysis to evaluate 3D shape that aligns with human evaluation, and its extended version Human-adjusted SAUCD further explores the sensitivity of human perception of each frequency band. To evaluate our new metrics, we build a user study dataset to compare our metrics with existing metrics. The results validate that both our new metrics are well aligned with human perceptions and outperform previous methods." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20162" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 20, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "type": "text", + "content": "[1] Gobotree - photos, cut-outs, 3d people. https://www.gobotree.com/." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 114, + 288, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 288, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 288, + 135 + ], + "type": "text", + "content": "[2] Sketchfab - the best 3d viewer on the web. https://sketchfab.com/." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 137, + 287, + 169 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 137, + 287, + 169 + ], + "spans": [ + { + "bbox": [ + 53, + 137, + 287, + 169 + ], + "type": "text", + "content": "[3] Panos Achlioptas, Olga Diamanti, Ioannis Mitliagkas, and Leonidas Guibas. 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Unsupervised 3d human mesh recovery from noisy point clouds. arXiv preprint arXiv:2107.07539, 2021." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20164" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Specularity Factorization for Low-Light Enhancement/f1d0299e-d664-4662-ab2f-1559d4f3b0a0_content_list.json b/2024/Specularity Factorization for Low-Light Enhancement/f1d0299e-d664-4662-ab2f-1559d4f3b0a0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..de14684633321a2687a8c02a1db8b73a46e39f61 --- /dev/null +++ b/2024/Specularity Factorization for Low-Light Enhancement/f1d0299e-d664-4662-ab2f-1559d4f3b0a0_content_list.json @@ -0,0 +1,1977 @@ +[ + { + "type": "text", + "text": "Specularity Factorization for Low-Light Enhancement", + "text_level": 1, + "bbox": [ + 207, + 130, + 759, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Saurabh Saini", + "bbox": [ + 310, + 181, + 424, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CVIT, KCIS", + "bbox": [ + 316, + 199, + 419, + 214 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "IIIT-Hyderabad, India", + "bbox": [ + 281, + 217, + 455, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "saurabh.saini@research.iit.ac.in", + "bbox": [ + 220, + 237, + 514, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "P J Narayanan", + "bbox": [ + 601, + 181, + 718, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "CVIT, KCIS", + "bbox": [ + 609, + 199, + 710, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "IIIT-Hyderabad, India", + "bbox": [ + 573, + 217, + 748, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "pjin@iiit.ac.in", + "bbox": [ + 594, + 237, + 720, + 250 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3bcd2373b54408ceec52e8f8c14def6058b0155cd9977a39c88cc7d778b015c3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 276, + 189, + 330 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e4d7666962218bffe8f583617bbcf3b95cfc55cf734fc1aa21a4f241e128bb21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 189, + 277, + 289, + 330 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0cf2e8dd49d54621cb672c1ad04cb5de0a5ff3b333c3ef92a47544d4a4aa6a61.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 290, + 277, + 388, + 330 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/03bc049edd905c46a34b7f1722939ca042217f7745dc7ab632277f8e3c4cf7fe.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 390, + 277, + 488, + 330 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cfd1fbed6aed75436089104a4790332b1ce3c351d48029bca69a9c646306959a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 277, + 589, + 330 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2bcba3876a3b74f3aaaa9edf676e0fd5860da4a17f93e0a31a3b775da07caf10.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 591, + 279, + 696, + 330 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5d56aece453457ab2ef5302613157fe199aa713d1d1123cff65d11316b5e0b38.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 337, + 202, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/614fda24059b29ce1809d0fe66d9146fbbea2d21384fbb57ec0a55ad4f93f926.jpg", + "image_caption": [ + "Figure 1. Sepcularity Factorization: We factorize a single input image (blue box, top row) into multiple soft specular factors (rescaled for visualization) based on their similar illumination characteristics (note table shadow and lamp reflection). Our factors directly enable zero-reference low-light enhancement and user controlled image relighting (bottom left). Additionally, they can also be used as a plug-and-play prior for various supervised image enhancement tasks like dehazing, deraining and deblurring. On right, our conceptual block diagram." + ], + "image_footnote": [], + "bbox": [ + 86, + 392, + 202, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5261b73b6dd45d5dd10311105207fbbeedfb67d01d777dedb7aa391d7b67844f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 204, + 337, + 323, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8ecb305ce4b8e242bc49f3b82a10ed598a139fa84cbdea19ce6420bbe1396bf5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 205, + 392, + 323, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4ddc2cd7c44d9b2917f4f7534f5f49b826a132e1308c0cbfcb2119f4c99d7fa7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 330, + 338, + 447, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a5ac2e2426631ef6065045aa00e8ad1a3483d8c847941cc883d85925be4cb40.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 330, + 392, + 449, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/495f45198e3be615596d664d7ea77586369a852c88938f3b7ec1f1b9cea9efd0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 450, + 338, + 571, + 391 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/90a9c9634e883617f0678dd8d579ff0bb313b5ab1669c74c5dcc99c8f3275a17.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 452, + 392, + 571, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/53c096b3b051bb8eb79d94bb0edf3709a6b219aa1d56bc7553594a1607210b72.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 573, + 338, + 692, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8d8f1ec5f7cd158dd5f7236e862656f1137e2be4648034d135110008c8a07270.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 573, + 391, + 692, + 446 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/9203037654e11cfb9c6d87ee30c7504c5fe4fc7e7378bddef7c2fee3c55085ea.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 728, + 273, + 888, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 532, + 312, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present a new additive image factorization technique that treats images to be composed of multiple latent specular components which can be simply estimated recursively by modulating the sparsity during decomposition. Our model-driven RSFNet estimates these factors by unrolling the optimization into network layers requiring only a few scalars to be learned. The resultant factors are interpretable by design and can be fused for different image enhancement tasks via a network or combined directly by the user in a controllable fashion. Based on RSFNet, we detail a zero-reference Low Light Enhancement (LLE) application trained without paired or unpaired supervision. Our system improves the state-of-the-art performance on standard benchmarks and achieves better generalization on multiple other datasets. We also integrate our factors with other task specific fusion networks for applications like de-earning, deblurring and dehazing with negligible overhead thereby highlighting the multi-domain and multi-task generalizability of our proposed RSFNet. The code and data is released for reproducibility on the project homepage1.", + "bbox": [ + 75, + 565, + 470, + 868 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 532, + 630, + 547 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A low-light image has most regions too dark for comprehension due to low exposure setting or insufficient scene lighting which makes images highly challenging for computer processing and aesthetically unpleasant. Low-Light Enhancement (LLE) aims to recovers a well-exposed image from a low-light input [46]. LLE can be a critical pre-processing step before the downstream applications [55, 57]. Core LLE challenge lies in modeling the degradation function which is spatially varying and has complex dependence on multiple variables like color, camera sensitivity, illuminant spectra, scene geometry, etc.", + "bbox": [ + 496, + 561, + 890, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most LLE solutions decompose the image into meaningful latent factors based on a relevant optical property (Tab. 1). This allows individual manipulation of each factor which simplifies the enhancement operation. A common factorization is based on the Retinex approximation [39, 58], which assumes a multiplicative disentangle-ment of image $I$ into two intrinsic factors: illumination-invariant, piecewise constant reflectance $R$ and color-invariant, smooth shading $S$ as $I = R\\cdot S$ . Other factorization criteria include frequency [35, 89], spatial scale [3, 50], spatio-frequency representation [18, 67], intensity", + "bbox": [ + 496, + 734, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://sophont01.github.io/data/projects/RSFNet/", + "bbox": [ + 94, + 886, + 439, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1", + "bbox": [ + 493, + 946, + 501, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "[33], reflectance rank [69, 76], etc. Fixed number of factors [35, 69, 87] and variable number that allow better representation [3, 33, 50] have been used. Some decompose image multiplicatively like Retinex [35, 87], while others split into additive factors which are numerically more stable [21, 32, 67]. Pixel segmentation could be soft or hard based on the membership across factors, with the former introducing fewer artifacts [4]. LLE solutions can be global or local. Global methods use whole image level statistics like gamma [27], histograms [96], etc., to enhance the images. Local methods employ spatially varying features like illumination maps [87], intensity/segmentation masks [33, 63], etc., for the same. Global methods are simpler but local ones can capture scene semantics better.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional LLE methods used manually-designed model-based optimisation by deriving specific priors from the image itself [23, 29, 100], needing no training. Data-driven, machine learning based solutions have done better recently. They use training datasets to tune the model which generalizes to other images [3, 87, 90]. Supervised methods require annotated input-output pairs of images [88, 90, 102]. Unsupervised methods require annotated training data but not necessarily paired [36, 91]. Zero-reference methods do not need annotated data and approach the problem by explicitly encoding the domain knowledge from training images [27, 57, 72]. They generalize better and are simpler, lighter, and more interpretable by design.", + "bbox": [ + 75, + 304, + 472, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we present a zero-reference LLE method that outperforms prior methods on the average. At core is a novel Recursive Specularity Factorization (RSF) of the image factorization based on image specularity. We decompose an image into additive specular factors by thresholding the amount of sparsity of each pixel recursively. Successive factor differences mark out newly discovered image regions which are then individually targeted for enhancement. Our RSFNet that computes the factorization is model-driven, task-agnostic, and light-weight, needing about 200 trainable parameters. The image factors are fused using a task-specific UNet-based module to enhance each region appropriately. RSF is useful to other applications when combined with other task-specific fusion modules. Our main contributions are:", + "bbox": [ + 75, + 505, + 472, + 731 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel image factorization criterion and optimization formulation based on recursive specularity estimation.", + "- A model-driven RSFNet to learn factorization thresholds in a data-driven fashion using algorithm unrolling.", + "- A simple and flexible zero-reference LLE solution that surpasses the state of the art on multiple benchmarks and in the average generalization performance.", + "- Demonstration of RSF's usability to tasks like dehazing, deraining, and deblurring. RSF has high potential as a structural prior for several image understanding and enhancement tasks." + ], + "bbox": [ + 76, + 734, + 468, + 898 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/898210056ff1ee594f92d5f3b90c770f1b991677430e18a87eaea710875b73a7.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Various LLE factorization criteria, with number of components (var. implies variable), type of factorization (+ additive/\\* multiplicative), types of output maps (local/global), pixel segmentation across maps (soft/hard) and corresponding exemplar methods. Our RSFNet proposes a novel specularity based factorization which allows a variable number of local soft-segmented factors." + ], + "table_body": "
CriteriaNo.TypeMapSegExample
Retinex2*globalsoft[72, 88]
Frequency2+, low/highglobalhard[89]
Spectral2*, fourierglobalsoft[35]
Low Rank2+globalsoft[69, 76]
Wavelets2n+, pyramidglobalsoft[18, 67]
Multiscale2n+, pyramidglobalsoft[3, 50]
Glare/Shadow3, 4*, +localhard[5, 78]
Intensityvar.+, bandslocalhard[32, 33]
Specularityvar.+localsoftRSFNet
", + "bbox": [ + 517, + 89, + 874, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 500, + 311, + 627, + 329 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-based LLE: Early LLE solutions used traditional optimization models using either global statistics [15, 43, 66, 70] or spatially varying illumination maps for local editing [22, 29, 85, 99]. They were more interpretable but required hand-crafted algorithms and heuristics.", + "bbox": [ + 496, + 337, + 890, + 412 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Data-driven LLE: Modern solutions take inspiration from traditional techniques and induce domain knowledge via loss terms or designed within the network architecture which are learned from large datasets in a data-driven fashion. They belong to one of the five training paradigms [46]. Supervised LLE methods require both low-light and well-lit paired images like Sharma and Tan [78], Wei et al. [87], Xu et al. [90], Yang et al. [95], Zhang et al. [103]. On the other hand, unsupervised methods like Jiang et al. [36], Ni et al. [64], Zhang et al. [96], require only unpaired low-light and well-lit image sets. Semi-supervised methods combine the previous two techniques and use both paired and unpaired annotations [73, 94]. Self-supervised solutions [48, 63] generate their own annotations using pseudo-labels or synthetic degradations. Contrary to all of these, zero-reference methods do not use ground truth reconstruction losses and assess the quality of output based upon encoded prior terms [27, 47, 57, 72, 98, 107]. These methods, like ours, possess improved generalizability due to explicit induction of domain knowledge and reduced chances of overfitting [27]. Zero-reference insights also provide direct valuable additions to the subsequent solutions in other paradigms.", + "bbox": [ + 496, + 415, + 892, + 748 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Model-Driven Networks: Data-driven solutions have good performance but lack interpretability, whereas model-based methods are explainable by design but often compromise with lower performance. Model-driven networks [61] are hybrids which bring the best of both together. Such networks unroll optimization steps as differentiable layers with learnable parameters, inducing data-driven priors in place of hand-crafted heuristics. Although data-driven solutions are plenty, only a few model-driven solutions exist for low-level vision tasks like image restoration [40, 41], shadow re", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "2", + "bbox": [ + 493, + 945, + 504, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/355f7c3923a3603e26949f43576930b86f182ecada5ac837d4e12e51be0d1751.jpg", + "image_caption": [ + "Figure 2. Categorization and Motivation: Left shows categorization of various LLE solution types (Sec. 2). Middle plot shows the relationship between five factor cluster centers w.r.t each other and the background comprising of shadow/non-shadow regions estimated using PCA dimensionality reduced DINO features [14]. Gradual progression of feature cluster centers from highlight region to shadow region indicates their capability to capture various illumination regions in an image. Top right shows one data point from CHUK dataset [34] with mask, processed shadow/highlight regions and extracted factors. Bottom right plots distinguish our specular fuzzy factors from intensity thresholding based binary division, with ours allowing more diverse distributions and richer representation." + ], + "image_footnote": [], + "bbox": [ + 81, + 92, + 356, + 242 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b4accd8fd4d71c18d75c5b7f7a40764205d461eab6191c8a71a7380bd372eb91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 357, + 93, + 630, + 244 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f59a79de1cf21e15deb2d46eeee35edb6811800378fcc3614f2388f70ffe6d20.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 630, + 93, + 888, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "moyal [108], dehazing [54], deraining [83], denoising [68] and super-resolution [7, 8]. Such solutions are concise and efficient due to underlying task specific formulation.", + "bbox": [ + 75, + 357, + 468, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Model-driven LLE solutions are very recent. UretinexNet [88] and UTVNet [104] are both supervised methods which respectively unroll the Retinex and total variational LLE formulations. RUAS [72] and SCI [57] are closest to our approach as they both propose model-driven zero-reference LLE solutions. RUAS [72] unrrolls illumination estimation and noise removal steps in their optimization and compliment it with learnable architecture search, towards a dynamic LLE framework. SCI [57] on the other hand propose a residual framework wherein reflectance estimation is done by a self-calibration module which is then used to iteratively refine illumination maps. In contrast, our method is inspired directly by image formation fundamentals and presents a novel factorization criterion which provides better interpretability, performance and flexibility.", + "bbox": [ + 75, + 405, + 470, + 632 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Retinex Factorization for LLE: Retinex [39, 58] is the most widely used factorization strategy for LLE [46, 72, 75, 87, 88] and beyond [9, 25, 74, 77]. One major Retinex limitation is due to the Lambertian reflection [38] assumption which approximates all surfaces as diffuse, thereby ignoring prevalent non-Lambertian effects in a real scene like specularity, translucency, caustics etc. Another issue is that pixelwise multiplicative nature of Retinex factors is cumbersome to handle numerically (especially in LLE with near zero pixel values) and the obtained illumination maps require further semantic analysis for downstream applications. Extensions of Retinex like dichromatic model [81] and shadow segmentation [5], separate one extra component each in addition to diffuse $R$ and $S$ e.g. Sharma and Tan [78] and Baslamisli et al. [5] used glare and shadow image decomposition respectively. From this perspective our recursive specular factorization can be understood as an extension of", + "bbox": [ + 75, + 643, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the same idea with continuously varying illumination characteristics starting from bright glares and ending with dark shadows (see Fig. 2 and Sec. 3 for details).", + "bbox": [ + 498, + 357, + 890, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Others Factorization Strategies: Apart from Retinex, other factorization techniques are listed in Tab. 1. Afifi et al. [3], Lim and Kim [50], Mertens et al. [59], Xu et al. [89] employ spatial or frequency based image decomposition. Recently, Yang et al. [94] used recursively concatenated features from a supervised encoder and Huang et al. [35] proposed a Fourier disentanglement based solution. Apart from these supervised factorizations, Zheng and Gupta [106] proposed semantic classification based ROI identification using a pretrained segmentation network. [27, 63] predict multiple gamma correction maps for enhancement. [32, 33] simulate single image exposure burst using piece-wise thresholded intensity functions whereas [69] uses low-rank decomposition for reflectance. Each factorization strategy harnesses crucial underlying optical observations and adds valuable insights to the low-level vision research. To the best of our knowledge, our proposed method here is the first to use recursive specularity estimation as a factorization strategy for LLE and other enhancement tasks.", + "bbox": [ + 496, + 415, + 892, + 702 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 722, + 609, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Outline: Our entire pipeline consists of two parts. We first decompose the image into $K$ factors using our Recursive Specularity Factorization Network (RSFNet), which consists of multiple factorization modules (FM) with each optimization step encoded as a differentiable network layer. Then we fuse, enhance, and denoise the factors using a fusion network, which is built using task dependent pre-existing architectures. This modular design allows easy adoption of our technique in several other tasks and learning paradigms (Sec. 4).", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "3", + "bbox": [ + 493, + 945, + 503, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8f5f4938fff2d8e5ec972e2105be4219573284994e1b6923b37ace949a57d55d.jpg", + "image_caption": [ + "Figure 3. Block Diagram: Our factorization module (RSFNet) splits a given image into multiple specular components using model-driven unrolled optimization. Then fusion module combines all the factors to generate the enhanced output." + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 883, + 281 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Factorization Network: RSFNet", + "text_level": 1, + "bbox": [ + 76, + 327, + 359, + 343 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specularity Estimation: Specularity removal is a well studied problem. Most specularity removal methods [1, 28, 79] exploit the relative sparsity of specular highlights and use pre-defined fixed sparsity thresholds to isolate the specular component. According to dichromatic reflection model [81] image consists of a diffuse $\\mathbf{A}$ and a specular $\\mathbf{E}$ term: $\\mathbf{X} = \\mathbf{A} + \\mathbf{E}$ for input $X$ where specular component can be estimated by minimizing the $L_{0}$ norm approximated as:", + "bbox": [ + 75, + 349, + 468, + 472 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\mathbf {E}, \\mathbf {A}} {\\operatorname {a r g m i n}} \\| \\mathbf {A} \\| _ {*} + \\lambda \\| \\mathbf {E} \\| _ {1} \\quad \\text {s . t .} \\mathbf {X} = \\mathbf {A} + \\mathbf {E}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 135, + 482, + 468, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $L_{1}$ is relaxation of $L_{0}$ , $*$ is Frobenius norm regularizer and $\\lambda$ is the sparsity parameter with higher values encouraging sparser results. Eq. (1) can be restated as augmented Lagrangian [10] using dual form and auxiliary parameters $(\\mathbf{Y},\\mu)$ , which are then solvable using iterative ADMM updates $(t\\in [0,T])$ [11] as given below:", + "bbox": [ + 75, + 515, + 468, + 606 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} _ {t + 1} = \\delta_ {\\alpha_ {t}} ^ {1} \\left(\\mathbf {X} - \\mathbf {A} _ {t} - \\mathbf {Y} _ {t} ^ {T} / \\mu_ {t}\\right) \\quad \\text {w h e r e} \\alpha : \\mathcal {F} (\\lambda , \\mu),\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 614, + 457, + 633 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {A} _ {t + 1} = \\delta_ {\\beta_ {t}} ^ {*} \\left(\\mathbf {X} - \\mathbf {E} _ {t + 1} - \\mathbf {Y} _ {t} ^ {T} / \\mu_ {t}\\right) \\quad \\text {w h e r e} \\beta : \\mathcal {F} (\\mu),\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 635, + 457, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} _ {t + 1} = \\mathbf {Y} _ {t} + \\mu_ {t} \\left(\\mathbf {A} _ {t + 1} + \\mathbf {E} _ {t + 1} - \\mathbf {X}\\right) \\quad \\text {w h e r e} \\mu : \\mathcal {F} (\\mathbf {X}). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 654, + 467, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here $\\delta_{\\alpha}^{p}$ is element-wise soft-thresholding operator [65]:", + "bbox": [ + 76, + 681, + 449, + 698 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {\\alpha} ^ {p} (x) = \\max \\left(1 - \\alpha / | x | _ {p}, 0\\right) \\cdot x.\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 705, + 385, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can back-propagate through updates in Eq. (2) [88, 104] and hence can unroll them as neural network layers with learnable parameters $\\alpha : \\{\\alpha\\}_0^T, \\beta : \\{\\beta\\}_0^T$ and $\\pmb{\\mu} : \\{\\pmb{\\mu}\\}_0^T$ .", + "bbox": [ + 75, + 733, + 467, + 781 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Relation with ISTA: Analyzing the structure of Eq. (2), we can draw parallels with the ISTA problem [17], which seeks a sparse solution to $\\mathbf{E}$ for the condition $\\mathbf{X} = \\mathcal{G}\\mathbf{E} + \\epsilon$ , with $\\mathcal{G}$ as a learnable dictionary and negligible $\\epsilon$ . In contrast, we have a non-negligible residue and identity dictionary. LISTA by Gregor and LeCun [26] showed how $\\mathbf{E}$ update step can be represented as a weighted function which can", + "bbox": [ + 75, + 794, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "then be approximated as finite network layers i.e.:", + "bbox": [ + 500, + 328, + 830, + 343 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {E} _ {t + 1} = \\delta_ {\\alpha_ {t}} \\left(\\mathbf {w} _ {t} ^ {1} \\mathbf {E} _ {t} + \\mathbf {w} _ {t} ^ {2} \\mathbf {X}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 351, + 890, + 368 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with learnable parameters $(\\alpha_{t},\\mathbf{w}_{t}^{1},\\mathbf{w}_{t}^{2})$ for each iteration $t\\in [0,T]$ . Based on the weight coupling between $\\mathbf{w}^1$ and $\\mathbf{w}^2$ , Chen et al. [16] simplified Eq. (3) by deriving both $\\mathbf{w}^1$ and $\\mathbf{w}^2$ from a single weight term, thereby halving the computation cost. A major simplification was further proposed by Liu et al. [51] as ALISTA, who proved how all weight terms could be analytically obtained for a known dictionary, thereby leaving only step sizes and thresholds i.e. $\\mu$ and $\\alpha_{t}$ to be estimated. Later on this idea was extended to other similar optimization formulations and improved upon by additional simplifications and guarantees e.g. Cai et al. [12] unrolled their ADMM updates into a network for robust principal component analysis.", + "bbox": [ + 496, + 377, + 892, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Recursive Factorization: Drawing parallels from ALISTA [51] and its applications [12], we propose to learn the analytically reduced sparsity thresholds and step sizes via unrolled network layers. After optimizing the above mentioned objective Eq. (1) we obtain one specular factor $\\mathbf{E}^k$ where index $k\\in [1,K]$ indicates the factor number. For multiple factors, we recursively solve Eq. (1) by resetting the input $X$ after removing the previous specular output and relaxing the initial sparsity weight. We initialize variables for each factor at $t = 0$ as:", + "bbox": [ + 496, + 589, + 890, + 739 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} ^ {k + 1} = \\mathbf {X} ^ {k} - \\mathbf {E} ^ {k}, \\quad \\mathbf {Y} ^ {k} = \\mathbf {X} ^ {k} / \\| \\mathbf {X} ^ {k} \\| _ {2} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 746, + 890, + 773 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha^ {k} = (1 - \\nu^ {k}) \\hat {X} ^ {k}, \\quad \\beta^ {k} = \\nu^ {k} \\hat {X} ^ {k}, \\quad \\nu^ {k} = k / K,\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 768, + 852, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{X}$ indicates input mean and $\\mathbf{X}^0 = \\mathbf{I}$ . Intuitively, this can be understood as progressively removing specularity $(E^{k})$ from the original image by gradually relaxing the sparsity weight $(\\alpha^{k + 1} < \\alpha^{k})$ . This lets us split the original image into multiple additive factors as:", + "bbox": [ + 496, + 799, + 890, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} = \\mathbf {E} ^ {1} + \\mathbf {E} ^ {2} + \\dots + \\mathbf {E} ^ {K} = \\sum_ {k = 1} ^ {K} \\mathbf {E} ^ {k} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4", + "bbox": [ + 493, + 946, + 503, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Unrolling: Based upon above discussion, we propose an unrolled network collecting all parameters in a single vector $\\pmb{\\theta}$ . In each iteration $t$ , we estimate three scalars: thresholds for both components $(\\alpha_{t},\\beta_{t})$ and the step size $(\\mu_t)$ . Hence for a factor $k$ , we have $3T$ parameters $\\pmb{\\theta}^{k} := (\\alpha^{k},\\beta^{k},\\mu^{k})$ and overall we have only $3KT$ parameters $\\pmb{\\theta} := \\{\\pmb{\\theta}_{1}^{k}\\}_{1}^{K}$ . Hence our model-driven factorization module is extremely light-weight compared to other decompositions (Tab. 2). We propose the following novel factorization loss:", + "bbox": [ + 76, + 106, + 472, + 243 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {f} = \\lambda_ {f} \\sum_ {k = 1} ^ {K} L _ {f} ^ {k} \\quad \\text {w h e r e} \\quad L _ {f} ^ {k} = \\left| \\hat {E} ^ {k} / \\hat {X} ^ {k} - \\nu^ {k} \\right|. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 250, + 470, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This constraints the ratio of signal energy in the $k^{th}$ factor compared to the input, to $\\nu^k$ . As $\\nu^k$ increases for higher factors, our factorization loss relaxes the sparsity constraint, thereby gradually increasing the number of pixels in the specular component. After training, we are left with $K$ specular factors which sum to $I$ . As shown in Fig. 1 and Fig. 2, each one of these factors highlights specific image regions with similar illumination characteristics which can be individually targeted for enhancement.", + "bbox": [ + 75, + 296, + 470, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motivation/Validation: The core assumption behind our factorization is that an image can be split into multiple specular factors with each representing specific illumination characteristic. Although such factorization quality assessment is difficult to estimate [9, 25, 30], we performed a toy experiment to validate our hypothesis using shadow detection dataset [34] which contains binary shadow masks in complex real world images (Fig. 2). We extract semantics-rich DINO image features [14] after masking shadow and non-shadow image regions and visualize them in 2D using PCA. This marks separation of feature space between shadowed and highlighted regions in the background. The regions with progressively degrading illumination characteristics (glare, direct light, indirect light, soft shadow, dark shadow, etc.) are expected to gradually lie between the two extremes. Next we factorize each image into five factors using our approach and plot the cluster mean for each factor feature distribution on the same graph. We can observe in Fig. 2 that successive factors gradually shift from the nonshadow towards the shadowed feature space region mirroring the expected illumination order. This confirms that our factorization decomposes the pixel values across fundamental illumination types like glare, direct light, indirect light, shadow, etc.", + "bbox": [ + 75, + 446, + 468, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also plot the respective factor distribution densities of intensity factorization [32, 33] and our specularity factorization (Fig. 2, bottom right). Intensity factorization allows little variation in the underlying factor distributions and imposes hard segmentation constraints with binary pixel masks. Our specular factors, on the other hand, permit", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: LLE Training" + ], + "code_body": "Input: Lowlight:I; Hyperparams: $\\lambda_{c|e|s}, K, T$ \nOutput: Enhanced: O; Params: $\\theta = \\{\\alpha\\}_{0}^{K}, \\{\\beta\\}_{0}^{K}, \\{\\mu\\}_{0}^{K}$ \nfor $e \\gets 0$ to num of epochs do \n// Train Factorization Module \nfor $k \\gets 0$ to $K$ do \nfor $t \\gets 0$ to $T$ do \nInitialize $E_0^k, A_0^k, Y_0^k$ ; // Eqn. 4 \n $E_t, A_t, Y_t \\gets$ ADMM updates; // Eqn. 2 \nend \n $F^k \\gets E^k - E^{k-1}$ ; // Eqn. 7 \nend \nCompute $L_f$ ; // Eqn. 6 \n// Train Fusion Module \nif $e >$ freeze epoch then \nFreeze all $\\alpha, \\beta, \\mu$ ; \n $L_f \\gets 0$ ; \nend \n $I_{fuse} \\gets$ Concatenate $[I, F^1, ..., F^K]$ ; \n $O \\gets$ Forward $(I_{fuse})$ ; \nCompute $L$ ; // Eqn. 9 \nBackpropagate $L$ ; \nend", + "bbox": [ + 506, + 109, + 890, + 362 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "higher variability and soft masks, with each pixel value spread across multiple factors. This provides more flexible representation and better optical approximation.", + "bbox": [ + 496, + 387, + 890, + 431 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Fusion Network", + "text_level": 1, + "bbox": [ + 500, + 434, + 660, + 449 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to adhere to the zero-reference paradigm, we choose our fusion module to be a small fully-convolutional UNet like architecture with symmetric skip connections similar to other zero-reference methods [27, 63, 106]. One fundamental difference is that we modify the architecture to harness multiple factors and simultaneously perform fusion, enhancement and denoising. Specifically, it comprises of seven $3 \\times 3$ convolutional layers with symmetric skip connections. We first pre-process all of our factors by subtracting the adjacent factors to discover the additional pixel values allowed in the current factor compared to the previous one as a soft mask:", + "bbox": [ + 496, + 457, + 890, + 636 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {F} ^ {k} = \\mathbf {E} ^ {k} - \\mathbf {E} ^ {k - 1} \\text {w h e r e} \\mathbf {F} ^ {1} = \\mathbf {E} ^ {1}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 641, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "These factors are weighted if required using fixed scalar values and are then passed as a concatenated tensor into the fusion network. The output gamma maps $\\mathbf{R}^k$ rescale different image regions differently and are applied directly on the original image inside the curve adjustment equation [27] for the fused result:", + "bbox": [ + 496, + 662, + 890, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nO = \\Phi \\left(\\sum_ {k = 0} ^ {K} I + R ^ {k}. \\left((I) ^ {2} - I\\right)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 756, + 890, + 792 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The fused output is finally passed through a differentiable bilateral filtering layer $\\Phi$ [71] for the final enhanced result $O$ . Note that all the parameters from both factorization and fusion networks are trained together in end-to-end manner.", + "bbox": [ + 496, + 797, + 890, + 856 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Loss Terms: We use two widely employed zero-reference losses for enhancement [27, 63, 96] and one image smoothing loss for denoising. First color loss $L_{c}$ [27, 96] is based", + "bbox": [ + 496, + 857, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5", + "bbox": [ + 493, + 945, + 503, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/77557ad2d6b1d7fbfe830c1bee7e67bcad48a9a28115e4dd456540147af89201.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ParadigmTraditional Model BasedZero-reference
MethodLIME [29]DUAL [100]SDD [31]ECNet [98]ZDCE [27]ZD++ [47]RUAS [72]SCI [57]PNet [63]GDP [20]RSFNet (Ours) 2.11
Params x103---16.5x10379.4210.563.430.2615.25552x103
Lolv1 [87] (dataset split: 485/15, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑16.2015.9715.1418.0116.7616.3818.4516.4519.8517.6822.17
SSIMy↑0.6950.6920.7540.6440.7340.6450.7660.7090.7180.6780.860
PSNRc↑14.2214.0213.3415.8114.8614.7416.4014.7817.5015.8019.39
SSIMc↑0.5210.5190.6340.4690.5620.4960.5030.5250.5500.5390.755
NIQE↓8.5838.6113.7068.8448.2238.1955.9278.3748.6296.4373.129
LPIPS↓0.3440.3460.2780.3580.3310.3460.3030.3270.3400.3750.265
Lolv2-real [95] (dataset split: 689/100, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑19.3119.1018.4718.8620.3119.3617.4919.3720.0815.8321.46
SSIMy↑0.7050.7040.7920.6130.7450.5850.7420.7220.6910.6270.836
PSNRc↑17.1416.9516.6416.2718.0617.3615.3317.3017.6314.0519.27
SSIMc↑0.5370.5350.6780.4590.5800.4420.4930.5400.5390.5020.738
NIQE↓9.0769.0834.1919.4754.1918.7096.1728.7399.1526.8673.769
LPIPS↓0.3220.3240.2800.3600.3100.3400.3250.2940.3400.3900.280
GENERALIZED PERFORMANCE Mean Scores (Lolv1 [87], Lolv2-real [95], Lolv2-syn [95] and VE-Lol [52])
PSNRy↑18.5017.8317.5018.4519.2618.7317.0918.0719.6515.8821.16
SSIMy↑0.7370.7280.7810.6770.7770.6740.7430.7450.7430.6340.854
PSNRc↑16.5315.8815.7716.2517.1916.7615.1216.2017.3514.1518.45
SSIMc↑0.5960.5830.6790.5380.6340.5480.5320.5870.6050.5040.758
NIQE↓7.8557.4784.0777.5434.2707.4685.8417.6267.7916.7263.763
LPIPS↓0.2910.2970.2660.3290.2730.2960.3460.2950.3020.3790.276
", + "bbox": [ + 76, + 89, + 890, + 405 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison of our method RSFNet with other traditional and zero-reference solutions on multiple lowlight benchmarks and six evaluation metrics. Shown here are scores for two datasets LOLv1 and LOLv2-real with mean value across all datasets in the last sub-table (key: ↑ higher better; ↓ lower better; bold: best; underline: second best).", + "bbox": [ + 75, + 410, + 892, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "on the gray-world assumption which tries to minimize the mean value difference between each color channel pair:", + "bbox": [ + 75, + 472, + 468, + 502 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {c} = \\sum_ {(i, j) \\in C} \\left(\\hat {O} ^ {i} - \\hat {O} ^ {j}\\right) ^ {2}, \\quad C \\in \\{(r, g), (g, b), (b, r) \\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 510, + 454, + 546 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Second is the exposure loss $L_{e}$ [27, 33, 59], which penalizes grayscale intensity deviation from the mid-tone value:", + "bbox": [ + 76, + 553, + 468, + 583 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {e} = \\frac {1}{| \\Omega |} \\sum_ {\\Omega} \\left(\\phi (O) - 0. 6\\right) ^ {2} \\text {w h e r e} \\Omega \\in \\{c \\times h \\times w \\},\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 590, + 460, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\phi$ represents the average value over a $16\\times 16$ window. Our third loss is the pixel-wise smoothing loss which controls the local gradients $\\nabla_{x|y}$ in the final output:", + "bbox": [ + 75, + 635, + 468, + 681 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s} = \\frac {1}{| \\Omega |} \\sum_ {\\Omega} \\left((\\nabla_ {x} O) ^ {2} + (\\nabla_ {y} O) ^ {2}\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 690, + 397, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Note that this differs from the previous works who focus on total variational loss of the gamma maps instead. Our final training loss with $\\lambda$ 's as respective loss weights, is given as:", + "bbox": [ + 75, + 734, + 468, + 779 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = \\lambda_ {f} L _ {f} + \\lambda_ {c} L _ {c} + \\lambda_ {e} L _ {e} + \\lambda_ {s} L _ {s}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 794, + 468, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments and Results", + "text_level": 1, + "bbox": [ + 76, + 829, + 310, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We now report our implementation details, results and extensions. Please see the supplementary document for additional details and results.", + "bbox": [ + 75, + 854, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Setup: We implement our combined network end-to-end on a single Nvidia 1080Ti GPU in PyTorch. We directly use low-light RGB images as inputs without any additional pre-processing. We first train factorization module for 25 epochs which we freeze and then optimize the fusion module for next 25 epochs. We use stochastic gradient descent for optimization with batch size of 10 and 0.01 as learning rate. Model hyper-parameters are fixed using grid search and the entire training take less than 30 minutes.", + "bbox": [ + 496, + 472, + 892, + 607 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: We evaluate our method using multiple LLE benchmark datasets (Lolv1 [87], Lolv2-real [95], Lolv2-synthetic [95] and VE-Lol [52]) with standard train/test splits (Tab. 2). These datasets comprise of several underexposed small-aperture inputs and corresponding well-exposed ground-truth pairs. Here we report results on two datasets: Lolv1 and Lolv2-real and finally show the mean scores on all four datasets combined in the last sub-table Tab. 2 and in Fig. 5. Furthermore, we report generalization results (Tab. 4) on five additional no-reference datasets which have significant domain shift: DICM [42], LIME [29], MEF [56], NPE [85] and VV [82].", + "bbox": [ + 496, + 608, + 892, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics: We report both single channel (Y from YCbCr) and multichannel (RGB) performance scores. As full-reference metrics (which require ground truth), we use Peak Signal to Noise-Ratio (PSNR), Structural Similarity Index Metric (SSIM) [86] and Learned Perceptual Image Patch Similarity (LPIPS) [101]. For no-reference assessment (without ground truth), we report Naturalness Image", + "bbox": [ + 496, + 789, + 893, + 895 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6", + "bbox": [ + 493, + 946, + 504, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/443db8f9dfbe3fdfb3ba7f2516dc4e85c72bb2813f97bca15982430cf54ce999.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
VariantsPSNRy↑SSIMy↑
w/o Le8.120.238
w/o Lc16.050.724
w/o Ls20.130.846
w/o Denoise19.510.756
w/o Fusion19.320.830
Full22.170.860
", + "bbox": [ + 78, + 89, + 277, + 202 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/68e307f5dc6e9600870bce03362f94b0f0ed9d7f325d4574d1a9646d8091188e.jpg", + "table_caption": [ + "Table 3. Ablation analysis on five variants of our RSFNet (Sec. 4)." + ], + "table_footnote": [], + "table_body": "
NIQE↓& LOE↓ECNet[98]ZDCE[27]ZD++[47]RUAS[72]PNet[63]SCI[57]RSFNet(Ours)
DICM [42]3.37—676.73.10—340.82.94—511.94.89—14213.00—590.33.61—321.93.23—303.1
LIME [29]3.75—685.13.79—135.03.89—332.24.26—719.93.84—223.24.14—75.53.80—68.3
MEF [56]3.30—863.33.31—164.33.18—458.54.08—784.23.25—363.03.43—95.03.00—100.7
NPE [85]3.24—936.13.52—312.93.27—532.25.75—13993.29—601.13.89—239.83.31—221.5
VV [82]2.15—292.42.75—145.42.53—222.93.82—583.72.56—260.22.30—109.01.96—109.0
Mean3.16—690.73.29—219.73.16—411.54.56—981.73.19—407.53.47—168.23.06—160.5
", + "bbox": [ + 305, + 90, + 888, + 200 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Qualitative comparison using naturalness preserving metrics (NIQE $\\downarrow$ - LOE $\\downarrow$ ) on five no-reference benchmarks: DICM, LIME, MEF, NPE and VV (best scores in bold, lower is better).", + "bbox": [ + 302, + 207, + 890, + 234 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6f3f2ecd3fbf3e4a7e090995bf2e745f1d03e551a150ab3394832e0b1cdaec96.jpg", + "image_caption": [ + "Figure 4. Results: Qualitative comparison of our method (green box) with other solutions (from top left 3 per row: SDD [31], ECNet [98], ZDCE [27]; ZD++ [47], RUAS [72], SCI [57]; PNet [63], GDP [20] and our RSFNet respectively). Our method generate natural looking images by handling noisy over and under exposed regions equally well, without over-saturating color or losing geometric details." + ], + "image_footnote": [], + "bbox": [ + 81, + 244, + 472, + 426 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e6a3a81c319bfa7a1486025f481c94529e72a70a76a719664ea46f134484f289.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 244, + 890, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quality Evaluator (NIQE) [60] and Lightness Order Error [84]. Note while PSNR and SSIM gauge performance quantitatively, other three metrics estimate perceptual quality.", + "bbox": [ + 76, + 491, + 468, + 537 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparisons: We compare against three model-based traditional optimization methods: LIME [29], DUAL [100] and SDD [31] (others ignored due to low performance). For data-driven methods we use seven recent zero-reference methods (chronologically ordered): ECNet [98], zeroDCE [27], zeroDCE++ [47], RUAS [72], SCI [57], PNet [63] and GDP [20]. We use the official code releases with pre", + "bbox": [ + 75, + 555, + 468, + 662 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/072db56d1026000780da4289e5e52077f06ff399eb3fcc6f065d489cfb71bd0c.jpg", + "image_caption": [ + "Figure 5. Analysis: On left, our average score on all datasets vs. other methods (more area implies better). On right, ablation analysis with varying number of factors." + ], + "image_footnote": [], + "bbox": [ + 81, + 691, + 460, + 857 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "trained weights and default parameters for results generation. Quantitative and qualitative performance comparison is shown in Tab. 2 and Fig. 4 respectively. Qualitatively, our method is cleaner with fewer artifacts and natural illumination (Fig. 4). This is validated by perceptual metrics like NIQE, LPIPS and LOE scores (Tabs. 2 and 4). Our method outperforms other similar category contemporary solutions on multiple metrics and achieves the best generalization performance across datasets. For a generalized performance, we take mean of all the scores across benchmarks and graphically show them in the polar plot in Fig. 5. Each polygon represents a separate LLE method with higher area inside indicating better performance.", + "bbox": [ + 496, + 491, + 890, + 688 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Ablation: To validate our design choices, we conduct ablation study on several variants of our methods using Lolv1 dataset. The effect of different number of factors $K$ on the final PSNR and SSIM scores are shown on right in Fig. 5. We choose the best observed hyper-parameter settings $K = 5$ for all our experiments. The effect of various loss terms after removing them one at a time (i.e. $w / o \\, L_{e|c|s}$ ) and the effect of the final denoising step are shown in Tab. 3. The last variant ( $w / o \\, Fusion$ ) represents an especially interesting setting where the fusion network is totally removed and inference uses only $3KT$ ( $= 3*5*3 = 45$ ) parameters. Fusion now reduces to a running average of the current image and", + "bbox": [ + 496, + 719, + 892, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7", + "bbox": [ + 493, + 945, + 503, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/326e21e8e5245c447e47ffc2983b841a5e3604fbbc3a31d4c70093e4ef704e43.jpg", + "image_caption": [ + "Dehaze" + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 210, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/94f01a4201cb500d9c436c101e14dad4f0b5abbe1ddde64eb32aed66fe521eb5.jpg", + "image_caption": [ + "Figure 6. Image enhancement applications using our specular factors as inputs on the AirNet [45] base model. Shown here left-to-right are our results for Dehazing [44], Deraining [93] and Deblurring [62] tasks respectively using AirNet [45] as base model." + ], + "image_footnote": [], + "bbox": [ + 214, + 90, + 346, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1f9d394aa1b236e21c2093d6070277f04c7e7c8f490289832eb524f6917adda4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 346, + 90, + 419, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f35334201e7560555e5c111c91e078629773c751048ae55961768637e35311ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 90, + 550, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ed92c50423a8f729e30b91f5763f2c60dd745d81fa3b1f447c9d02e62b706ea4.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 552, + 90, + 620, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/25387027c000af3e8f612966ab3de6a189e4fcc7e79763719656b8828805e4e6.jpg", + "image_caption": [ + "Deblur" + ], + "image_footnote": [], + "bbox": [ + 622, + 90, + 756, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/db888638aaf6b7d8f59bafef303db038a906b0f6fb5f16a273860014e92f5530.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 759, + 90, + 888, + 229 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the next factor, weighted by the normalized mean:", + "bbox": [ + 76, + 291, + 406, + 306 + ], + "page_idx": 7 + }, + { + "type": "equation", + "text": "\n$$\nO ^ {k + 1} = \\left(1 - w ^ {k}\\right) O ^ {k} + w ^ {k} F ^ {k}, \\text {w h e r e} w ^ {k} = \\hat {F} ^ {k} / \\sum_ {k} \\hat {F} ^ {k}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 311, + 468, + 330 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Even without any other zero-reference losses and using only a simple linear fusion, this method performs well, which demonstrates the effectiveness of our factors. Note here we have an order of magnitude smaller network size than SCI (0.045 vs. 0.26 thousand parameters in Tab. 2).", + "bbox": [ + 75, + 335, + 468, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Extensions: Our specular factors are easily interpretable and can be used directly for image manipulation as image layers in standard image editing tools like GIMP [80], Photoshop [2], etc. We show an image relighting example by varying the color and blending modes of factors in (Fig. 1 bottom left, Fig. 7). This indicates the potential of our factorization to complex downstream applications. We explore three diverse image enhancement tasks: dehazing, deraining and deblurring. Here our goal is to evaluate the use of specularity factorization as a pre-processing step on an existing base model. We chose the recent AirNet [45] as it allows experimentation on multiple image enhancement tasks with minor backbone modification. To induce our factors as prior information, we concatenate them along with the original input and alter the first convolutional layer input channels. Note that we do not introduce any new loss or layers and directly train the model for three tasks one by one: (i) Dehazing on RESIDE dataset [44] (ii) Deraining on Rain100L dataset [93] and (iii) Deblurring on GoPro dataset", + "bbox": [ + 75, + 426, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/804bf4b34903aa1c1a28eeafc4241d32bb575cd51ec068a79863f7010ad0272a.jpg", + "image_caption": [ + "Figure 7. Controllable relighting applications using our factors as layers [80] (top:inputs; bottom:results; from left:edited light specularity, indoor color and outdoor intensity respectively)." + ], + "image_footnote": [], + "bbox": [ + 81, + 734, + 205, + 854 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/61b67e2c4be726bf3d60096aa0aabbca6da8ccbebc9f799364d5e3d896631c30.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 210, + 734, + 334, + 857 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/efbc81a37b3fbc7ffcdd241d869584b6af60a470a1dffc6de8e2956bc3a23241.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 343, + 734, + 467, + 857 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/697ea6dde19b6f085e3e366967eee0cef1c09b845ac16d22ab41d0dc190921b1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TASK →DEHAZE [44]DERAIN [93]DEBLUR [62]
MethodPSNRSSIMPSNRSSIMPSNRSSIM
AirNet (multi-task)21.040.88432.980.95124.350.781
AirNet (uni-task)23.180.90034.900.965726.420.801
AirNet + Ours24.960.929236.190.971827.290.827
", + "bbox": [ + 501, + 289, + 888, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Our factors can induce structure prior in an existing base model and improve performance for multiple enhancement tasks.", + "bbox": [ + 500, + 371, + 890, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "[62]. As seen in Fig. 6 and Tab. 5, our results are perceptually more pleasing and improve the previously reported scores from multi-task methods consistently [45, 97]. We believe this is due to the induction of structural prior in the form of illumination based region categorization as the intensity and order of illumination at a pixel depends on the scene structure. See the supplementary for more results.", + "bbox": [ + 498, + 422, + 890, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations: Our method is sensitive to initialization conditions like the underlying algorithms [12, 51]. As a heuristic we use dataset mean for initialization. Another idea, to be explored in future, is to dynamically adapt to each input which is expected to further increase the performance.", + "bbox": [ + 498, + 529, + 890, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: We acknowledge the support of TCS Foundation and the Kohli Centre on Intelligent Systems for this research.", + "bbox": [ + 498, + 613, + 890, + 657 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 667, + 625, + 681 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a recursive specularity factorization (RSF) and its application to zero-reference LLE. We learn optimization hyperparameters in a data-driven fashion by unrolling the stages into a small neural network. The factors are fused using a network to yield the final result. We also demonstrate the utility of RSFs for image relighting as well as for image enhancement tasks like dehazing, deraining and deblurring. We are exploring the extension of RSFs to applications like image harmonization, foreground matting, white-balancing, depth estimation, etc., and extend the technique to other signals beyond the visible spectrum.", + "bbox": [ + 496, + 693, + 890, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethical Concerns: This work enhances captured images and poses no special ethical issues we are aware of.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8", + "bbox": [ + 493, + 945, + 503, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Amir Adler, Michael Elad, Yacov Hel-Or, and Ehud Rivlin. 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Sepcularity Factorization: We factorize a single input image (blue box, top row) into multiple soft specular factors (rescaled for visualization) based on their similar illumination characteristics (note table shadow and lamp reflection). Our factors directly enable zero-reference low-light enhancement and user controlled image relighting (bottom left). Additionally, they can also be used as a plug-and-play prior for various supervised image enhancement tasks like dehazing, deraining and deblurring. On right, our conceptual block diagram." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.533, + 0.313, + 0.548 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.566, + 0.471, + 0.869 + ], + "angle": 0, + "content": "We present a new additive image factorization technique that treats images to be composed of multiple latent specular components which can be simply estimated recursively by modulating the sparsity during decomposition. Our model-driven RSFNet estimates these factors by unrolling the optimization into network layers requiring only a few scalars to be learned. The resultant factors are interpretable by design and can be fused for different image enhancement tasks via a network or combined directly by the user in a controllable fashion. Based on RSFNet, we detail a zero-reference Low Light Enhancement (LLE) application trained without paired or unpaired supervision. Our system improves the state-of-the-art performance on standard benchmarks and achieves better generalization on multiple other datasets. We also integrate our factors with other task specific fusion networks for applications like de-earning, deblurring and dehazing with negligible overhead thereby highlighting the multi-domain and multi-task generalizability of our proposed RSFNet. The code and data is released for reproducibility on the project homepage1." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.533, + 0.631, + 0.548 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.563, + 0.892, + 0.73 + ], + "angle": 0, + "content": "A low-light image has most regions too dark for comprehension due to low exposure setting or insufficient scene lighting which makes images highly challenging for computer processing and aesthetically unpleasant. Low-Light Enhancement (LLE) aims to recovers a well-exposed image from a low-light input [46]. LLE can be a critical pre-processing step before the downstream applications [55, 57]. Core LLE challenge lies in modeling the degradation function which is spatially varying and has complex dependence on multiple variables like color, camera sensitivity, illuminant spectra, scene geometry, etc." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Most LLE solutions decompose the image into meaningful latent factors based on a relevant optical property (Tab. 1). This allows individual manipulation of each factor which simplifies the enhancement operation. A common factorization is based on the Retinex approximation [39, 58], which assumes a multiplicative disentangle-ment of image \\(I\\) into two intrinsic factors: illumination-invariant, piecewise constant reflectance \\(R\\) and color-invariant, smooth shading \\(S\\) as \\(I = R\\cdot S\\). Other factorization criteria include frequency [35, 89], spatial scale [3, 50], spatio-frequency representation [18, 67], intensity" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.441, + 0.9 + ], + "angle": 0, + "content": "1https://sophont01.github.io/data/projects/RSFNet/" + }, + { + "type": "page_number", + "bbox": [ + 0.495, + 0.947, + 0.503, + 0.956 + ], + "angle": 0, + "content": "1" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.304 + ], + "angle": 0, + "content": "[33], reflectance rank [69, 76], etc. Fixed number of factors [35, 69, 87] and variable number that allow better representation [3, 33, 50] have been used. Some decompose image multiplicatively like Retinex [35, 87], while others split into additive factors which are numerically more stable [21, 32, 67]. Pixel segmentation could be soft or hard based on the membership across factors, with the former introducing fewer artifacts [4]. LLE solutions can be global or local. Global methods use whole image level statistics like gamma [27], histograms [96], etc., to enhance the images. Local methods employ spatially varying features like illumination maps [87], intensity/segmentation masks [33, 63], etc., for the same. Global methods are simpler but local ones can capture scene semantics better." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.504 + ], + "angle": 0, + "content": "Traditional LLE methods used manually-designed model-based optimisation by deriving specific priors from the image itself [23, 29, 100], needing no training. Data-driven, machine learning based solutions have done better recently. They use training datasets to tune the model which generalizes to other images [3, 87, 90]. Supervised methods require annotated input-output pairs of images [88, 90, 102]. Unsupervised methods require annotated training data but not necessarily paired [36, 91]. Zero-reference methods do not need annotated data and approach the problem by explicitly encoding the domain knowledge from training images [27, 57, 72]. They generalize better and are simpler, lighter, and more interpretable by design." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.473, + 0.732 + ], + "angle": 0, + "content": "In this paper, we present a zero-reference LLE method that outperforms prior methods on the average. At core is a novel Recursive Specularity Factorization (RSF) of the image factorization based on image specularity. We decompose an image into additive specular factors by thresholding the amount of sparsity of each pixel recursively. Successive factor differences mark out newly discovered image regions which are then individually targeted for enhancement. Our RSFNet that computes the factorization is model-driven, task-agnostic, and light-weight, needing about 200 trainable parameters. The image factors are fused using a task-specific UNet-based module to enhance each region appropriately. RSF is useful to other applications when combined with other task-specific fusion modules. Our main contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.735, + 0.469, + 0.765 + ], + "angle": 0, + "content": "- A novel image factorization criterion and optimization formulation based on recursive specularity estimation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.766, + 0.469, + 0.795 + ], + "angle": 0, + "content": "- A model-driven RSFNet to learn factorization thresholds in a data-driven fashion using algorithm unrolling." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.796, + 0.469, + 0.841 + ], + "angle": 0, + "content": "- A simple and flexible zero-reference LLE solution that surpasses the state of the art on multiple benchmarks and in the average generalization performance." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.841, + 0.469, + 0.9 + ], + "angle": 0, + "content": "- Demonstration of RSF's usability to tasks like dehazing, deraining, and deblurring. RSF has high potential as a structural prior for several image understanding and enhancement tasks." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.735, + 0.469, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.09, + 0.875, + 0.213 + ], + "angle": 0, + "content": "
CriteriaNo.TypeMapSegExample
Retinex2*globalsoft[72, 88]
Frequency2+, low/highglobalhard[89]
Spectral2*, fourierglobalsoft[35]
Low Rank2+globalsoft[69, 76]
Wavelets2n+, pyramidglobalsoft[18, 67]
Multiscale2n+, pyramidglobalsoft[3, 50]
Glare/Shadow3, 4*, +localhard[5, 78]
Intensityvar.+, bandslocalhard[32, 33]
Specularityvar.+localsoftRSFNet
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.498, + 0.218, + 0.892, + 0.304 + ], + "angle": 0, + "content": "Table 1. Various LLE factorization criteria, with number of components (var. implies variable), type of factorization (+ additive/\\* multiplicative), types of output maps (local/global), pixel segmentation across maps (soft/hard) and corresponding exemplar methods. Our RSFNet proposes a novel specularity based factorization which allows a variable number of local soft-segmented factors." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.313, + 0.628, + 0.33 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.892, + 0.414 + ], + "angle": 0, + "content": "Model-based LLE: Early LLE solutions used traditional optimization models using either global statistics [15, 43, 66, 70] or spatially varying illumination maps for local editing [22, 29, 85, 99]. They were more interpretable but required hand-crafted algorithms and heuristics." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.893, + 0.749 + ], + "angle": 0, + "content": "Data-driven LLE: Modern solutions take inspiration from traditional techniques and induce domain knowledge via loss terms or designed within the network architecture which are learned from large datasets in a data-driven fashion. They belong to one of the five training paradigms [46]. Supervised LLE methods require both low-light and well-lit paired images like Sharma and Tan [78], Wei et al. [87], Xu et al. [90], Yang et al. [95], Zhang et al. [103]. On the other hand, unsupervised methods like Jiang et al. [36], Ni et al. [64], Zhang et al. [96], require only unpaired low-light and well-lit image sets. Semi-supervised methods combine the previous two techniques and use both paired and unpaired annotations [73, 94]. Self-supervised solutions [48, 63] generate their own annotations using pseudo-labels or synthetic degradations. Contrary to all of these, zero-reference methods do not use ground truth reconstruction losses and assess the quality of output based upon encoded prior terms [27, 47, 57, 72, 98, 107]. These methods, like ours, possess improved generalizability due to explicit induction of domain knowledge and reduced chances of overfitting [27]. Zero-reference insights also provide direct valuable additions to the subsequent solutions in other paradigms." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Model-Driven Networks: Data-driven solutions have good performance but lack interpretability, whereas model-based methods are explainable by design but often compromise with lower performance. Model-driven networks [61] are hybrids which bring the best of both together. Such networks unroll optimization steps as differentiable layers with learnable parameters, inducing data-driven priors in place of hand-crafted heuristics. Although data-driven solutions are plenty, only a few model-driven solutions exist for low-level vision tasks like image restoration [40, 41], shadow re" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.946, + 0.505, + 0.956 + ], + "angle": 0, + "content": "2" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.093, + 0.357, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.094, + 0.631, + 0.245 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.094, + 0.889, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.894, + 0.333 + ], + "angle": 0, + "content": "Figure 2. Categorization and Motivation: Left shows categorization of various LLE solution types (Sec. 2). Middle plot shows the relationship between five factor cluster centers w.r.t each other and the background comprising of shadow/non-shadow regions estimated using PCA dimensionality reduced DINO features [14]. Gradual progression of feature cluster centers from highlight region to shadow region indicates their capability to capture various illumination regions in an image. Top right shows one data point from CHUK dataset [34] with mask, processed shadow/highlight regions and extracted factors. Bottom right plots distinguish our specular fuzzy factors from intensity thresholding based binary division, with ours allowing more diverse distributions and richer representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.47, + 0.404 + ], + "angle": 0, + "content": "moyal [108], dehazing [54], deraining [83], denoising [68] and super-resolution [7, 8]. Such solutions are concise and efficient due to underlying task specific formulation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.406, + 0.471, + 0.633 + ], + "angle": 0, + "content": "Model-driven LLE solutions are very recent. UretinexNet [88] and UTVNet [104] are both supervised methods which respectively unroll the Retinex and total variational LLE formulations. RUAS [72] and SCI [57] are closest to our approach as they both propose model-driven zero-reference LLE solutions. RUAS [72] unrrolls illumination estimation and noise removal steps in their optimization and compliment it with learnable architecture search, towards a dynamic LLE framework. SCI [57] on the other hand propose a residual framework wherein reflectance estimation is done by a self-calibration module which is then used to iteratively refine illumination maps. In contrast, our method is inspired directly by image formation fundamentals and presents a novel factorization criterion which provides better interpretability, performance and flexibility." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Retinex Factorization for LLE: Retinex [39, 58] is the most widely used factorization strategy for LLE [46, 72, 75, 87, 88] and beyond [9, 25, 74, 77]. One major Retinex limitation is due to the Lambertian reflection [38] assumption which approximates all surfaces as diffuse, thereby ignoring prevalent non-Lambertian effects in a real scene like specularity, translucency, caustics etc. Another issue is that pixelwise multiplicative nature of Retinex factors is cumbersome to handle numerically (especially in LLE with near zero pixel values) and the obtained illumination maps require further semantic analysis for downstream applications. Extensions of Retinex like dichromatic model [81] and shadow segmentation [5], separate one extra component each in addition to diffuse \\( R \\) and \\( S \\) e.g. Sharma and Tan [78] and Baslamisli et al. [5] used glare and shadow image decomposition respectively. From this perspective our recursive specular factorization can be understood as an extension of" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.358, + 0.892, + 0.404 + ], + "angle": 0, + "content": "the same idea with continuously varying illumination characteristics starting from bright glares and ending with dark shadows (see Fig. 2 and Sec. 3 for details)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.893, + 0.703 + ], + "angle": 0, + "content": "Others Factorization Strategies: Apart from Retinex, other factorization techniques are listed in Tab. 1. Afifi et al. [3], Lim and Kim [50], Mertens et al. [59], Xu et al. [89] employ spatial or frequency based image decomposition. Recently, Yang et al. [94] used recursively concatenated features from a supervised encoder and Huang et al. [35] proposed a Fourier disentanglement based solution. Apart from these supervised factorizations, Zheng and Gupta [106] proposed semantic classification based ROI identification using a pretrained segmentation network. [27, 63] predict multiple gamma correction maps for enhancement. [32, 33] simulate single image exposure burst using piece-wise thresholded intensity functions whereas [69] uses low-rank decomposition for reflectance. Each factorization strategy harnesses crucial underlying optical observations and adds valuable insights to the low-level vision research. To the best of our knowledge, our proposed method here is the first to use recursive specularity estimation as a factorization strategy for LLE and other enhancement tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.723, + 0.61, + 0.74 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Outline: Our entire pipeline consists of two parts. We first decompose the image into \\( K \\) factors using our Recursive Specularity Factorization Network (RSFNet), which consists of multiple factorization modules (FM) with each optimization step encoded as a differentiable network layer. Then we fuse, enhance, and denoise the factors using a fusion network, which is built using task dependent pre-existing architectures. This modular design allows easy adoption of our technique in several other tasks and learning paradigms (Sec. 4)." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.946, + 0.504, + 0.956 + ], + "angle": 0, + "content": "3" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.885, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.289, + 0.893, + 0.318 + ], + "angle": 0, + "content": "Figure 3. Block Diagram: Our factorization module (RSFNet) splits a given image into multiple specular components using model-driven unrolled optimization. Then fusion module combines all the factors to generate the enhanced output." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.328, + 0.361, + 0.344 + ], + "angle": 0, + "content": "3.1. Factorization Network: RSFNet" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.473 + ], + "angle": 0, + "content": "Specularity Estimation: Specularity removal is a well studied problem. Most specularity removal methods [1, 28, 79] exploit the relative sparsity of specular highlights and use pre-defined fixed sparsity thresholds to isolate the specular component. According to dichromatic reflection model [81] image consists of a diffuse \\(\\mathbf{A}\\) and a specular \\(\\mathbf{E}\\) term: \\(\\mathbf{X} = \\mathbf{A} + \\mathbf{E}\\) for input \\(X\\) where specular component can be estimated by minimizing the \\(L_{0}\\) norm approximated as:" + }, + { + "type": "equation", + "bbox": [ + 0.137, + 0.483, + 0.469, + 0.506 + ], + "angle": 0, + "content": "\\[\n\\underset {\\mathbf {E}, \\mathbf {A}} {\\operatorname {a r g m i n}} \\| \\mathbf {A} \\| _ {*} + \\lambda \\| \\mathbf {E} \\| _ {1} \\quad \\text {s . t .} \\mathbf {X} = \\mathbf {A} + \\mathbf {E}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.607 + ], + "angle": 0, + "content": "where \\(L_{1}\\) is relaxation of \\(L_{0}\\), \\(*\\) is Frobenius norm regularizer and \\(\\lambda\\) is the sparsity parameter with higher values encouraging sparser results. Eq. (1) can be restated as augmented Lagrangian [10] using dual form and auxiliary parameters \\((\\mathbf{Y},\\mu)\\), which are then solvable using iterative ADMM updates \\((t\\in [0,T])\\) [11] as given below:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.616, + 0.458, + 0.635 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} _ {t + 1} = \\delta_ {\\alpha_ {t}} ^ {1} \\left(\\mathbf {X} - \\mathbf {A} _ {t} - \\mathbf {Y} _ {t} ^ {T} / \\mu_ {t}\\right) \\quad \\text {w h e r e} \\alpha : \\mathcal {F} (\\lambda , \\mu),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.636, + 0.458, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\mathbf {A} _ {t + 1} = \\delta_ {\\beta_ {t}} ^ {*} \\left(\\mathbf {X} - \\mathbf {E} _ {t + 1} - \\mathbf {Y} _ {t} ^ {T} / \\mu_ {t}\\right) \\quad \\text {w h e r e} \\beta : \\mathcal {F} (\\mu),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.091, + 0.655, + 0.468, + 0.682 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} _ {t + 1} = \\mathbf {Y} _ {t} + \\mu_ {t} \\left(\\mathbf {A} _ {t + 1} + \\mathbf {E} _ {t + 1} - \\mathbf {X}\\right) \\quad \\text {w h e r e} \\mu : \\mathcal {F} (\\mathbf {X}). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.683, + 0.45, + 0.699 + ], + "angle": 0, + "content": "Here \\(\\delta_{\\alpha}^{p}\\) is element-wise soft-thresholding operator [65]:" + }, + { + "type": "equation", + "bbox": [ + 0.159, + 0.707, + 0.386, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\delta_ {\\alpha} ^ {p} (x) = \\max \\left(1 - \\alpha / | x | _ {p}, 0\\right) \\cdot x.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.734, + 0.468, + 0.782 + ], + "angle": 0, + "content": "We can back-propagate through updates in Eq. (2) [88, 104] and hence can unroll them as neural network layers with learnable parameters \\(\\alpha : \\{\\alpha\\}_0^T, \\beta : \\{\\beta\\}_0^T\\) and \\(\\pmb{\\mu} : \\{\\pmb{\\mu}\\}_0^T\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Relation with ISTA: Analyzing the structure of Eq. (2), we can draw parallels with the ISTA problem [17], which seeks a sparse solution to \\(\\mathbf{E}\\) for the condition \\(\\mathbf{X} = \\mathcal{G}\\mathbf{E} + \\epsilon\\), with \\(\\mathcal{G}\\) as a learnable dictionary and negligible \\(\\epsilon\\). In contrast, we have a non-negligible residue and identity dictionary. LISTA by Gregor and LeCun [26] showed how \\(\\mathbf{E}\\) update step can be represented as a weighted function which can" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.329, + 0.831, + 0.344 + ], + "angle": 0, + "content": "then be approximated as finite network layers i.e.:" + }, + { + "type": "equation", + "bbox": [ + 0.605, + 0.352, + 0.892, + 0.369 + ], + "angle": 0, + "content": "\\[\n\\mathbf {E} _ {t + 1} = \\delta_ {\\alpha_ {t}} \\left(\\mathbf {w} _ {t} ^ {1} \\mathbf {E} _ {t} + \\mathbf {w} _ {t} ^ {2} \\mathbf {X}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.378, + 0.893, + 0.575 + ], + "angle": 0, + "content": "with learnable parameters \\((\\alpha_{t},\\mathbf{w}_{t}^{1},\\mathbf{w}_{t}^{2})\\) for each iteration \\(t\\in [0,T]\\). Based on the weight coupling between \\(\\mathbf{w}^1\\) and \\(\\mathbf{w}^2\\), Chen et al. [16] simplified Eq. (3) by deriving both \\(\\mathbf{w}^1\\) and \\(\\mathbf{w}^2\\) from a single weight term, thereby halving the computation cost. A major simplification was further proposed by Liu et al. [51] as ALISTA, who proved how all weight terms could be analytically obtained for a known dictionary, thereby leaving only step sizes and thresholds i.e. \\(\\mu\\) and \\(\\alpha_{t}\\) to be estimated. Later on this idea was extended to other similar optimization formulations and improved upon by additional simplifications and guarantees e.g. Cai et al. [12] unrolled their ADMM updates into a network for robust principal component analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.59, + 0.892, + 0.74 + ], + "angle": 0, + "content": "Recursive Factorization: Drawing parallels from ALISTA [51] and its applications [12], we propose to learn the analytically reduced sparsity thresholds and step sizes via unrolled network layers. After optimizing the above mentioned objective Eq. (1) we obtain one specular factor \\(\\mathbf{E}^k\\) where index \\(k\\in [1,K]\\) indicates the factor number. For multiple factors, we recursively solve Eq. (1) by resetting the input \\(X\\) after removing the previous specular output and relaxing the initial sparsity weight. We initialize variables for each factor at \\(t = 0\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.747, + 0.892, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} ^ {k + 1} = \\mathbf {X} ^ {k} - \\mathbf {E} ^ {k}, \\quad \\mathbf {Y} ^ {k} = \\mathbf {X} ^ {k} / \\| \\mathbf {X} ^ {k} \\| _ {2} \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.77, + 0.853, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\alpha^ {k} = (1 - \\nu^ {k}) \\hat {X} ^ {k}, \\quad \\beta^ {k} = \\nu^ {k} \\hat {X} ^ {k}, \\quad \\nu^ {k} = k / K,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.8, + 0.892, + 0.877 + ], + "angle": 0, + "content": "where \\(\\hat{X}\\) indicates input mean and \\(\\mathbf{X}^0 = \\mathbf{I}\\). Intuitively, this can be understood as progressively removing specularity \\((E^{k})\\) from the original image by gradually relaxing the sparsity weight \\((\\alpha^{k + 1} < \\alpha^{k})\\). This lets us split the original image into multiple additive factors as:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.884, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} = \\mathbf {E} ^ {1} + \\mathbf {E} ^ {2} + \\dots + \\mathbf {E} ^ {K} = \\sum_ {k = 1} ^ {K} \\mathbf {E} ^ {k} \\tag {5}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.947, + 0.504, + 0.956 + ], + "angle": 0, + "content": "4" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.107, + 0.473, + 0.244 + ], + "angle": 0, + "content": "Unrolling: Based upon above discussion, we propose an unrolled network collecting all parameters in a single vector \\(\\pmb{\\theta}\\). In each iteration \\(t\\), we estimate three scalars: thresholds for both components \\((\\alpha_{t},\\beta_{t})\\) and the step size \\((\\mu_t)\\). Hence for a factor \\(k\\), we have \\(3T\\) parameters \\(\\pmb{\\theta}^{k} := (\\alpha^{k},\\beta^{k},\\mu^{k})\\) and overall we have only \\(3KT\\) parameters \\(\\pmb{\\theta} := \\{\\pmb{\\theta}_{1}^{k}\\}_{1}^{K}\\). Hence our model-driven factorization module is extremely light-weight compared to other decompositions (Tab. 2). We propose the following novel factorization loss:" + }, + { + "type": "equation", + "bbox": [ + 0.097, + 0.251, + 0.472, + 0.288 + ], + "angle": 0, + "content": "\\[\nL _ {f} = \\lambda_ {f} \\sum_ {k = 1} ^ {K} L _ {f} ^ {k} \\quad \\text {w h e r e} \\quad L _ {f} ^ {k} = \\left| \\hat {E} ^ {k} / \\hat {X} ^ {k} - \\nu^ {k} \\right|. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.471, + 0.435 + ], + "angle": 0, + "content": "This constraints the ratio of signal energy in the \\(k^{th}\\) factor compared to the input, to \\(\\nu^k\\). As \\(\\nu^k\\) increases for higher factors, our factorization loss relaxes the sparsity constraint, thereby gradually increasing the number of pixels in the specular component. After training, we are left with \\(K\\) specular factors which sum to \\(I\\). As shown in Fig. 1 and Fig. 2, each one of these factors highlights specific image regions with similar illumination characteristics which can be individually targeted for enhancement." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.809 + ], + "angle": 0, + "content": "Motivation/Validation: The core assumption behind our factorization is that an image can be split into multiple specular factors with each representing specific illumination characteristic. Although such factorization quality assessment is difficult to estimate [9, 25, 30], we performed a toy experiment to validate our hypothesis using shadow detection dataset [34] which contains binary shadow masks in complex real world images (Fig. 2). We extract semantics-rich DINO image features [14] after masking shadow and non-shadow image regions and visualize them in 2D using PCA. This marks separation of feature space between shadowed and highlighted regions in the background. The regions with progressively degrading illumination characteristics (glare, direct light, indirect light, soft shadow, dark shadow, etc.) are expected to gradually lie between the two extremes. Next we factorize each image into five factors using our approach and plot the cluster mean for each factor feature distribution on the same graph. We can observe in Fig. 2 that successive factors gradually shift from the nonshadow towards the shadowed feature space region mirroring the expected illumination order. This confirms that our factorization decomposes the pixel values across fundamental illumination types like glare, direct light, indirect light, shadow, etc." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We also plot the respective factor distribution densities of intensity factorization [32, 33] and our specularity factorization (Fig. 2, bottom right). Intensity factorization allows little variation in the underlying factor distributions and imposes hard segmentation constraints with binary pixel masks. Our specular factors, on the other hand, permit" + }, + { + "type": "code_caption", + "bbox": [ + 0.508, + 0.095, + 0.682, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: LLE Training" + }, + { + "type": "algorithm", + "bbox": [ + 0.508, + 0.111, + 0.892, + 0.363 + ], + "angle": 0, + "content": "Input: Lowlight:I; Hyperparams: \\(\\lambda_{c|e|s}, K, T\\) \nOutput: Enhanced: O; Params: \\(\\theta = \\{\\alpha\\}_{0}^{K}, \\{\\beta\\}_{0}^{K}, \\{\\mu\\}_{0}^{K}\\) \nfor \\(e \\gets 0\\) to num of epochs do \n// Train Factorization Module \nfor \\(k \\gets 0\\) to \\(K\\) do \nfor \\(t \\gets 0\\) to \\(T\\) do \nInitialize \\(E_0^k, A_0^k, Y_0^k\\); // Eqn. 4 \n\\(E_t, A_t, Y_t \\gets\\) ADMM updates; // Eqn. 2 \nend \n\\(F^k \\gets E^k - E^{k-1}\\); // Eqn. 7 \nend \nCompute \\(L_f\\); // Eqn. 6 \n// Train Fusion Module \nif \\(e >\\) freeze epoch then \nFreeze all \\(\\alpha, \\beta, \\mu\\); \n\\(L_f \\gets 0\\); \nend \n\\(I_{fuse} \\gets\\) Concatenate \\([I, F^1, ..., F^K]\\); \n\\(O \\gets\\) Forward \\((I_{fuse})\\); \nCompute \\(L\\); // Eqn. 9 \nBackpropagate \\(L\\); \nend" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.433 + ], + "angle": 0, + "content": "higher variability and soft masks, with each pixel value spread across multiple factors. This provides more flexible representation and better optical approximation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.435, + 0.661, + 0.45 + ], + "angle": 0, + "content": "3.2. Fusion Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.892, + 0.637 + ], + "angle": 0, + "content": "In order to adhere to the zero-reference paradigm, we choose our fusion module to be a small fully-convolutional UNet like architecture with symmetric skip connections similar to other zero-reference methods [27, 63, 106]. One fundamental difference is that we modify the architecture to harness multiple factors and simultaneously perform fusion, enhancement and denoising. Specifically, it comprises of seven \\(3 \\times 3\\) convolutional layers with symmetric skip connections. We first pre-process all of our factors by subtracting the adjacent factors to discover the additional pixel values allowed in the current factor compared to the previous one as a soft mask:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.642, + 0.892, + 0.659 + ], + "angle": 0, + "content": "\\[\n\\mathbf {F} ^ {k} = \\mathbf {E} ^ {k} - \\mathbf {E} ^ {k - 1} \\text {w h e r e} \\mathbf {F} ^ {1} = \\mathbf {E} ^ {1}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.664, + 0.892, + 0.754 + ], + "angle": 0, + "content": "These factors are weighted if required using fixed scalar values and are then passed as a concatenated tensor into the fusion network. The output gamma maps \\(\\mathbf{R}^k\\) rescale different image regions differently and are applied directly on the original image inside the curve adjustment equation [27] for the fused result:" + }, + { + "type": "equation", + "bbox": [ + 0.593, + 0.757, + 0.892, + 0.794 + ], + "angle": 0, + "content": "\\[\nO = \\Phi \\left(\\sum_ {k = 0} ^ {K} I + R ^ {k}. \\left((I) ^ {2} - I\\right)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.857 + ], + "angle": 0, + "content": "The fused output is finally passed through a differentiable bilateral filtering layer \\(\\Phi\\) [71] for the final enhanced result \\(O\\). Note that all the parameters from both factorization and fusion networks are trained together in end-to-end manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.858, + 0.892, + 0.904 + ], + "angle": 0, + "content": "Loss Terms: We use two widely employed zero-reference losses for enhancement [27, 63, 96] and one image smoothing loss for denoising. First color loss \\( L_{c} \\) [27, 96] is based" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.946, + 0.504, + 0.956 + ], + "angle": 0, + "content": "5" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.09, + 0.891, + 0.406 + ], + "angle": 0, + "content": "
ParadigmTraditional Model BasedZero-reference
MethodLIME [29]DUAL [100]SDD [31]ECNet [98]ZDCE [27]ZD++ [47]RUAS [72]SCI [57]PNet [63]GDP [20]RSFNet (Ours) 2.11
Params x103---16.5x10379.4210.563.430.2615.25552x103
Lolv1 [87] (dataset split: 485/15, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑16.2015.9715.1418.0116.7616.3818.4516.4519.8517.6822.17
SSIMy↑0.6950.6920.7540.6440.7340.6450.7660.7090.7180.6780.860
PSNRc↑14.2214.0213.3415.8114.8614.7416.4014.7817.5015.8019.39
SSIMc↑0.5210.5190.6340.4690.5620.4960.5030.5250.5500.5390.755
NIQE↓8.5838.6113.7068.8448.2238.1955.9278.3748.6296.4373.129
LPIPS↓0.3440.3460.2780.3580.3310.3460.3030.3270.3400.3750.265
Lolv2-real [95] (dataset split: 689/100, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑19.3119.1018.4718.8620.3119.3617.4919.3720.0815.8321.46
SSIMy↑0.7050.7040.7920.6130.7450.5850.7420.7220.6910.6270.836
PSNRc↑17.1416.9516.6416.2718.0617.3615.3317.3017.6314.0519.27
SSIMc↑0.5370.5350.6780.4590.5800.4420.4930.5400.5390.5020.738
NIQE↓9.0769.0834.1919.4754.1918.7096.1728.7399.1526.8673.769
LPIPS↓0.3220.3240.2800.3600.3100.3400.3250.2940.3400.3900.280
GENERALIZED PERFORMANCE Mean Scores (Lolv1 [87], Lolv2-real [95], Lolv2-syn [95] and VE-Lol [52])
PSNRy↑18.5017.8317.5018.4519.2618.7317.0918.0719.6515.8821.16
SSIMy↑0.7370.7280.7810.6770.7770.6740.7430.7450.7430.6340.854
PSNRc↑16.5315.8815.7716.2517.1916.7615.1216.2017.3514.1518.45
SSIMc↑0.5960.5830.6790.5380.6340.5480.5320.5870.6050.5040.758
NIQE↓7.8557.4784.0777.5434.2707.4685.8417.6267.7916.7263.763
LPIPS↓0.2910.2970.2660.3290.2730.2960.3460.2950.3020.3790.276
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.411, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison of our method RSFNet with other traditional and zero-reference solutions on multiple lowlight benchmarks and six evaluation metrics. Shown here are scores for two datasets LOLv1 and LOLv2-real with mean value across all datasets in the last sub-table (key: ↑ higher better; ↓ lower better; bold: best; underline: second best)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.473, + 0.47, + 0.503 + ], + "angle": 0, + "content": "on the gray-world assumption which tries to minimize the mean value difference between each color channel pair:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.511, + 0.455, + 0.547 + ], + "angle": 0, + "content": "\\[\nL _ {c} = \\sum_ {(i, j) \\in C} \\left(\\hat {O} ^ {i} - \\hat {O} ^ {j}\\right) ^ {2}, \\quad C \\in \\{(r, g), (g, b), (b, r) \\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.554, + 0.47, + 0.584 + ], + "angle": 0, + "content": "Second is the exposure loss \\( L_{e} \\) [27, 33, 59], which penalizes grayscale intensity deviation from the mid-tone value:" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.592, + 0.462, + 0.628 + ], + "angle": 0, + "content": "\\[\nL _ {e} = \\frac {1}{| \\Omega |} \\sum_ {\\Omega} \\left(\\phi (O) - 0. 6\\right) ^ {2} \\text {w h e r e} \\Omega \\in \\{c \\times h \\times w \\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.636, + 0.47, + 0.682 + ], + "angle": 0, + "content": "where \\(\\phi\\) represents the average value over a \\(16\\times 16\\) window. Our third loss is the pixel-wise smoothing loss which controls the local gradients \\(\\nabla_{x|y}\\) in the final output:" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.691, + 0.398, + 0.726 + ], + "angle": 0, + "content": "\\[\nL _ {s} = \\frac {1}{| \\Omega |} \\sum_ {\\Omega} \\left((\\nabla_ {x} O) ^ {2} + (\\nabla_ {y} O) ^ {2}\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Note that this differs from the previous works who focus on total variational loss of the gamma maps instead. Our final training loss with \\(\\lambda\\) 's as respective loss weights, is given as:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.795, + 0.469, + 0.812 + ], + "angle": 0, + "content": "\\[\nL = \\lambda_ {f} L _ {f} + \\lambda_ {c} L _ {c} + \\lambda_ {e} L _ {e} + \\lambda_ {s} L _ {s}. \\tag {9}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.312, + 0.848 + ], + "angle": 0, + "content": "4. Experiments and Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.9 + ], + "angle": 0, + "content": "We now report our implementation details, results and extensions. Please see the supplementary document for additional details and results." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.893, + 0.608 + ], + "angle": 0, + "content": "Setup: We implement our combined network end-to-end on a single Nvidia 1080Ti GPU in PyTorch. We directly use low-light RGB images as inputs without any additional pre-processing. We first train factorization module for 25 epochs which we freeze and then optimize the fusion module for next 25 epochs. We use stochastic gradient descent for optimization with batch size of 10 and 0.01 as learning rate. Model hyper-parameters are fixed using grid search and the entire training take less than 30 minutes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.893, + 0.789 + ], + "angle": 0, + "content": "Datasets: We evaluate our method using multiple LLE benchmark datasets (Lolv1 [87], Lolv2-real [95], Lolv2-synthetic [95] and VE-Lol [52]) with standard train/test splits (Tab. 2). These datasets comprise of several underexposed small-aperture inputs and corresponding well-exposed ground-truth pairs. Here we report results on two datasets: Lolv1 and Lolv2-real and finally show the mean scores on all four datasets combined in the last sub-table Tab. 2 and in Fig. 5. Furthermore, we report generalization results (Tab. 4) on five additional no-reference datasets which have significant domain shift: DICM [42], LIME [29], MEF [56], NPE [85] and VV [82]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.79, + 0.894, + 0.896 + ], + "angle": 0, + "content": "Metrics: We report both single channel (Y from YCbCr) and multichannel (RGB) performance scores. As full-reference metrics (which require ground truth), we use Peak Signal to Noise-Ratio (PSNR), Structural Similarity Index Metric (SSIM) [86] and Learned Perceptual Image Patch Similarity (LPIPS) [101]. For no-reference assessment (without ground truth), we report Naturalness Image" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.947, + 0.505, + 0.957 + ], + "angle": 0, + "content": "6" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.079, + 0.09, + 0.278, + 0.203 + ], + "angle": 0, + "content": "
VariantsPSNRy↑SSIMy↑
w/o Le8.120.238
w/o Lc16.050.724
w/o Ls20.130.846
w/o Denoise19.510.756
w/o Fusion19.320.830
Full22.170.860
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.209, + 0.276, + 0.235 + ], + "angle": 0, + "content": "Table 3. Ablation analysis on five variants of our RSFNet (Sec. 4)." + }, + { + "type": "table", + "bbox": [ + 0.306, + 0.091, + 0.89, + 0.202 + ], + "angle": 0, + "content": "
NIQE↓& LOE↓ECNet[98]ZDCE[27]ZD++[47]RUAS[72]PNet[63]SCI[57]RSFNet(Ours)
DICM [42]3.37—676.73.10—340.82.94—511.94.89—14213.00—590.33.61—321.93.23—303.1
LIME [29]3.75—685.13.79—135.03.89—332.24.26—719.93.84—223.24.14—75.53.80—68.3
MEF [56]3.30—863.33.31—164.33.18—458.54.08—784.23.25—363.03.43—95.03.00—100.7
NPE [85]3.24—936.13.52—312.93.27—532.25.75—13993.29—601.13.89—239.83.31—221.5
VV [82]2.15—292.42.75—145.42.53—222.93.82—583.72.56—260.22.30—109.01.96—109.0
Mean3.16—690.73.29—219.73.16—411.54.56—981.73.19—407.53.47—168.23.06—160.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.303, + 0.208, + 0.892, + 0.235 + ], + "angle": 0, + "content": "Table 4. Qualitative comparison using naturalness preserving metrics (NIQE \\( \\downarrow \\) - LOE \\( \\downarrow \\) ) on five no-reference benchmarks: DICM, LIME, MEF, NPE and VV (best scores in bold, lower is better)." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.246, + 0.473, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.245, + 0.892, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.43, + 0.893, + 0.473 + ], + "angle": 0, + "content": "Figure 4. Results: Qualitative comparison of our method (green box) with other solutions (from top left 3 per row: SDD [31], ECNet [98], ZDCE [27]; ZD++ [47], RUAS [72], SCI [57]; PNet [63], GDP [20] and our RSFNet respectively). Our method generate natural looking images by handling noisy over and under exposed regions equally well, without over-saturating color or losing geometric details." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.492, + 0.47, + 0.539 + ], + "angle": 0, + "content": "Quality Evaluator (NIQE) [60] and Lightness Order Error [84]. Note while PSNR and SSIM gauge performance quantitatively, other three metrics estimate perceptual quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.556, + 0.47, + 0.663 + ], + "angle": 0, + "content": "Comparisons: We compare against three model-based traditional optimization methods: LIME [29], DUAL [100] and SDD [31] (others ignored due to low performance). For data-driven methods we use seven recent zero-reference methods (chronologically ordered): ECNet [98], zeroDCE [27], zeroDCE++ [47], RUAS [72], SCI [57], PNet [63] and GDP [20]. We use the official code releases with pre" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.692, + 0.462, + 0.858 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.863, + 0.468, + 0.904 + ], + "angle": 0, + "content": "Figure 5. Analysis: On left, our average score on all datasets vs. other methods (more area implies better). On right, ablation analysis with varying number of factors." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.689 + ], + "angle": 0, + "content": "trained weights and default parameters for results generation. Quantitative and qualitative performance comparison is shown in Tab. 2 and Fig. 4 respectively. Qualitatively, our method is cleaner with fewer artifacts and natural illumination (Fig. 4). This is validated by perceptual metrics like NIQE, LPIPS and LOE scores (Tabs. 2 and 4). Our method outperforms other similar category contemporary solutions on multiple metrics and achieves the best generalization performance across datasets. For a generalized performance, we take mean of all the scores across benchmarks and graphically show them in the polar plot in Fig. 5. Each polygon represents a separate LLE method with higher area inside indicating better performance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Ablation: To validate our design choices, we conduct ablation study on several variants of our methods using Lolv1 dataset. The effect of different number of factors \\( K \\) on the final PSNR and SSIM scores are shown on right in Fig. 5. We choose the best observed hyper-parameter settings \\( K = 5 \\) for all our experiments. The effect of various loss terms after removing them one at a time (i.e. \\( w / o \\, L_{e|c|s} \\)) and the effect of the final denoising step are shown in Tab. 3. The last variant (\\( w / o \\, Fusion \\)) represents an especially interesting setting where the fusion network is totally removed and inference uses only \\( 3KT \\) (\\( = 3*5*3 = 45 \\)) parameters. Fusion now reduces to a running average of the current image and" + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.946, + 0.504, + 0.956 + ], + "angle": 0, + "content": "7" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.091, + 0.212, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.199, + 0.232, + 0.231, + 0.242 + ], + "angle": 0, + "content": "Dehaze" + }, + { + "type": "image", + "bbox": [ + 0.215, + 0.091, + 0.347, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.348, + 0.091, + 0.42, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.421, + 0.092, + 0.552, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.553, + 0.092, + 0.622, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.624, + 0.092, + 0.758, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.76, + 0.092, + 0.889, + 0.231 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.232, + 0.776, + 0.241 + ], + "angle": 0, + "content": "Deblur" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.245, + 0.892, + 0.273 + ], + "angle": 0, + "content": "Figure 6. Image enhancement applications using our specular factors as inputs on the AirNet [45] base model. Shown here left-to-right are our results for Dehazing [44], Deraining [93] and Deblurring [62] tasks respectively using AirNet [45] as base model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.292, + 0.408, + 0.307 + ], + "angle": 0, + "content": "the next factor, weighted by the normalized mean:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.312, + 0.469, + 0.331 + ], + "angle": 0, + "content": "\\[\nO ^ {k + 1} = \\left(1 - w ^ {k}\\right) O ^ {k} + w ^ {k} F ^ {k}, \\text {w h e r e} w ^ {k} = \\hat {F} ^ {k} / \\sum_ {k} \\hat {F} ^ {k}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.469, + 0.413 + ], + "angle": 0, + "content": "Even without any other zero-reference losses and using only a simple linear fusion, this method performs well, which demonstrates the effectiveness of our factors. Note here we have an order of magnitude smaller network size than SCI (0.045 vs. 0.26 thousand parameters in Tab. 2)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.47, + 0.716 + ], + "angle": 0, + "content": "Extensions: Our specular factors are easily interpretable and can be used directly for image manipulation as image layers in standard image editing tools like GIMP [80], Photoshop [2], etc. We show an image relighting example by varying the color and blending modes of factors in (Fig. 1 bottom left, Fig. 7). This indicates the potential of our factorization to complex downstream applications. We explore three diverse image enhancement tasks: dehazing, deraining and deblurring. Here our goal is to evaluate the use of specularity factorization as a pre-processing step on an existing base model. We chose the recent AirNet [45] as it allows experimentation on multiple image enhancement tasks with minor backbone modification. To induce our factors as prior information, we concatenate them along with the original input and alter the first convolutional layer input channels. Note that we do not introduce any new loss or layers and directly train the model for three tasks one by one: (i) Dehazing on RESIDE dataset [44] (ii) Deraining on Rain100L dataset [93] and (iii) Deblurring on GoPro dataset" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.736, + 0.206, + 0.856 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.212, + 0.736, + 0.335, + 0.858 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.344, + 0.736, + 0.468, + 0.858 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.863, + 0.469, + 0.904 + ], + "angle": 0, + "content": "Figure 7. Controllable relighting applications using our factors as layers [80] (top:inputs; bottom:results; from left:edited light specularity, indoor color and outdoor intensity respectively)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.29, + 0.89, + 0.364 + ], + "angle": 0, + "content": "
TASK →DEHAZE [44]DERAIN [93]DEBLUR [62]
MethodPSNRSSIMPSNRSSIMPSNRSSIM
AirNet (multi-task)21.040.88432.980.95124.350.781
AirNet (uni-task)23.180.90034.900.965726.420.801
AirNet + Ours24.960.929236.190.971827.290.827
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.372, + 0.891, + 0.4 + ], + "angle": 0, + "content": "Table 5. Our factors can induce structure prior in an existing base model and improve performance for multiple enhancement tasks." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.423, + 0.892, + 0.529 + ], + "angle": 0, + "content": "[62]. As seen in Fig. 6 and Tab. 5, our results are perceptually more pleasing and improve the previously reported scores from multi-task methods consistently [45, 97]. We believe this is due to the induction of structural prior in the form of illumination based region categorization as the intensity and order of illumination at a pixel depends on the scene structure. See the supplementary for more results." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.53, + 0.892, + 0.606 + ], + "angle": 0, + "content": "Limitations: Our method is sensitive to initialization conditions like the underlying algorithms [12, 51]. As a heuristic we use dataset mean for initialization. Another idea, to be explored in future, is to dynamically adapt to each input which is expected to further increase the performance." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.614, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Acknowledgements: We acknowledge the support of TCS Foundation and the Kohli Centre on Intelligent Systems for this research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.668, + 0.627, + 0.683 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.694, + 0.892, + 0.86 + ], + "angle": 0, + "content": "In this paper, we presented a recursive specularity factorization (RSF) and its application to zero-reference LLE. We learn optimization hyperparameters in a data-driven fashion by unrolling the stages into a small neural network. The factors are fused using a network to yield the final result. We also demonstrate the utility of RSFs for image relighting as well as for image enhancement tasks like dehazing, deraining and deblurring. We are exploring the extension of RSFs to applications like image harmonization, foreground matting, white-balancing, depth estimation, etc., and extend the technique to other signals beyond the visible spectrum." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.901 + ], + "angle": 0, + "content": "Ethical Concerns: This work enhances captured images and poses no special ethical issues we are aware of." + }, + { + "type": "page_number", + "bbox": [ + 0.494, + 0.946, + 0.504, + 0.956 + ], + "angle": 0, + "content": "8" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.096, + 0.116, + 0.47, + 0.161 + ], + "angle": 0, + "content": "[1] Amir Adler, Michael Elad, Yacov Hel-Or, and Ehud Rivlin. 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Sepcularity Factorization: We factorize a single input image (blue box, top row) into multiple soft specular factors (rescaled for visualization) based on their similar illumination characteristics (note table shadow and lamp reflection). Our factors directly enable zero-reference low-light enhancement and user controlled image relighting (bottom left). Additionally, they can also be used as a plug-and-play prior for various supervised image enhancement tasks like dehazing, deraining and deblurring. On right, our conceptual block diagram. + +![](images/5261b73b6dd45d5dd10311105207fbbeedfb67d01d777dedb7aa391d7b67844f.jpg) + +![](images/8ecb305ce4b8e242bc49f3b82a10ed598a139fa84cbdea19ce6420bbe1396bf5.jpg) + +![](images/4ddc2cd7c44d9b2917f4f7534f5f49b826a132e1308c0cbfcb2119f4c99d7fa7.jpg) + +![](images/2a5ac2e2426631ef6065045aa00e8ad1a3483d8c847941cc883d85925be4cb40.jpg) + +![](images/495f45198e3be615596d664d7ea77586369a852c88938f3b7ec1f1b9cea9efd0.jpg) + +![](images/90a9c9634e883617f0678dd8d579ff0bb313b5ab1669c74c5dcc99c8f3275a17.jpg) + +![](images/53c096b3b051bb8eb79d94bb0edf3709a6b219aa1d56bc7553594a1607210b72.jpg) + +![](images/8d8f1ec5f7cd158dd5f7236e862656f1137e2be4648034d135110008c8a07270.jpg) + +![](images/9203037654e11cfb9c6d87ee30c7504c5fe4fc7e7378bddef7c2fee3c55085ea.jpg) + +# Abstract + +We present a new additive image factorization technique that treats images to be composed of multiple latent specular components which can be simply estimated recursively by modulating the sparsity during decomposition. Our model-driven RSFNet estimates these factors by unrolling the optimization into network layers requiring only a few scalars to be learned. The resultant factors are interpretable by design and can be fused for different image enhancement tasks via a network or combined directly by the user in a controllable fashion. Based on RSFNet, we detail a zero-reference Low Light Enhancement (LLE) application trained without paired or unpaired supervision. Our system improves the state-of-the-art performance on standard benchmarks and achieves better generalization on multiple other datasets. We also integrate our factors with other task specific fusion networks for applications like de-earning, deblurring and dehazing with negligible overhead thereby highlighting the multi-domain and multi-task generalizability of our proposed RSFNet. The code and data is released for reproducibility on the project homepage1. + +# 1. Introduction + +A low-light image has most regions too dark for comprehension due to low exposure setting or insufficient scene lighting which makes images highly challenging for computer processing and aesthetically unpleasant. Low-Light Enhancement (LLE) aims to recovers a well-exposed image from a low-light input [46]. LLE can be a critical pre-processing step before the downstream applications [55, 57]. Core LLE challenge lies in modeling the degradation function which is spatially varying and has complex dependence on multiple variables like color, camera sensitivity, illuminant spectra, scene geometry, etc. + +Most LLE solutions decompose the image into meaningful latent factors based on a relevant optical property (Tab. 1). This allows individual manipulation of each factor which simplifies the enhancement operation. A common factorization is based on the Retinex approximation [39, 58], which assumes a multiplicative disentangle-ment of image $I$ into two intrinsic factors: illumination-invariant, piecewise constant reflectance $R$ and color-invariant, smooth shading $S$ as $I = R\cdot S$ . Other factorization criteria include frequency [35, 89], spatial scale [3, 50], spatio-frequency representation [18, 67], intensity + +[33], reflectance rank [69, 76], etc. Fixed number of factors [35, 69, 87] and variable number that allow better representation [3, 33, 50] have been used. Some decompose image multiplicatively like Retinex [35, 87], while others split into additive factors which are numerically more stable [21, 32, 67]. Pixel segmentation could be soft or hard based on the membership across factors, with the former introducing fewer artifacts [4]. LLE solutions can be global or local. Global methods use whole image level statistics like gamma [27], histograms [96], etc., to enhance the images. Local methods employ spatially varying features like illumination maps [87], intensity/segmentation masks [33, 63], etc., for the same. Global methods are simpler but local ones can capture scene semantics better. + +Traditional LLE methods used manually-designed model-based optimisation by deriving specific priors from the image itself [23, 29, 100], needing no training. Data-driven, machine learning based solutions have done better recently. They use training datasets to tune the model which generalizes to other images [3, 87, 90]. Supervised methods require annotated input-output pairs of images [88, 90, 102]. Unsupervised methods require annotated training data but not necessarily paired [36, 91]. Zero-reference methods do not need annotated data and approach the problem by explicitly encoding the domain knowledge from training images [27, 57, 72]. They generalize better and are simpler, lighter, and more interpretable by design. + +In this paper, we present a zero-reference LLE method that outperforms prior methods on the average. At core is a novel Recursive Specularity Factorization (RSF) of the image factorization based on image specularity. We decompose an image into additive specular factors by thresholding the amount of sparsity of each pixel recursively. Successive factor differences mark out newly discovered image regions which are then individually targeted for enhancement. Our RSFNet that computes the factorization is model-driven, task-agnostic, and light-weight, needing about 200 trainable parameters. The image factors are fused using a task-specific UNet-based module to enhance each region appropriately. RSF is useful to other applications when combined with other task-specific fusion modules. Our main contributions are: + +- A novel image factorization criterion and optimization formulation based on recursive specularity estimation. +- A model-driven RSFNet to learn factorization thresholds in a data-driven fashion using algorithm unrolling. +- A simple and flexible zero-reference LLE solution that surpasses the state of the art on multiple benchmarks and in the average generalization performance. +- Demonstration of RSF's usability to tasks like dehazing, deraining, and deblurring. RSF has high potential as a structural prior for several image understanding and enhancement tasks. + +
CriteriaNo.TypeMapSegExample
Retinex2*globalsoft[72, 88]
Frequency2+, low/highglobalhard[89]
Spectral2*, fourierglobalsoft[35]
Low Rank2+globalsoft[69, 76]
Wavelets2n+, pyramidglobalsoft[18, 67]
Multiscale2n+, pyramidglobalsoft[3, 50]
Glare/Shadow3, 4*, +localhard[5, 78]
Intensityvar.+, bandslocalhard[32, 33]
Specularityvar.+localsoftRSFNet
+ +Table 1. Various LLE factorization criteria, with number of components (var. implies variable), type of factorization (+ additive/\* multiplicative), types of output maps (local/global), pixel segmentation across maps (soft/hard) and corresponding exemplar methods. Our RSFNet proposes a novel specularity based factorization which allows a variable number of local soft-segmented factors. + +# 2. Background + +Model-based LLE: Early LLE solutions used traditional optimization models using either global statistics [15, 43, 66, 70] or spatially varying illumination maps for local editing [22, 29, 85, 99]. They were more interpretable but required hand-crafted algorithms and heuristics. + +Data-driven LLE: Modern solutions take inspiration from traditional techniques and induce domain knowledge via loss terms or designed within the network architecture which are learned from large datasets in a data-driven fashion. They belong to one of the five training paradigms [46]. Supervised LLE methods require both low-light and well-lit paired images like Sharma and Tan [78], Wei et al. [87], Xu et al. [90], Yang et al. [95], Zhang et al. [103]. On the other hand, unsupervised methods like Jiang et al. [36], Ni et al. [64], Zhang et al. [96], require only unpaired low-light and well-lit image sets. Semi-supervised methods combine the previous two techniques and use both paired and unpaired annotations [73, 94]. Self-supervised solutions [48, 63] generate their own annotations using pseudo-labels or synthetic degradations. Contrary to all of these, zero-reference methods do not use ground truth reconstruction losses and assess the quality of output based upon encoded prior terms [27, 47, 57, 72, 98, 107]. These methods, like ours, possess improved generalizability due to explicit induction of domain knowledge and reduced chances of overfitting [27]. Zero-reference insights also provide direct valuable additions to the subsequent solutions in other paradigms. + +Model-Driven Networks: Data-driven solutions have good performance but lack interpretability, whereas model-based methods are explainable by design but often compromise with lower performance. Model-driven networks [61] are hybrids which bring the best of both together. Such networks unroll optimization steps as differentiable layers with learnable parameters, inducing data-driven priors in place of hand-crafted heuristics. Although data-driven solutions are plenty, only a few model-driven solutions exist for low-level vision tasks like image restoration [40, 41], shadow re + +![](images/355f7c3923a3603e26949f43576930b86f182ecada5ac837d4e12e51be0d1751.jpg) +Figure 2. Categorization and Motivation: Left shows categorization of various LLE solution types (Sec. 2). Middle plot shows the relationship between five factor cluster centers w.r.t each other and the background comprising of shadow/non-shadow regions estimated using PCA dimensionality reduced DINO features [14]. Gradual progression of feature cluster centers from highlight region to shadow region indicates their capability to capture various illumination regions in an image. Top right shows one data point from CHUK dataset [34] with mask, processed shadow/highlight regions and extracted factors. Bottom right plots distinguish our specular fuzzy factors from intensity thresholding based binary division, with ours allowing more diverse distributions and richer representation. + +![](images/b4accd8fd4d71c18d75c5b7f7a40764205d461eab6191c8a71a7380bd372eb91.jpg) + +![](images/f59a79de1cf21e15deb2d46eeee35edb6811800378fcc3614f2388f70ffe6d20.jpg) + +moyal [108], dehazing [54], deraining [83], denoising [68] and super-resolution [7, 8]. Such solutions are concise and efficient due to underlying task specific formulation. + +Model-driven LLE solutions are very recent. UretinexNet [88] and UTVNet [104] are both supervised methods which respectively unroll the Retinex and total variational LLE formulations. RUAS [72] and SCI [57] are closest to our approach as they both propose model-driven zero-reference LLE solutions. RUAS [72] unrrolls illumination estimation and noise removal steps in their optimization and compliment it with learnable architecture search, towards a dynamic LLE framework. SCI [57] on the other hand propose a residual framework wherein reflectance estimation is done by a self-calibration module which is then used to iteratively refine illumination maps. In contrast, our method is inspired directly by image formation fundamentals and presents a novel factorization criterion which provides better interpretability, performance and flexibility. + +Retinex Factorization for LLE: Retinex [39, 58] is the most widely used factorization strategy for LLE [46, 72, 75, 87, 88] and beyond [9, 25, 74, 77]. One major Retinex limitation is due to the Lambertian reflection [38] assumption which approximates all surfaces as diffuse, thereby ignoring prevalent non-Lambertian effects in a real scene like specularity, translucency, caustics etc. Another issue is that pixelwise multiplicative nature of Retinex factors is cumbersome to handle numerically (especially in LLE with near zero pixel values) and the obtained illumination maps require further semantic analysis for downstream applications. Extensions of Retinex like dichromatic model [81] and shadow segmentation [5], separate one extra component each in addition to diffuse $R$ and $S$ e.g. Sharma and Tan [78] and Baslamisli et al. [5] used glare and shadow image decomposition respectively. From this perspective our recursive specular factorization can be understood as an extension of + +the same idea with continuously varying illumination characteristics starting from bright glares and ending with dark shadows (see Fig. 2 and Sec. 3 for details). + +Others Factorization Strategies: Apart from Retinex, other factorization techniques are listed in Tab. 1. Afifi et al. [3], Lim and Kim [50], Mertens et al. [59], Xu et al. [89] employ spatial or frequency based image decomposition. Recently, Yang et al. [94] used recursively concatenated features from a supervised encoder and Huang et al. [35] proposed a Fourier disentanglement based solution. Apart from these supervised factorizations, Zheng and Gupta [106] proposed semantic classification based ROI identification using a pretrained segmentation network. [27, 63] predict multiple gamma correction maps for enhancement. [32, 33] simulate single image exposure burst using piece-wise thresholded intensity functions whereas [69] uses low-rank decomposition for reflectance. Each factorization strategy harnesses crucial underlying optical observations and adds valuable insights to the low-level vision research. To the best of our knowledge, our proposed method here is the first to use recursive specularity estimation as a factorization strategy for LLE and other enhancement tasks. + +# 3. Approach + +Outline: Our entire pipeline consists of two parts. We first decompose the image into $K$ factors using our Recursive Specularity Factorization Network (RSFNet), which consists of multiple factorization modules (FM) with each optimization step encoded as a differentiable network layer. Then we fuse, enhance, and denoise the factors using a fusion network, which is built using task dependent pre-existing architectures. This modular design allows easy adoption of our technique in several other tasks and learning paradigms (Sec. 4). + +![](images/8f5f4938fff2d8e5ec972e2105be4219573284994e1b6923b37ace949a57d55d.jpg) +Figure 3. Block Diagram: Our factorization module (RSFNet) splits a given image into multiple specular components using model-driven unrolled optimization. Then fusion module combines all the factors to generate the enhanced output. + +# 3.1. Factorization Network: RSFNet + +Specularity Estimation: Specularity removal is a well studied problem. Most specularity removal methods [1, 28, 79] exploit the relative sparsity of specular highlights and use pre-defined fixed sparsity thresholds to isolate the specular component. According to dichromatic reflection model [81] image consists of a diffuse $\mathbf{A}$ and a specular $\mathbf{E}$ term: $\mathbf{X} = \mathbf{A} + \mathbf{E}$ for input $X$ where specular component can be estimated by minimizing the $L_{0}$ norm approximated as: + +$$ +\underset {\mathbf {E}, \mathbf {A}} {\operatorname {a r g m i n}} \| \mathbf {A} \| _ {*} + \lambda \| \mathbf {E} \| _ {1} \quad \text {s . t .} \mathbf {X} = \mathbf {A} + \mathbf {E}, \tag {1} +$$ + +where $L_{1}$ is relaxation of $L_{0}$ , $*$ is Frobenius norm regularizer and $\lambda$ is the sparsity parameter with higher values encouraging sparser results. Eq. (1) can be restated as augmented Lagrangian [10] using dual form and auxiliary parameters $(\mathbf{Y},\mu)$ , which are then solvable using iterative ADMM updates $(t\in [0,T])$ [11] as given below: + +$$ +\mathbf {E} _ {t + 1} = \delta_ {\alpha_ {t}} ^ {1} \left(\mathbf {X} - \mathbf {A} _ {t} - \mathbf {Y} _ {t} ^ {T} / \mu_ {t}\right) \quad \text {w h e r e} \alpha : \mathcal {F} (\lambda , \mu), +$$ + +$$ +\mathbf {A} _ {t + 1} = \delta_ {\beta_ {t}} ^ {*} \left(\mathbf {X} - \mathbf {E} _ {t + 1} - \mathbf {Y} _ {t} ^ {T} / \mu_ {t}\right) \quad \text {w h e r e} \beta : \mathcal {F} (\mu), +$$ + +$$ +\mathbf {Y} _ {t + 1} = \mathbf {Y} _ {t} + \mu_ {t} \left(\mathbf {A} _ {t + 1} + \mathbf {E} _ {t + 1} - \mathbf {X}\right) \quad \text {w h e r e} \mu : \mathcal {F} (\mathbf {X}). \tag {2} +$$ + +Here $\delta_{\alpha}^{p}$ is element-wise soft-thresholding operator [65]: + +$$ +\delta_ {\alpha} ^ {p} (x) = \max \left(1 - \alpha / | x | _ {p}, 0\right) \cdot x. +$$ + +We can back-propagate through updates in Eq. (2) [88, 104] and hence can unroll them as neural network layers with learnable parameters $\alpha : \{\alpha\}_0^T, \beta : \{\beta\}_0^T$ and $\pmb{\mu} : \{\pmb{\mu}\}_0^T$ . + +Relation with ISTA: Analyzing the structure of Eq. (2), we can draw parallels with the ISTA problem [17], which seeks a sparse solution to $\mathbf{E}$ for the condition $\mathbf{X} = \mathcal{G}\mathbf{E} + \epsilon$ , with $\mathcal{G}$ as a learnable dictionary and negligible $\epsilon$ . In contrast, we have a non-negligible residue and identity dictionary. LISTA by Gregor and LeCun [26] showed how $\mathbf{E}$ update step can be represented as a weighted function which can + +then be approximated as finite network layers i.e.: + +$$ +\mathbf {E} _ {t + 1} = \delta_ {\alpha_ {t}} \left(\mathbf {w} _ {t} ^ {1} \mathbf {E} _ {t} + \mathbf {w} _ {t} ^ {2} \mathbf {X}\right), \tag {3} +$$ + +with learnable parameters $(\alpha_{t},\mathbf{w}_{t}^{1},\mathbf{w}_{t}^{2})$ for each iteration $t\in [0,T]$ . Based on the weight coupling between $\mathbf{w}^1$ and $\mathbf{w}^2$ , Chen et al. [16] simplified Eq. (3) by deriving both $\mathbf{w}^1$ and $\mathbf{w}^2$ from a single weight term, thereby halving the computation cost. A major simplification was further proposed by Liu et al. [51] as ALISTA, who proved how all weight terms could be analytically obtained for a known dictionary, thereby leaving only step sizes and thresholds i.e. $\mu$ and $\alpha_{t}$ to be estimated. Later on this idea was extended to other similar optimization formulations and improved upon by additional simplifications and guarantees e.g. Cai et al. [12] unrolled their ADMM updates into a network for robust principal component analysis. + +Recursive Factorization: Drawing parallels from ALISTA [51] and its applications [12], we propose to learn the analytically reduced sparsity thresholds and step sizes via unrolled network layers. After optimizing the above mentioned objective Eq. (1) we obtain one specular factor $\mathbf{E}^k$ where index $k\in [1,K]$ indicates the factor number. For multiple factors, we recursively solve Eq. (1) by resetting the input $X$ after removing the previous specular output and relaxing the initial sparsity weight. We initialize variables for each factor at $t = 0$ as: + +$$ +\mathbf {X} ^ {k + 1} = \mathbf {X} ^ {k} - \mathbf {E} ^ {k}, \quad \mathbf {Y} ^ {k} = \mathbf {X} ^ {k} / \| \mathbf {X} ^ {k} \| _ {2} \tag {4} +$$ + +$$ +\alpha^ {k} = (1 - \nu^ {k}) \hat {X} ^ {k}, \quad \beta^ {k} = \nu^ {k} \hat {X} ^ {k}, \quad \nu^ {k} = k / K, +$$ + +where $\hat{X}$ indicates input mean and $\mathbf{X}^0 = \mathbf{I}$ . Intuitively, this can be understood as progressively removing specularity $(E^{k})$ from the original image by gradually relaxing the sparsity weight $(\alpha^{k + 1} < \alpha^{k})$ . This lets us split the original image into multiple additive factors as: + +$$ +\mathbf {I} = \mathbf {E} ^ {1} + \mathbf {E} ^ {2} + \dots + \mathbf {E} ^ {K} = \sum_ {k = 1} ^ {K} \mathbf {E} ^ {k} \tag {5} +$$ + +Unrolling: Based upon above discussion, we propose an unrolled network collecting all parameters in a single vector $\pmb{\theta}$ . In each iteration $t$ , we estimate three scalars: thresholds for both components $(\alpha_{t},\beta_{t})$ and the step size $(\mu_t)$ . Hence for a factor $k$ , we have $3T$ parameters $\pmb{\theta}^{k} := (\alpha^{k},\beta^{k},\mu^{k})$ and overall we have only $3KT$ parameters $\pmb{\theta} := \{\pmb{\theta}_{1}^{k}\}_{1}^{K}$ . Hence our model-driven factorization module is extremely light-weight compared to other decompositions (Tab. 2). We propose the following novel factorization loss: + +$$ +L _ {f} = \lambda_ {f} \sum_ {k = 1} ^ {K} L _ {f} ^ {k} \quad \text {w h e r e} \quad L _ {f} ^ {k} = \left| \hat {E} ^ {k} / \hat {X} ^ {k} - \nu^ {k} \right|. \tag {6} +$$ + +This constraints the ratio of signal energy in the $k^{th}$ factor compared to the input, to $\nu^k$ . As $\nu^k$ increases for higher factors, our factorization loss relaxes the sparsity constraint, thereby gradually increasing the number of pixels in the specular component. After training, we are left with $K$ specular factors which sum to $I$ . As shown in Fig. 1 and Fig. 2, each one of these factors highlights specific image regions with similar illumination characteristics which can be individually targeted for enhancement. + +Motivation/Validation: The core assumption behind our factorization is that an image can be split into multiple specular factors with each representing specific illumination characteristic. Although such factorization quality assessment is difficult to estimate [9, 25, 30], we performed a toy experiment to validate our hypothesis using shadow detection dataset [34] which contains binary shadow masks in complex real world images (Fig. 2). We extract semantics-rich DINO image features [14] after masking shadow and non-shadow image regions and visualize them in 2D using PCA. This marks separation of feature space between shadowed and highlighted regions in the background. The regions with progressively degrading illumination characteristics (glare, direct light, indirect light, soft shadow, dark shadow, etc.) are expected to gradually lie between the two extremes. Next we factorize each image into five factors using our approach and plot the cluster mean for each factor feature distribution on the same graph. We can observe in Fig. 2 that successive factors gradually shift from the nonshadow towards the shadowed feature space region mirroring the expected illumination order. This confirms that our factorization decomposes the pixel values across fundamental illumination types like glare, direct light, indirect light, shadow, etc. + +We also plot the respective factor distribution densities of intensity factorization [32, 33] and our specularity factorization (Fig. 2, bottom right). Intensity factorization allows little variation in the underlying factor distributions and imposes hard segmentation constraints with binary pixel masks. Our specular factors, on the other hand, permit + +Algorithm 1: LLE Training +Input: Lowlight:I; Hyperparams: $\lambda_{c|e|s}, K, T$ +Output: Enhanced: O; Params: $\theta = \{\alpha\}_{0}^{K}, \{\beta\}_{0}^{K}, \{\mu\}_{0}^{K}$ +for $e \gets 0$ to num of epochs do +// Train Factorization Module +for $k \gets 0$ to $K$ do +for $t \gets 0$ to $T$ do +Initialize $E_0^k, A_0^k, Y_0^k$ ; // Eqn. 4 + $E_t, A_t, Y_t \gets$ ADMM updates; // Eqn. 2 +end + $F^k \gets E^k - E^{k-1}$ ; // Eqn. 7 +end +Compute $L_f$ ; // Eqn. 6 +// Train Fusion Module +if $e >$ freeze epoch then +Freeze all $\alpha, \beta, \mu$ ; + $L_f \gets 0$ ; +end + $I_{fuse} \gets$ Concatenate $[I, F^1, ..., F^K]$ ; + $O \gets$ Forward $(I_{fuse})$ ; +Compute $L$ ; // Eqn. 9 +Backpropagate $L$ ; +end + +higher variability and soft masks, with each pixel value spread across multiple factors. This provides more flexible representation and better optical approximation. + +# 3.2. Fusion Network + +In order to adhere to the zero-reference paradigm, we choose our fusion module to be a small fully-convolutional UNet like architecture with symmetric skip connections similar to other zero-reference methods [27, 63, 106]. One fundamental difference is that we modify the architecture to harness multiple factors and simultaneously perform fusion, enhancement and denoising. Specifically, it comprises of seven $3 \times 3$ convolutional layers with symmetric skip connections. We first pre-process all of our factors by subtracting the adjacent factors to discover the additional pixel values allowed in the current factor compared to the previous one as a soft mask: + +$$ +\mathbf {F} ^ {k} = \mathbf {E} ^ {k} - \mathbf {E} ^ {k - 1} \text {w h e r e} \mathbf {F} ^ {1} = \mathbf {E} ^ {1}. \tag {7} +$$ + +These factors are weighted if required using fixed scalar values and are then passed as a concatenated tensor into the fusion network. The output gamma maps $\mathbf{R}^k$ rescale different image regions differently and are applied directly on the original image inside the curve adjustment equation [27] for the fused result: + +$$ +O = \Phi \left(\sum_ {k = 0} ^ {K} I + R ^ {k}. \left((I) ^ {2} - I\right)\right). \tag {8} +$$ + +The fused output is finally passed through a differentiable bilateral filtering layer $\Phi$ [71] for the final enhanced result $O$ . Note that all the parameters from both factorization and fusion networks are trained together in end-to-end manner. + +Loss Terms: We use two widely employed zero-reference losses for enhancement [27, 63, 96] and one image smoothing loss for denoising. First color loss $L_{c}$ [27, 96] is based + +
ParadigmTraditional Model BasedZero-reference
MethodLIME [29]DUAL [100]SDD [31]ECNet [98]ZDCE [27]ZD++ [47]RUAS [72]SCI [57]PNet [63]GDP [20]RSFNet (Ours) 2.11
Params x103---16.5x10379.4210.563.430.2615.25552x103
Lolv1 [87] (dataset split: 485/15, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑16.2015.9715.1418.0116.7616.3818.4516.4519.8517.6822.17
SSIMy↑0.6950.6920.7540.6440.7340.6450.7660.7090.7180.6780.860
PSNRc↑14.2214.0213.3415.8114.8614.7416.4014.7817.5015.8019.39
SSIMc↑0.5210.5190.6340.4690.5620.4960.5030.5250.5500.5390.755
NIQE↓8.5838.6113.7068.8448.2238.1955.9278.3748.6296.4373.129
LPIPS↓0.3440.3460.2780.3580.3310.3460.3030.3270.3400.3750.265
Lolv2-real [95] (dataset split: 689/100, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑19.3119.1018.4718.8620.3119.3617.4919.3720.0815.8321.46
SSIMy↑0.7050.7040.7920.6130.7450.5850.7420.7220.6910.6270.836
PSNRc↑17.1416.9516.6416.2718.0617.3615.3317.3017.6314.0519.27
SSIMc↑0.5370.5350.6780.4590.5800.4420.4930.5400.5390.5020.738
NIQE↓9.0769.0834.1919.4754.1918.7096.1728.7399.1526.8673.769
LPIPS↓0.3220.3240.2800.3600.3100.3400.3250.2940.3400.3900.280
GENERALIZED PERFORMANCE Mean Scores (Lolv1 [87], Lolv2-real [95], Lolv2-syn [95] and VE-Lol [52])
PSNRy↑18.5017.8317.5018.4519.2618.7317.0918.0719.6515.8821.16
SSIMy↑0.7370.7280.7810.6770.7770.6740.7430.7450.7430.6340.854
PSNRc↑16.5315.8815.7716.2517.1916.7615.1216.2017.3514.1518.45
SSIMc↑0.5960.5830.6790.5380.6340.5480.5320.5870.6050.5040.758
NIQE↓7.8557.4784.0777.5434.2707.4685.8417.6267.7916.7263.763
LPIPS↓0.2910.2970.2660.3290.2730.2960.3460.2950.3020.3790.276
+ +Table 2. Quantitative comparison of our method RSFNet with other traditional and zero-reference solutions on multiple lowlight benchmarks and six evaluation metrics. Shown here are scores for two datasets LOLv1 and LOLv2-real with mean value across all datasets in the last sub-table (key: ↑ higher better; ↓ lower better; bold: best; underline: second best). + +on the gray-world assumption which tries to minimize the mean value difference between each color channel pair: + +$$ +L _ {c} = \sum_ {(i, j) \in C} \left(\hat {O} ^ {i} - \hat {O} ^ {j}\right) ^ {2}, \quad C \in \{(r, g), (g, b), (b, r) \}. +$$ + +Second is the exposure loss $L_{e}$ [27, 33, 59], which penalizes grayscale intensity deviation from the mid-tone value: + +$$ +L _ {e} = \frac {1}{| \Omega |} \sum_ {\Omega} \left(\phi (O) - 0. 6\right) ^ {2} \text {w h e r e} \Omega \in \{c \times h \times w \}, +$$ + +where $\phi$ represents the average value over a $16\times 16$ window. Our third loss is the pixel-wise smoothing loss which controls the local gradients $\nabla_{x|y}$ in the final output: + +$$ +L _ {s} = \frac {1}{| \Omega |} \sum_ {\Omega} \left((\nabla_ {x} O) ^ {2} + (\nabla_ {y} O) ^ {2}\right), +$$ + +Note that this differs from the previous works who focus on total variational loss of the gamma maps instead. Our final training loss with $\lambda$ 's as respective loss weights, is given as: + +$$ +L = \lambda_ {f} L _ {f} + \lambda_ {c} L _ {c} + \lambda_ {e} L _ {e} + \lambda_ {s} L _ {s}. \tag {9} +$$ + +# 4. Experiments and Results + +We now report our implementation details, results and extensions. Please see the supplementary document for additional details and results. + +Setup: We implement our combined network end-to-end on a single Nvidia 1080Ti GPU in PyTorch. We directly use low-light RGB images as inputs without any additional pre-processing. We first train factorization module for 25 epochs which we freeze and then optimize the fusion module for next 25 epochs. We use stochastic gradient descent for optimization with batch size of 10 and 0.01 as learning rate. Model hyper-parameters are fixed using grid search and the entire training take less than 30 minutes. + +Datasets: We evaluate our method using multiple LLE benchmark datasets (Lolv1 [87], Lolv2-real [95], Lolv2-synthetic [95] and VE-Lol [52]) with standard train/test splits (Tab. 2). These datasets comprise of several underexposed small-aperture inputs and corresponding well-exposed ground-truth pairs. Here we report results on two datasets: Lolv1 and Lolv2-real and finally show the mean scores on all four datasets combined in the last sub-table Tab. 2 and in Fig. 5. Furthermore, we report generalization results (Tab. 4) on five additional no-reference datasets which have significant domain shift: DICM [42], LIME [29], MEF [56], NPE [85] and VV [82]. + +Metrics: We report both single channel (Y from YCbCr) and multichannel (RGB) performance scores. As full-reference metrics (which require ground truth), we use Peak Signal to Noise-Ratio (PSNR), Structural Similarity Index Metric (SSIM) [86] and Learned Perceptual Image Patch Similarity (LPIPS) [101]. For no-reference assessment (without ground truth), we report Naturalness Image + +
VariantsPSNRy↑SSIMy↑
w/o Le8.120.238
w/o Lc16.050.724
w/o Ls20.130.846
w/o Denoise19.510.756
w/o Fusion19.320.830
Full22.170.860
+ +Table 3. Ablation analysis on five variants of our RSFNet (Sec. 4). + +
NIQE↓& LOE↓ECNet[98]ZDCE[27]ZD++[47]RUAS[72]PNet[63]SCI[57]RSFNet(Ours)
DICM [42]3.37—676.73.10—340.82.94—511.94.89—14213.00—590.33.61—321.93.23—303.1
LIME [29]3.75—685.13.79—135.03.89—332.24.26—719.93.84—223.24.14—75.53.80—68.3
MEF [56]3.30—863.33.31—164.33.18—458.54.08—784.23.25—363.03.43—95.03.00—100.7
NPE [85]3.24—936.13.52—312.93.27—532.25.75—13993.29—601.13.89—239.83.31—221.5
VV [82]2.15—292.42.75—145.42.53—222.93.82—583.72.56—260.22.30—109.01.96—109.0
Mean3.16—690.73.29—219.73.16—411.54.56—981.73.19—407.53.47—168.23.06—160.5
+ +Table 4. Qualitative comparison using naturalness preserving metrics (NIQE $\downarrow$ - LOE $\downarrow$ ) on five no-reference benchmarks: DICM, LIME, MEF, NPE and VV (best scores in bold, lower is better). + +![](images/6f3f2ecd3fbf3e4a7e090995bf2e745f1d03e551a150ab3394832e0b1cdaec96.jpg) +Figure 4. Results: Qualitative comparison of our method (green box) with other solutions (from top left 3 per row: SDD [31], ECNet [98], ZDCE [27]; ZD++ [47], RUAS [72], SCI [57]; PNet [63], GDP [20] and our RSFNet respectively). Our method generate natural looking images by handling noisy over and under exposed regions equally well, without over-saturating color or losing geometric details. + +![](images/e6a3a81c319bfa7a1486025f481c94529e72a70a76a719664ea46f134484f289.jpg) + +Quality Evaluator (NIQE) [60] and Lightness Order Error [84]. Note while PSNR and SSIM gauge performance quantitatively, other three metrics estimate perceptual quality. + +Comparisons: We compare against three model-based traditional optimization methods: LIME [29], DUAL [100] and SDD [31] (others ignored due to low performance). For data-driven methods we use seven recent zero-reference methods (chronologically ordered): ECNet [98], zeroDCE [27], zeroDCE++ [47], RUAS [72], SCI [57], PNet [63] and GDP [20]. We use the official code releases with pre + +![](images/072db56d1026000780da4289e5e52077f06ff399eb3fcc6f065d489cfb71bd0c.jpg) +Figure 5. Analysis: On left, our average score on all datasets vs. other methods (more area implies better). On right, ablation analysis with varying number of factors. + +trained weights and default parameters for results generation. Quantitative and qualitative performance comparison is shown in Tab. 2 and Fig. 4 respectively. Qualitatively, our method is cleaner with fewer artifacts and natural illumination (Fig. 4). This is validated by perceptual metrics like NIQE, LPIPS and LOE scores (Tabs. 2 and 4). Our method outperforms other similar category contemporary solutions on multiple metrics and achieves the best generalization performance across datasets. For a generalized performance, we take mean of all the scores across benchmarks and graphically show them in the polar plot in Fig. 5. Each polygon represents a separate LLE method with higher area inside indicating better performance. + +Ablation: To validate our design choices, we conduct ablation study on several variants of our methods using Lolv1 dataset. The effect of different number of factors $K$ on the final PSNR and SSIM scores are shown on right in Fig. 5. We choose the best observed hyper-parameter settings $K = 5$ for all our experiments. The effect of various loss terms after removing them one at a time (i.e. $w / o \, L_{e|c|s}$ ) and the effect of the final denoising step are shown in Tab. 3. The last variant ( $w / o \, Fusion$ ) represents an especially interesting setting where the fusion network is totally removed and inference uses only $3KT$ ( $= 3*5*3 = 45$ ) parameters. Fusion now reduces to a running average of the current image and + +![](images/326e21e8e5245c447e47ffc2983b841a5e3604fbbc3a31d4c70093e4ef704e43.jpg) +Dehaze + +![](images/94f01a4201cb500d9c436c101e14dad4f0b5abbe1ddde64eb32aed66fe521eb5.jpg) +Figure 6. Image enhancement applications using our specular factors as inputs on the AirNet [45] base model. Shown here left-to-right are our results for Dehazing [44], Deraining [93] and Deblurring [62] tasks respectively using AirNet [45] as base model. + +![](images/1f9d394aa1b236e21c2093d6070277f04c7e7c8f490289832eb524f6917adda4.jpg) + +![](images/f35334201e7560555e5c111c91e078629773c751048ae55961768637e35311ff.jpg) + +![](images/ed92c50423a8f729e30b91f5763f2c60dd745d81fa3b1f447c9d02e62b706ea4.jpg) + +![](images/25387027c000af3e8f612966ab3de6a189e4fcc7e79763719656b8828805e4e6.jpg) +Deblur + +![](images/db888638aaf6b7d8f59bafef303db038a906b0f6fb5f16a273860014e92f5530.jpg) + +the next factor, weighted by the normalized mean: + +$$ +O ^ {k + 1} = \left(1 - w ^ {k}\right) O ^ {k} + w ^ {k} F ^ {k}, \text {w h e r e} w ^ {k} = \hat {F} ^ {k} / \sum_ {k} \hat {F} ^ {k}. \tag {10} +$$ + +Even without any other zero-reference losses and using only a simple linear fusion, this method performs well, which demonstrates the effectiveness of our factors. Note here we have an order of magnitude smaller network size than SCI (0.045 vs. 0.26 thousand parameters in Tab. 2). + +Extensions: Our specular factors are easily interpretable and can be used directly for image manipulation as image layers in standard image editing tools like GIMP [80], Photoshop [2], etc. We show an image relighting example by varying the color and blending modes of factors in (Fig. 1 bottom left, Fig. 7). This indicates the potential of our factorization to complex downstream applications. We explore three diverse image enhancement tasks: dehazing, deraining and deblurring. Here our goal is to evaluate the use of specularity factorization as a pre-processing step on an existing base model. We chose the recent AirNet [45] as it allows experimentation on multiple image enhancement tasks with minor backbone modification. To induce our factors as prior information, we concatenate them along with the original input and alter the first convolutional layer input channels. Note that we do not introduce any new loss or layers and directly train the model for three tasks one by one: (i) Dehazing on RESIDE dataset [44] (ii) Deraining on Rain100L dataset [93] and (iii) Deblurring on GoPro dataset + +![](images/804bf4b34903aa1c1a28eeafc4241d32bb575cd51ec068a79863f7010ad0272a.jpg) +Figure 7. Controllable relighting applications using our factors as layers [80] (top:inputs; bottom:results; from left:edited light specularity, indoor color and outdoor intensity respectively). + +![](images/61b67e2c4be726bf3d60096aa0aabbca6da8ccbebc9f799364d5e3d896631c30.jpg) + +![](images/efbc81a37b3fbc7ffcdd241d869584b6af60a470a1dffc6de8e2956bc3a23241.jpg) + +
TASK →DEHAZE [44]DERAIN [93]DEBLUR [62]
MethodPSNRSSIMPSNRSSIMPSNRSSIM
AirNet (multi-task)21.040.88432.980.95124.350.781
AirNet (uni-task)23.180.90034.900.965726.420.801
AirNet + Ours24.960.929236.190.971827.290.827
+ +Table 5. Our factors can induce structure prior in an existing base model and improve performance for multiple enhancement tasks. + +[62]. As seen in Fig. 6 and Tab. 5, our results are perceptually more pleasing and improve the previously reported scores from multi-task methods consistently [45, 97]. We believe this is due to the induction of structural prior in the form of illumination based region categorization as the intensity and order of illumination at a pixel depends on the scene structure. See the supplementary for more results. + +Limitations: Our method is sensitive to initialization conditions like the underlying algorithms [12, 51]. As a heuristic we use dataset mean for initialization. Another idea, to be explored in future, is to dynamically adapt to each input which is expected to further increase the performance. + +Acknowledgements: We acknowledge the support of TCS Foundation and the Kohli Centre on Intelligent Systems for this research. + +# 5. Conclusions + +In this paper, we presented a recursive specularity factorization (RSF) and its application to zero-reference LLE. We learn optimization hyperparameters in a data-driven fashion by unrolling the stages into a small neural network. The factors are fused using a network to yield the final result. We also demonstrate the utility of RSFs for image relighting as well as for image enhancement tasks like dehazing, deraining and deblurring. We are exploring the extension of RSFs to applications like image harmonization, foreground matting, white-balancing, depth estimation, etc., and extend the technique to other signals beyond the visible spectrum. + +Ethical Concerns: This work enhances captured images and poses no special ethical issues we are aware of. + +# References + +[1] Amir Adler, Michael Elad, Yacov Hel-Or, and Ehud Rivlin. Sparse coding with anomaly detection. In 2013 IEEE MLSP, 2013. 4 +[2] Adobe Inc. 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354 + ], + "type": "image", + "image_path": "614fda24059b29ce1809d0fe66d9146fbbea2d21384fbb57ec0a55ad4f93f926.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "lines": [ + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 361, + 546, + 407 + ], + "type": "text", + "content": "Figure 1. Sepcularity Factorization: We factorize a single input image (blue box, top row) into multiple soft specular factors (rescaled for visualization) based on their similar illumination characteristics (note table shadow and lamp reflection). Our factors directly enable zero-reference low-light enhancement and user controlled image relighting (bottom left). Additionally, they can also be used as a plug-and-play prior for various supervised image enhancement tasks like dehazing, deraining and deblurring. On right, our conceptual block diagram." + } + ] + } + ], + "index": 28, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "type": "image", + "bbox": [ + 125, + 267, + 198, + 310 + ], + "blocks": [ + { + "bbox": [ + 125, + 267, + 198, + 310 + ], + "lines": [ + { + "bbox": [ + 125, + 267, + 198, + 310 + ], + "spans": [ + { + "bbox": [ + 125, + 267, + 198, + 310 + ], + "type": "image", + "image_path": "5261b73b6dd45d5dd10311105207fbbeedfb67d01d777dedb7aa391d7b67844f.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + } + ], + "index": 19 + }, + { + "type": "image", + "bbox": [ + 126, + 311, + 198, + 354 + ], + "blocks": [ + { + "bbox": [ + 126, + 311, + 198, + 354 + ], + "lines": [ + { + "bbox": [ + 126, + 311, + 198, + 354 + ], + "spans": [ + { + "bbox": [ + 126, + 311, + 198, + 354 + ], + "type": "image", + "image_path": "8ecb305ce4b8e242bc49f3b82a10ed598a139fa84cbdea19ce6420bbe1396bf5.jpg" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_body" + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 202, + 268, + 274, + 310 + ], + "blocks": [ + { + "bbox": [ + 202, + 268, + 274, + 310 + ], + "lines": [ + { + "bbox": [ + 202, + 268, + 274, + 310 + ], + "spans": [ + { + "bbox": [ + 202, + 268, + 274, + 310 + ], + "type": "image", + "image_path": "4ddc2cd7c44d9b2917f4f7534f5f49b826a132e1308c0cbfcb2119f4c99d7fa7.jpg" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_body" + } + ], + "index": 21 + }, + { + "type": "image", + "bbox": [ + 202, + 311, + 275, + 354 + ], + "blocks": [ + { + "bbox": [ + 202, + 311, + 275, + 354 + ], + "lines": [ + { + "bbox": [ + 202, + 311, + 275, + 354 + ], + "spans": [ + { + "bbox": [ + 202, + 311, + 275, + 354 + ], + "type": "image", + "image_path": "2a5ac2e2426631ef6065045aa00e8ad1a3483d8c847941cc883d85925be4cb40.jpg" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_body" + } + ], + "index": 22 + }, + { + "type": "image", + "bbox": [ + 276, + 268, + 350, + 310 + ], + "blocks": [ + { + "bbox": [ + 276, + 268, + 350, + 310 + ], + "lines": [ + { + "bbox": [ + 276, + 268, + 350, + 310 + ], + "spans": [ + { + "bbox": [ + 276, + 268, + 350, + 310 + ], + "type": "image", + "image_path": "495f45198e3be615596d664d7ea77586369a852c88938f3b7ec1f1b9cea9efd0.jpg" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_body" + } + ], + "index": 23 + }, + { + "type": "image", + "bbox": [ + 277, + 311, + 350, + 354 + ], + "blocks": [ + { + "bbox": [ + 277, + 311, + 350, + 354 + ], + "lines": [ + { + "bbox": [ + 277, + 311, + 350, + 354 + ], + "spans": [ + { + "bbox": [ + 277, + 311, + 350, + 354 + ], + "type": "image", + "image_path": "90a9c9634e883617f0678dd8d579ff0bb313b5ab1669c74c5dcc99c8f3275a17.jpg" + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_body" + } + ], + "index": 24 + }, + { + "type": "image", + "bbox": [ + 351, + 268, + 424, + 309 + ], + "blocks": [ + { + "bbox": [ + 351, + 268, + 424, + 309 + ], + "lines": [ + { + "bbox": [ + 351, + 268, + 424, + 309 + ], + "spans": [ + { + "bbox": [ + 351, + 268, + 424, + 309 + ], + "type": "image", + "image_path": "53c096b3b051bb8eb79d94bb0edf3709a6b219aa1d56bc7553594a1607210b72.jpg" + } + ] + } + ], + "index": 25, + "angle": 0, + "type": "image_body" + } + ], + "index": 25 + }, + { + "type": "image", + "bbox": [ + 351, + 310, + 424, + 354 + ], + "blocks": [ + { + "bbox": [ + 351, + 310, + 424, + 354 + ], + "lines": [ + { + "bbox": [ + 351, + 310, + 424, + 354 + ], + "spans": [ + { + "bbox": [ + 351, + 310, + 424, + 354 + ], + "type": "image", + "image_path": "8d8f1ec5f7cd158dd5f7236e862656f1137e2be4648034d135110008c8a07270.jpg" + } + ] + } + ], + "index": 26, + "angle": 0, + "type": "image_body" + } + ], + "index": 26 + }, + { + "type": "image", + "bbox": [ + 446, + 217, + 544, + 356 + ], + "blocks": [ + { + "bbox": [ + 446, + 217, + 544, + 356 + ], + "lines": [ + { + "bbox": [ + 446, + 217, + 544, + 356 + ], + "spans": [ + { + "bbox": [ + 446, + 217, + 544, + 356 + ], + "type": "image", + "image_path": "9203037654e11cfb9c6d87ee30c7504c5fe4fc7e7378bddef7c2fee3c55085ea.jpg" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_body" + } + ], + "index": 27 + }, + { + "bbox": [ + 143, + 422, + 191, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 422, + 191, + 434 + ], + "spans": [ + { + "bbox": [ + 143, + 422, + 191, + 434 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 448, + 288, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 448, + 288, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 448, + 288, + 688 + ], + "type": "text", + "content": "We present a new additive image factorization technique that treats images to be composed of multiple latent specular components which can be simply estimated recursively by modulating the sparsity during decomposition. Our model-driven RSFNet estimates these factors by unrolling the optimization into network layers requiring only a few scalars to be learned. The resultant factors are interpretable by design and can be fused for different image enhancement tasks via a network or combined directly by the user in a controllable fashion. Based on RSFNet, we detail a zero-reference Low Light Enhancement (LLE) application trained without paired or unpaired supervision. Our system improves the state-of-the-art performance on standard benchmarks and achieves better generalization on multiple other datasets. We also integrate our factors with other task specific fusion networks for applications like de-earning, deblurring and dehazing with negligible overhead thereby highlighting the multi-domain and multi-task generalizability of our proposed RSFNet. The code and data is released for reproducibility on the project homepage1." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 307, + 422, + 386, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 422, + 386, + 434 + ], + "spans": [ + { + "bbox": [ + 307, + 422, + 386, + 434 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 445, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 578 + ], + "type": "text", + "content": "A low-light image has most regions too dark for comprehension due to low exposure setting or insufficient scene lighting which makes images highly challenging for computer processing and aesthetically unpleasant. Low-Light Enhancement (LLE) aims to recovers a well-exposed image from a low-light input [46]. LLE can be a critical pre-processing step before the downstream applications [55, 57]. Core LLE challenge lies in modeling the degradation function which is spatially varying and has complex dependence on multiple variables like color, camera sensitivity, illuminant spectra, scene geometry, etc." + } + ] + } + ], + "index": 32 + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": "Most LLE solutions decompose the image into meaningful latent factors based on a relevant optical property (Tab. 1). This allows individual manipulation of each factor which simplifies the enhancement operation. A common factorization is based on the Retinex approximation [39, 58], which assumes a multiplicative disentangle-ment of image " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": " into two intrinsic factors: illumination-invariant, piecewise constant reflectance " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": " and color-invariant, smooth shading " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "inline_equation", + "content": "I = R\\cdot S" + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": ". Other factorization criteria include frequency [35, 89], spatial scale [3, 50], spatio-frequency representation [18, 67], intensity" + } + ] + } + ], + "index": 33 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 269, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 269, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 269, + 712 + ], + "type": "text", + "content": "1https://sophont01.github.io/data/projects/RSFNet/" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 302, + 750, + 307, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 750, + 307, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 307, + 757 + ], + "type": "text", + "content": "1" + } + ] + } + ], + "index": 35 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "[33], reflectance rank [69, 76], etc. Fixed number of factors [35, 69, 87] and variable number that allow better representation [3, 33, 50] have been used. Some decompose image multiplicatively like Retinex [35, 87], while others split into additive factors which are numerically more stable [21, 32, 67]. Pixel segmentation could be soft or hard based on the membership across factors, with the former introducing fewer artifacts [4]. LLE solutions can be global or local. Global methods use whole image level statistics like gamma [27], histograms [96], etc., to enhance the images. Local methods employ spatially varying features like illumination maps [87], intensity/segmentation masks [33, 63], etc., for the same. Global methods are simpler but local ones can capture scene semantics better." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 399 + ], + "type": "text", + "content": "Traditional LLE methods used manually-designed model-based optimisation by deriving specific priors from the image itself [23, 29, 100], needing no training. Data-driven, machine learning based solutions have done better recently. They use training datasets to tune the model which generalizes to other images [3, 87, 90]. Supervised methods require annotated input-output pairs of images [88, 90, 102]. Unsupervised methods require annotated training data but not necessarily paired [36, 91]. Zero-reference methods do not need annotated data and approach the problem by explicitly encoding the domain knowledge from training images [27, 57, 72]. They generalize better and are simpler, lighter, and more interpretable by design." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 400, + 289, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 289, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 289, + 579 + ], + "type": "text", + "content": "In this paper, we present a zero-reference LLE method that outperforms prior methods on the average. At core is a novel Recursive Specularity Factorization (RSF) of the image factorization based on image specularity. We decompose an image into additive specular factors by thresholding the amount of sparsity of each pixel recursively. Successive factor differences mark out newly discovered image regions which are then individually targeted for enhancement. Our RSFNet that computes the factorization is model-driven, task-agnostic, and light-weight, needing about 200 trainable parameters. The image factors are fused using a task-specific UNet-based module to enhance each region appropriately. RSF is useful to other applications when combined with other task-specific fusion modules. Our main contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 582, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 582, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 287, + 605 + ], + "type": "text", + "content": "- A novel image factorization criterion and optimization formulation based on recursive specularity estimation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 606, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 606, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 47, + 606, + 287, + 629 + ], + "type": "text", + "content": "- A model-driven RSFNet to learn factorization thresholds in a data-driven fashion using algorithm unrolling." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "content": "- A simple and flexible zero-reference LLE solution that surpasses the state of the art on multiple benchmarks and in the average generalization performance." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": "- Demonstration of RSF's usability to tasks like dehazing, deraining, and deblurring. RSF has high potential as a structural prior for several image understanding and enhancement tasks." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 317, + 71, + 535, + 168 + ], + "blocks": [ + { + "bbox": [ + 317, + 71, + 535, + 168 + ], + "lines": [ + { + "bbox": [ + 317, + 71, + 535, + 168 + ], + "spans": [ + { + "bbox": [ + 317, + 71, + 535, + 168 + ], + "type": "table", + "html": "
CriteriaNo.TypeMapSegExample
Retinex2*globalsoft[72, 88]
Frequency2+, low/highglobalhard[89]
Spectral2*, fourierglobalsoft[35]
Low Rank2+globalsoft[69, 76]
Wavelets2n+, pyramidglobalsoft[18, 67]
Multiscale2n+, pyramidglobalsoft[3, 50]
Glare/Shadow3, 4*, +localhard[5, 78]
Intensityvar.+, bandslocalhard[32, 33]
Specularityvar.+localsoftRSFNet
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Our RSFNet proposes a novel specularity based factorization which allows a variable number of local soft-segmented factors." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 247, + 384, + 261 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 247, + 384, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 247, + 384, + 261 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 267, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 545, + 327 + ], + "type": "text", + "content": "Model-based LLE: Early LLE solutions used traditional optimization models using either global statistics [15, 43, 66, 70] or spatially varying illumination maps for local editing [22, 29, 85, 99]. They were more interpretable but required hand-crafted algorithms and heuristics." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 329, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 546, + 593 + ], + "type": "text", + "content": "Data-driven LLE: Modern solutions take inspiration from traditional techniques and induce domain knowledge via loss terms or designed within the network architecture which are learned from large datasets in a data-driven fashion. They belong to one of the five training paradigms [46]. Supervised LLE methods require both low-light and well-lit paired images like Sharma and Tan [78], Wei et al. [87], Xu et al. [90], Yang et al. [95], Zhang et al. [103]. On the other hand, unsupervised methods like Jiang et al. [36], Ni et al. [64], Zhang et al. [96], require only unpaired low-light and well-lit image sets. Semi-supervised methods combine the previous two techniques and use both paired and unpaired annotations [73, 94]. Self-supervised solutions [48, 63] generate their own annotations using pseudo-labels or synthetic degradations. Contrary to all of these, zero-reference methods do not use ground truth reconstruction losses and assess the quality of output based upon encoded prior terms [27, 47, 57, 72, 98, 107]. These methods, like ours, possess improved generalizability due to explicit induction of domain knowledge and reduced chances of overfitting [27]. Zero-reference insights also provide direct valuable additions to the subsequent solutions in other paradigms." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Model-Driven Networks: Data-driven solutions have good performance but lack interpretability, whereas model-based methods are explainable by design but often compromise with lower performance. Model-driven networks [61] are hybrids which bring the best of both together. Such networks unroll optimization steps as differentiable layers with learnable parameters, inducing data-driven priors in place of hand-crafted heuristics. Although data-driven solutions are plenty, only a few model-driven solutions exist for low-level vision tasks like image restoration [40, 41], shadow re" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 749, + 309, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 749, + 309, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 749, + 309, + 757 + ], + "type": "text", + "content": "2" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 73, + 218, + 192 + ], + "blocks": [ + { + "bbox": [ + 50, + 73, + 218, + 192 + ], + "lines": [ + { + "bbox": [ + 50, + 73, + 218, + 192 + ], + "spans": [ + { + "bbox": [ + 50, + 73, + 218, + 192 + ], + "type": "image", + "image_path": "355f7c3923a3603e26949f43576930b86f182ecada5ac837d4e12e51be0d1751.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 547, + 263 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 547, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 547, + 263 + ], + "type": "text", + "content": "Figure 2. Categorization and Motivation: Left shows categorization of various LLE solution types (Sec. 2). Middle plot shows the relationship between five factor cluster centers w.r.t each other and the background comprising of shadow/non-shadow regions estimated using PCA dimensionality reduced DINO features [14]. Gradual progression of feature cluster centers from highlight region to shadow region indicates their capability to capture various illumination regions in an image. Top right shows one data point from CHUK dataset [34] with mask, processed shadow/highlight regions and extracted factors. Bottom right plots distinguish our specular fuzzy factors from intensity thresholding based binary division, with ours allowing more diverse distributions and richer representation." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 219, + 74, + 386, + 194 + ], + "blocks": [ + { + "bbox": [ + 219, + 74, + 386, + 194 + ], + "lines": [ + { + "bbox": [ + 219, + 74, + 386, + 194 + ], + "spans": [ + { + "bbox": [ + 219, + 74, + 386, + 194 + ], + "type": "image", + "image_path": "b4accd8fd4d71c18d75c5b7f7a40764205d461eab6191c8a71a7380bd372eb91.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 386, + 74, + 544, + 194 + ], + "blocks": [ + { + "bbox": [ + 386, + 74, + 544, + 194 + ], + "lines": [ + { + "bbox": [ + 386, + 74, + 544, + 194 + ], + "spans": [ + { + "bbox": [ + 386, + 74, + 544, + 194 + ], + "type": "image", + "image_path": "f59a79de1cf21e15deb2d46eeee35edb6811800378fcc3614f2388f70ffe6d20.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 283, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 287, + 319 + ], + "type": "text", + "content": "moyal [108], dehazing [54], deraining [83], denoising [68] and super-resolution [7, 8]. Such solutions are concise and efficient due to underlying task specific formulation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 321, + 288, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 321, + 288, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 288, + 501 + ], + "type": "text", + "content": "Model-driven LLE solutions are very recent. UretinexNet [88] and UTVNet [104] are both supervised methods which respectively unroll the Retinex and total variational LLE formulations. RUAS [72] and SCI [57] are closest to our approach as they both propose model-driven zero-reference LLE solutions. RUAS [72] unrrolls illumination estimation and noise removal steps in their optimization and compliment it with learnable architecture search, towards a dynamic LLE framework. SCI [57] on the other hand propose a residual framework wherein reflectance estimation is done by a self-calibration module which is then used to iteratively refine illumination maps. In contrast, our method is inspired directly by image formation fundamentals and presents a novel factorization criterion which provides better interpretability, performance and flexibility." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "content": "Retinex Factorization for LLE: Retinex [39, 58] is the most widely used factorization strategy for LLE [46, 72, 75, 87, 88] and beyond [9, 25, 74, 77]. One major Retinex limitation is due to the Lambertian reflection [38] assumption which approximates all surfaces as diffuse, thereby ignoring prevalent non-Lambertian effects in a real scene like specularity, translucency, caustics etc. Another issue is that pixelwise multiplicative nature of Retinex factors is cumbersome to handle numerically (especially in LLE with near zero pixel values) and the obtained illumination maps require further semantic analysis for downstream applications. Extensions of Retinex like dichromatic model [81] and shadow segmentation [5], separate one extra component each in addition to diffuse " + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 510, + 288, + 715 + ], + "type": "text", + "content": " e.g. Sharma and Tan [78] and Baslamisli et al. [5] used glare and shadow image decomposition respectively. From this perspective our recursive specular factorization can be understood as an extension of" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 283, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 283, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 283, + 545, + 319 + ], + "type": "text", + "content": "the same idea with continuously varying illumination characteristics starting from bright glares and ending with dark shadows (see Fig. 2 and Sec. 3 for details)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 329, + 546, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 546, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 546, + 556 + ], + "type": "text", + "content": "Others Factorization Strategies: Apart from Retinex, other factorization techniques are listed in Tab. 1. Afifi et al. [3], Lim and Kim [50], Mertens et al. [59], Xu et al. [89] employ spatial or frequency based image decomposition. Recently, Yang et al. [94] used recursively concatenated features from a supervised encoder and Huang et al. [35] proposed a Fourier disentanglement based solution. Apart from these supervised factorizations, Zheng and Gupta [106] proposed semantic classification based ROI identification using a pretrained segmentation network. [27, 63] predict multiple gamma correction maps for enhancement. [32, 33] simulate single image exposure burst using piece-wise thresholded intensity functions whereas [69] uses low-rank decomposition for reflectance. Each factorization strategy harnesses crucial underlying optical observations and adds valuable insights to the low-level vision research. To the best of our knowledge, our proposed method here is the first to use recursive specularity estimation as a factorization strategy for LLE and other enhancement tasks." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 572, + 373, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 572, + 373, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 572, + 373, + 586 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Outline: Our entire pipeline consists of two parts. We first decompose the image into " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " factors using our Recursive Specularity Factorization Network (RSFNet), which consists of multiple factorization modules (FM) with each optimization step encoded as a differentiable network layer. Then we fuse, enhance, and denoise the factors using a fusion network, which is built using task dependent pre-existing architectures. This modular design allows easy adoption of our technique in several other tasks and learning paradigms (Sec. 4)." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "text", + "content": "3" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 541, + 223 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 541, + 223 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 541, + 223 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 541, + 223 + ], + "type": "image", + "image_path": "8f5f4938fff2d8e5ec972e2105be4219573284994e1b6923b37ace949a57d55d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 546, + 251 + ], + "type": "text", + "content": "Figure 3. Block Diagram: Our factorization module (RSFNet) splits a given image into multiple specular components using model-driven unrolled optimization. Then fusion module combines all the factors to generate the enhanced output." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 259, + 220, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 259, + 220, + 272 + ], + "spans": [ + { + "bbox": [ + 47, + 259, + 220, + 272 + ], + "type": "text", + "content": "3.1. Factorization Network: RSFNet" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "content": "Specularity Estimation: Specularity removal is a well studied problem. Most specularity removal methods [1, 28, 79] exploit the relative sparsity of specular highlights and use pre-defined fixed sparsity thresholds to isolate the specular component. According to dichromatic reflection model [81] image consists of a diffuse " + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "content": " and a specular " + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "content": " term: " + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\mathbf{A} + \\mathbf{E}" + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "content": " for input " + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "content": " where specular component can be estimated by minimizing the " + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "inline_equation", + "content": "L_{0}" + }, + { + "bbox": [ + 46, + 277, + 287, + 374 + ], + "type": "text", + "content": " norm approximated as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 83, + 382, + 287, + 400 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 83, + 382, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 83, + 382, + 287, + 400 + ], + "type": "interline_equation", + "content": "\\underset {\\mathbf {E}, \\mathbf {A}} {\\operatorname {a r g m i n}} \\| \\mathbf {A} \\| _ {*} + \\lambda \\| \\mathbf {E} \\| _ {1} \\quad \\text {s . t .} \\mathbf {X} = \\mathbf {A} + \\mathbf {E}, \\tag {1}", + "image_path": "98cea5b5ecd354f5a7e753e59649e0a88aeb37bd0cd38ebab2b2db2cf84ffaef.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": " is relaxation of " + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "inline_equation", + "content": "L_{0}" + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": " is Frobenius norm regularizer and " + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": " is the sparsity parameter with higher values encouraging sparser results. Eq. (1) can be restated as augmented Lagrangian [10] using dual form and auxiliary parameters " + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "inline_equation", + "content": "(\\mathbf{Y},\\mu)" + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": ", which are then solvable using iterative ADMM updates " + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "inline_equation", + "content": "(t\\in [0,T])" + }, + { + "bbox": [ + 46, + 408, + 287, + 480 + ], + "type": "text", + "content": " [11] as given below:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 487, + 280, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 487, + 280, + 502 + ], + "spans": [ + { + "bbox": [ + 55, + 487, + 280, + 502 + ], + "type": "interline_equation", + "content": "\\mathbf {E} _ {t + 1} = \\delta_ {\\alpha_ {t}} ^ {1} \\left(\\mathbf {X} - \\mathbf {A} _ {t} - \\mathbf {Y} _ {t} ^ {T} / \\mu_ {t}\\right) \\quad \\text {w h e r e} \\alpha : \\mathcal {F} (\\lambda , \\mu),", + "image_path": "b640e2ec6eb5f9edf58ea3b69ca1cca7b6de462ec7d2c695226e17d66d3433ad.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 55, + 503, + 280, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 503, + 280, + 517 + ], + "spans": [ + { + "bbox": [ + 55, + 503, + 280, + 517 + ], + "type": "interline_equation", + "content": "\\mathbf {A} _ {t + 1} = \\delta_ {\\beta_ {t}} ^ {*} \\left(\\mathbf {X} - \\mathbf {E} _ {t + 1} - \\mathbf {Y} _ {t} ^ {T} / \\mu_ {t}\\right) \\quad \\text {w h e r e} \\beta : \\mathcal {F} (\\mu),", + "image_path": "966747aba5df701cbc5a25b63a404025d1c773379783063b4b6f267f3a5ba445.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 55, + 518, + 286, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 518, + 286, + 540 + ], + "spans": [ + { + "bbox": [ + 55, + 518, + 286, + 540 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} _ {t + 1} = \\mathbf {Y} _ {t} + \\mu_ {t} \\left(\\mathbf {A} _ {t + 1} + \\mathbf {E} _ {t + 1} - \\mathbf {X}\\right) \\quad \\text {w h e r e} \\mu : \\mathcal {F} (\\mathbf {X}). \\tag {2}", + "image_path": "70561870cafe210306fdc7f72498b451afffca778e730c9fd5bb2da5def83cc0.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 540, + 275, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 275, + 553 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 275, + 553 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 47, + 540, + 275, + 553 + ], + "type": "inline_equation", + "content": "\\delta_{\\alpha}^{p}" + }, + { + "bbox": [ + 47, + 540, + 275, + 553 + ], + "type": "text", + "content": " is element-wise soft-thresholding operator [65]:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 97, + 559, + 236, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 559, + 236, + 575 + ], + "spans": [ + { + "bbox": [ + 97, + 559, + 236, + 575 + ], + "type": "interline_equation", + "content": "\\delta_ {\\alpha} ^ {p} (x) = \\max \\left(1 - \\alpha / | x | _ {p}, 0\\right) \\cdot x.", + "image_path": "1d7fe4bd654f844da87ea3178ac20d24957b2818c847bc7d76f42223be58349f.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "type": "text", + "content": "We can back-propagate through updates in Eq. (2) [88, 104] and hence can unroll them as neural network layers with learnable parameters " + }, + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "type": "inline_equation", + "content": "\\alpha : \\{\\alpha\\}_0^T, \\beta : \\{\\beta\\}_0^T" + }, + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} : \\{\\pmb{\\mu}\\}_0^T" + }, + { + "bbox": [ + 46, + 581, + 286, + 619 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": "Relation with ISTA: Analyzing the structure of Eq. (2), we can draw parallels with the ISTA problem [17], which seeks a sparse solution to " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " for the condition " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\mathcal{G}\\mathbf{E} + \\epsilon" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " as a learnable dictionary and negligible " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": ". In contrast, we have a non-negligible residue and identity dictionary. LISTA by Gregor and LeCun [26] showed how " + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{E}" + }, + { + "bbox": [ + 46, + 629, + 286, + 713 + ], + "type": "text", + "content": " update step can be represented as a weighted function which can" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 260, + 508, + 272 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 260, + 508, + 272 + ], + "spans": [ + { + "bbox": [ + 306, + 260, + 508, + 272 + ], + "type": "text", + "content": "then be approximated as finite network layers i.e.:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 370, + 278, + 545, + 292 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 278, + 545, + 292 + ], + "spans": [ + { + "bbox": [ + 370, + 278, + 545, + 292 + ], + "type": "interline_equation", + "content": "\\mathbf {E} _ {t + 1} = \\delta_ {\\alpha_ {t}} \\left(\\mathbf {w} _ {t} ^ {1} \\mathbf {E} _ {t} + \\mathbf {w} _ {t} ^ {2} \\mathbf {X}\\right), \\tag {3}", + "image_path": "753fca494d272fe37d580852fa15cef7787c2fddd5c2ad044debd20360ab1683.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": "with learnable parameters " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "(\\alpha_{t},\\mathbf{w}_{t}^{1},\\mathbf{w}_{t}^{2})" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": " for each iteration " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "t\\in [0,T]" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": ". Based on the weight coupling between " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^1" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^2" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": ", Chen et al. [16] simplified Eq. (3) by deriving both " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^1" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\mathbf{w}^2" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": " from a single weight term, thereby halving the computation cost. A major simplification was further proposed by Liu et al. [51] as ALISTA, who proved how all weight terms could be analytically obtained for a known dictionary, thereby leaving only step sizes and thresholds i.e. " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\alpha_{t}" + }, + { + "bbox": [ + 304, + 299, + 546, + 455 + ], + "type": "text", + "content": " to be estimated. Later on this idea was extended to other similar optimization formulations and improved upon by additional simplifications and guarantees e.g. Cai et al. [12] unrolled their ADMM updates into a network for robust principal component analysis." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "text", + "content": "Recursive Factorization: Drawing parallels from ALISTA [51] and its applications [12], we propose to learn the analytically reduced sparsity thresholds and step sizes via unrolled network layers. After optimizing the above mentioned objective Eq. (1) we obtain one specular factor " + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\mathbf{E}^k" + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "text", + "content": " where index " + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "inline_equation", + "content": "k\\in [1,K]" + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "text", + "content": " indicates the factor number. For multiple factors, we recursively solve Eq. (1) by resetting the input " + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "text", + "content": " after removing the previous specular output and relaxing the initial sparsity weight. We initialize variables for each factor at " + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "inline_equation", + "content": "t = 0" + }, + { + "bbox": [ + 304, + 467, + 545, + 586 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 332, + 591, + 545, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 591, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 332, + 591, + 545, + 613 + ], + "type": "interline_equation", + "content": "\\mathbf {X} ^ {k + 1} = \\mathbf {X} ^ {k} - \\mathbf {E} ^ {k}, \\quad \\mathbf {Y} ^ {k} = \\mathbf {X} ^ {k} / \\| \\mathbf {X} ^ {k} \\| _ {2} \\tag {4}", + "image_path": "8c775a16e6d96b7f0af6da82f6c104be37db3b8b294395187aefb522f6709bc8.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 609, + 522, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 609, + 522, + 623 + ], + "spans": [ + { + "bbox": [ + 318, + 609, + 522, + 623 + ], + "type": "interline_equation", + "content": "\\alpha^ {k} = (1 - \\nu^ {k}) \\hat {X} ^ {k}, \\quad \\beta^ {k} = \\nu^ {k} \\hat {X} ^ {k}, \\quad \\nu^ {k} = k / K,", + "image_path": "2c516db7f30c5d8e2b9ac89998a6e235bd0e9a5a038490f351b3ed1c1dbe8cee.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\hat{X}" + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "text", + "content": " indicates input mean and " + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathbf{X}^0 = \\mathbf{I}" + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "text", + "content": ". Intuitively, this can be understood as progressively removing specularity " + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "inline_equation", + "content": "(E^{k})" + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "text", + "content": " from the original image by gradually relaxing the sparsity weight " + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "inline_equation", + "content": "(\\alpha^{k + 1} < \\alpha^{k})" + }, + { + "bbox": [ + 304, + 633, + 545, + 694 + ], + "type": "text", + "content": ". This lets us split the original image into multiple additive factors as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 351, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\mathbf {I} = \\mathbf {E} ^ {1} + \\mathbf {E} ^ {2} + \\dots + \\mathbf {E} ^ {K} = \\sum_ {k = 1} ^ {K} \\mathbf {E} ^ {k} \\tag {5}", + "image_path": "7a6cbf1aeafc7a555669e129080d39ad467be9e5684c901016c0e19649da0a40.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 750, + 308, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 750, + 308, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 308, + 757 + ], + "type": "text", + "content": "4" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": "Unrolling: Based upon above discussion, we propose an unrolled network collecting all parameters in a single vector " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": ". In each iteration " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": ", we estimate three scalars: thresholds for both components " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "(\\alpha_{t},\\beta_{t})" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": " and the step size " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "(\\mu_t)" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": ". Hence for a factor " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": ", we have " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "3T" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": " parameters " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta}^{k} := (\\alpha^{k},\\beta^{k},\\mu^{k})" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": " and overall we have only " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "3KT" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": " parameters " + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\pmb{\\theta} := \\{\\pmb{\\theta}_{1}^{k}\\}_{1}^{K}" + }, + { + "bbox": [ + 47, + 84, + 289, + 193 + ], + "type": "text", + "content": ". Hence our model-driven factorization module is extremely light-weight compared to other decompositions (Tab. 2). We propose the following novel factorization loss:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 198, + 288, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 198, + 288, + 228 + ], + "spans": [ + { + "bbox": [ + 59, + 198, + 288, + 228 + ], + "type": "interline_equation", + "content": "L _ {f} = \\lambda_ {f} \\sum_ {k = 1} ^ {K} L _ {f} ^ {k} \\quad \\text {w h e r e} \\quad L _ {f} ^ {k} = \\left| \\hat {E} ^ {k} / \\hat {X} ^ {k} - \\nu^ {k} \\right|. \\tag {6}", + "image_path": "63eb8272213d81bf3417d4acb5acf6d9a20fdb81b8c9f58d97d2e867a94fb580.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "content": "This constraints the ratio of signal energy in the " + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "inline_equation", + "content": "k^{th}" + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "content": " factor compared to the input, to " + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "inline_equation", + "content": "\\nu^k" + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "inline_equation", + "content": "\\nu^k" + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "content": " increases for higher factors, our factorization loss relaxes the sparsity constraint, thereby gradually increasing the number of pixels in the specular component. After training, we are left with " + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "content": " specular factors which sum to " + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 235, + 288, + 344 + ], + "type": "text", + "content": ". As shown in Fig. 1 and Fig. 2, each one of these factors highlights specific image regions with similar illumination characteristics which can be individually targeted for enhancement." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 354, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 640 + ], + "type": "text", + "content": "Motivation/Validation: The core assumption behind our factorization is that an image can be split into multiple specular factors with each representing specific illumination characteristic. Although such factorization quality assessment is difficult to estimate [9, 25, 30], we performed a toy experiment to validate our hypothesis using shadow detection dataset [34] which contains binary shadow masks in complex real world images (Fig. 2). We extract semantics-rich DINO image features [14] after masking shadow and non-shadow image regions and visualize them in 2D using PCA. This marks separation of feature space between shadowed and highlighted regions in the background. The regions with progressively degrading illumination characteristics (glare, direct light, indirect light, soft shadow, dark shadow, etc.) are expected to gradually lie between the two extremes. Next we factorize each image into five factors using our approach and plot the cluster mean for each factor feature distribution on the same graph. We can observe in Fig. 2 that successive factors gradually shift from the nonshadow towards the shadowed feature space region mirroring the expected illumination order. This confirms that our factorization decomposes the pixel values across fundamental illumination types like glare, direct light, indirect light, shadow, etc." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "We also plot the respective factor distribution densities of intensity factorization [32, 33] and our specularity factorization (Fig. 2, bottom right). Intensity factorization allows little variation in the underlying factor distributions and imposes hard segmentation constraints with binary pixel masks. Our specular factors, on the other hand, permit" + } + ] + } + ], + "index": 4 + }, + { + "type": "code", + "bbox": [ + 310, + 87, + 545, + 287 + ], + "blocks": [ + { + "bbox": [ + 310, + 75, + 417, + 87 + ], + "lines": [ + { + "bbox": [ + 310, + 75, + 417, + 87 + ], + "spans": [ + { + "bbox": [ + 310, + 75, + 417, + 87 + ], + "type": "text", + "content": "Algorithm 1: LLE Training" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "lines": [ + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "spans": [ + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "Input: Lowlight:I; Hyperparams: " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\lambda_{c|e|s}, K, T" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " \nOutput: Enhanced: O; Params: " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\theta = \\{\\alpha\\}_{0}^{K}, \\{\\beta\\}_{0}^{K}, \\{\\mu\\}_{0}^{K}" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " \nfor " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "e \\gets 0" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " to num of epochs do \n// Train Factorization Module \nfor " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "k \\gets 0" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " do \nfor " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "t \\gets 0" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " do \nInitialize " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "E_0^k, A_0^k, Y_0^k" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; // Eqn. 4 \n" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "E_t, A_t, Y_t \\gets" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " ADMM updates; // Eqn. 2 \nend \n" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "F^k \\gets E^k - E^{k-1}" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; // Eqn. 7 \nend \nCompute " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "L_f" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; // Eqn. 6 \n// Train Fusion Module \nif " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "e >" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " freeze epoch then \nFreeze all " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "\\alpha, \\beta, \\mu" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; \n" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "L_f \\gets 0" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; \nend \n" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "I_{fuse} \\gets" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " Concatenate " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "[I, F^1, ..., F^K]" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; \n" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "O \\gets" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": " Forward " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "(I_{fuse})" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; \nCompute " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; // Eqn. 9 \nBackpropagate " + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 310, + 87, + 545, + 287 + ], + "type": "text", + "content": "; \nend" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "code_body" + } + ], + "index": 6, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "text", + "content": "higher variability and soft masks, with each pixel value spread across multiple factors. This provides more flexible representation and better optical approximation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 344, + 404, + 356 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 344, + 404, + 356 + ], + "spans": [ + { + "bbox": [ + 306, + 344, + 404, + 356 + ], + "type": "text", + "content": "3.2. Fusion Network" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 362, + 545, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 545, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 545, + 504 + ], + "type": "text", + "content": "In order to adhere to the zero-reference paradigm, we choose our fusion module to be a small fully-convolutional UNet like architecture with symmetric skip connections similar to other zero-reference methods [27, 63, 106]. One fundamental difference is that we modify the architecture to harness multiple factors and simultaneously perform fusion, enhancement and denoising. Specifically, it comprises of seven " + }, + { + "bbox": [ + 304, + 362, + 545, + 504 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 362, + 545, + 504 + ], + "type": "text", + "content": " convolutional layers with symmetric skip connections. We first pre-process all of our factors by subtracting the adjacent factors to discover the additional pixel values allowed in the current factor compared to the previous one as a soft mask:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 356, + 508, + 545, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 508, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 356, + 508, + 545, + 521 + ], + "type": "interline_equation", + "content": "\\mathbf {F} ^ {k} = \\mathbf {E} ^ {k} - \\mathbf {E} ^ {k - 1} \\text {w h e r e} \\mathbf {F} ^ {1} = \\mathbf {E} ^ {1}. \\tag {7}", + "image_path": "f9e1e3fbeb0f52b00a86dc33522a3171237baa9a918443d91e43eb058e5e5501.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "spans": [ + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": "These factors are weighted if required using fixed scalar values and are then passed as a concatenated tensor into the fusion network. The output gamma maps " + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "inline_equation", + "content": "\\mathbf{R}^k" + }, + { + "bbox": [ + 304, + 525, + 545, + 597 + ], + "type": "text", + "content": " rescale different image regions differently and are applied directly on the original image inside the curve adjustment equation [27] for the fused result:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 362, + 599, + 545, + 628 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 599, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 362, + 599, + 545, + 628 + ], + "type": "interline_equation", + "content": "O = \\Phi \\left(\\sum_ {k = 0} ^ {K} I + R ^ {k}. \\left((I) ^ {2} - I\\right)\\right). \\tag {8}", + "image_path": "54f7638e377d5838747fa6b4543e6a7606787505ee7ca3fda163851cf22e147f.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "type": "text", + "content": "The fused output is finally passed through a differentiable bilateral filtering layer " + }, + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "type": "text", + "content": " [71] for the final enhanced result " + }, + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 304, + 632, + 545, + 678 + ], + "type": "text", + "content": ". Note that all the parameters from both factorization and fusion networks are trained together in end-to-end manner." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 679, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 679, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 679, + 545, + 715 + ], + "type": "text", + "content": "Loss Terms: We use two widely employed zero-reference losses for enhancement [27, 63, 96] and one image smoothing loss for denoising. First color loss " + }, + { + "bbox": [ + 304, + 679, + 545, + 715 + ], + "type": "inline_equation", + "content": "L_{c}" + }, + { + "bbox": [ + 304, + 679, + 545, + 715 + ], + "type": "text", + "content": " [27, 96] is based" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "text", + "content": "5" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 71, + 545, + 321 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 545, + 321 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 545, + 321 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 545, + 321 + ], + "type": "table", + "html": "
ParadigmTraditional Model BasedZero-reference
MethodLIME [29]DUAL [100]SDD [31]ECNet [98]ZDCE [27]ZD++ [47]RUAS [72]SCI [57]PNet [63]GDP [20]RSFNet (Ours) 2.11
Params x103---16.5x10379.4210.563.430.2615.25552x103
Lolv1 [87] (dataset split: 485/15, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑16.2015.9715.1418.0116.7616.3818.4516.4519.8517.6822.17
SSIMy↑0.6950.6920.7540.6440.7340.6450.7660.7090.7180.6780.860
PSNRc↑14.2214.0213.3415.8114.8614.7416.4014.7817.5015.8019.39
SSIMc↑0.5210.5190.6340.4690.5620.4960.5030.5250.5500.5390.755
NIQE↓8.5838.6113.7068.8448.2238.1955.9278.3748.6296.4373.129
LPIPS↓0.3440.3460.2780.3580.3310.3460.3030.3270.3400.3750.265
Lolv2-real [95] (dataset split: 689/100, mean≈ 0.05, resolution: 400 × 600)
PSNRy↑19.3119.1018.4718.8620.3119.3617.4919.3720.0815.8321.46
SSIMy↑0.7050.7040.7920.6130.7450.5850.7420.7220.6910.6270.836
PSNRc↑17.1416.9516.6416.2718.0617.3615.3317.3017.6314.0519.27
SSIMc↑0.5370.5350.6780.4590.5800.4420.4930.5400.5390.5020.738
NIQE↓9.0769.0834.1919.4754.1918.7096.1728.7399.1526.8673.769
LPIPS↓0.3220.3240.2800.3600.3100.3400.3250.2940.3400.3900.280
GENERALIZED PERFORMANCE Mean Scores (Lolv1 [87], Lolv2-real [95], Lolv2-syn [95] and VE-Lol [52])
PSNRy↑18.5017.8317.5018.4519.2618.7317.0918.0719.6515.8821.16
SSIMy↑0.7370.7280.7810.6770.7770.6740.7430.7450.7430.6340.854
PSNRc↑16.5315.8815.7716.2517.1916.7615.1216.2017.3514.1518.45
SSIMc↑0.5960.5830.6790.5380.6340.5480.5320.5870.6050.5040.758
NIQE↓7.8557.4784.0777.5434.2707.4685.8417.6267.7916.7263.763
LPIPS↓0.2910.2970.2660.3290.2730.2960.3460.2950.3020.3790.276
", + "image_path": "77557ad2d6b1d7fbfe830c1bee7e67bcad48a9a28115e4dd456540147af89201.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 325, + 546, + 361 + ], + "lines": [ + { + "bbox": [ + 46, + 325, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 546, + 361 + ], + "type": "text", + "content": "Table 2. Quantitative comparison of our method RSFNet with other traditional and zero-reference solutions on multiple lowlight benchmarks and six evaluation metrics. Shown here are scores for two datasets LOLv1 and LOLv2-real with mean value across all datasets in the last sub-table (key: ↑ higher better; ↓ lower better; bold: best; underline: second best)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 374, + 287, + 398 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 374, + 287, + 398 + ], + "spans": [ + { + "bbox": [ + 46, + 374, + 287, + 398 + ], + "type": "text", + "content": "on the gray-world assumption which tries to minimize the mean value difference between each color channel pair:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 55, + 404, + 278, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 404, + 278, + 433 + ], + "spans": [ + { + "bbox": [ + 55, + 404, + 278, + 433 + ], + "type": "interline_equation", + "content": "L _ {c} = \\sum_ {(i, j) \\in C} \\left(\\hat {O} ^ {i} - \\hat {O} ^ {j}\\right) ^ {2}, \\quad C \\in \\{(r, g), (g, b), (b, r) \\}.", + "image_path": "71fcbbdb238e1d1028223328065eab53133d94ef501e626326f91fa08aade015.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 438, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 438, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 438, + 287, + 462 + ], + "type": "text", + "content": "Second is the exposure loss " + }, + { + "bbox": [ + 47, + 438, + 287, + 462 + ], + "type": "inline_equation", + "content": "L_{e}" + }, + { + "bbox": [ + 47, + 438, + 287, + 462 + ], + "type": "text", + "content": " [27, 33, 59], which penalizes grayscale intensity deviation from the mid-tone value:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 52, + 468, + 282, + 497 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 468, + 282, + 497 + ], + "spans": [ + { + "bbox": [ + 52, + 468, + 282, + 497 + ], + "type": "interline_equation", + "content": "L _ {e} = \\frac {1}{| \\Omega |} \\sum_ {\\Omega} \\left(\\phi (O) - 0. 6\\right) ^ {2} \\text {w h e r e} \\Omega \\in \\{c \\times h \\times w \\},", + "image_path": "091cd80c3046a8375db0a62845c879e05840ea5daf96171012ae34d0c00b6e4f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "text", + "content": " represents the average value over a " + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "inline_equation", + "content": "16\\times 16" + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "text", + "content": " window. Our third loss is the pixel-wise smoothing loss which controls the local gradients " + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "inline_equation", + "content": "\\nabla_{x|y}" + }, + { + "bbox": [ + 46, + 503, + 287, + 540 + ], + "type": "text", + "content": " in the final output:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 91, + 547, + 243, + 574 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 547, + 243, + 574 + ], + "spans": [ + { + "bbox": [ + 91, + 547, + 243, + 574 + ], + "type": "interline_equation", + "content": "L _ {s} = \\frac {1}{| \\Omega |} \\sum_ {\\Omega} \\left((\\nabla_ {x} O) ^ {2} + (\\nabla_ {y} O) ^ {2}\\right),", + "image_path": "3cee81919060a07e15aef58673c41c5849fb01077b8300e20a493527f8db5ece.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 617 + ], + "type": "text", + "content": "Note that this differs from the previous works who focus on total variational loss of the gamma maps instead. Our final training loss with " + }, + { + "bbox": [ + 46, + 582, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 582, + 287, + 617 + ], + "type": "text", + "content": " 's as respective loss weights, is given as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 93, + 629, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 629, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 93, + 629, + 287, + 643 + ], + "type": "interline_equation", + "content": "L = \\lambda_ {f} L _ {f} + \\lambda_ {c} L _ {c} + \\lambda_ {e} L _ {e} + \\lambda_ {s} L _ {s}. \\tag {9}", + "image_path": "2dc2ad420ebb1eb486e58a0cfdffb079fb34219dcffcaee3bd74eb8841132408.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 657, + 190, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 190, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 190, + 671 + ], + "type": "text", + "content": "4. Experiments and Results" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 712 + ], + "type": "text", + "content": "We now report our implementation details, results and extensions. Please see the supplementary document for additional details and results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 374, + 546, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 546, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 546, + 481 + ], + "type": "text", + "content": "Setup: We implement our combined network end-to-end on a single Nvidia 1080Ti GPU in PyTorch. We directly use low-light RGB images as inputs without any additional pre-processing. We first train factorization module for 25 epochs which we freeze and then optimize the fusion module for next 25 epochs. We use stochastic gradient descent for optimization with batch size of 10 and 0.01 as learning rate. Model hyper-parameters are fixed using grid search and the entire training take less than 30 minutes." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 482, + 546, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 546, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 546, + 624 + ], + "type": "text", + "content": "Datasets: We evaluate our method using multiple LLE benchmark datasets (Lolv1 [87], Lolv2-real [95], Lolv2-synthetic [95] and VE-Lol [52]) with standard train/test splits (Tab. 2). These datasets comprise of several underexposed small-aperture inputs and corresponding well-exposed ground-truth pairs. Here we report results on two datasets: Lolv1 and Lolv2-real and finally show the mean scores on all four datasets combined in the last sub-table Tab. 2 and in Fig. 5. Furthermore, we report generalization results (Tab. 4) on five additional no-reference datasets which have significant domain shift: DICM [42], LIME [29], MEF [56], NPE [85] and VV [82]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 625, + 547, + 709 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 625, + 547, + 709 + ], + "spans": [ + { + "bbox": [ + 304, + 625, + 547, + 709 + ], + "type": "text", + "content": "Metrics: We report both single channel (Y from YCbCr) and multichannel (RGB) performance scores. As full-reference metrics (which require ground truth), we use Peak Signal to Noise-Ratio (PSNR), Structural Similarity Index Metric (SSIM) [86] and Learned Perceptual Image Patch Similarity (LPIPS) [101]. For no-reference assessment (without ground truth), we report Naturalness Image" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 750, + 309, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 757 + ], + "type": "text", + "content": "6" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 71, + 170, + 160 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 170, + 160 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 170, + 160 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 170, + 160 + ], + "type": "table", + "html": "
VariantsPSNRy↑SSIMy↑
w/o Le8.120.238
w/o Lc16.050.724
w/o Ls20.130.846
w/o Denoise19.510.756
w/o Fusion19.320.830
Full22.170.860
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NIQE↓& LOE↓ECNet[98]ZDCE[27]ZD++[47]RUAS[72]PNet[63]SCI[57]RSFNet(Ours)
DICM [42]3.37—676.73.10—340.82.94—511.94.89—14213.00—590.33.61—321.93.23—303.1
LIME [29]3.75—685.13.79—135.03.89—332.24.26—719.93.84—223.24.14—75.53.80—68.3
MEF [56]3.30—863.33.31—164.33.18—458.54.08—784.23.25—363.03.43—95.03.00—100.7
NPE [85]3.24—936.13.52—312.93.27—532.25.75—13993.29—601.13.89—239.83.31—221.5
VV [82]2.15—292.42.75—145.42.53—222.93.82—583.72.56—260.22.30—109.01.96—109.0
Mean3.16—690.73.29—219.73.16—411.54.56—981.73.19—407.53.47—168.23.06—160.5
", + "image_path": "68e307f5dc6e9600870bce03362f94b0f0ed9d7f325d4574d1a9646d8091188e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "type": "text", + "content": "Table 4. Qualitative comparison using naturalness preserving metrics (NIQE " + }, + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "type": "text", + "content": " - LOE " + }, + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "type": "inline_equation", + "content": "\\downarrow" + }, + { + "bbox": [ + 185, + 164, + 545, + 186 + ], + "type": "text", + "content": " ) on five no-reference benchmarks: DICM, LIME, MEF, NPE and VV (best scores in bold, lower is better)." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 194, + 289, + 338 + ], + "blocks": [ + { + "bbox": [ + 50, + 194, + 289, + 338 + ], + "lines": [ + { + "bbox": [ + 50, + 194, + 289, + 338 + ], + "spans": [ + { + "bbox": [ + 50, + 194, + 289, + 338 + ], + "type": "image", + "image_path": "6f3f2ecd3fbf3e4a7e090995bf2e745f1d03e551a150ab3394832e0b1cdaec96.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 340, + 546, + 374 + ], + "lines": [ + { + "bbox": [ + 46, + 340, + 546, + 374 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 546, + 374 + ], + "type": "text", + "content": "Figure 4. Results: Qualitative comparison of our method (green box) with other solutions (from top left 3 per row: SDD [31], ECNet [98], ZDCE [27]; ZD++ [47], RUAS [72], SCI [57]; PNet [63], GDP [20] and our RSFNet respectively). Our method generate natural looking images by handling noisy over and under exposed regions equally well, without over-saturating color or losing geometric details." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 306, + 194, + 545, + 338 + ], + "blocks": [ + { + "bbox": [ + 306, + 194, + 545, + 338 + ], + "lines": [ + { + "bbox": [ + 306, + 194, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 194, + 545, + 338 + ], + "type": "image", + "image_path": "e6a3a81c319bfa7a1486025f481c94529e72a70a76a719664ea46f134484f289.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 389, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 389, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 389, + 287, + 426 + ], + "type": "text", + "content": "Quality Evaluator (NIQE) [60] and Lightness Order Error [84]. Note while PSNR and SSIM gauge performance quantitatively, other three metrics estimate perceptual quality." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 440, + 287, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 440, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 440, + 287, + 525 + ], + "type": "text", + "content": "Comparisons: We compare against three model-based traditional optimization methods: LIME [29], DUAL [100] and SDD [31] (others ignored due to low performance). For data-driven methods we use seven recent zero-reference methods (chronologically ordered): ECNet [98], zeroDCE [27], zeroDCE++ [47], RUAS [72], SCI [57], PNet [63] and GDP [20]. We use the official code releases with pre" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 50, + 548, + 282, + 679 + ], + "blocks": [ + { + "bbox": [ + 50, + 548, + 282, + 679 + ], + "lines": [ + { + "bbox": [ + 50, + 548, + 282, + 679 + ], + "spans": [ + { + "bbox": [ + 50, + 548, + 282, + 679 + ], + "type": "image", + "image_path": "072db56d1026000780da4289e5e52077f06ff399eb3fcc6f065d489cfb71bd0c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 683, + 286, + 715 + ], + "lines": [ + { + "bbox": [ + 46, + 683, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 286, + 715 + ], + "type": "text", + "content": "Figure 5. Analysis: On left, our average score on all datasets vs. other methods (more area implies better). On right, ablation analysis with varying number of factors." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 389, + 545, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 545 + ], + "type": "text", + "content": "trained weights and default parameters for results generation. Quantitative and qualitative performance comparison is shown in Tab. 2 and Fig. 4 respectively. Qualitatively, our method is cleaner with fewer artifacts and natural illumination (Fig. 4). This is validated by perceptual metrics like NIQE, LPIPS and LOE scores (Tabs. 2 and 4). Our method outperforms other similar category contemporary solutions on multiple metrics and achieves the best generalization performance across datasets. For a generalized performance, we take mean of all the scores across benchmarks and graphically show them in the polar plot in Fig. 5. Each polygon represents a separate LLE method with higher area inside indicating better performance." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": "Ablation: To validate our design choices, we conduct ablation study on several variants of our methods using Lolv1 dataset. The effect of different number of factors " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " on the final PSNR and SSIM scores are shown on right in Fig. 5. We choose the best observed hyper-parameter settings " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "K = 5" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " for all our experiments. The effect of various loss terms after removing them one at a time (i.e. " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "w / o \\, L_{e|c|s}" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ") and the effect of the final denoising step are shown in Tab. 3. The last variant (" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "w / o \\, Fusion" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ") represents an especially interesting setting where the fusion network is totally removed and inference uses only " + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "3KT" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "inline_equation", + "content": "= 3*5*3 = 45" + }, + { + "bbox": [ + 304, + 570, + 546, + 713 + ], + "type": "text", + "content": ") parameters. Fusion now reduces to a running average of the current image and" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "text", + "content": "7" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 129, + 182 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 129, + 182 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 129, + 182 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 129, + 182 + ], + "type": "image", + "image_path": "326e21e8e5245c447e47ffc2983b841a5e3604fbbc3a31d4c70093e4ef704e43.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 121, + 183, + 141, + 191 + ], + "lines": [ + { + "bbox": [ + 121, + 183, + 141, + 191 + ], + "spans": [ + { + "bbox": [ + 121, + 183, + 141, + 191 + ], + "type": "text", + "content": "Dehaze" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 131, + 72, + 212, + 182 + ], + "blocks": [ + { + "bbox": [ + 131, + 72, + 212, + 182 + ], + "lines": [ + { + "bbox": [ + 131, + 72, + 212, + 182 + ], + "spans": [ + { + "bbox": [ + 131, + 72, + 212, + 182 + ], + "type": "image", + "image_path": "94f01a4201cb500d9c436c101e14dad4f0b5abbe1ddde64eb32aed66fe521eb5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 545, + 216 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 545, + 216 + ], + "type": "text", + "content": "Figure 6. Image enhancement applications using our specular factors as inputs on the AirNet [45] base model. Shown here left-to-right are our results for Dehazing [44], Deraining [93] and Deblurring [62] tasks respectively using AirNet [45] as base model." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 212, + 72, + 257, + 182 + ], + "blocks": [ + { + "bbox": [ + 212, + 72, + 257, + 182 + ], + "lines": [ + { + "bbox": [ + 212, + 72, + 257, + 182 + ], + "spans": [ + { + "bbox": [ + 212, + 72, + 257, + 182 + ], + "type": "image", + "image_path": "1f9d394aa1b236e21c2093d6070277f04c7e7c8f490289832eb524f6917adda4.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 257, + 72, + 337, + 182 + ], + "blocks": [ + { + "bbox": [ + 257, + 72, + 337, + 182 + ], + "lines": [ + { + "bbox": [ + 257, + 72, + 337, + 182 + ], + "spans": [ + { + "bbox": [ + 257, + 72, + 337, + 182 + ], + "type": "image", + "image_path": "f35334201e7560555e5c111c91e078629773c751048ae55961768637e35311ff.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 338, + 72, + 380, + 182 + ], + "blocks": [ + { + "bbox": [ + 338, + 72, + 380, + 182 + ], + "lines": [ + { + "bbox": [ + 338, + 72, + 380, + 182 + ], + "spans": [ + { + "bbox": [ + 338, + 72, + 380, + 182 + ], + "type": "image", + "image_path": "ed92c50423a8f729e30b91f5763f2c60dd745d81fa3b1f447c9d02e62b706ea4.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 381, + 72, + 463, + 182 + ], + "blocks": [ + { + "bbox": [ + 381, + 72, + 463, + 182 + ], + "lines": [ + { + "bbox": [ + 381, + 72, + 463, + 182 + ], + "spans": [ + { + "bbox": [ + 381, + 72, + 463, + 182 + ], + "type": "image", + "image_path": "25387027c000af3e8f612966ab3de6a189e4fcc7e79763719656b8828805e4e6.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 456, + 183, + 474, + 190 + ], + "lines": [ + { + "bbox": [ + 456, + 183, + 474, + 190 + ], + "spans": [ + { + "bbox": [ + 456, + 183, + 474, + 190 + ], + "type": "text", + "content": "Deblur" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 465, + 72, + 544, + 182 + ], + "blocks": [ + { + "bbox": [ + 465, + 72, + 544, + 182 + ], + "lines": [ + { + "bbox": [ + 465, + 72, + 544, + 182 + ], + "spans": [ + { + "bbox": [ + 465, + 72, + 544, + 182 + ], + "type": "image", + "image_path": "db888638aaf6b7d8f59bafef303db038a906b0f6fb5f16a273860014e92f5530.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 231, + 249, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 231, + 249, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 231, + 249, + 243 + ], + "type": "text", + "content": "the next factor, weighted by the normalized mean:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 51, + 247, + 287, + 262 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 247, + 287, + 262 + ], + "spans": [ + { + "bbox": [ + 51, + 247, + 287, + 262 + ], + "type": "interline_equation", + "content": "O ^ {k + 1} = \\left(1 - w ^ {k}\\right) O ^ {k} + w ^ {k} F ^ {k}, \\text {w h e r e} w ^ {k} = \\hat {F} ^ {k} / \\sum_ {k} \\hat {F} ^ {k}. \\tag {10}", + "image_path": "0eef016bbb1fccc8c4802aefe969502c0bd2a1ec7dcde643be55fc2cfa26ff73.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 266, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 287, + 327 + ], + "type": "text", + "content": "Even without any other zero-reference losses and using only a simple linear fusion, this method performs well, which demonstrates the effectiveness of our factors. Note here we have an order of magnitude smaller network size than SCI (0.045 vs. 0.26 thousand parameters in Tab. 2)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 338, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 567 + ], + "type": "text", + "content": "Extensions: Our specular factors are easily interpretable and can be used directly for image manipulation as image layers in standard image editing tools like GIMP [80], Photoshop [2], etc. We show an image relighting example by varying the color and blending modes of factors in (Fig. 1 bottom left, Fig. 7). This indicates the potential of our factorization to complex downstream applications. We explore three diverse image enhancement tasks: dehazing, deraining and deblurring. Here our goal is to evaluate the use of specularity factorization as a pre-processing step on an existing base model. We chose the recent AirNet [45] as it allows experimentation on multiple image enhancement tasks with minor backbone modification. To induce our factors as prior information, we concatenate them along with the original input and alter the first convolutional layer input channels. Note that we do not introduce any new loss or layers and directly train the model for three tasks one by one: (i) Dehazing on RESIDE dataset [44] (ii) Deraining on Rain100L dataset [93] and (iii) Deblurring on GoPro dataset" + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 50, + 582, + 126, + 677 + ], + "blocks": [ + { + "bbox": [ + 50, + 582, + 126, + 677 + ], + "lines": [ + { + "bbox": [ + 50, + 582, + 126, + 677 + ], + "spans": [ + { + "bbox": [ + 50, + 582, + 126, + 677 + ], + "type": "image", + "image_path": "804bf4b34903aa1c1a28eeafc4241d32bb575cd51ec068a79863f7010ad0272a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 683, + 287, + 715 + ], + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 715 + ], + "type": "text", + "content": "Figure 7. Controllable relighting applications using our factors as layers [80] (top:inputs; bottom:results; from left:edited light specularity, indoor color and outdoor intensity respectively)." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 129, + 582, + 205, + 679 + ], + "blocks": [ + { + "bbox": [ + 129, + 582, + 205, + 679 + ], + "lines": [ + { + "bbox": [ + 129, + 582, + 205, + 679 + ], + "spans": [ + { + "bbox": [ + 129, + 582, + 205, + 679 + ], + "type": "image", + "image_path": "61b67e2c4be726bf3d60096aa0aabbca6da8ccbebc9f799364d5e3d896631c30.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 210, + 582, + 286, + 679 + ], + "blocks": [ + { + "bbox": [ + 210, + 582, + 286, + 679 + ], + "lines": [ + { + "bbox": [ + 210, + 582, + 286, + 679 + ], + "spans": [ + { + "bbox": [ + 210, + 582, + 286, + 679 + ], + "type": "image", + "image_path": "efbc81a37b3fbc7ffcdd241d869584b6af60a470a1dffc6de8e2956bc3a23241.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "table", + "bbox": [ + 307, + 229, + 544, + 288 + ], + "blocks": [ + { + "bbox": [ + 307, + 229, + 544, + 288 + ], + "lines": [ + { + "bbox": [ + 307, + 229, + 544, + 288 + ], + "spans": [ + { + "bbox": [ + 307, + 229, + 544, + 288 + ], + "type": "table", + "html": "
TASK →DEHAZE [44]DERAIN [93]DEBLUR [62]
MethodPSNRSSIMPSNRSSIMPSNRSSIM
AirNet (multi-task)21.040.88432.980.95124.350.781
AirNet (uni-task)23.180.90034.900.965726.420.801
AirNet + Ours24.960.929236.190.971827.290.827
", + "image_path": "697ea6dde19b6f085e3e366967eee0cef1c09b845ac16d22ab41d0dc190921b1.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_body" + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 294, + 545, + 316 + ], + "lines": [ + { + "bbox": [ + 306, + 294, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 294, + 545, + 316 + ], + "type": "text", + "content": "Table 5. Our factors can induce structure prior in an existing base model and improve performance for multiple enhancement tasks." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 335, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 418 + ], + "type": "text", + "content": "[62]. As seen in Fig. 6 and Tab. 5, our results are perceptually more pleasing and improve the previously reported scores from multi-task methods consistently [45, 97]. We believe this is due to the induction of structural prior in the form of illumination based region categorization as the intensity and order of illumination at a pixel depends on the scene structure. See the supplementary for more results." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 419, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 419, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 419, + 545, + 479 + ], + "type": "text", + "content": "Limitations: Our method is sensitive to initialization conditions like the underlying algorithms [12, 51]. As a heuristic we use dataset mean for initialization. Another idea, to be explored in future, is to dynamically adapt to each input which is expected to further increase the performance." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 486, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 486, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 486, + 545, + 521 + ], + "type": "text", + "content": "Acknowledgements: We acknowledge the support of TCS Foundation and the Kohli Centre on Intelligent Systems for this research." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 529, + 383, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 383, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 383, + 540 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 549, + 545, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 549, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 304, + 549, + 545, + 681 + ], + "type": "text", + "content": "In this paper, we presented a recursive specularity factorization (RSF) and its application to zero-reference LLE. We learn optimization hyperparameters in a data-driven fashion by unrolling the stages into a small neural network. The factors are fused using a network to yield the final result. We also demonstrate the utility of RSFs for image relighting as well as for image enhancement tasks like dehazing, deraining and deblurring. We are exploring the extension of RSFs to applications like image harmonization, foreground matting, white-balancing, depth estimation, etc., and extend the technique to other signals beyond the visible spectrum." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "Ethical Concerns: This work enhances captured images and poses no special ethical issues we are aware of." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "spans": [ + { + "bbox": [ + 302, + 749, + 308, + 757 + ], + "type": "text", + "content": "8" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 58, + 91, + 287, + 127 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 91, + 287, + 127 + ], + "spans": [ + { + "bbox": [ + 58, + 91, + 287, + 127 + ], + "type": "text", + "content": "[1] Amir Adler, Michael Elad, Yacov Hel-Or, and Ehud Rivlin. 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AAAI, 2022. 3" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 301, + 749, + 310, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 301, + 749, + 310, + 757 + ], + "spans": [ + { + "bbox": [ + 301, + 749, + 310, + 757 + ], + "type": "text", + "content": "12" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_content_list.json b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b68d9f6c5ca319c02cf089c7b86ce213bcd26c55 --- /dev/null +++ b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_content_list.json @@ -0,0 +1,1686 @@ +[ + { + "type": "text", + "text": "Spherical Mask: Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation", + "text_level": 1, + "bbox": [ + 99, + 128, + 870, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sangyun Shin Kaichen Zhou Madhu Vankadari Andrew Markham Niki Trigoni Department of Computer Science University of Oxford", + "bbox": [ + 127, + 202, + 826, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "firstname.lastname@cs.ox.ac.uk", + "bbox": [ + 346, + 258, + 614, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Coarse-to-fine 3D instance segmentation methods show weak performances compared to recent Grouping-based, Kernel-based and Transformer-based methods. We argue that this is due to two limitations: 1) Instance size overestimation by axis-aligned bounding box(AABB) 2) False negative error accumulation from inaccurate box to the refinement phase. In this work, we introduce Spherical Mask, a novel coarse-to-fine approach based on spherical representation, overcoming those two limitations with several benefits. Specifically, our coarse detection estimates each instance with a 3D polygon using a center and radial distance predictions, which avoids excessive size estimation of AABB. To cut the error propagation in the existing coarse-to-fine approaches, we virtually migrate points based on the polygon, allowing all foreground points, including false negatives, to be refined. During inference, the proposal and point migration modules run in parallel and are assembled to form binary masks of instances. We also introduce two margin-based losses for the point migration to enforce corrections for the false positives/negatives and cohesion of foreground points, significantly improving the performance. Experimental results from three datasets, such as ScanNetV2, S3DIS, and STPLS3D, show that our proposed method outperforms existing works, demonstrating the effectiveness of the new instance representation with spherical coordinates. The code is available at: https://github.com/yunshin/SphericalMask", + "bbox": [ + 75, + 340, + 473, + 734 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 207, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3D instance segmentation has gained immense attention with its wide range of applications for Indoor Scanning[38], Augmented Reality(AR)[18], and Autonomous Driving[22]. Similar to 2D instance segmentation, the goal of the task is to identify each object along with its class label. Nevertheless, the sparse and unordered nature of point clouds has led to the development of methods different from 2D image segmentation.", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8f0926a4740271d01bcdbe162d28e7dd591d2b861dfecd38522d70f595e0122b.jpg", + "image_caption": [ + "Figure 1. Pipeline of Spherical Mask with coarse-to-fine framework. Given point cloud, instances are detected with 3D polygons defined in spherical coordinates. In the refinement phase, the points virtually migrate based on the polygon to estimate fine instance masks." + ], + "image_footnote": [], + "bbox": [ + 509, + 308, + 885, + 496 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Existing approaches for 3D instance segmentation are broadly categorized into coarse-to-fine based[12, 14, 20, 33, 34], grouping-based[4, 13, 19, 30, 36], kernel-based[10, 11, 13, 29, 31], and Transformer-based[1, 15, 21, 27, 28] approaches. Recent progress in clustering techniques and attention mechanisms have driven the performances of the last three approaches to state-of-the-art. Compared to these three approaches, the coarse-to-fine approach has received relatively less attention due to a low accuracy, caused by two limitations: 1) False negative error propagation from the coarse detection to the refinement stage. 2) Overestimation of instance size.", + "bbox": [ + 496, + 583, + 893, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Coarse-to-fine instance segmentation first performs coarse detection, followed by refinement using the coarse detection as hard reference. The basic assumption of the approach is that the coarse detection stage always provides a neat detection for refinement. However, this assumption is often violated as the coarse detection stage cannot always produce neat outputs, which causes an issue of upper bound accuracy. For example, if the first coarse detection does not include all foreground points, the following", + "bbox": [ + 496, + 763, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4060", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "refinement(binary classification) step has no means to include them, only possibly accumulating the error from false negative prediction. The other limitation is that the axis-aligned-bounding-box(AABB) estimation, which is typically used for the coarse detection, has been claimed to be an ill-defined problem[30] because commonly used box regression losses(L1, L2) result in overestimation of object sizes. For instance, the target values of AABB are minimum and maximum values in x,y,z cartesian coordinates, making the box include redundant empty space, as points only lie on the surface of the object.", + "bbox": [ + 75, + 90, + 472, + 257 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we address the aforementioned two limitations of coarse-to-fine instance segmentation. Our core intuition comes from the fact that the weakness of the coarse-to-fine approach is based on the structural disentanglement of coarse detection and fine refinement phase. Instead of assuming that the coarse part should be perfect, we take a relaxation approach, which regards the coarse detection as a soft reference during the refinement phase, providing more access for refinement yet restricting access to unnecessary background points. Specifically, to improve the coarse detection part, we estimate a 3D polygon in spherical coordinates instead of AABB, alleviating the issue of excessive object size estimation. To remove the error propagation from inaccurate coarse detection to the refinement stage, we virtually migrate points based on the 3D polygon with reduced complexity in spherical coordinates.", + "bbox": [ + 75, + 261, + 472, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our method Spherical Mask finds each instance by estimating a 3D polygon fitting to an instance in spherical coordinates and migrating points inside or outside the polygon to produce the fine instance mask. Our contributions are:", + "bbox": [ + 76, + 507, + 470, + 580 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a new alternative instance representation based on spherical coordinates, which overcomes the limitations in existing coarse-to-fine approaches.", + "- To circumvent the issue of excessive estimation of instance size, we propose Radial Instance Detection(RID) that formulates an instance into a 3D polygon as a coarse detection.", + "- To cut the error propagation from coarse detection to the refinement phase, we introduce Radial Point Migration(RPM), capable of refining both false positive and false negative points from RID.", + "- Extensive experiments on ScanNetV2 [7], S3DIS [2], and STPLS3D [3] show the effectiveness of our approach, pushing the boundary of current SOTA." + ], + "bbox": [ + 76, + 587, + 470, + 797 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 825, + 218, + 840 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing works on point cloud instance segmentation can be categorized into proposal-based, clustering-based, kernel-based and transformer-based methods.", + "bbox": [ + 75, + 854, + 470, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Coarse to Fine(Proposal-based) Approach", + "text_level": 1, + "bbox": [ + 500, + 90, + 857, + 107 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Coarse-to-fine-based methods are built on a conceptually simple design, where they first perform coarse detection, followed by a refinement stage to acquire fine segmentation. Typically, 3D bounding box is employed for the coarse detection. 3D-SIS[12] performs instance segmentation by first detecting the 3D boxes and refining points inside. 3D-BoNet[33] matches query AABBs and ground-truth instance using Hungarian algorithm for the supervision. The predicted AABBs are then concatenated with point features to produce binary masks for each instance. GSPN[34] adopts set-abstraction[24] to get query points and infer AABBs. The features inside the AABBs are extracted and used for per-point mask segmentation. More recently, TD3D [14] proposes a fully sparse-convolutional approach for point instance segmentation. It first detects AABBs and extracts perpoint features inside the boxes to perform binary classification. Most of the works use coarse detection(bounding box) directly as geometric features for predicting per-point binary instance masks. Thus, their accuracies greatly depend on the precision of the coarse detection, as inaccurate detection could easily lead to a large number of false negative points.", + "bbox": [ + 496, + 114, + 893, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Grouping-based Approach", + "text_level": 1, + "bbox": [ + 500, + 458, + 741, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Grouping-based methods learn latent embeddings to perform per-point predictions, such as semantic categories and clustering to acquire instances. PointGroup[13] predicts centroid offsets of each point and utilizes this shifted point cloud and original point cloud to obtain the clusters. Based on this concept, many studies improve the clustering technique with hierarchical intra-instance predictions[4], superpoint-based divisive grouping[19], soft grouping[30], and binary clustering[36]. The clustering-based methods have high expectations of the quality of per-point center prediction in 3D, which is challenging to generalize with various spatial extents of objects.", + "bbox": [ + 496, + 482, + 893, + 662 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.3. Kernel-based Approach", + "text_level": 1, + "bbox": [ + 500, + 674, + 718, + 691 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Kernel-based methods learn convolution kernels that aggregate point features to estimate instance masks. DyCo3D[10] proposes discriminative kernels by applying the clustering method from PointGroup[13]. Built on this, more recent works improved the performance by replacing the clustering part with farthest-point sampling[11], candidate localization[31], and instance-aware point sampling for the high-recall[29].", + "bbox": [ + 496, + 699, + 893, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.4. Transformer-based Approach", + "text_level": 1, + "bbox": [ + 500, + 830, + 764, + 847 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recently, transformer-based methods have set the new SOTA. Based on mask-attention[5, 6], Mask3D[27] and SPFormer[28] present the pipeline that learns to output", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4061", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "instance prediction directly from a fixed number of object queries from voxel and superpoint features, respectively. Based on these works, recent studies improve the performance with auxiliary center regression[15], query initialization and set grouping[21], spatial and semantic supervision[1]. Although the powerful architectural advantage has driven the performance of Transformer-based approaches, low-recall and how to distribute initial queries remain challenges.", + "bbox": [ + 75, + 90, + 472, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 239, + 166, + 255 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview", + "text_level": 1, + "bbox": [ + 76, + 265, + 187, + 279 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given an input point cloud $p_1 \\in \\mathbb{R}^{N_p \\times 3}$ in 3-dimensional cartesian coordinates and the corresponding color information $p_{\\mathrm{rgb}} \\in \\mathbb{R}^{N_p \\times 3}$ , we aim to design a system that segments the point cloud into local binary masks of instances $\\{o^{(i)} \\in \\mathbb{R}^{N_p \\times 1}\\}_{i=1}^{N_o}$ using a coarse to fine approach. Here, $N_p, N_o$ are the total number of points and the number of instances, respectively. This is achieved using the proposed method depicted in Figure 2. Our system consists of mainly two modules: 3D backbone and proposed instance mask estimation. The details of these modules are in Section 3.2 and Section 3.3, respectively.", + "bbox": [ + 75, + 286, + 472, + 455 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. 3D backbone", + "text_level": 1, + "bbox": [ + 76, + 463, + 215, + 478 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our 3D backbone is similar to [29] and is composed of two modules: a 3D encoder and a voting module. The 3D encoder uses U-Net [26] with sparse convolutions [9] to encode the given point cloud into deep features $F_{1} \\in \\mathbb{R}^{N_{p} \\times D}$ . Then, $F_{1}$ and the respective input points $p_{1}$ are fed into the voting module. The voting module performs set abstraction [24], producing $K$ votes with query points $p_{2} \\in \\mathbb{R}^{K \\times 3}$ and features $F_{2} \\in \\mathbb{R}^{K \\times D}$ . Please find the original paper [25] for more details about this procedure. These votes are spread in the scene, providing features to be further processed through the proposed instance mask estimation module. The details are explained in the following sections.", + "bbox": [ + 75, + 486, + 472, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Instance Mask Estimation", + "text_level": 1, + "bbox": [ + 76, + 691, + 313, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we estimate the instance masks from the votes predicted in the 3D backbone section using three modules: Radial Instance Detection, Radial Point Migration, and Mask Assembly. All of the modules are explained in the following sections. For the notation simplicity, we will explain how each vote feature is processed. Therefore, we write $f_{2}$ to refer to a single vote feature of $F_{2}$ from here onwards.", + "bbox": [ + 75, + 714, + 468, + 820 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3.1 Radial Instance Detection(Coarse Mask)", + "text_level": 1, + "bbox": [ + 76, + 830, + 413, + 847 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Radial Instance Detection(RID) aims to detect instances for further refinement. Similar to PolarMask[32] for 2D segmentation, we define an instance as a 3D polygon with a", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "center $f_{\\mathrm{center}}$ and multiple rays $f_{\\mathrm{ray}}$ emitting from the center forming each spherical sectors. Here, the sectors are defined by preset angles. Each ray then determines the distance to be considered for their corresponding sectors, as shown in Figure 3.", + "bbox": [ + 496, + 90, + 893, + 165 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We estimate the closest instances' center $f_{\\text{center}}$ using offsets predicted from an MLP network, CenterHead, which takes the respective $f_2$ as input and outputs offsets. The offsets are added to $p_2$ to infer $f_{\\text{center}}$ . After this, the input point cloud is converted into spherical coordinates using a transformation as $p_s = S(p_1)$ centered around $f_{\\text{center}}$ , where $S:(x,y,z) \\to (r,\\theta,\\varphi)$ as follows:", + "bbox": [ + 496, + 167, + 893, + 272 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} r = \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}, \\\\ \\theta = \\arctan \\frac {x}{y}, \\tag {1} \\\\ \\varphi = \\arctan {\\frac {z}{\\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}}}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 282, + 890, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $r$ , $\\theta$ , $\\varphi$ refer to radius, horizontal, and vertical angles in spherical coordinates, respectively. The $p_s$ is then divided uniformly with $N_{\\theta}$ and $N_{\\varphi}$ separations for horizontal and vertical direction respectively, resulting in $N_{\\theta} \\cdot N_{\\varphi}$ sectors, as shown in Figure 3 (b) and (c).", + "bbox": [ + 496, + 348, + 893, + 422 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider points inside the same sector to have identical $(\\theta, \\varphi)$ , which enables us to close the sector using a boundary estimated by $f_{\\mathrm{ray}}$ . To estimate $\\{f_{\\mathrm{ray}}^{(i)}\\}_{i=1}^{N_\\theta N_\\varphi}$ , another MLP named Ray Head is employed, which takes $f_2$ as input.", + "bbox": [ + 496, + 424, + 893, + 500 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "At this point, every point inside the corresponding sector's boundary from $f_{ray}$ is considered foreground. Using the boundary, RID offers tighter boundaries of instances than AABB in point cloud, as each sector is closed at the distance of the farthest foreground point in the sector, alleviating the problem of redundant space in AABB. Please refer to our supplementary material for additional visualizations.", + "bbox": [ + 496, + 501, + 893, + 606 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Coarse Instance Loss: During training, the estimated $f_{\\text{centre}}$ and $f_{\\text{ray}}$ are compared against their respective ground truth $\\mathbf{g}_{\\text{center}}$ and $\\mathbf{g}_{\\text{ray}}$ to calculate $L_{\\text{coarse}}$ :", + "bbox": [ + 496, + 607, + 890, + 654 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {c o a r s e}} = L _ {\\text {r a y}} + L _ {\\text {c e n t e r}}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 667, + 890, + 683 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $L_{\\mathrm{ray}}$ and $L_{\\mathrm{center}}$ are defined with L1 loss:", + "bbox": [ + 496, + 689, + 812, + 705 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {r a y}} = \\frac {1}{N _ {\\theta} N _ {\\varphi}} \\sum_ {i = 1} ^ {N _ {\\theta} N _ {\\varphi}} \\left| f _ {\\text {r a y}} ^ {(i)} - \\mathbf {g} _ {\\text {r a y}} ^ {(i)} \\right| _ {1} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 580, + 715, + 890, + 758 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {c e n t e r}} = \\left| f _ {\\text {c e n t e r}} - \\mathbf {g} _ {\\text {c e n t e r}} \\right| _ {1}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 768, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, the ground-truth instance $\\mathbf{g}$ is matched with $f_{\\mathrm{center}}$ by an injective mapping obtained using Hungarian algorithm as [29, 33]. For the details of the matching, please refer to Sec 3.4. $\\mathbf{g}_{\\mathrm{ray}}^{(i)}$ is set to the distance between $\\mathbf{g}_{\\mathrm{center}}$ and the furthest foreground point in the $i_{th}$ sector. If there are no foreground points in the sector, $\\mathbf{g}_{\\mathrm{ray}}^{(i)}$ is set to minimum as $1e - 5$ . The target center $\\mathbf{g}_{\\mathrm{center}}$ is calculated as mean values", + "bbox": [ + 496, + 790, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4062", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6b9c9d61e227658cdf1f8733a2962606d4b5a411addf09d257ce12dd594eb2ba.jpg", + "image_caption": [ + "Figure 2. Overall pipeline of our proposed method based on coarse to fine approach. Given the point cloud, the backbone produces base features with 3D UNet and Voting module. Based on this, RID performs coarse detection while RPM produces the virtual point offsets to refine the coarse detection. In Mask Assembly, $K$ local binary masks are generated, where each mask is a proposal for a single instance. 3D NMS is applied to acquire the final instance masks using local binary masks, classifications, and confidence scores." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 897, + 277 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "of foreground points of the matched groundtruth instance in cartesian coordinates.", + "bbox": [ + 75, + 359, + 468, + 390 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.2 Radial Point Migration(Mask Refinement)", + "text_level": 1, + "bbox": [ + 76, + 402, + 426, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce a refinement process to perform per-point fine-tuning. This is because the coarse detection will invariably include points belonging to the background or other instances (i.e. false positives) inside its boundary and neglect some instance points that fall outside (i.e. false negatives). We propose a conceptually simple yet effective dual that jitters individual points to belong to the correct instance. In particular, this is enabled by our innovative use of spherical coordinates - we only need to learn a single radial delta for each point to move it along the ray to the instance centroid while keeping angular quantities $\\phi$ and $\\theta$ constant. Note that this is a virtual point motion - we do not alter the final point cloud. We use this as a virtual offset to obtain clean instance labels without modifying the coarse sector.", + "bbox": [ + 75, + 425, + 468, + 651 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By estimating an offset value for each point $p_1$ , these misclassified points can be virtually migrated to being in the correct region. Based on its good performance on perpoint prediction, we adopt Dynamic Convolution in a similar manner to [10, 29] as our Point Migration Head, for predicting per-point offsets $F_{\\delta} \\in \\mathbb{R}^{K \\times N_p}$ using the vote features $F_2 \\in \\mathbb{R}^{K \\times D}$ as queries against the point features $F_1 \\in \\mathbb{R}^{N_p \\times D}$ . For the coherence with the notations, we write $f_{\\delta} \\in \\mathbb{R}^{N_p}$ to refer to an output of $F_{\\delta}$ , corresponding to one vote. For the learning of $f_{\\delta}$ , we divide points into two groups. The first is to learn the radial delta for the case of misclassification, and the second is to make instances more compact and cohesive by migrating points to the centroid of the sector.", + "bbox": [ + 75, + 652, + 470, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Misclassification Correction Loss: This process aims to estimate a radial delta to move the misclassified points either", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "inside or outside the estimated coarse sector. There are two possible cases where the misclassification could occur, as shown in Figure 4 (a): Instance points could lie outside the sector boundary, acting as false negatives, or background points could incorrectly lie within the sector boundary, acting as false positives. The goal is to move these points to the correct region.", + "bbox": [ + 496, + 359, + 890, + 464 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Formally, given the point indices of foreground points $\\{j^{+(i)}\\}_{i=1}^{N+}$ and background points $\\{j^{-(i)}\\}_{i=1}^{N-}$ from the groundtruth, the false negative points $p_{\\mathrm{fn}}$ and the false positive points $p_{\\mathrm{fp}}$ are defined as:", + "bbox": [ + 500, + 465, + 893, + 526 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathrm {f n}} = \\left\\{p _ {s} ^ {(j +)}: \\left(p _ {s} ^ {(j +)} + f _ {\\delta} ^ {(j +)}\\right) > f _ {\\text {r a y}} ^ {(\\tilde {j} +)} \\right\\}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 537, + 890, + 560 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathrm {f p}} = \\left\\{p _ {s} ^ {(j -)}: \\left(p _ {s} ^ {(j -)} + f _ {\\delta} ^ {(j -)}\\right) < f _ {\\text {r a y}} ^ {(j -)} \\right\\}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 580, + 890, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $N+$ and $N-$ stand for the number of foreground and background points, respectively. Here, $\\tilde{j} = \\text{findSector}(p_s^{(j)})$ where $\\text{findSector}(\\cdot)$ is a function that takes $p_s^{(j)}$ as input and returns the index of the sector that $p_s^{(j)}$ belongs to. Please refer to the supplementary material for our implementation of findSector().", + "bbox": [ + 496, + 607, + 893, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The union of $p_{\\mathrm{fp}}$ and $p_{\\mathrm{fn}}$ forms the misclassified points $p_{\\mathrm{miss}}$ that we are interested: $p_{\\mathrm{miss}} = p_{\\mathrm{fp}} \\cup p_{\\mathrm{fn}}$ . Our aim is to push or pull them inside/outside of the ray with margins. Thus, the loss function $L_{mc}$ is formulated with soft margin loss as:", + "bbox": [ + 496, + 702, + 893, + 776 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {m c} = \\frac {1}{N _ {\\text {m i s s}}} \\sum_ {i = 1} ^ {N _ {\\text {m i s s}}} \\log \\left(1 + \\exp \\left(y * \\tanh \\left(p _ {\\text {m i s s}} ^ {(i)} + f _ {\\delta} ^ {(\\hat {i})} - f _ {\\text {r a y}} ^ {(\\tilde {i})}\\right)\\right)\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 797, + 890, + 852 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where", + "bbox": [ + 519, + 853, + 563, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} p _ {\\mathrm {m i s s}} ^ {(i)} \\in p _ {\\mathrm {f p}}, \\\\ - 1 & \\text {i f} p _ {\\mathrm {m i s s}} ^ {(i)} \\in p _ {\\mathrm {f n}}, \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 863, + 890, + 904 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4063", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/5191c73ecb9c26b1081d4b574a4e565f9fc4fcf5f070dc30e2384fea12790528.jpg", + "image_caption": [ + "Figure 3. Process of RID. (a) Object points in cartesian coordinates (b) Converting points into a spherical coordinate system, using $f_{\\text{center}}$ , and preset angles $\\theta$ and $\\varphi$ . (c) Assigning points to each sector defined by $\\theta$ and $\\varphi$ . The example shows 3/3 for $\\theta / \\varphi$ . (d) For each sector, the distance between the farthest point and the center becomes the target of $f_{\\text{ray}}$ . During inference, points with smaller distance than $f_{\\text{ray}}$ are considered foreground." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 428, + 262 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, tanh is hyperbolic-tangent function and $L_{mc}$ is calculated for all the votes that are assigned to the ground truth instance. $N_{\\mathrm{miss}}$ stands for the number of element in $p_{\\mathrm{miss}}$ and $\\hat{i}$ is index of $f_{\\delta}$ corresponding to $p_{\\mathrm{miss}}^{(i)}$ . $f_{\\mathrm{ray}}$ is only used for reference and the gradient for learning $f_{ray}$ is not calculated.", + "bbox": [ + 75, + 375, + 470, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The misclassified points around the edge, $g_{\\mathrm{ray}}$ , of an instance are provided with comparably easy learning targets. In contrast, misclassified points far from the predicted rays are assigned targets with large discrepancies, encouraging larger gradients during the training.", + "bbox": [ + 75, + 452, + 470, + 527 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sector Cohesion Loss The goal of this block is to move true-positive points to the centroid of the sector. By doing so, the sector becomes more cohesive, encouraging the learning of common and shared features of an instance as the foreground features are getting close to each other. In addition, this helps to provide a learning signal for true-positive points, as $L_{\\mathrm{mc}}$ only considers false negatives/positives. This is shown more clearly in Figure 4 (b).", + "bbox": [ + 75, + 534, + 468, + 654 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Similar to $L_{mc}$ , using point indices of foreground points $j+$ , we extract true positives $p_{\\mathrm{tp}}$ as:", + "bbox": [ + 75, + 655, + 468, + 686 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np _ {\\mathrm {t p}} = \\left\\{p _ {s} ^ {(j +)}: \\left(p _ {s} ^ {(j +)} + f _ {\\delta} ^ {(j +)}\\right) < f _ {\\text {r a y}} ^ {(\\tilde {j} +)} \\right\\} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 696, + 468, + 719 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and formulate the loss with the soft margin calculation:", + "bbox": [ + 76, + 728, + 441, + 742 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s c} = \\frac {1}{N _ {\\mathrm {t p}}} \\sum_ {i = 1} ^ {N _ {\\mathrm {t p}}} \\log \\left(1 + \\exp \\left(\\tanh \\left(f _ {\\delta} ^ {(i)} + p _ {\\mathrm {t p}} ^ {(i)} - f _ {\\text {c e n t e r}}\\right)\\right)\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 750, + 468, + 805 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{\\mathrm{tp}}$ stands for the number of element in $p_{\\mathrm{tp}}$ and $\\hat{i}$ is index of $f_{\\delta}$ corresponding to $p_{\\mathrm{tp}}^{(i)}$ . Since $f_{\\mathrm{center}}$ is always 0 in centered spherical coordinate, the loss can be simplified as:", + "bbox": [ + 75, + 805, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {s c} = \\frac {1}{N _ {\\mathrm {t p}}} \\sum_ {i = 1} ^ {N _ {\\mathrm {t p}}} \\log \\left(1 + \\exp \\left(\\tanh \\left(f _ {\\delta} ^ {(i)} + p _ {\\mathrm {t p}} ^ {(i)}\\right)\\right)\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 861, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/643eb4d00da6ca92e1dbeee492fd35d4aa2202e21439c88706d257226dbdbd19.jpg", + "image_caption": [ + "(a) Misclassification Correction Loss", + "(b) Sector Cohesion Loss", + "Figure 4. Conceptual diagram showing per-point migration following both (a) $L_{\\mathrm{mc}}$ and (b) $L_{\\mathrm{sc}}$ . $\\Delta_{\\mathrm{FP}}$ and $\\Delta_{\\mathrm{FN}}$ are distances penalized by $L_{\\mathrm{mc}}$ with margin for misclassified points. $\\Delta_{\\mathrm{TP}}$ is the distance that $L_{\\mathrm{sc}}$ penalizes to enforce the learning of general features of an instance by making each sample close to the other around the center." + ], + "image_footnote": [], + "bbox": [ + 509, + 92, + 885, + 157 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$L_{mc}$ and $L_{sc}$ together form the refinement loss $L_{\\mathrm{fine}}$ as:", + "bbox": [ + 500, + 279, + 864, + 294 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {f i n e}} = L _ {m c} + L _ {s c}. \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 305, + 890, + 320 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our proposed virtual point migration brings three advantages for refinement over existing approaches that strictly disentangle coarse detection and refinement: 1) Instead of only focusing on points inside the coarse detection, predicting the offsets of all points allows the refinement of even false negative points outside of $f_{\\mathrm{ray}}$ , sidestepping the error accumulation from the coarse detection. 2) By considering the sector radius, $g_{\\mathrm{ray}}$ , it is possible to have a soft target for each point rather than a hard target which is the center of the sector/instance. For example, false negative points outside of the sector boundary only need to be migrated a small distance to being with the sector (soft), rather than being driven towards the center (hard). This makes it easier to learn how to perform the point migration. 3) We only need to learn a one-dimensional number to migrate the point virtually along the radial line. This is far simpler than having to learn a three-dimensional offset in cartesian coordinates.", + "bbox": [ + 496, + 330, + 893, + 587 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.3 Mask Assembly", + "text_level": 1, + "bbox": [ + 500, + 599, + 663, + 614 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our final mask is assembled by comparing virtually migrated points and $f_{ray}$ . Specifically, the local binary mask $\\{f_{\\mathrm{mask}}^{(i)}\\}_{i = 1}^{N_p}$ is formed as:", + "bbox": [ + 498, + 622, + 893, + 672 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\text {m a s k}} ^ {(i)} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\left(p _ {s} ^ {(i)} + f _ {\\delta} ^ {(i)}\\right) < f _ {\\text {r a y}} ^ {(\\tilde {i})} \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 680, + 890, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training", + "text_level": 1, + "bbox": [ + 500, + 729, + 604, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the training, we also learn classification and confidence with respective MLPs. For classification, we apply cross-entropy loss, $L_{\\mathrm{cls}}$ , for learning the classes of matched groundtruth instances. For the confidence scores of the proposals, we apply L2 loss to learn IoUs between the proposals and the groundtruth instances. Similar to [29], we also duplicate the number of groundtruth for 4 times and create a cost matrix $C$ :", + "bbox": [ + 496, + 753, + 893, + 872 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC (k, i) = L _ {\\text {c o a r s e}} (k, i) + L _ {\\text {f i n e}} (k, i) + L _ {\\text {c l s}} (k, i), \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 883, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4064", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $L(,)$ refers to the loss value calculated using $k_{th}$ vote and $i_{th}$ ground-truth instance. Referring $C$ , we apply Hungarian algorithm to find the least-cost injective mapping from each ground-truth instance to the votes. The final loss using the acquired ground-truths is:", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = \\lambda_ {1} L _ {\\mathrm {c l s}} + \\lambda_ {2} L _ {\\text {c o n f}} + \\lambda_ {3} L _ {\\text {c o a r s e}} + \\lambda_ {4} L _ {\\text {f i n e}} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 180, + 468, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 204, + 200, + 220 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Dataset", + "text_level": 1, + "bbox": [ + 76, + 229, + 171, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate our method on three datasets: ScanNetV2 [7], S3DIS [2], STPLS3D [3]. Following are descriptions of each dataset.", + "bbox": [ + 75, + 253, + 468, + 297 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ScanNetV2 ScanNetV2 dataset consists of 1201, 312, and 100 scans with 18 object classes for training, validation, and testing, respectively. We report the evaluation results on the validation and hidden test sets as in the existing works.", + "bbox": [ + 75, + 299, + 468, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "S3DIS S3DIS dataset contains 271 scenes from 6 areas with 13 categories. We report evaluations for both Area 5. Additional evaluation results with 6-fold cross-validation can be found in the supplementary material.", + "bbox": [ + 75, + 359, + 468, + 421 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "STPLS3D The STPLS3D dataset is an aerial photogrammetry point cloud dataset from real-world and synthetic environments. It includes 25 urban scenes of $6km^2$ and 14 instance categories. Following [4, 29, 30], we use scenes 5, 10, 15, 20, and 25 for validation and the rest for training.", + "bbox": [ + 75, + 421, + 468, + 497 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation Metric", + "text_level": 1, + "bbox": [ + 76, + 508, + 253, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We adopt average precision as our primary evaluation metric. Average precision is extensively used in vision tasks such as object detection and instance segmentation tasks. The metric calculates precisions by varying the IoU threshold. Following the existing works, we evaluate our model with three IoU thresholds: $AP$ , $AP_{50}$ , $AP_{25}$ . $AP_{50}$ and $AP_{25}$ stand for average precisions with IoU threshold as $25\\%$ and $50\\%$ , respectively. $AP$ is an averaged score by varying IoU thresholds from $50\\%$ to $95\\%$ by increasing the threshold with step size $5\\%$ . For S3DIS, we also evaluate our model with mean precision (mPrec50), and mean recall with IoU threshold as $50\\%$ (mRec50).", + "bbox": [ + 75, + 532, + 468, + 714 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Implementation Detail", + "text_level": 1, + "bbox": [ + 76, + 724, + 285, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We build our model on PyTorch framework [23] and train it for 300 epochs with AdamW optimizer with a single NVIDIA A10 GPU. The batch size is set to 10. The learning rate and weight decay are initialized to 0.001 and 0.0001. Cosine annealing [35] is used for scheduling the learning rate. Following [29, 30], the voxel size is set to $0.02\\mathrm{m}$ for ScanNetV2 and S3DIS, and to $0.3\\mathrm{m}$ for STPLS3D. For the augmentation during training, we use random cropping for each scene with a maximum number of 250,000 points. During testing, a whole scene is used as an input to the network.", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our backbone is similar to[29, 30], which outputs features $F_{1}$ with hidden dimension $D$ as 32 channels. For the voting, we use two set-abstraction [24, 25] layers with the ball query radius 0.2 and 0.4, respectively. The number seeds and votes are set to 1024 and 256, respectively. The number of neighbors is set to 32 for both layers, similar to [29]. For Point Migration Head, we use two layers of dynamic convolution[10], and their hidden dimensions are set to 32. $\\lambda 1$ , $\\lambda 2$ , $\\lambda 3$ , and $\\lambda 4$ are set to 0.5, 0.5, 1, and 1, respectively. For training and inference, we set $N_{\\theta}$ and $N_{\\varphi}$ to 5 and 5, respectively. During inference, Non-Maximum-Suppression is applied to the $K$ binary masks to delete redundant masks using a confidence score 0.2 as a threshold. Following [19, 21, 29, 31], we aggregate superpoints[16, 17] to align the final prediction masks on the ScanNetV2 dataset. Other details, such as the architecture of MLPs and runtime analysis, are included in the supplementary material.", + "bbox": [ + 496, + 90, + 893, + 349 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Main Results", + "text_level": 1, + "bbox": [ + 500, + 358, + 637, + 372 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ScanNetV2 Table 1 and Table 2 show the quantitative result of instance segmentation on the test and validation sets. Our proposed method achieves the highest AP and $\\mathrm{AP}_{50}$ surpassing the previous strongest method by the margin of $4.1\\%$ and $2.4\\%$ for the test set, and $6.7\\%$ and $5.7\\%$ for the validation set, respectively. Compared to the previous methods based on the coarse-to-fine approach, our method achieves $24.1\\%$ of the improvement in AP on the test set. In particular, for the test set, our method outperforms existing methods on instances that are typically located close to each other, such as pictures, desks, and bookshelves. This suggests that explicitly penalizing misclassified points around the edges of instances is helpful in RPM. Please refer to the supplementary material for more results about this.", + "bbox": [ + 496, + 381, + 893, + 592 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "S3DIS Table 3 illustrates the quantitative result on Area 5. Our proposed method outperforms the second best performing method with margins of 3.3 and 2.9 in mAP, $\\mathrm{AP}_{50}$ , and mRec $_{50}$ , improving the performance of SOTA $5.7\\%$ , $4.2\\%$ , and $5.6\\%$ respectively.", + "bbox": [ + 496, + 593, + 893, + 669 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "STPLS3D Table 4 shows the quantitative comparison on the validation set of STPLS3D dataset. Our method outperforms all of the existing methods, improving SOTA performance in mAP and $\\mathrm{AP}_{50}$ for 3.0 and 4.3, respectively.", + "bbox": [ + 496, + 669, + 890, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.5. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 739, + 681, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig.5 shows visual comparisons of ISBNet[29], MAFT[15], and our proposed Spherical Mask for challenging instances on ScanNetV2 validation set. Spherical Mask accurately segments large instances such as wall and book shelves(row 1), curtains and a window between them(row 2), a large sofa(row 3) and a circular shape sofa(row 4).", + "bbox": [ + 496, + 763, + 893, + 854 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ISBNet[29] struggles to segment large instances(wall and bookshelves in row 1) and a disconnected instance(curtains and a window between them in row 2). On the other hand,", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4065", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/329d742765c56b42be294d943ef2939194bdce883450a9e0acf8b42d88b815d0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodmAP\\( \\mathrm{mAP}_{50} \\)\\( bath \\)bedbk.shfcabinetchaircountercurtaindeskdoorotherpicturefridges. cur.sinksofatabletoiletwind.
3D-BoNet(C)[33]25.348.851.932.425.113.734.53.141.96.916.213.15.220.233.814.730.130.365.117.8
TD3D(C)[14]48.975.185.251.143.432.273.510.151.235.534.946.828.351.467.626.867.151.090.832.9
SoftGroup(G)[30]50.476.166.757.937.238.169.47.267.730.338.753.131.958.275.431.864.349.290.738.8
PBNet(G)[36]57.374.792.657.561.947.273.623.948.738.345.950.653.358.576.740.471.755.996.938.1
DKNet(K)[31]53.271.881.562.451.737.774.910.750.930.443.747.558.153.977.533.964.050.690.138.5
ISBNet(K)[29]55.975.793.965.538.342.676.318.053.438.649.950.962.142.770.446.764.957.194.840.1
MAFT(T)[15]57.878.688.972.144.846.076.825.155.840.850.453.961.661.885.848.268.455.193.145.0
QueryFormer(T)[21]58.378.792.670.239.350.473.327.652.737.347.953.453.369.772.043.674.559.295.836.3
Ours(C)61.681.294.665.455.543.476.927.160.444.750.554.969.871.677.548.074.757.592.543.6
", + "bbox": [ + 86, + 88, + 883, + 209 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison of top-performing methods for each approach on ScanNetV2 hidden test set. (C),(G),(K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. All the methods take the same input, such as point cloud and corresponding color information. The best results are in bold, and the second best ones are in underlined.", + "bbox": [ + 76, + 210, + 893, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/dfc9f12415c5c46f29cba97167fe29ac1629a56022017d487d1b7e8f8e25c693.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison of ISBNet[29], MAFT[15], and ours on ScanNetV2 validation set." + ], + "image_footnote": [], + "bbox": [ + 81, + 266, + 883, + 500 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/edb7417f3ed78979d7b5bb836cde0907bcbab6ae87ad77c058ec3ec944148714.jpg", + "image_caption": [ + "Figure 6. Visually comparing impacts of RID, $L_{mc}$ , and $L_{sh}$ ." + ], + "image_footnote": [], + "bbox": [ + 81, + 527, + 880, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "MAFT[15] shows better generalization capability for learning semantics(curtains and a window between them(row 2)). However, it struggles to segment some parts of an instance that look different, as shown in sofas(row 2,3) and oversegments the instance by considering physically further away points as the same instance(wall in row 2 and sofa in row 4), probably due to the local queries that overfit to certain semantics.", + "bbox": [ + 75, + 705, + 473, + 825 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.6. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 844, + 230, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we investigate Spherical Mask with ablation studies designed for its core components.", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Impact of $\\theta$ and $\\varphi$ is shown at Table 6. For this experiment, we fixed the backbone and the RPM with $L_{mc}$ and $L_{sc}$ , and change $N_{\\theta}$ and $N_{\\varphi}$ . In theory, increasing $N_{\\theta}$ and $N_{\\varphi}$ should always produce better results. However, in practice, increasing them faces an issue of high complexity, as can be seen. Using 4/4 and 5/5 of $N_{\\theta}$ and $N_{\\varphi}$ improves the mAP for $0.9\\%$ and $1.7\\%$ , respectively. However, increasing them from 5/5 to 6/6 results in $2.8\\%$ of the performance drop, suggesting that too large $N_{\\theta}$ and $N_{\\varphi}$ make a negative impact on the performance due to increased complexity. For example, too large $N_{\\theta}$ and $N_{\\varphi}$ would result in many sectors without any foreground points, leading to biased target values for learn-", + "bbox": [ + 496, + 705, + 895, + 888 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4066", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/a99c1db7f983dc087e0861d519b3e3fda9e1b5ee4042bf227fa8e2f35430e938.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodVenuemAPAP50AP25
3D-SIS(C)[12]CVPR19-18.735.7
GSPN(C)[34]CVPR19-37.853.4
TD3D(C)[14]WACV2347.371.281.9
PointGroup(G)[13]CVPR2034.851.771.3
SSTNet(G)[19]ICCV2149.464.374.0
MaskGroup(G)[37]ICME2227.442.063.3
SoftGroup(G)[30]CVPR2246.067.678.9
RPGN(G)[8]ECCV22-64.2-
PBNet(G)[36]ICCV2354.370.578.9
PointInst3D(K)[11]EECV2245.663.7
DKNet(K)[31]ECCV2250.866.976.9
ISBNet(K)[29]CVPR2354.573.182.5
Mask3D(T)[27]ICRA2355.273.782.9
3IS-ESSS(T)[1]ICCV2356.175.083.7
QueryFormer(T)[21]ICCV2356.574.283.3
MAFT(T)[15]ICCV2358.475.684.5
Ours(C)-62.379.988.2
", + "bbox": [ + 83, + 88, + 460, + 340 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1b3702d0c4d046c0210c089e725eb450afe74efaad27c60f9d94431623293331.jpg", + "table_caption": [ + "Table 2. Quantitative 3D instance segmentation results on ScanNetV2 validation set. (C), (G), (K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. The best results are in bold, and the second best ones are in underlined." + ], + "table_footnote": [], + "table_body": "
MethodmAPAP50mPrec50mRec50
GSPN [34]--36.028.7
PointGroup [13]-5.7861.962.1
HAIS [4]--71.165.0
SSTNet [19]42.759.365.664.2
SoftGroup [30]51.666.173.666.6
Mask3D [27]56.569.368.770.7
RPGN [8]--64.063.0
PointInst3D [11]--73.165.2
DKNet [31]--70.865.3
ISBNet [29]56.367.570.572.0
PBNet [36]53.566.474.965.4
QueryFormer [21]57.769.970.572.2
MAFT [15]-69.1--
Ours60.572.371.376.3
", + "bbox": [ + 88, + 419, + 455, + 631 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9ab767900776a380d993d7899fa0f79fb2e258732133158a9ab72e0e291b0a5b.jpg", + "table_caption": [ + "Table 3. Quantitative 3D instance segmentation results on S3DIS Area 5. The best results are in bold, and the second best ones are in underlined." + ], + "table_footnote": [], + "table_body": "
MethodmAP AP50RID Lmc LscmAP AP50AP25
HAIS [4]35.046.7✓51.669.486.8
PointGroup [13]23.338.5✓✓58.577.687.5
ISBNet [29]49.264.0✓56.577.187.1
Ours52.268.3✓✓62.379.988.2
", + "bbox": [ + 78, + 681, + 460, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing. Despite the variation, all configurations of $N_{\\theta}$ and $N_{\\varphi}$ still outperform existing methods in Table 2, implying that RID with RPM always improves the performance.", + "bbox": [ + 75, + 809, + 468, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Radial Point Migration is illustrated in Table 5. Here, we investigate the impact of the RPM and each loss for it. The baseline is the model trained with only RID, exclud", + "bbox": [ + 75, + 854, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/05bb5117bb962b8a4d4be209c5e5850585baa48fe8914255b94c1f5cb223fba2.jpg", + "table_caption": [ + "Table 4. Quantitative instance segmentation results on STPLS3D", + "Table 5. Impact of each component on ScanNetV2 validation set" + ], + "table_footnote": [], + "table_body": "
Nθ/NφmAPAP50AP25
1/159.677.185.3
2/260.077.786.1
3/360.678.487.1
4/461.280.089.3
5/562.379.988.2
6/660.678.588.2
", + "bbox": [ + 500, + 87, + 687, + 188 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/66551ffabd6b9138f696a9d5079648b9f5408c8ab3d2963f613ccd6c71300bcb.jpg", + "table_caption": [ + "Table 6. Impact of $N_{\\theta}$ and $N_{\\varphi}$ on ScanNetV2 validation set" + ], + "table_footnote": [], + "table_body": "
Seed/VotemAP\\( AP_{50} \\)\\( AP_{25} \\)
1024/12862.379.287.8
1024/25662.379.988.2
1024/51262.379.487.6
2048/12862.079.788.0
2048/25661.879.687.9
2048/51261.779.187.5
", + "bbox": [ + 696, + 88, + 883, + 188 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Impact of seed and vote numbers on ScanNetV2 validation set", + "bbox": [ + 696, + 189, + 888, + 229 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing RPM. As the baseline model cannot refine the false positive points inside radial predictions or false negative points outside, as shown in Figure 6 (parts of chairs included as tables), its performance with high iou thresholds(AP, $\\mathrm{AP}_{50}$ ) are $17.1\\%$ and $13.1\\%$ worse than the full model. Including RPM with $L_{mc}$ leads $13.3\\%$ of improvement in AP, suggesting refinement to push and pull misclassified points is crucial for the performance. $L_{sc}$ shows $9.4\\%$ improvement in AP from the baseline, suggesting that focusing on true positive samples also contributes significantly to learning fine granularity and common features shared within an instance. As shown in Figure 6(column 5,6), adding $L_{sc}$ improves the segmentation around the center of the objects, which was expected as the true positive samples near the instance centers could be neglected from $L_{mc}$ as they are usually inside rays. As $L_{mc}$ and $L_{sc}$ target different samples, the full model combining both $L_{mc}$ and $L_{sc}$ shows $20.7\\%$ and $15.1\\%$ improvements for AP and $\\mathrm{AP}_{50}$ , demonstrating the synergy of the two losses.", + "bbox": [ + 496, + 237, + 893, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Impact of Voting Parameters is shown in Table 7. In this experiment, we change the seed and vote numbers inside the backbone while fixing RID and RPM. As can be seen, a seed number of 1024 produces more reliable results without variation than 2048, suggesting too many seed points negatively impact the system. Despite the slight difference, we observe that changing the seed and vote produces comparably small variations of $\\pm 0.6$ in mAP for all settings.", + "bbox": [ + 496, + 523, + 893, + 645 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 654, + 619, + 671 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present Spherical Mask, a novel coarse-to-fine approach for 3D instance segmentation in point cloud. As a coarse detection, the RID module finds instances as 3D polygons defined with center and rays. In contrast to existing coarse-to-fine approaches, the RPM module uses the polygons as soft references and migrates points efficiently in spherical coordinates to acquire final masks. We demonstrate how each module contributes to the instance segmentation and achieves state-of-the-art performances on public benchmarks ScanNet-V2, S3DIS, and STPLS3D.", + "bbox": [ + 496, + 679, + 893, + 830 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 837, + 660, + 853 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This research was supported by ACE-OPS project (EP/S030832/1).", + "bbox": [ + 500, + 857, + 830, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4067", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Salwa Al Khatib, Mohamed El Amine Boudjoghra, Jean Lahoud, and Fahad Shahbaz Khan. 3d instance segmentation via enhanced spatial and semantic supervision. 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IEEE, 2022. 8" + ], + "bbox": [ + 78, + 90, + 468, + 900 + ], + "page_idx": 9 + }, + { + "type": "ref_text", + "text": "[38] Dingfu Zhou, Jin Fang, Xibin Song, Liu Liu, Junbo Yin, Yuchao Dai, Hongdong Li, and Ruigang Yang. Joint 3d instance segmentation and object detection for autonomous driving. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1839-1849, 2020. 1", + "bbox": [ + 501, + 90, + 890, + 174 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "4069", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_model.json b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_model.json new file mode 100644 index 0000000000000000000000000000000000000000..86e1377931910fc6023cc000114c06a47e11f68a --- /dev/null +++ b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_model.json @@ -0,0 +1,2167 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.1, + 0.13, + 0.872, + 0.177 + ], + "angle": 0, + "content": "Spherical Mask: Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.203, + 0.827, + 0.257 + ], + "angle": 0, + "content": "Sangyun Shin Kaichen Zhou Madhu Vankadari Andrew Markham Niki Trigoni Department of Computer Science University of Oxford" + }, + { + "type": "text", + "bbox": [ + 0.348, + 0.26, + 0.615, + 0.273 + ], + "angle": 0, + "content": "firstname.lastname@cs.ox.ac.uk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.326 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.735 + ], + "angle": 0, + "content": "Coarse-to-fine 3D instance segmentation methods show weak performances compared to recent Grouping-based, Kernel-based and Transformer-based methods. We argue that this is due to two limitations: 1) Instance size overestimation by axis-aligned bounding box(AABB) 2) False negative error accumulation from inaccurate box to the refinement phase. In this work, we introduce Spherical Mask, a novel coarse-to-fine approach based on spherical representation, overcoming those two limitations with several benefits. Specifically, our coarse detection estimates each instance with a 3D polygon using a center and radial distance predictions, which avoids excessive size estimation of AABB. To cut the error propagation in the existing coarse-to-fine approaches, we virtually migrate points based on the polygon, allowing all foreground points, including false negatives, to be refined. During inference, the proposal and point migration modules run in parallel and are assembled to form binary masks of instances. We also introduce two margin-based losses for the point migration to enforce corrections for the false positives/negatives and cohesion of foreground points, significantly improving the performance. Experimental results from three datasets, such as ScanNetV2, S3DIS, and STPLS3D, show that our proposed method outperforms existing works, demonstrating the effectiveness of the new instance representation with spherical coordinates. The code is available at: https://github.com/yunshin/SphericalMask" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.755, + 0.208, + 0.769 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "3D instance segmentation has gained immense attention with its wide range of applications for Indoor Scanning[38], Augmented Reality(AR)[18], and Autonomous Driving[22]. Similar to 2D instance segmentation, the goal of the task is to identify each object along with its class label. Nevertheless, the sparse and unordered nature of point clouds has led to the development of methods different from 2D image segmentation." + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.309, + 0.887, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.507, + 0.895, + 0.576 + ], + "angle": 0, + "content": "Figure 1. Pipeline of Spherical Mask with coarse-to-fine framework. Given point cloud, instances are detected with 3D polygons defined in spherical coordinates. In the refinement phase, the points virtually migrate based on the polygon to estimate fine instance masks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.763 + ], + "angle": 0, + "content": "Existing approaches for 3D instance segmentation are broadly categorized into coarse-to-fine based[12, 14, 20, 33, 34], grouping-based[4, 13, 19, 30, 36], kernel-based[10, 11, 13, 29, 31], and Transformer-based[1, 15, 21, 27, 28] approaches. Recent progress in clustering techniques and attention mechanisms have driven the performances of the last three approaches to state-of-the-art. Compared to these three approaches, the coarse-to-fine approach has received relatively less attention due to a low accuracy, caused by two limitations: 1) False negative error propagation from the coarse detection to the refinement stage. 2) Overestimation of instance size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Coarse-to-fine instance segmentation first performs coarse detection, followed by refinement using the coarse detection as hard reference. The basic assumption of the approach is that the coarse detection stage always provides a neat detection for refinement. However, this assumption is often violated as the coarse detection stage cannot always produce neat outputs, which causes an issue of upper bound accuracy. For example, if the first coarse detection does not include all foreground points, the following" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4060" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "refinement(binary classification) step has no means to include them, only possibly accumulating the error from false negative prediction. The other limitation is that the axis-aligned-bounding-box(AABB) estimation, which is typically used for the coarse detection, has been claimed to be an ill-defined problem[30] because commonly used box regression losses(L1, L2) result in overestimation of object sizes. For instance, the target values of AABB are minimum and maximum values in x,y,z cartesian coordinates, making the box include redundant empty space, as points only lie on the surface of the object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.473, + 0.504 + ], + "angle": 0, + "content": "In this work, we address the aforementioned two limitations of coarse-to-fine instance segmentation. Our core intuition comes from the fact that the weakness of the coarse-to-fine approach is based on the structural disentanglement of coarse detection and fine refinement phase. Instead of assuming that the coarse part should be perfect, we take a relaxation approach, which regards the coarse detection as a soft reference during the refinement phase, providing more access for refinement yet restricting access to unnecessary background points. Specifically, to improve the coarse detection part, we estimate a 3D polygon in spherical coordinates instead of AABB, alleviating the issue of excessive object size estimation. To remove the error propagation from inaccurate coarse detection to the refinement stage, we virtually migrate points based on the 3D polygon with reduced complexity in spherical coordinates." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.508, + 0.472, + 0.582 + ], + "angle": 0, + "content": "In summary, our method Spherical Mask finds each instance by estimating a 3D polygon fitting to an instance in spherical coordinates and migrating points inside or outside the polygon to produce the fine instance mask. Our contributions are:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.588, + 0.47, + 0.633 + ], + "angle": 0, + "content": "- We introduce a new alternative instance representation based on spherical coordinates, which overcomes the limitations in existing coarse-to-fine approaches." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.634, + 0.47, + 0.692 + ], + "angle": 0, + "content": "- To circumvent the issue of excessive estimation of instance size, we propose Radial Instance Detection(RID) that formulates an instance into a 3D polygon as a coarse detection." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.694, + 0.472, + 0.754 + ], + "angle": 0, + "content": "- To cut the error propagation from coarse detection to the refinement phase, we introduce Radial Point Migration(RPM), capable of refining both false positive and false negative points from RID." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.755, + 0.47, + 0.799 + ], + "angle": 0, + "content": "- Extensive experiments on ScanNetV2 [7], S3DIS [2], and STPLS3D [3] show the effectiveness of our approach, pushing the boundary of current SOTA." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.588, + 0.472, + 0.799 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.826, + 0.219, + 0.841 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.9 + ], + "angle": 0, + "content": "Existing works on point cloud instance segmentation can be categorized into proposal-based, clustering-based, kernel-based and transformer-based methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.859, + 0.108 + ], + "angle": 0, + "content": "2.1. Coarse to Fine(Proposal-based) Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.115, + 0.895, + 0.448 + ], + "angle": 0, + "content": "Coarse-to-fine-based methods are built on a conceptually simple design, where they first perform coarse detection, followed by a refinement stage to acquire fine segmentation. Typically, 3D bounding box is employed for the coarse detection. 3D-SIS[12] performs instance segmentation by first detecting the 3D boxes and refining points inside. 3D-BoNet[33] matches query AABBs and ground-truth instance using Hungarian algorithm for the supervision. The predicted AABBs are then concatenated with point features to produce binary masks for each instance. GSPN[34] adopts set-abstraction[24] to get query points and infer AABBs. The features inside the AABBs are extracted and used for per-point mask segmentation. More recently, TD3D [14] proposes a fully sparse-convolutional approach for point instance segmentation. It first detects AABBs and extracts perpoint features inside the boxes to perform binary classification. Most of the works use coarse detection(bounding box) directly as geometric features for predicting per-point binary instance masks. Thus, their accuracies greatly depend on the precision of the coarse detection, as inaccurate detection could easily lead to a large number of false negative points." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.459, + 0.742, + 0.475 + ], + "angle": 0, + "content": "2.2. Grouping-based Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.483, + 0.895, + 0.664 + ], + "angle": 0, + "content": "Grouping-based methods learn latent embeddings to perform per-point predictions, such as semantic categories and clustering to acquire instances. PointGroup[13] predicts centroid offsets of each point and utilizes this shifted point cloud and original point cloud to obtain the clusters. Based on this concept, many studies improve the clustering technique with hierarchical intra-instance predictions[4], superpoint-based divisive grouping[19], soft grouping[30], and binary clustering[36]. The clustering-based methods have high expectations of the quality of per-point center prediction in 3D, which is challenging to generalize with various spatial extents of objects." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.675, + 0.72, + 0.692 + ], + "angle": 0, + "content": "2.3. Kernel-based Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.894, + 0.82 + ], + "angle": 0, + "content": "Kernel-based methods learn convolution kernels that aggregate point features to estimate instance masks. DyCo3D[10] proposes discriminative kernels by applying the clustering method from PointGroup[13]. Built on this, more recent works improved the performance by replacing the clustering part with farthest-point sampling[11], candidate localization[31], and instance-aware point sampling for the high-recall[29]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.765, + 0.848 + ], + "angle": 0, + "content": "2.4. Transformer-based Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Recently, transformer-based methods have set the new SOTA. Based on mask-attention[5, 6], Mask3D[27] and SPFormer[28] present the pipeline that learns to output" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4061" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.228 + ], + "angle": 0, + "content": "instance prediction directly from a fixed number of object queries from voxel and superpoint features, respectively. Based on these works, recent studies improve the performance with auxiliary center regression[15], query initialization and set grouping[21], spatial and semantic supervision[1]. Although the powerful architectural advantage has driven the performance of Transformer-based approaches, low-recall and how to distribute initial queries remain challenges." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.241, + 0.168, + 0.256 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.266, + 0.188, + 0.28 + ], + "angle": 0, + "content": "3.1. Overview" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.287, + 0.473, + 0.456 + ], + "angle": 0, + "content": "Given an input point cloud \\( p_1 \\in \\mathbb{R}^{N_p \\times 3} \\) in 3-dimensional cartesian coordinates and the corresponding color information \\( p_{\\mathrm{rgb}} \\in \\mathbb{R}^{N_p \\times 3} \\), we aim to design a system that segments the point cloud into local binary masks of instances \\( \\{o^{(i)} \\in \\mathbb{R}^{N_p \\times 1}\\}_{i=1}^{N_o} \\) using a coarse to fine approach. Here, \\( N_p, N_o \\) are the total number of points and the number of instances, respectively. This is achieved using the proposed method depicted in Figure 2. Our system consists of mainly two modules: 3D backbone and proposed instance mask estimation. The details of these modules are in Section 3.2 and Section 3.3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.464, + 0.216, + 0.479 + ], + "angle": 0, + "content": "3.2. 3D backbone" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.487, + 0.473, + 0.683 + ], + "angle": 0, + "content": "Our 3D backbone is similar to [29] and is composed of two modules: a 3D encoder and a voting module. The 3D encoder uses U-Net [26] with sparse convolutions [9] to encode the given point cloud into deep features \\( F_{1} \\in \\mathbb{R}^{N_{p} \\times D} \\). Then, \\( F_{1} \\) and the respective input points \\( p_{1} \\) are fed into the voting module. The voting module performs set abstraction [24], producing \\( K \\) votes with query points \\( p_{2} \\in \\mathbb{R}^{K \\times 3} \\) and features \\( F_{2} \\in \\mathbb{R}^{K \\times D} \\). Please find the original paper [25] for more details about this procedure. These votes are spread in the scene, providing features to be further processed through the proposed instance mask estimation module. The details are explained in the following sections." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.315, + 0.707 + ], + "angle": 0, + "content": "3.3. Instance Mask Estimation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.715, + 0.47, + 0.821 + ], + "angle": 0, + "content": "In this section, we estimate the instance masks from the votes predicted in the 3D backbone section using three modules: Radial Instance Detection, Radial Point Migration, and Mask Assembly. All of the modules are explained in the following sections. For the notation simplicity, we will explain how each vote feature is processed. Therefore, we write \\( f_{2} \\) to refer to a single vote feature of \\( F_{2} \\) from here onwards." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.415, + 0.848 + ], + "angle": 0, + "content": "3.3.1 Radial Instance Detection(Coarse Mask)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Radial Instance Detection(RID) aims to detect instances for further refinement. Similar to PolarMask[32] for 2D segmentation, we define an instance as a 3D polygon with a" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.894, + 0.166 + ], + "angle": 0, + "content": "center \\( f_{\\mathrm{center}} \\) and multiple rays \\( f_{\\mathrm{ray}} \\) emitting from the center forming each spherical sectors. Here, the sectors are defined by preset angles. Each ray then determines the distance to be considered for their corresponding sectors, as shown in Figure 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.168, + 0.894, + 0.273 + ], + "angle": 0, + "content": "We estimate the closest instances' center \\( f_{\\text{center}} \\) using offsets predicted from an MLP network, CenterHead, which takes the respective \\( f_2 \\) as input and outputs offsets. The offsets are added to \\( p_2 \\) to infer \\( f_{\\text{center}} \\). After this, the input point cloud is converted into spherical coordinates using a transformation as \\( p_s = S(p_1) \\) centered around \\( f_{\\text{center}} \\), where \\( S:(x,y,z) \\to (r,\\theta,\\varphi) \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.283, + 0.892, + 0.34 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} r = \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}, \\\\ \\theta = \\arctan \\frac {x}{y}, \\tag {1} \\\\ \\varphi = \\arctan {\\frac {z}{\\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}}}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.894, + 0.424 + ], + "angle": 0, + "content": "Here, \\(r\\), \\(\\theta\\), \\(\\varphi\\) refer to radius, horizontal, and vertical angles in spherical coordinates, respectively. The \\(p_s\\) is then divided uniformly with \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) separations for horizontal and vertical direction respectively, resulting in \\(N_{\\theta} \\cdot N_{\\varphi}\\) sectors, as shown in Figure 3 (b) and (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.894, + 0.501 + ], + "angle": 0, + "content": "We consider points inside the same sector to have identical \\((\\theta, \\varphi)\\), which enables us to close the sector using a boundary estimated by \\(f_{\\mathrm{ray}}\\). To estimate \\(\\{f_{\\mathrm{ray}}^{(i)}\\}_{i=1}^{N_\\theta N_\\varphi}\\), another MLP named Ray Head is employed, which takes \\(f_2\\) as input." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.502, + 0.894, + 0.607 + ], + "angle": 0, + "content": "At this point, every point inside the corresponding sector's boundary from \\( f_{ray} \\) is considered foreground. Using the boundary, RID offers tighter boundaries of instances than AABB in point cloud, as each sector is closed at the distance of the farthest foreground point in the sector, alleviating the problem of redundant space in AABB. Please refer to our supplementary material for additional visualizations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.608, + 0.892, + 0.655 + ], + "angle": 0, + "content": "Coarse Instance Loss: During training, the estimated \\( f_{\\text{centre}} \\) and \\( f_{\\text{ray}} \\) are compared against their respective ground truth \\( \\mathbf{g}_{\\text{center}} \\) and \\( \\mathbf{g}_{\\text{ray}} \\) to calculate \\( L_{\\text{coarse}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.668, + 0.892, + 0.684 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {c o a r s e}} = L _ {\\text {r a y}} + L _ {\\text {c e n t e r}}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.69, + 0.813, + 0.706 + ], + "angle": 0, + "content": "where \\( L_{\\mathrm{ray}} \\) and \\( L_{\\mathrm{center}} \\) are defined with L1 loss:" + }, + { + "type": "equation", + "bbox": [ + 0.581, + 0.716, + 0.892, + 0.759 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {r a y}} = \\frac {1}{N _ {\\theta} N _ {\\varphi}} \\sum_ {i = 1} ^ {N _ {\\theta} N _ {\\varphi}} \\left| f _ {\\text {r a y}} ^ {(i)} - \\mathbf {g} _ {\\text {r a y}} ^ {(i)} \\right| _ {1} \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.769, + 0.892, + 0.786 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {c e n t e r}} = \\left| f _ {\\text {c e n t e r}} - \\mathbf {g} _ {\\text {c e n t e r}} \\right| _ {1}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.791, + 0.894, + 0.902 + ], + "angle": 0, + "content": "Here, the ground-truth instance \\(\\mathbf{g}\\) is matched with \\(f_{\\mathrm{center}}\\) by an injective mapping obtained using Hungarian algorithm as [29, 33]. For the details of the matching, please refer to Sec 3.4. \\(\\mathbf{g}_{\\mathrm{ray}}^{(i)}\\) is set to the distance between \\(\\mathbf{g}_{\\mathrm{center}}\\) and the furthest foreground point in the \\(i_{th}\\) sector. If there are no foreground points in the sector, \\(\\mathbf{g}_{\\mathrm{ray}}^{(i)}\\) is set to minimum as \\(1e - 5\\). The target center \\(\\mathbf{g}_{\\mathrm{center}}\\) is calculated as mean values" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4062" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.898, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.288, + 0.895, + 0.346 + ], + "angle": 0, + "content": "Figure 2. Overall pipeline of our proposed method based on coarse to fine approach. Given the point cloud, the backbone produces base features with 3D UNet and Voting module. Based on this, RID performs coarse detection while RPM produces the virtual point offsets to refine the coarse detection. In Mask Assembly, \\(K\\) local binary masks are generated, where each mask is a proposal for a single instance. 3D NMS is applied to acquire the final instance masks using local binary masks, classifications, and confidence scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.36, + 0.47, + 0.391 + ], + "angle": 0, + "content": "of foreground points of the matched groundtruth instance in cartesian coordinates." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.403, + 0.427, + 0.418 + ], + "angle": 0, + "content": "3.3.2 Radial Point Migration(Mask Refinement)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.47, + 0.652 + ], + "angle": 0, + "content": "In this section, we introduce a refinement process to perform per-point fine-tuning. This is because the coarse detection will invariably include points belonging to the background or other instances (i.e. false positives) inside its boundary and neglect some instance points that fall outside (i.e. false negatives). We propose a conceptually simple yet effective dual that jitters individual points to belong to the correct instance. In particular, this is enabled by our innovative use of spherical coordinates - we only need to learn a single radial delta for each point to move it along the ray to the instance centroid while keeping angular quantities \\(\\phi\\) and \\(\\theta\\) constant. Note that this is a virtual point motion - we do not alter the final point cloud. We use this as a virtual offset to obtain clean instance labels without modifying the coarse sector." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.654, + 0.471, + 0.864 + ], + "angle": 0, + "content": "By estimating an offset value for each point \\( p_1 \\), these misclassified points can be virtually migrated to being in the correct region. Based on its good performance on perpoint prediction, we adopt Dynamic Convolution in a similar manner to [10, 29] as our Point Migration Head, for predicting per-point offsets \\( F_{\\delta} \\in \\mathbb{R}^{K \\times N_p} \\) using the vote features \\( F_2 \\in \\mathbb{R}^{K \\times D} \\) as queries against the point features \\( F_1 \\in \\mathbb{R}^{N_p \\times D} \\). For the coherence with the notations, we write \\( f_{\\delta} \\in \\mathbb{R}^{N_p} \\) to refer to an output of \\( F_{\\delta} \\), corresponding to one vote. For the learning of \\( f_{\\delta} \\), we divide points into two groups. The first is to learn the radial delta for the case of misclassification, and the second is to make instances more compact and cohesive by migrating points to the centroid of the sector." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Misclassification Correction Loss: This process aims to estimate a radial delta to move the misclassified points either" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.36, + 0.892, + 0.465 + ], + "angle": 0, + "content": "inside or outside the estimated coarse sector. There are two possible cases where the misclassification could occur, as shown in Figure 4 (a): Instance points could lie outside the sector boundary, acting as false negatives, or background points could incorrectly lie within the sector boundary, acting as false positives. The goal is to move these points to the correct region." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.466, + 0.894, + 0.527 + ], + "angle": 0, + "content": "Formally, given the point indices of foreground points \\(\\{j^{+(i)}\\}_{i=1}^{N+}\\) and background points \\(\\{j^{-(i)}\\}_{i=1}^{N-}\\) from the groundtruth, the false negative points \\(p_{\\mathrm{fn}}\\) and the false positive points \\(p_{\\mathrm{fp}}\\) are defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.538, + 0.892, + 0.561 + ], + "angle": 0, + "content": "\\[\np _ {\\mathrm {f n}} = \\left\\{p _ {s} ^ {(j +)}: \\left(p _ {s} ^ {(j +)} + f _ {\\delta} ^ {(j +)}\\right) > f _ {\\text {r a y}} ^ {(\\tilde {j} +)} \\right\\}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.581, + 0.892, + 0.603 + ], + "angle": 0, + "content": "\\[\np _ {\\mathrm {f p}} = \\left\\{p _ {s} ^ {(j -)}: \\left(p _ {s} ^ {(j -)} + f _ {\\delta} ^ {(j -)}\\right) < f _ {\\text {r a y}} ^ {(j -)} \\right\\}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.608, + 0.894, + 0.702 + ], + "angle": 0, + "content": "where \\( N+ \\) and \\( N- \\) stand for the number of foreground and background points, respectively. Here, \\( \\tilde{j} = \\text{findSector}(p_s^{(j)}) \\) where \\( \\text{findSector}(\\cdot) \\) is a function that takes \\( p_s^{(j)} \\) as input and returns the index of the sector that \\( p_s^{(j)} \\) belongs to. Please refer to the supplementary material for our implementation of findSector()." + }, + { + "type": "text", + "bbox": [ + 0.497, + 0.703, + 0.894, + 0.777 + ], + "angle": 0, + "content": "The union of \\( p_{\\mathrm{fp}} \\) and \\( p_{\\mathrm{fn}} \\) forms the misclassified points \\( p_{\\mathrm{miss}} \\) that we are interested: \\( p_{\\mathrm{miss}} = p_{\\mathrm{fp}} \\cup p_{\\mathrm{fn}} \\). Our aim is to push or pull them inside/outside of the ray with margins. Thus, the loss function \\( L_{mc} \\) is formulated with soft margin loss as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.799, + 0.892, + 0.853 + ], + "angle": 0, + "content": "\\[\nL _ {m c} = \\frac {1}{N _ {\\text {m i s s}}} \\sum_ {i = 1} ^ {N _ {\\text {m i s s}}} \\log \\left(1 + \\exp \\left(y * \\tanh \\left(p _ {\\text {m i s s}} ^ {(i)} + f _ {\\delta} ^ {(\\hat {i})} - f _ {\\text {r a y}} ^ {(\\tilde {i})}\\right)\\right)\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.854, + 0.565, + 0.866 + ], + "angle": 0, + "content": "where" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.864, + 0.892, + 0.905 + ], + "angle": 0, + "content": "\\[\ny = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} p _ {\\mathrm {m i s s}} ^ {(i)} \\in p _ {\\mathrm {f p}}, \\\\ - 1 & \\text {i f} p _ {\\mathrm {m i s s}} ^ {(i)} \\in p _ {\\mathrm {f n}}, \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4063" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.089, + 0.429, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.271, + 0.47, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Process of RID. (a) Object points in cartesian coordinates (b) Converting points into a spherical coordinate system, using \\( f_{\\text{center}} \\), and preset angles \\( \\theta \\) and \\( \\varphi \\). (c) Assigning points to each sector defined by \\( \\theta \\) and \\( \\varphi \\). The example shows 3/3 for \\( \\theta / \\varphi \\). (d) For each sector, the distance between the farthest point and the center becomes the target of \\( f_{\\text{ray}} \\). During inference, points with smaller distance than \\( f_{\\text{ray}} \\) are considered foreground." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.471, + 0.453 + ], + "angle": 0, + "content": "Here, tanh is hyperbolic-tangent function and \\( L_{mc} \\) is calculated for all the votes that are assigned to the ground truth instance. \\( N_{\\mathrm{miss}} \\) stands for the number of element in \\( p_{\\mathrm{miss}} \\) and \\( \\hat{i} \\) is index of \\( f_{\\delta} \\) corresponding to \\( p_{\\mathrm{miss}}^{(i)} \\). \\( f_{\\mathrm{ray}} \\) is only used for reference and the gradient for learning \\( f_{ray} \\) is not calculated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.471, + 0.529 + ], + "angle": 0, + "content": "The misclassified points around the edge, \\( g_{\\mathrm{ray}} \\), of an instance are provided with comparably easy learning targets. In contrast, misclassified points far from the predicted rays are assigned targets with large discrepancies, encouraging larger gradients during the training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.47, + 0.655 + ], + "angle": 0, + "content": "Sector Cohesion Loss The goal of this block is to move true-positive points to the centroid of the sector. By doing so, the sector becomes more cohesive, encouraging the learning of common and shared features of an instance as the foreground features are getting close to each other. In addition, this helps to provide a learning signal for true-positive points, as \\( L_{\\mathrm{mc}} \\) only considers false negatives/positives. This is shown more clearly in Figure 4 (b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.469, + 0.687 + ], + "angle": 0, + "content": "Similar to \\( L_{mc} \\), using point indices of foreground points \\( j+ \\), we extract true positives \\( p_{\\mathrm{tp}} \\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.135, + 0.697, + 0.47, + 0.72 + ], + "angle": 0, + "content": "\\[\np _ {\\mathrm {t p}} = \\left\\{p _ {s} ^ {(j +)}: \\left(p _ {s} ^ {(j +)} + f _ {\\delta} ^ {(j +)}\\right) < f _ {\\text {r a y}} ^ {(\\tilde {j} +)} \\right\\} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.729, + 0.442, + 0.743 + ], + "angle": 0, + "content": "and formulate the loss with the soft margin calculation:" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.751, + 0.47, + 0.806 + ], + "angle": 0, + "content": "\\[\nL _ {s c} = \\frac {1}{N _ {\\mathrm {t p}}} \\sum_ {i = 1} ^ {N _ {\\mathrm {t p}}} \\log \\left(1 + \\exp \\left(\\tanh \\left(f _ {\\delta} ^ {(i)} + p _ {\\mathrm {t p}} ^ {(i)} - f _ {\\text {c e n t e r}}\\right)\\right)\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.806, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(N_{\\mathrm{tp}}\\) stands for the number of element in \\(p_{\\mathrm{tp}}\\) and \\(\\hat{i}\\) is index of \\(f_{\\delta}\\) corresponding to \\(p_{\\mathrm{tp}}^{(i)}\\). Since \\(f_{\\mathrm{center}}\\) is always 0 in centered spherical coordinate, the loss can be simplified as:" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.862, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\nL _ {s c} = \\frac {1}{N _ {\\mathrm {t p}}} \\sum_ {i = 1} ^ {N _ {\\mathrm {t p}}} \\log \\left(1 + \\exp \\left(\\tanh \\left(f _ {\\delta} ^ {(i)} + p _ {\\mathrm {t p}} ^ {(i)}\\right)\\right)\\right), \\tag {11}\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.51, + 0.093, + 0.887, + 0.159 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.166, + 0.708, + 0.179 + ], + "angle": 0, + "content": "(a) Misclassification Correction Loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.746, + 0.166, + 0.885, + 0.179 + ], + "angle": 0, + "content": "(b) Sector Cohesion Loss" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.185, + 0.894, + 0.268 + ], + "angle": 0, + "content": "Figure 4. Conceptual diagram showing per-point migration following both (a) \\( L_{\\mathrm{mc}} \\) and (b) \\( L_{\\mathrm{sc}} \\). \\( \\Delta_{\\mathrm{FP}} \\) and \\( \\Delta_{\\mathrm{FN}} \\) are distances penalized by \\( L_{\\mathrm{mc}} \\) with margin for misclassified points. \\( \\Delta_{\\mathrm{TP}} \\) is the distance that \\( L_{\\mathrm{sc}} \\) penalizes to enforce the learning of general features of an instance by making each sample close to the other around the center." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.28, + 0.866, + 0.295 + ], + "angle": 0, + "content": "\\(L_{mc}\\) and \\(L_{sc}\\) together form the refinement loss \\(L_{\\mathrm{fine}}\\) as:" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.306, + 0.892, + 0.321 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {f i n e}} = L _ {m c} + L _ {s c}. \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.332, + 0.895, + 0.588 + ], + "angle": 0, + "content": "Our proposed virtual point migration brings three advantages for refinement over existing approaches that strictly disentangle coarse detection and refinement: 1) Instead of only focusing on points inside the coarse detection, predicting the offsets of all points allows the refinement of even false negative points outside of \\( f_{\\mathrm{ray}} \\), sidestepping the error accumulation from the coarse detection. 2) By considering the sector radius, \\( g_{\\mathrm{ray}} \\), it is possible to have a soft target for each point rather than a hard target which is the center of the sector/instance. For example, false negative points outside of the sector boundary only need to be migrated a small distance to being with the sector (soft), rather than being driven towards the center (hard). This makes it easier to learn how to perform the point migration. 3) We only need to learn a one-dimensional number to migrate the point virtually along the radial line. This is far simpler than having to learn a three-dimensional offset in cartesian coordinates." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.6, + 0.664, + 0.615 + ], + "angle": 0, + "content": "3.3.3 Mask Assembly" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.623, + 0.894, + 0.673 + ], + "angle": 0, + "content": "Our final mask is assembled by comparing virtually migrated points and \\(f_{ray}\\). Specifically, the local binary mask \\(\\{f_{\\mathrm{mask}}^{(i)}\\}_{i = 1}^{N_p}\\) is formed as:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.681, + 0.892, + 0.723 + ], + "angle": 0, + "content": "\\[\nf _ {\\text {m a s k}} ^ {(i)} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\left(p _ {s} ^ {(i)} + f _ {\\delta} ^ {(i)}\\right) < f _ {\\text {r a y}} ^ {(\\tilde {i})} \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {13}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.731, + 0.605, + 0.747 + ], + "angle": 0, + "content": "3.4. Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.754, + 0.894, + 0.873 + ], + "angle": 0, + "content": "For the training, we also learn classification and confidence with respective MLPs. For classification, we apply cross-entropy loss, \\( L_{\\mathrm{cls}} \\), for learning the classes of matched groundtruth instances. For the confidence scores of the proposals, we apply L2 loss to learn IoUs between the proposals and the groundtruth instances. Similar to [29], we also duplicate the number of groundtruth for 4 times and create a cost matrix \\( C \\):" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.885, + 0.892, + 0.903 + ], + "angle": 0, + "content": "\\[\nC (k, i) = L _ {\\text {c o a r s e}} (k, i) + L _ {\\text {f i n e}} (k, i) + L _ {\\text {c l s}} (k, i), \\tag {14}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4064" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "where \\( L(,) \\) refers to the loss value calculated using \\( k_{th} \\) vote and \\( i_{th} \\) ground-truth instance. Referring \\( C \\), we apply Hungarian algorithm to find the least-cost injective mapping from each ground-truth instance to the votes. The final loss using the acquired ground-truths is:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.181, + 0.47, + 0.198 + ], + "angle": 0, + "content": "\\[\nL = \\lambda_ {1} L _ {\\mathrm {c l s}} + \\lambda_ {2} L _ {\\text {c o n f}} + \\lambda_ {3} L _ {\\text {c o a r s e}} + \\lambda_ {4} L _ {\\text {f i n e}} \\tag {15}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.205, + 0.201, + 0.222 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.231, + 0.173, + 0.245 + ], + "angle": 0, + "content": "4.1. Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.254, + 0.47, + 0.299 + ], + "angle": 0, + "content": "We evaluate our method on three datasets: ScanNetV2 [7], S3DIS [2], STPLS3D [3]. Following are descriptions of each dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.3, + 0.469, + 0.36 + ], + "angle": 0, + "content": "ScanNetV2 ScanNetV2 dataset consists of 1201, 312, and 100 scans with 18 object classes for training, validation, and testing, respectively. We report the evaluation results on the validation and hidden test sets as in the existing works." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.469, + 0.422 + ], + "angle": 0, + "content": "S3DIS S3DIS dataset contains 271 scenes from 6 areas with 13 categories. We report evaluations for both Area 5. Additional evaluation results with 6-fold cross-validation can be found in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.422, + 0.47, + 0.498 + ], + "angle": 0, + "content": "STPLS3D The STPLS3D dataset is an aerial photogrammetry point cloud dataset from real-world and synthetic environments. It includes 25 urban scenes of \\(6km^2\\) and 14 instance categories. Following [4, 29, 30], we use scenes 5, 10, 15, 20, and 25 for validation and the rest for training." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.51, + 0.254, + 0.525 + ], + "angle": 0, + "content": "4.2. Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.715 + ], + "angle": 0, + "content": "We adopt average precision as our primary evaluation metric. Average precision is extensively used in vision tasks such as object detection and instance segmentation tasks. The metric calculates precisions by varying the IoU threshold. Following the existing works, we evaluate our model with three IoU thresholds: \\(AP\\), \\(AP_{50}\\), \\(AP_{25}\\). \\(AP_{50}\\) and \\(AP_{25}\\) stand for average precisions with IoU threshold as \\(25\\%\\) and \\(50\\%\\), respectively. \\(AP\\) is an averaged score by varying IoU thresholds from \\(50\\%\\) to \\(95\\%\\) by increasing the threshold with step size \\(5\\%\\). For S3DIS, we also evaluate our model with mean precision (mPrec50), and mean recall with IoU threshold as \\(50\\%\\) (mRec50)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.726, + 0.287, + 0.741 + ], + "angle": 0, + "content": "4.3. Implementation Detail" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We build our model on PyTorch framework [23] and train it for 300 epochs with AdamW optimizer with a single NVIDIA A10 GPU. The batch size is set to 10. The learning rate and weight decay are initialized to 0.001 and 0.0001. Cosine annealing [35] is used for scheduling the learning rate. Following [29, 30], the voxel size is set to \\(0.02\\mathrm{m}\\) for ScanNetV2 and S3DIS, and to \\(0.3\\mathrm{m}\\) for STPLS3D. For the augmentation during training, we use random cropping for each scene with a maximum number of 250,000 points. During testing, a whole scene is used as an input to the network." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.35 + ], + "angle": 0, + "content": "Our backbone is similar to[29, 30], which outputs features \\( F_{1} \\) with hidden dimension \\( D \\) as 32 channels. For the voting, we use two set-abstraction [24, 25] layers with the ball query radius 0.2 and 0.4, respectively. The number seeds and votes are set to 1024 and 256, respectively. The number of neighbors is set to 32 for both layers, similar to [29]. For Point Migration Head, we use two layers of dynamic convolution[10], and their hidden dimensions are set to 32. \\( \\lambda 1 \\), \\( \\lambda 2 \\), \\( \\lambda 3 \\), and \\( \\lambda 4 \\) are set to 0.5, 0.5, 1, and 1, respectively. For training and inference, we set \\( N_{\\theta} \\) and \\( N_{\\varphi} \\) to 5 and 5, respectively. During inference, Non-Maximum-Suppression is applied to the \\( K \\) binary masks to delete redundant masks using a confidence score 0.2 as a threshold. Following [19, 21, 29, 31], we aggregate superpoints[16, 17] to align the final prediction masks on the ScanNetV2 dataset. Other details, such as the architecture of MLPs and runtime analysis, are included in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.359, + 0.638, + 0.373 + ], + "angle": 0, + "content": "4.4. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.382, + 0.895, + 0.593 + ], + "angle": 0, + "content": "ScanNetV2 Table 1 and Table 2 show the quantitative result of instance segmentation on the test and validation sets. Our proposed method achieves the highest AP and \\(\\mathrm{AP}_{50}\\) surpassing the previous strongest method by the margin of \\(4.1\\%\\) and \\(2.4\\%\\) for the test set, and \\(6.7\\%\\) and \\(5.7\\%\\) for the validation set, respectively. Compared to the previous methods based on the coarse-to-fine approach, our method achieves \\(24.1\\%\\) of the improvement in AP on the test set. In particular, for the test set, our method outperforms existing methods on instances that are typically located close to each other, such as pictures, desks, and bookshelves. This suggests that explicitly penalizing misclassified points around the edges of instances is helpful in RPM. Please refer to the supplementary material for more results about this." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.594, + 0.894, + 0.67 + ], + "angle": 0, + "content": "S3DIS Table 3 illustrates the quantitative result on Area 5. Our proposed method outperforms the second best performing method with margins of 3.3 and 2.9 in mAP, \\(\\mathrm{AP}_{50}\\), and mRec\\(_{50}\\), improving the performance of SOTA \\(5.7\\%\\), \\(4.2\\%\\), and \\(5.6\\%\\) respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.67, + 0.892, + 0.731 + ], + "angle": 0, + "content": "STPLS3D Table 4 shows the quantitative comparison on the validation set of STPLS3D dataset. Our method outperforms all of the existing methods, improving SOTA performance in mAP and \\(\\mathrm{AP}_{50}\\) for 3.0 and 4.3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.682, + 0.756 + ], + "angle": 0, + "content": "4.5. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.764, + 0.894, + 0.855 + ], + "angle": 0, + "content": "Fig.5 shows visual comparisons of ISBNet[29], MAFT[15], and our proposed Spherical Mask for challenging instances on ScanNetV2 validation set. Spherical Mask accurately segments large instances such as wall and book shelves(row 1), curtains and a window between them(row 2), a large sofa(row 3) and a circular shape sofa(row 4)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "ISBNet[29] struggles to segment large instances(wall and bookshelves in row 1) and a disconnected instance(curtains and a window between them in row 2). On the other hand," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4065" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.089, + 0.885, + 0.21 + ], + "angle": 0, + "content": "
MethodmAP\\( \\mathrm{mAP}_{50} \\)\\( bath \\)bedbk.shfcabinetchaircountercurtaindeskdoorotherpicturefridges. cur.sinksofatabletoiletwind.
3D-BoNet(C)[33]25.348.851.932.425.113.734.53.141.96.916.213.15.220.233.814.730.130.365.117.8
TD3D(C)[14]48.975.185.251.143.432.273.510.151.235.534.946.828.351.467.626.867.151.090.832.9
SoftGroup(G)[30]50.476.166.757.937.238.169.47.267.730.338.753.131.958.275.431.864.349.290.738.8
PBNet(G)[36]57.374.792.657.561.947.273.623.948.738.345.950.653.358.576.740.471.755.996.938.1
DKNet(K)[31]53.271.881.562.451.737.774.910.750.930.443.747.558.153.977.533.964.050.690.138.5
ISBNet(K)[29]55.975.793.965.538.342.676.318.053.438.649.950.962.142.770.446.764.957.194.840.1
MAFT(T)[15]57.878.688.972.144.846.076.825.155.840.850.453.961.661.885.848.268.455.193.145.0
QueryFormer(T)[21]58.378.792.670.239.350.473.327.652.737.347.953.453.369.772.043.674.559.295.836.3
Ours(C)61.681.294.665.455.543.476.927.160.444.750.554.969.871.677.548.074.757.592.543.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.211, + 0.894, + 0.255 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison of top-performing methods for each approach on ScanNetV2 hidden test set. (C),(G),(K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. All the methods take the same input, such as point cloud and corresponding color information. The best results are in bold, and the second best ones are in underlined." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.267, + 0.885, + 0.501 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.188, + 0.502, + 0.781, + 0.516 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison of ISBNet[29], MAFT[15], and ours on ScanNetV2 validation set." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.529, + 0.882, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.301, + 0.676, + 0.669, + 0.69 + ], + "angle": 0, + "content": "Figure 6. Visually comparing impacts of RID, \\( L_{mc} \\), and \\( L_{sh} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.706, + 0.475, + 0.826 + ], + "angle": 0, + "content": "MAFT[15] shows better generalization capability for learning semantics(curtains and a window between them(row 2)). However, it struggles to segment some parts of an instance that look different, as shown in sofas(row 2,3) and oversegments the instance by considering physically further away points as the same instance(wall in row 2 and sofa in row 4), probably due to the local queries that overfit to certain semantics." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.231, + 0.861 + ], + "angle": 0, + "content": "4.6. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this section, we investigate Spherical Mask with ablation studies designed for its core components." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.706, + 0.896, + 0.889 + ], + "angle": 0, + "content": "Impact of \\(\\theta\\) and \\(\\varphi\\) is shown at Table 6. For this experiment, we fixed the backbone and the RPM with \\(L_{mc}\\) and \\(L_{sc}\\), and change \\(N_{\\theta}\\) and \\(N_{\\varphi}\\). In theory, increasing \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) should always produce better results. However, in practice, increasing them faces an issue of high complexity, as can be seen. Using 4/4 and 5/5 of \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) improves the mAP for \\(0.9\\%\\) and \\(1.7\\%\\), respectively. However, increasing them from 5/5 to 6/6 results in \\(2.8\\%\\) of the performance drop, suggesting that too large \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) make a negative impact on the performance due to increased complexity. For example, too large \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) would result in many sectors without any foreground points, leading to biased target values for learn-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4066" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.462, + 0.342 + ], + "angle": 0, + "content": "
MethodVenuemAPAP50AP25
3D-SIS(C)[12]CVPR19-18.735.7
GSPN(C)[34]CVPR19-37.853.4
TD3D(C)[14]WACV2347.371.281.9
PointGroup(G)[13]CVPR2034.851.771.3
SSTNet(G)[19]ICCV2149.464.374.0
MaskGroup(G)[37]ICME2227.442.063.3
SoftGroup(G)[30]CVPR2246.067.678.9
RPGN(G)[8]ECCV22-64.2-
PBNet(G)[36]ICCV2354.370.578.9
PointInst3D(K)[11]EECV2245.663.7
DKNet(K)[31]ECCV2250.866.976.9
ISBNet(K)[29]CVPR2354.573.182.5
Mask3D(T)[27]ICRA2355.273.782.9
3IS-ESSS(T)[1]ICCV2356.175.083.7
QueryFormer(T)[21]ICCV2356.574.283.3
MAFT(T)[15]ICCV2358.475.684.5
Ours(C)-62.379.988.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.344, + 0.472, + 0.414 + ], + "angle": 0, + "content": "Table 2. Quantitative 3D instance segmentation results on ScanNetV2 validation set. (C), (G), (K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. The best results are in bold, and the second best ones are in underlined." + }, + { + "type": "table", + "bbox": [ + 0.089, + 0.42, + 0.456, + 0.632 + ], + "angle": 0, + "content": "
MethodmAPAP50mPrec50mRec50
GSPN [34]--36.028.7
PointGroup [13]-5.7861.962.1
HAIS [4]--71.165.0
SSTNet [19]42.759.365.664.2
SoftGroup [30]51.666.173.666.6
Mask3D [27]56.569.368.770.7
RPGN [8]--64.063.0
PointInst3D [11]--73.165.2
DKNet [31]--70.865.3
ISBNet [29]56.367.570.572.0
PBNet [36]53.566.474.965.4
QueryFormer [21]57.769.970.572.2
MAFT [15]-69.1--
Ours60.572.371.376.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.633, + 0.47, + 0.676 + ], + "angle": 0, + "content": "Table 3. Quantitative 3D instance segmentation results on S3DIS Area 5. The best results are in bold, and the second best ones are in underlined." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.683, + 0.462, + 0.755 + ], + "angle": 0, + "content": "
MethodmAP AP50RID Lmc LscmAP AP50AP25
HAIS [4]35.046.7✓51.669.486.8
PointGroup [13]23.338.5✓✓58.577.687.5
ISBNet [29]49.264.0✓56.577.187.1
Ours52.268.3✓✓62.379.988.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.757, + 0.245, + 0.798 + ], + "angle": 0, + "content": "Table 4. Quantitative instance segmentation results on STPLS3D" + }, + { + "type": "table_caption", + "bbox": [ + 0.266, + 0.756, + 0.468, + 0.784 + ], + "angle": 0, + "content": "Table 5. Impact of each component on ScanNetV2 validation set" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.856 + ], + "angle": 0, + "content": "ing. Despite the variation, all configurations of \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) still outperform existing methods in Table 2, implying that RID with RPM always improves the performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.901 + ], + "angle": 0, + "content": "Impact of Radial Point Migration is illustrated in Table 5. Here, we investigate the impact of the RPM and each loss for it. The baseline is the model trained with only RID, exclud" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.088, + 0.688, + 0.189 + ], + "angle": 0, + "content": "
Nθ/NφmAPAP50AP25
1/159.677.185.3
2/260.077.786.1
3/360.678.487.1
4/461.280.089.3
5/562.379.988.2
6/660.678.588.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.191, + 0.67, + 0.232 + ], + "angle": 0, + "content": "Table 6. Impact of \\(N_{\\theta}\\) and \\(N_{\\varphi}\\) on ScanNetV2 validation set" + }, + { + "type": "table", + "bbox": [ + 0.697, + 0.089, + 0.885, + 0.189 + ], + "angle": 0, + "content": "
Seed/VotemAP\\( AP_{50} \\)\\( AP_{25} \\)
1024/12862.379.287.8
1024/25662.379.988.2
1024/51262.379.487.6
2048/12862.079.788.0
2048/25661.879.687.9
2048/51261.779.187.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.697, + 0.19, + 0.89, + 0.23 + ], + "angle": 0, + "content": "Table 7. Impact of seed and vote numbers on ScanNetV2 validation set" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.895, + 0.524 + ], + "angle": 0, + "content": "ing RPM. As the baseline model cannot refine the false positive points inside radial predictions or false negative points outside, as shown in Figure 6 (parts of chairs included as tables), its performance with high iou thresholds(AP, \\(\\mathrm{AP}_{50}\\)) are \\(17.1\\%\\) and \\(13.1\\%\\) worse than the full model. Including RPM with \\(L_{mc}\\) leads \\(13.3\\%\\) of improvement in AP, suggesting refinement to push and pull misclassified points is crucial for the performance. \\(L_{sc}\\) shows \\(9.4\\%\\) improvement in AP from the baseline, suggesting that focusing on true positive samples also contributes significantly to learning fine granularity and common features shared within an instance. As shown in Figure 6(column 5,6), adding \\(L_{sc}\\) improves the segmentation around the center of the objects, which was expected as the true positive samples near the instance centers could be neglected from \\(L_{mc}\\) as they are usually inside rays. As \\(L_{mc}\\) and \\(L_{sc}\\) target different samples, the full model combining both \\(L_{mc}\\) and \\(L_{sc}\\) shows \\(20.7\\%\\) and \\(15.1\\%\\) improvements for AP and \\(\\mathrm{AP}_{50}\\), demonstrating the synergy of the two losses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.894, + 0.646 + ], + "angle": 0, + "content": "Impact of Voting Parameters is shown in Table 7. In this experiment, we change the seed and vote numbers inside the backbone while fixing RID and RPM. As can be seen, a seed number of 1024 produces more reliable results without variation than 2048, suggesting too many seed points negatively impact the system. Despite the slight difference, we observe that changing the seed and vote produces comparably small variations of \\(\\pm 0.6\\) in mAP for all settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.655, + 0.62, + 0.672 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.68, + 0.894, + 0.831 + ], + "angle": 0, + "content": "We present Spherical Mask, a novel coarse-to-fine approach for 3D instance segmentation in point cloud. As a coarse detection, the RID module finds instances as 3D polygons defined with center and rays. In contrast to existing coarse-to-fine approaches, the RPM module uses the polygons as soft references and migrates points efficiently in spherical coordinates to acquire final masks. We demonstrate how each module contributes to the instance segmentation and achieves state-of-the-art performances on public benchmarks ScanNet-V2, S3DIS, and STPLS3D." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.838, + 0.661, + 0.854 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.858, + 0.831, + 0.888 + ], + "angle": 0, + "content": "This research was supported by ACE-OPS project (EP/S030832/1)." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4067" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.184 + ], + "angle": 0, + "content": "[1] Salwa Al Khatib, Mohamed El Amine Boudjoghra, Jean Lahoud, and Fahad Shahbaz Khan. 3d instance segmentation via enhanced spatial and semantic supervision. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1839-1849, 2020. 1" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4069" + } + ] +] \ No newline at end of file diff --git a/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_origin.pdf b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2b4d340fb9c1b2b45a4bdbe5bfb3cc4209b35975 --- /dev/null +++ b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/adcaad31-f6bf-4625-9641-e0b1d8451ad5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:116d181c60f5f67f82d5c11f1187bd3a96619f3ddccc2c6377c56efebe579a60 +size 8395583 diff --git a/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/full.md b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..4748921c872efb9a47ddf641254658742ef7e5dd --- /dev/null +++ b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/full.md @@ -0,0 +1,340 @@ +# Spherical Mask: Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation + +Sangyun Shin Kaichen Zhou Madhu Vankadari Andrew Markham Niki Trigoni Department of Computer Science University of Oxford + +firstname.lastname@cs.ox.ac.uk + +# Abstract + +Coarse-to-fine 3D instance segmentation methods show weak performances compared to recent Grouping-based, Kernel-based and Transformer-based methods. We argue that this is due to two limitations: 1) Instance size overestimation by axis-aligned bounding box(AABB) 2) False negative error accumulation from inaccurate box to the refinement phase. In this work, we introduce Spherical Mask, a novel coarse-to-fine approach based on spherical representation, overcoming those two limitations with several benefits. Specifically, our coarse detection estimates each instance with a 3D polygon using a center and radial distance predictions, which avoids excessive size estimation of AABB. To cut the error propagation in the existing coarse-to-fine approaches, we virtually migrate points based on the polygon, allowing all foreground points, including false negatives, to be refined. During inference, the proposal and point migration modules run in parallel and are assembled to form binary masks of instances. We also introduce two margin-based losses for the point migration to enforce corrections for the false positives/negatives and cohesion of foreground points, significantly improving the performance. Experimental results from three datasets, such as ScanNetV2, S3DIS, and STPLS3D, show that our proposed method outperforms existing works, demonstrating the effectiveness of the new instance representation with spherical coordinates. The code is available at: https://github.com/yunshin/SphericalMask + +# 1. Introduction + +3D instance segmentation has gained immense attention with its wide range of applications for Indoor Scanning[38], Augmented Reality(AR)[18], and Autonomous Driving[22]. Similar to 2D instance segmentation, the goal of the task is to identify each object along with its class label. Nevertheless, the sparse and unordered nature of point clouds has led to the development of methods different from 2D image segmentation. + +![](images/8f0926a4740271d01bcdbe162d28e7dd591d2b861dfecd38522d70f595e0122b.jpg) +Figure 1. Pipeline of Spherical Mask with coarse-to-fine framework. Given point cloud, instances are detected with 3D polygons defined in spherical coordinates. In the refinement phase, the points virtually migrate based on the polygon to estimate fine instance masks. + +Existing approaches for 3D instance segmentation are broadly categorized into coarse-to-fine based[12, 14, 20, 33, 34], grouping-based[4, 13, 19, 30, 36], kernel-based[10, 11, 13, 29, 31], and Transformer-based[1, 15, 21, 27, 28] approaches. Recent progress in clustering techniques and attention mechanisms have driven the performances of the last three approaches to state-of-the-art. Compared to these three approaches, the coarse-to-fine approach has received relatively less attention due to a low accuracy, caused by two limitations: 1) False negative error propagation from the coarse detection to the refinement stage. 2) Overestimation of instance size. + +Coarse-to-fine instance segmentation first performs coarse detection, followed by refinement using the coarse detection as hard reference. The basic assumption of the approach is that the coarse detection stage always provides a neat detection for refinement. However, this assumption is often violated as the coarse detection stage cannot always produce neat outputs, which causes an issue of upper bound accuracy. For example, if the first coarse detection does not include all foreground points, the following + +refinement(binary classification) step has no means to include them, only possibly accumulating the error from false negative prediction. The other limitation is that the axis-aligned-bounding-box(AABB) estimation, which is typically used for the coarse detection, has been claimed to be an ill-defined problem[30] because commonly used box regression losses(L1, L2) result in overestimation of object sizes. For instance, the target values of AABB are minimum and maximum values in x,y,z cartesian coordinates, making the box include redundant empty space, as points only lie on the surface of the object. + +In this work, we address the aforementioned two limitations of coarse-to-fine instance segmentation. Our core intuition comes from the fact that the weakness of the coarse-to-fine approach is based on the structural disentanglement of coarse detection and fine refinement phase. Instead of assuming that the coarse part should be perfect, we take a relaxation approach, which regards the coarse detection as a soft reference during the refinement phase, providing more access for refinement yet restricting access to unnecessary background points. Specifically, to improve the coarse detection part, we estimate a 3D polygon in spherical coordinates instead of AABB, alleviating the issue of excessive object size estimation. To remove the error propagation from inaccurate coarse detection to the refinement stage, we virtually migrate points based on the 3D polygon with reduced complexity in spherical coordinates. + +In summary, our method Spherical Mask finds each instance by estimating a 3D polygon fitting to an instance in spherical coordinates and migrating points inside or outside the polygon to produce the fine instance mask. Our contributions are: + +- We introduce a new alternative instance representation based on spherical coordinates, which overcomes the limitations in existing coarse-to-fine approaches. +- To circumvent the issue of excessive estimation of instance size, we propose Radial Instance Detection(RID) that formulates an instance into a 3D polygon as a coarse detection. +- To cut the error propagation from coarse detection to the refinement phase, we introduce Radial Point Migration(RPM), capable of refining both false positive and false negative points from RID. +- Extensive experiments on ScanNetV2 [7], S3DIS [2], and STPLS3D [3] show the effectiveness of our approach, pushing the boundary of current SOTA. + +# 2. Related Work + +Existing works on point cloud instance segmentation can be categorized into proposal-based, clustering-based, kernel-based and transformer-based methods. + +# 2.1. Coarse to Fine(Proposal-based) Approach + +Coarse-to-fine-based methods are built on a conceptually simple design, where they first perform coarse detection, followed by a refinement stage to acquire fine segmentation. Typically, 3D bounding box is employed for the coarse detection. 3D-SIS[12] performs instance segmentation by first detecting the 3D boxes and refining points inside. 3D-BoNet[33] matches query AABBs and ground-truth instance using Hungarian algorithm for the supervision. The predicted AABBs are then concatenated with point features to produce binary masks for each instance. GSPN[34] adopts set-abstraction[24] to get query points and infer AABBs. The features inside the AABBs are extracted and used for per-point mask segmentation. More recently, TD3D [14] proposes a fully sparse-convolutional approach for point instance segmentation. It first detects AABBs and extracts perpoint features inside the boxes to perform binary classification. Most of the works use coarse detection(bounding box) directly as geometric features for predicting per-point binary instance masks. Thus, their accuracies greatly depend on the precision of the coarse detection, as inaccurate detection could easily lead to a large number of false negative points. + +# 2.2. Grouping-based Approach + +Grouping-based methods learn latent embeddings to perform per-point predictions, such as semantic categories and clustering to acquire instances. PointGroup[13] predicts centroid offsets of each point and utilizes this shifted point cloud and original point cloud to obtain the clusters. Based on this concept, many studies improve the clustering technique with hierarchical intra-instance predictions[4], superpoint-based divisive grouping[19], soft grouping[30], and binary clustering[36]. The clustering-based methods have high expectations of the quality of per-point center prediction in 3D, which is challenging to generalize with various spatial extents of objects. + +# 2.3. Kernel-based Approach + +Kernel-based methods learn convolution kernels that aggregate point features to estimate instance masks. DyCo3D[10] proposes discriminative kernels by applying the clustering method from PointGroup[13]. Built on this, more recent works improved the performance by replacing the clustering part with farthest-point sampling[11], candidate localization[31], and instance-aware point sampling for the high-recall[29]. + +# 2.4. Transformer-based Approach + +Recently, transformer-based methods have set the new SOTA. Based on mask-attention[5, 6], Mask3D[27] and SPFormer[28] present the pipeline that learns to output + +instance prediction directly from a fixed number of object queries from voxel and superpoint features, respectively. Based on these works, recent studies improve the performance with auxiliary center regression[15], query initialization and set grouping[21], spatial and semantic supervision[1]. Although the powerful architectural advantage has driven the performance of Transformer-based approaches, low-recall and how to distribute initial queries remain challenges. + +# 3. Method + +# 3.1. Overview + +Given an input point cloud $p_1 \in \mathbb{R}^{N_p \times 3}$ in 3-dimensional cartesian coordinates and the corresponding color information $p_{\mathrm{rgb}} \in \mathbb{R}^{N_p \times 3}$ , we aim to design a system that segments the point cloud into local binary masks of instances $\{o^{(i)} \in \mathbb{R}^{N_p \times 1}\}_{i=1}^{N_o}$ using a coarse to fine approach. Here, $N_p, N_o$ are the total number of points and the number of instances, respectively. This is achieved using the proposed method depicted in Figure 2. Our system consists of mainly two modules: 3D backbone and proposed instance mask estimation. The details of these modules are in Section 3.2 and Section 3.3, respectively. + +# 3.2. 3D backbone + +Our 3D backbone is similar to [29] and is composed of two modules: a 3D encoder and a voting module. The 3D encoder uses U-Net [26] with sparse convolutions [9] to encode the given point cloud into deep features $F_{1} \in \mathbb{R}^{N_{p} \times D}$ . Then, $F_{1}$ and the respective input points $p_{1}$ are fed into the voting module. The voting module performs set abstraction [24], producing $K$ votes with query points $p_{2} \in \mathbb{R}^{K \times 3}$ and features $F_{2} \in \mathbb{R}^{K \times D}$ . Please find the original paper [25] for more details about this procedure. These votes are spread in the scene, providing features to be further processed through the proposed instance mask estimation module. The details are explained in the following sections. + +# 3.3. Instance Mask Estimation + +In this section, we estimate the instance masks from the votes predicted in the 3D backbone section using three modules: Radial Instance Detection, Radial Point Migration, and Mask Assembly. All of the modules are explained in the following sections. For the notation simplicity, we will explain how each vote feature is processed. Therefore, we write $f_{2}$ to refer to a single vote feature of $F_{2}$ from here onwards. + +# 3.3.1 Radial Instance Detection(Coarse Mask) + +Radial Instance Detection(RID) aims to detect instances for further refinement. Similar to PolarMask[32] for 2D segmentation, we define an instance as a 3D polygon with a + +center $f_{\mathrm{center}}$ and multiple rays $f_{\mathrm{ray}}$ emitting from the center forming each spherical sectors. Here, the sectors are defined by preset angles. Each ray then determines the distance to be considered for their corresponding sectors, as shown in Figure 3. + +We estimate the closest instances' center $f_{\text{center}}$ using offsets predicted from an MLP network, CenterHead, which takes the respective $f_2$ as input and outputs offsets. The offsets are added to $p_2$ to infer $f_{\text{center}}$ . After this, the input point cloud is converted into spherical coordinates using a transformation as $p_s = S(p_1)$ centered around $f_{\text{center}}$ , where $S:(x,y,z) \to (r,\theta,\varphi)$ as follows: + +$$ +\begin{array}{l} r = \sqrt {x ^ {2} + y ^ {2} + z ^ {2}}, \\ \theta = \arctan \frac {x}{y}, \tag {1} \\ \varphi = \arctan {\frac {z}{\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}}}. \\ \end{array} +$$ + +Here, $r$ , $\theta$ , $\varphi$ refer to radius, horizontal, and vertical angles in spherical coordinates, respectively. The $p_s$ is then divided uniformly with $N_{\theta}$ and $N_{\varphi}$ separations for horizontal and vertical direction respectively, resulting in $N_{\theta} \cdot N_{\varphi}$ sectors, as shown in Figure 3 (b) and (c). + +We consider points inside the same sector to have identical $(\theta, \varphi)$ , which enables us to close the sector using a boundary estimated by $f_{\mathrm{ray}}$ . To estimate $\{f_{\mathrm{ray}}^{(i)}\}_{i=1}^{N_\theta N_\varphi}$ , another MLP named Ray Head is employed, which takes $f_2$ as input. + +At this point, every point inside the corresponding sector's boundary from $f_{ray}$ is considered foreground. Using the boundary, RID offers tighter boundaries of instances than AABB in point cloud, as each sector is closed at the distance of the farthest foreground point in the sector, alleviating the problem of redundant space in AABB. Please refer to our supplementary material for additional visualizations. + +Coarse Instance Loss: During training, the estimated $f_{\text{centre}}$ and $f_{\text{ray}}$ are compared against their respective ground truth $\mathbf{g}_{\text{center}}$ and $\mathbf{g}_{\text{ray}}$ to calculate $L_{\text{coarse}}$ : + +$$ +L _ {\text {c o a r s e}} = L _ {\text {r a y}} + L _ {\text {c e n t e r}}, \tag {2} +$$ + +where $L_{\mathrm{ray}}$ and $L_{\mathrm{center}}$ are defined with L1 loss: + +$$ +L _ {\text {r a y}} = \frac {1}{N _ {\theta} N _ {\varphi}} \sum_ {i = 1} ^ {N _ {\theta} N _ {\varphi}} \left| f _ {\text {r a y}} ^ {(i)} - \mathbf {g} _ {\text {r a y}} ^ {(i)} \right| _ {1} \tag {3} +$$ + +$$ +L _ {\text {c e n t e r}} = \left| f _ {\text {c e n t e r}} - \mathbf {g} _ {\text {c e n t e r}} \right| _ {1}, \tag {4} +$$ + +Here, the ground-truth instance $\mathbf{g}$ is matched with $f_{\mathrm{center}}$ by an injective mapping obtained using Hungarian algorithm as [29, 33]. For the details of the matching, please refer to Sec 3.4. $\mathbf{g}_{\mathrm{ray}}^{(i)}$ is set to the distance between $\mathbf{g}_{\mathrm{center}}$ and the furthest foreground point in the $i_{th}$ sector. If there are no foreground points in the sector, $\mathbf{g}_{\mathrm{ray}}^{(i)}$ is set to minimum as $1e - 5$ . The target center $\mathbf{g}_{\mathrm{center}}$ is calculated as mean values + +![](images/6b9c9d61e227658cdf1f8733a2962606d4b5a411addf09d257ce12dd594eb2ba.jpg) +Figure 2. Overall pipeline of our proposed method based on coarse to fine approach. Given the point cloud, the backbone produces base features with 3D UNet and Voting module. Based on this, RID performs coarse detection while RPM produces the virtual point offsets to refine the coarse detection. In Mask Assembly, $K$ local binary masks are generated, where each mask is a proposal for a single instance. 3D NMS is applied to acquire the final instance masks using local binary masks, classifications, and confidence scores. + +of foreground points of the matched groundtruth instance in cartesian coordinates. + +# 3.3.2 Radial Point Migration(Mask Refinement) + +In this section, we introduce a refinement process to perform per-point fine-tuning. This is because the coarse detection will invariably include points belonging to the background or other instances (i.e. false positives) inside its boundary and neglect some instance points that fall outside (i.e. false negatives). We propose a conceptually simple yet effective dual that jitters individual points to belong to the correct instance. In particular, this is enabled by our innovative use of spherical coordinates - we only need to learn a single radial delta for each point to move it along the ray to the instance centroid while keeping angular quantities $\phi$ and $\theta$ constant. Note that this is a virtual point motion - we do not alter the final point cloud. We use this as a virtual offset to obtain clean instance labels without modifying the coarse sector. + +By estimating an offset value for each point $p_1$ , these misclassified points can be virtually migrated to being in the correct region. Based on its good performance on perpoint prediction, we adopt Dynamic Convolution in a similar manner to [10, 29] as our Point Migration Head, for predicting per-point offsets $F_{\delta} \in \mathbb{R}^{K \times N_p}$ using the vote features $F_2 \in \mathbb{R}^{K \times D}$ as queries against the point features $F_1 \in \mathbb{R}^{N_p \times D}$ . For the coherence with the notations, we write $f_{\delta} \in \mathbb{R}^{N_p}$ to refer to an output of $F_{\delta}$ , corresponding to one vote. For the learning of $f_{\delta}$ , we divide points into two groups. The first is to learn the radial delta for the case of misclassification, and the second is to make instances more compact and cohesive by migrating points to the centroid of the sector. + +Misclassification Correction Loss: This process aims to estimate a radial delta to move the misclassified points either + +inside or outside the estimated coarse sector. There are two possible cases where the misclassification could occur, as shown in Figure 4 (a): Instance points could lie outside the sector boundary, acting as false negatives, or background points could incorrectly lie within the sector boundary, acting as false positives. The goal is to move these points to the correct region. + +Formally, given the point indices of foreground points $\{j^{+(i)}\}_{i=1}^{N+}$ and background points $\{j^{-(i)}\}_{i=1}^{N-}$ from the groundtruth, the false negative points $p_{\mathrm{fn}}$ and the false positive points $p_{\mathrm{fp}}$ are defined as: + +$$ +p _ {\mathrm {f n}} = \left\{p _ {s} ^ {(j +)}: \left(p _ {s} ^ {(j +)} + f _ {\delta} ^ {(j +)}\right) > f _ {\text {r a y}} ^ {(\tilde {j} +)} \right\}, \tag {5} +$$ + +$$ +p _ {\mathrm {f p}} = \left\{p _ {s} ^ {(j -)}: \left(p _ {s} ^ {(j -)} + f _ {\delta} ^ {(j -)}\right) < f _ {\text {r a y}} ^ {(j -)} \right\}, \tag {6} +$$ + +where $N+$ and $N-$ stand for the number of foreground and background points, respectively. Here, $\tilde{j} = \text{findSector}(p_s^{(j)})$ where $\text{findSector}(\cdot)$ is a function that takes $p_s^{(j)}$ as input and returns the index of the sector that $p_s^{(j)}$ belongs to. Please refer to the supplementary material for our implementation of findSector(). + +The union of $p_{\mathrm{fp}}$ and $p_{\mathrm{fn}}$ forms the misclassified points $p_{\mathrm{miss}}$ that we are interested: $p_{\mathrm{miss}} = p_{\mathrm{fp}} \cup p_{\mathrm{fn}}$ . Our aim is to push or pull them inside/outside of the ray with margins. Thus, the loss function $L_{mc}$ is formulated with soft margin loss as: + +$$ +L _ {m c} = \frac {1}{N _ {\text {m i s s}}} \sum_ {i = 1} ^ {N _ {\text {m i s s}}} \log \left(1 + \exp \left(y * \tanh \left(p _ {\text {m i s s}} ^ {(i)} + f _ {\delta} ^ {(\hat {i})} - f _ {\text {r a y}} ^ {(\tilde {i})}\right)\right)\right) \tag {7} +$$ + +where + +$$ +y = \left\{ \begin{array}{l l} 1 & \text {i f} p _ {\mathrm {m i s s}} ^ {(i)} \in p _ {\mathrm {f p}}, \\ - 1 & \text {i f} p _ {\mathrm {m i s s}} ^ {(i)} \in p _ {\mathrm {f n}}, \end{array} \right. \tag {8} +$$ + +![](images/5191c73ecb9c26b1081d4b574a4e565f9fc4fcf5f070dc30e2384fea12790528.jpg) +Figure 3. Process of RID. (a) Object points in cartesian coordinates (b) Converting points into a spherical coordinate system, using $f_{\text{center}}$ , and preset angles $\theta$ and $\varphi$ . (c) Assigning points to each sector defined by $\theta$ and $\varphi$ . The example shows 3/3 for $\theta / \varphi$ . (d) For each sector, the distance between the farthest point and the center becomes the target of $f_{\text{ray}}$ . During inference, points with smaller distance than $f_{\text{ray}}$ are considered foreground. + +Here, tanh is hyperbolic-tangent function and $L_{mc}$ is calculated for all the votes that are assigned to the ground truth instance. $N_{\mathrm{miss}}$ stands for the number of element in $p_{\mathrm{miss}}$ and $\hat{i}$ is index of $f_{\delta}$ corresponding to $p_{\mathrm{miss}}^{(i)}$ . $f_{\mathrm{ray}}$ is only used for reference and the gradient for learning $f_{ray}$ is not calculated. + +The misclassified points around the edge, $g_{\mathrm{ray}}$ , of an instance are provided with comparably easy learning targets. In contrast, misclassified points far from the predicted rays are assigned targets with large discrepancies, encouraging larger gradients during the training. + +Sector Cohesion Loss The goal of this block is to move true-positive points to the centroid of the sector. By doing so, the sector becomes more cohesive, encouraging the learning of common and shared features of an instance as the foreground features are getting close to each other. In addition, this helps to provide a learning signal for true-positive points, as $L_{\mathrm{mc}}$ only considers false negatives/positives. This is shown more clearly in Figure 4 (b). + +Similar to $L_{mc}$ , using point indices of foreground points $j+$ , we extract true positives $p_{\mathrm{tp}}$ as: + +$$ +p _ {\mathrm {t p}} = \left\{p _ {s} ^ {(j +)}: \left(p _ {s} ^ {(j +)} + f _ {\delta} ^ {(j +)}\right) < f _ {\text {r a y}} ^ {(\tilde {j} +)} \right\} \tag {9} +$$ + +and formulate the loss with the soft margin calculation: + +$$ +L _ {s c} = \frac {1}{N _ {\mathrm {t p}}} \sum_ {i = 1} ^ {N _ {\mathrm {t p}}} \log \left(1 + \exp \left(\tanh \left(f _ {\delta} ^ {(i)} + p _ {\mathrm {t p}} ^ {(i)} - f _ {\text {c e n t e r}}\right)\right)\right), \tag {10} +$$ + +where $N_{\mathrm{tp}}$ stands for the number of element in $p_{\mathrm{tp}}$ and $\hat{i}$ is index of $f_{\delta}$ corresponding to $p_{\mathrm{tp}}^{(i)}$ . Since $f_{\mathrm{center}}$ is always 0 in centered spherical coordinate, the loss can be simplified as: + +$$ +L _ {s c} = \frac {1}{N _ {\mathrm {t p}}} \sum_ {i = 1} ^ {N _ {\mathrm {t p}}} \log \left(1 + \exp \left(\tanh \left(f _ {\delta} ^ {(i)} + p _ {\mathrm {t p}} ^ {(i)}\right)\right)\right), \tag {11} +$$ + +![](images/643eb4d00da6ca92e1dbeee492fd35d4aa2202e21439c88706d257226dbdbd19.jpg) +(a) Misclassification Correction Loss +(b) Sector Cohesion Loss +Figure 4. Conceptual diagram showing per-point migration following both (a) $L_{\mathrm{mc}}$ and (b) $L_{\mathrm{sc}}$ . $\Delta_{\mathrm{FP}}$ and $\Delta_{\mathrm{FN}}$ are distances penalized by $L_{\mathrm{mc}}$ with margin for misclassified points. $\Delta_{\mathrm{TP}}$ is the distance that $L_{\mathrm{sc}}$ penalizes to enforce the learning of general features of an instance by making each sample close to the other around the center. + +$L_{mc}$ and $L_{sc}$ together form the refinement loss $L_{\mathrm{fine}}$ as: + +$$ +L _ {\text {f i n e}} = L _ {m c} + L _ {s c}. \tag {12} +$$ + +Our proposed virtual point migration brings three advantages for refinement over existing approaches that strictly disentangle coarse detection and refinement: 1) Instead of only focusing on points inside the coarse detection, predicting the offsets of all points allows the refinement of even false negative points outside of $f_{\mathrm{ray}}$ , sidestepping the error accumulation from the coarse detection. 2) By considering the sector radius, $g_{\mathrm{ray}}$ , it is possible to have a soft target for each point rather than a hard target which is the center of the sector/instance. For example, false negative points outside of the sector boundary only need to be migrated a small distance to being with the sector (soft), rather than being driven towards the center (hard). This makes it easier to learn how to perform the point migration. 3) We only need to learn a one-dimensional number to migrate the point virtually along the radial line. This is far simpler than having to learn a three-dimensional offset in cartesian coordinates. + +# 3.3.3 Mask Assembly + +Our final mask is assembled by comparing virtually migrated points and $f_{ray}$ . Specifically, the local binary mask $\{f_{\mathrm{mask}}^{(i)}\}_{i = 1}^{N_p}$ is formed as: + +$$ +f _ {\text {m a s k}} ^ {(i)} = \left\{ \begin{array}{l l} 1 & \text {i f} \left(p _ {s} ^ {(i)} + f _ {\delta} ^ {(i)}\right) < f _ {\text {r a y}} ^ {(\tilde {i})} \\ 0 & \text {o t h e r w i s e ,} \end{array} \right. \tag {13} +$$ + +# 3.4. Training + +For the training, we also learn classification and confidence with respective MLPs. For classification, we apply cross-entropy loss, $L_{\mathrm{cls}}$ , for learning the classes of matched groundtruth instances. For the confidence scores of the proposals, we apply L2 loss to learn IoUs between the proposals and the groundtruth instances. Similar to [29], we also duplicate the number of groundtruth for 4 times and create a cost matrix $C$ : + +$$ +C (k, i) = L _ {\text {c o a r s e}} (k, i) + L _ {\text {f i n e}} (k, i) + L _ {\text {c l s}} (k, i), \tag {14} +$$ + +where $L(,)$ refers to the loss value calculated using $k_{th}$ vote and $i_{th}$ ground-truth instance. Referring $C$ , we apply Hungarian algorithm to find the least-cost injective mapping from each ground-truth instance to the votes. The final loss using the acquired ground-truths is: + +$$ +L = \lambda_ {1} L _ {\mathrm {c l s}} + \lambda_ {2} L _ {\text {c o n f}} + \lambda_ {3} L _ {\text {c o a r s e}} + \lambda_ {4} L _ {\text {f i n e}} \tag {15} +$$ + +# 4. Experiment + +# 4.1. Dataset + +We evaluate our method on three datasets: ScanNetV2 [7], S3DIS [2], STPLS3D [3]. Following are descriptions of each dataset. + +ScanNetV2 ScanNetV2 dataset consists of 1201, 312, and 100 scans with 18 object classes for training, validation, and testing, respectively. We report the evaluation results on the validation and hidden test sets as in the existing works. + +S3DIS S3DIS dataset contains 271 scenes from 6 areas with 13 categories. We report evaluations for both Area 5. Additional evaluation results with 6-fold cross-validation can be found in the supplementary material. + +STPLS3D The STPLS3D dataset is an aerial photogrammetry point cloud dataset from real-world and synthetic environments. It includes 25 urban scenes of $6km^2$ and 14 instance categories. Following [4, 29, 30], we use scenes 5, 10, 15, 20, and 25 for validation and the rest for training. + +# 4.2. Evaluation Metric + +We adopt average precision as our primary evaluation metric. Average precision is extensively used in vision tasks such as object detection and instance segmentation tasks. The metric calculates precisions by varying the IoU threshold. Following the existing works, we evaluate our model with three IoU thresholds: $AP$ , $AP_{50}$ , $AP_{25}$ . $AP_{50}$ and $AP_{25}$ stand for average precisions with IoU threshold as $25\%$ and $50\%$ , respectively. $AP$ is an averaged score by varying IoU thresholds from $50\%$ to $95\%$ by increasing the threshold with step size $5\%$ . For S3DIS, we also evaluate our model with mean precision (mPrec50), and mean recall with IoU threshold as $50\%$ (mRec50). + +# 4.3. Implementation Detail + +We build our model on PyTorch framework [23] and train it for 300 epochs with AdamW optimizer with a single NVIDIA A10 GPU. The batch size is set to 10. The learning rate and weight decay are initialized to 0.001 and 0.0001. Cosine annealing [35] is used for scheduling the learning rate. Following [29, 30], the voxel size is set to $0.02\mathrm{m}$ for ScanNetV2 and S3DIS, and to $0.3\mathrm{m}$ for STPLS3D. For the augmentation during training, we use random cropping for each scene with a maximum number of 250,000 points. During testing, a whole scene is used as an input to the network. + +Our backbone is similar to[29, 30], which outputs features $F_{1}$ with hidden dimension $D$ as 32 channels. For the voting, we use two set-abstraction [24, 25] layers with the ball query radius 0.2 and 0.4, respectively. The number seeds and votes are set to 1024 and 256, respectively. The number of neighbors is set to 32 for both layers, similar to [29]. For Point Migration Head, we use two layers of dynamic convolution[10], and their hidden dimensions are set to 32. $\lambda 1$ , $\lambda 2$ , $\lambda 3$ , and $\lambda 4$ are set to 0.5, 0.5, 1, and 1, respectively. For training and inference, we set $N_{\theta}$ and $N_{\varphi}$ to 5 and 5, respectively. During inference, Non-Maximum-Suppression is applied to the $K$ binary masks to delete redundant masks using a confidence score 0.2 as a threshold. Following [19, 21, 29, 31], we aggregate superpoints[16, 17] to align the final prediction masks on the ScanNetV2 dataset. Other details, such as the architecture of MLPs and runtime analysis, are included in the supplementary material. + +# 4.4. Main Results + +ScanNetV2 Table 1 and Table 2 show the quantitative result of instance segmentation on the test and validation sets. Our proposed method achieves the highest AP and $\mathrm{AP}_{50}$ surpassing the previous strongest method by the margin of $4.1\%$ and $2.4\%$ for the test set, and $6.7\%$ and $5.7\%$ for the validation set, respectively. Compared to the previous methods based on the coarse-to-fine approach, our method achieves $24.1\%$ of the improvement in AP on the test set. In particular, for the test set, our method outperforms existing methods on instances that are typically located close to each other, such as pictures, desks, and bookshelves. This suggests that explicitly penalizing misclassified points around the edges of instances is helpful in RPM. Please refer to the supplementary material for more results about this. + +S3DIS Table 3 illustrates the quantitative result on Area 5. Our proposed method outperforms the second best performing method with margins of 3.3 and 2.9 in mAP, $\mathrm{AP}_{50}$ , and mRec $_{50}$ , improving the performance of SOTA $5.7\%$ , $4.2\%$ , and $5.6\%$ respectively. + +STPLS3D Table 4 shows the quantitative comparison on the validation set of STPLS3D dataset. Our method outperforms all of the existing methods, improving SOTA performance in mAP and $\mathrm{AP}_{50}$ for 3.0 and 4.3, respectively. + +# 4.5. Qualitative Results + +Fig.5 shows visual comparisons of ISBNet[29], MAFT[15], and our proposed Spherical Mask for challenging instances on ScanNetV2 validation set. Spherical Mask accurately segments large instances such as wall and book shelves(row 1), curtains and a window between them(row 2), a large sofa(row 3) and a circular shape sofa(row 4). + +ISBNet[29] struggles to segment large instances(wall and bookshelves in row 1) and a disconnected instance(curtains and a window between them in row 2). On the other hand, + +
MethodmAP\( \mathrm{mAP}_{50} \)\( bath \)bedbk.shfcabinetchaircountercurtaindeskdoorotherpicturefridges. cur.sinksofatabletoiletwind.
3D-BoNet(C)[33]25.348.851.932.425.113.734.53.141.96.916.213.15.220.233.814.730.130.365.117.8
TD3D(C)[14]48.975.185.251.143.432.273.510.151.235.534.946.828.351.467.626.867.151.090.832.9
SoftGroup(G)[30]50.476.166.757.937.238.169.47.267.730.338.753.131.958.275.431.864.349.290.738.8
PBNet(G)[36]57.374.792.657.561.947.273.623.948.738.345.950.653.358.576.740.471.755.996.938.1
DKNet(K)[31]53.271.881.562.451.737.774.910.750.930.443.747.558.153.977.533.964.050.690.138.5
ISBNet(K)[29]55.975.793.965.538.342.676.318.053.438.649.950.962.142.770.446.764.957.194.840.1
MAFT(T)[15]57.878.688.972.144.846.076.825.155.840.850.453.961.661.885.848.268.455.193.145.0
QueryFormer(T)[21]58.378.792.670.239.350.473.327.652.737.347.953.453.369.772.043.674.559.295.836.3
Ours(C)61.681.294.665.455.543.476.927.160.444.750.554.969.871.677.548.074.757.592.543.6
+ +Table 1. Quantitative comparison of top-performing methods for each approach on ScanNetV2 hidden test set. (C),(G),(K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. All the methods take the same input, such as point cloud and corresponding color information. The best results are in bold, and the second best ones are in underlined. + +![](images/dfc9f12415c5c46f29cba97167fe29ac1629a56022017d487d1b7e8f8e25c693.jpg) +Figure 5. Qualitative comparison of ISBNet[29], MAFT[15], and ours on ScanNetV2 validation set. + +![](images/edb7417f3ed78979d7b5bb836cde0907bcbab6ae87ad77c058ec3ec944148714.jpg) +Figure 6. Visually comparing impacts of RID, $L_{mc}$ , and $L_{sh}$ . + +MAFT[15] shows better generalization capability for learning semantics(curtains and a window between them(row 2)). However, it struggles to segment some parts of an instance that look different, as shown in sofas(row 2,3) and oversegments the instance by considering physically further away points as the same instance(wall in row 2 and sofa in row 4), probably due to the local queries that overfit to certain semantics. + +# 4.6. Ablation Study + +In this section, we investigate Spherical Mask with ablation studies designed for its core components. + +Impact of $\theta$ and $\varphi$ is shown at Table 6. For this experiment, we fixed the backbone and the RPM with $L_{mc}$ and $L_{sc}$ , and change $N_{\theta}$ and $N_{\varphi}$ . In theory, increasing $N_{\theta}$ and $N_{\varphi}$ should always produce better results. However, in practice, increasing them faces an issue of high complexity, as can be seen. Using 4/4 and 5/5 of $N_{\theta}$ and $N_{\varphi}$ improves the mAP for $0.9\%$ and $1.7\%$ , respectively. However, increasing them from 5/5 to 6/6 results in $2.8\%$ of the performance drop, suggesting that too large $N_{\theta}$ and $N_{\varphi}$ make a negative impact on the performance due to increased complexity. For example, too large $N_{\theta}$ and $N_{\varphi}$ would result in many sectors without any foreground points, leading to biased target values for learn- + +
MethodVenuemAPAP50AP25
3D-SIS(C)[12]CVPR19-18.735.7
GSPN(C)[34]CVPR19-37.853.4
TD3D(C)[14]WACV2347.371.281.9
PointGroup(G)[13]CVPR2034.851.771.3
SSTNet(G)[19]ICCV2149.464.374.0
MaskGroup(G)[37]ICME2227.442.063.3
SoftGroup(G)[30]CVPR2246.067.678.9
RPGN(G)[8]ECCV22-64.2-
PBNet(G)[36]ICCV2354.370.578.9
PointInst3D(K)[11]EECV2245.663.7
DKNet(K)[31]ECCV2250.866.976.9
ISBNet(K)[29]CVPR2354.573.182.5
Mask3D(T)[27]ICRA2355.273.782.9
3IS-ESSS(T)[1]ICCV2356.175.083.7
QueryFormer(T)[21]ICCV2356.574.283.3
MAFT(T)[15]ICCV2358.475.684.5
Ours(C)-62.379.988.2
+ +Table 2. Quantitative 3D instance segmentation results on ScanNetV2 validation set. (C), (G), (K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. The best results are in bold, and the second best ones are in underlined. + +
MethodmAPAP50mPrec50mRec50
GSPN [34]--36.028.7
PointGroup [13]-5.7861.962.1
HAIS [4]--71.165.0
SSTNet [19]42.759.365.664.2
SoftGroup [30]51.666.173.666.6
Mask3D [27]56.569.368.770.7
RPGN [8]--64.063.0
PointInst3D [11]--73.165.2
DKNet [31]--70.865.3
ISBNet [29]56.367.570.572.0
PBNet [36]53.566.474.965.4
QueryFormer [21]57.769.970.572.2
MAFT [15]-69.1--
Ours60.572.371.376.3
+ +Table 3. Quantitative 3D instance segmentation results on S3DIS Area 5. The best results are in bold, and the second best ones are in underlined. + +
MethodmAP AP50RID Lmc LscmAP AP50AP25
HAIS [4]35.046.7✓51.669.486.8
PointGroup [13]23.338.5✓✓58.577.687.5
ISBNet [29]49.264.0✓56.577.187.1
Ours52.268.3✓✓62.379.988.2
+ +ing. Despite the variation, all configurations of $N_{\theta}$ and $N_{\varphi}$ still outperform existing methods in Table 2, implying that RID with RPM always improves the performance. + +Impact of Radial Point Migration is illustrated in Table 5. Here, we investigate the impact of the RPM and each loss for it. The baseline is the model trained with only RID, exclud + +Table 4. Quantitative instance segmentation results on STPLS3D +Table 5. Impact of each component on ScanNetV2 validation set + +
Nθ/NφmAPAP50AP25
1/159.677.185.3
2/260.077.786.1
3/360.678.487.1
4/461.280.089.3
5/562.379.988.2
6/660.678.588.2
+ +Table 6. Impact of $N_{\theta}$ and $N_{\varphi}$ on ScanNetV2 validation set + +
Seed/VotemAP\( AP_{50} \)\( AP_{25} \)
1024/12862.379.287.8
1024/25662.379.988.2
1024/51262.379.487.6
2048/12862.079.788.0
2048/25661.879.687.9
2048/51261.779.187.5
+ +Table 7. Impact of seed and vote numbers on ScanNetV2 validation set + +ing RPM. As the baseline model cannot refine the false positive points inside radial predictions or false negative points outside, as shown in Figure 6 (parts of chairs included as tables), its performance with high iou thresholds(AP, $\mathrm{AP}_{50}$ ) are $17.1\%$ and $13.1\%$ worse than the full model. Including RPM with $L_{mc}$ leads $13.3\%$ of improvement in AP, suggesting refinement to push and pull misclassified points is crucial for the performance. $L_{sc}$ shows $9.4\%$ improvement in AP from the baseline, suggesting that focusing on true positive samples also contributes significantly to learning fine granularity and common features shared within an instance. As shown in Figure 6(column 5,6), adding $L_{sc}$ improves the segmentation around the center of the objects, which was expected as the true positive samples near the instance centers could be neglected from $L_{mc}$ as they are usually inside rays. As $L_{mc}$ and $L_{sc}$ target different samples, the full model combining both $L_{mc}$ and $L_{sc}$ shows $20.7\%$ and $15.1\%$ improvements for AP and $\mathrm{AP}_{50}$ , demonstrating the synergy of the two losses. + +Impact of Voting Parameters is shown in Table 7. In this experiment, we change the seed and vote numbers inside the backbone while fixing RID and RPM. As can be seen, a seed number of 1024 produces more reliable results without variation than 2048, suggesting too many seed points negatively impact the system. Despite the slight difference, we observe that changing the seed and vote produces comparably small variations of $\pm 0.6$ in mAP for all settings. + +# 5. Conclusion + +We present Spherical Mask, a novel coarse-to-fine approach for 3D instance segmentation in point cloud. As a coarse detection, the RID module finds instances as 3D polygons defined with center and rays. In contrast to existing coarse-to-fine approaches, the RPM module uses the polygons as soft references and migrates points efficiently in spherical coordinates to acquire final masks. We demonstrate how each module contributes to the instance segmentation and achieves state-of-the-art performances on public benchmarks ScanNet-V2, S3DIS, and STPLS3D. + +# Acknowledgement + +This research was supported by ACE-OPS project (EP/S030832/1). + +# References + +[1] Salwa Al Khatib, Mohamed El Amine Boudjoghra, Jean Lahoud, and Fahad Shahbaz Khan. 3d instance segmentation via enhanced spatial and semantic supervision. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1839-1849, 2020. 1 \ No newline at end of file diff --git a/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/images.zip b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..4e502b51a74a72cad2483f631f615abb79790593 --- /dev/null +++ b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4092a995384e86dd83351bd46a31b9121c9400fd2d5b306cb0ea7e733e32cf7c +size 774657 diff --git a/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/layout.json b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..aa38007ae525d379e0d3911ebcb3babbf520a0a3 --- /dev/null +++ b/2024/Spherical Mask_ Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation/layout.json @@ -0,0 +1,10550 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 61, + 102, + 533, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 102, + 533, + 140 + ], + "spans": [ + { + "bbox": [ + 61, + 102, + 533, + 140 + ], + "type": "text", + "content": "Spherical Mask: Coarse-to-Fine 3D Point Cloud Instance Segmentation with Spherical Representation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 78, + 160, + 506, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 160, + 506, + 203 + ], + "spans": [ + { + "bbox": [ + 78, + 160, + 506, + 203 + ], + "type": "text", + "content": "Sangyun Shin Kaichen Zhou Madhu Vankadari Andrew Markham Niki Trigoni Department of Computer Science University of Oxford" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 212, + 205, + 376, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 212, + 205, + 376, + 216 + ], + "spans": [ + { + "bbox": [ + 212, + 205, + 376, + 216 + ], + "type": "text", + "content": "firstname.lastname@cs.ox.ac.uk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "spans": [ + { + "bbox": [ + 143, + 244, + 192, + 258 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 270, + 290, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 582 + ], + "type": "text", + "content": "Coarse-to-fine 3D instance segmentation methods show weak performances compared to recent Grouping-based, Kernel-based and Transformer-based methods. We argue that this is due to two limitations: 1) Instance size overestimation by axis-aligned bounding box(AABB) 2) False negative error accumulation from inaccurate box to the refinement phase. In this work, we introduce Spherical Mask, a novel coarse-to-fine approach based on spherical representation, overcoming those two limitations with several benefits. Specifically, our coarse detection estimates each instance with a 3D polygon using a center and radial distance predictions, which avoids excessive size estimation of AABB. To cut the error propagation in the existing coarse-to-fine approaches, we virtually migrate points based on the polygon, allowing all foreground points, including false negatives, to be refined. During inference, the proposal and point migration modules run in parallel and are assembled to form binary masks of instances. We also introduce two margin-based losses for the point migration to enforce corrections for the false positives/negatives and cohesion of foreground points, significantly improving the performance. Experimental results from three datasets, such as ScanNetV2, S3DIS, and STPLS3D, show that our proposed method outperforms existing works, demonstrating the effectiveness of the new instance representation with spherical coordinates. The code is available at: https://github.com/yunshin/SphericalMask" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 597, + 127, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 127, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 127, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "3D instance segmentation has gained immense attention with its wide range of applications for Indoor Scanning[38], Augmented Reality(AR)[18], and Autonomous Driving[22]. Similar to 2D instance segmentation, the goal of the task is to identify each object along with its class label. Nevertheless, the sparse and unordered nature of point clouds has led to the development of methods different from 2D image segmentation." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 312, + 244, + 542, + 393 + ], + "blocks": [ + { + "bbox": [ + 312, + 244, + 542, + 393 + ], + "lines": [ + { + "bbox": [ + 312, + 244, + 542, + 393 + ], + "spans": [ + { + "bbox": [ + 312, + 244, + 542, + 393 + ], + "type": "image", + "image_path": "8f0926a4740271d01bcdbe162d28e7dd591d2b861dfecd38522d70f595e0122b.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 401, + 547, + 456 + ], + "lines": [ + { + "bbox": [ + 304, + 401, + 547, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 547, + 456 + ], + "type": "text", + "content": "Figure 1. Pipeline of Spherical Mask with coarse-to-fine framework. Given point cloud, instances are detected with 3D polygons defined in spherical coordinates. In the refinement phase, the points virtually migrate based on the polygon to estimate fine instance masks." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 462, + 547, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 604 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 604 + ], + "type": "text", + "content": "Existing approaches for 3D instance segmentation are broadly categorized into coarse-to-fine based[12, 14, 20, 33, 34], grouping-based[4, 13, 19, 30, 36], kernel-based[10, 11, 13, 29, 31], and Transformer-based[1, 15, 21, 27, 28] approaches. Recent progress in clustering techniques and attention mechanisms have driven the performances of the last three approaches to state-of-the-art. Compared to these three approaches, the coarse-to-fine approach has received relatively less attention due to a low accuracy, caused by two limitations: 1) False negative error propagation from the coarse detection to the refinement stage. 2) Overestimation of instance size." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 548, + 714 + ], + "type": "text", + "content": "Coarse-to-fine instance segmentation first performs coarse detection, followed by refinement using the coarse detection as hard reference. The basic assumption of the approach is that the coarse detection stage always provides a neat detection for refinement. However, this assumption is often violated as the coarse detection stage cannot always produce neat outputs, which causes an issue of upper bound accuracy. For example, if the first coarse detection does not include all foreground points, the following" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4060" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 204 + ], + "type": "text", + "content": "refinement(binary classification) step has no means to include them, only possibly accumulating the error from false negative prediction. The other limitation is that the axis-aligned-bounding-box(AABB) estimation, which is typically used for the coarse detection, has been claimed to be an ill-defined problem[30] because commonly used box regression losses(L1, L2) result in overestimation of object sizes. For instance, the target values of AABB are minimum and maximum values in x,y,z cartesian coordinates, making the box include redundant empty space, as points only lie on the surface of the object." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 207, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 289, + 399 + ], + "type": "text", + "content": "In this work, we address the aforementioned two limitations of coarse-to-fine instance segmentation. Our core intuition comes from the fact that the weakness of the coarse-to-fine approach is based on the structural disentanglement of coarse detection and fine refinement phase. Instead of assuming that the coarse part should be perfect, we take a relaxation approach, which regards the coarse detection as a soft reference during the refinement phase, providing more access for refinement yet restricting access to unnecessary background points. Specifically, to improve the coarse detection part, we estimate a 3D polygon in spherical coordinates instead of AABB, alleviating the issue of excessive object size estimation. To remove the error propagation from inaccurate coarse detection to the refinement stage, we virtually migrate points based on the 3D polygon with reduced complexity in spherical coordinates." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 402, + 288, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 402, + 288, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 402, + 288, + 460 + ], + "type": "text", + "content": "In summary, our method Spherical Mask finds each instance by estimating a 3D polygon fitting to an instance in spherical coordinates and migrating points inside or outside the polygon to produce the fine instance mask. Our contributions are:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 465, + 288, + 632 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 47, + 465, + 287, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 287, + 501 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 287, + 501 + ], + "type": "text", + "content": "- We introduce a new alternative instance representation based on spherical coordinates, which overcomes the limitations in existing coarse-to-fine approaches." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 502, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 502, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 502, + 287, + 548 + ], + "type": "text", + "content": "- To circumvent the issue of excessive estimation of instance size, we propose Radial Instance Detection(RID) that formulates an instance into a 3D polygon as a coarse detection." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 549, + 288, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 549, + 288, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 549, + 288, + 597 + ], + "type": "text", + "content": "- To cut the error propagation from coarse detection to the refinement phase, we introduce Radial Point Migration(RPM), capable of refining both false positive and false negative points from RID." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 597, + 287, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 287, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 287, + 632 + ], + "type": "text", + "content": "- Extensive experiments on ScanNetV2 [7], S3DIS [2], and STPLS3D [3] show the effectiveness of our approach, pushing the boundary of current SOTA." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 654, + 134, + 666 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 134, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 134, + 666 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 712 + ], + "type": "text", + "content": "Existing works on point cloud instance segmentation can be categorized into proposal-based, clustering-based, kernel-based and transformer-based methods." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 525, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 525, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 525, + 85 + ], + "type": "text", + "content": "2.1. Coarse to Fine(Proposal-based) Approach" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 547, + 354 + ], + "type": "text", + "content": "Coarse-to-fine-based methods are built on a conceptually simple design, where they first perform coarse detection, followed by a refinement stage to acquire fine segmentation. Typically, 3D bounding box is employed for the coarse detection. 3D-SIS[12] performs instance segmentation by first detecting the 3D boxes and refining points inside. 3D-BoNet[33] matches query AABBs and ground-truth instance using Hungarian algorithm for the supervision. The predicted AABBs are then concatenated with point features to produce binary masks for each instance. GSPN[34] adopts set-abstraction[24] to get query points and infer AABBs. The features inside the AABBs are extracted and used for per-point mask segmentation. More recently, TD3D [14] proposes a fully sparse-convolutional approach for point instance segmentation. It first detects AABBs and extracts perpoint features inside the boxes to perform binary classification. Most of the works use coarse detection(bounding box) directly as geometric features for predicting per-point binary instance masks. Thus, their accuracies greatly depend on the precision of the coarse detection, as inaccurate detection could easily lead to a large number of false negative points." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 363, + 454, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 363, + 454, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 363, + 454, + 376 + ], + "type": "text", + "content": "2.2. Grouping-based Approach" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 382, + 547, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 382, + 547, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 382, + 547, + 525 + ], + "type": "text", + "content": "Grouping-based methods learn latent embeddings to perform per-point predictions, such as semantic categories and clustering to acquire instances. PointGroup[13] predicts centroid offsets of each point and utilizes this shifted point cloud and original point cloud to obtain the clusters. Based on this concept, many studies improve the clustering technique with hierarchical intra-instance predictions[4], superpoint-based divisive grouping[19], soft grouping[30], and binary clustering[36]. The clustering-based methods have high expectations of the quality of per-point center prediction in 3D, which is challenging to generalize with various spatial extents of objects." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 534, + 440, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 534, + 440, + 548 + ], + "spans": [ + { + "bbox": [ + 306, + 534, + 440, + 548 + ], + "type": "text", + "content": "2.3. Kernel-based Approach" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 554, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 547, + 649 + ], + "type": "text", + "content": "Kernel-based methods learn convolution kernels that aggregate point features to estimate instance masks. DyCo3D[10] proposes discriminative kernels by applying the clustering method from PointGroup[13]. Built on this, more recent works improved the performance by replacing the clustering part with farthest-point sampling[11], candidate localization[31], and instance-aware point sampling for the high-recall[29]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 658, + 468, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 468, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 468, + 671 + ], + "type": "text", + "content": "2.4. Transformer-based Approach" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "Recently, transformer-based methods have set the new SOTA. Based on mask-attention[5, 6], Mask3D[27] and SPFormer[28] present the pipeline that learns to output" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4061" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 180 + ], + "type": "text", + "content": "instance prediction directly from a fixed number of object queries from voxel and superpoint features, respectively. Based on these works, recent studies improve the performance with auxiliary center regression[15], query initialization and set grouping[21], spatial and semantic supervision[1]. Although the powerful architectural advantage has driven the performance of Transformer-based approaches, low-recall and how to distribute initial queries remain challenges." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 190, + 102, + 202 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 190, + 102, + 202 + ], + "spans": [ + { + "bbox": [ + 47, + 190, + 102, + 202 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 210, + 115, + 221 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 210, + 115, + 221 + ], + "spans": [ + { + "bbox": [ + 47, + 210, + 115, + 221 + ], + "type": "text", + "content": "3.1. Overview" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "text", + "content": "Given an input point cloud " + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "inline_equation", + "content": "p_1 \\in \\mathbb{R}^{N_p \\times 3}" + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "text", + "content": " in 3-dimensional cartesian coordinates and the corresponding color information " + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{rgb}} \\in \\mathbb{R}^{N_p \\times 3}" + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "text", + "content": ", we aim to design a system that segments the point cloud into local binary masks of instances " + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "inline_equation", + "content": "\\{o^{(i)} \\in \\mathbb{R}^{N_p \\times 1}\\}_{i=1}^{N_o}" + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "text", + "content": " using a coarse to fine approach. Here, " + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "inline_equation", + "content": "N_p, N_o" + }, + { + "bbox": [ + 46, + 227, + 289, + 361 + ], + "type": "text", + "content": " are the total number of points and the number of instances, respectively. This is achieved using the proposed method depicted in Figure 2. Our system consists of mainly two modules: 3D backbone and proposed instance mask estimation. The details of these modules are in Section 3.2 and Section 3.3, respectively." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 367, + 132, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 367, + 132, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 367, + 132, + 379 + ], + "type": "text", + "content": "3.2. 3D backbone" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "spans": [ + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": "Our 3D backbone is similar to [29] and is composed of two modules: a 3D encoder and a voting module. The 3D encoder uses U-Net [26] with sparse convolutions [9] to encode the given point cloud into deep features " + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "inline_equation", + "content": "F_{1} \\in \\mathbb{R}^{N_{p} \\times D}" + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": ". Then, " + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": " and the respective input points " + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "inline_equation", + "content": "p_{1}" + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": " are fed into the voting module. The voting module performs set abstraction [24], producing " + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": " votes with query points " + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "inline_equation", + "content": "p_{2} \\in \\mathbb{R}^{K \\times 3}" + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": " and features " + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "inline_equation", + "content": "F_{2} \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 46, + 385, + 289, + 540 + ], + "type": "text", + "content": ". Please find the original paper [25] for more details about this procedure. These votes are spread in the scene, providing features to be further processed through the proposed instance mask estimation module. The details are explained in the following sections." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 548, + 192, + 559 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 192, + 559 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 192, + 559 + ], + "type": "text", + "content": "3.3. Instance Mask Estimation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "type": "text", + "content": "In this section, we estimate the instance masks from the votes predicted in the 3D backbone section using three modules: Radial Instance Detection, Radial Point Migration, and Mask Assembly. All of the modules are explained in the following sections. For the notation simplicity, we will explain how each vote feature is processed. Therefore, we write " + }, + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "type": "inline_equation", + "content": "f_{2}" + }, + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "type": "text", + "content": " to refer to a single vote feature of " + }, + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "type": "inline_equation", + "content": "F_{2}" + }, + { + "bbox": [ + 46, + 566, + 287, + 650 + ], + "type": "text", + "content": " from here onwards." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 658, + 253, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 253, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 253, + 671 + ], + "type": "text", + "content": "3.3.1 Radial Instance Detection(Coarse Mask)" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Radial Instance Detection(RID) aims to detect instances for further refinement. Similar to PolarMask[32] for 2D segmentation, we define an instance as a 3D polygon with a" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "type": "text", + "content": "center " + }, + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{center}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "type": "text", + "content": " and multiple rays " + }, + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{ray}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 131 + ], + "type": "text", + "content": " emitting from the center forming each spherical sectors. Here, the sectors are defined by preset angles. Each ray then determines the distance to be considered for their corresponding sectors, as shown in Figure 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": "We estimate the closest instances' center " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "f_{\\text{center}}" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": " using offsets predicted from an MLP network, CenterHead, which takes the respective " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "f_2" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": " as input and outputs offsets. The offsets are added to " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "p_2" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": " to infer " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "f_{\\text{center}}" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": ". After this, the input point cloud is converted into spherical coordinates using a transformation as " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "p_s = S(p_1)" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": " centered around " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "f_{\\text{center}}" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "inline_equation", + "content": "S:(x,y,z) \\to (r,\\theta,\\varphi)" + }, + { + "bbox": [ + 304, + 133, + 547, + 216 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 376, + 224, + 545, + 269 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 224, + 545, + 269 + ], + "spans": [ + { + "bbox": [ + 376, + 224, + 545, + 269 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} r = \\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}, \\\\ \\theta = \\arctan \\frac {x}{y}, \\tag {1} \\\\ \\varphi = \\arctan {\\frac {z}{\\sqrt {x ^ {2} + y ^ {2} + z ^ {2}}}}. \\\\ \\end{array}", + "image_path": "b0699ef789cc3e646649f8c46f75659fb450dc4841abc74dcc46fecf5fc314af.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": " refer to radius, horizontal, and vertical angles in spherical coordinates, respectively. The " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "p_s" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": " is then divided uniformly with " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": " separations for horizontal and vertical direction respectively, resulting in " + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "inline_equation", + "content": "N_{\\theta} \\cdot N_{\\varphi}" + }, + { + "bbox": [ + 304, + 276, + 547, + 335 + ], + "type": "text", + "content": " sectors, as shown in Figure 3 (b) and (c)." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "text", + "content": "We consider points inside the same sector to have identical " + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "inline_equation", + "content": "(\\theta, \\varphi)" + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "text", + "content": ", which enables us to close the sector using a boundary estimated by " + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{ray}}" + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "text", + "content": ". To estimate " + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "inline_equation", + "content": "\\{f_{\\mathrm{ray}}^{(i)}\\}_{i=1}^{N_\\theta N_\\varphi}" + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "text", + "content": ", another MLP named Ray Head is employed, which takes " + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "inline_equation", + "content": "f_2" + }, + { + "bbox": [ + 304, + 336, + 547, + 396 + ], + "type": "text", + "content": " as input." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 397, + 547, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 397, + 547, + 480 + ], + "spans": [ + { + "bbox": [ + 304, + 397, + 547, + 480 + ], + "type": "text", + "content": "At this point, every point inside the corresponding sector's boundary from " + }, + { + "bbox": [ + 304, + 397, + 547, + 480 + ], + "type": "inline_equation", + "content": "f_{ray}" + }, + { + "bbox": [ + 304, + 397, + 547, + 480 + ], + "type": "text", + "content": " is considered foreground. Using the boundary, RID offers tighter boundaries of instances than AABB in point cloud, as each sector is closed at the distance of the farthest foreground point in the sector, alleviating the problem of redundant space in AABB. Please refer to our supplementary material for additional visualizations." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "content": "Coarse Instance Loss: During training, the estimated " + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "inline_equation", + "content": "f_{\\text{centre}}" + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "inline_equation", + "content": "f_{\\text{ray}}" + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "content": " are compared against their respective ground truth " + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\text{center}}" + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\text{ray}}" + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "content": " to calculate " + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "inline_equation", + "content": "L_{\\text{coarse}}" + }, + { + "bbox": [ + 304, + 481, + 545, + 518 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 377, + 529, + 545, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 529, + 545, + 541 + ], + "spans": [ + { + "bbox": [ + 377, + 529, + 545, + 541 + ], + "type": "interline_equation", + "content": "L _ {\\text {c o a r s e}} = L _ {\\text {r a y}} + L _ {\\text {c e n t e r}}, \\tag {2}", + "image_path": "f00be8c6ed32ef4316f500b6ef0f115d39a9a275b43234ec69f461228587dd07.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{ray}}" + }, + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{center}}" + }, + { + "bbox": [ + 304, + 546, + 497, + 559 + ], + "type": "text", + "content": " are defined with L1 loss:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 355, + 567, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 355, + 567, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 355, + 567, + 545, + 601 + ], + "type": "interline_equation", + "content": "L _ {\\text {r a y}} = \\frac {1}{N _ {\\theta} N _ {\\varphi}} \\sum_ {i = 1} ^ {N _ {\\theta} N _ {\\varphi}} \\left| f _ {\\text {r a y}} ^ {(i)} - \\mathbf {g} _ {\\text {r a y}} ^ {(i)} \\right| _ {1} \\tag {3}", + "image_path": "8a389f23f6d4b04a450100d87b75a94151608f4a2d14db132347f4e6ff530ea4.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 370, + 609, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 609, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 370, + 609, + 545, + 622 + ], + "type": "interline_equation", + "content": "L _ {\\text {c e n t e r}} = \\left| f _ {\\text {c e n t e r}} - \\mathbf {g} _ {\\text {c e n t e r}} \\right| _ {1}, \\tag {4}", + "image_path": "e89726c9dfd478064beaffba16939345640986225b1ceff51878c907a7aff7ee.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": "Here, the ground-truth instance " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " is matched with " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{center}}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " by an injective mapping obtained using Hungarian algorithm as [29, 33]. For the details of the matching, please refer to Sec 3.4. " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\mathrm{ray}}^{(i)}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " is set to the distance between " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\mathrm{center}}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " and the furthest foreground point in the " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " sector. If there are no foreground points in the sector, " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\mathrm{ray}}^{(i)}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " is set to minimum as " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "1e - 5" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": ". The target center " + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\mathrm{center}}" + }, + { + "bbox": [ + 304, + 626, + 547, + 714 + ], + "type": "text", + "content": " is calculated as mean values" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4062" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 549, + 220 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 549, + 220 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 549, + 220 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 549, + 220 + ], + "type": "image", + "image_path": "6b9c9d61e227658cdf1f8733a2962606d4b5a411addf09d257ce12dd594eb2ba.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "lines": [ + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": "Figure 2. Overall pipeline of our proposed method based on coarse to fine approach. Given the point cloud, the backbone produces base features with 3D UNet and Voting module. Based on this, RID performs coarse detection while RPM produces the virtual point offsets to refine the coarse detection. In Mask Assembly, " + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 228, + 547, + 274 + ], + "type": "text", + "content": " local binary masks are generated, where each mask is a proposal for a single instance. 3D NMS is applied to acquire the final instance masks using local binary masks, classifications, and confidence scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 309 + ], + "type": "text", + "content": "of foreground points of the matched groundtruth instance in cartesian coordinates." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 261, + 331 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 261, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 261, + 331 + ], + "type": "text", + "content": "3.3.2 Radial Point Migration(Mask Refinement)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "type": "text", + "content": "In this section, we introduce a refinement process to perform per-point fine-tuning. This is because the coarse detection will invariably include points belonging to the background or other instances (i.e. false positives) inside its boundary and neglect some instance points that fall outside (i.e. false negatives). We propose a conceptually simple yet effective dual that jitters individual points to belong to the correct instance. In particular, this is enabled by our innovative use of spherical coordinates - we only need to learn a single radial delta for each point to move it along the ray to the instance centroid while keeping angular quantities " + }, + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 337, + 287, + 516 + ], + "type": "text", + "content": " constant. Note that this is a virtual point motion - we do not alter the final point cloud. We use this as a virtual offset to obtain clean instance labels without modifying the coarse sector." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": "By estimating an offset value for each point " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "p_1" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": ", these misclassified points can be virtually migrated to being in the correct region. Based on its good performance on perpoint prediction, we adopt Dynamic Convolution in a similar manner to [10, 29] as our Point Migration Head, for predicting per-point offsets " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "F_{\\delta} \\in \\mathbb{R}^{K \\times N_p}" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": " using the vote features " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "F_2 \\in \\mathbb{R}^{K \\times D}" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": " as queries against the point features " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "F_1 \\in \\mathbb{R}^{N_p \\times D}" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": ". For the coherence with the notations, we write " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "f_{\\delta} \\in \\mathbb{R}^{N_p}" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": " to refer to an output of " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "F_{\\delta}" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": ", corresponding to one vote. For the learning of " + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "inline_equation", + "content": "f_{\\delta}" + }, + { + "bbox": [ + 46, + 517, + 288, + 684 + ], + "type": "text", + "content": ", we divide points into two groups. The first is to learn the radial delta for the case of misclassification, and the second is to make instances more compact and cohesive by migrating points to the centroid of the sector." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Misclassification Correction Loss: This process aims to estimate a radial delta to move the misclassified points either" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 285, + 545, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 545, + 368 + ], + "type": "text", + "content": "inside or outside the estimated coarse sector. There are two possible cases where the misclassification could occur, as shown in Figure 4 (a): Instance points could lie outside the sector boundary, acting as false negatives, or background points could incorrectly lie within the sector boundary, acting as false positives. The goal is to move these points to the correct region." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "spans": [ + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "text", + "content": "Formally, given the point indices of foreground points " + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\{j^{+(i)}\\}_{i=1}^{N+}" + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "text", + "content": " and background points " + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "inline_equation", + "content": "\\{j^{-(i)}\\}_{i=1}^{N-}" + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "text", + "content": " from the groundtruth, the false negative points " + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{fn}}" + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "text", + "content": " and the false positive points " + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{fp}}" + }, + { + "bbox": [ + 306, + 369, + 547, + 417 + ], + "type": "text", + "content": " are defined as:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 340, + 426, + 545, + 444 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 426, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 340, + 426, + 545, + 444 + ], + "type": "interline_equation", + "content": "p _ {\\mathrm {f n}} = \\left\\{p _ {s} ^ {(j +)}: \\left(p _ {s} ^ {(j +)} + f _ {\\delta} ^ {(j +)}\\right) > f _ {\\text {r a y}} ^ {(\\tilde {j} +)} \\right\\}, \\tag {5}", + "image_path": "9364b4c5b8e1e1b2e15067a807d3dac59e6b153d6374e77ee5816a6e41b3f42a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 340, + 460, + 545, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 460, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 340, + 460, + 545, + 477 + ], + "type": "interline_equation", + "content": "p _ {\\mathrm {f p}} = \\left\\{p _ {s} ^ {(j -)}: \\left(p _ {s} ^ {(j -)} + f _ {\\delta} ^ {(j -)}\\right) < f _ {\\text {r a y}} ^ {(j -)} \\right\\}, \\tag {6}", + "image_path": "d761b2e30baeb401bc571cc32ecbda9e1a3aa70ce8ba39528496f1ebae00d9b3.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "inline_equation", + "content": "N+" + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "inline_equation", + "content": "N-" + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": " stand for the number of foreground and background points, respectively. Here, " + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\tilde{j} = \\text{findSector}(p_s^{(j)})" + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\text{findSector}(\\cdot)" + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": " is a function that takes " + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "inline_equation", + "content": "p_s^{(j)}" + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": " as input and returns the index of the sector that " + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "inline_equation", + "content": "p_s^{(j)}" + }, + { + "bbox": [ + 304, + 481, + 547, + 555 + ], + "type": "text", + "content": " belongs to. Please refer to the supplementary material for our implementation of findSector()." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "content": "The union of " + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{fp}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{fn}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "content": " forms the misclassified points " + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{miss}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "content": " that we are interested: " + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{miss}} = p_{\\mathrm{fp}} \\cup p_{\\mathrm{fn}}" + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "content": ". Our aim is to push or pull them inside/outside of the ray with margins. Thus, the loss function " + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 304, + 556, + 547, + 615 + ], + "type": "text", + "content": " is formulated with soft margin loss as:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 632, + 545, + 675 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 545, + 675 + ], + "type": "interline_equation", + "content": "L _ {m c} = \\frac {1}{N _ {\\text {m i s s}}} \\sum_ {i = 1} ^ {N _ {\\text {m i s s}}} \\log \\left(1 + \\exp \\left(y * \\tanh \\left(p _ {\\text {m i s s}} ^ {(i)} + f _ {\\delta} ^ {(\\hat {i})} - f _ {\\text {r a y}} ^ {(\\tilde {i})}\\right)\\right)\\right) \\tag {7}", + "image_path": "437425f5e1e8339ef9c37027bfa553f54042f905e2e063a0a1d1d84f61c7f473.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 676, + 345, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 676, + 345, + 685 + ], + "spans": [ + { + "bbox": [ + 318, + 676, + 345, + 685 + ], + "type": "text", + "content": "where" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 370, + 684, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 684, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 370, + 684, + 545, + 716 + ], + "type": "interline_equation", + "content": "y = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} p _ {\\mathrm {m i s s}} ^ {(i)} \\in p _ {\\mathrm {f p}}, \\\\ - 1 & \\text {i f} p _ {\\mathrm {m i s s}} ^ {(i)} \\in p _ {\\mathrm {f n}}, \\end{array} \\right. \\tag {8}", + "image_path": "1f5f0dbc137b9622fe2822445b9c53cfdce2eb572b2c12141e544ac59f1dc971.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4063" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 262, + 208 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 262, + 208 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 262, + 208 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 262, + 208 + ], + "type": "image", + "image_path": "5191c73ecb9c26b1081d4b574a4e565f9fc4fcf5f070dc30e2384fea12790528.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": "Figure 3. Process of RID. (a) Object points in cartesian coordinates (b) Converting points into a spherical coordinate system, using " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "f_{\\text{center}}" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": ", and preset angles " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": ". (c) Assigning points to each sector defined by " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": ". The example shows 3/3 for " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "\\theta / \\varphi" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": ". (d) For each sector, the distance between the farthest point and the center becomes the target of " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "f_{\\text{ray}}" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": ". During inference, points with smaller distance than " + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "inline_equation", + "content": "f_{\\text{ray}}" + }, + { + "bbox": [ + 46, + 214, + 287, + 291 + ], + "type": "text", + "content": " are considered foreground." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": "Here, tanh is hyperbolic-tangent function and " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " is calculated for all the votes that are assigned to the ground truth instance. " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{miss}}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " stands for the number of element in " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{miss}}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "\\hat{i}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " is index of " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "f_{\\delta}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{miss}}^{(i)}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{ray}}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " is only used for reference and the gradient for learning " + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "inline_equation", + "content": "f_{ray}" + }, + { + "bbox": [ + 46, + 297, + 288, + 358 + ], + "type": "text", + "content": " is not calculated." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 358, + 288, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 288, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 288, + 418 + ], + "type": "text", + "content": "The misclassified points around the edge, " + }, + { + "bbox": [ + 46, + 358, + 288, + 418 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{ray}}" + }, + { + "bbox": [ + 46, + 358, + 288, + 418 + ], + "type": "text", + "content": ", of an instance are provided with comparably easy learning targets. In contrast, misclassified points far from the predicted rays are assigned targets with large discrepancies, encouraging larger gradients during the training." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "content": "Sector Cohesion Loss The goal of this block is to move true-positive points to the centroid of the sector. By doing so, the sector becomes more cohesive, encouraging the learning of common and shared features of an instance as the foreground features are getting close to each other. In addition, this helps to provide a learning signal for true-positive points, as " + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mc}}" + }, + { + "bbox": [ + 46, + 423, + 287, + 518 + ], + "type": "text", + "content": " only considers false negatives/positives. This is shown more clearly in Figure 4 (b)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "text", + "content": "Similar to " + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "text", + "content": ", using point indices of foreground points " + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "inline_equation", + "content": "j+" + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "text", + "content": ", we extract true positives " + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{tp}}" + }, + { + "bbox": [ + 46, + 519, + 287, + 544 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 82, + 552, + 287, + 570 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 552, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 82, + 552, + 287, + 570 + ], + "type": "interline_equation", + "content": "p _ {\\mathrm {t p}} = \\left\\{p _ {s} ^ {(j +)}: \\left(p _ {s} ^ {(j +)} + f _ {\\delta} ^ {(j +)}\\right) < f _ {\\text {r a y}} ^ {(\\tilde {j} +)} \\right\\} \\tag {9}", + "image_path": "1138d29d2316eec9801030d84837c500ff02f7761ae026ae0531b49997846962.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 577, + 270, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 577, + 270, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 577, + 270, + 588 + ], + "type": "text", + "content": "and formulate the loss with the soft margin calculation:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 50, + 594, + 287, + 638 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 594, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 50, + 594, + 287, + 638 + ], + "type": "interline_equation", + "content": "L _ {s c} = \\frac {1}{N _ {\\mathrm {t p}}} \\sum_ {i = 1} ^ {N _ {\\mathrm {t p}}} \\log \\left(1 + \\exp \\left(\\tanh \\left(f _ {\\delta} ^ {(i)} + p _ {\\mathrm {t p}} ^ {(i)} - f _ {\\text {c e n t e r}}\\right)\\right)\\right), \\tag {10}", + "image_path": "f8ab2d644a4d6e70f71752c5471f742bd9e101b1ed83689cb4048501ec6412e3.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "inline_equation", + "content": "N_{\\mathrm{tp}}" + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": " stands for the number of element in " + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{tp}}" + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\hat{i}" + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": " is index of " + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "inline_equation", + "content": "f_{\\delta}" + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "inline_equation", + "content": "p_{\\mathrm{tp}}^{(i)}" + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{center}}" + }, + { + "bbox": [ + 46, + 638, + 287, + 677 + ], + "type": "text", + "content": " is always 0 in centered spherical coordinate, the loss can be simplified as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 682, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 682, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 59, + 682, + 287, + 715 + ], + "type": "interline_equation", + "content": "L _ {s c} = \\frac {1}{N _ {\\mathrm {t p}}} \\sum_ {i = 1} ^ {N _ {\\mathrm {t p}}} \\log \\left(1 + \\exp \\left(\\tanh \\left(f _ {\\delta} ^ {(i)} + p _ {\\mathrm {t p}} ^ {(i)}\\right)\\right)\\right), \\tag {11}", + "image_path": "68b11903481c7ecdcaa45dc4aeb9d17d81ae1392f0f90a90a1b0891898a4ed16.jpg" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 312, + 73, + 542, + 125 + ], + "blocks": [ + { + "bbox": [ + 312, + 73, + 542, + 125 + ], + "lines": [ + { + "bbox": [ + 312, + 73, + 542, + 125 + ], + "spans": [ + { + "bbox": [ + 312, + 73, + 542, + 125 + ], + "type": "image", + "image_path": "643eb4d00da6ca92e1dbeee492fd35d4aa2202e21439c88706d257226dbdbd19.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 131, + 433, + 141 + ], + "lines": [ + { + "bbox": [ + 307, + 131, + 433, + 141 + ], + "spans": [ + { + "bbox": [ + 307, + 131, + 433, + 141 + ], + "type": "text", + "content": "(a) Misclassification Correction Loss" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 456, + 131, + 541, + 141 + ], + "lines": [ + { + "bbox": [ + 456, + 131, + 541, + 141 + ], + "spans": [ + { + "bbox": [ + 456, + 131, + 541, + 141 + ], + "type": "text", + "content": "(b) Sector Cohesion Loss" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "lines": [ + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "spans": [ + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": "Figure 4. Conceptual diagram showing per-point migration following both (a) " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mc}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": " and (b) " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{sc}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathrm{FP}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathrm{FN}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": " are distances penalized by " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{mc}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": " with margin for misclassified points. " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "\\Delta_{\\mathrm{TP}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": " is the distance that " + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{sc}}" + }, + { + "bbox": [ + 305, + 146, + 547, + 212 + ], + "type": "text", + "content": " penalizes to enforce the learning of general features of an instance by making each sample close to the other around the center." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "spans": [ + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "text", + "content": " together form the refinement loss " + }, + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{fine}}" + }, + { + "bbox": [ + 306, + 221, + 529, + 233 + ], + "type": "text", + "content": " as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 384, + 242, + 545, + 254 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 242, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 384, + 242, + 545, + 254 + ], + "type": "interline_equation", + "content": "L _ {\\text {f i n e}} = L _ {m c} + L _ {s c}. \\tag {12}", + "image_path": "40fbd7ffe62cc5ade0621c2fc731838ea2419b678c24d11f325b9fafebcaac15.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "spans": [ + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "type": "text", + "content": "Our proposed virtual point migration brings three advantages for refinement over existing approaches that strictly disentangle coarse detection and refinement: 1) Instead of only focusing on points inside the coarse detection, predicting the offsets of all points allows the refinement of even false negative points outside of " + }, + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{ray}}" + }, + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "type": "text", + "content": ", sidestepping the error accumulation from the coarse detection. 2) By considering the sector radius, " + }, + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "type": "inline_equation", + "content": "g_{\\mathrm{ray}}" + }, + { + "bbox": [ + 304, + 262, + 547, + 465 + ], + "type": "text", + "content": ", it is possible to have a soft target for each point rather than a hard target which is the center of the sector/instance. For example, false negative points outside of the sector boundary only need to be migrated a small distance to being with the sector (soft), rather than being driven towards the center (hard). This makes it easier to learn how to perform the point migration. 3) We only need to learn a one-dimensional number to migrate the point virtually along the radial line. This is far simpler than having to learn a three-dimensional offset in cartesian coordinates." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 475, + 406, + 487 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 406, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 406, + 487 + ], + "type": "text", + "content": "3.3.3 Mask Assembly" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "spans": [ + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "type": "text", + "content": "Our final mask is assembled by comparing virtually migrated points and " + }, + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "type": "inline_equation", + "content": "f_{ray}" + }, + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "type": "text", + "content": ". Specifically, the local binary mask " + }, + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "type": "inline_equation", + "content": "\\{f_{\\mathrm{mask}}^{(i)}\\}_{i = 1}^{N_p}" + }, + { + "bbox": [ + 305, + 493, + 547, + 533 + ], + "type": "text", + "content": " is formed as:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 351, + 539, + 545, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 539, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 351, + 539, + 545, + 572 + ], + "type": "interline_equation", + "content": "f _ {\\text {m a s k}} ^ {(i)} = \\left\\{ \\begin{array}{l l} 1 & \\text {i f} \\left(p _ {s} ^ {(i)} + f _ {\\delta} ^ {(i)}\\right) < f _ {\\text {r a y}} ^ {(\\tilde {i})} \\\\ 0 & \\text {o t h e r w i s e ,} \\end{array} \\right. \\tag {13}", + "image_path": "15793a7fff4998490040b2e31624864471cffe7db1d6363619cc9df4ce301148.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 578, + 370, + 591 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 578, + 370, + 591 + ], + "spans": [ + { + "bbox": [ + 306, + 578, + 370, + 591 + ], + "type": "text", + "content": "3.4. Training" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "spans": [ + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "type": "text", + "content": "For the training, we also learn classification and confidence with respective MLPs. For classification, we apply cross-entropy loss, " + }, + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{cls}}" + }, + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "type": "text", + "content": ", for learning the classes of matched groundtruth instances. For the confidence scores of the proposals, we apply L2 loss to learn IoUs between the proposals and the groundtruth instances. Similar to [29], we also duplicate the number of groundtruth for 4 times and create a cost matrix " + }, + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 597, + 547, + 691 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 320, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 320, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "C (k, i) = L _ {\\text {c o a r s e}} (k, i) + L _ {\\text {f i n e}} (k, i) + L _ {\\text {c l s}} (k, i), \\tag {14}", + "image_path": "55198d0ae0e5e7c3b1f6f6e548d432fc9f025fbb96baa11e1195f2edb1af74e4.jpg" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4064" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "L(,)" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " refers to the loss value calculated using " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "k_{th}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " vote and " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "i_{th}" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " ground-truth instance. Referring " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": ", we apply Hungarian algorithm to find the least-cost injective mapping from each ground-truth instance to the votes. The final loss using the acquired ground-truths is:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 78, + 143, + 287, + 156 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 143, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 78, + 143, + 287, + 156 + ], + "type": "interline_equation", + "content": "L = \\lambda_ {1} L _ {\\mathrm {c l s}} + \\lambda_ {2} L _ {\\text {c o n f}} + \\lambda_ {3} L _ {\\text {c o a r s e}} + \\lambda_ {4} L _ {\\text {f i n e}} \\tag {15}", + "image_path": "7e4a9dc44ea9f343abc32c0f4ebc8b14d04bb6aa451a6a57d6aa104e6786e501.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 162, + 123, + 175 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 162, + 123, + 175 + ], + "spans": [ + { + "bbox": [ + 47, + 162, + 123, + 175 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 182, + 105, + 194 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 105, + 194 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 105, + 194 + ], + "type": "text", + "content": "4.1. Dataset" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 201, + 287, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 201, + 287, + 236 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 287, + 236 + ], + "type": "text", + "content": "We evaluate our method on three datasets: ScanNetV2 [7], S3DIS [2], STPLS3D [3]. Following are descriptions of each dataset." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 237, + 287, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 237, + 287, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 287, + 285 + ], + "type": "text", + "content": "ScanNetV2 ScanNetV2 dataset consists of 1201, 312, and 100 scans with 18 object classes for training, validation, and testing, respectively. We report the evaluation results on the validation and hidden test sets as in the existing works." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 334 + ], + "type": "text", + "content": "S3DIS S3DIS dataset contains 271 scenes from 6 areas with 13 categories. We report evaluations for both Area 5. Additional evaluation results with 6-fold cross-validation can be found in the supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 334, + 287, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 334, + 287, + 394 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 287, + 394 + ], + "type": "text", + "content": "STPLS3D The STPLS3D dataset is an aerial photogrammetry point cloud dataset from real-world and synthetic environments. It includes 25 urban scenes of " + }, + { + "bbox": [ + 46, + 334, + 287, + 394 + ], + "type": "inline_equation", + "content": "6km^2" + }, + { + "bbox": [ + 46, + 334, + 287, + 394 + ], + "type": "text", + "content": " and 14 instance categories. Following [4, 29, 30], we use scenes 5, 10, 15, 20, and 25 for validation and the rest for training." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 403, + 155, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 403, + 155, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 403, + 155, + 415 + ], + "type": "text", + "content": "4.2. Evaluation Metric" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": "We adopt average precision as our primary evaluation metric. Average precision is extensively used in vision tasks such as object detection and instance segmentation tasks. The metric calculates precisions by varying the IoU threshold. Following the existing works, we evaluate our model with three IoU thresholds: " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "AP_{50}" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "AP_{25}" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "AP_{50}" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "AP_{25}" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " stand for average precisions with IoU threshold as " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "AP" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " is an averaged score by varying IoU thresholds from " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "95\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " by increasing the threshold with step size " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": ". For S3DIS, we also evaluate our model with mean precision (mPrec50), and mean recall with IoU threshold as " + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 422, + 287, + 566 + ], + "type": "text", + "content": " (mRec50)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 574, + 175, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 175, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 175, + 586 + ], + "type": "text", + "content": "4.3. Implementation Detail" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "We build our model on PyTorch framework [23] and train it for 300 epochs with AdamW optimizer with a single NVIDIA A10 GPU. The batch size is set to 10. The learning rate and weight decay are initialized to 0.001 and 0.0001. Cosine annealing [35] is used for scheduling the learning rate. Following [29, 30], the voxel size is set to " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "0.02\\mathrm{m}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " for ScanNetV2 and S3DIS, and to " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "0.3\\mathrm{m}" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " for STPLS3D. For the augmentation during training, we use random cropping for each scene with a maximum number of 250,000 points. During testing, a whole scene is used as an input to the network." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": "Our backbone is similar to[29, 30], which outputs features " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "F_{1}" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " with hidden dimension " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " as 32 channels. For the voting, we use two set-abstraction [24, 25] layers with the ball query radius 0.2 and 0.4, respectively. The number seeds and votes are set to 1024 and 256, respectively. The number of neighbors is set to 32 for both layers, similar to [29]. For Point Migration Head, we use two layers of dynamic convolution[10], and their hidden dimensions are set to 32. " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\lambda 1" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\lambda 2" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\lambda 3" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "\\lambda 4" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " are set to 0.5, 0.5, 1, and 1, respectively. For training and inference, we set " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " to 5 and 5, respectively. During inference, Non-Maximum-Suppression is applied to the " + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 72, + 547, + 277 + ], + "type": "text", + "content": " binary masks to delete redundant masks using a confidence score 0.2 as a threshold. Following [19, 21, 29, 31], we aggregate superpoints[16, 17] to align the final prediction masks on the ScanNetV2 dataset. Other details, such as the architecture of MLPs and runtime analysis, are included in the supplementary material." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 284, + 390, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 284, + 390, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 284, + 390, + 295 + ], + "type": "text", + "content": "4.4. Main Results" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": "ScanNetV2 Table 1 and Table 2 show the quantitative result of instance segmentation on the test and validation sets. Our proposed method achieves the highest AP and " + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": " surpassing the previous strongest method by the margin of " + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "inline_equation", + "content": "4.1\\%" + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "inline_equation", + "content": "2.4\\%" + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": " for the test set, and " + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "inline_equation", + "content": "6.7\\%" + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": " for the validation set, respectively. Compared to the previous methods based on the coarse-to-fine approach, our method achieves " + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "inline_equation", + "content": "24.1\\%" + }, + { + "bbox": [ + 304, + 302, + 547, + 469 + ], + "type": "text", + "content": " of the improvement in AP on the test set. In particular, for the test set, our method outperforms existing methods on instances that are typically located close to each other, such as pictures, desks, and bookshelves. This suggests that explicitly penalizing misclassified points around the edges of instances is helpful in RPM. Please refer to the supplementary material for more results about this." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "content": "S3DIS Table 3 illustrates the quantitative result on Area 5. Our proposed method outperforms the second best performing method with margins of 3.3 and 2.9 in mAP, " + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "content": ", and mRec" + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "inline_equation", + "content": "_{50}" + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "content": ", improving the performance of SOTA " + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "inline_equation", + "content": "5.7\\%" + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "inline_equation", + "content": "5.6\\%" + }, + { + "bbox": [ + 304, + 470, + 547, + 530 + ], + "type": "text", + "content": " respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "text", + "content": "STPLS3D Table 4 shows the quantitative comparison on the validation set of STPLS3D dataset. Our method outperforms all of the existing methods, improving SOTA performance in mAP and " + }, + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 304, + 530, + 545, + 578 + ], + "type": "text", + "content": " for 3.0 and 4.3, respectively." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 586, + 417, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 417, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 417, + 598 + ], + "type": "text", + "content": "4.5. Qualitative Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 605, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 677 + ], + "type": "text", + "content": "Fig.5 shows visual comparisons of ISBNet[29], MAFT[15], and our proposed Spherical Mask for challenging instances on ScanNetV2 validation set. Spherical Mask accurately segments large instances such as wall and book shelves(row 1), curtains and a window between them(row 2), a large sofa(row 3) and a circular shape sofa(row 4)." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "ISBNet[29] struggles to segment large instances(wall and bookshelves in row 1) and a disconnected instance(curtains and a window between them in row 2). On the other hand," + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4065" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 541, + 166 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 541, + 166 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 541, + 166 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 541, + 166 + ], + "type": "table", + "html": "
MethodmAP\\( \\mathrm{mAP}_{50} \\)\\( bath \\)bedbk.shfcabinetchaircountercurtaindeskdoorotherpicturefridges. cur.sinksofatabletoiletwind.
3D-BoNet(C)[33]25.348.851.932.425.113.734.53.141.96.916.213.15.220.233.814.730.130.365.117.8
TD3D(C)[14]48.975.185.251.143.432.273.510.151.235.534.946.828.351.467.626.867.151.090.832.9
SoftGroup(G)[30]50.476.166.757.937.238.169.47.267.730.338.753.131.958.275.431.864.349.290.738.8
PBNet(G)[36]57.374.792.657.561.947.273.623.948.738.345.950.653.358.576.740.471.755.996.938.1
DKNet(K)[31]53.271.881.562.451.737.774.910.750.930.443.747.558.153.977.533.964.050.690.138.5
ISBNet(K)[29]55.975.793.965.538.342.676.318.053.438.649.950.962.142.770.446.764.957.194.840.1
MAFT(T)[15]57.878.688.972.144.846.076.825.155.840.850.453.961.661.885.848.268.455.193.145.0
QueryFormer(T)[21]58.378.792.670.239.350.473.327.652.737.347.953.453.369.772.043.674.559.295.836.3
Ours(C)61.681.294.665.455.543.476.927.160.444.750.554.969.871.677.548.074.757.592.543.6
", + "image_path": "329d742765c56b42be294d943ef2939194bdce883450a9e0acf8b42d88b815d0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 167, + 547, + 201 + ], + "lines": [ + { + "bbox": [ + 47, + 167, + 547, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 167, + 547, + 201 + ], + "type": "text", + "content": "Table 1. Quantitative comparison of top-performing methods for each approach on ScanNetV2 hidden test set. (C),(G),(K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. All the methods take the same input, such as point cloud and corresponding color information. The best results are in bold, and the second best ones are in underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 50, + 211, + 541, + 396 + ], + "blocks": [ + { + "bbox": [ + 50, + 211, + 541, + 396 + ], + "lines": [ + { + "bbox": [ + 50, + 211, + 541, + 396 + ], + "spans": [ + { + "bbox": [ + 50, + 211, + 541, + 396 + ], + "type": "image", + "image_path": "dfc9f12415c5c46f29cba97167fe29ac1629a56022017d487d1b7e8f8e25c693.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 115, + 397, + 477, + 408 + ], + "lines": [ + { + "bbox": [ + 115, + 397, + 477, + 408 + ], + "spans": [ + { + "bbox": [ + 115, + 397, + 477, + 408 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison of ISBNet[29], MAFT[15], and ours on ScanNetV2 validation set." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 418, + 539, + 529 + ], + "blocks": [ + { + "bbox": [ + 50, + 418, + 539, + 529 + ], + "lines": [ + { + "bbox": [ + 50, + 418, + 539, + 529 + ], + "spans": [ + { + "bbox": [ + 50, + 418, + 539, + 529 + ], + "type": "image", + "image_path": "edb7417f3ed78979d7b5bb836cde0907bcbab6ae87ad77c058ec3ec944148714.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "lines": [ + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "spans": [ + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "type": "text", + "content": "Figure 6. Visually comparing impacts of RID, " + }, + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "type": "inline_equation", + "content": "L_{sh}" + }, + { + "bbox": [ + 184, + 535, + 409, + 546 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 559, + 290, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 559, + 290, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 559, + 290, + 654 + ], + "type": "text", + "content": "MAFT[15] shows better generalization capability for learning semantics(curtains and a window between them(row 2)). However, it struggles to segment some parts of an instance that look different, as shown in sofas(row 2,3) and oversegments the instance by considering physically further away points as the same instance(wall in row 2 and sofa in row 4), probably due to the local queries that overfit to certain semantics." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 669, + 141, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 141, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 141, + 681 + ], + "type": "text", + "content": "4.6. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "In this section, we investigate Spherical Mask with ablation studies designed for its core components." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": "Impact of " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "\\varphi" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " is shown at Table 6. For this experiment, we fixed the backbone and the RPM with " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": ", and change " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": ". In theory, increasing " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " should always produce better results. However, in practice, increasing them faces an issue of high complexity, as can be seen. Using 4/4 and 5/5 of " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " improves the mAP for " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "0.9\\%" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "1.7\\%" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": ", respectively. However, increasing them from 5/5 to 6/6 results in " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "2.8\\%" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " of the performance drop, suggesting that too large " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " make a negative impact on the performance due to increased complexity. For example, too large " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 304, + 559, + 548, + 704 + ], + "type": "text", + "content": " would result in many sectors without any foreground points, leading to biased target values for learn-" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4066" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 282, + 270 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 282, + 270 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 282, + 270 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 282, + 270 + ], + "type": "table", + "html": "
MethodVenuemAPAP50AP25
3D-SIS(C)[12]CVPR19-18.735.7
GSPN(C)[34]CVPR19-37.853.4
TD3D(C)[14]WACV2347.371.281.9
PointGroup(G)[13]CVPR2034.851.771.3
SSTNet(G)[19]ICCV2149.464.374.0
MaskGroup(G)[37]ICME2227.442.063.3
SoftGroup(G)[30]CVPR2246.067.678.9
RPGN(G)[8]ECCV22-64.2-
PBNet(G)[36]ICCV2354.370.578.9
PointInst3D(K)[11]EECV2245.663.7
DKNet(K)[31]ECCV2250.866.976.9
ISBNet(K)[29]CVPR2354.573.182.5
Mask3D(T)[27]ICRA2355.273.782.9
3IS-ESSS(T)[1]ICCV2356.175.083.7
QueryFormer(T)[21]ICCV2356.574.283.3
MAFT(T)[15]ICCV2358.475.684.5
Ours(C)-62.379.988.2
", + "image_path": "a99c1db7f983dc087e0861d519b3e3fda9e1b5ee4042bf227fa8e2f35430e938.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 54, + 332, + 279, + 500 + ], + "blocks": [ + { + "bbox": [ + 47, + 272, + 288, + 327 + ], + "lines": [ + { + "bbox": [ + 47, + 272, + 288, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 272, + 288, + 327 + ], + "type": "text", + "content": "Table 2. Quantitative 3D instance segmentation results on ScanNetV2 validation set. (C), (G), (K), and (T) next to the names of the methods refer to coarse-to-fine, grouping, kernel, and Transformer based methods, respectively. The best results are in bold, and the second best ones are in underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 54, + 332, + 279, + 500 + ], + "lines": [ + { + "bbox": [ + 54, + 332, + 279, + 500 + ], + "spans": [ + { + "bbox": [ + 54, + 332, + 279, + 500 + ], + "type": "table", + "html": "
MethodmAPAP50mPrec50mRec50
GSPN [34]--36.028.7
PointGroup [13]-5.7861.962.1
HAIS [4]--71.165.0
SSTNet [19]42.759.365.664.2
SoftGroup [30]51.666.173.666.6
Mask3D [27]56.569.368.770.7
RPGN [8]--64.063.0
PointInst3D [11]--73.165.2
DKNet [31]--70.865.3
ISBNet [29]56.367.570.572.0
PBNet [36]53.566.474.965.4
QueryFormer [21]57.769.970.572.2
MAFT [15]-69.1--
Ours60.572.371.376.3
", + "image_path": "1b3702d0c4d046c0210c089e725eb450afe74efaad27c60f9d94431623293331.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 48, + 540, + 282, + 597 + ], + "blocks": [ + { + "bbox": [ + 47, + 501, + 287, + 535 + ], + "lines": [ + { + "bbox": [ + 47, + 501, + 287, + 535 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 287, + 535 + ], + "type": "text", + "content": "Table 3. Quantitative 3D instance segmentation results on S3DIS Area 5. The best results are in bold, and the second best ones are in underlined." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 540, + 282, + 597 + ], + "lines": [ + { + "bbox": [ + 48, + 540, + 282, + 597 + ], + "spans": [ + { + "bbox": [ + 48, + 540, + 282, + 597 + ], + "type": "table", + "html": "
MethodmAP AP50RID Lmc LscmAP AP50AP25
HAIS [4]35.046.7✓51.669.486.8
PointGroup [13]23.338.5✓✓58.577.687.5
ISBNet [29]49.264.0✓56.577.187.1
Ours52.268.3✓✓62.379.988.2
", + "image_path": "9ab767900776a380d993d7899fa0f79fb2e258732133158a9ab72e0e291b0a5b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": "ing. Despite the variation, all configurations of " + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 46, + 641, + 287, + 677 + ], + "type": "text", + "content": " still outperform existing methods in Table 2, implying that RID with RPM always improves the performance." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 713 + ], + "type": "text", + "content": "Impact of Radial Point Migration is illustrated in Table 5. Here, we investigate the impact of the RPM and each loss for it. The baseline is the model trained with only RID, exclud" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 306, + 69, + 421, + 149 + ], + "blocks": [ + { + "bbox": [ + 47, + 599, + 149, + 632 + ], + "lines": [ + { + "bbox": [ + 47, + 599, + 149, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 149, + 632 + ], + "type": "text", + "content": "Table 4. Quantitative instance segmentation results on STPLS3D" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 162, + 598, + 286, + 620 + ], + "lines": [ + { + "bbox": [ + 162, + 598, + 286, + 620 + ], + "spans": [ + { + "bbox": [ + 162, + 598, + 286, + 620 + ], + "type": "text", + "content": "Table 5. Impact of each component on ScanNetV2 validation set" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 69, + 421, + 149 + ], + "lines": [ + { + "bbox": [ + 306, + 69, + 421, + 149 + ], + "spans": [ + { + "bbox": [ + 306, + 69, + 421, + 149 + ], + "type": "table", + "html": "
Nθ/NφmAPAP50AP25
1/159.677.185.3
2/260.077.786.1
3/360.678.487.1
4/461.280.089.3
5/562.379.988.2
6/660.678.588.2
", + "image_path": "05bb5117bb962b8a4d4be209c5e5850585baa48fe8914255b94c1f5cb223fba2.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 426, + 70, + 541, + 149 + ], + "blocks": [ + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "lines": [ + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "spans": [ + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "type": "text", + "content": "Table 6. Impact of " + }, + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "type": "inline_equation", + "content": "N_{\\theta}" + }, + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "type": "inline_equation", + "content": "N_{\\varphi}" + }, + { + "bbox": [ + 306, + 151, + 410, + 183 + ], + "type": "text", + "content": " on ScanNetV2 validation set" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 426, + 70, + 541, + 149 + ], + "lines": [ + { + "bbox": [ + 426, + 70, + 541, + 149 + ], + "spans": [ + { + "bbox": [ + 426, + 70, + 541, + 149 + ], + "type": "table", + "html": "
Seed/VotemAP\\( AP_{50} \\)\\( AP_{25} \\)
1024/12862.379.287.8
1024/25662.379.988.2
1024/51262.379.487.6
2048/12862.079.788.0
2048/25661.879.687.9
2048/51261.779.187.5
", + "image_path": "66551ffabd6b9138f696a9d5079648b9f5408c8ab3d2963f613ccd6c71300bcb.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 426, + 150, + 544, + 182 + ], + "lines": [ + { + "bbox": [ + 426, + 150, + 544, + 182 + ], + "spans": [ + { + "bbox": [ + 426, + 150, + 544, + 182 + ], + "type": "text", + "content": "Table 7. Impact of seed and vote numbers on ScanNetV2 validation set" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": "ing RPM. As the baseline model cannot refine the false positive points inside radial predictions or false negative points outside, as shown in Figure 6 (parts of chairs included as tables), its performance with high iou thresholds(AP, " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": ") are " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "17.1\\%" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "13.1\\%" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " worse than the full model. Including RPM with " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " leads " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "13.3\\%" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " of improvement in AP, suggesting refinement to push and pull misclassified points is crucial for the performance. " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " shows " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "9.4\\%" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " improvement in AP from the baseline, suggesting that focusing on true positive samples also contributes significantly to learning fine granularity and common features shared within an instance. As shown in Figure 6(column 5,6), adding " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " improves the segmentation around the center of the objects, which was expected as the true positive samples near the instance centers could be neglected from " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " as they are usually inside rays. As " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " target different samples, the full model combining both " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{mc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "L_{sc}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " shows " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "20.7\\%" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "15.1\\%" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": " improvements for AP and " + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "inline_equation", + "content": "\\mathrm{AP}_{50}" + }, + { + "bbox": [ + 304, + 188, + 547, + 415 + ], + "type": "text", + "content": ", demonstrating the synergy of the two losses." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 415, + 547, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 547, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 547, + 511 + ], + "type": "text", + "content": "Impact of Voting Parameters is shown in Table 7. In this experiment, we change the seed and vote numbers inside the backbone while fixing RID and RPM. As can be seen, a seed number of 1024 produces more reliable results without variation than 2048, suggesting too many seed points negatively impact the system. Despite the slight difference, we observe that changing the seed and vote produces comparably small variations of " + }, + { + "bbox": [ + 304, + 415, + 547, + 511 + ], + "type": "inline_equation", + "content": "\\pm 0.6" + }, + { + "bbox": [ + 304, + 415, + 547, + 511 + ], + "type": "text", + "content": " in mAP for all settings." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 518, + 379, + 532 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 518, + 379, + 532 + ], + "spans": [ + { + "bbox": [ + 306, + 518, + 379, + 532 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 538, + 547, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 538, + 547, + 658 + ], + "spans": [ + { + "bbox": [ + 304, + 538, + 547, + 658 + ], + "type": "text", + "content": "We present Spherical Mask, a novel coarse-to-fine approach for 3D instance segmentation in point cloud. As a coarse detection, the RID module finds instances as 3D polygons defined with center and rays. In contrast to existing coarse-to-fine approaches, the RPM module uses the polygons as soft references and migrates points efficiently in spherical coordinates to acquire final masks. We demonstrate how each module contributes to the instance segmentation and achieves state-of-the-art performances on public benchmarks ScanNet-V2, S3DIS, and STPLS3D." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 663, + 404, + 676 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 663, + 404, + 676 + ], + "spans": [ + { + "bbox": [ + 306, + 663, + 404, + 676 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 679, + 508, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 679, + 508, + 703 + ], + "spans": [ + { + "bbox": [ + 306, + 679, + 508, + 703 + ], + "type": "text", + "content": "This research was supported by ACE-OPS project (EP/S030832/1)." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4067" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 145 + ], + "type": "text", + "content": "[1] Salwa Al Khatib, Mohamed El Amine Boudjoghra, Jean Lahoud, and Fahad Shahbaz Khan. 3d instance segmentation via enhanced spatial and semantic supervision. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 1839-1849, 2020. 1" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4069" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_content_list.json b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e616b59a60fdd73ae7b79de09bea4259016f87eb --- /dev/null +++ b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_content_list.json @@ -0,0 +1,1479 @@ +[ + { + "type": "text", + "text": "SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency", + "text_level": 1, + "bbox": [ + 250, + 130, + 718, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Paul Roetzer1 Florian Bernard1 \nUniversity of Bonn1", + "bbox": [ + 336, + 202, + 630, + 239 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bcb87a4e1a58ff91cab68dc8906372cf0e40b97283a541cb22b2225f303fa422.jpg", + "image_caption": [ + "Idea: Match Cyclic Path $\\mathcal{C}$ on $\\mathcal{X}$ to $\\mathcal{Y}$" + ], + "image_footnote": [], + "bbox": [ + 117, + 290, + 334, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/198351ef6c99d80f205e617d597ec1f9db10a03f2dd7ff8e95034c0682c6e183.jpg", + "image_caption": [ + "Dense Geometrically Consistent Shape Matching", + "Figure 1. (Left) Schematic illustration of our method: we extract a cyclic path $\\mathcal{C}$ on the surface of 3D shape $\\mathcal{X}$ , and match $\\mathcal{C}$ to the 3D target shape $\\mathcal{Y}$ . (Middle) If $\\mathcal{C}$ covers the whole source shape $\\mathcal{X}$ (not shown for clarity, see Sec. 4.1 for details), our method can be used to compute globally optimal results for dense non-rigid and geometrically consistent 3D shape matching. (Right) We show runtimes w.r.t. shape resolution and compare to Roetzer et al. [55] (which is the only existing method that achieves geometric consistency while having a global flavour and being initialization-free) and Cao et al. [14] (which does not provide any geometric consistency guarantees). Ours solves all instances to global optimality (with geometric consistency), while in addition being much faster than Roetzer et al." + ], + "image_footnote": [], + "bbox": [ + 370, + 290, + 635, + 436 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a7bbe0340e1e7d9281b218a4fa9d4b4f90f7807f59d36b977254ae3442653e0.jpg", + "image_caption": [ + "Scalability Analysis" + ], + "image_footnote": [], + "bbox": [ + 661, + 292, + 898, + 436 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 566, + 313, + 583 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Finding shortest paths on product spaces is a popular approach to tackle numerous variants of matching problems, including the dynamic time warping method for matching signals, the matching of curves, or the matching of a curve to a 3D shape. While these approaches admit the computation of globally optimal solutions in polynomial time, their natural generalisation to 3D shape matching is widely known to be intractable. In this work we address this issue by proposing a novel path-based formalism for 3D shape matching. More specifically, we consider an alternative shape discretisation in which one of the 3D shapes (the source shape) is represented as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. We then tackle the 3D shape matching problem as finding a shortest path in the product graph of the SpiderCurve and the target 3D shape. Our approach introduces a set of novel constraints that ensure a globally geometrically consistent matching. Overall, our formalism leads to an integer linear programming problem for which we experimentally show that it can efficiently be solved to global", + "bbox": [ + 73, + 599, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "optimality. We demonstrate that our approach is competitive with recent state-of-the-art shape matching methods, while in addition guaranteeing geometric consistency. $^{1}$", + "bbox": [ + 498, + 569, + 890, + 613 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 642, + 633, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The 3D shape matching problem refers to finding correspondences between given 3D shapes and has a high relevance across the broad field of visual computing. Examples of applications include texture transfer in graphics, statistical shape analysis in medical imaging, or 3D reconstruction or shape completion in computer vision. While the state of the art in 3D shape matching relies on data-driven deep learning methods [14], respective methods have the strong shortcoming that they lack guarantees about structural properties of obtained matchings. One crucial example, which is the main focus of our work, is geometric consistency: a matching between a given pair of 3D shapes is geometrically consistent if the neighbourhood between shape elements (e.g. triangles) is preserved under the matching.", + "bbox": [ + 496, + 667, + 890, + 878 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "1https://github.com/paul0noah/spider-match", + "bbox": [ + 517, + 888, + 849, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14543", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Loosely, geometric consistency (in the discrete domain) can be seen analogously to diffeomorphisms in the continuous domain [77].", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Achieving geometric consistency in learning-based shape matching solutions is extremely challenging, since it requires to impose complex structural constraints on the prediction. While there are some optimisation-based works that explicitly aim for geometric consistency, they require initial pre-matchings to handle the severe non-convexity of respective optimisation problems [23, 24, 43, 61, 62, 64, 66, 69, 75], or they employ heuristics and only find approximate solutions [55, 78]. To date, there do not exist any 3D shape matching methods that are able to find globally optimal solutions while guaranteeing geometric consistency.", + "bbox": [ + 75, + 136, + 468, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work we make a first step towards filling this gap. More specifically, motivated by recent advances in (polynomial-time solvable) matching problems between a curve and a 3D shape [37, 56], we propose to represent the source 3D shape as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D surface, loosely analogous to a spider web covering the shape surface. We then find a shortest path in the product graph of the SpiderCurve and the target 3D shape, while respecting geometric consistency constraints. We cast this as an integer linear program, for which we experimentally demonstrate that it can efficiently be solved to global optimality in all considered problem settings. Overall, we summarise our main contributions as follows (also cf. Tab. 1):", + "bbox": [ + 75, + 301, + 468, + 513 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- For the first time we enable to find globally optimal solutions for geometrically consistent 3D shape matching.", + "- To achieve this, we introduce a novel integer linear programme (ILP) that consistently matches our SpiderCurve 3D shape representation to the target 3D shape.", + "- Although ILP solvers employ branch and bound procedures that have exponential worst-case runtime in general, we experimentally demonstrate that our formalism allows to efficiently find solutions for problems with practically relevant sizes (e.g. we use the off-the-shelf ILP solver Gurobi to match shapes with 1000 triangles in $\\approx$ 100s.)." + ], + "bbox": [ + 76, + 513, + 467, + 679 + ], + "page_idx": 1 + }, + { + "type": "table", + "img_path": "images/fad2c6c2bc22359229cfb14930f88e29921005a982d4201898adb0045cd16e24.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodGeometrically ConsistentGlobally OptimalKeypoint FreePruning Free
SIGMA [26]X(✓)XX
MINA [10]X(✓)XX
PMSDP [47]XX✓X
Roetzer et al. [55](✓)X✓✓
Ours✓✓✓✓
", + "bbox": [ + 78, + 689, + 467, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Comparison of properties of shape matching methods. Ours is the only one that finds geometrically consistent and globally optimal solutions. Moreover, our method does not require the definition of keypoints, nor does it exploit any search space pruning scheme to solve the resulting integer linear program.", + "bbox": [ + 75, + 813, + 467, + 883 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 89, + 640, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the following we discuss works that are most relevant to our method. For a broad overview on 3D shape matching and registration we refer interested readers to the survey papers [17, 70, 73].", + "bbox": [ + 496, + 114, + 890, + 175 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep Shape Matching. Data-driven deep learning methods constitute the state of the art in 3D shape matching, as they can predict high-quality correspondences in short time. Most of these methods are based on the popular functional map framework [49], as it offers a convenient way to regularise the high-dimensional shape matching problem via a low-dimensional representation. Respective methods were trained both in a supervised manner [28, 40, 42, 72, 76], and in an unsupervised manner [5, 6, 12-14, 18, 19, 30, 33, 39, 46, 51, 57, 65, 68, 71]. A major leap forward was achieved with the introduction of DiffusionNet [68], which builds upon a simple diffusion process to perform learning on 3D surfaces. The method [14] builds on top of DiffusionNet while coupling functional maps with point maps, and thereby achieves state-of-the-art shape matching performance in very challenging scenarios (e.g. partial shapes and topological noisy shapes). Despite the astonishing performance of recent learning-based shape matching methods, they have the major shortcoming that the produced matchings are not geometrically consistent, see e.g. [21] for a recent demonstration.", + "bbox": [ + 496, + 176, + 890, + 492 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Geometrically Consistent Shape Matching. We argue that geometric consistency is an essential property of 3D shape matching. Geometric consistency is generally hard to achieve since it leads to challenging non-convex optimisation problems, see e.g. [77]. Thus, there exists many local methods that require given correspondences between a sparse set of points [64] (e.g. often user-defined). Among them is the work [66] based on heat diffusion, and the work [75] in which given matchings are smoothed with the so-called product manifold filter. Furthermore, the works [23, 24] also consider the refinement of an initial set of matchings. The works [61, 62, 69] solve for geometrically consistent intrinsic triangulations [67] via local optimisation. Many of these methods are parameterisation-based, i.e. they rely on mappings of given 3D shapes to simple parametric surfaces, such as planes [1, 2, 34, 43, 44, 48, 79] or spheres [1, 3, 4, 50, 61]. One shortcoming of parameterisation-based methods is that they are only applicable for matching shapes with a fixed genus. Furthermore, respective methods involve highly non-convex optimisation problems that depend on good initialisations (e.g. user-provided sparse matchings).", + "bbox": [ + 496, + 492, + 890, + 824 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Globally Optimal Shape Matching. While the polynomial-time solvable linear assignment problem (LAP) could in principle be used for 3D shape matching, it completely disregards geometric relations, so that neighbouring points may be matched to arbitrarily far away points. While", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14544", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the LAP matches vertices, the quadratic assignment problem (QAP) matches pairs of vertices (edges), so that neighbourhood relations can be better preserved. Yet, the QAP is NP-hard [54] so that shape matching instances with practically relevant sizes cannot efficiently be solved. Several attempts to tackle the QAP have been presented, including convex relaxations [9, 20, 36, 59], and heuristics based on local optimisation [31, 38, 74].", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Other attempts towards global shape matching are often based on some low-dimensional (or low-rank) representation, e.g. functional maps in the continuous domain [22, 27, 47, 49], functional maps coupled to point maps [53], or sparse matching representations in the discrete domain [10, 26]. Yet, functional map-based methods do not take geometric consistency into account, and sparse discrete models are typically slow and heavily rely on an aggressive pruning of the search space [10, 26, 47].", + "bbox": [ + 75, + 218, + 472, + 354 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A different class of global shape matching approaches is based on finding shortest paths in product graphs. These include the matching of signals in the popular dynamic time warping algorithm [58], the matching of 2D shapes to images to address shape-based image segmentation [16, 25, 63], or the matching of 2D shapes to each other [60]. Recently, a similar framework has been presented to match a 2D shape (a cyclic curve) to a 3D shape [37, 56]. All of these approaches have in common that solutions can efficiently be computed in polynomial time based on a shortest path algorithm (or some variant thereof). While product space formalisms have been generalised for the matching of 3D shapes [55, 77, 78], the respective problem is substantially harder and does not admit a solution via finding a shortest path - this is because in this case the matching cannot be represented as a one-dimensional path, but forms a two-dimensional surface in a four-dimensional product space. In this work we consider an alternative view that builds upon a different shape discretisation and thus allows to tackle 3D shape matching from a path-based perspective.", + "bbox": [ + 75, + 359, + 472, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Background on 2D-3D Shape Matching", + "text_level": 1, + "bbox": [ + 76, + 696, + 431, + 714 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following section, we summarise the important product graph formalism introduced in [37] for 2D-3D shape matching. It forms the foundation of our SpiderCurve-based 3D shape matching approach.", + "bbox": [ + 75, + 728, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Lähner et al. [37] aim to find correspondences between a 2D shape $\\mathcal{C} = (V^{\\mathcal{C}},E^{\\mathcal{C}})$ (a cyclic curve discretised as a cyclic chain graph, i.e. a graph with circular topology.) and a 3D shape $\\mathcal{Y} = (V^{\\mathcal{Y}},E^{\\mathcal{Y}})$ (interpreted as the undirected graph of a surface mesh). The matching between $\\mathcal{C}$ and $\\mathcal{Y}$ is found as a shortest path in the product graph", + "bbox": [ + 75, + 810, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/0d8c64e649a3561d68f69a690919a6bd07bd607a7ac58d995cbd075164527596.jpg", + "image_caption": [ + "Figure 2. The product graph $\\mathcal{P}$ is structured into layers (individual colours), where each layer corresponds to the product of a specific vertex $v^{\\mathcal{C}} \\in V^{\\mathcal{C}}$ of the 2D shape $\\mathcal{C}$ and the entire 3D shape $\\mathcal{Y}$ . $\\mathcal{P}$ contains intra-layer edges (edges within a layer) and inter-layer edges (edges connecting neighbouring layers). To avoid clutter, we only show the inter-layer connections for one vertex in the red and yellow layers. Like $\\mathcal{C}$ , the product graph $\\mathcal{P}$ is also cyclic." + ], + "image_footnote": [], + "bbox": [ + 550, + 87, + 851, + 362 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} = \\left(V ^ {\\mathcal {P}}, E ^ {\\mathcal {P}}\\right), \\text {w h e r e}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 492, + 656, + 508 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} V ^ {\\mathcal {P}} = V ^ {\\mathcal {C}} \\times V ^ {\\mathcal {Y}}, \\\\ E ^ {\\mathcal {P}} = \\left\\{\\left(e ^ {\\mathcal {C}}, e ^ {\\mathcal {Y}}\\right) \\in V ^ {\\mathcal {P}} \\times V ^ {\\mathcal {P}} \\mid e ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}} \\times V ^ {\\mathcal {C}}, \\right. \\tag {1} \\\\ e ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}} \\times V ^ {\\mathcal {Y}}, e ^ {\\mathcal {C}} \\text {o r} e ^ {\\mathcal {Y}} \\text {n o n - d e g .} \\}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 516, + 890, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Eq. (1), degenerate edges mean that they consist of the same vertex twice. This is necessary to handle different discretisations of the shapes. In Fig. 2 we show the structure of the product graph: $\\mathcal{P}$ is oragnised into layers, where each layer corresponds to the product of a specific vertex of the 2D shape $\\mathcal{C}$ and the entire 3D shape $\\mathcal{V}$ . Thus, every vertex $v = (v^{\\mathcal{C}}, v^{\\mathcal{V}}) \\in V^{\\mathcal{P}}$ consists of a vertex $v^{\\mathcal{C}} \\in V^{\\mathcal{C}}$ from the 2D shape $\\mathcal{C}$ , and a vertex $v^{\\mathcal{V}} \\in V^{\\mathcal{V}}$ from the 3D shape $\\mathcal{V}$ . Any cyclic path in the product graph $\\mathcal{P}$ that goes through all layers represents a (geometrically consistent) matching between $\\mathcal{C}$ and $\\mathcal{P}$ . By defining appropriate edge costs (e.g. based on shape feature similarity, or by penalising deformations), one can find a globally optimal and geometrically consistent matching between the 2D shape $\\mathcal{C}$ and the 3D shape $\\mathcal{V}$ via a (cyclic) shortest paths algorithm. The works [37, 56] propose custom algorithms that exploit the special structure of the product graph in order to efficiently find such matchings. Overall, our main idea is to generalise such 2D-3D shape matching formalisms towards 3D-3D shape matching with the help of a SpiderCurve representation.", + "bbox": [ + 496, + 583, + 893, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14545", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/4200a97dd30fcd9a0178a73e5628ced81bf5ce95a876ffd81d63c64ec9e9e382.jpg", + "image_caption": [ + "Figure 3. Overview of the pipeline of our method. We consider two 3D surface meshes $\\mathcal{X}$ and $\\mathcal{Y}$ for which we compute vertex-wise features with a pretrained feature extractor. After discretising $\\mathcal{X}$ into a SpiderCurve representation $\\mathcal{C}$ , we construct our cyclic shortest path ILP using constraints that ensure geometric and global 3D consistency of the matching. Solving the ILP (e.g. using Gurobi [29]) results in a globally optimal 3D shape matching represent as a shortest cyclic path in the product graph." + ], + "image_footnote": [], + "bbox": [ + 98, + 84, + 851, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. SpiderCurve-based 3D Shape Matching", + "text_level": 1, + "bbox": [ + 76, + 345, + 433, + 364 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We aim to find geometrically consistent correspondences between two non-rigidly deformed 3D shapes $\\mathcal{X}$ and $\\mathcal{Y}$ (with same genus and potentially having boundaries) represented as tuples of vertices and edges $\\mathcal{X} = (V^{\\mathcal{X}}, E^{\\mathcal{X}})$ and $\\mathcal{Y} = (V^{\\mathcal{Y}}, E^{\\mathcal{Y}})$ , respectively. Our notation is summarised in Tab. 2. Our main idea is to discretise the 3D shape $\\mathcal{X}$ using a long self-intersecting curve $\\mathcal{C}$ that traces the 3D surface $\\mathcal{X}$ - due to the resemblance to a spider web we call this representation SpiderCurve, cf. Fig. 4. With that, we match $\\mathcal{C}$ to the 3D shape $\\mathcal{Y}$ while ensuring that (i) existing self-intersections of $\\mathcal{C}$ are maintained, and that (ii) no additional self-intersections are introduces by the matching. We visualise our overall pipeline in Fig. 3.", + "bbox": [ + 75, + 376, + 470, + 571 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the following subsections we first discuss how to extract our SpiderCurve on $\\mathcal{X}$ , followed by the presentation of our integer linear programming (ILP) formulation.", + "bbox": [ + 75, + 577, + 470, + 622 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. SpiderCurve Extraction", + "text_level": 1, + "bbox": [ + 76, + 646, + 299, + 662 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To ensure that our SpiderCurve $\\mathcal{C} = (V^{\\mathcal{C}},E^{\\mathcal{C}})$ is a faithful discretisation of the 3D shape $V^{\\mathcal{X}}$ , we impose that $\\mathcal{C}$ covers all vertices of $V^{\\mathcal{X}}$ . Moreover, the start and end points of $\\mathcal{C}$ are equal, so that it forms a cycle. We explicitly strive for self-intersections in $\\mathcal{C}$ in order to consider geometric consistency in multiple directions along the shape surface (this is achieved by imposing that intersections are maintained by the matching, see Sec. 4.2). We have found that using an approximation algorithm for the (metric) travelling salesperson problem (TSP), i.e. the Christofides algorithm [15], leads to reasonable SpiderCurves for our purposes. We note that for technical reasons it is convenient to duplicate vertices in the SpiderCurve $\\mathcal{C}$ at the intersection points (so that $|V^{\\mathcal{C}}|\\geq |V^{\\mathcal{X}}|$ ). In Fig. 4, we visualise extracted SpiderCurves on different shapes.", + "bbox": [ + 75, + 672, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/2321a4a2b322c8209ae2c57eebf372694640a8c081af65a2ecec33f0945aa906.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
SymbolDescription
X=(Vx,Ex)3D surface shape X
|Vx|, |Ex|Number of vertices and edges
Vx∈R|Vx|×3Vertices of shape X
Ex∈N|Ex|×2Edges of shape X
Fx∈R|Vx|×128Features of shape X
Y=(Vy,Ey)3D surface shape Y
...(analogous to X)
C=(VC,Ec)Cyclic path on X (Spider Curve)
P=(VP,Ep)Product graph
x∈{0,1}|EP|Indicator representation of EP
c∈R|EP|Cost vector
x*Cyclic shortest path in P
(CYC)Cyclic path constraints
(CON)Path continuity constraints
(PES)Preservation of exist. self-inters. constraints
(ANS)Avoidance of new intersections constraints
", + "bbox": [ + 501, + 344, + 901, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 2. Summary of the notation used in this paper.", + "bbox": [ + 535, + 619, + 854, + 635 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/50e99f13283a84821c0de09e45d8297820a069e408d2114077c18a717e93159f.jpg", + "image_caption": [ + "Figure 4. Visualisation of SpiderCurves on various types of 3D shapes including humanoid shapes and animals. We can see that our SpiderCurves cover the whole surface and thus pose a faithful discretisation of the respective 3D shape." + ], + "image_footnote": [], + "bbox": [ + 516, + 657, + 879, + 787 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14546", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/abb3e88249b6a4c17a985fb46c4f3c9fd7dbf62dbb4766676d4db3f154e8230e.jpg", + "image_caption": [ + "Figure 5. Illustration of our four constraints. (Left) The sum of all $x_{i}$ that involve edges connecting two layers (e.g. the set of red or blue edges) should be equal to one, so that the cyclic path $x^{\\star}$ goes through all layers. (Middle-Left) The sum of all incoming edges (blue) of a product vertex (yellow) must be equal to the sum of all outgoing edges (red). This ensures that the path is continuous. (Middle-Right) Coupling of layers ensures that self-intersections of $\\mathcal{C}$ are preserved on $\\mathcal{V}$ under the matching. Coupling can be implemented by ensuring that the sum of outgoing edges (blue) of a product vertex on the bottom layer is equal to the sum of outgoing edges for a product vertex on the top layer (for corresponding vertices across layers, see yellow line). (Right) Self-intersections (other than the ones present in $\\mathcal{C}$ , see Middle-Right) can be avoided by allowing the cyclic path to only visit each vertex on $\\mathcal{V}$ once, i.e. the sum of outgoing product edges (red) must be less than or equal 1 (this does not include vertical inter-layer product edges, i.e. product edges that do not leave the vertex on $\\mathcal{V}$ )." + ], + "image_footnote": [], + "bbox": [ + 76, + 85, + 261, + 305 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/169996bf22bd3398b38e366ee4a42a1d155455116ff0e1ed620413c8c086abb7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 276, + 85, + 460, + 305 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a564660ee0ca7373817dbe0d22bd29d1aa145315fa2a95f672ee30eed94b447d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 85, + 681, + 305 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/b45754f3c9d4b34f19210536d7922509c024f7ebf81eb01340f9812416ea6107.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 85, + 880, + 305 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Our SpiderMatch Integer Linear Program", + "text_level": 1, + "bbox": [ + 75, + 457, + 439, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For finding a globally optimal matching, we construct the product graph $\\mathcal{P}$ of the SpiderCurve $\\mathcal{C}$ (a cyclic chain graph) and the 3D target shape $\\mathcal{V}$ . Then, we find a cyclic shortest path in $\\mathcal{P}$ in such way that the path goes through each layer of $\\mathcal{P}$ (cf. Fig. 2). In addition, we impose additional constraints that ensure geometric consistency in multiple directions along the shape surface.", + "bbox": [ + 75, + 484, + 468, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Contrary to [37, 56] that find shortest paths based on (a variant of) Dijkstra's algorithm, we formulate our optimisation problem as an ILP, so that we can directly integrate additional constraints. Most importantly, we impose that (i) self-intersections in $\\mathcal{C}$ are preserved under the matching, and that (ii) additional self-intersections are avoided. To formulate our optimisation problem, we introduce for each edge $e_i \\in E^{\\mathcal{P}}$ in the product graph $\\mathcal{P}$ a binary indicator variable $x_i \\in \\{0,1\\}$ . The value $x_i = 1$ means that product edge $e_i$ is part of our matching path, and $x_i = 0$ means that $e_i$ is not contained in the matching. Our overall objective is to find the optimal matching $x^\\star$ in the space of geometrically consistent matchings (to be defined in the following paragraphs) that minimises matching costs. We note that a product edge $e_i = (v_k, v_l) \\in E^{\\mathcal{P}}$ consists of two product vertices $v_k, v_l \\in V^{\\mathcal{P}}$ , where each product vertex consists of a vertex $v^{\\mathcal{C}} \\in V^{\\mathcal{C}}$ of the cyclic path $\\mathcal{C}$ and a vertex $v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}$ of 3D surface shape $\\mathcal{Y}$ .", + "bbox": [ + 75, + 594, + 470, + 867 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the following we introduce the constraints of our ILP that define the space of geometrically consistent matchings.", + "bbox": [ + 76, + 869, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We visualise all types of constraints in Fig. 5.", + "bbox": [ + 500, + 458, + 802, + 472 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cyclic Path. We want to ensure that every vertex of $\\mathcal{C}$ is matched at least once, i.e. the optimal cyclic path $x^{\\star}$ goes through all layers. This can be achieved by ensuring that the sum over all $x_{i}$ between any pair of adjacent layers (cf. Fig. 5 left) is equal to one. Formally, this is expressed as", + "bbox": [ + 496, + 473, + 890, + 549 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\forall \\left(v _ {1} ^ {\\mathcal {C}}, v _ {2} ^ {\\mathcal {C}}\\right) \\in E ^ {\\mathcal {C}}: \\sum_ {i: e _ {i} = \\left(\\left(v _ {1} ^ {\\mathcal {C}}, \\bullet\\right), \\left(v _ {2} ^ {\\mathcal {C}}, \\bullet\\right)\\right) \\in E ^ {\\mathcal {P}}} x _ {i} = 1.\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 559, + 890, + 611 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Path Continuity. Furthermore, we have to ensure that every product vertex $v_{l} \\in V^{\\mathcal{P}}$ with an active $(x_{i} = 1)$ incoming product edge $e_{i} = (v_{k}, v_{l})$ also has an active $(x_{j} = 1)$ outgoing product edge $e_{j} = (v_{l}, v_{m})$ , i.e. the path must be continuous (cf. Fig. 5 middle-left). This property can be formalised as", + "bbox": [ + 496, + 611, + 890, + 700 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\forall v _ {l} \\in V ^ {\\mathcal {P}}: \\sum_ {i: e _ {i} = (\\bullet , v _ {l}) \\in E ^ {\\mathcal {P}}} x _ {i} = \\sum_ {j: e _ {j} = (v _ {l}, \\bullet) \\in E ^ {\\mathcal {P}}} x _ {j}. \\tag {CON}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 710, + 890, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Preservation of Existing Self-Intersections. To ensure geometric consistency, i.e. neighbourhoods between shape elements $^2$ are preserved by the matching, every self-intersection of the SpiderCurve $\\mathcal{C}$ must result in a self-intersection that involves the same vertices when $\\mathcal{C}$ is matched to $\\mathcal{V}$ . We can ensure this by incorporating coupling constraints between product vertices that involve self", + "bbox": [ + 496, + 758, + 890, + 866 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "2In our formalism we can interpret polygons that are formed by our SpiderCurve as shape elements.", + "bbox": [ + 500, + 875, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14547", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "intersections. To be precise, we couple those product vertices $v_{p}^{\\mathcal{C}}$ and $v_{q}^{\\mathcal{C}}$ on (different) layers $p$ and $q$ that belong to the same vertex $v^{\\mathcal{V}}$ on $\\mathcal{V}$ (cf. Fig. 5 middle-right). Formally, this can be written as", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\forall v _ {p} ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}}, v _ {q} ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}}, p \\neq q, v _ {p} ^ {\\mathcal {C}} = v _ {q} ^ {\\mathcal {C}}: \\\\ \\sum_ {i: e _ {i} = \\left(\\left(v _ {p} ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}}\\right), \\bullet\\right) \\in E ^ {\\mathcal {P}}} x _ {i} = \\sum_ {j: e _ {j} = \\left(\\left(v _ {q} ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}}\\right), \\bullet\\right) \\in E ^ {\\mathcal {P}}} x _ {j}. \\tag {PES} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 101, + 162, + 468, + 233 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Avoidance of New Self-Intersections. Lastly, we forbid that new self-intersections are introduced by the matching. This can be ensured by constraining the matching path in such a way that every vertex $v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}$ can only be visited at most once. In other words, the sum (across all layers) over all outgoing edges of product vertices that contain a given $v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}$ must be smaller than or equal to one. In this constraint, we do not sum over inter-layer edges whose source and target product vertex contain the same vertex $v^{\\mathcal{Y}}$ on $\\mathcal{V}$ (since these edges can be interpreted as 'staying' in the same vertex $v^{\\mathcal{Y}}$ on $\\mathcal{V}$ ). The respective constraints are explained in Fig. 5 right. Mathematically, they read", + "bbox": [ + 75, + 234, + 468, + 416 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\forall v _ {k} ^ {\\mathcal {Y}}, v _ {l} ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}}, v _ {k} ^ {\\mathcal {Y}} \\neq v _ {l} ^ {\\mathcal {Y}}: \\sum_ {i: e _ {i} = \\left(\\left(v _ {k} ^ {\\mathcal {C}}, v _ {k} ^ {\\mathcal {Y}}\\right), \\left(v _ {l} ^ {\\mathcal {C}}, v _ {l} ^ {\\mathcal {Y}}\\right)\\right) \\in E ^ {\\mathcal {P}}} x _ {i} \\leq 1 \\tag {ANS}\n$$\n", + "text_format": "latex", + "bbox": [ + 81, + 429, + 467, + 478 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "with $v_{k}^{\\mathcal{C}}, v_{l}^{\\mathcal{C}} \\in V^{\\mathcal{C}}$ . Note that the sum will not include product vertices on layers which belong to coupling constraints, i.e. whenever $v_{k}^{\\mathcal{C}}$ or $v_{l}^{\\mathcal{C}}$ belong to a self-intersection of $\\mathcal{C}$ we do not include respective product edge $e_{i}$ in the sum.", + "bbox": [ + 76, + 479, + 468, + 539 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Matching Costs. We consider a cost vector $c \\in \\mathbb{R}^{|E^{\\mathcal{P}}|}$ based on vertex-wise 3D shape features $F^{\\mathcal{X}}$ and $F^{\\mathcal{Y}}$ . The entry at the $i$ -th position is given by", + "bbox": [ + 75, + 541, + 468, + 588 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nc _ {i} = c \\left(e _ {i}\\right) = \\Psi \\left(F _ {p} ^ {\\mathcal {X}} - F _ {r} ^ {\\mathcal {Y}}\\right) + \\Psi \\left(F _ {q} ^ {\\mathcal {X}} - F _ {s} ^ {\\mathcal {Y}}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 599, + 468, + 619 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $e_i = ((v_p^{\\mathcal{X}}, v_r^{\\mathcal{Y}}), (v_q^{\\mathcal{X}}, v_s^{\\mathcal{Y}}))$ , $v_p^{\\mathcal{X}}, v_q^{\\mathcal{X}} \\in V^{\\mathcal{C}}$ and $v_r^{\\mathcal{Y}}, v_s^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}$ . Furthermore, $\\Psi(\\cdot)$ is the robust loss function presented in [8].", + "bbox": [ + 76, + 632, + 468, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our SpiderMatch ILP. Putting our cost function and constraints together yields our final 3D shape matching formalism:", + "bbox": [ + 75, + 681, + 468, + 726 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {x \\in \\{0, 1 \\} ^ {| E ^ {\\mathcal {P}} |}} c ^ {T} x \\text {s . t (C Y C), (C O N), (P E S), (A N S).} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 739, + 468, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Essentially, Problem (3) can be seen as a cyclic shortest path problem (over product edges encoded in $x$ , cf. Sec. 4.2) that involves the additional constraints (PES), (ANS).", + "bbox": [ + 75, + 781, + 468, + 825 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 844, + 207, + 859 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section we evaluate the performance of our method. First, we explain the considered evaluation metric and the", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "competing methods. Subsequently, we evaluate the non-rigid shape matching performance of our method and compare it to other approaches. We conclude this section with ablation studies.", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We solve Problem (3) with the off-the-shelf ILP solver Gurobi [29] (Version 10.0.3) on an Intel Core i9 12900K with 64 GB DDR5 RAM. We decimate all shapes to 1000 triangles using the mesh decimation algorithm provided in [32]. We also compute matchings for methods Cao et al. [14], Ren et al. [53], and Eisenberger et al. [22] on 1000 triangles. Only for Roetzer et al. [55] we decimate shapes to 450 triangles so that runtimes are acceptable (cf. Fig. 1 right). For our robust loss function $\\Psi(\\cdot)$ [8] we choose parameters $\\alpha = 2$ and $c = 0.3$ and instead of a quadratic bowl we use a cubic bowl so that small differences in features are less relevant. We empirically observe that our method can solve all instances to global optimality in less than 200s.", + "bbox": [ + 496, + 155, + 890, + 364 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Evaluation Metric", + "text_level": 1, + "bbox": [ + 500, + 387, + 676, + 402 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate all shape matching methods using geodesic errors. Geodesic errors allow us to measure the correctness of the resulting matching w.r.t. to a ground-truth matching, i.e. how far is the resulting matching from the ground-truth matching. We follow the Princeton protocol [35] to compute geodesic errors which are normalised by the square-root of the area of a shape (see [35, Sec. 8.2]).", + "bbox": [ + 496, + 414, + 890, + 521 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Methods", + "text_level": 1, + "bbox": [ + 500, + 541, + 602, + 555 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We compare our method to four other methods:", + "bbox": [ + 500, + 568, + 813, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Cao et al. [14] is a recent functional map-based deep learning method which achieves state of the art performance by coupling functional maps with point maps during learning. We use this method as our feature extractor and thus consider it as our baseline. Moreover, the extensive evaluation in [14] confirms that it is indeed the state-of-the-art learning-based approach, so that we consider it as a representative for the broad body of learning-based shape matching methods.", + "bbox": [ + 496, + 587, + 890, + 722 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ren et al. [53] is a functional map-based method which associates a functional map with a point wise map as a hard constraint.", + "bbox": [ + 496, + 726, + 890, + 771 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Eisenberger et al. [22] is a functional map-based iterative alignment scheme of shapes, which incrementally refines the geometrical information used to perform the matching.", + "bbox": [ + 496, + 775, + 890, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Roetzer et al. [55] implements a combinatorial solver to solve a triangle-matching based ILP presented in [77]. This is the only competing approach that guarantees geometric consistency.", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14548", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6771b8c6690b308ee8620ca0ccfa28e3ecd3033950d23c631d2478352927f346.jpg", + "image_caption": [ + "Figure 6. Qualitative Results on the datasets FAUST, SMAL, DT4D-H (intra class and inter class). The state-of-the-art learning based method by Cao et al. produces matches with local geometric inconsistencies (cf. columns $③$ , $⑨$ ). Ren et al. yields visually the worst results due to large mismatches (cf. columns $④$ , $⑩$ ). Obvious large mismatches are not produced by Eisenberger et al., which however produces left-right flips (cf. columns $②$ , $⑧$ ) as well as local mismatches (cf. column $⑩$ ). Due to the geometric consistency of our method we produce smooth matchings for all shapes. Note that we show the lower-resolution matchings of Roetzer et al. in the appendix." + ], + "image_footnote": [], + "bbox": [ + 84, + 85, + 885, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Non-Rigid Shape Matching", + "text_level": 1, + "bbox": [ + 76, + 585, + 323, + 603 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section we evaluate our method on three different datasets: FAUST [11, 18, 52], SMAL [80], DT4D-H [45] (in intraclass and interclass settings). We show qualitative results in Fig. 6. We can see that our geometrically consistent formalism yields better matchings than Cao et al., since our approach does not produce local mismatches. Furthermore, we observe severe mismatches and geometric inconsistencies in the matchings by Eisenberger et al. and Ren et al.", + "bbox": [ + 75, + 611, + 470, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "FAUST. We test on the (more challenging) remeshed version [18, 52] of the FAUST dataset [11]. The dataset consists of 100 near-isometric human shapes (we randomly sample 100 pairs from the test set). In Fig. 7 left, we show geodesic errors on FAUST. Our geometrically consistent approach helps to resolve local missmatches (cf. Fig. 6) which yields improved geodesic error scores compared to Cao et al. The method by Ren et al. results in left-right flips due to intrinsic symmetries of human shapes of FAUST, which increases geodesic errors drastically.", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e2f52475df6d846b3d11175b2686347abab68b9d9e81b102f23683f917458564.jpg", + "image_caption": [ + "Figure 7. Geodesic errors on FAUST and SMAL datasets. Numbers in the legends are mean geodesic errors $(\\downarrow)$ . Our method yields best results w.r.t. to mean geodesic errors on both datasets." + ], + "image_footnote": [], + "bbox": [ + 496, + 577, + 898, + 693 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "SMAL. Next, we evaluate on the remeshed version of the SMAL dataset [80]. This dataset consists of 49 nonisometric deformed animal shapes of eight species (we randomly sample 100 pairs from the test set). In Fig. 7 right, we show geodesic errors on SMAL. Again, ours is the best among all methods. For this dataset, shapes are unaligned, which harms the performance of Eisenberger et al. since it has to heuristically find a pre-alignment necessary for the method.", + "bbox": [ + 496, + 763, + 893, + 898 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14549", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9d3426b320645db08636a490833cbc2b8a02a758537d29c29779eaaf7d0fa467.jpg", + "image_caption": [ + "Figure 8. Geodesic errors on DT4D-H dataset in the intra-class and inter-class setting. Numbers in the legends are mean geodesic errors $(\\downarrow)$ . In the intra-class settings our method produces best results among all competitors. In the inter-class setting ours is on par with Cao et al." + ], + "image_footnote": [], + "bbox": [ + 73, + 88, + 477, + 204 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "DT4D-H. Finally, we test on DT4D-H [45], which consist of 9 different classes of humanoid/game character shapes in different poses. These shapes are taken from DeformingThings 4D [41]. We sample 100 random intra-class pairs, i.e. near-isometric deformed shape pairs. We also sample 100 random inter-class pairs, i.e. non-isometric deformed shape pairs. In Fig. 8, we show geodesic errors for both settings. In the intra-class setting our method outperforms all methods. For inter-class shapes our method is on par with Cao et al. The method by Eisenberger et al. suffers from the unaligned shapes in both settings, while Ren et al. produces a significant amount of left-right flips. In Sec. 8 in the supp. material we provide additional geometric consistency comparisons among the methods.", + "bbox": [ + 75, + 296, + 468, + 507 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablations", + "text_level": 1, + "bbox": [ + 76, + 516, + 187, + 530 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Tab. 3, we summarise results of our ablation study. For that, we sample 25 random pairs of the FAUST dataset, downsample them to 500 triangles and compute matchings in the different settings reported in Tab. 3. We can see that constraints (PES), (ANS), and the robust loss function $\\Psi(\\cdot)$ contribute to the performance of our method. We also replace $F^{\\mathcal{X}}$ and $F^{\\mathcal{Y}}$ with wave kernel signatures (WKS) features [7] and compare this setting to our method where we extract $F^{\\mathcal{X}}$ and $F^{\\mathcal{Y}}$ with [14]. In Sec. 11 in the supp. material we study our method under different resolutions.", + "bbox": [ + 75, + 539, + 468, + 690 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/7e0d09a4b166e2b067623e6ad6fa103e7b9500cffa321a01b04f532e8c8528e1.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMean Geo. Err.
Ours w/o (PES), (ANS)0.036
Ours w/o (ANS)0.035
Ours w/o (PES)0.035
Ours with Ψ = ||·||20.036
Ours with WKS features0.213
Ours0.034
", + "bbox": [ + 138, + 700, + 405, + 814 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation studies of our method.", + "bbox": [ + 148, + 821, + 395, + 834 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Discussion and Limitations", + "text_level": 1, + "bbox": [ + 76, + 845, + 328, + 859 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Time complexity. We have introduced the first geometrically consistent and globally optimal method for 3D shape", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "matching. Our problem instances involve up to $2 \\cdot 10^{6}$ binary variables. Nevertheless, we experimentally demonstrate that we can find globally optimal solutions in all considered matching instances within about 100s, which indicates that our search space has a benign structure (likely stemming from the underlying shortest path-based motivation) that can effectively be exploited by off-the-shelf ILP solvers. Still, our proposed formalism belongs to the (generally difficult) class of integer programming problems. We observe that our constraints do not lead to a totally unimodular matrix, so that in general we may have exponential worst-case runtime. We leave a theoretical analysis of the time complexity of our proposed approach, and the question whether there may exist polynomial time algorithms that solves our problem (or related variants) for future work.", + "bbox": [ + 496, + 90, + 890, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "SpiderCurve extraction. The focus of this work was on presenting a novel framework that generalises path-based shape matching formalisms for 3D shape matching. Although our TSP-based SpiderCurve extraction leads to promising matchings in all conducted experiments, we believe that there may be potential using alternative curve-based shape discretisations. An in-depth analysis and comparison of different approaches was not our main focus and is an interesting direction for follow-up works.", + "bbox": [ + 496, + 320, + 890, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Feasibility. In theory, our SpiderMatch ILP (3) might be infeasible, which may for example stem from discretisation artefacts in low-resolution settings. Yet, our method is able to operate on (relatively) high resolution shapes so that we expect these cases to be rare (we found all of the 400 instances considered in our experiments to be feasible).", + "bbox": [ + 496, + 458, + 890, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 570, + 617, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present a fresh view on geometrically consistent 3D shape matching. Our key insight is to discretise one of the shapes using a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. This allows us to utilise ideas and concepts from shortest path-based formalisms that have so far not been applicable to the matching of 3D shapes. More specifically, our work is motivated by the recent shortest path-based curve to 3D shape matching formalism by Lähner et al. [37], which we augment with additional self-intersection constraints that allows us to ensure geometric consistency in multiple directions along the shape surface. Experimentally we showcase the great potential of our novel approach, which on the one hand leads us to state-of-the-art shape matching performance. Furthermore, at the same time we achieve both geometric consistency and global optimality – the latter two properties are highly desirable but have so far not been reached by any previous 3D shape matching method. Overall, we believe that our approach may be insightful and may inspire follow-up works in geometrically consistent shape matching and beyond.", + "bbox": [ + 496, + 598, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "14550", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Noam Aigerman and Yaron Lipman. OrbifoldiTutede embeddings.ACM Trans.Graph.,34(6):190-1,2015.2", + "[2] Noam Aigerman, Roi Poranne, and Yaron Lipman. Lifted bijections for low distortion surface mappings. ACM Transactions on Graphics (TOG), 33(4):1-12, 2014. 2", + "[3] Marc Alexa. Merging polyhedral shapes with scattered features. In Proceedings Shape Modeling International'99. International Conference on Shape Modeling and Applications, pages 202-210. 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In CVPR, 2017. 7" + ], + "bbox": [ + 501, + 90, + 890, + 176 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "14553", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_model.json b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_model.json new file mode 100644 index 0000000000000000000000000000000000000000..d25da3394ea6576dc151a909c4382f6cc9cc7223 --- /dev/null +++ b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_model.json @@ -0,0 +1,2378 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.251, + 0.131, + 0.72, + 0.177 + ], + "angle": 0, + "content": "SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency" + }, + { + "type": "text", + "bbox": [ + 0.338, + 0.203, + 0.631, + 0.24 + ], + "angle": 0, + "content": "Paul Roetzer1 Florian Bernard1 \nUniversity of Bonn1" + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.291, + 0.335, + 0.432 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.123, + 0.439, + 0.323, + 0.452 + ], + "angle": 0, + "content": "Idea: Match Cyclic Path \\(\\mathcal{C}\\) on \\(\\mathcal{X}\\) to \\(\\mathcal{Y}\\)" + }, + { + "type": "image", + "bbox": [ + 0.372, + 0.291, + 0.637, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.372, + 0.439, + 0.634, + 0.453 + ], + "angle": 0, + "content": "Dense Geometrically Consistent Shape Matching" + }, + { + "type": "image", + "bbox": [ + 0.662, + 0.293, + 0.9, + 0.437 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.44, + 0.829, + 0.452 + ], + "angle": 0, + "content": "Scalability Analysis" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.464, + 0.892, + 0.548 + ], + "angle": 0, + "content": "Figure 1. (Left) Schematic illustration of our method: we extract a cyclic path \\(\\mathcal{C}\\) on the surface of 3D shape \\(\\mathcal{X}\\), and match \\(\\mathcal{C}\\) to the 3D target shape \\(\\mathcal{Y}\\). (Middle) If \\(\\mathcal{C}\\) covers the whole source shape \\(\\mathcal{X}\\) (not shown for clarity, see Sec. 4.1 for details), our method can be used to compute globally optimal results for dense non-rigid and geometrically consistent 3D shape matching. (Right) We show runtimes w.r.t. shape resolution and compare to Roetzer et al. [55] (which is the only existing method that achieves geometric consistency while having a global flavour and being initialization-free) and Cao et al. [14] (which does not provide any geometric consistency guarantees). Ours solves all instances to global optimality (with geometric consistency), while in addition being much faster than Roetzer et al." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.567, + 0.314, + 0.584 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.601, + 0.474, + 0.904 + ], + "angle": 0, + "content": "Finding shortest paths on product spaces is a popular approach to tackle numerous variants of matching problems, including the dynamic time warping method for matching signals, the matching of curves, or the matching of a curve to a 3D shape. While these approaches admit the computation of globally optimal solutions in polynomial time, their natural generalisation to 3D shape matching is widely known to be intractable. In this work we address this issue by proposing a novel path-based formalism for 3D shape matching. More specifically, we consider an alternative shape discretisation in which one of the 3D shapes (the source shape) is represented as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. We then tackle the 3D shape matching problem as finding a shortest path in the product graph of the SpiderCurve and the target 3D shape. Our approach introduces a set of novel constraints that ensure a globally geometrically consistent matching. Overall, our formalism leads to an integer linear programming problem for which we experimentally show that it can efficiently be solved to global" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.57, + 0.892, + 0.614 + ], + "angle": 0, + "content": "optimality. We demonstrate that our approach is competitive with recent state-of-the-art shape matching methods, while in addition guaranteeing geometric consistency.\\(^{1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.643, + 0.634, + 0.658 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.668, + 0.892, + 0.88 + ], + "angle": 0, + "content": "The 3D shape matching problem refers to finding correspondences between given 3D shapes and has a high relevance across the broad field of visual computing. Examples of applications include texture transfer in graphics, statistical shape analysis in medical imaging, or 3D reconstruction or shape completion in computer vision. While the state of the art in 3D shape matching relies on data-driven deep learning methods [14], respective methods have the strong shortcoming that they lack guarantees about structural properties of obtained matchings. One crucial example, which is the main focus of our work, is geometric consistency: a matching between a given pair of 3D shapes is geometrically consistent if the neighbourhood between shape elements (e.g. triangles) is preserved under the matching." + }, + { + "type": "page_footnote", + "bbox": [ + 0.518, + 0.889, + 0.851, + 0.902 + ], + "angle": 0, + "content": "1https://github.com/paul0noah/spider-match" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14543" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "Loosely, geometric consistency (in the discrete domain) can be seen analogously to diffeomorphisms in the continuous domain [77]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.47, + 0.302 + ], + "angle": 0, + "content": "Achieving geometric consistency in learning-based shape matching solutions is extremely challenging, since it requires to impose complex structural constraints on the prediction. While there are some optimisation-based works that explicitly aim for geometric consistency, they require initial pre-matchings to handle the severe non-convexity of respective optimisation problems [23, 24, 43, 61, 62, 64, 66, 69, 75], or they employ heuristics and only find approximate solutions [55, 78]. To date, there do not exist any 3D shape matching methods that are able to find globally optimal solutions while guaranteeing geometric consistency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.469, + 0.514 + ], + "angle": 0, + "content": "In this work we make a first step towards filling this gap. More specifically, motivated by recent advances in (polynomial-time solvable) matching problems between a curve and a 3D shape [37, 56], we propose to represent the source 3D shape as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D surface, loosely analogous to a spider web covering the shape surface. We then find a shortest path in the product graph of the SpiderCurve and the target 3D shape, while respecting geometric consistency constraints. We cast this as an integer linear program, for which we experimentally demonstrate that it can efficiently be solved to global optimality in all considered problem settings. Overall, we summarise our main contributions as follows (also cf. Tab. 1):" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.515, + 0.468, + 0.543 + ], + "angle": 0, + "content": "- For the first time we enable to find globally optimal solutions for geometrically consistent 3D shape matching." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.545, + 0.468, + 0.589 + ], + "angle": 0, + "content": "- To achieve this, we introduce a novel integer linear programme (ILP) that consistently matches our SpiderCurve 3D shape representation to the target 3D shape." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.59, + 0.468, + 0.68 + ], + "angle": 0, + "content": "- Although ILP solvers employ branch and bound procedures that have exponential worst-case runtime in general, we experimentally demonstrate that our formalism allows to efficiently find solutions for problems with practically relevant sizes (e.g. we use the off-the-shelf ILP solver Gurobi to match shapes with 1000 triangles in \\(\\approx\\)100s.)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.515, + 0.468, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.69, + 0.468, + 0.803 + ], + "angle": 0, + "content": "
MethodGeometrically ConsistentGlobally OptimalKeypoint FreePruning Free
SIGMA [26]X(✓)XX
MINA [10]X(✓)XX
PMSDP [47]XX✓X
Roetzer et al. [55](✓)X✓✓
Ours✓✓✓✓
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.814, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Table 1. Comparison of properties of shape matching methods. Ours is the only one that finds geometrically consistent and globally optimal solutions. Moreover, our method does not require the definition of keypoints, nor does it exploit any search space pruning scheme to solve the resulting integer linear program." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.642, + 0.105 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.116, + 0.892, + 0.176 + ], + "angle": 0, + "content": "In the following we discuss works that are most relevant to our method. For a broad overview on 3D shape matching and registration we refer interested readers to the survey papers [17, 70, 73]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.177, + 0.892, + 0.493 + ], + "angle": 0, + "content": "Deep Shape Matching. Data-driven deep learning methods constitute the state of the art in 3D shape matching, as they can predict high-quality correspondences in short time. Most of these methods are based on the popular functional map framework [49], as it offers a convenient way to regularise the high-dimensional shape matching problem via a low-dimensional representation. Respective methods were trained both in a supervised manner [28, 40, 42, 72, 76], and in an unsupervised manner [5, 6, 12-14, 18, 19, 30, 33, 39, 46, 51, 57, 65, 68, 71]. A major leap forward was achieved with the introduction of DiffusionNet [68], which builds upon a simple diffusion process to perform learning on 3D surfaces. The method [14] builds on top of DiffusionNet while coupling functional maps with point maps, and thereby achieves state-of-the-art shape matching performance in very challenging scenarios (e.g. partial shapes and topological noisy shapes). Despite the astonishing performance of recent learning-based shape matching methods, they have the major shortcoming that the produced matchings are not geometrically consistent, see e.g. [21] for a recent demonstration." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.825 + ], + "angle": 0, + "content": "Geometrically Consistent Shape Matching. We argue that geometric consistency is an essential property of 3D shape matching. Geometric consistency is generally hard to achieve since it leads to challenging non-convex optimisation problems, see e.g. [77]. Thus, there exists many local methods that require given correspondences between a sparse set of points [64] (e.g. often user-defined). Among them is the work [66] based on heat diffusion, and the work [75] in which given matchings are smoothed with the so-called product manifold filter. Furthermore, the works [23, 24] also consider the refinement of an initial set of matchings. The works [61, 62, 69] solve for geometrically consistent intrinsic triangulations [67] via local optimisation. Many of these methods are parameterisation-based, i.e. they rely on mappings of given 3D shapes to simple parametric surfaces, such as planes [1, 2, 34, 43, 44, 48, 79] or spheres [1, 3, 4, 50, 61]. One shortcoming of parameterisation-based methods is that they are only applicable for matching shapes with a fixed genus. Furthermore, respective methods involve highly non-convex optimisation problems that depend on good initialisations (e.g. user-provided sparse matchings)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Globally Optimal Shape Matching. While the polynomial-time solvable linear assignment problem (LAP) could in principle be used for 3D shape matching, it completely disregards geometric relations, so that neighbouring points may be matched to arbitrarily far away points. While" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "14544" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "the LAP matches vertices, the quadratic assignment problem (QAP) matches pairs of vertices (edges), so that neighbourhood relations can be better preserved. Yet, the QAP is NP-hard [54] so that shape matching instances with practically relevant sizes cannot efficiently be solved. Several attempts to tackle the QAP have been presented, including convex relaxations [9, 20, 36, 59], and heuristics based on local optimisation [31, 38, 74]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.219, + 0.473, + 0.356 + ], + "angle": 0, + "content": "Other attempts towards global shape matching are often based on some low-dimensional (or low-rank) representation, e.g. functional maps in the continuous domain [22, 27, 47, 49], functional maps coupled to point maps [53], or sparse matching representations in the discrete domain [10, 26]. Yet, functional map-based methods do not take geometric consistency into account, and sparse discrete models are typically slow and heavily rely on an aggressive pruning of the search space [10, 26, 47]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.473, + 0.664 + ], + "angle": 0, + "content": "A different class of global shape matching approaches is based on finding shortest paths in product graphs. These include the matching of signals in the popular dynamic time warping algorithm [58], the matching of 2D shapes to images to address shape-based image segmentation [16, 25, 63], or the matching of 2D shapes to each other [60]. Recently, a similar framework has been presented to match a 2D shape (a cyclic curve) to a 3D shape [37, 56]. All of these approaches have in common that solutions can efficiently be computed in polynomial time based on a shortest path algorithm (or some variant thereof). While product space formalisms have been generalised for the matching of 3D shapes [55, 77, 78], the respective problem is substantially harder and does not admit a solution via finding a shortest path - this is because in this case the matching cannot be represented as a one-dimensional path, but forms a two-dimensional surface in a four-dimensional product space. In this work we consider an alternative view that builds upon a different shape discretisation and thus allows to tackle 3D shape matching from a path-based perspective." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.433, + 0.715 + ], + "angle": 0, + "content": "3. Background on 2D-3D Shape Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.729, + 0.47, + 0.79 + ], + "angle": 0, + "content": "In the following section, we summarise the important product graph formalism introduced in [37] for 2D-3D shape matching. It forms the foundation of our SpiderCurve-based 3D shape matching approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Lähner et al. [37] aim to find correspondences between a 2D shape \\(\\mathcal{C} = (V^{\\mathcal{C}},E^{\\mathcal{C}})\\) (a cyclic curve discretised as a cyclic chain graph, i.e. a graph with circular topology.) and a 3D shape \\(\\mathcal{Y} = (V^{\\mathcal{Y}},E^{\\mathcal{Y}})\\) (interpreted as the undirected graph of a surface mesh). The matching between \\(\\mathcal{C}\\) and \\(\\mathcal{Y}\\) is found as a shortest path in the product graph" + }, + { + "type": "image", + "bbox": [ + 0.551, + 0.088, + 0.852, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.373, + 0.895, + 0.472 + ], + "angle": 0, + "content": "Figure 2. The product graph \\(\\mathcal{P}\\) is structured into layers (individual colours), where each layer corresponds to the product of a specific vertex \\(v^{\\mathcal{C}} \\in V^{\\mathcal{C}}\\) of the 2D shape \\(\\mathcal{C}\\) and the entire 3D shape \\(\\mathcal{Y}\\). \\(\\mathcal{P}\\) contains intra-layer edges (edges within a layer) and inter-layer edges (edges connecting neighbouring layers). To avoid clutter, we only show the inter-layer connections for one vertex in the red and yellow layers. Like \\(\\mathcal{C}\\), the product graph \\(\\mathcal{P}\\) is also cyclic." + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.493, + 0.658, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} = \\left(V ^ {\\mathcal {P}}, E ^ {\\mathcal {P}}\\right), \\text {w h e r e}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.517, + 0.892, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} V ^ {\\mathcal {P}} = V ^ {\\mathcal {C}} \\times V ^ {\\mathcal {Y}}, \\\\ E ^ {\\mathcal {P}} = \\left\\{\\left(e ^ {\\mathcal {C}}, e ^ {\\mathcal {Y}}\\right) \\in V ^ {\\mathcal {P}} \\times V ^ {\\mathcal {P}} \\mid e ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}} \\times V ^ {\\mathcal {C}}, \\right. \\tag {1} \\\\ e ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}} \\times V ^ {\\mathcal {Y}}, e ^ {\\mathcal {C}} \\text {o r} e ^ {\\mathcal {Y}} \\text {n o n - d e g .} \\}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.895, + 0.901 + ], + "angle": 0, + "content": "In Eq. (1), degenerate edges mean that they consist of the same vertex twice. This is necessary to handle different discretisations of the shapes. In Fig. 2 we show the structure of the product graph: \\(\\mathcal{P}\\) is oragnised into layers, where each layer corresponds to the product of a specific vertex of the 2D shape \\(\\mathcal{C}\\) and the entire 3D shape \\(\\mathcal{V}\\). Thus, every vertex \\(v = (v^{\\mathcal{C}}, v^{\\mathcal{V}}) \\in V^{\\mathcal{P}}\\) consists of a vertex \\(v^{\\mathcal{C}} \\in V^{\\mathcal{C}}\\) from the 2D shape \\(\\mathcal{C}\\), and a vertex \\(v^{\\mathcal{V}} \\in V^{\\mathcal{V}}\\) from the 3D shape \\(\\mathcal{V}\\). Any cyclic path in the product graph \\(\\mathcal{P}\\) that goes through all layers represents a (geometrically consistent) matching between \\(\\mathcal{C}\\) and \\(\\mathcal{P}\\). By defining appropriate edge costs (e.g. based on shape feature similarity, or by penalising deformations), one can find a globally optimal and geometrically consistent matching between the 2D shape \\(\\mathcal{C}\\) and the 3D shape \\(\\mathcal{V}\\) via a (cyclic) shortest paths algorithm. The works [37, 56] propose custom algorithms that exploit the special structure of the product graph in order to efficiently find such matchings. Overall, our main idea is to generalise such 2D-3D shape matching formalisms towards 3D-3D shape matching with the help of a SpiderCurve representation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14545" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.085, + 0.852, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.265, + 0.895, + 0.322 + ], + "angle": 0, + "content": "Figure 3. Overview of the pipeline of our method. We consider two 3D surface meshes \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) for which we compute vertex-wise features with a pretrained feature extractor. After discretising \\(\\mathcal{X}\\) into a SpiderCurve representation \\(\\mathcal{C}\\), we construct our cyclic shortest path ILP using constraints that ensure geometric and global 3D consistency of the matching. Solving the ILP (e.g. using Gurobi [29]) results in a globally optimal 3D shape matching represent as a shortest cyclic path in the product graph." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.346, + 0.434, + 0.365 + ], + "angle": 0, + "content": "4. SpiderCurve-based 3D Shape Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.377, + 0.471, + 0.573 + ], + "angle": 0, + "content": "We aim to find geometrically consistent correspondences between two non-rigidly deformed 3D shapes \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) (with same genus and potentially having boundaries) represented as tuples of vertices and edges \\(\\mathcal{X} = (V^{\\mathcal{X}}, E^{\\mathcal{X}})\\) and \\(\\mathcal{Y} = (V^{\\mathcal{Y}}, E^{\\mathcal{Y}})\\), respectively. Our notation is summarised in Tab. 2. Our main idea is to discretise the 3D shape \\(\\mathcal{X}\\) using a long self-intersecting curve \\(\\mathcal{C}\\) that traces the 3D surface \\(\\mathcal{X}\\) - due to the resemblance to a spider web we call this representation SpiderCurve, cf. Fig. 4. With that, we match \\(\\mathcal{C}\\) to the 3D shape \\(\\mathcal{Y}\\) while ensuring that (i) existing self-intersections of \\(\\mathcal{C}\\) are maintained, and that (ii) no additional self-intersections are introduces by the matching. We visualise our overall pipeline in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.471, + 0.623 + ], + "angle": 0, + "content": "In the following subsections we first discuss how to extract our SpiderCurve on \\(\\mathcal{X}\\), followed by the presentation of our integer linear programming (ILP) formulation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.647, + 0.3, + 0.663 + ], + "angle": 0, + "content": "4.1. SpiderCurve Extraction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.901 + ], + "angle": 0, + "content": "To ensure that our SpiderCurve \\(\\mathcal{C} = (V^{\\mathcal{C}},E^{\\mathcal{C}})\\) is a faithful discretisation of the 3D shape \\(V^{\\mathcal{X}}\\), we impose that \\(\\mathcal{C}\\) covers all vertices of \\(V^{\\mathcal{X}}\\). Moreover, the start and end points of \\(\\mathcal{C}\\) are equal, so that it forms a cycle. We explicitly strive for self-intersections in \\(\\mathcal{C}\\) in order to consider geometric consistency in multiple directions along the shape surface (this is achieved by imposing that intersections are maintained by the matching, see Sec. 4.2). We have found that using an approximation algorithm for the (metric) travelling salesperson problem (TSP), i.e. the Christofides algorithm [15], leads to reasonable SpiderCurves for our purposes. We note that for technical reasons it is convenient to duplicate vertices in the SpiderCurve \\(\\mathcal{C}\\) at the intersection points (so that \\(|V^{\\mathcal{C}}|\\geq |V^{\\mathcal{X}}|\\)). In Fig. 4, we visualise extracted SpiderCurves on different shapes." + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.345, + 0.902, + 0.611 + ], + "angle": 0, + "content": "
SymbolDescription
X=(Vx,Ex)3D surface shape X
|Vx|, |Ex|Number of vertices and edges
Vx∈R|Vx|×3Vertices of shape X
Ex∈N|Ex|×2Edges of shape X
Fx∈R|Vx|×128Features of shape X
Y=(Vy,Ey)3D surface shape Y
...(analogous to X)
C=(VC,Ec)Cyclic path on X (Spider Curve)
P=(VP,Ep)Product graph
x∈{0,1}|EP|Indicator representation of EP
c∈R|EP|Cost vector
x*Cyclic shortest path in P
(CYC)Cyclic path constraints
(CON)Path continuity constraints
(PES)Preservation of exist. self-inters. constraints
(ANS)Avoidance of new intersections constraints
" + }, + { + "type": "table_caption", + "bbox": [ + 0.537, + 0.621, + 0.855, + 0.636 + ], + "angle": 0, + "content": "Table 2. Summary of the notation used in this paper." + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.659, + 0.88, + 0.789 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.804, + 0.894, + 0.86 + ], + "angle": 0, + "content": "Figure 4. Visualisation of SpiderCurves on various types of 3D shapes including humanoid shapes and animals. We can see that our SpiderCurves cover the whole surface and thus pose a faithful discretisation of the respective 3D shape." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14546" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.086, + 0.262, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.277, + 0.087, + 0.462, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.493, + 0.087, + 0.682, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.087, + 0.882, + 0.306 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.32, + 0.895, + 0.432 + ], + "angle": 0, + "content": "Figure 5. Illustration of our four constraints. (Left) The sum of all \\( x_{i} \\) that involve edges connecting two layers (e.g. the set of red or blue edges) should be equal to one, so that the cyclic path \\( x^{\\star} \\) goes through all layers. (Middle-Left) The sum of all incoming edges (blue) of a product vertex (yellow) must be equal to the sum of all outgoing edges (red). This ensures that the path is continuous. (Middle-Right) Coupling of layers ensures that self-intersections of \\( \\mathcal{C} \\) are preserved on \\( \\mathcal{V} \\) under the matching. Coupling can be implemented by ensuring that the sum of outgoing edges (blue) of a product vertex on the bottom layer is equal to the sum of outgoing edges for a product vertex on the top layer (for corresponding vertices across layers, see yellow line). (Right) Self-intersections (other than the ones present in \\( \\mathcal{C} \\), see Middle-Right) can be avoided by allowing the cyclic path to only visit each vertex on \\( \\mathcal{V} \\) once, i.e. the sum of outgoing product edges (red) must be less than or equal 1 (this does not include vertical inter-layer product edges, i.e. product edges that do not leave the vertex on \\( \\mathcal{V} \\))." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.458, + 0.441, + 0.475 + ], + "angle": 0, + "content": "4.2. Our SpiderMatch Integer Linear Program" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.485, + 0.47, + 0.592 + ], + "angle": 0, + "content": "For finding a globally optimal matching, we construct the product graph \\(\\mathcal{P}\\) of the SpiderCurve \\(\\mathcal{C}\\) (a cyclic chain graph) and the 3D target shape \\(\\mathcal{V}\\). Then, we find a cyclic shortest path in \\(\\mathcal{P}\\) in such way that the path goes through each layer of \\(\\mathcal{P}\\) (cf. Fig. 2). In addition, we impose additional constraints that ensure geometric consistency in multiple directions along the shape surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.471, + 0.868 + ], + "angle": 0, + "content": "Contrary to [37, 56] that find shortest paths based on (a variant of) Dijkstra's algorithm, we formulate our optimisation problem as an ILP, so that we can directly integrate additional constraints. Most importantly, we impose that (i) self-intersections in \\(\\mathcal{C}\\) are preserved under the matching, and that (ii) additional self-intersections are avoided. To formulate our optimisation problem, we introduce for each edge \\(e_i \\in E^{\\mathcal{P}}\\) in the product graph \\(\\mathcal{P}\\) a binary indicator variable \\(x_i \\in \\{0,1\\}\\). The value \\(x_i = 1\\) means that product edge \\(e_i\\) is part of our matching path, and \\(x_i = 0\\) means that \\(e_i\\) is not contained in the matching. Our overall objective is to find the optimal matching \\(x^\\star\\) in the space of geometrically consistent matchings (to be defined in the following paragraphs) that minimises matching costs. We note that a product edge \\(e_i = (v_k, v_l) \\in E^{\\mathcal{P}}\\) consists of two product vertices \\(v_k, v_l \\in V^{\\mathcal{P}}\\), where each product vertex consists of a vertex \\(v^{\\mathcal{C}} \\in V^{\\mathcal{C}}\\) of the cyclic path \\(\\mathcal{C}\\) and a vertex \\(v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}\\) of 3D surface shape \\(\\mathcal{Y}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In the following we introduce the constraints of our ILP that define the space of geometrically consistent matchings." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.459, + 0.803, + 0.473 + ], + "angle": 0, + "content": "We visualise all types of constraints in Fig. 5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.55 + ], + "angle": 0, + "content": "Cyclic Path. We want to ensure that every vertex of \\(\\mathcal{C}\\) is matched at least once, i.e. the optimal cyclic path \\(x^{\\star}\\) goes through all layers. This can be achieved by ensuring that the sum over all \\(x_{i}\\) between any pair of adjacent layers (cf. Fig. 5 left) is equal to one. Formally, this is expressed as" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.56, + 0.892, + 0.612 + ], + "angle": 0, + "content": "\\[\n\\forall \\left(v _ {1} ^ {\\mathcal {C}}, v _ {2} ^ {\\mathcal {C}}\\right) \\in E ^ {\\mathcal {C}}: \\sum_ {i: e _ {i} = \\left(\\left(v _ {1} ^ {\\mathcal {C}}, \\bullet\\right), \\left(v _ {2} ^ {\\mathcal {C}}, \\bullet\\right)\\right) \\in E ^ {\\mathcal {P}}} x _ {i} = 1.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.702 + ], + "angle": 0, + "content": "Path Continuity. Furthermore, we have to ensure that every product vertex \\( v_{l} \\in V^{\\mathcal{P}} \\) with an active \\( (x_{i} = 1) \\) incoming product edge \\( e_{i} = (v_{k}, v_{l}) \\) also has an active \\( (x_{j} = 1) \\) outgoing product edge \\( e_{j} = (v_{l}, v_{m}) \\), i.e. the path must be continuous (cf. Fig. 5 middle-left). This property can be formalised as" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.712, + 0.892, + 0.76 + ], + "angle": 0, + "content": "\\[\n\\forall v _ {l} \\in V ^ {\\mathcal {P}}: \\sum_ {i: e _ {i} = (\\bullet , v _ {l}) \\in E ^ {\\mathcal {P}}} x _ {i} = \\sum_ {j: e _ {j} = (v _ {l}, \\bullet) \\in E ^ {\\mathcal {P}}} x _ {j}. \\tag {CON}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.76, + 0.892, + 0.867 + ], + "angle": 0, + "content": "Preservation of Existing Self-Intersections. To ensure geometric consistency, i.e. neighbourhoods between shape elements\\(^2\\) are preserved by the matching, every self-intersection of the SpiderCurve \\(\\mathcal{C}\\) must result in a self-intersection that involves the same vertices when \\(\\mathcal{C}\\) is matched to \\(\\mathcal{V}\\). We can ensure this by incorporating coupling constraints between product vertices that involve self" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.901 + ], + "angle": 0, + "content": "2In our formalism we can interpret polygons that are formed by our SpiderCurve as shape elements." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14547" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "intersections. To be precise, we couple those product vertices \\( v_{p}^{\\mathcal{C}} \\) and \\( v_{q}^{\\mathcal{C}} \\) on (different) layers \\( p \\) and \\( q \\) that belong to the same vertex \\( v^{\\mathcal{V}} \\) on \\( \\mathcal{V} \\) (cf. Fig. 5 middle-right). Formally, this can be written as" + }, + { + "type": "equation", + "bbox": [ + 0.102, + 0.163, + 0.469, + 0.234 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\forall v _ {p} ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}}, v _ {q} ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}}, p \\neq q, v _ {p} ^ {\\mathcal {C}} = v _ {q} ^ {\\mathcal {C}}: \\\\ \\sum_ {i: e _ {i} = \\left(\\left(v _ {p} ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}}\\right), \\bullet\\right) \\in E ^ {\\mathcal {P}}} x _ {i} = \\sum_ {j: e _ {j} = \\left(\\left(v _ {q} ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}}\\right), \\bullet\\right) \\in E ^ {\\mathcal {P}}} x _ {j}. \\tag {PES} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.236, + 0.47, + 0.417 + ], + "angle": 0, + "content": "Avoidance of New Self-Intersections. Lastly, we forbid that new self-intersections are introduced by the matching. This can be ensured by constraining the matching path in such a way that every vertex \\( v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}} \\) can only be visited at most once. In other words, the sum (across all layers) over all outgoing edges of product vertices that contain a given \\( v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}} \\) must be smaller than or equal to one. In this constraint, we do not sum over inter-layer edges whose source and target product vertex contain the same vertex \\( v^{\\mathcal{Y}} \\) on \\( \\mathcal{V} \\) (since these edges can be interpreted as 'staying' in the same vertex \\( v^{\\mathcal{Y}} \\) on \\( \\mathcal{V} \\)). The respective constraints are explained in Fig. 5 right. Mathematically, they read" + }, + { + "type": "equation", + "bbox": [ + 0.082, + 0.43, + 0.468, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\forall v _ {k} ^ {\\mathcal {Y}}, v _ {l} ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}}, v _ {k} ^ {\\mathcal {Y}} \\neq v _ {l} ^ {\\mathcal {Y}}: \\sum_ {i: e _ {i} = \\left(\\left(v _ {k} ^ {\\mathcal {C}}, v _ {k} ^ {\\mathcal {Y}}\\right), \\left(v _ {l} ^ {\\mathcal {C}}, v _ {l} ^ {\\mathcal {Y}}\\right)\\right) \\in E ^ {\\mathcal {P}}} x _ {i} \\leq 1 \\tag {ANS}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.48, + 0.469, + 0.54 + ], + "angle": 0, + "content": "with \\( v_{k}^{\\mathcal{C}}, v_{l}^{\\mathcal{C}} \\in V^{\\mathcal{C}} \\). Note that the sum will not include product vertices on layers which belong to coupling constraints, i.e. whenever \\( v_{k}^{\\mathcal{C}} \\) or \\( v_{l}^{\\mathcal{C}} \\) belong to a self-intersection of \\( \\mathcal{C} \\) we do not include respective product edge \\( e_{i} \\) in the sum." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.542, + 0.469, + 0.589 + ], + "angle": 0, + "content": "Matching Costs. We consider a cost vector \\(c \\in \\mathbb{R}^{|E^{\\mathcal{P}}|}\\) based on vertex-wise 3D shape features \\(F^{\\mathcal{X}}\\) and \\(F^{\\mathcal{Y}}\\). The entry at the \\(i\\)-th position is given by" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.601, + 0.469, + 0.621 + ], + "angle": 0, + "content": "\\[\nc _ {i} = c \\left(e _ {i}\\right) = \\Psi \\left(F _ {p} ^ {\\mathcal {X}} - F _ {r} ^ {\\mathcal {Y}}\\right) + \\Psi \\left(F _ {q} ^ {\\mathcal {X}} - F _ {s} ^ {\\mathcal {Y}}\\right), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.633, + 0.469, + 0.681 + ], + "angle": 0, + "content": "where \\( e_i = ((v_p^{\\mathcal{X}}, v_r^{\\mathcal{Y}}), (v_q^{\\mathcal{X}}, v_s^{\\mathcal{Y}})) \\), \\( v_p^{\\mathcal{X}}, v_q^{\\mathcal{X}} \\in V^{\\mathcal{C}} \\) and \\( v_r^{\\mathcal{Y}}, v_s^{\\mathcal{Y}} \\in V^{\\mathcal{Y}} \\). Furthermore, \\( \\Psi(\\cdot) \\) is the robust loss function presented in [8]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.469, + 0.727 + ], + "angle": 0, + "content": "Our SpiderMatch ILP. Putting our cost function and constraints together yields our final 3D shape matching formalism:" + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.741, + 0.469, + 0.769 + ], + "angle": 0, + "content": "\\[\n\\min _ {x \\in \\{0, 1 \\} ^ {| E ^ {\\mathcal {P}} |}} c ^ {T} x \\text {s . t (C Y C), (C O N), (P E S), (A N S).} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.469, + 0.827 + ], + "angle": 0, + "content": "Essentially, Problem (3) can be seen as a cyclic shortest path problem (over product edges encoded in \\( x \\), cf. Sec. 4.2) that involves the additional constraints (PES), (ANS)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.209, + 0.861 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "In this section we evaluate the performance of our method. First, we explain the considered evaluation metric and the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "competing methods. Subsequently, we evaluate the non-rigid shape matching performance of our method and compare it to other approaches. We conclude this section with ablation studies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.156, + 0.892, + 0.366 + ], + "angle": 0, + "content": "We solve Problem (3) with the off-the-shelf ILP solver Gurobi [29] (Version 10.0.3) on an Intel Core i9 12900K with 64 GB DDR5 RAM. We decimate all shapes to 1000 triangles using the mesh decimation algorithm provided in [32]. We also compute matchings for methods Cao et al. [14], Ren et al. [53], and Eisenberger et al. [22] on 1000 triangles. Only for Roetzer et al. [55] we decimate shapes to 450 triangles so that runtimes are acceptable (cf. Fig. 1 right). For our robust loss function \\(\\Psi(\\cdot)\\) [8] we choose parameters \\(\\alpha = 2\\) and \\(c = 0.3\\) and instead of a quadratic bowl we use a cubic bowl so that small differences in features are less relevant. We empirically observe that our method can solve all instances to global optimality in less than 200s." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.388, + 0.677, + 0.403 + ], + "angle": 0, + "content": "5.1. Evaluation Metric" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.892, + 0.522 + ], + "angle": 0, + "content": "We evaluate all shape matching methods using geodesic errors. Geodesic errors allow us to measure the correctness of the resulting matching w.r.t. to a ground-truth matching, i.e. how far is the resulting matching from the ground-truth matching. We follow the Princeton protocol [35] to compute geodesic errors which are normalised by the square-root of the area of a shape (see [35, Sec. 8.2])." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.542, + 0.604, + 0.556 + ], + "angle": 0, + "content": "5.2. Methods" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.569, + 0.814, + 0.583 + ], + "angle": 0, + "content": "We compare our method to four other methods:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.588, + 0.892, + 0.723 + ], + "angle": 0, + "content": "Cao et al. [14] is a recent functional map-based deep learning method which achieves state of the art performance by coupling functional maps with point maps during learning. We use this method as our feature extractor and thus consider it as our baseline. Moreover, the extensive evaluation in [14] confirms that it is indeed the state-of-the-art learning-based approach, so that we consider it as a representative for the broad body of learning-based shape matching methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.727, + 0.892, + 0.772 + ], + "angle": 0, + "content": "Ren et al. [53] is a functional map-based method which associates a functional map with a point wise map as a hard constraint." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.776, + 0.892, + 0.837 + ], + "angle": 0, + "content": "Eisenberger et al. [22] is a functional map-based iterative alignment scheme of shapes, which incrementally refines the geometrical information used to perform the matching." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Roetzer et al. [55] implements a combinatorial solver to solve a triangle-matching based ILP presented in [77]. This is the only competing approach that guarantees geometric consistency." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14548" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.087, + 0.887, + 0.478 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.491, + 0.896, + 0.562 + ], + "angle": 0, + "content": "Figure 6. Qualitative Results on the datasets FAUST, SMAL, DT4D-H (intra class and inter class). The state-of-the-art learning based method by Cao et al. produces matches with local geometric inconsistencies (cf. columns \\(③\\), \\(⑨\\)). Ren et al. yields visually the worst results due to large mismatches (cf. columns \\(④\\), \\(⑩\\)). Obvious large mismatches are not produced by Eisenberger et al., which however produces left-right flips (cf. columns \\(②\\), \\(⑧\\)) as well as local mismatches (cf. column \\(⑩\\)). Due to the geometric consistency of our method we produce smooth matchings for all shapes. Note that we show the lower-resolution matchings of Roetzer et al. in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.586, + 0.325, + 0.604 + ], + "angle": 0, + "content": "5.3. Non-Rigid Shape Matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.471, + 0.747 + ], + "angle": 0, + "content": "In this section we evaluate our method on three different datasets: FAUST [11, 18, 52], SMAL [80], DT4D-H [45] (in intraclass and interclass settings). We show qualitative results in Fig. 6. We can see that our geometrically consistent formalism yields better matchings than Cao et al., since our approach does not produce local mismatches. Furthermore, we observe severe mismatches and geometric inconsistencies in the matchings by Eisenberger et al. and Ren et al." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "FAUST. We test on the (more challenging) remeshed version [18, 52] of the FAUST dataset [11]. The dataset consists of 100 near-isometric human shapes (we randomly sample 100 pairs from the test set). In Fig. 7 left, we show geodesic errors on FAUST. Our geometrically consistent approach helps to resolve local missmatches (cf. Fig. 6) which yields improved geodesic error scores compared to Cao et al. The method by Ren et al. results in left-right flips due to intrinsic symmetries of human shapes of FAUST, which increases geodesic errors drastically." + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.578, + 0.9, + 0.694 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.705, + 0.895, + 0.748 + ], + "angle": 0, + "content": "Figure 7. Geodesic errors on FAUST and SMAL datasets. Numbers in the legends are mean geodesic errors \\((\\downarrow)\\). Our method yields best results w.r.t. to mean geodesic errors on both datasets." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.9 + ], + "angle": 0, + "content": "SMAL. Next, we evaluate on the remeshed version of the SMAL dataset [80]. This dataset consists of 49 nonisometric deformed animal shapes of eight species (we randomly sample 100 pairs from the test set). In Fig. 7 right, we show geodesic errors on SMAL. Again, ours is the best among all methods. For this dataset, shapes are unaligned, which harms the performance of Eisenberger et al. since it has to heuristically find a pre-alignment necessary for the method." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "14549" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.075, + 0.089, + 0.478, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.217, + 0.47, + 0.286 + ], + "angle": 0, + "content": "Figure 8. Geodesic errors on DT4D-H dataset in the intra-class and inter-class setting. Numbers in the legends are mean geodesic errors \\((\\downarrow)\\). In the intra-class settings our method produces best results among all competitors. In the inter-class setting ours is on par with Cao et al." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.47, + 0.508 + ], + "angle": 0, + "content": "DT4D-H. Finally, we test on DT4D-H [45], which consist of 9 different classes of humanoid/game character shapes in different poses. These shapes are taken from DeformingThings 4D [41]. We sample 100 random intra-class pairs, i.e. near-isometric deformed shape pairs. We also sample 100 random inter-class pairs, i.e. non-isometric deformed shape pairs. In Fig. 8, we show geodesic errors for both settings. In the intra-class setting our method outperforms all methods. For inter-class shapes our method is on par with Cao et al. The method by Eisenberger et al. suffers from the unaligned shapes in both settings, while Ren et al. produces a significant amount of left-right flips. In Sec. 8 in the supp. material we provide additional geometric consistency comparisons among the methods." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.517, + 0.188, + 0.531 + ], + "angle": 0, + "content": "5.4. Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.47, + 0.691 + ], + "angle": 0, + "content": "In Tab. 3, we summarise results of our ablation study. For that, we sample 25 random pairs of the FAUST dataset, downsample them to 500 triangles and compute matchings in the different settings reported in Tab. 3. We can see that constraints (PES), (ANS), and the robust loss function \\(\\Psi(\\cdot)\\) contribute to the performance of our method. We also replace \\(F^{\\mathcal{X}}\\) and \\(F^{\\mathcal{Y}}\\) with wave kernel signatures (WKS) features [7] and compare this setting to our method where we extract \\(F^{\\mathcal{X}}\\) and \\(F^{\\mathcal{Y}}\\) with [14]. In Sec. 11 in the supp. material we study our method under different resolutions." + }, + { + "type": "table", + "bbox": [ + 0.139, + 0.702, + 0.406, + 0.815 + ], + "angle": 0, + "content": "
MethodMean Geo. Err.
Ours w/o (PES), (ANS)0.036
Ours w/o (ANS)0.035
Ours w/o (PES)0.035
Ours with Ψ = ||·||20.036
Ours with WKS features0.213
Ours0.034
" + }, + { + "type": "table_caption", + "bbox": [ + 0.149, + 0.822, + 0.397, + 0.835 + ], + "angle": 0, + "content": "Table 3. Ablation studies of our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.329, + 0.861 + ], + "angle": 0, + "content": "6. Discussion and Limitations" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Time complexity. We have introduced the first geometrically consistent and globally optimal method for 3D shape" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.091, + 0.892, + 0.318 + ], + "angle": 0, + "content": "matching. Our problem instances involve up to \\(2 \\cdot 10^{6}\\) binary variables. Nevertheless, we experimentally demonstrate that we can find globally optimal solutions in all considered matching instances within about 100s, which indicates that our search space has a benign structure (likely stemming from the underlying shortest path-based motivation) that can effectively be exploited by off-the-shelf ILP solvers. Still, our proposed formalism belongs to the (generally difficult) class of integer programming problems. We observe that our constraints do not lead to a totally unimodular matrix, so that in general we may have exponential worst-case runtime. We leave a theoretical analysis of the time complexity of our proposed approach, and the question whether there may exist polynomial time algorithms that solves our problem (or related variants) for future work." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.892, + 0.457 + ], + "angle": 0, + "content": "SpiderCurve extraction. The focus of this work was on presenting a novel framework that generalises path-based shape matching formalisms for 3D shape matching. Although our TSP-based SpiderCurve extraction leads to promising matchings in all conducted experiments, we believe that there may be potential using alternative curve-based shape discretisations. An in-depth analysis and comparison of different approaches was not our main focus and is an interesting direction for follow-up works." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.549 + ], + "angle": 0, + "content": "Feasibility. In theory, our SpiderMatch ILP (3) might be infeasible, which may for example stem from discretisation artefacts in low-resolution settings. Yet, our method is able to operate on (relatively) high resolution shapes so that we expect these cases to be rare (we found all of the 400 instances considered in our experiments to be feasible)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.571, + 0.619, + 0.587 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We present a fresh view on geometrically consistent 3D shape matching. Our key insight is to discretise one of the shapes using a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. This allows us to utilise ideas and concepts from shortest path-based formalisms that have so far not been applicable to the matching of 3D shapes. More specifically, our work is motivated by the recent shortest path-based curve to 3D shape matching formalism by Lähner et al. [37], which we augment with additional self-intersection constraints that allows us to ensure geometric consistency in multiple directions along the shape surface. Experimentally we showcase the great potential of our novel approach, which on the one hand leads us to state-of-the-art shape matching performance. Furthermore, at the same time we achieve both geometric consistency and global optimality – the latter two properties are highly desirable but have so far not been reached by any previous 3D shape matching method. Overall, we believe that our approach may be insightful and may inspire follow-up works in geometrically consistent shape matching and beyond." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14550" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.143 + ], + "angle": 0, + "content": "[1] Noam Aigerman and Yaron Lipman. OrbifoldiTutede embeddings.ACM Trans.Graph.,34(6):190-1,2015.2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.469, + 0.186 + ], + "angle": 0, + "content": "[2] Noam Aigerman, Roi Poranne, and Yaron Lipman. Lifted bijections for low distortion surface mappings. 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In CVPR, 2017. 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.178 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14553" + } + ] +] \ No newline at end of file diff --git a/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_origin.pdf b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..21092bdd089e5b26b0698a4be97ee30fb1e3c6c8 --- /dev/null +++ b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/dc02bdd8-9eaf-4562-b3e4-4eb5d67e4085_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0bb9e560d192ab16eb1b4ab2d7efe107b10ef0a71e721a43f5972a3ba664ac12 +size 8262797 diff --git a/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/full.md b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/full.md new file mode 100644 index 0000000000000000000000000000000000000000..2112ce9f16f84d47dc316e6f0f941ad22ba9e8df --- /dev/null +++ b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/full.md @@ -0,0 +1,311 @@ +# SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency + +Paul Roetzer1 Florian Bernard1 +University of Bonn1 + +![](images/bcb87a4e1a58ff91cab68dc8906372cf0e40b97283a541cb22b2225f303fa422.jpg) +Idea: Match Cyclic Path $\mathcal{C}$ on $\mathcal{X}$ to $\mathcal{Y}$ + +![](images/198351ef6c99d80f205e617d597ec1f9db10a03f2dd7ff8e95034c0682c6e183.jpg) +Dense Geometrically Consistent Shape Matching +Figure 1. (Left) Schematic illustration of our method: we extract a cyclic path $\mathcal{C}$ on the surface of 3D shape $\mathcal{X}$ , and match $\mathcal{C}$ to the 3D target shape $\mathcal{Y}$ . (Middle) If $\mathcal{C}$ covers the whole source shape $\mathcal{X}$ (not shown for clarity, see Sec. 4.1 for details), our method can be used to compute globally optimal results for dense non-rigid and geometrically consistent 3D shape matching. (Right) We show runtimes w.r.t. shape resolution and compare to Roetzer et al. [55] (which is the only existing method that achieves geometric consistency while having a global flavour and being initialization-free) and Cao et al. [14] (which does not provide any geometric consistency guarantees). Ours solves all instances to global optimality (with geometric consistency), while in addition being much faster than Roetzer et al. + +![](images/2a7bbe0340e1e7d9281b218a4fa9d4b4f90f7807f59d36b977254ae3442653e0.jpg) +Scalability Analysis + +# Abstract + +Finding shortest paths on product spaces is a popular approach to tackle numerous variants of matching problems, including the dynamic time warping method for matching signals, the matching of curves, or the matching of a curve to a 3D shape. While these approaches admit the computation of globally optimal solutions in polynomial time, their natural generalisation to 3D shape matching is widely known to be intractable. In this work we address this issue by proposing a novel path-based formalism for 3D shape matching. More specifically, we consider an alternative shape discretisation in which one of the 3D shapes (the source shape) is represented as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. We then tackle the 3D shape matching problem as finding a shortest path in the product graph of the SpiderCurve and the target 3D shape. Our approach introduces a set of novel constraints that ensure a globally geometrically consistent matching. Overall, our formalism leads to an integer linear programming problem for which we experimentally show that it can efficiently be solved to global + +optimality. We demonstrate that our approach is competitive with recent state-of-the-art shape matching methods, while in addition guaranteeing geometric consistency. $^{1}$ + +# 1. Introduction + +The 3D shape matching problem refers to finding correspondences between given 3D shapes and has a high relevance across the broad field of visual computing. Examples of applications include texture transfer in graphics, statistical shape analysis in medical imaging, or 3D reconstruction or shape completion in computer vision. While the state of the art in 3D shape matching relies on data-driven deep learning methods [14], respective methods have the strong shortcoming that they lack guarantees about structural properties of obtained matchings. One crucial example, which is the main focus of our work, is geometric consistency: a matching between a given pair of 3D shapes is geometrically consistent if the neighbourhood between shape elements (e.g. triangles) is preserved under the matching. + +Loosely, geometric consistency (in the discrete domain) can be seen analogously to diffeomorphisms in the continuous domain [77]. + +Achieving geometric consistency in learning-based shape matching solutions is extremely challenging, since it requires to impose complex structural constraints on the prediction. While there are some optimisation-based works that explicitly aim for geometric consistency, they require initial pre-matchings to handle the severe non-convexity of respective optimisation problems [23, 24, 43, 61, 62, 64, 66, 69, 75], or they employ heuristics and only find approximate solutions [55, 78]. To date, there do not exist any 3D shape matching methods that are able to find globally optimal solutions while guaranteeing geometric consistency. + +In this work we make a first step towards filling this gap. More specifically, motivated by recent advances in (polynomial-time solvable) matching problems between a curve and a 3D shape [37, 56], we propose to represent the source 3D shape as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D surface, loosely analogous to a spider web covering the shape surface. We then find a shortest path in the product graph of the SpiderCurve and the target 3D shape, while respecting geometric consistency constraints. We cast this as an integer linear program, for which we experimentally demonstrate that it can efficiently be solved to global optimality in all considered problem settings. Overall, we summarise our main contributions as follows (also cf. Tab. 1): + +- For the first time we enable to find globally optimal solutions for geometrically consistent 3D shape matching. +- To achieve this, we introduce a novel integer linear programme (ILP) that consistently matches our SpiderCurve 3D shape representation to the target 3D shape. +- Although ILP solvers employ branch and bound procedures that have exponential worst-case runtime in general, we experimentally demonstrate that our formalism allows to efficiently find solutions for problems with practically relevant sizes (e.g. we use the off-the-shelf ILP solver Gurobi to match shapes with 1000 triangles in $\approx$ 100s.). + +
MethodGeometrically ConsistentGlobally OptimalKeypoint FreePruning Free
SIGMA [26]X(✓)XX
MINA [10]X(✓)XX
PMSDP [47]XX✓X
Roetzer et al. [55](✓)X✓✓
Ours✓✓✓✓
+ +Table 1. Comparison of properties of shape matching methods. Ours is the only one that finds geometrically consistent and globally optimal solutions. Moreover, our method does not require the definition of keypoints, nor does it exploit any search space pruning scheme to solve the resulting integer linear program. + +# 2. Related Work + +In the following we discuss works that are most relevant to our method. For a broad overview on 3D shape matching and registration we refer interested readers to the survey papers [17, 70, 73]. + +Deep Shape Matching. Data-driven deep learning methods constitute the state of the art in 3D shape matching, as they can predict high-quality correspondences in short time. Most of these methods are based on the popular functional map framework [49], as it offers a convenient way to regularise the high-dimensional shape matching problem via a low-dimensional representation. Respective methods were trained both in a supervised manner [28, 40, 42, 72, 76], and in an unsupervised manner [5, 6, 12-14, 18, 19, 30, 33, 39, 46, 51, 57, 65, 68, 71]. A major leap forward was achieved with the introduction of DiffusionNet [68], which builds upon a simple diffusion process to perform learning on 3D surfaces. The method [14] builds on top of DiffusionNet while coupling functional maps with point maps, and thereby achieves state-of-the-art shape matching performance in very challenging scenarios (e.g. partial shapes and topological noisy shapes). Despite the astonishing performance of recent learning-based shape matching methods, they have the major shortcoming that the produced matchings are not geometrically consistent, see e.g. [21] for a recent demonstration. + +Geometrically Consistent Shape Matching. We argue that geometric consistency is an essential property of 3D shape matching. Geometric consistency is generally hard to achieve since it leads to challenging non-convex optimisation problems, see e.g. [77]. Thus, there exists many local methods that require given correspondences between a sparse set of points [64] (e.g. often user-defined). Among them is the work [66] based on heat diffusion, and the work [75] in which given matchings are smoothed with the so-called product manifold filter. Furthermore, the works [23, 24] also consider the refinement of an initial set of matchings. The works [61, 62, 69] solve for geometrically consistent intrinsic triangulations [67] via local optimisation. Many of these methods are parameterisation-based, i.e. they rely on mappings of given 3D shapes to simple parametric surfaces, such as planes [1, 2, 34, 43, 44, 48, 79] or spheres [1, 3, 4, 50, 61]. One shortcoming of parameterisation-based methods is that they are only applicable for matching shapes with a fixed genus. Furthermore, respective methods involve highly non-convex optimisation problems that depend on good initialisations (e.g. user-provided sparse matchings). + +Globally Optimal Shape Matching. While the polynomial-time solvable linear assignment problem (LAP) could in principle be used for 3D shape matching, it completely disregards geometric relations, so that neighbouring points may be matched to arbitrarily far away points. While + +the LAP matches vertices, the quadratic assignment problem (QAP) matches pairs of vertices (edges), so that neighbourhood relations can be better preserved. Yet, the QAP is NP-hard [54] so that shape matching instances with practically relevant sizes cannot efficiently be solved. Several attempts to tackle the QAP have been presented, including convex relaxations [9, 20, 36, 59], and heuristics based on local optimisation [31, 38, 74]. + +Other attempts towards global shape matching are often based on some low-dimensional (or low-rank) representation, e.g. functional maps in the continuous domain [22, 27, 47, 49], functional maps coupled to point maps [53], or sparse matching representations in the discrete domain [10, 26]. Yet, functional map-based methods do not take geometric consistency into account, and sparse discrete models are typically slow and heavily rely on an aggressive pruning of the search space [10, 26, 47]. + +A different class of global shape matching approaches is based on finding shortest paths in product graphs. These include the matching of signals in the popular dynamic time warping algorithm [58], the matching of 2D shapes to images to address shape-based image segmentation [16, 25, 63], or the matching of 2D shapes to each other [60]. Recently, a similar framework has been presented to match a 2D shape (a cyclic curve) to a 3D shape [37, 56]. All of these approaches have in common that solutions can efficiently be computed in polynomial time based on a shortest path algorithm (or some variant thereof). While product space formalisms have been generalised for the matching of 3D shapes [55, 77, 78], the respective problem is substantially harder and does not admit a solution via finding a shortest path - this is because in this case the matching cannot be represented as a one-dimensional path, but forms a two-dimensional surface in a four-dimensional product space. In this work we consider an alternative view that builds upon a different shape discretisation and thus allows to tackle 3D shape matching from a path-based perspective. + +# 3. Background on 2D-3D Shape Matching + +In the following section, we summarise the important product graph formalism introduced in [37] for 2D-3D shape matching. It forms the foundation of our SpiderCurve-based 3D shape matching approach. + +Lähner et al. [37] aim to find correspondences between a 2D shape $\mathcal{C} = (V^{\mathcal{C}},E^{\mathcal{C}})$ (a cyclic curve discretised as a cyclic chain graph, i.e. a graph with circular topology.) and a 3D shape $\mathcal{Y} = (V^{\mathcal{Y}},E^{\mathcal{Y}})$ (interpreted as the undirected graph of a surface mesh). The matching between $\mathcal{C}$ and $\mathcal{Y}$ is found as a shortest path in the product graph + +![](images/0d8c64e649a3561d68f69a690919a6bd07bd607a7ac58d995cbd075164527596.jpg) +Figure 2. The product graph $\mathcal{P}$ is structured into layers (individual colours), where each layer corresponds to the product of a specific vertex $v^{\mathcal{C}} \in V^{\mathcal{C}}$ of the 2D shape $\mathcal{C}$ and the entire 3D shape $\mathcal{Y}$ . $\mathcal{P}$ contains intra-layer edges (edges within a layer) and inter-layer edges (edges connecting neighbouring layers). To avoid clutter, we only show the inter-layer connections for one vertex in the red and yellow layers. Like $\mathcal{C}$ , the product graph $\mathcal{P}$ is also cyclic. + +$$ +\mathcal {P} = \left(V ^ {\mathcal {P}}, E ^ {\mathcal {P}}\right), \text {w h e r e} +$$ + +$$ +\begin{array}{l} V ^ {\mathcal {P}} = V ^ {\mathcal {C}} \times V ^ {\mathcal {Y}}, \\ E ^ {\mathcal {P}} = \left\{\left(e ^ {\mathcal {C}}, e ^ {\mathcal {Y}}\right) \in V ^ {\mathcal {P}} \times V ^ {\mathcal {P}} \mid e ^ {\mathcal {C}} \in V ^ {\mathcal {C}} \times V ^ {\mathcal {C}}, \right. \tag {1} \\ e ^ {\mathcal {Y}} \in V ^ {\mathcal {Y}} \times V ^ {\mathcal {Y}}, e ^ {\mathcal {C}} \text {o r} e ^ {\mathcal {Y}} \text {n o n - d e g .} \}. \\ \end{array} +$$ + +In Eq. (1), degenerate edges mean that they consist of the same vertex twice. This is necessary to handle different discretisations of the shapes. In Fig. 2 we show the structure of the product graph: $\mathcal{P}$ is oragnised into layers, where each layer corresponds to the product of a specific vertex of the 2D shape $\mathcal{C}$ and the entire 3D shape $\mathcal{V}$ . Thus, every vertex $v = (v^{\mathcal{C}}, v^{\mathcal{V}}) \in V^{\mathcal{P}}$ consists of a vertex $v^{\mathcal{C}} \in V^{\mathcal{C}}$ from the 2D shape $\mathcal{C}$ , and a vertex $v^{\mathcal{V}} \in V^{\mathcal{V}}$ from the 3D shape $\mathcal{V}$ . Any cyclic path in the product graph $\mathcal{P}$ that goes through all layers represents a (geometrically consistent) matching between $\mathcal{C}$ and $\mathcal{P}$ . By defining appropriate edge costs (e.g. based on shape feature similarity, or by penalising deformations), one can find a globally optimal and geometrically consistent matching between the 2D shape $\mathcal{C}$ and the 3D shape $\mathcal{V}$ via a (cyclic) shortest paths algorithm. The works [37, 56] propose custom algorithms that exploit the special structure of the product graph in order to efficiently find such matchings. Overall, our main idea is to generalise such 2D-3D shape matching formalisms towards 3D-3D shape matching with the help of a SpiderCurve representation. + +![](images/4200a97dd30fcd9a0178a73e5628ced81bf5ce95a876ffd81d63c64ec9e9e382.jpg) +Figure 3. Overview of the pipeline of our method. We consider two 3D surface meshes $\mathcal{X}$ and $\mathcal{Y}$ for which we compute vertex-wise features with a pretrained feature extractor. After discretising $\mathcal{X}$ into a SpiderCurve representation $\mathcal{C}$ , we construct our cyclic shortest path ILP using constraints that ensure geometric and global 3D consistency of the matching. Solving the ILP (e.g. using Gurobi [29]) results in a globally optimal 3D shape matching represent as a shortest cyclic path in the product graph. + +# 4. SpiderCurve-based 3D Shape Matching + +We aim to find geometrically consistent correspondences between two non-rigidly deformed 3D shapes $\mathcal{X}$ and $\mathcal{Y}$ (with same genus and potentially having boundaries) represented as tuples of vertices and edges $\mathcal{X} = (V^{\mathcal{X}}, E^{\mathcal{X}})$ and $\mathcal{Y} = (V^{\mathcal{Y}}, E^{\mathcal{Y}})$ , respectively. Our notation is summarised in Tab. 2. Our main idea is to discretise the 3D shape $\mathcal{X}$ using a long self-intersecting curve $\mathcal{C}$ that traces the 3D surface $\mathcal{X}$ - due to the resemblance to a spider web we call this representation SpiderCurve, cf. Fig. 4. With that, we match $\mathcal{C}$ to the 3D shape $\mathcal{Y}$ while ensuring that (i) existing self-intersections of $\mathcal{C}$ are maintained, and that (ii) no additional self-intersections are introduces by the matching. We visualise our overall pipeline in Fig. 3. + +In the following subsections we first discuss how to extract our SpiderCurve on $\mathcal{X}$ , followed by the presentation of our integer linear programming (ILP) formulation. + +# 4.1. SpiderCurve Extraction + +To ensure that our SpiderCurve $\mathcal{C} = (V^{\mathcal{C}},E^{\mathcal{C}})$ is a faithful discretisation of the 3D shape $V^{\mathcal{X}}$ , we impose that $\mathcal{C}$ covers all vertices of $V^{\mathcal{X}}$ . Moreover, the start and end points of $\mathcal{C}$ are equal, so that it forms a cycle. We explicitly strive for self-intersections in $\mathcal{C}$ in order to consider geometric consistency in multiple directions along the shape surface (this is achieved by imposing that intersections are maintained by the matching, see Sec. 4.2). We have found that using an approximation algorithm for the (metric) travelling salesperson problem (TSP), i.e. the Christofides algorithm [15], leads to reasonable SpiderCurves for our purposes. We note that for technical reasons it is convenient to duplicate vertices in the SpiderCurve $\mathcal{C}$ at the intersection points (so that $|V^{\mathcal{C}}|\geq |V^{\mathcal{X}}|$ ). In Fig. 4, we visualise extracted SpiderCurves on different shapes. + +
SymbolDescription
X=(Vx,Ex)3D surface shape X
|Vx|, |Ex|Number of vertices and edges
Vx∈R|Vx|×3Vertices of shape X
Ex∈N|Ex|×2Edges of shape X
Fx∈R|Vx|×128Features of shape X
Y=(Vy,Ey)3D surface shape Y
...(analogous to X)
C=(VC,Ec)Cyclic path on X (Spider Curve)
P=(VP,Ep)Product graph
x∈{0,1}|EP|Indicator representation of EP
c∈R|EP|Cost vector
x*Cyclic shortest path in P
(CYC)Cyclic path constraints
(CON)Path continuity constraints
(PES)Preservation of exist. self-inters. constraints
(ANS)Avoidance of new intersections constraints
+ +Table 2. Summary of the notation used in this paper. + +![](images/50e99f13283a84821c0de09e45d8297820a069e408d2114077c18a717e93159f.jpg) +Figure 4. Visualisation of SpiderCurves on various types of 3D shapes including humanoid shapes and animals. We can see that our SpiderCurves cover the whole surface and thus pose a faithful discretisation of the respective 3D shape. + +![](images/abb3e88249b6a4c17a985fb46c4f3c9fd7dbf62dbb4766676d4db3f154e8230e.jpg) +Figure 5. Illustration of our four constraints. (Left) The sum of all $x_{i}$ that involve edges connecting two layers (e.g. the set of red or blue edges) should be equal to one, so that the cyclic path $x^{\star}$ goes through all layers. (Middle-Left) The sum of all incoming edges (blue) of a product vertex (yellow) must be equal to the sum of all outgoing edges (red). This ensures that the path is continuous. (Middle-Right) Coupling of layers ensures that self-intersections of $\mathcal{C}$ are preserved on $\mathcal{V}$ under the matching. Coupling can be implemented by ensuring that the sum of outgoing edges (blue) of a product vertex on the bottom layer is equal to the sum of outgoing edges for a product vertex on the top layer (for corresponding vertices across layers, see yellow line). (Right) Self-intersections (other than the ones present in $\mathcal{C}$ , see Middle-Right) can be avoided by allowing the cyclic path to only visit each vertex on $\mathcal{V}$ once, i.e. the sum of outgoing product edges (red) must be less than or equal 1 (this does not include vertical inter-layer product edges, i.e. product edges that do not leave the vertex on $\mathcal{V}$ ). + +![](images/169996bf22bd3398b38e366ee4a42a1d155455116ff0e1ed620413c8c086abb7.jpg) + +![](images/a564660ee0ca7373817dbe0d22bd29d1aa145315fa2a95f672ee30eed94b447d.jpg) + +![](images/b45754f3c9d4b34f19210536d7922509c024f7ebf81eb01340f9812416ea6107.jpg) + +# 4.2. Our SpiderMatch Integer Linear Program + +For finding a globally optimal matching, we construct the product graph $\mathcal{P}$ of the SpiderCurve $\mathcal{C}$ (a cyclic chain graph) and the 3D target shape $\mathcal{V}$ . Then, we find a cyclic shortest path in $\mathcal{P}$ in such way that the path goes through each layer of $\mathcal{P}$ (cf. Fig. 2). In addition, we impose additional constraints that ensure geometric consistency in multiple directions along the shape surface. + +Contrary to [37, 56] that find shortest paths based on (a variant of) Dijkstra's algorithm, we formulate our optimisation problem as an ILP, so that we can directly integrate additional constraints. Most importantly, we impose that (i) self-intersections in $\mathcal{C}$ are preserved under the matching, and that (ii) additional self-intersections are avoided. To formulate our optimisation problem, we introduce for each edge $e_i \in E^{\mathcal{P}}$ in the product graph $\mathcal{P}$ a binary indicator variable $x_i \in \{0,1\}$ . The value $x_i = 1$ means that product edge $e_i$ is part of our matching path, and $x_i = 0$ means that $e_i$ is not contained in the matching. Our overall objective is to find the optimal matching $x^\star$ in the space of geometrically consistent matchings (to be defined in the following paragraphs) that minimises matching costs. We note that a product edge $e_i = (v_k, v_l) \in E^{\mathcal{P}}$ consists of two product vertices $v_k, v_l \in V^{\mathcal{P}}$ , where each product vertex consists of a vertex $v^{\mathcal{C}} \in V^{\mathcal{C}}$ of the cyclic path $\mathcal{C}$ and a vertex $v^{\mathcal{Y}} \in V^{\mathcal{Y}}$ of 3D surface shape $\mathcal{Y}$ . + +In the following we introduce the constraints of our ILP that define the space of geometrically consistent matchings. + +We visualise all types of constraints in Fig. 5. + +Cyclic Path. We want to ensure that every vertex of $\mathcal{C}$ is matched at least once, i.e. the optimal cyclic path $x^{\star}$ goes through all layers. This can be achieved by ensuring that the sum over all $x_{i}$ between any pair of adjacent layers (cf. Fig. 5 left) is equal to one. Formally, this is expressed as + +$$ +\forall \left(v _ {1} ^ {\mathcal {C}}, v _ {2} ^ {\mathcal {C}}\right) \in E ^ {\mathcal {C}}: \sum_ {i: e _ {i} = \left(\left(v _ {1} ^ {\mathcal {C}}, \bullet\right), \left(v _ {2} ^ {\mathcal {C}}, \bullet\right)\right) \in E ^ {\mathcal {P}}} x _ {i} = 1. +$$ + +Path Continuity. Furthermore, we have to ensure that every product vertex $v_{l} \in V^{\mathcal{P}}$ with an active $(x_{i} = 1)$ incoming product edge $e_{i} = (v_{k}, v_{l})$ also has an active $(x_{j} = 1)$ outgoing product edge $e_{j} = (v_{l}, v_{m})$ , i.e. the path must be continuous (cf. Fig. 5 middle-left). This property can be formalised as + +$$ +\forall v _ {l} \in V ^ {\mathcal {P}}: \sum_ {i: e _ {i} = (\bullet , v _ {l}) \in E ^ {\mathcal {P}}} x _ {i} = \sum_ {j: e _ {j} = (v _ {l}, \bullet) \in E ^ {\mathcal {P}}} x _ {j}. \tag {CON} +$$ + +Preservation of Existing Self-Intersections. To ensure geometric consistency, i.e. neighbourhoods between shape elements $^2$ are preserved by the matching, every self-intersection of the SpiderCurve $\mathcal{C}$ must result in a self-intersection that involves the same vertices when $\mathcal{C}$ is matched to $\mathcal{V}$ . We can ensure this by incorporating coupling constraints between product vertices that involve self + +intersections. To be precise, we couple those product vertices $v_{p}^{\mathcal{C}}$ and $v_{q}^{\mathcal{C}}$ on (different) layers $p$ and $q$ that belong to the same vertex $v^{\mathcal{V}}$ on $\mathcal{V}$ (cf. Fig. 5 middle-right). Formally, this can be written as + +$$ +\begin{array}{l} \forall v _ {p} ^ {\mathcal {C}} \in V ^ {\mathcal {C}}, v _ {q} ^ {\mathcal {C}} \in V ^ {\mathcal {C}}, v ^ {\mathcal {Y}} \in V ^ {\mathcal {Y}}, p \neq q, v _ {p} ^ {\mathcal {C}} = v _ {q} ^ {\mathcal {C}}: \\ \sum_ {i: e _ {i} = \left(\left(v _ {p} ^ {\mathcal {C}}, v ^ {\mathcal {Y}}\right), \bullet\right) \in E ^ {\mathcal {P}}} x _ {i} = \sum_ {j: e _ {j} = \left(\left(v _ {q} ^ {\mathcal {C}}, v ^ {\mathcal {Y}}\right), \bullet\right) \in E ^ {\mathcal {P}}} x _ {j}. \tag {PES} \\ \end{array} +$$ + +Avoidance of New Self-Intersections. Lastly, we forbid that new self-intersections are introduced by the matching. This can be ensured by constraining the matching path in such a way that every vertex $v^{\mathcal{Y}} \in V^{\mathcal{Y}}$ can only be visited at most once. In other words, the sum (across all layers) over all outgoing edges of product vertices that contain a given $v^{\mathcal{Y}} \in V^{\mathcal{Y}}$ must be smaller than or equal to one. In this constraint, we do not sum over inter-layer edges whose source and target product vertex contain the same vertex $v^{\mathcal{Y}}$ on $\mathcal{V}$ (since these edges can be interpreted as 'staying' in the same vertex $v^{\mathcal{Y}}$ on $\mathcal{V}$ ). The respective constraints are explained in Fig. 5 right. Mathematically, they read + +$$ +\forall v _ {k} ^ {\mathcal {Y}}, v _ {l} ^ {\mathcal {Y}} \in V ^ {\mathcal {Y}}, v _ {k} ^ {\mathcal {Y}} \neq v _ {l} ^ {\mathcal {Y}}: \sum_ {i: e _ {i} = \left(\left(v _ {k} ^ {\mathcal {C}}, v _ {k} ^ {\mathcal {Y}}\right), \left(v _ {l} ^ {\mathcal {C}}, v _ {l} ^ {\mathcal {Y}}\right)\right) \in E ^ {\mathcal {P}}} x _ {i} \leq 1 \tag {ANS} +$$ + +with $v_{k}^{\mathcal{C}}, v_{l}^{\mathcal{C}} \in V^{\mathcal{C}}$ . Note that the sum will not include product vertices on layers which belong to coupling constraints, i.e. whenever $v_{k}^{\mathcal{C}}$ or $v_{l}^{\mathcal{C}}$ belong to a self-intersection of $\mathcal{C}$ we do not include respective product edge $e_{i}$ in the sum. + +Matching Costs. We consider a cost vector $c \in \mathbb{R}^{|E^{\mathcal{P}}|}$ based on vertex-wise 3D shape features $F^{\mathcal{X}}$ and $F^{\mathcal{Y}}$ . The entry at the $i$ -th position is given by + +$$ +c _ {i} = c \left(e _ {i}\right) = \Psi \left(F _ {p} ^ {\mathcal {X}} - F _ {r} ^ {\mathcal {Y}}\right) + \Psi \left(F _ {q} ^ {\mathcal {X}} - F _ {s} ^ {\mathcal {Y}}\right), \tag {2} +$$ + +where $e_i = ((v_p^{\mathcal{X}}, v_r^{\mathcal{Y}}), (v_q^{\mathcal{X}}, v_s^{\mathcal{Y}}))$ , $v_p^{\mathcal{X}}, v_q^{\mathcal{X}} \in V^{\mathcal{C}}$ and $v_r^{\mathcal{Y}}, v_s^{\mathcal{Y}} \in V^{\mathcal{Y}}$ . Furthermore, $\Psi(\cdot)$ is the robust loss function presented in [8]. + +Our SpiderMatch ILP. Putting our cost function and constraints together yields our final 3D shape matching formalism: + +$$ +\min _ {x \in \{0, 1 \} ^ {| E ^ {\mathcal {P}} |}} c ^ {T} x \text {s . t (C Y C), (C O N), (P E S), (A N S).} \tag {3} +$$ + +Essentially, Problem (3) can be seen as a cyclic shortest path problem (over product edges encoded in $x$ , cf. Sec. 4.2) that involves the additional constraints (PES), (ANS). + +# 5. Experiments + +In this section we evaluate the performance of our method. First, we explain the considered evaluation metric and the + +competing methods. Subsequently, we evaluate the non-rigid shape matching performance of our method and compare it to other approaches. We conclude this section with ablation studies. + +We solve Problem (3) with the off-the-shelf ILP solver Gurobi [29] (Version 10.0.3) on an Intel Core i9 12900K with 64 GB DDR5 RAM. We decimate all shapes to 1000 triangles using the mesh decimation algorithm provided in [32]. We also compute matchings for methods Cao et al. [14], Ren et al. [53], and Eisenberger et al. [22] on 1000 triangles. Only for Roetzer et al. [55] we decimate shapes to 450 triangles so that runtimes are acceptable (cf. Fig. 1 right). For our robust loss function $\Psi(\cdot)$ [8] we choose parameters $\alpha = 2$ and $c = 0.3$ and instead of a quadratic bowl we use a cubic bowl so that small differences in features are less relevant. We empirically observe that our method can solve all instances to global optimality in less than 200s. + +# 5.1. Evaluation Metric + +We evaluate all shape matching methods using geodesic errors. Geodesic errors allow us to measure the correctness of the resulting matching w.r.t. to a ground-truth matching, i.e. how far is the resulting matching from the ground-truth matching. We follow the Princeton protocol [35] to compute geodesic errors which are normalised by the square-root of the area of a shape (see [35, Sec. 8.2]). + +# 5.2. Methods + +We compare our method to four other methods: + +Cao et al. [14] is a recent functional map-based deep learning method which achieves state of the art performance by coupling functional maps with point maps during learning. We use this method as our feature extractor and thus consider it as our baseline. Moreover, the extensive evaluation in [14] confirms that it is indeed the state-of-the-art learning-based approach, so that we consider it as a representative for the broad body of learning-based shape matching methods. + +Ren et al. [53] is a functional map-based method which associates a functional map with a point wise map as a hard constraint. + +Eisenberger et al. [22] is a functional map-based iterative alignment scheme of shapes, which incrementally refines the geometrical information used to perform the matching. + +Roetzer et al. [55] implements a combinatorial solver to solve a triangle-matching based ILP presented in [77]. This is the only competing approach that guarantees geometric consistency. + +![](images/6771b8c6690b308ee8620ca0ccfa28e3ecd3033950d23c631d2478352927f346.jpg) +Figure 6. Qualitative Results on the datasets FAUST, SMAL, DT4D-H (intra class and inter class). The state-of-the-art learning based method by Cao et al. produces matches with local geometric inconsistencies (cf. columns $③$ , $⑨$ ). Ren et al. yields visually the worst results due to large mismatches (cf. columns $④$ , $⑩$ ). Obvious large mismatches are not produced by Eisenberger et al., which however produces left-right flips (cf. columns $②$ , $⑧$ ) as well as local mismatches (cf. column $⑩$ ). Due to the geometric consistency of our method we produce smooth matchings for all shapes. Note that we show the lower-resolution matchings of Roetzer et al. in the appendix. + +# 5.3. Non-Rigid Shape Matching + +In this section we evaluate our method on three different datasets: FAUST [11, 18, 52], SMAL [80], DT4D-H [45] (in intraclass and interclass settings). We show qualitative results in Fig. 6. We can see that our geometrically consistent formalism yields better matchings than Cao et al., since our approach does not produce local mismatches. Furthermore, we observe severe mismatches and geometric inconsistencies in the matchings by Eisenberger et al. and Ren et al. + +FAUST. We test on the (more challenging) remeshed version [18, 52] of the FAUST dataset [11]. The dataset consists of 100 near-isometric human shapes (we randomly sample 100 pairs from the test set). In Fig. 7 left, we show geodesic errors on FAUST. Our geometrically consistent approach helps to resolve local missmatches (cf. Fig. 6) which yields improved geodesic error scores compared to Cao et al. The method by Ren et al. results in left-right flips due to intrinsic symmetries of human shapes of FAUST, which increases geodesic errors drastically. + +![](images/e2f52475df6d846b3d11175b2686347abab68b9d9e81b102f23683f917458564.jpg) +Figure 7. Geodesic errors on FAUST and SMAL datasets. Numbers in the legends are mean geodesic errors $(\downarrow)$ . Our method yields best results w.r.t. to mean geodesic errors on both datasets. + +SMAL. Next, we evaluate on the remeshed version of the SMAL dataset [80]. This dataset consists of 49 nonisometric deformed animal shapes of eight species (we randomly sample 100 pairs from the test set). In Fig. 7 right, we show geodesic errors on SMAL. Again, ours is the best among all methods. For this dataset, shapes are unaligned, which harms the performance of Eisenberger et al. since it has to heuristically find a pre-alignment necessary for the method. + +![](images/9d3426b320645db08636a490833cbc2b8a02a758537d29c29779eaaf7d0fa467.jpg) +Figure 8. Geodesic errors on DT4D-H dataset in the intra-class and inter-class setting. Numbers in the legends are mean geodesic errors $(\downarrow)$ . In the intra-class settings our method produces best results among all competitors. In the inter-class setting ours is on par with Cao et al. + +DT4D-H. Finally, we test on DT4D-H [45], which consist of 9 different classes of humanoid/game character shapes in different poses. These shapes are taken from DeformingThings 4D [41]. We sample 100 random intra-class pairs, i.e. near-isometric deformed shape pairs. We also sample 100 random inter-class pairs, i.e. non-isometric deformed shape pairs. In Fig. 8, we show geodesic errors for both settings. In the intra-class setting our method outperforms all methods. For inter-class shapes our method is on par with Cao et al. The method by Eisenberger et al. suffers from the unaligned shapes in both settings, while Ren et al. produces a significant amount of left-right flips. In Sec. 8 in the supp. material we provide additional geometric consistency comparisons among the methods. + +# 5.4. Ablations + +In Tab. 3, we summarise results of our ablation study. For that, we sample 25 random pairs of the FAUST dataset, downsample them to 500 triangles and compute matchings in the different settings reported in Tab. 3. We can see that constraints (PES), (ANS), and the robust loss function $\Psi(\cdot)$ contribute to the performance of our method. We also replace $F^{\mathcal{X}}$ and $F^{\mathcal{Y}}$ with wave kernel signatures (WKS) features [7] and compare this setting to our method where we extract $F^{\mathcal{X}}$ and $F^{\mathcal{Y}}$ with [14]. In Sec. 11 in the supp. material we study our method under different resolutions. + +
MethodMean Geo. Err.
Ours w/o (PES), (ANS)0.036
Ours w/o (ANS)0.035
Ours w/o (PES)0.035
Ours with Ψ = ||·||20.036
Ours with WKS features0.213
Ours0.034
+ +Table 3. Ablation studies of our method. + +# 6. Discussion and Limitations + +Time complexity. We have introduced the first geometrically consistent and globally optimal method for 3D shape + +matching. Our problem instances involve up to $2 \cdot 10^{6}$ binary variables. Nevertheless, we experimentally demonstrate that we can find globally optimal solutions in all considered matching instances within about 100s, which indicates that our search space has a benign structure (likely stemming from the underlying shortest path-based motivation) that can effectively be exploited by off-the-shelf ILP solvers. Still, our proposed formalism belongs to the (generally difficult) class of integer programming problems. We observe that our constraints do not lead to a totally unimodular matrix, so that in general we may have exponential worst-case runtime. We leave a theoretical analysis of the time complexity of our proposed approach, and the question whether there may exist polynomial time algorithms that solves our problem (or related variants) for future work. + +SpiderCurve extraction. The focus of this work was on presenting a novel framework that generalises path-based shape matching formalisms for 3D shape matching. Although our TSP-based SpiderCurve extraction leads to promising matchings in all conducted experiments, we believe that there may be potential using alternative curve-based shape discretisations. An in-depth analysis and comparison of different approaches was not our main focus and is an interesting direction for follow-up works. + +Feasibility. In theory, our SpiderMatch ILP (3) might be infeasible, which may for example stem from discretisation artefacts in low-resolution settings. Yet, our method is able to operate on (relatively) high resolution shapes so that we expect these cases to be rare (we found all of the 400 instances considered in our experiments to be feasible). + +# 7. Conclusion + +We present a fresh view on geometrically consistent 3D shape matching. Our key insight is to discretise one of the shapes using a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. This allows us to utilise ideas and concepts from shortest path-based formalisms that have so far not been applicable to the matching of 3D shapes. More specifically, our work is motivated by the recent shortest path-based curve to 3D shape matching formalism by Lähner et al. [37], which we augment with additional self-intersection constraints that allows us to ensure geometric consistency in multiple directions along the shape surface. 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In CVPR, 2017. 7 \ No newline at end of file diff --git a/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/images.zip b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..802d03074f7f0886c1c2cbbdead237ea710f1bfc --- /dev/null +++ b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:677bd20c9d49f8bf1fd4d374658a74a541f5343051f7481be3f2f5b322132b94 +size 644705 diff --git a/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/layout.json b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..a95e2be87a3ed641b6f89d7e9ff09c05e0059185 --- /dev/null +++ b/2024/SpiderMatch_ 3D Shape Matching with Global Optimality and Geometric Consistency/layout.json @@ -0,0 +1,10079 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 153, + 103, + 440, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 103, + 440, + 140 + ], + "spans": [ + { + "bbox": [ + 153, + 103, + 440, + 140 + ], + "type": "text", + "content": "SpiderMatch: 3D Shape Matching with Global Optimality and Geometric Consistency" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 206, + 160, + 386, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 206, + 160, + 386, + 190 + ], + "spans": [ + { + "bbox": [ + 206, + 160, + 386, + 190 + ], + "type": "text", + "content": "Paul Roetzer1 Florian Bernard1 \nUniversity of Bonn1" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 72, + 230, + 205, + 342 + ], + "blocks": [ + { + "bbox": [ + 72, + 230, + 205, + 342 + ], + "lines": [ + { + "bbox": [ + 72, + 230, + 205, + 342 + ], + "spans": [ + { + "bbox": [ + 72, + 230, + 205, + 342 + ], + "type": "image", + "image_path": "bcb87a4e1a58ff91cab68dc8906372cf0e40b97283a541cb22b2225f303fa422.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "lines": [ + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "spans": [ + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "type": "text", + "content": "Idea: Match Cyclic Path " + }, + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 75, + 347, + 197, + 357 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 227, + 230, + 389, + 346 + ], + "blocks": [ + { + "bbox": [ + 227, + 230, + 389, + 346 + ], + "lines": [ + { + "bbox": [ + 227, + 230, + 389, + 346 + ], + "spans": [ + { + "bbox": [ + 227, + 230, + 389, + 346 + ], + "type": "image", + "image_path": "198351ef6c99d80f205e617d597ec1f9db10a03f2dd7ff8e95034c0682c6e183.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 227, + 347, + 388, + 358 + ], + "lines": [ + { + "bbox": [ + 227, + 347, + 388, + 358 + ], + "spans": [ + { + "bbox": [ + 227, + 347, + 388, + 358 + ], + "type": "text", + "content": "Dense Geometrically Consistent Shape Matching" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": "Figure 1. (Left) Schematic illustration of our method: we extract a cyclic path " + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": " on the surface of 3D shape " + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": ", and match " + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": " to the 3D target shape " + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": ". (Middle) If " + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": " covers the whole source shape " + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 45, + 367, + 545, + 434 + ], + "type": "text", + "content": " (not shown for clarity, see Sec. 4.1 for details), our method can be used to compute globally optimal results for dense non-rigid and geometrically consistent 3D shape matching. (Right) We show runtimes w.r.t. shape resolution and compare to Roetzer et al. [55] (which is the only existing method that achieves geometric consistency while having a global flavour and being initialization-free) and Cao et al. [14] (which does not provide any geometric consistency guarantees). Ours solves all instances to global optimality (with geometric consistency), while in addition being much faster than Roetzer et al." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 405, + 232, + 550, + 346 + ], + "blocks": [ + { + "bbox": [ + 405, + 232, + 550, + 346 + ], + "lines": [ + { + "bbox": [ + 405, + 232, + 550, + 346 + ], + "spans": [ + { + "bbox": [ + 405, + 232, + 550, + 346 + ], + "type": "image", + "image_path": "2a7bbe0340e1e7d9281b218a4fa9d4b4f90f7807f59d36b977254ae3442653e0.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 441, + 348, + 507, + 357 + ], + "lines": [ + { + "bbox": [ + 441, + 348, + 507, + 357 + ], + "spans": [ + { + "bbox": [ + 441, + 348, + 507, + 357 + ], + "type": "text", + "content": "Scalability Analysis" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 143, + 449, + 192, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 449, + 192, + 462 + ], + "spans": [ + { + "bbox": [ + 143, + 449, + 192, + 462 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 45, + 475, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 475, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 475, + 290, + 715 + ], + "type": "text", + "content": "Finding shortest paths on product spaces is a popular approach to tackle numerous variants of matching problems, including the dynamic time warping method for matching signals, the matching of curves, or the matching of a curve to a 3D shape. While these approaches admit the computation of globally optimal solutions in polynomial time, their natural generalisation to 3D shape matching is widely known to be intractable. In this work we address this issue by proposing a novel path-based formalism for 3D shape matching. More specifically, we consider an alternative shape discretisation in which one of the 3D shapes (the source shape) is represented as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. We then tackle the 3D shape matching problem as finding a shortest path in the product graph of the SpiderCurve and the target 3D shape. Our approach introduces a set of novel constraints that ensure a globally geometrically consistent matching. Overall, our formalism leads to an integer linear programming problem for which we experimentally show that it can efficiently be solved to global" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 451, + 545, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 451, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 305, + 451, + 545, + 486 + ], + "type": "text", + "content": "optimality. We demonstrate that our approach is competitive with recent state-of-the-art shape matching methods, while in addition guaranteeing geometric consistency." + }, + { + "bbox": [ + 305, + 451, + 545, + 486 + ], + "type": "inline_equation", + "content": "^{1}" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 509, + 388, + 521 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 509, + 388, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 509, + 388, + 521 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 529, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 529, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 529, + 545, + 696 + ], + "type": "text", + "content": "The 3D shape matching problem refers to finding correspondences between given 3D shapes and has a high relevance across the broad field of visual computing. Examples of applications include texture transfer in graphics, statistical shape analysis in medical imaging, or 3D reconstruction or shape completion in computer vision. While the state of the art in 3D shape matching relies on data-driven deep learning methods [14], respective methods have the strong shortcoming that they lack guarantees about structural properties of obtained matchings. One crucial example, which is the main focus of our work, is geometric consistency: a matching between a given pair of 3D shapes is geometrically consistent if the neighbourhood between shape elements (e.g. triangles) is preserved under the matching." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 317, + 704, + 520, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 704, + 520, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 704, + 520, + 714 + ], + "type": "text", + "content": "1https://github.com/paul0noah/spider-match" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14543" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "Loosely, geometric consistency (in the discrete domain) can be seen analogously to diffeomorphisms in the continuous domain [77]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 287, + 239 + ], + "type": "text", + "content": "Achieving geometric consistency in learning-based shape matching solutions is extremely challenging, since it requires to impose complex structural constraints on the prediction. While there are some optimisation-based works that explicitly aim for geometric consistency, they require initial pre-matchings to handle the severe non-convexity of respective optimisation problems [23, 24, 43, 61, 62, 64, 66, 69, 75], or they employ heuristics and only find approximate solutions [55, 78]. To date, there do not exist any 3D shape matching methods that are able to find globally optimal solutions while guaranteeing geometric consistency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 239, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 407 + ], + "type": "text", + "content": "In this work we make a first step towards filling this gap. More specifically, motivated by recent advances in (polynomial-time solvable) matching problems between a curve and a 3D shape [37, 56], we propose to represent the source 3D shape as a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D surface, loosely analogous to a spider web covering the shape surface. We then find a shortest path in the product graph of the SpiderCurve and the target 3D shape, while respecting geometric consistency constraints. We cast this as an integer linear program, for which we experimentally demonstrate that it can efficiently be solved to global optimality in all considered problem settings. Overall, we summarise our main contributions as follows (also cf. Tab. 1):" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 407, + 286, + 538 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 407, + 286, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 286, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 286, + 430 + ], + "type": "text", + "content": "- For the first time we enable to find globally optimal solutions for geometrically consistent 3D shape matching." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 431, + 286, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 431, + 286, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 431, + 286, + 466 + ], + "type": "text", + "content": "- To achieve this, we introduce a novel integer linear programme (ILP) that consistently matches our SpiderCurve 3D shape representation to the target 3D shape." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 467, + 286, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 467, + 286, + 538 + ], + "spans": [ + { + "bbox": [ + 47, + 467, + 286, + 538 + ], + "type": "text", + "content": "- Although ILP solvers employ branch and bound procedures that have exponential worst-case runtime in general, we experimentally demonstrate that our formalism allows to efficiently find solutions for problems with practically relevant sizes (e.g. we use the off-the-shelf ILP solver Gurobi to match shapes with 1000 triangles in " + }, + { + "bbox": [ + 47, + 467, + 286, + 538 + ], + "type": "inline_equation", + "content": "\\approx" + }, + { + "bbox": [ + 47, + 467, + 286, + 538 + ], + "type": "text", + "content": "100s.)." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "type": "table", + "bbox": [ + 48, + 546, + 286, + 635 + ], + "blocks": [ + { + "bbox": [ + 48, + 546, + 286, + 635 + ], + "lines": [ + { + "bbox": [ + 48, + 546, + 286, + 635 + ], + "spans": [ + { + "bbox": [ + 48, + 546, + 286, + 635 + ], + "type": "table", + "html": "
MethodGeometrically ConsistentGlobally OptimalKeypoint FreePruning Free
SIGMA [26]X(✓)XX
MINA [10]X(✓)XX
PMSDP [47]XX✓X
Roetzer et al. [55](✓)X✓✓
Ours✓✓✓✓
", + "image_path": "fad2c6c2bc22359229cfb14930f88e29921005a982d4201898adb0045cd16e24.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 644, + 286, + 700 + ], + "lines": [ + { + "bbox": [ + 46, + 644, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 644, + 286, + 700 + ], + "type": "text", + "content": "Table 1. Comparison of properties of shape matching methods. Ours is the only one that finds geometrically consistent and globally optimal solutions. Moreover, our method does not require the definition of keypoints, nor does it exploit any search space pruning scheme to solve the resulting integer linear program." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 392, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 91, + 545, + 139 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 91, + 545, + 139 + ], + "spans": [ + { + "bbox": [ + 304, + 91, + 545, + 139 + ], + "type": "text", + "content": "In the following we discuss works that are most relevant to our method. For a broad overview on 3D shape matching and registration we refer interested readers to the survey papers [17, 70, 73]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 140, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 140, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 545, + 390 + ], + "type": "text", + "content": "Deep Shape Matching. Data-driven deep learning methods constitute the state of the art in 3D shape matching, as they can predict high-quality correspondences in short time. Most of these methods are based on the popular functional map framework [49], as it offers a convenient way to regularise the high-dimensional shape matching problem via a low-dimensional representation. Respective methods were trained both in a supervised manner [28, 40, 42, 72, 76], and in an unsupervised manner [5, 6, 12-14, 18, 19, 30, 33, 39, 46, 51, 57, 65, 68, 71]. A major leap forward was achieved with the introduction of DiffusionNet [68], which builds upon a simple diffusion process to perform learning on 3D surfaces. The method [14] builds on top of DiffusionNet while coupling functional maps with point maps, and thereby achieves state-of-the-art shape matching performance in very challenging scenarios (e.g. partial shapes and topological noisy shapes). Despite the astonishing performance of recent learning-based shape matching methods, they have the major shortcoming that the produced matchings are not geometrically consistent, see e.g. [21] for a recent demonstration." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 653 + ], + "type": "text", + "content": "Geometrically Consistent Shape Matching. We argue that geometric consistency is an essential property of 3D shape matching. Geometric consistency is generally hard to achieve since it leads to challenging non-convex optimisation problems, see e.g. [77]. Thus, there exists many local methods that require given correspondences between a sparse set of points [64] (e.g. often user-defined). Among them is the work [66] based on heat diffusion, and the work [75] in which given matchings are smoothed with the so-called product manifold filter. Furthermore, the works [23, 24] also consider the refinement of an initial set of matchings. The works [61, 62, 69] solve for geometrically consistent intrinsic triangulations [67] via local optimisation. Many of these methods are parameterisation-based, i.e. they rely on mappings of given 3D shapes to simple parametric surfaces, such as planes [1, 2, 34, 43, 44, 48, 79] or spheres [1, 3, 4, 50, 61]. One shortcoming of parameterisation-based methods is that they are only applicable for matching shapes with a fixed genus. Furthermore, respective methods involve highly non-convex optimisation problems that depend on good initialisations (e.g. user-provided sparse matchings)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "Globally Optimal Shape Matching. While the polynomial-time solvable linear assignment problem (LAP) could in principle be used for 3D shape matching, it completely disregards geometric relations, so that neighbouring points may be matched to arbitrarily far away points. While" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14544" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "the LAP matches vertices, the quadratic assignment problem (QAP) matches pairs of vertices (edges), so that neighbourhood relations can be better preserved. Yet, the QAP is NP-hard [54] so that shape matching instances with practically relevant sizes cannot efficiently be solved. Several attempts to tackle the QAP have been presented, including convex relaxations [9, 20, 36, 59], and heuristics based on local optimisation [31, 38, 74]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 173, + 289, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 173, + 289, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 289, + 281 + ], + "type": "text", + "content": "Other attempts towards global shape matching are often based on some low-dimensional (or low-rank) representation, e.g. functional maps in the continuous domain [22, 27, 47, 49], functional maps coupled to point maps [53], or sparse matching representations in the discrete domain [10, 26]. Yet, functional map-based methods do not take geometric consistency into account, and sparse discrete models are typically slow and heavily rely on an aggressive pruning of the search space [10, 26, 47]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 285, + 289, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 289, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 289, + 525 + ], + "type": "text", + "content": "A different class of global shape matching approaches is based on finding shortest paths in product graphs. These include the matching of signals in the popular dynamic time warping algorithm [58], the matching of 2D shapes to images to address shape-based image segmentation [16, 25, 63], or the matching of 2D shapes to each other [60]. Recently, a similar framework has been presented to match a 2D shape (a cyclic curve) to a 3D shape [37, 56]. All of these approaches have in common that solutions can efficiently be computed in polynomial time based on a shortest path algorithm (or some variant thereof). While product space formalisms have been generalised for the matching of 3D shapes [55, 77, 78], the respective problem is substantially harder and does not admit a solution via finding a shortest path - this is because in this case the matching cannot be represented as a one-dimensional path, but forms a two-dimensional surface in a four-dimensional product space. In this work we consider an alternative view that builds upon a different shape discretisation and thus allows to tackle 3D shape matching from a path-based perspective." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 552, + 264, + 566 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 264, + 566 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 264, + 566 + ], + "type": "text", + "content": "3. Background on 2D-3D Shape Matching" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 577, + 287, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 577, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 46, + 577, + 287, + 625 + ], + "type": "text", + "content": "In the following section, we summarise the important product graph formalism introduced in [37] for 2D-3D shape matching. It forms the foundation of our SpiderCurve-based 3D shape matching approach." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": "Lähner et al. [37] aim to find correspondences between a 2D shape " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = (V^{\\mathcal{C}},E^{\\mathcal{C}})" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " (a cyclic curve discretised as a cyclic chain graph, i.e. a graph with circular topology.) and a 3D shape " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = (V^{\\mathcal{Y}},E^{\\mathcal{Y}})" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " (interpreted as the undirected graph of a surface mesh). The matching between " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 642, + 288, + 714 + ], + "type": "text", + "content": " is found as a shortest path in the product graph" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 337, + 69, + 521, + 287 + ], + "blocks": [ + { + "bbox": [ + 337, + 69, + 521, + 287 + ], + "lines": [ + { + "bbox": [ + 337, + 69, + 521, + 287 + ], + "spans": [ + { + "bbox": [ + 337, + 69, + 521, + 287 + ], + "type": "image", + "image_path": "0d8c64e649a3561d68f69a690919a6bd07bd607a7ac58d995cbd075164527596.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "lines": [ + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "spans": [ + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": "Figure 2. The product graph " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": " is structured into layers (individual colours), where each layer corresponds to the product of a specific vertex " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{C}} \\in V^{\\mathcal{C}}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": " of the 2D shape " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": " and the entire 3D shape " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": " contains intra-layer edges (edges within a layer) and inter-layer edges (edges connecting neighbouring layers). To avoid clutter, we only show the inter-layer connections for one vertex in the red and yellow layers. Like " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": ", the product graph " + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 305, + 295, + 547, + 373 + ], + "type": "text", + "content": " is also cyclic." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 390, + 402, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 390, + 402, + 403 + ], + "spans": [ + { + "bbox": [ + 306, + 390, + 402, + 403 + ], + "type": "interline_equation", + "content": "\\mathcal {P} = \\left(V ^ {\\mathcal {P}}, E ^ {\\mathcal {P}}\\right), \\text {w h e r e}", + "image_path": "0acf573da5dfa6199716882aee46dedd4863d48520c739aa87974d0d51a1cffb.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 321, + 409, + 545, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 409, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 321, + 409, + 545, + 456 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} V ^ {\\mathcal {P}} = V ^ {\\mathcal {C}} \\times V ^ {\\mathcal {Y}}, \\\\ E ^ {\\mathcal {P}} = \\left\\{\\left(e ^ {\\mathcal {C}}, e ^ {\\mathcal {Y}}\\right) \\in V ^ {\\mathcal {P}} \\times V ^ {\\mathcal {P}} \\mid e ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}} \\times V ^ {\\mathcal {C}}, \\right. \\tag {1} \\\\ e ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}} \\times V ^ {\\mathcal {Y}}, e ^ {\\mathcal {C}} \\text {o r} e ^ {\\mathcal {Y}} \\text {n o n - d e g .} \\}. \\\\ \\end{array}", + "image_path": "b5b9b90eddc3ec7c1b42670d41eda4e0a052e2cfeb9f94af3f3fa66981ac9bac.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": "In Eq. (1), degenerate edges mean that they consist of the same vertex twice. This is necessary to handle different discretisations of the shapes. In Fig. 2 we show the structure of the product graph: " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " is oragnised into layers, where each layer corresponds to the product of a specific vertex of the 2D shape " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " and the entire 3D shape " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": ". Thus, every vertex " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "v = (v^{\\mathcal{C}}, v^{\\mathcal{V}}) \\in V^{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " consists of a vertex " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{C}} \\in V^{\\mathcal{C}}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " from the 2D shape " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": ", and a vertex " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{V}} \\in V^{\\mathcal{V}}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " from the 3D shape " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": ". Any cyclic path in the product graph " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " that goes through all layers represents a (geometrically consistent) matching between " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": ". By defining appropriate edge costs (e.g. based on shape feature similarity, or by penalising deformations), one can find a globally optimal and geometrically consistent matching between the 2D shape " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " and the 3D shape " + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 462, + 547, + 713 + ], + "type": "text", + "content": " via a (cyclic) shortest paths algorithm. The works [37, 56] propose custom algorithms that exploit the special structure of the product graph in order to efficiently find such matchings. Overall, our main idea is to generalise such 2D-3D shape matching formalisms towards 3D-3D shape matching with the help of a SpiderCurve representation." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14545" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 67, + 521, + 201 + ], + "blocks": [ + { + "bbox": [ + 60, + 67, + 521, + 201 + ], + "lines": [ + { + "bbox": [ + 60, + 67, + 521, + 201 + ], + "spans": [ + { + "bbox": [ + 60, + 67, + 521, + 201 + ], + "type": "image", + "image_path": "4200a97dd30fcd9a0178a73e5628ced81bf5ce95a876ffd81d63c64ec9e9e382.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "text", + "content": "Figure 3. Overview of the pipeline of our method. We consider two 3D surface meshes " + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "text", + "content": " for which we compute vertex-wise features with a pretrained feature extractor. After discretising " + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "text", + "content": " into a SpiderCurve representation " + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 209, + 547, + 255 + ], + "type": "text", + "content": ", we construct our cyclic shortest path ILP using constraints that ensure geometric and global 3D consistency of the matching. Solving the ILP (e.g. using Gurobi [29]) results in a globally optimal 3D shape matching represent as a shortest cyclic path in the product graph." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 274, + 265, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 265, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 265, + 289 + ], + "type": "text", + "content": "4. SpiderCurve-based 3D Shape Matching" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "spans": [ + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": "We aim to find geometrically consistent correspondences between two non-rigidly deformed 3D shapes " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " (with same genus and potentially having boundaries) represented as tuples of vertices and edges " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{X} = (V^{\\mathcal{X}}, E^{\\mathcal{X}})" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{Y} = (V^{\\mathcal{Y}}, E^{\\mathcal{Y}})" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": ", respectively. Our notation is summarised in Tab. 2. Our main idea is to discretise the 3D shape " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " using a long self-intersecting curve " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " that traces the 3D surface " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " - due to the resemblance to a spider web we call this representation SpiderCurve, cf. Fig. 4. With that, we match " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " to the 3D shape " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " while ensuring that (i) existing self-intersections of " + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 298, + 288, + 453 + ], + "type": "text", + "content": " are maintained, and that (ii) no additional self-intersections are introduces by the matching. We visualise our overall pipeline in Fig. 3." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 457, + 288, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 288, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 288, + 493 + ], + "type": "text", + "content": "In the following subsections we first discuss how to extract our SpiderCurve on " + }, + { + "bbox": [ + 46, + 457, + 288, + 493 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 457, + 288, + 493 + ], + "type": "text", + "content": ", followed by the presentation of our integer linear programming (ILP) formulation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 512, + 183, + 525 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 512, + 183, + 525 + ], + "spans": [ + { + "bbox": [ + 47, + 512, + 183, + 525 + ], + "type": "text", + "content": "4.1. SpiderCurve Extraction" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": "To ensure that our SpiderCurve " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C} = (V^{\\mathcal{C}},E^{\\mathcal{C}})" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": " is a faithful discretisation of the 3D shape " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "V^{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": ", we impose that " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": " covers all vertices of " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "V^{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": ". Moreover, the start and end points of " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": " are equal, so that it forms a cycle. We explicitly strive for self-intersections in " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": " in order to consider geometric consistency in multiple directions along the shape surface (this is achieved by imposing that intersections are maintained by the matching, see Sec. 4.2). We have found that using an approximation algorithm for the (metric) travelling salesperson problem (TSP), i.e. the Christofides algorithm [15], leads to reasonable SpiderCurves for our purposes. We note that for technical reasons it is convenient to duplicate vertices in the SpiderCurve " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": " at the intersection points (so that " + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "inline_equation", + "content": "|V^{\\mathcal{C}}|\\geq |V^{\\mathcal{X}}|" + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": "). In Fig. 4, we visualise extracted SpiderCurves on different shapes." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 307, + 273, + 552, + 483 + ], + "blocks": [ + { + "bbox": [ + 307, + 273, + 552, + 483 + ], + "lines": [ + { + "bbox": [ + 307, + 273, + 552, + 483 + ], + "spans": [ + { + "bbox": [ + 307, + 273, + 552, + 483 + ], + "type": "table", + "html": "
SymbolDescription
X=(Vx,Ex)3D surface shape X
|Vx|, |Ex|Number of vertices and edges
Vx∈R|Vx|×3Vertices of shape X
Ex∈N|Ex|×2Edges of shape X
Fx∈R|Vx|×128Features of shape X
Y=(Vy,Ey)3D surface shape Y
...(analogous to X)
C=(VC,Ec)Cyclic path on X (Spider Curve)
P=(VP,Ep)Product graph
x∈{0,1}|EP|Indicator representation of EP
c∈R|EP|Cost vector
x*Cyclic shortest path in P
(CYC)Cyclic path constraints
(CON)Path continuity constraints
(PES)Preservation of exist. self-inters. constraints
(ANS)Avoidance of new intersections constraints
", + "image_path": "2321a4a2b322c8209ae2c57eebf372694640a8c081af65a2ecec33f0945aa906.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 328, + 491, + 523, + 503 + ], + "lines": [ + { + "bbox": [ + 328, + 491, + 523, + 503 + ], + "spans": [ + { + "bbox": [ + 328, + 491, + 523, + 503 + ], + "type": "text", + "content": "Table 2. Summary of the notation used in this paper." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 316, + 521, + 538, + 624 + ], + "blocks": [ + { + "bbox": [ + 316, + 521, + 538, + 624 + ], + "lines": [ + { + "bbox": [ + 316, + 521, + 538, + 624 + ], + "spans": [ + { + "bbox": [ + 316, + 521, + 538, + 624 + ], + "type": "image", + "image_path": "50e99f13283a84821c0de09e45d8297820a069e408d2114077c18a717e93159f.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 636, + 547, + 681 + ], + "lines": [ + { + "bbox": [ + 305, + 636, + 547, + 681 + ], + "spans": [ + { + "bbox": [ + 305, + 636, + 547, + 681 + ], + "type": "text", + "content": "Figure 4. Visualisation of SpiderCurves on various types of 3D shapes including humanoid shapes and animals. We can see that our SpiderCurves cover the whole surface and thus pose a faithful discretisation of the respective 3D shape." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14546" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 68, + 160, + 242 + ], + "blocks": [ + { + "bbox": [ + 47, + 68, + 160, + 242 + ], + "lines": [ + { + "bbox": [ + 47, + 68, + 160, + 242 + ], + "spans": [ + { + "bbox": [ + 47, + 68, + 160, + 242 + ], + "type": "image", + "image_path": "abb3e88249b6a4c17a985fb46c4f3c9fd7dbf62dbb4766676d4db3f154e8230e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "lines": [ + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": "Figure 5. Illustration of our four constraints. (Left) The sum of all " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": " that involve edges connecting two layers (e.g. the set of red or blue edges) should be equal to one, so that the cyclic path " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "x^{\\star}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": " goes through all layers. (Middle-Left) The sum of all incoming edges (blue) of a product vertex (yellow) must be equal to the sum of all outgoing edges (red). This ensures that the path is continuous. (Middle-Right) Coupling of layers ensures that self-intersections of " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": " are preserved on " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": " under the matching. Coupling can be implemented by ensuring that the sum of outgoing edges (blue) of a product vertex on the bottom layer is equal to the sum of outgoing edges for a product vertex on the top layer (for corresponding vertices across layers, see yellow line). (Right) Self-intersections (other than the ones present in " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": ", see Middle-Right) can be avoided by allowing the cyclic path to only visit each vertex on " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": " once, i.e. the sum of outgoing product edges (red) must be less than or equal 1 (this does not include vertical inter-layer product edges, i.e. product edges that do not leave the vertex on " + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 253, + 547, + 342 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 169, + 68, + 282, + 242 + ], + "blocks": [ + { + "bbox": [ + 169, + 68, + 282, + 242 + ], + "lines": [ + { + "bbox": [ + 169, + 68, + 282, + 242 + ], + "spans": [ + { + "bbox": [ + 169, + 68, + 282, + 242 + ], + "type": "image", + "image_path": "169996bf22bd3398b38e366ee4a42a1d155455116ff0e1ed620413c8c086abb7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 301, + 68, + 417, + 242 + ], + "blocks": [ + { + "bbox": [ + 301, + 68, + 417, + 242 + ], + "lines": [ + { + "bbox": [ + 301, + 68, + 417, + 242 + ], + "spans": [ + { + "bbox": [ + 301, + 68, + 417, + 242 + ], + "type": "image", + "image_path": "a564660ee0ca7373817dbe0d22bd29d1aa145315fa2a95f672ee30eed94b447d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 427, + 68, + 539, + 242 + ], + "blocks": [ + { + "bbox": [ + 427, + 68, + 539, + 242 + ], + "lines": [ + { + "bbox": [ + 427, + 68, + 539, + 242 + ], + "spans": [ + { + "bbox": [ + 427, + 68, + 539, + 242 + ], + "type": "image", + "image_path": "b45754f3c9d4b34f19210536d7922509c024f7ebf81eb01340f9812416ea6107.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 362, + 269, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 362, + 269, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 362, + 269, + 376 + ], + "type": "text", + "content": "4.2. Our SpiderMatch Integer Linear Program" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "content": "For finding a globally optimal matching, we construct the product graph " + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "content": " of the SpiderCurve " + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "content": " (a cyclic chain graph) and the 3D target shape " + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "content": ". Then, we find a cyclic shortest path in " + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "content": " in such way that the path goes through each layer of " + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 384, + 287, + 468 + ], + "type": "text", + "content": " (cf. Fig. 2). In addition, we impose additional constraints that ensure geometric consistency in multiple directions along the shape surface." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": "Contrary to [37, 56] that find shortest paths based on (a variant of) Dijkstra's algorithm, we formulate our optimisation problem as an ILP, so that we can directly integrate additional constraints. Most importantly, we impose that (i) self-intersections in " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " are preserved under the matching, and that (ii) additional self-intersections are avoided. To formulate our optimisation problem, we introduce for each edge " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "e_i \\in E^{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " in the product graph " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " a binary indicator variable " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "x_i \\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": ". The value " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "x_i = 1" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " means that product edge " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " is part of our matching path, and " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "x_i = 0" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " means that " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "e_i" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " is not contained in the matching. Our overall objective is to find the optimal matching " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "x^\\star" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " in the space of geometrically consistent matchings (to be defined in the following paragraphs) that minimises matching costs. We note that a product edge " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "e_i = (v_k, v_l) \\in E^{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " consists of two product vertices " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "v_k, v_l \\in V^{\\mathcal{P}}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": ", where each product vertex consists of a vertex " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{C}} \\in V^{\\mathcal{C}}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " of the cyclic path " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " and a vertex " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": " of 3D surface shape " + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 471, + 288, + 687 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 715 + ], + "type": "text", + "content": "In the following we introduce the constraints of our ILP that define the space of geometrically consistent matchings." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 363, + 491, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 363, + 491, + 374 + ], + "spans": [ + { + "bbox": [ + 306, + 363, + 491, + 374 + ], + "type": "text", + "content": "We visualise all types of constraints in Fig. 5." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "text", + "content": "Cyclic Path. We want to ensure that every vertex of " + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "text", + "content": " is matched at least once, i.e. the optimal cyclic path " + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "inline_equation", + "content": "x^{\\star}" + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "text", + "content": " goes through all layers. This can be achieved by ensuring that the sum over all " + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 375, + 545, + 435 + ], + "type": "text", + "content": " between any pair of adjacent layers (cf. Fig. 5 left) is equal to one. Formally, this is expressed as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 322, + 443, + 545, + 484 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 443, + 545, + 484 + ], + "spans": [ + { + "bbox": [ + 322, + 443, + 545, + 484 + ], + "type": "interline_equation", + "content": "\\forall \\left(v _ {1} ^ {\\mathcal {C}}, v _ {2} ^ {\\mathcal {C}}\\right) \\in E ^ {\\mathcal {C}}: \\sum_ {i: e _ {i} = \\left(\\left(v _ {1} ^ {\\mathcal {C}}, \\bullet\\right), \\left(v _ {2} ^ {\\mathcal {C}}, \\bullet\\right)\\right) \\in E ^ {\\mathcal {P}}} x _ {i} = 1.", + "image_path": "3e1f0d27fd68efbaef58e41645558ccfae05c605f39630abd2ffd2fe9ca684cb.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": "Path Continuity. Furthermore, we have to ensure that every product vertex " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "v_{l} \\in V^{\\mathcal{P}}" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": " with an active " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "(x_{i} = 1)" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": " incoming product edge " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "e_{i} = (v_{k}, v_{l})" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": " also has an active " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "(x_{j} = 1)" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": " outgoing product edge " + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "inline_equation", + "content": "e_{j} = (v_{l}, v_{m})" + }, + { + "bbox": [ + 304, + 484, + 545, + 555 + ], + "type": "text", + "content": ", i.e. the path must be continuous (cf. Fig. 5 middle-left). This property can be formalised as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 563, + 545, + 601 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 563, + 545, + 601 + ], + "spans": [ + { + "bbox": [ + 321, + 563, + 545, + 601 + ], + "type": "interline_equation", + "content": "\\forall v _ {l} \\in V ^ {\\mathcal {P}}: \\sum_ {i: e _ {i} = (\\bullet , v _ {l}) \\in E ^ {\\mathcal {P}}} x _ {i} = \\sum_ {j: e _ {j} = (v _ {l}, \\bullet) \\in E ^ {\\mathcal {P}}} x _ {j}. \\tag {CON}", + "image_path": "76a0abd1a515c50b8545b8a37752a4f092b2dcf4909e1b4e7ffc420c65501f6e.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "text", + "content": "Preservation of Existing Self-Intersections. To ensure geometric consistency, i.e. neighbourhoods between shape elements" + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "text", + "content": " are preserved by the matching, every self-intersection of the SpiderCurve " + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "text", + "content": " must result in a self-intersection that involves the same vertices when " + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "text", + "content": " is matched to " + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 601, + 545, + 686 + ], + "type": "text", + "content": ". We can ensure this by incorporating coupling constraints between product vertices that involve self" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 713 + ], + "type": "text", + "content": "2In our formalism we can interpret polygons that are formed by our SpiderCurve as shape elements." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14547" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "intersections. To be precise, we couple those product vertices " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "v_{p}^{\\mathcal{C}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "v_{q}^{\\mathcal{C}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " on (different) layers " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " that belong to the same vertex " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{V}}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " (cf. Fig. 5 middle-right). Formally, this can be written as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 62, + 129, + 287, + 185 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 62, + 129, + 287, + 185 + ], + "spans": [ + { + "bbox": [ + 62, + 129, + 287, + 185 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\forall v _ {p} ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}}, v _ {q} ^ {\\mathcal {C}} \\in V ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}}, p \\neq q, v _ {p} ^ {\\mathcal {C}} = v _ {q} ^ {\\mathcal {C}}: \\\\ \\sum_ {i: e _ {i} = \\left(\\left(v _ {p} ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}}\\right), \\bullet\\right) \\in E ^ {\\mathcal {P}}} x _ {i} = \\sum_ {j: e _ {j} = \\left(\\left(v _ {q} ^ {\\mathcal {C}}, v ^ {\\mathcal {Y}}\\right), \\bullet\\right) \\in E ^ {\\mathcal {P}}} x _ {j}. \\tag {PES} \\\\ \\end{array}", + "image_path": "c7905ec09edbd4f9d52e53d23edea2a49a9bf91029f6d103c56a8b094a73e926.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": "Avoidance of New Self-Intersections. Lastly, we forbid that new self-intersections are introduced by the matching. This can be ensured by constraining the matching path in such a way that every vertex " + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": " can only be visited at most once. In other words, the sum (across all layers) over all outgoing edges of product vertices that contain a given " + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": " must be smaller than or equal to one. In this constraint, we do not sum over inter-layer edges whose source and target product vertex contain the same vertex " + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": " (since these edges can be interpreted as 'staying' in the same vertex " + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "inline_equation", + "content": "v^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 186, + 287, + 330 + ], + "type": "text", + "content": "). The respective constraints are explained in Fig. 5 right. Mathematically, they read" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 50, + 340, + 286, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 50, + 340, + 286, + 379 + ], + "spans": [ + { + "bbox": [ + 50, + 340, + 286, + 379 + ], + "type": "interline_equation", + "content": "\\forall v _ {k} ^ {\\mathcal {Y}}, v _ {l} ^ {\\mathcal {Y}} \\in V ^ {\\mathcal {Y}}, v _ {k} ^ {\\mathcal {Y}} \\neq v _ {l} ^ {\\mathcal {Y}}: \\sum_ {i: e _ {i} = \\left(\\left(v _ {k} ^ {\\mathcal {C}}, v _ {k} ^ {\\mathcal {Y}}\\right), \\left(v _ {l} ^ {\\mathcal {C}}, v _ {l} ^ {\\mathcal {Y}}\\right)\\right) \\in E ^ {\\mathcal {P}}} x _ {i} \\leq 1 \\tag {ANS}", + "image_path": "d7e01f53cfc6e55b0c3f2abd34d4f0631f36970a682d6984a35ce92657220ccf.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "inline_equation", + "content": "v_{k}^{\\mathcal{C}}, v_{l}^{\\mathcal{C}} \\in V^{\\mathcal{C}}" + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "content": ". Note that the sum will not include product vertices on layers which belong to coupling constraints, i.e. whenever " + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "inline_equation", + "content": "v_{k}^{\\mathcal{C}}" + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "inline_equation", + "content": "v_{l}^{\\mathcal{C}}" + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "content": " belong to a self-intersection of " + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "inline_equation", + "content": "\\mathcal{C}" + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "content": " we do not include respective product edge " + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "inline_equation", + "content": "e_{i}" + }, + { + "bbox": [ + 47, + 380, + 287, + 427 + ], + "type": "text", + "content": " in the sum." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "text", + "content": "Matching Costs. We consider a cost vector " + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}^{|E^{\\mathcal{P}}|}" + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "text", + "content": " based on vertex-wise 3D shape features " + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "inline_equation", + "content": "F^{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "inline_equation", + "content": "F^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "text", + "content": ". The entry at the " + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 429, + 287, + 466 + ], + "type": "text", + "content": "-th position is given by" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 73, + 475, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 475, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 73, + 475, + 287, + 491 + ], + "type": "interline_equation", + "content": "c _ {i} = c \\left(e _ {i}\\right) = \\Psi \\left(F _ {p} ^ {\\mathcal {X}} - F _ {r} ^ {\\mathcal {Y}}\\right) + \\Psi \\left(F _ {q} ^ {\\mathcal {X}} - F _ {s} ^ {\\mathcal {Y}}\\right), \\tag {2}", + "image_path": "aa44b4f01f01ed7255036a2f344a3bbc5c1eb1983c5d11b14e1eea8148f1ce06.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "inline_equation", + "content": "e_i = ((v_p^{\\mathcal{X}}, v_r^{\\mathcal{Y}}), (v_q^{\\mathcal{X}}, v_s^{\\mathcal{Y}}))" + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "inline_equation", + "content": "v_p^{\\mathcal{X}}, v_q^{\\mathcal{X}} \\in V^{\\mathcal{C}}" + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "inline_equation", + "content": "v_r^{\\mathcal{Y}}, v_s^{\\mathcal{Y}} \\in V^{\\mathcal{Y}}" + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "text", + "content": ". Furthermore, " + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\Psi(\\cdot)" + }, + { + "bbox": [ + 47, + 501, + 287, + 539 + ], + "type": "text", + "content": " is the robust loss function presented in [8]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 540, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 575 + ], + "type": "text", + "content": "Our SpiderMatch ILP. Putting our cost function and constraints together yields our final 3D shape matching formalism:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 53, + 586, + 287, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 586, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 53, + 586, + 287, + 609 + ], + "type": "interline_equation", + "content": "\\min _ {x \\in \\{0, 1 \\} ^ {| E ^ {\\mathcal {P}} |}} c ^ {T} x \\text {s . t (C Y C), (C O N), (P E S), (A N S).} \\tag {3}", + "image_path": "cb19969c99ec59752643f87e99054c8a4c3e69f67d650dfe5c374d70cf5d084c.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "text", + "content": "Essentially, Problem (3) can be seen as a cyclic shortest path problem (over product edges encoded in " + }, + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 619, + 287, + 654 + ], + "type": "text", + "content": ", cf. Sec. 4.2) that involves the additional constraints (PES), (ANS)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 127, + 681 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "In this section we evaluate the performance of our method. First, we explain the considered evaluation metric and the" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "competing methods. Subsequently, we evaluate the non-rigid shape matching performance of our method and compare it to other approaches. We conclude this section with ablation studies." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "text", + "content": "We solve Problem (3) with the off-the-shelf ILP solver Gurobi [29] (Version 10.0.3) on an Intel Core i9 12900K with 64 GB DDR5 RAM. We decimate all shapes to 1000 triangles using the mesh decimation algorithm provided in [32]. We also compute matchings for methods Cao et al. [14], Ren et al. [53], and Eisenberger et al. [22] on 1000 triangles. Only for Roetzer et al. [55] we decimate shapes to 450 triangles so that runtimes are acceptable (cf. Fig. 1 right). For our robust loss function " + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\Psi(\\cdot)" + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "text", + "content": " [8] we choose parameters " + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "inline_equation", + "content": "\\alpha = 2" + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "inline_equation", + "content": "c = 0.3" + }, + { + "bbox": [ + 304, + 123, + 545, + 289 + ], + "type": "text", + "content": " and instead of a quadratic bowl we use a cubic bowl so that small differences in features are less relevant. We empirically observe that our method can solve all instances to global optimality in less than 200s." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 307, + 414, + 319 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 307, + 414, + 319 + ], + "spans": [ + { + "bbox": [ + 306, + 307, + 414, + 319 + ], + "type": "text", + "content": "5.1. Evaluation Metric" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 328, + 545, + 413 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 545, + 413 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 545, + 413 + ], + "type": "text", + "content": "We evaluate all shape matching methods using geodesic errors. Geodesic errors allow us to measure the correctness of the resulting matching w.r.t. to a ground-truth matching, i.e. how far is the resulting matching from the ground-truth matching. We follow the Princeton protocol [35] to compute geodesic errors which are normalised by the square-root of the area of a shape (see [35, Sec. 8.2])." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 429, + 369, + 440 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 429, + 369, + 440 + ], + "spans": [ + { + "bbox": [ + 306, + 429, + 369, + 440 + ], + "type": "text", + "content": "5.2. Methods" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 450, + 498, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 450, + 498, + 461 + ], + "spans": [ + { + "bbox": [ + 306, + 450, + 498, + 461 + ], + "type": "text", + "content": "We compare our method to four other methods:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 465, + 545, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 465, + 545, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 465, + 545, + 572 + ], + "type": "text", + "content": "Cao et al. [14] is a recent functional map-based deep learning method which achieves state of the art performance by coupling functional maps with point maps during learning. We use this method as our feature extractor and thus consider it as our baseline. Moreover, the extensive evaluation in [14] confirms that it is indeed the state-of-the-art learning-based approach, so that we consider it as a representative for the broad body of learning-based shape matching methods." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 575, + 545, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 575, + 545, + 611 + ], + "spans": [ + { + "bbox": [ + 304, + 575, + 545, + 611 + ], + "type": "text", + "content": "Ren et al. [53] is a functional map-based method which associates a functional map with a point wise map as a hard constraint." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 614, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 614, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 614, + 545, + 662 + ], + "type": "text", + "content": "Eisenberger et al. [22] is a functional map-based iterative alignment scheme of shapes, which incrementally refines the geometrical information used to perform the matching." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "Roetzer et al. [55] implements a combinatorial solver to solve a triangle-matching based ILP presented in [77]. This is the only competing approach that guarantees geometric consistency." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14548" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 68, + 542, + 378 + ], + "blocks": [ + { + "bbox": [ + 52, + 68, + 542, + 378 + ], + "lines": [ + { + "bbox": [ + 52, + 68, + 542, + 378 + ], + "spans": [ + { + "bbox": [ + 52, + 68, + 542, + 378 + ], + "type": "image", + "image_path": "6771b8c6690b308ee8620ca0ccfa28e3ecd3033950d23c631d2478352927f346.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "lines": [ + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": "Figure 6. Qualitative Results on the datasets FAUST, SMAL, DT4D-H (intra class and inter class). The state-of-the-art learning based method by Cao et al. produces matches with local geometric inconsistencies (cf. columns " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "③" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "⑨" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": "). Ren et al. yields visually the worst results due to large mismatches (cf. columns " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "④" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "⑩" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": "). Obvious large mismatches are not produced by Eisenberger et al., which however produces left-right flips (cf. columns " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "②" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "⑧" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": ") as well as local mismatches (cf. column " + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "inline_equation", + "content": "⑩" + }, + { + "bbox": [ + 46, + 388, + 548, + 445 + ], + "type": "text", + "content": "). Due to the geometric consistency of our method we produce smooth matchings for all shapes. Note that we show the lower-resolution matchings of Roetzer et al. in the appendix." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 464, + 198, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 198, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 198, + 478 + ], + "type": "text", + "content": "5.3. Non-Rigid Shape Matching" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 484, + 288, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 591 + ], + "type": "text", + "content": "In this section we evaluate our method on three different datasets: FAUST [11, 18, 52], SMAL [80], DT4D-H [45] (in intraclass and interclass settings). We show qualitative results in Fig. 6. We can see that our geometrically consistent formalism yields better matchings than Cao et al., since our approach does not produce local mismatches. Furthermore, we observe severe mismatches and geometric inconsistencies in the matchings by Eisenberger et al. and Ren et al." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "FAUST. We test on the (more challenging) remeshed version [18, 52] of the FAUST dataset [11]. The dataset consists of 100 near-isometric human shapes (we randomly sample 100 pairs from the test set). In Fig. 7 left, we show geodesic errors on FAUST. Our geometrically consistent approach helps to resolve local missmatches (cf. Fig. 6) which yields improved geodesic error scores compared to Cao et al. The method by Ren et al. results in left-right flips due to intrinsic symmetries of human shapes of FAUST, which increases geodesic errors drastically." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 304, + 457, + 550, + 549 + ], + "blocks": [ + { + "bbox": [ + 304, + 457, + 550, + 549 + ], + "lines": [ + { + "bbox": [ + 304, + 457, + 550, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 457, + 550, + 549 + ], + "type": "image", + "image_path": "e2f52475df6d846b3d11175b2686347abab68b9d9e81b102f23683f917458564.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 558, + 547, + 592 + ], + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 592 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 592 + ], + "type": "text", + "content": "Figure 7. Geodesic errors on FAUST and SMAL datasets. Numbers in the legends are mean geodesic errors " + }, + { + "bbox": [ + 304, + 558, + 547, + 592 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 304, + 558, + 547, + 592 + ], + "type": "text", + "content": ". Our method yields best results w.r.t. to mean geodesic errors on both datasets." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 605, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 712 + ], + "type": "text", + "content": "SMAL. Next, we evaluate on the remeshed version of the SMAL dataset [80]. This dataset consists of 49 nonisometric deformed animal shapes of eight species (we randomly sample 100 pairs from the test set). In Fig. 7 right, we show geodesic errors on SMAL. Again, ours is the best among all methods. For this dataset, shapes are unaligned, which harms the performance of Eisenberger et al. since it has to heuristically find a pre-alignment necessary for the method." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "14549" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 45, + 70, + 292, + 162 + ], + "blocks": [ + { + "bbox": [ + 45, + 70, + 292, + 162 + ], + "lines": [ + { + "bbox": [ + 45, + 70, + 292, + 162 + ], + "spans": [ + { + "bbox": [ + 45, + 70, + 292, + 162 + ], + "type": "image", + "image_path": "9d3426b320645db08636a490833cbc2b8a02a758537d29c29779eaaf7d0fa467.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "lines": [ + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "text", + "content": "Figure 8. Geodesic errors on DT4D-H dataset in the intra-class and inter-class setting. Numbers in the legends are mean geodesic errors " + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "inline_equation", + "content": "(\\downarrow)" + }, + { + "bbox": [ + 46, + 171, + 287, + 226 + ], + "type": "text", + "content": ". In the intra-class settings our method produces best results among all competitors. In the inter-class setting ours is on par with Cao et al." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 235, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 287, + 402 + ], + "type": "text", + "content": "DT4D-H. Finally, we test on DT4D-H [45], which consist of 9 different classes of humanoid/game character shapes in different poses. These shapes are taken from DeformingThings 4D [41]. We sample 100 random intra-class pairs, i.e. near-isometric deformed shape pairs. We also sample 100 random inter-class pairs, i.e. non-isometric deformed shape pairs. In Fig. 8, we show geodesic errors for both settings. In the intra-class setting our method outperforms all methods. For inter-class shapes our method is on par with Cao et al. The method by Eisenberger et al. suffers from the unaligned shapes in both settings, while Ren et al. produces a significant amount of left-right flips. In Sec. 8 in the supp. material we provide additional geometric consistency comparisons among the methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 409, + 115, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 409, + 115, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 409, + 115, + 420 + ], + "type": "text", + "content": "5.4. Ablations" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "content": "In Tab. 3, we summarise results of our ablation study. For that, we sample 25 random pairs of the FAUST dataset, downsample them to 500 triangles and compute matchings in the different settings reported in Tab. 3. We can see that constraints (PES), (ANS), and the robust loss function " + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "inline_equation", + "content": "\\Psi(\\cdot)" + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "content": " contribute to the performance of our method. We also replace " + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "inline_equation", + "content": "F^{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "inline_equation", + "content": "F^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "content": " with wave kernel signatures (WKS) features [7] and compare this setting to our method where we extract " + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "inline_equation", + "content": "F^{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "inline_equation", + "content": "F^{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 427, + 287, + 547 + ], + "type": "text", + "content": " with [14]. In Sec. 11 in the supp. material we study our method under different resolutions." + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 85, + 555, + 248, + 645 + ], + "blocks": [ + { + "bbox": [ + 85, + 555, + 248, + 645 + ], + "lines": [ + { + "bbox": [ + 85, + 555, + 248, + 645 + ], + "spans": [ + { + "bbox": [ + 85, + 555, + 248, + 645 + ], + "type": "table", + "html": "
MethodMean Geo. Err.
Ours w/o (PES), (ANS)0.036
Ours w/o (ANS)0.035
Ours w/o (PES)0.035
Ours with Ψ = ||·||20.036
Ours with WKS features0.213
Ours0.034
", + "image_path": "7e0d09a4b166e2b067623e6ad6fa103e7b9500cffa321a01b04f532e8c8528e1.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 91, + 651, + 242, + 661 + ], + "lines": [ + { + "bbox": [ + 91, + 651, + 242, + 661 + ], + "spans": [ + { + "bbox": [ + 91, + 651, + 242, + 661 + ], + "type": "text", + "content": "Table 3. Ablation studies of our method." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 670, + 201, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 201, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 201, + 681 + ], + "type": "text", + "content": "6. Discussion and Limitations" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Time complexity. We have introduced the first geometrically consistent and globally optimal method for 3D shape" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": "matching. Our problem instances involve up to " + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "inline_equation", + "content": "2 \\cdot 10^{6}" + }, + { + "bbox": [ + 304, + 72, + 545, + 251 + ], + "type": "text", + "content": " binary variables. Nevertheless, we experimentally demonstrate that we can find globally optimal solutions in all considered matching instances within about 100s, which indicates that our search space has a benign structure (likely stemming from the underlying shortest path-based motivation) that can effectively be exploited by off-the-shelf ILP solvers. Still, our proposed formalism belongs to the (generally difficult) class of integer programming problems. We observe that our constraints do not lead to a totally unimodular matrix, so that in general we may have exponential worst-case runtime. We leave a theoretical analysis of the time complexity of our proposed approach, and the question whether there may exist polynomial time algorithms that solves our problem (or related variants) for future work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 254, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 545, + 361 + ], + "type": "text", + "content": "SpiderCurve extraction. The focus of this work was on presenting a novel framework that generalises path-based shape matching formalisms for 3D shape matching. Although our TSP-based SpiderCurve extraction leads to promising matchings in all conducted experiments, we believe that there may be potential using alternative curve-based shape discretisations. An in-depth analysis and comparison of different approaches was not our main focus and is an interesting direction for follow-up works." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 363, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 434 + ], + "type": "text", + "content": "Feasibility. In theory, our SpiderMatch ILP (3) might be infeasible, which may for example stem from discretisation artefacts in low-resolution settings. Yet, our method is able to operate on (relatively) high resolution shapes so that we expect these cases to be rare (we found all of the 400 instances considered in our experiments to be feasible)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 452, + 378, + 464 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 378, + 464 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 378, + 464 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 713 + ], + "type": "text", + "content": "We present a fresh view on geometrically consistent 3D shape matching. Our key insight is to discretise one of the shapes using a SpiderCurve, i.e. a long self-intersecting curve that traces the 3D shape surface. This allows us to utilise ideas and concepts from shortest path-based formalisms that have so far not been applicable to the matching of 3D shapes. More specifically, our work is motivated by the recent shortest path-based curve to 3D shape matching formalism by Lähner et al. [37], which we augment with additional self-intersection constraints that allows us to ensure geometric consistency in multiple directions along the shape surface. Experimentally we showcase the great potential of our novel approach, which on the one hand leads us to state-of-the-art shape matching performance. Furthermore, at the same time we achieve both geometric consistency and global optimality – the latter two properties are highly desirable but have so far not been reached by any previous 3D shape matching method. Overall, we believe that our approach may be insightful and may inspire follow-up works in geometrically consistent shape matching and beyond." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14550" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 286, + 113 + ], + "type": "text", + "content": "[1] Noam Aigerman and Yaron Lipman. 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In CVPR, 2017. 7" + } + ] + } + ], + "index": 17 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14553" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_content_list.json b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6d8fbf7167d94011e60eabca5bf26570019c981f --- /dev/null +++ b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_content_list.json @@ -0,0 +1,1616 @@ +[ + { + "type": "text", + "text": "Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment", + "text_level": 1, + "bbox": [ + 125, + 128, + 843, + 175 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Jiyuan Zhang $^{1,2}$ Shiyan Chen $^{1,2}$ Yajing Zheng $^{1,2*}$ Zhaofei Yu $^{1,2,3*}$ Tiejun Huang $^{1,2,3}$ $^{1}$ School of Computer Science, Peking University \n $^{2}$ National Key Laboratory for Multimedia Information Processing, Peking University \n $^{3}$ Institute for Artificial Intelligence, Peking University", + "bbox": [ + 148, + 200, + 815, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{jyzhang,2301112005}@stu.pku.edu.cn，{yj.zheng,yuzf12,tjhuang}@pku.edu.cn", + "bbox": [ + 158, + 276, + 800, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 312, + 342 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The traditional frame-based cameras that rely on exposure windows for imaging experience motion blur in high-speed scenarios. Frame-based deblurring methods lack reliable motion cues to restore sharp images under extreme blur conditions. The spike camera is a novel neuromorphic visual sensor that outputs spike streams with ultra-high temporal resolution. It can supplement the temporal information lost in traditional cameras and guide motion deblurring. However, in real-world scenarios, aligning discrete RGB images and continuous spike streams along both temporal and spatial axes is challenging due to the complexity of calibrating their coordinates, device displacements in vibrations, and time deviations. Misalignment of pixels leads to severe degradation of deblurring. We introduce the first framework for spike-guided motion deblurring without knowing the spatiotemporal alignment between spikes and images. To address the problem, we first propose a novel three-stage network containing a basic deblurring net, a carefully designed bi-directional deformable aligning module, and a flow-based multi-scale fusion net. Experimental results demonstrate that our approach can effectively guide the image deblurring with unknown alignment, surpassing the performance of other methods. Public project page: https://github.com/Leozhangjiyuan/UaSDN.", + "bbox": [ + 75, + 358, + 473, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 747, + 207, + 762 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The imaging principle of conventional frame-based cameras is based on the concept of exposure time windows. During the continuous imaging process, the time between the exposure windows of adjacent frames is unused. Due to the presence of exposure windows, when the camera is in high-speed motion or there are fast-moving objects in the scene, images may exhibit a blur effect. In recent years,", + "bbox": [ + 75, + 773, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d51f39e9240c9aa03129b66e16311207bc850af1594954d465bdb9f312a4a7a0.jpg", + "image_caption": [ + "Figure 1. Illustration of unknown spatiotemporal alignment between a spike camera and an RGB camera." + ], + "image_footnote": [], + "bbox": [ + 511, + 325, + 880, + 542 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "many studies have focused on addressing the challenging task of recovering clear images from blurry ones utilizing deep-learning routes [4, 5, 16]. However, the texture or structural information in blurry images is partially lost during the exposure, making it difficult to infer clear textures directly from blurry images, as in Fig. 2 (Orange Box).", + "bbox": [ + 496, + 611, + 890, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Introducing spike cameras as clues of deblurring. Bioinspired neuromorphic vision sensors have attracted increasing attention and achieved significant development. They possess advantages such as ultra-high temporal resolution, low latency, and high dynamic range. Due to the continuous recording of light intensity, neuromorphic cameras can be used to compensate for the lack of temporal information in image deblurring. Based on different sampling principles, they can be classified into event cameras [1, 21, 23] and spike cameras [12]. Event cameras asynchronously detect changes in light intensity and are highly sensitive to moving edges. Studies utilize events for image deblurring [28, 32]. Spike cameras accumulates", + "bbox": [ + 496, + 704, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 1, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 887, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "25047", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "photons and emits $20,000\\mathrm{Hz}$ spike streams. Due to the integration sampling principle, it can thoroughly record spatiotemporal information, including the texture and motion information of the scene. The precise texture information recorded in spikes can effectively guide the deblurring process. Our paper explores the effectiveness of using spike cameras to guide motion deblurring, uncovering the potential advantages of spike cameras in this novel task.", + "bbox": [ + 75, + 90, + 472, + 210 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Take misalignment between cameras in real application into consideration. At present, most deblurring works based on event cameras assume that the imaging planes of the two cameras are absolutely coaxial [32, 33] and that the event stream and video are fully synchronized on the time axis. Such assumptions facilitate model design but are overly idealistic. In the real world, achieving strict alignment of a spike camera and an RGB camera in both spatial and temporal dimensions is quite challenging. As shown in Fig. 1, in this work, we consider the unknown alignment factors in the real world:", + "bbox": [ + 75, + 214, + 472, + 378 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(A) Spatial alignment of the two cameras is challenging. Alignment of the coordinate systems of the two cameras can be achieved using methods such as beam splitters or manual calibration (e.g., chessboard calibration). However, beam splitters can result in significant loss of light, and differences in focal length, aperture, and relative positions between cameras, which can vary with the scene, make alignment operations complex and difficult.", + "(B) Position displacements. During motion, minor displacements in the relative positions of the two cameras occur due to vibrations. For current algorithms, pixel misalignment will lead to significant performance losses.", + "(C) Synchronizing discrete image sequences with continuous spike streams on the time axis is challenging. Technically, obtaining spikes strictly synchronized with blurry images requires acquiring the accurate exposure start and end times of the blurry images, which is complex. Moreover, in high-speed motion scenes, the two data streams are prone to small time deviations, leading to misalignment." + ], + "bbox": [ + 75, + 381, + 472, + 674 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "What we focus on and How we deal with the real-world misalignment? In response to the real-world misalignments mentioned above, we focus on investigating spike-guided motion deblurring with unknown spatiotemporal alignment between spikes and RGB images, as shown in Figs. 1 and 2. The proposed method allows for the use of two cameras simultaneously without the need for complex and rigorous spatial calibration and time alignment design. To address the problem, we propose an effective three-stage model Unaligned Spike-guided Deblur Net (UaSDN). (1) In the first stage, we employ a simplified off-the-shelf network to perform basic deblurring. In this stage, we aim to leverage existing technology to alleviate the blurring and enhance textures. (2) In the second stage, we first use a shallow net to estimate coarse light intensity", + "bbox": [ + 75, + 674, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "from the spike stream. Besides, we design a bidirectional deformable modal alignment module. The module achieves better alignment by learning bidirectional deformable convolutions between spike features and image features. (3) In the third stage, we design a multi-scale dense fusion network combining the optical flow, which performs feature fusion by aligning pixel motion offsets between modalities and fuse features in a multi-scale network. Through comparisons with various networks, experimental results demonstrate the effectiveness of our method in motion deblurring with unknown spatiotemporal alignment between modalities. To comprehensively validate the model's performance, we construct spike datasets for training and validation. Our contributions can be summarized as follows:", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We first explore the motion deblurring tasks guided by the spike camera and deal with the unknown spatiotemporal alignment between two modalities in the real world.", + "- We propose the three-stage UaSDN model which contains a bi-directional deformable modal alignment module and a flow-based fusion module.", + "- Experimental results demonstrate that our model significantly outperforms other methods on motion deblurring with unknown spatiotemporal alignment." + ], + "bbox": [ + 500, + 305, + 890, + 441 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 455, + 640, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Advances on Spike Cameras", + "text_level": 1, + "bbox": [ + 500, + 482, + 754, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The spike camera outputs spikes with an ultra-high temporal resolution of $20,000\\mathrm{Hz}$ [12]. Due to the sampling principle, it effectively captures texture in both moving and stationary areas, demonstrating potential in high-speed scenarios. Research focuses on utilizing spike cameras for image recovery or high-level visual tasks. Early studies involved direct statistics of spike counts or intervals for a rough estimation of light intensity [57]. Zhao et al. [52] introduces the first learning-based method. Zhang et al. [47] leverages wavelet transforms on spikes, and enhances the representational capability of spikes. Some bio-inspired works employ spiking neural networks (SNN) [53, 55] to process spikes. The introduction of self-supervised schemes enhanced the generalization capability [6]. Many applications have emerged, such as super-resolution reconstruction [51] and high-dynamic-range restoration [3], spike-guided video interpolation [41], denoising [11] and tracking [54].", + "bbox": [ + 496, + 505, + 893, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Frame-based Motion Deblurring", + "text_level": 1, + "bbox": [ + 500, + 771, + 790, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, with the rise of deep learning, CNN-based approaches have shown remarkable performance in frame-based deblurring tasks. Popular technical routes are employing end-to-end training [4, 9, 16, 24, 34, 44]. Some works [17, 18] employ generative networks. Rather than mapping a blurry image one-to-one to a single sharp image, some work [2, 13, 26, 27, 31, 38, 56, 58] attempts to mine", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "25048", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5026fa3bfb4b6f1e9d404ea6ada1e8bd767f5192d5d0cf50770a99f3a47a8ad3.jpg", + "image_caption": [ + "Figure 2. Illustration of the process of deblurring images in different scenarios. Orange box: deblurring directly from the RGB camera; blue box: deblurring with precise alignment of spike-RGB data; green box: unknown alignment in X-Y-T for spike-RGB data." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 478, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/3e65ce3b8687fecd8da5e90d1e017904701699a8bc076308a15ecbe776ea1e9d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 870, + 281 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "clues from video sequence input to assist in deblurring. However, video-based methods always use future frames, which is not applicable in the real world. Besides, many image-based image restoration models are able to deal with deblurring [4, 5, 19, 20, 39, 43-45].", + "bbox": [ + 75, + 348, + 468, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Event-guided Motion Deblurring", + "text_level": 1, + "bbox": [ + 76, + 434, + 367, + 450 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As neuromorphic vision sensors, event cameras have been used in deblurring. Pan et al. [28] builds a computational model between blurred images and events. Several works [14, 36] utilize motion information and recurrent networks for aligning. Shang et al. [29] enhances the deblurring by finding adjacent sharp frames. Kim et al. [15] and Weng et al. [40] deal with images with unknown exposure time. EFNet [32] introduces an attention-based module to better fuse events. Cho et al. [8] proposed a solution for cameras with spatial offsets. Zhang et al. [49] proposes to generalize the deblurring ability to various spatial resolutions and blur levels. Some works [22, 28, 33, 37, 42, 48] combine the motion deblurring and frame interpolation guided by events. However, most studies assume that scenes captured by the event camera and the traditional camera are entirely identical, i.e. two camera coordinates coincide perfectly along the spatial axis and events have the same center and duration as the exposure time of blurred images on the temporal axis. Our study aims to address motion deblurring in real scenes unknown of the alignment between cameras in both time and space.", + "bbox": [ + 75, + 458, + 472, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 790, + 166, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Analysis", + "text_level": 1, + "bbox": [ + 76, + 815, + 248, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We mainly focus on dealing with the motion deblurring in high-speed scenarios guided by a spike camera while not knowing the alignment between the RGB camera and spike camera on both the spatial axis and temporal axis. In this", + "bbox": [ + 75, + 839, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "section, we give a specific analysis of how to utilize spike data for deturbing spatiotemporal unaligned RGB frames.", + "bbox": [ + 496, + 348, + 890, + 377 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An RGB camera outputs discrete RGB blurry frames $\\mathbb{B} = \\{\\mathbf{B}_i|i\\in \\mathbf{N}\\}$ with the exposure time of $T_{B}$ , which is a shorter duration than the time duration between successive frames $T_{F}$ (the frame rate $f = \\frac{1}{T_F}$ ). A spike camera outputs the spike stream S with the rate of $20000\\mathrm{Hz}$ . Each pixel $(x,y)$ of a spike camera on the $H_{S}\\times W_{S}$ plane independently receives coming photons continuously at any timestamps $t$ , converts the light signals into electrical current $I_{x,y}(t)$ , and accumulates the voltage $V_{x,y}$ . Whenever the voltage reaches the preset threshold $\\Theta$ , the pixel fires a spike and resets the voltage to 0. The spike signals are read out with a very short interval ( $\\tau = \\frac{1}{20000Hz} = 50\\mu s$ ). The process can be formulated as follows:", + "bbox": [ + 496, + 378, + 892, + 574 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} _ {x, y} (c) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\exists t \\in ((c - 1) \\tau , c \\tau ], V _ {x, y} (t) = 0, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 580, + 890, + 621 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nV _ {x, y} ^ {+} (t) = \\left\\{ \\begin{array}{l l} V _ {x, y} ^ {-} (t) + I _ {x, y} (t), & \\text {i f} V _ {x, y} ^ {-} (t) < \\Theta , \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 636, + 890, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $V_{x,y}^{-}(t)$ and $V_{x,y}^{+}(t)$ denotes the voltage before and after receiving the electric current $I_{x,y}(t)$ , $c \\in \\mathbb{R}$ . The spike stream $S$ is output with the size of $H \\times W \\times C$ after $C$ times readout during $T\\mu s$ ( $C = \\frac{T}{\\tau}$ ).", + "bbox": [ + 496, + 684, + 890, + 744 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a blurred image $\\mathbf{B}_i$ , it can be represented as the average of the clear images $\\{\\mathbf{L}\\}$ over the exposure time, i.e.:", + "bbox": [ + 496, + 744, + 890, + 776 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {B} _ {i} = \\frac {1}{T _ {\\mathbf {B}}} \\int_ {T _ {i} - T _ {\\mathbf {B}} / 2} ^ {T _ {i} + T _ {\\mathbf {B}} / 2} \\mathbf {L} (t) d t, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 785, + 890, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T_{i}$ is the center of exposure time and $\\mathbf{L}_i$ at $T_{i}$ .", + "bbox": [ + 500, + 825, + 846, + 840 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Why spike cameras hold potential on image deblurring. The deblurring process can be formulated as:", + "bbox": [ + 496, + 840, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {M}} {\\arg \\min } \\| \\hat {\\mathbf {L}} _ {i} - \\mathbf {L} _ {i} \\|, \\text {w h e r e} \\hat {\\mathbf {L}} _ {i} = \\mathcal {F} \\left(\\mathbf {B} _ {i}: \\theta_ {M}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 877, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "25049", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b37a1bd1be3e3eab9f2b24342c98585bfc0e45cef81855993c0d6d616b9f1e9c.jpg", + "image_caption": [ + "Figure 3. The architecture of the proposed Unaligned Spike-guided Deblur Net (UaSDN)." + ], + "image_footnote": [], + "bbox": [ + 102, + 88, + 869, + 296 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\theta$ is the optimized parameters of the model $M$ and $\\hat{\\mathbf{L}}_i$ is the predicted clear image. The $\\theta$ is hard to optimize when $\\mathbf{B}_i$ holds extreme blur. Neglecting color information and differences in spatial resolution, when the spike camera and RGB camera are perfectly aligned, the clear image $\\mathbf{L}_i$ can also be approximated using spikes:", + "bbox": [ + 75, + 345, + 468, + 436 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {L}} _ {i} \\simeq \\mathcal {F} _ {M _ {S 2 I}} \\left(\\left\\{\\mathbf {S} (t) \\mid t \\in \\left[ T _ {i} - \\frac {T _ {\\mathbf {B}}}{2}, T _ {i} + \\frac {T _ {\\mathbf {B}}}{2} \\right] \\right\\}: \\theta_ {S 2 I}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 446, + 468, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $M_{S2I}$ is the model for reconstructing spikes to the approximated image $\\tilde{\\mathbf{L}}_i$ . Many existing models [47, 52] are able to reconstruct high-quality $\\tilde{\\mathbf{L}}_i$ . Despite that $\\hat{\\mathbf{L}}_i$ lacks color information and has lower spatial resolution compared to $\\mathbf{B}_i$ , its clear texture effectively provides deblurring clues for $\\mathbf{B}_i$ as shown in Fig. 2, which is proved by our experiments in Sec. 4.5. When not knowing the alignment between the RGB camera and spike camera on both spatial and temporal axis, we cannot get the accurate spikes $\\{\\mathbf{S}(t)\\}$ in Eq. (5). Thus textures in $\\tilde{\\mathbf{L}}_i$ are not aligned with $\\mathbf{L}_i$ , which raises challenges for spikes to guide the deblurring.", + "bbox": [ + 75, + 489, + 468, + 654 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "How to deal with unknown alignment? We set the situation of the unknown alignment as follows: (1) Spatial axis. There are blind plane displacements $\\Delta \\mathbf{P}$ between two cameras. Generally, we set the $\\Delta \\mathbf{P}$ not a constant but a variable parameter. (2) Temporal axis. Spike stream is continuous while RGB frames are discrete. When two streams cannot be precisely synchronized, in real situations, we can roughly fetch a segment of spikes $\\mathbf{S}_k$ around the corresponding exposure window $T_{i}$ of image $\\mathbf{B}_i$ . The temporal center of $\\mathbf{S}_k$ is unknown. In this case, we aim to build the model learning the aligning process adaptively.", + "bbox": [ + 75, + 655, + 468, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Overall Architecture", + "text_level": 1, + "bbox": [ + 76, + 830, + 272, + 845 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For not knowing the alignment, accurately matching the textures between the blurred image and spikes is challenging, requiring the model to have the ability for adaptive", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "feature matching. However, on one hand, the texture of the blurred image $\\mathbf{B}$ suffers from significant information loss. On the other hand, the irregular spike data cannot directly express scene textures like images. Therefore, we aim to progressively optimize the motion deblurring, gradually restoring clear textures of the blurred image and spikes. To achieve this, we propose a three-stage model named Unaligned Spike-guided Deblur Net (UaSDN). The network architecture of UaSDN is illustrated in Fig. 3.", + "bbox": [ + 496, + 345, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "UaSDN consists of three deblurring stages. (1) First Stage: Basic Image Deblurring Unclear texture in blurred images $\\mathbf{B}$ makes it difficult to match with features in spikes. We employ a simple network $M_{1}$ to learn basic deblurring for $\\mathbf{B}$ . The network takes the blurred image $\\mathbf{B}$ as input and outputs the predicted image $\\hat{\\mathbf{L}}_{1}$ (2) Second Stage: Bi-Deformable Aligning Enhancement. The texture of $\\mathbf{B}$ is enhanced after the stage 1. In this stage, we design a module $M_{2}$ based on deformable convolution to achieve basic alignment between spike features and blurred image features. Besides, to restore scene textures in spikes, we use shallow convolutional layers $M_{S2I}$ to input spikes and quickly infer the rough light intensity. We randomly sample $K$ segments of spikes $\\{\\mathbf{S}_k|k\\in [1,2,\\dots K]\\}$ as guidance input to $M_{2}$ , which outputs the enhanced image $\\hat{\\mathbf{L}}_{2}$ . (3) Third Stage: Flow-guided Dense Fusion. In this stage, we aim to utilize optical flows $v_{S2I}$ from spikes $\\mathbf{S}$ to the image $\\hat{\\mathbf{L}}_{2}$ as guidance for precise alignment. To achieve this, we design the multi-scale flow-guided deblurring module, which takes the sampled $K$ spike segments as input and predicts the final clear image $\\hat{\\mathbf{L}}_{3}$ . The process can be formulated as:", + "bbox": [ + 496, + 481, + 892, + 800 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {L}} _ {1} = \\mathcal {F} _ {M _ {1}} \\left(\\mathbf {B}: \\theta_ {M _ {1}}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 620, + 813, + 890, + 830 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {L}} _ {2} = \\mathcal {F} _ {M _ {2}} \\left(\\hat {\\mathbf {L}} _ {1}, \\left\\{\\mathbf {S} _ {k} \\mid k \\in [ 1, 2, \\dots , K ] \\right\\}: \\theta_ {M _ {2}}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 848, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {L}} _ {3} = \\mathcal {F} _ {M _ {3}} \\left(\\hat {\\mathbf {L}} _ {2}, \\left\\{\\mathbf {S} _ {k} \\mid k \\in [ 1, 2, \\dots , K ] \\right\\}: \\theta_ {M _ {3}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "25050", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d0aaab3376b6cf6d5d40259c4eeed7c05b52b060b636d7d5f7c50d442b546780.jpg", + "image_caption": [ + "Figure 4. The architecture of the proposed Bi-directional Deformable Modal Aligning (BiDMA) module." + ], + "image_footnote": [], + "bbox": [ + 88, + 87, + 459, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Stage 1: Basic Image Deblurring", + "text_level": 1, + "bbox": [ + 76, + 244, + 366, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the first stage, we employed one of the current state-of-the-art image restoration networks, NAFNet [5], as the basic deblurring module $M_{1}$ . We aim to use $M_{1}$ to lighten the blurring effect and enhance the texture of the blurred image $\\mathbf{B}$ , as shown in Fig. 3. Specifically, NAFNet is a U-shaped multi-scale network. $\\mathbf{B}$ undergoes 4 times down-sampling during feature extraction, followed by up-sampling. In the up-sampling process, features from each scale are fused, and the network finally outputs $\\hat{\\mathbf{L}}_{1}$ . To reduce parameter count and accelerate inference speed, the overall network channel number is halved. Detailed architectures are provided in the supplementary material.", + "bbox": [ + 75, + 268, + 470, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Stage 2: Bi-Deformable Aligning Enhancement", + "text_level": 1, + "bbox": [ + 76, + 458, + 468, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "At this stage, spikes are introduced. As in Eq. (5), if two cameras are perfectly aligned in space and time, spikes can be optimized to obtain a clear grayscale image $\\tilde{\\mathbf{L}}_{\\mathbf{S}}$ without color information and at a lower resolution. The reconstructed gray-scale image can effectively aid in deblurring the RGB image. Our goal is to learn an adaptive pixel alignment relationship between modalities through learning. We first pass the sampled spike fragments through a shallow convolutional module $M_{S2I}$ to quickly estimate the corresponding rough grayscale intensity $\\tilde{\\mathbf{L}}_{\\mathbf{S}}$ . $M_{S2I}$ consists of only 4 convolutional layers, which is formulated as:", + "bbox": [ + 75, + 481, + 468, + 647 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\mathbf {L}} _ {\\mathbf {S}} = \\mathcal {F} _ {M _ {S 2 I}} (\\mathbf {S}: \\theta_ {M _ {S 2 I}}), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 652, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we designed the bi-directional deformable modal align (BiDMA) module, as illustrated in Fig. 4. The spike and image features are extracted with downsampling, denoted as $\\mathbf{F_S} = \\{F_{\\mathbf{S}}^h\\}$ and $\\mathbf{F_L} = \\{F_{\\mathbf{L}}^h\\}$ , where $h \\in [1,2,\\dots,H]$ is the number of scales. A deformable convolution network(DCN) [10] $\\mathcal{F}_{DCN}$ can align two kinds of features, the principle can be denoted as:", + "bbox": [ + 76, + 676, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF (p) = \\sum_ {q = 1} ^ {Q} w _ {q} \\cdot F \\left(p + p _ {q} + \\Delta p _ {q}\\right) \\cdot \\Delta m _ {q}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 790, + 468, + 833 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p = (x,y)$ is the coordinate of the center pixel, Q denotes pixel numbers in the neighbor of $p$ , $p_q$ is the fixed offset from $p$ , $w_q$ denotes the weight, $\\Delta m_q$ denotes the modulation scalar. $\\Delta p_q$ is the learnable offset, which is predicted", + "bbox": [ + 76, + 839, + 468, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "by two modal features with a module $\\mathcal{F}_{\\Delta}$ consisting of several convolution layers. In each $h$ -level, we consider the bi-directional deformable aligning: 1) align $F_{\\mathbf{L}}^{h}$ of image to $F_{\\mathbf{S}}^{h}$ of spikes and get the $\\bar{F}_{\\mathbf{L}}^{h}$ ; 2) fuse the $\\bar{F}_{\\mathbf{L}}^{h}$ and $F_{\\mathbf{S}}^{h}$ , and get $\\bar{F}_{\\mathbf{S}}^{h}$ ; 3) align the $\\bar{F}_{\\mathbf{S}}^{h}$ back to $F_{\\mathbf{L}}^{h}$ , and get $\\bar{\\bar{F}}_{\\mathbf{S}}^{h}$ . The process can be formulated as:", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Delta P _ {I 2 S} ^ {h} = \\mathcal {F} _ {\\Delta} ([ F _ {\\mathbf {L}} ^ {h}, F _ {\\mathbf {S}} ^ {h} ], \\Delta P _ {I 2 S} ^ {h + 1}), \\\\ \\bar {F} _ {\\mathbf {L}} ^ {h} = \\mathcal {F} _ {\\oplus} \\left(\\mathcal {F} _ {D C N} \\left(F _ {\\mathbf {L}} ^ {h}, \\Delta P _ {I 2 S} ^ {h}\\right), \\mathbf {U} _ {\\mathbf {p}} \\left(\\bar {F} _ {\\mathbf {L}} ^ {h + 1}\\right)\\right), \\tag {11} \\\\ \\bar {F} _ {\\mathbf {S}} ^ {h} = \\mathcal {F} _ {\\oplus} (\\bar {F} _ {\\mathbf {L}} ^ {h}, F _ {\\mathbf {S}} ^ {h}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 190, + 890, + 251 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Delta P _ {S 2 I} ^ {h} = \\mathcal {F} _ {\\Delta} ([ \\bar {F} _ {\\mathbf {S}} ^ {h}, F _ {\\mathbf {L}} ^ {h} ], \\Delta P _ {S 2 I} ^ {h + 1}), \\\\ \\bar {\\bar {F}} _ {\\mathbf {S}} ^ {h} = \\mathcal {F} _ {\\oplus} \\left(\\mathcal {F} _ {D C N} \\left(\\bar {F} _ {\\mathbf {S}} ^ {h}, \\Delta P _ {S 2 I} ^ {h}\\right), \\mathbf {U p} \\left(\\bar {\\bar {F}} _ {\\mathbf {S}} ^ {h + 1}\\right)\\right), \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 273, + 890, + 314 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {a l i g n} = \\mathcal {F} _ {\\oplus} (\\bar {\\bar {F}} _ {\\mathbf {S}} ^ {1}, F _ {\\mathbf {L}} ^ {1}),\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 316, + 678, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{DCN}$ is the DCN network as in Eq. (10), $\\mathcal{F}_{\\oplus}$ is the feature fusion function with simple Conv layers, $\\mathbf{U}\\mathbf{p}(\\cdot)$ is the upsampling operation. Eq. (11) describe the align process from images to spikes, and Eq. (12) describe the align process from spikes back to images. In this way, at the 1-level, the aligned feature $F_{align}$ is fused by $\\mathcal{F}_{\\oplus}$ with several Conv layers. As described in Sec. 3.1, we sample $K$ segments of spikes for alignment with the image. Thus the output $\\hat{\\mathbf{L}}_2$ of stage 2 is formulated as:", + "bbox": [ + 496, + 345, + 890, + 481 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\mathbf {L}} _ {2} = \\mathcal {F} _ {p r e d} ([ F _ {a l i g n, 1}, F _ {a l i g n, 2}, \\dots , F _ {a l i g n, K} ]). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 491, + 890, + 510 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Stage 3: Flow-guided Dense Fusion", + "text_level": 1, + "bbox": [ + 500, + 518, + 805, + 535 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "After the alignment in stage 2, textures of $\\hat{\\mathbf{L}}_2$ are further enhanced by spikes. In this stage, we aim to achieve precise alignment of spike features through optical flow guidance, improving the deblurring effect by supplementing detailed textures from features in the spike. Thus, we build a flow-guided dense fusion network for the final refinement. as illustrated in Fig. 3. Firstly, $K$ coarse light intensity estimation $\\{\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}|k\\in [1,2,\\dots ,K]\\}$ are predicted as Eq. (9) described from the sampled spike segments $\\{\\mathbf{S}_k|k\\in$ $[1,2,\\ldots ,K]\\}$ . Then, we compute the optical flows $V_{\\mathbf{S}_k\\rightarrow \\hat{\\mathbf{L}}_2}$ between the $\\hat{\\mathbf{L}}_2$ and each $\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}$ , then warp the $\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}$ to $\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}^w$ according to the $V_{\\mathbf{S}_k\\rightarrow \\hat{\\mathbf{L}}_2}$ . The process is formulated as:", + "bbox": [ + 496, + 541, + 890, + 729 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} V _ {\\mathbf {S} _ {k} \\rightarrow \\hat {\\mathbf {L}} _ {2}} = \\mathcal {F} _ {f l o w} (\\tilde {\\mathbf {L}} _ {\\mathbf {S} _ {k}}, \\hat {\\mathbf {L}} _ {2}), \\tag {14} \\\\ \\tilde {\\bf L} _ {{\\bf S} _ {k}} ^ {w} = \\mathcal {G} (\\tilde {\\bf L} _ {{\\bf S} _ {k}}, V _ {{\\bf S} _ {k} \\rightarrow \\hat {{\\bf L}} _ {2}}), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 739, + 890, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}_{flow}$ is the pretrained image-based flow estimation network [35], and $\\mathcal{G}$ denotes the feature warp operator. Then, we concatenate $\\{\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}^w |k\\in [1,2,\\dots ,K]\\}$ and $\\hat{\\mathbf{L}}_2$ , and get the tiled image $\\hat{\\mathbf{L}}_{tile}$ . The U-shape network contains the encoder and decoder. In the encoder, the image features of $\\hat{\\mathbf{L}}_{tile}$ are extracted with downsampling, denoted as $\\mathbf{F}_{\\hat{\\mathbf{L}}_{tile}} = \\{F_{\\hat{\\mathbf{L}}_{tile}}^{h}\\} ,h = [1,2,\\dots ,H]$ . The feature $F_{\\hat{\\mathbf{L}}_{tile}}^{h}$ at", + "bbox": [ + 496, + 790, + 890, + 904 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "25051", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/f39971f68134817215343e2083093d84f6e9c3a452eb36a5851a23481b71908d.jpg", + "image_caption": [ + "Figure 5. The proposed Attention-base Dense Block (ADB)." + ], + "image_footnote": [], + "bbox": [ + 94, + 88, + 454, + 170 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "level $h$ doubles the channel number of $F_{\\hat{\\mathbf{L}}_t i t e}^{h - 1}$ at level $h - 1$ . In the decoder, features from the previous layer are upsampled through convolution layers and a pixel shuffle operation, then fuse with features at the current level. Each encoder and decoder at each level is an attention-base dense block(ADB) consisting of a channel attention layer (CA) and a residual dense block (RDB) [50], as in Fig. 5. The CA fuses two features from two modalities and the RDB aims to extract features effectively. In this way, the final deblurred image $\\hat{\\mathbf{L}}_3$ is predicted with the sum of the output of several convolutional layers and the input $\\hat{\\mathbf{L}}_2$ .", + "bbox": [ + 75, + 218, + 472, + 388 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.6. Loss functions", + "text_level": 1, + "bbox": [ + 76, + 396, + 225, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train the three stages separately, for each stage, we use the $\\mathcal{L}_1$ loss to optimize the network. For the coarse light intensity estimation module $M_{S2I}$ , $\\mathcal{L}_1$ loss is adopted too.", + "bbox": [ + 75, + 419, + 468, + 465 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d e b l u r} ^ {i} = \\left| \\hat {\\mathbf {L}} _ {1} ^ {i} - \\mathbf {L} _ {r g b} \\right|, \\text {w h e r e} i = 1, 2, 3, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 474, + 468, + 500 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {M _ {S 2 I}} ^ {i} = | \\bar {\\mathbf {L}} _ {\\mathbf {S}} - \\mathbf {L} _ {g r a y} |,\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 497, + 302, + 515 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $i$ is the stage index, $\\mathbf{L}_{rgb}$ is the ground-truth clear RGB image, and $\\mathbf{L}_{gray}$ is the clear gray image with equal spatial resolution as spikes.", + "bbox": [ + 75, + 522, + 468, + 568 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 76, + 580, + 200, + 598 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Training Settings", + "text_level": 1, + "bbox": [ + 76, + 604, + 348, + 622 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To train the network, we utilize datasets containing high-speed RGB images as the base and simulate the principle of a spike camera to generate continuous spike streams. Specifically, we conduct training and testing on two large datasets: the X4k1000FPS [30] and the REDS dataset [25]. The X4K1000FPS dataset includes high-definition 1000fps videos, while REDS comprises 1000fps videos, along with real or synthesized blurred images. To generate spike data, we employ the state-of-the-art video interpolation algorithm EMA-VFI [46] to increase the frame rate by 8 times for the image sequences in both datasets, resulting in ultra-high frame rate videos. Ultra-high frame rate videos can approximate the continuous changes in scene lighting, allowing us to use the working principle of a spike camera to generate corresponding spike streams as shown in Eq. (1). Additionally, since the X4K1000FPS dataset does not include blurred images, we simulate the blurry images using an average of 33 frames. In X4K1000FPS and REDS, the equiv", + "bbox": [ + 75, + 628, + 472, + 901 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/359052aaa8fb599711555613c8f4a1bf455828527becf8460800c87b65ec040a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image33.740.935
NAFNet [5]Image34.130.937
EFNet [32]Image+Spike33.280.928
REFID [33]Image+Spike34.220.939
SpkDeblurNet [7]Image+Spike34.470.941
UaSDN(Ours)Image+Spike35.780.964
", + "bbox": [ + 514, + 88, + 879, + 202 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/89b478f0601ea2358c84b6107b599bfc35b8a4eb63018b949bff61e25b72a52e.jpg", + "table_caption": [ + "Table 1. Comparison of various motion deblurring methods on X4K1000FPS [30]." + ], + "table_footnote": [], + "table_body": "
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image31.100.902
NAFNet [5]Image30.730.894
EFNet [32]Image+Spike31.740.912
REFID [33]Image+Spike31.230.904
SpkDeblurNet [7]Image+Spike31.160.911
UaSDN(Ours)Image+Spike33.610.942
", + "bbox": [ + 514, + 256, + 879, + 371 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison of various motion deblurring methods on REDS [25].", + "bbox": [ + 498, + 381, + 890, + 409 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "alent exposure time for the blurred images is 1/120 and 1/24 seconds, respectively.", + "bbox": [ + 498, + 436, + 890, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "How do we set the unknown spatiotemporal alignment between RGB frames and spikes? In the training set, along the spatial axis, we introduce random offsets in up, down, left, and right directions for the spikes compared to the blurred image, with a maximum offset of $10\\%$ . Along the temporal axis, the center timestamp of the sampled spike segments compared to the blurred image was set with random offsets in forward and backward directions, with a maximum offset of $25\\%$ . For testing, we set the above offset scheme as a fixed uniform distribution to ensure that all methods use the same test data in evaluation. Details of the dataset and training are in supplementary materials.", + "bbox": [ + 496, + 469, + 892, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Results on X4K1000FPS", + "text_level": 1, + "bbox": [ + 498, + 662, + 723, + 678 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the deblurring capability of our proposed model UaSDN, under modality misalignment, we compare it with five methods: two image-based networks, HINet [4] and NAFNet [5], two state-of-the-art event-based networks, EFNet [32] and REFID [33], and the spike-based SpkDeblurNet [7]. To ensure fairness in the experiments, we modify the inputs of EFNet and REFID to be the blurred images and spikes, with the spike length matching that of UaSDN. We transform the spikes to the input representation used by EFNet and REFID.", + "bbox": [ + 496, + 686, + 890, + 837 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As in Tab. 1, our method achieves 35.78dB in PSNR and 0.964 in SSIM, demonstrating a significant performance improvement compared to other methods. Compared to methods that only take the image as input, our approach", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "25052", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/238e25bd8304688abc66a79a98bdfc5f0a46275c5ef2e3694c2b217ab8a08614.jpg", + "image_caption": [ + "Figure 6. Visualized results of our method (UaSDN) on X4K1000FPS compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet." + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 872, + 328 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2013d0a41b03bb694b1fc8a882fe42ea33daa6b1cf6dc91fdc90f7d071f69e53.jpg", + "image_caption": [ + "Figure 7. Visualized results of our method (UaSDN) on REDS dataset compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet." + ], + "image_footnote": [], + "bbox": [ + 94, + 367, + 875, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "outperforms HINet and NAFNet by 2.04dB and 1.65dB in PSNR, respectively. It indicates the effectiveness of utilizing spikes as guidance for deblurring. Furthermore, compared to the other two event-based networks that take spikes as input, our approach surpasses EFNet and REFID by 2.50dB and 1.56dB in PSNR. It strongly validates the effectiveness of our model in aligning the two modal data in both time and space. As in Fig. 6, the visual results demonstrate that our method effectively obtains fine textures. For example, in the first row, our method successfully enhances the blurred textures without introducing any shape distortion, while other methods fail to address such extreme blurriness and result in shape distortions. It proves the precise spatiotemporal feature alignment achieved by our method.", + "bbox": [ + 75, + 621, + 470, + 833 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results on REDS", + "text_level": 1, + "bbox": [ + 76, + 845, + 245, + 859 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On the REDS dataset, as shown in Tab. 2, our method achieves a PSNR of 33.61dB and an SSIM of 0.942. Com", + "bbox": [ + 75, + 869, + 470, + 898 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pared to the image-based methods HINet and NAFNet, our method surpasses them by 2.51dB and 2.88dB, respectively. Compared to the event-based methods EFNet and REFID, our method outperforms them by 1.87dB and 2.38dB. As illustrated in Fig. 7, our method can significantly enhance deblurring performance in the presence of complex textures, such as text on license plates, text on ships, and details in faces. Through the comparison of the REDS dataset, we further demonstrate the deblurring capability of the model and its generalization ability to different datasets.", + "bbox": [ + 496, + 621, + 890, + 773 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Results on Real World Spikes", + "text_level": 1, + "bbox": [ + 500, + 785, + 761, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To assess the deblurring capability of our method in real-world scenarios, we set up a simple unaligned spike-RGB hybrid camera system. Fig. 8 shows real-world test cases, including fast-moving objects at close range and outdoor driving scenarios with rapid motion. As shown in Fig. 8, our method significantly outperforms other approaches in", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "25053", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8e407415c0d0806ae0130c0670420e1b8e173ac9cf66964a085061e99c7447f8.jpg", + "image_caption": [ + "Figure 8. Visualized results on real-world data captured with an RGB camera and a spike camera." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 462, + 193 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3aebc182f89d45500b129b4ceb324474a5b871441d1fd52af5ec3cd897073317.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Stage1Stage2Stage3PSNR ↑SSIM ↑
✓××32.300.914
✓✓×32.900.923
✓✓✓35.780.964
", + "bbox": [ + 99, + 247, + 446, + 325 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "motion deblurring. We also observed that due to the high dynamic information contained in the spike stream, our method excels of deblurring in scenes with overexposure.", + "bbox": [ + 75, + 378, + 468, + 425 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 436, + 241, + 452 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A. Performance Increases at each stage. To demonstrate the effectiveness of multi-stage model design, we conduct ablation experiments on the deblurring effects at each stage. As shown in Tab. 3, when performing the first stage training, the model possesses basic deblurring capabilities. With the introduction of the bi-directional deformable alignment in the second stage, the model shows a noticeable improvement of $0.6\\mathrm{dB}$ and 0.01 in PSNR and SSIM, respectively. The addition of the flow-guided feature fusion network in the third stage further increases the PSNR to the highest value of $35.78\\mathrm{dB}$ . These experimental results indicate that through progressive training, clear texture information from the spike stream can effectively be introduced into the image domain, guiding the deblurring process.", + "bbox": [ + 75, + 460, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "B. Deblurring Potentials under Precise Alignment. The above experiments demonstrate that our method effectively removes blur when spikes and images are unknownly aligned in both time and space. To further validate the potential of our method, we modify the X4k1000FPS and REDS datasets to strictly align spikes and images and test the model's performance under the condition of complete spatiotemporal alignment between modalities. As shown in Tab. 4, the results on the X4K1000FPS dataset include the quantitative results of two other methods, EFNET and REFID, which also take spikes as guiding input. The results show that our method achieves a PSNR of 36.92dB, surpassing the other two methods by 0.56dB and 0.62dB. We also test the performance improvement on REDS. The experiment shows that our method improves from 33.61dB", + "bbox": [ + 75, + 674, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/25e2278c0ba5ce8e2539d57a1853d5da757fb1f3be2356cfe49401483a3a9568.jpg", + "table_caption": [ + "Table 3. Experiments on the performance of the model stage." + ], + "table_footnote": [], + "table_body": "
MethodInput DataPSNR ↑SSIM ↑
EFNet [32]Image+Spike36.360.960
REFID [33]Image+Spike36.300.962
UaSDN(Ours)Image+Spike36.920.969
", + "bbox": [ + 517, + 88, + 877, + 165 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Comparison of various motion deblurring methods on X4K1000FPS [30] when spikes and images are precise aligned.", + "bbox": [ + 498, + 176, + 890, + 204 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/85e5976d4387ee59e11f198ef9ac1169204081033ae2e9aa581b78fa806032cc.jpg", + "image_caption": [ + "Figure 9. Influence of border areas when sampled spikes are totally not involved in the exposure of the image." + ], + "image_footnote": [], + "bbox": [ + 504, + 217, + 890, + 342 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to 34.60dB on REDS, indicating that our method has great potential for application in spike-guided deblurring. Visualized results are shown in the supplementary materials.", + "bbox": [ + 496, + 407, + 890, + 452 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "C. How the border areas are handled from spatial and temporal perspectives. Generally, the motion near the border is similar. The model learns motion clues in spikes that supplement textures. Besides, our image-based stage-1 in UaSDN performs basic deblurring without spikes. In Fig. 9, the image that is spatiotemporal unaligned with spikes is recovered well by UaSDN. The quality is close to the deblurred one with perfect alignment (28.58 dB). The curve shows the model maintains acceptable results though the PSNR declines when spikes are not involved in the image exposure time at all.", + "bbox": [ + 496, + 452, + 892, + 618 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 633, + 619, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We first explore the motion deblurring guided by a spike camera under unknown spatiotemporal alignment between two modalities. We believe the proposed method possesses potential in the real world. The proposed three-stage UaSDN contains a bi-directional deformable alignment and a flow-based fusion module. Results prove that UaSDN outperforms other methods on unaligned deblurring.", + "bbox": [ + 496, + 657, + 890, + 765 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 777, + 651, + 795 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (62176003, 62088102, 62306015), the China Postdoctoral Science Foundation (2022M720238, 2023T160015), the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), and the Beijing Nova Program (20230484362).", + "bbox": [ + 496, + 801, + 890, + 887 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "25054", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Christian Brandli, Raphael Berner, Minhao Yang, Shih-Chii Liu, and Tobi Delbruck. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12428-12437, 2023. 2" + ], + "bbox": [ + 78, + 90, + 468, + 681 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "25057", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_model.json b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_model.json new file mode 100644 index 0000000000000000000000000000000000000000..4d407599dccd37496317f31f7ebd27f0bc871a59 --- /dev/null +++ b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_model.json @@ -0,0 +1,2301 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.002, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.126, + 0.13, + 0.844, + 0.176 + ], + "angle": 0, + "content": "Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment" + }, + { + "type": "text", + "bbox": [ + 0.15, + 0.202, + 0.816, + 0.275 + ], + "angle": 0, + "content": "Jiyuan Zhang\\(^{1,2}\\) Shiyan Chen\\(^{1,2}\\) Yajing Zheng\\(^{1,2*}\\) Zhaofei Yu\\(^{1,2,3*}\\) Tiejun Huang\\(^{1,2,3}\\) \n\\(^{1}\\)School of Computer Science, Peking University \n\\(^{2}\\)National Key Laboratory for Multimedia Information Processing, Peking University \n\\(^{3}\\)Institute for Artificial Intelligence, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.16, + 0.277, + 0.802, + 0.293 + ], + "angle": 0, + "content": "{jyzhang,2301112005}@stu.pku.edu.cn，{yj.zheng,yuzf12,tjhuang}@pku.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.313, + 0.343 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.359, + 0.474, + 0.722 + ], + "angle": 0, + "content": "The traditional frame-based cameras that rely on exposure windows for imaging experience motion blur in high-speed scenarios. Frame-based deblurring methods lack reliable motion cues to restore sharp images under extreme blur conditions. The spike camera is a novel neuromorphic visual sensor that outputs spike streams with ultra-high temporal resolution. It can supplement the temporal information lost in traditional cameras and guide motion deblurring. However, in real-world scenarios, aligning discrete RGB images and continuous spike streams along both temporal and spatial axes is challenging due to the complexity of calibrating their coordinates, device displacements in vibrations, and time deviations. Misalignment of pixels leads to severe degradation of deblurring. We introduce the first framework for spike-guided motion deblurring without knowing the spatiotemporal alignment between spikes and images. To address the problem, we first propose a novel three-stage network containing a basic deblurring net, a carefully designed bi-directional deformable aligning module, and a flow-based multi-scale fusion net. Experimental results demonstrate that our approach can effectively guide the image deblurring with unknown alignment, surpassing the performance of other methods. Public project page: https://github.com/Leozhangjiyuan/UaSDN." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.748, + 0.208, + 0.763 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.774, + 0.47, + 0.88 + ], + "angle": 0, + "content": "The imaging principle of conventional frame-based cameras is based on the concept of exposure time windows. During the continuous imaging process, the time between the exposure windows of adjacent frames is unused. Due to the presence of exposure windows, when the camera is in high-speed motion or there are fast-moving objects in the scene, images may exhibit a blur effect. In recent years," + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.327, + 0.882, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.553, + 0.892, + 0.581 + ], + "angle": 0, + "content": "Figure 1. Illustration of unknown spatiotemporal alignment between a spike camera and an RGB camera." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.612, + 0.892, + 0.703 + ], + "angle": 0, + "content": "many studies have focused on addressing the challenging task of recovering clear images from blurry ones utilizing deep-learning routes [4, 5, 16]. However, the texture or structural information in blurry images is partially lost during the exposure, making it difficult to infer clear textures directly from blurry images, as in Fig. 2 (Orange Box)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Introducing spike cameras as clues of deblurring. Bioinspired neuromorphic vision sensors have attracted increasing attention and achieved significant development. They possess advantages such as ultra-high temporal resolution, low latency, and high dynamic range. Due to the continuous recording of light intensity, neuromorphic cameras can be used to compensate for the lack of temporal information in image deblurring. Based on different sampling principles, they can be classified into event cameras [1, 21, 23] and spike cameras [12]. Event cameras asynchronously detect changes in light intensity and are highly sensitive to moving edges. Studies utilize events for image deblurring [28, 32]. Spike cameras accumulates" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25047" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.212 + ], + "angle": 0, + "content": "photons and emits \\(20,000\\mathrm{Hz}\\) spike streams. Due to the integration sampling principle, it can thoroughly record spatiotemporal information, including the texture and motion information of the scene. The precise texture information recorded in spikes can effectively guide the deblurring process. Our paper explores the effectiveness of using spike cameras to guide motion deblurring, uncovering the potential advantages of spike cameras in this novel task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.473, + 0.38 + ], + "angle": 0, + "content": "Take misalignment between cameras in real application into consideration. At present, most deblurring works based on event cameras assume that the imaging planes of the two cameras are absolutely coaxial [32, 33] and that the event stream and video are fully synchronized on the time axis. Such assumptions facilitate model design but are overly idealistic. In the real world, achieving strict alignment of a spike camera and an RGB camera in both spatial and temporal dimensions is quite challenging. As shown in Fig. 1, in this work, we consider the unknown alignment factors in the real world:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.382, + 0.473, + 0.504 + ], + "angle": 0, + "content": "(A) Spatial alignment of the two cameras is challenging. Alignment of the coordinate systems of the two cameras can be achieved using methods such as beam splitters or manual calibration (e.g., chessboard calibration). However, beam splitters can result in significant loss of light, and differences in focal length, aperture, and relative positions between cameras, which can vary with the scene, make alignment operations complex and difficult." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.473, + 0.567 + ], + "angle": 0, + "content": "(B) Position displacements. During motion, minor displacements in the relative positions of the two cameras occur due to vibrations. For current algorithms, pixel misalignment will lead to significant performance losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.568, + 0.473, + 0.675 + ], + "angle": 0, + "content": "(C) Synchronizing discrete image sequences with continuous spike streams on the time axis is challenging. Technically, obtaining spikes strictly synchronized with blurry images requires acquiring the accurate exposure start and end times of the blurry images, which is complex. Moreover, in high-speed motion scenes, the two data streams are prone to small time deviations, leading to misalignment." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.382, + 0.473, + 0.675 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.473, + 0.903 + ], + "angle": 0, + "content": "What we focus on and How we deal with the real-world misalignment? In response to the real-world misalignments mentioned above, we focus on investigating spike-guided motion deblurring with unknown spatiotemporal alignment between spikes and RGB images, as shown in Figs. 1 and 2. The proposed method allows for the use of two cameras simultaneously without the need for complex and rigorous spatial calibration and time alignment design. To address the problem, we propose an effective three-stage model Unaligned Spike-guided Deblur Net (UaSDN). (1) In the first stage, we employ a simplified off-the-shelf network to perform basic deblurring. In this stage, we aim to leverage existing technology to alleviate the blurring and enhance textures. (2) In the second stage, we first use a shallow net to estimate coarse light intensity" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "from the spike stream. Besides, we design a bidirectional deformable modal alignment module. The module achieves better alignment by learning bidirectional deformable convolutions between spike features and image features. (3) In the third stage, we design a multi-scale dense fusion network combining the optical flow, which performs feature fusion by aligning pixel motion offsets between modalities and fuse features in a multi-scale network. Through comparisons with various networks, experimental results demonstrate the effectiveness of our method in motion deblurring with unknown spatiotemporal alignment between modalities. To comprehensively validate the model's performance, we construct spike datasets for training and validation. Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.306, + 0.892, + 0.351 + ], + "angle": 0, + "content": "- We first explore the motion deblurring tasks guided by the spike camera and deal with the unknown spatiotemporal alignment between two modalities in the real world." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.352, + 0.892, + 0.395 + ], + "angle": 0, + "content": "- We propose the three-stage UaSDN model which contains a bi-directional deformable modal alignment module and a flow-based fusion module." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.397, + 0.892, + 0.442 + ], + "angle": 0, + "content": "- Experimental results demonstrate that our model significantly outperforms other methods on motion deblurring with unknown spatiotemporal alignment." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.306, + 0.892, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.457, + 0.642, + 0.473 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.483, + 0.756, + 0.499 + ], + "angle": 0, + "content": "2.1. Advances on Spike Cameras" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.765 + ], + "angle": 0, + "content": "The spike camera outputs spikes with an ultra-high temporal resolution of \\(20,000\\mathrm{Hz}\\) [12]. Due to the sampling principle, it effectively captures texture in both moving and stationary areas, demonstrating potential in high-speed scenarios. Research focuses on utilizing spike cameras for image recovery or high-level visual tasks. Early studies involved direct statistics of spike counts or intervals for a rough estimation of light intensity [57]. Zhao et al. [52] introduces the first learning-based method. Zhang et al. [47] leverages wavelet transforms on spikes, and enhances the representational capability of spikes. Some bio-inspired works employ spiking neural networks (SNN) [53, 55] to process spikes. The introduction of self-supervised schemes enhanced the generalization capability [6]. Many applications have emerged, such as super-resolution reconstruction [51] and high-dynamic-range restoration [3], spike-guided video interpolation [41], denoising [11] and tracking [54]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.791, + 0.789 + ], + "angle": 0, + "content": "2.2. Frame-based Motion Deblurring" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In recent years, with the rise of deep learning, CNN-based approaches have shown remarkable performance in frame-based deblurring tasks. Popular technical routes are employing end-to-end training [4, 9, 16, 24, 34, 44]. Some works [17, 18] employ generative networks. Rather than mapping a blurry image one-to-one to a single sharp image, some work [2, 13, 26, 27, 31, 38, 56, 58] attempts to mine" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25048" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.089, + 0.48, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.871, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.293, + 0.893, + 0.325 + ], + "angle": 0, + "content": "Figure 2. Illustration of the process of deblurring images in different scenarios. Orange box: deblurring directly from the RGB camera; blue box: deblurring with precise alignment of spike-RGB data; green box: unknown alignment in X-Y-T for spike-RGB data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.349, + 0.47, + 0.425 + ], + "angle": 0, + "content": "clues from video sequence input to assist in deblurring. However, video-based methods always use future frames, which is not applicable in the real world. Besides, many image-based image restoration models are able to deal with deblurring [4, 5, 19, 20, 39, 43-45]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.435, + 0.369, + 0.452 + ], + "angle": 0, + "content": "2.3. Event-guided Motion Deblurring" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.473, + 0.779 + ], + "angle": 0, + "content": "As neuromorphic vision sensors, event cameras have been used in deblurring. Pan et al. [28] builds a computational model between blurred images and events. Several works [14, 36] utilize motion information and recurrent networks for aligning. Shang et al. [29] enhances the deblurring by finding adjacent sharp frames. Kim et al. [15] and Weng et al. [40] deal with images with unknown exposure time. EFNet [32] introduces an attention-based module to better fuse events. Cho et al. [8] proposed a solution for cameras with spatial offsets. Zhang et al. [49] proposes to generalize the deblurring ability to various spatial resolutions and blur levels. Some works [22, 28, 33, 37, 42, 48] combine the motion deblurring and frame interpolation guided by events. However, most studies assume that scenes captured by the event camera and the traditional camera are entirely identical, i.e. two camera coordinates coincide perfectly along the spatial axis and events have the same center and duration as the exposure time of blurred images on the temporal axis. Our study aims to address motion deblurring in real scenes unknown of the alignment between cameras in both time and space." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.791, + 0.168, + 0.807 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.816, + 0.249, + 0.833 + ], + "angle": 0, + "content": "3.1. Problem Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We mainly focus on dealing with the motion deblurring in high-speed scenarios guided by a spike camera while not knowing the alignment between the RGB camera and spike camera on both the spatial axis and temporal axis. In this" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.892, + 0.378 + ], + "angle": 0, + "content": "section, we give a specific analysis of how to utilize spike data for deturbing spatiotemporal unaligned RGB frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.893, + 0.575 + ], + "angle": 0, + "content": "An RGB camera outputs discrete RGB blurry frames \\(\\mathbb{B} = \\{\\mathbf{B}_i|i\\in \\mathbf{N}\\}\\) with the exposure time of \\(T_{B}\\), which is a shorter duration than the time duration between successive frames \\(T_{F}\\) (the frame rate \\(f = \\frac{1}{T_F}\\)). A spike camera outputs the spike stream S with the rate of \\(20000\\mathrm{Hz}\\). Each pixel \\((x,y)\\) of a spike camera on the \\(H_{S}\\times W_{S}\\) plane independently receives coming photons continuously at any timestamps \\(t\\), converts the light signals into electrical current \\(I_{x,y}(t)\\), and accumulates the voltage \\(V_{x,y}\\). Whenever the voltage reaches the preset threshold \\(\\Theta\\), the pixel fires a spike and resets the voltage to 0. The spike signals are read out with a very short interval (\\(\\tau = \\frac{1}{20000Hz} = 50\\mu s\\)). The process can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.582, + 0.892, + 0.622 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} _ {x, y} (c) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\exists t \\in ((c - 1) \\tau , c \\tau ], V _ {x, y} (t) = 0, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.637, + 0.892, + 0.678 + ], + "angle": 0, + "content": "\\[\nV _ {x, y} ^ {+} (t) = \\left\\{ \\begin{array}{l l} V _ {x, y} ^ {-} (t) + I _ {x, y} (t), & \\text {i f} V _ {x, y} ^ {-} (t) < \\Theta , \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.685, + 0.892, + 0.746 + ], + "angle": 0, + "content": "where \\( V_{x,y}^{-}(t) \\) and \\( V_{x,y}^{+}(t) \\) denotes the voltage before and after receiving the electric current \\( I_{x,y}(t) \\), \\( c \\in \\mathbb{R} \\). The spike stream \\( S \\) is output with the size of \\( H \\times W \\times C \\) after \\( C \\) times readout during \\( T\\mu s \\) (\\( C = \\frac{T}{\\tau} \\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.746, + 0.892, + 0.777 + ], + "angle": 0, + "content": "For a blurred image \\(\\mathbf{B}_i\\), it can be represented as the average of the clear images \\(\\{\\mathbf{L}\\}\\) over the exposure time, i.e.:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.786, + 0.892, + 0.824 + ], + "angle": 0, + "content": "\\[\n\\mathbf {B} _ {i} = \\frac {1}{T _ {\\mathbf {B}}} \\int_ {T _ {i} - T _ {\\mathbf {B}} / 2} ^ {T _ {i} + T _ {\\mathbf {B}} / 2} \\mathbf {L} (t) d t, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.826, + 0.848, + 0.841 + ], + "angle": 0, + "content": "where \\(T_{i}\\) is the center of exposure time and \\(\\mathbf{L}_i\\) at \\(T_{i}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.871 + ], + "angle": 0, + "content": "Why spike cameras hold potential on image deblurring. The deblurring process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.878, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {M}} {\\arg \\min } \\| \\hat {\\mathbf {L}} _ {i} - \\mathbf {L} _ {i} \\|, \\text {w h e r e} \\hat {\\mathbf {L}} _ {i} = \\mathcal {F} \\left(\\mathbf {B} _ {i}: \\theta_ {M}\\right), \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "25049" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.104, + 0.089, + 0.87, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.218, + 0.305, + 0.75, + 0.32 + ], + "angle": 0, + "content": "Figure 3. The architecture of the proposed Unaligned Spike-guided Deblur Net (UaSDN)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.346, + 0.47, + 0.437 + ], + "angle": 0, + "content": "where \\(\\theta\\) is the optimized parameters of the model \\(M\\) and \\(\\hat{\\mathbf{L}}_i\\) is the predicted clear image. The \\(\\theta\\) is hard to optimize when \\(\\mathbf{B}_i\\) holds extreme blur. Neglecting color information and differences in spatial resolution, when the spike camera and RGB camera are perfectly aligned, the clear image \\(\\mathbf{L}_i\\) can also be approximated using spikes:" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.448, + 0.469, + 0.489 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {L}} _ {i} \\simeq \\mathcal {F} _ {M _ {S 2 I}} \\left(\\left\\{\\mathbf {S} (t) \\mid t \\in \\left[ T _ {i} - \\frac {T _ {\\mathbf {B}}}{2}, T _ {i} + \\frac {T _ {\\mathbf {B}}}{2} \\right] \\right\\}: \\theta_ {S 2 I}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.469, + 0.655 + ], + "angle": 0, + "content": "where \\(M_{S2I}\\) is the model for reconstructing spikes to the approximated image \\(\\tilde{\\mathbf{L}}_i\\). Many existing models [47, 52] are able to reconstruct high-quality \\(\\tilde{\\mathbf{L}}_i\\). Despite that \\(\\hat{\\mathbf{L}}_i\\) lacks color information and has lower spatial resolution compared to \\(\\mathbf{B}_i\\), its clear texture effectively provides deblurring clues for \\(\\mathbf{B}_i\\) as shown in Fig. 2, which is proved by our experiments in Sec. 4.5. When not knowing the alignment between the RGB camera and spike camera on both spatial and temporal axis, we cannot get the accurate spikes \\(\\{\\mathbf{S}(t)\\}\\) in Eq. (5). Thus textures in \\(\\tilde{\\mathbf{L}}_i\\) are not aligned with \\(\\mathbf{L}_i\\), which raises challenges for spikes to guide the deblurring." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.469, + 0.822 + ], + "angle": 0, + "content": "How to deal with unknown alignment? We set the situation of the unknown alignment as follows: (1) Spatial axis. There are blind plane displacements \\(\\Delta \\mathbf{P}\\) between two cameras. Generally, we set the \\(\\Delta \\mathbf{P}\\) not a constant but a variable parameter. (2) Temporal axis. Spike stream is continuous while RGB frames are discrete. When two streams cannot be precisely synchronized, in real situations, we can roughly fetch a segment of spikes \\(\\mathbf{S}_k\\) around the corresponding exposure window \\(T_{i}\\) of image \\(\\mathbf{B}_i\\). The temporal center of \\(\\mathbf{S}_k\\) is unknown. In this case, we aim to build the model learning the aligning process adaptively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.274, + 0.846 + ], + "angle": 0, + "content": "3.2. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For not knowing the alignment, accurately matching the textures between the blurred image and spikes is challenging, requiring the model to have the ability for adaptive" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.892, + 0.481 + ], + "angle": 0, + "content": "feature matching. However, on one hand, the texture of the blurred image \\(\\mathbf{B}\\) suffers from significant information loss. On the other hand, the irregular spike data cannot directly express scene textures like images. Therefore, we aim to progressively optimize the motion deblurring, gradually restoring clear textures of the blurred image and spikes. To achieve this, we propose a three-stage model named Unaligned Spike-guided Deblur Net (UaSDN). The network architecture of UaSDN is illustrated in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.482, + 0.893, + 0.801 + ], + "angle": 0, + "content": "UaSDN consists of three deblurring stages. (1) First Stage: Basic Image Deblurring Unclear texture in blurred images \\(\\mathbf{B}\\) makes it difficult to match with features in spikes. We employ a simple network \\(M_{1}\\) to learn basic deblurring for \\(\\mathbf{B}\\). The network takes the blurred image \\(\\mathbf{B}\\) as input and outputs the predicted image \\(\\hat{\\mathbf{L}}_{1}\\) (2) Second Stage: Bi-Deformable Aligning Enhancement. The texture of \\(\\mathbf{B}\\) is enhanced after the stage 1. In this stage, we design a module \\(M_{2}\\) based on deformable convolution to achieve basic alignment between spike features and blurred image features. Besides, to restore scene textures in spikes, we use shallow convolutional layers \\(M_{S2I}\\) to input spikes and quickly infer the rough light intensity. We randomly sample \\(K\\) segments of spikes \\(\\{\\mathbf{S}_k|k\\in [1,2,\\dots K]\\}\\) as guidance input to \\(M_{2}\\), which outputs the enhanced image \\(\\hat{\\mathbf{L}}_{2}\\). (3) Third Stage: Flow-guided Dense Fusion. In this stage, we aim to utilize optical flows \\(v_{S2I}\\) from spikes \\(\\mathbf{S}\\) to the image \\(\\hat{\\mathbf{L}}_{2}\\) as guidance for precise alignment. To achieve this, we design the multi-scale flow-guided deblurring module, which takes the sampled \\(K\\) spike segments as input and predicts the final clear image \\(\\hat{\\mathbf{L}}_{3}\\). The process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.622, + 0.814, + 0.891, + 0.832 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {L}} _ {1} = \\mathcal {F} _ {M _ {1}} \\left(\\mathbf {B}: \\theta_ {M _ {1}}\\right), \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.849, + 0.891, + 0.867 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {L}} _ {2} = \\mathcal {F} _ {M _ {2}} \\left(\\hat {\\mathbf {L}} _ {1}, \\left\\{\\mathbf {S} _ {k} \\mid k \\in [ 1, 2, \\dots , K ] \\right\\}: \\theta_ {M _ {2}}\\right), \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.884, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {L}} _ {3} = \\mathcal {F} _ {M _ {3}} \\left(\\hat {\\mathbf {L}} _ {2}, \\left\\{\\mathbf {S} _ {k} \\mid k \\in [ 1, 2, \\dots , K ] \\right\\}: \\theta_ {M _ {3}}\\right). \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25050" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.089, + 0.088, + 0.46, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.196, + 0.47, + 0.225 + ], + "angle": 0, + "content": "Figure 4. The architecture of the proposed Bi-directional Deformable Modal Aligning (BiDMA) module." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.246, + 0.367, + 0.264 + ], + "angle": 0, + "content": "3.3. Stage 1: Basic Image Deblurring" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.471, + 0.452 + ], + "angle": 0, + "content": "In the first stage, we employed one of the current state-of-the-art image restoration networks, NAFNet [5], as the basic deblurring module \\( M_{1} \\). We aim to use \\( M_{1} \\) to lighten the blurring effect and enhance the texture of the blurred image \\( \\mathbf{B} \\), as shown in Fig. 3. Specifically, NAFNet is a U-shaped multi-scale network. \\( \\mathbf{B} \\) undergoes 4 times down-sampling during feature extraction, followed by up-sampling. In the up-sampling process, features from each scale are fused, and the network finally outputs \\( \\hat{\\mathbf{L}}_{1} \\). To reduce parameter count and accelerate inference speed, the overall network channel number is halved. Detailed architectures are provided in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.459, + 0.47, + 0.475 + ], + "angle": 0, + "content": "3.4. Stage 2: Bi-Deformable Aligning Enhancement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.47, + 0.648 + ], + "angle": 0, + "content": "At this stage, spikes are introduced. As in Eq. (5), if two cameras are perfectly aligned in space and time, spikes can be optimized to obtain a clear grayscale image \\(\\tilde{\\mathbf{L}}_{\\mathbf{S}}\\) without color information and at a lower resolution. The reconstructed gray-scale image can effectively aid in deblurring the RGB image. Our goal is to learn an adaptive pixel alignment relationship between modalities through learning. We first pass the sampled spike fragments through a shallow convolutional module \\(M_{S2I}\\) to quickly estimate the corresponding rough grayscale intensity \\(\\tilde{\\mathbf{L}}_{\\mathbf{S}}\\). \\(M_{S2I}\\) consists of only 4 convolutional layers, which is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.186, + 0.654, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\mathbf {L}} _ {\\mathbf {S}} = \\mathcal {F} _ {M _ {S 2 I}} (\\mathbf {S}: \\theta_ {M _ {S 2 I}}), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.678, + 0.47, + 0.784 + ], + "angle": 0, + "content": "In addition, we designed the bi-directional deformable modal align (BiDMA) module, as illustrated in Fig. 4. The spike and image features are extracted with downsampling, denoted as \\(\\mathbf{F_S} = \\{F_{\\mathbf{S}}^h\\}\\) and \\(\\mathbf{F_L} = \\{F_{\\mathbf{L}}^h\\}\\), where \\(h \\in [1,2,\\dots,H]\\) is the number of scales. A deformable convolution network(DCN) [10] \\(\\mathcal{F}_{DCN}\\) can align two kinds of features, the principle can be denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.791, + 0.469, + 0.834 + ], + "angle": 0, + "content": "\\[\nF (p) = \\sum_ {q = 1} ^ {Q} w _ {q} \\cdot F \\left(p + p _ {q} + \\Delta p _ {q}\\right) \\cdot \\Delta m _ {q}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "where \\(p = (x,y)\\) is the coordinate of the center pixel, Q denotes pixel numbers in the neighbor of \\(p\\), \\(p_q\\) is the fixed offset from \\(p\\), \\(w_q\\) denotes the weight, \\(\\Delta m_q\\) denotes the modulation scalar. \\(\\Delta p_q\\) is the learnable offset, which is predicted" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "by two modal features with a module \\(\\mathcal{F}_{\\Delta}\\) consisting of several convolution layers. In each \\(h\\)-level, we consider the bi-directional deformable aligning: 1) align \\(F_{\\mathbf{L}}^{h}\\) of image to \\(F_{\\mathbf{S}}^{h}\\) of spikes and get the \\(\\bar{F}_{\\mathbf{L}}^{h}\\); 2) fuse the \\(\\bar{F}_{\\mathbf{L}}^{h}\\) and \\(F_{\\mathbf{S}}^{h}\\), and get \\(\\bar{F}_{\\mathbf{S}}^{h}\\); 3) align the \\(\\bar{F}_{\\mathbf{S}}^{h}\\) back to \\(F_{\\mathbf{L}}^{h}\\), and get \\(\\bar{\\bar{F}}_{\\mathbf{S}}^{h}\\). The process can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.191, + 0.891, + 0.252 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Delta P _ {I 2 S} ^ {h} = \\mathcal {F} _ {\\Delta} ([ F _ {\\mathbf {L}} ^ {h}, F _ {\\mathbf {S}} ^ {h} ], \\Delta P _ {I 2 S} ^ {h + 1}), \\\\ \\bar {F} _ {\\mathbf {L}} ^ {h} = \\mathcal {F} _ {\\oplus} \\left(\\mathcal {F} _ {D C N} \\left(F _ {\\mathbf {L}} ^ {h}, \\Delta P _ {I 2 S} ^ {h}\\right), \\mathbf {U} _ {\\mathbf {p}} \\left(\\bar {F} _ {\\mathbf {L}} ^ {h + 1}\\right)\\right), \\tag {11} \\\\ \\bar {F} _ {\\mathbf {S}} ^ {h} = \\mathcal {F} _ {\\oplus} (\\bar {F} _ {\\mathbf {L}} ^ {h}, F _ {\\mathbf {S}} ^ {h}), \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.275, + 0.891, + 0.315 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Delta P _ {S 2 I} ^ {h} = \\mathcal {F} _ {\\Delta} ([ \\bar {F} _ {\\mathbf {S}} ^ {h}, F _ {\\mathbf {L}} ^ {h} ], \\Delta P _ {S 2 I} ^ {h + 1}), \\\\ \\bar {\\bar {F}} _ {\\mathbf {S}} ^ {h} = \\mathcal {F} _ {\\oplus} \\left(\\mathcal {F} _ {D C N} \\left(\\bar {F} _ {\\mathbf {S}} ^ {h}, \\Delta P _ {S 2 I} ^ {h}\\right), \\mathbf {U p} \\left(\\bar {\\bar {F}} _ {\\mathbf {S}} ^ {h + 1}\\right)\\right), \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.318, + 0.679, + 0.337 + ], + "angle": 0, + "content": "\\[\nF _ {a l i g n} = \\mathcal {F} _ {\\oplus} (\\bar {\\bar {F}} _ {\\mathbf {S}} ^ {1}, F _ {\\mathbf {L}} ^ {1}),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.346, + 0.892, + 0.482 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{DCN}\\) is the DCN network as in Eq. (10), \\(\\mathcal{F}_{\\oplus}\\) is the feature fusion function with simple Conv layers, \\(\\mathbf{U}\\mathbf{p}(\\cdot)\\) is the upsampling operation. Eq. (11) describe the align process from images to spikes, and Eq. (12) describe the align process from spikes back to images. In this way, at the 1-level, the aligned feature \\(F_{align}\\) is fused by \\(\\mathcal{F}_{\\oplus}\\) with several Conv layers. As described in Sec. 3.1, we sample \\(K\\) segments of spikes for alignment with the image. Thus the output \\(\\hat{\\mathbf{L}}_2\\) of stage 2 is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.492, + 0.891, + 0.511 + ], + "angle": 0, + "content": "\\[\n\\hat {\\mathbf {L}} _ {2} = \\mathcal {F} _ {p r e d} ([ F _ {a l i g n, 1}, F _ {a l i g n, 2}, \\dots , F _ {a l i g n, K} ]). \\tag {13}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.52, + 0.807, + 0.536 + ], + "angle": 0, + "content": "3.5. Stage 3: Flow-guided Dense Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.542, + 0.892, + 0.73 + ], + "angle": 0, + "content": "After the alignment in stage 2, textures of \\(\\hat{\\mathbf{L}}_2\\) are further enhanced by spikes. In this stage, we aim to achieve precise alignment of spike features through optical flow guidance, improving the deblurring effect by supplementing detailed textures from features in the spike. Thus, we build a flow-guided dense fusion network for the final refinement. as illustrated in Fig. 3. Firstly, \\(K\\) coarse light intensity estimation \\(\\{\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}|k\\in [1,2,\\dots ,K]\\}\\) are predicted as Eq. (9) described from the sampled spike segments \\(\\{\\mathbf{S}_k|k\\in\\) \\([1,2,\\ldots ,K]\\}\\). Then, we compute the optical flows \\(V_{\\mathbf{S}_k\\rightarrow \\hat{\\mathbf{L}}_2}\\) between the \\(\\hat{\\mathbf{L}}_2\\) and each \\(\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}\\), then warp the \\(\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}\\) to \\(\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}^w\\) according to the \\(V_{\\mathbf{S}_k\\rightarrow \\hat{\\mathbf{L}}_2}\\). The process is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.597, + 0.741, + 0.891, + 0.783 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} V _ {\\mathbf {S} _ {k} \\rightarrow \\hat {\\mathbf {L}} _ {2}} = \\mathcal {F} _ {f l o w} (\\tilde {\\mathbf {L}} _ {\\mathbf {S} _ {k}}, \\hat {\\mathbf {L}} _ {2}), \\tag {14} \\\\ \\tilde {\\bf L} _ {{\\bf S} _ {k}} ^ {w} = \\mathcal {G} (\\tilde {\\bf L} _ {{\\bf S} _ {k}}, V _ {{\\bf S} _ {k} \\rightarrow \\hat {{\\bf L}} _ {2}}), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.791, + 0.892, + 0.905 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}_{flow}\\) is the pretrained image-based flow estimation network [35], and \\(\\mathcal{G}\\) denotes the feature warp operator. Then, we concatenate \\(\\{\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}^w |k\\in [1,2,\\dots ,K]\\}\\) and \\(\\hat{\\mathbf{L}}_2\\) , and get the tiled image \\(\\hat{\\mathbf{L}}_{tile}\\) . The U-shape network contains the encoder and decoder. In the encoder, the image features of \\(\\hat{\\mathbf{L}}_{tile}\\) are extracted with downsampling, denoted as \\(\\mathbf{F}_{\\hat{\\mathbf{L}}_{tile}} = \\{F_{\\hat{\\mathbf{L}}_{tile}}^{h}\\} ,h = [1,2,\\dots ,H]\\) . The feature \\(F_{\\hat{\\mathbf{L}}_{tile}}^{h}\\) at" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25051" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.096, + 0.089, + 0.455, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.093, + 0.181, + 0.454, + 0.195 + ], + "angle": 0, + "content": "Figure 5. The proposed Attention-base Dense Block (ADB)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.219, + 0.473, + 0.389 + ], + "angle": 0, + "content": "level \\( h \\) doubles the channel number of \\( F_{\\hat{\\mathbf{L}}_t i t e}^{h - 1} \\) at level \\( h - 1 \\). In the decoder, features from the previous layer are upsampled through convolution layers and a pixel shuffle operation, then fuse with features at the current level. Each encoder and decoder at each level is an attention-base dense block(ADB) consisting of a channel attention layer (CA) and a residual dense block (RDB) [50], as in Fig. 5. The CA fuses two features from two modalities and the RDB aims to extract features effectively. In this way, the final deblurred image \\( \\hat{\\mathbf{L}}_3 \\) is predicted with the sum of the output of several convolutional layers and the input \\( \\hat{\\mathbf{L}}_2 \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.397, + 0.226, + 0.412 + ], + "angle": 0, + "content": "3.6. Loss functions" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.47, + 0.466 + ], + "angle": 0, + "content": "We train the three stages separately, for each stage, we use the \\(\\mathcal{L}_1\\) loss to optimize the network. For the coarse light intensity estimation module \\(M_{S2I}\\), \\(\\mathcal{L}_1\\) loss is adopted too." + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.475, + 0.469, + 0.501 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d e b l u r} ^ {i} = \\left| \\hat {\\mathbf {L}} _ {1} ^ {i} - \\mathbf {L} _ {r g b} \\right|, \\text {w h e r e} i = 1, 2, 3, \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.498, + 0.303, + 0.516 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {M _ {S 2 I}} ^ {i} = | \\bar {\\mathbf {L}} _ {\\mathbf {S}} - \\mathbf {L} _ {g r a y} |,\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.569 + ], + "angle": 0, + "content": "where \\(i\\) is the stage index, \\(\\mathbf{L}_{rgb}\\) is the ground-truth clear RGB image, and \\(\\mathbf{L}_{gray}\\) is the clear gray image with equal spatial resolution as spikes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.202, + 0.599 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.349, + 0.623 + ], + "angle": 0, + "content": "4.1. Datasets and Training Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To train the network, we utilize datasets containing high-speed RGB images as the base and simulate the principle of a spike camera to generate continuous spike streams. Specifically, we conduct training and testing on two large datasets: the X4k1000FPS [30] and the REDS dataset [25]. The X4K1000FPS dataset includes high-definition 1000fps videos, while REDS comprises 1000fps videos, along with real or synthesized blurred images. To generate spike data, we employ the state-of-the-art video interpolation algorithm EMA-VFI [46] to increase the frame rate by 8 times for the image sequences in both datasets, resulting in ultra-high frame rate videos. Ultra-high frame rate videos can approximate the continuous changes in scene lighting, allowing us to use the working principle of a spike camera to generate corresponding spike streams as shown in Eq. (1). Additionally, since the X4K1000FPS dataset does not include blurred images, we simulate the blurry images using an average of 33 frames. In X4K1000FPS and REDS, the equiv" + }, + { + "type": "table", + "bbox": [ + 0.516, + 0.089, + 0.88, + 0.203 + ], + "angle": 0, + "content": "
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image33.740.935
NAFNet [5]Image34.130.937
EFNet [32]Image+Spike33.280.928
REFID [33]Image+Spike34.220.939
SpkDeblurNet [7]Image+Spike34.470.941
UaSDN(Ours)Image+Spike35.780.964
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.213, + 0.892, + 0.241 + ], + "angle": 0, + "content": "Table 1. Comparison of various motion deblurring methods on X4K1000FPS [30]." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.257, + 0.88, + 0.372 + ], + "angle": 0, + "content": "
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image31.100.902
NAFNet [5]Image30.730.894
EFNet [32]Image+Spike31.740.912
REFID [33]Image+Spike31.230.904
SpkDeblurNet [7]Image+Spike31.160.911
UaSDN(Ours)Image+Spike33.610.942
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.382, + 0.892, + 0.41 + ], + "angle": 0, + "content": "Table 2. Comparison of various motion deblurring methods on REDS [25]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.438, + 0.892, + 0.469 + ], + "angle": 0, + "content": "alent exposure time for the blurred images is 1/120 and 1/24 seconds, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.47, + 0.893, + 0.652 + ], + "angle": 0, + "content": "How do we set the unknown spatiotemporal alignment between RGB frames and spikes? In the training set, along the spatial axis, we introduce random offsets in up, down, left, and right directions for the spikes compared to the blurred image, with a maximum offset of \\(10\\%\\). Along the temporal axis, the center timestamp of the sampled spike segments compared to the blurred image was set with random offsets in forward and backward directions, with a maximum offset of \\(25\\%\\). For testing, we set the above offset scheme as a fixed uniform distribution to ensure that all methods use the same test data in evaluation. Details of the dataset and training are in supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.664, + 0.724, + 0.679 + ], + "angle": 0, + "content": "4.2. Results on X4K1000FPS" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.838 + ], + "angle": 0, + "content": "To demonstrate the deblurring capability of our proposed model UaSDN, under modality misalignment, we compare it with five methods: two image-based networks, HINet [4] and NAFNet [5], two state-of-the-art event-based networks, EFNet [32] and REFID [33], and the spike-based SpkDeblurNet [7]. To ensure fairness in the experiments, we modify the inputs of EFNet and REFID to be the blurred images and spikes, with the spike length matching that of UaSDN. We transform the spikes to the input representation used by EFNet and REFID." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "As in Tab. 1, our method achieves 35.78dB in PSNR and 0.964 in SSIM, demonstrating a significant performance improvement compared to other methods. Compared to methods that only take the image as input, our approach" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25052" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.874, + 0.329 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.337, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Figure 6. Visualized results of our method (UaSDN) on X4K1000FPS compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.368, + 0.877, + 0.571 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.581, + 0.892, + 0.597 + ], + "angle": 0, + "content": "Figure 7. Visualized results of our method (UaSDN) on REDS dataset compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.471, + 0.834 + ], + "angle": 0, + "content": "outperforms HINet and NAFNet by 2.04dB and 1.65dB in PSNR, respectively. It indicates the effectiveness of utilizing spikes as guidance for deblurring. Furthermore, compared to the other two event-based networks that take spikes as input, our approach surpasses EFNet and REFID by 2.50dB and 1.56dB in PSNR. It strongly validates the effectiveness of our model in aligning the two modal data in both time and space. As in Fig. 6, the visual results demonstrate that our method effectively obtains fine textures. For example, in the first row, our method successfully enhances the blurred textures without introducing any shape distortion, while other methods fail to address such extreme blurriness and result in shape distortions. It proves the precise spatiotemporal feature alignment achieved by our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.246, + 0.861 + ], + "angle": 0, + "content": "4.3. Results on REDS" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.9 + ], + "angle": 0, + "content": "On the REDS dataset, as shown in Tab. 2, our method achieves a PSNR of 33.61dB and an SSIM of 0.942. Com" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.774 + ], + "angle": 0, + "content": "pared to the image-based methods HINet and NAFNet, our method surpasses them by 2.51dB and 2.88dB, respectively. Compared to the event-based methods EFNet and REFID, our method outperforms them by 1.87dB and 2.38dB. As illustrated in Fig. 7, our method can significantly enhance deblurring performance in the presence of complex textures, such as text on license plates, text on ships, and details in faces. Through the comparison of the REDS dataset, we further demonstrate the deblurring capability of the model and its generalization ability to different datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.786, + 0.763, + 0.803 + ], + "angle": 0, + "content": "4.4. Results on Real World Spikes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To assess the deblurring capability of our method in real-world scenarios, we set up a simple unaligned spike-RGB hybrid camera system. Fig. 8 shows real-world test cases, including fast-moving objects at close range and outdoor driving scenarios with rapid motion. As shown in Fig. 8, our method significantly outperforms other approaches in" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "25053" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.464, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.204, + 0.47, + 0.233 + ], + "angle": 0, + "content": "Figure 8. Visualized results on real-world data captured with an RGB camera and a spike camera." + }, + { + "type": "table", + "bbox": [ + 0.101, + 0.248, + 0.447, + 0.326 + ], + "angle": 0, + "content": "
Stage1Stage2Stage3PSNR ↑SSIM ↑
✓××32.300.914
✓✓×32.900.923
✓✓✓35.780.964
" + }, + { + "type": "table_caption", + "bbox": [ + 0.091, + 0.336, + 0.454, + 0.351 + ], + "angle": 0, + "content": "Table 3. Experiments on the performance of the model stage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.379, + 0.47, + 0.426 + ], + "angle": 0, + "content": "motion deblurring. We also observed that due to the high dynamic information contained in the spike stream, our method excels of deblurring in scenes with overexposure." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.438, + 0.242, + 0.453 + ], + "angle": 0, + "content": "4.5. Ablation Studies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.47, + 0.674 + ], + "angle": 0, + "content": "A. Performance Increases at each stage. To demonstrate the effectiveness of multi-stage model design, we conduct ablation experiments on the deblurring effects at each stage. As shown in Tab. 3, when performing the first stage training, the model possesses basic deblurring capabilities. With the introduction of the bi-directional deformable alignment in the second stage, the model shows a noticeable improvement of \\(0.6\\mathrm{dB}\\) and 0.01 in PSNR and SSIM, respectively. The addition of the flow-guided feature fusion network in the third stage further increases the PSNR to the highest value of \\(35.78\\mathrm{dB}\\). These experimental results indicate that through progressive training, clear texture information from the spike stream can effectively be introduced into the image domain, guiding the deblurring process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.675, + 0.471, + 0.902 + ], + "angle": 0, + "content": "B. Deblurring Potentials under Precise Alignment. The above experiments demonstrate that our method effectively removes blur when spikes and images are unknownly aligned in both time and space. To further validate the potential of our method, we modify the X4k1000FPS and REDS datasets to strictly align spikes and images and test the model's performance under the condition of complete spatiotemporal alignment between modalities. As shown in Tab. 4, the results on the X4K1000FPS dataset include the quantitative results of two other methods, EFNET and REFID, which also take spikes as guiding input. The results show that our method achieves a PSNR of 36.92dB, surpassing the other two methods by 0.56dB and 0.62dB. We also test the performance improvement on REDS. The experiment shows that our method improves from 33.61dB" + }, + { + "type": "table", + "bbox": [ + 0.519, + 0.089, + 0.878, + 0.166 + ], + "angle": 0, + "content": "
MethodInput DataPSNR ↑SSIM ↑
EFNet [32]Image+Spike36.360.960
REFID [33]Image+Spike36.300.962
UaSDN(Ours)Image+Spike36.920.969
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.177, + 0.892, + 0.205 + ], + "angle": 0, + "content": "Table 4. Comparison of various motion deblurring methods on X4K1000FPS [30] when spikes and images are precise aligned." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.218, + 0.891, + 0.343 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.353, + 0.892, + 0.381 + ], + "angle": 0, + "content": "Figure 9. Influence of border areas when sampled spikes are totally not involved in the exposure of the image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.453 + ], + "angle": 0, + "content": "to 34.60dB on REDS, indicating that our method has great potential for application in spike-guided deblurring. Visualized results are shown in the supplementary materials." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.453, + 0.893, + 0.619 + ], + "angle": 0, + "content": "C. How the border areas are handled from spatial and temporal perspectives. Generally, the motion near the border is similar. The model learns motion clues in spikes that supplement textures. Besides, our image-based stage-1 in UaSDN performs basic deblurring without spikes. In Fig. 9, the image that is spatiotemporal unaligned with spikes is recovered well by UaSDN. The quality is close to the deblurred one with perfect alignment (28.58 dB). The curve shows the model maintains acceptable results though the PSNR declines when spikes are not involved in the image exposure time at all." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.634, + 0.62, + 0.649 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.766 + ], + "angle": 0, + "content": "We first explore the motion deblurring guided by a spike camera under unknown spatiotemporal alignment between two modalities. We believe the proposed method possesses potential in the real world. The proposed three-stage UaSDN contains a bi-directional deformable alignment and a flow-based fusion module. Results prove that UaSDN outperforms other methods on unaligned deblurring." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.779, + 0.652, + 0.796 + ], + "angle": 0, + "content": "Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.803, + 0.892, + 0.888 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (62176003, 62088102, 62306015), the China Postdoctoral Science Foundation (2022M720238, 2023T160015), the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), and the Beijing Nova Program (20230484362)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "25054" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Christian Brandli, Raphael Berner, Minhao Yang, Shih-Chii Liu, and Tobi Delbruck. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12428-12437, 2023. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.682 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "25057" + } + ] +] \ No newline at end of file diff --git a/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_origin.pdf b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..69eafca3434b49f2da08abbff85637843b48f172 --- /dev/null +++ b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/fc7703e6-e447-4073-bf40-f253b97da714_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:9995b8434e2e1862e7fecfc8dc9f94d4d8f059507c9bc7aeab4396ccb3325bc5 +size 4016696 diff --git a/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/full.md b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/full.md new file mode 100644 index 0000000000000000000000000000000000000000..98d83ad3eceeedfb322344b5510df60298b00e95 --- /dev/null +++ b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/full.md @@ -0,0 +1,340 @@ +# Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment + +Jiyuan Zhang $^{1,2}$ Shiyan Chen $^{1,2}$ Yajing Zheng $^{1,2*}$ Zhaofei Yu $^{1,2,3*}$ Tiejun Huang $^{1,2,3}$ $^{1}$ School of Computer Science, Peking University + $^{2}$ National Key Laboratory for Multimedia Information Processing, Peking University + $^{3}$ Institute for Artificial Intelligence, Peking University + +{jyzhang,2301112005}@stu.pku.edu.cn，{yj.zheng,yuzf12,tjhuang}@pku.edu.cn + +# Abstract + +The traditional frame-based cameras that rely on exposure windows for imaging experience motion blur in high-speed scenarios. Frame-based deblurring methods lack reliable motion cues to restore sharp images under extreme blur conditions. The spike camera is a novel neuromorphic visual sensor that outputs spike streams with ultra-high temporal resolution. It can supplement the temporal information lost in traditional cameras and guide motion deblurring. However, in real-world scenarios, aligning discrete RGB images and continuous spike streams along both temporal and spatial axes is challenging due to the complexity of calibrating their coordinates, device displacements in vibrations, and time deviations. Misalignment of pixels leads to severe degradation of deblurring. We introduce the first framework for spike-guided motion deblurring without knowing the spatiotemporal alignment between spikes and images. To address the problem, we first propose a novel three-stage network containing a basic deblurring net, a carefully designed bi-directional deformable aligning module, and a flow-based multi-scale fusion net. Experimental results demonstrate that our approach can effectively guide the image deblurring with unknown alignment, surpassing the performance of other methods. Public project page: https://github.com/Leozhangjiyuan/UaSDN. + +# 1. Introduction + +The imaging principle of conventional frame-based cameras is based on the concept of exposure time windows. During the continuous imaging process, the time between the exposure windows of adjacent frames is unused. Due to the presence of exposure windows, when the camera is in high-speed motion or there are fast-moving objects in the scene, images may exhibit a blur effect. In recent years, + +![](images/d51f39e9240c9aa03129b66e16311207bc850af1594954d465bdb9f312a4a7a0.jpg) +Figure 1. Illustration of unknown spatiotemporal alignment between a spike camera and an RGB camera. + +many studies have focused on addressing the challenging task of recovering clear images from blurry ones utilizing deep-learning routes [4, 5, 16]. However, the texture or structural information in blurry images is partially lost during the exposure, making it difficult to infer clear textures directly from blurry images, as in Fig. 2 (Orange Box). + +Introducing spike cameras as clues of deblurring. Bioinspired neuromorphic vision sensors have attracted increasing attention and achieved significant development. They possess advantages such as ultra-high temporal resolution, low latency, and high dynamic range. Due to the continuous recording of light intensity, neuromorphic cameras can be used to compensate for the lack of temporal information in image deblurring. Based on different sampling principles, they can be classified into event cameras [1, 21, 23] and spike cameras [12]. Event cameras asynchronously detect changes in light intensity and are highly sensitive to moving edges. Studies utilize events for image deblurring [28, 32]. Spike cameras accumulates + +photons and emits $20,000\mathrm{Hz}$ spike streams. Due to the integration sampling principle, it can thoroughly record spatiotemporal information, including the texture and motion information of the scene. The precise texture information recorded in spikes can effectively guide the deblurring process. Our paper explores the effectiveness of using spike cameras to guide motion deblurring, uncovering the potential advantages of spike cameras in this novel task. + +Take misalignment between cameras in real application into consideration. At present, most deblurring works based on event cameras assume that the imaging planes of the two cameras are absolutely coaxial [32, 33] and that the event stream and video are fully synchronized on the time axis. Such assumptions facilitate model design but are overly idealistic. In the real world, achieving strict alignment of a spike camera and an RGB camera in both spatial and temporal dimensions is quite challenging. As shown in Fig. 1, in this work, we consider the unknown alignment factors in the real world: + +(A) Spatial alignment of the two cameras is challenging. Alignment of the coordinate systems of the two cameras can be achieved using methods such as beam splitters or manual calibration (e.g., chessboard calibration). However, beam splitters can result in significant loss of light, and differences in focal length, aperture, and relative positions between cameras, which can vary with the scene, make alignment operations complex and difficult. +(B) Position displacements. During motion, minor displacements in the relative positions of the two cameras occur due to vibrations. For current algorithms, pixel misalignment will lead to significant performance losses. +(C) Synchronizing discrete image sequences with continuous spike streams on the time axis is challenging. Technically, obtaining spikes strictly synchronized with blurry images requires acquiring the accurate exposure start and end times of the blurry images, which is complex. Moreover, in high-speed motion scenes, the two data streams are prone to small time deviations, leading to misalignment. + +What we focus on and How we deal with the real-world misalignment? In response to the real-world misalignments mentioned above, we focus on investigating spike-guided motion deblurring with unknown spatiotemporal alignment between spikes and RGB images, as shown in Figs. 1 and 2. The proposed method allows for the use of two cameras simultaneously without the need for complex and rigorous spatial calibration and time alignment design. To address the problem, we propose an effective three-stage model Unaligned Spike-guided Deblur Net (UaSDN). (1) In the first stage, we employ a simplified off-the-shelf network to perform basic deblurring. In this stage, we aim to leverage existing technology to alleviate the blurring and enhance textures. (2) In the second stage, we first use a shallow net to estimate coarse light intensity + +from the spike stream. Besides, we design a bidirectional deformable modal alignment module. The module achieves better alignment by learning bidirectional deformable convolutions between spike features and image features. (3) In the third stage, we design a multi-scale dense fusion network combining the optical flow, which performs feature fusion by aligning pixel motion offsets between modalities and fuse features in a multi-scale network. Through comparisons with various networks, experimental results demonstrate the effectiveness of our method in motion deblurring with unknown spatiotemporal alignment between modalities. To comprehensively validate the model's performance, we construct spike datasets for training and validation. Our contributions can be summarized as follows: + +- We first explore the motion deblurring tasks guided by the spike camera and deal with the unknown spatiotemporal alignment between two modalities in the real world. +- We propose the three-stage UaSDN model which contains a bi-directional deformable modal alignment module and a flow-based fusion module. +- Experimental results demonstrate that our model significantly outperforms other methods on motion deblurring with unknown spatiotemporal alignment. + +# 2. Related Work + +# 2.1. Advances on Spike Cameras + +The spike camera outputs spikes with an ultra-high temporal resolution of $20,000\mathrm{Hz}$ [12]. Due to the sampling principle, it effectively captures texture in both moving and stationary areas, demonstrating potential in high-speed scenarios. Research focuses on utilizing spike cameras for image recovery or high-level visual tasks. Early studies involved direct statistics of spike counts or intervals for a rough estimation of light intensity [57]. Zhao et al. [52] introduces the first learning-based method. Zhang et al. [47] leverages wavelet transforms on spikes, and enhances the representational capability of spikes. Some bio-inspired works employ spiking neural networks (SNN) [53, 55] to process spikes. The introduction of self-supervised schemes enhanced the generalization capability [6]. Many applications have emerged, such as super-resolution reconstruction [51] and high-dynamic-range restoration [3], spike-guided video interpolation [41], denoising [11] and tracking [54]. + +# 2.2. Frame-based Motion Deblurring + +In recent years, with the rise of deep learning, CNN-based approaches have shown remarkable performance in frame-based deblurring tasks. Popular technical routes are employing end-to-end training [4, 9, 16, 24, 34, 44]. Some works [17, 18] employ generative networks. Rather than mapping a blurry image one-to-one to a single sharp image, some work [2, 13, 26, 27, 31, 38, 56, 58] attempts to mine + +![](images/5026fa3bfb4b6f1e9d404ea6ada1e8bd767f5192d5d0cf50770a99f3a47a8ad3.jpg) +Figure 2. Illustration of the process of deblurring images in different scenarios. Orange box: deblurring directly from the RGB camera; blue box: deblurring with precise alignment of spike-RGB data; green box: unknown alignment in X-Y-T for spike-RGB data. + +![](images/3e65ce3b8687fecd8da5e90d1e017904701699a8bc076308a15ecbe776ea1e9d.jpg) + +clues from video sequence input to assist in deblurring. However, video-based methods always use future frames, which is not applicable in the real world. Besides, many image-based image restoration models are able to deal with deblurring [4, 5, 19, 20, 39, 43-45]. + +# 2.3. Event-guided Motion Deblurring + +As neuromorphic vision sensors, event cameras have been used in deblurring. Pan et al. [28] builds a computational model between blurred images and events. Several works [14, 36] utilize motion information and recurrent networks for aligning. Shang et al. [29] enhances the deblurring by finding adjacent sharp frames. Kim et al. [15] and Weng et al. [40] deal with images with unknown exposure time. EFNet [32] introduces an attention-based module to better fuse events. Cho et al. [8] proposed a solution for cameras with spatial offsets. Zhang et al. [49] proposes to generalize the deblurring ability to various spatial resolutions and blur levels. Some works [22, 28, 33, 37, 42, 48] combine the motion deblurring and frame interpolation guided by events. However, most studies assume that scenes captured by the event camera and the traditional camera are entirely identical, i.e. two camera coordinates coincide perfectly along the spatial axis and events have the same center and duration as the exposure time of blurred images on the temporal axis. Our study aims to address motion deblurring in real scenes unknown of the alignment between cameras in both time and space. + +# 3. Method + +# 3.1. Problem Analysis + +We mainly focus on dealing with the motion deblurring in high-speed scenarios guided by a spike camera while not knowing the alignment between the RGB camera and spike camera on both the spatial axis and temporal axis. In this + +section, we give a specific analysis of how to utilize spike data for deturbing spatiotemporal unaligned RGB frames. + +An RGB camera outputs discrete RGB blurry frames $\mathbb{B} = \{\mathbf{B}_i|i\in \mathbf{N}\}$ with the exposure time of $T_{B}$ , which is a shorter duration than the time duration between successive frames $T_{F}$ (the frame rate $f = \frac{1}{T_F}$ ). A spike camera outputs the spike stream S with the rate of $20000\mathrm{Hz}$ . Each pixel $(x,y)$ of a spike camera on the $H_{S}\times W_{S}$ plane independently receives coming photons continuously at any timestamps $t$ , converts the light signals into electrical current $I_{x,y}(t)$ , and accumulates the voltage $V_{x,y}$ . Whenever the voltage reaches the preset threshold $\Theta$ , the pixel fires a spike and resets the voltage to 0. The spike signals are read out with a very short interval ( $\tau = \frac{1}{20000Hz} = 50\mu s$ ). The process can be formulated as follows: + +$$ +\mathbf {S} _ {x, y} (c) = \left\{ \begin{array}{l l} 1, & \text {i f} \exists t \in ((c - 1) \tau , c \tau ], V _ {x, y} (t) = 0, \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {1} +$$ + +$$ +V _ {x, y} ^ {+} (t) = \left\{ \begin{array}{l l} V _ {x, y} ^ {-} (t) + I _ {x, y} (t), & \text {i f} V _ {x, y} ^ {-} (t) < \Theta , \\ 0, & \text {o t h e r w i s e}, \end{array} \right. \tag {2} +$$ + +where $V_{x,y}^{-}(t)$ and $V_{x,y}^{+}(t)$ denotes the voltage before and after receiving the electric current $I_{x,y}(t)$ , $c \in \mathbb{R}$ . The spike stream $S$ is output with the size of $H \times W \times C$ after $C$ times readout during $T\mu s$ ( $C = \frac{T}{\tau}$ ). + +For a blurred image $\mathbf{B}_i$ , it can be represented as the average of the clear images $\{\mathbf{L}\}$ over the exposure time, i.e.: + +$$ +\mathbf {B} _ {i} = \frac {1}{T _ {\mathbf {B}}} \int_ {T _ {i} - T _ {\mathbf {B}} / 2} ^ {T _ {i} + T _ {\mathbf {B}} / 2} \mathbf {L} (t) d t, \tag {3} +$$ + +where $T_{i}$ is the center of exposure time and $\mathbf{L}_i$ at $T_{i}$ . + +Why spike cameras hold potential on image deblurring. The deblurring process can be formulated as: + +$$ +\underset {\theta_ {M}} {\arg \min } \| \hat {\mathbf {L}} _ {i} - \mathbf {L} _ {i} \|, \text {w h e r e} \hat {\mathbf {L}} _ {i} = \mathcal {F} \left(\mathbf {B} _ {i}: \theta_ {M}\right), \tag {4} +$$ + +![](images/b37a1bd1be3e3eab9f2b24342c98585bfc0e45cef81855993c0d6d616b9f1e9c.jpg) +Figure 3. The architecture of the proposed Unaligned Spike-guided Deblur Net (UaSDN). + +where $\theta$ is the optimized parameters of the model $M$ and $\hat{\mathbf{L}}_i$ is the predicted clear image. The $\theta$ is hard to optimize when $\mathbf{B}_i$ holds extreme blur. Neglecting color information and differences in spatial resolution, when the spike camera and RGB camera are perfectly aligned, the clear image $\mathbf{L}_i$ can also be approximated using spikes: + +$$ +\tilde {\mathbf {L}} _ {i} \simeq \mathcal {F} _ {M _ {S 2 I}} \left(\left\{\mathbf {S} (t) \mid t \in \left[ T _ {i} - \frac {T _ {\mathbf {B}}}{2}, T _ {i} + \frac {T _ {\mathbf {B}}}{2} \right] \right\}: \theta_ {S 2 I}\right), \tag {5} +$$ + +where $M_{S2I}$ is the model for reconstructing spikes to the approximated image $\tilde{\mathbf{L}}_i$ . Many existing models [47, 52] are able to reconstruct high-quality $\tilde{\mathbf{L}}_i$ . Despite that $\hat{\mathbf{L}}_i$ lacks color information and has lower spatial resolution compared to $\mathbf{B}_i$ , its clear texture effectively provides deblurring clues for $\mathbf{B}_i$ as shown in Fig. 2, which is proved by our experiments in Sec. 4.5. When not knowing the alignment between the RGB camera and spike camera on both spatial and temporal axis, we cannot get the accurate spikes $\{\mathbf{S}(t)\}$ in Eq. (5). Thus textures in $\tilde{\mathbf{L}}_i$ are not aligned with $\mathbf{L}_i$ , which raises challenges for spikes to guide the deblurring. + +How to deal with unknown alignment? We set the situation of the unknown alignment as follows: (1) Spatial axis. There are blind plane displacements $\Delta \mathbf{P}$ between two cameras. Generally, we set the $\Delta \mathbf{P}$ not a constant but a variable parameter. (2) Temporal axis. Spike stream is continuous while RGB frames are discrete. When two streams cannot be precisely synchronized, in real situations, we can roughly fetch a segment of spikes $\mathbf{S}_k$ around the corresponding exposure window $T_{i}$ of image $\mathbf{B}_i$ . The temporal center of $\mathbf{S}_k$ is unknown. In this case, we aim to build the model learning the aligning process adaptively. + +# 3.2. Overall Architecture + +For not knowing the alignment, accurately matching the textures between the blurred image and spikes is challenging, requiring the model to have the ability for adaptive + +feature matching. However, on one hand, the texture of the blurred image $\mathbf{B}$ suffers from significant information loss. On the other hand, the irregular spike data cannot directly express scene textures like images. Therefore, we aim to progressively optimize the motion deblurring, gradually restoring clear textures of the blurred image and spikes. To achieve this, we propose a three-stage model named Unaligned Spike-guided Deblur Net (UaSDN). The network architecture of UaSDN is illustrated in Fig. 3. + +UaSDN consists of three deblurring stages. (1) First Stage: Basic Image Deblurring Unclear texture in blurred images $\mathbf{B}$ makes it difficult to match with features in spikes. We employ a simple network $M_{1}$ to learn basic deblurring for $\mathbf{B}$ . The network takes the blurred image $\mathbf{B}$ as input and outputs the predicted image $\hat{\mathbf{L}}_{1}$ (2) Second Stage: Bi-Deformable Aligning Enhancement. The texture of $\mathbf{B}$ is enhanced after the stage 1. In this stage, we design a module $M_{2}$ based on deformable convolution to achieve basic alignment between spike features and blurred image features. Besides, to restore scene textures in spikes, we use shallow convolutional layers $M_{S2I}$ to input spikes and quickly infer the rough light intensity. We randomly sample $K$ segments of spikes $\{\mathbf{S}_k|k\in [1,2,\dots K]\}$ as guidance input to $M_{2}$ , which outputs the enhanced image $\hat{\mathbf{L}}_{2}$ . (3) Third Stage: Flow-guided Dense Fusion. In this stage, we aim to utilize optical flows $v_{S2I}$ from spikes $\mathbf{S}$ to the image $\hat{\mathbf{L}}_{2}$ as guidance for precise alignment. To achieve this, we design the multi-scale flow-guided deblurring module, which takes the sampled $K$ spike segments as input and predicts the final clear image $\hat{\mathbf{L}}_{3}$ . The process can be formulated as: + +$$ +\hat {\mathbf {L}} _ {1} = \mathcal {F} _ {M _ {1}} \left(\mathbf {B}: \theta_ {M _ {1}}\right), \tag {6} +$$ + +$$ +\hat {\mathbf {L}} _ {2} = \mathcal {F} _ {M _ {2}} \left(\hat {\mathbf {L}} _ {1}, \left\{\mathbf {S} _ {k} \mid k \in [ 1, 2, \dots , K ] \right\}: \theta_ {M _ {2}}\right), \tag {7} +$$ + +$$ +\hat {\mathbf {L}} _ {3} = \mathcal {F} _ {M _ {3}} \left(\hat {\mathbf {L}} _ {2}, \left\{\mathbf {S} _ {k} \mid k \in [ 1, 2, \dots , K ] \right\}: \theta_ {M _ {3}}\right). \tag {8} +$$ + +![](images/d0aaab3376b6cf6d5d40259c4eeed7c05b52b060b636d7d5f7c50d442b546780.jpg) +Figure 4. The architecture of the proposed Bi-directional Deformable Modal Aligning (BiDMA) module. + +# 3.3. Stage 1: Basic Image Deblurring + +In the first stage, we employed one of the current state-of-the-art image restoration networks, NAFNet [5], as the basic deblurring module $M_{1}$ . We aim to use $M_{1}$ to lighten the blurring effect and enhance the texture of the blurred image $\mathbf{B}$ , as shown in Fig. 3. Specifically, NAFNet is a U-shaped multi-scale network. $\mathbf{B}$ undergoes 4 times down-sampling during feature extraction, followed by up-sampling. In the up-sampling process, features from each scale are fused, and the network finally outputs $\hat{\mathbf{L}}_{1}$ . To reduce parameter count and accelerate inference speed, the overall network channel number is halved. Detailed architectures are provided in the supplementary material. + +# 3.4. Stage 2: Bi-Deformable Aligning Enhancement + +At this stage, spikes are introduced. As in Eq. (5), if two cameras are perfectly aligned in space and time, spikes can be optimized to obtain a clear grayscale image $\tilde{\mathbf{L}}_{\mathbf{S}}$ without color information and at a lower resolution. The reconstructed gray-scale image can effectively aid in deblurring the RGB image. Our goal is to learn an adaptive pixel alignment relationship between modalities through learning. We first pass the sampled spike fragments through a shallow convolutional module $M_{S2I}$ to quickly estimate the corresponding rough grayscale intensity $\tilde{\mathbf{L}}_{\mathbf{S}}$ . $M_{S2I}$ consists of only 4 convolutional layers, which is formulated as: + +$$ +\tilde {\mathbf {L}} _ {\mathbf {S}} = \mathcal {F} _ {M _ {S 2 I}} (\mathbf {S}: \theta_ {M _ {S 2 I}}), \tag {9} +$$ + +In addition, we designed the bi-directional deformable modal align (BiDMA) module, as illustrated in Fig. 4. The spike and image features are extracted with downsampling, denoted as $\mathbf{F_S} = \{F_{\mathbf{S}}^h\}$ and $\mathbf{F_L} = \{F_{\mathbf{L}}^h\}$ , where $h \in [1,2,\dots,H]$ is the number of scales. A deformable convolution network(DCN) [10] $\mathcal{F}_{DCN}$ can align two kinds of features, the principle can be denoted as: + +$$ +F (p) = \sum_ {q = 1} ^ {Q} w _ {q} \cdot F \left(p + p _ {q} + \Delta p _ {q}\right) \cdot \Delta m _ {q}, \tag {10} +$$ + +where $p = (x,y)$ is the coordinate of the center pixel, Q denotes pixel numbers in the neighbor of $p$ , $p_q$ is the fixed offset from $p$ , $w_q$ denotes the weight, $\Delta m_q$ denotes the modulation scalar. $\Delta p_q$ is the learnable offset, which is predicted + +by two modal features with a module $\mathcal{F}_{\Delta}$ consisting of several convolution layers. In each $h$ -level, we consider the bi-directional deformable aligning: 1) align $F_{\mathbf{L}}^{h}$ of image to $F_{\mathbf{S}}^{h}$ of spikes and get the $\bar{F}_{\mathbf{L}}^{h}$ ; 2) fuse the $\bar{F}_{\mathbf{L}}^{h}$ and $F_{\mathbf{S}}^{h}$ , and get $\bar{F}_{\mathbf{S}}^{h}$ ; 3) align the $\bar{F}_{\mathbf{S}}^{h}$ back to $F_{\mathbf{L}}^{h}$ , and get $\bar{\bar{F}}_{\mathbf{S}}^{h}$ . The process can be formulated as: + +$$ +\begin{array}{l} \Delta P _ {I 2 S} ^ {h} = \mathcal {F} _ {\Delta} ([ F _ {\mathbf {L}} ^ {h}, F _ {\mathbf {S}} ^ {h} ], \Delta P _ {I 2 S} ^ {h + 1}), \\ \bar {F} _ {\mathbf {L}} ^ {h} = \mathcal {F} _ {\oplus} \left(\mathcal {F} _ {D C N} \left(F _ {\mathbf {L}} ^ {h}, \Delta P _ {I 2 S} ^ {h}\right), \mathbf {U} _ {\mathbf {p}} \left(\bar {F} _ {\mathbf {L}} ^ {h + 1}\right)\right), \tag {11} \\ \bar {F} _ {\mathbf {S}} ^ {h} = \mathcal {F} _ {\oplus} (\bar {F} _ {\mathbf {L}} ^ {h}, F _ {\mathbf {S}} ^ {h}), \\ \end{array} +$$ + +$$ +\begin{array}{l} \Delta P _ {S 2 I} ^ {h} = \mathcal {F} _ {\Delta} ([ \bar {F} _ {\mathbf {S}} ^ {h}, F _ {\mathbf {L}} ^ {h} ], \Delta P _ {S 2 I} ^ {h + 1}), \\ \bar {\bar {F}} _ {\mathbf {S}} ^ {h} = \mathcal {F} _ {\oplus} \left(\mathcal {F} _ {D C N} \left(\bar {F} _ {\mathbf {S}} ^ {h}, \Delta P _ {S 2 I} ^ {h}\right), \mathbf {U p} \left(\bar {\bar {F}} _ {\mathbf {S}} ^ {h + 1}\right)\right), \tag {12} \\ \end{array} +$$ + +$$ +F _ {a l i g n} = \mathcal {F} _ {\oplus} (\bar {\bar {F}} _ {\mathbf {S}} ^ {1}, F _ {\mathbf {L}} ^ {1}), +$$ + +where $\mathcal{F}_{DCN}$ is the DCN network as in Eq. (10), $\mathcal{F}_{\oplus}$ is the feature fusion function with simple Conv layers, $\mathbf{U}\mathbf{p}(\cdot)$ is the upsampling operation. Eq. (11) describe the align process from images to spikes, and Eq. (12) describe the align process from spikes back to images. In this way, at the 1-level, the aligned feature $F_{align}$ is fused by $\mathcal{F}_{\oplus}$ with several Conv layers. As described in Sec. 3.1, we sample $K$ segments of spikes for alignment with the image. Thus the output $\hat{\mathbf{L}}_2$ of stage 2 is formulated as: + +$$ +\hat {\mathbf {L}} _ {2} = \mathcal {F} _ {p r e d} ([ F _ {a l i g n, 1}, F _ {a l i g n, 2}, \dots , F _ {a l i g n, K} ]). \tag {13} +$$ + +# 3.5. Stage 3: Flow-guided Dense Fusion + +After the alignment in stage 2, textures of $\hat{\mathbf{L}}_2$ are further enhanced by spikes. In this stage, we aim to achieve precise alignment of spike features through optical flow guidance, improving the deblurring effect by supplementing detailed textures from features in the spike. Thus, we build a flow-guided dense fusion network for the final refinement. as illustrated in Fig. 3. Firstly, $K$ coarse light intensity estimation $\{\tilde{\mathbf{L}}_{\mathbf{S}_k}|k\in [1,2,\dots ,K]\}$ are predicted as Eq. (9) described from the sampled spike segments $\{\mathbf{S}_k|k\in$ $[1,2,\ldots ,K]\}$ . Then, we compute the optical flows $V_{\mathbf{S}_k\rightarrow \hat{\mathbf{L}}_2}$ between the $\hat{\mathbf{L}}_2$ and each $\tilde{\mathbf{L}}_{\mathbf{S}_k}$ , then warp the $\tilde{\mathbf{L}}_{\mathbf{S}_k}$ to $\tilde{\mathbf{L}}_{\mathbf{S}_k}^w$ according to the $V_{\mathbf{S}_k\rightarrow \hat{\mathbf{L}}_2}$ . The process is formulated as: + +$$ +\begin{array}{l} V _ {\mathbf {S} _ {k} \rightarrow \hat {\mathbf {L}} _ {2}} = \mathcal {F} _ {f l o w} (\tilde {\mathbf {L}} _ {\mathbf {S} _ {k}}, \hat {\mathbf {L}} _ {2}), \tag {14} \\ \tilde {\bf L} _ {{\bf S} _ {k}} ^ {w} = \mathcal {G} (\tilde {\bf L} _ {{\bf S} _ {k}}, V _ {{\bf S} _ {k} \rightarrow \hat {{\bf L}} _ {2}}), \\ \end{array} +$$ + +where $\mathcal{F}_{flow}$ is the pretrained image-based flow estimation network [35], and $\mathcal{G}$ denotes the feature warp operator. Then, we concatenate $\{\tilde{\mathbf{L}}_{\mathbf{S}_k}^w |k\in [1,2,\dots ,K]\}$ and $\hat{\mathbf{L}}_2$ , and get the tiled image $\hat{\mathbf{L}}_{tile}$ . The U-shape network contains the encoder and decoder. In the encoder, the image features of $\hat{\mathbf{L}}_{tile}$ are extracted with downsampling, denoted as $\mathbf{F}_{\hat{\mathbf{L}}_{tile}} = \{F_{\hat{\mathbf{L}}_{tile}}^{h}\} ,h = [1,2,\dots ,H]$ . The feature $F_{\hat{\mathbf{L}}_{tile}}^{h}$ at + +![](images/f39971f68134817215343e2083093d84f6e9c3a452eb36a5851a23481b71908d.jpg) +Figure 5. The proposed Attention-base Dense Block (ADB). + +level $h$ doubles the channel number of $F_{\hat{\mathbf{L}}_t i t e}^{h - 1}$ at level $h - 1$ . In the decoder, features from the previous layer are upsampled through convolution layers and a pixel shuffle operation, then fuse with features at the current level. Each encoder and decoder at each level is an attention-base dense block(ADB) consisting of a channel attention layer (CA) and a residual dense block (RDB) [50], as in Fig. 5. The CA fuses two features from two modalities and the RDB aims to extract features effectively. In this way, the final deblurred image $\hat{\mathbf{L}}_3$ is predicted with the sum of the output of several convolutional layers and the input $\hat{\mathbf{L}}_2$ . + +# 3.6. Loss functions + +We train the three stages separately, for each stage, we use the $\mathcal{L}_1$ loss to optimize the network. For the coarse light intensity estimation module $M_{S2I}$ , $\mathcal{L}_1$ loss is adopted too. + +$$ +\mathcal {L} _ {d e b l u r} ^ {i} = \left| \hat {\mathbf {L}} _ {1} ^ {i} - \mathbf {L} _ {r g b} \right|, \text {w h e r e} i = 1, 2, 3, \tag {15} +$$ + +$$ +\mathcal {L} _ {M _ {S 2 I}} ^ {i} = | \bar {\mathbf {L}} _ {\mathbf {S}} - \mathbf {L} _ {g r a y} |, +$$ + +where $i$ is the stage index, $\mathbf{L}_{rgb}$ is the ground-truth clear RGB image, and $\mathbf{L}_{gray}$ is the clear gray image with equal spatial resolution as spikes. + +# 4. Experiment + +# 4.1. Datasets and Training Settings + +To train the network, we utilize datasets containing high-speed RGB images as the base and simulate the principle of a spike camera to generate continuous spike streams. Specifically, we conduct training and testing on two large datasets: the X4k1000FPS [30] and the REDS dataset [25]. The X4K1000FPS dataset includes high-definition 1000fps videos, while REDS comprises 1000fps videos, along with real or synthesized blurred images. To generate spike data, we employ the state-of-the-art video interpolation algorithm EMA-VFI [46] to increase the frame rate by 8 times for the image sequences in both datasets, resulting in ultra-high frame rate videos. Ultra-high frame rate videos can approximate the continuous changes in scene lighting, allowing us to use the working principle of a spike camera to generate corresponding spike streams as shown in Eq. (1). Additionally, since the X4K1000FPS dataset does not include blurred images, we simulate the blurry images using an average of 33 frames. In X4K1000FPS and REDS, the equiv + +
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image33.740.935
NAFNet [5]Image34.130.937
EFNet [32]Image+Spike33.280.928
REFID [33]Image+Spike34.220.939
SpkDeblurNet [7]Image+Spike34.470.941
UaSDN(Ours)Image+Spike35.780.964
+ +Table 1. Comparison of various motion deblurring methods on X4K1000FPS [30]. + +
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image31.100.902
NAFNet [5]Image30.730.894
EFNet [32]Image+Spike31.740.912
REFID [33]Image+Spike31.230.904
SpkDeblurNet [7]Image+Spike31.160.911
UaSDN(Ours)Image+Spike33.610.942
+ +Table 2. Comparison of various motion deblurring methods on REDS [25]. + +alent exposure time for the blurred images is 1/120 and 1/24 seconds, respectively. + +How do we set the unknown spatiotemporal alignment between RGB frames and spikes? In the training set, along the spatial axis, we introduce random offsets in up, down, left, and right directions for the spikes compared to the blurred image, with a maximum offset of $10\%$ . Along the temporal axis, the center timestamp of the sampled spike segments compared to the blurred image was set with random offsets in forward and backward directions, with a maximum offset of $25\%$ . For testing, we set the above offset scheme as a fixed uniform distribution to ensure that all methods use the same test data in evaluation. Details of the dataset and training are in supplementary materials. + +# 4.2. Results on X4K1000FPS + +To demonstrate the deblurring capability of our proposed model UaSDN, under modality misalignment, we compare it with five methods: two image-based networks, HINet [4] and NAFNet [5], two state-of-the-art event-based networks, EFNet [32] and REFID [33], and the spike-based SpkDeblurNet [7]. To ensure fairness in the experiments, we modify the inputs of EFNet and REFID to be the blurred images and spikes, with the spike length matching that of UaSDN. We transform the spikes to the input representation used by EFNet and REFID. + +As in Tab. 1, our method achieves 35.78dB in PSNR and 0.964 in SSIM, demonstrating a significant performance improvement compared to other methods. Compared to methods that only take the image as input, our approach + +![](images/238e25bd8304688abc66a79a98bdfc5f0a46275c5ef2e3694c2b217ab8a08614.jpg) +Figure 6. Visualized results of our method (UaSDN) on X4K1000FPS compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet. + +![](images/2013d0a41b03bb694b1fc8a882fe42ea33daa6b1cf6dc91fdc90f7d071f69e53.jpg) +Figure 7. Visualized results of our method (UaSDN) on REDS dataset compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet. + +outperforms HINet and NAFNet by 2.04dB and 1.65dB in PSNR, respectively. It indicates the effectiveness of utilizing spikes as guidance for deblurring. Furthermore, compared to the other two event-based networks that take spikes as input, our approach surpasses EFNet and REFID by 2.50dB and 1.56dB in PSNR. It strongly validates the effectiveness of our model in aligning the two modal data in both time and space. As in Fig. 6, the visual results demonstrate that our method effectively obtains fine textures. For example, in the first row, our method successfully enhances the blurred textures without introducing any shape distortion, while other methods fail to address such extreme blurriness and result in shape distortions. It proves the precise spatiotemporal feature alignment achieved by our method. + +# 4.3. Results on REDS + +On the REDS dataset, as shown in Tab. 2, our method achieves a PSNR of 33.61dB and an SSIM of 0.942. Com + +pared to the image-based methods HINet and NAFNet, our method surpasses them by 2.51dB and 2.88dB, respectively. Compared to the event-based methods EFNet and REFID, our method outperforms them by 1.87dB and 2.38dB. As illustrated in Fig. 7, our method can significantly enhance deblurring performance in the presence of complex textures, such as text on license plates, text on ships, and details in faces. Through the comparison of the REDS dataset, we further demonstrate the deblurring capability of the model and its generalization ability to different datasets. + +# 4.4. Results on Real World Spikes + +To assess the deblurring capability of our method in real-world scenarios, we set up a simple unaligned spike-RGB hybrid camera system. Fig. 8 shows real-world test cases, including fast-moving objects at close range and outdoor driving scenarios with rapid motion. As shown in Fig. 8, our method significantly outperforms other approaches in + +![](images/8e407415c0d0806ae0130c0670420e1b8e173ac9cf66964a085061e99c7447f8.jpg) +Figure 8. Visualized results on real-world data captured with an RGB camera and a spike camera. + +
Stage1Stage2Stage3PSNR ↑SSIM ↑
✓××32.300.914
✓✓×32.900.923
✓✓✓35.780.964
+ +motion deblurring. We also observed that due to the high dynamic information contained in the spike stream, our method excels of deblurring in scenes with overexposure. + +# 4.5. Ablation Studies + +A. Performance Increases at each stage. To demonstrate the effectiveness of multi-stage model design, we conduct ablation experiments on the deblurring effects at each stage. As shown in Tab. 3, when performing the first stage training, the model possesses basic deblurring capabilities. With the introduction of the bi-directional deformable alignment in the second stage, the model shows a noticeable improvement of $0.6\mathrm{dB}$ and 0.01 in PSNR and SSIM, respectively. The addition of the flow-guided feature fusion network in the third stage further increases the PSNR to the highest value of $35.78\mathrm{dB}$ . These experimental results indicate that through progressive training, clear texture information from the spike stream can effectively be introduced into the image domain, guiding the deblurring process. + +B. Deblurring Potentials under Precise Alignment. The above experiments demonstrate that our method effectively removes blur when spikes and images are unknownly aligned in both time and space. To further validate the potential of our method, we modify the X4k1000FPS and REDS datasets to strictly align spikes and images and test the model's performance under the condition of complete spatiotemporal alignment between modalities. As shown in Tab. 4, the results on the X4K1000FPS dataset include the quantitative results of two other methods, EFNET and REFID, which also take spikes as guiding input. The results show that our method achieves a PSNR of 36.92dB, surpassing the other two methods by 0.56dB and 0.62dB. We also test the performance improvement on REDS. The experiment shows that our method improves from 33.61dB + +Table 3. Experiments on the performance of the model stage. + +
MethodInput DataPSNR ↑SSIM ↑
EFNet [32]Image+Spike36.360.960
REFID [33]Image+Spike36.300.962
UaSDN(Ours)Image+Spike36.920.969
+ +Table 4. Comparison of various motion deblurring methods on X4K1000FPS [30] when spikes and images are precise aligned. + +![](images/85e5976d4387ee59e11f198ef9ac1169204081033ae2e9aa581b78fa806032cc.jpg) +Figure 9. Influence of border areas when sampled spikes are totally not involved in the exposure of the image. + +to 34.60dB on REDS, indicating that our method has great potential for application in spike-guided deblurring. Visualized results are shown in the supplementary materials. + +C. How the border areas are handled from spatial and temporal perspectives. Generally, the motion near the border is similar. The model learns motion clues in spikes that supplement textures. Besides, our image-based stage-1 in UaSDN performs basic deblurring without spikes. In Fig. 9, the image that is spatiotemporal unaligned with spikes is recovered well by UaSDN. The quality is close to the deblurred one with perfect alignment (28.58 dB). The curve shows the model maintains acceptable results though the PSNR declines when spikes are not involved in the image exposure time at all. + +# 5. Conclusion + +We first explore the motion deblurring guided by a spike camera under unknown spatiotemporal alignment between two modalities. We believe the proposed method possesses potential in the real world. The proposed three-stage UaSDN contains a bi-directional deformable alignment and a flow-based fusion module. Results prove that UaSDN outperforms other methods on unaligned deblurring. + +# Acknowledgment + +This work was supported by the National Natural Science Foundation of China (62176003, 62088102, 62306015), the China Postdoctoral Science Foundation (2022M720238, 2023T160015), the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), and the Beijing Nova Program (20230484362). + +# References + +[1] Christian Brandli, Raphael Berner, Minhao Yang, Shih-Chii Liu, and Tobi Delbruck. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12428-12437, 2023. 2 \ No newline at end of file diff --git a/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/images.zip b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e248c4e78d24db354f30a626936b61fa981ec072 --- /dev/null +++ b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:abc13c8154e81f144c0857a0056987217cba6d857e6739a659c1a531153bf6a3 +size 847077 diff --git a/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/layout.json b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..e25b4b48442db4f4f79f74cfbba405e80b5e8975 --- /dev/null +++ b/2024/Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment/layout.json @@ -0,0 +1,10034 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 77, + 102, + 516, + 139 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 102, + 516, + 139 + ], + "spans": [ + { + "bbox": [ + 77, + 102, + 516, + 139 + ], + "type": "text", + "content": "Spike-guided Motion Deblurring with Unknown Modal Spatiotemporal Alignment" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "spans": [ + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": "Jiyuan Zhang" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": " Shiyan Chen" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,2}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": " Yajing Zheng" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,2*}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": " Zhaofei Yu" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,2,3*}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": " Tiejun Huang" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1,2,3}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": "School of Computer Science, Peking University \n" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": "National Key Laboratory for Multimedia Information Processing, Peking University \n" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 91, + 159, + 499, + 217 + ], + "type": "text", + "content": "Institute for Artificial Intelligence, Peking University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 97, + 219, + 490, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 219, + 490, + 232 + ], + "spans": [ + { + "bbox": [ + 97, + 219, + 490, + 232 + ], + "type": "text", + "content": "{jyzhang,2301112005}@stu.pku.edu.cn，{yj.zheng,yuzf12,tjhuang}@pku.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 258, + 191, + 271 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 191, + 271 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 191, + 271 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 284, + 290, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 284, + 290, + 571 + ], + "spans": [ + { + "bbox": [ + 46, + 284, + 290, + 571 + ], + "type": "text", + "content": "The traditional frame-based cameras that rely on exposure windows for imaging experience motion blur in high-speed scenarios. Frame-based deblurring methods lack reliable motion cues to restore sharp images under extreme blur conditions. The spike camera is a novel neuromorphic visual sensor that outputs spike streams with ultra-high temporal resolution. It can supplement the temporal information lost in traditional cameras and guide motion deblurring. However, in real-world scenarios, aligning discrete RGB images and continuous spike streams along both temporal and spatial axes is challenging due to the complexity of calibrating their coordinates, device displacements in vibrations, and time deviations. Misalignment of pixels leads to severe degradation of deblurring. We introduce the first framework for spike-guided motion deblurring without knowing the spatiotemporal alignment between spikes and images. To address the problem, we first propose a novel three-stage network containing a basic deblurring net, a carefully designed bi-directional deformable aligning module, and a flow-based multi-scale fusion net. Experimental results demonstrate that our approach can effectively guide the image deblurring with unknown alignment, surpassing the performance of other methods. Public project page: https://github.com/Leozhangjiyuan/UaSDN." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 592, + 127, + 604 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 592, + 127, + 604 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 127, + 604 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 613, + 287, + 696 + ], + "type": "text", + "content": "The imaging principle of conventional frame-based cameras is based on the concept of exposure time windows. During the continuous imaging process, the time between the exposure windows of adjacent frames is unused. Due to the presence of exposure windows, when the camera is in high-speed motion or there are fast-moving objects in the scene, images may exhibit a blur effect. In recent years," + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 313, + 258, + 539, + 430 + ], + "blocks": [ + { + "bbox": [ + 313, + 258, + 539, + 430 + ], + "lines": [ + { + "bbox": [ + 313, + 258, + 539, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 258, + 539, + 430 + ], + "type": "image", + "image_path": "d51f39e9240c9aa03129b66e16311207bc850af1594954d465bdb9f312a4a7a0.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 437, + 545, + 460 + ], + "lines": [ + { + "bbox": [ + 305, + 437, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 305, + 437, + 545, + 460 + ], + "type": "text", + "content": "Figure 1. Illustration of unknown spatiotemporal alignment between a spike camera and an RGB camera." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 484, + 545, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 484, + 545, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 484, + 545, + 556 + ], + "type": "text", + "content": "many studies have focused on addressing the challenging task of recovering clear images from blurry ones utilizing deep-learning routes [4, 5, 16]. However, the texture or structural information in blurry images is partially lost during the exposure, making it difficult to infer clear textures directly from blurry images, as in Fig. 2 (Orange Box)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 546, + 713 + ], + "type": "text", + "content": "Introducing spike cameras as clues of deblurring. Bioinspired neuromorphic vision sensors have attracted increasing attention and achieved significant development. They possess advantages such as ultra-high temporal resolution, low latency, and high dynamic range. Due to the continuous recording of light intensity, neuromorphic cameras can be used to compensate for the lack of temporal information in image deblurring. Based on different sampling principles, they can be classified into event cameras [1, 21, 23] and spike cameras [12]. Event cameras asynchronously detect changes in light intensity and are highly sensitive to moving edges. Studies utilize events for image deblurring [28, 32]. Spike cameras accumulates" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 1, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25047" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": "photons and emits " + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "inline_equation", + "content": "20,000\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 72, + 289, + 167 + ], + "type": "text", + "content": " spike streams. Due to the integration sampling principle, it can thoroughly record spatiotemporal information, including the texture and motion information of the scene. The precise texture information recorded in spikes can effectively guide the deblurring process. Our paper explores the effectiveness of using spike cameras to guide motion deblurring, uncovering the potential advantages of spike cameras in this novel task." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 170, + 289, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 289, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 289, + 300 + ], + "type": "text", + "content": "Take misalignment between cameras in real application into consideration. At present, most deblurring works based on event cameras assume that the imaging planes of the two cameras are absolutely coaxial [32, 33] and that the event stream and video are fully synchronized on the time axis. Such assumptions facilitate model design but are overly idealistic. In the real world, achieving strict alignment of a spike camera and an RGB camera in both spatial and temporal dimensions is quite challenging. As shown in Fig. 1, in this work, we consider the unknown alignment factors in the real world:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 302, + 289, + 534 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 46, + 302, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 302, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 302, + 289, + 399 + ], + "type": "text", + "content": "(A) Spatial alignment of the two cameras is challenging. Alignment of the coordinate systems of the two cameras can be achieved using methods such as beam splitters or manual calibration (e.g., chessboard calibration). However, beam splitters can result in significant loss of light, and differences in focal length, aperture, and relative positions between cameras, which can vary with the scene, make alignment operations complex and difficult." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 399, + 289, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 289, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 289, + 449 + ], + "type": "text", + "content": "(B) Position displacements. During motion, minor displacements in the relative positions of the two cameras occur due to vibrations. For current algorithms, pixel misalignment will lead to significant performance losses." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 449, + 289, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 534 + ], + "type": "text", + "content": "(C) Synchronizing discrete image sequences with continuous spike streams on the time axis is challenging. Technically, obtaining spikes strictly synchronized with blurry images requires acquiring the accurate exposure start and end times of the blurry images, which is complex. Moreover, in high-speed motion scenes, the two data streams are prone to small time deviations, leading to misalignment." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 289, + 715 + ], + "type": "text", + "content": "What we focus on and How we deal with the real-world misalignment? In response to the real-world misalignments mentioned above, we focus on investigating spike-guided motion deblurring with unknown spatiotemporal alignment between spikes and RGB images, as shown in Figs. 1 and 2. The proposed method allows for the use of two cameras simultaneously without the need for complex and rigorous spatial calibration and time alignment design. To address the problem, we propose an effective three-stage model Unaligned Spike-guided Deblur Net (UaSDN). (1) In the first stage, we employ a simplified off-the-shelf network to perform basic deblurring. In this stage, we aim to leverage existing technology to alleviate the blurring and enhance textures. (2) In the second stage, we first use a shallow net to estimate coarse light intensity" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "from the spike stream. Besides, we design a bidirectional deformable modal alignment module. The module achieves better alignment by learning bidirectional deformable convolutions between spike features and image features. (3) In the third stage, we design a multi-scale dense fusion network combining the optical flow, which performs feature fusion by aligning pixel motion offsets between modalities and fuse features in a multi-scale network. Through comparisons with various networks, experimental results demonstrate the effectiveness of our method in motion deblurring with unknown spatiotemporal alignment between modalities. To comprehensively validate the model's performance, we construct spike datasets for training and validation. Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 242, + 545, + 350 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 306, + 242, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 242, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 306, + 242, + 545, + 277 + ], + "type": "text", + "content": "- We first explore the motion deblurring tasks guided by the spike camera and deal with the unknown spatiotemporal alignment between two modalities in the real world." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 278, + 545, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 278, + 545, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 278, + 545, + 312 + ], + "type": "text", + "content": "- We propose the three-stage UaSDN model which contains a bi-directional deformable modal alignment module and a flow-based fusion module." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 314, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 545, + 350 + ], + "type": "text", + "content": "- Experimental results demonstrate that our model significantly outperforms other methods on motion deblurring with unknown spatiotemporal alignment." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 361, + 392, + 374 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 361, + 392, + 374 + ], + "spans": [ + { + "bbox": [ + 306, + 361, + 392, + 374 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 382, + 462, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 382, + 462, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 382, + 462, + 395 + ], + "type": "text", + "content": "2.1. Advances on Spike Cameras" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 400, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 605 + ], + "type": "text", + "content": "The spike camera outputs spikes with an ultra-high temporal resolution of " + }, + { + "bbox": [ + 304, + 400, + 547, + 605 + ], + "type": "inline_equation", + "content": "20,000\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 400, + 547, + 605 + ], + "type": "text", + "content": " [12]. Due to the sampling principle, it effectively captures texture in both moving and stationary areas, demonstrating potential in high-speed scenarios. Research focuses on utilizing spike cameras for image recovery or high-level visual tasks. Early studies involved direct statistics of spike counts or intervals for a rough estimation of light intensity [57]. Zhao et al. [52] introduces the first learning-based method. Zhang et al. [47] leverages wavelet transforms on spikes, and enhances the representational capability of spikes. Some bio-inspired works employ spiking neural networks (SNN) [53, 55] to process spikes. The introduction of self-supervised schemes enhanced the generalization capability [6]. Many applications have emerged, such as super-resolution reconstruction [51] and high-dynamic-range restoration [3], spike-guided video interpolation [41], denoising [11] and tracking [54]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 611, + 484, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 484, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 484, + 624 + ], + "type": "text", + "content": "2.2. Frame-based Motion Deblurring" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "In recent years, with the rise of deep learning, CNN-based approaches have shown remarkable performance in frame-based deblurring tasks. Popular technical routes are employing end-to-end training [4, 9, 16, 24, 34, 44]. Some works [17, 18] employ generative networks. Rather than mapping a blurry image one-to-one to a single sharp image, some work [2, 13, 26, 27, 31, 38, 56, 58] attempts to mine" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25048" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 293, + 223 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 293, + 223 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 293, + 223 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 293, + 223 + ], + "type": "image", + "image_path": "5026fa3bfb4b6f1e9d404ea6ada1e8bd767f5192d5d0cf50770a99f3a47a8ad3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "lines": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 546, + 257 + ], + "type": "text", + "content": "Figure 2. Illustration of the process of deblurring images in different scenarios. Orange box: deblurring directly from the RGB camera; blue box: deblurring with precise alignment of spike-RGB data; green box: unknown alignment in X-Y-T for spike-RGB data." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 533, + 223 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 533, + 223 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 533, + 223 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 533, + 223 + ], + "type": "image", + "image_path": "3e65ce3b8687fecd8da5e90d1e017904701699a8bc076308a15ecbe776ea1e9d.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 276, + 287, + 336 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 276, + 287, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 276, + 287, + 336 + ], + "type": "text", + "content": "clues from video sequence input to assist in deblurring. However, video-based methods always use future frames, which is not applicable in the real world. Besides, many image-based image restoration models are able to deal with deblurring [4, 5, 19, 20, 39, 43-45]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 344, + 225, + 357 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 344, + 225, + 357 + ], + "spans": [ + { + "bbox": [ + 47, + 344, + 225, + 357 + ], + "type": "text", + "content": "2.3. Event-guided Motion Deblurring" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 363, + 289, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 289, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 289, + 616 + ], + "type": "text", + "content": "As neuromorphic vision sensors, event cameras have been used in deblurring. Pan et al. [28] builds a computational model between blurred images and events. Several works [14, 36] utilize motion information and recurrent networks for aligning. Shang et al. [29] enhances the deblurring by finding adjacent sharp frames. Kim et al. [15] and Weng et al. [40] deal with images with unknown exposure time. EFNet [32] introduces an attention-based module to better fuse events. Cho et al. [8] proposed a solution for cameras with spatial offsets. Zhang et al. [49] proposes to generalize the deblurring ability to various spatial resolutions and blur levels. Some works [22, 28, 33, 37, 42, 48] combine the motion deblurring and frame interpolation guided by events. However, most studies assume that scenes captured by the event camera and the traditional camera are entirely identical, i.e. two camera coordinates coincide perfectly along the spatial axis and events have the same center and duration as the exposure time of blurred images on the temporal axis. Our study aims to address motion deblurring in real scenes unknown of the alignment between cameras in both time and space." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 626, + 102, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 102, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 102, + 639 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 646, + 152, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 646, + 152, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 646, + 152, + 659 + ], + "type": "text", + "content": "3.1. Problem Analysis" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 715 + ], + "type": "text", + "content": "We mainly focus on dealing with the motion deblurring in high-speed scenarios guided by a spike camera while not knowing the alignment between the RGB camera and spike camera on both the spatial axis and temporal axis. In this" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 276, + 545, + 299 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 545, + 299 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 545, + 299 + ], + "type": "text", + "content": "section, we give a specific analysis of how to utilize spike data for deturbing spatiotemporal unaligned RGB frames." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": "An RGB camera outputs discrete RGB blurry frames " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\mathbb{B} = \\{\\mathbf{B}_i|i\\in \\mathbf{N}\\}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": " with the exposure time of " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "T_{B}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": ", which is a shorter duration than the time duration between successive frames " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "T_{F}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": " (the frame rate " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "f = \\frac{1}{T_F}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": "). A spike camera outputs the spike stream S with the rate of " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "20000\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": ". Each pixel " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": " of a spike camera on the " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "H_{S}\\times W_{S}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": " plane independently receives coming photons continuously at any timestamps " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": ", converts the light signals into electrical current " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "I_{x,y}(t)" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": ", and accumulates the voltage " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "V_{x,y}" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": ". Whenever the voltage reaches the preset threshold " + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": ", the pixel fires a spike and resets the voltage to 0. The spike signals are read out with a very short interval (" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "inline_equation", + "content": "\\tau = \\frac{1}{20000Hz} = 50\\mu s" + }, + { + "bbox": [ + 304, + 300, + 546, + 455 + ], + "type": "text", + "content": "). The process can be formulated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 313, + 460, + 545, + 492 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 460, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 313, + 460, + 545, + 492 + ], + "type": "interline_equation", + "content": "\\mathbf {S} _ {x, y} (c) = \\left\\{ \\begin{array}{l l} 1, & \\text {i f} \\exists t \\in ((c - 1) \\tau , c \\tau ], V _ {x, y} (t) = 0, \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {1}", + "image_path": "956592ae8de68c1d1e46765f01c5e7fa4ac0bf96c752451fae8fc60e283d2972.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 321, + 504, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 504, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 321, + 504, + 545, + 536 + ], + "type": "interline_equation", + "content": "V _ {x, y} ^ {+} (t) = \\left\\{ \\begin{array}{l l} V _ {x, y} ^ {-} (t) + I _ {x, y} (t), & \\text {i f} V _ {x, y} ^ {-} (t) < \\Theta , \\\\ 0, & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {2}", + "image_path": "fb74fb52a9fb709a938ee26bf8cf8bc9731396bcb1b1cffdac6ae9b9fd3dfdda.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "V_{x,y}^{-}(t)" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "V_{x,y}^{+}(t)" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": " denotes the voltage before and after receiving the electric current " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "I_{x,y}(t)" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "c \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": ". The spike stream " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": " is output with the size of " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "H \\times W \\times C" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": " after " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": " times readout during " + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "T\\mu s" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "inline_equation", + "content": "C = \\frac{T}{\\tau}" + }, + { + "bbox": [ + 304, + 542, + 545, + 590 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "type": "text", + "content": "For a blurred image " + }, + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "type": "text", + "content": ", it can be represented as the average of the clear images " + }, + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{L}\\}" + }, + { + "bbox": [ + 304, + 590, + 545, + 615 + ], + "type": "text", + "content": " over the exposure time, i.e.:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 365, + 622, + 545, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 622, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 365, + 622, + 545, + 652 + ], + "type": "interline_equation", + "content": "\\mathbf {B} _ {i} = \\frac {1}{T _ {\\mathbf {B}}} \\int_ {T _ {i} - T _ {\\mathbf {B}} / 2} ^ {T _ {i} + T _ {\\mathbf {B}} / 2} \\mathbf {L} (t) d t, \\tag {3}", + "image_path": "a3435957e8435fc1e8c1ebc9ec163a8e5b731a2dd12e5e63ee9920db213f2949.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "spans": [ + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "text", + "content": " is the center of exposure time and " + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_i" + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 306, + 654, + 518, + 666 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 666, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 689 + ], + "type": "text", + "content": "Why spike cameras hold potential on image deblurring. The deblurring process can be formulated as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 332, + 695, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 695, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 332, + 695, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {M}} {\\arg \\min } \\| \\hat {\\mathbf {L}} _ {i} - \\mathbf {L} _ {i} \\|, \\text {w h e r e} \\hat {\\mathbf {L}} _ {i} = \\mathcal {F} \\left(\\mathbf {B} _ {i}: \\theta_ {M}\\right), \\tag {4}", + "image_path": "d62191e19a749f2d60048db53093afc48858fccdbaa9ce071f6586a6983bdc3c.jpg" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25049" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 63, + 70, + 532, + 235 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 532, + 235 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 532, + 235 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 532, + 235 + ], + "type": "image", + "image_path": "b37a1bd1be3e3eab9f2b24342c98585bfc0e45cef81855993c0d6d616b9f1e9c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 133, + 241, + 459, + 253 + ], + "lines": [ + { + "bbox": [ + 133, + 241, + 459, + 253 + ], + "spans": [ + { + "bbox": [ + 133, + 241, + 459, + 253 + ], + "type": "text", + "content": "Figure 3. The architecture of the proposed Unaligned Spike-guided Deblur Net (UaSDN)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": " is the optimized parameters of the model " + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_i" + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": " is the predicted clear image. The " + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": " is hard to optimize when " + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": " holds extreme blur. Neglecting color information and differences in spatial resolution, when the spike camera and RGB camera are perfectly aligned, the clear image " + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_i" + }, + { + "bbox": [ + 46, + 274, + 287, + 346 + ], + "type": "text", + "content": " can also be approximated using spikes:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 56, + 354, + 287, + 387 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 354, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 56, + 354, + 287, + 387 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {L}} _ {i} \\simeq \\mathcal {F} _ {M _ {S 2 I}} \\left(\\left\\{\\mathbf {S} (t) \\mid t \\in \\left[ T _ {i} - \\frac {T _ {\\mathbf {B}}}{2}, T _ {i} + \\frac {T _ {\\mathbf {B}}}{2} \\right] \\right\\}: \\theta_ {S 2 I}\\right), \\tag {5}", + "image_path": "0ab676b44808c5ed289345a2d4b3c6f12cc555f12c0be769dcb476a5e2fa7aa5.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "M_{S2I}" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": " is the model for reconstructing spikes to the approximated image " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": ". Many existing models [47, 52] are able to reconstruct high-quality " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": ". Despite that " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": " lacks color information and has lower spatial resolution compared to " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": ", its clear texture effectively provides deblurring clues for " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": " as shown in Fig. 2, which is proved by our experiments in Sec. 4.5. When not knowing the alignment between the RGB camera and spike camera on both spatial and temporal axis, we cannot get the accurate spikes " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}(t)\\}" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": " in Eq. (5). Thus textures in " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": " are not aligned with " + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_i" + }, + { + "bbox": [ + 46, + 388, + 287, + 518 + ], + "type": "text", + "content": ", which raises challenges for spikes to guide the deblurring." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": "How to deal with unknown alignment? We set the situation of the unknown alignment as follows: (1) Spatial axis. There are blind plane displacements " + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{P}" + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": " between two cameras. Generally, we set the " + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\Delta \\mathbf{P}" + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": " not a constant but a variable parameter. (2) Temporal axis. Spike stream is continuous while RGB frames are discrete. When two streams cannot be precisely synchronized, in real situations, we can roughly fetch a segment of spikes " + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_k" + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": " around the corresponding exposure window " + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": " of image " + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{B}_i" + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": ". The temporal center of " + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "inline_equation", + "content": "\\mathbf{S}_k" + }, + { + "bbox": [ + 46, + 519, + 287, + 651 + ], + "type": "text", + "content": " is unknown. In this case, we aim to build the model learning the aligning process adaptively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 658, + 167, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 167, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 167, + 670 + ], + "type": "text", + "content": "3.2. Overall Architecture" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "For not knowing the alignment, accurately matching the textures between the blurred image and spikes is challenging, requiring the model to have the ability for adaptive" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 274, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 380 + ], + "type": "text", + "content": "feature matching. However, on one hand, the texture of the blurred image " + }, + { + "bbox": [ + 304, + 274, + 545, + 380 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 274, + 545, + 380 + ], + "type": "text", + "content": " suffers from significant information loss. On the other hand, the irregular spike data cannot directly express scene textures like images. Therefore, we aim to progressively optimize the motion deblurring, gradually restoring clear textures of the blurred image and spikes. To achieve this, we propose a three-stage model named Unaligned Spike-guided Deblur Net (UaSDN). The network architecture of UaSDN is illustrated in Fig. 3." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": "UaSDN consists of three deblurring stages. (1) First Stage: Basic Image Deblurring Unclear texture in blurred images " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " makes it difficult to match with features in spikes. We employ a simple network " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "M_{1}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " to learn basic deblurring for " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": ". The network takes the blurred image " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " as input and outputs the predicted image " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{1}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " (2) Second Stage: Bi-Deformable Aligning Enhancement. The texture of " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " is enhanced after the stage 1. In this stage, we design a module " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "M_{2}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " based on deformable convolution to achieve basic alignment between spike features and blurred image features. Besides, to restore scene textures in spikes, we use shallow convolutional layers " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "M_{S2I}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " to input spikes and quickly infer the rough light intensity. We randomly sample " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " segments of spikes " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}_k|k\\in [1,2,\\dots K]\\}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " as guidance input to " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "M_{2}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": ", which outputs the enhanced image " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{2}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": ". (3) Third Stage: Flow-guided Dense Fusion. In this stage, we aim to utilize optical flows " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "v_{S2I}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " from spikes " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\mathbf{S}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " to the image " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{2}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " as guidance for precise alignment. To achieve this, we design the multi-scale flow-guided deblurring module, which takes the sampled " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": " spike segments as input and predicts the final clear image " + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{3}" + }, + { + "bbox": [ + 304, + 381, + 546, + 634 + ], + "type": "text", + "content": ". The process can be formulated as:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 380, + 644, + 545, + 658 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 380, + 644, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 380, + 644, + 545, + 658 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {L}} _ {1} = \\mathcal {F} _ {M _ {1}} \\left(\\mathbf {B}: \\theta_ {M _ {1}}\\right), \\tag {6}", + "image_path": "5d3e47a9b2d17de52265e8b274f584eaa0b3b63bdcc21725d41578779f019af1.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 330, + 672, + 545, + 686 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 672, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 330, + 672, + 545, + 686 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {L}} _ {2} = \\mathcal {F} _ {M _ {2}} \\left(\\hat {\\mathbf {L}} _ {1}, \\left\\{\\mathbf {S} _ {k} \\mid k \\in [ 1, 2, \\dots , K ] \\right\\}: \\theta_ {M _ {2}}\\right), \\tag {7}", + "image_path": "c5cc68e706de050dafa34e10856c0107be0e75520eb57f4298cff803936bd8dd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 330, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 330, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {L}} _ {3} = \\mathcal {F} _ {M _ {3}} \\left(\\hat {\\mathbf {L}} _ {2}, \\left\\{\\mathbf {S} _ {k} \\mid k \\in [ 1, 2, \\dots , K ] \\right\\}: \\theta_ {M _ {3}}\\right). \\tag {8}", + "image_path": "e234268693f0f9c1c0ffb79742add1b539d2d4d3b2d40198353574ea27b495c1.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25050" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 54, + 69, + 281, + 148 + ], + "blocks": [ + { + "bbox": [ + 54, + 69, + 281, + 148 + ], + "lines": [ + { + "bbox": [ + 54, + 69, + 281, + 148 + ], + "spans": [ + { + "bbox": [ + 54, + 69, + 281, + 148 + ], + "type": "image", + "image_path": "d0aaab3376b6cf6d5d40259c4eeed7c05b52b060b636d7d5f7c50d442b546780.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 155, + 287, + 178 + ], + "lines": [ + { + "bbox": [ + 46, + 155, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 46, + 155, + 287, + 178 + ], + "type": "text", + "content": "Figure 4. The architecture of the proposed Bi-directional Deformable Modal Aligning (BiDMA) module." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 194, + 224, + 209 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 194, + 224, + 209 + ], + "spans": [ + { + "bbox": [ + 47, + 194, + 224, + 209 + ], + "type": "text", + "content": "3.3. Stage 1: Basic Image Deblurring" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "content": "In the first stage, we employed one of the current state-of-the-art image restoration networks, NAFNet [5], as the basic deblurring module " + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "inline_equation", + "content": "M_{1}" + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "content": ". We aim to use " + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "inline_equation", + "content": "M_{1}" + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "content": " to lighten the blurring effect and enhance the texture of the blurred image " + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "content": ", as shown in Fig. 3. Specifically, NAFNet is a U-shaped multi-scale network. " + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "content": " undergoes 4 times down-sampling during feature extraction, followed by up-sampling. In the up-sampling process, features from each scale are fused, and the network finally outputs " + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{1}" + }, + { + "bbox": [ + 46, + 213, + 288, + 357 + ], + "type": "text", + "content": ". To reduce parameter count and accelerate inference speed, the overall network channel number is halved. Detailed architectures are provided in the supplementary material." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 363, + 287, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 363, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 47, + 363, + 287, + 376 + ], + "type": "text", + "content": "3.4. Stage 2: Bi-Deformable Aligning Enhancement" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "text", + "content": "At this stage, spikes are introduced. As in Eq. (5), if two cameras are perfectly aligned in space and time, spikes can be optimized to obtain a clear grayscale image " + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_{\\mathbf{S}}" + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "text", + "content": " without color information and at a lower resolution. The reconstructed gray-scale image can effectively aid in deblurring the RGB image. Our goal is to learn an adaptive pixel alignment relationship between modalities through learning. We first pass the sampled spike fragments through a shallow convolutional module " + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "inline_equation", + "content": "M_{S2I}" + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "text", + "content": " to quickly estimate the corresponding rough grayscale intensity " + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_{\\mathbf{S}}" + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "inline_equation", + "content": "M_{S2I}" + }, + { + "bbox": [ + 46, + 381, + 287, + 513 + ], + "type": "text", + "content": " consists of only 4 convolutional layers, which is formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 517, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 517, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 113, + 517, + 287, + 533 + ], + "type": "interline_equation", + "content": "\\tilde {\\mathbf {L}} _ {\\mathbf {S}} = \\mathcal {F} _ {M _ {S 2 I}} (\\mathbf {S}: \\theta_ {M _ {S 2 I}}), \\tag {9}", + "image_path": "f25d58ab5c96372677331e5f949948235fd2cd74092c12f689f3f1ea9ea25310.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "text", + "content": "In addition, we designed the bi-directional deformable modal align (BiDMA) module, as illustrated in Fig. 4. The spike and image features are extracted with downsampling, denoted as " + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{F_S} = \\{F_{\\mathbf{S}}^h\\}" + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathbf{F_L} = \\{F_{\\mathbf{L}}^h\\}" + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "inline_equation", + "content": "h \\in [1,2,\\dots,H]" + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "text", + "content": " is the number of scales. A deformable convolution network(DCN) [10] " + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{DCN}" + }, + { + "bbox": [ + 47, + 536, + 287, + 620 + ], + "type": "text", + "content": " can align two kinds of features, the principle can be denoted as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 70, + 626, + 287, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 626, + 287, + 660 + ], + "spans": [ + { + "bbox": [ + 70, + 626, + 287, + 660 + ], + "type": "interline_equation", + "content": "F (p) = \\sum_ {q = 1} ^ {Q} w _ {q} \\cdot F \\left(p + p _ {q} + \\Delta p _ {q}\\right) \\cdot \\Delta m _ {q}, \\tag {10}", + "image_path": "935facb413d07bd490fe9fcd97aa4564759b0a0233b7f086a73429775b3a9459.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "p = (x,y)" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " is the coordinate of the center pixel, Q denotes pixel numbers in the neighbor of " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "p_q" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " is the fixed offset from " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "w_q" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " denotes the weight, " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\Delta m_q" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " denotes the modulation scalar. " + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "inline_equation", + "content": "\\Delta p_q" + }, + { + "bbox": [ + 47, + 665, + 287, + 715 + ], + "type": "text", + "content": " is the learnable offset, which is predicted" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "by two modal features with a module " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\Delta}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " consisting of several convolution layers. In each " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "-level, we consider the bi-directional deformable aligning: 1) align " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "F_{\\mathbf{L}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " of image to " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "F_{\\mathbf{S}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " of spikes and get the " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\bar{F}_{\\mathbf{L}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "; 2) fuse the " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\bar{F}_{\\mathbf{L}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "F_{\\mathbf{S}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", and get " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\bar{F}_{\\mathbf{S}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "; 3) align the " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\bar{F}_{\\mathbf{S}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": " back to " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "F_{\\mathbf{L}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ", and get " + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "\\bar{\\bar{F}}_{\\mathbf{S}}^{h}" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": ". The process can be formulated as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 317, + 151, + 545, + 199 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 151, + 545, + 199 + ], + "spans": [ + { + "bbox": [ + 317, + 151, + 545, + 199 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Delta P _ {I 2 S} ^ {h} = \\mathcal {F} _ {\\Delta} ([ F _ {\\mathbf {L}} ^ {h}, F _ {\\mathbf {S}} ^ {h} ], \\Delta P _ {I 2 S} ^ {h + 1}), \\\\ \\bar {F} _ {\\mathbf {L}} ^ {h} = \\mathcal {F} _ {\\oplus} \\left(\\mathcal {F} _ {D C N} \\left(F _ {\\mathbf {L}} ^ {h}, \\Delta P _ {I 2 S} ^ {h}\\right), \\mathbf {U} _ {\\mathbf {p}} \\left(\\bar {F} _ {\\mathbf {L}} ^ {h + 1}\\right)\\right), \\tag {11} \\\\ \\bar {F} _ {\\mathbf {S}} ^ {h} = \\mathcal {F} _ {\\oplus} (\\bar {F} _ {\\mathbf {L}} ^ {h}, F _ {\\mathbf {S}} ^ {h}), \\\\ \\end{array}", + "image_path": "a27c6e106e46707ca167226d82305c4da2668d3ee9d3d6325dffe0cc714109c6.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 217, + 545, + 249 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 217, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 317, + 217, + 545, + 249 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Delta P _ {S 2 I} ^ {h} = \\mathcal {F} _ {\\Delta} ([ \\bar {F} _ {\\mathbf {S}} ^ {h}, F _ {\\mathbf {L}} ^ {h} ], \\Delta P _ {S 2 I} ^ {h + 1}), \\\\ \\bar {\\bar {F}} _ {\\mathbf {S}} ^ {h} = \\mathcal {F} _ {\\oplus} \\left(\\mathcal {F} _ {D C N} \\left(\\bar {F} _ {\\mathbf {S}} ^ {h}, \\Delta P _ {S 2 I} ^ {h}\\right), \\mathbf {U p} \\left(\\bar {\\bar {F}} _ {\\mathbf {S}} ^ {h + 1}\\right)\\right), \\tag {12} \\\\ \\end{array}", + "image_path": "a68693b0321e089c5620c0fb293d560c5fbd2bdbcdd1ff1d4282b7eb3bff6ab2.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 320, + 251, + 415, + 266 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 251, + 415, + 266 + ], + "spans": [ + { + "bbox": [ + 320, + 251, + 415, + 266 + ], + "type": "interline_equation", + "content": "F _ {a l i g n} = \\mathcal {F} _ {\\oplus} (\\bar {\\bar {F}} _ {\\mathbf {S}} ^ {1}, F _ {\\mathbf {L}} ^ {1}),", + "image_path": "ac494374123dbed557c8f0010a70c0be0c7826110616f44c1d925202c15fcfe7.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{DCN}" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " is the DCN network as in Eq. (10), " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\oplus}" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " is the feature fusion function with simple Conv layers, " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\mathbf{U}\\mathbf{p}(\\cdot)" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " is the upsampling operation. Eq. (11) describe the align process from images to spikes, and Eq. (12) describe the align process from spikes back to images. In this way, at the 1-level, the aligned feature " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "F_{align}" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " is fused by " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\oplus}" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " with several Conv layers. As described in Sec. 3.1, we sample " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " segments of spikes for alignment with the image. Thus the output " + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_2" + }, + { + "bbox": [ + 304, + 274, + 545, + 381 + ], + "type": "text", + "content": " of stage 2 is formulated as:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 322, + 389, + 545, + 404 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 389, + 545, + 404 + ], + "spans": [ + { + "bbox": [ + 322, + 389, + 545, + 404 + ], + "type": "interline_equation", + "content": "\\hat {\\mathbf {L}} _ {2} = \\mathcal {F} _ {p r e d} ([ F _ {a l i g n, 1}, F _ {a l i g n, 2}, \\dots , F _ {a l i g n, K} ]). \\tag {13}", + "image_path": "8af37e7ae91137aa3cf832b75cb9a4a7ac1b1b6fe3960f2cda6547e409fd1eed.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 411, + 493, + 424 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 411, + 493, + 424 + ], + "spans": [ + { + "bbox": [ + 306, + 411, + 493, + 424 + ], + "type": "text", + "content": "3.5. Stage 3: Flow-guided Dense Fusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "spans": [ + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": "After the alignment in stage 2, textures of " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_2" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " are further enhanced by spikes. In this stage, we aim to achieve precise alignment of spike features through optical flow guidance, improving the deblurring effect by supplementing detailed textures from features in the spike. Thus, we build a flow-guided dense fusion network for the final refinement. as illustrated in Fig. 3. Firstly, " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " coarse light intensity estimation " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\{\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}|k\\in [1,2,\\dots ,K]\\}" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " are predicted as Eq. (9) described from the sampled spike segments " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{S}_k|k\\in" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "[1,2,\\ldots ,K]\\}" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": ". Then, we compute the optical flows " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "V_{\\mathbf{S}_k\\rightarrow \\hat{\\mathbf{L}}_2}" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " between the " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_2" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " and each " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": ", then warp the " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}^w" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": " according to the " + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "inline_equation", + "content": "V_{\\mathbf{S}_k\\rightarrow \\hat{\\mathbf{L}}_2}" + }, + { + "bbox": [ + 304, + 429, + 545, + 578 + ], + "type": "text", + "content": ". The process is formulated as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 365, + 586, + 545, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 586, + 545, + 620 + ], + "spans": [ + { + "bbox": [ + 365, + 586, + 545, + 620 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} V _ {\\mathbf {S} _ {k} \\rightarrow \\hat {\\mathbf {L}} _ {2}} = \\mathcal {F} _ {f l o w} (\\tilde {\\mathbf {L}} _ {\\mathbf {S} _ {k}}, \\hat {\\mathbf {L}} _ {2}), \\tag {14} \\\\ \\tilde {\\bf L} _ {{\\bf S} _ {k}} ^ {w} = \\mathcal {G} (\\tilde {\\bf L} _ {{\\bf S} _ {k}}, V _ {{\\bf S} _ {k} \\rightarrow \\hat {{\\bf L}} _ {2}}), \\\\ \\end{array}", + "image_path": "9f4cf345e5e1ab91ea23ef5ec8f08b9610b5cf3f43e0d7fb58e20ff2bcbf89cf.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{flow}" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " is the pretrained image-based flow estimation network [35], and " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " denotes the feature warp operator. Then, we concatenate " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\{\\tilde{\\mathbf{L}}_{\\mathbf{S}_k}^w |k\\in [1,2,\\dots ,K]\\}" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_2" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " , and get the tiled image " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{tile}" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " . The U-shape network contains the encoder and decoder. In the encoder, the image features of " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_{tile}" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " are extracted with downsampling, denoted as " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "\\mathbf{F}_{\\hat{\\mathbf{L}}_{tile}} = \\{F_{\\hat{\\mathbf{L}}_{tile}}^{h}\\} ,h = [1,2,\\dots ,H]" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " . The feature " + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "inline_equation", + "content": "F_{\\hat{\\mathbf{L}}_{tile}}^{h}" + }, + { + "bbox": [ + 304, + 626, + 545, + 716 + ], + "type": "text", + "content": " at" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25051" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 58, + 70, + 278, + 135 + ], + "blocks": [ + { + "bbox": [ + 58, + 70, + 278, + 135 + ], + "lines": [ + { + "bbox": [ + 58, + 70, + 278, + 135 + ], + "spans": [ + { + "bbox": [ + 58, + 70, + 278, + 135 + ], + "type": "image", + "image_path": "f39971f68134817215343e2083093d84f6e9c3a452eb36a5851a23481b71908d.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 56, + 143, + 277, + 154 + ], + "lines": [ + { + "bbox": [ + 56, + 143, + 277, + 154 + ], + "spans": [ + { + "bbox": [ + 56, + 143, + 277, + 154 + ], + "type": "text", + "content": "Figure 5. The proposed Attention-base Dense Block (ADB)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "content": "level " + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "content": " doubles the channel number of " + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "inline_equation", + "content": "F_{\\hat{\\mathbf{L}}_t i t e}^{h - 1}" + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "content": " at level " + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "inline_equation", + "content": "h - 1" + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "content": ". In the decoder, features from the previous layer are upsampled through convolution layers and a pixel shuffle operation, then fuse with features at the current level. Each encoder and decoder at each level is an attention-base dense block(ADB) consisting of a channel attention layer (CA) and a residual dense block (RDB) [50], as in Fig. 5. The CA fuses two features from two modalities and the RDB aims to extract features effectively. In this way, the final deblurred image " + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_3" + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "content": " is predicted with the sum of the output of several convolutional layers and the input " + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{L}}_2" + }, + { + "bbox": [ + 46, + 173, + 289, + 308 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 314, + 138, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 314, + 138, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 314, + 138, + 326 + ], + "type": "text", + "content": "3.6. Loss functions" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": "We train the three stages separately, for each stage, we use the " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": " loss to optimize the network. For the coarse light intensity estimation module " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "M_{S2I}" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 332, + 287, + 369 + ], + "type": "text", + "content": " loss is adopted too." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 82, + 376, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 376, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 82, + 376, + 287, + 396 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d e b l u r} ^ {i} = \\left| \\hat {\\mathbf {L}} _ {1} ^ {i} - \\mathbf {L} _ {r g b} \\right|, \\text {w h e r e} i = 1, 2, 3, \\tag {15}", + "image_path": "fc468c60c471c0f166327ce98aaf164a6ea47a3bfee93a9e08d6c5148e64f9d6.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 87, + 394, + 185, + 408 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 394, + 185, + 408 + ], + "spans": [ + { + "bbox": [ + 87, + 394, + 185, + 408 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {M _ {S 2 I}} ^ {i} = | \\bar {\\mathbf {L}} _ {\\mathbf {S}} - \\mathbf {L} _ {g r a y} |,", + "image_path": "682803ed0aa663520d905c5fe266dd32d1c1e0d435698f4794d7d8358f6dbaf0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "content": " is the stage index, " + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_{rgb}" + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "content": " is the ground-truth clear RGB image, and " + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "inline_equation", + "content": "\\mathbf{L}_{gray}" + }, + { + "bbox": [ + 46, + 414, + 287, + 450 + ], + "type": "text", + "content": " is the clear gray image with equal spatial resolution as spikes." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 460, + 123, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 123, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 123, + 474 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 479, + 213, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 213, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 213, + 493 + ], + "type": "text", + "content": "4.1. Datasets and Training Settings" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 714 + ], + "type": "text", + "content": "To train the network, we utilize datasets containing high-speed RGB images as the base and simulate the principle of a spike camera to generate continuous spike streams. Specifically, we conduct training and testing on two large datasets: the X4k1000FPS [30] and the REDS dataset [25]. The X4K1000FPS dataset includes high-definition 1000fps videos, while REDS comprises 1000fps videos, along with real or synthesized blurred images. To generate spike data, we employ the state-of-the-art video interpolation algorithm EMA-VFI [46] to increase the frame rate by 8 times for the image sequences in both datasets, resulting in ultra-high frame rate videos. Ultra-high frame rate videos can approximate the continuous changes in scene lighting, allowing us to use the working principle of a spike camera to generate corresponding spike streams as shown in Eq. (1). Additionally, since the X4K1000FPS dataset does not include blurred images, we simulate the blurry images using an average of 33 frames. In X4K1000FPS and REDS, the equiv" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 315, + 70, + 538, + 160 + ], + "blocks": [ + { + "bbox": [ + 315, + 70, + 538, + 160 + ], + "lines": [ + { + "bbox": [ + 315, + 70, + 538, + 160 + ], + "spans": [ + { + "bbox": [ + 315, + 70, + 538, + 160 + ], + "type": "table", + "html": "
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image33.740.935
NAFNet [5]Image34.130.937
EFNet [32]Image+Spike33.280.928
REFID [33]Image+Spike34.220.939
SpkDeblurNet [7]Image+Spike34.470.941
UaSDN(Ours)Image+Spike35.780.964
", + "image_path": "359052aaa8fb599711555613c8f4a1bf455828527becf8460800c87b65ec040a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 315, + 203, + 538, + 294 + ], + "blocks": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "lines": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "spans": [ + { + "bbox": [ + 305, + 168, + 545, + 190 + ], + "type": "text", + "content": "Table 1. Comparison of various motion deblurring methods on X4K1000FPS [30]." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 203, + 538, + 294 + ], + "lines": [ + { + "bbox": [ + 315, + 203, + 538, + 294 + ], + "spans": [ + { + "bbox": [ + 315, + 203, + 538, + 294 + ], + "type": "table", + "html": "
MethodInput DataPSNR ↑SSIM ↑
HINet [4]Image31.100.902
NAFNet [5]Image30.730.894
EFNet [32]Image+Spike31.740.912
REFID [33]Image+Spike31.230.904
SpkDeblurNet [7]Image+Spike31.160.911
UaSDN(Ours)Image+Spike33.610.942
", + "image_path": "89b478f0601ea2358c84b6107b599bfc35b8a4eb63018b949bff61e25b72a52e.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 302, + 545, + 324 + ], + "lines": [ + { + "bbox": [ + 305, + 302, + 545, + 324 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 545, + 324 + ], + "type": "text", + "content": "Table 2. Comparison of various motion deblurring methods on REDS [25]." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 346, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 545, + 371 + ], + "type": "text", + "content": "alent exposure time for the blurred images is 1/120 and 1/24 seconds, respectively." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "type": "text", + "content": "How do we set the unknown spatiotemporal alignment between RGB frames and spikes? In the training set, along the spatial axis, we introduce random offsets in up, down, left, and right directions for the spikes compared to the blurred image, with a maximum offset of " + }, + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "type": "text", + "content": ". Along the temporal axis, the center timestamp of the sampled spike segments compared to the blurred image was set with random offsets in forward and backward directions, with a maximum offset of " + }, + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "type": "inline_equation", + "content": "25\\%" + }, + { + "bbox": [ + 304, + 372, + 546, + 516 + ], + "type": "text", + "content": ". For testing, we set the above offset scheme as a fixed uniform distribution to ensure that all methods use the same test data in evaluation. Details of the dataset and training are in supplementary materials." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 525, + 443, + 537 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 525, + 443, + 537 + ], + "spans": [ + { + "bbox": [ + 305, + 525, + 443, + 537 + ], + "type": "text", + "content": "4.2. Results on X4K1000FPS" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 544, + 545, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 663 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 663 + ], + "type": "text", + "content": "To demonstrate the deblurring capability of our proposed model UaSDN, under modality misalignment, we compare it with five methods: two image-based networks, HINet [4] and NAFNet [5], two state-of-the-art event-based networks, EFNet [32] and REFID [33], and the spike-based SpkDeblurNet [7]. To ensure fairness in the experiments, we modify the inputs of EFNet and REFID to be the blurred images and spikes, with the spike length matching that of UaSDN. We transform the spikes to the input representation used by EFNet and REFID." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "As in Tab. 1, our method achieves 35.78dB in PSNR and 0.964 in SSIM, demonstrating a significant performance improvement compared to other methods. Compared to methods that only take the image as input, our approach" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25052" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 534, + 260 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 534, + 260 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 534, + 260 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 534, + 260 + ], + "type": "image", + "image_path": "238e25bd8304688abc66a79a98bdfc5f0a46275c5ef2e3694c2b217ab8a08614.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 266, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 47, + 266, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 47, + 266, + 545, + 278 + ], + "type": "text", + "content": "Figure 6. Visualized results of our method (UaSDN) on X4K1000FPS compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 58, + 291, + 536, + 452 + ], + "blocks": [ + { + "bbox": [ + 58, + 291, + 536, + 452 + ], + "lines": [ + { + "bbox": [ + 58, + 291, + 536, + 452 + ], + "spans": [ + { + "bbox": [ + 58, + 291, + 536, + 452 + ], + "type": "image", + "image_path": "2013d0a41b03bb694b1fc8a882fe42ea33daa6b1cf6dc91fdc90f7d071f69e53.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 460, + 545, + 472 + ], + "lines": [ + { + "bbox": [ + 47, + 460, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 545, + 472 + ], + "type": "text", + "content": "Figure 7. Visualized results of our method (UaSDN) on REDS dataset compared with HINet, NAFNet, EFNet, REFID and SpkDeblurNet." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 492, + 288, + 660 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 288, + 660 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 288, + 660 + ], + "type": "text", + "content": "outperforms HINet and NAFNet by 2.04dB and 1.65dB in PSNR, respectively. It indicates the effectiveness of utilizing spikes as guidance for deblurring. Furthermore, compared to the other two event-based networks that take spikes as input, our approach surpasses EFNet and REFID by 2.50dB and 1.56dB in PSNR. It strongly validates the effectiveness of our model in aligning the two modal data in both time and space. As in Fig. 6, the visual results demonstrate that our method effectively obtains fine textures. For example, in the first row, our method successfully enhances the blurred textures without introducing any shape distortion, while other methods fail to address such extreme blurriness and result in shape distortions. It proves the precise spatiotemporal feature alignment achieved by our method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 670, + 150, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 150, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 150, + 681 + ], + "type": "text", + "content": "4.3. Results on REDS" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 712 + ], + "type": "text", + "content": "On the REDS dataset, as shown in Tab. 2, our method achieves a PSNR of 33.61dB and an SSIM of 0.942. Com" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 492, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 613 + ], + "type": "text", + "content": "pared to the image-based methods HINet and NAFNet, our method surpasses them by 2.51dB and 2.88dB, respectively. Compared to the event-based methods EFNet and REFID, our method outperforms them by 1.87dB and 2.38dB. As illustrated in Fig. 7, our method can significantly enhance deblurring performance in the presence of complex textures, such as text on license plates, text on ships, and details in faces. Through the comparison of the REDS dataset, we further demonstrate the deblurring capability of the model and its generalization ability to different datasets." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 622, + 466, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 622, + 466, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 622, + 466, + 635 + ], + "type": "text", + "content": "4.4. Results on Real World Spikes" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "To assess the deblurring capability of our method in real-world scenarios, we set up a simple unaligned spike-RGB hybrid camera system. Fig. 8 shows real-world test cases, including fast-moving objects at close range and outdoor driving scenarios with rapid motion. As shown in Fig. 8, our method significantly outperforms other approaches in" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25053" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 283, + 153 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 283, + 153 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 283, + 153 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 283, + 153 + ], + "type": "image", + "image_path": "8e407415c0d0806ae0130c0670420e1b8e173ac9cf66964a085061e99c7447f8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 161, + 287, + 184 + ], + "lines": [ + { + "bbox": [ + 47, + 161, + 287, + 184 + ], + "spans": [ + { + "bbox": [ + 47, + 161, + 287, + 184 + ], + "type": "text", + "content": "Figure 8. Visualized results on real-world data captured with an RGB camera and a spike camera." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 61, + 196, + 273, + 258 + ], + "blocks": [ + { + "bbox": [ + 61, + 196, + 273, + 258 + ], + "lines": [ + { + "bbox": [ + 61, + 196, + 273, + 258 + ], + "spans": [ + { + "bbox": [ + 61, + 196, + 273, + 258 + ], + "type": "table", + "html": "
Stage1Stage2Stage3PSNR ↑SSIM ↑
✓××32.300.914
✓✓×32.900.923
✓✓✓35.780.964
", + "image_path": "3aebc182f89d45500b129b4ceb324474a5b871441d1fd52af5ec3cd897073317.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 300, + 287, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 337 + ], + "type": "text", + "content": "motion deblurring. We also observed that due to the high dynamic information contained in the spike stream, our method excels of deblurring in scenes with overexposure." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 148, + 358 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 148, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 148, + 358 + ], + "type": "text", + "content": "4.5. Ablation Studies" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "type": "text", + "content": "A. Performance Increases at each stage. To demonstrate the effectiveness of multi-stage model design, we conduct ablation experiments on the deblurring effects at each stage. As shown in Tab. 3, when performing the first stage training, the model possesses basic deblurring capabilities. With the introduction of the bi-directional deformable alignment in the second stage, the model shows a noticeable improvement of " + }, + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "type": "inline_equation", + "content": "0.6\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "type": "text", + "content": " and 0.01 in PSNR and SSIM, respectively. The addition of the flow-guided feature fusion network in the third stage further increases the PSNR to the highest value of " + }, + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "type": "inline_equation", + "content": "35.78\\mathrm{dB}" + }, + { + "bbox": [ + 46, + 365, + 287, + 533 + ], + "type": "text", + "content": ". These experimental results indicate that through progressive training, clear texture information from the spike stream can effectively be introduced into the image domain, guiding the deblurring process." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 534, + 288, + 714 + ], + "type": "text", + "content": "B. Deblurring Potentials under Precise Alignment. The above experiments demonstrate that our method effectively removes blur when spikes and images are unknownly aligned in both time and space. To further validate the potential of our method, we modify the X4k1000FPS and REDS datasets to strictly align spikes and images and test the model's performance under the condition of complete spatiotemporal alignment between modalities. As shown in Tab. 4, the results on the X4K1000FPS dataset include the quantitative results of two other methods, EFNET and REFID, which also take spikes as guiding input. The results show that our method achieves a PSNR of 36.92dB, surpassing the other two methods by 0.56dB and 0.62dB. We also test the performance improvement on REDS. The experiment shows that our method improves from 33.61dB" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 70, + 537, + 131 + ], + "blocks": [ + { + "bbox": [ + 55, + 266, + 277, + 277 + ], + "lines": [ + { + "bbox": [ + 55, + 266, + 277, + 277 + ], + "spans": [ + { + "bbox": [ + 55, + 266, + 277, + 277 + ], + "type": "text", + "content": "Table 3. Experiments on the performance of the model stage." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 70, + 537, + 131 + ], + "lines": [ + { + "bbox": [ + 317, + 70, + 537, + 131 + ], + "spans": [ + { + "bbox": [ + 317, + 70, + 537, + 131 + ], + "type": "table", + "html": "
MethodInput DataPSNR ↑SSIM ↑
EFNet [32]Image+Spike36.360.960
REFID [33]Image+Spike36.300.962
UaSDN(Ours)Image+Spike36.920.969
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Comparison of various motion deblurring methods on X4K1000FPS [30] when spikes and images are precise aligned." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 309, + 172, + 545, + 271 + ], + "blocks": [ + { + "bbox": [ + 309, + 172, + 545, + 271 + ], + "lines": [ + { + "bbox": [ + 309, + 172, + 545, + 271 + ], + "spans": [ + { + "bbox": [ + 309, + 172, + 545, + 271 + ], + "type": "image", + "image_path": "85e5976d4387ee59e11f198ef9ac1169204081033ae2e9aa581b78fa806032cc.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 279, + 545, + 301 + ], + "lines": [ + { + "bbox": [ + 305, + 279, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 305, + 279, + 545, + 301 + ], + "type": "text", + "content": "Figure 9. Influence of border areas when sampled spikes are totally not involved in the exposure of the image." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 323, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 358 + ], + "type": "text", + "content": "to 34.60dB on REDS, indicating that our method has great potential for application in spike-guided deblurring. Visualized results are shown in the supplementary materials." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 358, + 546, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 358, + 546, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 358, + 546, + 490 + ], + "type": "text", + "content": "C. How the border areas are handled from spatial and temporal perspectives. Generally, the motion near the border is similar. The model learns motion clues in spikes that supplement textures. Besides, our image-based stage-1 in UaSDN performs basic deblurring without spikes. In Fig. 9, the image that is spatiotemporal unaligned with spikes is recovered well by UaSDN. The quality is close to the deblurred one with perfect alignment (28.58 dB). The curve shows the model maintains acceptable results though the PSNR declines when spikes are not involved in the image exposure time at all." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 502, + 379, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 502, + 379, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 502, + 379, + 514 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 521, + 545, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 606 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 606 + ], + "type": "text", + "content": "We first explore the motion deblurring guided by a spike camera under unknown spatiotemporal alignment between two modalities. We believe the proposed method possesses potential in the real world. The proposed three-stage UaSDN contains a bi-directional deformable alignment and a flow-based fusion module. Results prove that UaSDN outperforms other methods on unaligned deblurring." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 616, + 399, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 399, + 630 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 399, + 630 + ], + "type": "text", + "content": "Acknowledgment" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 635, + 545, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 635, + 545, + 703 + ], + "spans": [ + { + "bbox": [ + 304, + 635, + 545, + 703 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China (62176003, 62088102, 62306015), the China Postdoctoral Science Foundation (2022M720238, 2023T160015), the Young Elite Scientists Sponsorship Program by CAST (2023QNRC001), and the Beijing Nova Program (20230484362)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "25054" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Christian Brandli, Raphael Berner, Minhao Yang, Shih-Chii Liu, and Tobi Delbruck. 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In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 12428-12437, 2023. 2" + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "25057" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SpikeNeRF_ Learning Neural Radiance Fields from Continuous Spike Stream/028c841a-a56f-4e19-871e-e3d2e2b3ec7c_content_list.json b/2024/SpikeNeRF_ Learning Neural Radiance Fields from Continuous Spike Stream/028c841a-a56f-4e19-871e-e3d2e2b3ec7c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..eefe744acf3079a031d8102aed046fb124aa97c2 --- /dev/null +++ b/2024/SpikeNeRF_ Learning Neural Radiance Fields from Continuous Spike Stream/028c841a-a56f-4e19-871e-e3d2e2b3ec7c_content_list.json @@ -0,0 +1,1552 @@ +[ + { + "type": "text", + "text": "SpikeNeRF: Learning Neural Radiance Fields from Continuous Spike Stream", + "text_level": 1, + "bbox": [ + 91, + 130, + 875, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lin Zhu", + "bbox": [ + 89, + 179, + 163, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhu $^{1}$ Kangmin Jia $^{1}$", + "bbox": [ + 122, + 179, + 313, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yifan Zhao2", + "bbox": [ + 348, + 180, + 449, + 196 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yunshan Qi2", + "bbox": [ + 485, + 180, + 586, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Lizhi Wang", + "bbox": [ + 622, + 180, + 723, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hua Huang $^{3,1,*}$", + "bbox": [ + 763, + 180, + 883, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1Beijing Institute of Technology", + "bbox": [ + 122, + 199, + 375, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Beihang University", + "bbox": [ + 418, + 199, + 581, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Beijing Normal University", + "bbox": [ + 622, + 199, + 841, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 312, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Spike cameras, leveraging spike-based integration sampling and high temporal resolution, offer distinct advantages over standard cameras. However, existing approaches reliant on spike cameras often assume optimal illumination, a condition frequently unmet in real-world scenarios. To address this, we introduce SpikeNeRF, the first work that derives a NeRF-based volumetric scene representation from spike camera data. Our approach leverages NeRF's multiview consistency to establish robust self-supervision, effectively eliminating erroneous measurements and uncovering coherent structures within exceedingly noisy input amidst diverse real-world illumination scenarios. The framework comprises two core elements: a spike generation model incorporating an integrate-and-fire neuron layer and parameters accounting for non-idealities, such as threshold variation, and a spike rendering loss capable of generalizing across varying illumination conditions. We describe how to effectively optimize neural radiance fields to render photorealistic novel views from the novel continuous spike stream, demonstrating advantages over other vision sensors in certain scenes. Empirical evaluations conducted on both real and novel realistically simulated sequences affirm the efficacy of our methodology. The dataset and source code are released at https://github.com/BIT-Vision/SpikeNeRF.", + "bbox": [ + 76, + 282, + 473, + 660 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 686, + 209, + 703 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, there has been significant progress in the development of neuromorphic cameras, with notable advancements such as event cameras [2, 4] and spike cameras [15, 46]. These innovative devices excel in capturing light intensity changes in high-speed scenes, presenting a breakthrough in the realm of visual perception [9, 11, 13, 31, 32, 38, 49]. Spike camera, wherein each pixel responds independently to the accumulation of photons by generating asynchronous spikes [46]. This distinctive feature enables the spike camera to record full visual details with an ultra-high temporal resolution of up to $40\\mathrm{kHz}$ (or $20\\mathrm{kHz}$ for the", + "bbox": [ + 75, + 712, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "portable version). These advantages include the capability to capture rapid changes in scenes and efficiently represent dynamic environments. With these unique features, spike cameras have demonstrated superiority in handling multiple computer vision tasks [12, 14, 33, 37, 45, 47-49, 51].", + "bbox": [ + 500, + 252, + 890, + 329 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In parallel, there has been a growing trend in the computer vision community to explore neural radiance fields (NeRFs) as a solution for scene representation and novel view synthesis [5, 8, 17, 18, 20, 22, 27, 29, 39]. NeRFs employ a multilayer perceptron (MLP) combined with differentiable rendering to represent scenes, allowing for the synthesis of novel views from unseen perspectives. So far, NeRFs have predominantly undergone examination using simulated data and high-quality real-world images acquired under optimal conditions. Some studies have explored the application of NeRF to a distinct type of neuromorphic camera known as an event camera, characterized by differential sampling. Noteworthy among these endeavors are Ev-NeRF [17] and EventNeRF [29], both of which introduced neural radiance fields derived exclusively from event streams. However, the inherent lack of texture details in event data has constrained the effectiveness of these approaches, resulting in limited outcomes. Instead, a spike camera can offer fine texture details through a high temporal resolution spike stream.", + "bbox": [ + 496, + 332, + 892, + 635 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, their application to spike camera data poses a unique challenge due to the distinctive data modality. The output of a spike camera is a spike stream, fundamentally different from traditional images. Each pixel in a spike camera generates a spike, and the accumulation is reset when the photon accumulation exceeds a predefined threshold. At each timestamp, the spike camera outputs a binary matrix, referred to as a spike frame, indicating the presence of spikes at all pixels. Currently, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. Therefore, the challenge tackled in this paper is: Can we reconstruct a dense volumetric 3D representation of the scene from a spike stream captured by a moving spike camera?", + "bbox": [ + 496, + 638, + 893, + 851 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Addressing the aforementioned challenges, this paper introduces SpikeNeRF, the first approach for deriving a volumetric scene representation from spike camera data using", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: Hua Huang.", + "bbox": [ + 94, + 886, + 290, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "6285", + "bbox": [ + 482, + 944, + 514, + 957 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/086dd65d5771a97bb36f728381ed6e0df670756e9c6139d43679b4bccd89bfbb.jpg", + "image_caption": [ + "Figure 1. Comparing novel views across various vision sensors, our SpikeNeRF stands out as the first method to learn neural radiance fields from a continuous spike stream. The Spike camera, operating at $20,000\\mathrm{Hz}$ , eliminates motion blur, distinguishing it from traditional cameras. Notably, when contrasted with other methods (e.g., TFI+NeRF [46], Spk2img+NeRF [45], and EventNeRF [29]) and sensors (e.g., event camera), the rendered views of objects or scenes exhibit significantly enhanced sharpness." + ], + "image_footnote": [], + "bbox": [ + 89, + 88, + 751, + 354 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/bc01535143b9e89ac2b7b5a2b4640545b68d6fa706126ea1bd738ccb8a295058.jpg", + "image_caption": [ + "Event input" + ], + "image_footnote": [], + "bbox": [ + 774, + 95, + 898, + 159 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2ebe2ac8d569e8338902a9f354b1fb21b35e0ca3a7c96296813e3de178e9275b.jpg", + "image_caption": [ + "Novel Views from EventNeRF" + ], + "image_footnote": [], + "bbox": [ + 777, + 176, + 898, + 239 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/156f0cefec9d94fc7316fc5169dfeddde8fef3225f9503bce17cf765012c48c7.jpg", + "image_caption": [ + "Novel Views from Image+NeRF" + ], + "image_footnote": [], + "bbox": [ + 777, + 263, + 897, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Radiance Fields (NeRF). Our method is designed for purely spike-based supervision, preserving texture and motion details in high temporal resolution. We evaluate the efficacy of SpikeNeRF for the task of novel view synthesis on a new dataset of synthetic and real spike sequences. SpikeNeRF leverages NeRF's inherent multi-view consistency to establish robust self-supervision, mitigating the impact of erroneous measurements in the presence of high noise levels and diverse illumination conditions. Specifically, SpikeNeRF incorporates a spike generation model based on a spiking neuron layer, which considers intrinsic parameters and non-idealities associated with spike cameras. This model enhances the fidelity of spike data, providing a more accurate representation of the scene under varying lighting conditions (see Fig. 1). To enable generalization across diverse illumination scenarios, SpikeNeRF introduces a long-term spike rendering loss. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry, even in challenging lighting conditions. The main contributions of this paper are:", + "bbox": [ + 75, + 436, + 472, + 739 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1) We present the first approach for inferring a NeRF volume from only a spike stream. SpikeNeRF is highly robust to various illumination conditions and builds a coherent 3D structure that can provide high-quality observations.", + "2) We develop a long-term spike rendering loss based on a spiking neuron layer and threshold variation simulation, which are effective in enhancing neural volumetric representation learning.", + "3) We build both synthetic and real-world datasets for training and testing our model. Experimental results" + ], + "bbox": [ + 75, + 743, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "demonstrate that our method outperforms existing methods. We release the newly recorded spike dataset and source code to facilitate the research field.", + "bbox": [ + 498, + 436, + 890, + 482 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 501, + 640, + 517 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Neural Radiance Fields", + "text_level": 1, + "bbox": [ + 500, + 527, + 717, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In recent years, Neural Radiance Fields have garnered significant attention for their remarkable performance in tasks involving neural implicit 3D representation and novel view synthesis. Various enhancements, such as FastNeRF [8] and Depth-supervised NeRF [5], aim to expedite NeRF's learning speed. Neural scene flow fields [18] delve into 3D Scene Representation Learning for dynamic scenes. Approaches like PixelNeRF [39] and RegNeRF [27] leverage a minimal number of input images for high-quality novel view synthesis. Mip-NeRF [1] introduces a frustum-based sampling strategy for NeRF-based anti-aliasing, addressing artifacts while enhancing training speed. Beyond speed and data augmentation, some works focus on enhancing NeRF with low-quality input images. For instance, NeRF in the wild [21] utilizes low-quality images captured by tourists, tackling occlusions and inconsistent lighting conditions. NeRF in the dark [23] and HDR-NeRF [16] enable the synthesis of high dynamic range new view images from noisy low dynamic images. Additionally, Deblur-NeRF [20] introduces the DSK module for simulating the blurring process, facilitating novel view synthesis from blurry to sharp images. However, Deblur-NeRF may face challenges in scenarios where the camera coincidentally shakes uniformly across", + "bbox": [ + 496, + 553, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "6286", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "all views or the input images exhibit strong blur.", + "bbox": [ + 76, + 90, + 395, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Scene Reconstruction based on Neuromorphic Camera", + "text_level": 1, + "bbox": [ + 76, + 114, + 467, + 143 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Generally speaking, there are two types of bio-inspired visual sampling manner: temporal contrast sampling and integral sampling. Dynamic Vision Sensor (DVS), also known as an event camera, generates events when pixel brightness changes exceed a threshold. Recently, Ev-NeRF [17] and EventNeRF [29] proposed neural radiance fields derived exclusively from event streams. However, due to the absence of texture details in event data, these approaches yield limited results. Ev-NeRF [17] is confined to learning grayscale NeRF, while EventNeRF [29] exhibits noticeable artifacts and chromatic aberration, lacking RGB data for supervision. [28] first introduces event data and blurry RGB frames to achieve high quality clear scene reconstruction. [19] proposes Robust e-NeRF to robustly reconstruct NeRFs from moving event cameras under various real-world conditions,", + "bbox": [ + 75, + 152, + 467, + 378 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our work is based on spike camera, where each pixel responds independently to the accumulation of photons by generating spikes. It records full visual details with an ultra-high temporal resolution (up to $40\\mathrm{kHz}$ ). Image reconstruction based on spike cameras has emerged by analyzing spike intervals and counts [46]. Leveraging the spiking neuron model, a fovea-like texture reconstruction framework reconstructs images [48]. Spike camera methods have been developed for tone mapping [43], motion deblurring [12], and super resolution [37, 44]. Recent deep learning-based image reconstruction methods [3, 45, 49, 51] for spike cameras outperform traditional methods significantly. The noise characteristics of spike cameras differ substantially from those of traditional cameras. A preliminary analysis in [49] demonstrates that the noise distribution varies under different lighting conditions.", + "bbox": [ + 75, + 380, + 467, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "However, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. The challenge is to explore the texture details hidden in the spike stream, understanding the spike distribution is crucial for spike-based applications.", + "bbox": [ + 76, + 621, + 467, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 709, + 174, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Neural Radiance Fields", + "text_level": 1, + "bbox": [ + 76, + 734, + 292, + 750 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The fundamental idea of NeRF is to employ a Multilayer Perceptron (MLP) to learn a 3D volume representation [22]. The MLP takes 3D position $\\mathbf{o}$ and 2D ray direction $\\mathbf{d}$ as inputs and produces color $\\mathbf{c}$ and density $\\sigma$ as outputs. In Eq. (1), $F_{\\theta}$ represents the MLP network with $\\theta$ as its parameters:", + "bbox": [ + 76, + 757, + 467, + 845 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n(\\mathbf {c}, \\sigma) = F _ {\\theta} \\left(\\gamma_ {o} (\\mathbf {o}), \\gamma_ {d} (\\mathbf {d})\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 848, + 467, + 864 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The functions $\\gamma_{o}(\\cdot)$ and $\\gamma_{d}(\\cdot)$ , defined in Eq. (1), map the input 5D coordinates to a higher-dimensional space, en", + "bbox": [ + 76, + 869, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "abling the neural network to better capture color and geometry information in the scene. To generate views from the scene representation, NeRF employs a classical volume rendering method described in Eq. 2. For a given ray $\\mathbf{r}(t) = \\mathbf{o} + l\\mathbf{d}$ emitted from the camera, the expected color projected on the pixel is denoted as $C(\\mathbf{r})$ . The near and far bounds of the ray are represented by $l_{n}$ and $l_{f}$ , respectively. NeRF divides the interval $[l_n,l_f]$ into $N$ discrete bins, where $\\mathbf{c}_i$ and $\\sigma i$ are the outputs of $F_{\\theta}$ , indicating the color and density of each bin through which the ray passes. The distance between adjacent samples is $\\delta_i = l_{i + 1} - l_i$ , and $T_{i}$ represents the transparency of particles between $l_{n}$ and bin $i$ .", + "bbox": [ + 496, + 90, + 890, + 286 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nC (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) \\mathbf {c} _ {i}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 292, + 890, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $T(i) = \\exp(-\\sum_{j=1}^{i-1} \\sigma_j \\delta_j)$ . To ensure reasonable sampling in the final model, NeRF utilizes a Hierarchical volume sampling strategy, simultaneously optimizing the coarse and fine models and using the density obtained by the coarse model to determine the sampling weight of the fine model.", + "bbox": [ + 496, + 343, + 890, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Spike Sampling Mechanism", + "text_level": 1, + "bbox": [ + 500, + 444, + 750, + 459 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the field of frame-free neuromorphic vision, the spike camera operates by converting the intensity of light into voltage through photoreceptors [7, 46]. Upon reaching a predefined threshold, a one-bit spike is generated, accompanied by a signal to reset the integrator. This mechanism resembles that of an integrate-and-fire neuron. Luminance stimuli $I$ lead to varying spike firing rates, with asynchronous triggering of output and reset across pixels. Brighter light results in faster firing, governed by the inequality $\\int I dt \\geq \\phi$ .", + "bbox": [ + 496, + 467, + 890, + 618 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The raw data from the spike camera is a three-dimensional spike stream, focusing solely on luminance intensity integration and firing ultra-high frequency spikes. At each sampling moment, a digital signal of \"1\" (spike) or \"0\" is output based on whether a spike was fired. The spike firing status of pixel $(i,j)$ at moment $t$ is represented as $S_{i,j}(t)\\in 0,1$ . The spike signal model is defined as:", + "bbox": [ + 496, + 619, + 890, + 724 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nS (x, y, t) = S (x, y, n t _ {0}) = \\epsilon \\left(\\int_ {t ^ {\\prime}} ^ {n t _ {0}} \\frac {C \\Delta V}{I _ {p h} (x , y , \\tau)} d \\tau - 1\\right). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 732, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t'$ is the start time of the current integration phase, reset at the phase's end. $\\Delta V$ denotes the voltage, $nt_0$ denotes the $n$ -th clock signal, with $t_0$ as the unit time interval $(50\\mu s)$ , and $I_{ph}$ represents the magnitude of the current for photoelectric conversion. $C$ is the capacitor in parallel with the photodiode, which is used to store electrons for photoconversion. $\\epsilon(x)$ is a step function where $\\epsilon(x) = 1$ when $x \\geq 0$ otherwise $\\epsilon(x) = 0$ .", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "6287", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ec5ee23f389f434d376916a4b081e4b0df5463b84293f8dc2f757de40f01294c.jpg", + "image_caption": [ + "Figure 2. The architecture of SpikeNeRF. Motivated by the objective of learning NeRFs from a continuous spike stream, we establish the connection between the pixel ray $r$ and the real-world spike stream $S$ . To quantify the rendering loss in the spike domain, we integrate a spiking neuron layer following the NeRF MLP. The nonuniformity is captured through pixel-to-pixel threshold variation, simulated by the spiking neuron layer. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 893, + 333 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The noise of the spike camera differs significantly from traditional cameras due to circuit variations. The noise components encompass Shot Noise, wherein the photosensor converts photons into photo-electrons, resulting in a photo-current subject to shot noise $N_{p}$ even in uniform light scenarios. Dark Current Noise arises from thermal diffusion and defects, causing the spike circuit to produce signals even in the absence of scene light, with dark current noise denoted as $N_{d}$ . Response Nonuniformity stems from chip manufacturing limitations, causing pixel units to exhibit varying sensitivity to light intensity, leading to photo response nonuniformity noise $N_{nru}$ . Lastly, Quantization Noise arises from the delay in the release time of the spike signal relative to the generation time of the reset signal, introducing quantization noise $N_{q}$ .", + "bbox": [ + 75, + 429, + 472, + 656 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Self-Supervision with Volumetric Rendering", + "text_level": 1, + "bbox": [ + 76, + 669, + 452, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "An overview of the training pipeline is illustrated in Fig. 2. In line with the spike generation model, we propose self-supervision with volumetric rendering in this section. Different from traditional RGB frames, a binary spike frame can not accurately represent the light intensity at the current timestamp. Let us denote the intensity values of the pixel ray $r$ at time $T_{i}$ as $\\hat{I}(T_{i}(r))$ . Since the high temporal resolution of the spike camera, the estimated short-term light intensity $\\hat{L}_{T_i}$ can record motion details hidden in the spike stream. A straightforward approach is to calculate the light intensity $\\hat{L}_{T_i}$ at time $T_{i}$ based on the original spike stream:", + "bbox": [ + 75, + 693, + 468, + 861 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {L} _ {T _ {i}} = \\frac {\\theta}{n - m}, m < n, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 875, + 468, + 905 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $m$ and $n$ are the timestamps corresponding to two adjacent spikes, $\\theta$ controls the gray-scale level.", + "bbox": [ + 498, + 429, + 890, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, $\\hat{L}_{T_i}$ is influenced by various sources of noise, particularly the temporal sampling noise [49]. The firing intervals of spikes fluctuate even in constant illumination conditions due to the inherent spike sampling mechanism. For instance, in the integrate-and-fire mechanism, if the membrane potential of the neuron (pixel) is not reset, an object with a light intensity corresponding to an inter-spike interval of 2 might be recorded as 1 or 3. Consequently, $\\hat{L}_{T_i}$ is suitable for capturing motion details in the intensity values of the pixel ray $r$ , but texture details are often affected. $\\hat{L}_{T_i}$ is susceptible to non-uniform pixel response, akin to standard image sensors. This is manifested by pixel-to-pixel variations in the contrast threshold, analogous to the spike camera's version of Fixed-Pattern Noise (FPN). Hence, relying solely on the rendered and degraded estimated light intensity values for NeRF training supervision can yield suboptimal results.", + "bbox": [ + 496, + 459, + 892, + 717 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Measuring Rendering Loss in Spike Domain", + "text_level": 1, + "bbox": [ + 500, + 739, + 862, + 755 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In order to capture the precise distribution of the spike stream, we advocate for employing a long-term spike rate rendering loss rather than directly assessing short-term light intensity. To account for the various noise sources, inspired by the spike simulator [51], we introduce a layer of spiking neurons that generate spike streams based on the intensity values of the pixel ray $r$ emulating the spike sampling process. We then compute the long-term spike rate rendering loss directly on both the generated spike stream and the", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "6288", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/9a7939f270a5048f37cbb4d6bcc0de22a2082ff0957db54abcd829adb19a50ca.jpg", + "image_caption": [ + "Figure 3. The backpropagation process of spiking neurons. The spiking neuron layer, comprising 256 time steps, follows the NeRF MLP. The weight of the last layer of MLP can be updated through Backpropagation Through Time (BPTT) using Eq. 10." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 467, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "original spike stream.", + "bbox": [ + 76, + 286, + 222, + 300 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our findings indicate that by combining NeRF's inherent multi-view consistency with our long-term spike rendering loss, our framework can establish robust self-supervision. This approach proves effective in mitigating the impact of erroneous measurements, particularly in the presence of high noise levels and diverse illumination conditions.", + "bbox": [ + 75, + 301, + 468, + 390 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relationship between the Pixel Ray $r$ and Real-world Spike Stream $S$ . The objective is to estimate intensity values $\\hat{I}(T_i(r))$ corresponding to the real light of the scene. Assuming that $\\hat{I}(T_i(r))$ is clear, to supervise the $\\hat{I}(T_i(r))$ with the real noisy spike stream, we need to consider multiple noises. Inspired by [51], we can define the relationship between $\\hat{I}(T_i(r))$ and spike noise as:", + "bbox": [ + 75, + 391, + 468, + 498 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {I} \\left(T _ {i} (r)\\right) = I \\left(T _ {i} (S)\\right) - I \\left(T _ {i} (N)\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 507, + 468, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $I(T_{i}(S)) = \\frac{1}{\\frac{Q_{r}}{L + N_{p} + N_{d}} + N_{rnu} + N_{q}} + N_{c}, I(T_{i}(N))$ denotes the intensity changes caused by noise, $L$ represents the scene light intensity, $Q_{r}$ is relative quantity matrix of electric charge. $N_{p}, N_{d}, N_{rnu}, N_{q}$ , and $N_{c}$ represent shot noise, dark current noise, response nonuniformity noise, quantization noise, and truncation noise, respectively.", + "bbox": [ + 75, + 536, + 468, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Spiking Neuron Layer. To accurately represent the spike distribution, we introduce an additional layer of spiking neurons following the NeRF MLP to generate the spike stream. Given that the spike camera employs an integrate-and-fire mechanism to convert the light intensity of the scene into spike streams, our framework utilizes the Integrate-and-Fire (IF) neuron model. The Integrate-and-Fire (IF) model [10] is a widely employed neuron model in Spiking Neural Networks (SNN) known for its biological realism [36]. For better representation, we represent the function of IF neuron as the discrete form:", + "bbox": [ + 75, + 633, + 468, + 799 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nV _ {t} = V _ {t - 1} + X _ {t}, \\quad S _ {t} = H \\left(V _ {t} - V _ {t h}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 811, + 468, + 829 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $V(t)$ denotes the membrane potential after neuronal dynamics at $t$ , $X(t)$ represents the input to neuron. A spike fires if $V(t)$ exceeds the threshold $V_{th}$ , $V_{rest}$ is the resting potential after firing, $S_t$ denotes the spike output at $t$ ,", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$H(\\cdot)$ denotes the Heaviside step function which is defined as $H(x) = 1$ for $x \\geq 0$ and $H(x) = 0$ for $x < 0$ .", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Threshold Variation Simulation. The response nonuniformity noise can be characterized by the pixel-to-pixel variation in the firing threshold. In fact, the deviation matrix corresponding to the response nonuniformity noise can be obtained by capturing a uniform light scene and recording the intensity. Thus, the threshold variation of each spiking neuron can be modeled by Eq. 7, and the spike stream can be generated by", + "bbox": [ + 496, + 121, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {S} (x, y) = \\operatorname {S N} \\left(I \\left(T _ {i} (r)\\right)\\right) \\cdot R (x, y), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 251, + 890, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{SN}(\\cdot)$ denotes the spiking neuron, $R(x,y)$ is the nonuniformity matrix and can be obtained by capturing a uniform light scene and recording the intensity1.", + "bbox": [ + 496, + 279, + 890, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Long-term Spike Rendering Loss. The spike stream can be mapped into an RKHS (reproducing kernel Hilbert space) as continuous-time functions which incorporate a statistical description of spike trains. Based on the RKHS, the kernel method [6] is employed for measuring spike train distances. Additionally, [47] introduces an intensity-based distance metric to quantify spike distances. Nevertheless, the complexity of these two methods is excessively high, rendering NeRF training inefficient.", + "bbox": [ + 496, + 325, + 890, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to measure the distance between the generated spike stream $\\hat{S}$ and the input spike stream $S$ , we propose a long-term spike rendering loss, which can be expressed by", + "bbox": [ + 496, + 460, + 890, + 506 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nD (r, S) = \\sum_ {t} \\operatorname {S N} \\left(I \\left(T _ {i} (r)\\right)\\right) \\cdot R (x, y) - \\sum_ {t} I \\left(T _ {i} (S)\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 516, + 890, + 547 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In theory, employing a longer spike stream for measurement has the potential to mitigate excessive truncation noise. In our experiment, the parameter $t$ is configured to 256, aligning with the time steps of the spiking neuron. The final loss function can be expressed as follows:", + "bbox": [ + 496, + 556, + 890, + 632 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} [ \\| D (r _ {c}, S) \\| _ {2} ^ {2} + \\| D (r _ {f}, S) \\| _ {2} ^ {2} ], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 643, + 890, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $r_c$ and $r_f$ are the pixel rays of coarse and fine models, respectively. In this way, the loss function of NeRF with spike stream as input is converted into Eq. 9. We adopt the design of the joint optimization of NeRF's coarse model and fine model, which is still beneficial in our framework.", + "bbox": [ + 496, + 681, + 890, + 756 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 Backpropagation Training", + "text_level": 1, + "bbox": [ + 500, + 775, + 738, + 789 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The spike generation function of an IF neuron is a hard threshold function that emits a spike when the membrane", + "bbox": [ + 496, + 797, + 890, + 825 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "1 Choose the pixel $(x_{m},y_{m})$ which is closest to the average response value as the reference pixel. $R(x,y)$ is then obtained by calculating the ratio of the reference pixel's response value to the response values of other pixels: $R(x,y) = \\frac{(L_2 + L_d(x_m,y_m))T_2(x_m,y_m)}{(L_2 + L_d(x,y))T_2}$ , where $L$ and $T$ are variables to be calibrated. See our supplementary materials for details.", + "bbox": [ + 496, + 834, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "6289", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/08e439a639766542fcf64306288b64cd996ebc60e30ca3a28b5b22e3b2dafbb5.jpg", + "image_caption": [ + "Figure 4. Quantitative results on synthetic spike data." + ], + "image_footnote": [], + "bbox": [ + 80, + 89, + 890, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "potential exceeds a firing threshold. Due to this discontinuous and non-differentiable neuron model, standard backpropagation algorithms cannot be applied to SNNs in their native form [40, 41]. As shown in Fig. 3, the backpropagated errors pass through the spiking neuron layer using BackPropagation Through Time (BPTT) [35]. Since the spiking neurons are one-to-one connected to the neurons of the last layer of NeRF MLP, the weight of the last layer of NeRF MLP $w^{l}$ is updated by BPTT. In BPTT, the network is unrolled for all discrete time steps, and $w^{l}$ update is computed as the sum of gradients from each time step as follows:", + "bbox": [ + 75, + 489, + 473, + 656 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta w ^ {l} = \\sum_ {t - 1} ^ {T} \\frac {\\partial \\mathcal {L} _ {t o t a l}}{\\partial o _ {t} ^ {l}} \\frac {\\partial o _ {t} ^ {l}}{\\partial V _ {t} ^ {l}} \\frac {\\partial V _ {t} ^ {l}}{\\partial w ^ {l}}, \\text {w h e r e} \\frac {\\partial o _ {t} ^ {l}}{\\partial V _ {t} ^ {l}} = H _ {1} ^ {\\prime} \\left(V _ {t} - V _ {t h}\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 661, + 482, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $o_t^l$ is the output of the neuron at time $t$ , $\\frac{\\partial o_t^l}{\\partial V_t^l}$ denotes the derivative of spike with respect to the membrane potential after charging at time step $t$ . Since $\\frac{\\partial o_t^l}{\\partial V_t^l}$ is not differentiable, we adopt surrogate gradient method [26] to calculate it. In our work, the approximate IF gradient is computed as $H_1(x) = \\frac{1}{V_{th}}$ , where the threshold value accounts for the change of the spiking output with respect to the input.", + "bbox": [ + 76, + 708, + 468, + 824 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on the above, a learnable realistic noise-embedded spike stream generation pipeline is proposed. Each time step of the spiking neuron represents a readout circuit process that verifies the reset signal in a clock signal corresponding to a spike camera. The dark current noise,", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/2b1202752cd7e0532074b96a0e602ff0462184b407a4685d8be857c47621559e.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation on synthetic dataset." + ], + "table_footnote": [], + "table_body": "
Method / MetricPSNR ↑SSIM ↑LPIPS ↓
TFP (32) + NeRF16.21/16.630.142/0.6480.662/0.058
TFP (256) + NeRF15.07/19.240.094/0.8640.741/0.085
TFI + NeRF14.93/19.340.108/0.8620.752/0.090
Spk2img + NeRF13.41/14.050.064/0.7490.729/0.133
Ours20.78/22.070.209/0.9160.617/0.053
", + "bbox": [ + 501, + 513, + 903, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "nonuniformity noise, and quantization noise are collectively treated as nonuniformity noise. These components are incorporated into the generated spike stream through a simulation of threshold variation.", + "bbox": [ + 496, + 637, + 893, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 498, + 714, + 624, + 732 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 498, + 739, + 689, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Synthetic Spike Data. We utilize six synthetic scenes (chair, ficus, hotdog, lego, materials, and mic) to generate synthetic spike data in NeRF. Using the spike generator provided by [51], we simulate spike streams for each viewpoint under different illumination conditions. The original image size is resized to $400 \\times 400$ , resulting in generated spike streams with a resolution of $400 \\times 400 \\times 256$ , where 256 represents the time length of each spike stream. In addition to generating spike streams from static viewpoint images,", + "bbox": [ + 496, + 763, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "6290", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b86ef7771c84516522f91145315300a40c8c2ab3bbb00daa3e9f9f06ac181fc0.jpg", + "table_caption": [ + "Table 2. Ablation study on synthetic dataset." + ], + "table_footnote": [], + "table_body": "
MethodLossStaticDynamicAverage
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRFMSE15.26/15.570.154/0.7850.588/0.06514.93/15.220.112/0.7450.626/0.10915.10/15.400.133/0.7650.607/0.087
TFP(256)+NeRFMSE14.44/16.410.127/0.7940.652/0.08814.34/16.290.099/0.7700.693/0.11414.39/16.350.113/0.7820.672/0.101
TFI+NeRFMSE13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810.682/0.101
Spk2img+NeRFMSE13.42/14.050.066/0.7260.724/0.12913.39/14.040.062/0.7720.735/0.13713.41/14.050.064/0.0750.729/0.133
OursLi*13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810. 682/0.101
Li18.55/19.760.237/0.8780.527/0.05116.63/17.790.167/0.7970.593/0.09717.59/18.770.202/0.8370.560/0.074
Ls+Li18.50/19.590.237/0.8760.524/0.05117.61/18.410.179/0.8160.590/0.08918.05/19.000.208/0.8460.557/0.070
Ls18.72/19.380.251/0.8800.517/0.05018.16/18.800.187/0.8200.601/0.09318.44/19.090.219/0.8500.559/0.072
", + "bbox": [ + 78, + 101, + 893, + 234 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f27bda079ba120cfec58c2b7c9d834f7c4f2fe82c466274098c6ccb07d73db6d.jpg", + "table_caption": [ + "Table 3. Quantitative evaluation of different light intensities on synthetic dataset." + ], + "table_footnote": [], + "table_body": "
MethodLight intensity (16)Light intensity (32)Light intensity (64)
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRF15.27/15.570.154/0.7850.588/0.06517.81/18.550.191/0.8270.562/0.07720.63/21.860.239/0.8720.528/0.067
TFP(256)+NeRF14.44/16.410.127/0.7940.652/0.08815.82/18.680.170/0.8350.616/0.07717.28/21.270.189/0.8520.596/0.081
TFI+NeRF13.77/16.630.120/0.7930.670/0.09315.07/18.530.156/0.8250.634/0.08316.16/20.560.187/0.8520.602/0.077
Spk2img+NeRF13.42/14.050.066/0.7260.724/0.12914.59/15.390.109/0.7680.651/0.09316.37/17.730.169/0.8370.595/0.073
Ours18.72/19.380.251/0.8800.517/0.05022.05/23.660.300/0.9260.477/0.05023.89/24.460.411/0.9290.428/0.049
", + "bbox": [ + 78, + 266, + 892, + 364 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3ceba9a99074fd02b289b05df4871ac2f678a8a66d00b83e2b0ca6a80e9f87fc.jpg", + "image_caption": [ + "Figure 5. Quantitative results on real-world spike data." + ], + "image_footnote": [], + "bbox": [ + 81, + 392, + 467, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "we render 16 high-resolution images captured by the camera and feed them into the spike generator to replicate the dynamic recording process of the spike camera. Each scene comprises 100 sets of images and their corresponding event data. Further details about the synthetic data can be found in our supplementary material.", + "bbox": [ + 75, + 595, + 468, + 686 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Real-world Spike Data. We employ the spike camera [15] to record real-world spike data. This camera is capable of capturing spike streams with a spatial resolution of $250 \\times 400$ and a temporal resolution of $20,000\\mathrm{Hz}$ . Holding the camera by hand, we capture data from five real-world scenarios, each featuring texture details under different illumination conditions. Each dataset comprises approximately 35 images from various viewpoints along with their corresponding spike data. To facilitate a comprehensive comparison of different cameras, we also use the DAVIS346 color event camera [30] to capture event and RGB data. This camera is equipped to capture spatial-temporally aligned event data and RGB frames, with a resolution of $346 \\times 260$ and an exposure time set to $33\\mathrm{ms}$ for the RGB frames.", + "bbox": [ + 75, + 688, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Baselines. Given the absence of existing spike-based NeRF methods, we compare our approach with three spike-based image reconstruction methods: TFI [46, 50], TFP [46, 50], and Spk2imgNet [45]. In a two-stage process, we reconstruct images using TFI and TFP (with window sizes of 32 and 256), which are commonly employed spike-based reconstruction methods, and Spk2imgNet, a learning-based method leveraging neural networks. While there are other learning-based methods for spike-based reconstruction [3], those methods aim to simultaneously estimate flow and image. The approach by [51] requires long spike sequences for recurrently optimizing the reconstruction process. Consequently, Spk2imgNet is well-suited for the NeRF setting, demonstrating stable performance. To ensure a fair comparison, all methods adopt a common NeRF backbone.", + "bbox": [ + 496, + 393, + 890, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Training Details. For the simulated data, we use the poses provided by the Blender and the generated spike stream as the input of the NeRF framework. For real-world data, we first reconstruct the spike stream into images, and then use COLMAP to estimate the poses. For a fair comparison, all comparison methods use the same poses as the input of the network. At each optimization iteration, we randomly sample a batch of camera rays from the set of all pixels in the dataset. We use the Adam optimizer with a learning rate that begins at $5 \\times 10^{-4}$ and decays exponentially to $5 \\times 10^{-5}$ . The optimization for a single scene typically takes about 20 hours to converge on a single NVIDIA 3090 GPU.", + "bbox": [ + 496, + 622, + 890, + 803 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Quantitative Experiment", + "text_level": 1, + "bbox": [ + 500, + 815, + 728, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We utilize three standard metrics: PSNR, SSIM [34], and LPIPS [42]. These metrics are employed to quantify the similarity between the synthesized novel views and the provided target novel views. The quantitative results on the", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "6291", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e7f746852b0605217f2d984e962f260e6d67cd4a617bd973e115ea30e7762d5c.jpg", + "image_caption": [ + "Figure 6. Quantitative results on different light intensities." + ], + "image_footnote": [], + "bbox": [ + 78, + 89, + 890, + 287 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9d8e2cb7d0ab7bb1392935cd6405e9d5dfde8dc4e23acc7261c4a69fb4798932.jpg", + "table_caption": [ + "Table 4. Quantitative evaluation on real-world data." + ], + "table_footnote": [], + "table_body": "
CameraMethodBrisque ↓NIQE ↓
APSImage+NeRF52.079.06
APSImage+NeRF*53.0510.06
DVSEvent+ENeRF83.9812.71
Spike cameraTFP+NeRF42.646.16
Spike cameraTFI+NeRF47.927.49
Spike cameraOurs35.946.09
", + "bbox": [ + 96, + 357, + 447, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "synthetic dataset are presented in Table 1. Since only the object will produce firing spikes in the synthetic dataset, we provide two measurement approaches: the left one utilizes the entire image for measurement, while the right one focuses solely on measurements within the object region. The results show that our model performs better than other two-stage methods, proving the effectiveness of the proposed framework. Table 4 presents the results on real-world data. As the real data lacks ground truth, we assess the results using no-reference quality assessment methods, specifically Brique [24] and NIQE [25]. The results indicate that our method outperforms other models. Additional experimental results can be found in our supplementary materials.", + "bbox": [ + 75, + 491, + 468, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Qualitative Experiment", + "text_level": 1, + "bbox": [ + 76, + 696, + 294, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We perform qualitative experiments on both synthetic and real-world data. As shown in Fig. 6, the rendered views from our method show markedly improved sharpness. TFP $(\\mathrm{W} = 32)$ struggles to generate novel views for the \"mic\" and \"materials\" scenes due to their low light intensity. The short window used by TFP fails to gather sufficient information. Similarly, Spk2img also exhibits suboptimal performance. This learning-based method is designed for ideal illumination conditions, and its performance sharply degrades when confronted with noisy spikes. In Fig. 5, three real-world scenes with varying illumination conditions are depicted. \"toys\" exhibits high light intensity, \"grid\" features medium", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "light, and \"box\" has low illumination. The results illustrate that our model performs effectively across different scenes and lighting conditions in real spike data.", + "bbox": [ + 496, + 334, + 890, + 380 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Ablation Study", + "text_level": 1, + "bbox": [ + 498, + 388, + 653, + 406 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We perform ablation studies on the proposed long-term spike rendering loss, and the results are presented in Table 2. In the table, $\\mathcal{L}_s$ represents the proposed spike rendering loss, $\\mathcal{L}_i$ involves using the light intensity of rays plus threshold correction, and the reconstructed images from spikes as supervision, while $\\mathcal{L}_i^*$ directly employs the estimated light intensity and reconstructed images as supervision. The experiments are conducted in both static and dynamic settings, affirming the effectiveness of our framework. Furthermore, we assess the performance under varying light intensities on the synthetic dataset. The results, presented in Table 3 and Fig. 6, demonstrate the robustness of our framework across different illumination conditions.", + "bbox": [ + 496, + 414, + 892, + 609 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 498, + 625, + 619, + 641 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper introduces SpikeNeRF as a pioneering approach to derive a volumetric scene representation from spike camera data using NeRF. With a focus on purely spike-based supervision, SpikeNeRF preserves texture and motion details in high temporal resolution, addressing the challenges associated with real-world spike sequences. Our evaluations on a newly curated dataset of synthetic and real spike sequences demonstrate the efficacy of SpikeNeRF for novel view synthesis. We hope that our work will shed light on the research of high quality 3D representation learning with novel spike stream techniques.", + "bbox": [ + 496, + 650, + 890, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement This work is partially supported by National Natural Science Foundation of China under Grant No.62302041, 62322204, 62131003, China National Postdoctoral Program under contract No.BX20230469, and Beijing Institute of Technology Research Fund Program for Young Scholars.", + "bbox": [ + 496, + 816, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "6292", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 118, + 174, + 133 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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Neuspike-net: High speed video reconstruc" + ], + "bbox": [ + 501, + 92, + 893, + 900 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "6294", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "tion via bio-inspired neuromorphic cameras. In IEEE Int. Conf. Comput. Vis. (ICCV), pages 2400-2409, 2021. 1, 3, 4", + "[50] Lin Zhu, Siwei Dong, Jianing Li, Tiejun Huang, and Yonghong Tian. Ultra-high temporal resolution visual reconstruction from a fovea-like spike camera via spiking neuron model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(1):1233-1249, 2022. 7", + "[51] Lin Zhu, Yunlong Zheng, Mengyue Geng, Lizhi Wang, and Hua Huang. Recurrent spike-based image restoration under general illumination. In Proceedings of the 31st ACM International Conference on Multimedia, pages 8251-8260, 2023. 1, 3, 4, 5, 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 260 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "6295", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SpikeNeRF_ Learning Neural Radiance Fields from Continuous Spike Stream/028c841a-a56f-4e19-871e-e3d2e2b3ec7c_model.json b/2024/SpikeNeRF_ Learning Neural Radiance Fields from Continuous Spike Stream/028c841a-a56f-4e19-871e-e3d2e2b3ec7c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..c485581226ae8c5c37b495c6ab85c67609eceb87 --- /dev/null +++ b/2024/SpikeNeRF_ Learning Neural Radiance Fields from Continuous Spike Stream/028c841a-a56f-4e19-871e-e3d2e2b3ec7c_model.json @@ -0,0 +1,2180 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.093, + 0.131, + 0.877, + 0.153 + ], + "angle": 0, + "content": "SpikeNeRF: Learning Neural Radiance Fields from Continuous Spike Stream" + }, + { + "type": "text", + "bbox": [ + 0.09, + 0.18, + 0.165, + 0.198 + ], + "angle": 0, + "content": "Lin Zhu" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.18, + 0.314, + 0.199 + ], + "angle": 0, + "content": "Zhu\\(^{1}\\) Kangmin Jia\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.349, + 0.181, + 0.45, + 0.198 + ], + "angle": 0, + "content": "Yifan Zhao2" + }, + { + "type": "text", + "bbox": [ + 0.486, + 0.181, + 0.588, + 0.199 + ], + "angle": 0, + "content": "Yunshan Qi2" + }, + { + "type": "text", + "bbox": [ + 0.623, + 0.181, + 0.725, + 0.199 + ], + "angle": 0, + "content": "Lizhi Wang" + }, + { + "type": "text", + "bbox": [ + 0.764, + 0.181, + 0.885, + 0.199 + ], + "angle": 0, + "content": "Hua Huang\\(^{3,1,*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.124, + 0.2, + 0.377, + 0.218 + ], + "angle": 0, + "content": "1Beijing Institute of Technology" + }, + { + "type": "text", + "bbox": [ + 0.419, + 0.2, + 0.582, + 0.217 + ], + "angle": 0, + "content": "\\(^{2}\\)Beihang University" + }, + { + "type": "text", + "bbox": [ + 0.624, + 0.2, + 0.843, + 0.217 + ], + "angle": 0, + "content": "\\(^{3}\\)Beijing Normal University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.313, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.283, + 0.474, + 0.661 + ], + "angle": 0, + "content": "Spike cameras, leveraging spike-based integration sampling and high temporal resolution, offer distinct advantages over standard cameras. However, existing approaches reliant on spike cameras often assume optimal illumination, a condition frequently unmet in real-world scenarios. To address this, we introduce SpikeNeRF, the first work that derives a NeRF-based volumetric scene representation from spike camera data. Our approach leverages NeRF's multiview consistency to establish robust self-supervision, effectively eliminating erroneous measurements and uncovering coherent structures within exceedingly noisy input amidst diverse real-world illumination scenarios. The framework comprises two core elements: a spike generation model incorporating an integrate-and-fire neuron layer and parameters accounting for non-idealities, such as threshold variation, and a spike rendering loss capable of generalizing across varying illumination conditions. We describe how to effectively optimize neural radiance fields to render photorealistic novel views from the novel continuous spike stream, demonstrating advantages over other vision sensors in certain scenes. Empirical evaluations conducted on both real and novel realistically simulated sequences affirm the efficacy of our methodology. The dataset and source code are released at https://github.com/BIT-Vision/SpikeNeRF." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.688, + 0.21, + 0.704 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.713, + 0.47, + 0.88 + ], + "angle": 0, + "content": "In recent years, there has been significant progress in the development of neuromorphic cameras, with notable advancements such as event cameras [2, 4] and spike cameras [15, 46]. These innovative devices excel in capturing light intensity changes in high-speed scenes, presenting a breakthrough in the realm of visual perception [9, 11, 13, 31, 32, 38, 49]. Spike camera, wherein each pixel responds independently to the accumulation of photons by generating asynchronous spikes [46]. This distinctive feature enables the spike camera to record full visual details with an ultra-high temporal resolution of up to \\(40\\mathrm{kHz}\\) (or \\(20\\mathrm{kHz}\\) for the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.253, + 0.892, + 0.33 + ], + "angle": 0, + "content": "portable version). These advantages include the capability to capture rapid changes in scenes and efficiently represent dynamic environments. With these unique features, spike cameras have demonstrated superiority in handling multiple computer vision tasks [12, 14, 33, 37, 45, 47-49, 51]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.333, + 0.893, + 0.636 + ], + "angle": 0, + "content": "In parallel, there has been a growing trend in the computer vision community to explore neural radiance fields (NeRFs) as a solution for scene representation and novel view synthesis [5, 8, 17, 18, 20, 22, 27, 29, 39]. NeRFs employ a multilayer perceptron (MLP) combined with differentiable rendering to represent scenes, allowing for the synthesis of novel views from unseen perspectives. So far, NeRFs have predominantly undergone examination using simulated data and high-quality real-world images acquired under optimal conditions. Some studies have explored the application of NeRF to a distinct type of neuromorphic camera known as an event camera, characterized by differential sampling. Noteworthy among these endeavors are Ev-NeRF [17] and EventNeRF [29], both of which introduced neural radiance fields derived exclusively from event streams. However, the inherent lack of texture details in event data has constrained the effectiveness of these approaches, resulting in limited outcomes. Instead, a spike camera can offer fine texture details through a high temporal resolution spike stream." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.895, + 0.852 + ], + "angle": 0, + "content": "However, their application to spike camera data poses a unique challenge due to the distinctive data modality. The output of a spike camera is a spike stream, fundamentally different from traditional images. Each pixel in a spike camera generates a spike, and the accumulation is reset when the photon accumulation exceeds a predefined threshold. At each timestamp, the spike camera outputs a binary matrix, referred to as a spike frame, indicating the presence of spikes at all pixels. Currently, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. Therefore, the challenge tackled in this paper is: Can we reconstruct a dense volumetric 3D representation of the scene from a spike stream captured by a moving spike camera?" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Addressing the aforementioned challenges, this paper introduces SpikeNeRF, the first approach for deriving a volumetric scene representation from spike camera data using" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.292, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: Hua Huang." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "6285" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.089, + 0.752, + 0.356 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.776, + 0.096, + 0.9, + 0.16 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.806, + 0.161, + 0.871, + 0.172 + ], + "angle": 0, + "content": "Event input" + }, + { + "type": "image", + "bbox": [ + 0.778, + 0.178, + 0.899, + 0.241 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.241, + 0.89, + 0.263 + ], + "angle": 0, + "content": "Novel Views from EventNeRF" + }, + { + "type": "image", + "bbox": [ + 0.779, + 0.264, + 0.898, + 0.331 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.787, + 0.332, + 0.89, + 0.356 + ], + "angle": 0, + "content": "Novel Views from Image+NeRF" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.363, + 0.894, + 0.419 + ], + "angle": 0, + "content": "Figure 1. Comparing novel views across various vision sensors, our SpikeNeRF stands out as the first method to learn neural radiance fields from a continuous spike stream. The Spike camera, operating at \\(20,000\\mathrm{Hz}\\), eliminates motion blur, distinguishing it from traditional cameras. Notably, when contrasted with other methods (e.g., TFI+NeRF [46], Spk2img+NeRF [45], and EventNeRF [29]) and sensors (e.g., event camera), the rendered views of objects or scenes exhibit significantly enhanced sharpness." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.438, + 0.473, + 0.741 + ], + "angle": 0, + "content": "Neural Radiance Fields (NeRF). Our method is designed for purely spike-based supervision, preserving texture and motion details in high temporal resolution. We evaluate the efficacy of SpikeNeRF for the task of novel view synthesis on a new dataset of synthetic and real spike sequences. SpikeNeRF leverages NeRF's inherent multi-view consistency to establish robust self-supervision, mitigating the impact of erroneous measurements in the presence of high noise levels and diverse illumination conditions. Specifically, SpikeNeRF incorporates a spike generation model based on a spiking neuron layer, which considers intrinsic parameters and non-idealities associated with spike cameras. This model enhances the fidelity of spike data, providing a more accurate representation of the scene under varying lighting conditions (see Fig. 1). To enable generalization across diverse illumination scenarios, SpikeNeRF introduces a long-term spike rendering loss. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry, even in challenging lighting conditions. The main contributions of this paper are:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.804 + ], + "angle": 0, + "content": "1) We present the first approach for inferring a NeRF volume from only a spike stream. SpikeNeRF is highly robust to various illumination conditions and builds a coherent 3D structure that can provide high-quality observations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.807, + 0.47, + 0.868 + ], + "angle": 0, + "content": "2) We develop a long-term spike rendering loss based on a spiking neuron layer and threshold variation simulation, which are effective in enhancing neural volumetric representation learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "3) We build both synthetic and real-world datasets for training and testing our model. Experimental results" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.744, + 0.47, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.438, + 0.892, + 0.483 + ], + "angle": 0, + "content": "demonstrate that our method outperforms existing methods. We release the newly recorded spike dataset and source code to facilitate the research field." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.502, + 0.642, + 0.518 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.529, + 0.718, + 0.544 + ], + "angle": 0, + "content": "2.1. Neural Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.554, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In recent years, Neural Radiance Fields have garnered significant attention for their remarkable performance in tasks involving neural implicit 3D representation and novel view synthesis. Various enhancements, such as FastNeRF [8] and Depth-supervised NeRF [5], aim to expedite NeRF's learning speed. Neural scene flow fields [18] delve into 3D Scene Representation Learning for dynamic scenes. Approaches like PixelNeRF [39] and RegNeRF [27] leverage a minimal number of input images for high-quality novel view synthesis. Mip-NeRF [1] introduces a frustum-based sampling strategy for NeRF-based anti-aliasing, addressing artifacts while enhancing training speed. Beyond speed and data augmentation, some works focus on enhancing NeRF with low-quality input images. For instance, NeRF in the wild [21] utilizes low-quality images captured by tourists, tackling occlusions and inconsistent lighting conditions. NeRF in the dark [23] and HDR-NeRF [16] enable the synthesis of high dynamic range new view images from noisy low dynamic images. Additionally, Deblur-NeRF [20] introduces the DSK module for simulating the blurring process, facilitating novel view synthesis from blurry to sharp images. However, Deblur-NeRF may face challenges in scenarios where the camera coincidentally shakes uniformly across" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6286" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.396, + 0.107 + ], + "angle": 0, + "content": "all views or the input images exhibit strong blur." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.468, + 0.145 + ], + "angle": 0, + "content": "2.2. Scene Reconstruction based on Neuromorphic Camera" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.154, + 0.468, + 0.379 + ], + "angle": 0, + "content": "Generally speaking, there are two types of bio-inspired visual sampling manner: temporal contrast sampling and integral sampling. Dynamic Vision Sensor (DVS), also known as an event camera, generates events when pixel brightness changes exceed a threshold. Recently, Ev-NeRF [17] and EventNeRF [29] proposed neural radiance fields derived exclusively from event streams. However, due to the absence of texture details in event data, these approaches yield limited results. Ev-NeRF [17] is confined to learning grayscale NeRF, while EventNeRF [29] exhibits noticeable artifacts and chromatic aberration, lacking RGB data for supervision. [28] first introduces event data and blurry RGB frames to achieve high quality clear scene reconstruction. [19] proposes Robust e-NeRF to robustly reconstruct NeRFs from moving event cameras under various real-world conditions," + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.381, + 0.468, + 0.621 + ], + "angle": 0, + "content": "Our work is based on spike camera, where each pixel responds independently to the accumulation of photons by generating spikes. It records full visual details with an ultra-high temporal resolution (up to \\(40\\mathrm{kHz}\\)). Image reconstruction based on spike cameras has emerged by analyzing spike intervals and counts [46]. Leveraging the spiking neuron model, a fovea-like texture reconstruction framework reconstructs images [48]. Spike camera methods have been developed for tone mapping [43], motion deblurring [12], and super resolution [37, 44]. Recent deep learning-based image reconstruction methods [3, 45, 49, 51] for spike cameras outperform traditional methods significantly. The noise characteristics of spike cameras differ substantially from those of traditional cameras. A preliminary analysis in [49] demonstrates that the noise distribution varies under different lighting conditions." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.622, + 0.468, + 0.698 + ], + "angle": 0, + "content": "However, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. The challenge is to explore the texture details hidden in the spike stream, understanding the spike distribution is crucial for spike-based applications." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.175, + 0.725 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.735, + 0.294, + 0.75 + ], + "angle": 0, + "content": "3.1. Neural Radiance Fields" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.758, + 0.468, + 0.846 + ], + "angle": 0, + "content": "The fundamental idea of NeRF is to employ a Multilayer Perceptron (MLP) to learn a 3D volume representation [22]. The MLP takes 3D position \\(\\mathbf{o}\\) and 2D ray direction \\(\\mathbf{d}\\) as inputs and produces color \\(\\mathbf{c}\\) and density \\(\\sigma\\) as outputs. In Eq. (1), \\(F_{\\theta}\\) represents the MLP network with \\(\\theta\\) as its parameters:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.849, + 0.468, + 0.865 + ], + "angle": 0, + "content": "\\[\n(\\mathbf {c}, \\sigma) = F _ {\\theta} \\left(\\gamma_ {o} (\\mathbf {o}), \\gamma_ {d} (\\mathbf {d})\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The functions \\(\\gamma_{o}(\\cdot)\\) and \\(\\gamma_{d}(\\cdot)\\), defined in Eq. (1), map the input 5D coordinates to a higher-dimensional space, en" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.287 + ], + "angle": 0, + "content": "abling the neural network to better capture color and geometry information in the scene. To generate views from the scene representation, NeRF employs a classical volume rendering method described in Eq. 2. For a given ray \\(\\mathbf{r}(t) = \\mathbf{o} + l\\mathbf{d}\\) emitted from the camera, the expected color projected on the pixel is denoted as \\(C(\\mathbf{r})\\). The near and far bounds of the ray are represented by \\(l_{n}\\) and \\(l_{f}\\), respectively. NeRF divides the interval \\([l_n,l_f]\\) into \\(N\\) discrete bins, where \\(\\mathbf{c}_i\\) and \\(\\sigma i\\) are the outputs of \\(F_{\\theta}\\), indicating the color and density of each bin through which the ray passes. The distance between adjacent samples is \\(\\delta_i = l_{i + 1} - l_i\\), and \\(T_{i}\\) represents the transparency of particles between \\(l_{n}\\) and bin \\(i\\)." + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.294, + 0.892, + 0.335 + ], + "angle": 0, + "content": "\\[\nC (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) \\mathbf {c} _ {i}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.435 + ], + "angle": 0, + "content": "where \\( T(i) = \\exp(-\\sum_{j=1}^{i-1} \\sigma_j \\delta_j) \\). To ensure reasonable sampling in the final model, NeRF utilizes a Hierarchical volume sampling strategy, simultaneously optimizing the coarse and fine models and using the density obtained by the coarse model to determine the sampling weight of the fine model." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.445, + 0.75, + 0.46 + ], + "angle": 0, + "content": "3.2. Spike Sampling Mechanism" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.619 + ], + "angle": 0, + "content": "In the field of frame-free neuromorphic vision, the spike camera operates by converting the intensity of light into voltage through photoreceptors [7, 46]. Upon reaching a predefined threshold, a one-bit spike is generated, accompanied by a signal to reset the integrator. This mechanism resembles that of an integrate-and-fire neuron. Luminance stimuli \\(I\\) lead to varying spike firing rates, with asynchronous triggering of output and reset across pixels. Brighter light results in faster firing, governed by the inequality \\(\\int I dt \\geq \\phi\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.62, + 0.892, + 0.726 + ], + "angle": 0, + "content": "The raw data from the spike camera is a three-dimensional spike stream, focusing solely on luminance intensity integration and firing ultra-high frequency spikes. At each sampling moment, a digital signal of \"1\" (spike) or \"0\" is output based on whether a spike was fired. The spike firing status of pixel \\((i,j)\\) at moment \\(t\\) is represented as \\(S_{i,j}(t)\\in 0,1\\). The spike signal model is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.733, + 0.892, + 0.78 + ], + "angle": 0, + "content": "\\[\nS (x, y, t) = S (x, y, n t _ {0}) = \\epsilon \\left(\\int_ {t ^ {\\prime}} ^ {n t _ {0}} \\frac {C \\Delta V}{I _ {p h} (x , y , \\tau)} d \\tau - 1\\right). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( t' \\) is the start time of the current integration phase, reset at the phase's end. \\( \\Delta V \\) denotes the voltage, \\( nt_0 \\) denotes the \\( n \\)-th clock signal, with \\( t_0 \\) as the unit time interval \\( (50\\mu s) \\), and \\( I_{ph} \\) represents the magnitude of the current for photoelectric conversion. \\( C \\) is the capacitor in parallel with the photodiode, which is used to store electrons for photoconversion. \\( \\epsilon(x) \\) is a step function where \\( \\epsilon(x) = 1 \\) when \\( x \\geq 0 \\) otherwise \\( \\epsilon(x) = 0 \\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6287" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.334 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.347, + 0.895, + 0.406 + ], + "angle": 0, + "content": "Figure 2. The architecture of SpikeNeRF. Motivated by the objective of learning NeRFs from a continuous spike stream, we establish the connection between the pixel ray \\( r \\) and the real-world spike stream \\( S \\). To quantify the rendering loss in the spike domain, we integrate a spiking neuron layer following the NeRF MLP. The nonuniformity is captured through pixel-to-pixel threshold variation, simulated by the spiking neuron layer. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.473, + 0.657 + ], + "angle": 0, + "content": "The noise of the spike camera differs significantly from traditional cameras due to circuit variations. The noise components encompass Shot Noise, wherein the photosensor converts photons into photo-electrons, resulting in a photo-current subject to shot noise \\( N_{p} \\) even in uniform light scenarios. Dark Current Noise arises from thermal diffusion and defects, causing the spike circuit to produce signals even in the absence of scene light, with dark current noise denoted as \\( N_{d} \\). Response Nonuniformity stems from chip manufacturing limitations, causing pixel units to exhibit varying sensitivity to light intensity, leading to photo response nonuniformity noise \\( N_{nru} \\). Lastly, Quantization Noise arises from the delay in the release time of the spike signal relative to the generation time of the reset signal, introducing quantization noise \\( N_{q} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.67, + 0.454, + 0.687 + ], + "angle": 0, + "content": "3.3. Self-Supervision with Volumetric Rendering" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.694, + 0.47, + 0.862 + ], + "angle": 0, + "content": "An overview of the training pipeline is illustrated in Fig. 2. In line with the spike generation model, we propose self-supervision with volumetric rendering in this section. Different from traditional RGB frames, a binary spike frame can not accurately represent the light intensity at the current timestamp. Let us denote the intensity values of the pixel ray \\( r \\) at time \\( T_{i} \\) as \\( \\hat{I}(T_{i}(r)) \\). Since the high temporal resolution of the spike camera, the estimated short-term light intensity \\( \\hat{L}_{T_i} \\) can record motion details hidden in the spike stream. A straightforward approach is to calculate the light intensity \\( \\hat{L}_{T_i} \\) at time \\( T_{i} \\) based on the original spike stream:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.875, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\hat {L} _ {T _ {i}} = \\frac {\\theta}{n - m}, m < n, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.43, + 0.892, + 0.459 + ], + "angle": 0, + "content": "where \\(m\\) and \\(n\\) are the timestamps corresponding to two adjacent spikes, \\(\\theta\\) controls the gray-scale level." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.893, + 0.718 + ], + "angle": 0, + "content": "However, \\(\\hat{L}_{T_i}\\) is influenced by various sources of noise, particularly the temporal sampling noise [49]. The firing intervals of spikes fluctuate even in constant illumination conditions due to the inherent spike sampling mechanism. For instance, in the integrate-and-fire mechanism, if the membrane potential of the neuron (pixel) is not reset, an object with a light intensity corresponding to an inter-spike interval of 2 might be recorded as 1 or 3. Consequently, \\(\\hat{L}_{T_i}\\) is suitable for capturing motion details in the intensity values of the pixel ray \\(r\\), but texture details are often affected. \\(\\hat{L}_{T_i}\\) is susceptible to non-uniform pixel response, akin to standard image sensors. This is manifested by pixel-to-pixel variations in the contrast threshold, analogous to the spike camera's version of Fixed-Pattern Noise (FPN). Hence, relying solely on the rendered and degraded estimated light intensity values for NeRF training supervision can yield suboptimal results." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.74, + 0.863, + 0.756 + ], + "angle": 0, + "content": "3.3.1 Measuring Rendering Loss in Spike Domain" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In order to capture the precise distribution of the spike stream, we advocate for employing a long-term spike rate rendering loss rather than directly assessing short-term light intensity. To account for the various noise sources, inspired by the spike simulator [51], we introduce a layer of spiking neurons that generate spike streams based on the intensity values of the pixel ray \\( r \\) emulating the spike sampling process. We then compute the long-term spike rate rendering loss directly on both the generated spike stream and the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6288" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.468, + 0.205 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.218, + 0.471, + 0.275 + ], + "angle": 0, + "content": "Figure 3. The backpropagation process of spiking neurons. The spiking neuron layer, comprising 256 time steps, follows the NeRF MLP. The weight of the last layer of MLP can be updated through Backpropagation Through Time (BPTT) using Eq. 10." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.287, + 0.223, + 0.301 + ], + "angle": 0, + "content": "original spike stream." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.47, + 0.391 + ], + "angle": 0, + "content": "Our findings indicate that by combining NeRF's inherent multi-view consistency with our long-term spike rendering loss, our framework can establish robust self-supervision. This approach proves effective in mitigating the impact of erroneous measurements, particularly in the presence of high noise levels and diverse illumination conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.469, + 0.499 + ], + "angle": 0, + "content": "Relationship between the Pixel Ray \\( r \\) and Real-world Spike Stream \\( S \\). The objective is to estimate intensity values \\( \\hat{I}(T_i(r)) \\) corresponding to the real light of the scene. Assuming that \\( \\hat{I}(T_i(r)) \\) is clear, to supervise the \\( \\hat{I}(T_i(r)) \\) with the real noisy spike stream, we need to consider multiple noises. Inspired by [51], we can define the relationship between \\( \\hat{I}(T_i(r)) \\) and spike noise as:" + }, + { + "type": "equation", + "bbox": [ + 0.157, + 0.508, + 0.469, + 0.527 + ], + "angle": 0, + "content": "\\[\n\\hat {I} \\left(T _ {i} (r)\\right) = I \\left(T _ {i} (S)\\right) - I \\left(T _ {i} (N)\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.469, + 0.635 + ], + "angle": 0, + "content": "where \\( I(T_{i}(S)) = \\frac{1}{\\frac{Q_{r}}{L + N_{p} + N_{d}} + N_{rnu} + N_{q}} + N_{c}, I(T_{i}(N)) \\) denotes the intensity changes caused by noise, \\( L \\) represents the scene light intensity, \\( Q_{r} \\) is relative quantity matrix of electric charge. \\( N_{p}, N_{d}, N_{rnu}, N_{q} \\), and \\( N_{c} \\) represent shot noise, dark current noise, response nonuniformity noise, quantization noise, and truncation noise, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.635, + 0.469, + 0.8 + ], + "angle": 0, + "content": "Spiking Neuron Layer. To accurately represent the spike distribution, we introduce an additional layer of spiking neurons following the NeRF MLP to generate the spike stream. Given that the spike camera employs an integrate-and-fire mechanism to convert the light intensity of the scene into spike streams, our framework utilizes the Integrate-and-Fire (IF) neuron model. The Integrate-and-Fire (IF) model [10] is a widely employed neuron model in Spiking Neural Networks (SNN) known for its biological realism [36]. For better representation, we represent the function of IF neuron as the discrete form:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.813, + 0.469, + 0.83 + ], + "angle": 0, + "content": "\\[\nV _ {t} = V _ {t - 1} + X _ {t}, \\quad S _ {t} = H \\left(V _ {t} - V _ {t h}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\( V(t) \\) denotes the membrane potential after neuronal dynamics at \\( t \\), \\( X(t) \\) represents the input to neuron. A spike fires if \\( V(t) \\) exceeds the threshold \\( V_{th} \\), \\( V_{rest} \\) is the resting potential after firing, \\( S_t \\) denotes the spike output at \\( t \\)," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "\\(H(\\cdot)\\) denotes the Heaviside step function which is defined as \\(H(x) = 1\\) for \\(x \\geq 0\\) and \\(H(x) = 0\\) for \\(x < 0\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.892, + 0.243 + ], + "angle": 0, + "content": "Threshold Variation Simulation. The response nonuniformity noise can be characterized by the pixel-to-pixel variation in the firing threshold. In fact, the deviation matrix corresponding to the response nonuniformity noise can be obtained by capturing a uniform light scene and recording the intensity. Thus, the threshold variation of each spiking neuron can be modeled by Eq. 7, and the spike stream can be generated by" + }, + { + "type": "equation", + "bbox": [ + 0.579, + 0.252, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\hat {S} (x, y) = \\operatorname {S N} \\left(I \\left(T _ {i} (r)\\right)\\right) \\cdot R (x, y), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.28, + 0.892, + 0.326 + ], + "angle": 0, + "content": "where \\(\\mathrm{SN}(\\cdot)\\) denotes the spiking neuron, \\(R(x,y)\\) is the nonuniformity matrix and can be obtained by capturing a uniform light scene and recording the intensity1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.892, + 0.462 + ], + "angle": 0, + "content": "Long-term Spike Rendering Loss. The spike stream can be mapped into an RKHS (reproducing kernel Hilbert space) as continuous-time functions which incorporate a statistical description of spike trains. Based on the RKHS, the kernel method [6] is employed for measuring spike train distances. Additionally, [47] introduces an intensity-based distance metric to quantify spike distances. Nevertheless, the complexity of these two methods is excessively high, rendering NeRF training inefficient." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.507 + ], + "angle": 0, + "content": "In order to measure the distance between the generated spike stream \\(\\hat{S}\\) and the input spike stream \\(S\\), we propose a long-term spike rendering loss, which can be expressed by" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.517, + 0.892, + 0.548 + ], + "angle": 0, + "content": "\\[\nD (r, S) = \\sum_ {t} \\operatorname {S N} \\left(I \\left(T _ {i} (r)\\right)\\right) \\cdot R (x, y) - \\sum_ {t} I \\left(T _ {i} (S)\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.892, + 0.633 + ], + "angle": 0, + "content": "In theory, employing a longer spike stream for measurement has the potential to mitigate excessive truncation noise. In our experiment, the parameter \\( t \\) is configured to 256, aligning with the time steps of the spiking neuron. The final loss function can be expressed as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.645, + 0.892, + 0.677 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} [ \\| D (r _ {c}, S) \\| _ {2} ^ {2} + \\| D (r _ {f}, S) \\| _ {2} ^ {2} ], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.682, + 0.892, + 0.757 + ], + "angle": 0, + "content": "where \\( r_c \\) and \\( r_f \\) are the pixel rays of coarse and fine models, respectively. In this way, the loss function of NeRF with spike stream as input is converted into Eq. 9. We adopt the design of the joint optimization of NeRF's coarse model and fine model, which is still beneficial in our framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.776, + 0.74, + 0.79 + ], + "angle": 0, + "content": "3.3.2 Backpropagation Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.798, + 0.892, + 0.827 + ], + "angle": 0, + "content": "The spike generation function of an IF neuron is a hard threshold function that emits a spike when the membrane" + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.835, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1 Choose the pixel \\((x_{m},y_{m})\\) which is closest to the average response value as the reference pixel. \\(R(x,y)\\) is then obtained by calculating the ratio of the reference pixel's response value to the response values of other pixels: \\(R(x,y) = \\frac{(L_2 + L_d(x_m,y_m))T_2(x_m,y_m)}{(L_2 + L_d(x,y))T_2}\\), where \\(L\\) and \\(T\\) are variables to be calibrated. See our supplementary materials for details." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6289" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.09, + 0.891, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.325, + 0.45, + 0.644, + 0.464 + ], + "angle": 0, + "content": "Figure 4. Quantitative results on synthetic spike data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.49, + 0.475, + 0.657 + ], + "angle": 0, + "content": "potential exceeds a firing threshold. Due to this discontinuous and non-differentiable neuron model, standard backpropagation algorithms cannot be applied to SNNs in their native form [40, 41]. As shown in Fig. 3, the backpropagated errors pass through the spiking neuron layer using BackPropagation Through Time (BPTT) [35]. Since the spiking neurons are one-to-one connected to the neurons of the last layer of NeRF MLP, the weight of the last layer of NeRF MLP \\( w^{l} \\) is updated by BPTT. In BPTT, the network is unrolled for all discrete time steps, and \\( w^{l} \\) update is computed as the sum of gradients from each time step as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.662, + 0.483, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\Delta w ^ {l} = \\sum_ {t - 1} ^ {T} \\frac {\\partial \\mathcal {L} _ {t o t a l}}{\\partial o _ {t} ^ {l}} \\frac {\\partial o _ {t} ^ {l}}{\\partial V _ {t} ^ {l}} \\frac {\\partial V _ {t} ^ {l}}{\\partial w ^ {l}}, \\text {w h e r e} \\frac {\\partial o _ {t} ^ {l}}{\\partial V _ {t} ^ {l}} = H _ {1} ^ {\\prime} \\left(V _ {t} - V _ {t h}\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.709, + 0.47, + 0.825 + ], + "angle": 0, + "content": "where \\(o_t^l\\) is the output of the neuron at time \\(t\\), \\(\\frac{\\partial o_t^l}{\\partial V_t^l}\\) denotes the derivative of spike with respect to the membrane potential after charging at time step \\(t\\). Since \\(\\frac{\\partial o_t^l}{\\partial V_t^l}\\) is not differentiable, we adopt surrogate gradient method [26] to calculate it. In our work, the approximate IF gradient is computed as \\(H_1(x) = \\frac{1}{V_{th}}\\), where the threshold value accounts for the change of the spiking output with respect to the input." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Based on the above, a learnable realistic noise-embedded spike stream generation pipeline is proposed. Each time step of the spiking neuron represents a readout circuit process that verifies the reset signal in a clock signal corresponding to a spike camera. The dark current noise," + }, + { + "type": "table_caption", + "bbox": [ + 0.538, + 0.488, + 0.854, + 0.503 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation on synthetic dataset." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.514, + 0.905, + 0.607 + ], + "angle": 0, + "content": "
Method / MetricPSNR ↑SSIM ↑LPIPS ↓
TFP (32) + NeRF16.21/16.630.142/0.6480.662/0.058
TFP (256) + NeRF15.07/19.240.094/0.8640.741/0.085
TFI + NeRF14.93/19.340.108/0.8620.752/0.090
Spk2img + NeRF13.41/14.050.064/0.7490.729/0.133
Ours20.78/22.070.209/0.9160.617/0.053
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.894, + 0.7 + ], + "angle": 0, + "content": "nonuniformity noise, and quantization noise are collectively treated as nonuniformity noise. These components are incorporated into the generated spike stream through a simulation of threshold variation." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.715, + 0.625, + 0.733 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.74, + 0.691, + 0.758 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Synthetic Spike Data. We utilize six synthetic scenes (chair, ficus, hotdog, lego, materials, and mic) to generate synthetic spike data in NeRF. Using the spike generator provided by [51], we simulate spike streams for each viewpoint under different illumination conditions. The original image size is resized to \\(400 \\times 400\\), resulting in generated spike streams with a resolution of \\(400 \\times 400 \\times 256\\), where 256 represents the time length of each spike stream. In addition to generating spike streams from static viewpoint images," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6290" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.352, + 0.09, + 0.616, + 0.103 + ], + "angle": 0, + "content": "Table 2. Ablation study on synthetic dataset." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.102, + 0.894, + 0.236 + ], + "angle": 0, + "content": "
MethodLossStaticDynamicAverage
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRFMSE15.26/15.570.154/0.7850.588/0.06514.93/15.220.112/0.7450.626/0.10915.10/15.400.133/0.7650.607/0.087
TFP(256)+NeRFMSE14.44/16.410.127/0.7940.652/0.08814.34/16.290.099/0.7700.693/0.11414.39/16.350.113/0.7820.672/0.101
TFI+NeRFMSE13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810.682/0.101
Spk2img+NeRFMSE13.42/14.050.066/0.7260.724/0.12913.39/14.040.062/0.7720.735/0.13713.41/14.050.064/0.0750.729/0.133
OursLi*13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810. 682/0.101
Li18.55/19.760.237/0.8780.527/0.05116.63/17.790.167/0.7970.593/0.09717.59/18.770.202/0.8370.560/0.074
Ls+Li18.50/19.590.237/0.8760.524/0.05117.61/18.410.179/0.8160.590/0.08918.05/19.000.208/0.8460.557/0.070
Ls18.72/19.380.251/0.8800.517/0.05018.16/18.800.187/0.8200.601/0.09318.44/19.090.219/0.8500.559/0.072
" + }, + { + "type": "table_caption", + "bbox": [ + 0.245, + 0.254, + 0.722, + 0.267 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation of different light intensities on synthetic dataset." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.267, + 0.893, + 0.365 + ], + "angle": 0, + "content": "
MethodLight intensity (16)Light intensity (32)Light intensity (64)
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRF15.27/15.570.154/0.7850.588/0.06517.81/18.550.191/0.8270.562/0.07720.63/21.860.239/0.8720.528/0.067
TFP(256)+NeRF14.44/16.410.127/0.7940.652/0.08815.82/18.680.170/0.8350.616/0.07717.28/21.270.189/0.8520.596/0.081
TFI+NeRF13.77/16.630.120/0.7930.670/0.09315.07/18.530.156/0.8250.634/0.08316.16/20.560.187/0.8520.602/0.077
Spk2img+NeRF13.42/14.050.066/0.7260.724/0.12914.59/15.390.109/0.7680.651/0.09316.37/17.730.169/0.8370.595/0.073
Ours18.72/19.380.251/0.8800.517/0.05022.05/23.660.300/0.9260.477/0.05023.89/24.460.411/0.9290.428/0.049
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.393, + 0.468, + 0.543 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.11, + 0.553, + 0.435, + 0.567 + ], + "angle": 0, + "content": "Figure 5. Quantitative results on real-world spike data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.47, + 0.688 + ], + "angle": 0, + "content": "we render 16 high-resolution images captured by the camera and feed them into the spike generator to replicate the dynamic recording process of the spike camera. Each scene comprises 100 sets of images and their corresponding event data. Further details about the synthetic data can be found in our supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Real-world Spike Data. We employ the spike camera [15] to record real-world spike data. This camera is capable of capturing spike streams with a spatial resolution of \\(250 \\times 400\\) and a temporal resolution of \\(20,000\\mathrm{Hz}\\). Holding the camera by hand, we capture data from five real-world scenarios, each featuring texture details under different illumination conditions. Each dataset comprises approximately 35 images from various viewpoints along with their corresponding spike data. To facilitate a comprehensive comparison of different cameras, we also use the DAVIS346 color event camera [30] to capture event and RGB data. This camera is equipped to capture spatial-temporally aligned event data and RGB frames, with a resolution of \\(346 \\times 260\\) and an exposure time set to \\(33\\mathrm{ms}\\) for the RGB frames." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.394, + 0.892, + 0.621 + ], + "angle": 0, + "content": "Baselines. Given the absence of existing spike-based NeRF methods, we compare our approach with three spike-based image reconstruction methods: TFI [46, 50], TFP [46, 50], and Spk2imgNet [45]. In a two-stage process, we reconstruct images using TFI and TFP (with window sizes of 32 and 256), which are commonly employed spike-based reconstruction methods, and Spk2imgNet, a learning-based method leveraging neural networks. While there are other learning-based methods for spike-based reconstruction [3], those methods aim to simultaneously estimate flow and image. The approach by [51] requires long spike sequences for recurrently optimizing the reconstruction process. Consequently, Spk2imgNet is well-suited for the NeRF setting, demonstrating stable performance. To ensure a fair comparison, all methods adopt a common NeRF backbone." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.623, + 0.892, + 0.804 + ], + "angle": 0, + "content": "Training Details. For the simulated data, we use the poses provided by the Blender and the generated spike stream as the input of the NeRF framework. For real-world data, we first reconstruct the spike stream into images, and then use COLMAP to estimate the poses. For a fair comparison, all comparison methods use the same poses as the input of the network. At each optimization iteration, we randomly sample a batch of camera rays from the set of all pixels in the dataset. We use the Adam optimizer with a learning rate that begins at \\(5 \\times 10^{-4}\\) and decays exponentially to \\(5 \\times 10^{-5}\\). The optimization for a single scene typically takes about 20 hours to converge on a single NVIDIA 3090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.729, + 0.832 + ], + "angle": 0, + "content": "4.2. Quantitative Experiment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We utilize three standard metrics: PSNR, SSIM [34], and LPIPS [42]. These metrics are employed to quantify the similarity between the synthesized novel views and the provided target novel views. The quantitative results on the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "6291" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.09, + 0.891, + 0.289 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.311, + 0.293, + 0.658, + 0.308 + ], + "angle": 0, + "content": "Figure 6. Quantitative results on different light intensities." + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.333, + 0.427, + 0.346 + ], + "angle": 0, + "content": "Table 4. Quantitative evaluation on real-world data." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.358, + 0.449, + 0.466 + ], + "angle": 0, + "content": "
CameraMethodBrisque ↓NIQE ↓
APSImage+NeRF52.079.06
APSImage+NeRF*53.0510.06
DVSEvent+ENeRF83.9812.71
Spike cameraTFP+NeRF42.646.16
Spike cameraTFI+NeRF47.927.49
Spike cameraOurs35.946.09
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.47, + 0.688 + ], + "angle": 0, + "content": "synthetic dataset are presented in Table 1. Since only the object will produce firing spikes in the synthetic dataset, we provide two measurement approaches: the left one utilizes the entire image for measurement, while the right one focuses solely on measurements within the object region. The results show that our model performs better than other two-stage methods, proving the effectiveness of the proposed framework. Table 4 presents the results on real-world data. As the real data lacks ground truth, we assess the results using no-reference quality assessment methods, specifically Brique [24] and NIQE [25]. The results indicate that our method outperforms other models. Additional experimental results can be found in our supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.697, + 0.295, + 0.713 + ], + "angle": 0, + "content": "4.3. Qualitative Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We perform qualitative experiments on both synthetic and real-world data. As shown in Fig. 6, the rendered views from our method show markedly improved sharpness. TFP \\((\\mathrm{W} = 32)\\) struggles to generate novel views for the \"mic\" and \"materials\" scenes due to their low light intensity. The short window used by TFP fails to gather sufficient information. Similarly, Spk2img also exhibits suboptimal performance. This learning-based method is designed for ideal illumination conditions, and its performance sharply degrades when confronted with noisy spikes. In Fig. 5, three real-world scenes with varying illumination conditions are depicted. \"toys\" exhibits high light intensity, \"grid\" features medium" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.892, + 0.381 + ], + "angle": 0, + "content": "light, and \"box\" has low illumination. The results illustrate that our model performs effectively across different scenes and lighting conditions in real spike data." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.39, + 0.654, + 0.407 + ], + "angle": 0, + "content": "4.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.415, + 0.893, + 0.61 + ], + "angle": 0, + "content": "We perform ablation studies on the proposed long-term spike rendering loss, and the results are presented in Table 2. In the table, \\(\\mathcal{L}_s\\) represents the proposed spike rendering loss, \\(\\mathcal{L}_i\\) involves using the light intensity of rays plus threshold correction, and the reconstructed images from spikes as supervision, while \\(\\mathcal{L}_i^*\\) directly employs the estimated light intensity and reconstructed images as supervision. The experiments are conducted in both static and dynamic settings, affirming the effectiveness of our framework. Furthermore, we assess the performance under varying light intensities on the synthetic dataset. The results, presented in Table 3 and Fig. 6, demonstrate the robustness of our framework across different illumination conditions." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.626, + 0.62, + 0.642 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.651, + 0.892, + 0.816 + ], + "angle": 0, + "content": "This paper introduces SpikeNeRF as a pioneering approach to derive a volumetric scene representation from spike camera data using NeRF. With a focus on purely spike-based supervision, SpikeNeRF preserves texture and motion details in high temporal resolution, addressing the challenges associated with real-world spike sequences. Our evaluations on a newly curated dataset of synthetic and real spike sequences demonstrate the efficacy of SpikeNeRF for novel view synthesis. We hope that our work will shed light on the research of high quality 3D representation learning with novel spike stream techniques." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.817, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Acknowledgement This work is partially supported by National Natural Science Foundation of China under Grant No.62302041, 62322204, 62131003, China National Postdoctoral Program under contract No.BX20230469, and Beijing Institute of Technology Research Fund Program for Young Scholars." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "6292" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.119, + 0.176, + 0.135 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.145, + 0.47, + 0.226 + ], + "angle": 0, + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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However, existing approaches reliant on spike cameras often assume optimal illumination, a condition frequently unmet in real-world scenarios. To address this, we introduce SpikeNeRF, the first work that derives a NeRF-based volumetric scene representation from spike camera data. Our approach leverages NeRF's multiview consistency to establish robust self-supervision, effectively eliminating erroneous measurements and uncovering coherent structures within exceedingly noisy input amidst diverse real-world illumination scenarios. The framework comprises two core elements: a spike generation model incorporating an integrate-and-fire neuron layer and parameters accounting for non-idealities, such as threshold variation, and a spike rendering loss capable of generalizing across varying illumination conditions. We describe how to effectively optimize neural radiance fields to render photorealistic novel views from the novel continuous spike stream, demonstrating advantages over other vision sensors in certain scenes. Empirical evaluations conducted on both real and novel realistically simulated sequences affirm the efficacy of our methodology. The dataset and source code are released at https://github.com/BIT-Vision/SpikeNeRF. + +# 1. Introduction + +In recent years, there has been significant progress in the development of neuromorphic cameras, with notable advancements such as event cameras [2, 4] and spike cameras [15, 46]. These innovative devices excel in capturing light intensity changes in high-speed scenes, presenting a breakthrough in the realm of visual perception [9, 11, 13, 31, 32, 38, 49]. Spike camera, wherein each pixel responds independently to the accumulation of photons by generating asynchronous spikes [46]. This distinctive feature enables the spike camera to record full visual details with an ultra-high temporal resolution of up to $40\mathrm{kHz}$ (or $20\mathrm{kHz}$ for the + +portable version). These advantages include the capability to capture rapid changes in scenes and efficiently represent dynamic environments. With these unique features, spike cameras have demonstrated superiority in handling multiple computer vision tasks [12, 14, 33, 37, 45, 47-49, 51]. + +In parallel, there has been a growing trend in the computer vision community to explore neural radiance fields (NeRFs) as a solution for scene representation and novel view synthesis [5, 8, 17, 18, 20, 22, 27, 29, 39]. NeRFs employ a multilayer perceptron (MLP) combined with differentiable rendering to represent scenes, allowing for the synthesis of novel views from unseen perspectives. So far, NeRFs have predominantly undergone examination using simulated data and high-quality real-world images acquired under optimal conditions. Some studies have explored the application of NeRF to a distinct type of neuromorphic camera known as an event camera, characterized by differential sampling. Noteworthy among these endeavors are Ev-NeRF [17] and EventNeRF [29], both of which introduced neural radiance fields derived exclusively from event streams. However, the inherent lack of texture details in event data has constrained the effectiveness of these approaches, resulting in limited outcomes. Instead, a spike camera can offer fine texture details through a high temporal resolution spike stream. + +However, their application to spike camera data poses a unique challenge due to the distinctive data modality. The output of a spike camera is a spike stream, fundamentally different from traditional images. Each pixel in a spike camera generates a spike, and the accumulation is reset when the photon accumulation exceeds a predefined threshold. At each timestamp, the spike camera outputs a binary matrix, referred to as a spike frame, indicating the presence of spikes at all pixels. Currently, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. Therefore, the challenge tackled in this paper is: Can we reconstruct a dense volumetric 3D representation of the scene from a spike stream captured by a moving spike camera? + +Addressing the aforementioned challenges, this paper introduces SpikeNeRF, the first approach for deriving a volumetric scene representation from spike camera data using + +![](images/086dd65d5771a97bb36f728381ed6e0df670756e9c6139d43679b4bccd89bfbb.jpg) +Figure 1. Comparing novel views across various vision sensors, our SpikeNeRF stands out as the first method to learn neural radiance fields from a continuous spike stream. The Spike camera, operating at $20,000\mathrm{Hz}$ , eliminates motion blur, distinguishing it from traditional cameras. Notably, when contrasted with other methods (e.g., TFI+NeRF [46], Spk2img+NeRF [45], and EventNeRF [29]) and sensors (e.g., event camera), the rendered views of objects or scenes exhibit significantly enhanced sharpness. + +![](images/bc01535143b9e89ac2b7b5a2b4640545b68d6fa706126ea1bd738ccb8a295058.jpg) +Event input + +![](images/2ebe2ac8d569e8338902a9f354b1fb21b35e0ca3a7c96296813e3de178e9275b.jpg) +Novel Views from EventNeRF + +![](images/156f0cefec9d94fc7316fc5169dfeddde8fef3225f9503bce17cf765012c48c7.jpg) +Novel Views from Image+NeRF + +Neural Radiance Fields (NeRF). Our method is designed for purely spike-based supervision, preserving texture and motion details in high temporal resolution. We evaluate the efficacy of SpikeNeRF for the task of novel view synthesis on a new dataset of synthetic and real spike sequences. SpikeNeRF leverages NeRF's inherent multi-view consistency to establish robust self-supervision, mitigating the impact of erroneous measurements in the presence of high noise levels and diverse illumination conditions. Specifically, SpikeNeRF incorporates a spike generation model based on a spiking neuron layer, which considers intrinsic parameters and non-idealities associated with spike cameras. This model enhances the fidelity of spike data, providing a more accurate representation of the scene under varying lighting conditions (see Fig. 1). To enable generalization across diverse illumination scenarios, SpikeNeRF introduces a long-term spike rendering loss. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry, even in challenging lighting conditions. The main contributions of this paper are: + +1) We present the first approach for inferring a NeRF volume from only a spike stream. SpikeNeRF is highly robust to various illumination conditions and builds a coherent 3D structure that can provide high-quality observations. +2) We develop a long-term spike rendering loss based on a spiking neuron layer and threshold variation simulation, which are effective in enhancing neural volumetric representation learning. +3) We build both synthetic and real-world datasets for training and testing our model. Experimental results + +demonstrate that our method outperforms existing methods. We release the newly recorded spike dataset and source code to facilitate the research field. + +# 2. Related Work + +# 2.1. Neural Radiance Fields + +In recent years, Neural Radiance Fields have garnered significant attention for their remarkable performance in tasks involving neural implicit 3D representation and novel view synthesis. Various enhancements, such as FastNeRF [8] and Depth-supervised NeRF [5], aim to expedite NeRF's learning speed. Neural scene flow fields [18] delve into 3D Scene Representation Learning for dynamic scenes. Approaches like PixelNeRF [39] and RegNeRF [27] leverage a minimal number of input images for high-quality novel view synthesis. Mip-NeRF [1] introduces a frustum-based sampling strategy for NeRF-based anti-aliasing, addressing artifacts while enhancing training speed. Beyond speed and data augmentation, some works focus on enhancing NeRF with low-quality input images. For instance, NeRF in the wild [21] utilizes low-quality images captured by tourists, tackling occlusions and inconsistent lighting conditions. NeRF in the dark [23] and HDR-NeRF [16] enable the synthesis of high dynamic range new view images from noisy low dynamic images. Additionally, Deblur-NeRF [20] introduces the DSK module for simulating the blurring process, facilitating novel view synthesis from blurry to sharp images. However, Deblur-NeRF may face challenges in scenarios where the camera coincidentally shakes uniformly across + +all views or the input images exhibit strong blur. + +# 2.2. Scene Reconstruction based on Neuromorphic Camera + +Generally speaking, there are two types of bio-inspired visual sampling manner: temporal contrast sampling and integral sampling. Dynamic Vision Sensor (DVS), also known as an event camera, generates events when pixel brightness changes exceed a threshold. Recently, Ev-NeRF [17] and EventNeRF [29] proposed neural radiance fields derived exclusively from event streams. However, due to the absence of texture details in event data, these approaches yield limited results. Ev-NeRF [17] is confined to learning grayscale NeRF, while EventNeRF [29] exhibits noticeable artifacts and chromatic aberration, lacking RGB data for supervision. [28] first introduces event data and blurry RGB frames to achieve high quality clear scene reconstruction. [19] proposes Robust e-NeRF to robustly reconstruct NeRFs from moving event cameras under various real-world conditions, + +Our work is based on spike camera, where each pixel responds independently to the accumulation of photons by generating spikes. It records full visual details with an ultra-high temporal resolution (up to $40\mathrm{kHz}$ ). Image reconstruction based on spike cameras has emerged by analyzing spike intervals and counts [46]. Leveraging the spiking neuron model, a fovea-like texture reconstruction framework reconstructs images [48]. Spike camera methods have been developed for tone mapping [43], motion deblurring [12], and super resolution [37, 44]. Recent deep learning-based image reconstruction methods [3, 45, 49, 51] for spike cameras outperform traditional methods significantly. The noise characteristics of spike cameras differ substantially from those of traditional cameras. A preliminary analysis in [49] demonstrates that the noise distribution varies under different lighting conditions. + +However, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. The challenge is to explore the texture details hidden in the spike stream, understanding the spike distribution is crucial for spike-based applications. + +# 3. Methods + +# 3.1. Neural Radiance Fields + +The fundamental idea of NeRF is to employ a Multilayer Perceptron (MLP) to learn a 3D volume representation [22]. The MLP takes 3D position $\mathbf{o}$ and 2D ray direction $\mathbf{d}$ as inputs and produces color $\mathbf{c}$ and density $\sigma$ as outputs. In Eq. (1), $F_{\theta}$ represents the MLP network with $\theta$ as its parameters: + +$$ +(\mathbf {c}, \sigma) = F _ {\theta} \left(\gamma_ {o} (\mathbf {o}), \gamma_ {d} (\mathbf {d})\right). \tag {1} +$$ + +The functions $\gamma_{o}(\cdot)$ and $\gamma_{d}(\cdot)$ , defined in Eq. (1), map the input 5D coordinates to a higher-dimensional space, en + +abling the neural network to better capture color and geometry information in the scene. To generate views from the scene representation, NeRF employs a classical volume rendering method described in Eq. 2. For a given ray $\mathbf{r}(t) = \mathbf{o} + l\mathbf{d}$ emitted from the camera, the expected color projected on the pixel is denoted as $C(\mathbf{r})$ . The near and far bounds of the ray are represented by $l_{n}$ and $l_{f}$ , respectively. NeRF divides the interval $[l_n,l_f]$ into $N$ discrete bins, where $\mathbf{c}_i$ and $\sigma i$ are the outputs of $F_{\theta}$ , indicating the color and density of each bin through which the ray passes. The distance between adjacent samples is $\delta_i = l_{i + 1} - l_i$ , and $T_{i}$ represents the transparency of particles between $l_{n}$ and bin $i$ . + +$$ +C (\mathbf {r}) = \sum_ {i = 1} ^ {N} T _ {i} \left(1 - \exp \left(- \sigma_ {i} \delta_ {i}\right)\right) \mathbf {c} _ {i}, \tag {2} +$$ + +where $T(i) = \exp(-\sum_{j=1}^{i-1} \sigma_j \delta_j)$ . To ensure reasonable sampling in the final model, NeRF utilizes a Hierarchical volume sampling strategy, simultaneously optimizing the coarse and fine models and using the density obtained by the coarse model to determine the sampling weight of the fine model. + +# 3.2. Spike Sampling Mechanism + +In the field of frame-free neuromorphic vision, the spike camera operates by converting the intensity of light into voltage through photoreceptors [7, 46]. Upon reaching a predefined threshold, a one-bit spike is generated, accompanied by a signal to reset the integrator. This mechanism resembles that of an integrate-and-fire neuron. Luminance stimuli $I$ lead to varying spike firing rates, with asynchronous triggering of output and reset across pixels. Brighter light results in faster firing, governed by the inequality $\int I dt \geq \phi$ . + +The raw data from the spike camera is a three-dimensional spike stream, focusing solely on luminance intensity integration and firing ultra-high frequency spikes. At each sampling moment, a digital signal of "1" (spike) or "0" is output based on whether a spike was fired. The spike firing status of pixel $(i,j)$ at moment $t$ is represented as $S_{i,j}(t)\in 0,1$ . The spike signal model is defined as: + +$$ +S (x, y, t) = S (x, y, n t _ {0}) = \epsilon \left(\int_ {t ^ {\prime}} ^ {n t _ {0}} \frac {C \Delta V}{I _ {p h} (x , y , \tau)} d \tau - 1\right). \tag {3} +$$ + +where $t'$ is the start time of the current integration phase, reset at the phase's end. $\Delta V$ denotes the voltage, $nt_0$ denotes the $n$ -th clock signal, with $t_0$ as the unit time interval $(50\mu s)$ , and $I_{ph}$ represents the magnitude of the current for photoelectric conversion. $C$ is the capacitor in parallel with the photodiode, which is used to store electrons for photoconversion. $\epsilon(x)$ is a step function where $\epsilon(x) = 1$ when $x \geq 0$ otherwise $\epsilon(x) = 0$ . + +![](images/ec5ee23f389f434d376916a4b081e4b0df5463b84293f8dc2f757de40f01294c.jpg) +Figure 2. The architecture of SpikeNeRF. Motivated by the objective of learning NeRFs from a continuous spike stream, we establish the connection between the pixel ray $r$ and the real-world spike stream $S$ . To quantify the rendering loss in the spike domain, we integrate a spiking neuron layer following the NeRF MLP. The nonuniformity is captured through pixel-to-pixel threshold variation, simulated by the spiking neuron layer. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry. + +The noise of the spike camera differs significantly from traditional cameras due to circuit variations. The noise components encompass Shot Noise, wherein the photosensor converts photons into photo-electrons, resulting in a photo-current subject to shot noise $N_{p}$ even in uniform light scenarios. Dark Current Noise arises from thermal diffusion and defects, causing the spike circuit to produce signals even in the absence of scene light, with dark current noise denoted as $N_{d}$ . Response Nonuniformity stems from chip manufacturing limitations, causing pixel units to exhibit varying sensitivity to light intensity, leading to photo response nonuniformity noise $N_{nru}$ . Lastly, Quantization Noise arises from the delay in the release time of the spike signal relative to the generation time of the reset signal, introducing quantization noise $N_{q}$ . + +# 3.3. Self-Supervision with Volumetric Rendering + +An overview of the training pipeline is illustrated in Fig. 2. In line with the spike generation model, we propose self-supervision with volumetric rendering in this section. Different from traditional RGB frames, a binary spike frame can not accurately represent the light intensity at the current timestamp. Let us denote the intensity values of the pixel ray $r$ at time $T_{i}$ as $\hat{I}(T_{i}(r))$ . Since the high temporal resolution of the spike camera, the estimated short-term light intensity $\hat{L}_{T_i}$ can record motion details hidden in the spike stream. A straightforward approach is to calculate the light intensity $\hat{L}_{T_i}$ at time $T_{i}$ based on the original spike stream: + +$$ +\hat {L} _ {T _ {i}} = \frac {\theta}{n - m}, m < n, \tag {4} +$$ + +where $m$ and $n$ are the timestamps corresponding to two adjacent spikes, $\theta$ controls the gray-scale level. + +However, $\hat{L}_{T_i}$ is influenced by various sources of noise, particularly the temporal sampling noise [49]. The firing intervals of spikes fluctuate even in constant illumination conditions due to the inherent spike sampling mechanism. For instance, in the integrate-and-fire mechanism, if the membrane potential of the neuron (pixel) is not reset, an object with a light intensity corresponding to an inter-spike interval of 2 might be recorded as 1 or 3. Consequently, $\hat{L}_{T_i}$ is suitable for capturing motion details in the intensity values of the pixel ray $r$ , but texture details are often affected. $\hat{L}_{T_i}$ is susceptible to non-uniform pixel response, akin to standard image sensors. This is manifested by pixel-to-pixel variations in the contrast threshold, analogous to the spike camera's version of Fixed-Pattern Noise (FPN). Hence, relying solely on the rendered and degraded estimated light intensity values for NeRF training supervision can yield suboptimal results. + +# 3.3.1 Measuring Rendering Loss in Spike Domain + +In order to capture the precise distribution of the spike stream, we advocate for employing a long-term spike rate rendering loss rather than directly assessing short-term light intensity. To account for the various noise sources, inspired by the spike simulator [51], we introduce a layer of spiking neurons that generate spike streams based on the intensity values of the pixel ray $r$ emulating the spike sampling process. We then compute the long-term spike rate rendering loss directly on both the generated spike stream and the + +![](images/9a7939f270a5048f37cbb4d6bcc0de22a2082ff0957db54abcd829adb19a50ca.jpg) +Figure 3. The backpropagation process of spiking neurons. The spiking neuron layer, comprising 256 time steps, follows the NeRF MLP. The weight of the last layer of MLP can be updated through Backpropagation Through Time (BPTT) using Eq. 10. + +original spike stream. + +Our findings indicate that by combining NeRF's inherent multi-view consistency with our long-term spike rendering loss, our framework can establish robust self-supervision. This approach proves effective in mitigating the impact of erroneous measurements, particularly in the presence of high noise levels and diverse illumination conditions. + +Relationship between the Pixel Ray $r$ and Real-world Spike Stream $S$ . The objective is to estimate intensity values $\hat{I}(T_i(r))$ corresponding to the real light of the scene. Assuming that $\hat{I}(T_i(r))$ is clear, to supervise the $\hat{I}(T_i(r))$ with the real noisy spike stream, we need to consider multiple noises. Inspired by [51], we can define the relationship between $\hat{I}(T_i(r))$ and spike noise as: + +$$ +\hat {I} \left(T _ {i} (r)\right) = I \left(T _ {i} (S)\right) - I \left(T _ {i} (N)\right), \tag {5} +$$ + +where $I(T_{i}(S)) = \frac{1}{\frac{Q_{r}}{L + N_{p} + N_{d}} + N_{rnu} + N_{q}} + N_{c}, I(T_{i}(N))$ denotes the intensity changes caused by noise, $L$ represents the scene light intensity, $Q_{r}$ is relative quantity matrix of electric charge. $N_{p}, N_{d}, N_{rnu}, N_{q}$ , and $N_{c}$ represent shot noise, dark current noise, response nonuniformity noise, quantization noise, and truncation noise, respectively. + +Spiking Neuron Layer. To accurately represent the spike distribution, we introduce an additional layer of spiking neurons following the NeRF MLP to generate the spike stream. Given that the spike camera employs an integrate-and-fire mechanism to convert the light intensity of the scene into spike streams, our framework utilizes the Integrate-and-Fire (IF) neuron model. The Integrate-and-Fire (IF) model [10] is a widely employed neuron model in Spiking Neural Networks (SNN) known for its biological realism [36]. For better representation, we represent the function of IF neuron as the discrete form: + +$$ +V _ {t} = V _ {t - 1} + X _ {t}, \quad S _ {t} = H \left(V _ {t} - V _ {t h}\right), \tag {6} +$$ + +where $V(t)$ denotes the membrane potential after neuronal dynamics at $t$ , $X(t)$ represents the input to neuron. A spike fires if $V(t)$ exceeds the threshold $V_{th}$ , $V_{rest}$ is the resting potential after firing, $S_t$ denotes the spike output at $t$ , + +$H(\cdot)$ denotes the Heaviside step function which is defined as $H(x) = 1$ for $x \geq 0$ and $H(x) = 0$ for $x < 0$ . + +Threshold Variation Simulation. The response nonuniformity noise can be characterized by the pixel-to-pixel variation in the firing threshold. In fact, the deviation matrix corresponding to the response nonuniformity noise can be obtained by capturing a uniform light scene and recording the intensity. Thus, the threshold variation of each spiking neuron can be modeled by Eq. 7, and the spike stream can be generated by + +$$ +\hat {S} (x, y) = \operatorname {S N} \left(I \left(T _ {i} (r)\right)\right) \cdot R (x, y), \tag {7} +$$ + +where $\mathrm{SN}(\cdot)$ denotes the spiking neuron, $R(x,y)$ is the nonuniformity matrix and can be obtained by capturing a uniform light scene and recording the intensity1. + +Long-term Spike Rendering Loss. The spike stream can be mapped into an RKHS (reproducing kernel Hilbert space) as continuous-time functions which incorporate a statistical description of spike trains. Based on the RKHS, the kernel method [6] is employed for measuring spike train distances. Additionally, [47] introduces an intensity-based distance metric to quantify spike distances. Nevertheless, the complexity of these two methods is excessively high, rendering NeRF training inefficient. + +In order to measure the distance between the generated spike stream $\hat{S}$ and the input spike stream $S$ , we propose a long-term spike rendering loss, which can be expressed by + +$$ +D (r, S) = \sum_ {t} \operatorname {S N} \left(I \left(T _ {i} (r)\right)\right) \cdot R (x, y) - \sum_ {t} I \left(T _ {i} (S)\right). \tag {8} +$$ + +In theory, employing a longer spike stream for measurement has the potential to mitigate excessive truncation noise. In our experiment, the parameter $t$ is configured to 256, aligning with the time steps of the spiking neuron. The final loss function can be expressed as follows: + +$$ +\mathcal {L} = \sum_ {\mathbf {r} \in \mathcal {R}} [ \| D (r _ {c}, S) \| _ {2} ^ {2} + \| D (r _ {f}, S) \| _ {2} ^ {2} ], \tag {9} +$$ + +where $r_c$ and $r_f$ are the pixel rays of coarse and fine models, respectively. In this way, the loss function of NeRF with spike stream as input is converted into Eq. 9. We adopt the design of the joint optimization of NeRF's coarse model and fine model, which is still beneficial in our framework. + +# 3.3.2 Backpropagation Training + +The spike generation function of an IF neuron is a hard threshold function that emits a spike when the membrane + +![](images/08e439a639766542fcf64306288b64cd996ebc60e30ca3a28b5b22e3b2dafbb5.jpg) +Figure 4. Quantitative results on synthetic spike data. + +potential exceeds a firing threshold. Due to this discontinuous and non-differentiable neuron model, standard backpropagation algorithms cannot be applied to SNNs in their native form [40, 41]. As shown in Fig. 3, the backpropagated errors pass through the spiking neuron layer using BackPropagation Through Time (BPTT) [35]. Since the spiking neurons are one-to-one connected to the neurons of the last layer of NeRF MLP, the weight of the last layer of NeRF MLP $w^{l}$ is updated by BPTT. In BPTT, the network is unrolled for all discrete time steps, and $w^{l}$ update is computed as the sum of gradients from each time step as follows: + +$$ +\Delta w ^ {l} = \sum_ {t - 1} ^ {T} \frac {\partial \mathcal {L} _ {t o t a l}}{\partial o _ {t} ^ {l}} \frac {\partial o _ {t} ^ {l}}{\partial V _ {t} ^ {l}} \frac {\partial V _ {t} ^ {l}}{\partial w ^ {l}}, \text {w h e r e} \frac {\partial o _ {t} ^ {l}}{\partial V _ {t} ^ {l}} = H _ {1} ^ {\prime} \left(V _ {t} - V _ {t h}\right), \tag {10} +$$ + +where $o_t^l$ is the output of the neuron at time $t$ , $\frac{\partial o_t^l}{\partial V_t^l}$ denotes the derivative of spike with respect to the membrane potential after charging at time step $t$ . Since $\frac{\partial o_t^l}{\partial V_t^l}$ is not differentiable, we adopt surrogate gradient method [26] to calculate it. In our work, the approximate IF gradient is computed as $H_1(x) = \frac{1}{V_{th}}$ , where the threshold value accounts for the change of the spiking output with respect to the input. + +Based on the above, a learnable realistic noise-embedded spike stream generation pipeline is proposed. Each time step of the spiking neuron represents a readout circuit process that verifies the reset signal in a clock signal corresponding to a spike camera. The dark current noise, + +Table 1. Quantitative evaluation on synthetic dataset. + +
Method / MetricPSNR ↑SSIM ↑LPIPS ↓
TFP (32) + NeRF16.21/16.630.142/0.6480.662/0.058
TFP (256) + NeRF15.07/19.240.094/0.8640.741/0.085
TFI + NeRF14.93/19.340.108/0.8620.752/0.090
Spk2img + NeRF13.41/14.050.064/0.7490.729/0.133
Ours20.78/22.070.209/0.9160.617/0.053
+ +nonuniformity noise, and quantization noise are collectively treated as nonuniformity noise. These components are incorporated into the generated spike stream through a simulation of threshold variation. + +# 4. Experiment + +# 4.1. Experimental Setup + +Synthetic Spike Data. We utilize six synthetic scenes (chair, ficus, hotdog, lego, materials, and mic) to generate synthetic spike data in NeRF. Using the spike generator provided by [51], we simulate spike streams for each viewpoint under different illumination conditions. The original image size is resized to $400 \times 400$ , resulting in generated spike streams with a resolution of $400 \times 400 \times 256$ , where 256 represents the time length of each spike stream. In addition to generating spike streams from static viewpoint images, + +Table 2. Ablation study on synthetic dataset. + +
MethodLossStaticDynamicAverage
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRFMSE15.26/15.570.154/0.7850.588/0.06514.93/15.220.112/0.7450.626/0.10915.10/15.400.133/0.7650.607/0.087
TFP(256)+NeRFMSE14.44/16.410.127/0.7940.652/0.08814.34/16.290.099/0.7700.693/0.11414.39/16.350.113/0.7820.672/0.101
TFI+NeRFMSE13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810.682/0.101
Spk2img+NeRFMSE13.42/14.050.066/0.7260.724/0.12913.39/14.040.062/0.7720.735/0.13713.41/14.050.064/0.0750.729/0.133
OursLi*13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810. 682/0.101
Li18.55/19.760.237/0.8780.527/0.05116.63/17.790.167/0.7970.593/0.09717.59/18.770.202/0.8370.560/0.074
Ls+Li18.50/19.590.237/0.8760.524/0.05117.61/18.410.179/0.8160.590/0.08918.05/19.000.208/0.8460.557/0.070
Ls18.72/19.380.251/0.8800.517/0.05018.16/18.800.187/0.8200.601/0.09318.44/19.090.219/0.8500.559/0.072
+ +Table 3. Quantitative evaluation of different light intensities on synthetic dataset. + +
MethodLight intensity (16)Light intensity (32)Light intensity (64)
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRF15.27/15.570.154/0.7850.588/0.06517.81/18.550.191/0.8270.562/0.07720.63/21.860.239/0.8720.528/0.067
TFP(256)+NeRF14.44/16.410.127/0.7940.652/0.08815.82/18.680.170/0.8350.616/0.07717.28/21.270.189/0.8520.596/0.081
TFI+NeRF13.77/16.630.120/0.7930.670/0.09315.07/18.530.156/0.8250.634/0.08316.16/20.560.187/0.8520.602/0.077
Spk2img+NeRF13.42/14.050.066/0.7260.724/0.12914.59/15.390.109/0.7680.651/0.09316.37/17.730.169/0.8370.595/0.073
Ours18.72/19.380.251/0.8800.517/0.05022.05/23.660.300/0.9260.477/0.05023.89/24.460.411/0.9290.428/0.049
+ +![](images/3ceba9a99074fd02b289b05df4871ac2f678a8a66d00b83e2b0ca6a80e9f87fc.jpg) +Figure 5. Quantitative results on real-world spike data. + +we render 16 high-resolution images captured by the camera and feed them into the spike generator to replicate the dynamic recording process of the spike camera. Each scene comprises 100 sets of images and their corresponding event data. Further details about the synthetic data can be found in our supplementary material. + +Real-world Spike Data. We employ the spike camera [15] to record real-world spike data. This camera is capable of capturing spike streams with a spatial resolution of $250 \times 400$ and a temporal resolution of $20,000\mathrm{Hz}$ . Holding the camera by hand, we capture data from five real-world scenarios, each featuring texture details under different illumination conditions. Each dataset comprises approximately 35 images from various viewpoints along with their corresponding spike data. To facilitate a comprehensive comparison of different cameras, we also use the DAVIS346 color event camera [30] to capture event and RGB data. This camera is equipped to capture spatial-temporally aligned event data and RGB frames, with a resolution of $346 \times 260$ and an exposure time set to $33\mathrm{ms}$ for the RGB frames. + +Baselines. Given the absence of existing spike-based NeRF methods, we compare our approach with three spike-based image reconstruction methods: TFI [46, 50], TFP [46, 50], and Spk2imgNet [45]. In a two-stage process, we reconstruct images using TFI and TFP (with window sizes of 32 and 256), which are commonly employed spike-based reconstruction methods, and Spk2imgNet, a learning-based method leveraging neural networks. While there are other learning-based methods for spike-based reconstruction [3], those methods aim to simultaneously estimate flow and image. The approach by [51] requires long spike sequences for recurrently optimizing the reconstruction process. Consequently, Spk2imgNet is well-suited for the NeRF setting, demonstrating stable performance. To ensure a fair comparison, all methods adopt a common NeRF backbone. + +Training Details. For the simulated data, we use the poses provided by the Blender and the generated spike stream as the input of the NeRF framework. For real-world data, we first reconstruct the spike stream into images, and then use COLMAP to estimate the poses. For a fair comparison, all comparison methods use the same poses as the input of the network. At each optimization iteration, we randomly sample a batch of camera rays from the set of all pixels in the dataset. We use the Adam optimizer with a learning rate that begins at $5 \times 10^{-4}$ and decays exponentially to $5 \times 10^{-5}$ . The optimization for a single scene typically takes about 20 hours to converge on a single NVIDIA 3090 GPU. + +# 4.2. Quantitative Experiment + +We utilize three standard metrics: PSNR, SSIM [34], and LPIPS [42]. These metrics are employed to quantify the similarity between the synthesized novel views and the provided target novel views. The quantitative results on the + +![](images/e7f746852b0605217f2d984e962f260e6d67cd4a617bd973e115ea30e7762d5c.jpg) +Figure 6. Quantitative results on different light intensities. + +Table 4. Quantitative evaluation on real-world data. + +
CameraMethodBrisque ↓NIQE ↓
APSImage+NeRF52.079.06
APSImage+NeRF*53.0510.06
DVSEvent+ENeRF83.9812.71
Spike cameraTFP+NeRF42.646.16
Spike cameraTFI+NeRF47.927.49
Spike cameraOurs35.946.09
+ +synthetic dataset are presented in Table 1. Since only the object will produce firing spikes in the synthetic dataset, we provide two measurement approaches: the left one utilizes the entire image for measurement, while the right one focuses solely on measurements within the object region. The results show that our model performs better than other two-stage methods, proving the effectiveness of the proposed framework. Table 4 presents the results on real-world data. As the real data lacks ground truth, we assess the results using no-reference quality assessment methods, specifically Brique [24] and NIQE [25]. The results indicate that our method outperforms other models. Additional experimental results can be found in our supplementary materials. + +# 4.3. Qualitative Experiment + +We perform qualitative experiments on both synthetic and real-world data. As shown in Fig. 6, the rendered views from our method show markedly improved sharpness. TFP $(\mathrm{W} = 32)$ struggles to generate novel views for the "mic" and "materials" scenes due to their low light intensity. The short window used by TFP fails to gather sufficient information. Similarly, Spk2img also exhibits suboptimal performance. This learning-based method is designed for ideal illumination conditions, and its performance sharply degrades when confronted with noisy spikes. In Fig. 5, three real-world scenes with varying illumination conditions are depicted. "toys" exhibits high light intensity, "grid" features medium + +light, and "box" has low illumination. The results illustrate that our model performs effectively across different scenes and lighting conditions in real spike data. + +# 4.4. Ablation Study + +We perform ablation studies on the proposed long-term spike rendering loss, and the results are presented in Table 2. In the table, $\mathcal{L}_s$ represents the proposed spike rendering loss, $\mathcal{L}_i$ involves using the light intensity of rays plus threshold correction, and the reconstructed images from spikes as supervision, while $\mathcal{L}_i^*$ directly employs the estimated light intensity and reconstructed images as supervision. The experiments are conducted in both static and dynamic settings, affirming the effectiveness of our framework. Furthermore, we assess the performance under varying light intensities on the synthetic dataset. The results, presented in Table 3 and Fig. 6, demonstrate the robustness of our framework across different illumination conditions. + +# 5. Conclusion + +This paper introduces SpikeNeRF as a pioneering approach to derive a volumetric scene representation from spike camera data using NeRF. With a focus on purely spike-based supervision, SpikeNeRF preserves texture and motion details in high temporal resolution, addressing the challenges associated with real-world spike sequences. Our evaluations on a newly curated dataset of synthetic and real spike sequences demonstrate the efficacy of SpikeNeRF for novel view synthesis. We hope that our work will shed light on the research of high quality 3D representation learning with novel spike stream techniques. + +Acknowledgement This work is partially supported by National Natural Science Foundation of China under Grant No.62302041, 62322204, 62131003, China National Postdoctoral Program under contract No.BX20230469, and Beijing Institute of Technology Research Fund Program for Young Scholars. + +# References + +[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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(ICCV), pages 2400-2409, 2021. 1, 3, 4 +[50] Lin Zhu, Siwei Dong, Jianing Li, Tiejun Huang, and Yonghong Tian. Ultra-high temporal resolution visual reconstruction from a fovea-like spike camera via spiking neuron model. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(1):1233-1249, 2022. 7 +[51] Lin Zhu, Yunlong Zheng, Mengyue Geng, Lizhi Wang, and Hua Huang. Recurrent spike-based image restoration under general illumination. 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However, existing approaches reliant on spike cameras often assume optimal illumination, a condition frequently unmet in real-world scenarios. To address this, we introduce SpikeNeRF, the first work that derives a NeRF-based volumetric scene representation from spike camera data. Our approach leverages NeRF's multiview consistency to establish robust self-supervision, effectively eliminating erroneous measurements and uncovering coherent structures within exceedingly noisy input amidst diverse real-world illumination scenarios. The framework comprises two core elements: a spike generation model incorporating an integrate-and-fire neuron layer and parameters accounting for non-idealities, such as threshold variation, and a spike rendering loss capable of generalizing across varying illumination conditions. 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Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "type": "text", + "content": "In recent years, there has been significant progress in the development of neuromorphic cameras, with notable advancements such as event cameras [2, 4] and spike cameras [15, 46]. These innovative devices excel in capturing light intensity changes in high-speed scenes, presenting a breakthrough in the realm of visual perception [9, 11, 13, 31, 32, 38, 49]. Spike camera, wherein each pixel responds independently to the accumulation of photons by generating asynchronous spikes [46]. This distinctive feature enables the spike camera to record full visual details with an ultra-high temporal resolution of up to " + }, + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "type": "inline_equation", + "content": "40\\mathrm{kHz}" + }, + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "type": "text", + "content": " (or " + }, + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "type": "inline_equation", + "content": "20\\mathrm{kHz}" + }, + { + "bbox": [ + 46, + 564, + 287, + 696 + ], + "type": "text", + "content": " for the" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 200, + 545, + 261 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 200, + 545, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 200, + 545, + 261 + ], + "type": "text", + "content": "portable version). These advantages include the capability to capture rapid changes in scenes and efficiently represent dynamic environments. With these unique features, spike cameras have demonstrated superiority in handling multiple computer vision tasks [12, 14, 33, 37, 45, 47-49, 51]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 263, + 546, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 263, + 546, + 503 + ], + "spans": [ + { + "bbox": [ + 304, + 263, + 546, + 503 + ], + "type": "text", + "content": "In parallel, there has been a growing trend in the computer vision community to explore neural radiance fields (NeRFs) as a solution for scene representation and novel view synthesis [5, 8, 17, 18, 20, 22, 27, 29, 39]. NeRFs employ a multilayer perceptron (MLP) combined with differentiable rendering to represent scenes, allowing for the synthesis of novel views from unseen perspectives. So far, NeRFs have predominantly undergone examination using simulated data and high-quality real-world images acquired under optimal conditions. Some studies have explored the application of NeRF to a distinct type of neuromorphic camera known as an event camera, characterized by differential sampling. Noteworthy among these endeavors are Ev-NeRF [17] and EventNeRF [29], both of which introduced neural radiance fields derived exclusively from event streams. However, the inherent lack of texture details in event data has constrained the effectiveness of these approaches, resulting in limited outcomes. Instead, a spike camera can offer fine texture details through a high temporal resolution spike stream." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 506, + 547, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 674 + ], + "type": "text", + "content": "However, their application to spike camera data poses a unique challenge due to the distinctive data modality. The output of a spike camera is a spike stream, fundamentally different from traditional images. Each pixel in a spike camera generates a spike, and the accumulation is reset when the photon accumulation exceeds a predefined threshold. At each timestamp, the spike camera outputs a binary matrix, referred to as a spike frame, indicating the presence of spikes at all pixels. Currently, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. Therefore, the challenge tackled in this paper is: Can we reconstruct a dense volumetric 3D representation of the scene from a spike stream captured by a moving spike camera?" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Addressing the aforementioned challenges, this paper introduces SpikeNeRF, the first approach for deriving a volumetric scene representation from spike camera data using" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 178, + 713 + ], + "type": "text", + "content": "*Corresponding author: Hua Huang." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 758 + ], + "type": "text", + "content": "6285" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 70, + 460, + 281 + ], + "blocks": [ + { + "bbox": [ + 55, + 70, + 460, + 281 + ], + "lines": [ + { + "bbox": [ + 55, + 70, + 460, + 281 + ], + "spans": [ + { + "bbox": [ + 55, + 70, + 460, + 281 + ], + "type": "image", + "image_path": "086dd65d5771a97bb36f728381ed6e0df670756e9c6139d43679b4bccd89bfbb.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "lines": [ + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "text", + "content": "Figure 1. Comparing novel views across various vision sensors, our SpikeNeRF stands out as the first method to learn neural radiance fields from a continuous spike stream. The Spike camera, operating at " + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "inline_equation", + "content": "20,000\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 287, + 547, + 331 + ], + "type": "text", + "content": ", eliminates motion blur, distinguishing it from traditional cameras. Notably, when contrasted with other methods (e.g., TFI+NeRF [46], Spk2img+NeRF [45], and EventNeRF [29]) and sensors (e.g., event camera), the rendered views of objects or scenes exhibit significantly enhanced sharpness." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 474, + 76, + 550, + 126 + ], + "blocks": [ + { + "bbox": [ + 474, + 76, + 550, + 126 + ], + "lines": [ + { + "bbox": [ + 474, + 76, + 550, + 126 + ], + "spans": [ + { + "bbox": [ + 474, + 76, + 550, + 126 + ], + "type": "image", + "image_path": "bc01535143b9e89ac2b7b5a2b4640545b68d6fa706126ea1bd738ccb8a295058.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 493, + 127, + 533, + 136 + ], + "lines": [ + { + "bbox": [ + 493, + 127, + 533, + 136 + ], + "spans": [ + { + "bbox": [ + 493, + 127, + 533, + 136 + ], + "type": "text", + "content": "Event input" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 476, + 140, + 550, + 190 + ], + "blocks": [ + { + "bbox": [ + 476, + 140, + 550, + 190 + ], + "lines": [ + { + "bbox": [ + 476, + 140, + 550, + 190 + ], + "spans": [ + { + "bbox": [ + 476, + 140, + 550, + 190 + ], + "type": "image", + "image_path": "2ebe2ac8d569e8338902a9f354b1fb21b35e0ca3a7c96296813e3de178e9275b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 190, + 544, + 208 + ], + "lines": [ + { + "bbox": [ + 481, + 190, + 544, + 208 + ], + "spans": [ + { + "bbox": [ + 481, + 190, + 544, + 208 + ], + "type": "text", + "content": "Novel Views from EventNeRF" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 476, + 209, + 549, + 262 + ], + "blocks": [ + { + "bbox": [ + 476, + 209, + 549, + 262 + ], + "lines": [ + { + "bbox": [ + 476, + 209, + 549, + 262 + ], + "spans": [ + { + "bbox": [ + 476, + 209, + 549, + 262 + ], + "type": "image", + "image_path": "156f0cefec9d94fc7316fc5169dfeddde8fef3225f9503bce17cf765012c48c7.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 481, + 262, + 544, + 281 + ], + "lines": [ + { + "bbox": [ + 481, + 262, + 544, + 281 + ], + "spans": [ + { + "bbox": [ + 481, + 262, + 544, + 281 + ], + "type": "text", + "content": "Novel Views from Image+NeRF" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 346, + 289, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 289, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 289, + 586 + ], + "type": "text", + "content": "Neural Radiance Fields (NeRF). Our method is designed for purely spike-based supervision, preserving texture and motion details in high temporal resolution. We evaluate the efficacy of SpikeNeRF for the task of novel view synthesis on a new dataset of synthetic and real spike sequences. SpikeNeRF leverages NeRF's inherent multi-view consistency to establish robust self-supervision, mitigating the impact of erroneous measurements in the presence of high noise levels and diverse illumination conditions. Specifically, SpikeNeRF incorporates a spike generation model based on a spiking neuron layer, which considers intrinsic parameters and non-idealities associated with spike cameras. This model enhances the fidelity of spike data, providing a more accurate representation of the scene under varying lighting conditions (see Fig. 1). To enable generalization across diverse illumination scenarios, SpikeNeRF introduces a long-term spike rendering loss. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry, even in challenging lighting conditions. The main contributions of this paper are:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 589, + 287, + 714 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 46, + 589, + 287, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 636 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 636 + ], + "type": "text", + "content": "1) We present the first approach for inferring a NeRF volume from only a spike stream. SpikeNeRF is highly robust to various illumination conditions and builds a coherent 3D structure that can provide high-quality observations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 287, + 687 + ], + "type": "text", + "content": "2) We develop a long-term spike rendering loss based on a spiking neuron layer and threshold variation simulation, which are effective in enhancing neural volumetric representation learning." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "3) We build both synthetic and real-world datasets for training and testing our model. Experimental results" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 305, + 346, + 545, + 382 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 545, + 382 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 545, + 382 + ], + "type": "text", + "content": "demonstrate that our method outperforms existing methods. We release the newly recorded spike dataset and source code to facilitate the research field." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 397, + 392, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 397, + 392, + 410 + ], + "spans": [ + { + "bbox": [ + 306, + 397, + 392, + 410 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 418, + 439, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 418, + 439, + 430 + ], + "spans": [ + { + "bbox": [ + 306, + 418, + 439, + 430 + ], + "type": "text", + "content": "2.1. Neural Radiance Fields" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 545, + 713 + ], + "type": "text", + "content": "In recent years, Neural Radiance Fields have garnered significant attention for their remarkable performance in tasks involving neural implicit 3D representation and novel view synthesis. Various enhancements, such as FastNeRF [8] and Depth-supervised NeRF [5], aim to expedite NeRF's learning speed. Neural scene flow fields [18] delve into 3D Scene Representation Learning for dynamic scenes. Approaches like PixelNeRF [39] and RegNeRF [27] leverage a minimal number of input images for high-quality novel view synthesis. Mip-NeRF [1] introduces a frustum-based sampling strategy for NeRF-based anti-aliasing, addressing artifacts while enhancing training speed. Beyond speed and data augmentation, some works focus on enhancing NeRF with low-quality input images. For instance, NeRF in the wild [21] utilizes low-quality images captured by tourists, tackling occlusions and inconsistent lighting conditions. NeRF in the dark [23] and HDR-NeRF [16] enable the synthesis of high dynamic range new view images from noisy low dynamic images. Additionally, Deblur-NeRF [20] introduces the DSK module for simulating the blurring process, facilitating novel view synthesis from blurry to sharp images. However, Deblur-NeRF may face challenges in scenarios where the camera coincidentally shakes uniformly across" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "6286" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 242, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 242, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 242, + 84 + ], + "type": "text", + "content": "all views or the input images exhibit strong blur." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 286, + 114 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 286, + 114 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 286, + 114 + ], + "type": "text", + "content": "2.2. Scene Reconstruction based on Neuromorphic Camera" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 121, + 286, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 121, + 286, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 121, + 286, + 300 + ], + "type": "text", + "content": "Generally speaking, there are two types of bio-inspired visual sampling manner: temporal contrast sampling and integral sampling. Dynamic Vision Sensor (DVS), also known as an event camera, generates events when pixel brightness changes exceed a threshold. Recently, Ev-NeRF [17] and EventNeRF [29] proposed neural radiance fields derived exclusively from event streams. However, due to the absence of texture details in event data, these approaches yield limited results. Ev-NeRF [17] is confined to learning grayscale NeRF, while EventNeRF [29] exhibits noticeable artifacts and chromatic aberration, lacking RGB data for supervision. [28] first introduces event data and blurry RGB frames to achieve high quality clear scene reconstruction. [19] proposes Robust e-NeRF to robustly reconstruct NeRFs from moving event cameras under various real-world conditions," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 301, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 301, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 301, + 286, + 491 + ], + "type": "text", + "content": "Our work is based on spike camera, where each pixel responds independently to the accumulation of photons by generating spikes. It records full visual details with an ultra-high temporal resolution (up to " + }, + { + "bbox": [ + 46, + 301, + 286, + 491 + ], + "type": "inline_equation", + "content": "40\\mathrm{kHz}" + }, + { + "bbox": [ + 46, + 301, + 286, + 491 + ], + "type": "text", + "content": "). Image reconstruction based on spike cameras has emerged by analyzing spike intervals and counts [46]. Leveraging the spiking neuron model, a fovea-like texture reconstruction framework reconstructs images [48]. Spike camera methods have been developed for tone mapping [43], motion deblurring [12], and super resolution [37, 44]. Recent deep learning-based image reconstruction methods [3, 45, 49, 51] for spike cameras outperform traditional methods significantly. The noise characteristics of spike cameras differ substantially from those of traditional cameras. A preliminary analysis in [49] demonstrates that the noise distribution varies under different lighting conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 492, + 286, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 492, + 286, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 492, + 286, + 552 + ], + "type": "text", + "content": "However, there is no established spike-based method for addressing the challenge of generating dense, photorealistic 3D representations of scenes. The challenge is to explore the texture details hidden in the spike stream, understanding the spike distribution is crucial for spike-based applications." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 562, + 107, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 107, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 107, + 574 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 582, + 179, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 179, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 179, + 594 + ], + "type": "text", + "content": "3.1. Neural Radiance Fields" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": "The fundamental idea of NeRF is to employ a Multilayer Perceptron (MLP) to learn a 3D volume representation [22]. The MLP takes 3D position " + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{o}" + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": " and 2D ray direction " + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{d}" + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": " as inputs and produces color " + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": " and density " + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": " as outputs. In Eq. (1), " + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": " represents the MLP network with " + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 600, + 286, + 670 + ], + "type": "text", + "content": " as its parameters:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 111, + 672, + 286, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 672, + 286, + 685 + ], + "spans": [ + { + "bbox": [ + 111, + 672, + 286, + 685 + ], + "type": "interline_equation", + "content": "(\\mathbf {c}, \\sigma) = F _ {\\theta} \\left(\\gamma_ {o} (\\mathbf {o}), \\gamma_ {d} (\\mathbf {d})\\right). \\tag {1}", + "image_path": "93e87116c500d43a350a21db3503ec5d067fc42f69d29b15f6872479ce2b6ae4.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": "The functions " + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\gamma_{o}(\\cdot)" + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "\\gamma_{d}(\\cdot)" + }, + { + "bbox": [ + 47, + 689, + 286, + 713 + ], + "type": "text", + "content": ", defined in Eq. (1), map the input 5D coordinates to a higher-dimensional space, en" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": "abling the neural network to better capture color and geometry information in the scene. To generate views from the scene representation, NeRF employs a classical volume rendering method described in Eq. 2. For a given ray " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + l\\mathbf{d}" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " emitted from the camera, the expected color projected on the pixel is denoted as " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "C(\\mathbf{r})" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": ". The near and far bounds of the ray are represented by " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "l_{f}" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": ", respectively. NeRF divides the interval " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "[l_n,l_f]" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " discrete bins, where " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\mathbf{c}_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\sigma i" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " are the outputs of " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": ", indicating the color and density of each bin through which the ray passes. The distance between adjacent samples is " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "\\delta_i = l_{i + 1} - l_i" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " represents the transparency of particles between " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "l_{n}" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": " and bin " + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 72, + 545, + 227 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 352, + 232, + 545, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 232, + 545, + 265 + ], + "spans": [ + { + "bbox": [ + 352, + 232, + 545, + 265 + ], + "type": "interline_equation", + "content": "C (\\mathbf {r}) = \\sum_ {i = 1} ^ {N} T _ {i} \\left(1 - \\exp \\left(- \\sigma_ {i} \\delta_ {i}\\right)\\right) \\mathbf {c} _ {i}, \\tag {2}", + "image_path": "457d385f75450afe563be4d46b76895388ffeb79de51632d64908df177c8ab26.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "inline_equation", + "content": "T(i) = \\exp(-\\sum_{j=1}^{i-1} \\sigma_j \\delta_j)" + }, + { + "bbox": [ + 304, + 272, + 545, + 344 + ], + "type": "text", + "content": ". To ensure reasonable sampling in the final model, NeRF utilizes a Hierarchical volume sampling strategy, simultaneously optimizing the coarse and fine models and using the density obtained by the coarse model to determine the sampling weight of the fine model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 352, + 459, + 364 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 459, + 364 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 459, + 364 + ], + "type": "text", + "content": "3.2. Spike Sampling Mechanism" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "type": "text", + "content": "In the field of frame-free neuromorphic vision, the spike camera operates by converting the intensity of light into voltage through photoreceptors [7, 46]. Upon reaching a predefined threshold, a one-bit spike is generated, accompanied by a signal to reset the integrator. This mechanism resembles that of an integrate-and-fire neuron. Luminance stimuli " + }, + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "type": "text", + "content": " lead to varying spike firing rates, with asynchronous triggering of output and reset across pixels. Brighter light results in faster firing, governed by the inequality " + }, + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "type": "inline_equation", + "content": "\\int I dt \\geq \\phi" + }, + { + "bbox": [ + 304, + 370, + 545, + 490 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "text", + "content": "The raw data from the spike camera is a three-dimensional spike stream, focusing solely on luminance intensity integration and firing ultra-high frequency spikes. At each sampling moment, a digital signal of \"1\" (spike) or \"0\" is output based on whether a spike was fired. The spike firing status of pixel " + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "inline_equation", + "content": "(i,j)" + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "text", + "content": " at moment " + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "text", + "content": " is represented as " + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "inline_equation", + "content": "S_{i,j}(t)\\in 0,1" + }, + { + "bbox": [ + 304, + 491, + 545, + 574 + ], + "type": "text", + "content": ". The spike signal model is defined as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 580, + 545, + 617 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 580, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 306, + 580, + 545, + 617 + ], + "type": "interline_equation", + "content": "S (x, y, t) = S (x, y, n t _ {0}) = \\epsilon \\left(\\int_ {t ^ {\\prime}} ^ {n t _ {0}} \\frac {C \\Delta V}{I _ {p h} (x , y , \\tau)} d \\tau - 1\\right). \\tag {3}", + "image_path": "97bd56e67f87fbdb350266564ed5a2f9827bda5fe6f683033149d9e11b215646.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "t'" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " is the start time of the current integration phase, reset at the phase's end. " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\Delta V" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " denotes the voltage, " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "nt_0" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "-th clock signal, with " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "t_0" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " as the unit time interval " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "(50\\mu s)" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_{ph}" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " represents the magnitude of the current for photoelectric conversion. " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " is the capacitor in parallel with the photodiode, which is used to store electrons for photoconversion. " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon(x)" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " is a step function where " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon(x) = 1" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " when " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "x \\geq 0" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": " otherwise " + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon(x) = 0" + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6287" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 547, + 264 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 264 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 264 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 264 + ], + "type": "image", + "image_path": "ec5ee23f389f434d376916a4b081e4b0df5463b84293f8dc2f757de40f01294c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "lines": [ + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "type": "text", + "content": "Figure 2. The architecture of SpikeNeRF. Motivated by the objective of learning NeRFs from a continuous spike stream, we establish the connection between the pixel ray " + }, + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "type": "text", + "content": " and the real-world spike stream " + }, + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 274, + 547, + 321 + ], + "type": "text", + "content": ". To quantify the rendering loss in the spike domain, we integrate a spiking neuron layer following the NeRF MLP. The nonuniformity is captured through pixel-to-pixel threshold variation, simulated by the spiking neuron layer. This tandem of loss functions ensures that the model can effectively capture and represent scene geometry." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "text", + "content": "The noise of the spike camera differs significantly from traditional cameras due to circuit variations. The noise components encompass Shot Noise, wherein the photosensor converts photons into photo-electrons, resulting in a photo-current subject to shot noise " + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "inline_equation", + "content": "N_{p}" + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "text", + "content": " even in uniform light scenarios. Dark Current Noise arises from thermal diffusion and defects, causing the spike circuit to produce signals even in the absence of scene light, with dark current noise denoted as " + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "text", + "content": ". Response Nonuniformity stems from chip manufacturing limitations, causing pixel units to exhibit varying sensitivity to light intensity, leading to photo response nonuniformity noise " + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "inline_equation", + "content": "N_{nru}" + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "text", + "content": ". Lastly, Quantization Noise arises from the delay in the release time of the spike signal relative to the generation time of the reset signal, introducing quantization noise " + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "inline_equation", + "content": "N_{q}" + }, + { + "bbox": [ + 46, + 340, + 289, + 520 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 530, + 277, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 530, + 277, + 544 + ], + "spans": [ + { + "bbox": [ + 47, + 530, + 277, + 544 + ], + "type": "text", + "content": "3.3. Self-Supervision with Volumetric Rendering" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": "An overview of the training pipeline is illustrated in Fig. 2. In line with the spike generation model, we propose self-supervision with volumetric rendering in this section. Different from traditional RGB frames, a binary spike frame can not accurately represent the light intensity at the current timestamp. Let us denote the intensity values of the pixel ray " + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\hat{I}(T_{i}(r))" + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": ". Since the high temporal resolution of the spike camera, the estimated short-term light intensity " + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\hat{L}_{T_i}" + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": " can record motion details hidden in the spike stream. A straightforward approach is to calculate the light intensity " + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "inline_equation", + "content": "\\hat{L}_{T_i}" + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 549, + 287, + 682 + ], + "type": "text", + "content": " based on the original spike stream:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 116, + 693, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 693, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 116, + 693, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\hat {L} _ {T _ {i}} = \\frac {\\theta}{n - m}, m < n, \\tag {4}", + "image_path": "5b2cf9faa1e9d54692690c755b402848a9b08cec3cb50a69b9643aa86d3315f5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "text", + "content": " are the timestamps corresponding to two adjacent spikes, " + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 340, + 545, + 363 + ], + "type": "text", + "content": " controls the gray-scale level." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "text", + "content": "However, " + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\hat{L}_{T_i}" + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "text", + "content": " is influenced by various sources of noise, particularly the temporal sampling noise [49]. The firing intervals of spikes fluctuate even in constant illumination conditions due to the inherent spike sampling mechanism. For instance, in the integrate-and-fire mechanism, if the membrane potential of the neuron (pixel) is not reset, an object with a light intensity corresponding to an inter-spike interval of 2 might be recorded as 1 or 3. Consequently, " + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\hat{L}_{T_i}" + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "text", + "content": " is suitable for capturing motion details in the intensity values of the pixel ray " + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "text", + "content": ", but texture details are often affected. " + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "inline_equation", + "content": "\\hat{L}_{T_i}" + }, + { + "bbox": [ + 304, + 364, + 546, + 568 + ], + "type": "text", + "content": " is susceptible to non-uniform pixel response, akin to standard image sensors. This is manifested by pixel-to-pixel variations in the contrast threshold, analogous to the spike camera's version of Fixed-Pattern Noise (FPN). Hence, relying solely on the rendered and degraded estimated light intensity values for NeRF training supervision can yield suboptimal results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 586, + 528, + 598 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 528, + 598 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 528, + 598 + ], + "type": "text", + "content": "3.3.1 Measuring Rendering Loss in Spike Domain" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "In order to capture the precise distribution of the spike stream, we advocate for employing a long-term spike rate rendering loss rather than directly assessing short-term light intensity. To account for the various noise sources, inspired by the spike simulator [51], we introduce a layer of spiking neurons that generate spike streams based on the intensity values of the pixel ray " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " emulating the spike sampling process. We then compute the long-term spike rate rendering loss directly on both the generated spike stream and the" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6288" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 286, + 162 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 286, + 162 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 286, + 162 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 286, + 162 + ], + "type": "image", + "image_path": "9a7939f270a5048f37cbb4d6bcc0de22a2082ff0957db54abcd829adb19a50ca.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 172, + 288, + 217 + ], + "lines": [ + { + "bbox": [ + 46, + 172, + 288, + 217 + ], + "spans": [ + { + "bbox": [ + 46, + 172, + 288, + 217 + ], + "type": "text", + "content": "Figure 3. The backpropagation process of spiking neurons. The spiking neuron layer, comprising 256 time steps, follows the NeRF MLP. The weight of the last layer of MLP can be updated through Backpropagation Through Time (BPTT) using Eq. 10." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 227, + 136, + 238 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 227, + 136, + 238 + ], + "spans": [ + { + "bbox": [ + 47, + 227, + 136, + 238 + ], + "type": "text", + "content": "original spike stream." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 239, + 287, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 287, + 309 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 287, + 309 + ], + "type": "text", + "content": "Our findings indicate that by combining NeRF's inherent multi-view consistency with our long-term spike rendering loss, our framework can establish robust self-supervision. This approach proves effective in mitigating the impact of erroneous measurements, particularly in the presence of high noise levels and diverse illumination conditions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": "Relationship between the Pixel Ray " + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": " and Real-world Spike Stream " + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": ". The objective is to estimate intensity values " + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\hat{I}(T_i(r))" + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": " corresponding to the real light of the scene. Assuming that " + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\hat{I}(T_i(r))" + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": " is clear, to supervise the " + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\hat{I}(T_i(r))" + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": " with the real noisy spike stream, we need to consider multiple noises. Inspired by [51], we can define the relationship between " + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "inline_equation", + "content": "\\hat{I}(T_i(r))" + }, + { + "bbox": [ + 46, + 310, + 287, + 395 + ], + "type": "text", + "content": " and spike noise as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 402, + 287, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 402, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 96, + 402, + 287, + 417 + ], + "type": "interline_equation", + "content": "\\hat {I} \\left(T _ {i} (r)\\right) = I \\left(T _ {i} (S)\\right) - I \\left(T _ {i} (N)\\right), \\tag {5}", + "image_path": "6fb840336fdd1a413064d03860e1dba4a11b117c93aa4f14ddf59f101d948387.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "inline_equation", + "content": "I(T_{i}(S)) = \\frac{1}{\\frac{Q_{r}}{L + N_{p} + N_{d}} + N_{rnu} + N_{q}} + N_{c}, I(T_{i}(N))" + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "content": " denotes the intensity changes caused by noise, " + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "content": " represents the scene light intensity, " + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "inline_equation", + "content": "Q_{r}" + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "content": " is relative quantity matrix of electric charge. " + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "inline_equation", + "content": "N_{p}, N_{d}, N_{rnu}, N_{q}" + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "inline_equation", + "content": "N_{c}" + }, + { + "bbox": [ + 46, + 425, + 287, + 502 + ], + "type": "text", + "content": " represent shot noise, dark current noise, response nonuniformity noise, quantization noise, and truncation noise, respectively." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 502, + 287, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 502, + 287, + 633 + ], + "spans": [ + { + "bbox": [ + 46, + 502, + 287, + 633 + ], + "type": "text", + "content": "Spiking Neuron Layer. To accurately represent the spike distribution, we introduce an additional layer of spiking neurons following the NeRF MLP to generate the spike stream. Given that the spike camera employs an integrate-and-fire mechanism to convert the light intensity of the scene into spike streams, our framework utilizes the Integrate-and-Fire (IF) neuron model. The Integrate-and-Fire (IF) model [10] is a widely employed neuron model in Spiking Neural Networks (SNN) known for its biological realism [36]. For better representation, we represent the function of IF neuron as the discrete form:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 78, + 643, + 287, + 657 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 643, + 287, + 657 + ], + "spans": [ + { + "bbox": [ + 78, + 643, + 287, + 657 + ], + "type": "interline_equation", + "content": "V _ {t} = V _ {t - 1} + X _ {t}, \\quad S _ {t} = H \\left(V _ {t} - V _ {t h}\\right), \\tag {6}", + "image_path": "7f462acb7dcd50c2c25dc1505ceb84e9cfb80a1fa3c628d0686d628d19500083.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "V(t)" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " denotes the membrane potential after neuronal dynamics at " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "X(t)" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " represents the input to neuron. A spike fires if " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "V(t)" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " exceeds the threshold " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "V_{th}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "V_{rest}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " is the resting potential after firing, " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "S_t" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " denotes the spike output at " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "H(\\cdot)" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " denotes the Heaviside step function which is defined as " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "H(x) = 1" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "x \\geq 0" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "H(x) = 0" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "x < 0" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 545, + 192 + ], + "type": "text", + "content": "Threshold Variation Simulation. The response nonuniformity noise can be characterized by the pixel-to-pixel variation in the firing threshold. In fact, the deviation matrix corresponding to the response nonuniformity noise can be obtained by capturing a uniform light scene and recording the intensity. Thus, the threshold variation of each spiking neuron can be modeled by Eq. 7, and the spike stream can be generated by" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 354, + 199, + 545, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 199, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 354, + 199, + 545, + 214 + ], + "type": "interline_equation", + "content": "\\hat {S} (x, y) = \\operatorname {S N} \\left(I \\left(T _ {i} (r)\\right)\\right) \\cdot R (x, y), \\tag {7}", + "image_path": "5e08fbdef82be798546cf507d2e0932602fad5add4267fee41d98bb8cc6c27cc.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "type": "inline_equation", + "content": "\\mathrm{SN}(\\cdot)" + }, + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "type": "text", + "content": " denotes the spiking neuron, " + }, + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "type": "inline_equation", + "content": "R(x,y)" + }, + { + "bbox": [ + 304, + 221, + 545, + 258 + ], + "type": "text", + "content": " is the nonuniformity matrix and can be obtained by capturing a uniform light scene and recording the intensity1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 545, + 365 + ], + "type": "text", + "content": "Long-term Spike Rendering Loss. The spike stream can be mapped into an RKHS (reproducing kernel Hilbert space) as continuous-time functions which incorporate a statistical description of spike trains. Based on the RKHS, the kernel method [6] is employed for measuring spike train distances. Additionally, [47] introduces an intensity-based distance metric to quantify spike distances. Nevertheless, the complexity of these two methods is excessively high, rendering NeRF training inefficient." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "type": "text", + "content": "In order to measure the distance between the generated spike stream " + }, + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "type": "inline_equation", + "content": "\\hat{S}" + }, + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "type": "text", + "content": " and the input spike stream " + }, + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 365, + 545, + 401 + ], + "type": "text", + "content": ", we propose a long-term spike rendering loss, which can be expressed by" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 310, + 409, + 545, + 434 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 409, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 310, + 409, + 545, + 434 + ], + "type": "interline_equation", + "content": "D (r, S) = \\sum_ {t} \\operatorname {S N} \\left(I \\left(T _ {i} (r)\\right)\\right) \\cdot R (x, y) - \\sum_ {t} I \\left(T _ {i} (S)\\right). \\tag {8}", + "image_path": "9f1fbbc22f06bb4633953842968a23008bf807c25b513a3038b0c8dde08d0736.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 441, + 545, + 501 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 545, + 501 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 545, + 501 + ], + "type": "text", + "content": "In theory, employing a longer spike stream for measurement has the potential to mitigate excessive truncation noise. In our experiment, the parameter " + }, + { + "bbox": [ + 304, + 441, + 545, + 501 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 441, + 545, + 501 + ], + "type": "text", + "content": " is configured to 256, aligning with the time steps of the spiking neuron. The final loss function can be expressed as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 344, + 510, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 510, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 344, + 510, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} [ \\| D (r _ {c}, S) \\| _ {2} ^ {2} + \\| D (r _ {f}, S) \\| _ {2} ^ {2} ], \\tag {9}", + "image_path": "11f8dfd3064cd84c3f561c6721526d71e3dfe360d63c1050e97ca004e794f462.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "type": "inline_equation", + "content": "r_c" + }, + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "type": "inline_equation", + "content": "r_f" + }, + { + "bbox": [ + 304, + 540, + 545, + 599 + ], + "type": "text", + "content": " are the pixel rays of coarse and fine models, respectively. In this way, the loss function of NeRF with spike stream as input is converted into Eq. 9. We adopt the design of the joint optimization of NeRF's coarse model and fine model, which is still beneficial in our framework." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 614, + 452, + 625 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 614, + 452, + 625 + ], + "spans": [ + { + "bbox": [ + 306, + 614, + 452, + 625 + ], + "type": "text", + "content": "3.3.2 Backpropagation Training" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 632, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 632, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 632, + 545, + 654 + ], + "type": "text", + "content": "The spike generation function of an IF neuron is a hard threshold function that emits a spike when the membrane" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "text", + "content": "1 Choose the pixel " + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "inline_equation", + "content": "(x_{m},y_{m})" + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "text", + "content": " which is closest to the average response value as the reference pixel. " + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "inline_equation", + "content": "R(x,y)" + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "text", + "content": " is then obtained by calculating the ratio of the reference pixel's response value to the response values of other pixels: " + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "inline_equation", + "content": "R(x,y) = \\frac{(L_2 + L_d(x_m,y_m))T_2(x_m,y_m)}{(L_2 + L_d(x,y))T_2}" + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 661, + 545, + 713 + ], + "type": "text", + "content": " are variables to be calibrated. See our supplementary materials for details." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6289" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 71, + 545, + 348 + ], + "blocks": [ + { + "bbox": [ + 49, + 71, + 545, + 348 + ], + "lines": [ + { + "bbox": [ + 49, + 71, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 49, + 71, + 545, + 348 + ], + "type": "image", + "image_path": "08e439a639766542fcf64306288b64cd996ebc60e30ca3a28b5b22e3b2dafbb5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 198, + 356, + 394, + 367 + ], + "lines": [ + { + "bbox": [ + 198, + 356, + 394, + 367 + ], + "spans": [ + { + "bbox": [ + 198, + 356, + 394, + 367 + ], + "type": "text", + "content": "Figure 4. Quantitative results on synthetic spike data." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "type": "text", + "content": "potential exceeds a firing threshold. Due to this discontinuous and non-differentiable neuron model, standard backpropagation algorithms cannot be applied to SNNs in their native form [40, 41]. As shown in Fig. 3, the backpropagated errors pass through the spiking neuron layer using BackPropagation Through Time (BPTT) [35]. Since the spiking neurons are one-to-one connected to the neurons of the last layer of NeRF MLP, the weight of the last layer of NeRF MLP " + }, + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "type": "inline_equation", + "content": "w^{l}" + }, + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "type": "text", + "content": " is updated by BPTT. In BPTT, the network is unrolled for all discrete time steps, and " + }, + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "type": "inline_equation", + "content": "w^{l}" + }, + { + "bbox": [ + 46, + 388, + 290, + 520 + ], + "type": "text", + "content": " update is computed as the sum of gradients from each time step as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 524, + 295, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 524, + 295, + 554 + ], + "spans": [ + { + "bbox": [ + 47, + 524, + 295, + 554 + ], + "type": "interline_equation", + "content": "\\Delta w ^ {l} = \\sum_ {t - 1} ^ {T} \\frac {\\partial \\mathcal {L} _ {t o t a l}}{\\partial o _ {t} ^ {l}} \\frac {\\partial o _ {t} ^ {l}}{\\partial V _ {t} ^ {l}} \\frac {\\partial V _ {t} ^ {l}}{\\partial w ^ {l}}, \\text {w h e r e} \\frac {\\partial o _ {t} ^ {l}}{\\partial V _ {t} ^ {l}} = H _ {1} ^ {\\prime} \\left(V _ {t} - V _ {t h}\\right), \\tag {10}", + "image_path": "88c756e954aa6bb2859b148fed4da642a4f26462ed09c130a60cffe09eefa223.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "inline_equation", + "content": "o_t^l" + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": " is the output of the neuron at time " + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\frac{\\partial o_t^l}{\\partial V_t^l}" + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": " denotes the derivative of spike with respect to the membrane potential after charging at time step " + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "inline_equation", + "content": "\\frac{\\partial o_t^l}{\\partial V_t^l}" + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": " is not differentiable, we adopt surrogate gradient method [26] to calculate it. In our work, the approximate IF gradient is computed as " + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "inline_equation", + "content": "H_1(x) = \\frac{1}{V_{th}}" + }, + { + "bbox": [ + 47, + 561, + 287, + 653 + ], + "type": "text", + "content": ", where the threshold value accounts for the change of the spiking output with respect to the input." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Based on the above, a learnable realistic noise-embedded spike stream generation pipeline is proposed. Each time step of the spiking neuron represents a readout circuit process that verifies the reset signal in a clock signal corresponding to a spike camera. The dark current noise," + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 307, + 407, + 553, + 480 + ], + "blocks": [ + { + "bbox": [ + 329, + 386, + 522, + 398 + ], + "lines": [ + { + "bbox": [ + 329, + 386, + 522, + 398 + ], + "spans": [ + { + "bbox": [ + 329, + 386, + 522, + 398 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation on synthetic dataset." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 407, + 553, + 480 + ], + "lines": [ + { + "bbox": [ + 307, + 407, + 553, + 480 + ], + "spans": [ + { + "bbox": [ + 307, + 407, + 553, + 480 + ], + "type": "table", + "html": "
Method / MetricPSNR ↑SSIM ↑LPIPS ↓
TFP (32) + NeRF16.21/16.630.142/0.6480.662/0.058
TFP (256) + NeRF15.07/19.240.094/0.8640.741/0.085
TFI + NeRF14.93/19.340.108/0.8620.752/0.090
Spk2img + NeRF13.41/14.050.064/0.7490.729/0.133
Ours20.78/22.070.209/0.9160.617/0.053
", + "image_path": "2b1202752cd7e0532074b96a0e602ff0462184b407a4685d8be857c47621559e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 505, + 547, + 554 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 554 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 554 + ], + "type": "text", + "content": "nonuniformity noise, and quantization noise are collectively treated as nonuniformity noise. These components are incorporated into the generated spike stream through a simulation of threshold variation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 566, + 382, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 566, + 382, + 580 + ], + "spans": [ + { + "bbox": [ + 305, + 566, + 382, + 580 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 586, + 422, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 586, + 422, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 586, + 422, + 600 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": "Synthetic Spike Data. We utilize six synthetic scenes (chair, ficus, hotdog, lego, materials, and mic) to generate synthetic spike data in NeRF. Using the spike generator provided by [51], we simulate spike streams for each viewpoint under different illumination conditions. The original image size is resized to " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "400 \\times 400" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ", resulting in generated spike streams with a resolution of " + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "inline_equation", + "content": "400 \\times 400 \\times 256" + }, + { + "bbox": [ + 304, + 605, + 547, + 715 + ], + "type": "text", + "content": ", where 256 represents the time length of each spike stream. In addition to generating spike streams from static viewpoint images," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6290" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 80, + 547, + 186 + ], + "blocks": [ + { + "bbox": [ + 215, + 71, + 376, + 81 + ], + "lines": [ + { + "bbox": [ + 215, + 71, + 376, + 81 + ], + "spans": [ + { + "bbox": [ + 215, + 71, + 376, + 81 + ], + "type": "text", + "content": "Table 2. Ablation study on synthetic dataset." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 80, + 547, + 186 + ], + "lines": [ + { + "bbox": [ + 48, + 80, + 547, + 186 + ], + "spans": [ + { + "bbox": [ + 48, + 80, + 547, + 186 + ], + "type": "table", + "html": "
MethodLossStaticDynamicAverage
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRFMSE15.26/15.570.154/0.7850.588/0.06514.93/15.220.112/0.7450.626/0.10915.10/15.400.133/0.7650.607/0.087
TFP(256)+NeRFMSE14.44/16.410.127/0.7940.652/0.08814.34/16.290.099/0.7700.693/0.11414.39/16.350.113/0.7820.672/0.101
TFI+NeRFMSE13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810.682/0.101
Spk2img+NeRFMSE13.42/14.050.066/0.7260.724/0.12913.39/14.040.062/0.7720.735/0.13713.41/14.050.064/0.0750.729/0.133
OursLi*13.77/16.630.120/0.7930.670/0.09313.76/16.110.096/0.7690.694/0.11013.76/16.370.108/0.7810. 682/0.101
Li18.55/19.760.237/0.8780.527/0.05116.63/17.790.167/0.7970.593/0.09717.59/18.770.202/0.8370.560/0.074
Ls+Li18.50/19.590.237/0.8760.524/0.05117.61/18.410.179/0.8160.590/0.08918.05/19.000.208/0.8460.557/0.070
Ls18.72/19.380.251/0.8800.517/0.05018.16/18.800.187/0.8200.601/0.09318.44/19.090.219/0.8500.559/0.072
", + "image_path": "b86ef7771c84516522f91145315300a40c8c2ab3bbb00daa3e9f9f06ac181fc0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 48, + 211, + 546, + 289 + ], + "blocks": [ + { + "bbox": [ + 149, + 201, + 441, + 211 + ], + "lines": [ + { + "bbox": [ + 149, + 201, + 441, + 211 + ], + "spans": [ + { + "bbox": [ + 149, + 201, + 441, + 211 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation of different light intensities on synthetic dataset." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 211, + 546, + 289 + ], + "lines": [ + { + "bbox": [ + 48, + 211, + 546, + 289 + ], + "spans": [ + { + "bbox": [ + 48, + 211, + 546, + 289 + ], + "type": "table", + "html": "
MethodLight intensity (16)Light intensity (32)Light intensity (64)
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
TFP(32)+NeRF15.27/15.570.154/0.7850.588/0.06517.81/18.550.191/0.8270.562/0.07720.63/21.860.239/0.8720.528/0.067
TFP(256)+NeRF14.44/16.410.127/0.7940.652/0.08815.82/18.680.170/0.8350.616/0.07717.28/21.270.189/0.8520.596/0.081
TFI+NeRF13.77/16.630.120/0.7930.670/0.09315.07/18.530.156/0.8250.634/0.08316.16/20.560.187/0.8520.602/0.077
Spk2img+NeRF13.42/14.050.066/0.7260.724/0.12914.59/15.390.109/0.7680.651/0.09316.37/17.730.169/0.8370.595/0.073
Ours18.72/19.380.251/0.8800.517/0.05022.05/23.660.300/0.9260.477/0.05023.89/24.460.411/0.9290.428/0.049
", + "image_path": "f27bda079ba120cfec58c2b7c9d834f7c4f2fe82c466274098c6ccb07d73db6d.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 50, + 311, + 286, + 430 + ], + "blocks": [ + { + "bbox": [ + 50, + 311, + 286, + 430 + ], + "lines": [ + { + "bbox": [ + 50, + 311, + 286, + 430 + ], + "spans": [ + { + "bbox": [ + 50, + 311, + 286, + 430 + ], + "type": "image", + "image_path": "3ceba9a99074fd02b289b05df4871ac2f678a8a66d00b83e2b0ca6a80e9f87fc.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 67, + 437, + 266, + 449 + ], + "lines": [ + { + "bbox": [ + 67, + 437, + 266, + 449 + ], + "spans": [ + { + "bbox": [ + 67, + 437, + 266, + 449 + ], + "type": "text", + "content": "Figure 5. Quantitative results on real-world spike data." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 544 + ], + "type": "text", + "content": "we render 16 high-resolution images captured by the camera and feed them into the spike generator to replicate the dynamic recording process of the spike camera. Each scene comprises 100 sets of images and their corresponding event data. Further details about the synthetic data can be found in our supplementary material." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": "Real-world Spike Data. We employ the spike camera [15] to record real-world spike data. This camera is capable of capturing spike streams with a spatial resolution of " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "250 \\times 400" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " and a temporal resolution of " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "20,000\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": ". Holding the camera by hand, we capture data from five real-world scenarios, each featuring texture details under different illumination conditions. Each dataset comprises approximately 35 images from various viewpoints along with their corresponding spike data. To facilitate a comprehensive comparison of different cameras, we also use the DAVIS346 color event camera [30] to capture event and RGB data. This camera is equipped to capture spatial-temporally aligned event data and RGB frames, with a resolution of " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "346 \\times 260" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " and an exposure time set to " + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "inline_equation", + "content": "33\\mathrm{ms}" + }, + { + "bbox": [ + 46, + 545, + 288, + 713 + ], + "type": "text", + "content": " for the RGB frames." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 312, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 491 + ], + "type": "text", + "content": "Baselines. Given the absence of existing spike-based NeRF methods, we compare our approach with three spike-based image reconstruction methods: TFI [46, 50], TFP [46, 50], and Spk2imgNet [45]. In a two-stage process, we reconstruct images using TFI and TFP (with window sizes of 32 and 256), which are commonly employed spike-based reconstruction methods, and Spk2imgNet, a learning-based method leveraging neural networks. While there are other learning-based methods for spike-based reconstruction [3], those methods aim to simultaneously estimate flow and image. The approach by [51] requires long spike sequences for recurrently optimizing the reconstruction process. Consequently, Spk2imgNet is well-suited for the NeRF setting, demonstrating stable performance. To ensure a fair comparison, all methods adopt a common NeRF backbone." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "type": "text", + "content": "Training Details. For the simulated data, we use the poses provided by the Blender and the generated spike stream as the input of the NeRF framework. For real-world data, we first reconstruct the spike stream into images, and then use COLMAP to estimate the poses. For a fair comparison, all comparison methods use the same poses as the input of the network. At each optimization iteration, we randomly sample a batch of camera rays from the set of all pixels in the dataset. We use the Adam optimizer with a learning rate that begins at " + }, + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "type": "text", + "content": " and decays exponentially to " + }, + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "type": "inline_equation", + "content": "5 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 493, + 545, + 636 + ], + "type": "text", + "content": ". The optimization for a single scene typically takes about 20 hours to converge on a single NVIDIA 3090 GPU." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 646, + 446, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 446, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 446, + 658 + ], + "type": "text", + "content": "4.2. Quantitative Experiment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "We utilize three standard metrics: PSNR, SSIM [34], and LPIPS [42]. These metrics are employed to quantify the similarity between the synthesized novel views and the provided target novel views. The quantitative results on the" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "6291" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 71, + 545, + 228 + ], + "blocks": [ + { + "bbox": [ + 48, + 71, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 48, + 71, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 545, + 228 + ], + "type": "image", + "image_path": "e7f746852b0605217f2d984e962f260e6d67cd4a617bd973e115ea30e7762d5c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 190, + 232, + 402, + 243 + ], + "lines": [ + { + "bbox": [ + 190, + 232, + 402, + 243 + ], + "spans": [ + { + "bbox": [ + 190, + 232, + 402, + 243 + ], + "type": "text", + "content": "Figure 6. Quantitative results on different light intensities." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 59, + 283, + 274, + 369 + ], + "blocks": [ + { + "bbox": [ + 73, + 263, + 261, + 274 + ], + "lines": [ + { + "bbox": [ + 73, + 263, + 261, + 274 + ], + "spans": [ + { + "bbox": [ + 73, + 263, + 261, + 274 + ], + "type": "text", + "content": "Table 4. Quantitative evaluation on real-world data." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 283, + 274, + 369 + ], + "lines": [ + { + "bbox": [ + 59, + 283, + 274, + 369 + ], + "spans": [ + { + "bbox": [ + 59, + 283, + 274, + 369 + ], + "type": "table", + "html": "
CameraMethodBrisque ↓NIQE ↓
APSImage+NeRF52.079.06
APSImage+NeRF*53.0510.06
DVSEvent+ENeRF83.9812.71
Spike cameraTFP+NeRF42.646.16
Spike cameraTFI+NeRF47.927.49
Spike cameraOurs35.946.09
", + "image_path": "9d8e2cb7d0ab7bb1392935cd6405e9d5dfde8dc4e23acc7261c4a69fb4798932.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 287, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 544 + ], + "type": "text", + "content": "synthetic dataset are presented in Table 1. Since only the object will produce firing spikes in the synthetic dataset, we provide two measurement approaches: the left one utilizes the entire image for measurement, while the right one focuses solely on measurements within the object region. The results show that our model performs better than other two-stage methods, proving the effectiveness of the proposed framework. Table 4 presents the results on real-world data. As the real data lacks ground truth, we assess the results using no-reference quality assessment methods, specifically Brique [24] and NIQE [25]. The results indicate that our method outperforms other models. Additional experimental results can be found in our supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 552, + 180, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 180, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 180, + 564 + ], + "type": "text", + "content": "4.3. Qualitative Experiment" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "We perform qualitative experiments on both synthetic and real-world data. As shown in Fig. 6, the rendered views from our method show markedly improved sharpness. TFP " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathrm{W} = 32)" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " struggles to generate novel views for the \"mic\" and \"materials\" scenes due to their low light intensity. The short window used by TFP fails to gather sufficient information. Similarly, Spk2img also exhibits suboptimal performance. This learning-based method is designed for ideal illumination conditions, and its performance sharply degrades when confronted with noisy spikes. In Fig. 5, three real-world scenes with varying illumination conditions are depicted. \"toys\" exhibits high light intensity, \"grid\" features medium" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 265, + 545, + 301 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 545, + 301 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 545, + 301 + ], + "type": "text", + "content": "light, and \"box\" has low illumination. The results illustrate that our model performs effectively across different scenes and lighting conditions in real spike data." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 308, + 400, + 322 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 400, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 400, + 322 + ], + "type": "text", + "content": "4.4. Ablation Study" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "text", + "content": "We perform ablation studies on the proposed long-term spike rendering loss, and the results are presented in Table 2. In the table, " + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "text", + "content": " represents the proposed spike rendering loss, " + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i" + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "text", + "content": " involves using the light intensity of rays plus threshold correction, and the reconstructed images from spikes as supervision, while " + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_i^*" + }, + { + "bbox": [ + 304, + 328, + 546, + 483 + ], + "type": "text", + "content": " directly employs the estimated light intensity and reconstructed images as supervision. The experiments are conducted in both static and dynamic settings, affirming the effectiveness of our framework. Furthermore, we assess the performance under varying light intensities on the synthetic dataset. The results, presented in Table 3 and Fig. 6, demonstrate the robustness of our framework across different illumination conditions." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 495, + 379, + 508 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 495, + 379, + 508 + ], + "spans": [ + { + "bbox": [ + 305, + 495, + 379, + 508 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 515, + 545, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 515, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 515, + 545, + 646 + ], + "type": "text", + "content": "This paper introduces SpikeNeRF as a pioneering approach to derive a volumetric scene representation from spike camera data using NeRF. With a focus on purely spike-based supervision, SpikeNeRF preserves texture and motion details in high temporal resolution, addressing the challenges associated with real-world spike sequences. Our evaluations on a newly curated dataset of synthetic and real spike sequences demonstrate the efficacy of SpikeNeRF for novel view synthesis. We hope that our work will shed light on the research of high quality 3D representation learning with novel spike stream techniques." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 647, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 647, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 647, + 545, + 714 + ], + "type": "text", + "content": "Acknowledgement This work is partially supported by National Natural Science Foundation of China under Grant No.62302041, 62322204, 62131003, China National Postdoctoral Program under contract No.BX20230469, and Beijing Institute of Technology Research Fund Program for Young Scholars." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "6292" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 94, + 107, + 106 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 94, + 107, + 106 + ], + "spans": [ + { + "bbox": [ + 48, + 94, + 107, + 106 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 114, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 114, + 287, + 178 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 114, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 53, + 114, + 287, + 178 + ], + "type": "text", + "content": "[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. 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While existing methods propose spiking self-attention mechanisms that are compatible with SNNs, they lack reasonable scaling methods, and the overall architectures proposed by these methods suffer from a bottleneck in effectively extracting local features. To address these challenges, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA) with a reasonable scaling method. Based on DSSA, we propose a novel spiking Vision Transformer architecture called SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to improve both performance and energy efficiency while reducing parameters. Experimental results show that SpikingResformer achieves higher accuracy with fewer parameters and lower energy consumption than other spiking Vision Transformer counterparts. Notably, our SpikingResformer-L achieves $79.40\\%$ top-1 accuracy on ImageNet with 4 time-steps, which is the state-of-the-art result in the SNN field. Codes are available at https://github.com/xyshi2000/SpikingResformer", + "bbox": [ + 76, + 323, + 473, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 715, + 209, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Spiking Neural Networks (SNNs), considered as the third generation of Artificial Neural Networks (ANNs) [27], have garnered significant attention due to their notable advantages such as low power consumption, biological plausibility, and event-driven characteristics that are compatible with neuromorphic hardware. In comparison to ANNs, SNNs exhibit an energy-saving advantage when deployed on neuromorphic hardware [11, 29, 32], and have become popular in the field of neuromorphic computing in recent years [33].", + "bbox": [ + 75, + 739, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c83c5ee7eb46085195ceeb07a127dd65632894289d0059ed8acf1dda25e8ac69.jpg", + "image_caption": [ + "Figure 1. Comparison of Top-1 accuracy on ImageNet with respect to energy consumption per image for inference (left) and the number of parameters (right). The input size is $224 \\times 224$ ." + ], + "image_footnote": [], + "bbox": [ + 501, + 291, + 893, + 462 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "However, the performance of existing SNNs still lags behind that of ANNs, particularly on challenging vision tasks, which limits further application of SNNs.", + "bbox": [ + 498, + 547, + 892, + 593 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Researchers make great efforts to enhance the performance of SNNs. Recently, inspired by the remarkable achievements of vision transformers [8, 26] in ANNs, some attempts have been made to introduce transformer-based architecture into SNNs. The main challenge in incorporating transformer structures into SNNs lies in designing a self-attention mechanism suitable for SNNs. The vanilla self-attention mechanism in ANNs relies on float-point matrix multiplication and softmax operations. However, these operations involve float-point multiplication, division, and exponentiation, which do not comply with the spike-driven nature of SNNs. Moreover, commonly used components in ANN Transformers, such as layer normalization (LN) and GELU activation, are not directly applicable in SNNs. Therefore, the introduction of transformer architectures into SNNs necessitates circumventing these operations and catering to the unique requirements of SNNs.", + "bbox": [ + 496, + 595, + 892, + 852 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Some work has attempted to partially preserve floating-point operations [37], or run an SNN and an ANN Transformer in parallel [48]. Although these approaches en", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: yuzf12@puk.edu.cn", + "bbox": [ + 94, + 886, + 333, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5610", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "hance performance, they do not fully address the incompatibility between vanilla self-attention and SNNs. There are also works that propose spiking self-attention mechanisms and spiking Vision Transformer architectures, which are entirely based on synaptic operations [45] and fully spikedriven [41, 44]. These works completely resolve the incompatibility of the self-attention mechanism with SNNs, significantly outperforming existing spiking convolutional neural networks. However, these approaches have certain limitations. Specifically, the spiking transformer architectures of these methods exhibit a bottleneck in extracting local features. They employ a shallow convolutional network before the Transformer encoder to extract local features and reduce the size of feature maps. However, the effectiveness of such a shallow network is limited compared to Transformer encoders. Replacing this shallow network with a Transformer encoder is not feasible. This is because their spiking self-attention mechanisms lack reasonable scaling methods, making them suitable only for small feature maps. Designing proper scaling factors for these mechanisms is challenging as the input currents to neurons, which generate self-attention, do not possess simple mean and variance forms. Thus, there is a pressing need to design a new spiking self-attention mechanism with a reasonable scaling method that can effectively handle large feature maps.", + "bbox": [ + 76, + 90, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address these problems, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven, compatible with SNNs, and eliminates the need for direct spike multiplications. In addition, we detail the scaling method in DSSA, enabling it to adapt to adapt to feature maps of arbitrary scales. Building upon DSSA, we propose SpikingResformer, a novel spiking Vision Transformer architecture. This architecture combines the ResNet-based multistage design with our proposed spiking self-attention mechanism. Experimental results show that our proposed SpikingResformer significantly outperforms the performance of existing spiking Vision Transformers with fewer parameters and less energy consumption. The main contributions of this paper can be summarized as follows:", + "bbox": [ + 76, + 473, + 472, + 715 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the Dual Spike Self-Attention (DSSA), a novel spiking self-attention mechanism. It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs.", + "- We detail the scaling factors employed in DSSA, enabling DSSA to handle feature maps of arbitrary scales.", + "- We propose the SpikingResformer architecture, which combines the ResNet-based multi-stage architecture with our proposed DSSA.", + "- Experimental results show that the proposed SpikingReformer significantly outperforms other spiking Vision Transformer counterparts with fewer parame" + ], + "bbox": [ + 76, + 719, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ters and lower energy consumption. Notably, our SpikingResformer-L achieves up to $79.40\\%$ top-1 accuracy on ImageNet.", + "bbox": [ + 511, + 90, + 890, + 137 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 147, + 640, + 162 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spiking Convolutional Neural Networks. Spiking convolutional neural networks (SCNNs) have been extensively developed due to the remarkable success of surrogate gradient learning [30, 42] and are widely used in handling challenging vision tasks, including object recognition [1, 20], detection [17, 35], and segmentation [18, 31]. To improve the performance of SCNNs on these challenging tasks, researchers have dedicated great efforts to exploring training methods [6, 12, 21, 28, 38, 40, 46, 47] and ANN-to-SNN conversion techniques [2, 3, 5, 7, 13-16, 22, 24, 34, 39]. Moreover, many deep spiking convolutional architectures [9, 14, 21, 34, 43] have been proposed to achieve high performance. The success of SpikingVGG [21, 34] demonstrates that SCNNs can achieve comparable performance to ANNs in recognition tasks. SpikingResNet [14, 43] further explores SCNNs with residual structure and achieves deeper SCNN with ResNet-based architecture. Moreover, SEW ResNet [9] meticulously analyzes the identity mapping in directly-trained spiking residual networks and successfully trains a 152-layer SCNN directly. These architectures leverage large-scale SNNs with numerous layers and demonstrate superior performance on various tasks.", + "bbox": [ + 496, + 172, + 890, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spiking Vision Transformers. Spikformer [45] is the first directly-trained spiking vision transformer with a pure SNN architecture. It introduces a spiking self-attention mechanism that eliminates multiplication by activating Query, Key, and Value with spiking neurons and replacing softmax with spiking neurons. In addition, it replaces layer normalization and GELU activation in the Transformer with batch normalization and spiking neurons. Based on Spikformer, Spikingformer [44] achieves a purely spike-driven Vision Transformer by modifying the residual connection paradigm. Spike-driven Transformer [41] proposes a spikedriven self-attention mechanism with linear complexity, effectively reducing energy consumption. However, all of these efforts employ a shallow convolutional network to pre-extract local information to form a sequence of patches and lack proper scaling methods.", + "bbox": [ + 496, + 505, + 892, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 500, + 757, + 625, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We describe the dynamics of the Leaky Integrate-and-Fire (LIF) neuron used in this paper by the following discrete-time model:", + "bbox": [ + 496, + 782, + 890, + 825 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nv _ {i} [ t ] = u _ {i} [ t ] + \\frac {1}{\\tau} \\left(I _ {i} [ t ] - \\left(u _ {i} [ t ] - u _ {\\text {r e s t}}\\right)\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 830, + 890, + 859 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\ns _ {i} [ t ] = H \\left(v _ {i} [ t ] - u _ {\\mathrm {t h}}\\right), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 861, + 890, + 878 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nu _ {i} [ t + 1 ] = s _ {i} [ t ] u _ {\\text {r e s t}} + (1 - s _ {i} [ t ]) v _ {i} [ t ]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 880, + 890, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5611", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Eq. (1) describes the charging process. Here $u_{i}[t]$ and $v_{i}[t]$ denote the membrane potential of $i$ -th postsynaptic neuron before and after charging. $\\tau$ is the membrane time constant. $I_{i}[t]$ denotes the input current. In general, $I_{i}[t] = \\sum_{j} w_{i,j} s_{j}[t]$ , where $s_{j}[t] \\in \\{0, 1\\}$ represents the spike output of the $j$ -th presynaptic neuron at time-step $t$ , and $w_{i,j}$ represents the weight of the corresponding synaptic connection from neuron $j$ to neuron $i$ . Eq. (2) describes the firing process, where $H(\\cdot)$ is the Heaviside function, $s_{i}[t] \\in \\{0, 1\\}$ is the spike output of the spiking neuron, $u_{\\mathrm{th}}$ denotes the firing threshold. Eq. (3) describes the resetting process, with $u_{\\mathrm{rest}}$ denoting the resting potential.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For the sake of simplicity and clarity in subsequent sections, we represent the spiking neuron model as follows:", + "bbox": [ + 76, + 272, + 468, + 301 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {S} = \\operatorname {S N} (\\mathbf {I}), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 230, + 313, + 468, + 329 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{SN}(\\cdot)$ denotes the spiking neuron layer, omitting the dynamic processes within the neuron, $\\mathbf{I}\\in \\mathbb{R}^{T\\times n}$ is the input current, where $T$ is the time step and $n$ is the number of neurons, $\\mathbf{S}\\in \\{0,1\\}^{T\\times n}$ is the corresponding spike output.", + "bbox": [ + 75, + 340, + 468, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Dual Spike Self-Attention", + "text_level": 1, + "bbox": [ + 76, + 412, + 316, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section first revisits the vanilla self-attention (VSA) mechanism commonly used in ANNs and analyzes why VSA is not suitable for SNNs. Then, we propose dual spike self-attention (DSSA), specifically designed for compatibility. We further discuss the significance of the scaling factor in DSSA and the spike-driven characteristic of DSSA.", + "bbox": [ + 75, + 438, + 468, + 529 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Vanilla Self-Attention", + "text_level": 1, + "bbox": [ + 76, + 537, + 279, + 553 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The vanilla self-attention in Transformer [36] can be formulated as follows:", + "bbox": [ + 75, + 561, + 468, + 590 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {V}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 603, + 468, + 619 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\mathrm {T}}}{\\sqrt {d}}\\right) \\mathbf {V} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 622, + 468, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here $\\mathbf{Q},\\mathbf{K},\\mathbf{V}\\in \\mathbb{R}^{n\\times d}$ denote Query, Key and Value, respectively. $n$ is the number of patches, $d$ is the embedding dimension. We assume that $\\mathbf{Q},\\mathbf{K},\\mathbf{V}$ have the same embedding dimension. $\\mathbf{X}\\in \\mathbb{R}^{n\\times d}$ is the input of selfattention block, $\\mathbf{W}_Q,\\mathbf{W}_K,\\mathbf{W}_V\\in \\mathbb{R}^{d\\times d}$ are the weights of the linear transformations corresponding to $\\mathbf{Q},\\mathbf{K},\\mathbf{V}$ , respectively.", + "bbox": [ + 75, + 672, + 468, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The vanilla self-attention commonly used in ANNs is not suitable for SNNs due to the following two types of operations involved: 1) the float-point matrix multiplication of $\\mathbf{Q}$ and $\\mathbf{K}$ , as well as between the attention map and $\\mathbf{V}$ ; 2) the softmax function, which contains exponentiation and division operations. These operations rely on float-point multiplication, division, and exponentiation operations, which are not compatible with the restrictions of SNNs.", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. Dual Spike Self-Attention", + "text_level": 1, + "bbox": [ + 500, + 90, + 733, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To introduce the self-attention mechanism into SNNs and efficiently handle the multi-scale feature maps, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). DSSA only utilizes Dual Spike Transformation (DST), thereby eliminating the need for the float-point matrix multiplication and softmax function. We first define the DST as follows:", + "bbox": [ + 496, + 113, + 890, + 218 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {D S T} (\\mathbf {X}, \\mathbf {Y}; f (\\cdot)) = \\mathbf {X} f (\\mathbf {Y}) = \\mathbf {X Y W}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 549, + 224, + 890, + 242 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {D S T} _ {\\mathrm {T}} (\\mathbf {X}, \\mathbf {Y}; f (\\cdot)) = \\mathbf {X} f (\\mathbf {Y}) ^ {\\mathrm {T}} = \\mathbf {X} \\mathbf {W} ^ {\\mathrm {T}} \\mathbf {Y} ^ {\\mathrm {T}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 540, + 244, + 890, + 263 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Eq. (7), $\\mathbf{X} \\in \\{0,1\\}^{T \\times p \\times m}$ and $\\mathbf{Y} \\in \\{0,1\\}^{T \\times m \\times q}$ represent the dual spike inputs. $T$ is the time steps, $p, m, q$ denote arbitrary dimensions. Here $f(\\cdot)$ is a generalized linear transformation on $\\mathbf{Y}$ , with $\\mathbf{W} \\in \\mathbb{R}^{q \\times q}$ denoting its weight matrix. It represents any operation that can be equated to a linear transformation, including convolution, batch normalization (ignoring bias), etc. A detailed discussion on the equivalence of convolution operations to linear transformations can be found in the supplementary. Similarly, in Eq. (8), we have $\\mathbf{Y} \\in \\{0,1\\}^{T \\times q \\times m}$ , $\\mathbf{W} \\in \\mathbb{R}^{m \\times m}$ . Since $\\mathbf{X}$ and $\\mathbf{Y}$ are both spike matrices, all matrix multiplications are equivalent to the summation of weights. Consequently, the DST avoids floating-point multiplication, making it compatible with SNNs. Further discussion of the compatibility and the spike-driven characteristic of DST can be found in Sec. 4.4. Based on DST, the attention map in DSSA can be formulated as follows:", + "bbox": [ + 496, + 268, + 892, + 526 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {A t t n M a p} (\\mathbf {X}) = \\operatorname {S N} \\left(\\mathrm {D S T} _ {\\mathrm {T}} (\\mathbf {X}, \\mathbf {X}; f (\\cdot)) * c _ {1}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 534, + 890, + 550 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {\\mathrm {p}} (\\mathbf {X})\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 551, + 890, + 569 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{X} \\in \\{0,1\\}^{T \\times HW \\times d}$ is the spike input, with $H$ and $W$ denoting the spatial height and width of the input, $d$ denoting the embedding dimension. $\\mathrm{BN}(\\cdot)$ refers to the batch normalization layer, $\\mathrm{Conv}_{\\mathrm{p}}(\\cdot)$ denotes a $p \\times p$ convolution with a stride of $p$ , and $c_{1}$ is the scaling factor. Since the convolution operation is equivalent to a generalized linear transformation, and batch normalization can be absorbed into the convolution (ignoring bias), $\\mathrm{BN}(\\mathrm{Conv}_{\\mathrm{p}}(\\cdot))$ can be viewed as a generalized linear transformation. Here we use the $p \\times p$ convolution with a stride of $p$ to reduce the spatial size to handle the multi-scale feature map and reduce the computational overhead. In DSSA, there is no need for the softmax function since the spiking neuron layer inherently generates a binary attention map composed of spikes. Each spike $s_{ij}$ in this spiking attention map signifies attention between patch $i$ and patch $j$ . We believe that such a spiking attention map is more interpretable compared to the attention map in ANN activated with softmax. With the spiking attention map, the DSSA can be formulated as follows:", + "bbox": [ + 496, + 575, + 892, + 863 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {D S S A} (\\mathbf {X}) = \\operatorname {S N} (\\operatorname {D S T} (\\operatorname {A t t n M a p} (\\mathbf {X}), \\mathbf {X}; f (\\cdot)) * c _ {2}), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 869, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5612", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d9f54d23994e6f7fac53498446fa400e08c44b6dd68168c3dcbfac0002b99286.jpg", + "image_caption": [ + "Figure 2. Left: Architecture of SpikingResformer and components including Dual Spike Self-Attention (DSSA), Multi-Head DSSA (MHDSSA), and Group-Wise Spiking Feed-Forward Network (GWSFFN). Right: Architecture of SEW ResNet-50 and Spikformer." + ], + "image_footnote": [], + "bbox": [ + 76, + 92, + 883, + 398 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $c_{2}$ is the second scaling factor. Since the form of DSSA is quite different from VSA and existing spiking self-attention mechanisms, we further discuss how DSSA achieves self-attention in the supplementary.", + "bbox": [ + 75, + 464, + 470, + 525 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Scaling Factors in DSSA", + "text_level": 1, + "bbox": [ + 76, + 534, + 302, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the vanilla self-attention mechanism [36], the product of matrices $\\mathbf{Q}$ and $\\mathbf{K}$ in Eq. (6) is scaled by a factor of $1 / \\sqrt{d}$ before applying the softmax operation. This scaling is necessary because the magnitude of $\\mathbf{Q}\\mathbf{K}^{\\mathrm{T}}$ grows with the embedding dimension $d_{k}$ , which can result in gradient vanishing issues after the softmax operation. Formally, assume that all the elements in $\\mathbf{Q}$ and $\\mathbf{K}$ are independent random variables with a mean of 0 and a variance of 1, then each element in their product $\\mathbf{Q}\\mathbf{K}^{\\mathrm{T}}$ has mean 0 and variance $d$ . By multiplying the product with a factor of $1 / \\sqrt{d}$ , the variance of the product is scaled to 1.", + "bbox": [ + 75, + 556, + 468, + 722 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While DSSA does not employ the softmax function, the surrogate gradient also suffers gradient vanishes without scaling. However, directly using the scaling factor of VSA is not feasible. Due to the spike-based nature of the input in DST and the attention map in DSSA, we cannot assume that they possess a mean of 0 and a variance of 1. Therefore, the scaling factor values in DSSA should be different from those used in VSA. In the following theorem, we present the mean and variance of DST.", + "bbox": [ + 75, + 724, + 468, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 (Mean and variance of DST). Given spike input $\\mathbf{X} \\in \\{0,1\\}^{T \\times p \\times m}$ , $\\mathbf{Y} \\in \\{0,1\\}^{T \\times m \\times q}$ and linear", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "transformation $f(\\cdot)$ with weight matrix $\\mathbf{W} \\in \\mathbb{R}^{q \\times q}$ , $\\mathbf{I} \\in \\mathbb{R}^{T \\times p \\times q}$ is the output of DST, $\\mathbf{I} = \\mathrm{DST}(\\mathbf{X},\\mathbf{Y};f(\\cdot))$ . Assume that all elements in $\\mathbf{X}$ and $\\mathbf{Y}$ are independent random variables, $x_{i_x,j_x}[t]$ in $\\mathbf{X}$ subject to Bernoulli distribution $x_{i_x,j_x}[t] \\sim B(f_x)$ , and the output of linear transformation $f(\\mathbf{Y})$ has mean 0 and variance 1, we have $\\operatorname{E}(I_{i_I,j_I}[t]) = 0$ , $\\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm$ . Similarly, for $\\mathbf{I} = \\mathrm{DST}_{\\mathrm{T}}(\\mathbf{X},\\mathbf{Y};f(\\cdot))$ and $\\mathbf{Y} \\in \\{0,1\\}^{T \\times q \\times m}$ , $\\mathbf{W} \\in \\mathbb{R}^{m \\times m}$ , we also have $\\operatorname{E}(I_{i_I,j_I}[t]) = 0$ , $\\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm$ .", + "bbox": [ + 496, + 463, + 892, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proof of Theorem 1 can be found in the supplementary. According to Theorem 1, we have $c_{1} = 1 / \\sqrt{f_{X}d}$ , $c_{2} = 1 / \\sqrt{f_{Attn}HW / p^{2}}$ . Here $f_{X}$ and $f_{Attn}$ are the average firing rate of $\\mathbf{X}$ and spiking attention map, respectively.", + "bbox": [ + 496, + 612, + 890, + 674 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.4. Spike-driven Characteristic of DSSA", + "text_level": 1, + "bbox": [ + 500, + 684, + 818, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The spike-driven characteristic is important for SNNs, i.e., the computation is sparsely triggered with spikes and requires only synaptic operations. Previous work has made a great effort in achieving spike-driven Transformers [41, 44]. In this subsection, we delve into the spike-driven characteristic of DSSA and prove that DSSA is spike-driven. We first give the formal definition of the spike-driven characteristic.", + "bbox": [ + 496, + 707, + 890, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 1. A spiking neural network is spike-driven if the input currents of all neurons satisfy the following form:", + "bbox": [ + 496, + 825, + 890, + 857 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {i} [ t ] = \\sum_ {j} w _ {i, j} s _ {j} [ t ] = \\sum_ {j, s _ {j} [ t ] \\neq 0} w _ {i, j}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 868, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5613", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I_{i}[t]$ is the input current of the $i$ -th postsynaptic neuron at time step $t$ , $s_{j}[t] \\in \\{0,1\\}$ is the spike output of the $j$ -th presynaptic neuron, $w_{i,j}$ is the weight of the synaptic connection from neuron $j$ to neuron $i$ .", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This definition reveals the nature of the spike-driven characteristic, i.e., the accumulation of input current is sparsely triggered by spikes emitted from presynaptic neurons. It is evident that commonly used linear layers and convolution layers satisfy this definition.", + "bbox": [ + 75, + 162, + 468, + 238 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The DSSA has only two spiking neuron layers, including the spiking attention map layer and the output layer. Both of these layers receive input currents derived from DST. Thus, we only need to validate that the DST satisfies the form in Definition 1. We first validate the $\\mathrm{DST}_{\\mathrm{T}}$ in Eq. (8)", + "bbox": [ + 75, + 238, + 468, + 314 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} = \\mathbf {X} \\mathbf {W} ^ {\\mathrm {T}} \\mathbf {Y} ^ {\\mathrm {T}}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 325, + 468, + 342 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {i, j} [ t ] = \\sum_ {k = 1} ^ {m} \\sum_ {l = 1} ^ {m} x _ {i, k} [ t ] w _ {l, k} y _ {j, l} [ t ] = \\sum_ {\\substack {k, l \\\\ (x _ {i, k} [ t ] \\wedge y _ {j, l} [ t ]) \\neq 0}} w _ {l, k}. \\tag{14}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 345, + 468, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Slightly different from Definition 1, the spike input here is the logical AND of dual spikes. This can be viewed as a synaptic operation requiring dual spikes to trigger, which is the reason it is called dual spike transformation. Similar to the $\\mathrm{DST}_{\\mathrm{T}}$ , the DST in Eq. (7) can also be formulated as:", + "bbox": [ + 75, + 426, + 468, + 501 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {I} = \\mathbf {X Y W}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 116, + 529, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI _ {i, j} [ t ] = \\sum_ {k = 1} ^ {m} \\sum_ {l = 1} ^ {q} x _ {i, k} [ t ] y _ {k, l} [ t ] w _ {l, j} = \\sum_ {\\substack {k, l \\\\ (x _ {i, k} [ t ] \\wedge y _ {k, l} [ t ]) \\neq 0}} w _ {l, j}. \\tag{16}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 549, + 468, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Thus, DSSA is spike-driven.", + "bbox": [ + 76, + 628, + 267, + 643 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. SpikingResformer", + "text_level": 1, + "bbox": [ + 76, + 659, + 254, + 676 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first introduce the overall architecture of the proposed SpikingResformer and compare it with existing SEW ResNet [9] and Spikformer [45]. Then we detail the design of the spiking resformer block.", + "bbox": [ + 75, + 684, + 468, + 744 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Overall Architecture", + "text_level": 1, + "bbox": [ + 76, + 756, + 272, + 770 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The overall pipeline of SEW ResNet [9], Spikformer [45], and the proposed SpikingResformer are shown in Fig. 2. As shown in Fig. 2, Spikformer employs a Spiking Patch Splitting (SPS) module to project an image to $d$ dimensional feature with reduced spatial size. However, the local information can only be poorly modeled by this shallow spiking convolutional module and it only generates single-scale feature maps. On the other hand, SEW ResNet is much", + "bbox": [ + 75, + 779, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "deeper than the SPS in Spikformer and have a greater capability in extracting multi-scale feature with the multi-stage architecture, but lacks the global self-attention mechanism which helps extract global information. To overcome the limitations of these architectures while exploiting their advantages, we propose SpikingResformer, which combines the ResNet-based architecture and the spiking self-attention mechanism.", + "bbox": [ + 496, + 90, + 890, + 210 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The details of the overall architecture of SpikingResformer series are listed in Tab. 1. Similar to the ResNet-based SNNs [9, 14], our model starts with a stem architecture consisting of a $7 \\times 7$ convolution and a $3 \\times 3$ max pooling to pre-extract localized features and employs a multistage backbone to generate multi-scale feature maps. In each stage, multiple spiking Resformer blocks are stacked sequentially. Each spiking Resformer block consists of two modules, named Multi-Head Dual Spike Self-Attention (MHDSSA) block and Group-Wise Spiking Feed-Forward Network (GWSFFN). A downsample layer is applied before each stage (except the first stage) to reduce the size of the feature maps and project them to a higher dimension ( $2 \\times$ downsampling of resolution with $2 \\times$ enlargement of dimension). Finally, the model ends with a global average pooling layer and a classification layer.", + "bbox": [ + 496, + 210, + 892, + 454 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Spiking Resformer Block", + "text_level": 1, + "bbox": [ + 500, + 460, + 728, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As illustrated in Fig. 2, the spiking Resformer block consists of a Multi-Head Dual Spike Self-Attention (MHDSSA) module and a Group-Wise Spiking Feed-Forward Network (GWSFFN). We first introduce the two modules and then derive the form of the spiking Resformer block.", + "bbox": [ + 496, + 484, + 890, + 573 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Multi-Head Convolutional Spiking Self-Attention. In Sec. 4, we propose the single-head form of DSSA. It can be easily extended to the multi-head DSSA (MHDSSA) following a similar approach to the vanilla Transformer [36]. In MHDSSA, we first split the results of linear transformation in DST into $h$ heads, then perform DSSA on each head and concatenate them together. Finally, we use point-wise convolution to project the concatenated features thus fusing the features in different heads. The MHDSSA can be formulated as follows:", + "bbox": [ + 496, + 574, + 890, + 726 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {M H D S S A} (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {1} \\left([ \\mathrm {D S S A} _ {i} (\\operatorname {S N} (\\mathbf {X})) ] _ {i = 1} ^ {h}\\right)\\right), \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 732, + 890, + 763 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $[\\ldots]$ denotes the concatenate operation, $\\mathrm{Conv}_1$ denotes the point-wise convolution.", + "bbox": [ + 496, + 763, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Group-Wise Spiking Feed-Forward Network. The spiking feed-forward network (SFFN) proposed in previous spiking vision transformers is composed of two linear layers with batch normalization and spiking neuron activation [41, 45]. Moreover, the expansion ratio is usually set to 4, i.e., the first layer raises the dimension by a factor of 4 while the second layer reduces to the original dimension.", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5614", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7f28f8c23c93ae2972c05c26a30d7a8111c2a1d65358e53c4f64838d11e54fbb.jpg", + "table_caption": [ + "Table 1. Architectures of SpikingResformer series. The output size corresponds to the input size of $224 \\times 224$ . $D_{i}$ and $H_{i}$ are the embedding dimension and number of heads of MHDSSA in stage $i$ , respectively. $p_i$ denotes that the MHDSSA in stage $i$ uses $p_i \\times p_i$ convolution in DST. $R_{i}$ and $G_{i}$ denote the expansion ratio and embedding dimension per group of GWSFFN in stage $i$ , respectively." + ], + "table_footnote": [], + "table_body": "
StageOutput SizeLayer NameSpikingResformer-TiSpikingResformer-SSpikingResformer-MSpikingResformer-L
Stem56×56StemConv 7×7, stride 2, Maxpooling 3×3, stride 2
Stage 156×56MHDSSA[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=128H1=1,p1=4R1=4,G1=64] × 1
GWSFFN
Stage 228×28DownsampleConv 3×3, 192, stride 2Conv 3×3, 256, stride 2Conv 3×3, 384, stride 2Conv 3×3, 512, stride 2
MHDSSA[D2=192H2=3,p2=2R2=4,G2=64] × 2[D2=256H2=4,p2=2R2=4,G2=64] × 2[D2=384H2=6,p2=2R2=4,G2=64] × 2[D2=512H2=8,p2=2R2=4,G2=64] × 2
GWSFFN
Stage 314×14DownsampleConv 3×3, 384, stride 2Conv 3×3, 512, stride 2Conv 3×3, 768, stride 2Conv 3×3, 1024, stride 2
MHDSSA[D3=384H3=6,p3=1R3=4,G3=64] × 3[D3=512H3=8,p3=1R3=4,G3=64] × 3[D3=768H3=12,p3=1R3=4,G3=64] × 3[D3=1024H3=16,p3=1R3=4,G3=64] × 3
GWSFFN
Classifier1×1Linear1000-FC
", + "bbox": [ + 80, + 142, + 890, + 353 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on SFFN, we insert a $3 \\times 3$ convolution layer with the residual connection between two linear layers to enable SFFN to extract local features. Since the dimension of the hidden features between the two linear layers is expanded by a factor of 4 compared to the input, in order to reduce the number of parameters and computational overhead, we use group-wise convolution and set every 64 channels as 1 group. We also employ the spike-driven design in [41, 44]. The group-wise spiking feed-forward network (GWSFFN) can be formulated as follows:", + "bbox": [ + 75, + 377, + 472, + 527 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {F F L} _ {i} (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {1} (\\operatorname {S N} (\\mathbf {X}))\\right), i = 1, 2, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 540, + 468, + 556 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {G W L} (\\mathbf {X}) = \\operatorname {B N} (\\operatorname {G W C o n v} (\\operatorname {S N} (\\mathbf {X}))) + \\mathbf {X}, \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 125, + 559, + 468, + 575 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {G W S F F N} (\\mathbf {X}) = \\operatorname {F F L} _ {2} (\\operatorname {G W L} (\\operatorname {F F L} _ {1} (\\mathbf {X}))). \\tag {20}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 578, + 468, + 594 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here $\\mathrm{FFL}_i(\\cdot), i = 1,2$ denote the feed-forward layers, $\\mathrm{Conv}_1(\\cdot)$ is point-wise convolution ( $1 \\times 1$ convolution), which equal to the linear transformation. $\\mathrm{GWL}(\\cdot)$ denotes group-wise convolution layer, $\\mathrm{GWConv}(\\cdot)$ denotes the group-wise convolution.", + "bbox": [ + 75, + 606, + 468, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Spiking Resformer Block. With the MHDSSA module and GWSFFN above, the spiking resformer block can be formulated as:", + "bbox": [ + 75, + 681, + 468, + 724 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} _ {i} = \\operatorname {M H D S S A} \\left(\\mathbf {X} _ {i}\\right) + \\mathbf {X} _ {i}, \\tag {21}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 739, + 468, + 755 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} _ {i + 1} = \\operatorname {G W S F N} \\left(\\mathbf {Y} _ {i}\\right) + \\mathbf {Y} _ {i}. \\tag {22}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 757, + 468, + 773 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\mathbf{Y}_i$ denotes the output features of MHDSSA module in the $i$ -th spiking reformer block.", + "bbox": [ + 75, + 785, + 468, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 76, + 830, + 209, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we first evaluate the performance and energy efficiency of SpikingResformer on the ImageNet classification task. Then, we perform ablation experiments on key", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "components in SpikingResformer. Finally, we evaluate the transfer learning ability of SpikingResformer.", + "bbox": [ + 498, + 377, + 890, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. ImageNet Classification", + "text_level": 1, + "bbox": [ + 500, + 417, + 718, + 434 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ImageNet [4] is one of the most typical static image datasets widely used for image classification. For a fair comparison, we generally follow the data augmentation strategy and training setup in [41]. More details of the experimental setup can be found in the supplementary.", + "bbox": [ + 498, + 441, + 890, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Results. Our experimental results are listed in Tab. 2. For comparison, we also list the results of existing spiking convolutional networks and spiking Vision Transformers. As shown in Tab. 2, SpikingResformer achieves higher accuracy, fewer parameters, and lower energy consumption at the same time compared to existing methods. For instance, SpikingResformer-Ti achieves $74.34\\%$ accuracy with only 11.14M parameters and 2.73G SOPs $(2.46\\mathrm{mJ})$ , outperforming Spike-driven Transformer-8-384 by $2.06\\%$ , saving 5.67M parameters and $1.44\\mathrm{mJ}$ energy. SpikingResformer-M achieves $77.24\\%$ accuracy with 35.52M parameters and 6.07G SOPs $(5.46\\mathrm{mJ})$ , outperforming Spike-driven Transformer-8-768 by $0.92\\%$ while saving 30.82M parameters. Particularly, the SpikingResformer-L achieves up to $79.40\\%$ accuracy when the input size is enlarged to $288\\times 288$ , which is the state-of-the-art result in SNN field.", + "bbox": [ + 498, + 518, + 892, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 771, + 653, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We perform ablation experiments on key components in SpikingResformer, including the multi-stage architecture, the group-wise convolution layer in GWSFFN, and our proposed spiking self-attention mechanism. The ablation experiments are conducted on the ImageNet100 dataset, which is a subset of the ImageNet dataset and consists of 100 categories from the ImageNet dataset. The experiment", + "bbox": [ + 498, + 795, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5615", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/fe2f025e7b2ef990e4883e6bf3c99ab93c253efd3816fa75d4417bbcb66de0b4.jpg", + "table_caption": [ + "Table 2. Evaluation on ImageNet. SOPs denotes the average synaptic operations of an image inference on ImageNet validation data. Energy is the estimation of energy consumption same as [41, 45]. The default input resolution for training and inference is $224 \\times 224$ . $\\dagger$ means the input is enlarged to $288 \\times 288$ in inference. - means the data is not provided in the original paper." + ], + "table_footnote": [], + "table_body": "
MethodTypeArchitectureTParam (M)SOPs (G)Energy (mJ)Top-1 Acc. (%)
Spiking ResNet [14]ANN-to-SNNResNet-3435021.7965.2859.3071.61
ResNet-5035025.5678.2970.9372.75
STBP-tdBN [43]Direct TrainingSpiking ResNet-34621.796.506.3963.72
TET [6]Direct TrainingSpiking ResNet-34621.79--64.79
SEW ResNet-34421.79--68.00
SEW ResNet [9]Direct TrainingSEW ResNet-34421.793.884.0467.04
SEW ResNet-50425.564.834.8967.78
SEW ResNet-101444.559.308.9168.76
SEW ResNet-152460.1913.7212.8969.26
Spikformer [45]Direct TrainingSpikformer-8-384416.816.827.7370.24
Spikformer-8-512429.6811.0911.5873.38
Spikformer-8-768466.3422.0921.4874.81
Spikingformer [44]Direct TrainingSpikingformer-8-384416.81-4.6972.45
Spikingformer-8-512429.68-7.4674.79
Spikingformer-8-768466.34-13.6875.85
Spike-driven Transformer [41]Direct TrainingSpike-driven Transformer-8-384416.81-3.9072.28
Spike-driven Transformer-8-512429.68-4.5074.57
Spike-driven Transformer-8-768466.34-/-6.09/-76.32/77.07†
SpikingResformer (Ours)Direct TrainingSpikingResformer-Ti411.142.73/4.71†2.46/4.24†74.34/75.57†
SpikingResformer-S417.763.74/6.40†3.37/5.76†75.95/76.90†
SpikingResformer-M435.526.07/10.24†5.46/9.22†77.24/78.06†
SpikingResformer-L460.389.74/16.40†8.76/14.76†78.77/79.40†
", + "bbox": [ + 80, + 142, + 890, + 489 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b5c48a893a4363dda20c6aea7cbaaabc1746b8345ef88bf58d1b72206b0efee1.jpg", + "table_caption": [ + "Table 3. Ablation Study on ImageNet100 dataset. The number of parameters for all variants is comparable to SpikingResformer-S." + ], + "table_footnote": [], + "table_body": "
ModelSOPs (G)Energy (mJ)Acc. (%)
SpikingResformer-S2.432.1888.06
w/o multi-stage architecture1.841.6685.32
w/o group-wise convolution2.372.1384.64
w/o DSSAnot converge
w/o p × p convolution4.343.9186.14
w/o scalingnot converge
", + "bbox": [ + 81, + 553, + 465, + 654 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tal setup basically follows the one in Sec. 6.1. Detailed settings are listed in the supplementary.", + "bbox": [ + 75, + 684, + 468, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Multi-Stage Architecture. To verify the effectiveness of the multi-stage architecture, we replace it with the Spikingformer-based architecture, while the structure of the spiking Resformer block remains unchanged. We adjust the embedding dimensions to make the model parameters comparable to SpikingResformer-S. As shown in Tab. 3, SpikingResformer-S outperforms the variant without multi-stage architecture by $2.74\\%$ , demonstrating the effectiveness of multi-stage architecture.", + "bbox": [ + 75, + 715, + 468, + 852 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Group-Wise Convolution Layer. In comparison to the point-wise SFFN, GWSFFN employs a $3 \\times 3$ group-wise convolution layer between the two linear layers. We", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "evaluate its effect by removing the group-wise convolution layer and increasing the dimension to keep the number of parameters constant. As demonstrated in Tab. 3, SpikingResformer-S achieves $3.42\\%$ higher accuracy in contrast to the variant without the group-wise convolution layer. This difference highlights the benefits of the group-wise convolution layer in GWSFFN.", + "bbox": [ + 496, + 516, + 890, + 625 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Dual Spike Self-Attention. To validate the effectiveness of DSSA, we first replace DSSA with existing spiking self-attention mechanisms, including Spiking Self-Attention (SSA) in Spikformer and Spike-Driven Self-Attention (SDSA) in Spike-driven Transformer. However, neither SSA nor SDSA converges. We believe this is because SSA and SDSA do not fit the multi-scale input. To further validate the key factors that help DSSA fit for the multi-scale input, we conduct two more sets of experiments. One set replaces all $p \\times p$ convolutions with $1 \\times 1$ convolutions in DST to validate the effect of reducing spatial size. The other removes the scaling factor or replaces our proposed scaling factors with $1 / \\sqrt{d}$ to validate the effect of scaling. As a result, the first group converges but only achieves $86.14\\%$ accuracy with a higher energy consumption of $3.91\\mathrm{mJ}$ , while the second set does not converge. This shows that the scaling factor is the key to convergence. We believe that both SSA and SDSA lack proper scaling meth", + "bbox": [ + 496, + 628, + 892, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5616", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/cdc3f3be8d18dee33e93966322f35998f14e656de8748350db8f49c2dd85c600.jpg", + "table_caption": [ + "Table 4. Transfer learning results on CIFAR10, CIFAR100, CIFAR10-DVS, DVSGesture datasets." + ], + "table_footnote": [], + "table_body": "
MethodTypeCIFAR10CIFAR100CIFAR10-DVSDVSGesture
TAcc.TAcc.TAcc.TAcc.
STBP-tdBN [43]Direct Training693.16--1067.84096.87
PLIF [10]Direct Training893.50--2074.82097.57
Dspike [25]Direct Training694.25674.241075.4--
Spikformer [45]Direct Training495.19477.861680.61697.9
Spikingformer [44]Direct Training495.61479.091681.31698.3
Spike-driven Transformer [41]Direct Training495.6478.41680.01699.3
Spikformer [45]Transfer Learning497.03483.83----
SpikingResformer (Ours)Transfer Learning497.40485.981084.81093.4
", + "bbox": [ + 161, + 114, + 805, + 273 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ods, thus do not apply to multi-stage architecture. SSA employs the same scaling factor as vanilla self-attention, i.e., $1 / \\sqrt{d}$ . However, this does not apply to spike matrix multiplication, since spikes do not have mean 0 and variance 1. SDSA has no scaling method, which may be feasible when the feature map is small but not for multi-scale inputs.", + "bbox": [ + 75, + 297, + 470, + 388 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.3. Transfer Learning", + "text_level": 1, + "bbox": [ + 76, + 402, + 256, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "High transfer learning ability is a key advantage of Vision Transformer. We evaluate the transfer learning ability of the proposed SpikingResformer on static dataset CIFAR10 and CIFAR100 [19] and neuromorphic dataset CIFAR10-DVS [23] and DVSGesture [1] by fine-tuning the models pre-trained on ImageNet. Among the existing spiking Vision Transformers, only Spikformer provides transfer learning results, and only on the static image datasets CIFAR10 and CIFAR100. Thus, we also compared our results with the direct training results for a comprehensive comparison. Tab. 4 lists the highest accuracy achieved by these methods. The experimental setup and a more detailed comparison can be found in the supplementary.", + "bbox": [ + 75, + 429, + 468, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Static Image Datasets. As shown in Tab. 4, SpikingResformer achieves $97.40\\%$ accuracy on CIFAR10 dataset and $85.98\\%$ accuracy on CIFAR100 dataset, which is the state-of-the-art result, outperforming the transfer learning results of Spikformer by $0.37\\%$ on CIFAR10 and $2.15\\%$ on CIFAR100. Compared to direct training methods, SpikingResformer obtained from transfer learning has significantly better performance. For example, SpikingResformer outperforms Spikingformer by $6.89\\%$ on CIFAR100 dataset, demonstrating the advantage of transfer learning.", + "bbox": [ + 75, + 627, + 468, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Neuromorphic Datasets. Neuromorphic datasets differ significantly from traditional static image datasets. The samples of the neuromorphic dataset consist of event streams instead of RGB images. As a result, there is a large gap between the source and target domain for models pre-trained on static image datasets. To bridge this gap, we stack the events over a period of time to form a frame. The RGB channels are replaced with positive events,", + "bbox": [ + 75, + 779, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "negative events, and the sum of events channels, respectively. As shown in Tab. 4, transfer learning results of SpikingResformer significantly outperform the direct training ones on CIFAR10-DVS. SpikingResformer achieves $84.8\\%$ accuracy on CIFAR10-DVS, outperforming Spikingformer by $3.5\\%$ . However, the transfer learning results on DVS-Gesture fail to achieve comparable performance to direct training. SpikingResformer only achieves $93.4\\%$ accuracy on DVSGesture, falling behind the state-of-the-art method Spike-driven Transformer by $5.9\\%$ . We believe that this is mainly due to the way CIFAR10-DVS is constructed differs from DVSGesture. CIFAR10-DVS is converted from CIFAR10, which does not contain temporal information. Thus, models pre-trained on static datasets can transfer to CIFAR10-DVS well. However, DVSGesture is directly created from human gestures using a dynamic vision sensor, thus containing rich temporal information. As a result, models pre-trained on static datasets do not transfer well to DVSGesture. We hope our exploration of transfer learning on neuromorphic datasets could pave the way for further transfer learning research of SNNs.", + "bbox": [ + 496, + 297, + 893, + 616 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 627, + 619, + 642 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs. We detail the scaling factors in DSSA enabling it to handle feature maps of arbitrary scales. Based on DSSA, we propose SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to achieve superior performance and energy efficiency with fewer parameters. Extensive experiments demonstrate the effectiveness and superiority of the proposed SpikingResformer.", + "bbox": [ + 496, + 652, + 893, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 830, + 660, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (62176003, 62088102) and by the Beijing Nova Program (20230484362).", + "bbox": [ + 496, + 854, + 890, + 902 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5617", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. 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Event-based human pose tracking by spiking spatiotemporal transformer. arXiv preprint arXiv:2303.09681, pages 1-12, 2023. 1" + ], + "bbox": [ + 503, + 92, + 890, + 796 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5619", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SpikingResformer_ Bridging ResNet and Vision Transformer in Spiking Neural Networks/02fe2792-da1c-4c04-8cc2-8f8d42352f7c_model.json b/2024/SpikingResformer_ Bridging ResNet and Vision Transformer in Spiking Neural Networks/02fe2792-da1c-4c04-8cc2-8f8d42352f7c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5e8fa013fc38584da4f3a3efc8c1a68454cde474 --- /dev/null +++ b/2024/SpikingResformer_ Bridging ResNet and Vision Transformer in Spiking Neural Networks/02fe2792-da1c-4c04-8cc2-8f8d42352f7c_model.json @@ -0,0 +1,2134 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.086, + 0.13, + 0.885, + 0.175 + ], + "angle": 0, + "content": "SpikingResformer: Bridging ResNet and Vision Transformer in Spiking Neural Networks" + }, + { + "type": "text", + "bbox": [ + 0.316, + 0.203, + 0.66, + 0.221 + ], + "angle": 0, + "content": "Xinyu Shi\\(^{1,2}\\), Zecheng Hao\\(^{2}\\), Zhaofei Yu\\(^{1,2*}\\)" + }, + { + "type": "text", + "bbox": [ + 0.27, + 0.221, + 0.7, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\) Institute for Artificial Intelligence, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.289, + 0.24, + 0.681, + 0.258 + ], + "angle": 0, + "content": "2 School of Computer Science, Peking University" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.324, + 0.474, + 0.687 + ], + "angle": 0, + "content": "The remarkable success of Vision Transformers in Artificial Neural Networks (ANNs) has led to a growing interest in incorporating the self-attention mechanism and transformer-based architecture into Spiking Neural Networks (SNNs). While existing methods propose spiking self-attention mechanisms that are compatible with SNNs, they lack reasonable scaling methods, and the overall architectures proposed by these methods suffer from a bottleneck in effectively extracting local features. To address these challenges, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA) with a reasonable scaling method. Based on DSSA, we propose a novel spiking Vision Transformer architecture called SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to improve both performance and energy efficiency while reducing parameters. Experimental results show that SpikingResformer achieves higher accuracy with fewer parameters and lower energy consumption than other spiking Vision Transformer counterparts. Notably, our SpikingResformer-L achieves \\(79.40\\%\\) top-1 accuracy on ImageNet with 4 time-steps, which is the state-of-the-art result in the SNN field. Codes are available at https://github.com/xyshi2000/SpikingResformer" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.716, + 0.21, + 0.731 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.741, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Spiking Neural Networks (SNNs), considered as the third generation of Artificial Neural Networks (ANNs) [27], have garnered significant attention due to their notable advantages such as low power consumption, biological plausibility, and event-driven characteristics that are compatible with neuromorphic hardware. In comparison to ANNs, SNNs exhibit an energy-saving advantage when deployed on neuromorphic hardware [11, 29, 32], and have become popular in the field of neuromorphic computing in recent years [33]." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.292, + 0.895, + 0.463 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.473, + 0.894, + 0.517 + ], + "angle": 0, + "content": "Figure 1. Comparison of Top-1 accuracy on ImageNet with respect to energy consumption per image for inference (left) and the number of parameters (right). The input size is \\(224 \\times 224\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.548, + 0.893, + 0.594 + ], + "angle": 0, + "content": "However, the performance of existing SNNs still lags behind that of ANNs, particularly on challenging vision tasks, which limits further application of SNNs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.893, + 0.853 + ], + "angle": 0, + "content": "Researchers make great efforts to enhance the performance of SNNs. Recently, inspired by the remarkable achievements of vision transformers [8, 26] in ANNs, some attempts have been made to introduce transformer-based architecture into SNNs. The main challenge in incorporating transformer structures into SNNs lies in designing a self-attention mechanism suitable for SNNs. The vanilla self-attention mechanism in ANNs relies on float-point matrix multiplication and softmax operations. However, these operations involve float-point multiplication, division, and exponentiation, which do not comply with the spike-driven nature of SNNs. Moreover, commonly used components in ANN Transformers, such as layer normalization (LN) and GELU activation, are not directly applicable in SNNs. Therefore, the introduction of transformer architectures into SNNs necessitates circumventing these operations and catering to the unique requirements of SNNs." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Some work has attempted to partially preserve floating-point operations [37], or run an SNN and an ANN Transformer in parallel [48]. Although these approaches en" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.334, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: yuzf12@puk.edu.cn" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5610" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.471 + ], + "angle": 0, + "content": "hance performance, they do not fully address the incompatibility between vanilla self-attention and SNNs. There are also works that propose spiking self-attention mechanisms and spiking Vision Transformer architectures, which are entirely based on synaptic operations [45] and fully spikedriven [41, 44]. These works completely resolve the incompatibility of the self-attention mechanism with SNNs, significantly outperforming existing spiking convolutional neural networks. However, these approaches have certain limitations. Specifically, the spiking transformer architectures of these methods exhibit a bottleneck in extracting local features. They employ a shallow convolutional network before the Transformer encoder to extract local features and reduce the size of feature maps. However, the effectiveness of such a shallow network is limited compared to Transformer encoders. Replacing this shallow network with a Transformer encoder is not feasible. This is because their spiking self-attention mechanisms lack reasonable scaling methods, making them suitable only for small feature maps. Designing proper scaling factors for these mechanisms is challenging as the input currents to neurons, which generate self-attention, do not possess simple mean and variance forms. Thus, there is a pressing need to design a new spiking self-attention mechanism with a reasonable scaling method that can effectively handle large feature maps." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.473, + 0.716 + ], + "angle": 0, + "content": "To address these problems, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven, compatible with SNNs, and eliminates the need for direct spike multiplications. In addition, we detail the scaling method in DSSA, enabling it to adapt to adapt to feature maps of arbitrary scales. Building upon DSSA, we propose SpikingResformer, a novel spiking Vision Transformer architecture. This architecture combines the ResNet-based multistage design with our proposed spiking self-attention mechanism. Experimental results show that our proposed SpikingResformer significantly outperforms the performance of existing spiking Vision Transformers with fewer parameters and less energy consumption. The main contributions of this paper can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.72, + 0.47, + 0.78 + ], + "angle": 0, + "content": "- We propose the Dual Spike Self-Attention (DSSA), a novel spiking self-attention mechanism. It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.781, + 0.47, + 0.81 + ], + "angle": 0, + "content": "- We detail the scaling factors employed in DSSA, enabling DSSA to handle feature maps of arbitrary scales." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.469, + 0.856 + ], + "angle": 0, + "content": "- We propose the SpikingResformer architecture, which combines the ResNet-based multi-stage architecture with our proposed DSSA." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.857, + 0.469, + 0.901 + ], + "angle": 0, + "content": "- Experimental results show that the proposed SpikingReformer significantly outperforms other spiking Vision Transformer counterparts with fewer parame" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.092, + 0.892, + 0.138 + ], + "angle": 0, + "content": "ters and lower energy consumption. Notably, our SpikingResformer-L achieves up to \\(79.40\\%\\) top-1 accuracy on ImageNet." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.148, + 0.642, + 0.164 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.173, + 0.892, + 0.505 + ], + "angle": 0, + "content": "Spiking Convolutional Neural Networks. Spiking convolutional neural networks (SCNNs) have been extensively developed due to the remarkable success of surrogate gradient learning [30, 42] and are widely used in handling challenging vision tasks, including object recognition [1, 20], detection [17, 35], and segmentation [18, 31]. To improve the performance of SCNNs on these challenging tasks, researchers have dedicated great efforts to exploring training methods [6, 12, 21, 28, 38, 40, 46, 47] and ANN-to-SNN conversion techniques [2, 3, 5, 7, 13-16, 22, 24, 34, 39]. Moreover, many deep spiking convolutional architectures [9, 14, 21, 34, 43] have been proposed to achieve high performance. The success of SpikingVGG [21, 34] demonstrates that SCNNs can achieve comparable performance to ANNs in recognition tasks. SpikingResNet [14, 43] further explores SCNNs with residual structure and achieves deeper SCNN with ResNet-based architecture. Moreover, SEW ResNet [9] meticulously analyzes the identity mapping in directly-trained spiking residual networks and successfully trains a 152-layer SCNN directly. These architectures leverage large-scale SNNs with numerous layers and demonstrate superior performance on various tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.893, + 0.747 + ], + "angle": 0, + "content": "Spiking Vision Transformers. Spikformer [45] is the first directly-trained spiking vision transformer with a pure SNN architecture. It introduces a spiking self-attention mechanism that eliminates multiplication by activating Query, Key, and Value with spiking neurons and replacing softmax with spiking neurons. In addition, it replaces layer normalization and GELU activation in the Transformer with batch normalization and spiking neurons. Based on Spikformer, Spikingformer [44] achieves a purely spike-driven Vision Transformer by modifying the residual connection paradigm. Spike-driven Transformer [41] proposes a spikedriven self-attention mechanism with linear complexity, effectively reducing energy consumption. However, all of these efforts employ a shallow convolutional network to pre-extract local information to form a sequence of patches and lack proper scaling methods." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.758, + 0.627, + 0.775 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.784, + 0.892, + 0.827 + ], + "angle": 0, + "content": "We describe the dynamics of the Leaky Integrate-and-Fire (LIF) neuron used in this paper by the following discrete-time model:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.831, + 0.892, + 0.86 + ], + "angle": 0, + "content": "\\[\nv _ {i} [ t ] = u _ {i} [ t ] + \\frac {1}{\\tau} \\left(I _ {i} [ t ] - \\left(u _ {i} [ t ] - u _ {\\text {r e s t}}\\right)\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.862, + 0.892, + 0.879 + ], + "angle": 0, + "content": "\\[\ns _ {i} [ t ] = H \\left(v _ {i} [ t ] - u _ {\\mathrm {t h}}\\right), \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.881, + 0.892, + 0.898 + ], + "angle": 0, + "content": "\\[\nu _ {i} [ t + 1 ] = s _ {i} [ t ] u _ {\\text {r e s t}} + (1 - s _ {i} [ t ]) v _ {i} [ t ]. \\tag {3}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5611" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.273 + ], + "angle": 0, + "content": "Eq. (1) describes the charging process. Here \\( u_{i}[t] \\) and \\( v_{i}[t] \\) denote the membrane potential of \\( i \\)-th postsynaptic neuron before and after charging. \\( \\tau \\) is the membrane time constant. \\( I_{i}[t] \\) denotes the input current. In general, \\( I_{i}[t] = \\sum_{j} w_{i,j} s_{j}[t] \\), where \\( s_{j}[t] \\in \\{0, 1\\} \\) represents the spike output of the \\( j \\)-th presynaptic neuron at time-step \\( t \\), and \\( w_{i,j} \\) represents the weight of the corresponding synaptic connection from neuron \\( j \\) to neuron \\( i \\). Eq. (2) describes the firing process, where \\( H(\\cdot) \\) is the Heaviside function, \\( s_{i}[t] \\in \\{0, 1\\} \\) is the spike output of the spiking neuron, \\( u_{\\mathrm{th}} \\) denotes the firing threshold. Eq. (3) describes the resetting process, with \\( u_{\\mathrm{rest}} \\) denoting the resting potential." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.273, + 0.47, + 0.303 + ], + "angle": 0, + "content": "For the sake of simplicity and clarity in subsequent sections, we represent the spiking neuron model as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.231, + 0.314, + 0.47, + 0.33 + ], + "angle": 0, + "content": "\\[\n\\mathbf {S} = \\operatorname {S N} (\\mathbf {I}), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.341, + 0.47, + 0.402 + ], + "angle": 0, + "content": "where \\(\\mathrm{SN}(\\cdot)\\) denotes the spiking neuron layer, omitting the dynamic processes within the neuron, \\(\\mathbf{I}\\in \\mathbb{R}^{T\\times n}\\) is the input current, where \\(T\\) is the time step and \\(n\\) is the number of neurons, \\(\\mathbf{S}\\in \\{0,1\\}^{T\\times n}\\) is the corresponding spike output." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.414, + 0.317, + 0.431 + ], + "angle": 0, + "content": "4. Dual Spike Self-Attention" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.439, + 0.469, + 0.53 + ], + "angle": 0, + "content": "This section first revisits the vanilla self-attention (VSA) mechanism commonly used in ANNs and analyzes why VSA is not suitable for SNNs. Then, we propose dual spike self-attention (DSSA), specifically designed for compatibility. We further discuss the significance of the scaling factor in DSSA and the spike-driven characteristic of DSSA." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.539, + 0.281, + 0.554 + ], + "angle": 0, + "content": "4.1. Vanilla Self-Attention" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.562, + 0.469, + 0.592 + ], + "angle": 0, + "content": "The vanilla self-attention in Transformer [36] can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.604, + 0.469, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {V}, \\tag {5}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.116, + 0.623, + 0.469, + 0.664 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\mathrm {T}}}{\\sqrt {d}}\\right) \\mathbf {V} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Here \\(\\mathbf{Q},\\mathbf{K},\\mathbf{V}\\in \\mathbb{R}^{n\\times d}\\) denote Query, Key and Value, respectively. \\(n\\) is the number of patches, \\(d\\) is the embedding dimension. We assume that \\(\\mathbf{Q},\\mathbf{K},\\mathbf{V}\\) have the same embedding dimension. \\(\\mathbf{X}\\in \\mathbb{R}^{n\\times d}\\) is the input of selfattention block, \\(\\mathbf{W}_Q,\\mathbf{W}_K,\\mathbf{W}_V\\in \\mathbb{R}^{d\\times d}\\) are the weights of the linear transformations corresponding to \\(\\mathbf{Q},\\mathbf{K},\\mathbf{V}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The vanilla self-attention commonly used in ANNs is not suitable for SNNs due to the following two types of operations involved: 1) the float-point matrix multiplication of \\(\\mathbf{Q}\\) and \\(\\mathbf{K}\\), as well as between the attention map and \\(\\mathbf{V}\\); 2) the softmax function, which contains exponentiation and division operations. These operations rely on float-point multiplication, division, and exponentiation operations, which are not compatible with the restrictions of SNNs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.734, + 0.107 + ], + "angle": 0, + "content": "4.2. Dual Spike Self-Attention" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.219 + ], + "angle": 0, + "content": "To introduce the self-attention mechanism into SNNs and efficiently handle the multi-scale feature maps, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). DSSA only utilizes Dual Spike Transformation (DST), thereby eliminating the need for the float-point matrix multiplication and softmax function. We first define the DST as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.55, + 0.226, + 0.892, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\operatorname {D S T} (\\mathbf {X}, \\mathbf {Y}; f (\\cdot)) = \\mathbf {X} f (\\mathbf {Y}) = \\mathbf {X Y W}, \\tag {7}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.541, + 0.245, + 0.892, + 0.265 + ], + "angle": 0, + "content": "\\[\n\\mathrm {D S T} _ {\\mathrm {T}} (\\mathbf {X}, \\mathbf {Y}; f (\\cdot)) = \\mathbf {X} f (\\mathbf {Y}) ^ {\\mathrm {T}} = \\mathbf {X} \\mathbf {W} ^ {\\mathrm {T}} \\mathbf {Y} ^ {\\mathrm {T}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.27, + 0.893, + 0.527 + ], + "angle": 0, + "content": "In Eq. (7), \\(\\mathbf{X} \\in \\{0,1\\}^{T \\times p \\times m}\\) and \\(\\mathbf{Y} \\in \\{0,1\\}^{T \\times m \\times q}\\) represent the dual spike inputs. \\(T\\) is the time steps, \\(p, m, q\\) denote arbitrary dimensions. Here \\(f(\\cdot)\\) is a generalized linear transformation on \\(\\mathbf{Y}\\), with \\(\\mathbf{W} \\in \\mathbb{R}^{q \\times q}\\) denoting its weight matrix. It represents any operation that can be equated to a linear transformation, including convolution, batch normalization (ignoring bias), etc. A detailed discussion on the equivalence of convolution operations to linear transformations can be found in the supplementary. Similarly, in Eq. (8), we have \\(\\mathbf{Y} \\in \\{0,1\\}^{T \\times q \\times m}\\), \\(\\mathbf{W} \\in \\mathbb{R}^{m \\times m}\\). Since \\(\\mathbf{X}\\) and \\(\\mathbf{Y}\\) are both spike matrices, all matrix multiplications are equivalent to the summation of weights. Consequently, the DST avoids floating-point multiplication, making it compatible with SNNs. Further discussion of the compatibility and the spike-driven characteristic of DST can be found in Sec. 4.4. Based on DST, the attention map in DSSA can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.535, + 0.892, + 0.551 + ], + "angle": 0, + "content": "\\[\n\\operatorname {A t t n M a p} (\\mathbf {X}) = \\operatorname {S N} \\left(\\mathrm {D S T} _ {\\mathrm {T}} (\\mathbf {X}, \\mathbf {X}; f (\\cdot)) * c _ {1}\\right), \\tag {9}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.553, + 0.892, + 0.57 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {\\mathrm {p}} (\\mathbf {X})\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.893, + 0.864 + ], + "angle": 0, + "content": "where \\(\\mathbf{X} \\in \\{0,1\\}^{T \\times HW \\times d}\\) is the spike input, with \\(H\\) and \\(W\\) denoting the spatial height and width of the input, \\(d\\) denoting the embedding dimension. \\(\\mathrm{BN}(\\cdot)\\) refers to the batch normalization layer, \\(\\mathrm{Conv}_{\\mathrm{p}}(\\cdot)\\) denotes a \\(p \\times p\\) convolution with a stride of \\(p\\), and \\(c_{1}\\) is the scaling factor. Since the convolution operation is equivalent to a generalized linear transformation, and batch normalization can be absorbed into the convolution (ignoring bias), \\(\\mathrm{BN}(\\mathrm{Conv}_{\\mathrm{p}}(\\cdot))\\) can be viewed as a generalized linear transformation. Here we use the \\(p \\times p\\) convolution with a stride of \\(p\\) to reduce the spatial size to handle the multi-scale feature map and reduce the computational overhead. In DSSA, there is no need for the softmax function since the spiking neuron layer inherently generates a binary attention map composed of spikes. Each spike \\(s_{ij}\\) in this spiking attention map signifies attention between patch \\(i\\) and patch \\(j\\). We believe that such a spiking attention map is more interpretable compared to the attention map in ANN activated with softmax. With the spiking attention map, the DSSA can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.516, + 0.87, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\operatorname {D S S A} (\\mathbf {X}) = \\operatorname {S N} (\\operatorname {D S T} (\\operatorname {A t t n M a p} (\\mathbf {X}), \\mathbf {X}; f (\\cdot)) * c _ {2}), \\tag {11}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5612" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.093, + 0.885, + 0.399 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.41, + 0.893, + 0.438 + ], + "angle": 0, + "content": "Figure 2. Left: Architecture of SpikingResformer and components including Dual Spike Self-Attention (DSSA), Multi-Head DSSA (MHDSSA), and Group-Wise Spiking Feed-Forward Network (GWSFFN). Right: Architecture of SEW ResNet-50 and Spikformer." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.465, + 0.471, + 0.526 + ], + "angle": 0, + "content": "where \\( c_{2} \\) is the second scaling factor. Since the form of DSSA is quite different from VSA and existing spiking self-attention mechanisms, we further discuss how DSSA achieves self-attention in the supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.535, + 0.303, + 0.551 + ], + "angle": 0, + "content": "4.3. Scaling Factors in DSSA" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.47, + 0.723 + ], + "angle": 0, + "content": "In the vanilla self-attention mechanism [36], the product of matrices \\(\\mathbf{Q}\\) and \\(\\mathbf{K}\\) in Eq. (6) is scaled by a factor of \\(1 / \\sqrt{d}\\) before applying the softmax operation. This scaling is necessary because the magnitude of \\(\\mathbf{Q}\\mathbf{K}^{\\mathrm{T}}\\) grows with the embedding dimension \\(d_{k}\\), which can result in gradient vanishing issues after the softmax operation. Formally, assume that all the elements in \\(\\mathbf{Q}\\) and \\(\\mathbf{K}\\) are independent random variables with a mean of 0 and a variance of 1, then each element in their product \\(\\mathbf{Q}\\mathbf{K}^{\\mathrm{T}}\\) has mean 0 and variance \\(d\\). By multiplying the product with a factor of \\(1 / \\sqrt{d}\\), the variance of the product is scaled to 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.86 + ], + "angle": 0, + "content": "While DSSA does not employ the softmax function, the surrogate gradient also suffers gradient vanishes without scaling. However, directly using the scaling factor of VSA is not feasible. Due to the spike-based nature of the input in DST and the attention map in DSSA, we cannot assume that they possess a mean of 0 and a variance of 1. Therefore, the scaling factor values in DSSA should be different from those used in VSA. In the following theorem, we present the mean and variance of DST." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Theorem 1 (Mean and variance of DST). Given spike input \\(\\mathbf{X} \\in \\{0,1\\}^{T \\times p \\times m}\\), \\(\\mathbf{Y} \\in \\{0,1\\}^{T \\times m \\times q}\\) and linear" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.893, + 0.603 + ], + "angle": 0, + "content": "transformation \\(f(\\cdot)\\) with weight matrix \\(\\mathbf{W} \\in \\mathbb{R}^{q \\times q}\\), \\(\\mathbf{I} \\in \\mathbb{R}^{T \\times p \\times q}\\) is the output of DST, \\(\\mathbf{I} = \\mathrm{DST}(\\mathbf{X},\\mathbf{Y};f(\\cdot))\\). Assume that all elements in \\(\\mathbf{X}\\) and \\(\\mathbf{Y}\\) are independent random variables, \\(x_{i_x,j_x}[t]\\) in \\(\\mathbf{X}\\) subject to Bernoulli distribution \\(x_{i_x,j_x}[t] \\sim B(f_x)\\), and the output of linear transformation \\(f(\\mathbf{Y})\\) has mean 0 and variance 1, we have \\(\\operatorname{E}(I_{i_I,j_I}[t]) = 0\\), \\(\\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm\\). Similarly, for \\(\\mathbf{I} = \\mathrm{DST}_{\\mathrm{T}}(\\mathbf{X},\\mathbf{Y};f(\\cdot))\\) and \\(\\mathbf{Y} \\in \\{0,1\\}^{T \\times q \\times m}\\), \\(\\mathbf{W} \\in \\mathbb{R}^{m \\times m}\\), we also have \\(\\operatorname{E}(I_{i_I,j_I}[t]) = 0\\), \\(\\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.892, + 0.675 + ], + "angle": 0, + "content": "The proof of Theorem 1 can be found in the supplementary. According to Theorem 1, we have \\( c_{1} = 1 / \\sqrt{f_{X}d} \\), \\( c_{2} = 1 / \\sqrt{f_{Attn}HW / p^{2}} \\). Here \\( f_{X} \\) and \\( f_{Attn} \\) are the average firing rate of \\( \\mathbf{X} \\) and spiking attention map, respectively." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.685, + 0.819, + 0.701 + ], + "angle": 0, + "content": "4.4. Spike-driven Characteristic of DSSA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.708, + 0.892, + 0.815 + ], + "angle": 0, + "content": "The spike-driven characteristic is important for SNNs, i.e., the computation is sparsely triggered with spikes and requires only synaptic operations. Previous work has made a great effort in achieving spike-driven Transformers [41, 44]. In this subsection, we delve into the spike-driven characteristic of DSSA and prove that DSSA is spike-driven. We first give the formal definition of the spike-driven characteristic." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.827, + 0.892, + 0.858 + ], + "angle": 0, + "content": "Definition 1. A spiking neural network is spike-driven if the input currents of all neurons satisfy the following form:" + }, + { + "type": "equation", + "bbox": [ + 0.574, + 0.869, + 0.892, + 0.904 + ], + "angle": 0, + "content": "\\[\nI _ {i} [ t ] = \\sum_ {j} w _ {i, j} s _ {j} [ t ] = \\sum_ {j, s _ {j} [ t ] \\neq 0} w _ {i, j}, \\tag {12}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5613" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "where \\( I_{i}[t] \\) is the input current of the \\( i \\)-th postsynaptic neuron at time step \\( t \\), \\( s_{j}[t] \\in \\{0,1\\} \\) is the spike output of the \\( j \\)-th presynaptic neuron, \\( w_{i,j} \\) is the weight of the synaptic connection from neuron \\( j \\) to neuron \\( i \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.163, + 0.469, + 0.239 + ], + "angle": 0, + "content": "This definition reveals the nature of the spike-driven characteristic, i.e., the accumulation of input current is sparsely triggered by spikes emitted from presynaptic neurons. It is evident that commonly used linear layers and convolution layers satisfy this definition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.239, + 0.47, + 0.315 + ], + "angle": 0, + "content": "The DSSA has only two spiking neuron layers, including the spiking attention map layer and the output layer. Both of these layers receive input currents derived from DST. Thus, we only need to validate that the DST satisfies the form in Definition 1. We first validate the \\(\\mathrm{DST}_{\\mathrm{T}}\\) in Eq. (8)" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.326, + 0.469, + 0.343 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} = \\mathbf {X} \\mathbf {W} ^ {\\mathrm {T}} \\mathbf {Y} ^ {\\mathrm {T}}, \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.086, + 0.347, + 0.469, + 0.414 + ], + "angle": 0, + "content": "\\[\nI _ {i, j} [ t ] = \\sum_ {k = 1} ^ {m} \\sum_ {l = 1} ^ {m} x _ {i, k} [ t ] w _ {l, k} y _ {j, l} [ t ] = \\sum_ {\\substack {k, l \\\\ (x _ {i, k} [ t ] \\wedge y _ {j, l} [ t ]) \\neq 0}} w _ {l, k}. \\tag{14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.469, + 0.502 + ], + "angle": 0, + "content": "Slightly different from Definition 1, the spike input here is the logical AND of dual spikes. This can be viewed as a synaptic operation requiring dual spikes to trigger, which is the reason it is called dual spike transformation. Similar to the \\(\\mathrm{DST}_{\\mathrm{T}}\\), the DST in Eq. (7) can also be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.117, + 0.53, + 0.469, + 0.546 + ], + "angle": 0, + "content": "\\[\n\\mathbf {I} = \\mathbf {X Y W}, \\tag {15}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.55, + 0.469, + 0.617 + ], + "angle": 0, + "content": "\\[\nI _ {i, j} [ t ] = \\sum_ {k = 1} ^ {m} \\sum_ {l = 1} ^ {q} x _ {i, k} [ t ] y _ {k, l} [ t ] w _ {l, j} = \\sum_ {\\substack {k, l \\\\ (x _ {i, k} [ t ] \\wedge y _ {k, l} [ t ]) \\neq 0}} w _ {l, j}. \\tag{16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.63, + 0.268, + 0.645 + ], + "angle": 0, + "content": "Thus, DSSA is spike-driven." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.66, + 0.255, + 0.677 + ], + "angle": 0, + "content": "5. SpikingResformer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.469, + 0.746 + ], + "angle": 0, + "content": "In this section, we first introduce the overall architecture of the proposed SpikingResformer and compare it with existing SEW ResNet [9] and Spikformer [45]. Then we detail the design of the spiking resformer block." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.274, + 0.771 + ], + "angle": 0, + "content": "5.1. Overall Architecture" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The overall pipeline of SEW ResNet [9], Spikformer [45], and the proposed SpikingResformer are shown in Fig. 2. As shown in Fig. 2, Spikformer employs a Spiking Patch Splitting (SPS) module to project an image to \\(d\\) dimensional feature with reduced spatial size. However, the local information can only be poorly modeled by this shallow spiking convolutional module and it only generates single-scale feature maps. On the other hand, SEW ResNet is much" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.212 + ], + "angle": 0, + "content": "deeper than the SPS in Spikformer and have a greater capability in extracting multi-scale feature with the multi-stage architecture, but lacks the global self-attention mechanism which helps extract global information. To overcome the limitations of these architectures while exploiting their advantages, we propose SpikingResformer, which combines the ResNet-based architecture and the spiking self-attention mechanism." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.212, + 0.893, + 0.455 + ], + "angle": 0, + "content": "The details of the overall architecture of SpikingResformer series are listed in Tab. 1. Similar to the ResNet-based SNNs [9, 14], our model starts with a stem architecture consisting of a \\(7 \\times 7\\) convolution and a \\(3 \\times 3\\) max pooling to pre-extract localized features and employs a multistage backbone to generate multi-scale feature maps. In each stage, multiple spiking Resformer blocks are stacked sequentially. Each spiking Resformer block consists of two modules, named Multi-Head Dual Spike Self-Attention (MHDSSA) block and Group-Wise Spiking Feed-Forward Network (GWSFFN). A downsample layer is applied before each stage (except the first stage) to reduce the size of the feature maps and project them to a higher dimension (\\(2 \\times\\) downsampling of resolution with \\(2 \\times\\) enlargement of dimension). Finally, the model ends with a global average pooling layer and a classification layer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.462, + 0.729, + 0.478 + ], + "angle": 0, + "content": "5.2. Spiking Resformer Block" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.574 + ], + "angle": 0, + "content": "As illustrated in Fig. 2, the spiking Resformer block consists of a Multi-Head Dual Spike Self-Attention (MHDSSA) module and a Group-Wise Spiking Feed-Forward Network (GWSFFN). We first introduce the two modules and then derive the form of the spiking Resformer block." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.575, + 0.892, + 0.727 + ], + "angle": 0, + "content": "Multi-Head Convolutional Spiking Self-Attention. In Sec. 4, we propose the single-head form of DSSA. It can be easily extended to the multi-head DSSA (MHDSSA) following a similar approach to the vanilla Transformer [36]. In MHDSSA, we first split the results of linear transformation in DST into \\( h \\) heads, then perform DSSA on each head and concatenate them together. Finally, we use point-wise convolution to project the concatenated features thus fusing the features in different heads. The MHDSSA can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.733, + 0.891, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\operatorname {M H D S S A} (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {1} \\left([ \\mathrm {D S S A} _ {i} (\\operatorname {S N} (\\mathbf {X})) ] _ {i = 1} ^ {h}\\right)\\right), \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.891, + 0.795 + ], + "angle": 0, + "content": "where \\([\\ldots]\\) denotes the concatenate operation, \\(\\mathrm{Conv}_1\\) denotes the point-wise convolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Group-Wise Spiking Feed-Forward Network. The spiking feed-forward network (SFFN) proposed in previous spiking vision transformers is composed of two linear layers with batch normalization and spiking neuron activation [41, 45]. Moreover, the expansion ratio is usually set to 4, i.e., the first layer raises the dimension by a factor of 4 while the second layer reduces to the original dimension." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5614" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Architectures of SpikingResformer series. The output size corresponds to the input size of \\(224 \\times 224\\). \\(D_{i}\\) and \\(H_{i}\\) are the embedding dimension and number of heads of MHDSSA in stage \\(i\\), respectively. \\(p_i\\) denotes that the MHDSSA in stage \\(i\\) uses \\(p_i \\times p_i\\) convolution in DST. \\(R_{i}\\) and \\(G_{i}\\) denote the expansion ratio and embedding dimension per group of GWSFFN in stage \\(i\\), respectively." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.143, + 0.892, + 0.354 + ], + "angle": 0, + "content": "
StageOutput SizeLayer NameSpikingResformer-TiSpikingResformer-SSpikingResformer-MSpikingResformer-L
Stem56×56StemConv 7×7, stride 2, Maxpooling 3×3, stride 2
Stage 156×56MHDSSA[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=128H1=1,p1=4R1=4,G1=64] × 1
GWSFFN
Stage 228×28DownsampleConv 3×3, 192, stride 2Conv 3×3, 256, stride 2Conv 3×3, 384, stride 2Conv 3×3, 512, stride 2
MHDSSA[D2=192H2=3,p2=2R2=4,G2=64] × 2[D2=256H2=4,p2=2R2=4,G2=64] × 2[D2=384H2=6,p2=2R2=4,G2=64] × 2[D2=512H2=8,p2=2R2=4,G2=64] × 2
GWSFFN
Stage 314×14DownsampleConv 3×3, 384, stride 2Conv 3×3, 512, stride 2Conv 3×3, 768, stride 2Conv 3×3, 1024, stride 2
MHDSSA[D3=384H3=6,p3=1R3=4,G3=64] × 3[D3=512H3=8,p3=1R3=4,G3=64] × 3[D3=768H3=12,p3=1R3=4,G3=64] × 3[D3=1024H3=16,p3=1R3=4,G3=64] × 3
GWSFFN
Classifier1×1Linear1000-FC
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.378, + 0.473, + 0.528 + ], + "angle": 0, + "content": "Based on SFFN, we insert a \\(3 \\times 3\\) convolution layer with the residual connection between two linear layers to enable SFFN to extract local features. Since the dimension of the hidden features between the two linear layers is expanded by a factor of 4 compared to the input, in order to reduce the number of parameters and computational overhead, we use group-wise convolution and set every 64 channels as 1 group. We also employ the spike-driven design in [41, 44]. The group-wise spiking feed-forward network (GWSFFN) can be formulated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.127, + 0.541, + 0.469, + 0.558 + ], + "angle": 0, + "content": "\\[\n\\operatorname {F F L} _ {i} (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {1} (\\operatorname {S N} (\\mathbf {X}))\\right), i = 1, 2, \\tag {18}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.126, + 0.56, + 0.469, + 0.576 + ], + "angle": 0, + "content": "\\[\n\\operatorname {G W L} (\\mathbf {X}) = \\operatorname {B N} (\\operatorname {G W C o n v} (\\operatorname {S N} (\\mathbf {X}))) + \\mathbf {X}, \\tag {19}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.579, + 0.469, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\operatorname {G W S F F N} (\\mathbf {X}) = \\operatorname {F F L} _ {2} (\\operatorname {G W L} (\\operatorname {F F L} _ {1} (\\mathbf {X}))). \\tag {20}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.607, + 0.469, + 0.681 + ], + "angle": 0, + "content": "Here \\(\\mathrm{FFL}_i(\\cdot), i = 1,2\\) denote the feed-forward layers, \\(\\mathrm{Conv}_1(\\cdot)\\) is point-wise convolution (\\(1 \\times 1\\) convolution), which equal to the linear transformation. \\(\\mathrm{GWL}(\\cdot)\\) denotes group-wise convolution layer, \\(\\mathrm{GWConv}(\\cdot)\\) denotes the group-wise convolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.682, + 0.47, + 0.726 + ], + "angle": 0, + "content": "Spiking Resformer Block. With the MHDSSA module and GWSFFN above, the spiking resformer block can be formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.74, + 0.469, + 0.756 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} _ {i} = \\operatorname {M H D S S A} \\left(\\mathbf {X} _ {i}\\right) + \\mathbf {X} _ {i}, \\tag {21}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.758, + 0.469, + 0.775 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} _ {i + 1} = \\operatorname {G W S F N} \\left(\\mathbf {Y} _ {i}\\right) + \\mathbf {Y} _ {i}. \\tag {22}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.786, + 0.47, + 0.817 + ], + "angle": 0, + "content": "where \\(\\mathbf{Y}_i\\) denotes the output features of MHDSSA module in the \\(i\\)-th spiking reformer block." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.21, + 0.848 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this section, we first evaluate the performance and energy efficiency of SpikingResformer on the ImageNet classification task. Then, we perform ablation experiments on key" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.378, + 0.892, + 0.409 + ], + "angle": 0, + "content": "components in SpikingResformer. Finally, we evaluate the transfer learning ability of SpikingResformer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.419, + 0.72, + 0.435 + ], + "angle": 0, + "content": "6.1. ImageNet Classification" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.443, + 0.892, + 0.518 + ], + "angle": 0, + "content": "ImageNet [4] is one of the most typical static image datasets widely used for image classification. For a fair comparison, we generally follow the data augmentation strategy and training setup in [41]. More details of the experimental setup can be found in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.519, + 0.893, + 0.76 + ], + "angle": 0, + "content": "Results. Our experimental results are listed in Tab. 2. For comparison, we also list the results of existing spiking convolutional networks and spiking Vision Transformers. As shown in Tab. 2, SpikingResformer achieves higher accuracy, fewer parameters, and lower energy consumption at the same time compared to existing methods. For instance, SpikingResformer-Ti achieves \\(74.34\\%\\) accuracy with only 11.14M parameters and 2.73G SOPs \\((2.46\\mathrm{mJ})\\), outperforming Spike-driven Transformer-8-384 by \\(2.06\\%\\), saving 5.67M parameters and \\(1.44\\mathrm{mJ}\\) energy. SpikingResformer-M achieves \\(77.24\\%\\) accuracy with 35.52M parameters and 6.07G SOPs \\((5.46\\mathrm{mJ})\\), outperforming Spike-driven Transformer-8-768 by \\(0.92\\%\\) while saving 30.82M parameters. Particularly, the SpikingResformer-L achieves up to \\(79.40\\%\\) accuracy when the input size is enlarged to \\(288\\times 288\\), which is the state-of-the-art result in SNN field." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.655, + 0.789 + ], + "angle": 0, + "content": "6.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.796, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We perform ablation experiments on key components in SpikingResformer, including the multi-stage architecture, the group-wise convolution layer in GWSFFN, and our proposed spiking self-attention mechanism. The ablation experiments are conducted on the ImageNet100 dataset, which is a subset of the ImageNet dataset and consists of 100 categories from the ImageNet dataset. The experiment" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5615" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.133 + ], + "angle": 0, + "content": "Table 2. Evaluation on ImageNet. SOPs denotes the average synaptic operations of an image inference on ImageNet validation data. Energy is the estimation of energy consumption same as [41, 45]. The default input resolution for training and inference is \\(224 \\times 224\\). \\(\\dagger\\) means the input is enlarged to \\(288 \\times 288\\) in inference. - means the data is not provided in the original paper." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.143, + 0.892, + 0.491 + ], + "angle": 0, + "content": "
MethodTypeArchitectureTParam (M)SOPs (G)Energy (mJ)Top-1 Acc. (%)
Spiking ResNet [14]ANN-to-SNNResNet-3435021.7965.2859.3071.61
ResNet-5035025.5678.2970.9372.75
STBP-tdBN [43]Direct TrainingSpiking ResNet-34621.796.506.3963.72
TET [6]Direct TrainingSpiking ResNet-34621.79--64.79
SEW ResNet-34421.79--68.00
SEW ResNet [9]Direct TrainingSEW ResNet-34421.793.884.0467.04
SEW ResNet-50425.564.834.8967.78
SEW ResNet-101444.559.308.9168.76
SEW ResNet-152460.1913.7212.8969.26
Spikformer [45]Direct TrainingSpikformer-8-384416.816.827.7370.24
Spikformer-8-512429.6811.0911.5873.38
Spikformer-8-768466.3422.0921.4874.81
Spikingformer [44]Direct TrainingSpikingformer-8-384416.81-4.6972.45
Spikingformer-8-512429.68-7.4674.79
Spikingformer-8-768466.34-13.6875.85
Spike-driven Transformer [41]Direct TrainingSpike-driven Transformer-8-384416.81-3.9072.28
Spike-driven Transformer-8-512429.68-4.5074.57
Spike-driven Transformer-8-768466.34-/-6.09/-76.32/77.07†
SpikingResformer (Ours)Direct TrainingSpikingResformer-Ti411.142.73/4.71†2.46/4.24†74.34/75.57†
SpikingResformer-S417.763.74/6.40†3.37/5.76†75.95/76.90†
SpikingResformer-M435.526.07/10.24†5.46/9.22†77.24/78.06†
SpikingResformer-L460.389.74/16.40†8.76/14.76†78.77/79.40†
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.515, + 0.472, + 0.545 + ], + "angle": 0, + "content": "Table 3. Ablation Study on ImageNet100 dataset. The number of parameters for all variants is comparable to SpikingResformer-S." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.554, + 0.466, + 0.655 + ], + "angle": 0, + "content": "
ModelSOPs (G)Energy (mJ)Acc. (%)
SpikingResformer-S2.432.1888.06
w/o multi-stage architecture1.841.6685.32
w/o group-wise convolution2.372.1384.64
w/o DSSAnot converge
w/o p × p convolution4.343.9186.14
w/o scalingnot converge
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.685, + 0.47, + 0.716 + ], + "angle": 0, + "content": "tal setup basically follows the one in Sec. 6.1. Detailed settings are listed in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.717, + 0.47, + 0.853 + ], + "angle": 0, + "content": "Multi-Stage Architecture. To verify the effectiveness of the multi-stage architecture, we replace it with the Spikingformer-based architecture, while the structure of the spiking Resformer block remains unchanged. We adjust the embedding dimensions to make the model parameters comparable to SpikingResformer-S. As shown in Tab. 3, SpikingResformer-S outperforms the variant without multi-stage architecture by \\(2.74\\%\\), demonstrating the effectiveness of multi-stage architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Group-Wise Convolution Layer. In comparison to the point-wise SFFN, GWSFFN employs a \\(3 \\times 3\\) group-wise convolution layer between the two linear layers. We" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.892, + 0.625 + ], + "angle": 0, + "content": "evaluate its effect by removing the group-wise convolution layer and increasing the dimension to keep the number of parameters constant. As demonstrated in Tab. 3, SpikingResformer-S achieves \\(3.42\\%\\) higher accuracy in contrast to the variant without the group-wise convolution layer. This difference highlights the benefits of the group-wise convolution layer in GWSFFN." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Dual Spike Self-Attention. To validate the effectiveness of DSSA, we first replace DSSA with existing spiking self-attention mechanisms, including Spiking Self-Attention (SSA) in Spikformer and Spike-Driven Self-Attention (SDSA) in Spike-driven Transformer. However, neither SSA nor SDSA converges. We believe this is because SSA and SDSA do not fit the multi-scale input. To further validate the key factors that help DSSA fit for the multi-scale input, we conduct two more sets of experiments. One set replaces all \\( p \\times p \\) convolutions with \\( 1 \\times 1 \\) convolutions in DST to validate the effect of reducing spatial size. The other removes the scaling factor or replaces our proposed scaling factors with \\( 1 / \\sqrt{d} \\) to validate the effect of scaling. As a result, the first group converges but only achieves \\( 86.14\\% \\) accuracy with a higher energy consumption of \\( 3.91\\mathrm{mJ} \\), while the second set does not converge. This shows that the scaling factor is the key to convergence. We believe that both SSA and SDSA lack proper scaling meth" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5616" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.193, + 0.089, + 0.776, + 0.104 + ], + "angle": 0, + "content": "Table 4. Transfer learning results on CIFAR10, CIFAR100, CIFAR10-DVS, DVSGesture datasets." + }, + { + "type": "table", + "bbox": [ + 0.162, + 0.115, + 0.807, + 0.274 + ], + "angle": 0, + "content": "
MethodTypeCIFAR10CIFAR100CIFAR10-DVSDVSGesture
TAcc.TAcc.TAcc.TAcc.
STBP-tdBN [43]Direct Training693.16--1067.84096.87
PLIF [10]Direct Training893.50--2074.82097.57
Dspike [25]Direct Training694.25674.241075.4--
Spikformer [45]Direct Training495.19477.861680.61697.9
Spikingformer [44]Direct Training495.61479.091681.31698.3
Spike-driven Transformer [41]Direct Training495.6478.41680.01699.3
Spikformer [45]Transfer Learning497.03483.83----
SpikingResformer (Ours)Transfer Learning497.40485.981084.81093.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.299, + 0.471, + 0.39 + ], + "angle": 0, + "content": "ods, thus do not apply to multi-stage architecture. SSA employs the same scaling factor as vanilla self-attention, i.e., \\(1 / \\sqrt{d}\\). However, this does not apply to spike matrix multiplication, since spikes do not have mean 0 and variance 1. SDSA has no scaling method, which may be feasible when the feature map is small but not for multi-scale inputs." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.404, + 0.258, + 0.421 + ], + "angle": 0, + "content": "6.3. Transfer Learning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.43, + 0.47, + 0.626 + ], + "angle": 0, + "content": "High transfer learning ability is a key advantage of Vision Transformer. We evaluate the transfer learning ability of the proposed SpikingResformer on static dataset CIFAR10 and CIFAR100 [19] and neuromorphic dataset CIFAR10-DVS [23] and DVSGesture [1] by fine-tuning the models pre-trained on ImageNet. Among the existing spiking Vision Transformers, only Spikformer provides transfer learning results, and only on the static image datasets CIFAR10 and CIFAR100. Thus, we also compared our results with the direct training results for a comprehensive comparison. Tab. 4 lists the highest accuracy achieved by these methods. The experimental setup and a more detailed comparison can be found in the supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Static Image Datasets. As shown in Tab. 4, SpikingResformer achieves \\(97.40\\%\\) accuracy on CIFAR10 dataset and \\(85.98\\%\\) accuracy on CIFAR100 dataset, which is the state-of-the-art result, outperforming the transfer learning results of Spikformer by \\(0.37\\%\\) on CIFAR10 and \\(2.15\\%\\) on CIFAR100. Compared to direct training methods, SpikingResformer obtained from transfer learning has significantly better performance. For example, SpikingResformer outperforms Spikingformer by \\(6.89\\%\\) on CIFAR100 dataset, demonstrating the advantage of transfer learning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Neuromorphic Datasets. Neuromorphic datasets differ significantly from traditional static image datasets. The samples of the neuromorphic dataset consist of event streams instead of RGB images. As a result, there is a large gap between the source and target domain for models pre-trained on static image datasets. To bridge this gap, we stack the events over a period of time to form a frame. The RGB channels are replaced with positive events," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.299, + 0.895, + 0.617 + ], + "angle": 0, + "content": "negative events, and the sum of events channels, respectively. As shown in Tab. 4, transfer learning results of SpikingResformer significantly outperform the direct training ones on CIFAR10-DVS. SpikingResformer achieves \\(84.8\\%\\) accuracy on CIFAR10-DVS, outperforming Spikingformer by \\(3.5\\%\\). However, the transfer learning results on DVS-Gesture fail to achieve comparable performance to direct training. SpikingResformer only achieves \\(93.4\\%\\) accuracy on DVSGesture, falling behind the state-of-the-art method Spike-driven Transformer by \\(5.9\\%\\). We believe that this is mainly due to the way CIFAR10-DVS is constructed differs from DVSGesture. CIFAR10-DVS is converted from CIFAR10, which does not contain temporal information. Thus, models pre-trained on static datasets can transfer to CIFAR10-DVS well. However, DVSGesture is directly created from human gestures using a dynamic vision sensor, thus containing rich temporal information. As a result, models pre-trained on static datasets do not transfer well to DVSGesture. We hope our exploration of transfer learning on neuromorphic datasets could pave the way for further transfer learning research of SNNs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.628, + 0.62, + 0.643 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.653, + 0.894, + 0.82 + ], + "angle": 0, + "content": "In this paper, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs. We detail the scaling factors in DSSA enabling it to handle feature maps of arbitrary scales. Based on DSSA, we propose SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to achieve superior performance and energy efficiency with fewer parameters. Extensive experiments demonstrate the effectiveness and superiority of the proposed SpikingResformer." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.661, + 0.848 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.903 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (62176003, 62088102) and by the Beijing Nova Program (20230484362)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5617" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.198 + ], + "angle": 0, + "content": "[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. 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While existing methods propose spiking self-attention mechanisms that are compatible with SNNs, they lack reasonable scaling methods, and the overall architectures proposed by these methods suffer from a bottleneck in effectively extracting local features. To address these challenges, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA) with a reasonable scaling method. Based on DSSA, we propose a novel spiking Vision Transformer architecture called SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to improve both performance and energy efficiency while reducing parameters. Experimental results show that SpikingResformer achieves higher accuracy with fewer parameters and lower energy consumption than other spiking Vision Transformer counterparts. Notably, our SpikingResformer-L achieves $79.40\%$ top-1 accuracy on ImageNet with 4 time-steps, which is the state-of-the-art result in the SNN field. Codes are available at https://github.com/xyshi2000/SpikingResformer + +# 1. Introduction + +Spiking Neural Networks (SNNs), considered as the third generation of Artificial Neural Networks (ANNs) [27], have garnered significant attention due to their notable advantages such as low power consumption, biological plausibility, and event-driven characteristics that are compatible with neuromorphic hardware. In comparison to ANNs, SNNs exhibit an energy-saving advantage when deployed on neuromorphic hardware [11, 29, 32], and have become popular in the field of neuromorphic computing in recent years [33]. + +![](images/c83c5ee7eb46085195ceeb07a127dd65632894289d0059ed8acf1dda25e8ac69.jpg) +Figure 1. Comparison of Top-1 accuracy on ImageNet with respect to energy consumption per image for inference (left) and the number of parameters (right). The input size is $224 \times 224$ . + +However, the performance of existing SNNs still lags behind that of ANNs, particularly on challenging vision tasks, which limits further application of SNNs. + +Researchers make great efforts to enhance the performance of SNNs. Recently, inspired by the remarkable achievements of vision transformers [8, 26] in ANNs, some attempts have been made to introduce transformer-based architecture into SNNs. The main challenge in incorporating transformer structures into SNNs lies in designing a self-attention mechanism suitable for SNNs. The vanilla self-attention mechanism in ANNs relies on float-point matrix multiplication and softmax operations. However, these operations involve float-point multiplication, division, and exponentiation, which do not comply with the spike-driven nature of SNNs. Moreover, commonly used components in ANN Transformers, such as layer normalization (LN) and GELU activation, are not directly applicable in SNNs. Therefore, the introduction of transformer architectures into SNNs necessitates circumventing these operations and catering to the unique requirements of SNNs. + +Some work has attempted to partially preserve floating-point operations [37], or run an SNN and an ANN Transformer in parallel [48]. Although these approaches en + +hance performance, they do not fully address the incompatibility between vanilla self-attention and SNNs. There are also works that propose spiking self-attention mechanisms and spiking Vision Transformer architectures, which are entirely based on synaptic operations [45] and fully spikedriven [41, 44]. These works completely resolve the incompatibility of the self-attention mechanism with SNNs, significantly outperforming existing spiking convolutional neural networks. However, these approaches have certain limitations. Specifically, the spiking transformer architectures of these methods exhibit a bottleneck in extracting local features. They employ a shallow convolutional network before the Transformer encoder to extract local features and reduce the size of feature maps. However, the effectiveness of such a shallow network is limited compared to Transformer encoders. Replacing this shallow network with a Transformer encoder is not feasible. This is because their spiking self-attention mechanisms lack reasonable scaling methods, making them suitable only for small feature maps. Designing proper scaling factors for these mechanisms is challenging as the input currents to neurons, which generate self-attention, do not possess simple mean and variance forms. Thus, there is a pressing need to design a new spiking self-attention mechanism with a reasonable scaling method that can effectively handle large feature maps. + +To address these problems, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven, compatible with SNNs, and eliminates the need for direct spike multiplications. In addition, we detail the scaling method in DSSA, enabling it to adapt to adapt to feature maps of arbitrary scales. Building upon DSSA, we propose SpikingResformer, a novel spiking Vision Transformer architecture. This architecture combines the ResNet-based multistage design with our proposed spiking self-attention mechanism. Experimental results show that our proposed SpikingResformer significantly outperforms the performance of existing spiking Vision Transformers with fewer parameters and less energy consumption. The main contributions of this paper can be summarized as follows: + +- We propose the Dual Spike Self-Attention (DSSA), a novel spiking self-attention mechanism. It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs. +- We detail the scaling factors employed in DSSA, enabling DSSA to handle feature maps of arbitrary scales. +- We propose the SpikingResformer architecture, which combines the ResNet-based multi-stage architecture with our proposed DSSA. +- Experimental results show that the proposed SpikingReformer significantly outperforms other spiking Vision Transformer counterparts with fewer parame + +ters and lower energy consumption. Notably, our SpikingResformer-L achieves up to $79.40\%$ top-1 accuracy on ImageNet. + +# 2. Related Work + +Spiking Convolutional Neural Networks. Spiking convolutional neural networks (SCNNs) have been extensively developed due to the remarkable success of surrogate gradient learning [30, 42] and are widely used in handling challenging vision tasks, including object recognition [1, 20], detection [17, 35], and segmentation [18, 31]. To improve the performance of SCNNs on these challenging tasks, researchers have dedicated great efforts to exploring training methods [6, 12, 21, 28, 38, 40, 46, 47] and ANN-to-SNN conversion techniques [2, 3, 5, 7, 13-16, 22, 24, 34, 39]. Moreover, many deep spiking convolutional architectures [9, 14, 21, 34, 43] have been proposed to achieve high performance. The success of SpikingVGG [21, 34] demonstrates that SCNNs can achieve comparable performance to ANNs in recognition tasks. SpikingResNet [14, 43] further explores SCNNs with residual structure and achieves deeper SCNN with ResNet-based architecture. Moreover, SEW ResNet [9] meticulously analyzes the identity mapping in directly-trained spiking residual networks and successfully trains a 152-layer SCNN directly. These architectures leverage large-scale SNNs with numerous layers and demonstrate superior performance on various tasks. + +Spiking Vision Transformers. Spikformer [45] is the first directly-trained spiking vision transformer with a pure SNN architecture. It introduces a spiking self-attention mechanism that eliminates multiplication by activating Query, Key, and Value with spiking neurons and replacing softmax with spiking neurons. In addition, it replaces layer normalization and GELU activation in the Transformer with batch normalization and spiking neurons. Based on Spikformer, Spikingformer [44] achieves a purely spike-driven Vision Transformer by modifying the residual connection paradigm. Spike-driven Transformer [41] proposes a spikedriven self-attention mechanism with linear complexity, effectively reducing energy consumption. However, all of these efforts employ a shallow convolutional network to pre-extract local information to form a sequence of patches and lack proper scaling methods. + +# 3. Preliminary + +We describe the dynamics of the Leaky Integrate-and-Fire (LIF) neuron used in this paper by the following discrete-time model: + +$$ +v _ {i} [ t ] = u _ {i} [ t ] + \frac {1}{\tau} \left(I _ {i} [ t ] - \left(u _ {i} [ t ] - u _ {\text {r e s t}}\right)\right), \tag {1} +$$ + +$$ +s _ {i} [ t ] = H \left(v _ {i} [ t ] - u _ {\mathrm {t h}}\right), \tag {2} +$$ + +$$ +u _ {i} [ t + 1 ] = s _ {i} [ t ] u _ {\text {r e s t}} + (1 - s _ {i} [ t ]) v _ {i} [ t ]. \tag {3} +$$ + +Eq. (1) describes the charging process. Here $u_{i}[t]$ and $v_{i}[t]$ denote the membrane potential of $i$ -th postsynaptic neuron before and after charging. $\tau$ is the membrane time constant. $I_{i}[t]$ denotes the input current. In general, $I_{i}[t] = \sum_{j} w_{i,j} s_{j}[t]$ , where $s_{j}[t] \in \{0, 1\}$ represents the spike output of the $j$ -th presynaptic neuron at time-step $t$ , and $w_{i,j}$ represents the weight of the corresponding synaptic connection from neuron $j$ to neuron $i$ . Eq. (2) describes the firing process, where $H(\cdot)$ is the Heaviside function, $s_{i}[t] \in \{0, 1\}$ is the spike output of the spiking neuron, $u_{\mathrm{th}}$ denotes the firing threshold. Eq. (3) describes the resetting process, with $u_{\mathrm{rest}}$ denoting the resting potential. + +For the sake of simplicity and clarity in subsequent sections, we represent the spiking neuron model as follows: + +$$ +\mathbf {S} = \operatorname {S N} (\mathbf {I}), \tag {4} +$$ + +where $\mathrm{SN}(\cdot)$ denotes the spiking neuron layer, omitting the dynamic processes within the neuron, $\mathbf{I}\in \mathbb{R}^{T\times n}$ is the input current, where $T$ is the time step and $n$ is the number of neurons, $\mathbf{S}\in \{0,1\}^{T\times n}$ is the corresponding spike output. + +# 4. Dual Spike Self-Attention + +This section first revisits the vanilla self-attention (VSA) mechanism commonly used in ANNs and analyzes why VSA is not suitable for SNNs. Then, we propose dual spike self-attention (DSSA), specifically designed for compatibility. We further discuss the significance of the scaling factor in DSSA and the spike-driven characteristic of DSSA. + +# 4.1. Vanilla Self-Attention + +The vanilla self-attention in Transformer [36] can be formulated as follows: + +$$ +\mathbf {Q} = \mathbf {X} \mathbf {W} _ {Q}, \mathbf {K} = \mathbf {X} \mathbf {W} _ {K}, \mathbf {V} = \mathbf {X} \mathbf {W} _ {V}, \tag {5} +$$ + +$$ +\operatorname {A t t e n t i o n} (\mathbf {Q}, \mathbf {K}, \mathbf {V}) = \operatorname {S o f t m a x} \left(\frac {\mathbf {Q} \mathbf {K} ^ {\mathrm {T}}}{\sqrt {d}}\right) \mathbf {V} \tag {6} +$$ + +Here $\mathbf{Q},\mathbf{K},\mathbf{V}\in \mathbb{R}^{n\times d}$ denote Query, Key and Value, respectively. $n$ is the number of patches, $d$ is the embedding dimension. We assume that $\mathbf{Q},\mathbf{K},\mathbf{V}$ have the same embedding dimension. $\mathbf{X}\in \mathbb{R}^{n\times d}$ is the input of selfattention block, $\mathbf{W}_Q,\mathbf{W}_K,\mathbf{W}_V\in \mathbb{R}^{d\times d}$ are the weights of the linear transformations corresponding to $\mathbf{Q},\mathbf{K},\mathbf{V}$ , respectively. + +The vanilla self-attention commonly used in ANNs is not suitable for SNNs due to the following two types of operations involved: 1) the float-point matrix multiplication of $\mathbf{Q}$ and $\mathbf{K}$ , as well as between the attention map and $\mathbf{V}$ ; 2) the softmax function, which contains exponentiation and division operations. These operations rely on float-point multiplication, division, and exponentiation operations, which are not compatible with the restrictions of SNNs. + +# 4.2. Dual Spike Self-Attention + +To introduce the self-attention mechanism into SNNs and efficiently handle the multi-scale feature maps, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). DSSA only utilizes Dual Spike Transformation (DST), thereby eliminating the need for the float-point matrix multiplication and softmax function. We first define the DST as follows: + +$$ +\operatorname {D S T} (\mathbf {X}, \mathbf {Y}; f (\cdot)) = \mathbf {X} f (\mathbf {Y}) = \mathbf {X Y W}, \tag {7} +$$ + +$$ +\mathrm {D S T} _ {\mathrm {T}} (\mathbf {X}, \mathbf {Y}; f (\cdot)) = \mathbf {X} f (\mathbf {Y}) ^ {\mathrm {T}} = \mathbf {X} \mathbf {W} ^ {\mathrm {T}} \mathbf {Y} ^ {\mathrm {T}}. \tag {8} +$$ + +In Eq. (7), $\mathbf{X} \in \{0,1\}^{T \times p \times m}$ and $\mathbf{Y} \in \{0,1\}^{T \times m \times q}$ represent the dual spike inputs. $T$ is the time steps, $p, m, q$ denote arbitrary dimensions. Here $f(\cdot)$ is a generalized linear transformation on $\mathbf{Y}$ , with $\mathbf{W} \in \mathbb{R}^{q \times q}$ denoting its weight matrix. It represents any operation that can be equated to a linear transformation, including convolution, batch normalization (ignoring bias), etc. A detailed discussion on the equivalence of convolution operations to linear transformations can be found in the supplementary. Similarly, in Eq. (8), we have $\mathbf{Y} \in \{0,1\}^{T \times q \times m}$ , $\mathbf{W} \in \mathbb{R}^{m \times m}$ . Since $\mathbf{X}$ and $\mathbf{Y}$ are both spike matrices, all matrix multiplications are equivalent to the summation of weights. Consequently, the DST avoids floating-point multiplication, making it compatible with SNNs. Further discussion of the compatibility and the spike-driven characteristic of DST can be found in Sec. 4.4. Based on DST, the attention map in DSSA can be formulated as follows: + +$$ +\operatorname {A t t n M a p} (\mathbf {X}) = \operatorname {S N} \left(\mathrm {D S T} _ {\mathrm {T}} (\mathbf {X}, \mathbf {X}; f (\cdot)) * c _ {1}\right), \tag {9} +$$ + +$$ +f (\mathbf {X}) = \operatorname {B N} \left(\operatorname {C o n v} _ {\mathrm {p}} (\mathbf {X})\right), \tag {10} +$$ + +where $\mathbf{X} \in \{0,1\}^{T \times HW \times d}$ is the spike input, with $H$ and $W$ denoting the spatial height and width of the input, $d$ denoting the embedding dimension. $\mathrm{BN}(\cdot)$ refers to the batch normalization layer, $\mathrm{Conv}_{\mathrm{p}}(\cdot)$ denotes a $p \times p$ convolution with a stride of $p$ , and $c_{1}$ is the scaling factor. Since the convolution operation is equivalent to a generalized linear transformation, and batch normalization can be absorbed into the convolution (ignoring bias), $\mathrm{BN}(\mathrm{Conv}_{\mathrm{p}}(\cdot))$ can be viewed as a generalized linear transformation. Here we use the $p \times p$ convolution with a stride of $p$ to reduce the spatial size to handle the multi-scale feature map and reduce the computational overhead. In DSSA, there is no need for the softmax function since the spiking neuron layer inherently generates a binary attention map composed of spikes. Each spike $s_{ij}$ in this spiking attention map signifies attention between patch $i$ and patch $j$ . We believe that such a spiking attention map is more interpretable compared to the attention map in ANN activated with softmax. With the spiking attention map, the DSSA can be formulated as follows: + +$$ +\operatorname {D S S A} (\mathbf {X}) = \operatorname {S N} (\operatorname {D S T} (\operatorname {A t t n M a p} (\mathbf {X}), \mathbf {X}; f (\cdot)) * c _ {2}), \tag {11} +$$ + +![](images/d9f54d23994e6f7fac53498446fa400e08c44b6dd68168c3dcbfac0002b99286.jpg) +Figure 2. Left: Architecture of SpikingResformer and components including Dual Spike Self-Attention (DSSA), Multi-Head DSSA (MHDSSA), and Group-Wise Spiking Feed-Forward Network (GWSFFN). Right: Architecture of SEW ResNet-50 and Spikformer. + +where $c_{2}$ is the second scaling factor. Since the form of DSSA is quite different from VSA and existing spiking self-attention mechanisms, we further discuss how DSSA achieves self-attention in the supplementary. + +# 4.3. Scaling Factors in DSSA + +In the vanilla self-attention mechanism [36], the product of matrices $\mathbf{Q}$ and $\mathbf{K}$ in Eq. (6) is scaled by a factor of $1 / \sqrt{d}$ before applying the softmax operation. This scaling is necessary because the magnitude of $\mathbf{Q}\mathbf{K}^{\mathrm{T}}$ grows with the embedding dimension $d_{k}$ , which can result in gradient vanishing issues after the softmax operation. Formally, assume that all the elements in $\mathbf{Q}$ and $\mathbf{K}$ are independent random variables with a mean of 0 and a variance of 1, then each element in their product $\mathbf{Q}\mathbf{K}^{\mathrm{T}}$ has mean 0 and variance $d$ . By multiplying the product with a factor of $1 / \sqrt{d}$ , the variance of the product is scaled to 1. + +While DSSA does not employ the softmax function, the surrogate gradient also suffers gradient vanishes without scaling. However, directly using the scaling factor of VSA is not feasible. Due to the spike-based nature of the input in DST and the attention map in DSSA, we cannot assume that they possess a mean of 0 and a variance of 1. Therefore, the scaling factor values in DSSA should be different from those used in VSA. In the following theorem, we present the mean and variance of DST. + +Theorem 1 (Mean and variance of DST). Given spike input $\mathbf{X} \in \{0,1\}^{T \times p \times m}$ , $\mathbf{Y} \in \{0,1\}^{T \times m \times q}$ and linear + +transformation $f(\cdot)$ with weight matrix $\mathbf{W} \in \mathbb{R}^{q \times q}$ , $\mathbf{I} \in \mathbb{R}^{T \times p \times q}$ is the output of DST, $\mathbf{I} = \mathrm{DST}(\mathbf{X},\mathbf{Y};f(\cdot))$ . Assume that all elements in $\mathbf{X}$ and $\mathbf{Y}$ are independent random variables, $x_{i_x,j_x}[t]$ in $\mathbf{X}$ subject to Bernoulli distribution $x_{i_x,j_x}[t] \sim B(f_x)$ , and the output of linear transformation $f(\mathbf{Y})$ has mean 0 and variance 1, we have $\operatorname{E}(I_{i_I,j_I}[t]) = 0$ , $\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm$ . Similarly, for $\mathbf{I} = \mathrm{DST}_{\mathrm{T}}(\mathbf{X},\mathbf{Y};f(\cdot))$ and $\mathbf{Y} \in \{0,1\}^{T \times q \times m}$ , $\mathbf{W} \in \mathbb{R}^{m \times m}$ , we also have $\operatorname{E}(I_{i_I,j_I}[t]) = 0$ , $\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm$ . + +The proof of Theorem 1 can be found in the supplementary. According to Theorem 1, we have $c_{1} = 1 / \sqrt{f_{X}d}$ , $c_{2} = 1 / \sqrt{f_{Attn}HW / p^{2}}$ . Here $f_{X}$ and $f_{Attn}$ are the average firing rate of $\mathbf{X}$ and spiking attention map, respectively. + +# 4.4. Spike-driven Characteristic of DSSA + +The spike-driven characteristic is important for SNNs, i.e., the computation is sparsely triggered with spikes and requires only synaptic operations. Previous work has made a great effort in achieving spike-driven Transformers [41, 44]. In this subsection, we delve into the spike-driven characteristic of DSSA and prove that DSSA is spike-driven. We first give the formal definition of the spike-driven characteristic. + +Definition 1. A spiking neural network is spike-driven if the input currents of all neurons satisfy the following form: + +$$ +I _ {i} [ t ] = \sum_ {j} w _ {i, j} s _ {j} [ t ] = \sum_ {j, s _ {j} [ t ] \neq 0} w _ {i, j}, \tag {12} +$$ + +where $I_{i}[t]$ is the input current of the $i$ -th postsynaptic neuron at time step $t$ , $s_{j}[t] \in \{0,1\}$ is the spike output of the $j$ -th presynaptic neuron, $w_{i,j}$ is the weight of the synaptic connection from neuron $j$ to neuron $i$ . + +This definition reveals the nature of the spike-driven characteristic, i.e., the accumulation of input current is sparsely triggered by spikes emitted from presynaptic neurons. It is evident that commonly used linear layers and convolution layers satisfy this definition. + +The DSSA has only two spiking neuron layers, including the spiking attention map layer and the output layer. Both of these layers receive input currents derived from DST. Thus, we only need to validate that the DST satisfies the form in Definition 1. We first validate the $\mathrm{DST}_{\mathrm{T}}$ in Eq. (8) + +$$ +\mathbf {I} = \mathbf {X} \mathbf {W} ^ {\mathrm {T}} \mathbf {Y} ^ {\mathrm {T}}, \tag {13} +$$ + +$$ +I _ {i, j} [ t ] = \sum_ {k = 1} ^ {m} \sum_ {l = 1} ^ {m} x _ {i, k} [ t ] w _ {l, k} y _ {j, l} [ t ] = \sum_ {\substack {k, l \\ (x _ {i, k} [ t ] \wedge y _ {j, l} [ t ]) \neq 0}} w _ {l, k}. \tag{14} +$$ + +Slightly different from Definition 1, the spike input here is the logical AND of dual spikes. This can be viewed as a synaptic operation requiring dual spikes to trigger, which is the reason it is called dual spike transformation. Similar to the $\mathrm{DST}_{\mathrm{T}}$ , the DST in Eq. (7) can also be formulated as: + +$$ +\mathbf {I} = \mathbf {X Y W}, \tag {15} +$$ + +$$ +I _ {i, j} [ t ] = \sum_ {k = 1} ^ {m} \sum_ {l = 1} ^ {q} x _ {i, k} [ t ] y _ {k, l} [ t ] w _ {l, j} = \sum_ {\substack {k, l \\ (x _ {i, k} [ t ] \wedge y _ {k, l} [ t ]) \neq 0}} w _ {l, j}. \tag{16} +$$ + +Thus, DSSA is spike-driven. + +# 5. SpikingResformer + +In this section, we first introduce the overall architecture of the proposed SpikingResformer and compare it with existing SEW ResNet [9] and Spikformer [45]. Then we detail the design of the spiking resformer block. + +# 5.1. Overall Architecture + +The overall pipeline of SEW ResNet [9], Spikformer [45], and the proposed SpikingResformer are shown in Fig. 2. As shown in Fig. 2, Spikformer employs a Spiking Patch Splitting (SPS) module to project an image to $d$ dimensional feature with reduced spatial size. However, the local information can only be poorly modeled by this shallow spiking convolutional module and it only generates single-scale feature maps. On the other hand, SEW ResNet is much + +deeper than the SPS in Spikformer and have a greater capability in extracting multi-scale feature with the multi-stage architecture, but lacks the global self-attention mechanism which helps extract global information. To overcome the limitations of these architectures while exploiting their advantages, we propose SpikingResformer, which combines the ResNet-based architecture and the spiking self-attention mechanism. + +The details of the overall architecture of SpikingResformer series are listed in Tab. 1. Similar to the ResNet-based SNNs [9, 14], our model starts with a stem architecture consisting of a $7 \times 7$ convolution and a $3 \times 3$ max pooling to pre-extract localized features and employs a multistage backbone to generate multi-scale feature maps. In each stage, multiple spiking Resformer blocks are stacked sequentially. Each spiking Resformer block consists of two modules, named Multi-Head Dual Spike Self-Attention (MHDSSA) block and Group-Wise Spiking Feed-Forward Network (GWSFFN). A downsample layer is applied before each stage (except the first stage) to reduce the size of the feature maps and project them to a higher dimension ( $2 \times$ downsampling of resolution with $2 \times$ enlargement of dimension). Finally, the model ends with a global average pooling layer and a classification layer. + +# 5.2. Spiking Resformer Block + +As illustrated in Fig. 2, the spiking Resformer block consists of a Multi-Head Dual Spike Self-Attention (MHDSSA) module and a Group-Wise Spiking Feed-Forward Network (GWSFFN). We first introduce the two modules and then derive the form of the spiking Resformer block. + +Multi-Head Convolutional Spiking Self-Attention. In Sec. 4, we propose the single-head form of DSSA. It can be easily extended to the multi-head DSSA (MHDSSA) following a similar approach to the vanilla Transformer [36]. In MHDSSA, we first split the results of linear transformation in DST into $h$ heads, then perform DSSA on each head and concatenate them together. Finally, we use point-wise convolution to project the concatenated features thus fusing the features in different heads. The MHDSSA can be formulated as follows: + +$$ +\operatorname {M H D S S A} (\mathbf {X}) = \operatorname {B N} \left(\operatorname {C o n v} _ {1} \left([ \mathrm {D S S A} _ {i} (\operatorname {S N} (\mathbf {X})) ] _ {i = 1} ^ {h}\right)\right), \tag {17} +$$ + +where $[\ldots]$ denotes the concatenate operation, $\mathrm{Conv}_1$ denotes the point-wise convolution. + +Group-Wise Spiking Feed-Forward Network. The spiking feed-forward network (SFFN) proposed in previous spiking vision transformers is composed of two linear layers with batch normalization and spiking neuron activation [41, 45]. Moreover, the expansion ratio is usually set to 4, i.e., the first layer raises the dimension by a factor of 4 while the second layer reduces to the original dimension. + +Table 1. Architectures of SpikingResformer series. The output size corresponds to the input size of $224 \times 224$ . $D_{i}$ and $H_{i}$ are the embedding dimension and number of heads of MHDSSA in stage $i$ , respectively. $p_i$ denotes that the MHDSSA in stage $i$ uses $p_i \times p_i$ convolution in DST. $R_{i}$ and $G_{i}$ denote the expansion ratio and embedding dimension per group of GWSFFN in stage $i$ , respectively. + +
StageOutput SizeLayer NameSpikingResformer-TiSpikingResformer-SSpikingResformer-MSpikingResformer-L
Stem56×56StemConv 7×7, stride 2, Maxpooling 3×3, stride 2
Stage 156×56MHDSSA[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=128H1=1,p1=4R1=4,G1=64] × 1
GWSFFN
Stage 228×28DownsampleConv 3×3, 192, stride 2Conv 3×3, 256, stride 2Conv 3×3, 384, stride 2Conv 3×3, 512, stride 2
MHDSSA[D2=192H2=3,p2=2R2=4,G2=64] × 2[D2=256H2=4,p2=2R2=4,G2=64] × 2[D2=384H2=6,p2=2R2=4,G2=64] × 2[D2=512H2=8,p2=2R2=4,G2=64] × 2
GWSFFN
Stage 314×14DownsampleConv 3×3, 384, stride 2Conv 3×3, 512, stride 2Conv 3×3, 768, stride 2Conv 3×3, 1024, stride 2
MHDSSA[D3=384H3=6,p3=1R3=4,G3=64] × 3[D3=512H3=8,p3=1R3=4,G3=64] × 3[D3=768H3=12,p3=1R3=4,G3=64] × 3[D3=1024H3=16,p3=1R3=4,G3=64] × 3
GWSFFN
Classifier1×1Linear1000-FC
+ +Based on SFFN, we insert a $3 \times 3$ convolution layer with the residual connection between two linear layers to enable SFFN to extract local features. Since the dimension of the hidden features between the two linear layers is expanded by a factor of 4 compared to the input, in order to reduce the number of parameters and computational overhead, we use group-wise convolution and set every 64 channels as 1 group. We also employ the spike-driven design in [41, 44]. The group-wise spiking feed-forward network (GWSFFN) can be formulated as follows: + +$$ +\operatorname {F F L} _ {i} (\mathbf {X}) = \operatorname {B N} \left(\operatorname {C o n v} _ {1} (\operatorname {S N} (\mathbf {X}))\right), i = 1, 2, \tag {18} +$$ + +$$ +\operatorname {G W L} (\mathbf {X}) = \operatorname {B N} (\operatorname {G W C o n v} (\operatorname {S N} (\mathbf {X}))) + \mathbf {X}, \tag {19} +$$ + +$$ +\operatorname {G W S F F N} (\mathbf {X}) = \operatorname {F F L} _ {2} (\operatorname {G W L} (\operatorname {F F L} _ {1} (\mathbf {X}))). \tag {20} +$$ + +Here $\mathrm{FFL}_i(\cdot), i = 1,2$ denote the feed-forward layers, $\mathrm{Conv}_1(\cdot)$ is point-wise convolution ( $1 \times 1$ convolution), which equal to the linear transformation. $\mathrm{GWL}(\cdot)$ denotes group-wise convolution layer, $\mathrm{GWConv}(\cdot)$ denotes the group-wise convolution. + +Spiking Resformer Block. With the MHDSSA module and GWSFFN above, the spiking resformer block can be formulated as: + +$$ +\mathbf {Y} _ {i} = \operatorname {M H D S S A} \left(\mathbf {X} _ {i}\right) + \mathbf {X} _ {i}, \tag {21} +$$ + +$$ +\mathbf {X} _ {i + 1} = \operatorname {G W S F N} \left(\mathbf {Y} _ {i}\right) + \mathbf {Y} _ {i}. \tag {22} +$$ + +where $\mathbf{Y}_i$ denotes the output features of MHDSSA module in the $i$ -th spiking reformer block. + +# 6. Experiments + +In this section, we first evaluate the performance and energy efficiency of SpikingResformer on the ImageNet classification task. Then, we perform ablation experiments on key + +components in SpikingResformer. Finally, we evaluate the transfer learning ability of SpikingResformer. + +# 6.1. ImageNet Classification + +ImageNet [4] is one of the most typical static image datasets widely used for image classification. For a fair comparison, we generally follow the data augmentation strategy and training setup in [41]. More details of the experimental setup can be found in the supplementary. + +Results. Our experimental results are listed in Tab. 2. For comparison, we also list the results of existing spiking convolutional networks and spiking Vision Transformers. As shown in Tab. 2, SpikingResformer achieves higher accuracy, fewer parameters, and lower energy consumption at the same time compared to existing methods. For instance, SpikingResformer-Ti achieves $74.34\%$ accuracy with only 11.14M parameters and 2.73G SOPs $(2.46\mathrm{mJ})$ , outperforming Spike-driven Transformer-8-384 by $2.06\%$ , saving 5.67M parameters and $1.44\mathrm{mJ}$ energy. SpikingResformer-M achieves $77.24\%$ accuracy with 35.52M parameters and 6.07G SOPs $(5.46\mathrm{mJ})$ , outperforming Spike-driven Transformer-8-768 by $0.92\%$ while saving 30.82M parameters. Particularly, the SpikingResformer-L achieves up to $79.40\%$ accuracy when the input size is enlarged to $288\times 288$ , which is the state-of-the-art result in SNN field. + +# 6.2. Ablation Study + +We perform ablation experiments on key components in SpikingResformer, including the multi-stage architecture, the group-wise convolution layer in GWSFFN, and our proposed spiking self-attention mechanism. The ablation experiments are conducted on the ImageNet100 dataset, which is a subset of the ImageNet dataset and consists of 100 categories from the ImageNet dataset. The experiment + +Table 2. Evaluation on ImageNet. SOPs denotes the average synaptic operations of an image inference on ImageNet validation data. Energy is the estimation of energy consumption same as [41, 45]. The default input resolution for training and inference is $224 \times 224$ . $\dagger$ means the input is enlarged to $288 \times 288$ in inference. - means the data is not provided in the original paper. + +
MethodTypeArchitectureTParam (M)SOPs (G)Energy (mJ)Top-1 Acc. (%)
Spiking ResNet [14]ANN-to-SNNResNet-3435021.7965.2859.3071.61
ResNet-5035025.5678.2970.9372.75
STBP-tdBN [43]Direct TrainingSpiking ResNet-34621.796.506.3963.72
TET [6]Direct TrainingSpiking ResNet-34621.79--64.79
SEW ResNet-34421.79--68.00
SEW ResNet [9]Direct TrainingSEW ResNet-34421.793.884.0467.04
SEW ResNet-50425.564.834.8967.78
SEW ResNet-101444.559.308.9168.76
SEW ResNet-152460.1913.7212.8969.26
Spikformer [45]Direct TrainingSpikformer-8-384416.816.827.7370.24
Spikformer-8-512429.6811.0911.5873.38
Spikformer-8-768466.3422.0921.4874.81
Spikingformer [44]Direct TrainingSpikingformer-8-384416.81-4.6972.45
Spikingformer-8-512429.68-7.4674.79
Spikingformer-8-768466.34-13.6875.85
Spike-driven Transformer [41]Direct TrainingSpike-driven Transformer-8-384416.81-3.9072.28
Spike-driven Transformer-8-512429.68-4.5074.57
Spike-driven Transformer-8-768466.34-/-6.09/-76.32/77.07†
SpikingResformer (Ours)Direct TrainingSpikingResformer-Ti411.142.73/4.71†2.46/4.24†74.34/75.57†
SpikingResformer-S417.763.74/6.40†3.37/5.76†75.95/76.90†
SpikingResformer-M435.526.07/10.24†5.46/9.22†77.24/78.06†
SpikingResformer-L460.389.74/16.40†8.76/14.76†78.77/79.40†
+ +Table 3. Ablation Study on ImageNet100 dataset. The number of parameters for all variants is comparable to SpikingResformer-S. + +
ModelSOPs (G)Energy (mJ)Acc. (%)
SpikingResformer-S2.432.1888.06
w/o multi-stage architecture1.841.6685.32
w/o group-wise convolution2.372.1384.64
w/o DSSAnot converge
w/o p × p convolution4.343.9186.14
w/o scalingnot converge
+ +tal setup basically follows the one in Sec. 6.1. Detailed settings are listed in the supplementary. + +Multi-Stage Architecture. To verify the effectiveness of the multi-stage architecture, we replace it with the Spikingformer-based architecture, while the structure of the spiking Resformer block remains unchanged. We adjust the embedding dimensions to make the model parameters comparable to SpikingResformer-S. As shown in Tab. 3, SpikingResformer-S outperforms the variant without multi-stage architecture by $2.74\%$ , demonstrating the effectiveness of multi-stage architecture. + +Group-Wise Convolution Layer. In comparison to the point-wise SFFN, GWSFFN employs a $3 \times 3$ group-wise convolution layer between the two linear layers. We + +evaluate its effect by removing the group-wise convolution layer and increasing the dimension to keep the number of parameters constant. As demonstrated in Tab. 3, SpikingResformer-S achieves $3.42\%$ higher accuracy in contrast to the variant without the group-wise convolution layer. This difference highlights the benefits of the group-wise convolution layer in GWSFFN. + +Dual Spike Self-Attention. To validate the effectiveness of DSSA, we first replace DSSA with existing spiking self-attention mechanisms, including Spiking Self-Attention (SSA) in Spikformer and Spike-Driven Self-Attention (SDSA) in Spike-driven Transformer. However, neither SSA nor SDSA converges. We believe this is because SSA and SDSA do not fit the multi-scale input. To further validate the key factors that help DSSA fit for the multi-scale input, we conduct two more sets of experiments. One set replaces all $p \times p$ convolutions with $1 \times 1$ convolutions in DST to validate the effect of reducing spatial size. The other removes the scaling factor or replaces our proposed scaling factors with $1 / \sqrt{d}$ to validate the effect of scaling. As a result, the first group converges but only achieves $86.14\%$ accuracy with a higher energy consumption of $3.91\mathrm{mJ}$ , while the second set does not converge. This shows that the scaling factor is the key to convergence. We believe that both SSA and SDSA lack proper scaling meth + +Table 4. Transfer learning results on CIFAR10, CIFAR100, CIFAR10-DVS, DVSGesture datasets. + +
MethodTypeCIFAR10CIFAR100CIFAR10-DVSDVSGesture
TAcc.TAcc.TAcc.TAcc.
STBP-tdBN [43]Direct Training693.16--1067.84096.87
PLIF [10]Direct Training893.50--2074.82097.57
Dspike [25]Direct Training694.25674.241075.4--
Spikformer [45]Direct Training495.19477.861680.61697.9
Spikingformer [44]Direct Training495.61479.091681.31698.3
Spike-driven Transformer [41]Direct Training495.6478.41680.01699.3
Spikformer [45]Transfer Learning497.03483.83----
SpikingResformer (Ours)Transfer Learning497.40485.981084.81093.4
+ +ods, thus do not apply to multi-stage architecture. SSA employs the same scaling factor as vanilla self-attention, i.e., $1 / \sqrt{d}$ . However, this does not apply to spike matrix multiplication, since spikes do not have mean 0 and variance 1. SDSA has no scaling method, which may be feasible when the feature map is small but not for multi-scale inputs. + +# 6.3. Transfer Learning + +High transfer learning ability is a key advantage of Vision Transformer. We evaluate the transfer learning ability of the proposed SpikingResformer on static dataset CIFAR10 and CIFAR100 [19] and neuromorphic dataset CIFAR10-DVS [23] and DVSGesture [1] by fine-tuning the models pre-trained on ImageNet. Among the existing spiking Vision Transformers, only Spikformer provides transfer learning results, and only on the static image datasets CIFAR10 and CIFAR100. Thus, we also compared our results with the direct training results for a comprehensive comparison. Tab. 4 lists the highest accuracy achieved by these methods. The experimental setup and a more detailed comparison can be found in the supplementary. + +Static Image Datasets. As shown in Tab. 4, SpikingResformer achieves $97.40\%$ accuracy on CIFAR10 dataset and $85.98\%$ accuracy on CIFAR100 dataset, which is the state-of-the-art result, outperforming the transfer learning results of Spikformer by $0.37\%$ on CIFAR10 and $2.15\%$ on CIFAR100. Compared to direct training methods, SpikingResformer obtained from transfer learning has significantly better performance. For example, SpikingResformer outperforms Spikingformer by $6.89\%$ on CIFAR100 dataset, demonstrating the advantage of transfer learning. + +Neuromorphic Datasets. Neuromorphic datasets differ significantly from traditional static image datasets. The samples of the neuromorphic dataset consist of event streams instead of RGB images. As a result, there is a large gap between the source and target domain for models pre-trained on static image datasets. To bridge this gap, we stack the events over a period of time to form a frame. The RGB channels are replaced with positive events, + +negative events, and the sum of events channels, respectively. As shown in Tab. 4, transfer learning results of SpikingResformer significantly outperform the direct training ones on CIFAR10-DVS. SpikingResformer achieves $84.8\%$ accuracy on CIFAR10-DVS, outperforming Spikingformer by $3.5\%$ . However, the transfer learning results on DVS-Gesture fail to achieve comparable performance to direct training. SpikingResformer only achieves $93.4\%$ accuracy on DVSGesture, falling behind the state-of-the-art method Spike-driven Transformer by $5.9\%$ . We believe that this is mainly due to the way CIFAR10-DVS is constructed differs from DVSGesture. CIFAR10-DVS is converted from CIFAR10, which does not contain temporal information. Thus, models pre-trained on static datasets can transfer to CIFAR10-DVS well. However, DVSGesture is directly created from human gestures using a dynamic vision sensor, thus containing rich temporal information. As a result, models pre-trained on static datasets do not transfer well to DVSGesture. We hope our exploration of transfer learning on neuromorphic datasets could pave the way for further transfer learning research of SNNs. + +# 7. Conclusion + +In this paper, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs. We detail the scaling factors in DSSA enabling it to handle feature maps of arbitrary scales. Based on DSSA, we propose SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to achieve superior performance and energy efficiency with fewer parameters. Extensive experiments demonstrate the effectiveness and superiority of the proposed SpikingResformer. + +# Acknowledgments + +This work was supported by the National Natural Science Foundation of China (62176003, 62088102) and by the Beijing Nova Program (20230484362). + +# References + +[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. A low power, fully event-based gesture recognition system. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 7243-7252, 2017. 2, 8 +[2] Tong Bu, Jianhao Ding, Zhaofei Yu, and Tiejun Huang. Optimized potential initialization for low-latency spiking neural networks. In In Proceedings of the AAAI Conference on Artificial Intelligence, pages 11-20, 2022. 2 +[3] Tong Bu, Wei Fang, Jianhao Ding, PengLin Dai, Zhaofei Yu, and Tiejun Huang. 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While existing methods propose spiking self-attention mechanisms that are compatible with SNNs, they lack reasonable scaling methods, and the overall architectures proposed by these methods suffer from a bottleneck in effectively extracting local features. To address these challenges, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA) with a reasonable scaling method. Based on DSSA, we propose a novel spiking Vision Transformer architecture called SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to improve both performance and energy efficiency while reducing parameters. Experimental results show that SpikingResformer achieves higher accuracy with fewer parameters and lower energy consumption than other spiking Vision Transformer counterparts. Notably, our SpikingResformer-L achieves " + }, + { + "bbox": [ + 47, + 256, + 290, + 544 + ], + "type": "inline_equation", + "content": "79.40\\%" + }, + { + "bbox": [ + 47, + 256, + 290, + 544 + ], + "type": "text", + "content": " top-1 accuracy on ImageNet with 4 time-steps, which is the state-of-the-art result in the SNN field. Codes are available at https://github.com/xyshi2000/SpikingResformer" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 567, + 128, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 128, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 128, + 578 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 586, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 586, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 586, + 287, + 696 + ], + "type": "text", + "content": "Spiking Neural Networks (SNNs), considered as the third generation of Artificial Neural Networks (ANNs) [27], have garnered significant attention due to their notable advantages such as low power consumption, biological plausibility, and event-driven characteristics that are compatible with neuromorphic hardware. In comparison to ANNs, SNNs exhibit an energy-saving advantage when deployed on neuromorphic hardware [11, 29, 32], and have become popular in the field of neuromorphic computing in recent years [33]." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 231, + 547, + 366 + ], + "blocks": [ + { + "bbox": [ + 307, + 231, + 547, + 366 + ], + "lines": [ + { + "bbox": [ + 307, + 231, + 547, + 366 + ], + "spans": [ + { + "bbox": [ + 307, + 231, + 547, + 366 + ], + "type": "image", + "image_path": "c83c5ee7eb46085195ceeb07a127dd65632894289d0059ed8acf1dda25e8ac69.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 374, + 547, + 409 + ], + "lines": [ + { + "bbox": [ + 305, + 374, + 547, + 409 + ], + "spans": [ + { + "bbox": [ + 305, + 374, + 547, + 409 + ], + "type": "text", + "content": "Figure 1. Comparison of Top-1 accuracy on ImageNet with respect to energy consumption per image for inference (left) and the number of parameters (right). The input size is " + }, + { + "bbox": [ + 305, + 374, + 547, + 409 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 305, + 374, + 547, + 409 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 434, + 546, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 434, + 546, + 470 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 546, + 470 + ], + "type": "text", + "content": "However, the performance of existing SNNs still lags behind that of ANNs, particularly on challenging vision tasks, which limits further application of SNNs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 675 + ], + "type": "text", + "content": "Researchers make great efforts to enhance the performance of SNNs. Recently, inspired by the remarkable achievements of vision transformers [8, 26] in ANNs, some attempts have been made to introduce transformer-based architecture into SNNs. The main challenge in incorporating transformer structures into SNNs lies in designing a self-attention mechanism suitable for SNNs. The vanilla self-attention mechanism in ANNs relies on float-point matrix multiplication and softmax operations. However, these operations involve float-point multiplication, division, and exponentiation, which do not comply with the spike-driven nature of SNNs. Moreover, commonly used components in ANN Transformers, such as layer normalization (LN) and GELU activation, are not directly applicable in SNNs. Therefore, the introduction of transformer architectures into SNNs necessitates circumventing these operations and catering to the unique requirements of SNNs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Some work has attempted to partially preserve floating-point operations [37], or run an SNN and an ANN Transformer in parallel [48]. Although these approaches en" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 204, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 204, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 204, + 713 + ], + "type": "text", + "content": "*Corresponding author: yuzf12@puk.edu.cn" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5610" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 373 + ], + "type": "text", + "content": "hance performance, they do not fully address the incompatibility between vanilla self-attention and SNNs. There are also works that propose spiking self-attention mechanisms and spiking Vision Transformer architectures, which are entirely based on synaptic operations [45] and fully spikedriven [41, 44]. These works completely resolve the incompatibility of the self-attention mechanism with SNNs, significantly outperforming existing spiking convolutional neural networks. However, these approaches have certain limitations. Specifically, the spiking transformer architectures of these methods exhibit a bottleneck in extracting local features. They employ a shallow convolutional network before the Transformer encoder to extract local features and reduce the size of feature maps. However, the effectiveness of such a shallow network is limited compared to Transformer encoders. Replacing this shallow network with a Transformer encoder is not feasible. This is because their spiking self-attention mechanisms lack reasonable scaling methods, making them suitable only for small feature maps. Designing proper scaling factors for these mechanisms is challenging as the input currents to neurons, which generate self-attention, do not possess simple mean and variance forms. Thus, there is a pressing need to design a new spiking self-attention mechanism with a reasonable scaling method that can effectively handle large feature maps." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 375, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 289, + 567 + ], + "type": "text", + "content": "To address these problems, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven, compatible with SNNs, and eliminates the need for direct spike multiplications. In addition, we detail the scaling method in DSSA, enabling it to adapt to adapt to feature maps of arbitrary scales. Building upon DSSA, we propose SpikingResformer, a novel spiking Vision Transformer architecture. This architecture combines the ResNet-based multistage design with our proposed spiking self-attention mechanism. Experimental results show that our proposed SpikingResformer significantly outperforms the performance of existing spiking Vision Transformers with fewer parameters and less energy consumption. The main contributions of this paper can be summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 570, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 570, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 617 + ], + "type": "text", + "content": "- We propose the Dual Spike Self-Attention (DSSA), a novel spiking self-attention mechanism. It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 618, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 641 + ], + "type": "text", + "content": "- We detail the scaling factors employed in DSSA, enabling DSSA to handle feature maps of arbitrary scales." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 677 + ], + "type": "text", + "content": "- We propose the SpikingResformer architecture, which combines the ResNet-based multi-stage architecture with our proposed DSSA." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "type": "text", + "content": "- Experimental results show that the proposed SpikingReformer significantly outperforms other spiking Vision Transformer counterparts with fewer parame" + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "type": "text", + "content": "ters and lower energy consumption. Notably, our SpikingResformer-L achieves up to " + }, + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "type": "inline_equation", + "content": "79.40\\%" + }, + { + "bbox": [ + 313, + 72, + 545, + 109 + ], + "type": "text", + "content": " top-1 accuracy on ImageNet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 117, + 392, + 129 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 117, + 392, + 129 + ], + "spans": [ + { + "bbox": [ + 306, + 117, + 392, + 129 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 137, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 545, + 399 + ], + "type": "text", + "content": "Spiking Convolutional Neural Networks. Spiking convolutional neural networks (SCNNs) have been extensively developed due to the remarkable success of surrogate gradient learning [30, 42] and are widely used in handling challenging vision tasks, including object recognition [1, 20], detection [17, 35], and segmentation [18, 31]. To improve the performance of SCNNs on these challenging tasks, researchers have dedicated great efforts to exploring training methods [6, 12, 21, 28, 38, 40, 46, 47] and ANN-to-SNN conversion techniques [2, 3, 5, 7, 13-16, 22, 24, 34, 39]. Moreover, many deep spiking convolutional architectures [9, 14, 21, 34, 43] have been proposed to achieve high performance. The success of SpikingVGG [21, 34] demonstrates that SCNNs can achieve comparable performance to ANNs in recognition tasks. SpikingResNet [14, 43] further explores SCNNs with residual structure and achieves deeper SCNN with ResNet-based architecture. Moreover, SEW ResNet [9] meticulously analyzes the identity mapping in directly-trained spiking residual networks and successfully trains a 152-layer SCNN directly. These architectures leverage large-scale SNNs with numerous layers and demonstrate superior performance on various tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 546, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 546, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 546, + 591 + ], + "type": "text", + "content": "Spiking Vision Transformers. Spikformer [45] is the first directly-trained spiking vision transformer with a pure SNN architecture. It introduces a spiking self-attention mechanism that eliminates multiplication by activating Query, Key, and Value with spiking neurons and replacing softmax with spiking neurons. In addition, it replaces layer normalization and GELU activation in the Transformer with batch normalization and spiking neurons. Based on Spikformer, Spikingformer [44] achieves a purely spike-driven Vision Transformer by modifying the residual connection paradigm. Spike-driven Transformer [41] proposes a spikedriven self-attention mechanism with linear complexity, effectively reducing energy consumption. However, all of these efforts employ a shallow convolutional network to pre-extract local information to form a sequence of patches and lack proper scaling methods." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 600, + 383, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 600, + 383, + 613 + ], + "spans": [ + { + "bbox": [ + 306, + 600, + 383, + 613 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 620, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 620, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 620, + 545, + 654 + ], + "type": "text", + "content": "We describe the dynamics of the Leaky Integrate-and-Fire (LIF) neuron used in this paper by the following discrete-time model:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 350, + 658, + 545, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 658, + 545, + 681 + ], + "spans": [ + { + "bbox": [ + 350, + 658, + 545, + 681 + ], + "type": "interline_equation", + "content": "v _ {i} [ t ] = u _ {i} [ t ] + \\frac {1}{\\tau} \\left(I _ {i} [ t ] - \\left(u _ {i} [ t ] - u _ {\\text {r e s t}}\\right)\\right), \\tag {1}", + "image_path": "b3f158c0a51c6b803efdfad2ce5f30646c67939bec2a7473be31d46b70ea0a17.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 351, + 682, + 545, + 696 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 682, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 351, + 682, + 545, + 696 + ], + "type": "interline_equation", + "content": "s _ {i} [ t ] = H \\left(v _ {i} [ t ] - u _ {\\mathrm {t h}}\\right), \\tag {2}", + "image_path": "c288ecf3a72a1fc4332148815b083e2b4b27c128c1a4f6558d51daaa5be9b7df.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 333, + 697, + 545, + 711 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 697, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 333, + 697, + 545, + 711 + ], + "type": "interline_equation", + "content": "u _ {i} [ t + 1 ] = s _ {i} [ t ] u _ {\\text {r e s t}} + (1 - s _ {i} [ t ]) v _ {i} [ t ]. \\tag {3}", + "image_path": "e1eddd2ae652809db0b9a2c2e4752a6723519aaf2b75b0f8c26e08f07430e820.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5611" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "Eq. (1) describes the charging process. Here " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "u_{i}[t]" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "v_{i}[t]" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " denote the membrane potential of " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "-th postsynaptic neuron before and after charging. " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " is the membrane time constant. " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "I_{i}[t]" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " denotes the input current. In general, " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "I_{i}[t] = \\sum_{j} w_{i,j} s_{j}[t]" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "s_{j}[t] \\in \\{0, 1\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " represents the spike output of the " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "-th presynaptic neuron at time-step " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "w_{i,j}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " represents the weight of the corresponding synaptic connection from neuron " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " to neuron " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": ". Eq. (2) describes the firing process, where " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "H(\\cdot)" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " is the Heaviside function, " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "s_{i}[t] \\in \\{0, 1\\}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " is the spike output of the spiking neuron, " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "u_{\\mathrm{th}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " denotes the firing threshold. Eq. (3) describes the resetting process, with " + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "inline_equation", + "content": "u_{\\mathrm{rest}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": " denoting the resting potential." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 216, + 287, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 216, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 47, + 216, + 287, + 239 + ], + "type": "text", + "content": "For the sake of simplicity and clarity in subsequent sections, we represent the spiking neuron model as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 141, + 248, + 287, + 261 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 141, + 248, + 287, + 261 + ], + "spans": [ + { + "bbox": [ + 141, + 248, + 287, + 261 + ], + "type": "interline_equation", + "content": "\\mathbf {S} = \\operatorname {S N} (\\mathbf {I}), \\tag {4}", + "image_path": "ae26d76b2c925c3d27ffb1dc683c3caa80ceb6ada000934b09d125e56919ba39.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "inline_equation", + "content": "\\mathrm{SN}(\\cdot)" + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": " denotes the spiking neuron layer, omitting the dynamic processes within the neuron, " + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{I}\\in \\mathbb{R}^{T\\times n}" + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": " is the input current, where " + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": " is the time step and " + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": " is the number of neurons, " + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "inline_equation", + "content": "\\mathbf{S}\\in \\{0,1\\}^{T\\times n}" + }, + { + "bbox": [ + 46, + 270, + 287, + 318 + ], + "type": "text", + "content": " is the corresponding spike output." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 327, + 194, + 341 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 194, + 341 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 194, + 341 + ], + "type": "text", + "content": "4. Dual Spike Self-Attention" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "spans": [ + { + "bbox": [ + 46, + 347, + 287, + 419 + ], + "type": "text", + "content": "This section first revisits the vanilla self-attention (VSA) mechanism commonly used in ANNs and analyzes why VSA is not suitable for SNNs. Then, we propose dual spike self-attention (DSSA), specifically designed for compatibility. We further discuss the significance of the scaling factor in DSSA and the spike-driven characteristic of DSSA." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 426, + 171, + 438 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 171, + 438 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 171, + 438 + ], + "type": "text", + "content": "4.1. Vanilla Self-Attention" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 445, + 287, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 468 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 468 + ], + "type": "text", + "content": "The vanilla self-attention in Transformer [36] can be formulated as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 70, + 478, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 478, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 70, + 478, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} = \\mathbf {X} \\mathbf {W} _ {Q}, \\mathbf {K} = \\mathbf {X} \\mathbf {W} _ {K}, \\mathbf {V} = \\mathbf {X} \\mathbf {W} _ {V}, \\tag {5}", + "image_path": "b6749104f85d1a846c664abf39eb558176d85666f4e2a15563dca3dd80df686e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 70, + 493, + 287, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 493, + 287, + 525 + ], + "spans": [ + { + "bbox": [ + 70, + 493, + 287, + 525 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t e n t i o n} (\\mathbf {Q}, \\mathbf {K}, \\mathbf {V}) = \\operatorname {S o f t m a x} \\left(\\frac {\\mathbf {Q} \\mathbf {K} ^ {\\mathrm {T}}}{\\sqrt {d}}\\right) \\mathbf {V} \\tag {6}", + "image_path": "54ff0ecba72b4a73ee2a13a429631d0a8ce18db5d9da45f41447d2bbdda4272b.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{Q},\\mathbf{K},\\mathbf{V}\\in \\mathbb{R}^{n\\times d}" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": " denote Query, Key and Value, respectively. " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": " is the number of patches, " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": " is the embedding dimension. We assume that " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{Q},\\mathbf{K},\\mathbf{V}" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": " have the same embedding dimension. " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\in \\mathbb{R}^{n\\times d}" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": " is the input of selfattention block, " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_Q,\\mathbf{W}_K,\\mathbf{W}_V\\in \\mathbb{R}^{d\\times d}" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": " are the weights of the linear transformations corresponding to " + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "inline_equation", + "content": "\\mathbf{Q},\\mathbf{K},\\mathbf{V}" + }, + { + "bbox": [ + 46, + 533, + 287, + 617 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "The vanilla self-attention commonly used in ANNs is not suitable for SNNs due to the following two types of operations involved: 1) the float-point matrix multiplication of " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": ", as well as between the attention map and " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{V}" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "; 2) the softmax function, which contains exponentiation and division operations. These operations rely on float-point multiplication, division, and exponentiation operations, which are not compatible with the restrictions of SNNs." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 449, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 449, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 449, + 84 + ], + "type": "text", + "content": "4.2. Dual Spike Self-Attention" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 90, + 545, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 173 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 173 + ], + "type": "text", + "content": "To introduce the self-attention mechanism into SNNs and efficiently handle the multi-scale feature maps, we propose a novel spiking self-attention mechanism, named Dual Spike Self-Attention (DSSA). DSSA only utilizes Dual Spike Transformation (DST), thereby eliminating the need for the float-point matrix multiplication and softmax function. We first define the DST as follows:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 336, + 178, + 545, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 336, + 178, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 336, + 178, + 545, + 192 + ], + "type": "interline_equation", + "content": "\\operatorname {D S T} (\\mathbf {X}, \\mathbf {Y}; f (\\cdot)) = \\mathbf {X} f (\\mathbf {Y}) = \\mathbf {X Y W}, \\tag {7}", + "image_path": "7c7d961d0d6db7c8840e0bec797b8b73b1a35bdcad8dea68dcf3f85955051045.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 331, + 194, + 545, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 331, + 194, + 545, + 209 + ], + "spans": [ + { + "bbox": [ + 331, + 194, + 545, + 209 + ], + "type": "interline_equation", + "content": "\\mathrm {D S T} _ {\\mathrm {T}} (\\mathbf {X}, \\mathbf {Y}; f (\\cdot)) = \\mathbf {X} f (\\mathbf {Y}) ^ {\\mathrm {T}} = \\mathbf {X} \\mathbf {W} ^ {\\mathrm {T}} \\mathbf {Y} ^ {\\mathrm {T}}. \\tag {8}", + "image_path": "ff2fac1c03126be6d08dca666cec141cd09129c3ff7eb43bd2856004c08c434b.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": "In Eq. (7), " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\{0,1\\}^{T \\times p \\times m}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\{0,1\\}^{T \\times m \\times q}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " represent the dual spike inputs. " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " is the time steps, " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "p, m, q" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " denote arbitrary dimensions. Here " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " is a generalized linear transformation on " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{q \\times q}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " denoting its weight matrix. It represents any operation that can be equated to a linear transformation, including convolution, batch normalization (ignoring bias), etc. A detailed discussion on the equivalence of convolution operations to linear transformations can be found in the supplementary. Similarly, in Eq. (8), we have " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\{0,1\\}^{T \\times q \\times m}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{m \\times m}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": ". Since " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 213, + 546, + 417 + ], + "type": "text", + "content": " are both spike matrices, all matrix multiplications are equivalent to the summation of weights. Consequently, the DST avoids floating-point multiplication, making it compatible with SNNs. Further discussion of the compatibility and the spike-driven characteristic of DST can be found in Sec. 4.4. Based on DST, the attention map in DSSA can be formulated as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 330, + 423, + 545, + 436 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 423, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 330, + 423, + 545, + 436 + ], + "type": "interline_equation", + "content": "\\operatorname {A t t n M a p} (\\mathbf {X}) = \\operatorname {S N} \\left(\\mathrm {D S T} _ {\\mathrm {T}} (\\mathbf {X}, \\mathbf {X}; f (\\cdot)) * c _ {1}\\right), \\tag {9}", + "image_path": "53e2ea2cbac2610f88fcb93de29aadf07b65c802e20709d6b5ee659e705eeb31.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 364, + 437, + 545, + 451 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 437, + 545, + 451 + ], + "spans": [ + { + "bbox": [ + 364, + 437, + 545, + 451 + ], + "type": "interline_equation", + "content": "f (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {\\mathrm {p}} (\\mathbf {X})\\right), \\tag {10}", + "image_path": "aca62e99ad6fa09658df19e573a8384dcb115825a14c578fc3db01b813ab127a.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\{0,1\\}^{T \\times HW \\times d}" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " is the spike input, with " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "H" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " denoting the spatial height and width of the input, " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " denoting the embedding dimension. " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "\\mathrm{BN}(\\cdot)" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " refers to the batch normalization layer, " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_{\\mathrm{p}}(\\cdot)" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " denotes a " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "p \\times p" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " convolution with a stride of " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "c_{1}" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " is the scaling factor. Since the convolution operation is equivalent to a generalized linear transformation, and batch normalization can be absorbed into the convolution (ignoring bias), " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "\\mathrm{BN}(\\mathrm{Conv}_{\\mathrm{p}}(\\cdot))" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " can be viewed as a generalized linear transformation. Here we use the " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "p \\times p" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " convolution with a stride of " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " to reduce the spatial size to handle the multi-scale feature map and reduce the computational overhead. In DSSA, there is no need for the softmax function since the spiking neuron layer inherently generates a binary attention map composed of spikes. Each spike " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "s_{ij}" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " in this spiking attention map signifies attention between patch " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": " and patch " + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 456, + 546, + 684 + ], + "type": "text", + "content": ". We believe that such a spiking attention map is more interpretable compared to the attention map in ANN activated with softmax. With the spiking attention map, the DSSA can be formulated as follows:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 315, + 689, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 315, + 689, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\operatorname {D S S A} (\\mathbf {X}) = \\operatorname {S N} (\\operatorname {D S T} (\\operatorname {A t t n M a p} (\\mathbf {X}), \\mathbf {X}; f (\\cdot)) * c _ {2}), \\tag {11}", + "image_path": "41c22b6ebc788b640cfd428c6b261d0db165c137cecf5a0828e10c932623417f.jpg" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5612" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 73, + 541, + 316 + ], + "blocks": [ + { + "bbox": [ + 47, + 73, + 541, + 316 + ], + "lines": [ + { + "bbox": [ + 47, + 73, + 541, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 73, + 541, + 316 + ], + "type": "image", + "image_path": "d9f54d23994e6f7fac53498446fa400e08c44b6dd68168c3dcbfac0002b99286.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 324, + 546, + 346 + ], + "lines": [ + { + "bbox": [ + 46, + 324, + 546, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 324, + 546, + 346 + ], + "type": "text", + "content": "Figure 2. Left: Architecture of SpikingResformer and components including Dual Spike Self-Attention (DSSA), Multi-Head DSSA (MHDSSA), and Group-Wise Spiking Feed-Forward Network (GWSFFN). Right: Architecture of SEW ResNet-50 and Spikformer." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 368, + 288, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 368, + 288, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 368, + 288, + 416 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 368, + 288, + 416 + ], + "type": "inline_equation", + "content": "c_{2}" + }, + { + "bbox": [ + 46, + 368, + 288, + 416 + ], + "type": "text", + "content": " is the second scaling factor. Since the form of DSSA is quite different from VSA and existing spiking self-attention mechanisms, we further discuss how DSSA achieves self-attention in the supplementary." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 423, + 185, + 436 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 423, + 185, + 436 + ], + "spans": [ + { + "bbox": [ + 47, + 423, + 185, + 436 + ], + "type": "text", + "content": "4.3. Scaling Factors in DSSA" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": "In the vanilla self-attention mechanism [36], the product of matrices " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " in Eq. (6) is scaled by a factor of " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "1 / \\sqrt{d}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " before applying the softmax operation. This scaling is necessary because the magnitude of " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}\\mathbf{K}^{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " grows with the embedding dimension " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "d_{k}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": ", which can result in gradient vanishing issues after the softmax operation. Formally, assume that all the elements in " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{K}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " are independent random variables with a mean of 0 and a variance of 1, then each element in their product " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}\\mathbf{K}^{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": " has mean 0 and variance " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": ". By multiplying the product with a factor of " + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "inline_equation", + "content": "1 / \\sqrt{d}" + }, + { + "bbox": [ + 46, + 441, + 287, + 572 + ], + "type": "text", + "content": ", the variance of the product is scaled to 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 574, + 287, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 681 + ], + "type": "text", + "content": "While DSSA does not employ the softmax function, the surrogate gradient also suffers gradient vanishes without scaling. However, directly using the scaling factor of VSA is not feasible. Due to the spike-based nature of the input in DST and the attention map in DSSA, we cannot assume that they possess a mean of 0 and a variance of 1. Therefore, the scaling factor values in DSSA should be different from those used in VSA. In the following theorem, we present the mean and variance of DST." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Theorem 1 (Mean and variance of DST). Given spike input " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\{0,1\\}^{T \\times p \\times m}" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\{0,1\\}^{T \\times m \\times q}" + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": " and linear" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": "transformation " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "f(\\cdot)" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " with weight matrix " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{q \\times q}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{T \\times p \\times q}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " is the output of DST, " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{I} = \\mathrm{DST}(\\mathbf{X},\\mathbf{Y};f(\\cdot))" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ". Assume that all elements in " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " are independent random variables, " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "x_{i_x,j_x}[t]" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " subject to Bernoulli distribution " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "x_{i_x,j_x}[t] \\sim B(f_x)" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ", and the output of linear transformation " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "f(\\mathbf{Y})" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " has mean 0 and variance 1, we have " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\operatorname{E}(I_{i_I,j_I}[t]) = 0" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ". Similarly, for " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{I} = \\mathrm{DST}_{\\mathrm{T}}(\\mathbf{X},\\mathbf{Y};f(\\cdot))" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} \\in \\{0,1\\}^{T \\times q \\times m}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{m \\times m}" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ", we also have " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\operatorname{E}(I_{i_I,j_I}[t]) = 0" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "inline_equation", + "content": "\\operatorname{Var}(I_{i_I,j_I}[t]) = f_xm" + }, + { + "bbox": [ + 304, + 367, + 546, + 477 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "content": "The proof of Theorem 1 can be found in the supplementary. According to Theorem 1, we have " + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "inline_equation", + "content": "c_{1} = 1 / \\sqrt{f_{X}d}" + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "inline_equation", + "content": "c_{2} = 1 / \\sqrt{f_{Attn}HW / p^{2}}" + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "inline_equation", + "content": "f_{X}" + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "inline_equation", + "content": "f_{Attn}" + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "content": " are the average firing rate of " + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 485, + 545, + 534 + ], + "type": "text", + "content": " and spiking attention map, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 542, + 501, + 555 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 542, + 501, + 555 + ], + "spans": [ + { + "bbox": [ + 306, + 542, + 501, + 555 + ], + "type": "text", + "content": "4.4. Spike-driven Characteristic of DSSA" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 560, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 560, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 304, + 560, + 545, + 645 + ], + "type": "text", + "content": "The spike-driven characteristic is important for SNNs, i.e., the computation is sparsely triggered with spikes and requires only synaptic operations. Previous work has made a great effort in achieving spike-driven Transformers [41, 44]. In this subsection, we delve into the spike-driven characteristic of DSSA and prove that DSSA is spike-driven. We first give the formal definition of the spike-driven characteristic." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 679 + ], + "type": "text", + "content": "Definition 1. A spiking neural network is spike-driven if the input currents of all neurons satisfy the following form:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 351, + 688, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 688, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 351, + 688, + 545, + 715 + ], + "type": "interline_equation", + "content": "I _ {i} [ t ] = \\sum_ {j} w _ {i, j} s _ {j} [ t ] = \\sum_ {j, s _ {j} [ t ] \\neq 0} w _ {i, j}, \\tag {12}", + "image_path": "79617228d7e0a2a94ea0b1b0430f74b4de986ab9deab0a479732554d20764d8f.jpg" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5613" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "I_{i}[t]" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " is the input current of the " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "-th postsynaptic neuron at time step " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "s_{j}[t] \\in \\{0,1\\}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " is the spike output of the " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "-th presynaptic neuron, " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "w_{i,j}" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " is the weight of the synaptic connection from neuron " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " to neuron " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 129, + 287, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 129, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 46, + 129, + 287, + 189 + ], + "type": "text", + "content": "This definition reveals the nature of the spike-driven characteristic, i.e., the accumulation of input current is sparsely triggered by spikes emitted from presynaptic neurons. It is evident that commonly used linear layers and convolution layers satisfy this definition." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 189, + 287, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 189, + 287, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 287, + 249 + ], + "type": "text", + "content": "The DSSA has only two spiking neuron layers, including the spiking attention map layer and the output layer. Both of these layers receive input currents derived from DST. Thus, we only need to validate that the DST satisfies the form in Definition 1. We first validate the " + }, + { + "bbox": [ + 46, + 189, + 287, + 249 + ], + "type": "inline_equation", + "content": "\\mathrm{DST}_{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 189, + 287, + 249 + ], + "type": "text", + "content": " in Eq. (8)" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 71, + 258, + 287, + 271 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 258, + 287, + 271 + ], + "spans": [ + { + "bbox": [ + 71, + 258, + 287, + 271 + ], + "type": "interline_equation", + "content": "\\mathbf {I} = \\mathbf {X} \\mathbf {W} ^ {\\mathrm {T}} \\mathbf {Y} ^ {\\mathrm {T}}, \\tag {13}", + "image_path": "c7c478c25332d13288299a55bf959e54184445f10ae006476fe0cb201ef846a1.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 52, + 274, + 287, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 274, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 52, + 274, + 287, + 327 + ], + "type": "interline_equation", + "content": "I _ {i, j} [ t ] = \\sum_ {k = 1} ^ {m} \\sum_ {l = 1} ^ {m} x _ {i, k} [ t ] w _ {l, k} y _ {j, l} [ t ] = \\sum_ {\\substack {k, l \\\\ (x _ {i, k} [ t ] \\wedge y _ {j, l} [ t ]) \\neq 0}} w _ {l, k}. \\tag{14}", + "image_path": "93eec280f69511958e5e3e7d1549ad016e4cb8b611c5b37f94f2645d6aff6137.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 338, + 287, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 287, + 397 + ], + "type": "text", + "content": "Slightly different from Definition 1, the spike input here is the logical AND of dual spikes. This can be viewed as a synaptic operation requiring dual spikes to trigger, which is the reason it is called dual spike transformation. Similar to the " + }, + { + "bbox": [ + 46, + 338, + 287, + 397 + ], + "type": "inline_equation", + "content": "\\mathrm{DST}_{\\mathrm{T}}" + }, + { + "bbox": [ + 46, + 338, + 287, + 397 + ], + "type": "text", + "content": ", the DST in Eq. (7) can also be formulated as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 71, + 419, + 287, + 432 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 71, + 419, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 71, + 419, + 287, + 432 + ], + "type": "interline_equation", + "content": "\\mathbf {I} = \\mathbf {X Y W}, \\tag {15}", + "image_path": "0cd70f34f8970cda2f996bd24aa68e8f1cde7221ab9bb502869e309fe15e88ce.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 52, + 435, + 287, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 435, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 52, + 435, + 287, + 488 + ], + "type": "interline_equation", + "content": "I _ {i, j} [ t ] = \\sum_ {k = 1} ^ {m} \\sum_ {l = 1} ^ {q} x _ {i, k} [ t ] y _ {k, l} [ t ] w _ {l, j} = \\sum_ {\\substack {k, l \\\\ (x _ {i, k} [ t ] \\wedge y _ {k, l} [ t ]) \\neq 0}} w _ {l, j}. \\tag{16}", + "image_path": "71c450477e2798b8781bbac3ffb1f86afd58ad80b32fa55e5af77dd0db0fbe02.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 498, + 164, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 164, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 164, + 510 + ], + "type": "text", + "content": "Thus, DSSA is spike-driven." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 522, + 156, + 536 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 522, + 156, + 536 + ], + "spans": [ + { + "bbox": [ + 47, + 522, + 156, + 536 + ], + "type": "text", + "content": "5. SpikingResformer" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 542, + 287, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 590 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 590 + ], + "type": "text", + "content": "In this section, we first introduce the overall architecture of the proposed SpikingResformer and compare it with existing SEW ResNet [9] and Spikformer [45]. Then we detail the design of the spiking resformer block." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 599, + 167, + 610 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 167, + 610 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 167, + 610 + ], + "type": "text", + "content": "5.1. Overall Architecture" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": "The overall pipeline of SEW ResNet [9], Spikformer [45], and the proposed SpikingResformer are shown in Fig. 2. As shown in Fig. 2, Spikformer employs a Spiking Patch Splitting (SPS) module to project an image to " + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 617, + 287, + 713 + ], + "type": "text", + "content": " dimensional feature with reduced spatial size. However, the local information can only be poorly modeled by this shallow spiking convolutional module and it only generates single-scale feature maps. On the other hand, SEW ResNet is much" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 167 + ], + "type": "text", + "content": "deeper than the SPS in Spikformer and have a greater capability in extracting multi-scale feature with the multi-stage architecture, but lacks the global self-attention mechanism which helps extract global information. To overcome the limitations of these architectures while exploiting their advantages, we propose SpikingResformer, which combines the ResNet-based architecture and the spiking self-attention mechanism." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "text", + "content": "The details of the overall architecture of SpikingResformer series are listed in Tab. 1. Similar to the ResNet-based SNNs [9, 14], our model starts with a stem architecture consisting of a " + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "inline_equation", + "content": "7 \\times 7" + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "text", + "content": " convolution and a " + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "text", + "content": " max pooling to pre-extract localized features and employs a multistage backbone to generate multi-scale feature maps. In each stage, multiple spiking Resformer blocks are stacked sequentially. Each spiking Resformer block consists of two modules, named Multi-Head Dual Spike Self-Attention (MHDSSA) block and Group-Wise Spiking Feed-Forward Network (GWSFFN). A downsample layer is applied before each stage (except the first stage) to reduce the size of the feature maps and project them to a higher dimension (" + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "text", + "content": " downsampling of resolution with " + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 304, + 167, + 546, + 360 + ], + "type": "text", + "content": " enlargement of dimension). Finally, the model ends with a global average pooling layer and a classification layer." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 365, + 446, + 378 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 446, + 378 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 446, + 378 + ], + "type": "text", + "content": "5.2. Spiking Resformer Block" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 384, + 545, + 454 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 454 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 454 + ], + "type": "text", + "content": "As illustrated in Fig. 2, the spiking Resformer block consists of a Multi-Head Dual Spike Self-Attention (MHDSSA) module and a Group-Wise Spiking Feed-Forward Network (GWSFFN). We first introduce the two modules and then derive the form of the spiking Resformer block." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 455, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 455, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 455, + 545, + 575 + ], + "type": "text", + "content": "Multi-Head Convolutional Spiking Self-Attention. In Sec. 4, we propose the single-head form of DSSA. It can be easily extended to the multi-head DSSA (MHDSSA) following a similar approach to the vanilla Transformer [36]. In MHDSSA, we first split the results of linear transformation in DST into " + }, + { + "bbox": [ + 304, + 455, + 545, + 575 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 304, + 455, + 545, + 575 + ], + "type": "text", + "content": " heads, then perform DSSA on each head and concatenate them together. Finally, we use point-wise convolution to project the concatenated features thus fusing the features in different heads. The MHDSSA can be formulated as follows:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 315, + 580, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 580, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 315, + 580, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\operatorname {M H D S S A} (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {1} \\left([ \\mathrm {D S S A} _ {i} (\\operatorname {S N} (\\mathbf {X})) ] _ {i = 1} ^ {h}\\right)\\right), \\tag {17}", + "image_path": "7a06b6d13c2d075d86122c22e4d9c758e3f349f1c02dd3f7d5faf32cce52c787.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "inline_equation", + "content": "[\\ldots]" + }, + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "text", + "content": " denotes the concatenate operation, " + }, + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_1" + }, + { + "bbox": [ + 304, + 605, + 545, + 629 + ], + "type": "text", + "content": " denotes the point-wise convolution." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "Group-Wise Spiking Feed-Forward Network. The spiking feed-forward network (SFFN) proposed in previous spiking vision transformers is composed of two linear layers with batch normalization and spiking neuron activation [41, 45]. Moreover, the expansion ratio is usually set to 4, i.e., the first layer raises the dimension by a factor of 4 while the second layer reduces to the original dimension." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5614" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 113, + 545, + 280 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Architectures of SpikingResformer series. The output size corresponds to the input size of " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "D_{i}" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "H_{i}" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " are the embedding dimension and number of heads of MHDSSA in stage " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "p_i" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " denotes that the MHDSSA in stage " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " uses " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "p_i \\times p_i" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " convolution in DST. " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "R_{i}" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "G_{i}" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": " denote the expansion ratio and embedding dimension per group of GWSFFN in stage " + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 70, + 547, + 105 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 113, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 49, + 113, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 49, + 113, + 545, + 280 + ], + "type": "table", + "html": "
StageOutput SizeLayer NameSpikingResformer-TiSpikingResformer-SSpikingResformer-MSpikingResformer-L
Stem56×56StemConv 7×7, stride 2, Maxpooling 3×3, stride 2
Stage 156×56MHDSSA[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=64H1=1,p1=4R1=4,G1=64] × 1[D1=128H1=1,p1=4R1=4,G1=64] × 1
GWSFFN
Stage 228×28DownsampleConv 3×3, 192, stride 2Conv 3×3, 256, stride 2Conv 3×3, 384, stride 2Conv 3×3, 512, stride 2
MHDSSA[D2=192H2=3,p2=2R2=4,G2=64] × 2[D2=256H2=4,p2=2R2=4,G2=64] × 2[D2=384H2=6,p2=2R2=4,G2=64] × 2[D2=512H2=8,p2=2R2=4,G2=64] × 2
GWSFFN
Stage 314×14DownsampleConv 3×3, 384, stride 2Conv 3×3, 512, stride 2Conv 3×3, 768, stride 2Conv 3×3, 1024, stride 2
MHDSSA[D3=384H3=6,p3=1R3=4,G3=64] × 3[D3=512H3=8,p3=1R3=4,G3=64] × 3[D3=768H3=12,p3=1R3=4,G3=64] × 3[D3=1024H3=16,p3=1R3=4,G3=64] × 3
GWSFFN
Classifier1×1Linear1000-FC
", + "image_path": "7f28f8c23c93ae2972c05c26a30d7a8111c2a1d65358e53c4f64838d11e54fbb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 299, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 299, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 299, + 289, + 418 + ], + "type": "text", + "content": "Based on SFFN, we insert a " + }, + { + "bbox": [ + 46, + 299, + 289, + 418 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 299, + 289, + 418 + ], + "type": "text", + "content": " convolution layer with the residual connection between two linear layers to enable SFFN to extract local features. Since the dimension of the hidden features between the two linear layers is expanded by a factor of 4 compared to the input, in order to reduce the number of parameters and computational overhead, we use group-wise convolution and set every 64 channels as 1 group. We also employ the spike-driven design in [41, 44]. The group-wise spiking feed-forward network (GWSFFN) can be formulated as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 77, + 428, + 287, + 441 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 428, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 77, + 428, + 287, + 441 + ], + "type": "interline_equation", + "content": "\\operatorname {F F L} _ {i} (\\mathbf {X}) = \\operatorname {B N} \\left(\\operatorname {C o n v} _ {1} (\\operatorname {S N} (\\mathbf {X}))\\right), i = 1, 2, \\tag {18}", + "image_path": "9698d3609b89841147a3592a921d1071c2bcb18d38bc1d4d1c46f9eaa991a8a4.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 77, + 443, + 287, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 77, + 443, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 77, + 443, + 287, + 456 + ], + "type": "interline_equation", + "content": "\\operatorname {G W L} (\\mathbf {X}) = \\operatorname {B N} (\\operatorname {G W C o n v} (\\operatorname {S N} (\\mathbf {X}))) + \\mathbf {X}, \\tag {19}", + "image_path": "93ab1d949c564e101665c3c7f45c17de3099c3e97d0bac991426e96f8a77bb0f.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 458, + 287, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 458, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 56, + 458, + 287, + 471 + ], + "type": "interline_equation", + "content": "\\operatorname {G W S F F N} (\\mathbf {X}) = \\operatorname {F F L} _ {2} (\\operatorname {G W L} (\\operatorname {F F L} _ {1} (\\mathbf {X}))). \\tag {20}", + "image_path": "b40d2cd3d5715607db3628b2d7c7ace25cdacfa1b2b8856964055c9f3e413974.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathrm{FFL}_i(\\cdot), i = 1,2" + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "content": " denote the feed-forward layers, " + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathrm{Conv}_1(\\cdot)" + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "content": " is point-wise convolution (" + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "content": " convolution), which equal to the linear transformation. " + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathrm{GWL}(\\cdot)" + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "content": " denotes group-wise convolution layer, " + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "inline_equation", + "content": "\\mathrm{GWConv}(\\cdot)" + }, + { + "bbox": [ + 46, + 480, + 287, + 539 + ], + "type": "text", + "content": " denotes the group-wise convolution." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 540, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 574 + ], + "type": "text", + "content": "Spiking Resformer Block. With the MHDSSA module and GWSFFN above, the spiking resformer block can be formulated as:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 113, + 586, + 287, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 586, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 113, + 586, + 287, + 598 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} _ {i} = \\operatorname {M H D S S A} \\left(\\mathbf {X} _ {i}\\right) + \\mathbf {X} _ {i}, \\tag {21}", + "image_path": "2e2d024771e65dedd128bf36b10db1d07dc735aa35edca80c7a2ba6ece36ee3a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 102, + 600, + 287, + 613 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 600, + 287, + 613 + ], + "spans": [ + { + "bbox": [ + 102, + 600, + 287, + 613 + ], + "type": "interline_equation", + "content": "\\mathbf {X} _ {i + 1} = \\operatorname {G W S F N} \\left(\\mathbf {Y} _ {i}\\right) + \\mathbf {Y} _ {i}. \\tag {22}", + "image_path": "b637e4ecfb5077c8905f94e92d6b0310252ef3dc7782fd08862d045243420140.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_i" + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "content": " denotes the output features of MHDSSA module in the " + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 622, + 287, + 647 + ], + "type": "text", + "content": "-th spiking reformer block." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 658, + 128, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 128, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 128, + 671 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "In this section, we first evaluate the performance and energy efficiency of SpikingResformer on the ImageNet classification task. Then, we perform ablation experiments on key" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 299, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 299, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 305, + 299, + 545, + 323 + ], + "type": "text", + "content": "components in SpikingResformer. Finally, we evaluate the transfer learning ability of SpikingResformer." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 331, + 440, + 344 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 331, + 440, + 344 + ], + "spans": [ + { + "bbox": [ + 306, + 331, + 440, + 344 + ], + "type": "text", + "content": "6.1. ImageNet Classification" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 350, + 545, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 410 + ], + "type": "text", + "content": "ImageNet [4] is one of the most typical static image datasets widely used for image classification. For a fair comparison, we generally follow the data augmentation strategy and training setup in [41]. More details of the experimental setup can be found in the supplementary." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "spans": [ + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": "Results. Our experimental results are listed in Tab. 2. For comparison, we also list the results of existing spiking convolutional networks and spiking Vision Transformers. As shown in Tab. 2, SpikingResformer achieves higher accuracy, fewer parameters, and lower energy consumption at the same time compared to existing methods. For instance, SpikingResformer-Ti achieves " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "74.34\\%" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": " accuracy with only 11.14M parameters and 2.73G SOPs " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "(2.46\\mathrm{mJ})" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": ", outperforming Spike-driven Transformer-8-384 by " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "2.06\\%" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": ", saving 5.67M parameters and " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "1.44\\mathrm{mJ}" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": " energy. SpikingResformer-M achieves " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "77.24\\%" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": " accuracy with 35.52M parameters and 6.07G SOPs " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "(5.46\\mathrm{mJ})" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": ", outperforming Spike-driven Transformer-8-768 by " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "0.92\\%" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": " while saving 30.82M parameters. Particularly, the SpikingResformer-L achieves up to " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "79.40\\%" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": " accuracy when the input size is enlarged to " + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "inline_equation", + "content": "288\\times 288" + }, + { + "bbox": [ + 305, + 411, + 546, + 601 + ], + "type": "text", + "content": ", which is the state-of-the-art result in SNN field." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 400, + 624 + ], + "type": "text", + "content": "6.2. Ablation Study" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 630, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 630, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 630, + 547, + 713 + ], + "type": "text", + "content": "We perform ablation experiments on key components in SpikingResformer, including the multi-stage architecture, the group-wise convolution layer in GWSFFN, and our proposed spiking self-attention mechanism. The ablation experiments are conducted on the ImageNet100 dataset, which is a subset of the ImageNet dataset and consists of 100 categories from the ImageNet dataset. The experiment" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5615" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 113, + 545, + 388 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "text", + "content": "Table 2. Evaluation on ImageNet. SOPs denotes the average synaptic operations of an image inference on ImageNet validation data. Energy is the estimation of energy consumption same as [41, 45]. The default input resolution for training and inference is " + }, + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "inline_equation", + "content": "224 \\times 224" + }, + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "text", + "content": " means the input is enlarged to " + }, + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "inline_equation", + "content": "288 \\times 288" + }, + { + "bbox": [ + 47, + 70, + 545, + 105 + ], + "type": "text", + "content": " in inference. - means the data is not provided in the original paper." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 113, + 545, + 388 + ], + "lines": [ + { + "bbox": [ + 49, + 113, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 49, + 113, + 545, + 388 + ], + "type": "table", + "html": "
MethodTypeArchitectureTParam (M)SOPs (G)Energy (mJ)Top-1 Acc. (%)
Spiking ResNet [14]ANN-to-SNNResNet-3435021.7965.2859.3071.61
ResNet-5035025.5678.2970.9372.75
STBP-tdBN [43]Direct TrainingSpiking ResNet-34621.796.506.3963.72
TET [6]Direct TrainingSpiking ResNet-34621.79--64.79
SEW ResNet-34421.79--68.00
SEW ResNet [9]Direct TrainingSEW ResNet-34421.793.884.0467.04
SEW ResNet-50425.564.834.8967.78
SEW ResNet-101444.559.308.9168.76
SEW ResNet-152460.1913.7212.8969.26
Spikformer [45]Direct TrainingSpikformer-8-384416.816.827.7370.24
Spikformer-8-512429.6811.0911.5873.38
Spikformer-8-768466.3422.0921.4874.81
Spikingformer [44]Direct TrainingSpikingformer-8-384416.81-4.6972.45
Spikingformer-8-512429.68-7.4674.79
Spikingformer-8-768466.34-13.6875.85
Spike-driven Transformer [41]Direct TrainingSpike-driven Transformer-8-384416.81-3.9072.28
Spike-driven Transformer-8-512429.68-4.5074.57
Spike-driven Transformer-8-768466.34-/-6.09/-76.32/77.07†
SpikingResformer (Ours)Direct TrainingSpikingResformer-Ti411.142.73/4.71†2.46/4.24†74.34/75.57†
SpikingResformer-S417.763.74/6.40†3.37/5.76†75.95/76.90†
SpikingResformer-M435.526.07/10.24†5.46/9.22†77.24/78.06†
SpikingResformer-L460.389.74/16.40†8.76/14.76†78.77/79.40†
", + "image_path": "fe2f025e7b2ef990e4883e6bf3c99ab93c253efd3816fa75d4417bbcb66de0b4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 438, + 285, + 518 + ], + "blocks": [ + { + "bbox": [ + 47, + 407, + 288, + 431 + ], + "lines": [ + { + "bbox": [ + 47, + 407, + 288, + 431 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 288, + 431 + ], + "type": "text", + "content": "Table 3. Ablation Study on ImageNet100 dataset. The number of parameters for all variants is comparable to SpikingResformer-S." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 438, + 285, + 518 + ], + "lines": [ + { + "bbox": [ + 50, + 438, + 285, + 518 + ], + "spans": [ + { + "bbox": [ + 50, + 438, + 285, + 518 + ], + "type": "table", + "html": "
ModelSOPs (G)Energy (mJ)Acc. (%)
SpikingResformer-S2.432.1888.06
w/o multi-stage architecture1.841.6685.32
w/o group-wise convolution2.372.1384.64
w/o DSSAnot converge
w/o p × p convolution4.343.9186.14
w/o scalingnot converge
", + "image_path": "b5c48a893a4363dda20c6aea7cbaaabc1746b8345ef88bf58d1b72206b0efee1.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 542, + 287, + 567 + ], + "type": "text", + "content": "tal setup basically follows the one in Sec. 6.1. Detailed settings are listed in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 567, + 287, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 675 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 675 + ], + "type": "text", + "content": "Multi-Stage Architecture. To verify the effectiveness of the multi-stage architecture, we replace it with the Spikingformer-based architecture, while the structure of the spiking Resformer block remains unchanged. We adjust the embedding dimensions to make the model parameters comparable to SpikingResformer-S. As shown in Tab. 3, SpikingResformer-S outperforms the variant without multi-stage architecture by " + }, + { + "bbox": [ + 46, + 567, + 287, + 675 + ], + "type": "inline_equation", + "content": "2.74\\%" + }, + { + "bbox": [ + 46, + 567, + 287, + 675 + ], + "type": "text", + "content": ", demonstrating the effectiveness of multi-stage architecture." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Group-Wise Convolution Layer. In comparison to the point-wise SFFN, GWSFFN employs a " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "3 \\times 3" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " group-wise convolution layer between the two linear layers. We" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 409, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 545, + 495 + ], + "type": "text", + "content": "evaluate its effect by removing the group-wise convolution layer and increasing the dimension to keep the number of parameters constant. As demonstrated in Tab. 3, SpikingResformer-S achieves " + }, + { + "bbox": [ + 304, + 409, + 545, + 495 + ], + "type": "inline_equation", + "content": "3.42\\%" + }, + { + "bbox": [ + 304, + 409, + 545, + 495 + ], + "type": "text", + "content": " higher accuracy in contrast to the variant without the group-wise convolution layer. This difference highlights the benefits of the group-wise convolution layer in GWSFFN." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": "Dual Spike Self-Attention. To validate the effectiveness of DSSA, we first replace DSSA with existing spiking self-attention mechanisms, including Spiking Self-Attention (SSA) in Spikformer and Spike-Driven Self-Attention (SDSA) in Spike-driven Transformer. However, neither SSA nor SDSA converges. We believe this is because SSA and SDSA do not fit the multi-scale input. To further validate the key factors that help DSSA fit for the multi-scale input, we conduct two more sets of experiments. One set replaces all " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "p \\times p" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " convolutions with " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " convolutions in DST to validate the effect of reducing spatial size. The other removes the scaling factor or replaces our proposed scaling factors with " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "1 / \\sqrt{d}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " to validate the effect of scaling. As a result, the first group converges but only achieves " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "86.14\\%" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": " accuracy with a higher energy consumption of " + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "inline_equation", + "content": "3.91\\mathrm{mJ}" + }, + { + "bbox": [ + 304, + 498, + 546, + 714 + ], + "type": "text", + "content": ", while the second set does not converge. This shows that the scaling factor is the key to convergence. We believe that both SSA and SDSA lack proper scaling meth" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5616" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 99, + 91, + 493, + 217 + ], + "blocks": [ + { + "bbox": [ + 118, + 70, + 474, + 82 + ], + "lines": [ + { + "bbox": [ + 118, + 70, + 474, + 82 + ], + "spans": [ + { + "bbox": [ + 118, + 70, + 474, + 82 + ], + "type": "text", + "content": "Table 4. Transfer learning results on CIFAR10, CIFAR100, CIFAR10-DVS, DVSGesture datasets." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 91, + 493, + 217 + ], + "lines": [ + { + "bbox": [ + 99, + 91, + 493, + 217 + ], + "spans": [ + { + "bbox": [ + 99, + 91, + 493, + 217 + ], + "type": "table", + "html": "
MethodTypeCIFAR10CIFAR100CIFAR10-DVSDVSGesture
TAcc.TAcc.TAcc.TAcc.
STBP-tdBN [43]Direct Training693.16--1067.84096.87
PLIF [10]Direct Training893.50--2074.82097.57
Dspike [25]Direct Training694.25674.241075.4--
Spikformer [45]Direct Training495.19477.861680.61697.9
Spikingformer [44]Direct Training495.61479.091681.31698.3
Spike-driven Transformer [41]Direct Training495.6478.41680.01699.3
Spikformer [45]Transfer Learning497.03483.83----
SpikingResformer (Ours)Transfer Learning497.40485.981084.81093.4
", + "image_path": "cdc3f3be8d18dee33e93966322f35998f14e656de8748350db8f49c2dd85c600.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 236, + 288, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 236, + 288, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 288, + 308 + ], + "type": "text", + "content": "ods, thus do not apply to multi-stage architecture. SSA employs the same scaling factor as vanilla self-attention, i.e., " + }, + { + "bbox": [ + 46, + 236, + 288, + 308 + ], + "type": "inline_equation", + "content": "1 / \\sqrt{d}" + }, + { + "bbox": [ + 46, + 236, + 288, + 308 + ], + "type": "text", + "content": ". However, this does not apply to spike matrix multiplication, since spikes do not have mean 0 and variance 1. SDSA has no scaling method, which may be feasible when the feature map is small but not for multi-scale inputs." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 319, + 157, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 319, + 157, + 333 + ], + "spans": [ + { + "bbox": [ + 47, + 319, + 157, + 333 + ], + "type": "text", + "content": "6.3. Transfer Learning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 340, + 287, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 340, + 287, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 340, + 287, + 495 + ], + "type": "text", + "content": "High transfer learning ability is a key advantage of Vision Transformer. We evaluate the transfer learning ability of the proposed SpikingResformer on static dataset CIFAR10 and CIFAR100 [19] and neuromorphic dataset CIFAR10-DVS [23] and DVSGesture [1] by fine-tuning the models pre-trained on ImageNet. Among the existing spiking Vision Transformers, only Spikformer provides transfer learning results, and only on the static image datasets CIFAR10 and CIFAR100. Thus, we also compared our results with the direct training results for a comprehensive comparison. Tab. 4 lists the highest accuracy achieved by these methods. The experimental setup and a more detailed comparison can be found in the supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": "Static Image Datasets. As shown in Tab. 4, SpikingResformer achieves " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "97.40\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " accuracy on CIFAR10 dataset and " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "85.98\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " accuracy on CIFAR100 dataset, which is the state-of-the-art result, outperforming the transfer learning results of Spikformer by " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "0.37\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " on CIFAR10 and " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "2.15\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " on CIFAR100. Compared to direct training methods, SpikingResformer obtained from transfer learning has significantly better performance. For example, SpikingResformer outperforms Spikingformer by " + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "inline_equation", + "content": "6.89\\%" + }, + { + "bbox": [ + 46, + 497, + 287, + 616 + ], + "type": "text", + "content": " on CIFAR100 dataset, demonstrating the advantage of transfer learning." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 715 + ], + "type": "text", + "content": "Neuromorphic Datasets. Neuromorphic datasets differ significantly from traditional static image datasets. The samples of the neuromorphic dataset consist of event streams instead of RGB images. As a result, there is a large gap between the source and target domain for models pre-trained on static image datasets. To bridge this gap, we stack the events over a period of time to form a frame. The RGB channels are replaced with positive events," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "text", + "content": "negative events, and the sum of events channels, respectively. As shown in Tab. 4, transfer learning results of SpikingResformer significantly outperform the direct training ones on CIFAR10-DVS. SpikingResformer achieves " + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "inline_equation", + "content": "84.8\\%" + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "text", + "content": " accuracy on CIFAR10-DVS, outperforming Spikingformer by " + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "text", + "content": ". However, the transfer learning results on DVS-Gesture fail to achieve comparable performance to direct training. SpikingResformer only achieves " + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "inline_equation", + "content": "93.4\\%" + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "text", + "content": " accuracy on DVSGesture, falling behind the state-of-the-art method Spike-driven Transformer by " + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "inline_equation", + "content": "5.9\\%" + }, + { + "bbox": [ + 304, + 236, + 547, + 488 + ], + "type": "text", + "content": ". We believe that this is mainly due to the way CIFAR10-DVS is constructed differs from DVSGesture. CIFAR10-DVS is converted from CIFAR10, which does not contain temporal information. Thus, models pre-trained on static datasets can transfer to CIFAR10-DVS well. However, DVSGesture is directly created from human gestures using a dynamic vision sensor, thus containing rich temporal information. As a result, models pre-trained on static datasets do not transfer well to DVSGesture. We hope our exploration of transfer learning on neuromorphic datasets could pave the way for further transfer learning research of SNNs." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "spans": [ + { + "bbox": [ + 306, + 497, + 379, + 509 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 517, + 547, + 649 + ], + "type": "text", + "content": "In this paper, we propose a novel spiking self-attention mechanism named Dual Spike Self-Attention (DSSA). It produces spiking self-attention via Dual Spike Transformation, which is fully spike-driven and compatible with SNNs. We detail the scaling factors in DSSA enabling it to handle feature maps of arbitrary scales. Based on DSSA, we propose SpikingResformer, which combines the ResNet-based multi-stage architecture with our proposed DSSA to achieve superior performance and energy efficiency with fewer parameters. Extensive experiments demonstrate the effectiveness and superiority of the proposed SpikingResformer." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 658, + 404, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 404, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 404, + 671 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 715 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China (62176003, 62088102) and by the Beijing Nova Program (20230484362)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5617" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 156 + ], + "type": "text", + "content": "[1] Arnon Amir, Brian Taba, David Berg, Timothy Melano, Jeffrey McKinstry, Carmelo Di Nolfo, Tapan Nayak, Alexander Andreopoulos, Guillaume Garreau, Marcela Mendoza, et al. 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However, due to the intrinsic ill-posedness and high-dimensional ambiguities, addressing NaUPS is still an open question. Existing works impose strong assumptions on the environment lights and objects' material, restricting the effectiveness in more general scenarios. Alternatively, some methods leverage supervised learning with intricate models while lacking interpretability, resulting in a biased estimation. In this work, we propose Spin Light Uncalibrated Photometric Stereo (Spin-UP), an unsupervised method to tackle NaUPS in various environment lights and objects. The proposed method uses a novel setup that captures the object's images on a rotatable platform, which mitigates NaUPS's ill-posedness by reducing unknowns and provides reliable priors to alleviate NaUPS's ambiguities. Leveraging neural inverse rendering and the proposed training strategies, Spin-UP recovers surface normals, environment light, and isotropic reflectance under complex natural light with low computational cost. Experiments have shown that Spin-UP outperforms other supervised / unsupervised NaUPS methods and achieves state-of-the-art performance on synthetic and real-world datasets. Codes and data are available at https://github.com/LMozart/CVPR2024-SpinUP.", + "bbox": [ + 76, + 391, + 472, + 785 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 799, + 209, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Natural light uncalibrated photometric stereo (NaUPS) [6] is proposed to relieve the dark room and directional light as", + "bbox": [ + 75, + 824, + 468, + 854 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sumption in classical uncalibrated photometric stereo, aiming to reconstruct the surface normal given images of an object captured at arbitrary environment light. The implications of NaUPS are far-reaching: it makes photometric stereo universal. However, solving NaUPS is still an open question because of the intrinsic ill-posedness introduced by the varying light of each image and the high dimensional ambiguities between the light and objects [6].", + "bbox": [ + 500, + 362, + 890, + 483 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous optimization-based methods use the simple light model to represent the varying environment lights and Lambertian reflectance to represent the material [6, 7, 21]. These models help mitigate the ill-posedness and ambiguities to some extent but become ineffective in handling objects with general reflectance (e.g., non-Lambertian reflectance) under complex environment light, leading to unsatisfactory reconstruction outcomes. Besides, since they solely model the varying lights in each image, the unknowns introduced by the light model may increase with the resolution and numbers of the images, restricting their method to low-resolution and insufficient images.", + "bbox": [ + 496, + 486, + 892, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Considering the difficulties of explicitly mitigating the ill-posedness and ambiguities, recent advances [10, 11] turn to data-driven methods: they train a deep learning model on large-scale datasets and implicitly exploit deep light features from images to improve performance. However, those methods lack interpretability, making them hard to constrain during training. Consequently, the model may be affected by the data bias and prone to specific types of light sources [10] or reflection variations [11] among images.", + "bbox": [ + 496, + 670, + 893, + 806 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite a persistent exploration in this research field, a method capable of handling general objects under natural light while free from data bias is still missing. In this paper, we provide a new perspective on solving NaUPS. Specifically, we propose a novel setup that acquires images on a rotatable platform under a static environment light. In such a", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Co-first author. ‡Corresponding author.", + "bbox": [ + 94, + 862, + 316, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger$ Work completed while interning at the State Key Lab of BrainMachine Intelligence, Zhejiang University.", + "bbox": [ + 94, + 875, + 468, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11905", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "case, the object is illuminated by rotated environment lights. Representing such rotated lights requires fewer parameters than solely modeling varying lights in each image since we model the lights as a uniform environment light varied by low degree-of-freedom (DOF [5]) rotation. This frees us from significantly increasing unknowns when implementing advanced parametric light models (e.g., spherical Gaussian) and reflectance models to handle general scenarios. Additionally, based on such a setup, we further derive a reliable light initialization method by analyzing the pixel value at object's occluding boundary. Such light initialization will help the model converge at the beginning and alleviate the ambiguity between light and objects during training.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the help of the proposed setup and light initialization method, we develop Spin Light Uncalibrated Photometric Stereo (Spin-UP), addressing NaUPS by optimizing inverse rendering framework in an unsupervised manner. To our best knowledge, this is the first unsupervised method that can handle general objects under natural light. Unlike previous methods, Spin-UP can jointly reconstruct environment light, isotropic reflectance, and complicated shapes through iterative optimization. To reduce the computational cost and improve convergence, we propose two strategies: interval sampling and shrinking range computing, which help optimize Spin-UP in low GPU usage (5 GB) and fast running time (25 mins). Experiments on synthetic and real-world datasets demonstrate our superior performance over previous methods on general scenarios. Overall, our contributions are summarized as follows:", + "bbox": [ + 75, + 287, + 472, + 527 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We design a novel setup for NaUPS, which reduces unknowns of light representation and facilitates solving NaUPS in an unsupervised manner.", + "2. We introduce a light prior, which leverages an object's occluding boundaries to initialize a reliable environment light. Based on the setup and light prior, we propose the unsupervised NaUPS method named Spin-UP.", + "3. We present two training strategies for fast training and convergence of Spin-UP." + ], + "bbox": [ + 76, + 530, + 468, + 667 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 679, + 218, + 694 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly review recent supervised and unsupervised NaUPS methods. We also summarize other techniques that exploit priors from occluding boundaries. Additionally, we discuss recent advances in 3D vision to distinguish Spin-UP from other neural inverse rendering approaches. Given that the focus of this paper is on NaUPS, a group of works reconstructing 3D surfaces from a single image by deep learning under natural light [15] or shading [4, 12, 32] are not included.", + "bbox": [ + 75, + 703, + 468, + 839 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Natural Light Uncalibrated Photometric Stereo. Unsupervised NaUPS methods jointly recover the light, reflectance properties, and surface normal. These methods explicitly model the environment light by low-order spheri", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cal harmonics (SH) [2, 21], spatially varying spherical harmonics (SV-SH) [7, 18] or equivalent directional light (Eqv-Dir) [6] to mitigate the ill-posedness, and use integrability constraint [2], shape initialization [7], non-physical lighting regularization [21], or graph-based ambiguity relaxation [6] to alleviate the ambiguity. In contrast, supervised NaUPS methods [10, 11] apply deep learning models like transformers to reconstruct normal maps without explicitly estimating the environment light. The models are trained on a dataset containing images of diverse objects captured under various lighting conditions, including directional, point, and environment light. Compared to previous work, the proposed Spin-UP distinguishes itself in three key aspects: 1) it features a novel setup explicitly designed to model correlations among observed images to mitigate the ill-posedness of NaUPS, 2) leveraging this unique setup, a novel light initialization method is introduced to mitigate ambiguities, and 3) an advanced light and material model is implemented to address a broader range of scenarios.", + "bbox": [ + 496, + 90, + 890, + 378 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Priors from the Boundaries. The occluding boundaries of an object are considered to reveal adequate information about the object's shape and the scene's light. Given the fact that the projection of the boundaries' normal to xy-plane is perpendicular to the boundaries in orthographic projection, methods are developed to constraint the surface normal estimation during iterative optimization [16] or recover a rough shape to initialize the geometry in multi-view [8] or photometric stereo [7]. Other methods associate the boundaries normal with the reflectance to estimate a rough position of the directional lights [27]. However, none of them derive the environment light from the boundary reflectance. Given the setup in Spin-UP, we can roughly estimate the environment by analyzing occluding boundaries and the corresponding pixel points. This approach provides a reliable initialization for lighting that alleviates ambiguity in NaUPS.", + "bbox": [ + 496, + 378, + 892, + 619 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Inverse rendering in 3D Vision. Neural Radiance Fields (NeRF) [19] implicitly store the scene's shape and reflectance through MLPs optimized by inverse volume rendering. While NeRF can only recover coarse 3D shapes, several subsequent works [3, 25, 26, 29, 31, 33] have been proposed to combine the surface rendering and volume rendering techniques, recovering fine shapes under varying viewpoints but static environment light. In contrast, viewpoints in Spin-UP are relatively static to the objects. While most neural field methods aim to recover the whole 3D geometries, Spin-UP only recovers the object's surface.", + "bbox": [ + 496, + 621, + 890, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 500, + 797, + 671, + 815 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In Sec. 3.1, we explain the Spin-UP's setup and how it reduces the unknowns. In Sec. 3.2, we introduce the light prior that alleviates ambiguities in NaUPS, including details of the light initialization method based on that prior. In Sec. 3.3, we describe the implementation details of the", + "bbox": [ + 496, + 824, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11906", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/7a6c86879d55ac5889e65e52e95fbdfb6631fc1127d0315e5d44db26fe7970a5.jpg", + "image_caption": [ + "Figure 1. The proposed image capturing setup. Left: an illustration of image-capturing equipment consisting of a rotatable platform, a camera, and the target object. We spin the platform in $360^{\\circ}$ and capture images of the object. The object and camera rotate together with the platform. Right-top: Four observed images at different positions. Right-bottom: Ground truth environment light. Dashed color boxes indicate the corresponding camera views." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 467, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "proposed Spin-UP framework and losses. In Sec. 3.4, we demonstrate two proposed training strategies.", + "bbox": [ + 75, + 351, + 468, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Spin Light Setup", + "text_level": 1, + "bbox": [ + 76, + 393, + 243, + 411 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 1, we capture a sequence of images $\\pmb{I} \\triangleq \\{I_j | j \\in [1, \\dots, N_I]\\}$ for an object by rotating it together with a linear perspective camera in $360^\\circ$ on a rotatable platform. Since the relative positions and orientations between the camera and the object are fixed during rotation, each observed image is aligned with the rotated environment light $L(R_j \\cdot \\omega)$ , where $\\omega \\in \\mathbb{R}^3$ indicates the incident light's direction, $R_j = R(\\theta_j)$ is the 1-DoF [5] rotation matrix representing rotation about the vertical axis, $\\theta_j$ is the rotation angle, $\\theta_1 = 0$ . As we conduct $360^\\circ$ rotation and assume a constant velocity (despite not strictly required in practice), $R_j$ can be initialized given $\\theta_j = 2\\pi (j - 1) / N_I$ . Given a sequence of images $I$ and the initialized $R$ , Spin-UP iteratively optimizes the normal map $N$ , the environment light $L$ , isotropic BRDF map $M$ , and rotation angle $R$ by solving", + "bbox": [ + 75, + 417, + 472, + 660 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\boldsymbol {L}, \\boldsymbol {M}, \\boldsymbol {N}, \\boldsymbol {R}} {\\arg \\min } \\sum_ {i = 1} ^ {N _ {P}} \\sum_ {j = 1} ^ {N _ {I}} \\mathcal {E} \\left(\\boldsymbol {m} _ {i j}, \\hat {\\boldsymbol {m}} _ {i j}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 662, + 468, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $N_P$ is the number of sampled points on the surface, $\\pmb{m}_{ij}$ and $\\hat{\\pmb{m}}_{ij}$ indicate the ground truth and estimation of point $i$ 's color in image $I_j$ , respectively. $\\mathcal{E}(\\cdot ,\\cdot)$ is loss function between $\\pmb{m}_{ij}$ and $\\hat{\\pmb{m}}_{ij}$ (i.e., mean absolute error). We adopt the rendering equation to calculate the color $\\hat{\\pmb{m}}^2$", + "bbox": [ + 75, + 707, + 468, + 782 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {\\boldsymbol {m}} = \\int_ {\\Omega} s \\boldsymbol {L} (\\boldsymbol {\\omega}) \\rho (\\boldsymbol {\\omega} \\cdot \\boldsymbol {n}) \\mathrm {d} \\boldsymbol {\\omega}, \\\\ = \\int_ {\\Omega} s \\boldsymbol {L} (\\boldsymbol {\\omega}) \\left(\\rho^ {s} + \\rho^ {d}\\right) (\\boldsymbol {\\omega} \\cdot \\boldsymbol {n}) \\mathrm {d} \\boldsymbol {\\omega}. \\end{array} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 784, + 468, + 851 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/2788daca40f9e2b875ca1853204fee7670a816e5cdd379d44670afc2fa303648.jpg", + "table_caption": [ + "Table 1. A comparison of type, unknowns' number (number), and representation capacity (rep. capacity) of light model among Spin-UP and representative unsupervised NaUPS methods. The unknown number is calculated on 50 images $(512 \\times 512)$ . 'freq.' represents frequency." + ], + "table_footnote": [], + "table_body": "
QL15 [21]HY19 [7]GM21 [6]Spin-UP
typeSV-SHGlobal SHEqv-DirSG
number1.5K4501.4M434
rep. capacitylow-freq.low-freq.low-freq.high-freq.
", + "bbox": [ + 503, + 164, + 888, + 212 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/1fabe228253706e1c6b33412be24413c0e6c3b6e2f9914976c9579624a35957d.jpg", + "image_caption": [ + "Figure 2. The proposed light initialization method in Spin-UP. We crop the boundary pixels $m_{b}$ and normal $\\pmb{n}_{b}$ from input images. Then, we remap them on the sphere and rotate them with their corresponding rotations $\\pmb{R}$ . Based on a light probe composed of gray-scale boundary pixels, we optimize the SG light model to obtain the environment light." + ], + "image_footnote": [], + "bbox": [ + 501, + 223, + 890, + 362 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Omega$ represents the upper hemisphere centered at the normal vector $\\pmb{n}$ . $s$ is the first shadow. $\\rho^s$ and $\\rho^d$ indicate the specular and diffuse reflectance, respectively. The ambiguities between the light $L$ and reflectance of the object $\\pmb{M}$ are often disregarded [13, 16].", + "bbox": [ + 496, + 474, + 890, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Unkowns reduction. The proposed spin light setup reduces the unknowns of the light representation $L$ by exploiting correlations between different images. Unlike premodel the light for ionization in the nucleus is modeled using the method shown in the setup, we can exploit from the object's boundary to light initialization. The idea is motivated by the observation that the light map has no effect on the image. We consider the images into the environment light (see Fig. 2). For an object with a light boundary, the normal of those boundaries can roughly derive a light map indicating the light sources' positions at the object. We then use the recently measured light map at $N_{1}$ to calculate the ionized and ground state image. As such, the unknowns consist of the environment light model's parameters and the number of rotational angles that are quantitatively equal to $N_{I}$ . The total unknown amount is reduced compared to other methods (Table 1), which helps mitigate the ill-posedness and facilitates solving NaUPS with advanced light and reflectance models in an unsupervised manner.", + "bbox": [ + 488, + 551, + 890, + 762 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Light Prior from Boundaries", + "text_level": 1, + "bbox": [ + 500, + 771, + 758, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Based on the spin light setup, we can exploit priors from the object boundary for light initialization to alleviate the ambiguity. The idea is motivated by the observation that the pixel value $m_{b}$ at an object's boundary provides insights into the environment light (see Fig. 2). For an object with occluding boundaries, the normal of those boundaries $\\mathbf{n}_b$ can be pre-computed [13, 16]. By bonding $m_{b}, n_{b}$ , and $R$ , we can", + "bbox": [ + 496, + 794, + 890, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "1We assume the object's boundary is geometrically smooth (occluding boundary).", + "bbox": [ + 76, + 862, + 468, + 887 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2The subscripts are omitted for simplicity.", + "bbox": [ + 94, + 887, + 318, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11907", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/72a22c394c32f9bb276f419d5e469fcd4fd938f9419f85a7b47b443207ab6f8c.jpg", + "image_caption": [ + "(a)", + "Figure 3. An illustration of mismatched light source positions. Rows from top to bottom: an illustration of reflection on materials with different roughness; the initial environment light before applying any filters given objects' boundary pixels; the ground truth environment light. Objects are (a) the diffuse-dominant sphere, (b) the diffuse and specular mixture sphere, and (c) the specular dominant sphere. The yellow and red lines in rows 2 and 3 indicate a rough position of the light sources." + ], + "image_footnote": [], + "bbox": [ + 112, + 93, + 207, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/51ec9e0fb3fe2aa89b8d65e38bd4938ef8350af1e91c95754a18fef0eabc2d1f.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 223, + 88, + 321, + 215 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/910595d469e5d2077ddfaad19583c6308d9eacfb9f341ef3795235e7ea080289.jpg", + "image_caption": [ + "(c)" + ], + "image_footnote": [], + "bbox": [ + 336, + 88, + 434, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "roughly derive a light map indicating the light sources' positions and intensities, where $m_b$ directly represent the light intensity $L(\\omega_b)$ at $\\boldsymbol{\\omega}_b = \\boldsymbol{R} \\cdot \\boldsymbol{n}_b$ . However, the derived light map for objects with different materials may contain mismatched light source positions and chromatic bias, leading to inaccurate light initialization.", + "bbox": [ + 75, + 361, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The mismatched light source positions are caused by the specular component $m_b^s$ in $m_b$ . When $m_b^s$ dominates, approximating $L(\\omega_b)$ by $m_b$ becomes a biased estimation as $m_b^s$ is a reflection of lights in different directions than $\\omega_b$ (Fig. 3). By contrast, the approximation is more reasonable when the diffuse component $(m_b^d)$ dominates since $m_b^d = \\int_{\\Omega} L(\\omega) \\rho^d (\\omega \\cdot \\omega_b) \\mathrm{d}\\omega$ indicates that $L(\\omega_b)$ contributes most to the actual pixel value, making it less biased to use $m_b^d$ to represent $L(\\omega_b)$ . Therefore, to facilitate a less biased estimation of environment light for initialization, a diffuse filter $\\mathcal{F}^d(.)$ is necessary on $m_b^d$ , alleviating the mismatched light source positions issue. Similarly, a chromatic filter $\\mathcal{F}^c(.)$ is also required to reduce the chromatic bias caused by the spatially varying material at boundaries. The filtered pixel value $\\hat{m}_b^d = \\mathcal{F}^c(\\mathcal{F}^d(m_b))$ are the basis for our light initialization method.", + "bbox": [ + 75, + 452, + 468, + 694 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Light initialization method. The procedure of light initialization method is summarized in Algorithm 1. This method aims to derive an initial environment light model with parameter $\\Theta$ . Specifically, we use $N_{L} = 64$ spherical Gaussian (SG) bases [28] as the light model, where $\\pmb{L}(\\pmb{\\omega}|\\pmb{\\xi}_t,\\lambda_t,\\pmb{\\mu}_t) = \\sum_{t=1}^{N_L} G(\\pmb{\\omega};\\pmb{\\xi}_t,\\lambda_t,\\pmb{\\mu}_t)$ . $\\pmb{\\xi}_t$ , $\\lambda_t$ , and $\\pmb{\\mu}_t$ stands for Gaussian lobes' direction, sharpness, and amplitude, respectively3. Inspired by [23] indicating that diffuse reflectance can be approximated by the low-frequency reflectance, we design $\\mathcal{F}^d(.)$ as a combination of a threshold filter $\\mathcal{F}_{TH}^d(.)$ that removes high-intensity reflectance (top", + "bbox": [ + 75, + 695, + 468, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$20\\%$ bright) based on boundary points' intensity profile [23] and a low-pass filter (i.e., 3-order spherical harmonics filter4) noted as $\\mathcal{F}_{SH}^{d}$ [22, 23]. While $\\mathcal{F}_{TH}^{d}(.)$ reduces the bias by removing the brightest parts that are usually aligned with specular reflectance in observed images. $\\mathcal{F}_{SH}^{d}(.)$ helps extract the low-frequency reflectance. For $\\mathcal{F}^c(.)$ , we design it as a converter transferring pixel values into gray-scale5, mitigating biases from spatially varying material.", + "bbox": [ + 500, + 90, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1 Light Initialization Method", + "text_level": 1, + "bbox": [ + 501, + 218, + 769, + 233 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Input: pre-computed boundary normal $\\mathbf{n}_b$ , initial relative rotation matrices $\\{\\pmb{R}_1\\ldots ,\\pmb{R}_{N_I}\\}$ , boundary pixels $\\{m_{b1},\\dots,m_{bN_I}\\}$ , diffuse filters $\\mathcal{F}_{TH}^{d}(\\cdot)$ and $\\mathcal{F}_{SH}^{d}(\\cdot)$ , chromatic filter $\\mathcal{F}^c (\\cdot)$ , fitting epochs $N$ , environment light with parameters $L(|\\Theta\\rangle)$ , learning rate $\\eta$ .", + "bbox": [ + 522, + 237, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Output: an initial environment light model $L(|\\Theta^{\\prime})$", + "bbox": [ + 524, + 306, + 836, + 321 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {f o r} j = 1, \\dots , N _ {I} \\mathbf {d o}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 321, + 651, + 334 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\omega} _ {b j} = \\boldsymbol {R} _ {j} \\cdot \\boldsymbol {n} _ {b}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 335, + 642, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\hat {m} _ {b} ^ {d} = \\mathcal {F} ^ {c} \\left(\\mathcal {F} _ {S H} ^ {d} \\left(\\mathcal {F} _ {T H} ^ {d} (m _ {b}))\\right)\\right) \\\\ \\mathbf {f o r} e = 1, \\dots , N \\mathbf {d o} \\\\ J = \\sum (\\boldsymbol {L} (\\omega_ {b} | \\Theta) - \\hat {m} _ {b} ^ {d}) ^ {2} \\\\ \\Theta \\leftarrow \\Theta - \\eta \\partial J / \\partial \\Theta \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 526, + 349, + 709, + 407 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta^ {\\prime} = \\Theta\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 407, + 575, + 416 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Framework of Spin-UP", + "text_level": 1, + "bbox": [ + 500, + 430, + 715, + 446 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With reliable initial SG lights and rotation matrices $\\mathbf{R}$ , we develop Spin-UP based on neural inverse rendering [3, 13, 16, 31] given the rendering equation in Eq. (2).", + "bbox": [ + 498, + 453, + 890, + 498 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shape model. We use the neural depth field to represent the 3D surface. A multi-layer perceptron (MLP) predicts the depth value given the image coordinates. To compute normal given the depth map, we extend the normal fitting method described in [16] to the perspective projection6.", + "bbox": [ + 498, + 500, + 890, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Material model. We represent the spatially varying and isotropic reflectance as a modified Disney Model [31]. The diffuse albedo $\\rho^d$ is predicted by another MLP with a similar structure given the image coordinate. The spatially varying specular reflectance is calculated as a weighted sum of $N_{S} = 12$ SG bases, so $\\rho^{s} = \\sum_{n = 1}^{N_{S}}c^{n}\\mathcal{D}(\\pmb {v},\\pmb {\\omega})\\mathcal{F}(\\pmb {h},\\pmb {\\omega})\\mathcal{G}(\\pmb {n},\\pmb {\\omega},\\pmb {v},\\lambda_{n})$ , where $\\mathcal{D}$ , $\\mathcal{F}$ , and $\\mathcal{G}$ accounts for micro-facet's normal distribution, Fresnel effects, and self-occlusion, respectively. $\\pmb{v}$ is the view direction. $\\pmb{h}$ is the half-vector, calculated by $\\pmb {h} = (\\pmb {v} + \\pmb {\\omega}) / \\| \\pmb {v} + \\pmb {\\omega}\\|$ , $\\lambda_{n}$ is the roughness terms initialized as $(0.1 + 0.9(n - 1)) / (N_S - 1)$ and set as learnable parameters, $c^n$ is the weights predicted by the MLP.", + "bbox": [ + 498, + 574, + 890, + 770 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Shadow model. We apply a shadow mask similar in [13] to handle the cast shadow.", + "bbox": [ + 498, + 771, + 890, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Loss functions. Similar to other inverse rendering-based methods [13, 16], we use the inverse rendering loss", + "bbox": [ + 498, + 801, + 890, + 830 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "4We implement a Gaussian filter and rescale the pixel value's range to $\\mathcal{F}_{TH}^{d}(m_{b})$ 's range to suppress ringing effect and negative energy in SH.", + "bbox": [ + 500, + 838, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "We use gray-scale value to initialize the RGB value of light model.", + "bbox": [ + 524, + 864, + 877, + 875 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "6Please refer to the supplementary material for more details about the network structures and modified normal fitting method.", + "bbox": [ + 500, + 875, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "In practice, we find that initializing Gaussians' parameters by Fibonacci lattice [31] and freezing $\\lambda_{t}$ gives the best results.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11908", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/80242f5cfc3644696e395af39d8cf3902ba96691ec81ea34c6a9bc2b19a6381a.jpg", + "image_caption": [ + "Figure 4. Proposed training strategies. (Top) Interval sampling (IS). The high-resolution images are down-sampled into several low-resolution sub-images by extracting pixels with an interval of $N_B$ , where $N_B = 2$ in this example. (Bottom) Shrinking range computing (SRC). Far points (yellow circles) that are $k$ ( $k = 3$ in this example) point away w.r.t the query position is selected to interpolate the close points (blue circles)'s depth for normal calculation. During optimization, $k$ will be gradually reduced to 1." + ], + "image_footnote": [], + "bbox": [ + 0, + 0, + 496, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "(i.e, Eq. (1)) to train the framework. The three-stage schema [16] is applied, as well as other smoothness terms (total variance regularization [13, 16]) calculate as $\\mathrm{TV}(.) = \\frac{1}{N_P}\\sum_{i = 1}^{N_P}\\left|\\frac{\\partial(.)}{\\partial x} +\\frac{\\partial(.)}{\\partial y}\\right|$ , where $(x,y)$ is the image coordinates. We implement $\\mathrm{TV}(.)$ on the normal map $(N)$ , diffuse albedo map $(A)$ , and the Gaussian bases' weights $(c)$ for the material, and gradually drop it following the three-stage training schema [16]. Similar to [30], the normalized color loss calculated as $\\| \\operatorname {Nor}(A) - \\operatorname {Nor}(I)\\|$ is implemented to help Spin-UP learn a better albedo representation, where $\\operatorname {Nor}(.)$ is the vector normalization. Following [16], we calculate the boundary loss as the cosine similarity between the pre-computed and estimated boundary normal", + "bbox": [ + 75, + 398, + 468, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Strategies", + "text_level": 1, + "bbox": [ + 76, + 613, + 261, + 628 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimizing Spin-UP requires smoothness terms to facilitate convergence and avoid local optima. However, those terms are often implemented on full-resolution images, leading to high computational costs. To reduce those costs, we propose to use a sampling strategy noted as interval sampling (IS). To further improve convergence, we introduce another technique noted as shrinking range computing (SRC).", + "bbox": [ + 75, + 637, + 468, + 743 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Interval sampling (IS). IS samples ray batches from images to reduce the costs. Unlike random ray sampling [19] or patch-based sampling [20], IS preserves the object's shape. The idea is similar to downsampled techniques in [11, 24], but we don't merge the sub-images to full resolution. We experimentally find this strategy important for training on down-sampled sub-images with smoothness terms to avoid local optima (Sec. 5.2). Specifically,", + "bbox": [ + 75, + 743, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "we divide the image in full resolution into non-overlapping blocks, and each block contains $N_B \\times N_B$ pixel points. By extracting pixel points from the same position in each block (e.g., the left-top pixel), we obtain $N_B \\times N_B$ sub-images with a down-sampled resolution (See Fig. 4 for illustration). During training, those sub-images are randomly sampled in each epoch, and the smoothness terms are calculated based on the sub-images resolution, which reduces the computational cost and ensures the effectiveness of those terms.", + "bbox": [ + 500, + 90, + 890, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Shrinking range computing (SRC). Without merging sub-images back to a full-resolution image in IS, there will be an aliasing issue in the inverse rendering process. Such an issue is caused by the fact that the normal calculation in our framework on sub-images requires four adjacent points' depths in sub-images resolution [16], which degrades the precision of normal calculation8. Therefore, SRC is applied for anti-aliasing. It uses points adjacent to the query point (blue circles in Fig. 4) in the full-resolution image coordinates to calculate the normal for each pixel in the sub-images. Such a strategy maintains the precision of normal calculation. However, at the early stage of training, calculating the normal based on the blue circles' depth is vulnerable to perturbation in per-pixel training. Therefore, SRC gradually selects points (yellow circles) from far ( $k = 3$ points away) to close (blue circles) w.r.t query points to interpolate the blue circles' depth, as normal calculation on far points' depth will lead to a more smooth and stable normal map at the early stage, which eventually improves convergence, as validated in Sec. 5.2.", + "bbox": [ + 496, + 227, + 892, + 529 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 547, + 632, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We validate the effectiveness of the proposed Spin-UP on synthetic and real-world data. We use mean angle error (MAE) to evaluate the normal map's reconstructed quality and PU-PSNR [1], and PU-SSIM [1] to evaluate the reconstructed environment light. Since no existing datasets follow our spin light setup, we collect the dataset using Blender and our device.", + "bbox": [ + 496, + 573, + 890, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Evaluation on Synthetic Datasets", + "text_level": 1, + "bbox": [ + 500, + 691, + 790, + 707 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We collect several objects, environment maps, and materials to render the synthetic dataset in Blender by Cycles. Specifically, five shapes from the DiLiGenT-MV dataset [14] (i.e, BUDDHA, BEAR, COW, POT2, and READING) and a generated shape (BALL), five HDR environment maps (i.e, LANDSCAPE, QUARRY, URBAN, ATTIC, STUDIO), two PBR materials (i.e, RUSTY STEEL, LEATHER), and four synthetic materials (i.e, VORONOI DIFF, VORONOI SPEC,", + "bbox": [ + 496, + 715, + 890, + 835 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "7Please refer to the supplementary material for more details about the setup of hyperparameters.", + "bbox": [ + 76, + 875, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_footnote", + "text": "8 According to normal's definition, the smaller the distance between the adjacent points and the query points (red circle in Fig. 4), the more accurately representing the geometry at query points. Therefore, the blue circles' depths are preferred for normal calculation.", + "bbox": [ + 498, + 849, + 890, + 898 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11909", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8cdf0ad331600b6053416191c37a61b01670e7c077bc183bce125914a8424e65.jpg", + "table_caption": [ + "Table 2. Qualitative comparison results in terms of MAE on shape group (left-top), light group (left-bottom), reflectance group (right-top), and spatially varying material group (right-bottom). Bold numbers indicate the best results in MAE. In light group, {U., A., S., L.} stand for environment map named URBAN, ATTIC, STUDIO, and LANDSCAPE, respectively. In the reflectance group, {D., S.} stand for material named GREEN DIFF and GREEN SPEC, respectively. In spatially varying material group, {D., S.} stand for material named VORONOI DIFF and VORONOI SPEC, respectively." + ], + "table_footnote": [], + "table_body": "
MethodShape GroupReflectance Group
BALLBEARBUDDHAREADINGAVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]41.3253.8867.9054.8554.4957.4537.4365.4858.0454.60
S22 [10]7.3514.0326.3718.7716.6315.5611.8318.9718.3816.19
S23 [11]5.5610.3718.5415.1012.3913.469.7516.2212.6713.03
Spin-UP3.546.3317.307.718.725.837.1113.0910.309.08
MethodLight GroupSpatially Varying Material Group
Cow (U.)Cow (A.)Cow (S.)Cow (L.)AVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]67.6339.2140.2848.4748.8940.9737.4649.2748.9644.17
S22 [10]17.1712.7417.1111.3514.5918.5917.6322.8023.7520.69
S23 [11]11.937.5212.3811.6010.8414.2211.0014.5814.3113.53
Spin-UP5.504.403.334.944.545.586.9712.5411.529.15
", + "bbox": [ + 80, + 169, + 893, + 357 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GREEN DIFF, GREEN SPEC) are used for evaluation. We devise four groups of data for evaluation: shape group, light group, reflectance group, and spatially varying material group, each containing four scenes. For each scene, 50 observed images with a resolution of $512 \\times 512$ are rendered by a perspective camera with the focal of $50\\mathrm{mm}$ and a frame size of $36\\mathrm{mm} \\times 36\\mathrm{mm}$ . The camera rotation $\\theta$ for consecutive images follows a non-uniform rotation velocity. We compare Spin-UP with three advanced NaUPS methods, including two supervised NaUPS methods (S22 [10] and S23 [11]) and one unsupervised UPS method (HY19 [7])10.", + "bbox": [ + 75, + 369, + 468, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Normal estimation comparison. According to results in Table 2, Spin-UP presents a superior performance compared to all other NaUPS methods. Specifically, in shape group, the low MAE on BALL, BEAR, BUDDHA, READING in RUSTY STEEL rendered under QUARRY indicate the practicability of Spin-UP to various shapes. In light group, the low-variance of MAE $(0.81^{\\circ}$ for Spin-UP vs. $1.94^{\\circ}$ for S23 [11]) on COW in LEATHER rendered under QUARRY, URBAN, ATTIC, and STUDIO demonstrates robustness toward different environment lights. In reflectance group, the results on POT2 and READING in GREEN DIFF and GREEN SPEC rendered under LANDSCAPE demonstrate the ability to handle non-Lambertian objects. In spatially varying material group, results on POT2 and READING rendered in VORONOI DIFF or VORONOI SPEC under LANDSCAPE prove adaptability to challenging scenarios. A comparative analysis of the outcomes of the reflectance group and the spatially varying material group in our method reveals that the MAE remains relatively consistent across identical ob", + "bbox": [ + 75, + 536, + 472, + 824 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fee7cb9086f51e186505047276097eae38bf8b80f9e501af9dec43804ee0f3eb.jpg", + "image_caption": [ + "Figure 5. The visual quality comparison of light between the estimated one by Spin-UP (columns 2-5) and the ground truth (column 1) on the four groups, i.e., shape (row 1), reflectance (row 2), spatially varying material (row 3), and light group (row 4-5). The intensity of the estimated light maps is scaled for visualization." + ], + "image_footnote": [], + "bbox": [ + 501, + 367, + 890, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "jects with different materials, underscoring the robustness of Spin-UP in handling diverse materials. Also, we find that Spin-UP sometimes performs better on specular objects than on diffuse objects (i.e., READING). We attribute this to the high-frequency details in specular reflectance that may be useful for shape-light reconstruction.", + "bbox": [ + 496, + 638, + 893, + 731 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Light estimation comparison. Fig. 5 provides a qualitative comparison between the estimated environment light and the ground truth on four groups. We can observe that the learned light map reflects the position of the light source, especially in Cow (S.) given such a challenging setup without any prior information about the object material or shape. It also reconstructs a reasonable light map for objects with diffuse reflectance, such as POT2 (D.) and READING (D.), further highlighting the effectiveness of the proposed light initialization. However, it should be noted that the estimated environment light is influenced by the object material, par", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "The generated pattern for VORONOI DIFF and VORONOI SPEC follow similar setup in CNN-PS [9]. Please refer to the supplementary material for all the qualitative comparison between Spin-UP and other methods on the synthetic and realworld dataset.", + "bbox": [ + 76, + 837, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11910", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/87faaf44c16a4cf3d57ebca1ed4da6653eb643bbbf160e8ff68aabe0138fffb5.jpg", + "image_caption": [ + "Capture System" + ], + "image_footnote": [], + "bbox": [ + 53, + 89, + 261, + 195 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b2e98dfb957480b582514429a7108b5dab6ab883cb9cc325dcb43d895fa08b3b.jpg", + "image_caption": [ + "Captured Images and Light References" + ], + "image_footnote": [], + "bbox": [ + 272, + 89, + 468, + 193 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/831702f2c33bb20dc3eb06dd81f3b34990399e21d221c99828bf021eb1ef0a3d.jpg", + "image_caption": [ + "Figure 6. Illustration of the device for real data collection. Please refer to the supplementary material for more details. Left: the capture system contains a camera, a spin platform, and an object. Right: Captured images and paired mirror balls (as light reference) of two objects in the indoor and outdoor scenes, respectively.", + "Figure 7. Qualitative comparison for the estimated normal map and environment light on SOLDIER and PLAYER capturing under outdoor (columns 1-6) and indoor (columns 7-12) between ours (column 3, 9), S23 [11] (column 5, 11), and S22 [10] (column 6, 12). We also show the reference sphere and reference environment light (columns 2, 7), and estimated light (columns 4, 10)." + ], + "image_footnote": [], + "bbox": [ + 81, + 295, + 468, + 496 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ticularly when handling objects with a nearly uniform base color (e.g., reflectance group) or spatially varying material, which may generate unpleasant artifacts (e.g., inconsistent color in estimated environment light of READING (D.) in the spatially varying material group). Those artifacts are hard to eliminate without priors.", + "bbox": [ + 75, + 604, + 468, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation on Real-world Datasets", + "text_level": 1, + "bbox": [ + 76, + 708, + 380, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We set up our spin light capture system to collect real data under indoor and outdoor scenes, as shown in Fig. 6. After preprocessing, we end up with 50 images for each object, with a $540 \\times 540$ resolution. Here, we showcase the normal estimation results on two objects (i.e., SOLDIER, and PLAYER) under indoor and outdoor environment lights in Fig. 7, compared with S23 [11], S22 [10]. We do not show HY19 [7]'s result as it failed on the captured data.", + "bbox": [ + 75, + 732, + 468, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Normal estimation comparison. According to the Fig. 7, Spin-UP has competitive performance compared to the state-of-the-art supervised method [11]. In some scenar", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/720f10d83a4a6174f44d65b28123bfb78dd0dda24e9aabf649fd2e45d4917be7.jpg", + "table_caption": [ + "Table 3. Ablation studies on Spin-UP's alternatives regarding average PU-PSNR [1] and PU-SSIM [1] on synthetic dataset. 'Fib.' and 'Rand.' represent the Fibonacci and random initialization method, respectively. Bold number indicates the best results." + ], + "table_footnote": [], + "table_body": "
w Rand.w Fib.Spin-UP
PU-PSNR [1]↑16.8618.9822.06
PU-SSIM [1]↑0.450.520.60
", + "bbox": [ + 540, + 151, + 852, + 191 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "ios, we recover more reasonable results regarding the overall normal distribution than the reference sphere, particularly for SOLDIER indoor and PLAYER indoor. Spin-UP can effectively capture high-frequency details such as wrinkles on clothes in PLAYER and SOLDIER. By contrast, S23 [11] may contain artifacts (i.e., an incorrect normal map distribution) even though they have more details than ours, and S22 [10] generates over-smooth results. By comparing indoor and outdoor results, we observe that the performance of S23 [11] degrades significantly in indoor scenarios, which may be attributed to the data bias and low pixel variance, while our method is not greatly affected.", + "bbox": [ + 496, + 199, + 893, + 381 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 396, + 651, + 414 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1. Light Initialization Validation", + "text_level": 1, + "bbox": [ + 500, + 421, + 764, + 438 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To comprehensively validate the effectiveness of our light initialization method, we conduct experiments in two aspects: a comparison of different light initialization methods and the effectiveness of the filters.", + "bbox": [ + 496, + 446, + 892, + 505 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on light initialization methods. We compare our light initialization method with two widely used SG light initialization methods, i.e., the random initialization noted as 'w Rand.' and Fibonacci lattice [31] noted as 'w Fib.' A quantitative comparison of reconstructed normal and light maps is shown in Table 3 and Table 4. Compared with 'w Rand,' the improvement in average $(1.75^{\\circ}$ reduction in MAE on normal estimation and $5.20 / 0.15$ increase in PU-PSNR / PU-SSIM on light estimation, respectively) indicates our method's adaptability. Compared with 'w Fib,' we observe an obvious advantage in the shape group $(0.61^{\\circ}$ reduction in MAE), while a smaller advantage in the spatially varying material group $(0.19^{\\circ}$ reduction in MAE). This is because the material and shape will affect the initial environment light's quality. While the estimated environment light is most accurate on smooth geometry with simple material, the quality will degrade on complex geometry and spatially varying material.", + "bbox": [ + 496, + 507, + 892, + 779 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison on the designed filters. We compare Spin-UP with three alternatives (i.e, $w / o \\mathcal{F}^c$ , $w / o \\mathcal{F}_{SH}^d$ , and $w / o \\mathcal{F}_{TH}^d$ ). The results in Table 4 demonstrate the effectiveness of those filters. Specifically, dropping $\\mathcal{F}_{TH}^d$ will lead to mismatching light source position in the initialized environment light introduced by the specular reflectance, which eventually affects the accuracy of the estimated normal; dropping $\\mathcal{F}_{SH}^d$ will harm the performance, especially", + "bbox": [ + 496, + 780, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "(1)细胞壁：脑聚糖体膜、高尔基体膜、内质网等", + "bbox": [ + 71, + 0, + 261, + 55 + ], + "page_idx": 6 + }, + { + "type": "header", + "text": "\\( \\left\\{ {1,2}\\right\\} \\Rightarrow \\left\\{ {1,3}\\right\\} \\Rightarrow \\left\\{ {2,4}\\right\\} \\Rightarrow \\left\\{ {3,4}\\right\\} \\Rightarrow \\left\\{ {4,5}\\right\\} \\Rightarrow \\left\\{ {5,6}\\right\\} \\Rightarrow \\left\\{ {6,7}\\right\\} \\Rightarrow \\left\\{ {7,8}\\right\\} \\Rightarrow \\left\\{ {8,9}\\right\\} \\Rightarrow \\left\\{ {9,10}\\right\\} \\Rightarrow \\left\\{ {10,11}\\right\\} \\Rightarrow \\left\\{ {11,12}\\right\\} \\Rightarrow \\left\\{ {12,13}\\right\\} \\Rightarrow \\left\\{ {13,14}\\right\\} \\Rightarrow \\left\\{ {14,15}\\right\\} \\Rightarrow \\left\\{ {15,16}\\right\\} \\Rightarrow \\left\\{ {16,17}\\right\\} \\Rightarrow \\left\\{ {17,18}\\right\\} \\Rightarrow \\left\\{ {18,19}\\right\\} \\Rightarrow \\left\\{ {19,20}\\right\\} \\Rightarrow \\left\\{ {20,21}\\right\\} \\Rightarrow \\left\\{ {21,22}\\right\\} \\Rightarrow \\left\\{ {22,23}\\right\\} \\Rightarrow \\left\\{ {23,24}\\right\\} \\Rightarrow \\left\\{ {24,25}\\right\\} \\Rightarrow \\left\\{ {25,26}\\right\\} \\Rightarrow \\left\\{ {26,27}\\right\\} \\Rightarrow \\left\\{ {27,28}\\right\\} \\Rightarrow \\left\\{ {28,29}\\right\\} \\Rightarrow \\left\\{ {29,30}\\right\\} \\Rightarrow \\left\\{ {30,31}\\right\\} \\Rightarrow \\left\\{ {31,32}\\right\\} \\Rightarrow \\left\\{ {32,33}\\right\\} \\Rightarrow \\left\\{ {33,34}\\right\\} \\Rightarrow \\left\\{ {34,35}\\right\\} \\Rightarrow \\left\\{ {35,36}\\right\\} \\Rightarrow \\left\\{ {36,37}\\right\\} \\Rightarrow \\left\\{ {37,38}\\right\\} \\Rightarrow \\left\\{ {38,39}\\right\\} \\Rightarrow \\left\\{ {39,40}\\right\\} \\Rightarrow \\left\\{ {40,41}\\right\\} \\Rightarrow \\left\\{ {41,42}\\right\\} \\Rightarrow \\left\\{ {42,43}\\right\\} \\Rightarrow \\left\\{ {43,44}\\right\\} \\Rightarrow \\left\\{ {44,45}\\right\\} \\Rightarrow \\left\\{ {45,46}\\right\\} \\Rightarrow \\left\\{ {46,47}\\right\\} \\Rightarrow \\left\\{ {47,48}\\right\\} \\Rightarrow \\left\\{ {48,49}\\right\\} \\Rightarrow \\left\\{ {49,50}\\right\\} \\Rightarrow \\left\\{ {50,51}\\right\\} \\Rightarrow \\left\\{ {51,52}\\right\\} \\Rightarrow \\left\\{ {52,53}\\right\\} \\Rightarrow \\left\\{ {53,54}\\right\\} \\Rightarrow \\left\\{ {54,55}\\right\\} \\Rightarrow \\left\\{ {55,56}\\right\\} \\Rightarrow \\left\\{ {56,57}\\right\\} \\Rightarrow \\left\\{ {57,58}\\right\\} \\Rightarrow \\left\\{ {58,59}\\right\\} \\Rightarrow \\left\\{ {59,60}\\right\\} \\Rightarrow \\left\\{ {60,61}\\right\\} \\Rightarrow \\left\\{ {61,62}\\right\\} \\Rightarrow \\left\\{ {62,63}\\right\\} \\Rightarrow \\left\\{ {63,64}\\right\\} \\Rightarrow \\left\\{ {64,65}\\right\\} \\Rightarrow \\left\\{ {65,66}\\right\\} \\Rightarrow \\left\\{ {66,67}\\right\\} \\Rightarrow \\left\\{ {67,68}\\right\\} \\Rightarrow }.\\;\\left( {{QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq@qq", + "bbox": [ + 351, + 0, + 540, + 53 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11911", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/715cf3b1fef59ff66711f4c32b359ec97ea9ffd02b278d348d226f3e1644232a.jpg", + "table_caption": [ + "Table 4. Ablation studies on Spin-UP's alternatives regarding average MAE on four groups (shape, light, reflectance, and spatially varying material group). 'Fib.', 'Rand.', 'Intv.', and 'Shrk.' represent the Fibonacci initialization method, random initialization, interval sampling, and shrinking range computing, respectively. Bold number indicates the best results in MAE." + ], + "table_footnote": [ + "$\\dagger$ Method with $\\dagger$ is tested on dataset with point light $^+$ environment light Sec. 5.3." + ], + "table_body": "
ShapeLightRef.SV.AVG
w Rand.12.026.449.7910.289.60
w Fib.9.335.3410.209.348.55
w/o Intv.8.875.029.8310.128.37
w/o Shrk.10.104.9210.1210.438.81
w/o Fc9.444.619.249.408.17
w/o FSh9.758.298.9315.7310.41
w/o FTh9.305.049.1812.498.82
Spin-UP8.724.549.089.157.85
S23 [11]†12.428.5612.5212.3311.46
Spin-UP†11.629.2511.079.079.48
", + "bbox": [ + 81, + 179, + 467, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in the spatially varying material group $(6.58^{\\circ}$ increase in MAE) since $\\mathcal{F}_{SH}^{d}$ is essential in extracting low-frequency reflectance to initialize the environment light; dropping $\\mathcal{F}^c$ will increase MAE in average $(0.32^{\\circ})$ , illustrating the necessity of reducing chromatic bias.", + "bbox": [ + 75, + 333, + 467, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.2. Training Strategies Validation", + "text_level": 1, + "bbox": [ + 76, + 415, + 344, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The interval sampling will facilitate the training of Spin-UP in two ways. First, the training time is two times shorter (25 min per object on average vs. 60 min on average, depending on the image's valid points for the object), and the GPU memory occupation is five times smaller (around 5 GB vs. 25 GB during training) than directly training on full-image resolution. Second, comparing Spin-UP with 'w/o Intv.', which applies a random sampling strategy and calculates the smoothness terms on patches (3 × 3 pixels), we find that the performance drops $0.52^{\\circ}$ on average, and most $(0.97^{\\circ})$ on the spatially varying material group. This is because the patch-based smoothness may not work uniformly on different parts of the object, diminishing the effectiveness of smoothness terms, especially on objects in spatially varying material with abrupt texture changes. The shrinking range computing helps avoid local optima when training Spin-UP on down-sampled images while still using full-resolution image coordinates for normal calculation. We compared Spin-UP with the alternative 'w/o Shrk.', which does not implement this strategy. The average MAE on normal estimation for four groups increases $0.96^{\\circ}$ , highlighting the importance of this strategy.", + "bbox": [ + 75, + 435, + 472, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Additional Validation on Point Light Source", + "text_level": 1, + "bbox": [ + 76, + 777, + 450, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To ensure a more fair comparison with the state-of-the-art supervised methods (S23 [11]), we add a dominant point light to the environment light in synthetic and real-world dataset11. According to Table 4, the proposed Spin-UP has a lower MAE on estimated normal maps than S23 [11] on", + "bbox": [ + 75, + 801, + 468, + 878 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/27e91bf9217fa5337d58e38c26d9e5a3c049700841666a4eb6f85525c8307ae1.jpg", + "image_caption": [ + "Point Light + Environment Light", + "(a)" + ], + "image_footnote": [], + "bbox": [ + 506, + 99, + 669, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9054fcb82d0f83787934bf4dd22989dabab545ea6d4cceca298c94390f3ba2b1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 686, + 88, + 720, + 176 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a25ca09de8da3a786682a755eaa268c8af6f4adc67efeced6763ba73de67e5a3.jpg", + "image_caption": [ + "(b)" + ], + "image_footnote": [], + "bbox": [ + 733, + 89, + 803, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4d5b24164b0537eb879a4a69607f720392cb70d32e0c09a96f3973a9377300ba.jpg", + "image_caption": [ + "Figure 8. (a) Illustration of new light setup. (b) Qualitative comparison on SOLDIER between our method and S23 [11] with dominant point light." + ], + "image_footnote": [], + "bbox": [ + 813, + 89, + 887, + 186 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the synthetic dataset (9.48° ours v.s. 11.46° S23 [11]). As shown in Fig. 8, we have a visually comparable result on the real-world dataset given far-field point light (2m) and a better result given near-field point light (0.4m), validating the adaptability of Spin-UP on unseen light sources.", + "bbox": [ + 496, + 258, + 890, + 335 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 345, + 617, + 361 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This paper proposes Spin-UP to address NaUPS in an unsupervised manner. Thanks to our setup to mitigate the ill-posedness, the light initialization method to alleviate the ambiguities of NaUPS, and the proposed training strategies to facilitate fast convergence, Spin-UP can recover surfaces with isotropic reflectance under various lights. Experiments in synthetic and real-world datasets have shown that Spin-UP is robust to various shapes, lights, and reflectances.", + "bbox": [ + 496, + 368, + 890, + 488 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. Although Spin-UP is efficient and robust in solving NaUPS, it has several limitations: 1) Spin-UP assumes infinitely far light sources, which omit the spatially varying lighting; 2) the materials' base color will bias the estimated environment light; 3) Spin-UP assumes objects to have isotropic reflectance, ignoring inter-reflections and anisotropic features, meaning that it cannot perform well on objects with anisotropic reflectance, such as aluminum, or strong inter-reflections, such as a glass bowl; 4) Spin-UP doesn't compute the shadow iteratively, which may result in artifacts on objects with complicated shapes. Overcoming the above limitations will be regarded as our future work. Besides, the rotation axis of our device does not align with the object's center due to the consideration of structural stability, which may introduce bias from the spatially varying light in observed images. Redesigning the image capture device is also one of the future works. At last, we find it interesting to improve the setup by relieving the requirement for single-axis $360^{\\circ}$ rotation to free rotations for easier implementation on portable devices.", + "bbox": [ + 496, + 489, + 892, + 790 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work is supported by the National Natural Science Foundation of China under Grant No. 62136001, 62088102, Rapid-Rich Object Search (ROSE) Lab, Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, and the State Key Lab of Brain-Machine Intelligence, Zhejiang University, Hangzhou, China.", + "bbox": [ + 496, + 791, + 890, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "11Point light's setup follows [11] and [17].", + "bbox": [ + 89, + 885, + 316, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11912", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Maryam Azimi et al. PU21: A novel perceptually uniform encoding for adapting existing quality metrics for HDR. 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Ref-NeRF: Structured view-dependent appearance for neural radiance fields. In Proc. Computer Vision and Pattern Recognition (CVPR), 2021. 2", + "[27] George Vogiatzis, Carlos Hernandez, and Roberto Cipolla. Reconstruction in the round using photometric normals and silhouettes. In Proc. Computer Vision and Pattern Recognition (CVPR), 2006. 2", + "[28] Jiaping Wang, Peiran Ren, Minmin Gong, John Snyder, and Baining Guo. All-frequency rendering of dynamic, spatially-varying reflectance. In ACM SIGGRAPH Asia, 2009. 4" + ], + "bbox": [ + 501, + 92, + 890, + 900 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "11913", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[29] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. NeuS: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. In Proc. 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In ACM Transactions on Graphics (TOG), 2021. 2" + ], + "bbox": [ + 78, + 90, + 468, + 428 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11914", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/6c1acd6f-00c1-4dc9-a5c3-6c6dd410bb2c_model.json b/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/6c1acd6f-00c1-4dc9-a5c3-6c6dd410bb2c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..931f2a8b25e52ea7923889b5ab42461606211a0f --- /dev/null +++ b/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/6c1acd6f-00c1-4dc9-a5c3-6c6dd410bb2c_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.121, + 0.131, + 0.849, + 0.154 + ], + "angle": 0, + "content": "Spin-UP: Spin Light for Natural Light Uncalibrated Photometric Stereo" + }, + { + "type": "text", + "bbox": [ + 0.086, + 0.179, + 0.886, + 0.201 + ], + "angle": 0, + "content": "Zongrui \\(\\mathrm{Li}^{1,2,*}\\) Zhan \\(\\mathrm{Lu}^{2,4,*,\\dagger}\\) Haojie Yan\\(^{3,4}\\) Boxin Shi\\(^{5,6}\\) Gang Pan\\(^{3,4}\\) Qian Zheng\\(^{3,4,\\ddagger}\\) Xudong Jiang\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.145, + 0.203, + 0.834, + 0.219 + ], + "angle": 0, + "content": "\\(^{1}\\)Rapid-Rich Object Search (ROSE) Lab, Interdisciplinary Graduate Programme, Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.221, + 0.741, + 0.238 + ], + "angle": 0, + "content": "\\(^{2}\\)School of Electrical and Electronic Engineering, Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.285, + 0.238, + 0.692, + 0.256 + ], + "angle": 0, + "content": "3College of Computer Science and Technology, Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.276, + 0.256, + 0.703, + 0.273 + ], + "angle": 0, + "content": "4The State Key Lab of Brain-Machine Intelligence, Zhejiang University" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.273, + 0.829, + 0.291 + ], + "angle": 0, + "content": "\\(^{5}\\)National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.161, + 0.291, + 0.816, + 0.308 + ], + "angle": 0, + "content": "\\(^{6}\\)National Engineering Research Center of Visual Technology, School of Computer Science, Peking University" + }, + { + "type": "text", + "bbox": [ + 0.161, + 0.311, + 0.815, + 0.326 + ], + "angle": 0, + "content": "{zongrui001, zhan007, EXDJiang} @ntu.edu.sg, {hjyan, gpan, qianzheng} @zju.edu.cn, shiboxin@pku.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.361, + 0.314, + 0.377 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.392, + 0.473, + 0.786 + ], + "angle": 0, + "content": "Natural Light Uncalibrated Photometric Stereo (NaUPS) relieves the strict environment and light assumptions in classical Uncalibrated Photometric Stereo (UPS) methods. However, due to the intrinsic ill-posedness and high-dimensional ambiguities, addressing NaUPS is still an open question. Existing works impose strong assumptions on the environment lights and objects' material, restricting the effectiveness in more general scenarios. Alternatively, some methods leverage supervised learning with intricate models while lacking interpretability, resulting in a biased estimation. In this work, we propose Spin Light Uncalibrated Photometric Stereo (Spin-UP), an unsupervised method to tackle NaUPS in various environment lights and objects. The proposed method uses a novel setup that captures the object's images on a rotatable platform, which mitigates NaUPS's ill-posedness by reducing unknowns and provides reliable priors to alleviate NaUPS's ambiguities. Leveraging neural inverse rendering and the proposed training strategies, Spin-UP recovers surface normals, environment light, and isotropic reflectance under complex natural light with low computational cost. Experiments have shown that Spin-UP outperforms other supervised / unsupervised NaUPS methods and achieves state-of-the-art performance on synthetic and real-world datasets. Codes and data are available at https://github.com/LMozart/CVPR2024-SpinUP." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.8, + 0.21, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.856 + ], + "angle": 0, + "content": "Natural light uncalibrated photometric stereo (NaUPS) [6] is proposed to relieve the dark room and directional light as" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.363, + 0.892, + 0.484 + ], + "angle": 0, + "content": "sumption in classical uncalibrated photometric stereo, aiming to reconstruct the surface normal given images of an object captured at arbitrary environment light. The implications of NaUPS are far-reaching: it makes photometric stereo universal. However, solving NaUPS is still an open question because of the intrinsic ill-posedness introduced by the varying light of each image and the high dimensional ambiguities between the light and objects [6]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.893, + 0.669 + ], + "angle": 0, + "content": "Previous optimization-based methods use the simple light model to represent the varying environment lights and Lambertian reflectance to represent the material [6, 7, 21]. These models help mitigate the ill-posedness and ambiguities to some extent but become ineffective in handling objects with general reflectance (e.g., non-Lambertian reflectance) under complex environment light, leading to unsatisfactory reconstruction outcomes. Besides, since they solely model the varying lights in each image, the unknowns introduced by the light model may increase with the resolution and numbers of the images, restricting their method to low-resolution and insufficient images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.895, + 0.808 + ], + "angle": 0, + "content": "Considering the difficulties of explicitly mitigating the ill-posedness and ambiguities, recent advances [10, 11] turn to data-driven methods: they train a deep learning model on large-scale datasets and implicitly exploit deep light features from images to improve performance. However, those methods lack interpretability, making them hard to constrain during training. Consequently, the model may be affected by the data bias and prone to specific types of light sources [10] or reflection variations [11] among images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Despite a persistent exploration in this research field, a method capable of handling general objects under natural light while free from data bias is still missing. In this paper, we provide a new perspective on solving NaUPS. Specifically, we propose a novel setup that acquires images on a rotatable platform under a static environment light. In such a" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.863, + 0.318, + 0.876 + ], + "angle": 0, + "content": "*Co-first author. ‡Corresponding author." + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.876, + 0.469, + 0.901 + ], + "angle": 0, + "content": "\\(\\dagger\\)Work completed while interning at the State Key Lab of BrainMachine Intelligence, Zhejiang University." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11905" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "case, the object is illuminated by rotated environment lights. Representing such rotated lights requires fewer parameters than solely modeling varying lights in each image since we model the lights as a uniform environment light varied by low degree-of-freedom (DOF [5]) rotation. This frees us from significantly increasing unknowns when implementing advanced parametric light models (e.g., spherical Gaussian) and reflectance models to handle general scenarios. Additionally, based on such a setup, we further derive a reliable light initialization method by analyzing the pixel value at object's occluding boundary. Such light initialization will help the model converge at the beginning and alleviate the ambiguity between light and objects during training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.288, + 0.473, + 0.529 + ], + "angle": 0, + "content": "With the help of the proposed setup and light initialization method, we develop Spin Light Uncalibrated Photometric Stereo (Spin-UP), addressing NaUPS by optimizing inverse rendering framework in an unsupervised manner. To our best knowledge, this is the first unsupervised method that can handle general objects under natural light. Unlike previous methods, Spin-UP can jointly reconstruct environment light, isotropic reflectance, and complicated shapes through iterative optimization. To reduce the computational cost and improve convergence, we propose two strategies: interval sampling and shrinking range computing, which help optimize Spin-UP in low GPU usage (5 GB) and fast running time (25 mins). Experiments on synthetic and real-world datasets demonstrate our superior performance over previous methods on general scenarios. Overall, our contributions are summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.531, + 0.47, + 0.576 + ], + "angle": 0, + "content": "1. We design a novel setup for NaUPS, which reduces unknowns of light representation and facilitates solving NaUPS in an unsupervised manner." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.577, + 0.47, + 0.637 + ], + "angle": 0, + "content": "2. We introduce a light prior, which leverages an object's occluding boundaries to initialize a reliable environment light. Based on the setup and light prior, we propose the unsupervised NaUPS method named Spin-UP." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.638, + 0.47, + 0.668 + ], + "angle": 0, + "content": "3. We present two training strategies for fast training and convergence of Spin-UP." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.531, + 0.47, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.22, + 0.695 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.47, + 0.84 + ], + "angle": 0, + "content": "In this section, we briefly review recent supervised and unsupervised NaUPS methods. We also summarize other techniques that exploit priors from occluding boundaries. Additionally, we discuss recent advances in 3D vision to distinguish Spin-UP from other neural inverse rendering approaches. Given that the focus of this paper is on NaUPS, a group of works reconstructing 3D surfaces from a single image by deep learning under natural light [15] or shading [4, 12, 32] are not included." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Natural Light Uncalibrated Photometric Stereo. Unsupervised NaUPS methods jointly recover the light, reflectance properties, and surface normal. These methods explicitly model the environment light by low-order spheri" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.379 + ], + "angle": 0, + "content": "cal harmonics (SH) [2, 21], spatially varying spherical harmonics (SV-SH) [7, 18] or equivalent directional light (Eqv-Dir) [6] to mitigate the ill-posedness, and use integrability constraint [2], shape initialization [7], non-physical lighting regularization [21], or graph-based ambiguity relaxation [6] to alleviate the ambiguity. In contrast, supervised NaUPS methods [10, 11] apply deep learning models like transformers to reconstruct normal maps without explicitly estimating the environment light. The models are trained on a dataset containing images of diverse objects captured under various lighting conditions, including directional, point, and environment light. Compared to previous work, the proposed Spin-UP distinguishes itself in three key aspects: 1) it features a novel setup explicitly designed to model correlations among observed images to mitigate the ill-posedness of NaUPS, 2) leveraging this unique setup, a novel light initialization method is introduced to mitigate ambiguities, and 3) an advanced light and material model is implemented to address a broader range of scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.379, + 0.893, + 0.621 + ], + "angle": 0, + "content": "Priors from the Boundaries. The occluding boundaries of an object are considered to reveal adequate information about the object's shape and the scene's light. Given the fact that the projection of the boundaries' normal to xy-plane is perpendicular to the boundaries in orthographic projection, methods are developed to constraint the surface normal estimation during iterative optimization [16] or recover a rough shape to initialize the geometry in multi-view [8] or photometric stereo [7]. Other methods associate the boundaries normal with the reflectance to estimate a rough position of the directional lights [27]. However, none of them derive the environment light from the boundary reflectance. Given the setup in Spin-UP, we can roughly estimate the environment by analyzing occluding boundaries and the corresponding pixel points. This approach provides a reliable initialization for lighting that alleviates ambiguity in NaUPS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.622, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Inverse rendering in 3D Vision. Neural Radiance Fields (NeRF) [19] implicitly store the scene's shape and reflectance through MLPs optimized by inverse volume rendering. While NeRF can only recover coarse 3D shapes, several subsequent works [3, 25, 26, 29, 31, 33] have been proposed to combine the surface rendering and volume rendering techniques, recovering fine shapes under varying viewpoints but static environment light. In contrast, viewpoints in Spin-UP are relatively static to the objects. While most neural field methods aim to recover the whole 3D geometries, Spin-UP only recovers the object's surface." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.799, + 0.673, + 0.816 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In Sec. 3.1, we explain the Spin-UP's setup and how it reduces the unknowns. In Sec. 3.2, we introduce the light prior that alleviates ambiguities in NaUPS, including details of the light initialization method based on that prior. In Sec. 3.3, we describe the implementation details of the" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11906" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.468, + 0.228 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.239, + 0.473, + 0.337 + ], + "angle": 0, + "content": "Figure 1. The proposed image capturing setup. Left: an illustration of image-capturing equipment consisting of a rotatable platform, a camera, and the target object. We spin the platform in \\(360^{\\circ}\\) and capture images of the object. The object and camera rotate together with the platform. Right-top: Four observed images at different positions. Right-bottom: Ground truth environment light. Dashed color boxes indicate the corresponding camera views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.47, + 0.385 + ], + "angle": 0, + "content": "proposed Spin-UP framework and losses. In Sec. 3.4, we demonstrate two proposed training strategies." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.395, + 0.245, + 0.412 + ], + "angle": 0, + "content": "3.1. Spin Light Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.419, + 0.473, + 0.661 + ], + "angle": 0, + "content": "As shown in Fig. 1, we capture a sequence of images \\( \\pmb{I} \\triangleq \\{I_j | j \\in [1, \\dots, N_I]\\} \\) for an object by rotating it together with a linear perspective camera in \\( 360^\\circ \\) on a rotatable platform. Since the relative positions and orientations between the camera and the object are fixed during rotation, each observed image is aligned with the rotated environment light \\( L(R_j \\cdot \\omega) \\), where \\( \\omega \\in \\mathbb{R}^3 \\) indicates the incident light's direction, \\( R_j = R(\\theta_j) \\) is the 1-DoF [5] rotation matrix representing rotation about the vertical axis, \\( \\theta_j \\) is the rotation angle, \\( \\theta_1 = 0 \\). As we conduct \\( 360^\\circ \\) rotation and assume a constant velocity (despite not strictly required in practice), \\( R_j \\) can be initialized given \\( \\theta_j = 2\\pi (j - 1) / N_I \\). Given a sequence of images \\( I \\) and the initialized \\( R \\), Spin-UP iteratively optimizes the normal map \\( N \\), the environment light \\( L \\), isotropic BRDF map \\( M \\), and rotation angle \\( R \\) by solving" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.663, + 0.47, + 0.707 + ], + "angle": 0, + "content": "\\[\n\\underset {\\boldsymbol {L}, \\boldsymbol {M}, \\boldsymbol {N}, \\boldsymbol {R}} {\\arg \\min } \\sum_ {i = 1} ^ {N _ {P}} \\sum_ {j = 1} ^ {N _ {I}} \\mathcal {E} \\left(\\boldsymbol {m} _ {i j}, \\hat {\\boldsymbol {m}} _ {i j}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.708, + 0.47, + 0.784 + ], + "angle": 0, + "content": "where \\(N_P\\) is the number of sampled points on the surface, \\(\\pmb{m}_{ij}\\) and \\(\\hat{\\pmb{m}}_{ij}\\) indicate the ground truth and estimation of point \\(i\\)'s color in image \\(I_j\\), respectively. \\(\\mathcal{E}(\\cdot ,\\cdot)\\) is loss function between \\(\\pmb{m}_{ij}\\) and \\(\\hat{\\pmb{m}}_{ij}\\) (i.e., mean absolute error). We adopt the rendering equation to calculate the color \\(\\hat{\\pmb{m}}^2\\)" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.785, + 0.47, + 0.852 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {\\boldsymbol {m}} = \\int_ {\\Omega} s \\boldsymbol {L} (\\boldsymbol {\\omega}) \\rho (\\boldsymbol {\\omega} \\cdot \\boldsymbol {n}) \\mathrm {d} \\boldsymbol {\\omega}, \\\\ = \\int_ {\\Omega} s \\boldsymbol {L} (\\boldsymbol {\\omega}) \\left(\\rho^ {s} + \\rho^ {d}\\right) (\\boldsymbol {\\omega} \\cdot \\boldsymbol {n}) \\mathrm {d} \\boldsymbol {\\omega}. \\end{array} \\tag {2}\n\\]" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.863, + 0.469, + 0.888 + ], + "angle": 0, + "content": "1We assume the object's boundary is geometrically smooth (occluding boundary)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.095, + 0.888, + 0.32, + 0.901 + ], + "angle": 0, + "content": "2The subscripts are omitted for simplicity." + }, + { + "type": "list", + "bbox": [ + 0.077, + 0.863, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.093, + 0.892, + 0.163 + ], + "angle": 0, + "content": "Table 1. A comparison of type, unknowns' number (number), and representation capacity (rep. capacity) of light model among Spin-UP and representative unsupervised NaUPS methods. The unknown number is calculated on 50 images \\((512 \\times 512)\\). 'freq.' represents frequency." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.165, + 0.89, + 0.213 + ], + "angle": 0, + "content": "
QL15 [21]HY19 [7]GM21 [6]Spin-UP
typeSV-SHGlobal SHEqv-DirSG
number1.5K4501.4M434
rep. capacitylow-freq.low-freq.low-freq.high-freq.
" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.224, + 0.892, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.373, + 0.893, + 0.457 + ], + "angle": 0, + "content": "Figure 2. The proposed light initialization method in Spin-UP. We crop the boundary pixels \\( m_{b} \\) and normal \\( \\pmb{n}_{b} \\) from input images. Then, we remap them on the sphere and rotate them with their corresponding rotations \\( \\pmb{R} \\). Based on a light probe composed of gray-scale boundary pixels, we optimize the SG light model to obtain the environment light." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.892, + 0.553 + ], + "angle": 0, + "content": "where \\(\\Omega\\) represents the upper hemisphere centered at the normal vector \\(\\pmb{n}\\). \\(s\\) is the first shadow. \\(\\rho^s\\) and \\(\\rho^d\\) indicate the specular and diffuse reflectance, respectively. The ambiguities between the light \\(L\\) and reflectance of the object \\(\\pmb{M}\\) are often disregarded [13, 16]." + }, + { + "type": "text", + "bbox": [ + 0.49, + 0.553, + 0.892, + 0.763 + ], + "angle": 0, + "content": "Unkowns reduction. The proposed spin light setup reduces the unknowns of the light representation \\(L\\) by exploiting correlations between different images. Unlike premodel the light for ionization in the nucleus is modeled using the method shown in the setup, we can exploit from the object's boundary to light initialization. The idea is motivated by the observation that the light map has no effect on the image. We consider the images into the environment light (see Fig. 2). For an object with a light boundary, the normal of those boundaries can roughly derive a light map indicating the light sources' positions at the object. We then use the recently measured light map at \\(N_{1}\\) to calculate the ionized and ground state image. As such, the unknowns consist of the environment light model's parameters and the number of rotational angles that are quantitatively equal to \\(N_{I}\\). The total unknown amount is reduced compared to other methods (Table 1), which helps mitigate the ill-posedness and facilitates solving NaUPS with advanced light and reflectance models in an unsupervised manner." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.759, + 0.789 + ], + "angle": 0, + "content": "3.2. Light Prior from Boundaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Based on the spin light setup, we can exploit priors from the object boundary for light initialization to alleviate the ambiguity. The idea is motivated by the observation that the pixel value \\( m_{b} \\) at an object's boundary provides insights into the environment light (see Fig. 2). For an object with occluding boundaries, the normal of those boundaries \\( \\mathbf{n}_b \\) can be pre-computed [13, 16]. By bonding \\( m_{b}, n_{b} \\), and \\( R \\), we can" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11907" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.094, + 0.208, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.155, + 0.217, + 0.169, + 0.226 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.225, + 0.089, + 0.323, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.266, + 0.217, + 0.281, + 0.227 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.338, + 0.089, + 0.435, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.379, + 0.217, + 0.394, + 0.226 + ], + "angle": 0, + "content": "(c)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.241, + 0.47, + 0.352 + ], + "angle": 0, + "content": "Figure 3. An illustration of mismatched light source positions. Rows from top to bottom: an illustration of reflection on materials with different roughness; the initial environment light before applying any filters given objects' boundary pixels; the ground truth environment light. Objects are (a) the diffuse-dominant sphere, (b) the diffuse and specular mixture sphere, and (c) the specular dominant sphere. The yellow and red lines in rows 2 and 3 indicate a rough position of the light sources." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.469, + 0.452 + ], + "angle": 0, + "content": "roughly derive a light map indicating the light sources' positions and intensities, where \\( m_b \\) directly represent the light intensity \\( L(\\omega_b) \\) at \\( \\boldsymbol{\\omega}_b = \\boldsymbol{R} \\cdot \\boldsymbol{n}_b \\). However, the derived light map for objects with different materials may contain mismatched light source positions and chromatic bias, leading to inaccurate light initialization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.453, + 0.469, + 0.695 + ], + "angle": 0, + "content": "The mismatched light source positions are caused by the specular component \\( m_b^s \\) in \\( m_b \\). When \\( m_b^s \\) dominates, approximating \\( L(\\omega_b) \\) by \\( m_b \\) becomes a biased estimation as \\( m_b^s \\) is a reflection of lights in different directions than \\( \\omega_b \\) (Fig. 3). By contrast, the approximation is more reasonable when the diffuse component \\( (m_b^d) \\) dominates since \\( m_b^d = \\int_{\\Omega} L(\\omega) \\rho^d (\\omega \\cdot \\omega_b) \\mathrm{d}\\omega \\) indicates that \\( L(\\omega_b) \\) contributes most to the actual pixel value, making it less biased to use \\( m_b^d \\) to represent \\( L(\\omega_b) \\). Therefore, to facilitate a less biased estimation of environment light for initialization, a diffuse filter \\( \\mathcal{F}^d(.) \\) is necessary on \\( m_b^d \\), alleviating the mismatched light source positions issue. Similarly, a chromatic filter \\( \\mathcal{F}^c(.) \\) is also required to reduce the chromatic bias caused by the spatially varying material at boundaries. The filtered pixel value \\( \\hat{m}_b^d = \\mathcal{F}^c(\\mathcal{F}^d(m_b)) \\) are the basis for our light initialization method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.469, + 0.864 + ], + "angle": 0, + "content": "Light initialization method. The procedure of light initialization method is summarized in Algorithm 1. This method aims to derive an initial environment light model with parameter \\(\\Theta\\). Specifically, we use \\(N_{L} = 64\\) spherical Gaussian (SG) bases [28] as the light model, where \\(\\pmb{L}(\\pmb{\\omega}|\\pmb{\\xi}_t,\\lambda_t,\\pmb{\\mu}_t) = \\sum_{t=1}^{N_L} G(\\pmb{\\omega};\\pmb{\\xi}_t,\\lambda_t,\\pmb{\\mu}_t)\\). \\(\\pmb{\\xi}_t\\), \\(\\lambda_t\\), and \\(\\pmb{\\mu}_t\\) stands for Gaussian lobes' direction, sharpness, and amplitude, respectively3. Inspired by [23] indicating that diffuse reflectance can be approximated by the low-frequency reflectance, we design \\(\\mathcal{F}^d(.)\\) as a combination of a threshold filter \\(\\mathcal{F}_{TH}^d(.)\\) that removes high-intensity reflectance (top" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.091, + 0.892, + 0.213 + ], + "angle": 0, + "content": "\\(20\\%\\) bright) based on boundary points' intensity profile [23] and a low-pass filter (i.e., 3-order spherical harmonics filter4) noted as \\(\\mathcal{F}_{SH}^{d}\\) [22, 23]. While \\(\\mathcal{F}_{TH}^{d}(.)\\) reduces the bias by removing the brightest parts that are usually aligned with specular reflectance in observed images. \\(\\mathcal{F}_{SH}^{d}(.)\\) helps extract the low-frequency reflectance. For \\(\\mathcal{F}^c(.)\\), we design it as a converter transferring pixel values into gray-scale5, mitigating biases from spatially varying material." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.219, + 0.771, + 0.234 + ], + "angle": 0, + "content": "Algorithm 1 Light Initialization Method" + }, + { + "type": "text", + "bbox": [ + 0.524, + 0.238, + 0.892, + 0.307 + ], + "angle": 0, + "content": "Input: pre-computed boundary normal \\( \\mathbf{n}_b \\), initial relative rotation matrices \\( \\{\\pmb{R}_1\\ldots ,\\pmb{R}_{N_I}\\} \\), boundary pixels \\( \\{m_{b1},\\dots,m_{bN_I}\\} \\), diffuse filters \\( \\mathcal{F}_{TH}^{d}(\\cdot) \\) and \\( \\mathcal{F}_{SH}^{d}(\\cdot) \\), chromatic filter \\( \\mathcal{F}^c (\\cdot) \\), fitting epochs \\( N \\), environment light with parameters \\( L(|\\Theta\\rangle) \\), learning rate \\( \\eta \\)." + }, + { + "type": "text", + "bbox": [ + 0.525, + 0.308, + 0.838, + 0.322 + ], + "angle": 0, + "content": "Output: an initial environment light model \\(L(|\\Theta^{\\prime})\\)" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.322, + 0.652, + 0.335 + ], + "angle": 0, + "content": "\\[\n\\mathbf {f o r} j = 1, \\dots , N _ {I} \\mathbf {d o}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.337, + 0.643, + 0.35 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\omega} _ {b j} = \\boldsymbol {R} _ {j} \\cdot \\boldsymbol {n} _ {b}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.527, + 0.351, + 0.71, + 0.408 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\hat {m} _ {b} ^ {d} = \\mathcal {F} ^ {c} \\left(\\mathcal {F} _ {S H} ^ {d} \\left(\\mathcal {F} _ {T H} ^ {d} (m _ {b}))\\right)\\right) \\\\ \\mathbf {f o r} e = 1, \\dots , N \\mathbf {d o} \\\\ J = \\sum (\\boldsymbol {L} (\\omega_ {b} | \\Theta) - \\hat {m} _ {b} ^ {d}) ^ {2} \\\\ \\Theta \\leftarrow \\Theta - \\eta \\partial J / \\partial \\Theta \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.528, + 0.408, + 0.576, + 0.417 + ], + "angle": 0, + "content": "\\[\n\\Theta^ {\\prime} = \\Theta\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.431, + 0.716, + 0.447 + ], + "angle": 0, + "content": "3.3. Framework of Spin-UP" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.454, + 0.892, + 0.499 + ], + "angle": 0, + "content": "With reliable initial SG lights and rotation matrices \\( \\mathbf{R} \\), we develop Spin-UP based on neural inverse rendering [3, 13, 16, 31] given the rendering equation in Eq. (2)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.5, + 0.892, + 0.575 + ], + "angle": 0, + "content": "Shape model. We use the neural depth field to represent the 3D surface. A multi-layer perceptron (MLP) predicts the depth value given the image coordinates. To compute normal given the depth map, we extend the normal fitting method described in [16] to the perspective projection6." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.575, + 0.892, + 0.771 + ], + "angle": 0, + "content": "Material model. We represent the spatially varying and isotropic reflectance as a modified Disney Model [31]. The diffuse albedo \\(\\rho^d\\) is predicted by another MLP with a similar structure given the image coordinate. The spatially varying specular reflectance is calculated as a weighted sum of \\(N_{S} = 12\\) SG bases, so \\(\\rho^{s} = \\sum_{n = 1}^{N_{S}}c^{n}\\mathcal{D}(\\pmb {v},\\pmb {\\omega})\\mathcal{F}(\\pmb {h},\\pmb {\\omega})\\mathcal{G}(\\pmb {n},\\pmb {\\omega},\\pmb {v},\\lambda_{n})\\), where \\(\\mathcal{D}\\), \\(\\mathcal{F}\\), and \\(\\mathcal{G}\\) accounts for micro-facet's normal distribution, Fresnel effects, and self-occlusion, respectively. \\(\\pmb{v}\\) is the view direction. \\(\\pmb{h}\\) is the half-vector, calculated by \\(\\pmb {h} = (\\pmb {v} + \\pmb {\\omega}) / \\| \\pmb {v} + \\pmb {\\omega}\\|\\), \\(\\lambda_{n}\\) is the roughness terms initialized as \\((0.1 + 0.9(n - 1)) / (N_S - 1)\\) and set as learnable parameters, \\(c^n\\) is the weights predicted by the MLP." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.772, + 0.891, + 0.8 + ], + "angle": 0, + "content": "Shadow model. We apply a shadow mask similar in [13] to handle the cast shadow." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.802, + 0.892, + 0.832 + ], + "angle": 0, + "content": "Loss functions. Similar to other inverse rendering-based methods [13, 16], we use the inverse rendering loss" + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.839, + 0.892, + 0.866 + ], + "angle": 0, + "content": "4We implement a Gaussian filter and rescale the pixel value's range to \\(\\mathcal{F}_{TH}^{d}(m_{b})\\) 's range to suppress ringing effect and negative energy in SH." + }, + { + "type": "page_footnote", + "bbox": [ + 0.525, + 0.865, + 0.878, + 0.876 + ], + "angle": 0, + "content": "We use gray-scale value to initialize the RGB value of light model." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.876, + 0.891, + 0.9 + ], + "angle": 0, + "content": "6Please refer to the supplementary material for more details about the network structures and modified normal fitting method." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.839, + 0.891, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "In practice, we find that initializing Gaussians' parameters by Fibonacci lattice [31] and freezing \\(\\lambda_{t}\\) gives the best results." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11908" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.0, + 0.0, + 0.498, + 0.269 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.47, + 0.39 + ], + "angle": 0, + "content": "Figure 4. Proposed training strategies. (Top) Interval sampling (IS). The high-resolution images are down-sampled into several low-resolution sub-images by extracting pixels with an interval of \\( N_B \\), where \\( N_B = 2 \\) in this example. (Bottom) Shrinking range computing (SRC). Far points (yellow circles) that are \\( k \\) (\\( k = 3 \\) in this example) point away w.r.t the query position is selected to interpolate the close points (blue circles)'s depth for normal calculation. During optimization, \\( k \\) will be gradually reduced to 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.47, + 0.603 + ], + "angle": 0, + "content": "(i.e, Eq. (1)) to train the framework. The three-stage schema [16] is applied, as well as other smoothness terms (total variance regularization [13, 16]) calculate as \\(\\mathrm{TV}(.) = \\frac{1}{N_P}\\sum_{i = 1}^{N_P}\\left|\\frac{\\partial(.)}{\\partial x} +\\frac{\\partial(.)}{\\partial y}\\right|\\), where \\((x,y)\\) is the image coordinates. We implement \\(\\mathrm{TV}(.)\\) on the normal map \\((N)\\), diffuse albedo map \\((A)\\), and the Gaussian bases' weights \\((c)\\) for the material, and gradually drop it following the three-stage training schema [16]. Similar to [30], the normalized color loss calculated as \\(\\| \\operatorname {Nor}(A) - \\operatorname {Nor}(I)\\|\\) is implemented to help Spin-UP learn a better albedo representation, where \\(\\operatorname {Nor}(.)\\) is the vector normalization. Following [16], we calculate the boundary loss as the cosine similarity between the pre-computed and estimated boundary normal" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.614, + 0.262, + 0.63 + ], + "angle": 0, + "content": "3.4. Training Strategies" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.638, + 0.469, + 0.744 + ], + "angle": 0, + "content": "Optimizing Spin-UP requires smoothness terms to facilitate convergence and avoid local optima. However, those terms are often implemented on full-resolution images, leading to high computational costs. To reduce those costs, we propose to use a sampling strategy noted as interval sampling (IS). To further improve convergence, we introduce another technique noted as shrinking range computing (SRC)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.744, + 0.469, + 0.865 + ], + "angle": 0, + "content": "Interval sampling (IS). IS samples ray batches from images to reduce the costs. Unlike random ray sampling [19] or patch-based sampling [20], IS preserves the object's shape. The idea is similar to downsampled techniques in [11, 24], but we don't merge the sub-images to full resolution. We experimentally find this strategy important for training on down-sampled sub-images with smoothness terms to avoid local optima (Sec. 5.2). Specifically," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.226 + ], + "angle": 0, + "content": "we divide the image in full resolution into non-overlapping blocks, and each block contains \\( N_B \\times N_B \\) pixel points. By extracting pixel points from the same position in each block (e.g., the left-top pixel), we obtain \\( N_B \\times N_B \\) sub-images with a down-sampled resolution (See Fig. 4 for illustration). During training, those sub-images are randomly sampled in each epoch, and the smoothness terms are calculated based on the sub-images resolution, which reduces the computational cost and ensures the effectiveness of those terms." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.228, + 0.893, + 0.53 + ], + "angle": 0, + "content": "Shrinking range computing (SRC). Without merging sub-images back to a full-resolution image in IS, there will be an aliasing issue in the inverse rendering process. Such an issue is caused by the fact that the normal calculation in our framework on sub-images requires four adjacent points' depths in sub-images resolution [16], which degrades the precision of normal calculation8. Therefore, SRC is applied for anti-aliasing. It uses points adjacent to the query point (blue circles in Fig. 4) in the full-resolution image coordinates to calculate the normal for each pixel in the sub-images. Such a strategy maintains the precision of normal calculation. However, at the early stage of training, calculating the normal based on the blue circles' depth is vulnerable to perturbation in per-pixel training. Therefore, SRC gradually selects points (yellow circles) from far (\\(k = 3\\) points away) to close (blue circles) w.r.t query points to interpolate the blue circles' depth, as normal calculation on far points' depth will lead to a more smooth and stable normal map at the early stage, which eventually improves convergence, as validated in Sec. 5.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.548, + 0.633, + 0.565 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.574, + 0.892, + 0.679 + ], + "angle": 0, + "content": "We validate the effectiveness of the proposed Spin-UP on synthetic and real-world data. We use mean angle error (MAE) to evaluate the normal map's reconstructed quality and PU-PSNR [1], and PU-SSIM [1] to evaluate the reconstructed environment light. Since no existing datasets follow our spin light setup, we collect the dataset using Blender and our device." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.791, + 0.708 + ], + "angle": 0, + "content": "4.1. Evaluation on Synthetic Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.717, + 0.892, + 0.837 + ], + "angle": 0, + "content": "We collect several objects, environment maps, and materials to render the synthetic dataset in Blender by Cycles. Specifically, five shapes from the DiLiGenT-MV dataset [14] (i.e, BUDDHA, BEAR, COW, POT2, and READING) and a generated shape (BALL), five HDR environment maps (i.e, LANDSCAPE, QUARRY, URBAN, ATTIC, STUDIO), two PBR materials (i.e, RUSTY STEEL, LEATHER), and four synthetic materials (i.e, VORONOI DIFF, VORONOI SPEC," + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.469, + 0.9 + ], + "angle": 0, + "content": "7Please refer to the supplementary material for more details about the setup of hyperparameters." + }, + { + "type": "page_footnote", + "bbox": [ + 0.499, + 0.851, + 0.892, + 0.9 + ], + "angle": 0, + "content": "8 According to normal's definition, the smaller the distance between the adjacent points and the query points (red circle in Fig. 4), the more accurately representing the geometry at query points. Therefore, the blue circles' depths are preferred for normal calculation." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11909" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.089, + 0.895, + 0.16 + ], + "angle": 0, + "content": "Table 2. Qualitative comparison results in terms of MAE on shape group (left-top), light group (left-bottom), reflectance group (right-top), and spatially varying material group (right-bottom). Bold numbers indicate the best results in MAE. In light group, {U., A., S., L.} stand for environment map named URBAN, ATTIC, STUDIO, and LANDSCAPE, respectively. In the reflectance group, {D., S.} stand for material named GREEN DIFF and GREEN SPEC, respectively. In spatially varying material group, {D., S.} stand for material named VORONOI DIFF and VORONOI SPEC, respectively." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.17, + 0.895, + 0.358 + ], + "angle": 0, + "content": "
MethodShape GroupReflectance Group
BALLBEARBUDDHAREADINGAVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]41.3253.8867.9054.8554.4957.4537.4365.4858.0454.60
S22 [10]7.3514.0326.3718.7716.6315.5611.8318.9718.3816.19
S23 [11]5.5610.3718.5415.1012.3913.469.7516.2212.6713.03
Spin-UP3.546.3317.307.718.725.837.1113.0910.309.08
MethodLight GroupSpatially Varying Material Group
Cow (U.)Cow (A.)Cow (S.)Cow (L.)AVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]67.6339.2140.2848.4748.8940.9737.4649.2748.9644.17
S22 [10]17.1712.7417.1111.3514.5918.5917.6322.8023.7520.69
S23 [11]11.937.5212.3811.6010.8414.2211.0014.5814.3113.53
Spin-UP5.504.403.334.944.545.586.9712.5411.529.15
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.537 + ], + "angle": 0, + "content": "GREEN DIFF, GREEN SPEC) are used for evaluation. We devise four groups of data for evaluation: shape group, light group, reflectance group, and spatially varying material group, each containing four scenes. For each scene, 50 observed images with a resolution of \\(512 \\times 512\\) are rendered by a perspective camera with the focal of \\(50\\mathrm{mm}\\) and a frame size of \\(36\\mathrm{mm} \\times 36\\mathrm{mm}\\). The camera rotation \\(\\theta\\) for consecutive images follows a non-uniform rotation velocity. We compare Spin-UP with three advanced NaUPS methods, including two supervised NaUPS methods (S22 [10] and S23 [11]) and one unsupervised UPS method (HY19 [7])10." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.537, + 0.473, + 0.825 + ], + "angle": 0, + "content": "Normal estimation comparison. According to results in Table 2, Spin-UP presents a superior performance compared to all other NaUPS methods. Specifically, in shape group, the low MAE on BALL, BEAR, BUDDHA, READING in RUSTY STEEL rendered under QUARRY indicate the practicability of Spin-UP to various shapes. In light group, the low-variance of MAE \\((0.81^{\\circ}\\) for Spin-UP vs. \\(1.94^{\\circ}\\) for S23 [11]) on COW in LEATHER rendered under QUARRY, URBAN, ATTIC, and STUDIO demonstrates robustness toward different environment lights. In reflectance group, the results on POT2 and READING in GREEN DIFF and GREEN SPEC rendered under LANDSCAPE demonstrate the ability to handle non-Lambertian objects. In spatially varying material group, results on POT2 and READING rendered in VORONOI DIFF or VORONOI SPEC under LANDSCAPE prove adaptability to challenging scenarios. A comparative analysis of the outcomes of the reflectance group and the spatially varying material group in our method reveals that the MAE remains relatively consistent across identical ob" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.368, + 0.892, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.554, + 0.895, + 0.626 + ], + "angle": 0, + "content": "Figure 5. The visual quality comparison of light between the estimated one by Spin-UP (columns 2-5) and the ground truth (column 1) on the four groups, i.e., shape (row 1), reflectance (row 2), spatially varying material (row 3), and light group (row 4-5). The intensity of the estimated light maps is scaled for visualization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.64, + 0.895, + 0.732 + ], + "angle": 0, + "content": "jects with different materials, underscoring the robustness of Spin-UP in handling diverse materials. Also, we find that Spin-UP sometimes performs better on specular objects than on diffuse objects (i.e., READING). We attribute this to the high-frequency details in specular reflectance that may be useful for shape-light reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Light estimation comparison. Fig. 5 provides a qualitative comparison between the estimated environment light and the ground truth on four groups. We can observe that the learned light map reflects the position of the light source, especially in Cow (S.) given such a challenging setup without any prior information about the object material or shape. It also reconstructs a reasonable light map for objects with diffuse reflectance, such as POT2 (D.) and READING (D.), further highlighting the effectiveness of the proposed light initialization. However, it should be noted that the estimated environment light is influenced by the object material, par" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.838, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The generated pattern for VORONOI DIFF and VORONOI SPEC follow similar setup in CNN-PS [9]. Please refer to the supplementary material for all the qualitative comparison between Spin-UP and other methods on the synthetic and realworld dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "11910" + } + ], + [ + { + "type": "header", + "bbox": [ + 0.073, + 0.0, + 0.262, + 0.056 + ], + "angle": 0, + "content": "(1)细胞壁：脑聚糖体膜、高尔基体膜、内质网等" + }, + { + "type": "header", + "bbox": [ + 0.352, + 0.0, + 0.541, + 0.054 + ], + "angle": 0, + "content": "\\( \\left\\{ {1,2}\\right\\} \\Rightarrow \\left\\{ {1,3}\\right\\} \\Rightarrow \\left\\{ {2,4}\\right\\} \\Rightarrow \\left\\{ {3,4}\\right\\} \\Rightarrow \\left\\{ {4,5}\\right\\} \\Rightarrow \\left\\{ {5,6}\\right\\} \\Rightarrow \\left\\{ {6,7}\\right\\} \\Rightarrow \\left\\{ {7,8}\\right\\} \\Rightarrow \\left\\{ {8,9}\\right\\} \\Rightarrow \\left\\{ {9,10}\\right\\} \\Rightarrow \\left\\{ {10,11}\\right\\} \\Rightarrow \\left\\{ {11,12}\\right\\} \\Rightarrow \\left\\{ {12,13}\\right\\} \\Rightarrow \\left\\{ {13,14}\\right\\} \\Rightarrow \\left\\{ {14,15}\\right\\} \\Rightarrow \\left\\{ {15,16}\\right\\} \\Rightarrow \\left\\{ {16,17}\\right\\} \\Rightarrow \\left\\{ {17,18}\\right\\} \\Rightarrow \\left\\{ {18,19}\\right\\} \\Rightarrow \\left\\{ {19,20}\\right\\} \\Rightarrow \\left\\{ {20,21}\\right\\} \\Rightarrow \\left\\{ {21,22}\\right\\} \\Rightarrow \\left\\{ {22,23}\\right\\} \\Rightarrow \\left\\{ {23,24}\\right\\} \\Rightarrow \\left\\{ {24,25}\\right\\} \\Rightarrow \\left\\{ {25,26}\\right\\} \\Rightarrow \\left\\{ {26,27}\\right\\} \\Rightarrow \\left\\{ {27,28}\\right\\} \\Rightarrow \\left\\{ {28,29}\\right\\} \\Rightarrow \\left\\{ {29,30}\\right\\} \\Rightarrow \\left\\{ {30,31}\\right\\} \\Rightarrow \\left\\{ {31,32}\\right\\} \\Rightarrow \\left\\{ {32,33}\\right\\} \\Rightarrow \\left\\{ {33,34}\\right\\} \\Rightarrow \\left\\{ {34,35}\\right\\} \\Rightarrow \\left\\{ {35,36}\\right\\} \\Rightarrow \\left\\{ {36,37}\\right\\} \\Rightarrow \\left\\{ {37,38}\\right\\} \\Rightarrow \\left\\{ {38,39}\\right\\} \\Rightarrow \\left\\{ {39,40}\\right\\} \\Rightarrow \\left\\{ {40,41}\\right\\} \\Rightarrow \\left\\{ {41,42}\\right\\} \\Rightarrow \\left\\{ {42,43}\\right\\} \\Rightarrow \\left\\{ {43,44}\\right\\} \\Rightarrow \\left\\{ {44,45}\\right\\} \\Rightarrow \\left\\{ {45,46}\\right\\} \\Rightarrow \\left\\{ {46,47}\\right\\} \\Rightarrow \\left\\{ {47,48}\\right\\} \\Rightarrow \\left\\{ {48,49}\\right\\} \\Rightarrow \\left\\{ {49,50}\\right\\} \\Rightarrow \\left\\{ {50,51}\\right\\} \\Rightarrow \\left\\{ {51,52}\\right\\} \\Rightarrow \\left\\{ {52,53}\\right\\} \\Rightarrow \\left\\{ {53,54}\\right\\} \\Rightarrow \\left\\{ {54,55}\\right\\} \\Rightarrow \\left\\{ {55,56}\\right\\} \\Rightarrow \\left\\{ {56,57}\\right\\} \\Rightarrow \\left\\{ {57,58}\\right\\} \\Rightarrow \\left\\{ {58,59}\\right\\} \\Rightarrow \\left\\{ {59,60}\\right\\} \\Rightarrow \\left\\{ {60,61}\\right\\} \\Rightarrow \\left\\{ {61,62}\\right\\} \\Rightarrow \\left\\{ {62,63}\\right\\} \\Rightarrow \\left\\{ {63,64}\\right\\} \\Rightarrow \\left\\{ {64,65}\\right\\} \\Rightarrow \\left\\{ {65,66}\\right\\} \\Rightarrow \\left\\{ {66,67}\\right\\} \\Rightarrow \\left\\{ {67,68}\\right\\} \\Rightarrow }.\\;\\left( {{QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq@qq" + }, + { + "type": "image", + "bbox": [ + 0.054, + 0.09, + 0.262, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.133, + 0.199, + 0.21, + 0.21 + ], + "angle": 0, + "content": "Capture System" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.09, + 0.47, + 0.194 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.279, + 0.199, + 0.46, + 0.21 + ], + "angle": 0, + "content": "Captured Images and Light References" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.222, + 0.47, + 0.293 + ], + "angle": 0, + "content": "Figure 6. Illustration of the device for real data collection. Please refer to the supplementary material for more details. Left: the capture system contains a camera, a spin platform, and an object. Right: Captured images and paired mirror balls (as light reference) of two objects in the indoor and outdoor scenes, respectively." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.296, + 0.47, + 0.497 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.511, + 0.47, + 0.595 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison for the estimated normal map and environment light on SOLDIER and PLAYER capturing under outdoor (columns 1-6) and indoor (columns 7-12) between ours (column 3, 9), S23 [11] (column 5, 11), and S22 [10] (column 6, 12). We also show the reference sphere and reference environment light (columns 2, 7), and estimated light (columns 4, 10)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.47, + 0.697 + ], + "angle": 0, + "content": "ticularly when handling objects with a nearly uniform base color (e.g., reflectance group) or spatially varying material, which may generate unpleasant artifacts (e.g., inconsistent color in estimated environment light of READING (D.) in the spatially varying material group). Those artifacts are hard to eliminate without priors." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.709, + 0.382, + 0.725 + ], + "angle": 0, + "content": "4.2. Evaluation on Real-world Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.47, + 0.854 + ], + "angle": 0, + "content": "We set up our spin light capture system to collect real data under indoor and outdoor scenes, as shown in Fig. 6. After preprocessing, we end up with 50 images for each object, with a \\(540 \\times 540\\) resolution. Here, we showcase the normal estimation results on two objects (i.e., SOLDIER, and PLAYER) under indoor and outdoor environment lights in Fig. 7, compared with S23 [11], S22 [10]. We do not show HY19 [7]'s result as it failed on the captured data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Normal estimation comparison. According to the Fig. 7, Spin-UP has competitive performance compared to the state-of-the-art supervised method [11]. In some scenar" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.894, + 0.146 + ], + "angle": 0, + "content": "Table 3. Ablation studies on Spin-UP's alternatives regarding average PU-PSNR [1] and PU-SSIM [1] on synthetic dataset. 'Fib.' and 'Rand.' represent the Fibonacci and random initialization method, respectively. Bold number indicates the best results." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.152, + 0.853, + 0.193 + ], + "angle": 0, + "content": "
w Rand.w Fib.Spin-UP
PU-PSNR [1]↑16.8618.9822.06
PU-SSIM [1]↑0.450.520.60
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.2, + 0.894, + 0.382 + ], + "angle": 0, + "content": "ios, we recover more reasonable results regarding the overall normal distribution than the reference sphere, particularly for SOLDIER indoor and PLAYER indoor. Spin-UP can effectively capture high-frequency details such as wrinkles on clothes in PLAYER and SOLDIER. By contrast, S23 [11] may contain artifacts (i.e., an incorrect normal map distribution) even though they have more details than ours, and S22 [10] generates over-smooth results. By comparing indoor and outdoor results, we observe that the performance of S23 [11] degrades significantly in indoor scenarios, which may be attributed to the data bias and low pixel variance, while our method is not greatly affected." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.397, + 0.652, + 0.415 + ], + "angle": 0, + "content": "5. Ablation Study" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.766, + 0.439 + ], + "angle": 0, + "content": "5.1. Light Initialization Validation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.447, + 0.893, + 0.506 + ], + "angle": 0, + "content": "To comprehensively validate the effectiveness of our light initialization method, we conduct experiments in two aspects: a comparison of different light initialization methods and the effectiveness of the filters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.893, + 0.78 + ], + "angle": 0, + "content": "Comparison on light initialization methods. We compare our light initialization method with two widely used SG light initialization methods, i.e., the random initialization noted as 'w Rand.' and Fibonacci lattice [31] noted as 'w Fib.' A quantitative comparison of reconstructed normal and light maps is shown in Table 3 and Table 4. Compared with 'w Rand,' the improvement in average \\((1.75^{\\circ}\\) reduction in MAE on normal estimation and \\(5.20 / 0.15\\) increase in PU-PSNR / PU-SSIM on light estimation, respectively) indicates our method's adaptability. Compared with 'w Fib,' we observe an obvious advantage in the shape group \\((0.61^{\\circ}\\) reduction in MAE), while a smaller advantage in the spatially varying material group \\((0.19^{\\circ}\\) reduction in MAE). This is because the material and shape will affect the initial environment light's quality. While the estimated environment light is most accurate on smooth geometry with simple material, the quality will degrade on complex geometry and spatially varying material." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Comparison on the designed filters. We compare Spin-UP with three alternatives (i.e, \\( w / o \\mathcal{F}^c \\), \\( w / o \\mathcal{F}_{SH}^d \\), and \\( w / o \\mathcal{F}_{TH}^d \\)). The results in Table 4 demonstrate the effectiveness of those filters. Specifically, dropping \\( \\mathcal{F}_{TH}^d \\) will lead to mismatching light source position in the initialized environment light introduced by the specular reflectance, which eventually affects the accuracy of the estimated normal; dropping \\( \\mathcal{F}_{SH}^d \\) will harm the performance, especially" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11911" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.173 + ], + "angle": 0, + "content": "Table 4. Ablation studies on Spin-UP's alternatives regarding average MAE on four groups (shape, light, reflectance, and spatially varying material group). 'Fib.', 'Rand.', 'Intv.', and 'Shrk.' represent the Fibonacci initialization method, random initialization, interval sampling, and shrinking range computing, respectively. Bold number indicates the best results in MAE." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.18, + 0.468, + 0.315 + ], + "angle": 0, + "content": "
ShapeLightRef.SV.AVG
w Rand.12.026.449.7910.289.60
w Fib.9.335.3410.209.348.55
w/o Intv.8.875.029.8310.128.37
w/o Shrk.10.104.9210.1210.438.81
w/o Fc9.444.619.249.408.17
w/o FSh9.758.298.9315.7310.41
w/o FTh9.305.049.1812.498.82
Spin-UP8.724.549.089.157.85
S23 [11]†12.428.5612.5212.3311.46
Spin-UP†11.629.2511.079.079.48
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.094, + 0.316, + 0.432, + 0.326 + ], + "angle": 0, + "content": "\\(\\dagger\\) Method with \\(\\dagger\\) is tested on dataset with point light \\(^+\\) environment light Sec. 5.3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.468, + 0.41 + ], + "angle": 0, + "content": "in the spatially varying material group \\((6.58^{\\circ}\\) increase in MAE) since \\(\\mathcal{F}_{SH}^{d}\\) is essential in extracting low-frequency reflectance to initialize the environment light; dropping \\(\\mathcal{F}^c\\) will increase MAE in average \\((0.32^{\\circ})\\), illustrating the necessity of reducing chromatic bias." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.416, + 0.345, + 0.432 + ], + "angle": 0, + "content": "5.2. Training Strategies Validation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.473, + 0.769 + ], + "angle": 0, + "content": "The interval sampling will facilitate the training of Spin-UP in two ways. First, the training time is two times shorter (25 min per object on average vs. 60 min on average, depending on the image's valid points for the object), and the GPU memory occupation is five times smaller (around 5 GB vs. 25 GB during training) than directly training on full-image resolution. Second, comparing Spin-UP with 'w/o Intv.', which applies a random sampling strategy and calculates the smoothness terms on patches (3 × 3 pixels), we find that the performance drops \\(0.52^{\\circ}\\) on average, and most \\((0.97^{\\circ})\\) on the spatially varying material group. This is because the patch-based smoothness may not work uniformly on different parts of the object, diminishing the effectiveness of smoothness terms, especially on objects in spatially varying material with abrupt texture changes. The shrinking range computing helps avoid local optima when training Spin-UP on down-sampled images while still using full-resolution image coordinates for normal calculation. We compared Spin-UP with the alternative 'w/o Shrk.', which does not implement this strategy. The average MAE on normal estimation for four groups increases \\(0.96^{\\circ}\\), highlighting the importance of this strategy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.778, + 0.452, + 0.794 + ], + "angle": 0, + "content": "5.3. Additional Validation on Point Light Source" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.802, + 0.47, + 0.879 + ], + "angle": 0, + "content": "To ensure a more fair comparison with the state-of-the-art supervised methods (S23 [11]), we add a dominant point light to the environment light in synthetic and real-world dataset11. According to Table 4, the proposed Spin-UP has a lower MAE on estimated normal maps than S23 [11] on" + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.09, + 0.652, + 0.1 + ], + "angle": 0, + "content": "Point Light + Environment Light" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.1, + 0.671, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.586, + 0.189, + 0.6, + 0.199 + ], + "angle": 0, + "content": "(a)" + }, + { + "type": "image", + "bbox": [ + 0.687, + 0.089, + 0.721, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.735, + 0.09, + 0.804, + 0.186 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.188, + 0.779, + 0.198 + ], + "angle": 0, + "content": "(b)" + }, + { + "type": "image", + "bbox": [ + 0.814, + 0.09, + 0.888, + 0.187 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.21, + 0.892, + 0.254 + ], + "angle": 0, + "content": "Figure 8. (a) Illustration of new light setup. (b) Qualitative comparison on SOLDIER between our method and S23 [11] with dominant point light." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.259, + 0.892, + 0.336 + ], + "angle": 0, + "content": "the synthetic dataset (9.48° ours v.s. 11.46° S23 [11]). As shown in Fig. 8, we have a visually comparable result on the real-world dataset given far-field point light (2m) and a better result given near-field point light (0.4m), validating the adaptability of Spin-UP on unseen light sources." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.619, + 0.362 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.489 + ], + "angle": 0, + "content": "This paper proposes Spin-UP to address NaUPS in an unsupervised manner. Thanks to our setup to mitigate the ill-posedness, the light initialization method to alleviate the ambiguities of NaUPS, and the proposed training strategies to facilitate fast convergence, Spin-UP can recover surfaces with isotropic reflectance under various lights. Experiments in synthetic and real-world datasets have shown that Spin-UP is robust to various shapes, lights, and reflectances." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.893, + 0.791 + ], + "angle": 0, + "content": "Limitations and future work. Although Spin-UP is efficient and robust in solving NaUPS, it has several limitations: 1) Spin-UP assumes infinitely far light sources, which omit the spatially varying lighting; 2) the materials' base color will bias the estimated environment light; 3) Spin-UP assumes objects to have isotropic reflectance, ignoring inter-reflections and anisotropic features, meaning that it cannot perform well on objects with anisotropic reflectance, such as aluminum, or strong inter-reflections, such as a glass bowl; 4) Spin-UP doesn't compute the shadow iteratively, which may result in artifacts on objects with complicated shapes. Overcoming the above limitations will be regarded as our future work. Besides, the rotation axis of our device does not align with the object's center due to the consideration of structural stability, which may introduce bias from the spatially varying light in observed images. Redesigning the image capture device is also one of the future works. At last, we find it interesting to improve the setup by relieving the requirement for single-axis \\(360^{\\circ}\\) rotation to free rotations for easier implementation on portable devices." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.892, + 0.898 + ], + "angle": 0, + "content": "Acknowledgments. This work is supported by the National Natural Science Foundation of China under Grant No. 62136001, 62088102, Rapid-Rich Object Search (ROSE) Lab, Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, and the State Key Lab of Brain-Machine Intelligence, Zhejiang University, Hangzhou, China." + }, + { + "type": "page_footnote", + "bbox": [ + 0.091, + 0.886, + 0.318, + 0.901 + ], + "angle": 0, + "content": "11Point light's setup follows [11] and [17]." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11912" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.469, + 0.156 + ], + "angle": 0, + "content": "[1] Maryam Azimi et al. PU21: A novel perceptually uniform encoding for adapting existing quality metrics for HDR. 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In ACM Transactions on Graphics (TOG), 2021. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.429 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11914" + } + ] +] \ No newline at end of file diff --git a/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/6c1acd6f-00c1-4dc9-a5c3-6c6dd410bb2c_origin.pdf b/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/6c1acd6f-00c1-4dc9-a5c3-6c6dd410bb2c_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7e1a20a71fae0fa3240ec5295ecb6b778d6451d1 --- /dev/null +++ b/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/6c1acd6f-00c1-4dc9-a5c3-6c6dd410bb2c_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:05ebe84f67d12c456ad0c0d2b699018e50e42a22d5a554ddb269f065c346b11f +size 4340654 diff --git a/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/full.md b/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f6197a4da7576e08539bd0c1a7b03e1019c9dad3 --- /dev/null +++ b/2024/Spin-UP_ Spin Light for Natural Light Uncalibrated Photometric Stereo/full.md @@ -0,0 +1,291 @@ +# Spin-UP: Spin Light for Natural Light Uncalibrated Photometric Stereo + +Zongrui $\mathrm{Li}^{1,2,*}$ Zhan $\mathrm{Lu}^{2,4,*,\dagger}$ Haojie Yan $^{3,4}$ Boxin Shi $^{5,6}$ Gang Pan $^{3,4}$ Qian Zheng $^{3,4,\ddagger}$ Xudong Jiang $^{1,2}$ + +$^{1}$ Rapid-Rich Object Search (ROSE) Lab, Interdisciplinary Graduate Programme, Nanyang Technological University + +$^{2}$ School of Electrical and Electronic Engineering, Nanyang Technological University + +3College of Computer Science and Technology, Zhejiang University + +4The State Key Lab of Brain-Machine Intelligence, Zhejiang University + +$^{5}$ National Key Laboratory for Multimedia Information Processing, School of Computer Science, Peking University + +$^{6}$ National Engineering Research Center of Visual Technology, School of Computer Science, Peking University + +{zongrui001, zhan007, EXDJiang} @ntu.edu.sg, {hjyan, gpan, qianzheng} @zju.edu.cn, shiboxin@pku.edu.cn + +# Abstract + +Natural Light Uncalibrated Photometric Stereo (NaUPS) relieves the strict environment and light assumptions in classical Uncalibrated Photometric Stereo (UPS) methods. However, due to the intrinsic ill-posedness and high-dimensional ambiguities, addressing NaUPS is still an open question. Existing works impose strong assumptions on the environment lights and objects' material, restricting the effectiveness in more general scenarios. Alternatively, some methods leverage supervised learning with intricate models while lacking interpretability, resulting in a biased estimation. In this work, we propose Spin Light Uncalibrated Photometric Stereo (Spin-UP), an unsupervised method to tackle NaUPS in various environment lights and objects. The proposed method uses a novel setup that captures the object's images on a rotatable platform, which mitigates NaUPS's ill-posedness by reducing unknowns and provides reliable priors to alleviate NaUPS's ambiguities. Leveraging neural inverse rendering and the proposed training strategies, Spin-UP recovers surface normals, environment light, and isotropic reflectance under complex natural light with low computational cost. Experiments have shown that Spin-UP outperforms other supervised / unsupervised NaUPS methods and achieves state-of-the-art performance on synthetic and real-world datasets. Codes and data are available at https://github.com/LMozart/CVPR2024-SpinUP. + +# 1. Introduction + +Natural light uncalibrated photometric stereo (NaUPS) [6] is proposed to relieve the dark room and directional light as + +sumption in classical uncalibrated photometric stereo, aiming to reconstruct the surface normal given images of an object captured at arbitrary environment light. The implications of NaUPS are far-reaching: it makes photometric stereo universal. However, solving NaUPS is still an open question because of the intrinsic ill-posedness introduced by the varying light of each image and the high dimensional ambiguities between the light and objects [6]. + +Previous optimization-based methods use the simple light model to represent the varying environment lights and Lambertian reflectance to represent the material [6, 7, 21]. These models help mitigate the ill-posedness and ambiguities to some extent but become ineffective in handling objects with general reflectance (e.g., non-Lambertian reflectance) under complex environment light, leading to unsatisfactory reconstruction outcomes. Besides, since they solely model the varying lights in each image, the unknowns introduced by the light model may increase with the resolution and numbers of the images, restricting their method to low-resolution and insufficient images. + +Considering the difficulties of explicitly mitigating the ill-posedness and ambiguities, recent advances [10, 11] turn to data-driven methods: they train a deep learning model on large-scale datasets and implicitly exploit deep light features from images to improve performance. However, those methods lack interpretability, making them hard to constrain during training. Consequently, the model may be affected by the data bias and prone to specific types of light sources [10] or reflection variations [11] among images. + +Despite a persistent exploration in this research field, a method capable of handling general objects under natural light while free from data bias is still missing. In this paper, we provide a new perspective on solving NaUPS. Specifically, we propose a novel setup that acquires images on a rotatable platform under a static environment light. In such a + +case, the object is illuminated by rotated environment lights. Representing such rotated lights requires fewer parameters than solely modeling varying lights in each image since we model the lights as a uniform environment light varied by low degree-of-freedom (DOF [5]) rotation. This frees us from significantly increasing unknowns when implementing advanced parametric light models (e.g., spherical Gaussian) and reflectance models to handle general scenarios. Additionally, based on such a setup, we further derive a reliable light initialization method by analyzing the pixel value at object's occluding boundary. Such light initialization will help the model converge at the beginning and alleviate the ambiguity between light and objects during training. + +With the help of the proposed setup and light initialization method, we develop Spin Light Uncalibrated Photometric Stereo (Spin-UP), addressing NaUPS by optimizing inverse rendering framework in an unsupervised manner. To our best knowledge, this is the first unsupervised method that can handle general objects under natural light. Unlike previous methods, Spin-UP can jointly reconstruct environment light, isotropic reflectance, and complicated shapes through iterative optimization. To reduce the computational cost and improve convergence, we propose two strategies: interval sampling and shrinking range computing, which help optimize Spin-UP in low GPU usage (5 GB) and fast running time (25 mins). Experiments on synthetic and real-world datasets demonstrate our superior performance over previous methods on general scenarios. Overall, our contributions are summarized as follows: + +1. We design a novel setup for NaUPS, which reduces unknowns of light representation and facilitates solving NaUPS in an unsupervised manner. +2. We introduce a light prior, which leverages an object's occluding boundaries to initialize a reliable environment light. Based on the setup and light prior, we propose the unsupervised NaUPS method named Spin-UP. +3. We present two training strategies for fast training and convergence of Spin-UP. + +# 2. Related Work + +In this section, we briefly review recent supervised and unsupervised NaUPS methods. We also summarize other techniques that exploit priors from occluding boundaries. Additionally, we discuss recent advances in 3D vision to distinguish Spin-UP from other neural inverse rendering approaches. Given that the focus of this paper is on NaUPS, a group of works reconstructing 3D surfaces from a single image by deep learning under natural light [15] or shading [4, 12, 32] are not included. + +Natural Light Uncalibrated Photometric Stereo. Unsupervised NaUPS methods jointly recover the light, reflectance properties, and surface normal. These methods explicitly model the environment light by low-order spheri + +cal harmonics (SH) [2, 21], spatially varying spherical harmonics (SV-SH) [7, 18] or equivalent directional light (Eqv-Dir) [6] to mitigate the ill-posedness, and use integrability constraint [2], shape initialization [7], non-physical lighting regularization [21], or graph-based ambiguity relaxation [6] to alleviate the ambiguity. In contrast, supervised NaUPS methods [10, 11] apply deep learning models like transformers to reconstruct normal maps without explicitly estimating the environment light. The models are trained on a dataset containing images of diverse objects captured under various lighting conditions, including directional, point, and environment light. Compared to previous work, the proposed Spin-UP distinguishes itself in three key aspects: 1) it features a novel setup explicitly designed to model correlations among observed images to mitigate the ill-posedness of NaUPS, 2) leveraging this unique setup, a novel light initialization method is introduced to mitigate ambiguities, and 3) an advanced light and material model is implemented to address a broader range of scenarios. + +Priors from the Boundaries. The occluding boundaries of an object are considered to reveal adequate information about the object's shape and the scene's light. Given the fact that the projection of the boundaries' normal to xy-plane is perpendicular to the boundaries in orthographic projection, methods are developed to constraint the surface normal estimation during iterative optimization [16] or recover a rough shape to initialize the geometry in multi-view [8] or photometric stereo [7]. Other methods associate the boundaries normal with the reflectance to estimate a rough position of the directional lights [27]. However, none of them derive the environment light from the boundary reflectance. Given the setup in Spin-UP, we can roughly estimate the environment by analyzing occluding boundaries and the corresponding pixel points. This approach provides a reliable initialization for lighting that alleviates ambiguity in NaUPS. + +Inverse rendering in 3D Vision. Neural Radiance Fields (NeRF) [19] implicitly store the scene's shape and reflectance through MLPs optimized by inverse volume rendering. While NeRF can only recover coarse 3D shapes, several subsequent works [3, 25, 26, 29, 31, 33] have been proposed to combine the surface rendering and volume rendering techniques, recovering fine shapes under varying viewpoints but static environment light. In contrast, viewpoints in Spin-UP are relatively static to the objects. While most neural field methods aim to recover the whole 3D geometries, Spin-UP only recovers the object's surface. + +# 3. Proposed Method + +In Sec. 3.1, we explain the Spin-UP's setup and how it reduces the unknowns. In Sec. 3.2, we introduce the light prior that alleviates ambiguities in NaUPS, including details of the light initialization method based on that prior. In Sec. 3.3, we describe the implementation details of the + +![](images/7a6c86879d55ac5889e65e52e95fbdfb6631fc1127d0315e5d44db26fe7970a5.jpg) +Figure 1. The proposed image capturing setup. Left: an illustration of image-capturing equipment consisting of a rotatable platform, a camera, and the target object. We spin the platform in $360^{\circ}$ and capture images of the object. The object and camera rotate together with the platform. Right-top: Four observed images at different positions. Right-bottom: Ground truth environment light. Dashed color boxes indicate the corresponding camera views. + +proposed Spin-UP framework and losses. In Sec. 3.4, we demonstrate two proposed training strategies. + +# 3.1. Spin Light Setup + +As shown in Fig. 1, we capture a sequence of images $\pmb{I} \triangleq \{I_j | j \in [1, \dots, N_I]\}$ for an object by rotating it together with a linear perspective camera in $360^\circ$ on a rotatable platform. Since the relative positions and orientations between the camera and the object are fixed during rotation, each observed image is aligned with the rotated environment light $L(R_j \cdot \omega)$ , where $\omega \in \mathbb{R}^3$ indicates the incident light's direction, $R_j = R(\theta_j)$ is the 1-DoF [5] rotation matrix representing rotation about the vertical axis, $\theta_j$ is the rotation angle, $\theta_1 = 0$ . As we conduct $360^\circ$ rotation and assume a constant velocity (despite not strictly required in practice), $R_j$ can be initialized given $\theta_j = 2\pi (j - 1) / N_I$ . Given a sequence of images $I$ and the initialized $R$ , Spin-UP iteratively optimizes the normal map $N$ , the environment light $L$ , isotropic BRDF map $M$ , and rotation angle $R$ by solving + +$$ +\underset {\boldsymbol {L}, \boldsymbol {M}, \boldsymbol {N}, \boldsymbol {R}} {\arg \min } \sum_ {i = 1} ^ {N _ {P}} \sum_ {j = 1} ^ {N _ {I}} \mathcal {E} \left(\boldsymbol {m} _ {i j}, \hat {\boldsymbol {m}} _ {i j}\right), \tag {1} +$$ + +where $N_P$ is the number of sampled points on the surface, $\pmb{m}_{ij}$ and $\hat{\pmb{m}}_{ij}$ indicate the ground truth and estimation of point $i$ 's color in image $I_j$ , respectively. $\mathcal{E}(\cdot ,\cdot)$ is loss function between $\pmb{m}_{ij}$ and $\hat{\pmb{m}}_{ij}$ (i.e., mean absolute error). We adopt the rendering equation to calculate the color $\hat{\pmb{m}}^2$ + +$$ +\begin{array}{l} \hat {\boldsymbol {m}} = \int_ {\Omega} s \boldsymbol {L} (\boldsymbol {\omega}) \rho (\boldsymbol {\omega} \cdot \boldsymbol {n}) \mathrm {d} \boldsymbol {\omega}, \\ = \int_ {\Omega} s \boldsymbol {L} (\boldsymbol {\omega}) \left(\rho^ {s} + \rho^ {d}\right) (\boldsymbol {\omega} \cdot \boldsymbol {n}) \mathrm {d} \boldsymbol {\omega}. \end{array} \tag {2} +$$ + +Table 1. A comparison of type, unknowns' number (number), and representation capacity (rep. capacity) of light model among Spin-UP and representative unsupervised NaUPS methods. The unknown number is calculated on 50 images $(512 \times 512)$ . 'freq.' represents frequency. + +
QL15 [21]HY19 [7]GM21 [6]Spin-UP
typeSV-SHGlobal SHEqv-DirSG
number1.5K4501.4M434
rep. capacitylow-freq.low-freq.low-freq.high-freq.
+ +![](images/1fabe228253706e1c6b33412be24413c0e6c3b6e2f9914976c9579624a35957d.jpg) +Figure 2. The proposed light initialization method in Spin-UP. We crop the boundary pixels $m_{b}$ and normal $\pmb{n}_{b}$ from input images. Then, we remap them on the sphere and rotate them with their corresponding rotations $\pmb{R}$ . Based on a light probe composed of gray-scale boundary pixels, we optimize the SG light model to obtain the environment light. + +where $\Omega$ represents the upper hemisphere centered at the normal vector $\pmb{n}$ . $s$ is the first shadow. $\rho^s$ and $\rho^d$ indicate the specular and diffuse reflectance, respectively. The ambiguities between the light $L$ and reflectance of the object $\pmb{M}$ are often disregarded [13, 16]. + +Unkowns reduction. The proposed spin light setup reduces the unknowns of the light representation $L$ by exploiting correlations between different images. Unlike premodel the light for ionization in the nucleus is modeled using the method shown in the setup, we can exploit from the object's boundary to light initialization. The idea is motivated by the observation that the light map has no effect on the image. We consider the images into the environment light (see Fig. 2). For an object with a light boundary, the normal of those boundaries can roughly derive a light map indicating the light sources' positions at the object. We then use the recently measured light map at $N_{1}$ to calculate the ionized and ground state image. As such, the unknowns consist of the environment light model's parameters and the number of rotational angles that are quantitatively equal to $N_{I}$ . The total unknown amount is reduced compared to other methods (Table 1), which helps mitigate the ill-posedness and facilitates solving NaUPS with advanced light and reflectance models in an unsupervised manner. + +# 3.2. Light Prior from Boundaries + +Based on the spin light setup, we can exploit priors from the object boundary for light initialization to alleviate the ambiguity. The idea is motivated by the observation that the pixel value $m_{b}$ at an object's boundary provides insights into the environment light (see Fig. 2). For an object with occluding boundaries, the normal of those boundaries $\mathbf{n}_b$ can be pre-computed [13, 16]. By bonding $m_{b}, n_{b}$ , and $R$ , we can + +![](images/72a22c394c32f9bb276f419d5e469fcd4fd938f9419f85a7b47b443207ab6f8c.jpg) +(a) +Figure 3. An illustration of mismatched light source positions. Rows from top to bottom: an illustration of reflection on materials with different roughness; the initial environment light before applying any filters given objects' boundary pixels; the ground truth environment light. Objects are (a) the diffuse-dominant sphere, (b) the diffuse and specular mixture sphere, and (c) the specular dominant sphere. The yellow and red lines in rows 2 and 3 indicate a rough position of the light sources. + +![](images/51ec9e0fb3fe2aa89b8d65e38bd4938ef8350af1e91c95754a18fef0eabc2d1f.jpg) +(b) + +![](images/910595d469e5d2077ddfaad19583c6308d9eacfb9f341ef3795235e7ea080289.jpg) +(c) + +roughly derive a light map indicating the light sources' positions and intensities, where $m_b$ directly represent the light intensity $L(\omega_b)$ at $\boldsymbol{\omega}_b = \boldsymbol{R} \cdot \boldsymbol{n}_b$ . However, the derived light map for objects with different materials may contain mismatched light source positions and chromatic bias, leading to inaccurate light initialization. + +The mismatched light source positions are caused by the specular component $m_b^s$ in $m_b$ . When $m_b^s$ dominates, approximating $L(\omega_b)$ by $m_b$ becomes a biased estimation as $m_b^s$ is a reflection of lights in different directions than $\omega_b$ (Fig. 3). By contrast, the approximation is more reasonable when the diffuse component $(m_b^d)$ dominates since $m_b^d = \int_{\Omega} L(\omega) \rho^d (\omega \cdot \omega_b) \mathrm{d}\omega$ indicates that $L(\omega_b)$ contributes most to the actual pixel value, making it less biased to use $m_b^d$ to represent $L(\omega_b)$ . Therefore, to facilitate a less biased estimation of environment light for initialization, a diffuse filter $\mathcal{F}^d(.)$ is necessary on $m_b^d$ , alleviating the mismatched light source positions issue. Similarly, a chromatic filter $\mathcal{F}^c(.)$ is also required to reduce the chromatic bias caused by the spatially varying material at boundaries. The filtered pixel value $\hat{m}_b^d = \mathcal{F}^c(\mathcal{F}^d(m_b))$ are the basis for our light initialization method. + +Light initialization method. The procedure of light initialization method is summarized in Algorithm 1. This method aims to derive an initial environment light model with parameter $\Theta$ . Specifically, we use $N_{L} = 64$ spherical Gaussian (SG) bases [28] as the light model, where $\pmb{L}(\pmb{\omega}|\pmb{\xi}_t,\lambda_t,\pmb{\mu}_t) = \sum_{t=1}^{N_L} G(\pmb{\omega};\pmb{\xi}_t,\lambda_t,\pmb{\mu}_t)$ . $\pmb{\xi}_t$ , $\lambda_t$ , and $\pmb{\mu}_t$ stands for Gaussian lobes' direction, sharpness, and amplitude, respectively3. Inspired by [23] indicating that diffuse reflectance can be approximated by the low-frequency reflectance, we design $\mathcal{F}^d(.)$ as a combination of a threshold filter $\mathcal{F}_{TH}^d(.)$ that removes high-intensity reflectance (top + +$20\%$ bright) based on boundary points' intensity profile [23] and a low-pass filter (i.e., 3-order spherical harmonics filter4) noted as $\mathcal{F}_{SH}^{d}$ [22, 23]. While $\mathcal{F}_{TH}^{d}(.)$ reduces the bias by removing the brightest parts that are usually aligned with specular reflectance in observed images. $\mathcal{F}_{SH}^{d}(.)$ helps extract the low-frequency reflectance. For $\mathcal{F}^c(.)$ , we design it as a converter transferring pixel values into gray-scale5, mitigating biases from spatially varying material. + +# Algorithm 1 Light Initialization Method + +Input: pre-computed boundary normal $\mathbf{n}_b$ , initial relative rotation matrices $\{\pmb{R}_1\ldots ,\pmb{R}_{N_I}\}$ , boundary pixels $\{m_{b1},\dots,m_{bN_I}\}$ , diffuse filters $\mathcal{F}_{TH}^{d}(\cdot)$ and $\mathcal{F}_{SH}^{d}(\cdot)$ , chromatic filter $\mathcal{F}^c (\cdot)$ , fitting epochs $N$ , environment light with parameters $L(|\Theta\rangle)$ , learning rate $\eta$ . + +Output: an initial environment light model $L(|\Theta^{\prime})$ + +$$ +\mathbf {f o r} j = 1, \dots , N _ {I} \mathbf {d o} +$$ + +$$ +\boldsymbol {\omega} _ {b j} = \boldsymbol {R} _ {j} \cdot \boldsymbol {n} _ {b} +$$ + +$$ +\begin{array}{l} \hat {m} _ {b} ^ {d} = \mathcal {F} ^ {c} \left(\mathcal {F} _ {S H} ^ {d} \left(\mathcal {F} _ {T H} ^ {d} (m _ {b}))\right)\right) \\ \mathbf {f o r} e = 1, \dots , N \mathbf {d o} \\ J = \sum (\boldsymbol {L} (\omega_ {b} | \Theta) - \hat {m} _ {b} ^ {d}) ^ {2} \\ \Theta \leftarrow \Theta - \eta \partial J / \partial \Theta \\ \end{array} +$$ + +$$ +\Theta^ {\prime} = \Theta +$$ + +# 3.3. Framework of Spin-UP + +With reliable initial SG lights and rotation matrices $\mathbf{R}$ , we develop Spin-UP based on neural inverse rendering [3, 13, 16, 31] given the rendering equation in Eq. (2). + +Shape model. We use the neural depth field to represent the 3D surface. A multi-layer perceptron (MLP) predicts the depth value given the image coordinates. To compute normal given the depth map, we extend the normal fitting method described in [16] to the perspective projection6. + +Material model. We represent the spatially varying and isotropic reflectance as a modified Disney Model [31]. The diffuse albedo $\rho^d$ is predicted by another MLP with a similar structure given the image coordinate. The spatially varying specular reflectance is calculated as a weighted sum of $N_{S} = 12$ SG bases, so $\rho^{s} = \sum_{n = 1}^{N_{S}}c^{n}\mathcal{D}(\pmb {v},\pmb {\omega})\mathcal{F}(\pmb {h},\pmb {\omega})\mathcal{G}(\pmb {n},\pmb {\omega},\pmb {v},\lambda_{n})$ , where $\mathcal{D}$ , $\mathcal{F}$ , and $\mathcal{G}$ accounts for micro-facet's normal distribution, Fresnel effects, and self-occlusion, respectively. $\pmb{v}$ is the view direction. $\pmb{h}$ is the half-vector, calculated by $\pmb {h} = (\pmb {v} + \pmb {\omega}) / \| \pmb {v} + \pmb {\omega}\|$ , $\lambda_{n}$ is the roughness terms initialized as $(0.1 + 0.9(n - 1)) / (N_S - 1)$ and set as learnable parameters, $c^n$ is the weights predicted by the MLP. + +Shadow model. We apply a shadow mask similar in [13] to handle the cast shadow. + +Loss functions. Similar to other inverse rendering-based methods [13, 16], we use the inverse rendering loss + +![](images/80242f5cfc3644696e395af39d8cf3902ba96691ec81ea34c6a9bc2b19a6381a.jpg) +Figure 4. Proposed training strategies. (Top) Interval sampling (IS). The high-resolution images are down-sampled into several low-resolution sub-images by extracting pixels with an interval of $N_B$ , where $N_B = 2$ in this example. (Bottom) Shrinking range computing (SRC). Far points (yellow circles) that are $k$ ( $k = 3$ in this example) point away w.r.t the query position is selected to interpolate the close points (blue circles)'s depth for normal calculation. During optimization, $k$ will be gradually reduced to 1. + +(i.e, Eq. (1)) to train the framework. The three-stage schema [16] is applied, as well as other smoothness terms (total variance regularization [13, 16]) calculate as $\mathrm{TV}(.) = \frac{1}{N_P}\sum_{i = 1}^{N_P}\left|\frac{\partial(.)}{\partial x} +\frac{\partial(.)}{\partial y}\right|$ , where $(x,y)$ is the image coordinates. We implement $\mathrm{TV}(.)$ on the normal map $(N)$ , diffuse albedo map $(A)$ , and the Gaussian bases' weights $(c)$ for the material, and gradually drop it following the three-stage training schema [16]. Similar to [30], the normalized color loss calculated as $\| \operatorname {Nor}(A) - \operatorname {Nor}(I)\|$ is implemented to help Spin-UP learn a better albedo representation, where $\operatorname {Nor}(.)$ is the vector normalization. Following [16], we calculate the boundary loss as the cosine similarity between the pre-computed and estimated boundary normal + +# 3.4. Training Strategies + +Optimizing Spin-UP requires smoothness terms to facilitate convergence and avoid local optima. However, those terms are often implemented on full-resolution images, leading to high computational costs. To reduce those costs, we propose to use a sampling strategy noted as interval sampling (IS). To further improve convergence, we introduce another technique noted as shrinking range computing (SRC). + +Interval sampling (IS). IS samples ray batches from images to reduce the costs. Unlike random ray sampling [19] or patch-based sampling [20], IS preserves the object's shape. The idea is similar to downsampled techniques in [11, 24], but we don't merge the sub-images to full resolution. We experimentally find this strategy important for training on down-sampled sub-images with smoothness terms to avoid local optima (Sec. 5.2). Specifically, + +we divide the image in full resolution into non-overlapping blocks, and each block contains $N_B \times N_B$ pixel points. By extracting pixel points from the same position in each block (e.g., the left-top pixel), we obtain $N_B \times N_B$ sub-images with a down-sampled resolution (See Fig. 4 for illustration). During training, those sub-images are randomly sampled in each epoch, and the smoothness terms are calculated based on the sub-images resolution, which reduces the computational cost and ensures the effectiveness of those terms. + +Shrinking range computing (SRC). Without merging sub-images back to a full-resolution image in IS, there will be an aliasing issue in the inverse rendering process. Such an issue is caused by the fact that the normal calculation in our framework on sub-images requires four adjacent points' depths in sub-images resolution [16], which degrades the precision of normal calculation8. Therefore, SRC is applied for anti-aliasing. It uses points adjacent to the query point (blue circles in Fig. 4) in the full-resolution image coordinates to calculate the normal for each pixel in the sub-images. Such a strategy maintains the precision of normal calculation. However, at the early stage of training, calculating the normal based on the blue circles' depth is vulnerable to perturbation in per-pixel training. Therefore, SRC gradually selects points (yellow circles) from far ( $k = 3$ points away) to close (blue circles) w.r.t query points to interpolate the blue circles' depth, as normal calculation on far points' depth will lead to a more smooth and stable normal map at the early stage, which eventually improves convergence, as validated in Sec. 5.2. + +# 4. Experiments + +We validate the effectiveness of the proposed Spin-UP on synthetic and real-world data. We use mean angle error (MAE) to evaluate the normal map's reconstructed quality and PU-PSNR [1], and PU-SSIM [1] to evaluate the reconstructed environment light. Since no existing datasets follow our spin light setup, we collect the dataset using Blender and our device. + +# 4.1. Evaluation on Synthetic Datasets + +We collect several objects, environment maps, and materials to render the synthetic dataset in Blender by Cycles. Specifically, five shapes from the DiLiGenT-MV dataset [14] (i.e, BUDDHA, BEAR, COW, POT2, and READING) and a generated shape (BALL), five HDR environment maps (i.e, LANDSCAPE, QUARRY, URBAN, ATTIC, STUDIO), two PBR materials (i.e, RUSTY STEEL, LEATHER), and four synthetic materials (i.e, VORONOI DIFF, VORONOI SPEC, + +Table 2. Qualitative comparison results in terms of MAE on shape group (left-top), light group (left-bottom), reflectance group (right-top), and spatially varying material group (right-bottom). Bold numbers indicate the best results in MAE. In light group, {U., A., S., L.} stand for environment map named URBAN, ATTIC, STUDIO, and LANDSCAPE, respectively. In the reflectance group, {D., S.} stand for material named GREEN DIFF and GREEN SPEC, respectively. In spatially varying material group, {D., S.} stand for material named VORONOI DIFF and VORONOI SPEC, respectively. + +
MethodShape GroupReflectance Group
BALLBEARBUDDHAREADINGAVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]41.3253.8867.9054.8554.4957.4537.4365.4858.0454.60
S22 [10]7.3514.0326.3718.7716.6315.5611.8318.9718.3816.19
S23 [11]5.5610.3718.5415.1012.3913.469.7516.2212.6713.03
Spin-UP3.546.3317.307.718.725.837.1113.0910.309.08
MethodLight GroupSpatially Varying Material Group
Cow (U.)Cow (A.)Cow (S.)Cow (L.)AVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]67.6339.2140.2848.4748.8940.9737.4649.2748.9644.17
S22 [10]17.1712.7417.1111.3514.5918.5917.6322.8023.7520.69
S23 [11]11.937.5212.3811.6010.8414.2211.0014.5814.3113.53
Spin-UP5.504.403.334.944.545.586.9712.5411.529.15
+ +GREEN DIFF, GREEN SPEC) are used for evaluation. We devise four groups of data for evaluation: shape group, light group, reflectance group, and spatially varying material group, each containing four scenes. For each scene, 50 observed images with a resolution of $512 \times 512$ are rendered by a perspective camera with the focal of $50\mathrm{mm}$ and a frame size of $36\mathrm{mm} \times 36\mathrm{mm}$ . The camera rotation $\theta$ for consecutive images follows a non-uniform rotation velocity. We compare Spin-UP with three advanced NaUPS methods, including two supervised NaUPS methods (S22 [10] and S23 [11]) and one unsupervised UPS method (HY19 [7])10. + +Normal estimation comparison. According to results in Table 2, Spin-UP presents a superior performance compared to all other NaUPS methods. Specifically, in shape group, the low MAE on BALL, BEAR, BUDDHA, READING in RUSTY STEEL rendered under QUARRY indicate the practicability of Spin-UP to various shapes. In light group, the low-variance of MAE $(0.81^{\circ}$ for Spin-UP vs. $1.94^{\circ}$ for S23 [11]) on COW in LEATHER rendered under QUARRY, URBAN, ATTIC, and STUDIO demonstrates robustness toward different environment lights. In reflectance group, the results on POT2 and READING in GREEN DIFF and GREEN SPEC rendered under LANDSCAPE demonstrate the ability to handle non-Lambertian objects. In spatially varying material group, results on POT2 and READING rendered in VORONOI DIFF or VORONOI SPEC under LANDSCAPE prove adaptability to challenging scenarios. A comparative analysis of the outcomes of the reflectance group and the spatially varying material group in our method reveals that the MAE remains relatively consistent across identical ob + +![](images/fee7cb9086f51e186505047276097eae38bf8b80f9e501af9dec43804ee0f3eb.jpg) +Figure 5. The visual quality comparison of light between the estimated one by Spin-UP (columns 2-5) and the ground truth (column 1) on the four groups, i.e., shape (row 1), reflectance (row 2), spatially varying material (row 3), and light group (row 4-5). The intensity of the estimated light maps is scaled for visualization. + +jects with different materials, underscoring the robustness of Spin-UP in handling diverse materials. Also, we find that Spin-UP sometimes performs better on specular objects than on diffuse objects (i.e., READING). We attribute this to the high-frequency details in specular reflectance that may be useful for shape-light reconstruction. + +Light estimation comparison. Fig. 5 provides a qualitative comparison between the estimated environment light and the ground truth on four groups. We can observe that the learned light map reflects the position of the light source, especially in Cow (S.) given such a challenging setup without any prior information about the object material or shape. It also reconstructs a reasonable light map for objects with diffuse reflectance, such as POT2 (D.) and READING (D.), further highlighting the effectiveness of the proposed light initialization. However, it should be noted that the estimated environment light is influenced by the object material, par + +![](images/87faaf44c16a4cf3d57ebca1ed4da6653eb643bbbf160e8ff68aabe0138fffb5.jpg) +Capture System + +![](images/b2e98dfb957480b582514429a7108b5dab6ab883cb9cc325dcb43d895fa08b3b.jpg) +Captured Images and Light References + +![](images/831702f2c33bb20dc3eb06dd81f3b34990399e21d221c99828bf021eb1ef0a3d.jpg) +Figure 6. Illustration of the device for real data collection. Please refer to the supplementary material for more details. Left: the capture system contains a camera, a spin platform, and an object. Right: Captured images and paired mirror balls (as light reference) of two objects in the indoor and outdoor scenes, respectively. +Figure 7. Qualitative comparison for the estimated normal map and environment light on SOLDIER and PLAYER capturing under outdoor (columns 1-6) and indoor (columns 7-12) between ours (column 3, 9), S23 [11] (column 5, 11), and S22 [10] (column 6, 12). We also show the reference sphere and reference environment light (columns 2, 7), and estimated light (columns 4, 10). + +ticularly when handling objects with a nearly uniform base color (e.g., reflectance group) or spatially varying material, which may generate unpleasant artifacts (e.g., inconsistent color in estimated environment light of READING (D.) in the spatially varying material group). Those artifacts are hard to eliminate without priors. + +# 4.2. Evaluation on Real-world Datasets + +We set up our spin light capture system to collect real data under indoor and outdoor scenes, as shown in Fig. 6. After preprocessing, we end up with 50 images for each object, with a $540 \times 540$ resolution. Here, we showcase the normal estimation results on two objects (i.e., SOLDIER, and PLAYER) under indoor and outdoor environment lights in Fig. 7, compared with S23 [11], S22 [10]. We do not show HY19 [7]'s result as it failed on the captured data. + +Normal estimation comparison. According to the Fig. 7, Spin-UP has competitive performance compared to the state-of-the-art supervised method [11]. In some scenar + +Table 3. Ablation studies on Spin-UP's alternatives regarding average PU-PSNR [1] and PU-SSIM [1] on synthetic dataset. 'Fib.' and 'Rand.' represent the Fibonacci and random initialization method, respectively. Bold number indicates the best results. + +
w Rand.w Fib.Spin-UP
PU-PSNR [1]↑16.8618.9822.06
PU-SSIM [1]↑0.450.520.60
+ +ios, we recover more reasonable results regarding the overall normal distribution than the reference sphere, particularly for SOLDIER indoor and PLAYER indoor. Spin-UP can effectively capture high-frequency details such as wrinkles on clothes in PLAYER and SOLDIER. By contrast, S23 [11] may contain artifacts (i.e., an incorrect normal map distribution) even though they have more details than ours, and S22 [10] generates over-smooth results. By comparing indoor and outdoor results, we observe that the performance of S23 [11] degrades significantly in indoor scenarios, which may be attributed to the data bias and low pixel variance, while our method is not greatly affected. + +# 5. Ablation Study + +# 5.1. Light Initialization Validation + +To comprehensively validate the effectiveness of our light initialization method, we conduct experiments in two aspects: a comparison of different light initialization methods and the effectiveness of the filters. + +Comparison on light initialization methods. We compare our light initialization method with two widely used SG light initialization methods, i.e., the random initialization noted as 'w Rand.' and Fibonacci lattice [31] noted as 'w Fib.' A quantitative comparison of reconstructed normal and light maps is shown in Table 3 and Table 4. Compared with 'w Rand,' the improvement in average $(1.75^{\circ}$ reduction in MAE on normal estimation and $5.20 / 0.15$ increase in PU-PSNR / PU-SSIM on light estimation, respectively) indicates our method's adaptability. Compared with 'w Fib,' we observe an obvious advantage in the shape group $(0.61^{\circ}$ reduction in MAE), while a smaller advantage in the spatially varying material group $(0.19^{\circ}$ reduction in MAE). This is because the material and shape will affect the initial environment light's quality. While the estimated environment light is most accurate on smooth geometry with simple material, the quality will degrade on complex geometry and spatially varying material. + +Comparison on the designed filters. We compare Spin-UP with three alternatives (i.e, $w / o \mathcal{F}^c$ , $w / o \mathcal{F}_{SH}^d$ , and $w / o \mathcal{F}_{TH}^d$ ). The results in Table 4 demonstrate the effectiveness of those filters. Specifically, dropping $\mathcal{F}_{TH}^d$ will lead to mismatching light source position in the initialized environment light introduced by the specular reflectance, which eventually affects the accuracy of the estimated normal; dropping $\mathcal{F}_{SH}^d$ will harm the performance, especially + +Table 4. Ablation studies on Spin-UP's alternatives regarding average MAE on four groups (shape, light, reflectance, and spatially varying material group). 'Fib.', 'Rand.', 'Intv.', and 'Shrk.' represent the Fibonacci initialization method, random initialization, interval sampling, and shrinking range computing, respectively. Bold number indicates the best results in MAE. + +
ShapeLightRef.SV.AVG
w Rand.12.026.449.7910.289.60
w Fib.9.335.3410.209.348.55
w/o Intv.8.875.029.8310.128.37
w/o Shrk.10.104.9210.1210.438.81
w/o Fc9.444.619.249.408.17
w/o FSh9.758.298.9315.7310.41
w/o FTh9.305.049.1812.498.82
Spin-UP8.724.549.089.157.85
S23 [11]†12.428.5612.5212.3311.46
Spin-UP†11.629.2511.079.079.48
+ +$\dagger$ Method with $\dagger$ is tested on dataset with point light $^+$ environment light Sec. 5.3. + +in the spatially varying material group $(6.58^{\circ}$ increase in MAE) since $\mathcal{F}_{SH}^{d}$ is essential in extracting low-frequency reflectance to initialize the environment light; dropping $\mathcal{F}^c$ will increase MAE in average $(0.32^{\circ})$ , illustrating the necessity of reducing chromatic bias. + +# 5.2. Training Strategies Validation + +The interval sampling will facilitate the training of Spin-UP in two ways. First, the training time is two times shorter (25 min per object on average vs. 60 min on average, depending on the image's valid points for the object), and the GPU memory occupation is five times smaller (around 5 GB vs. 25 GB during training) than directly training on full-image resolution. Second, comparing Spin-UP with 'w/o Intv.', which applies a random sampling strategy and calculates the smoothness terms on patches (3 × 3 pixels), we find that the performance drops $0.52^{\circ}$ on average, and most $(0.97^{\circ})$ on the spatially varying material group. This is because the patch-based smoothness may not work uniformly on different parts of the object, diminishing the effectiveness of smoothness terms, especially on objects in spatially varying material with abrupt texture changes. The shrinking range computing helps avoid local optima when training Spin-UP on down-sampled images while still using full-resolution image coordinates for normal calculation. We compared Spin-UP with the alternative 'w/o Shrk.', which does not implement this strategy. The average MAE on normal estimation for four groups increases $0.96^{\circ}$ , highlighting the importance of this strategy. + +# 5.3. Additional Validation on Point Light Source + +To ensure a more fair comparison with the state-of-the-art supervised methods (S23 [11]), we add a dominant point light to the environment light in synthetic and real-world dataset11. According to Table 4, the proposed Spin-UP has a lower MAE on estimated normal maps than S23 [11] on + +![](images/27e91bf9217fa5337d58e38c26d9e5a3c049700841666a4eb6f85525c8307ae1.jpg) +Point Light + Environment Light +(a) + +![](images/9054fcb82d0f83787934bf4dd22989dabab545ea6d4cceca298c94390f3ba2b1.jpg) + +![](images/a25ca09de8da3a786682a755eaa268c8af6f4adc67efeced6763ba73de67e5a3.jpg) +(b) + +![](images/4d5b24164b0537eb879a4a69607f720392cb70d32e0c09a96f3973a9377300ba.jpg) +Figure 8. (a) Illustration of new light setup. (b) Qualitative comparison on SOLDIER between our method and S23 [11] with dominant point light. + +the synthetic dataset (9.48° ours v.s. 11.46° S23 [11]). As shown in Fig. 8, we have a visually comparable result on the real-world dataset given far-field point light (2m) and a better result given near-field point light (0.4m), validating the adaptability of Spin-UP on unseen light sources. + +# 6. Conclusion + +This paper proposes Spin-UP to address NaUPS in an unsupervised manner. Thanks to our setup to mitigate the ill-posedness, the light initialization method to alleviate the ambiguities of NaUPS, and the proposed training strategies to facilitate fast convergence, Spin-UP can recover surfaces with isotropic reflectance under various lights. Experiments in synthetic and real-world datasets have shown that Spin-UP is robust to various shapes, lights, and reflectances. + +Limitations and future work. Although Spin-UP is efficient and robust in solving NaUPS, it has several limitations: 1) Spin-UP assumes infinitely far light sources, which omit the spatially varying lighting; 2) the materials' base color will bias the estimated environment light; 3) Spin-UP assumes objects to have isotropic reflectance, ignoring inter-reflections and anisotropic features, meaning that it cannot perform well on objects with anisotropic reflectance, such as aluminum, or strong inter-reflections, such as a glass bowl; 4) Spin-UP doesn't compute the shadow iteratively, which may result in artifacts on objects with complicated shapes. Overcoming the above limitations will be regarded as our future work. Besides, the rotation axis of our device does not align with the object's center due to the consideration of structural stability, which may introduce bias from the spatially varying light in observed images. Redesigning the image capture device is also one of the future works. At last, we find it interesting to improve the setup by relieving the requirement for single-axis $360^{\circ}$ rotation to free rotations for easier implementation on portable devices. + +Acknowledgments. This work is supported by the National Natural Science Foundation of China under Grant No. 62136001, 62088102, Rapid-Rich Object Search (ROSE) Lab, Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, and the State Key Lab of Brain-Machine Intelligence, Zhejiang University, Hangzhou, China. + +# References + +[1] Maryam Azimi et al. PU21: A novel perceptually uniform encoding for adapting existing quality metrics for HDR. In Picture Coding Symposium (PCS), 2021. 5, 7 +[2] Ronen Basri, David Jacobs, and Ira Kemelmacher. Photometric stereo with general, unknown lighting. International Journal of Computer Vision (IJCV), 2007. 2 +[3] Mark Boss, Raphael Braun, Varun Jampani, Jonathan T. Barron, Ce Liu, and Hendrik P.A. Lensch. 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International Conference on Computational Photography (ICCP), 2018. 8 +[18] Robert Maier, Kihwan Kim, Daniel Cremers, Jan Kautz, and Matthias Nießner. Intrinsic3D: High-quality 3D reconstruction by joint appearance and geometry optimization with spatially-varying lighting. In Proc. International Conference on Computer Vision (ICCV), 2017. 2 +[19] Ben Mildenhall, Pratul P Srinivasan, Matthew Tancik, Jonathan T Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing scenes as neural radiance fields for view synthesis. In Proc. European Conference on Computer Vision (ECCV), 2020. 2, 5 +[20] Michael Niemeyer, Jonathan T Barron, Ben Mildenhall, Mehdi SM Sajjadi, Andreas Geiger, and Noha Radwan. Reg-NeRf: Regularizing neural radiance fields for view synthesis from sparse inputs. In Proc. Computer Vision and Pattern Recognition (CVPR), 2022. 5 +[21] Yvain Queau, François Lauze, and Jean-Denis Durou. A $\mathbf{L}^{1}$ -TV algorithm for robust perspective photometric stereo with spatially-varying lightings. In International Conference on Scale Space and Variational Methods in Computer Vision, 2015. 1, 2, 3 +[22] Robert T Seeley. Spherical harmonics. The American Mathematical Monthly, 1966. 4 +[23] Boxin Shi, Ping Tan, Yasuyuki Matsushita, and Katsushi Ikeuchi. Bi-polynomial modeling of low-frequency reflectances. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 2013. 4 +[24] Wenzhe Shi, Jose Caballero, Ferenc Huszár, Johannes Totz, Andrew P Aitken, Rob Bishop, Daniel Rueckert, and Zehan Wang. Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network. In Proc. Computer Vision and Pattern Recognition (CVPR), 2016. 5 +[25] Pratul P. Srinivasan, Boyang Deng, Xiuming Zhang, Matthew Tancik, Ben Mildenhall, and Jonathan T. Barron. NeRV: Neural reflectance and visibility fields for relighting and view synthesis. In Proc. Computer Vision and Pattern Recognition (CVPR), 2021. 2 +[26] Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T Barron, and Pratul P Srinivasan. Ref-NeRF: Structured view-dependent appearance for neural radiance fields. In Proc. Computer Vision and Pattern Recognition (CVPR), 2021. 2 +[27] George Vogiatzis, Carlos Hernandez, and Roberto Cipolla. Reconstruction in the round using photometric normals and silhouettes. In Proc. Computer Vision and Pattern Recognition (CVPR), 2006. 2 +[28] Jiaping Wang, Peiran Ren, Minmin Gong, John Snyder, and Baining Guo. All-frequency rendering of dynamic, spatially-varying reflectance. In ACM SIGGRAPH Asia, 2009. 4 + +[29] Peng Wang, Lingjie Liu, Yuan Liu, Christian Theobalt, Taku Komura, and Wenping Wang. NeuS: Learning neural implicit surfaces by volume rendering for multi-view reconstruction. In Proc. Conference on Neural Information Processing Systems (NeurIPS), 2021. 2 +[30] Weicai Ye, Shuo Chen, Chong Bao, Hujun Bao, Marc Pollefeys, Zhaopeng Cui, and Guofeng Zhang. IntrinsicNeRF: Learning intrinsic neural radiance fields for editable novel view synthesis. Proc. International Conference on Computer Vision (ICCV), 2023. 5 +[31] Kai Zhang, Fujun Luan, Qianqian Wang, Kavita Bala, and Noah Snively. PhySG: Inverse rendering with spherical gaussians for physics-based material editing and relighting. In Proc. Computer Vision and Pattern Recognition (CVPR), 2021. 2, 4, 7 +[32] Ruo Zhang, Ping-Sing Tsai, James Edwin Cryer, and Mubarak Shah. Shape-from-shading: a survey. IEEE Transactions on Pattern Analysis and Machine Intelligence (TPAMI), 1999. 2 +[33] Xiuming Zhang, Pratul P Srinivasan, Boyang Deng, Paul Debevec, William T Freeman, and Jonathan T Barron. NeR-Factor: Neural factorization of shape and reflectance under an unknown illumination. 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+ { + "bbox": [ + 143, + 285, + 192, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 285, + 192, + 298 + ], + "spans": [ + { + "bbox": [ + 143, + 285, + 192, + 298 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 310, + 289, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 310, + 289, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 310, + 289, + 622 + ], + "type": "text", + "content": "Natural Light Uncalibrated Photometric Stereo (NaUPS) relieves the strict environment and light assumptions in classical Uncalibrated Photometric Stereo (UPS) methods. However, due to the intrinsic ill-posedness and high-dimensional ambiguities, addressing NaUPS is still an open question. Existing works impose strong assumptions on the environment lights and objects' material, restricting the effectiveness in more general scenarios. Alternatively, some methods leverage supervised learning with intricate models while lacking interpretability, resulting in a biased estimation. In this work, we propose Spin Light Uncalibrated Photometric Stereo (Spin-UP), an unsupervised method to tackle NaUPS in various environment lights and objects. The proposed method uses a novel setup that captures the object's images on a rotatable platform, which mitigates NaUPS's ill-posedness by reducing unknowns and provides reliable priors to alleviate NaUPS's ambiguities. Leveraging neural inverse rendering and the proposed training strategies, Spin-UP recovers surface normals, environment light, and isotropic reflectance under complex natural light with low computational cost. Experiments have shown that Spin-UP outperforms other supervised / unsupervised NaUPS methods and achieves state-of-the-art performance on synthetic and real-world datasets. Codes and data are available at https://github.com/LMozart/CVPR2024-SpinUP." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 633, + 128, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 633, + 128, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 633, + 128, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": "Natural light uncalibrated photometric stereo (NaUPS) [6] is proposed to relieve the dark room and directional light as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 287, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 545, + 383 + ], + "type": "text", + "content": "sumption in classical uncalibrated photometric stereo, aiming to reconstruct the surface normal given images of an object captured at arbitrary environment light. The implications of NaUPS are far-reaching: it makes photometric stereo universal. However, solving NaUPS is still an open question because of the intrinsic ill-posedness introduced by the varying light of each image and the high dimensional ambiguities between the light and objects [6]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 385, + 546, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 546, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 546, + 529 + ], + "type": "text", + "content": "Previous optimization-based methods use the simple light model to represent the varying environment lights and Lambertian reflectance to represent the material [6, 7, 21]. These models help mitigate the ill-posedness and ambiguities to some extent but become ineffective in handling objects with general reflectance (e.g., non-Lambertian reflectance) under complex environment light, leading to unsatisfactory reconstruction outcomes. Besides, since they solely model the varying lights in each image, the unknowns introduced by the light model may increase with the resolution and numbers of the images, restricting their method to low-resolution and insufficient images." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 531, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 547, + 639 + ], + "type": "text", + "content": "Considering the difficulties of explicitly mitigating the ill-posedness and ambiguities, recent advances [10, 11] turn to data-driven methods: they train a deep learning model on large-scale datasets and implicitly exploit deep light features from images to improve performance. However, those methods lack interpretability, making them hard to constrain during training. Consequently, the model may be affected by the data bias and prone to specific types of light sources [10] or reflection variations [11] among images." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Despite a persistent exploration in this research field, a method capable of handling general objects under natural light while free from data bias is still missing. In this paper, we provide a new perspective on solving NaUPS. Specifically, we propose a novel setup that acquires images on a rotatable platform under a static environment light. In such a" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 683, + 194, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 683, + 194, + 693 + ], + "spans": [ + { + "bbox": [ + 58, + 683, + 194, + 693 + ], + "type": "text", + "content": "*Co-first author. ‡Corresponding author." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 58, + 693, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 58, + 693, + 287, + 713 + ], + "type": "text", + "content": "Work completed while interning at the State Key Lab of BrainMachine Intelligence, Zhejiang University." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11905" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "case, the object is illuminated by rotated environment lights. Representing such rotated lights requires fewer parameters than solely modeling varying lights in each image since we model the lights as a uniform environment light varied by low degree-of-freedom (DOF [5]) rotation. This frees us from significantly increasing unknowns when implementing advanced parametric light models (e.g., spherical Gaussian) and reflectance models to handle general scenarios. Additionally, based on such a setup, we further derive a reliable light initialization method by analyzing the pixel value at object's occluding boundary. Such light initialization will help the model converge at the beginning and alleviate the ambiguity between light and objects during training." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 228, + 289, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 228, + 289, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 228, + 289, + 418 + ], + "type": "text", + "content": "With the help of the proposed setup and light initialization method, we develop Spin Light Uncalibrated Photometric Stereo (Spin-UP), addressing NaUPS by optimizing inverse rendering framework in an unsupervised manner. To our best knowledge, this is the first unsupervised method that can handle general objects under natural light. Unlike previous methods, Spin-UP can jointly reconstruct environment light, isotropic reflectance, and complicated shapes through iterative optimization. To reduce the computational cost and improve convergence, we propose two strategies: interval sampling and shrinking range computing, which help optimize Spin-UP in low GPU usage (5 GB) and fast running time (25 mins). Experiments on synthetic and real-world datasets demonstrate our superior performance over previous methods on general scenarios. Overall, our contributions are summarized as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 420, + 287, + 529 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 420, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 287, + 456 + ], + "type": "text", + "content": "1. We design a novel setup for NaUPS, which reduces unknowns of light representation and facilitates solving NaUPS in an unsupervised manner." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 456, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 504 + ], + "type": "text", + "content": "2. We introduce a light prior, which leverages an object's occluding boundaries to initialize a reliable environment light. Based on the setup and light prior, we propose the unsupervised NaUPS method named Spin-UP." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 505, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 505, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 505, + 287, + 529 + ], + "type": "text", + "content": "3. We present two training strategies for fast training and convergence of Spin-UP." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 538, + 134, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 134, + 550 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 134, + 550 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 557, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 665 + ], + "type": "text", + "content": "In this section, we briefly review recent supervised and unsupervised NaUPS methods. We also summarize other techniques that exploit priors from occluding boundaries. Additionally, we discuss recent advances in 3D vision to distinguish Spin-UP from other neural inverse rendering approaches. Given that the focus of this paper is on NaUPS, a group of works reconstructing 3D surfaces from a single image by deep learning under natural light [15] or shading [4, 12, 32] are not included." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Natural Light Uncalibrated Photometric Stereo. Unsupervised NaUPS methods jointly recover the light, reflectance properties, and surface normal. These methods explicitly model the environment light by low-order spheri" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 300 + ], + "type": "text", + "content": "cal harmonics (SH) [2, 21], spatially varying spherical harmonics (SV-SH) [7, 18] or equivalent directional light (Eqv-Dir) [6] to mitigate the ill-posedness, and use integrability constraint [2], shape initialization [7], non-physical lighting regularization [21], or graph-based ambiguity relaxation [6] to alleviate the ambiguity. In contrast, supervised NaUPS methods [10, 11] apply deep learning models like transformers to reconstruct normal maps without explicitly estimating the environment light. The models are trained on a dataset containing images of diverse objects captured under various lighting conditions, including directional, point, and environment light. Compared to previous work, the proposed Spin-UP distinguishes itself in three key aspects: 1) it features a novel setup explicitly designed to model correlations among observed images to mitigate the ill-posedness of NaUPS, 2) leveraging this unique setup, a novel light initialization method is introduced to mitigate ambiguities, and 3) an advanced light and material model is implemented to address a broader range of scenarios." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 300, + 546, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 546, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 546, + 491 + ], + "type": "text", + "content": "Priors from the Boundaries. The occluding boundaries of an object are considered to reveal adequate information about the object's shape and the scene's light. Given the fact that the projection of the boundaries' normal to xy-plane is perpendicular to the boundaries in orthographic projection, methods are developed to constraint the surface normal estimation during iterative optimization [16] or recover a rough shape to initialize the geometry in multi-view [8] or photometric stereo [7]. Other methods associate the boundaries normal with the reflectance to estimate a rough position of the directional lights [27]. However, none of them derive the environment light from the boundary reflectance. Given the setup in Spin-UP, we can roughly estimate the environment by analyzing occluding boundaries and the corresponding pixel points. This approach provides a reliable initialization for lighting that alleviates ambiguity in NaUPS." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 492, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 492, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 492, + 545, + 624 + ], + "type": "text", + "content": "Inverse rendering in 3D Vision. Neural Radiance Fields (NeRF) [19] implicitly store the scene's shape and reflectance through MLPs optimized by inverse volume rendering. While NeRF can only recover coarse 3D shapes, several subsequent works [3, 25, 26, 29, 31, 33] have been proposed to combine the surface rendering and volume rendering techniques, recovering fine shapes under varying viewpoints but static environment light. In contrast, viewpoints in Spin-UP are relatively static to the objects. While most neural field methods aim to recover the whole 3D geometries, Spin-UP only recovers the object's surface." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 632, + 411, + 646 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 632, + 411, + 646 + ], + "spans": [ + { + "bbox": [ + 306, + 632, + 411, + 646 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 545, + 713 + ], + "type": "text", + "content": "In Sec. 3.1, we explain the Spin-UP's setup and how it reduces the unknowns. In Sec. 3.2, we introduce the light prior that alleviates ambiguities in NaUPS, including details of the light initialization method based on that prior. In Sec. 3.3, we describe the implementation details of the" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11906" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 286, + 180 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 286, + 180 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 286, + 180 + ], + "type": "image", + "image_path": "7a6c86879d55ac5889e65e52e95fbdfb6631fc1127d0315e5d44db26fe7970a5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 189, + 289, + 266 + ], + "lines": [ + { + "bbox": [ + 46, + 189, + 289, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 189, + 289, + 266 + ], + "type": "text", + "content": "Figure 1. The proposed image capturing setup. Left: an illustration of image-capturing equipment consisting of a rotatable platform, a camera, and the target object. We spin the platform in " + }, + { + "bbox": [ + 46, + 189, + 289, + 266 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 189, + 289, + 266 + ], + "type": "text", + "content": " and capture images of the object. The object and camera rotate together with the platform. Right-top: Four observed images at different positions. Right-bottom: Ground truth environment light. Dashed color boxes indicate the corresponding camera views." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 278, + 287, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 287, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 287, + 304 + ], + "type": "text", + "content": "proposed Spin-UP framework and losses. In Sec. 3.4, we demonstrate two proposed training strategies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 312, + 149, + 326 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 149, + 326 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 149, + 326 + ], + "type": "text", + "content": "3.1. Spin Light Setup" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": "As shown in Fig. 1, we capture a sequence of images " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\pmb{I} \\triangleq \\{I_j | j \\in [1, \\dots, N_I]\\}" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": " for an object by rotating it together with a linear perspective camera in " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "360^\\circ" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": " on a rotatable platform. 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As we conduct " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "360^\\circ" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": " rotation and assume a constant velocity (despite not strictly required in practice), " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "R_j" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": " can be initialized given " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\theta_j = 2\\pi (j - 1) / N_I" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": ". Given a sequence of images " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": " and the initialized " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": ", Spin-UP iteratively optimizes the normal map " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": ", the environment light " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": ", isotropic BRDF map " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": ", and rotation angle " + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 46, + 331, + 289, + 523 + ], + "type": "text", + "content": " by solving" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 100, + 525, + 287, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 525, + 287, + 559 + ], + "spans": [ + { + "bbox": [ + 100, + 525, + 287, + 559 + ], + "type": "interline_equation", + "content": "\\underset {\\boldsymbol {L}, \\boldsymbol {M}, \\boldsymbol {N}, \\boldsymbol {R}} {\\arg \\min } \\sum_ {i = 1} ^ {N _ {P}} \\sum_ {j = 1} ^ {N _ {I}} \\mathcal {E} \\left(\\boldsymbol {m} _ {i j}, \\hat {\\boldsymbol {m}} _ {i j}\\right), \\tag {1}", + "image_path": "9b4192067150a122553677fc3f4594a21da131609891a422f0e8593e3bb6ee61.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "N_P" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": " is the number of sampled points on the surface, " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\pmb{m}_{ij}" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{m}}_{ij}" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": " indicate the ground truth and estimation of point " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": "'s color in image " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "I_j" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": ", respectively. " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{E}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": " is loss function between " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\pmb{m}_{ij}" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{m}}_{ij}" + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "text", + "content": " (i.e., mean absolute error). We adopt the rendering equation to calculate the color " + }, + { + "bbox": [ + 46, + 560, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{m}}^2" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 86, + 621, + 287, + 674 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 621, + 287, + 674 + ], + "spans": [ + { + "bbox": [ + 86, + 621, + 287, + 674 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {\\boldsymbol {m}} = \\int_ {\\Omega} s \\boldsymbol {L} (\\boldsymbol {\\omega}) \\rho (\\boldsymbol {\\omega} \\cdot \\boldsymbol {n}) \\mathrm {d} \\boldsymbol {\\omega}, \\\\ = \\int_ {\\Omega} s \\boldsymbol {L} (\\boldsymbol {\\omega}) \\left(\\rho^ {s} + \\rho^ {d}\\right) (\\boldsymbol {\\omega} \\cdot \\boldsymbol {n}) \\mathrm {d} \\boldsymbol {\\omega}. \\end{array} \\tag {2}", + "image_path": "59cb3c0fb8779d9a107b5e11cd384d0c9db32b65c800824f8d1ce7849003bdad.jpg" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 130, + 544, + 168 + ], + "blocks": [ + { + "bbox": [ + 305, + 73, + 545, + 129 + ], + "lines": [ + { + "bbox": [ + 305, + 73, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 305, + 73, + 545, + 129 + ], + "type": "text", + "content": "Table 1. A comparison of type, unknowns' number (number), and representation capacity (rep. capacity) of light model among Spin-UP and representative unsupervised NaUPS methods. The unknown number is calculated on 50 images " + }, + { + "bbox": [ + 305, + 73, + 545, + 129 + ], + "type": "inline_equation", + "content": "(512 \\times 512)" + }, + { + "bbox": [ + 305, + 73, + 545, + 129 + ], + "type": "text", + "content": ". 'freq.' represents frequency." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 130, + 544, + 168 + ], + "lines": [ + { + "bbox": [ + 308, + 130, + 544, + 168 + ], + "spans": [ + { + "bbox": [ + 308, + 130, + 544, + 168 + ], + "type": "table", + "html": "
QL15 [21]HY19 [7]GM21 [6]Spin-UP
typeSV-SHGlobal SHEqv-DirSG
number1.5K4501.4M434
rep. capacitylow-freq.low-freq.low-freq.high-freq.
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We crop the boundary pixels " + }, + { + "bbox": [ + 304, + 295, + 546, + 361 + ], + "type": "inline_equation", + "content": "m_{b}" + }, + { + "bbox": [ + 304, + 295, + 546, + 361 + ], + "type": "text", + "content": " and normal " + }, + { + "bbox": [ + 304, + 295, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{n}_{b}" + }, + { + "bbox": [ + 304, + 295, + 546, + 361 + ], + "type": "text", + "content": " from input images. Then, we remap them on the sphere and rotate them with their corresponding rotations " + }, + { + "bbox": [ + 304, + 295, + 546, + 361 + ], + "type": "inline_equation", + "content": "\\pmb{R}" + }, + { + "bbox": [ + 304, + 295, + 546, + 361 + ], + "type": "text", + "content": ". Based on a light probe composed of gray-scale boundary pixels, we optimize the SG light model to obtain the environment light." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\Omega" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " represents the upper hemisphere centered at the normal vector " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{n}" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " is the first shadow. " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\rho^s" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\rho^d" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " indicate the specular and diffuse reflectance, respectively. The ambiguities between the light " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " and reflectance of the object " + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "inline_equation", + "content": "\\pmb{M}" + }, + { + "bbox": [ + 304, + 376, + 545, + 437 + ], + "type": "text", + "content": " are often disregarded [13, 16]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "text", + "content": "Unkowns reduction. The proposed spin light setup reduces the unknowns of the light representation " + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "text", + "content": " by exploiting correlations between different images. Unlike premodel the light for ionization in the nucleus is modeled using the method shown in the setup, we can exploit from the object's boundary to light initialization. The idea is motivated by the observation that the light map has no effect on the image. We consider the images into the environment light (see Fig. 2). For an object with a light boundary, the normal of those boundaries can roughly derive a light map indicating the light sources' positions at the object. We then use the recently measured light map at " + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{1}" + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "text", + "content": " to calculate the ionized and ground state image. As such, the unknowns consist of the environment light model's parameters and the number of rotational angles that are quantitatively equal to " + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "inline_equation", + "content": "N_{I}" + }, + { + "bbox": [ + 299, + 437, + 545, + 604 + ], + "type": "text", + "content": ". The total unknown amount is reduced compared to other methods (Table 1), which helps mitigate the ill-posedness and facilitates solving NaUPS with advanced light and reflectance models in an unsupervised manner." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 611, + 464, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 464, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 464, + 624 + ], + "type": "text", + "content": "3.2. Light Prior from Boundaries" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": "Based on the spin light setup, we can exploit priors from the object boundary for light initialization to alleviate the ambiguity. The idea is motivated by the observation that the pixel value " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "m_{b}" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": " at an object's boundary provides insights into the environment light (see Fig. 2). For an object with occluding boundaries, the normal of those boundaries " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_b" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": " can be pre-computed [13, 16]. By bonding " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "m_{b}, n_{b}" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "inline_equation", + "content": "R" + }, + { + "bbox": [ + 304, + 629, + 545, + 715 + ], + "type": "text", + "content": ", we can" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 683, + 287, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 683, + 287, + 703 + ], + "spans": [ + { + "bbox": [ + 47, + 683, + 287, + 703 + ], + "type": "text", + "content": "1We assume the object's boundary is geometrically smooth (occluding boundary)." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 703, + 195, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 195, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 195, + 713 + ], + "type": "text", + "content": "2The subscripts are omitted for simplicity." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11907" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 74, + 127, + 171 + ], + "blocks": [ + { + "bbox": [ + 69, + 74, + 127, + 171 + ], + "lines": [ + { + "bbox": [ + 69, + 74, + 127, + 171 + ], + "spans": [ + { + "bbox": [ + 69, + 74, + 127, + 171 + ], + "type": "image", + "image_path": "72a22c394c32f9bb276f419d5e469fcd4fd938f9419f85a7b47b443207ab6f8c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 94, + 171, + 103, + 178 + ], + "lines": [ + { + "bbox": [ + 94, + 171, + 103, + 178 + ], + "spans": [ + { + "bbox": [ + 94, + 171, + 103, + 178 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 190, + 287, + 278 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 278 + ], + "type": "text", + "content": "Figure 3. An illustration of mismatched light source positions. Rows from top to bottom: an illustration of reflection on materials with different roughness; the initial environment light before applying any filters given objects' boundary pixels; the ground truth environment light. Objects are (a) the diffuse-dominant sphere, (b) the diffuse and specular mixture sphere, and (c) the specular dominant sphere. The yellow and red lines in rows 2 and 3 indicate a rough position of the light sources." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 137, + 70, + 197, + 171 + ], + "blocks": [ + { + "bbox": [ + 137, + 70, + 197, + 171 + ], + "lines": [ + { + "bbox": [ + 137, + 70, + 197, + 171 + ], + "spans": [ + { + "bbox": [ + 137, + 70, + 197, + 171 + ], + "type": "image", + "image_path": "51ec9e0fb3fe2aa89b8d65e38bd4938ef8350af1e91c95754a18fef0eabc2d1f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 162, + 171, + 171, + 179 + ], + "lines": [ + { + "bbox": [ + 162, + 171, + 171, + 179 + ], + "spans": [ + { + "bbox": [ + 162, + 171, + 171, + 179 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 206, + 70, + 266, + 171 + ], + "blocks": [ + { + "bbox": [ + 206, + 70, + 266, + 171 + ], + "lines": [ + { + "bbox": [ + 206, + 70, + 266, + 171 + ], + "spans": [ + { + "bbox": [ + 206, + 70, + 266, + 171 + ], + "type": "image", + "image_path": "910595d469e5d2077ddfaad19583c6308d9eacfb9f341ef3795235e7ea080289.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 231, + 171, + 241, + 178 + ], + "lines": [ + { + "bbox": [ + 231, + 171, + 241, + 178 + ], + "spans": [ + { + "bbox": [ + 231, + 171, + 241, + 178 + ], + "type": "text", + "content": "(c)" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "text", + "content": "roughly derive a light map indicating the light sources' positions and intensities, where " + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "inline_equation", + "content": "m_b" + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "text", + "content": " directly represent the light intensity " + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "inline_equation", + "content": "L(\\omega_b)" + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\omega}_b = \\boldsymbol{R} \\cdot \\boldsymbol{n}_b" + }, + { + "bbox": [ + 46, + 286, + 287, + 357 + ], + "type": "text", + "content": ". However, the derived light map for objects with different materials may contain mismatched light source positions and chromatic bias, leading to inaccurate light initialization." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": "The mismatched light source positions are caused by the specular component " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b^s" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": ". When " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b^s" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " dominates, approximating " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "L(\\omega_b)" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " becomes a biased estimation as " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b^s" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " is a reflection of lights in different directions than " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\omega_b" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " (Fig. 3). By contrast, the approximation is more reasonable when the diffuse component " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "(m_b^d)" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " dominates since " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b^d = \\int_{\\Omega} L(\\omega) \\rho^d (\\omega \\cdot \\omega_b) \\mathrm{d}\\omega" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " indicates that " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "L(\\omega_b)" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " contributes most to the actual pixel value, making it less biased to use " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b^d" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " to represent " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "L(\\omega_b)" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": ". Therefore, to facilitate a less biased estimation of environment light for initialization, a diffuse filter " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^d(.)" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " is necessary on " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "m_b^d" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": ", alleviating the mismatched light source positions issue. Similarly, a chromatic filter " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^c(.)" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " is also required to reduce the chromatic bias caused by the spatially varying material at boundaries. The filtered pixel value " + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "inline_equation", + "content": "\\hat{m}_b^d = \\mathcal{F}^c(\\mathcal{F}^d(m_b))" + }, + { + "bbox": [ + 46, + 358, + 287, + 550 + ], + "type": "text", + "content": " are the basis for our light initialization method." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": "Light initialization method. The procedure of light initialization method is summarized in Algorithm 1. This method aims to derive an initial environment light model with parameter " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": ". Specifically, we use " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "N_{L} = 64" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": " spherical Gaussian (SG) bases [28] as the light model, where " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\pmb{L}(\\pmb{\\omega}|\\pmb{\\xi}_t,\\lambda_t,\\pmb{\\mu}_t) = \\sum_{t=1}^{N_L} G(\\pmb{\\omega};\\pmb{\\xi}_t,\\lambda_t,\\pmb{\\mu}_t)" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\pmb{\\xi}_t" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\lambda_t" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_t" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": " stands for Gaussian lobes' direction, sharpness, and amplitude, respectively3. Inspired by [23] indicating that diffuse reflectance can be approximated by the low-frequency reflectance, we design " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^d(.)" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": " as a combination of a threshold filter " + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{TH}^d(.)" + }, + { + "bbox": [ + 46, + 551, + 287, + 684 + ], + "type": "text", + "content": " that removes high-intensity reflectance (top" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " bright) based on boundary points' intensity profile [23] and a low-pass filter (i.e., 3-order spherical harmonics filter4) noted as " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{SH}^{d}" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " [22, 23]. While " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{TH}^{d}(.)" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " reduces the bias by removing the brightest parts that are usually aligned with specular reflectance in observed images. " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{SH}^{d}(.)" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": " helps extract the low-frequency reflectance. For " + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^c(.)" + }, + { + "bbox": [ + 306, + 72, + 545, + 168 + ], + "type": "text", + "content": ", we design it as a converter transferring pixel values into gray-scale5, mitigating biases from spatially varying material." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 173, + 471, + 185 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 173, + 471, + 185 + ], + "spans": [ + { + "bbox": [ + 307, + 173, + 471, + 185 + ], + "type": "text", + "content": "Algorithm 1 Light Initialization Method" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": "Input: pre-computed boundary normal " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\mathbf{n}_b" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", initial relative rotation matrices " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\{\\pmb{R}_1\\ldots ,\\pmb{R}_{N_I}\\}" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", boundary pixels " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\{m_{b1},\\dots,m_{bN_I}\\}" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", diffuse filters " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{TH}^{d}(\\cdot)" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{SH}^{d}(\\cdot)" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", chromatic filter " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^c (\\cdot)" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", fitting epochs " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", environment light with parameters " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "L(|\\Theta\\rangle)" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": ", learning rate " + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "inline_equation", + "content": "\\eta" + }, + { + "bbox": [ + 320, + 188, + 545, + 243 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 321, + 243, + 512, + 255 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 243, + 512, + 255 + ], + "spans": [ + { + "bbox": [ + 321, + 243, + 512, + 255 + ], + "type": "text", + "content": "Output: an initial environment light model " + }, + { + "bbox": [ + 321, + 243, + 512, + 255 + ], + "type": "inline_equation", + "content": "L(|\\Theta^{\\prime})" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 255, + 399, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 255, + 399, + 265 + ], + "spans": [ + { + "bbox": [ + 321, + 255, + 399, + 265 + ], + "type": "interline_equation", + "content": "\\mathbf {f o r} j = 1, \\dots , N _ {I} \\mathbf {d o}", + "image_path": "f82bc9490444952fa74472faebdeb7837324d2a9b6a98e2abbf019862bf9b39c.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 335, + 266, + 393, + 277 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 266, + 393, + 277 + ], + "spans": [ + { + "bbox": [ + 335, + 266, + 393, + 277 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\omega} _ {b j} = \\boldsymbol {R} _ {j} \\cdot \\boldsymbol {n} _ {b}", + "image_path": "f7673c2a0d3177966e502a75d12b9a9c16f3921e824b9bfb5a306a86f3730f58.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 322, + 277, + 434, + 323 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 322, + 277, + 434, + 323 + ], + "spans": [ + { + "bbox": [ + 322, + 277, + 434, + 323 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\hat {m} _ {b} ^ {d} = \\mathcal {F} ^ {c} \\left(\\mathcal {F} _ {S H} ^ {d} \\left(\\mathcal {F} _ {T H} ^ {d} (m _ {b}))\\right)\\right) \\\\ \\mathbf {f o r} e = 1, \\dots , N \\mathbf {d o} \\\\ J = \\sum (\\boldsymbol {L} (\\omega_ {b} | \\Theta) - \\hat {m} _ {b} ^ {d}) ^ {2} \\\\ \\Theta \\leftarrow \\Theta - \\eta \\partial J / \\partial \\Theta \\\\ \\end{array}", + "image_path": "74edb983cd6bf747b6b52ba5a170c8f7b85905df2f27962deca04ef097348f18.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 323, + 323, + 352, + 330 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 323, + 352, + 330 + ], + "spans": [ + { + "bbox": [ + 323, + 323, + 352, + 330 + ], + "type": "interline_equation", + "content": "\\Theta^ {\\prime} = \\Theta", + "image_path": "fd0d08fda6ee3e5159a9dbb81bcd3f0e9fec631c86bbb57fe1c580836624f3b3.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 341, + 438, + 354 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 341, + 438, + 354 + ], + "spans": [ + { + "bbox": [ + 306, + 341, + 438, + 354 + ], + "type": "text", + "content": "3.3. Framework of Spin-UP" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 359, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 359, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 305, + 359, + 545, + 395 + ], + "type": "text", + "content": "With reliable initial SG lights and rotation matrices " + }, + { + "bbox": [ + 305, + 359, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathbf{R}" + }, + { + "bbox": [ + 305, + 359, + 545, + 395 + ], + "type": "text", + "content": ", we develop Spin-UP based on neural inverse rendering [3, 13, 16, 31] given the rendering equation in Eq. (2)." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 396, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 396, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 305, + 396, + 545, + 455 + ], + "type": "text", + "content": "Shape model. We use the neural depth field to represent the 3D surface. A multi-layer perceptron (MLP) predicts the depth value given the image coordinates. To compute normal given the depth map, we extend the normal fitting method described in [16] to the perspective projection6." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": "Material model. We represent the spatially varying and isotropic reflectance as a modified Disney Model [31]. The diffuse albedo " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\rho^d" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " is predicted by another MLP with a similar structure given the image coordinate. The spatially varying specular reflectance is calculated as a weighted sum of " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "N_{S} = 12" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " SG bases, so " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\rho^{s} = \\sum_{n = 1}^{N_{S}}c^{n}\\mathcal{D}(\\pmb {v},\\pmb {\\omega})\\mathcal{F}(\\pmb {h},\\pmb {\\omega})\\mathcal{G}(\\pmb {n},\\pmb {\\omega},\\pmb {v},\\lambda_{n})" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " accounts for micro-facet's normal distribution, Fresnel effects, and self-occlusion, respectively. " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\pmb{v}" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " is the view direction. " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\pmb{h}" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " is the half-vector, calculated by " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\pmb {h} = (\\pmb {v} + \\pmb {\\omega}) / \\| \\pmb {v} + \\pmb {\\omega}\\|" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "\\lambda_{n}" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " is the roughness terms initialized as " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "(0.1 + 0.9(n - 1)) / (N_S - 1)" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " and set as learnable parameters, " + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "inline_equation", + "content": "c^n" + }, + { + "bbox": [ + 305, + 455, + 545, + 610 + ], + "type": "text", + "content": " is the weights predicted by the MLP." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 611, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 611, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 305, + 611, + 545, + 633 + ], + "type": "text", + "content": "Shadow model. We apply a shadow mask similar in [13] to handle the cast shadow." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 635, + 545, + 658 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 635, + 545, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 635, + 545, + 658 + ], + "type": "text", + "content": "Loss functions. Similar to other inverse rendering-based methods [13, 16], we use the inverse rendering loss" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 664, + 545, + 685 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 664, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 306, + 664, + 545, + 685 + ], + "type": "text", + "content": "4We implement a Gaussian filter and rescale the pixel value's range to " + }, + { + "bbox": [ + 306, + 664, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{TH}^{d}(m_{b})" + }, + { + "bbox": [ + 306, + 664, + 545, + 685 + ], + "type": "text", + "content": " 's range to suppress ringing effect and negative energy in SH." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 321, + 685, + 537, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 685, + 537, + 693 + ], + "spans": [ + { + "bbox": [ + 321, + 685, + 537, + 693 + ], + "type": "text", + "content": "We use gray-scale value to initialize the RGB value of light model." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 712 + ], + "type": "text", + "content": "6Please refer to the supplementary material for more details about the network structures and modified normal fitting method." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "In practice, we find that initializing Gaussians' parameters by Fibonacci lattice [31] and freezing " + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\lambda_{t}" + }, + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": " gives the best results." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11908" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 0, + 0, + 304, + 213 + ], + "blocks": [ + { + "bbox": [ + 0, + 0, + 304, + 213 + ], + "lines": [ + { + "bbox": [ + 0, + 0, + 304, + 213 + ], + "spans": [ + { + "bbox": [ + 0, + 0, + 304, + 213 + ], + "type": "image", + "image_path": "80242f5cfc3644696e395af39d8cf3902ba96691ec81ea34c6a9bc2b19a6381a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "text", + "content": "Figure 4. Proposed training strategies. (Top) Interval sampling (IS). The high-resolution images are down-sampled into several low-resolution sub-images by extracting pixels with an interval of " + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "inline_equation", + "content": "N_B" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "inline_equation", + "content": "N_B = 2" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "text", + "content": " in this example. (Bottom) Shrinking range computing (SRC). Far points (yellow circles) that are " + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "text", + "content": " in this example) point away w.r.t the query position is selected to interpolate the close points (blue circles)'s depth for normal calculation. During optimization, " + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 220, + 287, + 308 + ], + "type": "text", + "content": " will be gradually reduced to 1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": "(i.e, Eq. (1)) to train the framework. The three-stage schema [16] is applied, as well as other smoothness terms (total variance regularization [13, 16]) calculate as " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathrm{TV}(.) = \\frac{1}{N_P}\\sum_{i = 1}^{N_P}\\left|\\frac{\\partial(.)}{\\partial x} +\\frac{\\partial(.)}{\\partial y}\\right|" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": " is the image coordinates. We implement " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\mathrm{TV}(.)" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": " on the normal map " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "(N)" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": ", diffuse albedo map " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "(A)" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": ", and the Gaussian bases' weights " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "(c)" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": " for the material, and gradually drop it following the three-stage training schema [16]. Similar to [30], the normalized color loss calculated as " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\| \\operatorname {Nor}(A) - \\operatorname {Nor}(I)\\|" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": " is implemented to help Spin-UP learn a better albedo representation, where " + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "inline_equation", + "content": "\\operatorname {Nor}(.)" + }, + { + "bbox": [ + 46, + 316, + 287, + 477 + ], + "type": "text", + "content": " is the vector normalization. Following [16], we calculate the boundary loss as the cosine similarity between the pre-computed and estimated boundary normal" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 486, + 160, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 160, + 498 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 160, + 498 + ], + "type": "text", + "content": "3.4. Training Strategies" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 287, + 589 + ], + "type": "text", + "content": "Optimizing Spin-UP requires smoothness terms to facilitate convergence and avoid local optima. However, those terms are often implemented on full-resolution images, leading to high computational costs. To reduce those costs, we propose to use a sampling strategy noted as interval sampling (IS). To further improve convergence, we introduce another technique noted as shrinking range computing (SRC)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 589, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 589, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 589, + 287, + 685 + ], + "type": "text", + "content": "Interval sampling (IS). IS samples ray batches from images to reduce the costs. Unlike random ray sampling [19] or patch-based sampling [20], IS preserves the object's shape. The idea is similar to downsampled techniques in [11, 24], but we don't merge the sub-images to full resolution. We experimentally find this strategy important for training on down-sampled sub-images with smoothness terms to avoid local optima (Sec. 5.2). Specifically," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "type": "text", + "content": "we divide the image in full resolution into non-overlapping blocks, and each block contains " + }, + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "type": "inline_equation", + "content": "N_B \\times N_B" + }, + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "type": "text", + "content": " pixel points. By extracting pixel points from the same position in each block (e.g., the left-top pixel), we obtain " + }, + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "type": "inline_equation", + "content": "N_B \\times N_B" + }, + { + "bbox": [ + 306, + 72, + 545, + 178 + ], + "type": "text", + "content": " sub-images with a down-sampled resolution (See Fig. 4 for illustration). During training, those sub-images are randomly sampled in each epoch, and the smoothness terms are calculated based on the sub-images resolution, which reduces the computational cost and ensures the effectiveness of those terms." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 180, + 546, + 419 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 180, + 546, + 419 + ], + "spans": [ + { + "bbox": [ + 304, + 180, + 546, + 419 + ], + "type": "text", + "content": "Shrinking range computing (SRC). Without merging sub-images back to a full-resolution image in IS, there will be an aliasing issue in the inverse rendering process. Such an issue is caused by the fact that the normal calculation in our framework on sub-images requires four adjacent points' depths in sub-images resolution [16], which degrades the precision of normal calculation8. Therefore, SRC is applied for anti-aliasing. It uses points adjacent to the query point (blue circles in Fig. 4) in the full-resolution image coordinates to calculate the normal for each pixel in the sub-images. Such a strategy maintains the precision of normal calculation. However, at the early stage of training, calculating the normal based on the blue circles' depth is vulnerable to perturbation in per-pixel training. Therefore, SRC gradually selects points (yellow circles) from far (" + }, + { + "bbox": [ + 304, + 180, + 546, + 419 + ], + "type": "inline_equation", + "content": "k = 3" + }, + { + "bbox": [ + 304, + 180, + 546, + 419 + ], + "type": "text", + "content": " points away) to close (blue circles) w.r.t query points to interpolate the blue circles' depth, as normal calculation on far points' depth will lead to a more smooth and stable normal map at the early stage, which eventually improves convergence, as validated in Sec. 5.2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 434, + 387, + 447 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 434, + 387, + 447 + ], + "spans": [ + { + "bbox": [ + 306, + 434, + 387, + 447 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 454, + 545, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 454, + 545, + 537 + ], + "spans": [ + { + "bbox": [ + 304, + 454, + 545, + 537 + ], + "type": "text", + "content": "We validate the effectiveness of the proposed Spin-UP on synthetic and real-world data. We use mean angle error (MAE) to evaluate the normal map's reconstructed quality and PU-PSNR [1], and PU-SSIM [1] to evaluate the reconstructed environment light. Since no existing datasets follow our spin light setup, we collect the dataset using Blender and our device." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 548, + 484, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 484, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 484, + 560 + ], + "type": "text", + "content": "4.1. Evaluation on Synthetic Datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 567, + 545, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 567, + 545, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 567, + 545, + 662 + ], + "type": "text", + "content": "We collect several objects, environment maps, and materials to render the synthetic dataset in Blender by Cycles. Specifically, five shapes from the DiLiGenT-MV dataset [14] (i.e, BUDDHA, BEAR, COW, POT2, and READING) and a generated shape (BALL), five HDR environment maps (i.e, LANDSCAPE, QUARRY, URBAN, ATTIC, STUDIO), two PBR materials (i.e, RUSTY STEEL, LEATHER), and four synthetic materials (i.e, VORONOI DIFF, VORONOI SPEC," + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 287, + 712 + ], + "type": "text", + "content": "7Please refer to the supplementary material for more details about the setup of hyperparameters." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 673, + 545, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 673, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 305, + 673, + 545, + 712 + ], + "type": "text", + "content": "8 According to normal's definition, the smaller the distance between the adjacent points and the query points (red circle in Fig. 4), the more accurately representing the geometry at query points. Therefore, the blue circles' depths are preferred for normal calculation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11909" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 134, + 547, + 283 + ], + "blocks": [ + { + "bbox": [ + 46, + 70, + 547, + 126 + ], + "lines": [ + { + "bbox": [ + 46, + 70, + 547, + 126 + ], + "spans": [ + { + "bbox": [ + 46, + 70, + 547, + 126 + ], + "type": "text", + "content": "Table 2. Qualitative comparison results in terms of MAE on shape group (left-top), light group (left-bottom), reflectance group (right-top), and spatially varying material group (right-bottom). Bold numbers indicate the best results in MAE. In light group, {U., A., S., L.} stand for environment map named URBAN, ATTIC, STUDIO, and LANDSCAPE, respectively. In the reflectance group, {D., S.} stand for material named GREEN DIFF and GREEN SPEC, respectively. In spatially varying material group, {D., S.} stand for material named VORONOI DIFF and VORONOI SPEC, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 134, + 547, + 283 + ], + "lines": [ + { + "bbox": [ + 49, + 134, + 547, + 283 + ], + "spans": [ + { + "bbox": [ + 49, + 134, + 547, + 283 + ], + "type": "table", + "html": "
MethodShape GroupReflectance Group
BALLBEARBUDDHAREADINGAVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]41.3253.8867.9054.8554.4957.4537.4365.4858.0454.60
S22 [10]7.3514.0326.3718.7716.6315.5611.8318.9718.3816.19
S23 [11]5.5610.3718.5415.1012.3913.469.7516.2212.6713.03
Spin-UP3.546.3317.307.718.725.837.1113.0910.309.08
MethodLight GroupSpatially Varying Material Group
Cow (U.)Cow (A.)Cow (S.)Cow (L.)AVGPOT2 (D.)POT2 (S.)READING (D.)READING (S.)AVG
HY19 [7]67.6339.2140.2848.4748.8940.9737.4649.2748.9644.17
S22 [10]17.1712.7417.1111.3514.5918.5917.6322.8023.7520.69
S23 [11]11.937.5212.3811.6010.8414.2211.0014.5814.3113.53
Spin-UP5.504.403.334.944.545.586.9712.5411.529.15
", + "image_path": "8cdf0ad331600b6053416191c37a61b01670e7c077bc183bce125914a8424e65.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "text", + "content": "GREEN DIFF, GREEN SPEC) are used for evaluation. We devise four groups of data for evaluation: shape group, light group, reflectance group, and spatially varying material group, each containing four scenes. For each scene, 50 observed images with a resolution of " + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "text", + "content": " are rendered by a perspective camera with the focal of " + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "inline_equation", + "content": "50\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "text", + "content": " and a frame size of " + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "inline_equation", + "content": "36\\mathrm{mm} \\times 36\\mathrm{mm}" + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "text", + "content": ". The camera rotation " + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 293, + 287, + 425 + ], + "type": "text", + "content": " for consecutive images follows a non-uniform rotation velocity. We compare Spin-UP with three advanced NaUPS methods, including two supervised NaUPS methods (S22 [10] and S23 [11]) and one unsupervised UPS method (HY19 [7])10." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "type": "text", + "content": "Normal estimation comparison. According to results in Table 2, Spin-UP presents a superior performance compared to all other NaUPS methods. Specifically, in shape group, the low MAE on BALL, BEAR, BUDDHA, READING in RUSTY STEEL rendered under QUARRY indicate the practicability of Spin-UP to various shapes. In light group, the low-variance of MAE " + }, + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "type": "inline_equation", + "content": "(0.81^{\\circ}" + }, + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "type": "text", + "content": " for Spin-UP vs. " + }, + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "type": "inline_equation", + "content": "1.94^{\\circ}" + }, + { + "bbox": [ + 46, + 425, + 289, + 653 + ], + "type": "text", + "content": " for S23 [11]) on COW in LEATHER rendered under QUARRY, URBAN, ATTIC, and STUDIO demonstrates robustness toward different environment lights. In reflectance group, the results on POT2 and READING in GREEN DIFF and GREEN SPEC rendered under LANDSCAPE demonstrate the ability to handle non-Lambertian objects. In spatially varying material group, results on POT2 and READING rendered in VORONOI DIFF or VORONOI SPEC under LANDSCAPE prove adaptability to challenging scenarios. A comparative analysis of the outcomes of the reflectance group and the spatially varying material group in our method reveals that the MAE remains relatively consistent across identical ob" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 307, + 291, + 545, + 432 + ], + "blocks": [ + { + "bbox": [ + 307, + 291, + 545, + 432 + ], + "lines": [ + { + "bbox": [ + 307, + 291, + 545, + 432 + ], + "spans": [ + { + "bbox": [ + 307, + 291, + 545, + 432 + ], + "type": "image", + "image_path": "fee7cb9086f51e186505047276097eae38bf8b80f9e501af9dec43804ee0f3eb.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 438, + 547, + 495 + ], + "lines": [ + { + "bbox": [ + 304, + 438, + 547, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 438, + 547, + 495 + ], + "type": "text", + "content": "Figure 5. The visual quality comparison of light between the estimated one by Spin-UP (columns 2-5) and the ground truth (column 1) on the four groups, i.e., shape (row 1), reflectance (row 2), spatially varying material (row 3), and light group (row 4-5). The intensity of the estimated light maps is scaled for visualization." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 547, + 579 + ], + "type": "text", + "content": "jects with different materials, underscoring the robustness of Spin-UP in handling diverse materials. Also, we find that Spin-UP sometimes performs better on specular objects than on diffuse objects (i.e., READING). We attribute this to the high-frequency details in specular reflectance that may be useful for shape-light reconstruction." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "Light estimation comparison. Fig. 5 provides a qualitative comparison between the estimated environment light and the ground truth on four groups. We can observe that the learned light map reflects the position of the light source, especially in Cow (S.) given such a challenging setup without any prior information about the object material or shape. It also reconstructs a reasonable light map for objects with diffuse reflectance, such as POT2 (D.) and READING (D.), further highlighting the effectiveness of the proposed light initialization. However, it should be noted that the estimated environment light is influenced by the object material, par" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 47, + 663, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 663, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 663, + 287, + 713 + ], + "type": "text", + "content": "The generated pattern for VORONOI DIFF and VORONOI SPEC follow similar setup in CNN-PS [9]. Please refer to the supplementary material for all the qualitative comparison between Spin-UP and other methods on the synthetic and realworld dataset." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11910" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 33, + 71, + 160, + 155 + ], + "blocks": [ + { + "bbox": [ + 33, + 71, + 160, + 155 + ], + "lines": [ + { + "bbox": [ + 33, + 71, + 160, + 155 + ], + "spans": [ + { + "bbox": [ + 33, + 71, + 160, + 155 + ], + "type": "image", + "image_path": "87faaf44c16a4cf3d57ebca1ed4da6653eb643bbbf160e8ff68aabe0138fffb5.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 81, + 157, + 128, + 166 + ], + "lines": [ + { + "bbox": [ + 81, + 157, + 128, + 166 + ], + "spans": [ + { + "bbox": [ + 81, + 157, + 128, + 166 + ], + "type": "text", + "content": "Capture System" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 71, + 287, + 153 + ], + "blocks": [ + { + "bbox": [ + 167, + 71, + 287, + 153 + ], + "lines": [ + { + "bbox": [ + 167, + 71, + 287, + 153 + ], + "spans": [ + { + "bbox": [ + 167, + 71, + 287, + 153 + ], + "type": "image", + "image_path": "b2e98dfb957480b582514429a7108b5dab6ab883cb9cc325dcb43d895fa08b3b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 170, + 157, + 281, + 166 + ], + "lines": [ + { + "bbox": [ + 170, + 157, + 281, + 166 + ], + "spans": [ + { + "bbox": [ + 170, + 157, + 281, + 166 + ], + "type": "text", + "content": "Captured Images and Light References" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 50, + 234, + 287, + 393 + ], + "blocks": [ + { + "bbox": [ + 46, + 175, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 287, + 232 + ], + "type": "text", + "content": "Figure 6. Illustration of the device for real data collection. Please refer to the supplementary material for more details. Left: the capture system contains a camera, a spin platform, and an object. Right: Captured images and paired mirror balls (as light reference) of two objects in the indoor and outdoor scenes, respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 234, + 287, + 393 + ], + "lines": [ + { + "bbox": [ + 50, + 234, + 287, + 393 + ], + "spans": [ + { + "bbox": [ + 50, + 234, + 287, + 393 + ], + "type": "image", + "image_path": "831702f2c33bb20dc3eb06dd81f3b34990399e21d221c99828bf021eb1ef0a3d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 404, + 287, + 471 + ], + "lines": [ + { + "bbox": [ + 46, + 404, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 404, + 287, + 471 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison for the estimated normal map and environment light on SOLDIER and PLAYER capturing under outdoor (columns 1-6) and indoor (columns 7-12) between ours (column 3, 9), S23 [11] (column 5, 11), and S22 [10] (column 6, 12). We also show the reference sphere and reference environment light (columns 2, 7), and estimated light (columns 4, 10)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 552 + ], + "type": "text", + "content": "ticularly when handling objects with a nearly uniform base color (e.g., reflectance group) or spatially varying material, which may generate unpleasant artifacts (e.g., inconsistent color in estimated environment light of READING (D.) in the spatially varying material group). Those artifacts are hard to eliminate without priors." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 561, + 233, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 233, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 233, + 574 + ], + "type": "text", + "content": "4.2. Evaluation on Real-world Datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "type": "text", + "content": "We set up our spin light capture system to collect real data under indoor and outdoor scenes, as shown in Fig. 6. After preprocessing, we end up with 50 images for each object, with a " + }, + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "type": "inline_equation", + "content": "540 \\times 540" + }, + { + "bbox": [ + 46, + 580, + 287, + 676 + ], + "type": "text", + "content": " resolution. Here, we showcase the normal estimation results on two objects (i.e., SOLDIER, and PLAYER) under indoor and outdoor environment lights in Fig. 7, compared with S23 [11], S22 [10]. We do not show HY19 [7]'s result as it failed on the captured data." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Normal estimation comparison. According to the Fig. 7, Spin-UP has competitive performance compared to the state-of-the-art supervised method [11]. In some scenar" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 331, + 120, + 522, + 152 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 115 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 115 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 115 + ], + "type": "text", + "content": "Table 3. Ablation studies on Spin-UP's alternatives regarding average PU-PSNR [1] and PU-SSIM [1] on synthetic dataset. 'Fib.' and 'Rand.' represent the Fibonacci and random initialization method, respectively. Bold number indicates the best results." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 120, + 522, + 152 + ], + "lines": [ + { + "bbox": [ + 331, + 120, + 522, + 152 + ], + "spans": [ + { + "bbox": [ + 331, + 120, + 522, + 152 + ], + "type": "table", + "html": "
w Rand.w Fib.Spin-UP
PU-PSNR [1]↑16.8618.9822.06
PU-SSIM [1]↑0.450.520.60
", + "image_path": "720f10d83a4a6174f44d65b28123bfb78dd0dda24e9aabf649fd2e45d4917be7.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 158, + 547, + 302 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 158, + 547, + 302 + ], + "spans": [ + { + "bbox": [ + 304, + 158, + 547, + 302 + ], + "type": "text", + "content": "ios, we recover more reasonable results regarding the overall normal distribution than the reference sphere, particularly for SOLDIER indoor and PLAYER indoor. Spin-UP can effectively capture high-frequency details such as wrinkles on clothes in PLAYER and SOLDIER. By contrast, S23 [11] may contain artifacts (i.e., an incorrect normal map distribution) even though they have more details than ours, and S22 [10] generates over-smooth results. By comparing indoor and outdoor results, we observe that the performance of S23 [11] degrades significantly in indoor scenarios, which may be attributed to the data bias and low pixel variance, while our method is not greatly affected." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 314, + 399, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 399, + 328 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 399, + 328 + ], + "type": "text", + "content": "5. Ablation Study" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 334, + 468, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 468, + 347 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 468, + 347 + ], + "type": "text", + "content": "5.1. Light Initialization Validation" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 354, + 546, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 546, + 400 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 546, + 400 + ], + "type": "text", + "content": "To comprehensively validate the effectiveness of our light initialization method, we conduct experiments in two aspects: a comparison of different light initialization methods and the effectiveness of the filters." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "text", + "content": "Comparison on light initialization methods. We compare our light initialization method with two widely used SG light initialization methods, i.e., the random initialization noted as 'w Rand.' and Fibonacci lattice [31] noted as 'w Fib.' A quantitative comparison of reconstructed normal and light maps is shown in Table 3 and Table 4. Compared with 'w Rand,' the improvement in average " + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "inline_equation", + "content": "(1.75^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "text", + "content": " reduction in MAE on normal estimation and " + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "inline_equation", + "content": "5.20 / 0.15" + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "text", + "content": " increase in PU-PSNR / PU-SSIM on light estimation, respectively) indicates our method's adaptability. Compared with 'w Fib,' we observe an obvious advantage in the shape group " + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "inline_equation", + "content": "(0.61^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "text", + "content": " reduction in MAE), while a smaller advantage in the spatially varying material group " + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "inline_equation", + "content": "(0.19^{\\circ}" + }, + { + "bbox": [ + 304, + 402, + 546, + 617 + ], + "type": "text", + "content": " reduction in MAE). This is because the material and shape will affect the initial environment light's quality. While the estimated environment light is most accurate on smooth geometry with simple material, the quality will degrade on complex geometry and spatially varying material." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "Comparison on the designed filters. We compare Spin-UP with three alternatives (i.e, " + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o \\mathcal{F}^c" + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o \\mathcal{F}_{SH}^d" + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "inline_equation", + "content": "w / o \\mathcal{F}_{TH}^d" + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": "). The results in Table 4 demonstrate the effectiveness of those filters. Specifically, dropping " + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{TH}^d" + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": " will lead to mismatching light source position in the initialized environment light introduced by the specular reflectance, which eventually affects the accuracy of the estimated normal; dropping " + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{SH}^d" + }, + { + "bbox": [ + 304, + 618, + 547, + 715 + ], + "type": "text", + "content": " will harm the performance, especially" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 44, + 0, + 160, + 44 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 44, + 0, + 160, + 44 + ], + "spans": [ + { + "bbox": [ + 44, + 0, + 160, + 44 + ], + "type": "text", + "content": "(1)细胞壁：脑聚糖体膜、高尔基体膜、内质网等" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 215, + 0, + 331, + 42 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 215, + 0, + 331, + 42 + ], + "spans": [ + { + "bbox": [ + 215, + 0, + 331, + 42 + ], + "type": "text", + "content": "\\( \\left\\{ {1,2}\\right\\} \\Rightarrow \\left\\{ {1,3}\\right\\} \\Rightarrow \\left\\{ {2,4}\\right\\} \\Rightarrow \\left\\{ {3,4}\\right\\} \\Rightarrow \\left\\{ {4,5}\\right\\} \\Rightarrow \\left\\{ {5,6}\\right\\} \\Rightarrow \\left\\{ {6,7}\\right\\} \\Rightarrow \\left\\{ {7,8}\\right\\} \\Rightarrow \\left\\{ {8,9}\\right\\} \\Rightarrow \\left\\{ {9,10}\\right\\} \\Rightarrow \\left\\{ {10,11}\\right\\} \\Rightarrow \\left\\{ {11,12}\\right\\} \\Rightarrow \\left\\{ {12,13}\\right\\} \\Rightarrow \\left\\{ {13,14}\\right\\} \\Rightarrow \\left\\{ {14,15}\\right\\} \\Rightarrow \\left\\{ {15,16}\\right\\} \\Rightarrow \\left\\{ {16,17}\\right\\} \\Rightarrow \\left\\{ {17,18}\\right\\} \\Rightarrow \\left\\{ {18,19}\\right\\} \\Rightarrow \\left\\{ {19,20}\\right\\} \\Rightarrow \\left\\{ {20,21}\\right\\} \\Rightarrow \\left\\{ {21,22}\\right\\} \\Rightarrow \\left\\{ {22,23}\\right\\} \\Rightarrow \\left\\{ {23,24}\\right\\} \\Rightarrow \\left\\{ {24,25}\\right\\} \\Rightarrow \\left\\{ {25,26}\\right\\} \\Rightarrow \\left\\{ {26,27}\\right\\} \\Rightarrow \\left\\{ {27,28}\\right\\} \\Rightarrow \\left\\{ {28,29}\\right\\} \\Rightarrow \\left\\{ {29,30}\\right\\} \\Rightarrow \\left\\{ {30,31}\\right\\} \\Rightarrow \\left\\{ {31,32}\\right\\} \\Rightarrow \\left\\{ {32,33}\\right\\} \\Rightarrow \\left\\{ {33,34}\\right\\} \\Rightarrow \\left\\{ {34,35}\\right\\} \\Rightarrow \\left\\{ {35,36}\\right\\} \\Rightarrow \\left\\{ {36,37}\\right\\} \\Rightarrow \\left\\{ {37,38}\\right\\} \\Rightarrow \\left\\{ {38,39}\\right\\} \\Rightarrow \\left\\{ {39,40}\\right\\} \\Rightarrow \\left\\{ {40,41}\\right\\} \\Rightarrow \\left\\{ {41,42}\\right\\} \\Rightarrow \\left\\{ {42,43}\\right\\} \\Rightarrow \\left\\{ {43,44}\\right\\} \\Rightarrow \\left\\{ {44,45}\\right\\} \\Rightarrow \\left\\{ {45,46}\\right\\} \\Rightarrow \\left\\{ {46,47}\\right\\} \\Rightarrow \\left\\{ {47,48}\\right\\} \\Rightarrow \\left\\{ {48,49}\\right\\} \\Rightarrow \\left\\{ {49,50}\\right\\} \\Rightarrow \\left\\{ {50,51}\\right\\} \\Rightarrow \\left\\{ {51,52}\\right\\} \\Rightarrow \\left\\{ {52,53}\\right\\} \\Rightarrow \\left\\{ {53,54}\\right\\} \\Rightarrow \\left\\{ {54,55}\\right\\} \\Rightarrow \\left\\{ {55,56}\\right\\} \\Rightarrow \\left\\{ {56,57}\\right\\} \\Rightarrow \\left\\{ {57,58}\\right\\} \\Rightarrow \\left\\{ {58,59}\\right\\} \\Rightarrow \\left\\{ {59,60}\\right\\} \\Rightarrow \\left\\{ {60,61}\\right\\} \\Rightarrow \\left\\{ {61,62}\\right\\} \\Rightarrow \\left\\{ {62,63}\\right\\} \\Rightarrow \\left\\{ {63,64}\\right\\} \\Rightarrow \\left\\{ {64,65}\\right\\} \\Rightarrow \\left\\{ {65,66}\\right\\} \\Rightarrow \\left\\{ {66,67}\\right\\} \\Rightarrow \\left\\{ {67,68}\\right\\} \\Rightarrow }.\\;\\left( {{QQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQQ QQQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ qqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqqq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq.qq@qq" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11911" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 142, + 286, + 249 + ], + "blocks": [ + { + 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Ablation studies on Spin-UP's alternatives regarding average MAE on four groups (shape, light, reflectance, and spatially varying material group). 'Fib.', 'Rand.', 'Intv.', and 'Shrk.' represent the Fibonacci initialization method, random initialization, interval sampling, and shrinking range computing, respectively. Bold number indicates the best results in MAE." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 142, + 286, + 249 + ], + "lines": [ + { + "bbox": [ + 50, + 142, + 286, + 249 + ], + "spans": [ + { + "bbox": [ + 50, + 142, + 286, + 249 + ], + "type": "table", + "html": "
ShapeLightRef.SV.AVG
w Rand.12.026.449.7910.289.60
w Fib.9.335.3410.209.348.55
w/o Intv.8.875.029.8310.128.37
w/o Shrk.10.104.9210.1210.438.81
w/o Fc9.444.619.249.408.17
w/o FSh9.758.298.9315.7310.41
w/o FTh9.305.049.1812.498.82
Spin-UP8.724.549.089.157.85
S23 [11]†12.428.5612.5212.3311.46
Spin-UP†11.629.2511.079.079.48
", + "image_path": "715cf3b1fef59ff66711f4c32b359ec97ea9ffd02b278d348d226f3e1644232a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "lines": [ + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "spans": [ + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "type": "text", + "content": " Method with " + }, + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "type": "text", + "content": " is tested on dataset with point light " + }, + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "type": "inline_equation", + "content": "^+" + }, + { + "bbox": [ + 57, + 250, + 264, + 258 + ], + "type": "text", + "content": " environment light Sec. 5.3." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "text", + "content": "in the spatially varying material group " + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "inline_equation", + "content": "(6.58^{\\circ}" + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "text", + "content": " increase in MAE) since " + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{SH}^{d}" + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "text", + "content": " is essential in extracting low-frequency reflectance to initialize the environment light; dropping " + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^c" + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "text", + "content": " will increase MAE in average " + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "inline_equation", + "content": "(0.32^{\\circ})" + }, + { + "bbox": [ + 46, + 264, + 286, + 324 + ], + "type": "text", + "content": ", illustrating the necessity of reducing chromatic bias." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 329, + 211, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 329, + 211, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 329, + 211, + 342 + ], + "type": "text", + "content": "5.2. Training Strategies Validation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "text", + "content": "The interval sampling will facilitate the training of Spin-UP in two ways. First, the training time is two times shorter (25 min per object on average vs. 60 min on average, depending on the image's valid points for the object), and the GPU memory occupation is five times smaller (around 5 GB vs. 25 GB during training) than directly training on full-image resolution. Second, comparing Spin-UP with 'w/o Intv.', which applies a random sampling strategy and calculates the smoothness terms on patches (3 × 3 pixels), we find that the performance drops " + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "inline_equation", + "content": "0.52^{\\circ}" + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "text", + "content": " on average, and most " + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "inline_equation", + "content": "(0.97^{\\circ})" + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "text", + "content": " on the spatially varying material group. This is because the patch-based smoothness may not work uniformly on different parts of the object, diminishing the effectiveness of smoothness terms, especially on objects in spatially varying material with abrupt texture changes. The shrinking range computing helps avoid local optima when training Spin-UP on down-sampled images while still using full-resolution image coordinates for normal calculation. We compared Spin-UP with the alternative 'w/o Shrk.', which does not implement this strategy. The average MAE on normal estimation for four groups increases " + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "inline_equation", + "content": "0.96^{\\circ}" + }, + { + "bbox": [ + 46, + 345, + 289, + 609 + ], + "type": "text", + "content": ", highlighting the importance of this strategy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 616, + 276, + 628 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 276, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 276, + 628 + ], + "type": "text", + "content": "5.3. Additional Validation on Point Light Source" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 635, + 287, + 696 + ], + "type": "text", + "content": "To ensure a more fair comparison with the state-of-the-art supervised methods (S23 [11]), we add a dominant point light to the environment light in synthetic and real-world dataset11. According to Table 4, the proposed Spin-UP has a lower MAE on estimated normal maps than S23 [11] on" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 79, + 410, + 140 + ], + "blocks": [ + { + "bbox": [ + 321, + 71, + 399, + 79 + ], + "lines": [ + { + "bbox": [ + 321, + 71, + 399, + 79 + ], + "spans": [ + { + "bbox": [ + 321, + 71, + 399, + 79 + ], + "type": "text", + "content": "Point Light + Environment Light" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 79, + 410, + 140 + ], + "lines": [ + { + "bbox": [ + 310, + 79, + 410, + 140 + ], + "spans": [ + { + "bbox": [ + 310, + 79, + 410, + 140 + ], + "type": "image", + "image_path": "27e91bf9217fa5337d58e38c26d9e5a3c049700841666a4eb6f85525c8307ae1.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 358, + 149, + 367, + 157 + ], + "lines": [ + { + "bbox": [ + 358, + 149, + 367, + 157 + ], + "spans": [ + { + "bbox": [ + 358, + 149, + 367, + 157 + ], + "type": "text", + "content": "(a)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 420, + 70, + 441, + 140 + ], + "blocks": [ + { + "bbox": [ + 420, + 70, + 441, + 140 + ], + "lines": [ + { + "bbox": [ + 420, + 70, + 441, + 140 + ], + "spans": [ + { + "bbox": [ + 420, + 70, + 441, + 140 + ], + "type": "image", + "image_path": "9054fcb82d0f83787934bf4dd22989dabab545ea6d4cceca298c94390f3ba2b1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 449, + 71, + 492, + 147 + ], + "blocks": [ + { + "bbox": [ + 449, + 71, + 492, + 147 + ], + "lines": [ + { + "bbox": [ + 449, + 71, + 492, + 147 + ], + "spans": [ + { + "bbox": [ + 449, + 71, + 492, + 147 + ], + "type": "image", + "image_path": "a25ca09de8da3a786682a755eaa268c8af6f4adc67efeced6763ba73de67e5a3.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 468, + 148, + 476, + 156 + ], + "lines": [ + { + "bbox": [ + 468, + 148, + 476, + 156 + ], + "spans": [ + { + "bbox": [ + 468, + 148, + 476, + 156 + ], + "type": "text", + "content": "(b)" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 498, + 71, + 543, + 148 + ], + "blocks": [ + { + "bbox": [ + 498, + 71, + 543, + 148 + ], + "lines": [ + { + "bbox": [ + 498, + 71, + 543, + 148 + ], + "spans": [ + { + "bbox": [ + 498, + 71, + 543, + 148 + ], + "type": "image", + "image_path": "4d5b24164b0537eb879a4a69607f720392cb70d32e0c09a96f3973a9377300ba.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 166, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 304, + 166, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 304, + 166, + 545, + 201 + ], + "type": "text", + "content": "Figure 8. (a) Illustration of new light setup. (b) Qualitative comparison on SOLDIER between our method and S23 [11] with dominant point light." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 205, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 205, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 205, + 545, + 266 + ], + "type": "text", + "content": "the synthetic dataset (9.48° ours v.s. 11.46° S23 [11]). As shown in Fig. 8, we have a visually comparable result on the real-world dataset given far-field point light (2m) and a better result given near-field point light (0.4m), validating the adaptability of Spin-UP on unseen light sources." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 274, + 378, + 286 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 378, + 286 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 378, + 286 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 292, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 387 + ], + "type": "text", + "content": "This paper proposes Spin-UP to address NaUPS in an unsupervised manner. Thanks to our setup to mitigate the ill-posedness, the light initialization method to alleviate the ambiguities of NaUPS, and the proposed training strategies to facilitate fast convergence, Spin-UP can recover surfaces with isotropic reflectance under various lights. Experiments in synthetic and real-world datasets have shown that Spin-UP is robust to various shapes, lights, and reflectances." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 388, + 546, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 546, + 626 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 546, + 626 + ], + "type": "text", + "content": "Limitations and future work. Although Spin-UP is efficient and robust in solving NaUPS, it has several limitations: 1) Spin-UP assumes infinitely far light sources, which omit the spatially varying lighting; 2) the materials' base color will bias the estimated environment light; 3) Spin-UP assumes objects to have isotropic reflectance, ignoring inter-reflections and anisotropic features, meaning that it cannot perform well on objects with anisotropic reflectance, such as aluminum, or strong inter-reflections, such as a glass bowl; 4) Spin-UP doesn't compute the shadow iteratively, which may result in artifacts on objects with complicated shapes. Overcoming the above limitations will be regarded as our future work. Besides, the rotation axis of our device does not align with the object's center due to the consideration of structural stability, which may introduce bias from the spatially varying light in observed images. Redesigning the image capture device is also one of the future works. At last, we find it interesting to improve the setup by relieving the requirement for single-axis " + }, + { + "bbox": [ + 304, + 388, + 546, + 626 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 388, + 546, + 626 + ], + "type": "text", + "content": " rotation to free rotations for easier implementation on portable devices." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 627, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 545, + 711 + ], + "type": "text", + "content": "Acknowledgments. This work is supported by the National Natural Science Foundation of China under Grant No. 62136001, 62088102, Rapid-Rich Object Search (ROSE) Lab, Interdisciplinary Graduate Programme, Nanyang Technological University, Singapore, and the State Key Lab of Brain-Machine Intelligence, Zhejiang University, Hangzhou, China." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 55, + 701, + 194, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 701, + 194, + 713 + ], + "spans": [ + { + "bbox": [ + 55, + 701, + 194, + 713 + ], + "type": "text", + "content": "11Point light's setup follows [11] and [17]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11912" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Maryam Azimi et al. 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SPLaTAM enables precise camera tracking and high-fidelity reconstruction for dense simultaneous localization and mapping (SLAM) in challenging real-world scenarios. SPLaTAM achieves this by online optimization of an explicit volumetric representation, 3D Gaussian Splatting [14], using differentiable rendering. Left: We showcase the high-fidelity 3D Gaussian Map along with the train (SLAM-input) & novel view camera frustums. It can be noticed that SPLaTAM achieves sub-cm localization despite the large motion between subsequent cameras in the texture-less environment. This is particularly challenging for state-of-the-art baselines leading to the failure of tracking. Right: SPLaTAM enables photo-realistic rendering of both train & novel views at 400 FPS for a resolution of $876 \\times 584$ ." + ], + "image_footnote": [], + "bbox": [ + 630, + 400, + 720, + 448 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c17ffd141d9b091cd6624a0418a96309d67f5a32e4100db0aeed5a8bd42e30e3.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 722, + 352, + 813, + 400 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7c703e8740815dddb91c567c048227810e228546173da7ef9f7c3ee895ac97ac.jpg", + "image_caption": [ + "Depth L1: 1.9 cm", + "SplaTAM" + ], + "image_footnote": [], + "bbox": [ + 722, + 400, + 815, + 448 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 566, + 313, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dense simultaneous localization and mapping (SLAM) is crucial for robotics and augmented reality applications. However, current methods are often hampered by the nonvolumetric or implicit way they represent a scene. This work introduces SplaTAM, an approach that, for the first time, leverages explicit volumetric representations, i.e., 3D Gaussians, to enable high-fidelity reconstruction from a single unposed RGB-D camera, surpassing the capabilities of existing methods. SplaTAM employs a simple online tracking and mapping system tailored to the underlying Gaussian representation. It utilizes a silhouette mask to elegantly capture the presence of scene density. This combination enables several benefits over prior representations, including fast rendering and dense optimization, quickly determining if areas have been previously mapped, and structured map expansion by adding more Gaussians. Extensive experiments show that SplaTAM achieves up to $2 \\times$ superior performance in camera pose estimation, map construction, and novel-view synthesis over existing methods, paving the way for more immersive high-fidelity SLAM applications.", + "bbox": [ + 73, + 583, + 473, + 886 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 566, + 630, + 580 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual simultaneous localization and mapping (SLAM)—the task of estimating the pose of a vision sensor (such as a depth camera) and a map of the environment—is an essential capability for vision or robotic systems to operate in previously unseen 3D environments. For the past three decades, SLAM research has extensively centered around the question of map representation—resulting in a variety of sparse [2, 3, 7, 23], dense [4, 6, 8, 13, 15, 25, 26, 34, 42, 43], and neural scene representations [21, 29, 30, 37, 46, 55]. Map representation is a fundamental choice that dramatically impacts the design of every processing block within the SLAM system, as well as of the downstream tasks that depend on the outputs of SLAM.", + "bbox": [ + 496, + 595, + 892, + 792 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In terms of dense visual SLAM, the most successful handcrafted representations are points, surfels/flats, and signed distance fields. While systems based on such map representations have matured to production level over the past years, there are still significant shortcomings that need to be addressed. Tracking explicit representations relies crucially on the availability of rich 3D geometric fea", + "bbox": [ + 496, + 794, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "21357", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "tures and high-framerate captures. Furthermore, these approaches only reliably explain the observed parts of the scene; many applications, such as mixed reality and high-fidelity 3D capture, require techniques that can also explain/synthesize unobserved/novel camera viewpoints [32].", + "bbox": [ + 75, + 90, + 467, + 167 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The shortcomings of handcrafted representations, combined with the emergence of radiance field representations [21] for high-quality image synthesis, have fueled a recent class of methods that attempt to encode the scene into the weight space of a neural network. These radiance-field-based SLAM algorithms [30, 54] benefit from high-fidelity global maps and image reconstruction losses that capture dense photometric information via differentiable rendering. However, current methods use implicit neural representations to model the volumetric radiance fields, which causes a number of issues in the SLAM setting - they are computationally inefficient, not easy to edit, do not model spatial geometry explicitly, and suffer from catastrophic forgetting.", + "bbox": [ + 75, + 170, + 467, + 366 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this context, we explore the question, \"How can one use an explicit volumetric representation to design a SLAM solution?\" Specifically, we use a radiance field based on 3D Gaussians [14] to Splat (Render), Track, and Map for SLAM. We believe that this representation has the following benefits over existing map representations:", + "bbox": [ + 75, + 369, + 467, + 459 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Fast rendering and rich optimization: Gaussian Splating can be rendered at speeds up to 400 FPS, making it significantly faster to visualize and optimize than implicit alternatives. The key enabling factor for fast optimization is the rasterization of 3D primitives. We introduce several simple modifications that make splattering even faster for SLAM, including the removal of view-dependent appearance and the use of isotropic Gaussians. Furthermore, this allows us to use dense photometric loss for SLAM in real-time, in contrast to traditional & implicit map representations that rely respectively on sparse 3D geometric features or pixel-sampling to maintain efficiency.", + "- Maps with explicit spatial extent: The spatial frontier of the existing map can be easily controlled by adding Gaussians only in parts of the scene that have been observed in the past. Given a new image frame, this allows one to efficiently identify which portions of the scene are new content (outside the map's spatial frontier) by rendering a silhouette. This is crucial for camera tracking as we only want to compare mapped areas of the scene to new images. However, this is difficult for implicit map representations, as the network is subject to global changes during gradient-based optimization for the unmapped space.", + "- Explicit map: We can arbitrarily increase the map capacity by simply adding more Gaussians. Furthermore, this explicit volumetric representation enables us to edit parts of the scene, while still allowing photo-realistic rendering. Implicit approaches cannot easily increase their capacity or edit their represented scene." + ], + "bbox": [ + 76, + 462, + 467, + 898 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Direct gradient flow to parameters: As the scene is represented by Gaussians with physical 3D locations, colors, and sizes, there is a direct, almost linear (projective) gradient flow between the parameters and the rendering. Because camera motion can be thought of as keeping the camera still and moving the scene, we also have a direct gradient into the camera parameters, which enables fast optimization. Neural-based representations don't have this as the gradient needs to flow through (potentially many) non-linear neural network layers.", + "bbox": [ + 500, + 90, + 890, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Given all of the above advantages, an explicit volumetric representation is a natural way for efficiently inferring a high-fidelity spatial map while simultaneously estimating camera motion, as is also visible from Fig. 1. We show across all our experiments on simulated and real data that our approach, SplaTAM, achieves state-of-the-art results compared to all previous approaches for camera pose estimation, map estimation, and novel-view synthesis.", + "bbox": [ + 496, + 243, + 890, + 364 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 377, + 640, + 393 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this section, we briefly review various approaches to dense SLAM, with a particular emphasis on recent approaches that leverage implicit representations encoded in overfit neural networks for tracking and mapping. For a more detailed review of traditional SLAM methods, we refer the interested reader to this excellent survey [2].", + "bbox": [ + 496, + 402, + 890, + 492 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional approaches to dense SLAM have explored a variety of explicit representations, including 2.5D images [15, 34], (truncated) signed-distance functions [6, 25, 26, 42], gaussian mixture models [9, 10] and circular surfels [13, 33, 43]. Of particular relevance to this work is surfels, which are colored circular surface elements and can be optimized in real-time from RGB-D image inputs as shown in [13, 33, 43]. While the aforementioned SLAM approaches do not assume the visibility function to be differentiable, there exist modern differentiable rasterizers that enable gradient flow through depth discontinuities [50]. However, since 2D surfels are discontinuous, they need careful regularization to prevent holes [33, 50]. In this work, we use volumetric (as opposed to surface-only) scene representations in the form of 3D Gaussians, enabling easy continuous optimization for fast and accurate SLAM.", + "bbox": [ + 496, + 493, + 890, + 733 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pretrained neural network representations have been integrated with traditional SLAM techniques, largely focusing on predicting depth from RGB images. These approaches range from directly integrating depth predictions from a neural network into SLAM [38], to learning a variational autoencoder that decodes compact estimizable latent codes to depth maps [1, 52], to approaches that simultaneously learn to predict a depth cost volume and tracking [53].", + "bbox": [ + 496, + 734, + 890, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Implicit scene representations: iMAP [37] first performed both tracking and mapping using neural implicit representations. To improve scalability, NICE-SLAM [54] proposed", + "bbox": [ + 496, + 854, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "21358", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/0b9a3f698960632db53cf77051563ac0360374645a4daad46b89373e8413eee5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 99, + 93, + 478, + 234 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/d0f4525f8b1c81d7034ed7562a132f2cd1d6c7f30889f0220a54e124559daef7.jpg", + "image_caption": [ + "Figure 2. Overview of SplaTAM. Top-Left: The input to our approach at each timestep is the current RGB-D frame and the 3D Gaussian Map Representation that we have built representing all of the scene seen so far. Top-Right: Step (1) estimates the camera pose for the new image, using silhouette-guided differentiable rendering. Bottom-Right: Step (2) increases the map capacity by adding new Gaussians based on the rendered silhouette and input depth. Bottom-Left: Step (3) updates the underlying Gaussian map with differentiable rendering." + ], + "image_footnote": [], + "bbox": [ + 99, + 234, + 478, + 356 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/54352ae94e06df53469045007024152d1711c7ac296d53a50c81b25e2203af41.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 93, + 870, + 234 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/bff135a5897e48faf10bd615be447d8fe6c821dc135ea05b62018b848d002e22.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 234, + 867, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the use of hierarchical multi-feature grids. On similar lines, iSDF [28] used implicit representations to efficiently compute signed-distances, compared to [25, 27]. Following this, a number of works [11, 18, 19, 22, 29, 31, 41, 51, 55], have recently advanced implicit-based SLAM through a number of ways - by reducing catastrophic forgetting via continual learning(experience replay), capturing semantics, incorporating uncertainty, employing efficient resolution hash-frames and encodings, and using improved losses. More recently, Point-SLAM [30], proposes an alternative route, similar to [45] by using neural point clouds and performing volumetric rendering with feature interpolation, offering better 3-D reconstruction, especially for robotics. However, like other implicit representations, volumetric ray sampling greatly limits its efficiency, thereby resorting to optimization over a sparse set of pixels as opposed to per-pixel dense photometric error. Instead, SplaTAM's explicit volumetric radiance model leverages fast rasterization, enabling complete use of per-pixel dense photometric errors.", + "bbox": [ + 75, + 446, + 472, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3D Gaussian Splatting: Recently, 3D Gaussians have emerged as a promising 3D scene representation [14, 16, 17, 40], in particular with the ability to differentiably render them extremely quickly via splatting [14]. This approach has also been extended to model dynamic scenes [20, 44, 47, 48] with dense 6-DOF motion [20]. Such approaches for both static and dynamic scenes require that each input frame has an accurately known 6-DOF camera pose, in order to successfully optimize the representation. For the first time our approach removes this constraint, simultaneously", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "estimating the camera poses while also fitting the underlying Gaussian representation.", + "bbox": [ + 498, + 448, + 890, + 479 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 491, + 591, + 507 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "SplaTAM is the first dense RGB-D SLAM solution to use 3D Gaussian Splatting [14]. By modeling the world as a collection of 3D Gaussians which can be rendered into high-fidelity color and depth images, we are able to directly use differentiable-rendering and gradient-based-optimization to optimize both the camera pose for each frame and an underlying volumetric discretized map of the world.", + "bbox": [ + 496, + 517, + 890, + 625 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gaussian Map Representation. We represent the underlying map of the scene as a set of 3D Gaussians. We made a number of simplifications to the representation proposed in [14], by using only view-independent color and forcing Gaussians to be isotropic. This implies each Gaussian is parameterized by only 8 values: three for its RGB color $\\mathbf{c}$ , three for its center position $\\pmb{\\mu} \\in \\mathbb{R}^3$ , one for its radius $r$ and one for its opacity $o \\in [0,1]$ . Each Gaussian influences a point in 3D space $\\mathbf{x} \\in \\mathbb{R}^3$ according to the standard (unnormized) Gaussian equation weighted by its opacity:", + "bbox": [ + 496, + 642, + 890, + 792 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf (\\mathbf {x}) = o \\exp \\left(- \\frac {\\| \\mathbf {x} - \\boldsymbol {\\mu} \\| ^ {2}}{2 r ^ {2}}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 594, + 804, + 890, + 839 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Differentiable Rendering via Splatting. The core of our approach is the ability to render high-fidelity color, depth, and silhouette images from our underlying Gaussian Map", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "21359", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "into any possible camera reference frame in a differentiable way. This differentiable rendering allows us to directly calculate the gradients in the underlying scene representation (Gaussians) and camera parameters with respect to the error between the renders and provided RGB-D frames, and update both the Gaussians and camera parameters to minimize this error, thus fitting both accurate camera poses and an accurate volumetric representation of the world.", + "bbox": [ + 75, + 90, + 468, + 210 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gaussian Splatting [14] renders an RGB image as follows: Given a collection of 3D Gaussians and camera pose, first sort all Gaussians from front-to-back. RGB images can then be efficiently rendered by alpha-compositing the splatted 2D projection of each Gaussian in order in pixel space. The rendered color of pixel $\\mathbf{p} = (u,\\nu)$ can be written as:", + "bbox": [ + 75, + 210, + 468, + 303 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} \\mathbf {c} _ {i} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 315, + 468, + 352 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{i}(\\mathbf{p})$ is computed as in Eq. (1) but with $\\boldsymbol{\\mu}$ and $r$ of the splatted 2D Gaussians in pixel-space:", + "bbox": [ + 76, + 364, + 468, + 396 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} ^ {2 \\mathrm {D}} = K \\frac {E _ {t} \\boldsymbol {\\mu}}{d}, \\quad r ^ {2 \\mathrm {D}} = \\frac {f r}{d}, \\quad \\text {w h e r e} \\quad d = \\left(E _ {t} \\boldsymbol {\\mu}\\right) _ {z}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 405, + 468, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, $K$ is the (known) camera intrinsic matrix, $E_{t}$ is the extrinsic matrix capturing the rotation and translation of the camera at frame $t$ , $f$ is the (known) focal length, and $d$ is the depth of the $i^{th}$ Gaussian in camera coordinates.", + "bbox": [ + 76, + 445, + 468, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We propose to similarly differentiably render depth:", + "bbox": [ + 96, + 505, + 439, + 520 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nD (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} d _ {i} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 532, + 468, + 570 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "which can be compared against the input depth map and return gradients with respect to the 3D map.", + "bbox": [ + 76, + 577, + 468, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We also render a silhouette image to determine visibility - e.g. if a pixel contains information from the current map:", + "bbox": [ + 76, + 607, + 467, + 638 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nS (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 648, + 468, + 686 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SLAM System. We build a SLAM system from our Gaussian representation and differentiable renderer. We begin with a brief overview and then describe each module in detail. Assume we have an existing map (represented via a set of 3D Gaussians) that has been fitted from a set of camera frames 1 to t. Given a new RGB-D frame $t + 1$ , our SLAM system performs the following steps (see Fig. 2):", + "bbox": [ + 76, + 704, + 468, + 810 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) Camera Tracking. We minimize the image and depth reconstruction error of the RGB-D frame with respect to camera pose parameters for $t + 1$ , but only evaluate errors over pixels within the visible silhouette.", + "(2) Gaussian Densification. We add new Gaussians to the map based on the rendered silhouette and input depth." + ], + "bbox": [ + 76, + 810, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "(3) Map Update. Given the camera poses from frame 1 to $t + 1$ , we update the parameters of all the Gaussians in the scene by minimizing the RGB and depth errors over all images up to $t + 1$ . In practice, to keep the batch size manageable, a selected subset of keyframes that overlap with the most recent frame are optimized.", + "bbox": [ + 500, + 90, + 890, + 181 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Initialization. For the first frame, the tracking step is skipped, and the camera pose is set to identity. In the densification step, since the rendered silhouette is empty, all pixels are used to initialize new Gaussians. Specifically, for each pixel, we add a new Gaussian with the color of that pixel, the center at the location of the unprojection of that pixel depth, an opacity of 0.5, and a radius equal to having a one-pixel radius upon projection into the 2D image given by dividing the depth by the focal length:", + "bbox": [ + 496, + 200, + 890, + 335 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nr = \\frac {D _ {\\mathrm {G T}}}{f} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 661, + 347, + 890, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Camera Tracking. Camera Tracking aims to estimate the camera pose of the current incoming online RGB-D image. The camera pose is initialized for a new timestep by a constant velocity forward projection of the pose parameters in the camera center + quaternion space. E.g. the camera parameters are initialized using the following:", + "bbox": [ + 496, + 393, + 890, + 484 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nE _ {t + 1} = E _ {t} + \\left(E _ {t} - E _ {t - 1}\\right) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 498, + 890, + 513 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The camera pose is then updated iteratively by gradient-based optimization through differentiably rendering RGB, depth, and silhouette maps, and updating the camera parameters to minimize the following loss while keeping the Gaussian parameters fixed:", + "bbox": [ + 496, + 525, + 890, + 601 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {t} = \\sum_ {\\mathbf {p}} \\left(S (\\mathbf {p}) > 0. 9 9\\right) \\left(\\mathrm {L} _ {1} (D (\\mathbf {p})) + 0. 5 \\mathrm {L} _ {1} (C (\\mathbf {p}))\\right) \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 612, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This is an L1 loss on both the depth and color renders, with color weighted down by half. The color weighting is empirically selected, where we observe the range of $C(\\mathbf{p})$ to be [0.01, 0.03] & $D(\\mathbf{p})$ to be [0.002, 0.006]. We only apply the loss over pixels that are rendered from well-optimized parts of the map by using our rendered visibility silhouette which captures the epistemic uncertainty of the map. This is very important for tracking new camera poses, as often new frames contain new information that hasn't been captured or well optimized in our map yet. The L1 loss also gives a value of 0 if there is no ground-truth depth for a pixel.", + "bbox": [ + 496, + 655, + 890, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Gaussian Densification. Gaussian Densification aims to initialize new Gaussians in our Map at each incoming online frame. After tracking we have an accurate estimate for the camera pose for this frame, and with a depth image we have", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "21360", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a good estimate for where Gaussians in the scene should be. However, we don't want to add Gaussians where the current Gaussians already accurately represent the scene geometry. Thus we create a densification mask to determine which pixels should be densified:", + "bbox": [ + 75, + 90, + 470, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} M (\\mathbf {p}) = \\left(S (\\mathbf {p}) < 0. 5\\right) + \\\\ \\left(D _ {\\mathrm {G T}} (\\mathbf {p}) < D (\\mathbf {p})\\right) \\left(\\mathrm {L} _ {1} (D (\\mathbf {p})) > \\lambda \\mathrm {M D E}\\right) \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 181, + 468, + 237 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This mask indicates where the map isn't adequately dense ( $S < 0.5$ ), or where there should be new geometry in front of the current estimated geometry (i.e., the ground-truth depth is in front of the predicted depth, and the depth error is greater than $\\lambda$ times the median depth error (MDE), where $\\lambda$ is empirically selected as 50). For each pixel, based on this mask, we add a new Gaussian following the same procedure as first-frame initialization.", + "bbox": [ + 75, + 247, + 470, + 367 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Gaussian Map Updating. This aims to update the parameters of the 3D Gaussian Map given the set of online camera poses estimated so far. This is done again by differentiable-rendering and gradient-based-optimization, however unlike tracking, in this setting the camera poses are fixed, and the parameters of the Gaussians are updated.", + "bbox": [ + 75, + 391, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This is equivalent to the \"classic\" problem of fitting a radiance field to images with known poses. However, we make two important modifications. Instead of starting from scratch, we warm-start the optimization from the most recently constructed map. We also do not optimize over all previous (key)frames but select frames that are likely to influence the newly added Gaussians. We save each $n^{\\mathrm{th}}$ frame as a keyframe and select $k$ frames to optimize, including the current frame, the most recent keyframe, and $k - 2$ previous keyframes which have the highest overlap with the current frame. Overlap is determined by taking the point cloud of the current frame depth map and determining the number of points inside the frustum of each keyframe.", + "bbox": [ + 75, + 482, + 470, + 678 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This phase optimizes a similar loss as during tracking, except we don't use the silhouette mask as we want to optimize over all pixels. Furthermore, we add an SSIM loss to RGB rendering and cull useless Gaussians that have near 0 opacity or are too large, as done partly in [14].", + "bbox": [ + 75, + 679, + 468, + 755 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 768, + 269, + 786 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets and Evaluation Settings. We evaluate our approach on four datasets: ScanNet++ [49], Replica [35], TUM-RGBD [36] and the original ScanNet [5]. The last three are chosen in order to follow the evaluation procedure of previous radiance-field-based SLAM methods Point-SLAM [30] and NICE-SLAM [54]. However, we also add ScanNet++ [49] evaluation because none of the", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "other three benchmarks have the ability to evaluate rendering quality on hold out novel views and only evaluate camera pose estimation and rendering on the training views.", + "bbox": [ + 496, + 90, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Replica [35] is the simplest benchmark as it contains synthetic scenes, highly accurate and complete (synthetic) depth maps, and small displacements between consecutive camera poses. TUM-RGBD [36] and the original ScanNet are harder, especially for dense methods, due to poor RGB and depth image quality as they both use old low-quality cameras. Depth images are quite sparse with lots of missing information, and the color images have a very high amount of motion blur. For ScanNet++ [49] we use the DSLR captures from two scenes (8b5caf3398 (S1) and b20a261fdf (S2)), where complete dense trajectories are present. In contrast to other benchmarks, ScanNet++ color and depth images are very high quality, and provide a second capture loop for each scene to evaluate completely novel hold-out views. However, each camera pose is very far apart from one another making pose-estimation very difficult. The difference between consecutive frames on ScanNet++ is about the same as a 30-frame gap on Replica. For all benchmarks except ScanNet++, we take baseline numbers from Point-SLAM [30]. Similar to Point-SLAM, we evaluate every 5th frame for the training view rendering benchmarking on Replica. Furthermore, for all comparisons to prior baselines, we present results as the average of 3 seeds (0-2) and use seed 0 for the ablations.", + "bbox": [ + 496, + 138, + 892, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics. We follow all evaluation metrics for camera pose estimation and rendering performance as [30]. For measuring RGB rendering performance we use PSNR, SSIM and LPIPS. For depth rendering performance we use Depth L1 loss. For camera pose estimation tracking we use the average absolute trajectory error (ATE RMSE).", + "bbox": [ + 496, + 511, + 890, + 602 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. The main baseline method we compare to is Point-SLAM [30], the previous state-of-the-art (SOTA) method for dense radiance-field-based SLAM. We also compare to older dense SLAM approaches such as NICE-SLAM [54], Vox-Fusion [46], and ESLAM [12] where appropriate. Lastly, we compare against traditional SLAM systems such as Kintinous [42], ElasticFusion [43], and ORB-SLAM2 [23] on TUM-RGBD, DROID-SLAM [39] on Replica, and ORB-SLAM3 [3] on ScanNet++.", + "bbox": [ + 496, + 614, + 890, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Results & Discussion", + "text_level": 1, + "bbox": [ + 500, + 768, + 699, + 784 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we first discuss our evaluation results on camera pose estimation for the four benchmark datasets. Then, we further showcase our high-fidelity 3D Gaussian reconstructions and provide qualitative and quantitative comparisons of our rendering quality (both for novel views and input training views). Finally, we discuss pipeline ablations and provide a runtime comparison.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "21361", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/330c71f74784380965ea0d73f618571fc541c5678a0dc0f07395ab5cb3d55dcd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsAvg.S1S2
Point-SLAM [30]343.8296.7390.8
ORB-SLAM3 [3]158.2156.8159.7
SplaTAM1.20.61.9
", + "bbox": [ + 196, + 85, + 429, + 143 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/ccbfec7fb34f40ef5b89aec18065af63952dbae0410d44f54df853871fe42dae.jpg", + "table_caption": [ + "ScanNet++[49]" + ], + "table_footnote": [], + "table_body": "
MethodsAvg.R0R1R2Of0Of1Of2Of3Of4
DROID-SLAM [39]0.380.530.380.450.350.240.360.330.43
Vox-Fusion [46]3.091.374.701.478.482.042.581.112.94
NICE-SLAM [54]1.060.971.311.070.881.001.061.101.13
ESLAM [12]0.630.710.700.520.570.550.580.720.63
Point-SLAM [30]0.520.610.410.370.380.480.540.690.72
SplaTAM0.360.310.400.290.470.270.290.320.55
", + "bbox": [ + 478, + 85, + 807, + 178 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4f98a792a1bfd2f947622fab98b83a5606657458c8ca7b8d321f16fb54d4e6e5.jpg", + "table_caption": [ + "Replica [35]" + ], + "table_footnote": [], + "table_body": "
MethodsAvg.fr1/ deskfr1/ desk2fr1/ roomfr2/ xyzfr3/ off.
Kintinous [42]4.843.707.107.502.903.00
ElasticFusion [43]6.912.536.8321.491.172.52
ORB-SLAM2 [23]1.981.602.204.700.401.00
NICE-SLAM [54]15.874.264.9934.4931.733.87
Vox-Fusion [46]11.313.526.0019.531.4926.01
Point-SLAM [30]8.924.344.5430.921.313.48
SplaTAM5.483.356.5411.131.245.16
", + "bbox": [ + 161, + 184, + 457, + 296 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/712de6e5006477355243e797a8c939903babeeba5d4f748f3ef59ba9e1851711.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsAvg.000000590106016901810207
Vox-Fusion [46]26.9068.8424.188.4127.2823.309.41
NICE-SLAM [54]10.7012.0014.007.9010.9013.406.20
Point-SLAM [30]12.1910.247.818.6522.1614.779.54
SplaTAM11.8812.8310.1017.7212.0811.107.46
", + "bbox": [ + 483, + 208, + 800, + 273 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Orig-ScanNet [5]", + "bbox": [ + 599, + 281, + 684, + 292 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "TUM-RGBD [36]", + "text_level": 1, + "bbox": [ + 264, + 304, + 354, + 316 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Online Camera-Pose Estimation Results on Four Datasets (ATE RMSE $\\downarrow[\\mathrm{cm}]$ ). Our method consistently outperforms all the SOTA-dense baselines on ScanNet++, Replica, and TUM-RGBD, while providing competitive performance on Orig-ScanNet [5]. Best results are highlighted as first, second, and third. Numbers for the baselines on Orig-ScanNet [5], TUM-RGBD [36] and Replica [35] are taken from Point-SLAM [30].", + "bbox": [ + 75, + 327, + 893, + 385 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Camera Pose Estimation Results. In Table 1, we compare our method's camera pose estimation results to a number of baselines on four datasets [5, 35, 36, 49].", + "bbox": [ + 75, + 411, + 468, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On ScanNet++ [49], both SOTA SLAM approaches Point-SLAM [30] and ORB-SLAM3 [3] (RGB-D variant) completely fail to correctly track the camera pose due to the very large displacement between contiguous cameras, and thus give very large pose-estimation errors. In particular, for ORB-SLAM3, we observe that the texture-less ScanNet++ scans cause the tracking to re-initialize multiple times due to the lack of features. In contrast, our approach successfully manages to track the camera over both sequences giving an average trajectory error of only $1.2\\mathrm{cm}$ .", + "bbox": [ + 75, + 458, + 468, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On the relatively easy synthetic Replica [35] dataset, the de-facto evaluation benchmark, our approach reduces the trajectory error over the prior SOTA-dense baseline [30] by more than $30\\%$ from $0.52\\mathrm{cm}$ to $0.36\\mathrm{cm}$ . Furthermore, SPLaTAM provides better or competitive performance to a feature-based tracking method such as DROID-SLAM [39].", + "bbox": [ + 75, + 611, + 468, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On TUM-RGBD [36], all the volumetric methods struggle immensely due to both poor depth sensor information (very sparse) and poor RGB image quality (extremely high motion blur). Compared to prior methods in this category [30, 54], SplaTAM still significantly outperforms, decreasing the trajectory error of the prior SOTA in this category [30] by almost $40\\%$ , from $8.92\\mathrm{cm}$ to $5.48\\mathrm{cm}$ . Also, we observe that feature-based methods (ORB-SLAM2 [23]) still outperform dense methods on this benchmark.", + "bbox": [ + 75, + 702, + 468, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The original ScanNet [5] benchmark has similar issues to TUM-RGBD, where no dense volumetric method is able to obtain results with less than $10\\mathrm{cm}$ error & SPLaTAM performs similarly to the two prior SOTA methods [30, 54].", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Overall these camera pose estimation results are extremely promising and show off the strengths of our SplaTAM method. The results on ScanNet++ show that if you have high-quality clean input images, our approach can successfully and accurately perform SLAM even with extremely large motions between camera positions, which is not something that is possible with previous SOTA approaches such as Point-SLAM [30] and ORB-SLAM3 [3].", + "bbox": [ + 496, + 412, + 890, + 532 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "**Rendering Quality Results.** In Table 2, we evaluate our method's rendering quality on the input views of Replica dataset [35] (as is the standard evaluation approach from Point-SLAM [30] and NICE-SLAM [54]). Our approach achieves similar PSNR, SSIM, and LPIPS results as Point-SLAM [30], although the comparison is not fair as Point-SLAM has the unfair advantage as it takes the ground-truth depth of these images as an input for where to sample its 3D volume for rendering. Our approach achieves much better results than the other baselines Vox-Fusion [46] and NICE-SLAM [54], improving over both by around 10dB in PSNR.", + "bbox": [ + 496, + 537, + 892, + 703 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In general, we believe that the rendering results on Replica in Table 2 are irrelevant because the rendering performance is evaluated on the same training views that were passed in as input, and methods can simply have a high capacity and overfit to these images. We only show this as this is the de-facto evaluation for prior methods, and we wish to have some way to compare against them.", + "bbox": [ + 496, + 704, + 890, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hence, a better evaluation is to evaluate novel-view rendering. However, all current SLAM benchmarks don't have a hold-out set of images separate from the camera trajectory that the SLAM algorithm estimates, so they cannot be used for this purpose. Therefore, we set up a novel benchmark for this using the new high-quality ScanNet++ [49] dataset.", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "21362", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b28a0746b0f1467b3397ecdb85ded1aecf1289417d94e114243aa86be2af0c72.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsMetricsAvg.R0R1R2Of0Of1Of2Of3Of4
Vox-Fusion [46]PSNR ↑24.4122.3922.3623.9227.7929.8320.3323.4725.21
SSIM ↑0.800.680.750.800.860.880.790.800.85
LPIPS ↓0.240.300.270.230.240.180.240.210.20
NICE-SLAM [54]PSNR ↑24.4222.1222.4724.5229.0730.3419.6622.2324.94
SSIM ↑0.810.690.760.810.870.890.800.800.86
LPIPS ↓0.230.330.270.210.230.180.240.210.20
Point-SLAM [30]PSNR ↑35.1732.4034.0835.5038.2639.1633.9933.4833.49
SSIM ↑0.980.970.980.980.980.990.960.960.98
LPIPS ↓0.120.110.120.110.100.120.160.130.14
SplaTAMPSNR ↑34.1132.8633.8935.2538.2639.1731.9729.7031.81
SSIM ↑0.970.980.970.980.980.980.970.950.95
LPIPS ↓0.100.070.100.080.090.090.100.120.15
", + "bbox": [ + 76, + 89, + 475, + 253 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The results for both novel-view and training-view rendering on this ScanNet++ benchmark can be found in Table 3. Our approach achieves a good novel-view synthesis result of 24.41 PSNR on average and slightly higher on training views with 27.98 PSNR. Note that for novel-view synthesis, we use the ground-truth pose of the novel view to align it with the origin of the SLAM map, i.e., the first SLAM frame. Since Point-SLAM [30] fails to successfully estimate the camera poses and build a good map, it also completely fails on the task of novel-view synthesis.", + "bbox": [ + 75, + 375, + 468, + 526 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We can also evaluate the geometric reconstruction of the scene by evaluating the rendered depth and comparing it to the ground-truth depth, again for both training and novel views. Our method obtains an incredibly accurate reconstruction with a depth error of only around $2\\mathrm{cm}$ in novel views and $1.3\\mathrm{cm}$ in training views.", + "bbox": [ + 75, + 526, + 468, + 618 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visual results of both novel-view and training-view rendering for RGB and depth can be seen in Fig. 3. As can be seen, our methods achieve visually excellent results over both scenes for both novel and training views. In contrast, Point-SLAM [30] fails at camera-pose tracking and overfits to the training views, and isn't able to successfully render novel views at all. Point-SLAM also takes the ground-truth depth as an input for rendering to determine where to sample, and as such the depth maps look similar to the ground-truth, while color rendering is completely wrong.", + "bbox": [ + 75, + 618, + 468, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "With this novel benchmark that is able to correctly evaluate Novel-View Synthesis and SLAM simultaneously, as well as our approach as a strong initial baseline for this benchmark, we hope to inspire many future approaches that improve upon these results for both tasks.", + "bbox": [ + 75, + 768, + 468, + 845 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Color and Depth Loss Ablation. Our SplaTAM involves fitting the camera poses (during tracking) and the scene map (during mapping) using both a photometric (RGB) and", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/60978e7b7aefb7d90a37e9b538a5765290d3603f094e5698f51edec233dc0c10.jpg", + "table_caption": [ + "Table 2. Quantitative Train View Rendering Performance on Replica [35]. SplaTAM is comparable to the SOTA baseline, Point-SLAM [30] and consistently outperforms the other dense SLAM methods by a large margin. Numbers for the baselines are taken from Point-SLAM [30]. Note that Point-SLAM uses ground-truth depth for rendering." + ], + "table_footnote": [], + "table_body": "
MethodsMetricsNovel ViewTraining View
Avg.S1S2Avg.S1S2
Point-SLAM [30]PSNR [dB] ↑11.9112.1011.7314.4614.6214.30
SSIM ↑0.280.310.260.380.350.41
LPIPS ↓0.680.620.740.650.680.62
Depth L1 [cm] ↓XXXXXX
SplaTAMPSNR [dB] ↑24.4123.9924.8427.9827.8228.14
SSIM ↑0.880.880.870.940.940.94
LPIPS ↓0.240.210.260.120.120.13
Depth L1 [cm] ↓2.071.912.231.280.931.64
", + "bbox": [ + 500, + 88, + 908, + 212 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/8b25a8bbee766d4974c3f091eb194f74367f48615dff10a366687288693b77c9.jpg", + "table_caption": [ + "Table 3. Novel & Train View Rendering Performance on ScanNet++ [49]. SplaTAM provides high-fidelity performance on both training views seen during SLAM and held-out novel views from any camera pose. On the other hand, Point-SLAM [30] requires ground-truth depth & performs poorly." + ], + "table_footnote": [], + "table_body": "
Track. ColorMap. ColorTrack. DepthMap. DepthATE [cm]↓Dep. L1 [cm]↓PSNR [dB]↑
XX✓✓86.03XX
✓✓XX1.3812.5831.30
✓✓✓✓0.270.4932.81
", + "bbox": [ + 521, + 305, + 870, + 375 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/863e3cb7f9618181a0c4be7d80c6906bcbf086561d3aea08b3b1208b11612943.jpg", + "table_caption": [ + "Table 4. Color & Depth Loss Ablation on Replica/Room 0." + ], + "table_footnote": [], + "table_body": "
Velo. \nProp.Sil. \nMaskSil. \nThresh.ATE \n[cm]↓Dep. L1 \n[cm]↓PSNR \n[dB]↑
X✓0.992.952.1525.40
✓X0.99115.800.2914.16
✓✓0.51.300.7431.36
✓✓0.990.270.4932.81
", + "bbox": [ + 544, + 412, + 849, + 491 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Camera Tracking Ablations on Replica/Room 0.", + "bbox": [ + 516, + 501, + 874, + 515 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "depth loss. In Table 4, we ablate the decision to use both and investigate the performance of only one or the other for both tracking and mapping. We do this using Room 0 of Replica. With only depth our method completely fails to track the camera trajectory, because the L1 depth loss doesn't provide adequate information in the x-y image plane. Using only an RGB loss successfully tracks the camera trajectory (although with more than $5\\mathrm{x}$ the error as using both). Both the RGB and depth work together to achieve excellent results. With only the color loss, reconstruction PSNR is really high, only 1.5 PSNR lower than the full model. However, the depth L1 is much higher using only color vs directly optimizing this depth error. In the color-only experiments, the depth is not used for tracking & mapping, but it is used for the densification and initialization of Gaussians.", + "bbox": [ + 496, + 542, + 890, + 770 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Camera Tracking Ablation. In Table 5, we ablate three aspects of our camera tracking: (1) the use of forward velocity propagation, (2) the use of a silhouette mask to mask out invalid map areas in the loss, and (3) setting the silhouette threshold to 0.99 instead of 0.5. All three are critical to excellent results. Without forward velocity propagation, tracking still works, but the overall error is more than $10\\mathrm{x}$ higher, which subsequently degrades the map and render", + "bbox": [ + 496, + 779, + 890, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "21363", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a3e76135e2f46b1b248703f25e92a4fb2206ea420a9e3065eae419c9e5624b96.jpg", + "image_caption": [ + "Figure 3. Renderings on ScanNet++ [49]. Our method, SplaTAM, renders color & depth for the novel & train views with fidelity comparable to the ground truth. It can also be observed that Point-SLAM [30] fails to provide good renderings on both novel & train view images. Note that Point-SLAM (PS) uses the ground-truth depth to render the train & novel view images. Despite the use of ground-truth depth, the failure of PS can be attributed to the failure of tracking as shown in Tab. 1." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 903, + 262 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/e92f39f17d4e314d0bfe36bdcac712826d489813e653c89786a1cc35bec5bc35.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsTracking /IterationMapping /IterationTracking /FrameMapping /FrameATE RMSE [cm] ↓
NICE-SLAM [54]30 ms166 ms1.18 s2.04 s0.97
Point-SLAM [30]19 ms30 ms0.76 s4.50 s0.61
SplaTAM25 ms24 ms1.00 s1.44 s0.27
SplaTAM-S19 ms22 ms0.19 s0.33 s0.39
", + "bbox": [ + 83, + 354, + 464, + 431 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Runtime on Replica/R0 using a RTX 3080 Ti.", + "bbox": [ + 102, + 441, + 442, + 455 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "ing. Silhouette is critical as without it tracking completely fails. Setting the silhouette threshold to 0.99 allows the loss to be applied on well-optimized pixels in the map, thereby leading to an important $5\\mathrm{x}$ reduction in the error compared to the threshold of 0.5, which is used for the densification.", + "bbox": [ + 75, + 481, + 468, + 556 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Runtime Comparison. In Table 6, we compare our runtime to NICE-SLAM [54] and Point-SLAM [30] on a Nvidia RTX 3080 Ti. Each iteration of our approach renders a full $1200 \\times 980$ pixel image ( $\\sim 1.2$ mil pixels) to apply the loss for both tracking and mapping. Other methods use only 200 pixels for tracking and 1000 pixels for mapping each iteration (but attempt to cleverly sample these pixels). Even though we differentiably render 3 orders of magnitude more pixels, our approach incurs similar runtime, primarily due to the efficiency of rasterizing 3D Gaussians. Additionally, we show a version of our method with fewer iterations and half-resolution densification, SplaTAM-S, which works 5x faster with only a minor degradation in performance. In particular, SplaTAM uses 40 and 60 iterations per frame for tracking & mapping respectively on Replica, while SplaTAM-S uses 10 and 15 iterations per frame.", + "bbox": [ + 75, + 561, + 468, + 805 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations & Future Work. Although SplaTAM achieves state-of-the-art performance, we find our method to show some sensitivity to motion blur, large depth noise, and aggressive rotation. We believe a possible solution would be to temporally model these effects and wish to tackle this in future work. Furthermore, SplaTAM", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "can be scaled up to large-scale scenes through efficient representations like OpenVDB [24]. Finally, our method requires known camera intrinsics and dense depth as input for performing SLAM, and removing these dependencies is an interesting avenue for the future.", + "bbox": [ + 496, + 356, + 893, + 434 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 446, + 619, + 463 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present SPLaTAM, a novel SLAM system that leverages 3D Gaussians as its underlying map representation to enable fast rendering and dense optimization, explicit knowledge of map spatial extent, and streamlined map densification. We demonstrate its effectiveness in achieving state-of-the-art results in camera pose estimation, scene reconstruction, and novel-view synthesis. We believe that SPLaTAM not only sets a new benchmark in both the SLAM and novel-view synthesis domains but also opens up exciting avenues, where the integration of 3D Gaussian Splatting with SLAM offers a robust framework for further exploration and innovation in scene understanding. Our work underscores the potential of this integration, paving the way for more sophisticated and efficient SLAM systems in the future.", + "bbox": [ + 496, + 472, + 890, + 684 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. This work was supported in part by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. This work used Bridges-2 at PSC through allocation cis220039p from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program which is supported by NSF grants #2138259, #2138286, #2138307, #2137603, and #213296, and also supported by a hardware grant from Nvidia.", + "bbox": [ + 496, + 695, + 892, + 851 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The authors thank Yao He for his support with testing ORB-SLAM3 & Jeff Tan for testing the code & demos. We also thank Chonghyuk (Andrew) Song, Margaret Hansen, John Kim & Michael Kaess for their insightful feedback & discussion on initial versions of the work.", + "bbox": [ + 496, + 851, + 893, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "21364", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Michael Bloesch, Jan Czarnowski, Ronald Clark, Stefan Leutenegger, and Andrew J Davison. Codeslam—learning a compact, optimisable representation for dense visual slam. In CVPR, 2018. 2", + "[2] Cesar Cadena, Luca Carlone, Henry Carrillo, Yasir Latif, Davide Scaramuzza, José Neira, Ian Reid, and John J Leonard. Past, present, and future of simultaneous localization and mapping: Toward the robust-perception age. 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Nicer-slam: Neural implicit scene encoding for rgb slam. arXiv preprint arXiv:2302.03594, 2023. 1, 3" + ], + "bbox": [ + 501, + 92, + 890, + 897 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "21366", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/177d5eaf-8449-4cd5-ba1f-ab6fb569d8d8_model.json b/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/177d5eaf-8449-4cd5-ba1f-ab6fb569d8d8_model.json new file mode 100644 index 0000000000000000000000000000000000000000..312ede3c18e361f53f0852633668f03559ed3454 --- /dev/null +++ b/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/177d5eaf-8449-4cd5-ba1f-ab6fb569d8d8_model.json @@ -0,0 +1,2354 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.129, + 0.13, + 0.842, + 0.176 + ], + "angle": 0, + "content": "SplaTAM: Splat, Track & Map 3D Gaussians for Dense RGB-D SLAM SPLa-tam.github.io" + }, + { + "type": "text", + "bbox": [ + 0.163, + 0.178, + 0.807, + 0.216 + ], + "angle": 0, + "content": "Nikhil Keetha1, Jay Karhade1, Krishna Murthy Jatavallabhula2, Gengshan Yang1, Sebastian Scherer1, Deva Ramanan1, and Jonathon Luiten1" + }, + { + "type": "text", + "bbox": [ + 0.423, + 0.219, + 0.544, + 0.236 + ], + "angle": 0, + "content": "\\(^{1}\\)CMU \\(^{2}\\)MIT" + }, + { + "type": "image", + "bbox": [ + 0.102, + 0.244, + 0.59, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.594, + 0.285, + 0.623, + 0.304 + ], + "angle": 0, + "content": "Train View" + }, + { + "type": "image_caption", + "bbox": [ + 0.593, + 0.361, + 0.623, + 0.41 + ], + "angle": 0, + "content": "Novel View" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.245, + 0.722, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.293, + 0.721, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.341, + 0.711, + 0.351 + ], + "angle": 0, + "content": "PSNR: 27.4 dB" + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.245, + 0.814, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.293, + 0.815, + 0.341 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.341, + 0.808, + 0.351 + ], + "angle": 0, + "content": "Depth L1: 0.9 cm" + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.353, + 0.722, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.631, + 0.401, + 0.722, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.643, + 0.449, + 0.712, + 0.459 + ], + "angle": 0, + "content": "PSNR: 24.2 dB" + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.353, + 0.815, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.401, + 0.816, + 0.449 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.45, + 0.809, + 0.459 + ], + "angle": 0, + "content": "Depth L1: 1.9 cm" + }, + { + "type": "image_caption", + "bbox": [ + 0.822, + 0.258, + 0.86, + 0.278 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.311, + 0.864, + 0.321 + ], + "angle": 0, + "content": "SplaTAM" + }, + { + "type": "image_caption", + "bbox": [ + 0.821, + 0.367, + 0.86, + 0.387 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image_caption", + "bbox": [ + 0.82, + 0.419, + 0.864, + 0.429 + ], + "angle": 0, + "content": "SplaTAM" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.471, + 0.895, + 0.555 + ], + "angle": 0, + "content": "Figure 1. SPLaTAM enables precise camera tracking and high-fidelity reconstruction for dense simultaneous localization and mapping (SLAM) in challenging real-world scenarios. SPLaTAM achieves this by online optimization of an explicit volumetric representation, 3D Gaussian Splatting [14], using differentiable rendering. Left: We showcase the high-fidelity 3D Gaussian Map along with the train (SLAM-input) & novel view camera frustums. It can be noticed that SPLaTAM achieves sub-cm localization despite the large motion between subsequent cameras in the texture-less environment. This is particularly challenging for state-of-the-art baselines leading to the failure of tracking. Right: SPLaTAM enables photo-realistic rendering of both train & novel views at 400 FPS for a resolution of \\(876 \\times 584\\)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.567, + 0.314, + 0.582 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.584, + 0.474, + 0.887 + ], + "angle": 0, + "content": "Dense simultaneous localization and mapping (SLAM) is crucial for robotics and augmented reality applications. However, current methods are often hampered by the nonvolumetric or implicit way they represent a scene. This work introduces SplaTAM, an approach that, for the first time, leverages explicit volumetric representations, i.e., 3D Gaussians, to enable high-fidelity reconstruction from a single unposed RGB-D camera, surpassing the capabilities of existing methods. SplaTAM employs a simple online tracking and mapping system tailored to the underlying Gaussian representation. It utilizes a silhouette mask to elegantly capture the presence of scene density. This combination enables several benefits over prior representations, including fast rendering and dense optimization, quickly determining if areas have been previously mapped, and structured map expansion by adding more Gaussians. Extensive experiments show that SplaTAM achieves up to \\(2 \\times\\) superior performance in camera pose estimation, map construction, and novel-view synthesis over existing methods, paving the way for more immersive high-fidelity SLAM applications." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.567, + 0.631, + 0.582 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.596, + 0.893, + 0.793 + ], + "angle": 0, + "content": "Visual simultaneous localization and mapping (SLAM)—the task of estimating the pose of a vision sensor (such as a depth camera) and a map of the environment—is an essential capability for vision or robotic systems to operate in previously unseen 3D environments. For the past three decades, SLAM research has extensively centered around the question of map representation—resulting in a variety of sparse [2, 3, 7, 23], dense [4, 6, 8, 13, 15, 25, 26, 34, 42, 43], and neural scene representations [21, 29, 30, 37, 46, 55]. Map representation is a fundamental choice that dramatically impacts the design of every processing block within the SLAM system, as well as of the downstream tasks that depend on the outputs of SLAM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.903 + ], + "angle": 0, + "content": "In terms of dense visual SLAM, the most successful handcrafted representations are points, surfels/flats, and signed distance fields. While systems based on such map representations have matured to production level over the past years, there are still significant shortcomings that need to be addressed. Tracking explicit representations relies crucially on the availability of rich 3D geometric fea" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "21357" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.468, + 0.168 + ], + "angle": 0, + "content": "tures and high-framerate captures. Furthermore, these approaches only reliably explain the observed parts of the scene; many applications, such as mixed reality and high-fidelity 3D capture, require techniques that can also explain/synthesize unobserved/novel camera viewpoints [32]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.171, + 0.468, + 0.367 + ], + "angle": 0, + "content": "The shortcomings of handcrafted representations, combined with the emergence of radiance field representations [21] for high-quality image synthesis, have fueled a recent class of methods that attempt to encode the scene into the weight space of a neural network. These radiance-field-based SLAM algorithms [30, 54] benefit from high-fidelity global maps and image reconstruction losses that capture dense photometric information via differentiable rendering. However, current methods use implicit neural representations to model the volumetric radiance fields, which causes a number of issues in the SLAM setting - they are computationally inefficient, not easy to edit, do not model spatial geometry explicitly, and suffer from catastrophic forgetting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.468, + 0.46 + ], + "angle": 0, + "content": "In this context, we explore the question, \"How can one use an explicit volumetric representation to design a SLAM solution?\" Specifically, we use a radiance field based on 3D Gaussians [14] to Splat (Render), Track, and Map for SLAM. We believe that this representation has the following benefits over existing map representations:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.463, + 0.468, + 0.643 + ], + "angle": 0, + "content": "- Fast rendering and rich optimization: Gaussian Splating can be rendered at speeds up to 400 FPS, making it significantly faster to visualize and optimize than implicit alternatives. The key enabling factor for fast optimization is the rasterization of 3D primitives. We introduce several simple modifications that make splattering even faster for SLAM, including the removal of view-dependent appearance and the use of isotropic Gaussians. Furthermore, this allows us to use dense photometric loss for SLAM in real-time, in contrast to traditional & implicit map representations that rely respectively on sparse 3D geometric features or pixel-sampling to maintain efficiency." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.645, + 0.468, + 0.81 + ], + "angle": 0, + "content": "- Maps with explicit spatial extent: The spatial frontier of the existing map can be easily controlled by adding Gaussians only in parts of the scene that have been observed in the past. Given a new image frame, this allows one to efficiently identify which portions of the scene are new content (outside the map's spatial frontier) by rendering a silhouette. This is crucial for camera tracking as we only want to compare mapped areas of the scene to new images. However, this is difficult for implicit map representations, as the network is subject to global changes during gradient-based optimization for the unmapped space." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.468, + 0.9 + ], + "angle": 0, + "content": "- Explicit map: We can arbitrarily increase the map capacity by simply adding more Gaussians. Furthermore, this explicit volumetric representation enables us to edit parts of the scene, while still allowing photo-realistic rendering. Implicit approaches cannot easily increase their capacity or edit their represented scene." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.463, + 0.468, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.242 + ], + "angle": 0, + "content": "- Direct gradient flow to parameters: As the scene is represented by Gaussians with physical 3D locations, colors, and sizes, there is a direct, almost linear (projective) gradient flow between the parameters and the rendering. Because camera motion can be thought of as keeping the camera still and moving the scene, we also have a direct gradient into the camera parameters, which enables fast optimization. Neural-based representations don't have this as the gradient needs to flow through (potentially many) non-linear neural network layers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.244, + 0.892, + 0.365 + ], + "angle": 0, + "content": "Given all of the above advantages, an explicit volumetric representation is a natural way for efficiently inferring a high-fidelity spatial map while simultaneously estimating camera motion, as is also visible from Fig. 1. We show across all our experiments on simulated and real data that our approach, SplaTAM, achieves state-of-the-art results compared to all previous approaches for camera pose estimation, map estimation, and novel-view synthesis." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.378, + 0.642, + 0.394 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.403, + 0.892, + 0.493 + ], + "angle": 0, + "content": "In this section, we briefly review various approaches to dense SLAM, with a particular emphasis on recent approaches that leverage implicit representations encoded in overfit neural networks for tracking and mapping. For a more detailed review of traditional SLAM methods, we refer the interested reader to this excellent survey [2]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.494, + 0.892, + 0.734 + ], + "angle": 0, + "content": "Traditional approaches to dense SLAM have explored a variety of explicit representations, including 2.5D images [15, 34], (truncated) signed-distance functions [6, 25, 26, 42], gaussian mixture models [9, 10] and circular surfels [13, 33, 43]. Of particular relevance to this work is surfels, which are colored circular surface elements and can be optimized in real-time from RGB-D image inputs as shown in [13, 33, 43]. While the aforementioned SLAM approaches do not assume the visibility function to be differentiable, there exist modern differentiable rasterizers that enable gradient flow through depth discontinuities [50]. However, since 2D surfels are discontinuous, they need careful regularization to prevent holes [33, 50]. In this work, we use volumetric (as opposed to surface-only) scene representations in the form of 3D Gaussians, enabling easy continuous optimization for fast and accurate SLAM." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Pretrained neural network representations have been integrated with traditional SLAM techniques, largely focusing on predicting depth from RGB images. These approaches range from directly integrating depth predictions from a neural network into SLAM [38], to learning a variational autoencoder that decodes compact estimizable latent codes to depth maps [1, 52], to approaches that simultaneously learn to predict a depth cost volume and tracking [53]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Implicit scene representations: iMAP [37] first performed both tracking and mapping using neural implicit representations. To improve scalability, NICE-SLAM [54] proposed" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21358" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.101, + 0.094, + 0.48, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.101, + 0.236, + 0.48, + 0.357 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.094, + 0.871, + 0.235 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.236, + 0.869, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.895, + 0.424 + ], + "angle": 0, + "content": "Figure 2. Overview of SplaTAM. Top-Left: The input to our approach at each timestep is the current RGB-D frame and the 3D Gaussian Map Representation that we have built representing all of the scene seen so far. Top-Right: Step (1) estimates the camera pose for the new image, using silhouette-guided differentiable rendering. Bottom-Right: Step (2) increases the map capacity by adding new Gaussians based on the rendered silhouette and input depth. Bottom-Left: Step (3) updates the underlying Gaussian map with differentiable rendering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.473, + 0.736 + ], + "angle": 0, + "content": "the use of hierarchical multi-feature grids. On similar lines, iSDF [28] used implicit representations to efficiently compute signed-distances, compared to [25, 27]. Following this, a number of works [11, 18, 19, 22, 29, 31, 41, 51, 55], have recently advanced implicit-based SLAM through a number of ways - by reducing catastrophic forgetting via continual learning(experience replay), capturing semantics, incorporating uncertainty, employing efficient resolution hash-frames and encodings, and using improved losses. More recently, Point-SLAM [30], proposes an alternative route, similar to [45] by using neural point clouds and performing volumetric rendering with feature interpolation, offering better 3-D reconstruction, especially for robotics. However, like other implicit representations, volumetric ray sampling greatly limits its efficiency, thereby resorting to optimization over a sparse set of pixels as opposed to per-pixel dense photometric error. Instead, SplaTAM's explicit volumetric radiance model leverages fast rasterization, enabling complete use of per-pixel dense photometric errors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "3D Gaussian Splatting: Recently, 3D Gaussians have emerged as a promising 3D scene representation [14, 16, 17, 40], in particular with the ability to differentiably render them extremely quickly via splatting [14]. This approach has also been extended to model dynamic scenes [20, 44, 47, 48] with dense 6-DOF motion [20]. Such approaches for both static and dynamic scenes require that each input frame has an accurately known 6-DOF camera pose, in order to successfully optimize the representation. For the first time our approach removes this constraint, simultaneously" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.449, + 0.892, + 0.48 + ], + "angle": 0, + "content": "estimating the camera poses while also fitting the underlying Gaussian representation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.492, + 0.593, + 0.508 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.892, + 0.625 + ], + "angle": 0, + "content": "SplaTAM is the first dense RGB-D SLAM solution to use 3D Gaussian Splatting [14]. By modeling the world as a collection of 3D Gaussians which can be rendered into high-fidelity color and depth images, we are able to directly use differentiable-rendering and gradient-based-optimization to optimize both the camera pose for each frame and an underlying volumetric discretized map of the world." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Gaussian Map Representation. We represent the underlying map of the scene as a set of 3D Gaussians. We made a number of simplifications to the representation proposed in [14], by using only view-independent color and forcing Gaussians to be isotropic. This implies each Gaussian is parameterized by only 8 values: three for its RGB color \\(\\mathbf{c}\\), three for its center position \\(\\pmb{\\mu} \\in \\mathbb{R}^3\\), one for its radius \\(r\\) and one for its opacity \\(o \\in [0,1]\\). Each Gaussian influences a point in 3D space \\(\\mathbf{x} \\in \\mathbb{R}^3\\) according to the standard (unnormized) Gaussian equation weighted by its opacity:" + }, + { + "type": "equation", + "bbox": [ + 0.596, + 0.805, + 0.892, + 0.84 + ], + "angle": 0, + "content": "\\[\nf (\\mathbf {x}) = o \\exp \\left(- \\frac {\\| \\mathbf {x} - \\boldsymbol {\\mu} \\| ^ {2}}{2 r ^ {2}}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Differentiable Rendering via Splatting. The core of our approach is the ability to render high-fidelity color, depth, and silhouette images from our underlying Gaussian Map" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21359" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.212 + ], + "angle": 0, + "content": "into any possible camera reference frame in a differentiable way. This differentiable rendering allows us to directly calculate the gradients in the underlying scene representation (Gaussians) and camera parameters with respect to the error between the renders and provided RGB-D frames, and update both the Gaussians and camera parameters to minimize this error, thus fitting both accurate camera poses and an accurate volumetric representation of the world." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.212, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Gaussian Splatting [14] renders an RGB image as follows: Given a collection of 3D Gaussians and camera pose, first sort all Gaussians from front-to-back. RGB images can then be efficiently rendered by alpha-compositing the splatted 2D projection of each Gaussian in order in pixel space. The rendered color of pixel \\(\\mathbf{p} = (u,\\nu)\\) can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.316, + 0.469, + 0.353 + ], + "angle": 0, + "content": "\\[\nC (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} \\mathbf {c} _ {i} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.366, + 0.47, + 0.397 + ], + "angle": 0, + "content": "where \\( f_{i}(\\mathbf{p}) \\) is computed as in Eq. (1) but with \\( \\boldsymbol{\\mu} \\) and \\( r \\) of the splatted 2D Gaussians in pixel-space:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.406, + 0.469, + 0.436 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} ^ {2 \\mathrm {D}} = K \\frac {E _ {t} \\boldsymbol {\\mu}}{d}, \\quad r ^ {2 \\mathrm {D}} = \\frac {f r}{d}, \\quad \\text {w h e r e} \\quad d = \\left(E _ {t} \\boldsymbol {\\mu}\\right) _ {z}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.446, + 0.469, + 0.505 + ], + "angle": 0, + "content": "Here, \\(K\\) is the (known) camera intrinsic matrix, \\(E_{t}\\) is the extrinsic matrix capturing the rotation and translation of the camera at frame \\(t\\), \\(f\\) is the (known) focal length, and \\(d\\) is the depth of the \\(i^{th}\\) Gaussian in camera coordinates." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.506, + 0.441, + 0.521 + ], + "angle": 0, + "content": "We propose to similarly differentiably render depth:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.533, + 0.469, + 0.571 + ], + "angle": 0, + "content": "\\[\nD (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} d _ {i} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.578, + 0.469, + 0.607 + ], + "angle": 0, + "content": "which can be compared against the input depth map and return gradients with respect to the 3D map." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.608, + 0.468, + 0.639 + ], + "angle": 0, + "content": "We also render a silhouette image to determine visibility - e.g. if a pixel contains information from the current map:" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.649, + 0.469, + 0.687 + ], + "angle": 0, + "content": "\\[\nS (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.705, + 0.469, + 0.811 + ], + "angle": 0, + "content": "SLAM System. We build a SLAM system from our Gaussian representation and differentiable renderer. We begin with a brief overview and then describe each module in detail. Assume we have an existing map (represented via a set of 3D Gaussians) that has been fitted from a set of camera frames 1 to t. Given a new RGB-D frame \\(t + 1\\), our SLAM system performs the following steps (see Fig. 2):" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.811, + 0.469, + 0.87 + ], + "angle": 0, + "content": "(1) Camera Tracking. We minimize the image and depth reconstruction error of the RGB-D frame with respect to camera pose parameters for \\( t + 1 \\), but only evaluate errors over pixels within the visible silhouette." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "(2) Gaussian Densification. We add new Gaussians to the map based on the rendered silhouette and input depth." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.811, + 0.469, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "(3) Map Update. Given the camera poses from frame 1 to \\( t + 1 \\), we update the parameters of all the Gaussians in the scene by minimizing the RGB and depth errors over all images up to \\( t + 1 \\). In practice, to keep the batch size manageable, a selected subset of keyframes that overlap with the most recent frame are optimized." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.201, + 0.892, + 0.337 + ], + "angle": 0, + "content": "Initialization. For the first frame, the tracking step is skipped, and the camera pose is set to identity. In the densification step, since the rendered silhouette is empty, all pixels are used to initialize new Gaussians. Specifically, for each pixel, we add a new Gaussian with the color of that pixel, the center at the location of the unprojection of that pixel depth, an opacity of 0.5, and a radius equal to having a one-pixel radius upon projection into the 2D image given by dividing the depth by the focal length:" + }, + { + "type": "equation", + "bbox": [ + 0.663, + 0.348, + 0.892, + 0.379 + ], + "angle": 0, + "content": "\\[\nr = \\frac {D _ {\\mathrm {G T}}}{f} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.892, + 0.485 + ], + "angle": 0, + "content": "Camera Tracking. Camera Tracking aims to estimate the camera pose of the current incoming online RGB-D image. The camera pose is initialized for a new timestep by a constant velocity forward projection of the pose parameters in the camera center + quaternion space. E.g. the camera parameters are initialized using the following:" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.499, + 0.891, + 0.514 + ], + "angle": 0, + "content": "\\[\nE _ {t + 1} = E _ {t} + \\left(E _ {t} - E _ {t - 1}\\right) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.526, + 0.892, + 0.602 + ], + "angle": 0, + "content": "The camera pose is then updated iteratively by gradient-based optimization through differentiably rendering RGB, depth, and silhouette maps, and updating the camera parameters to minimize the following loss while keeping the Gaussian parameters fixed:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.613, + 0.891, + 0.645 + ], + "angle": 0, + "content": "\\[\nL _ {t} = \\sum_ {\\mathbf {p}} \\left(S (\\mathbf {p}) > 0. 9 9\\right) \\left(\\mathrm {L} _ {1} (D (\\mathbf {p})) + 0. 5 \\mathrm {L} _ {1} (C (\\mathbf {p}))\\right) \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.822 + ], + "angle": 0, + "content": "This is an L1 loss on both the depth and color renders, with color weighted down by half. The color weighting is empirically selected, where we observe the range of \\( C(\\mathbf{p}) \\) to be [0.01, 0.03] & \\( D(\\mathbf{p}) \\) to be [0.002, 0.006]. We only apply the loss over pixels that are rendered from well-optimized parts of the map by using our rendered visibility silhouette which captures the epistemic uncertainty of the map. This is very important for tracking new camera poses, as often new frames contain new information that hasn't been captured or well optimized in our map yet. The L1 loss also gives a value of 0 if there is no ground-truth depth for a pixel." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Gaussian Densification. Gaussian Densification aims to initialize new Gaussians in our Map at each incoming online frame. After tracking we have an accurate estimate for the camera pose for this frame, and with a depth image we have" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21360" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.168 + ], + "angle": 0, + "content": "a good estimate for where Gaussians in the scene should be. However, we don't want to add Gaussians where the current Gaussians already accurately represent the scene geometry. Thus we create a densification mask to determine which pixels should be densified:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.183, + 0.47, + 0.238 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} M (\\mathbf {p}) = \\left(S (\\mathbf {p}) < 0. 5\\right) + \\\\ \\left(D _ {\\mathrm {G T}} (\\mathbf {p}) < D (\\mathbf {p})\\right) \\left(\\mathrm {L} _ {1} (D (\\mathbf {p})) > \\lambda \\mathrm {M D E}\\right) \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.471, + 0.368 + ], + "angle": 0, + "content": "This mask indicates where the map isn't adequately dense (\\(S < 0.5\\)), or where there should be new geometry in front of the current estimated geometry (i.e., the ground-truth depth is in front of the predicted depth, and the depth error is greater than \\(\\lambda\\) times the median depth error (MDE), where \\(\\lambda\\) is empirically selected as 50). For each pixel, based on this mask, we add a new Gaussian following the same procedure as first-frame initialization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.47, + 0.481 + ], + "angle": 0, + "content": "Gaussian Map Updating. This aims to update the parameters of the 3D Gaussian Map given the set of online camera poses estimated so far. This is done again by differentiable-rendering and gradient-based-optimization, however unlike tracking, in this setting the camera poses are fixed, and the parameters of the Gaussians are updated." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.483, + 0.471, + 0.679 + ], + "angle": 0, + "content": "This is equivalent to the \"classic\" problem of fitting a radiance field to images with known poses. However, we make two important modifications. Instead of starting from scratch, we warm-start the optimization from the most recently constructed map. We also do not optimize over all previous (key)frames but select frames that are likely to influence the newly added Gaussians. We save each \\( n^{\\mathrm{th}} \\) frame as a keyframe and select \\( k \\) frames to optimize, including the current frame, the most recent keyframe, and \\( k - 2 \\) previous keyframes which have the highest overlap with the current frame. Overlap is determined by taking the point cloud of the current frame depth map and determining the number of points inside the frustum of each keyframe." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.47, + 0.756 + ], + "angle": 0, + "content": "This phase optimizes a similar loss as during tracking, except we don't use the silhouette mask as we want to optimize over all pixels. Furthermore, we add an SSIM loss to RGB rendering and cull useless Gaussians that have near 0 opacity or are too large, as done partly in [14]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.769, + 0.27, + 0.787 + ], + "angle": 0, + "content": "4. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Datasets and Evaluation Settings. We evaluate our approach on four datasets: ScanNet++ [49], Replica [35], TUM-RGBD [36] and the original ScanNet [5]. The last three are chosen in order to follow the evaluation procedure of previous radiance-field-based SLAM methods Point-SLAM [30] and NICE-SLAM [54]. However, we also add ScanNet++ [49] evaluation because none of the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.137 + ], + "angle": 0, + "content": "other three benchmarks have the ability to evaluate rendering quality on hold out novel views and only evaluate camera pose estimation and rendering on the training views." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.139, + 0.893, + 0.501 + ], + "angle": 0, + "content": "Replica [35] is the simplest benchmark as it contains synthetic scenes, highly accurate and complete (synthetic) depth maps, and small displacements between consecutive camera poses. TUM-RGBD [36] and the original ScanNet are harder, especially for dense methods, due to poor RGB and depth image quality as they both use old low-quality cameras. Depth images are quite sparse with lots of missing information, and the color images have a very high amount of motion blur. For ScanNet++ [49] we use the DSLR captures from two scenes (8b5caf3398 (S1) and b20a261fdf (S2)), where complete dense trajectories are present. In contrast to other benchmarks, ScanNet++ color and depth images are very high quality, and provide a second capture loop for each scene to evaluate completely novel hold-out views. However, each camera pose is very far apart from one another making pose-estimation very difficult. The difference between consecutive frames on ScanNet++ is about the same as a 30-frame gap on Replica. For all benchmarks except ScanNet++, we take baseline numbers from Point-SLAM [30]. Similar to Point-SLAM, we evaluate every 5th frame for the training view rendering benchmarking on Replica. Furthermore, for all comparisons to prior baselines, we present results as the average of 3 seeds (0-2) and use seed 0 for the ablations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.512, + 0.892, + 0.603 + ], + "angle": 0, + "content": "Evaluation Metrics. We follow all evaluation metrics for camera pose estimation and rendering performance as [30]. For measuring RGB rendering performance we use PSNR, SSIM and LPIPS. For depth rendering performance we use Depth L1 loss. For camera pose estimation tracking we use the average absolute trajectory error (ATE RMSE)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.615, + 0.892, + 0.751 + ], + "angle": 0, + "content": "Baselines. The main baseline method we compare to is Point-SLAM [30], the previous state-of-the-art (SOTA) method for dense radiance-field-based SLAM. We also compare to older dense SLAM approaches such as NICE-SLAM [54], Vox-Fusion [46], and ESLAM [12] where appropriate. Lastly, we compare against traditional SLAM systems such as Kintinous [42], ElasticFusion [43], and ORB-SLAM2 [23] on TUM-RGBD, DROID-SLAM [39] on Replica, and ORB-SLAM3 [3] on ScanNet++." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.769, + 0.7, + 0.785 + ], + "angle": 0, + "content": "5. Results & Discussion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we first discuss our evaluation results on camera pose estimation for the four benchmark datasets. Then, we further showcase our high-fidelity 3D Gaussian reconstructions and provide qualitative and quantitative comparisons of our rendering quality (both for novel views and input training views). Finally, we discuss pipeline ablations and provide a runtime comparison." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "21361" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.197, + 0.087, + 0.431, + 0.144 + ], + "angle": 0, + "content": "
MethodsAvg.S1S2
Point-SLAM [30]343.8296.7390.8
ORB-SLAM3 [3]158.2156.8159.7
SplaTAM1.20.61.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.272, + 0.151, + 0.352, + 0.163 + ], + "angle": 0, + "content": "ScanNet++[49]" + }, + { + "type": "table", + "bbox": [ + 0.479, + 0.087, + 0.808, + 0.179 + ], + "angle": 0, + "content": "
MethodsAvg.R0R1R2Of0Of1Of2Of3Of4
DROID-SLAM [39]0.380.530.380.450.350.240.360.330.43
Vox-Fusion [46]3.091.374.701.478.482.042.581.112.94
NICE-SLAM [54]1.060.971.311.070.881.001.061.101.13
ESLAM [12]0.630.710.700.520.570.550.580.720.63
Point-SLAM [30]0.520.610.410.370.380.480.540.690.72
SplaTAM0.360.310.400.290.470.270.290.320.55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.612, + 0.187, + 0.674, + 0.199 + ], + "angle": 0, + "content": "Replica [35]" + }, + { + "type": "table", + "bbox": [ + 0.163, + 0.185, + 0.458, + 0.297 + ], + "angle": 0, + "content": "
MethodsAvg.fr1/ deskfr1/ desk2fr1/ roomfr2/ xyzfr3/ off.
Kintinous [42]4.843.707.107.502.903.00
ElasticFusion [43]6.912.536.8321.491.172.52
ORB-SLAM2 [23]1.981.602.204.700.401.00
NICE-SLAM [54]15.874.264.9934.4931.733.87
Vox-Fusion [46]11.313.526.0019.531.4926.01
Point-SLAM [30]8.924.344.5430.921.313.48
SplaTAM5.483.356.5411.131.245.16
" + }, + { + "type": "table", + "bbox": [ + 0.485, + 0.209, + 0.802, + 0.274 + ], + "angle": 0, + "content": "
MethodsAvg.000000590106016901810207
Vox-Fusion [46]26.9068.8424.188.4127.2823.309.41
NICE-SLAM [54]10.7012.0014.007.9010.9013.406.20
Point-SLAM [30]12.1910.247.818.6522.1614.779.54
SplaTAM11.8812.8310.1017.7212.0811.107.46
" + }, + { + "type": "table_caption", + "bbox": [ + 0.6, + 0.282, + 0.686, + 0.293 + ], + "angle": 0, + "content": "Orig-ScanNet [5]" + }, + { + "type": "title", + "bbox": [ + 0.266, + 0.305, + 0.356, + 0.317 + ], + "angle": 0, + "content": "TUM-RGBD [36]" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.328, + 0.895, + 0.386 + ], + "angle": 0, + "content": "Table 1. Online Camera-Pose Estimation Results on Four Datasets (ATE RMSE \\(\\downarrow[\\mathrm{cm}]\\)). Our method consistently outperforms all the SOTA-dense baselines on ScanNet++, Replica, and TUM-RGBD, while providing competitive performance on Orig-ScanNet [5]. Best results are highlighted as first, second, and third. Numbers for the baselines on Orig-ScanNet [5], TUM-RGBD [36] and Replica [35] are taken from Point-SLAM [30]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.412, + 0.469, + 0.457 + ], + "angle": 0, + "content": "Camera Pose Estimation Results. In Table 1, we compare our method's camera pose estimation results to a number of baselines on four datasets [5, 35, 36, 49]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.459, + 0.47, + 0.61 + ], + "angle": 0, + "content": "On ScanNet++ [49], both SOTA SLAM approaches Point-SLAM [30] and ORB-SLAM3 [3] (RGB-D variant) completely fail to correctly track the camera pose due to the very large displacement between contiguous cameras, and thus give very large pose-estimation errors. In particular, for ORB-SLAM3, we observe that the texture-less ScanNet++ scans cause the tracking to re-initialize multiple times due to the lack of features. In contrast, our approach successfully manages to track the camera over both sequences giving an average trajectory error of only \\(1.2\\mathrm{cm}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.47, + 0.702 + ], + "angle": 0, + "content": "On the relatively easy synthetic Replica [35] dataset, the de-facto evaluation benchmark, our approach reduces the trajectory error over the prior SOTA-dense baseline [30] by more than \\(30\\%\\) from \\(0.52\\mathrm{cm}\\) to \\(0.36\\mathrm{cm}\\). Furthermore, SPLaTAM provides better or competitive performance to a feature-based tracking method such as DROID-SLAM [39]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.469, + 0.839 + ], + "angle": 0, + "content": "On TUM-RGBD [36], all the volumetric methods struggle immensely due to both poor depth sensor information (very sparse) and poor RGB image quality (extremely high motion blur). Compared to prior methods in this category [30, 54], SplaTAM still significantly outperforms, decreasing the trajectory error of the prior SOTA in this category [30] by almost \\(40\\%\\), from \\(8.92\\mathrm{cm}\\) to \\(5.48\\mathrm{cm}\\). Also, we observe that feature-based methods (ORB-SLAM2 [23]) still outperform dense methods on this benchmark." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The original ScanNet [5] benchmark has similar issues to TUM-RGBD, where no dense volumetric method is able to obtain results with less than \\(10\\mathrm{cm}\\) error & SPLaTAM performs similarly to the two prior SOTA methods [30, 54]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.413, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Overall these camera pose estimation results are extremely promising and show off the strengths of our SplaTAM method. The results on ScanNet++ show that if you have high-quality clean input images, our approach can successfully and accurately perform SLAM even with extremely large motions between camera positions, which is not something that is possible with previous SOTA approaches such as Point-SLAM [30] and ORB-SLAM3 [3]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.538, + 0.893, + 0.704 + ], + "angle": 0, + "content": "**Rendering Quality Results.** In Table 2, we evaluate our method's rendering quality on the input views of Replica dataset [35] (as is the standard evaluation approach from Point-SLAM [30] and NICE-SLAM [54]). Our approach achieves similar PSNR, SSIM, and LPIPS results as Point-SLAM [30], although the comparison is not fair as Point-SLAM has the unfair advantage as it takes the ground-truth depth of these images as an input for where to sample its 3D volume for rendering. Our approach achieves much better results than the other baselines Vox-Fusion [46] and NICE-SLAM [54], improving over both by around 10dB in PSNR." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.81 + ], + "angle": 0, + "content": "In general, we believe that the rendering results on Replica in Table 2 are irrelevant because the rendering performance is evaluated on the same training views that were passed in as input, and methods can simply have a high capacity and overfit to these images. We only show this as this is the de-facto evaluation for prior methods, and we wish to have some way to compare against them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Hence, a better evaluation is to evaluate novel-view rendering. However, all current SLAM benchmarks don't have a hold-out set of images separate from the camera trajectory that the SLAM algorithm estimates, so they cannot be used for this purpose. Therefore, we set up a novel benchmark for this using the new high-quality ScanNet++ [49] dataset." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "21362" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.09, + 0.477, + 0.254 + ], + "angle": 0, + "content": "
MethodsMetricsAvg.R0R1R2Of0Of1Of2Of3Of4
Vox-Fusion [46]PSNR ↑24.4122.3922.3623.9227.7929.8320.3323.4725.21
SSIM ↑0.800.680.750.800.860.880.790.800.85
LPIPS ↓0.240.300.270.230.240.180.240.210.20
NICE-SLAM [54]PSNR ↑24.4222.1222.4724.5229.0730.3419.6622.2324.94
SSIM ↑0.810.690.760.810.870.890.800.800.86
LPIPS ↓0.230.330.270.210.230.180.240.210.20
Point-SLAM [30]PSNR ↑35.1732.4034.0835.5038.2639.1633.9933.4833.49
SSIM ↑0.980.970.980.980.980.990.960.960.98
LPIPS ↓0.120.110.120.110.100.120.160.130.14
SplaTAMPSNR ↑34.1132.8633.8935.2538.2639.1731.9729.7031.81
SSIM ↑0.970.980.970.980.980.980.970.950.95
LPIPS ↓0.100.070.100.080.090.090.100.120.15
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.264, + 0.471, + 0.349 + ], + "angle": 0, + "content": "Table 2. Quantitative Train View Rendering Performance on Replica [35]. SplaTAM is comparable to the SOTA baseline, Point-SLAM [30] and consistently outperforms the other dense SLAM methods by a large margin. Numbers for the baselines are taken from Point-SLAM [30]. Note that Point-SLAM uses ground-truth depth for rendering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.47, + 0.527 + ], + "angle": 0, + "content": "The results for both novel-view and training-view rendering on this ScanNet++ benchmark can be found in Table 3. Our approach achieves a good novel-view synthesis result of 24.41 PSNR on average and slightly higher on training views with 27.98 PSNR. Note that for novel-view synthesis, we use the ground-truth pose of the novel view to align it with the origin of the SLAM map, i.e., the first SLAM frame. Since Point-SLAM [30] fails to successfully estimate the camera poses and build a good map, it also completely fails on the task of novel-view synthesis." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.619 + ], + "angle": 0, + "content": "We can also evaluate the geometric reconstruction of the scene by evaluating the rendered depth and comparing it to the ground-truth depth, again for both training and novel views. Our method obtains an incredibly accurate reconstruction with a depth error of only around \\(2\\mathrm{cm}\\) in novel views and \\(1.3\\mathrm{cm}\\) in training views." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.619, + 0.47, + 0.77 + ], + "angle": 0, + "content": "Visual results of both novel-view and training-view rendering for RGB and depth can be seen in Fig. 3. As can be seen, our methods achieve visually excellent results over both scenes for both novel and training views. In contrast, Point-SLAM [30] fails at camera-pose tracking and overfits to the training views, and isn't able to successfully render novel views at all. Point-SLAM also takes the ground-truth depth as an input for rendering to determine where to sample, and as such the depth maps look similar to the ground-truth, while color rendering is completely wrong." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.77, + 0.47, + 0.847 + ], + "angle": 0, + "content": "With this novel benchmark that is able to correctly evaluate Novel-View Synthesis and SLAM simultaneously, as well as our approach as a strong initial baseline for this benchmark, we hope to inspire many future approaches that improve upon these results for both tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Color and Depth Loss Ablation. Our SplaTAM involves fitting the camera poses (during tracking) and the scene map (during mapping) using both a photometric (RGB) and" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.089, + 0.91, + 0.213 + ], + "angle": 0, + "content": "
MethodsMetricsNovel ViewTraining View
Avg.S1S2Avg.S1S2
Point-SLAM [30]PSNR [dB] ↑11.9112.1011.7314.4614.6214.30
SSIM ↑0.280.310.260.380.350.41
LPIPS ↓0.680.620.740.650.680.62
Depth L1 [cm] ↓XXXXXX
SplaTAMPSNR [dB] ↑24.4123.9924.8427.9827.8228.14
SSIM ↑0.880.880.870.940.940.94
LPIPS ↓0.240.210.260.120.120.13
Depth L1 [cm] ↓2.071.912.231.280.931.64
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.223, + 0.894, + 0.294 + ], + "angle": 0, + "content": "Table 3. Novel & Train View Rendering Performance on ScanNet++ [49]. SplaTAM provides high-fidelity performance on both training views seen during SLAM and held-out novel views from any camera pose. On the other hand, Point-SLAM [30] requires ground-truth depth & performs poorly." + }, + { + "type": "table", + "bbox": [ + 0.522, + 0.306, + 0.872, + 0.375 + ], + "angle": 0, + "content": "
Track. ColorMap. ColorTrack. DepthMap. DepthATE [cm]↓Dep. L1 [cm]↓PSNR [dB]↑
XX✓✓86.03XX
✓✓XX1.3812.5831.30
✓✓✓✓0.270.4932.81
" + }, + { + "type": "table_caption", + "bbox": [ + 0.513, + 0.385, + 0.88, + 0.4 + ], + "angle": 0, + "content": "Table 4. Color & Depth Loss Ablation on Replica/Room 0." + }, + { + "type": "table", + "bbox": [ + 0.545, + 0.414, + 0.85, + 0.492 + ], + "angle": 0, + "content": "
Velo. \nProp.Sil. \nMaskSil. \nThresh.ATE \n[cm]↓Dep. L1 \n[cm]↓PSNR \n[dB]↑
X✓0.992.952.1525.40
✓X0.99115.800.2914.16
✓✓0.51.300.7431.36
✓✓0.990.270.4932.81
" + }, + { + "type": "table_caption", + "bbox": [ + 0.517, + 0.502, + 0.875, + 0.516 + ], + "angle": 0, + "content": "Table 5. Camera Tracking Ablations on Replica/Room 0." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.544, + 0.892, + 0.771 + ], + "angle": 0, + "content": "depth loss. In Table 4, we ablate the decision to use both and investigate the performance of only one or the other for both tracking and mapping. We do this using Room 0 of Replica. With only depth our method completely fails to track the camera trajectory, because the L1 depth loss doesn't provide adequate information in the x-y image plane. Using only an RGB loss successfully tracks the camera trajectory (although with more than \\(5\\mathrm{x}\\) the error as using both). Both the RGB and depth work together to achieve excellent results. With only the color loss, reconstruction PSNR is really high, only 1.5 PSNR lower than the full model. However, the depth L1 is much higher using only color vs directly optimizing this depth error. In the color-only experiments, the depth is not used for tracking & mapping, but it is used for the densification and initialization of Gaussians." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Camera Tracking Ablation. In Table 5, we ablate three aspects of our camera tracking: (1) the use of forward velocity propagation, (2) the use of a silhouette mask to mask out invalid map areas in the loss, and (3) setting the silhouette threshold to 0.99 instead of 0.5. All three are critical to excellent results. Without forward velocity propagation, tracking still works, but the overall error is more than \\(10\\mathrm{x}\\) higher, which subsequently degrades the map and render" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21363" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.904, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.275, + 0.895, + 0.332 + ], + "angle": 0, + "content": "Figure 3. Renderings on ScanNet++ [49]. Our method, SplaTAM, renders color & depth for the novel & train views with fidelity comparable to the ground truth. It can also be observed that Point-SLAM [30] fails to provide good renderings on both novel & train view images. Note that Point-SLAM (PS) uses the ground-truth depth to render the train & novel view images. Despite the use of ground-truth depth, the failure of PS can be attributed to the failure of tracking as shown in Tab. 1." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.355, + 0.465, + 0.433 + ], + "angle": 0, + "content": "
MethodsTracking /IterationMapping /IterationTracking /FrameMapping /FrameATE RMSE [cm] ↓
NICE-SLAM [54]30 ms166 ms1.18 s2.04 s0.97
Point-SLAM [30]19 ms30 ms0.76 s4.50 s0.61
SplaTAM25 ms24 ms1.00 s1.44 s0.27
SplaTAM-S19 ms22 ms0.19 s0.33 s0.39
" + }, + { + "type": "table_caption", + "bbox": [ + 0.104, + 0.442, + 0.443, + 0.456 + ], + "angle": 0, + "content": "Table 6. Runtime on Replica/R0 using a RTX 3080 Ti." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.482, + 0.47, + 0.558 + ], + "angle": 0, + "content": "ing. Silhouette is critical as without it tracking completely fails. Setting the silhouette threshold to 0.99 allows the loss to be applied on well-optimized pixels in the map, thereby leading to an important \\(5\\mathrm{x}\\) reduction in the error compared to the threshold of 0.5, which is used for the densification." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.563, + 0.47, + 0.806 + ], + "angle": 0, + "content": "Runtime Comparison. In Table 6, we compare our runtime to NICE-SLAM [54] and Point-SLAM [30] on a Nvidia RTX 3080 Ti. Each iteration of our approach renders a full \\(1200 \\times 980\\) pixel image (\\(\\sim 1.2\\) mil pixels) to apply the loss for both tracking and mapping. Other methods use only 200 pixels for tracking and 1000 pixels for mapping each iteration (but attempt to cleverly sample these pixels). Even though we differentiably render 3 orders of magnitude more pixels, our approach incurs similar runtime, primarily due to the efficiency of rasterizing 3D Gaussians. Additionally, we show a version of our method with fewer iterations and half-resolution densification, SplaTAM-S, which works 5x faster with only a minor degradation in performance. In particular, SplaTAM uses 40 and 60 iterations per frame for tracking & mapping respectively on Replica, while SplaTAM-S uses 10 and 15 iterations per frame." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Limitations & Future Work. Although SplaTAM achieves state-of-the-art performance, we find our method to show some sensitivity to motion blur, large depth noise, and aggressive rotation. We believe a possible solution would be to temporally model these effects and wish to tackle this in future work. Furthermore, SplaTAM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.895, + 0.435 + ], + "angle": 0, + "content": "can be scaled up to large-scale scenes through efficient representations like OpenVDB [24]. Finally, our method requires known camera intrinsics and dense depth as input for performing SLAM, and removing these dependencies is an interesting avenue for the future." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.448, + 0.62, + 0.464 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.685 + ], + "angle": 0, + "content": "We present SPLaTAM, a novel SLAM system that leverages 3D Gaussians as its underlying map representation to enable fast rendering and dense optimization, explicit knowledge of map spatial extent, and streamlined map densification. We demonstrate its effectiveness in achieving state-of-the-art results in camera pose estimation, scene reconstruction, and novel-view synthesis. We believe that SPLaTAM not only sets a new benchmark in both the SLAM and novel-view synthesis domains but also opens up exciting avenues, where the integration of 3D Gaussian Splatting with SLAM offers a robust framework for further exploration and innovation in scene understanding. Our work underscores the potential of this integration, paving the way for more sophisticated and efficient SLAM systems in the future." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.893, + 0.852 + ], + "angle": 0, + "content": "Acknowledgments. This work was supported in part by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. This work used Bridges-2 at PSC through allocation cis220039p from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program which is supported by NSF grants #2138259, #2138286, #2138307, #2137603, and #213296, and also supported by a hardware grant from Nvidia." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.852, + 0.894, + 0.9 + ], + "angle": 0, + "content": "The authors thank Yao He for his support with testing ORB-SLAM3 & Jeff Tan for testing the code & demos. We also thank Chonghyuk (Andrew) Song, Margaret Hansen, John Kim & Michael Kaess for their insightful feedback & discussion on initial versions of the work." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "21364" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Michael Bloesch, Jan Czarnowski, Ronald Clark, Stefan Leutenegger, and Andrew J Davison. Codeslam—learning a compact, optimisable representation for dense visual slam. In CVPR, 2018. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.472, + 0.24 + ], + "angle": 0, + "content": "[2] Cesar Cadena, Luca Carlone, Henry Carrillo, Yasir Latif, Davide Scaramuzza, José Neira, Ian Reid, and John J Leonard. 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Nicer-slam: Neural implicit scene encoding for rgb slam. arXiv preprint arXiv:2302.03594, 2023. 1, 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "21366" + } + ] +] \ No newline at end of file diff --git a/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/177d5eaf-8449-4cd5-ba1f-ab6fb569d8d8_origin.pdf b/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/177d5eaf-8449-4cd5-ba1f-ab6fb569d8d8_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..82841dea9e6e0aa95c153922ea8053b381c2abb9 --- /dev/null +++ b/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/177d5eaf-8449-4cd5-ba1f-ab6fb569d8d8_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:740197e6521d1f8bbb062e72d16e9a333dad6180c8730071e4b0712b7ae7ceda +size 752496 diff --git a/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/full.md b/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/full.md new file mode 100644 index 0000000000000000000000000000000000000000..08bab172d0fa3667df3106c7a848aa8a4beb9a20 --- /dev/null +++ b/2024/SplaTAM_ Splat Track & Map 3D Gaussians for Dense RGB-D SLAM/full.md @@ -0,0 +1,342 @@ +# SplaTAM: Splat, Track & Map 3D Gaussians for Dense RGB-D SLAM SPLa-tam.github.io + +Nikhil Keetha1, Jay Karhade1, Krishna Murthy Jatavallabhula2, Gengshan Yang1, Sebastian Scherer1, Deva Ramanan1, and Jonathon Luiten1 + +$^{1}$ CMU $^{2}$ MIT + +![](images/173b35c76566c5aec6a5d52976453d8c9663367484fda2c2b0bfa32e75644165.jpg) +Novel View + +![](images/ad32ba380c57d10fbf88f9441109cd65b238d7782cc2350176db8e83a5d4b8c8.jpg) +Train View + +![](images/555b0db5ce150c21d850a6c2cb8d9fcd098f5f2a91afb3d8fc8a5daac5d0f544.jpg) +PSNR: 27.4 dB + +![](images/ddf7b45935a4d5ba19feabef286a78c7d7f9469b2c3196ede6b050196af800af.jpg) +Ground Truth + +![](images/0028961f5fa277644ec0430c1c99f86dc61a24e2bdc0a304ad5f82328a7bbb62.jpg) +Depth L1: 0.9 cm +SplaTAM + +![](images/77bd9d08e41faeb92a29ceb0caa816db7e7724630c0268a4f14fabd565be1c50.jpg) + +![](images/ccd6049fda276dd9ae8a3f13993d2a3909e1d3b974203d8553e1aabe4769f25e.jpg) +PSNR: 24.2 dB +Figure 1. SPLaTAM enables precise camera tracking and high-fidelity reconstruction for dense simultaneous localization and mapping (SLAM) in challenging real-world scenarios. SPLaTAM achieves this by online optimization of an explicit volumetric representation, 3D Gaussian Splatting [14], using differentiable rendering. Left: We showcase the high-fidelity 3D Gaussian Map along with the train (SLAM-input) & novel view camera frustums. It can be noticed that SPLaTAM achieves sub-cm localization despite the large motion between subsequent cameras in the texture-less environment. This is particularly challenging for state-of-the-art baselines leading to the failure of tracking. Right: SPLaTAM enables photo-realistic rendering of both train & novel views at 400 FPS for a resolution of $876 \times 584$ . + +![](images/c17ffd141d9b091cd6624a0418a96309d67f5a32e4100db0aeed5a8bd42e30e3.jpg) +Ground Truth + +![](images/7c703e8740815dddb91c567c048227810e228546173da7ef9f7c3ee895ac97ac.jpg) +Depth L1: 1.9 cm +SplaTAM + +# Abstract + +Dense simultaneous localization and mapping (SLAM) is crucial for robotics and augmented reality applications. However, current methods are often hampered by the nonvolumetric or implicit way they represent a scene. This work introduces SplaTAM, an approach that, for the first time, leverages explicit volumetric representations, i.e., 3D Gaussians, to enable high-fidelity reconstruction from a single unposed RGB-D camera, surpassing the capabilities of existing methods. SplaTAM employs a simple online tracking and mapping system tailored to the underlying Gaussian representation. It utilizes a silhouette mask to elegantly capture the presence of scene density. This combination enables several benefits over prior representations, including fast rendering and dense optimization, quickly determining if areas have been previously mapped, and structured map expansion by adding more Gaussians. Extensive experiments show that SplaTAM achieves up to $2 \times$ superior performance in camera pose estimation, map construction, and novel-view synthesis over existing methods, paving the way for more immersive high-fidelity SLAM applications. + +# 1. Introduction + +Visual simultaneous localization and mapping (SLAM)—the task of estimating the pose of a vision sensor (such as a depth camera) and a map of the environment—is an essential capability for vision or robotic systems to operate in previously unseen 3D environments. For the past three decades, SLAM research has extensively centered around the question of map representation—resulting in a variety of sparse [2, 3, 7, 23], dense [4, 6, 8, 13, 15, 25, 26, 34, 42, 43], and neural scene representations [21, 29, 30, 37, 46, 55]. Map representation is a fundamental choice that dramatically impacts the design of every processing block within the SLAM system, as well as of the downstream tasks that depend on the outputs of SLAM. + +In terms of dense visual SLAM, the most successful handcrafted representations are points, surfels/flats, and signed distance fields. While systems based on such map representations have matured to production level over the past years, there are still significant shortcomings that need to be addressed. Tracking explicit representations relies crucially on the availability of rich 3D geometric fea + +tures and high-framerate captures. Furthermore, these approaches only reliably explain the observed parts of the scene; many applications, such as mixed reality and high-fidelity 3D capture, require techniques that can also explain/synthesize unobserved/novel camera viewpoints [32]. + +The shortcomings of handcrafted representations, combined with the emergence of radiance field representations [21] for high-quality image synthesis, have fueled a recent class of methods that attempt to encode the scene into the weight space of a neural network. These radiance-field-based SLAM algorithms [30, 54] benefit from high-fidelity global maps and image reconstruction losses that capture dense photometric information via differentiable rendering. However, current methods use implicit neural representations to model the volumetric radiance fields, which causes a number of issues in the SLAM setting - they are computationally inefficient, not easy to edit, do not model spatial geometry explicitly, and suffer from catastrophic forgetting. + +In this context, we explore the question, "How can one use an explicit volumetric representation to design a SLAM solution?" Specifically, we use a radiance field based on 3D Gaussians [14] to Splat (Render), Track, and Map for SLAM. We believe that this representation has the following benefits over existing map representations: + +- Fast rendering and rich optimization: Gaussian Splating can be rendered at speeds up to 400 FPS, making it significantly faster to visualize and optimize than implicit alternatives. The key enabling factor for fast optimization is the rasterization of 3D primitives. We introduce several simple modifications that make splattering even faster for SLAM, including the removal of view-dependent appearance and the use of isotropic Gaussians. Furthermore, this allows us to use dense photometric loss for SLAM in real-time, in contrast to traditional & implicit map representations that rely respectively on sparse 3D geometric features or pixel-sampling to maintain efficiency. +- Maps with explicit spatial extent: The spatial frontier of the existing map can be easily controlled by adding Gaussians only in parts of the scene that have been observed in the past. Given a new image frame, this allows one to efficiently identify which portions of the scene are new content (outside the map's spatial frontier) by rendering a silhouette. This is crucial for camera tracking as we only want to compare mapped areas of the scene to new images. However, this is difficult for implicit map representations, as the network is subject to global changes during gradient-based optimization for the unmapped space. +- Explicit map: We can arbitrarily increase the map capacity by simply adding more Gaussians. Furthermore, this explicit volumetric representation enables us to edit parts of the scene, while still allowing photo-realistic rendering. Implicit approaches cannot easily increase their capacity or edit their represented scene. + +- Direct gradient flow to parameters: As the scene is represented by Gaussians with physical 3D locations, colors, and sizes, there is a direct, almost linear (projective) gradient flow between the parameters and the rendering. Because camera motion can be thought of as keeping the camera still and moving the scene, we also have a direct gradient into the camera parameters, which enables fast optimization. Neural-based representations don't have this as the gradient needs to flow through (potentially many) non-linear neural network layers. + +Given all of the above advantages, an explicit volumetric representation is a natural way for efficiently inferring a high-fidelity spatial map while simultaneously estimating camera motion, as is also visible from Fig. 1. We show across all our experiments on simulated and real data that our approach, SplaTAM, achieves state-of-the-art results compared to all previous approaches for camera pose estimation, map estimation, and novel-view synthesis. + +# 2. Related Work + +In this section, we briefly review various approaches to dense SLAM, with a particular emphasis on recent approaches that leverage implicit representations encoded in overfit neural networks for tracking and mapping. For a more detailed review of traditional SLAM methods, we refer the interested reader to this excellent survey [2]. + +Traditional approaches to dense SLAM have explored a variety of explicit representations, including 2.5D images [15, 34], (truncated) signed-distance functions [6, 25, 26, 42], gaussian mixture models [9, 10] and circular surfels [13, 33, 43]. Of particular relevance to this work is surfels, which are colored circular surface elements and can be optimized in real-time from RGB-D image inputs as shown in [13, 33, 43]. While the aforementioned SLAM approaches do not assume the visibility function to be differentiable, there exist modern differentiable rasterizers that enable gradient flow through depth discontinuities [50]. However, since 2D surfels are discontinuous, they need careful regularization to prevent holes [33, 50]. In this work, we use volumetric (as opposed to surface-only) scene representations in the form of 3D Gaussians, enabling easy continuous optimization for fast and accurate SLAM. + +Pretrained neural network representations have been integrated with traditional SLAM techniques, largely focusing on predicting depth from RGB images. These approaches range from directly integrating depth predictions from a neural network into SLAM [38], to learning a variational autoencoder that decodes compact estimizable latent codes to depth maps [1, 52], to approaches that simultaneously learn to predict a depth cost volume and tracking [53]. + +Implicit scene representations: iMAP [37] first performed both tracking and mapping using neural implicit representations. To improve scalability, NICE-SLAM [54] proposed + +![](images/0b9a3f698960632db53cf77051563ac0360374645a4daad46b89373e8413eee5.jpg) + +![](images/d0f4525f8b1c81d7034ed7562a132f2cd1d6c7f30889f0220a54e124559daef7.jpg) +Figure 2. Overview of SplaTAM. Top-Left: The input to our approach at each timestep is the current RGB-D frame and the 3D Gaussian Map Representation that we have built representing all of the scene seen so far. Top-Right: Step (1) estimates the camera pose for the new image, using silhouette-guided differentiable rendering. Bottom-Right: Step (2) increases the map capacity by adding new Gaussians based on the rendered silhouette and input depth. Bottom-Left: Step (3) updates the underlying Gaussian map with differentiable rendering. + +![](images/54352ae94e06df53469045007024152d1711c7ac296d53a50c81b25e2203af41.jpg) + +![](images/bff135a5897e48faf10bd615be447d8fe6c821dc135ea05b62018b848d002e22.jpg) + +the use of hierarchical multi-feature grids. On similar lines, iSDF [28] used implicit representations to efficiently compute signed-distances, compared to [25, 27]. Following this, a number of works [11, 18, 19, 22, 29, 31, 41, 51, 55], have recently advanced implicit-based SLAM through a number of ways - by reducing catastrophic forgetting via continual learning(experience replay), capturing semantics, incorporating uncertainty, employing efficient resolution hash-frames and encodings, and using improved losses. More recently, Point-SLAM [30], proposes an alternative route, similar to [45] by using neural point clouds and performing volumetric rendering with feature interpolation, offering better 3-D reconstruction, especially for robotics. However, like other implicit representations, volumetric ray sampling greatly limits its efficiency, thereby resorting to optimization over a sparse set of pixels as opposed to per-pixel dense photometric error. Instead, SplaTAM's explicit volumetric radiance model leverages fast rasterization, enabling complete use of per-pixel dense photometric errors. + +3D Gaussian Splatting: Recently, 3D Gaussians have emerged as a promising 3D scene representation [14, 16, 17, 40], in particular with the ability to differentiably render them extremely quickly via splatting [14]. This approach has also been extended to model dynamic scenes [20, 44, 47, 48] with dense 6-DOF motion [20]. Such approaches for both static and dynamic scenes require that each input frame has an accurately known 6-DOF camera pose, in order to successfully optimize the representation. For the first time our approach removes this constraint, simultaneously + +estimating the camera poses while also fitting the underlying Gaussian representation. + +# 3. Method + +SplaTAM is the first dense RGB-D SLAM solution to use 3D Gaussian Splatting [14]. By modeling the world as a collection of 3D Gaussians which can be rendered into high-fidelity color and depth images, we are able to directly use differentiable-rendering and gradient-based-optimization to optimize both the camera pose for each frame and an underlying volumetric discretized map of the world. + +Gaussian Map Representation. We represent the underlying map of the scene as a set of 3D Gaussians. We made a number of simplifications to the representation proposed in [14], by using only view-independent color and forcing Gaussians to be isotropic. This implies each Gaussian is parameterized by only 8 values: three for its RGB color $\mathbf{c}$ , three for its center position $\pmb{\mu} \in \mathbb{R}^3$ , one for its radius $r$ and one for its opacity $o \in [0,1]$ . Each Gaussian influences a point in 3D space $\mathbf{x} \in \mathbb{R}^3$ according to the standard (unnormized) Gaussian equation weighted by its opacity: + +$$ +f (\mathbf {x}) = o \exp \left(- \frac {\| \mathbf {x} - \boldsymbol {\mu} \| ^ {2}}{2 r ^ {2}}\right). \tag {1} +$$ + +Differentiable Rendering via Splatting. The core of our approach is the ability to render high-fidelity color, depth, and silhouette images from our underlying Gaussian Map + +into any possible camera reference frame in a differentiable way. This differentiable rendering allows us to directly calculate the gradients in the underlying scene representation (Gaussians) and camera parameters with respect to the error between the renders and provided RGB-D frames, and update both the Gaussians and camera parameters to minimize this error, thus fitting both accurate camera poses and an accurate volumetric representation of the world. + +Gaussian Splatting [14] renders an RGB image as follows: Given a collection of 3D Gaussians and camera pose, first sort all Gaussians from front-to-back. RGB images can then be efficiently rendered by alpha-compositing the splatted 2D projection of each Gaussian in order in pixel space. The rendered color of pixel $\mathbf{p} = (u,\nu)$ can be written as: + +$$ +C (\mathbf {p}) = \sum_ {i = 1} ^ {n} \mathbf {c} _ {i} f _ {i} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\mathbf {p})), \tag {2} +$$ + +where $f_{i}(\mathbf{p})$ is computed as in Eq. (1) but with $\boldsymbol{\mu}$ and $r$ of the splatted 2D Gaussians in pixel-space: + +$$ +\boldsymbol {\mu} ^ {2 \mathrm {D}} = K \frac {E _ {t} \boldsymbol {\mu}}{d}, \quad r ^ {2 \mathrm {D}} = \frac {f r}{d}, \quad \text {w h e r e} \quad d = \left(E _ {t} \boldsymbol {\mu}\right) _ {z}. \tag {3} +$$ + +Here, $K$ is the (known) camera intrinsic matrix, $E_{t}$ is the extrinsic matrix capturing the rotation and translation of the camera at frame $t$ , $f$ is the (known) focal length, and $d$ is the depth of the $i^{th}$ Gaussian in camera coordinates. + +We propose to similarly differentiably render depth: + +$$ +D (\mathbf {p}) = \sum_ {i = 1} ^ {n} d _ {i} f _ {i} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\mathbf {p})), \tag {4} +$$ + +which can be compared against the input depth map and return gradients with respect to the 3D map. + +We also render a silhouette image to determine visibility - e.g. if a pixel contains information from the current map: + +$$ +S (\mathbf {p}) = \sum_ {i = 1} ^ {n} f _ {i} (\mathbf {p}) \prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\mathbf {p})). \tag {5} +$$ + +SLAM System. We build a SLAM system from our Gaussian representation and differentiable renderer. We begin with a brief overview and then describe each module in detail. Assume we have an existing map (represented via a set of 3D Gaussians) that has been fitted from a set of camera frames 1 to t. Given a new RGB-D frame $t + 1$ , our SLAM system performs the following steps (see Fig. 2): + +(1) Camera Tracking. We minimize the image and depth reconstruction error of the RGB-D frame with respect to camera pose parameters for $t + 1$ , but only evaluate errors over pixels within the visible silhouette. +(2) Gaussian Densification. We add new Gaussians to the map based on the rendered silhouette and input depth. + +(3) Map Update. Given the camera poses from frame 1 to $t + 1$ , we update the parameters of all the Gaussians in the scene by minimizing the RGB and depth errors over all images up to $t + 1$ . In practice, to keep the batch size manageable, a selected subset of keyframes that overlap with the most recent frame are optimized. + +Initialization. For the first frame, the tracking step is skipped, and the camera pose is set to identity. In the densification step, since the rendered silhouette is empty, all pixels are used to initialize new Gaussians. Specifically, for each pixel, we add a new Gaussian with the color of that pixel, the center at the location of the unprojection of that pixel depth, an opacity of 0.5, and a radius equal to having a one-pixel radius upon projection into the 2D image given by dividing the depth by the focal length: + +$$ +r = \frac {D _ {\mathrm {G T}}}{f} \tag {6} +$$ + +Camera Tracking. Camera Tracking aims to estimate the camera pose of the current incoming online RGB-D image. The camera pose is initialized for a new timestep by a constant velocity forward projection of the pose parameters in the camera center + quaternion space. E.g. the camera parameters are initialized using the following: + +$$ +E _ {t + 1} = E _ {t} + \left(E _ {t} - E _ {t - 1}\right) \tag {7} +$$ + +The camera pose is then updated iteratively by gradient-based optimization through differentiably rendering RGB, depth, and silhouette maps, and updating the camera parameters to minimize the following loss while keeping the Gaussian parameters fixed: + +$$ +L _ {t} = \sum_ {\mathbf {p}} \left(S (\mathbf {p}) > 0. 9 9\right) \left(\mathrm {L} _ {1} (D (\mathbf {p})) + 0. 5 \mathrm {L} _ {1} (C (\mathbf {p}))\right) \tag {8} +$$ + +This is an L1 loss on both the depth and color renders, with color weighted down by half. The color weighting is empirically selected, where we observe the range of $C(\mathbf{p})$ to be [0.01, 0.03] & $D(\mathbf{p})$ to be [0.002, 0.006]. We only apply the loss over pixels that are rendered from well-optimized parts of the map by using our rendered visibility silhouette which captures the epistemic uncertainty of the map. This is very important for tracking new camera poses, as often new frames contain new information that hasn't been captured or well optimized in our map yet. The L1 loss also gives a value of 0 if there is no ground-truth depth for a pixel. + +Gaussian Densification. Gaussian Densification aims to initialize new Gaussians in our Map at each incoming online frame. After tracking we have an accurate estimate for the camera pose for this frame, and with a depth image we have + +a good estimate for where Gaussians in the scene should be. However, we don't want to add Gaussians where the current Gaussians already accurately represent the scene geometry. Thus we create a densification mask to determine which pixels should be densified: + +$$ +\begin{array}{l} M (\mathbf {p}) = \left(S (\mathbf {p}) < 0. 5\right) + \\ \left(D _ {\mathrm {G T}} (\mathbf {p}) < D (\mathbf {p})\right) \left(\mathrm {L} _ {1} (D (\mathbf {p})) > \lambda \mathrm {M D E}\right) \tag {9} \\ \end{array} +$$ + +This mask indicates where the map isn't adequately dense ( $S < 0.5$ ), or where there should be new geometry in front of the current estimated geometry (i.e., the ground-truth depth is in front of the predicted depth, and the depth error is greater than $\lambda$ times the median depth error (MDE), where $\lambda$ is empirically selected as 50). For each pixel, based on this mask, we add a new Gaussian following the same procedure as first-frame initialization. + +Gaussian Map Updating. This aims to update the parameters of the 3D Gaussian Map given the set of online camera poses estimated so far. This is done again by differentiable-rendering and gradient-based-optimization, however unlike tracking, in this setting the camera poses are fixed, and the parameters of the Gaussians are updated. + +This is equivalent to the "classic" problem of fitting a radiance field to images with known poses. However, we make two important modifications. Instead of starting from scratch, we warm-start the optimization from the most recently constructed map. We also do not optimize over all previous (key)frames but select frames that are likely to influence the newly added Gaussians. We save each $n^{\mathrm{th}}$ frame as a keyframe and select $k$ frames to optimize, including the current frame, the most recent keyframe, and $k - 2$ previous keyframes which have the highest overlap with the current frame. Overlap is determined by taking the point cloud of the current frame depth map and determining the number of points inside the frustum of each keyframe. + +This phase optimizes a similar loss as during tracking, except we don't use the silhouette mask as we want to optimize over all pixels. Furthermore, we add an SSIM loss to RGB rendering and cull useless Gaussians that have near 0 opacity or are too large, as done partly in [14]. + +# 4. Experimental Setup + +Datasets and Evaluation Settings. We evaluate our approach on four datasets: ScanNet++ [49], Replica [35], TUM-RGBD [36] and the original ScanNet [5]. The last three are chosen in order to follow the evaluation procedure of previous radiance-field-based SLAM methods Point-SLAM [30] and NICE-SLAM [54]. However, we also add ScanNet++ [49] evaluation because none of the + +other three benchmarks have the ability to evaluate rendering quality on hold out novel views and only evaluate camera pose estimation and rendering on the training views. + +Replica [35] is the simplest benchmark as it contains synthetic scenes, highly accurate and complete (synthetic) depth maps, and small displacements between consecutive camera poses. TUM-RGBD [36] and the original ScanNet are harder, especially for dense methods, due to poor RGB and depth image quality as they both use old low-quality cameras. Depth images are quite sparse with lots of missing information, and the color images have a very high amount of motion blur. For ScanNet++ [49] we use the DSLR captures from two scenes (8b5caf3398 (S1) and b20a261fdf (S2)), where complete dense trajectories are present. In contrast to other benchmarks, ScanNet++ color and depth images are very high quality, and provide a second capture loop for each scene to evaluate completely novel hold-out views. However, each camera pose is very far apart from one another making pose-estimation very difficult. The difference between consecutive frames on ScanNet++ is about the same as a 30-frame gap on Replica. For all benchmarks except ScanNet++, we take baseline numbers from Point-SLAM [30]. Similar to Point-SLAM, we evaluate every 5th frame for the training view rendering benchmarking on Replica. Furthermore, for all comparisons to prior baselines, we present results as the average of 3 seeds (0-2) and use seed 0 for the ablations. + +Evaluation Metrics. We follow all evaluation metrics for camera pose estimation and rendering performance as [30]. For measuring RGB rendering performance we use PSNR, SSIM and LPIPS. For depth rendering performance we use Depth L1 loss. For camera pose estimation tracking we use the average absolute trajectory error (ATE RMSE). + +Baselines. The main baseline method we compare to is Point-SLAM [30], the previous state-of-the-art (SOTA) method for dense radiance-field-based SLAM. We also compare to older dense SLAM approaches such as NICE-SLAM [54], Vox-Fusion [46], and ESLAM [12] where appropriate. Lastly, we compare against traditional SLAM systems such as Kintinous [42], ElasticFusion [43], and ORB-SLAM2 [23] on TUM-RGBD, DROID-SLAM [39] on Replica, and ORB-SLAM3 [3] on ScanNet++. + +# 5. Results & Discussion + +In this section, we first discuss our evaluation results on camera pose estimation for the four benchmark datasets. Then, we further showcase our high-fidelity 3D Gaussian reconstructions and provide qualitative and quantitative comparisons of our rendering quality (both for novel views and input training views). Finally, we discuss pipeline ablations and provide a runtime comparison. + +
MethodsAvg.S1S2
Point-SLAM [30]343.8296.7390.8
ORB-SLAM3 [3]158.2156.8159.7
SplaTAM1.20.61.9
+ +ScanNet++[49] + +
MethodsAvg.R0R1R2Of0Of1Of2Of3Of4
DROID-SLAM [39]0.380.530.380.450.350.240.360.330.43
Vox-Fusion [46]3.091.374.701.478.482.042.581.112.94
NICE-SLAM [54]1.060.971.311.070.881.001.061.101.13
ESLAM [12]0.630.710.700.520.570.550.580.720.63
Point-SLAM [30]0.520.610.410.370.380.480.540.690.72
SplaTAM0.360.310.400.290.470.270.290.320.55
+ +Replica [35] + +
MethodsAvg.fr1/ deskfr1/ desk2fr1/ roomfr2/ xyzfr3/ off.
Kintinous [42]4.843.707.107.502.903.00
ElasticFusion [43]6.912.536.8321.491.172.52
ORB-SLAM2 [23]1.981.602.204.700.401.00
NICE-SLAM [54]15.874.264.9934.4931.733.87
Vox-Fusion [46]11.313.526.0019.531.4926.01
Point-SLAM [30]8.924.344.5430.921.313.48
SplaTAM5.483.356.5411.131.245.16
+ +
MethodsAvg.000000590106016901810207
Vox-Fusion [46]26.9068.8424.188.4127.2823.309.41
NICE-SLAM [54]10.7012.0014.007.9010.9013.406.20
Point-SLAM [30]12.1910.247.818.6522.1614.779.54
SplaTAM11.8812.8310.1017.7212.0811.107.46
+ +Orig-ScanNet [5] + +# TUM-RGBD [36] + +Table 1. Online Camera-Pose Estimation Results on Four Datasets (ATE RMSE $\downarrow[\mathrm{cm}]$ ). Our method consistently outperforms all the SOTA-dense baselines on ScanNet++, Replica, and TUM-RGBD, while providing competitive performance on Orig-ScanNet [5]. Best results are highlighted as first, second, and third. Numbers for the baselines on Orig-ScanNet [5], TUM-RGBD [36] and Replica [35] are taken from Point-SLAM [30]. + +Camera Pose Estimation Results. In Table 1, we compare our method's camera pose estimation results to a number of baselines on four datasets [5, 35, 36, 49]. + +On ScanNet++ [49], both SOTA SLAM approaches Point-SLAM [30] and ORB-SLAM3 [3] (RGB-D variant) completely fail to correctly track the camera pose due to the very large displacement between contiguous cameras, and thus give very large pose-estimation errors. In particular, for ORB-SLAM3, we observe that the texture-less ScanNet++ scans cause the tracking to re-initialize multiple times due to the lack of features. In contrast, our approach successfully manages to track the camera over both sequences giving an average trajectory error of only $1.2\mathrm{cm}$ . + +On the relatively easy synthetic Replica [35] dataset, the de-facto evaluation benchmark, our approach reduces the trajectory error over the prior SOTA-dense baseline [30] by more than $30\%$ from $0.52\mathrm{cm}$ to $0.36\mathrm{cm}$ . Furthermore, SPLaTAM provides better or competitive performance to a feature-based tracking method such as DROID-SLAM [39]. + +On TUM-RGBD [36], all the volumetric methods struggle immensely due to both poor depth sensor information (very sparse) and poor RGB image quality (extremely high motion blur). Compared to prior methods in this category [30, 54], SplaTAM still significantly outperforms, decreasing the trajectory error of the prior SOTA in this category [30] by almost $40\%$ , from $8.92\mathrm{cm}$ to $5.48\mathrm{cm}$ . Also, we observe that feature-based methods (ORB-SLAM2 [23]) still outperform dense methods on this benchmark. + +The original ScanNet [5] benchmark has similar issues to TUM-RGBD, where no dense volumetric method is able to obtain results with less than $10\mathrm{cm}$ error & SPLaTAM performs similarly to the two prior SOTA methods [30, 54]. + +Overall these camera pose estimation results are extremely promising and show off the strengths of our SplaTAM method. The results on ScanNet++ show that if you have high-quality clean input images, our approach can successfully and accurately perform SLAM even with extremely large motions between camera positions, which is not something that is possible with previous SOTA approaches such as Point-SLAM [30] and ORB-SLAM3 [3]. + +**Rendering Quality Results.** In Table 2, we evaluate our method's rendering quality on the input views of Replica dataset [35] (as is the standard evaluation approach from Point-SLAM [30] and NICE-SLAM [54]). Our approach achieves similar PSNR, SSIM, and LPIPS results as Point-SLAM [30], although the comparison is not fair as Point-SLAM has the unfair advantage as it takes the ground-truth depth of these images as an input for where to sample its 3D volume for rendering. Our approach achieves much better results than the other baselines Vox-Fusion [46] and NICE-SLAM [54], improving over both by around 10dB in PSNR. + +In general, we believe that the rendering results on Replica in Table 2 are irrelevant because the rendering performance is evaluated on the same training views that were passed in as input, and methods can simply have a high capacity and overfit to these images. We only show this as this is the de-facto evaluation for prior methods, and we wish to have some way to compare against them. + +Hence, a better evaluation is to evaluate novel-view rendering. However, all current SLAM benchmarks don't have a hold-out set of images separate from the camera trajectory that the SLAM algorithm estimates, so they cannot be used for this purpose. Therefore, we set up a novel benchmark for this using the new high-quality ScanNet++ [49] dataset. + +
MethodsMetricsAvg.R0R1R2Of0Of1Of2Of3Of4
Vox-Fusion [46]PSNR ↑24.4122.3922.3623.9227.7929.8320.3323.4725.21
SSIM ↑0.800.680.750.800.860.880.790.800.85
LPIPS ↓0.240.300.270.230.240.180.240.210.20
NICE-SLAM [54]PSNR ↑24.4222.1222.4724.5229.0730.3419.6622.2324.94
SSIM ↑0.810.690.760.810.870.890.800.800.86
LPIPS ↓0.230.330.270.210.230.180.240.210.20
Point-SLAM [30]PSNR ↑35.1732.4034.0835.5038.2639.1633.9933.4833.49
SSIM ↑0.980.970.980.980.980.990.960.960.98
LPIPS ↓0.120.110.120.110.100.120.160.130.14
SplaTAMPSNR ↑34.1132.8633.8935.2538.2639.1731.9729.7031.81
SSIM ↑0.970.980.970.980.980.980.970.950.95
LPIPS ↓0.100.070.100.080.090.090.100.120.15
+ +The results for both novel-view and training-view rendering on this ScanNet++ benchmark can be found in Table 3. Our approach achieves a good novel-view synthesis result of 24.41 PSNR on average and slightly higher on training views with 27.98 PSNR. Note that for novel-view synthesis, we use the ground-truth pose of the novel view to align it with the origin of the SLAM map, i.e., the first SLAM frame. Since Point-SLAM [30] fails to successfully estimate the camera poses and build a good map, it also completely fails on the task of novel-view synthesis. + +We can also evaluate the geometric reconstruction of the scene by evaluating the rendered depth and comparing it to the ground-truth depth, again for both training and novel views. Our method obtains an incredibly accurate reconstruction with a depth error of only around $2\mathrm{cm}$ in novel views and $1.3\mathrm{cm}$ in training views. + +Visual results of both novel-view and training-view rendering for RGB and depth can be seen in Fig. 3. As can be seen, our methods achieve visually excellent results over both scenes for both novel and training views. In contrast, Point-SLAM [30] fails at camera-pose tracking and overfits to the training views, and isn't able to successfully render novel views at all. Point-SLAM also takes the ground-truth depth as an input for rendering to determine where to sample, and as such the depth maps look similar to the ground-truth, while color rendering is completely wrong. + +With this novel benchmark that is able to correctly evaluate Novel-View Synthesis and SLAM simultaneously, as well as our approach as a strong initial baseline for this benchmark, we hope to inspire many future approaches that improve upon these results for both tasks. + +Color and Depth Loss Ablation. Our SplaTAM involves fitting the camera poses (during tracking) and the scene map (during mapping) using both a photometric (RGB) and + +Table 2. Quantitative Train View Rendering Performance on Replica [35]. SplaTAM is comparable to the SOTA baseline, Point-SLAM [30] and consistently outperforms the other dense SLAM methods by a large margin. Numbers for the baselines are taken from Point-SLAM [30]. Note that Point-SLAM uses ground-truth depth for rendering. + +
MethodsMetricsNovel ViewTraining View
Avg.S1S2Avg.S1S2
Point-SLAM [30]PSNR [dB] ↑11.9112.1011.7314.4614.6214.30
SSIM ↑0.280.310.260.380.350.41
LPIPS ↓0.680.620.740.650.680.62
Depth L1 [cm] ↓XXXXXX
SplaTAMPSNR [dB] ↑24.4123.9924.8427.9827.8228.14
SSIM ↑0.880.880.870.940.940.94
LPIPS ↓0.240.210.260.120.120.13
Depth L1 [cm] ↓2.071.912.231.280.931.64
+ +Table 3. Novel & Train View Rendering Performance on ScanNet++ [49]. SplaTAM provides high-fidelity performance on both training views seen during SLAM and held-out novel views from any camera pose. On the other hand, Point-SLAM [30] requires ground-truth depth & performs poorly. + +
Track. ColorMap. ColorTrack. DepthMap. DepthATE [cm]↓Dep. L1 [cm]↓PSNR [dB]↑
XX✓✓86.03XX
✓✓XX1.3812.5831.30
✓✓✓✓0.270.4932.81
+ +Table 4. Color & Depth Loss Ablation on Replica/Room 0. + +
Velo. +Prop.Sil. +MaskSil. +Thresh.ATE +[cm]↓Dep. L1 +[cm]↓PSNR +[dB]↑
X✓0.992.952.1525.40
✓X0.99115.800.2914.16
✓✓0.51.300.7431.36
✓✓0.990.270.4932.81
+ +Table 5. Camera Tracking Ablations on Replica/Room 0. + +depth loss. In Table 4, we ablate the decision to use both and investigate the performance of only one or the other for both tracking and mapping. We do this using Room 0 of Replica. With only depth our method completely fails to track the camera trajectory, because the L1 depth loss doesn't provide adequate information in the x-y image plane. Using only an RGB loss successfully tracks the camera trajectory (although with more than $5\mathrm{x}$ the error as using both). Both the RGB and depth work together to achieve excellent results. With only the color loss, reconstruction PSNR is really high, only 1.5 PSNR lower than the full model. However, the depth L1 is much higher using only color vs directly optimizing this depth error. In the color-only experiments, the depth is not used for tracking & mapping, but it is used for the densification and initialization of Gaussians. + +Camera Tracking Ablation. In Table 5, we ablate three aspects of our camera tracking: (1) the use of forward velocity propagation, (2) the use of a silhouette mask to mask out invalid map areas in the loss, and (3) setting the silhouette threshold to 0.99 instead of 0.5. All three are critical to excellent results. Without forward velocity propagation, tracking still works, but the overall error is more than $10\mathrm{x}$ higher, which subsequently degrades the map and render + +![](images/a3e76135e2f46b1b248703f25e92a4fb2206ea420a9e3065eae419c9e5624b96.jpg) +Figure 3. Renderings on ScanNet++ [49]. Our method, SplaTAM, renders color & depth for the novel & train views with fidelity comparable to the ground truth. It can also be observed that Point-SLAM [30] fails to provide good renderings on both novel & train view images. Note that Point-SLAM (PS) uses the ground-truth depth to render the train & novel view images. Despite the use of ground-truth depth, the failure of PS can be attributed to the failure of tracking as shown in Tab. 1. + +
MethodsTracking /IterationMapping /IterationTracking /FrameMapping /FrameATE RMSE [cm] ↓
NICE-SLAM [54]30 ms166 ms1.18 s2.04 s0.97
Point-SLAM [30]19 ms30 ms0.76 s4.50 s0.61
SplaTAM25 ms24 ms1.00 s1.44 s0.27
SplaTAM-S19 ms22 ms0.19 s0.33 s0.39
+ +Table 6. Runtime on Replica/R0 using a RTX 3080 Ti. + +ing. Silhouette is critical as without it tracking completely fails. Setting the silhouette threshold to 0.99 allows the loss to be applied on well-optimized pixels in the map, thereby leading to an important $5\mathrm{x}$ reduction in the error compared to the threshold of 0.5, which is used for the densification. + +Runtime Comparison. In Table 6, we compare our runtime to NICE-SLAM [54] and Point-SLAM [30] on a Nvidia RTX 3080 Ti. Each iteration of our approach renders a full $1200 \times 980$ pixel image ( $\sim 1.2$ mil pixels) to apply the loss for both tracking and mapping. Other methods use only 200 pixels for tracking and 1000 pixels for mapping each iteration (but attempt to cleverly sample these pixels). Even though we differentiably render 3 orders of magnitude more pixels, our approach incurs similar runtime, primarily due to the efficiency of rasterizing 3D Gaussians. Additionally, we show a version of our method with fewer iterations and half-resolution densification, SplaTAM-S, which works 5x faster with only a minor degradation in performance. In particular, SplaTAM uses 40 and 60 iterations per frame for tracking & mapping respectively on Replica, while SplaTAM-S uses 10 and 15 iterations per frame. + +Limitations & Future Work. Although SplaTAM achieves state-of-the-art performance, we find our method to show some sensitivity to motion blur, large depth noise, and aggressive rotation. We believe a possible solution would be to temporally model these effects and wish to tackle this in future work. Furthermore, SplaTAM + +can be scaled up to large-scale scenes through efficient representations like OpenVDB [24]. Finally, our method requires known camera intrinsics and dense depth as input for performing SLAM, and removing these dependencies is an interesting avenue for the future. + +# 6. Conclusion + +We present SPLaTAM, a novel SLAM system that leverages 3D Gaussians as its underlying map representation to enable fast rendering and dense optimization, explicit knowledge of map spatial extent, and streamlined map densification. We demonstrate its effectiveness in achieving state-of-the-art results in camera pose estimation, scene reconstruction, and novel-view synthesis. We believe that SPLaTAM not only sets a new benchmark in both the SLAM and novel-view synthesis domains but also opens up exciting avenues, where the integration of 3D Gaussian Splatting with SLAM offers a robust framework for further exploration and innovation in scene understanding. Our work underscores the potential of this integration, paving the way for more sophisticated and efficient SLAM systems in the future. + +Acknowledgments. This work was supported in part by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. This work used Bridges-2 at PSC through allocation cis220039p from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program which is supported by NSF grants #2138259, #2138286, #2138307, #2137603, and #213296, and also supported by a hardware grant from Nvidia. + +The authors thank Yao He for his support with testing ORB-SLAM3 & Jeff Tan for testing the code & demos. 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SPLaTAM enables precise camera tracking and high-fidelity reconstruction for dense simultaneous localization and mapping (SLAM) in challenging real-world scenarios. SPLaTAM achieves this by online optimization of an explicit volumetric representation, 3D Gaussian Splatting [14], using differentiable rendering. Left: We showcase the high-fidelity 3D Gaussian Map along with the train (SLAM-input) & novel view camera frustums. It can be noticed that SPLaTAM achieves sub-cm localization despite the large motion between subsequent cameras in the texture-less environment. This is particularly challenging for state-of-the-art baselines leading to the failure of tracking. Right: SPLaTAM enables photo-realistic rendering of both train & novel views at 400 FPS for a resolution of " + }, + { + "bbox": [ + 46, + 373, + 547, + 439 + ], + "type": "inline_equation", + "content": "876 \\times 584" + }, + { + "bbox": [ + 46, + 373, + 547, + 439 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 442, + 279, + 498, + 317 + ], + "blocks": [ + { + "bbox": [ + 442, + 279, + 498, + 317 + ], + "lines": [ + { + "bbox": [ + 442, + 279, + 498, + 317 + ], + "spans": [ + { + "bbox": [ + 442, + 279, + 498, + 317 + ], + "type": "image", + "image_path": "c17ffd141d9b091cd6624a0418a96309d67f5a32e4100db0aeed5a8bd42e30e3.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 502, + 290, + 526, + 306 + ], + "lines": [ + { + "bbox": [ + 502, + 290, + 526, + 306 + ], + "spans": [ + { + "bbox": [ + 502, + 290, + 526, + 306 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 442, + 317, + 499, + 355 + ], + "blocks": [ + { + "bbox": [ + 442, + 317, + 499, + 355 + ], + "lines": [ + { + "bbox": [ + 442, + 317, + 499, + 355 + ], + "spans": [ + { + "bbox": [ + 442, + 317, + 499, + 355 + ], + "type": "image", + "image_path": "7c703e8740815dddb91c567c048227810e228546173da7ef9f7c3ee895ac97ac.jpg" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 446, + 356, + 495, + 363 + ], + "lines": [ + { + "bbox": [ + 446, + 356, + 495, + 363 + ], + "spans": [ + { + "bbox": [ + 446, + 356, + 495, + 363 + ], + "type": "text", + "content": "Depth L1: 1.9 cm" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 501, + 331, + 528, + 339 + ], + "lines": [ + { + "bbox": [ + 501, + 331, + 528, + 339 + ], + "spans": [ + { + "bbox": [ + 501, + 331, + 528, + 339 + ], + "type": "text", + "content": "SplaTAM" + } + ] + } + ], + "index": 23, + "angle": 0, + "type": "image_caption" + } + ], + "index": 18 + }, + { + "bbox": [ + 143, + 449, + 192, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 449, + 192, + 460 + ], + "spans": [ + { + "bbox": [ + 143, + 449, + 192, + 460 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 45, + 462, + 290, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 462, + 290, + 702 + ], + "spans": [ + { + "bbox": [ + 45, + 462, + 290, + 702 + ], + "type": "text", + "content": "Dense simultaneous localization and mapping (SLAM) is crucial for robotics and augmented reality applications. However, current methods are often hampered by the nonvolumetric or implicit way they represent a scene. This work introduces SplaTAM, an approach that, for the first time, leverages explicit volumetric representations, i.e., 3D Gaussians, to enable high-fidelity reconstruction from a single unposed RGB-D camera, surpassing the capabilities of existing methods. SplaTAM employs a simple online tracking and mapping system tailored to the underlying Gaussian representation. It utilizes a silhouette mask to elegantly capture the presence of scene density. This combination enables several benefits over prior representations, including fast rendering and dense optimization, quickly determining if areas have been previously mapped, and structured map expansion by adding more Gaussians. Extensive experiments show that SplaTAM achieves up to " + }, + { + "bbox": [ + 45, + 462, + 290, + 702 + ], + "type": "inline_equation", + "content": "2 \\times" + }, + { + "bbox": [ + 45, + 462, + 290, + 702 + ], + "type": "text", + "content": " superior performance in camera pose estimation, map construction, and novel-view synthesis over existing methods, paving the way for more immersive high-fidelity SLAM applications." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 307, + 449, + 386, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 449, + 386, + 460 + ], + "spans": [ + { + "bbox": [ + 307, + 449, + 386, + 460 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 472, + 546, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 546, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 546, + 628 + ], + "type": "text", + "content": "Visual simultaneous localization and mapping (SLAM)—the task of estimating the pose of a vision sensor (such as a depth camera) and a map of the environment—is an essential capability for vision or robotic systems to operate in previously unseen 3D environments. For the past three decades, SLAM research has extensively centered around the question of map representation—resulting in a variety of sparse [2, 3, 7, 23], dense [4, 6, 8, 13, 15, 25, 26, 34, 42, 43], and neural scene representations [21, 29, 30, 37, 46, 55]. Map representation is a fundamental choice that dramatically impacts the design of every processing block within the SLAM system, as well as of the downstream tasks that depend on the outputs of SLAM." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 715 + ], + "type": "text", + "content": "In terms of dense visual SLAM, the most successful handcrafted representations are points, surfels/flats, and signed distance fields. While systems based on such map representations have matured to production level over the past years, there are still significant shortcomings that need to be addressed. Tracking explicit representations relies crucially on the availability of rich 3D geometric fea" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21357" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 286, + 133 + ], + "type": "text", + "content": "tures and high-framerate captures. Furthermore, these approaches only reliably explain the observed parts of the scene; many applications, such as mixed reality and high-fidelity 3D capture, require techniques that can also explain/synthesize unobserved/novel camera viewpoints [32]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 135, + 286, + 290 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 135, + 286, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 135, + 286, + 290 + ], + "type": "text", + "content": "The shortcomings of handcrafted representations, combined with the emergence of radiance field representations [21] for high-quality image synthesis, have fueled a recent class of methods that attempt to encode the scene into the weight space of a neural network. These radiance-field-based SLAM algorithms [30, 54] benefit from high-fidelity global maps and image reconstruction losses that capture dense photometric information via differentiable rendering. However, current methods use implicit neural representations to model the volumetric radiance fields, which causes a number of issues in the SLAM setting - they are computationally inefficient, not easy to edit, do not model spatial geometry explicitly, and suffer from catastrophic forgetting." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 293, + 286, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 286, + 364 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 286, + 364 + ], + "type": "text", + "content": "In this context, we explore the question, \"How can one use an explicit volumetric representation to design a SLAM solution?\" Specifically, we use a radiance field based on 3D Gaussians [14] to Splat (Render), Track, and Map for SLAM. We believe that this representation has the following benefits over existing map representations:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 366, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 6, + "blocks": [ + { + "bbox": [ + 47, + 366, + 286, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 286, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 286, + 509 + ], + "type": "text", + "content": "- Fast rendering and rich optimization: Gaussian Splating can be rendered at speeds up to 400 FPS, making it significantly faster to visualize and optimize than implicit alternatives. The key enabling factor for fast optimization is the rasterization of 3D primitives. We introduce several simple modifications that make splattering even faster for SLAM, including the removal of view-dependent appearance and the use of isotropic Gaussians. Furthermore, this allows us to use dense photometric loss for SLAM in real-time, in contrast to traditional & implicit map representations that rely respectively on sparse 3D geometric features or pixel-sampling to maintain efficiency." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 510, + 286, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 510, + 286, + 641 + ], + "spans": [ + { + "bbox": [ + 47, + 510, + 286, + 641 + ], + "type": "text", + "content": "- Maps with explicit spatial extent: The spatial frontier of the existing map can be easily controlled by adding Gaussians only in parts of the scene that have been observed in the past. Given a new image frame, this allows one to efficiently identify which portions of the scene are new content (outside the map's spatial frontier) by rendering a silhouette. This is crucial for camera tracking as we only want to compare mapped areas of the scene to new images. However, this is difficult for implicit map representations, as the network is subject to global changes during gradient-based optimization for the unmapped space." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 642, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 286, + 712 + ], + "type": "text", + "content": "- Explicit map: We can arbitrarily increase the map capacity by simply adding more Gaussians. Furthermore, this explicit volumetric representation enables us to edit parts of the scene, while still allowing photo-realistic rendering. Implicit approaches cannot easily increase their capacity or edit their represented scene." + } + ] + } + ], + "index": 5 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 191 + ], + "type": "text", + "content": "- Direct gradient flow to parameters: As the scene is represented by Gaussians with physical 3D locations, colors, and sizes, there is a direct, almost linear (projective) gradient flow between the parameters and the rendering. Because camera motion can be thought of as keeping the camera still and moving the scene, we also have a direct gradient into the camera parameters, which enables fast optimization. Neural-based representations don't have this as the gradient needs to flow through (potentially many) non-linear neural network layers." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 193, + 545, + 289 + ], + "type": "text", + "content": "Given all of the above advantages, an explicit volumetric representation is a natural way for efficiently inferring a high-fidelity spatial map while simultaneously estimating camera motion, as is also visible from Fig. 1. We show across all our experiments on simulated and real data that our approach, SplaTAM, achieves state-of-the-art results compared to all previous approaches for camera pose estimation, map estimation, and novel-view synthesis." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 299, + 392, + 312 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 299, + 392, + 312 + ], + "spans": [ + { + "bbox": [ + 306, + 299, + 392, + 312 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 319, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 319, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 304, + 319, + 545, + 390 + ], + "type": "text", + "content": "In this section, we briefly review various approaches to dense SLAM, with a particular emphasis on recent approaches that leverage implicit representations encoded in overfit neural networks for tracking and mapping. For a more detailed review of traditional SLAM methods, we refer the interested reader to this excellent survey [2]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 391, + 545, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 391, + 545, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 391, + 545, + 581 + ], + "type": "text", + "content": "Traditional approaches to dense SLAM have explored a variety of explicit representations, including 2.5D images [15, 34], (truncated) signed-distance functions [6, 25, 26, 42], gaussian mixture models [9, 10] and circular surfels [13, 33, 43]. Of particular relevance to this work is surfels, which are colored circular surface elements and can be optimized in real-time from RGB-D image inputs as shown in [13, 33, 43]. While the aforementioned SLAM approaches do not assume the visibility function to be differentiable, there exist modern differentiable rasterizers that enable gradient flow through depth discontinuities [50]. However, since 2D surfels are discontinuous, they need careful regularization to prevent holes [33, 50]. In this work, we use volumetric (as opposed to surface-only) scene representations in the form of 3D Gaussians, enabling easy continuous optimization for fast and accurate SLAM." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 677 + ], + "type": "text", + "content": "Pretrained neural network representations have been integrated with traditional SLAM techniques, largely focusing on predicting depth from RGB images. These approaches range from directly integrating depth predictions from a neural network into SLAM [38], to learning a variational autoencoder that decodes compact estimizable latent codes to depth maps [1, 52], to approaches that simultaneously learn to predict a depth cost volume and tracking [53]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 713 + ], + "type": "text", + "content": "Implicit scene representations: iMAP [37] first performed both tracking and mapping using neural implicit representations. To improve scalability, NICE-SLAM [54] proposed" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21358" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 74, + 293, + 186 + ], + "blocks": [ + { + "bbox": [ + 61, + 74, + 293, + 186 + ], + "lines": [ + { + "bbox": [ + 61, + 74, + 293, + 186 + ], + "spans": [ + { + "bbox": [ + 61, + 74, + 293, + 186 + ], + "type": "image", + "image_path": "0b9a3f698960632db53cf77051563ac0360374645a4daad46b89373e8413eee5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 61, + 186, + 293, + 282 + ], + "blocks": [ + { + "bbox": [ + 61, + 186, + 293, + 282 + ], + "lines": [ + { + "bbox": [ + 61, + 186, + 293, + 282 + ], + "spans": [ + { + "bbox": [ + 61, + 186, + 293, + 282 + ], + "type": "image", + "image_path": "d0f4525f8b1c81d7034ed7562a132f2cd1d6c7f30889f0220a54e124559daef7.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 547, + 335 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 547, + 335 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 547, + 335 + ], + "type": "text", + "content": "Figure 2. Overview of SplaTAM. Top-Left: The input to our approach at each timestep is the current RGB-D frame and the 3D Gaussian Map Representation that we have built representing all of the scene seen so far. Top-Right: Step (1) estimates the camera pose for the new image, using silhouette-guided differentiable rendering. Bottom-Right: Step (2) increases the map capacity by adding new Gaussians based on the rendered silhouette and input depth. Bottom-Left: Step (3) updates the underlying Gaussian map with differentiable rendering." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 299, + 74, + 533, + 186 + ], + "blocks": [ + { + "bbox": [ + 299, + 74, + 533, + 186 + ], + "lines": [ + { + "bbox": [ + 299, + 74, + 533, + 186 + ], + "spans": [ + { + "bbox": [ + 299, + 74, + 533, + 186 + ], + "type": "image", + "image_path": "54352ae94e06df53469045007024152d1711c7ac296d53a50c81b25e2203af41.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 301, + 186, + 531, + 274 + ], + "blocks": [ + { + "bbox": [ + 301, + 186, + 531, + 274 + ], + "lines": [ + { + "bbox": [ + 301, + 186, + 531, + 274 + ], + "spans": [ + { + "bbox": [ + 301, + 186, + 531, + 274 + ], + "type": "image", + "image_path": "bff135a5897e48faf10bd615be447d8fe6c821dc135ea05b62018b848d002e22.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 354, + 289, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 289, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 289, + 582 + ], + "type": "text", + "content": "the use of hierarchical multi-feature grids. On similar lines, iSDF [28] used implicit representations to efficiently compute signed-distances, compared to [25, 27]. Following this, a number of works [11, 18, 19, 22, 29, 31, 41, 51, 55], have recently advanced implicit-based SLAM through a number of ways - by reducing catastrophic forgetting via continual learning(experience replay), capturing semantics, incorporating uncertainty, employing efficient resolution hash-frames and encodings, and using improved losses. More recently, Point-SLAM [30], proposes an alternative route, similar to [45] by using neural point clouds and performing volumetric rendering with feature interpolation, offering better 3-D reconstruction, especially for robotics. However, like other implicit representations, volumetric ray sampling greatly limits its efficiency, thereby resorting to optimization over a sparse set of pixels as opposed to per-pixel dense photometric error. Instead, SplaTAM's explicit volumetric radiance model leverages fast rasterization, enabling complete use of per-pixel dense photometric errors." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "3D Gaussian Splatting: Recently, 3D Gaussians have emerged as a promising 3D scene representation [14, 16, 17, 40], in particular with the ability to differentiably render them extremely quickly via splatting [14]. This approach has also been extended to model dynamic scenes [20, 44, 47, 48] with dense 6-DOF motion [20]. Such approaches for both static and dynamic scenes require that each input frame has an accurately known 6-DOF camera pose, in order to successfully optimize the representation. For the first time our approach removes this constraint, simultaneously" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 355, + 545, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 355, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 305, + 355, + 545, + 380 + ], + "type": "text", + "content": "estimating the camera poses while also fitting the underlying Gaussian representation." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 389, + 362, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 389, + 362, + 402 + ], + "spans": [ + { + "bbox": [ + 306, + 389, + 362, + 402 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 410, + 545, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 545, + 495 + ], + "type": "text", + "content": "SplaTAM is the first dense RGB-D SLAM solution to use 3D Gaussian Splatting [14]. By modeling the world as a collection of 3D Gaussians which can be rendered into high-fidelity color and depth images, we are able to directly use differentiable-rendering and gradient-based-optimization to optimize both the camera pose for each frame and an underlying volumetric discretized map of the world." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": "Gaussian Map Representation. We represent the underlying map of the scene as a set of 3D Gaussians. We made a number of simplifications to the representation proposed in [14], by using only view-independent color and forcing Gaussians to be isotropic. This implies each Gaussian is parameterized by only 8 values: three for its RGB color " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": ", three for its center position " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": ", one for its radius " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": " and one for its opacity " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "o \\in [0,1]" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": ". Each Gaussian influences a point in 3D space " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": " according to the standard (unnormized) Gaussian equation weighted by its opacity:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 364, + 637, + 545, + 665 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 364, + 637, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 364, + 637, + 545, + 665 + ], + "type": "interline_equation", + "content": "f (\\mathbf {x}) = o \\exp \\left(- \\frac {\\| \\mathbf {x} - \\boldsymbol {\\mu} \\| ^ {2}}{2 r ^ {2}}\\right). \\tag {1}", + "image_path": "dcbd2043c8c3e4335b9a8724d13847f34117e81ff632da96fa806a903f7694f4.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Differentiable Rendering via Splatting. The core of our approach is the ability to render high-fidelity color, depth, and silhouette images from our underlying Gaussian Map" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21359" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 167 + ], + "type": "text", + "content": "into any possible camera reference frame in a differentiable way. This differentiable rendering allows us to directly calculate the gradients in the underlying scene representation (Gaussians) and camera parameters with respect to the error between the renders and provided RGB-D frames, and update both the Gaussians and camera parameters to minimize this error, thus fitting both accurate camera poses and an accurate volumetric representation of the world." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 167, + 287, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 167, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 167, + 287, + 240 + ], + "type": "text", + "content": "Gaussian Splatting [14] renders an RGB image as follows: Given a collection of 3D Gaussians and camera pose, first sort all Gaussians from front-to-back. RGB images can then be efficiently rendered by alpha-compositing the splatted 2D projection of each Gaussian in order in pixel space. The rendered color of pixel " + }, + { + "bbox": [ + 46, + 167, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\mathbf{p} = (u,\\nu)" + }, + { + "bbox": [ + 46, + 167, + 287, + 240 + ], + "type": "text", + "content": " can be written as:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 97, + 250, + 287, + 279 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 250, + 287, + 279 + ], + "spans": [ + { + "bbox": [ + 97, + 250, + 287, + 279 + ], + "type": "interline_equation", + "content": "C (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} \\mathbf {c} _ {i} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})), \\tag {2}", + "image_path": "0171a7ae53707190bdc4efaa0e5db87e8182a39127e123df6f36a44060d35671.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "inline_equation", + "content": "f_{i}(\\mathbf{p})" + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "content": " is computed as in Eq. (1) but with " + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "inline_equation", + "content": "\\boldsymbol{\\mu}" + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 47, + 289, + 287, + 314 + ], + "type": "text", + "content": " of the splatted 2D Gaussians in pixel-space:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 51, + 321, + 287, + 345 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 321, + 287, + 345 + ], + "spans": [ + { + "bbox": [ + 51, + 321, + 287, + 345 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} ^ {2 \\mathrm {D}} = K \\frac {E _ {t} \\boldsymbol {\\mu}}{d}, \\quad r ^ {2 \\mathrm {D}} = \\frac {f r}{d}, \\quad \\text {w h e r e} \\quad d = \\left(E _ {t} \\boldsymbol {\\mu}\\right) _ {z}. \\tag {3}", + "image_path": "fb714ff14a24b5f9cd2e5d0176df5b4e9056c027791704f7d6d9490a450c020a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": " is the (known) camera intrinsic matrix, " + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "inline_equation", + "content": "E_{t}" + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": " is the extrinsic matrix capturing the rotation and translation of the camera at frame " + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": " is the (known) focal length, and " + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": " is the depth of the " + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 47, + 353, + 287, + 399 + ], + "type": "text", + "content": " Gaussian in camera coordinates." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 400, + 269, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 400, + 269, + 412 + ], + "spans": [ + { + "bbox": [ + 59, + 400, + 269, + 412 + ], + "type": "text", + "content": "We propose to similarly differentiably render depth:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 97, + 422, + 287, + 452 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 422, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 97, + 422, + 287, + 452 + ], + "type": "interline_equation", + "content": "D (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} d _ {i} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})), \\tag {4}", + "image_path": "f183524cbb18400b605cb6687902f8fe097f5ffe8e8de7062a002b0fcf9f4603.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 457, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 457, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 457, + 287, + 480 + ], + "type": "text", + "content": "which can be compared against the input depth map and return gradients with respect to the 3D map." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 481, + 286, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 481, + 286, + 506 + ], + "spans": [ + { + "bbox": [ + 47, + 481, + 286, + 506 + ], + "type": "text", + "content": "We also render a silhouette image to determine visibility - e.g. if a pixel contains information from the current map:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 102, + 514, + 287, + 544 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 514, + 287, + 544 + ], + "spans": [ + { + "bbox": [ + 102, + 514, + 287, + 544 + ], + "type": "interline_equation", + "content": "S (\\mathbf {p}) = \\sum_ {i = 1} ^ {n} f _ {i} (\\mathbf {p}) \\prod_ {j = 1} ^ {i - 1} (1 - f _ {j} (\\mathbf {p})). \\tag {5}", + "image_path": "cbe843be77b3593f79f0adcc1290294ee689aac7af30700049a22cfe786cb9ab.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 558, + 287, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 558, + 287, + 642 + ], + "spans": [ + { + "bbox": [ + 47, + 558, + 287, + 642 + ], + "type": "text", + "content": "SLAM System. We build a SLAM system from our Gaussian representation and differentiable renderer. We begin with a brief overview and then describe each module in detail. Assume we have an existing map (represented via a set of 3D Gaussians) that has been fitted from a set of camera frames 1 to t. Given a new RGB-D frame " + }, + { + "bbox": [ + 47, + 558, + 287, + 642 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 47, + 558, + 287, + 642 + ], + "type": "text", + "content": ", our SLAM system performs the following steps (see Fig. 2):" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 642, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "type": "text", + "content": "(1) Camera Tracking. We minimize the image and depth reconstruction error of the RGB-D frame with respect to camera pose parameters for " + }, + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 47, + 642, + 287, + 689 + ], + "type": "text", + "content": ", but only evaluate errors over pixels within the visible silhouette." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "(2) Gaussian Densification. We add new Gaussians to the map based on the rendered silhouette and input depth." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "type": "text", + "content": "(3) Map Update. Given the camera poses from frame 1 to " + }, + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "type": "text", + "content": ", we update the parameters of all the Gaussians in the scene by minimizing the RGB and depth errors over all images up to " + }, + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "type": "inline_equation", + "content": "t + 1" + }, + { + "bbox": [ + 306, + 72, + 545, + 144 + ], + "type": "text", + "content": ". In practice, to keep the batch size manageable, a selected subset of keyframes that overlap with the most recent frame are optimized." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 159, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 545, + 266 + ], + "type": "text", + "content": "Initialization. For the first frame, the tracking step is skipped, and the camera pose is set to identity. In the densification step, since the rendered silhouette is empty, all pixels are used to initialize new Gaussians. Specifically, for each pixel, we add a new Gaussian with the color of that pixel, the center at the location of the unprojection of that pixel depth, an opacity of 0.5, and a radius equal to having a one-pixel radius upon projection into the 2D image given by dividing the depth by the focal length:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 405, + 275, + 545, + 300 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 405, + 275, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 405, + 275, + 545, + 300 + ], + "type": "interline_equation", + "content": "r = \\frac {D _ {\\mathrm {G T}}}{f} \\tag {6}", + "image_path": "bdea54c39301f2f39b7096e0c51f1524a8eace6c0440e2b060fd94786fba0e2b.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 312, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 545, + 384 + ], + "type": "text", + "content": "Camera Tracking. Camera Tracking aims to estimate the camera pose of the current incoming online RGB-D image. The camera pose is initialized for a new timestep by a constant velocity forward projection of the pose parameters in the camera center + quaternion space. E.g. the camera parameters are initialized using the following:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 377, + 395, + 545, + 407 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 395, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 377, + 395, + 545, + 407 + ], + "type": "interline_equation", + "content": "E _ {t + 1} = E _ {t} + \\left(E _ {t} - E _ {t - 1}\\right) \\tag {7}", + "image_path": "826ede2e22bf30c19fe386bc2077cfc7f47b73c53bde335b955f2a6668f6fab2.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 416, + 545, + 476 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 416, + 545, + 476 + ], + "spans": [ + { + "bbox": [ + 304, + 416, + 545, + 476 + ], + "type": "text", + "content": "The camera pose is then updated iteratively by gradient-based optimization through differentiably rendering RGB, depth, and silhouette maps, and updating the camera parameters to minimize the following loss while keeping the Gaussian parameters fixed:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 315, + 485, + 545, + 510 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 485, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 315, + 485, + 545, + 510 + ], + "type": "interline_equation", + "content": "L _ {t} = \\sum_ {\\mathbf {p}} \\left(S (\\mathbf {p}) > 0. 9 9\\right) \\left(\\mathrm {L} _ {1} (D (\\mathbf {p})) + 0. 5 \\mathrm {L} _ {1} (C (\\mathbf {p}))\\right) \\tag {8}", + "image_path": "11fef4a65c1c9a91ee2d1e84fe850bcc03a1c03c9333da3cec5a5f3d6fbea4ea.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "type": "text", + "content": "This is an L1 loss on both the depth and color renders, with color weighted down by half. The color weighting is empirically selected, where we observe the range of " + }, + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "type": "inline_equation", + "content": "C(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "type": "text", + "content": " to be [0.01, 0.03] & " + }, + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "type": "inline_equation", + "content": "D(\\mathbf{p})" + }, + { + "bbox": [ + 304, + 519, + 545, + 651 + ], + "type": "text", + "content": " to be [0.002, 0.006]. We only apply the loss over pixels that are rendered from well-optimized parts of the map by using our rendered visibility silhouette which captures the epistemic uncertainty of the map. This is very important for tracking new camera poses, as often new frames contain new information that hasn't been captured or well optimized in our map yet. The L1 loss also gives a value of 0 if there is no ground-truth depth for a pixel." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Gaussian Densification. Gaussian Densification aims to initialize new Gaussians in our Map at each incoming online frame. After tracking we have an accurate estimate for the camera pose for this frame, and with a depth image we have" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21360" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 133 + ], + "type": "text", + "content": "a good estimate for where Gaussians in the scene should be. However, we don't want to add Gaussians where the current Gaussians already accurately represent the scene geometry. Thus we create a densification mask to determine which pixels should be densified:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 144, + 287, + 188 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 144, + 287, + 188 + ], + "spans": [ + { + "bbox": [ + 56, + 144, + 287, + 188 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} M (\\mathbf {p}) = \\left(S (\\mathbf {p}) < 0. 5\\right) + \\\\ \\left(D _ {\\mathrm {G T}} (\\mathbf {p}) < D (\\mathbf {p})\\right) \\left(\\mathrm {L} _ {1} (D (\\mathbf {p})) > \\lambda \\mathrm {M D E}\\right) \\tag {9} \\\\ \\end{array}", + "image_path": "9fb02796a5e1ae1c5626b68693d4d023510fb1b856f836bf6b88b2dc942e8365.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "text", + "content": "This mask indicates where the map isn't adequately dense (" + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "inline_equation", + "content": "S < 0.5" + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "text", + "content": "), or where there should be new geometry in front of the current estimated geometry (i.e., the ground-truth depth is in front of the predicted depth, and the depth error is greater than " + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "text", + "content": " times the median depth error (MDE), where " + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 46, + 196, + 288, + 291 + ], + "type": "text", + "content": " is empirically selected as 50). For each pixel, based on this mask, we add a new Gaussian following the same procedure as first-frame initialization." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 310, + 287, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 287, + 380 + ], + "type": "text", + "content": "Gaussian Map Updating. This aims to update the parameters of the 3D Gaussian Map given the set of online camera poses estimated so far. This is done again by differentiable-rendering and gradient-based-optimization, however unlike tracking, in this setting the camera poses are fixed, and the parameters of the Gaussians are updated." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "spans": [ + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "text", + "content": "This is equivalent to the \"classic\" problem of fitting a radiance field to images with known poses. However, we make two important modifications. Instead of starting from scratch, we warm-start the optimization from the most recently constructed map. We also do not optimize over all previous (key)frames but select frames that are likely to influence the newly added Gaussians. We save each " + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "inline_equation", + "content": "n^{\\mathrm{th}}" + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "text", + "content": " frame as a keyframe and select " + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "text", + "content": " frames to optimize, including the current frame, the most recent keyframe, and " + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "inline_equation", + "content": "k - 2" + }, + { + "bbox": [ + 46, + 382, + 288, + 537 + ], + "type": "text", + "content": " previous keyframes which have the highest overlap with the current frame. Overlap is determined by taking the point cloud of the current frame depth map and determining the number of points inside the frustum of each keyframe." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 538, + 287, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 538, + 287, + 598 + ], + "spans": [ + { + "bbox": [ + 46, + 538, + 287, + 598 + ], + "type": "text", + "content": "This phase optimizes a similar loss as during tracking, except we don't use the silhouette mask as we want to optimize over all pixels. Furthermore, we add an SSIM loss to RGB rendering and cull useless Gaussians that have near 0 opacity or are too large, as done partly in [14]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 609, + 165, + 623 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 165, + 623 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 165, + 623 + ], + "type": "text", + "content": "4. Experimental Setup" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Datasets and Evaluation Settings. We evaluate our approach on four datasets: ScanNet++ [49], Replica [35], TUM-RGBD [36] and the original ScanNet [5]. The last three are chosen in order to follow the evaluation procedure of previous radiance-field-based SLAM methods Point-SLAM [30] and NICE-SLAM [54]. However, we also add ScanNet++ [49] evaluation because none of the" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 108 + ], + "type": "text", + "content": "other three benchmarks have the ability to evaluate rendering quality on hold out novel views and only evaluate camera pose estimation and rendering on the training views." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 110, + 546, + 396 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 546, + 396 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 546, + 396 + ], + "type": "text", + "content": "Replica [35] is the simplest benchmark as it contains synthetic scenes, highly accurate and complete (synthetic) depth maps, and small displacements between consecutive camera poses. TUM-RGBD [36] and the original ScanNet are harder, especially for dense methods, due to poor RGB and depth image quality as they both use old low-quality cameras. Depth images are quite sparse with lots of missing information, and the color images have a very high amount of motion blur. For ScanNet++ [49] we use the DSLR captures from two scenes (8b5caf3398 (S1) and b20a261fdf (S2)), where complete dense trajectories are present. In contrast to other benchmarks, ScanNet++ color and depth images are very high quality, and provide a second capture loop for each scene to evaluate completely novel hold-out views. However, each camera pose is very far apart from one another making pose-estimation very difficult. The difference between consecutive frames on ScanNet++ is about the same as a 30-frame gap on Replica. For all benchmarks except ScanNet++, we take baseline numbers from Point-SLAM [30]. Similar to Point-SLAM, we evaluate every 5th frame for the training view rendering benchmarking on Replica. Furthermore, for all comparisons to prior baselines, we present results as the average of 3 seeds (0-2) and use seed 0 for the ablations." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 405, + 545, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 405, + 545, + 477 + ], + "spans": [ + { + "bbox": [ + 304, + 405, + 545, + 477 + ], + "type": "text", + "content": "Evaluation Metrics. We follow all evaluation metrics for camera pose estimation and rendering performance as [30]. For measuring RGB rendering performance we use PSNR, SSIM and LPIPS. For depth rendering performance we use Depth L1 loss. For camera pose estimation tracking we use the average absolute trajectory error (ATE RMSE)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 487, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 487, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 487, + 545, + 594 + ], + "type": "text", + "content": "Baselines. The main baseline method we compare to is Point-SLAM [30], the previous state-of-the-art (SOTA) method for dense radiance-field-based SLAM. We also compare to older dense SLAM approaches such as NICE-SLAM [54], Vox-Fusion [46], and ESLAM [12] where appropriate. Lastly, we compare against traditional SLAM systems such as Kintinous [42], ElasticFusion [43], and ORB-SLAM2 [23] on TUM-RGBD, DROID-SLAM [39] on Replica, and ORB-SLAM3 [3] on ScanNet++." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 609, + 428, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 609, + 428, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 609, + 428, + 621 + ], + "type": "text", + "content": "5. Results & Discussion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "In this section, we first discuss our evaluation results on camera pose estimation for the four benchmark datasets. Then, we further showcase our high-fidelity 3D Gaussian reconstructions and provide qualitative and quantitative comparisons of our rendering quality (both for novel views and input training views). Finally, we discuss pipeline ablations and provide a runtime comparison." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "21361" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 120, + 68, + 263, + 114 + ], + "blocks": [ + { + "bbox": [ + 120, + 68, + 263, + 114 + ], + "lines": [ + { + "bbox": [ + 120, + 68, + 263, + 114 + ], + "spans": [ + { + "bbox": [ + 120, + 68, + 263, + 114 + ], + "type": "table", + "html": "
MethodsAvg.S1S2
Point-SLAM [30]343.8296.7390.8
ORB-SLAM3 [3]158.2156.8159.7
SplaTAM1.20.61.9
", + "image_path": "330c71f74784380965ea0d73f618571fc541c5678a0dc0f07395ab5cb3d55dcd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 293, + 68, + 494, + 141 + ], + "blocks": [ + { + "bbox": [ + 166, + 119, + 215, + 129 + ], + "lines": [ + { + "bbox": [ + 166, + 119, + 215, + 129 + ], + "spans": [ + { + "bbox": [ + 166, + 119, + 215, + 129 + ], + "type": "text", + "content": "ScanNet++[49]" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 293, + 68, + 494, + 141 + ], + "lines": [ + { + "bbox": [ + 293, + 68, + 494, + 141 + ], + "spans": [ + { + "bbox": [ + 293, + 68, + 494, + 141 + ], + "type": "table", + "html": "
MethodsAvg.R0R1R2Of0Of1Of2Of3Of4
DROID-SLAM [39]0.380.530.380.450.350.240.360.330.43
Vox-Fusion [46]3.091.374.701.478.482.042.581.112.94
NICE-SLAM [54]1.060.971.311.070.881.001.061.101.13
ESLAM [12]0.630.710.700.520.570.550.580.720.63
Point-SLAM [30]0.520.610.410.370.380.480.540.690.72
SplaTAM0.360.310.400.290.470.270.290.320.55
", + "image_path": "ccbfec7fb34f40ef5b89aec18065af63952dbae0410d44f54df853871fe42dae.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 99, + 146, + 280, + 235 + ], + "blocks": [ + { + "bbox": [ + 374, + 148, + 412, + 157 + ], + "lines": [ + { + "bbox": [ + 374, + 148, + 412, + 157 + ], + "spans": [ + { + "bbox": [ + 374, + 148, + 412, + 157 + ], + "type": "text", + "content": "Replica [35]" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 99, + 146, + 280, + 235 + ], + "lines": [ + { + "bbox": [ + 99, + 146, + 280, + 235 + ], + "spans": [ + { + "bbox": [ + 99, + 146, + 280, + 235 + ], + "type": "table", + "html": "
MethodsAvg.fr1/ deskfr1/ desk2fr1/ roomfr2/ xyzfr3/ off.
Kintinous [42]4.843.707.107.502.903.00
ElasticFusion [43]6.912.536.8321.491.172.52
ORB-SLAM2 [23]1.981.602.204.700.401.00
NICE-SLAM [54]15.874.264.9934.4931.733.87
Vox-Fusion [46]11.313.526.0019.531.4926.01
Point-SLAM [30]8.924.344.5430.921.313.48
SplaTAM5.483.356.5411.131.245.16
", + "image_path": "4f98a792a1bfd2f947622fab98b83a5606657458c8ca7b8d321f16fb54d4e6e5.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 296, + 165, + 490, + 217 + ], + "blocks": [ + { + "bbox": [ + 296, + 165, + 490, + 217 + ], + "lines": [ + { + "bbox": [ + 296, + 165, + 490, + 217 + ], + "spans": [ + { + "bbox": [ + 296, + 165, + 490, + 217 + ], + "type": "table", + "html": "
MethodsAvg.000000590106016901810207
Vox-Fusion [46]26.9068.8424.188.4127.2823.309.41
NICE-SLAM [54]10.7012.0014.007.9010.9013.406.20
Point-SLAM [30]12.1910.247.818.6522.1614.779.54
SplaTAM11.8812.8310.1017.7212.0811.107.46
", + "image_path": "712de6e5006477355243e797a8c939903babeeba5d4f748f3ef59ba9e1851711.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 367, + 223, + 419, + 232 + ], + "lines": [ + { + "bbox": [ + 367, + 223, + 419, + 232 + ], + "spans": [ + { + "bbox": [ + 367, + 223, + 419, + 232 + ], + "type": "text", + "content": "Orig-ScanNet [5]" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 162, + 241, + 217, + 251 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 162, + 241, + 217, + 251 + ], + "spans": [ + { + "bbox": [ + 162, + 241, + 217, + 251 + ], + "type": "text", + "content": "TUM-RGBD [36]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 259, + 547, + 305 + ], + "lines": [ + { + "bbox": [ + 46, + 259, + 547, + 305 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 547, + 305 + ], + "type": "text", + "content": "Table 1. Online Camera-Pose Estimation Results on Four Datasets (ATE RMSE " + }, + { + "bbox": [ + 46, + 259, + 547, + 305 + ], + "type": "inline_equation", + "content": "\\downarrow[\\mathrm{cm}]" + }, + { + "bbox": [ + 46, + 259, + 547, + 305 + ], + "type": "text", + "content": "). Our method consistently outperforms all the SOTA-dense baselines on ScanNet++, Replica, and TUM-RGBD, while providing competitive performance on Orig-ScanNet [5]. Best results are highlighted as first, second, and third. Numbers for the baselines on Orig-ScanNet [5], TUM-RGBD [36] and Replica [35] are taken from Point-SLAM [30]." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 326, + 287, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 326, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 46, + 326, + 287, + 361 + ], + "type": "text", + "content": "Camera Pose Estimation Results. In Table 1, we compare our method's camera pose estimation results to a number of baselines on four datasets [5, 35, 36, 49]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "type": "text", + "content": "On ScanNet++ [49], both SOTA SLAM approaches Point-SLAM [30] and ORB-SLAM3 [3] (RGB-D variant) completely fail to correctly track the camera pose due to the very large displacement between contiguous cameras, and thus give very large pose-estimation errors. In particular, for ORB-SLAM3, we observe that the texture-less ScanNet++ scans cause the tracking to re-initialize multiple times due to the lack of features. In contrast, our approach successfully manages to track the camera over both sequences giving an average trajectory error of only " + }, + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "type": "inline_equation", + "content": "1.2\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 363, + 287, + 483 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": "On the relatively easy synthetic Replica [35] dataset, the de-facto evaluation benchmark, our approach reduces the trajectory error over the prior SOTA-dense baseline [30] by more than " + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "inline_equation", + "content": "30\\%" + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "inline_equation", + "content": "0.52\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "inline_equation", + "content": "0.36\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 484, + 287, + 555 + ], + "type": "text", + "content": ". Furthermore, SPLaTAM provides better or competitive performance to a feature-based tracking method such as DROID-SLAM [39]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "content": "On TUM-RGBD [36], all the volumetric methods struggle immensely due to both poor depth sensor information (very sparse) and poor RGB image quality (extremely high motion blur). Compared to prior methods in this category [30, 54], SplaTAM still significantly outperforms, decreasing the trajectory error of the prior SOTA in this category [30] by almost " + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "inline_equation", + "content": "40\\%" + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "content": ", from " + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "inline_equation", + "content": "8.92\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "inline_equation", + "content": "5.48\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 556, + 287, + 664 + ], + "type": "text", + "content": ". Also, we observe that feature-based methods (ORB-SLAM2 [23]) still outperform dense methods on this benchmark." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "The original ScanNet [5] benchmark has similar issues to TUM-RGBD, where no dense volumetric method is able to obtain results with less than " + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": " error & SPLaTAM performs similarly to the two prior SOTA methods [30, 54]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 327, + 545, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 327, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 304, + 327, + 545, + 422 + ], + "type": "text", + "content": "Overall these camera pose estimation results are extremely promising and show off the strengths of our SplaTAM method. The results on ScanNet++ show that if you have high-quality clean input images, our approach can successfully and accurately perform SLAM even with extremely large motions between camera positions, which is not something that is possible with previous SOTA approaches such as Point-SLAM [30] and ORB-SLAM3 [3]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 426, + 546, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 546, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 546, + 557 + ], + "type": "text", + "content": "**Rendering Quality Results.** In Table 2, we evaluate our method's rendering quality on the input views of Replica dataset [35] (as is the standard evaluation approach from Point-SLAM [30] and NICE-SLAM [54]). Our approach achieves similar PSNR, SSIM, and LPIPS results as Point-SLAM [30], although the comparison is not fair as Point-SLAM has the unfair advantage as it takes the ground-truth depth of these images as an input for where to sample its 3D volume for rendering. Our approach achieves much better results than the other baselines Vox-Fusion [46] and NICE-SLAM [54], improving over both by around 10dB in PSNR." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 641 + ], + "type": "text", + "content": "In general, we believe that the rendering results on Replica in Table 2 are irrelevant because the rendering performance is evaluated on the same training views that were passed in as input, and methods can simply have a high capacity and overfit to these images. We only show this as this is the de-facto evaluation for prior methods, and we wish to have some way to compare against them." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Hence, a better evaluation is to evaluate novel-view rendering. However, all current SLAM benchmarks don't have a hold-out set of images separate from the camera trajectory that the SLAM algorithm estimates, so they cannot be used for this purpose. Therefore, we set up a novel benchmark for this using the new high-quality ScanNet++ [49] dataset." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "21362" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 71, + 291, + 201 + ], + "blocks": [ + { + "bbox": [ + 47, + 71, + 291, + 201 + ], + "lines": [ + { + "bbox": [ + 47, + 71, + 291, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 291, + 201 + ], + "type": "table", + "html": "
MethodsMetricsAvg.R0R1R2Of0Of1Of2Of3Of4
Vox-Fusion [46]PSNR ↑24.4122.3922.3623.9227.7929.8320.3323.4725.21
SSIM ↑0.800.680.750.800.860.880.790.800.85
LPIPS ↓0.240.300.270.230.240.180.240.210.20
NICE-SLAM [54]PSNR ↑24.4222.1222.4724.5229.0730.3419.6622.2324.94
SSIM ↑0.810.690.760.810.870.890.800.800.86
LPIPS ↓0.230.330.270.210.230.180.240.210.20
Point-SLAM [30]PSNR ↑35.1732.4034.0835.5038.2639.1633.9933.4833.49
SSIM ↑0.980.970.980.980.980.990.960.960.98
LPIPS ↓0.120.110.120.110.100.120.160.130.14
SplaTAMPSNR ↑34.1132.8633.8935.2538.2639.1731.9729.7031.81
SSIM ↑0.970.980.970.980.980.980.970.950.95
LPIPS ↓0.100.070.100.080.090.090.100.120.15
", + "image_path": "b28a0746b0f1467b3397ecdb85ded1aecf1289417d94e114243aa86be2af0c72.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 297, + 287, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 417 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 417 + ], + "type": "text", + "content": "The results for both novel-view and training-view rendering on this ScanNet++ benchmark can be found in Table 3. Our approach achieves a good novel-view synthesis result of 24.41 PSNR on average and slightly higher on training views with 27.98 PSNR. Note that for novel-view synthesis, we use the ground-truth pose of the novel view to align it with the origin of the SLAM map, i.e., the first SLAM frame. Since Point-SLAM [30] fails to successfully estimate the camera poses and build a good map, it also completely fails on the task of novel-view synthesis." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "type": "text", + "content": "We can also evaluate the geometric reconstruction of the scene by evaluating the rendered depth and comparing it to the ground-truth depth, again for both training and novel views. Our method obtains an incredibly accurate reconstruction with a depth error of only around " + }, + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "type": "inline_equation", + "content": "2\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "type": "text", + "content": " in novel views and " + }, + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "type": "inline_equation", + "content": "1.3\\mathrm{cm}" + }, + { + "bbox": [ + 46, + 417, + 287, + 490 + ], + "type": "text", + "content": " in training views." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 490, + 287, + 609 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 490, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 46, + 490, + 287, + 609 + ], + "type": "text", + "content": "Visual results of both novel-view and training-view rendering for RGB and depth can be seen in Fig. 3. As can be seen, our methods achieve visually excellent results over both scenes for both novel and training views. In contrast, Point-SLAM [30] fails at camera-pose tracking and overfits to the training views, and isn't able to successfully render novel views at all. Point-SLAM also takes the ground-truth depth as an input for rendering to determine where to sample, and as such the depth maps look similar to the ground-truth, while color rendering is completely wrong." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 609, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 609, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 609, + 287, + 670 + ], + "type": "text", + "content": "With this novel benchmark that is able to correctly evaluate Novel-View Synthesis and SLAM simultaneously, as well as our approach as a strong initial baseline for this benchmark, we hope to inspire many future approaches that improve upon these results for both tasks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "Color and Depth Loss Ablation. Our SplaTAM involves fitting the camera poses (during tracking) and the scene map (during mapping) using both a photometric (RGB) and" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 70, + 556, + 168 + ], + "blocks": [ + { + "bbox": [ + 46, + 209, + 288, + 276 + ], + "lines": [ + { + "bbox": [ + 46, + 209, + 288, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 288, + 276 + ], + "type": "text", + "content": "Table 2. Quantitative Train View Rendering Performance on Replica [35]. SplaTAM is comparable to the SOTA baseline, Point-SLAM [30] and consistently outperforms the other dense SLAM methods by a large margin. Numbers for the baselines are taken from Point-SLAM [30]. Note that Point-SLAM uses ground-truth depth for rendering." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 70, + 556, + 168 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 556, + 168 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 556, + 168 + ], + "type": "table", + "html": "
MethodsMetricsNovel ViewTraining View
Avg.S1S2Avg.S1S2
Point-SLAM [30]PSNR [dB] ↑11.9112.1011.7314.4614.6214.30
SSIM ↑0.280.310.260.380.350.41
LPIPS ↓0.680.620.740.650.680.62
Depth L1 [cm] ↓XXXXXX
SplaTAMPSNR [dB] ↑24.4123.9924.8427.9827.8228.14
SSIM ↑0.880.880.870.940.940.94
LPIPS ↓0.240.210.260.120.120.13
Depth L1 [cm] ↓2.071.912.231.280.931.64
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Track. ColorMap. ColorTrack. DepthMap. DepthATE [cm]↓Dep. L1 [cm]↓PSNR [dB]↑
XX✓✓86.03XX
✓✓XX1.3812.5831.30
✓✓✓✓0.270.4932.81
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Velo. \nProp.Sil. \nMaskSil. \nThresh.ATE \n[cm]↓Dep. L1 \n[cm]↓PSNR \n[dB]↑
X✓0.992.952.1525.40
✓X0.99115.800.2914.16
✓✓0.51.300.7431.36
✓✓0.990.270.4932.81
", + "image_path": "863e3cb7f9618181a0c4be7d80c6906bcbf086561d3aea08b3b1208b11612943.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 316, + 397, + 535, + 408 + ], + "lines": [ + { + "bbox": [ + 316, + 397, + 535, + 408 + ], + "spans": [ + { + "bbox": [ + 316, + 397, + 535, + 408 + ], + "type": "text", + "content": "Table 5. Camera Tracking Ablations on Replica/Room 0." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 430, + 545, + 610 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 430, + 545, + 610 + ], + "spans": [ + { + "bbox": [ + 304, + 430, + 545, + 610 + ], + "type": "text", + "content": "depth loss. In Table 4, we ablate the decision to use both and investigate the performance of only one or the other for both tracking and mapping. We do this using Room 0 of Replica. With only depth our method completely fails to track the camera trajectory, because the L1 depth loss doesn't provide adequate information in the x-y image plane. Using only an RGB loss successfully tracks the camera trajectory (although with more than " + }, + { + "bbox": [ + 304, + 430, + 545, + 610 + ], + "type": "inline_equation", + "content": "5\\mathrm{x}" + }, + { + "bbox": [ + 304, + 430, + 545, + 610 + ], + "type": "text", + "content": " the error as using both). Both the RGB and depth work together to achieve excellent results. With only the color loss, reconstruction PSNR is really high, only 1.5 PSNR lower than the full model. However, the depth L1 is much higher using only color vs directly optimizing this depth error. In the color-only experiments, the depth is not used for tracking & mapping, but it is used for the densification and initialization of Gaussians." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": "Camera Tracking Ablation. In Table 5, we ablate three aspects of our camera tracking: (1) the use of forward velocity propagation, (2) the use of a silhouette mask to mask out invalid map areas in the loss, and (3) setting the silhouette threshold to 0.99 instead of 0.5. All three are critical to excellent results. Without forward velocity propagation, tracking still works, but the overall error is more than " + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "inline_equation", + "content": "10\\mathrm{x}" + }, + { + "bbox": [ + 304, + 617, + 545, + 715 + ], + "type": "text", + "content": " higher, which subsequently degrades the map and render" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21363" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 553, + 208 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 553, + 208 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 553, + 208 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 553, + 208 + ], + "type": "image", + "image_path": "a3e76135e2f46b1b248703f25e92a4fb2206ea420a9e3065eae419c9e5624b96.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 217, + 547, + 262 + ], + "lines": [ + { + "bbox": [ + 46, + 217, + 547, + 262 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 547, + 262 + ], + "type": "text", + "content": "Figure 3. Renderings on ScanNet++ [49]. Our method, SplaTAM, renders color & depth for the novel & train views with fidelity comparable to the ground truth. It can also be observed that Point-SLAM [30] fails to provide good renderings on both novel & train view images. Note that Point-SLAM (PS) uses the ground-truth depth to render the train & novel view images. Despite the use of ground-truth depth, the failure of PS can be attributed to the failure of tracking as shown in Tab. 1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 281, + 284, + 342 + ], + "blocks": [ + { + "bbox": [ + 51, + 281, + 284, + 342 + ], + "lines": [ + { + "bbox": [ + 51, + 281, + 284, + 342 + ], + "spans": [ + { + "bbox": [ + 51, + 281, + 284, + 342 + ], + "type": "table", + "html": "
MethodsTracking /IterationMapping /IterationTracking /FrameMapping /FrameATE RMSE [cm] ↓
NICE-SLAM [54]30 ms166 ms1.18 s2.04 s0.97
Point-SLAM [30]19 ms30 ms0.76 s4.50 s0.61
SplaTAM25 ms24 ms1.00 s1.44 s0.27
SplaTAM-S19 ms22 ms0.19 s0.33 s0.39
", + "image_path": "e92f39f17d4e314d0bfe36bdcac712826d489813e653c89786a1cc35bec5bc35.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 63, + 350, + 271, + 361 + ], + "lines": [ + { + "bbox": [ + 63, + 350, + 271, + 361 + ], + "spans": [ + { + "bbox": [ + 63, + 350, + 271, + 361 + ], + "type": "text", + "content": "Table 6. Runtime on Replica/R0 using a RTX 3080 Ti." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 381, + 287, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 381, + 287, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 381, + 287, + 441 + ], + "type": "text", + "content": "ing. Silhouette is critical as without it tracking completely fails. Setting the silhouette threshold to 0.99 allows the loss to be applied on well-optimized pixels in the map, thereby leading to an important " + }, + { + "bbox": [ + 46, + 381, + 287, + 441 + ], + "type": "inline_equation", + "content": "5\\mathrm{x}" + }, + { + "bbox": [ + 46, + 381, + 287, + 441 + ], + "type": "text", + "content": " reduction in the error compared to the threshold of 0.5, which is used for the densification." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "spans": [ + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "type": "text", + "content": "Runtime Comparison. In Table 6, we compare our runtime to NICE-SLAM [54] and Point-SLAM [30] on a Nvidia RTX 3080 Ti. Each iteration of our approach renders a full " + }, + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "type": "inline_equation", + "content": "1200 \\times 980" + }, + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "type": "text", + "content": " pixel image (" + }, + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "type": "inline_equation", + "content": "\\sim 1.2" + }, + { + "bbox": [ + 46, + 445, + 287, + 638 + ], + "type": "text", + "content": " mil pixels) to apply the loss for both tracking and mapping. Other methods use only 200 pixels for tracking and 1000 pixels for mapping each iteration (but attempt to cleverly sample these pixels). Even though we differentiably render 3 orders of magnitude more pixels, our approach incurs similar runtime, primarily due to the efficiency of rasterizing 3D Gaussians. Additionally, we show a version of our method with fewer iterations and half-resolution densification, SplaTAM-S, which works 5x faster with only a minor degradation in performance. In particular, SplaTAM uses 40 and 60 iterations per frame for tracking & mapping respectively on Replica, while SplaTAM-S uses 10 and 15 iterations per frame." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "Limitations & Future Work. Although SplaTAM achieves state-of-the-art performance, we find our method to show some sensitivity to motion blur, large depth noise, and aggressive rotation. We believe a possible solution would be to temporally model these effects and wish to tackle this in future work. Furthermore, SplaTAM" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 282, + 547, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 547, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 547, + 344 + ], + "type": "text", + "content": "can be scaled up to large-scale scenes through efficient representations like OpenVDB [24]. Finally, our method requires known camera intrinsics and dense depth as input for performing SLAM, and removing these dependencies is an interesting avenue for the future." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 354, + 379, + 367 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 354, + 379, + 367 + ], + "spans": [ + { + "bbox": [ + 306, + 354, + 379, + 367 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 374, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 542 + ], + "type": "text", + "content": "We present SPLaTAM, a novel SLAM system that leverages 3D Gaussians as its underlying map representation to enable fast rendering and dense optimization, explicit knowledge of map spatial extent, and streamlined map densification. We demonstrate its effectiveness in achieving state-of-the-art results in camera pose estimation, scene reconstruction, and novel-view synthesis. We believe that SPLaTAM not only sets a new benchmark in both the SLAM and novel-view synthesis domains but also opens up exciting avenues, where the integration of 3D Gaussian Splatting with SLAM offers a robust framework for further exploration and innovation in scene understanding. Our work underscores the potential of this integration, paving the way for more sophisticated and efficient SLAM systems in the future." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 551, + 546, + 674 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 546, + 674 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 546, + 674 + ], + "type": "text", + "content": "Acknowledgments. This work was supported in part by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0074. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. This work used Bridges-2 at PSC through allocation cis220039p from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program which is supported by NSF grants #2138259, #2138286, #2138307, #2137603, and #213296, and also supported by a hardware grant from Nvidia." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 674, + 547, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 674, + 547, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 674, + 547, + 712 + ], + "type": "text", + "content": "The authors thank Yao He for his support with testing ORB-SLAM3 & Jeff Tan for testing the code & demos. We also thank Chonghyuk (Andrew) Song, Margaret Hansen, John Kim & Michael Kaess for their insightful feedback & discussion on initial versions of the work." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "21364" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Michael Bloesch, Jan Czarnowski, Ronald Clark, Stefan Leutenegger, and Andrew J Davison. 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Nicer-slam: Neural implicit scene encoding for rgb slam. arXiv preprint arXiv:2302.03594, 2023. 1, 3" + } + ] + } + ], + "index": 29 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "21366" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Splatter Image_ Ultra-Fast Single-View 3D Reconstruction/a13161ef-830a-482f-925a-3b60cfe25a4d_content_list.json b/2024/Splatter Image_ Ultra-Fast Single-View 3D Reconstruction/a13161ef-830a-482f-925a-3b60cfe25a4d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..3443b3cdc7764683111031bd24b9d9d7f75cc558 --- /dev/null +++ b/2024/Splatter Image_ Ultra-Fast Single-View 3D Reconstruction/a13161ef-830a-482f-925a-3b60cfe25a4d_content_list.json @@ -0,0 +1,1641 @@ +[ + { + "type": "text", + "text": "Splatter Image: Ultra-Fast Single-View 3D Reconstruction", + "text_level": 1, + "bbox": [ + 189, + 130, + 779, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Stanislaw Szymanowicz Christian Rupprecht Andrea Vedaldi", + "bbox": [ + 222, + 180, + 746, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Visual Geometry Group — University of Oxford", + "bbox": [ + 292, + 203, + 676, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{stan, chrisr, vedaldi} @ robots.ox.ac.uk", + "bbox": [ + 321, + 223, + 648, + 238 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/1bd3e082f15c951631ff73b003fe1b68079163057e56587c13575e9625835632.jpg", + "image_caption": [ + "Figure 1. The Splatter Image is an ultra-efficient method for single- and few-view 3D reconstruction. It uses an image-to-image neural network to map the input image to another image that holds the parameters of one coloured 3D Gaussian per pixel. Splatter Image achieves excellent 3D reconstruction quality on synthetic, real and large-scale datasets while using a single GPU for training." + ], + "image_footnote": [], + "bbox": [ + 76, + 272, + 483, + 431 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0f6dd5b5e2edf5f1141648a74f1c4ff46a2b834a4167b34a310ee66c4fdbc2bc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 272, + 890, + 439 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 516, + 313, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We introduce the Splatter Image, an ultra-efficient approach for monocular 3D object reconstruction. Splatter Image is based on Gaussian Splatting, which allows fast and high-quality reconstruction of 3D scenes from multiple images. We apply Gaussian Splatting to monocular reconstruction by learning a neural network that, at test time, performs reconstruction in a feed-forward manner, at 38 FPS. Our main innovation is the surprisingly straightforward design of this network, which, using 2D operators, maps the input image to one 3D Gaussian per pixel. The resulting set of Gaussians thus has the form an image, the Splatter Image. We further extend the method to several images as input via cross-view attention. Owning to the speed of the renderer (588 FPS), we use a single GPU for training while generating entire images at each iteration to optimize perceptual metrics like LPIPS. On several synthetic, real, multi-category and large-scale benchmark datasets, we achieve better results in terms of PSNR, LPIPS, and other metrics while training and evaluating much faster than prior works. Code, models and more results are available at https://szymanowicz.github.io/splatter-image.", + "bbox": [ + 73, + 551, + 473, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 516, + 630, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We contribute Splatter Image, a method that achieves ultrafast single-view reconstruction of the 3D shape and appearance of objects. Splatter Image uses a set of 3D Gaussians as the 3D representation, taking advantage of the rendering quality and speed of Gaussian Splatting [22]. Splatter Image works by predicting a 3D Gaussian for each of the input image pixels, using an image-to-image neural network. Remarkably, the predicted 3D Gaussians provide $360^{\\circ}$ reconstructions of quality comparable or superior to much slower methods (Fig. 1).", + "bbox": [ + 496, + 544, + 890, + 696 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We formulate monocular 3D reconstruction as the problem of designing a neural network that takes an image of an object as input and produces as output a corresponding Gaussian mixture that represents all sides of it. While a Gaussian mixture is a set, i.e., an unordered collection, it can still be stored in an ordered data structure. Splatter Image takes advantage of this fact by using a $2D$ image as the container of the 3D Gaussians, storing the parameters of one Gaussian (i.e., its opacity, position, shape, and colour) per pixel. The Gaussians predominantly lie on the rays from the camera to the object, but they can also be placed off the rays (Fig. 2), enabling $360^{\\circ}$ object representation.", + "bbox": [ + 496, + 699, + 892, + 881 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The advantage of storing a set of 3D Gaussians in an im", + "bbox": [ + 519, + 885, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "10208", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "age is that it reduces the reconstruction problem to learning an image-to-image neural network. In this manner, the recon- constructor can be implemented utilizing only efficient 2D operators (e.g., 2D convolution instead of 3D convolution). We use in particular a U-Net [42] as those have demonstrated excellent performance in image generation [41]. In our case, their ability to capture small image details [55] helps to obtain higher-quality reconstructions.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Since the 3D representation in Splatter Image is a mixture of 3D Gaussians, it enjoys the rendering and space efficiency of Gaussian Splattering, which benefits inference and training. In particular, rendering stops being a training bottleneck [34] and we can afford to generate complete views of the object to optimize perceptual metrics like LPIPS [56]. More importantly, the efficiency is such that our model can be trained on a single GPU on standard benchmarks of 3D objects or two GPUs on large datasets such as Objverse [10], whereas alternative methods typically require distributed training on dozens [26] or even hundreds [17] of GPUs. We also extend Splatter Image to take several views as input. This is achieved by taking the union of the Gaussian mixtures predicted from individual views, after registering them to a common coordinate frame. The different views communicate during prediction via lightweight cross-view attention layers in the architecture.", + "bbox": [ + 75, + 213, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Empirically, we show that, while the network only sees one side of the object, it can still produce a $360^{\\circ}$ reconstruction of it by using the prior acquired during training. The $360^{\\circ}$ information is encoded in the 2D image by allocating different Gaussians in a given 2D neighbourhood to different parts of the 3D object.", + "bbox": [ + 75, + 473, + 470, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We validate Splatter Image by comparing it to alternative, slower reconstructors on standard benchmark datasets like ShapeNet [5] and CO3D [38]. To assess scalability and generalization, we also apply Splatter Image to multicategory reconstruction and train it on Objaverse [10], and evaluate it on Google Scanned Objects [12]. We obtain results of quality comparable to the recent Large Reconstruction Model of [15, 17], which is $50 \\times$ more expensive to train. In fact, in several cases we even outperform slower methods in PSNR and LPIPS. We argue that this is because the very efficient design allows training the model very effectively, including using image-level losses like LPIPS.", + "bbox": [ + 75, + 566, + 472, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To summarise, our contributions are: (1) to port Gaussian Splatting to learning-based monocular reconstruction; (2) to do so with the Splatter Image, a straightforward, efficient and performant 3D reconstruction approach that operates at 38 FPS on a standard GPU and affords single-GPU training; (3) to also extend the method to multi-view reconstruction; (4) and to obtain state-of-the-art reconstruction performance in multiple standard benchmarks, including synthetic, real, multi-category and large-scale datasets, in terms of reconstruction quality and speed.", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 89, + 638, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Representations for single-view 3D reconstruction. In recent years, implicit representations like NeRF [34] have dominated learning-based few-view reconstruction, parameterising the MLP in NeRF using global [19, 39], local [55] or both global and local codes [26]. However, implicit representations, particularly MLP-based ones, are notoriously slow to render, up to 2s for a single $128 \\times 128$ image.", + "bbox": [ + 496, + 116, + 893, + 222 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Follow-up works [14, 48] used faster, explicit, voxel grid representations that encode opacities and colours directly. Similar to DVGO [47], they achieve significant speed-ups, but, due to their voxel-based representation, they scale poorly with resolution. They also assume the knowledge of the absolute viewpoint of each object image.", + "bbox": [ + 496, + 223, + 893, + 314 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The triplane representation [3, 7] was proposed as a compromise between rendering speed and memory consumption. While they are not as fast to render as explicit representations, they allow view-space reconstruction [13] and are fast enough to be effectively used for single-view reconstruction [1, 13]. Triplane-based reconstructors were shown to scale to large datasets like Objaverse [9, 10], albeit at the cost of hundreds of GPUs for multiple days [17, 50].", + "bbox": [ + 496, + 315, + 893, + 436 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In contrast to these works, our method predicts a mixture of 3D Gaussians in a feed-forward manner. As a result, our method is cheap to train (1-2 GPUs), fast at inference and achieves real-time rendering speeds while achieving state-of-the-art image quality across multiple metrics on multiple standard single-view reconstruction benchmarks, including single- [45] and multi-category ShapeNet [5, 21].", + "bbox": [ + 496, + 436, + 893, + 544 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "When more than one view is available at the input, one can use them to estimate the scene geometry [6, 31], learn a view interpolation function [51] or optimize a 3D representation of a scene using priors [18]. Our method is primarily a single-view reconstruction network, but we do show how Splatter Image can be extended to fuse multiple views. However, we focus our work on object-centric reconstruction rather than on generalising to unseen scenes.", + "bbox": [ + 496, + 545, + 893, + 666 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3D Reconstruction with Point Clouds. PointOutNet [11] took image encoding as input and trained point cloud prediction networks [37] using 3D point cloud supervision. PVD [58] and $\\mathrm{PC^2}$ [32] extended this approach using Diffusion Models [16] by conditioning the denoising process on partial point clouds and RGB images, respectively. These approaches require ground truth 3D point clouds, limiting their applicability. Other works [27, 40, 53] use point clouds as intermediate 3D representations for conditioning 2D inpainting or generation networks. However, these point clouds are assumed to correspond to only visible object points. In contrast, our Gaussians can model any part of the object, and thus afford $360^{\\circ}$ reconstruction.", + "bbox": [ + 496, + 672, + 893, + 869 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Point cloud-based representations have also been used for high-quality reconstruction from multi-view images.", + "bbox": [ + 496, + 869, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "10209", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Novel views can be rendered with 2D inpainting networks for hole-filling [43], or by using non-isotropic 3D Gaussians with variable scale [22]. While showing high-quality results, Gaussian Splitting [22] requires many images per scene and has not yet been used in a learning-based reconstruction framework as we do here.", + "bbox": [ + 75, + 90, + 468, + 180 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method also uses 3D Gaussians as an underlying representation but predicts them from as few as a single image. Moreover, it outputs a full $360^{\\circ}$ 3D reconstruction without using 2D or 3D inpainting networks.", + "bbox": [ + 75, + 181, + 470, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Probabilistic 3D Reconstruction. Single-view 3D reconstruction is an ambiguous problem, so recently it has been tackled as a conditional generation task. Diffusion Models have been employed for conditional novel view synthesis [4, 29, 52]. Due to generating images without underlying geometries, the output images exhibit noticeable flicker. This can be mitigated by simultaneously generating multiview images [30, 44], reconstructing a geometry at every step of the denoising process [48, 49, 54] or training a robust reconstructor [25, 28]. Other works build and use a 3D [8, 35] or 2D [13, 33] prior which can be used in an image-conditioned auto-decoding framework.", + "bbox": [ + 75, + 250, + 468, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, we focus on deterministic reconstruction. However, few-view reconstruction is required to output 3D geometries from feed-forward methods [30, 44, 48, 49, 54]. Our method is capable of few-view 3D reconstruction, thus it is complementary to these generative methods and could lead to improvements in generation speed and quality.", + "bbox": [ + 75, + 431, + 468, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 537, + 166, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We discuss Gaussian Splatting in Sec. 3.1 for background, and then describe the Splatter Image in Secs. 3.2 to 3.6.", + "bbox": [ + 75, + 563, + 468, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overview of Gaussian Splitting", + "text_level": 1, + "bbox": [ + 76, + 604, + 356, + 622 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A radiance field [34] is a pair of functions, assigning an opacity $\\sigma(\\pmb{x}) \\in \\mathbb{R}_+$ and a colour $c(\\pmb{x},\\pmb{\\nu}) \\in \\mathbb{R}^3$ to each 3D point $\\pmb{x} \\in \\mathbb{R}^3$ and viewing direction $\\pmb{\\nu} \\in \\mathbb{S}^2$ . Gaussian Splatting [60] represents the two functions $\\sigma$ and $c$ as a mixture $\\theta$ of $G$ colored 3D Gaussians", + "bbox": [ + 75, + 628, + 468, + 704 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ng _ {i} (\\pmb {x}) = \\exp \\left(- \\frac {1}{2} (\\pmb {x} - \\pmb {\\mu} _ {i}) ^ {\\top} \\Sigma_ {i} ^ {- 1} (\\pmb {x} - \\pmb {\\mu} _ {i})\\right),\n$$\n", + "text_format": "latex", + "bbox": [ + 117, + 714, + 426, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $1 \\leq i \\leq G$ , $\\pmb{\\mu}_i \\in \\mathbb{R}^3$ is the Gaussian mean or center and $\\Sigma_i \\in \\mathbb{R}^{3 \\times 3}$ is its covariance, specifying its shape and size. Each Gaussian has also an opacity $\\sigma_i \\in [0,1]$ and a view-dependent colour $c_i(\\pmb{v}) \\in \\mathbb{R}^3$ . Together, they define a radiance field as follows:", + "bbox": [ + 75, + 758, + 468, + 835 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma (\\boldsymbol {x}) = \\sum_ {i = 1} ^ {G} \\sigma_ {i} g _ {i} (\\boldsymbol {x}), \\quad c (\\boldsymbol {x}, \\boldsymbol {\\nu}) = \\frac {\\sum_ {i = 1} ^ {G} c _ {i} (\\boldsymbol {\\nu}) \\sigma_ {i} g _ {i} (\\boldsymbol {x})}{\\sum_ {j = 1} ^ {G} \\sigma_ {i} g _ {i} (\\boldsymbol {x})}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 845, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The mixture of Gaussians is thus given by the set", + "bbox": [ + 500, + 90, + 825, + 106 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\theta = \\left\\{\\left(\\sigma_ {i}, \\boldsymbol {\\mu} _ {i}, \\Sigma_ {i}, c _ {i}\\right), i = 1, \\dots , G \\right\\}.\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 118, + 816, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A raidance field is rendered into an image $I(\\pmb{u})$ by integrating the colors observed along the ray $\\pmb{x}_{\\tau} = \\pmb{x}_0 - \\tau \\pmb{\\nu}$ , $\\tau \\in \\mathbb{R}_+$ that passes through each image pixel $\\pmb{u}$ via the equation:", + "bbox": [ + 498, + 148, + 890, + 208 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nI (\\boldsymbol {u}) = \\int_ {0} ^ {\\infty} c \\left(\\boldsymbol {x} _ {\\tau}, \\boldsymbol {\\nu}\\right) \\sigma \\left(\\boldsymbol {x} _ {\\tau}\\right) e ^ {- \\int_ {0} ^ {\\tau} \\sigma \\left(\\boldsymbol {x} _ {\\mu}\\right) d \\mu} d \\tau . \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 219, + 890, + 252 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gaussian Splatting [22, 60] provides a very fast differentiable renderer $I = \\mathcal{R}(\\theta, \\pi)$ that approximates Eq. (2), mapping the mixture $\\theta$ and the viewpoint $\\pi$ to an image $I$ .", + "bbox": [ + 498, + 262, + 890, + 308 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. The Splatter Image", + "text_level": 1, + "bbox": [ + 500, + 318, + 684, + 334 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To perform monocular reconstruction we seek for a function $\\theta = S(I)$ which is the 'inverse' of the renderer $\\mathcal{R}$ , mapping an image $I$ to a mixture of 3D Gaussians $\\theta$ . Our key innovation is to propose an extremely simple and yet effective design for such a function. Specifically, we predict a Gaussian for each pixel of the input image $I$ using a standard image-to-image neural network architecture. We call its output image $M$ the Splatter Image.", + "bbox": [ + 496, + 340, + 890, + 462 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In more detail, Let $\\pmb{u} = (u_{1}, u_{2}, 1)$ denote one of the $H \\times W$ image pixels. This corresponds to ray $\\pmb{x} = \\pmb{u}d$ in camera space, where $d$ is the depth of the ray point. Our network $f$ takes as input the $H \\times W \\times 3$ RGB image $I$ , and outputs directly a $H \\times W \\times K$ tensor $M$ , where each pixel is associated to the $K$ -dimensional feature vector packing the parameters $M_{\\pmb{u}} = (\\sigma, \\pmb{\\mu}, \\Sigma, c)$ of a corresponding Gaussian.", + "bbox": [ + 498, + 463, + 890, + 568 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We assume that Gaussians are expressed in the same reference frame of the camera. As illustrated in Fig. 2, the network predicts the depth $d$ and offset $(\\Delta_x, \\Delta_y, \\Delta_y)$ , setting", + "bbox": [ + 498, + 569, + 890, + 628 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {\\mu} = \\left[ \\begin{array}{l} u _ {1} d + \\Delta_ {x} \\\\ u _ {2} d + \\Delta_ {y} \\\\ d + \\Delta_ {z} \\end{array} \\right]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 628, + 890, + 676 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The network also predicts the opacity $\\sigma$ , the shape $\\Sigma$ and the colour $c$ . For now, we assume that the colour is Lambertian, i.e., $c(\\nu) = c \\in \\mathbb{R}^3$ , and relax this assumption in Sec. 3.5. Section 3.6 provides more detail on the network architecture.", + "bbox": [ + 498, + 681, + 890, + 757 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Discussion. One may wonder how this design can predict a full $360^{\\circ}$ reconstruction of the object when the reconstruction is aligned a single input view. We find that the network adjusts the 3D offsets $\\Delta$ and depths $d$ to allocate some of the 3D Gaussians to reconstruct the input view, and some to reconstruct unseen portions of the object, automatically. The network can also decide to switch off any Gaussian by simply predicting $\\sigma = 0$ , if needed. These points are then not rendered and can be culled in post-processing.", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "10210", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2b5514cc74e6d526b55061d89c12c0902f0a0c07e32a2b62a9217eba2cb8a692.jpg", + "image_caption": [ + "Figure 2. Predicting locations. The location of each Gaussian is parameterised by depth $d$ and a 3D offset $\\Delta = (\\Delta_x, \\Delta_y, \\Delta_z)$ . The 3D Gaussians are projected to depth $d$ (blue) along camera rays (green) and moved by the 3D offset $\\Delta$ (red)." + ], + "image_footnote": [], + "bbox": [ + 81, + 90, + 460, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our design can also be seen as an extension of depth prediction networks which only predicting the depth of each pixel. Here, we also predict unobserved parts of the geometry, as well as the shape and appearance of each Gaussian.", + "bbox": [ + 75, + 325, + 467, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Learning formulation", + "text_level": 1, + "bbox": [ + 76, + 393, + 279, + 410 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning to predict the Splatter Image is simple and efficient. It can be done on a single GPU using at most 20GB of memory at training time in most of our single-view reconstruction experiments (except for Objaverse, where we use 2 GPUs and using 26GB of memory on each). For training, we assume a multi-view dataset, either real or synthetic. The dataset $\\mathcal{D}$ consists of triplets $(I,J,\\pi)$ , where $I$ is a source image, $J$ a target image, and $\\pi$ the viewpoint change between the source and the target cameras. Then we simply feed the source $I$ as input to Splatter Image, and minimize the average reconstruction loss of target view $J$ :", + "bbox": [ + 75, + 417, + 468, + 583 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} (\\mathcal {S}) = \\frac {1}{| \\mathcal {D} |} \\sum_ {(I, J, \\pi) \\in \\mathcal {D}} \\| J - \\mathcal {R} (\\mathcal {S} (I), \\pi) \\| ^ {2}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 590, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Image-level losses. A main advantage of the speed and efficiency of our method is that it allows for rendering entire images at each training iteration, even for relatively large batches (this differs from NeRF [34], which only generates a certain number of pixels in a batch). In particular, this means that, in addition to decomposable losses like the $L2$ loss above, we can use image-level losses like LPIPS [56], which do not decompose into per-pixel losses. In practice, we experiment with a combination of such losses.", + "bbox": [ + 75, + 636, + 467, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regularisations. We also add generic regularisers to prevent parameters from taking on unreasonable values (e.g., Gaussians which are larger than the reconstructed objects, or vanishingly small). Please see the sup. mat. for details.", + "bbox": [ + 75, + 777, + 467, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Extension to multiple input viewpoints", + "text_level": 1, + "bbox": [ + 76, + 847, + 408, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "If two or more input views $I_j$ , $j \\in \\{1, \\dots, N\\}$ are provided, we can apply network $S$ multiple times to obtain", + "bbox": [ + 75, + 869, + 467, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "multiple Splatter Images $M_{j}$ , one per view. If $(R, T)$ is the relative camera pose change from an additional view to the reference view, we can take the mixture of 3D Gaussians $\\theta$ defined in the additional view's coordinates and warp it to the reference view. Specifically, a Gaussian of parameters $(\\sigma, \\mu, \\Sigma, c)$ maps to Gaussian of parameters $(\\sigma, \\tilde{\\mu}, \\tilde{\\Sigma}, \\tilde{c})$ where $\\tilde{\\mu} = R\\mu + T$ , $\\tilde{\\Sigma} = R\\Sigma R^{\\top}$ , $\\tilde{c} = c$ . We use the symbol $\\phi[\\theta]$ to denote the Gaussian mixture obtained by warping each Gaussian in $\\theta$ . Here we have also assumed a Lambertian colour model and will discuss in Sec. 3.5 how more complex models transform.", + "bbox": [ + 496, + 90, + 890, + 256 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given $N$ different views $I_{j}$ and corresponding warps $\\phi$ , we can obtain a composite mixture of 3D Gaussians simply by taking their union $\\Theta = \\bigcup_{j=1}^{N} \\phi_{j}[S(I_{j})]$ . Note that this set of 3D Gaussians is defined in the coordinate system of the reference camera.", + "bbox": [ + 496, + 257, + 890, + 332 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. View-dependent colour", + "text_level": 1, + "bbox": [ + 498, + 344, + 714, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Generalising beyond the Lambertian colour model, we use spherical harmonics [22] to represent view-dependent colours. For a particular Gaussian $(\\sigma, \\mu, \\Sigma, c)$ , we then define $[c(\\pmb{\\nu}; \\pmb{\\alpha})]_i = \\sum_{l=0}^L \\sum_{m=-L}^L \\alpha_{ilm} Y_l^m(\\pmb{\\nu})$ where $\\alpha_{ilm}$ are coefficients predicted by the network and $Y_l^m$ are spherical harmonics, $L$ is the order of the expansion, and $\\pmb{\\nu} \\in \\mathbb{S}^2$ is the viewing direction.", + "bbox": [ + 496, + 368, + 890, + 474 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The viewpoint change of Sec. 3.4 transforms a viewing direction $\\pmb{\\nu}$ in the source camera to the corresponding viewing direction in the reference frame as $\\tilde{\\pmb{\\nu}} = R\\pmb{\\nu}$ . We can then find the transformed colour function by finding the coefficients $\\tilde{\\alpha}$ such that $c(\\pmb{\\nu};\\pmb{\\alpha}) = c(\\tilde{\\pmb{\\nu}};\\tilde{\\pmb{\\alpha}})$ . This is possible because (each order of) spherical harmonics are closed under rotation. However, the general case requires the computation of Wigner matrices. For simplicity, we only consider orders $L = 0$ (Lambertian) and $L = 1$ . Hence, the first level has one constant component $Y_0^0$ and the second level has three components which we can write collectively as $Y_{1} = [Y_{1}^{-1},Y_{1}^{0},Y_{1}^{1}]$ such that", + "bbox": [ + 496, + 476, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nY _ {1} (\\boldsymbol {\\nu}) = \\sqrt {\\frac {3}{4 \\pi}} \\Pi \\boldsymbol {\\nu}, \\quad \\Pi = \\left[ \\begin{array}{c c c} 0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\ 1 & 0 & 0 \\end{array} \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 558, + 669, + 830, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can then conveniently rewrite $[c(\\pmb {\\nu};\\pmb {\\alpha})]_i = \\alpha_{i0} +$ $\\pmb{\\alpha}_{i1}^{\\top}Y_{1}(\\pmb {\\nu})$ . From this and $c(\\pmb {\\nu};\\alpha_0,\\pmb {\\alpha}_1) = c(\\tilde{\\pmb{\\nu}};\\tilde{\\alpha}_0,\\tilde{\\alpha}_1)$ we conclude that $\\tilde{\\alpha}_{i0} = \\tilde{\\alpha}_{i0}$ , and $\\tilde{\\alpha}_{i1} = \\Pi^{-1}R\\Pi \\alpha_{i1}$", + "bbox": [ + 496, + 729, + 890, + 775 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.6. Neural network architecture", + "text_level": 1, + "bbox": [ + 500, + 786, + 754, + 800 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The bulk of the predictor $S$ mapping the input image $I$ to the mixture of Gaussians $\\theta$ is architecturally identical to the SongUNet of [46]. The last layer is replaced with a $1\\times 1$ convolutional layer with $12 + k_{c}$ output channels, where $k_{c}\\in \\{3,12\\}$ depending on the colour model. Given $I\\in \\mathbb{R}^{3\\times H\\times W}$ as input, the network thus produces", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "10211", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "a $(12 + k_{c})\\times H\\times W$ tensor as output, coding, for each pixel $\\pmb{u}$ channels, the parameters $(\\hat{\\sigma},\\Delta ,\\hat{d},\\hat{s},\\hat{q},\\alpha)$ which are then transformed to opacity, offset, depth, scale, rotation and colour, respectively. These are activated by nonlinear functions to obtain the Gaussian parameters. Specifically, the opacity is obtained using the sigmoid operator as $\\sigma =$ sigmoid( $\\hat{\\sigma}$ ). The depth is obtained as $d =$ $(z_{\\mathrm{far}} - z_{\\mathrm{near}})$ sigmoid $(\\hat{d}) + z_{\\mathrm{near}}$ . The mean $\\mu$ is then obtained using Eq. (3). Following [22], the covariance is obtained as $\\Sigma = R(\\pmb {q})\\mathrm{diag}(\\exp \\hat{s})^{2}R(\\pmb {q})^{\\top}$ where $R(\\pmb {q})$ is the rotation matrix with quaternion $\\pmb {q} = \\hat{\\pmb{q}} /\\| \\hat{\\pmb{q}}\\|$ and $\\hat{\\pmb{q}}\\in \\mathbb{R}^4$", + "bbox": [ + 75, + 90, + 472, + 261 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For multi-view reconstruction, we apply the same network to each input view and then use the approach of Sec. 3.4 to fuse the individual reconstructions. In order to allow the network to coordinate and exchange information between views, we apply two modifications to it.", + "bbox": [ + 75, + 261, + 470, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "First, we condition the network with the corresponding camera pose $(R,T)$ (we only assume access to the relative camera pose to a common but otherwise arbitrary reference frame). In fact, since we consider cameras in a turn-table-like configuration, we only pass vectors $(Re_3,T)$ where $e_3 = (0,0,1)$ . We do so by encoding each entry via a sinusoidal positional embedding of order 9, resulting in 60 dimensions in total. Finally, these are applied to the U-Net blocks via FiLM [36] embeddings.", + "bbox": [ + 75, + 335, + 472, + 473 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Second, we add cross-attention layers to allow communication between the features of different views. We do so in a manner similar to [44], but only at the lowest UNet resolution, which maintains the computational cost very low.", + "bbox": [ + 75, + 473, + 470, + 534 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 549, + 209, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our method extensively for single-view reconstruction on six standard benchmarks. Next, we assess the quality of multi-view reconstruction, and finish with an evaluation of the speed of the method.", + "bbox": [ + 75, + 575, + 468, + 637 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. The standard benchmark for evaluating single-view 3D reconstruction is ShapeNet-SRN [45]. We train our method in the single-class setting and report results on the \"Car\" and \"Chair\" classes, following prior work. Moreover, we challenge our method with two classes of real objects from the CO3D [38] dataset: Hydrants and Teddybears. In this challenging dataset ripe with ambiguities we set $z_{\\mathrm{far}}$ and $z_{\\mathrm{near}}$ to depend on ground truth distance $z_{\\mathrm{gt}}$ between the object and camera.", + "bbox": [ + 75, + 642, + 468, + 779 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We further test our method on two multi-category datasets. First, we use the standard benchmark of multicategory ShapeNet (with objects from 13 largest categories), and use the renderings, standard splits and target views from NMR [21]. Secondly, we train one model on renderings of objects from Objaverse-LVIS [10] which contains over 1k object categories, using the renderings from Zero-1-to-3 [29]. We evaluate this model on all objects", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/617c289e29fba77b448a43d354c00473e03cbf416d3ce98a2dd8ea88132b8bc6.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRC1-view Cars1-view Chairs
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
SRN✗22.250.880.12922.890.890.104
CodeNeRF✗23.800.910.12823.660.900.166
FE-NVS✗22.830.910.09923.210.920.077
ViewsetDiff w/o D✗23.210.900.11624.160.910.088
PixelNeRF✓23.170.890.14623.720.900.128
VisionNeRF✓22.880.900.08424.480.920.077
NeRFDiff w/o NGD✓23.950.920.09224.800.930.070
Ours✓24.000.920.07824.430.930.067
", + "bbox": [ + 498, + 88, + 893, + 238 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Table 1. ShapeNet-SRN: Single-View Reconstruction. Our method achieves State-of-the-Art reconstruction quality on all metrics on the Car dataset and on two metrics in the Chair dataset, while performing reconstruction in the camera view-space. 'RC' indicates if a method can operate using only relative camera poses.", + "bbox": [ + 496, + 247, + 893, + 319 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "from the Google Scanned Objects dataset [12], using the same renderings as used for evaluation in Free3D [57]. We train and evaluate all models at $128 \\times 128$ resolution, apart from multi-category ShapeNet which is at $64 \\times 64$ . Finally, we use the ShapeNet-SRN Cars dataset for the evaluation of the two-view reconstruction quality. For more details on datasets see supp. mat.", + "bbox": [ + 496, + 344, + 893, + 450 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. For ShapeNet (both single-class and multiclass), we compare against implicit [19, 26, 45, 55], hybrid implicit-explicit [13] and explicit methods [2, 14, 48]. We use the deterministic variants of [13, 48] by using their reconstruction network in a single forward pass. For CO3D we compare against PixelNeRF which we train for 400,000 iterations with their officially released code on the same data as used for our method. Finally, on Objaverse-LVIS we compare to OpenLRM [15] (open-source version of LRM [17]): a large triplane-based reconstructor, trained on the full Objaverse dataset. Since we are proposing a deterministic reconstruction method, we do not compare to methods that employ Score Distillation [29, 59] or feedforward diffusion models [4, 28, 52, 54].", + "bbox": [ + 496, + 457, + 893, + 669 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details can be found in the supp. mat.", + "bbox": [ + 517, + 669, + 872, + 686 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Evaluation of reconstruction quality", + "text_level": 1, + "bbox": [ + 498, + 695, + 815, + 712 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In line with related works [26, 55], we assess the quality of the reconstructions by measuring novel view synthesis quality and report Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and a perceptual loss (LPIPS). We perform reconstruction from a given source view and render the 3D shape to unseen target views following standard protocols as detailed in the supp. mat.", + "bbox": [ + 496, + 718, + 893, + 825 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Single-view 3D reconstruction", + "text_level": 1, + "bbox": [ + 498, + 845, + 764, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ShapeNet. In Tab. 1 and Fig. 3 we compare the single-view reconstruction quality on the ShapeNet-SRN benchmark.", + "bbox": [ + 496, + 869, + 892, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "10212", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/4d67f4d94fb59ab9ecfbd4e7b9d0e71c42e009ec4355fde59440c475d05e08e7.jpg", + "image_caption": [ + "Figure 3. ShapeNet-SRN Comparison. Our method outputs more accurate reconstructions (cars' backs, top chair) and better represents thin regions (bottom chair)." + ], + "image_footnote": [], + "bbox": [ + 83, + 87, + 472, + 349 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9f587cd21209c02f03c17118984af638a43d5ff7d5ee6c4375651bf0ae2e6c74.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PixelNeRF [55]FE-NVS [14]FWD [2]VisionNeRF [26]Ours
PSNR ↑26.8027.0826.6628.7629.38
SSIM ↑0.910.920.910.930.95
LPIPS ↓0.1080.0820.0550.0650.047
", + "bbox": [ + 78, + 420, + 465, + 472 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/19fd537415fcc0c2fe059ea853b0fca196ee848a7ba3b8ce6b62d412ee6ec960.jpg", + "table_caption": [ + "Table 2. Our method achieves State-of-the-Art quality of single-view reconstruction on multi-class ShapeNet dataset." + ], + "table_footnote": [], + "table_body": "
ObjectMethodPSNR ↑SSIM ↑LPIPS ↓
HydrantPixelNeRF21.760.780.203
HydrantOurs21.800.800.150
TeddybearPixelNeRF19.380.650.290
TeddybearOurs19.440.730.231
", + "bbox": [ + 84, + 517, + 459, + 609 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our method outperforms all deterministic reconstructors in SSIM and LPIPS, obtaining sharper new views. Furthermore, our method requires only relative camera poses instead of absolute/canonical ones. Qualitatively, our method does well in challenging situations with limited visibility and thin structures. In Tab. 2, we use instead the multicategory ShapeNet protocol we observe that our method outperforms more expensive baselines [26] across all metrics in the multi-category ShapeNet setting.", + "bbox": [ + 75, + 676, + 468, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CO3D. On CO3D bears and hydrants, our model outperforms PixelNeRF on all metrics (Tab. 3), and qualitatively produces sharper images (Fig. 4) while being $1,000 \\times$ faster.", + "bbox": [ + 75, + 818, + 468, + 864 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Objaverse-LVIS and Google Scanned Objects. We compare our method to OpenLRM [15], an open-source ver", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/37df622fc055cf5ea3c81c0f05207f525630a581b9355e8786a2094999c62318.jpg", + "image_caption": [ + "Figure 4. CO3D Hydrants and Teddybears. Our method outputs sharper reconstructions than PixelNeRF while being $100\\mathrm{x}$ faster in inference." + ], + "image_footnote": [], + "bbox": [ + 501, + 88, + 890, + 268 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/28e3f87aac4b4a8bfc13b0ffbd3091e9bf360cdb22268b560fac2e4e48d46a34.jpg", + "table_caption": [ + "Table 3. CO3D: Single-View. Our method outperforms PixelNeRF on this challenging benchmark across all metrics." + ], + "table_footnote": [], + "table_body": "
MethodPSNR ↑SSIM ↑LPIPS ↓
OpenLRM18.060.840.129
Ours21.060.880.111
", + "bbox": [ + 540, + 345, + 849, + 407 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 4. Google Scanned Objects: Single-View. Our method outperforms the much more expensive LRM [15, 17] on single-view open-world reconstruction.", + "bbox": [ + 498, + 417, + 890, + 460 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/f4fcc57bbd0f2cd4869dce799c7d4c76eb839246499c7741d0d6f9fda4a98bde.jpg", + "image_caption": [ + "Figure 5. Google Scanned Objects. On large datasets our model has similar quality to much more expensive baselines (shoe). Our reconstructions have more accurate lighting (Jenga), object pose (horse) and shape (toy)." + ], + "image_footnote": [], + "bbox": [ + 509, + 483, + 877, + 667 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sion of the LRM model [17], on the Google Scanned Objects [12] evaluation renderings from Free3D [57]. Quantitatively, in Tab. 4 Splatter Image outperforms OpenLRM and, qualitatively (Fig. 5), it is comparable. Our models perform well even on images collected from the Internet Fig. 6, after removing backgrounds and resizing. Remarkably, our method, trained for 7 GPU days, is able to compete with OpenLRM, which uses hundreds of GPUs for several days [15, 17].", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "10213", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6d0803740f828c39a676d86c3d33cd8ca2a2555925e84cf622cd1ee8249814b0.jpg", + "image_caption": [ + "Figure 6. Our models trained on single classes (top) and on Objaverse (bottom) can be used on in-the-wild Internet images (right)." + ], + "image_footnote": [], + "bbox": [ + 89, + 85, + 459, + 339 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/aa6fa5a89801c4d9125070c28de45d177ce51734ad6dc85dbd248eb7f06c2951.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodRelative Pose2-view Cars
PSNR ↑SSIM ↑
SRNX24.840.92
CodeNeRFX25.710.91
FE-NVSX24.640.93
PixelNeRF✓25.660.94
Ours✓26.010.94
", + "bbox": [ + 142, + 383, + 403, + 492 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Two-view reconstruction on ShapeNet-SRN Cars.", + "bbox": [ + 96, + 502, + 446, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.2 Two-view 3D reconstruction", + "text_level": 1, + "bbox": [ + 76, + 530, + 328, + 542 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We compare our multi-view reconstruction model on ShapeNet-SRN Cars by training it for two-view predictions (see Tab. 5). Prior work often relies on absolute camera pose conditioning, meaning that the model learns to rely on the canonical orientation of the object in the dataset. This limits the applicability of these models, as in practice for a new image of an object, the absolute camera pose is of course unknown. Here, only ours and PixelNeRF can deal with relative camera poses as input. Interestingly, our method shows not only better performance than PixelNeRF in both real and synthetic data but also improves over SRN, CodeNeRF, and FE-NVS that rely on absolute camera poses.", + "bbox": [ + 75, + 554, + 468, + 734 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.1.3 Ablations", + "text_level": 1, + "bbox": [ + 76, + 755, + 199, + 768 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate the influence of individual components of our method, using a shorter training schedule than models in Tab. 1 for efficiency. Ablations of the multi-view model are given in the supp. mat.", + "bbox": [ + 75, + 779, + 468, + 840 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We show the results of our ablation study for the single-view model in Tab. 6. We train a model (w/o image) that uses a fully connected, unstructured output instead of a Splatter Image. This model cannot transfer image informa", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bbd629e48d621962ef0b99e2c4b83d409d533dcd56973729ac2052e7c3bc2396.jpg", + "image_caption": [ + "Figure 7. Analysis. Splatter Images represent full $360^{\\circ}$ of objects by allocating background pixels to appropriate 3D locations (third row) to predict occluded elements like wheels (left) or chair legs (middle). Alternatively, it predicts offsets in the foreground pixels to represent occluded chair parts (right)." + ], + "image_footnote": [], + "bbox": [ + 501, + 87, + 893, + 369 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tion directly to their corresponding Gaussians and does not achieve good performance. We also ablate predicting the depth along the ray by simply predicting 3D coordinates for each Gaussian. This version also suffers from its inability to easily align the input image with the output. Removing the 3D offset prediction mainly harms the backside of the object while leaving the front faces the same. This results in a lower impact on the overall performance of this component. Changing the degrees of freedom of appearance predictions (by fixing Gaussians to be isotropic or removing view-dependence) also reduced the image fidelity. Finally, removing perceptual loss (w/o $\\mathcal{L}_{\\mathrm{LPIPS}}$ ) results in a significant worsening of LPIPS, indicating this loss is important for perceptual sharpness of reconstructions. Being able to use LPIPS in optimisation is a direct consequence of employing a fast-to-render representation and being able to render full images at training time.", + "bbox": [ + 496, + 465, + 892, + 722 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis. In Fig. 7, we analyse how 3D information is stored inside a Splatter Image. Since all information is arranged in an image format, we can visualise each of the modalities: opacity, depth, and location. Pixels of the input image that belong to the object tend to describe their corresponding 3D structure, while pixels outside of the object wrap around to close the object on the back.", + "bbox": [ + 496, + 729, + 890, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Evaluation of reconstruction efficiency", + "text_level": 1, + "bbox": [ + 500, + 845, + 831, + 862 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "A key advantage of the Splatter Image is its training and test time efficiency, which we assess below.", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "10214", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/791f821a8a7223986a9c44c016beb74137f82ec00e5c9b78ac9e897f30b0e949.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
PSNR ↑SSIM ↑LPIPS ↓
Full model22.250.900.115
w/o image20.600.870.152
w/o depth21.210.880.145
w/o view dir.21.770.890.121
isotropic22.010.890.118
w/o offset22.060.900.119
w/o LPIPS22.220.890.141
", + "bbox": [ + 109, + 88, + 436, + 232 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/9fd9ba4ae0f56989abda4006fa7521a40cacfc0374c958673945a6c85996be87.jpg", + "table_caption": [ + "Table 6. Ablations: Single-View Reconstruction." + ], + "table_footnote": [ + "Table 7. Speed. Time required for image encoding (E), rendering (R), the 'Forward' time, indicative of train-time efficiency and the 'Test' time, indicative of test-time efficiency. Our method is the most efficient in both train and test time across open-source available methods and only requires relative camera poses. 'RP' indicates if a method can operate using only relative camera poses." + ], + "table_body": "
RPE↓R↓Forward↓Test↓
NeRFDiff✓(0.031)(0.0180)(0.103)(4.531)
FE-NVS✗(0.015)(0.0032)(0.028)(0.815)
VisionNeRF✓0.0082.43129.733607.8
PixelNeRF✓0.0031.85727.432463.3
ViewsetDiff✗0.0250.00640.0511.625
Ours 2-view✓0.0300.00170.0370.455
Ours 1-view✓0.0260.00170.0330.451
", + "bbox": [ + 83, + 272, + 459, + 398 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Test-time efficiency. First, we assess the 'Test' time speed, i.e., the time it takes for the trained model to reconstruct an object and generate a certain number of images. We reference the evaluation protocol of the standard ShapeNet-SRN benchmark [45] and render 250 images at $128^{2}$ resolution.", + "bbox": [ + 75, + 521, + 468, + 597 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Assessing wall-clock time fairly is challenging as it depends on many factors. All measurements reported here are done on a single NVIDIA V100 GPU. We use officially released code of Viewset Diffusion [48], PixelNeRF [55] and VisionNeRF [26] and rerun those on our hardware. NeRFDiff [13] and FE-NVS [14] do not have code available, so we use their self-reported metrics. According to the authors, FE-NVS was evaluated on the same type of GPU, while NeRFDiff does not include information about the hardware used and we were unable to obtain more information. Since we could not perfectly control these experiments, the comparisons to NeRFDiff and FE-NVS are only indicative. For Viewset Diffusion and NeRFDiff we report the time for a single pass through the reconstruction network.", + "bbox": [ + 75, + 598, + 468, + 808 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 7 reports the 'Encoding' (E) time, spent by the network to compute the object's 3D representation from an image, and the 'Rendering' (R) time, spent by the network to render new images from the 3D representation. From those, we calculate the 'Test' time, equal to the 'Encoding' time plus 250 'Rendering' time. As shown in the last column", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "of Tab. 7, our method is more than $1000 \\times$ faster in testing than PixelNeRF and VisionNeRF (while achieving equal or superior quality of reconstruction in Tab. 1). Our method is also faster than voxel-based Viewset Diffusion even though it does not require knowing the absolute camera pose. The efficiency of our method is very useful to iterate quickly in research; for instance, evaluating our method on the full ShapeNet-Car validation set takes less than 10 minutes on a single GPU. In contrast, PixelNeRF takes 45 GPU-hours.", + "bbox": [ + 496, + 90, + 890, + 227 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Train-time efficiency. Next, we assess the efficiency of the method during training. Here, the encoding time becomes more significant because one typically renders only a few images to compute the reconstruction loss and obtain a gradient (e.g., because there are only so many views available in the training dataset, or because generating more views provides diminishing returns in terms of supervision). As typical values (and as used by us in this work), we assume that the method is tasked with generating 4 new views at each iteration instead of 250 as before. We call this the 'Forward' time and measure it the same way. As shown in the 'Forward' column of Tab. 7, our method is $246 \\times$ faster at training time than implicit methods and $1.5 \\times$ than Viewset Diffusion, which uses an explicit representation. With this, we can train models achieving state-of-the-art quality on a single A6000 GPU in 7 days, while VisionNeRF requires 16 A100 GPUs for 5 days. What is even more remarkable, we can train models on large datasets such as Objaverse on two A6000 GPUs in 3.5 days, while triplane-based methods such as LRM require 128 A100 GPUs for 3 days [17].", + "bbox": [ + 496, + 234, + 892, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 556, + 617, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have presented Splatter Image, a simple method for single- or few-view 3D reconstruction. The method uses an off-the-shelf 2D image-to-image network and predicts a pseudo-image containing one colored 3D Gaussian per pixel. By combining fast inference with fast rendering via Gaussian Splatting, Splatter Image can be trained and evaluated quickly on synthetic and real benchmarks. Splatter Image achieves state-of-the-art reconstruction performance without requiring absolute/canonical camera poses at test time, is simple to implement, and can be trained and tested much faster than many alternatives.", + "bbox": [ + 496, + 582, + 890, + 750 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ethics. We use various datasets in a manner compatible with their terms. There is no processing of personal data. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html.", + "bbox": [ + 496, + 756, + 890, + 832 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. S. Szymanowicz is supported by an EPSRC Doctoral Training Partnerships Scholarship (DTP) EP/R513295/1 and the Oxford-Ashton Scholarship. A. Vedaldi is supported by ERC-CoG UNION 101001212.", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "10215", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Titas Anciukevicius, Zexiang Xu, Matthew Fisher, Paul Henderson, Hakan Bilen, Niloy J. Mitra, and Paul Guerrero. RenderDiffusion: Image diffusion for 3d reconstruction, inpainting and generation. In Proc. CVPR, 2022. 2", + "[2] Ang Cao, Chris Rockwell, and Justin Johnson. Fwd: Realtime novel view synthesis with forward warping and depth. In Proc. CVPR, 2022. 5, 6", + "[3] Eric R. Chan, Connor Z. Lin, Matthew A. Chan, Koki Nagano, Boxiao Pan, Shalini De Mello, Orazio Gallo, Leonidas J. Guibas, Jonathan Tremblay, Sameh Khamis, Tero Karras, and Gordon Wetzstein. 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PixelNeRF: Neural radiance fields from one or few images. In Proc. CVPR, 2021. 2, 5, 6, 8, 1", + "[56] Richard Zhang, Phillip Isola, Alexei A Efros, Eli Shechtman, and Oliver Wang. The unreasonable effectiveness of deep features as a perceptual metric. In Proc. CVPR, 2018. 2, 4", + "[57] Chuanxia Zheng and Andrea Vedaldi. Free3d: Consistent novel view synthesis without 3d representation. In Proc. CVPR, 2024. 5, 6, 1", + "[58] Linqi Zhou, Yilun Du, and Jiajun Wu. 3d shape generation and completion through point-voxel diffusion. In Proc. ICCV, 2021. 2", + "[59] Zhizhuo Zhou and Shubham Tulsiani. Sparsefusion: Distilling view-conditioned diffusion for 3d reconstruction. In Proc. CVPR, 2023. 5, 1", + "[60] Matthias Zwicker, Hanspeter Pfister, Jeroen van Baar, and Markus H. Gross. EWA volume splatting. In Proc. IEEE Visualization Conference., 2001. 3" + ], + "bbox": [ + 501, + 92, + 890, + 842 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "10217", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Splatter Image_ Ultra-Fast Single-View 3D Reconstruction/a13161ef-830a-482f-925a-3b60cfe25a4d_model.json b/2024/Splatter Image_ Ultra-Fast Single-View 3D Reconstruction/a13161ef-830a-482f-925a-3b60cfe25a4d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a7fd543e03ba8bb1949af0c8855debd26d5596d9 --- /dev/null +++ b/2024/Splatter Image_ Ultra-Fast Single-View 3D Reconstruction/a13161ef-830a-482f-925a-3b60cfe25a4d_model.json @@ -0,0 +1,2299 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.19, + 0.131, + 0.78, + 0.154 + ], + "angle": 0, + "content": "Splatter Image: Ultra-Fast Single-View 3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.181, + 0.747, + 0.2 + ], + "angle": 0, + "content": "Stanislaw Szymanowicz Christian Rupprecht Andrea Vedaldi" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.204, + 0.678, + 0.222 + ], + "angle": 0, + "content": "Visual Geometry Group — University of Oxford" + }, + { + "type": "text", + "bbox": [ + 0.322, + 0.224, + 0.65, + 0.239 + ], + "angle": 0, + "content": "{stan, chrisr, vedaldi} @ robots.ox.ac.uk" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.273, + 0.485, + 0.433 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.273, + 0.892, + 0.44 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.449, + 0.894, + 0.493 + ], + "angle": 0, + "content": "Figure 1. The Splatter Image is an ultra-efficient method for single- and few-view 3D reconstruction. It uses an image-to-image neural network to map the input image to another image that holds the parameters of one coloured 3D Gaussian per pixel. Splatter Image achieves excellent 3D reconstruction quality on synthetic, real and large-scale datasets while using a single GPU for training." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.517, + 0.314, + 0.533 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.552, + 0.474, + 0.884 + ], + "angle": 0, + "content": "We introduce the Splatter Image, an ultra-efficient approach for monocular 3D object reconstruction. Splatter Image is based on Gaussian Splatting, which allows fast and high-quality reconstruction of 3D scenes from multiple images. We apply Gaussian Splatting to monocular reconstruction by learning a neural network that, at test time, performs reconstruction in a feed-forward manner, at 38 FPS. Our main innovation is the surprisingly straightforward design of this network, which, using 2D operators, maps the input image to one 3D Gaussian per pixel. The resulting set of Gaussians thus has the form an image, the Splatter Image. We further extend the method to several images as input via cross-view attention. Owning to the speed of the renderer (588 FPS), we use a single GPU for training while generating entire images at each iteration to optimize perceptual metrics like LPIPS. On several synthetic, real, multi-category and large-scale benchmark datasets, we achieve better results in terms of PSNR, LPIPS, and other metrics while training and evaluating much faster than prior works. Code, models and more results are available at https://szymanowicz.github.io/splatter-image." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.517, + 0.631, + 0.533 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.698 + ], + "angle": 0, + "content": "We contribute Splatter Image, a method that achieves ultrafast single-view reconstruction of the 3D shape and appearance of objects. Splatter Image uses a set of 3D Gaussians as the 3D representation, taking advantage of the rendering quality and speed of Gaussian Splatting [22]. Splatter Image works by predicting a 3D Gaussian for each of the input image pixels, using an image-to-image neural network. Remarkably, the predicted 3D Gaussians provide \\(360^{\\circ}\\) reconstructions of quality comparable or superior to much slower methods (Fig. 1)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.893, + 0.882 + ], + "angle": 0, + "content": "We formulate monocular 3D reconstruction as the problem of designing a neural network that takes an image of an object as input and produces as output a corresponding Gaussian mixture that represents all sides of it. While a Gaussian mixture is a set, i.e., an unordered collection, it can still be stored in an ordered data structure. Splatter Image takes advantage of this fact by using a \\(2D\\) image as the container of the 3D Gaussians, storing the parameters of one Gaussian (i.e., its opacity, position, shape, and colour) per pixel. The Gaussians predominantly lie on the rays from the camera to the object, but they can also be placed off the rays (Fig. 2), enabling \\(360^{\\circ}\\) object representation." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The advantage of storing a set of 3D Gaussians in an im" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10208" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "age is that it reduces the reconstruction problem to learning an image-to-image neural network. In this manner, the recon- constructor can be implemented utilizing only efficient 2D operators (e.g., 2D convolution instead of 3D convolution). We use in particular a U-Net [42] as those have demonstrated excellent performance in image generation [41]. In our case, their ability to capture small image details [55] helps to obtain higher-quality reconstructions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.214, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Since the 3D representation in Splatter Image is a mixture of 3D Gaussians, it enjoys the rendering and space efficiency of Gaussian Splattering, which benefits inference and training. In particular, rendering stops being a training bottleneck [34] and we can afford to generate complete views of the object to optimize perceptual metrics like LPIPS [56]. More importantly, the efficiency is such that our model can be trained on a single GPU on standard benchmarks of 3D objects or two GPUs on large datasets such as Objverse [10], whereas alternative methods typically require distributed training on dozens [26] or even hundreds [17] of GPUs. We also extend Splatter Image to take several views as input. This is achieved by taking the union of the Gaussian mixtures predicted from individual views, after registering them to a common coordinate frame. The different views communicate during prediction via lightweight cross-view attention layers in the architecture." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.472, + 0.566 + ], + "angle": 0, + "content": "Empirically, we show that, while the network only sees one side of the object, it can still produce a \\(360^{\\circ}\\) reconstruction of it by using the prior acquired during training. The \\(360^{\\circ}\\) information is encoded in the 2D image by allocating different Gaussians in a given 2D neighbourhood to different parts of the 3D object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.473, + 0.748 + ], + "angle": 0, + "content": "We validate Splatter Image by comparing it to alternative, slower reconstructors on standard benchmark datasets like ShapeNet [5] and CO3D [38]. To assess scalability and generalization, we also apply Splatter Image to multicategory reconstruction and train it on Objaverse [10], and evaluate it on Google Scanned Objects [12]. We obtain results of quality comparable to the recent Large Reconstruction Model of [15, 17], which is \\(50 \\times\\) more expensive to train. In fact, in several cases we even outperform slower methods in PSNR and LPIPS. We argue that this is because the very efficient design allows training the model very effectively, including using image-level losses like LPIPS." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To summarise, our contributions are: (1) to port Gaussian Splatting to learning-based monocular reconstruction; (2) to do so with the Splatter Image, a straightforward, efficient and performant 3D reconstruction approach that operates at 38 FPS on a standard GPU and affords single-GPU training; (3) to also extend the method to multi-view reconstruction; (4) and to obtain state-of-the-art reconstruction performance in multiple standard benchmarks, including synthetic, real, multi-category and large-scale datasets, in terms of reconstruction quality and speed." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.09, + 0.64, + 0.107 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.117, + 0.895, + 0.223 + ], + "angle": 0, + "content": "Representations for single-view 3D reconstruction. In recent years, implicit representations like NeRF [34] have dominated learning-based few-view reconstruction, parameterising the MLP in NeRF using global [19, 39], local [55] or both global and local codes [26]. However, implicit representations, particularly MLP-based ones, are notoriously slow to render, up to 2s for a single \\(128 \\times 128\\) image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.224, + 0.895, + 0.315 + ], + "angle": 0, + "content": "Follow-up works [14, 48] used faster, explicit, voxel grid representations that encode opacities and colours directly. Similar to DVGO [47], they achieve significant speed-ups, but, due to their voxel-based representation, they scale poorly with resolution. They also assume the knowledge of the absolute viewpoint of each object image." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.316, + 0.895, + 0.437 + ], + "angle": 0, + "content": "The triplane representation [3, 7] was proposed as a compromise between rendering speed and memory consumption. While they are not as fast to render as explicit representations, they allow view-space reconstruction [13] and are fast enough to be effectively used for single-view reconstruction [1, 13]. Triplane-based reconstructors were shown to scale to large datasets like Objaverse [9, 10], albeit at the cost of hundreds of GPUs for multiple days [17, 50]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.895, + 0.545 + ], + "angle": 0, + "content": "In contrast to these works, our method predicts a mixture of 3D Gaussians in a feed-forward manner. As a result, our method is cheap to train (1-2 GPUs), fast at inference and achieves real-time rendering speeds while achieving state-of-the-art image quality across multiple metrics on multiple standard single-view reconstruction benchmarks, including single- [45] and multi-category ShapeNet [5, 21]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.546, + 0.895, + 0.667 + ], + "angle": 0, + "content": "When more than one view is available at the input, one can use them to estimate the scene geometry [6, 31], learn a view interpolation function [51] or optimize a 3D representation of a scene using priors [18]. Our method is primarily a single-view reconstruction network, but we do show how Splatter Image can be extended to fuse multiple views. However, we focus our work on object-centric reconstruction rather than on generalising to unseen scenes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.895, + 0.87 + ], + "angle": 0, + "content": "3D Reconstruction with Point Clouds. PointOutNet [11] took image encoding as input and trained point cloud prediction networks [37] using 3D point cloud supervision. PVD [58] and \\(\\mathrm{PC^2}\\) [32] extended this approach using Diffusion Models [16] by conditioning the denoising process on partial point clouds and RGB images, respectively. These approaches require ground truth 3D point clouds, limiting their applicability. Other works [27, 40, 53] use point clouds as intermediate 3D representations for conditioning 2D inpainting or generation networks. However, these point clouds are assumed to correspond to only visible object points. In contrast, our Gaussians can model any part of the object, and thus afford \\(360^{\\circ}\\) reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Point cloud-based representations have also been used for high-quality reconstruction from multi-view images." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "10209" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.181 + ], + "angle": 0, + "content": "Novel views can be rendered with 2D inpainting networks for hole-filling [43], or by using non-isotropic 3D Gaussians with variable scale [22]. While showing high-quality results, Gaussian Splitting [22] requires many images per scene and has not yet been used in a learning-based reconstruction framework as we do here." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.471, + 0.245 + ], + "angle": 0, + "content": "Our method also uses 3D Gaussians as an underlying representation but predicts them from as few as a single image. Moreover, it outputs a full \\(360^{\\circ}\\) 3D reconstruction without using 2D or 3D inpainting networks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.25, + 0.469, + 0.431 + ], + "angle": 0, + "content": "Probabilistic 3D Reconstruction. Single-view 3D reconstruction is an ambiguous problem, so recently it has been tackled as a conditional generation task. Diffusion Models have been employed for conditional novel view synthesis [4, 29, 52]. Due to generating images without underlying geometries, the output images exhibit noticeable flicker. This can be mitigated by simultaneously generating multiview images [30, 44], reconstructing a geometry at every step of the denoising process [48, 49, 54] or training a robust reconstructor [25, 28]. Other works build and use a 3D [8, 35] or 2D [13, 33] prior which can be used in an image-conditioned auto-decoding framework." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.432, + 0.47, + 0.523 + ], + "angle": 0, + "content": "Here, we focus on deterministic reconstruction. However, few-view reconstruction is required to output 3D geometries from feed-forward methods [30, 44, 48, 49, 54]. Our method is capable of few-view 3D reconstruction, thus it is complementary to these generative methods and could lead to improvements in generation speed and quality." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.538, + 0.168, + 0.552 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.564, + 0.469, + 0.595 + ], + "angle": 0, + "content": "We discuss Gaussian Splatting in Sec. 3.1 for background, and then describe the Splatter Image in Secs. 3.2 to 3.6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.606, + 0.357, + 0.623 + ], + "angle": 0, + "content": "3.1. Overview of Gaussian Splitting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.705 + ], + "angle": 0, + "content": "A radiance field [34] is a pair of functions, assigning an opacity \\(\\sigma(\\pmb{x}) \\in \\mathbb{R}_+\\) and a colour \\(c(\\pmb{x},\\pmb{\\nu}) \\in \\mathbb{R}^3\\) to each 3D point \\(\\pmb{x} \\in \\mathbb{R}^3\\) and viewing direction \\(\\pmb{\\nu} \\in \\mathbb{S}^2\\). Gaussian Splatting [60] represents the two functions \\(\\sigma\\) and \\(c\\) as a mixture \\(\\theta\\) of \\(G\\) colored 3D Gaussians" + }, + { + "type": "equation", + "bbox": [ + 0.118, + 0.715, + 0.427, + 0.749 + ], + "angle": 0, + "content": "\\[\ng _ {i} (\\pmb {x}) = \\exp \\left(- \\frac {1}{2} (\\pmb {x} - \\pmb {\\mu} _ {i}) ^ {\\top} \\Sigma_ {i} ^ {- 1} (\\pmb {x} - \\pmb {\\mu} _ {i})\\right),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.76, + 0.47, + 0.837 + ], + "angle": 0, + "content": "where \\(1 \\leq i \\leq G\\), \\(\\pmb{\\mu}_i \\in \\mathbb{R}^3\\) is the Gaussian mean or center and \\(\\Sigma_i \\in \\mathbb{R}^{3 \\times 3}\\) is its covariance, specifying its shape and size. Each Gaussian has also an opacity \\(\\sigma_i \\in [0,1]\\) and a view-dependent colour \\(c_i(\\pmb{v}) \\in \\mathbb{R}^3\\). Together, they define a radiance field as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.847, + 0.469, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\sigma (\\boldsymbol {x}) = \\sum_ {i = 1} ^ {G} \\sigma_ {i} g _ {i} (\\boldsymbol {x}), \\quad c (\\boldsymbol {x}, \\boldsymbol {\\nu}) = \\frac {\\sum_ {i = 1} ^ {G} c _ {i} (\\boldsymbol {\\nu}) \\sigma_ {i} g _ {i} (\\boldsymbol {x})}{\\sum_ {j = 1} ^ {G} \\sigma_ {i} g _ {i} (\\boldsymbol {x})}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.826, + 0.107 + ], + "angle": 0, + "content": "The mixture of Gaussians is thus given by the set" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.119, + 0.818, + 0.136 + ], + "angle": 0, + "content": "\\[\n\\theta = \\left\\{\\left(\\sigma_ {i}, \\boldsymbol {\\mu} _ {i}, \\Sigma_ {i}, c _ {i}\\right), i = 1, \\dots , G \\right\\}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.149, + 0.892, + 0.209 + ], + "angle": 0, + "content": "A raidance field is rendered into an image \\(I(\\pmb{u})\\) by integrating the colors observed along the ray \\(\\pmb{x}_{\\tau} = \\pmb{x}_0 - \\tau \\pmb{\\nu}\\), \\(\\tau \\in \\mathbb{R}_+\\) that passes through each image pixel \\(\\pmb{u}\\) via the equation:" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.22, + 0.892, + 0.253 + ], + "angle": 0, + "content": "\\[\nI (\\boldsymbol {u}) = \\int_ {0} ^ {\\infty} c \\left(\\boldsymbol {x} _ {\\tau}, \\boldsymbol {\\nu}\\right) \\sigma \\left(\\boldsymbol {x} _ {\\tau}\\right) e ^ {- \\int_ {0} ^ {\\tau} \\sigma \\left(\\boldsymbol {x} _ {\\mu}\\right) d \\mu} d \\tau . \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.263, + 0.892, + 0.309 + ], + "angle": 0, + "content": "Gaussian Splatting [22, 60] provides a very fast differentiable renderer \\( I = \\mathcal{R}(\\theta, \\pi) \\) that approximates Eq. (2), mapping the mixture \\( \\theta \\) and the viewpoint \\( \\pi \\) to an image \\( I \\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.319, + 0.686, + 0.335 + ], + "angle": 0, + "content": "3.2. The Splatter Image" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.463 + ], + "angle": 0, + "content": "To perform monocular reconstruction we seek for a function \\(\\theta = S(I)\\) which is the 'inverse' of the renderer \\(\\mathcal{R}\\), mapping an image \\(I\\) to a mixture of 3D Gaussians \\(\\theta\\). Our key innovation is to propose an extremely simple and yet effective design for such a function. Specifically, we predict a Gaussian for each pixel of the input image \\(I\\) using a standard image-to-image neural network architecture. We call its output image \\(M\\) the Splatter Image." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.464, + 0.892, + 0.569 + ], + "angle": 0, + "content": "In more detail, Let \\(\\pmb{u} = (u_{1}, u_{2}, 1)\\) denote one of the \\(H \\times W\\) image pixels. This corresponds to ray \\(\\pmb{x} = \\pmb{u}d\\) in camera space, where \\(d\\) is the depth of the ray point. Our network \\(f\\) takes as input the \\(H \\times W \\times 3\\) RGB image \\(I\\), and outputs directly a \\(H \\times W \\times K\\) tensor \\(M\\), where each pixel is associated to the \\(K\\)-dimensional feature vector packing the parameters \\(M_{\\pmb{u}} = (\\sigma, \\pmb{\\mu}, \\Sigma, c)\\) of a corresponding Gaussian." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.57, + 0.892, + 0.629 + ], + "angle": 0, + "content": "We assume that Gaussians are expressed in the same reference frame of the camera. As illustrated in Fig. 2, the network predicts the depth \\(d\\) and offset \\((\\Delta_x, \\Delta_y, \\Delta_y)\\), setting" + }, + { + "type": "equation", + "bbox": [ + 0.628, + 0.629, + 0.892, + 0.678 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {\\mu} = \\left[ \\begin{array}{l} u _ {1} d + \\Delta_ {x} \\\\ u _ {2} d + \\Delta_ {y} \\\\ d + \\Delta_ {z} \\end{array} \\right]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.683, + 0.892, + 0.758 + ], + "angle": 0, + "content": "The network also predicts the opacity \\(\\sigma\\), the shape \\(\\Sigma\\) and the colour \\(c\\). For now, we assume that the colour is Lambertian, i.e., \\(c(\\nu) = c \\in \\mathbb{R}^3\\), and relax this assumption in Sec. 3.5. Section 3.6 provides more detail on the network architecture." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Discussion. One may wonder how this design can predict a full \\(360^{\\circ}\\) reconstruction of the object when the reconstruction is aligned a single input view. We find that the network adjusts the 3D offsets \\(\\Delta\\) and depths \\(d\\) to allocate some of the 3D Gaussians to reconstruct the input view, and some to reconstruct unseen portions of the object, automatically. The network can also decide to switch off any Gaussian by simply predicting \\(\\sigma = 0\\), if needed. These points are then not rendered and can be culled in post-processing." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "10210" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.092, + 0.462, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.246, + 0.47, + 0.304 + ], + "angle": 0, + "content": "Figure 2. Predicting locations. The location of each Gaussian is parameterised by depth \\( d \\) and a 3D offset \\( \\Delta = (\\Delta_x, \\Delta_y, \\Delta_z) \\). The 3D Gaussians are projected to depth \\( d \\) (blue) along camera rays (green) and moved by the 3D offset \\( \\Delta \\) (red)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.326, + 0.468, + 0.388 + ], + "angle": 0, + "content": "Our design can also be seen as an extension of depth prediction networks which only predicting the depth of each pixel. Here, we also predict unobserved parts of the geometry, as well as the shape and appearance of each Gaussian." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.395, + 0.281, + 0.411 + ], + "angle": 0, + "content": "3.3. Learning formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.584 + ], + "angle": 0, + "content": "Learning to predict the Splatter Image is simple and efficient. It can be done on a single GPU using at most 20GB of memory at training time in most of our single-view reconstruction experiments (except for Objaverse, where we use 2 GPUs and using 26GB of memory on each). For training, we assume a multi-view dataset, either real or synthetic. The dataset \\(\\mathcal{D}\\) consists of triplets \\((I,J,\\pi)\\), where \\(I\\) is a source image, \\(J\\) a target image, and \\(\\pi\\) the viewpoint change between the source and the target cameras. Then we simply feed the source \\(I\\) as input to Splatter Image, and minimize the average reconstruction loss of target view \\(J\\):" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.591, + 0.47, + 0.629 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} (\\mathcal {S}) = \\frac {1}{| \\mathcal {D} |} \\sum_ {(I, J, \\pi) \\in \\mathcal {D}} \\| J - \\mathcal {R} (\\mathcal {S} (I), \\pi) \\| ^ {2}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.637, + 0.468, + 0.773 + ], + "angle": 0, + "content": "Image-level losses. A main advantage of the speed and efficiency of our method is that it allows for rendering entire images at each training iteration, even for relatively large batches (this differs from NeRF [34], which only generates a certain number of pixels in a batch). In particular, this means that, in addition to decomposable losses like the \\(L2\\) loss above, we can use image-level losses like LPIPS [56], which do not decompose into per-pixel losses. In practice, we experiment with a combination of such losses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.468, + 0.84 + ], + "angle": 0, + "content": "Regularisations. We also add generic regularisers to prevent parameters from taking on unreasonable values (e.g., Gaussians which are larger than the reconstructed objects, or vanishingly small). Please see the sup. mat. for details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.409, + 0.864 + ], + "angle": 0, + "content": "3.4. Extension to multiple input viewpoints" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.468, + 0.901 + ], + "angle": 0, + "content": "If two or more input views \\(I_j\\), \\(j \\in \\{1, \\dots, N\\}\\) are provided, we can apply network \\(S\\) multiple times to obtain" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.257 + ], + "angle": 0, + "content": "multiple Splatter Images \\(M_{j}\\), one per view. If \\((R, T)\\) is the relative camera pose change from an additional view to the reference view, we can take the mixture of 3D Gaussians \\(\\theta\\) defined in the additional view's coordinates and warp it to the reference view. Specifically, a Gaussian of parameters \\((\\sigma, \\mu, \\Sigma, c)\\) maps to Gaussian of parameters \\((\\sigma, \\tilde{\\mu}, \\tilde{\\Sigma}, \\tilde{c})\\) where \\(\\tilde{\\mu} = R\\mu + T\\), \\(\\tilde{\\Sigma} = R\\Sigma R^{\\top}\\), \\(\\tilde{c} = c\\). We use the symbol \\(\\phi[\\theta]\\) to denote the Gaussian mixture obtained by warping each Gaussian in \\(\\theta\\). Here we have also assumed a Lambertian colour model and will discuss in Sec. 3.5 how more complex models transform." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.258, + 0.892, + 0.333 + ], + "angle": 0, + "content": "Given \\(N\\) different views \\(I_{j}\\) and corresponding warps \\(\\phi\\), we can obtain a composite mixture of 3D Gaussians simply by taking their union \\(\\Theta = \\bigcup_{j=1}^{N} \\phi_{j}[S(I_{j})]\\). Note that this set of 3D Gaussians is defined in the coordinate system of the reference camera." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.345, + 0.715, + 0.361 + ], + "angle": 0, + "content": "3.5. View-dependent colour" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.369, + 0.892, + 0.476 + ], + "angle": 0, + "content": "Generalising beyond the Lambertian colour model, we use spherical harmonics [22] to represent view-dependent colours. For a particular Gaussian \\((\\sigma, \\mu, \\Sigma, c)\\), we then define \\([c(\\pmb{\\nu}; \\pmb{\\alpha})]_i = \\sum_{l=0}^L \\sum_{m=-L}^L \\alpha_{ilm} Y_l^m(\\pmb{\\nu})\\) where \\(\\alpha_{ilm}\\) are coefficients predicted by the network and \\(Y_l^m\\) are spherical harmonics, \\(L\\) is the order of the expansion, and \\(\\pmb{\\nu} \\in \\mathbb{S}^2\\) is the viewing direction." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.477, + 0.892, + 0.658 + ], + "angle": 0, + "content": "The viewpoint change of Sec. 3.4 transforms a viewing direction \\(\\pmb{\\nu}\\) in the source camera to the corresponding viewing direction in the reference frame as \\(\\tilde{\\pmb{\\nu}} = R\\pmb{\\nu}\\). We can then find the transformed colour function by finding the coefficients \\(\\tilde{\\alpha}\\) such that \\(c(\\pmb{\\nu};\\pmb{\\alpha}) = c(\\tilde{\\pmb{\\nu}};\\tilde{\\pmb{\\alpha}})\\). This is possible because (each order of) spherical harmonics are closed under rotation. However, the general case requires the computation of Wigner matrices. For simplicity, we only consider orders \\(L = 0\\) (Lambertian) and \\(L = 1\\). Hence, the first level has one constant component \\(Y_0^0\\) and the second level has three components which we can write collectively as \\(Y_{1} = [Y_{1}^{-1},Y_{1}^{0},Y_{1}^{1}]\\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.56, + 0.67, + 0.831, + 0.719 + ], + "angle": 0, + "content": "\\[\nY _ {1} (\\boldsymbol {\\nu}) = \\sqrt {\\frac {3}{4 \\pi}} \\Pi \\boldsymbol {\\nu}, \\quad \\Pi = \\left[ \\begin{array}{c c c} 0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\ 1 & 0 & 0 \\end{array} \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.892, + 0.776 + ], + "angle": 0, + "content": "We can then conveniently rewrite \\([c(\\pmb {\\nu};\\pmb {\\alpha})]_i = \\alpha_{i0} +\\) \\(\\pmb{\\alpha}_{i1}^{\\top}Y_{1}(\\pmb {\\nu})\\) . From this and \\(c(\\pmb {\\nu};\\alpha_0,\\pmb {\\alpha}_1) = c(\\tilde{\\pmb{\\nu}};\\tilde{\\alpha}_0,\\tilde{\\alpha}_1)\\) we conclude that \\(\\tilde{\\alpha}_{i0} = \\tilde{\\alpha}_{i0}\\) , and \\(\\tilde{\\alpha}_{i1} = \\Pi^{-1}R\\Pi \\alpha_{i1}\\)" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.755, + 0.801 + ], + "angle": 0, + "content": "3.6. Neural network architecture" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The bulk of the predictor \\(S\\) mapping the input image \\(I\\) to the mixture of Gaussians \\(\\theta\\) is architecturally identical to the SongUNet of [46]. The last layer is replaced with a \\(1\\times 1\\) convolutional layer with \\(12 + k_{c}\\) output channels, where \\(k_{c}\\in \\{3,12\\}\\) depending on the colour model. Given \\(I\\in \\mathbb{R}^{3\\times H\\times W}\\) as input, the network thus produces" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10211" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.262 + ], + "angle": 0, + "content": "a \\((12 + k_{c})\\times H\\times W\\) tensor as output, coding, for each pixel \\(\\pmb{u}\\) channels, the parameters \\((\\hat{\\sigma},\\Delta ,\\hat{d},\\hat{s},\\hat{q},\\alpha)\\) which are then transformed to opacity, offset, depth, scale, rotation and colour, respectively. These are activated by nonlinear functions to obtain the Gaussian parameters. Specifically, the opacity is obtained using the sigmoid operator as \\(\\sigma =\\) sigmoid( \\(\\hat{\\sigma}\\) ). The depth is obtained as \\(d =\\) \\((z_{\\mathrm{far}} - z_{\\mathrm{near}})\\) sigmoid \\((\\hat{d}) + z_{\\mathrm{near}}\\) . The mean \\(\\mu\\) is then obtained using Eq. (3). Following [22], the covariance is obtained as \\(\\Sigma = R(\\pmb {q})\\mathrm{diag}(\\exp \\hat{s})^{2}R(\\pmb {q})^{\\top}\\) where \\(R(\\pmb {q})\\) is the rotation matrix with quaternion \\(\\pmb {q} = \\hat{\\pmb{q}} /\\| \\hat{\\pmb{q}}\\|\\) and \\(\\hat{\\pmb{q}}\\in \\mathbb{R}^4\\)" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.262, + 0.472, + 0.337 + ], + "angle": 0, + "content": "For multi-view reconstruction, we apply the same network to each input view and then use the approach of Sec. 3.4 to fuse the individual reconstructions. In order to allow the network to coordinate and exchange information between views, we apply two modifications to it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.337, + 0.473, + 0.474 + ], + "angle": 0, + "content": "First, we condition the network with the corresponding camera pose \\((R,T)\\) (we only assume access to the relative camera pose to a common but otherwise arbitrary reference frame). In fact, since we consider cameras in a turn-table-like configuration, we only pass vectors \\((Re_3,T)\\) where \\(e_3 = (0,0,1)\\). We do so by encoding each entry via a sinusoidal positional embedding of order 9, resulting in 60 dimensions in total. Finally, these are applied to the U-Net blocks via FiLM [36] embeddings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.472, + 0.535 + ], + "angle": 0, + "content": "Second, we add cross-attention layers to allow communication between the features of different views. We do so in a manner similar to [44], but only at the lowest UNet resolution, which maintains the computational cost very low." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.55, + 0.21, + 0.568 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.576, + 0.47, + 0.638 + ], + "angle": 0, + "content": "We evaluate our method extensively for single-view reconstruction on six standard benchmarks. Next, we assess the quality of multi-view reconstruction, and finish with an evaluation of the speed of the method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Datasets. The standard benchmark for evaluating single-view 3D reconstruction is ShapeNet-SRN [45]. We train our method in the single-class setting and report results on the \"Car\" and \"Chair\" classes, following prior work. Moreover, we challenge our method with two classes of real objects from the CO3D [38] dataset: Hydrants and Teddybears. In this challenging dataset ripe with ambiguities we set \\( z_{\\mathrm{far}} \\) and \\( z_{\\mathrm{near}} \\) to depend on ground truth distance \\( z_{\\mathrm{gt}} \\) between the object and camera." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We further test our method on two multi-category datasets. First, we use the standard benchmark of multicategory ShapeNet (with objects from 13 largest categories), and use the renderings, standard splits and target views from NMR [21]. Secondly, we train one model on renderings of objects from Objaverse-LVIS [10] which contains over 1k object categories, using the renderings from Zero-1-to-3 [29]. We evaluate this model on all objects" + }, + { + "type": "table", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.239 + ], + "angle": 0, + "content": "
MethodRC1-view Cars1-view Chairs
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
SRN✗22.250.880.12922.890.890.104
CodeNeRF✗23.800.910.12823.660.900.166
FE-NVS✗22.830.910.09923.210.920.077
ViewsetDiff w/o D✗23.210.900.11624.160.910.088
PixelNeRF✓23.170.890.14623.720.900.128
VisionNeRF✓22.880.900.08424.480.920.077
NeRFDiff w/o NGD✓23.950.920.09224.800.930.070
Ours✓24.000.920.07824.430.930.067
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.248, + 0.895, + 0.32 + ], + "angle": 0, + "content": "Table 1. ShapeNet-SRN: Single-View Reconstruction. Our method achieves State-of-the-Art reconstruction quality on all metrics on the Car dataset and on two metrics in the Chair dataset, while performing reconstruction in the camera view-space. 'RC' indicates if a method can operate using only relative camera poses." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.895, + 0.452 + ], + "angle": 0, + "content": "from the Google Scanned Objects dataset [12], using the same renderings as used for evaluation in Free3D [57]. We train and evaluate all models at \\( 128 \\times 128 \\) resolution, apart from multi-category ShapeNet which is at \\( 64 \\times 64 \\). Finally, we use the ShapeNet-SRN Cars dataset for the evaluation of the two-view reconstruction quality. For more details on datasets see supp. mat." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.458, + 0.895, + 0.67 + ], + "angle": 0, + "content": "Baselines. For ShapeNet (both single-class and multiclass), we compare against implicit [19, 26, 45, 55], hybrid implicit-explicit [13] and explicit methods [2, 14, 48]. We use the deterministic variants of [13, 48] by using their reconstruction network in a single forward pass. For CO3D we compare against PixelNeRF which we train for 400,000 iterations with their officially released code on the same data as used for our method. Finally, on Objaverse-LVIS we compare to OpenLRM [15] (open-source version of LRM [17]): a large triplane-based reconstructor, trained on the full Objaverse dataset. Since we are proposing a deterministic reconstruction method, we do not compare to methods that employ Score Distillation [29, 59] or feedforward diffusion models [4, 28, 52, 54]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.67, + 0.874, + 0.687 + ], + "angle": 0, + "content": "Implementation details can be found in the supp. mat." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.696, + 0.816, + 0.713 + ], + "angle": 0, + "content": "4.1. Evaluation of reconstruction quality" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.894, + 0.827 + ], + "angle": 0, + "content": "In line with related works [26, 55], we assess the quality of the reconstructions by measuring novel view synthesis quality and report Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and a perceptual loss (LPIPS). We perform reconstruction from a given source view and render the 3D shape to unseen target views following standard protocols as detailed in the supp. mat." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.846, + 0.766, + 0.862 + ], + "angle": 0, + "content": "4.1.1 Single-view 3D reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.893, + 0.903 + ], + "angle": 0, + "content": "ShapeNet. In Tab. 1 and Fig. 3 we compare the single-view reconstruction quality on the ShapeNet-SRN benchmark." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "10212" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.473, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.366, + 0.471, + 0.409 + ], + "angle": 0, + "content": "Figure 3. ShapeNet-SRN Comparison. Our method outputs more accurate reconstructions (cars' backs, top chair) and better represents thin regions (bottom chair)." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.421, + 0.466, + 0.473 + ], + "angle": 0, + "content": "
PixelNeRF [55]FE-NVS [14]FWD [2]VisionNeRF [26]Ours
PSNR ↑26.8027.0826.6628.7629.38
SSIM ↑0.910.920.910.930.95
LPIPS ↓0.1080.0820.0550.0650.047
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.476, + 0.469, + 0.504 + ], + "angle": 0, + "content": "Table 2. Our method achieves State-of-the-Art quality of single-view reconstruction on multi-class ShapeNet dataset." + }, + { + "type": "table", + "bbox": [ + 0.085, + 0.518, + 0.46, + 0.611 + ], + "angle": 0, + "content": "
ObjectMethodPSNR ↑SSIM ↑LPIPS ↓
HydrantPixelNeRF21.760.780.203
HydrantOurs21.800.800.150
TeddybearPixelNeRF19.380.650.290
TeddybearOurs19.440.730.231
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.621, + 0.468, + 0.65 + ], + "angle": 0, + "content": "Table 3. CO3D: Single-View. Our method outperforms PixelNeRF on this challenging benchmark across all metrics." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.677, + 0.469, + 0.812 + ], + "angle": 0, + "content": "Our method outperforms all deterministic reconstructors in SSIM and LPIPS, obtaining sharper new views. Furthermore, our method requires only relative camera poses instead of absolute/canonical ones. Qualitatively, our method does well in challenging situations with limited visibility and thin structures. In Tab. 2, we use instead the multicategory ShapeNet protocol we observe that our method outperforms more expensive baselines [26] across all metrics in the multi-category ShapeNet setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.819, + 0.469, + 0.865 + ], + "angle": 0, + "content": "CO3D. On CO3D bears and hydrants, our model outperforms PixelNeRF on all metrics (Tab. 3), and qualitatively produces sharper images (Fig. 4) while being \\(1,000 \\times\\) faster." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Objaverse-LVIS and Google Scanned Objects. We compare our method to OpenLRM [15], an open-source ver" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.089, + 0.892, + 0.27 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.28, + 0.892, + 0.321 + ], + "angle": 0, + "content": "Figure 4. CO3D Hydrants and Teddybears. Our method outputs sharper reconstructions than PixelNeRF while being \\(100\\mathrm{x}\\) faster in inference." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.346, + 0.851, + 0.408 + ], + "angle": 0, + "content": "
MethodPSNR ↑SSIM ↑LPIPS ↓
OpenLRM18.060.840.129
Ours21.060.880.111
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.419, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Table 4. Google Scanned Objects: Single-View. Our method outperforms the much more expensive LRM [15, 17] on single-view open-world reconstruction." + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.484, + 0.878, + 0.668 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.673, + 0.892, + 0.729 + ], + "angle": 0, + "content": "Figure 5. Google Scanned Objects. On large datasets our model has similar quality to much more expensive baselines (shoe). Our reconstructions have more accurate lighting (Jenga), object pose (horse) and shape (toy)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "sion of the LRM model [17], on the Google Scanned Objects [12] evaluation renderings from Free3D [57]. Quantitatively, in Tab. 4 Splatter Image outperforms OpenLRM and, qualitatively (Fig. 5), it is comparable. Our models perform well even on images collected from the Internet Fig. 6, after removing backgrounds and resizing. Remarkably, our method, trained for 7 GPU days, is able to compete with OpenLRM, which uses hundreds of GPUs for several days [15, 17]." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10213" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.09, + 0.087, + 0.46, + 0.34 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.343, + 0.47, + 0.371 + ], + "angle": 0, + "content": "Figure 6. Our models trained on single classes (top) and on Objaverse (bottom) can be used on in-the-wild Internet images (right)." + }, + { + "type": "table", + "bbox": [ + 0.143, + 0.385, + 0.404, + 0.493 + ], + "angle": 0, + "content": "
MethodRelative Pose2-view Cars
PSNR ↑SSIM ↑
SRNX24.840.92
CodeNeRFX25.710.91
FE-NVSX24.640.93
PixelNeRF✓25.660.94
Ours✓26.010.94
" + }, + { + "type": "table_caption", + "bbox": [ + 0.098, + 0.503, + 0.447, + 0.517 + ], + "angle": 0, + "content": "Table 5. Two-view reconstruction on ShapeNet-SRN Cars." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.531, + 0.329, + 0.544 + ], + "angle": 0, + "content": "4.1.2 Two-view 3D reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.555, + 0.47, + 0.736 + ], + "angle": 0, + "content": "We compare our multi-view reconstruction model on ShapeNet-SRN Cars by training it for two-view predictions (see Tab. 5). Prior work often relies on absolute camera pose conditioning, meaning that the model learns to rely on the canonical orientation of the object in the dataset. This limits the applicability of these models, as in practice for a new image of an object, the absolute camera pose is of course unknown. Here, only ours and PixelNeRF can deal with relative camera poses as input. Interestingly, our method shows not only better performance than PixelNeRF in both real and synthetic data but also improves over SRN, CodeNeRF, and FE-NVS that rely on absolute camera poses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.2, + 0.77 + ], + "angle": 0, + "content": "4.1.3 Ablations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.841 + ], + "angle": 0, + "content": "We evaluate the influence of individual components of our method, using a shorter training schedule than models in Tab. 1 for efficiency. Ablations of the multi-view model are given in the supp. mat." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We show the results of our ablation study for the single-view model in Tab. 6. We train a model (w/o image) that uses a fully connected, unstructured output instead of a Splatter Image. This model cannot transfer image informa" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.088, + 0.895, + 0.371 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.383, + 0.893, + 0.453 + ], + "angle": 0, + "content": "Figure 7. Analysis. Splatter Images represent full \\(360^{\\circ}\\) of objects by allocating background pixels to appropriate 3D locations (third row) to predict occluded elements like wheels (left) or chair legs (middle). Alternatively, it predicts offsets in the foreground pixels to represent occluded chair parts (right)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.466, + 0.893, + 0.723 + ], + "angle": 0, + "content": "tion directly to their corresponding Gaussians and does not achieve good performance. We also ablate predicting the depth along the ray by simply predicting 3D coordinates for each Gaussian. This version also suffers from its inability to easily align the input image with the output. Removing the 3D offset prediction mainly harms the backside of the object while leaving the front faces the same. This results in a lower impact on the overall performance of this component. Changing the degrees of freedom of appearance predictions (by fixing Gaussians to be isotropic or removing view-dependence) also reduced the image fidelity. Finally, removing perceptual loss (w/o \\(\\mathcal{L}_{\\mathrm{LPIPS}}\\)) results in a significant worsening of LPIPS, indicating this loss is important for perceptual sharpness of reconstructions. Being able to use LPIPS in optimisation is a direct consequence of employing a fast-to-render representation and being able to render full images at training time." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.73, + 0.892, + 0.835 + ], + "angle": 0, + "content": "Analysis. In Fig. 7, we analyse how 3D information is stored inside a Splatter Image. Since all information is arranged in an image format, we can visualise each of the modalities: opacity, depth, and location. Pixels of the input image that belong to the object tend to describe their corresponding 3D structure, while pixels outside of the object wrap around to close the object on the back." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.833, + 0.863 + ], + "angle": 0, + "content": "4.2. Evaluation of reconstruction efficiency" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "A key advantage of the Splatter Image is its training and test time efficiency, which we assess below." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "10214" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.111, + 0.089, + 0.437, + 0.233 + ], + "angle": 0, + "content": "
PSNR ↑SSIM ↑LPIPS ↓
Full model22.250.900.115
w/o image20.600.870.152
w/o depth21.210.880.145
w/o view dir.21.770.890.121
isotropic22.010.890.118
w/o offset22.060.900.119
w/o LPIPS22.220.890.141
" + }, + { + "type": "table_caption", + "bbox": [ + 0.122, + 0.243, + 0.424, + 0.257 + ], + "angle": 0, + "content": "Table 6. Ablations: Single-View Reconstruction." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.273, + 0.46, + 0.4 + ], + "angle": 0, + "content": "
RPE↓R↓Forward↓Test↓
NeRFDiff✓(0.031)(0.0180)(0.103)(4.531)
FE-NVS✗(0.015)(0.0032)(0.028)(0.815)
VisionNeRF✓0.0082.43129.733607.8
PixelNeRF✓0.0031.85727.432463.3
ViewsetDiff✗0.0250.00640.0511.625
Ours 2-view✓0.0300.00170.0370.455
Ours 1-view✓0.0260.00170.0330.451
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.411, + 0.469, + 0.495 + ], + "angle": 0, + "content": "Table 7. Speed. Time required for image encoding (E), rendering (R), the 'Forward' time, indicative of train-time efficiency and the 'Test' time, indicative of test-time efficiency. Our method is the most efficient in both train and test time across open-source available methods and only requires relative camera poses. 'RP' indicates if a method can operate using only relative camera poses." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.522, + 0.469, + 0.598 + ], + "angle": 0, + "content": "Test-time efficiency. First, we assess the 'Test' time speed, i.e., the time it takes for the trained model to reconstruct an object and generate a certain number of images. We reference the evaluation protocol of the standard ShapeNet-SRN benchmark [45] and render 250 images at \\(128^{2}\\) resolution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.809 + ], + "angle": 0, + "content": "Assessing wall-clock time fairly is challenging as it depends on many factors. All measurements reported here are done on a single NVIDIA V100 GPU. We use officially released code of Viewset Diffusion [48], PixelNeRF [55] and VisionNeRF [26] and rerun those on our hardware. NeRFDiff [13] and FE-NVS [14] do not have code available, so we use their self-reported metrics. According to the authors, FE-NVS was evaluated on the same type of GPU, while NeRFDiff does not include information about the hardware used and we were unable to obtain more information. Since we could not perfectly control these experiments, the comparisons to NeRFDiff and FE-NVS are only indicative. For Viewset Diffusion and NeRFDiff we report the time for a single pass through the reconstruction network." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Tab. 7 reports the 'Encoding' (E) time, spent by the network to compute the object's 3D representation from an image, and the 'Rendering' (R) time, spent by the network to render new images from the 3D representation. From those, we calculate the 'Test' time, equal to the 'Encoding' time plus 250 'Rendering' time. As shown in the last column" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.228 + ], + "angle": 0, + "content": "of Tab. 7, our method is more than \\(1000 \\times\\) faster in testing than PixelNeRF and VisionNeRF (while achieving equal or superior quality of reconstruction in Tab. 1). Our method is also faster than voxel-based Viewset Diffusion even though it does not require knowing the absolute camera pose. The efficiency of our method is very useful to iterate quickly in research; for instance, evaluating our method on the full ShapeNet-Car validation set takes less than 10 minutes on a single GPU. In contrast, PixelNeRF takes 45 GPU-hours." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.235, + 0.893, + 0.538 + ], + "angle": 0, + "content": "Train-time efficiency. Next, we assess the efficiency of the method during training. Here, the encoding time becomes more significant because one typically renders only a few images to compute the reconstruction loss and obtain a gradient (e.g., because there are only so many views available in the training dataset, or because generating more views provides diminishing returns in terms of supervision). As typical values (and as used by us in this work), we assume that the method is tasked with generating 4 new views at each iteration instead of 250 as before. We call this the 'Forward' time and measure it the same way. As shown in the 'Forward' column of Tab. 7, our method is \\(246 \\times\\) faster at training time than implicit methods and \\(1.5 \\times\\) than Viewset Diffusion, which uses an explicit representation. With this, we can train models achieving state-of-the-art quality on a single A6000 GPU in 7 days, while VisionNeRF requires 16 A100 GPUs for 5 days. What is even more remarkable, we can train models on large datasets such as Objaverse on two A6000 GPUs in 3.5 days, while triplane-based methods such as LRM require 128 A100 GPUs for 3 days [17]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.557, + 0.618, + 0.572 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.583, + 0.892, + 0.75 + ], + "angle": 0, + "content": "We have presented Splatter Image, a simple method for single- or few-view 3D reconstruction. The method uses an off-the-shelf 2D image-to-image network and predicts a pseudo-image containing one colored 3D Gaussian per pixel. By combining fast inference with fast rendering via Gaussian Splatting, Splatter Image can be trained and evaluated quickly on synthetic and real benchmarks. Splatter Image achieves state-of-the-art reconstruction performance without requiring absolute/canonical camera poses at test time, is simple to implement, and can be trained and tested much faster than many alternatives." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.757, + 0.892, + 0.833 + ], + "angle": 0, + "content": "Ethics. We use various datasets in a manner compatible with their terms. There is no processing of personal data. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements. S. Szymanowicz is supported by an EPSRC Doctoral Training Partnerships Scholarship (DTP) EP/R513295/1 and the Oxford-Ashton Scholarship. A. Vedaldi is supported by ERC-CoG UNION 101001212." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "10215" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Titas Anciukevicius, Zexiang Xu, Matthew Fisher, Paul Henderson, Hakan Bilen, Niloy J. Mitra, and Paul Guerrero. RenderDiffusion: Image diffusion for 3d reconstruction, inpainting and generation. In Proc. CVPR, 2022. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.171, + 0.47, + 0.212 + ], + "angle": 0, + "content": "[2] Ang Cao, Chris Rockwell, and Justin Johnson. Fwd: Realtime novel view synthesis with forward warping and depth. 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The Splatter Image is an ultra-efficient method for single- and few-view 3D reconstruction. It uses an image-to-image neural network to map the input image to another image that holds the parameters of one coloured 3D Gaussian per pixel. Splatter Image achieves excellent 3D reconstruction quality on synthetic, real and large-scale datasets while using a single GPU for training. + +![](images/0f6dd5b5e2edf5f1141648a74f1c4ff46a2b834a4167b34a310ee66c4fdbc2bc.jpg) + +# Abstract + +We introduce the Splatter Image, an ultra-efficient approach for monocular 3D object reconstruction. Splatter Image is based on Gaussian Splatting, which allows fast and high-quality reconstruction of 3D scenes from multiple images. We apply Gaussian Splatting to monocular reconstruction by learning a neural network that, at test time, performs reconstruction in a feed-forward manner, at 38 FPS. Our main innovation is the surprisingly straightforward design of this network, which, using 2D operators, maps the input image to one 3D Gaussian per pixel. The resulting set of Gaussians thus has the form an image, the Splatter Image. We further extend the method to several images as input via cross-view attention. Owning to the speed of the renderer (588 FPS), we use a single GPU for training while generating entire images at each iteration to optimize perceptual metrics like LPIPS. On several synthetic, real, multi-category and large-scale benchmark datasets, we achieve better results in terms of PSNR, LPIPS, and other metrics while training and evaluating much faster than prior works. Code, models and more results are available at https://szymanowicz.github.io/splatter-image. + +# 1. Introduction + +We contribute Splatter Image, a method that achieves ultrafast single-view reconstruction of the 3D shape and appearance of objects. Splatter Image uses a set of 3D Gaussians as the 3D representation, taking advantage of the rendering quality and speed of Gaussian Splatting [22]. Splatter Image works by predicting a 3D Gaussian for each of the input image pixels, using an image-to-image neural network. Remarkably, the predicted 3D Gaussians provide $360^{\circ}$ reconstructions of quality comparable or superior to much slower methods (Fig. 1). + +We formulate monocular 3D reconstruction as the problem of designing a neural network that takes an image of an object as input and produces as output a corresponding Gaussian mixture that represents all sides of it. While a Gaussian mixture is a set, i.e., an unordered collection, it can still be stored in an ordered data structure. Splatter Image takes advantage of this fact by using a $2D$ image as the container of the 3D Gaussians, storing the parameters of one Gaussian (i.e., its opacity, position, shape, and colour) per pixel. The Gaussians predominantly lie on the rays from the camera to the object, but they can also be placed off the rays (Fig. 2), enabling $360^{\circ}$ object representation. + +The advantage of storing a set of 3D Gaussians in an im + +age is that it reduces the reconstruction problem to learning an image-to-image neural network. In this manner, the recon- constructor can be implemented utilizing only efficient 2D operators (e.g., 2D convolution instead of 3D convolution). We use in particular a U-Net [42] as those have demonstrated excellent performance in image generation [41]. In our case, their ability to capture small image details [55] helps to obtain higher-quality reconstructions. + +Since the 3D representation in Splatter Image is a mixture of 3D Gaussians, it enjoys the rendering and space efficiency of Gaussian Splattering, which benefits inference and training. In particular, rendering stops being a training bottleneck [34] and we can afford to generate complete views of the object to optimize perceptual metrics like LPIPS [56]. More importantly, the efficiency is such that our model can be trained on a single GPU on standard benchmarks of 3D objects or two GPUs on large datasets such as Objverse [10], whereas alternative methods typically require distributed training on dozens [26] or even hundreds [17] of GPUs. We also extend Splatter Image to take several views as input. This is achieved by taking the union of the Gaussian mixtures predicted from individual views, after registering them to a common coordinate frame. The different views communicate during prediction via lightweight cross-view attention layers in the architecture. + +Empirically, we show that, while the network only sees one side of the object, it can still produce a $360^{\circ}$ reconstruction of it by using the prior acquired during training. The $360^{\circ}$ information is encoded in the 2D image by allocating different Gaussians in a given 2D neighbourhood to different parts of the 3D object. + +We validate Splatter Image by comparing it to alternative, slower reconstructors on standard benchmark datasets like ShapeNet [5] and CO3D [38]. To assess scalability and generalization, we also apply Splatter Image to multicategory reconstruction and train it on Objaverse [10], and evaluate it on Google Scanned Objects [12]. We obtain results of quality comparable to the recent Large Reconstruction Model of [15, 17], which is $50 \times$ more expensive to train. In fact, in several cases we even outperform slower methods in PSNR and LPIPS. We argue that this is because the very efficient design allows training the model very effectively, including using image-level losses like LPIPS. + +To summarise, our contributions are: (1) to port Gaussian Splatting to learning-based monocular reconstruction; (2) to do so with the Splatter Image, a straightforward, efficient and performant 3D reconstruction approach that operates at 38 FPS on a standard GPU and affords single-GPU training; (3) to also extend the method to multi-view reconstruction; (4) and to obtain state-of-the-art reconstruction performance in multiple standard benchmarks, including synthetic, real, multi-category and large-scale datasets, in terms of reconstruction quality and speed. + +# 2. Related work + +Representations for single-view 3D reconstruction. In recent years, implicit representations like NeRF [34] have dominated learning-based few-view reconstruction, parameterising the MLP in NeRF using global [19, 39], local [55] or both global and local codes [26]. However, implicit representations, particularly MLP-based ones, are notoriously slow to render, up to 2s for a single $128 \times 128$ image. + +Follow-up works [14, 48] used faster, explicit, voxel grid representations that encode opacities and colours directly. Similar to DVGO [47], they achieve significant speed-ups, but, due to their voxel-based representation, they scale poorly with resolution. They also assume the knowledge of the absolute viewpoint of each object image. + +The triplane representation [3, 7] was proposed as a compromise between rendering speed and memory consumption. While they are not as fast to render as explicit representations, they allow view-space reconstruction [13] and are fast enough to be effectively used for single-view reconstruction [1, 13]. Triplane-based reconstructors were shown to scale to large datasets like Objaverse [9, 10], albeit at the cost of hundreds of GPUs for multiple days [17, 50]. + +In contrast to these works, our method predicts a mixture of 3D Gaussians in a feed-forward manner. As a result, our method is cheap to train (1-2 GPUs), fast at inference and achieves real-time rendering speeds while achieving state-of-the-art image quality across multiple metrics on multiple standard single-view reconstruction benchmarks, including single- [45] and multi-category ShapeNet [5, 21]. + +When more than one view is available at the input, one can use them to estimate the scene geometry [6, 31], learn a view interpolation function [51] or optimize a 3D representation of a scene using priors [18]. Our method is primarily a single-view reconstruction network, but we do show how Splatter Image can be extended to fuse multiple views. However, we focus our work on object-centric reconstruction rather than on generalising to unseen scenes. + +3D Reconstruction with Point Clouds. PointOutNet [11] took image encoding as input and trained point cloud prediction networks [37] using 3D point cloud supervision. PVD [58] and $\mathrm{PC^2}$ [32] extended this approach using Diffusion Models [16] by conditioning the denoising process on partial point clouds and RGB images, respectively. These approaches require ground truth 3D point clouds, limiting their applicability. Other works [27, 40, 53] use point clouds as intermediate 3D representations for conditioning 2D inpainting or generation networks. However, these point clouds are assumed to correspond to only visible object points. In contrast, our Gaussians can model any part of the object, and thus afford $360^{\circ}$ reconstruction. + +Point cloud-based representations have also been used for high-quality reconstruction from multi-view images. + +Novel views can be rendered with 2D inpainting networks for hole-filling [43], or by using non-isotropic 3D Gaussians with variable scale [22]. While showing high-quality results, Gaussian Splitting [22] requires many images per scene and has not yet been used in a learning-based reconstruction framework as we do here. + +Our method also uses 3D Gaussians as an underlying representation but predicts them from as few as a single image. Moreover, it outputs a full $360^{\circ}$ 3D reconstruction without using 2D or 3D inpainting networks. + +Probabilistic 3D Reconstruction. Single-view 3D reconstruction is an ambiguous problem, so recently it has been tackled as a conditional generation task. Diffusion Models have been employed for conditional novel view synthesis [4, 29, 52]. Due to generating images without underlying geometries, the output images exhibit noticeable flicker. This can be mitigated by simultaneously generating multiview images [30, 44], reconstructing a geometry at every step of the denoising process [48, 49, 54] or training a robust reconstructor [25, 28]. Other works build and use a 3D [8, 35] or 2D [13, 33] prior which can be used in an image-conditioned auto-decoding framework. + +Here, we focus on deterministic reconstruction. However, few-view reconstruction is required to output 3D geometries from feed-forward methods [30, 44, 48, 49, 54]. Our method is capable of few-view 3D reconstruction, thus it is complementary to these generative methods and could lead to improvements in generation speed and quality. + +# 3. Method + +We discuss Gaussian Splatting in Sec. 3.1 for background, and then describe the Splatter Image in Secs. 3.2 to 3.6. + +# 3.1. Overview of Gaussian Splitting + +A radiance field [34] is a pair of functions, assigning an opacity $\sigma(\pmb{x}) \in \mathbb{R}_+$ and a colour $c(\pmb{x},\pmb{\nu}) \in \mathbb{R}^3$ to each 3D point $\pmb{x} \in \mathbb{R}^3$ and viewing direction $\pmb{\nu} \in \mathbb{S}^2$ . Gaussian Splatting [60] represents the two functions $\sigma$ and $c$ as a mixture $\theta$ of $G$ colored 3D Gaussians + +$$ +g _ {i} (\pmb {x}) = \exp \left(- \frac {1}{2} (\pmb {x} - \pmb {\mu} _ {i}) ^ {\top} \Sigma_ {i} ^ {- 1} (\pmb {x} - \pmb {\mu} _ {i})\right), +$$ + +where $1 \leq i \leq G$ , $\pmb{\mu}_i \in \mathbb{R}^3$ is the Gaussian mean or center and $\Sigma_i \in \mathbb{R}^{3 \times 3}$ is its covariance, specifying its shape and size. Each Gaussian has also an opacity $\sigma_i \in [0,1]$ and a view-dependent colour $c_i(\pmb{v}) \in \mathbb{R}^3$ . Together, they define a radiance field as follows: + +$$ +\sigma (\boldsymbol {x}) = \sum_ {i = 1} ^ {G} \sigma_ {i} g _ {i} (\boldsymbol {x}), \quad c (\boldsymbol {x}, \boldsymbol {\nu}) = \frac {\sum_ {i = 1} ^ {G} c _ {i} (\boldsymbol {\nu}) \sigma_ {i} g _ {i} (\boldsymbol {x})}{\sum_ {j = 1} ^ {G} \sigma_ {i} g _ {i} (\boldsymbol {x})}. \tag {1} +$$ + +The mixture of Gaussians is thus given by the set + +$$ +\theta = \left\{\left(\sigma_ {i}, \boldsymbol {\mu} _ {i}, \Sigma_ {i}, c _ {i}\right), i = 1, \dots , G \right\}. +$$ + +A raidance field is rendered into an image $I(\pmb{u})$ by integrating the colors observed along the ray $\pmb{x}_{\tau} = \pmb{x}_0 - \tau \pmb{\nu}$ , $\tau \in \mathbb{R}_+$ that passes through each image pixel $\pmb{u}$ via the equation: + +$$ +I (\boldsymbol {u}) = \int_ {0} ^ {\infty} c \left(\boldsymbol {x} _ {\tau}, \boldsymbol {\nu}\right) \sigma \left(\boldsymbol {x} _ {\tau}\right) e ^ {- \int_ {0} ^ {\tau} \sigma \left(\boldsymbol {x} _ {\mu}\right) d \mu} d \tau . \tag {2} +$$ + +Gaussian Splatting [22, 60] provides a very fast differentiable renderer $I = \mathcal{R}(\theta, \pi)$ that approximates Eq. (2), mapping the mixture $\theta$ and the viewpoint $\pi$ to an image $I$ . + +# 3.2. The Splatter Image + +To perform monocular reconstruction we seek for a function $\theta = S(I)$ which is the 'inverse' of the renderer $\mathcal{R}$ , mapping an image $I$ to a mixture of 3D Gaussians $\theta$ . Our key innovation is to propose an extremely simple and yet effective design for such a function. Specifically, we predict a Gaussian for each pixel of the input image $I$ using a standard image-to-image neural network architecture. We call its output image $M$ the Splatter Image. + +In more detail, Let $\pmb{u} = (u_{1}, u_{2}, 1)$ denote one of the $H \times W$ image pixels. This corresponds to ray $\pmb{x} = \pmb{u}d$ in camera space, where $d$ is the depth of the ray point. Our network $f$ takes as input the $H \times W \times 3$ RGB image $I$ , and outputs directly a $H \times W \times K$ tensor $M$ , where each pixel is associated to the $K$ -dimensional feature vector packing the parameters $M_{\pmb{u}} = (\sigma, \pmb{\mu}, \Sigma, c)$ of a corresponding Gaussian. + +We assume that Gaussians are expressed in the same reference frame of the camera. As illustrated in Fig. 2, the network predicts the depth $d$ and offset $(\Delta_x, \Delta_y, \Delta_y)$ , setting + +$$ +\boldsymbol {\mu} = \left[ \begin{array}{l} u _ {1} d + \Delta_ {x} \\ u _ {2} d + \Delta_ {y} \\ d + \Delta_ {z} \end{array} \right]. \tag {3} +$$ + +The network also predicts the opacity $\sigma$ , the shape $\Sigma$ and the colour $c$ . For now, we assume that the colour is Lambertian, i.e., $c(\nu) = c \in \mathbb{R}^3$ , and relax this assumption in Sec. 3.5. Section 3.6 provides more detail on the network architecture. + +Discussion. One may wonder how this design can predict a full $360^{\circ}$ reconstruction of the object when the reconstruction is aligned a single input view. We find that the network adjusts the 3D offsets $\Delta$ and depths $d$ to allocate some of the 3D Gaussians to reconstruct the input view, and some to reconstruct unseen portions of the object, automatically. The network can also decide to switch off any Gaussian by simply predicting $\sigma = 0$ , if needed. These points are then not rendered and can be culled in post-processing. + +![](images/2b5514cc74e6d526b55061d89c12c0902f0a0c07e32a2b62a9217eba2cb8a692.jpg) +Figure 2. Predicting locations. The location of each Gaussian is parameterised by depth $d$ and a 3D offset $\Delta = (\Delta_x, \Delta_y, \Delta_z)$ . The 3D Gaussians are projected to depth $d$ (blue) along camera rays (green) and moved by the 3D offset $\Delta$ (red). + +Our design can also be seen as an extension of depth prediction networks which only predicting the depth of each pixel. Here, we also predict unobserved parts of the geometry, as well as the shape and appearance of each Gaussian. + +# 3.3. Learning formulation + +Learning to predict the Splatter Image is simple and efficient. It can be done on a single GPU using at most 20GB of memory at training time in most of our single-view reconstruction experiments (except for Objaverse, where we use 2 GPUs and using 26GB of memory on each). For training, we assume a multi-view dataset, either real or synthetic. The dataset $\mathcal{D}$ consists of triplets $(I,J,\pi)$ , where $I$ is a source image, $J$ a target image, and $\pi$ the viewpoint change between the source and the target cameras. Then we simply feed the source $I$ as input to Splatter Image, and minimize the average reconstruction loss of target view $J$ : + +$$ +\mathcal {L} (\mathcal {S}) = \frac {1}{| \mathcal {D} |} \sum_ {(I, J, \pi) \in \mathcal {D}} \| J - \mathcal {R} (\mathcal {S} (I), \pi) \| ^ {2}. \tag {4} +$$ + +Image-level losses. A main advantage of the speed and efficiency of our method is that it allows for rendering entire images at each training iteration, even for relatively large batches (this differs from NeRF [34], which only generates a certain number of pixels in a batch). In particular, this means that, in addition to decomposable losses like the $L2$ loss above, we can use image-level losses like LPIPS [56], which do not decompose into per-pixel losses. In practice, we experiment with a combination of such losses. + +Regularisations. We also add generic regularisers to prevent parameters from taking on unreasonable values (e.g., Gaussians which are larger than the reconstructed objects, or vanishingly small). Please see the sup. mat. for details. + +# 3.4. Extension to multiple input viewpoints + +If two or more input views $I_j$ , $j \in \{1, \dots, N\}$ are provided, we can apply network $S$ multiple times to obtain + +multiple Splatter Images $M_{j}$ , one per view. If $(R, T)$ is the relative camera pose change from an additional view to the reference view, we can take the mixture of 3D Gaussians $\theta$ defined in the additional view's coordinates and warp it to the reference view. Specifically, a Gaussian of parameters $(\sigma, \mu, \Sigma, c)$ maps to Gaussian of parameters $(\sigma, \tilde{\mu}, \tilde{\Sigma}, \tilde{c})$ where $\tilde{\mu} = R\mu + T$ , $\tilde{\Sigma} = R\Sigma R^{\top}$ , $\tilde{c} = c$ . We use the symbol $\phi[\theta]$ to denote the Gaussian mixture obtained by warping each Gaussian in $\theta$ . Here we have also assumed a Lambertian colour model and will discuss in Sec. 3.5 how more complex models transform. + +Given $N$ different views $I_{j}$ and corresponding warps $\phi$ , we can obtain a composite mixture of 3D Gaussians simply by taking their union $\Theta = \bigcup_{j=1}^{N} \phi_{j}[S(I_{j})]$ . Note that this set of 3D Gaussians is defined in the coordinate system of the reference camera. + +# 3.5. View-dependent colour + +Generalising beyond the Lambertian colour model, we use spherical harmonics [22] to represent view-dependent colours. For a particular Gaussian $(\sigma, \mu, \Sigma, c)$ , we then define $[c(\pmb{\nu}; \pmb{\alpha})]_i = \sum_{l=0}^L \sum_{m=-L}^L \alpha_{ilm} Y_l^m(\pmb{\nu})$ where $\alpha_{ilm}$ are coefficients predicted by the network and $Y_l^m$ are spherical harmonics, $L$ is the order of the expansion, and $\pmb{\nu} \in \mathbb{S}^2$ is the viewing direction. + +The viewpoint change of Sec. 3.4 transforms a viewing direction $\pmb{\nu}$ in the source camera to the corresponding viewing direction in the reference frame as $\tilde{\pmb{\nu}} = R\pmb{\nu}$ . We can then find the transformed colour function by finding the coefficients $\tilde{\alpha}$ such that $c(\pmb{\nu};\pmb{\alpha}) = c(\tilde{\pmb{\nu}};\tilde{\pmb{\alpha}})$ . This is possible because (each order of) spherical harmonics are closed under rotation. However, the general case requires the computation of Wigner matrices. For simplicity, we only consider orders $L = 0$ (Lambertian) and $L = 1$ . Hence, the first level has one constant component $Y_0^0$ and the second level has three components which we can write collectively as $Y_{1} = [Y_{1}^{-1},Y_{1}^{0},Y_{1}^{1}]$ such that + +$$ +Y _ {1} (\boldsymbol {\nu}) = \sqrt {\frac {3}{4 \pi}} \Pi \boldsymbol {\nu}, \quad \Pi = \left[ \begin{array}{c c c} 0 & 1 & 0 \\ 0 & 0 & 1 \\ 1 & 0 & 0 \end{array} \right]. +$$ + +We can then conveniently rewrite $[c(\pmb {\nu};\pmb {\alpha})]_i = \alpha_{i0} +$ $\pmb{\alpha}_{i1}^{\top}Y_{1}(\pmb {\nu})$ . From this and $c(\pmb {\nu};\alpha_0,\pmb {\alpha}_1) = c(\tilde{\pmb{\nu}};\tilde{\alpha}_0,\tilde{\alpha}_1)$ we conclude that $\tilde{\alpha}_{i0} = \tilde{\alpha}_{i0}$ , and $\tilde{\alpha}_{i1} = \Pi^{-1}R\Pi \alpha_{i1}$ + +# 3.6. Neural network architecture + +The bulk of the predictor $S$ mapping the input image $I$ to the mixture of Gaussians $\theta$ is architecturally identical to the SongUNet of [46]. The last layer is replaced with a $1\times 1$ convolutional layer with $12 + k_{c}$ output channels, where $k_{c}\in \{3,12\}$ depending on the colour model. Given $I\in \mathbb{R}^{3\times H\times W}$ as input, the network thus produces + +a $(12 + k_{c})\times H\times W$ tensor as output, coding, for each pixel $\pmb{u}$ channels, the parameters $(\hat{\sigma},\Delta ,\hat{d},\hat{s},\hat{q},\alpha)$ which are then transformed to opacity, offset, depth, scale, rotation and colour, respectively. These are activated by nonlinear functions to obtain the Gaussian parameters. Specifically, the opacity is obtained using the sigmoid operator as $\sigma =$ sigmoid( $\hat{\sigma}$ ). The depth is obtained as $d =$ $(z_{\mathrm{far}} - z_{\mathrm{near}})$ sigmoid $(\hat{d}) + z_{\mathrm{near}}$ . The mean $\mu$ is then obtained using Eq. (3). Following [22], the covariance is obtained as $\Sigma = R(\pmb {q})\mathrm{diag}(\exp \hat{s})^{2}R(\pmb {q})^{\top}$ where $R(\pmb {q})$ is the rotation matrix with quaternion $\pmb {q} = \hat{\pmb{q}} /\| \hat{\pmb{q}}\|$ and $\hat{\pmb{q}}\in \mathbb{R}^4$ + +For multi-view reconstruction, we apply the same network to each input view and then use the approach of Sec. 3.4 to fuse the individual reconstructions. In order to allow the network to coordinate and exchange information between views, we apply two modifications to it. + +First, we condition the network with the corresponding camera pose $(R,T)$ (we only assume access to the relative camera pose to a common but otherwise arbitrary reference frame). In fact, since we consider cameras in a turn-table-like configuration, we only pass vectors $(Re_3,T)$ where $e_3 = (0,0,1)$ . We do so by encoding each entry via a sinusoidal positional embedding of order 9, resulting in 60 dimensions in total. Finally, these are applied to the U-Net blocks via FiLM [36] embeddings. + +Second, we add cross-attention layers to allow communication between the features of different views. We do so in a manner similar to [44], but only at the lowest UNet resolution, which maintains the computational cost very low. + +# 4. Experiments + +We evaluate our method extensively for single-view reconstruction on six standard benchmarks. Next, we assess the quality of multi-view reconstruction, and finish with an evaluation of the speed of the method. + +Datasets. The standard benchmark for evaluating single-view 3D reconstruction is ShapeNet-SRN [45]. We train our method in the single-class setting and report results on the "Car" and "Chair" classes, following prior work. Moreover, we challenge our method with two classes of real objects from the CO3D [38] dataset: Hydrants and Teddybears. In this challenging dataset ripe with ambiguities we set $z_{\mathrm{far}}$ and $z_{\mathrm{near}}$ to depend on ground truth distance $z_{\mathrm{gt}}$ between the object and camera. + +We further test our method on two multi-category datasets. First, we use the standard benchmark of multicategory ShapeNet (with objects from 13 largest categories), and use the renderings, standard splits and target views from NMR [21]. Secondly, we train one model on renderings of objects from Objaverse-LVIS [10] which contains over 1k object categories, using the renderings from Zero-1-to-3 [29]. We evaluate this model on all objects + +
MethodRC1-view Cars1-view Chairs
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
SRN✗22.250.880.12922.890.890.104
CodeNeRF✗23.800.910.12823.660.900.166
FE-NVS✗22.830.910.09923.210.920.077
ViewsetDiff w/o D✗23.210.900.11624.160.910.088
PixelNeRF✓23.170.890.14623.720.900.128
VisionNeRF✓22.880.900.08424.480.920.077
NeRFDiff w/o NGD✓23.950.920.09224.800.930.070
Ours✓24.000.920.07824.430.930.067
+ +Table 1. ShapeNet-SRN: Single-View Reconstruction. Our method achieves State-of-the-Art reconstruction quality on all metrics on the Car dataset and on two metrics in the Chair dataset, while performing reconstruction in the camera view-space. 'RC' indicates if a method can operate using only relative camera poses. + +from the Google Scanned Objects dataset [12], using the same renderings as used for evaluation in Free3D [57]. We train and evaluate all models at $128 \times 128$ resolution, apart from multi-category ShapeNet which is at $64 \times 64$ . Finally, we use the ShapeNet-SRN Cars dataset for the evaluation of the two-view reconstruction quality. For more details on datasets see supp. mat. + +Baselines. For ShapeNet (both single-class and multiclass), we compare against implicit [19, 26, 45, 55], hybrid implicit-explicit [13] and explicit methods [2, 14, 48]. We use the deterministic variants of [13, 48] by using their reconstruction network in a single forward pass. For CO3D we compare against PixelNeRF which we train for 400,000 iterations with their officially released code on the same data as used for our method. Finally, on Objaverse-LVIS we compare to OpenLRM [15] (open-source version of LRM [17]): a large triplane-based reconstructor, trained on the full Objaverse dataset. Since we are proposing a deterministic reconstruction method, we do not compare to methods that employ Score Distillation [29, 59] or feedforward diffusion models [4, 28, 52, 54]. + +Implementation details can be found in the supp. mat. + +# 4.1. Evaluation of reconstruction quality + +In line with related works [26, 55], we assess the quality of the reconstructions by measuring novel view synthesis quality and report Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and a perceptual loss (LPIPS). We perform reconstruction from a given source view and render the 3D shape to unseen target views following standard protocols as detailed in the supp. mat. + +# 4.1.1 Single-view 3D reconstruction + +ShapeNet. In Tab. 1 and Fig. 3 we compare the single-view reconstruction quality on the ShapeNet-SRN benchmark. + +![](images/4d67f4d94fb59ab9ecfbd4e7b9d0e71c42e009ec4355fde59440c475d05e08e7.jpg) +Figure 3. ShapeNet-SRN Comparison. Our method outputs more accurate reconstructions (cars' backs, top chair) and better represents thin regions (bottom chair). + +
PixelNeRF [55]FE-NVS [14]FWD [2]VisionNeRF [26]Ours
PSNR ↑26.8027.0826.6628.7629.38
SSIM ↑0.910.920.910.930.95
LPIPS ↓0.1080.0820.0550.0650.047
+ +Table 2. Our method achieves State-of-the-Art quality of single-view reconstruction on multi-class ShapeNet dataset. + +
ObjectMethodPSNR ↑SSIM ↑LPIPS ↓
HydrantPixelNeRF21.760.780.203
HydrantOurs21.800.800.150
TeddybearPixelNeRF19.380.650.290
TeddybearOurs19.440.730.231
+ +Our method outperforms all deterministic reconstructors in SSIM and LPIPS, obtaining sharper new views. Furthermore, our method requires only relative camera poses instead of absolute/canonical ones. Qualitatively, our method does well in challenging situations with limited visibility and thin structures. In Tab. 2, we use instead the multicategory ShapeNet protocol we observe that our method outperforms more expensive baselines [26] across all metrics in the multi-category ShapeNet setting. + +CO3D. On CO3D bears and hydrants, our model outperforms PixelNeRF on all metrics (Tab. 3), and qualitatively produces sharper images (Fig. 4) while being $1,000 \times$ faster. + +Objaverse-LVIS and Google Scanned Objects. We compare our method to OpenLRM [15], an open-source ver + +![](images/37df622fc055cf5ea3c81c0f05207f525630a581b9355e8786a2094999c62318.jpg) +Figure 4. CO3D Hydrants and Teddybears. Our method outputs sharper reconstructions than PixelNeRF while being $100\mathrm{x}$ faster in inference. + +Table 3. CO3D: Single-View. Our method outperforms PixelNeRF on this challenging benchmark across all metrics. + +
MethodPSNR ↑SSIM ↑LPIPS ↓
OpenLRM18.060.840.129
Ours21.060.880.111
+ +Table 4. Google Scanned Objects: Single-View. Our method outperforms the much more expensive LRM [15, 17] on single-view open-world reconstruction. + +![](images/f4fcc57bbd0f2cd4869dce799c7d4c76eb839246499c7741d0d6f9fda4a98bde.jpg) +Figure 5. Google Scanned Objects. On large datasets our model has similar quality to much more expensive baselines (shoe). Our reconstructions have more accurate lighting (Jenga), object pose (horse) and shape (toy). + +sion of the LRM model [17], on the Google Scanned Objects [12] evaluation renderings from Free3D [57]. Quantitatively, in Tab. 4 Splatter Image outperforms OpenLRM and, qualitatively (Fig. 5), it is comparable. Our models perform well even on images collected from the Internet Fig. 6, after removing backgrounds and resizing. Remarkably, our method, trained for 7 GPU days, is able to compete with OpenLRM, which uses hundreds of GPUs for several days [15, 17]. + +![](images/6d0803740f828c39a676d86c3d33cd8ca2a2555925e84cf622cd1ee8249814b0.jpg) +Figure 6. Our models trained on single classes (top) and on Objaverse (bottom) can be used on in-the-wild Internet images (right). + +
MethodRelative Pose2-view Cars
PSNR ↑SSIM ↑
SRNX24.840.92
CodeNeRFX25.710.91
FE-NVSX24.640.93
PixelNeRF✓25.660.94
Ours✓26.010.94
+ +Table 5. Two-view reconstruction on ShapeNet-SRN Cars. + +# 4.1.2 Two-view 3D reconstruction + +We compare our multi-view reconstruction model on ShapeNet-SRN Cars by training it for two-view predictions (see Tab. 5). Prior work often relies on absolute camera pose conditioning, meaning that the model learns to rely on the canonical orientation of the object in the dataset. This limits the applicability of these models, as in practice for a new image of an object, the absolute camera pose is of course unknown. Here, only ours and PixelNeRF can deal with relative camera poses as input. Interestingly, our method shows not only better performance than PixelNeRF in both real and synthetic data but also improves over SRN, CodeNeRF, and FE-NVS that rely on absolute camera poses. + +# 4.1.3 Ablations + +We evaluate the influence of individual components of our method, using a shorter training schedule than models in Tab. 1 for efficiency. Ablations of the multi-view model are given in the supp. mat. + +We show the results of our ablation study for the single-view model in Tab. 6. We train a model (w/o image) that uses a fully connected, unstructured output instead of a Splatter Image. This model cannot transfer image informa + +![](images/bbd629e48d621962ef0b99e2c4b83d409d533dcd56973729ac2052e7c3bc2396.jpg) +Figure 7. Analysis. Splatter Images represent full $360^{\circ}$ of objects by allocating background pixels to appropriate 3D locations (third row) to predict occluded elements like wheels (left) or chair legs (middle). Alternatively, it predicts offsets in the foreground pixels to represent occluded chair parts (right). + +tion directly to their corresponding Gaussians and does not achieve good performance. We also ablate predicting the depth along the ray by simply predicting 3D coordinates for each Gaussian. This version also suffers from its inability to easily align the input image with the output. Removing the 3D offset prediction mainly harms the backside of the object while leaving the front faces the same. This results in a lower impact on the overall performance of this component. Changing the degrees of freedom of appearance predictions (by fixing Gaussians to be isotropic or removing view-dependence) also reduced the image fidelity. Finally, removing perceptual loss (w/o $\mathcal{L}_{\mathrm{LPIPS}}$ ) results in a significant worsening of LPIPS, indicating this loss is important for perceptual sharpness of reconstructions. Being able to use LPIPS in optimisation is a direct consequence of employing a fast-to-render representation and being able to render full images at training time. + +Analysis. In Fig. 7, we analyse how 3D information is stored inside a Splatter Image. Since all information is arranged in an image format, we can visualise each of the modalities: opacity, depth, and location. Pixels of the input image that belong to the object tend to describe their corresponding 3D structure, while pixels outside of the object wrap around to close the object on the back. + +# 4.2. Evaluation of reconstruction efficiency + +A key advantage of the Splatter Image is its training and test time efficiency, which we assess below. + +
PSNR ↑SSIM ↑LPIPS ↓
Full model22.250.900.115
w/o image20.600.870.152
w/o depth21.210.880.145
w/o view dir.21.770.890.121
isotropic22.010.890.118
w/o offset22.060.900.119
w/o LPIPS22.220.890.141
+ +Table 6. Ablations: Single-View Reconstruction. + +
RPE↓R↓Forward↓Test↓
NeRFDiff✓(0.031)(0.0180)(0.103)(4.531)
FE-NVS✗(0.015)(0.0032)(0.028)(0.815)
VisionNeRF✓0.0082.43129.733607.8
PixelNeRF✓0.0031.85727.432463.3
ViewsetDiff✗0.0250.00640.0511.625
Ours 2-view✓0.0300.00170.0370.455
Ours 1-view✓0.0260.00170.0330.451
+ +Table 7. Speed. Time required for image encoding (E), rendering (R), the 'Forward' time, indicative of train-time efficiency and the 'Test' time, indicative of test-time efficiency. Our method is the most efficient in both train and test time across open-source available methods and only requires relative camera poses. 'RP' indicates if a method can operate using only relative camera poses. + +Test-time efficiency. First, we assess the 'Test' time speed, i.e., the time it takes for the trained model to reconstruct an object and generate a certain number of images. We reference the evaluation protocol of the standard ShapeNet-SRN benchmark [45] and render 250 images at $128^{2}$ resolution. + +Assessing wall-clock time fairly is challenging as it depends on many factors. All measurements reported here are done on a single NVIDIA V100 GPU. We use officially released code of Viewset Diffusion [48], PixelNeRF [55] and VisionNeRF [26] and rerun those on our hardware. NeRFDiff [13] and FE-NVS [14] do not have code available, so we use their self-reported metrics. According to the authors, FE-NVS was evaluated on the same type of GPU, while NeRFDiff does not include information about the hardware used and we were unable to obtain more information. Since we could not perfectly control these experiments, the comparisons to NeRFDiff and FE-NVS are only indicative. For Viewset Diffusion and NeRFDiff we report the time for a single pass through the reconstruction network. + +Tab. 7 reports the 'Encoding' (E) time, spent by the network to compute the object's 3D representation from an image, and the 'Rendering' (R) time, spent by the network to render new images from the 3D representation. From those, we calculate the 'Test' time, equal to the 'Encoding' time plus 250 'Rendering' time. As shown in the last column + +of Tab. 7, our method is more than $1000 \times$ faster in testing than PixelNeRF and VisionNeRF (while achieving equal or superior quality of reconstruction in Tab. 1). Our method is also faster than voxel-based Viewset Diffusion even though it does not require knowing the absolute camera pose. The efficiency of our method is very useful to iterate quickly in research; for instance, evaluating our method on the full ShapeNet-Car validation set takes less than 10 minutes on a single GPU. In contrast, PixelNeRF takes 45 GPU-hours. + +Train-time efficiency. Next, we assess the efficiency of the method during training. Here, the encoding time becomes more significant because one typically renders only a few images to compute the reconstruction loss and obtain a gradient (e.g., because there are only so many views available in the training dataset, or because generating more views provides diminishing returns in terms of supervision). As typical values (and as used by us in this work), we assume that the method is tasked with generating 4 new views at each iteration instead of 250 as before. We call this the 'Forward' time and measure it the same way. As shown in the 'Forward' column of Tab. 7, our method is $246 \times$ faster at training time than implicit methods and $1.5 \times$ than Viewset Diffusion, which uses an explicit representation. With this, we can train models achieving state-of-the-art quality on a single A6000 GPU in 7 days, while VisionNeRF requires 16 A100 GPUs for 5 days. What is even more remarkable, we can train models on large datasets such as Objaverse on two A6000 GPUs in 3.5 days, while triplane-based methods such as LRM require 128 A100 GPUs for 3 days [17]. + +# 5. Conclusion + +We have presented Splatter Image, a simple method for single- or few-view 3D reconstruction. The method uses an off-the-shelf 2D image-to-image network and predicts a pseudo-image containing one colored 3D Gaussian per pixel. By combining fast inference with fast rendering via Gaussian Splatting, Splatter Image can be trained and evaluated quickly on synthetic and real benchmarks. Splatter Image achieves state-of-the-art reconstruction performance without requiring absolute/canonical camera poses at test time, is simple to implement, and can be trained and tested much faster than many alternatives. + +Ethics. We use various datasets in a manner compatible with their terms. There is no processing of personal data. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html. + +Acknowledgements. S. Szymanowicz is supported by an EPSRC Doctoral Training Partnerships Scholarship (DTP) EP/R513295/1 and the Oxford-Ashton Scholarship. A. 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The Splatter Image is an ultra-efficient method for single- and few-view 3D reconstruction. It uses an image-to-image neural network to map the input image to another image that holds the parameters of one coloured 3D Gaussian per pixel. Splatter Image achieves excellent 3D reconstruction quality on synthetic, real and large-scale datasets while using a single GPU for training." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 310, + 216, + 545, + 348 + ], + "blocks": [ + { + "bbox": [ + 310, + 216, + 545, + 348 + ], + "lines": [ + { + "bbox": [ + 310, + 216, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 310, + 216, + 545, + 348 + ], + "type": "image", + "image_path": "0f6dd5b5e2edf5f1141648a74f1c4ff46a2b834a4167b34a310ee66c4fdbc2bc.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 409, + 192, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 409, + 192, + 422 + ], + "spans": [ + { + "bbox": [ + 143, + 409, + 192, + 422 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 45, + 437, + 290, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 437, + 290, + 700 + ], + "spans": [ + { + "bbox": [ + 45, + 437, + 290, + 700 + ], + "type": "text", + "content": "We introduce the Splatter Image, an ultra-efficient approach for monocular 3D object reconstruction. Splatter Image is based on Gaussian Splatting, which allows fast and high-quality reconstruction of 3D scenes from multiple images. We apply Gaussian Splatting to monocular reconstruction by learning a neural network that, at test time, performs reconstruction in a feed-forward manner, at 38 FPS. Our main innovation is the surprisingly straightforward design of this network, which, using 2D operators, maps the input image to one 3D Gaussian per pixel. The resulting set of Gaussians thus has the form an image, the Splatter Image. We further extend the method to several images as input via cross-view attention. Owning to the speed of the renderer (588 FPS), we use a single GPU for training while generating entire images at each iteration to optimize perceptual metrics like LPIPS. On several synthetic, real, multi-category and large-scale benchmark datasets, we achieve better results in terms of PSNR, LPIPS, and other metrics while training and evaluating much faster than prior works. Code, models and more results are available at https://szymanowicz.github.io/splatter-image." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 409, + 386, + 422 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 409, + 386, + 422 + ], + "spans": [ + { + "bbox": [ + 307, + 409, + 386, + 422 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 431, + 545, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 545, + 552 + ], + "type": "text", + "content": "We contribute Splatter Image, a method that achieves ultrafast single-view reconstruction of the 3D shape and appearance of objects. Splatter Image uses a set of 3D Gaussians as the 3D representation, taking advantage of the rendering quality and speed of Gaussian Splatting [22]. Splatter Image works by predicting a 3D Gaussian for each of the input image pixels, using an image-to-image neural network. Remarkably, the predicted 3D Gaussians provide " + }, + { + "bbox": [ + 304, + 431, + 545, + 552 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 431, + 545, + 552 + ], + "type": "text", + "content": " reconstructions of quality comparable or superior to much slower methods (Fig. 1)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "type": "text", + "content": "We formulate monocular 3D reconstruction as the problem of designing a neural network that takes an image of an object as input and produces as output a corresponding Gaussian mixture that represents all sides of it. While a Gaussian mixture is a set, i.e., an unordered collection, it can still be stored in an ordered data structure. Splatter Image takes advantage of this fact by using a " + }, + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "type": "inline_equation", + "content": "2D" + }, + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "type": "text", + "content": " image as the container of the 3D Gaussians, storing the parameters of one Gaussian (i.e., its opacity, position, shape, and colour) per pixel. The Gaussians predominantly lie on the rays from the camera to the object, but they can also be placed off the rays (Fig. 2), enabling " + }, + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 554, + 546, + 698 + ], + "type": "text", + "content": " object representation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 713 + ], + "type": "text", + "content": "The advantage of storing a set of 3D Gaussians in an im" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10208" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "age is that it reduces the reconstruction problem to learning an image-to-image neural network. In this manner, the recon- constructor can be implemented utilizing only efficient 2D operators (e.g., 2D convolution instead of 3D convolution). We use in particular a U-Net [42] as those have demonstrated excellent performance in image generation [41]. In our case, their ability to capture small image details [55] helps to obtain higher-quality reconstructions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 169, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 169, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 169, + 289, + 373 + ], + "type": "text", + "content": "Since the 3D representation in Splatter Image is a mixture of 3D Gaussians, it enjoys the rendering and space efficiency of Gaussian Splattering, which benefits inference and training. In particular, rendering stops being a training bottleneck [34] and we can afford to generate complete views of the object to optimize perceptual metrics like LPIPS [56]. More importantly, the efficiency is such that our model can be trained on a single GPU on standard benchmarks of 3D objects or two GPUs on large datasets such as Objverse [10], whereas alternative methods typically require distributed training on dozens [26] or even hundreds [17] of GPUs. We also extend Splatter Image to take several views as input. This is achieved by taking the union of the Gaussian mixtures predicted from individual views, after registering them to a common coordinate frame. The different views communicate during prediction via lightweight cross-view attention layers in the architecture." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "type": "text", + "content": "Empirically, we show that, while the network only sees one side of the object, it can still produce a " + }, + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "type": "text", + "content": " reconstruction of it by using the prior acquired during training. The " + }, + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 375, + 288, + 448 + ], + "type": "text", + "content": " information is encoded in the 2D image by allocating different Gaussians in a given 2D neighbourhood to different parts of the 3D object." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 289, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 289, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 289, + 592 + ], + "type": "text", + "content": "We validate Splatter Image by comparing it to alternative, slower reconstructors on standard benchmark datasets like ShapeNet [5] and CO3D [38]. To assess scalability and generalization, we also apply Splatter Image to multicategory reconstruction and train it on Objaverse [10], and evaluate it on Google Scanned Objects [12]. We obtain results of quality comparable to the recent Large Reconstruction Model of [15, 17], which is " + }, + { + "bbox": [ + 46, + 449, + 289, + 592 + ], + "type": "inline_equation", + "content": "50 \\times" + }, + { + "bbox": [ + 46, + 449, + 289, + 592 + ], + "type": "text", + "content": " more expensive to train. In fact, in several cases we even outperform slower methods in PSNR and LPIPS. We argue that this is because the very efficient design allows training the model very effectively, including using image-level losses like LPIPS." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "To summarise, our contributions are: (1) to port Gaussian Splatting to learning-based monocular reconstruction; (2) to do so with the Splatter Image, a straightforward, efficient and performant 3D reconstruction approach that operates at 38 FPS on a standard GPU and affords single-GPU training; (3) to also extend the method to multi-view reconstruction; (4) and to obtain state-of-the-art reconstruction performance in multiple standard benchmarks, including synthetic, real, multi-category and large-scale datasets, in terms of reconstruction quality and speed." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 71, + 391, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 71, + 391, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 71, + 391, + 84 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "spans": [ + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "type": "text", + "content": "Representations for single-view 3D reconstruction. In recent years, implicit representations like NeRF [34] have dominated learning-based few-view reconstruction, parameterising the MLP in NeRF using global [19, 39], local [55] or both global and local codes [26]. However, implicit representations, particularly MLP-based ones, are notoriously slow to render, up to 2s for a single " + }, + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 92, + 547, + 176 + ], + "type": "text", + "content": " image." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 177, + 547, + 249 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 177, + 547, + 249 + ], + "spans": [ + { + "bbox": [ + 304, + 177, + 547, + 249 + ], + "type": "text", + "content": "Follow-up works [14, 48] used faster, explicit, voxel grid representations that encode opacities and colours directly. Similar to DVGO [47], they achieve significant speed-ups, but, due to their voxel-based representation, they scale poorly with resolution. They also assume the knowledge of the absolute viewpoint of each object image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 250, + 547, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 250, + 547, + 346 + ], + "spans": [ + { + "bbox": [ + 304, + 250, + 547, + 346 + ], + "type": "text", + "content": "The triplane representation [3, 7] was proposed as a compromise between rendering speed and memory consumption. While they are not as fast to render as explicit representations, they allow view-space reconstruction [13] and are fast enough to be effectively used for single-view reconstruction [1, 13]. Triplane-based reconstructors were shown to scale to large datasets like Objaverse [9, 10], albeit at the cost of hundreds of GPUs for multiple days [17, 50]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 346, + 547, + 431 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 547, + 431 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 547, + 431 + ], + "type": "text", + "content": "In contrast to these works, our method predicts a mixture of 3D Gaussians in a feed-forward manner. As a result, our method is cheap to train (1-2 GPUs), fast at inference and achieves real-time rendering speeds while achieving state-of-the-art image quality across multiple metrics on multiple standard single-view reconstruction benchmarks, including single- [45] and multi-category ShapeNet [5, 21]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 432, + 547, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 432, + 547, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 432, + 547, + 528 + ], + "type": "text", + "content": "When more than one view is available at the input, one can use them to estimate the scene geometry [6, 31], learn a view interpolation function [51] or optimize a 3D representation of a scene using priors [18]. Our method is primarily a single-view reconstruction network, but we do show how Splatter Image can be extended to fuse multiple views. However, we focus our work on object-centric reconstruction rather than on generalising to unseen scenes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "type": "text", + "content": "3D Reconstruction with Point Clouds. PointOutNet [11] took image encoding as input and trained point cloud prediction networks [37] using 3D point cloud supervision. PVD [58] and " + }, + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "type": "inline_equation", + "content": "\\mathrm{PC^2}" + }, + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "type": "text", + "content": " [32] extended this approach using Diffusion Models [16] by conditioning the denoising process on partial point clouds and RGB images, respectively. These approaches require ground truth 3D point clouds, limiting their applicability. Other works [27, 40, 53] use point clouds as intermediate 3D representations for conditioning 2D inpainting or generation networks. However, these point clouds are assumed to correspond to only visible object points. In contrast, our Gaussians can model any part of the object, and thus afford " + }, + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 533, + 547, + 689 + ], + "type": "text", + "content": " reconstruction." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "content": "Point cloud-based representations have also been used for high-quality reconstruction from multi-view images." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10209" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 143 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 143 + ], + "type": "text", + "content": "Novel views can be rendered with 2D inpainting networks for hole-filling [43], or by using non-isotropic 3D Gaussians with variable scale [22]. While showing high-quality results, Gaussian Splitting [22] requires many images per scene and has not yet been used in a learning-based reconstruction framework as we do here." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 288, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 288, + 194 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 288, + 194 + ], + "type": "text", + "content": "Our method also uses 3D Gaussians as an underlying representation but predicts them from as few as a single image. Moreover, it outputs a full " + }, + { + "bbox": [ + 46, + 144, + 288, + 194 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 46, + 144, + 288, + 194 + ], + "type": "text", + "content": " 3D reconstruction without using 2D or 3D inpainting networks." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 198, + 287, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 198, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 46, + 198, + 287, + 341 + ], + "type": "text", + "content": "Probabilistic 3D Reconstruction. Single-view 3D reconstruction is an ambiguous problem, so recently it has been tackled as a conditional generation task. Diffusion Models have been employed for conditional novel view synthesis [4, 29, 52]. Due to generating images without underlying geometries, the output images exhibit noticeable flicker. This can be mitigated by simultaneously generating multiview images [30, 44], reconstructing a geometry at every step of the denoising process [48, 49, 54] or training a robust reconstructor [25, 28]. Other works build and use a 3D [8, 35] or 2D [13, 33] prior which can be used in an image-conditioned auto-decoding framework." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 342, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 342, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 342, + 287, + 414 + ], + "type": "text", + "content": "Here, we focus on deterministic reconstruction. However, few-view reconstruction is required to output 3D geometries from feed-forward methods [30, 44, 48, 49, 54]. Our method is capable of few-view 3D reconstruction, thus it is complementary to these generative methods and could lead to improvements in generation speed and quality." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 426, + 102, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 426, + 102, + 437 + ], + "spans": [ + { + "bbox": [ + 47, + 426, + 102, + 437 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 446, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 446, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 46, + 446, + 287, + 471 + ], + "type": "text", + "content": "We discuss Gaussian Splatting in Sec. 3.1 for background, and then describe the Splatter Image in Secs. 3.2 to 3.6." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 479, + 218, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 218, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 218, + 493 + ], + "type": "text", + "content": "3.1. Overview of Gaussian Splitting" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": "A radiance field [34] is a pair of functions, assigning an opacity " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "\\sigma(\\pmb{x}) \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " and a colour " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "c(\\pmb{x},\\pmb{\\nu}) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " to each 3D point " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "\\pmb{x} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " and viewing direction " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu} \\in \\mathbb{S}^2" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": ". Gaussian Splatting [60] represents the two functions " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " as a mixture " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 498, + 287, + 558 + ], + "type": "text", + "content": " colored 3D Gaussians" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 72, + 566, + 261, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 72, + 566, + 261, + 593 + ], + "spans": [ + { + "bbox": [ + 72, + 566, + 261, + 593 + ], + "type": "interline_equation", + "content": "g _ {i} (\\pmb {x}) = \\exp \\left(- \\frac {1}{2} (\\pmb {x} - \\pmb {\\mu} _ {i}) ^ {\\top} \\Sigma_ {i} ^ {- 1} (\\pmb {x} - \\pmb {\\mu} _ {i})\\right),", + "image_path": "c2226f99db7508b2142bd682b940ec7e6b403485146e3053ab9a247f5459352a.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "1 \\leq i \\leq G" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\pmb{\\mu}_i \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": " is the Gaussian mean or center and " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\Sigma_i \\in \\mathbb{R}^{3 \\times 3}" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": " is its covariance, specifying its shape and size. Each Gaussian has also an opacity " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "\\sigma_i \\in [0,1]" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": " and a view-dependent colour " + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "inline_equation", + "content": "c_i(\\pmb{v}) \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 601, + 287, + 662 + ], + "type": "text", + "content": ". Together, they define a radiance field as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 53, + 670, + 287, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 670, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 53, + 670, + 287, + 713 + ], + "type": "interline_equation", + "content": "\\sigma (\\boldsymbol {x}) = \\sum_ {i = 1} ^ {G} \\sigma_ {i} g _ {i} (\\boldsymbol {x}), \\quad c (\\boldsymbol {x}, \\boldsymbol {\\nu}) = \\frac {\\sum_ {i = 1} ^ {G} c _ {i} (\\boldsymbol {\\nu}) \\sigma_ {i} g _ {i} (\\boldsymbol {x})}{\\sum_ {j = 1} ^ {G} \\sigma_ {i} g _ {i} (\\boldsymbol {x})}. \\tag {1}", + "image_path": "271e4c71715832797c34721c1818887dfca624ed3030f97971ac54f392c4f987.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 72, + 505, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 505, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 505, + 84 + ], + "type": "text", + "content": "The mixture of Gaussians is thus given by the set" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 350, + 94, + 500, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 94, + 500, + 107 + ], + "spans": [ + { + "bbox": [ + 350, + 94, + 500, + 107 + ], + "type": "interline_equation", + "content": "\\theta = \\left\\{\\left(\\sigma_ {i}, \\boldsymbol {\\mu} _ {i}, \\Sigma_ {i}, c _ {i}\\right), i = 1, \\dots , G \\right\\}.", + "image_path": "6d3a345b51994bbecf0218ffbc160ccaa89fecb50905107969dfdf5eaf2f2c7c.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "spans": [ + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "text", + "content": "A raidance field is rendered into an image " + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "inline_equation", + "content": "I(\\pmb{u})" + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "text", + "content": " by integrating the colors observed along the ray " + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "inline_equation", + "content": "\\pmb{x}_{\\tau} = \\pmb{x}_0 - \\tau \\pmb{\\nu}" + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "inline_equation", + "content": "\\tau \\in \\mathbb{R}_+" + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "text", + "content": " that passes through each image pixel " + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "inline_equation", + "content": "\\pmb{u}" + }, + { + "bbox": [ + 305, + 118, + 545, + 165 + ], + "type": "text", + "content": " via the equation:" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 332, + 174, + 545, + 200 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 174, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 332, + 174, + 545, + 200 + ], + "type": "interline_equation", + "content": "I (\\boldsymbol {u}) = \\int_ {0} ^ {\\infty} c \\left(\\boldsymbol {x} _ {\\tau}, \\boldsymbol {\\nu}\\right) \\sigma \\left(\\boldsymbol {x} _ {\\tau}\\right) e ^ {- \\int_ {0} ^ {\\tau} \\sigma \\left(\\boldsymbol {x} _ {\\mu}\\right) d \\mu} d \\tau . \\tag {2}", + "image_path": "de8aed68c9b1fbad81dd014786bb3da7e13b52edbc8e6eed5226291ff927f291.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "spans": [ + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "text", + "content": "Gaussian Splatting [22, 60] provides a very fast differentiable renderer " + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "inline_equation", + "content": "I = \\mathcal{R}(\\theta, \\pi)" + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "text", + "content": " that approximates Eq. (2), mapping the mixture " + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "text", + "content": " and the viewpoint " + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "text", + "content": " to an image " + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 208, + 545, + 244 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 252, + 419, + 265 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 252, + 419, + 265 + ], + "spans": [ + { + "bbox": [ + 306, + 252, + 419, + 265 + ], + "type": "text", + "content": "3.2. The Splatter Image" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": "To perform monocular reconstruction we seek for a function " + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\theta = S(I)" + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": " which is the 'inverse' of the renderer " + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": ", mapping an image " + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": " to a mixture of 3D Gaussians " + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": ". Our key innovation is to propose an extremely simple and yet effective design for such a function. Specifically, we predict a Gaussian for each pixel of the input image " + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": " using a standard image-to-image neural network architecture. We call its output image " + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 270, + 545, + 366 + ], + "type": "text", + "content": " the Splatter Image." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "spans": [ + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": "In more detail, Let " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\pmb{u} = (u_{1}, u_{2}, 1)" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " denote one of the " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " image pixels. This corresponds to ray " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "\\pmb{x} = \\pmb{u}d" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " in camera space, where " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " is the depth of the ray point. Our network " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " takes as input the " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "H \\times W \\times 3" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " RGB image " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": ", and outputs directly a " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "H \\times W \\times K" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " tensor " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": ", where each pixel is associated to the " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": "-dimensional feature vector packing the parameters " + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "inline_equation", + "content": "M_{\\pmb{u}} = (\\sigma, \\pmb{\\mu}, \\Sigma, c)" + }, + { + "bbox": [ + 305, + 367, + 545, + 450 + ], + "type": "text", + "content": " of a corresponding Gaussian." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": "We assume that Gaussians are expressed in the same reference frame of the camera. As illustrated in Fig. 2, the network predicts the depth " + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": " and offset " + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "inline_equation", + "content": "(\\Delta_x, \\Delta_y, \\Delta_y)" + }, + { + "bbox": [ + 305, + 451, + 545, + 498 + ], + "type": "text", + "content": ", setting" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 384, + 498, + 545, + 536 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 498, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 384, + 498, + 545, + 536 + ], + "type": "interline_equation", + "content": "\\boldsymbol {\\mu} = \\left[ \\begin{array}{l} u _ {1} d + \\Delta_ {x} \\\\ u _ {2} d + \\Delta_ {y} \\\\ d + \\Delta_ {z} \\end{array} \\right]. \\tag {3}", + "image_path": "1273613a215ef05c1eb2d7ae37c15bcb6303ed62b6a3c84aee4359adf4e8145f.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "spans": [ + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "text", + "content": "The network also predicts the opacity " + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "text", + "content": ", the shape " + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "text", + "content": " and the colour " + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "text", + "content": ". For now, we assume that the colour is Lambertian, i.e., " + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "inline_equation", + "content": "c(\\nu) = c \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 305, + 540, + 545, + 600 + ], + "type": "text", + "content": ", and relax this assumption in Sec. 3.5. Section 3.6 provides more detail on the network architecture." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Discussion. One may wonder how this design can predict a full " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " reconstruction of the object when the reconstruction is aligned a single input view. We find that the network adjusts the 3D offsets " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " and depths " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": " to allocate some of the 3D Gaussians to reconstruct the input view, and some to reconstruct unseen portions of the object, automatically. The network can also decide to switch off any Gaussian by simply predicting " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\sigma = 0" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": ", if needed. These points are then not rendered and can be culled in post-processing." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10210" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 72, + 282, + 182 + ], + "blocks": [ + { + "bbox": [ + 50, + 72, + 282, + 182 + ], + "lines": [ + { + "bbox": [ + 50, + 72, + 282, + 182 + ], + "spans": [ + { + "bbox": [ + 50, + 72, + 282, + 182 + ], + "type": "image", + "image_path": "2b5514cc74e6d526b55061d89c12c0902f0a0c07e32a2b62a9217eba2cb8a692.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "text", + "content": "Figure 2. Predicting locations. The location of each Gaussian is parameterised by depth " + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "text", + "content": " and a 3D offset " + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\Delta = (\\Delta_x, \\Delta_y, \\Delta_z)" + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "text", + "content": ". The 3D Gaussians are projected to depth " + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "text", + "content": " (blue) along camera rays (green) and moved by the 3D offset " + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 46, + 194, + 287, + 240 + ], + "type": "text", + "content": " (red)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 258, + 286, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 258, + 286, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 258, + 286, + 307 + ], + "type": "text", + "content": "Our design can also be seen as an extension of depth prediction networks which only predicting the depth of each pixel. Here, we also predict unobserved parts of the geometry, as well as the shape and appearance of each Gaussian." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 312, + 171, + 325 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 171, + 325 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 171, + 325 + ], + "type": "text", + "content": "3.3. Learning formulation" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": "Learning to predict the Splatter Image is simple and efficient. It can be done on a single GPU using at most 20GB of memory at training time in most of our single-view reconstruction experiments (except for Objaverse, where we use 2 GPUs and using 26GB of memory on each). For training, we assume a multi-view dataset, either real or synthetic. The dataset " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": " consists of triplets " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "(I,J,\\pi)" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": " is a source image, " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": " a target image, and " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "\\pi" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": " the viewpoint change between the source and the target cameras. Then we simply feed the source " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": " as input to Splatter Image, and minimize the average reconstruction loss of target view " + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 46, + 331, + 287, + 462 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 79, + 468, + 287, + 498 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 468, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 79, + 468, + 287, + 498 + ], + "type": "interline_equation", + "content": "\\mathcal {L} (\\mathcal {S}) = \\frac {1}{| \\mathcal {D} |} \\sum_ {(I, J, \\pi) \\in \\mathcal {D}} \\| J - \\mathcal {R} (\\mathcal {S} (I), \\pi) \\| ^ {2}. \\tag {4}", + "image_path": "4799ac9af31286b1844a7b59619119b32739e8ec29093e46fb70ccb3ae3fe106.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 504, + 286, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 504, + 286, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 504, + 286, + 612 + ], + "type": "text", + "content": "Image-level losses. A main advantage of the speed and efficiency of our method is that it allows for rendering entire images at each training iteration, even for relatively large batches (this differs from NeRF [34], which only generates a certain number of pixels in a batch). In particular, this means that, in addition to decomposable losses like the " + }, + { + "bbox": [ + 46, + 504, + 286, + 612 + ], + "type": "inline_equation", + "content": "L2" + }, + { + "bbox": [ + 46, + 504, + 286, + 612 + ], + "type": "text", + "content": " loss above, we can use image-level losses like LPIPS [56], which do not decompose into per-pixel losses. In practice, we experiment with a combination of such losses." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 616, + 286, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 286, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 286, + 665 + ], + "type": "text", + "content": "Regularisations. We also add generic regularisers to prevent parameters from taking on unreasonable values (e.g., Gaussians which are larger than the reconstructed objects, or vanishingly small). Please see the sup. mat. for details." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 671, + 250, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 250, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 250, + 684 + ], + "type": "text", + "content": "3.4. Extension to multiple input viewpoints" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": "If two or more input views " + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "I_j" + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "j \\in \\{1, \\dots, N\\}" + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": " are provided, we can apply network " + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 689, + 286, + 713 + ], + "type": "text", + "content": " multiple times to obtain" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": "multiple Splatter Images " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "M_{j}" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": ", one per view. If " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "(R, T)" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " is the relative camera pose change from an additional view to the reference view, we can take the mixture of 3D Gaussians " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " defined in the additional view's coordinates and warp it to the reference view. Specifically, a Gaussian of parameters " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "(\\sigma, \\mu, \\Sigma, c)" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " maps to Gaussian of parameters " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "(\\sigma, \\tilde{\\mu}, \\tilde{\\Sigma}, \\tilde{c})" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "\\tilde{\\mu} = R\\mu + T" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "\\tilde{\\Sigma} = R\\Sigma R^{\\top}" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "\\tilde{c} = c" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": ". We use the symbol " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "\\phi[\\theta]" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": " to denote the Gaussian mixture obtained by warping each Gaussian in " + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 72, + 545, + 203 + ], + "type": "text", + "content": ". Here we have also assumed a Lambertian colour model and will discuss in Sec. 3.5 how more complex models transform." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "spans": [ + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "content": "Given " + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "content": " different views " + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "inline_equation", + "content": "I_{j}" + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "content": " and corresponding warps " + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "content": ", we can obtain a composite mixture of 3D Gaussians simply by taking their union " + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "inline_equation", + "content": "\\Theta = \\bigcup_{j=1}^{N} \\phi_{j}[S(I_{j})]" + }, + { + "bbox": [ + 304, + 204, + 545, + 263 + ], + "type": "text", + "content": ". Note that this set of 3D Gaussians is defined in the coordinate system of the reference camera." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 273, + 437, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 273, + 437, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 273, + 437, + 285 + ], + "type": "text", + "content": "3.5. View-dependent colour" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": "Generalising beyond the Lambertian colour model, we use spherical harmonics [22] to represent view-dependent colours. For a particular Gaussian " + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "inline_equation", + "content": "(\\sigma, \\mu, \\Sigma, c)" + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": ", we then define " + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "inline_equation", + "content": "[c(\\pmb{\\nu}; \\pmb{\\alpha})]_i = \\sum_{l=0}^L \\sum_{m=-L}^L \\alpha_{ilm} Y_l^m(\\pmb{\\nu})" + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\alpha_{ilm}" + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": " are coefficients predicted by the network and " + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "inline_equation", + "content": "Y_l^m" + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": " are spherical harmonics, " + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "inline_equation", + "content": "L" + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": " is the order of the expansion, and " + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu} \\in \\mathbb{S}^2" + }, + { + "bbox": [ + 304, + 292, + 545, + 376 + ], + "type": "text", + "content": " is the viewing direction." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": "The viewpoint change of Sec. 3.4 transforms a viewing direction " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\pmb{\\nu}" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": " in the source camera to the corresponding viewing direction in the reference frame as " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{\\nu}} = R\\pmb{\\nu}" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": ". We can then find the transformed colour function by finding the coefficients " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\tilde{\\alpha}" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "c(\\pmb{\\nu};\\pmb{\\alpha}) = c(\\tilde{\\pmb{\\nu}};\\tilde{\\pmb{\\alpha}})" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": ". This is possible because (each order of) spherical harmonics are closed under rotation. However, the general case requires the computation of Wigner matrices. For simplicity, we only consider orders " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "L = 0" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": " (Lambertian) and " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "L = 1" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": ". Hence, the first level has one constant component " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "Y_0^0" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": " and the second level has three components which we can write collectively as " + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "inline_equation", + "content": "Y_{1} = [Y_{1}^{-1},Y_{1}^{0},Y_{1}^{1}]" + }, + { + "bbox": [ + 304, + 377, + 545, + 521 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 342, + 530, + 508, + 569 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 342, + 530, + 508, + 569 + ], + "spans": [ + { + "bbox": [ + 342, + 530, + 508, + 569 + ], + "type": "interline_equation", + "content": "Y _ {1} (\\boldsymbol {\\nu}) = \\sqrt {\\frac {3}{4 \\pi}} \\Pi \\boldsymbol {\\nu}, \\quad \\Pi = \\left[ \\begin{array}{c c c} 0 & 1 & 0 \\\\ 0 & 0 & 1 \\\\ 1 & 0 & 0 \\end{array} \\right].", + "image_path": "5778245c5f89350846d67270e2dfb59182f52843cf9a9acd35b8b33ab80a10d9.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": "We can then conveniently rewrite " + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "[c(\\pmb {\\nu};\\pmb {\\alpha})]_i = \\alpha_{i0} +" + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\pmb{\\alpha}_{i1}^{\\top}Y_{1}(\\pmb {\\nu})" + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": " . From this and " + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "c(\\pmb {\\nu};\\alpha_0,\\pmb {\\alpha}_1) = c(\\tilde{\\pmb{\\nu}};\\tilde{\\alpha}_0,\\tilde{\\alpha}_1)" + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": " we conclude that " + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\tilde{\\alpha}_{i0} = \\tilde{\\alpha}_{i0}" + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "text", + "content": " , and " + }, + { + "bbox": [ + 304, + 578, + 545, + 614 + ], + "type": "inline_equation", + "content": "\\tilde{\\alpha}_{i1} = \\Pi^{-1}R\\Pi \\alpha_{i1}" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 623, + 462, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 462, + 634 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 462, + 634 + ], + "type": "text", + "content": "3.6. Neural network architecture" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "The bulk of the predictor " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " mapping the input image " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " to the mixture of Gaussians " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " is architecturally identical to the SongUNet of [46]. The last layer is replaced with a " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "1\\times 1" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " convolutional layer with " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "12 + k_{c}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " output channels, where " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "k_{c}\\in \\{3,12\\}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " depending on the colour model. Given " + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "inline_equation", + "content": "I\\in \\mathbb{R}^{3\\times H\\times W}" + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": " as input, the network thus produces" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10211" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": "a " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "(12 + k_{c})\\times H\\times W" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " tensor as output, coding, for each pixel " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\pmb{u}" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " channels, the parameters " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "(\\hat{\\sigma},\\Delta ,\\hat{d},\\hat{s},\\hat{q},\\alpha)" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " which are then transformed to opacity, offset, depth, scale, rotation and colour, respectively. These are activated by nonlinear functions to obtain the Gaussian parameters. Specifically, the opacity is obtained using the sigmoid operator as " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\sigma =" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " sigmoid( " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\hat{\\sigma}" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " ). The depth is obtained as " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "d =" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "(z_{\\mathrm{far}} - z_{\\mathrm{near}})" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " sigmoid " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "(\\hat{d}) + z_{\\mathrm{near}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " . The mean " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " is then obtained using Eq. (3). Following [22], the covariance is obtained as " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\Sigma = R(\\pmb {q})\\mathrm{diag}(\\exp \\hat{s})^{2}R(\\pmb {q})^{\\top}" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "R(\\pmb {q})" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " is the rotation matrix with quaternion " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\pmb {q} = \\hat{\\pmb{q}} /\\| \\hat{\\pmb{q}}\\|" + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 72, + 289, + 207 + ], + "type": "inline_equation", + "content": "\\hat{\\pmb{q}}\\in \\mathbb{R}^4" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 207, + 288, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 207, + 288, + 266 + ], + "spans": [ + { + "bbox": [ + 46, + 207, + 288, + 266 + ], + "type": "text", + "content": "For multi-view reconstruction, we apply the same network to each input view and then use the approach of Sec. 3.4 to fuse the individual reconstructions. In order to allow the network to coordinate and exchange information between views, we apply two modifications to it." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "text", + "content": "First, we condition the network with the corresponding camera pose " + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "inline_equation", + "content": "(R,T)" + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "text", + "content": " (we only assume access to the relative camera pose to a common but otherwise arbitrary reference frame). In fact, since we consider cameras in a turn-table-like configuration, we only pass vectors " + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "inline_equation", + "content": "(Re_3,T)" + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "inline_equation", + "content": "e_3 = (0,0,1)" + }, + { + "bbox": [ + 46, + 266, + 289, + 375 + ], + "type": "text", + "content": ". We do so by encoding each entry via a sinusoidal positional embedding of order 9, resulting in 60 dimensions in total. Finally, these are applied to the U-Net blocks via FiLM [36] embeddings." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 375, + 288, + 423 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 288, + 423 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 288, + 423 + ], + "type": "text", + "content": "Second, we add cross-attention layers to allow communication between the features of different views. We do so in a manner similar to [44], but only at the lowest UNet resolution, which maintains the computational cost very low." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 435, + 128, + 449 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 435, + 128, + 449 + ], + "spans": [ + { + "bbox": [ + 47, + 435, + 128, + 449 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "spans": [ + { + "bbox": [ + 46, + 456, + 287, + 505 + ], + "type": "text", + "content": "We evaluate our method extensively for single-view reconstruction on six standard benchmarks. Next, we assess the quality of multi-view reconstruction, and finish with an evaluation of the speed of the method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "text", + "content": "Datasets. The standard benchmark for evaluating single-view 3D reconstruction is ShapeNet-SRN [45]. We train our method in the single-class setting and report results on the \"Car\" and \"Chair\" classes, following prior work. Moreover, we challenge our method with two classes of real objects from the CO3D [38] dataset: Hydrants and Teddybears. In this challenging dataset ripe with ambiguities we set " + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{far}}" + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{near}}" + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "text", + "content": " to depend on ground truth distance " + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gt}}" + }, + { + "bbox": [ + 46, + 509, + 287, + 617 + ], + "type": "text", + "content": " between the object and camera." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "We further test our method on two multi-category datasets. First, we use the standard benchmark of multicategory ShapeNet (with objects from 13 largest categories), and use the renderings, standard splits and target views from NMR [21]. Secondly, we train one model on renderings of objects from Objaverse-LVIS [10] which contains over 1k object categories, using the renderings from Zero-1-to-3 [29]. We evaluate this model on all objects" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 305, + 70, + 547, + 189 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 189 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 189 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 189 + ], + "type": "table", + "html": "
MethodRC1-view Cars1-view Chairs
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
SRN✗22.250.880.12922.890.890.104
CodeNeRF✗23.800.910.12823.660.900.166
FE-NVS✗22.830.910.09923.210.920.077
ViewsetDiff w/o D✗23.210.900.11624.160.910.088
PixelNeRF✓23.170.890.14623.720.900.128
VisionNeRF✓22.880.900.08424.480.920.077
NeRFDiff w/o NGD✓23.950.920.09224.800.930.070
Ours✓24.000.920.07824.430.930.067
", + "image_path": "617c289e29fba77b448a43d354c00473e03cbf416d3ce98a2dd8ea88132b8bc6.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 196, + 547, + 253 + ], + "lines": [ + { + "bbox": [ + 304, + 196, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 196, + 547, + 253 + ], + "type": "text", + "content": "Table 1. ShapeNet-SRN: Single-View Reconstruction. Our method achieves State-of-the-Art reconstruction quality on all metrics on the Car dataset and on two metrics in the Chair dataset, while performing reconstruction in the camera view-space. 'RC' indicates if a method can operate using only relative camera poses." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "type": "text", + "content": "from the Google Scanned Objects dataset [12], using the same renderings as used for evaluation in Free3D [57]. We train and evaluate all models at " + }, + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "type": "inline_equation", + "content": "128 \\times 128" + }, + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "type": "text", + "content": " resolution, apart from multi-category ShapeNet which is at " + }, + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "type": "inline_equation", + "content": "64 \\times 64" + }, + { + "bbox": [ + 304, + 273, + 547, + 357 + ], + "type": "text", + "content": ". Finally, we use the ShapeNet-SRN Cars dataset for the evaluation of the two-view reconstruction quality. For more details on datasets see supp. mat." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 362, + 547, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 362, + 547, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 362, + 547, + 530 + ], + "type": "text", + "content": "Baselines. For ShapeNet (both single-class and multiclass), we compare against implicit [19, 26, 45, 55], hybrid implicit-explicit [13] and explicit methods [2, 14, 48]. We use the deterministic variants of [13, 48] by using their reconstruction network in a single forward pass. For CO3D we compare against PixelNeRF which we train for 400,000 iterations with their officially released code on the same data as used for our method. Finally, on Objaverse-LVIS we compare to OpenLRM [15] (open-source version of LRM [17]): a large triplane-based reconstructor, trained on the full Objaverse dataset. Since we are proposing a deterministic reconstruction method, we do not compare to methods that employ Score Distillation [29, 59] or feedforward diffusion models [4, 28, 52, 54]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 530, + 534, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 530, + 534, + 544 + ], + "spans": [ + { + "bbox": [ + 317, + 530, + 534, + 544 + ], + "type": "text", + "content": "Implementation details can be found in the supp. mat." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 551, + 499, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 551, + 499, + 564 + ], + "spans": [ + { + "bbox": [ + 305, + 551, + 499, + 564 + ], + "type": "text", + "content": "4.1. Evaluation of reconstruction quality" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 569, + 547, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 547, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 547, + 654 + ], + "type": "text", + "content": "In line with related works [26, 55], we assess the quality of the reconstructions by measuring novel view synthesis quality and report Peak Signal-to-Noise Ratio (PSNR), Structural Similarity (SSIM) and a perceptual loss (LPIPS). We perform reconstruction from a given source view and render the 3D shape to unseen target views following standard protocols as detailed in the supp. mat." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 670, + 468, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 670, + 468, + 682 + ], + "spans": [ + { + "bbox": [ + 305, + 670, + 468, + 682 + ], + "type": "text", + "content": "4.1.1 Single-view 3D reconstruction" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 689, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 546, + 715 + ], + "type": "text", + "content": "ShapeNet. In Tab. 1 and Fig. 3 we compare the single-view reconstruction quality on the ShapeNet-SRN benchmark." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "10212" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 289, + 277 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 289, + 277 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 289, + 277 + ], + "type": "image", + "image_path": "4d67f4d94fb59ab9ecfbd4e7b9d0e71c42e009ec4355fde59440c475d05e08e7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 288, + 323 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 288, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 288, + 323 + ], + "type": "text", + "content": "Figure 3. ShapeNet-SRN Comparison. Our method outputs more accurate reconstructions (cars' backs, top chair) and better represents thin regions (bottom chair)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 333, + 285, + 374 + ], + "blocks": [ + { + "bbox": [ + 48, + 333, + 285, + 374 + ], + "lines": [ + { + "bbox": [ + 48, + 333, + 285, + 374 + ], + "spans": [ + { + "bbox": [ + 48, + 333, + 285, + 374 + ], + "type": "table", + "html": "
PixelNeRF [55]FE-NVS [14]FWD [2]VisionNeRF [26]Ours
PSNR ↑26.8027.0826.6628.7629.38
SSIM ↑0.910.920.910.930.95
LPIPS ↓0.1080.0820.0550.0650.047
", + "image_path": "9f587cd21209c02f03c17118984af638a43d5ff7d5ee6c4375651bf0ae2e6c74.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 52, + 410, + 281, + 483 + ], + "blocks": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "lines": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 287, + 399 + ], + "type": "text", + "content": "Table 2. Our method achieves State-of-the-Art quality of single-view reconstruction on multi-class ShapeNet dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 410, + 281, + 483 + ], + "lines": [ + { + "bbox": [ + 52, + 410, + 281, + 483 + ], + "spans": [ + { + "bbox": [ + 52, + 410, + 281, + 483 + ], + "type": "table", + "html": "
ObjectMethodPSNR ↑SSIM ↑LPIPS ↓
HydrantPixelNeRF21.760.780.203
HydrantOurs21.800.800.150
TeddybearPixelNeRF19.380.650.290
TeddybearOurs19.440.730.231
", + "image_path": "19fd537415fcc0c2fe059ea853b0fca196ee848a7ba3b8ce6b62d412ee6ec960.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 536, + 287, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 536, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 46, + 536, + 287, + 643 + ], + "type": "text", + "content": "Our method outperforms all deterministic reconstructors in SSIM and LPIPS, obtaining sharper new views. Furthermore, our method requires only relative camera poses instead of absolute/canonical ones. Qualitatively, our method does well in challenging situations with limited visibility and thin structures. In Tab. 2, we use instead the multicategory ShapeNet protocol we observe that our method outperforms more expensive baselines [26] across all metrics in the multi-category ShapeNet setting." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 648, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 648, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 648, + 287, + 685 + ], + "type": "text", + "content": "CO3D. On CO3D bears and hydrants, our model outperforms PixelNeRF on all metrics (Tab. 3), and qualitatively produces sharper images (Fig. 4) while being " + }, + { + "bbox": [ + 46, + 648, + 287, + 685 + ], + "type": "inline_equation", + "content": "1,000 \\times" + }, + { + "bbox": [ + 46, + 648, + 287, + 685 + ], + "type": "text", + "content": " faster." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "Objaverse-LVIS and Google Scanned Objects. We compare our method to OpenLRM [15], an open-source ver" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 70, + 545, + 213 + ], + "blocks": [ + { + "bbox": [ + 307, + 70, + 545, + 213 + ], + "lines": [ + { + "bbox": [ + 307, + 70, + 545, + 213 + ], + "spans": [ + { + "bbox": [ + 307, + 70, + 545, + 213 + ], + "type": "image", + "image_path": "37df622fc055cf5ea3c81c0f05207f525630a581b9355e8786a2094999c62318.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 221, + 545, + 254 + ], + "lines": [ + { + "bbox": [ + 305, + 221, + 545, + 254 + ], + "spans": [ + { + "bbox": [ + 305, + 221, + 545, + 254 + ], + "type": "text", + "content": "Figure 4. CO3D Hydrants and Teddybears. Our method outputs sharper reconstructions than PixelNeRF while being " + }, + { + "bbox": [ + 305, + 221, + 545, + 254 + ], + "type": "inline_equation", + "content": "100\\mathrm{x}" + }, + { + "bbox": [ + 305, + 221, + 545, + 254 + ], + "type": "text", + "content": " faster in inference." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 331, + 274, + 520, + 323 + ], + "blocks": [ + { + "bbox": [ + 46, + 491, + 286, + 514 + ], + "lines": [ + { + "bbox": [ + 46, + 491, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 286, + 514 + ], + "type": "text", + "content": "Table 3. CO3D: Single-View. Our method outperforms PixelNeRF on this challenging benchmark across all metrics." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 274, + 520, + 323 + ], + "lines": [ + { + "bbox": [ + 331, + 274, + 520, + 323 + ], + "spans": [ + { + "bbox": [ + 331, + 274, + 520, + 323 + ], + "type": "table", + "html": "
MethodPSNR ↑SSIM ↑LPIPS ↓
OpenLRM18.060.840.129
Ours21.060.880.111
", + "image_path": "28e3f87aac4b4a8bfc13b0ffbd3091e9bf360cdb22268b560fac2e4e48d46a34.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 331, + 545, + 365 + ], + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 365 + ], + "type": "text", + "content": "Table 4. Google Scanned Objects: Single-View. Our method outperforms the much more expensive LRM [15, 17] on single-view open-world reconstruction." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 312, + 383, + 537, + 529 + ], + "blocks": [ + { + "bbox": [ + 312, + 383, + 537, + 529 + ], + "lines": [ + { + "bbox": [ + 312, + 383, + 537, + 529 + ], + "spans": [ + { + "bbox": [ + 312, + 383, + 537, + 529 + ], + "type": "image", + "image_path": "f4fcc57bbd0f2cd4869dce799c7d4c76eb839246499c7741d0d6f9fda4a98bde.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 533, + 545, + 577 + ], + "lines": [ + { + "bbox": [ + 305, + 533, + 545, + 577 + ], + "spans": [ + { + "bbox": [ + 305, + 533, + 545, + 577 + ], + "type": "text", + "content": "Figure 5. Google Scanned Objects. On large datasets our model has similar quality to much more expensive baselines (shoe). Our reconstructions have more accurate lighting (Jenga), object pose (horse) and shape (toy)." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "sion of the LRM model [17], on the Google Scanned Objects [12] evaluation renderings from Free3D [57]. Quantitatively, in Tab. 4 Splatter Image outperforms OpenLRM and, qualitatively (Fig. 5), it is comparable. Our models perform well even on images collected from the Internet Fig. 6, after removing backgrounds and resizing. Remarkably, our method, trained for 7 GPU days, is able to compete with OpenLRM, which uses hundreds of GPUs for several days [15, 17]." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10213" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 68, + 281, + 269 + ], + "blocks": [ + { + "bbox": [ + 55, + 68, + 281, + 269 + ], + "lines": [ + { + "bbox": [ + 55, + 68, + 281, + 269 + ], + "spans": [ + { + "bbox": [ + 55, + 68, + 281, + 269 + ], + "type": "image", + "image_path": "6d0803740f828c39a676d86c3d33cd8ca2a2555925e84cf622cd1ee8249814b0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 271, + 287, + 293 + ], + "lines": [ + { + "bbox": [ + 47, + 271, + 287, + 293 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 287, + 293 + ], + "type": "text", + "content": "Figure 6. Our models trained on single classes (top) and on Objaverse (bottom) can be used on in-the-wild Internet images (right)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 87, + 304, + 247, + 390 + ], + "blocks": [ + { + "bbox": [ + 87, + 304, + 247, + 390 + ], + "lines": [ + { + "bbox": [ + 87, + 304, + 247, + 390 + ], + "spans": [ + { + "bbox": [ + 87, + 304, + 247, + 390 + ], + "type": "table", + "html": "
MethodRelative Pose2-view Cars
PSNR ↑SSIM ↑
SRNX24.840.92
CodeNeRFX25.710.91
FE-NVSX24.640.93
PixelNeRF✓25.660.94
Ours✓26.010.94
", + "image_path": "aa6fa5a89801c4d9125070c28de45d177ce51734ad6dc85dbd248eb7f06c2951.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 59, + 398, + 273, + 409 + ], + "lines": [ + { + "bbox": [ + 59, + 398, + 273, + 409 + ], + "spans": [ + { + "bbox": [ + 59, + 398, + 273, + 409 + ], + "type": "text", + "content": "Table 5. Two-view reconstruction on ShapeNet-SRN Cars." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 420, + 201, + 430 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 201, + 430 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 201, + 430 + ], + "type": "text", + "content": "4.1.2 Two-view 3D reconstruction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 439, + 287, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 439, + 287, + 582 + ], + "spans": [ + { + "bbox": [ + 46, + 439, + 287, + 582 + ], + "type": "text", + "content": "We compare our multi-view reconstruction model on ShapeNet-SRN Cars by training it for two-view predictions (see Tab. 5). Prior work often relies on absolute camera pose conditioning, meaning that the model learns to rely on the canonical orientation of the object in the dataset. This limits the applicability of these models, as in practice for a new image of an object, the absolute camera pose is of course unknown. Here, only ours and PixelNeRF can deal with relative camera poses as input. Interestingly, our method shows not only better performance than PixelNeRF in both real and synthetic data but also improves over SRN, CodeNeRF, and FE-NVS that rely on absolute camera poses." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 598, + 122, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 122, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 122, + 609 + ], + "type": "text", + "content": "4.1.3 Ablations" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 666 + ], + "type": "text", + "content": "We evaluate the influence of individual components of our method, using a shorter training schedule than models in Tab. 1 for efficiency. Ablations of the multi-view model are given in the supp. mat." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "We show the results of our ablation study for the single-view model in Tab. 6. We train a model (w/o image) that uses a fully connected, unstructured output instead of a Splatter Image. This model cannot transfer image informa" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 69, + 547, + 293 + ], + "blocks": [ + { + "bbox": [ + 307, + 69, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 307, + 69, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 307, + 69, + 547, + 293 + ], + "type": "image", + "image_path": "bbd629e48d621962ef0b99e2c4b83d409d533dcd56973729ac2052e7c3bc2396.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 303, + 546, + 358 + ], + "lines": [ + { + "bbox": [ + 305, + 303, + 546, + 358 + ], + "spans": [ + { + "bbox": [ + 305, + 303, + 546, + 358 + ], + "type": "text", + "content": "Figure 7. Analysis. Splatter Images represent full " + }, + { + "bbox": [ + 305, + 303, + 546, + 358 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 305, + 303, + 546, + 358 + ], + "type": "text", + "content": " of objects by allocating background pixels to appropriate 3D locations (third row) to predict occluded elements like wheels (left) or chair legs (middle). Alternatively, it predicts offsets in the foreground pixels to represent occluded chair parts (right)." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 369, + 546, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 546, + 572 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 546, + 572 + ], + "type": "text", + "content": "tion directly to their corresponding Gaussians and does not achieve good performance. We also ablate predicting the depth along the ray by simply predicting 3D coordinates for each Gaussian. This version also suffers from its inability to easily align the input image with the output. Removing the 3D offset prediction mainly harms the backside of the object while leaving the front faces the same. This results in a lower impact on the overall performance of this component. Changing the degrees of freedom of appearance predictions (by fixing Gaussians to be isotropic or removing view-dependence) also reduced the image fidelity. Finally, removing perceptual loss (w/o " + }, + { + "bbox": [ + 304, + 369, + 546, + 572 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{LPIPS}}" + }, + { + "bbox": [ + 304, + 369, + 546, + 572 + ], + "type": "text", + "content": ") results in a significant worsening of LPIPS, indicating this loss is important for perceptual sharpness of reconstructions. Being able to use LPIPS in optimisation is a direct consequence of employing a fast-to-render representation and being able to render full images at training time." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 578, + 545, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 578, + 545, + 661 + ], + "spans": [ + { + "bbox": [ + 304, + 578, + 545, + 661 + ], + "type": "text", + "content": "Analysis. In Fig. 7, we analyse how 3D information is stored inside a Splatter Image. Since all information is arranged in an image format, we can visualise each of the modalities: opacity, depth, and location. Pixels of the input image that belong to the object tend to describe their corresponding 3D structure, while pixels outside of the object wrap around to close the object on the back." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 670, + 509, + 683 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 509, + 683 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 509, + 683 + ], + "type": "text", + "content": "4.2. Evaluation of reconstruction efficiency" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "A key advantage of the Splatter Image is its training and test time efficiency, which we assess below." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10214" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 267, + 184 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 267, + 184 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 267, + 184 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 267, + 184 + ], + "type": "table", + "html": "
PSNR ↑SSIM ↑LPIPS ↓
Full model22.250.900.115
w/o image20.600.870.152
w/o depth21.210.880.145
w/o view dir.21.770.890.121
isotropic22.010.890.118
w/o offset22.060.900.119
w/o LPIPS22.220.890.141
", + "image_path": "791f821a8a7223986a9c44c016beb74137f82ec00e5c9b78ac9e897f30b0e949.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 51, + 216, + 281, + 316 + ], + "blocks": [ + { + "bbox": [ + 74, + 192, + 259, + 203 + ], + "lines": [ + { + "bbox": [ + 74, + 192, + 259, + 203 + ], + "spans": [ + { + "bbox": [ + 74, + 192, + 259, + 203 + ], + "type": "text", + "content": "Table 6. Ablations: Single-View Reconstruction." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 51, + 216, + 281, + 316 + ], + "lines": [ + { + "bbox": [ + 51, + 216, + 281, + 316 + ], + "spans": [ + { + "bbox": [ + 51, + 216, + 281, + 316 + ], + "type": "table", + "html": "
RPE↓R↓Forward↓Test↓
NeRFDiff✓(0.031)(0.0180)(0.103)(4.531)
FE-NVS✗(0.015)(0.0032)(0.028)(0.815)
VisionNeRF✓0.0082.43129.733607.8
PixelNeRF✓0.0031.85727.432463.3
ViewsetDiff✗0.0250.00640.0511.625
Ours 2-view✓0.0300.00170.0370.455
Ours 1-view✓0.0260.00170.0330.451
", + "image_path": "9fd9ba4ae0f56989abda4006fa7521a40cacfc0374c958673945a6c85996be87.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 325, + 287, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 325, + 287, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 287, + 392 + ], + "type": "text", + "content": "Table 7. Speed. Time required for image encoding (E), rendering (R), the 'Forward' time, indicative of train-time efficiency and the 'Test' time, indicative of test-time efficiency. Our method is the most efficient in both train and test time across open-source available methods and only requires relative camera poses. 'RP' indicates if a method can operate using only relative camera poses." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 413, + 287, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 413, + 287, + 473 + ], + "spans": [ + { + "bbox": [ + 46, + 413, + 287, + 473 + ], + "type": "text", + "content": "Test-time efficiency. First, we assess the 'Test' time speed, i.e., the time it takes for the trained model to reconstruct an object and generate a certain number of images. We reference the evaluation protocol of the standard ShapeNet-SRN benchmark [45] and render 250 images at " + }, + { + "bbox": [ + 46, + 413, + 287, + 473 + ], + "type": "inline_equation", + "content": "128^{2}" + }, + { + "bbox": [ + 46, + 413, + 287, + 473 + ], + "type": "text", + "content": " resolution." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 474, + 287, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 640 + ], + "type": "text", + "content": "Assessing wall-clock time fairly is challenging as it depends on many factors. All measurements reported here are done on a single NVIDIA V100 GPU. We use officially released code of Viewset Diffusion [48], PixelNeRF [55] and VisionNeRF [26] and rerun those on our hardware. NeRFDiff [13] and FE-NVS [14] do not have code available, so we use their self-reported metrics. According to the authors, FE-NVS was evaluated on the same type of GPU, while NeRFDiff does not include information about the hardware used and we were unable to obtain more information. Since we could not perfectly control these experiments, the comparisons to NeRFDiff and FE-NVS are only indicative. For Viewset Diffusion and NeRFDiff we report the time for a single pass through the reconstruction network." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Tab. 7 reports the 'Encoding' (E) time, spent by the network to compute the object's 3D representation from an image, and the 'Rendering' (R) time, spent by the network to render new images from the 3D representation. From those, we calculate the 'Test' time, equal to the 'Encoding' time plus 250 'Rendering' time. As shown in the last column" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": "of Tab. 7, our method is more than " + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "inline_equation", + "content": "1000 \\times" + }, + { + "bbox": [ + 304, + 72, + 545, + 180 + ], + "type": "text", + "content": " faster in testing than PixelNeRF and VisionNeRF (while achieving equal or superior quality of reconstruction in Tab. 1). Our method is also faster than voxel-based Viewset Diffusion even though it does not require knowing the absolute camera pose. The efficiency of our method is very useful to iterate quickly in research; for instance, evaluating our method on the full ShapeNet-Car validation set takes less than 10 minutes on a single GPU. In contrast, PixelNeRF takes 45 GPU-hours." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "type": "text", + "content": "Train-time efficiency. Next, we assess the efficiency of the method during training. Here, the encoding time becomes more significant because one typically renders only a few images to compute the reconstruction loss and obtain a gradient (e.g., because there are only so many views available in the training dataset, or because generating more views provides diminishing returns in terms of supervision). As typical values (and as used by us in this work), we assume that the method is tasked with generating 4 new views at each iteration instead of 250 as before. We call this the 'Forward' time and measure it the same way. As shown in the 'Forward' column of Tab. 7, our method is " + }, + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "type": "inline_equation", + "content": "246 \\times" + }, + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "type": "text", + "content": " faster at training time than implicit methods and " + }, + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "type": "inline_equation", + "content": "1.5 \\times" + }, + { + "bbox": [ + 304, + 186, + 546, + 426 + ], + "type": "text", + "content": " than Viewset Diffusion, which uses an explicit representation. With this, we can train models achieving state-of-the-art quality on a single A6000 GPU in 7 days, while VisionNeRF requires 16 A100 GPUs for 5 days. What is even more remarkable, we can train models on large datasets such as Objaverse on two A6000 GPUs in 3.5 days, while triplane-based methods such as LRM require 128 A100 GPUs for 3 days [17]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 378, + 453 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 461, + 545, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 461, + 545, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 461, + 545, + 594 + ], + "type": "text", + "content": "We have presented Splatter Image, a simple method for single- or few-view 3D reconstruction. The method uses an off-the-shelf 2D image-to-image network and predicts a pseudo-image containing one colored 3D Gaussian per pixel. By combining fast inference with fast rendering via Gaussian Splatting, Splatter Image can be trained and evaluated quickly on synthetic and real benchmarks. Splatter Image achieves state-of-the-art reconstruction performance without requiring absolute/canonical camera poses at test time, is simple to implement, and can be trained and tested much faster than many alternatives." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 599, + 545, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 599, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 304, + 599, + 545, + 659 + ], + "type": "text", + "content": "Ethics. We use various datasets in a manner compatible with their terms. There is no processing of personal data. For further details on ethics, data protection, and copyright please see https://www.robots.ox.ac.uk/~vedaldi/research/union/ethics.html." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Acknowledgements. S. Szymanowicz is supported by an EPSRC Doctoral Training Partnerships Scholarship (DTP) EP/R513295/1 and the Oxford-Ashton Scholarship. A. Vedaldi is supported by ERC-CoG UNION 101001212." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "10215" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Titas Anciukevicius, Zexiang Xu, Matthew Fisher, Paul Henderson, Hakan Bilen, Niloy J. 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IEEE Visualization Conference., 2001. 3" + } + ] + } + ], + "index": 31 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "10217" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SplattingAvatar_ Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting/2a923612-0df2-4faf-a040-0816baf81069_content_list.json b/2024/SplattingAvatar_ Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting/2a923612-0df2-4faf-a040-0816baf81069_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..432c138e05cbb72dfc8871999d7a4f423121aee1 --- /dev/null +++ b/2024/SplattingAvatar_ Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting/2a923612-0df2-4faf-a040-0816baf81069_content_list.json @@ -0,0 +1,1533 @@ +[ + { + "type": "text", + "text": "SplattingAvatar: Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting", + "text_level": 1, + "bbox": [ + 215, + 130, + 756, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhijing Shao $^{1,2}$ \nXiangu Lin $^{2}$ \nZhaolong Wang $^{2}$ \nZhuang Li $^{2}$ \nDuotun Wang $^{1}$ \nXiangru Lin $^{2}$ \nYu Zhang $^{2}$ \nMingming Fan $^{1,3}$ \nZeyu Wang $^{1,3}$ $^{1}$ The Hong Kong University of Science and Technology (Guangzhou) \n $^{2}$ Prometheus Vision Technology Co., Ltd. \n $^{3}$ The Hong Kong University of Science and Technology", + "bbox": [ + 183, + 200, + 781, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2bb73886a2abb1488eb7304c86ebaa70adf937a115f124fd50877fbea0607f4b.jpg", + "image_caption": [ + "Figure 1. Overview of SplattingAvatar featuring Mesh-Embedded Gaussian Splatting. Our method takes (a) monocular videos as input, while employing (b) a trainable embedding technique for Gaussian-Mesh association. (c) Animated by mesh through the learned embedding, the Gaussians render into high-fidelity human avatars. (d) SplattingAvatar demonstrates real-time rendering capabilities in Unity, achieving over 300 FPS on an NVIDIA RTX 3090 GPU and 30 FPS on an iPhone 13 (images captured in action)." + ], + "image_footnote": [], + "bbox": [ + 86, + 324, + 480, + 518 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/adf2b2b599e15bb9c5501b304e5530f51ed7526f521079cebbba7d50c3832da3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 480, + 325, + 880, + 517 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 595, + 313, + 611 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We present SplattingAvatar, a hybrid 3D representation of photorealistic human avatars with Gaussian Splatting embedded on a triangle mesh, which renders over 300 FPS on a modern GPU and 30 FPS on a mobile device. We disentangle the motion and appearance of a virtual human with explicit mesh geometry and implicit appearance modeling with Gaussian Splatting. The Gaussians are defined by barycentric coordinates and displacement on a triangle mesh as Phong surfaces. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians while walking on the triangle mesh. SplattingAvatar is a hybrid representation of virtual humans where the mesh represents low-frequency motion and surface deformation, while the Gaussians take over the high-frequency geometry and detailed appearance. Unlike existing deformation methods that rely on an MLP-based linear blend skinning (LBS) field for motion, we control the rotation and translation of the Gaussians directly by mesh, which empowers its compatibility with various animation", + "bbox": [ + 75, + 628, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "techniques, e.g., skeletal animation, blend shapes, and mesh editing. Trainable from monocular videos for both full-body and head avatars, SplattingAvatar shows state-of-the-art rendering quality across multiple datasets. Code and data are available at https://github.com/initialneil/SplattingAvatar.", + "bbox": [ + 498, + 597, + 895, + 688 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 722, + 632, + 738 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The demand for personalized, photorealistic, and animatable human avatars that render in real-time spans a wide array of applications, including gaming [48], extended reality (XR) storytelling [10, 19], and tele-presentation [22, 24]. As the quest for digital realism intensifies, practitioners face a growing challenge: improving the quality of 3D human models often means increasing the complexity of these models. This is typically achieved by adding more polygons, layering skin textures [5], and integrating advanced hair systems [42]. However, these enhancements invariably lead to", + "bbox": [ + 496, + 750, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "1606", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "higher computational demands, creating obstacles in achieving efficiency and portability in avatar rendering.", + "bbox": [ + 75, + 90, + 470, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In our approach, we categorize the representation of mesh-based virtual humans into three distinct levels of detail. The first two levels encompass body motion and surface deformation, both of which are effectively captured by a mesh [11, 16, 39]. The third level, however, focuses on geometric details that are crucial for enhancing realism but challenging to represent with traditional meshes. This level is not only computationally demanding to render [31] but also faces limitations due to the rigid connectivity of mesh vertices, which hinders the adaptability to topological changes and complex or thin structures.", + "bbox": [ + 75, + 123, + 470, + 289 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Recent advances in the field have seen a shift towards using Neural Radiance Fields (NeRF) [32], especially for capturing high-frequency details in 3D avatar modeling [3, 18, 21, 26, 27, 34, 35, 53]. A typical process involves constructing NeRF in a canonical space and then performing volume rendering in the posed space. This is done by tracing ray samples backward from their posed positions to their canonical origins [21, 34, 35, 53]. However, this reverse mapping process introduces ambiguities, as a single point in the posed space might correspond to multiple points in the canonical space [8, 9], leading to challenges in accurately rendering details. Additionally, the prevalent use of multilayer perceptron (MLPs) for motion control [21, 39, 51] tends to overlook the advantages of mesh-based representations for capturing surface deformations, an aspect crucial for realistic avatar movement as highlighted in studies like DECA [12], CAPE [30], and TalkSHOW [45].", + "bbox": [ + 75, + 291, + 470, + 547 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To address the challenges posed by the limitations of NeRF and MLP-based motion control in capturing high-frequency details and realistic surface deformations, we introduce a novel solution. Inspired by the recently proposed Gaussian Splatting technique [23], we propose explicit motion control of the Gaussians with trainable embeddings on a mesh. The embedding is described by $(k,u,v,d)$ on the mesh as Phong surface [38], where $(u,v)$ represents the local barycentric coordinates of the embedding triangle $k$ , and $d$ is the displacement along the interpolated normal vector. The pose-dependent rotation and scaling adjust dynamically in response to the mesh warping, while the pose-invariant properties, i.e., canonical rotation and scaling, color, and opacity, remain stable and consistent across various poses. Because the embedding point defined in barycentric coordinates is differentiable only inside the corresponding triangle, cross-triangle updates must be handled properly [40, 41]. During training, we conduct lifted optimization [38] with the embedding points walking on the triangle mesh.", + "bbox": [ + 75, + 550, + 470, + 838 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our hybrid representation, Gaussians embedded on a mesh, can be trained from a monocular video and efficiently port to Unity that runs in real time (Figure 1) by bringing together three key advantages. First, the use of the mesh", + "bbox": [ + 75, + 839, + 470, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for representing body motion and surface deformation not only proves efficient but also allows for high editability. This flexibility is crucial for adapting the avatar to various scenarios and movements. Second, the application of Gaussian Splatting enriches this model by providing a robust means to capture high-frequency geometry and appearance details. This is vital for achieving a level of realism that conventional meshes alone cannot offer. Third, the embedding technique empowers the Gaussians to be explicitly controlled by the mesh movements. This integration results in an efficient, clear, and non-ambiguous method for motion control, significantly reducing the computational load compared to MLP-based methods.", + "bbox": [ + 496, + 90, + 893, + 286 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Furthermore, our approach is distinct from existing hybrid models such as AvatarReX [52] and DELTA [14], which typically segment avatars into body parts like hair, hands, clothes, and face. Instead, our method achieves a disentanglement of motion and appearance. In the SplattingAvatar framework, although different parts may have specific motion control, the rendering is uniformly conducted through Gaussian Splatting. This uniformity achieved by our method ensures a cohesive and harmonious appearance across all parts of the avatar.", + "bbox": [ + 496, + 287, + 893, + 439 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We summarize our main contributions as follows:", + "bbox": [ + 503, + 446, + 831, + 460 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce a framework that integrates Gaussian Splating with meshes, offering a new avatar representation that achieves realism and computational efficiency.", + "- Our approach applies lifted optimization to avatar modeling, allowing for joint optimization of Gaussian parameters and mesh embeddings for accurate reconstruction.", + "- We demonstrate the capability of real-time rendering and adaptability to creating diverse avatars through comprehensive evaluation and a Unity implementation." + ], + "bbox": [ + 504, + 468, + 890, + 616 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 632, + 640, + 648 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Mesh-based avatar. The rise of free-viewpoint video in sequences of textured meshes has shown the expressiveness of detailed texture atlas along with as few as 10k triangles [11]. Many efforts [18, 20] have been put into extending this line of work to build controllable avatars. With the help of human shape models with strong prior [6, 25, 28, 33] that unwrap to a unified UV space, texture atlas can be obtained by 2D image generation supervised through differentiable rendering [31, 43]. Such prior models provide consistency across large motions and can be recovered from monocular videos or even a single image. To cope with the shape details of identities and clothes, CAPE [30] predicts displacements on the vertices with pose-conditioned VAE. Due to the limitation of the base model to topological changes, some treat the textured mesh as input conditions [31, 36] for image rendering, while others resort to implicit representations of", + "bbox": [ + 496, + 657, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "1607", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/c809f53ba168abcbf1bacf32a0339f36ecb84694deaead04feb645b14e04fa4c.jpg", + "image_caption": [ + "Figure 2. The pipeline of our method. SplittingAvatar learns 3D Gaussians with trainable embedding on the canonical mesh. The motion and deformation of the mesh explicitly bring the Gaussians to the posed space for differentiable rasterization. Both the Gaussians and embedding parameters are optimized during training. The position $\\mu$ is the barycentric point $P$ plus a displacement $d$ along the interpolated normal vector $\\mathbf{n}$ . Pose-dependent quaternion and scaling $(\\delta q, \\delta s)$ and pose-invariant quaternion, scaling, opacity, and color $(\\overline{q}, \\overline{s}, o, c)$ together define the properties of the Gaussians." + ], + "image_footnote": [], + "bbox": [ + 91, + 85, + 893, + 290 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the mesh [8, 9, 20, 39], color [16, 20, 39], or materials [4].", + "bbox": [ + 75, + 396, + 464, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Implicit neural avatar. To achieve convincing rendering beyond the limitation of triangle mesh, especially on the hair, glasses, and clothes, some recent works [3, 16, 21, 26, 34, 35, 44, 47, 53] focus on constructing NeRF in the canonical space (usually T-pose of SMPL [28] or neutral expression of FLAME [25]) and conduct volume rendering at the posed space. The required backward tracing from pose to canonical is non-trivial and raises an ambiguity issue. Existing works propose to adopt pose conditioned inverse LBS field [17, 34] or to optimize a root-finding loop with multiple initialization [8, 9, 21]. The increased computational load upon volume rendering prohibits the potential real-time applications.", + "bbox": [ + 75, + 412, + 470, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PointAvatar [51], with explicit point primitives, takes advantage of forward rasterization that only requires nonambiguous forward deformation from canonical to pose, producing photo-realistic appearance and detailed challenging geometries such as hair and glasses. In transforming to Gaussian Splatting, we further increase the efficiency and compatibility with our mesh embedding mechanism instead of the LBS-based deformation field and achieve two magnitude faster rendering speed with on-par quality.", + "bbox": [ + 75, + 611, + 470, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Hybrid avatar representation. First attempts have been proposed to disentangle human avatar modeling into separate parts with varying properties. AvatarRex [52] learns disentangled models for face, body, and hands. SCARF [13] and DELTA [14] propose hybrid modeling with textured mesh for body, and NeRF for hair and clothing. In contrast, our method handles the disentanglement in terms of motion and appearance to explicit mesh geometry and implicit Gaussian Splatting rendering. Different from existing works [3, 20] that attach features to fixed locations on mesh like mesh", + "bbox": [ + 75, + 750, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "vertices, our trainable embedding enables the Gaussians to optimize their locations on mesh and distribute unevenly according to the texture complexity.", + "bbox": [ + 496, + 396, + 893, + 443 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 460, + 591, + 476 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Overview. Given a sequence of monocular images, each with a registered mesh template, i.e., the deformed mesh of SMPL [28] or FLAME [25], we train a hybrid representation of human avatar as 3D Gaussians [23] embedded on the canonical mesh. The Gaussians, parameterized by position, rotation, scale, color, and opacity, are semi-transparent 3D particles that render into camera views through splattering-based rasterization.", + "bbox": [ + 496, + 487, + 893, + 607 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Each 3D Gaussian is embedded on one triangle of the canonical mesh in its local $(u, v, d)$ coordinates. The embedding directly defines the position of the Gaussians in both canonical and posed space. Other than position, each Gaussian has its own parameters of rotation, scaling, color, and opacity. With the mesh deformed by animation, the embedding also provides additional rotation and scaling upon each Gaussian. The additional pose-dependent rotation is defined by barycentric interpolated per-vertex quaternion while the additional scaling is defined by the area change of the embedded triangle.", + "bbox": [ + 496, + 609, + 895, + 776 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "During optimization, the Gaussian parameters and the embedding parameters are updated simultaneously. When the update of $(u,v)$ moves the embedding across the triangle boundary, the barycentric update is re-expressed in the neighboring triangle as if the Gaussian is walking on the mesh. To support embedding, we adapt the clone and split scheme of 3D Gaussians [23] to better suit our needs.", + "bbox": [ + 496, + 777, + 893, + 883 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Embedding on mesh. Inspired by the Phong shading in", + "bbox": [ + 500, + 885, + 892, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "1608", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "computer graphics, Phong surface [38] defines the position and normal of a point inside a triangle. For the point $P$ on triangle $k$ with barycentric coordinate $(u,v)$ , its position and normal is a linear interpolation of the triangle's vertices $\\{V_1,V_2,V_3\\}$ and per-vertex normals $\\{\\pmb{n}_1,\\pmb{n}_2,\\pmb{n}_3\\}$ :", + "bbox": [ + 76, + 90, + 472, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nP = \\mathcal {V} (k, u, v) = u * V _ {1} + v * V _ {2} + (1 - u - v) * V _ {3} \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 176, + 468, + 193 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {n} = \\mathcal {N} (k, u, v) = u * \\boldsymbol {n} _ {1} + v * \\boldsymbol {n} _ {2} + (1 - u - v) * \\boldsymbol {n} _ {3} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 203, + 468, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{V}$ maps triangle index $k$ and barycentric coordinates $(u,v)$ to a point on the mesh and $\\mathcal{N}$ the interpolated normal.", + "bbox": [ + 75, + 229, + 468, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We define the position of a Gaussian, i.e., the mean $\\mu$ , by a displacement $d$ along the interpolated normal vector:", + "bbox": [ + 76, + 261, + 468, + 290 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mu = P + d * \\boldsymbol {n} \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 301, + 468, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Embedding $E = \\{k, u, v, d\\}$ approximates a first-order continuous space around the mesh surface.", + "bbox": [ + 75, + 327, + 468, + 356 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As proposed by Zielonka et al. [53], for the corresponding triangle in the canonical and posed space at frame $t$ we compute the matrix $\\{R_{\\text{cano}}, R_{\\text{pose}}\\}$ based on the triangle's tangent, bitangent, and normal to track the triangle rotation from canonical to pose, noted that the notation $t$ is skipped. The rotation matrix is then converted to a quaternion, and we calculate the per-vertex quaternion $q_V$ by area-weighted average from surrounding neighbor triangles:", + "bbox": [ + 75, + 357, + 470, + 478 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nR _ {k} = R _ {\\text {c a n o}} R _ {\\text {p o s e}} ^ {- 1} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 209, + 487, + 468, + 506 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {V} = \\frac {\\sum_ {k \\in \\Omega_ {V}} A _ {k} q _ {k}}{\\sum_ {k \\in \\Omega_ {V}} A _ {k}} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 512, + 468, + 549 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Omega_V$ is the neighbor triangles of vertex $V$ , $A_k$ and $q_k$ are the triangle's area and quaternion respectively. For an embedding $E_i$ with quaternions $\\{q_1, q_2, q_3\\}$ calculated on the corresponding triangle vertices at frame $t$ , the barycentric interpolated rotation $\\delta q_{i,t}$ is multiplied to the canonical rotation $\\overline{q}_i$ of the Gaussian in the canonical space:", + "bbox": [ + 75, + 551, + 468, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\delta q _ {i, t} = u * q _ {1} + v * q _ {2} + (1 - u - v) * q _ {3} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 654, + 468, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nq _ {i, t} = \\delta q _ {i, t} * \\bar {q} _ {i} \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 683, + 468, + 699 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The same applies to scaling where the area change of the embedded triangle is used to represent the scaling caused by deformation: $s_{i,t} = (A_{\\text{pose}} / A_{\\text{cano}}) \\overline{s}_i$ . While the original implementation of Gaussian Splatting [23] represents color in view-dependent spherical harmonics, we choose to turn it off for simplicity [29].", + "bbox": [ + 75, + 704, + 468, + 795 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We perform initialization by randomly selecting $10\\mathrm{k}$ pairs of triangle indices and barycentric coordinates on the canonical mesh. We set the barycentric coordinates to be the current $(u,v)$ of embeddings and initialize all the $d$ to be zero. With the position of the Gaussians calculated from the embeddings, we initialize other properties of the Gaussians according to their original definitions [23]. Initially, the Gaussians", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/03ac5e5ad6ed0bba6cbaf91b4603ac27afca759cd1e7a1073c55ceea02722b97.jpg", + "image_caption": [ + "Figure 3. The development of Gaussian embeddings on mesh. Each line segment indicates the position of one Gaussian displaced from its embedding point on mesh. Gaussians for off-surface geometries like the hair have positive displacements while others turn to have negative displacements because when the mesh surface is correctly aligned to the geometry like in the facial area, the means for the Gaussians will be inside the mesh." + ], + "image_footnote": [], + "bbox": [ + 511, + 89, + 616, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/fbe688147623148f4bceaf7aba006639a4d4e892cafb792c744247d41d2532ab.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 645, + 89, + 746, + 172 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/d93a12c3d42cfc4d8df22b4e9efe959216124939801c996e6e72e8b6d1393a03.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 772, + 90, + 874, + 172 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "are positioned on the surface of the mesh. With the training proceeds with more poses, the embeddings generally bring the Gaussians to approximate the actual geometry and densify in the regions with rich texture. Figure 3 illustrates the development of the embeddings.", + "bbox": [ + 498, + 306, + 893, + 382 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Differentiable rendering of Gaussian Splatting. With the position, rotation, and scaling of the Gaussians updated by the mesh deformation at frame $t$ , we perform differentiable Gaussian rendering [23] to the observed camera view(s). The Gaussian in space is defined by its mean $\\mu$ and a 3D covariance matrix $\\Sigma$ .", + "bbox": [ + 498, + 383, + 892, + 473 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nG _ {i, t} (x) = e ^ {- \\frac {1}{2} (x) ^ {T} \\Sigma_ {i, t} ^ {- 1} (x)} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 483, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma_ {i, t} = R _ {i, t} S _ {i, t} S _ {i, t} ^ {T} R _ {i, t} ^ {T} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 518, + 890, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $R_{i,t}$ is the rotation matrix constructed from $q_{i,t}$ , and $S_{i,t}$ the scaling matrix from $s_{i,t}$ . Given the world-to-camera view matrix $W$ and the Jacobian $J$ of the point projection matrix. The influence of the Gaussian is splatted to 2D [54]:", + "bbox": [ + 498, + 544, + 890, + 604 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Sigma^ {\\prime} = J W \\Sigma W ^ {T} J ^ {T} \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 616, + 890, + 633 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The image formation of Gaussian Splatting is akin to NeRF, where the same volume rendering formula is applied to the blending from near to far. The color $C$ of a pixel rendered by $N$ Gaussians is given by a series of $\\alpha$ -blending:", + "bbox": [ + 498, + 646, + 893, + 708 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC = \\sum_ {i = 1} ^ {N} c _ {i} \\alpha_ {i} \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 604, + 719, + 890, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\alpha_{i}$ evaluated from the 2D covariance, and an opacity in logit $o_{i}$ with $\\mathrm{sigm}()$ being the standard sigmoid function:", + "bbox": [ + 498, + 773, + 890, + 804 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\alpha_ {i} (P) = \\operatorname {s i g m} \\left(o _ {i}\\right) \\exp \\left(- \\frac {1}{2} \\left(P - \\mu_ {i}\\right) \\left(\\Sigma_ {i}\\right) ^ {- 1} \\left(P - \\mu_ {i}\\right)\\right) \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 815, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The Equation 11 is implemented in CUDA with a for loop for each pixel, while in our Unity implementation, each Gaussian is drawn by a front-parallel Quad primitive based", + "bbox": [ + 498, + 854, + 892, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "1609", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on the projection and 2D covariance. We resort to the standard rasterization pipeline of the rendering engine to enable $\\alpha$ -blending with these semi-transparent Gaussians.", + "bbox": [ + 75, + 90, + 470, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Due to limited viewing angle and pose variations from monocular video, we propose a scaling regularization term to prevent Gaussians from growing long and thin. A random background color is generated every iteration to mix with the rendered image $I$ and ground truth image $I_{gt}$ , providing important cues for the silhouette. The loss is the sum of $\\mathcal{L}_1$ , $\\mathcal{L}_{mse}$ , a perceptual loss [49], and a scaling regularization.", + "bbox": [ + 75, + 137, + 472, + 243 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {1} + \\lambda_ {l _ {m s e}} \\mathcal {L} _ {m s e} + \\lambda_ {l} \\mathcal {L} _ {l p i p s} + \\lambda_ {s} \\mathcal {L} _ {\\text {s c a l i n g}} \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 270, + 470, + 287 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {s c a l i n g}} (i) = \\left\\{ \\begin{array}{c c} | \\hat {s} _ {i} |, & \\hat {s} _ {i} > \\max \\left(T _ {s}, T _ {r} \\check {s} _ {i}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 310, + 470, + 344 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With $s_i \\in \\mathbb{R}^3$ being the scaling of a Gaussian, $\\hat{s}_i$ and $\\check{s}_i$ are the maximum and minimum scaling values respectively. The scaling regularization is posed on $\\hat{s}_i$ when it is both long (larger than $T_s$ ) and thin (larger than $T_r$ times $\\check{s}_i$ ). Please see Section 4.3 for an ablation study on the regularization term. Walking on a triangle mesh. The notion Lifted Optimization arises in the model-point registration for hand tracking [38, 40, 41] in contrast to Iterative Closest Point (ICP), where the solve for model pose and correspondences are lifted to be simultaneous. We extend this notion to our avatar training, where the properties of the Gaussians and the trainable embeddings are optimized simultaneously. The barycentric coordinate of a point $P$ is $(k, u, v)$ defined within triangle $k$ . When the learned update $Q = (k, u, v) + (\\delta u, \\delta v)$ is outside triangle $k$ , we find the intersection $P'$ on the shared edge of the adjacent triangle $k'$ and re-express the remaining update in $k'$ as $Q' = P' + (\\delta u', \\delta v')$ . Because the barycentric coordinates are agnostic to the triangle shape, without loss of generality, the re-expression is conducted by conceptually treating two adjacent triangles as right triangles with the intersection on the hypotenuse. The update is iteratively re-expressed until it ends inside the final triangle. We show the re-expression process in Figure 4. The detailed steps are presented in Algorithm 1. Noted that we omit the conceptual re-ordering of the vertices.", + "bbox": [ + 75, + 354, + 472, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Optimization. We use Adam to optimize the Gaussian parameters and the embedding parameters. The original learning rate attenuation on position [23] is instead applied to the embedding parameters. We record the current barycentric $(u,v)$ and optimize for $(\\delta u,\\delta v,d)$ . The triangle walking in Algorithm 1 is implemented as a pybind11 module in C++. When an embedding is being transferred to another triangle, we reset its corresponding optimizer state of the $(\\delta u,\\delta v,d)$ .", + "bbox": [ + 75, + 734, + 470, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The densification process [23] plays an important role in allocating more Gaussians to where in need. In the clone and prune process, the embedding parameters are copied", + "bbox": [ + 75, + 854, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/7795c9900a40067eb63d56c9c20284a77c9f1e1994851ed8f68a284970605864.jpg", + "image_caption": [ + "a) Barycentric update starting from P", + "Figure 4. Walking on triangles for embedding update. a) The recursion process of walking on a triangle mesh. b) The update $P + \\delta$ starting from triangle $CAB$ is re-expressed as $P' + \\delta'$ in triangle $DBA$ , and c) re-expressed again in $EDA$ . The re-expression between two triangles is conducted by conceptually treating them as two right triangles adjacent to each other on the hypotenuse." + ], + "image_footnote": [], + "bbox": [ + 511, + 90, + 632, + 178 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/167ac849a7c105b07d26e8ffcb28ac4d1f0c39f86538172d1a24963b0fee2283.jpg", + "image_caption": [ + "b) Triangle walking $CAB \\rightarrow DBA$" + ], + "image_footnote": [], + "bbox": [ + 650, + 99, + 754, + 174 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/199c34ee6a90979ad7477756bb3d63be67fcf3d9e0c1d064e752592d95b19cd1.jpg", + "image_caption": [ + "c) Triangle walking $BAD \\to EDA$" + ], + "image_footnote": [], + "bbox": [ + 774, + 99, + 872, + 174 + ], + "page_idx": 4 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 Walking on triangles" + ], + "code_body": "Input: $k, u, v, \\delta u, \\delta v$ \nOutput: $\\hat{k}, \\hat{u}, \\hat{v}$ \nfunction WALKONTRIANGLES $(k, u, v, \\delta u, \\delta v)$ $P \\leftarrow (u, v)$ $Q \\leftarrow (u + \\delta u, v + \\delta v)$ \nif Q is inside triangle then \nReturn $(k, Q.u, Q.v)$ \nend if \nIntersect $P-Q$ with hypotenuse* on $(u', v')$ $\\triangleright$ *reorder vertices if needed \n $\\delta u' \\leftarrow \\delta u - (u' - u)$ $\\delta v' \\leftarrow \\delta v - (v' - v)$ \nReturn ReExpress $(k, u', v', \\delta u', \\delta v')$ \nend function \nfunction REEXPRESS $(k, u', v', \\delta u', \\delta v')$ $\\hat{k} \\leftarrow$ adjacent of $k$ $\\hat{u} \\leftarrow 1 - u'$ , $\\hat{v} \\leftarrow 1 - v'$ $\\delta \\hat{u} \\leftarrow -\\delta u'$ , $\\delta \\hat{v} \\leftarrow -\\delta v'$ \nReturn WalkOnTriangles $(\\hat{k}, \\hat{u}, \\hat{v}, \\delta \\hat{u}, \\delta \\hat{v})$ \nend function \n $(\\hat{k}, \\hat{u}, \\hat{v}) \\leftarrow$ WalkOnTriangles $(k, u, v, \\delta u, \\delta v)$", + "bbox": [ + 500, + 330, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "or deleted in the same way as Gaussian parameters. In the split process, when a new position $\\hat{\\mu}$ is sampled from the Gaussian, we solve a mini problem with triangle walking to find the new embedding:", + "bbox": [ + 496, + 683, + 890, + 744 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {E} = \\underset {k, u, v, d} {\\arg \\min } \\| \\mathcal {V} (k, u, v) + d * \\mathcal {N} (k, u, v) - \\hat {\\mu} \\| _ {2} ^ {2} \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 755, + 890, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unity implementation for mobile device. With maximum compatibility in mind, we made SplattingAvatar solely rely on the warped mesh. Before exporting to Unity, we uploaded the canonical mesh in .obj format to Mixamo [1] for autorigging. In total, we exported one .ply file of the Gaussians, one .json file describing the embedding, and one .fbx file from Mixamo to Unity. Note that the .fbx file can be rigged", + "bbox": [ + 496, + 794, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "1610", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/a72704280f49ada581aa1f28b6e9038a965c5cefe0db5ca8ddf8e105dcb57c1c.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison on head avatars. SplattingAvatar produces photorealistic rendering for avatars with high-quality details especially in the eye and hair regions. Even the light reflection on the glasses is well reconstructed. Both PointAvatar [51] and NHA [16] can reconstruct good geometries but the rendering quality is limited by their underlying representations, i.e., points and texture atlas respectively. Compared to INSTA [53], our trainable embedding scheme produces better quality for off-surface geometries, especially for the glasses. The green arrows highlight where our results have better consistency with Ground Truth, while the red arrows point to where other methods show significant artifacts or noise. Please see the supplemental materials for illustrations of the error map." + ], + "image_footnote": [], + "bbox": [ + 86, + 87, + 885, + 468 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "by any other software for customized needs, as long as the triangle order is maintained.", + "bbox": [ + 75, + 585, + 468, + 616 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We implemented the Gaussian renderer in Unity's compute shaders, starting from sorting all Gaussians by the z-axis in camera coordinates from near to far. Based on the calculated 2D covariance $\\Sigma'$ , one front-parallel quad primitive is drawn for every visible Gaussian centered at its position. This one-primitive-one-Gaussian strategy is important for the game engine to properly handle the occlusion of other regular objects. For every pixel to draw in the fragment Shader, our implementation emits color with alpha pre-multiplication and sets the blend function to (ONE, ONE_MINUS_SRC_alpha). Our Unity program achieves a high performance of over 300 FPS on a modern GPU while maintaining a steady 30 FPS on an iPhone 13.", + "bbox": [ + 75, + 617, + 472, + 815 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 829, + 209, + 847 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To demonstrate the effectiveness of SplittingAvatar, we compared it with state-of-the-art (SoTA) methods in two different types of datasets for head and full-body avatars.", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/e3d7d10c221fc54f14b280ba419ee156a98350a66186e7cb4784b0ecacd5b2c3.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodPSNR↑SSIM↑LPIPS↓
NHA [16]20.290.8830.145
INSTA [53]26.420.9240.080
PointAvatar [51]27.840.9130.067
Ours+FLAME28.190.9310.063
Ours+NHA28.860.9310.060
", + "bbox": [ + 527, + 583, + 864, + 698 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparison on head avatars. Both variations of our method outperform existing methods in terms of average photometric errors. With detailed meshes from NHA [16], Ours+NHA performs the best based on the metrics. However, we observe better visual quality with Ours+FLAME in the inner regions of the rendered image.", + "bbox": [ + 496, + 708, + 895, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 500, + 815, + 602, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Monocular video for head avatar. Taking a single monocular video to construct a head avatar for the given subject, our method takes as input images, masks, camera parameters, and tracked FLAME meshes, denoting Ours+FLAME. We", + "bbox": [ + 496, + 839, + 895, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "1611", + "bbox": [ + 483, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/90f59808529981c35eb299632ae45cea4ba5008d047a39777258f583fc630f0b.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison on PeopleSnapshot [2]. We show the results on PeopleSnapshot (columns 2-4) and novel pose animation (columns 5-6). SplittingAvatar produces photorealistic rendering for full-body avatars, especially in the facial area, and captures thin structures like the accessory on the wrist." + ], + "image_footnote": [], + "bbox": [ + 84, + 87, + 883, + 388 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/d1bdbbaa6cc2375b1a6a4761d96fdc2e3c4ca2619d0a13e73d7a47291c01e041.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
male-3-casualmale-4-casualfemale-3-casualfemale-4-casual
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
Anim-NeRF [7]29.370.9700.01728.370.9600.02728.910.9740.02228.900.9680.017
InstantAvatar [21]30.910.9770.02229.770.9800.02529.730.9750.02530.920.9770.021
Ours33.010.9820.02030.990.9820.02930.810.9780.02832.570.9810.018
", + "bbox": [ + 78, + 455, + 890, + 541 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparison on PeopleSnapshot. Compared to two SoTA methods, we achieve significant improvements in pixel-wise quality with PSNR and SSIM. All three methods achieve good perceptual quality in terms of LPIPS where the metrics are close.", + "bbox": [ + 75, + 549, + 892, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "evaluated our approach with several SoTA methods on a combined dataset from NHA [16], NerFace [15], INSTA [53] and PointAvatar [51], including 10 subjects covering different videos captured with DSLR, smartphones and from the Internet. The pre-processing pipeline of IMavatar [50] and INSTA [53] was altered to apply DECA [12] for face tracking, RVM [37] for segmentation, and BisenetV2 [46] for face parsing. For each video, the last 350 frames were used as testing samples. Because our method can directly be animated by the given mesh, we further unleashed its potential by training and testing on the generated meshes from NHA [16] which have more geometry details. This variation is referred to as Ours+NHA.", + "bbox": [ + 75, + 599, + 473, + 797 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PeopleSnapshot. We conducted a quantitative evaluation of the rendering quality of full-body avatars on the PeopleSnapshot [2] dataset. Following the protocol of InstantAvatar [21], we used SMPL meshes refined by Anim-NeRF [7]. Our method demonstrates the generalizability to novel poses through qualitative analysis in Section 4.2.", + "bbox": [ + 75, + 809, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparison with SoTA", + "text_level": 1, + "bbox": [ + 500, + 599, + 718, + 616 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Head avatar. To evaluate the rendering quality of the learned avatars, we animated SplattingAvatar with the registered meshes of testing images. For Ours+NHA, we trained NHA [16] on the training set and extracted the final meshes for both the training and testing images, which were further used for the training and testing of our method respectively.", + "bbox": [ + 496, + 625, + 893, + 715 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conducted a comparative analysis of SplittingAvatar against INSTA [53], PointAvatar [51], and NHA [16]. As depicted in Figure 5, our method achieves superior quality in terms of improved details in the eye and hair regions, and even being able to capture the light reflection on the glasses. For Ours+FLAME, though the off-surface geometries like hair and glasses are not fully represented by meshes, our method can handle the rendering decently because the embeddings are optimized to find correct motions from nearby triangles. Please see Table 1 for quantitative evaluations.", + "bbox": [ + 496, + 717, + 895, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Full-body avatar. We made a comparison to InstantAvatar [21] and Anim-NeRF [7] on PeopleSnapshot. For In", + "bbox": [ + 498, + 869, + 895, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "1612", + "bbox": [ + 483, + 944, + 514, + 957 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "stantAvatar [21], a complete training was performed for 200 epochs as suggested in the most recent version of the author's code. Image quality metrics in Table 2 demonstrate the effectiveness of our method in terms of the lowest pixelwise errors. We qualitatively show the comparison of rendering quality of testing images in Figure 6, together with the demonstration of generalizability to novel poses. Our representation is friendly to thin structures like the accessory on the wrist. Our approach produced better quality overall and especially in the facial area compared to InstantAvatar [21], but slightly more artifacts under the shoulder due to very limited pose variations in the training set. We believe this can be much improved with more training poses.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 297, + 230, + 313 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Trainable embedding. The key component of our method is the trainable embedding on the mesh. We conducted an ablation experiment by replacing it with fixed embedding on mesh and a trainable local shift $\\Delta x \\in \\mathbb{R}^3$ per Gaussian. Without trainable embedding, the Gaussians encountered difficulties in following the mesh correctly. The right column of Figure 7 shows the irregular rendering artifacts without trainable embedding.", + "bbox": [ + 75, + 320, + 468, + 440 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Regularization. In the optimization process of Gaussian Splatting, some Gaussians turn to become long and thin, generating artifacts when rendered into novel poses. We show the results without the scaling regularization in the middle column of Figure 7.", + "bbox": [ + 75, + 441, + 468, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "underlying mesh. In the comparison between Ours+FLAME and Ours+NHA, we observe that the driving mesh should focus on the motion instead of fully reconstructing the exact geometry. In Figure 8 we show that when the mesh with vertex offsets from NHA [16] is applied, the detailed surface deformation improves the generalizability of SplattingAvatar to large poses. However, in the second and third row of Figure 5, the mesh from FLAME that captures the correct motion of the glasses rather than the shape is driving the best rendering quality of SplattingAvatar. To perform textured mesh rendering, the mesh of NHA [16] is seamed in the mouth region and deformed to fit the shape of the glasses, yet both being unhelpful to the quality of Ours+NHA.", + "bbox": [ + 500, + 90, + 893, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations and future work. As discussed above, our method depends on the motion representation ability of the driving mesh. With current FLAME and SMPL models, we do not have separate motion representations for clothes and hair. We believe SplattingAvatar can support future works on human avatars with disentangled mesh representations, e.g., separate meshes for clothes and hair stands.", + "bbox": [ + 498, + 287, + 893, + 393 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ca0fca2348664c809ad0cd94ca7368986bfc766babea73539e74194ac456d840.jpg", + "image_caption": [ + "Figure 8. Comparison between Ours+FLAME and Ours+NHA. The better aligned mesh from NHA [16] improves the generalizability of SplattingAvatar to large pose variations." + ], + "image_footnote": [], + "bbox": [ + 506, + 402, + 888, + 513 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/d33b11b4690962ff013b31561a635dc1d66a23dedbb5cdbbfd3e1c0826e9a884.jpg", + "image_caption": [ + "Figure 7. Ablation study. Without the scaling regularization term, Gaussians that are long and thin cause needle-like artifacts. Without trainable embedding, Gaussians do not follow the movement of the mesh tightly, leading to irregular rendering results. The application of our trainable embedding and the scaling term successfully removes most of the artifacts when rendered into novel poses." + ], + "image_footnote": [], + "bbox": [ + 81, + 529, + 464, + 708 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Discussion", + "text_level": 1, + "bbox": [ + 76, + 830, + 194, + 845 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Discussion on driving mesh. Considering efficiency, compatibility, and portability, SplattingAvatar is designed to tightly rely on the motion and surface deformation of the", + "bbox": [ + 75, + 854, + 472, + 900 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 595, + 617, + 611 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have proposed a hybrid representation for human avatar modeling featuring Gaussian Splatting with trainable embeddings on a mesh. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians and their embeddings. Our method leverages the advantages of the explicit motion representation with a mesh and implicit rendering capability of Gaussian Splatting. Compared with SoTA methods, our approach achieves the best rendering quality for both head and full-body avatars reconstructed from monocular videos and runs at real-time frame rates on a mobile device. Our method lays a foundation for future work in Gaussian Splatting manipulation with mesh-based motion control.", + "bbox": [ + 498, + 621, + 893, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments", + "text_level": 1, + "bbox": [ + 500, + 830, + 658, + 847 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was partially supported by Guangzhou-HKUST(GZ) Joint Funding #2023A03J0670 and Guangzhou Basic Research Scheme #2024A04J4229.", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "1613", + "bbox": [ + 483, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Mixamo. https://www MIXamo.com/. 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Association for Computing Machinery. 4" + ], + "bbox": [ + 78, + 90, + 470, + 415 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "1616", + "bbox": [ + 483, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/SplattingAvatar_ Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting/2a923612-0df2-4faf-a040-0816baf81069_model.json b/2024/SplattingAvatar_ Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting/2a923612-0df2-4faf-a040-0816baf81069_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8872736938af9a1f6fb6373212233988e54e043b --- /dev/null +++ b/2024/SplattingAvatar_ Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting/2a923612-0df2-4faf-a040-0816baf81069_model.json @@ -0,0 +1,2180 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.216, + 0.131, + 0.757, + 0.177 + ], + "angle": 0, + "content": "SplattingAvatar: Realistic Real-Time Human Avatars with Mesh-Embedded Gaussian Splatting" + }, + { + "type": "text", + "bbox": [ + 0.184, + 0.202, + 0.782, + 0.294 + ], + "angle": 0, + "content": "Zhijing Shao\\(^{1,2}\\) \nXiangu Lin\\(^{2}\\) \nZhaolong Wang\\(^{2}\\) \nZhuang Li\\(^{2}\\) \nDuotun Wang\\(^{1}\\) \nXiangru Lin\\(^{2}\\) \nYu Zhang\\(^{2}\\) \nMingming Fan\\(^{1,3}\\) \nZeyu Wang\\(^{1,3}\\) \n\\(^{1}\\)The Hong Kong University of Science and Technology (Guangzhou) \n\\(^{2}\\)Prometheus Vision Technology Co., Ltd. \n\\(^{3}\\)The Hong Kong University of Science and Technology" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.325, + 0.482, + 0.519 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.482, + 0.327, + 0.882, + 0.518 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.527, + 0.897, + 0.584 + ], + "angle": 0, + "content": "Figure 1. Overview of SplattingAvatar featuring Mesh-Embedded Gaussian Splatting. Our method takes (a) monocular videos as input, while employing (b) a trainable embedding technique for Gaussian-Mesh association. (c) Animated by mesh through the learned embedding, the Gaussians render into high-fidelity human avatars. (d) SplattingAvatar demonstrates real-time rendering capabilities in Unity, achieving over 300 FPS on an NVIDIA RTX 3090 GPU and 30 FPS on an iPhone 13 (images captured in action)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.596, + 0.314, + 0.612 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.474, + 0.903 + ], + "angle": 0, + "content": "We present SplattingAvatar, a hybrid 3D representation of photorealistic human avatars with Gaussian Splatting embedded on a triangle mesh, which renders over 300 FPS on a modern GPU and 30 FPS on a mobile device. We disentangle the motion and appearance of a virtual human with explicit mesh geometry and implicit appearance modeling with Gaussian Splatting. The Gaussians are defined by barycentric coordinates and displacement on a triangle mesh as Phong surfaces. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians while walking on the triangle mesh. SplattingAvatar is a hybrid representation of virtual humans where the mesh represents low-frequency motion and surface deformation, while the Gaussians take over the high-frequency geometry and detailed appearance. Unlike existing deformation methods that rely on an MLP-based linear blend skinning (LBS) field for motion, we control the rotation and translation of the Gaussians directly by mesh, which empowers its compatibility with various animation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.598, + 0.896, + 0.689 + ], + "angle": 0, + "content": "techniques, e.g., skeletal animation, blend shapes, and mesh editing. Trainable from monocular videos for both full-body and head avatars, SplattingAvatar shows state-of-the-art rendering quality across multiple datasets. Code and data are available at https://github.com/initialneil/SplattingAvatar." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.723, + 0.633, + 0.739 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.897, + 0.903 + ], + "angle": 0, + "content": "The demand for personalized, photorealistic, and animatable human avatars that render in real-time spans a wide array of applications, including gaming [48], extended reality (XR) storytelling [10, 19], and tele-presentation [22, 24]. As the quest for digital realism intensifies, practitioners face a growing challenge: improving the quality of 3D human models often means increasing the complexity of these models. This is typically achieved by adding more polygons, layering skin textures [5], and integrating advanced hair systems [42]. However, these enhancements invariably lead to" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1606" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.122 + ], + "angle": 0, + "content": "higher computational demands, creating obstacles in achieving efficiency and portability in avatar rendering." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.124, + 0.472, + 0.29 + ], + "angle": 0, + "content": "In our approach, we categorize the representation of mesh-based virtual humans into three distinct levels of detail. The first two levels encompass body motion and surface deformation, both of which are effectively captured by a mesh [11, 16, 39]. The third level, however, focuses on geometric details that are crucial for enhancing realism but challenging to represent with traditional meshes. This level is not only computationally demanding to render [31] but also faces limitations due to the rigid connectivity of mesh vertices, which hinders the adaptability to topological changes and complex or thin structures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.472, + 0.549 + ], + "angle": 0, + "content": "Recent advances in the field have seen a shift towards using Neural Radiance Fields (NeRF) [32], especially for capturing high-frequency details in 3D avatar modeling [3, 18, 21, 26, 27, 34, 35, 53]. A typical process involves constructing NeRF in a canonical space and then performing volume rendering in the posed space. This is done by tracing ray samples backward from their posed positions to their canonical origins [21, 34, 35, 53]. However, this reverse mapping process introduces ambiguities, as a single point in the posed space might correspond to multiple points in the canonical space [8, 9], leading to challenges in accurately rendering details. Additionally, the prevalent use of multilayer perceptron (MLPs) for motion control [21, 39, 51] tends to overlook the advantages of mesh-based representations for capturing surface deformations, an aspect crucial for realistic avatar movement as highlighted in studies like DECA [12], CAPE [30], and TalkSHOW [45]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.551, + 0.472, + 0.839 + ], + "angle": 0, + "content": "To address the challenges posed by the limitations of NeRF and MLP-based motion control in capturing high-frequency details and realistic surface deformations, we introduce a novel solution. Inspired by the recently proposed Gaussian Splatting technique [23], we propose explicit motion control of the Gaussians with trainable embeddings on a mesh. The embedding is described by \\((k,u,v,d)\\) on the mesh as Phong surface [38], where \\((u,v)\\) represents the local barycentric coordinates of the embedding triangle \\(k\\), and \\(d\\) is the displacement along the interpolated normal vector. The pose-dependent rotation and scaling adjust dynamically in response to the mesh warping, while the pose-invariant properties, i.e., canonical rotation and scaling, color, and opacity, remain stable and consistent across various poses. Because the embedding point defined in barycentric coordinates is differentiable only inside the corresponding triangle, cross-triangle updates must be handled properly [40, 41]. During training, we conduct lifted optimization [38] with the embedding points walking on the triangle mesh." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Our hybrid representation, Gaussians embedded on a mesh, can be trained from a monocular video and efficiently port to Unity that runs in real time (Figure 1) by bringing together three key advantages. First, the use of the mesh" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.287 + ], + "angle": 0, + "content": "for representing body motion and surface deformation not only proves efficient but also allows for high editability. This flexibility is crucial for adapting the avatar to various scenarios and movements. Second, the application of Gaussian Splatting enriches this model by providing a robust means to capture high-frequency geometry and appearance details. This is vital for achieving a level of realism that conventional meshes alone cannot offer. Third, the embedding technique empowers the Gaussians to be explicitly controlled by the mesh movements. This integration results in an efficient, clear, and non-ambiguous method for motion control, significantly reducing the computational load compared to MLP-based methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.289, + 0.895, + 0.44 + ], + "angle": 0, + "content": "Furthermore, our approach is distinct from existing hybrid models such as AvatarReX [52] and DELTA [14], which typically segment avatars into body parts like hair, hands, clothes, and face. Instead, our method achieves a disentanglement of motion and appearance. In the SplattingAvatar framework, although different parts may have specific motion control, the rendering is uniformly conducted through Gaussian Splatting. This uniformity achieved by our method ensures a cohesive and harmonious appearance across all parts of the avatar." + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.447, + 0.833, + 0.461 + ], + "angle": 0, + "content": "We summarize our main contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.469, + 0.892, + 0.514 + ], + "angle": 0, + "content": "- We introduce a framework that integrates Gaussian Splating with meshes, offering a new avatar representation that achieves realism and computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.521, + 0.892, + 0.566 + ], + "angle": 0, + "content": "- Our approach applies lifted optimization to avatar modeling, allowing for joint optimization of Gaussian parameters and mesh embeddings for accurate reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.506, + 0.572, + 0.892, + 0.617 + ], + "angle": 0, + "content": "- We demonstrate the capability of real-time rendering and adaptability to creating diverse avatars through comprehensive evaluation and a Unity implementation." + }, + { + "type": "list", + "bbox": [ + 0.506, + 0.469, + 0.892, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.633, + 0.642, + 0.649 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Mesh-based avatar. The rise of free-viewpoint video in sequences of textured meshes has shown the expressiveness of detailed texture atlas along with as few as 10k triangles [11]. Many efforts [18, 20] have been put into extending this line of work to build controllable avatars. With the help of human shape models with strong prior [6, 25, 28, 33] that unwrap to a unified UV space, texture atlas can be obtained by 2D image generation supervised through differentiable rendering [31, 43]. Such prior models provide consistency across large motions and can be recovered from monocular videos or even a single image. To cope with the shape details of identities and clothes, CAPE [30] predicts displacements on the vertices with pose-conditioned VAE. Due to the limitation of the base model to topological changes, some treat the textured mesh as input conditions [31, 36] for image rendering, while others resort to implicit representations of" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1607" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.092, + 0.087, + 0.895, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.301, + 0.897, + 0.373 + ], + "angle": 0, + "content": "Figure 2. The pipeline of our method. SplittingAvatar learns 3D Gaussians with trainable embedding on the canonical mesh. The motion and deformation of the mesh explicitly bring the Gaussians to the posed space for differentiable rasterization. Both the Gaussians and embedding parameters are optimized during training. The position \\(\\mu\\) is the barycentric point \\(P\\) plus a displacement \\(d\\) along the interpolated normal vector \\(\\mathbf{n}\\). Pose-dependent quaternion and scaling \\((\\delta q, \\delta s)\\) and pose-invariant quaternion, scaling, opacity, and color \\((\\overline{q}, \\overline{s}, o, c)\\) together define the properties of the Gaussians." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.397, + 0.465, + 0.413 + ], + "angle": 0, + "content": "the mesh [8, 9, 20, 39], color [16, 20, 39], or materials [4]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.414, + 0.471, + 0.61 + ], + "angle": 0, + "content": "Implicit neural avatar. To achieve convincing rendering beyond the limitation of triangle mesh, especially on the hair, glasses, and clothes, some recent works [3, 16, 21, 26, 34, 35, 44, 47, 53] focus on constructing NeRF in the canonical space (usually T-pose of SMPL [28] or neutral expression of FLAME [25]) and conduct volume rendering at the posed space. The required backward tracing from pose to canonical is non-trivial and raises an ambiguity issue. Existing works propose to adopt pose conditioned inverse LBS field [17, 34] or to optimize a root-finding loop with multiple initialization [8, 9, 21]. The increased computational load upon volume rendering prohibits the potential real-time applications." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.472, + 0.749 + ], + "angle": 0, + "content": "PointAvatar [51], with explicit point primitives, takes advantage of forward rasterization that only requires nonambiguous forward deformation from canonical to pose, producing photo-realistic appearance and detailed challenging geometries such as hair and glasses. In transforming to Gaussian Splatting, we further increase the efficiency and compatibility with our mesh embedding mechanism instead of the LBS-based deformation field and achieve two magnitude faster rendering speed with on-par quality." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Hybrid avatar representation. First attempts have been proposed to disentangle human avatar modeling into separate parts with varying properties. AvatarRex [52] learns disentangled models for face, body, and hands. SCARF [13] and DELTA [14] propose hybrid modeling with textured mesh for body, and NeRF for hair and clothing. In contrast, our method handles the disentanglement in terms of motion and appearance to explicit mesh geometry and implicit Gaussian Splatting rendering. Different from existing works [3, 20] that attach features to fixed locations on mesh like mesh" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.397, + 0.895, + 0.444 + ], + "angle": 0, + "content": "vertices, our trainable embedding enables the Gaussians to optimize their locations on mesh and distribute unevenly according to the texture complexity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.461, + 0.593, + 0.477 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.488, + 0.895, + 0.608 + ], + "angle": 0, + "content": "Overview. Given a sequence of monocular images, each with a registered mesh template, i.e., the deformed mesh of SMPL [28] or FLAME [25], we train a hybrid representation of human avatar as 3D Gaussians [23] embedded on the canonical mesh. The Gaussians, parameterized by position, rotation, scale, color, and opacity, are semi-transparent 3D particles that render into camera views through splattering-based rasterization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.896, + 0.777 + ], + "angle": 0, + "content": "Each 3D Gaussian is embedded on one triangle of the canonical mesh in its local \\((u, v, d)\\) coordinates. The embedding directly defines the position of the Gaussians in both canonical and posed space. Other than position, each Gaussian has its own parameters of rotation, scaling, color, and opacity. With the mesh deformed by animation, the embedding also provides additional rotation and scaling upon each Gaussian. The additional pose-dependent rotation is defined by barycentric interpolated per-vertex quaternion while the additional scaling is defined by the area change of the embedded triangle." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.779, + 0.895, + 0.884 + ], + "angle": 0, + "content": "During optimization, the Gaussian parameters and the embedding parameters are updated simultaneously. When the update of \\((u,v)\\) moves the embedding across the triangle boundary, the barycentric update is re-expressed in the neighboring triangle as if the Gaussian is walking on the mesh. To support embedding, we adapt the clone and split scheme of 3D Gaussians [23] to better suit our needs." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.893, + 0.902 + ], + "angle": 0, + "content": "Embedding on mesh. Inspired by the Phong shading in" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1608" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.169 + ], + "angle": 0, + "content": "computer graphics, Phong surface [38] defines the position and normal of a point inside a triangle. For the point \\(P\\) on triangle \\(k\\) with barycentric coordinate \\((u,v)\\), its position and normal is a linear interpolation of the triangle's vertices \\(\\{V_1,V_2,V_3\\}\\) and per-vertex normals \\(\\{\\pmb{n}_1,\\pmb{n}_2,\\pmb{n}_3\\}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.178, + 0.47, + 0.194 + ], + "angle": 0, + "content": "\\[\nP = \\mathcal {V} (k, u, v) = u * V _ {1} + v * V _ {2} + (1 - u - v) * V _ {3} \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.204, + 0.47, + 0.22 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {n} = \\mathcal {N} (k, u, v) = u * \\boldsymbol {n} _ {1} + v * \\boldsymbol {n} _ {2} + (1 - u - v) * \\boldsymbol {n} _ {3} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.231, + 0.47, + 0.26 + ], + "angle": 0, + "content": "where \\(\\mathcal{V}\\) maps triangle index \\(k\\) and barycentric coordinates \\((u,v)\\) to a point on the mesh and \\(\\mathcal{N}\\) the interpolated normal." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.262, + 0.47, + 0.291 + ], + "angle": 0, + "content": "We define the position of a Gaussian, i.e., the mean \\(\\mu\\), by a displacement \\(d\\) along the interpolated normal vector:" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.302, + 0.47, + 0.318 + ], + "angle": 0, + "content": "\\[\n\\mu = P + d * \\boldsymbol {n} \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.328, + 0.47, + 0.357 + ], + "angle": 0, + "content": "Embedding \\( E = \\{k, u, v, d\\} \\) approximates a first-order continuous space around the mesh surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.471, + 0.479 + ], + "angle": 0, + "content": "As proposed by Zielonka et al. [53], for the corresponding triangle in the canonical and posed space at frame \\( t \\) we compute the matrix \\( \\{R_{\\text{cano}}, R_{\\text{pose}}\\} \\) based on the triangle's tangent, bitangent, and normal to track the triangle rotation from canonical to pose, noted that the notation \\( t \\) is skipped. The rotation matrix is then converted to a quaternion, and we calculate the per-vertex quaternion \\( q_V \\) by area-weighted average from surrounding neighbor triangles:" + }, + { + "type": "equation", + "bbox": [ + 0.21, + 0.488, + 0.47, + 0.507 + ], + "angle": 0, + "content": "\\[\nR _ {k} = R _ {\\text {c a n o}} R _ {\\text {p o s e}} ^ {- 1} \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.202, + 0.513, + 0.47, + 0.55 + ], + "angle": 0, + "content": "\\[\nq _ {V} = \\frac {\\sum_ {k \\in \\Omega_ {V}} A _ {k} q _ {k}}{\\sum_ {k \\in \\Omega_ {V}} A _ {k}} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.553, + 0.47, + 0.645 + ], + "angle": 0, + "content": "where \\(\\Omega_V\\) is the neighbor triangles of vertex \\(V\\), \\(A_k\\) and \\(q_k\\) are the triangle's area and quaternion respectively. For an embedding \\(E_i\\) with quaternions \\(\\{q_1, q_2, q_3\\}\\) calculated on the corresponding triangle vertices at frame \\(t\\), the barycentric interpolated rotation \\(\\delta q_{i,t}\\) is multiplied to the canonical rotation \\(\\overline{q}_i\\) of the Gaussian in the canonical space:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.655, + 0.47, + 0.671 + ], + "angle": 0, + "content": "\\[\n\\delta q _ {i, t} = u * q _ {1} + v * q _ {2} + (1 - u - v) * q _ {3} \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.684, + 0.47, + 0.7 + ], + "angle": 0, + "content": "\\[\nq _ {i, t} = \\delta q _ {i, t} * \\bar {q} _ {i} \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.796 + ], + "angle": 0, + "content": "The same applies to scaling where the area change of the embedded triangle is used to represent the scaling caused by deformation: \\( s_{i,t} = (A_{\\text{pose}} / A_{\\text{cano}}) \\overline{s}_i \\). While the original implementation of Gaussian Splatting [23] represents color in view-dependent spherical harmonics, we choose to turn it off for simplicity [29]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We perform initialization by randomly selecting \\(10\\mathrm{k}\\) pairs of triangle indices and barycentric coordinates on the canonical mesh. We set the barycentric coordinates to be the current \\((u,v)\\) of embeddings and initialize all the \\(d\\) to be zero. With the position of the Gaussians calculated from the embeddings, we initialize other properties of the Gaussians according to their original definitions [23]. Initially, the Gaussians" + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.09, + 0.617, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.647, + 0.09, + 0.748, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.774, + 0.091, + 0.875, + 0.173 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.184, + 0.894, + 0.28 + ], + "angle": 0, + "content": "Figure 3. The development of Gaussian embeddings on mesh. Each line segment indicates the position of one Gaussian displaced from its embedding point on mesh. Gaussians for off-surface geometries like the hair have positive displacements while others turn to have negative displacements because when the mesh surface is correctly aligned to the geometry like in the facial area, the means for the Gaussians will be inside the mesh." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.308, + 0.894, + 0.383 + ], + "angle": 0, + "content": "are positioned on the surface of the mesh. With the training proceeds with more poses, the embeddings generally bring the Gaussians to approximate the actual geometry and densify in the regions with rich texture. Figure 3 illustrates the development of the embeddings." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.384, + 0.893, + 0.474 + ], + "angle": 0, + "content": "Differentiable rendering of Gaussian Splatting. With the position, rotation, and scaling of the Gaussians updated by the mesh deformation at frame \\( t \\), we perform differentiable Gaussian rendering [23] to the observed camera view(s). The Gaussian in space is defined by its mean \\( \\mu \\) and a 3D covariance matrix \\( \\Sigma \\)." + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.484, + 0.892, + 0.505 + ], + "angle": 0, + "content": "\\[\nG _ {i, t} (x) = e ^ {- \\frac {1}{2} (x) ^ {T} \\Sigma_ {i, t} ^ {- 1} (x)} \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.519, + 0.892, + 0.538 + ], + "angle": 0, + "content": "\\[\n\\Sigma_ {i, t} = R _ {i, t} S _ {i, t} S _ {i, t} ^ {T} R _ {i, t} ^ {T} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.545, + 0.892, + 0.605 + ], + "angle": 0, + "content": "where \\(R_{i,t}\\) is the rotation matrix constructed from \\(q_{i,t}\\), and \\(S_{i,t}\\) the scaling matrix from \\(s_{i,t}\\). Given the world-to-camera view matrix \\(W\\) and the Jacobian \\(J\\) of the point projection matrix. The influence of the Gaussian is splatted to 2D [54]:" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.617, + 0.892, + 0.634 + ], + "angle": 0, + "content": "\\[\n\\Sigma^ {\\prime} = J W \\Sigma W ^ {T} J ^ {T} \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.647, + 0.894, + 0.709 + ], + "angle": 0, + "content": "The image formation of Gaussian Splatting is akin to NeRF, where the same volume rendering formula is applied to the blending from near to far. The color \\(C\\) of a pixel rendered by \\(N\\) Gaussians is given by a series of \\(\\alpha\\)-blending:" + }, + { + "type": "equation", + "bbox": [ + 0.606, + 0.72, + 0.892, + 0.763 + ], + "angle": 0, + "content": "\\[\nC = \\sum_ {i = 1} ^ {N} c _ {i} \\alpha_ {i} \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.774, + 0.892, + 0.805 + ], + "angle": 0, + "content": "with \\(\\alpha_{i}\\) evaluated from the 2D covariance, and an opacity in logit \\(o_{i}\\) with \\(\\mathrm{sigm}()\\) being the standard sigmoid function:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.816, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\alpha_ {i} (P) = \\operatorname {s i g m} \\left(o _ {i}\\right) \\exp \\left(- \\frac {1}{2} \\left(P - \\mu_ {i}\\right) \\left(\\Sigma_ {i}\\right) ^ {- 1} \\left(P - \\mu_ {i}\\right)\\right) \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.893, + 0.901 + ], + "angle": 0, + "content": "The Equation 11 is implemented in CUDA with a for loop for each pixel, while in our Unity implementation, each Gaussian is drawn by a front-parallel Quad primitive based" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1609" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.137 + ], + "angle": 0, + "content": "on the projection and 2D covariance. We resort to the standard rasterization pipeline of the rendering engine to enable \\(\\alpha\\)-blending with these semi-transparent Gaussians." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.473, + 0.244 + ], + "angle": 0, + "content": "Due to limited viewing angle and pose variations from monocular video, we propose a scaling regularization term to prevent Gaussians from growing long and thin. A random background color is generated every iteration to mix with the rendered image \\(I\\) and ground truth image \\(I_{gt}\\), providing important cues for the silhouette. The loss is the sum of \\(\\mathcal{L}_1\\), \\(\\mathcal{L}_{mse}\\), a perceptual loss [49], and a scaling regularization." + }, + { + "type": "equation", + "bbox": [ + 0.103, + 0.271, + 0.471, + 0.288 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {1} + \\lambda_ {l _ {m s e}} \\mathcal {L} _ {m s e} + \\lambda_ {l} \\mathcal {L} _ {l p i p s} + \\lambda_ {s} \\mathcal {L} _ {\\text {s c a l i n g}} \\tag {13}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.311, + 0.471, + 0.345 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {s c a l i n g}} (i) = \\left\\{ \\begin{array}{c c} | \\hat {s} _ {i} |, & \\hat {s} _ {i} > \\max \\left(T _ {s}, T _ {r} \\check {s} _ {i}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.473, + 0.734 + ], + "angle": 0, + "content": "With \\( s_i \\in \\mathbb{R}^3 \\) being the scaling of a Gaussian, \\( \\hat{s}_i \\) and \\( \\check{s}_i \\) are the maximum and minimum scaling values respectively. The scaling regularization is posed on \\( \\hat{s}_i \\) when it is both long (larger than \\( T_s \\)) and thin (larger than \\( T_r \\) times \\( \\check{s}_i \\)). Please see Section 4.3 for an ablation study on the regularization term. Walking on a triangle mesh. The notion Lifted Optimization arises in the model-point registration for hand tracking [38, 40, 41] in contrast to Iterative Closest Point (ICP), where the solve for model pose and correspondences are lifted to be simultaneous. We extend this notion to our avatar training, where the properties of the Gaussians and the trainable embeddings are optimized simultaneously. The barycentric coordinate of a point \\( P \\) is \\( (k, u, v) \\) defined within triangle \\( k \\). When the learned update \\( Q = (k, u, v) + (\\delta u, \\delta v) \\) is outside triangle \\( k \\), we find the intersection \\( P' \\) on the shared edge of the adjacent triangle \\( k' \\) and re-express the remaining update in \\( k' \\) as \\( Q' = P' + (\\delta u', \\delta v') \\). Because the barycentric coordinates are agnostic to the triangle shape, without loss of generality, the re-expression is conducted by conceptually treating two adjacent triangles as right triangles with the intersection on the hypotenuse. The update is iteratively re-expressed until it ends inside the final triangle. We show the re-expression process in Figure 4. The detailed steps are presented in Algorithm 1. Noted that we omit the conceptual re-ordering of the vertices." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.472, + 0.856 + ], + "angle": 0, + "content": "Optimization. We use Adam to optimize the Gaussian parameters and the embedding parameters. The original learning rate attenuation on position [23] is instead applied to the embedding parameters. We record the current barycentric \\((u,v)\\) and optimize for \\((\\delta u,\\delta v,d)\\). The triangle walking in Algorithm 1 is implemented as a pybind11 module in C++. When an embedding is being transferred to another triangle, we reset its corresponding optimizer state of the \\((\\delta u,\\delta v,d)\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.902 + ], + "angle": 0, + "content": "The densification process [23] plays an important role in allocating more Gaussians to where in need. In the clone and prune process, the embedding parameters are copied" + }, + { + "type": "image", + "bbox": [ + 0.512, + 0.092, + 0.633, + 0.179 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.513, + 0.179, + 0.621, + 0.201 + ], + "angle": 0, + "content": "a) Barycentric update starting from P" + }, + { + "type": "image", + "bbox": [ + 0.651, + 0.1, + 0.756, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.648, + 0.178, + 0.747, + 0.2 + ], + "angle": 0, + "content": "b) Triangle walking \\( CAB \\rightarrow DBA \\)" + }, + { + "type": "image", + "bbox": [ + 0.775, + 0.1, + 0.874, + 0.175 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.771, + 0.178, + 0.871, + 0.2 + ], + "angle": 0, + "content": "c) Triangle walking \\(BAD \\to EDA\\)" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.214, + 0.894, + 0.299 + ], + "angle": 0, + "content": "Figure 4. Walking on triangles for embedding update. a) The recursion process of walking on a triangle mesh. b) The update \\( P + \\delta \\) starting from triangle \\( CAB \\) is re-expressed as \\( P' + \\delta' \\) in triangle \\( DBA \\), and c) re-expressed again in \\( EDA \\). The re-expression between two triangles is conducted by conceptually treating them as two right triangles adjacent to each other on the hypotenuse." + }, + { + "type": "code_caption", + "bbox": [ + 0.501, + 0.315, + 0.729, + 0.331 + ], + "angle": 0, + "content": "Algorithm 1 Walking on triangles" + }, + { + "type": "algorithm", + "bbox": [ + 0.5, + 0.332, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Input: \\(k, u, v, \\delta u, \\delta v\\) \nOutput: \\(\\hat{k}, \\hat{u}, \\hat{v}\\) \nfunction WALKONTRIANGLES\\((k, u, v, \\delta u, \\delta v)\\) \n\\(P \\leftarrow (u, v)\\) \n\\(Q \\leftarrow (u + \\delta u, v + \\delta v)\\) \nif Q is inside triangle then \nReturn \\((k, Q.u, Q.v)\\) \nend if \nIntersect \\(P-Q\\) with hypotenuse* on \\((u', v')\\) \n\\(\\triangleright\\) *reorder vertices if needed \n\\(\\delta u' \\leftarrow \\delta u - (u' - u)\\) \n\\(\\delta v' \\leftarrow \\delta v - (v' - v)\\) \nReturn ReExpress\\((k, u', v', \\delta u', \\delta v')\\) \nend function \nfunction REEXPRESS\\((k, u', v', \\delta u', \\delta v')\\) \n\\(\\hat{k} \\leftarrow\\) adjacent of \\(k\\) \n\\(\\hat{u} \\leftarrow 1 - u'\\), \\(\\hat{v} \\leftarrow 1 - v'\\) \n\\(\\delta \\hat{u} \\leftarrow -\\delta u'\\), \\(\\delta \\hat{v} \\leftarrow -\\delta v'\\) \nReturn WalkOnTriangles\\((\\hat{k}, \\hat{u}, \\hat{v}, \\delta \\hat{u}, \\delta \\hat{v})\\) \nend function \n\\((\\hat{k}, \\hat{u}, \\hat{v}) \\leftarrow\\) WalkOnTriangles\\((k, u, v, \\delta u, \\delta v)\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.892, + 0.745 + ], + "angle": 0, + "content": "or deleted in the same way as Gaussian parameters. In the split process, when a new position \\(\\hat{\\mu}\\) is sampled from the Gaussian, we solve a mini problem with triangle walking to find the new embedding:" + }, + { + "type": "equation", + "bbox": [ + 0.52, + 0.756, + 0.892, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\hat {E} = \\underset {k, u, v, d} {\\arg \\min } \\| \\mathcal {V} (k, u, v) + d * \\mathcal {N} (k, u, v) - \\hat {\\mu} \\| _ {2} ^ {2} \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Unity implementation for mobile device. With maximum compatibility in mind, we made SplattingAvatar solely rely on the warped mesh. Before exporting to Unity, we uploaded the canonical mesh in .obj format to Mixamo [1] for autorigging. In total, we exported one .ply file of the Gaussians, one .json file describing the embedding, and one .fbx file from Mixamo to Unity. Note that the .fbx file can be rigged" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1610" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.088, + 0.887, + 0.469 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.477, + 0.896, + 0.562 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison on head avatars. SplattingAvatar produces photorealistic rendering for avatars with high-quality details especially in the eye and hair regions. Even the light reflection on the glasses is well reconstructed. Both PointAvatar [51] and NHA [16] can reconstruct good geometries but the rendering quality is limited by their underlying representations, i.e., points and texture atlas respectively. Compared to INSTA [53], our trainable embedding scheme produces better quality for off-surface geometries, especially for the glasses. The green arrows highlight where our results have better consistency with Ground Truth, while the red arrows point to where other methods show significant artifacts or noise. Please see the supplemental materials for illustrations of the error map." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.47, + 0.617 + ], + "angle": 0, + "content": "by any other software for customized needs, as long as the triangle order is maintained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.618, + 0.473, + 0.816 + ], + "angle": 0, + "content": "We implemented the Gaussian renderer in Unity's compute shaders, starting from sorting all Gaussians by the z-axis in camera coordinates from near to far. Based on the calculated 2D covariance \\(\\Sigma'\\), one front-parallel quad primitive is drawn for every visible Gaussian centered at its position. This one-primitive-one-Gaussian strategy is important for the game engine to properly handle the occlusion of other regular objects. For every pixel to draw in the fragment Shader, our implementation emits color with alpha pre-multiplication and sets the blend function to (ONE, ONE_MINUS_SRC_alpha). Our Unity program achieves a high performance of over 300 FPS on a modern GPU while maintaining a steady 30 FPS on an iPhone 13." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.83, + 0.21, + 0.848 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To demonstrate the effectiveness of SplittingAvatar, we compared it with state-of-the-art (SoTA) methods in two different types of datasets for head and full-body avatars." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.584, + 0.866, + 0.699 + ], + "angle": 0, + "content": "
MethodPSNR↑SSIM↑LPIPS↓
NHA [16]20.290.8830.145
INSTA [53]26.420.9240.080
PointAvatar [51]27.840.9130.067
Ours+FLAME28.190.9310.063
Ours+NHA28.860.9310.060
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.709, + 0.896, + 0.793 + ], + "angle": 0, + "content": "Table 1. Quantitative comparison on head avatars. Both variations of our method outperform existing methods in terms of average photometric errors. With detailed meshes from NHA [16], Ours+NHA performs the best based on the metrics. However, we observe better visual quality with Ours+FLAME in the inner regions of the rendered image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.816, + 0.603, + 0.831 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.896, + 0.901 + ], + "angle": 0, + "content": "Monocular video for head avatar. Taking a single monocular video to construct a head avatar for the given subject, our method takes as input images, masks, camera parameters, and tracked FLAME meshes, denoting Ours+FLAME. We" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "1611" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.088, + 0.885, + 0.39 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.4, + 0.893, + 0.445 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison on PeopleSnapshot [2]. We show the results on PeopleSnapshot (columns 2-4) and novel pose animation (columns 5-6). SplittingAvatar produces photorealistic rendering for full-body avatars, especially in the facial area, and captures thin structures like the accessory on the wrist." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.456, + 0.891, + 0.542 + ], + "angle": 0, + "content": "
male-3-casualmale-4-casualfemale-3-casualfemale-4-casual
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
Anim-NeRF [7]29.370.9700.01728.370.9600.02728.910.9740.02228.900.9680.017
InstantAvatar [21]30.910.9770.02229.770.9800.02529.730.9750.02530.920.9770.021
Ours33.010.9820.02030.990.9820.02930.810.9780.02832.570.9810.018
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.55, + 0.893, + 0.581 + ], + "angle": 0, + "content": "Table 2. Quantitative comparison on PeopleSnapshot. Compared to two SoTA methods, we achieve significant improvements in pixel-wise quality with PSNR and SSIM. All three methods achieve good perceptual quality in terms of LPIPS where the metrics are close." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.601, + 0.475, + 0.798 + ], + "angle": 0, + "content": "evaluated our approach with several SoTA methods on a combined dataset from NHA [16], NerFace [15], INSTA [53] and PointAvatar [51], including 10 subjects covering different videos captured with DSLR, smartphones and from the Internet. The pre-processing pipeline of IMavatar [50] and INSTA [53] was altered to apply DECA [12] for face tracking, RVM [37] for segmentation, and BisenetV2 [46] for face parsing. For each video, the last 350 frames were used as testing samples. Because our method can directly be animated by the given mesh, we further unleashed its potential by training and testing on the generated meshes from NHA [16] which have more geometry details. This variation is referred to as Ours+NHA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.473, + 0.903 + ], + "angle": 0, + "content": "PeopleSnapshot. We conducted a quantitative evaluation of the rendering quality of full-body avatars on the PeopleSnapshot [2] dataset. Following the protocol of InstantAvatar [21], we used SMPL meshes refined by Anim-NeRF [7]. Our method demonstrates the generalizability to novel poses through qualitative analysis in Section 4.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.6, + 0.719, + 0.617 + ], + "angle": 0, + "content": "4.2. Comparison with SoTA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.895, + 0.716 + ], + "angle": 0, + "content": "Head avatar. To evaluate the rendering quality of the learned avatars, we animated SplattingAvatar with the registered meshes of testing images. For Ours+NHA, we trained NHA [16] on the training set and extracted the final meshes for both the training and testing images, which were further used for the training and testing of our method respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.896, + 0.869 + ], + "angle": 0, + "content": "We conducted a comparative analysis of SplittingAvatar against INSTA [53], PointAvatar [51], and NHA [16]. As depicted in Figure 5, our method achieves superior quality in terms of improved details in the eye and hair regions, and even being able to capture the light reflection on the glasses. For Ours+FLAME, though the off-surface geometries like hair and glasses are not fully represented by meshes, our method can handle the rendering decently because the embeddings are optimized to find correct motions from nearby triangles. Please see Table 1 for quantitative evaluations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Full-body avatar. We made a comparison to InstantAvatar [21] and Anim-NeRF [7] on PeopleSnapshot. For In" + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.958 + ], + "angle": 0, + "content": "1612" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "stantAvatar [21], a complete training was performed for 200 epochs as suggested in the most recent version of the author's code. Image quality metrics in Table 2 demonstrate the effectiveness of our method in terms of the lowest pixelwise errors. We qualitatively show the comparison of rendering quality of testing images in Figure 6, together with the demonstration of generalizability to novel poses. Our representation is friendly to thin structures like the accessory on the wrist. Our approach produced better quality overall and especially in the facial area compared to InstantAvatar [21], but slightly more artifacts under the shoulder due to very limited pose variations in the training set. We believe this can be much improved with more training poses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.298, + 0.231, + 0.314 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.321, + 0.47, + 0.441 + ], + "angle": 0, + "content": "Trainable embedding. The key component of our method is the trainable embedding on the mesh. We conducted an ablation experiment by replacing it with fixed embedding on mesh and a trainable local shift \\(\\Delta x \\in \\mathbb{R}^3\\) per Gaussian. Without trainable embedding, the Gaussians encountered difficulties in following the mesh correctly. The right column of Figure 7 shows the irregular rendering artifacts without trainable embedding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.442, + 0.47, + 0.517 + ], + "angle": 0, + "content": "Regularization. In the optimization process of Gaussian Splatting, some Gaussians turn to become long and thin, generating artifacts when rendered into novel poses. We show the results without the scaling regularization in the middle column of Figure 7." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.895, + 0.288 + ], + "angle": 0, + "content": "underlying mesh. In the comparison between Ours+FLAME and Ours+NHA, we observe that the driving mesh should focus on the motion instead of fully reconstructing the exact geometry. In Figure 8 we show that when the mesh with vertex offsets from NHA [16] is applied, the detailed surface deformation improves the generalizability of SplattingAvatar to large poses. However, in the second and third row of Figure 5, the mesh from FLAME that captures the correct motion of the glasses rather than the shape is driving the best rendering quality of SplattingAvatar. To perform textured mesh rendering, the mesh of NHA [16] is seamed in the mouth region and deformed to fit the shape of the glasses, yet both being unhelpful to the quality of Ours+NHA." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.288, + 0.895, + 0.394 + ], + "angle": 0, + "content": "Limitations and future work. As discussed above, our method depends on the motion representation ability of the driving mesh. With current FLAME and SMPL models, we do not have separate motion representations for clothes and hair. We believe SplattingAvatar can support future works on human avatars with disentangled mesh representations, e.g., separate meshes for clothes and hair stands." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.404, + 0.889, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.527, + 0.895, + 0.569 + ], + "angle": 0, + "content": "Figure 8. Comparison between Ours+FLAME and Ours+NHA. The better aligned mesh from NHA [16] improves the generalizability of SplattingAvatar to large pose variations." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.53, + 0.465, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.722, + 0.471, + 0.807 + ], + "angle": 0, + "content": "Figure 7. Ablation study. Without the scaling regularization term, Gaussians that are long and thin cause needle-like artifacts. Without trainable embedding, Gaussians do not follow the movement of the mesh tightly, leading to irregular rendering results. The application of our trainable embedding and the scaling term successfully removes most of the artifacts when rendered into novel poses." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.832, + 0.195, + 0.847 + ], + "angle": 0, + "content": "4.4. Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Discussion on driving mesh. Considering efficiency, compatibility, and portability, SplattingAvatar is designed to tightly rely on the motion and surface deformation of the" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.596, + 0.619, + 0.612 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.622, + 0.895, + 0.817 + ], + "angle": 0, + "content": "In this paper, we have proposed a hybrid representation for human avatar modeling featuring Gaussian Splatting with trainable embeddings on a mesh. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians and their embeddings. Our method leverages the advantages of the explicit motion representation with a mesh and implicit rendering capability of Gaussian Splatting. Compared with SoTA methods, our approach achieves the best rendering quality for both head and full-body avatars reconstructed from monocular videos and runs at real-time frame rates on a mobile device. Our method lays a foundation for future work in Gaussian Splatting manipulation with mesh-based motion control." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.66, + 0.848 + ], + "angle": 0, + "content": "Acknowledgments" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This work was partially supported by Guangzhou-HKUST(GZ) Joint Funding #2023A03J0670 and Guangzhou Basic Research Scheme #2024A04J4229." + }, + { + "type": "page_number", + "bbox": [ + 0.484, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "1613" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.471, + 0.142 + ], + "angle": 0, + "content": "[1] Mixamo. https://www MIXamo.com/. 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Overview of SplattingAvatar featuring Mesh-Embedded Gaussian Splatting. Our method takes (a) monocular videos as input, while employing (b) a trainable embedding technique for Gaussian-Mesh association. (c) Animated by mesh through the learned embedding, the Gaussians render into high-fidelity human avatars. (d) SplattingAvatar demonstrates real-time rendering capabilities in Unity, achieving over 300 FPS on an NVIDIA RTX 3090 GPU and 30 FPS on an iPhone 13 (images captured in action). + +![](images/adf2b2b599e15bb9c5501b304e5530f51ed7526f521079cebbba7d50c3832da3.jpg) + +# Abstract + +We present SplattingAvatar, a hybrid 3D representation of photorealistic human avatars with Gaussian Splatting embedded on a triangle mesh, which renders over 300 FPS on a modern GPU and 30 FPS on a mobile device. We disentangle the motion and appearance of a virtual human with explicit mesh geometry and implicit appearance modeling with Gaussian Splatting. The Gaussians are defined by barycentric coordinates and displacement on a triangle mesh as Phong surfaces. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians while walking on the triangle mesh. SplattingAvatar is a hybrid representation of virtual humans where the mesh represents low-frequency motion and surface deformation, while the Gaussians take over the high-frequency geometry and detailed appearance. Unlike existing deformation methods that rely on an MLP-based linear blend skinning (LBS) field for motion, we control the rotation and translation of the Gaussians directly by mesh, which empowers its compatibility with various animation + +techniques, e.g., skeletal animation, blend shapes, and mesh editing. Trainable from monocular videos for both full-body and head avatars, SplattingAvatar shows state-of-the-art rendering quality across multiple datasets. Code and data are available at https://github.com/initialneil/SplattingAvatar. + +# 1. Introduction + +The demand for personalized, photorealistic, and animatable human avatars that render in real-time spans a wide array of applications, including gaming [48], extended reality (XR) storytelling [10, 19], and tele-presentation [22, 24]. As the quest for digital realism intensifies, practitioners face a growing challenge: improving the quality of 3D human models often means increasing the complexity of these models. This is typically achieved by adding more polygons, layering skin textures [5], and integrating advanced hair systems [42]. However, these enhancements invariably lead to + +higher computational demands, creating obstacles in achieving efficiency and portability in avatar rendering. + +In our approach, we categorize the representation of mesh-based virtual humans into three distinct levels of detail. The first two levels encompass body motion and surface deformation, both of which are effectively captured by a mesh [11, 16, 39]. The third level, however, focuses on geometric details that are crucial for enhancing realism but challenging to represent with traditional meshes. This level is not only computationally demanding to render [31] but also faces limitations due to the rigid connectivity of mesh vertices, which hinders the adaptability to topological changes and complex or thin structures. + +Recent advances in the field have seen a shift towards using Neural Radiance Fields (NeRF) [32], especially for capturing high-frequency details in 3D avatar modeling [3, 18, 21, 26, 27, 34, 35, 53]. A typical process involves constructing NeRF in a canonical space and then performing volume rendering in the posed space. This is done by tracing ray samples backward from their posed positions to their canonical origins [21, 34, 35, 53]. However, this reverse mapping process introduces ambiguities, as a single point in the posed space might correspond to multiple points in the canonical space [8, 9], leading to challenges in accurately rendering details. Additionally, the prevalent use of multilayer perceptron (MLPs) for motion control [21, 39, 51] tends to overlook the advantages of mesh-based representations for capturing surface deformations, an aspect crucial for realistic avatar movement as highlighted in studies like DECA [12], CAPE [30], and TalkSHOW [45]. + +To address the challenges posed by the limitations of NeRF and MLP-based motion control in capturing high-frequency details and realistic surface deformations, we introduce a novel solution. Inspired by the recently proposed Gaussian Splatting technique [23], we propose explicit motion control of the Gaussians with trainable embeddings on a mesh. The embedding is described by $(k,u,v,d)$ on the mesh as Phong surface [38], where $(u,v)$ represents the local barycentric coordinates of the embedding triangle $k$ , and $d$ is the displacement along the interpolated normal vector. The pose-dependent rotation and scaling adjust dynamically in response to the mesh warping, while the pose-invariant properties, i.e., canonical rotation and scaling, color, and opacity, remain stable and consistent across various poses. Because the embedding point defined in barycentric coordinates is differentiable only inside the corresponding triangle, cross-triangle updates must be handled properly [40, 41]. During training, we conduct lifted optimization [38] with the embedding points walking on the triangle mesh. + +Our hybrid representation, Gaussians embedded on a mesh, can be trained from a monocular video and efficiently port to Unity that runs in real time (Figure 1) by bringing together three key advantages. First, the use of the mesh + +for representing body motion and surface deformation not only proves efficient but also allows for high editability. This flexibility is crucial for adapting the avatar to various scenarios and movements. Second, the application of Gaussian Splatting enriches this model by providing a robust means to capture high-frequency geometry and appearance details. This is vital for achieving a level of realism that conventional meshes alone cannot offer. Third, the embedding technique empowers the Gaussians to be explicitly controlled by the mesh movements. This integration results in an efficient, clear, and non-ambiguous method for motion control, significantly reducing the computational load compared to MLP-based methods. + +Furthermore, our approach is distinct from existing hybrid models such as AvatarReX [52] and DELTA [14], which typically segment avatars into body parts like hair, hands, clothes, and face. Instead, our method achieves a disentanglement of motion and appearance. In the SplattingAvatar framework, although different parts may have specific motion control, the rendering is uniformly conducted through Gaussian Splatting. This uniformity achieved by our method ensures a cohesive and harmonious appearance across all parts of the avatar. + +We summarize our main contributions as follows: + +- We introduce a framework that integrates Gaussian Splating with meshes, offering a new avatar representation that achieves realism and computational efficiency. +- Our approach applies lifted optimization to avatar modeling, allowing for joint optimization of Gaussian parameters and mesh embeddings for accurate reconstruction. +- We demonstrate the capability of real-time rendering and adaptability to creating diverse avatars through comprehensive evaluation and a Unity implementation. + +# 2. Related Work + +Mesh-based avatar. The rise of free-viewpoint video in sequences of textured meshes has shown the expressiveness of detailed texture atlas along with as few as 10k triangles [11]. Many efforts [18, 20] have been put into extending this line of work to build controllable avatars. With the help of human shape models with strong prior [6, 25, 28, 33] that unwrap to a unified UV space, texture atlas can be obtained by 2D image generation supervised through differentiable rendering [31, 43]. Such prior models provide consistency across large motions and can be recovered from monocular videos or even a single image. To cope with the shape details of identities and clothes, CAPE [30] predicts displacements on the vertices with pose-conditioned VAE. Due to the limitation of the base model to topological changes, some treat the textured mesh as input conditions [31, 36] for image rendering, while others resort to implicit representations of + +![](images/c809f53ba168abcbf1bacf32a0339f36ecb84694deaead04feb645b14e04fa4c.jpg) +Figure 2. The pipeline of our method. SplittingAvatar learns 3D Gaussians with trainable embedding on the canonical mesh. The motion and deformation of the mesh explicitly bring the Gaussians to the posed space for differentiable rasterization. Both the Gaussians and embedding parameters are optimized during training. The position $\mu$ is the barycentric point $P$ plus a displacement $d$ along the interpolated normal vector $\mathbf{n}$ . Pose-dependent quaternion and scaling $(\delta q, \delta s)$ and pose-invariant quaternion, scaling, opacity, and color $(\overline{q}, \overline{s}, o, c)$ together define the properties of the Gaussians. + +the mesh [8, 9, 20, 39], color [16, 20, 39], or materials [4]. + +Implicit neural avatar. To achieve convincing rendering beyond the limitation of triangle mesh, especially on the hair, glasses, and clothes, some recent works [3, 16, 21, 26, 34, 35, 44, 47, 53] focus on constructing NeRF in the canonical space (usually T-pose of SMPL [28] or neutral expression of FLAME [25]) and conduct volume rendering at the posed space. The required backward tracing from pose to canonical is non-trivial and raises an ambiguity issue. Existing works propose to adopt pose conditioned inverse LBS field [17, 34] or to optimize a root-finding loop with multiple initialization [8, 9, 21]. The increased computational load upon volume rendering prohibits the potential real-time applications. + +PointAvatar [51], with explicit point primitives, takes advantage of forward rasterization that only requires nonambiguous forward deformation from canonical to pose, producing photo-realistic appearance and detailed challenging geometries such as hair and glasses. In transforming to Gaussian Splatting, we further increase the efficiency and compatibility with our mesh embedding mechanism instead of the LBS-based deformation field and achieve two magnitude faster rendering speed with on-par quality. + +Hybrid avatar representation. First attempts have been proposed to disentangle human avatar modeling into separate parts with varying properties. AvatarRex [52] learns disentangled models for face, body, and hands. SCARF [13] and DELTA [14] propose hybrid modeling with textured mesh for body, and NeRF for hair and clothing. In contrast, our method handles the disentanglement in terms of motion and appearance to explicit mesh geometry and implicit Gaussian Splatting rendering. Different from existing works [3, 20] that attach features to fixed locations on mesh like mesh + +vertices, our trainable embedding enables the Gaussians to optimize their locations on mesh and distribute unevenly according to the texture complexity. + +# 3. Method + +Overview. Given a sequence of monocular images, each with a registered mesh template, i.e., the deformed mesh of SMPL [28] or FLAME [25], we train a hybrid representation of human avatar as 3D Gaussians [23] embedded on the canonical mesh. The Gaussians, parameterized by position, rotation, scale, color, and opacity, are semi-transparent 3D particles that render into camera views through splattering-based rasterization. + +Each 3D Gaussian is embedded on one triangle of the canonical mesh in its local $(u, v, d)$ coordinates. The embedding directly defines the position of the Gaussians in both canonical and posed space. Other than position, each Gaussian has its own parameters of rotation, scaling, color, and opacity. With the mesh deformed by animation, the embedding also provides additional rotation and scaling upon each Gaussian. The additional pose-dependent rotation is defined by barycentric interpolated per-vertex quaternion while the additional scaling is defined by the area change of the embedded triangle. + +During optimization, the Gaussian parameters and the embedding parameters are updated simultaneously. When the update of $(u,v)$ moves the embedding across the triangle boundary, the barycentric update is re-expressed in the neighboring triangle as if the Gaussian is walking on the mesh. To support embedding, we adapt the clone and split scheme of 3D Gaussians [23] to better suit our needs. + +Embedding on mesh. Inspired by the Phong shading in + +computer graphics, Phong surface [38] defines the position and normal of a point inside a triangle. For the point $P$ on triangle $k$ with barycentric coordinate $(u,v)$ , its position and normal is a linear interpolation of the triangle's vertices $\{V_1,V_2,V_3\}$ and per-vertex normals $\{\pmb{n}_1,\pmb{n}_2,\pmb{n}_3\}$ : + +$$ +P = \mathcal {V} (k, u, v) = u * V _ {1} + v * V _ {2} + (1 - u - v) * V _ {3} \tag {1} +$$ + +$$ +\boldsymbol {n} = \mathcal {N} (k, u, v) = u * \boldsymbol {n} _ {1} + v * \boldsymbol {n} _ {2} + (1 - u - v) * \boldsymbol {n} _ {3} \tag {2} +$$ + +where $\mathcal{V}$ maps triangle index $k$ and barycentric coordinates $(u,v)$ to a point on the mesh and $\mathcal{N}$ the interpolated normal. + +We define the position of a Gaussian, i.e., the mean $\mu$ , by a displacement $d$ along the interpolated normal vector: + +$$ +\mu = P + d * \boldsymbol {n} \tag {3} +$$ + +Embedding $E = \{k, u, v, d\}$ approximates a first-order continuous space around the mesh surface. + +As proposed by Zielonka et al. [53], for the corresponding triangle in the canonical and posed space at frame $t$ we compute the matrix $\{R_{\text{cano}}, R_{\text{pose}}\}$ based on the triangle's tangent, bitangent, and normal to track the triangle rotation from canonical to pose, noted that the notation $t$ is skipped. The rotation matrix is then converted to a quaternion, and we calculate the per-vertex quaternion $q_V$ by area-weighted average from surrounding neighbor triangles: + +$$ +R _ {k} = R _ {\text {c a n o}} R _ {\text {p o s e}} ^ {- 1} \tag {4} +$$ + +$$ +q _ {V} = \frac {\sum_ {k \in \Omega_ {V}} A _ {k} q _ {k}}{\sum_ {k \in \Omega_ {V}} A _ {k}} \tag {5} +$$ + +where $\Omega_V$ is the neighbor triangles of vertex $V$ , $A_k$ and $q_k$ are the triangle's area and quaternion respectively. For an embedding $E_i$ with quaternions $\{q_1, q_2, q_3\}$ calculated on the corresponding triangle vertices at frame $t$ , the barycentric interpolated rotation $\delta q_{i,t}$ is multiplied to the canonical rotation $\overline{q}_i$ of the Gaussian in the canonical space: + +$$ +\delta q _ {i, t} = u * q _ {1} + v * q _ {2} + (1 - u - v) * q _ {3} \tag {6} +$$ + +$$ +q _ {i, t} = \delta q _ {i, t} * \bar {q} _ {i} \tag {7} +$$ + +The same applies to scaling where the area change of the embedded triangle is used to represent the scaling caused by deformation: $s_{i,t} = (A_{\text{pose}} / A_{\text{cano}}) \overline{s}_i$ . While the original implementation of Gaussian Splatting [23] represents color in view-dependent spherical harmonics, we choose to turn it off for simplicity [29]. + +We perform initialization by randomly selecting $10\mathrm{k}$ pairs of triangle indices and barycentric coordinates on the canonical mesh. We set the barycentric coordinates to be the current $(u,v)$ of embeddings and initialize all the $d$ to be zero. With the position of the Gaussians calculated from the embeddings, we initialize other properties of the Gaussians according to their original definitions [23]. Initially, the Gaussians + +![](images/03ac5e5ad6ed0bba6cbaf91b4603ac27afca759cd1e7a1073c55ceea02722b97.jpg) +Figure 3. The development of Gaussian embeddings on mesh. Each line segment indicates the position of one Gaussian displaced from its embedding point on mesh. Gaussians for off-surface geometries like the hair have positive displacements while others turn to have negative displacements because when the mesh surface is correctly aligned to the geometry like in the facial area, the means for the Gaussians will be inside the mesh. + +![](images/fbe688147623148f4bceaf7aba006639a4d4e892cafb792c744247d41d2532ab.jpg) + +![](images/d93a12c3d42cfc4d8df22b4e9efe959216124939801c996e6e72e8b6d1393a03.jpg) + +are positioned on the surface of the mesh. With the training proceeds with more poses, the embeddings generally bring the Gaussians to approximate the actual geometry and densify in the regions with rich texture. Figure 3 illustrates the development of the embeddings. + +Differentiable rendering of Gaussian Splatting. With the position, rotation, and scaling of the Gaussians updated by the mesh deformation at frame $t$ , we perform differentiable Gaussian rendering [23] to the observed camera view(s). The Gaussian in space is defined by its mean $\mu$ and a 3D covariance matrix $\Sigma$ . + +$$ +G _ {i, t} (x) = e ^ {- \frac {1}{2} (x) ^ {T} \Sigma_ {i, t} ^ {- 1} (x)} \tag {8} +$$ + +$$ +\Sigma_ {i, t} = R _ {i, t} S _ {i, t} S _ {i, t} ^ {T} R _ {i, t} ^ {T} \tag {9} +$$ + +where $R_{i,t}$ is the rotation matrix constructed from $q_{i,t}$ , and $S_{i,t}$ the scaling matrix from $s_{i,t}$ . Given the world-to-camera view matrix $W$ and the Jacobian $J$ of the point projection matrix. The influence of the Gaussian is splatted to 2D [54]: + +$$ +\Sigma^ {\prime} = J W \Sigma W ^ {T} J ^ {T} \tag {10} +$$ + +The image formation of Gaussian Splatting is akin to NeRF, where the same volume rendering formula is applied to the blending from near to far. The color $C$ of a pixel rendered by $N$ Gaussians is given by a series of $\alpha$ -blending: + +$$ +C = \sum_ {i = 1} ^ {N} c _ {i} \alpha_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {j}) \tag {11} +$$ + +with $\alpha_{i}$ evaluated from the 2D covariance, and an opacity in logit $o_{i}$ with $\mathrm{sigm}()$ being the standard sigmoid function: + +$$ +\alpha_ {i} (P) = \operatorname {s i g m} \left(o _ {i}\right) \exp \left(- \frac {1}{2} \left(P - \mu_ {i}\right) \left(\Sigma_ {i}\right) ^ {- 1} \left(P - \mu_ {i}\right)\right) \tag {12} +$$ + +The Equation 11 is implemented in CUDA with a for loop for each pixel, while in our Unity implementation, each Gaussian is drawn by a front-parallel Quad primitive based + +on the projection and 2D covariance. We resort to the standard rasterization pipeline of the rendering engine to enable $\alpha$ -blending with these semi-transparent Gaussians. + +Due to limited viewing angle and pose variations from monocular video, we propose a scaling regularization term to prevent Gaussians from growing long and thin. A random background color is generated every iteration to mix with the rendered image $I$ and ground truth image $I_{gt}$ , providing important cues for the silhouette. The loss is the sum of $\mathcal{L}_1$ , $\mathcal{L}_{mse}$ , a perceptual loss [49], and a scaling regularization. + +$$ +\mathcal {L} = \mathcal {L} _ {1} + \lambda_ {l _ {m s e}} \mathcal {L} _ {m s e} + \lambda_ {l} \mathcal {L} _ {l p i p s} + \lambda_ {s} \mathcal {L} _ {\text {s c a l i n g}} \tag {13} +$$ + +$$ +\mathcal {L} _ {\text {s c a l i n g}} (i) = \left\{ \begin{array}{c c} | \hat {s} _ {i} |, & \hat {s} _ {i} > \max \left(T _ {s}, T _ {r} \check {s} _ {i}\right) \\ 0, & \text {o t h e r w i s e} \end{array} \right. \tag {14} +$$ + +With $s_i \in \mathbb{R}^3$ being the scaling of a Gaussian, $\hat{s}_i$ and $\check{s}_i$ are the maximum and minimum scaling values respectively. The scaling regularization is posed on $\hat{s}_i$ when it is both long (larger than $T_s$ ) and thin (larger than $T_r$ times $\check{s}_i$ ). Please see Section 4.3 for an ablation study on the regularization term. Walking on a triangle mesh. The notion Lifted Optimization arises in the model-point registration for hand tracking [38, 40, 41] in contrast to Iterative Closest Point (ICP), where the solve for model pose and correspondences are lifted to be simultaneous. We extend this notion to our avatar training, where the properties of the Gaussians and the trainable embeddings are optimized simultaneously. The barycentric coordinate of a point $P$ is $(k, u, v)$ defined within triangle $k$ . When the learned update $Q = (k, u, v) + (\delta u, \delta v)$ is outside triangle $k$ , we find the intersection $P'$ on the shared edge of the adjacent triangle $k'$ and re-express the remaining update in $k'$ as $Q' = P' + (\delta u', \delta v')$ . Because the barycentric coordinates are agnostic to the triangle shape, without loss of generality, the re-expression is conducted by conceptually treating two adjacent triangles as right triangles with the intersection on the hypotenuse. The update is iteratively re-expressed until it ends inside the final triangle. We show the re-expression process in Figure 4. The detailed steps are presented in Algorithm 1. Noted that we omit the conceptual re-ordering of the vertices. + +Optimization. We use Adam to optimize the Gaussian parameters and the embedding parameters. The original learning rate attenuation on position [23] is instead applied to the embedding parameters. We record the current barycentric $(u,v)$ and optimize for $(\delta u,\delta v,d)$ . The triangle walking in Algorithm 1 is implemented as a pybind11 module in C++. When an embedding is being transferred to another triangle, we reset its corresponding optimizer state of the $(\delta u,\delta v,d)$ . + +The densification process [23] plays an important role in allocating more Gaussians to where in need. In the clone and prune process, the embedding parameters are copied + +![](images/7795c9900a40067eb63d56c9c20284a77c9f1e1994851ed8f68a284970605864.jpg) +a) Barycentric update starting from P +Figure 4. Walking on triangles for embedding update. a) The recursion process of walking on a triangle mesh. b) The update $P + \delta$ starting from triangle $CAB$ is re-expressed as $P' + \delta'$ in triangle $DBA$ , and c) re-expressed again in $EDA$ . The re-expression between two triangles is conducted by conceptually treating them as two right triangles adjacent to each other on the hypotenuse. + +![](images/167ac849a7c105b07d26e8ffcb28ac4d1f0c39f86538172d1a24963b0fee2283.jpg) +b) Triangle walking $CAB \rightarrow DBA$ + +![](images/199c34ee6a90979ad7477756bb3d63be67fcf3d9e0c1d064e752592d95b19cd1.jpg) +c) Triangle walking $BAD \to EDA$ + +Algorithm 1 Walking on triangles +Input: $k, u, v, \delta u, \delta v$ +Output: $\hat{k}, \hat{u}, \hat{v}$ +function WALKONTRIANGLES $(k, u, v, \delta u, \delta v)$ $P \leftarrow (u, v)$ $Q \leftarrow (u + \delta u, v + \delta v)$ +if Q is inside triangle then +Return $(k, Q.u, Q.v)$ +end if +Intersect $P-Q$ with hypotenuse* on $(u', v')$ $\triangleright$ *reorder vertices if needed + $\delta u' \leftarrow \delta u - (u' - u)$ $\delta v' \leftarrow \delta v - (v' - v)$ +Return ReExpress $(k, u', v', \delta u', \delta v')$ +end function +function REEXPRESS $(k, u', v', \delta u', \delta v')$ $\hat{k} \leftarrow$ adjacent of $k$ $\hat{u} \leftarrow 1 - u'$ , $\hat{v} \leftarrow 1 - v'$ $\delta \hat{u} \leftarrow -\delta u'$ , $\delta \hat{v} \leftarrow -\delta v'$ +Return WalkOnTriangles $(\hat{k}, \hat{u}, \hat{v}, \delta \hat{u}, \delta \hat{v})$ +end function + $(\hat{k}, \hat{u}, \hat{v}) \leftarrow$ WalkOnTriangles $(k, u, v, \delta u, \delta v)$ + +or deleted in the same way as Gaussian parameters. In the split process, when a new position $\hat{\mu}$ is sampled from the Gaussian, we solve a mini problem with triangle walking to find the new embedding: + +$$ +\hat {E} = \underset {k, u, v, d} {\arg \min } \| \mathcal {V} (k, u, v) + d * \mathcal {N} (k, u, v) - \hat {\mu} \| _ {2} ^ {2} \tag {15} +$$ + +Unity implementation for mobile device. With maximum compatibility in mind, we made SplattingAvatar solely rely on the warped mesh. Before exporting to Unity, we uploaded the canonical mesh in .obj format to Mixamo [1] for autorigging. In total, we exported one .ply file of the Gaussians, one .json file describing the embedding, and one .fbx file from Mixamo to Unity. Note that the .fbx file can be rigged + +![](images/a72704280f49ada581aa1f28b6e9038a965c5cefe0db5ca8ddf8e105dcb57c1c.jpg) +Figure 5. Qualitative comparison on head avatars. SplattingAvatar produces photorealistic rendering for avatars with high-quality details especially in the eye and hair regions. Even the light reflection on the glasses is well reconstructed. Both PointAvatar [51] and NHA [16] can reconstruct good geometries but the rendering quality is limited by their underlying representations, i.e., points and texture atlas respectively. Compared to INSTA [53], our trainable embedding scheme produces better quality for off-surface geometries, especially for the glasses. The green arrows highlight where our results have better consistency with Ground Truth, while the red arrows point to where other methods show significant artifacts or noise. Please see the supplemental materials for illustrations of the error map. + +by any other software for customized needs, as long as the triangle order is maintained. + +We implemented the Gaussian renderer in Unity's compute shaders, starting from sorting all Gaussians by the z-axis in camera coordinates from near to far. Based on the calculated 2D covariance $\Sigma'$ , one front-parallel quad primitive is drawn for every visible Gaussian centered at its position. This one-primitive-one-Gaussian strategy is important for the game engine to properly handle the occlusion of other regular objects. For every pixel to draw in the fragment Shader, our implementation emits color with alpha pre-multiplication and sets the blend function to (ONE, ONE_MINUS_SRC_alpha). Our Unity program achieves a high performance of over 300 FPS on a modern GPU while maintaining a steady 30 FPS on an iPhone 13. + +# 4. Experiments + +To demonstrate the effectiveness of SplittingAvatar, we compared it with state-of-the-art (SoTA) methods in two different types of datasets for head and full-body avatars. + +
MethodPSNR↑SSIM↑LPIPS↓
NHA [16]20.290.8830.145
INSTA [53]26.420.9240.080
PointAvatar [51]27.840.9130.067
Ours+FLAME28.190.9310.063
Ours+NHA28.860.9310.060
+ +Table 1. Quantitative comparison on head avatars. Both variations of our method outperform existing methods in terms of average photometric errors. With detailed meshes from NHA [16], Ours+NHA performs the best based on the metrics. However, we observe better visual quality with Ours+FLAME in the inner regions of the rendered image. + +# 4.1. Datasets + +Monocular video for head avatar. Taking a single monocular video to construct a head avatar for the given subject, our method takes as input images, masks, camera parameters, and tracked FLAME meshes, denoting Ours+FLAME. We + +![](images/90f59808529981c35eb299632ae45cea4ba5008d047a39777258f583fc630f0b.jpg) +Figure 6. Qualitative comparison on PeopleSnapshot [2]. We show the results on PeopleSnapshot (columns 2-4) and novel pose animation (columns 5-6). SplittingAvatar produces photorealistic rendering for full-body avatars, especially in the facial area, and captures thin structures like the accessory on the wrist. + +
male-3-casualmale-4-casualfemale-3-casualfemale-4-casual
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
Anim-NeRF [7]29.370.9700.01728.370.9600.02728.910.9740.02228.900.9680.017
InstantAvatar [21]30.910.9770.02229.770.9800.02529.730.9750.02530.920.9770.021
Ours33.010.9820.02030.990.9820.02930.810.9780.02832.570.9810.018
+ +Table 2. Quantitative comparison on PeopleSnapshot. Compared to two SoTA methods, we achieve significant improvements in pixel-wise quality with PSNR and SSIM. All three methods achieve good perceptual quality in terms of LPIPS where the metrics are close. + +evaluated our approach with several SoTA methods on a combined dataset from NHA [16], NerFace [15], INSTA [53] and PointAvatar [51], including 10 subjects covering different videos captured with DSLR, smartphones and from the Internet. The pre-processing pipeline of IMavatar [50] and INSTA [53] was altered to apply DECA [12] for face tracking, RVM [37] for segmentation, and BisenetV2 [46] for face parsing. For each video, the last 350 frames were used as testing samples. Because our method can directly be animated by the given mesh, we further unleashed its potential by training and testing on the generated meshes from NHA [16] which have more geometry details. This variation is referred to as Ours+NHA. + +PeopleSnapshot. We conducted a quantitative evaluation of the rendering quality of full-body avatars on the PeopleSnapshot [2] dataset. Following the protocol of InstantAvatar [21], we used SMPL meshes refined by Anim-NeRF [7]. Our method demonstrates the generalizability to novel poses through qualitative analysis in Section 4.2. + +# 4.2. Comparison with SoTA + +Head avatar. To evaluate the rendering quality of the learned avatars, we animated SplattingAvatar with the registered meshes of testing images. For Ours+NHA, we trained NHA [16] on the training set and extracted the final meshes for both the training and testing images, which were further used for the training and testing of our method respectively. + +We conducted a comparative analysis of SplittingAvatar against INSTA [53], PointAvatar [51], and NHA [16]. As depicted in Figure 5, our method achieves superior quality in terms of improved details in the eye and hair regions, and even being able to capture the light reflection on the glasses. For Ours+FLAME, though the off-surface geometries like hair and glasses are not fully represented by meshes, our method can handle the rendering decently because the embeddings are optimized to find correct motions from nearby triangles. Please see Table 1 for quantitative evaluations. + +Full-body avatar. We made a comparison to InstantAvatar [21] and Anim-NeRF [7] on PeopleSnapshot. For In + +stantAvatar [21], a complete training was performed for 200 epochs as suggested in the most recent version of the author's code. Image quality metrics in Table 2 demonstrate the effectiveness of our method in terms of the lowest pixelwise errors. We qualitatively show the comparison of rendering quality of testing images in Figure 6, together with the demonstration of generalizability to novel poses. Our representation is friendly to thin structures like the accessory on the wrist. Our approach produced better quality overall and especially in the facial area compared to InstantAvatar [21], but slightly more artifacts under the shoulder due to very limited pose variations in the training set. We believe this can be much improved with more training poses. + +# 4.3. Ablation Study + +Trainable embedding. The key component of our method is the trainable embedding on the mesh. We conducted an ablation experiment by replacing it with fixed embedding on mesh and a trainable local shift $\Delta x \in \mathbb{R}^3$ per Gaussian. Without trainable embedding, the Gaussians encountered difficulties in following the mesh correctly. The right column of Figure 7 shows the irregular rendering artifacts without trainable embedding. + +Regularization. In the optimization process of Gaussian Splatting, some Gaussians turn to become long and thin, generating artifacts when rendered into novel poses. We show the results without the scaling regularization in the middle column of Figure 7. + +underlying mesh. In the comparison between Ours+FLAME and Ours+NHA, we observe that the driving mesh should focus on the motion instead of fully reconstructing the exact geometry. In Figure 8 we show that when the mesh with vertex offsets from NHA [16] is applied, the detailed surface deformation improves the generalizability of SplattingAvatar to large poses. However, in the second and third row of Figure 5, the mesh from FLAME that captures the correct motion of the glasses rather than the shape is driving the best rendering quality of SplattingAvatar. To perform textured mesh rendering, the mesh of NHA [16] is seamed in the mouth region and deformed to fit the shape of the glasses, yet both being unhelpful to the quality of Ours+NHA. + +Limitations and future work. As discussed above, our method depends on the motion representation ability of the driving mesh. With current FLAME and SMPL models, we do not have separate motion representations for clothes and hair. We believe SplattingAvatar can support future works on human avatars with disentangled mesh representations, e.g., separate meshes for clothes and hair stands. + +![](images/ca0fca2348664c809ad0cd94ca7368986bfc766babea73539e74194ac456d840.jpg) +Figure 8. Comparison between Ours+FLAME and Ours+NHA. The better aligned mesh from NHA [16] improves the generalizability of SplattingAvatar to large pose variations. + +![](images/d33b11b4690962ff013b31561a635dc1d66a23dedbb5cdbbfd3e1c0826e9a884.jpg) +Figure 7. Ablation study. Without the scaling regularization term, Gaussians that are long and thin cause needle-like artifacts. Without trainable embedding, Gaussians do not follow the movement of the mesh tightly, leading to irregular rendering results. The application of our trainable embedding and the scaling term successfully removes most of the artifacts when rendered into novel poses. + +# 4.4. Discussion + +Discussion on driving mesh. Considering efficiency, compatibility, and portability, SplattingAvatar is designed to tightly rely on the motion and surface deformation of the + +# 5. Conclusion + +In this paper, we have proposed a hybrid representation for human avatar modeling featuring Gaussian Splatting with trainable embeddings on a mesh. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians and their embeddings. Our method leverages the advantages of the explicit motion representation with a mesh and implicit rendering capability of Gaussian Splatting. Compared with SoTA methods, our approach achieves the best rendering quality for both head and full-body avatars reconstructed from monocular videos and runs at real-time frame rates on a mobile device. Our method lays a foundation for future work in Gaussian Splatting manipulation with mesh-based motion control. + +# Acknowledgments + +This work was partially supported by Guangzhou-HKUST(GZ) Joint Funding #2023A03J0670 and Guangzhou Basic Research Scheme #2024A04J4229. + +# References + +[1] Mixamo. https://www MIXamo.com/. Accessed: November 10, 2023. 5 +[2] Thiemo Alldieck, Marcus Magnor, Weipeng Xu, Christian Theobalt, and Gerard Pons-Moll. Detailed Human Avatars from Monocular Video. In International Conference on 3D Vision, pages 98-109, 2018. 7 +[3] Ziqian Bai, Feitong Tan, Zeng Huang, Kripasindhu Sarkar, Danhang Tang, Di Qiu, Abhinitra Meka, Ruofei Du, Ming-song Dou, Sergio Orts-Escolano, Rohit Pandey, Ping Tan, Thabo Beeler, Sean Fanello, and Yinda Zhang. Learning Personalized High Quality Volumetric Head Avatars From Monocular RGB Videos. 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Overview of SplattingAvatar featuring Mesh-Embedded Gaussian Splatting. Our method takes (a) monocular videos as input, while employing (b) a trainable embedding technique for Gaussian-Mesh association. (c) Animated by mesh through the learned embedding, the Gaussians render into high-fidelity human avatars. 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We disentangle the motion and appearance of a virtual human with explicit mesh geometry and implicit appearance modeling with Gaussian Splatting. The Gaussians are defined by barycentric coordinates and displacement on a triangle mesh as Phong surfaces. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians while walking on the triangle mesh. SplattingAvatar is a hybrid representation of virtual humans where the mesh represents low-frequency motion and surface deformation, while the Gaussians take over the high-frequency geometry and detailed appearance. Unlike existing deformation methods that rely on an MLP-based linear blend skinning (LBS) field for motion, we control the rotation and translation of the Gaussians directly by mesh, which empowers its compatibility with various animation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 473, + 548, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 473, + 548, + 545 + ], + "spans": [ + { + "bbox": [ + 305, + 473, + 548, + 545 + ], + "type": "text", + "content": "techniques, e.g., skeletal animation, blend shapes, and mesh editing. Trainable from monocular videos for both full-body and head avatars, SplattingAvatar shows state-of-the-art rendering quality across multiple datasets. Code and data are available at https://github.com/initialneil/SplattingAvatar." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 572, + 387, + 585 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 572, + 387, + 585 + ], + "spans": [ + { + "bbox": [ + 306, + 572, + 387, + 585 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 715 + ], + "type": "text", + "content": "The demand for personalized, photorealistic, and animatable human avatars that render in real-time spans a wide array of applications, including gaming [48], extended reality (XR) storytelling [10, 19], and tele-presentation [22, 24]. As the quest for digital realism intensifies, practitioners face a growing challenge: improving the quality of 3D human models often means increasing the complexity of these models. This is typically achieved by adding more polygons, layering skin textures [5], and integrating advanced hair systems [42]. However, these enhancements invariably lead to" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1606" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 96 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 96 + ], + "type": "text", + "content": "higher computational demands, creating obstacles in achieving efficiency and portability in avatar rendering." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 98, + 288, + 229 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 98, + 288, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 98, + 288, + 229 + ], + "type": "text", + "content": "In our approach, we categorize the representation of mesh-based virtual humans into three distinct levels of detail. The first two levels encompass body motion and surface deformation, both of which are effectively captured by a mesh [11, 16, 39]. The third level, however, focuses on geometric details that are crucial for enhancing realism but challenging to represent with traditional meshes. This level is not only computationally demanding to render [31] but also faces limitations due to the rigid connectivity of mesh vertices, which hinders the adaptability to topological changes and complex or thin structures." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 231, + 288, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 288, + 434 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 288, + 434 + ], + "type": "text", + "content": "Recent advances in the field have seen a shift towards using Neural Radiance Fields (NeRF) [32], especially for capturing high-frequency details in 3D avatar modeling [3, 18, 21, 26, 27, 34, 35, 53]. A typical process involves constructing NeRF in a canonical space and then performing volume rendering in the posed space. This is done by tracing ray samples backward from their posed positions to their canonical origins [21, 34, 35, 53]. However, this reverse mapping process introduces ambiguities, as a single point in the posed space might correspond to multiple points in the canonical space [8, 9], leading to challenges in accurately rendering details. Additionally, the prevalent use of multilayer perceptron (MLPs) for motion control [21, 39, 51] tends to overlook the advantages of mesh-based representations for capturing surface deformations, an aspect crucial for realistic avatar movement as highlighted in studies like DECA [12], CAPE [30], and TalkSHOW [45]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "text", + "content": "To address the challenges posed by the limitations of NeRF and MLP-based motion control in capturing high-frequency details and realistic surface deformations, we introduce a novel solution. Inspired by the recently proposed Gaussian Splatting technique [23], we propose explicit motion control of the Gaussians with trainable embeddings on a mesh. The embedding is described by " + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "inline_equation", + "content": "(k,u,v,d)" + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "text", + "content": " on the mesh as Phong surface [38], where " + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "text", + "content": " represents the local barycentric coordinates of the embedding triangle " + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 436, + 288, + 664 + ], + "type": "text", + "content": " is the displacement along the interpolated normal vector. The pose-dependent rotation and scaling adjust dynamically in response to the mesh warping, while the pose-invariant properties, i.e., canonical rotation and scaling, color, and opacity, remain stable and consistent across various poses. Because the embedding point defined in barycentric coordinates is differentiable only inside the corresponding triangle, cross-triangle updates must be handled properly [40, 41]. During training, we conduct lifted optimization [38] with the embedding points walking on the triangle mesh." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 713 + ], + "type": "text", + "content": "Our hybrid representation, Gaussians embedded on a mesh, can be trained from a monocular video and efficiently port to Unity that runs in real time (Figure 1) by bringing together three key advantages. First, the use of the mesh" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 227 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 227 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 227 + ], + "type": "text", + "content": "for representing body motion and surface deformation not only proves efficient but also allows for high editability. This flexibility is crucial for adapting the avatar to various scenarios and movements. Second, the application of Gaussian Splatting enriches this model by providing a robust means to capture high-frequency geometry and appearance details. This is vital for achieving a level of realism that conventional meshes alone cannot offer. Third, the embedding technique empowers the Gaussians to be explicitly controlled by the mesh movements. This integration results in an efficient, clear, and non-ambiguous method for motion control, significantly reducing the computational load compared to MLP-based methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 228, + 547, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 228, + 547, + 348 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 547, + 348 + ], + "type": "text", + "content": "Furthermore, our approach is distinct from existing hybrid models such as AvatarReX [52] and DELTA [14], which typically segment avatars into body parts like hair, hands, clothes, and face. Instead, our method achieves a disentanglement of motion and appearance. In the SplattingAvatar framework, although different parts may have specific motion control, the rendering is uniformly conducted through Gaussian Splatting. This uniformity achieved by our method ensures a cohesive and harmonious appearance across all parts of the avatar." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 308, + 354, + 509, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 354, + 509, + 365 + ], + "spans": [ + { + "bbox": [ + 308, + 354, + 509, + 365 + ], + "type": "text", + "content": "We summarize our main contributions as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 309, + 371, + 545, + 488 + ], + "type": "list", + "angle": 0, + "index": 11, + "blocks": [ + { + "bbox": [ + 309, + 371, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 371, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 309, + 371, + 545, + 407 + ], + "type": "text", + "content": "- We introduce a framework that integrates Gaussian Splating with meshes, offering a new avatar representation that achieves realism and computational efficiency." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 309, + 412, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 412, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 309, + 412, + 545, + 448 + ], + "type": "text", + "content": "- Our approach applies lifted optimization to avatar modeling, allowing for joint optimization of Gaussian parameters and mesh embeddings for accurate reconstruction." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 309, + 453, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 309, + 453, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 309, + 453, + 545, + 488 + ], + "type": "text", + "content": "- We demonstrate the capability of real-time rendering and adaptability to creating diverse avatars through comprehensive evaluation and a Unity implementation." + } + ] + } + ], + "index": 10 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 501, + 392, + 514 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 501, + 392, + 514 + ], + "spans": [ + { + "bbox": [ + 306, + 501, + 392, + 514 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 713 + ], + "type": "text", + "content": "Mesh-based avatar. The rise of free-viewpoint video in sequences of textured meshes has shown the expressiveness of detailed texture atlas along with as few as 10k triangles [11]. Many efforts [18, 20] have been put into extending this line of work to build controllable avatars. With the help of human shape models with strong prior [6, 25, 28, 33] that unwrap to a unified UV space, texture atlas can be obtained by 2D image generation supervised through differentiable rendering [31, 43]. Such prior models provide consistency across large motions and can be recovered from monocular videos or even a single image. To cope with the shape details of identities and clothes, CAPE [30] predicts displacements on the vertices with pose-conditioned VAE. Due to the limitation of the base model to topological changes, some treat the textured mesh as input conditions [31, 36] for image rendering, while others resort to implicit representations of" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1607" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 56, + 68, + 547, + 230 + ], + "blocks": [ + { + "bbox": [ + 56, + 68, + 547, + 230 + ], + "lines": [ + { + "bbox": [ + 56, + 68, + 547, + 230 + ], + "spans": [ + { + "bbox": [ + 56, + 68, + 547, + 230 + ], + "type": "image", + "image_path": "c809f53ba168abcbf1bacf32a0339f36ecb84694deaead04feb645b14e04fa4c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": "Figure 2. The pipeline of our method. SplittingAvatar learns 3D Gaussians with trainable embedding on the canonical mesh. The motion and deformation of the mesh explicitly bring the Gaussians to the posed space for differentiable rasterization. Both the Gaussians and embedding parameters are optimized during training. The position " + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": " is the barycentric point " + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": " plus a displacement " + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": " along the interpolated normal vector " + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "inline_equation", + "content": "\\mathbf{n}" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": ". Pose-dependent quaternion and scaling " + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "inline_equation", + "content": "(\\delta q, \\delta s)" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": " and pose-invariant quaternion, scaling, opacity, and color " + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "inline_equation", + "content": "(\\overline{q}, \\overline{s}, o, c)" + }, + { + "bbox": [ + 46, + 238, + 548, + 295 + ], + "type": "text", + "content": " together define the properties of the Gaussians." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 314, + 284, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 314, + 284, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 314, + 284, + 327 + ], + "type": "text", + "content": "the mesh [8, 9, 20, 39], color [16, 20, 39], or materials [4]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 327, + 288, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 288, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 288, + 483 + ], + "type": "text", + "content": "Implicit neural avatar. To achieve convincing rendering beyond the limitation of triangle mesh, especially on the hair, glasses, and clothes, some recent works [3, 16, 21, 26, 34, 35, 44, 47, 53] focus on constructing NeRF in the canonical space (usually T-pose of SMPL [28] or neutral expression of FLAME [25]) and conduct volume rendering at the posed space. The required backward tracing from pose to canonical is non-trivial and raises an ambiguity issue. Existing works propose to adopt pose conditioned inverse LBS field [17, 34] or to optimize a root-finding loop with multiple initialization [8, 9, 21]. The increased computational load upon volume rendering prohibits the potential real-time applications." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 484, + 288, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 288, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 288, + 593 + ], + "type": "text", + "content": "PointAvatar [51], with explicit point primitives, takes advantage of forward rasterization that only requires nonambiguous forward deformation from canonical to pose, producing photo-realistic appearance and detailed challenging geometries such as hair and glasses. In transforming to Gaussian Splatting, we further increase the efficiency and compatibility with our mesh embedding mechanism instead of the LBS-based deformation field and achieve two magnitude faster rendering speed with on-par quality." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 713 + ], + "type": "text", + "content": "Hybrid avatar representation. First attempts have been proposed to disentangle human avatar modeling into separate parts with varying properties. AvatarRex [52] learns disentangled models for face, body, and hands. SCARF [13] and DELTA [14] propose hybrid modeling with textured mesh for body, and NeRF for hair and clothing. In contrast, our method handles the disentanglement in terms of motion and appearance to explicit mesh geometry and implicit Gaussian Splatting rendering. Different from existing works [3, 20] that attach features to fixed locations on mesh like mesh" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 314, + 547, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 314, + 547, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 314, + 547, + 351 + ], + "type": "text", + "content": "vertices, our trainable embedding enables the Gaussians to optimize their locations on mesh and distribute unevenly according to the texture complexity." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 365, + 362, + 377 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 362, + 377 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 362, + 377 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 386, + 547, + 481 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 386, + 547, + 481 + ], + "spans": [ + { + "bbox": [ + 304, + 386, + 547, + 481 + ], + "type": "text", + "content": "Overview. Given a sequence of monocular images, each with a registered mesh template, i.e., the deformed mesh of SMPL [28] or FLAME [25], we train a hybrid representation of human avatar as 3D Gaussians [23] embedded on the canonical mesh. The Gaussians, parameterized by position, rotation, scale, color, and opacity, are semi-transparent 3D particles that render into camera views through splattering-based rasterization." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 483, + 548, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 548, + 615 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 548, + 615 + ], + "type": "text", + "content": "Each 3D Gaussian is embedded on one triangle of the canonical mesh in its local " + }, + { + "bbox": [ + 304, + 483, + 548, + 615 + ], + "type": "inline_equation", + "content": "(u, v, d)" + }, + { + "bbox": [ + 304, + 483, + 548, + 615 + ], + "type": "text", + "content": " coordinates. The embedding directly defines the position of the Gaussians in both canonical and posed space. Other than position, each Gaussian has its own parameters of rotation, scaling, color, and opacity. With the mesh deformed by animation, the embedding also provides additional rotation and scaling upon each Gaussian. The additional pose-dependent rotation is defined by barycentric interpolated per-vertex quaternion while the additional scaling is defined by the area change of the embedded triangle." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "type": "text", + "content": "During optimization, the Gaussian parameters and the embedding parameters are updated simultaneously. When the update of " + }, + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 304, + 616, + 547, + 700 + ], + "type": "text", + "content": " moves the embedding across the triangle boundary, the barycentric update is re-expressed in the neighboring triangle as if the Gaussian is walking on the mesh. To support embedding, we adapt the clone and split scheme of 3D Gaussians [23] to better suit our needs." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 701, + 546, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 546, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 546, + 714 + ], + "type": "text", + "content": "Embedding on mesh. Inspired by the Phong shading in" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1608" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": "computer graphics, Phong surface [38] defines the position and normal of a point inside a triangle. For the point " + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": " on triangle " + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": " with barycentric coordinate " + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": ", its position and normal is a linear interpolation of the triangle's vertices " + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\{V_1,V_2,V_3\\}" + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": " and per-vertex normals " + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "inline_equation", + "content": "\\{\\pmb{n}_1,\\pmb{n}_2,\\pmb{n}_3\\}" + }, + { + "bbox": [ + 47, + 72, + 289, + 133 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 52, + 140, + 287, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 140, + 287, + 153 + ], + "spans": [ + { + "bbox": [ + 52, + 140, + 287, + 153 + ], + "type": "interline_equation", + "content": "P = \\mathcal {V} (k, u, v) = u * V _ {1} + v * V _ {2} + (1 - u - v) * V _ {3} \\tag {1}", + "image_path": "783826817e80ac826d94a74650c8ddc8b086afe77cd26bccc47eedd8f362f39b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 52, + 161, + 287, + 174 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 161, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 52, + 161, + 287, + 174 + ], + "type": "interline_equation", + "content": "\\boldsymbol {n} = \\mathcal {N} (k, u, v) = u * \\boldsymbol {n} _ {1} + v * \\boldsymbol {n} _ {2} + (1 - u - v) * \\boldsymbol {n} _ {3} \\tag {2}", + "image_path": "f6caf915048aa1d8462b2209664b6abaaa125ddf363765113e0c4bcea88e33c6.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": " maps triangle index " + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": " and barycentric coordinates " + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": " to a point on the mesh and " + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 182, + 287, + 205 + ], + "type": "text", + "content": " the interpolated normal." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "spans": [ + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "type": "text", + "content": "We define the position of a Gaussian, i.e., the mean " + }, + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "type": "text", + "content": ", by a displacement " + }, + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 47, + 207, + 287, + 230 + ], + "type": "text", + "content": " along the interpolated normal vector:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 239, + 287, + 251 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 239, + 287, + 251 + ], + "spans": [ + { + "bbox": [ + 134, + 239, + 287, + 251 + ], + "type": "interline_equation", + "content": "\\mu = P + d * \\boldsymbol {n} \\tag {3}", + "image_path": "532f4af76daf8e852b0fff50b2a1ea0cdc5cece75562864a6ccd8228d60eb041.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 259, + 287, + 282 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 259, + 287, + 282 + ], + "spans": [ + { + "bbox": [ + 46, + 259, + 287, + 282 + ], + "type": "text", + "content": "Embedding " + }, + { + "bbox": [ + 46, + 259, + 287, + 282 + ], + "type": "inline_equation", + "content": "E = \\{k, u, v, d\\}" + }, + { + "bbox": [ + 46, + 259, + 287, + 282 + ], + "type": "text", + "content": " approximates a first-order continuous space around the mesh surface." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "text", + "content": "As proposed by Zielonka et al. [53], for the corresponding triangle in the canonical and posed space at frame " + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "text", + "content": " we compute the matrix " + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\{R_{\\text{cano}}, R_{\\text{pose}}\\}" + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "text", + "content": " based on the triangle's tangent, bitangent, and normal to track the triangle rotation from canonical to pose, noted that the notation " + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "text", + "content": " is skipped. The rotation matrix is then converted to a quaternion, and we calculate the per-vertex quaternion " + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "inline_equation", + "content": "q_V" + }, + { + "bbox": [ + 46, + 283, + 288, + 379 + ], + "type": "text", + "content": " by area-weighted average from surrounding neighbor triangles:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 128, + 386, + 287, + 401 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 128, + 386, + 287, + 401 + ], + "spans": [ + { + "bbox": [ + 128, + 386, + 287, + 401 + ], + "type": "interline_equation", + "content": "R _ {k} = R _ {\\text {c a n o}} R _ {\\text {p o s e}} ^ {- 1} \\tag {4}", + "image_path": "78d470a923d7c4167b9b330f86aeeeb357862e0648c9f0cbc1bb8da5ca6b98f6.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 123, + 406, + 287, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 406, + 287, + 435 + ], + "spans": [ + { + "bbox": [ + 123, + 406, + 287, + 435 + ], + "type": "interline_equation", + "content": "q _ {V} = \\frac {\\sum_ {k \\in \\Omega_ {V}} A _ {k} q _ {k}}{\\sum_ {k \\in \\Omega_ {V}} A _ {k}} \\tag {5}", + "image_path": "772ff4b85ddc3deba5feade90fa766260bbf47e1b43cbbee28a8434ce6df10b7.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\Omega_V" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " is the neighbor triangles of vertex " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "A_k" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "q_k" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " are the triangle's area and quaternion respectively. For an embedding " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "E_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " with quaternions " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\{q_1, q_2, q_3\\}" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " calculated on the corresponding triangle vertices at frame " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": ", the barycentric interpolated rotation " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\delta q_{i,t}" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " is multiplied to the canonical rotation " + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "inline_equation", + "content": "\\overline{q}_i" + }, + { + "bbox": [ + 46, + 437, + 287, + 510 + ], + "type": "text", + "content": " of the Gaussian in the canonical space:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 80, + 518, + 287, + 531 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 518, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 80, + 518, + 287, + 531 + ], + "type": "interline_equation", + "content": "\\delta q _ {i, t} = u * q _ {1} + v * q _ {2} + (1 - u - v) * q _ {3} \\tag {6}", + "image_path": "30aacd9346cce40704b64d4057b0eb56b6e2c08b633a40b9b1d1c3a3388f9f3c.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 134, + 541, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 541, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 134, + 541, + 287, + 554 + ], + "type": "interline_equation", + "content": "q _ {i, t} = \\delta q _ {i, t} * \\bar {q} _ {i} \\tag {7}", + "image_path": "b62399c9ffd83956553640796aaec0cd5379bbab7b78216e8fa8606d91ff13c3.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": "The same applies to scaling where the area change of the embedded triangle is used to represent the scaling caused by deformation: " + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "inline_equation", + "content": "s_{i,t} = (A_{\\text{pose}} / A_{\\text{cano}}) \\overline{s}_i" + }, + { + "bbox": [ + 46, + 558, + 287, + 630 + ], + "type": "text", + "content": ". While the original implementation of Gaussian Splatting [23] represents color in view-dependent spherical harmonics, we choose to turn it off for simplicity [29]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "We perform initialization by randomly selecting " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{k}" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " pairs of triangle indices and barycentric coordinates on the canonical mesh. We set the barycentric coordinates to be the current " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " of embeddings and initialize all the " + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": " to be zero. With the position of the Gaussians calculated from the embeddings, we initialize other properties of the Gaussians according to their original definitions [23]. Initially, the Gaussians" + } + ] + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 313, + 71, + 377, + 137 + ], + "blocks": [ + { + "bbox": [ + 313, + 71, + 377, + 137 + ], + "lines": [ + { + "bbox": [ + 313, + 71, + 377, + 137 + ], + "spans": [ + { + "bbox": [ + 313, + 71, + 377, + 137 + ], + "type": "image", + "image_path": "03ac5e5ad6ed0bba6cbaf91b4603ac27afca759cd1e7a1073c55ceea02722b97.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 145, + 547, + 221 + ], + "lines": [ + { + "bbox": [ + 305, + 145, + 547, + 221 + ], + "spans": [ + { + "bbox": [ + 305, + 145, + 547, + 221 + ], + "type": "text", + "content": "Figure 3. The development of Gaussian embeddings on mesh. Each line segment indicates the position of one Gaussian displaced from its embedding point on mesh. Gaussians for off-surface geometries like the hair have positive displacements while others turn to have negative displacements because when the mesh surface is correctly aligned to the geometry like in the facial area, the means for the Gaussians will be inside the mesh." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 395, + 71, + 457, + 137 + ], + "blocks": [ + { + "bbox": [ + 395, + 71, + 457, + 137 + ], + "lines": [ + { + "bbox": [ + 395, + 71, + 457, + 137 + ], + "spans": [ + { + "bbox": [ + 395, + 71, + 457, + 137 + ], + "type": "image", + "image_path": "fbe688147623148f4bceaf7aba006639a4d4e892cafb792c744247d41d2532ab.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 473, + 72, + 535, + 137 + ], + "blocks": [ + { + "bbox": [ + 473, + 72, + 535, + 137 + ], + "lines": [ + { + "bbox": [ + 473, + 72, + 535, + 137 + ], + "spans": [ + { + "bbox": [ + 473, + 72, + 535, + 137 + ], + "type": "image", + "image_path": "d93a12c3d42cfc4d8df22b4e9efe959216124939801c996e6e72e8b6d1393a03.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 243, + 547, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 243, + 547, + 303 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 547, + 303 + ], + "type": "text", + "content": "are positioned on the surface of the mesh. With the training proceeds with more poses, the embeddings generally bring the Gaussians to approximate the actual geometry and densify in the regions with rich texture. Figure 3 illustrates the development of the embeddings." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "text", + "content": "Differentiable rendering of Gaussian Splatting. With the position, rotation, and scaling of the Gaussians updated by the mesh deformation at frame " + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "text", + "content": ", we perform differentiable Gaussian rendering [23] to the observed camera view(s). The Gaussian in space is defined by its mean " + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "inline_equation", + "content": "\\mu" + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "text", + "content": " and a 3D covariance matrix " + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "inline_equation", + "content": "\\Sigma" + }, + { + "bbox": [ + 305, + 304, + 546, + 375 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 372, + 383, + 545, + 399 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 383, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 372, + 383, + 545, + 399 + ], + "type": "interline_equation", + "content": "G _ {i, t} (x) = e ^ {- \\frac {1}{2} (x) ^ {T} \\Sigma_ {i, t} ^ {- 1} (x)} \\tag {8}", + "image_path": "0ee5c91e51c79be6b6b8689f08bf904f5d4c127196a9ece7f08ba525561765d6.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 378, + 411, + 545, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 411, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 378, + 411, + 545, + 426 + ], + "type": "interline_equation", + "content": "\\Sigma_ {i, t} = R _ {i, t} S _ {i, t} S _ {i, t} ^ {T} R _ {i, t} ^ {T} \\tag {9}", + "image_path": "da4c083966fb3f1d15501bb9bc2887b8b0b9ff28ca01901d830afa8fd8b7dab6.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "inline_equation", + "content": "R_{i,t}" + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": " is the rotation matrix constructed from " + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "inline_equation", + "content": "q_{i,t}" + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "inline_equation", + "content": "S_{i,t}" + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": " the scaling matrix from " + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "inline_equation", + "content": "s_{i,t}" + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": ". Given the world-to-camera view matrix " + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": " and the Jacobian " + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "inline_equation", + "content": "J" + }, + { + "bbox": [ + 305, + 431, + 545, + 479 + ], + "type": "text", + "content": " of the point projection matrix. The influence of the Gaussian is splatted to 2D [54]:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 384, + 488, + 545, + 502 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 488, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 384, + 488, + 545, + 502 + ], + "type": "interline_equation", + "content": "\\Sigma^ {\\prime} = J W \\Sigma W ^ {T} J ^ {T} \\tag {10}", + "image_path": "ed1fca628e04ce69a9b0630aeaa779f83114c52c33001de7fc9aefeaf893dfef.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "spans": [ + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "text", + "content": "The image formation of Gaussian Splatting is akin to NeRF, where the same volume rendering formula is applied to the blending from near to far. The color " + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "text", + "content": " of a pixel rendered by " + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "text", + "content": " Gaussians is given by a series of " + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 512, + 547, + 561 + ], + "type": "text", + "content": "-blending:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 370, + 570, + 545, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 370, + 570, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 370, + 570, + 545, + 604 + ], + "type": "interline_equation", + "content": "C = \\sum_ {i = 1} ^ {N} c _ {i} \\alpha_ {i} \\prod_ {j = 1} ^ {i - 1} (1 - \\alpha_ {j}) \\tag {11}", + "image_path": "042efcd37763deb46f27e61d19d6b45fe41bf34d58b8b3eed64ac5262e2fc11d.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "spans": [ + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\alpha_{i}" + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "text", + "content": " evaluated from the 2D covariance, and an opacity in logit " + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "inline_equation", + "content": "o_{i}" + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "inline_equation", + "content": "\\mathrm{sigm}()" + }, + { + "bbox": [ + 305, + 613, + 545, + 637 + ], + "type": "text", + "content": " being the standard sigmoid function:" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 310, + 646, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 646, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 310, + 646, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\alpha_ {i} (P) = \\operatorname {s i g m} \\left(o _ {i}\\right) \\exp \\left(- \\frac {1}{2} \\left(P - \\mu_ {i}\\right) \\left(\\Sigma_ {i}\\right) ^ {- 1} \\left(P - \\mu_ {i}\\right)\\right) \\tag {12}", + "image_path": "d0c3d9adb81b7aaf7ac13e66f23c7687fa7cc1c9ced93a56b7004dc20f10b782.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 546, + 713 + ], + "type": "text", + "content": "The Equation 11 is implemented in CUDA with a for loop for each pixel, while in our Unity implementation, each Gaussian is drawn by a front-parallel Quad primitive based" + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1609" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "type": "text", + "content": "on the projection and 2D covariance. We resort to the standard rasterization pipeline of the rendering engine to enable " + }, + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 288, + 108 + ], + "type": "text", + "content": "-blending with these semi-transparent Gaussians." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "text", + "content": "Due to limited viewing angle and pose variations from monocular video, we propose a scaling regularization term to prevent Gaussians from growing long and thin. A random background color is generated every iteration to mix with the rendered image " + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "text", + "content": " and ground truth image " + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "inline_equation", + "content": "I_{gt}" + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "text", + "content": ", providing important cues for the silhouette. The loss is the sum of " + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_1" + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{mse}" + }, + { + "bbox": [ + 46, + 109, + 289, + 193 + ], + "type": "text", + "content": ", a perceptual loss [49], and a scaling regularization." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 63, + 214, + 288, + 228 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 214, + 288, + 228 + ], + "spans": [ + { + "bbox": [ + 63, + 214, + 288, + 228 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {1} + \\lambda_ {l _ {m s e}} \\mathcal {L} _ {m s e} + \\lambda_ {l} \\mathcal {L} _ {l p i p s} + \\lambda_ {s} \\mathcal {L} _ {\\text {s c a l i n g}} \\tag {13}", + "image_path": "04a2244c2b68a8910762e831400c0738ec413b319f2563ed519e4b482d5b987e.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 66, + 246, + 288, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 246, + 288, + 273 + ], + "spans": [ + { + "bbox": [ + 66, + 246, + 288, + 273 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {s c a l i n g}} (i) = \\left\\{ \\begin{array}{c c} | \\hat {s} _ {i} |, & \\hat {s} _ {i} > \\max \\left(T _ {s}, T _ {r} \\check {s} _ {i}\\right) \\\\ 0, & \\text {o t h e r w i s e} \\end{array} \\right. \\tag {14}", + "image_path": "138bddbc6c5ea14d7d4925cd5bdcd7e75b6ee041a0f89c108ccfa6e01755ae62.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": "With " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "s_i \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " being the scaling of a Gaussian, " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\hat{s}_i" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\check{s}_i" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " are the maximum and minimum scaling values respectively. The scaling regularization is posed on " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\hat{s}_i" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " when it is both long (larger than " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "T_s" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": ") and thin (larger than " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "T_r" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " times " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\check{s}_i" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": "). Please see Section 4.3 for an ablation study on the regularization term. Walking on a triangle mesh. The notion Lifted Optimization arises in the model-point registration for hand tracking [38, 40, 41] in contrast to Iterative Closest Point (ICP), where the solve for model pose and correspondences are lifted to be simultaneous. We extend this notion to our avatar training, where the properties of the Gaussians and the trainable embeddings are optimized simultaneously. The barycentric coordinate of a point " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "P" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "(k, u, v)" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " defined within triangle " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": ". When the learned update " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "Q = (k, u, v) + (\\delta u, \\delta v)" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " is outside triangle " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": ", we find the intersection " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "P'" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " on the shared edge of the adjacent triangle " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "k'" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " and re-express the remaining update in " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "k'" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "inline_equation", + "content": "Q' = P' + (\\delta u', \\delta v')" + }, + { + "bbox": [ + 46, + 281, + 289, + 581 + ], + "type": "text", + "content": ". Because the barycentric coordinates are agnostic to the triangle shape, without loss of generality, the re-expression is conducted by conceptually treating two adjacent triangles as right triangles with the intersection on the hypotenuse. The update is iteratively re-expressed until it ends inside the final triangle. We show the re-expression process in Figure 4. The detailed steps are presented in Algorithm 1. Noted that we omit the conceptual re-ordering of the vertices." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": "Optimization. We use Adam to optimize the Gaussian parameters and the embedding parameters. The original learning rate attenuation on position [23] is instead applied to the embedding parameters. We record the current barycentric " + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "inline_equation", + "content": "(u,v)" + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": " and optimize for " + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "inline_equation", + "content": "(\\delta u,\\delta v,d)" + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": ". The triangle walking in Algorithm 1 is implemented as a pybind11 module in C++. When an embedding is being transferred to another triangle, we reset its corresponding optimizer state of the " + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "inline_equation", + "content": "(\\delta u,\\delta v,d)" + }, + { + "bbox": [ + 46, + 582, + 288, + 677 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 714 + ], + "type": "text", + "content": "The densification process [23] plays an important role in allocating more Gaussians to where in need. In the clone and prune process, the embedding parameters are copied" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 313, + 72, + 387, + 141 + ], + "blocks": [ + { + "bbox": [ + 313, + 72, + 387, + 141 + ], + "lines": [ + { + "bbox": [ + 313, + 72, + 387, + 141 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 387, + 141 + ], + "type": "image", + "image_path": "7795c9900a40067eb63d56c9c20284a77c9f1e1994851ed8f68a284970605864.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 313, + 141, + 380, + 159 + ], + "lines": [ + { + "bbox": [ + 313, + 141, + 380, + 159 + ], + "spans": [ + { + "bbox": [ + 313, + 141, + 380, + 159 + ], + "type": "text", + "content": "a) Barycentric update starting from P" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "lines": [ + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "text", + "content": "Figure 4. Walking on triangles for embedding update. a) The recursion process of walking on a triangle mesh. b) The update " + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "inline_equation", + "content": "P + \\delta" + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "text", + "content": " starting from triangle " + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "inline_equation", + "content": "CAB" + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "text", + "content": " is re-expressed as " + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "inline_equation", + "content": "P' + \\delta'" + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "text", + "content": " in triangle " + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "inline_equation", + "content": "DBA" + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "text", + "content": ", and c) re-expressed again in " + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "inline_equation", + "content": "EDA" + }, + { + "bbox": [ + 304, + 169, + 547, + 236 + ], + "type": "text", + "content": ". The re-expression between two triangles is conducted by conceptually treating them as two right triangles adjacent to each other on the hypotenuse." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 398, + 79, + 462, + 138 + ], + "blocks": [ + { + "bbox": [ + 398, + 79, + 462, + 138 + ], + "lines": [ + { + "bbox": [ + 398, + 79, + 462, + 138 + ], + "spans": [ + { + "bbox": [ + 398, + 79, + 462, + 138 + ], + "type": "image", + "image_path": "167ac849a7c105b07d26e8ffcb28ac4d1f0c39f86538172d1a24963b0fee2283.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 396, + 140, + 457, + 158 + ], + "lines": [ + { + "bbox": [ + 396, + 140, + 457, + 158 + ], + "spans": [ + { + "bbox": [ + 396, + 140, + 457, + 158 + ], + "type": "text", + "content": "b) Triangle walking " + }, + { + "bbox": [ + 396, + 140, + 457, + 158 + ], + "type": "inline_equation", + "content": "CAB \\rightarrow DBA" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 474, + 79, + 534, + 138 + ], + "blocks": [ + { + "bbox": [ + 474, + 79, + 534, + 138 + ], + "lines": [ + { + "bbox": [ + 474, + 79, + 534, + 138 + ], + "spans": [ + { + "bbox": [ + 474, + 79, + 534, + 138 + ], + "type": "image", + "image_path": "199c34ee6a90979ad7477756bb3d63be67fcf3d9e0c1d064e752592d95b19cd1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 471, + 140, + 533, + 158 + ], + "lines": [ + { + "bbox": [ + 471, + 140, + 533, + 158 + ], + "spans": [ + { + "bbox": [ + 471, + 140, + 533, + 158 + ], + "type": "text", + "content": "c) Triangle walking " + }, + { + "bbox": [ + 471, + 140, + 533, + 158 + ], + "type": "inline_equation", + "content": "BAD \\to EDA" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "code", + "bbox": [ + 306, + 262, + 545, + 521 + ], + "blocks": [ + { + "bbox": [ + 306, + 249, + 446, + 262 + ], + "lines": [ + { + "bbox": [ + 306, + 249, + 446, + 262 + ], + "spans": [ + { + "bbox": [ + 306, + 249, + 446, + 262 + ], + "type": "text", + "content": "Algorithm 1 Walking on triangles" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "lines": [ + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": "Input: " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "k, u, v, \\delta u, \\delta v" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nOutput: " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\hat{k}, \\hat{u}, \\hat{v}" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nfunction WALKONTRIANGLES" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(k, u, v, \\delta u, \\delta v)" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "P \\leftarrow (u, v)" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "Q \\leftarrow (u + \\delta u, v + \\delta v)" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nif Q is inside triangle then \nReturn " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(k, Q.u, Q.v)" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nend if \nIntersect " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "P-Q" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " with hypotenuse* on " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(u', v')" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\triangleright" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " *reorder vertices if needed \n" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\delta u' \\leftarrow \\delta u - (u' - u)" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\delta v' \\leftarrow \\delta v - (v' - v)" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nReturn ReExpress" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(k, u', v', \\delta u', \\delta v')" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nend function \nfunction REEXPRESS" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(k, u', v', \\delta u', \\delta v')" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\hat{k} \\leftarrow" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " adjacent of " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\hat{u} \\leftarrow 1 - u'" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\hat{v} \\leftarrow 1 - v'" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\delta \\hat{u} \\leftarrow -\\delta u'" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\delta \\hat{v} \\leftarrow -\\delta v'" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nReturn WalkOnTriangles" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(\\hat{k}, \\hat{u}, \\hat{v}, \\delta \\hat{u}, \\delta \\hat{v})" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " \nend function \n" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(\\hat{k}, \\hat{u}, \\hat{v}) \\leftarrow" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "text", + "content": " WalkOnTriangles" + }, + { + "bbox": [ + 306, + 262, + 545, + 521 + ], + "type": "inline_equation", + "content": "(k, u, v, \\delta u, \\delta v)" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "code_body" + } + ], + "index": 15, + "sub_type": "algorithm" + }, + { + "bbox": [ + 304, + 541, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 545, + 590 + ], + "type": "text", + "content": "or deleted in the same way as Gaussian parameters. In the split process, when a new position " + }, + { + "bbox": [ + 304, + 541, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\hat{\\mu}" + }, + { + "bbox": [ + 304, + 541, + 545, + 590 + ], + "type": "text", + "content": " is sampled from the Gaussian, we solve a mini problem with triangle walking to find the new embedding:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 318, + 598, + 545, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 598, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 318, + 598, + 545, + 619 + ], + "type": "interline_equation", + "content": "\\hat {E} = \\underset {k, u, v, d} {\\arg \\min } \\| \\mathcal {V} (k, u, v) + d * \\mathcal {N} (k, u, v) - \\hat {\\mu} \\| _ {2} ^ {2} \\tag {15}", + "image_path": "4902ce7f9a152f1bf248781f4807ab7706ef5caf8b5564624889688f87ca3f91.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 629, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 547, + 714 + ], + "type": "text", + "content": "Unity implementation for mobile device. With maximum compatibility in mind, we made SplattingAvatar solely rely on the warped mesh. Before exporting to Unity, we uploaded the canonical mesh in .obj format to Mixamo [1] for autorigging. In total, we exported one .ply file of the Gaussians, one .json file describing the embedding, and one .fbx file from Mixamo to Unity. Note that the .fbx file can be rigged" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1610" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 69, + 542, + 371 + ], + "blocks": [ + { + "bbox": [ + 53, + 69, + 542, + 371 + ], + "lines": [ + { + "bbox": [ + 53, + 69, + 542, + 371 + ], + "spans": [ + { + "bbox": [ + 53, + 69, + 542, + 371 + ], + "type": "image", + "image_path": "a72704280f49ada581aa1f28b6e9038a965c5cefe0db5ca8ddf8e105dcb57c1c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 377, + 548, + 445 + ], + "lines": [ + { + "bbox": [ + 46, + 377, + 548, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 548, + 445 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison on head avatars. SplattingAvatar produces photorealistic rendering for avatars with high-quality details especially in the eye and hair regions. Even the light reflection on the glasses is well reconstructed. Both PointAvatar [51] and NHA [16] can reconstruct good geometries but the rendering quality is limited by their underlying representations, i.e., points and texture atlas respectively. Compared to INSTA [53], our trainable embedding scheme produces better quality for off-surface geometries, especially for the glasses. The green arrows highlight where our results have better consistency with Ground Truth, while the red arrows point to where other methods show significant artifacts or noise. Please see the supplemental materials for illustrations of the error map." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 464, + 287, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 488 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 488 + ], + "type": "text", + "content": "by any other software for customized needs, as long as the triangle order is maintained." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 489, + 289, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 489, + 289, + 646 + ], + "spans": [ + { + "bbox": [ + 46, + 489, + 289, + 646 + ], + "type": "text", + "content": "We implemented the Gaussian renderer in Unity's compute shaders, starting from sorting all Gaussians by the z-axis in camera coordinates from near to far. Based on the calculated 2D covariance " + }, + { + "bbox": [ + 46, + 489, + 289, + 646 + ], + "type": "inline_equation", + "content": "\\Sigma'" + }, + { + "bbox": [ + 46, + 489, + 289, + 646 + ], + "type": "text", + "content": ", one front-parallel quad primitive is drawn for every visible Gaussian centered at its position. This one-primitive-one-Gaussian strategy is important for the game engine to properly handle the occlusion of other regular objects. For every pixel to draw in the fragment Shader, our implementation emits color with alpha pre-multiplication and sets the blend function to (ONE, ONE_MINUS_SRC_alpha). Our Unity program achieves a high performance of over 300 FPS on a modern GPU while maintaining a steady 30 FPS on an iPhone 13." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 657, + 128, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 657, + 128, + 671 + ], + "spans": [ + { + "bbox": [ + 47, + 657, + 128, + 671 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "To demonstrate the effectiveness of SplittingAvatar, we compared it with state-of-the-art (SoTA) methods in two different types of datasets for head and full-body avatars." + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 323, + 462, + 529, + 553 + ], + "blocks": [ + { + "bbox": [ + 323, + 462, + 529, + 553 + ], + "lines": [ + { + "bbox": [ + 323, + 462, + 529, + 553 + ], + "spans": [ + { + "bbox": [ + 323, + 462, + 529, + 553 + ], + "type": "table", + "html": "
MethodPSNR↑SSIM↑LPIPS↓
NHA [16]20.290.8830.145
INSTA [53]26.420.9240.080
PointAvatar [51]27.840.9130.067
Ours+FLAME28.190.9310.063
Ours+NHA28.860.9310.060
", + "image_path": "e3d7d10c221fc54f14b280ba419ee156a98350a66186e7cb4784b0ecacd5b2c3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 561, + 548, + 628 + ], + "lines": [ + { + "bbox": [ + 304, + 561, + 548, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 561, + 548, + 628 + ], + "type": "text", + "content": "Table 1. Quantitative comparison on head avatars. Both variations of our method outperform existing methods in terms of average photometric errors. With detailed meshes from NHA [16], Ours+NHA performs the best based on the metrics. However, we observe better visual quality with Ours+FLAME in the inner regions of the rendered image." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 646, + 369, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 646, + 369, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 646, + 369, + 658 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 548, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 548, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 548, + 713 + ], + "type": "text", + "content": "Monocular video for head avatar. Taking a single monocular video to construct a head avatar for the given subject, our method takes as input images, masks, camera parameters, and tracked FLAME meshes, denoting Ours+FLAME. We" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 314, + 757 + ], + "type": "text", + "content": "1611" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 69, + 541, + 308 + ], + "blocks": [ + { + "bbox": [ + 52, + 69, + 541, + 308 + ], + "lines": [ + { + "bbox": [ + 52, + 69, + 541, + 308 + ], + "spans": [ + { + "bbox": [ + 52, + 69, + 541, + 308 + ], + "type": "image", + "image_path": "90f59808529981c35eb299632ae45cea4ba5008d047a39777258f583fc630f0b.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 316, + 546, + 352 + ], + "lines": [ + { + "bbox": [ + 46, + 316, + 546, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 546, + 352 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison on PeopleSnapshot [2]. We show the results on PeopleSnapshot (columns 2-4) and novel pose animation (columns 5-6). SplittingAvatar produces photorealistic rendering for full-body avatars, especially in the facial area, and captures thin structures like the accessory on the wrist." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 361, + 545, + 429 + ], + "blocks": [ + { + "bbox": [ + 48, + 361, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 48, + 361, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 48, + 361, + 545, + 429 + ], + "type": "table", + "html": "
male-3-casualmale-4-casualfemale-3-casualfemale-4-casual
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
Anim-NeRF [7]29.370.9700.01728.370.9600.02728.910.9740.02228.900.9680.017
InstantAvatar [21]30.910.9770.02229.770.9800.02529.730.9750.02530.920.9770.021
Ours33.010.9820.02030.990.9820.02930.810.9780.02832.570.9810.018
", + "image_path": "d1bdbbaa6cc2375b1a6a4761d96fdc2e3c4ca2619d0a13e73d7a47291c01e041.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 435, + 546, + 460 + ], + "lines": [ + { + "bbox": [ + 46, + 435, + 546, + 460 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 546, + 460 + ], + "type": "text", + "content": "Table 2. Quantitative comparison on PeopleSnapshot. Compared to two SoTA methods, we achieve significant improvements in pixel-wise quality with PSNR and SSIM. All three methods achieve good perceptual quality in terms of LPIPS where the metrics are close." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 475, + 290, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 290, + 632 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 290, + 632 + ], + "type": "text", + "content": "evaluated our approach with several SoTA methods on a combined dataset from NHA [16], NerFace [15], INSTA [53] and PointAvatar [51], including 10 subjects covering different videos captured with DSLR, smartphones and from the Internet. The pre-processing pipeline of IMavatar [50] and INSTA [53] was altered to apply DECA [12] for face tracking, RVM [37] for segmentation, and BisenetV2 [46] for face parsing. For each video, the last 350 frames were used as testing samples. Because our method can directly be animated by the given mesh, we further unleashed its potential by training and testing on the generated meshes from NHA [16] which have more geometry details. This variation is referred to as Ours+NHA." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": "PeopleSnapshot. We conducted a quantitative evaluation of the rendering quality of full-body avatars on the PeopleSnapshot [2] dataset. Following the protocol of InstantAvatar [21], we used SMPL meshes refined by Anim-NeRF [7]. Our method demonstrates the generalizability to novel poses through qualitative analysis in Section 4.2." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 475, + 440, + 488 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 475, + 440, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 475, + 440, + 488 + ], + "type": "text", + "content": "4.2. Comparison with SoTA" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 547, + 567 + ], + "type": "text", + "content": "Head avatar. To evaluate the rendering quality of the learned avatars, we animated SplattingAvatar with the registered meshes of testing images. For Ours+NHA, we trained NHA [16] on the training set and extracted the final meshes for both the training and testing images, which were further used for the training and testing of our method respectively." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 568, + 548, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 548, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 548, + 688 + ], + "type": "text", + "content": "We conducted a comparative analysis of SplittingAvatar against INSTA [53], PointAvatar [51], and NHA [16]. As depicted in Figure 5, our method achieves superior quality in terms of improved details in the eye and hair regions, and even being able to capture the light reflection on the glasses. For Ours+FLAME, though the off-surface geometries like hair and glasses are not fully represented by meshes, our method can handle the rendering decently because the embeddings are optimized to find correct motions from nearby triangles. Please see Table 1 for quantitative evaluations." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 689, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 548, + 715 + ], + "type": "text", + "content": "Full-body avatar. We made a comparison to InstantAvatar [21] and Anim-NeRF [7] on PeopleSnapshot. For In" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 758 + ], + "type": "text", + "content": "1612" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "stantAvatar [21], a complete training was performed for 200 epochs as suggested in the most recent version of the author's code. Image quality metrics in Table 2 demonstrate the effectiveness of our method in terms of the lowest pixelwise errors. We qualitatively show the comparison of rendering quality of testing images in Figure 6, together with the demonstration of generalizability to novel poses. Our representation is friendly to thin structures like the accessory on the wrist. Our approach produced better quality overall and especially in the facial area compared to InstantAvatar [21], but slightly more artifacts under the shoulder due to very limited pose variations in the training set. We believe this can be much improved with more training poses." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 236, + 141, + 248 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 236, + 141, + 248 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 141, + 248 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 254, + 287, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 254, + 287, + 349 + ], + "spans": [ + { + "bbox": [ + 46, + 254, + 287, + 349 + ], + "type": "text", + "content": "Trainable embedding. The key component of our method is the trainable embedding on the mesh. We conducted an ablation experiment by replacing it with fixed embedding on mesh and a trainable local shift " + }, + { + "bbox": [ + 46, + 254, + 287, + 349 + ], + "type": "inline_equation", + "content": "\\Delta x \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 46, + 254, + 287, + 349 + ], + "type": "text", + "content": " per Gaussian. Without trainable embedding, the Gaussians encountered difficulties in following the mesh correctly. The right column of Figure 7 shows the irregular rendering artifacts without trainable embedding." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 350, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 350, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 350, + 287, + 409 + ], + "type": "text", + "content": "Regularization. In the optimization process of Gaussian Splatting, some Gaussians turn to become long and thin, generating artifacts when rendered into novel poses. We show the results without the scaling regularization in the middle column of Figure 7." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 72, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 547, + 228 + ], + "type": "text", + "content": "underlying mesh. In the comparison between Ours+FLAME and Ours+NHA, we observe that the driving mesh should focus on the motion instead of fully reconstructing the exact geometry. In Figure 8 we show that when the mesh with vertex offsets from NHA [16] is applied, the detailed surface deformation improves the generalizability of SplattingAvatar to large poses. However, in the second and third row of Figure 5, the mesh from FLAME that captures the correct motion of the glasses rather than the shape is driving the best rendering quality of SplattingAvatar. To perform textured mesh rendering, the mesh of NHA [16] is seamed in the mouth region and deformed to fit the shape of the glasses, yet both being unhelpful to the quality of Ours+NHA." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 228, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 228, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 305, + 228, + 547, + 312 + ], + "type": "text", + "content": "Limitations and future work. As discussed above, our method depends on the motion representation ability of the driving mesh. With current FLAME and SMPL models, we do not have separate motion representations for clothes and hair. We believe SplattingAvatar can support future works on human avatars with disentangled mesh representations, e.g., separate meshes for clothes and hair stands." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 310, + 319, + 544, + 407 + ], + "blocks": [ + { + "bbox": [ + 310, + 319, + 544, + 407 + ], + "lines": [ + { + "bbox": [ + 310, + 319, + 544, + 407 + ], + "spans": [ + { + "bbox": [ + 310, + 319, + 544, + 407 + ], + "type": "image", + "image_path": "ca0fca2348664c809ad0cd94ca7368986bfc766babea73539e74194ac456d840.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 417, + 547, + 450 + ], + "lines": [ + { + "bbox": [ + 305, + 417, + 547, + 450 + ], + "spans": [ + { + "bbox": [ + 305, + 417, + 547, + 450 + ], + "type": "text", + "content": "Figure 8. Comparison between Ours+FLAME and Ours+NHA. The better aligned mesh from NHA [16] improves the generalizability of SplattingAvatar to large pose variations." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 50, + 419, + 284, + 561 + ], + "blocks": [ + { + "bbox": [ + 50, + 419, + 284, + 561 + ], + "lines": [ + { + "bbox": [ + 50, + 419, + 284, + 561 + ], + "spans": [ + { + "bbox": [ + 50, + 419, + 284, + 561 + ], + "type": "image", + "image_path": "d33b11b4690962ff013b31561a635dc1d66a23dedbb5cdbbfd3e1c0826e9a884.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 571, + 288, + 639 + ], + "lines": [ + { + "bbox": [ + 46, + 571, + 288, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 288, + 639 + ], + "type": "text", + "content": "Figure 7. Ablation study. Without the scaling regularization term, Gaussians that are long and thin cause needle-like artifacts. Without trainable embedding, Gaussians do not follow the movement of the mesh tightly, leading to irregular rendering results. The application of our trainable embedding and the scaling term successfully removes most of the artifacts when rendered into novel poses." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 658, + 119, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 119, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 119, + 670 + ], + "type": "text", + "content": "4.4. Discussion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 713 + ], + "type": "text", + "content": "Discussion on driving mesh. Considering efficiency, compatibility, and portability, SplattingAvatar is designed to tightly rely on the motion and surface deformation of the" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 472, + 378, + 484 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 472, + 378, + 484 + ], + "spans": [ + { + "bbox": [ + 306, + 472, + 378, + 484 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 492, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 492, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 305, + 492, + 547, + 647 + ], + "type": "text", + "content": "In this paper, we have proposed a hybrid representation for human avatar modeling featuring Gaussian Splatting with trainable embeddings on a mesh. We extend lifted optimization to simultaneously optimize the parameters of the Gaussians and their embeddings. Our method leverages the advantages of the explicit motion representation with a mesh and implicit rendering capability of Gaussian Splatting. Compared with SoTA methods, our approach achieves the best rendering quality for both head and full-body avatars reconstructed from monocular videos and runs at real-time frame rates on a mobile device. Our method lays a foundation for future work in Gaussian Splatting manipulation with mesh-based motion control." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 403, + 671 + ], + "type": "text", + "content": "Acknowledgments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "This work was partially supported by Guangzhou-HKUST(GZ) Joint Funding #2023A03J0670 and Guangzhou Basic Research Scheme #2024A04J4229." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 748, + 315, + 757 + ], + "type": "text", + "content": "1613" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 288, + 112 + ], + "type": "text", + "content": "[1] Mixamo. https://www MIXamo.com/. 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Association for Computing Machinery. 4" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 296, + 749, + 315, + 757 + ], + "type": "text", + "content": "1616" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/0b95bf41-b7e1-4df0-9ad3-d873e89c86e9_content_list.json b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/0b95bf41-b7e1-4df0-9ad3-d873e89c86e9_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f59212c1f5d83291c6f3d1e0d165162506d9975a --- /dev/null +++ b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/0b95bf41-b7e1-4df0-9ad3-d873e89c86e9_content_list.json @@ -0,0 +1,1742 @@ +[ + { + "type": "text", + "text": "Split to Merge: Unifying Separated Modalities for Unsupervised Domain Adaptation", + "text_level": 1, + "bbox": [ + 233, + 130, + 736, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xinyao Li $^{1}$ Yuke Li $^{2*}$ Zhekai Du $^{1}$ Fengling Li $^{3}$ Ke Lu $^{1}$ Jingjing Li $^{1*}$ $^{1}$ University of Electronic Science and Technology of China \n $^{2}$ Boston College $^{3}$ University of Technology Sydney", + "bbox": [ + 171, + 202, + 803, + 256 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "xinyao326@outlook.com, lidwh@bc.edu, zhekaid@std.uestc.edu.cn", + "bbox": [ + 210, + 258, + 754, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "fenglingli2023@gmail.com, kel@uestc.edu.cn, lijin117@yeah.net", + "bbox": [ + 210, + 277, + 753, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Large vision-language models (VLMs) like CLIP have demonstrated good zero-shot learning performance in the unsupervised domain adaptation task. Yet, most transfer approaches for VLMs focus on either the language or visual branches, overlooking the nuanced interplay between both modalities. In this work, we introduce a Unified Modality Separation (UniMoS) framework for unsupervised domain adaptation. Leveraging insights from modality gap studies, we craft a nimble modality separation network that distinctly disentangles CLIP's features into language-associated and vision-associated components. Our proposed Modality-Ensemble Training (MET) method fosters the exchange of modality-agnostic information while maintaining modality-specific nuances. We align features across domains using a modality discriminator. Comprehensive evaluations on three benchmarks reveal our approach sets a new state-of-the-art with minimal computational costs. Code: https://github.com/TL-UESTC/UniMoS.", + "bbox": [ + 75, + 357, + 473, + 630 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 657, + 209, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unsupervised domain adaptation (UDA) [2, 7, 29, 30] aims to apply knowledge trained on a source domain to an unlabeled target domain, a process invaluable in data-scarce scenarios. Conventional methods often struggle with bridging the gap between source and target domains, finding it challenging to develop consistent features across domains [19, 39]. In image classification, aligning vision features while neglecting semantic content can lead to difficulties in differentiating complex samples [10, 41]. Vision-language models (VLMs) such as CLIP [36] and ALIGN [13] circumvent these issues through joint multimodal pretraining on images and texts. This extensive pretraining endows publicly available VLMs with robust zero-shot transfer abl-", + "bbox": [ + 75, + 681, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/33cbdc16c5614d7b3ad158a09fee11ee6450b9bf8b3c153969fda50c87b164cb.jpg", + "image_caption": [ + "Figure 1. Examples of modality-specific information from task Art $\\rightarrow$ RealWorld in Office-Home dataset. The digits are top-2 highest classification probabilities given by both modalities." + ], + "image_footnote": [], + "bbox": [ + 522, + 335, + 661, + 406 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/5f231e916ff007618f1564f626900c53d4f478be314016a1b54c2d718c4a00fb.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Modality / Prob.couchchair (√)
image modality0.0020.998
text modality0.8320.130
", + "bbox": [ + 522, + 407, + 679, + 449 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f063ea6fb9027d8c91ba7e4cff3d54c0b84e293e0ad20e083f25a2f45dd37a91.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 712, + 327, + 846, + 406 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/7257245fdc27123806835b73bcafa48dbe17080be743bebca12b426aea8bd071.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Modality / Prob.shelffile cabinet ( \\( \\checkmark \\) )
image modality0.8990.101
text modality0.0620.928
", + "bbox": [ + 694, + 407, + 864, + 449 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ities and a broad base of conceptual knowledge, making them highly suitable for comprehensive UDA. They facilitate alignment across both visual and textual modalities, enhancing adaptability and applicability in diverse contexts.", + "bbox": [ + 496, + 506, + 890, + 566 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Previous studies have shown promising results by adapting VLMs like CLIP for unsupervised domain adaptation (UDA). For instance, DAPrompt [10] introduces learning both domain-agnostic and domain-specific text embeddings, while PADCLIP [17] focuses on fine-tuning the vision branch of CLIP for adaptive visual feature extraction. However, recent research [14, 24] highlights a modality gap in VLMs, revealing that, despite training efforts, vision and text features often remain distinctly distributed. We argue that adapting a single modality is less than ideal due to the existence of unique, modality-specific cues in misaligned textual and visual components. We suggest that certain samples are best classified using specific modalities, a hypothesis supported by empirical observations in Fig. 1. This figure shows differing classification patterns when each modality is adapted independently to the unlabeled target data. Text modality results derive from CLIP's zero-shot capabilities, while image results come from linear probing with target pseudo-labels. For instance, visually straightforward items like a cushioned chair are accurately classified by the vision linear classifier after tuning on target dataset. However, pretrained CLIP can erroneously cat", + "bbox": [ + 496, + 568, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23364", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "egorize such items under visually similar classes. In contrast, complex items with nuanced semantic details, like a file cabinet resembling a shelf, may confuse the vision classifier, while CLIP's broader knowledge base facilitates correct zero-shot predictions. In summary, while the vision branch effectively discerns class-specific visual patterns, the text branch leverages semantic information to clarify ambiguous cases. This observation lays the groundwork for a multimodal adaptation framework that synergistically combines the strengths of both modalities.", + "bbox": [ + 75, + 90, + 470, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A direct approach to domain adaptation involves concurrently fine-tuning vision branch and crafting textual prompts, which risks disturbing the image-text representation pairs in pretrained CLIP and is computationally intensive [9, 57]. As a more efficient alternative, we propose to explicitly disentangle CLIP-extracted visual features into two complementary parts. The first component retains the language-associated semantic knowledge inherent in CLIP, while the second focuses on vision-specific attributes crucial for distinguishing between nuanced visual categories.", + "bbox": [ + 75, + 244, + 468, + 396 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We devised a set of modality separation networks with dual branches to project CLIP-encoded visual features into distinct language-associated components (LAC) and vision-associated components (VAC). An orthogonal regularization is employed to ensure these branches yield discrete, disentangled representations. Each component is optimized based on its inherent modality strengths. For the LAC branch, we utilize knowledge distillation on target data to harness the rich semantic content from the original pretrained CLIP model. Additionally, we implement a debiasing method to mitigate dataset bias in CLIP's zero-shot results. For the VAC branch, the locality structure within visual feature spaces [20, 53, 54] is leveraged to generate visual pseudo-labels for supervised learning on target data. We then introduce a novel Modality-Ensemble Training (MET) strategy that synergistically merges outputs from both modalities. A weight generator dynamically assembles these predictions, supervised by VAC pseudo-labels on target data and actual labels on source data. Importantly, the text modality output remains isolated during MET to preserve independent training and maintain pretrained semantics. Additionally, a modality discriminator is utilized to align LAC and VAC across domains for unsupervised domain adaptation. Trained on source data to distinguish between LAC and VAC, this discriminator is frozen on the target domain, directly updating the separation networks to produce domain-invariant LAC and VAC. This approach ensures a consistent modality separation across domains, facilitating simultaneous adaptation in both modalities.", + "bbox": [ + 75, + 398, + 470, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions: 1. We investigate the modality gap phenomenon in the context of applying Vision-Language Models (VLMs) to unsupervised domain adaptation, revealing the limitations of adapting a single modality; 2. We intro-", + "bbox": [ + 76, + 839, + 468, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "duce a novel framework, Unified Modality Separation (UniMoS), which, coupled with a Modality-Ensemble Training (MET) approach, facilitates effective multimodal adaptation; 3. Our comprehensive analysis and validations underscore and efficiency of the proposed UniMoS, demonstrating its ability to set new state-of-the-art benchmarks while maintaining low computational demands.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 500, + 210, + 637, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised domain adaptation (UDA). A core challenge in UDA is aligning representations between the source domain and unlabeled target domain. Prior techniques can be categorized as discrepancy-based [18, 28, 59] and adversarial methods [7, 30, 39]. Discrepancy-based methods explicitly minimizes divergence metrics including MMD [18], MDD [59], etc. Adversarial methods extract domain invariant features via a min-max game between the feature extractor and domain discriminator [7, 30]. Recent works focus on exploiting target data structures via self-training techniques [15, 53-55, 60]. ICON [55] learns an invariant classifier with consistent predictions to remove the spurious correlation inconsistency in the target domain. EIDCo [60] combines Mixup [56] with IDCo loss [5, 12] to explore target data distribution. Vision transformer (ViT) [6] and its variants have also gained popularity due to their superior performance [51, 52, 63]. PMTrans [63] mixes patch representations in SwinTransformer [27] as an intermediate domain bridge. CDTrans [51] aligns features extracted by DeiT [44] via cross-attention.", + "bbox": [ + 496, + 234, + 890, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Vision-language models (VLMs) have shown great generalization abilities due to extensive multimodal pretraining [13, 36, 47, 48]. CLIP [36] is trained from 400 million text-image pairs, while ALIGN [13] leverages more than one billion text-image pairs. Subsequent works have built on pretrained VLMs in various ways. Some learn prompt texts to transfer VLMs to downstream tasks [10, 33, 38, 61, 62], while others incorporate additional tunable layers on the frozen pretrained encoder [9, 57]. Beyond utilizing existing VLMs, research also aims to improve VLM training [14, 31]. Liang et al. [24] reveal that VLMs exhibit a modality gap, failing to perfectly align multimodal features. Jiang et al. [14] conduct theoretical analysis on modality gap and propose latent space regularization to preserve modality-specific information. MaPLe [16] utilize prompt learning on both modality branches to improve alignment. Our approach is fundamentally different since we disentangle VLM-extracted features posteriorly instead of training VLM from scratch, requiring far less computation costs. Besides, our method requires no labeling on target domain. VLMs have also been adopted for UDA [10, 17, 41]. DAPrompt [10] learns domain-specific and domain-agnostic textual prompts for each class. ADCLIP [41] learns domain invariant prompts by conditioning", + "bbox": [ + 496, + 537, + 890, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23365", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/25449e5ea3aa30d8207f56872986ac020ecf191956a4fae6681e40f3fb1e2969.jpg", + "image_caption": [ + "Figure 2. Framework of our method. We freeze the pretrained vision and text encoder of CLIP. CLIP-extracted vision features are disentangled into language-associated components $(f_{lac})$ and vision-associated components $(f_{vac})$ by the modality separation networks. We obtain zero-shot results from CLIP as teacher knowledge, and distill the knowledge to LAC. We then introduce a weight generator to assemble the modality outputs to train VAC. A modality discriminator is applied to align LAC and VAC from both domains." + ], + "image_footnote": [], + "bbox": [ + 125, + 89, + 851, + 299 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "on image style and content features. PADCLIP [17] dynamically adjusts learning rate while tuning CLIP to prevent catastrophic forgetting. However, these methods perform adaptation on either the visual or textual modality in isolation. Our work addresses this limitation by proposing a unified adaptation framework for the multimodal features.", + "bbox": [ + 75, + 369, + 472, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 472, + 171, + 488 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem formulation", + "text_level": 1, + "bbox": [ + 76, + 497, + 274, + 512 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this study, superscripts differentiate domains, with symbols lacking superscripts applicable to both domains. We consider a labeled source domain $\\mathcal{D}^s = \\{(x_i^s,y_i^s)\\}_{i = 1}^{N^s}$ and aim to develop a model generalizable to an unlabeled target domain $\\mathcal{D}^t = \\{(x_i^t)\\}_{i = 1}^{N^t}$ . CLIP [36] features a vision encoder $g_{vis}$ and a text encoder $g_{txt}$ . The vision feature for an image input $x$ is denoted as $f_{v} = g_{vis}(x)$ . Employing the zero-shot inference strategy from [17], we construct naive prompts $\\{(t_i)\\}_{i = 1}^K$ as a [DOMAIN] photo of a [CLASS], with $K$ representing the number of classes, [DOMAIN] indicating domain specifics, and [CLASS] the class name. Text features are then derived as $\\mu_{i} = g_{txt}(t_{i})$ . $\\mu_{i}$ and $f_{v}$ are both features with $d_v$ dimension. Classification is based on the highest cosine similarity between $f_{v}$ and $\\mu_{i}$ :", + "bbox": [ + 75, + 520, + 472, + 733 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {z s} = \\underset {i} {\\arg \\max } \\cos \\left(\\mu_ {i}, f _ {v}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 176, + 739, + 468, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Eq. (1) may not be ideal for unlabeled target data due to the existence of modality gap [24]. To tackle this, we conceptualize vision inputs as a composite of a vision-associated component (VAC) and a language-associated component (LAC), denoted as $f_{v} = \\{f_{vac}, f_{lac}\\}$ . This leads us to obtain modality-specific classification results $y_{vac}$ and $y_{lac}$ , before constructing a cross-modality output:", + "bbox": [ + 75, + 770, + 472, + 878 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny _ {e n s} = w \\cdot y _ {v a c} + (1 - w) \\cdot y _ {l a c}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 160, + 885, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $w$ is a set of learnable weights harmonizing the contributions of VAC and LAC. This design seeks to balance modality-agnostic information sharing and modality-specific information capturing.", + "bbox": [ + 496, + 369, + 890, + 430 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Instead of separating LAC and VAC during training, we utilize $y_{ens}$ to guide VAC learning, incorporating complementary modality information for a holistic cross-modal training. Furthermore, a fixed weight $w$ may lack flexibility across diverse datasets and scenarios, potentially obscuring the distinction between VAC and LAC. Addressing this, we introduce a dynamic $w$ that adeptly discriminates between modalities within $y_{ens}$ , calibrating their influence in the training. This strategy ensures tailored training approaches for different datasets or training stages, facilitating modality-specific information utilization. Next we detail on the training and aligning of LAC and VAC.", + "bbox": [ + 496, + 430, + 892, + 613 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Modality separation networks", + "text_level": 1, + "bbox": [ + 500, + 622, + 767, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first introduce the modality separation networks that disentangles CLIP-extracted features, which comprise two separators as shown in Fig. 2. These networks partition CLIP-extracted vision features into LAC and VAC using the text separator $G_{txt}$ and the vision separator $G_{vis}$ , respectively. The separated components are defined as $f_{lac} = G_{txt}(f_v)$ and $f_{vac} = G_{vis}(f_v)$ . Both separators are linear layers preserving the dimensionality of $f_v$ , such that $f_{vac}, f_{lac} \\in \\mathbb{R}^{d_v}$ . Drawing on deep feature separation principles [3], we apply an orthogonal loss to maintain the distinctness of LAC and VAC:", + "bbox": [ + 496, + 646, + 893, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {o r t h o}} = \\left| f _ {l a c} ^ {s} \\cdot f _ {v a c} ^ {s} \\right. ^ {\\top} | _ {F} ^ {2} + \\left| f _ {l a c} ^ {t} \\cdot f _ {v a c} ^ {t} \\right. ^ {\\top} | _ {F} ^ {2}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 821, + 892, + 843 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Different outputs for LAC and VAC are then generated. For the text modality, we utilize the zero-shot inference of CLIP to classify LAC by calculating the cosine similarity", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23366", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "between LAC and CLIP's text features, forming logits:", + "bbox": [ + 76, + 90, + 439, + 106 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {l a c} = \\left(\\hat {l} _ {1}, \\hat {l} _ {2}, \\dots \\hat {l} _ {k}\\right), \\quad \\hat {l} _ {i} = \\cos \\left(\\mu_ {i}, f _ {l a c}\\right) / T, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 111, + 468, + 130 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $T$ is temperature in pretrained CLIP. For VAC, we route it through a linear classifier with layers $\\Phi_1 \\in \\mathbb{R}^{d_v \\times d_b}$ and $\\Phi_2 \\in \\mathbb{R}^{d_b \\times K}$ , producing the bottleneck feature with dimension $d_b$ and output via:", + "bbox": [ + 76, + 136, + 468, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {b} = \\Phi_ {1} \\left(f _ {v a c}\\right), \\quad \\hat {y} _ {v a c} = \\Phi_ {2} \\left(f _ {b}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 205, + 468, + 220 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We provide implementation details in Supplementary.", + "bbox": [ + 76, + 228, + 431, + 243 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Modality-ensemble training", + "text_level": 1, + "bbox": [ + 76, + 250, + 326, + 266 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Having obtained disentangled components, we design customized training paradigm for each modality. A learnable weight further connects both modalities, establishing a unified modality-ensemble training framework.", + "bbox": [ + 76, + 273, + 468, + 334 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning LAC. To preserve the rich semantic content in pretrained CLIP, we distill this knowledge to LAC. For the target data, zero-shot similarity scores derived from pretrained CLIP serve as the teacher knowledge:", + "bbox": [ + 76, + 334, + 468, + 393 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {l a c} ^ {t} = \\left(l _ {1} - \\bar {l}, l _ {2} - \\bar {l}, \\dots , l _ {k} - \\bar {l}\\right), \\quad l _ {i} = \\cos \\left(\\mu_ {i}, f _ {v} ^ {t}\\right) / T, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 400, + 468, + 419 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\bar{l} = \\frac{1}{K}\\sum_{k=1}^{K}l_k$ normalizing the CLIP outputs and $T$ the temperature of pretrained CLIP. The teacher knowledge in Eq. (6) guides the distillation for the unlabeled target LAC, while for the source data, cross-entropy loss is applied directly using labeled source data. The overall training loss for LAC combines Eq. (4) and Eq. (6) as follows:", + "bbox": [ + 76, + 425, + 468, + 517 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {l a c} = \\mathrm {K L} \\left(\\hat {y} _ {l a c} ^ {t}, y _ {l a c} ^ {t}\\right) + \\alpha \\mathrm {C E} \\left(\\hat {y} _ {l a c} ^ {s}, y ^ {s}\\right), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 523, + 468, + 542 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha$ adjusts the influence of source data supervision, $\\mathrm{KL}(\\cdot ,\\cdot)$ is the Kullback-Leibler divergence, and $\\mathrm{CE}(\\cdot ,\\cdot)$ represents the standard cross-entropy loss.", + "bbox": [ + 76, + 547, + 468, + 593 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Obtaining pseudo label for VAC. Focusing on image modality, we aim to enhance the locality structure of vision representations—high inter-class discriminability and tight intra-class distribution—a feature that CLIP-extracted vision features lack, as detailed in Fig. 4a. To instill these locality structures within VAC, we utilize a K-means-based deep clustering approach [4, 21] to generate pseudo-labels for unlabeled target data. We calculate the clustering centroids for class $k$ as follows:", + "bbox": [ + 76, + 594, + 468, + 728 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\phi_ {k} = \\frac {\\sum_ {x ^ {t}} \\delta_ {k} \\left(\\operatorname {s o f t m a x} \\left(\\hat {y} _ {e n s} ^ {t}\\right)\\right) \\cdot f _ {b} ^ {t}}{\\sum_ {x ^ {t}} \\delta_ {k} \\left(\\operatorname {s o f t m a x} \\left(\\hat {y} _ {e n s} ^ {t}\\right)\\right)}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 733, + 468, + 767 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\hat{y}_{ens}^{t}$ represents target ensemble outputs discussed below, and $\\delta_{k}$ selects the $k_{th}$ logit. To mitigate imbalances in text modality predictions from CLIP [17, 49], we implement Approximated Controlled Direct Effect (ACDE) [49] to adjust similarity scores obtained in Eq. (4):", + "bbox": [ + 76, + 773, + 468, + 849 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {y} _ {l a c} ^ {t} = \\hat {y} _ {l a c} ^ {t} - \\tau \\log \\hat {p}, \\hat {p} \\leftarrow m \\hat {p} + (1 - m) \\frac {1}{B} \\sum_ {i = 1} ^ {B} p _ {i}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 856, + 468, + 896 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $m$ is momentum, $\\tau$ is a debiasing factor, $B$ is the batch size, and $p_i = \\mathrm{softmax}(\\hat{y}_{lac}^t)$ denotes classification probability of LAC. The ensemble outputs, used in the centroid calculation, are then defined as $\\hat{y}_{ens}^{t} = w\\cdot \\hat{y}_{vac}^{t} + (1 - w)\\cdot \\tilde{y}_{lac}^{t}$ . For any given target bottleneck feature $f_{b}^{t}$ , we compute its cosine similarity with all centroids, assigning the class with the highest similarity as the pseudo-label:", + "bbox": [ + 498, + 90, + 890, + 196 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {v a c} ^ {t} = \\arg \\max _ {k} \\cos \\left(f _ {b} ^ {t}, \\phi_ {k}\\right). \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 208, + 890, + 229 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Learning VAC. We now train vision component on unifies outputs from both modalities. Utilizing Eq. (9) and Eq. (5), the target ensemble output $\\hat{y}_{\\text {ens }}^{t}$ is formulated as:", + "bbox": [ + 498, + 241, + 890, + 287 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {y} _ {e n s} ^ {t} = w \\cdot \\hat {y} _ {v a c} ^ {t} + (1 - w) \\cdot \\tilde {y} _ {l a c} ^ {t}, \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 297, + 890, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with the weight $w = W(VAC^t)$ produced by the weight generator $W$ , as depicted in Fig. 2. Referring to Sec. 3.1, we optimize $\\hat{y}_{\\text{ens}}^t$ rather than $\\hat{y}_{\\text{vac}}^t$ directly, with $\\tilde{y}_{\\text{lac}}^t$ serving as an auxiliary in training VAC and thus detached from the computational graph in Eq. (11).", + "bbox": [ + 498, + 325, + 890, + 402 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To enhance individual discriminability and global diversity, thereby preserving the locality structure of vision representations, we follow state-of-the-art [1, 20, 21] to apply an information maximization loss $\\mathcal{L}_{im}$ comprising two components. The entropy loss $\\mathcal{L}_{ent}$ improves individual certainty:", + "bbox": [ + 498, + 402, + 890, + 492 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {e n t} = - \\mathbb {E} _ {x ^ {t} \\in \\mathcal {D} ^ {t}} \\left[ \\sum_ {k = 1} ^ {K} \\delta_ {k} \\left(\\hat {y} _ {e n s} ^ {t}\\right) \\log \\delta_ {k} \\left(\\hat {y} _ {e n s} ^ {t}\\right) \\right], \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 503, + 890, + 546 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "and the diversity loss fosters diverse class distributions:", + "bbox": [ + 500, + 556, + 864, + 571 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {d i v} = - \\sum_ {k = 1} ^ {K} \\bar {q} _ {k} \\log \\bar {q} _ {k}, \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 614, + 582, + 890, + 625 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\overline{q}_k = -\\mathbb{E}_{x^t\\in \\mathcal{D}^t}\\delta_k(\\hat{y}_{ens}^t)$ . Hence, $\\mathcal{L}_{im}$ is defined as:", + "bbox": [ + 500, + 635, + 880, + 652 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {i m} = \\mathcal {L} _ {e n t} - \\mathcal {L} _ {d i v}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 664, + 890, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The training of VAC is supervised by target pseudo labels for the vision modality, obtained through Eq. (10), while source labels directly optimize $\\hat{y}_{vac}^{s}$ :", + "bbox": [ + 498, + 691, + 890, + 738 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {v a c} = C E \\left(\\hat {y} _ {\\text {e n s}} ^ {t}, y _ {v a c} ^ {t}\\right) + \\beta C E \\left(\\hat {y} _ {v a c} ^ {s}, y ^ {s}\\right) + \\mathcal {L} _ {i m}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 748, + 890, + 766 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\beta$ modulates the impact of source data supervision.", + "bbox": [ + 500, + 777, + 879, + 792 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Aligning source and target by discriminator", + "text_level": 1, + "bbox": [ + 500, + 801, + 870, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To achieve domain adaptation on both modalities, we introduce a modality discriminator $D$ to align VAC and LAC from both domains. Our approach utilizes a singular modality discriminator trained on the source domain to differentiate LAC from VAC, and then assesses alignment on the", + "bbox": [ + 498, + 824, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23367", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "target domain. Proper alignment across domains would enable $D$ to discern LAC and VAC on the target domain without direct training. The modality discriminator is trained using binary cross-entropy loss:", + "bbox": [ + 75, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b c e} = - \\left[ y _ {d i s} \\log \\hat {y} _ {d i s} + \\left(1 - y _ {d i s}\\right) \\log \\left(1 - \\hat {y} _ {d i s}\\right) \\right], \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 164, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $y_{dis}$ represents the modality label (0 for VAC, 1 for LAC) and $\\hat{y}_{dis}$ is the output of $D$ .", + "bbox": [ + 75, + 193, + 468, + 222 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Notably, $D$ is only trained on the source domain using Eq. (16). On the target domain, only the separators $G_{vis}$ and $G_{txt}$ are updated to minimize Eq. (16), aligning target LAC and VAC with the source ones.", + "bbox": [ + 75, + 223, + 468, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Training and inference", + "text_level": 1, + "bbox": [ + 76, + 294, + 289, + 310 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training. As depicted in Fig. 2, the pretrained text encoder and vision encoder are frozen, and we optimize parameters of $G_{txt}$ , $G_{vis}$ , $\\Phi_1$ , $\\Phi_2$ , $W$ , $D$ , denoted as $\\theta_{G_{txt}}$ , $\\theta_{G_{vis}}$ , $\\theta_{\\Phi_1}$ , $\\theta_{\\Phi_2}$ , $\\theta_W$ , $\\theta_D$ , respectively. Combining Eq. (7), Eq. (3), Eq. (15), Eq. (16), we define the following optimization problem:", + "bbox": [ + 75, + 316, + 468, + 407 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {G _ {t x t}} = \\underset {\\theta_ {G _ {t x t}}} {\\arg \\min } \\mathcal {L} _ {l a c} + \\gamma \\mathcal {L} _ {o r t h o} + \\gamma \\mathcal {L} _ {b c e}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 422, + 468, + 446 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_{G_{vis}} = \\operatorname *{arg min}_{\\theta_{G_{vis}}}\\mathcal{L}_{vac} + \\gamma \\mathcal{L}_{ortho} + \\gamma \\mathcal{L}_{bce},\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 453, + 415, + 478 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_ {W}, \\theta_ {\\Phi_ {1}}, \\theta_ {\\Phi_ {2}} = \\operatorname * {a r g m i n} _ {\\theta_ {W}, \\bar {\\theta} _ {\\Phi_ {1}}, \\theta_ {\\Phi_ {2}}} \\mathcal {L} _ {v a c},\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 484, + 354, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\theta_{D} = \\operatorname *{arg min}_{\\theta_{D}}\\gamma \\mathcal{L}_{bce},\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 515, + 274, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\gamma$ is hyperparameter controlling regularization terms $\\mathcal{L}_{bce}$ and $\\mathcal{L}_{ortho}$ . We present detailed training procedure of UniMoS in Supplementary.", + "bbox": [ + 76, + 550, + 468, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inference. At inference, the final mixed prediction on target data is obtained using $\\hat{y}_{ens}^{t}$ from Eq. (11), with a fixed mixup weight $w$ . The objective is to maximize accuracy by leveraging the strengths of both modalities for improved classification, as supported by our observations (Fig. 1), thus integrating outputs from both modalities to harness their combined advantages.", + "bbox": [ + 75, + 595, + 468, + 702 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 715, + 207, + 732 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and implementation details", + "text_level": 1, + "bbox": [ + 76, + 741, + 390, + 757 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We extensively evaluate our method on three mainstream UDA benchmarks. Office-Home [46] consists of 65 categories divided into 4 distinct domains. On VisDA2017 [34], the goal is to transfer knowledge from 152k synthetic images (source domain) to 55k images of real items (target domain). DomainNet [35] is the most challenging UDA benchmark so far, containing 0.6 million samples from 345 categories divided into 6 distinct domains. Following previous works, we additionally provide results on", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Mini-DomainNet [25, 40, 58], a subset of DomainNet with 4 domains and 126 categories.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conduct all experiments on an NVIDIA RTX 2080Ti GPU. Since our method does not involve updating CLIP's pretrained parameters or prompts, the CLIP-extracted vision and text features are obtained via one single forward and saved in memory, thus greatly saving computation costs. For all tasks, we adopt SGD optimizer with batch size 32, and set momentum $m$ in Eq. (9) to 0.99 and debias factor $\\tau$ in Eq. (9) to 0.5. For Office-Home and DomainNet, we train 50 epochs with initial learning rate 3e-3 and adopt annealing strategy [8] for learning rate decay. We train for 10 epochs with initial learning rate 9e-4 on VisDA due to fast convergence. The fixed mixup weight described in Sec. 3.5 is set to 0.3 for all tasks. We set regularization weight $\\gamma$ in Eq. (17) to 0.01 across all datasets.", + "bbox": [ + 496, + 122, + 890, + 333 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Benchmark results", + "text_level": 1, + "bbox": [ + 500, + 345, + 679, + 359 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Office-Home. Tab. 1 gives classification accuracies on 12 adaptation tasks on Office-Home using the ResNet50 [11] backbone. To ensure a fair comparison, we categorize CLIP-based methods into two groups: 'none-tuning' and 'full-tuning'. The former involves learning prompts or additional modules without adjusting the pretrained CLIP backbones, while the latter optimizes the pretrained parameters of CLIP for specific tasks. It is evident from the results that our proposed UniMoS consistently outperforms both 'none-tuning' and 'full-tuning' methods. Notably, we obtain $+1.3\\%$ performance boost than the strong baseline PADCLIP, which fine-tunes the CLIP vision backbone. Our method requires no parameter update or data forwarding of CLIP backbones, thus is much computationally cheaper. Especially on tasks that take P as target domain, we achieve up to $+5.4\\%$ performance boost than PADCLIP, demonstrating the superiority of multimodal adaptation.", + "bbox": [ + 496, + 369, + 890, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "VisDA-2017. Tab. 2 shows class-wise classification accuracies on VisDA using ResNet101 [11]. Our method achieves the best performance among 'none-tuning' CLIP methods, while slightly falling behind PADCLIP. The reason is that CLIP has not been trained on the synthetic images like those from source domain of VisDA, resulting in incompatibilities between the VisDA dataset and CLIP. Similar observations are made by PADCLIP [17], which opts to fine-tune the vision branch of CLIP to address this challenge. Nevertheless, our approach outperforms typical UDA methods.", + "bbox": [ + 496, + 628, + 890, + 777 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "DomainNet. Tab. 3 presents classification accuracies of 30 cross-domain adaptation tasks on the most challenging benchmark DomainNet. Rows represent source domains and columns represent target domains. Our method reaches comparable performance with the strong baseline PADCLIP. One significant observation is that our UniMoS obtains lower accuracy than PADCLIP (6.6% lower in average) on tasks with qdr as target. This discrepancy arises", + "bbox": [ + 496, + 779, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23368", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/e9a4d7b1602bd9b25ce511af1b5a7aefd36a039f9e13041d1dfa83c662b9562a.jpg", + "table_caption": [ + "Table 1. UDA results on Office-Home. Best results are marked in bold font. Methods with $*$ ’ are based on CLIP." + ], + "table_footnote": [], + "table_body": "
MethodBackboneA→CA→PA→RC→AC→PC→RP→AP→CP→RR→AR→CR→PAvg.
SourceOnly [11]ResNet5034.950.058.037.441.946.238.531.260.453.941.259.946.1
ParetoDA [22]56.875.980.564.473.573.765.655.281.375.261.183.970.6
SDAT [37]58.277.182.266.377.676.863.357.082.274.964.786.072.2
MSGD [50]58.776.978.970.176.276.669.057.282.374.962.784.572.3
Fixbi [32]58.177.380.467.779.578.165.857.981.776.462.986.772.7
CST [26]59.079.683.468.477.176.768.956.483.075.362.285.172.9
ATDOC [23]60.277.882.268.578.677.968.458.483.174.861.587.273.2
KUDA [42]58.280.082.971.180.380.771.356.883.275.560.386.673.9
EIDCo [60]63.880.882.671.580.180.972.161.384.578.665.887.175.8
ICON [55]63.381.384.570.382.181.070.361.883.775.668.687.375.8
PADCLIP* [17]ResNet50-full-tuning57.584.083.877.885.584.776.359.285.478.160.286.776.6
CLIP* [36]ResNet50-none-tuning51.781.582.371.781.582.371.751.782.371.751.781.571.8
DAPrompt* [10]54.184.384.874.483.785.074.554.684.875.254.783.874.5
ADCLIP* [41]55.485.285.676.185.886.276.756.185.476.856.185.575.9
UniMoS* (ours)59.589.486.975.289.686.875.458.487.276.959.589.777.9
", + "bbox": [ + 81, + 104, + 893, + 344 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/acf9f10a9193bf412eb96be3b5077641886c5afa8e979e7d9b6d793403e6738b.jpg", + "table_caption": [ + "Table 2. UDA results on VisDA-2017. Best results are marked in bold font. Methods with \\* are based on CLIP." + ], + "table_footnote": [], + "table_body": "
MethodBackboneplanebicyclebuscarhorseknifemcyclpersonplantsktbrdtraintruckAvg.
SourceOnly [11]ResNet10155.153.361.959.180.617.979.731.281.026.573.58.552.4
ParetoDA [22]95.982.881.358.793.993.785.983.091.992.087.151.883.2
MSGD [50]97.583.484.469.495.994.190.975.595.594.688.144.984.5
ATDOC [23]95.384.782.475.695.897.788.776.694.091.791.561.986.3
CAN [15]97.087.282.574.397.896.290.880.796.696.387.559.987.2
FixBi [32]96.187.890.590.396.895.392.888.797.294.290.925.787.2
PADCLIP* [17]ResNet101-full-tuning96.788.887.082.897.193.091.383.095.591.891.563.088.5
CLIP* [36]ResNet101-none-tuning98.283.990.573.597.284.095.365.779.489.991.863.384.4
DAPrompt* [10]97.883.188.877.997.491.594.279.788.689.392.562.086.9
ADCLIP* [41]98.183.691.276.698.193.496.081.486.491.592.164.287.7
UniMoS* (ours)97.788.290.174.696.895.892.484.190.889.091.865.388.1
", + "bbox": [ + 81, + 369, + 890, + 550 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "from a significant domain gap between qdr and other domains, which is challenging to bridge without tuning the CLIP backbones. However, despite this, we manage to achieve superior performance to PADCLIP on all other tasks, thereby mitigating the overall $6.6\\%$ performance drop. We also surpass all competing methods significantly. Tab. 4 compares UniMoS with available CLIP-based non-tuning methods on Mini-DomainNet, where our method achieves significant performance boost. Detailed results on Mini-DomainNet are given in Supplementary.", + "bbox": [ + 75, + 568, + 468, + 718 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 726, + 227, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section we validate the efficacy of each module in UniMoS. Tab. 5 presents averaged accuracies on Office-Home and VisDA-2017 by removing specific modules while maintaining other settings identical. The 'w/o debiasing' is obtained by skipping the debias procedure in Eq. (9). A primary observation is that the removal of any module leads to a performance drop to varying degrees, underscoring the positive contribution of each module to the overall outcome. The 'w/o learnable weight' row is obtained by replacing $w$ in Eq. (11) with a constant 0.5, re", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sulting in the most pronounced performance decline. This emphasizes the significance of dynamic weights, which enables VAC to focus on vision-specific parts. Further insights into the effects of dynamic $w$ are detailed in Sec. 4.4.", + "bbox": [ + 496, + 566, + 890, + 627 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 6 ablates on the choice of backbones. We experiment with three backbones on Office-Home, and our UniMoS consistently outperforms all competing methods, proving that our method is generalizable across various models. Detailed results are given in Supplementary.", + "bbox": [ + 496, + 628, + 890, + 704 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Discussions", + "text_level": 1, + "bbox": [ + 500, + 710, + 624, + 724 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Effectiveness of learnable weight $w$ . To better understand how the learnable ensemble weight $w$ in Eq. (2) boosts performance, Fig. 3 compares the training process with and without dynamic $w$ . We set a fixed weight of 0.5 for both LAC and VAC in 'w/o learnable w', and learn dynamic weights (shown as 'Learned weight w' in the figure) in other settings. Our first observation is that in our full design, accuracy of VAC increases steadily as the training progresses. Leveraging complementary modality-specific information from LAC, the final mixed outputs achieve higher accuracy than VAC alone. As stated in Sec. 3.1, the goal of", + "bbox": [ + 496, + 734, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23369", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/4badaec65960c3caf17e98d8545d3f5bf97cc24dea10a798d71ae98eed7f68e0.jpg", + "table_caption": [ + "Table 3. UDA results on DomainNet. Best results are marked in bold font. Methods with $*$ ’ are based on CLIP." + ], + "table_footnote": [], + "table_body": "
DeiT-B [44]clpinfpptqdrrelsktavgViT-B [6]clpinfpptqdrrelsktavgSSRT-B [43]clpinfpptqdrrelsktavg
clp-24.349.615.865.352.141.4clp-27.253.113.271.253.343.6clp33.860.219.475.859.849.8
inf45.9-45.96.761.439.539.9inf51.4-49.34.066.341.142.4inf55.5-54.09.068.244.746.3
ppt53.223.8-6.566.444.738.9ppt53.125.6-4.870.041.839.1ppt61.728.5-8.471.455.245.0
qdr31.96.815.4-23.420.619.6qdr30.54.516.0-27.019.319.5qdr42.58.824.2-37.633.629.3
rel59.025.856.39.2-44.839.0rel58.429.060.06.0-45.839.9rel69.937.166.010.1-58.948.4
skt60.620.648.416.561.2-41.5skt63.923.852.314.467.4-44.4skt70.632.862.221.773.2-52.1
avg50.120.343.110.955.540.336.7avg51.522.046.18.560.440.338.1avg60.028.253.313.765.350.445.2
CDTrans -DeiT [51]clpinfpptqdrrelsktavgPMTrans -Swin [63]clpinfpptqdrrelsktavgCLIP -B* [36]clpinfpptqdrrelsktavg
clp-29.457.226.072.658.148.7clp-34.262.732.579.363.754.5clp-70.170.170.170.170.170.1
inf57.0-54.412.869.548.448.4inf67.4-61.122.278.057.657.3inf46.4-46.446.446.446.446.4
ppt62.927.4-15.872.153.946.4ppt69.733.5-23.979.861.253.6ppt61.761.7-61.761.761.761.7
qdr44.68.929.0-42.628.530.7qdr54.617.438.9-49.541.040.3qdr13.713.713.7-13.713.713.7
rel66.231.061.516.2-52.945.6rel74.135.370.025.4-61.153.2rel82.982.982.9-82.982.982.9
skt69.029.659.027.272.5-51.5skt73.833.062.630.977.5-55.6skt62.662.662.662.6-62.6
avg59.925.352.219.665.948.445.2avg67.930.759.127.072.856.952.4avg53.558.255.164.750.955.056.2
DAPrompt -B* [10]clpinfpptqdrrelsktavgPADCLIP -B* [17]clpinfpptqdrrelsktavgUniMoS -B* (ours)clpinfpptqdrrelsktavg
clp-73.073.872.673.973.573.4clp-73.675.474.676.476.375.3clp-76.577.276.677.577.877.1
inf50.8-50.149.650.650.350.3inf55.1-54.353.654.954.954.6inf55.1-55.054.655.355.255.0
ppt70.269.6-68.970.469.969.8ppt71.170.6-70.072.771.771.2ppt72.371.5-69.472.572.671.7
qdr17.214.413.9-14.313.914.7qdr36.818.032.0-31.734.930.7qdr25.022.923.6-23.725.124.1
rel84.984.884.984.7-84.684.8rel84.283.583.583.1-83.683.6rel86.085.985.885.5-85.985.8
skt65.865.465.864.965.9-65.6skt68.166.667.266.167.5-67.1skt68.567.868.267.568.0-68.0
avg57.861.457.768.155.058.459.8avg63.162.562.569.560.664.363.7avg61.464.962.070.759.463.363.6
", + "bbox": [ + 80, + 104, + 893, + 364 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/3f2fed690ac19204c78832d8f823471965df6bae5e673bc07bbdeb2f4a92f104.jpg", + "table_caption": [ + "Table 4. UDA results on Mini-DomainNet. Best results are marked in bold font. All compared methods are CLIP-based." + ], + "table_footnote": [], + "table_body": "
MethodBackboneAcc.MethodBackboneAcc.
CLIPResNet5071.2CLIPViT-B82.8
DAPrompt74.8DAPrompt85.8
ADCLIP75.2ADCLIP86.9
UniMoS (ours)78.0UniMoS (ours)87.3
", + "bbox": [ + 81, + 412, + 468, + 481 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1c5847ec6fc10c8538aa773310a064db75d05fe27ff5ded60ddc5f8e05706947.jpg", + "table_caption": [ + "Table 5. Ablation study on Office-Home and VisDA-2017." + ], + "table_footnote": [], + "table_body": "
MethodOffice-HomeVisDA-2017
w/o Lortho77.487.6
w/o debiasing77.387.7
w/o Lim77.087.8
w/o Ldistill77.087.6
w/o learnable weight76.986.2
w/o modality discriminator77.687.9
UniMoS (full design)77.988.1
", + "bbox": [ + 102, + 512, + 444, + 627 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "dynamic ensemble weight is to adaptively identify and preserve modality-specific information. We show in Fig. 3 that, the learned weight changes in each epoch to fit the training process. Without its support (w/o learnable w), the accuracy of VAC outputs drops significantly and finally converges with LAC. This occurs because employing a static weight would compromise the modality separation effects, causing both modalities to collapse to poor performance. In the example given by Fig. 3, accuracy of 'VAC output w/o learnable w' is $3.5\\%$ lower than that of the full design 'VAC output'. The phenomenon indicates the significance of training with dynamic ensemble weights in our design. More examples are given in Supplementary.", + "bbox": [ + 75, + 641, + 468, + 838 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Computation analysis. Tab. 7 compares computation costs of different methods on VisDA dataset. Our method necessitates training only a few linear layers without updating CLIP backbones, bringing great parameter efficiency.", + "bbox": [ + 75, + 839, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3a76308d52f2419f5adb32e4a24abfeab96aa20d7537a9cd077e332ad5be3ce8.jpg", + "image_caption": [ + "Figure 3. Effects of learnable ensemble weight $w$ on Office-Home." + ], + "image_footnote": [], + "bbox": [ + 547, + 380, + 846, + 551 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/50e63ea2d87a20ac51ea8a5c31c5ab338e2bd35e130b5f317e30a38879dc86a9.jpg", + "table_caption": [ + "Table 6. Results with different backbones on Office-Home. Best results are in bold. All compared methods are based on CLIP." + ], + "table_footnote": [], + "table_body": "
MethodBackboneAcc.MethodBackboneAcc.
UniMoS (ours)ResNet5077.9CLIP82.4
CLIPViT-L87.0DAPromptViT-B84.4
DAPrompt88.7ADCLIP86.1
ADCLIP90.5PADCLIP86.7
UniMoS (ours)90.7UniMoS (ours)86.9
", + "bbox": [ + 504, + 618, + 890, + 704 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Furthermore, only one forward through CLIP is needed, which allows UniMoS achieve more than $47 \\times$ training speed boost than PADCLIP. Prompt learning methods like DAPrompt also requires no training on CLIP backbones, but they require extensive iterative forwarding of data through CLIP to learn optimal prompts per class, leading to low computing efficiency and scalability to larger datasets. When running on DomainNet with 345 classes, DAPrompt requires more than 22G GPU memory, while our method requires less than 3G. More details are in Supplementary.", + "bbox": [ + 496, + 717, + 890, + 868 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Feature distribution visualization. To demonstrate the efficacy of modality separation and feature alignment, we per", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23370", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/da613e85b47013da81c14148ebe07ac7f9f8977c50157741053f4ef1721a5916.jpg", + "image_caption": [ + "(a) CLIP-extracted feature distribution." + ], + "image_footnote": [], + "bbox": [ + 96, + 90, + 346, + 238 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/05e6a1cd3d72af8426c06e4eca41d7d1cd4a0dcf4d4bc7443cb9dc30dd086d62.jpg", + "image_caption": [ + "(b) Modality separation effect." + ], + "image_footnote": [], + "bbox": [ + 357, + 90, + 612, + 237 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/e0398b853fc9e1188c0af74fc4e1571ccf97b92173737a2ea6603e67fe5d8176.jpg", + "image_caption": [ + "(c) Aligned bottleneck feature distribution." + ], + "image_footnote": [], + "bbox": [ + 622, + 90, + 874, + 237 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0498327a2dba20dda13110aca0f7ac3bd5ac95d724ee2ccf901e18e3488b3009.jpg", + "table_caption": [ + "Table 7. Computation analysis on VisDA-2017. Best results are marked in bold font. Methods with \\* are based on CLIP." + ], + "table_footnote": [], + "table_body": "
MethodBkb.Param.Throughput (images/s)Train timeFLOPsAcc.
DAPrompt*ResNet1011.2M2444.3H11.3G86.9
FixBi86.1M1025.5H15.73G87.2
CAN42.5M3110.5H7.9G87.2
PADCLIP*--23.5H*-88.5
UniMoS* (ours)0.79M26670.5H<0.01G88.1
", + "bbox": [ + 81, + 339, + 468, + 428 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "form t-sne [45] visualization on various features at different phases of our method. Fig. 4a shows CLIP-extracted vision features from source (green) and target (blue) domain, along with CLIP-extracted text features (red) of naive prompts. The text features distribute distantly with vision features, proving the existence of modality gap. Besides, CLIP-extracted vision features form poor class discriminability and locality structures. Fig. 4b showcases the separated LAC and VAC of our method. A clear boundary can be observed between the features of both modalities, indicating the effectiveness of modality separation. Additionally, the text features distribute closer to LAC, proving that the separated LAC is indeed more relevant to the text modality. Following feature alignment and VAC training, the bottleneck features $f_{b}$ from both domains display a compact class-level locality structure, as demonstrated in Fig. 4c. This compact structure contributes significantly to the accuracy of the final classification results.", + "bbox": [ + 75, + 444, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Hyperparameter sensitivity. In the calibration of UniMoS, we encounter three hyperparameters to determine: $\\alpha$ in Eq. (7), $\\beta$ in Eq. (15), and $\\gamma$ in Eq. (17). We empirically discover that alternating $\\gamma$ has little impact within each dataset, so we focus on exploring the effects of $\\alpha$ and $\\beta$ . As illustrated in Fig. 5a, the performance on VisDA is notably influenced by $\\alpha$ , with smaller values leading to improved accuracy. This outcome is attributed to the fact, as discussed in Sec. 4.2, that CLIP struggles to adequately iden", + "bbox": [ + 75, + 717, + 468, + 853 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/eca940e3e1893db4d802a889b9cd72c959e7d5960f81195fb2fb9495cb0e1ae3.jpg", + "image_caption": [ + "Figure 4. T-sne visualization [45] of the effects of UniMoS on $\\mathrm{A}\\rightarrow \\mathrm{P}$ task from Office-Home. UniMoS effectively disentangles CLIP-extracted vision features (Fig. 4a) into LAC and VAC (Fig. 4b, obtained by randomly selecting 25 classes), and constructs clear cross-domain locality structures (Fig. 4c).", + "(a) VisDA-2017", + "Figure 5. Parameter sensitivity analysis on $\\alpha$ and $\\beta$ of UniMoS." + ], + "image_footnote": [], + "bbox": [ + 506, + 310, + 694, + 426 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4178cd35b931fedfc0fc58a55ef736ff9eb1fbcf4b340dd4692ec0dbda1c8e9b.jpg", + "image_caption": [ + "(b) Office-Home" + ], + "image_footnote": [], + "bbox": [ + 697, + 311, + 883, + 426 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tify source synthetic images from VisDA. Consequently, down-weighting source supervision on LAC proves beneficial. Conversely, source supervision from both modalities of Office-Home are important. They positively and equally contributes to the adaptation process, so $\\alpha = 1$ and $\\beta = 1$ brings the best result, as shown in Fig. 5b.", + "bbox": [ + 496, + 473, + 890, + 565 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 579, + 627, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inspired by the theory of modality gap, in this paper we propose a Unified Modality Separation framework for unsupervised domain adaptation. The CLIP-extracted vision features are explicitly disentangled into vision-associated and language-associated components, which are trained differently according to their modality strengths and further aligned by a modality discriminator. A modality-ensemble training paradigm unifies both components to leverage modality-specific information while preserving modality-shared contexts, contributing to successful classification. This work is hope to inspire further analysis and exploitation of the multimodal features in pretrained VLMs.", + "bbox": [ + 496, + 604, + 892, + 785 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 799, + 687, + 816 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China under Grant 62176042, and in part by Sichuan Science and Technology Program under Grant 2023NSFSC0483, and in part by Tencent Marketing Solution Rhino-Bird Focused Research Program.", + "bbox": [ + 496, + 824, + 892, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "*Cited from PADCLIP [17]. PADCLIP conducts the experiments on an NVIDIA Tesla V100 GPU. Results on other metrics are unavailable since the authors have not released the code implementations yet.", + "bbox": [ + 75, + 862, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23371", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sk Miraj Ahmed, Dripta S Raychaudhuri, Sujoy Paul, Samet Oymak, and Amit K Roy-Chowdhury. Unsupervised multisource domain adaptation without access to source data. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10103-10112, 2021.", + "[2] Shai Ben-David, John Blitzer, Koby Crammer, Alex Kulesza, Fernando Pereira, and Jennifer Wortman Vaughan. A theory of learning from different domains. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3561-3571, 2023." + ], + "bbox": [ + 78, + 90, + 470, + 881 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "23374", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/0b95bf41-b7e1-4df0-9ad3-d873e89c86e9_model.json b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/0b95bf41-b7e1-4df0-9ad3-d873e89c86e9_model.json new file mode 100644 index 0000000000000000000000000000000000000000..566c2ab40a51bb3223cf8f861dc290b2296a30f1 --- /dev/null +++ b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/0b95bf41-b7e1-4df0-9ad3-d873e89c86e9_model.json @@ -0,0 +1,2466 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.234, + 0.131, + 0.738, + 0.177 + ], + "angle": 0, + "content": "Split to Merge: Unifying Separated Modalities for Unsupervised Domain Adaptation" + }, + { + "type": "text", + "bbox": [ + 0.172, + 0.203, + 0.805, + 0.257 + ], + "angle": 0, + "content": "Xinyao Li\\(^{1}\\) Yuke Li\\(^{2*}\\) Zhekai Du\\(^{1}\\) Fengling Li\\(^{3}\\) Ke Lu\\(^{1}\\) Jingjing Li\\(^{1*}\\) \n\\(^{1}\\)University of Electronic Science and Technology of China \n\\(^{2}\\)Boston College \\(^{3}\\)University of Technology Sydney" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.26, + 0.756, + 0.275 + ], + "angle": 0, + "content": "xinyao326@outlook.com, lidwh@bc.edu, zhekaid@std.uestc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.212, + 0.278, + 0.754, + 0.293 + ], + "angle": 0, + "content": "fenglingli2023@gmail.com, kel@uestc.edu.cn, lijin117@yeah.net" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.358, + 0.474, + 0.631 + ], + "angle": 0, + "content": "Large vision-language models (VLMs) like CLIP have demonstrated good zero-shot learning performance in the unsupervised domain adaptation task. Yet, most transfer approaches for VLMs focus on either the language or visual branches, overlooking the nuanced interplay between both modalities. In this work, we introduce a Unified Modality Separation (UniMoS) framework for unsupervised domain adaptation. Leveraging insights from modality gap studies, we craft a nimble modality separation network that distinctly disentangles CLIP's features into language-associated and vision-associated components. Our proposed Modality-Ensemble Training (MET) method fosters the exchange of modality-agnostic information while maintaining modality-specific nuances. We align features across domains using a modality discriminator. Comprehensive evaluations on three benchmarks reveal our approach sets a new state-of-the-art with minimal computational costs. Code: https://github.com/TL-UESTC/UniMoS." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.658, + 0.21, + 0.673 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.683, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Unsupervised domain adaptation (UDA) [2, 7, 29, 30] aims to apply knowledge trained on a source domain to an unlabeled target domain, a process invaluable in data-scarce scenarios. Conventional methods often struggle with bridging the gap between source and target domains, finding it challenging to develop consistent features across domains [19, 39]. In image classification, aligning vision features while neglecting semantic content can lead to difficulties in differentiating complex samples [10, 41]. Vision-language models (VLMs) such as CLIP [36] and ALIGN [13] circumvent these issues through joint multimodal pretraining on images and texts. This extensive pretraining endows publicly available VLMs with robust zero-shot transfer abl-" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.336, + 0.662, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.523, + 0.409, + 0.681, + 0.45 + ], + "angle": 0, + "content": "
Modality / Prob.couchchair (√)
image modality0.0020.998
text modality0.8320.130
" + }, + { + "type": "image", + "bbox": [ + 0.713, + 0.328, + 0.848, + 0.407 + ], + "angle": 0, + "content": null + }, + { + "type": "table", + "bbox": [ + 0.695, + 0.409, + 0.866, + 0.45 + ], + "angle": 0, + "content": "
Modality / Prob.shelffile cabinet ( \\( \\checkmark \\) )
image modality0.8990.101
text modality0.0620.928
" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.454, + 0.893, + 0.497 + ], + "angle": 0, + "content": "Figure 1. Examples of modality-specific information from task Art \\(\\rightarrow\\) RealWorld in Office-Home dataset. The digits are top-2 highest classification probabilities given by both modalities." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.507, + 0.892, + 0.568 + ], + "angle": 0, + "content": "ities and a broad base of conceptual knowledge, making them highly suitable for comprehensive UDA. They facilitate alignment across both visual and textual modalities, enhancing adaptability and applicability in diverse contexts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Previous studies have shown promising results by adapting VLMs like CLIP for unsupervised domain adaptation (UDA). For instance, DAPrompt [10] introduces learning both domain-agnostic and domain-specific text embeddings, while PADCLIP [17] focuses on fine-tuning the vision branch of CLIP for adaptive visual feature extraction. However, recent research [14, 24] highlights a modality gap in VLMs, revealing that, despite training efforts, vision and text features often remain distinctly distributed. We argue that adapting a single modality is less than ideal due to the existence of unique, modality-specific cues in misaligned textual and visual components. We suggest that certain samples are best classified using specific modalities, a hypothesis supported by empirical observations in Fig. 1. This figure shows differing classification patterns when each modality is adapted independently to the unlabeled target data. Text modality results derive from CLIP's zero-shot capabilities, while image results come from linear probing with target pseudo-labels. For instance, visually straightforward items like a cushioned chair are accurately classified by the vision linear classifier after tuning on target dataset. However, pretrained CLIP can erroneously cat" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23364" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.242 + ], + "angle": 0, + "content": "egorize such items under visually similar classes. In contrast, complex items with nuanced semantic details, like a file cabinet resembling a shelf, may confuse the vision classifier, while CLIP's broader knowledge base facilitates correct zero-shot predictions. In summary, while the vision branch effectively discerns class-specific visual patterns, the text branch leverages semantic information to clarify ambiguous cases. This observation lays the groundwork for a multimodal adaptation framework that synergistically combines the strengths of both modalities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.246, + 0.47, + 0.397 + ], + "angle": 0, + "content": "A direct approach to domain adaptation involves concurrently fine-tuning vision branch and crafting textual prompts, which risks disturbing the image-text representation pairs in pretrained CLIP and is computationally intensive [9, 57]. As a more efficient alternative, we propose to explicitly disentangle CLIP-extracted visual features into two complementary parts. The first component retains the language-associated semantic knowledge inherent in CLIP, while the second focuses on vision-specific attributes crucial for distinguishing between nuanced visual categories." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.399, + 0.471, + 0.838 + ], + "angle": 0, + "content": "We devised a set of modality separation networks with dual branches to project CLIP-encoded visual features into distinct language-associated components (LAC) and vision-associated components (VAC). An orthogonal regularization is employed to ensure these branches yield discrete, disentangled representations. Each component is optimized based on its inherent modality strengths. For the LAC branch, we utilize knowledge distillation on target data to harness the rich semantic content from the original pretrained CLIP model. Additionally, we implement a debiasing method to mitigate dataset bias in CLIP's zero-shot results. For the VAC branch, the locality structure within visual feature spaces [20, 53, 54] is leveraged to generate visual pseudo-labels for supervised learning on target data. We then introduce a novel Modality-Ensemble Training (MET) strategy that synergistically merges outputs from both modalities. A weight generator dynamically assembles these predictions, supervised by VAC pseudo-labels on target data and actual labels on source data. Importantly, the text modality output remains isolated during MET to preserve independent training and maintain pretrained semantics. Additionally, a modality discriminator is utilized to align LAC and VAC across domains for unsupervised domain adaptation. Trained on source data to distinguish between LAC and VAC, this discriminator is frozen on the target domain, directly updating the separation networks to produce domain-invariant LAC and VAC. This approach ensures a consistent modality separation across domains, facilitating simultaneous adaptation in both modalities." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Contributions: 1. We investigate the modality gap phenomenon in the context of applying Vision-Language Models (VLMs) to unsupervised domain adaptation, revealing the limitations of adapting a single modality; 2. We intro-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "duce a novel framework, Unified Modality Separation (UniMoS), which, coupled with a Modality-Ensemble Training (MET) approach, facilitates effective multimodal adaptation; 3. Our comprehensive analysis and validations underscore and efficiency of the proposed UniMoS, demonstrating its ability to set new state-of-the-art benchmarks while maintaining low computational demands." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.211, + 0.638, + 0.227 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.236, + 0.892, + 0.538 + ], + "angle": 0, + "content": "Unsupervised domain adaptation (UDA). A core challenge in UDA is aligning representations between the source domain and unlabeled target domain. Prior techniques can be categorized as discrepancy-based [18, 28, 59] and adversarial methods [7, 30, 39]. Discrepancy-based methods explicitly minimizes divergence metrics including MMD [18], MDD [59], etc. Adversarial methods extract domain invariant features via a min-max game between the feature extractor and domain discriminator [7, 30]. Recent works focus on exploiting target data structures via self-training techniques [15, 53-55, 60]. ICON [55] learns an invariant classifier with consistent predictions to remove the spurious correlation inconsistency in the target domain. EIDCo [60] combines Mixup [56] with IDCo loss [5, 12] to explore target data distribution. Vision transformer (ViT) [6] and its variants have also gained popularity due to their superior performance [51, 52, 63]. PMTrans [63] mixes patch representations in SwinTransformer [27] as an intermediate domain bridge. CDTrans [51] aligns features extracted by DeiT [44] via cross-attention." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.539, + 0.892, + 0.903 + ], + "angle": 0, + "content": "Vision-language models (VLMs) have shown great generalization abilities due to extensive multimodal pretraining [13, 36, 47, 48]. CLIP [36] is trained from 400 million text-image pairs, while ALIGN [13] leverages more than one billion text-image pairs. Subsequent works have built on pretrained VLMs in various ways. Some learn prompt texts to transfer VLMs to downstream tasks [10, 33, 38, 61, 62], while others incorporate additional tunable layers on the frozen pretrained encoder [9, 57]. Beyond utilizing existing VLMs, research also aims to improve VLM training [14, 31]. Liang et al. [24] reveal that VLMs exhibit a modality gap, failing to perfectly align multimodal features. Jiang et al. [14] conduct theoretical analysis on modality gap and propose latent space regularization to preserve modality-specific information. MaPLe [16] utilize prompt learning on both modality branches to improve alignment. Our approach is fundamentally different since we disentangle VLM-extracted features posteriorly instead of training VLM from scratch, requiring far less computation costs. Besides, our method requires no labeling on target domain. VLMs have also been adopted for UDA [10, 17, 41]. DAPrompt [10] learns domain-specific and domain-agnostic textual prompts for each class. ADCLIP [41] learns domain invariant prompts by conditioning" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23365" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.127, + 0.09, + 0.852, + 0.3 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. Framework of our method. We freeze the pretrained vision and text encoder of CLIP. CLIP-extracted vision features are disentangled into language-associated components \\((f_{lac})\\) and vision-associated components \\((f_{vac})\\) by the modality separation networks. We obtain zero-shot results from CLIP as teacher knowledge, and distill the knowledge to LAC. We then introduce a weight generator to assemble the modality outputs to train VAC. A modality discriminator is applied to align LAC and VAC from both domains." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.371, + 0.473, + 0.462 + ], + "angle": 0, + "content": "on image style and content features. PADCLIP [17] dynamically adjusts learning rate while tuning CLIP to prevent catastrophic forgetting. However, these methods perform adaptation on either the visual or textual modality in isolation. Our work addresses this limitation by proposing a unified adaptation framework for the multimodal features." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.473, + 0.172, + 0.489 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.498, + 0.276, + 0.513 + ], + "angle": 0, + "content": "3.1. Problem formulation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.521, + 0.473, + 0.734 + ], + "angle": 0, + "content": "In this study, superscripts differentiate domains, with symbols lacking superscripts applicable to both domains. We consider a labeled source domain \\(\\mathcal{D}^s = \\{(x_i^s,y_i^s)\\}_{i = 1}^{N^s}\\) and aim to develop a model generalizable to an unlabeled target domain \\(\\mathcal{D}^t = \\{(x_i^t)\\}_{i = 1}^{N^t}\\). CLIP [36] features a vision encoder \\(g_{vis}\\) and a text encoder \\(g_{txt}\\). The vision feature for an image input \\(x\\) is denoted as \\(f_{v} = g_{vis}(x)\\). Employing the zero-shot inference strategy from [17], we construct naive prompts \\(\\{(t_i)\\}_{i = 1}^K\\) as a [DOMAIN] photo of a [CLASS], with \\(K\\) representing the number of classes, [DOMAIN] indicating domain specifics, and [CLASS] the class name. Text features are then derived as \\(\\mu_{i} = g_{txt}(t_{i})\\). \\(\\mu_{i}\\) and \\(f_{v}\\) are both features with \\(d_v\\) dimension. Classification is based on the highest cosine similarity between \\(f_{v}\\) and \\(\\mu_{i}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.178, + 0.741, + 0.47, + 0.765 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {z s} = \\underset {i} {\\arg \\max } \\cos \\left(\\mu_ {i}, f _ {v}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.771, + 0.473, + 0.879 + ], + "angle": 0, + "content": "Eq. (1) may not be ideal for unlabeled target data due to the existence of modality gap [24]. To tackle this, we conceptualize vision inputs as a composite of a vision-associated component (VAC) and a language-associated component (LAC), denoted as \\( f_{v} = \\{f_{vac}, f_{lac}\\} \\). This leads us to obtain modality-specific classification results \\( y_{vac} \\) and \\( y_{lac} \\), before constructing a cross-modality output:" + }, + { + "type": "equation", + "bbox": [ + 0.161, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "\\[\ny _ {e n s} = w \\cdot y _ {v a c} + (1 - w) \\cdot y _ {l a c}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.431 + ], + "angle": 0, + "content": "where \\( w \\) is a set of learnable weights harmonizing the contributions of VAC and LAC. This design seeks to balance modality-agnostic information sharing and modality-specific information capturing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.893, + 0.614 + ], + "angle": 0, + "content": "Instead of separating LAC and VAC during training, we utilize \\( y_{ens} \\) to guide VAC learning, incorporating complementary modality information for a holistic cross-modal training. Furthermore, a fixed weight \\( w \\) may lack flexibility across diverse datasets and scenarios, potentially obscuring the distinction between VAC and LAC. Addressing this, we introduce a dynamic \\( w \\) that adeptly discriminates between modalities within \\( y_{ens} \\), calibrating their influence in the training. This strategy ensures tailored training approaches for different datasets or training stages, facilitating modality-specific information utilization. Next we detail on the training and aligning of LAC and VAC." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.623, + 0.768, + 0.64 + ], + "angle": 0, + "content": "3.2. Modality separation networks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.647, + 0.895, + 0.812 + ], + "angle": 0, + "content": "We first introduce the modality separation networks that disentangles CLIP-extracted features, which comprise two separators as shown in Fig. 2. These networks partition CLIP-extracted vision features into LAC and VAC using the text separator \\( G_{txt} \\) and the vision separator \\( G_{vis} \\), respectively. The separated components are defined as \\( f_{lac} = G_{txt}(f_v) \\) and \\( f_{vac} = G_{vis}(f_v) \\). Both separators are linear layers preserving the dimensionality of \\( f_v \\), such that \\( f_{vac}, f_{lac} \\in \\mathbb{R}^{d_v} \\). Drawing on deep feature separation principles [3], we apply an orthogonal loss to maintain the distinctness of LAC and VAC:" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.822, + 0.893, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {o r t h o}} = \\left| f _ {l a c} ^ {s} \\cdot f _ {v a c} ^ {s} \\right. ^ {\\top} | _ {F} ^ {2} + \\left| f _ {l a c} ^ {t} \\cdot f _ {v a c} ^ {t} \\right. ^ {\\top} | _ {F} ^ {2}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Different outputs for LAC and VAC are then generated. For the text modality, we utilize the zero-shot inference of CLIP to classify LAC by calculating the cosine similarity" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23366" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.441, + 0.107 + ], + "angle": 0, + "content": "between LAC and CLIP's text features, forming logits:" + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.112, + 0.469, + 0.131 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {l a c} = \\left(\\hat {l} _ {1}, \\hat {l} _ {2}, \\dots \\hat {l} _ {k}\\right), \\quad \\hat {l} _ {i} = \\cos \\left(\\mu_ {i}, f _ {l a c}\\right) / T, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.137, + 0.469, + 0.198 + ], + "angle": 0, + "content": "where \\(T\\) is temperature in pretrained CLIP. For VAC, we route it through a linear classifier with layers \\(\\Phi_1 \\in \\mathbb{R}^{d_v \\times d_b}\\) and \\(\\Phi_2 \\in \\mathbb{R}^{d_b \\times K}\\), producing the bottleneck feature with dimension \\(d_b\\) and output via:" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.206, + 0.469, + 0.222 + ], + "angle": 0, + "content": "\\[\nf _ {b} = \\Phi_ {1} \\left(f _ {v a c}\\right), \\quad \\hat {y} _ {v a c} = \\Phi_ {2} \\left(f _ {b}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.229, + 0.432, + 0.244 + ], + "angle": 0, + "content": "We provide implementation details in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.251, + 0.327, + 0.267 + ], + "angle": 0, + "content": "3.3. Modality-ensemble training" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.275, + 0.469, + 0.335 + ], + "angle": 0, + "content": "Having obtained disentangled components, we design customized training paradigm for each modality. A learnable weight further connects both modalities, establishing a unified modality-ensemble training framework." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.335, + 0.469, + 0.395 + ], + "angle": 0, + "content": "Learning LAC. To preserve the rich semantic content in pretrained CLIP, we distill this knowledge to LAC. For the target data, zero-shot similarity scores derived from pretrained CLIP serve as the teacher knowledge:" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.401, + 0.469, + 0.42 + ], + "angle": 0, + "content": "\\[\ny _ {l a c} ^ {t} = \\left(l _ {1} - \\bar {l}, l _ {2} - \\bar {l}, \\dots , l _ {k} - \\bar {l}\\right), \\quad l _ {i} = \\cos \\left(\\mu_ {i}, f _ {v} ^ {t}\\right) / T, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.426, + 0.469, + 0.518 + ], + "angle": 0, + "content": "with \\(\\bar{l} = \\frac{1}{K}\\sum_{k=1}^{K}l_k\\) normalizing the CLIP outputs and \\(T\\) the temperature of pretrained CLIP. The teacher knowledge in Eq. (6) guides the distillation for the unlabeled target LAC, while for the source data, cross-entropy loss is applied directly using labeled source data. The overall training loss for LAC combines Eq. (4) and Eq. (6) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.525, + 0.469, + 0.543 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {l a c} = \\mathrm {K L} \\left(\\hat {y} _ {l a c} ^ {t}, y _ {l a c} ^ {t}\\right) + \\alpha \\mathrm {C E} \\left(\\hat {y} _ {l a c} ^ {s}, y ^ {s}\\right), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.549, + 0.469, + 0.594 + ], + "angle": 0, + "content": "where \\(\\alpha\\) adjusts the influence of source data supervision, \\(\\mathrm{KL}(\\cdot ,\\cdot)\\) is the Kullback-Leibler divergence, and \\(\\mathrm{CE}(\\cdot ,\\cdot)\\) represents the standard cross-entropy loss." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.595, + 0.469, + 0.729 + ], + "angle": 0, + "content": "Obtaining pseudo label for VAC. Focusing on image modality, we aim to enhance the locality structure of vision representations—high inter-class discriminability and tight intra-class distribution—a feature that CLIP-extracted vision features lack, as detailed in Fig. 4a. To instill these locality structures within VAC, we utilize a K-means-based deep clustering approach [4, 21] to generate pseudo-labels for unlabeled target data. We calculate the clustering centroids for class \\( k \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.153, + 0.734, + 0.469, + 0.768 + ], + "angle": 0, + "content": "\\[\n\\phi_ {k} = \\frac {\\sum_ {x ^ {t}} \\delta_ {k} \\left(\\operatorname {s o f t m a x} \\left(\\hat {y} _ {e n s} ^ {t}\\right)\\right) \\cdot f _ {b} ^ {t}}{\\sum_ {x ^ {t}} \\delta_ {k} \\left(\\operatorname {s o f t m a x} \\left(\\hat {y} _ {e n s} ^ {t}\\right)\\right)}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.774, + 0.469, + 0.85 + ], + "angle": 0, + "content": "where \\(\\hat{y}_{ens}^{t}\\) represents target ensemble outputs discussed below, and \\(\\delta_{k}\\) selects the \\(k_{th}\\) logit. To mitigate imbalances in text modality predictions from CLIP [17, 49], we implement Approximated Controlled Direct Effect (ACDE) [49] to adjust similarity scores obtained in Eq. (4):" + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.857, + 0.469, + 0.897 + ], + "angle": 0, + "content": "\\[\n\\tilde {y} _ {l a c} ^ {t} = \\hat {y} _ {l a c} ^ {t} - \\tau \\log \\hat {p}, \\hat {p} \\leftarrow m \\hat {p} + (1 - m) \\frac {1}{B} \\sum_ {i = 1} ^ {B} p _ {i}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "where \\(m\\) is momentum, \\(\\tau\\) is a debiasing factor, \\(B\\) is the batch size, and \\(p_i = \\mathrm{softmax}(\\hat{y}_{lac}^t)\\) denotes classification probability of LAC. The ensemble outputs, used in the centroid calculation, are then defined as \\(\\hat{y}_{ens}^{t} = w\\cdot \\hat{y}_{vac}^{t} + (1 - w)\\cdot \\tilde{y}_{lac}^{t}\\). For any given target bottleneck feature \\(f_{b}^{t}\\), we compute its cosine similarity with all centroids, assigning the class with the highest similarity as the pseudo-label:" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.209, + 0.892, + 0.231 + ], + "angle": 0, + "content": "\\[\ny _ {v a c} ^ {t} = \\arg \\max _ {k} \\cos \\left(f _ {b} ^ {t}, \\phi_ {k}\\right). \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.242, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Learning VAC. We now train vision component on unifies outputs from both modalities. Utilizing Eq. (9) and Eq. (5), the target ensemble output \\(\\hat{y}_{\\text {ens }}^{t}\\) is formulated as:" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.298, + 0.891, + 0.316 + ], + "angle": 0, + "content": "\\[\n\\hat {y} _ {e n s} ^ {t} = w \\cdot \\hat {y} _ {v a c} ^ {t} + (1 - w) \\cdot \\tilde {y} _ {l a c} ^ {t}, \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.327, + 0.892, + 0.403 + ], + "angle": 0, + "content": "with the weight \\( w = W(VAC^t) \\) produced by the weight generator \\( W \\), as depicted in Fig. 2. Referring to Sec. 3.1, we optimize \\( \\hat{y}_{\\text{ens}}^t \\) rather than \\( \\hat{y}_{\\text{vac}}^t \\) directly, with \\( \\tilde{y}_{\\text{lac}}^t \\) serving as an auxiliary in training VAC and thus detached from the computational graph in Eq. (11)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.403, + 0.892, + 0.493 + ], + "angle": 0, + "content": "To enhance individual discriminability and global diversity, thereby preserving the locality structure of vision representations, we follow state-of-the-art [1, 20, 21] to apply an information maximization loss \\(\\mathcal{L}_{im}\\) comprising two components. The entropy loss \\(\\mathcal{L}_{ent}\\) improves individual certainty:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.504, + 0.891, + 0.547 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {e n t} = - \\mathbb {E} _ {x ^ {t} \\in \\mathcal {D} ^ {t}} \\left[ \\sum_ {k = 1} ^ {K} \\delta_ {k} \\left(\\hat {y} _ {e n s} ^ {t}\\right) \\log \\delta_ {k} \\left(\\hat {y} _ {e n s} ^ {t}\\right) \\right], \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.557, + 0.866, + 0.572 + ], + "angle": 0, + "content": "and the diversity loss fosters diverse class distributions:" + }, + { + "type": "equation", + "bbox": [ + 0.615, + 0.583, + 0.891, + 0.625 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {d i v} = - \\sum_ {k = 1} ^ {K} \\bar {q} _ {k} \\log \\bar {q} _ {k}, \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.636, + 0.882, + 0.653 + ], + "angle": 0, + "content": "where \\(\\overline{q}_k = -\\mathbb{E}_{x^t\\in \\mathcal{D}^t}\\delta_k(\\hat{y}_{ens}^t)\\). Hence, \\(\\mathcal{L}_{im}\\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.665, + 0.891, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {i m} = \\mathcal {L} _ {e n t} - \\mathcal {L} _ {d i v}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.692, + 0.891, + 0.739 + ], + "angle": 0, + "content": "The training of VAC is supervised by target pseudo labels for the vision modality, obtained through Eq. (10), while source labels directly optimize \\(\\hat{y}_{vac}^{s}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.749, + 0.891, + 0.767 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {v a c} = C E \\left(\\hat {y} _ {\\text {e n s}} ^ {t}, y _ {v a c} ^ {t}\\right) + \\beta C E \\left(\\hat {y} _ {v a c} ^ {s}, y ^ {s}\\right) + \\mathcal {L} _ {i m}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.778, + 0.88, + 0.793 + ], + "angle": 0, + "content": "where \\(\\beta\\) modulates the impact of source data supervision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.872, + 0.818 + ], + "angle": 0, + "content": "3.4. Aligning source and target by discriminator" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.892, + 0.901 + ], + "angle": 0, + "content": "To achieve domain adaptation on both modalities, we introduce a modality discriminator \\(D\\) to align VAC and LAC from both domains. Our approach utilizes a singular modality discriminator trained on the source domain to differentiate LAC from VAC, and then assesses alignment on the" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23367" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.152 + ], + "angle": 0, + "content": "target domain. Proper alignment across domains would enable \\( D \\) to discern LAC and VAC on the target domain without direct training. The modality discriminator is trained using binary cross-entropy loss:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.165, + 0.47, + 0.182 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b c e} = - \\left[ y _ {d i s} \\log \\hat {y} _ {d i s} + \\left(1 - y _ {d i s}\\right) \\log \\left(1 - \\hat {y} _ {d i s}\\right) \\right], \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.194, + 0.469, + 0.223 + ], + "angle": 0, + "content": "where \\( y_{dis} \\) represents the modality label (0 for VAC, 1 for LAC) and \\( \\hat{y}_{dis} \\) is the output of \\( D \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.224, + 0.469, + 0.284 + ], + "angle": 0, + "content": "Notably, \\(D\\) is only trained on the source domain using Eq. (16). On the target domain, only the separators \\(G_{vis}\\) and \\(G_{txt}\\) are updated to minimize Eq. (16), aligning target LAC and VAC with the source ones." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.295, + 0.29, + 0.311 + ], + "angle": 0, + "content": "3.5. Training and inference" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.318, + 0.469, + 0.409 + ], + "angle": 0, + "content": "Training. As depicted in Fig. 2, the pretrained text encoder and vision encoder are frozen, and we optimize parameters of \\( G_{txt} \\), \\( G_{vis} \\), \\( \\Phi_1 \\), \\( \\Phi_2 \\), \\( W \\), \\( D \\), denoted as \\( \\theta_{G_{txt}} \\), \\( \\theta_{G_{vis}} \\), \\( \\theta_{\\Phi_1} \\), \\( \\theta_{\\Phi_2} \\), \\( \\theta_W \\), \\( \\theta_D \\), respectively. Combining Eq. (7), Eq. (3), Eq. (15), Eq. (16), we define the following optimization problem:" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.424, + 0.469, + 0.448 + ], + "angle": 0, + "content": "\\[\n\\theta_ {G _ {t x t}} = \\underset {\\theta_ {G _ {t x t}}} {\\arg \\min } \\mathcal {L} _ {l a c} + \\gamma \\mathcal {L} _ {o r t h o} + \\gamma \\mathcal {L} _ {b c e}, \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.454, + 0.416, + 0.479 + ], + "angle": 0, + "content": "\\[\n\\theta_{G_{vis}} = \\operatorname *{arg min}_{\\theta_{G_{vis}}}\\mathcal{L}_{vac} + \\gamma \\mathcal{L}_{ortho} + \\gamma \\mathcal{L}_{bce},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.485, + 0.356, + 0.51 + ], + "angle": 0, + "content": "\\[\n\\theta_ {W}, \\theta_ {\\Phi_ {1}}, \\theta_ {\\Phi_ {2}} = \\operatorname * {a r g m i n} _ {\\theta_ {W}, \\bar {\\theta} _ {\\Phi_ {1}}, \\theta_ {\\Phi_ {2}}} \\mathcal {L} _ {v a c},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.516, + 0.276, + 0.539 + ], + "angle": 0, + "content": "\\[\n\\theta_{D} = \\operatorname *{arg min}_{\\theta_{D}}\\gamma \\mathcal{L}_{bce},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.551, + 0.469, + 0.596 + ], + "angle": 0, + "content": "where \\(\\gamma\\) is hyperparameter controlling regularization terms \\(\\mathcal{L}_{bce}\\) and \\(\\mathcal{L}_{ortho}\\). We present detailed training procedure of UniMoS in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.469, + 0.703 + ], + "angle": 0, + "content": "Inference. At inference, the final mixed prediction on target data is obtained using \\(\\hat{y}_{ens}^{t}\\) from Eq. (11), with a fixed mixup weight \\(w\\). The objective is to maximize accuracy by leveraging the strengths of both modalities for improved classification, as supported by our observations (Fig. 1), thus integrating outputs from both modalities to harness their combined advantages." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.717, + 0.209, + 0.733 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.742, + 0.391, + 0.758 + ], + "angle": 0, + "content": "4.1. Datasets and implementation details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "We extensively evaluate our method on three mainstream UDA benchmarks. Office-Home [46] consists of 65 categories divided into 4 distinct domains. On VisDA2017 [34], the goal is to transfer knowledge from 152k synthetic images (source domain) to 55k images of real items (target domain). DomainNet [35] is the most challenging UDA benchmark so far, containing 0.6 million samples from 345 categories divided into 6 distinct domains. Following previous works, we additionally provide results on" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "Mini-DomainNet [25, 40, 58], a subset of DomainNet with 4 domains and 126 categories." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.892, + 0.334 + ], + "angle": 0, + "content": "We conduct all experiments on an NVIDIA RTX 2080Ti GPU. Since our method does not involve updating CLIP's pretrained parameters or prompts, the CLIP-extracted vision and text features are obtained via one single forward and saved in memory, thus greatly saving computation costs. For all tasks, we adopt SGD optimizer with batch size 32, and set momentum \\( m \\) in Eq. (9) to 0.99 and debias factor \\( \\tau \\) in Eq. (9) to 0.5. For Office-Home and DomainNet, we train 50 epochs with initial learning rate 3e-3 and adopt annealing strategy [8] for learning rate decay. We train for 10 epochs with initial learning rate 9e-4 on VisDA due to fast convergence. The fixed mixup weight described in Sec. 3.5 is set to 0.3 for all tasks. We set regularization weight \\( \\gamma \\) in Eq. (17) to 0.01 across all datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.347, + 0.681, + 0.361 + ], + "angle": 0, + "content": "4.2. Benchmark results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.627 + ], + "angle": 0, + "content": "Office-Home. Tab. 1 gives classification accuracies on 12 adaptation tasks on Office-Home using the ResNet50 [11] backbone. To ensure a fair comparison, we categorize CLIP-based methods into two groups: 'none-tuning' and 'full-tuning'. The former involves learning prompts or additional modules without adjusting the pretrained CLIP backbones, while the latter optimizes the pretrained parameters of CLIP for specific tasks. It is evident from the results that our proposed UniMoS consistently outperforms both 'none-tuning' and 'full-tuning' methods. Notably, we obtain \\(+1.3\\%\\) performance boost than the strong baseline PADCLIP, which fine-tunes the CLIP vision backbone. Our method requires no parameter update or data forwarding of CLIP backbones, thus is much computationally cheaper. Especially on tasks that take P as target domain, we achieve up to \\(+5.4\\%\\) performance boost than PADCLIP, demonstrating the superiority of multimodal adaptation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.779 + ], + "angle": 0, + "content": "VisDA-2017. Tab. 2 shows class-wise classification accuracies on VisDA using ResNet101 [11]. Our method achieves the best performance among 'none-tuning' CLIP methods, while slightly falling behind PADCLIP. The reason is that CLIP has not been trained on the synthetic images like those from source domain of VisDA, resulting in incompatibilities between the VisDA dataset and CLIP. Similar observations are made by PADCLIP [17], which opts to fine-tune the vision branch of CLIP to address this challenge. Nevertheless, our approach outperforms typical UDA methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.901 + ], + "angle": 0, + "content": "DomainNet. Tab. 3 presents classification accuracies of 30 cross-domain adaptation tasks on the most challenging benchmark DomainNet. Rows represent source domains and columns represent target domains. Our method reaches comparable performance with the strong baseline PADCLIP. One significant observation is that our UniMoS obtains lower accuracy than PADCLIP (6.6% lower in average) on tasks with qdr as target. This discrepancy arises" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23368" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.15, + 0.09, + 0.82, + 0.103 + ], + "angle": 0, + "content": "Table 1. UDA results on Office-Home. Best results are marked in bold font. Methods with \\( * \\) ’ are based on CLIP." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.106, + 0.894, + 0.345 + ], + "angle": 0, + "content": "
MethodBackboneA→CA→PA→RC→AC→PC→RP→AP→CP→RR→AR→CR→PAvg.
SourceOnly [11]ResNet5034.950.058.037.441.946.238.531.260.453.941.259.946.1
ParetoDA [22]56.875.980.564.473.573.765.655.281.375.261.183.970.6
SDAT [37]58.277.182.266.377.676.863.357.082.274.964.786.072.2
MSGD [50]58.776.978.970.176.276.669.057.282.374.962.784.572.3
Fixbi [32]58.177.380.467.779.578.165.857.981.776.462.986.772.7
CST [26]59.079.683.468.477.176.768.956.483.075.362.285.172.9
ATDOC [23]60.277.882.268.578.677.968.458.483.174.861.587.273.2
KUDA [42]58.280.082.971.180.380.771.356.883.275.560.386.673.9
EIDCo [60]63.880.882.671.580.180.972.161.384.578.665.887.175.8
ICON [55]63.381.384.570.382.181.070.361.883.775.668.687.375.8
PADCLIP* [17]ResNet50-full-tuning57.584.083.877.885.584.776.359.285.478.160.286.776.6
CLIP* [36]ResNet50-none-tuning51.781.582.371.781.582.371.751.782.371.751.781.571.8
DAPrompt* [10]54.184.384.874.483.785.074.554.684.875.254.783.874.5
ADCLIP* [41]55.485.285.676.185.886.276.756.185.476.856.185.575.9
UniMoS* (ours)59.589.486.975.289.686.875.458.487.276.959.589.777.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.151, + 0.353, + 0.819, + 0.367 + ], + "angle": 0, + "content": "Table 2. UDA results on VisDA-2017. Best results are marked in bold font. Methods with \\* are based on CLIP." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.37, + 0.892, + 0.551 + ], + "angle": 0, + "content": "
MethodBackboneplanebicyclebuscarhorseknifemcyclpersonplantsktbrdtraintruckAvg.
SourceOnly [11]ResNet10155.153.361.959.180.617.979.731.281.026.573.58.552.4
ParetoDA [22]95.982.881.358.793.993.785.983.091.992.087.151.883.2
MSGD [50]97.583.484.469.495.994.190.975.595.594.688.144.984.5
ATDOC [23]95.384.782.475.695.897.788.776.694.091.791.561.986.3
CAN [15]97.087.282.574.397.896.290.880.796.696.387.559.987.2
FixBi [32]96.187.890.590.396.895.392.888.797.294.290.925.787.2
PADCLIP* [17]ResNet101-full-tuning96.788.887.082.897.193.091.383.095.591.891.563.088.5
CLIP* [36]ResNet101-none-tuning98.283.990.573.597.284.095.365.779.489.991.863.384.4
DAPrompt* [10]97.883.188.877.997.491.594.279.788.689.392.562.086.9
ADCLIP* [41]98.183.691.276.698.193.496.081.486.491.592.164.287.7
UniMoS* (ours)97.788.290.174.696.895.892.484.190.889.091.865.388.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.47, + 0.719 + ], + "angle": 0, + "content": "from a significant domain gap between qdr and other domains, which is challenging to bridge without tuning the CLIP backbones. However, despite this, we manage to achieve superior performance to PADCLIP on all other tasks, thereby mitigating the overall \\(6.6\\%\\) performance drop. We also surpass all competing methods significantly. Tab. 4 compares UniMoS with available CLIP-based non-tuning methods on Mini-DomainNet, where our method achieves significant performance boost. Detailed results on Mini-DomainNet are given in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.727, + 0.228, + 0.743 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this section we validate the efficacy of each module in UniMoS. Tab. 5 presents averaged accuracies on Office-Home and VisDA-2017 by removing specific modules while maintaining other settings identical. The 'w/o debiasing' is obtained by skipping the debias procedure in Eq. (9). A primary observation is that the removal of any module leads to a performance drop to varying degrees, underscoring the positive contribution of each module to the overall outcome. The 'w/o learnable weight' row is obtained by replacing \\( w \\) in Eq. (11) with a constant 0.5, re" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.628 + ], + "angle": 0, + "content": "sulting in the most pronounced performance decline. This emphasizes the significance of dynamic weights, which enables VAC to focus on vision-specific parts. Further insights into the effects of dynamic \\( w \\) are detailed in Sec. 4.4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.705 + ], + "angle": 0, + "content": "Tab. 6 ablates on the choice of backbones. We experiment with three backbones on Office-Home, and our UniMoS consistently outperforms all competing methods, proving that our method is generalizable across various models. Detailed results are given in Supplementary." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.712, + 0.625, + 0.726 + ], + "angle": 0, + "content": "4.4. Discussions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Effectiveness of learnable weight \\( w \\). To better understand how the learnable ensemble weight \\( w \\) in Eq. (2) boosts performance, Fig. 3 compares the training process with and without dynamic \\( w \\). We set a fixed weight of 0.5 for both LAC and VAC in 'w/o learnable w', and learn dynamic weights (shown as 'Learned weight w' in the figure) in other settings. Our first observation is that in our full design, accuracy of VAC increases steadily as the training progresses. Leveraging complementary modality-specific information from LAC, the final mixed outputs achieve higher accuracy than VAC alone. As stated in Sec. 3.1, the goal of" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23369" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.154, + 0.09, + 0.816, + 0.103 + ], + "angle": 0, + "content": "Table 3. UDA results on DomainNet. Best results are marked in bold font. Methods with \\( * \\) ’ are based on CLIP." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.105, + 0.894, + 0.366 + ], + "angle": 0, + "content": "
DeiT-B [44]clpinfpptqdrrelsktavgViT-B [6]clpinfpptqdrrelsktavgSSRT-B [43]clpinfpptqdrrelsktavg
clp-24.349.615.865.352.141.4clp-27.253.113.271.253.343.6clp33.860.219.475.859.849.8
inf45.9-45.96.761.439.539.9inf51.4-49.34.066.341.142.4inf55.5-54.09.068.244.746.3
ppt53.223.8-6.566.444.738.9ppt53.125.6-4.870.041.839.1ppt61.728.5-8.471.455.245.0
qdr31.96.815.4-23.420.619.6qdr30.54.516.0-27.019.319.5qdr42.58.824.2-37.633.629.3
rel59.025.856.39.2-44.839.0rel58.429.060.06.0-45.839.9rel69.937.166.010.1-58.948.4
skt60.620.648.416.561.2-41.5skt63.923.852.314.467.4-44.4skt70.632.862.221.773.2-52.1
avg50.120.343.110.955.540.336.7avg51.522.046.18.560.440.338.1avg60.028.253.313.765.350.445.2
CDTrans -DeiT [51]clpinfpptqdrrelsktavgPMTrans -Swin [63]clpinfpptqdrrelsktavgCLIP -B* [36]clpinfpptqdrrelsktavg
clp-29.457.226.072.658.148.7clp-34.262.732.579.363.754.5clp-70.170.170.170.170.170.1
inf57.0-54.412.869.548.448.4inf67.4-61.122.278.057.657.3inf46.4-46.446.446.446.446.4
ppt62.927.4-15.872.153.946.4ppt69.733.5-23.979.861.253.6ppt61.761.7-61.761.761.761.7
qdr44.68.929.0-42.628.530.7qdr54.617.438.9-49.541.040.3qdr13.713.713.7-13.713.713.7
rel66.231.061.516.2-52.945.6rel74.135.370.025.4-61.153.2rel82.982.982.9-82.982.982.9
skt69.029.659.027.272.5-51.5skt73.833.062.630.977.5-55.6skt62.662.662.662.6-62.6
avg59.925.352.219.665.948.445.2avg67.930.759.127.072.856.952.4avg53.558.255.164.750.955.056.2
DAPrompt -B* [10]clpinfpptqdrrelsktavgPADCLIP -B* [17]clpinfpptqdrrelsktavgUniMoS -B* (ours)clpinfpptqdrrelsktavg
clp-73.073.872.673.973.573.4clp-73.675.474.676.476.375.3clp-76.577.276.677.577.877.1
inf50.8-50.149.650.650.350.3inf55.1-54.353.654.954.954.6inf55.1-55.054.655.355.255.0
ppt70.269.6-68.970.469.969.8ppt71.170.6-70.072.771.771.2ppt72.371.5-69.472.572.671.7
qdr17.214.413.9-14.313.914.7qdr36.818.032.0-31.734.930.7qdr25.022.923.6-23.725.124.1
rel84.984.884.984.7-84.684.8rel84.283.583.583.1-83.683.6rel86.085.985.885.5-85.985.8
skt65.865.465.864.965.9-65.6skt68.166.667.266.167.5-67.1skt68.567.868.267.568.0-68.0
avg57.861.457.768.155.058.459.8avg63.162.562.569.560.664.363.7avg61.464.962.070.759.463.363.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.379, + 0.47, + 0.407 + ], + "angle": 0, + "content": "Table 4. UDA results on Mini-DomainNet. Best results are marked in bold font. All compared methods are CLIP-based." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.413, + 0.47, + 0.482 + ], + "angle": 0, + "content": "
MethodBackboneAcc.MethodBackboneAcc.
CLIPResNet5071.2CLIPViT-B82.8
DAPrompt74.8DAPrompt85.8
ADCLIP75.2ADCLIP86.9
UniMoS (ours)78.0UniMoS (ours)87.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.1, + 0.494, + 0.447, + 0.508 + ], + "angle": 0, + "content": "Table 5. Ablation study on Office-Home and VisDA-2017." + }, + { + "type": "table", + "bbox": [ + 0.104, + 0.513, + 0.445, + 0.628 + ], + "angle": 0, + "content": "
MethodOffice-HomeVisDA-2017
w/o Lortho77.487.6
w/o debiasing77.387.7
w/o Lim77.087.8
w/o Ldistill77.087.6
w/o learnable weight76.986.2
w/o modality discriminator77.687.9
UniMoS (full design)77.988.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.839 + ], + "angle": 0, + "content": "dynamic ensemble weight is to adaptively identify and preserve modality-specific information. We show in Fig. 3 that, the learned weight changes in each epoch to fit the training process. Without its support (w/o learnable w), the accuracy of VAC outputs drops significantly and finally converges with LAC. This occurs because employing a static weight would compromise the modality separation effects, causing both modalities to collapse to poor performance. In the example given by Fig. 3, accuracy of 'VAC output w/o learnable w' is \\(3.5\\%\\) lower than that of the full design 'VAC output'. The phenomenon indicates the significance of training with dynamic ensemble weights in our design. More examples are given in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Computation analysis. Tab. 7 compares computation costs of different methods on VisDA dataset. Our method necessitates training only a few linear layers without updating CLIP backbones, bringing great parameter efficiency." + }, + { + "type": "image", + "bbox": [ + 0.549, + 0.381, + 0.848, + 0.553 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.558, + 0.89, + 0.573 + ], + "angle": 0, + "content": "Figure 3. Effects of learnable ensemble weight \\( w \\) on Office-Home." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.587, + 0.892, + 0.615 + ], + "angle": 0, + "content": "Table 6. Results with different backbones on Office-Home. Best results are in bold. All compared methods are based on CLIP." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.619, + 0.892, + 0.705 + ], + "angle": 0, + "content": "
MethodBackboneAcc.MethodBackboneAcc.
UniMoS (ours)ResNet5077.9CLIP82.4
CLIPViT-L87.0DAPromptViT-B84.4
DAPrompt88.7ADCLIP86.1
ADCLIP90.5PADCLIP86.7
UniMoS (ours)90.7UniMoS (ours)86.9
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.718, + 0.892, + 0.869 + ], + "angle": 0, + "content": "Furthermore, only one forward through CLIP is needed, which allows UniMoS achieve more than \\(47 \\times\\) training speed boost than PADCLIP. Prompt learning methods like DAPrompt also requires no training on CLIP backbones, but they require extensive iterative forwarding of data through CLIP to learn optimal prompts per class, leading to low computing efficiency and scalability to larger datasets. When running on DomainNet with 345 classes, DAPrompt requires more than 22G GPU memory, while our method requires less than 3G. More details are in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.891, + 0.902 + ], + "angle": 0, + "content": "Feature distribution visualization. To demonstrate the efficacy of modality separation and feature alignment, we per" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23370" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.097, + 0.092, + 0.348, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.116, + 0.245, + 0.324, + 0.257 + ], + "angle": 0, + "content": "(a) CLIP-extracted feature distribution." + }, + { + "type": "image", + "bbox": [ + 0.359, + 0.092, + 0.613, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.402, + 0.245, + 0.565, + 0.258 + ], + "angle": 0, + "content": "(b) Modality separation effect." + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.092, + 0.875, + 0.238 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.632, + 0.244, + 0.86, + 0.258 + ], + "angle": 0, + "content": "(c) Aligned bottleneck feature distribution." + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.26, + 0.894, + 0.302 + ], + "angle": 0, + "content": "Figure 4. T-sne visualization [45] of the effects of UniMoS on \\(\\mathrm{A}\\rightarrow \\mathrm{P}\\) task from Office-Home. UniMoS effectively disentangles CLIP-extracted vision features (Fig. 4a) into LAC and VAC (Fig. 4b, obtained by randomly selecting 25 classes), and constructs clear cross-domain locality structures (Fig. 4c)." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.311, + 0.47, + 0.338 + ], + "angle": 0, + "content": "Table 7. Computation analysis on VisDA-2017. Best results are marked in bold font. Methods with \\* are based on CLIP." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.34, + 0.47, + 0.429 + ], + "angle": 0, + "content": "
MethodBkb.Param.Throughput (images/s)Train timeFLOPsAcc.
DAPrompt*ResNet1011.2M2444.3H11.3G86.9
FixBi86.1M1025.5H15.73G87.2
CAN42.5M3110.5H7.9G87.2
PADCLIP*--23.5H*-88.5
UniMoS* (ours)0.79M26670.5H<0.01G88.1
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.47, + 0.717 + ], + "angle": 0, + "content": "form t-sne [45] visualization on various features at different phases of our method. Fig. 4a shows CLIP-extracted vision features from source (green) and target (blue) domain, along with CLIP-extracted text features (red) of naive prompts. The text features distribute distantly with vision features, proving the existence of modality gap. Besides, CLIP-extracted vision features form poor class discriminability and locality structures. Fig. 4b showcases the separated LAC and VAC of our method. A clear boundary can be observed between the features of both modalities, indicating the effectiveness of modality separation. Additionally, the text features distribute closer to LAC, proving that the separated LAC is indeed more relevant to the text modality. Following feature alignment and VAC training, the bottleneck features \\( f_{b} \\) from both domains display a compact class-level locality structure, as demonstrated in Fig. 4c. This compact structure contributes significantly to the accuracy of the final classification results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Hyperparameter sensitivity. In the calibration of UniMoS, we encounter three hyperparameters to determine: \\(\\alpha\\) in Eq. (7), \\(\\beta\\) in Eq. (15), and \\(\\gamma\\) in Eq. (17). We empirically discover that alternating \\(\\gamma\\) has little impact within each dataset, so we focus on exploring the effects of \\(\\alpha\\) and \\(\\beta\\). As illustrated in Fig. 5a, the performance on VisDA is notably influenced by \\(\\alpha\\), with smaller values leading to improved accuracy. This outcome is attributed to the fact, as discussed in Sec. 4.2, that CLIP struggles to adequately iden" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.311, + 0.695, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.556, + 0.434, + 0.643, + 0.446 + ], + "angle": 0, + "content": "(a) VisDA-2017" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.312, + 0.884, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.745, + 0.434, + 0.836, + 0.446 + ], + "angle": 0, + "content": "(b) Office-Home" + }, + { + "type": "image_caption", + "bbox": [ + 0.505, + 0.449, + 0.885, + 0.464 + ], + "angle": 0, + "content": "Figure 5. Parameter sensitivity analysis on \\(\\alpha\\) and \\(\\beta\\) of UniMoS." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.474, + 0.892, + 0.566 + ], + "angle": 0, + "content": "tify source synthetic images from VisDA. Consequently, down-weighting source supervision on LAC proves beneficial. Conversely, source supervision from both modalities of Office-Home are important. They positively and equally contributes to the adaptation process, so \\(\\alpha = 1\\) and \\(\\beta = 1\\) brings the best result, as shown in Fig. 5b." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.58, + 0.628, + 0.595 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.605, + 0.893, + 0.786 + ], + "angle": 0, + "content": "Inspired by the theory of modality gap, in this paper we propose a Unified Modality Separation framework for unsupervised domain adaptation. The CLIP-extracted vision features are explicitly disentangled into vision-associated and language-associated components, which are trained differently according to their modality strengths and further aligned by a modality discriminator. A modality-ensemble training paradigm unifies both components to leverage modality-specific information while preserving modality-shared contexts, contributing to successful classification. This work is hope to inspire further analysis and exploitation of the multimodal features in pretrained VLMs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.8, + 0.688, + 0.817 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.893, + 0.901 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62176042, and in part by Sichuan Science and Technology Program under Grant 2023NSFSC0483, and in part by Tencent Marketing Solution Rhino-Bird Focused Research Program." + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.863, + 0.47, + 0.901 + ], + "angle": 0, + "content": "*Cited from PADCLIP [17]. PADCLIP conducts the experiments on an NVIDIA Tesla V100 GPU. Results on other metrics are unavailable since the authors have not released the code implementations yet." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23371" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Sk Miraj Ahmed, Dripta S Raychaudhuri, Sujoy Paul, Samet Oymak, and Amit K Roy-Chowdhury. Unsupervised multisource domain adaptation without access to source data. 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Yet, most transfer approaches for VLMs focus on either the language or visual branches, overlooking the nuanced interplay between both modalities. In this work, we introduce a Unified Modality Separation (UniMoS) framework for unsupervised domain adaptation. Leveraging insights from modality gap studies, we craft a nimble modality separation network that distinctly disentangles CLIP's features into language-associated and vision-associated components. Our proposed Modality-Ensemble Training (MET) method fosters the exchange of modality-agnostic information while maintaining modality-specific nuances. We align features across domains using a modality discriminator. Comprehensive evaluations on three benchmarks reveal our approach sets a new state-of-the-art with minimal computational costs. Code: https://github.com/TL-UESTC/UniMoS. + +# 1. Introduction + +Unsupervised domain adaptation (UDA) [2, 7, 29, 30] aims to apply knowledge trained on a source domain to an unlabeled target domain, a process invaluable in data-scarce scenarios. Conventional methods often struggle with bridging the gap between source and target domains, finding it challenging to develop consistent features across domains [19, 39]. In image classification, aligning vision features while neglecting semantic content can lead to difficulties in differentiating complex samples [10, 41]. Vision-language models (VLMs) such as CLIP [36] and ALIGN [13] circumvent these issues through joint multimodal pretraining on images and texts. This extensive pretraining endows publicly available VLMs with robust zero-shot transfer abl- + +![](images/33cbdc16c5614d7b3ad158a09fee11ee6450b9bf8b3c153969fda50c87b164cb.jpg) +Figure 1. Examples of modality-specific information from task Art $\rightarrow$ RealWorld in Office-Home dataset. The digits are top-2 highest classification probabilities given by both modalities. + +
Modality / Prob.couchchair (√)
image modality0.0020.998
text modality0.8320.130
+ +![](images/f063ea6fb9027d8c91ba7e4cff3d54c0b84e293e0ad20e083f25a2f45dd37a91.jpg) + +
Modality / Prob.shelffile cabinet ( \( \checkmark \) )
image modality0.8990.101
text modality0.0620.928
+ +ities and a broad base of conceptual knowledge, making them highly suitable for comprehensive UDA. They facilitate alignment across both visual and textual modalities, enhancing adaptability and applicability in diverse contexts. + +Previous studies have shown promising results by adapting VLMs like CLIP for unsupervised domain adaptation (UDA). For instance, DAPrompt [10] introduces learning both domain-agnostic and domain-specific text embeddings, while PADCLIP [17] focuses on fine-tuning the vision branch of CLIP for adaptive visual feature extraction. However, recent research [14, 24] highlights a modality gap in VLMs, revealing that, despite training efforts, vision and text features often remain distinctly distributed. We argue that adapting a single modality is less than ideal due to the existence of unique, modality-specific cues in misaligned textual and visual components. We suggest that certain samples are best classified using specific modalities, a hypothesis supported by empirical observations in Fig. 1. This figure shows differing classification patterns when each modality is adapted independently to the unlabeled target data. Text modality results derive from CLIP's zero-shot capabilities, while image results come from linear probing with target pseudo-labels. For instance, visually straightforward items like a cushioned chair are accurately classified by the vision linear classifier after tuning on target dataset. However, pretrained CLIP can erroneously cat + +egorize such items under visually similar classes. In contrast, complex items with nuanced semantic details, like a file cabinet resembling a shelf, may confuse the vision classifier, while CLIP's broader knowledge base facilitates correct zero-shot predictions. In summary, while the vision branch effectively discerns class-specific visual patterns, the text branch leverages semantic information to clarify ambiguous cases. This observation lays the groundwork for a multimodal adaptation framework that synergistically combines the strengths of both modalities. + +A direct approach to domain adaptation involves concurrently fine-tuning vision branch and crafting textual prompts, which risks disturbing the image-text representation pairs in pretrained CLIP and is computationally intensive [9, 57]. As a more efficient alternative, we propose to explicitly disentangle CLIP-extracted visual features into two complementary parts. The first component retains the language-associated semantic knowledge inherent in CLIP, while the second focuses on vision-specific attributes crucial for distinguishing between nuanced visual categories. + +We devised a set of modality separation networks with dual branches to project CLIP-encoded visual features into distinct language-associated components (LAC) and vision-associated components (VAC). An orthogonal regularization is employed to ensure these branches yield discrete, disentangled representations. Each component is optimized based on its inherent modality strengths. For the LAC branch, we utilize knowledge distillation on target data to harness the rich semantic content from the original pretrained CLIP model. Additionally, we implement a debiasing method to mitigate dataset bias in CLIP's zero-shot results. For the VAC branch, the locality structure within visual feature spaces [20, 53, 54] is leveraged to generate visual pseudo-labels for supervised learning on target data. We then introduce a novel Modality-Ensemble Training (MET) strategy that synergistically merges outputs from both modalities. A weight generator dynamically assembles these predictions, supervised by VAC pseudo-labels on target data and actual labels on source data. Importantly, the text modality output remains isolated during MET to preserve independent training and maintain pretrained semantics. Additionally, a modality discriminator is utilized to align LAC and VAC across domains for unsupervised domain adaptation. Trained on source data to distinguish between LAC and VAC, this discriminator is frozen on the target domain, directly updating the separation networks to produce domain-invariant LAC and VAC. This approach ensures a consistent modality separation across domains, facilitating simultaneous adaptation in both modalities. + +Contributions: 1. We investigate the modality gap phenomenon in the context of applying Vision-Language Models (VLMs) to unsupervised domain adaptation, revealing the limitations of adapting a single modality; 2. We intro- + +duce a novel framework, Unified Modality Separation (UniMoS), which, coupled with a Modality-Ensemble Training (MET) approach, facilitates effective multimodal adaptation; 3. Our comprehensive analysis and validations underscore and efficiency of the proposed UniMoS, demonstrating its ability to set new state-of-the-art benchmarks while maintaining low computational demands. + +# 2. Related work + +Unsupervised domain adaptation (UDA). A core challenge in UDA is aligning representations between the source domain and unlabeled target domain. Prior techniques can be categorized as discrepancy-based [18, 28, 59] and adversarial methods [7, 30, 39]. Discrepancy-based methods explicitly minimizes divergence metrics including MMD [18], MDD [59], etc. Adversarial methods extract domain invariant features via a min-max game between the feature extractor and domain discriminator [7, 30]. Recent works focus on exploiting target data structures via self-training techniques [15, 53-55, 60]. ICON [55] learns an invariant classifier with consistent predictions to remove the spurious correlation inconsistency in the target domain. EIDCo [60] combines Mixup [56] with IDCo loss [5, 12] to explore target data distribution. Vision transformer (ViT) [6] and its variants have also gained popularity due to their superior performance [51, 52, 63]. PMTrans [63] mixes patch representations in SwinTransformer [27] as an intermediate domain bridge. CDTrans [51] aligns features extracted by DeiT [44] via cross-attention. + +Vision-language models (VLMs) have shown great generalization abilities due to extensive multimodal pretraining [13, 36, 47, 48]. CLIP [36] is trained from 400 million text-image pairs, while ALIGN [13] leverages more than one billion text-image pairs. Subsequent works have built on pretrained VLMs in various ways. Some learn prompt texts to transfer VLMs to downstream tasks [10, 33, 38, 61, 62], while others incorporate additional tunable layers on the frozen pretrained encoder [9, 57]. Beyond utilizing existing VLMs, research also aims to improve VLM training [14, 31]. Liang et al. [24] reveal that VLMs exhibit a modality gap, failing to perfectly align multimodal features. Jiang et al. [14] conduct theoretical analysis on modality gap and propose latent space regularization to preserve modality-specific information. MaPLe [16] utilize prompt learning on both modality branches to improve alignment. Our approach is fundamentally different since we disentangle VLM-extracted features posteriorly instead of training VLM from scratch, requiring far less computation costs. Besides, our method requires no labeling on target domain. VLMs have also been adopted for UDA [10, 17, 41]. DAPrompt [10] learns domain-specific and domain-agnostic textual prompts for each class. ADCLIP [41] learns domain invariant prompts by conditioning + +![](images/25449e5ea3aa30d8207f56872986ac020ecf191956a4fae6681e40f3fb1e2969.jpg) +Figure 2. Framework of our method. We freeze the pretrained vision and text encoder of CLIP. CLIP-extracted vision features are disentangled into language-associated components $(f_{lac})$ and vision-associated components $(f_{vac})$ by the modality separation networks. We obtain zero-shot results from CLIP as teacher knowledge, and distill the knowledge to LAC. We then introduce a weight generator to assemble the modality outputs to train VAC. A modality discriminator is applied to align LAC and VAC from both domains. + +on image style and content features. PADCLIP [17] dynamically adjusts learning rate while tuning CLIP to prevent catastrophic forgetting. However, these methods perform adaptation on either the visual or textual modality in isolation. Our work addresses this limitation by proposing a unified adaptation framework for the multimodal features. + +# 3. Method + +# 3.1. Problem formulation + +In this study, superscripts differentiate domains, with symbols lacking superscripts applicable to both domains. We consider a labeled source domain $\mathcal{D}^s = \{(x_i^s,y_i^s)\}_{i = 1}^{N^s}$ and aim to develop a model generalizable to an unlabeled target domain $\mathcal{D}^t = \{(x_i^t)\}_{i = 1}^{N^t}$ . CLIP [36] features a vision encoder $g_{vis}$ and a text encoder $g_{txt}$ . The vision feature for an image input $x$ is denoted as $f_{v} = g_{vis}(x)$ . Employing the zero-shot inference strategy from [17], we construct naive prompts $\{(t_i)\}_{i = 1}^K$ as a [DOMAIN] photo of a [CLASS], with $K$ representing the number of classes, [DOMAIN] indicating domain specifics, and [CLASS] the class name. Text features are then derived as $\mu_{i} = g_{txt}(t_{i})$ . $\mu_{i}$ and $f_{v}$ are both features with $d_v$ dimension. Classification is based on the highest cosine similarity between $f_{v}$ and $\mu_{i}$ : + +$$ +\hat {y} _ {z s} = \underset {i} {\arg \max } \cos \left(\mu_ {i}, f _ {v}\right). \tag {1} +$$ + +Eq. (1) may not be ideal for unlabeled target data due to the existence of modality gap [24]. To tackle this, we conceptualize vision inputs as a composite of a vision-associated component (VAC) and a language-associated component (LAC), denoted as $f_{v} = \{f_{vac}, f_{lac}\}$ . This leads us to obtain modality-specific classification results $y_{vac}$ and $y_{lac}$ , before constructing a cross-modality output: + +$$ +y _ {e n s} = w \cdot y _ {v a c} + (1 - w) \cdot y _ {l a c}, \tag {2} +$$ + +where $w$ is a set of learnable weights harmonizing the contributions of VAC and LAC. This design seeks to balance modality-agnostic information sharing and modality-specific information capturing. + +Instead of separating LAC and VAC during training, we utilize $y_{ens}$ to guide VAC learning, incorporating complementary modality information for a holistic cross-modal training. Furthermore, a fixed weight $w$ may lack flexibility across diverse datasets and scenarios, potentially obscuring the distinction between VAC and LAC. Addressing this, we introduce a dynamic $w$ that adeptly discriminates between modalities within $y_{ens}$ , calibrating their influence in the training. This strategy ensures tailored training approaches for different datasets or training stages, facilitating modality-specific information utilization. Next we detail on the training and aligning of LAC and VAC. + +# 3.2. Modality separation networks + +We first introduce the modality separation networks that disentangles CLIP-extracted features, which comprise two separators as shown in Fig. 2. These networks partition CLIP-extracted vision features into LAC and VAC using the text separator $G_{txt}$ and the vision separator $G_{vis}$ , respectively. The separated components are defined as $f_{lac} = G_{txt}(f_v)$ and $f_{vac} = G_{vis}(f_v)$ . Both separators are linear layers preserving the dimensionality of $f_v$ , such that $f_{vac}, f_{lac} \in \mathbb{R}^{d_v}$ . Drawing on deep feature separation principles [3], we apply an orthogonal loss to maintain the distinctness of LAC and VAC: + +$$ +\mathcal {L} _ {\text {o r t h o}} = \left| f _ {l a c} ^ {s} \cdot f _ {v a c} ^ {s} \right. ^ {\top} | _ {F} ^ {2} + \left| f _ {l a c} ^ {t} \cdot f _ {v a c} ^ {t} \right. ^ {\top} | _ {F} ^ {2}. \tag {3} +$$ + +Different outputs for LAC and VAC are then generated. For the text modality, we utilize the zero-shot inference of CLIP to classify LAC by calculating the cosine similarity + +between LAC and CLIP's text features, forming logits: + +$$ +\hat {y} _ {l a c} = \left(\hat {l} _ {1}, \hat {l} _ {2}, \dots \hat {l} _ {k}\right), \quad \hat {l} _ {i} = \cos \left(\mu_ {i}, f _ {l a c}\right) / T, \tag {4} +$$ + +where $T$ is temperature in pretrained CLIP. For VAC, we route it through a linear classifier with layers $\Phi_1 \in \mathbb{R}^{d_v \times d_b}$ and $\Phi_2 \in \mathbb{R}^{d_b \times K}$ , producing the bottleneck feature with dimension $d_b$ and output via: + +$$ +f _ {b} = \Phi_ {1} \left(f _ {v a c}\right), \quad \hat {y} _ {v a c} = \Phi_ {2} \left(f _ {b}\right). \tag {5} +$$ + +We provide implementation details in Supplementary. + +# 3.3. Modality-ensemble training + +Having obtained disentangled components, we design customized training paradigm for each modality. A learnable weight further connects both modalities, establishing a unified modality-ensemble training framework. + +Learning LAC. To preserve the rich semantic content in pretrained CLIP, we distill this knowledge to LAC. For the target data, zero-shot similarity scores derived from pretrained CLIP serve as the teacher knowledge: + +$$ +y _ {l a c} ^ {t} = \left(l _ {1} - \bar {l}, l _ {2} - \bar {l}, \dots , l _ {k} - \bar {l}\right), \quad l _ {i} = \cos \left(\mu_ {i}, f _ {v} ^ {t}\right) / T, \tag {6} +$$ + +with $\bar{l} = \frac{1}{K}\sum_{k=1}^{K}l_k$ normalizing the CLIP outputs and $T$ the temperature of pretrained CLIP. The teacher knowledge in Eq. (6) guides the distillation for the unlabeled target LAC, while for the source data, cross-entropy loss is applied directly using labeled source data. The overall training loss for LAC combines Eq. (4) and Eq. (6) as follows: + +$$ +\mathcal {L} _ {l a c} = \mathrm {K L} \left(\hat {y} _ {l a c} ^ {t}, y _ {l a c} ^ {t}\right) + \alpha \mathrm {C E} \left(\hat {y} _ {l a c} ^ {s}, y ^ {s}\right), \tag {7} +$$ + +where $\alpha$ adjusts the influence of source data supervision, $\mathrm{KL}(\cdot ,\cdot)$ is the Kullback-Leibler divergence, and $\mathrm{CE}(\cdot ,\cdot)$ represents the standard cross-entropy loss. + +Obtaining pseudo label for VAC. Focusing on image modality, we aim to enhance the locality structure of vision representations—high inter-class discriminability and tight intra-class distribution—a feature that CLIP-extracted vision features lack, as detailed in Fig. 4a. To instill these locality structures within VAC, we utilize a K-means-based deep clustering approach [4, 21] to generate pseudo-labels for unlabeled target data. We calculate the clustering centroids for class $k$ as follows: + +$$ +\phi_ {k} = \frac {\sum_ {x ^ {t}} \delta_ {k} \left(\operatorname {s o f t m a x} \left(\hat {y} _ {e n s} ^ {t}\right)\right) \cdot f _ {b} ^ {t}}{\sum_ {x ^ {t}} \delta_ {k} \left(\operatorname {s o f t m a x} \left(\hat {y} _ {e n s} ^ {t}\right)\right)}, \tag {8} +$$ + +where $\hat{y}_{ens}^{t}$ represents target ensemble outputs discussed below, and $\delta_{k}$ selects the $k_{th}$ logit. To mitigate imbalances in text modality predictions from CLIP [17, 49], we implement Approximated Controlled Direct Effect (ACDE) [49] to adjust similarity scores obtained in Eq. (4): + +$$ +\tilde {y} _ {l a c} ^ {t} = \hat {y} _ {l a c} ^ {t} - \tau \log \hat {p}, \hat {p} \leftarrow m \hat {p} + (1 - m) \frac {1}{B} \sum_ {i = 1} ^ {B} p _ {i}, \tag {9} +$$ + +where $m$ is momentum, $\tau$ is a debiasing factor, $B$ is the batch size, and $p_i = \mathrm{softmax}(\hat{y}_{lac}^t)$ denotes classification probability of LAC. The ensemble outputs, used in the centroid calculation, are then defined as $\hat{y}_{ens}^{t} = w\cdot \hat{y}_{vac}^{t} + (1 - w)\cdot \tilde{y}_{lac}^{t}$ . For any given target bottleneck feature $f_{b}^{t}$ , we compute its cosine similarity with all centroids, assigning the class with the highest similarity as the pseudo-label: + +$$ +y _ {v a c} ^ {t} = \arg \max _ {k} \cos \left(f _ {b} ^ {t}, \phi_ {k}\right). \tag {10} +$$ + +Learning VAC. We now train vision component on unifies outputs from both modalities. Utilizing Eq. (9) and Eq. (5), the target ensemble output $\hat{y}_{\text {ens }}^{t}$ is formulated as: + +$$ +\hat {y} _ {e n s} ^ {t} = w \cdot \hat {y} _ {v a c} ^ {t} + (1 - w) \cdot \tilde {y} _ {l a c} ^ {t}, \tag {11} +$$ + +with the weight $w = W(VAC^t)$ produced by the weight generator $W$ , as depicted in Fig. 2. Referring to Sec. 3.1, we optimize $\hat{y}_{\text{ens}}^t$ rather than $\hat{y}_{\text{vac}}^t$ directly, with $\tilde{y}_{\text{lac}}^t$ serving as an auxiliary in training VAC and thus detached from the computational graph in Eq. (11). + +To enhance individual discriminability and global diversity, thereby preserving the locality structure of vision representations, we follow state-of-the-art [1, 20, 21] to apply an information maximization loss $\mathcal{L}_{im}$ comprising two components. The entropy loss $\mathcal{L}_{ent}$ improves individual certainty: + +$$ +\mathcal {L} _ {e n t} = - \mathbb {E} _ {x ^ {t} \in \mathcal {D} ^ {t}} \left[ \sum_ {k = 1} ^ {K} \delta_ {k} \left(\hat {y} _ {e n s} ^ {t}\right) \log \delta_ {k} \left(\hat {y} _ {e n s} ^ {t}\right) \right], \tag {12} +$$ + +and the diversity loss fosters diverse class distributions: + +$$ +\mathcal {L} _ {d i v} = - \sum_ {k = 1} ^ {K} \bar {q} _ {k} \log \bar {q} _ {k}, \tag {13} +$$ + +where $\overline{q}_k = -\mathbb{E}_{x^t\in \mathcal{D}^t}\delta_k(\hat{y}_{ens}^t)$ . Hence, $\mathcal{L}_{im}$ is defined as: + +$$ +\mathcal {L} _ {i m} = \mathcal {L} _ {e n t} - \mathcal {L} _ {d i v}. \tag {14} +$$ + +The training of VAC is supervised by target pseudo labels for the vision modality, obtained through Eq. (10), while source labels directly optimize $\hat{y}_{vac}^{s}$ : + +$$ +\mathcal {L} _ {v a c} = C E \left(\hat {y} _ {\text {e n s}} ^ {t}, y _ {v a c} ^ {t}\right) + \beta C E \left(\hat {y} _ {v a c} ^ {s}, y ^ {s}\right) + \mathcal {L} _ {i m}, \tag {15} +$$ + +where $\beta$ modulates the impact of source data supervision. + +# 3.4. Aligning source and target by discriminator + +To achieve domain adaptation on both modalities, we introduce a modality discriminator $D$ to align VAC and LAC from both domains. Our approach utilizes a singular modality discriminator trained on the source domain to differentiate LAC from VAC, and then assesses alignment on the + +target domain. Proper alignment across domains would enable $D$ to discern LAC and VAC on the target domain without direct training. The modality discriminator is trained using binary cross-entropy loss: + +$$ +\mathcal {L} _ {b c e} = - \left[ y _ {d i s} \log \hat {y} _ {d i s} + \left(1 - y _ {d i s}\right) \log \left(1 - \hat {y} _ {d i s}\right) \right], \tag {16} +$$ + +where $y_{dis}$ represents the modality label (0 for VAC, 1 for LAC) and $\hat{y}_{dis}$ is the output of $D$ . + +Notably, $D$ is only trained on the source domain using Eq. (16). On the target domain, only the separators $G_{vis}$ and $G_{txt}$ are updated to minimize Eq. (16), aligning target LAC and VAC with the source ones. + +# 3.5. Training and inference + +Training. As depicted in Fig. 2, the pretrained text encoder and vision encoder are frozen, and we optimize parameters of $G_{txt}$ , $G_{vis}$ , $\Phi_1$ , $\Phi_2$ , $W$ , $D$ , denoted as $\theta_{G_{txt}}$ , $\theta_{G_{vis}}$ , $\theta_{\Phi_1}$ , $\theta_{\Phi_2}$ , $\theta_W$ , $\theta_D$ , respectively. Combining Eq. (7), Eq. (3), Eq. (15), Eq. (16), we define the following optimization problem: + +$$ +\theta_ {G _ {t x t}} = \underset {\theta_ {G _ {t x t}}} {\arg \min } \mathcal {L} _ {l a c} + \gamma \mathcal {L} _ {o r t h o} + \gamma \mathcal {L} _ {b c e}, \tag {17} +$$ + +$$ +\theta_{G_{vis}} = \operatorname *{arg min}_{\theta_{G_{vis}}}\mathcal{L}_{vac} + \gamma \mathcal{L}_{ortho} + \gamma \mathcal{L}_{bce}, +$$ + +$$ +\theta_ {W}, \theta_ {\Phi_ {1}}, \theta_ {\Phi_ {2}} = \operatorname * {a r g m i n} _ {\theta_ {W}, \bar {\theta} _ {\Phi_ {1}}, \theta_ {\Phi_ {2}}} \mathcal {L} _ {v a c}, +$$ + +$$ +\theta_{D} = \operatorname *{arg min}_{\theta_{D}}\gamma \mathcal{L}_{bce}, +$$ + +where $\gamma$ is hyperparameter controlling regularization terms $\mathcal{L}_{bce}$ and $\mathcal{L}_{ortho}$ . We present detailed training procedure of UniMoS in Supplementary. + +Inference. At inference, the final mixed prediction on target data is obtained using $\hat{y}_{ens}^{t}$ from Eq. (11), with a fixed mixup weight $w$ . The objective is to maximize accuracy by leveraging the strengths of both modalities for improved classification, as supported by our observations (Fig. 1), thus integrating outputs from both modalities to harness their combined advantages. + +# 4. Experiments + +# 4.1. Datasets and implementation details + +We extensively evaluate our method on three mainstream UDA benchmarks. Office-Home [46] consists of 65 categories divided into 4 distinct domains. On VisDA2017 [34], the goal is to transfer knowledge from 152k synthetic images (source domain) to 55k images of real items (target domain). DomainNet [35] is the most challenging UDA benchmark so far, containing 0.6 million samples from 345 categories divided into 6 distinct domains. Following previous works, we additionally provide results on + +Mini-DomainNet [25, 40, 58], a subset of DomainNet with 4 domains and 126 categories. + +We conduct all experiments on an NVIDIA RTX 2080Ti GPU. Since our method does not involve updating CLIP's pretrained parameters or prompts, the CLIP-extracted vision and text features are obtained via one single forward and saved in memory, thus greatly saving computation costs. For all tasks, we adopt SGD optimizer with batch size 32, and set momentum $m$ in Eq. (9) to 0.99 and debias factor $\tau$ in Eq. (9) to 0.5. For Office-Home and DomainNet, we train 50 epochs with initial learning rate 3e-3 and adopt annealing strategy [8] for learning rate decay. We train for 10 epochs with initial learning rate 9e-4 on VisDA due to fast convergence. The fixed mixup weight described in Sec. 3.5 is set to 0.3 for all tasks. We set regularization weight $\gamma$ in Eq. (17) to 0.01 across all datasets. + +# 4.2. Benchmark results + +Office-Home. Tab. 1 gives classification accuracies on 12 adaptation tasks on Office-Home using the ResNet50 [11] backbone. To ensure a fair comparison, we categorize CLIP-based methods into two groups: 'none-tuning' and 'full-tuning'. The former involves learning prompts or additional modules without adjusting the pretrained CLIP backbones, while the latter optimizes the pretrained parameters of CLIP for specific tasks. It is evident from the results that our proposed UniMoS consistently outperforms both 'none-tuning' and 'full-tuning' methods. Notably, we obtain $+1.3\%$ performance boost than the strong baseline PADCLIP, which fine-tunes the CLIP vision backbone. Our method requires no parameter update or data forwarding of CLIP backbones, thus is much computationally cheaper. Especially on tasks that take P as target domain, we achieve up to $+5.4\%$ performance boost than PADCLIP, demonstrating the superiority of multimodal adaptation. + +VisDA-2017. Tab. 2 shows class-wise classification accuracies on VisDA using ResNet101 [11]. Our method achieves the best performance among 'none-tuning' CLIP methods, while slightly falling behind PADCLIP. The reason is that CLIP has not been trained on the synthetic images like those from source domain of VisDA, resulting in incompatibilities between the VisDA dataset and CLIP. Similar observations are made by PADCLIP [17], which opts to fine-tune the vision branch of CLIP to address this challenge. Nevertheless, our approach outperforms typical UDA methods. + +DomainNet. Tab. 3 presents classification accuracies of 30 cross-domain adaptation tasks on the most challenging benchmark DomainNet. Rows represent source domains and columns represent target domains. Our method reaches comparable performance with the strong baseline PADCLIP. One significant observation is that our UniMoS obtains lower accuracy than PADCLIP (6.6% lower in average) on tasks with qdr as target. This discrepancy arises + +Table 1. UDA results on Office-Home. Best results are marked in bold font. Methods with $*$ ’ are based on CLIP. + +
MethodBackboneA→CA→PA→RC→AC→PC→RP→AP→CP→RR→AR→CR→PAvg.
SourceOnly [11]ResNet5034.950.058.037.441.946.238.531.260.453.941.259.946.1
ParetoDA [22]56.875.980.564.473.573.765.655.281.375.261.183.970.6
SDAT [37]58.277.182.266.377.676.863.357.082.274.964.786.072.2
MSGD [50]58.776.978.970.176.276.669.057.282.374.962.784.572.3
Fixbi [32]58.177.380.467.779.578.165.857.981.776.462.986.772.7
CST [26]59.079.683.468.477.176.768.956.483.075.362.285.172.9
ATDOC [23]60.277.882.268.578.677.968.458.483.174.861.587.273.2
KUDA [42]58.280.082.971.180.380.771.356.883.275.560.386.673.9
EIDCo [60]63.880.882.671.580.180.972.161.384.578.665.887.175.8
ICON [55]63.381.384.570.382.181.070.361.883.775.668.687.375.8
PADCLIP* [17]ResNet50-full-tuning57.584.083.877.885.584.776.359.285.478.160.286.776.6
CLIP* [36]ResNet50-none-tuning51.781.582.371.781.582.371.751.782.371.751.781.571.8
DAPrompt* [10]54.184.384.874.483.785.074.554.684.875.254.783.874.5
ADCLIP* [41]55.485.285.676.185.886.276.756.185.476.856.185.575.9
UniMoS* (ours)59.589.486.975.289.686.875.458.487.276.959.589.777.9
+ +Table 2. UDA results on VisDA-2017. Best results are marked in bold font. Methods with \* are based on CLIP. + +
MethodBackboneplanebicyclebuscarhorseknifemcyclpersonplantsktbrdtraintruckAvg.
SourceOnly [11]ResNet10155.153.361.959.180.617.979.731.281.026.573.58.552.4
ParetoDA [22]95.982.881.358.793.993.785.983.091.992.087.151.883.2
MSGD [50]97.583.484.469.495.994.190.975.595.594.688.144.984.5
ATDOC [23]95.384.782.475.695.897.788.776.694.091.791.561.986.3
CAN [15]97.087.282.574.397.896.290.880.796.696.387.559.987.2
FixBi [32]96.187.890.590.396.895.392.888.797.294.290.925.787.2
PADCLIP* [17]ResNet101-full-tuning96.788.887.082.897.193.091.383.095.591.891.563.088.5
CLIP* [36]ResNet101-none-tuning98.283.990.573.597.284.095.365.779.489.991.863.384.4
DAPrompt* [10]97.883.188.877.997.491.594.279.788.689.392.562.086.9
ADCLIP* [41]98.183.691.276.698.193.496.081.486.491.592.164.287.7
UniMoS* (ours)97.788.290.174.696.895.892.484.190.889.091.865.388.1
+ +from a significant domain gap between qdr and other domains, which is challenging to bridge without tuning the CLIP backbones. However, despite this, we manage to achieve superior performance to PADCLIP on all other tasks, thereby mitigating the overall $6.6\%$ performance drop. We also surpass all competing methods significantly. Tab. 4 compares UniMoS with available CLIP-based non-tuning methods on Mini-DomainNet, where our method achieves significant performance boost. Detailed results on Mini-DomainNet are given in Supplementary. + +# 4.3. Ablation study + +In this section we validate the efficacy of each module in UniMoS. Tab. 5 presents averaged accuracies on Office-Home and VisDA-2017 by removing specific modules while maintaining other settings identical. The 'w/o debiasing' is obtained by skipping the debias procedure in Eq. (9). A primary observation is that the removal of any module leads to a performance drop to varying degrees, underscoring the positive contribution of each module to the overall outcome. The 'w/o learnable weight' row is obtained by replacing $w$ in Eq. (11) with a constant 0.5, re + +sulting in the most pronounced performance decline. This emphasizes the significance of dynamic weights, which enables VAC to focus on vision-specific parts. Further insights into the effects of dynamic $w$ are detailed in Sec. 4.4. + +Tab. 6 ablates on the choice of backbones. We experiment with three backbones on Office-Home, and our UniMoS consistently outperforms all competing methods, proving that our method is generalizable across various models. Detailed results are given in Supplementary. + +# 4.4. Discussions + +Effectiveness of learnable weight $w$ . To better understand how the learnable ensemble weight $w$ in Eq. (2) boosts performance, Fig. 3 compares the training process with and without dynamic $w$ . We set a fixed weight of 0.5 for both LAC and VAC in 'w/o learnable w', and learn dynamic weights (shown as 'Learned weight w' in the figure) in other settings. Our first observation is that in our full design, accuracy of VAC increases steadily as the training progresses. Leveraging complementary modality-specific information from LAC, the final mixed outputs achieve higher accuracy than VAC alone. As stated in Sec. 3.1, the goal of + +Table 3. UDA results on DomainNet. Best results are marked in bold font. Methods with $*$ ’ are based on CLIP. + +
DeiT-B [44]clpinfpptqdrrelsktavgViT-B [6]clpinfpptqdrrelsktavgSSRT-B [43]clpinfpptqdrrelsktavg
clp-24.349.615.865.352.141.4clp-27.253.113.271.253.343.6clp33.860.219.475.859.849.8
inf45.9-45.96.761.439.539.9inf51.4-49.34.066.341.142.4inf55.5-54.09.068.244.746.3
ppt53.223.8-6.566.444.738.9ppt53.125.6-4.870.041.839.1ppt61.728.5-8.471.455.245.0
qdr31.96.815.4-23.420.619.6qdr30.54.516.0-27.019.319.5qdr42.58.824.2-37.633.629.3
rel59.025.856.39.2-44.839.0rel58.429.060.06.0-45.839.9rel69.937.166.010.1-58.948.4
skt60.620.648.416.561.2-41.5skt63.923.852.314.467.4-44.4skt70.632.862.221.773.2-52.1
avg50.120.343.110.955.540.336.7avg51.522.046.18.560.440.338.1avg60.028.253.313.765.350.445.2
CDTrans -DeiT [51]clpinfpptqdrrelsktavgPMTrans -Swin [63]clpinfpptqdrrelsktavgCLIP -B* [36]clpinfpptqdrrelsktavg
clp-29.457.226.072.658.148.7clp-34.262.732.579.363.754.5clp-70.170.170.170.170.170.1
inf57.0-54.412.869.548.448.4inf67.4-61.122.278.057.657.3inf46.4-46.446.446.446.446.4
ppt62.927.4-15.872.153.946.4ppt69.733.5-23.979.861.253.6ppt61.761.7-61.761.761.761.7
qdr44.68.929.0-42.628.530.7qdr54.617.438.9-49.541.040.3qdr13.713.713.7-13.713.713.7
rel66.231.061.516.2-52.945.6rel74.135.370.025.4-61.153.2rel82.982.982.9-82.982.982.9
skt69.029.659.027.272.5-51.5skt73.833.062.630.977.5-55.6skt62.662.662.662.6-62.6
avg59.925.352.219.665.948.445.2avg67.930.759.127.072.856.952.4avg53.558.255.164.750.955.056.2
DAPrompt -B* [10]clpinfpptqdrrelsktavgPADCLIP -B* [17]clpinfpptqdrrelsktavgUniMoS -B* (ours)clpinfpptqdrrelsktavg
clp-73.073.872.673.973.573.4clp-73.675.474.676.476.375.3clp-76.577.276.677.577.877.1
inf50.8-50.149.650.650.350.3inf55.1-54.353.654.954.954.6inf55.1-55.054.655.355.255.0
ppt70.269.6-68.970.469.969.8ppt71.170.6-70.072.771.771.2ppt72.371.5-69.472.572.671.7
qdr17.214.413.9-14.313.914.7qdr36.818.032.0-31.734.930.7qdr25.022.923.6-23.725.124.1
rel84.984.884.984.7-84.684.8rel84.283.583.583.1-83.683.6rel86.085.985.885.5-85.985.8
skt65.865.465.864.965.9-65.6skt68.166.667.266.167.5-67.1skt68.567.868.267.568.0-68.0
avg57.861.457.768.155.058.459.8avg63.162.562.569.560.664.363.7avg61.464.962.070.759.463.363.6
+ +Table 4. UDA results on Mini-DomainNet. Best results are marked in bold font. All compared methods are CLIP-based. + +
MethodBackboneAcc.MethodBackboneAcc.
CLIPResNet5071.2CLIPViT-B82.8
DAPrompt74.8DAPrompt85.8
ADCLIP75.2ADCLIP86.9
UniMoS (ours)78.0UniMoS (ours)87.3
+ +Table 5. Ablation study on Office-Home and VisDA-2017. + +
MethodOffice-HomeVisDA-2017
w/o Lortho77.487.6
w/o debiasing77.387.7
w/o Lim77.087.8
w/o Ldistill77.087.6
w/o learnable weight76.986.2
w/o modality discriminator77.687.9
UniMoS (full design)77.988.1
+ +dynamic ensemble weight is to adaptively identify and preserve modality-specific information. We show in Fig. 3 that, the learned weight changes in each epoch to fit the training process. Without its support (w/o learnable w), the accuracy of VAC outputs drops significantly and finally converges with LAC. This occurs because employing a static weight would compromise the modality separation effects, causing both modalities to collapse to poor performance. In the example given by Fig. 3, accuracy of 'VAC output w/o learnable w' is $3.5\%$ lower than that of the full design 'VAC output'. The phenomenon indicates the significance of training with dynamic ensemble weights in our design. More examples are given in Supplementary. + +Computation analysis. Tab. 7 compares computation costs of different methods on VisDA dataset. Our method necessitates training only a few linear layers without updating CLIP backbones, bringing great parameter efficiency. + +![](images/3a76308d52f2419f5adb32e4a24abfeab96aa20d7537a9cd077e332ad5be3ce8.jpg) +Figure 3. Effects of learnable ensemble weight $w$ on Office-Home. + +Table 6. Results with different backbones on Office-Home. Best results are in bold. All compared methods are based on CLIP. + +
MethodBackboneAcc.MethodBackboneAcc.
UniMoS (ours)ResNet5077.9CLIP82.4
CLIPViT-L87.0DAPromptViT-B84.4
DAPrompt88.7ADCLIP86.1
ADCLIP90.5PADCLIP86.7
UniMoS (ours)90.7UniMoS (ours)86.9
+ +Furthermore, only one forward through CLIP is needed, which allows UniMoS achieve more than $47 \times$ training speed boost than PADCLIP. Prompt learning methods like DAPrompt also requires no training on CLIP backbones, but they require extensive iterative forwarding of data through CLIP to learn optimal prompts per class, leading to low computing efficiency and scalability to larger datasets. When running on DomainNet with 345 classes, DAPrompt requires more than 22G GPU memory, while our method requires less than 3G. More details are in Supplementary. + +Feature distribution visualization. To demonstrate the efficacy of modality separation and feature alignment, we per + +![](images/da613e85b47013da81c14148ebe07ac7f9f8977c50157741053f4ef1721a5916.jpg) +(a) CLIP-extracted feature distribution. + +![](images/05e6a1cd3d72af8426c06e4eca41d7d1cd4a0dcf4d4bc7443cb9dc30dd086d62.jpg) +(b) Modality separation effect. + +![](images/e0398b853fc9e1188c0af74fc4e1571ccf97b92173737a2ea6603e67fe5d8176.jpg) +(c) Aligned bottleneck feature distribution. + +Table 7. Computation analysis on VisDA-2017. Best results are marked in bold font. Methods with \* are based on CLIP. + +
MethodBkb.Param.Throughput (images/s)Train timeFLOPsAcc.
DAPrompt*ResNet1011.2M2444.3H11.3G86.9
FixBi86.1M1025.5H15.73G87.2
CAN42.5M3110.5H7.9G87.2
PADCLIP*--23.5H*-88.5
UniMoS* (ours)0.79M26670.5H<0.01G88.1
+ +form t-sne [45] visualization on various features at different phases of our method. Fig. 4a shows CLIP-extracted vision features from source (green) and target (blue) domain, along with CLIP-extracted text features (red) of naive prompts. The text features distribute distantly with vision features, proving the existence of modality gap. Besides, CLIP-extracted vision features form poor class discriminability and locality structures. Fig. 4b showcases the separated LAC and VAC of our method. A clear boundary can be observed between the features of both modalities, indicating the effectiveness of modality separation. Additionally, the text features distribute closer to LAC, proving that the separated LAC is indeed more relevant to the text modality. Following feature alignment and VAC training, the bottleneck features $f_{b}$ from both domains display a compact class-level locality structure, as demonstrated in Fig. 4c. This compact structure contributes significantly to the accuracy of the final classification results. + +Hyperparameter sensitivity. In the calibration of UniMoS, we encounter three hyperparameters to determine: $\alpha$ in Eq. (7), $\beta$ in Eq. (15), and $\gamma$ in Eq. (17). We empirically discover that alternating $\gamma$ has little impact within each dataset, so we focus on exploring the effects of $\alpha$ and $\beta$ . As illustrated in Fig. 5a, the performance on VisDA is notably influenced by $\alpha$ , with smaller values leading to improved accuracy. This outcome is attributed to the fact, as discussed in Sec. 4.2, that CLIP struggles to adequately iden + +![](images/eca940e3e1893db4d802a889b9cd72c959e7d5960f81195fb2fb9495cb0e1ae3.jpg) +Figure 4. T-sne visualization [45] of the effects of UniMoS on $\mathrm{A}\rightarrow \mathrm{P}$ task from Office-Home. UniMoS effectively disentangles CLIP-extracted vision features (Fig. 4a) into LAC and VAC (Fig. 4b, obtained by randomly selecting 25 classes), and constructs clear cross-domain locality structures (Fig. 4c). +(a) VisDA-2017 +Figure 5. Parameter sensitivity analysis on $\alpha$ and $\beta$ of UniMoS. + +![](images/4178cd35b931fedfc0fc58a55ef736ff9eb1fbcf4b340dd4692ec0dbda1c8e9b.jpg) +(b) Office-Home + +tify source synthetic images from VisDA. Consequently, down-weighting source supervision on LAC proves beneficial. Conversely, source supervision from both modalities of Office-Home are important. They positively and equally contributes to the adaptation process, so $\alpha = 1$ and $\beta = 1$ brings the best result, as shown in Fig. 5b. + +# 5. Conclusions + +Inspired by the theory of modality gap, in this paper we propose a Unified Modality Separation framework for unsupervised domain adaptation. The CLIP-extracted vision features are explicitly disentangled into vision-associated and language-associated components, which are trained differently according to their modality strengths and further aligned by a modality discriminator. A modality-ensemble training paradigm unifies both components to leverage modality-specific information while preserving modality-shared contexts, contributing to successful classification. This work is hope to inspire further analysis and exploitation of the multimodal features in pretrained VLMs. + +# 6. Acknowledgements + +This work was supported in part by the National Natural Science Foundation of China under Grant 62176042, and in part by Sichuan Science and Technology Program under Grant 2023NSFSC0483, and in part by Tencent Marketing Solution Rhino-Bird Focused Research Program. + +# References + +[1] Sk Miraj Ahmed, Dripta S Raychaudhuri, Sujoy Paul, Samet Oymak, and Amit K Roy-Chowdhury. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3561-3571, 2023. \ No newline at end of file diff --git a/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/images.zip b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..77cd0284e37fa348dba75136d48e504940ad6f31 --- /dev/null +++ b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:e4bfc1b1cc7feee303d7a74c068a8eda274c79e0d886f62eb8f40f59127a7b3d +size 792108 diff --git a/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/layout.json b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..76c3ba00715dcdd473c4e9e82fbe3c7d08960e75 --- /dev/null +++ b/2024/Split to Merge_ Unifying Separated Modalities for Unsupervised Domain Adaptation/layout.json @@ -0,0 +1,10093 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 143, + 103, + 451, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 103, + 451, + 140 + ], + "spans": [ + { + "bbox": [ + 143, + 103, + 451, + 140 + ], + "type": "text", + "content": "Split to Merge: Unifying Separated Modalities for Unsupervised Domain Adaptation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": "Xinyao Li" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": " Yuke Li" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{2*}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": " Zhekai Du" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": " Fengling Li" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": " Ke Lu" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": " Jingjing Li" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": "University of Electronic Science and Technology of China \n" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": "Boston College " + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 105, + 160, + 492, + 203 + ], + "type": "text", + "content": "University of Technology Sydney" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 129, + 205, + 462, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 205, + 462, + 217 + ], + "spans": [ + { + "bbox": [ + 129, + 205, + 462, + 217 + ], + "type": "text", + "content": "xinyao326@outlook.com, lidwh@bc.edu, zhekaid@std.uestc.edu.cn" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 129, + 220, + 461, + 232 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 220, + 461, + 232 + ], + "spans": [ + { + "bbox": [ + 129, + 220, + 461, + 232 + ], + "type": "text", + "content": "fenglingli2023@gmail.com, kel@uestc.edu.cn, lijin117@yeah.net" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "spans": [ + { + "bbox": [ + 143, + 258, + 192, + 272 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 283, + 290, + 499 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 283, + 290, + 499 + ], + "spans": [ + { + "bbox": [ + 46, + 283, + 290, + 499 + ], + "type": "text", + "content": "Large vision-language models (VLMs) like CLIP have demonstrated good zero-shot learning performance in the unsupervised domain adaptation task. Yet, most transfer approaches for VLMs focus on either the language or visual branches, overlooking the nuanced interplay between both modalities. In this work, we introduce a Unified Modality Separation (UniMoS) framework for unsupervised domain adaptation. Leveraging insights from modality gap studies, we craft a nimble modality separation network that distinctly disentangles CLIP's features into language-associated and vision-associated components. Our proposed Modality-Ensemble Training (MET) method fosters the exchange of modality-agnostic information while maintaining modality-specific nuances. We align features across domains using a modality discriminator. Comprehensive evaluations on three benchmarks reveal our approach sets a new state-of-the-art with minimal computational costs. Code: https://github.com/TL-UESTC/UniMoS." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 521, + 128, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 521, + 128, + 533 + ], + "spans": [ + { + "bbox": [ + 47, + 521, + 128, + 533 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 540, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 540, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 540, + 287, + 696 + ], + "type": "text", + "content": "Unsupervised domain adaptation (UDA) [2, 7, 29, 30] aims to apply knowledge trained on a source domain to an unlabeled target domain, a process invaluable in data-scarce scenarios. Conventional methods often struggle with bridging the gap between source and target domains, finding it challenging to develop consistent features across domains [19, 39]. 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Examples of modality-specific information from task Art " + }, + { + "bbox": [ + 305, + 359, + 546, + 393 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 305, + 359, + 546, + 393 + ], + "type": "text", + "content": " RealWorld in Office-Home dataset. The digits are top-2 highest classification probabilities given by both modalities." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 320, + 323, + 416, + 356 + ], + "blocks": [ + { + "bbox": [ + 320, + 323, + 416, + 356 + ], + "lines": [ + { + "bbox": [ + 320, + 323, + 416, + 356 + ], + "spans": [ + { + "bbox": [ + 320, + 323, + 416, + 356 + ], + "type": "table", + "html": "
Modality / Prob.couchchair (√)
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Modality / Prob.shelffile cabinet ( \\( \\checkmark \\) )
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", + "image_path": "7257245fdc27123806835b73bcafa48dbe17080be743bebca12b426aea8bd071.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 401, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 401, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 401, + 545, + 449 + ], + "type": "text", + "content": "ities and a broad base of conceptual knowledge, making them highly suitable for comprehensive UDA. They facilitate alignment across both visual and textual modalities, enhancing adaptability and applicability in diverse contexts." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 546, + 715 + ], + "type": "text", + "content": "Previous studies have shown promising results by adapting VLMs like CLIP for unsupervised domain adaptation (UDA). For instance, DAPrompt [10] introduces learning both domain-agnostic and domain-specific text embeddings, while PADCLIP [17] focuses on fine-tuning the vision branch of CLIP for adaptive visual feature extraction. However, recent research [14, 24] highlights a modality gap in VLMs, revealing that, despite training efforts, vision and text features often remain distinctly distributed. We argue that adapting a single modality is less than ideal due to the existence of unique, modality-specific cues in misaligned textual and visual components. We suggest that certain samples are best classified using specific modalities, a hypothesis supported by empirical observations in Fig. 1. This figure shows differing classification patterns when each modality is adapted independently to the unlabeled target data. Text modality results derive from CLIP's zero-shot capabilities, while image results come from linear probing with target pseudo-labels. For instance, visually straightforward items like a cushioned chair are accurately classified by the vision linear classifier after tuning on target dataset. However, pretrained CLIP can erroneously cat" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23364" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 191 + ], + "type": "text", + "content": "egorize such items under visually similar classes. In contrast, complex items with nuanced semantic details, like a file cabinet resembling a shelf, may confuse the vision classifier, while CLIP's broader knowledge base facilitates correct zero-shot predictions. In summary, while the vision branch effectively discerns class-specific visual patterns, the text branch leverages semantic information to clarify ambiguous cases. This observation lays the groundwork for a multimodal adaptation framework that synergistically combines the strengths of both modalities." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 194, + 287, + 314 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 194, + 287, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 194, + 287, + 314 + ], + "type": "text", + "content": "A direct approach to domain adaptation involves concurrently fine-tuning vision branch and crafting textual prompts, which risks disturbing the image-text representation pairs in pretrained CLIP and is computationally intensive [9, 57]. As a more efficient alternative, we propose to explicitly disentangle CLIP-extracted visual features into two complementary parts. The first component retains the language-associated semantic knowledge inherent in CLIP, while the second focuses on vision-specific attributes crucial for distinguishing between nuanced visual categories." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 316, + 288, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 316, + 288, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 316, + 288, + 663 + ], + "type": "text", + "content": "We devised a set of modality separation networks with dual branches to project CLIP-encoded visual features into distinct language-associated components (LAC) and vision-associated components (VAC). An orthogonal regularization is employed to ensure these branches yield discrete, disentangled representations. Each component is optimized based on its inherent modality strengths. For the LAC branch, we utilize knowledge distillation on target data to harness the rich semantic content from the original pretrained CLIP model. Additionally, we implement a debiasing method to mitigate dataset bias in CLIP's zero-shot results. For the VAC branch, the locality structure within visual feature spaces [20, 53, 54] is leveraged to generate visual pseudo-labels for supervised learning on target data. We then introduce a novel Modality-Ensemble Training (MET) strategy that synergistically merges outputs from both modalities. A weight generator dynamically assembles these predictions, supervised by VAC pseudo-labels on target data and actual labels on source data. Importantly, the text modality output remains isolated during MET to preserve independent training and maintain pretrained semantics. Additionally, a modality discriminator is utilized to align LAC and VAC across domains for unsupervised domain adaptation. Trained on source data to distinguish between LAC and VAC, this discriminator is frozen on the target domain, directly updating the separation networks to produce domain-invariant LAC and VAC. This approach ensures a consistent modality separation across domains, facilitating simultaneous adaptation in both modalities." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 665, + 287, + 714 + ], + "type": "text", + "content": "Contributions: 1. We investigate the modality gap phenomenon in the context of applying Vision-Language Models (VLMs) to unsupervised domain adaptation, revealing the limitations of adapting a single modality; 2. We intro-" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "duce a novel framework, Unified Modality Separation (UniMoS), which, coupled with a Modality-Ensemble Training (MET) approach, facilitates effective multimodal adaptation; 3. Our comprehensive analysis and validations underscore and efficiency of the proposed UniMoS, demonstrating its ability to set new state-of-the-art benchmarks while maintaining low computational demands." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 167, + 390, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 167, + 390, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 167, + 390, + 179 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 186, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 545, + 426 + ], + "type": "text", + "content": "Unsupervised domain adaptation (UDA). A core challenge in UDA is aligning representations between the source domain and unlabeled target domain. Prior techniques can be categorized as discrepancy-based [18, 28, 59] and adversarial methods [7, 30, 39]. Discrepancy-based methods explicitly minimizes divergence metrics including MMD [18], MDD [59], etc. Adversarial methods extract domain invariant features via a min-max game between the feature extractor and domain discriminator [7, 30]. Recent works focus on exploiting target data structures via self-training techniques [15, 53-55, 60]. ICON [55] learns an invariant classifier with consistent predictions to remove the spurious correlation inconsistency in the target domain. EIDCo [60] combines Mixup [56] with IDCo loss [5, 12] to explore target data distribution. Vision transformer (ViT) [6] and its variants have also gained popularity due to their superior performance [51, 52, 63]. PMTrans [63] mixes patch representations in SwinTransformer [27] as an intermediate domain bridge. CDTrans [51] aligns features extracted by DeiT [44] via cross-attention." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 426, + 545, + 715 + ], + "type": "text", + "content": "Vision-language models (VLMs) have shown great generalization abilities due to extensive multimodal pretraining [13, 36, 47, 48]. CLIP [36] is trained from 400 million text-image pairs, while ALIGN [13] leverages more than one billion text-image pairs. Subsequent works have built on pretrained VLMs in various ways. Some learn prompt texts to transfer VLMs to downstream tasks [10, 33, 38, 61, 62], while others incorporate additional tunable layers on the frozen pretrained encoder [9, 57]. Beyond utilizing existing VLMs, research also aims to improve VLM training [14, 31]. Liang et al. [24] reveal that VLMs exhibit a modality gap, failing to perfectly align multimodal features. Jiang et al. [14] conduct theoretical analysis on modality gap and propose latent space regularization to preserve modality-specific information. MaPLe [16] utilize prompt learning on both modality branches to improve alignment. Our approach is fundamentally different since we disentangle VLM-extracted features posteriorly instead of training VLM from scratch, requiring far less computation costs. Besides, our method requires no labeling on target domain. VLMs have also been adopted for UDA [10, 17, 41]. DAPrompt [10] learns domain-specific and domain-agnostic textual prompts for each class. ADCLIP [41] learns domain invariant prompts by conditioning" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23365" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 71, + 521, + 237 + ], + "blocks": [ + { + "bbox": [ + 77, + 71, + 521, + 237 + ], + "lines": [ + { + "bbox": [ + 77, + 71, + 521, + 237 + ], + "spans": [ + { + "bbox": [ + 77, + 71, + 521, + 237 + ], + "type": "image", + "image_path": "25449e5ea3aa30d8207f56872986ac020ecf191956a4fae6681e40f3fb1e2969.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. Framework of our method. We freeze the pretrained vision and text encoder of CLIP. CLIP-extracted vision features are disentangled into language-associated components " + }, + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "type": "inline_equation", + "content": "(f_{lac})" + }, + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "type": "text", + "content": " and vision-associated components " + }, + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "type": "inline_equation", + "content": "(f_{vac})" + }, + { + "bbox": [ + 46, + 239, + 547, + 285 + ], + "type": "text", + "content": " by the modality separation networks. We obtain zero-shot results from CLIP as teacher knowledge, and distill the knowledge to LAC. We then introduce a weight generator to assemble the modality outputs to train VAC. A modality discriminator is applied to align LAC and VAC from both domains." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 293, + 289, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 289, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 289, + 365 + ], + "type": "text", + "content": "on image style and content features. PADCLIP [17] dynamically adjusts learning rate while tuning CLIP to prevent catastrophic forgetting. However, these methods perform adaptation on either the visual or textual modality in isolation. Our work addresses this limitation by proposing a unified adaptation framework for the multimodal features." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 374, + 105, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 374, + 105, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 374, + 105, + 387 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 394, + 168, + 406 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 394, + 168, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 394, + 168, + 406 + ], + "type": "text", + "content": "3.1. Problem formulation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": "In this study, superscripts differentiate domains, with symbols lacking superscripts applicable to both domains. We consider a labeled source domain " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^s = \\{(x_i^s,y_i^s)\\}_{i = 1}^{N^s}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " and aim to develop a model generalizable to an unlabeled target domain " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{D}^t = \\{(x_i^t)\\}_{i = 1}^{N^t}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": ". CLIP [36] features a vision encoder " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "g_{vis}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " and a text encoder " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "g_{txt}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": ". The vision feature for an image input " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " is denoted as " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "f_{v} = g_{vis}(x)" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": ". Employing the zero-shot inference strategy from [17], we construct naive prompts " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\{(t_i)\\}_{i = 1}^K" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " as a [DOMAIN] photo of a [CLASS], with " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " representing the number of classes, [DOMAIN] indicating domain specifics, and [CLASS] the class name. Text features are then derived as " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mu_{i} = g_{txt}(t_{i})" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " are both features with " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "d_v" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " dimension. Classification is based on the highest cosine similarity between " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "f_{v}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "inline_equation", + "content": "\\mu_{i}" + }, + { + "bbox": [ + 46, + 412, + 289, + 581 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 108, + 586, + 287, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 108, + 586, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 108, + 586, + 287, + 605 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {z s} = \\underset {i} {\\arg \\max } \\cos \\left(\\mu_ {i}, f _ {v}\\right). \\tag {1}", + "image_path": "054a99cc75e28a90859bd6ff7e4c4f4c7668f0b68a3bba593f8392a78e31243c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "text", + "content": "Eq. (1) may not be ideal for unlabeled target data due to the existence of modality gap [24]. To tackle this, we conceptualize vision inputs as a composite of a vision-associated component (VAC) and a language-associated component (LAC), denoted as " + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "inline_equation", + "content": "f_{v} = \\{f_{vac}, f_{lac}\\}" + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "text", + "content": ". This leads us to obtain modality-specific classification results " + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "inline_equation", + "content": "y_{vac}" + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "inline_equation", + "content": "y_{lac}" + }, + { + "bbox": [ + 46, + 610, + 289, + 696 + ], + "type": "text", + "content": ", before constructing a cross-modality output:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 98, + 701, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 98, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 98, + 701, + 287, + 714 + ], + "type": "interline_equation", + "content": "y _ {e n s} = w \\cdot y _ {v a c} + (1 - w) \\cdot y _ {l a c}, \\tag {2}", + "image_path": "82ed423a060867a582da6cc7dcc94929ed19ef9c73ee2baa155e0c4ff3383119.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 293, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 341 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 293, + 545, + 341 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 293, + 545, + 341 + ], + "type": "text", + "content": " is a set of learnable weights harmonizing the contributions of VAC and LAC. This design seeks to balance modality-agnostic information sharing and modality-specific information capturing." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "text", + "content": "Instead of separating LAC and VAC during training, we utilize " + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "inline_equation", + "content": "y_{ens}" + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "text", + "content": " to guide VAC learning, incorporating complementary modality information for a holistic cross-modal training. Furthermore, a fixed weight " + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "text", + "content": " may lack flexibility across diverse datasets and scenarios, potentially obscuring the distinction between VAC and LAC. Addressing this, we introduce a dynamic " + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "text", + "content": " that adeptly discriminates between modalities within " + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "inline_equation", + "content": "y_{ens}" + }, + { + "bbox": [ + 304, + 341, + 546, + 486 + ], + "type": "text", + "content": ", calibrating their influence in the training. This strategy ensures tailored training approaches for different datasets or training stages, facilitating modality-specific information utilization. Next we detail on the training and aligning of LAC and VAC." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 493, + 470, + 506 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 493, + 470, + 506 + ], + "spans": [ + { + "bbox": [ + 306, + 493, + 470, + 506 + ], + "type": "text", + "content": "3.2. Modality separation networks" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": "We first introduce the modality separation networks that disentangles CLIP-extracted features, which comprise two separators as shown in Fig. 2. These networks partition CLIP-extracted vision features into LAC and VAC using the text separator " + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "inline_equation", + "content": "G_{txt}" + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": " and the vision separator " + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "inline_equation", + "content": "G_{vis}" + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": ", respectively. The separated components are defined as " + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "inline_equation", + "content": "f_{lac} = G_{txt}(f_v)" + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "inline_equation", + "content": "f_{vac} = G_{vis}(f_v)" + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": ". Both separators are linear layers preserving the dimensionality of " + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "inline_equation", + "content": "f_v" + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "inline_equation", + "content": "f_{vac}, f_{lac} \\in \\mathbb{R}^{d_v}" + }, + { + "bbox": [ + 304, + 512, + 547, + 643 + ], + "type": "text", + "content": ". Drawing on deep feature separation principles [3], we apply an orthogonal loss to maintain the distinctness of LAC and VAC:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 337, + 651, + 546, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 651, + 546, + 668 + ], + "spans": [ + { + "bbox": [ + 337, + 651, + 546, + 668 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {o r t h o}} = \\left| f _ {l a c} ^ {s} \\cdot f _ {v a c} ^ {s} \\right. ^ {\\top} | _ {F} ^ {2} + \\left| f _ {l a c} ^ {t} \\cdot f _ {v a c} ^ {t} \\right. ^ {\\top} | _ {F} ^ {2}. \\tag {3}", + "image_path": "434f1dca1692403993b0063dac961cdcfcd768b231c5ca3889c9f413405fa81a.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Different outputs for LAC and VAC are then generated. For the text modality, we utilize the zero-shot inference of CLIP to classify LAC by calculating the cosine similarity" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23366" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 269, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 269, + 84 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 269, + 84 + ], + "type": "text", + "content": "between LAC and CLIP's text features, forming logits:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 74, + 88, + 287, + 103 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 88, + 287, + 103 + ], + "spans": [ + { + "bbox": [ + 74, + 88, + 287, + 103 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {l a c} = \\left(\\hat {l} _ {1}, \\hat {l} _ {2}, \\dots \\hat {l} _ {k}\\right), \\quad \\hat {l} _ {i} = \\cos \\left(\\mu_ {i}, f _ {l a c}\\right) / T, \\tag {4}", + "image_path": "5169c99fe7a34f642e397a0b4cf8ab057ecf35097410641cdea28c430454fe6e.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "text", + "content": " is temperature in pretrained CLIP. For VAC, we route it through a linear classifier with layers " + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\Phi_1 \\in \\mathbb{R}^{d_v \\times d_b}" + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "inline_equation", + "content": "\\Phi_2 \\in \\mathbb{R}^{d_b \\times K}" + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "text", + "content": ", producing the bottleneck feature with dimension " + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "inline_equation", + "content": "d_b" + }, + { + "bbox": [ + 47, + 108, + 287, + 156 + ], + "type": "text", + "content": " and output via:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 97, + 163, + 287, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 163, + 287, + 175 + ], + "spans": [ + { + "bbox": [ + 97, + 163, + 287, + 175 + ], + "type": "interline_equation", + "content": "f _ {b} = \\Phi_ {1} \\left(f _ {v a c}\\right), \\quad \\hat {y} _ {v a c} = \\Phi_ {2} \\left(f _ {b}\\right). \\tag {5}", + "image_path": "d199b9e6ddd819e3feacdb38eeb4f485fe1b9543cf1565cba98f7d71a98eb382.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 181, + 264, + 193 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 181, + 264, + 193 + ], + "spans": [ + { + "bbox": [ + 47, + 181, + 264, + 193 + ], + "type": "text", + "content": "We provide implementation details in Supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 198, + 200, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 198, + 200, + 211 + ], + "spans": [ + { + "bbox": [ + 47, + 198, + 200, + 211 + ], + "type": "text", + "content": "3.3. Modality-ensemble training" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 287, + 265 + ], + "type": "text", + "content": "Having obtained disentangled components, we design customized training paradigm for each modality. A learnable weight further connects both modalities, establishing a unified modality-ensemble training framework." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 265, + 287, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 287, + 312 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 287, + 312 + ], + "type": "text", + "content": "Learning LAC. To preserve the rich semantic content in pretrained CLIP, we distill this knowledge to LAC. For the target data, zero-shot similarity scores derived from pretrained CLIP serve as the teacher knowledge:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 51, + 317, + 287, + 332 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 317, + 287, + 332 + ], + "spans": [ + { + "bbox": [ + 51, + 317, + 287, + 332 + ], + "type": "interline_equation", + "content": "y _ {l a c} ^ {t} = \\left(l _ {1} - \\bar {l}, l _ {2} - \\bar {l}, \\dots , l _ {k} - \\bar {l}\\right), \\quad l _ {i} = \\cos \\left(\\mu_ {i}, f _ {v} ^ {t}\\right) / T, \\tag {6}", + "image_path": "6122e7856c445fea2cc0965baa17424182327e2efc8a7310272d54bc1324838e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "type": "inline_equation", + "content": "\\bar{l} = \\frac{1}{K}\\sum_{k=1}^{K}l_k" + }, + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "type": "text", + "content": " normalizing the CLIP outputs and " + }, + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 47, + 337, + 287, + 410 + ], + "type": "text", + "content": " the temperature of pretrained CLIP. The teacher knowledge in Eq. (6) guides the distillation for the unlabeled target LAC, while for the source data, cross-entropy loss is applied directly using labeled source data. The overall training loss for LAC combines Eq. (4) and Eq. (6) as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 84, + 415, + 287, + 430 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 415, + 287, + 430 + ], + "spans": [ + { + "bbox": [ + 84, + 415, + 287, + 430 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {l a c} = \\mathrm {K L} \\left(\\hat {y} _ {l a c} ^ {t}, y _ {l a c} ^ {t}\\right) + \\alpha \\mathrm {C E} \\left(\\hat {y} _ {l a c} ^ {s}, y ^ {s}\\right), \\tag {7}", + "image_path": "c510cfefd59d09508215e11dbc9d9eb1b0443a1adb9a6a7132cdfd808720aa18.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "text", + "content": " adjusts the influence of source data supervision, " + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\mathrm{KL}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "text", + "content": " is the Kullback-Leibler divergence, and " + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "inline_equation", + "content": "\\mathrm{CE}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 434, + 287, + 470 + ], + "type": "text", + "content": " represents the standard cross-entropy loss." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 471, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 471, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 47, + 471, + 287, + 577 + ], + "type": "text", + "content": "Obtaining pseudo label for VAC. Focusing on image modality, we aim to enhance the locality structure of vision representations—high inter-class discriminability and tight intra-class distribution—a feature that CLIP-extracted vision features lack, as detailed in Fig. 4a. To instill these locality structures within VAC, we utilize a K-means-based deep clustering approach [4, 21] to generate pseudo-labels for unlabeled target data. We calculate the clustering centroids for class " + }, + { + "bbox": [ + 47, + 471, + 287, + 577 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 47, + 471, + 287, + 577 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 93, + 581, + 287, + 608 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 581, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 93, + 581, + 287, + 608 + ], + "type": "interline_equation", + "content": "\\phi_ {k} = \\frac {\\sum_ {x ^ {t}} \\delta_ {k} \\left(\\operatorname {s o f t m a x} \\left(\\hat {y} _ {e n s} ^ {t}\\right)\\right) \\cdot f _ {b} ^ {t}}{\\sum_ {x ^ {t}} \\delta_ {k} \\left(\\operatorname {s o f t m a x} \\left(\\hat {y} _ {e n s} ^ {t}\\right)\\right)}, \\tag {8}", + "image_path": "13c09dbe8a0eaa7c7d765ebc9d07ae97d57e18c48d6684dd234ac56af189616f.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\hat{y}_{ens}^{t}" + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": " represents target ensemble outputs discussed below, and " + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "inline_equation", + "content": "\\delta_{k}" + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": " selects the " + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "inline_equation", + "content": "k_{th}" + }, + { + "bbox": [ + 47, + 613, + 287, + 673 + ], + "type": "text", + "content": " logit. To mitigate imbalances in text modality predictions from CLIP [17, 49], we implement Approximated Controlled Direct Effect (ACDE) [49] to adjust similarity scores obtained in Eq. (4):" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 53, + 678, + 287, + 710 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 678, + 287, + 710 + ], + "spans": [ + { + "bbox": [ + 53, + 678, + 287, + 710 + ], + "type": "interline_equation", + "content": "\\tilde {y} _ {l a c} ^ {t} = \\hat {y} _ {l a c} ^ {t} - \\tau \\log \\hat {p}, \\hat {p} \\leftarrow m \\hat {p} + (1 - m) \\frac {1}{B} \\sum_ {i = 1} ^ {B} p _ {i}, \\tag {9}", + "image_path": "72700b3deee1cc3e572cee426438913376bada335ffd6349cc899ff5eb40e3ec.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is momentum, " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is a debiasing factor, " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " is the batch size, and " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "p_i = \\mathrm{softmax}(\\hat{y}_{lac}^t)" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": " denotes classification probability of LAC. The ensemble outputs, used in the centroid calculation, are then defined as " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "\\hat{y}_{ens}^{t} = w\\cdot \\hat{y}_{vac}^{t} + (1 - w)\\cdot \\tilde{y}_{lac}^{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": ". For any given target bottleneck feature " + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "f_{b}^{t}" + }, + { + "bbox": [ + 305, + 72, + 545, + 156 + ], + "type": "text", + "content": ", we compute its cosine similarity with all centroids, assigning the class with the highest similarity as the pseudo-label:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 365, + 165, + 545, + 182 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 165, + 545, + 182 + ], + "spans": [ + { + "bbox": [ + 365, + 165, + 545, + 182 + ], + "type": "interline_equation", + "content": "y _ {v a c} ^ {t} = \\arg \\max _ {k} \\cos \\left(f _ {b} ^ {t}, \\phi_ {k}\\right). \\tag {10}", + "image_path": "abace0c7c18cf00c0ec6cfb2f5c7d3dd3f7b2b8d16a93c622b6f0822892dd58e.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 191, + 545, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 545, + 228 + ], + "type": "text", + "content": "Learning VAC. We now train vision component on unifies outputs from both modalities. Utilizing Eq. (9) and Eq. (5), the target ensemble output " + }, + { + "bbox": [ + 305, + 191, + 545, + 228 + ], + "type": "inline_equation", + "content": "\\hat{y}_{\\text {ens }}^{t}" + }, + { + "bbox": [ + 305, + 191, + 545, + 228 + ], + "type": "text", + "content": " is formulated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 357, + 236, + 545, + 250 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 236, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 357, + 236, + 545, + 250 + ], + "type": "interline_equation", + "content": "\\hat {y} _ {e n s} ^ {t} = w \\cdot \\hat {y} _ {v a c} ^ {t} + (1 - w) \\cdot \\tilde {y} _ {l a c} ^ {t}, \\tag {11}", + "image_path": "0ed161bc1d0019c934b5fac85224cb110b84aa8abb5fdca39ec89bf12c5e0d3d.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "content": "with the weight " + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "inline_equation", + "content": "w = W(VAC^t)" + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "content": " produced by the weight generator " + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "content": ", as depicted in Fig. 2. Referring to Sec. 3.1, we optimize " + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\hat{y}_{\\text{ens}}^t" + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "content": " rather than " + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\hat{y}_{\\text{vac}}^t" + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "content": " directly, with " + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{\\text{lac}}^t" + }, + { + "bbox": [ + 305, + 258, + 545, + 319 + ], + "type": "text", + "content": " serving as an auxiliary in training VAC and thus detached from the computational graph in Eq. (11)." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "spans": [ + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "type": "text", + "content": "To enhance individual discriminability and global diversity, thereby preserving the locality structure of vision representations, we follow state-of-the-art [1, 20, 21] to apply an information maximization loss " + }, + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{im}" + }, + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "type": "text", + "content": " comprising two components. The entropy loss " + }, + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ent}" + }, + { + "bbox": [ + 305, + 319, + 545, + 390 + ], + "type": "text", + "content": " improves individual certainty:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 320, + 399, + 545, + 433 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 399, + 545, + 433 + ], + "spans": [ + { + "bbox": [ + 320, + 399, + 545, + 433 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {e n t} = - \\mathbb {E} _ {x ^ {t} \\in \\mathcal {D} ^ {t}} \\left[ \\sum_ {k = 1} ^ {K} \\delta_ {k} \\left(\\hat {y} _ {e n s} ^ {t}\\right) \\log \\delta_ {k} \\left(\\hat {y} _ {e n s} ^ {t}\\right) \\right], \\tag {12}", + "image_path": "0946cc67f821204bf21847e5341e9bab11ac35284e4158af863241bf861d67e9.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 441, + 529, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 441, + 529, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 529, + 453 + ], + "type": "text", + "content": "and the diversity loss fosters diverse class distributions:" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 376, + 461, + 545, + 495 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 376, + 461, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 376, + 461, + 545, + 495 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {d i v} = - \\sum_ {k = 1} ^ {K} \\bar {q} _ {k} \\log \\bar {q} _ {k}, \\tag {13}", + "image_path": "08043c49dafc64b5fb86fea354521f0a5eb4ebdfbc3dfa8140c5220ac5e2a6f9.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "spans": [ + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "type": "inline_equation", + "content": "\\overline{q}_k = -\\mathbb{E}_{x^t\\in \\mathcal{D}^t}\\delta_k(\\hat{y}_{ens}^t)" + }, + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "type": "text", + "content": ". Hence, " + }, + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{im}" + }, + { + "bbox": [ + 306, + 503, + 539, + 517 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 382, + 526, + 545, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 526, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 382, + 526, + 545, + 538 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {i m} = \\mathcal {L} _ {e n t} - \\mathcal {L} _ {d i v}. \\tag {14}", + "image_path": "6c9bef6539f50fe3865ca7ab24b4442f47c495a028f788b95200c315c38cbc38.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "spans": [ + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "text", + "content": "The training of VAC is supervised by target pseudo labels for the vision modality, obtained through Eq. (10), while source labels directly optimize " + }, + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "inline_equation", + "content": "\\hat{y}_{vac}^{s}" + }, + { + "bbox": [ + 305, + 548, + 545, + 585 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 315, + 593, + 545, + 607 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 593, + 545, + 607 + ], + "spans": [ + { + "bbox": [ + 315, + 593, + 545, + 607 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {v a c} = C E \\left(\\hat {y} _ {\\text {e n s}} ^ {t}, y _ {v a c} ^ {t}\\right) + \\beta C E \\left(\\hat {y} _ {v a c} ^ {s}, y ^ {s}\\right) + \\mathcal {L} _ {i m}, \\tag {15}", + "image_path": "d77a6a812eb3cfa9c15f6ff4309e442926f9137f7d234135bbe5d8210423ac7c.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 616, + 538, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 538, + 628 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 538, + 628 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 616, + 538, + 628 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 306, + 616, + 538, + 628 + ], + "type": "text", + "content": " modulates the impact of source data supervision." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 635, + 533, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 533, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 533, + 647 + ], + "type": "text", + "content": "3.4. Aligning source and target by discriminator" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": "To achieve domain adaptation on both modalities, we introduce a modality discriminator " + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 653, + 545, + 713 + ], + "type": "text", + "content": " to align VAC and LAC from both domains. Our approach utilizes a singular modality discriminator trained on the source domain to differentiate LAC from VAC, and then assesses alignment on the" + } + ] + } + ], + "index": 31 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23367" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": "target domain. Proper alignment across domains would enable " + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 72, + 287, + 120 + ], + "type": "text", + "content": " to discern LAC and VAC on the target domain without direct training. The modality discriminator is trained using binary cross-entropy loss:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 55, + 130, + 287, + 144 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 130, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 55, + 130, + 287, + 144 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b c e} = - \\left[ y _ {d i s} \\log \\hat {y} _ {d i s} + \\left(1 - y _ {d i s}\\right) \\log \\left(1 - \\hat {y} _ {d i s}\\right) \\right], \\tag {16}", + "image_path": "f8ccef26ec7f135d48d44f47005bfdc2cee744f00e2e7ca090e0dd721f6d16bf.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "spans": [ + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "inline_equation", + "content": "y_{dis}" + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "text", + "content": " represents the modality label (0 for VAC, 1 for LAC) and " + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "inline_equation", + "content": "\\hat{y}_{dis}" + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "text", + "content": " is the output of " + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 153, + 287, + 176 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "spans": [ + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "text", + "content": "Notably, " + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "text", + "content": " is only trained on the source domain using Eq. (16). On the target domain, only the separators " + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "inline_equation", + "content": "G_{vis}" + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "inline_equation", + "content": "G_{txt}" + }, + { + "bbox": [ + 46, + 177, + 287, + 224 + ], + "type": "text", + "content": " are updated to minimize Eq. (16), aligning target LAC and VAC with the source ones." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 233, + 177, + 246 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 233, + 177, + 246 + ], + "spans": [ + { + "bbox": [ + 47, + 233, + 177, + 246 + ], + "type": "text", + "content": "3.5. Training and inference" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "spans": [ + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": "Training. As depicted in Fig. 2, the pretrained text encoder and vision encoder are frozen, and we optimize parameters of " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "G_{txt}" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "G_{vis}" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\Phi_1" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\Phi_2" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\theta_{G_{txt}}" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\theta_{G_{vis}}" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\theta_{\\Phi_1}" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\theta_{\\Phi_2}" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\theta_W" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "inline_equation", + "content": "\\theta_D" + }, + { + "bbox": [ + 46, + 251, + 287, + 323 + ], + "type": "text", + "content": ", respectively. Combining Eq. (7), Eq. (3), Eq. (15), Eq. (16), we define the following optimization problem:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 80, + 335, + 287, + 354 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 335, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 80, + 335, + 287, + 354 + ], + "type": "interline_equation", + "content": "\\theta_ {G _ {t x t}} = \\underset {\\theta_ {G _ {t x t}}} {\\arg \\min } \\mathcal {L} _ {l a c} + \\gamma \\mathcal {L} _ {o r t h o} + \\gamma \\mathcal {L} _ {b c e}, \\tag {17}", + "image_path": "d55afa89874b8eea34692563551286233e7cd06378b119a9990fa32bad61f5ac.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 80, + 359, + 254, + 379 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 359, + 254, + 379 + ], + "spans": [ + { + "bbox": [ + 80, + 359, + 254, + 379 + ], + "type": "interline_equation", + "content": "\\theta_{G_{vis}} = \\operatorname *{arg min}_{\\theta_{G_{vis}}}\\mathcal{L}_{vac} + \\gamma \\mathcal{L}_{ortho} + \\gamma \\mathcal{L}_{bce},", + "image_path": "8d1a0204e2024679077b809b63aa2c3ca3fad14f00b6d71fba7f4f37a014b6d5.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 80, + 384, + 217, + 403 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 384, + 217, + 403 + ], + "spans": [ + { + "bbox": [ + 80, + 384, + 217, + 403 + ], + "type": "interline_equation", + "content": "\\theta_ {W}, \\theta_ {\\Phi_ {1}}, \\theta_ {\\Phi_ {2}} = \\operatorname * {a r g m i n} _ {\\theta_ {W}, \\bar {\\theta} _ {\\Phi_ {1}}, \\theta_ {\\Phi_ {2}}} \\mathcal {L} _ {v a c},", + "image_path": "91df19e54d9644dc3d8aae8f6d3bdc015887f34b4957f5a2490f1b8f0b2ba651.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 80, + 408, + 168, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 408, + 168, + 426 + ], + "spans": [ + { + "bbox": [ + 80, + 408, + 168, + 426 + ], + "type": "interline_equation", + "content": "\\theta_{D} = \\operatorname *{arg min}_{\\theta_{D}}\\gamma \\mathcal{L}_{bce},", + "image_path": "c68c0c3ee43a9c65dcb6c9d7b965b3d75b8f2004a54a01a0efb004caa38f0047.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "text", + "content": " is hyperparameter controlling regularization terms " + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{bce}" + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ortho}" + }, + { + "bbox": [ + 47, + 436, + 287, + 472 + ], + "type": "text", + "content": ". We present detailed training procedure of UniMoS in Supplementary." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "text", + "content": "Inference. At inference, the final mixed prediction on target data is obtained using " + }, + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "inline_equation", + "content": "\\hat{y}_{ens}^{t}" + }, + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "text", + "content": " from Eq. (11), with a fixed mixup weight " + }, + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 472, + 287, + 556 + ], + "type": "text", + "content": ". The objective is to maximize accuracy by leveraging the strengths of both modalities for improved classification, as supported by our observations (Fig. 1), thus integrating outputs from both modalities to harness their combined advantages." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 567, + 127, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 127, + 580 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 127, + 580 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 587, + 239, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 587, + 239, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 587, + 239, + 600 + ], + "type": "text", + "content": "4.1. Datasets and implementation details" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "We extensively evaluate our method on three mainstream UDA benchmarks. Office-Home [46] consists of 65 categories divided into 4 distinct domains. On VisDA2017 [34], the goal is to transfer knowledge from 152k synthetic images (source domain) to 55k images of real items (target domain). DomainNet [35] is the most challenging UDA benchmark so far, containing 0.6 million samples from 345 categories divided into 6 distinct domains. Following previous works, we additionally provide results on" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "Mini-DomainNet [25, 40, 58], a subset of DomainNet with 4 domains and 126 categories." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "text", + "content": "We conduct all experiments on an NVIDIA RTX 2080Ti GPU. Since our method does not involve updating CLIP's pretrained parameters or prompts, the CLIP-extracted vision and text features are obtained via one single forward and saved in memory, thus greatly saving computation costs. For all tasks, we adopt SGD optimizer with batch size 32, and set momentum " + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "text", + "content": " in Eq. (9) to 0.99 and debias factor " + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "text", + "content": " in Eq. (9) to 0.5. For Office-Home and DomainNet, we train 50 epochs with initial learning rate 3e-3 and adopt annealing strategy [8] for learning rate decay. We train for 10 epochs with initial learning rate 9e-4 on VisDA due to fast convergence. The fixed mixup weight described in Sec. 3.5 is set to 0.3 for all tasks. We set regularization weight " + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 304, + 97, + 545, + 264 + ], + "type": "text", + "content": " in Eq. (17) to 0.01 across all datasets." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 274, + 416, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 274, + 416, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 274, + 416, + 285 + ], + "type": "text", + "content": "4.2. Benchmark results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "type": "text", + "content": "Office-Home. Tab. 1 gives classification accuracies on 12 adaptation tasks on Office-Home using the ResNet50 [11] backbone. To ensure a fair comparison, we categorize CLIP-based methods into two groups: 'none-tuning' and 'full-tuning'. The former involves learning prompts or additional modules without adjusting the pretrained CLIP backbones, while the latter optimizes the pretrained parameters of CLIP for specific tasks. It is evident from the results that our proposed UniMoS consistently outperforms both 'none-tuning' and 'full-tuning' methods. Notably, we obtain " + }, + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "type": "inline_equation", + "content": "+1.3\\%" + }, + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "type": "text", + "content": " performance boost than the strong baseline PADCLIP, which fine-tunes the CLIP vision backbone. Our method requires no parameter update or data forwarding of CLIP backbones, thus is much computationally cheaper. Especially on tasks that take P as target domain, we achieve up to " + }, + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "type": "inline_equation", + "content": "+5.4\\%" + }, + { + "bbox": [ + 304, + 293, + 545, + 496 + ], + "type": "text", + "content": " performance boost than PADCLIP, demonstrating the superiority of multimodal adaptation." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 498, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 616 + ], + "type": "text", + "content": "VisDA-2017. Tab. 2 shows class-wise classification accuracies on VisDA using ResNet101 [11]. Our method achieves the best performance among 'none-tuning' CLIP methods, while slightly falling behind PADCLIP. The reason is that CLIP has not been trained on the synthetic images like those from source domain of VisDA, resulting in incompatibilities between the VisDA dataset and CLIP. Similar observations are made by PADCLIP [17], which opts to fine-tune the vision branch of CLIP to address this challenge. Nevertheless, our approach outperforms typical UDA methods." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 713 + ], + "type": "text", + "content": "DomainNet. Tab. 3 presents classification accuracies of 30 cross-domain adaptation tasks on the most challenging benchmark DomainNet. Rows represent source domains and columns represent target domains. Our method reaches comparable performance with the strong baseline PADCLIP. One significant observation is that our UniMoS obtains lower accuracy than PADCLIP (6.6% lower in average) on tasks with qdr as target. This discrepancy arises" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23368" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 83, + 547, + 273 + ], + "blocks": [ + { + "bbox": [ + 91, + 71, + 501, + 81 + ], + "lines": [ + { + "bbox": [ + 91, + 71, + 501, + 81 + ], + "spans": [ + { + "bbox": [ + 91, + 71, + 501, + 81 + ], + "type": "text", + "content": "Table 1. UDA results on Office-Home. Best results are marked in bold font. Methods with " + }, + { + "bbox": [ + 91, + 71, + 501, + 81 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 91, + 71, + 501, + 81 + ], + "type": "text", + "content": " ’ are based on CLIP." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 83, + 547, + 273 + ], + "lines": [ + { + "bbox": [ + 50, + 83, + 547, + 273 + ], + "spans": [ + { + "bbox": [ + 50, + 83, + 547, + 273 + ], + "type": "table", + "html": "
MethodBackboneA→CA→PA→RC→AC→PC→RP→AP→CP→RR→AR→CR→PAvg.
SourceOnly [11]ResNet5034.950.058.037.441.946.238.531.260.453.941.259.946.1
ParetoDA [22]56.875.980.564.473.573.765.655.281.375.261.183.970.6
SDAT [37]58.277.182.266.377.676.863.357.082.274.964.786.072.2
MSGD [50]58.776.978.970.176.276.669.057.282.374.962.784.572.3
Fixbi [32]58.177.380.467.779.578.165.857.981.776.462.986.772.7
CST [26]59.079.683.468.477.176.768.956.483.075.362.285.172.9
ATDOC [23]60.277.882.268.578.677.968.458.483.174.861.587.273.2
KUDA [42]58.280.082.971.180.380.771.356.883.275.560.386.673.9
EIDCo [60]63.880.882.671.580.180.972.161.384.578.665.887.175.8
ICON [55]63.381.384.570.382.181.070.361.883.775.668.687.375.8
PADCLIP* [17]ResNet50-full-tuning57.584.083.877.885.584.776.359.285.478.160.286.776.6
CLIP* [36]ResNet50-none-tuning51.781.582.371.781.582.371.751.782.371.751.781.571.8
DAPrompt* [10]54.184.384.874.483.785.074.554.684.875.254.783.874.5
ADCLIP* [41]55.485.285.676.185.886.276.756.185.476.856.185.575.9
UniMoS* (ours)59.589.486.975.289.686.875.458.487.276.959.589.777.9
", + "image_path": "e9a4d7b1602bd9b25ce511af1b5a7aefd36a039f9e13041d1dfa83c662b9562a.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 293, + 545, + 436 + ], + "blocks": [ + { + "bbox": [ + 92, + 279, + 501, + 290 + ], + "lines": [ + { + "bbox": [ + 92, + 279, + 501, + 290 + ], + "spans": [ + { + "bbox": [ + 92, + 279, + 501, + 290 + ], + "type": "text", + "content": "Table 2. UDA results on VisDA-2017. Best results are marked in bold font. Methods with \\* are based on CLIP." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 293, + 545, + 436 + ], + "lines": [ + { + "bbox": [ + 50, + 293, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 50, + 293, + 545, + 436 + ], + "type": "table", + "html": "
MethodBackboneplanebicyclebuscarhorseknifemcyclpersonplantsktbrdtraintruckAvg.
SourceOnly [11]ResNet10155.153.361.959.180.617.979.731.281.026.573.58.552.4
ParetoDA [22]95.982.881.358.793.993.785.983.091.992.087.151.883.2
MSGD [50]97.583.484.469.495.994.190.975.595.594.688.144.984.5
ATDOC [23]95.384.782.475.695.897.788.776.694.091.791.561.986.3
CAN [15]97.087.282.574.397.896.290.880.796.696.387.559.987.2
FixBi [32]96.187.890.590.396.895.392.888.797.294.290.925.787.2
PADCLIP* [17]ResNet101-full-tuning96.788.887.082.897.193.091.383.095.591.891.563.088.5
CLIP* [36]ResNet101-none-tuning98.283.990.573.597.284.095.365.779.489.991.863.384.4
DAPrompt* [10]97.883.188.877.997.491.594.279.788.689.392.562.086.9
ADCLIP* [41]98.183.691.276.698.193.496.081.486.491.592.164.287.7
UniMoS* (ours)97.788.290.174.696.895.892.484.190.889.091.865.388.1
", + "image_path": "acf9f10a9193bf412eb96be3b5077641886c5afa8e979e7d9b6d793403e6738b.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": "from a significant domain gap between qdr and other domains, which is challenging to bridge without tuning the CLIP backbones. However, despite this, we manage to achieve superior performance to PADCLIP on all other tasks, thereby mitigating the overall " + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "inline_equation", + "content": "6.6\\%" + }, + { + "bbox": [ + 46, + 450, + 287, + 569 + ], + "type": "text", + "content": " performance drop. We also surpass all competing methods significantly. Tab. 4 compares UniMoS with available CLIP-based non-tuning methods on Mini-DomainNet, where our method achieves significant performance boost. Detailed results on Mini-DomainNet are given in Supplementary." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 575, + 139, + 588 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 139, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 139, + 588 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "In this section we validate the efficacy of each module in UniMoS. Tab. 5 presents averaged accuracies on Office-Home and VisDA-2017 by removing specific modules while maintaining other settings identical. The 'w/o debiasing' is obtained by skipping the debias procedure in Eq. (9). A primary observation is that the removal of any module leads to a performance drop to varying degrees, underscoring the positive contribution of each module to the overall outcome. The 'w/o learnable weight' row is obtained by replacing " + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": " in Eq. (11) with a constant 0.5, re" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 449, + 545, + 497 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 497 + ], + "type": "text", + "content": "sulting in the most pronounced performance decline. This emphasizes the significance of dynamic weights, which enables VAC to focus on vision-specific parts. Further insights into the effects of dynamic " + }, + { + "bbox": [ + 304, + 449, + 545, + 497 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 449, + 545, + 497 + ], + "type": "text", + "content": " are detailed in Sec. 4.4." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 498, + 545, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 558 + ], + "type": "text", + "content": "Tab. 6 ablates on the choice of backbones. We experiment with three backbones on Office-Home, and our UniMoS consistently outperforms all competing methods, proving that our method is generalizable across various models. Detailed results are given in Supplementary." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 563, + 382, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 563, + 382, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 563, + 382, + 574 + ], + "type": "text", + "content": "4.4. Discussions" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": "Effectiveness of learnable weight " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": ". To better understand how the learnable ensemble weight " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": " in Eq. (2) boosts performance, Fig. 3 compares the training process with and without dynamic " + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 582, + 547, + 713 + ], + "type": "text", + "content": ". We set a fixed weight of 0.5 for both LAC and VAC in 'w/o learnable w', and learn dynamic weights (shown as 'Learned weight w' in the figure) in other settings. Our first observation is that in our full design, accuracy of VAC increases steadily as the training progresses. Leveraging complementary modality-specific information from LAC, the final mixed outputs achieve higher accuracy than VAC alone. As stated in Sec. 3.1, the goal of" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23369" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 83, + 547, + 289 + ], + "blocks": [ + { + "bbox": [ + 94, + 71, + 499, + 81 + ], + "lines": [ + { + "bbox": [ + 94, + 71, + 499, + 81 + ], + "spans": [ + { + "bbox": [ + 94, + 71, + 499, + 81 + ], + "type": "text", + "content": "Table 3. UDA results on DomainNet. Best results are marked in bold font. Methods with " + }, + { + "bbox": [ + 94, + 71, + 499, + 81 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 94, + 71, + 499, + 81 + ], + "type": "text", + "content": " ’ are based on CLIP." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 83, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 49, + 83, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 49, + 83, + 547, + 289 + ], + "type": "table", + "html": "
DeiT-B [44]clpinfpptqdrrelsktavgViT-B [6]clpinfpptqdrrelsktavgSSRT-B [43]clpinfpptqdrrelsktavg
clp-24.349.615.865.352.141.4clp-27.253.113.271.253.343.6clp33.860.219.475.859.849.8
inf45.9-45.96.761.439.539.9inf51.4-49.34.066.341.142.4inf55.5-54.09.068.244.746.3
ppt53.223.8-6.566.444.738.9ppt53.125.6-4.870.041.839.1ppt61.728.5-8.471.455.245.0
qdr31.96.815.4-23.420.619.6qdr30.54.516.0-27.019.319.5qdr42.58.824.2-37.633.629.3
rel59.025.856.39.2-44.839.0rel58.429.060.06.0-45.839.9rel69.937.166.010.1-58.948.4
skt60.620.648.416.561.2-41.5skt63.923.852.314.467.4-44.4skt70.632.862.221.773.2-52.1
avg50.120.343.110.955.540.336.7avg51.522.046.18.560.440.338.1avg60.028.253.313.765.350.445.2
CDTrans -DeiT [51]clpinfpptqdrrelsktavgPMTrans -Swin [63]clpinfpptqdrrelsktavgCLIP -B* [36]clpinfpptqdrrelsktavg
clp-29.457.226.072.658.148.7clp-34.262.732.579.363.754.5clp-70.170.170.170.170.170.1
inf57.0-54.412.869.548.448.4inf67.4-61.122.278.057.657.3inf46.4-46.446.446.446.446.4
ppt62.927.4-15.872.153.946.4ppt69.733.5-23.979.861.253.6ppt61.761.7-61.761.761.761.7
qdr44.68.929.0-42.628.530.7qdr54.617.438.9-49.541.040.3qdr13.713.713.7-13.713.713.7
rel66.231.061.516.2-52.945.6rel74.135.370.025.4-61.153.2rel82.982.982.9-82.982.982.9
skt69.029.659.027.272.5-51.5skt73.833.062.630.977.5-55.6skt62.662.662.662.6-62.6
avg59.925.352.219.665.948.445.2avg67.930.759.127.072.856.952.4avg53.558.255.164.750.955.056.2
DAPrompt -B* [10]clpinfpptqdrrelsktavgPADCLIP -B* [17]clpinfpptqdrrelsktavgUniMoS -B* (ours)clpinfpptqdrrelsktavg
clp-73.073.872.673.973.573.4clp-73.675.474.676.476.375.3clp-76.577.276.677.577.877.1
inf50.8-50.149.650.650.350.3inf55.1-54.353.654.954.954.6inf55.1-55.054.655.355.255.0
ppt70.269.6-68.970.469.969.8ppt71.170.6-70.072.771.771.2ppt72.371.5-69.472.572.671.7
qdr17.214.413.9-14.313.914.7qdr36.818.032.0-31.734.930.7qdr25.022.923.6-23.725.124.1
rel84.984.884.984.7-84.684.8rel84.283.583.583.1-83.683.6rel86.085.985.885.5-85.985.8
skt65.865.465.864.965.9-65.6skt68.166.667.266.167.5-67.1skt68.567.868.267.568.0-68.0
avg57.861.457.768.155.058.459.8avg63.162.562.569.560.664.363.7avg61.464.962.070.759.463.363.6
", + "image_path": "4badaec65960c3caf17e98d8545d3f5bf97cc24dea10a798d71ae98eed7f68e0.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 50, + 327, + 287, + 381 + ], + "blocks": [ + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "lines": [ + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 287, + 322 + ], + "type": "text", + "content": "Table 4. UDA results on Mini-DomainNet. Best results are marked in bold font. All compared methods are CLIP-based." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 327, + 287, + 381 + ], + "lines": [ + { + "bbox": [ + 50, + 327, + 287, + 381 + ], + "spans": [ + { + "bbox": [ + 50, + 327, + 287, + 381 + ], + "type": "table", + "html": "
MethodBackboneAcc.MethodBackboneAcc.
CLIPResNet5071.2CLIPViT-B82.8
DAPrompt74.8DAPrompt85.8
ADCLIP75.2ADCLIP86.9
UniMoS (ours)78.0UniMoS (ours)87.3
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MethodOffice-HomeVisDA-2017
w/o Lortho77.487.6
w/o debiasing77.387.7
w/o Lim77.087.8
w/o Ldistill77.087.6
w/o learnable weight76.986.2
w/o modality discriminator77.687.9
UniMoS (full design)77.988.1
", + "image_path": "1c5847ec6fc10c8538aa773310a064db75d05fe27ff5ded60ddc5f8e05706947.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 508, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 664 + ], + "type": "text", + "content": "dynamic ensemble weight is to adaptively identify and preserve modality-specific information. We show in Fig. 3 that, the learned weight changes in each epoch to fit the training process. Without its support (w/o learnable w), the accuracy of VAC outputs drops significantly and finally converges with LAC. This occurs because employing a static weight would compromise the modality separation effects, causing both modalities to collapse to poor performance. In the example given by Fig. 3, accuracy of 'VAC output w/o learnable w' is " + }, + { + "bbox": [ + 46, + 508, + 287, + 664 + ], + "type": "inline_equation", + "content": "3.5\\%" + }, + { + "bbox": [ + 46, + 508, + 287, + 664 + ], + "type": "text", + "content": " lower than that of the full design 'VAC output'. The phenomenon indicates the significance of training with dynamic ensemble weights in our design. More examples are given in Supplementary." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 715 + ], + "type": "text", + "content": "Computation analysis. Tab. 7 compares computation costs of different methods on VisDA dataset. Our method necessitates training only a few linear layers without updating CLIP backbones, bringing great parameter efficiency." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 335, + 301, + 518, + 437 + ], + "blocks": [ + { + "bbox": [ + 335, + 301, + 518, + 437 + ], + "lines": [ + { + "bbox": [ + 335, + 301, + 518, + 437 + ], + "spans": [ + { + "bbox": [ + 335, + 301, + 518, + 437 + ], + "type": "image", + "image_path": "3a76308d52f2419f5adb32e4a24abfeab96aa20d7537a9cd077e332ad5be3ce8.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 441, + 544, + 453 + ], + "lines": [ + { + "bbox": [ + 306, + 441, + 544, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 441, + 544, + 453 + ], + "type": "text", + "content": "Figure 3. Effects of learnable ensemble weight " + }, + { + "bbox": [ + 306, + 441, + 544, + 453 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 306, + 441, + 544, + 453 + ], + "type": "text", + "content": " on Office-Home." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 490, + 545, + 558 + ], + "blocks": [ + { + "bbox": [ + 306, + 464, + 545, + 487 + ], + "lines": [ + { + "bbox": [ + 306, + 464, + 545, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 545, + 487 + ], + "type": "text", + "content": "Table 6. Results with different backbones on Office-Home. Best results are in bold. All compared methods are based on CLIP." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 490, + 545, + 558 + ], + "lines": [ + { + "bbox": [ + 309, + 490, + 545, + 558 + ], + "spans": [ + { + "bbox": [ + 309, + 490, + 545, + 558 + ], + "type": "table", + "html": "
MethodBackboneAcc.MethodBackboneAcc.
UniMoS (ours)ResNet5077.9CLIP82.4
CLIPViT-L87.0DAPromptViT-B84.4
DAPrompt88.7ADCLIP86.1
ADCLIP90.5PADCLIP86.7
UniMoS (ours)90.7UniMoS (ours)86.9
", + "image_path": "50e63ea2d87a20ac51ea8a5c31c5ab338e2bd35e130b5f317e30a38879dc86a9.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "spans": [ + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "content": "Furthermore, only one forward through CLIP is needed, which allows UniMoS achieve more than " + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "inline_equation", + "content": "47 \\times" + }, + { + "bbox": [ + 304, + 568, + 545, + 688 + ], + "type": "text", + "content": " training speed boost than PADCLIP. Prompt learning methods like DAPrompt also requires no training on CLIP backbones, but they require extensive iterative forwarding of data through CLIP to learn optimal prompts per class, leading to low computing efficiency and scalability to larger datasets. When running on DomainNet with 345 classes, DAPrompt requires more than 22G GPU memory, while our method requires less than 3G. More details are in Supplementary." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "Feature distribution visualization. To demonstrate the efficacy of modality separation and feature alignment, we per" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23370" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 59, + 72, + 212, + 189 + ], + "blocks": [ + { + "bbox": [ + 59, + 72, + 212, + 189 + ], + "lines": [ + { + "bbox": [ + 59, + 72, + 212, + 189 + ], + "spans": [ + { + "bbox": [ + 59, + 72, + 212, + 189 + ], + "type": "image", + "image_path": "da613e85b47013da81c14148ebe07ac7f9f8977c50157741053f4ef1721a5916.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 194, + 198, + 203 + ], + "lines": [ + { + "bbox": [ + 70, + 194, + 198, + 203 + ], + "spans": [ + { + "bbox": [ + 70, + 194, + 198, + 203 + ], + "type": "text", + "content": "(a) CLIP-extracted feature distribution." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 219, + 72, + 375, + 188 + ], + "blocks": [ + { + "bbox": [ + 219, + 72, + 375, + 188 + ], + "lines": [ + { + "bbox": [ + 219, + 72, + 375, + 188 + ], + "spans": [ + { + "bbox": [ + 219, + 72, + 375, + 188 + ], + "type": "image", + "image_path": "05e6a1cd3d72af8426c06e4eca41d7d1cd4a0dcf4d4bc7443cb9dc30dd086d62.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 246, + 194, + 345, + 204 + ], + "lines": [ + { + "bbox": [ + 246, + 194, + 345, + 204 + ], + "spans": [ + { + "bbox": [ + 246, + 194, + 345, + 204 + ], + "type": "text", + "content": "(b) Modality separation effect." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 381, + 72, + 535, + 188 + ], + "blocks": [ + { + "bbox": [ + 381, + 72, + 535, + 188 + ], + "lines": [ + { + "bbox": [ + 381, + 72, + 535, + 188 + ], + "spans": [ + { + "bbox": [ + 381, + 72, + 535, + 188 + ], + "type": "image", + "image_path": "e0398b853fc9e1188c0af74fc4e1571ccf97b92173737a2ea6603e67fe5d8176.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 386, + 193, + 526, + 204 + ], + "lines": [ + { + "bbox": [ + 386, + 193, + 526, + 204 + ], + "spans": [ + { + "bbox": [ + 386, + 193, + 526, + 204 + ], + "type": "text", + "content": "(c) Aligned bottleneck feature distribution." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 50, + 269, + 287, + 339 + ], + "blocks": [ + { + "bbox": [ + 47, + 246, + 287, + 267 + ], + "lines": [ + { + "bbox": [ + 47, + 246, + 287, + 267 + ], + "spans": [ + { + "bbox": [ + 47, + 246, + 287, + 267 + ], + "type": "text", + "content": "Table 7. Computation analysis on VisDA-2017. Best results are marked in bold font. Methods with \\* are based on CLIP." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 269, + 287, + 339 + ], + "lines": [ + { + "bbox": [ + 50, + 269, + 287, + 339 + ], + "spans": [ + { + "bbox": [ + 50, + 269, + 287, + 339 + ], + "type": "table", + "html": "
MethodBkb.Param.Throughput (images/s)Train timeFLOPsAcc.
DAPrompt*ResNet1011.2M2444.3H11.3G86.9
FixBi86.1M1025.5H15.73G87.2
CAN42.5M3110.5H7.9G87.2
PADCLIP*--23.5H*-88.5
UniMoS* (ours)0.79M26670.5H<0.01G88.1
", + "image_path": "0498327a2dba20dda13110aca0f7ac3bd5ac95d724ee2ccf901e18e3488b3009.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 352, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 287, + 567 + ], + "type": "text", + "content": "form t-sne [45] visualization on various features at different phases of our method. Fig. 4a shows CLIP-extracted vision features from source (green) and target (blue) domain, along with CLIP-extracted text features (red) of naive prompts. The text features distribute distantly with vision features, proving the existence of modality gap. Besides, CLIP-extracted vision features form poor class discriminability and locality structures. Fig. 4b showcases the separated LAC and VAC of our method. A clear boundary can be observed between the features of both modalities, indicating the effectiveness of modality separation. Additionally, the text features distribute closer to LAC, proving that the separated LAC is indeed more relevant to the text modality. Following feature alignment and VAC training, the bottleneck features " + }, + { + "bbox": [ + 46, + 352, + 287, + 567 + ], + "type": "inline_equation", + "content": "f_{b}" + }, + { + "bbox": [ + 46, + 352, + 287, + 567 + ], + "type": "text", + "content": " from both domains display a compact class-level locality structure, as demonstrated in Fig. 4c. This compact structure contributes significantly to the accuracy of the final classification results." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": "Hyperparameter sensitivity. In the calibration of UniMoS, we encounter three hyperparameters to determine: " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": " in Eq. (7), " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": " in Eq. (15), and " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": " in Eq. (17). We empirically discover that alternating " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": " has little impact within each dataset, so we focus on exploring the effects of " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": ". As illustrated in Fig. 5a, the performance on VisDA is notably influenced by " + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 568, + 287, + 676 + ], + "type": "text", + "content": ", with smaller values leading to improved accuracy. This outcome is attributed to the fact, as discussed in Sec. 4.2, that CLIP struggles to adequately iden" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 246, + 425, + 338 + ], + "blocks": [ + { + "bbox": [ + 45, + 205, + 547, + 239 + ], + "lines": [ + { + "bbox": [ + 45, + 205, + 547, + 239 + ], + "spans": [ + { + "bbox": [ + 45, + 205, + 547, + 239 + ], + "type": "text", + "content": "Figure 4. T-sne visualization [45] of the effects of UniMoS on " + }, + { + "bbox": [ + 45, + 205, + 547, + 239 + ], + "type": "inline_equation", + "content": "\\mathrm{A}\\rightarrow \\mathrm{P}" + }, + { + "bbox": [ + 45, + 205, + 547, + 239 + ], + "type": "text", + "content": " task from Office-Home. UniMoS effectively disentangles CLIP-extracted vision features (Fig. 4a) into LAC and VAC (Fig. 4b, obtained by randomly selecting 25 classes), and constructs clear cross-domain locality structures (Fig. 4c)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 246, + 425, + 338 + ], + "lines": [ + { + "bbox": [ + 310, + 246, + 425, + 338 + ], + "spans": [ + { + "bbox": [ + 310, + 246, + 425, + 338 + ], + "type": "image", + "image_path": "eca940e3e1893db4d802a889b9cd72c959e7d5960f81195fb2fb9495cb0e1ae3.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 340, + 343, + 393, + 353 + ], + "lines": [ + { + "bbox": [ + 340, + 343, + 393, + 353 + ], + "spans": [ + { + "bbox": [ + 340, + 343, + 393, + 353 + ], + "type": "text", + "content": "(a) VisDA-2017" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "lines": [ + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "spans": [ + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "type": "text", + "content": "Figure 5. Parameter sensitivity analysis on " + }, + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 309, + 355, + 541, + 367 + ], + "type": "text", + "content": " of UniMoS." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 247, + 541, + 338 + ], + "blocks": [ + { + "bbox": [ + 427, + 247, + 541, + 338 + ], + "lines": [ + { + "bbox": [ + 427, + 247, + 541, + 338 + ], + "spans": [ + { + "bbox": [ + 427, + 247, + 541, + 338 + ], + "type": "image", + "image_path": "4178cd35b931fedfc0fc58a55ef736ff9eb1fbcf4b340dd4692ec0dbda1c8e9b.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 455, + 343, + 511, + 353 + ], + "lines": [ + { + "bbox": [ + 455, + 343, + 511, + 353 + ], + "spans": [ + { + "bbox": [ + 455, + 343, + 511, + 353 + ], + "type": "text", + "content": "(b) Office-Home" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "spans": [ + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "type": "text", + "content": "tify source synthetic images from VisDA. Consequently, down-weighting source supervision on LAC proves beneficial. Conversely, source supervision from both modalities of Office-Home are important. They positively and equally contributes to the adaptation process, so " + }, + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\alpha = 1" + }, + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "type": "inline_equation", + "content": "\\beta = 1" + }, + { + "bbox": [ + 304, + 375, + 545, + 448 + ], + "type": "text", + "content": " brings the best result, as shown in Fig. 5b." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 459, + 384, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 459, + 384, + 471 + ], + "spans": [ + { + "bbox": [ + 306, + 459, + 384, + 471 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 479, + 546, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 546, + 622 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 546, + 622 + ], + "type": "text", + "content": "Inspired by the theory of modality gap, in this paper we propose a Unified Modality Separation framework for unsupervised domain adaptation. The CLIP-extracted vision features are explicitly disentangled into vision-associated and language-associated components, which are trained differently according to their modality strengths and further aligned by a modality discriminator. A modality-ensemble training paradigm unifies both components to leverage modality-specific information while preserving modality-shared contexts, contributing to successful classification. This work is hope to inspire further analysis and exploitation of the multimodal features in pretrained VLMs." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 633, + 421, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 633, + 421, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 633, + 421, + 647 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China under Grant 62176042, and in part by Sichuan Science and Technology Program under Grant 2023NSFSC0483, and in part by Tencent Marketing Solution Rhino-Bird Focused Research Program." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 683, + 287, + 713 + ], + "type": "text", + "content": "*Cited from PADCLIP [17]. PADCLIP conducts the experiments on an NVIDIA Tesla V100 GPU. Results on other metrics are unavailable since the authors have not released the code implementations yet." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23371" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 146 + ], + "type": "text", + "content": "[1] Sk Miraj Ahmed, Dripta S Raychaudhuri, Sujoy Paul, Samet Oymak, and Amit K Roy-Chowdhury. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3561-3571, 2023." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23374" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_content_list.json b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..d140fa1f87d24e527bdb08da367f41ef88bff019 --- /dev/null +++ b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_content_list.json @@ -0,0 +1,1506 @@ +[ + { + "type": "text", + "text": "SportsHHI: A Dataset for Human-Human Interaction Detection in Sports Videos", + "text_level": 1, + "bbox": [ + 76, + 130, + 890, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tao $\\mathbf{W}\\mathbf{u}^{1,*}$ Runyu He $^{1,*}$ Gangshan $\\mathbf{W}\\mathbf{u}^{1}$ Limin Wang $^{1,2,\\boxtimes}$", + "bbox": [ + 200, + 178, + 767, + 198 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ State Key Laboratory for Novel Software Technology, Nanjing University $^{2}$ Shanghai AI Lab", + "bbox": [ + 107, + 198, + 861, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "wt, runyu.he}@smail.nju.edu.cn, {gswu, lmwang}@nju.edu.cn", + "bbox": [ + 235, + 218, + 732, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "https://github.com/MCG-NJU/SportsHHI", + "bbox": [ + 303, + 234, + 658, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 310, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video-based visual relation detection tasks, such as video scene graph generation, play important roles in fine-grained video understanding. However, current video visual relation detection datasets have two main limitations that hinder the progress of research in this area. First, they do not explore complex human-human interactions in multi-person scenarios. Second, the relation types of existing datasets have relatively low-level semantics and can be often recognized by appearance or simple prior information, without the need for detailed spatio-temporal context reasoning. Nevertheless, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. To address this issue, we propose a new video visual relation detection task: video human-human interaction detection, and build a dataset named SportsHHI for it. SportsHHI contains 34 high-level interaction classes from basketball and volleyball sports. 118,075 human bounding boxes and 50,649 interaction instances are annotated on 11,398 keyframes. To benchmark this, we propose a two-stage baseline method and conduct extensive experiments to reveal the key factors for a successful human-human interaction detector. We hope that SportsHHI can stimulate research on human interaction understanding in videos and promote the development of spatio-temporal context modeling techniques in video visual relation detection.", + "bbox": [ + 76, + 319, + 473, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 742, + 207, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video understanding is a fundamental research field in computer vision, which has wide applications in security monitoring, internet video recommendation, and sports video analysis. Remarkable progress has been made in the action recognition task [3, 4, 13, 22, 23, 39, 40] with the advances of video convolution neural networks [3, 11, 45, 46, 49, 50, 52, 55] and video transformers [1, 2, 10, 29, 44, 51, 58].", + "bbox": [ + 76, + 768, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3422ee33eec44e6c3d69531293a7dac4806aa802f9e35f1dce7139837b0057ad.jpg", + "image_caption": [ + "" + ], + "image_footnote": [], + "bbox": [ + 504, + 284, + 696, + 366 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/8889d04a7c3e3db844a634032fe90504c8ed3d102b41af00d915a679142a3f29.jpg", + "image_caption": [ + "" + ], + "image_footnote": [], + "bbox": [ + 697, + 284, + 797, + 366 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ea07afbbabc970e14672dd51be95e0d7f26e64b3e149c566ae5d2ce79764a3a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 802, + 285, + 890, + 366 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3c384324447107dc63b430fca1d46a0925e21593c1a35c30f15fa63bf2ef344b.jpg", + "image_caption": [ + "<#5,attack-defend,#11><#5,attack-protect,#2><#5,attack-block,#9>", + "Figure 1. Comparison between previous video visual relation detection datasets and our SportsHHI. In the upper row, we show three relation instances from VidVRD and AG datasets. These datasets rarely involve human-human interaction and define semantically simple relations that can be recognized by appearance or prior information. In contrast, the bottom row shows interaction annotations in two sample keyframes of SportsHHI. The bounding boxes and interaction annotation of the same instance are displayed in the same color. SportsHHI provides complex multi-person scenes where various interactions between human pairs occur concurrently. It focuses on high-level interactions that require detailed spatio-temporal context reasoning." + ], + "image_footnote": [], + "bbox": [ + 504, + 371, + 696, + 455 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/40a53d3c426fe36ed24322095d48af473ad6f865cf1700d806d93799b7632d06.jpg", + "image_caption": [ + "", + "<#2, close defense, #8> <#1, close defense, #9> <#3, close defense, #6>", + "<#4, close defense, #7> <#0, interfere-shot, #5>" + ], + "image_footnote": [], + "bbox": [ + 697, + 371, + 890, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The action recognition task requires tagging each video clip with a single action label. However, real-world applications usually require a more detailed and in-depth understanding of videos, thus more attention has been attracted to fine-grained video understanding tasks such as video action detection [14, 18, 24, 26, 31, 42, 54] and video visual relation detection tasks [7, 19, 20, 35, 36].", + "bbox": [ + 496, + 654, + 890, + 760 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video action detection involves localizing action performers in both space and time, as well as recognizing their action class. While earlier datasets like UCF101-24 [40] and JHMDB [18] primarily focuses on action detection in single-person scenarios, recent large-scale datasets such as AVA [14] and MultiSports [26] have emphasized the importance of modeling human-human interactions for a better recognition of individual actions in multi-person scenes. However, while AVA and MultiSports provide ample multi", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*: Equal contribution. $\\boxtimes$ Corresponding author.", + "bbox": [ + 99, + 886, + 370, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18537", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "person scenes, neither of them offers explicit human-human interaction definitions and annotations.", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video scene graph generation is a popular video visual relation detection task, which requires the model to localize objects of interest in the video and recognize the relation of each pair of objects. While current datasets like AG [19], VidVRD [35], and VidOR [36] provide explicit relation instance annotations, human-human interactions are barely involved. Moreover, the relation categories defined in these benchmarks primarily include spatial relations, atomic actions, and simple visual comparisons, which are semantically straightforward and often recognizable by appearance information or simple prior knowledge, such as $\\langle \\text{dog}, \\text{larger}, \\text{frisbee} \\rangle$ and $\\langle \\text{person}, \\text{stand on}, \\text{floor} \\rangle$ in the upper row of Figure 1. This makes current research pay more attention to the recognition of object categories and the utilization of category priors while ignoring reasoning based on spatio-temporal context. However, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. Spatio-temporal context modeling is an important technology that makes video relation detection different from image relation detection. We argue that there is a need for new datasets that comprehensively explore human-human interactions in complex multiperson scenarios, with high-level relation categories that require detailed spatio-temporal context reasoning.", + "bbox": [ + 75, + 125, + 472, + 503 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we propose a new video visual relation detection task: video human-human interaction detection. This task requires detecting human-human interaction instances in video frames. Each human-human interaction instance is formulated as a triplet $\\langle S, I, O \\rangle$ , where $S$ and $O$ denote the bounding boxes of two different people and $I$ denotes the interaction category. For this task, we develop a dataset named SportsHHI, short for Sports Human-Human Interaction. We label interaction instances on the keyframes of basketball and volleyball videos at 5FPS. Two samples of keyframes are shown in the bottom row of Figure 1. SportsHHI has several unique characteristics that distinguish it from other visual relation detection datasets: 1) It is built on basketball and volleyball sports videos, thus containing a large number of complex multiplayer scenes with various interactions between athlete pairs occurring concurrently. 2) The interactions between each pair of humans are transient and change rapidly due to the fast movements of the players. 3) The defined interactions are of high-level semantic, including technical actions, tactical cooperation, and confrontation in sports. Recognizing an interaction instance in SportsHHI usually requires detailed spatiotemporal context reasoning. We hope that SportsHHI can attract more research attention to human-human interaction understanding in complex multi-person videos and promote the development of spatio-temporal context modeling tech", + "bbox": [ + 75, + 507, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "niques in video visual relation detection.", + "bbox": [ + 498, + 90, + 769, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We test existing action detection and video scene graph generation methods on the SportsHHI dataset and propose a simple and neat baseline method based on these methods. Our baseline method adopts a Faster-RCNN-alike two-stage pipeline [33]: In the first stage, we use an offline human detector to detect person bounding boxes on the keyframe. We exhaust bounding box pairs to generate interaction proposals. In the second stage, we extract features for each proposal and categorize each proposal into an interaction class or background. Our experiments demonstrate that motion features, context information, relative position encoding, and information exchange among proposals are important for human-human interaction detection.", + "bbox": [ + 496, + 106, + 890, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In summary, our contribution is three-fold: 1) We propose a new video relation detection task of human-human interaction detection which aims at exploring the complex interaction between people in multi-person scenarios; 2) We develop the SportsHHI dataset of multi-person sports videos on which high-level human-human interaction is well-defined and finely-labeled; 3) We design a two-stage baseline model and conduct extensive experiments on the SportsHHI dataset to discover the key factors for a successful interaction detector.", + "bbox": [ + 496, + 301, + 890, + 452 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 467, + 640, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video action detection. Video action detection aims to locate and recognize action instances on video frames. Earlier datasets like UCF Sports [34], UCF101-24 [40], and J-HMDB [18] typically only include single-person videos. Datasets like DALY [53], AVA [14], AVA-Kinetics [24], and MultiSports [26] contain scenes where multiple people are performing various actions concurrently. AVA sparsely annotates keyframes of movie videos at 1FPS. MultiSports collects videos from sports competitions. Many interaction-related action classes are defined, such as listen to in AVA and second pass in MultiSports. As they claim, it is important to model the interaction between people to recognize the action category of each person. However, as no interaction annotation is provided, interaction modeling can only be performed implicitly. SportsHHI annotates interactions on keyframes of basketball and volleyball videos from MultiSports at 5FPS. With interaction definitions and annotations provided in SportHHI, human-human interaction detection can be explicitly performed and evaluated.", + "bbox": [ + 496, + 492, + 890, + 779 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Video visual relation detection. Video scene graph generation requires localizing object pairs in the video and recognizing the relation of each pair of objects. AG [19] is a large-scale dataset built on Charades [38]. All videos in AG contain only one person, thus no human-human interaction is involved. In VidVRD [35] and VidOR [36], most of the videos contain only one person. Though human-human interaction is involved, the exploration of it is very", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18538", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "limited. Similar to AG, video human-object interaction detection [5, 41] datasets only focus on relations between humans and objects. Besides, the relation categories defined in these datasets only include spatial relations (e.g. above), atomic actions (e.g. lean on), and simple visual comparisons (e.g. larger). The relations are usually semantically simple and can be easily recognized by appearance information. Some trivial relations are also defined like $\\langle dog, larger, frisbee \\rangle$ in VidVRD. The category of the subject and object can often provide enough cues for relation recognition [7, 20, 28, 32, 43, 47], such as $\\langle person, ride, horse \\rangle$ . Moreover, the relation between two objects changes very slowly in a video. Our SportHHI annotates human-human interaction instances in complex multi-person sports videos. The defined interactions are of high-level semantics and the interaction between two people changes rapidly.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Sports video understanding. Researchers have built many different benchmarks in the sports domain for its challenges in spatio-temporal reasoning and promising application prospects, such as UCF101-24 [40] and MultiSports [26] for video action detection, FineGym [37] and Diving48 [25] for action recognition and temporal action detection, SoccerNet [12] for action spotting, SportsMOT [8] for multiobject tracking, and NBA [56], CAD [6] and Volleyball [17] for group action recognition, etc. Group action recognition (GAR) requires tagging each video clip with a group action label. Implicit modeling of interactions among the players is often performed to improve the accuracy of label predictions. The proposed SportsHHI dataset provides interaction definitions and annotations for explicit human-human interaction exploration.", + "bbox": [ + 75, + 347, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. The SportsHHI Dataset", + "text_level": 1, + "bbox": [ + 76, + 585, + 302, + 603 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Sec. 3.1, we will explain several key choices we made while creating the SportsHHI dataset and outline the annotation process. Then in Sec. 3.2, we will present a detailed analysis of the statistics and characteristics of SportsHHI.", + "bbox": [ + 75, + 612, + 468, + 674 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Dataset Construction", + "text_level": 1, + "bbox": [ + 76, + 681, + 277, + 696 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Selection of the data domain. First, we select to annotate human-human interaction in team sports videos for the following reasons: 1) The field of sports is itself a very promising application area for interaction detection. 2) Team sports videos provide ample multi-person scenes where various interactions between athlete pairs occur concurrently, which are rarely seen in daily-life videos. 3) Team sports videos involve many interactions with high-level semantics, such as tactics coordination or confrontation. 4) Interactions between people in sports game videos can be clearly and comprehensively defined according to game rules and professional athletes' advice. 5) High-quality, diverse sports game videos are easily accessible,", + "bbox": [ + 75, + 704, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/e0049393c50939f6cf96efaefb9c536e8603a18f7f2df8b69dae1594bf4b5969.jpg", + "image_caption": [ + "Figure 2. User interface for interaction annotation. The person bounding boxes and ids in the keyframe are shown in the left. We can play the video for context information. To add an interaction instance in the current keyframe, the subject person id, object person id, and interaction class should be specified." + ], + "image_footnote": [], + "bbox": [ + 503, + 88, + 887, + 290 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ed8cf76d618c47c3b666e604d44f4f290892fbf9bbf44db02e4e94c3204ba1a4.jpg", + "image_caption": [ + "Figure 3. Interaction classes hierarchy. There are 34 interaction classes of high-level semantics in total in SportsHHI. 16 for basketball and 18 for volleyball." + ], + "image_footnote": [], + "bbox": [ + 501, + 369, + 887, + 465 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "while surveillance videos are usually of lower quality and harder to obtain because of privacy. Furthermore, we decide to build the dataset on two popular team sports basketball and volleyball because: 1) The methods can be validated on two different subsets to evaluate their generalization performance on different sports. 2) Football is not included because the instance sparsity and class imbalance (which will be discussed in Sec. 3.2) would be more prominent in football videos.", + "bbox": [ + 496, + 522, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Interaction classes definition. There are existing benchmarks focusing on atomic relations, which can be recognized by appearance information or prior knowledge. These interaction classes are out of our scope (it does not mean they are solved or not important). Instead, we focus on high-level interactions between athletes, which are semantically complex and require detailed spatio-temporal context reasoning to recognize. With the guidance of professional athletes, we generated the final interaction vocabulary through iterative trial labeling and modification, which is shown in Figure 3. Our defined interaction classes include technical action (e.g. pass-catch in basketball), tactical coordination (e.g. co-block in volleyball), or confrontation (e.g. attack-defend in volleyball).", + "bbox": [ + 496, + 657, + 890, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Interaction instance formulation. Following common practice in AVA and AG datasets, we define interaction in", + "bbox": [ + 496, + 869, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18539", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/a5e35501bae7cc4f28601f7f406727b06e8b204325eb37639e2dcaf19a969138.jpg", + "image_caption": [ + "Figure 4. The number of interaction instances of each class sorted by descending order." + ], + "image_footnote": [], + "bbox": [ + 107, + 88, + 861, + 253 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/80376e924605107752419676f7837da4f7fdcd7db6629a12b3c45edf1adf45d3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 84, + 282, + 264, + 376 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/24b88d24b6d9f0896fc90564385e3950cafa8d7a72f5190fce5fa0fdf64a7bb0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 266, + 282, + 459, + 376 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a717f2d113d30e8872a93c8e44bc56e6ae6da41eafc7f939ef0d01b7ac3f3eda.jpg", + "image_caption": [ + "Figure 5. Statistics comparisons between SportsHHI and VidVRD. In the left, we compare the distribution of the number of instances in each keyframe. SportsHHI has more keyframes of fewer instances because of the high-level interaction class definition and the property of sports videos. In the right, we compare the distribution of GIoU between the subject and object. The proportion of instances of extremely high and extremely low GIoU between subject and object are both higher than VidVRD," + ], + "image_footnote": [], + "bbox": [ + 84, + 378, + 264, + 473 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1bc3bb600c20b444440b566fd8ca024fbc6843d70fa010a9404111c88813b16f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 267, + 378, + 459, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "stances at the frame level, with reference to a long-term spatial-temporal context. Each interaction instance can be formulated as a triplet $\\langle S, I, O \\rangle$ where $S$ and $O$ denote the bounding boxes of the subject and object person and $I$ denotes the interaction category between them from the interaction vocabulary. When the subject person or the object person is out of view, we annotate $S$ or $O$ as \"invisible\". This happens infrequently and we will provide statistics about it in the appendix.", + "bbox": [ + 75, + 597, + 467, + 733 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Data preparation. We carefully selected 80 basketball and 80 volleyball videos from the MultiSports [26] dataset to cover various types of games including men's, women's, national team, and club games. The average length of the videos is 603 frames and the frame rate of the videos is 25FPS. All videos have a high resolution of 720P.", + "bbox": [ + 75, + 734, + 467, + 823 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Annotation. We follow the sparse annotation strategy of AVA [14] and AG [19] to reduce redundancy and save labor costs, but we annotate keyframes at a higher rate of 5FPS, because in sports videos, the change of interactions is very frequent and fast. In our practice, 5FPS can avoid lots of", + "bbox": [ + 75, + 824, + 467, + 898 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/387fb1fc83bd33e75d741e0d9d079fb46419ee45cf03fbd7d1f036231022406a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
#keyframes#interact.#inst.#obj. bbox#hum. bboxavg. hum.
AG [19]234253251.7M4762292342531.00
VidVRD [35]5834134556311270522240.38
SportsHHI113983450649-11807510.36
", + "bbox": [ + 501, + 282, + 888, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 1. Comparison of statistics between video scene graph generation datasets and SportsHHI. SportsHHI has a comparable scale to VidVRD. The average number of human bounding boxes per frame of SportsHHI is much higher than AG or VidVRD.", + "bbox": [ + 498, + 340, + 890, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "redundancy and keep up with the changes of interactions.", + "bbox": [ + 498, + 407, + 877, + 422 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We take a two-stage annotation pipeline. The first stage is for person localization and tracking and the second stage is for interaction instance annotation. The user interface of the software for interaction instance annotation is shown in Figure 2. Though we annotate interaction instances at the frame level, as person id tracking is provided, we can easily generate interaction tubes by linking the same pair of persons with the same interaction class and provide temporal boundaries at a granularity of 5 frames. We will exemplify this in the appendix.", + "bbox": [ + 496, + 424, + 890, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Quality control. For the first stage, all annotations are complemented manually without using detection or tracking models. We double-check each video and manually correct inaccurate bounding boxes and inconsistent person numbers. For the second stage, all the annotators are professional athletes or veteran amateurs. To improve annotation accuracy and completeness, we perform repeated annotation. Each video is distributed to two different annotators. If the two annotators disagree on an annotation record, this record will be checked and decided by the meta-annotator.", + "bbox": [ + 496, + 575, + 890, + 727 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Dataset Statistics and Characteristics", + "text_level": 1, + "bbox": [ + 500, + 739, + 821, + 753 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our SportsHHI provides interaction instance annotations on keyframes of basketball and volleyball videos. As shown in Table 1, SportHHI contains 34 interaction classes, and 11398 keyframes in total are annotated with instances. Current video scene graph datasets deal with general relations between various kinds of objects while our SportsHHI focuses on high-level interaction between humans. It is reasonable that datasets for video scene graph generation have a larger scale than SportsHHI. However, our SportHHI still", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18540", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "has a comparable size to the popular VidVRD dataset for video scene graph generation. Our SportsHHI has more annotated keyframes (11398 versus 5834) and the number of interaction instances is close (55631 versus 50649). One important characteristic of our SportsHHI is the multiperson scenarios. The average number of people per frame in our SportsHHI is much higher than AG and VidVRD. AG only contains one person in each video and there is virtually no multi-person scenario in videos of VidVRD. Human-human interaction is barely involved in these datasets.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We further show some important characteristics of our SportsHHI: 1) As shown in Figure 4, the distribution of the number of interaction instances per class roughly follows Zipf's law. This long-tail distribution requires us to put more attention to classes with fewer instances. 2) As shown in Figure 5 left, compared with VidVRD [35], our SportsHHI has more keyframes with fewer instances. That is because we focus on interaction classes of coordination or confrontation in sports. In long plain segments (e.g. segments of dribbling in basketball), few interactions of interest happen, and there are much more interaction instances in video segments with fierce confrontation. The videos are in crowd multi-person scenarios but the interaction instances are relatively sparse, which requires the model to distinguish two people without interaction from real interaction instances. 3) As shown in Figure 5 right, the proportion of instances of low GIoU between subject and object in SportsHHI is significantly higher than in VidVRD, which indicates that the subject and object of many instances are spatially far apart in SportsHHI. The proportion of extremely high GIoU is also higher, which indicates the occlusion is severe in some instances. VidVRD deals with simple relations in daily life videos, where the subject and object usually have a moderate distance.", + "bbox": [ + 75, + 242, + 472, + 604 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 617, + 169, + 633 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose a baseline method for the human-human interaction detection task. As illustrated in Fig. 6, our method adopts a two-stage pipeline. In the first stage, interaction proposals are generated. In the second stage, we construct a representation for each proposal and classify each proposal into an interaction class or background. The following part of this section explains our method in detail.", + "bbox": [ + 75, + 642, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Interaction proposal generation", + "text_level": 1, + "bbox": [ + 76, + 756, + 357, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We use an offline human detector for human detection on keyframes. We enumerate all human bounding box pairs as interaction proposals. Formally, for a keyframe at timestamp $t$ , let $N$ denote the number of human boxes in the frame and $B = \\{b_{1}, b_{2}, \\dots, b_{N}\\}$ denote the boxes. The interaction proposals can be denoted as $P = \\{p_{1}, p_{2}, \\dots, p_{K}\\}$ , where $p_{k} = (b_{s_{k}}, b_{o_{k}})$ and $K = N \\times (N - 1)$ .", + "bbox": [ + 76, + 780, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Positive proposals and negative proposals sampling. We label a proposal $p_k$ as a positive proposal when its subject and object bounding boxes both have an IoU overlap higher than 0.7 with their counterparts in a ground-truth interaction instance. For training, it is possible to input all the interaction proposals to the classification network for loss function calculation, but this will consume large GPU memory and the network optimization will bias towards negative samples as they are dominant. Instead, we use all positive proposals and sample negative proposals by a fixed positive-negative ratio. To increase the proportion of positive proposals and avoid the situation that a ground truth has no corresponding positive proposal, we add all ground-truth human box pairs as positive proposals for training.", + "bbox": [ + 496, + 90, + 893, + 303 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Interaction classification", + "text_level": 1, + "bbox": [ + 498, + 311, + 723, + 325 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The presentation of each interaction proposal comprises three parts: the motion features of the subject and object persons, the context features, and the relative position of the subject and object encoding.", + "bbox": [ + 496, + 334, + 893, + 393 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Motion features and context features. We sample a video clip centered at the keyframe and employ a 3D video backbone on it for feature map extraction. For an interaction proposal $p_k$ , we apply RoIAlign operation [16] on the feature maps with the bounding boxes $b_{s_k}$ and $b_{o_k}$ and then transform the RoIAligned feature to dimension $d_v$ with a linear layer. The motion features are denoted as $f_k^{ms} \\in \\mathbb{R}^{d_v}$ and $f_k^{mo} \\in \\mathbb{R}^{d_v}$ . We apply the RoIAlign operation on the features map using the union box of the subject and object for context information. The context feature is also transformed to dimension $d_v$ , denoted as $f_k^c \\in \\mathbb{R}^{d_v}$", + "bbox": [ + 496, + 395, + 890, + 561 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relative position information encoding. Following [7, 57], given an interaction proposal $p_k$ , we generate a spatial mask for the subject and object person respectively. We resize the union box of $b_{s_k}$ and $b_{o_k}$ to a fixed size of $M \\times M$ . We then generate the spatial mask of the subject bounding box $m_k^s \\in \\mathbb{R}^{M \\times M}$ . For each pixel in $m_k^s$ , if it is inside the subject bounding box $b_{s_k}$ , its value is set to 1, else 0. The spatial mask of the object bounding box $m_k^o \\in \\mathbb{R}^{M \\times M}$ is generated in the same way. The two spatial masks are flattened, concatenated, and transformed to dimension $d_p$ . We use the final vector $f_k^p \\in \\mathbb{R}^{d_p}$ as relative position encoding.", + "bbox": [ + 496, + 561, + 893, + 728 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposal representation. We use the concatenation of motions features $f_{k}^{ms}$ and $f_{k}^{mo}$ , context features $f_{k}^{c}$ , and relative position encoding $f_{k}^{p}$ as the representation $x_{k}$ of interaction proposal $p_{k}$ . Formally,", + "bbox": [ + 496, + 728, + 890, + 787 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {k} = \\left\\langle f _ {k} ^ {m s}, f _ {k} ^ {m o}, f _ {k} ^ {c}, f _ {k} ^ {p} \\right\\rangle , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 606, + 797, + 890, + 815 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\langle ,\\rangle$ is the concatenation operation.", + "bbox": [ + 498, + 824, + 772, + 839 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Information exchange among proposals. We denote the representation of the $K$ interaction proposals as $X = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_K\\}$ . Sometimes, recognizing an interaction requires information from other interaction instances. For", + "bbox": [ + 498, + 840, + 893, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18541", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/89a5967740a170852da57efba261395e31967eeca43e038ac8072334adf3ec8e.jpg", + "image_caption": [ + "Figure 6. An overview of our baseline method. Given a video clip centered at a keyframe, we first use an offline human detector to detect human bounding boxes on the keyframe. All the human bounding box pairs are enumerated as interaction proposals. Then, we construct representations for the proposals. We perform the RoIAlign operation on the video feature maps extracted by a video backbone for motion features and context features. We generate spatial masks for each proposal, which are flattened and transformed into a vector. The vector is used as relative position encoding. The motion features, context features, and relative position encoding are concatenated as proposal representations. Multi-head self-attention is applied to the representations for information exchange. Finally, an FCN classification head is used to predict the classification scores." + ], + "image_footnote": [], + "bbox": [ + 78, + 88, + 890, + 234 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "example, to recognize an interaction of co-defend in volleyball, we need to know there exists an interaction of attack-defend. To capture the information from other interaction proposals, we apply a standard multi-head self-attention (MHSA) [48] operation on $X$ . Formally,", + "bbox": [ + 75, + 349, + 470, + 425 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nX ^ {\\prime} = \\operatorname {M H S A} (X). \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 210, + 436, + 468, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Classification head. Finally, $X'$ is input to a fully connected network (FCN) for classification score prediction. Let $S$ denote the predicted scores. Formally,", + "bbox": [ + 76, + 465, + 468, + 512 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nS = \\operatorname {F C N} \\left(X ^ {\\prime}\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 218, + 522, + 468, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $S\\in \\mathbb{R}^{K\\times (C + 1)}$ $C$ denotes the number of interaction classes.", + "bbox": [ + 75, + 549, + 468, + 582 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 595, + 209, + 613 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 619, + 267, + 637 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset. We train and validate our model on the SportsHHI Dataset. The dataset is split into the training and validation set by video. Evaluation on a very small number of examples could be unreliable, so we evaluate the 28 classes that have at least 10 instances in both the training and validation set. Instances with an invisible subject or object are excluded from evaluation. In total, the current version contains 38,527 instances from 8,719 keyframes for training and 12,122 instances from 2,679 keyframes for validation. We report results on the validation set.", + "bbox": [ + 75, + 643, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. A prediction is considered as a true positive if and only if its subject and object bounding boxes both have an IoU overlap higher than a preset threshold with their counterparts in a ground-truth interaction instance and the predicted interaction class matches the ground truth. Following VidVRD [35], we set the IoU threshold to 0.5. Following the video scene graph generation task, we use Recall@K", + "bbox": [ + 75, + 795, + 470, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "(K is the number of predictions) as the evaluation metric. Mean average precision is adopted as an evaluation metric for many detection tasks [27]. However, this metric is discarded by many former visual relation detection benchmarks [19, 30] because of their incomplete annotation. This issue does not exist in SportsHHI. In our experiments, mAP is also reported for the interaction detection task. We argue that mAP is a more difficult and informative metric. Two different modes for model training and evaluation are used: 1) human-human interaction detection (HHIDet) which expects input video frames and predicts human boxes and interaction labels; 2) human-human interaction classification (HHICls) which directly uses ground-truth human bounding boxes and predicts human-human interaction classes.", + "bbox": [ + 496, + 349, + 890, + 560 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. The human detector we use is a Faster-RCNN [33] detector with a ResNeXt-101-FPN backbone, which is pre-trained on ImageNet [9] and COCO [27] and finetuned on keyframes of SportsHHI. The ratio of positive and negative proposals is set to 1:10. The SlowFast-R50 backbone [11] pre-trained on Kinetics-400 [22] is adopted for video feature extraction. The dimension of features $d_v$ and the dimension of relative position encoding $d_p$ are set to 512 and 256 respectively. We scale the short side of the video frames to 256. We use SGD optimizer with momentum 0.9 and weight decay $1 \\times 10^{-5}$ . The batch size is set to 8. The learning rate is 0.002 for HHICls and 0.004 for HHIDet. The models are trained for 20 epochs.", + "bbox": [ + 496, + 561, + 892, + 758 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 770, + 653, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We conduct ablation experiments on SportsHHI to investigate the influence of each design and component of our baseline method. Unless otherwise stated, all ablation experiments are conducted in the HHICls mode, that is, the ground-truth human bounding boxes are used. HHICls mode allows us to study the key factors to predict interactions without the limitations of human detection.", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18542", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Positive and negative proposal ratio. We investigate the influence of the ratio of positive and negative proposals in Table 3. A moderate proportion of negative samples help the model to distinguish interactions from backgrounds. However, when the positive-negative ratio gets too low, the model optimization will be overwhelmed by negative samples, and thus the performance drops.", + "bbox": [ + 75, + 90, + 470, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spatial mask generation. We generate two separate spatial masks for the subject and object person. Therefore, the positions of the subject and object can be distinguished. For comparison, we generate a single mask for the two people by setting the values in any box to 1. As shown in Table 4, model performance degrades when using a single mask. As the triplet $\\langle S, I, O \\rangle$ is ordered in SportsHHI, it is important to distinguish the position of the subject and object.", + "bbox": [ + 75, + 198, + 468, + 318 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Interaction proposal representation. We show the importance of motion features $f^{mo}$ and $f^{ms}$ , context feature $f^c$ and relative position encoding $f^p$ in interaction representation in Table 2. We first show the results of using each feature in lines 1-3 and 8-10. Using only motions features $f^{mo}$ and $f^{ms}$ can achieve acceptable results, which indicates the modeling of the actions of the subject and object person is very important for the recognition of the interaction between them. The performance is much worse when using context feature $f^c$ or relative position encoding $f^p$ only. Using only the context feature cannot provide specific information of the subject and object and as the subject and object person are often far apart in spatial, the context feature may include much noise. Without visual information, pure prior information of the relative position of the subject and object person is not discriminative enough for interaction recognition. As shown in lines 5-7 and 12-14, when coupling position encoding with motion and context features, the performance improves a lot, which indicates that position information is complementary to visual information. As shown in lines 7 and 14, using all three types of features achieves the best results.", + "bbox": [ + 75, + 319, + 470, + 651 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Information exchange among proposals. We ablate the multi-head self-attention module to show the importance of information exchange among proposals. As shown in Table 2, regardless of the representation of the proposal, exchanging information among proposals always brings performance improvement.", + "bbox": [ + 75, + 652, + 468, + 743 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3.Quantitative Results", + "text_level": 1, + "bbox": [ + 76, + 755, + 271, + 771 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Human box detection and interaction proposals generation results. We first show the human detection and interaction results in Table 5. Under IoU threshold of 0.5, both human boxes and interactions have a high recall rate of 98.6 and 98.4. When the threshold improves to 0.7, recall of human boxes drops by 2.6 points and recall of interactions drops by 5.3 points. When improving the IoU threshold to 0.9, both recall rates drop significantly. The results indi", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f16a0c282145c4c60c7025b9ba78be983eba88575d4692cbb72104db092d1b44.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
fmo&fmsfcfpInfo. Ex.mAPR@150R@100R@50R@20
✓---5.0081.6674.0052.7326.82
-✓--2.0771.7561.4338.9719.12
--✓-1.1350.7145.2439.7230.83
✓✓--5.1981.9874.8154.8928.51
✓-✓-5.5483.0575.4557.7131.92
-✓✓-3.8576.7668.5749.6527.68
✓✓✓-5.4381.7174.8458.1634.20
✓--✓6.1584.0976.5955.5528.10
-✓-✓3.5173.4163.1141.4720.91
--✓✓2.0158.7651.6038.8826.35
✓✓-✓6.8284.0177.1158.1431.86
✓-✓✓6.9484.4176.7257.4431.05
-✓✓✓5.9780.7571.8251.7831.04
✓✓✓✓7.5285.7878.5259.5332.76
", + "bbox": [ + 514, + 89, + 883, + 258 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9edf6abee964abb54975a28c12c28abde18299eadf0c42130cdb66f853187c2b.jpg", + "table_caption": [ + "Table 2. Ablation study on the interaction representation and information exchanging. “√” indicates the corresponding element is enabled while - indicates disabled. “fmo & fms” denotes motion features of the subject and object person. “fc” stands for context features of the union area. “fp” stands for the relative position information encoding. “Info. Ex.” stands for the multi-head self-attention operation to exchange information among proposals." + ], + "table_footnote": [], + "table_body": "
Pos:NegmAPR@150R@100R@50R@20
1:16.9785.9279.6460.9632.59
1:57.3986.2577.8759.8632.82
1:107.5285.7878.5259.5332.76
1:157.0285.3977.8758.5631.16
1:207.0885.3578.4360.5132.77
1:256.8985.4478.3158.8531.61
", + "bbox": [ + 560, + 364, + 834, + 452 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/6c5f77727def65e47c0d368b595ea6f1cfe3b473217fc7cea316c606144489be.jpg", + "table_caption": [ + "Table 3. Ablation on the positive and negative proposals ratio. The best results are obtained at 1:10." + ], + "table_footnote": [], + "table_body": "
mAPR@150R@100R@50R@20
Single Mask6.7784.5777.4158.2731.63
Separate Mask7.5285.7878.5259.5332.76
", + "bbox": [ + 550, + 489, + 844, + 531 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/964b64fcba2341da081cc9c9f837b70887312121865cea1e986ba4241d3c01b2.jpg", + "table_caption": [ + "Table 4. Ablation on spatial mask generation. \"Separate Masks\" means generating a spatial mask for the subject and object person respectively while \"Single Mask\" means using only one spatial mask to represent the pair." + ], + "table_footnote": [], + "table_body": "
mAPAP@0.5R@0.5R@0.7R@0.9
Human Boxes73.592.698.696.058.2
Interactions--98.493.237.7
", + "bbox": [ + 540, + 595, + 851, + 640 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 5. Human detection and interaction proposal generation results. For human box detection, we report mAP, AP, and Recall. For interaction proposal generation, Recall is reported. We calculate recall under IoU thresholds of 0.5, 0.7, and 0.9.", + "bbox": [ + 496, + 642, + 890, + 696 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "cate that, despite high recall under a relatively lower IoU threshold, there is still a lot of room for improvement in the quality of human boxes and interaction proposals.", + "bbox": [ + 496, + 718, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "HHICls and HHIDet results. We provide HHICls and HHIDet results of some existing methods and our baseline in Table 6. STTran [7] and HORT [20] are two well-established video scene graph generation methods. They share two common properties: 1) Using appearance features extracted by image backbone. This is because the semantic level of relation classes defined by previous datasets is relatively low and the appearance feature is often sufficient for recognition, such as $\\langle \\text{dog}, \\text{larger}, \\text{frisbee} \\rangle$ . However,", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18543", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/68a55402684c7d70e4f1d9714aef986fc1d90f3ed3cfb96293ed7af852701931.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneHHICIsHHIDet
mAPR@150R@100R@50R@20mAPR@150R@100R@50R@20
STTran [7]ResNet-101 [15]3.3171.2962.9142.6722.141.4351.6546.5437.6220.81
HORT [20]ResNet-101 [15]3.7578.5767.7850.3326.961.5452.4746.7336.8920/93
SlowFast [11]SlowFast-R50 [11]5.0081.6674.0052.7326.822.4462.1752.7737.8322.45
ACARN [31]SlowFast-R50 [11]5.4482.8575.2256.5331.772.5362.2552.8437.5021.85
Our baselineSlowFast-R50 [11]7.5285.7878.5259.5332.763.3664.8254.6237.7221.26
SlowFast-R101 [11]8.6787.3580.3560.1829.703.5265.2454.7637.0320.21
ViT-B [44]10.6989.2582.9368.1343.724.9372.2261.9242.9923.89
", + "bbox": [ + 161, + 88, + 807, + 198 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. HHICs and HHIDet results. We test existing video scene graph generation methods (STTran [7] and HORT [20]) and action detection methods (SlowFast [11] and ACARN [31]) on SportsHHI. Our baseline method achieves the best performance.", + "bbox": [ + 75, + 202, + 892, + 232 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/47085546cca7a24eaa6893515bd2b11e72b666f25e9c6d61aeed08df406a0a90.jpg", + "image_caption": [ + "Figure 7. Error analysis in HHIDet mode. We show the proportion of each error type among false positives." + ], + "image_footnote": [], + "bbox": [ + 83, + 239, + 459, + 344 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "action modeling is very important for interaction recognition on SportsHHI. 2) Dependent on the object detection results. They add the category encoding of the objects to the relation representation, which provides strong prior information. For example, knowing that the subject and object are human and horse respectively, the relation category is very likely to be ride. However, SportsHHI does not have such prior as all subjects and objects are humans. Since video backbones are used to extract the motion features of each person, the performance of the action detection methods like SlowFast [11] and ACARN [31] is relatively better. Our baseline follows these action detectors to adopt a video backbone for motion features and introduce extra relative position and spatio-temporal context modeling between the subject and object person. Our simple baseline achieves leading performance with the same SlowFast-R50 backbone. When using the stronger VideoMAE [44] pretrained ViT-B backbone, the performance is significantly improved, which shows the importance of spatio-temporal representation.", + "bbox": [ + 73, + 391, + 468, + 694 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Error Analysis", + "text_level": 1, + "bbox": [ + 76, + 709, + 227, + 724 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Following ACT [21] and MultiSports [26], we analyze error types of the false positives in the predictions to better understand the challenges of human-human interaction detection in SportsHHI. We analyze the predictions of the baseline model with a SlowFast-R50 backbone. We classify false positives in the predictions into 9 mutually exclusive error types. $E_{R}$ : a prediction targets a ground-truth instance that has already been matched. $E_{C}$ : a prediction that has an accurate subject and object localization, but wrong interaction class. $E_{O}$ : a prediction that has accurate subject localization and correct interaction class, but inaccurate object lo", + "bbox": [ + 75, + 734, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "calization. $E_S$ : a prediction that has accurate object localization and correct interaction class, but inaccurate subject localization. $E_{S\\& O}$ , $E_{O\\& C}$ , $E_{S\\& C}$ , $E_{S\\& O\\& C}$ : a prediction that is inaccurate in corresponding aspects while acceptable in other aspects (if any). $E_N$ : a prediction that both the subject and object of it have no overlap with any ground truth.", + "bbox": [ + 496, + 242, + 890, + 333 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As shown in Figure 7, $E_N$ is one of the most common error types. This is because SportsHHI is annotated in crowd multi-person scenarios but the interaction instances are relatively sparse due to the characteristic of sports videos and our high-level interaction definition. It is important but difficult to distinguish two people without interaction from real interaction instances. In video action detection [26], localization is relatively accurate and most errors are about classification. However, in interaction detection, the localization of people involved in interaction and the classification of interaction are inseparable. Pure localization errors $(E_S$ and $E_O$ ) or pure classification errors $(E_C)$ are relatively rare. The error types that coexisted with localization error and classification error $(E_{O\\& C}, E_{S\\& C}, E_{S\\& O\\& C})$ account for a relatively large proportion.", + "bbox": [ + 496, + 334, + 892, + 561 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 573, + 617, + 589 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we proposed a new video visual relation detection task with a focus on sports human-human interaction understanding. This task deals with the complex interactions between humans in multi-person scenarios. We build a dataset named SportsHHI based on sports videos for this task. Human boxes and interaction instances are exhaustively annotated on keyframes at 5FPS. To benchmark this, we test several existing methods on SportsHHI and propose a baseline method. We conduct extensive experiments on SportsHHI and reveal the importance of motion information, context information, and position information for interaction recognition. We hope our SportHHI dataset and baseline method can inspire future research on human-human interaction understanding in videos.", + "bbox": [ + 496, + 599, + 890, + 811 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006), and Collaborative Innovation Center of Novel Software Technology and Industrialization.", + "bbox": [ + 496, + 821, + 890, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18544", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. 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In ICCV, pages 13577-13587, 2021. 1" + ], + "bbox": [ + 501, + 92, + 890, + 616 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18546", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_model.json b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9ce824fa99d412f36eab898292ddca734b4f379a --- /dev/null +++ b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_model.json @@ -0,0 +1,2189 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.131, + 0.892, + 0.153 + ], + "angle": 0, + "content": "SportsHHI: A Dataset for Human-Human Interaction Detection in Sports Videos" + }, + { + "type": "text", + "bbox": [ + 0.201, + 0.179, + 0.768, + 0.199 + ], + "angle": 0, + "content": "Tao \\(\\mathbf{W}\\mathbf{u}^{1,*}\\) Runyu He\\(^{1,*}\\) Gangshan \\(\\mathbf{W}\\mathbf{u}^{1}\\) Limin Wang\\(^{1,2,\\boxtimes}\\)" + }, + { + "type": "text", + "bbox": [ + 0.108, + 0.199, + 0.862, + 0.217 + ], + "angle": 0, + "content": "\\(^{1}\\)State Key Laboratory for Novel Software Technology, Nanjing University \\(^{2}\\)Shanghai AI Lab" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.219, + 0.733, + 0.234 + ], + "angle": 0, + "content": "wt, runyu.he}@smail.nju.edu.cn, {gswu, lmwang}@nju.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.304, + 0.236, + 0.66, + 0.251 + ], + "angle": 0, + "content": "https://github.com/MCG-NJU/SportsHHI" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.312, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.32, + 0.474, + 0.712 + ], + "angle": 0, + "content": "Video-based visual relation detection tasks, such as video scene graph generation, play important roles in fine-grained video understanding. However, current video visual relation detection datasets have two main limitations that hinder the progress of research in this area. First, they do not explore complex human-human interactions in multi-person scenarios. Second, the relation types of existing datasets have relatively low-level semantics and can be often recognized by appearance or simple prior information, without the need for detailed spatio-temporal context reasoning. Nevertheless, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. To address this issue, we propose a new video visual relation detection task: video human-human interaction detection, and build a dataset named SportsHHI for it. SportsHHI contains 34 high-level interaction classes from basketball and volleyball sports. 118,075 human bounding boxes and 50,649 interaction instances are annotated on 11,398 keyframes. To benchmark this, we propose a two-stage baseline method and conduct extensive experiments to reveal the key factors for a successful human-human interaction detector. We hope that SportsHHI can stimulate research on human interaction understanding in videos and promote the development of spatio-temporal context modeling techniques in video visual relation detection." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.208, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.47, + 0.876 + ], + "angle": 0, + "content": "Video understanding is a fundamental research field in computer vision, which has wide applications in security monitoring, internet video recommendation, and sports video analysis. Remarkable progress has been made in the action recognition task [3, 4, 13, 22, 23, 39, 40] with the advances of video convolution neural networks [3, 11, 45, 46, 49, 50, 52, 55] and video transformers [1, 2, 10, 29, 44, 51, 58]." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.285, + 0.697, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.571, + 0.366, + 0.624, + 0.372 + ], + "angle": 0, + "content": "" + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.285, + 0.798, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.721, + 0.366, + 0.769, + 0.372 + ], + "angle": 0, + "content": "" + }, + { + "type": "image", + "bbox": [ + 0.803, + 0.286, + 0.891, + 0.367 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.819, + 0.366, + 0.882, + 0.372 + ], + "angle": 0, + "content": "" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.372, + 0.697, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.507, + 0.457, + 0.696, + 0.463 + ], + "angle": 0, + "content": "<#5,attack-defend,#11><#5,attack-protect,#2><#5,attack-block,#9>" + }, + { + "type": "image", + "bbox": [ + 0.698, + 0.372, + 0.892, + 0.457 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.7, + 0.457, + 0.889, + 0.463 + ], + "angle": 0, + "content": "<#2, close defense, #8> <#1, close defense, #9> <#3, close defense, #6>" + }, + { + "type": "image_caption", + "bbox": [ + 0.701, + 0.463, + 0.825, + 0.468 + ], + "angle": 0, + "content": "<#4, close defense, #7> <#0, interfere-shot, #5>" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.473, + 0.892, + 0.639 + ], + "angle": 0, + "content": "Figure 1. Comparison between previous video visual relation detection datasets and our SportsHHI. In the upper row, we show three relation instances from VidVRD and AG datasets. These datasets rarely involve human-human interaction and define semantically simple relations that can be recognized by appearance or prior information. In contrast, the bottom row shows interaction annotations in two sample keyframes of SportsHHI. The bounding boxes and interaction annotation of the same instance are displayed in the same color. SportsHHI provides complex multi-person scenes where various interactions between human pairs occur concurrently. It focuses on high-level interactions that require detailed spatio-temporal context reasoning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.655, + 0.892, + 0.761 + ], + "angle": 0, + "content": "The action recognition task requires tagging each video clip with a single action label. However, real-world applications usually require a more detailed and in-depth understanding of videos, thus more attention has been attracted to fine-grained video understanding tasks such as video action detection [14, 18, 24, 26, 31, 42, 54] and video visual relation detection tasks [7, 19, 20, 35, 36]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Video action detection involves localizing action performers in both space and time, as well as recognizing their action class. While earlier datasets like UCF101-24 [40] and JHMDB [18] primarily focuses on action detection in single-person scenarios, recent large-scale datasets such as AVA [14] and MultiSports [26] have emphasized the importance of modeling human-human interactions for a better recognition of individual actions in multi-person scenes. However, while AVA and MultiSports provide ample multi" + }, + { + "type": "page_footnote", + "bbox": [ + 0.101, + 0.887, + 0.371, + 0.901 + ], + "angle": 0, + "content": "*: Equal contribution. \\(\\boxtimes\\) Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18537" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "person scenes, neither of them offers explicit human-human interaction definitions and annotations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.126, + 0.473, + 0.504 + ], + "angle": 0, + "content": "Video scene graph generation is a popular video visual relation detection task, which requires the model to localize objects of interest in the video and recognize the relation of each pair of objects. While current datasets like AG [19], VidVRD [35], and VidOR [36] provide explicit relation instance annotations, human-human interactions are barely involved. Moreover, the relation categories defined in these benchmarks primarily include spatial relations, atomic actions, and simple visual comparisons, which are semantically straightforward and often recognizable by appearance information or simple prior knowledge, such as \\(\\langle \\text{dog}, \\text{larger}, \\text{frisbee} \\rangle\\) and \\(\\langle \\text{person}, \\text{stand on}, \\text{floor} \\rangle\\) in the upper row of Figure 1. This makes current research pay more attention to the recognition of object categories and the utilization of category priors while ignoring reasoning based on spatio-temporal context. However, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. Spatio-temporal context modeling is an important technology that makes video relation detection different from image relation detection. We argue that there is a need for new datasets that comprehensively explore human-human interactions in complex multiperson scenarios, with high-level relation categories that require detailed spatio-temporal context reasoning." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.903 + ], + "angle": 0, + "content": "In this paper, we propose a new video visual relation detection task: video human-human interaction detection. This task requires detecting human-human interaction instances in video frames. Each human-human interaction instance is formulated as a triplet \\(\\langle S, I, O \\rangle\\), where \\(S\\) and \\(O\\) denote the bounding boxes of two different people and \\(I\\) denotes the interaction category. For this task, we develop a dataset named SportsHHI, short for Sports Human-Human Interaction. We label interaction instances on the keyframes of basketball and volleyball videos at 5FPS. Two samples of keyframes are shown in the bottom row of Figure 1. SportsHHI has several unique characteristics that distinguish it from other visual relation detection datasets: 1) It is built on basketball and volleyball sports videos, thus containing a large number of complex multiplayer scenes with various interactions between athlete pairs occurring concurrently. 2) The interactions between each pair of humans are transient and change rapidly due to the fast movements of the players. 3) The defined interactions are of high-level semantic, including technical actions, tactical cooperation, and confrontation in sports. Recognizing an interaction instance in SportsHHI usually requires detailed spatiotemporal context reasoning. We hope that SportsHHI can attract more research attention to human-human interaction understanding in complex multi-person videos and promote the development of spatio-temporal context modeling tech" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.77, + 0.106 + ], + "angle": 0, + "content": "niques in video visual relation detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.892, + 0.302 + ], + "angle": 0, + "content": "We test existing action detection and video scene graph generation methods on the SportsHHI dataset and propose a simple and neat baseline method based on these methods. Our baseline method adopts a Faster-RCNN-alike two-stage pipeline [33]: In the first stage, we use an offline human detector to detect person bounding boxes on the keyframe. We exhaust bounding box pairs to generate interaction proposals. In the second stage, we extract features for each proposal and categorize each proposal into an interaction class or background. Our experiments demonstrate that motion features, context information, relative position encoding, and information exchange among proposals are important for human-human interaction detection." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.303, + 0.892, + 0.453 + ], + "angle": 0, + "content": "In summary, our contribution is three-fold: 1) We propose a new video relation detection task of human-human interaction detection which aims at exploring the complex interaction between people in multi-person scenarios; 2) We develop the SportsHHI dataset of multi-person sports videos on which high-level human-human interaction is well-defined and finely-labeled; 3) We design a two-stage baseline model and conduct extensive experiments on the SportsHHI dataset to discover the key factors for a successful interaction detector." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.642, + 0.484 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.78 + ], + "angle": 0, + "content": "Video action detection. Video action detection aims to locate and recognize action instances on video frames. Earlier datasets like UCF Sports [34], UCF101-24 [40], and J-HMDB [18] typically only include single-person videos. Datasets like DALY [53], AVA [14], AVA-Kinetics [24], and MultiSports [26] contain scenes where multiple people are performing various actions concurrently. AVA sparsely annotates keyframes of movie videos at 1FPS. MultiSports collects videos from sports competitions. Many interaction-related action classes are defined, such as listen to in AVA and second pass in MultiSports. As they claim, it is important to model the interaction between people to recognize the action category of each person. However, as no interaction annotation is provided, interaction modeling can only be performed implicitly. SportsHHI annotates interactions on keyframes of basketball and volleyball videos from MultiSports at 5FPS. With interaction definitions and annotations provided in SportHHI, human-human interaction detection can be explicitly performed and evaluated." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Video visual relation detection. Video scene graph generation requires localizing object pairs in the video and recognizing the relation of each pair of objects. AG [19] is a large-scale dataset built on Charades [38]. All videos in AG contain only one person, thus no human-human interaction is involved. In VidVRD [35] and VidOR [36], most of the videos contain only one person. Though human-human interaction is involved, the exploration of it is very" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18538" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.348 + ], + "angle": 0, + "content": "limited. Similar to AG, video human-object interaction detection [5, 41] datasets only focus on relations between humans and objects. Besides, the relation categories defined in these datasets only include spatial relations (e.g. above), atomic actions (e.g. lean on), and simple visual comparisons (e.g. larger). The relations are usually semantically simple and can be easily recognized by appearance information. Some trivial relations are also defined like \\(\\langle dog, larger, frisbee \\rangle\\) in VidVRD. The category of the subject and object can often provide enough cues for relation recognition [7, 20, 28, 32, 43, 47], such as \\(\\langle person, ride, horse \\rangle\\). Moreover, the relation between two objects changes very slowly in a video. Our SportHHI annotates human-human interaction instances in complex multi-person sports videos. The defined interactions are of high-level semantics and the interaction between two people changes rapidly." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Sports video understanding. Researchers have built many different benchmarks in the sports domain for its challenges in spatio-temporal reasoning and promising application prospects, such as UCF101-24 [40] and MultiSports [26] for video action detection, FineGym [37] and Diving48 [25] for action recognition and temporal action detection, SoccerNet [12] for action spotting, SportsMOT [8] for multiobject tracking, and NBA [56], CAD [6] and Volleyball [17] for group action recognition, etc. Group action recognition (GAR) requires tagging each video clip with a group action label. Implicit modeling of interactions among the players is often performed to improve the accuracy of label predictions. The proposed SportsHHI dataset provides interaction definitions and annotations for explicit human-human interaction exploration." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.303, + 0.604 + ], + "angle": 0, + "content": "3. The SportsHHI Dataset" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.613, + 0.47, + 0.675 + ], + "angle": 0, + "content": "In Sec. 3.1, we will explain several key choices we made while creating the SportsHHI dataset and outline the annotation process. Then in Sec. 3.2, we will present a detailed analysis of the statistics and characteristics of SportsHHI." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.682, + 0.279, + 0.697 + ], + "angle": 0, + "content": "3.1. Dataset Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Selection of the data domain. First, we select to annotate human-human interaction in team sports videos for the following reasons: 1) The field of sports is itself a very promising application area for interaction detection. 2) Team sports videos provide ample multi-person scenes where various interactions between athlete pairs occur concurrently, which are rarely seen in daily-life videos. 3) Team sports videos involve many interactions with high-level semantics, such as tactics coordination or confrontation. 4) Interactions between people in sports game videos can be clearly and comprehensively defined according to game rules and professional athletes' advice. 5) High-quality, diverse sports game videos are easily accessible," + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.089, + 0.888, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.295, + 0.895, + 0.365 + ], + "angle": 0, + "content": "Figure 2. User interface for interaction annotation. The person bounding boxes and ids in the keyframe are shown in the left. We can play the video for context information. To add an interaction instance in the current keyframe, the subject person id, object person id, and interaction class should be specified." + }, + { + "type": "image", + "bbox": [ + 0.502, + 0.371, + 0.888, + 0.466 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.469, + 0.895, + 0.512 + ], + "angle": 0, + "content": "Figure 3. Interaction classes hierarchy. There are 34 interaction classes of high-level semantics in total in SportsHHI. 16 for basketball and 18 for volleyball." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.892, + 0.658 + ], + "angle": 0, + "content": "while surveillance videos are usually of lower quality and harder to obtain because of privacy. Furthermore, we decide to build the dataset on two popular team sports basketball and volleyball because: 1) The methods can be validated on two different subsets to evaluate their generalization performance on different sports. 2) Football is not included because the instance sparsity and class imbalance (which will be discussed in Sec. 3.2) would be more prominent in football videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Interaction classes definition. There are existing benchmarks focusing on atomic relations, which can be recognized by appearance information or prior knowledge. These interaction classes are out of our scope (it does not mean they are solved or not important). Instead, we focus on high-level interactions between athletes, which are semantically complex and require detailed spatio-temporal context reasoning to recognize. With the guidance of professional athletes, we generated the final interaction vocabulary through iterative trial labeling and modification, which is shown in Figure 3. Our defined interaction classes include technical action (e.g. pass-catch in basketball), tactical coordination (e.g. co-block in volleyball), or confrontation (e.g. attack-defend in volleyball)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Interaction instance formulation. Following common practice in AVA and AG datasets, we define interaction in" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "18539" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.089, + 0.862, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.225, + 0.256, + 0.744, + 0.271 + ], + "angle": 0, + "content": "Figure 4. The number of interaction instances of each class sorted by descending order." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.283, + 0.265, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.267, + 0.283, + 0.46, + 0.377 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.38, + 0.265, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.38, + 0.46, + 0.474 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.588 + ], + "angle": 0, + "content": "Figure 5. Statistics comparisons between SportsHHI and VidVRD. In the left, we compare the distribution of the number of instances in each keyframe. SportsHHI has more keyframes of fewer instances because of the high-level interaction class definition and the property of sports videos. In the right, we compare the distribution of GIoU between the subject and object. The proportion of instances of extremely high and extremely low GIoU between subject and object are both higher than VidVRD," + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.598, + 0.468, + 0.734 + ], + "angle": 0, + "content": "stances at the frame level, with reference to a long-term spatial-temporal context. Each interaction instance can be formulated as a triplet \\(\\langle S, I, O \\rangle\\) where \\(S\\) and \\(O\\) denote the bounding boxes of the subject and object person and \\(I\\) denotes the interaction category between them from the interaction vocabulary. When the subject person or the object person is out of view, we annotate \\(S\\) or \\(O\\) as \"invisible\". This happens infrequently and we will provide statistics about it in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Data preparation. We carefully selected 80 basketball and 80 volleyball videos from the MultiSports [26] dataset to cover various types of games including men's, women's, national team, and club games. The average length of the videos is 603 frames and the frame rate of the videos is 25FPS. All videos have a high resolution of 720P." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.468, + 0.9 + ], + "angle": 0, + "content": "Annotation. We follow the sparse annotation strategy of AVA [14] and AG [19] to reduce redundancy and save labor costs, but we annotate keyframes at a higher rate of 5FPS, because in sports videos, the change of interactions is very frequent and fast. In our practice, 5FPS can avoid lots of" + }, + { + "type": "table", + "bbox": [ + 0.503, + 0.283, + 0.89, + 0.336 + ], + "angle": 0, + "content": "
#keyframes#interact.#inst.#obj. bbox#hum. bboxavg. hum.
AG [19]234253251.7M4762292342531.00
VidVRD [35]5834134556311270522240.38
SportsHHI113983450649-11807510.36
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.342, + 0.892, + 0.397 + ], + "angle": 0, + "content": "Table 1. Comparison of statistics between video scene graph generation datasets and SportsHHI. SportsHHI has a comparable scale to VidVRD. The average number of human bounding boxes per frame of SportsHHI is much higher than AG or VidVRD." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.409, + 0.878, + 0.424 + ], + "angle": 0, + "content": "redundancy and keep up with the changes of interactions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.425, + 0.892, + 0.576 + ], + "angle": 0, + "content": "We take a two-stage annotation pipeline. The first stage is for person localization and tracking and the second stage is for interaction instance annotation. The user interface of the software for interaction instance annotation is shown in Figure 2. Though we annotate interaction instances at the frame level, as person id tracking is provided, we can easily generate interaction tubes by linking the same pair of persons with the same interaction class and provide temporal boundaries at a granularity of 5 frames. We will exemplify this in the appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.728 + ], + "angle": 0, + "content": "Quality control. For the first stage, all annotations are complemented manually without using detection or tracking models. We double-check each video and manually correct inaccurate bounding boxes and inconsistent person numbers. For the second stage, all the annotators are professional athletes or veteran amateurs. To improve annotation accuracy and completeness, we perform repeated annotation. Each video is distributed to two different annotators. If the two annotators disagree on an annotation record, this record will be checked and decided by the meta-annotator." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.741, + 0.822, + 0.755 + ], + "angle": 0, + "content": "3.2. Dataset Statistics and Characteristics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Our SportsHHI provides interaction instance annotations on keyframes of basketball and volleyball videos. As shown in Table 1, SportHHI contains 34 interaction classes, and 11398 keyframes in total are annotated with instances. Current video scene graph datasets deal with general relations between various kinds of objects while our SportsHHI focuses on high-level interaction between humans. It is reasonable that datasets for video scene graph generation have a larger scale than SportsHHI. However, our SportHHI still" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18540" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "has a comparable size to the popular VidVRD dataset for video scene graph generation. Our SportsHHI has more annotated keyframes (11398 versus 5834) and the number of interaction instances is close (55631 versus 50649). One important characteristic of our SportsHHI is the multiperson scenarios. The average number of people per frame in our SportsHHI is much higher than AG and VidVRD. AG only contains one person in each video and there is virtually no multi-person scenario in videos of VidVRD. Human-human interaction is barely involved in these datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.606 + ], + "angle": 0, + "content": "We further show some important characteristics of our SportsHHI: 1) As shown in Figure 4, the distribution of the number of interaction instances per class roughly follows Zipf's law. This long-tail distribution requires us to put more attention to classes with fewer instances. 2) As shown in Figure 5 left, compared with VidVRD [35], our SportsHHI has more keyframes with fewer instances. That is because we focus on interaction classes of coordination or confrontation in sports. In long plain segments (e.g. segments of dribbling in basketball), few interactions of interest happen, and there are much more interaction instances in video segments with fierce confrontation. The videos are in crowd multi-person scenarios but the interaction instances are relatively sparse, which requires the model to distinguish two people without interaction from real interaction instances. 3) As shown in Figure 5 right, the proportion of instances of low GIoU between subject and object in SportsHHI is significantly higher than in VidVRD, which indicates that the subject and object of many instances are spatially far apart in SportsHHI. The proportion of extremely high GIoU is also higher, which indicates the occlusion is severe in some instances. VidVRD deals with simple relations in daily life videos, where the subject and object usually have a moderate distance." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.618, + 0.17, + 0.634 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.643, + 0.47, + 0.749 + ], + "angle": 0, + "content": "We propose a baseline method for the human-human interaction detection task. As illustrated in Fig. 6, our method adopts a two-stage pipeline. In the first stage, interaction proposals are generated. In the second stage, we construct a representation for each proposal and classify each proposal into an interaction class or background. The following part of this section explains our method in detail." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.358, + 0.773 + ], + "angle": 0, + "content": "4.1. Interaction proposal generation" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.781, + 0.47, + 0.902 + ], + "angle": 0, + "content": "We use an offline human detector for human detection on keyframes. We enumerate all human bounding box pairs as interaction proposals. Formally, for a keyframe at timestamp \\( t \\), let \\( N \\) denote the number of human boxes in the frame and \\( B = \\{b_{1}, b_{2}, \\dots, b_{N}\\} \\) denote the boxes. The interaction proposals can be denoted as \\( P = \\{p_{1}, p_{2}, \\dots, p_{K}\\} \\), where \\( p_{k} = (b_{s_{k}}, b_{o_{k}}) \\) and \\( K = N \\times (N - 1) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.304 + ], + "angle": 0, + "content": "Positive proposals and negative proposals sampling. We label a proposal \\( p_k \\) as a positive proposal when its subject and object bounding boxes both have an IoU overlap higher than 0.7 with their counterparts in a ground-truth interaction instance. For training, it is possible to input all the interaction proposals to the classification network for loss function calculation, but this will consume large GPU memory and the network optimization will bias towards negative samples as they are dominant. Instead, we use all positive proposals and sample negative proposals by a fixed positive-negative ratio. To increase the proportion of positive proposals and avoid the situation that a ground truth has no corresponding positive proposal, we add all ground-truth human box pairs as positive proposals for training." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.312, + 0.725, + 0.327 + ], + "angle": 0, + "content": "4.2. Interaction classification" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.894, + 0.395 + ], + "angle": 0, + "content": "The presentation of each interaction proposal comprises three parts: the motion features of the subject and object persons, the context features, and the relative position of the subject and object encoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.396, + 0.892, + 0.562 + ], + "angle": 0, + "content": "Motion features and context features. We sample a video clip centered at the keyframe and employ a 3D video backbone on it for feature map extraction. For an interaction proposal \\( p_k \\), we apply RoIAlign operation [16] on the feature maps with the bounding boxes \\( b_{s_k} \\) and \\( b_{o_k} \\) and then transform the RoIAligned feature to dimension \\( d_v \\) with a linear layer. The motion features are denoted as \\( f_k^{ms} \\in \\mathbb{R}^{d_v} \\) and \\( f_k^{mo} \\in \\mathbb{R}^{d_v} \\). We apply the RoIAlign operation on the features map using the union box of the subject and object for context information. The context feature is also transformed to dimension \\( d_v \\), denoted as \\( f_k^c \\in \\mathbb{R}^{d_v} \\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.894, + 0.729 + ], + "angle": 0, + "content": "Relative position information encoding. Following [7, 57], given an interaction proposal \\( p_k \\), we generate a spatial mask for the subject and object person respectively. We resize the union box of \\( b_{s_k} \\) and \\( b_{o_k} \\) to a fixed size of \\( M \\times M \\). We then generate the spatial mask of the subject bounding box \\( m_k^s \\in \\mathbb{R}^{M \\times M} \\). For each pixel in \\( m_k^s \\), if it is inside the subject bounding box \\( b_{s_k} \\), its value is set to 1, else 0. The spatial mask of the object bounding box \\( m_k^o \\in \\mathbb{R}^{M \\times M} \\) is generated in the same way. The two spatial masks are flattened, concatenated, and transformed to dimension \\( d_p \\). We use the final vector \\( f_k^p \\in \\mathbb{R}^{d_p} \\) as relative position encoding." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.729, + 0.892, + 0.789 + ], + "angle": 0, + "content": "Proposal representation. We use the concatenation of motions features \\( f_{k}^{ms} \\) and \\( f_{k}^{mo} \\), context features \\( f_{k}^{c} \\), and relative position encoding \\( f_{k}^{p} \\) as the representation \\( x_{k} \\) of interaction proposal \\( p_{k} \\). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.607, + 0.798, + 0.892, + 0.816 + ], + "angle": 0, + "content": "\\[\nx _ {k} = \\left\\langle f _ {k} ^ {m s}, f _ {k} ^ {m o}, f _ {k} ^ {c}, f _ {k} ^ {p} \\right\\rangle , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.825, + 0.774, + 0.84 + ], + "angle": 0, + "content": "where \\(\\langle ,\\rangle\\) is the concatenation operation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.841, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Information exchange among proposals. We denote the representation of the \\(K\\) interaction proposals as \\(X = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_K\\}\\). Sometimes, recognizing an interaction requires information from other interaction instances. For" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18541" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.089, + 0.891, + 0.236 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.244, + 0.895, + 0.342 + ], + "angle": 0, + "content": "Figure 6. An overview of our baseline method. Given a video clip centered at a keyframe, we first use an offline human detector to detect human bounding boxes on the keyframe. All the human bounding box pairs are enumerated as interaction proposals. Then, we construct representations for the proposals. We perform the RoIAlign operation on the video feature maps extracted by a video backbone for motion features and context features. We generate spatial masks for each proposal, which are flattened and transformed into a vector. The vector is used as relative position encoding. The motion features, context features, and relative position encoding are concatenated as proposal representations. Multi-head self-attention is applied to the representations for information exchange. Finally, an FCN classification head is used to predict the classification scores." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.35, + 0.471, + 0.426 + ], + "angle": 0, + "content": "example, to recognize an interaction of co-defend in volleyball, we need to know there exists an interaction of attack-defend. To capture the information from other interaction proposals, we apply a standard multi-head self-attention (MHSA) [48] operation on \\( X \\). Formally," + }, + { + "type": "equation", + "bbox": [ + 0.211, + 0.438, + 0.47, + 0.457 + ], + "angle": 0, + "content": "\\[\nX ^ {\\prime} = \\operatorname {M H S A} (X). \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.466, + 0.47, + 0.513 + ], + "angle": 0, + "content": "Classification head. Finally, \\( X' \\) is input to a fully connected network (FCN) for classification score prediction. Let \\( S \\) denote the predicted scores. Formally," + }, + { + "type": "equation", + "bbox": [ + 0.22, + 0.523, + 0.47, + 0.541 + ], + "angle": 0, + "content": "\\[\nS = \\operatorname {F C N} \\left(X ^ {\\prime}\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.55, + 0.47, + 0.583 + ], + "angle": 0, + "content": "where \\(S\\in \\mathbb{R}^{K\\times (C + 1)}\\) \\(C\\) denotes the number of interaction classes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.596, + 0.21, + 0.614 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.268, + 0.638 + ], + "angle": 0, + "content": "5.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.47, + 0.794 + ], + "angle": 0, + "content": "Dataset. We train and validate our model on the SportsHHI Dataset. The dataset is split into the training and validation set by video. Evaluation on a very small number of examples could be unreliable, so we evaluate the 28 classes that have at least 10 instances in both the training and validation set. Instances with an invisible subject or object are excluded from evaluation. In total, the current version contains 38,527 instances from 8,719 keyframes for training and 12,122 instances from 2,679 keyframes for validation. We report results on the validation set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Metrics. A prediction is considered as a true positive if and only if its subject and object bounding boxes both have an IoU overlap higher than a preset threshold with their counterparts in a ground-truth interaction instance and the predicted interaction class matches the ground truth. Following VidVRD [35], we set the IoU threshold to 0.5. Following the video scene graph generation task, we use Recall@K" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.35, + 0.892, + 0.561 + ], + "angle": 0, + "content": "(K is the number of predictions) as the evaluation metric. Mean average precision is adopted as an evaluation metric for many detection tasks [27]. However, this metric is discarded by many former visual relation detection benchmarks [19, 30] because of their incomplete annotation. This issue does not exist in SportsHHI. In our experiments, mAP is also reported for the interaction detection task. We argue that mAP is a more difficult and informative metric. Two different modes for model training and evaluation are used: 1) human-human interaction detection (HHIDet) which expects input video frames and predicts human boxes and interaction labels; 2) human-human interaction classification (HHICls) which directly uses ground-truth human bounding boxes and predicts human-human interaction classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.893, + 0.76 + ], + "angle": 0, + "content": "Implementation details. The human detector we use is a Faster-RCNN [33] detector with a ResNeXt-101-FPN backbone, which is pre-trained on ImageNet [9] and COCO [27] and finetuned on keyframes of SportsHHI. The ratio of positive and negative proposals is set to 1:10. The SlowFast-R50 backbone [11] pre-trained on Kinetics-400 [22] is adopted for video feature extraction. The dimension of features \\( d_v \\) and the dimension of relative position encoding \\( d_p \\) are set to 512 and 256 respectively. We scale the short side of the video frames to 256. We use SGD optimizer with momentum 0.9 and weight decay \\( 1 \\times 10^{-5} \\). The batch size is set to 8. The learning rate is 0.002 for HHICls and 0.004 for HHIDet. The models are trained for 20 epochs." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.771, + 0.655, + 0.789 + ], + "angle": 0, + "content": "5.2. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We conduct ablation experiments on SportsHHI to investigate the influence of each design and component of our baseline method. Unless otherwise stated, all ablation experiments are conducted in the HHICls mode, that is, the ground-truth human bounding boxes are used. HHICls mode allows us to study the key factors to predict interactions without the limitations of human detection." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18542" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.471, + 0.198 + ], + "angle": 0, + "content": "Positive and negative proposal ratio. We investigate the influence of the ratio of positive and negative proposals in Table 3. A moderate proportion of negative samples help the model to distinguish interactions from backgrounds. However, when the positive-negative ratio gets too low, the model optimization will be overwhelmed by negative samples, and thus the performance drops." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.199, + 0.47, + 0.319 + ], + "angle": 0, + "content": "Spatial mask generation. We generate two separate spatial masks for the subject and object person. Therefore, the positions of the subject and object can be distinguished. For comparison, we generate a single mask for the two people by setting the values in any box to 1. As shown in Table 4, model performance degrades when using a single mask. As the triplet \\(\\langle S, I, O \\rangle\\) is ordered in SportsHHI, it is important to distinguish the position of the subject and object." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.471, + 0.652 + ], + "angle": 0, + "content": "Interaction proposal representation. We show the importance of motion features \\( f^{mo} \\) and \\( f^{ms} \\), context feature \\( f^c \\) and relative position encoding \\( f^p \\) in interaction representation in Table 2. We first show the results of using each feature in lines 1-3 and 8-10. Using only motions features \\( f^{mo} \\) and \\( f^{ms} \\) can achieve acceptable results, which indicates the modeling of the actions of the subject and object person is very important for the recognition of the interaction between them. The performance is much worse when using context feature \\( f^c \\) or relative position encoding \\( f^p \\) only. Using only the context feature cannot provide specific information of the subject and object and as the subject and object person are often far apart in spatial, the context feature may include much noise. Without visual information, pure prior information of the relative position of the subject and object person is not discriminative enough for interaction recognition. As shown in lines 5-7 and 12-14, when coupling position encoding with motion and context features, the performance improves a lot, which indicates that position information is complementary to visual information. As shown in lines 7 and 14, using all three types of features achieves the best results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.653, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Information exchange among proposals. We ablate the multi-head self-attention module to show the importance of information exchange among proposals. As shown in Table 2, regardless of the representation of the proposal, exchanging information among proposals always brings performance improvement." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.756, + 0.272, + 0.772 + ], + "angle": 0, + "content": "5.3.Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Human box detection and interaction proposals generation results. We first show the human detection and interaction results in Table 5. Under IoU threshold of 0.5, both human boxes and interactions have a high recall rate of 98.6 and 98.4. When the threshold improves to 0.7, recall of human boxes drops by 2.6 points and recall of interactions drops by 5.3 points. When improving the IoU threshold to 0.9, both recall rates drop significantly. The results indi" + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.09, + 0.885, + 0.259 + ], + "angle": 0, + "content": "
fmo&fmsfcfpInfo. Ex.mAPR@150R@100R@50R@20
✓---5.0081.6674.0052.7326.82
-✓--2.0771.7561.4338.9719.12
--✓-1.1350.7145.2439.7230.83
✓✓--5.1981.9874.8154.8928.51
✓-✓-5.5483.0575.4557.7131.92
-✓✓-3.8576.7668.5749.6527.68
✓✓✓-5.4381.7174.8458.1634.20
✓--✓6.1584.0976.5955.5528.10
-✓-✓3.5173.4163.1141.4720.91
--✓✓2.0158.7651.6038.8826.35
✓✓-✓6.8284.0177.1158.1431.86
✓-✓✓6.9484.4176.7257.4431.05
-✓✓✓5.9780.7571.8251.7831.04
✓✓✓✓7.5285.7878.5259.5332.76
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.262, + 0.892, + 0.359 + ], + "angle": 0, + "content": "Table 2. Ablation study on the interaction representation and information exchanging. “√” indicates the corresponding element is enabled while - indicates disabled. “fmo & fms” denotes motion features of the subject and object person. “fc” stands for context features of the union area. “fp” stands for the relative position information encoding. “Info. Ex.” stands for the multi-head self-attention operation to exchange information among proposals." + }, + { + "type": "table", + "bbox": [ + 0.562, + 0.366, + 0.836, + 0.453 + ], + "angle": 0, + "content": "
Pos:NegmAPR@150R@100R@50R@20
1:16.9785.9279.6460.9632.59
1:57.3986.2577.8759.8632.82
1:107.5285.7878.5259.5332.76
1:157.0285.3977.8758.5631.16
1:207.0885.3578.4360.5132.77
1:256.8985.4478.3158.8531.61
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.456, + 0.892, + 0.482 + ], + "angle": 0, + "content": "Table 3. Ablation on the positive and negative proposals ratio. The best results are obtained at 1:10." + }, + { + "type": "table", + "bbox": [ + 0.552, + 0.49, + 0.846, + 0.532 + ], + "angle": 0, + "content": "
mAPR@150R@100R@50R@20
Single Mask6.7784.5777.4158.2731.63
Separate Mask7.5285.7878.5259.5332.76
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.535, + 0.892, + 0.59 + ], + "angle": 0, + "content": "Table 4. Ablation on spatial mask generation. \"Separate Masks\" means generating a spatial mask for the subject and object person respectively while \"Single Mask\" means using only one spatial mask to represent the pair." + }, + { + "type": "table", + "bbox": [ + 0.541, + 0.596, + 0.852, + 0.641 + ], + "angle": 0, + "content": "
mAPAP@0.5R@0.5R@0.7R@0.9
Human Boxes73.592.698.696.058.2
Interactions--98.493.237.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.698 + ], + "angle": 0, + "content": "Table 5. Human detection and interaction proposal generation results. For human box detection, we report mAP, AP, and Recall. For interaction proposal generation, Recall is reported. We calculate recall under IoU thresholds of 0.5, 0.7, and 0.9." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.764 + ], + "angle": 0, + "content": "cate that, despite high recall under a relatively lower IoU threshold, there is still a lot of room for improvement in the quality of human boxes and interaction proposals." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "HHICls and HHIDet results. We provide HHICls and HHIDet results of some existing methods and our baseline in Table 6. STTran [7] and HORT [20] are two well-established video scene graph generation methods. They share two common properties: 1) Using appearance features extracted by image backbone. This is because the semantic level of relation classes defined by previous datasets is relatively low and the appearance feature is often sufficient for recognition, such as \\(\\langle \\text{dog}, \\text{larger}, \\text{frisbee} \\rangle\\). However," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18543" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.162, + 0.089, + 0.808, + 0.199 + ], + "angle": 0, + "content": "
MethodBackboneHHICIsHHIDet
mAPR@150R@100R@50R@20mAPR@150R@100R@50R@20
STTran [7]ResNet-101 [15]3.3171.2962.9142.6722.141.4351.6546.5437.6220.81
HORT [20]ResNet-101 [15]3.7578.5767.7850.3326.961.5452.4746.7336.8920/93
SlowFast [11]SlowFast-R50 [11]5.0081.6674.0052.7326.822.4462.1752.7737.8322.45
ACARN [31]SlowFast-R50 [11]5.4482.8575.2256.5331.772.5362.2552.8437.5021.85
Our baselineSlowFast-R50 [11]7.5285.7878.5259.5332.763.3664.8254.6237.7221.26
SlowFast-R101 [11]8.6787.3580.3560.1829.703.5265.2454.7637.0320.21
ViT-B [44]10.6989.2582.9368.1343.724.9372.2261.9242.9923.89
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.203, + 0.893, + 0.233 + ], + "angle": 0, + "content": "Table 6. HHICs and HHIDet results. We test existing video scene graph generation methods (STTran [7] and HORT [20]) and action detection methods (SlowFast [11] and ACARN [31]) on SportsHHI. Our baseline method achieves the best performance." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.241, + 0.46, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.348, + 0.468, + 0.378 + ], + "angle": 0, + "content": "Figure 7. Error analysis in HHIDet mode. We show the proportion of each error type among false positives." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.392, + 0.47, + 0.695 + ], + "angle": 0, + "content": "action modeling is very important for interaction recognition on SportsHHI. 2) Dependent on the object detection results. They add the category encoding of the objects to the relation representation, which provides strong prior information. For example, knowing that the subject and object are human and horse respectively, the relation category is very likely to be ride. However, SportsHHI does not have such prior as all subjects and objects are humans. Since video backbones are used to extract the motion features of each person, the performance of the action detection methods like SlowFast [11] and ACARN [31] is relatively better. Our baseline follows these action detectors to adopt a video backbone for motion features and introduce extra relative position and spatio-temporal context modeling between the subject and object person. Our simple baseline achieves leading performance with the same SlowFast-R50 backbone. When using the stronger VideoMAE [44] pretrained ViT-B backbone, the performance is significantly improved, which shows the importance of spatio-temporal representation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.71, + 0.228, + 0.726 + ], + "angle": 0, + "content": "5.4. Error Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Following ACT [21] and MultiSports [26], we analyze error types of the false positives in the predictions to better understand the challenges of human-human interaction detection in SportsHHI. We analyze the predictions of the baseline model with a SlowFast-R50 backbone. We classify false positives in the predictions into 9 mutually exclusive error types. \\( E_{R} \\): a prediction targets a ground-truth instance that has already been matched. \\( E_{C} \\): a prediction that has an accurate subject and object localization, but wrong interaction class. \\( E_{O} \\): a prediction that has accurate subject localization and correct interaction class, but inaccurate object lo" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.243, + 0.892, + 0.334 + ], + "angle": 0, + "content": "calization. \\( E_S \\): a prediction that has accurate object localization and correct interaction class, but inaccurate subject localization. \\( E_{S\\& O} \\), \\( E_{O\\& C} \\), \\( E_{S\\& C} \\), \\( E_{S\\& O\\& C} \\): a prediction that is inaccurate in corresponding aspects while acceptable in other aspects (if any). \\( E_N \\): a prediction that both the subject and object of it have no overlap with any ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.335, + 0.893, + 0.562 + ], + "angle": 0, + "content": "As shown in Figure 7, \\( E_N \\) is one of the most common error types. This is because SportsHHI is annotated in crowd multi-person scenarios but the interaction instances are relatively sparse due to the characteristic of sports videos and our high-level interaction definition. It is important but difficult to distinguish two people without interaction from real interaction instances. In video action detection [26], localization is relatively accurate and most errors are about classification. However, in interaction detection, the localization of people involved in interaction and the classification of interaction are inseparable. Pure localization errors \\( (E_S \\) and \\( E_O \\)) or pure classification errors \\( (E_C) \\) are relatively rare. The error types that coexisted with localization error and classification error \\( (E_{O\\& C}, E_{S\\& C}, E_{S\\& O\\& C}) \\) account for a relatively large proportion." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.574, + 0.619, + 0.59 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.812 + ], + "angle": 0, + "content": "In this paper, we proposed a new video visual relation detection task with a focus on sports human-human interaction understanding. This task deals with the complex interactions between humans in multi-person scenarios. We build a dataset named SportsHHI based on sports videos for this task. Human boxes and interaction instances are exhaustively annotated on keyframes at 5FPS. To benchmark this, we test several existing methods on SportsHHI and propose a baseline method. We conduct extensive experiments on SportsHHI and reveal the importance of motion information, context information, and position information for interaction recognition. We hope our SportHHI dataset and baseline method can inspire future research on human-human interaction understanding in videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.823, + 0.892, + 0.898 + ], + "angle": 0, + "content": "Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006), and Collaborative Innovation Center of Novel Software Technology and Industrialization." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18544" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.157 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. Vivit: A video vision transformer. 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In ICCV, pages 13577-13587, 2021. 1" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.617 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18546" + } + ] +] \ No newline at end of file diff --git a/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_origin.pdf b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..575ade0ecf705938a9dd9b2687a81cc2a9bb1303 --- /dev/null +++ b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/c0955323-ec6c-46f0-bf26-c3cb285a2d3d_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:53c3230004d48f9c810beaaee83843f2f43a74313dd11586a1e0ba28d1829fa2 +size 2361839 diff --git a/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/full.md b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/full.md new file mode 100644 index 0000000000000000000000000000000000000000..28b03ed91b3fcc7bccab768d827058cac858c2ed --- /dev/null +++ b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/full.md @@ -0,0 +1,297 @@ +# SportsHHI: A Dataset for Human-Human Interaction Detection in Sports Videos + +Tao $\mathbf{W}\mathbf{u}^{1,*}$ Runyu He $^{1,*}$ Gangshan $\mathbf{W}\mathbf{u}^{1}$ Limin Wang $^{1,2,\boxtimes}$ + +$^{1}$ State Key Laboratory for Novel Software Technology, Nanjing University $^{2}$ Shanghai AI Lab + +wt, runyu.he}@smail.nju.edu.cn, {gswu, lmwang}@nju.edu.cn + +https://github.com/MCG-NJU/SportsHHI + +# Abstract + +Video-based visual relation detection tasks, such as video scene graph generation, play important roles in fine-grained video understanding. However, current video visual relation detection datasets have two main limitations that hinder the progress of research in this area. First, they do not explore complex human-human interactions in multi-person scenarios. Second, the relation types of existing datasets have relatively low-level semantics and can be often recognized by appearance or simple prior information, without the need for detailed spatio-temporal context reasoning. Nevertheless, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. To address this issue, we propose a new video visual relation detection task: video human-human interaction detection, and build a dataset named SportsHHI for it. SportsHHI contains 34 high-level interaction classes from basketball and volleyball sports. 118,075 human bounding boxes and 50,649 interaction instances are annotated on 11,398 keyframes. To benchmark this, we propose a two-stage baseline method and conduct extensive experiments to reveal the key factors for a successful human-human interaction detector. We hope that SportsHHI can stimulate research on human interaction understanding in videos and promote the development of spatio-temporal context modeling techniques in video visual relation detection. + +# 1. Introduction + +Video understanding is a fundamental research field in computer vision, which has wide applications in security monitoring, internet video recommendation, and sports video analysis. Remarkable progress has been made in the action recognition task [3, 4, 13, 22, 23, 39, 40] with the advances of video convolution neural networks [3, 11, 45, 46, 49, 50, 52, 55] and video transformers [1, 2, 10, 29, 44, 51, 58]. + +![](images/3422ee33eec44e6c3d69531293a7dac4806aa802f9e35f1dce7139837b0057ad.jpg) + + +![](images/8889d04a7c3e3db844a634032fe90504c8ed3d102b41af00d915a679142a3f29.jpg) + + +![](images/ea07afbbabc970e14672dd51be95e0d7f26e64b3e149c566ae5d2ce79764a3a3.jpg) + +![](images/3c384324447107dc63b430fca1d46a0925e21593c1a35c30f15fa63bf2ef344b.jpg) +<#5,attack-defend,#11><#5,attack-protect,#2><#5,attack-block,#9> +Figure 1. Comparison between previous video visual relation detection datasets and our SportsHHI. In the upper row, we show three relation instances from VidVRD and AG datasets. These datasets rarely involve human-human interaction and define semantically simple relations that can be recognized by appearance or prior information. In contrast, the bottom row shows interaction annotations in two sample keyframes of SportsHHI. The bounding boxes and interaction annotation of the same instance are displayed in the same color. SportsHHI provides complex multi-person scenes where various interactions between human pairs occur concurrently. It focuses on high-level interactions that require detailed spatio-temporal context reasoning. + +![](images/40a53d3c426fe36ed24322095d48af473ad6f865cf1700d806d93799b7632d06.jpg) + +<#2, close defense, #8> <#1, close defense, #9> <#3, close defense, #6> +<#4, close defense, #7> <#0, interfere-shot, #5> + +The action recognition task requires tagging each video clip with a single action label. However, real-world applications usually require a more detailed and in-depth understanding of videos, thus more attention has been attracted to fine-grained video understanding tasks such as video action detection [14, 18, 24, 26, 31, 42, 54] and video visual relation detection tasks [7, 19, 20, 35, 36]. + +Video action detection involves localizing action performers in both space and time, as well as recognizing their action class. While earlier datasets like UCF101-24 [40] and JHMDB [18] primarily focuses on action detection in single-person scenarios, recent large-scale datasets such as AVA [14] and MultiSports [26] have emphasized the importance of modeling human-human interactions for a better recognition of individual actions in multi-person scenes. However, while AVA and MultiSports provide ample multi + +person scenes, neither of them offers explicit human-human interaction definitions and annotations. + +Video scene graph generation is a popular video visual relation detection task, which requires the model to localize objects of interest in the video and recognize the relation of each pair of objects. While current datasets like AG [19], VidVRD [35], and VidOR [36] provide explicit relation instance annotations, human-human interactions are barely involved. Moreover, the relation categories defined in these benchmarks primarily include spatial relations, atomic actions, and simple visual comparisons, which are semantically straightforward and often recognizable by appearance information or simple prior knowledge, such as $\langle \text{dog}, \text{larger}, \text{frisbee} \rangle$ and $\langle \text{person}, \text{stand on}, \text{floor} \rangle$ in the upper row of Figure 1. This makes current research pay more attention to the recognition of object categories and the utilization of category priors while ignoring reasoning based on spatio-temporal context. However, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. Spatio-temporal context modeling is an important technology that makes video relation detection different from image relation detection. We argue that there is a need for new datasets that comprehensively explore human-human interactions in complex multiperson scenarios, with high-level relation categories that require detailed spatio-temporal context reasoning. + +In this paper, we propose a new video visual relation detection task: video human-human interaction detection. This task requires detecting human-human interaction instances in video frames. Each human-human interaction instance is formulated as a triplet $\langle S, I, O \rangle$ , where $S$ and $O$ denote the bounding boxes of two different people and $I$ denotes the interaction category. For this task, we develop a dataset named SportsHHI, short for Sports Human-Human Interaction. We label interaction instances on the keyframes of basketball and volleyball videos at 5FPS. Two samples of keyframes are shown in the bottom row of Figure 1. SportsHHI has several unique characteristics that distinguish it from other visual relation detection datasets: 1) It is built on basketball and volleyball sports videos, thus containing a large number of complex multiplayer scenes with various interactions between athlete pairs occurring concurrently. 2) The interactions between each pair of humans are transient and change rapidly due to the fast movements of the players. 3) The defined interactions are of high-level semantic, including technical actions, tactical cooperation, and confrontation in sports. Recognizing an interaction instance in SportsHHI usually requires detailed spatiotemporal context reasoning. We hope that SportsHHI can attract more research attention to human-human interaction understanding in complex multi-person videos and promote the development of spatio-temporal context modeling tech + +niques in video visual relation detection. + +We test existing action detection and video scene graph generation methods on the SportsHHI dataset and propose a simple and neat baseline method based on these methods. Our baseline method adopts a Faster-RCNN-alike two-stage pipeline [33]: In the first stage, we use an offline human detector to detect person bounding boxes on the keyframe. We exhaust bounding box pairs to generate interaction proposals. In the second stage, we extract features for each proposal and categorize each proposal into an interaction class or background. Our experiments demonstrate that motion features, context information, relative position encoding, and information exchange among proposals are important for human-human interaction detection. + +In summary, our contribution is three-fold: 1) We propose a new video relation detection task of human-human interaction detection which aims at exploring the complex interaction between people in multi-person scenarios; 2) We develop the SportsHHI dataset of multi-person sports videos on which high-level human-human interaction is well-defined and finely-labeled; 3) We design a two-stage baseline model and conduct extensive experiments on the SportsHHI dataset to discover the key factors for a successful interaction detector. + +# 2. Related Work + +Video action detection. Video action detection aims to locate and recognize action instances on video frames. Earlier datasets like UCF Sports [34], UCF101-24 [40], and J-HMDB [18] typically only include single-person videos. Datasets like DALY [53], AVA [14], AVA-Kinetics [24], and MultiSports [26] contain scenes where multiple people are performing various actions concurrently. AVA sparsely annotates keyframes of movie videos at 1FPS. MultiSports collects videos from sports competitions. Many interaction-related action classes are defined, such as listen to in AVA and second pass in MultiSports. As they claim, it is important to model the interaction between people to recognize the action category of each person. However, as no interaction annotation is provided, interaction modeling can only be performed implicitly. SportsHHI annotates interactions on keyframes of basketball and volleyball videos from MultiSports at 5FPS. With interaction definitions and annotations provided in SportHHI, human-human interaction detection can be explicitly performed and evaluated. + +Video visual relation detection. Video scene graph generation requires localizing object pairs in the video and recognizing the relation of each pair of objects. AG [19] is a large-scale dataset built on Charades [38]. All videos in AG contain only one person, thus no human-human interaction is involved. In VidVRD [35] and VidOR [36], most of the videos contain only one person. Though human-human interaction is involved, the exploration of it is very + +limited. Similar to AG, video human-object interaction detection [5, 41] datasets only focus on relations between humans and objects. Besides, the relation categories defined in these datasets only include spatial relations (e.g. above), atomic actions (e.g. lean on), and simple visual comparisons (e.g. larger). The relations are usually semantically simple and can be easily recognized by appearance information. Some trivial relations are also defined like $\langle dog, larger, frisbee \rangle$ in VidVRD. The category of the subject and object can often provide enough cues for relation recognition [7, 20, 28, 32, 43, 47], such as $\langle person, ride, horse \rangle$ . Moreover, the relation between two objects changes very slowly in a video. Our SportHHI annotates human-human interaction instances in complex multi-person sports videos. The defined interactions are of high-level semantics and the interaction between two people changes rapidly. + +Sports video understanding. Researchers have built many different benchmarks in the sports domain for its challenges in spatio-temporal reasoning and promising application prospects, such as UCF101-24 [40] and MultiSports [26] for video action detection, FineGym [37] and Diving48 [25] for action recognition and temporal action detection, SoccerNet [12] for action spotting, SportsMOT [8] for multiobject tracking, and NBA [56], CAD [6] and Volleyball [17] for group action recognition, etc. Group action recognition (GAR) requires tagging each video clip with a group action label. Implicit modeling of interactions among the players is often performed to improve the accuracy of label predictions. The proposed SportsHHI dataset provides interaction definitions and annotations for explicit human-human interaction exploration. + +# 3. The SportsHHI Dataset + +In Sec. 3.1, we will explain several key choices we made while creating the SportsHHI dataset and outline the annotation process. Then in Sec. 3.2, we will present a detailed analysis of the statistics and characteristics of SportsHHI. + +# 3.1. Dataset Construction + +Selection of the data domain. First, we select to annotate human-human interaction in team sports videos for the following reasons: 1) The field of sports is itself a very promising application area for interaction detection. 2) Team sports videos provide ample multi-person scenes where various interactions between athlete pairs occur concurrently, which are rarely seen in daily-life videos. 3) Team sports videos involve many interactions with high-level semantics, such as tactics coordination or confrontation. 4) Interactions between people in sports game videos can be clearly and comprehensively defined according to game rules and professional athletes' advice. 5) High-quality, diverse sports game videos are easily accessible, + +![](images/e0049393c50939f6cf96efaefb9c536e8603a18f7f2df8b69dae1594bf4b5969.jpg) +Figure 2. User interface for interaction annotation. The person bounding boxes and ids in the keyframe are shown in the left. We can play the video for context information. To add an interaction instance in the current keyframe, the subject person id, object person id, and interaction class should be specified. + +![](images/ed8cf76d618c47c3b666e604d44f4f290892fbf9bbf44db02e4e94c3204ba1a4.jpg) +Figure 3. Interaction classes hierarchy. There are 34 interaction classes of high-level semantics in total in SportsHHI. 16 for basketball and 18 for volleyball. + +while surveillance videos are usually of lower quality and harder to obtain because of privacy. Furthermore, we decide to build the dataset on two popular team sports basketball and volleyball because: 1) The methods can be validated on two different subsets to evaluate their generalization performance on different sports. 2) Football is not included because the instance sparsity and class imbalance (which will be discussed in Sec. 3.2) would be more prominent in football videos. + +Interaction classes definition. There are existing benchmarks focusing on atomic relations, which can be recognized by appearance information or prior knowledge. These interaction classes are out of our scope (it does not mean they are solved or not important). Instead, we focus on high-level interactions between athletes, which are semantically complex and require detailed spatio-temporal context reasoning to recognize. With the guidance of professional athletes, we generated the final interaction vocabulary through iterative trial labeling and modification, which is shown in Figure 3. Our defined interaction classes include technical action (e.g. pass-catch in basketball), tactical coordination (e.g. co-block in volleyball), or confrontation (e.g. attack-defend in volleyball). + +Interaction instance formulation. Following common practice in AVA and AG datasets, we define interaction in + +![](images/a5e35501bae7cc4f28601f7f406727b06e8b204325eb37639e2dcaf19a969138.jpg) +Figure 4. The number of interaction instances of each class sorted by descending order. + +![](images/80376e924605107752419676f7837da4f7fdcd7db6629a12b3c45edf1adf45d3.jpg) + +![](images/24b88d24b6d9f0896fc90564385e3950cafa8d7a72f5190fce5fa0fdf64a7bb0.jpg) + +![](images/a717f2d113d30e8872a93c8e44bc56e6ae6da41eafc7f939ef0d01b7ac3f3eda.jpg) +Figure 5. Statistics comparisons between SportsHHI and VidVRD. In the left, we compare the distribution of the number of instances in each keyframe. SportsHHI has more keyframes of fewer instances because of the high-level interaction class definition and the property of sports videos. In the right, we compare the distribution of GIoU between the subject and object. The proportion of instances of extremely high and extremely low GIoU between subject and object are both higher than VidVRD, + +![](images/1bc3bb600c20b444440b566fd8ca024fbc6843d70fa010a9404111c88813b16f.jpg) + +stances at the frame level, with reference to a long-term spatial-temporal context. Each interaction instance can be formulated as a triplet $\langle S, I, O \rangle$ where $S$ and $O$ denote the bounding boxes of the subject and object person and $I$ denotes the interaction category between them from the interaction vocabulary. When the subject person or the object person is out of view, we annotate $S$ or $O$ as "invisible". This happens infrequently and we will provide statistics about it in the appendix. + +Data preparation. We carefully selected 80 basketball and 80 volleyball videos from the MultiSports [26] dataset to cover various types of games including men's, women's, national team, and club games. The average length of the videos is 603 frames and the frame rate of the videos is 25FPS. All videos have a high resolution of 720P. + +Annotation. We follow the sparse annotation strategy of AVA [14] and AG [19] to reduce redundancy and save labor costs, but we annotate keyframes at a higher rate of 5FPS, because in sports videos, the change of interactions is very frequent and fast. In our practice, 5FPS can avoid lots of + +
#keyframes#interact.#inst.#obj. bbox#hum. bboxavg. hum.
AG [19]234253251.7M4762292342531.00
VidVRD [35]5834134556311270522240.38
SportsHHI113983450649-11807510.36
+ +Table 1. Comparison of statistics between video scene graph generation datasets and SportsHHI. SportsHHI has a comparable scale to VidVRD. The average number of human bounding boxes per frame of SportsHHI is much higher than AG or VidVRD. + +redundancy and keep up with the changes of interactions. + +We take a two-stage annotation pipeline. The first stage is for person localization and tracking and the second stage is for interaction instance annotation. The user interface of the software for interaction instance annotation is shown in Figure 2. Though we annotate interaction instances at the frame level, as person id tracking is provided, we can easily generate interaction tubes by linking the same pair of persons with the same interaction class and provide temporal boundaries at a granularity of 5 frames. We will exemplify this in the appendix. + +Quality control. For the first stage, all annotations are complemented manually without using detection or tracking models. We double-check each video and manually correct inaccurate bounding boxes and inconsistent person numbers. For the second stage, all the annotators are professional athletes or veteran amateurs. To improve annotation accuracy and completeness, we perform repeated annotation. Each video is distributed to two different annotators. If the two annotators disagree on an annotation record, this record will be checked and decided by the meta-annotator. + +# 3.2. Dataset Statistics and Characteristics + +Our SportsHHI provides interaction instance annotations on keyframes of basketball and volleyball videos. As shown in Table 1, SportHHI contains 34 interaction classes, and 11398 keyframes in total are annotated with instances. Current video scene graph datasets deal with general relations between various kinds of objects while our SportsHHI focuses on high-level interaction between humans. It is reasonable that datasets for video scene graph generation have a larger scale than SportsHHI. However, our SportHHI still + +has a comparable size to the popular VidVRD dataset for video scene graph generation. Our SportsHHI has more annotated keyframes (11398 versus 5834) and the number of interaction instances is close (55631 versus 50649). One important characteristic of our SportsHHI is the multiperson scenarios. The average number of people per frame in our SportsHHI is much higher than AG and VidVRD. AG only contains one person in each video and there is virtually no multi-person scenario in videos of VidVRD. Human-human interaction is barely involved in these datasets. + +We further show some important characteristics of our SportsHHI: 1) As shown in Figure 4, the distribution of the number of interaction instances per class roughly follows Zipf's law. This long-tail distribution requires us to put more attention to classes with fewer instances. 2) As shown in Figure 5 left, compared with VidVRD [35], our SportsHHI has more keyframes with fewer instances. That is because we focus on interaction classes of coordination or confrontation in sports. In long plain segments (e.g. segments of dribbling in basketball), few interactions of interest happen, and there are much more interaction instances in video segments with fierce confrontation. The videos are in crowd multi-person scenarios but the interaction instances are relatively sparse, which requires the model to distinguish two people without interaction from real interaction instances. 3) As shown in Figure 5 right, the proportion of instances of low GIoU between subject and object in SportsHHI is significantly higher than in VidVRD, which indicates that the subject and object of many instances are spatially far apart in SportsHHI. The proportion of extremely high GIoU is also higher, which indicates the occlusion is severe in some instances. VidVRD deals with simple relations in daily life videos, where the subject and object usually have a moderate distance. + +# 4. Method + +We propose a baseline method for the human-human interaction detection task. As illustrated in Fig. 6, our method adopts a two-stage pipeline. In the first stage, interaction proposals are generated. In the second stage, we construct a representation for each proposal and classify each proposal into an interaction class or background. The following part of this section explains our method in detail. + +# 4.1. Interaction proposal generation + +We use an offline human detector for human detection on keyframes. We enumerate all human bounding box pairs as interaction proposals. Formally, for a keyframe at timestamp $t$ , let $N$ denote the number of human boxes in the frame and $B = \{b_{1}, b_{2}, \dots, b_{N}\}$ denote the boxes. The interaction proposals can be denoted as $P = \{p_{1}, p_{2}, \dots, p_{K}\}$ , where $p_{k} = (b_{s_{k}}, b_{o_{k}})$ and $K = N \times (N - 1)$ . + +Positive proposals and negative proposals sampling. We label a proposal $p_k$ as a positive proposal when its subject and object bounding boxes both have an IoU overlap higher than 0.7 with their counterparts in a ground-truth interaction instance. For training, it is possible to input all the interaction proposals to the classification network for loss function calculation, but this will consume large GPU memory and the network optimization will bias towards negative samples as they are dominant. Instead, we use all positive proposals and sample negative proposals by a fixed positive-negative ratio. To increase the proportion of positive proposals and avoid the situation that a ground truth has no corresponding positive proposal, we add all ground-truth human box pairs as positive proposals for training. + +# 4.2. Interaction classification + +The presentation of each interaction proposal comprises three parts: the motion features of the subject and object persons, the context features, and the relative position of the subject and object encoding. + +Motion features and context features. We sample a video clip centered at the keyframe and employ a 3D video backbone on it for feature map extraction. For an interaction proposal $p_k$ , we apply RoIAlign operation [16] on the feature maps with the bounding boxes $b_{s_k}$ and $b_{o_k}$ and then transform the RoIAligned feature to dimension $d_v$ with a linear layer. The motion features are denoted as $f_k^{ms} \in \mathbb{R}^{d_v}$ and $f_k^{mo} \in \mathbb{R}^{d_v}$ . We apply the RoIAlign operation on the features map using the union box of the subject and object for context information. The context feature is also transformed to dimension $d_v$ , denoted as $f_k^c \in \mathbb{R}^{d_v}$ + +Relative position information encoding. Following [7, 57], given an interaction proposal $p_k$ , we generate a spatial mask for the subject and object person respectively. We resize the union box of $b_{s_k}$ and $b_{o_k}$ to a fixed size of $M \times M$ . We then generate the spatial mask of the subject bounding box $m_k^s \in \mathbb{R}^{M \times M}$ . For each pixel in $m_k^s$ , if it is inside the subject bounding box $b_{s_k}$ , its value is set to 1, else 0. The spatial mask of the object bounding box $m_k^o \in \mathbb{R}^{M \times M}$ is generated in the same way. The two spatial masks are flattened, concatenated, and transformed to dimension $d_p$ . We use the final vector $f_k^p \in \mathbb{R}^{d_p}$ as relative position encoding. + +Proposal representation. We use the concatenation of motions features $f_{k}^{ms}$ and $f_{k}^{mo}$ , context features $f_{k}^{c}$ , and relative position encoding $f_{k}^{p}$ as the representation $x_{k}$ of interaction proposal $p_{k}$ . Formally, + +$$ +x _ {k} = \left\langle f _ {k} ^ {m s}, f _ {k} ^ {m o}, f _ {k} ^ {c}, f _ {k} ^ {p} \right\rangle , \tag {1} +$$ + +where $\langle ,\rangle$ is the concatenation operation. + +Information exchange among proposals. We denote the representation of the $K$ interaction proposals as $X = \{\pmb{x}_1, \pmb{x}_2, \dots, \pmb{x}_K\}$ . Sometimes, recognizing an interaction requires information from other interaction instances. For + +![](images/89a5967740a170852da57efba261395e31967eeca43e038ac8072334adf3ec8e.jpg) +Figure 6. An overview of our baseline method. Given a video clip centered at a keyframe, we first use an offline human detector to detect human bounding boxes on the keyframe. All the human bounding box pairs are enumerated as interaction proposals. Then, we construct representations for the proposals. We perform the RoIAlign operation on the video feature maps extracted by a video backbone for motion features and context features. We generate spatial masks for each proposal, which are flattened and transformed into a vector. The vector is used as relative position encoding. The motion features, context features, and relative position encoding are concatenated as proposal representations. Multi-head self-attention is applied to the representations for information exchange. Finally, an FCN classification head is used to predict the classification scores. + +example, to recognize an interaction of co-defend in volleyball, we need to know there exists an interaction of attack-defend. To capture the information from other interaction proposals, we apply a standard multi-head self-attention (MHSA) [48] operation on $X$ . Formally, + +$$ +X ^ {\prime} = \operatorname {M H S A} (X). \tag {2} +$$ + +Classification head. Finally, $X'$ is input to a fully connected network (FCN) for classification score prediction. Let $S$ denote the predicted scores. Formally, + +$$ +S = \operatorname {F C N} \left(X ^ {\prime}\right), \tag {3} +$$ + +where $S\in \mathbb{R}^{K\times (C + 1)}$ $C$ denotes the number of interaction classes. + +# 5. Experiments + +# 5.1. Experimental Setup + +Dataset. We train and validate our model on the SportsHHI Dataset. The dataset is split into the training and validation set by video. Evaluation on a very small number of examples could be unreliable, so we evaluate the 28 classes that have at least 10 instances in both the training and validation set. Instances with an invisible subject or object are excluded from evaluation. In total, the current version contains 38,527 instances from 8,719 keyframes for training and 12,122 instances from 2,679 keyframes for validation. We report results on the validation set. + +Metrics. A prediction is considered as a true positive if and only if its subject and object bounding boxes both have an IoU overlap higher than a preset threshold with their counterparts in a ground-truth interaction instance and the predicted interaction class matches the ground truth. Following VidVRD [35], we set the IoU threshold to 0.5. Following the video scene graph generation task, we use Recall@K + +(K is the number of predictions) as the evaluation metric. Mean average precision is adopted as an evaluation metric for many detection tasks [27]. However, this metric is discarded by many former visual relation detection benchmarks [19, 30] because of their incomplete annotation. This issue does not exist in SportsHHI. In our experiments, mAP is also reported for the interaction detection task. We argue that mAP is a more difficult and informative metric. Two different modes for model training and evaluation are used: 1) human-human interaction detection (HHIDet) which expects input video frames and predicts human boxes and interaction labels; 2) human-human interaction classification (HHICls) which directly uses ground-truth human bounding boxes and predicts human-human interaction classes. + +Implementation details. The human detector we use is a Faster-RCNN [33] detector with a ResNeXt-101-FPN backbone, which is pre-trained on ImageNet [9] and COCO [27] and finetuned on keyframes of SportsHHI. The ratio of positive and negative proposals is set to 1:10. The SlowFast-R50 backbone [11] pre-trained on Kinetics-400 [22] is adopted for video feature extraction. The dimension of features $d_v$ and the dimension of relative position encoding $d_p$ are set to 512 and 256 respectively. We scale the short side of the video frames to 256. We use SGD optimizer with momentum 0.9 and weight decay $1 \times 10^{-5}$ . The batch size is set to 8. The learning rate is 0.002 for HHICls and 0.004 for HHIDet. The models are trained for 20 epochs. + +# 5.2. Ablation Study + +We conduct ablation experiments on SportsHHI to investigate the influence of each design and component of our baseline method. Unless otherwise stated, all ablation experiments are conducted in the HHICls mode, that is, the ground-truth human bounding boxes are used. HHICls mode allows us to study the key factors to predict interactions without the limitations of human detection. + +Positive and negative proposal ratio. We investigate the influence of the ratio of positive and negative proposals in Table 3. A moderate proportion of negative samples help the model to distinguish interactions from backgrounds. However, when the positive-negative ratio gets too low, the model optimization will be overwhelmed by negative samples, and thus the performance drops. + +Spatial mask generation. We generate two separate spatial masks for the subject and object person. Therefore, the positions of the subject and object can be distinguished. For comparison, we generate a single mask for the two people by setting the values in any box to 1. As shown in Table 4, model performance degrades when using a single mask. As the triplet $\langle S, I, O \rangle$ is ordered in SportsHHI, it is important to distinguish the position of the subject and object. + +Interaction proposal representation. We show the importance of motion features $f^{mo}$ and $f^{ms}$ , context feature $f^c$ and relative position encoding $f^p$ in interaction representation in Table 2. We first show the results of using each feature in lines 1-3 and 8-10. Using only motions features $f^{mo}$ and $f^{ms}$ can achieve acceptable results, which indicates the modeling of the actions of the subject and object person is very important for the recognition of the interaction between them. The performance is much worse when using context feature $f^c$ or relative position encoding $f^p$ only. Using only the context feature cannot provide specific information of the subject and object and as the subject and object person are often far apart in spatial, the context feature may include much noise. Without visual information, pure prior information of the relative position of the subject and object person is not discriminative enough for interaction recognition. As shown in lines 5-7 and 12-14, when coupling position encoding with motion and context features, the performance improves a lot, which indicates that position information is complementary to visual information. As shown in lines 7 and 14, using all three types of features achieves the best results. + +Information exchange among proposals. We ablate the multi-head self-attention module to show the importance of information exchange among proposals. As shown in Table 2, regardless of the representation of the proposal, exchanging information among proposals always brings performance improvement. + +# 5.3.Quantitative Results + +Human box detection and interaction proposals generation results. We first show the human detection and interaction results in Table 5. Under IoU threshold of 0.5, both human boxes and interactions have a high recall rate of 98.6 and 98.4. When the threshold improves to 0.7, recall of human boxes drops by 2.6 points and recall of interactions drops by 5.3 points. When improving the IoU threshold to 0.9, both recall rates drop significantly. The results indi + +
fmo&fmsfcfpInfo. Ex.mAPR@150R@100R@50R@20
✓---5.0081.6674.0052.7326.82
-✓--2.0771.7561.4338.9719.12
--✓-1.1350.7145.2439.7230.83
✓✓--5.1981.9874.8154.8928.51
✓-✓-5.5483.0575.4557.7131.92
-✓✓-3.8576.7668.5749.6527.68
✓✓✓-5.4381.7174.8458.1634.20
✓--✓6.1584.0976.5955.5528.10
-✓-✓3.5173.4163.1141.4720.91
--✓✓2.0158.7651.6038.8826.35
✓✓-✓6.8284.0177.1158.1431.86
✓-✓✓6.9484.4176.7257.4431.05
-✓✓✓5.9780.7571.8251.7831.04
✓✓✓✓7.5285.7878.5259.5332.76
+ +Table 2. Ablation study on the interaction representation and information exchanging. “√” indicates the corresponding element is enabled while - indicates disabled. “fmo & fms” denotes motion features of the subject and object person. “fc” stands for context features of the union area. “fp” stands for the relative position information encoding. “Info. Ex.” stands for the multi-head self-attention operation to exchange information among proposals. + +
Pos:NegmAPR@150R@100R@50R@20
1:16.9785.9279.6460.9632.59
1:57.3986.2577.8759.8632.82
1:107.5285.7878.5259.5332.76
1:157.0285.3977.8758.5631.16
1:207.0885.3578.4360.5132.77
1:256.8985.4478.3158.8531.61
+ +Table 3. Ablation on the positive and negative proposals ratio. The best results are obtained at 1:10. + +
mAPR@150R@100R@50R@20
Single Mask6.7784.5777.4158.2731.63
Separate Mask7.5285.7878.5259.5332.76
+ +Table 4. Ablation on spatial mask generation. "Separate Masks" means generating a spatial mask for the subject and object person respectively while "Single Mask" means using only one spatial mask to represent the pair. + +
mAPAP@0.5R@0.5R@0.7R@0.9
Human Boxes73.592.698.696.058.2
Interactions--98.493.237.7
+ +Table 5. Human detection and interaction proposal generation results. For human box detection, we report mAP, AP, and Recall. For interaction proposal generation, Recall is reported. We calculate recall under IoU thresholds of 0.5, 0.7, and 0.9. + +cate that, despite high recall under a relatively lower IoU threshold, there is still a lot of room for improvement in the quality of human boxes and interaction proposals. + +HHICls and HHIDet results. We provide HHICls and HHIDet results of some existing methods and our baseline in Table 6. STTran [7] and HORT [20] are two well-established video scene graph generation methods. They share two common properties: 1) Using appearance features extracted by image backbone. This is because the semantic level of relation classes defined by previous datasets is relatively low and the appearance feature is often sufficient for recognition, such as $\langle \text{dog}, \text{larger}, \text{frisbee} \rangle$ . However, + +
MethodBackboneHHICIsHHIDet
mAPR@150R@100R@50R@20mAPR@150R@100R@50R@20
STTran [7]ResNet-101 [15]3.3171.2962.9142.6722.141.4351.6546.5437.6220.81
HORT [20]ResNet-101 [15]3.7578.5767.7850.3326.961.5452.4746.7336.8920/93
SlowFast [11]SlowFast-R50 [11]5.0081.6674.0052.7326.822.4462.1752.7737.8322.45
ACARN [31]SlowFast-R50 [11]5.4482.8575.2256.5331.772.5362.2552.8437.5021.85
Our baselineSlowFast-R50 [11]7.5285.7878.5259.5332.763.3664.8254.6237.7221.26
SlowFast-R101 [11]8.6787.3580.3560.1829.703.5265.2454.7637.0320.21
ViT-B [44]10.6989.2582.9368.1343.724.9372.2261.9242.9923.89
+ +Table 6. HHICs and HHIDet results. We test existing video scene graph generation methods (STTran [7] and HORT [20]) and action detection methods (SlowFast [11] and ACARN [31]) on SportsHHI. Our baseline method achieves the best performance. + +![](images/47085546cca7a24eaa6893515bd2b11e72b666f25e9c6d61aeed08df406a0a90.jpg) +Figure 7. Error analysis in HHIDet mode. We show the proportion of each error type among false positives. + +action modeling is very important for interaction recognition on SportsHHI. 2) Dependent on the object detection results. They add the category encoding of the objects to the relation representation, which provides strong prior information. For example, knowing that the subject and object are human and horse respectively, the relation category is very likely to be ride. However, SportsHHI does not have such prior as all subjects and objects are humans. Since video backbones are used to extract the motion features of each person, the performance of the action detection methods like SlowFast [11] and ACARN [31] is relatively better. Our baseline follows these action detectors to adopt a video backbone for motion features and introduce extra relative position and spatio-temporal context modeling between the subject and object person. Our simple baseline achieves leading performance with the same SlowFast-R50 backbone. When using the stronger VideoMAE [44] pretrained ViT-B backbone, the performance is significantly improved, which shows the importance of spatio-temporal representation. + +# 5.4. Error Analysis + +Following ACT [21] and MultiSports [26], we analyze error types of the false positives in the predictions to better understand the challenges of human-human interaction detection in SportsHHI. We analyze the predictions of the baseline model with a SlowFast-R50 backbone. We classify false positives in the predictions into 9 mutually exclusive error types. $E_{R}$ : a prediction targets a ground-truth instance that has already been matched. $E_{C}$ : a prediction that has an accurate subject and object localization, but wrong interaction class. $E_{O}$ : a prediction that has accurate subject localization and correct interaction class, but inaccurate object lo + +calization. $E_S$ : a prediction that has accurate object localization and correct interaction class, but inaccurate subject localization. $E_{S\& O}$ , $E_{O\& C}$ , $E_{S\& C}$ , $E_{S\& O\& C}$ : a prediction that is inaccurate in corresponding aspects while acceptable in other aspects (if any). $E_N$ : a prediction that both the subject and object of it have no overlap with any ground truth. + +As shown in Figure 7, $E_N$ is one of the most common error types. This is because SportsHHI is annotated in crowd multi-person scenarios but the interaction instances are relatively sparse due to the characteristic of sports videos and our high-level interaction definition. It is important but difficult to distinguish two people without interaction from real interaction instances. In video action detection [26], localization is relatively accurate and most errors are about classification. However, in interaction detection, the localization of people involved in interaction and the classification of interaction are inseparable. Pure localization errors $(E_S$ and $E_O$ ) or pure classification errors $(E_C)$ are relatively rare. The error types that coexisted with localization error and classification error $(E_{O\& C}, E_{S\& C}, E_{S\& O\& C})$ account for a relatively large proportion. + +# 6. Conclusion + +In this paper, we proposed a new video visual relation detection task with a focus on sports human-human interaction understanding. This task deals with the complex interactions between humans in multi-person scenarios. We build a dataset named SportsHHI based on sports videos for this task. Human boxes and interaction instances are exhaustively annotated on keyframes at 5FPS. To benchmark this, we test several existing methods on SportsHHI and propose a baseline method. We conduct extensive experiments on SportsHHI and reveal the importance of motion information, context information, and position information for interaction recognition. We hope our SportHHI dataset and baseline method can inspire future research on human-human interaction understanding in videos. + +Acknowledgements. 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In ICCV, pages 13577-13587, 2021. 1 \ No newline at end of file diff --git a/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/images.zip b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..f3ad240f7fdeb705d65130a8c9b2d6bfdb42790b --- /dev/null +++ b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:ce6379e660a2ee758d98dd10ff45f97f3827b162f98e8d9b99f42bb51d37c359 +size 468186 diff --git a/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/layout.json b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6a42314f91572bab1fcf650bf143283191182ce0 --- /dev/null +++ b/2024/SportsHHI_ A Dataset for Human-Human Interaction Detection in Sports Videos/layout.json @@ -0,0 +1,8490 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 47, + 103, + 545, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 103, + 545, + 121 + ], + "spans": [ + { + "bbox": [ + 47, + 103, + 545, + 121 + ], + "type": "text", + "content": "SportsHHI: A Dataset for Human-Human Interaction Detection in Sports Videos" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "spans": [ + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "text", + "content": "Tao " + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{W}\\mathbf{u}^{1,*}" + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "text", + "content": " Runyu He" + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "inline_equation", + "content": "^{1,*}" + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "text", + "content": " Gangshan " + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "inline_equation", + "content": "\\mathbf{W}\\mathbf{u}^{1}" + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "text", + "content": " Limin Wang" + }, + { + "bbox": [ + 123, + 141, + 470, + 157 + ], + "type": "inline_equation", + "content": "^{1,2,\\boxtimes}" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 66, + 157, + 527, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 157, + 527, + 171 + ], + "spans": [ + { + "bbox": [ + 66, + 157, + 527, + 171 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 66, + 157, + 527, + 171 + ], + "type": "text", + "content": "State Key Laboratory for Novel Software Technology, Nanjing University " + }, + { + "bbox": [ + 66, + 157, + 527, + 171 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 66, + 157, + 527, + 171 + ], + "type": "text", + "content": "Shanghai AI Lab" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 144, + 173, + 448, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 144, + 173, + 448, + 185 + ], + "spans": [ + { + "bbox": [ + 144, + 173, + 448, + 185 + ], + "type": "text", + "content": "wt, runyu.he}@smail.nju.edu.cn, {gswu, lmwang}@nju.edu.cn" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 186, + 186, + 403, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 186, + 186, + 403, + 198 + ], + "spans": [ + { + "bbox": [ + 186, + 186, + 403, + 198 + ], + "type": "text", + "content": "https://github.com/MCG-NJU/SportsHHI" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 190, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 253, + 290, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 253, + 290, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 253, + 290, + 563 + ], + "type": "text", + "content": "Video-based visual relation detection tasks, such as video scene graph generation, play important roles in fine-grained video understanding. However, current video visual relation detection datasets have two main limitations that hinder the progress of research in this area. First, they do not explore complex human-human interactions in multi-person scenarios. Second, the relation types of existing datasets have relatively low-level semantics and can be often recognized by appearance or simple prior information, without the need for detailed spatio-temporal context reasoning. Nevertheless, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. To address this issue, we propose a new video visual relation detection task: video human-human interaction detection, and build a dataset named SportsHHI for it. SportsHHI contains 34 high-level interaction classes from basketball and volleyball sports. 118,075 human bounding boxes and 50,649 interaction instances are annotated on 11,398 keyframes. To benchmark this, we propose a two-stage baseline method and conduct extensive experiments to reveal the key factors for a successful human-human interaction detector. We hope that SportsHHI can stimulate research on human interaction understanding in videos and promote the development of spatio-temporal context modeling techniques in video visual relation detection." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 588, + 127, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 127, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 127, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 609, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 693 + ], + "type": "text", + "content": "Video understanding is a fundamental research field in computer vision, which has wide applications in security monitoring, internet video recommendation, and sports video analysis. Remarkable progress has been made in the action recognition task [3, 4, 13, 22, 23, 39, 40] with the advances of video convolution neural networks [3, 11, 45, 46, 49, 50, 52, 55] and video transformers [1, 2, 10, 29, 44, 51, 58]." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 309, + 225, + 426, + 290 + ], + "blocks": [ + { + "bbox": [ + 309, + 225, + 426, + 290 + ], + "lines": [ + { + "bbox": [ + 309, + 225, + 426, + 290 + ], + "spans": [ + { + "bbox": [ + 309, + 225, + 426, + 290 + ], + "type": "image", + "image_path": "3422ee33eec44e6c3d69531293a7dac4806aa802f9e35f1dce7139837b0057ad.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 349, + 289, + 381, + 294 + ], + "lines": [ + { + "bbox": [ + 349, + 289, + 381, + 294 + ], + "spans": [ + { + "bbox": [ + 349, + 289, + 381, + 294 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 427, + 225, + 488, + 290 + ], + "blocks": [ + { + "bbox": [ + 427, + 225, + 488, + 290 + ], + "lines": [ + { + "bbox": [ + 427, + 225, + 488, + 290 + ], + "spans": [ + { + "bbox": [ + 427, + 225, + 488, + 290 + ], + "type": "image", + "image_path": "8889d04a7c3e3db844a634032fe90504c8ed3d102b41af00d915a679142a3f29.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 441, + 289, + 470, + 294 + ], + "lines": [ + { + "bbox": [ + 441, + 289, + 470, + 294 + ], + "spans": [ + { + "bbox": [ + 441, + 289, + 470, + 294 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 491, + 226, + 545, + 290 + ], + "blocks": [ + { + "bbox": [ + 491, + 226, + 545, + 290 + ], + "lines": [ + { + "bbox": [ + 491, + 226, + 545, + 290 + ], + "spans": [ + { + "bbox": [ + 491, + 226, + 545, + 290 + ], + "type": "image", + "image_path": "ea07afbbabc970e14672dd51be95e0d7f26e64b3e149c566ae5d2ce79764a3a3.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 309, + 294, + 426, + 361 + ], + "blocks": [ + { + "bbox": [ + 309, + 294, + 426, + 361 + ], + "lines": [ + { + "bbox": [ + 309, + 294, + 426, + 361 + ], + "spans": [ + { + "bbox": [ + 309, + 294, + 426, + 361 + ], + "type": "image", + "image_path": "3c384324447107dc63b430fca1d46a0925e21593c1a35c30f15fa63bf2ef344b.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 310, + 361, + 425, + 366 + ], + "lines": [ + { + "bbox": [ + 310, + 361, + 425, + 366 + ], + "spans": [ + { + "bbox": [ + 310, + 361, + 425, + 366 + ], + "type": "text", + "content": "<#5,attack-defend,#11><#5,attack-protect,#2><#5,attack-block,#9>" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 304, + 374, + 545, + 506 + ], + "lines": [ + { + "bbox": [ + 304, + 374, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 304, + 374, + 545, + 506 + ], + "type": "text", + "content": "Figure 1. Comparison between previous video visual relation detection datasets and our SportsHHI. In the upper row, we show three relation instances from VidVRD and AG datasets. These datasets rarely involve human-human interaction and define semantically simple relations that can be recognized by appearance or prior information. In contrast, the bottom row shows interaction annotations in two sample keyframes of SportsHHI. The bounding boxes and interaction annotation of the same instance are displayed in the same color. SportsHHI provides complex multi-person scenes where various interactions between human pairs occur concurrently. It focuses on high-level interactions that require detailed spatio-temporal context reasoning." + } + ] + } + ], + "index": 22, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "type": "image", + "bbox": [ + 427, + 294, + 545, + 361 + ], + "blocks": [ + { + "bbox": [ + 501, + 289, + 539, + 294 + ], + "lines": [ + { + "bbox": [ + 501, + 289, + 539, + 294 + ], + "spans": [ + { + "bbox": [ + 501, + 289, + 539, + 294 + ], + "type": "text", + "content": "" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 427, + 294, + 545, + 361 + ], + "lines": [ + { + "bbox": [ + 427, + 294, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 427, + 294, + 545, + 361 + ], + "type": "image", + "image_path": "40a53d3c426fe36ed24322095d48af473ad6f865cf1700d806d93799b7632d06.jpg" + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 428, + 361, + 544, + 366 + ], + "lines": [ + { + "bbox": [ + 428, + 361, + 544, + 366 + ], + "spans": [ + { + "bbox": [ + 428, + 361, + 544, + 366 + ], + "type": "text", + "content": "<#2, close defense, #8> <#1, close defense, #9> <#3, close defense, #6>" + } + ] + } + ], + "index": 20, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 429, + 366, + 504, + 370 + ], + "lines": [ + { + "bbox": [ + 429, + 366, + 504, + 370 + ], + "spans": [ + { + "bbox": [ + 429, + 366, + 504, + 370 + ], + "type": "text", + "content": "<#4, close defense, #7> <#0, interfere-shot, #5>" + } + ] + } + ], + "index": 21, + "angle": 0, + "type": "image_caption" + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 518, + 545, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 518, + 545, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 518, + 545, + 602 + ], + "type": "text", + "content": "The action recognition task requires tagging each video clip with a single action label. However, real-world applications usually require a more detailed and in-depth understanding of videos, thus more attention has been attracted to fine-grained video understanding tasks such as video action detection [14, 18, 24, 26, 31, 42, 54] and video visual relation detection tasks [7, 19, 20, 35, 36]." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Video action detection involves localizing action performers in both space and time, as well as recognizing their action class. While earlier datasets like UCF101-24 [40] and JHMDB [18] primarily focuses on action detection in single-person scenarios, recent large-scale datasets such as AVA [14] and MultiSports [26] have emphasized the importance of modeling human-human interactions for a better recognition of individual actions in multi-person scenes. However, while AVA and MultiSports provide ample multi" + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 702, + 227, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 702, + 227, + 713 + ], + "spans": [ + { + "bbox": [ + 61, + 702, + 227, + 713 + ], + "type": "text", + "content": "*: Equal contribution. " + }, + { + "bbox": [ + 61, + 702, + 227, + 713 + ], + "type": "inline_equation", + "content": "\\boxtimes" + }, + { + "bbox": [ + 61, + 702, + 227, + 713 + ], + "type": "text", + "content": " Corresponding author." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18537" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "person scenes, neither of them offers explicit human-human interaction definitions and annotations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "type": "text", + "content": "Video scene graph generation is a popular video visual relation detection task, which requires the model to localize objects of interest in the video and recognize the relation of each pair of objects. While current datasets like AG [19], VidVRD [35], and VidOR [36] provide explicit relation instance annotations, human-human interactions are barely involved. Moreover, the relation categories defined in these benchmarks primarily include spatial relations, atomic actions, and simple visual comparisons, which are semantically straightforward and often recognizable by appearance information or simple prior knowledge, such as " + }, + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "type": "inline_equation", + "content": "\\langle \\text{dog}, \\text{larger}, \\text{frisbee} \\rangle" + }, + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "type": "inline_equation", + "content": "\\langle \\text{person}, \\text{stand on}, \\text{floor} \\rangle" + }, + { + "bbox": [ + 46, + 99, + 289, + 399 + ], + "type": "text", + "content": " in the upper row of Figure 1. This makes current research pay more attention to the recognition of object categories and the utilization of category priors while ignoring reasoning based on spatio-temporal context. However, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. Spatio-temporal context modeling is an important technology that makes video relation detection different from image relation detection. We argue that there is a need for new datasets that comprehensively explore human-human interactions in complex multiperson scenarios, with high-level relation categories that require detailed spatio-temporal context reasoning." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": "In this paper, we propose a new video visual relation detection task: video human-human interaction detection. This task requires detecting human-human interaction instances in video frames. Each human-human interaction instance is formulated as a triplet " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\langle S, I, O \\rangle" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": " denote the bounding boxes of two different people and " + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 402, + 289, + 715 + ], + "type": "text", + "content": " denotes the interaction category. For this task, we develop a dataset named SportsHHI, short for Sports Human-Human Interaction. We label interaction instances on the keyframes of basketball and volleyball videos at 5FPS. Two samples of keyframes are shown in the bottom row of Figure 1. SportsHHI has several unique characteristics that distinguish it from other visual relation detection datasets: 1) It is built on basketball and volleyball sports videos, thus containing a large number of complex multiplayer scenes with various interactions between athlete pairs occurring concurrently. 2) The interactions between each pair of humans are transient and change rapidly due to the fast movements of the players. 3) The defined interactions are of high-level semantic, including technical actions, tactical cooperation, and confrontation in sports. Recognizing an interaction instance in SportsHHI usually requires detailed spatiotemporal context reasoning. We hope that SportsHHI can attract more research attention to human-human interaction understanding in complex multi-person videos and promote the development of spatio-temporal context modeling tech" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 471, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 471, + 83 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 471, + 83 + ], + "type": "text", + "content": "niques in video visual relation detection." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 84, + 545, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 545, + 239 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 545, + 239 + ], + "type": "text", + "content": "We test existing action detection and video scene graph generation methods on the SportsHHI dataset and propose a simple and neat baseline method based on these methods. Our baseline method adopts a Faster-RCNN-alike two-stage pipeline [33]: In the first stage, we use an offline human detector to detect person bounding boxes on the keyframe. We exhaust bounding box pairs to generate interaction proposals. In the second stage, we extract features for each proposal and categorize each proposal into an interaction class or background. Our experiments demonstrate that motion features, context information, relative position encoding, and information exchange among proposals are important for human-human interaction detection." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 239, + 545, + 358 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 239, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 304, + 239, + 545, + 358 + ], + "type": "text", + "content": "In summary, our contribution is three-fold: 1) We propose a new video relation detection task of human-human interaction detection which aims at exploring the complex interaction between people in multi-person scenarios; 2) We develop the SportsHHI dataset of multi-person sports videos on which high-level human-human interaction is well-defined and finely-labeled; 3) We design a two-stage baseline model and conduct extensive experiments on the SportsHHI dataset to discover the key factors for a successful interaction detector." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 390, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 617 + ], + "type": "text", + "content": "Video action detection. Video action detection aims to locate and recognize action instances on video frames. Earlier datasets like UCF Sports [34], UCF101-24 [40], and J-HMDB [18] typically only include single-person videos. Datasets like DALY [53], AVA [14], AVA-Kinetics [24], and MultiSports [26] contain scenes where multiple people are performing various actions concurrently. AVA sparsely annotates keyframes of movie videos at 1FPS. MultiSports collects videos from sports competitions. Many interaction-related action classes are defined, such as listen to in AVA and second pass in MultiSports. As they claim, it is important to model the interaction between people to recognize the action category of each person. However, as no interaction annotation is provided, interaction modeling can only be performed implicitly. SportsHHI annotates interactions on keyframes of basketball and volleyball videos from MultiSports at 5FPS. With interaction definitions and annotations provided in SportHHI, human-human interaction detection can be explicitly performed and evaluated." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "Video visual relation detection. Video scene graph generation requires localizing object pairs in the video and recognizing the relation of each pair of objects. AG [19] is a large-scale dataset built on Charades [38]. All videos in AG contain only one person, thus no human-human interaction is involved. In VidVRD [35] and VidOR [36], most of the videos contain only one person. Though human-human interaction is involved, the exploration of it is very" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18538" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "limited. Similar to AG, video human-object interaction detection [5, 41] datasets only focus on relations between humans and objects. Besides, the relation categories defined in these datasets only include spatial relations (e.g. above), atomic actions (e.g. lean on), and simple visual comparisons (e.g. larger). The relations are usually semantically simple and can be easily recognized by appearance information. Some trivial relations are also defined like " + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\langle dog, larger, frisbee \\rangle" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": " in VidVRD. The category of the subject and object can often provide enough cues for relation recognition [7, 20, 28, 32, 43, 47], such as " + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "inline_equation", + "content": "\\langle person, ride, horse \\rangle" + }, + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": ". Moreover, the relation between two objects changes very slowly in a video. Our SportHHI annotates human-human interaction instances in complex multi-person sports videos. The defined interactions are of high-level semantics and the interaction between two people changes rapidly." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 456 + ], + "type": "text", + "content": "Sports video understanding. Researchers have built many different benchmarks in the sports domain for its challenges in spatio-temporal reasoning and promising application prospects, such as UCF101-24 [40] and MultiSports [26] for video action detection, FineGym [37] and Diving48 [25] for action recognition and temporal action detection, SoccerNet [12] for action spotting, SportsMOT [8] for multiobject tracking, and NBA [56], CAD [6] and Volleyball [17] for group action recognition, etc. Group action recognition (GAR) requires tagging each video clip with a group action label. Implicit modeling of interactions among the players is often performed to improve the accuracy of label predictions. The proposed SportsHHI dataset provides interaction definitions and annotations for explicit human-human interaction exploration." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 464, + 185, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 185, + 478 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 185, + 478 + ], + "type": "text", + "content": "3. The SportsHHI Dataset" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 485, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 485, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 485, + 287, + 534 + ], + "type": "text", + "content": "In Sec. 3.1, we will explain several key choices we made while creating the SportsHHI dataset and outline the annotation process. Then in Sec. 3.2, we will present a detailed analysis of the statistics and characteristics of SportsHHI." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 540, + 170, + 552 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 170, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 170, + 552 + ], + "type": "text", + "content": "3.1. Dataset Construction" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 289, + 715 + ], + "type": "text", + "content": "Selection of the data domain. First, we select to annotate human-human interaction in team sports videos for the following reasons: 1) The field of sports is itself a very promising application area for interaction detection. 2) Team sports videos provide ample multi-person scenes where various interactions between athlete pairs occur concurrently, which are rarely seen in daily-life videos. 3) Team sports videos involve many interactions with high-level semantics, such as tactics coordination or confrontation. 4) Interactions between people in sports game videos can be clearly and comprehensively defined according to game rules and professional athletes' advice. 5) High-quality, diverse sports game videos are easily accessible," + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 308, + 70, + 543, + 230 + ], + "blocks": [ + { + "bbox": [ + 308, + 70, + 543, + 230 + ], + "lines": [ + { + "bbox": [ + 308, + 70, + 543, + 230 + ], + "spans": [ + { + "bbox": [ + 308, + 70, + 543, + 230 + ], + "type": "image", + "image_path": "e0049393c50939f6cf96efaefb9c536e8603a18f7f2df8b69dae1594bf4b5969.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 233, + 547, + 289 + ], + "lines": [ + { + "bbox": [ + 304, + 233, + 547, + 289 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 547, + 289 + ], + "type": "text", + "content": "Figure 2. User interface for interaction annotation. The person bounding boxes and ids in the keyframe are shown in the left. We can play the video for context information. To add an interaction instance in the current keyframe, the subject person id, object person id, and interaction class should be specified." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 307, + 293, + 543, + 369 + ], + "blocks": [ + { + "bbox": [ + 307, + 293, + 543, + 369 + ], + "lines": [ + { + "bbox": [ + 307, + 293, + 543, + 369 + ], + "spans": [ + { + "bbox": [ + 307, + 293, + 543, + 369 + ], + "type": "image", + "image_path": "ed8cf76d618c47c3b666e604d44f4f290892fbf9bbf44db02e4e94c3204ba1a4.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 371, + 547, + 405 + ], + "lines": [ + { + "bbox": [ + 304, + 371, + 547, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 547, + 405 + ], + "type": "text", + "content": "Figure 3. Interaction classes hierarchy. There are 34 interaction classes of high-level semantics in total in SportsHHI. 16 for basketball and 18 for volleyball." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 414, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 545, + 521 + ], + "type": "text", + "content": "while surveillance videos are usually of lower quality and harder to obtain because of privacy. Furthermore, we decide to build the dataset on two popular team sports basketball and volleyball because: 1) The methods can be validated on two different subsets to evaluate their generalization performance on different sports. 2) Football is not included because the instance sparsity and class imbalance (which will be discussed in Sec. 3.2) would be more prominent in football videos." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 521, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 689 + ], + "type": "text", + "content": "Interaction classes definition. There are existing benchmarks focusing on atomic relations, which can be recognized by appearance information or prior knowledge. These interaction classes are out of our scope (it does not mean they are solved or not important). Instead, we focus on high-level interactions between athletes, which are semantically complex and require detailed spatio-temporal context reasoning to recognize. With the guidance of professional athletes, we generated the final interaction vocabulary through iterative trial labeling and modification, which is shown in Figure 3. Our defined interaction classes include technical action (e.g. pass-catch in basketball), tactical coordination (e.g. co-block in volleyball), or confrontation (e.g. attack-defend in volleyball)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 547, + 715 + ], + "type": "text", + "content": "Interaction instance formulation. Following common practice in AVA and AG datasets, we define interaction in" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "18539" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 66, + 70, + 527, + 201 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 527, + 201 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 527, + 201 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 527, + 201 + ], + "type": "image", + "image_path": "a5e35501bae7cc4f28601f7f406727b06e8b204325eb37639e2dcaf19a969138.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 137, + 202, + 455, + 214 + ], + "lines": [ + { + "bbox": [ + 137, + 202, + 455, + 214 + ], + "spans": [ + { + "bbox": [ + 137, + 202, + 455, + 214 + ], + "type": "text", + "content": "Figure 4. The number of interaction instances of each class sorted by descending order." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 52, + 224, + 162, + 298 + ], + "blocks": [ + { + "bbox": [ + 52, + 224, + 162, + 298 + ], + "lines": [ + { + "bbox": [ + 52, + 224, + 162, + 298 + ], + "spans": [ + { + "bbox": [ + 52, + 224, + 162, + 298 + ], + "type": "image", + "image_path": "80376e924605107752419676f7837da4f7fdcd7db6629a12b3c45edf1adf45d3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 163, + 224, + 281, + 298 + ], + "blocks": [ + { + "bbox": [ + 163, + 224, + 281, + 298 + ], + "lines": [ + { + "bbox": [ + 163, + 224, + 281, + 298 + ], + "spans": [ + { + "bbox": [ + 163, + 224, + 281, + 298 + ], + "type": "image", + "image_path": "24b88d24b6d9f0896fc90564385e3950cafa8d7a72f5190fce5fa0fdf64a7bb0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 52, + 300, + 162, + 375 + ], + "blocks": [ + { + "bbox": [ + 52, + 300, + 162, + 375 + ], + "lines": [ + { + "bbox": [ + 52, + 300, + 162, + 375 + ], + "spans": [ + { + "bbox": [ + 52, + 300, + 162, + 375 + ], + "type": "image", + "image_path": "a717f2d113d30e8872a93c8e44bc56e6ae6da41eafc7f939ef0d01b7ac3f3eda.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 377, + 287, + 465 + ], + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 465 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 465 + ], + "type": "text", + "content": "Figure 5. Statistics comparisons between SportsHHI and VidVRD. In the left, we compare the distribution of the number of instances in each keyframe. SportsHHI has more keyframes of fewer instances because of the high-level interaction class definition and the property of sports videos. In the right, we compare the distribution of GIoU between the subject and object. The proportion of instances of extremely high and extremely low GIoU between subject and object are both higher than VidVRD," + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 164, + 300, + 281, + 375 + ], + "blocks": [ + { + "bbox": [ + 164, + 300, + 281, + 375 + ], + "lines": [ + { + "bbox": [ + 164, + 300, + 281, + 375 + ], + "spans": [ + { + "bbox": [ + 164, + 300, + 281, + 375 + ], + "type": "image", + "image_path": "1bc3bb600c20b444440b566fd8ca024fbc6843d70fa010a9404111c88813b16f.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": "stances at the frame level, with reference to a long-term spatial-temporal context. Each interaction instance can be formulated as a triplet " + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "inline_equation", + "content": "\\langle S, I, O \\rangle" + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": " denote the bounding boxes of the subject and object person and " + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": " denotes the interaction category between them from the interaction vocabulary. When the subject person or the object person is out of view, we annotate " + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "inline_equation", + "content": "O" + }, + { + "bbox": [ + 46, + 473, + 286, + 581 + ], + "type": "text", + "content": " as \"invisible\". This happens infrequently and we will provide statistics about it in the appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 582, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 286, + 652 + ], + "type": "text", + "content": "Data preparation. We carefully selected 80 basketball and 80 volleyball videos from the MultiSports [26] dataset to cover various types of games including men's, women's, national team, and club games. The average length of the videos is 603 frames and the frame rate of the videos is 25FPS. All videos have a high resolution of 720P." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 286, + 712 + ], + "type": "text", + "content": "Annotation. We follow the sparse annotation strategy of AVA [14] and AG [19] to reduce redundancy and save labor costs, but we annotate keyframes at a higher rate of 5FPS, because in sports videos, the change of interactions is very frequent and fast. In our practice, 5FPS can avoid lots of" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 224, + 544, + 266 + ], + "blocks": [ + { + "bbox": [ + 307, + 224, + 544, + 266 + ], + "lines": [ + { + "bbox": [ + 307, + 224, + 544, + 266 + ], + "spans": [ + { + "bbox": [ + 307, + 224, + 544, + 266 + ], + "type": "table", + "html": "
#keyframes#interact.#inst.#obj. bbox#hum. bboxavg. hum.
AG [19]234253251.7M4762292342531.00
VidVRD [35]5834134556311270522240.38
SportsHHI113983450649-11807510.36
", + "image_path": "387fb1fc83bd33e75d741e0d9d079fb46419ee45cf03fbd7d1f036231022406a.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 270, + 545, + 314 + ], + "lines": [ + { + "bbox": [ + 305, + 270, + 545, + 314 + ], + "spans": [ + { + "bbox": [ + 305, + 270, + 545, + 314 + ], + "type": "text", + "content": "Table 1. Comparison of statistics between video scene graph generation datasets and SportsHHI. SportsHHI has a comparable scale to VidVRD. The average number of human bounding boxes per frame of SportsHHI is much higher than AG or VidVRD." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 323, + 537, + 335 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 323, + 537, + 335 + ], + "spans": [ + { + "bbox": [ + 305, + 323, + 537, + 335 + ], + "type": "text", + "content": "redundancy and keep up with the changes of interactions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 336, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 336, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 336, + 545, + 456 + ], + "type": "text", + "content": "We take a two-stage annotation pipeline. The first stage is for person localization and tracking and the second stage is for interaction instance annotation. The user interface of the software for interaction instance annotation is shown in Figure 2. Though we annotate interaction instances at the frame level, as person id tracking is provided, we can easily generate interaction tubes by linking the same pair of persons with the same interaction class and provide temporal boundaries at a granularity of 5 frames. We will exemplify this in the appendix." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 456, + 545, + 576 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 576 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 576 + ], + "type": "text", + "content": "Quality control. For the first stage, all annotations are complemented manually without using detection or tracking models. We double-check each video and manually correct inaccurate bounding boxes and inconsistent person numbers. For the second stage, all the annotators are professional athletes or veteran amateurs. To improve annotation accuracy and completeness, we perform repeated annotation. Each video is distributed to two different annotators. If the two annotators disagree on an annotation record, this record will be checked and decided by the meta-annotator." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 586, + 503, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 503, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 503, + 597 + ], + "type": "text", + "content": "3.2. Dataset Statistics and Characteristics" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "Our SportsHHI provides interaction instance annotations on keyframes of basketball and volleyball videos. As shown in Table 1, SportHHI contains 34 interaction classes, and 11398 keyframes in total are annotated with instances. Current video scene graph datasets deal with general relations between various kinds of objects while our SportsHHI focuses on high-level interaction between humans. It is reasonable that datasets for video scene graph generation have a larger scale than SportsHHI. However, our SportHHI still" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18540" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "has a comparable size to the popular VidVRD dataset for video scene graph generation. Our SportsHHI has more annotated keyframes (11398 versus 5834) and the number of interaction instances is close (55631 versus 50649). One important characteristic of our SportsHHI is the multiperson scenarios. The average number of people per frame in our SportsHHI is much higher than AG and VidVRD. AG only contains one person in each video and there is virtually no multi-person scenario in videos of VidVRD. Human-human interaction is barely involved in these datasets." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 479 + ], + "type": "text", + "content": "We further show some important characteristics of our SportsHHI: 1) As shown in Figure 4, the distribution of the number of interaction instances per class roughly follows Zipf's law. This long-tail distribution requires us to put more attention to classes with fewer instances. 2) As shown in Figure 5 left, compared with VidVRD [35], our SportsHHI has more keyframes with fewer instances. That is because we focus on interaction classes of coordination or confrontation in sports. In long plain segments (e.g. segments of dribbling in basketball), few interactions of interest happen, and there are much more interaction instances in video segments with fierce confrontation. The videos are in crowd multi-person scenarios but the interaction instances are relatively sparse, which requires the model to distinguish two people without interaction from real interaction instances. 3) As shown in Figure 5 right, the proportion of instances of low GIoU between subject and object in SportsHHI is significantly higher than in VidVRD, which indicates that the subject and object of many instances are spatially far apart in SportsHHI. The proportion of extremely high GIoU is also higher, which indicates the occlusion is severe in some instances. VidVRD deals with simple relations in daily life videos, where the subject and object usually have a moderate distance." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 489, + 104, + 502 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 489, + 104, + 502 + ], + "spans": [ + { + "bbox": [ + 47, + 489, + 104, + 502 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 509, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 509, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 509, + 287, + 593 + ], + "type": "text", + "content": "We propose a baseline method for the human-human interaction detection task. As illustrated in Fig. 6, our method adopts a two-stage pipeline. In the first stage, interaction proposals are generated. In the second stage, we construct a representation for each proposal and classify each proposal into an interaction class or background. The following part of this section explains our method in detail." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 599, + 219, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 219, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 219, + 612 + ], + "type": "text", + "content": "4.1. Interaction proposal generation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": "We use an offline human detector for human detection on keyframes. We enumerate all human bounding box pairs as interaction proposals. Formally, for a keyframe at timestamp " + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": ", let " + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": " denote the number of human boxes in the frame and " + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "B = \\{b_{1}, b_{2}, \\dots, b_{N}\\}" + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": " denote the boxes. The interaction proposals can be denoted as " + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "P = \\{p_{1}, p_{2}, \\dots, p_{K}\\}" + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "p_{k} = (b_{s_{k}}, b_{o_{k}})" + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "inline_equation", + "content": "K = N \\times (N - 1)" + }, + { + "bbox": [ + 47, + 618, + 287, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": "Positive proposals and negative proposals sampling. We label a proposal " + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 304, + 72, + 547, + 240 + ], + "type": "text", + "content": " as a positive proposal when its subject and object bounding boxes both have an IoU overlap higher than 0.7 with their counterparts in a ground-truth interaction instance. For training, it is possible to input all the interaction proposals to the classification network for loss function calculation, but this will consume large GPU memory and the network optimization will bias towards negative samples as they are dominant. Instead, we use all positive proposals and sample negative proposals by a fixed positive-negative ratio. To increase the proportion of positive proposals and avoid the situation that a ground truth has no corresponding positive proposal, we add all ground-truth human box pairs as positive proposals for training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 247, + 443, + 258 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 247, + 443, + 258 + ], + "spans": [ + { + "bbox": [ + 305, + 247, + 443, + 258 + ], + "type": "text", + "content": "4.2. Interaction classification" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 265, + 547, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 547, + 312 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 547, + 312 + ], + "type": "text", + "content": "The presentation of each interaction proposal comprises three parts: the motion features of the subject and object persons, the context features, and the relative position of the subject and object encoding." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": "Motion features and context features. We sample a video clip centered at the keyframe and employ a 3D video backbone on it for feature map extraction. For an interaction proposal " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": ", we apply RoIAlign operation [16] on the feature maps with the bounding boxes " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "b_{s_k}" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "b_{o_k}" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": " and then transform the RoIAligned feature to dimension " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "d_v" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": " with a linear layer. The motion features are denoted as " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "f_k^{ms} \\in \\mathbb{R}^{d_v}" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "f_k^{mo} \\in \\mathbb{R}^{d_v}" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": ". We apply the RoIAlign operation on the features map using the union box of the subject and object for context information. The context feature is also transformed to dimension " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "d_v" + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "text", + "content": ", denoted as " + }, + { + "bbox": [ + 304, + 313, + 545, + 445 + ], + "type": "inline_equation", + "content": "f_k^c \\in \\mathbb{R}^{d_v}" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": "Relative position information encoding. Following [7, 57], given an interaction proposal " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "p_k" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": ", we generate a spatial mask for the subject and object person respectively. We resize the union box of " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "b_{s_k}" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "b_{o_k}" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": " to a fixed size of " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "M \\times M" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": ". We then generate the spatial mask of the subject bounding box " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "m_k^s \\in \\mathbb{R}^{M \\times M}" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": ". For each pixel in " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "m_k^s" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": ", if it is inside the subject bounding box " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "b_{s_k}" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": ", its value is set to 1, else 0. The spatial mask of the object bounding box " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "m_k^o \\in \\mathbb{R}^{M \\times M}" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": " is generated in the same way. The two spatial masks are flattened, concatenated, and transformed to dimension " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "d_p" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": ". We use the final vector " + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "inline_equation", + "content": "f_k^p \\in \\mathbb{R}^{d_p}" + }, + { + "bbox": [ + 304, + 445, + 547, + 577 + ], + "type": "text", + "content": " as relative position encoding." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": "Proposal representation. We use the concatenation of motions features " + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "inline_equation", + "content": "f_{k}^{ms}" + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "inline_equation", + "content": "f_{k}^{mo}" + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": ", context features " + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "inline_equation", + "content": "f_{k}^{c}" + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": ", and relative position encoding " + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "inline_equation", + "content": "f_{k}^{p}" + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": " as the representation " + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "inline_equation", + "content": "x_{k}" + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": " of interaction proposal " + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "inline_equation", + "content": "p_{k}" + }, + { + "bbox": [ + 304, + 577, + 545, + 624 + ], + "type": "text", + "content": ". Formally," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 371, + 632, + 545, + 646 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 371, + 632, + 545, + 646 + ], + "spans": [ + { + "bbox": [ + 371, + 632, + 545, + 646 + ], + "type": "interline_equation", + "content": "x _ {k} = \\left\\langle f _ {k} ^ {m s}, f _ {k} ^ {m o}, f _ {k} ^ {c}, f _ {k} ^ {p} \\right\\rangle , \\tag {1}", + "image_path": "1ca2d673d5f640557da2917df0de95ed8a0cb9f75ef021627a401c094ce1ed97.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 653, + 473, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 653, + 473, + 665 + ], + "spans": [ + { + "bbox": [ + 305, + 653, + 473, + 665 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 653, + 473, + 665 + ], + "type": "inline_equation", + "content": "\\langle ,\\rangle" + }, + { + "bbox": [ + 305, + 653, + 473, + 665 + ], + "type": "text", + "content": " is the concatenation operation." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "text", + "content": "Information exchange among proposals. We denote the representation of the " + }, + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "text", + "content": " interaction proposals as " + }, + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "inline_equation", + "content": "X = \\{\\pmb{x}_1, \\pmb{x}_2, \\dots, \\pmb{x}_K\\}" + }, + { + "bbox": [ + 305, + 666, + 547, + 713 + ], + "type": "text", + "content": ". Sometimes, recognizing an interaction requires information from other interaction instances. For" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18541" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 70, + 545, + 186 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 545, + 186 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 545, + 186 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 545, + 186 + ], + "type": "image", + "image_path": "89a5967740a170852da57efba261395e31967eeca43e038ac8072334adf3ec8e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 193, + 547, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 193, + 547, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 193, + 547, + 270 + ], + "type": "text", + "content": "Figure 6. An overview of our baseline method. Given a video clip centered at a keyframe, we first use an offline human detector to detect human bounding boxes on the keyframe. All the human bounding box pairs are enumerated as interaction proposals. Then, we construct representations for the proposals. We perform the RoIAlign operation on the video feature maps extracted by a video backbone for motion features and context features. We generate spatial masks for each proposal, which are flattened and transformed into a vector. The vector is used as relative position encoding. The motion features, context features, and relative position encoding are concatenated as proposal representations. Multi-head self-attention is applied to the representations for information exchange. Finally, an FCN classification head is used to predict the classification scores." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 277, + 288, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 288, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 288, + 337 + ], + "type": "text", + "content": "example, to recognize an interaction of co-defend in volleyball, we need to know there exists an interaction of attack-defend. To capture the information from other interaction proposals, we apply a standard multi-head self-attention (MHSA) [48] operation on " + }, + { + "bbox": [ + 46, + 277, + 288, + 337 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 277, + 288, + 337 + ], + "type": "text", + "content": ". Formally," + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 129, + 346, + 287, + 361 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 129, + 346, + 287, + 361 + ], + "spans": [ + { + "bbox": [ + 129, + 346, + 287, + 361 + ], + "type": "interline_equation", + "content": "X ^ {\\prime} = \\operatorname {M H S A} (X). \\tag {2}", + "image_path": "099a4d28e0867e60e3ec8166292d586b6016b059ee261e5ef24753f17bce07d9.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "type": "text", + "content": "Classification head. Finally, " + }, + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "type": "inline_equation", + "content": "X'" + }, + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "type": "text", + "content": " is input to a fully connected network (FCN) for classification score prediction. Let " + }, + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 47, + 369, + 287, + 406 + ], + "type": "text", + "content": " denote the predicted scores. Formally," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 134, + 414, + 287, + 428 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 134, + 414, + 287, + 428 + ], + "spans": [ + { + "bbox": [ + 134, + 414, + 287, + 428 + ], + "type": "interline_equation", + "content": "S = \\operatorname {F C N} \\left(X ^ {\\prime}\\right), \\tag {3}", + "image_path": "6ad4ea74949c8294752e2105ff1edd28b5248724d8c6327c9816a990bbea6401.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 435, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 435, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 46, + 435, + 287, + 461 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 435, + 287, + 461 + ], + "type": "inline_equation", + "content": "S\\in \\mathbb{R}^{K\\times (C + 1)}" + }, + { + "bbox": [ + 46, + 435, + 287, + 461 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 435, + 287, + 461 + ], + "type": "text", + "content": " denotes the number of interaction classes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 472, + 128, + 486 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 472, + 128, + 486 + ], + "spans": [ + { + "bbox": [ + 47, + 472, + 128, + 486 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 491, + 164, + 505 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 164, + 505 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 164, + 505 + ], + "type": "text", + "content": "5.1. Experimental Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 510, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 287, + 628 + ], + "type": "text", + "content": "Dataset. We train and validate our model on the SportsHHI Dataset. The dataset is split into the training and validation set by video. Evaluation on a very small number of examples could be unreliable, so we evaluate the 28 classes that have at least 10 instances in both the training and validation set. Instances with an invisible subject or object are excluded from evaluation. In total, the current version contains 38,527 instances from 8,719 keyframes for training and 12,122 instances from 2,679 keyframes for validation. We report results on the validation set." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 288, + 714 + ], + "type": "text", + "content": "Metrics. A prediction is considered as a true positive if and only if its subject and object bounding boxes both have an IoU overlap higher than a preset threshold with their counterparts in a ground-truth interaction instance and the predicted interaction class matches the ground truth. Following VidVRD [35], we set the IoU threshold to 0.5. Following the video scene graph generation task, we use Recall@K" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 277, + 545, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 277, + 545, + 444 + ], + "spans": [ + { + "bbox": [ + 304, + 277, + 545, + 444 + ], + "type": "text", + "content": "(K is the number of predictions) as the evaluation metric. Mean average precision is adopted as an evaluation metric for many detection tasks [27]. However, this metric is discarded by many former visual relation detection benchmarks [19, 30] because of their incomplete annotation. This issue does not exist in SportsHHI. In our experiments, mAP is also reported for the interaction detection task. We argue that mAP is a more difficult and informative metric. Two different modes for model training and evaluation are used: 1) human-human interaction detection (HHIDet) which expects input video frames and predicts human boxes and interaction labels; 2) human-human interaction classification (HHICls) which directly uses ground-truth human bounding boxes and predicts human-human interaction classes." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "text", + "content": "Implementation details. The human detector we use is a Faster-RCNN [33] detector with a ResNeXt-101-FPN backbone, which is pre-trained on ImageNet [9] and COCO [27] and finetuned on keyframes of SportsHHI. The ratio of positive and negative proposals is set to 1:10. The SlowFast-R50 backbone [11] pre-trained on Kinetics-400 [22] is adopted for video feature extraction. The dimension of features " + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "inline_equation", + "content": "d_v" + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "text", + "content": " and the dimension of relative position encoding " + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "inline_equation", + "content": "d_p" + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "text", + "content": " are set to 512 and 256 respectively. We scale the short side of the video frames to 256. We use SGD optimizer with momentum 0.9 and weight decay " + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-5}" + }, + { + "bbox": [ + 304, + 445, + 546, + 601 + ], + "type": "text", + "content": ". The batch size is set to 8. The learning rate is 0.002 for HHICls and 0.004 for HHIDet. The models are trained for 20 epochs." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 610, + 400, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 610, + 400, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 610, + 400, + 624 + ], + "type": "text", + "content": "5.2. Ablation Study" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "We conduct ablation experiments on SportsHHI to investigate the influence of each design and component of our baseline method. Unless otherwise stated, all ablation experiments are conducted in the HHICls mode, that is, the ground-truth human bounding boxes are used. HHICls mode allows us to study the key factors to predict interactions without the limitations of human detection." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18542" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 288, + 156 + ], + "type": "text", + "content": "Positive and negative proposal ratio. We investigate the influence of the ratio of positive and negative proposals in Table 3. A moderate proportion of negative samples help the model to distinguish interactions from backgrounds. However, when the positive-negative ratio gets too low, the model optimization will be overwhelmed by negative samples, and thus the performance drops." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "spans": [ + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "type": "text", + "content": "Spatial mask generation. We generate two separate spatial masks for the subject and object person. Therefore, the positions of the subject and object can be distinguished. For comparison, we generate a single mask for the two people by setting the values in any box to 1. As shown in Table 4, model performance degrades when using a single mask. As the triplet " + }, + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "type": "inline_equation", + "content": "\\langle S, I, O \\rangle" + }, + { + "bbox": [ + 46, + 157, + 287, + 252 + ], + "type": "text", + "content": " is ordered in SportsHHI, it is important to distinguish the position of the subject and object." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": "Interaction proposal representation. We show the importance of motion features " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^{mo}" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^{ms}" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": ", context feature " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^c" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " and relative position encoding " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^p" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " in interaction representation in Table 2. We first show the results of using each feature in lines 1-3 and 8-10. Using only motions features " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^{mo}" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^{ms}" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " can achieve acceptable results, which indicates the modeling of the actions of the subject and object person is very important for the recognition of the interaction between them. The performance is much worse when using context feature " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^c" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " or relative position encoding " + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "inline_equation", + "content": "f^p" + }, + { + "bbox": [ + 46, + 253, + 288, + 516 + ], + "type": "text", + "content": " only. Using only the context feature cannot provide specific information of the subject and object and as the subject and object person are often far apart in spatial, the context feature may include much noise. Without visual information, pure prior information of the relative position of the subject and object person is not discriminative enough for interaction recognition. As shown in lines 5-7 and 12-14, when coupling position encoding with motion and context features, the performance improves a lot, which indicates that position information is complementary to visual information. As shown in lines 7 and 14, using all three types of features achieves the best results." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 517, + 287, + 589 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 517, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 287, + 589 + ], + "type": "text", + "content": "Information exchange among proposals. We ablate the multi-head self-attention module to show the importance of information exchange among proposals. As shown in Table 2, regardless of the representation of the proposal, exchanging information among proposals always brings performance improvement." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 598, + 166, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 598, + 166, + 611 + ], + "spans": [ + { + "bbox": [ + 47, + 598, + 166, + 611 + ], + "type": "text", + "content": "5.3.Quantitative Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "Human box detection and interaction proposals generation results. We first show the human detection and interaction results in Table 5. Under IoU threshold of 0.5, both human boxes and interactions have a high recall rate of 98.6 and 98.4. When the threshold improves to 0.7, recall of human boxes drops by 2.6 points and recall of interactions drops by 5.3 points. When improving the IoU threshold to 0.9, both recall rates drop significantly. The results indi" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 315, + 71, + 541, + 205 + ], + "blocks": [ + { + "bbox": [ + 315, + 71, + 541, + 205 + ], + "lines": [ + { + "bbox": [ + 315, + 71, + 541, + 205 + ], + "spans": [ + { + "bbox": [ + 315, + 71, + 541, + 205 + ], + "type": "table", + "html": "
fmo&fmsfcfpInfo. Ex.mAPR@150R@100R@50R@20
✓---5.0081.6674.0052.7326.82
-✓--2.0771.7561.4338.9719.12
--✓-1.1350.7145.2439.7230.83
✓✓--5.1981.9874.8154.8928.51
✓-✓-5.5483.0575.4557.7131.92
-✓✓-3.8576.7668.5749.6527.68
✓✓✓-5.4381.7174.8458.1634.20
✓--✓6.1584.0976.5955.5528.10
-✓-✓3.5173.4163.1141.4720.91
--✓✓2.0158.7651.6038.8826.35
✓✓-✓6.8284.0177.1158.1431.86
✓-✓✓6.9484.4176.7257.4431.05
-✓✓✓5.9780.7571.8251.7831.04
✓✓✓✓7.5285.7878.5259.5332.76
", + "image_path": "f16a0c282145c4c60c7025b9ba78be983eba88575d4692cbb72104db092d1b44.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_body" + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 343, + 289, + 511, + 358 + ], + "blocks": [ + { + "bbox": [ + 304, + 207, + 545, + 284 + ], + "lines": [ + { + "bbox": [ + 304, + 207, + 545, + 284 + ], + "spans": [ + { + "bbox": [ + 304, + 207, + 545, + 284 + ], + "type": "text", + "content": "Table 2. Ablation study on the interaction representation and information exchanging. “√” indicates the corresponding element is enabled while - indicates disabled. “fmo & fms” denotes motion features of the subject and object person. “fc” stands for context features of the union area. “fp” stands for the relative position information encoding. “Info. Ex.” stands for the multi-head self-attention operation to exchange information among proposals." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 343, + 289, + 511, + 358 + ], + "lines": [ + { + "bbox": [ + 343, + 289, + 511, + 358 + ], + "spans": [ + { + "bbox": [ + 343, + 289, + 511, + 358 + ], + "type": "table", + "html": "
Pos:NegmAPR@150R@100R@50R@20
1:16.9785.9279.6460.9632.59
1:57.3986.2577.8759.8632.82
1:107.5285.7878.5259.5332.76
1:157.0285.3977.8758.5631.16
1:207.0885.3578.4360.5132.77
1:256.8985.4478.3158.8531.61
", + "image_path": "9edf6abee964abb54975a28c12c28abde18299eadf0c42130cdb66f853187c2b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 337, + 388, + 517, + 421 + ], + "blocks": [ + { + "bbox": [ + 305, + 361, + 545, + 381 + ], + "lines": [ + { + "bbox": [ + 305, + 361, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 305, + 361, + 545, + 381 + ], + "type": "text", + "content": "Table 3. Ablation on the positive and negative proposals ratio. The best results are obtained at 1:10." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 337, + 388, + 517, + 421 + ], + "lines": [ + { + "bbox": [ + 337, + 388, + 517, + 421 + ], + "spans": [ + { + "bbox": [ + 337, + 388, + 517, + 421 + ], + "type": "table", + "html": "
mAPR@150R@100R@50R@20
Single Mask6.7784.5777.4158.2731.63
Separate Mask7.5285.7878.5259.5332.76
", + "image_path": "6c5f77727def65e47c0d368b595ea6f1cfe3b473217fc7cea316c606144489be.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 331, + 472, + 521, + 507 + ], + "blocks": [ + { + "bbox": [ + 304, + 423, + 545, + 467 + ], + "lines": [ + { + "bbox": [ + 304, + 423, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 423, + 545, + 467 + ], + "type": "text", + "content": "Table 4. Ablation on spatial mask generation. \"Separate Masks\" means generating a spatial mask for the subject and object person respectively while \"Single Mask\" means using only one spatial mask to represent the pair." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 331, + 472, + 521, + 507 + ], + "lines": [ + { + "bbox": [ + 331, + 472, + 521, + 507 + ], + "spans": [ + { + "bbox": [ + 331, + 472, + 521, + 507 + ], + "type": "table", + "html": "
mAPAP@0.5R@0.5R@0.7R@0.9
Human Boxes73.592.698.696.058.2
Interactions--98.493.237.7
", + "image_path": "964b64fcba2341da081cc9c9f837b70887312121865cea1e986ba4241d3c01b2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 509, + 545, + 552 + ], + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 552 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 552 + ], + "type": "text", + "content": "Table 5. Human detection and interaction proposal generation results. For human box detection, we report mAP, AP, and Recall. For interaction proposal generation, Recall is reported. We calculate recall under IoU thresholds of 0.5, 0.7, and 0.9." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 569, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 605 + ], + "type": "text", + "content": "cate that, despite high recall under a relatively lower IoU threshold, there is still a lot of room for improvement in the quality of human boxes and interaction proposals." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "HHICls and HHIDet results. We provide HHICls and HHIDet results of some existing methods and our baseline in Table 6. STTran [7] and HORT [20] are two well-established video scene graph generation methods. They share two common properties: 1) Using appearance features extracted by image backbone. This is because the semantic level of relation classes defined by previous datasets is relatively low and the appearance feature is often sufficient for recognition, such as " + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\langle \\text{dog}, \\text{larger}, \\text{frisbee} \\rangle" + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": ". However," + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18543" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 99, + 70, + 494, + 157 + ], + "blocks": [ + { + "bbox": [ + 99, + 70, + 494, + 157 + ], + "lines": [ + { + "bbox": [ + 99, + 70, + 494, + 157 + ], + "spans": [ + { + "bbox": [ + 99, + 70, + 494, + 157 + ], + "type": "table", + "html": "
MethodBackboneHHICIsHHIDet
mAPR@150R@100R@50R@20mAPR@150R@100R@50R@20
STTran [7]ResNet-101 [15]3.3171.2962.9142.6722.141.4351.6546.5437.6220.81
HORT [20]ResNet-101 [15]3.7578.5767.7850.3326.961.5452.4746.7336.8920/93
SlowFast [11]SlowFast-R50 [11]5.0081.6674.0052.7326.822.4462.1752.7737.8322.45
ACARN [31]SlowFast-R50 [11]5.4482.8575.2256.5331.772.5362.2552.8437.5021.85
Our baselineSlowFast-R50 [11]7.5285.7878.5259.5332.763.3664.8254.6237.7221.26
SlowFast-R101 [11]8.6787.3580.3560.1829.703.5265.2454.7637.0320.21
ViT-B [44]10.6989.2582.9368.1343.724.9372.2261.9242.9923.89
", + "image_path": "68a55402684c7d70e4f1d9714aef986fc1d90f3ed3cfb96293ed7af852701931.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "lines": [ + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "spans": [ + { + "bbox": [ + 46, + 160, + 546, + 184 + ], + "type": "text", + "content": "Table 6. HHICs and HHIDet results. We test existing video scene graph generation methods (STTran [7] and HORT [20]) and action detection methods (SlowFast [11] and ACARN [31]) on SportsHHI. Our baseline method achieves the best performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 51, + 190, + 281, + 273 + ], + "blocks": [ + { + "bbox": [ + 51, + 190, + 281, + 273 + ], + "lines": [ + { + "bbox": [ + 51, + 190, + 281, + 273 + ], + "spans": [ + { + "bbox": [ + 51, + 190, + 281, + 273 + ], + "type": "image", + "image_path": "47085546cca7a24eaa6893515bd2b11e72b666f25e9c6d61aeed08df406a0a90.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 275, + 286, + 299 + ], + "lines": [ + { + "bbox": [ + 46, + 275, + 286, + 299 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 286, + 299 + ], + "type": "text", + "content": "Figure 7. Error analysis in HHIDet mode. We show the proportion of each error type among false positives." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 45, + 310, + 287, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 310, + 287, + 550 + ], + "spans": [ + { + "bbox": [ + 45, + 310, + 287, + 550 + ], + "type": "text", + "content": "action modeling is very important for interaction recognition on SportsHHI. 2) Dependent on the object detection results. They add the category encoding of the objects to the relation representation, which provides strong prior information. For example, knowing that the subject and object are human and horse respectively, the relation category is very likely to be ride. However, SportsHHI does not have such prior as all subjects and objects are humans. Since video backbones are used to extract the motion features of each person, the performance of the action detection methods like SlowFast [11] and ACARN [31] is relatively better. Our baseline follows these action detectors to adopt a video backbone for motion features and introduce extra relative position and spatio-temporal context modeling between the subject and object person. Our simple baseline achieves leading performance with the same SlowFast-R50 backbone. When using the stronger VideoMAE [44] pretrained ViT-B backbone, the performance is significantly improved, which shows the importance of spatio-temporal representation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 562, + 139, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 139, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 139, + 574 + ], + "type": "text", + "content": "5.4. Error Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": "Following ACT [21] and MultiSports [26], we analyze error types of the false positives in the predictions to better understand the challenges of human-human interaction detection in SportsHHI. We analyze the predictions of the baseline model with a SlowFast-R50 backbone. We classify false positives in the predictions into 9 mutually exclusive error types. " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "E_{R}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": ": a prediction targets a ground-truth instance that has already been matched. " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "E_{C}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": ": a prediction that has an accurate subject and object localization, but wrong interaction class. " + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "inline_equation", + "content": "E_{O}" + }, + { + "bbox": [ + 46, + 582, + 287, + 715 + ], + "type": "text", + "content": ": a prediction that has accurate subject localization and correct interaction class, but inaccurate object lo" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "spans": [ + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": "calization. " + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "inline_equation", + "content": "E_S" + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": ": a prediction that has accurate object localization and correct interaction class, but inaccurate subject localization. " + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "inline_equation", + "content": "E_{S\\& O}" + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "inline_equation", + "content": "E_{O\\& C}" + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "inline_equation", + "content": "E_{S\\& C}" + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "inline_equation", + "content": "E_{S\\& O\\& C}" + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": ": a prediction that is inaccurate in corresponding aspects while acceptable in other aspects (if any). " + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "inline_equation", + "content": "E_N" + }, + { + "bbox": [ + 304, + 192, + 545, + 264 + ], + "type": "text", + "content": ": a prediction that both the subject and object of it have no overlap with any ground truth." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "spans": [ + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "content": "As shown in Figure 7, " + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "inline_equation", + "content": "E_N" + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "content": " is one of the most common error types. This is because SportsHHI is annotated in crowd multi-person scenarios but the interaction instances are relatively sparse due to the characteristic of sports videos and our high-level interaction definition. It is important but difficult to distinguish two people without interaction from real interaction instances. In video action detection [26], localization is relatively accurate and most errors are about classification. However, in interaction detection, the localization of people involved in interaction and the classification of interaction are inseparable. Pure localization errors " + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "inline_equation", + "content": "(E_S" + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "inline_equation", + "content": "E_O" + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "content": ") or pure classification errors " + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "inline_equation", + "content": "(E_C)" + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "content": " are relatively rare. The error types that coexisted with localization error and classification error " + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "inline_equation", + "content": "(E_{O\\& C}, E_{S\\& C}, E_{S\\& O\\& C})" + }, + { + "bbox": [ + 304, + 265, + 546, + 445 + ], + "type": "text", + "content": " account for a relatively large proportion." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 454, + 378, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 454, + 378, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 454, + 378, + 467 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 475, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 643 + ], + "type": "text", + "content": "In this paper, we proposed a new video visual relation detection task with a focus on sports human-human interaction understanding. This task deals with the complex interactions between humans in multi-person scenarios. We build a dataset named SportsHHI based on sports videos for this task. Human boxes and interaction instances are exhaustively annotated on keyframes at 5FPS. To benchmark this, we test several existing methods on SportsHHI and propose a baseline method. We conduct extensive experiments on SportsHHI and reveal the importance of motion information, context information, and position information for interaction recognition. We hope our SportHHI dataset and baseline method can inspire future research on human-human interaction understanding in videos." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 651, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 545, + 711 + ], + "type": "text", + "content": "Acknowledgements. This work is supported by National Key R&D Program of China (No. 2022ZD0160900), National Natural Science Foundation of China (No. 62076119, No. 61921006), and Collaborative Innovation Center of Novel Software Technology and Industrialization." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18544" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 124 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lučić, and Cordelia Schmid. 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In ICCV, pages 13577-13587, 2021. 1" + } + ] + } + ], + "index": 28 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18546" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation/06cbf727-53a9-4ece-bc0b-04416037b63c_content_list.json b/2024/Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation/06cbf727-53a9-4ece-bc0b-04416037b63c_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7854feef00db07c89fd478ad02446b2d671424f8 --- /dev/null +++ b/2024/Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation/06cbf727-53a9-4ece-bc0b-04416037b63c_content_list.json @@ -0,0 +1,1641 @@ +[ + { + "type": "text", + "text": "Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation", + "text_level": 1, + "bbox": [ + 107, + 130, + 861, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dong Zhao $^{1}$ , Shuang Wang $^{1}$ , Qi Zang $^{1}$ , Licheng Jiao $^{1}$ , Nicu Sebe $^{2}$ , Zhun Zhong $^{3,4}$", + "bbox": [ + 140, + 179, + 826, + 199 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 School of Artificial Intelligence, Xidian University, Shaanxi, China", + "bbox": [ + 212, + 196, + 756, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Department of Information Engineering and Computer Science, University of Trento, Italy \n $^{3}$ School of Computer Science and Information Engineering, Hefei University of Technology, China \n $^{4}$ School of Computer Science, University of Nottingham, NG8 1BB Nottingham, UK", + "bbox": [ + 91, + 215, + 875, + 271 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 304, + 312, + 319 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We study source-free unsupervised domain adaptation (SFUDA) for semantic segmentation, which aims to adapt a source-trained model to the target domain without accessing the source data. Many works have been proposed to address this challenging problem, among which uncertainty-based self-training is a predominant approach. However, without comprehensive denoising mechanisms, they still largely fall into biased estimates when dealing with different domains and confirmation bias. In this paper, we observe that pseudo-label noise is mainly contained in unstable samples in which the predictions of most pixels undergo significant variations during self-training. Inspired by this, we propose a novel mechanism to denoise unstable samples with stable ones. Specifically, we introduce the Stable Neighbor Denoising (SND) approach, which effectively discovers highly correlated stable and unstable samples by nearest neighbor retrieval and guides the reliable optimization of unstable samples by bi-level learning. Moreover, we compensate for the stable set by object-level object paste, which can further eliminate the bias caused by less learned classes. Our SND enjoys two advantages. First, SND does not require a specific segmentor structure, endowing its universality. Second, SND simultaneously addresses the issues of class, domain, and confirmation biases during adaptation, ensuring its effectiveness. Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings. In addition, SND can be easily integrated with other approaches, obtaining further improvements. The source code is available at https://github.com/DZhaoXd/SND.", + "bbox": [ + 76, + 329, + 473, + 782 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/edb7565aa5605ad3bc1578fc5aa2da72679318e20e37980d41e27e764eb11ffa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 508, + 319, + 684, + 402 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4a5ef134ce13a6d1a21b2813605aef23d35fbec932584b01a6e6f289625f31c3.jpg", + "image_caption": [ + "Generic Structure Class debiasing Domain debiasing Confirmation debiasing" + ], + "image_footnote": [], + "bbox": [ + 687, + 318, + 885, + 402 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b99ac96548eb2df04817c67e60b6c77026bc4438e4840a00f6255e6b982fac3d.jpg", + "image_caption": [ + "Figure 1. Comparison of advantages of different uncertain estimation strategies in self-training method for SFUDA." + ], + "image_footnote": [], + "bbox": [ + 506, + 407, + 683, + 502 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba99403b1c0cfb6858230c3eb9cb693fa82d98d9248a65104de4a8d2157951f1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 407, + 883, + 502 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 558, + 632, + 571 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Unsupervised domain adaptation (UDA) [47] transfers knowledge of the labeled-rich source domains to the unlabeled target domains, providing an effective solution for semantic segmentation towards lower annotation burden [20] and strong generalization in an open environment [50, 71]. However, the access requirements of source domain data make it impossible to handle scenarios involving privacy, property rights protection, and confidentiality [15]. Thus, this work focuses on a more practical task in semantic segmentation, source-free unsupervised domain adaptation (SFUDA) [38, 75], which aims to adapt a source-trained model to a target domain without accessing the source data.", + "bbox": [ + 496, + 579, + 890, + 761 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Currently, self-training is the mainstream technology to address the SFUDA problem in semantic segmentation, which strives to adapt the model with high-quality pseudo-labels produced by uncertain estimation functions, e.g., probability thresholding [1, 21-23, 35, 73, 85], perturbation consistency [15, 29, 76], or discrepancy classifier voting [5, 29, 56, 65, 82, 89]. Generally, a strong cross-domain self-training method should comprehensively consider the following aspects. Generic structure: It does not require", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "This work was supported in part by the National Natural Science Foundation of China No. 62271377, the Key Research and Development Program of Shannxi Program No. 2021ZDLGY0106 and No. 2022ZDLGY0112, the National Key R&D Program of China under Grant 2021ZD0110400 and 2021ZD0110404 the Key Scientific Technological Innovation Research Project by Ministry of Education, the Joint Funds of the National Natural Science Foundation of China (U22B2054).", + "bbox": [ + 75, + 803, + 468, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\mathbf{\\bar{C}}$ Co-corresponding author.", + "bbox": [ + 76, + 887, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "23416", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "the adoption of a specific structural design (e.g., a specific segmentation head) on the source side; otherwise, it would not be conducive to target deployment [46]. Class debbiasing: the less-learned (hard) categories in the source model should be paid more attention, as the class imbalance problem often exists in segmentation tasks [1, 21, 43, 58, 90]. Domain debiasing: the self-training method needs to maintain the adaptability of distinct domains, since the cross-domain segmentation tasks often face multiple or compound domains, e.g., different weather conditions. Confirmation debiasing: since the running confidence of the model will increase with self-training [3, 86], a strong self-training method should be able to dynamically adjust the uncertain estimation function for addressing the confirmation bias. However, existing self-training methods for SFUDA, lacking a comprehensive denoising mechanism, often fall short in one or more aspects (see Fig. 1(a-c)), leading to inefficiency and under-adaptation.", + "bbox": [ + 76, + 90, + 472, + 363 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our motivation comes from experimental observations of implementing the vanilla self-training [1] on SFUDA. As shown in Fig. 2, for each target training sample at different iterations, we record 1) its mIoU scores with the ground truth (mIoU-axis); and 2) the change degrees between the segmentation results of the current step and the ones obtained by the initial step (stability-axis). Throughout the training process, we observe that samples with high stability consistently maintain high mIoU scores, while those with low stability consistently show low mIoU scores. This indicates that noise in samples with low stability is the main contributor to error accumulation during self-training. Moreover, this issue does not significantly improve as training progresses. This motivates us to identify stable samples (i.e., whose pseudo-label change degree are low) and unstable samples to address the above issue.", + "bbox": [ + 76, + 367, + 472, + 609 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose a novel denoising approach, called Stable Neighbor Denoising (SND), which can effectively discover highly correlated stable and unstable samples by nearest neighbor retrieval and denoise unstable samples with the guidance of the stable ones by bi-level optimization. Specifically, we resort to bi-level optimization [48, 70] to establish the connection between the stable and unstable sets and guide the evolution direction of unstable samples. The principle here is that if the model is trained on unstable samples with correct pseudo-labels, the loss on stable samples will be also minimized. Importantly, by the analysis of the gradient of bi-level optimization (detailed in Section 3.2), we find that matching unbiased and highly correlated stable samples for unstable samples is the key to achieving this principle. This is because the loss gradients of biased/low-correlation samples often have non-intersecting/different optimization directions, leading to bias in bi-level optimization for denoising. To tackle this problem, we propose retrieving stable", + "bbox": [ + 76, + 613, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3b55355efb89e8d98903e18d38d2c5d77a99a4664f739e1f24363c09db609e9a.jpg", + "image_caption": [ + "Figure 2. The plot of the mIoU scores versus stability for each target sample throughout training. Stability is calculated by the difference between the initial and the current segmentation. It shows a positive correlation between mIoU (pseudo-label quality) and stability. This observation holds during the whole training process. Experiments are from the GTA5 $\\rightarrow$ Cityscapes SFUDA task." + ], + "image_footnote": [], + "bbox": [ + 550, + 95, + 857, + 287 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "neighbors by image style and spatial layout factors to eliminate the domain bias in one-step bi-level denoising optimization. In addition, we propose refining the stable samples into two sets: a whole-stable set and a category-stable set. Then, we compensate for stable neighbors using diverse object-level pasting to eliminate category bias. In this way, bi-level optimization can efficiently denoise unstable samples with stable ones under the principle.", + "bbox": [ + 496, + 393, + 893, + 516 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Through the above techniques, the proposed SND shows superiority over previous works as follows. 1 Generic structure: SND does not require a specific network structure on both the source and target sides, endowing its universality. 2 Class debiasing: SND constructs stable neighbors with balanced categories and uses them to guide the adaptation of less-learned categories. 3 Domain debiasing: SND denoises distinct domains by retrieving neighbors with similar domain factors and can handle complex compound domain scenarios (See Table. 3). 4 Confirmation debiasing: SND designs a stability-oriented denoising mechanism that filters out noisy pseudo-labels without the need for probability or prototype distance, thereby mitigating confirmation bias (See Fig. 6). Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings.", + "bbox": [ + 496, + 517, + 895, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 771, + 640, + 787 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Unsupervised Domain Adaptation. Domain adaptive semantic segmentation has achieved significant adaptability improvements in multiple adaptation scenarios such as synthesis-to-reality [10, 21-23, 56], cross-weather [31, 53, 54], multi-source [18, 69], etc. Overall, the current work mainly realizes cross-domain transfer from the following aspects. 1) Use the source domain data to learn a gener", + "bbox": [ + 496, + 795, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "23417", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "alized representation [8]. This line of work employs data augmentation (e.g. copy-paste [58], random masking [23]) and domain randomization (e.g. expanding image styles [12, 24, 30, 56, 81, 88]) to expand the representation space of source domain models. 2) Align the source and target domains. The following works adopt a variety of domain alignment strategies (e.g. adversarial training or statistical matching) in a variety of alignment spaces (e.g. pixels space [7, 20], Fourier space [77], features space [49, 63, 66], output space [41, 59, 61], etc.), reducing the statistical difference of both domains. 3) Target characteristic mining. Most of such works use augmentation consistency [2, 11, 44, 82] and pseudo-labels [6, 81] to further improve the model's adaptive ability, e.g. tail category and local distribution.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Source-Free Unsupervised Domain Adaptation (SFUDA). In classification tasks, prior SFUDA works propose implicit distribution alignment [14, 37], instance contrast [83], and model perturbation [27] to align domains without source data. In segmentation tasks, the above idea is hard to adopt due to complex semantic feature spaces. Most SFUDA works for segmentation adopt self-training, which filters and retransmits the well-adapted pixels or regions through probability thresholds [85], data [25] or model discrepancy [15, 29], but they often fall into various biases.", + "bbox": [ + 75, + 301, + 472, + 453 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Noisy Label Learning. SFUDA can be viewed as a noisy label learning problem [74, 78, 87]. Currently, noisy label learning is mostly discussed on classification tasks. The mainstream technologies include robust loss design [42, 67, 84], self-label correction [9, 33], prototype denoising [17], meta-learning based denoising [48, 70], etc. Most of those methods are designed for instance-level and are not suitable for pixel-level segmentation tasks. In particular, the prototype [34, 82] and meta-learning [16] based denoising methods have been applied to UDA segmentation tasks, but their dependence on source data limits on SFUDA.", + "bbox": [ + 75, + 454, + 472, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 627, + 169, + 643 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminary. In the setting of source-free unsupervised domain adaptation (SFUDA), we are given a segmentation model $\\mathcal{H}$ with parameter $\\Theta$ pre-trained on the labeled source dataset $\\mathcal{D}_s = \\{(x_s^i,y_s^i)\\}_{i}^{N_s}$ , and the unlabeled target dataset $\\mathcal{D}_t = \\{x_t^i\\}_i^{N_t}$ . The goal is to adapt the network $\\mathcal{H}$ and achieve low risk on the target dataset without accessing the source data $\\mathcal{D}_s$ . To achieve this goal, most works mainly conduct self-training to optimize the $\\mathcal{H}$ as follows,", + "bbox": [ + 75, + 648, + 468, + 772 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta^ {\\star} = \\underset {\\Theta} {\\arg \\min } \\sum_ {i} ^ {N _ {t}} \\sum_ {l} ^ {H \\times W} \\omega^ {(i, l)} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta\\right), \\hat {y} _ {t} ^ {(i, l)} \\right], \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 777, + 468, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathcal{L}$ is the cross-entropy loss and $\\hat{y}_t$ is the pseudo-label. $\\omega$ is a weighting factor calculated by uncertainty, in which the lower the uncertainty, the closer the value is to 0. This paper proposes stable neighbor denoising techniques to estimate $\\omega$ in an unbiased way.", + "bbox": [ + 75, + 824, + 468, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Division of Stable & Unstable Sets", + "text_level": 1, + "bbox": [ + 498, + 90, + 799, + 106 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following the observation in Fig 2, we aim to divide target domain samples into stable and unstable sets by the change degree (also called evolution stability) of their segmentation results during the vanilla self-training [1]. Formally, for each target sample $x_{t}^{i}$ , we define its evolution stability (ES) at $\\tau$ -th iteration as follow,", + "bbox": [ + 496, + 109, + 890, + 200 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {E S} ^ {i, \\tau} = \\sum_ {l} ^ {H \\times W} \\operatorname {S I M} \\left[ \\mathcal {H} \\left(x _ {t} ^ {i, l} \\mid \\Theta^ {0}\\right), \\mathcal {H} \\left(x _ {t} ^ {i, l} \\mid \\Theta^ {\\tau}\\right) \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 205, + 890, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathrm{SIM}[\\cdot ]$ is the cosine similarity. $\\Theta^{\\tau}$ represent the parameters of the model at $\\tau$ -th iteration during self-training. The larger the ES value of the sample, the more stable it is. As ES may fluctuate in different degrees of domain shift tasks, it is hard to set a suitable threshold to determine whether it is stable. Instead, we take the top- $k\\%$ ranked highly stable samples to divide the $\\mathcal{D}_t$ into the stable set $\\mathcal{D}_{se}$ and the unstable set $\\mathcal{D}_{ue}$ as follows,", + "bbox": [ + 496, + 252, + 890, + 375 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {s e} = \\left\\{\\left(x _ {t} ^ {i}, \\bar {y} ^ {i}\\right) \\mid x _ {t} ^ {i} \\in \\mathcal {D} _ {t}, \\mathrm {E S} ^ {i, \\tau} \\in \\top_ {k} \\right\\}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 381, + 890, + 400 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {D} _ {u e} = \\left\\{x _ {t} ^ {i} \\mid x _ {t} ^ {i} \\in \\mathcal {D} _ {t}, \\mathrm {E S} ^ {i, \\tau} \\notin \\top_ {k} \\right\\}. \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 407, + 890, + 425 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Next, the main challenge is how to utilize $\\mathcal{D}_{se}$ to assist in predicting unbiased $\\omega$ of $\\mathcal{D}_{ue}$ .", + "bbox": [ + 496, + 430, + 890, + 460 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Build Relations between Stable & Unstable Sets", + "text_level": 1, + "bbox": [ + 498, + 468, + 890, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An intuitive way is to exploit the cross-image feature similarity [68] of samples in the two sets to build relations. However, we find that the un-adapted source-trained model fails to capture this cross-image feature similarity because the representation ability of deep networks is always insufficient under the domain shift (see Table 3). Instead, we propose to build relations between the two sets from an optimization perspective and utilize bi-level learning [48, 70] to achieve this. In a nutshell, we formulate each optimization step as the inner- and outer loops, in which the former learns uncertainty parameter $\\omega$ for the latter.", + "bbox": [ + 496, + 491, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, for $m$ -th optimization step, in the inner loop, the estimizable $\\omega$ is first initialized as $\\omega_0$ and the model with parameters $\\Theta^m$ is optimized on unstable samples by Eq.1,", + "bbox": [ + 496, + 657, + 890, + 718 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta_ {\\text {i n n e r}} ^ {m + 1} = \\arg \\min _ {\\Theta} \\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\sum_ {l} ^ {H \\times W} \\omega_ {0} ^ {i} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta^ {m}\\right), \\hat {y} _ {t} ^ {(i, l)} \\right]. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 720, + 890, + 775 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "$\\omega_0^i$ is simply set to be an all-one matrix. For optimization, Eq. 5 can be approximated by one- or multi-step gradient calculation, i.e., $\\Theta_{inner}^{m + 1} = \\Theta^m - \\alpha \\sum_{x_t \\in \\mathcal{D}_{ue}} \\omega_0^i \\frac{\\partial \\mathcal{L}(x_t^i | \\Theta^m)}{\\partial \\Theta} |_{\\Theta^m}$ , where $\\alpha$ is the inner-loop learning rate. It can be seen that $\\omega$ is differentiable relative to $\\Theta_{inner}^{m + 1}$ . Subsequently, we optimize the $\\omega$ by enforcing the optimized model with parameters $\\Theta_{inner}^{m + 1}$ also achieves low risk on the stable samples in $\\mathcal{D}_{se}$ ,", + "bbox": [ + 496, + 775, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "23418", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f6d1bc28f2488502568d9c85120bc8979c0d392aee47b2db8d6502952b9aa5ff.jpg", + "image_caption": [ + "Figure 3. The pipeline of the proposed Stable Neighbor Denoising (SND). It is formed by the student-teacher model [57]. In each optimization, SND performs the inner and outer optimizations sequentially. In the inner loop (red line), SND utilizes the style $\\mathcal{Q}_{\\text{style}}$ and the layout $\\mathcal{Q}_{\\text{layout}}$ factors to retrieve stable neighbors for unstable samples and then performs category compensation to reduce category bias. Thereafter, SND executes Eq. 8 using the teacher model to obtain the unbiased uncertainty map $\\omega_{\\star}$ and initial pseudo-label $\\hat{y}_t$ . In the outer loop (black line), SND performs Eq. 7 to optimize the student model. EMA denotes the Exponential Moving Average." + ], + "image_footnote": [], + "bbox": [ + 112, + 88, + 857, + 286 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\omega_ {\\star} = \\arg \\min _ {\\omega} \\sum_ {\\left(x _ {t}, \\bar {y} _ {t}\\right) \\in \\mathcal {D} _ {s e}} \\sum_ {l} ^ {H \\times W} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta_ {\\text {i n n e r}} ^ {m + 1}\\right), \\bar {y} _ {t} ^ {(i, l)} \\right]. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 377, + 468, + 434 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This object is driven by the following principle: $\\omega$ is optimized to increase/decrease the weight of these regions so that the model optimized on the unstable set samples has a small/large loss on the stable set. In this way, we establish an implicit relation between stable and unstable sets, because optimizing noisy regions of unstable samples has misleading optimization goals. Finally, in the outer loop, the model can be optimized by the learned $\\omega_{\\star}$ ,", + "bbox": [ + 75, + 435, + 470, + 556 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Theta_ {\\text {o u t e r}} ^ {m + 1} = \\arg \\min _ {\\Theta} \\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\sum_ {l} ^ {H \\times W} \\omega_ {\\star} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta^ {m}\\right), \\hat {y} _ {t} ^ {(i, l)} \\right]. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 559, + 468, + 614 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Problem Discussion. One important question in the above learning strategy is, does this principle work by taking arbitrary samples from the stable and unstable set to optimize? We present further analysis of the optimization of $\\omega$ to answer this question. For optimization, Eq. 6 is performed by gradient descent as follows,", + "bbox": [ + 75, + 614, + 468, + 698 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\omega_ {\\star} = \\omega_ {0} - \\beta \\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} (x _ {t} ^ {i} | \\Theta_ {i n n e r} ^ {m + 1})}{\\partial \\omega} | _ {\\omega_ {0}} \\\\ = \\omega_ {0} - \\beta \\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} (x _ {t} ^ {i} | \\Theta_ {i n n e r} ^ {m + 1})}{\\partial \\Theta} | _ {\\Theta_ {i n n e r} ^ {m + 1}} \\cdot \\frac {\\partial \\Theta_ {i n n e r} ^ {m + 1}}{\\partial \\omega} | _ {\\omega_ {0}} \\\\ = \\omega_ {0} + \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 705, + 439, + 797 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\beta \\underbrace {\\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} \\left(x _ {t} ^ {i} \\mid \\Theta_ {i n n e r} ^ {m + 1}\\right)}{\\partial \\Theta} \\mid_ {\\Theta_ {i n n e r} ^ {m + 1}}} _ {\\text {L o s s g r a d i e n t o f s t a b l e s e t}} \\cdot \\alpha \\underbrace {\\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\frac {\\partial \\mathcal {L} \\left(x _ {t} ^ {i} \\mid \\Theta^ {m}\\right)}{\\partial \\Theta} \\mid_ {\\Theta^ {m}}} _ {\\text {L o s s g r a d i e n t o f u n s t a b l e s e t}}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 801, + 472, + 875 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thus, when the continuous loss gradient on the stable", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/45cf9f18bf32ac3ff449618e1033105da3e51defb50a2b47e5b84bbd264e1a18.jpg", + "image_caption": [ + "Figure 4. Loss gradient directions in bi-level optimization. It is shown by computing the average gradient direction of different sets of classifier weights (ASPP) using the true labels. The black lines are inner-loop and the other colored lines are outer-loop." + ], + "image_footnote": [], + "bbox": [ + 506, + 381, + 687, + 479 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7bb049772898497df7ef616221865fd5394256b5ce19483c5f8825a36ef5518c.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 696, + 386, + 890, + 481 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "samples in $\\mathcal{D}_{se}$ has a similar direction to that on the unstable samples in $\\mathcal{D}_{ue}$ , the $\\omega$ value of the corresponding area of the unstable samples will increase, and vice versa. This indicates that optimizing noisy pseudo-labels would deviate from the optimization goal of stable samples and thus explains why noise in pseudo-labels can be estimated. Moreover, Eq. 8 also gives us the answer that arbitrarily selecting samples from the two sets will induce bias in the estimation on $\\omega$ , especially for samples with low correlation. This is because heterogeneous data always enjoy different optimal weight spaces [26], which will mislead the estimation of $\\omega$ . We provide below a detailed analysis.", + "bbox": [ + 496, + 564, + 892, + 744 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Reason & Analysis (1) We find that samples from both sets suffering large domain shifts tend to have large differences in optimization directions, which will cause the optimization of $\\omega$ in Eq. 8 to be weakened by domain differences rather than the pseudo-label noise. As shown in Fig. 4, despite using real labels in bi-level optimization, domain factors (e.g. the spatial layout or image style) will still bias the optimization direction. (2) We find that samples from both sets with inconsistent category distribution cannot produce intersecting gradients in Eq. 8, causing the corresponding", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "23419", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "gradient of $\\omega$ to be 0 as well. Moreover, in actual optimization, it is unacceptable to use massive stable samples to perform multi-step gradient descent for Eq. 6 due to huge computational and memory overhead. As a result, stable and unstable samples always suffer from mismatched class distributions, resulting in no gradient for missing classes.", + "bbox": [ + 75, + 90, + 468, + 181 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In conclusion, it is reasonable to argue that matching highly correlated samples from two sets is critical for unbiased uncertain estimation.", + "bbox": [ + 75, + 181, + 468, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Stable Neighbor Denoising", + "text_level": 1, + "bbox": [ + 76, + 236, + 318, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We propose to query the stable neighbor with similar domain properties for each unstable sample and compensate for missing categories for the neighbor, resulting in an unbiased estimate of $\\omega$ . In the querying part, following the observation in Eq. 4, we specify domain factors, namely image style and spatial layout, as the proxy for querying.", + "bbox": [ + 75, + 258, + 468, + 349 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Specifically, for image style, a series of works [36, 77] pointed out that the Fourier amplitude spectrum has a strong correlation with the image style. Thus, we adopt the flattened vector of the low-frequency Fourier amplitude spectrum as the style proxy, i.e., $\\mathcal{Q}_{style} = \\text{Low}(\\mathcal{A}(\\mathcal{F}(x))$ . For spatial layout, [32] shows that the row-wise and column-wise label statistical histogram vectors can represent the spatial distribution. Thus, we use the pseudolabels of both sets samples for computation as an alternative, i.e., $\\mathcal{Q}_{layout} = [\\mathcal{Q}_{layout}^{row}, \\mathcal{Q}_{layout}^{col}]$ , where $\\mathcal{Q}_{layout}^{row,c} = \\frac{\\sum_{row} \\arg\\max[\\mathcal{H}(x_t^l|\\Theta^m)] = c}{\\sum_{row} \\sum_{column} \\arg\\max[\\mathcal{H}(x_t^l|\\Theta^m)] = c}$ , $c \\in [0,1,\\dots C]$ , and $C$ is the number of categories. With $\\mathcal{Q}_{style}$ and $\\mathcal{Q}_{layout}$ , we can retrieve the nearest stable neighbor $x_{neib}^i \\in \\mathcal{D}_{se}$ for the unstable sample $x^i \\in \\mathcal{D}_{ue}$ via the similarity between the proxy vectors.", + "bbox": [ + 75, + 351, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The retrieved domain-associated neighbors may still suffer from missing categories, leading to problems described in the analysis (2). Thus, we further propose to borrow the missing class objects from other stable samples and paste them to the neighbor as compensation. However, the tail categories in the stable set $\\mathcal{D}_{se}$ may be scarce, making the objects to be copied far less abundant. To enrich the diversity of tail categories, we additionally maintain top- $k$ ranked stable category sets $\\mathcal{D}_{sec}^{c} = \\{(x^{i},\\bar{y}^{i})|x^{i}\\in \\mathcal{D}_{t},\\mathrm{ES}^{i,m,c}\\in \\top_{k}\\}$ for each category $c$ as the supplement. We name the $\\mathcal{D}_{se}$ as a stable whole set and the $\\mathcal{D}_{sec}^{c}$ as a stable category set for distinction. Subsequently, the nearest stable neighbor $x_{neib}^{i}\\in \\mathcal{D}_{se}$ can be compensated as follows,", + "bbox": [ + 75, + 585, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {x} _ {n e i b} ^ {i}, \\bar {y} _ {n e i b} ^ {i} = \\mathrm {C P} \\left[ \\left(x _ {n e i b} ^ {i}, \\bar {y} _ {n e i b} ^ {i}\\right), \\left(x _ {m i x}, \\bar {y} _ {m i x}\\right) \\in \\mathcal {D} _ {\\text {s e c}} ^ {c} \\right], \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 792, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathrm{CP}[\\cdot, \\cdot]$ is the copy-paste operation [58] that copies objects from the latter to the former.", + "bbox": [ + 75, + 824, + 468, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through these efforts, we can use unbiased stable neighbors $\\bar{x}_{neib}^{i}$ for Eq. 6 to denoise unstable samples in an unbiased way. Fig. 3 shows the pipeline of the proposed SND", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1 The training step of SND.", + "text_level": 1, + "bbox": [ + 500, + 90, + 761, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Input: Target data $\\mathcal{D}_t$ , source-trained segmentation network $\\mathcal{H}$ with parameter $\\Theta$ , max iteration $M$ .", + "bbox": [ + 500, + 108, + 890, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: Well-adapted segmentation model $\\mathcal{H}$", + "bbox": [ + 506, + 137, + 816, + 152 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Split $\\mathcal{D}_t$ into $\\mathcal{D}_{se}$ and $\\mathcal{D}_{ue}$ via vanilla self-training by Eq. 2, Eq. 3 and Eq. 4", + "2: Initialize the teacher student model as $\\Theta_{tea}$ and $\\Theta_{stu}$", + "3: for $m \\gets 0$ to $M - 1$ do", + "4: Sample batch samples $\\{x_{t}^{i}\\}_{i = 1}^{B}\\in \\mathcal{D}_{ue}$", + "5: Inner loop Optimization:", + "6: Retrieve nearest stable neighbor $(x_{neib}^{i},y_{neib}^{i})\\in$ $\\mathcal{D}_{se}$ for each unstable sample $x_{t}^{i}$ by $\\mathcal{Q}_{style}$ and $\\mathcal{Q}_{layout}$", + "7: Compensate $(x_{neib}^{i},y_{neib}^{i})$ by Eq. 9", + "8: Optimize $\\Theta_{tea}$ by Eq. 8 to obtain the uncertainty $\\omega_{\\star}$ and pseudo-label $\\hat{y}_t$", + "9: Outer loop Optimization:", + "10: Update $\\Theta_{stu}$ by Eq. 7 with $\\omega_{\\star}$ and $\\hat{y}_t$", + "11: Update $\\Theta_{tea}$ by exponential moving average", + "12: end for", + "13: Return Adapted model $\\mathcal{H}$ with $\\Theta_{tea}$ ." + ], + "bbox": [ + 506, + 154, + 890, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "and the corresponding is shown in Algorithm 1. Algorithm 1 implements our SND within the student-teacher framework [57] to align with existing methods. See detailed explanations and ablation in the Appendix.", + "bbox": [ + 498, + 430, + 890, + 491 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 505, + 632, + 522 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets & Setup", + "text_level": 1, + "bbox": [ + 500, + 530, + 668, + 546 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. GTA5 [51] dataset provides 24,999 game-rendering urban scene images with a resolution of $1914 \\times 1024$ . SYNTHIA [52] dataset includes 9,400 virtual images with a resolution of $1280 \\times 760$ . We use 19 and 16 common categories in these two datasets respectively as source data. Cityscapes [13] dataset contains 3,975 real urban scene images from 50 different cities in primarily Germany, with a resolution of $2048 \\times 1024$ . ACDC [55] is the real-world dataset on adverse visual conditions, which comprises diverse weather scene images with a resolution of $1280 \\times 720$ . BDD100K [80] is a compound real-world dataset consists of 8000 training images and 1000 verification images with a resolution of $1280 \\times 720$ .", + "bbox": [ + 496, + 551, + 890, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setup. We conduct experiments using the Convolutional and Transformer structures respectively. For Convolutional structures, we adopt the Deeplab-v2 [4] with ResNet-101 [19] as the segmentation model. SGD optimizers are used for both inner and outer optimization, where the outer optimizer is set an initial learning rate $(\\beta)$ to $2.5 \\times 10^{-4}$ with weight decay 0.01 while the inner optimizer is set a fixed learning rate $(\\alpha)$ of 0.01. The batch size is set as 4, and the framework is trained for 20,000 iterations on all SFUDA tasks. For Transformer structures, we adopt the SegFormer", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "23420", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/5039d0c6609374177ee1b6f78e2151c099a0471d51ecc7073ca187c6614cea75.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
roadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
Source-free Synthetic-to-Real: GTA → Cityscapes (Val.)
HCL (NIPS'21) [25]92.654.682.833.226.239.838.131.984.538.685.361.330.285.433.141.614.427.344.049.7
SFDASEG (ICCV'21)† [29]91.753.486.137.632.137.438.235.686.748.589.962.634.387.251.050.84.242.753.953.4
DTST (CVPR'23) [85]93.557.684.736.525.233.444.736.786.842.881.362.337.288.148.750.635.548.359.155.4
CrossMatch(ICCV'23)† [79]95.167.887.751.341.536.347.451.387.847.887.36734.287.54151.8042.646.456.4
CROTS(IJV'24) [40]9252.485.937.335.834.642.238.486.945.691.165.136.187.341.651.1041.456.253.7
SND (Ours)93.054.084.635.630.331.041.941.687.644.686.462.638.587.548.742.936.649.558.755.6
DTST + SND (Ours)93.960.086.738.635.937.543.448.387.644.690.165.339.988.554.944.433.149.960.958.1
Source-free Synthetic-to-Real: Synthia → Cityscapes (Val.)
HCL (NIPS'21) [25]86.738.182.7100.630.325.429.782.8-85.961.924.884.5-38.9-22.637.946.4
SFDASEG (ICCV'21)† [29]90.550.081.613.32.834.725.733.183.8-89.266.034.985.3-53.4-46.146.652.3
DTST (CVPR'23) [85]88.945.883.313.70.832.731.620.885.7-82.564.427.888.1-50.9-37.657.350.7
CrossMatch(ICCV'23)† [79]91.555.585.434.48.340.840.044.486.6-84.362.422.088.3-60.0-40.645.655.6
CROTS(IJV'24) [40]89.441.682.715.11.234.733.725.783.7-87.966.634.685.4-45.9-43.549.651.3
SND (Ours)88.147.480.128.132.234.933.641.383.3-86.759.927.286.7-48.1-36.252.554.1
DTST + SND (Ours)88.743.783.632.126.032.438.044.787.2-87.962.235.587.4-40.4-46.957.255.9
Source-free clean-Adverse-Weather: Cityscapes → ACDC (Test)
URMDA (CVPR'2021)† [15]74.125.643.519.524.325.948.643.266.227.579.845.020.970.736.835.932.727.729.940.9
HCL (NIPS'2021) [25]72.624.768.521.419.431.051.846.571.828.581.243.821.576.842.844.436.130.124.044.0
SFDASEG (ICCV'21)† [29]73.529.070.719.721.936.153.251.472.031.185.341.526.276.441.946.139.833.332.046.4
DTST (CVPR'2023) [85]73.428.569.716.720.532.850.251.171.530.885.050.822.371.640.341.735.631.938.245.4
SND (Ours)74.827.669.323.626.336.552.854.675.535.084.852.525.578.844.948.137.631.134.948.1
DTST + SND (Ours)73.429.470.922.025.138.554.655.577.735.286.653.427.480.945.649.041.036.740.449.6
Source-free Open-compound: GTA → BDD100k (Test)
URMDA (CVPR'21)† [15]83.938.378.79.67.329.111.14.970.7-74.253.815.081.2-35.0-22.830.540.4
HCL (NIPS'21) [25]88.639.281.08.27.928.411.45.771.0-77.254.216.081.8-41.4-22.631.441.6
SFDASEG (ICCV'21)† [29]87.940.280.613.18.230.222.817.171.1-78.151.427.980.2-43.7-30.342.345.3
DTST (CVPR'23) [85]83.139.964.98.914.529.527.027.171.9-83.252.931.374.7-41.1-30.042.145.2
SND (Ours)84.142.674.115.221.231.131.025.570.4-83.952.833.979.9-39.1-37.541.947.8
SND + DTST (Ours)86.544.477.321.322.932.433.027.469.6-86.754.334.382.1-39.4-38.342.449.5
", + "bbox": [ + 80, + 88, + 890, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "[72] with MiT-B5 [72]. AdamW [39] and Adam [28] optimizer are used for inner and outer optimization respectively, where the outer optimizer is set an initial learning rate $(\\beta) 6 \\times 10^{-5}$ with weight decay 0.01, while the inner optimizer is set a fixed learning rate $(\\alpha)$ of 0.01. The batch size is set as 2 and the model is trained for 20,000 iterations on all tasks. For set dividing, we use the stability (ES) evaluated at $10k(\\tau)$ iterations and regard the top $5\\%$ ( $k\\%$ ) ranked stable samples as the stable set for all adaptation tasks.", + "bbox": [ + 75, + 546, + 468, + 683 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-the-art Alternatives", + "text_level": 1, + "bbox": [ + 76, + 695, + 467, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Performance Comparison on SFUDA. We compare our methods with the state-of-the-art approaches on source-free unsupervised domain adaptive semantic segmentation (SFUDA), including adapting to single and compound target domains. Table 1 shows that the proposed SND achieves the best performance on all SFUDA tasks. Moreover, SND can be combined with other method (DTST [85]) and achieves further significant improvements. In the two synthetic-to-real SFUDA adaptation tasks, our approach (SND+DTST) surpasses the second-highest methods by $2.7\\%$ and $3.1\\%$ , respectively. On real-to-real adaptation tasks, i.e., ACDC with various weather conditions, our ap", + "bbox": [ + 75, + 719, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/88594d1b4321bdf64e74dadb45ec1dc45792f837e5e590efad9a44ff03cb4d16.jpg", + "table_caption": [ + "Table 1. Comparison of SND with state-of-the-art works on the tasks of source-free domain adaptation in semantic segmentation. The model is deeplab-v2 with ResNet101. The report metric is IoU(\\%). $\\dagger$ denotes using the specific network on the source side, e.g., SFDASEG using multiple heads, CrossMatch using two segmentation models with depth estimation. DTST+SND means using the minority class resampling strategy in DTST [85], as minority class adaptation is very challenging in source-free UDA." + ], + "table_footnote": [], + "table_body": "
Continual source-free adaptation: Cityscapes→ACDC
Timet →
FogNightRainSnowmIoU
Source model [72]69.140.359.757.856.7
TENT * [62]68.536.359.954.754.9
CoTTA * [64]70.441.663.960.859.2
HCL [25]70.039.963.761.258.7
SFDASEG † [29]70.142.162.461.859.1
SND72.143.166.365.661.8
", + "bbox": [ + 524, + 544, + 867, + 670 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Comparison on the tasks of continual source-free domain adaptation semantic segmentation. The segmentation model is SegFormer with MiT-B5 as the backbone. *means we use the target domain data for multiple round adaptations rather than one round in the original paper.", + "bbox": [ + 496, + 672, + 890, + 742 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "proach (SND+DTST) still maintains excellent performance, improving the performance of the current best method (SF-DASEG [29]) by $3.2\\%$ . When adapted to the more challenging open-compound domain BDD100k, the proposed method (SND+DTST) achieves a large performance gain, surpassing the second-highest method by $4.2\\%$ . The performance under various conditions proves that our method can effectively cope with the pseudo-label noise in complex environments, and alleviate the bias problem in SFUDA tasks.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "23421", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/95993d7e325adc994325bc4893a640feb35dd2c94314d8c9bf9d94019e092e58.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
UnweightedPE. [62]MCC. [89]DAC. [29]MPC. [15]PD. [82]CIA. [68]SND
GTA → Cityscapes49.650.5 (+0.9)52.1 (+2.5)51.7 (+2.1)51.6 (+2.0)50.9 (+1.3)49.8 (+0.2)55.6 (+6.0)
Synthia → Cityscapes48.249.5 (+1.3)52.9 (+2.7)49.4 (+1.2)51.5 (+3.3)49.7 (+1.5)47.2 (-1.0)54.1 (+5.9)
Cityscapes → ACDC43.141.3 (-1.8)45.1 (+2.0)42.9 (-0.3)43.0 (-0.1)39.1 (-4.0)39.2 (-3.9)48.1 (+5.0)
GTA → BDD100k42.141.5 (-0.6)44.8 (+2.7)41.2 (-0.9)42.9 (+0.8)40.5 (-1.6)37.1 (-5.0)47.8 (+5.7)
", + "bbox": [ + 140, + 88, + 828, + 159 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5316279f2700925da58d212ad764bee515ff13d99e131de2c36e01b35fddf3a7.jpg", + "table_caption": [ + "Table 3. Ablation experiments on uncertainty estimation for source-free cross-domain segmentation tasks. We compared the following uncertainty estimation methods, probability entropy (PE.) [62], multi-classifier consistency (MCC.) [89], data augmentation consistency (DAC.) [29], model perturbation consistency (MPC.) [15], prototype distance (PD.) [82], cross-image association [68](CIA.). 'Unweighted' means original pseudo labels." + ], + "table_footnote": [], + "table_body": "
Division metricGTA → CityscapesCityscapes → ACDC
Image-level entropy [45]52.945.1
Patch-level entropy [59]51.743.6
Image-level loss [74]52.744.1
Domain distance [60]51.642.4
Stability55.648.1
", + "bbox": [ + 91, + 233, + 455, + 316 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7b3db39005eb151c7d47188f919e7f78cb0cbe18f4df1204db9398de0b18ca6f.jpg", + "table_caption": [ + "Table 4. Comparison of the subset division metrics." + ], + "table_footnote": [], + "table_body": "
QueryGTA → CityscapesCityscapes → ACDC
Random54.244.7
Qlayout55.344.9
Qstyle55.147.5
Qlayout + Qstyle55.648.1
", + "bbox": [ + 109, + 337, + 434, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance Comparison on Continual SFUDA. As real-world machine systems always operate in nonstationary environments, we also verify the effectiveness of our approach in the continual adaptation setting. In Table 2, our method maintains good performance, with an average adaptability increase of $5.1\\%$ in multiple domains under continual settings, showing obvious advantages compared with other methods. It is verified that our method can better adapt to multi-domain environments and alleviate model degradation caused by domain bias and confirmation bias.", + "bbox": [ + 75, + 448, + 468, + 599 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 606, + 230, + 622 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of denoising module. In Table 3, we ablate the denoising part, i.e., SND, and compare it with alternatives. In two synthetic-to-real SFUDA experiments, SND achieves a performance improvement of nearly $6\\%$ , showing optimal competitiveness than other alternatives. In multiple and compound adaptation tasks, SND produces a performance improvement of nearly $5\\%$ . On difficult transfer tasks, SND exhibits stable cross-domain adaptability, whereas other alternatives suffer from severe performance degradation. The effectiveness of SND is mainly contributed to its accurate estimation of uncertain and comprehensive denoising capabilities.", + "bbox": [ + 75, + 628, + 467, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of the Stability Metric. In Table 4, we compare the proposed stability with other adaptability metrics for subset division, including regional entropy [45,59], image-level loss [74], and domain distance [60]. Denoising using stability metrics shows obvious advantages on two adaptive tasks, with gains increased by $2.7\\%$ and $3.0\\%$ com", + "bbox": [ + 75, + 810, + 467, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/435641e02607bbbc8ea291039e4f4a6460ad23e53c2980a89b9b103478544519.jpg", + "table_caption": [ + "Table 5. Ablation study of querying stable neighbor strategies. Random means randomly selecting stable samples from $\\mathcal{D}_{se}$ ." + ], + "table_footnote": [], + "table_body": "
Category compensationGTA → CityscapesCityscapes → ACDC
None53.046.3
Dse54.247.1
Dsec55.648.1
", + "bbox": [ + 513, + 233, + 879, + 292 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Variants of category compensation methods. 'None' means not applying compensation. $\\mathcal{D}_{se}$ and $\\mathcal{D}_{sec}$ means we select samples from $\\mathcal{D}_{se}$ and $\\mathcal{D}_{sec}$ for compensation.", + "bbox": [ + 498, + 294, + 890, + 337 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pared to the second competitor. We think it contributes to the ability to screen more reliable samples to provide effective support for denoising.", + "bbox": [ + 498, + 354, + 890, + 398 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Query Methods. In Table 5, we verify the impact of different retrieval factors on adaptability. It shows that gradually adding domain-related factors for retrieving stable neighbors can improve adaptability. In special, on complex compound domain adaptation task, Cityscapes $\\rightarrow$ ACDC, retrieving by domain factors shows greater improvements. This further verifies matching highly correlated neighbors is crucial for bi-level optimization.", + "bbox": [ + 498, + 400, + 892, + 520 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effectiveness of Category Compensation. In Table 6, we verify the impact of category compensation on adaptability. Using the stable set $\\mathcal{D}_{se}$ as the copy object for compensation improves performance by $1.2\\%$ and $0.8\\%$ on two tasks respectively, verifying the impact of missing categories on denoising. Furthermore, adding category stable sets as replication objects can improve the performance by $1.4\\%$ and $1.0\\%$ , showing that diversity compensation is more conducive to reducing the bias of bi-level optimization.", + "bbox": [ + 498, + 521, + 890, + 657 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Qualitative assessment", + "text_level": 1, + "bbox": [ + 500, + 666, + 710, + 681 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Visualization of the Learned Uncertainty Map. Fig. 5 presents the learned uncertain map $\\omega$ on two SFUDA tasks. It can be seen that the uncertainty maps from probability entropy [61] and multi-classifier voting [56,82] contain a large amount of noise. Moreover, in the harder open-compound task Cityscapes $\\rightarrow$ ACDC, the estimation bias of their methods is more obvious in difficult domain data, which will be a predisposing factor for error accumulation. In contrast, SND alleviates bias estimation and presents more reasonable uncertainty maps for different categories and domains. Moreover, our SND even can give accurate estimation against noise at the segmentation edges.", + "bbox": [ + 496, + 688, + 890, + 869 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Denoising Effect during Training. In Fig. 6, we plot the mIoU scores on the validation during training to show", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "23422", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3d5be07296ba9c4c3d3dd4f44f304d5ad8adbe595cb7e25c21cd4ee787ac864.jpg", + "image_caption": [ + "(a). Single-target source-free adaptation" + ], + "image_footnote": [], + "bbox": [ + 98, + 87, + 872, + 229 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/cd6b422502e3f4fff6f0ece47d2dfbb6c7add9897cef1015cf2b59db72a0134d.jpg", + "image_caption": [ + "(b). Open-compound source-free adaptation" + ], + "image_footnote": [], + "bbox": [ + 98, + 241, + 869, + 388 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4e1850c9a3b781825a4659240177897e566da421c9925d3c1c3d6a60079a9f09.jpg", + "image_caption": [ + "Figure 5. Visualization of different uncertainty estimation results on both GTA $\\rightarrow$ Cityscapes and GTA $\\rightarrow$ BDD100k tasks. Diff.GT denotes the ground truth estimation mask. Entropy map is shown by probability entropy [61]. Prototype map is shown by the difference between the Aspp classifier and prototype classifier [56,82].", + "Figure 6. Comparison of the mIoU score $(\\%)$ curve on the validation set during training on two transfer tasks." + ], + "image_footnote": [], + "bbox": [ + 81, + 455, + 274, + 590 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1cae91168d8e4daab93c2a7e239d0b758d3df3b12d3d214ce6d6cdf8f541c083.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 455, + 464, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the denoising effect. In single-target adaptation (a), compared with DTST [85], SND shows stronger denoising ability, allowing the model to achieve faster convergence speed during training and to obtain better performance. In multi-target adaptation (b), DTST degrades in the later stages of training, which shows that more difficult adaptation tasks place higher requirements on denoising. In contrast, SND shows a better denoising effect and can effectively alleviate model degradation.", + "bbox": [ + 75, + 640, + 468, + 775 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Hyperparameter Sensitivity", + "text_level": 1, + "bbox": [ + 76, + 786, + 326, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In Table 7, we analyze the sensitivity of the hyperparameter top- $k\\%$ and $\\tau$ in Eq. 2 on the two SFUDA tasks across three runs. For $k$ , we set the range from 1 to 10, because too small $k$ cannot select enough valuable samples, while too large $k$ will inject massive noise into the stable set. On the two tasks, the fluctuation range of mIoU is", + "bbox": [ + 75, + 810, + 468, + 898 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6d14e37db1ece55970b9b4f152c1bc3b4561204b10b074d944449cb50a1153ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
k (%)1.02.55.07.510.0
GTA → Cityscapes57.857.958.157.857.8
Cityscapes → ACDC49.950.250.750.449.8
τ (×1000)2481012
GTA → Cityscapes57.958.058.158.158.1
Cityscapes → ACDC50.550.650.750.750.7
", + "bbox": [ + 524, + 453, + 867, + 560 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 7. Sensitivity study of the hyper-parameter $k$ and $\\tau$ .", + "bbox": [ + 522, + 561, + 866, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "within $0.5\\%$ and $0.8\\%$ , showing that SND is not sensitive to $k$ . For $\\tau$ , we set the range from 2,000 to 12,000 to verify the impact of the stability evaluation iteration on SND for selecting stable samples. Results show that SND has very small fluctuations in performance, within $0.3\\%$ . This indicates that SND is not sensitive to $\\tau$ and also verifies the observation in Fig. 2 from the side.", + "bbox": [ + 496, + 580, + 890, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 696, + 617, + 712 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we propose Stable Neighbor Denoising to perform unbiased denoising for the SFUDA semantic segmentation tasks. SND detects and suppresses noise in unstable samples by establishing the connection between the stable and unstable samples through bi-level optimization. The proposed retrieval nearest neighbor strategy and category compensation strategy further reduce the bias of bi-level optimization, thereby achieving effective denoising. Extensive experiments on different source-free adaptation scenarios, backbones, and ablations show that SND effectively estimates the noise of pseudo-labels and achieves state-of-the-art performance on all benchmarks.", + "bbox": [ + 496, + 719, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "23423", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15384-15394, 2021. 1, 2, 3", + "[2] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. 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In Proceedings of the European conference on computer vision (ECCV), pages 289-305, 2018. 2" + ], + "bbox": [ + 501, + 92, + 893, + 443 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "23427", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation/06cbf727-53a9-4ece-bc0b-04416037b63c_model.json b/2024/Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation/06cbf727-53a9-4ece-bc0b-04416037b63c_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3c1495784943dead0dbc7bc285a561ef30c6c22e --- /dev/null +++ b/2024/Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation/06cbf727-53a9-4ece-bc0b-04416037b63c_model.json @@ -0,0 +1,2754 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.108, + 0.131, + 0.862, + 0.154 + ], + "angle": 0, + "content": "Stable Neighbor Denoising for Source-free Domain Adaptive Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.141, + 0.18, + 0.828, + 0.2 + ], + "angle": 0, + "content": "Dong Zhao\\(^{1}\\), Shuang Wang\\(^{1}\\), Qi Zang\\(^{1}\\), Licheng Jiao\\(^{1}\\), Nicu Sebe\\(^{2}\\), Zhun Zhong\\(^{3,4}\\)" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.198, + 0.757, + 0.216 + ], + "angle": 0, + "content": "1 School of Artificial Intelligence, Xidian University, Shaanxi, China" + }, + { + "type": "text", + "bbox": [ + 0.092, + 0.216, + 0.877, + 0.272 + ], + "angle": 0, + "content": "\\(^{2}\\) Department of Information Engineering and Computer Science, University of Trento, Italy \n\\(^{3}\\) School of Computer Science and Information Engineering, Hefei University of Technology, China \n\\(^{4}\\) School of Computer Science, University of Nottingham, NG8 1BB Nottingham, UK" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.305, + 0.313, + 0.32 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.33, + 0.474, + 0.784 + ], + "angle": 0, + "content": "We study source-free unsupervised domain adaptation (SFUDA) for semantic segmentation, which aims to adapt a source-trained model to the target domain without accessing the source data. Many works have been proposed to address this challenging problem, among which uncertainty-based self-training is a predominant approach. However, without comprehensive denoising mechanisms, they still largely fall into biased estimates when dealing with different domains and confirmation bias. In this paper, we observe that pseudo-label noise is mainly contained in unstable samples in which the predictions of most pixels undergo significant variations during self-training. Inspired by this, we propose a novel mechanism to denoise unstable samples with stable ones. Specifically, we introduce the Stable Neighbor Denoising (SND) approach, which effectively discovers highly correlated stable and unstable samples by nearest neighbor retrieval and guides the reliable optimization of unstable samples by bi-level learning. Moreover, we compensate for the stable set by object-level object paste, which can further eliminate the bias caused by less learned classes. Our SND enjoys two advantages. First, SND does not require a specific segmentor structure, endowing its universality. Second, SND simultaneously addresses the issues of class, domain, and confirmation biases during adaptation, ensuring its effectiveness. Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings. In addition, SND can be easily integrated with other approaches, obtaining further improvements. The source code is available at https://github.com/DZhaoXd/SND." + }, + { + "type": "image_caption", + "bbox": [ + 0.503, + 0.305, + 0.892, + 0.318 + ], + "angle": 0, + "content": "Generic Structure Class debiasing Domain debiasing Confirmation debiasing" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.32, + 0.685, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.319, + 0.886, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.408, + 0.684, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.408, + 0.885, + 0.503 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.514, + 0.892, + 0.542 + ], + "angle": 0, + "content": "Figure 1. Comparison of advantages of different uncertain estimation strategies in self-training method for SFUDA." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.559, + 0.633, + 0.573 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.58, + 0.892, + 0.762 + ], + "angle": 0, + "content": "Unsupervised domain adaptation (UDA) [47] transfers knowledge of the labeled-rich source domains to the unlabeled target domains, providing an effective solution for semantic segmentation towards lower annotation burden [20] and strong generalization in an open environment [50, 71]. However, the access requirements of source domain data make it impossible to handle scenarios involving privacy, property rights protection, and confidentiality [15]. Thus, this work focuses on a more practical task in semantic segmentation, source-free unsupervised domain adaptation (SFUDA) [38, 75], which aims to adapt a source-trained model to a target domain without accessing the source data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Currently, self-training is the mainstream technology to address the SFUDA problem in semantic segmentation, which strives to adapt the model with high-quality pseudo-labels produced by uncertain estimation functions, e.g., probability thresholding [1, 21-23, 35, 73, 85], perturbation consistency [15, 29, 76], or discrepancy classifier voting [5, 29, 56, 65, 82, 89]. Generally, a strong cross-domain self-training method should comprehensively consider the following aspects. Generic structure: It does not require" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.888 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China No. 62271377, the Key Research and Development Program of Shannxi Program No. 2021ZDLGY0106 and No. 2022ZDLGY0112, the National Key R&D Program of China under Grant 2021ZD0110400 and 2021ZD0110404 the Key Scientific Technological Innovation Research Project by Ministry of Education, the Joint Funds of the National Natural Science Foundation of China (U22B2054)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.078, + 0.888, + 0.227, + 0.9 + ], + "angle": 0, + "content": "\\(\\mathbf{\\bar{C}}\\) Co-corresponding author." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23416" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.364 + ], + "angle": 0, + "content": "the adoption of a specific structural design (e.g., a specific segmentation head) on the source side; otherwise, it would not be conducive to target deployment [46]. Class debbiasing: the less-learned (hard) categories in the source model should be paid more attention, as the class imbalance problem often exists in segmentation tasks [1, 21, 43, 58, 90]. Domain debiasing: the self-training method needs to maintain the adaptability of distinct domains, since the cross-domain segmentation tasks often face multiple or compound domains, e.g., different weather conditions. Confirmation debiasing: since the running confidence of the model will increase with self-training [3, 86], a strong self-training method should be able to dynamically adjust the uncertain estimation function for addressing the confirmation bias. However, existing self-training methods for SFUDA, lacking a comprehensive denoising mechanism, often fall short in one or more aspects (see Fig. 1(a-c)), leading to inefficiency and under-adaptation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.368, + 0.473, + 0.61 + ], + "angle": 0, + "content": "Our motivation comes from experimental observations of implementing the vanilla self-training [1] on SFUDA. As shown in Fig. 2, for each target training sample at different iterations, we record 1) its mIoU scores with the ground truth (mIoU-axis); and 2) the change degrees between the segmentation results of the current step and the ones obtained by the initial step (stability-axis). Throughout the training process, we observe that samples with high stability consistently maintain high mIoU scores, while those with low stability consistently show low mIoU scores. This indicates that noise in samples with low stability is the main contributor to error accumulation during self-training. Moreover, this issue does not significantly improve as training progresses. This motivates us to identify stable samples (i.e., whose pseudo-label change degree are low) and unstable samples to address the above issue." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.614, + 0.473, + 0.903 + ], + "angle": 0, + "content": "To this end, we propose a novel denoising approach, called Stable Neighbor Denoising (SND), which can effectively discover highly correlated stable and unstable samples by nearest neighbor retrieval and denoise unstable samples with the guidance of the stable ones by bi-level optimization. Specifically, we resort to bi-level optimization [48, 70] to establish the connection between the stable and unstable sets and guide the evolution direction of unstable samples. The principle here is that if the model is trained on unstable samples with correct pseudo-labels, the loss on stable samples will be also minimized. Importantly, by the analysis of the gradient of bi-level optimization (detailed in Section 3.2), we find that matching unbiased and highly correlated stable samples for unstable samples is the key to achieving this principle. This is because the loss gradients of biased/low-correlation samples often have non-intersecting/different optimization directions, leading to bias in bi-level optimization for denoising. To tackle this problem, we propose retrieving stable" + }, + { + "type": "image", + "bbox": [ + 0.551, + 0.096, + 0.858, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.299, + 0.895, + 0.385 + ], + "angle": 0, + "content": "Figure 2. The plot of the mIoU scores versus stability for each target sample throughout training. Stability is calculated by the difference between the initial and the current segmentation. It shows a positive correlation between mIoU (pseudo-label quality) and stability. This observation holds during the whole training process. Experiments are from the GTA5 \\(\\rightarrow\\) Cityscapes SFUDA task." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.395, + 0.895, + 0.517 + ], + "angle": 0, + "content": "neighbors by image style and spatial layout factors to eliminate the domain bias in one-step bi-level denoising optimization. In addition, we propose refining the stable samples into two sets: a whole-stable set and a category-stable set. Then, we compensate for stable neighbors using diverse object-level pasting to eliminate category bias. In this way, bi-level optimization can efficiently denoise unstable samples with stable ones under the principle." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.518, + 0.896, + 0.761 + ], + "angle": 0, + "content": "Through the above techniques, the proposed SND shows superiority over previous works as follows. 1 Generic structure: SND does not require a specific network structure on both the source and target sides, endowing its universality. 2 Class debiasing: SND constructs stable neighbors with balanced categories and uses them to guide the adaptation of less-learned categories. 3 Domain debiasing: SND denoises distinct domains by retrieving neighbors with similar domain factors and can handle complex compound domain scenarios (See Table. 3). 4 Confirmation debiasing: SND designs a stability-oriented denoising mechanism that filters out noisy pseudo-labels without the need for probability or prototype distance, thereby mitigating confirmation bias (See Fig. 6). Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.772, + 0.642, + 0.789 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Unsupervised Domain Adaptation. Domain adaptive semantic segmentation has achieved significant adaptability improvements in multiple adaptation scenarios such as synthesis-to-reality [10, 21-23, 56], cross-weather [31, 53, 54], multi-source [18, 69], etc. Overall, the current work mainly realizes cross-domain transfer from the following aspects. 1) Use the source domain data to learn a gener" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23417" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "alized representation [8]. This line of work employs data augmentation (e.g. copy-paste [58], random masking [23]) and domain randomization (e.g. expanding image styles [12, 24, 30, 56, 81, 88]) to expand the representation space of source domain models. 2) Align the source and target domains. The following works adopt a variety of domain alignment strategies (e.g. adversarial training or statistical matching) in a variety of alignment spaces (e.g. pixels space [7, 20], Fourier space [77], features space [49, 63, 66], output space [41, 59, 61], etc.), reducing the statistical difference of both domains. 3) Target characteristic mining. Most of such works use augmentation consistency [2, 11, 44, 82] and pseudo-labels [6, 81] to further improve the model's adaptive ability, e.g. tail category and local distribution." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.454 + ], + "angle": 0, + "content": "Source-Free Unsupervised Domain Adaptation (SFUDA). In classification tasks, prior SFUDA works propose implicit distribution alignment [14, 37], instance contrast [83], and model perturbation [27] to align domains without source data. In segmentation tasks, the above idea is hard to adopt due to complex semantic feature spaces. Most SFUDA works for segmentation adopt self-training, which filters and retransmits the well-adapted pixels or regions through probability thresholds [85], data [25] or model discrepancy [15, 29], but they often fall into various biases." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.473, + 0.621 + ], + "angle": 0, + "content": "Noisy Label Learning. SFUDA can be viewed as a noisy label learning problem [74, 78, 87]. Currently, noisy label learning is mostly discussed on classification tasks. The mainstream technologies include robust loss design [42, 67, 84], self-label correction [9, 33], prototype denoising [17], meta-learning based denoising [48, 70], etc. Most of those methods are designed for instance-level and are not suitable for pixel-level segmentation tasks. In particular, the prototype [34, 82] and meta-learning [16] based denoising methods have been applied to UDA segmentation tasks, but their dependence on source data limits on SFUDA." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.628, + 0.17, + 0.644 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Preliminary. In the setting of source-free unsupervised domain adaptation (SFUDA), we are given a segmentation model \\(\\mathcal{H}\\) with parameter \\(\\Theta\\) pre-trained on the labeled source dataset \\(\\mathcal{D}_s = \\{(x_s^i,y_s^i)\\}_{i}^{N_s}\\), and the unlabeled target dataset \\(\\mathcal{D}_t = \\{x_t^i\\}_i^{N_t}\\). The goal is to adapt the network \\(\\mathcal{H}\\) and achieve low risk on the target dataset without accessing the source data \\(\\mathcal{D}_s\\). To achieve this goal, most works mainly conduct self-training to optimize the \\(\\mathcal{H}\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.778, + 0.47, + 0.82 + ], + "angle": 0, + "content": "\\[\n\\Theta^ {\\star} = \\underset {\\Theta} {\\arg \\min } \\sum_ {i} ^ {N _ {t}} \\sum_ {l} ^ {H \\times W} \\omega^ {(i, l)} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta\\right), \\hat {y} _ {t} ^ {(i, l)} \\right], \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.47, + 0.902 + ], + "angle": 0, + "content": "where \\(\\mathcal{L}\\) is the cross-entropy loss and \\(\\hat{y}_t\\) is the pseudo-label. \\(\\omega\\) is a weighting factor calculated by uncertainty, in which the lower the uncertainty, the closer the value is to 0. This paper proposes stable neighbor denoising techniques to estimate \\(\\omega\\) in an unbiased way." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.8, + 0.107 + ], + "angle": 0, + "content": "3.1. Division of Stable & Unstable Sets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.111, + 0.892, + 0.202 + ], + "angle": 0, + "content": "Following the observation in Fig 2, we aim to divide target domain samples into stable and unstable sets by the change degree (also called evolution stability) of their segmentation results during the vanilla self-training [1]. Formally, for each target sample \\( x_{t}^{i} \\), we define its evolution stability (ES) at \\( \\tau \\)-th iteration as follow," + }, + { + "type": "equation", + "bbox": [ + 0.544, + 0.206, + 0.892, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\operatorname {E S} ^ {i, \\tau} = \\sum_ {l} ^ {H \\times W} \\operatorname {S I M} \\left[ \\mathcal {H} \\left(x _ {t} ^ {i, l} \\mid \\Theta^ {0}\\right), \\mathcal {H} \\left(x _ {t} ^ {i, l} \\mid \\Theta^ {\\tau}\\right) \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.253, + 0.892, + 0.375 + ], + "angle": 0, + "content": "where \\(\\mathrm{SIM}[\\cdot ]\\) is the cosine similarity. \\(\\Theta^{\\tau}\\) represent the parameters of the model at \\(\\tau\\)-th iteration during self-training. The larger the ES value of the sample, the more stable it is. As ES may fluctuate in different degrees of domain shift tasks, it is hard to set a suitable threshold to determine whether it is stable. Instead, we take the top-\\(k\\%\\) ranked highly stable samples to divide the \\(\\mathcal{D}_t\\) into the stable set \\(\\mathcal{D}_{se}\\) and the unstable set \\(\\mathcal{D}_{ue}\\) as follows," + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.382, + 0.892, + 0.401 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {s e} = \\left\\{\\left(x _ {t} ^ {i}, \\bar {y} ^ {i}\\right) \\mid x _ {t} ^ {i} \\in \\mathcal {D} _ {t}, \\mathrm {E S} ^ {i, \\tau} \\in \\top_ {k} \\right\\}, \\tag {3}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.408, + 0.892, + 0.426 + ], + "angle": 0, + "content": "\\[\n\\mathcal {D} _ {u e} = \\left\\{x _ {t} ^ {i} \\mid x _ {t} ^ {i} \\in \\mathcal {D} _ {t}, \\mathrm {E S} ^ {i, \\tau} \\notin \\top_ {k} \\right\\}. \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.892, + 0.461 + ], + "angle": 0, + "content": "Next, the main challenge is how to utilize \\(\\mathcal{D}_{se}\\) to assist in predicting unbiased \\(\\omega\\) of \\(\\mathcal{D}_{ue}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.469, + 0.892, + 0.485 + ], + "angle": 0, + "content": "3.2. Build Relations between Stable & Unstable Sets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.657 + ], + "angle": 0, + "content": "An intuitive way is to exploit the cross-image feature similarity [68] of samples in the two sets to build relations. However, we find that the un-adapted source-trained model fails to capture this cross-image feature similarity because the representation ability of deep networks is always insufficient under the domain shift (see Table 3). Instead, we propose to build relations between the two sets from an optimization perspective and utilize bi-level learning [48, 70] to achieve this. In a nutshell, we formulate each optimization step as the inner- and outer loops, in which the former learns uncertainty parameter \\(\\omega\\) for the latter." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.719 + ], + "angle": 0, + "content": "Specifically, for \\(m\\)-th optimization step, in the inner loop, the estimizable \\(\\omega\\) is first initialized as \\(\\omega_0\\) and the model with parameters \\(\\Theta^m\\) is optimized on unstable samples by Eq.1," + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.721, + 0.892, + 0.776 + ], + "angle": 0, + "content": "\\[\n\\Theta_ {\\text {i n n e r}} ^ {m + 1} = \\arg \\min _ {\\Theta} \\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\sum_ {l} ^ {H \\times W} \\omega_ {0} ^ {i} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta^ {m}\\right), \\hat {y} _ {t} ^ {(i, l)} \\right]. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.776, + 0.892, + 0.902 + ], + "angle": 0, + "content": "\\(\\omega_0^i\\) is simply set to be an all-one matrix. For optimization, Eq. 5 can be approximated by one- or multi-step gradient calculation, i.e., \\(\\Theta_{inner}^{m + 1} = \\Theta^m - \\alpha \\sum_{x_t \\in \\mathcal{D}_{ue}} \\omega_0^i \\frac{\\partial \\mathcal{L}(x_t^i | \\Theta^m)}{\\partial \\Theta} |_{\\Theta^m}\\), where \\(\\alpha\\) is the inner-loop learning rate. It can be seen that \\(\\omega\\) is differentiable relative to \\(\\Theta_{inner}^{m + 1}\\). Subsequently, we optimize the \\(\\omega\\) by enforcing the optimized model with parameters \\(\\Theta_{inner}^{m + 1}\\) also achieves low risk on the stable samples in \\(\\mathcal{D}_{se}\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "23418" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.114, + 0.089, + 0.859, + 0.287 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.295, + 0.896, + 0.368 + ], + "angle": 0, + "content": "Figure 3. The pipeline of the proposed Stable Neighbor Denoising (SND). It is formed by the student-teacher model [57]. In each optimization, SND performs the inner and outer optimizations sequentially. In the inner loop (red line), SND utilizes the style \\(\\mathcal{Q}_{\\text{style}}\\) and the layout \\(\\mathcal{Q}_{\\text{layout}}\\) factors to retrieve stable neighbors for unstable samples and then performs category compensation to reduce category bias. Thereafter, SND executes Eq. 8 using the teacher model to obtain the unbiased uncertainty map \\(\\omega_{\\star}\\) and initial pseudo-label \\(\\hat{y}_t\\). In the outer loop (black line), SND performs Eq. 7 to optimize the student model. EMA denotes the Exponential Moving Average." + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.378, + 0.47, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\omega_ {\\star} = \\arg \\min _ {\\omega} \\sum_ {\\left(x _ {t}, \\bar {y} _ {t}\\right) \\in \\mathcal {D} _ {s e}} \\sum_ {l} ^ {H \\times W} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta_ {\\text {i n n e r}} ^ {m + 1}\\right), \\bar {y} _ {t} ^ {(i, l)} \\right]. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.436, + 0.471, + 0.557 + ], + "angle": 0, + "content": "This object is driven by the following principle: \\(\\omega\\) is optimized to increase/decrease the weight of these regions so that the model optimized on the unstable set samples has a small/large loss on the stable set. In this way, we establish an implicit relation between stable and unstable sets, because optimizing noisy regions of unstable samples has misleading optimization goals. Finally, in the outer loop, the model can be optimized by the learned \\(\\omega_{\\star}\\)," + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.56, + 0.469, + 0.615 + ], + "angle": 0, + "content": "\\[\n\\Theta_ {\\text {o u t e r}} ^ {m + 1} = \\arg \\min _ {\\Theta} \\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\sum_ {l} ^ {H \\times W} \\omega_ {\\star} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta^ {m}\\right), \\hat {y} _ {t} ^ {(i, l)} \\right]. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.615, + 0.47, + 0.699 + ], + "angle": 0, + "content": "Problem Discussion. One important question in the above learning strategy is, does this principle work by taking arbitrary samples from the stable and unstable set to optimize? We present further analysis of the optimization of \\(\\omega\\) to answer this question. For optimization, Eq. 6 is performed by gradient descent as follows," + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.707, + 0.441, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\omega_ {\\star} = \\omega_ {0} - \\beta \\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} (x _ {t} ^ {i} | \\Theta_ {i n n e r} ^ {m + 1})}{\\partial \\omega} | _ {\\omega_ {0}} \\\\ = \\omega_ {0} - \\beta \\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} (x _ {t} ^ {i} | \\Theta_ {i n n e r} ^ {m + 1})}{\\partial \\Theta} | _ {\\Theta_ {i n n e r} ^ {m + 1}} \\cdot \\frac {\\partial \\Theta_ {i n n e r} ^ {m + 1}}{\\partial \\omega} | _ {\\omega_ {0}} \\\\ = \\omega_ {0} + \\\\ \\end{array}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.093, + 0.803, + 0.473, + 0.876 + ], + "angle": 0, + "content": "\\[\n\\beta \\underbrace {\\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} \\left(x _ {t} ^ {i} \\mid \\Theta_ {i n n e r} ^ {m + 1}\\right)}{\\partial \\Theta} \\mid_ {\\Theta_ {i n n e r} ^ {m + 1}}} _ {\\text {L o s s g r a d i e n t o f s t a b l e s e t}} \\cdot \\alpha \\underbrace {\\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\frac {\\partial \\mathcal {L} \\left(x _ {t} ^ {i} \\mid \\Theta^ {m}\\right)}{\\partial \\Theta} \\mid_ {\\Theta^ {m}}} _ {\\text {L o s s g r a d i e n t o f u n s t a b l e s e t}}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Thus, when the continuous loss gradient on the stable" + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.382, + 0.688, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.697, + 0.387, + 0.892, + 0.482 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.489, + 0.893, + 0.547 + ], + "angle": 0, + "content": "Figure 4. Loss gradient directions in bi-level optimization. It is shown by computing the average gradient direction of different sets of classifier weights (ASPP) using the true labels. The black lines are inner-loop and the other colored lines are outer-loop." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.565, + 0.893, + 0.746 + ], + "angle": 0, + "content": "samples in \\(\\mathcal{D}_{se}\\) has a similar direction to that on the unstable samples in \\(\\mathcal{D}_{ue}\\), the \\(\\omega\\) value of the corresponding area of the unstable samples will increase, and vice versa. This indicates that optimizing noisy pseudo-labels would deviate from the optimization goal of stable samples and thus explains why noise in pseudo-labels can be estimated. Moreover, Eq. 8 also gives us the answer that arbitrarily selecting samples from the two sets will induce bias in the estimation on \\(\\omega\\), especially for samples with low correlation. This is because heterogeneous data always enjoy different optimal weight spaces [26], which will mislead the estimation of \\(\\omega\\). We provide below a detailed analysis." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Reason & Analysis (1) We find that samples from both sets suffering large domain shifts tend to have large differences in optimization directions, which will cause the optimization of \\(\\omega\\) in Eq. 8 to be weakened by domain differences rather than the pseudo-label noise. As shown in Fig. 4, despite using real labels in bi-level optimization, domain factors (e.g. the spatial layout or image style) will still bias the optimization direction. (2) We find that samples from both sets with inconsistent category distribution cannot produce intersecting gradients in Eq. 8, causing the corresponding" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "23419" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.182 + ], + "angle": 0, + "content": "gradient of \\(\\omega\\) to be 0 as well. Moreover, in actual optimization, it is unacceptable to use massive stable samples to perform multi-step gradient descent for Eq. 6 due to huge computational and memory overhead. As a result, stable and unstable samples always suffer from mismatched class distributions, resulting in no gradient for missing classes." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.183, + 0.47, + 0.227 + ], + "angle": 0, + "content": "In conclusion, it is reasonable to argue that matching highly correlated samples from two sets is critical for unbiased uncertain estimation." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.237, + 0.32, + 0.254 + ], + "angle": 0, + "content": "3.3. Stable Neighbor Denoising" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.26, + 0.469, + 0.351 + ], + "angle": 0, + "content": "We propose to query the stable neighbor with similar domain properties for each unstable sample and compensate for missing categories for the neighbor, resulting in an unbiased estimate of \\(\\omega\\). In the querying part, following the observation in Eq. 4, we specify domain factors, namely image style and spatial layout, as the proxy for querying." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.47, + 0.586 + ], + "angle": 0, + "content": "Specifically, for image style, a series of works [36, 77] pointed out that the Fourier amplitude spectrum has a strong correlation with the image style. Thus, we adopt the flattened vector of the low-frequency Fourier amplitude spectrum as the style proxy, i.e., \\(\\mathcal{Q}_{style} = \\text{Low}(\\mathcal{A}(\\mathcal{F}(x))\\). For spatial layout, [32] shows that the row-wise and column-wise label statistical histogram vectors can represent the spatial distribution. Thus, we use the pseudolabels of both sets samples for computation as an alternative, i.e., \\(\\mathcal{Q}_{layout} = [\\mathcal{Q}_{layout}^{row}, \\mathcal{Q}_{layout}^{col}]\\), where \\(\\mathcal{Q}_{layout}^{row,c} = \\frac{\\sum_{row} \\arg\\max[\\mathcal{H}(x_t^l|\\Theta^m)] = c}{\\sum_{row} \\sum_{column} \\arg\\max[\\mathcal{H}(x_t^l|\\Theta^m)] = c}\\), \\(c \\in [0,1,\\dots C]\\), and \\(C\\) is the number of categories. With \\(\\mathcal{Q}_{style}\\) and \\(\\mathcal{Q}_{layout}\\), we can retrieve the nearest stable neighbor \\(x_{neib}^i \\in \\mathcal{D}_{se}\\) for the unstable sample \\(x^i \\in \\mathcal{D}_{ue}\\) via the similarity between the proxy vectors." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.587, + 0.469, + 0.784 + ], + "angle": 0, + "content": "The retrieved domain-associated neighbors may still suffer from missing categories, leading to problems described in the analysis (2). Thus, we further propose to borrow the missing class objects from other stable samples and paste them to the neighbor as compensation. However, the tail categories in the stable set \\(\\mathcal{D}_{se}\\) may be scarce, making the objects to be copied far less abundant. To enrich the diversity of tail categories, we additionally maintain top-\\(k\\) ranked stable category sets \\(\\mathcal{D}_{sec}^{c} = \\{(x^{i},\\bar{y}^{i})|x^{i}\\in \\mathcal{D}_{t},\\mathrm{ES}^{i,m,c}\\in \\top_{k}\\}\\) for each category \\(c\\) as the supplement. We name the \\(\\mathcal{D}_{se}\\) as a stable whole set and the \\(\\mathcal{D}_{sec}^{c}\\) as a stable category set for distinction. Subsequently, the nearest stable neighbor \\(x_{neib}^{i}\\in \\mathcal{D}_{se}\\) can be compensated as follows," + }, + { + "type": "equation", + "bbox": [ + 0.087, + 0.793, + 0.469, + 0.825 + ], + "angle": 0, + "content": "\\[\n\\bar {x} _ {n e i b} ^ {i}, \\bar {y} _ {n e i b} ^ {i} = \\mathrm {C P} \\left[ \\left(x _ {n e i b} ^ {i}, \\bar {y} _ {n e i b} ^ {i}\\right), \\left(x _ {m i x}, \\bar {y} _ {m i x}\\right) \\in \\mathcal {D} _ {\\text {s e c}} ^ {c} \\right], \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.469, + 0.855 + ], + "angle": 0, + "content": "where \\(\\mathrm{CP}[\\cdot, \\cdot]\\) is the copy-paste operation [58] that copies objects from the latter to the former." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Through these efforts, we can use unbiased stable neighbors \\(\\bar{x}_{neib}^{i}\\) for Eq. 6 to denoise unstable samples in an unbiased way. Fig. 3 shows the pipeline of the proposed SND" + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.091, + 0.762, + 0.107 + ], + "angle": 0, + "content": "Algorithm 1 The training step of SND." + }, + { + "type": "text", + "bbox": [ + 0.501, + 0.109, + 0.892, + 0.137 + ], + "angle": 0, + "content": "Input: Target data \\(\\mathcal{D}_t\\), source-trained segmentation network \\(\\mathcal{H}\\) with parameter \\(\\Theta\\), max iteration \\(M\\)." + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.138, + 0.817, + 0.153 + ], + "angle": 0, + "content": "Output: Well-adapted segmentation model \\(\\mathcal{H}\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.155, + 0.891, + 0.186 + ], + "angle": 0, + "content": "1: Split \\(\\mathcal{D}_t\\) into \\(\\mathcal{D}_{se}\\) and \\(\\mathcal{D}_{ue}\\) via vanilla self-training by Eq. 2, Eq. 3 and Eq. 4" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.186, + 0.878, + 0.201 + ], + "angle": 0, + "content": "2: Initialize the teacher student model as \\(\\Theta_{tea}\\) and \\(\\Theta_{stu}\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.202, + 0.694, + 0.215 + ], + "angle": 0, + "content": "3: for \\( m \\gets 0 \\) to \\( M - 1 \\) do" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.216, + 0.806, + 0.232 + ], + "angle": 0, + "content": "4: Sample batch samples \\(\\{x_{t}^{i}\\}_{i = 1}^{B}\\in \\mathcal{D}_{ue}\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.233, + 0.731, + 0.246 + ], + "angle": 0, + "content": "5: Inner loop Optimization:" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.246, + 0.892, + 0.277 + ], + "angle": 0, + "content": "6: Retrieve nearest stable neighbor \\((x_{neib}^{i},y_{neib}^{i})\\in\\) \\(\\mathcal{D}_{se}\\) for each unstable sample \\(x_{t}^{i}\\) by \\(\\mathcal{Q}_{style}\\) and \\(\\mathcal{Q}_{layout}\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.278, + 0.79, + 0.293 + ], + "angle": 0, + "content": "7: Compensate \\((x_{neib}^{i},y_{neib}^{i})\\) by Eq. 9" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.293, + 0.89, + 0.322 + ], + "angle": 0, + "content": "8: Optimize \\(\\Theta_{tea}\\) by Eq. 8 to obtain the uncertainty \\(\\omega_{\\star}\\) and pseudo-label \\(\\hat{y}_t\\)" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.323, + 0.733, + 0.337 + ], + "angle": 0, + "content": "9: Outer loop Optimization:" + }, + { + "type": "text", + "bbox": [ + 0.509, + 0.338, + 0.804, + 0.353 + ], + "angle": 0, + "content": "10: Update \\(\\Theta_{stu}\\) by Eq. 7 with \\(\\omega_{\\star}\\) and \\(\\hat{y}_t\\)" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.354, + 0.848, + 0.368 + ], + "angle": 0, + "content": "11: Update \\(\\Theta_{tea}\\) by exponential moving average" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.371, + 0.583, + 0.383 + ], + "angle": 0, + "content": "12: end for" + }, + { + "type": "text", + "bbox": [ + 0.507, + 0.385, + 0.777, + 0.4 + ], + "angle": 0, + "content": "13: Return Adapted model \\(\\mathcal{H}\\) with \\(\\Theta_{tea}\\)." + }, + { + "type": "list", + "bbox": [ + 0.507, + 0.155, + 0.892, + 0.4 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.431, + 0.892, + 0.492 + ], + "angle": 0, + "content": "and the corresponding is shown in Algorithm 1. Algorithm 1 implements our SND within the student-teacher framework [57] to align with existing methods. See detailed explanations and ablation in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.633, + 0.523 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.531, + 0.669, + 0.547 + ], + "angle": 0, + "content": "4.1. Datasets & Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.749 + ], + "angle": 0, + "content": "Datasets. GTA5 [51] dataset provides 24,999 game-rendering urban scene images with a resolution of \\(1914 \\times 1024\\). SYNTHIA [52] dataset includes 9,400 virtual images with a resolution of \\(1280 \\times 760\\). We use 19 and 16 common categories in these two datasets respectively as source data. Cityscapes [13] dataset contains 3,975 real urban scene images from 50 different cities in primarily Germany, with a resolution of \\(2048 \\times 1024\\). ACDC [55] is the real-world dataset on adverse visual conditions, which comprises diverse weather scene images with a resolution of \\(1280 \\times 720\\). BDD100K [80] is a compound real-world dataset consists of 8000 training images and 1000 verification images with a resolution of \\(1280 \\times 720\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Setup. We conduct experiments using the Convolutional and Transformer structures respectively. For Convolutional structures, we adopt the Deeplab-v2 [4] with ResNet-101 [19] as the segmentation model. SGD optimizers are used for both inner and outer optimization, where the outer optimizer is set an initial learning rate \\((\\beta)\\) to \\(2.5 \\times 10^{-4}\\) with weight decay 0.01 while the inner optimizer is set a fixed learning rate \\((\\alpha)\\) of 0.01. The batch size is set as 4, and the framework is trained for 20,000 iterations on all SFUDA tasks. For Transformer structures, we adopt the SegFormer" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "23420" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.081, + 0.089, + 0.892, + 0.476 + ], + "angle": 0, + "content": "
roadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
Source-free Synthetic-to-Real: GTA → Cityscapes (Val.)
HCL (NIPS'21) [25]92.654.682.833.226.239.838.131.984.538.685.361.330.285.433.141.614.427.344.049.7
SFDASEG (ICCV'21)† [29]91.753.486.137.632.137.438.235.686.748.589.962.634.387.251.050.84.242.753.953.4
DTST (CVPR'23) [85]93.557.684.736.525.233.444.736.786.842.881.362.337.288.148.750.635.548.359.155.4
CrossMatch(ICCV'23)† [79]95.167.887.751.341.536.347.451.387.847.887.36734.287.54151.8042.646.456.4
CROTS(IJV'24) [40]9252.485.937.335.834.642.238.486.945.691.165.136.187.341.651.1041.456.253.7
SND (Ours)93.054.084.635.630.331.041.941.687.644.686.462.638.587.548.742.936.649.558.755.6
DTST + SND (Ours)93.960.086.738.635.937.543.448.387.644.690.165.339.988.554.944.433.149.960.958.1
Source-free Synthetic-to-Real: Synthia → Cityscapes (Val.)
HCL (NIPS'21) [25]86.738.182.7100.630.325.429.782.8-85.961.924.884.5-38.9-22.637.946.4
SFDASEG (ICCV'21)† [29]90.550.081.613.32.834.725.733.183.8-89.266.034.985.3-53.4-46.146.652.3
DTST (CVPR'23) [85]88.945.883.313.70.832.731.620.885.7-82.564.427.888.1-50.9-37.657.350.7
CrossMatch(ICCV'23)† [79]91.555.585.434.48.340.840.044.486.6-84.362.422.088.3-60.0-40.645.655.6
CROTS(IJV'24) [40]89.441.682.715.11.234.733.725.783.7-87.966.634.685.4-45.9-43.549.651.3
SND (Ours)88.147.480.128.132.234.933.641.383.3-86.759.927.286.7-48.1-36.252.554.1
DTST + SND (Ours)88.743.783.632.126.032.438.044.787.2-87.962.235.587.4-40.4-46.957.255.9
Source-free clean-Adverse-Weather: Cityscapes → ACDC (Test)
URMDA (CVPR'2021)† [15]74.125.643.519.524.325.948.643.266.227.579.845.020.970.736.835.932.727.729.940.9
HCL (NIPS'2021) [25]72.624.768.521.419.431.051.846.571.828.581.243.821.576.842.844.436.130.124.044.0
SFDASEG (ICCV'21)† [29]73.529.070.719.721.936.153.251.472.031.185.341.526.276.441.946.139.833.332.046.4
DTST (CVPR'2023) [85]73.428.569.716.720.532.850.251.171.530.885.050.822.371.640.341.735.631.938.245.4
SND (Ours)74.827.669.323.626.336.552.854.675.535.084.852.525.578.844.948.137.631.134.948.1
DTST + SND (Ours)73.429.470.922.025.138.554.655.577.735.286.653.427.480.945.649.041.036.740.449.6
Source-free Open-compound: GTA → BDD100k (Test)
URMDA (CVPR'21)† [15]83.938.378.79.67.329.111.14.970.7-74.253.815.081.2-35.0-22.830.540.4
HCL (NIPS'21) [25]88.639.281.08.27.928.411.45.771.0-77.254.216.081.8-41.4-22.631.441.6
SFDASEG (ICCV'21)† [29]87.940.280.613.18.230.222.817.171.1-78.151.427.980.2-43.7-30.342.345.3
DTST (CVPR'23) [85]83.139.964.98.914.529.527.027.171.9-83.252.931.374.7-41.1-30.042.145.2
SND (Ours)84.142.674.115.221.231.131.025.570.4-83.952.833.979.9-39.1-37.541.947.8
SND + DTST (Ours)86.544.477.321.322.932.433.027.469.6-86.754.334.382.1-39.4-38.342.449.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.479, + 0.892, + 0.536 + ], + "angle": 0, + "content": "Table 1. Comparison of SND with state-of-the-art works on the tasks of source-free domain adaptation in semantic segmentation. The model is deeplab-v2 with ResNet101. The report metric is IoU(\\%). \\(\\dagger\\) denotes using the specific network on the source side, e.g., SFDASEG using multiple heads, CrossMatch using two segmentation models with depth estimation. DTST+SND means using the minority class resampling strategy in DTST [85], as minority class adaptation is very challenging in source-free UDA." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.547, + 0.47, + 0.684 + ], + "angle": 0, + "content": "[72] with MiT-B5 [72]. AdamW [39] and Adam [28] optimizer are used for inner and outer optimization respectively, where the outer optimizer is set an initial learning rate \\((\\beta) 6 \\times 10^{-5}\\) with weight decay 0.01, while the inner optimizer is set a fixed learning rate \\((\\alpha)\\) of 0.01. The batch size is set as 2 and the model is trained for 20,000 iterations on all tasks. For set dividing, we use the stability (ES) evaluated at \\(10k(\\tau)\\) iterations and regard the top \\(5\\%\\) (\\(k\\%\\)) ranked stable samples as the stable set for all adaptation tasks." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.696, + 0.468, + 0.712 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-the-art Alternatives" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Performance Comparison on SFUDA. We compare our methods with the state-of-the-art approaches on source-free unsupervised domain adaptive semantic segmentation (SFUDA), including adapting to single and compound target domains. Table 1 shows that the proposed SND achieves the best performance on all SFUDA tasks. Moreover, SND can be combined with other method (DTST [85]) and achieves further significant improvements. In the two synthetic-to-real SFUDA adaptation tasks, our approach (SND+DTST) surpasses the second-highest methods by \\(2.7\\%\\) and \\(3.1\\%\\), respectively. On real-to-real adaptation tasks, i.e., ACDC with various weather conditions, our ap" + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.545, + 0.869, + 0.671 + ], + "angle": 0, + "content": "
Continual source-free adaptation: Cityscapes→ACDC
Timet →
FogNightRainSnowmIoU
Source model [72]69.140.359.757.856.7
TENT * [62]68.536.359.954.754.9
CoTTA * [64]70.441.663.960.859.2
HCL [25]70.039.963.761.258.7
SFDASEG † [29]70.142.162.461.859.1
SND72.143.166.365.661.8
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.743 + ], + "angle": 0, + "content": "Table 2. Comparison on the tasks of continual source-free domain adaptation semantic segmentation. The segmentation model is SegFormer with MiT-B5 as the backbone. *means we use the target domain data for multiple round adaptations rather than one round in the original paper." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "proach (SND+DTST) still maintains excellent performance, improving the performance of the current best method (SF-DASEG [29]) by \\(3.2\\%\\). When adapted to the more challenging open-compound domain BDD100k, the proposed method (SND+DTST) achieves a large performance gain, surpassing the second-highest method by \\(4.2\\%\\). The performance under various conditions proves that our method can effectively cope with the pseudo-label noise in complex environments, and alleviate the bias problem in SFUDA tasks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23421" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.141, + 0.089, + 0.83, + 0.16 + ], + "angle": 0, + "content": "
UnweightedPE. [62]MCC. [89]DAC. [29]MPC. [15]PD. [82]CIA. [68]SND
GTA → Cityscapes49.650.5 (+0.9)52.1 (+2.5)51.7 (+2.1)51.6 (+2.0)50.9 (+1.3)49.8 (+0.2)55.6 (+6.0)
Synthia → Cityscapes48.249.5 (+1.3)52.9 (+2.7)49.4 (+1.2)51.5 (+3.3)49.7 (+1.5)47.2 (-1.0)54.1 (+5.9)
Cityscapes → ACDC43.141.3 (-1.8)45.1 (+2.0)42.9 (-0.3)43.0 (-0.1)39.1 (-4.0)39.2 (-3.9)48.1 (+5.0)
GTA → BDD100k42.141.5 (-0.6)44.8 (+2.7)41.2 (-0.9)42.9 (+0.8)40.5 (-1.6)37.1 (-5.0)47.8 (+5.7)
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.162, + 0.895, + 0.22 + ], + "angle": 0, + "content": "Table 3. Ablation experiments on uncertainty estimation for source-free cross-domain segmentation tasks. We compared the following uncertainty estimation methods, probability entropy (PE.) [62], multi-classifier consistency (MCC.) [89], data augmentation consistency (DAC.) [29], model perturbation consistency (MPC.) [15], prototype distance (PD.) [82], cross-image association [68](CIA.). 'Unweighted' means original pseudo labels." + }, + { + "type": "table", + "bbox": [ + 0.092, + 0.234, + 0.457, + 0.317 + ], + "angle": 0, + "content": "
Division metricGTA → CityscapesCityscapes → ACDC
Image-level entropy [45]52.945.1
Patch-level entropy [59]51.743.6
Image-level loss [74]52.744.1
Domain distance [60]51.642.4
Stability55.648.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.12, + 0.318, + 0.427, + 0.332 + ], + "angle": 0, + "content": "Table 4. Comparison of the subset division metrics." + }, + { + "type": "table", + "bbox": [ + 0.111, + 0.338, + 0.436, + 0.407 + ], + "angle": 0, + "content": "
QueryGTA → CityscapesCityscapes → ACDC
Random54.244.7
Qlayout55.344.9
Qstyle55.147.5
Qlayout + Qstyle55.648.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.409, + 0.468, + 0.438 + ], + "angle": 0, + "content": "Table 5. Ablation study of querying stable neighbor strategies. Random means randomly selecting stable samples from \\( \\mathcal{D}_{se} \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.601 + ], + "angle": 0, + "content": "Performance Comparison on Continual SFUDA. As real-world machine systems always operate in nonstationary environments, we also verify the effectiveness of our approach in the continual adaptation setting. In Table 2, our method maintains good performance, with an average adaptability increase of \\(5.1\\%\\) in multiple domains under continual settings, showing obvious advantages compared with other methods. It is verified that our method can better adapt to multi-domain environments and alleviate model degradation caused by domain bias and confirmation bias." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.607, + 0.231, + 0.623 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.468, + 0.81 + ], + "angle": 0, + "content": "Effectiveness of denoising module. In Table 3, we ablate the denoising part, i.e., SND, and compare it with alternatives. In two synthetic-to-real SFUDA experiments, SND achieves a performance improvement of nearly \\(6\\%\\), showing optimal competitiveness than other alternatives. In multiple and compound adaptation tasks, SND produces a performance improvement of nearly \\(5\\%\\). On difficult transfer tasks, SND exhibits stable cross-domain adaptability, whereas other alternatives suffer from severe performance degradation. The effectiveness of SND is mainly contributed to its accurate estimation of uncertain and comprehensive denoising capabilities." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Effectiveness of the Stability Metric. In Table 4, we compare the proposed stability with other adaptability metrics for subset division, including regional entropy [45,59], image-level loss [74], and domain distance [60]. Denoising using stability metrics shows obvious advantages on two adaptive tasks, with gains increased by \\(2.7\\%\\) and \\(3.0\\%\\) com" + }, + { + "type": "table", + "bbox": [ + 0.514, + 0.234, + 0.88, + 0.294 + ], + "angle": 0, + "content": "
Category compensationGTA → CityscapesCityscapes → ACDC
None53.046.3
Dse54.247.1
Dsec55.648.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.295, + 0.892, + 0.338 + ], + "angle": 0, + "content": "Table 6. Variants of category compensation methods. 'None' means not applying compensation. \\( \\mathcal{D}_{se} \\) and \\( \\mathcal{D}_{sec} \\) means we select samples from \\( \\mathcal{D}_{se} \\) and \\( \\mathcal{D}_{sec} \\) for compensation." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.355, + 0.892, + 0.4 + ], + "angle": 0, + "content": "pared to the second competitor. We think it contributes to the ability to screen more reliable samples to provide effective support for denoising." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.401, + 0.893, + 0.521 + ], + "angle": 0, + "content": "Effectiveness of Query Methods. In Table 5, we verify the impact of different retrieval factors on adaptability. It shows that gradually adding domain-related factors for retrieving stable neighbors can improve adaptability. In special, on complex compound domain adaptation task, Cityscapes \\(\\rightarrow\\) ACDC, retrieving by domain factors shows greater improvements. This further verifies matching highly correlated neighbors is crucial for bi-level optimization." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.522, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Effectiveness of Category Compensation. In Table 6, we verify the impact of category compensation on adaptability. Using the stable set \\(\\mathcal{D}_{se}\\) as the copy object for compensation improves performance by \\(1.2\\%\\) and \\(0.8\\%\\) on two tasks respectively, verifying the impact of missing categories on denoising. Furthermore, adding category stable sets as replication objects can improve the performance by \\(1.4\\%\\) and \\(1.0\\%\\), showing that diversity compensation is more conducive to reducing the bias of bi-level optimization." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.667, + 0.712, + 0.683 + ], + "angle": 0, + "content": "4.4. Qualitative assessment" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.87 + ], + "angle": 0, + "content": "Visualization of the Learned Uncertainty Map. Fig. 5 presents the learned uncertain map \\(\\omega\\) on two SFUDA tasks. It can be seen that the uncertainty maps from probability entropy [61] and multi-classifier voting [56,82] contain a large amount of noise. Moreover, in the harder open-compound task Cityscapes \\(\\rightarrow\\) ACDC, the estimation bias of their methods is more obvious in difficult domain data, which will be a predisposing factor for error accumulation. In contrast, SND alleviates bias estimation and presents more reasonable uncertainty maps for different categories and domains. Moreover, our SND even can give accurate estimation against noise at the segmentation edges." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Denoising Effect during Training. In Fig. 6, we plot the mIoU scores on the validation during training to show" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "23422" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.088, + 0.873, + 0.23 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.368, + 0.23, + 0.615, + 0.242 + ], + "angle": 0, + "content": "(a). Single-target source-free adaptation" + }, + { + "type": "image", + "bbox": [ + 0.099, + 0.242, + 0.87, + 0.389 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.361, + 0.39, + 0.634, + 0.403 + ], + "angle": 0, + "content": "(b). Open-compound source-free adaptation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.404, + 0.893, + 0.446 + ], + "angle": 0, + "content": "Figure 5. Visualization of different uncertainty estimation results on both GTA \\(\\rightarrow\\) Cityscapes and GTA \\(\\rightarrow\\) BDD100k tasks. Diff.GT denotes the ground truth estimation mask. Entropy map is shown by probability entropy [61]. Prototype map is shown by the difference between the Aspp classifier and prototype classifier [56,82]." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.456, + 0.275, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.279, + 0.456, + 0.465, + 0.591 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.601, + 0.47, + 0.629 + ], + "angle": 0, + "content": "Figure 6. Comparison of the mIoU score \\((\\%)\\) curve on the validation set during training on two transfer tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.641, + 0.47, + 0.776 + ], + "angle": 0, + "content": "the denoising effect. In single-target adaptation (a), compared with DTST [85], SND shows stronger denoising ability, allowing the model to achieve faster convergence speed during training and to obtain better performance. In multi-target adaptation (b), DTST degrades in the later stages of training, which shows that more difficult adaptation tasks place higher requirements on denoising. In contrast, SND shows a better denoising effect and can effectively alleviate model degradation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.787, + 0.327, + 0.803 + ], + "angle": 0, + "content": "4.5. Hyperparameter Sensitivity" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.9 + ], + "angle": 0, + "content": "In Table 7, we analyze the sensitivity of the hyperparameter top- \\(k\\%\\) and \\(\\tau\\) in Eq. 2 on the two SFUDA tasks across three runs. For \\(k\\), we set the range from 1 to 10, because too small \\(k\\) cannot select enough valuable samples, while too large \\(k\\) will inject massive noise into the stable set. On the two tasks, the fluctuation range of mIoU is" + }, + { + "type": "table", + "bbox": [ + 0.526, + 0.454, + 0.868, + 0.561 + ], + "angle": 0, + "content": "
k (%)1.02.55.07.510.0
GTA → Cityscapes57.857.958.157.857.8
Cityscapes → ACDC49.950.250.750.449.8
τ (×1000)2481012
GTA → Cityscapes57.958.058.158.158.1
Cityscapes → ACDC50.550.650.750.750.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.524, + 0.563, + 0.867, + 0.577 + ], + "angle": 0, + "content": "Table 7. Sensitivity study of the hyper-parameter \\( k \\) and \\( \\tau \\) ." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.582, + 0.892, + 0.688 + ], + "angle": 0, + "content": "within \\(0.5\\%\\) and \\(0.8\\%\\), showing that SND is not sensitive to \\(k\\). For \\(\\tau\\), we set the range from 2,000 to 12,000 to verify the impact of the stability evaluation iteration on SND for selecting stable samples. Results show that SND has very small fluctuations in performance, within \\(0.3\\%\\). This indicates that SND is not sensitive to \\(\\tau\\) and also verifies the observation in Fig. 2 from the side." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.698, + 0.619, + 0.713 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.9 + ], + "angle": 0, + "content": "In this work, we propose Stable Neighbor Denoising to perform unbiased denoising for the SFUDA semantic segmentation tasks. SND detects and suppresses noise in unstable samples by establishing the connection between the stable and unstable samples through bi-level optimization. The proposed retrieval nearest neighbor strategy and category compensation strategy further reduce the bias of bi-level optimization, thereby achieving effective denoising. Extensive experiments on different source-free adaptation scenarios, backbones, and ablations show that SND effectively estimates the noise of pseudo-labels and achieves state-of-the-art performance on all benchmarks." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "23423" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.116, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15384-15394, 2021. 1, 2, 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.187, + 0.472, + 0.256 + ], + "angle": 0, + "content": "[2] Nikita Araslanov and Stefan Roth. 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Many works have been proposed to address this challenging problem, among which uncertainty-based self-training is a predominant approach. However, without comprehensive denoising mechanisms, they still largely fall into biased estimates when dealing with different domains and confirmation bias. In this paper, we observe that pseudo-label noise is mainly contained in unstable samples in which the predictions of most pixels undergo significant variations during self-training. Inspired by this, we propose a novel mechanism to denoise unstable samples with stable ones. Specifically, we introduce the Stable Neighbor Denoising (SND) approach, which effectively discovers highly correlated stable and unstable samples by nearest neighbor retrieval and guides the reliable optimization of unstable samples by bi-level learning. Moreover, we compensate for the stable set by object-level object paste, which can further eliminate the bias caused by less learned classes. Our SND enjoys two advantages. First, SND does not require a specific segmentor structure, endowing its universality. Second, SND simultaneously addresses the issues of class, domain, and confirmation biases during adaptation, ensuring its effectiveness. Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings. In addition, SND can be easily integrated with other approaches, obtaining further improvements. The source code is available at https://github.com/DZhaoXd/SND. + +![](images/edb7565aa5605ad3bc1578fc5aa2da72679318e20e37980d41e27e764eb11ffa.jpg) + +![](images/4a5ef134ce13a6d1a21b2813605aef23d35fbec932584b01a6e6f289625f31c3.jpg) +Generic Structure Class debiasing Domain debiasing Confirmation debiasing + +![](images/b99ac96548eb2df04817c67e60b6c77026bc4438e4840a00f6255e6b982fac3d.jpg) +Figure 1. Comparison of advantages of different uncertain estimation strategies in self-training method for SFUDA. + +![](images/ba99403b1c0cfb6858230c3eb9cb693fa82d98d9248a65104de4a8d2157951f1.jpg) + +# 1. Introduction + +Unsupervised domain adaptation (UDA) [47] transfers knowledge of the labeled-rich source domains to the unlabeled target domains, providing an effective solution for semantic segmentation towards lower annotation burden [20] and strong generalization in an open environment [50, 71]. However, the access requirements of source domain data make it impossible to handle scenarios involving privacy, property rights protection, and confidentiality [15]. Thus, this work focuses on a more practical task in semantic segmentation, source-free unsupervised domain adaptation (SFUDA) [38, 75], which aims to adapt a source-trained model to a target domain without accessing the source data. + +Currently, self-training is the mainstream technology to address the SFUDA problem in semantic segmentation, which strives to adapt the model with high-quality pseudo-labels produced by uncertain estimation functions, e.g., probability thresholding [1, 21-23, 35, 73, 85], perturbation consistency [15, 29, 76], or discrepancy classifier voting [5, 29, 56, 65, 82, 89]. Generally, a strong cross-domain self-training method should comprehensively consider the following aspects. Generic structure: It does not require + +the adoption of a specific structural design (e.g., a specific segmentation head) on the source side; otherwise, it would not be conducive to target deployment [46]. Class debbiasing: the less-learned (hard) categories in the source model should be paid more attention, as the class imbalance problem often exists in segmentation tasks [1, 21, 43, 58, 90]. Domain debiasing: the self-training method needs to maintain the adaptability of distinct domains, since the cross-domain segmentation tasks often face multiple or compound domains, e.g., different weather conditions. Confirmation debiasing: since the running confidence of the model will increase with self-training [3, 86], a strong self-training method should be able to dynamically adjust the uncertain estimation function for addressing the confirmation bias. However, existing self-training methods for SFUDA, lacking a comprehensive denoising mechanism, often fall short in one or more aspects (see Fig. 1(a-c)), leading to inefficiency and under-adaptation. + +Our motivation comes from experimental observations of implementing the vanilla self-training [1] on SFUDA. As shown in Fig. 2, for each target training sample at different iterations, we record 1) its mIoU scores with the ground truth (mIoU-axis); and 2) the change degrees between the segmentation results of the current step and the ones obtained by the initial step (stability-axis). Throughout the training process, we observe that samples with high stability consistently maintain high mIoU scores, while those with low stability consistently show low mIoU scores. This indicates that noise in samples with low stability is the main contributor to error accumulation during self-training. Moreover, this issue does not significantly improve as training progresses. This motivates us to identify stable samples (i.e., whose pseudo-label change degree are low) and unstable samples to address the above issue. + +To this end, we propose a novel denoising approach, called Stable Neighbor Denoising (SND), which can effectively discover highly correlated stable and unstable samples by nearest neighbor retrieval and denoise unstable samples with the guidance of the stable ones by bi-level optimization. Specifically, we resort to bi-level optimization [48, 70] to establish the connection between the stable and unstable sets and guide the evolution direction of unstable samples. The principle here is that if the model is trained on unstable samples with correct pseudo-labels, the loss on stable samples will be also minimized. Importantly, by the analysis of the gradient of bi-level optimization (detailed in Section 3.2), we find that matching unbiased and highly correlated stable samples for unstable samples is the key to achieving this principle. This is because the loss gradients of biased/low-correlation samples often have non-intersecting/different optimization directions, leading to bias in bi-level optimization for denoising. To tackle this problem, we propose retrieving stable + +![](images/3b55355efb89e8d98903e18d38d2c5d77a99a4664f739e1f24363c09db609e9a.jpg) +Figure 2. The plot of the mIoU scores versus stability for each target sample throughout training. Stability is calculated by the difference between the initial and the current segmentation. It shows a positive correlation between mIoU (pseudo-label quality) and stability. This observation holds during the whole training process. Experiments are from the GTA5 $\rightarrow$ Cityscapes SFUDA task. + +neighbors by image style and spatial layout factors to eliminate the domain bias in one-step bi-level denoising optimization. In addition, we propose refining the stable samples into two sets: a whole-stable set and a category-stable set. Then, we compensate for stable neighbors using diverse object-level pasting to eliminate category bias. In this way, bi-level optimization can efficiently denoise unstable samples with stable ones under the principle. + +Through the above techniques, the proposed SND shows superiority over previous works as follows. 1 Generic structure: SND does not require a specific network structure on both the source and target sides, endowing its universality. 2 Class debiasing: SND constructs stable neighbors with balanced categories and uses them to guide the adaptation of less-learned categories. 3 Domain debiasing: SND denoises distinct domains by retrieving neighbors with similar domain factors and can handle complex compound domain scenarios (See Table. 3). 4 Confirmation debiasing: SND designs a stability-oriented denoising mechanism that filters out noisy pseudo-labels without the need for probability or prototype distance, thereby mitigating confirmation bias (See Fig. 6). Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings. + +# 2. Related Work + +Unsupervised Domain Adaptation. Domain adaptive semantic segmentation has achieved significant adaptability improvements in multiple adaptation scenarios such as synthesis-to-reality [10, 21-23, 56], cross-weather [31, 53, 54], multi-source [18, 69], etc. Overall, the current work mainly realizes cross-domain transfer from the following aspects. 1) Use the source domain data to learn a gener + +alized representation [8]. This line of work employs data augmentation (e.g. copy-paste [58], random masking [23]) and domain randomization (e.g. expanding image styles [12, 24, 30, 56, 81, 88]) to expand the representation space of source domain models. 2) Align the source and target domains. The following works adopt a variety of domain alignment strategies (e.g. adversarial training or statistical matching) in a variety of alignment spaces (e.g. pixels space [7, 20], Fourier space [77], features space [49, 63, 66], output space [41, 59, 61], etc.), reducing the statistical difference of both domains. 3) Target characteristic mining. Most of such works use augmentation consistency [2, 11, 44, 82] and pseudo-labels [6, 81] to further improve the model's adaptive ability, e.g. tail category and local distribution. + +Source-Free Unsupervised Domain Adaptation (SFUDA). In classification tasks, prior SFUDA works propose implicit distribution alignment [14, 37], instance contrast [83], and model perturbation [27] to align domains without source data. In segmentation tasks, the above idea is hard to adopt due to complex semantic feature spaces. Most SFUDA works for segmentation adopt self-training, which filters and retransmits the well-adapted pixels or regions through probability thresholds [85], data [25] or model discrepancy [15, 29], but they often fall into various biases. + +Noisy Label Learning. SFUDA can be viewed as a noisy label learning problem [74, 78, 87]. Currently, noisy label learning is mostly discussed on classification tasks. The mainstream technologies include robust loss design [42, 67, 84], self-label correction [9, 33], prototype denoising [17], meta-learning based denoising [48, 70], etc. Most of those methods are designed for instance-level and are not suitable for pixel-level segmentation tasks. In particular, the prototype [34, 82] and meta-learning [16] based denoising methods have been applied to UDA segmentation tasks, but their dependence on source data limits on SFUDA. + +# 3. Method + +Preliminary. In the setting of source-free unsupervised domain adaptation (SFUDA), we are given a segmentation model $\mathcal{H}$ with parameter $\Theta$ pre-trained on the labeled source dataset $\mathcal{D}_s = \{(x_s^i,y_s^i)\}_{i}^{N_s}$ , and the unlabeled target dataset $\mathcal{D}_t = \{x_t^i\}_i^{N_t}$ . The goal is to adapt the network $\mathcal{H}$ and achieve low risk on the target dataset without accessing the source data $\mathcal{D}_s$ . To achieve this goal, most works mainly conduct self-training to optimize the $\mathcal{H}$ as follows, + +$$ +\Theta^ {\star} = \underset {\Theta} {\arg \min } \sum_ {i} ^ {N _ {t}} \sum_ {l} ^ {H \times W} \omega^ {(i, l)} \mathcal {L} \left[ \mathcal {H} \left(x _ {t} ^ {(i, l)} \mid \Theta\right), \hat {y} _ {t} ^ {(i, l)} \right], \tag {1} +$$ + +where $\mathcal{L}$ is the cross-entropy loss and $\hat{y}_t$ is the pseudo-label. $\omega$ is a weighting factor calculated by uncertainty, in which the lower the uncertainty, the closer the value is to 0. This paper proposes stable neighbor denoising techniques to estimate $\omega$ in an unbiased way. + +# 3.1. Division of Stable & Unstable Sets + +Following the observation in Fig 2, we aim to divide target domain samples into stable and unstable sets by the change degree (also called evolution stability) of their segmentation results during the vanilla self-training [1]. Formally, for each target sample $x_{t}^{i}$ , we define its evolution stability (ES) at $\tau$ -th iteration as follow, + +$$ +\operatorname {E S} ^ {i, \tau} = \sum_ {l} ^ {H \times W} \operatorname {S I M} \left[ \mathcal {H} \left(x _ {t} ^ {i, l} \mid \Theta^ {0}\right), \mathcal {H} \left(x _ {t} ^ {i, l} \mid \Theta^ {\tau}\right) \right], \tag {2} +$$ + +where $\mathrm{SIM}[\cdot ]$ is the cosine similarity. $\Theta^{\tau}$ represent the parameters of the model at $\tau$ -th iteration during self-training. The larger the ES value of the sample, the more stable it is. As ES may fluctuate in different degrees of domain shift tasks, it is hard to set a suitable threshold to determine whether it is stable. Instead, we take the top- $k\%$ ranked highly stable samples to divide the $\mathcal{D}_t$ into the stable set $\mathcal{D}_{se}$ and the unstable set $\mathcal{D}_{ue}$ as follows, + +$$ +\mathcal {D} _ {s e} = \left\{\left(x _ {t} ^ {i}, \bar {y} ^ {i}\right) \mid x _ {t} ^ {i} \in \mathcal {D} _ {t}, \mathrm {E S} ^ {i, \tau} \in \top_ {k} \right\}, \tag {3} +$$ + +$$ +\mathcal {D} _ {u e} = \left\{x _ {t} ^ {i} \mid x _ {t} ^ {i} \in \mathcal {D} _ {t}, \mathrm {E S} ^ {i, \tau} \notin \top_ {k} \right\}. \tag {4} +$$ + +Next, the main challenge is how to utilize $\mathcal{D}_{se}$ to assist in predicting unbiased $\omega$ of $\mathcal{D}_{ue}$ . + +# 3.2. Build Relations between Stable & Unstable Sets + +An intuitive way is to exploit the cross-image feature similarity [68] of samples in the two sets to build relations. However, we find that the un-adapted source-trained model fails to capture this cross-image feature similarity because the representation ability of deep networks is always insufficient under the domain shift (see Table 3). Instead, we propose to build relations between the two sets from an optimization perspective and utilize bi-level learning [48, 70] to achieve this. In a nutshell, we formulate each optimization step as the inner- and outer loops, in which the former learns uncertainty parameter $\omega$ for the latter. + +Specifically, for $m$ -th optimization step, in the inner loop, the estimizable $\omega$ is first initialized as $\omega_0$ and the model with parameters $\Theta^m$ is optimized on unstable samples by Eq.1, + +$$ +\Theta_ {\text {i n n e r}} ^ {m + 1} = \arg \min _ {\Theta} \sum_ {x _ {t} \in \mathcal {D} _ {u e}} \sum_ {l} ^ {H \times W} \omega_ {0} ^ {i} \mathcal {L} \left[ \mathcal {H} \left(x _ {t} ^ {(i, l)} \mid \Theta^ {m}\right), \hat {y} _ {t} ^ {(i, l)} \right]. \tag {5} +$$ + +$\omega_0^i$ is simply set to be an all-one matrix. For optimization, Eq. 5 can be approximated by one- or multi-step gradient calculation, i.e., $\Theta_{inner}^{m + 1} = \Theta^m - \alpha \sum_{x_t \in \mathcal{D}_{ue}} \omega_0^i \frac{\partial \mathcal{L}(x_t^i | \Theta^m)}{\partial \Theta} |_{\Theta^m}$ , where $\alpha$ is the inner-loop learning rate. It can be seen that $\omega$ is differentiable relative to $\Theta_{inner}^{m + 1}$ . Subsequently, we optimize the $\omega$ by enforcing the optimized model with parameters $\Theta_{inner}^{m + 1}$ also achieves low risk on the stable samples in $\mathcal{D}_{se}$ , + +![](images/f6d1bc28f2488502568d9c85120bc8979c0d392aee47b2db8d6502952b9aa5ff.jpg) +Figure 3. The pipeline of the proposed Stable Neighbor Denoising (SND). It is formed by the student-teacher model [57]. In each optimization, SND performs the inner and outer optimizations sequentially. In the inner loop (red line), SND utilizes the style $\mathcal{Q}_{\text{style}}$ and the layout $\mathcal{Q}_{\text{layout}}$ factors to retrieve stable neighbors for unstable samples and then performs category compensation to reduce category bias. Thereafter, SND executes Eq. 8 using the teacher model to obtain the unbiased uncertainty map $\omega_{\star}$ and initial pseudo-label $\hat{y}_t$ . In the outer loop (black line), SND performs Eq. 7 to optimize the student model. EMA denotes the Exponential Moving Average. + +$$ +\omega_ {\star} = \arg \min _ {\omega} \sum_ {\left(x _ {t}, \bar {y} _ {t}\right) \in \mathcal {D} _ {s e}} \sum_ {l} ^ {H \times W} \mathcal {L} \left[ \mathcal {H} \left(x _ {t} ^ {(i, l)} \mid \Theta_ {\text {i n n e r}} ^ {m + 1}\right), \bar {y} _ {t} ^ {(i, l)} \right]. \tag {6} +$$ + +This object is driven by the following principle: $\omega$ is optimized to increase/decrease the weight of these regions so that the model optimized on the unstable set samples has a small/large loss on the stable set. In this way, we establish an implicit relation between stable and unstable sets, because optimizing noisy regions of unstable samples has misleading optimization goals. Finally, in the outer loop, the model can be optimized by the learned $\omega_{\star}$ , + +$$ +\Theta_ {\text {o u t e r}} ^ {m + 1} = \arg \min _ {\Theta} \sum_ {x _ {t} \in \mathcal {D} _ {u e}} \sum_ {l} ^ {H \times W} \omega_ {\star} \mathcal {L} \left[ \mathcal {H} \left(x _ {t} ^ {(i, l)} \mid \Theta^ {m}\right), \hat {y} _ {t} ^ {(i, l)} \right]. \tag {7} +$$ + +Problem Discussion. One important question in the above learning strategy is, does this principle work by taking arbitrary samples from the stable and unstable set to optimize? We present further analysis of the optimization of $\omega$ to answer this question. For optimization, Eq. 6 is performed by gradient descent as follows, + +$$ +\begin{array}{l} \omega_ {\star} = \omega_ {0} - \beta \sum_ {x _ {t} \in \mathcal {D} _ {s e}} \frac {\partial \mathcal {L} (x _ {t} ^ {i} | \Theta_ {i n n e r} ^ {m + 1})}{\partial \omega} | _ {\omega_ {0}} \\ = \omega_ {0} - \beta \sum_ {x _ {t} \in \mathcal {D} _ {s e}} \frac {\partial \mathcal {L} (x _ {t} ^ {i} | \Theta_ {i n n e r} ^ {m + 1})}{\partial \Theta} | _ {\Theta_ {i n n e r} ^ {m + 1}} \cdot \frac {\partial \Theta_ {i n n e r} ^ {m + 1}}{\partial \omega} | _ {\omega_ {0}} \\ = \omega_ {0} + \\ \end{array} +$$ + +$$ +\beta \underbrace {\sum_ {x _ {t} \in \mathcal {D} _ {s e}} \frac {\partial \mathcal {L} \left(x _ {t} ^ {i} \mid \Theta_ {i n n e r} ^ {m + 1}\right)}{\partial \Theta} \mid_ {\Theta_ {i n n e r} ^ {m + 1}}} _ {\text {L o s s g r a d i e n t o f s t a b l e s e t}} \cdot \alpha \underbrace {\sum_ {x _ {t} \in \mathcal {D} _ {u e}} \frac {\partial \mathcal {L} \left(x _ {t} ^ {i} \mid \Theta^ {m}\right)}{\partial \Theta} \mid_ {\Theta^ {m}}} _ {\text {L o s s g r a d i e n t o f u n s t a b l e s e t}}. \tag {8} +$$ + +Thus, when the continuous loss gradient on the stable + +![](images/45cf9f18bf32ac3ff449618e1033105da3e51defb50a2b47e5b84bbd264e1a18.jpg) +Figure 4. Loss gradient directions in bi-level optimization. It is shown by computing the average gradient direction of different sets of classifier weights (ASPP) using the true labels. The black lines are inner-loop and the other colored lines are outer-loop. + +![](images/7bb049772898497df7ef616221865fd5394256b5ce19483c5f8825a36ef5518c.jpg) + +samples in $\mathcal{D}_{se}$ has a similar direction to that on the unstable samples in $\mathcal{D}_{ue}$ , the $\omega$ value of the corresponding area of the unstable samples will increase, and vice versa. This indicates that optimizing noisy pseudo-labels would deviate from the optimization goal of stable samples and thus explains why noise in pseudo-labels can be estimated. Moreover, Eq. 8 also gives us the answer that arbitrarily selecting samples from the two sets will induce bias in the estimation on $\omega$ , especially for samples with low correlation. This is because heterogeneous data always enjoy different optimal weight spaces [26], which will mislead the estimation of $\omega$ . We provide below a detailed analysis. + +Reason & Analysis (1) We find that samples from both sets suffering large domain shifts tend to have large differences in optimization directions, which will cause the optimization of $\omega$ in Eq. 8 to be weakened by domain differences rather than the pseudo-label noise. As shown in Fig. 4, despite using real labels in bi-level optimization, domain factors (e.g. the spatial layout or image style) will still bias the optimization direction. (2) We find that samples from both sets with inconsistent category distribution cannot produce intersecting gradients in Eq. 8, causing the corresponding + +gradient of $\omega$ to be 0 as well. Moreover, in actual optimization, it is unacceptable to use massive stable samples to perform multi-step gradient descent for Eq. 6 due to huge computational and memory overhead. As a result, stable and unstable samples always suffer from mismatched class distributions, resulting in no gradient for missing classes. + +In conclusion, it is reasonable to argue that matching highly correlated samples from two sets is critical for unbiased uncertain estimation. + +# 3.3. Stable Neighbor Denoising + +We propose to query the stable neighbor with similar domain properties for each unstable sample and compensate for missing categories for the neighbor, resulting in an unbiased estimate of $\omega$ . In the querying part, following the observation in Eq. 4, we specify domain factors, namely image style and spatial layout, as the proxy for querying. + +Specifically, for image style, a series of works [36, 77] pointed out that the Fourier amplitude spectrum has a strong correlation with the image style. Thus, we adopt the flattened vector of the low-frequency Fourier amplitude spectrum as the style proxy, i.e., $\mathcal{Q}_{style} = \text{Low}(\mathcal{A}(\mathcal{F}(x))$ . For spatial layout, [32] shows that the row-wise and column-wise label statistical histogram vectors can represent the spatial distribution. Thus, we use the pseudolabels of both sets samples for computation as an alternative, i.e., $\mathcal{Q}_{layout} = [\mathcal{Q}_{layout}^{row}, \mathcal{Q}_{layout}^{col}]$ , where $\mathcal{Q}_{layout}^{row,c} = \frac{\sum_{row} \arg\max[\mathcal{H}(x_t^l|\Theta^m)] = c}{\sum_{row} \sum_{column} \arg\max[\mathcal{H}(x_t^l|\Theta^m)] = c}$ , $c \in [0,1,\dots C]$ , and $C$ is the number of categories. With $\mathcal{Q}_{style}$ and $\mathcal{Q}_{layout}$ , we can retrieve the nearest stable neighbor $x_{neib}^i \in \mathcal{D}_{se}$ for the unstable sample $x^i \in \mathcal{D}_{ue}$ via the similarity between the proxy vectors. + +The retrieved domain-associated neighbors may still suffer from missing categories, leading to problems described in the analysis (2). Thus, we further propose to borrow the missing class objects from other stable samples and paste them to the neighbor as compensation. However, the tail categories in the stable set $\mathcal{D}_{se}$ may be scarce, making the objects to be copied far less abundant. To enrich the diversity of tail categories, we additionally maintain top- $k$ ranked stable category sets $\mathcal{D}_{sec}^{c} = \{(x^{i},\bar{y}^{i})|x^{i}\in \mathcal{D}_{t},\mathrm{ES}^{i,m,c}\in \top_{k}\}$ for each category $c$ as the supplement. We name the $\mathcal{D}_{se}$ as a stable whole set and the $\mathcal{D}_{sec}^{c}$ as a stable category set for distinction. Subsequently, the nearest stable neighbor $x_{neib}^{i}\in \mathcal{D}_{se}$ can be compensated as follows, + +$$ +\bar {x} _ {n e i b} ^ {i}, \bar {y} _ {n e i b} ^ {i} = \mathrm {C P} \left[ \left(x _ {n e i b} ^ {i}, \bar {y} _ {n e i b} ^ {i}\right), \left(x _ {m i x}, \bar {y} _ {m i x}\right) \in \mathcal {D} _ {\text {s e c}} ^ {c} \right], \tag {9} +$$ + +where $\mathrm{CP}[\cdot, \cdot]$ is the copy-paste operation [58] that copies objects from the latter to the former. + +Through these efforts, we can use unbiased stable neighbors $\bar{x}_{neib}^{i}$ for Eq. 6 to denoise unstable samples in an unbiased way. Fig. 3 shows the pipeline of the proposed SND + +# Algorithm 1 The training step of SND. + +Input: Target data $\mathcal{D}_t$ , source-trained segmentation network $\mathcal{H}$ with parameter $\Theta$ , max iteration $M$ . + +Output: Well-adapted segmentation model $\mathcal{H}$ + +1: Split $\mathcal{D}_t$ into $\mathcal{D}_{se}$ and $\mathcal{D}_{ue}$ via vanilla self-training by Eq. 2, Eq. 3 and Eq. 4 +2: Initialize the teacher student model as $\Theta_{tea}$ and $\Theta_{stu}$ +3: for $m \gets 0$ to $M - 1$ do +4: Sample batch samples $\{x_{t}^{i}\}_{i = 1}^{B}\in \mathcal{D}_{ue}$ +5: Inner loop Optimization: +6: Retrieve nearest stable neighbor $(x_{neib}^{i},y_{neib}^{i})\in$ $\mathcal{D}_{se}$ for each unstable sample $x_{t}^{i}$ by $\mathcal{Q}_{style}$ and $\mathcal{Q}_{layout}$ +7: Compensate $(x_{neib}^{i},y_{neib}^{i})$ by Eq. 9 +8: Optimize $\Theta_{tea}$ by Eq. 8 to obtain the uncertainty $\omega_{\star}$ and pseudo-label $\hat{y}_t$ +9: Outer loop Optimization: +10: Update $\Theta_{stu}$ by Eq. 7 with $\omega_{\star}$ and $\hat{y}_t$ +11: Update $\Theta_{tea}$ by exponential moving average +12: end for +13: Return Adapted model $\mathcal{H}$ with $\Theta_{tea}$ . + +and the corresponding is shown in Algorithm 1. Algorithm 1 implements our SND within the student-teacher framework [57] to align with existing methods. See detailed explanations and ablation in the Appendix. + +# 4. Experiments + +# 4.1. Datasets & Setup + +Datasets. GTA5 [51] dataset provides 24,999 game-rendering urban scene images with a resolution of $1914 \times 1024$ . SYNTHIA [52] dataset includes 9,400 virtual images with a resolution of $1280 \times 760$ . We use 19 and 16 common categories in these two datasets respectively as source data. Cityscapes [13] dataset contains 3,975 real urban scene images from 50 different cities in primarily Germany, with a resolution of $2048 \times 1024$ . ACDC [55] is the real-world dataset on adverse visual conditions, which comprises diverse weather scene images with a resolution of $1280 \times 720$ . BDD100K [80] is a compound real-world dataset consists of 8000 training images and 1000 verification images with a resolution of $1280 \times 720$ . + +Setup. We conduct experiments using the Convolutional and Transformer structures respectively. For Convolutional structures, we adopt the Deeplab-v2 [4] with ResNet-101 [19] as the segmentation model. SGD optimizers are used for both inner and outer optimization, where the outer optimizer is set an initial learning rate $(\beta)$ to $2.5 \times 10^{-4}$ with weight decay 0.01 while the inner optimizer is set a fixed learning rate $(\alpha)$ of 0.01. The batch size is set as 4, and the framework is trained for 20,000 iterations on all SFUDA tasks. For Transformer structures, we adopt the SegFormer + +
roadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
Source-free Synthetic-to-Real: GTA → Cityscapes (Val.)
HCL (NIPS'21) [25]92.654.682.833.226.239.838.131.984.538.685.361.330.285.433.141.614.427.344.049.7
SFDASEG (ICCV'21)† [29]91.753.486.137.632.137.438.235.686.748.589.962.634.387.251.050.84.242.753.953.4
DTST (CVPR'23) [85]93.557.684.736.525.233.444.736.786.842.881.362.337.288.148.750.635.548.359.155.4
CrossMatch(ICCV'23)† [79]95.167.887.751.341.536.347.451.387.847.887.36734.287.54151.8042.646.456.4
CROTS(IJV'24) [40]9252.485.937.335.834.642.238.486.945.691.165.136.187.341.651.1041.456.253.7
SND (Ours)93.054.084.635.630.331.041.941.687.644.686.462.638.587.548.742.936.649.558.755.6
DTST + SND (Ours)93.960.086.738.635.937.543.448.387.644.690.165.339.988.554.944.433.149.960.958.1
Source-free Synthetic-to-Real: Synthia → Cityscapes (Val.)
HCL (NIPS'21) [25]86.738.182.7100.630.325.429.782.8-85.961.924.884.5-38.9-22.637.946.4
SFDASEG (ICCV'21)† [29]90.550.081.613.32.834.725.733.183.8-89.266.034.985.3-53.4-46.146.652.3
DTST (CVPR'23) [85]88.945.883.313.70.832.731.620.885.7-82.564.427.888.1-50.9-37.657.350.7
CrossMatch(ICCV'23)† [79]91.555.585.434.48.340.840.044.486.6-84.362.422.088.3-60.0-40.645.655.6
CROTS(IJV'24) [40]89.441.682.715.11.234.733.725.783.7-87.966.634.685.4-45.9-43.549.651.3
SND (Ours)88.147.480.128.132.234.933.641.383.3-86.759.927.286.7-48.1-36.252.554.1
DTST + SND (Ours)88.743.783.632.126.032.438.044.787.2-87.962.235.587.4-40.4-46.957.255.9
Source-free clean-Adverse-Weather: Cityscapes → ACDC (Test)
URMDA (CVPR'2021)† [15]74.125.643.519.524.325.948.643.266.227.579.845.020.970.736.835.932.727.729.940.9
HCL (NIPS'2021) [25]72.624.768.521.419.431.051.846.571.828.581.243.821.576.842.844.436.130.124.044.0
SFDASEG (ICCV'21)† [29]73.529.070.719.721.936.153.251.472.031.185.341.526.276.441.946.139.833.332.046.4
DTST (CVPR'2023) [85]73.428.569.716.720.532.850.251.171.530.885.050.822.371.640.341.735.631.938.245.4
SND (Ours)74.827.669.323.626.336.552.854.675.535.084.852.525.578.844.948.137.631.134.948.1
DTST + SND (Ours)73.429.470.922.025.138.554.655.577.735.286.653.427.480.945.649.041.036.740.449.6
Source-free Open-compound: GTA → BDD100k (Test)
URMDA (CVPR'21)† [15]83.938.378.79.67.329.111.14.970.7-74.253.815.081.2-35.0-22.830.540.4
HCL (NIPS'21) [25]88.639.281.08.27.928.411.45.771.0-77.254.216.081.8-41.4-22.631.441.6
SFDASEG (ICCV'21)† [29]87.940.280.613.18.230.222.817.171.1-78.151.427.980.2-43.7-30.342.345.3
DTST (CVPR'23) [85]83.139.964.98.914.529.527.027.171.9-83.252.931.374.7-41.1-30.042.145.2
SND (Ours)84.142.674.115.221.231.131.025.570.4-83.952.833.979.9-39.1-37.541.947.8
SND + DTST (Ours)86.544.477.321.322.932.433.027.469.6-86.754.334.382.1-39.4-38.342.449.5
+ +[72] with MiT-B5 [72]. AdamW [39] and Adam [28] optimizer are used for inner and outer optimization respectively, where the outer optimizer is set an initial learning rate $(\beta) 6 \times 10^{-5}$ with weight decay 0.01, while the inner optimizer is set a fixed learning rate $(\alpha)$ of 0.01. The batch size is set as 2 and the model is trained for 20,000 iterations on all tasks. For set dividing, we use the stability (ES) evaluated at $10k(\tau)$ iterations and regard the top $5\%$ ( $k\%$ ) ranked stable samples as the stable set for all adaptation tasks. + +# 4.2. Comparison with State-of-the-art Alternatives + +Performance Comparison on SFUDA. We compare our methods with the state-of-the-art approaches on source-free unsupervised domain adaptive semantic segmentation (SFUDA), including adapting to single and compound target domains. Table 1 shows that the proposed SND achieves the best performance on all SFUDA tasks. Moreover, SND can be combined with other method (DTST [85]) and achieves further significant improvements. In the two synthetic-to-real SFUDA adaptation tasks, our approach (SND+DTST) surpasses the second-highest methods by $2.7\%$ and $3.1\%$ , respectively. On real-to-real adaptation tasks, i.e., ACDC with various weather conditions, our ap + +Table 1. Comparison of SND with state-of-the-art works on the tasks of source-free domain adaptation in semantic segmentation. The model is deeplab-v2 with ResNet101. The report metric is IoU(\%). $\dagger$ denotes using the specific network on the source side, e.g., SFDASEG using multiple heads, CrossMatch using two segmentation models with depth estimation. DTST+SND means using the minority class resampling strategy in DTST [85], as minority class adaptation is very challenging in source-free UDA. + +
Continual source-free adaptation: Cityscapes→ACDC
Timet →
FogNightRainSnowmIoU
Source model [72]69.140.359.757.856.7
TENT * [62]68.536.359.954.754.9
CoTTA * [64]70.441.663.960.859.2
HCL [25]70.039.963.761.258.7
SFDASEG † [29]70.142.162.461.859.1
SND72.143.166.365.661.8
+ +Table 2. Comparison on the tasks of continual source-free domain adaptation semantic segmentation. The segmentation model is SegFormer with MiT-B5 as the backbone. *means we use the target domain data for multiple round adaptations rather than one round in the original paper. + +proach (SND+DTST) still maintains excellent performance, improving the performance of the current best method (SF-DASEG [29]) by $3.2\%$ . When adapted to the more challenging open-compound domain BDD100k, the proposed method (SND+DTST) achieves a large performance gain, surpassing the second-highest method by $4.2\%$ . The performance under various conditions proves that our method can effectively cope with the pseudo-label noise in complex environments, and alleviate the bias problem in SFUDA tasks. + +
UnweightedPE. [62]MCC. [89]DAC. [29]MPC. [15]PD. [82]CIA. [68]SND
GTA → Cityscapes49.650.5 (+0.9)52.1 (+2.5)51.7 (+2.1)51.6 (+2.0)50.9 (+1.3)49.8 (+0.2)55.6 (+6.0)
Synthia → Cityscapes48.249.5 (+1.3)52.9 (+2.7)49.4 (+1.2)51.5 (+3.3)49.7 (+1.5)47.2 (-1.0)54.1 (+5.9)
Cityscapes → ACDC43.141.3 (-1.8)45.1 (+2.0)42.9 (-0.3)43.0 (-0.1)39.1 (-4.0)39.2 (-3.9)48.1 (+5.0)
GTA → BDD100k42.141.5 (-0.6)44.8 (+2.7)41.2 (-0.9)42.9 (+0.8)40.5 (-1.6)37.1 (-5.0)47.8 (+5.7)
+ +Table 3. Ablation experiments on uncertainty estimation for source-free cross-domain segmentation tasks. We compared the following uncertainty estimation methods, probability entropy (PE.) [62], multi-classifier consistency (MCC.) [89], data augmentation consistency (DAC.) [29], model perturbation consistency (MPC.) [15], prototype distance (PD.) [82], cross-image association [68](CIA.). 'Unweighted' means original pseudo labels. + +
Division metricGTA → CityscapesCityscapes → ACDC
Image-level entropy [45]52.945.1
Patch-level entropy [59]51.743.6
Image-level loss [74]52.744.1
Domain distance [60]51.642.4
Stability55.648.1
+ +Table 4. Comparison of the subset division metrics. + +
QueryGTA → CityscapesCityscapes → ACDC
Random54.244.7
Qlayout55.344.9
Qstyle55.147.5
Qlayout + Qstyle55.648.1
+ +Performance Comparison on Continual SFUDA. As real-world machine systems always operate in nonstationary environments, we also verify the effectiveness of our approach in the continual adaptation setting. In Table 2, our method maintains good performance, with an average adaptability increase of $5.1\%$ in multiple domains under continual settings, showing obvious advantages compared with other methods. It is verified that our method can better adapt to multi-domain environments and alleviate model degradation caused by domain bias and confirmation bias. + +# 4.3. Ablation Study + +Effectiveness of denoising module. In Table 3, we ablate the denoising part, i.e., SND, and compare it with alternatives. In two synthetic-to-real SFUDA experiments, SND achieves a performance improvement of nearly $6\%$ , showing optimal competitiveness than other alternatives. In multiple and compound adaptation tasks, SND produces a performance improvement of nearly $5\%$ . On difficult transfer tasks, SND exhibits stable cross-domain adaptability, whereas other alternatives suffer from severe performance degradation. The effectiveness of SND is mainly contributed to its accurate estimation of uncertain and comprehensive denoising capabilities. + +Effectiveness of the Stability Metric. In Table 4, we compare the proposed stability with other adaptability metrics for subset division, including regional entropy [45,59], image-level loss [74], and domain distance [60]. Denoising using stability metrics shows obvious advantages on two adaptive tasks, with gains increased by $2.7\%$ and $3.0\%$ com + +Table 5. Ablation study of querying stable neighbor strategies. Random means randomly selecting stable samples from $\mathcal{D}_{se}$ . + +
Category compensationGTA → CityscapesCityscapes → ACDC
None53.046.3
Dse54.247.1
Dsec55.648.1
+ +Table 6. Variants of category compensation methods. 'None' means not applying compensation. $\mathcal{D}_{se}$ and $\mathcal{D}_{sec}$ means we select samples from $\mathcal{D}_{se}$ and $\mathcal{D}_{sec}$ for compensation. + +pared to the second competitor. We think it contributes to the ability to screen more reliable samples to provide effective support for denoising. + +Effectiveness of Query Methods. In Table 5, we verify the impact of different retrieval factors on adaptability. It shows that gradually adding domain-related factors for retrieving stable neighbors can improve adaptability. In special, on complex compound domain adaptation task, Cityscapes $\rightarrow$ ACDC, retrieving by domain factors shows greater improvements. This further verifies matching highly correlated neighbors is crucial for bi-level optimization. + +Effectiveness of Category Compensation. In Table 6, we verify the impact of category compensation on adaptability. Using the stable set $\mathcal{D}_{se}$ as the copy object for compensation improves performance by $1.2\%$ and $0.8\%$ on two tasks respectively, verifying the impact of missing categories on denoising. Furthermore, adding category stable sets as replication objects can improve the performance by $1.4\%$ and $1.0\%$ , showing that diversity compensation is more conducive to reducing the bias of bi-level optimization. + +# 4.4. Qualitative assessment + +Visualization of the Learned Uncertainty Map. Fig. 5 presents the learned uncertain map $\omega$ on two SFUDA tasks. It can be seen that the uncertainty maps from probability entropy [61] and multi-classifier voting [56,82] contain a large amount of noise. Moreover, in the harder open-compound task Cityscapes $\rightarrow$ ACDC, the estimation bias of their methods is more obvious in difficult domain data, which will be a predisposing factor for error accumulation. In contrast, SND alleviates bias estimation and presents more reasonable uncertainty maps for different categories and domains. Moreover, our SND even can give accurate estimation against noise at the segmentation edges. + +Denoising Effect during Training. In Fig. 6, we plot the mIoU scores on the validation during training to show + +![](images/e3d5be07296ba9c4c3d3dd4f44f304d5ad8adbe595cb7e25c21cd4ee787ac864.jpg) +(a). Single-target source-free adaptation + +![](images/cd6b422502e3f4fff6f0ece47d2dfbb6c7add9897cef1015cf2b59db72a0134d.jpg) +(b). Open-compound source-free adaptation + +![](images/4e1850c9a3b781825a4659240177897e566da421c9925d3c1c3d6a60079a9f09.jpg) +Figure 5. Visualization of different uncertainty estimation results on both GTA $\rightarrow$ Cityscapes and GTA $\rightarrow$ BDD100k tasks. Diff.GT denotes the ground truth estimation mask. Entropy map is shown by probability entropy [61]. Prototype map is shown by the difference between the Aspp classifier and prototype classifier [56,82]. +Figure 6. Comparison of the mIoU score $(\%)$ curve on the validation set during training on two transfer tasks. + +![](images/1cae91168d8e4daab93c2a7e239d0b758d3df3b12d3d214ce6d6cdf8f541c083.jpg) + +the denoising effect. In single-target adaptation (a), compared with DTST [85], SND shows stronger denoising ability, allowing the model to achieve faster convergence speed during training and to obtain better performance. In multi-target adaptation (b), DTST degrades in the later stages of training, which shows that more difficult adaptation tasks place higher requirements on denoising. In contrast, SND shows a better denoising effect and can effectively alleviate model degradation. + +# 4.5. Hyperparameter Sensitivity + +In Table 7, we analyze the sensitivity of the hyperparameter top- $k\%$ and $\tau$ in Eq. 2 on the two SFUDA tasks across three runs. For $k$ , we set the range from 1 to 10, because too small $k$ cannot select enough valuable samples, while too large $k$ will inject massive noise into the stable set. On the two tasks, the fluctuation range of mIoU is + +
k (%)1.02.55.07.510.0
GTA → Cityscapes57.857.958.157.857.8
Cityscapes → ACDC49.950.250.750.449.8
τ (×1000)2481012
GTA → Cityscapes57.958.058.158.158.1
Cityscapes → ACDC50.550.650.750.750.7
+ +Table 7. Sensitivity study of the hyper-parameter $k$ and $\tau$ . + +within $0.5\%$ and $0.8\%$ , showing that SND is not sensitive to $k$ . For $\tau$ , we set the range from 2,000 to 12,000 to verify the impact of the stability evaluation iteration on SND for selecting stable samples. Results show that SND has very small fluctuations in performance, within $0.3\%$ . This indicates that SND is not sensitive to $\tau$ and also verifies the observation in Fig. 2 from the side. + +# 5. Conclusion + +In this work, we propose Stable Neighbor Denoising to perform unbiased denoising for the SFUDA semantic segmentation tasks. SND detects and suppresses noise in unstable samples by establishing the connection between the stable and unstable samples through bi-level optimization. The proposed retrieval nearest neighbor strategy and category compensation strategy further reduce the bias of bi-level optimization, thereby achieving effective denoising. Extensive experiments on different source-free adaptation scenarios, backbones, and ablations show that SND effectively estimates the noise of pseudo-labels and achieves state-of-the-art performance on all benchmarks. + +# References + +[1] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 15384-15394, 2021. 1, 2, 3 +[2] Nikita Araslanov and Stefan Roth. Self-supervised augmentation consistency for adapting semantic segmentation. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 15384-15394, June 2021. 3 +[3] Baixu Chen, Junguang Jiang, Ximei Wang, Pengfei Wan, Jianmin Wang, and Mingsheng Long. Debiased self-training for semi-supervised learning. Advances in Neural Information Processing Systems, 35:32424-32437, 2022. 2 +[4] L. Chen, G. Papandreou, I. Kokkinos, K. Murphy, and A. L. 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Many works have been proposed to address this challenging problem, among which uncertainty-based self-training is a predominant approach. However, without comprehensive denoising mechanisms, they still largely fall into biased estimates when dealing with different domains and confirmation bias. In this paper, we observe that pseudo-label noise is mainly contained in unstable samples in which the predictions of most pixels undergo significant variations during self-training. Inspired by this, we propose a novel mechanism to denoise unstable samples with stable ones. Specifically, we introduce the Stable Neighbor Denoising (SND) approach, which effectively discovers highly correlated stable and unstable samples by nearest neighbor retrieval and guides the reliable optimization of unstable samples by bi-level learning. Moreover, we compensate for the stable set by object-level object paste, which can further eliminate the bias caused by less learned classes. Our SND enjoys two advantages. First, SND does not require a specific segmentor structure, endowing its universality. Second, SND simultaneously addresses the issues of class, domain, and confirmation biases during adaptation, ensuring its effectiveness. Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings. In addition, SND can be easily integrated with other approaches, obtaining further improvements. The source code is available at https://github.com/DZhaoXd/SND." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 311, + 253, + 419, + 319 + ], + "blocks": [ + { + "bbox": [ + 311, + 253, + 419, + 319 + ], + "lines": [ + { + "bbox": [ + 311, + 253, + 419, + 319 + ], + "spans": [ + { + "bbox": [ + 311, + 253, + 419, + 319 + ], + "type": "image", + "image_path": "edb7565aa5605ad3bc1578fc5aa2da72679318e20e37980d41e27e764eb11ffa.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 421, + 252, + 542, + 319 + ], + "blocks": [ + { + "bbox": [ + 307, + 241, + 545, + 251 + ], + "lines": [ + { + "bbox": [ + 307, + 241, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 307, + 241, + 545, + 251 + ], + "type": "text", + "content": "Generic Structure Class debiasing Domain debiasing Confirmation debiasing" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 421, + 252, + 542, + 319 + ], + "lines": [ + { + "bbox": [ + 421, + 252, + 542, + 319 + ], + "spans": [ + { + "bbox": [ + 421, + 252, + 542, + 319 + ], + "type": "image", + "image_path": "4a5ef134ce13a6d1a21b2813605aef23d35fbec932584b01a6e6f289625f31c3.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 310, + 323, + 418, + 398 + ], + "blocks": [ + { + "bbox": [ + 310, + 323, + 418, + 398 + ], + "lines": [ + { + "bbox": [ + 310, + 323, + 418, + 398 + ], + "spans": [ + { + "bbox": [ + 310, + 323, + 418, + 398 + ], + "type": "image", + "image_path": "b99ac96548eb2df04817c67e60b6c77026bc4438e4840a00f6255e6b982fac3d.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 407, + 545, + 429 + ], + "lines": [ + { + "bbox": [ + 306, + 407, + 545, + 429 + ], + "spans": [ + { + "bbox": [ + 306, + 407, + 545, + 429 + ], + "type": "text", + "content": "Figure 1. Comparison of advantages of different uncertain estimation strategies in self-training method for SFUDA." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 421, + 323, + 541, + 398 + ], + "blocks": [ + { + "bbox": [ + 421, + 323, + 541, + 398 + ], + "lines": [ + { + "bbox": [ + 421, + 323, + 541, + 398 + ], + "spans": [ + { + "bbox": [ + 421, + 323, + 541, + 398 + ], + "type": "image", + "image_path": "ba99403b1c0cfb6858230c3eb9cb693fa82d98d9248a65104de4a8d2157951f1.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 442, + 387, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 442, + 387, + 453 + ], + "spans": [ + { + "bbox": [ + 306, + 442, + 387, + 453 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 459, + 545, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 459, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 304, + 459, + 545, + 603 + ], + "type": "text", + "content": "Unsupervised domain adaptation (UDA) [47] transfers knowledge of the labeled-rich source domains to the unlabeled target domains, providing an effective solution for semantic segmentation towards lower annotation burden [20] and strong generalization in an open environment [50, 71]. However, the access requirements of source domain data make it impossible to handle scenarios involving privacy, property rights protection, and confidentiality [15]. Thus, this work focuses on a more practical task in semantic segmentation, source-free unsupervised domain adaptation (SFUDA) [38, 75], which aims to adapt a source-trained model to a target domain without accessing the source data." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "Currently, self-training is the mainstream technology to address the SFUDA problem in semantic segmentation, which strives to adapt the model with high-quality pseudo-labels produced by uncertain estimation functions, e.g., probability thresholding [1, 21-23, 35, 73, 85], perturbation consistency [15, 29, 76], or discrepancy classifier voting [5, 29, 56, 65, 82, 89]. Generally, a strong cross-domain self-training method should comprehensively consider the following aspects. Generic structure: It does not require" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 636, + 287, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 703 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 703 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China No. 62271377, the Key Research and Development Program of Shannxi Program No. 2021ZDLGY0106 and No. 2022ZDLGY0112, the National Key R&D Program of China under Grant 2021ZD0110400 and 2021ZD0110404 the Key Scientific Technological Innovation Research Project by Ministry of Education, the Joint Funds of the National Natural Science Foundation of China (U22B2054)." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 703, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 703, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 703, + 138, + 712 + ], + "type": "inline_equation", + "content": "\\mathbf{\\bar{C}}" + }, + { + "bbox": [ + 47, + 703, + 138, + 712 + ], + "type": "text", + "content": " Co-corresponding author." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23416" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 288 + ], + "type": "text", + "content": "the adoption of a specific structural design (e.g., a specific segmentation head) on the source side; otherwise, it would not be conducive to target deployment [46]. Class debbiasing: the less-learned (hard) categories in the source model should be paid more attention, as the class imbalance problem often exists in segmentation tasks [1, 21, 43, 58, 90]. Domain debiasing: the self-training method needs to maintain the adaptability of distinct domains, since the cross-domain segmentation tasks often face multiple or compound domains, e.g., different weather conditions. Confirmation debiasing: since the running confidence of the model will increase with self-training [3, 86], a strong self-training method should be able to dynamically adjust the uncertain estimation function for addressing the confirmation bias. However, existing self-training methods for SFUDA, lacking a comprehensive denoising mechanism, often fall short in one or more aspects (see Fig. 1(a-c)), leading to inefficiency and under-adaptation." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 291, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 291, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 47, + 291, + 289, + 483 + ], + "type": "text", + "content": "Our motivation comes from experimental observations of implementing the vanilla self-training [1] on SFUDA. As shown in Fig. 2, for each target training sample at different iterations, we record 1) its mIoU scores with the ground truth (mIoU-axis); and 2) the change degrees between the segmentation results of the current step and the ones obtained by the initial step (stability-axis). Throughout the training process, we observe that samples with high stability consistently maintain high mIoU scores, while those with low stability consistently show low mIoU scores. This indicates that noise in samples with low stability is the main contributor to error accumulation during self-training. Moreover, this issue does not significantly improve as training progresses. This motivates us to identify stable samples (i.e., whose pseudo-label change degree are low) and unstable samples to address the above issue." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 486, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 486, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 486, + 289, + 715 + ], + "type": "text", + "content": "To this end, we propose a novel denoising approach, called Stable Neighbor Denoising (SND), which can effectively discover highly correlated stable and unstable samples by nearest neighbor retrieval and denoise unstable samples with the guidance of the stable ones by bi-level optimization. Specifically, we resort to bi-level optimization [48, 70] to establish the connection between the stable and unstable sets and guide the evolution direction of unstable samples. The principle here is that if the model is trained on unstable samples with correct pseudo-labels, the loss on stable samples will be also minimized. Importantly, by the analysis of the gradient of bi-level optimization (detailed in Section 3.2), we find that matching unbiased and highly correlated stable samples for unstable samples is the key to achieving this principle. This is because the loss gradients of biased/low-correlation samples often have non-intersecting/different optimization directions, leading to bias in bi-level optimization for denoising. To tackle this problem, we propose retrieving stable" + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 337, + 76, + 525, + 228 + ], + "blocks": [ + { + "bbox": [ + 337, + 76, + 525, + 228 + ], + "lines": [ + { + "bbox": [ + 337, + 76, + 525, + 228 + ], + "spans": [ + { + "bbox": [ + 337, + 76, + 525, + 228 + ], + "type": "image", + "image_path": "3b55355efb89e8d98903e18d38d2c5d77a99a4664f739e1f24363c09db609e9a.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 236, + 547, + 304 + ], + "lines": [ + { + "bbox": [ + 304, + 236, + 547, + 304 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 547, + 304 + ], + "type": "text", + "content": "Figure 2. The plot of the mIoU scores versus stability for each target sample throughout training. Stability is calculated by the difference between the initial and the current segmentation. It shows a positive correlation between mIoU (pseudo-label quality) and stability. This observation holds during the whole training process. Experiments are from the GTA5 " + }, + { + "bbox": [ + 304, + 236, + 547, + 304 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 236, + 547, + 304 + ], + "type": "text", + "content": " Cityscapes SFUDA task." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 312, + 547, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 312, + 547, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 312, + 547, + 409 + ], + "type": "text", + "content": "neighbors by image style and spatial layout factors to eliminate the domain bias in one-step bi-level denoising optimization. In addition, we propose refining the stable samples into two sets: a whole-stable set and a category-stable set. Then, we compensate for stable neighbors using diverse object-level pasting to eliminate category bias. In this way, bi-level optimization can efficiently denoise unstable samples with stable ones under the principle." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 410, + 548, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 410, + 548, + 602 + ], + "spans": [ + { + "bbox": [ + 304, + 410, + 548, + 602 + ], + "type": "text", + "content": "Through the above techniques, the proposed SND shows superiority over previous works as follows. 1 Generic structure: SND does not require a specific network structure on both the source and target sides, endowing its universality. 2 Class debiasing: SND constructs stable neighbors with balanced categories and uses them to guide the adaptation of less-learned categories. 3 Domain debiasing: SND denoises distinct domains by retrieving neighbors with similar domain factors and can handle complex compound domain scenarios (See Table. 3). 4 Confirmation debiasing: SND designs a stability-oriented denoising mechanism that filters out noisy pseudo-labels without the need for probability or prototype distance, thereby mitigating confirmation bias (See Fig. 6). Extensive experiments show that SND consistently outperforms state-of-the-art methods in various SFUDA semantic segmentation settings." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 611, + 392, + 624 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 611, + 392, + 624 + ], + "spans": [ + { + "bbox": [ + 306, + 611, + 392, + 624 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 547, + 715 + ], + "type": "text", + "content": "Unsupervised Domain Adaptation. Domain adaptive semantic segmentation has achieved significant adaptability improvements in multiple adaptation scenarios such as synthesis-to-reality [10, 21-23, 56], cross-weather [31, 53, 54], multi-source [18, 69], etc. Overall, the current work mainly realizes cross-domain transfer from the following aspects. 1) Use the source domain data to learn a gener" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23417" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "alized representation [8]. This line of work employs data augmentation (e.g. copy-paste [58], random masking [23]) and domain randomization (e.g. expanding image styles [12, 24, 30, 56, 81, 88]) to expand the representation space of source domain models. 2) Align the source and target domains. The following works adopt a variety of domain alignment strategies (e.g. adversarial training or statistical matching) in a variety of alignment spaces (e.g. pixels space [7, 20], Fourier space [77], features space [49, 63, 66], output space [41, 59, 61], etc.), reducing the statistical difference of both domains. 3) Target characteristic mining. Most of such works use augmentation consistency [2, 11, 44, 82] and pseudo-labels [6, 81] to further improve the model's adaptive ability, e.g. tail category and local distribution." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 359 + ], + "type": "text", + "content": "Source-Free Unsupervised Domain Adaptation (SFUDA). In classification tasks, prior SFUDA works propose implicit distribution alignment [14, 37], instance contrast [83], and model perturbation [27] to align domains without source data. In segmentation tasks, the above idea is hard to adopt due to complex semantic feature spaces. Most SFUDA works for segmentation adopt self-training, which filters and retransmits the well-adapted pixels or regions through probability thresholds [85], data [25] or model discrepancy [15, 29], but they often fall into various biases." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 360, + 289, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 289, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 289, + 491 + ], + "type": "text", + "content": "Noisy Label Learning. SFUDA can be viewed as a noisy label learning problem [74, 78, 87]. Currently, noisy label learning is mostly discussed on classification tasks. The mainstream technologies include robust loss design [42, 67, 84], self-label correction [9, 33], prototype denoising [17], meta-learning based denoising [48, 70], etc. Most of those methods are designed for instance-level and are not suitable for pixel-level segmentation tasks. In particular, the prototype [34, 82] and meta-learning [16] based denoising methods have been applied to UDA segmentation tasks, but their dependence on source data limits on SFUDA." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 497, + 104, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 497, + 104, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 497, + 104, + 510 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": "Preliminary. In the setting of source-free unsupervised domain adaptation (SFUDA), we are given a segmentation model " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": " with parameter " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": " pre-trained on the labeled source dataset " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s = \\{(x_s^i,y_s^i)\\}_{i}^{N_s}" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": ", and the unlabeled target dataset " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t = \\{x_t^i\\}_i^{N_t}" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": ". The goal is to adapt the network " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": " and achieve low risk on the target dataset without accessing the source data " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_s" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": ". To achieve this goal, most works mainly conduct self-training to optimize the " + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 514, + 287, + 612 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 56, + 616, + 287, + 649 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 616, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 56, + 616, + 287, + 649 + ], + "type": "interline_equation", + "content": "\\Theta^ {\\star} = \\underset {\\Theta} {\\arg \\min } \\sum_ {i} ^ {N _ {t}} \\sum_ {l} ^ {H \\times W} \\omega^ {(i, l)} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta\\right), \\hat {y} _ {t} ^ {(i, l)} \\right], \\tag {1}", + "image_path": "2a43808b2891fed0d675a6039555959a7ab0148a09c578dd4e9a159760a384bc.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " is the cross-entropy loss and " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\hat{y}_t" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " is the pseudo-label. " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " is a weighting factor calculated by uncertainty, in which the lower the uncertainty, the closer the value is to 0. This paper proposes stable neighbor denoising techniques to estimate " + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 653, + 287, + 714 + ], + "type": "text", + "content": " in an unbiased way." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 489, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 489, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 489, + 84 + ], + "type": "text", + "content": "3.1. Division of Stable & Unstable Sets" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "spans": [ + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "type": "text", + "content": "Following the observation in Fig 2, we aim to divide target domain samples into stable and unstable sets by the change degree (also called evolution stability) of their segmentation results during the vanilla self-training [1]. Formally, for each target sample " + }, + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "type": "inline_equation", + "content": "x_{t}^{i}" + }, + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "type": "text", + "content": ", we define its evolution stability (ES) at " + }, + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 87, + 545, + 159 + ], + "type": "text", + "content": "-th iteration as follow," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 332, + 163, + 545, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 163, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 332, + 163, + 545, + 196 + ], + "type": "interline_equation", + "content": "\\operatorname {E S} ^ {i, \\tau} = \\sum_ {l} ^ {H \\times W} \\operatorname {S I M} \\left[ \\mathcal {H} \\left(x _ {t} ^ {i, l} \\mid \\Theta^ {0}\\right), \\mathcal {H} \\left(x _ {t} ^ {i, l} \\mid \\Theta^ {\\tau}\\right) \\right], \\tag {2}", + "image_path": "6e96b0deff3537817f1b10bc5fbf0d0bf6faaca6ef9b12b04b594bb798afdab1.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathrm{SIM}[\\cdot ]" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": " is the cosine similarity. " + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\Theta^{\\tau}" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": " represent the parameters of the model at " + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": "-th iteration during self-training. The larger the ES value of the sample, the more stable it is. As ES may fluctuate in different degrees of domain shift tasks, it is hard to set a suitable threshold to determine whether it is stable. Instead, we take the top-" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "k\\%" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": " ranked highly stable samples to divide the " + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": " into the stable set " + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": " and the unstable set " + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{ue}" + }, + { + "bbox": [ + 304, + 200, + 545, + 297 + ], + "type": "text", + "content": " as follows," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 344, + 302, + 545, + 317 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 302, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 344, + 302, + 545, + 317 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {s e} = \\left\\{\\left(x _ {t} ^ {i}, \\bar {y} ^ {i}\\right) \\mid x _ {t} ^ {i} \\in \\mathcal {D} _ {t}, \\mathrm {E S} ^ {i, \\tau} \\in \\top_ {k} \\right\\}, \\tag {3}", + "image_path": "68ab8ee13ca2d99b687e90640b51a9477f85df784acff96348835945cab9ca75.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 354, + 323, + 545, + 337 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 354, + 323, + 545, + 337 + ], + "spans": [ + { + "bbox": [ + 354, + 323, + 545, + 337 + ], + "type": "interline_equation", + "content": "\\mathcal {D} _ {u e} = \\left\\{x _ {t} ^ {i} \\mid x _ {t} ^ {i} \\in \\mathcal {D} _ {t}, \\mathrm {E S} ^ {i, \\tau} \\notin \\top_ {k} \\right\\}. \\tag {4}", + "image_path": "7d1cbddc12e190269d25744088f8cd5f174ba2e26630e2e38eba693797cbb2b5.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "text", + "content": "Next, the main challenge is how to utilize " + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "text", + "content": " to assist in predicting unbiased " + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{ue}" + }, + { + "bbox": [ + 304, + 341, + 545, + 365 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 371, + 545, + 384 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 371, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 371, + 545, + 384 + ], + "type": "text", + "content": "3.2. Build Relations between Stable & Unstable Sets" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 389, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 520 + ], + "type": "text", + "content": "An intuitive way is to exploit the cross-image feature similarity [68] of samples in the two sets to build relations. However, we find that the un-adapted source-trained model fails to capture this cross-image feature similarity because the representation ability of deep networks is always insufficient under the domain shift (see Table 3). Instead, we propose to build relations between the two sets from an optimization perspective and utilize bi-level learning [48, 70] to achieve this. In a nutshell, we formulate each optimization step as the inner- and outer loops, in which the former learns uncertainty parameter " + }, + { + "bbox": [ + 304, + 389, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 389, + 545, + 520 + ], + "type": "text", + "content": " for the latter." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": "Specifically, for " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": "-th optimization step, in the inner loop, the estimizable " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": " is first initialized as " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\omega_0" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": " and the model with parameters " + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "inline_equation", + "content": "\\Theta^m" + }, + { + "bbox": [ + 304, + 521, + 545, + 569 + ], + "type": "text", + "content": " is optimized on unstable samples by Eq.1," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 571, + 545, + 614 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 571, + 545, + 614 + ], + "spans": [ + { + "bbox": [ + 306, + 571, + 545, + 614 + ], + "type": "interline_equation", + "content": "\\Theta_ {\\text {i n n e r}} ^ {m + 1} = \\arg \\min _ {\\Theta} \\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\sum_ {l} ^ {H \\times W} \\omega_ {0} ^ {i} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta^ {m}\\right), \\hat {y} _ {t} ^ {(i, l)} \\right]. \\tag {5}", + "image_path": "b26c44a589cd3b7dc8b3a95c337fc97ca9d337bd177b91567ff4ae208c5bb757.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\omega_0^i" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": " is simply set to be an all-one matrix. For optimization, Eq. 5 can be approximated by one- or multi-step gradient calculation, i.e., " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Theta_{inner}^{m + 1} = \\Theta^m - \\alpha \\sum_{x_t \\in \\mathcal{D}_{ue}} \\omega_0^i \\frac{\\partial \\mathcal{L}(x_t^i | \\Theta^m)}{\\partial \\Theta} |_{\\Theta^m}" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": " is the inner-loop learning rate. It can be seen that " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": " is differentiable relative to " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Theta_{inner}^{m + 1}" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": ". Subsequently, we optimize the " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": " by enforcing the optimized model with parameters " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Theta_{inner}^{m + 1}" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": " also achieves low risk on the stable samples in " + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 304, + 614, + 545, + 714 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "23418" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 70, + 525, + 227 + ], + "blocks": [ + { + "bbox": [ + 69, + 70, + 525, + 227 + ], + "lines": [ + { + "bbox": [ + 69, + 70, + 525, + 227 + ], + "spans": [ + { + "bbox": [ + 69, + 70, + 525, + 227 + ], + "type": "image", + "image_path": "f6d1bc28f2488502568d9c85120bc8979c0d392aee47b2db8d6502952b9aa5ff.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "lines": [ + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "spans": [ + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "text", + "content": "Figure 3. The pipeline of the proposed Stable Neighbor Denoising (SND). It is formed by the student-teacher model [57]. In each optimization, SND performs the inner and outer optimizations sequentially. In the inner loop (red line), SND utilizes the style " + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{\\text{style}}" + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "text", + "content": " and the layout " + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{\\text{layout}}" + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "text", + "content": " factors to retrieve stable neighbors for unstable samples and then performs category compensation to reduce category bias. Thereafter, SND executes Eq. 8 using the teacher model to obtain the unbiased uncertainty map " + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "inline_equation", + "content": "\\omega_{\\star}" + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "text", + "content": " and initial pseudo-label " + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "inline_equation", + "content": "\\hat{y}_t" + }, + { + "bbox": [ + 45, + 233, + 548, + 291 + ], + "type": "text", + "content": ". In the outer loop (black line), SND performs Eq. 7 to optimize the student model. EMA denotes the Exponential Moving Average." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 299, + 287, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 299, + 287, + 344 + ], + "spans": [ + { + "bbox": [ + 47, + 299, + 287, + 344 + ], + "type": "interline_equation", + "content": "\\omega_ {\\star} = \\arg \\min _ {\\omega} \\sum_ {\\left(x _ {t}, \\bar {y} _ {t}\\right) \\in \\mathcal {D} _ {s e}} \\sum_ {l} ^ {H \\times W} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta_ {\\text {i n n e r}} ^ {m + 1}\\right), \\bar {y} _ {t} ^ {(i, l)} \\right]. \\tag {6}", + "image_path": "ba3d8dcf472f919697bc0ee9e32c3eb0831c768af1dac44fbd53b459336adb80.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "type": "text", + "content": "This object is driven by the following principle: " + }, + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "type": "text", + "content": " is optimized to increase/decrease the weight of these regions so that the model optimized on the unstable set samples has a small/large loss on the stable set. In this way, we establish an implicit relation between stable and unstable sets, because optimizing noisy regions of unstable samples has misleading optimization goals. Finally, in the outer loop, the model can be optimized by the learned " + }, + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "type": "inline_equation", + "content": "\\omega_{\\star}" + }, + { + "bbox": [ + 46, + 345, + 288, + 441 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 48, + 443, + 287, + 487 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 443, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 48, + 443, + 287, + 487 + ], + "type": "interline_equation", + "content": "\\Theta_ {\\text {o u t e r}} ^ {m + 1} = \\arg \\min _ {\\Theta} \\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\sum_ {l} ^ {H \\times W} \\omega_ {\\star} \\mathcal {L} \\left[ \\mathcal {H} \\left(x _ {t} ^ {(i, l)} \\mid \\Theta^ {m}\\right), \\hat {y} _ {t} ^ {(i, l)} \\right]. \\tag {7}", + "image_path": "e8b1af39b52b76b5911e900cf8bc1e02e5e28c620da67960f85550f532b1286a.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 487, + 287, + 553 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 487, + 287, + 553 + ], + "spans": [ + { + "bbox": [ + 46, + 487, + 287, + 553 + ], + "type": "text", + "content": "Problem Discussion. One important question in the above learning strategy is, does this principle work by taking arbitrary samples from the stable and unstable set to optimize? We present further analysis of the optimization of " + }, + { + "bbox": [ + 46, + 487, + 287, + 553 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 487, + 287, + 553 + ], + "type": "text", + "content": " to answer this question. For optimization, Eq. 6 is performed by gradient descent as follows," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 559, + 269, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 559, + 269, + 632 + ], + "spans": [ + { + "bbox": [ + 47, + 559, + 269, + 632 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\omega_ {\\star} = \\omega_ {0} - \\beta \\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} (x _ {t} ^ {i} | \\Theta_ {i n n e r} ^ {m + 1})}{\\partial \\omega} | _ {\\omega_ {0}} \\\\ = \\omega_ {0} - \\beta \\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} (x _ {t} ^ {i} | \\Theta_ {i n n e r} ^ {m + 1})}{\\partial \\Theta} | _ {\\Theta_ {i n n e r} ^ {m + 1}} \\cdot \\frac {\\partial \\Theta_ {i n n e r} ^ {m + 1}}{\\partial \\omega} | _ {\\omega_ {0}} \\\\ = \\omega_ {0} + \\\\ \\end{array}", + "image_path": "8d296e1bbcad38f58cfdbd9aaeb1403b726127d5d8836465c9d525748b8bbc0c.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 56, + 635, + 289, + 693 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 635, + 289, + 693 + ], + "spans": [ + { + "bbox": [ + 56, + 635, + 289, + 693 + ], + "type": "interline_equation", + "content": "\\beta \\underbrace {\\sum_ {x _ {t} \\in \\mathcal {D} _ {s e}} \\frac {\\partial \\mathcal {L} \\left(x _ {t} ^ {i} \\mid \\Theta_ {i n n e r} ^ {m + 1}\\right)}{\\partial \\Theta} \\mid_ {\\Theta_ {i n n e r} ^ {m + 1}}} _ {\\text {L o s s g r a d i e n t o f s t a b l e s e t}} \\cdot \\alpha \\underbrace {\\sum_ {x _ {t} \\in \\mathcal {D} _ {u e}} \\frac {\\partial \\mathcal {L} \\left(x _ {t} ^ {i} \\mid \\Theta^ {m}\\right)}{\\partial \\Theta} \\mid_ {\\Theta^ {m}}} _ {\\text {L o s s g r a d i e n t o f u n s t a b l e s e t}}. \\tag {8}", + "image_path": "a15e0c93d68b2ea3bfe8e7cb5339fa86139a0c012e4a548f7a4e2a123943d70f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Thus, when the continuous loss gradient on the stable" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 310, + 302, + 421, + 380 + ], + "blocks": [ + { + "bbox": [ + 310, + 302, + 421, + 380 + ], + "lines": [ + { + "bbox": [ + 310, + 302, + 421, + 380 + ], + "spans": [ + { + "bbox": [ + 310, + 302, + 421, + 380 + ], + "type": "image", + "image_path": "45cf9f18bf32ac3ff449618e1033105da3e51defb50a2b47e5b84bbd264e1a18.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 387, + 546, + 433 + ], + "lines": [ + { + "bbox": [ + 305, + 387, + 546, + 433 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 546, + 433 + ], + "type": "text", + "content": "Figure 4. Loss gradient directions in bi-level optimization. It is shown by computing the average gradient direction of different sets of classifier weights (ASPP) using the true labels. The black lines are inner-loop and the other colored lines are outer-loop." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 426, + 306, + 545, + 381 + ], + "blocks": [ + { + "bbox": [ + 426, + 306, + 545, + 381 + ], + "lines": [ + { + "bbox": [ + 426, + 306, + 545, + 381 + ], + "spans": [ + { + "bbox": [ + 426, + 306, + 545, + 381 + ], + "type": "image", + "image_path": "7bb049772898497df7ef616221865fd5394256b5ce19483c5f8825a36ef5518c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "content": "samples in " + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "content": " has a similar direction to that on the unstable samples in " + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{ue}" + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "content": ", the " + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "content": " value of the corresponding area of the unstable samples will increase, and vice versa. This indicates that optimizing noisy pseudo-labels would deviate from the optimization goal of stable samples and thus explains why noise in pseudo-labels can be estimated. Moreover, Eq. 8 also gives us the answer that arbitrarily selecting samples from the two sets will induce bias in the estimation on " + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "content": ", especially for samples with low correlation. This is because heterogeneous data always enjoy different optimal weight spaces [26], which will mislead the estimation of " + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 447, + 546, + 590 + ], + "type": "text", + "content": ". We provide below a detailed analysis." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Reason & Analysis (1) We find that samples from both sets suffering large domain shifts tend to have large differences in optimization directions, which will cause the optimization of " + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": " in Eq. 8 to be weakened by domain differences rather than the pseudo-label noise. As shown in Fig. 4, despite using real labels in bi-level optimization, domain factors (e.g. the spatial layout or image style) will still bias the optimization direction. (2) We find that samples from both sets with inconsistent category distribution cannot produce intersecting gradients in Eq. 8, causing the corresponding" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "23419" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": "gradient of " + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 72, + 287, + 144 + ], + "type": "text", + "content": " to be 0 as well. Moreover, in actual optimization, it is unacceptable to use massive stable samples to perform multi-step gradient descent for Eq. 6 due to huge computational and memory overhead. As a result, stable and unstable samples always suffer from mismatched class distributions, resulting in no gradient for missing classes." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 144, + 287, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 144, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 46, + 144, + 287, + 179 + ], + "type": "text", + "content": "In conclusion, it is reasonable to argue that matching highly correlated samples from two sets is critical for unbiased uncertain estimation." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 187, + 195, + 201 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 187, + 195, + 201 + ], + "spans": [ + { + "bbox": [ + 47, + 187, + 195, + 201 + ], + "type": "text", + "content": "3.3. Stable Neighbor Denoising" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "type": "text", + "content": "We propose to query the stable neighbor with similar domain properties for each unstable sample and compensate for missing categories for the neighbor, resulting in an unbiased estimate of " + }, + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 205, + 287, + 277 + ], + "type": "text", + "content": ". In the querying part, following the observation in Eq. 4, we specify domain factors, namely image style and spatial layout, as the proxy for querying." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": "Specifically, for image style, a series of works [36, 77] pointed out that the Fourier amplitude spectrum has a strong correlation with the image style. Thus, we adopt the flattened vector of the low-frequency Fourier amplitude spectrum as the style proxy, i.e., " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{style} = \\text{Low}(\\mathcal{A}(\\mathcal{F}(x))" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": ". For spatial layout, [32] shows that the row-wise and column-wise label statistical histogram vectors can represent the spatial distribution. Thus, we use the pseudolabels of both sets samples for computation as an alternative, i.e., " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{layout} = [\\mathcal{Q}_{layout}^{row}, \\mathcal{Q}_{layout}^{col}]" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{layout}^{row,c} = \\frac{\\sum_{row} \\arg\\max[\\mathcal{H}(x_t^l|\\Theta^m)] = c}{\\sum_{row} \\sum_{column} \\arg\\max[\\mathcal{H}(x_t^l|\\Theta^m)] = c}" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "c \\in [0,1,\\dots C]" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": " is the number of categories. With " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{style}" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}_{layout}" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": ", we can retrieve the nearest stable neighbor " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "x_{neib}^i \\in \\mathcal{D}_{se}" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": " for the unstable sample " + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "inline_equation", + "content": "x^i \\in \\mathcal{D}_{ue}" + }, + { + "bbox": [ + 46, + 278, + 287, + 464 + ], + "type": "text", + "content": " via the similarity between the proxy vectors." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": "The retrieved domain-associated neighbors may still suffer from missing categories, leading to problems described in the analysis (2). Thus, we further propose to borrow the missing class objects from other stable samples and paste them to the neighbor as compensation. However, the tail categories in the stable set " + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " may be scarce, making the objects to be copied far less abundant. To enrich the diversity of tail categories, we additionally maintain top-" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " ranked stable category sets " + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{sec}^{c} = \\{(x^{i},\\bar{y}^{i})|x^{i}\\in \\mathcal{D}_{t},\\mathrm{ES}^{i,m,c}\\in \\top_{k}\\}" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " for each category " + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " as the supplement. We name the " + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " as a stable whole set and the " + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{sec}^{c}" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " as a stable category set for distinction. Subsequently, the nearest stable neighbor " + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "inline_equation", + "content": "x_{neib}^{i}\\in \\mathcal{D}_{se}" + }, + { + "bbox": [ + 46, + 464, + 287, + 620 + ], + "type": "text", + "content": " can be compensated as follows," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 53, + 628, + 287, + 653 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 628, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 53, + 628, + 287, + 653 + ], + "type": "interline_equation", + "content": "\\bar {x} _ {n e i b} ^ {i}, \\bar {y} _ {n e i b} ^ {i} = \\mathrm {C P} \\left[ \\left(x _ {n e i b} ^ {i}, \\bar {y} _ {n e i b} ^ {i}\\right), \\left(x _ {m i x}, \\bar {y} _ {m i x}\\right) \\in \\mathcal {D} _ {\\text {s e c}} ^ {c} \\right], \\tag {9}", + "image_path": "d2ced8da84eab99b96840c1a48ab1505ade69a375344dd38f125b203fa1a7fe3.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\mathrm{CP}[\\cdot, \\cdot]" + }, + { + "bbox": [ + 46, + 653, + 287, + 677 + ], + "type": "text", + "content": " is the copy-paste operation [58] that copies objects from the latter to the former." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Through these efforts, we can use unbiased stable neighbors " + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\bar{x}_{neib}^{i}" + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": " for Eq. 6 to denoise unstable samples in an unbiased way. Fig. 3 shows the pipeline of the proposed SND" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 72, + 466, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 466, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 466, + 84 + ], + "type": "text", + "content": "Algorithm 1 The training step of SND." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "text", + "content": "Input: Target data " + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_t" + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "text", + "content": ", source-trained segmentation network " + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "text", + "content": " with parameter " + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "text", + "content": ", max iteration " + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 306, + 86, + 545, + 108 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 310, + 109, + 500, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 109, + 500, + 121 + ], + "spans": [ + { + "bbox": [ + 310, + 109, + 500, + 121 + ], + "type": "text", + "content": "Output: Well-adapted segmentation model " + }, + { + "bbox": [ + 310, + 109, + 500, + 121 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 310, + 122, + 545, + 316 + ], + "type": "list", + 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Algorithm 1 implements our SND within the student-teacher framework [57] to align with existing methods. See detailed explanations and ablation in the Appendix." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 400, + 387, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 387, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 387, + 414 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 306, + 420, + 409, + 433 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 420, + 409, + 433 + ], + "spans": [ + { + "bbox": [ + 306, + 420, + 409, + 433 + ], + "type": "text", + "content": "4.1. Datasets & Setup" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "content": "Datasets. GTA5 [51] dataset provides 24,999 game-rendering urban scene images with a resolution of " + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "inline_equation", + "content": "1914 \\times 1024" + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "content": ". SYNTHIA [52] dataset includes 9,400 virtual images with a resolution of " + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "inline_equation", + "content": "1280 \\times 760" + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "content": ". We use 19 and 16 common categories in these two datasets respectively as source data. Cityscapes [13] dataset contains 3,975 real urban scene images from 50 different cities in primarily Germany, with a resolution of " + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "inline_equation", + "content": "2048 \\times 1024" + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "content": ". ACDC [55] is the real-world dataset on adverse visual conditions, which comprises diverse weather scene images with a resolution of " + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "inline_equation", + "content": "1280 \\times 720" + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "content": ". BDD100K [80] is a compound real-world dataset consists of 8000 training images and 1000 verification images with a resolution of " + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "inline_equation", + "content": "1280 \\times 720" + }, + { + "bbox": [ + 304, + 437, + 545, + 593 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Setup. We conduct experiments using the Convolutional and Transformer structures respectively. For Convolutional structures, we adopt the Deeplab-v2 [4] with ResNet-101 [19] as the segmentation model. SGD optimizers are used for both inner and outer optimization, where the outer optimizer is set an initial learning rate " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\beta)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "2.5 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " with weight decay 0.01 while the inner optimizer is set a fixed learning rate " + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha)" + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": " of 0.01. The batch size is set as 4, and the framework is trained for 20,000 iterations on all SFUDA tasks. 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roadsidewalkBuildingWallfencepolelightsignvege.terrainskypersonridercartruckbustrainmbikebikemIoU
Source-free Synthetic-to-Real: GTA → Cityscapes (Val.)
HCL (NIPS'21) [25]92.654.682.833.226.239.838.131.984.538.685.361.330.285.433.141.614.427.344.049.7
SFDASEG (ICCV'21)† [29]91.753.486.137.632.137.438.235.686.748.589.962.634.387.251.050.84.242.753.953.4
DTST (CVPR'23) [85]93.557.684.736.525.233.444.736.786.842.881.362.337.288.148.750.635.548.359.155.4
CrossMatch(ICCV'23)† [79]95.167.887.751.341.536.347.451.387.847.887.36734.287.54151.8042.646.456.4
CROTS(IJV'24) [40]9252.485.937.335.834.642.238.486.945.691.165.136.187.341.651.1041.456.253.7
SND (Ours)93.054.084.635.630.331.041.941.687.644.686.462.638.587.548.742.936.649.558.755.6
DTST + SND (Ours)93.960.086.738.635.937.543.448.387.644.690.165.339.988.554.944.433.149.960.958.1
Source-free Synthetic-to-Real: Synthia → Cityscapes (Val.)
HCL (NIPS'21) [25]86.738.182.7100.630.325.429.782.8-85.961.924.884.5-38.9-22.637.946.4
SFDASEG (ICCV'21)† [29]90.550.081.613.32.834.725.733.183.8-89.266.034.985.3-53.4-46.146.652.3
DTST (CVPR'23) [85]88.945.883.313.70.832.731.620.885.7-82.564.427.888.1-50.9-37.657.350.7
CrossMatch(ICCV'23)† [79]91.555.585.434.48.340.840.044.486.6-84.362.422.088.3-60.0-40.645.655.6
CROTS(IJV'24) [40]89.441.682.715.11.234.733.725.783.7-87.966.634.685.4-45.9-43.549.651.3
SND (Ours)88.147.480.128.132.234.933.641.383.3-86.759.927.286.7-48.1-36.252.554.1
DTST + SND (Ours)88.743.783.632.126.032.438.044.787.2-87.962.235.587.4-40.4-46.957.255.9
Source-free clean-Adverse-Weather: Cityscapes → ACDC (Test)
URMDA (CVPR'2021)† [15]74.125.643.519.524.325.948.643.266.227.579.845.020.970.736.835.932.727.729.940.9
HCL (NIPS'2021) [25]72.624.768.521.419.431.051.846.571.828.581.243.821.576.842.844.436.130.124.044.0
SFDASEG (ICCV'21)† [29]73.529.070.719.721.936.153.251.472.031.185.341.526.276.441.946.139.833.332.046.4
DTST (CVPR'2023) [85]73.428.569.716.720.532.850.251.171.530.885.050.822.371.640.341.735.631.938.245.4
SND (Ours)74.827.669.323.626.336.552.854.675.535.084.852.525.578.844.948.137.631.134.948.1
DTST + SND (Ours)73.429.470.922.025.138.554.655.577.735.286.653.427.480.945.649.041.036.740.449.6
Source-free Open-compound: GTA → BDD100k (Test)
URMDA (CVPR'21)† [15]83.938.378.79.67.329.111.14.970.7-74.253.815.081.2-35.0-22.830.540.4
HCL (NIPS'21) [25]88.639.281.08.27.928.411.45.771.0-77.254.216.081.8-41.4-22.631.441.6
SFDASEG (ICCV'21)† [29]87.940.280.613.18.230.222.817.171.1-78.151.427.980.2-43.7-30.342.345.3
DTST (CVPR'23) [85]83.139.964.98.914.529.527.027.171.9-83.252.931.374.7-41.1-30.042.145.2
SND (Ours)84.142.674.115.221.231.131.025.570.4-83.952.833.979.9-39.1-37.541.947.8
SND + DTST (Ours)86.544.477.321.322.932.433.027.469.6-86.754.334.382.1-39.4-38.342.449.5
", + "image_path": "5039d0c6609374177ee1b6f78e2151c099a0471d51ecc7073ca187c6614cea75.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "spans": [ + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "content": "[72] with MiT-B5 [72]. AdamW [39] and Adam [28] optimizer are used for inner and outer optimization respectively, where the outer optimizer is set an initial learning rate " + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "inline_equation", + "content": "(\\beta) 6 \\times 10^{-5}" + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "content": " with weight decay 0.01, while the inner optimizer is set a fixed learning rate " + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "inline_equation", + "content": "(\\alpha)" + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "content": " of 0.01. The batch size is set as 2 and the model is trained for 20,000 iterations on all tasks. For set dividing, we use the stability (ES) evaluated at " + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "inline_equation", + "content": "10k(\\tau)" + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "content": " iterations and regard the top " + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "inline_equation", + "content": "k\\%" + }, + { + "bbox": [ + 46, + 433, + 287, + 541 + ], + "type": "text", + "content": ") ranked stable samples as the stable set for all adaptation tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 551, + 286, + 563 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 551, + 286, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 551, + 286, + 563 + ], + "type": "text", + "content": "4.2. Comparison with State-of-the-art Alternatives" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": "Performance Comparison on SFUDA. We compare our methods with the state-of-the-art approaches on source-free unsupervised domain adaptive semantic segmentation (SFUDA), including adapting to single and compound target domains. Table 1 shows that the proposed SND achieves the best performance on all SFUDA tasks. Moreover, SND can be combined with other method (DTST [85]) and achieves further significant improvements. In the two synthetic-to-real SFUDA adaptation tasks, our approach (SND+DTST) surpasses the second-highest methods by " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "inline_equation", + "content": "3.1\\%" + }, + { + "bbox": [ + 46, + 570, + 287, + 713 + ], + "type": "text", + "content": ", respectively. On real-to-real adaptation tasks, i.e., ACDC with various weather conditions, our ap" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 321, + 431, + 531, + 531 + ], + "blocks": [ + { + "bbox": [ + 46, + 379, + 545, + 424 + ], + "lines": [ + { + "bbox": [ + 46, + 379, + 545, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 545, + 424 + ], + "type": "text", + "content": "Table 1. Comparison of SND with state-of-the-art works on the tasks of source-free domain adaptation in semantic segmentation. The model is deeplab-v2 with ResNet101. The report metric is IoU(\\%). " + }, + { + "bbox": [ + 46, + 379, + 545, + 424 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 379, + 545, + 424 + ], + "type": "text", + "content": " denotes using the specific network on the source side, e.g., SFDASEG using multiple heads, CrossMatch using two segmentation models with depth estimation. DTST+SND means using the minority class resampling strategy in DTST [85], as minority class adaptation is very challenging in source-free UDA." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 321, + 431, + 531, + 531 + ], + "lines": [ + { + "bbox": [ + 321, + 431, + 531, + 531 + ], + "spans": [ + { + "bbox": [ + 321, + 431, + 531, + 531 + ], + "type": "table", + "html": "
Continual source-free adaptation: Cityscapes→ACDC
Timet →
FogNightRainSnowmIoU
Source model [72]69.140.359.757.856.7
TENT * [62]68.536.359.954.754.9
CoTTA * [64]70.441.663.960.859.2
HCL [25]70.039.963.761.258.7
SFDASEG † [29]70.142.162.461.859.1
SND72.143.166.365.661.8
", + "image_path": "88594d1b4321bdf64e74dadb45ec1dc45792f837e5e590efad9a44ff03cb4d16.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 533, + 545, + 588 + ], + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 588 + ], + "type": "text", + "content": "Table 2. Comparison on the tasks of continual source-free domain adaptation semantic segmentation. The segmentation model is SegFormer with MiT-B5 as the backbone. *means we use the target domain data for multiple round adaptations rather than one round in the original paper." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "proach (SND+DTST) still maintains excellent performance, improving the performance of the current best method (SF-DASEG [29]) by " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "3.2\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". When adapted to the more challenging open-compound domain BDD100k, the proposed method (SND+DTST) achieves a large performance gain, surpassing the second-highest method by " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "4.2\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": ". The performance under various conditions proves that our method can effectively cope with the pseudo-label noise in complex environments, and alleviate the bias problem in SFUDA tasks." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23421" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 86, + 70, + 507, + 126 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 507, + 126 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 507, + 126 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 507, + 126 + ], + "type": "table", + "html": "
UnweightedPE. [62]MCC. [89]DAC. [29]MPC. [15]PD. [82]CIA. [68]SND
GTA → Cityscapes49.650.5 (+0.9)52.1 (+2.5)51.7 (+2.1)51.6 (+2.0)50.9 (+1.3)49.8 (+0.2)55.6 (+6.0)
Synthia → Cityscapes48.249.5 (+1.3)52.9 (+2.7)49.4 (+1.2)51.5 (+3.3)49.7 (+1.5)47.2 (-1.0)54.1 (+5.9)
Cityscapes → ACDC43.141.3 (-1.8)45.1 (+2.0)42.9 (-0.3)43.0 (-0.1)39.1 (-4.0)39.2 (-3.9)48.1 (+5.0)
GTA → BDD100k42.141.5 (-0.6)44.8 (+2.7)41.2 (-0.9)42.9 (+0.8)40.5 (-1.6)37.1 (-5.0)47.8 (+5.7)
", + "image_path": "95993d7e325adc994325bc4893a640feb35dd2c94314d8c9bf9d94019e092e58.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 56, + 185, + 279, + 251 + ], + "blocks": [ + { + "bbox": [ + 46, + 128, + 547, + 174 + ], + "lines": [ + { + "bbox": [ + 46, + 128, + 547, + 174 + ], + "spans": [ + { + "bbox": [ + 46, + 128, + 547, + 174 + ], + "type": "text", + "content": "Table 3. Ablation experiments on uncertainty estimation for source-free cross-domain segmentation tasks. We compared the following uncertainty estimation methods, probability entropy (PE.) [62], multi-classifier consistency (MCC.) [89], data augmentation consistency (DAC.) [29], model perturbation consistency (MPC.) [15], prototype distance (PD.) [82], cross-image association [68](CIA.). 'Unweighted' means original pseudo labels." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 56, + 185, + 279, + 251 + ], + "lines": [ + { + "bbox": [ + 56, + 185, + 279, + 251 + ], + "spans": [ + { + "bbox": [ + 56, + 185, + 279, + 251 + ], + "type": "table", + "html": "
Division metricGTA → CityscapesCityscapes → ACDC
Image-level entropy [45]52.945.1
Patch-level entropy [59]51.743.6
Image-level loss [74]52.744.1
Domain distance [60]51.642.4
Stability55.648.1
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QueryGTA → CityscapesCityscapes → ACDC
Random54.244.7
Qlayout55.344.9
Qstyle55.147.5
Qlayout + Qstyle55.648.1
", + "image_path": "7b3db39005eb151c7d47188f919e7f78cb0cbe18f4df1204db9398de0b18ca6f.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 355, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 475 + ], + "type": "text", + "content": "Performance Comparison on Continual SFUDA. As real-world machine systems always operate in nonstationary environments, we also verify the effectiveness of our approach in the continual adaptation setting. In Table 2, our method maintains good performance, with an average adaptability increase of " + }, + { + "bbox": [ + 46, + 355, + 287, + 475 + ], + "type": "inline_equation", + "content": "5.1\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 475 + ], + "type": "text", + "content": " in multiple domains under continual settings, showing obvious advantages compared with other methods. It is verified that our method can better adapt to multi-domain environments and alleviate model degradation caused by domain bias and confirmation bias." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 480, + 141, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 141, + 493 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 141, + 493 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "type": "text", + "content": "Effectiveness of denoising module. In Table 3, we ablate the denoising part, i.e., SND, and compare it with alternatives. In two synthetic-to-real SFUDA experiments, SND achieves a performance improvement of nearly " + }, + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "type": "inline_equation", + "content": "6\\%" + }, + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "type": "text", + "content": ", showing optimal competitiveness than other alternatives. In multiple and compound adaptation tasks, SND produces a performance improvement of nearly " + }, + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 46, + 498, + 286, + 641 + ], + "type": "text", + "content": ". On difficult transfer tasks, SND exhibits stable cross-domain adaptability, whereas other alternatives suffer from severe performance degradation. The effectiveness of SND is mainly contributed to its accurate estimation of uncertain and comprehensive denoising capabilities." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "content": "Effectiveness of the Stability Metric. In Table 4, we compare the proposed stability with other adaptability metrics for subset division, including regional entropy [45,59], image-level loss [74], and domain distance [60]. Denoising using stability metrics shows obvious advantages on two adaptive tasks, with gains increased by " + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "inline_equation", + "content": "2.7\\%" + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "inline_equation", + "content": "3.0\\%" + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "content": " com" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 314, + 185, + 538, + 232 + ], + "blocks": [ + { + "bbox": [ + 47, + 323, + 286, + 346 + ], + "lines": [ + { + "bbox": [ + 47, + 323, + 286, + 346 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 286, + 346 + ], + "type": "text", + "content": "Table 5. Ablation study of querying stable neighbor strategies. Random means randomly selecting stable samples from " + }, + { + "bbox": [ + 47, + 323, + 286, + 346 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 47, + 323, + 286, + 346 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 314, + 185, + 538, + 232 + ], + "lines": [ + { + "bbox": [ + 314, + 185, + 538, + 232 + ], + "spans": [ + { + "bbox": [ + 314, + 185, + 538, + 232 + ], + "type": "table", + "html": "
Category compensationGTA → CityscapesCityscapes → ACDC
None53.046.3
Dse54.247.1
Dsec55.648.1
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" + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{sec}" + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "text", + "content": " means we select samples from " + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{sec}" + }, + { + "bbox": [ + 305, + 233, + 545, + 267 + ], + "type": "text", + "content": " for compensation." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 281, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 281, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 305, + 281, + 545, + 316 + ], + "type": "text", + "content": "pared to the second competitor. We think it contributes to the ability to screen more reliable samples to provide effective support for denoising." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 317, + 546, + 412 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 317, + 546, + 412 + ], + "spans": [ + { + "bbox": [ + 305, + 317, + 546, + 412 + ], + "type": "text", + "content": "Effectiveness of Query Methods. In Table 5, we verify the impact of different retrieval factors on adaptability. It shows that gradually adding domain-related factors for retrieving stable neighbors can improve adaptability. In special, on complex compound domain adaptation task, Cityscapes " + }, + { + "bbox": [ + 305, + 317, + 546, + 412 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 305, + 317, + 546, + 412 + ], + "type": "text", + "content": " ACDC, retrieving by domain factors shows greater improvements. This further verifies matching highly correlated neighbors is crucial for bi-level optimization." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "content": "Effectiveness of Category Compensation. In Table 6, we verify the impact of category compensation on adaptability. Using the stable set " + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{se}" + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "content": " as the copy object for compensation improves performance by " + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "content": " on two tasks respectively, verifying the impact of missing categories on denoising. Furthermore, adding category stable sets as replication objects can improve the performance by " + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "inline_equation", + "content": "1.0\\%" + }, + { + "bbox": [ + 305, + 413, + 545, + 521 + ], + "type": "text", + "content": ", showing that diversity compensation is more conducive to reducing the bias of bi-level optimization." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 528, + 435, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 528, + 435, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 528, + 435, + 540 + ], + "type": "text", + "content": "4.4. Qualitative assessment" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": "Visualization of the Learned Uncertainty Map. Fig. 5 presents the learned uncertain map " + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": " on two SFUDA tasks. It can be seen that the uncertainty maps from probability entropy [61] and multi-classifier voting [56,82] contain a large amount of noise. Moreover, in the harder open-compound task Cityscapes " + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 304, + 545, + 545, + 689 + ], + "type": "text", + "content": " ACDC, the estimation bias of their methods is more obvious in difficult domain data, which will be a predisposing factor for error accumulation. In contrast, SND alleviates bias estimation and presents more reasonable uncertainty maps for different categories and domains. Moreover, our SND even can give accurate estimation against noise at the segmentation edges." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Denoising Effect during Training. In Fig. 6, we plot the mIoU scores on the validation during training to show" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "23422" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 69, + 534, + 182 + ], + "blocks": [ + { + "bbox": [ + 60, + 69, + 534, + 182 + ], + "lines": [ + { + "bbox": [ + 60, + 69, + 534, + 182 + ], + "spans": [ + { + "bbox": [ + 60, + 69, + 534, + 182 + ], + "type": "image", + "image_path": "e3d5be07296ba9c4c3d3dd4f44f304d5ad8adbe595cb7e25c21cd4ee787ac864.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 225, + 182, + 376, + 191 + ], + "lines": [ + { + "bbox": [ + 225, + 182, + 376, + 191 + ], + "spans": [ + { + "bbox": [ + 225, + 182, + 376, + 191 + ], + "type": "text", + "content": "(a). Single-target source-free adaptation" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 60, + 191, + 532, + 308 + ], + "blocks": [ + { + "bbox": [ + 60, + 191, + 532, + 308 + ], + "lines": [ + { + "bbox": [ + 60, + 191, + 532, + 308 + ], + "spans": [ + { + "bbox": [ + 60, + 191, + 532, + 308 + ], + "type": "image", + "image_path": "cd6b422502e3f4fff6f0ece47d2dfbb6c7add9897cef1015cf2b59db72a0134d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 220, + 308, + 388, + 319 + ], + "lines": [ + { + "bbox": [ + 220, + 308, + 388, + 319 + ], + "spans": [ + { + "bbox": [ + 220, + 308, + 388, + 319 + ], + "type": "text", + "content": "(b). Open-compound source-free adaptation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 361, + 168, + 468 + ], + "blocks": [ + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "lines": [ + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "type": "text", + "content": "Figure 5. Visualization of different uncertainty estimation results on both GTA " + }, + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "type": "text", + "content": " Cityscapes and GTA " + }, + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 319, + 546, + 353 + ], + "type": "text", + "content": " BDD100k tasks. Diff.GT denotes the ground truth estimation mask. Entropy map is shown by probability entropy [61]. Prototype map is shown by the difference between the Aspp classifier and prototype classifier [56,82]." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 361, + 168, + 468 + ], + "lines": [ + { + "bbox": [ + 50, + 361, + 168, + 468 + ], + "spans": [ + { + "bbox": [ + 50, + 361, + 168, + 468 + ], + "type": "image", + "image_path": "4e1850c9a3b781825a4659240177897e566da421c9925d3c1c3d6a60079a9f09.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 475, + 287, + 498 + ], + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 498 + ], + "type": "text", + "content": "Figure 6. Comparison of the mIoU score " + }, + { + "bbox": [ + 46, + 475, + 287, + 498 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 475, + 287, + 498 + ], + "type": "text", + "content": " curve on the validation set during training on two transfer tasks." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 170, + 361, + 284, + 468 + ], + "blocks": [ + { + "bbox": [ + 170, + 361, + 284, + 468 + ], + "lines": [ + { + "bbox": [ + 170, + 361, + 284, + 468 + ], + "spans": [ + { + "bbox": [ + 170, + 361, + 284, + 468 + ], + "type": "image", + "image_path": "1cae91168d8e4daab93c2a7e239d0b758d3df3b12d3d214ce6d6cdf8f541c083.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 46, + 507, + 287, + 614 + ], + "type": "text", + "content": "the denoising effect. In single-target adaptation (a), compared with DTST [85], SND shows stronger denoising ability, allowing the model to achieve faster convergence speed during training and to obtain better performance. In multi-target adaptation (b), DTST degrades in the later stages of training, which shows that more difficult adaptation tasks place higher requirements on denoising. In contrast, SND shows a better denoising effect and can effectively alleviate model degradation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 623, + 200, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 623, + 200, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 623, + 200, + 635 + ], + "type": "text", + "content": "4.5. Hyperparameter Sensitivity" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": "In Table 7, we analyze the sensitivity of the hyperparameter top- " + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "inline_equation", + "content": "k\\%" + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": " in Eq. 2 on the two SFUDA tasks across three runs. For " + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": ", we set the range from 1 to 10, because too small " + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": " cannot select enough valuable samples, while too large " + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 642, + 287, + 712 + ], + "type": "text", + "content": " will inject massive noise into the stable set. On the two tasks, the fluctuation range of mIoU is" + } + ] + } + ], + "index": 10 + }, + { + "type": "table", + "bbox": [ + 321, + 359, + 531, + 444 + ], + "blocks": [ + { + "bbox": [ + 321, + 359, + 531, + 444 + ], + "lines": [ + { + "bbox": [ + 321, + 359, + 531, + 444 + ], + "spans": [ + { + "bbox": [ + 321, + 359, + 531, + 444 + ], + "type": "table", + "html": "
k (%)1.02.55.07.510.0
GTA → Cityscapes57.857.958.157.857.8
Cityscapes → ACDC49.950.250.750.449.8
τ (×1000)2481012
GTA → Cityscapes57.958.058.158.158.1
Cityscapes → ACDC50.550.650.750.750.7
", + "image_path": "6d14e37db1ece55970b9b4f152c1bc3b4561204b10b074d944449cb50a1153ff.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "lines": [ + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "spans": [ + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "type": "text", + "content": "Table 7. Sensitivity study of the hyper-parameter " + }, + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 320, + 445, + 530, + 456 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": "within " + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "inline_equation", + "content": "0.5\\%" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "inline_equation", + "content": "0.8\\%" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": ", showing that SND is not sensitive to " + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": ". For " + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": ", we set the range from 2,000 to 12,000 to verify the impact of the stability evaluation iteration on SND for selecting stable samples. Results show that SND has very small fluctuations in performance, within " + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "inline_equation", + "content": "0.3\\%" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": ". This indicates that SND is not sensitive to " + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 460, + 545, + 544 + ], + "type": "text", + "content": " and also verifies the observation in Fig. 2 from the side." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 552, + 378, + 564 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 552, + 378, + 564 + ], + "spans": [ + { + "bbox": [ + 306, + 552, + 378, + 564 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 570, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 712 + ], + "type": "text", + "content": "In this work, we propose Stable Neighbor Denoising to perform unbiased denoising for the SFUDA semantic segmentation tasks. SND detects and suppresses noise in unstable samples by establishing the connection between the stable and unstable samples through bi-level optimization. The proposed retrieval nearest neighbor strategy and category compensation strategy further reduce the bias of bi-level optimization, thereby achieving effective denoising. Extensive experiments on different source-free adaptation scenarios, backbones, and ablations show that SND effectively estimates the noise of pseudo-labels and achieves state-of-the-art performance on all benchmarks." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "23423" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Nikita Araslanov and Stefan Roth. 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Generated results of StableVITON: VITON-HD (the first row), SHHQ-1.0 (the first two images in the second row), and web-crawled images (the last two images in the second row). All results are generated using StableVITON trained on VITON-HD dataset." + ], + "image_footnote": [], + "bbox": [ + 78, + 462, + 279, + 657 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/24e1f96c2aeacdfa80fdc955fe826b8788a7616a35b04934f807110d473761d5.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 462, + 483, + 657 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d883e59fa85a56cdd514abe3f54352df80d7300b775719abcf4592faa7336d2f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 486, + 462, + 686, + 657 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c3bd79f0004f279cbb424a9302ec7cdc9e225aec24dda2f7838fed635d40dca1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 687, + 462, + 890, + 657 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 698, + 313, + 713 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Given a clothing image and a person image, an image-based virtual try-on aims to generate a customized image that appears natural and accurately reflects the characteristics of the clothing image. In this work, we aim to expand the applicability of the pre-trained diffusion model so that it can be utilized independently for the virtual try-on task. The main challenge is to preserve the clothing details while effectively utilizing the robust generative capability of the pre-trained model. In order to tackle these issues, we propose StableVITON, learning the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model in an end-to", + "bbox": [ + 75, + 720, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "end manner. Our proposed zero cross-attention blocks not only preserve the clothing details by learning the semantic correspondence but also generate high-fidelity images by utilizing the inherent knowledge of the pre-trained model in the warping process. Through our proposed novel attention total variation loss and applying augmentation, we achieve the sharp attention map, resulting in a more precise representation of clothing details. StableVITON outperforms the baselines in qualitative and quantitative evaluation, showing promising quality in arbitrary person images. Our code is available at https://github.com/rlawjdghek/StableVITON.", + "bbox": [ + 496, + 699, + 893, + 880 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8176", + "bbox": [ + 480, + 945, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 89, + 209, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The objective of an image-based virtual try-on is to dress a given clothing image on a target person image. Most of the previous virtual try-on approaches [3, 7, 10, 14, 15, 29, 31, 33] leverage paired datasets consisting of clothing images and person images wearing those garments for training purposes. These methods typically include two modules: (1) a warping network to learn the semantic correspondence between the clothing and the human body, and (2) a generator that fuses the warped clothing and the person image.", + "bbox": [ + 75, + 114, + 468, + 251 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite achieving significant advancements, previous methods [3, 8, 15, 31] still have limitations in achieving generalizability, particularly in maintaining the complex background in an arbitrary person image. The nature of matching clothing and individuals in the virtual try-on dataset [3, 10, 18] makes it challenging to collect data in diverse environments [20], which in turn leads to limitations in the generator's generative capability.", + "bbox": [ + 75, + 251, + 468, + 371 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Meanwhile, recent advancements in large-scale pretrained diffusion models [23, 24, 27] have led to the emergence of downstream tasks [6, 8, 16, 19, 26, 34, 36] that control the pre-trained diffusion models for task-specific image generation. Thanks to the powerful generative ability, several works [17, 34] have succeeded in synthesizing high-fidelity human images using the prior knowledge of the pre-trained models, which signifies the potential for extension to the virtual try-on task.", + "bbox": [ + 75, + 371, + 468, + 507 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this paper, we aim to expand the applicability of the pre-trained diffusion model to provide a standalone model for the virtual try-on task. In the effort to adapt the pretrained diffusion model for virtual try-on, a significant challenge is to preserve the clothing details while harnessing the knowledge of the pre-trained diffusion model. This can be achieved by learning the semantic correspondence between clothing and the human body using the provided dataset. Recent research [8, 19] that has employed pretrained diffusion models in virtual try-on has shown limitations due to the following two issues: (1) insufficient spatial information available for learning the semantic correspondence [19], and (2) the pre-trained diffusion model not being fully utilized, as it pastes the warped clothing in the RGB space, relying on external warping networks as previous approaches [3, 7, 15, 31, 33] for aligning the input condition.", + "bbox": [ + 75, + 507, + 468, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To overcome these issues, we propose StableVITON, which learns the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model. To incorporate the spatial information of the clothing for learning semantic correspondence, we introduce an encoder [34] that takes clothing as input and conditions the U-Net with the intermediate features of the encoder via zero cross-attention blocks. Warping through the zero cross-attention block in a pre-trained", + "bbox": [ + 75, + 763, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/56e4aeb4aa0681bf8b1c198b61335b5816eb48f488ad07b80f019ada6c8db8a3.jpg", + "image_caption": [ + "Figure 2. Visualization of the semantic correspondence learned by our StableVITON. We overlay the attention map for the clothing regions onto the generated images for visualization." + ], + "image_footnote": [], + "bbox": [ + 504, + 88, + 890, + 284 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "diffusion model has the following two advantages: (1) preserving the clothing details by learning the semantic correspondence; (2) synthesizing high-fidelity images by leveraging the pre-trained models' inherent knowledge about humans in the warping process. As shown in Fig. 2, the attention mechanism in the latent space performs patch-wise warping by activating each token corresponding to clothing alignment within the generation region.", + "bbox": [ + 496, + 364, + 890, + 487 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To further sharpen attention maps, we propose a novel attention total variation loss and apply the augmentation, which yields improved preservation of clothing details. By not impairing the pre-trained diffusion model, this architecture generates high-quality images even when images with complex backgrounds are provided, only using an existing virtual try-on dataset. Our extensive experiments show that StableVITON outperforms the existing virtual try-on method by a large margin. In summary, our contributions are as follows:", + "bbox": [ + 496, + 494, + 890, + 645 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Our proposed StableVITON, to the best of our knowledge, is the first end-to-end virtual try-on method finetuned on the pre-trained diffusion model without an independent warping process.", + "- We propose a zero cross-attention block, which learns semantic correspondence between the clothing and the human body, to condition the intermediate features from the spatial encoder.", + "- We propose a novel attention total variation loss and apply augmentation for further precise semantic correspondence learning.", + "- StableVITON shows state-of-the-art performance over existing virtual try-on models in both qualitative and quantitative results. Moreover, through the evaluation of a trained model on multiple datasets, StableVITON demonstrates its promising quality in a real-world setting." + ], + "bbox": [ + 500, + 656, + 890, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8177", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "GAN-based Virtual Try-On. To properly try-on the given clothing image to the target person, existing approaches [3, 7, 15, 31] based on generative adversarial network (GAN) have attempted to address the virtual try-on problem using a two-stage strategy: (1) deforming the clothing to the proposal region and (2) fusing the warped clothing via try-on generator based on GAN. In order to achieve precise clothing deformation, previous methods [1, 7, 11, 15, 31] leverage a trainable network that estimates a dense flow map [37] to deform the clothing to the human body. At the same time, several approaches [3, 7, 14, 15, 31, 33] have been attempted to address the misalignment between the warped clothing and the human body, such as using a normalization [3] or distillation [7, 14]. However, the existing approaches still are not generalized well, leading to significant performance degradation in arbitrary person images with complex backgrounds. In this paper, we effectively address such issues by proposing a method that leverages the powerful generation ability of the pre-trained model.", + "bbox": [ + 76, + 114, + 472, + 402 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion-based Virtual Try-On. Due to the remarkable generative capabilities, research on virtual try-on has extensively discussed the application of the diffusion models. While TryOnDiffusion [38] introduces an architecture for try-on using two U-Nets, this method requires a large-scale and challenging-to-collect dataset, consisting of image pairs of the same person wearing the same clothing in two different poses. Therefore, much recent research has shifted their focus towards using the prior of a large-scale pre-trained diffusion models [13, 22, 24, 32] in the virtual try-on task. LADI-VTON [19] represents the clothing as pseudo-words, and DCI-VTON [8] applies a warping network to input the clothing as conditions for the pre-trained diffusion models. While both models deal with background-related issues, they suffer from preserving high-frequency details due to the excessive loss of spatial information from the CLIP encoder [19] and drawbacks such as incorrectly warped clothing inherited from the independent warping network [8]. On the other hand, we propose to condition the intermediate feature maps of a spatial encoder through zero cross-attention block, which allows for using the prior knowledge of the pre-trained model in the warping process.", + "bbox": [ + 76, + 404, + 472, + 737 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 753, + 204, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Stable Diffusion Model. Stable Diffusion model [24] is a large-scale diffusion model trained on LAION dataset [28], built upon the Latent Diffusion model (LDM) [24], which performs a denoising process in the latent space of an autoencoder. With a fixed encoder $(\\mathcal{E})$ , an input image $\\mathbf{x}$ is first transformed to latent feature $\\mathbf{z}_0 = \\mathcal{E}(\\mathbf{x})$ . Given a predefined variance schedule $\\beta_{t}$ , we can define a forward diffusion process in the latent space following denoising diffu", + "bbox": [ + 76, + 779, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "sion probabilistic models [13]:", + "bbox": [ + 500, + 90, + 705, + 106 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 116, + 890, + 135 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $t \\in \\{1, \\dots, T\\}$ , $T$ represents the number of steps in the forward diffusion process, $\\alpha_{t} \\coloneqq 1 - \\beta_{t}$ , and $\\bar{\\alpha}_{t} \\coloneqq \\Pi_{s=1}^{t} \\alpha_{s}$ . As a training loss, Stable Diffusion model employs the simplified objective function from LDM [15]:", + "bbox": [ + 496, + 143, + 893, + 205 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\mathcal {E} (\\mathbf {x}), \\mathbf {y}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\tau_ {\\theta} (\\mathbf {y})\\right) \\| _ {2} ^ {2} \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 215, + 890, + 247 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where the denoising network $\\epsilon_{\\theta}(\\cdot)$ is implemented with a U-Net architecture [25] and $\\tau_{\\theta}(\\cdot)$ is the CLIP [22] text encoder to condition the text prompt $y$ .", + "bbox": [ + 496, + 247, + 893, + 294 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 500, + 306, + 591, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Model Overview", + "text_level": 1, + "bbox": [ + 500, + 330, + 663, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "An overview of StableVITON is presented in Fig. 3(a). Given a person image $\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}$ , the clothing-agnostic person representation $\\mathbf{x}_a \\in \\mathbb{R}^{H \\times W \\times 3}$ (we call it as 'agnostic map') [3] is proposed to eliminate any clothing information in $\\mathbf{x}$ . In this work, we approach the virtual try-on as an exemplar-based image inpainting problem [32] to fill theagnostic map $\\mathbf{x}_a$ with the clothing image $\\mathbf{x}_c$ . As the input of the U-Net, we concatenate four components: (1) the noisy image $(\\mathbf{z}_t)$ , (2) latentagnostic map $(\\mathcal{E}(\\mathbf{x}_a))$ , (3) the resized clothing-agnostic mask $(\\mathbf{x}_{m_a})$ , (4) latent dense pose condition $(\\mathcal{E}(\\mathbf{x}_p))$ [9] to preserve the person's pose. To align the input channels, we expand the initial convolution layer of the U-Net to 13 (i.e., $4 + 4 + 1 + 4 = 13$ ) channels with a convolution layer initialized with zero weights. For exemplar conditioning, we input the $\\mathbf{x}_c$ to the CLIP image encoder [32].", + "bbox": [ + 496, + 354, + 890, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To preserve the fine details of the clothing, we introduce a spatial encoder, which takes latent clothing $(\\mathcal{E}(\\mathbf{x}_c))$ as input. This spatial encoder copies the weight of the pre-trained U-Net [34] and conditions the intermediate feature maps of the encoder to U-Net via zero cross-attention blocks. During training, we apply augmentation and further finetune the model with our proposed attention total variation loss, which makes the attention region on the clothing sharper. The detailed model architecture is described in the supplementary material.", + "bbox": [ + 496, + 597, + 893, + 748 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.2. StableVITON", + "text_level": 1, + "bbox": [ + 500, + 756, + 643, + 771 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Zero Cross-Attention Block. We aim to condition the intermediate feature maps of the clothing to U-Net, properly aligning with the human body. The operation of adding the unaligned clothing feature map to the human feature map is insufficient to preserve clothing details due to misalignment between the human body and the clothing. Therefore, we proposed a zero cross-attention block to be a flexible operation by applying an attention mechanism for conditioning.", + "bbox": [ + 496, + 779, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8178", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/de6b6a92a84da2f943eca46edd5addd21db7f1937427b67156c7cc3e4a567358.jpg", + "image_caption": [ + "(a) Overview of StableVITON" + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 599, + 345 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/66aac335d69389b123521d8f2373401d2a76370cecb94ecd369555201760a3f7.jpg", + "image_caption": [ + "(b) Zero Cross-Attention Block", + "Figure 3. For the virtual try-on task, StableVITON additionally takes three conditions: agnostic map, agnostic mask, and dense pose, as the input of the pre-trained U-Net, which serves as the query (Q) for the cross-attention. The feature map of the clothing is used as the key (K) and value (V) for the cross-attention and is conditioned on the UNet, as depicted in (b)." + ], + "image_footnote": [], + "bbox": [ + 668, + 103, + 864, + 330 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, as shown in Fig. 3(b), the feature map of the U-Net decoder block inputs to self-attention, followed by the cross-attention layer where the query (Q) comes from the previous self-attention layer and the spatial encoder's feature map serves as the key (K) and value (V). To eliminate harmful noise, we introduce a linear layer initialized with zero weight after the feed-forward operation [34].", + "bbox": [ + 75, + 425, + 470, + 532 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To successfully align the clothing to the human body part via cross-attention, it is crucial to ensure semantic correspondence between the key tokens (clothing) and the query tokens (human body). For instance, when dealing with a query token related to the right shoulder, the corresponding key tokens should exhibit higher attention scores in the corresponding right shoulder area of the clothing. In Fig. 4(a), we averaged the attention maps of the resolution of $32 \\times 24$ across the head dimension and arranged them flatly. For clear visualization, we downsample the generated image to a resolution of $32 \\times 24$ and then resize it back to $32^2 \\times 24^2$ . Subsequently, we overlay this generated image with the attention map corresponding to each query token. Zooming in on the upper and middle of the generated clothing area, we observe that the key tokens unrelated to the corresponding query token, such as the bottom of the clothing, are activated in the attention map. This indicates that the cross-attention layer fails to learn the exact semantic correspondence between query and key tokens, combining the several key tokens of the clothing to generate the color corresponding to the query token during training. Therefore, as shown in Fig. 4, the stripes on the clothing are not distinctly visible.", + "bbox": [ + 75, + 534, + 470, + 881 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Augmentation. To mitigate such issues of key tokens unre", + "bbox": [ + 76, + 885, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "lated to query tokens being attended to, we alter the feature map by applying augmentation, including random shifts to input conditions. Detailed settings of augmentation are described in supplementary material. Along with the augmented input conditions, we train our model with the objective function defined as follows:", + "bbox": [ + 496, + 425, + 890, + 516 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\zeta , \\mathbf {x} _ {c}, \\mathcal {E} (\\mathbf {x} _ {c}), \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\zeta , t, \\tau_ {\\phi} (\\mathbf {x} _ {c}), \\mathcal {E} (\\mathbf {x} _ {c})) \\| _ {2} ^ {2} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 521, + 890, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\zeta = [\\mathbf{z}_t;\\mathcal{E}(\\mathbf{x}_a);\\mathbf{x}_{m_a};\\mathcal{E}(\\mathbf{x}_p)]$ , and $\\tau_{\\phi}$ is the CLIP image encoder. Note that we do not update the parameters of the original blocks, as depicted in Fig. 3(a).", + "bbox": [ + 496, + 551, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The rationale behind this strategy is to force the model to learn fine-grained semantic correspondence using augmentation, instead of just moderately injecting the clothes at similar positions. As shown in Fig. 4(b), we can confirm that key tokens related to query tokens have high attention scores, signifying that the cross-attention layer has learned the high semantic correspondence between the clothing-agnostic region and clothing.", + "bbox": [ + 496, + 598, + 890, + 718 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Attention Total Variation Loss. While the cross-attention layer successfully aligns the clothing to the agnostic map, the points with high attention scores appear in dispersed positions, as shown in the attention map of Fig. 4(b). This causes inaccurate details in generated images, such as color discrepancies.", + "bbox": [ + 496, + 719, + 890, + 808 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To address such an issue, we propose attention total variation loss. As the attention scores are the weight for the output, we calculate the center coordinates as a weighted sum of the attention map and the grid. Therefore, given the $H_{q}W_{q}$ query tokens and $h_k w_k$ key tokens, we calculate center coordinate map $F \\in \\mathbb{R}^{H_q \\times W_q \\times 2}$ as follows:", + "bbox": [ + 496, + 810, + 890, + 898 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8179", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/b6ef1068bff360dc5c1412015ff1d0775461730b00458cc4bf9fcc0137081f43.jpg", + "image_caption": [ + "Figure 4. Visualization of attention map from a zero cross-attention block of 32 resolution." + ], + "image_footnote": [], + "bbox": [ + 81, + 85, + 893, + 261 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nF _ {i j n} = \\frac {1}{h _ {k} w _ {k}} \\sum_ {k = 1} ^ {h _ {k}} \\sum_ {l = 1} ^ {w _ {k}} \\left(A _ {i j k l} \\odot G _ {k l n}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 292, + 468, + 334 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where we average the attention map over the head dimension and reshape it as $A \\in \\mathbb{R}^{H_q \\times W_q \\times h_k \\times w_k}$ , and $G \\in [-1, 1]^{h_k \\times w_k \\times 2}$ is a 2D normalized coordinate. $n \\in \\{0, 1\\}$ in Eq. 4 denotes the dimension of attention map coordinates and $\\odot$ indicates element-wise multiplication operation.", + "bbox": [ + 76, + 342, + 468, + 417 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For each query token in each clothing-agnostic region, the center coordinates should be evenly distributed, and the attention total variation loss $\\mathcal{L}_{ATV}$ is defined as follows:", + "bbox": [ + 76, + 417, + 468, + 462 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {A T V} = \\left\\| \\nabla (F \\odot M) \\right\\| _ {1}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 472, + 468, + 489 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $M \\in \\{0,1\\}^{H_q \\times W_q}$ is the ground truth clothing mask to only affect the clothing region. The attention total variation loss $\\mathcal{L}_{ATV}$ is designed to enforce the center coordinates on the attention map uniformly distributed, thereby alleviating interference among attention scores located at dispersed positions. As illustrated in Figure (c), this leads to the generation of a sharper attention map, thereby more accurately reflecting the color of the clothing.", + "bbox": [ + 75, + 497, + 468, + 618 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, we finetune our StableVITON by adding $\\mathcal{L}_{ATV}$ to Eq. 3:", + "bbox": [ + 76, + 619, + 467, + 648 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {f i n e t u n e}} = \\mathcal {L} _ {L D M} + \\lambda_ {A T V} \\mathcal {L} _ {A T V}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 150, + 656, + 468, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\lambda_{ATV}$ is a weight hyper-parameter.", + "bbox": [ + 76, + 681, + 356, + 696 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiment", + "text_level": 1, + "bbox": [ + 76, + 709, + 200, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines. We compare StableVITON with three GAN-based virtual try-on methods, VITON-HD [3], HRVITON [15], and GP-VTON [31], and two diffusion-based virtual try-on methods, LADI-VTON [19] and DCIVTON [8]. We also evaluate a diffusion-based inpainting method, Paint-by-Example [32]. We use pre-trained weights if available; otherwise, we train the models following the official code.", + "bbox": [ + 75, + 734, + 468, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset. We conduct the experiments using two publicly available virtual try-on datasets, VITON-HD [3] and DressCode [18], and one human image dataset, SHHQ-1.0 [5].", + "bbox": [ + 75, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train our model with VITON-HD and upper-body images in DressCode, respectively. For the evaluation of SHHQ-1.0, we use the first 2,032 images and follow the preprocessing instruction of VITON-HD [3] to obtain the input conditions such as the agnostic maps or the dense pose.", + "bbox": [ + 496, + 294, + 890, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation. We evaluate the performances in two test settings. Specifically, the paired setting uses a pair of a person and the original clothes for reconstruction, whereas the unpaired setting involves changing the clothing of a person image with a different clothing item. As previous work [3], training and evaluation within a single dataset are referred to as 'single dataset evaluation'. On the other hand, we extend our evaluation on other datasets (e.g., SHHQ-1.0), which we refer to as a 'cross dataset evaluation'. This evaluation enables an in-depth assessment of the model's generalizability in handling arbitrary person images, demonstrating applicability in real-world scenarios. Our model is capable of training at a $1024 \\times 768$ resolution, but for a fair evaluation with baselines, we used a model trained at a $512 \\times 384$ resolution. More results and details about experiments are described in the supplementary material.", + "bbox": [ + 496, + 369, + 892, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Qualitative Results", + "text_level": 1, + "bbox": [ + 500, + 619, + 683, + 636 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Single Dataset Evaluation. As shown in Fig. 5, StableVITON generates realistic images and effectively preserves the text and clothing textures compared to the six baseline methods. Specifically, in the first row of Fig. 5, GAN-based methods such as GP-VTON struggle to generate the arms of the target person naturally. Moreover, other diffusion-based models either fail to preserve the text (Paint-by-Example and LADI-VTON) or show an overlapped artifact between the clothing and the target person (DCI-VTON). On the other hand, despite some parts of the arm being covered by clothing, our model produces a high-fidelity result that omits the 'L' in 'Love'.", + "bbox": [ + 496, + 643, + 890, + 823 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Cross Dataset Evaluation. We visualize the generation images of the models trained on VITON-HD for DressCode and SHHQ-1.0 datasets in Fig. 6 and Fig. 7, respectively. The results clearly demonstrate that StableVITON generates high-fidelity images while preserving the details of the", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8180", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/00336f9be79e64d53683de0f80e560792f6a234e0a7f25355c518213bef59315.jpg", + "image_caption": [ + "Figure 5. Qualitative comparison with baselines in a single dataset setting (VITON-HD / VITON-HD). Best viewed when zoomed in." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 848, + 290 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/153f71905918fc1561aa61dc46b91cdc2d29b48f0707f9c7e912ed9254216b85.jpg", + "image_caption": [ + "Figure 6. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / DressCode). Best viewed when zoomed in." + ], + "image_footnote": [], + "bbox": [ + 117, + 311, + 849, + 513 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a150eeb418ed5a7165495b05ec582c5a0c48668be837e3f6cfd7e48611784d67.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Train / Test MethodVITON-HD / VITON-HDD.C. Upper / D.C. Upper
SSIMLPIPSFIDKIDSSIMLPIPSFIDKID
VITON-HD [3]0.8620.11712.1173.23----
HR-VITON [15]0.8780.104511.2652.730.9360.065213.8202.71
LADI-VTON [19]0.8640.09649.4801.990.9220.062814.173.04
Paint-by-Example [32]0.8020.142811.9393.850.8970.077515.3324.64
DCI-VTON [8]0.8800.08048.7541.100.9370.042111.9201.89
GP-VTON [31]0.8840.08149.0720.880.7690.267920.1108.17
Ours0.8520.08428.6980.880.9110.050011.2660.72
Ours (RePaint [17])0.8880.07328.2330.490.9370.03889.9400.12
", + "bbox": [ + 243, + 537, + 728, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons in single dataset settings, VITON-HD and DressCode upper-body (D.C. Upper) datasets. Bold and underline denote the best and the second best result, respectively.", + "bbox": [ + 75, + 652, + 890, + 680 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "clothing. GAN-based methods especially show significant artifacts on the target person and fail to maintain background. While diffusion-based methods generate natural images, they fail to preserve clothing details or the shape of the clothing. Furthermore, even when applying the augmentation we used to DCI-VTON (denoted as DCI-VTON (Aug.)), as depicted in Fig. 7, a significant improvement in the performance of the warping network is not achieved, failing to preserve clothing details.", + "bbox": [ + 75, + 695, + 468, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Quantitative Results", + "text_level": 1, + "bbox": [ + 76, + 845, + 271, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Metrics. For quantitative evaluation, we use SSIM [30] and LPIPS [35] in the paired setting. In an unpaired setting,", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "we assess the realism using FID [12] and KID [2] score. We follow the evaluation paradigm [19] for the implementation [4, 21].", + "bbox": [ + 496, + 695, + 890, + 741 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Single Dataset Evaluation. We evaluate our StableViTON and existing baselines on a single dataset setting and report the results in Table 1. In the unpaired setting (i.e., FID and KID), StableViTON outperforms all the baselines. We observe that the performance degradation in the paired setting occurs due to the autoencoder's reconstruction error of the agnostic map. To mitigate this issue, we adapt RePaint [17], which samples the known region (i.e., agnostic map) and replaces it in each denoising steps during the inference, used in DCI-VTON. Applying RePaint, Stable-", + "bbox": [ + 496, + 750, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8181", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b795af6fd36ec0ba4121345289a3e9293083f77f3a3db7d931f9b8d762212729.jpg", + "image_caption": [ + "Figure 7. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / SHHQ-1.0). Best viewed when zoomed in." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 849, + 335 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7d9407d384155c5986e63d404205dca4a960d4460b6bd2ee705a5dc83cb241a8.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Train / Test \nMethodVITON-HD / D.C. UpperD.C. Upper / VITON-HDVITON-HD / SHHQ-1.0
SSIMLPIPSFIDKIDSSIMLPIPSFIDKIDFIDKID
VITON-HD [3]0.8530.187444.25728.82----71.14952.01
HR-VITON [15]0.9090.107719.9707.350.8110.227845.92336.6952.73231.22
LADI-VTON [19]0.9010.100916.3365.360.7950.27228.2719.324.9046.07
Paint-by-Example [32]0.8890.086716.3984.780.7840.181415.6257.5226.2749.830
DCI-VTON [8]0.9030.121723.07612.030.8250.187016.6706.4024.8506.68
DCI-VTON (Aug.) [8]0.8980.124018.8098.02----24.3686.11
GP-VTON [31]0.7240.384665.71166.010.8040.262152.35148.68--
Ours0.9110.060312.5811.700.8170.130810.1041.7223.5315.68
Ours (RePaint [17])0.9380.047010.4800.410.8550.11739.7141.3521.0775.10
", + "bbox": [ + 161, + 362, + 807, + 484 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparisons in cross dataset settings. We train the models on VITON-HD and DressCode upper-body (D.C. Upper) datasets and evaluate them on different datasets. Bold and underline denote the best and the second best result, respectively.", + "bbox": [ + 75, + 488, + 888, + 516 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "VITON outperforms the baselines for all evaluation metrics. Since RePaint greatly helps maintain regions unrelated to clothing, it shows notable performance improvement in the paired setting. Nevertheless, even without RePaint, our method demonstrates superior performance in terms of FID and KID in the unpaired setting compared to the baselines.", + "bbox": [ + 75, + 529, + 468, + 619 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cross Dataset Evaluation. Table 2 presents that our StableVITON shows state-of-the-art performance for all the evaluation metrics with a large margin. GAN-based methods fail to maintain background consistency, resulting in significantly high FID and KID scores. While diffusion-based methods exhibit better performance due to the plausible generation outcomes enabled by pre-trained diffusion models, they fail to preserve clothing details. Consequently, they exhibit lower similarity scores in the paired setting (i.e., SSIM and LPIPS) compared to our method.", + "bbox": [ + 75, + 621, + 468, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. User Study", + "text_level": 1, + "bbox": [ + 76, + 785, + 197, + 801 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "For the models trained on the VITON-HD dataset, we conducted a user study with 40 participants. Each participant was shown one image generated by the baseline and the other by our model. They were asked to choose the better image based on three criteria: (1) fidelity, (2) person attributes, and (3) clothing identity. We added a question", + "bbox": [ + 75, + 809, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/2dc606c788efb5f813f4d4fe85867a1558ec6dc23a045196135cdfc6e8b61c3b.jpg", + "image_caption": [ + "Figure 8. User study results. We compare our StableVITON with six baselines, involving a total of 40 participants." + ], + "image_footnote": [], + "bbox": [ + 504, + 527, + 890, + 707 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "about (4) background quality for the cross dataset setting. Detailed questions can be found in the supplementary material. As shown in Fig. 8, StableVITON outperforms in most of the criteria, and especially in the cross dataset setting, our method is overwhelming in human evaluations. While LADI-VTON shows better preference in the evaluation of fidelity and person attributes on the VITON-HD dataset, it fails to preserve clothing details, resulting in a $35\\%$ preference in the clothing identity criteria.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8182", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/91c44c90a5f4603f28647b5223612b44fe602f0d9c550504a9a23813d0d5cce4.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Train / Test on VITON-HDSSIMLPIPSFIDKID
ControlNet + Aug.0.8320.11579.811.81
ControlNet-W + Aug.0.8220.11249.661.57
Zero Cross-Attention Block + Aug.0.8500.08518.740.91
", + "bbox": [ + 107, + 88, + 436, + 135 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/de3d8b3b7b8dd2bafe33a390f700e8614c2eda75c75800f729a8f098bb8c8436.jpg", + "table_caption": [ + "Table 3. Quantitative comparison results between our zero cross-attention block and ControlNet. We train ControlNet with clothing and warped clothing [15] (ControlNet-W). We apply augmentation to all the models in training." + ], + "table_footnote": [], + "table_body": "
Aug.Attention TV LossSSIMLPIPSFIDFID
XX0.8470.09699.351.33
✓X0.8500.08518.7440.91
✓✓0.8520.0428.6980.88
", + "bbox": [ + 137, + 213, + 410, + 276 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 4. Ablation study of our proposed training components on VITON-HD dataset.", + "bbox": [ + 76, + 279, + 468, + 306 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 334, + 228, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Comparison with ControlNet. To demonstrate the effectiveness of StableVITON in tackling the alignment issue compared to ControlNet [34], we train ControlNet under two different input conditions: (1) clothing, and (2) warped clothing [15] (dubbed as ControlNet-W). We apply our proposed augmentation to both models during training. Using the warping network to align the clothing helps ControlNet capture coarse features, such as the overall shape and color of the logo, as shown in Fig. 9(b) and (c). However, since the misalignment still exists between warped clothing and the human body in the training phase, ControlNet-W struggles to reflect more fine-grained clothing details to the generation results. These observations highlight that ControlNet is highly sensitive to subtle misalignment across the input, stemming from the limitations of the ControlNet's direct addition operation in conditioning. In contrast, as shown in Fig. 9(d), the zero cross-attention block, free from the alignment constraints, successfully preserves the logos and patterns and leads to a qualitative performance improvement, as shown in Table 3.", + "bbox": [ + 75, + 361, + 472, + 662 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of Training Components. We investigate the effect of the two proposed components during training: augmentation and attention total variation loss. In Fig. 10, we visualize the generated images while incrementally introducing the proposed training components one by one. Compared to Fig 10(a) and (b), we observe that detailed features such as logos and patterns of the clothing are more preserved when augmentation is applied. However, as the attention maps are not sufficiently distinct, we observe inaccuracies in the generated images, such as the 'M' in 'PUMA' being incorrectly depicted or lines blurring, as shown in Fig. 10(b). After finetuning with our proposed attention total variation loss, these finer details are significantly improved. Such visual enhancements correspond to quantitative performance improvements as demonstrated in Table 4.", + "bbox": [ + 75, + 672, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1a098365e78edee7a2abb9a263691d70c015e6014bfacdb8daccc604b9f5cbc9.jpg", + "image_caption": [ + "(a) Target Person", + "(b) ControlNet", + "(c) ControlNet-W", + "(d) Ours" + ], + "image_footnote": [], + "bbox": [ + 504, + 89, + 890, + 258 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/99ff958f43611ed13e493971dca37ebf82d02b66fdb086713514bf96a67d5c8f.jpg", + "image_caption": [ + "Figure 9. Comparison our StableVITON to ControlNets under the two different input conditions: (1) clothing, and (2) warped clothing [15] (ControlNet-W). Best viewed when zoomed in.", + "Figure 10. Visual comparisons according to our training components. Best viewed when zoomed in." + ], + "image_footnote": [], + "bbox": [ + 506, + 318, + 890, + 547 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 588, + 617, + 603 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose StableVITON, a novel image-based virtual try-on method using the pre-trained diffusion model. Our proposed zero cross-attention block learns semantic correspondence between the clothing and the human body, enabling try-on in the latent feature space. A novel attention total variation loss and augmentation are designed to preserve the clothing details better. Extensive experiments, including cross dataset evaluation, clearly demonstrate that StableVITON shows the state-of-the-art performance compared to the existing methods and its promising quality in the real-world setting.", + "bbox": [ + 496, + 613, + 890, + 779 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements. Sunghyun Park is the corresponding author. This work was supported by the Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913).", + "bbox": [ + 496, + 779, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8183", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Shuai Bai, Huiling Zhou, Zhikang Li, Chang Zhou, and Hongxia Yang. Single stage virtual try-on via deformable attention flows. In European Conference on Computer Vision, pages 409-425. 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In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4606-4615, 2023. 3" + ], + "bbox": [ + 78, + 90, + 468, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8185", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/StableVITON_ Learning Semantic Correspondence with Latent Diffusion Model for Virtual Try-On/d486dcf7-d514-4538-af86-ab7be3d92c46_model.json b/2024/StableVITON_ Learning Semantic Correspondence with Latent Diffusion Model for Virtual Try-On/d486dcf7-d514-4538-af86-ab7be3d92c46_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2aa016d7e1272bd1254a6ca03684e2ceb8d7d6fc --- /dev/null +++ b/2024/StableVITON_ Learning Semantic Correspondence with Latent Diffusion Model for Virtual Try-On/d486dcf7-d514-4538-af86-ab7be3d92c46_model.json @@ -0,0 +1,1969 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.226, + 0.131, + 0.745, + 0.175 + ], + "angle": 0, + "content": "StableVITON: Learning Semantic Correspondence with Latent Diffusion Model for Virtual Try-On" + }, + { + "type": "text", + "bbox": [ + 0.149, + 0.204, + 0.26, + 0.222 + ], + "angle": 0, + "content": "Jeongho Kim" + }, + { + "type": "text", + "bbox": [ + 0.293, + 0.204, + 0.395, + 0.222 + ], + "angle": 0, + "content": "Gyojung Gu" + }, + { + "type": "text", + "bbox": [ + 0.43, + 0.204, + 0.526, + 0.222 + ], + "angle": 0, + "content": "Minho Park" + }, + { + "type": "text", + "bbox": [ + 0.562, + 0.204, + 0.685, + 0.222 + ], + "angle": 0, + "content": "Sunghyun Park" + }, + { + "type": "text", + "bbox": [ + 0.72, + 0.204, + 0.82, + 0.222 + ], + "angle": 0, + "content": "Jaegul Choo" + }, + { + "type": "text", + "bbox": [ + 0.365, + 0.223, + 0.607, + 0.24 + ], + "angle": 0, + "content": "KAIST, Daejeon, South Korea" + }, + { + "type": "text", + "bbox": [ + 0.214, + 0.242, + 0.751, + 0.257 + ], + "angle": 0, + "content": "{rlawjdghek, gyojung.gu, m.park, psh01087, jchoo}@kaist.ac.kr" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.277, + 0.348, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.352, + 0.277, + 0.619, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.623, + 0.277, + 0.892, + 0.462 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.079, + 0.463, + 0.28, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.463, + 0.485, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.487, + 0.463, + 0.687, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.463, + 0.892, + 0.658 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.66, + 0.891, + 0.689 + ], + "angle": 0, + "content": "Figure 1. Generated results of StableVITON: VITON-HD (the first row), SHHQ-1.0 (the first two images in the second row), and web-crawled images (the last two images in the second row). All results are generated using StableVITON trained on VITON-HD dataset." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.699, + 0.314, + 0.714 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.721, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Given a clothing image and a person image, an image-based virtual try-on aims to generate a customized image that appears natural and accurately reflects the characteristics of the clothing image. In this work, we aim to expand the applicability of the pre-trained diffusion model so that it can be utilized independently for the virtual try-on task. The main challenge is to preserve the clothing details while effectively utilizing the robust generative capability of the pre-trained model. In order to tackle these issues, we propose StableVITON, learning the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model in an end-to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.895, + 0.881 + ], + "angle": 0, + "content": "end manner. Our proposed zero cross-attention blocks not only preserve the clothing details by learning the semantic correspondence but also generate high-fidelity images by utilizing the inherent knowledge of the pre-trained model in the warping process. Through our proposed novel attention total variation loss and applying augmentation, we achieve the sharp attention map, resulting in a more precise representation of clothing details. StableVITON outperforms the baselines in qualitative and quantitative evaluation, showing promising quality in arbitrary person images. Our code is available at https://github.com/rlawjdghek/StableVITON." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8176" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.21, + 0.106 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.115, + 0.47, + 0.252 + ], + "angle": 0, + "content": "The objective of an image-based virtual try-on is to dress a given clothing image on a target person image. Most of the previous virtual try-on approaches [3, 7, 10, 14, 15, 29, 31, 33] leverage paired datasets consisting of clothing images and person images wearing those garments for training purposes. These methods typically include two modules: (1) a warping network to learn the semantic correspondence between the clothing and the human body, and (2) a generator that fuses the warped clothing and the person image." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.252, + 0.469, + 0.372 + ], + "angle": 0, + "content": "Despite achieving significant advancements, previous methods [3, 8, 15, 31] still have limitations in achieving generalizability, particularly in maintaining the complex background in an arbitrary person image. The nature of matching clothing and individuals in the virtual try-on dataset [3, 10, 18] makes it challenging to collect data in diverse environments [20], which in turn leads to limitations in the generator's generative capability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.372, + 0.469, + 0.508 + ], + "angle": 0, + "content": "Meanwhile, recent advancements in large-scale pretrained diffusion models [23, 24, 27] have led to the emergence of downstream tasks [6, 8, 16, 19, 26, 34, 36] that control the pre-trained diffusion models for task-specific image generation. Thanks to the powerful generative ability, several works [17, 34] have succeeded in synthesizing high-fidelity human images using the prior knowledge of the pre-trained models, which signifies the potential for extension to the virtual try-on task." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.469, + 0.764 + ], + "angle": 0, + "content": "In this paper, we aim to expand the applicability of the pre-trained diffusion model to provide a standalone model for the virtual try-on task. In the effort to adapt the pretrained diffusion model for virtual try-on, a significant challenge is to preserve the clothing details while harnessing the knowledge of the pre-trained diffusion model. This can be achieved by learning the semantic correspondence between clothing and the human body using the provided dataset. Recent research [8, 19] that has employed pretrained diffusion models in virtual try-on has shown limitations due to the following two issues: (1) insufficient spatial information available for learning the semantic correspondence [19], and (2) the pre-trained diffusion model not being fully utilized, as it pastes the warped clothing in the RGB space, relying on external warping networks as previous approaches [3, 7, 15, 31, 33] for aligning the input condition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.469, + 0.901 + ], + "angle": 0, + "content": "To overcome these issues, we propose StableVITON, which learns the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model. To incorporate the spatial information of the clothing for learning semantic correspondence, we introduce an encoder [34] that takes clothing as input and conditions the U-Net with the intermediate features of the encoder via zero cross-attention blocks. Warping through the zero cross-attention block in a pre-trained" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.089, + 0.891, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.293, + 0.892, + 0.336 + ], + "angle": 0, + "content": "Figure 2. Visualization of the semantic correspondence learned by our StableVITON. We overlay the attention map for the clothing regions onto the generated images for visualization." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.366, + 0.892, + 0.488 + ], + "angle": 0, + "content": "diffusion model has the following two advantages: (1) preserving the clothing details by learning the semantic correspondence; (2) synthesizing high-fidelity images by leveraging the pre-trained models' inherent knowledge about humans in the warping process. As shown in Fig. 2, the attention mechanism in the latent space performs patch-wise warping by activating each token corresponding to clothing alignment within the generation region." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.496, + 0.892, + 0.646 + ], + "angle": 0, + "content": "To further sharpen attention maps, we propose a novel attention total variation loss and apply the augmentation, which yields improved preservation of clothing details. By not impairing the pre-trained diffusion model, this architecture generates high-quality images even when images with complex backgrounds are provided, only using an existing virtual try-on dataset. Our extensive experiments show that StableVITON outperforms the existing virtual try-on method by a large margin. In summary, our contributions are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.657, + 0.891, + 0.717 + ], + "angle": 0, + "content": "- Our proposed StableVITON, to the best of our knowledge, is the first end-to-end virtual try-on method finetuned on the pre-trained diffusion model without an independent warping process." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.718, + 0.89, + 0.776 + ], + "angle": 0, + "content": "- We propose a zero cross-attention block, which learns semantic correspondence between the clothing and the human body, to condition the intermediate features from the spatial encoder." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.778, + 0.89, + 0.822 + ], + "angle": 0, + "content": "- We propose a novel attention total variation loss and apply augmentation for further precise semantic correspondence learning." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.822, + 0.891, + 0.898 + ], + "angle": 0, + "content": "- StableVITON shows state-of-the-art performance over existing virtual try-on models in both qualitative and quantitative results. Moreover, through the evaluation of a trained model on multiple datasets, StableVITON demonstrates its promising quality in a real-world setting." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.657, + 0.891, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8177" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.116, + 0.473, + 0.404 + ], + "angle": 0, + "content": "GAN-based Virtual Try-On. To properly try-on the given clothing image to the target person, existing approaches [3, 7, 15, 31] based on generative adversarial network (GAN) have attempted to address the virtual try-on problem using a two-stage strategy: (1) deforming the clothing to the proposal region and (2) fusing the warped clothing via try-on generator based on GAN. In order to achieve precise clothing deformation, previous methods [1, 7, 11, 15, 31] leverage a trainable network that estimates a dense flow map [37] to deform the clothing to the human body. At the same time, several approaches [3, 7, 14, 15, 31, 33] have been attempted to address the misalignment between the warped clothing and the human body, such as using a normalization [3] or distillation [7, 14]. However, the existing approaches still are not generalized well, leading to significant performance degradation in arbitrary person images with complex backgrounds. In this paper, we effectively address such issues by proposing a method that leverages the powerful generation ability of the pre-trained model." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.405, + 0.473, + 0.738 + ], + "angle": 0, + "content": "Diffusion-based Virtual Try-On. Due to the remarkable generative capabilities, research on virtual try-on has extensively discussed the application of the diffusion models. While TryOnDiffusion [38] introduces an architecture for try-on using two U-Nets, this method requires a large-scale and challenging-to-collect dataset, consisting of image pairs of the same person wearing the same clothing in two different poses. Therefore, much recent research has shifted their focus towards using the prior of a large-scale pre-trained diffusion models [13, 22, 24, 32] in the virtual try-on task. LADI-VTON [19] represents the clothing as pseudo-words, and DCI-VTON [8] applies a warping network to input the clothing as conditions for the pre-trained diffusion models. While both models deal with background-related issues, they suffer from preserving high-frequency details due to the excessive loss of spatial information from the CLIP encoder [19] and drawbacks such as incorrectly warped clothing inherited from the independent warping network [8]. On the other hand, we propose to condition the intermediate feature maps of a spatial encoder through zero cross-attention block, which allows for using the prior knowledge of the pre-trained model in the warping process." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.205, + 0.77 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.78, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Stable Diffusion Model. Stable Diffusion model [24] is a large-scale diffusion model trained on LAION dataset [28], built upon the Latent Diffusion model (LDM) [24], which performs a denoising process in the latent space of an autoencoder. With a fixed encoder \\((\\mathcal{E})\\), an input image \\(\\mathbf{x}\\) is first transformed to latent feature \\(\\mathbf{z}_0 = \\mathcal{E}(\\mathbf{x})\\). Given a predefined variance schedule \\(\\beta_{t}\\), we can define a forward diffusion process in the latent space following denoising diffu" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.707, + 0.107 + ], + "angle": 0, + "content": "sion probabilistic models [13]:" + }, + { + "type": "equation", + "bbox": [ + 0.569, + 0.117, + 0.892, + 0.136 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.145, + 0.894, + 0.207 + ], + "angle": 0, + "content": "where \\(t \\in \\{1, \\dots, T\\}\\), \\(T\\) represents the number of steps in the forward diffusion process, \\(\\alpha_{t} \\coloneqq 1 - \\beta_{t}\\), and \\(\\bar{\\alpha}_{t} \\coloneqq \\Pi_{s=1}^{t} \\alpha_{s}\\). As a training loss, Stable Diffusion model employs the simplified objective function from LDM [15]:" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.216, + 0.892, + 0.248 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\mathcal {E} (\\mathbf {x}), \\mathbf {y}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\tau_ {\\theta} (\\mathbf {y})\\right) \\| _ {2} ^ {2} \\right], \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.248, + 0.895, + 0.295 + ], + "angle": 0, + "content": "where the denoising network \\(\\epsilon_{\\theta}(\\cdot)\\) is implemented with a U-Net architecture [25] and \\(\\tau_{\\theta}(\\cdot)\\) is the CLIP [22] text encoder to condition the text prompt \\(y\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.307, + 0.593, + 0.323 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.332, + 0.664, + 0.347 + ], + "angle": 0, + "content": "4.1. Model Overview" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.355, + 0.892, + 0.597 + ], + "angle": 0, + "content": "An overview of StableVITON is presented in Fig. 3(a). Given a person image \\(\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}\\), the clothing-agnostic person representation \\(\\mathbf{x}_a \\in \\mathbb{R}^{H \\times W \\times 3}\\) (we call it as 'agnostic map') [3] is proposed to eliminate any clothing information in \\(\\mathbf{x}\\). In this work, we approach the virtual try-on as an exemplar-based image inpainting problem [32] to fill theagnostic map \\(\\mathbf{x}_a\\) with the clothing image \\(\\mathbf{x}_c\\). As the input of the U-Net, we concatenate four components: (1) the noisy image \\((\\mathbf{z}_t)\\), (2) latentagnostic map \\((\\mathcal{E}(\\mathbf{x}_a))\\), (3) the resized clothing-agnostic mask \\((\\mathbf{x}_{m_a})\\), (4) latent dense pose condition \\((\\mathcal{E}(\\mathbf{x}_p))\\) [9] to preserve the person's pose. To align the input channels, we expand the initial convolution layer of the U-Net to 13 (i.e., \\(4 + 4 + 1 + 4 = 13\\)) channels with a convolution layer initialized with zero weights. For exemplar conditioning, we input the \\(\\mathbf{x}_c\\) to the CLIP image encoder [32]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.749 + ], + "angle": 0, + "content": "To preserve the fine details of the clothing, we introduce a spatial encoder, which takes latent clothing \\((\\mathcal{E}(\\mathbf{x}_c))\\) as input. This spatial encoder copies the weight of the pre-trained U-Net [34] and conditions the intermediate feature maps of the encoder to U-Net via zero cross-attention blocks. During training, we apply augmentation and further finetune the model with our proposed attention total variation loss, which makes the attention region on the clothing sharper. The detailed model architecture is described in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.757, + 0.644, + 0.772 + ], + "angle": 0, + "content": "4.2. StableVITON" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Zero Cross-Attention Block. We aim to condition the intermediate feature maps of the clothing to U-Net, properly aligning with the human body. The operation of adding the unaligned clothing feature map to the human feature map is insufficient to preserve clothing details due to misalignment between the human body and the clothing. Therefore, we proposed a zero cross-attention block to be a flexible operation by applying an attention mechanism for conditioning." + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8178" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.6, + 0.346 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.243, + 0.349, + 0.441, + 0.362 + ], + "angle": 0, + "content": "(a) Overview of StableVITON" + }, + { + "type": "image", + "bbox": [ + 0.669, + 0.104, + 0.865, + 0.332 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.665, + 0.349, + 0.869, + 0.362 + ], + "angle": 0, + "content": "(b) Zero Cross-Attention Block" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.37, + 0.895, + 0.414 + ], + "angle": 0, + "content": "Figure 3. For the virtual try-on task, StableVITON additionally takes three conditions: agnostic map, agnostic mask, and dense pose, as the input of the pre-trained U-Net, which serves as the query (Q) for the cross-attention. The feature map of the clothing is used as the key (K) and value (V) for the cross-attention and is conditioned on the UNet, as depicted in (b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.426, + 0.471, + 0.533 + ], + "angle": 0, + "content": "Specifically, as shown in Fig. 3(b), the feature map of the U-Net decoder block inputs to self-attention, followed by the cross-attention layer where the query (Q) comes from the previous self-attention layer and the spatial encoder's feature map serves as the key (K) and value (V). To eliminate harmful noise, we introduce a linear layer initialized with zero weight after the feed-forward operation [34]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.535, + 0.471, + 0.882 + ], + "angle": 0, + "content": "To successfully align the clothing to the human body part via cross-attention, it is crucial to ensure semantic correspondence between the key tokens (clothing) and the query tokens (human body). For instance, when dealing with a query token related to the right shoulder, the corresponding key tokens should exhibit higher attention scores in the corresponding right shoulder area of the clothing. In Fig. 4(a), we averaged the attention maps of the resolution of \\(32 \\times 24\\) across the head dimension and arranged them flatly. For clear visualization, we downsample the generated image to a resolution of \\(32 \\times 24\\) and then resize it back to \\(32^2 \\times 24^2\\). Subsequently, we overlay this generated image with the attention map corresponding to each query token. Zooming in on the upper and middle of the generated clothing area, we observe that the key tokens unrelated to the corresponding query token, such as the bottom of the clothing, are activated in the attention map. This indicates that the cross-attention layer fails to learn the exact semantic correspondence between query and key tokens, combining the several key tokens of the clothing to generate the color corresponding to the query token during training. Therefore, as shown in Fig. 4, the stripes on the clothing are not distinctly visible." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Augmentation. To mitigate such issues of key tokens unre" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.426, + 0.892, + 0.517 + ], + "angle": 0, + "content": "lated to query tokens being attended to, we alter the feature map by applying augmentation, including random shifts to input conditions. Detailed settings of augmentation are described in supplementary material. Along with the augmented input conditions, we train our model with the objective function defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.522, + 0.892, + 0.553 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\zeta , \\mathbf {x} _ {c}, \\mathcal {E} (\\mathbf {x} _ {c}), \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\zeta , t, \\tau_ {\\phi} (\\mathbf {x} _ {c}), \\mathcal {E} (\\mathbf {x} _ {c})) \\| _ {2} ^ {2} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.553, + 0.892, + 0.599 + ], + "angle": 0, + "content": "where \\(\\zeta = [\\mathbf{z}_t;\\mathcal{E}(\\mathbf{x}_a);\\mathbf{x}_{m_a};\\mathcal{E}(\\mathbf{x}_p)]\\), and \\(\\tau_{\\phi}\\) is the CLIP image encoder. Note that we do not update the parameters of the original blocks, as depicted in Fig. 3(a)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.719 + ], + "angle": 0, + "content": "The rationale behind this strategy is to force the model to learn fine-grained semantic correspondence using augmentation, instead of just moderately injecting the clothes at similar positions. As shown in Fig. 4(b), we can confirm that key tokens related to query tokens have high attention scores, signifying that the cross-attention layer has learned the high semantic correspondence between the clothing-agnostic region and clothing." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.809 + ], + "angle": 0, + "content": "Attention Total Variation Loss. While the cross-attention layer successfully aligns the clothing to the agnostic map, the points with high attention scores appear in dispersed positions, as shown in the attention map of Fig. 4(b). This causes inaccurate details in generated images, such as color discrepancies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.9 + ], + "angle": 0, + "content": "To address such an issue, we propose attention total variation loss. As the attention scores are the weight for the output, we calculate the center coordinates as a weighted sum of the attention map and the grid. Therefore, given the \\(H_{q}W_{q}\\) query tokens and \\(h_k w_k\\) key tokens, we calculate center coordinate map \\(F \\in \\mathbb{R}^{H_q \\times W_q \\times 2}\\) as follows:" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8179" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.087, + 0.895, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.215, + 0.265, + 0.755, + 0.28 + ], + "angle": 0, + "content": "Figure 4. Visualization of attention map from a zero cross-attention block of 32 resolution." + }, + { + "type": "equation", + "bbox": [ + 0.142, + 0.293, + 0.47, + 0.335 + ], + "angle": 0, + "content": "\\[\nF _ {i j n} = \\frac {1}{h _ {k} w _ {k}} \\sum_ {k = 1} ^ {h _ {k}} \\sum_ {l = 1} ^ {w _ {k}} \\left(A _ {i j k l} \\odot G _ {k l n}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.47, + 0.418 + ], + "angle": 0, + "content": "where we average the attention map over the head dimension and reshape it as \\( A \\in \\mathbb{R}^{H_q \\times W_q \\times h_k \\times w_k} \\), and \\( G \\in [-1, 1]^{h_k \\times w_k \\times 2} \\) is a 2D normalized coordinate. \\( n \\in \\{0, 1\\} \\) in Eq. 4 denotes the dimension of attention map coordinates and \\( \\odot \\) indicates element-wise multiplication operation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.419, + 0.469, + 0.463 + ], + "angle": 0, + "content": "For each query token in each clothing-agnostic region, the center coordinates should be evenly distributed, and the attention total variation loss \\(\\mathcal{L}_{ATV}\\) is defined as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.473, + 0.469, + 0.49 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {A T V} = \\left\\| \\nabla (F \\odot M) \\right\\| _ {1}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.498, + 0.469, + 0.619 + ], + "angle": 0, + "content": "where \\( M \\in \\{0,1\\}^{H_q \\times W_q} \\) is the ground truth clothing mask to only affect the clothing region. The attention total variation loss \\( \\mathcal{L}_{ATV} \\) is designed to enforce the center coordinates on the attention map uniformly distributed, thereby alleviating interference among attention scores located at dispersed positions. As illustrated in Figure (c), this leads to the generation of a sharper attention map, thereby more accurately reflecting the color of the clothing." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.62, + 0.468, + 0.65 + ], + "angle": 0, + "content": "Finally, we finetune our StableVITON by adding \\(\\mathcal{L}_{ATV}\\) to Eq. 3:" + }, + { + "type": "equation", + "bbox": [ + 0.151, + 0.657, + 0.469, + 0.673 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {f i n e t u n e}} = \\mathcal {L} _ {L D M} + \\lambda_ {A T V} \\mathcal {L} _ {A T V}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.682, + 0.357, + 0.697 + ], + "angle": 0, + "content": "where \\(\\lambda_{ATV}\\) is a weight hyper-parameter." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.71, + 0.202, + 0.726 + ], + "angle": 0, + "content": "5. Experiment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.854 + ], + "angle": 0, + "content": "Baselines. We compare StableVITON with three GAN-based virtual try-on methods, VITON-HD [3], HRVITON [15], and GP-VTON [31], and two diffusion-based virtual try-on methods, LADI-VTON [19] and DCIVTON [8]. We also evaluate a diffusion-based inpainting method, Paint-by-Example [32]. We use pre-trained weights if available; otherwise, we train the models following the official code." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Dataset. We conduct the experiments using two publicly available virtual try-on datasets, VITON-HD [3] and DressCode [18], and one human image dataset, SHHQ-1.0 [5]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.295, + 0.892, + 0.371 + ], + "angle": 0, + "content": "We train our model with VITON-HD and upper-body images in DressCode, respectively. For the evaluation of SHHQ-1.0, we use the first 2,032 images and follow the preprocessing instruction of VITON-HD [3] to obtain the input conditions such as the agnostic maps or the dense pose." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.893, + 0.613 + ], + "angle": 0, + "content": "Evaluation. We evaluate the performances in two test settings. Specifically, the paired setting uses a pair of a person and the original clothes for reconstruction, whereas the unpaired setting involves changing the clothing of a person image with a different clothing item. As previous work [3], training and evaluation within a single dataset are referred to as 'single dataset evaluation'. On the other hand, we extend our evaluation on other datasets (e.g., SHHQ-1.0), which we refer to as a 'cross dataset evaluation'. This evaluation enables an in-depth assessment of the model's generalizability in handling arbitrary person images, demonstrating applicability in real-world scenarios. Our model is capable of training at a \\(1024 \\times 768\\) resolution, but for a fair evaluation with baselines, we used a model trained at a \\(512 \\times 384\\) resolution. More results and details about experiments are described in the supplementary material." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.621, + 0.684, + 0.637 + ], + "angle": 0, + "content": "5.1. Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.644, + 0.892, + 0.824 + ], + "angle": 0, + "content": "Single Dataset Evaluation. As shown in Fig. 5, StableVITON generates realistic images and effectively preserves the text and clothing textures compared to the six baseline methods. Specifically, in the first row of Fig. 5, GAN-based methods such as GP-VTON struggle to generate the arms of the target person naturally. Moreover, other diffusion-based models either fail to preserve the text (Paint-by-Example and LADI-VTON) or show an overlapped artifact between the clothing and the target person (DCI-VTON). On the other hand, despite some parts of the arm being covered by clothing, our model produces a high-fidelity result that omits the 'L' in 'Love'." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Cross Dataset Evaluation. We visualize the generation images of the models trained on VITON-HD for DressCode and SHHQ-1.0 datasets in Fig. 6 and Fig. 7, respectively. The results clearly demonstrate that StableVITON generates high-fidelity images while preserving the details of the" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8180" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.849, + 0.291 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.09, + 0.292, + 0.878, + 0.306 + ], + "angle": 0, + "content": "Figure 5. Qualitative comparison with baselines in a single dataset setting (VITON-HD / VITON-HD). Best viewed when zoomed in." + }, + { + "type": "image", + "bbox": [ + 0.118, + 0.313, + 0.851, + 0.515 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.095, + 0.516, + 0.872, + 0.53 + ], + "angle": 0, + "content": "Figure 6. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / DressCode). Best viewed when zoomed in." + }, + { + "type": "table", + "bbox": [ + 0.244, + 0.538, + 0.729, + 0.653 + ], + "angle": 0, + "content": "
Train / Test MethodVITON-HD / VITON-HDD.C. Upper / D.C. Upper
SSIMLPIPSFIDKIDSSIMLPIPSFIDKID
VITON-HD [3]0.8620.11712.1173.23----
HR-VITON [15]0.8780.104511.2652.730.9360.065213.8202.71
LADI-VTON [19]0.8640.09649.4801.990.9220.062814.173.04
Paint-by-Example [32]0.8020.142811.9393.850.8970.077515.3324.64
DCI-VTON [8]0.8800.08048.7541.100.9370.042111.9201.89
GP-VTON [31]0.8840.08149.0720.880.7690.267920.1108.17
Ours0.8520.08428.6980.880.9110.050011.2660.72
Ours (RePaint [17])0.8880.07328.2330.490.9370.03889.9400.12
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.654, + 0.892, + 0.681 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons in single dataset settings, VITON-HD and DressCode upper-body (D.C. Upper) datasets. Bold and underline denote the best and the second best result, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.696, + 0.47, + 0.833 + ], + "angle": 0, + "content": "clothing. GAN-based methods especially show significant artifacts on the target person and fail to maintain background. While diffusion-based methods generate natural images, they fail to preserve clothing details or the shape of the clothing. Furthermore, even when applying the augmentation we used to DCI-VTON (denoted as DCI-VTON (Aug.)), as depicted in Fig. 7, a significant improvement in the performance of the warping network is not achieved, failing to preserve clothing details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.272, + 0.862 + ], + "angle": 0, + "content": "5.2. Quantitative Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Metrics. For quantitative evaluation, we use SSIM [30] and LPIPS [35] in the paired setting. In an unpaired setting," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.892, + 0.742 + ], + "angle": 0, + "content": "we assess the realism using FID [12] and KID [2] score. We follow the evaluation paradigm [19] for the implementation [4, 21]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Single Dataset Evaluation. We evaluate our StableViTON and existing baselines on a single dataset setting and report the results in Table 1. In the unpaired setting (i.e., FID and KID), StableViTON outperforms all the baselines. We observe that the performance degradation in the paired setting occurs due to the autoencoder's reconstruction error of the agnostic map. To mitigate this issue, we adapt RePaint [17], which samples the known region (i.e., agnostic map) and replaces it in each denoising steps during the inference, used in DCI-VTON. Applying RePaint, Stable-" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8181" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.089, + 0.85, + 0.337 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.097, + 0.341, + 0.872, + 0.356 + ], + "angle": 0, + "content": "Figure 7. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / SHHQ-1.0). Best viewed when zoomed in." + }, + { + "type": "table", + "bbox": [ + 0.162, + 0.363, + 0.808, + 0.486 + ], + "angle": 0, + "content": "
Train / Test \nMethodVITON-HD / D.C. UpperD.C. Upper / VITON-HDVITON-HD / SHHQ-1.0
SSIMLPIPSFIDKIDSSIMLPIPSFIDKIDFIDKID
VITON-HD [3]0.8530.187444.25728.82----71.14952.01
HR-VITON [15]0.9090.107719.9707.350.8110.227845.92336.6952.73231.22
LADI-VTON [19]0.9010.100916.3365.360.7950.27228.2719.324.9046.07
Paint-by-Example [32]0.8890.086716.3984.780.7840.181415.6257.5226.2749.830
DCI-VTON [8]0.9030.121723.07612.030.8250.187016.6706.4024.8506.68
DCI-VTON (Aug.) [8]0.8980.124018.8098.02----24.3686.11
GP-VTON [31]0.7240.384665.71166.010.8040.262152.35148.68--
Ours0.9110.060312.5811.700.8170.130810.1041.7223.5315.68
Ours (RePaint [17])0.9380.047010.4800.410.8550.11739.7141.3521.0775.10
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.489, + 0.89, + 0.517 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons in cross dataset settings. We train the models on VITON-HD and DressCode upper-body (D.C. Upper) datasets and evaluate them on different datasets. Bold and underline denote the best and the second best result, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.469, + 0.621 + ], + "angle": 0, + "content": "VITON outperforms the baselines for all evaluation metrics. Since RePaint greatly helps maintain regions unrelated to clothing, it shows notable performance improvement in the paired setting. Nevertheless, even without RePaint, our method demonstrates superior performance in terms of FID and KID in the unpaired setting compared to the baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.622, + 0.469, + 0.773 + ], + "angle": 0, + "content": "Cross Dataset Evaluation. Table 2 presents that our StableVITON shows state-of-the-art performance for all the evaluation metrics with a large margin. GAN-based methods fail to maintain background consistency, resulting in significantly high FID and KID scores. While diffusion-based methods exhibit better performance due to the plausible generation outcomes enabled by pre-trained diffusion models, they fail to preserve clothing details. Consequently, they exhibit lower similarity scores in the paired setting (i.e., SSIM and LPIPS) compared to our method." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.786, + 0.199, + 0.803 + ], + "angle": 0, + "content": "5.3. User Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.469, + 0.901 + ], + "angle": 0, + "content": "For the models trained on the VITON-HD dataset, we conducted a user study with 40 participants. Each participant was shown one image generated by the baseline and the other by our model. They were asked to choose the better image based on three criteria: (1) fidelity, (2) person attributes, and (3) clothing identity. We added a question" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.528, + 0.891, + 0.708 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.713, + 0.892, + 0.741 + ], + "angle": 0, + "content": "Figure 8. User study results. We compare our StableVITON with six baselines, involving a total of 40 participants." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "about (4) background quality for the cross dataset setting. Detailed questions can be found in the supplementary material. As shown in Fig. 8, StableVITON outperforms in most of the criteria, and especially in the cross dataset setting, our method is overwhelming in human evaluations. While LADI-VTON shows better preference in the evaluation of fidelity and person attributes on the VITON-HD dataset, it fails to preserve clothing details, resulting in a \\(35\\%\\) preference in the clothing identity criteria." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8182" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.109, + 0.089, + 0.437, + 0.136 + ], + "angle": 0, + "content": "
Train / Test on VITON-HDSSIMLPIPSFIDKID
ControlNet + Aug.0.8320.11579.811.81
ControlNet-W + Aug.0.8220.11249.661.57
Zero Cross-Attention Block + Aug.0.8500.08518.740.91
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.142, + 0.47, + 0.198 + ], + "angle": 0, + "content": "Table 3. Quantitative comparison results between our zero cross-attention block and ControlNet. We train ControlNet with clothing and warped clothing [15] (ControlNet-W). We apply augmentation to all the models in training." + }, + { + "type": "table", + "bbox": [ + 0.138, + 0.214, + 0.411, + 0.277 + ], + "angle": 0, + "content": "
Aug.Attention TV LossSSIMLPIPSFIDFID
XX0.8470.09699.351.33
✓X0.8500.08518.7440.91
✓✓0.8520.0428.6980.88
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.28, + 0.469, + 0.307 + ], + "angle": 0, + "content": "Table 4. Ablation study of our proposed training components on VITON-HD dataset." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.335, + 0.229, + 0.351 + ], + "angle": 0, + "content": "5.4. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.362, + 0.473, + 0.664 + ], + "angle": 0, + "content": "Comparison with ControlNet. To demonstrate the effectiveness of StableVITON in tackling the alignment issue compared to ControlNet [34], we train ControlNet under two different input conditions: (1) clothing, and (2) warped clothing [15] (dubbed as ControlNet-W). We apply our proposed augmentation to both models during training. Using the warping network to align the clothing helps ControlNet capture coarse features, such as the overall shape and color of the logo, as shown in Fig. 9(b) and (c). However, since the misalignment still exists between warped clothing and the human body in the training phase, ControlNet-W struggles to reflect more fine-grained clothing details to the generation results. These observations highlight that ControlNet is highly sensitive to subtle misalignment across the input, stemming from the limitations of the ControlNet's direct addition operation in conditioning. In contrast, as shown in Fig. 9(d), the zero cross-attention block, free from the alignment constraints, successfully preserves the logos and patterns and leads to a qualitative performance improvement, as shown in Table 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.674, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Effect of Training Components. We investigate the effect of the two proposed components during training: augmentation and attention total variation loss. In Fig. 10, we visualize the generated images while incrementally introducing the proposed training components one by one. Compared to Fig 10(a) and (b), we observe that detailed features such as logos and patterns of the clothing are more preserved when augmentation is applied. However, as the attention maps are not sufficiently distinct, we observe inaccuracies in the generated images, such as the 'M' in 'PUMA' being incorrectly depicted or lines blurring, as shown in Fig. 10(b). After finetuning with our proposed attention total variation loss, these finer details are significantly improved. Such visual enhancements correspond to quantitative performance improvements as demonstrated in Table 4." + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.09, + 0.892, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.565, + 0.261, + 0.641, + 0.27 + ], + "angle": 0, + "content": "(a) Target Person" + }, + { + "type": "image_caption", + "bbox": [ + 0.652, + 0.261, + 0.717, + 0.27 + ], + "angle": 0, + "content": "(b) ControlNet" + }, + { + "type": "image_caption", + "bbox": [ + 0.727, + 0.261, + 0.805, + 0.27 + ], + "angle": 0, + "content": "(c) ControlNet-W" + }, + { + "type": "image_caption", + "bbox": [ + 0.832, + 0.261, + 0.868, + 0.27 + ], + "angle": 0, + "content": "(d) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.274, + 0.892, + 0.315 + ], + "angle": 0, + "content": "Figure 9. Comparison our StableVITON to ControlNets under the two different input conditions: (1) clothing, and (2) warped clothing [15] (ControlNet-W). Best viewed when zoomed in." + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.319, + 0.891, + 0.549 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.5, + 0.553, + 0.891, + 0.58 + ], + "angle": 0, + "content": "Figure 10. Visual comparisons according to our training components. Best viewed when zoomed in." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.589, + 0.619, + 0.604 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.892, + 0.78 + ], + "angle": 0, + "content": "We propose StableVITON, a novel image-based virtual try-on method using the pre-trained diffusion model. Our proposed zero cross-attention block learns semantic correspondence between the clothing and the human body, enabling try-on in the latent feature space. A novel attention total variation loss and augmentation are designed to preserve the clothing details better. Extensive experiments, including cross dataset evaluation, clearly demonstrate that StableVITON shows the state-of-the-art performance compared to the existing methods and its promising quality in the real-world setting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements. Sunghyun Park is the corresponding author. This work was supported by the Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8183" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Shuai Bai, Huiling Zhou, Zhikang Li, Chang Zhou, and Hongxia Yang. Single stage virtual try-on via deformable attention flows. In European Conference on Computer Vision, pages 409-425. 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Generated results of StableVITON: VITON-HD (the first row), SHHQ-1.0 (the first two images in the second row), and web-crawled images (the last two images in the second row). All results are generated using StableVITON trained on VITON-HD dataset. + +![](images/24e1f96c2aeacdfa80fdc955fe826b8788a7616a35b04934f807110d473761d5.jpg) + +![](images/d883e59fa85a56cdd514abe3f54352df80d7300b775719abcf4592faa7336d2f.jpg) + +![](images/c3bd79f0004f279cbb424a9302ec7cdc9e225aec24dda2f7838fed635d40dca1.jpg) + +# Abstract + +Given a clothing image and a person image, an image-based virtual try-on aims to generate a customized image that appears natural and accurately reflects the characteristics of the clothing image. In this work, we aim to expand the applicability of the pre-trained diffusion model so that it can be utilized independently for the virtual try-on task. The main challenge is to preserve the clothing details while effectively utilizing the robust generative capability of the pre-trained model. In order to tackle these issues, we propose StableVITON, learning the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model in an end-to + +end manner. Our proposed zero cross-attention blocks not only preserve the clothing details by learning the semantic correspondence but also generate high-fidelity images by utilizing the inherent knowledge of the pre-trained model in the warping process. Through our proposed novel attention total variation loss and applying augmentation, we achieve the sharp attention map, resulting in a more precise representation of clothing details. StableVITON outperforms the baselines in qualitative and quantitative evaluation, showing promising quality in arbitrary person images. Our code is available at https://github.com/rlawjdghek/StableVITON. + +# 1. Introduction + +The objective of an image-based virtual try-on is to dress a given clothing image on a target person image. Most of the previous virtual try-on approaches [3, 7, 10, 14, 15, 29, 31, 33] leverage paired datasets consisting of clothing images and person images wearing those garments for training purposes. These methods typically include two modules: (1) a warping network to learn the semantic correspondence between the clothing and the human body, and (2) a generator that fuses the warped clothing and the person image. + +Despite achieving significant advancements, previous methods [3, 8, 15, 31] still have limitations in achieving generalizability, particularly in maintaining the complex background in an arbitrary person image. The nature of matching clothing and individuals in the virtual try-on dataset [3, 10, 18] makes it challenging to collect data in diverse environments [20], which in turn leads to limitations in the generator's generative capability. + +Meanwhile, recent advancements in large-scale pretrained diffusion models [23, 24, 27] have led to the emergence of downstream tasks [6, 8, 16, 19, 26, 34, 36] that control the pre-trained diffusion models for task-specific image generation. Thanks to the powerful generative ability, several works [17, 34] have succeeded in synthesizing high-fidelity human images using the prior knowledge of the pre-trained models, which signifies the potential for extension to the virtual try-on task. + +In this paper, we aim to expand the applicability of the pre-trained diffusion model to provide a standalone model for the virtual try-on task. In the effort to adapt the pretrained diffusion model for virtual try-on, a significant challenge is to preserve the clothing details while harnessing the knowledge of the pre-trained diffusion model. This can be achieved by learning the semantic correspondence between clothing and the human body using the provided dataset. Recent research [8, 19] that has employed pretrained diffusion models in virtual try-on has shown limitations due to the following two issues: (1) insufficient spatial information available for learning the semantic correspondence [19], and (2) the pre-trained diffusion model not being fully utilized, as it pastes the warped clothing in the RGB space, relying on external warping networks as previous approaches [3, 7, 15, 31, 33] for aligning the input condition. + +To overcome these issues, we propose StableVITON, which learns the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model. To incorporate the spatial information of the clothing for learning semantic correspondence, we introduce an encoder [34] that takes clothing as input and conditions the U-Net with the intermediate features of the encoder via zero cross-attention blocks. Warping through the zero cross-attention block in a pre-trained + +![](images/56e4aeb4aa0681bf8b1c198b61335b5816eb48f488ad07b80f019ada6c8db8a3.jpg) +Figure 2. Visualization of the semantic correspondence learned by our StableVITON. We overlay the attention map for the clothing regions onto the generated images for visualization. + +diffusion model has the following two advantages: (1) preserving the clothing details by learning the semantic correspondence; (2) synthesizing high-fidelity images by leveraging the pre-trained models' inherent knowledge about humans in the warping process. As shown in Fig. 2, the attention mechanism in the latent space performs patch-wise warping by activating each token corresponding to clothing alignment within the generation region. + +To further sharpen attention maps, we propose a novel attention total variation loss and apply the augmentation, which yields improved preservation of clothing details. By not impairing the pre-trained diffusion model, this architecture generates high-quality images even when images with complex backgrounds are provided, only using an existing virtual try-on dataset. Our extensive experiments show that StableVITON outperforms the existing virtual try-on method by a large margin. In summary, our contributions are as follows: + +- Our proposed StableVITON, to the best of our knowledge, is the first end-to-end virtual try-on method finetuned on the pre-trained diffusion model without an independent warping process. +- We propose a zero cross-attention block, which learns semantic correspondence between the clothing and the human body, to condition the intermediate features from the spatial encoder. +- We propose a novel attention total variation loss and apply augmentation for further precise semantic correspondence learning. +- StableVITON shows state-of-the-art performance over existing virtual try-on models in both qualitative and quantitative results. Moreover, through the evaluation of a trained model on multiple datasets, StableVITON demonstrates its promising quality in a real-world setting. + +# 2. Related Work + +GAN-based Virtual Try-On. To properly try-on the given clothing image to the target person, existing approaches [3, 7, 15, 31] based on generative adversarial network (GAN) have attempted to address the virtual try-on problem using a two-stage strategy: (1) deforming the clothing to the proposal region and (2) fusing the warped clothing via try-on generator based on GAN. In order to achieve precise clothing deformation, previous methods [1, 7, 11, 15, 31] leverage a trainable network that estimates a dense flow map [37] to deform the clothing to the human body. At the same time, several approaches [3, 7, 14, 15, 31, 33] have been attempted to address the misalignment between the warped clothing and the human body, such as using a normalization [3] or distillation [7, 14]. However, the existing approaches still are not generalized well, leading to significant performance degradation in arbitrary person images with complex backgrounds. In this paper, we effectively address such issues by proposing a method that leverages the powerful generation ability of the pre-trained model. + +Diffusion-based Virtual Try-On. Due to the remarkable generative capabilities, research on virtual try-on has extensively discussed the application of the diffusion models. While TryOnDiffusion [38] introduces an architecture for try-on using two U-Nets, this method requires a large-scale and challenging-to-collect dataset, consisting of image pairs of the same person wearing the same clothing in two different poses. Therefore, much recent research has shifted their focus towards using the prior of a large-scale pre-trained diffusion models [13, 22, 24, 32] in the virtual try-on task. LADI-VTON [19] represents the clothing as pseudo-words, and DCI-VTON [8] applies a warping network to input the clothing as conditions for the pre-trained diffusion models. While both models deal with background-related issues, they suffer from preserving high-frequency details due to the excessive loss of spatial information from the CLIP encoder [19] and drawbacks such as incorrectly warped clothing inherited from the independent warping network [8]. On the other hand, we propose to condition the intermediate feature maps of a spatial encoder through zero cross-attention block, which allows for using the prior knowledge of the pre-trained model in the warping process. + +# 3. Preliminary + +Stable Diffusion Model. Stable Diffusion model [24] is a large-scale diffusion model trained on LAION dataset [28], built upon the Latent Diffusion model (LDM) [24], which performs a denoising process in the latent space of an autoencoder. With a fixed encoder $(\mathcal{E})$ , an input image $\mathbf{x}$ is first transformed to latent feature $\mathbf{z}_0 = \mathcal{E}(\mathbf{x})$ . Given a predefined variance schedule $\beta_{t}$ , we can define a forward diffusion process in the latent space following denoising diffu + +sion probabilistic models [13]: + +$$ +q \left(\mathbf {z} _ {t} \mid \mathbf {z} _ {0}\right) = \mathcal {N} \left(\mathbf {z} _ {t}; \sqrt {\bar {\alpha} _ {t}} \mathbf {z} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {1} +$$ + +where $t \in \{1, \dots, T\}$ , $T$ represents the number of steps in the forward diffusion process, $\alpha_{t} \coloneqq 1 - \beta_{t}$ , and $\bar{\alpha}_{t} \coloneqq \Pi_{s=1}^{t} \alpha_{s}$ . As a training loss, Stable Diffusion model employs the simplified objective function from LDM [15]: + +$$ +\mathcal {L} _ {L D M} = \mathbb {E} _ {\mathcal {E} (\mathbf {x}), \mathbf {y}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(\mathbf {z} _ {t}, t, \tau_ {\theta} (\mathbf {y})\right) \| _ {2} ^ {2} \right], \tag {2} +$$ + +where the denoising network $\epsilon_{\theta}(\cdot)$ is implemented with a U-Net architecture [25] and $\tau_{\theta}(\cdot)$ is the CLIP [22] text encoder to condition the text prompt $y$ . + +# 4. Method + +# 4.1. Model Overview + +An overview of StableVITON is presented in Fig. 3(a). Given a person image $\mathbf{x} \in \mathbb{R}^{H \times W \times 3}$ , the clothing-agnostic person representation $\mathbf{x}_a \in \mathbb{R}^{H \times W \times 3}$ (we call it as 'agnostic map') [3] is proposed to eliminate any clothing information in $\mathbf{x}$ . In this work, we approach the virtual try-on as an exemplar-based image inpainting problem [32] to fill theagnostic map $\mathbf{x}_a$ with the clothing image $\mathbf{x}_c$ . As the input of the U-Net, we concatenate four components: (1) the noisy image $(\mathbf{z}_t)$ , (2) latentagnostic map $(\mathcal{E}(\mathbf{x}_a))$ , (3) the resized clothing-agnostic mask $(\mathbf{x}_{m_a})$ , (4) latent dense pose condition $(\mathcal{E}(\mathbf{x}_p))$ [9] to preserve the person's pose. To align the input channels, we expand the initial convolution layer of the U-Net to 13 (i.e., $4 + 4 + 1 + 4 = 13$ ) channels with a convolution layer initialized with zero weights. For exemplar conditioning, we input the $\mathbf{x}_c$ to the CLIP image encoder [32]. + +To preserve the fine details of the clothing, we introduce a spatial encoder, which takes latent clothing $(\mathcal{E}(\mathbf{x}_c))$ as input. This spatial encoder copies the weight of the pre-trained U-Net [34] and conditions the intermediate feature maps of the encoder to U-Net via zero cross-attention blocks. During training, we apply augmentation and further finetune the model with our proposed attention total variation loss, which makes the attention region on the clothing sharper. The detailed model architecture is described in the supplementary material. + +# 4.2. StableVITON + +Zero Cross-Attention Block. We aim to condition the intermediate feature maps of the clothing to U-Net, properly aligning with the human body. The operation of adding the unaligned clothing feature map to the human feature map is insufficient to preserve clothing details due to misalignment between the human body and the clothing. Therefore, we proposed a zero cross-attention block to be a flexible operation by applying an attention mechanism for conditioning. + +![](images/de6b6a92a84da2f943eca46edd5addd21db7f1937427b67156c7cc3e4a567358.jpg) +(a) Overview of StableVITON + +![](images/66aac335d69389b123521d8f2373401d2a76370cecb94ecd369555201760a3f7.jpg) +(b) Zero Cross-Attention Block +Figure 3. For the virtual try-on task, StableVITON additionally takes three conditions: agnostic map, agnostic mask, and dense pose, as the input of the pre-trained U-Net, which serves as the query (Q) for the cross-attention. The feature map of the clothing is used as the key (K) and value (V) for the cross-attention and is conditioned on the UNet, as depicted in (b). + +Specifically, as shown in Fig. 3(b), the feature map of the U-Net decoder block inputs to self-attention, followed by the cross-attention layer where the query (Q) comes from the previous self-attention layer and the spatial encoder's feature map serves as the key (K) and value (V). To eliminate harmful noise, we introduce a linear layer initialized with zero weight after the feed-forward operation [34]. + +To successfully align the clothing to the human body part via cross-attention, it is crucial to ensure semantic correspondence between the key tokens (clothing) and the query tokens (human body). For instance, when dealing with a query token related to the right shoulder, the corresponding key tokens should exhibit higher attention scores in the corresponding right shoulder area of the clothing. In Fig. 4(a), we averaged the attention maps of the resolution of $32 \times 24$ across the head dimension and arranged them flatly. For clear visualization, we downsample the generated image to a resolution of $32 \times 24$ and then resize it back to $32^2 \times 24^2$ . Subsequently, we overlay this generated image with the attention map corresponding to each query token. Zooming in on the upper and middle of the generated clothing area, we observe that the key tokens unrelated to the corresponding query token, such as the bottom of the clothing, are activated in the attention map. This indicates that the cross-attention layer fails to learn the exact semantic correspondence between query and key tokens, combining the several key tokens of the clothing to generate the color corresponding to the query token during training. Therefore, as shown in Fig. 4, the stripes on the clothing are not distinctly visible. + +Augmentation. To mitigate such issues of key tokens unre + +lated to query tokens being attended to, we alter the feature map by applying augmentation, including random shifts to input conditions. Detailed settings of augmentation are described in supplementary material. Along with the augmented input conditions, we train our model with the objective function defined as follows: + +$$ +\mathcal {L} _ {L D M} = \mathbb {E} _ {\zeta , \mathbf {x} _ {c}, \mathcal {E} (\mathbf {x} _ {c}), \epsilon , t} \left[ \| \epsilon - \epsilon_ {\theta} (\zeta , t, \tau_ {\phi} (\mathbf {x} _ {c}), \mathcal {E} (\mathbf {x} _ {c})) \| _ {2} ^ {2} \right], \tag {3} +$$ + +where $\zeta = [\mathbf{z}_t;\mathcal{E}(\mathbf{x}_a);\mathbf{x}_{m_a};\mathcal{E}(\mathbf{x}_p)]$ , and $\tau_{\phi}$ is the CLIP image encoder. Note that we do not update the parameters of the original blocks, as depicted in Fig. 3(a). + +The rationale behind this strategy is to force the model to learn fine-grained semantic correspondence using augmentation, instead of just moderately injecting the clothes at similar positions. As shown in Fig. 4(b), we can confirm that key tokens related to query tokens have high attention scores, signifying that the cross-attention layer has learned the high semantic correspondence between the clothing-agnostic region and clothing. + +Attention Total Variation Loss. While the cross-attention layer successfully aligns the clothing to the agnostic map, the points with high attention scores appear in dispersed positions, as shown in the attention map of Fig. 4(b). This causes inaccurate details in generated images, such as color discrepancies. + +To address such an issue, we propose attention total variation loss. As the attention scores are the weight for the output, we calculate the center coordinates as a weighted sum of the attention map and the grid. Therefore, given the $H_{q}W_{q}$ query tokens and $h_k w_k$ key tokens, we calculate center coordinate map $F \in \mathbb{R}^{H_q \times W_q \times 2}$ as follows: + +![](images/b6ef1068bff360dc5c1412015ff1d0775461730b00458cc4bf9fcc0137081f43.jpg) +Figure 4. Visualization of attention map from a zero cross-attention block of 32 resolution. + +$$ +F _ {i j n} = \frac {1}{h _ {k} w _ {k}} \sum_ {k = 1} ^ {h _ {k}} \sum_ {l = 1} ^ {w _ {k}} \left(A _ {i j k l} \odot G _ {k l n}\right), \tag {4} +$$ + +where we average the attention map over the head dimension and reshape it as $A \in \mathbb{R}^{H_q \times W_q \times h_k \times w_k}$ , and $G \in [-1, 1]^{h_k \times w_k \times 2}$ is a 2D normalized coordinate. $n \in \{0, 1\}$ in Eq. 4 denotes the dimension of attention map coordinates and $\odot$ indicates element-wise multiplication operation. + +For each query token in each clothing-agnostic region, the center coordinates should be evenly distributed, and the attention total variation loss $\mathcal{L}_{ATV}$ is defined as follows: + +$$ +\mathcal {L} _ {A T V} = \left\| \nabla (F \odot M) \right\| _ {1}, \tag {5} +$$ + +where $M \in \{0,1\}^{H_q \times W_q}$ is the ground truth clothing mask to only affect the clothing region. The attention total variation loss $\mathcal{L}_{ATV}$ is designed to enforce the center coordinates on the attention map uniformly distributed, thereby alleviating interference among attention scores located at dispersed positions. As illustrated in Figure (c), this leads to the generation of a sharper attention map, thereby more accurately reflecting the color of the clothing. + +Finally, we finetune our StableVITON by adding $\mathcal{L}_{ATV}$ to Eq. 3: + +$$ +\mathcal {L} _ {\text {f i n e t u n e}} = \mathcal {L} _ {L D M} + \lambda_ {A T V} \mathcal {L} _ {A T V}, \tag {6} +$$ + +where $\lambda_{ATV}$ is a weight hyper-parameter. + +# 5. Experiment + +Baselines. We compare StableVITON with three GAN-based virtual try-on methods, VITON-HD [3], HRVITON [15], and GP-VTON [31], and two diffusion-based virtual try-on methods, LADI-VTON [19] and DCIVTON [8]. We also evaluate a diffusion-based inpainting method, Paint-by-Example [32]. We use pre-trained weights if available; otherwise, we train the models following the official code. + +Dataset. We conduct the experiments using two publicly available virtual try-on datasets, VITON-HD [3] and DressCode [18], and one human image dataset, SHHQ-1.0 [5]. + +We train our model with VITON-HD and upper-body images in DressCode, respectively. For the evaluation of SHHQ-1.0, we use the first 2,032 images and follow the preprocessing instruction of VITON-HD [3] to obtain the input conditions such as the agnostic maps or the dense pose. + +Evaluation. We evaluate the performances in two test settings. Specifically, the paired setting uses a pair of a person and the original clothes for reconstruction, whereas the unpaired setting involves changing the clothing of a person image with a different clothing item. As previous work [3], training and evaluation within a single dataset are referred to as 'single dataset evaluation'. On the other hand, we extend our evaluation on other datasets (e.g., SHHQ-1.0), which we refer to as a 'cross dataset evaluation'. This evaluation enables an in-depth assessment of the model's generalizability in handling arbitrary person images, demonstrating applicability in real-world scenarios. Our model is capable of training at a $1024 \times 768$ resolution, but for a fair evaluation with baselines, we used a model trained at a $512 \times 384$ resolution. More results and details about experiments are described in the supplementary material. + +# 5.1. Qualitative Results + +Single Dataset Evaluation. As shown in Fig. 5, StableVITON generates realistic images and effectively preserves the text and clothing textures compared to the six baseline methods. Specifically, in the first row of Fig. 5, GAN-based methods such as GP-VTON struggle to generate the arms of the target person naturally. Moreover, other diffusion-based models either fail to preserve the text (Paint-by-Example and LADI-VTON) or show an overlapped artifact between the clothing and the target person (DCI-VTON). On the other hand, despite some parts of the arm being covered by clothing, our model produces a high-fidelity result that omits the 'L' in 'Love'. + +Cross Dataset Evaluation. We visualize the generation images of the models trained on VITON-HD for DressCode and SHHQ-1.0 datasets in Fig. 6 and Fig. 7, respectively. The results clearly demonstrate that StableVITON generates high-fidelity images while preserving the details of the + +![](images/00336f9be79e64d53683de0f80e560792f6a234e0a7f25355c518213bef59315.jpg) +Figure 5. Qualitative comparison with baselines in a single dataset setting (VITON-HD / VITON-HD). Best viewed when zoomed in. + +![](images/153f71905918fc1561aa61dc46b91cdc2d29b48f0707f9c7e912ed9254216b85.jpg) +Figure 6. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / DressCode). Best viewed when zoomed in. + +
Train / Test MethodVITON-HD / VITON-HDD.C. Upper / D.C. Upper
SSIMLPIPSFIDKIDSSIMLPIPSFIDKID
VITON-HD [3]0.8620.11712.1173.23----
HR-VITON [15]0.8780.104511.2652.730.9360.065213.8202.71
LADI-VTON [19]0.8640.09649.4801.990.9220.062814.173.04
Paint-by-Example [32]0.8020.142811.9393.850.8970.077515.3324.64
DCI-VTON [8]0.8800.08048.7541.100.9370.042111.9201.89
GP-VTON [31]0.8840.08149.0720.880.7690.267920.1108.17
Ours0.8520.08428.6980.880.9110.050011.2660.72
Ours (RePaint [17])0.8880.07328.2330.490.9370.03889.9400.12
+ +Table 1. Quantitative comparisons in single dataset settings, VITON-HD and DressCode upper-body (D.C. Upper) datasets. Bold and underline denote the best and the second best result, respectively. + +clothing. GAN-based methods especially show significant artifacts on the target person and fail to maintain background. While diffusion-based methods generate natural images, they fail to preserve clothing details or the shape of the clothing. Furthermore, even when applying the augmentation we used to DCI-VTON (denoted as DCI-VTON (Aug.)), as depicted in Fig. 7, a significant improvement in the performance of the warping network is not achieved, failing to preserve clothing details. + +# 5.2. Quantitative Results + +Metrics. For quantitative evaluation, we use SSIM [30] and LPIPS [35] in the paired setting. In an unpaired setting, + +we assess the realism using FID [12] and KID [2] score. We follow the evaluation paradigm [19] for the implementation [4, 21]. + +Single Dataset Evaluation. We evaluate our StableViTON and existing baselines on a single dataset setting and report the results in Table 1. In the unpaired setting (i.e., FID and KID), StableViTON outperforms all the baselines. We observe that the performance degradation in the paired setting occurs due to the autoencoder's reconstruction error of the agnostic map. To mitigate this issue, we adapt RePaint [17], which samples the known region (i.e., agnostic map) and replaces it in each denoising steps during the inference, used in DCI-VTON. Applying RePaint, Stable- + +![](images/b795af6fd36ec0ba4121345289a3e9293083f77f3a3db7d931f9b8d762212729.jpg) +Figure 7. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / SHHQ-1.0). Best viewed when zoomed in. + +
Train / Test +MethodVITON-HD / D.C. UpperD.C. Upper / VITON-HDVITON-HD / SHHQ-1.0
SSIMLPIPSFIDKIDSSIMLPIPSFIDKIDFIDKID
VITON-HD [3]0.8530.187444.25728.82----71.14952.01
HR-VITON [15]0.9090.107719.9707.350.8110.227845.92336.6952.73231.22
LADI-VTON [19]0.9010.100916.3365.360.7950.27228.2719.324.9046.07
Paint-by-Example [32]0.8890.086716.3984.780.7840.181415.6257.5226.2749.830
DCI-VTON [8]0.9030.121723.07612.030.8250.187016.6706.4024.8506.68
DCI-VTON (Aug.) [8]0.8980.124018.8098.02----24.3686.11
GP-VTON [31]0.7240.384665.71166.010.8040.262152.35148.68--
Ours0.9110.060312.5811.700.8170.130810.1041.7223.5315.68
Ours (RePaint [17])0.9380.047010.4800.410.8550.11739.7141.3521.0775.10
+ +Table 2. Quantitative comparisons in cross dataset settings. We train the models on VITON-HD and DressCode upper-body (D.C. Upper) datasets and evaluate them on different datasets. Bold and underline denote the best and the second best result, respectively. + +VITON outperforms the baselines for all evaluation metrics. Since RePaint greatly helps maintain regions unrelated to clothing, it shows notable performance improvement in the paired setting. Nevertheless, even without RePaint, our method demonstrates superior performance in terms of FID and KID in the unpaired setting compared to the baselines. + +Cross Dataset Evaluation. Table 2 presents that our StableVITON shows state-of-the-art performance for all the evaluation metrics with a large margin. GAN-based methods fail to maintain background consistency, resulting in significantly high FID and KID scores. While diffusion-based methods exhibit better performance due to the plausible generation outcomes enabled by pre-trained diffusion models, they fail to preserve clothing details. Consequently, they exhibit lower similarity scores in the paired setting (i.e., SSIM and LPIPS) compared to our method. + +# 5.3. User Study + +For the models trained on the VITON-HD dataset, we conducted a user study with 40 participants. Each participant was shown one image generated by the baseline and the other by our model. They were asked to choose the better image based on three criteria: (1) fidelity, (2) person attributes, and (3) clothing identity. We added a question + +![](images/2dc606c788efb5f813f4d4fe85867a1558ec6dc23a045196135cdfc6e8b61c3b.jpg) +Figure 8. User study results. We compare our StableVITON with six baselines, involving a total of 40 participants. + +about (4) background quality for the cross dataset setting. Detailed questions can be found in the supplementary material. As shown in Fig. 8, StableVITON outperforms in most of the criteria, and especially in the cross dataset setting, our method is overwhelming in human evaluations. While LADI-VTON shows better preference in the evaluation of fidelity and person attributes on the VITON-HD dataset, it fails to preserve clothing details, resulting in a $35\%$ preference in the clothing identity criteria. + +
Train / Test on VITON-HDSSIMLPIPSFIDKID
ControlNet + Aug.0.8320.11579.811.81
ControlNet-W + Aug.0.8220.11249.661.57
Zero Cross-Attention Block + Aug.0.8500.08518.740.91
+ +Table 3. Quantitative comparison results between our zero cross-attention block and ControlNet. We train ControlNet with clothing and warped clothing [15] (ControlNet-W). We apply augmentation to all the models in training. + +
Aug.Attention TV LossSSIMLPIPSFIDFID
XX0.8470.09699.351.33
✓X0.8500.08518.7440.91
✓✓0.8520.0428.6980.88
+ +Table 4. Ablation study of our proposed training components on VITON-HD dataset. + +# 5.4. Ablation Study + +Comparison with ControlNet. To demonstrate the effectiveness of StableVITON in tackling the alignment issue compared to ControlNet [34], we train ControlNet under two different input conditions: (1) clothing, and (2) warped clothing [15] (dubbed as ControlNet-W). We apply our proposed augmentation to both models during training. Using the warping network to align the clothing helps ControlNet capture coarse features, such as the overall shape and color of the logo, as shown in Fig. 9(b) and (c). However, since the misalignment still exists between warped clothing and the human body in the training phase, ControlNet-W struggles to reflect more fine-grained clothing details to the generation results. These observations highlight that ControlNet is highly sensitive to subtle misalignment across the input, stemming from the limitations of the ControlNet's direct addition operation in conditioning. In contrast, as shown in Fig. 9(d), the zero cross-attention block, free from the alignment constraints, successfully preserves the logos and patterns and leads to a qualitative performance improvement, as shown in Table 3. + +Effect of Training Components. We investigate the effect of the two proposed components during training: augmentation and attention total variation loss. In Fig. 10, we visualize the generated images while incrementally introducing the proposed training components one by one. Compared to Fig 10(a) and (b), we observe that detailed features such as logos and patterns of the clothing are more preserved when augmentation is applied. However, as the attention maps are not sufficiently distinct, we observe inaccuracies in the generated images, such as the 'M' in 'PUMA' being incorrectly depicted or lines blurring, as shown in Fig. 10(b). After finetuning with our proposed attention total variation loss, these finer details are significantly improved. Such visual enhancements correspond to quantitative performance improvements as demonstrated in Table 4. + +![](images/1a098365e78edee7a2abb9a263691d70c015e6014bfacdb8daccc604b9f5cbc9.jpg) +(a) Target Person +(b) ControlNet +(c) ControlNet-W +(d) Ours + +![](images/99ff958f43611ed13e493971dca37ebf82d02b66fdb086713514bf96a67d5c8f.jpg) +Figure 9. Comparison our StableVITON to ControlNets under the two different input conditions: (1) clothing, and (2) warped clothing [15] (ControlNet-W). Best viewed when zoomed in. +Figure 10. Visual comparisons according to our training components. Best viewed when zoomed in. + +# 6. Conclusion + +We propose StableVITON, a novel image-based virtual try-on method using the pre-trained diffusion model. Our proposed zero cross-attention block learns semantic correspondence between the clothing and the human body, enabling try-on in the latent feature space. A novel attention total variation loss and augmentation are designed to preserve the clothing details better. Extensive experiments, including cross dataset evaluation, clearly demonstrate that StableVITON shows the state-of-the-art performance compared to the existing methods and its promising quality in the real-world setting. + +Acknowledgements. Sunghyun Park is the corresponding author. This work was supported by the Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913). + +# References + +[1] Shuai Bai, Huiling Zhou, Zhikang Li, Chang Zhou, and Hongxia Yang. Single stage virtual try-on via deformable attention flows. In European Conference on Computer Vision, pages 409-425. Springer, 2022. 3 +[2] Mikołaj Binkowski, Danica J Sutherland, Michael Arbel, and Arthur Gretton. Demystifying mmd gans. arXiv preprint arXiv:1801.01401, 2018. 6 +[3] Seunghwan Choi, Sunghyun Park, Minsoo Lee, and Jaegul Choo. Viton-hd: High-resolution virtual try-on via misalignment-aware normalization. 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Generated results of StableVITON: VITON-HD (the first row), SHHQ-1.0 (the first two images in the second row), and web-crawled images (the last two images in the second row). All results are generated using StableVITON trained on VITON-HD dataset." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 173, + 366, + 296, + 521 + ], + "blocks": [ + { + "bbox": [ + 173, + 366, + 296, + 521 + ], + "lines": [ + { + "bbox": [ + 173, + 366, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 173, + 366, + 296, + 521 + ], + "type": "image", + "image_path": "24e1f96c2aeacdfa80fdc955fe826b8788a7616a35b04934f807110d473761d5.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 298, + 366, + 420, + 521 + ], + "blocks": [ + { + "bbox": [ + 298, + 366, + 420, + 521 + ], + "lines": [ + { + "bbox": [ + 298, + 366, + 420, + 521 + ], + "spans": [ + { + "bbox": [ + 298, + 366, + 420, + 521 + ], + "type": "image", + "image_path": "d883e59fa85a56cdd514abe3f54352df80d7300b775719abcf4592faa7336d2f.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 421, + 366, + 545, + 521 + ], + "blocks": [ + { + "bbox": [ + 421, + 366, + 545, + 521 + ], + "lines": [ + { + "bbox": [ + 421, + 366, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 421, + 366, + 545, + 521 + ], + "type": "image", + "image_path": "c3bd79f0004f279cbb424a9302ec7cdc9e225aec24dda2f7838fed635d40dca1.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 143, + 553, + 192, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 553, + 192, + 565 + ], + "spans": [ + { + "bbox": [ + 143, + 553, + 192, + 565 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 571, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 571, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 571, + 288, + 715 + ], + "type": "text", + "content": "Given a clothing image and a person image, an image-based virtual try-on aims to generate a customized image that appears natural and accurately reflects the characteristics of the clothing image. In this work, we aim to expand the applicability of the pre-trained diffusion model so that it can be utilized independently for the virtual try-on task. The main challenge is to preserve the clothing details while effectively utilizing the robust generative capability of the pre-trained model. In order to tackle these issues, we propose StableVITON, learning the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model in an end-to" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 554, + 547, + 697 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 547, + 697 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 547, + 697 + ], + "type": "text", + "content": "end manner. Our proposed zero cross-attention blocks not only preserve the clothing details by learning the semantic correspondence but also generate high-fidelity images by utilizing the inherent knowledge of the pre-trained model in the warping process. Through our proposed novel attention total variation loss and applying augmentation, we achieve the sharp attention map, resulting in a more precise representation of clothing details. StableVITON outperforms the baselines in qualitative and quantitative evaluation, showing promising quality in arbitrary person images. Our code is available at https://github.com/rlawjdghek/StableVITON." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 315, + 757 + ], + "type": "text", + "content": "8176" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 128, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 128, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 128, + 83 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 287, + 199 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 287, + 199 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 287, + 199 + ], + "type": "text", + "content": "The objective of an image-based virtual try-on is to dress a given clothing image on a target person image. Most of the previous virtual try-on approaches [3, 7, 10, 14, 15, 29, 31, 33] leverage paired datasets consisting of clothing images and person images wearing those garments for training purposes. These methods typically include two modules: (1) a warping network to learn the semantic correspondence between the clothing and the human body, and (2) a generator that fuses the warped clothing and the person image." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 199, + 287, + 294 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 199, + 287, + 294 + ], + "spans": [ + { + "bbox": [ + 46, + 199, + 287, + 294 + ], + "type": "text", + "content": "Despite achieving significant advancements, previous methods [3, 8, 15, 31] still have limitations in achieving generalizability, particularly in maintaining the complex background in an arbitrary person image. The nature of matching clothing and individuals in the virtual try-on dataset [3, 10, 18] makes it challenging to collect data in diverse environments [20], which in turn leads to limitations in the generator's generative capability." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 294, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 294, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 294, + 287, + 402 + ], + "type": "text", + "content": "Meanwhile, recent advancements in large-scale pretrained diffusion models [23, 24, 27] have led to the emergence of downstream tasks [6, 8, 16, 19, 26, 34, 36] that control the pre-trained diffusion models for task-specific image generation. Thanks to the powerful generative ability, several works [17, 34] have succeeded in synthesizing high-fidelity human images using the prior knowledge of the pre-trained models, which signifies the potential for extension to the virtual try-on task." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 605 + ], + "type": "text", + "content": "In this paper, we aim to expand the applicability of the pre-trained diffusion model to provide a standalone model for the virtual try-on task. In the effort to adapt the pretrained diffusion model for virtual try-on, a significant challenge is to preserve the clothing details while harnessing the knowledge of the pre-trained diffusion model. This can be achieved by learning the semantic correspondence between clothing and the human body using the provided dataset. Recent research [8, 19] that has employed pretrained diffusion models in virtual try-on has shown limitations due to the following two issues: (1) insufficient spatial information available for learning the semantic correspondence [19], and (2) the pre-trained diffusion model not being fully utilized, as it pastes the warped clothing in the RGB space, relying on external warping networks as previous approaches [3, 7, 15, 31, 33] for aligning the input condition." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 713 + ], + "type": "text", + "content": "To overcome these issues, we propose StableVITON, which learns the semantic correspondence between the clothing and the human body within the latent space of the pre-trained diffusion model. To incorporate the spatial information of the clothing for learning semantic correspondence, we introduce an encoder [34] that takes clothing as input and conditions the U-Net with the intermediate features of the encoder via zero cross-attention blocks. Warping through the zero cross-attention block in a pre-trained" + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 309, + 70, + 545, + 225 + ], + "blocks": [ + { + "bbox": [ + 309, + 70, + 545, + 225 + ], + "lines": [ + { + "bbox": [ + 309, + 70, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 309, + 70, + 545, + 225 + ], + "type": "image", + "image_path": "56e4aeb4aa0681bf8b1c198b61335b5816eb48f488ad07b80f019ada6c8db8a3.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 232, + 545, + 266 + ], + "lines": [ + { + "bbox": [ + 305, + 232, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 232, + 545, + 266 + ], + "type": "text", + "content": "Figure 2. Visualization of the semantic correspondence learned by our StableVITON. We overlay the attention map for the clothing regions onto the generated images for visualization." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 289, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 289, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 304, + 289, + 545, + 386 + ], + "type": "text", + "content": "diffusion model has the following two advantages: (1) preserving the clothing details by learning the semantic correspondence; (2) synthesizing high-fidelity images by leveraging the pre-trained models' inherent knowledge about humans in the warping process. As shown in Fig. 2, the attention mechanism in the latent space performs patch-wise warping by activating each token corresponding to clothing alignment within the generation region." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 392, + 545, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 392, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 392, + 545, + 511 + ], + "type": "text", + "content": "To further sharpen attention maps, we propose a novel attention total variation loss and apply the augmentation, which yields improved preservation of clothing details. By not impairing the pre-trained diffusion model, this architecture generates high-quality images even when images with complex backgrounds are provided, only using an existing virtual try-on dataset. Our extensive experiments show that StableVITON outperforms the existing virtual try-on method by a large margin. In summary, our contributions are as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 520, + 545, + 711 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 306, + 520, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 520, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 306, + 520, + 545, + 567 + ], + "type": "text", + "content": "- Our proposed StableVITON, to the best of our knowledge, is the first end-to-end virtual try-on method finetuned on the pre-trained diffusion model without an independent warping process." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 568, + 544, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 568, + 544, + 614 + ], + "spans": [ + { + "bbox": [ + 306, + 568, + 544, + 614 + ], + "type": "text", + "content": "- We propose a zero cross-attention block, which learns semantic correspondence between the clothing and the human body, to condition the intermediate features from the spatial encoder." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 616, + 544, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 544, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 544, + 651 + ], + "type": "text", + "content": "- We propose a novel attention total variation loss and apply augmentation for further precise semantic correspondence learning." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 545, + 711 + ], + "type": "text", + "content": "- StableVITON shows state-of-the-art performance over existing virtual try-on models in both qualitative and quantitative results. Moreover, through the evaluation of a trained model on multiple datasets, StableVITON demonstrates its promising quality in a real-world setting." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8177" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 289, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 289, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 289, + 319 + ], + "type": "text", + "content": "GAN-based Virtual Try-On. To properly try-on the given clothing image to the target person, existing approaches [3, 7, 15, 31] based on generative adversarial network (GAN) have attempted to address the virtual try-on problem using a two-stage strategy: (1) deforming the clothing to the proposal region and (2) fusing the warped clothing via try-on generator based on GAN. In order to achieve precise clothing deformation, previous methods [1, 7, 11, 15, 31] leverage a trainable network that estimates a dense flow map [37] to deform the clothing to the human body. At the same time, several approaches [3, 7, 14, 15, 31, 33] have been attempted to address the misalignment between the warped clothing and the human body, such as using a normalization [3] or distillation [7, 14]. However, the existing approaches still are not generalized well, leading to significant performance degradation in arbitrary person images with complex backgrounds. In this paper, we effectively address such issues by proposing a method that leverages the powerful generation ability of the pre-trained model." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 320, + 289, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 320, + 289, + 584 + ], + "spans": [ + { + "bbox": [ + 47, + 320, + 289, + 584 + ], + "type": "text", + "content": "Diffusion-based Virtual Try-On. Due to the remarkable generative capabilities, research on virtual try-on has extensively discussed the application of the diffusion models. While TryOnDiffusion [38] introduces an architecture for try-on using two U-Nets, this method requires a large-scale and challenging-to-collect dataset, consisting of image pairs of the same person wearing the same clothing in two different poses. Therefore, much recent research has shifted their focus towards using the prior of a large-scale pre-trained diffusion models [13, 22, 24, 32] in the virtual try-on task. LADI-VTON [19] represents the clothing as pseudo-words, and DCI-VTON [8] applies a warping network to input the clothing as conditions for the pre-trained diffusion models. While both models deal with background-related issues, they suffer from preserving high-frequency details due to the excessive loss of spatial information from the CLIP encoder [19] and drawbacks such as incorrectly warped clothing inherited from the independent warping network [8]. On the other hand, we propose to condition the intermediate feature maps of a spatial encoder through zero cross-attention block, which allows for using the prior knowledge of the pre-trained model in the warping process." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 597, + 125, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 125, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 125, + 609 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": "Stable Diffusion Model. Stable Diffusion model [24] is a large-scale diffusion model trained on LAION dataset [28], built upon the Latent Diffusion model (LDM) [24], which performs a denoising process in the latent space of an autoencoder. With a fixed encoder " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "(\\mathcal{E})" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": ", an input image " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": " is first transformed to latent feature " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{z}_0 = \\mathcal{E}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": ". Given a predefined variance schedule " + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 47, + 617, + 288, + 714 + ], + "type": "text", + "content": ", we can define a forward diffusion process in the latent space following denoising diffu" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 72, + 432, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 432, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 432, + 84 + ], + "type": "text", + "content": "sion probabilistic models [13]:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 348, + 92, + 545, + 107 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 92, + 545, + 107 + ], + "spans": [ + { + "bbox": [ + 348, + 92, + 545, + 107 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {z} _ {t} \\mid \\mathbf {z} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {z} _ {t}; \\sqrt {\\bar {\\alpha} _ {t}} \\mathbf {z} _ {0}, (1 - \\bar {\\alpha} _ {t}) \\mathbf {I}\\right), \\tag {1}", + "image_path": "bbc5da2d5febff9655f4437d48be6e6e05bdb52a3a4d7da2b8005fd888a5a5af.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "spans": [ + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "t \\in \\{1, \\dots, T\\}" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": " represents the number of steps in the forward diffusion process, " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "\\alpha_{t} \\coloneqq 1 - \\beta_{t}" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "inline_equation", + "content": "\\bar{\\alpha}_{t} \\coloneqq \\Pi_{s=1}^{t} \\alpha_{s}" + }, + { + "bbox": [ + 304, + 114, + 547, + 163 + ], + "type": "text", + "content": ". As a training loss, Stable Diffusion model employs the simplified objective function from LDM [15]:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 315, + 171, + 545, + 196 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 171, + 545, + 196 + ], + "spans": [ + { + "bbox": [ + 315, + 171, + 545, + 196 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\mathcal {E} (\\mathbf {x}), \\mathbf {y}, \\epsilon \\sim \\mathcal {N} (0, 1), t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} \\left(\\mathbf {z} _ {t}, t, \\tau_ {\\theta} (\\mathbf {y})\\right) \\| _ {2} ^ {2} \\right], \\tag {2}", + "image_path": "cb19e60ff84c23371ee7b248c38e8aff3c618b99a8af5217d64cc888a2e9fa98.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "spans": [ + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "text", + "content": "where the denoising network " + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "text", + "content": " is implemented with a U-Net architecture [25] and " + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "inline_equation", + "content": "\\tau_{\\theta}(\\cdot)" + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "text", + "content": " is the CLIP [22] text encoder to condition the text prompt " + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 196, + 547, + 233 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 243, + 362, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 243, + 362, + 255 + ], + "spans": [ + { + "bbox": [ + 306, + 243, + 362, + 255 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 262, + 406, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 406, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 406, + 274 + ], + "type": "text", + "content": "4.1. Model Overview" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": "An overview of StableVITON is presented in Fig. 3(a). Given a person image " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ", the clothing-agnostic person representation " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_a \\in \\mathbb{R}^{H \\times W \\times 3}" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": " (we call it as 'agnostic map') [3] is proposed to eliminate any clothing information in " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ". In this work, we approach the virtual try-on as an exemplar-based image inpainting problem [32] to fill theagnostic map " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_a" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": " with the clothing image " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_c" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ". As the input of the U-Net, we concatenate four components: (1) the noisy image " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "(\\mathbf{z}_t)" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ", (2) latentagnostic map " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "(\\mathcal{E}(\\mathbf{x}_a))" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ", (3) the resized clothing-agnostic mask " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "(\\mathbf{x}_{m_a})" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ", (4) latent dense pose condition " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "(\\mathcal{E}(\\mathbf{x}_p))" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": " [9] to preserve the person's pose. To align the input channels, we expand the initial convolution layer of the U-Net to 13 (i.e., " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "4 + 4 + 1 + 4 = 13" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": ") channels with a convolution layer initialized with zero weights. For exemplar conditioning, we input the " + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_c" + }, + { + "bbox": [ + 304, + 281, + 545, + 472 + ], + "type": "text", + "content": " to the CLIP image encoder [32]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 473, + 547, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 593 + ], + "type": "text", + "content": "To preserve the fine details of the clothing, we introduce a spatial encoder, which takes latent clothing " + }, + { + "bbox": [ + 304, + 473, + 547, + 593 + ], + "type": "inline_equation", + "content": "(\\mathcal{E}(\\mathbf{x}_c))" + }, + { + "bbox": [ + 304, + 473, + 547, + 593 + ], + "type": "text", + "content": " as input. This spatial encoder copies the weight of the pre-trained U-Net [34] and conditions the intermediate feature maps of the encoder to U-Net via zero cross-attention blocks. During training, we apply augmentation and further finetune the model with our proposed attention total variation loss, which makes the attention region on the clothing sharper. The detailed model architecture is described in the supplementary material." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 599, + 394, + 611 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 394, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 394, + 611 + ], + "type": "text", + "content": "4.2. StableVITON" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 715 + ], + "type": "text", + "content": "Zero Cross-Attention Block. We aim to condition the intermediate feature maps of the clothing to U-Net, properly aligning with the human body. The operation of adding the unaligned clothing feature map to the human feature map is insufficient to preserve clothing details due to misalignment between the human body and the clothing. Therefore, we proposed a zero cross-attention block to be a flexible operation by applying an attention mechanism for conditioning." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "8178" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 367, + 274 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 367, + 274 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 367, + 274 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 367, + 274 + ], + "type": "image", + "image_path": "de6b6a92a84da2f943eca46edd5addd21db7f1937427b67156c7cc3e4a567358.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 148, + 276, + 269, + 286 + ], + "lines": [ + { + "bbox": [ + 148, + 276, + 269, + 286 + ], + "spans": [ + { + "bbox": [ + 148, + 276, + 269, + 286 + ], + "type": "text", + "content": "(a) Overview of StableVITON" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 409, + 82, + 529, + 262 + ], + "blocks": [ + { + "bbox": [ + 409, + 82, + 529, + 262 + ], + "lines": [ + { + "bbox": [ + 409, + 82, + 529, + 262 + ], + "spans": [ + { + "bbox": [ + 409, + 82, + 529, + 262 + ], + "type": "image", + "image_path": "66aac335d69389b123521d8f2373401d2a76370cecb94ecd369555201760a3f7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 406, + 276, + 531, + 286 + ], + "lines": [ + { + "bbox": [ + 406, + 276, + 531, + 286 + ], + "spans": [ + { + "bbox": [ + 406, + 276, + 531, + 286 + ], + "type": "text", + "content": "(b) Zero Cross-Attention Block" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 293, + 547, + 327 + ], + "lines": [ + { + "bbox": [ + 46, + 293, + 547, + 327 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 547, + 327 + ], + "type": "text", + "content": "Figure 3. For the virtual try-on task, StableVITON additionally takes three conditions: agnostic map, agnostic mask, and dense pose, as the input of the pre-trained U-Net, which serves as the query (Q) for the cross-attention. The feature map of the clothing is used as the key (K) and value (V) for the cross-attention and is conditioned on the UNet, as depicted in (b)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 337, + 288, + 422 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 337, + 288, + 422 + ], + "spans": [ + { + "bbox": [ + 46, + 337, + 288, + 422 + ], + "type": "text", + "content": "Specifically, as shown in Fig. 3(b), the feature map of the U-Net decoder block inputs to self-attention, followed by the cross-attention layer where the query (Q) comes from the previous self-attention layer and the spatial encoder's feature map serves as the key (K) and value (V). To eliminate harmful noise, we introduce a linear layer initialized with zero weight after the feed-forward operation [34]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "spans": [ + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "text", + "content": "To successfully align the clothing to the human body part via cross-attention, it is crucial to ensure semantic correspondence between the key tokens (clothing) and the query tokens (human body). For instance, when dealing with a query token related to the right shoulder, the corresponding key tokens should exhibit higher attention scores in the corresponding right shoulder area of the clothing. In Fig. 4(a), we averaged the attention maps of the resolution of " + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "inline_equation", + "content": "32 \\times 24" + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "text", + "content": " across the head dimension and arranged them flatly. For clear visualization, we downsample the generated image to a resolution of " + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "inline_equation", + "content": "32 \\times 24" + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "text", + "content": " and then resize it back to " + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "inline_equation", + "content": "32^2 \\times 24^2" + }, + { + "bbox": [ + 46, + 423, + 288, + 698 + ], + "type": "text", + "content": ". Subsequently, we overlay this generated image with the attention map corresponding to each query token. Zooming in on the upper and middle of the generated clothing area, we observe that the key tokens unrelated to the corresponding query token, such as the bottom of the clothing, are activated in the attention map. This indicates that the cross-attention layer fails to learn the exact semantic correspondence between query and key tokens, combining the several key tokens of the clothing to generate the color corresponding to the query token during training. Therefore, as shown in Fig. 4, the stripes on the clothing are not distinctly visible." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 701, + 287, + 713 + ], + "type": "text", + "content": "Augmentation. To mitigate such issues of key tokens unre" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 337, + 545, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 337, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 304, + 337, + 545, + 409 + ], + "type": "text", + "content": "lated to query tokens being attended to, we alter the feature map by applying augmentation, including random shifts to input conditions. Detailed settings of augmentation are described in supplementary material. Along with the augmented input conditions, we train our model with the objective function defined as follows:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 308, + 413, + 545, + 437 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 413, + 545, + 437 + ], + "spans": [ + { + "bbox": [ + 308, + 413, + 545, + 437 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {L D M} = \\mathbb {E} _ {\\zeta , \\mathbf {x} _ {c}, \\mathcal {E} (\\mathbf {x} _ {c}), \\epsilon , t} \\left[ \\| \\epsilon - \\epsilon_ {\\theta} (\\zeta , t, \\tau_ {\\phi} (\\mathbf {x} _ {c}), \\mathcal {E} (\\mathbf {x} _ {c})) \\| _ {2} ^ {2} \\right], \\tag {3}", + "image_path": "6ab1c3f9eb8a69a29daf19273b0317428dab3553514e402ece7c40e05091332a.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\zeta = [\\mathbf{z}_t;\\mathcal{E}(\\mathbf{x}_a);\\mathbf{x}_{m_a};\\mathcal{E}(\\mathbf{x}_p)]" + }, + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\tau_{\\phi}" + }, + { + "bbox": [ + 304, + 437, + 545, + 474 + ], + "type": "text", + "content": " is the CLIP image encoder. Note that we do not update the parameters of the original blocks, as depicted in Fig. 3(a)." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 569 + ], + "type": "text", + "content": "The rationale behind this strategy is to force the model to learn fine-grained semantic correspondence using augmentation, instead of just moderately injecting the clothes at similar positions. As shown in Fig. 4(b), we can confirm that key tokens related to query tokens have high attention scores, signifying that the cross-attention layer has learned the high semantic correspondence between the clothing-agnostic region and clothing." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 640 + ], + "type": "text", + "content": "Attention Total Variation Loss. While the cross-attention layer successfully aligns the clothing to the agnostic map, the points with high attention scores appear in dispersed positions, as shown in the attention map of Fig. 4(b). This causes inaccurate details in generated images, such as color discrepancies." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": "To address such an issue, we propose attention total variation loss. As the attention scores are the weight for the output, we calculate the center coordinates as a weighted sum of the attention map and the grid. Therefore, given the " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "H_{q}W_{q}" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": " query tokens and " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "h_k w_k" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": " key tokens, we calculate center coordinate map " + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "inline_equation", + "content": "F \\in \\mathbb{R}^{H_q \\times W_q \\times 2}" + }, + { + "bbox": [ + 304, + 642, + 545, + 712 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8179" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 68, + 547, + 207 + ], + "blocks": [ + { + "bbox": [ + 50, + 68, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 50, + 68, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 50, + 68, + 547, + 207 + ], + "type": "image", + "image_path": "b6ef1068bff360dc5c1412015ff1d0775461730b00458cc4bf9fcc0137081f43.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 131, + 209, + 462, + 221 + ], + "lines": [ + { + "bbox": [ + 131, + 209, + 462, + 221 + ], + "spans": [ + { + "bbox": [ + 131, + 209, + 462, + 221 + ], + "type": "text", + "content": "Figure 4. Visualization of attention map from a zero cross-attention block of 32 resolution." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 86, + 232, + 287, + 265 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 232, + 287, + 265 + ], + "spans": [ + { + "bbox": [ + 86, + 232, + 287, + 265 + ], + "type": "interline_equation", + "content": "F _ {i j n} = \\frac {1}{h _ {k} w _ {k}} \\sum_ {k = 1} ^ {h _ {k}} \\sum_ {l = 1} ^ {w _ {k}} \\left(A _ {i j k l} \\odot G _ {k l n}\\right), \\tag {4}", + "image_path": "d9ff1627648fa8cf45a433946afff03088023f6e0e2488539241cf37ce507403.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "text", + "content": "where we average the attention map over the head dimension and reshape it as " + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "inline_equation", + "content": "A \\in \\mathbb{R}^{H_q \\times W_q \\times h_k \\times w_k}" + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "inline_equation", + "content": "G \\in [-1, 1]^{h_k \\times w_k \\times 2}" + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "text", + "content": " is a 2D normalized coordinate. " + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "inline_equation", + "content": "n \\in \\{0, 1\\}" + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "text", + "content": " in Eq. 4 denotes the dimension of attention map coordinates and " + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 271, + 287, + 331 + ], + "type": "text", + "content": " indicates element-wise multiplication operation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 331, + 287, + 366 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 287, + 366 + ], + "type": "text", + "content": "For each query token in each clothing-agnostic region, the center coordinates should be evenly distributed, and the attention total variation loss " + }, + { + "bbox": [ + 47, + 331, + 287, + 366 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ATV}" + }, + { + "bbox": [ + 47, + 331, + 287, + 366 + ], + "type": "text", + "content": " is defined as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 374, + 287, + 388 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 374, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 112, + 374, + 287, + 388 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {A T V} = \\left\\| \\nabla (F \\odot M) \\right\\| _ {1}, \\tag {5}", + "image_path": "309fce957999fe71bbd918dfac4b9081f2e486d4ce323b5a82e7527a14d9f8d7.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "spans": [ + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "type": "inline_equation", + "content": "M \\in \\{0,1\\}^{H_q \\times W_q}" + }, + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "type": "text", + "content": " is the ground truth clothing mask to only affect the clothing region. The attention total variation loss " + }, + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ATV}" + }, + { + "bbox": [ + 46, + 394, + 287, + 490 + ], + "type": "text", + "content": " is designed to enforce the center coordinates on the attention map uniformly distributed, thereby alleviating interference among attention scores located at dispersed positions. As illustrated in Figure (c), this leads to the generation of a sharper attention map, thereby more accurately reflecting the color of the clothing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 491, + 286, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 286, + 514 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 286, + 514 + ], + "type": "text", + "content": "Finally, we finetune our StableVITON by adding " + }, + { + "bbox": [ + 47, + 491, + 286, + 514 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{ATV}" + }, + { + "bbox": [ + 47, + 491, + 286, + 514 + ], + "type": "text", + "content": " to Eq. 3:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 92, + 520, + 287, + 533 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 92, + 520, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 92, + 520, + 287, + 533 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {f i n e t u n e}} = \\mathcal {L} _ {L D M} + \\lambda_ {A T V} \\mathcal {L} _ {A T V}, \\tag {6}", + "image_path": "8f36cf869c7002eeea6ae154af732e8b5eb0ae2a5def7f996b8bebcc330e87d9.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 540, + 218, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 218, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 218, + 552 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 540, + 218, + 552 + ], + "type": "inline_equation", + "content": "\\lambda_{ATV}" + }, + { + "bbox": [ + 47, + 540, + 218, + 552 + ], + "type": "text", + "content": " is a weight hyper-parameter." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 562, + 123, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 123, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 123, + 574 + ], + "type": "text", + "content": "5. Experiment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 582, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 676 + ], + "type": "text", + "content": "Baselines. We compare StableVITON with three GAN-based virtual try-on methods, VITON-HD [3], HRVITON [15], and GP-VTON [31], and two diffusion-based virtual try-on methods, LADI-VTON [19] and DCIVTON [8]. We also evaluate a diffusion-based inpainting method, Paint-by-Example [32]. We use pre-trained weights if available; otherwise, we train the models following the official code." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 714 + ], + "type": "text", + "content": "Dataset. We conduct the experiments using two publicly available virtual try-on datasets, VITON-HD [3] and DressCode [18], and one human image dataset, SHHQ-1.0 [5]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 233, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 233, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 233, + 545, + 293 + ], + "type": "text", + "content": "We train our model with VITON-HD and upper-body images in DressCode, respectively. For the evaluation of SHHQ-1.0, we use the first 2,032 images and follow the preprocessing instruction of VITON-HD [3] to obtain the input conditions such as the agnostic maps or the dense pose." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "type": "text", + "content": "Evaluation. We evaluate the performances in two test settings. Specifically, the paired setting uses a pair of a person and the original clothes for reconstruction, whereas the unpaired setting involves changing the clothing of a person image with a different clothing item. As previous work [3], training and evaluation within a single dataset are referred to as 'single dataset evaluation'. On the other hand, we extend our evaluation on other datasets (e.g., SHHQ-1.0), which we refer to as a 'cross dataset evaluation'. This evaluation enables an in-depth assessment of the model's generalizability in handling arbitrary person images, demonstrating applicability in real-world scenarios. Our model is capable of training at a " + }, + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "type": "inline_equation", + "content": "1024 \\times 768" + }, + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "type": "text", + "content": " resolution, but for a fair evaluation with baselines, we used a model trained at a " + }, + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "type": "inline_equation", + "content": "512 \\times 384" + }, + { + "bbox": [ + 304, + 293, + 546, + 485 + ], + "type": "text", + "content": " resolution. More results and details about experiments are described in the supplementary material." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 491, + 418, + 504 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 491, + 418, + 504 + ], + "spans": [ + { + "bbox": [ + 306, + 491, + 418, + 504 + ], + "type": "text", + "content": "5.1. Qualitative Results" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 510, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 652 + ], + "type": "text", + "content": "Single Dataset Evaluation. As shown in Fig. 5, StableVITON generates realistic images and effectively preserves the text and clothing textures compared to the six baseline methods. Specifically, in the first row of Fig. 5, GAN-based methods such as GP-VTON struggle to generate the arms of the target person naturally. Moreover, other diffusion-based models either fail to preserve the text (Paint-by-Example and LADI-VTON) or show an overlapped artifact between the clothing and the target person (DCI-VTON). On the other hand, despite some parts of the arm being covered by clothing, our model produces a high-fidelity result that omits the 'L' in 'Love'." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Cross Dataset Evaluation. We visualize the generation images of the models trained on VITON-HD for DressCode and SHHQ-1.0 datasets in Fig. 6 and Fig. 7, respectively. The results clearly demonstrate that StableVITON generates high-fidelity images while preserving the details of the" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8180" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 519, + 230 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 519, + 230 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 519, + 230 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 519, + 230 + ], + "type": "image", + "image_path": "00336f9be79e64d53683de0f80e560792f6a234e0a7f25355c518213bef59315.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 55, + 231, + 537, + 242 + ], + "lines": [ + { + "bbox": [ + 55, + 231, + 537, + 242 + ], + "spans": [ + { + "bbox": [ + 55, + 231, + 537, + 242 + ], + "type": "text", + "content": "Figure 5. Qualitative comparison with baselines in a single dataset setting (VITON-HD / VITON-HD). Best viewed when zoomed in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 72, + 247, + 520, + 407 + ], + "blocks": [ + { + "bbox": [ + 72, + 247, + 520, + 407 + ], + "lines": [ + { + "bbox": [ + 72, + 247, + 520, + 407 + ], + "spans": [ + { + "bbox": [ + 72, + 247, + 520, + 407 + ], + "type": "image", + "image_path": "153f71905918fc1561aa61dc46b91cdc2d29b48f0707f9c7e912ed9254216b85.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 58, + 408, + 533, + 419 + ], + "lines": [ + { + "bbox": [ + 58, + 408, + 533, + 419 + ], + "spans": [ + { + "bbox": [ + 58, + 408, + 533, + 419 + ], + "type": "text", + "content": "Figure 6. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / DressCode). Best viewed when zoomed in." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 149, + 426, + 446, + 517 + ], + "blocks": [ + { + "bbox": [ + 149, + 426, + 446, + 517 + ], + "lines": [ + { + "bbox": [ + 149, + 426, + 446, + 517 + ], + "spans": [ + { + "bbox": [ + 149, + 426, + 446, + 517 + ], + "type": "table", + "html": "
Train / Test MethodVITON-HD / VITON-HDD.C. Upper / D.C. Upper
SSIMLPIPSFIDKIDSSIMLPIPSFIDKID
VITON-HD [3]0.8620.11712.1173.23----
HR-VITON [15]0.8780.104511.2652.730.9360.065213.8202.71
LADI-VTON [19]0.8640.09649.4801.990.9220.062814.173.04
Paint-by-Example [32]0.8020.142811.9393.850.8970.077515.3324.64
DCI-VTON [8]0.8800.08048.7541.100.9370.042111.9201.89
GP-VTON [31]0.8840.08149.0720.880.7690.267920.1108.17
Ours0.8520.08428.6980.880.9110.050011.2660.72
Ours (RePaint [17])0.8880.07328.2330.490.9370.03889.9400.12
", + "image_path": "a150eeb418ed5a7165495b05ec582c5a0c48668be837e3f6cfd7e48611784d67.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 517, + 545, + 539 + ], + "lines": [ + { + "bbox": [ + 46, + 517, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 46, + 517, + 545, + 539 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons in single dataset settings, VITON-HD and DressCode upper-body (D.C. Upper) datasets. Bold and underline denote the best and the second best result, respectively." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 551, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 551, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 551, + 287, + 659 + ], + "type": "text", + "content": "clothing. GAN-based methods especially show significant artifacts on the target person and fail to maintain background. While diffusion-based methods generate natural images, they fail to preserve clothing details or the shape of the clothing. Furthermore, even when applying the augmentation we used to DCI-VTON (denoted as DCI-VTON (Aug.)), as depicted in Fig. 7, a significant improvement in the performance of the warping network is not achieved, failing to preserve clothing details." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 670, + 166, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 166, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 166, + 682 + ], + "type": "text", + "content": "5.2. Quantitative Results" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "Metrics. For quantitative evaluation, we use SSIM [30] and LPIPS [35] in the paired setting. In an unpaired setting," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 551, + 545, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 545, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 545, + 587 + ], + "type": "text", + "content": "we assess the realism using FID [12] and KID [2] score. We follow the evaluation paradigm [19] for the implementation [4, 21]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 546, + 713 + ], + "type": "text", + "content": "Single Dataset Evaluation. We evaluate our StableViTON and existing baselines on a single dataset setting and report the results in Table 1. In the unpaired setting (i.e., FID and KID), StableViTON outperforms all the baselines. We observe that the performance degradation in the paired setting occurs due to the autoencoder's reconstruction error of the agnostic map. To mitigate this issue, we adapt RePaint [17], which samples the known region (i.e., agnostic map) and replaces it in each denoising steps during the inference, used in DCI-VTON. Applying RePaint, Stable-" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "8181" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 520, + 266 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 520, + 266 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 520, + 266 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 520, + 266 + ], + "type": "image", + "image_path": "b795af6fd36ec0ba4121345289a3e9293083f77f3a3db7d931f9b8d762212729.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 59, + 270, + 533, + 281 + ], + "lines": [ + { + "bbox": [ + 59, + 270, + 533, + 281 + ], + "spans": [ + { + "bbox": [ + 59, + 270, + 533, + 281 + ], + "type": "text", + "content": "Figure 7. Qualitative comparison with baselines in a cross dataset setting (VITON-HD / SHHQ-1.0). Best viewed when zoomed in." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 99, + 287, + 494, + 384 + ], + "blocks": [ + { + "bbox": [ + 99, + 287, + 494, + 384 + ], + "lines": [ + { + "bbox": [ + 99, + 287, + 494, + 384 + ], + "spans": [ + { + "bbox": [ + 99, + 287, + 494, + 384 + ], + "type": "table", + "html": "
Train / Test \nMethodVITON-HD / D.C. UpperD.C. Upper / VITON-HDVITON-HD / SHHQ-1.0
SSIMLPIPSFIDKIDSSIMLPIPSFIDKIDFIDKID
VITON-HD [3]0.8530.187444.25728.82----71.14952.01
HR-VITON [15]0.9090.107719.9707.350.8110.227845.92336.6952.73231.22
LADI-VTON [19]0.9010.100916.3365.360.7950.27228.2719.324.9046.07
Paint-by-Example [32]0.8890.086716.3984.780.7840.181415.6257.5226.2749.830
DCI-VTON [8]0.9030.121723.07612.030.8250.187016.6706.4024.8506.68
DCI-VTON (Aug.) [8]0.8980.124018.8098.02----24.3686.11
GP-VTON [31]0.7240.384665.71166.010.8040.262152.35148.68--
Ours0.9110.060312.5811.700.8170.130810.1041.7223.5315.68
Ours (RePaint [17])0.9380.047010.4800.410.8550.11739.7141.3521.0775.10
", + "image_path": "7d9407d384155c5986e63d404205dca4a960d4460b6bd2ee705a5dc83cb241a8.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 387, + 544, + 409 + ], + "lines": [ + { + "bbox": [ + 46, + 387, + 544, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 544, + 409 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons in cross dataset settings. We train the models on VITON-HD and DressCode upper-body (D.C. Upper) datasets and evaluate them on different datasets. Bold and underline denote the best and the second best result, respectively." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 287, + 491 + ], + "type": "text", + "content": "VITON outperforms the baselines for all evaluation metrics. Since RePaint greatly helps maintain regions unrelated to clothing, it shows notable performance improvement in the paired setting. Nevertheless, even without RePaint, our method demonstrates superior performance in terms of FID and KID in the unpaired setting compared to the baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 492, + 287, + 612 + ], + "type": "text", + "content": "Cross Dataset Evaluation. Table 2 presents that our StableVITON shows state-of-the-art performance for all the evaluation metrics with a large margin. GAN-based methods fail to maintain background consistency, resulting in significantly high FID and KID scores. While diffusion-based methods exhibit better performance due to the plausible generation outcomes enabled by pre-trained diffusion models, they fail to preserve clothing details. Consequently, they exhibit lower similarity scores in the paired setting (i.e., SSIM and LPIPS) compared to our method." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 622, + 121, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 622, + 121, + 635 + ], + "spans": [ + { + "bbox": [ + 47, + 622, + 121, + 635 + ], + "type": "text", + "content": "5.3. User Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 713 + ], + "type": "text", + "content": "For the models trained on the VITON-HD dataset, we conducted a user study with 40 participants. Each participant was shown one image generated by the baseline and the other by our model. They were asked to choose the better image based on three criteria: (1) fidelity, (2) person attributes, and (3) clothing identity. We added a question" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 309, + 418, + 545, + 560 + ], + "blocks": [ + { + "bbox": [ + 309, + 418, + 545, + 560 + ], + "lines": [ + { + "bbox": [ + 309, + 418, + 545, + 560 + ], + "spans": [ + { + "bbox": [ + 309, + 418, + 545, + 560 + ], + "type": "image", + "image_path": "2dc606c788efb5f813f4d4fe85867a1558ec6dc23a045196135cdfc6e8b61c3b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 564, + 545, + 586 + ], + "lines": [ + { + "bbox": [ + 305, + 564, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 305, + 564, + 545, + 586 + ], + "type": "text", + "content": "Figure 8. User study results. We compare our StableVITON with six baselines, involving a total of 40 participants." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "about (4) background quality for the cross dataset setting. Detailed questions can be found in the supplementary material. As shown in Fig. 8, StableVITON outperforms in most of the criteria, and especially in the cross dataset setting, our method is overwhelming in human evaluations. While LADI-VTON shows better preference in the evaluation of fidelity and person attributes on the VITON-HD dataset, it fails to preserve clothing details, resulting in a " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "35\\%" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " preference in the clothing identity criteria." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8182" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 70, + 267, + 107 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 267, + 107 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 267, + 107 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 267, + 107 + ], + "type": "table", + "html": "
Train / Test on VITON-HDSSIMLPIPSFIDKID
ControlNet + Aug.0.8320.11579.811.81
ControlNet-W + Aug.0.8220.11249.661.57
Zero Cross-Attention Block + Aug.0.8500.08518.740.91
", + "image_path": "91c44c90a5f4603f28647b5223612b44fe602f0d9c550504a9a23813d0d5cce4.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 84, + 169, + 251, + 219 + ], + "blocks": [ + { + "bbox": [ + 47, + 112, + 287, + 156 + ], + "lines": [ + { + "bbox": [ + 47, + 112, + 287, + 156 + ], + "spans": [ + { + "bbox": [ + 47, + 112, + 287, + 156 + ], + "type": "text", + "content": "Table 3. Quantitative comparison results between our zero cross-attention block and ControlNet. We train ControlNet with clothing and warped clothing [15] (ControlNet-W). We apply augmentation to all the models in training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 84, + 169, + 251, + 219 + ], + "lines": [ + { + "bbox": [ + 84, + 169, + 251, + 219 + ], + "spans": [ + { + "bbox": [ + 84, + 169, + 251, + 219 + ], + "type": "table", + "html": "
Aug.Attention TV LossSSIMLPIPSFIDFID
XX0.8470.09699.351.33
✓X0.8500.08518.7440.91
✓✓0.8520.0428.6980.88
", + "image_path": "de3d8b3b7b8dd2bafe33a390f700e8614c2eda75c75800f729a8f098bb8c8436.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 221, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 47, + 221, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 221, + 287, + 243 + ], + "type": "text", + "content": "Table 4. Ablation study of our proposed training components on VITON-HD dataset." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 265, + 140, + 277 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 265, + 140, + 277 + ], + "spans": [ + { + "bbox": [ + 47, + 265, + 140, + 277 + ], + "type": "text", + "content": "5.4. Ablation Study" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 286, + 289, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 286, + 289, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 286, + 289, + 525 + ], + "type": "text", + "content": "Comparison with ControlNet. To demonstrate the effectiveness of StableVITON in tackling the alignment issue compared to ControlNet [34], we train ControlNet under two different input conditions: (1) clothing, and (2) warped clothing [15] (dubbed as ControlNet-W). We apply our proposed augmentation to both models during training. Using the warping network to align the clothing helps ControlNet capture coarse features, such as the overall shape and color of the logo, as shown in Fig. 9(b) and (c). However, since the misalignment still exists between warped clothing and the human body in the training phase, ControlNet-W struggles to reflect more fine-grained clothing details to the generation results. These observations highlight that ControlNet is highly sensitive to subtle misalignment across the input, stemming from the limitations of the ControlNet's direct addition operation in conditioning. In contrast, as shown in Fig. 9(d), the zero cross-attention block, free from the alignment constraints, successfully preserves the logos and patterns and leads to a qualitative performance improvement, as shown in Table 3." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 533, + 287, + 713 + ], + "type": "text", + "content": "Effect of Training Components. We investigate the effect of the two proposed components during training: augmentation and attention total variation loss. In Fig. 10, we visualize the generated images while incrementally introducing the proposed training components one by one. Compared to Fig 10(a) and (b), we observe that detailed features such as logos and patterns of the clothing are more preserved when augmentation is applied. However, as the attention maps are not sufficiently distinct, we observe inaccuracies in the generated images, such as the 'M' in 'PUMA' being incorrectly depicted or lines blurring, as shown in Fig. 10(b). After finetuning with our proposed attention total variation loss, these finer details are significantly improved. Such visual enhancements correspond to quantitative performance improvements as demonstrated in Table 4." + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 309, + 71, + 545, + 205 + ], + "blocks": [ + { + "bbox": [ + 309, + 71, + 545, + 205 + ], + "lines": [ + { + "bbox": [ + 309, + 71, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 309, + 71, + 545, + 205 + ], + "type": "image", + "image_path": "1a098365e78edee7a2abb9a263691d70c015e6014bfacdb8daccc604b9f5cbc9.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 345, + 206, + 392, + 213 + ], + "lines": [ + { + "bbox": [ + 345, + 206, + 392, + 213 + ], + "spans": [ + { + "bbox": [ + 345, + 206, + 392, + 213 + ], + "type": "text", + "content": "(a) Target Person" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 399, + 206, + 438, + 213 + ], + "lines": [ + { + "bbox": [ + 399, + 206, + 438, + 213 + ], + "spans": [ + { + "bbox": [ + 399, + 206, + 438, + 213 + ], + "type": "text", + "content": "(b) ControlNet" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 444, + 206, + 492, + 213 + ], + "lines": [ + { + "bbox": [ + 444, + 206, + 492, + 213 + ], + "spans": [ + { + "bbox": [ + 444, + 206, + 492, + 213 + ], + "type": "text", + "content": "(c) ControlNet-W" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 509, + 206, + 531, + 213 + ], + "lines": [ + { + "bbox": [ + 509, + 206, + 531, + 213 + ], + "spans": [ + { + "bbox": [ + 509, + 206, + 531, + 213 + ], + "type": "text", + "content": "(d) Ours" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 310, + 252, + 545, + 434 + ], + "blocks": [ + { + "bbox": [ + 306, + 217, + 545, + 249 + ], + "lines": [ + { + "bbox": [ + 306, + 217, + 545, + 249 + ], + "spans": [ + { + "bbox": [ + 306, + 217, + 545, + 249 + ], + "type": "text", + "content": "Figure 9. Comparison our StableVITON to ControlNets under the two different input conditions: (1) clothing, and (2) warped clothing [15] (ControlNet-W). Best viewed when zoomed in." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 310, + 252, + 545, + 434 + ], + "lines": [ + { + "bbox": [ + 310, + 252, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 310, + 252, + 545, + 434 + ], + "type": "image", + "image_path": "99ff958f43611ed13e493971dca37ebf82d02b66fdb086713514bf96a67d5c8f.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 306, + 437, + 545, + 459 + ], + "lines": [ + { + "bbox": [ + 306, + 437, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 545, + 459 + ], + "type": "text", + "content": "Figure 10. Visual comparisons according to our training components. Best viewed when zoomed in." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 466, + 378, + 478 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 378, + 478 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 378, + 478 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 486, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 545, + 617 + ], + "type": "text", + "content": "We propose StableVITON, a novel image-based virtual try-on method using the pre-trained diffusion model. Our proposed zero cross-attention block learns semantic correspondence between the clothing and the human body, enabling try-on in the latent feature space. A novel attention total variation loss and augmentation are designed to preserve the clothing details better. Extensive experiments, including cross dataset evaluation, clearly demonstrate that StableVITON shows the state-of-the-art performance compared to the existing methods and its promising quality in the real-world setting." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements. Sunghyun Park is the corresponding author. This work was supported by the Institute for Information & communications Technology Promotion(IITP) grant funded by the Korea government(MSIT) (No.2019-0-00075, Artificial Intelligence Graduate School Program(KAIST) and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. NRF-2022R1A2B5B02001913)." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8183" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 16, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Shuai Bai, Huiling Zhou, Zhikang Li, Chang Zhou, and Hongxia Yang. 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Springer, 2016. 3" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 48, + 648, + 287, + 712 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 648, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 48, + 648, + 287, + 712 + ], + "type": "text", + "content": "[38] Luyang Zhu, Dawei Yang, Tyler Zhu, Fitsum Reda, William Chan, Chitwan Sahara, Mohammad Norouzi, and Ira Kemelmacher-Shlizerman. Tryondiffusion: A tale of two unets. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4606-4615, 2023. 3" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "8185" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_content_list.json b/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..37d0dfd681a886d1b0504c38df8df4447c7c13cb --- /dev/null +++ b/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_content_list.json @@ -0,0 +1,1567 @@ +[ + { + "type": "text", + "text": "State Space Models for Event Cameras", + "text_level": 1, + "bbox": [ + 287, + 130, + 684, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Nikola Zubić, Mathias Gehrig, Davide Scaramuzza \nRobotics and Perception Group, University of Zurich, Switzerland", + "bbox": [ + 222, + 180, + 746, + 218 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/b26124d083158f6234fcebdce73cd247470ebb0c06a28ed95ec2111a8d1b31de.jpg", + "image_caption": [ + "Figure 1. Top-Left Previous works [12, 29] use RNN architectures with convolutional or attention mechanisms to train models that have superior performance on downstream tasks. However, the use of RNNs leads to slower training and the learned weights only generalize well to data deployed at the same frequency as that used at training time. Bottom-Left We solve this problem by utilizing SSMs for temporal aggregation, which enables faster training by either utilizing the S4 model [16] or S5 [36] parallel scans. By their nature, these models allow deployment at different frequencies than those used at training time since they have a learnable timescale parameter. Right Our SSM-based models achieve an average performance drop between training and testing frequencies of $3.31\\mathrm{mAP}$ averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and $24.53\\mathrm{mAP}$ , respectively." + ], + "image_footnote": [], + "bbox": [ + 76, + 233, + 390, + 486 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/edd855e2bebae16a33dd0e16f441b312398a59212f60d78d85ad08cf4444faa7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 419, + 239, + 890, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 608, + 313, + 625 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Today, state-of-the-art deep neural networks that process event-camera data first convert a temporal window of events into dense, grid-like input representations. As such, they exhibit poor generalizability when deployed at higher inference frequencies (i.e., smaller temporal windows) than the ones they were trained on. We address this challenge by introducing state-space models (SSMs) with learnable timescale parameters to event-based vision. This design adapts to varying frequencies without the need to retrain the network at different frequencies. Additionally, we investigate two strategies to counteract aliasing effects when deploying the model at higher frequencies. We comprehensively evaluate our approach against existing methods based on RNN and Transformer architectures across various benchmarks, including Gen1 and 1 Mpx event camera datasets. Our results demonstrate that SSM-based models train $33\\%$ faster and also exhibit minimal performance degradation when tested at higher frequencies than the", + "bbox": [ + 73, + 628, + 473, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "training input. Traditional RNN and Transformer models exhibit performance drops of more than 20 mAP, with SSMs having a drop of 3.31 mAP, highlighting the effectiveness of SSMs in event-based vision tasks.", + "bbox": [ + 498, + 609, + 895, + 670 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 690, + 632, + 707 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Event cameras emerged as a class of sensor technologies that noticeably deviate from the operational mechanics of conventional frame-based cameras [9]. While standard frame-based cameras [42] capture full-frame luminance levels at fixed intervals, event cameras record per-pixel relative brightness changes in a scene at the time they occur. The output is, therefore, an asynchronous stream of events in a four-dimensional spatio-temporal space. Each event is represented by its spatial coordinates on the pixel array, the temporal instance of the occurrence, and its polarity, which denotes the direction of the brightness change and encapsulates the increase or decrease in luminance. The", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 47 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "5819", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "power of event cameras primarily lies in their ability to capture dynamic scenes with unparalleled temporal resolution (microseconds). This property becomes invaluable in rapidly changing environments or applications requiring very fast response times [8, 39]. However, the richness of the spatio-temporal data they generate introduces complexities in data interpretation and processing. Sophisticated algorithms are required to efficiently parse and make sense of the high-dimensional data space. As such, while event cameras represent a promising frontier in visual sensor technologies, their pervasive utilization depends upon solving these inherent computational challenges.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Current methodologies for addressing problems with event cameras fall predominantly into two categories. The first involves converting the raw stream of spatio-temporal events into dense representations akin to multi-channel images [12, 22, 40, 43]. This transformation allows leveraging conventional computer vision techniques designed for frame-based data. The second category employs sparse computational paradigms, often utilizing spiking neural networks or graph-based architectures [4, 11]. While promising, these methods are not without limitations; they frequently encounter hardware incompatibility issues and compromised accuracy. In this work, we utilize dense representations for their advantages in computational efficiency.", + "bbox": [ + 75, + 273, + 472, + 470 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Despite the advances in both paradigms, models trained on event representations at a specific frequency exhibit poor generalizability when deployed in settings with higher frequencies which is crucial for high-speed, dynamical visual scenarios. Additionally, to achieve high performance, it is necessary to include recurrent memory, thereby sacrificing computational efficiency during the training phase. An ideal model would seamlessly merge the training speed of convolutional architectures with the temporal sensitivity and memory benefits inherent to recurrent models.", + "bbox": [ + 75, + 470, + 472, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While recent advancements have introduced efficient recurrent vision transformer architectures [12, 24] to achieve better performance, they face several limitations. Specifically, these architectures suffer from longer training cycles due to their reliance on conventional recurrent mechanisms.", + "bbox": [ + 75, + 623, + 472, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The issue of slow training and generalization at higher event representation frequency than the lower one we trained on remains unresolved as conventional recurrent training methodologies are predominantly utilized in event-based vision. These methods do not incorporate learnable timescale parameters, thus inhibiting the model's capacity to generalize across varying inference frequencies.", + "bbox": [ + 75, + 700, + 472, + 808 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we address this limitation by introducing structured variations of state-space models [16, 36] as layers within our neural network framework.", + "bbox": [ + 76, + 808, + 472, + 854 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "State-space models [14] function as CNN during training and are converted to an efficient RNN at test time. To achieve this, S4 [16] employs a technique where the SSM,", + "bbox": [ + 76, + 854, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "which is not practical for training on modern hardware due to its sequential nature, is transformed into a CNN by unrolling. S5 [36] uses parallel scans during training, and is employed as RNN during inference. State-space models [14] can be deployed at different frequencies at inference time because they are Linear Time-Invariant (LTI) continuous-time systems that can be transformed into a discrete-time system with an arbitrary step size. This feature permits inference at arbitrary frequencies by globally adjusting the timescale parameter based on the ratio between the new and old frequency sampling rates. Consequently, we tackle the longstanding issue in event-based vision, which requires multiple training cycles with different frequencies to adapt the neural network for various frequencies during inference.", + "bbox": [ + 496, + 90, + 893, + 319 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "For the task of object detection, we find that incorporating state-space layers accelerates the training by up to $33\\%$ relative to existing recurrent vision transformer approaches [12, 24]. This is achieved while maintaining performance comparable to existing methods. Notably, our approach demonstrates superior generalization to higher temporal frequencies with a drop of only $3.31\\mathrm{mAP}$ , while previous methods experience a drop of $21.25\\mathrm{mAP}$ or more. Also, we achieve comparable performance to RVT although we use a linear state-space model rather than a non-linear LSTM model. This also shows that the complexity of the LSTM might not be needed. For this to work, we introduce two strategies (frequency-selective masking and $H_{2}$ norm) to counteract the aliasing effect encountered with increased temporal frequencies in event cameras. First one is a low-pass bandlimiting modification to SSM that encourages the learned convolutional kernels to be smooth. Second one mitigates the aliasing problem by attenuating the frequency response after a chosen frequency. We argue that state-space modeling offers a significant new direction for research in event-based vision, offering promising solutions to the challenges inherent in processing event-based data effectively and efficiently.", + "bbox": [ + 496, + 339, + 893, + 689 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions are concisely outlined as follows:", + "bbox": [ + 519, + 709, + 862, + 724 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce state-space models for event cameras to address two key challenges in event-based vision: (i) model performance degradation when operating event cameras at temporal frequencies different from their training conditions and (ii) training efficiency.", + "- Our experimental results outperform existing methods at higher frequencies by $20\\mathrm{mAP}$ on average and show $33\\%$ increase in the training speed.", + "- We introduce two strategies (bandlimiting & $H_{2}$ norm) designed to alleviate aliasing issues." + ], + "bbox": [ + 500, + 746, + 890, + 897 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "5820", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 89, + 218, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Object detection with Event Cameras", + "text_level": 1, + "bbox": [ + 76, + 114, + 401, + 131 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Approaches in event camera literature, thus in object detection, can be broadly classified into two branches.", + "bbox": [ + 76, + 138, + 468, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The first research branch investigates dense feed-forward methods. Early attempts in this direction relied on a constrained temporal window for generating event representations [3, 17, 19]. The resultant models were deficient in tracking slow-moving or stationary objects, as they failed to incorporate data beyond this limited time-frame. To mitigate these drawbacks, later studies introduced recurrent neural network (RNN) layers [29] into the architecture. The RNN component enhanced the model's capacity for temporal understanding, thereby improving its object detection capabilities. The work of Zubic et al. [43] takes this a step further by optimizing event representations and incorporating cutting-edge swim transformer architecture. Nonetheless, their approach was limited in its ability to re-detect slowly moving objects following extended periods of absence. Subsequent research [12, 24], merged the transformer and RNN architectures, pushing the performance further. However, this significantly increased computational demands during the training phase. Importantly, all methodologies examined to date suffer from an inability to adapt when deployed at variable frequencies.", + "bbox": [ + 75, + 169, + 468, + 487 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The second research branch investigates the use of Graph Neural Networks (GNNs) or Spiking Neural Networks (SNNs). GNNs dynamically construct a spatiotemporal graph where new nodes and edges are instantiated by selectively sub-sampling events and identifying pre-existing nodes that are proximate in the space-time continuum [11, 18, 38]. A pivotal challenge lies in architecting the network such that information can disseminate effectively across extensive regions of the space-time volume. This becomes particularly important when dealing with large objects that exhibit slow relative motion to the camera. Moreover, while aggressive sub-sampling is often necessary to achieve low-latency inference, it introduces the risk of omitting important information from the event stream. On the other hand, SNNs [1, 6, 34] transmit information sparsely within the system. Unlike RNNs, SNNs emit spikes only when a threshold is met, making them hard to optimize due to the non-differentiable spike mechanism. Some solutions [27] bypass the threshold, but this sacrifices sparsity in deeper layers. Overall, SNNs remain a challenging area needing more foundational research for optimized performance.", + "bbox": [ + 75, + 488, + 470, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Continuous-time Models", + "text_level": 1, + "bbox": [ + 76, + 830, + 303, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gu et al. [16] introduced the S4 model as an alternative to CNNs and Transformers for capturing long-range dependencies through LTI systems. This was followed by", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the S4D model [15], designed for easier understanding and implementation, offering similar performance to S4. The S5 model [36] improved efficiency by avoiding frequency domain computations and utilizing time-domain parallel scans. However, these models have not been thoroughly evaluated on complex, high-dimensional visual data with significant temporal resolution.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our study, we empirically show that S4, S4D and S5 models achieve results on-par with state-of-the-art when combined with attention mechanisms on complex data. We also identify and address aliasing issues in these models, proposing two corrective strategies. Our work extends the range and robustness of continuous-time models for complex sequence modeling tasks such as object detection for event cameras.", + "bbox": [ + 496, + 198, + 890, + 316 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 500, + 329, + 591, + 345 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we firstly formalize the operating mechanism of event cameras and provide a notation used for describing state-space models in the preliminaries (Sec. 3.1). Secondly, we describe our approach of incorporating variants of state-space models as layers within our block (Sec. 3.2). This innovative design solves the problems associated with slow training and the variable frequency inference for event cameras.", + "bbox": [ + 496, + 354, + 890, + 474 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 483, + 640, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Event cameras. Event cameras are bio-inspired vision sensors that capture changes in log intensity per pixel asynchronously, rather than capturing entire frames at fixed intervals. Formally, let $I(x,y,t)$ denote the log intensity at pixel coordinates $(x,y)$ and time $t$ . An event $e$ is generated at $(x,y,t)$ whenever the change in log intensity $\\Delta I$ exceeds a certain threshold $C$ :", + "bbox": [ + 496, + 507, + 890, + 612 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta I (x, y, t) = I (x, y, t) - I (x, y, t - \\Delta t) \\geq C \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 621, + 890, + 638 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Each event $e$ is a tuple $(x, y, t, p)$ , where $(x, y)$ are the pixel coordinates, $t$ is the timestamp, and $p = \\{-1, 1\\}$ is the polarity of the event, indicating the direction of the intensity change.", + "bbox": [ + 496, + 645, + 890, + 705 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "State-Space Models (SSMs). Linear State-Space Models (SSMs) form the crucial part of the backbone in our architecture, where we compare S4 [16], S4D [15] and S5 [36] layer variants. Given an input vector $\\mathbf{u}(t) \\in \\mathbb{R}^U$ , a latent state vector $\\mathbf{x}(t) \\in \\mathbb{R}^P$ , and an output vector $\\mathbf{y}(t) \\in \\mathbb{R}^M$ , the governing equations of a continuous-time linear SSM can be mathematically represented as:", + "bbox": [ + 496, + 705, + 890, + 811 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\mathrm {d} \\mathbf {x} (t)}{\\mathrm {d} t} = \\mathbf {A} \\mathbf {x} (t) + \\mathbf {B} \\mathbf {u} (t), \\quad \\mathbf {y} (t) = \\mathbf {C} \\mathbf {x} (t) + \\mathbf {D} \\mathbf {u} (t), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 819, + 890, + 849 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The model is parameterized by a state transition matrix $\\mathbf{A} \\in \\mathbb{R}^{P \\times P}$ , an input matrix $\\mathbf{B} \\in \\mathbb{R}^{P \\times U}$ , an output matrix $\\mathbf{C} \\in \\mathbb{R}^{M \\times P}$ , and a direct transmission matrix $\\mathbf{D} \\in \\mathbb{R}^{M \\times U}$ .", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "5821", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a fixed step size $\\Delta$ , this continuous-time model can be discretized into a linear recurrence using various methods such as Euler, bilinear, or zero-order hold (ZOH):", + "bbox": [ + 76, + 90, + 468, + 135 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {k} = \\overline {{\\mathbf {A}}} \\mathbf {x} _ {k - 1} + \\overline {{\\mathbf {B}}} \\mathbf {u} _ {k}, \\quad \\mathbf {y} _ {k} = \\overline {{\\mathbf {C}}} \\mathbf {x} _ {k} + \\overline {{\\mathbf {D}}} \\mathbf {u} _ {k}, \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 107, + 147, + 468, + 165 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The parameters in the discrete-time model are functions of the continuous-time parameters, defined by the chosen discretization method. Details on SSMs are available in the appendix.", + "bbox": [ + 76, + 176, + 468, + 236 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ac8e807a07578454697f8b983da8958522d23d15c4d4aaf8597162287003a6ec.jpg", + "image_caption": [ + "Figure 2. SSM-ViT block structure" + ], + "image_footnote": [], + "bbox": [ + 81, + 256, + 467, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. SSM-ViT block", + "text_level": 1, + "bbox": [ + 76, + 393, + 230, + 407 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce the SSM-ViT block, a novel block depicted in Figure 2, which showcases the structured flow of the proposed block structure, designed for efficient event-based information processing.", + "bbox": [ + 76, + 417, + 468, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We build a 4-stage hierarchical backbone like in [12] where in each stage we utilize our proposed SSM-ViT block. Events are processed into a tensor representation like in [12] before they are used as input to the first stage. Each stage takes the previous features as input and reuses the SSM state from the last timestep to compute features for the next stage. By saving SSM states, each stage retains temporal information for the whole feature map, while also being able to generalize to different frequencies since we use SSM instead of RNN that is used in [12].", + "bbox": [ + 75, + 478, + 468, + 628 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Regarding the block structure, initially, the input undergoes convolution with a defined kernel of size $k \\times k$ with a stride $s$ . This operation effectively captures the essential spatial features of the input. Following the convolution operation, the structure introduces a 'Block-SA' module. This module is pivotal in implementing self-attention mechanisms, but it does so specifically within local windows. The localized nature of the attention in this block ensures a focus on immediate spatial relations, allowing for a detailed representation of close-proximity features.", + "bbox": [ + 75, + 628, + 468, + 779 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequent to 'Block-SA', the 'Grid-SA' module comes into play. In contrast to the localized approach of the previous block, 'Grid-SA' employs dilated attention, ensuring a global perspective. This module, by considering a broader scope, encapsulates a more comprehensive understanding of the spatial relations and the overall structure of the input.", + "bbox": [ + 75, + 779, + 468, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The final and crucial component of the block structure is the State-Space Model (SSM) block, that is designed to", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "compute both the output and the state in parallel, either by using S4 [16], S4D [15] or S5 [36] model variant. This ensures temporal consistency and a seamless transition of information between consecutive time steps. Efficient computation is crucial since it allows for the faster training than RNN, and timescale parameter on temporal aggregation is important since we can rescale it during inference and deploy at any frequency we want.", + "bbox": [ + 496, + 90, + 890, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Low-pass bandlimiting", + "text_level": 1, + "bbox": [ + 500, + 220, + 712, + 237 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "However, the capability to deploy state space models at resolutions higher than those encountered during training is not without its drawbacks. It gives rise to the well-documented issue of aliasing [32, 33], which occurs when the kernel bandwidth surpasses the Nyquist frequency. We adress this challenge in following two subsections - 3.3.1 & 3.3.2.", + "bbox": [ + 496, + 244, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3.1 Output Masking", + "text_level": 1, + "bbox": [ + 500, + 363, + 669, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In the realm of signal processing, frequency content beyond the Nyquist rate can lead to aliasing, adversely affecting model performance. To address this, we integrate a frequency-selective masking strategy into the training and inference processes. This bandlimiting method has been empirically validated to be crucial for generalizing across different frequencies [32, 33], with ablation studies indicating a decrease in accuracy by as much as $20\\%$ in its absence.", + "bbox": [ + 496, + 387, + 890, + 508 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let the SSM be governed by a matrix $\\mathbf{A}$ , with its diagonal elements $a_{n}$ influencing the temporal evolution of the system states. The kernel's basis function for the $n$ -th state is given by $K_{n}(t) = e^{ta_{n}}B_{n}$ , where the frequency characteristics are primarily dictated by the imaginary part of $a_{n} - \\Im(a_{n})$ and $B_{n}$ represents the $B$ matrix.", + "bbox": [ + 496, + 508, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To modulate the frequency spectrum of the model, we define a hyperparameter $\\alpha$ , which is used for masking of the computed effective frequency $f_{n}$ for each state:", + "bbox": [ + 496, + 599, + 890, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {n} = \\frac {\\Delta t}{r} \\cdot \\frac {| \\Im (a _ {n}) |}{2 \\pi}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 655, + 890, + 685 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Delta t$ denotes the discrete time-step, and $r$ is the rate at which we train the model, by default it is 1, rate gets halved when deploying at twice the trained frequency etc.", + "bbox": [ + 496, + 695, + 890, + 739 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The bandlimiting mask is then applied as follows:", + "bbox": [ + 517, + 739, + 848, + 755 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nC _ {n} = \\left\\{ \\begin{array}{l l} C _ {n} & \\text {i f} f _ {n} \\leq \\frac {\\alpha}{2}, \\\\ 0 & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 766, + 890, + 799 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $C_n$ represents the coefficients in the state representation. The selection of $\\alpha$ is critical, with $\\alpha = 1.0$ representing the Nyquist limit under idealized conditions. However, practical considerations and model constraints typically necessitate a lower empirical threshold. Our findings suggest that setting $\\alpha = 0.5$ yields optimal outcomes for systems", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "5822", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with diagonal state matrices, such as in S4D and S5 configurations.", + "bbox": [ + 76, + 90, + 467, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This frequency-selective masking is proven to be a cornerstone for the adaptability of our SSMs, significantly contributing to their generalization across differing frequencies.", + "bbox": [ + 76, + 121, + 467, + 167 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3.2 $\\mathbf{H}_2$ Norm", + "text_level": 1, + "bbox": [ + 76, + 184, + 194, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section introduces another strategy to mitigate the aliasing problem by suppressing the frequency response of the continuous-time state-space model beyond a selected frequency $\\omega_{\\mathrm{min}}$ .", + "bbox": [ + 76, + 208, + 467, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This approach makes use of the $H_{2}$ norm of a continuous-time linear system which measures the power (or steady-state covariance) of the output response to unit white-noise input.", + "bbox": [ + 76, + 268, + 467, + 328 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given a continuous-time system described by matrices $\\mathbf{A}$ , $\\mathbf{B}$ , and $\\mathbf{C}$ , the transfer function $\\mathbf{G}(s)$ from the Laplace transform can be defined in the frequency domain as:", + "bbox": [ + 76, + 329, + 467, + 375 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {G} (j \\omega) = \\mathbf {C} (j \\omega \\mathbf {I} - \\mathbf {A}) ^ {- 1} \\mathbf {B}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 387, + 467, + 405 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\omega$ denotes the frequency, and $\\mathbf{I}$ is the identity matrix. The $H_{2}$ norm is computed as the integral of the squared magnitude of the frequency response over the range of interest, typically the entire frequency spectrum. However, in our case, we would like to suppress the frequency response of the system to frequencies beyond $\\omega_{\\mathrm{min}}$ which can be done by minimizing the following:", + "bbox": [ + 75, + 410, + 467, + 515 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| \\mathbf {G} \\right\\| _ {H _ {2} \\left(\\omega_ {\\min }, \\infty\\right)} = \\sqrt {\\frac {1}{\\pi} \\int_ {\\omega_ {\\min }} ^ {\\infty} \\left\\| \\mathbf {G} \\left(j \\omega_ {k}\\right) \\right\\| _ {F} ^ {2} d \\omega}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 535, + 467, + 575 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "as part of the loss function, where $\\| \\cdot \\| _F$ is the Frobenius norm. In practice, to numerically estimate this integral, we choose a maximum frequency $\\omega_{\\mathrm{max}}$ and discretize the frequency range $[\\omega_{\\mathrm{min}},\\omega_{\\mathrm{max}}]$ into $N$ points and apply numerical integration methods to the squared Frobenius norm of $\\mathbf{G}(j\\omega)$ . This yields an approximate $H_{2}$ norm of the system in the desired frequency range.", + "bbox": [ + 75, + 584, + 467, + 690 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 696, + 207, + 713 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We perform ablation studies and systematic evaluations of our proposed models utilizing both the Gen1 [7] and 1 Mpx [29] event-based camera datasets. We assess the model's proficiency in adapting to unseen inference frequencies during training time on both datasets. We employed two variants for training across both datasets: the base model ViT-SSM-B, alongside its scaled-down derivative ViT-SSM-S (small). Additionally, to study the robustness and generalization capabilities of our architecture, we subject it to empirical testing on the DSEC dataset [13], which was not part of the original training corpus and the visual results are provided in the appendix.", + "bbox": [ + 75, + 722, + 467, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 500, + 90, + 581, + 106 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. Our models are trained using 32-bit precision arithmetic across 400k iterations, making use of the ADAM optimizer [20] and a OneCycle learning rate schedule [37] that decays linearly from its highest value. We adopt a mixed batching technique that applies standard Backpropagation Through Time (BPTT) to half of the batch samples and Truncated BPTT (TBPTT) to the other half. This technique was introduced in the RVT [12] and ablated in their supplementary material. We found it to be equally effective also for SSMs. For the S4(D) method, details can be found in [15, 16]. As for S5 [36], we utilize an efficient implementation from scratch in PyTorch; original public version of S5 is available in JAX. Data augmentation is carried out through random horizontal flips and zooming operations, both inward and outward. Event representations are formed based on $50~\\mathrm{ms}$ time windows that correspond to $20\\mathrm{Hz}$ sampling frequency, divided into $\\mathrm{T} = 10$ discrete bins. We incorporate a YOLOX detection head [10] that integrates IOU, class, and regression losses, averaged across both batch and sequence lengths during each optimization phase. Bandlimiting is implemented during training and inference of the SSM model by masking the output matrix $\\mathbf{C}$ as explained in 3.3.1. In case of $H_{2}$ norm, we add it as term to the loss function of the model. We conduct training on the GEN1 dataset using A100 GPU, employing a batch size of 8 and a sequence length of 21. We use a global learning rate of 2e-4, which is propagated to the SSM components. For the 1 Mpx dataset, we train with a batch size of 12 and a sequence length of 10, using a learning rate of 3.5e-4 across two A100 GPUs.", + "bbox": [ + 496, + 113, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Datasets. The Gen1 Automotive Detection dataset [7] comprises 39 hours of event camera footage with a resolution of $304 \\times 240$ pixels. It includes 228k bounding boxes for cars and 28k for pedestrians. Using original evaluation criteria [7], we discard bounding boxes having a side length shorter than 10 pixels or a diagonal less than 30 pixels.", + "bbox": [ + 496, + 566, + 890, + 656 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The 1 Mpx dataset [29] similarly focuses on driving environments but offers recordings at a higher resolution of $720 \\times 1280$ pixels, captured over multiple months during both day-time and night-time. It contains roughly 15 hours of event data and accumulates around 25 million bounding box labels, spread across three classes: cars, pedestrians, and two-wheelers. Following original evaluation criteria, we eliminate bounding boxes with a side length under 20 pixels and a diagonal less than 60 pixels, while also reducing the input resolution to $640 \\times 360$ pixels.", + "bbox": [ + 496, + 657, + 890, + 808 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Benchmark comparisons", + "text_level": 1, + "bbox": [ + 500, + 816, + 725, + 832 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present a detailed comparison of our proposed methods, S4D-ViT-B and S5-ViT-B, with the SotA approaches in the domain of event-based vision for object detection, which can be seen in Table 1. The evalua", + "bbox": [ + 496, + 840, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "5823", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/39646e48a601e53a94100fb4bbf3b2c70a90d1573349b9647f04e7a5cf2571d0.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
Asynet [27]Sparse CNNYOLOv1 [31]14.5---11.4
AEGNN [35]GNNYOLOv116.3---20.0
Spiking DenseNet [5]SNNSSD [23]18.9---8.2
Inception + SSD [17]CNNSSD30.119.434.045.2>60*
RRC-Events [3]CNNYOLOv3 [30]30.721.534.346.4>100*
MatrixLSTM [2]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [19]CNNYOLOv331.222.334.649.4>60*
RED [29]CNN + RNNSSD40.016.743.039.324.1
ERGO-12 [43]TransformerYOLOv6 [21]50.469.940.6100.059.6
RVT-B [12]Transformer + RNNYOLOX [10]47.210.247.411.918.5
Swin-T v2 [25]Transformer + RNNYOLOX45.526.646.434.521.1
Nested-T [28, 41]Transformer + RNNYOLOX46.325.946.033.522.2
GET-T [28]Transformer + RNNYOLOX47.916.848.418.221.9
S4D-ViT-B (ours)Transformer + SSMYOLOX46.29.4046.810.916.5
S5-ViT-B (ours)Transformer + SSMYOLOX47.48.1647.29.5718.2
", + "bbox": [ + 83, + 88, + 883, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion is conducted on two distinct datasets: Gen1 and 1 Mpx, to assess the performance and robustness of these methods under varying conditions.", + "bbox": [ + 75, + 467, + 468, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The comparative analysis, as summarized in Table 1, encompasses different backbones and detection heads. These include Sparse CNNs, GNNs, SNNs, RNNs, and various implementations of Transformers.", + "bbox": [ + 75, + 515, + 468, + 575 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our S4D-ViT-B and S5-ViT-B models, which integrate SSMs with Attention (3.2), demonstrate competitive performance across both datasets. Specifically, on the 1 Mpx dataset, our models achieve mAP scores of 46.8 and 47.2, respectively, which are competitive with the leading scores in this benchmark. While our models do not outperform the top-performing ERGO-12 [43] and GET-T [28] in terms of mAP, they exhibit a notable balance between accuracy and model complexity, as indicated by their parameter counts of 16.5M and 17.5M, respectively.", + "bbox": [ + 75, + 577, + 468, + 729 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Notably, our models perform consistently well across different frequencies as it can be seen in Table 2, highlighting their robustness and generalizability in comparison to RVT and GET-T, which tend to exhibit large performance drops. We achieve an average performance drop between training and testing frequencies of $3.31\\mathrm{mAP}$ averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and $24.53\\mathrm{mAP}$ , respectively.", + "bbox": [ + 75, + 731, + 468, + 853 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In summary, our proposed S4D-ViT-B and S5-ViT-B models establish themselves as effective and efficient contenders in the field of event-based vision for object detec", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "tion. Their competitive performance metrics, coupled with their generalization capabilities across various inference frequencies, make them valuable contributions to event-based vision community.", + "bbox": [ + 496, + 467, + 890, + 527 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b556197dd6618e3f06602b99b5862f5f9bd8fc5ffc4f5948ee37ee863f15f805.jpg", + "table_caption": [ + "Table 1. Comparisons on test sets of Gen1 and 1 Mpx datasets (20 Hz). Best results in bold and second best underlined. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for SSM-ViT to compare against indicated timings in prior work [29] on comparable GPUs (Titan Xp). Ours achieves comparable results with other SotA approaches and generalizes well to other frequencies where others fail." + ], + "table_footnote": [], + "table_body": "
ModelDatasetFrequency Evaluation (Hz)Perf. Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVTGen147.1635.1321.9818.618.3526.14
1Mpx47.4042.5133.2030.2918.1516.36
S5Gen147.4046.4445.0842.4939.843.94
1Mpx47.2046.4946.1145.8039.702.68
GETGen147.9034.1519.9715.135.3529.25
1Mpx48.4040.5130.3028.1115.4419.81
", + "bbox": [ + 503, + 539, + 890, + 642 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 2. Evaluation of RVT [12], S5 [36], and GET [28] across different frequencies on test datasets", + "bbox": [ + 496, + 651, + 890, + 679 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Ablation study", + "text_level": 1, + "bbox": [ + 500, + 683, + 650, + 699 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section we investigate different SSMs and their initializations with and without bandlimiting parameter for event-based vision to address the problem of inference at different frequencies (4.3.1). After that, we study the importance of SSM layers in various stages during training of the model (4.3.2). Finally, we evaluate models on differing frequencies with two proposed strategies (4.3.3).", + "bbox": [ + 496, + 705, + 890, + 811 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3.1 SSMs: initializations & bandlimiting", + "text_level": 1, + "bbox": [ + 498, + 816, + 810, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "This section presents an ablation study focusing on the performance impact of various SSM variants and their initialization strategies in conjunction with the bandlimiting parameter $\\alpha$ . The SSM variants under consideration are S4", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "5824", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/246b6b269726701210b448ecf005ec10657abdcb289be44664379223c2257a1a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelMean Average Precision - mAP val
α = 0α = 0.5α = 1Average
S4-legS46.66--46.66
S4D-legS46.9347.3346.5046.92
S4D-inv46.1546.2346.1146.16
S4D-lin44.8246.0245.0445.29
S5-legS48.3348.4848.0048.27
S5-inv47.2647.4346.9847.22
S5-lin46.1246.4045.5946.04
", + "bbox": [ + 98, + 88, + 450, + 229 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "[16], S4D [15], and the more recent S5 [36]. The analysis is conducted on the Gen1 [7] validation dataset, with the mean Average Precision (mAP) serving as the performance metric. Table 3 provides a comprehensive view of how different initialization strategies (legS, inv, lin) introduced in [15] and values of $\\alpha \\in \\{0,0.5,1\\}$ influence model performance. The S4-legS model, not equipped for bandlimiting in non-diagonal matrix scenarios, achieves a baseline mAP of 46.66 at $\\alpha = 0$ . The S4D variants demonstrate a diverse performance spectrum. The S4D-legS variant, particularly at $\\alpha = 0.5$ , achieves the highest mAP of 47.33 among the S4D models, also maintaining the best average mAP of 46.92. The S4D-inv and S4D-lin variants show less favorable outcomes, with mAPs peaking at 46.23 and 46.02, respectively, for $\\alpha = 0.5$ .", + "bbox": [ + 75, + 310, + 467, + 536 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, the S5 model variants exhibit an improvement over their predecessors. The S5-legS variant achieves the highest mAP of 48.48 at $\\alpha = 0.5$ , and also records the best average mAP of 48.27. This result is not only the best in its category but also the best overall. The S5-inv and S5-ln models also demonstrate comparable performance, with the former reaching its peak mAP of 47.43 at $\\alpha = 0.5$ .", + "bbox": [ + 75, + 537, + 467, + 643 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "This study emphasizes the critical role of initialization strategies and bandlimiting in optimizing SSM-based neural networks for event-based vision tasks. The distinct performance variations across different models and configurations underscore the importance of selecting appropriate initializations and $\\alpha$ values, as these choices impact the efficacy of the models in handling the dynamic and complex nature of event-based vision data. Higher values of parameter $\\alpha$ encourage SSM to learn smoother kernels and discard more complex and higher-frequency convolution kernels.", + "bbox": [ + 75, + 645, + 467, + 795 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.2 SSM Utilization Analysis", + "text_level": 1, + "bbox": [ + 76, + 814, + 303, + 829 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this ablation study, we examine the impact of employing temporal recurrence exclusively in a subset of network stages, or not using it at all. Our methodology involves manipulating the SSMs within the network by resetting their", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "states at predetermined stages during each timestep. This approach enables us to isolate and evaluate the impact of SSM layers' presence or absence while maintaining a consistent parameter count across different model configurations.", + "bbox": [ + 498, + 90, + 890, + 165 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/e3471fa7215e4af192415cc920e892919caf14dc5171ec09fd50f277c0cfae7b.jpg", + "table_caption": [ + "Table 3. Performance comparison between the S4 [16], S4D [15] and S5 [36] models for different values of $\\alpha$ and initializations on Gen1 [7] validation dataset." + ], + "table_footnote": [], + "table_body": "
S1S2S3S4mAPRVTmAPS4D5mAPS5
33.9039.9943.67
✓41.6843.1146.10
✓✓46.1045.3347.52
✓✓✓48.8247.0248.41
✓✓✓✓49.5247.3348.48
", + "bbox": [ + 501, + 176, + 890, + 272 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. SSM contribution in various stages on the Gen1 dataset.", + "bbox": [ + 501, + 282, + 887, + 296 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4 shows the outcomes of these manipulations on the Gen1 validation dataset. $S4D_{.5}$ represents S4D model, and $S5_{.5}$ is S5 model with $\\alpha = 0.5$ . The data clearly indicate that the complete removal of SSMs from the network leads to a highest decrease in detection performance. This underscores the pivotal role of SSMs in enhancing the model's capability. On the other hand, initiating the use of SSMs from the fourth stage onwards consistently enhances performance, suggesting a critical threshold for the impact of temporal information processing in the later stages of the network. Another intriguing observation is the performance boost obtained by incorporating an SSM at the very initial stage. This suggests that the early integration of temporal information is also beneficial for the overall detection performance. As a result of these findings, our preferred configuration includes the SSM component right from the initial stage, thereby leveraging the advantages of temporal information processing throughout the entire network. Noteworthy is the observation that the performance drop when employing SSMs is less pronounced than with RVT, suggesting our approach's superior robustness to temporal aggregation from certain stages compared to RVT.", + "bbox": [ + 496, + 316, + 890, + 648 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3.3 Evaluation at different frequencies", + "text_level": 1, + "bbox": [ + 500, + 657, + 795, + 672 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, we delve into the comparative performance analysis of three models: RVT [12], S4D [15], and S5 [36], across various frequency ranges. This evaluation is crucial in determining the robustness and adaptability of these models under diverse inference frequencies, specifically at $20\\mathrm{Hz}$ , $40\\mathrm{Hz}$ , $80\\mathrm{Hz}$ , $100\\mathrm{Hz}$ , and $200\\mathrm{Hz}$ . Our model is trained with event representations formed based on $50\\mathrm{ms}$ time windows that correspond to $20\\mathrm{Hz}$ sampling frequency. Evaluation is done at this frequency, and others above mentioned. With RVT, there are no changes when evaluating at different frequencies, while with SSMs rate $r$ is halved for the double the inference frequency etc.", + "bbox": [ + 496, + 674, + 890, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Each model in Table 5 is assessed across datasets and model sizes, including Gen1 $\\text{Base}$ , Gen1 $\\text{Small}$ , and 1 $\\text{Mpx}$ $\\text{Base}$ . Base and Small represent two variants of mod", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "5825", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f6c97f1d689a3479fe21d0acdc7a8b7e6b0e1d3480c1e4140c82e7bd4c1d0c61.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ModelDataset/SizeStrategyFrequency Evaluation (Hz)Performance Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVT [12]Gen1Base-49.5237.1623.2519.367.8327.62
Gen1Small-48.6835.2819.9516.055.7529.42
1MpxBase-45.9540.9331.7029.0018.1616.00
S4D [15]Gen1BaseH2norm46.8345.9843.9140.1036.115.31
α = 0.547.3346.3644.5140.0235.985.61
Gen1SmallH2norm45.8845.1141.0538.0034.056.33
α = 0.546.3045.2142.1138.6133.006.57
1MpxBaseH2norm46.6645.8543.3341.8037.014.66
α = 0.547.9346.7844.5641.1136.185.77
S5 [36]Gen1BaseH2norm48.6047.1146.0643.8040.514.23
α = 0.548.4847.3446.1143.2340.034.30
Gen1SmallH2norm47.3346.3244.0341.1238.984.72
α = 0.547.8346.5844.4641.1138.955.06
1MpxBaseH2norm48.6547.5347.1146.6340.913.11
α = 0.548.3547.6047.2146.5040.802.82
", + "bbox": [ + 125, + 87, + 843, + 349 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. Evaluation of RVT, S4D, and S5 across different frequencies on validation datasets", + "bbox": [ + 210, + 359, + 754, + 376 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "els on the Gen1 and 1 Mpx datasets, the base one being the larger one with 16.5M parameters for the S4D model and 18.2M parameters for the S5 model (as presented in Table 1 parameters' column), and small one with 8.8M parameters for S4D and 9.7M parameters for S5 model. The focal point of this analysis is the performance drop, calculated as the average difference between the original performance at $20\\mathrm{Hz}$ and performances at higher frequencies. A notable aspect of this study is the inherent advantage of the S4D and S5 models due to their incorporation of a learnable timescale parameter. This significantly enhances their adaptability, allowing them to dynamically adjust to varying frequencies. This feature is particularly salient in the S4D and S5 models, which are further analyzed based on different operational strategies: the $H_{2}$ norm and bandlimiting with $\\alpha = 0.5$ . The inclusion of the learnable timescale parameter in these models underscores their capability to maintain performance across a wide range of frequencies.", + "bbox": [ + 75, + 401, + 468, + 674 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The analysis reveals that both the $H_{2}$ norm and bandlimiting strategies with $\\alpha = 0.5$ offer comparable performance across the assessed frequency ranges. However, a slight edge is observed with the $H_{2}$ norm, particularly at very high frequencies. This marginal superiority can be attributed to the fact that $H_{2}$ norm approach does not explicitly mask output's $(C)$ matrix columns.", + "bbox": [ + 75, + 675, + 468, + 781 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In the Appendix, we study pure-SSM and SSM models in combination with ConvNext [26].", + "bbox": [ + 76, + 782, + 468, + 813 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 827, + 194, + 843 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we presented a novel approach for enhancing the adaptability and training efficiency of models designed for event-based vision, particularly in object detec", + "bbox": [ + 76, + 854, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion tasks. Our methodology leverages the integration of SSMs with a Vision Transformer (ViT) architecture, creating a hybrid SSM-ViT model. This integration not only addresses the long-standing challenge of performance degradation at varying temporal frequencies but also significantly accelerates the training process.", + "bbox": [ + 496, + 401, + 890, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The key innovation of our work lies in the use of learnable timescale parameters within the SSMs, enabling the model to adapt dynamically to different inference frequencies without necessitating multiple training cycles. This feature represents a substantial advancement over existing methods, which require retraining for different frequencies.", + "bbox": [ + 496, + 500, + 890, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The SSM-ViT model outperforms existing methods by $20\\mathrm{mAP}$ at higher frequencies and exhibits a $33\\%$ increase in training speed. Furthermore, our introduction of two novel strategies to counteract the aliasing effect (a crucial consideration in high-frequency deployment) further reinforces the model's suitability for real-world applications. These strategies, involving frequency-selective masking and $H_{2}$ norm adjustments, effectively mitigate the adverse effects of aliasing, ensuring the model's reliability across a spectrum of temporal resolutions. We believe that our approach opens new avenues for research and application in high-speed, dynamic visual environments, setting a new benchmark in the domain of event-based vision.", + "bbox": [ + 496, + 598, + 890, + 794 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgment", + "text_level": 1, + "bbox": [ + 500, + 830, + 669, + 848 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT).", + "bbox": [ + 500, + 854, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "5826", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Julian Büchel, Gregor Lenz, Yalun Hu, Sadique Sheik, and Martino Sorbaro. Adversarial attacks on spiking convolutional neural networks for event-based vision. Front. Neurosci., 16, 2022. 3", + "[2] Marco Cannici, Marco Ciccone, Andrea Romanoni, and Matteo Matteucci. Asynchronous convolutional networks for object detection in neuromorphic cameras. 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In ICCV, pages 12846-12856, 2023. 2, 3, 6" + ], + "bbox": [ + 78, + 90, + 467, + 672 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "5828", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_model.json b/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2ed741575f3e11793305531b6b83aae1e058c15c --- /dev/null +++ b/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_model.json @@ -0,0 +1,2035 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.048 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.288, + 0.131, + 0.685, + 0.154 + ], + "angle": 0, + "content": "State Space Models for Event Cameras" + }, + { + "type": "text", + "bbox": [ + 0.223, + 0.181, + 0.748, + 0.219 + ], + "angle": 0, + "content": "Nikola Zubić, Mathias Gehrig, Davide Scaramuzza \nRobotics and Perception Group, University of Zurich, Switzerland" + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.234, + 0.391, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.42, + 0.24, + 0.891, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.498, + 0.896, + 0.598 + ], + "angle": 0, + "content": "Figure 1. Top-Left Previous works [12, 29] use RNN architectures with convolutional or attention mechanisms to train models that have superior performance on downstream tasks. However, the use of RNNs leads to slower training and the learned weights only generalize well to data deployed at the same frequency as that used at training time. Bottom-Left We solve this problem by utilizing SSMs for temporal aggregation, which enables faster training by either utilizing the S4 model [16] or S5 [36] parallel scans. By their nature, these models allow deployment at different frequencies than those used at training time since they have a learnable timescale parameter. Right Our SSM-based models achieve an average performance drop between training and testing frequencies of \\(3.31\\mathrm{mAP}\\) averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and \\(24.53\\mathrm{mAP}\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.609, + 0.314, + 0.625 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.629, + 0.474, + 0.903 + ], + "angle": 0, + "content": "Today, state-of-the-art deep neural networks that process event-camera data first convert a temporal window of events into dense, grid-like input representations. As such, they exhibit poor generalizability when deployed at higher inference frequencies (i.e., smaller temporal windows) than the ones they were trained on. We address this challenge by introducing state-space models (SSMs) with learnable timescale parameters to event-based vision. This design adapts to varying frequencies without the need to retrain the network at different frequencies. Additionally, we investigate two strategies to counteract aliasing effects when deploying the model at higher frequencies. We comprehensively evaluate our approach against existing methods based on RNN and Transformer architectures across various benchmarks, including Gen1 and 1 Mpx event camera datasets. Our results demonstrate that SSM-based models train \\(33\\%\\) faster and also exhibit minimal performance degradation when tested at higher frequencies than the" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.61, + 0.896, + 0.671 + ], + "angle": 0, + "content": "training input. Traditional RNN and Transformer models exhibit performance drops of more than 20 mAP, with SSMs having a drop of 3.31 mAP, highlighting the effectiveness of SSMs in event-based vision tasks." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.691, + 0.633, + 0.708 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Event cameras emerged as a class of sensor technologies that noticeably deviate from the operational mechanics of conventional frame-based cameras [9]. While standard frame-based cameras [42] capture full-frame luminance levels at fixed intervals, event cameras record per-pixel relative brightness changes in a scene at the time they occur. The output is, therefore, an asynchronous stream of events in a four-dimensional spatio-temporal space. Each event is represented by its spatial coordinates on the pixel array, the temporal instance of the occurrence, and its polarity, which denotes the direction of the brightness change and encapsulates the increase or decrease in luminance. The" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5819" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "power of event cameras primarily lies in their ability to capture dynamic scenes with unparalleled temporal resolution (microseconds). This property becomes invaluable in rapidly changing environments or applications requiring very fast response times [8, 39]. However, the richness of the spatio-temporal data they generate introduces complexities in data interpretation and processing. Sophisticated algorithms are required to efficiently parse and make sense of the high-dimensional data space. As such, while event cameras represent a promising frontier in visual sensor technologies, their pervasive utilization depends upon solving these inherent computational challenges." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.274, + 0.473, + 0.472 + ], + "angle": 0, + "content": "Current methodologies for addressing problems with event cameras fall predominantly into two categories. The first involves converting the raw stream of spatio-temporal events into dense representations akin to multi-channel images [12, 22, 40, 43]. This transformation allows leveraging conventional computer vision techniques designed for frame-based data. The second category employs sparse computational paradigms, often utilizing spiking neural networks or graph-based architectures [4, 11]. While promising, these methods are not without limitations; they frequently encounter hardware incompatibility issues and compromised accuracy. In this work, we utilize dense representations for their advantages in computational efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.473, + 0.625 + ], + "angle": 0, + "content": "Despite the advances in both paradigms, models trained on event representations at a specific frequency exhibit poor generalizability when deployed in settings with higher frequencies which is crucial for high-speed, dynamical visual scenarios. Additionally, to achieve high performance, it is necessary to include recurrent memory, thereby sacrificing computational efficiency during the training phase. An ideal model would seamlessly merge the training speed of convolutional architectures with the temporal sensitivity and memory benefits inherent to recurrent models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.624, + 0.473, + 0.701 + ], + "angle": 0, + "content": "While recent advancements have introduced efficient recurrent vision transformer architectures [12, 24] to achieve better performance, they face several limitations. Specifically, these architectures suffer from longer training cycles due to their reliance on conventional recurrent mechanisms." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.473, + 0.809 + ], + "angle": 0, + "content": "The issue of slow training and generalization at higher event representation frequency than the lower one we trained on remains unresolved as conventional recurrent training methodologies are predominantly utilized in event-based vision. These methods do not incorporate learnable timescale parameters, thus inhibiting the model's capacity to generalize across varying inference frequencies." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.809, + 0.473, + 0.855 + ], + "angle": 0, + "content": "In this work, we address this limitation by introducing structured variations of state-space models [16, 36] as layers within our neural network framework." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "State-space models [14] function as CNN during training and are converted to an efficient RNN at test time. To achieve this, S4 [16] employs a technique where the SSM," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.32 + ], + "angle": 0, + "content": "which is not practical for training on modern hardware due to its sequential nature, is transformed into a CNN by unrolling. S5 [36] uses parallel scans during training, and is employed as RNN during inference. State-space models [14] can be deployed at different frequencies at inference time because they are Linear Time-Invariant (LTI) continuous-time systems that can be transformed into a discrete-time system with an arbitrary step size. This feature permits inference at arbitrary frequencies by globally adjusting the timescale parameter based on the ratio between the new and old frequency sampling rates. Consequently, we tackle the longstanding issue in event-based vision, which requires multiple training cycles with different frequencies to adapt the neural network for various frequencies during inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.34, + 0.895, + 0.69 + ], + "angle": 0, + "content": "For the task of object detection, we find that incorporating state-space layers accelerates the training by up to \\(33\\%\\) relative to existing recurrent vision transformer approaches [12, 24]. This is achieved while maintaining performance comparable to existing methods. Notably, our approach demonstrates superior generalization to higher temporal frequencies with a drop of only \\(3.31\\mathrm{mAP}\\), while previous methods experience a drop of \\(21.25\\mathrm{mAP}\\) or more. Also, we achieve comparable performance to RVT although we use a linear state-space model rather than a non-linear LSTM model. This also shows that the complexity of the LSTM might not be needed. For this to work, we introduce two strategies (frequency-selective masking and \\(H_{2}\\) norm) to counteract the aliasing effect encountered with increased temporal frequencies in event cameras. First one is a low-pass bandlimiting modification to SSM that encourages the learned convolutional kernels to be smooth. Second one mitigates the aliasing problem by attenuating the frequency response after a chosen frequency. We argue that state-space modeling offers a significant new direction for research in event-based vision, offering promising solutions to the challenges inherent in processing event-based data effectively and efficiently." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.71, + 0.864, + 0.726 + ], + "angle": 0, + "content": "Our contributions are concisely outlined as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.747, + 0.892, + 0.822 + ], + "angle": 0, + "content": "- We introduce state-space models for event cameras to address two key challenges in event-based vision: (i) model performance degradation when operating event cameras at temporal frequencies different from their training conditions and (ii) training efficiency." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.823, + 0.892, + 0.868 + ], + "angle": 0, + "content": "- Our experimental results outperform existing methods at higher frequencies by \\(20\\mathrm{mAP}\\) on average and show \\(33\\%\\) increase in the training speed." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.868, + 0.892, + 0.898 + ], + "angle": 0, + "content": "- We introduce two strategies (bandlimiting & \\( H_{2} \\) norm) designed to alleviate aliasing issues." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.747, + 0.892, + 0.898 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "5820" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.09, + 0.22, + 0.106 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.115, + 0.403, + 0.132 + ], + "angle": 0, + "content": "2.1. Object detection with Event Cameras" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.14, + 0.47, + 0.169 + ], + "angle": 0, + "content": "Approaches in event camera literature, thus in object detection, can be broadly classified into two branches." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.17, + 0.47, + 0.488 + ], + "angle": 0, + "content": "The first research branch investigates dense feed-forward methods. Early attempts in this direction relied on a constrained temporal window for generating event representations [3, 17, 19]. The resultant models were deficient in tracking slow-moving or stationary objects, as they failed to incorporate data beyond this limited time-frame. To mitigate these drawbacks, later studies introduced recurrent neural network (RNN) layers [29] into the architecture. The RNN component enhanced the model's capacity for temporal understanding, thereby improving its object detection capabilities. The work of Zubic et al. [43] takes this a step further by optimizing event representations and incorporating cutting-edge swim transformer architecture. Nonetheless, their approach was limited in its ability to re-detect slowly moving objects following extended periods of absence. Subsequent research [12, 24], merged the transformer and RNN architectures, pushing the performance further. However, this significantly increased computational demands during the training phase. Importantly, all methodologies examined to date suffer from an inability to adapt when deployed at variable frequencies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.489, + 0.471, + 0.82 + ], + "angle": 0, + "content": "The second research branch investigates the use of Graph Neural Networks (GNNs) or Spiking Neural Networks (SNNs). GNNs dynamically construct a spatiotemporal graph where new nodes and edges are instantiated by selectively sub-sampling events and identifying pre-existing nodes that are proximate in the space-time continuum [11, 18, 38]. A pivotal challenge lies in architecting the network such that information can disseminate effectively across extensive regions of the space-time volume. This becomes particularly important when dealing with large objects that exhibit slow relative motion to the camera. Moreover, while aggressive sub-sampling is often necessary to achieve low-latency inference, it introduces the risk of omitting important information from the event stream. On the other hand, SNNs [1, 6, 34] transmit information sparsely within the system. Unlike RNNs, SNNs emit spikes only when a threshold is met, making them hard to optimize due to the non-differentiable spike mechanism. Some solutions [27] bypass the threshold, but this sacrifices sparsity in deeper layers. Overall, SNNs remain a challenging area needing more foundational research for optimized performance." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.832, + 0.305, + 0.847 + ], + "angle": 0, + "content": "2.2. Continuous-time Models" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Gu et al. [16] introduced the S4 model as an alternative to CNNs and Transformers for capturing long-range dependencies through LTI systems. This was followed by" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "the S4D model [15], designed for easier understanding and implementation, offering similar performance to S4. The S5 model [36] improved efficiency by avoiding frequency domain computations and utilizing time-domain parallel scans. However, these models have not been thoroughly evaluated on complex, high-dimensional visual data with significant temporal resolution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.892, + 0.318 + ], + "angle": 0, + "content": "In our study, we empirically show that S4, S4D and S5 models achieve results on-par with state-of-the-art when combined with attention mechanisms on complex data. We also identify and address aliasing issues in these models, proposing two corrective strategies. Our work extends the range and robustness of continuous-time models for complex sequence modeling tasks such as object detection for event cameras." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.33, + 0.593, + 0.346 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.356, + 0.892, + 0.476 + ], + "angle": 0, + "content": "In this section, we firstly formalize the operating mechanism of event cameras and provide a notation used for describing state-space models in the preliminaries (Sec. 3.1). Secondly, we describe our approach of incorporating variants of state-space models as layers within our block (Sec. 3.2). This innovative design solves the problems associated with slow training and the variable frequency inference for event cameras." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.484, + 0.642, + 0.499 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Event cameras. Event cameras are bio-inspired vision sensors that capture changes in log intensity per pixel asynchronously, rather than capturing entire frames at fixed intervals. Formally, let \\( I(x,y,t) \\) denote the log intensity at pixel coordinates \\( (x,y) \\) and time \\( t \\). An event \\( e \\) is generated at \\( (x,y,t) \\) whenever the change in log intensity \\( \\Delta I \\) exceeds a certain threshold \\( C \\):" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.622, + 0.892, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\Delta I (x, y, t) = I (x, y, t) - I (x, y, t - \\Delta t) \\geq C \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.646, + 0.892, + 0.707 + ], + "angle": 0, + "content": "Each event \\( e \\) is a tuple \\( (x, y, t, p) \\), where \\( (x, y) \\) are the pixel coordinates, \\( t \\) is the timestamp, and \\( p = \\{-1, 1\\} \\) is the polarity of the event, indicating the direction of the intensity change." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.813 + ], + "angle": 0, + "content": "State-Space Models (SSMs). Linear State-Space Models (SSMs) form the crucial part of the backbone in our architecture, where we compare S4 [16], S4D [15] and S5 [36] layer variants. Given an input vector \\(\\mathbf{u}(t) \\in \\mathbb{R}^U\\), a latent state vector \\(\\mathbf{x}(t) \\in \\mathbb{R}^P\\), and an output vector \\(\\mathbf{y}(t) \\in \\mathbb{R}^M\\), the governing equations of a continuous-time linear SSM can be mathematically represented as:" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.82, + 0.892, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\frac {\\mathrm {d} \\mathbf {x} (t)}{\\mathrm {d} t} = \\mathbf {A} \\mathbf {x} (t) + \\mathbf {B} \\mathbf {u} (t), \\quad \\mathbf {y} (t) = \\mathbf {C} \\mathbf {x} (t) + \\mathbf {D} \\mathbf {u} (t), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The model is parameterized by a state transition matrix \\(\\mathbf{A} \\in \\mathbb{R}^{P \\times P}\\), an input matrix \\(\\mathbf{B} \\in \\mathbb{R}^{P \\times U}\\), an output matrix \\(\\mathbf{C} \\in \\mathbb{R}^{M \\times P}\\), and a direct transmission matrix \\(\\mathbf{D} \\in \\mathbb{R}^{M \\times U}\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "5821" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "Given a fixed step size \\(\\Delta\\), this continuous-time model can be discretized into a linear recurrence using various methods such as Euler, bilinear, or zero-order hold (ZOH):" + }, + { + "type": "equation", + "bbox": [ + 0.108, + 0.148, + 0.469, + 0.166 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {k} = \\overline {{\\mathbf {A}}} \\mathbf {x} _ {k - 1} + \\overline {{\\mathbf {B}}} \\mathbf {u} _ {k}, \\quad \\mathbf {y} _ {k} = \\overline {{\\mathbf {C}}} \\mathbf {x} _ {k} + \\overline {{\\mathbf {D}}} \\mathbf {u} _ {k}, \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.177, + 0.47, + 0.237 + ], + "angle": 0, + "content": "The parameters in the discrete-time model are functions of the continuous-time parameters, defined by the chosen discretization method. Details on SSMs are available in the appendix." + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.257, + 0.468, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.163, + 0.362, + 0.384, + 0.375 + ], + "angle": 0, + "content": "Figure 2. SSM-ViT block structure" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.395, + 0.232, + 0.409 + ], + "angle": 0, + "content": "3.2. SSM-ViT block" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.418, + 0.469, + 0.478 + ], + "angle": 0, + "content": "In this section, we introduce the SSM-ViT block, a novel block depicted in Figure 2, which showcases the structured flow of the proposed block structure, designed for efficient event-based information processing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.469, + 0.629 + ], + "angle": 0, + "content": "We build a 4-stage hierarchical backbone like in [12] where in each stage we utilize our proposed SSM-ViT block. Events are processed into a tensor representation like in [12] before they are used as input to the first stage. Each stage takes the previous features as input and reuses the SSM state from the last timestep to compute features for the next stage. By saving SSM states, each stage retains temporal information for the whole feature map, while also being able to generalize to different frequencies since we use SSM instead of RNN that is used in [12]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.78 + ], + "angle": 0, + "content": "Regarding the block structure, initially, the input undergoes convolution with a defined kernel of size \\( k \\times k \\) with a stride \\( s \\). This operation effectively captures the essential spatial features of the input. Following the convolution operation, the structure introduces a 'Block-SA' module. This module is pivotal in implementing self-attention mechanisms, but it does so specifically within local windows. The localized nature of the attention in this block ensures a focus on immediate spatial relations, allowing for a detailed representation of close-proximity features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.87 + ], + "angle": 0, + "content": "Subsequent to 'Block-SA', the 'Grid-SA' module comes into play. In contrast to the localized approach of the previous block, 'Grid-SA' employs dilated attention, ensuring a global perspective. This module, by considering a broader scope, encapsulates a more comprehensive understanding of the spatial relations and the overall structure of the input." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "The final and crucial component of the block structure is the State-Space Model (SSM) block, that is designed to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.213 + ], + "angle": 0, + "content": "compute both the output and the state in parallel, either by using S4 [16], S4D [15] or S5 [36] model variant. This ensures temporal consistency and a seamless transition of information between consecutive time steps. Efficient computation is crucial since it allows for the faster training than RNN, and timescale parameter on temporal aggregation is important since we can rescale it during inference and deploy at any frequency we want." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.222, + 0.714, + 0.238 + ], + "angle": 0, + "content": "3.3. Low-pass bandlimiting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.245, + 0.892, + 0.35 + ], + "angle": 0, + "content": "However, the capability to deploy state space models at resolutions higher than those encountered during training is not without its drawbacks. It gives rise to the well-documented issue of aliasing [32, 33], which occurs when the kernel bandwidth surpasses the Nyquist frequency. We adress this challenge in following two subsections - 3.3.1 & 3.3.2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.364, + 0.671, + 0.38 + ], + "angle": 0, + "content": "3.3.1 Output Masking" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.509 + ], + "angle": 0, + "content": "In the realm of signal processing, frequency content beyond the Nyquist rate can lead to aliasing, adversely affecting model performance. To address this, we integrate a frequency-selective masking strategy into the training and inference processes. This bandlimiting method has been empirically validated to be crucial for generalizing across different frequencies [32, 33], with ablation studies indicating a decrease in accuracy by as much as \\(20\\%\\) in its absence." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.892, + 0.599 + ], + "angle": 0, + "content": "Let the SSM be governed by a matrix \\(\\mathbf{A}\\), with its diagonal elements \\(a_{n}\\) influencing the temporal evolution of the system states. The kernel's basis function for the \\(n\\)-th state is given by \\(K_{n}(t) = e^{ta_{n}}B_{n}\\), where the frequency characteristics are primarily dictated by the imaginary part of \\(a_{n} - \\Im(a_{n})\\) and \\(B_{n}\\) represents the \\(B\\) matrix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.6, + 0.892, + 0.645 + ], + "angle": 0, + "content": "To modulate the frequency spectrum of the model, we define a hyperparameter \\(\\alpha\\), which is used for masking of the computed effective frequency \\(f_{n}\\) for each state:" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.656, + 0.891, + 0.686 + ], + "angle": 0, + "content": "\\[\nf _ {n} = \\frac {\\Delta t}{r} \\cdot \\frac {| \\Im (a _ {n}) |}{2 \\pi}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.696, + 0.892, + 0.741 + ], + "angle": 0, + "content": "where \\(\\Delta t\\) denotes the discrete time-step, and \\(r\\) is the rate at which we train the model, by default it is 1, rate gets halved when deploying at twice the trained frequency etc." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.741, + 0.849, + 0.756 + ], + "angle": 0, + "content": "The bandlimiting mask is then applied as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.603, + 0.767, + 0.891, + 0.8 + ], + "angle": 0, + "content": "\\[\nC _ {n} = \\left\\{ \\begin{array}{l l} C _ {n} & \\text {i f} f _ {n} \\leq \\frac {\\alpha}{2}, \\\\ 0 & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( C_n \\) represents the coefficients in the state representation. The selection of \\( \\alpha \\) is critical, with \\( \\alpha = 1.0 \\) representing the Nyquist limit under idealized conditions. However, practical considerations and model constraints typically necessitate a lower empirical threshold. Our findings suggest that setting \\( \\alpha = 0.5 \\) yields optimal outcomes for systems" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5822" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.12 + ], + "angle": 0, + "content": "with diagonal state matrices, such as in S4D and S5 configurations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.122, + 0.468, + 0.168 + ], + "angle": 0, + "content": "This frequency-selective masking is proven to be a cornerstone for the adaptability of our SSMs, significantly contributing to their generalization across differing frequencies." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.185, + 0.195, + 0.2 + ], + "angle": 0, + "content": "3.3.2 \\(\\mathbf{H}_2\\) Norm" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.209, + 0.468, + 0.269 + ], + "angle": 0, + "content": "This section introduces another strategy to mitigate the aliasing problem by suppressing the frequency response of the continuous-time state-space model beyond a selected frequency \\(\\omega_{\\mathrm{min}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.27, + 0.468, + 0.329 + ], + "angle": 0, + "content": "This approach makes use of the \\( H_{2} \\) norm of a continuous-time linear system which measures the power (or steady-state covariance) of the output response to unit white-noise input." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.33, + 0.468, + 0.375 + ], + "angle": 0, + "content": "Given a continuous-time system described by matrices \\(\\mathbf{A}\\), \\(\\mathbf{B}\\), and \\(\\mathbf{C}\\), the transfer function \\(\\mathbf{G}(s)\\) from the Laplace transform can be defined in the frequency domain as:" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.388, + 0.468, + 0.406 + ], + "angle": 0, + "content": "\\[\n\\mathbf {G} (j \\omega) = \\mathbf {C} (j \\omega \\mathbf {I} - \\mathbf {A}) ^ {- 1} \\mathbf {B}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.411, + 0.468, + 0.516 + ], + "angle": 0, + "content": "where \\(\\omega\\) denotes the frequency, and \\(\\mathbf{I}\\) is the identity matrix. The \\(H_{2}\\) norm is computed as the integral of the squared magnitude of the frequency response over the range of interest, typically the entire frequency spectrum. However, in our case, we would like to suppress the frequency response of the system to frequencies beyond \\(\\omega_{\\mathrm{min}}\\) which can be done by minimizing the following:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.536, + 0.468, + 0.577 + ], + "angle": 0, + "content": "\\[\n\\left\\| \\mathbf {G} \\right\\| _ {H _ {2} \\left(\\omega_ {\\min }, \\infty\\right)} = \\sqrt {\\frac {1}{\\pi} \\int_ {\\omega_ {\\min }} ^ {\\infty} \\left\\| \\mathbf {G} \\left(j \\omega_ {k}\\right) \\right\\| _ {F} ^ {2} d \\omega}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.585, + 0.468, + 0.691 + ], + "angle": 0, + "content": "as part of the loss function, where \\(\\| \\cdot \\| _F\\) is the Frobenius norm. In practice, to numerically estimate this integral, we choose a maximum frequency \\(\\omega_{\\mathrm{max}}\\) and discretize the frequency range \\([\\omega_{\\mathrm{min}},\\omega_{\\mathrm{max}}]\\) into \\(N\\) points and apply numerical integration methods to the squared Frobenius norm of \\(\\mathbf{G}(j\\omega)\\). This yields an approximate \\(H_{2}\\) norm of the system in the desired frequency range." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.698, + 0.209, + 0.714 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.468, + 0.904 + ], + "angle": 0, + "content": "We perform ablation studies and systematic evaluations of our proposed models utilizing both the Gen1 [7] and 1 Mpx [29] event-based camera datasets. We assess the model's proficiency in adapting to unseen inference frequencies during training time on both datasets. We employed two variants for training across both datasets: the base model ViT-SSM-B, alongside its scaled-down derivative ViT-SSM-S (small). Additionally, to study the robustness and generalization capabilities of our architecture, we subject it to empirical testing on the DSEC dataset [13], which was not part of the original training corpus and the visual results are provided in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.582, + 0.107 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Implementation details. Our models are trained using 32-bit precision arithmetic across 400k iterations, making use of the ADAM optimizer [20] and a OneCycle learning rate schedule [37] that decays linearly from its highest value. We adopt a mixed batching technique that applies standard Backpropagation Through Time (BPTT) to half of the batch samples and Truncated BPTT (TBPTT) to the other half. This technique was introduced in the RVT [12] and ablated in their supplementary material. We found it to be equally effective also for SSMs. For the S4(D) method, details can be found in [15, 16]. As for S5 [36], we utilize an efficient implementation from scratch in PyTorch; original public version of S5 is available in JAX. Data augmentation is carried out through random horizontal flips and zooming operations, both inward and outward. Event representations are formed based on \\(50~\\mathrm{ms}\\) time windows that correspond to \\(20\\mathrm{Hz}\\) sampling frequency, divided into \\(\\mathrm{T} = 10\\) discrete bins. We incorporate a YOLOX detection head [10] that integrates IOU, class, and regression losses, averaged across both batch and sequence lengths during each optimization phase. Bandlimiting is implemented during training and inference of the SSM model by masking the output matrix \\(\\mathbf{C}\\) as explained in 3.3.1. In case of \\(H_{2}\\) norm, we add it as term to the loss function of the model. We conduct training on the GEN1 dataset using A100 GPU, employing a batch size of 8 and a sequence length of 21. We use a global learning rate of 2e-4, which is propagated to the SSM components. For the 1 Mpx dataset, we train with a batch size of 12 and a sequence length of 10, using a learning rate of 3.5e-4 across two A100 GPUs." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.568, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Datasets. The Gen1 Automotive Detection dataset [7] comprises 39 hours of event camera footage with a resolution of \\(304 \\times 240\\) pixels. It includes 228k bounding boxes for cars and 28k for pedestrians. Using original evaluation criteria [7], we discard bounding boxes having a side length shorter than 10 pixels or a diagonal less than 30 pixels." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.892, + 0.809 + ], + "angle": 0, + "content": "The 1 Mpx dataset [29] similarly focuses on driving environments but offers recordings at a higher resolution of \\(720 \\times 1280\\) pixels, captured over multiple months during both day-time and night-time. It contains roughly 15 hours of event data and accumulates around 25 million bounding box labels, spread across three classes: cars, pedestrians, and two-wheelers. Following original evaluation criteria, we eliminate bounding boxes with a side length under 20 pixels and a diagonal less than 60 pixels, while also reducing the input resolution to \\(640 \\times 360\\) pixels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.818, + 0.727, + 0.833 + ], + "angle": 0, + "content": "4.2. Benchmark comparisons" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.841, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we present a detailed comparison of our proposed methods, S4D-ViT-B and S5-ViT-B, with the SotA approaches in the domain of event-based vision for object detection, which can be seen in Table 1. The evalua" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5823" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.885, + 0.375 + ], + "angle": 0, + "content": "
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
Asynet [27]Sparse CNNYOLOv1 [31]14.5---11.4
AEGNN [35]GNNYOLOv116.3---20.0
Spiking DenseNet [5]SNNSSD [23]18.9---8.2
Inception + SSD [17]CNNSSD30.119.434.045.2>60*
RRC-Events [3]CNNYOLOv3 [30]30.721.534.346.4>100*
MatrixLSTM [2]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [19]CNNYOLOv331.222.334.649.4>60*
RED [29]CNN + RNNSSD40.016.743.039.324.1
ERGO-12 [43]TransformerYOLOv6 [21]50.469.940.6100.059.6
RVT-B [12]Transformer + RNNYOLOX [10]47.210.247.411.918.5
Swin-T v2 [25]Transformer + RNNYOLOX45.526.646.434.521.1
Nested-T [28, 41]Transformer + RNNYOLOX46.325.946.033.522.2
GET-T [28]Transformer + RNNYOLOX47.916.848.418.221.9
S4D-ViT-B (ours)Transformer + SSMYOLOX46.29.4046.810.916.5
S5-ViT-B (ours)Transformer + SSMYOLOX47.48.1647.29.5718.2
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.385, + 0.893, + 0.442 + ], + "angle": 0, + "content": "Table 1. Comparisons on test sets of Gen1 and 1 Mpx datasets (20 Hz). Best results in bold and second best underlined. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for SSM-ViT to compare against indicated timings in prior work [29] on comparable GPUs (Titan Xp). Ours achieves comparable results with other SotA approaches and generalizes well to other frequencies where others fail." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.468, + 0.47, + 0.514 + ], + "angle": 0, + "content": "tion is conducted on two distinct datasets: Gen1 and 1 Mpx, to assess the performance and robustness of these methods under varying conditions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.516, + 0.47, + 0.576 + ], + "angle": 0, + "content": "The comparative analysis, as summarized in Table 1, encompasses different backbones and detection heads. These include Sparse CNNs, GNNs, SNNs, RNNs, and various implementations of Transformers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.578, + 0.47, + 0.731 + ], + "angle": 0, + "content": "Our S4D-ViT-B and S5-ViT-B models, which integrate SSMs with Attention (3.2), demonstrate competitive performance across both datasets. Specifically, on the 1 Mpx dataset, our models achieve mAP scores of 46.8 and 47.2, respectively, which are competitive with the leading scores in this benchmark. While our models do not outperform the top-performing ERGO-12 [43] and GET-T [28] in terms of mAP, they exhibit a notable balance between accuracy and model complexity, as indicated by their parameter counts of 16.5M and 17.5M, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.732, + 0.47, + 0.854 + ], + "angle": 0, + "content": "Notably, our models perform consistently well across different frequencies as it can be seen in Table 2, highlighting their robustness and generalizability in comparison to RVT and GET-T, which tend to exhibit large performance drops. We achieve an average performance drop between training and testing frequencies of \\(3.31\\mathrm{mAP}\\) averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and \\(24.53\\mathrm{mAP}\\), respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "In summary, our proposed S4D-ViT-B and S5-ViT-B models establish themselves as effective and efficient contenders in the field of event-based vision for object detec" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.468, + 0.892, + 0.529 + ], + "angle": 0, + "content": "tion. Their competitive performance metrics, coupled with their generalization capabilities across various inference frequencies, make them valuable contributions to event-based vision community." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.54, + 0.892, + 0.643 + ], + "angle": 0, + "content": "
ModelDatasetFrequency Evaluation (Hz)Perf. Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVTGen147.1635.1321.9818.618.3526.14
1Mpx47.4042.5133.2030.2918.1516.36
S5Gen147.4046.4445.0842.4939.843.94
1Mpx47.2046.4946.1145.8039.702.68
GETGen147.9034.1519.9715.135.3529.25
1Mpx48.4040.5130.3028.1115.4419.81
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.652, + 0.892, + 0.68 + ], + "angle": 0, + "content": "Table 2. Evaluation of RVT [12], S5 [36], and GET [28] across different frequencies on test datasets" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.684, + 0.651, + 0.7 + ], + "angle": 0, + "content": "4.3. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.892, + 0.813 + ], + "angle": 0, + "content": "In this section we investigate different SSMs and their initializations with and without bandlimiting parameter for event-based vision to address the problem of inference at different frequencies (4.3.1). After that, we study the importance of SSM layers in various stages during training of the model (4.3.2). Finally, we evaluate models on differing frequencies with two proposed strategies (4.3.3)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.817, + 0.812, + 0.832 + ], + "angle": 0, + "content": "4.3.1 SSMs: initializations & bandlimiting" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This section presents an ablation study focusing on the performance impact of various SSM variants and their initialization strategies in conjunction with the bandlimiting parameter \\(\\alpha\\). The SSM variants under consideration are S4" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5824" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.099, + 0.089, + 0.451, + 0.23 + ], + "angle": 0, + "content": "
ModelMean Average Precision - mAP val
α = 0α = 0.5α = 1Average
S4-legS46.66--46.66
S4D-legS46.9347.3346.5046.92
S4D-inv46.1546.2346.1146.16
S4D-lin44.8246.0245.0445.29
S5-legS48.3348.4848.0048.27
S5-inv47.2647.4346.9847.22
S5-lin46.1246.4045.5946.04
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.24, + 0.47, + 0.282 + ], + "angle": 0, + "content": "Table 3. Performance comparison between the S4 [16], S4D [15] and S5 [36] models for different values of \\(\\alpha\\) and initializations on Gen1 [7] validation dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.311, + 0.468, + 0.537 + ], + "angle": 0, + "content": "[16], S4D [15], and the more recent S5 [36]. The analysis is conducted on the Gen1 [7] validation dataset, with the mean Average Precision (mAP) serving as the performance metric. Table 3 provides a comprehensive view of how different initialization strategies (legS, inv, lin) introduced in [15] and values of \\(\\alpha \\in \\{0,0.5,1\\}\\) influence model performance. The S4-legS model, not equipped for bandlimiting in non-diagonal matrix scenarios, achieves a baseline mAP of 46.66 at \\(\\alpha = 0\\). The S4D variants demonstrate a diverse performance spectrum. The S4D-legS variant, particularly at \\(\\alpha = 0.5\\), achieves the highest mAP of 47.33 among the S4D models, also maintaining the best average mAP of 46.92. The S4D-inv and S4D-lin variants show less favorable outcomes, with mAPs peaking at 46.23 and 46.02, respectively, for \\(\\alpha = 0.5\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.468, + 0.644 + ], + "angle": 0, + "content": "Notably, the S5 model variants exhibit an improvement over their predecessors. The S5-legS variant achieves the highest mAP of 48.48 at \\(\\alpha = 0.5\\), and also records the best average mAP of 48.27. This result is not only the best in its category but also the best overall. The S5-inv and S5-ln models also demonstrate comparable performance, with the former reaching its peak mAP of 47.43 at \\(\\alpha = 0.5\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.646, + 0.468, + 0.796 + ], + "angle": 0, + "content": "This study emphasizes the critical role of initialization strategies and bandlimiting in optimizing SSM-based neural networks for event-based vision tasks. The distinct performance variations across different models and configurations underscore the importance of selecting appropriate initializations and \\(\\alpha\\) values, as these choices impact the efficacy of the models in handling the dynamic and complex nature of event-based vision data. Higher values of parameter \\(\\alpha\\) encourage SSM to learn smoother kernels and discard more complex and higher-frequency convolution kernels." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.305, + 0.83 + ], + "angle": 0, + "content": "4.3.2 SSM Utilization Analysis" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "In this ablation study, we examine the impact of employing temporal recurrence exclusively in a subset of network stages, or not using it at all. Our methodology involves manipulating the SSMs within the network by resetting their" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "states at predetermined stages during each timestep. This approach enables us to isolate and evaluate the impact of SSM layers' presence or absence while maintaining a consistent parameter count across different model configurations." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.178, + 0.892, + 0.273 + ], + "angle": 0, + "content": "
S1S2S3S4mAPRVTmAPS4D5mAPS5
33.9039.9943.67
✓41.6843.1146.10
✓✓46.1045.3347.52
✓✓✓48.8247.0248.41
✓✓✓✓49.5247.3348.48
" + }, + { + "type": "table_caption", + "bbox": [ + 0.503, + 0.283, + 0.888, + 0.297 + ], + "angle": 0, + "content": "Table 4. SSM contribution in various stages on the Gen1 dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.318, + 0.892, + 0.65 + ], + "angle": 0, + "content": "Table 4 shows the outcomes of these manipulations on the Gen1 validation dataset. \\( S4D_{.5} \\) represents S4D model, and \\( S5_{.5} \\) is S5 model with \\( \\alpha = 0.5 \\). The data clearly indicate that the complete removal of SSMs from the network leads to a highest decrease in detection performance. This underscores the pivotal role of SSMs in enhancing the model's capability. On the other hand, initiating the use of SSMs from the fourth stage onwards consistently enhances performance, suggesting a critical threshold for the impact of temporal information processing in the later stages of the network. Another intriguing observation is the performance boost obtained by incorporating an SSM at the very initial stage. This suggests that the early integration of temporal information is also beneficial for the overall detection performance. As a result of these findings, our preferred configuration includes the SSM component right from the initial stage, thereby leveraging the advantages of temporal information processing throughout the entire network. Noteworthy is the observation that the performance drop when employing SSMs is less pronounced than with RVT, suggesting our approach's superior robustness to temporal aggregation from certain stages compared to RVT." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.659, + 0.796, + 0.674 + ], + "angle": 0, + "content": "4.3.3 Evaluation at different frequencies" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.854 + ], + "angle": 0, + "content": "In this section, we delve into the comparative performance analysis of three models: RVT [12], S4D [15], and S5 [36], across various frequency ranges. This evaluation is crucial in determining the robustness and adaptability of these models under diverse inference frequencies, specifically at \\(20\\mathrm{Hz}\\), \\(40\\mathrm{Hz}\\), \\(80\\mathrm{Hz}\\), \\(100\\mathrm{Hz}\\), and \\(200\\mathrm{Hz}\\). Our model is trained with event representations formed based on \\(50\\mathrm{ms}\\) time windows that correspond to \\(20\\mathrm{Hz}\\) sampling frequency. Evaluation is done at this frequency, and others above mentioned. With RVT, there are no changes when evaluating at different frequencies, while with SSMs rate \\(r\\) is halved for the double the inference frequency etc." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Each model in Table 5 is assessed across datasets and model sizes, including Gen1 \\( \\text{Base} \\), Gen1 \\( \\text{Small} \\), and 1 \\( \\text{Mpx} \\) \\( \\text{Base} \\). Base and Small represent two variants of mod" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5825" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.127, + 0.088, + 0.844, + 0.351 + ], + "angle": 0, + "content": "
ModelDataset/SizeStrategyFrequency Evaluation (Hz)Performance Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVT [12]Gen1Base-49.5237.1623.2519.367.8327.62
Gen1Small-48.6835.2819.9516.055.7529.42
1MpxBase-45.9540.9331.7029.0018.1616.00
S4D [15]Gen1BaseH2norm46.8345.9843.9140.1036.115.31
α = 0.547.3346.3644.5140.0235.985.61
Gen1SmallH2norm45.8845.1141.0538.0034.056.33
α = 0.546.3045.2142.1138.6133.006.57
1MpxBaseH2norm46.6645.8543.3341.8037.014.66
α = 0.547.9346.7844.5641.1136.185.77
S5 [36]Gen1BaseH2norm48.6047.1146.0643.8040.514.23
α = 0.548.4847.3446.1143.2340.034.30
Gen1SmallH2norm47.3346.3244.0341.1238.984.72
α = 0.547.8346.5844.4641.1138.955.06
1MpxBaseH2norm48.6547.5347.1146.6340.913.11
α = 0.548.3547.6047.2146.5040.802.82
" + }, + { + "type": "table_caption", + "bbox": [ + 0.212, + 0.361, + 0.756, + 0.377 + ], + "angle": 0, + "content": "Table 5. Evaluation of RVT, S4D, and S5 across different frequencies on validation datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.402, + 0.47, + 0.675 + ], + "angle": 0, + "content": "els on the Gen1 and 1 Mpx datasets, the base one being the larger one with 16.5M parameters for the S4D model and 18.2M parameters for the S5 model (as presented in Table 1 parameters' column), and small one with 8.8M parameters for S4D and 9.7M parameters for S5 model. The focal point of this analysis is the performance drop, calculated as the average difference between the original performance at \\(20\\mathrm{Hz}\\) and performances at higher frequencies. A notable aspect of this study is the inherent advantage of the S4D and S5 models due to their incorporation of a learnable timescale parameter. This significantly enhances their adaptability, allowing them to dynamically adjust to varying frequencies. This feature is particularly salient in the S4D and S5 models, which are further analyzed based on different operational strategies: the \\(H_{2}\\) norm and bandlimiting with \\(\\alpha = 0.5\\). The inclusion of the learnable timescale parameter in these models underscores their capability to maintain performance across a wide range of frequencies." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.47, + 0.782 + ], + "angle": 0, + "content": "The analysis reveals that both the \\( H_{2} \\) norm and bandlimiting strategies with \\( \\alpha = 0.5 \\) offer comparable performance across the assessed frequency ranges. However, a slight edge is observed with the \\( H_{2} \\) norm, particularly at very high frequencies. This marginal superiority can be attributed to the fact that \\( H_{2} \\) norm approach does not explicitly mask output's \\( (C) \\) matrix columns." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.784, + 0.47, + 0.814 + ], + "angle": 0, + "content": "In the Appendix, we study pure-SSM and SSM models in combination with ConvNext [26]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.828, + 0.196, + 0.844 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.903 + ], + "angle": 0, + "content": "In this paper, we presented a novel approach for enhancing the adaptability and training efficiency of models designed for event-based vision, particularly in object detec" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.402, + 0.892, + 0.495 + ], + "angle": 0, + "content": "tion tasks. Our methodology leverages the integration of SSMs with a Vision Transformer (ViT) architecture, creating a hybrid SSM-ViT model. This integration not only addresses the long-standing challenge of performance degradation at varying temporal frequencies but also significantly accelerates the training process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.593 + ], + "angle": 0, + "content": "The key innovation of our work lies in the use of learnable timescale parameters within the SSMs, enabling the model to adapt dynamically to different inference frequencies without necessitating multiple training cycles. This feature represents a substantial advancement over existing methods, which require retraining for different frequencies." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.795 + ], + "angle": 0, + "content": "The SSM-ViT model outperforms existing methods by \\(20\\mathrm{mAP}\\) at higher frequencies and exhibits a \\(33\\%\\) increase in training speed. Furthermore, our introduction of two novel strategies to counteract the aliasing effect (a crucial consideration in high-frequency deployment) further reinforces the model's suitability for real-world applications. These strategies, involving frequency-selective masking and \\(H_{2}\\) norm adjustments, effectively mitigate the adverse effects of aliasing, ensuring the model's reliability across a spectrum of temporal resolutions. We believe that our approach opens new avenues for research and application in high-speed, dynamic visual environments, setting a new benchmark in the domain of event-based vision." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.832, + 0.671, + 0.849 + ], + "angle": 0, + "content": "6. Acknowledgment" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This work was supported by the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.516, + 0.957 + ], + "angle": 0, + "content": "5826" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Julian Büchel, Gregor Lenz, Yalun Hu, Sadique Sheik, and Martino Sorbaro. Adversarial attacks on spiking convolutional neural networks for event-based vision. Front. Neurosci., 16, 2022. 3" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.172, + 0.472, + 0.226 + ], + "angle": 0, + "content": "[2] Marco Cannici, Marco Ciccone, Andrea Romanoni, and Matteo Matteucci. 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In ICCV, pages 12846-12856, 2023. 2, 3, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.468, + 0.674 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "5828" + } + ] +] \ No newline at end of file diff --git a/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_origin.pdf b/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e23d751eb88463ce09f82a2df5ca453d42427820 --- /dev/null +++ b/2024/State Space Models for Event Cameras/04cf8976-65e9-4903-adef-22c48bc5447f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:61c648f58cde467801b837c75d50ff2b6d81e58079f975af5f1fd084cd9489ab +size 564358 diff --git a/2024/State Space Models for Event Cameras/full.md b/2024/State Space Models for Event Cameras/full.md new file mode 100644 index 0000000000000000000000000000000000000000..1b6d54e22224988f2551ef025863d6ed940592e6 --- /dev/null +++ b/2024/State Space Models for Event Cameras/full.md @@ -0,0 +1,303 @@ +# State Space Models for Event Cameras + +Nikola Zubić, Mathias Gehrig, Davide Scaramuzza +Robotics and Perception Group, University of Zurich, Switzerland + +![](images/b26124d083158f6234fcebdce73cd247470ebb0c06a28ed95ec2111a8d1b31de.jpg) +Figure 1. Top-Left Previous works [12, 29] use RNN architectures with convolutional or attention mechanisms to train models that have superior performance on downstream tasks. However, the use of RNNs leads to slower training and the learned weights only generalize well to data deployed at the same frequency as that used at training time. Bottom-Left We solve this problem by utilizing SSMs for temporal aggregation, which enables faster training by either utilizing the S4 model [16] or S5 [36] parallel scans. By their nature, these models allow deployment at different frequencies than those used at training time since they have a learnable timescale parameter. Right Our SSM-based models achieve an average performance drop between training and testing frequencies of $3.31\mathrm{mAP}$ averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and $24.53\mathrm{mAP}$ , respectively. + +![](images/edd855e2bebae16a33dd0e16f441b312398a59212f60d78d85ad08cf4444faa7.jpg) + +# Abstract + +Today, state-of-the-art deep neural networks that process event-camera data first convert a temporal window of events into dense, grid-like input representations. As such, they exhibit poor generalizability when deployed at higher inference frequencies (i.e., smaller temporal windows) than the ones they were trained on. We address this challenge by introducing state-space models (SSMs) with learnable timescale parameters to event-based vision. This design adapts to varying frequencies without the need to retrain the network at different frequencies. Additionally, we investigate two strategies to counteract aliasing effects when deploying the model at higher frequencies. We comprehensively evaluate our approach against existing methods based on RNN and Transformer architectures across various benchmarks, including Gen1 and 1 Mpx event camera datasets. Our results demonstrate that SSM-based models train $33\%$ faster and also exhibit minimal performance degradation when tested at higher frequencies than the + +training input. Traditional RNN and Transformer models exhibit performance drops of more than 20 mAP, with SSMs having a drop of 3.31 mAP, highlighting the effectiveness of SSMs in event-based vision tasks. + +# 1. Introduction + +Event cameras emerged as a class of sensor technologies that noticeably deviate from the operational mechanics of conventional frame-based cameras [9]. While standard frame-based cameras [42] capture full-frame luminance levels at fixed intervals, event cameras record per-pixel relative brightness changes in a scene at the time they occur. The output is, therefore, an asynchronous stream of events in a four-dimensional spatio-temporal space. Each event is represented by its spatial coordinates on the pixel array, the temporal instance of the occurrence, and its polarity, which denotes the direction of the brightness change and encapsulates the increase or decrease in luminance. The + +power of event cameras primarily lies in their ability to capture dynamic scenes with unparalleled temporal resolution (microseconds). This property becomes invaluable in rapidly changing environments or applications requiring very fast response times [8, 39]. However, the richness of the spatio-temporal data they generate introduces complexities in data interpretation and processing. Sophisticated algorithms are required to efficiently parse and make sense of the high-dimensional data space. As such, while event cameras represent a promising frontier in visual sensor technologies, their pervasive utilization depends upon solving these inherent computational challenges. + +Current methodologies for addressing problems with event cameras fall predominantly into two categories. The first involves converting the raw stream of spatio-temporal events into dense representations akin to multi-channel images [12, 22, 40, 43]. This transformation allows leveraging conventional computer vision techniques designed for frame-based data. The second category employs sparse computational paradigms, often utilizing spiking neural networks or graph-based architectures [4, 11]. While promising, these methods are not without limitations; they frequently encounter hardware incompatibility issues and compromised accuracy. In this work, we utilize dense representations for their advantages in computational efficiency. + +Despite the advances in both paradigms, models trained on event representations at a specific frequency exhibit poor generalizability when deployed in settings with higher frequencies which is crucial for high-speed, dynamical visual scenarios. Additionally, to achieve high performance, it is necessary to include recurrent memory, thereby sacrificing computational efficiency during the training phase. An ideal model would seamlessly merge the training speed of convolutional architectures with the temporal sensitivity and memory benefits inherent to recurrent models. + +While recent advancements have introduced efficient recurrent vision transformer architectures [12, 24] to achieve better performance, they face several limitations. Specifically, these architectures suffer from longer training cycles due to their reliance on conventional recurrent mechanisms. + +The issue of slow training and generalization at higher event representation frequency than the lower one we trained on remains unresolved as conventional recurrent training methodologies are predominantly utilized in event-based vision. These methods do not incorporate learnable timescale parameters, thus inhibiting the model's capacity to generalize across varying inference frequencies. + +In this work, we address this limitation by introducing structured variations of state-space models [16, 36] as layers within our neural network framework. + +State-space models [14] function as CNN during training and are converted to an efficient RNN at test time. To achieve this, S4 [16] employs a technique where the SSM, + +which is not practical for training on modern hardware due to its sequential nature, is transformed into a CNN by unrolling. S5 [36] uses parallel scans during training, and is employed as RNN during inference. State-space models [14] can be deployed at different frequencies at inference time because they are Linear Time-Invariant (LTI) continuous-time systems that can be transformed into a discrete-time system with an arbitrary step size. This feature permits inference at arbitrary frequencies by globally adjusting the timescale parameter based on the ratio between the new and old frequency sampling rates. Consequently, we tackle the longstanding issue in event-based vision, which requires multiple training cycles with different frequencies to adapt the neural network for various frequencies during inference. + +For the task of object detection, we find that incorporating state-space layers accelerates the training by up to $33\%$ relative to existing recurrent vision transformer approaches [12, 24]. This is achieved while maintaining performance comparable to existing methods. Notably, our approach demonstrates superior generalization to higher temporal frequencies with a drop of only $3.31\mathrm{mAP}$ , while previous methods experience a drop of $21.25\mathrm{mAP}$ or more. Also, we achieve comparable performance to RVT although we use a linear state-space model rather than a non-linear LSTM model. This also shows that the complexity of the LSTM might not be needed. For this to work, we introduce two strategies (frequency-selective masking and $H_{2}$ norm) to counteract the aliasing effect encountered with increased temporal frequencies in event cameras. First one is a low-pass bandlimiting modification to SSM that encourages the learned convolutional kernels to be smooth. Second one mitigates the aliasing problem by attenuating the frequency response after a chosen frequency. We argue that state-space modeling offers a significant new direction for research in event-based vision, offering promising solutions to the challenges inherent in processing event-based data effectively and efficiently. + +Our contributions are concisely outlined as follows: + +- We introduce state-space models for event cameras to address two key challenges in event-based vision: (i) model performance degradation when operating event cameras at temporal frequencies different from their training conditions and (ii) training efficiency. +- Our experimental results outperform existing methods at higher frequencies by $20\mathrm{mAP}$ on average and show $33\%$ increase in the training speed. +- We introduce two strategies (bandlimiting & $H_{2}$ norm) designed to alleviate aliasing issues. + +# 2. Related Work + +# 2.1. Object detection with Event Cameras + +Approaches in event camera literature, thus in object detection, can be broadly classified into two branches. + +The first research branch investigates dense feed-forward methods. Early attempts in this direction relied on a constrained temporal window for generating event representations [3, 17, 19]. The resultant models were deficient in tracking slow-moving or stationary objects, as they failed to incorporate data beyond this limited time-frame. To mitigate these drawbacks, later studies introduced recurrent neural network (RNN) layers [29] into the architecture. The RNN component enhanced the model's capacity for temporal understanding, thereby improving its object detection capabilities. The work of Zubic et al. [43] takes this a step further by optimizing event representations and incorporating cutting-edge swim transformer architecture. Nonetheless, their approach was limited in its ability to re-detect slowly moving objects following extended periods of absence. Subsequent research [12, 24], merged the transformer and RNN architectures, pushing the performance further. However, this significantly increased computational demands during the training phase. Importantly, all methodologies examined to date suffer from an inability to adapt when deployed at variable frequencies. + +The second research branch investigates the use of Graph Neural Networks (GNNs) or Spiking Neural Networks (SNNs). GNNs dynamically construct a spatiotemporal graph where new nodes and edges are instantiated by selectively sub-sampling events and identifying pre-existing nodes that are proximate in the space-time continuum [11, 18, 38]. A pivotal challenge lies in architecting the network such that information can disseminate effectively across extensive regions of the space-time volume. This becomes particularly important when dealing with large objects that exhibit slow relative motion to the camera. Moreover, while aggressive sub-sampling is often necessary to achieve low-latency inference, it introduces the risk of omitting important information from the event stream. On the other hand, SNNs [1, 6, 34] transmit information sparsely within the system. Unlike RNNs, SNNs emit spikes only when a threshold is met, making them hard to optimize due to the non-differentiable spike mechanism. Some solutions [27] bypass the threshold, but this sacrifices sparsity in deeper layers. Overall, SNNs remain a challenging area needing more foundational research for optimized performance. + +# 2.2. Continuous-time Models + +Gu et al. [16] introduced the S4 model as an alternative to CNNs and Transformers for capturing long-range dependencies through LTI systems. This was followed by + +the S4D model [15], designed for easier understanding and implementation, offering similar performance to S4. The S5 model [36] improved efficiency by avoiding frequency domain computations and utilizing time-domain parallel scans. However, these models have not been thoroughly evaluated on complex, high-dimensional visual data with significant temporal resolution. + +In our study, we empirically show that S4, S4D and S5 models achieve results on-par with state-of-the-art when combined with attention mechanisms on complex data. We also identify and address aliasing issues in these models, proposing two corrective strategies. Our work extends the range and robustness of continuous-time models for complex sequence modeling tasks such as object detection for event cameras. + +# 3. Method + +In this section, we firstly formalize the operating mechanism of event cameras and provide a notation used for describing state-space models in the preliminaries (Sec. 3.1). Secondly, we describe our approach of incorporating variants of state-space models as layers within our block (Sec. 3.2). This innovative design solves the problems associated with slow training and the variable frequency inference for event cameras. + +# 3.1. Preliminaries + +Event cameras. Event cameras are bio-inspired vision sensors that capture changes in log intensity per pixel asynchronously, rather than capturing entire frames at fixed intervals. Formally, let $I(x,y,t)$ denote the log intensity at pixel coordinates $(x,y)$ and time $t$ . An event $e$ is generated at $(x,y,t)$ whenever the change in log intensity $\Delta I$ exceeds a certain threshold $C$ : + +$$ +\Delta I (x, y, t) = I (x, y, t) - I (x, y, t - \Delta t) \geq C \tag {1} +$$ + +Each event $e$ is a tuple $(x, y, t, p)$ , where $(x, y)$ are the pixel coordinates, $t$ is the timestamp, and $p = \{-1, 1\}$ is the polarity of the event, indicating the direction of the intensity change. + +State-Space Models (SSMs). Linear State-Space Models (SSMs) form the crucial part of the backbone in our architecture, where we compare S4 [16], S4D [15] and S5 [36] layer variants. Given an input vector $\mathbf{u}(t) \in \mathbb{R}^U$ , a latent state vector $\mathbf{x}(t) \in \mathbb{R}^P$ , and an output vector $\mathbf{y}(t) \in \mathbb{R}^M$ , the governing equations of a continuous-time linear SSM can be mathematically represented as: + +$$ +\frac {\mathrm {d} \mathbf {x} (t)}{\mathrm {d} t} = \mathbf {A} \mathbf {x} (t) + \mathbf {B} \mathbf {u} (t), \quad \mathbf {y} (t) = \mathbf {C} \mathbf {x} (t) + \mathbf {D} \mathbf {u} (t), \tag {2} +$$ + +The model is parameterized by a state transition matrix $\mathbf{A} \in \mathbb{R}^{P \times P}$ , an input matrix $\mathbf{B} \in \mathbb{R}^{P \times U}$ , an output matrix $\mathbf{C} \in \mathbb{R}^{M \times P}$ , and a direct transmission matrix $\mathbf{D} \in \mathbb{R}^{M \times U}$ . + +Given a fixed step size $\Delta$ , this continuous-time model can be discretized into a linear recurrence using various methods such as Euler, bilinear, or zero-order hold (ZOH): + +$$ +\mathbf {x} _ {k} = \overline {{\mathbf {A}}} \mathbf {x} _ {k - 1} + \overline {{\mathbf {B}}} \mathbf {u} _ {k}, \quad \mathbf {y} _ {k} = \overline {{\mathbf {C}}} \mathbf {x} _ {k} + \overline {{\mathbf {D}}} \mathbf {u} _ {k}, \tag {3} +$$ + +The parameters in the discrete-time model are functions of the continuous-time parameters, defined by the chosen discretization method. Details on SSMs are available in the appendix. + +![](images/ac8e807a07578454697f8b983da8958522d23d15c4d4aaf8597162287003a6ec.jpg) +Figure 2. SSM-ViT block structure + +# 3.2. SSM-ViT block + +In this section, we introduce the SSM-ViT block, a novel block depicted in Figure 2, which showcases the structured flow of the proposed block structure, designed for efficient event-based information processing. + +We build a 4-stage hierarchical backbone like in [12] where in each stage we utilize our proposed SSM-ViT block. Events are processed into a tensor representation like in [12] before they are used as input to the first stage. Each stage takes the previous features as input and reuses the SSM state from the last timestep to compute features for the next stage. By saving SSM states, each stage retains temporal information for the whole feature map, while also being able to generalize to different frequencies since we use SSM instead of RNN that is used in [12]. + +Regarding the block structure, initially, the input undergoes convolution with a defined kernel of size $k \times k$ with a stride $s$ . This operation effectively captures the essential spatial features of the input. Following the convolution operation, the structure introduces a 'Block-SA' module. This module is pivotal in implementing self-attention mechanisms, but it does so specifically within local windows. The localized nature of the attention in this block ensures a focus on immediate spatial relations, allowing for a detailed representation of close-proximity features. + +Subsequent to 'Block-SA', the 'Grid-SA' module comes into play. In contrast to the localized approach of the previous block, 'Grid-SA' employs dilated attention, ensuring a global perspective. This module, by considering a broader scope, encapsulates a more comprehensive understanding of the spatial relations and the overall structure of the input. + +The final and crucial component of the block structure is the State-Space Model (SSM) block, that is designed to + +compute both the output and the state in parallel, either by using S4 [16], S4D [15] or S5 [36] model variant. This ensures temporal consistency and a seamless transition of information between consecutive time steps. Efficient computation is crucial since it allows for the faster training than RNN, and timescale parameter on temporal aggregation is important since we can rescale it during inference and deploy at any frequency we want. + +# 3.3. Low-pass bandlimiting + +However, the capability to deploy state space models at resolutions higher than those encountered during training is not without its drawbacks. It gives rise to the well-documented issue of aliasing [32, 33], which occurs when the kernel bandwidth surpasses the Nyquist frequency. We adress this challenge in following two subsections - 3.3.1 & 3.3.2. + +# 3.3.1 Output Masking + +In the realm of signal processing, frequency content beyond the Nyquist rate can lead to aliasing, adversely affecting model performance. To address this, we integrate a frequency-selective masking strategy into the training and inference processes. This bandlimiting method has been empirically validated to be crucial for generalizing across different frequencies [32, 33], with ablation studies indicating a decrease in accuracy by as much as $20\%$ in its absence. + +Let the SSM be governed by a matrix $\mathbf{A}$ , with its diagonal elements $a_{n}$ influencing the temporal evolution of the system states. The kernel's basis function for the $n$ -th state is given by $K_{n}(t) = e^{ta_{n}}B_{n}$ , where the frequency characteristics are primarily dictated by the imaginary part of $a_{n} - \Im(a_{n})$ and $B_{n}$ represents the $B$ matrix. + +To modulate the frequency spectrum of the model, we define a hyperparameter $\alpha$ , which is used for masking of the computed effective frequency $f_{n}$ for each state: + +$$ +f _ {n} = \frac {\Delta t}{r} \cdot \frac {| \Im (a _ {n}) |}{2 \pi}, \tag {4} +$$ + +where $\Delta t$ denotes the discrete time-step, and $r$ is the rate at which we train the model, by default it is 1, rate gets halved when deploying at twice the trained frequency etc. + +The bandlimiting mask is then applied as follows: + +$$ +C _ {n} = \left\{ \begin{array}{l l} C _ {n} & \text {i f} f _ {n} \leq \frac {\alpha}{2}, \\ 0 & \text {o t h e r w i s e}, \end{array} \right. \tag {5} +$$ + +where $C_n$ represents the coefficients in the state representation. The selection of $\alpha$ is critical, with $\alpha = 1.0$ representing the Nyquist limit under idealized conditions. However, practical considerations and model constraints typically necessitate a lower empirical threshold. Our findings suggest that setting $\alpha = 0.5$ yields optimal outcomes for systems + +with diagonal state matrices, such as in S4D and S5 configurations. + +This frequency-selective masking is proven to be a cornerstone for the adaptability of our SSMs, significantly contributing to their generalization across differing frequencies. + +# 3.3.2 $\mathbf{H}_2$ Norm + +This section introduces another strategy to mitigate the aliasing problem by suppressing the frequency response of the continuous-time state-space model beyond a selected frequency $\omega_{\mathrm{min}}$ . + +This approach makes use of the $H_{2}$ norm of a continuous-time linear system which measures the power (or steady-state covariance) of the output response to unit white-noise input. + +Given a continuous-time system described by matrices $\mathbf{A}$ , $\mathbf{B}$ , and $\mathbf{C}$ , the transfer function $\mathbf{G}(s)$ from the Laplace transform can be defined in the frequency domain as: + +$$ +\mathbf {G} (j \omega) = \mathbf {C} (j \omega \mathbf {I} - \mathbf {A}) ^ {- 1} \mathbf {B}, \tag {6} +$$ + +where $\omega$ denotes the frequency, and $\mathbf{I}$ is the identity matrix. The $H_{2}$ norm is computed as the integral of the squared magnitude of the frequency response over the range of interest, typically the entire frequency spectrum. However, in our case, we would like to suppress the frequency response of the system to frequencies beyond $\omega_{\mathrm{min}}$ which can be done by minimizing the following: + +$$ +\left\| \mathbf {G} \right\| _ {H _ {2} \left(\omega_ {\min }, \infty\right)} = \sqrt {\frac {1}{\pi} \int_ {\omega_ {\min }} ^ {\infty} \left\| \mathbf {G} \left(j \omega_ {k}\right) \right\| _ {F} ^ {2} d \omega}, \tag {7} +$$ + +as part of the loss function, where $\| \cdot \| _F$ is the Frobenius norm. In practice, to numerically estimate this integral, we choose a maximum frequency $\omega_{\mathrm{max}}$ and discretize the frequency range $[\omega_{\mathrm{min}},\omega_{\mathrm{max}}]$ into $N$ points and apply numerical integration methods to the squared Frobenius norm of $\mathbf{G}(j\omega)$ . This yields an approximate $H_{2}$ norm of the system in the desired frequency range. + +# 4. Experiments + +We perform ablation studies and systematic evaluations of our proposed models utilizing both the Gen1 [7] and 1 Mpx [29] event-based camera datasets. We assess the model's proficiency in adapting to unseen inference frequencies during training time on both datasets. We employed two variants for training across both datasets: the base model ViT-SSM-B, alongside its scaled-down derivative ViT-SSM-S (small). Additionally, to study the robustness and generalization capabilities of our architecture, we subject it to empirical testing on the DSEC dataset [13], which was not part of the original training corpus and the visual results are provided in the appendix. + +# 4.1. Setup + +Implementation details. Our models are trained using 32-bit precision arithmetic across 400k iterations, making use of the ADAM optimizer [20] and a OneCycle learning rate schedule [37] that decays linearly from its highest value. We adopt a mixed batching technique that applies standard Backpropagation Through Time (BPTT) to half of the batch samples and Truncated BPTT (TBPTT) to the other half. This technique was introduced in the RVT [12] and ablated in their supplementary material. We found it to be equally effective also for SSMs. For the S4(D) method, details can be found in [15, 16]. As for S5 [36], we utilize an efficient implementation from scratch in PyTorch; original public version of S5 is available in JAX. Data augmentation is carried out through random horizontal flips and zooming operations, both inward and outward. Event representations are formed based on $50~\mathrm{ms}$ time windows that correspond to $20\mathrm{Hz}$ sampling frequency, divided into $\mathrm{T} = 10$ discrete bins. We incorporate a YOLOX detection head [10] that integrates IOU, class, and regression losses, averaged across both batch and sequence lengths during each optimization phase. Bandlimiting is implemented during training and inference of the SSM model by masking the output matrix $\mathbf{C}$ as explained in 3.3.1. In case of $H_{2}$ norm, we add it as term to the loss function of the model. We conduct training on the GEN1 dataset using A100 GPU, employing a batch size of 8 and a sequence length of 21. We use a global learning rate of 2e-4, which is propagated to the SSM components. For the 1 Mpx dataset, we train with a batch size of 12 and a sequence length of 10, using a learning rate of 3.5e-4 across two A100 GPUs. + +Datasets. The Gen1 Automotive Detection dataset [7] comprises 39 hours of event camera footage with a resolution of $304 \times 240$ pixels. It includes 228k bounding boxes for cars and 28k for pedestrians. Using original evaluation criteria [7], we discard bounding boxes having a side length shorter than 10 pixels or a diagonal less than 30 pixels. + +The 1 Mpx dataset [29] similarly focuses on driving environments but offers recordings at a higher resolution of $720 \times 1280$ pixels, captured over multiple months during both day-time and night-time. It contains roughly 15 hours of event data and accumulates around 25 million bounding box labels, spread across three classes: cars, pedestrians, and two-wheelers. Following original evaluation criteria, we eliminate bounding boxes with a side length under 20 pixels and a diagonal less than 60 pixels, while also reducing the input resolution to $640 \times 360$ pixels. + +# 4.2. Benchmark comparisons + +In this section, we present a detailed comparison of our proposed methods, S4D-ViT-B and S5-ViT-B, with the SotA approaches in the domain of event-based vision for object detection, which can be seen in Table 1. The evalua + +
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
Asynet [27]Sparse CNNYOLOv1 [31]14.5---11.4
AEGNN [35]GNNYOLOv116.3---20.0
Spiking DenseNet [5]SNNSSD [23]18.9---8.2
Inception + SSD [17]CNNSSD30.119.434.045.2>60*
RRC-Events [3]CNNYOLOv3 [30]30.721.534.346.4>100*
MatrixLSTM [2]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [19]CNNYOLOv331.222.334.649.4>60*
RED [29]CNN + RNNSSD40.016.743.039.324.1
ERGO-12 [43]TransformerYOLOv6 [21]50.469.940.6100.059.6
RVT-B [12]Transformer + RNNYOLOX [10]47.210.247.411.918.5
Swin-T v2 [25]Transformer + RNNYOLOX45.526.646.434.521.1
Nested-T [28, 41]Transformer + RNNYOLOX46.325.946.033.522.2
GET-T [28]Transformer + RNNYOLOX47.916.848.418.221.9
S4D-ViT-B (ours)Transformer + SSMYOLOX46.29.4046.810.916.5
S5-ViT-B (ours)Transformer + SSMYOLOX47.48.1647.29.5718.2
+ +tion is conducted on two distinct datasets: Gen1 and 1 Mpx, to assess the performance and robustness of these methods under varying conditions. + +The comparative analysis, as summarized in Table 1, encompasses different backbones and detection heads. These include Sparse CNNs, GNNs, SNNs, RNNs, and various implementations of Transformers. + +Our S4D-ViT-B and S5-ViT-B models, which integrate SSMs with Attention (3.2), demonstrate competitive performance across both datasets. Specifically, on the 1 Mpx dataset, our models achieve mAP scores of 46.8 and 47.2, respectively, which are competitive with the leading scores in this benchmark. While our models do not outperform the top-performing ERGO-12 [43] and GET-T [28] in terms of mAP, they exhibit a notable balance between accuracy and model complexity, as indicated by their parameter counts of 16.5M and 17.5M, respectively. + +Notably, our models perform consistently well across different frequencies as it can be seen in Table 2, highlighting their robustness and generalizability in comparison to RVT and GET-T, which tend to exhibit large performance drops. We achieve an average performance drop between training and testing frequencies of $3.31\mathrm{mAP}$ averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and $24.53\mathrm{mAP}$ , respectively. + +In summary, our proposed S4D-ViT-B and S5-ViT-B models establish themselves as effective and efficient contenders in the field of event-based vision for object detec + +tion. Their competitive performance metrics, coupled with their generalization capabilities across various inference frequencies, make them valuable contributions to event-based vision community. + +Table 1. Comparisons on test sets of Gen1 and 1 Mpx datasets (20 Hz). Best results in bold and second best underlined. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for SSM-ViT to compare against indicated timings in prior work [29] on comparable GPUs (Titan Xp). Ours achieves comparable results with other SotA approaches and generalizes well to other frequencies where others fail. + +
ModelDatasetFrequency Evaluation (Hz)Perf. Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVTGen147.1635.1321.9818.618.3526.14
1Mpx47.4042.5133.2030.2918.1516.36
S5Gen147.4046.4445.0842.4939.843.94
1Mpx47.2046.4946.1145.8039.702.68
GETGen147.9034.1519.9715.135.3529.25
1Mpx48.4040.5130.3028.1115.4419.81
+ +Table 2. Evaluation of RVT [12], S5 [36], and GET [28] across different frequencies on test datasets + +# 4.3. Ablation study + +In this section we investigate different SSMs and their initializations with and without bandlimiting parameter for event-based vision to address the problem of inference at different frequencies (4.3.1). After that, we study the importance of SSM layers in various stages during training of the model (4.3.2). Finally, we evaluate models on differing frequencies with two proposed strategies (4.3.3). + +# 4.3.1 SSMs: initializations & bandlimiting + +This section presents an ablation study focusing on the performance impact of various SSM variants and their initialization strategies in conjunction with the bandlimiting parameter $\alpha$ . The SSM variants under consideration are S4 + +
ModelMean Average Precision - mAP val
α = 0α = 0.5α = 1Average
S4-legS46.66--46.66
S4D-legS46.9347.3346.5046.92
S4D-inv46.1546.2346.1146.16
S4D-lin44.8246.0245.0445.29
S5-legS48.3348.4848.0048.27
S5-inv47.2647.4346.9847.22
S5-lin46.1246.4045.5946.04
+ +[16], S4D [15], and the more recent S5 [36]. The analysis is conducted on the Gen1 [7] validation dataset, with the mean Average Precision (mAP) serving as the performance metric. Table 3 provides a comprehensive view of how different initialization strategies (legS, inv, lin) introduced in [15] and values of $\alpha \in \{0,0.5,1\}$ influence model performance. The S4-legS model, not equipped for bandlimiting in non-diagonal matrix scenarios, achieves a baseline mAP of 46.66 at $\alpha = 0$ . The S4D variants demonstrate a diverse performance spectrum. The S4D-legS variant, particularly at $\alpha = 0.5$ , achieves the highest mAP of 47.33 among the S4D models, also maintaining the best average mAP of 46.92. The S4D-inv and S4D-lin variants show less favorable outcomes, with mAPs peaking at 46.23 and 46.02, respectively, for $\alpha = 0.5$ . + +Notably, the S5 model variants exhibit an improvement over their predecessors. The S5-legS variant achieves the highest mAP of 48.48 at $\alpha = 0.5$ , and also records the best average mAP of 48.27. This result is not only the best in its category but also the best overall. The S5-inv and S5-ln models also demonstrate comparable performance, with the former reaching its peak mAP of 47.43 at $\alpha = 0.5$ . + +This study emphasizes the critical role of initialization strategies and bandlimiting in optimizing SSM-based neural networks for event-based vision tasks. The distinct performance variations across different models and configurations underscore the importance of selecting appropriate initializations and $\alpha$ values, as these choices impact the efficacy of the models in handling the dynamic and complex nature of event-based vision data. Higher values of parameter $\alpha$ encourage SSM to learn smoother kernels and discard more complex and higher-frequency convolution kernels. + +# 4.3.2 SSM Utilization Analysis + +In this ablation study, we examine the impact of employing temporal recurrence exclusively in a subset of network stages, or not using it at all. Our methodology involves manipulating the SSMs within the network by resetting their + +states at predetermined stages during each timestep. This approach enables us to isolate and evaluate the impact of SSM layers' presence or absence while maintaining a consistent parameter count across different model configurations. + +Table 3. Performance comparison between the S4 [16], S4D [15] and S5 [36] models for different values of $\alpha$ and initializations on Gen1 [7] validation dataset. + +
S1S2S3S4mAPRVTmAPS4D5mAPS5
33.9039.9943.67
✓41.6843.1146.10
✓✓46.1045.3347.52
✓✓✓48.8247.0248.41
✓✓✓✓49.5247.3348.48
+ +Table 4. SSM contribution in various stages on the Gen1 dataset. + +Table 4 shows the outcomes of these manipulations on the Gen1 validation dataset. $S4D_{.5}$ represents S4D model, and $S5_{.5}$ is S5 model with $\alpha = 0.5$ . The data clearly indicate that the complete removal of SSMs from the network leads to a highest decrease in detection performance. This underscores the pivotal role of SSMs in enhancing the model's capability. On the other hand, initiating the use of SSMs from the fourth stage onwards consistently enhances performance, suggesting a critical threshold for the impact of temporal information processing in the later stages of the network. Another intriguing observation is the performance boost obtained by incorporating an SSM at the very initial stage. This suggests that the early integration of temporal information is also beneficial for the overall detection performance. As a result of these findings, our preferred configuration includes the SSM component right from the initial stage, thereby leveraging the advantages of temporal information processing throughout the entire network. Noteworthy is the observation that the performance drop when employing SSMs is less pronounced than with RVT, suggesting our approach's superior robustness to temporal aggregation from certain stages compared to RVT. + +# 4.3.3 Evaluation at different frequencies + +In this section, we delve into the comparative performance analysis of three models: RVT [12], S4D [15], and S5 [36], across various frequency ranges. This evaluation is crucial in determining the robustness and adaptability of these models under diverse inference frequencies, specifically at $20\mathrm{Hz}$ , $40\mathrm{Hz}$ , $80\mathrm{Hz}$ , $100\mathrm{Hz}$ , and $200\mathrm{Hz}$ . Our model is trained with event representations formed based on $50\mathrm{ms}$ time windows that correspond to $20\mathrm{Hz}$ sampling frequency. Evaluation is done at this frequency, and others above mentioned. With RVT, there are no changes when evaluating at different frequencies, while with SSMs rate $r$ is halved for the double the inference frequency etc. + +Each model in Table 5 is assessed across datasets and model sizes, including Gen1 $\text{Base}$ , Gen1 $\text{Small}$ , and 1 $\text{Mpx}$ $\text{Base}$ . Base and Small represent two variants of mod + +
ModelDataset/SizeStrategyFrequency Evaluation (Hz)Performance Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVT [12]Gen1Base-49.5237.1623.2519.367.8327.62
Gen1Small-48.6835.2819.9516.055.7529.42
1MpxBase-45.9540.9331.7029.0018.1616.00
S4D [15]Gen1BaseH2norm46.8345.9843.9140.1036.115.31
α = 0.547.3346.3644.5140.0235.985.61
Gen1SmallH2norm45.8845.1141.0538.0034.056.33
α = 0.546.3045.2142.1138.6133.006.57
1MpxBaseH2norm46.6645.8543.3341.8037.014.66
α = 0.547.9346.7844.5641.1136.185.77
S5 [36]Gen1BaseH2norm48.6047.1146.0643.8040.514.23
α = 0.548.4847.3446.1143.2340.034.30
Gen1SmallH2norm47.3346.3244.0341.1238.984.72
α = 0.547.8346.5844.4641.1138.955.06
1MpxBaseH2norm48.6547.5347.1146.6340.913.11
α = 0.548.3547.6047.2146.5040.802.82
+ +Table 5. Evaluation of RVT, S4D, and S5 across different frequencies on validation datasets + +els on the Gen1 and 1 Mpx datasets, the base one being the larger one with 16.5M parameters for the S4D model and 18.2M parameters for the S5 model (as presented in Table 1 parameters' column), and small one with 8.8M parameters for S4D and 9.7M parameters for S5 model. The focal point of this analysis is the performance drop, calculated as the average difference between the original performance at $20\mathrm{Hz}$ and performances at higher frequencies. A notable aspect of this study is the inherent advantage of the S4D and S5 models due to their incorporation of a learnable timescale parameter. This significantly enhances their adaptability, allowing them to dynamically adjust to varying frequencies. This feature is particularly salient in the S4D and S5 models, which are further analyzed based on different operational strategies: the $H_{2}$ norm and bandlimiting with $\alpha = 0.5$ . The inclusion of the learnable timescale parameter in these models underscores their capability to maintain performance across a wide range of frequencies. + +The analysis reveals that both the $H_{2}$ norm and bandlimiting strategies with $\alpha = 0.5$ offer comparable performance across the assessed frequency ranges. However, a slight edge is observed with the $H_{2}$ norm, particularly at very high frequencies. This marginal superiority can be attributed to the fact that $H_{2}$ norm approach does not explicitly mask output's $(C)$ matrix columns. + +In the Appendix, we study pure-SSM and SSM models in combination with ConvNext [26]. + +# 5. Conclusion + +In this paper, we presented a novel approach for enhancing the adaptability and training efficiency of models designed for event-based vision, particularly in object detec + +tion tasks. Our methodology leverages the integration of SSMs with a Vision Transformer (ViT) architecture, creating a hybrid SSM-ViT model. This integration not only addresses the long-standing challenge of performance degradation at varying temporal frequencies but also significantly accelerates the training process. + +The key innovation of our work lies in the use of learnable timescale parameters within the SSMs, enabling the model to adapt dynamically to different inference frequencies without necessitating multiple training cycles. This feature represents a substantial advancement over existing methods, which require retraining for different frequencies. + +The SSM-ViT model outperforms existing methods by $20\mathrm{mAP}$ at higher frequencies and exhibits a $33\%$ increase in training speed. Furthermore, our introduction of two novel strategies to counteract the aliasing effect (a crucial consideration in high-frequency deployment) further reinforces the model's suitability for real-world applications. 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In ICCV, pages 12846-12856, 2023. 2, 3, 6 \ No newline at end of file diff --git a/2024/State Space Models for Event Cameras/images.zip b/2024/State Space Models for Event Cameras/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..eb4d67c0fc6948b07a620e4909124df4d83f2c91 --- /dev/null +++ b/2024/State Space Models for Event Cameras/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:18eae2b6c3aadb3212f811b4b87d5fc58bf4b27d4225b9442f04167d59284d47 +size 446097 diff --git a/2024/State Space Models for Event Cameras/layout.json b/2024/State Space Models for Event Cameras/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ccc66b929a581da44e7b6fc92e38305e17fad242 --- /dev/null +++ b/2024/State Space Models for Event Cameras/layout.json @@ -0,0 +1,8397 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 176, + 103, + 419, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 176, + 103, + 419, + 121 + ], + "spans": [ + { + "bbox": [ + 176, + 103, + 419, + 121 + ], + "type": "text", + "content": "State Space Models for Event Cameras" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 136, + 143, + 457, + 173 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 136, + 143, + 457, + 173 + ], + "spans": [ + { + "bbox": [ + 136, + 143, + 457, + 173 + ], + "type": "text", + "content": "Nikola Zubić, Mathias Gehrig, Davide Scaramuzza \nRobotics and Perception Group, University of Zurich, Switzerland" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 47, + 185, + 239, + 385 + ], + "blocks": [ + { + "bbox": [ + 47, + 185, + 239, + 385 + ], + "lines": [ + { + "bbox": [ + 47, + 185, + 239, + 385 + ], + "spans": [ + { + "bbox": [ + 47, + 185, + 239, + 385 + ], + "type": "image", + "image_path": "b26124d083158f6234fcebdce73cd247470ebb0c06a28ed95ec2111a8d1b31de.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "lines": [ + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "spans": [ + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "type": "text", + "content": "Figure 1. Top-Left Previous works [12, 29] use RNN architectures with convolutional or attention mechanisms to train models that have superior performance on downstream tasks. However, the use of RNNs leads to slower training and the learned weights only generalize well to data deployed at the same frequency as that used at training time. Bottom-Left We solve this problem by utilizing SSMs for temporal aggregation, which enables faster training by either utilizing the S4 model [16] or S5 [36] parallel scans. By their nature, these models allow deployment at different frequencies than those used at training time since they have a learnable timescale parameter. Right Our SSM-based models achieve an average performance drop between training and testing frequencies of " + }, + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "type": "inline_equation", + "content": "3.31\\mathrm{mAP}" + }, + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "type": "text", + "content": " averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and " + }, + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "type": "inline_equation", + "content": "24.53\\mathrm{mAP}" + }, + { + "bbox": [ + 45, + 394, + 548, + 473 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 257, + 190, + 545, + 380 + ], + "blocks": [ + { + "bbox": [ + 257, + 190, + 545, + 380 + ], + "lines": [ + { + "bbox": [ + 257, + 190, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 257, + 190, + 545, + 380 + ], + "type": "image", + "image_path": "edd855e2bebae16a33dd0e16f441b312398a59212f60d78d85ad08cf4444faa7.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 482, + 192, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 482, + 192, + 495 + ], + "spans": [ + { + "bbox": [ + 143, + 482, + 192, + 495 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "type": "text", + "content": "Today, state-of-the-art deep neural networks that process event-camera data first convert a temporal window of events into dense, grid-like input representations. As such, they exhibit poor generalizability when deployed at higher inference frequencies (i.e., smaller temporal windows) than the ones they were trained on. We address this challenge by introducing state-space models (SSMs) with learnable timescale parameters to event-based vision. This design adapts to varying frequencies without the need to retrain the network at different frequencies. Additionally, we investigate two strategies to counteract aliasing effects when deploying the model at higher frequencies. We comprehensively evaluate our approach against existing methods based on RNN and Transformer architectures across various benchmarks, including Gen1 and 1 Mpx event camera datasets. Our results demonstrate that SSM-based models train " + }, + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 45, + 498, + 290, + 715 + ], + "type": "text", + "content": " faster and also exhibit minimal performance degradation when tested at higher frequencies than the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 483, + 548, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 483, + 548, + 531 + ], + "spans": [ + { + "bbox": [ + 305, + 483, + 548, + 531 + ], + "type": "text", + "content": "training input. Traditional RNN and Transformer models exhibit performance drops of more than 20 mAP, with SSMs having a drop of 3.31 mAP, highlighting the effectiveness of SSMs in event-based vision tasks." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 547, + 387, + 560 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 547, + 387, + 560 + ], + "spans": [ + { + "bbox": [ + 306, + 547, + 387, + 560 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Event cameras emerged as a class of sensor technologies that noticeably deviate from the operational mechanics of conventional frame-based cameras [9]. While standard frame-based cameras [42] capture full-frame luminance levels at fixed intervals, event cameras record per-pixel relative brightness changes in a scene at the time they occur. The output is, therefore, an asynchronous stream of events in a four-dimensional spatio-temporal space. Each event is represented by its spatial coordinates on the pixel array, the temporal instance of the occurrence, and its polarity, which denotes the direction of the brightness change and encapsulates the increase or decrease in luminance. The" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 38 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5819" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "power of event cameras primarily lies in their ability to capture dynamic scenes with unparalleled temporal resolution (microseconds). This property becomes invaluable in rapidly changing environments or applications requiring very fast response times [8, 39]. However, the richness of the spatio-temporal data they generate introduces complexities in data interpretation and processing. Sophisticated algorithms are required to efficiently parse and make sense of the high-dimensional data space. As such, while event cameras represent a promising frontier in visual sensor technologies, their pervasive utilization depends upon solving these inherent computational challenges." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 217, + 289, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 289, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 289, + 373 + ], + "type": "text", + "content": "Current methodologies for addressing problems with event cameras fall predominantly into two categories. The first involves converting the raw stream of spatio-temporal events into dense representations akin to multi-channel images [12, 22, 40, 43]. This transformation allows leveraging conventional computer vision techniques designed for frame-based data. The second category employs sparse computational paradigms, often utilizing spiking neural networks or graph-based architectures [4, 11]. While promising, these methods are not without limitations; they frequently encounter hardware incompatibility issues and compromised accuracy. In this work, we utilize dense representations for their advantages in computational efficiency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 373, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 289, + 495 + ], + "type": "text", + "content": "Despite the advances in both paradigms, models trained on event representations at a specific frequency exhibit poor generalizability when deployed in settings with higher frequencies which is crucial for high-speed, dynamical visual scenarios. Additionally, to achieve high performance, it is necessary to include recurrent memory, thereby sacrificing computational efficiency during the training phase. An ideal model would seamlessly merge the training speed of convolutional architectures with the temporal sensitivity and memory benefits inherent to recurrent models." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 494, + 289, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 494, + 289, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 494, + 289, + 555 + ], + "type": "text", + "content": "While recent advancements have introduced efficient recurrent vision transformer architectures [12, 24] to achieve better performance, they face several limitations. Specifically, these architectures suffer from longer training cycles due to their reliance on conventional recurrent mechanisms." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 555, + 289, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 289, + 640 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 289, + 640 + ], + "type": "text", + "content": "The issue of slow training and generalization at higher event representation frequency than the lower one we trained on remains unresolved as conventional recurrent training methodologies are predominantly utilized in event-based vision. These methods do not incorporate learnable timescale parameters, thus inhibiting the model's capacity to generalize across varying inference frequencies." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 640, + 289, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 640, + 289, + 677 + ], + "spans": [ + { + "bbox": [ + 47, + 640, + 289, + 677 + ], + "type": "text", + "content": "In this work, we address this limitation by introducing structured variations of state-space models [16, 36] as layers within our neural network framework." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 289, + 715 + ], + "type": "text", + "content": "State-space models [14] function as CNN during training and are converted to an efficient RNN at test time. To achieve this, S4 [16] employs a technique where the SSM," + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 253 + ], + "type": "text", + "content": "which is not practical for training on modern hardware due to its sequential nature, is transformed into a CNN by unrolling. S5 [36] uses parallel scans during training, and is employed as RNN during inference. State-space models [14] can be deployed at different frequencies at inference time because they are Linear Time-Invariant (LTI) continuous-time systems that can be transformed into a discrete-time system with an arbitrary step size. This feature permits inference at arbitrary frequencies by globally adjusting the timescale parameter based on the ratio between the new and old frequency sampling rates. Consequently, we tackle the longstanding issue in event-based vision, which requires multiple training cycles with different frequencies to adapt the neural network for various frequencies during inference." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "spans": [ + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "text", + "content": "For the task of object detection, we find that incorporating state-space layers accelerates the training by up to " + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "text", + "content": " relative to existing recurrent vision transformer approaches [12, 24]. This is achieved while maintaining performance comparable to existing methods. Notably, our approach demonstrates superior generalization to higher temporal frequencies with a drop of only " + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "inline_equation", + "content": "3.31\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "text", + "content": ", while previous methods experience a drop of " + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "inline_equation", + "content": "21.25\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "text", + "content": " or more. Also, we achieve comparable performance to RVT although we use a linear state-space model rather than a non-linear LSTM model. This also shows that the complexity of the LSTM might not be needed. For this to work, we introduce two strategies (frequency-selective masking and " + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 304, + 269, + 547, + 546 + ], + "type": "text", + "content": " norm) to counteract the aliasing effect encountered with increased temporal frequencies in event cameras. First one is a low-pass bandlimiting modification to SSM that encourages the learned convolutional kernels to be smooth. Second one mitigates the aliasing problem by attenuating the frequency response after a chosen frequency. We argue that state-space modeling offers a significant new direction for research in event-based vision, offering promising solutions to the challenges inherent in processing event-based data effectively and efficiently." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 562, + 528, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 562, + 528, + 574 + ], + "spans": [ + { + "bbox": [ + 318, + 562, + 528, + 574 + ], + "type": "text", + "content": "Our contributions are concisely outlined as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 591, + 545, + 711 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 306, + 591, + 545, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 591, + 545, + 651 + ], + "spans": [ + { + "bbox": [ + 306, + 591, + 545, + 651 + ], + "type": "text", + "content": "- We introduce state-space models for event cameras to address two key challenges in event-based vision: (i) model performance degradation when operating event cameras at temporal frequencies different from their training conditions and (ii) training efficiency." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "spans": [ + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "type": "text", + "content": "- Our experimental results outperform existing methods at higher frequencies by " + }, + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "type": "inline_equation", + "content": "20\\mathrm{mAP}" + }, + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "type": "text", + "content": " on average and show " + }, + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 306, + 651, + 545, + 687 + ], + "type": "text", + "content": " increase in the training speed." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "spans": [ + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "type": "text", + "content": "- We introduce two strategies (bandlimiting & " + }, + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 306, + 687, + 545, + 711 + ], + "type": "text", + "content": " norm) designed to alleviate aliasing issues." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "5820" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 71, + 134, + 83 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 246, + 104 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 91, + 246, + 104 + ], + "spans": [ + { + "bbox": [ + 47, + 91, + 246, + 104 + ], + "type": "text", + "content": "2.1. Object detection with Event Cameras" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 110, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 110, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 110, + 287, + 133 + ], + "type": "text", + "content": "Approaches in event camera literature, thus in object detection, can be broadly classified into two branches." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 134, + 287, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 134, + 287, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 134, + 287, + 386 + ], + "type": "text", + "content": "The first research branch investigates dense feed-forward methods. Early attempts in this direction relied on a constrained temporal window for generating event representations [3, 17, 19]. The resultant models were deficient in tracking slow-moving or stationary objects, as they failed to incorporate data beyond this limited time-frame. To mitigate these drawbacks, later studies introduced recurrent neural network (RNN) layers [29] into the architecture. The RNN component enhanced the model's capacity for temporal understanding, thereby improving its object detection capabilities. The work of Zubic et al. [43] takes this a step further by optimizing event representations and incorporating cutting-edge swim transformer architecture. Nonetheless, their approach was limited in its ability to re-detect slowly moving objects following extended periods of absence. Subsequent research [12, 24], merged the transformer and RNN architectures, pushing the performance further. However, this significantly increased computational demands during the training phase. Importantly, all methodologies examined to date suffer from an inability to adapt when deployed at variable frequencies." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 387, + 288, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 387, + 288, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 387, + 288, + 649 + ], + "type": "text", + "content": "The second research branch investigates the use of Graph Neural Networks (GNNs) or Spiking Neural Networks (SNNs). GNNs dynamically construct a spatiotemporal graph where new nodes and edges are instantiated by selectively sub-sampling events and identifying pre-existing nodes that are proximate in the space-time continuum [11, 18, 38]. A pivotal challenge lies in architecting the network such that information can disseminate effectively across extensive regions of the space-time volume. This becomes particularly important when dealing with large objects that exhibit slow relative motion to the camera. Moreover, while aggressive sub-sampling is often necessary to achieve low-latency inference, it introduces the risk of omitting important information from the event stream. On the other hand, SNNs [1, 6, 34] transmit information sparsely within the system. Unlike RNNs, SNNs emit spikes only when a threshold is met, making them hard to optimize due to the non-differentiable spike mechanism. Some solutions [27] bypass the threshold, but this sacrifices sparsity in deeper layers. Overall, SNNs remain a challenging area needing more foundational research for optimized performance." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 186, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 186, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 186, + 670 + ], + "type": "text", + "content": "2.2. Continuous-time Models" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "Gu et al. [16] introduced the S4 model as an alternative to CNNs and Transformers for capturing long-range dependencies through LTI systems. This was followed by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "the S4D model [15], designed for easier understanding and implementation, offering similar performance to S4. The S5 model [36] improved efficiency by avoiding frequency domain computations and utilizing time-domain parallel scans. However, these models have not been thoroughly evaluated on complex, high-dimensional visual data with significant temporal resolution." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 157, + 545, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 545, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 545, + 251 + ], + "type": "text", + "content": "In our study, we empirically show that S4, S4D and S5 models achieve results on-par with state-of-the-art when combined with attention mechanisms on complex data. We also identify and address aliasing issues in these models, proposing two corrective strategies. Our work extends the range and robustness of continuous-time models for complex sequence modeling tasks such as object detection for event cameras." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 261, + 362, + 274 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 261, + 362, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 261, + 362, + 274 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 281, + 545, + 376 + ], + "type": "text", + "content": "In this section, we firstly formalize the operating mechanism of event cameras and provide a notation used for describing state-space models in the preliminaries (Sec. 3.1). Secondly, we describe our approach of incorporating variants of state-space models as layers within our block (Sec. 3.2). This innovative design solves the problems associated with slow training and the variable frequency inference for event cameras." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 383, + 392, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 383, + 392, + 395 + ], + "spans": [ + { + "bbox": [ + 306, + 383, + 392, + 395 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": "Event cameras. Event cameras are bio-inspired vision sensors that capture changes in log intensity per pixel asynchronously, rather than capturing entire frames at fixed intervals. Formally, let " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "I(x,y,t)" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": " denote the log intensity at pixel coordinates " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "(x,y)" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": " and time " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": ". An event " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": " is generated at " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "(x,y,t)" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": " whenever the change in log intensity " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "\\Delta I" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": " exceeds a certain threshold " + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 304, + 402, + 545, + 485 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 330, + 492, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 492, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 330, + 492, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\Delta I (x, y, t) = I (x, y, t) - I (x, y, t - \\Delta t) \\geq C \\tag {1}", + "image_path": "a68a2f83ba4b31aa98ef11dcf6351eb6da26da21afaab0e0824dec4d564bebe1.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "content": "Each event " + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "inline_equation", + "content": "e" + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "content": " is a tuple " + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "inline_equation", + "content": "(x, y, t, p)" + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "inline_equation", + "content": "(x, y)" + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "content": " are the pixel coordinates, " + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "content": " is the timestamp, and " + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "inline_equation", + "content": "p = \\{-1, 1\\}" + }, + { + "bbox": [ + 304, + 511, + 545, + 559 + ], + "type": "text", + "content": " is the polarity of the event, indicating the direction of the intensity change." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "content": "State-Space Models (SSMs). Linear State-Space Models (SSMs) form the crucial part of the backbone in our architecture, where we compare S4 [16], S4D [15] and S5 [36] layer variants. Given an input vector " + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{u}(t) \\in \\mathbb{R}^U" + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "content": ", a latent state vector " + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{x}(t) \\in \\mathbb{R}^P" + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "content": ", and an output vector " + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "inline_equation", + "content": "\\mathbf{y}(t) \\in \\mathbb{R}^M" + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "content": ", the governing equations of a continuous-time linear SSM can be mathematically represented as:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 312, + 649, + 545, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 649, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 312, + 649, + 545, + 673 + ], + "type": "interline_equation", + "content": "\\frac {\\mathrm {d} \\mathbf {x} (t)}{\\mathrm {d} t} = \\mathbf {A} \\mathbf {x} (t) + \\mathbf {B} \\mathbf {u} (t), \\quad \\mathbf {y} (t) = \\mathbf {C} \\mathbf {x} (t) + \\mathbf {D} \\mathbf {u} (t), \\tag {2}", + "image_path": "b22937a89536615aa2667423aa1c705ab792f907b173ed23fc92fabaa93760cc.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "The model is parameterized by a state transition matrix " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{P \\times P}" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": ", an input matrix " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{B} \\in \\mathbb{R}^{P \\times U}" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": ", an output matrix " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{C} \\in \\mathbb{R}^{M \\times P}" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": ", and a direct transmission matrix " + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\in \\mathbb{R}^{M \\times U}" + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "5821" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": "Given a fixed step size " + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 47, + 72, + 287, + 107 + ], + "type": "text", + "content": ", this continuous-time model can be discretized into a linear recurrence using various methods such as Euler, bilinear, or zero-order hold (ZOH):" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 66, + 117, + 287, + 131 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 66, + 117, + 287, + 131 + ], + "spans": [ + { + "bbox": [ + 66, + 117, + 287, + 131 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {k} = \\overline {{\\mathbf {A}}} \\mathbf {x} _ {k - 1} + \\overline {{\\mathbf {B}}} \\mathbf {u} _ {k}, \\quad \\mathbf {y} _ {k} = \\overline {{\\mathbf {C}}} \\mathbf {x} _ {k} + \\overline {{\\mathbf {D}}} \\mathbf {u} _ {k}, \\tag {3}", + "image_path": "f92e5c8df2a36c81b0c651a984ece04a8ad738a2b72532731ada07df3fb620c4.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 287, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 187 + ], + "type": "text", + "content": "The parameters in the discrete-time model are functions of the continuous-time parameters, defined by the chosen discretization method. Details on SSMs are available in the appendix." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 203, + 286, + 277 + ], + "blocks": [ + { + "bbox": [ + 50, + 203, + 286, + 277 + ], + "lines": [ + { + "bbox": [ + 50, + 203, + 286, + 277 + ], + "spans": [ + { + "bbox": [ + 50, + 203, + 286, + 277 + ], + "type": "image", + "image_path": "ac8e807a07578454697f8b983da8958522d23d15c4d4aaf8597162287003a6ec.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 99, + 286, + 235, + 297 + ], + "lines": [ + { + "bbox": [ + 99, + 286, + 235, + 297 + ], + "spans": [ + { + "bbox": [ + 99, + 286, + 235, + 297 + ], + "type": "text", + "content": "Figure 2. SSM-ViT block structure" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 312, + 141, + 323 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 312, + 141, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 312, + 141, + 323 + ], + "type": "text", + "content": "3.2. SSM-ViT block" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 331, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 331, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 47, + 331, + 287, + 378 + ], + "type": "text", + "content": "In this section, we introduce the SSM-ViT block, a novel block depicted in Figure 2, which showcases the structured flow of the proposed block structure, designed for efficient event-based information processing." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 379, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 498 + ], + "type": "text", + "content": "We build a 4-stage hierarchical backbone like in [12] where in each stage we utilize our proposed SSM-ViT block. Events are processed into a tensor representation like in [12] before they are used as input to the first stage. Each stage takes the previous features as input and reuses the SSM state from the last timestep to compute features for the next stage. By saving SSM states, each stage retains temporal information for the whole feature map, while also being able to generalize to different frequencies since we use SSM instead of RNN that is used in [12]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "content": "Regarding the block structure, initially, the input undergoes convolution with a defined kernel of size " + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "inline_equation", + "content": "k \\times k" + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "content": " with a stride " + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "inline_equation", + "content": "s" + }, + { + "bbox": [ + 46, + 498, + 287, + 617 + ], + "type": "text", + "content": ". This operation effectively captures the essential spatial features of the input. Following the convolution operation, the structure introduces a 'Block-SA' module. This module is pivotal in implementing self-attention mechanisms, but it does so specifically within local windows. The localized nature of the attention in this block ensures a focus on immediate spatial relations, allowing for a detailed representation of close-proximity features." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 617, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 689 + ], + "type": "text", + "content": "Subsequent to 'Block-SA', the 'Grid-SA' module comes into play. In contrast to the localized approach of the previous block, 'Grid-SA' employs dilated attention, ensuring a global perspective. This module, by considering a broader scope, encapsulates a more comprehensive understanding of the spatial relations and the overall structure of the input." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The final and crucial component of the block structure is the State-Space Model (SSM) block, that is designed to" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 168 + ], + "type": "text", + "content": "compute both the output and the state in parallel, either by using S4 [16], S4D [15] or S5 [36] model variant. This ensures temporal consistency and a seamless transition of information between consecutive time steps. Efficient computation is crucial since it allows for the faster training than RNN, and timescale parameter on temporal aggregation is important since we can rescale it during inference and deploy at any frequency we want." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 175, + 436, + 188 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 175, + 436, + 188 + ], + "spans": [ + { + "bbox": [ + 306, + 175, + 436, + 188 + ], + "type": "text", + "content": "3.3. Low-pass bandlimiting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 194, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 194, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 194, + 545, + 277 + ], + "type": "text", + "content": "However, the capability to deploy state space models at resolutions higher than those encountered during training is not without its drawbacks. It gives rise to the well-documented issue of aliasing [32, 33], which occurs when the kernel bandwidth surpasses the Nyquist frequency. We adress this challenge in following two subsections - 3.3.1 & 3.3.2." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 288, + 410, + 300 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 288, + 410, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 288, + 410, + 300 + ], + "type": "text", + "content": "3.3.1 Output Masking" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 307, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 403 + ], + "type": "text", + "content": "In the realm of signal processing, frequency content beyond the Nyquist rate can lead to aliasing, adversely affecting model performance. To address this, we integrate a frequency-selective masking strategy into the training and inference processes. This bandlimiting method has been empirically validated to be crucial for generalizing across different frequencies [32, 33], with ablation studies indicating a decrease in accuracy by as much as " + }, + { + "bbox": [ + 304, + 307, + 545, + 403 + ], + "type": "inline_equation", + "content": "20\\%" + }, + { + "bbox": [ + 304, + 307, + 545, + 403 + ], + "type": "text", + "content": " in its absence." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": "Let the SSM be governed by a matrix " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": ", with its diagonal elements " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "a_{n}" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": " influencing the temporal evolution of the system states. The kernel's basis function for the " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": "-th state is given by " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "K_{n}(t) = e^{ta_{n}}B_{n}" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": ", where the frequency characteristics are primarily dictated by the imaginary part of " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "a_{n} - \\Im(a_{n})" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "B_{n}" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": " represents the " + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 403, + 545, + 474 + ], + "type": "text", + "content": " matrix." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "text", + "content": "To modulate the frequency spectrum of the model, we define a hyperparameter " + }, + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "text", + "content": ", which is used for masking of the computed effective frequency " + }, + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "inline_equation", + "content": "f_{n}" + }, + { + "bbox": [ + 304, + 475, + 545, + 510 + ], + "type": "text", + "content": " for each state:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 383, + 519, + 545, + 543 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 519, + 545, + 543 + ], + "spans": [ + { + "bbox": [ + 383, + 519, + 545, + 543 + ], + "type": "interline_equation", + "content": "f _ {n} = \\frac {\\Delta t}{r} \\cdot \\frac {| \\Im (a _ {n}) |}{2 \\pi}, \\tag {4}", + "image_path": "915d706cd8f34cb80933af3b183c0708c4b7173a97f78f4987a8c46fb7dd4f6f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "spans": [ + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "type": "text", + "content": " denotes the discrete time-step, and " + }, + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 551, + 545, + 586 + ], + "type": "text", + "content": " is the rate at which we train the model, by default it is 1, rate gets halved when deploying at twice the trained frequency etc." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 317, + 586, + 519, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 586, + 519, + 598 + ], + "spans": [ + { + "bbox": [ + 317, + 586, + 519, + 598 + ], + "type": "text", + "content": "The bandlimiting mask is then applied as follows:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 369, + 607, + 545, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 607, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 369, + 607, + 545, + 633 + ], + "type": "interline_equation", + "content": "C _ {n} = \\left\\{ \\begin{array}{l l} C _ {n} & \\text {i f} f _ {n} \\leq \\frac {\\alpha}{2}, \\\\ 0 & \\text {o t h e r w i s e}, \\end{array} \\right. \\tag {5}", + "image_path": "2f3c7984acf588d85ab73e23123c1c2345a35d688cf4713edc49120379d334ec.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "C_n" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " represents the coefficients in the state representation. The selection of " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " is critical, with " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha = 1.0" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " representing the Nyquist limit under idealized conditions. However, practical considerations and model constraints typically necessitate a lower empirical threshold. Our findings suggest that setting " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " yields optimal outcomes for systems" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5822" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 95 + ], + "type": "text", + "content": "with diagonal state matrices, such as in S4D and S5 configurations." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 96, + 286, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 96, + 286, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 96, + 286, + 133 + ], + "type": "text", + "content": "This frequency-selective masking is proven to be a cornerstone for the adaptability of our SSMs, significantly contributing to their generalization across differing frequencies." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 146, + 119, + 158 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 146, + 119, + 158 + ], + "spans": [ + { + "bbox": [ + 47, + 146, + 119, + 158 + ], + "type": "text", + "content": "3.3.2 " + }, + { + "bbox": [ + 47, + 146, + 119, + 158 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_2" + }, + { + "bbox": [ + 47, + 146, + 119, + 158 + ], + "type": "text", + "content": " Norm" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 165, + 286, + 213 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 165, + 286, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 165, + 286, + 213 + ], + "type": "text", + "content": "This section introduces another strategy to mitigate the aliasing problem by suppressing the frequency response of the continuous-time state-space model beyond a selected frequency " + }, + { + "bbox": [ + 47, + 165, + 286, + 213 + ], + "type": "inline_equation", + "content": "\\omega_{\\mathrm{min}}" + }, + { + "bbox": [ + 47, + 165, + 286, + 213 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 213, + 286, + 260 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 213, + 286, + 260 + ], + "spans": [ + { + "bbox": [ + 47, + 213, + 286, + 260 + ], + "type": "text", + "content": "This approach makes use of the " + }, + { + "bbox": [ + 47, + 213, + 286, + 260 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 47, + 213, + 286, + 260 + ], + "type": "text", + "content": " norm of a continuous-time linear system which measures the power (or steady-state covariance) of the output response to unit white-noise input." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "text", + "content": "Given a continuous-time system described by matrices " + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{B}" + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "text", + "content": ", the transfer function " + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "inline_equation", + "content": "\\mathbf{G}(s)" + }, + { + "bbox": [ + 47, + 261, + 286, + 297 + ], + "type": "text", + "content": " from the Laplace transform can be defined in the frequency domain as:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 107, + 307, + 286, + 321 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 307, + 286, + 321 + ], + "spans": [ + { + "bbox": [ + 107, + 307, + 286, + 321 + ], + "type": "interline_equation", + "content": "\\mathbf {G} (j \\omega) = \\mathbf {C} (j \\omega \\mathbf {I} - \\mathbf {A}) ^ {- 1} \\mathbf {B}, \\tag {6}", + "image_path": "7a8a96d56cddfdc41f760fbc1ee24c9981fb7046145a378cdb6e85022ab87fe8.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "inline_equation", + "content": "\\omega" + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "text", + "content": " denotes the frequency, and " + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "inline_equation", + "content": "\\mathbf{I}" + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "text", + "content": " is the identity matrix. The " + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "text", + "content": " norm is computed as the integral of the squared magnitude of the frequency response over the range of interest, typically the entire frequency spectrum. However, in our case, we would like to suppress the frequency response of the system to frequencies beyond " + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "inline_equation", + "content": "\\omega_{\\mathrm{min}}" + }, + { + "bbox": [ + 46, + 325, + 286, + 408 + ], + "type": "text", + "content": " which can be done by minimizing the following:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 75, + 424, + 286, + 456 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 424, + 286, + 456 + ], + "spans": [ + { + "bbox": [ + 75, + 424, + 286, + 456 + ], + "type": "interline_equation", + "content": "\\left\\| \\mathbf {G} \\right\\| _ {H _ {2} \\left(\\omega_ {\\min }, \\infty\\right)} = \\sqrt {\\frac {1}{\\pi} \\int_ {\\omega_ {\\min }} ^ {\\infty} \\left\\| \\mathbf {G} \\left(j \\omega_ {k}\\right) \\right\\| _ {F} ^ {2} d \\omega}, \\tag {7}", + "image_path": "a14e51e50640a6f287aae1d10508cc14fa0026f10d488c95a37bb451a0829fa7.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "spans": [ + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": "as part of the loss function, where " + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\| _F" + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": " is the Frobenius norm. In practice, to numerically estimate this integral, we choose a maximum frequency " + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "inline_equation", + "content": "\\omega_{\\mathrm{max}}" + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": " and discretize the frequency range " + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "inline_equation", + "content": "[\\omega_{\\mathrm{min}},\\omega_{\\mathrm{max}}]" + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": " points and apply numerical integration methods to the squared Frobenius norm of " + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "inline_equation", + "content": "\\mathbf{G}(j\\omega)" + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": ". This yields an approximate " + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 463, + 286, + 547 + ], + "type": "text", + "content": " norm of the system in the desired frequency range." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 552, + 127, + 565 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 552, + 127, + 565 + ], + "spans": [ + { + "bbox": [ + 47, + 552, + 127, + 565 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 572, + 286, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 286, + 715 + ], + "type": "text", + "content": "We perform ablation studies and systematic evaluations of our proposed models utilizing both the Gen1 [7] and 1 Mpx [29] event-based camera datasets. We assess the model's proficiency in adapting to unseen inference frequencies during training time on both datasets. We employed two variants for training across both datasets: the base model ViT-SSM-B, alongside its scaled-down derivative ViT-SSM-S (small). Additionally, to study the robustness and generalization capabilities of our architecture, we subject it to empirical testing on the DSEC dataset [13], which was not part of the original training corpus and the visual results are provided in the appendix." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 72, + 356, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 356, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 356, + 84 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "content": "Implementation details. Our models are trained using 32-bit precision arithmetic across 400k iterations, making use of the ADAM optimizer [20] and a OneCycle learning rate schedule [37] that decays linearly from its highest value. We adopt a mixed batching technique that applies standard Backpropagation Through Time (BPTT) to half of the batch samples and Truncated BPTT (TBPTT) to the other half. This technique was introduced in the RVT [12] and ablated in their supplementary material. We found it to be equally effective also for SSMs. For the S4(D) method, details can be found in [15, 16]. As for S5 [36], we utilize an efficient implementation from scratch in PyTorch; original public version of S5 is available in JAX. Data augmentation is carried out through random horizontal flips and zooming operations, both inward and outward. Event representations are formed based on " + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "inline_equation", + "content": "50~\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "content": " time windows that correspond to " + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "inline_equation", + "content": "20\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "content": " sampling frequency, divided into " + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\mathrm{T} = 10" + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "content": " discrete bins. We incorporate a YOLOX detection head [10] that integrates IOU, class, and regression losses, averaged across both batch and sequence lengths during each optimization phase. Bandlimiting is implemented during training and inference of the SSM model by masking the output matrix " + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "content": " as explained in 3.3.1. In case of " + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 304, + 90, + 545, + 447 + ], + "type": "text", + "content": " norm, we add it as term to the loss function of the model. We conduct training on the GEN1 dataset using A100 GPU, employing a batch size of 8 and a sequence length of 21. We use a global learning rate of 2e-4, which is propagated to the SSM components. For the 1 Mpx dataset, we train with a batch size of 12 and a sequence length of 10, using a learning rate of 3.5e-4 across two A100 GPUs." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": "Datasets. The Gen1 Automotive Detection dataset [7] comprises 39 hours of event camera footage with a resolution of " + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "inline_equation", + "content": "304 \\times 240" + }, + { + "bbox": [ + 304, + 449, + 545, + 520 + ], + "type": "text", + "content": " pixels. It includes 228k bounding boxes for cars and 28k for pedestrians. Using original evaluation criteria [7], we discard bounding boxes having a side length shorter than 10 pixels or a diagonal less than 30 pixels." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "text", + "content": "The 1 Mpx dataset [29] similarly focuses on driving environments but offers recordings at a higher resolution of " + }, + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "inline_equation", + "content": "720 \\times 1280" + }, + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "text", + "content": " pixels, captured over multiple months during both day-time and night-time. It contains roughly 15 hours of event data and accumulates around 25 million bounding box labels, spread across three classes: cars, pedestrians, and two-wheelers. Following original evaluation criteria, we eliminate bounding boxes with a side length under 20 pixels and a diagonal less than 60 pixels, while also reducing the input resolution to " + }, + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "inline_equation", + "content": "640 \\times 360" + }, + { + "bbox": [ + 304, + 521, + 545, + 640 + ], + "type": "text", + "content": " pixels." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 647, + 444, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 444, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 444, + 659 + ], + "type": "text", + "content": "4.2. Benchmark comparisons" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 545, + 713 + ], + "type": "text", + "content": "In this section, we present a detailed comparison of our proposed methods, S4D-ViT-B and S5-ViT-B, with the SotA approaches in the domain of event-based vision for object detection, which can be seen in Table 1. The evalua" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5823" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 541, + 297 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 541, + 297 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 541, + 297 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 541, + 297 + ], + "type": "table", + "html": "
MethodBackboneDetection HeadGen11 MpxParams (M)
mAPTime (ms)mAPTime (ms)
Asynet [27]Sparse CNNYOLOv1 [31]14.5---11.4
AEGNN [35]GNNYOLOv116.3---20.0
Spiking DenseNet [5]SNNSSD [23]18.9---8.2
Inception + SSD [17]CNNSSD30.119.434.045.2>60*
RRC-Events [3]CNNYOLOv3 [30]30.721.534.346.4>100*
MatrixLSTM [2]RNN + CNNYOLOv331.0---61.5
YOLOv3 Events [19]CNNYOLOv331.222.334.649.4>60*
RED [29]CNN + RNNSSD40.016.743.039.324.1
ERGO-12 [43]TransformerYOLOv6 [21]50.469.940.6100.059.6
RVT-B [12]Transformer + RNNYOLOX [10]47.210.247.411.918.5
Swin-T v2 [25]Transformer + RNNYOLOX45.526.646.434.521.1
Nested-T [28, 41]Transformer + RNNYOLOX46.325.946.033.522.2
GET-T [28]Transformer + RNNYOLOX47.916.848.418.221.9
S4D-ViT-B (ours)Transformer + SSMYOLOX46.29.4046.810.916.5
S5-ViT-B (ours)Transformer + SSMYOLOX47.48.1647.29.5718.2
", + "image_path": "39646e48a601e53a94100fb4bbf3b2c70a90d1573349b9647f04e7a5cf2571d0.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 370, + 287, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 370, + 287, + 407 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 287, + 407 + ], + "type": "text", + "content": "tion is conducted on two distinct datasets: Gen1 and 1 Mpx, to assess the performance and robustness of these methods under varying conditions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 408, + 287, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 408, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 408, + 287, + 456 + ], + "type": "text", + "content": "The comparative analysis, as summarized in Table 1, encompasses different backbones and detection heads. These include Sparse CNNs, GNNs, SNNs, RNNs, and various implementations of Transformers." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 457, + 287, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 457, + 287, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 457, + 287, + 578 + ], + "type": "text", + "content": "Our S4D-ViT-B and S5-ViT-B models, which integrate SSMs with Attention (3.2), demonstrate competitive performance across both datasets. Specifically, on the 1 Mpx dataset, our models achieve mAP scores of 46.8 and 47.2, respectively, which are competitive with the leading scores in this benchmark. While our models do not outperform the top-performing ERGO-12 [43] and GET-T [28] in terms of mAP, they exhibit a notable balance between accuracy and model complexity, as indicated by their parameter counts of 16.5M and 17.5M, respectively." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "spans": [ + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "type": "text", + "content": "Notably, our models perform consistently well across different frequencies as it can be seen in Table 2, highlighting their robustness and generalizability in comparison to RVT and GET-T, which tend to exhibit large performance drops. We achieve an average performance drop between training and testing frequencies of " + }, + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "type": "inline_equation", + "content": "3.31\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "type": "text", + "content": " averaged on both Gen1 [7] and 1 Mpx [29] datasets, while RVT [12] and GET [28] have a drop of 21.25 and " + }, + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "type": "inline_equation", + "content": "24.53\\mathrm{mAP}" + }, + { + "bbox": [ + 46, + 579, + 287, + 676 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "In summary, our proposed S4D-ViT-B and S5-ViT-B models establish themselves as effective and efficient contenders in the field of event-based vision for object detec" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 370, + 545, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 370, + 545, + 418 + ], + "spans": [ + { + "bbox": [ + 304, + 370, + 545, + 418 + ], + "type": "text", + "content": "tion. Their competitive performance metrics, coupled with their generalization capabilities across various inference frequencies, make them valuable contributions to event-based vision community." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 308, + 427, + 545, + 509 + ], + "blocks": [ + { + "bbox": [ + 46, + 304, + 546, + 350 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 546, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 546, + 350 + ], + "type": "text", + "content": "Table 1. Comparisons on test sets of Gen1 and 1 Mpx datasets (20 Hz). Best results in bold and second best underlined. A star * suggests that this information was not directly available and estimated based on the publications. Runtime is measured in milliseconds for a batch size of 1. We used a T4 GPU for SSM-ViT to compare against indicated timings in prior work [29] on comparable GPUs (Titan Xp). Ours achieves comparable results with other SotA approaches and generalizes well to other frequencies where others fail." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 427, + 545, + 509 + ], + "lines": [ + { + "bbox": [ + 308, + 427, + 545, + 509 + ], + "spans": [ + { + "bbox": [ + 308, + 427, + 545, + 509 + ], + "type": "table", + "html": "
ModelDatasetFrequency Evaluation (Hz)Perf. Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVTGen147.1635.1321.9818.618.3526.14
1Mpx47.4042.5133.2030.2918.1516.36
S5Gen147.4046.4445.0842.4939.843.94
1Mpx47.2046.4946.1145.8039.702.68
GETGen147.9034.1519.9715.135.3529.25
1Mpx48.4040.5130.3028.1115.4419.81
", + "image_path": "b556197dd6618e3f06602b99b5862f5f9bd8fc5ffc4f5948ee37ee863f15f805.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 516, + 545, + 538 + ], + "lines": [ + { + "bbox": [ + 304, + 516, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 545, + 538 + ], + "type": "text", + "content": "Table 2. Evaluation of RVT [12], S5 [36], and GET [28] across different frequencies on test datasets" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 541, + 398, + 554 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 541, + 398, + 554 + ], + "spans": [ + { + "bbox": [ + 306, + 541, + 398, + 554 + ], + "type": "text", + "content": "4.3. Ablation study" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 545, + 643 + ], + "type": "text", + "content": "In this section we investigate different SSMs and their initializations with and without bandlimiting parameter for event-based vision to address the problem of inference at different frequencies (4.3.1). After that, we study the importance of SSM layers in various stages during training of the model (4.3.2). Finally, we evaluate models on differing frequencies with two proposed strategies (4.3.3)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 647, + 496, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 647, + 496, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 647, + 496, + 658 + ], + "type": "text", + "content": "4.3.1 SSMs: initializations & bandlimiting" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "This section presents an ablation study focusing on the performance impact of various SSM variants and their initialization strategies in conjunction with the bandlimiting parameter " + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": ". The SSM variants under consideration are S4" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5824" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 60, + 70, + 276, + 182 + ], + "blocks": [ + { + "bbox": [ + 60, + 70, + 276, + 182 + ], + "lines": [ + { + "bbox": [ + 60, + 70, + 276, + 182 + ], + "spans": [ + { + "bbox": [ + 60, + 70, + 276, + 182 + ], + "type": "table", + "html": "
ModelMean Average Precision - mAP val
α = 0α = 0.5α = 1Average
S4-legS46.66--46.66
S4D-legS46.9347.3346.5046.92
S4D-inv46.1546.2346.1146.16
S4D-lin44.8246.0245.0445.29
S5-legS48.3348.4848.0048.27
S5-inv47.2647.4346.9847.22
S5-lin46.1246.4045.5946.04
", + "image_path": "246b6b269726701210b448ecf005ec10657abdcb289be44664379223c2257a1a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "text", + "content": "[16], S4D [15], and the more recent S5 [36]. The analysis is conducted on the Gen1 [7] validation dataset, with the mean Average Precision (mAP) serving as the performance metric. Table 3 provides a comprehensive view of how different initialization strategies (legS, inv, lin) introduced in [15] and values of " + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "inline_equation", + "content": "\\alpha \\in \\{0,0.5,1\\}" + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "text", + "content": " influence model performance. The S4-legS model, not equipped for bandlimiting in non-diagonal matrix scenarios, achieves a baseline mAP of 46.66 at " + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "inline_equation", + "content": "\\alpha = 0" + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "text", + "content": ". The S4D variants demonstrate a diverse performance spectrum. The S4D-legS variant, particularly at " + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "text", + "content": ", achieves the highest mAP of 47.33 among the S4D models, also maintaining the best average mAP of 46.92. The S4D-inv and S4D-lin variants show less favorable outcomes, with mAPs peaking at 46.23 and 46.02, respectively, for " + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 246, + 286, + 425 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": "Notably, the S5 model variants exhibit an improvement over their predecessors. The S5-legS variant achieves the highest mAP of 48.48 at " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": ", and also records the best average mAP of 48.27. This result is not only the best in its category but also the best overall. The S5-inv and S5-ln models also demonstrate comparable performance, with the former reaching its peak mAP of 47.43 at " + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 426, + 286, + 510 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "spans": [ + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "type": "text", + "content": "This study emphasizes the critical role of initialization strategies and bandlimiting in optimizing SSM-based neural networks for event-based vision tasks. The distinct performance variations across different models and configurations underscore the importance of selecting appropriate initializations and " + }, + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "type": "text", + "content": " values, as these choices impact the efficacy of the models in handling the dynamic and complex nature of event-based vision data. Higher values of parameter " + }, + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 511, + 286, + 630 + ], + "type": "text", + "content": " encourage SSM to learn smoother kernels and discard more complex and higher-frequency convolution kernels." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 645, + 186, + 657 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 186, + 657 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 186, + 657 + ], + "type": "text", + "content": "4.3.2 SSM Utilization Analysis" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "In this ablation study, we examine the impact of employing temporal recurrence exclusively in a subset of network stages, or not using it at all. Our methodology involves manipulating the SSMs within the network by resetting their" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "text", + "content": "states at predetermined stages during each timestep. This approach enables us to isolate and evaluate the impact of SSM layers' presence or absence while maintaining a consistent parameter count across different model configurations." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 140, + 545, + 216 + ], + "blocks": [ + { + "bbox": [ + 46, + 190, + 287, + 223 + ], + "lines": [ + { + "bbox": [ + 46, + 190, + 287, + 223 + ], + "spans": [ + { + "bbox": [ + 46, + 190, + 287, + 223 + ], + "type": "text", + "content": "Table 3. Performance comparison between the S4 [16], S4D [15] and S5 [36] models for different values of " + }, + { + "bbox": [ + 46, + 190, + 287, + 223 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 190, + 287, + 223 + ], + "type": "text", + "content": " and initializations on Gen1 [7] validation dataset." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 140, + 545, + 216 + ], + "lines": [ + { + "bbox": [ + 307, + 140, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 307, + 140, + 545, + 216 + ], + "type": "table", + "html": "
S1S2S3S4mAPRVTmAPS4D5mAPS5
33.9039.9943.67
✓41.6843.1146.10
✓✓46.1045.3347.52
✓✓✓48.8247.0248.41
✓✓✓✓49.5247.3348.48
", + "image_path": "e3471fa7215e4af192415cc920e892919caf14dc5171ec09fd50f277c0cfae7b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 307, + 224, + 543, + 235 + ], + "lines": [ + { + "bbox": [ + 307, + 224, + 543, + 235 + ], + "spans": [ + { + "bbox": [ + 307, + 224, + 543, + 235 + ], + "type": "text", + "content": "Table 4. SSM contribution in various stages on the Gen1 dataset." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "spans": [ + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "text", + "content": "Table 4 shows the outcomes of these manipulations on the Gen1 validation dataset. " + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "inline_equation", + "content": "S4D_{.5}" + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "text", + "content": " represents S4D model, and " + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "inline_equation", + "content": "S5_{.5}" + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "text", + "content": " is S5 model with " + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 304, + 251, + 545, + 514 + ], + "type": "text", + "content": ". The data clearly indicate that the complete removal of SSMs from the network leads to a highest decrease in detection performance. This underscores the pivotal role of SSMs in enhancing the model's capability. On the other hand, initiating the use of SSMs from the fourth stage onwards consistently enhances performance, suggesting a critical threshold for the impact of temporal information processing in the later stages of the network. Another intriguing observation is the performance boost obtained by incorporating an SSM at the very initial stage. This suggests that the early integration of temporal information is also beneficial for the overall detection performance. As a result of these findings, our preferred configuration includes the SSM component right from the initial stage, thereby leveraging the advantages of temporal information processing throughout the entire network. Noteworthy is the observation that the performance drop when employing SSMs is less pronounced than with RVT, suggesting our approach's superior robustness to temporal aggregation from certain stages compared to RVT." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 521, + 487, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 487, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 487, + 533 + ], + "type": "text", + "content": "4.3.3 Evaluation at different frequencies" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": "In this section, we delve into the comparative performance analysis of three models: RVT [12], S4D [15], and S5 [36], across various frequency ranges. This evaluation is crucial in determining the robustness and adaptability of these models under diverse inference frequencies, specifically at " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "20\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "40\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "80\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "100\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "200\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": ". Our model is trained with event representations formed based on " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "50\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": " time windows that correspond to " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "20\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": " sampling frequency. Evaluation is done at this frequency, and others above mentioned. With RVT, there are no changes when evaluating at different frequencies, while with SSMs rate " + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 304, + 534, + 545, + 676 + ], + "type": "text", + "content": " is halved for the double the inference frequency etc." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Each model in Table 5 is assessed across datasets and model sizes, including Gen1 " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\text{Base}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ", Gen1 " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\text{Small}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ", and 1 " + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\text{Mpx}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\text{Base}" + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": ". Base and Small represent two variants of mod" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5825" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 77, + 69, + 516, + 277 + ], + "blocks": [ + { + "bbox": [ + 77, + 69, + 516, + 277 + ], + "lines": [ + { + "bbox": [ + 77, + 69, + 516, + 277 + ], + "spans": [ + { + "bbox": [ + 77, + 69, + 516, + 277 + ], + "type": "table", + "html": "
ModelDataset/SizeStrategyFrequency Evaluation (Hz)Performance Drop
20 Hz40 Hz80 Hz100 Hz200 Hz
RVT [12]Gen1Base-49.5237.1623.2519.367.8327.62
Gen1Small-48.6835.2819.9516.055.7529.42
1MpxBase-45.9540.9331.7029.0018.1616.00
S4D [15]Gen1BaseH2norm46.8345.9843.9140.1036.115.31
α = 0.547.3346.3644.5140.0235.985.61
Gen1SmallH2norm45.8845.1141.0538.0034.056.33
α = 0.546.3045.2142.1138.6133.006.57
1MpxBaseH2norm46.6645.8543.3341.8037.014.66
α = 0.547.9346.7844.5641.1136.185.77
S5 [36]Gen1BaseH2norm48.6047.1146.0643.8040.514.23
α = 0.548.4847.3446.1143.2340.034.30
Gen1SmallH2norm47.3346.3244.0341.1238.984.72
α = 0.547.8346.5844.4641.1138.955.06
1MpxBaseH2norm48.6547.5347.1146.6340.913.11
α = 0.548.3547.6047.2146.5040.802.82
", + "image_path": "f6c97f1d689a3479fe21d0acdc7a8b7e6b0e1d3480c1e4140c82e7bd4c1d0c61.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 129, + 285, + 462, + 298 + ], + "lines": [ + { + "bbox": [ + 129, + 285, + 462, + 298 + ], + "spans": [ + { + "bbox": [ + 129, + 285, + 462, + 298 + ], + "type": "text", + "content": "Table 5. Evaluation of RVT, S4D, and S5 across different frequencies on validation datasets" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "spans": [ + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "text", + "content": "els on the Gen1 and 1 Mpx datasets, the base one being the larger one with 16.5M parameters for the S4D model and 18.2M parameters for the S5 model (as presented in Table 1 parameters' column), and small one with 8.8M parameters for S4D and 9.7M parameters for S5 model. The focal point of this analysis is the performance drop, calculated as the average difference between the original performance at " + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "inline_equation", + "content": "20\\mathrm{Hz}" + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "text", + "content": " and performances at higher frequencies. A notable aspect of this study is the inherent advantage of the S4D and S5 models due to their incorporation of a learnable timescale parameter. This significantly enhances their adaptability, allowing them to dynamically adjust to varying frequencies. This feature is particularly salient in the S4D and S5 models, which are further analyzed based on different operational strategies: the " + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "text", + "content": " norm and bandlimiting with " + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 318, + 287, + 534 + ], + "type": "text", + "content": ". The inclusion of the learnable timescale parameter in these models underscores their capability to maintain performance across a wide range of frequencies." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "content": "The analysis reveals that both the " + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "content": " norm and bandlimiting strategies with " + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\alpha = 0.5" + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "content": " offer comparable performance across the assessed frequency ranges. However, a slight edge is observed with the " + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "content": " norm, particularly at very high frequencies. This marginal superiority can be attributed to the fact that " + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "content": " norm approach does not explicitly mask output's " + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "inline_equation", + "content": "(C)" + }, + { + "bbox": [ + 46, + 535, + 287, + 619 + ], + "type": "text", + "content": " matrix columns." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 620, + 287, + 644 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 287, + 644 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 287, + 644 + ], + "type": "text", + "content": "In the Appendix, we study pure-SSM and SSM models in combination with ConvNext [26]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 655, + 119, + 668 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 655, + 119, + 668 + ], + "spans": [ + { + "bbox": [ + 47, + 655, + 119, + 668 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 715 + ], + "type": "text", + "content": "In this paper, we presented a novel approach for enhancing the adaptability and training efficiency of models designed for event-based vision, particularly in object detec" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 318, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 318, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 304, + 318, + 545, + 392 + ], + "type": "text", + "content": "tion tasks. Our methodology leverages the integration of SSMs with a Vision Transformer (ViT) architecture, creating a hybrid SSM-ViT model. This integration not only addresses the long-standing challenge of performance degradation at varying temporal frequencies but also significantly accelerates the training process." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 396, + 545, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 469 + ], + "type": "text", + "content": "The key innovation of our work lies in the use of learnable timescale parameters within the SSMs, enabling the model to adapt dynamically to different inference frequencies without necessitating multiple training cycles. This feature represents a substantial advancement over existing methods, which require retraining for different frequencies." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "text", + "content": "The SSM-ViT model outperforms existing methods by " + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "inline_equation", + "content": "20\\mathrm{mAP}" + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "text", + "content": " at higher frequencies and exhibits a " + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "text", + "content": " increase in training speed. Furthermore, our introduction of two novel strategies to counteract the aliasing effect (a crucial consideration in high-frequency deployment) further reinforces the model's suitability for real-world applications. These strategies, involving frequency-selective masking and " + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "inline_equation", + "content": "H_{2}" + }, + { + "bbox": [ + 304, + 474, + 545, + 629 + ], + "type": "text", + "content": " norm adjustments, effectively mitigate the adverse effects of aliasing, ensuring the model's reliability across a spectrum of temporal resolutions. We believe that our approach opens new avenues for research and application in high-speed, dynamic visual environments, setting a new benchmark in the domain of event-based vision." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 658, + 410, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 410, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 410, + 672 + ], + "type": "text", + "content": "6. Acknowledgment" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 677, + 545, + 713 + ], + "type": "text", + "content": "This work was supported by the European Research Council (ERC) under grant agreement No. 864042 (AGILEFLIGHT)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "5826" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Julian Büchel, Gregor Lenz, Yalun Hu, Sadique Sheik, and Martino Sorbaro. 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In ICCV, pages 12846-12856, 2023. 2, 3, 6" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "5828" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_content_list.json b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c18845117b8e5d675612369367dda6d98272f1e5 --- /dev/null +++ b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_content_list.json @@ -0,0 +1,1511 @@ +[ + { + "type": "text", + "text": "Stationary Representations: Optimally Approximating Compatibility and Implications for Improved Model Replacements", + "text_level": 1, + "bbox": [ + 114, + 130, + 854, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Niccolò Biondi Federico Pernici Simone Ricci Alberto Del Bimbo \nDINFO (Department of Information Engineering), University of Florence, Italy, \nMICCC (Media Integration and Communication Center), \nname.surname@unifi.it", + "bbox": [ + 169, + 203, + 800, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 308, + 313, + 325 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pretrained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pretrained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamc12r.", + "bbox": [ + 76, + 342, + 473, + 720 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 753, + 209, + 768 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "By learning powerful internal feature representations from data, Deep Neural Networks (DNNs) [1-4] have made tremendous progress in some of the most challenging search tasks such as face recognition [5-9], person re-identification [10-12], image retrieval [13-15] and this significance also extends to a variety of other data modalities [16, 17]. Although all of the works mentioned above have focused on learning feature representations from static and,", + "bbox": [ + 75, + 779, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e7cdfc1cbe186ab8d0b88e37850155adbeefb629c048effa3dad0343b6644885.jpg", + "image_caption": [ + "Figure 1. Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL $^2$ R pronounced \"I am clear\"). In the process of lifelong learning, a model is sequentially fine-tuned and asynchronously replaced with improved third-party models that are pre-trained externally. Stationary representations ensure seamless retrieval services and better performance, without the need to reprocess gallery images." + ], + "image_footnote": [], + "bbox": [ + 526, + 309, + 870, + 554 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "more recently, dynamic datasets [18-21], the now-standard practice is downloading and fine-tuning representations from models pre-trained elsewhere [22, 23]. These \"third-party\" pre-trained models often incorporate new data, utilize alternative architectures, adopt different loss functions or more in general provide novel methodologies. Whether applied individually or combined, these advancements aim to encapsulate the field's rapid progress within a single unified model [24]. This greatly facilitates the exploitation of internally learned semantic representations, particularly as models, datasets, and computational infrastructure continue to expand in size, complexity, and cost [25, 26].", + "bbox": [ + 496, + 686, + 893, + 867 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The challenge of fully exploiting such standard practice in retrieval/search systems has to deal with the underlying", + "bbox": [ + 498, + 869, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28793", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "problem of compatible learning [27-29]. That is the desire to align the representation of different models trained with different data, initialization seeds, loss functions, or alternative architectures—either individually or in combination. In such applications, maintaining alignment is crucial to minimize the need for repeated reprocessing of gallery images for feature extraction each time a new pre-trained model becomes available [24]. Reprocessing is not only computationally intensive but may also be unsustainable for extensive gallery sets [25, 26, 30] or unfeasible if the original images are no longer accessible due to privacy concerns [31]. This holds across various typical galleries: social networks update millions of images every month, while in robotics and automotive domains, the update rate can be as rapid as hundreds of images every second. Similarly, in textual domains, books can be structured into chapters, paragraphs, and sentences, enabling the capture of semantic relationships between these segments. While a similar organizational principle can be structured for the web with LLMs [17, 32], the challenge lies in the impracticality of reprocessing such extensive content with each advancement in representation models. Although recent research has shown the effectiveness of compatible representation learning [27-29, 33-41], there is still a lack of comprehensive theoretical understanding about compatibility.", + "bbox": [ + 76, + 90, + 472, + 468 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper introduces a theorem that demonstrates how the stationary representations proposed in [42, 43] optimally approximate compatibility according to the two inequality constraints of its formal definition as provided in [27]. This not only establishes a solid foundation for future works, but also presents implications that can be exploited fine-tuning third-party models without the need of reprocessing gallery images. Specifically, we show that a continuously fine-tuned model can be asynchronously replaced by downloading a higher-performing, pre-trained model from an external source. Due to stationarity (and therefore optimal compatibility), such a replacement provides seamless retrieval services with improved performance, eliminating the need for image gallery reprocessing. We refer to this scenario as Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL $^2$ R pronounced \"I am clear\"). Fig. 1 illustrates the relationship between sequential fine-tuning and model replacement. Furthermore, as will be elaborated in the related work section, our foundation draws connections with the Neural Collapse phenomenon [44] and its associated theory.", + "bbox": [ + 76, + 473, + 472, + 789 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our second contribution is related to a specific challenge that arises: the tendency of the old and the new replaced models to align at their first-order statistics, an inherent property of stationary representation. Consequently, cross-entropy based prediction errors alone, when fine-tuning the representation, may not fully capture higher-order dependencies. To address this issue while preserving compatibility, we show", + "bbox": [ + 76, + 795, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "that learning stationary representations using a convex combination of the cross-entropy loss and the infoNCE loss [45] is equivalent to training under one of the compatibility inequality constraints in [27]. This combined loss, termed Higher-Order Compatibility (HOC), distinguishes itself from the use of cross-entropy alone by capturing higher-order dependencies and optimally approximating compatibility.", + "bbox": [ + 496, + 90, + 893, + 198 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 210, + 640, + 226 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural Collapse. Neural Collapse (NC) is an empirical phenomenon that demonstrates the alignment between features and the classifier in a symmetric configuration [44]. Specifically, each class feature vector and its corresponding class prototype vector align with each other (i.e., collapse onto the same vector), forming a regular Simplex geometry in a subspace of the representation space. This particular configuration, which results in maximal separation of the collapsed vectors, is also referred to as a regular Simplex ETF (Equiangular Tight Frame). As training progresses and the training phase goes beyond zero classification error, the network increasingly approaches collapse. Notably, this also agrees with the double descent generalization regime observed within the same training phase [46]. The two phenomena together indicate a form of stable steady-state for the internal representations of Deep Neural Networks.", + "bbox": [ + 496, + 234, + 893, + 477 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Prior to the observation of neural collapse, other research applied the steady-state of the Simplex geometry directly from the beginning of training. The fixed classifier with mutually orthogonal prototypes, introduced in [47], firstly demonstrates no degradation in classification performance. Building on this initial model, the regular polytope fixed classifiers—such as the $d$ -Simplex, $d$ -Cube, and $d$ -Orthoplex—advance the concept further by observing stationary and maximally separated representations, as introduced in [48] and further detailed in [42]. Prior to these developments, [49] delved into the early energy-based investigations of symmetric and maximal separation in the representation space. The distinction between the natural emergence of a regular Simplex ETF and intentionally fixing the regular Simplex geometry at the beginning of training is that prior fixing can preserve regions in the representation space for future classes, as introduced in [50] and more recently in [51] and [52]. Our work takes advantage of this preservation for future classes, allowing third-party representation models to be trained from scratch and fine-tuned, while mitigating the interference in the representation space of the classes involved in both processes.", + "bbox": [ + 496, + 478, + 895, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As neural collapse is related to the interaction between the neural network's final and penultimate layers, it offers a tool to examine training dynamics and convergence, as introduced in [53] and [54] under the name of Unconstrained Feature Model (UFM) and Layered Peeled Model (LPM), respectively. In both [55] and [56], the favorable conver", + "bbox": [ + 496, + 810, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28794", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "gence of fixing the final classifier according to the UFM is demonstrated. In [54], it is shown that training on imbalanced datasets does not necessarily result in NC. Additional observations from [57] suggest that NC can emerge in both imbalanced and long-tail scenarios when the classifier is fixed to a $d$ -Simplex geometry. Further detailed results on NC are presented in [58]. Our proof is based on the assumption from the UFM and LPM that the backbone has sufficient expressiveness to allow for the independent study of each feature. Our proof is also based on the assumption of $d$ -Simplex fixed classifier, whose inherent symmetry allows to reduce the extent of the analysis to a single pairwise class interaction, as it causes all the interactions to be identical.", + "bbox": [ + 75, + 90, + 472, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Compatible Representations Learning. Compatible representations broadly refer to the ability to align different learned representations, as discussed in [59-63]. The distinction outlined in [27] is that the alignment of models should be achieved without wasting the information learned from new data. This capability is typically evaluated in a query and gallery setting, where query and gallery features are extracted from two different representation models. The model for the query is trained using an extended dataset that includes additional data not present in the one used for training the gallery's model. The study in [27] further presents a method called Backward Compatible Training (BCT), which applies regularization to a new model using the classifier from the previous learning phase. This approach implicitly aligns the current improved model with the previously trained classifier, which is kept fixed. Several other methods have adopted this basic working principle: The fundamental aspect of this principle is that the challenge of model alignment is primarily demanded by the new model, which must learn from both the additional and the old data how to compensate for the inadequate representations of the previously learned models. Conversely, as also recently highlighted in [41], methods such as [64] or the more recent [28, 65, 66] train a lightweight transformation to convert old representations into new ones for backward compatibility. However, these methods do not entirely eliminate the re-processing cost. As the number of chained mappings increases, the entire chain necessitates re-evaluation each time the representation model is updated. This makes them unsuitable for sequential learning and large gallery-sets. While its primary focus is on classification, the study in [37] is one of the first methods employing sequential chaining transformations for aligning representations within a common reference space. The works in [39] and [38] bypass the use of chaining transformations, focusing instead on aligning representations for compatibility purposes in lifelong learning scenarios. Both approaches leverage auxiliary losses to ensure similarity among previously learned representations. Additionally, [39] achieves alignment with an absolute reference through the use of fixed classifiers, in line with the", + "bbox": [ + 75, + 296, + 472, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "neural collapse phenomenon.", + "bbox": [ + 500, + 90, + 694, + 104 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The work in [41] argues that there is an inherent trade-off in the definition of compatibility introduced in [27], which inspires them to \"hold\" incompatible information of the new model on additional orthogonal dimensions to avoid this conflict. Their argument seems to be in line with the recent work [29] and [39] based on stationarity in which (nearly) orthogonal dimensions are pre-allocated from the beginning using a regular $d$ -Simplex fixed classifier. In this paper, we establish a formal relationship among compatibility, neural collapse, and stationarity, showing that stationarity provides an optimal approximation to the compatibility definition formulated in [27].", + "bbox": [ + 496, + 106, + 893, + 287 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Theoretical Results", + "text_level": 1, + "bbox": [ + 498, + 297, + 686, + 314 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Stationarity and Compatibility", + "text_level": 1, + "bbox": [ + 500, + 323, + 772, + 339 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Preliminaries. Let $\\mathcal{G} = \\{\\mathbf{x}_i\\}_{i=1}^{N_g}$ be a gallery-set composed of a set of $N_g$ images $\\mathbf{x}_i \\in \\mathbb{R}^D$ with class labels from $\\mathcal{V} = \\{y_i\\}_{i=1}^L$ and $\\Phi^\\mathcal{G} = \\{\\phi(\\mathbf{x}_i) \\in \\mathbb{R}^d | \\forall \\mathbf{x}_i \\in \\mathcal{G}\\}$ be the set of feature vectors of the gallery-set $\\mathcal{G}$ obtained with representation model $\\phi$ . Let $\\mathcal{Q} = \\{\\mathbf{x}_i\\}_{i=1}^{N_q}$ be a query-set composed of $N_q$ images $\\mathbf{x}_i \\in \\mathbb{R}^D$ and $\\Phi^\\mathcal{Q} = \\{\\phi(\\mathbf{x}_i) \\in \\mathbb{R}^d | \\forall \\mathbf{x}_i \\in \\mathcal{Q}\\}$ be the set of feature vectors of the query-set $\\mathcal{Q}$ obtained with $\\phi$ . Visual search is performed using a distance function $\\mathrm{d}(\\cdot, \\cdot)$ to identify the closest gallery features to the query features.", + "bbox": [ + 496, + 345, + 893, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Let $\\mathcal{T}_1, \\mathcal{T}_2, \\ldots, \\mathcal{T}_T$ be a sequence of $T$ tasks, where each task $\\mathcal{T}$ is composed of labeled images $\\mathbf{x}_i$ of class $y_i \\in \\mathcal{K}$ with $\\mathcal{K}$ the set of classes in $\\mathcal{T}$ . At task $t$ , the model $\\phi_t$ is finetuned starting from the previous representation model $\\phi_{t-1}$ . Compatibility between the current model $\\phi_t$ and a previous model $\\phi_k$ , with $k < t$ , is achieved when the feature vector of any query image obtained with $\\phi_t$ , the set $\\Phi_t^{\\mathcal{Q}}$ , can be compared with feature vectors in $\\Phi_k^{\\mathcal{G}}$ without reprocessing the gallery-set. The following provides a formal definition of compatibility [27]:", + "bbox": [ + 496, + 484, + 893, + 637 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 1 (Compatibility) Given two representation models $\\phi_t$ and $\\phi_k$ , with $\\phi_t$ learned after $\\phi_k$ , $\\phi_t$ and $\\phi_k$ are compatible according to the distance function $d(\\cdot, \\cdot)$ if it holds:", + "bbox": [ + 496, + 642, + 893, + 702 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right) \\leq \\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {k} \\left(\\mathbf {x} _ {j}\\right)\\right) \\tag {1a}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 707, + 893, + 726 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\forall (i, j) \\in \\left\\{(i, j) \\mid y _ {i} = y _ {j} \\right\\}\n$$\n", + "text_format": "latex", + "bbox": [ + 681, + 728, + 861, + 747 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and", + "bbox": [ + 692, + 750, + 723, + 761 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right) \\geq \\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {k} \\left(\\mathbf {x} _ {j}\\right)\\right) \\tag {1b}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 767, + 890, + 785 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\forall (i, j) \\in \\left\\{(i, j) \\mid y _ {i} \\neq y _ {j} \\right\\}\n$$\n", + "text_format": "latex", + "bbox": [ + 681, + 787, + 861, + 806 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nw i t h k < t, \\quad t = (2, 3, \\dots , T), \\quad k = (1, 2, \\dots , T - 1).\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 806, + 874, + 823 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Main Result. In this paragraph, we state and prove that learning stationary feature representations according to a $d$ -Simplex fixed classifier necessarily implies optimal approximation of the compatibility as defined in Eqs. 1a and 1b.", + "bbox": [ + 496, + 839, + 895, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28795", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/2eff6fe739fb7df06c087bdb409f61e0c8800b5a50359107ffcac487911cfff6.jpg", + "image_caption": [ + "(a) Same class" + ], + "image_footnote": [], + "bbox": [ + 212, + 104, + 379, + 231 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/7679c8255f67d0ca17852d3e5098ad24565751c03bcbdbc1f0d1a790d1cd8d74.jpg", + "image_caption": [ + "(b) Different class", + "Figure 2. Key concepts and relationships underlying Theorem 1. Distances in feature space of two distinct samples within their hyperballs before and after model update, with the update process represented by a dotted arrow. (a): Distances between samples $\\mathbf{x}_i$ and $\\mathbf{x}_j$ of the same class $y$ before (red) and after (cyan) model update. (b): Distances between samples $\\mathbf{x}_i$ of class $y_i$ and $\\mathbf{x}_j$ of class $y_j$ , before (red) and after (cyan) model update. Compatibility is verified by computing the expected lengths of the segments and verifying if they satisfy the inequalities of the compatibility definition. A transparently colored instance shows counter-intuitive distance behavior. Expectation reveals the underlying pattern of approximation." + ], + "image_footnote": [], + "bbox": [ + 428, + 101, + 810, + 231 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The formulation involves examining the expected distance between feature points before and after a learning update in a high-dimensional space, where the feature points are assumed to be distributed in hyperballs (i.e., high dimensional ball) centered at the prototypes of the $d$ -Simplex fixed classifier. This abstraction allows for mathematical manipulation and analysis of the cluster as a single entity rather than individual points.", + "bbox": [ + 75, + 366, + 470, + 488 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 1 (Stationarity $\\Rightarrow$ Compatibility) Let $\\mathbf{W} = [\\mathbf{w}_1, \\mathbf{w}_2, \\ldots, \\mathbf{w}_K]$ be the $d \\times K$ matrix of a $d$ -Simplex fixed classifier with $K$ pre-allocated classes. Given two tasks, $\\mathcal{T}_k$ and $\\mathcal{T}_t$ . The task $\\mathcal{T}_t$ is derived from $\\mathcal{T}_k$ by incorporating an additional training set $\\Delta \\mathcal{T}$ , such that $\\mathcal{T}_t = \\mathcal{T}_k \\cup \\Delta \\mathcal{T}$ . The combined task, $\\mathcal{T}_t$ , comprises a set of classes each denoted by $y$ , where $y \\in \\{1, 2, \\ldots, K_t\\}$ and $K_t < K$ . Under the assumption that learning the new task $\\mathcal{T}_t$ causes the hyperball $\\mathcal{B}_k(\\mathbf{w}_y)$ with radius $r_k^y$ to shrink into a smaller hyperball $\\mathcal{B}_t(\\mathbf{w}_y)$ , i.e., $r_t^y \\leq r_k^y$ for all $y$ in the set $\\{1, 2, \\ldots, K_k\\}$ , then it necessarily follows that $\\phi_t$ and $\\phi_k$ optimally approximate the compatibility inequality constraints as defined in Def. 1 in expectation.", + "bbox": [ + 75, + 500, + 470, + 696 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The proof is available in the Appendix.", + "bbox": [ + 76, + 709, + 334, + 724 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Discussion. The Theorem relies on two main assumptions: the use of a $d$ -Simplex fixed classifier [42] and the model's sufficient expressiveness, as described in the UFM abstraction [53, 54]. The latter assumption enables us to consider features independently1. While the former allows focusing", + "bbox": [ + 75, + 742, + 468, + 819 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "on a single pairwise class interaction, since interactions with all other classes are symmetrically similar and cannot change. Fig. 2 illustrates the key concepts and relationships presented in Theorem 1.", + "bbox": [ + 500, + 367, + 893, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Without loss of generality, the Theorem considers two distinct hyperballs of different radius $\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)$ and $\\mathcal{B}_{\\mathrm{old}}(\\mathbf{w}_y)$ representing the semantic clusters of a generic class $y$ , respectively before and after a generic learning update. The assumption that features are distributed in hyperballs stems from the margin-based softmax loss $^2$ introduced in [67]. This interpretation has since been utilized in various studies, such as SphereFace [68] and ArcFace [8]. Besides the margin formulation, empirical evidence, such as Neural Collapse [44], shows that class features not only cluster around their associated prototypes but also, with sufficient training epochs, collapse into them, resulting in hyperballs tightening around the prototypes. Due to the stationarity property induced by the $d$ -Simplex classifier $\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)$ and $\\mathcal{B}_{\\mathrm{old}}(\\mathbf{w}_y)$ hyperballs have the same center in the representation space on the classifier prototype $\\mathbf{w}_y$ . After the learning step, $\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)$ has a shorter radius (i.e., adding new information improves the discrimination capability of the model [69-72]).", + "bbox": [ + 496, + 428, + 893, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In particular, Fig. 2a shows the case in which feature vectors are from samples of the same class. As defined in Eq. 1a compatibility requires that, after updating, the distance between $\\phi_{\\mathrm{new}}(\\mathbf{x}_i)$ (in the cyan hyperball) and $\\phi_{\\mathrm{old}}(\\mathbf{x}_j)$ (in red hyperball) is less than or equal to distance between $\\phi_{\\mathrm{old}}(\\mathbf{x}_i)$ and $\\phi_{\\mathrm{old}}(\\mathbf{x}_j)$ . The figure displays two configurations: one where the condition is met and another where it is not met (shown in transparent colors).", + "bbox": [ + 496, + 700, + 893, + 821 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 2b shows the case in which the feature vectors are", + "bbox": [ + 517, + 823, + 890, + 838 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "Essentially, the Neural Collapse phenomenon, which is observed across various networks and datasets, also appears in a two-layer neural network when assuming input feature independence (i.e., a UFM). This equivalence supports the assumption that: 1) real network backbones are typically expressive enough to learn features as independent entities, and 2) UFM can be used as a tool to study neural networks properties.", + "bbox": [ + 78, + 825, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_footnote", + "text": "2The margin enforces the confinement of features within a hyperball or a hyperdisc (the local approximation of a hypercap) around class prototypes. A disc in high-dimensional space can be considered a hyperball when referring to its filled volume.", + "bbox": [ + 500, + 849, + 893, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28796", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "from samples of different classes. As defined in Eq. 1b compatibility requires that, after updating, the distance between $\\phi_{\\mathrm{new}}(\\mathbf{x}_i)$ of class $y_i$ (in the cyan hyperball centered in $\\mathbf{w}_{y_i}$ ) and $\\phi_{\\mathrm{old}}(\\mathbf{x}_j)$ of class $y_j$ (in the red hyperball centered in $\\mathbf{w}_{y_j}$ ) is greater than or equal to than the distance between $\\phi_{\\mathrm{old}}(\\mathbf{x}_i)$ and $\\phi_{\\mathrm{old}}(\\mathbf{x}_j)$ . The Theorem establishes that, on average, this condition cannot be optimally satisfied and that stationarity is the best approximation achievable under the given constraints. A detailed justification for this is provided in the proof of Theorem 1, with a clearer and more focused exposition presented as a Corollary in the Appendix.", + "bbox": [ + 76, + 90, + 472, + 257 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Informally, the proof of the Theorem starts with the premise that, upon retraining a model, the probability of finding a class feature near the corresponding class prototype from the old model—an indicator of compatibility between the two models—is nearly zero. Subsequently, the proof establishes that the optimal approximation for a compatible representation is obtained when the average distance between the same hyperball in two distinct learned models is minimized. This minimization occurs when the two corresponding hyperballs are centered at the same class prototype and when adding more classes does not alter this distance, i.e., the stationarity condition.", + "bbox": [ + 75, + 260, + 472, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our formulation calculates the average distance between hyperballs based on the Ball Line Picking problem, which determines the expected length of a line segment that connects two random points inside a hyperball [73-78]. Differently from that problem, our theorem considers a line segment connecting two random points in two distinct hyperballs, each with a different radius. Specifically, we analyze the cases as shown in Fig. 2. These hyperballs represent the \"class-state\" before and after the learning step during each model update. Closed-form solutions are not available for this problem, except in a specific two-dimensional case [79].", + "bbox": [ + 75, + 444, + 472, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.2. Stationarity and Higher-Order Alignment", + "text_level": 1, + "bbox": [ + 76, + 628, + 434, + 645 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "A specific challenge arises when fine-tuning stationary learned representation models, for example in the IAM-CL $^2$ R setting of Fig. 1. In this case the old and the new models align at the first-order statistics, an inherent property of stationarity [42]. The consequence is that cross-entropy based prediction errors may not fully capture higher-order dependencies in representation space. We conjecture that simple cross-entropy mostly focuses on prediction errors related to the forgetting of the internal representation which may not promote compatibility when the representation model is largely aligned. To address this problem, we show that adding the infoNCE loss function [45, 80] is equivalent to training with the cross-entropy loss under one of the compatibility constraints while capturing higher-order dependencies.", + "bbox": [ + 75, + 656, + 470, + 882 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The loss for training at task $t$ the stationary representation", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "model $\\phi_t$ assumes the form [42]:", + "bbox": [ + 500, + 90, + 718, + 106 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {S C E}} \\left(\\phi_ {t}\\right) = \\\\ = - \\sum_ {B} \\log \\left(\\frac {\\exp \\left(\\mathbf {W} _ {y _ {i}} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right)}{\\sum_ {j = 1} ^ {K _ {t}} \\exp \\left(\\mathbf {W} _ {j} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right) + \\sum_ {j = K _ {t} + 1} ^ {K} \\exp \\left(\\mathbf {W} _ {j} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right)}\\right) \\tag {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 114, + 890, + 199 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_j^\\top \\in \\mathbb{R}^d$ denotes the $j$ -th column of the $d$ -Simplex classifier matrix $\\mathbf{W} \\in \\mathbb{R}^{d \\times K}$ , being $K$ the number of preallocated classes, $K_t = |\\bigcup_{i=1}^t \\mathcal{K}_i|$ the number of classes learned until time $t$ with $K_t < K$ , and $B$ is a mini-batch of samples of $\\mathcal{T}_t$ . The first term in the denominator accounts for the classes learned until $t$ . The second term accounts for future classes, preserving dedicated regions in the representation space. This ensures that adding new classes minimally impacts the representation of previously learned classes [29, 39, 50, 81]. We train the representation model $\\phi_t$ with the following convex combination, namely:", + "bbox": [ + 496, + 200, + 893, + 368 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {H O C}} \\left(\\phi_ {t}\\right) = \\lambda \\mathcal {L} _ {\\mathrm {S C E}} \\left(\\phi_ {t}\\right) + (1 - \\lambda) \\mathcal {L} _ {\\mathrm {N C E}} \\left(\\phi_ {t}, \\phi_ {t - 1}\\right), \\tag {3} \\\\ \\text {w i t h} \\quad \\lambda \\in [ 0, 1 ] \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 378, + 890, + 412 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where: $\\mathcal{L}_{\\mathrm{SCE}}(\\phi_t)$ is the cross-entropy loss of Eq. 2, and", + "bbox": [ + 498, + 422, + 861, + 439 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {N C E}} \\left(\\phi_ {t}, \\phi_ {t - 1}\\right) = - \\sum_ {B} \\log \\left(\\frac {\\Delta \\left(\\phi_ {t - 1} \\left(\\mathbf {x} _ {i}\\right) , \\phi_ {t} \\left(\\mathbf {x} _ {i}\\right)\\right)}{\\sum_ {j \\neq i} \\Delta \\left(\\phi_ {t - 1} \\left(\\mathbf {x} _ {i}\\right) , \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right)}\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 501, + 468, + 890, + 539 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "with", + "bbox": [ + 500, + 549, + 534, + 561 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\left(\\phi_ {t - 1} (\\mathbf {x} _ {i}), \\phi_ {t} (\\mathbf {x} _ {j})\\right) = \\exp \\left(\\tau \\cdot \\frac {\\phi_ {t - 1} (\\mathbf {x} _ {i}) \\phi_ {t} (\\mathbf {x} _ {j})}{\\left| \\left| \\phi_ {t - 1} (\\mathbf {x} _ {i}) \\phi_ {t} (\\mathbf {x} _ {j}) \\right|\\right|}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 570, + 890, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "is the contrastive loss [45, 80] based on $\\tau$ -scaled cosine similarity between $\\phi_{t-1}(\\mathbf{x}_i)$ and $\\phi_t(\\mathbf{x}_j)$ . We show that training the representation model with the $\\mathcal{L}_{\\mathrm{HOC}}$ of Eq. 3 is both: (1) able to capture higher-order dependencies between old and new model representations and (2) equivalent to learning under the compatibility constraints in Def. 1a. We refer to this loss as the Higher-Order Compatibility loss ( $\\mathcal{L}_{\\mathrm{HOC}}$ ).", + "bbox": [ + 496, + 616, + 893, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Through Theorem 1 presented in the previous section, we establish that the constraint of Eq. 1a cannot be exploited in combination with the constraint of Eq. 1b. Based on this result we show that, under no specific conditions, the constrained optimization problem using solely the inequality constraint of Eq. 1a:", + "bbox": [ + 496, + 722, + 893, + 811 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname * {a r g m i n} _ {\\phi_ {t}} \\mathcal {L} _ {\\text {S C E}} (\\phi_ {t}) \\\\ \\mathrm {s . t .} \\quad \\mathrm {d} \\left(\\phi_ {k} (\\mathbf {x} _ {i}), \\phi_ {t} (\\mathbf {x} _ {j})\\right) - \\mathrm {d} \\left(\\phi_ {k} (\\mathbf {x} _ {i}), \\phi_ {k} (\\mathbf {x} _ {j})\\right) \\leq 0 \\\\ \\forall y _ {i} = y _ {j} \\tag {6} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 821, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28797", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/51b5926c6a665b7911f4c226f04a454b67c1fc53c2dc604314acd5664d3fdb67.jpg", + "image_caption": [ + "Figure 3. Training loss of a $d$ -Simplex fixed classifier during a model update. Values are the cross-entropy loss of Eq. 2 (red line) and the loss of Eq. 3 (blue line). Models are trained on MNIST." + ], + "image_footnote": [], + "bbox": [ + 138, + 92, + 410, + 247 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "can be transformed into a tractable form. Rooted in the work of [82], this transformation not only provides an approach to solve the tractability issue but, within the context of compatibility, it also allows preserving the optimality as outlined in the proof of Theorem 1. As shown in [82], the model for a constrained problem like Eq. 6 can be equivalently learned with a convex combination of the cross-entropy loss and the Kullback-Leibler divergence function.", + "bbox": [ + 75, + 329, + 468, + 449 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "On the other hand, as discussed in [83], the contrastive loss $\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})$ can be approximated as the Kullback-Leibler divergence between the product of the marginals of the joint distribution of $\\phi_t$ and $\\phi_{t - 1}$ . Moreover, $\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})$ also approximates the mutual information between $\\phi_t$ and $\\phi_{t - 1}$ , thereby enabling to capture higher-order dependencies between consecutive updates of the model. As a consequence, training with the loss in Eq. 3 is equivalent to the optimal classifier for the constrained optimization problem stated in Eq. 6 and at the same time, thanks to the term $\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})$ , takes into account higher-order variations between $\\phi_{t - 1}(\\mathbf{x}_i)$ and $\\phi_t(\\mathbf{x}_j)$ . In the following, we call training the representation model using $d$ -Simplex with $\\mathcal{L}_{\\mathrm{HOC}}$ as $d$ -Simplex-HOC.", + "bbox": [ + 75, + 450, + 470, + 662 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In Fig. 3, we illustrate the effects of $\\mathcal{L}_{\\mathrm{HOC}}$ compared to the cross-entropy loss. We use a toy example with the LeNet++ CNN architecture [84] with the $d$ -Simplex fixed classifier. The model is initially trained on the first five MNIST classes and then fine-tuned on all ten classes. The cross-entropy training error (red curve) converges rapidly to low values. In contrast, the convergence with the $\\mathcal{L}_{\\mathrm{HOC}}$ loss (blue curve) is more gradual, which allows for the capture of richer information during back-propagation.", + "bbox": [ + 75, + 662, + 468, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experimental Verification", + "text_level": 1, + "bbox": [ + 76, + 814, + 316, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Referring to the IAM-CL $^2$ R learning scenario presented in Fig. 1, this section provides empirical evidence to verify the practical implications of the theoretical results discussed earlier.", + "bbox": [ + 75, + 839, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets and Settings", + "text_level": 1, + "bbox": [ + 500, + 90, + 699, + 107 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Pre-trained Models. We pre-train our models in a supervised manner using the ImageNet32 [85]. Three distinct models are pre-trained on ImageNet32 with 100, 300, and 600 classes. The model trained with 100 classes is used to initialize the model before fine-tuning on the sequence of tasks. The other two models are used to simulate the practice of downloading and fine-tuning pre-trained models and serve as third-party models that will replace the current one undergoing fine-tuning.", + "bbox": [ + 496, + 113, + 893, + 250 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fine-tuning. We replicate the fact that dataset size for training third-party models is typically significantly larger than the dataset size used for fine-tuning [86]. According to this, pre-trained models are fine-tuned with a reduced version of CIFAR100 [87] denoted in this paper as CIFAR100R.", + "bbox": [ + 496, + 250, + 893, + 325 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We considered two distinct task sequences consisting of 7 and 31 tasks each. We fine-tune the pre-trained model with an initial task comprising 10 classes. Subsequently, for the sequences of 7 and 31 tasks, the respective tasks contain 15 and 3 classes each. The fine-tuning process incorporates incoming task data, consisting of 300 images per class, and utilizes an episodic memory that stores 20 images from each class of previous tasks.", + "bbox": [ + 496, + 325, + 892, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Model Replacement. In our experiments, we verify the impact of replacing the current fine-tuned model with two improved models pre-trained elsewhere. The two replacements occur while fine-tuning on CIFAR100R: at the third and fifth tasks in the shorter sequence, and at the eleventh and twenty-first tasks in the longer sequence. We also consider the challenging scenario of improved model replacement considering more sophisticated network architectures.", + "bbox": [ + 496, + 446, + 893, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The $d$ -Simplex fixed classifier is pre-allocated with a number of classes $K$ , ensuring enough space to accommodate future classes for both pre-training and fine-tuning. Class assignments for pre-training are made from left to right, and for fine-tuning, from right to left. This straightforward convention is used to ensure that classes assigned for pre-training and fine-tuning remain distinct, without overlap. Other non-overlapping assignment methods could also be used.", + "bbox": [ + 496, + 568, + 893, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Network Architectures. We use ResNet18 [88] as network architecture. In the scenario using more sophisticated network architectures, we initially replace ResNet18 with SENet18 [89], followed by a subsequent replacement with a RegNetY_400MF [90].", + "bbox": [ + 496, + 688, + 893, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Hyper-parameters. The ResNet18, SENet18, and RegNetY_400MF models were pre-trained on ImageNet32 using the following hyper-parameters: 300 epochs, a batch size of 128, and an initial SGD optimizer learning rate of 0.1, which was adjusted using a Cosine Annealing schedule. For each task used for fine-tuning, the model is trained for 70 epochs with a batch size of 128, starting with a learning rate of 0.001 that was reduced by a factor of 10 after the 50th and 64th epochs. The $d$ -Simplex was pre-allocated with $K = 1024$", + "bbox": [ + 496, + 763, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28798", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/daf12376188a7578eda5c33dac4097b5be3399f75659d393e2304cffba46cc02.jpg", + "image_caption": [ + "(a) Two replacements" + ], + "image_footnote": [], + "bbox": [ + 98, + 89, + 465, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/c28a1e1b1bfff5061ec4cabfa7d32b1bda83e8b47436d44b711ecf395b07b51c.jpg", + "image_caption": [ + "(b) No replacements" + ], + "image_footnote": [], + "bbox": [ + 465, + 90, + 872, + 277 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/90def011759f1a932dda13471ce617d13616a3dad4114e20366884e0647f5724.jpg", + "image_caption": [ + "Figure 4. Average multi-model Accuracy $(AA_{t})$ evaluated across 31 tasks using CIFAR100R/10, showing: (a) model replacements at tasks 11 and 21 (indicated by yellow markers); (b) no model replacement.", + "(a) CVS [38]", + "Figure 5. Compatibility Matrices for $d$ -Simplex-HOC, CVS, BCT-ER, and $d$ -Simplex-FD on CIFAR100R/10 across 7 tasks. Model replacements at tasks 3 and 5 are highlighted in bold. Entries failing to meet compatibility criteria as defined in [27] are marked with a light-red background." + ], + "image_footnote": [], + "bbox": [ + 76, + 344, + 267, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/d892ae816ee6affdd5d2a9603a05a8c50240f93018a036714cfdca4608f9c43e.jpg", + "image_caption": [ + "(b) BCT-ER [27]" + ], + "image_footnote": [], + "bbox": [ + 267, + 345, + 457, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3d3372b5327f7237a91ff50a6919172dc7b30f2fb41b1b5f4d5a90feeb70e99e.jpg", + "image_caption": [ + "(c) $d$ -Simplex-FD [39]" + ], + "image_footnote": [], + "bbox": [ + 457, + 345, + 645, + 494 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e57ccf828d516be7cdc327d2a959188689fb8eef1b91cd428fc917a96b7bd98e.jpg", + "image_caption": [ + "(d) $d$ -Simplex-HOC (in this paper)" + ], + "image_footnote": [], + "bbox": [ + 647, + 345, + 870, + 494 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "classes (i.e., $d = K - 1$ ).", + "bbox": [ + 76, + 578, + 246, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Performance Evaluation. The evaluation focuses on the open-set recognition task, in which separated datasets for training and evaluation are required. The standard 1:N search protocol, applicable to re-identification and similar tasks [27], is employed in the evaluation. To ensure strict separation between datasets, the CIFAR10 dataset is utilized for evaluation during fine-tuning with CIFAR100R. Specifically, the test set of CIFAR10, comprising 10,000 images, is used as the gallery set, while its training set of 50,000 images serves as the query set.", + "bbox": [ + 75, + 595, + 470, + 747 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Following [27] and [29], we measure performance progression across the two sequences of tasks using two established metrics: Average Compatibility $(AC)$ and Average multi-model Accuracy (referred shortly as to $AA_{t}$ ). The metric $AC$ quantifies the extent of compatibility across all possible pairs of model combinations by providing a normalized count of times in which compatibility is achieved. Conversely, $AA_{t}$ calculates the mean accuracy across all combinations of the previously learned models until task $t$ , providing an overall measure of accuracy.", + "bbox": [ + 75, + 750, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. IAM-CL $^2$ R: Comparative Results", + "text_level": 1, + "bbox": [ + 500, + 577, + 795, + 593 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We performed a comparative analysis of $d$ -Simplex-HOC against FAN [37], CVS [38], $d$ -Simplex-FD [39], and the lifelong adapted versions of BCT [27] (BCT-ER), LCE [28] (LCE-ER), and AdvBCT [36] (AdvBCT-ER). The experiments also incorporate a baseline method, Experience Replay (ER), in which the model is fine-tuned using cross-entropy loss on data of the new task and an episodic memory. Ablation studies of IAM-CL $^2$ R with the $d$ -Simplex-HOC are provided in the Appendix.", + "bbox": [ + 496, + 613, + 893, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Replacing: Same Architecture, Expanded Data. Fig. 4 presents the Average multi-model Accuracy at task $t(AA_{t})$ for learning scenarios with model replacement as depicted in Fig. 4a and for those without as depicted in Fig. 4b. The experiment involves fine-tuning a ResNet18 model across 31 tasks. The comparison provides insights into the performance benefits that can be obtained by replacing models when representations are trained in a compatible manner. The $d$ -Simplex-HOC effectively incorporates improvements from model replacements, showing increased performance", + "bbox": [ + 496, + 750, + 893, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28799", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/7d76aaa98ec5fdfdffd8fb2bee47ff1d1b2a129b99612185b842040c060d65cd.jpg", + "image_caption": [ + "Figure 6. Plots of Average multi-model Accuracy $(AA_{t})$ for 31 tasks on CIFAR100R/10, showing the impact of model replacements with different network architectures at tasks 11 and 21." + ], + "image_footnote": [], + "bbox": [ + 86, + 88, + 462, + 287 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "compared to the case without model replacement, as indicated in Fig. 4b. The $d$ -Simplex-FD demonstrates a similar capability, though to a reduced extent. The other methods have a clear performance decay after model replacements and end up with a worse performance than the case without replacement. This can be attributed to the fact that after replacement, fine-tuning is applied to a model obtained by retraining the network from scratch, leading to an entirely different representation.", + "bbox": [ + 75, + 369, + 468, + 505 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Further performance details, as indicated by the self and cross-test accuracy values, are shown according to the compatibility matrices [27, 29]. Fig. 5 shows these values for CVS, BCT-ER, $d$ -Simplex-FD, and $d$ -Simplex-HOC in the 7 tasks sequence. The values reveal that the $d$ -Simplex-HOC effectively leverages the improved expressive power of the models after replacement, except in one instance. This exception, where the model is not compatible and the cross-test accuracy falls below the self-test accuracy, is shown in Fig. 5d. Both CVS and BCT-ER score near zero cros-tests accuracy after model replacements as indicated by the values in the blue sub matrix blocks shown in Fig. 5a and Fig. 5b. This leads to mostly non-compatible representations. Although both $d$ -Simplex-HOC and $d$ -Simplex-FD utilize the $d$ -Simplex fixed classifier to learn stationary representations, the former shows better performance. This can be attributed to the high-order alignment achievable through the HOC loss. To provide a full evaluation of compatibility, the $AA_{t}$ of Fig. 4 is complemented with the Average Compatibility $AC$ in Tab. 1. We also report the Average multi-model Accuracy $AA_{7}$ and $AA_{31}$ for methods compared at the end of the 7-th and 31-th task, respectively. It is observed that, in both instances, all models—with the exception of $d$ -Simplex-HOC—fail to achieve significant compatibility performance.", + "bbox": [ + 75, + 506, + 473, + 869 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Replacing: Different Architectures, Expanded Data. Fig. 6 shows the performance of the evaluated methods when", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/86641bcf4dacf1b6a4a0fc02e464eb5d2ecb4e0bc5cbea199e8696c8af1decab.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
METHOD7 tasks31 tasks
\\( {AC} \\)\\( A{A}_{7} \\)\\( {AC} \\)\\( A{A}_{31} \\)
ER baseline×36.22<0.0131.30
FAN [37]×36.32<0.0130.79
BCT-ER [27]×35.59×29.88
LCE-ER [28]×34.89×29.30
AdvBCT-ER [36]×35.73×30.10
CVS [38]×36.310.0131.34
d-Simplex-FD [39]0.0556.580.2156.27
d-Simplex-HOC0.9568.130.6567.40
", + "bbox": [ + 506, + 88, + 887, + 250 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 1. Compatibility metrics with CIFAR100R/10 for 7 tasks with model replacements at task 3 and task 5, and 31 tasks with model replacements at task 11 and task 21. “×” indicates the case in which compatibility is not achieved.", + "bbox": [ + 498, + 258, + 893, + 316 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "the original ResNet18 is replaced first by a SENet18 and then by a more expressive RegNetY_400MF. It is observed that the change of network architecture not only does not adversely affect compatibility in the $d$ -Simplex-HOC but takes advantage of their more expressive representation power. In particular, direct comparison of Fig. 6 with Fig. 5 shows that $d$ -Simplex-HOC improves performance gradually with each model replacement. This is in contrast to $d$ -SimplexFD, which does not demonstrate the same trends leading to a plateau around the 20-th task. Given the different feature sizes before and after the second model replacement with the RegNetY_400MF architecture—512 and 384, respectively—all methods except $d$ -Simplex-HOC and $d$ -Simplex-FD require non-trivial extensions to adapt to the changed feature size. According to this, for these methods, evaluation cannot be reported.", + "bbox": [ + 496, + 348, + 893, + 590 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 612, + 619, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we have investigated the concept of learning compatible representations through the principle of stationarity. We demonstrated that stationary representations optimally approximate compatibility according to its definition. We demonstrated that better model alignment through higher-order dependencies can be obtained by training with a loss derived from one of the compatibility inequality constraints. Finally, empirical evidence confirmed that stationary representations enable uninterrupted retrieval service allowing for fine-tuning and model replacement to occur concurrently and asynchronously with limited interference.", + "bbox": [ + 496, + 640, + 893, + 806 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgment: This work was partially supported by the European Commission under European Horizon 2020 Programme, grant number 951911 - AI4Media.", + "bbox": [ + 496, + 809, + 893, + 854 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support (ISCRA-C ID: HP10C4TIIM).", + "bbox": [ + 496, + 854, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28800", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Sumit Chopra, Raia Hadsell, and Yann LeCun. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10428-10436, 2020. 6" + ], + "bbox": [ + 78, + 90, + 470, + 460 + ], + "page_idx": 11 + }, + { + "type": "page_number", + "text": "28804", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 11 + } +] \ No newline at end of file diff --git a/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_model.json b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a3a14453245b6ab77aa7dccff428291e2ef48068 --- /dev/null +++ b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_model.json @@ -0,0 +1,2523 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.115, + 0.131, + 0.856, + 0.177 + ], + "angle": 0, + "content": "Stationary Representations: Optimally Approximating Compatibility and Implications for Improved Model Replacements" + }, + { + "type": "text", + "bbox": [ + 0.17, + 0.204, + 0.802, + 0.275 + ], + "angle": 0, + "content": "Niccolò Biondi Federico Pernici Simone Ricci Alberto Del Bimbo \nDINFO (Department of Information Engineering), University of Florence, Italy, \nMICCC (Media Integration and Communication Center), \nname.surname@unifi.it" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.309, + 0.314, + 0.327 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.474, + 0.721 + ], + "angle": 0, + "content": "Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pretrained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pretrained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamc12r." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.754, + 0.21, + 0.769 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.902 + ], + "angle": 0, + "content": "By learning powerful internal feature representations from data, Deep Neural Networks (DNNs) [1-4] have made tremendous progress in some of the most challenging search tasks such as face recognition [5-9], person re-identification [10-12], image retrieval [13-15] and this significance also extends to a variety of other data modalities [16, 17]. Although all of the works mentioned above have focused on learning feature representations from static and," + }, + { + "type": "image", + "bbox": [ + 0.527, + 0.31, + 0.871, + 0.555 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.567, + 0.895, + 0.667 + ], + "angle": 0, + "content": "Figure 1. Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL\\(^2\\)R pronounced \"I am clear\"). In the process of lifelong learning, a model is sequentially fine-tuned and asynchronously replaced with improved third-party models that are pre-trained externally. Stationary representations ensure seamless retrieval services and better performance, without the need to reprocess gallery images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.687, + 0.895, + 0.868 + ], + "angle": 0, + "content": "more recently, dynamic datasets [18-21], the now-standard practice is downloading and fine-tuning representations from models pre-trained elsewhere [22, 23]. These \"third-party\" pre-trained models often incorporate new data, utilize alternative architectures, adopt different loss functions or more in general provide novel methodologies. Whether applied individually or combined, these advancements aim to encapsulate the field's rapid progress within a single unified model [24]. This greatly facilitates the exploitation of internally learned semantic representations, particularly as models, datasets, and computational infrastructure continue to expand in size, complexity, and cost [25, 26]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.895, + 0.903 + ], + "angle": 0, + "content": "The challenge of fully exploiting such standard practice in retrieval/search systems has to deal with the underlying" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28793" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.469 + ], + "angle": 0, + "content": "problem of compatible learning [27-29]. That is the desire to align the representation of different models trained with different data, initialization seeds, loss functions, or alternative architectures—either individually or in combination. In such applications, maintaining alignment is crucial to minimize the need for repeated reprocessing of gallery images for feature extraction each time a new pre-trained model becomes available [24]. Reprocessing is not only computationally intensive but may also be unsustainable for extensive gallery sets [25, 26, 30] or unfeasible if the original images are no longer accessible due to privacy concerns [31]. This holds across various typical galleries: social networks update millions of images every month, while in robotics and automotive domains, the update rate can be as rapid as hundreds of images every second. Similarly, in textual domains, books can be structured into chapters, paragraphs, and sentences, enabling the capture of semantic relationships between these segments. While a similar organizational principle can be structured for the web with LLMs [17, 32], the challenge lies in the impracticality of reprocessing such extensive content with each advancement in representation models. Although recent research has shown the effectiveness of compatible representation learning [27-29, 33-41], there is still a lack of comprehensive theoretical understanding about compatibility." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.473, + 0.79 + ], + "angle": 0, + "content": "This paper introduces a theorem that demonstrates how the stationary representations proposed in [42, 43] optimally approximate compatibility according to the two inequality constraints of its formal definition as provided in [27]. This not only establishes a solid foundation for future works, but also presents implications that can be exploited fine-tuning third-party models without the need of reprocessing gallery images. Specifically, we show that a continuously fine-tuned model can be asynchronously replaced by downloading a higher-performing, pre-trained model from an external source. Due to stationarity (and therefore optimal compatibility), such a replacement provides seamless retrieval services with improved performance, eliminating the need for image gallery reprocessing. We refer to this scenario as Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL\\(^2\\)R pronounced \"I am clear\"). Fig. 1 illustrates the relationship between sequential fine-tuning and model replacement. Furthermore, as will be elaborated in the related work section, our foundation draws connections with the Neural Collapse phenomenon [44] and its associated theory." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.796, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Our second contribution is related to a specific challenge that arises: the tendency of the old and the new replaced models to align at their first-order statistics, an inherent property of stationary representation. Consequently, cross-entropy based prediction errors alone, when fine-tuning the representation, may not fully capture higher-order dependencies. To address this issue while preserving compatibility, we show" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.199 + ], + "angle": 0, + "content": "that learning stationary representations using a convex combination of the cross-entropy loss and the infoNCE loss [45] is equivalent to training under one of the compatibility inequality constraints in [27]. This combined loss, termed Higher-Order Compatibility (HOC), distinguishes itself from the use of cross-entropy alone by capturing higher-order dependencies and optimally approximating compatibility." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.211, + 0.642, + 0.227 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.236, + 0.895, + 0.478 + ], + "angle": 0, + "content": "Neural Collapse. Neural Collapse (NC) is an empirical phenomenon that demonstrates the alignment between features and the classifier in a symmetric configuration [44]. Specifically, each class feature vector and its corresponding class prototype vector align with each other (i.e., collapse onto the same vector), forming a regular Simplex geometry in a subspace of the representation space. This particular configuration, which results in maximal separation of the collapsed vectors, is also referred to as a regular Simplex ETF (Equiangular Tight Frame). As training progresses and the training phase goes beyond zero classification error, the network increasingly approaches collapse. Notably, this also agrees with the double descent generalization regime observed within the same training phase [46]. The two phenomena together indicate a form of stable steady-state for the internal representations of Deep Neural Networks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.897, + 0.81 + ], + "angle": 0, + "content": "Prior to the observation of neural collapse, other research applied the steady-state of the Simplex geometry directly from the beginning of training. The fixed classifier with mutually orthogonal prototypes, introduced in [47], firstly demonstrates no degradation in classification performance. Building on this initial model, the regular polytope fixed classifiers—such as the \\(d\\)-Simplex, \\(d\\)-Cube, and \\(d\\)-Orthoplex—advance the concept further by observing stationary and maximally separated representations, as introduced in [48] and further detailed in [42]. Prior to these developments, [49] delved into the early energy-based investigations of symmetric and maximal separation in the representation space. The distinction between the natural emergence of a regular Simplex ETF and intentionally fixing the regular Simplex geometry at the beginning of training is that prior fixing can preserve regions in the representation space for future classes, as introduced in [50] and more recently in [51] and [52]. Our work takes advantage of this preservation for future classes, allowing third-party representation models to be trained from scratch and fine-tuned, while mitigating the interference in the representation space of the classes involved in both processes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.897, + 0.903 + ], + "angle": 0, + "content": "As neural collapse is related to the interaction between the neural network's final and penultimate layers, it offers a tool to examine training dynamics and convergence, as introduced in [53] and [54] under the name of Unconstrained Feature Model (UFM) and Layered Peeled Model (LPM), respectively. In both [55] and [56], the favorable conver" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28794" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.288 + ], + "angle": 0, + "content": "gence of fixing the final classifier according to the UFM is demonstrated. In [54], it is shown that training on imbalanced datasets does not necessarily result in NC. Additional observations from [57] suggest that NC can emerge in both imbalanced and long-tail scenarios when the classifier is fixed to a \\(d\\)-Simplex geometry. Further detailed results on NC are presented in [58]. Our proof is based on the assumption from the UFM and LPM that the backbone has sufficient expressiveness to allow for the independent study of each feature. Our proof is also based on the assumption of \\(d\\)-Simplex fixed classifier, whose inherent symmetry allows to reduce the extent of the analysis to a single pairwise class interaction, as it causes all the interactions to be identical." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.297, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Compatible Representations Learning. Compatible representations broadly refer to the ability to align different learned representations, as discussed in [59-63]. The distinction outlined in [27] is that the alignment of models should be achieved without wasting the information learned from new data. This capability is typically evaluated in a query and gallery setting, where query and gallery features are extracted from two different representation models. The model for the query is trained using an extended dataset that includes additional data not present in the one used for training the gallery's model. The study in [27] further presents a method called Backward Compatible Training (BCT), which applies regularization to a new model using the classifier from the previous learning phase. This approach implicitly aligns the current improved model with the previously trained classifier, which is kept fixed. Several other methods have adopted this basic working principle: The fundamental aspect of this principle is that the challenge of model alignment is primarily demanded by the new model, which must learn from both the additional and the old data how to compensate for the inadequate representations of the previously learned models. Conversely, as also recently highlighted in [41], methods such as [64] or the more recent [28, 65, 66] train a lightweight transformation to convert old representations into new ones for backward compatibility. However, these methods do not entirely eliminate the re-processing cost. As the number of chained mappings increases, the entire chain necessitates re-evaluation each time the representation model is updated. This makes them unsuitable for sequential learning and large gallery-sets. While its primary focus is on classification, the study in [37] is one of the first methods employing sequential chaining transformations for aligning representations within a common reference space. The works in [39] and [38] bypass the use of chaining transformations, focusing instead on aligning representations for compatibility purposes in lifelong learning scenarios. Both approaches leverage auxiliary losses to ensure similarity among previously learned representations. Additionally, [39] achieves alignment with an absolute reference through the use of fixed classifiers, in line with the" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.695, + 0.106 + ], + "angle": 0, + "content": "neural collapse phenomenon." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.107, + 0.895, + 0.289 + ], + "angle": 0, + "content": "The work in [41] argues that there is an inherent trade-off in the definition of compatibility introduced in [27], which inspires them to \"hold\" incompatible information of the new model on additional orthogonal dimensions to avoid this conflict. Their argument seems to be in line with the recent work [29] and [39] based on stationarity in which (nearly) orthogonal dimensions are pre-allocated from the beginning using a regular \\(d\\)-Simplex fixed classifier. In this paper, we establish a formal relationship among compatibility, neural collapse, and stationarity, showing that stationarity provides an optimal approximation to the compatibility definition formulated in [27]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.299, + 0.687, + 0.315 + ], + "angle": 0, + "content": "3. Theoretical Results" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.324, + 0.774, + 0.34 + ], + "angle": 0, + "content": "3.1. Stationarity and Compatibility" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.895, + 0.486 + ], + "angle": 0, + "content": "Preliminaries. Let \\(\\mathcal{G} = \\{\\mathbf{x}_i\\}_{i=1}^{N_g}\\) be a gallery-set composed of a set of \\(N_g\\) images \\(\\mathbf{x}_i \\in \\mathbb{R}^D\\) with class labels from \\(\\mathcal{V} = \\{y_i\\}_{i=1}^L\\) and \\(\\Phi^\\mathcal{G} = \\{\\phi(\\mathbf{x}_i) \\in \\mathbb{R}^d | \\forall \\mathbf{x}_i \\in \\mathcal{G}\\}\\) be the set of feature vectors of the gallery-set \\(\\mathcal{G}\\) obtained with representation model \\(\\phi\\). Let \\(\\mathcal{Q} = \\{\\mathbf{x}_i\\}_{i=1}^{N_q}\\) be a query-set composed of \\(N_q\\) images \\(\\mathbf{x}_i \\in \\mathbb{R}^D\\) and \\(\\Phi^\\mathcal{Q} = \\{\\phi(\\mathbf{x}_i) \\in \\mathbb{R}^d | \\forall \\mathbf{x}_i \\in \\mathcal{Q}\\}\\) be the set of feature vectors of the query-set \\(\\mathcal{Q}\\) obtained with \\(\\phi\\). Visual search is performed using a distance function \\(\\mathrm{d}(\\cdot, \\cdot)\\) to identify the closest gallery features to the query features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.895, + 0.638 + ], + "angle": 0, + "content": "Let \\(\\mathcal{T}_1, \\mathcal{T}_2, \\ldots, \\mathcal{T}_T\\) be a sequence of \\(T\\) tasks, where each task \\(\\mathcal{T}\\) is composed of labeled images \\(\\mathbf{x}_i\\) of class \\(y_i \\in \\mathcal{K}\\) with \\(\\mathcal{K}\\) the set of classes in \\(\\mathcal{T}\\). At task \\(t\\), the model \\(\\phi_t\\) is finetuned starting from the previous representation model \\(\\phi_{t-1}\\). Compatibility between the current model \\(\\phi_t\\) and a previous model \\(\\phi_k\\), with \\(k < t\\), is achieved when the feature vector of any query image obtained with \\(\\phi_t\\), the set \\(\\Phi_t^{\\mathcal{Q}}\\), can be compared with feature vectors in \\(\\Phi_k^{\\mathcal{G}}\\) without reprocessing the gallery-set. The following provides a formal definition of compatibility [27]:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.894, + 0.703 + ], + "angle": 0, + "content": "Definition 1 (Compatibility) Given two representation models \\(\\phi_t\\) and \\(\\phi_k\\), with \\(\\phi_t\\) learned after \\(\\phi_k\\), \\(\\phi_t\\) and \\(\\phi_k\\) are compatible according to the distance function \\(d(\\cdot, \\cdot)\\) if it holds:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.708, + 0.894, + 0.727 + ], + "angle": 0, + "content": "\\[\n\\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right) \\leq \\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {k} \\left(\\mathbf {x} _ {j}\\right)\\right) \\tag {1a}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.682, + 0.729, + 0.862, + 0.748 + ], + "angle": 0, + "content": "\\[\n\\forall (i, j) \\in \\left\\{(i, j) \\mid y _ {i} = y _ {j} \\right\\}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.694, + 0.75, + 0.724, + 0.762 + ], + "angle": 0, + "content": "and" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.768, + 0.892, + 0.786 + ], + "angle": 0, + "content": "\\[\n\\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right) \\geq \\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {k} \\left(\\mathbf {x} _ {j}\\right)\\right) \\tag {1b}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.682, + 0.789, + 0.862, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\forall (i, j) \\in \\left\\{(i, j) \\mid y _ {i} \\neq y _ {j} \\right\\}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.808, + 0.875, + 0.824 + ], + "angle": 0, + "content": "\\[\nw i t h k < t, \\quad t = (2, 3, \\dots , T), \\quad k = (1, 2, \\dots , T - 1).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Main Result. In this paragraph, we state and prove that learning stationary feature representations according to a \\(d\\)-Simplex fixed classifier necessarily implies optimal approximation of the compatibility as defined in Eqs. 1a and 1b." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28795" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.214, + 0.105, + 0.38, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.273, + 0.243, + 0.352, + 0.256 + ], + "angle": 0, + "content": "(a) Same class" + }, + { + "type": "image", + "bbox": [ + 0.429, + 0.102, + 0.811, + 0.232 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.573, + 0.243, + 0.671, + 0.256 + ], + "angle": 0, + "content": "(b) Different class" + }, + { + "type": "image_caption", + "bbox": [ + 0.075, + 0.268, + 0.892, + 0.352 + ], + "angle": 0, + "content": "Figure 2. Key concepts and relationships underlying Theorem 1. Distances in feature space of two distinct samples within their hyperballs before and after model update, with the update process represented by a dotted arrow. (a): Distances between samples \\(\\mathbf{x}_i\\) and \\(\\mathbf{x}_j\\) of the same class \\(y\\) before (red) and after (cyan) model update. (b): Distances between samples \\(\\mathbf{x}_i\\) of class \\(y_i\\) and \\(\\mathbf{x}_j\\) of class \\(y_j\\), before (red) and after (cyan) model update. Compatibility is verified by computing the expected lengths of the segments and verifying if they satisfy the inequalities of the compatibility definition. A transparently colored instance shows counter-intuitive distance behavior. Expectation reveals the underlying pattern of approximation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.471, + 0.489 + ], + "angle": 0, + "content": "The formulation involves examining the expected distance between feature points before and after a learning update in a high-dimensional space, where the feature points are assumed to be distributed in hyperballs (i.e., high dimensional ball) centered at the prototypes of the \\(d\\)-Simplex fixed classifier. This abstraction allows for mathematical manipulation and analysis of the cluster as a single entity rather than individual points." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.501, + 0.471, + 0.698 + ], + "angle": 0, + "content": "Theorem 1 (Stationarity \\(\\Rightarrow\\) Compatibility) Let \\(\\mathbf{W} = [\\mathbf{w}_1, \\mathbf{w}_2, \\ldots, \\mathbf{w}_K]\\) be the \\(d \\times K\\) matrix of a \\(d\\)-Simplex fixed classifier with \\(K\\) pre-allocated classes. Given two tasks, \\(\\mathcal{T}_k\\) and \\(\\mathcal{T}_t\\). The task \\(\\mathcal{T}_t\\) is derived from \\(\\mathcal{T}_k\\) by incorporating an additional training set \\(\\Delta \\mathcal{T}\\), such that \\(\\mathcal{T}_t = \\mathcal{T}_k \\cup \\Delta \\mathcal{T}\\). The combined task, \\(\\mathcal{T}_t\\), comprises a set of classes each denoted by \\(y\\), where \\(y \\in \\{1, 2, \\ldots, K_t\\}\\) and \\(K_t < K\\). Under the assumption that learning the new task \\(\\mathcal{T}_t\\) causes the hyperball \\(\\mathcal{B}_k(\\mathbf{w}_y)\\) with radius \\(r_k^y\\) to shrink into a smaller hyperball \\(\\mathcal{B}_t(\\mathbf{w}_y)\\), i.e., \\(r_t^y \\leq r_k^y\\) for all \\(y\\) in the set \\(\\{1, 2, \\ldots, K_k\\}\\), then it necessarily follows that \\(\\phi_t\\) and \\(\\phi_k\\) optimally approximate the compatibility inequality constraints as defined in Def. 1 in expectation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.71, + 0.336, + 0.725 + ], + "angle": 0, + "content": "The proof is available in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.743, + 0.47, + 0.82 + ], + "angle": 0, + "content": "Discussion. The Theorem relies on two main assumptions: the use of a \\(d\\)-Simplex fixed classifier [42] and the model's sufficient expressiveness, as described in the UFM abstraction [53, 54]. The latter assumption enables us to consider features independently1. While the former allows focusing" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.368, + 0.894, + 0.427 + ], + "angle": 0, + "content": "on a single pairwise class interaction, since interactions with all other classes are symmetrically similar and cannot change. Fig. 2 illustrates the key concepts and relationships presented in Theorem 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.895, + 0.701 + ], + "angle": 0, + "content": "Without loss of generality, the Theorem considers two distinct hyperballs of different radius \\(\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)\\) and \\(\\mathcal{B}_{\\mathrm{old}}(\\mathbf{w}_y)\\) representing the semantic clusters of a generic class \\(y\\), respectively before and after a generic learning update. The assumption that features are distributed in hyperballs stems from the margin-based softmax loss\\(^2\\) introduced in [67]. This interpretation has since been utilized in various studies, such as SphereFace [68] and ArcFace [8]. Besides the margin formulation, empirical evidence, such as Neural Collapse [44], shows that class features not only cluster around their associated prototypes but also, with sufficient training epochs, collapse into them, resulting in hyperballs tightening around the prototypes. Due to the stationarity property induced by the \\(d\\)-Simplex classifier \\(\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)\\) and \\(\\mathcal{B}_{\\mathrm{old}}(\\mathbf{w}_y)\\) hyperballs have the same center in the representation space on the classifier prototype \\(\\mathbf{w}_y\\). After the learning step, \\(\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)\\) has a shorter radius (i.e., adding new information improves the discrimination capability of the model [69-72])." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.702, + 0.894, + 0.822 + ], + "angle": 0, + "content": "In particular, Fig. 2a shows the case in which feature vectors are from samples of the same class. As defined in Eq. 1a compatibility requires that, after updating, the distance between \\(\\phi_{\\mathrm{new}}(\\mathbf{x}_i)\\) (in the cyan hyperball) and \\(\\phi_{\\mathrm{old}}(\\mathbf{x}_j)\\) (in red hyperball) is less than or equal to distance between \\(\\phi_{\\mathrm{old}}(\\mathbf{x}_i)\\) and \\(\\phi_{\\mathrm{old}}(\\mathbf{x}_j)\\). The figure displays two configurations: one where the condition is met and another where it is not met (shown in transparent colors)." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.824, + 0.892, + 0.839 + ], + "angle": 0, + "content": "Fig. 2b shows the case in which the feature vectors are" + }, + { + "type": "page_footnote", + "bbox": [ + 0.08, + 0.827, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Essentially, the Neural Collapse phenomenon, which is observed across various networks and datasets, also appears in a two-layer neural network when assuming input feature independence (i.e., a UFM). This equivalence supports the assumption that: 1) real network backbones are typically expressive enough to learn features as independent entities, and 2) UFM can be used as a tool to study neural networks properties." + }, + { + "type": "page_footnote", + "bbox": [ + 0.501, + 0.851, + 0.894, + 0.901 + ], + "angle": 0, + "content": "2The margin enforces the confinement of features within a hyperball or a hyperdisc (the local approximation of a hypercap) around class prototypes. A disc in high-dimensional space can be considered a hyperball when referring to its filled volume." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28796" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.258 + ], + "angle": 0, + "content": "from samples of different classes. As defined in Eq. 1b compatibility requires that, after updating, the distance between \\(\\phi_{\\mathrm{new}}(\\mathbf{x}_i)\\) of class \\(y_i\\) (in the cyan hyperball centered in \\(\\mathbf{w}_{y_i}\\)) and \\(\\phi_{\\mathrm{old}}(\\mathbf{x}_j)\\) of class \\(y_j\\) (in the red hyperball centered in \\(\\mathbf{w}_{y_j}\\)) is greater than or equal to than the distance between \\(\\phi_{\\mathrm{old}}(\\mathbf{x}_i)\\) and \\(\\phi_{\\mathrm{old}}(\\mathbf{x}_j)\\). The Theorem establishes that, on average, this condition cannot be optimally satisfied and that stationarity is the best approximation achievable under the given constraints. A detailed justification for this is provided in the proof of Theorem 1, with a clearer and more focused exposition presented as a Corollary in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.473, + 0.442 + ], + "angle": 0, + "content": "Informally, the proof of the Theorem starts with the premise that, upon retraining a model, the probability of finding a class feature near the corresponding class prototype from the old model—an indicator of compatibility between the two models—is nearly zero. Subsequently, the proof establishes that the optimal approximation for a compatible representation is obtained when the average distance between the same hyperball in two distinct learned models is minimized. This minimization occurs when the two corresponding hyperballs are centered at the same class prototype and when adding more classes does not alter this distance, i.e., the stationarity condition." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.445, + 0.473, + 0.611 + ], + "angle": 0, + "content": "Our formulation calculates the average distance between hyperballs based on the Ball Line Picking problem, which determines the expected length of a line segment that connects two random points inside a hyperball [73-78]. Differently from that problem, our theorem considers a line segment connecting two random points in two distinct hyperballs, each with a different radius. Specifically, we analyze the cases as shown in Fig. 2. These hyperballs represent the \"class-state\" before and after the learning step during each model update. Closed-form solutions are not available for this problem, except in a specific two-dimensional case [79]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.63, + 0.436, + 0.646 + ], + "angle": 0, + "content": "3.2. Stationarity and Higher-Order Alignment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.472, + 0.883 + ], + "angle": 0, + "content": "A specific challenge arises when fine-tuning stationary learned representation models, for example in the IAM-CL\\(^2\\)R setting of Fig. 1. In this case the old and the new models align at the first-order statistics, an inherent property of stationarity [42]. The consequence is that cross-entropy based prediction errors may not fully capture higher-order dependencies in representation space. We conjecture that simple cross-entropy mostly focuses on prediction errors related to the forgetting of the internal representation which may not promote compatibility when the representation model is largely aligned. To address this problem, we show that adding the infoNCE loss function [45, 80] is equivalent to training with the cross-entropy loss under one of the compatibility constraints while capturing higher-order dependencies." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The loss for training at task \\(t\\) the stationary representation" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.72, + 0.107 + ], + "angle": 0, + "content": "model \\(\\phi_t\\) assumes the form [42]:" + }, + { + "type": "equation", + "bbox": [ + 0.502, + 0.116, + 0.892, + 0.2 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {S C E}} \\left(\\phi_ {t}\\right) = \\\\ = - \\sum_ {B} \\log \\left(\\frac {\\exp \\left(\\mathbf {W} _ {y _ {i}} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right)}{\\sum_ {j = 1} ^ {K _ {t}} \\exp \\left(\\mathbf {W} _ {j} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right) + \\sum_ {j = K _ {t} + 1} ^ {K} \\exp \\left(\\mathbf {W} _ {j} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right)}\\right) \\tag {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.201, + 0.895, + 0.369 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_j^\\top \\in \\mathbb{R}^d\\) denotes the \\(j\\)-th column of the \\(d\\)-Simplex classifier matrix \\(\\mathbf{W} \\in \\mathbb{R}^{d \\times K}\\), being \\(K\\) the number of preallocated classes, \\(K_t = |\\bigcup_{i=1}^t \\mathcal{K}_i|\\) the number of classes learned until time \\(t\\) with \\(K_t < K\\), and \\(B\\) is a mini-batch of samples of \\(\\mathcal{T}_t\\). The first term in the denominator accounts for the classes learned until \\(t\\). The second term accounts for future classes, preserving dedicated regions in the representation space. This ensures that adding new classes minimally impacts the representation of previously learned classes [29, 39, 50, 81]. We train the representation model \\(\\phi_t\\) with the following convex combination, namely:" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.38, + 0.892, + 0.414 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {H O C}} \\left(\\phi_ {t}\\right) = \\lambda \\mathcal {L} _ {\\mathrm {S C E}} \\left(\\phi_ {t}\\right) + (1 - \\lambda) \\mathcal {L} _ {\\mathrm {N C E}} \\left(\\phi_ {t}, \\phi_ {t - 1}\\right), \\tag {3} \\\\ \\text {w i t h} \\quad \\lambda \\in [ 0, 1 ] \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.424, + 0.862, + 0.44 + ], + "angle": 0, + "content": "where: \\(\\mathcal{L}_{\\mathrm{SCE}}(\\phi_t)\\) is the cross-entropy loss of Eq. 2, and" + }, + { + "type": "equation", + "bbox": [ + 0.503, + 0.469, + 0.892, + 0.54 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {N C E}} \\left(\\phi_ {t}, \\phi_ {t - 1}\\right) = - \\sum_ {B} \\log \\left(\\frac {\\Delta \\left(\\phi_ {t - 1} \\left(\\mathbf {x} _ {i}\\right) , \\phi_ {t} \\left(\\mathbf {x} _ {i}\\right)\\right)}{\\sum_ {j \\neq i} \\Delta \\left(\\phi_ {t - 1} \\left(\\mathbf {x} _ {i}\\right) , \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right)}\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.55, + 0.535, + 0.562 + ], + "angle": 0, + "content": "with" + }, + { + "type": "equation", + "bbox": [ + 0.511, + 0.571, + 0.892, + 0.617 + ], + "angle": 0, + "content": "\\[\n\\Delta \\left(\\phi_ {t - 1} (\\mathbf {x} _ {i}), \\phi_ {t} (\\mathbf {x} _ {j})\\right) = \\exp \\left(\\tau \\cdot \\frac {\\phi_ {t - 1} (\\mathbf {x} _ {i}) \\phi_ {t} (\\mathbf {x} _ {j})}{\\left| \\left| \\phi_ {t - 1} (\\mathbf {x} _ {i}) \\phi_ {t} (\\mathbf {x} _ {j}) \\right|\\right|}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.617, + 0.894, + 0.722 + ], + "angle": 0, + "content": "is the contrastive loss [45, 80] based on \\(\\tau\\)-scaled cosine similarity between \\(\\phi_{t-1}(\\mathbf{x}_i)\\) and \\(\\phi_t(\\mathbf{x}_j)\\). We show that training the representation model with the \\(\\mathcal{L}_{\\mathrm{HOC}}\\) of Eq. 3 is both: (1) able to capture higher-order dependencies between old and new model representations and (2) equivalent to learning under the compatibility constraints in Def. 1a. We refer to this loss as the Higher-Order Compatibility loss (\\(\\mathcal{L}_{\\mathrm{HOC}}\\))." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.723, + 0.894, + 0.813 + ], + "angle": 0, + "content": "Through Theorem 1 presented in the previous section, we establish that the constraint of Eq. 1a cannot be exploited in combination with the constraint of Eq. 1b. Based on this result we show that, under no specific conditions, the constrained optimization problem using solely the inequality constraint of Eq. 1a:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.823, + 0.892, + 0.901 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname * {a r g m i n} _ {\\phi_ {t}} \\mathcal {L} _ {\\text {S C E}} (\\phi_ {t}) \\\\ \\mathrm {s . t .} \\quad \\mathrm {d} \\left(\\phi_ {k} (\\mathbf {x} _ {i}), \\phi_ {t} (\\mathbf {x} _ {j})\\right) - \\mathrm {d} \\left(\\phi_ {k} (\\mathbf {x} _ {i}), \\phi_ {k} (\\mathbf {x} _ {j})\\right) \\leq 0 \\\\ \\forall y _ {i} = y _ {j} \\tag {6} \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28797" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.139, + 0.093, + 0.411, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.259, + 0.47, + 0.302 + ], + "angle": 0, + "content": "Figure 3. Training loss of a \\(d\\)-Simplex fixed classifier during a model update. Values are the cross-entropy loss of Eq. 2 (red line) and the loss of Eq. 3 (blue line). Models are trained on MNIST." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.45 + ], + "angle": 0, + "content": "can be transformed into a tractable form. Rooted in the work of [82], this transformation not only provides an approach to solve the tractability issue but, within the context of compatibility, it also allows preserving the optimality as outlined in the proof of Theorem 1. As shown in [82], the model for a constrained problem like Eq. 6 can be equivalently learned with a convex combination of the cross-entropy loss and the Kullback-Leibler divergence function." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.471, + 0.663 + ], + "angle": 0, + "content": "On the other hand, as discussed in [83], the contrastive loss \\(\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})\\) can be approximated as the Kullback-Leibler divergence between the product of the marginals of the joint distribution of \\(\\phi_t\\) and \\(\\phi_{t - 1}\\). Moreover, \\(\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})\\) also approximates the mutual information between \\(\\phi_t\\) and \\(\\phi_{t - 1}\\), thereby enabling to capture higher-order dependencies between consecutive updates of the model. As a consequence, training with the loss in Eq. 3 is equivalent to the optimal classifier for the constrained optimization problem stated in Eq. 6 and at the same time, thanks to the term \\(\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})\\), takes into account higher-order variations between \\(\\phi_{t - 1}(\\mathbf{x}_i)\\) and \\(\\phi_t(\\mathbf{x}_j)\\). In the following, we call training the representation model using \\(d\\)-Simplex with \\(\\mathcal{L}_{\\mathrm{HOC}}\\) as \\(d\\)-Simplex-HOC." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.663, + 0.47, + 0.801 + ], + "angle": 0, + "content": "In Fig. 3, we illustrate the effects of \\(\\mathcal{L}_{\\mathrm{HOC}}\\) compared to the cross-entropy loss. We use a toy example with the LeNet++ CNN architecture [84] with the \\(d\\)-Simplex fixed classifier. The model is initially trained on the first five MNIST classes and then fine-tuned on all ten classes. The cross-entropy training error (red curve) converges rapidly to low values. In contrast, the convergence with the \\(\\mathcal{L}_{\\mathrm{HOC}}\\) loss (blue curve) is more gradual, which allows for the capture of richer information during back-propagation." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.318, + 0.831 + ], + "angle": 0, + "content": "4. Experimental Verification" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.9 + ], + "angle": 0, + "content": "Referring to the IAM-CL\\(^2\\)R learning scenario presented in Fig. 1, this section provides empirical evidence to verify the practical implications of the theoretical results discussed earlier." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.092, + 0.7, + 0.108 + ], + "angle": 0, + "content": "4.1. Datasets and Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.894, + 0.251 + ], + "angle": 0, + "content": "Pre-trained Models. We pre-train our models in a supervised manner using the ImageNet32 [85]. Three distinct models are pre-trained on ImageNet32 with 100, 300, and 600 classes. The model trained with 100 classes is used to initialize the model before fine-tuning on the sequence of tasks. The other two models are used to simulate the practice of downloading and fine-tuning pre-trained models and serve as third-party models that will replace the current one undergoing fine-tuning." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.894, + 0.326 + ], + "angle": 0, + "content": "Fine-tuning. We replicate the fact that dataset size for training third-party models is typically significantly larger than the dataset size used for fine-tuning [86]. According to this, pre-trained models are fine-tuned with a reduced version of CIFAR100 [87] denoted in this paper as CIFAR100R." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.327, + 0.893, + 0.447 + ], + "angle": 0, + "content": "We considered two distinct task sequences consisting of 7 and 31 tasks each. We fine-tune the pre-trained model with an initial task comprising 10 classes. Subsequently, for the sequences of 7 and 31 tasks, the respective tasks contain 15 and 3 classes each. The fine-tuning process incorporates incoming task data, consisting of 300 images per class, and utilizes an episodic memory that stores 20 images from each class of previous tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.894, + 0.568 + ], + "angle": 0, + "content": "Model Replacement. In our experiments, we verify the impact of replacing the current fine-tuned model with two improved models pre-trained elsewhere. The two replacements occur while fine-tuning on CIFAR100R: at the third and fifth tasks in the shorter sequence, and at the eleventh and twenty-first tasks in the longer sequence. We also consider the challenging scenario of improved model replacement considering more sophisticated network architectures." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.569, + 0.894, + 0.689 + ], + "angle": 0, + "content": "The \\(d\\)-Simplex fixed classifier is pre-allocated with a number of classes \\(K\\), ensuring enough space to accommodate future classes for both pre-training and fine-tuning. Class assignments for pre-training are made from left to right, and for fine-tuning, from right to left. This straightforward convention is used to ensure that classes assigned for pre-training and fine-tuning remain distinct, without overlap. Other non-overlapping assignment methods could also be used." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.894, + 0.764 + ], + "angle": 0, + "content": "Network Architectures. We use ResNet18 [88] as network architecture. In the scenario using more sophisticated network architectures, we initially replace ResNet18 with SENet18 [89], followed by a subsequent replacement with a RegNetY_400MF [90]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Hyper-parameters. The ResNet18, SENet18, and RegNetY_400MF models were pre-trained on ImageNet32 using the following hyper-parameters: 300 epochs, a batch size of 128, and an initial SGD optimizer learning rate of 0.1, which was adjusted using a Cosine Annealing schedule. For each task used for fine-tuning, the model is trained for 70 epochs with a batch size of 128, starting with a learning rate of 0.001 that was reduced by a factor of 10 after the 50th and 64th epochs. The \\(d\\)-Simplex was pre-allocated with \\(K = 1024\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "28798" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.099, + 0.09, + 0.466, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.221, + 0.28, + 0.337, + 0.293 + ], + "angle": 0, + "content": "(a) Two replacements" + }, + { + "type": "image", + "bbox": [ + 0.467, + 0.091, + 0.874, + 0.278 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.638, + 0.28, + 0.746, + 0.293 + ], + "angle": 0, + "content": "(b) No replacements" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.893, + 0.334 + ], + "angle": 0, + "content": "Figure 4. Average multi-model Accuracy \\((AA_{t})\\) evaluated across 31 tasks using CIFAR100R/10, showing: (a) model replacements at tasks 11 and 21 (indicated by yellow markers); (b) no model replacement." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.345, + 0.268, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.138, + 0.497, + 0.208, + 0.509 + ], + "angle": 0, + "content": "(a) CVS [38]" + }, + { + "type": "image", + "bbox": [ + 0.268, + 0.346, + 0.458, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.318, + 0.497, + 0.409, + 0.509 + ], + "angle": 0, + "content": "(b) BCT-ER [27]" + }, + { + "type": "image", + "bbox": [ + 0.458, + 0.346, + 0.647, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.493, + 0.497, + 0.614, + 0.509 + ], + "angle": 0, + "content": "(c) \\(d\\) -Simplex-FD [39]" + }, + { + "type": "image", + "bbox": [ + 0.648, + 0.346, + 0.871, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.651, + 0.497, + 0.835, + 0.509 + ], + "angle": 0, + "content": "(d) \\(d\\)-Simplex-HOC (in this paper)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.521, + 0.893, + 0.564 + ], + "angle": 0, + "content": "Figure 5. Compatibility Matrices for \\(d\\)-Simplex-HOC, CVS, BCT-ER, and \\(d\\)-Simplex-FD on CIFAR100R/10 across 7 tasks. Model replacements at tasks 3 and 5 are highlighted in bold. Entries failing to meet compatibility criteria as defined in [27] are marked with a light-red background." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.579, + 0.248, + 0.594 + ], + "angle": 0, + "content": "classes (i.e., \\(d = K - 1\\))." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.597, + 0.471, + 0.748 + ], + "angle": 0, + "content": "Performance Evaluation. The evaluation focuses on the open-set recognition task, in which separated datasets for training and evaluation are required. The standard 1:N search protocol, applicable to re-identification and similar tasks [27], is employed in the evaluation. To ensure strict separation between datasets, the CIFAR10 dataset is utilized for evaluation during fine-tuning with CIFAR100R. Specifically, the test set of CIFAR10, comprising 10,000 images, is used as the gallery set, while its training set of 50,000 images serves as the query set." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Following [27] and [29], we measure performance progression across the two sequences of tasks using two established metrics: Average Compatibility \\((AC)\\) and Average multi-model Accuracy (referred shortly as to \\(AA_{t}\\)). The metric \\(AC\\) quantifies the extent of compatibility across all possible pairs of model combinations by providing a normalized count of times in which compatibility is achieved. Conversely, \\(AA_{t}\\) calculates the mean accuracy across all combinations of the previously learned models until task \\(t\\), providing an overall measure of accuracy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.578, + 0.796, + 0.594 + ], + "angle": 0, + "content": "4.2. IAM-CL\\(^2\\)R: Comparative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.614, + 0.895, + 0.75 + ], + "angle": 0, + "content": "We performed a comparative analysis of \\(d\\)-Simplex-HOC against FAN [37], CVS [38], \\(d\\)-Simplex-FD [39], and the lifelong adapted versions of BCT [27] (BCT-ER), LCE [28] (LCE-ER), and AdvBCT [36] (AdvBCT-ER). The experiments also incorporate a baseline method, Experience Replay (ER), in which the model is fine-tuned using cross-entropy loss on data of the new task and an episodic memory. Ablation studies of IAM-CL\\(^2\\)R with the \\(d\\)-Simplex-HOC are provided in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Replacing: Same Architecture, Expanded Data. Fig. 4 presents the Average multi-model Accuracy at task \\( t(AA_{t}) \\) for learning scenarios with model replacement as depicted in Fig. 4a and for those without as depicted in Fig. 4b. The experiment involves fine-tuning a ResNet18 model across 31 tasks. The comparison provides insights into the performance benefits that can be obtained by replacing models when representations are trained in a compatible manner. The \\( d \\)-Simplex-HOC effectively incorporates improvements from model replacements, showing increased performance" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28799" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.089, + 0.464, + 0.288 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.299, + 0.472, + 0.342 + ], + "angle": 0, + "content": "Figure 6. Plots of Average multi-model Accuracy \\((AA_{t})\\) for 31 tasks on CIFAR100R/10, showing the impact of model replacements with different network architectures at tasks 11 and 21." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.37, + 0.47, + 0.506 + ], + "angle": 0, + "content": "compared to the case without model replacement, as indicated in Fig. 4b. The \\(d\\)-Simplex-FD demonstrates a similar capability, though to a reduced extent. The other methods have a clear performance decay after model replacements and end up with a worse performance than the case without replacement. This can be attributed to the fact that after replacement, fine-tuning is applied to a model obtained by retraining the network from scratch, leading to an entirely different representation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.474, + 0.871 + ], + "angle": 0, + "content": "Further performance details, as indicated by the self and cross-test accuracy values, are shown according to the compatibility matrices [27, 29]. Fig. 5 shows these values for CVS, BCT-ER, \\(d\\)-Simplex-FD, and \\(d\\)-Simplex-HOC in the 7 tasks sequence. The values reveal that the \\(d\\)-Simplex-HOC effectively leverages the improved expressive power of the models after replacement, except in one instance. This exception, where the model is not compatible and the cross-test accuracy falls below the self-test accuracy, is shown in Fig. 5d. Both CVS and BCT-ER score near zero cros-tests accuracy after model replacements as indicated by the values in the blue sub matrix blocks shown in Fig. 5a and Fig. 5b. This leads to mostly non-compatible representations. Although both \\(d\\)-Simplex-HOC and \\(d\\)-Simplex-FD utilize the \\(d\\)-Simplex fixed classifier to learn stationary representations, the former shows better performance. This can be attributed to the high-order alignment achievable through the HOC loss. To provide a full evaluation of compatibility, the \\(AA_{t}\\) of Fig. 4 is complemented with the Average Compatibility \\(AC\\) in Tab. 1. We also report the Average multi-model Accuracy \\(AA_{7}\\) and \\(AA_{31}\\) for methods compared at the end of the 7-th and 31-th task, respectively. It is observed that, in both instances, all models—with the exception of \\(d\\)-Simplex-HOC—fail to achieve significant compatibility performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.472, + 0.902 + ], + "angle": 0, + "content": "Replacing: Different Architectures, Expanded Data. Fig. 6 shows the performance of the evaluated methods when" + }, + { + "type": "table", + "bbox": [ + 0.507, + 0.089, + 0.888, + 0.25 + ], + "angle": 0, + "content": "
METHOD7 tasks31 tasks
\\( {AC} \\)\\( A{A}_{7} \\)\\( {AC} \\)\\( A{A}_{31} \\)
ER baseline×36.22<0.0131.30
FAN [37]×36.32<0.0130.79
BCT-ER [27]×35.59×29.88
LCE-ER [28]×34.89×29.30
AdvBCT-ER [36]×35.73×30.10
CVS [38]×36.310.0131.34
d-Simplex-FD [39]0.0556.580.2156.27
d-Simplex-HOC0.9568.130.6567.40
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.26, + 0.895, + 0.318 + ], + "angle": 0, + "content": "Table 1. Compatibility metrics with CIFAR100R/10 for 7 tasks with model replacements at task 3 and task 5, and 31 tasks with model replacements at task 11 and task 21. “×” indicates the case in which compatibility is not achieved." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.349, + 0.895, + 0.591 + ], + "angle": 0, + "content": "the original ResNet18 is replaced first by a SENet18 and then by a more expressive RegNetY_400MF. It is observed that the change of network architecture not only does not adversely affect compatibility in the \\(d\\)-Simplex-HOC but takes advantage of their more expressive representation power. In particular, direct comparison of Fig. 6 with Fig. 5 shows that \\(d\\)-Simplex-HOC improves performance gradually with each model replacement. This is in contrast to \\(d\\)-SimplexFD, which does not demonstrate the same trends leading to a plateau around the 20-th task. Given the different feature sizes before and after the second model replacement with the RegNetY_400MF architecture—512 and 384, respectively—all methods except \\(d\\)-Simplex-HOC and \\(d\\)-Simplex-FD require non-trivial extensions to adapt to the changed feature size. According to this, for these methods, evaluation cannot be reported." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.613, + 0.62, + 0.63 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.641, + 0.895, + 0.807 + ], + "angle": 0, + "content": "In this paper, we have investigated the concept of learning compatible representations through the principle of stationarity. We demonstrated that stationary representations optimally approximate compatibility according to its definition. We demonstrated that better model alignment through higher-order dependencies can be obtained by training with a loss derived from one of the compatibility inequality constraints. Finally, empirical evidence confirmed that stationary representations enable uninterrupted retrieval service allowing for fine-tuning and model replacement to occur concurrently and asynchronously with limited interference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.894, + 0.856 + ], + "angle": 0, + "content": "Acknowledgment: This work was partially supported by the European Commission under European Horizon 2020 Programme, grant number 951911 - AI4Media." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "We acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support (ISCRA-C ID: HP10C4TIIM)." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28800" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.184 + ], + "angle": 0, + "content": "[1] Sumit Chopra, Raia Hadsell, and Yann LeCun. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10428-10436, 2020. 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.461 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.956 + ], + "angle": 0, + "content": "28804" + } + ] +] \ No newline at end of file diff --git a/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_origin.pdf b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..00dfcd34298e97eaf3b53347c00efde2fa8134cc --- /dev/null +++ b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/554d31c6-935e-4439-a512-f2ee4bfee481_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:baab955fbd4db17d42fc5dc7994c52f309d1a36e8974cac8c63ede41f1721a91 +size 753457 diff --git a/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/full.md b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/full.md new file mode 100644 index 0000000000000000000000000000000000000000..ad3a4a457fef35f7d5c88c1b1005762183beec95 --- /dev/null +++ b/2024/Stationary Representations_ Optimally Approximating Compatibility and Implications for Improved Model Replacements/full.md @@ -0,0 +1,331 @@ +# Stationary Representations: Optimally Approximating Compatibility and Implications for Improved Model Replacements + +Niccolò Biondi Federico Pernici Simone Ricci Alberto Del Bimbo +DINFO (Department of Information Engineering), University of Florence, Italy, +MICCC (Media Integration and Communication Center), +name.surname@unifi.it + +# Abstract + +Learning compatible representations enables the interchangeable use of semantic features as models are updated over time. This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pretrained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pretrained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamc12r. + +# 1. Introduction + +By learning powerful internal feature representations from data, Deep Neural Networks (DNNs) [1-4] have made tremendous progress in some of the most challenging search tasks such as face recognition [5-9], person re-identification [10-12], image retrieval [13-15] and this significance also extends to a variety of other data modalities [16, 17]. Although all of the works mentioned above have focused on learning feature representations from static and, + +![](images/e7cdfc1cbe186ab8d0b88e37850155adbeefb629c048effa3dad0343b6644885.jpg) +Figure 1. Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL $^2$ R pronounced "I am clear"). In the process of lifelong learning, a model is sequentially fine-tuned and asynchronously replaced with improved third-party models that are pre-trained externally. Stationary representations ensure seamless retrieval services and better performance, without the need to reprocess gallery images. + +more recently, dynamic datasets [18-21], the now-standard practice is downloading and fine-tuning representations from models pre-trained elsewhere [22, 23]. These "third-party" pre-trained models often incorporate new data, utilize alternative architectures, adopt different loss functions or more in general provide novel methodologies. Whether applied individually or combined, these advancements aim to encapsulate the field's rapid progress within a single unified model [24]. This greatly facilitates the exploitation of internally learned semantic representations, particularly as models, datasets, and computational infrastructure continue to expand in size, complexity, and cost [25, 26]. + +The challenge of fully exploiting such standard practice in retrieval/search systems has to deal with the underlying + +problem of compatible learning [27-29]. That is the desire to align the representation of different models trained with different data, initialization seeds, loss functions, or alternative architectures—either individually or in combination. In such applications, maintaining alignment is crucial to minimize the need for repeated reprocessing of gallery images for feature extraction each time a new pre-trained model becomes available [24]. Reprocessing is not only computationally intensive but may also be unsustainable for extensive gallery sets [25, 26, 30] or unfeasible if the original images are no longer accessible due to privacy concerns [31]. This holds across various typical galleries: social networks update millions of images every month, while in robotics and automotive domains, the update rate can be as rapid as hundreds of images every second. Similarly, in textual domains, books can be structured into chapters, paragraphs, and sentences, enabling the capture of semantic relationships between these segments. While a similar organizational principle can be structured for the web with LLMs [17, 32], the challenge lies in the impracticality of reprocessing such extensive content with each advancement in representation models. Although recent research has shown the effectiveness of compatible representation learning [27-29, 33-41], there is still a lack of comprehensive theoretical understanding about compatibility. + +This paper introduces a theorem that demonstrates how the stationary representations proposed in [42, 43] optimally approximate compatibility according to the two inequality constraints of its formal definition as provided in [27]. This not only establishes a solid foundation for future works, but also presents implications that can be exploited fine-tuning third-party models without the need of reprocessing gallery images. Specifically, we show that a continuously fine-tuned model can be asynchronously replaced by downloading a higher-performing, pre-trained model from an external source. Due to stationarity (and therefore optimal compatibility), such a replacement provides seamless retrieval services with improved performance, eliminating the need for image gallery reprocessing. We refer to this scenario as Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL $^2$ R pronounced "I am clear"). Fig. 1 illustrates the relationship between sequential fine-tuning and model replacement. Furthermore, as will be elaborated in the related work section, our foundation draws connections with the Neural Collapse phenomenon [44] and its associated theory. + +Our second contribution is related to a specific challenge that arises: the tendency of the old and the new replaced models to align at their first-order statistics, an inherent property of stationary representation. Consequently, cross-entropy based prediction errors alone, when fine-tuning the representation, may not fully capture higher-order dependencies. To address this issue while preserving compatibility, we show + +that learning stationary representations using a convex combination of the cross-entropy loss and the infoNCE loss [45] is equivalent to training under one of the compatibility inequality constraints in [27]. This combined loss, termed Higher-Order Compatibility (HOC), distinguishes itself from the use of cross-entropy alone by capturing higher-order dependencies and optimally approximating compatibility. + +# 2. Related Work + +Neural Collapse. Neural Collapse (NC) is an empirical phenomenon that demonstrates the alignment between features and the classifier in a symmetric configuration [44]. Specifically, each class feature vector and its corresponding class prototype vector align with each other (i.e., collapse onto the same vector), forming a regular Simplex geometry in a subspace of the representation space. This particular configuration, which results in maximal separation of the collapsed vectors, is also referred to as a regular Simplex ETF (Equiangular Tight Frame). As training progresses and the training phase goes beyond zero classification error, the network increasingly approaches collapse. Notably, this also agrees with the double descent generalization regime observed within the same training phase [46]. The two phenomena together indicate a form of stable steady-state for the internal representations of Deep Neural Networks. + +Prior to the observation of neural collapse, other research applied the steady-state of the Simplex geometry directly from the beginning of training. The fixed classifier with mutually orthogonal prototypes, introduced in [47], firstly demonstrates no degradation in classification performance. Building on this initial model, the regular polytope fixed classifiers—such as the $d$ -Simplex, $d$ -Cube, and $d$ -Orthoplex—advance the concept further by observing stationary and maximally separated representations, as introduced in [48] and further detailed in [42]. Prior to these developments, [49] delved into the early energy-based investigations of symmetric and maximal separation in the representation space. The distinction between the natural emergence of a regular Simplex ETF and intentionally fixing the regular Simplex geometry at the beginning of training is that prior fixing can preserve regions in the representation space for future classes, as introduced in [50] and more recently in [51] and [52]. Our work takes advantage of this preservation for future classes, allowing third-party representation models to be trained from scratch and fine-tuned, while mitigating the interference in the representation space of the classes involved in both processes. + +As neural collapse is related to the interaction between the neural network's final and penultimate layers, it offers a tool to examine training dynamics and convergence, as introduced in [53] and [54] under the name of Unconstrained Feature Model (UFM) and Layered Peeled Model (LPM), respectively. In both [55] and [56], the favorable conver + +gence of fixing the final classifier according to the UFM is demonstrated. In [54], it is shown that training on imbalanced datasets does not necessarily result in NC. Additional observations from [57] suggest that NC can emerge in both imbalanced and long-tail scenarios when the classifier is fixed to a $d$ -Simplex geometry. Further detailed results on NC are presented in [58]. Our proof is based on the assumption from the UFM and LPM that the backbone has sufficient expressiveness to allow for the independent study of each feature. Our proof is also based on the assumption of $d$ -Simplex fixed classifier, whose inherent symmetry allows to reduce the extent of the analysis to a single pairwise class interaction, as it causes all the interactions to be identical. + +Compatible Representations Learning. Compatible representations broadly refer to the ability to align different learned representations, as discussed in [59-63]. The distinction outlined in [27] is that the alignment of models should be achieved without wasting the information learned from new data. This capability is typically evaluated in a query and gallery setting, where query and gallery features are extracted from two different representation models. The model for the query is trained using an extended dataset that includes additional data not present in the one used for training the gallery's model. The study in [27] further presents a method called Backward Compatible Training (BCT), which applies regularization to a new model using the classifier from the previous learning phase. This approach implicitly aligns the current improved model with the previously trained classifier, which is kept fixed. Several other methods have adopted this basic working principle: The fundamental aspect of this principle is that the challenge of model alignment is primarily demanded by the new model, which must learn from both the additional and the old data how to compensate for the inadequate representations of the previously learned models. Conversely, as also recently highlighted in [41], methods such as [64] or the more recent [28, 65, 66] train a lightweight transformation to convert old representations into new ones for backward compatibility. However, these methods do not entirely eliminate the re-processing cost. As the number of chained mappings increases, the entire chain necessitates re-evaluation each time the representation model is updated. This makes them unsuitable for sequential learning and large gallery-sets. While its primary focus is on classification, the study in [37] is one of the first methods employing sequential chaining transformations for aligning representations within a common reference space. The works in [39] and [38] bypass the use of chaining transformations, focusing instead on aligning representations for compatibility purposes in lifelong learning scenarios. Both approaches leverage auxiliary losses to ensure similarity among previously learned representations. Additionally, [39] achieves alignment with an absolute reference through the use of fixed classifiers, in line with the + +neural collapse phenomenon. + +The work in [41] argues that there is an inherent trade-off in the definition of compatibility introduced in [27], which inspires them to "hold" incompatible information of the new model on additional orthogonal dimensions to avoid this conflict. Their argument seems to be in line with the recent work [29] and [39] based on stationarity in which (nearly) orthogonal dimensions are pre-allocated from the beginning using a regular $d$ -Simplex fixed classifier. In this paper, we establish a formal relationship among compatibility, neural collapse, and stationarity, showing that stationarity provides an optimal approximation to the compatibility definition formulated in [27]. + +# 3. Theoretical Results + +# 3.1. Stationarity and Compatibility + +Preliminaries. Let $\mathcal{G} = \{\mathbf{x}_i\}_{i=1}^{N_g}$ be a gallery-set composed of a set of $N_g$ images $\mathbf{x}_i \in \mathbb{R}^D$ with class labels from $\mathcal{V} = \{y_i\}_{i=1}^L$ and $\Phi^\mathcal{G} = \{\phi(\mathbf{x}_i) \in \mathbb{R}^d | \forall \mathbf{x}_i \in \mathcal{G}\}$ be the set of feature vectors of the gallery-set $\mathcal{G}$ obtained with representation model $\phi$ . Let $\mathcal{Q} = \{\mathbf{x}_i\}_{i=1}^{N_q}$ be a query-set composed of $N_q$ images $\mathbf{x}_i \in \mathbb{R}^D$ and $\Phi^\mathcal{Q} = \{\phi(\mathbf{x}_i) \in \mathbb{R}^d | \forall \mathbf{x}_i \in \mathcal{Q}\}$ be the set of feature vectors of the query-set $\mathcal{Q}$ obtained with $\phi$ . Visual search is performed using a distance function $\mathrm{d}(\cdot, \cdot)$ to identify the closest gallery features to the query features. + +Let $\mathcal{T}_1, \mathcal{T}_2, \ldots, \mathcal{T}_T$ be a sequence of $T$ tasks, where each task $\mathcal{T}$ is composed of labeled images $\mathbf{x}_i$ of class $y_i \in \mathcal{K}$ with $\mathcal{K}$ the set of classes in $\mathcal{T}$ . At task $t$ , the model $\phi_t$ is finetuned starting from the previous representation model $\phi_{t-1}$ . Compatibility between the current model $\phi_t$ and a previous model $\phi_k$ , with $k < t$ , is achieved when the feature vector of any query image obtained with $\phi_t$ , the set $\Phi_t^{\mathcal{Q}}$ , can be compared with feature vectors in $\Phi_k^{\mathcal{G}}$ without reprocessing the gallery-set. The following provides a formal definition of compatibility [27]: + +Definition 1 (Compatibility) Given two representation models $\phi_t$ and $\phi_k$ , with $\phi_t$ learned after $\phi_k$ , $\phi_t$ and $\phi_k$ are compatible according to the distance function $d(\cdot, \cdot)$ if it holds: + +$$ +\mathrm {d} \left(\phi_ {k} \left(\mathbf {x} _ {i}\right), \phi_ {t} \left(\mathbf {x} _ {j}\right)\right) \leq \mathrm {d} \left(\phi_ {k} \left(\mathbf {x} _ {i}\right), \phi_ {k} \left(\mathbf {x} _ {j}\right)\right) \tag {1a} +$$ + +$$ +\forall (i, j) \in \left\{(i, j) \mid y _ {i} = y _ {j} \right\} +$$ + +and + +$$ +\mathrm {d} \left(\phi_ {k} \left(\mathbf {x} _ {i}\right), \phi_ {t} \left(\mathbf {x} _ {j}\right)\right) \geq \mathrm {d} \left(\phi_ {k} \left(\mathbf {x} _ {i}\right), \phi_ {k} \left(\mathbf {x} _ {j}\right)\right) \tag {1b} +$$ + +$$ +\forall (i, j) \in \left\{(i, j) \mid y _ {i} \neq y _ {j} \right\} +$$ + +$$ +w i t h k < t, \quad t = (2, 3, \dots , T), \quad k = (1, 2, \dots , T - 1). +$$ + +Main Result. In this paragraph, we state and prove that learning stationary feature representations according to a $d$ -Simplex fixed classifier necessarily implies optimal approximation of the compatibility as defined in Eqs. 1a and 1b. + +![](images/2eff6fe739fb7df06c087bdb409f61e0c8800b5a50359107ffcac487911cfff6.jpg) +(a) Same class + +![](images/7679c8255f67d0ca17852d3e5098ad24565751c03bcbdbc1f0d1a790d1cd8d74.jpg) +(b) Different class +Figure 2. Key concepts and relationships underlying Theorem 1. Distances in feature space of two distinct samples within their hyperballs before and after model update, with the update process represented by a dotted arrow. (a): Distances between samples $\mathbf{x}_i$ and $\mathbf{x}_j$ of the same class $y$ before (red) and after (cyan) model update. (b): Distances between samples $\mathbf{x}_i$ of class $y_i$ and $\mathbf{x}_j$ of class $y_j$ , before (red) and after (cyan) model update. Compatibility is verified by computing the expected lengths of the segments and verifying if they satisfy the inequalities of the compatibility definition. A transparently colored instance shows counter-intuitive distance behavior. Expectation reveals the underlying pattern of approximation. + +The formulation involves examining the expected distance between feature points before and after a learning update in a high-dimensional space, where the feature points are assumed to be distributed in hyperballs (i.e., high dimensional ball) centered at the prototypes of the $d$ -Simplex fixed classifier. This abstraction allows for mathematical manipulation and analysis of the cluster as a single entity rather than individual points. + +Theorem 1 (Stationarity $\Rightarrow$ Compatibility) Let $\mathbf{W} = [\mathbf{w}_1, \mathbf{w}_2, \ldots, \mathbf{w}_K]$ be the $d \times K$ matrix of a $d$ -Simplex fixed classifier with $K$ pre-allocated classes. Given two tasks, $\mathcal{T}_k$ and $\mathcal{T}_t$ . The task $\mathcal{T}_t$ is derived from $\mathcal{T}_k$ by incorporating an additional training set $\Delta \mathcal{T}$ , such that $\mathcal{T}_t = \mathcal{T}_k \cup \Delta \mathcal{T}$ . The combined task, $\mathcal{T}_t$ , comprises a set of classes each denoted by $y$ , where $y \in \{1, 2, \ldots, K_t\}$ and $K_t < K$ . Under the assumption that learning the new task $\mathcal{T}_t$ causes the hyperball $\mathcal{B}_k(\mathbf{w}_y)$ with radius $r_k^y$ to shrink into a smaller hyperball $\mathcal{B}_t(\mathbf{w}_y)$ , i.e., $r_t^y \leq r_k^y$ for all $y$ in the set $\{1, 2, \ldots, K_k\}$ , then it necessarily follows that $\phi_t$ and $\phi_k$ optimally approximate the compatibility inequality constraints as defined in Def. 1 in expectation. + +The proof is available in the Appendix. + +Discussion. The Theorem relies on two main assumptions: the use of a $d$ -Simplex fixed classifier [42] and the model's sufficient expressiveness, as described in the UFM abstraction [53, 54]. The latter assumption enables us to consider features independently1. While the former allows focusing + +on a single pairwise class interaction, since interactions with all other classes are symmetrically similar and cannot change. Fig. 2 illustrates the key concepts and relationships presented in Theorem 1. + +Without loss of generality, the Theorem considers two distinct hyperballs of different radius $\mathcal{B}_{\mathrm{new}}(\mathbf{w}_y)$ and $\mathcal{B}_{\mathrm{old}}(\mathbf{w}_y)$ representing the semantic clusters of a generic class $y$ , respectively before and after a generic learning update. The assumption that features are distributed in hyperballs stems from the margin-based softmax loss $^2$ introduced in [67]. This interpretation has since been utilized in various studies, such as SphereFace [68] and ArcFace [8]. Besides the margin formulation, empirical evidence, such as Neural Collapse [44], shows that class features not only cluster around their associated prototypes but also, with sufficient training epochs, collapse into them, resulting in hyperballs tightening around the prototypes. Due to the stationarity property induced by the $d$ -Simplex classifier $\mathcal{B}_{\mathrm{new}}(\mathbf{w}_y)$ and $\mathcal{B}_{\mathrm{old}}(\mathbf{w}_y)$ hyperballs have the same center in the representation space on the classifier prototype $\mathbf{w}_y$ . After the learning step, $\mathcal{B}_{\mathrm{new}}(\mathbf{w}_y)$ has a shorter radius (i.e., adding new information improves the discrimination capability of the model [69-72]). + +In particular, Fig. 2a shows the case in which feature vectors are from samples of the same class. As defined in Eq. 1a compatibility requires that, after updating, the distance between $\phi_{\mathrm{new}}(\mathbf{x}_i)$ (in the cyan hyperball) and $\phi_{\mathrm{old}}(\mathbf{x}_j)$ (in red hyperball) is less than or equal to distance between $\phi_{\mathrm{old}}(\mathbf{x}_i)$ and $\phi_{\mathrm{old}}(\mathbf{x}_j)$ . The figure displays two configurations: one where the condition is met and another where it is not met (shown in transparent colors). + +Fig. 2b shows the case in which the feature vectors are + +from samples of different classes. As defined in Eq. 1b compatibility requires that, after updating, the distance between $\phi_{\mathrm{new}}(\mathbf{x}_i)$ of class $y_i$ (in the cyan hyperball centered in $\mathbf{w}_{y_i}$ ) and $\phi_{\mathrm{old}}(\mathbf{x}_j)$ of class $y_j$ (in the red hyperball centered in $\mathbf{w}_{y_j}$ ) is greater than or equal to than the distance between $\phi_{\mathrm{old}}(\mathbf{x}_i)$ and $\phi_{\mathrm{old}}(\mathbf{x}_j)$ . The Theorem establishes that, on average, this condition cannot be optimally satisfied and that stationarity is the best approximation achievable under the given constraints. A detailed justification for this is provided in the proof of Theorem 1, with a clearer and more focused exposition presented as a Corollary in the Appendix. + +Informally, the proof of the Theorem starts with the premise that, upon retraining a model, the probability of finding a class feature near the corresponding class prototype from the old model—an indicator of compatibility between the two models—is nearly zero. Subsequently, the proof establishes that the optimal approximation for a compatible representation is obtained when the average distance between the same hyperball in two distinct learned models is minimized. This minimization occurs when the two corresponding hyperballs are centered at the same class prototype and when adding more classes does not alter this distance, i.e., the stationarity condition. + +Our formulation calculates the average distance between hyperballs based on the Ball Line Picking problem, which determines the expected length of a line segment that connects two random points inside a hyperball [73-78]. Differently from that problem, our theorem considers a line segment connecting two random points in two distinct hyperballs, each with a different radius. Specifically, we analyze the cases as shown in Fig. 2. These hyperballs represent the "class-state" before and after the learning step during each model update. Closed-form solutions are not available for this problem, except in a specific two-dimensional case [79]. + +# 3.2. Stationarity and Higher-Order Alignment + +A specific challenge arises when fine-tuning stationary learned representation models, for example in the IAM-CL $^2$ R setting of Fig. 1. In this case the old and the new models align at the first-order statistics, an inherent property of stationarity [42]. The consequence is that cross-entropy based prediction errors may not fully capture higher-order dependencies in representation space. We conjecture that simple cross-entropy mostly focuses on prediction errors related to the forgetting of the internal representation which may not promote compatibility when the representation model is largely aligned. To address this problem, we show that adding the infoNCE loss function [45, 80] is equivalent to training with the cross-entropy loss under one of the compatibility constraints while capturing higher-order dependencies. + +The loss for training at task $t$ the stationary representation + +model $\phi_t$ assumes the form [42]: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {S C E}} \left(\phi_ {t}\right) = \\ = - \sum_ {B} \log \left(\frac {\exp \left(\mathbf {W} _ {y _ {i}} ^ {\top} \phi_ {t} (\mathbf {x} _ {i})\right)}{\sum_ {j = 1} ^ {K _ {t}} \exp \left(\mathbf {W} _ {j} ^ {\top} \phi_ {t} (\mathbf {x} _ {i})\right) + \sum_ {j = K _ {t} + 1} ^ {K} \exp \left(\mathbf {W} _ {j} ^ {\top} \phi_ {t} (\mathbf {x} _ {i})\right)}\right) \tag {2} \\ \end{array} +$$ + +where $\mathbf{W}_j^\top \in \mathbb{R}^d$ denotes the $j$ -th column of the $d$ -Simplex classifier matrix $\mathbf{W} \in \mathbb{R}^{d \times K}$ , being $K$ the number of preallocated classes, $K_t = |\bigcup_{i=1}^t \mathcal{K}_i|$ the number of classes learned until time $t$ with $K_t < K$ , and $B$ is a mini-batch of samples of $\mathcal{T}_t$ . The first term in the denominator accounts for the classes learned until $t$ . The second term accounts for future classes, preserving dedicated regions in the representation space. This ensures that adding new classes minimally impacts the representation of previously learned classes [29, 39, 50, 81]. We train the representation model $\phi_t$ with the following convex combination, namely: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {H O C}} \left(\phi_ {t}\right) = \lambda \mathcal {L} _ {\mathrm {S C E}} \left(\phi_ {t}\right) + (1 - \lambda) \mathcal {L} _ {\mathrm {N C E}} \left(\phi_ {t}, \phi_ {t - 1}\right), \tag {3} \\ \text {w i t h} \quad \lambda \in [ 0, 1 ] \\ \end{array} +$$ + +where: $\mathcal{L}_{\mathrm{SCE}}(\phi_t)$ is the cross-entropy loss of Eq. 2, and + +$$ +\mathcal {L} _ {\mathrm {N C E}} \left(\phi_ {t}, \phi_ {t - 1}\right) = - \sum_ {B} \log \left(\frac {\Delta \left(\phi_ {t - 1} \left(\mathbf {x} _ {i}\right) , \phi_ {t} \left(\mathbf {x} _ {i}\right)\right)}{\sum_ {j \neq i} \Delta \left(\phi_ {t - 1} \left(\mathbf {x} _ {i}\right) , \phi_ {t} \left(\mathbf {x} _ {j}\right)\right)}\right) \tag {4} +$$ + +with + +$$ +\Delta \left(\phi_ {t - 1} (\mathbf {x} _ {i}), \phi_ {t} (\mathbf {x} _ {j})\right) = \exp \left(\tau \cdot \frac {\phi_ {t - 1} (\mathbf {x} _ {i}) \phi_ {t} (\mathbf {x} _ {j})}{\left| \left| \phi_ {t - 1} (\mathbf {x} _ {i}) \phi_ {t} (\mathbf {x} _ {j}) \right|\right|}\right) \tag {5} +$$ + +is the contrastive loss [45, 80] based on $\tau$ -scaled cosine similarity between $\phi_{t-1}(\mathbf{x}_i)$ and $\phi_t(\mathbf{x}_j)$ . We show that training the representation model with the $\mathcal{L}_{\mathrm{HOC}}$ of Eq. 3 is both: (1) able to capture higher-order dependencies between old and new model representations and (2) equivalent to learning under the compatibility constraints in Def. 1a. We refer to this loss as the Higher-Order Compatibility loss ( $\mathcal{L}_{\mathrm{HOC}}$ ). + +Through Theorem 1 presented in the previous section, we establish that the constraint of Eq. 1a cannot be exploited in combination with the constraint of Eq. 1b. Based on this result we show that, under no specific conditions, the constrained optimization problem using solely the inequality constraint of Eq. 1a: + +$$ +\begin{array}{l} \operatorname * {a r g m i n} _ {\phi_ {t}} \mathcal {L} _ {\text {S C E}} (\phi_ {t}) \\ \mathrm {s . t .} \quad \mathrm {d} \left(\phi_ {k} (\mathbf {x} _ {i}), \phi_ {t} (\mathbf {x} _ {j})\right) - \mathrm {d} \left(\phi_ {k} (\mathbf {x} _ {i}), \phi_ {k} (\mathbf {x} _ {j})\right) \leq 0 \\ \forall y _ {i} = y _ {j} \tag {6} \\ \end{array} +$$ + +![](images/51b5926c6a665b7911f4c226f04a454b67c1fc53c2dc604314acd5664d3fdb67.jpg) +Figure 3. Training loss of a $d$ -Simplex fixed classifier during a model update. Values are the cross-entropy loss of Eq. 2 (red line) and the loss of Eq. 3 (blue line). Models are trained on MNIST. + +can be transformed into a tractable form. Rooted in the work of [82], this transformation not only provides an approach to solve the tractability issue but, within the context of compatibility, it also allows preserving the optimality as outlined in the proof of Theorem 1. As shown in [82], the model for a constrained problem like Eq. 6 can be equivalently learned with a convex combination of the cross-entropy loss and the Kullback-Leibler divergence function. + +On the other hand, as discussed in [83], the contrastive loss $\mathcal{L}_{\mathrm{NCE}}(\phi_t,\phi_{t - 1})$ can be approximated as the Kullback-Leibler divergence between the product of the marginals of the joint distribution of $\phi_t$ and $\phi_{t - 1}$ . Moreover, $\mathcal{L}_{\mathrm{NCE}}(\phi_t,\phi_{t - 1})$ also approximates the mutual information between $\phi_t$ and $\phi_{t - 1}$ , thereby enabling to capture higher-order dependencies between consecutive updates of the model. As a consequence, training with the loss in Eq. 3 is equivalent to the optimal classifier for the constrained optimization problem stated in Eq. 6 and at the same time, thanks to the term $\mathcal{L}_{\mathrm{NCE}}(\phi_t,\phi_{t - 1})$ , takes into account higher-order variations between $\phi_{t - 1}(\mathbf{x}_i)$ and $\phi_t(\mathbf{x}_j)$ . In the following, we call training the representation model using $d$ -Simplex with $\mathcal{L}_{\mathrm{HOC}}$ as $d$ -Simplex-HOC. + +In Fig. 3, we illustrate the effects of $\mathcal{L}_{\mathrm{HOC}}$ compared to the cross-entropy loss. We use a toy example with the LeNet++ CNN architecture [84] with the $d$ -Simplex fixed classifier. The model is initially trained on the first five MNIST classes and then fine-tuned on all ten classes. The cross-entropy training error (red curve) converges rapidly to low values. In contrast, the convergence with the $\mathcal{L}_{\mathrm{HOC}}$ loss (blue curve) is more gradual, which allows for the capture of richer information during back-propagation. + +# 4. Experimental Verification + +Referring to the IAM-CL $^2$ R learning scenario presented in Fig. 1, this section provides empirical evidence to verify the practical implications of the theoretical results discussed earlier. + +# 4.1. Datasets and Settings + +Pre-trained Models. We pre-train our models in a supervised manner using the ImageNet32 [85]. Three distinct models are pre-trained on ImageNet32 with 100, 300, and 600 classes. The model trained with 100 classes is used to initialize the model before fine-tuning on the sequence of tasks. The other two models are used to simulate the practice of downloading and fine-tuning pre-trained models and serve as third-party models that will replace the current one undergoing fine-tuning. + +Fine-tuning. We replicate the fact that dataset size for training third-party models is typically significantly larger than the dataset size used for fine-tuning [86]. According to this, pre-trained models are fine-tuned with a reduced version of CIFAR100 [87] denoted in this paper as CIFAR100R. + +We considered two distinct task sequences consisting of 7 and 31 tasks each. We fine-tune the pre-trained model with an initial task comprising 10 classes. Subsequently, for the sequences of 7 and 31 tasks, the respective tasks contain 15 and 3 classes each. The fine-tuning process incorporates incoming task data, consisting of 300 images per class, and utilizes an episodic memory that stores 20 images from each class of previous tasks. + +Model Replacement. In our experiments, we verify the impact of replacing the current fine-tuned model with two improved models pre-trained elsewhere. The two replacements occur while fine-tuning on CIFAR100R: at the third and fifth tasks in the shorter sequence, and at the eleventh and twenty-first tasks in the longer sequence. We also consider the challenging scenario of improved model replacement considering more sophisticated network architectures. + +The $d$ -Simplex fixed classifier is pre-allocated with a number of classes $K$ , ensuring enough space to accommodate future classes for both pre-training and fine-tuning. Class assignments for pre-training are made from left to right, and for fine-tuning, from right to left. This straightforward convention is used to ensure that classes assigned for pre-training and fine-tuning remain distinct, without overlap. Other non-overlapping assignment methods could also be used. + +Network Architectures. We use ResNet18 [88] as network architecture. In the scenario using more sophisticated network architectures, we initially replace ResNet18 with SENet18 [89], followed by a subsequent replacement with a RegNetY_400MF [90]. + +Hyper-parameters. The ResNet18, SENet18, and RegNetY_400MF models were pre-trained on ImageNet32 using the following hyper-parameters: 300 epochs, a batch size of 128, and an initial SGD optimizer learning rate of 0.1, which was adjusted using a Cosine Annealing schedule. For each task used for fine-tuning, the model is trained for 70 epochs with a batch size of 128, starting with a learning rate of 0.001 that was reduced by a factor of 10 after the 50th and 64th epochs. The $d$ -Simplex was pre-allocated with $K = 1024$ + +![](images/daf12376188a7578eda5c33dac4097b5be3399f75659d393e2304cffba46cc02.jpg) +(a) Two replacements + +![](images/c28a1e1b1bfff5061ec4cabfa7d32b1bda83e8b47436d44b711ecf395b07b51c.jpg) +(b) No replacements + +![](images/90def011759f1a932dda13471ce617d13616a3dad4114e20366884e0647f5724.jpg) +Figure 4. Average multi-model Accuracy $(AA_{t})$ evaluated across 31 tasks using CIFAR100R/10, showing: (a) model replacements at tasks 11 and 21 (indicated by yellow markers); (b) no model replacement. +(a) CVS [38] +Figure 5. Compatibility Matrices for $d$ -Simplex-HOC, CVS, BCT-ER, and $d$ -Simplex-FD on CIFAR100R/10 across 7 tasks. Model replacements at tasks 3 and 5 are highlighted in bold. Entries failing to meet compatibility criteria as defined in [27] are marked with a light-red background. + +![](images/d892ae816ee6affdd5d2a9603a05a8c50240f93018a036714cfdca4608f9c43e.jpg) +(b) BCT-ER [27] + +![](images/3d3372b5327f7237a91ff50a6919172dc7b30f2fb41b1b5f4d5a90feeb70e99e.jpg) +(c) $d$ -Simplex-FD [39] + +![](images/e57ccf828d516be7cdc327d2a959188689fb8eef1b91cd428fc917a96b7bd98e.jpg) +(d) $d$ -Simplex-HOC (in this paper) + +classes (i.e., $d = K - 1$ ). + +Performance Evaluation. The evaluation focuses on the open-set recognition task, in which separated datasets for training and evaluation are required. The standard 1:N search protocol, applicable to re-identification and similar tasks [27], is employed in the evaluation. To ensure strict separation between datasets, the CIFAR10 dataset is utilized for evaluation during fine-tuning with CIFAR100R. Specifically, the test set of CIFAR10, comprising 10,000 images, is used as the gallery set, while its training set of 50,000 images serves as the query set. + +Following [27] and [29], we measure performance progression across the two sequences of tasks using two established metrics: Average Compatibility $(AC)$ and Average multi-model Accuracy (referred shortly as to $AA_{t}$ ). The metric $AC$ quantifies the extent of compatibility across all possible pairs of model combinations by providing a normalized count of times in which compatibility is achieved. Conversely, $AA_{t}$ calculates the mean accuracy across all combinations of the previously learned models until task $t$ , providing an overall measure of accuracy. + +# 4.2. IAM-CL $^2$ R: Comparative Results + +We performed a comparative analysis of $d$ -Simplex-HOC against FAN [37], CVS [38], $d$ -Simplex-FD [39], and the lifelong adapted versions of BCT [27] (BCT-ER), LCE [28] (LCE-ER), and AdvBCT [36] (AdvBCT-ER). The experiments also incorporate a baseline method, Experience Replay (ER), in which the model is fine-tuned using cross-entropy loss on data of the new task and an episodic memory. Ablation studies of IAM-CL $^2$ R with the $d$ -Simplex-HOC are provided in the Appendix. + +Replacing: Same Architecture, Expanded Data. Fig. 4 presents the Average multi-model Accuracy at task $t(AA_{t})$ for learning scenarios with model replacement as depicted in Fig. 4a and for those without as depicted in Fig. 4b. The experiment involves fine-tuning a ResNet18 model across 31 tasks. The comparison provides insights into the performance benefits that can be obtained by replacing models when representations are trained in a compatible manner. The $d$ -Simplex-HOC effectively incorporates improvements from model replacements, showing increased performance + +![](images/7d76aaa98ec5fdfdffd8fb2bee47ff1d1b2a129b99612185b842040c060d65cd.jpg) +Figure 6. Plots of Average multi-model Accuracy $(AA_{t})$ for 31 tasks on CIFAR100R/10, showing the impact of model replacements with different network architectures at tasks 11 and 21. + +compared to the case without model replacement, as indicated in Fig. 4b. The $d$ -Simplex-FD demonstrates a similar capability, though to a reduced extent. The other methods have a clear performance decay after model replacements and end up with a worse performance than the case without replacement. This can be attributed to the fact that after replacement, fine-tuning is applied to a model obtained by retraining the network from scratch, leading to an entirely different representation. + +Further performance details, as indicated by the self and cross-test accuracy values, are shown according to the compatibility matrices [27, 29]. Fig. 5 shows these values for CVS, BCT-ER, $d$ -Simplex-FD, and $d$ -Simplex-HOC in the 7 tasks sequence. The values reveal that the $d$ -Simplex-HOC effectively leverages the improved expressive power of the models after replacement, except in one instance. This exception, where the model is not compatible and the cross-test accuracy falls below the self-test accuracy, is shown in Fig. 5d. Both CVS and BCT-ER score near zero cros-tests accuracy after model replacements as indicated by the values in the blue sub matrix blocks shown in Fig. 5a and Fig. 5b. This leads to mostly non-compatible representations. Although both $d$ -Simplex-HOC and $d$ -Simplex-FD utilize the $d$ -Simplex fixed classifier to learn stationary representations, the former shows better performance. This can be attributed to the high-order alignment achievable through the HOC loss. To provide a full evaluation of compatibility, the $AA_{t}$ of Fig. 4 is complemented with the Average Compatibility $AC$ in Tab. 1. We also report the Average multi-model Accuracy $AA_{7}$ and $AA_{31}$ for methods compared at the end of the 7-th and 31-th task, respectively. It is observed that, in both instances, all models—with the exception of $d$ -Simplex-HOC—fail to achieve significant compatibility performance. + +Replacing: Different Architectures, Expanded Data. Fig. 6 shows the performance of the evaluated methods when + +
METHOD7 tasks31 tasks
\( {AC} \)\( A{A}_{7} \)\( {AC} \)\( A{A}_{31} \)
ER baseline×36.22<0.0131.30
FAN [37]×36.32<0.0130.79
BCT-ER [27]×35.59×29.88
LCE-ER [28]×34.89×29.30
AdvBCT-ER [36]×35.73×30.10
CVS [38]×36.310.0131.34
d-Simplex-FD [39]0.0556.580.2156.27
d-Simplex-HOC0.9568.130.6567.40
+ +Table 1. Compatibility metrics with CIFAR100R/10 for 7 tasks with model replacements at task 3 and task 5, and 31 tasks with model replacements at task 11 and task 21. “×” indicates the case in which compatibility is not achieved. + +the original ResNet18 is replaced first by a SENet18 and then by a more expressive RegNetY_400MF. It is observed that the change of network architecture not only does not adversely affect compatibility in the $d$ -Simplex-HOC but takes advantage of their more expressive representation power. In particular, direct comparison of Fig. 6 with Fig. 5 shows that $d$ -Simplex-HOC improves performance gradually with each model replacement. This is in contrast to $d$ -SimplexFD, which does not demonstrate the same trends leading to a plateau around the 20-th task. Given the different feature sizes before and after the second model replacement with the RegNetY_400MF architecture—512 and 384, respectively—all methods except $d$ -Simplex-HOC and $d$ -Simplex-FD require non-trivial extensions to adapt to the changed feature size. According to this, for these methods, evaluation cannot be reported. + +# 5. Conclusion + +In this paper, we have investigated the concept of learning compatible representations through the principle of stationarity. We demonstrated that stationary representations optimally approximate compatibility according to its definition. We demonstrated that better model alignment through higher-order dependencies can be obtained by training with a loss derived from one of the compatibility inequality constraints. Finally, empirical evidence confirmed that stationary representations enable uninterrupted retrieval service allowing for fine-tuning and model replacement to occur concurrently and asynchronously with limited interference. + +Acknowledgment: This work was partially supported by the European Commission under European Horizon 2020 Programme, grant number 951911 - AI4Media. + +We acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support (ISCRA-C ID: HP10C4TIIM). + +# References + +[1] Sumit Chopra, Raia Hadsell, and Yann LeCun. Learning a similarity metric discriminatively, with application to face verification. In 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05), volume 1, pages 539-546. IEEE, 2005. 1 +[2] Yoshua Bengio, Aaron Courville, and Pascal Vincent. Representation learning: A review and new perspectives. 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This is particularly relevant in search and retrieval systems where it is crucial to avoid reprocessing of the gallery images with the updated model. While recent research has shown promising empirical evidence, there is still a lack of comprehensive theoretical understanding about learning compatible representations. In this paper, we demonstrate that the stationary representations learned by the d-Simplex fixed classifier optimally approximate compatibility representation according to the two inequality constraints of its formal definition. This not only establishes a solid foundation for future works in this line of research but also presents implications that can be exploited in practical learning scenarios. An exemplary application is the now-standard practice of downloading and fine-tuning new pretrained models. Specifically, we show the strengths and critical issues of stationary representations in the case in which a model undergoing sequential fine-tuning is asynchronously replaced by downloading a better-performing model pretrained elsewhere. Such a representation enables seamless delivery of retrieval service (i.e., no reprocessing of gallery images) and offers improved performance without operational disruptions during model replacement. Code available at: https://github.com/miccunifi/iamc12r." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 128, + 609 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 714 + ], + "type": "text", + "content": "By learning powerful internal feature representations from data, Deep Neural Networks (DNNs) [1-4] have made tremendous progress in some of the most challenging search tasks such as face recognition [5-9], person re-identification [10-12], image retrieval [13-15] and this significance also extends to a variety of other data modalities [16, 17]. Although all of the works mentioned above have focused on learning feature representations from static and," + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 322, + 245, + 533, + 439 + ], + "blocks": [ + { + "bbox": [ + 322, + 245, + 533, + 439 + ], + "lines": [ + { + "bbox": [ + 322, + 245, + 533, + 439 + ], + "spans": [ + { + "bbox": [ + 322, + 245, + 533, + 439 + ], + "type": "image", + "image_path": "e7cdfc1cbe186ab8d0b88e37850155adbeefb629c048effa3dad0343b6644885.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 449, + 547, + 528 + ], + "lines": [ + { + "bbox": [ + 304, + 449, + 547, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 449, + 547, + 528 + ], + "type": "text", + "content": "Figure 1. Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL" + }, + { + "bbox": [ + 304, + 449, + 547, + 528 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 449, + 547, + 528 + ], + "type": "text", + "content": "R pronounced \"I am clear\"). In the process of lifelong learning, a model is sequentially fine-tuned and asynchronously replaced with improved third-party models that are pre-trained externally. Stationary representations ensure seamless retrieval services and better performance, without the need to reprocess gallery images." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 544, + 547, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 547, + 687 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 547, + 687 + ], + "type": "text", + "content": "more recently, dynamic datasets [18-21], the now-standard practice is downloading and fine-tuning representations from models pre-trained elsewhere [22, 23]. These \"third-party\" pre-trained models often incorporate new data, utilize alternative architectures, adopt different loss functions or more in general provide novel methodologies. Whether applied individually or combined, these advancements aim to encapsulate the field's rapid progress within a single unified model [24]. This greatly facilitates the exploitation of internally learned semantic representations, particularly as models, datasets, and computational infrastructure continue to expand in size, complexity, and cost [25, 26]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 547, + 715 + ], + "type": "text", + "content": "The challenge of fully exploiting such standard practice in retrieval/search systems has to deal with the underlying" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28793" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 371 + ], + "type": "text", + "content": "problem of compatible learning [27-29]. That is the desire to align the representation of different models trained with different data, initialization seeds, loss functions, or alternative architectures—either individually or in combination. In such applications, maintaining alignment is crucial to minimize the need for repeated reprocessing of gallery images for feature extraction each time a new pre-trained model becomes available [24]. Reprocessing is not only computationally intensive but may also be unsustainable for extensive gallery sets [25, 26, 30] or unfeasible if the original images are no longer accessible due to privacy concerns [31]. This holds across various typical galleries: social networks update millions of images every month, while in robotics and automotive domains, the update rate can be as rapid as hundreds of images every second. Similarly, in textual domains, books can be structured into chapters, paragraphs, and sentences, enabling the capture of semantic relationships between these segments. While a similar organizational principle can be structured for the web with LLMs [17, 32], the challenge lies in the impracticality of reprocessing such extensive content with each advancement in representation models. Although recent research has shown the effectiveness of compatible representation learning [27-29, 33-41], there is still a lack of comprehensive theoretical understanding about compatibility." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 375, + 289, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 289, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 289, + 625 + ], + "type": "text", + "content": "This paper introduces a theorem that demonstrates how the stationary representations proposed in [42, 43] optimally approximate compatibility according to the two inequality constraints of its formal definition as provided in [27]. This not only establishes a solid foundation for future works, but also presents implications that can be exploited fine-tuning third-party models without the need of reprocessing gallery images. Specifically, we show that a continuously fine-tuned model can be asynchronously replaced by downloading a higher-performing, pre-trained model from an external source. Due to stationarity (and therefore optimal compatibility), such a replacement provides seamless retrieval services with improved performance, eliminating the need for image gallery reprocessing. We refer to this scenario as Improved Asynchronous Model Compatible Lifelong Learning Representation (IAM-CL" + }, + { + "bbox": [ + 47, + 375, + 289, + 625 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 47, + 375, + 289, + 625 + ], + "type": "text", + "content": "R pronounced \"I am clear\"). Fig. 1 illustrates the relationship between sequential fine-tuning and model replacement. Furthermore, as will be elaborated in the related work section, our foundation draws connections with the Neural Collapse phenomenon [44] and its associated theory." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 630, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 289, + 715 + ], + "type": "text", + "content": "Our second contribution is related to a specific challenge that arises: the tendency of the old and the new replaced models to align at their first-order statistics, an inherent property of stationary representation. Consequently, cross-entropy based prediction errors alone, when fine-tuning the representation, may not fully capture higher-order dependencies. To address this issue while preserving compatibility, we show" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 157 + ], + "type": "text", + "content": "that learning stationary representations using a convex combination of the cross-entropy loss and the infoNCE loss [45] is equivalent to training under one of the compatibility inequality constraints in [27]. This combined loss, termed Higher-Order Compatibility (HOC), distinguishes itself from the use of cross-entropy alone by capturing higher-order dependencies and optimally approximating compatibility." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 167, + 392, + 179 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 167, + 392, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 167, + 392, + 179 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 186, + 547, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 186, + 547, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 186, + 547, + 378 + ], + "type": "text", + "content": "Neural Collapse. Neural Collapse (NC) is an empirical phenomenon that demonstrates the alignment between features and the classifier in a symmetric configuration [44]. Specifically, each class feature vector and its corresponding class prototype vector align with each other (i.e., collapse onto the same vector), forming a regular Simplex geometry in a subspace of the representation space. This particular configuration, which results in maximal separation of the collapsed vectors, is also referred to as a regular Simplex ETF (Equiangular Tight Frame). As training progresses and the training phase goes beyond zero classification error, the network increasingly approaches collapse. Notably, this also agrees with the double descent generalization regime observed within the same training phase [46]. The two phenomena together indicate a form of stable steady-state for the internal representations of Deep Neural Networks." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "text", + "content": "Prior to the observation of neural collapse, other research applied the steady-state of the Simplex geometry directly from the beginning of training. The fixed classifier with mutually orthogonal prototypes, introduced in [47], firstly demonstrates no degradation in classification performance. Building on this initial model, the regular polytope fixed classifiers—such as the " + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "text", + "content": "-Simplex, " + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "text", + "content": "-Cube, and " + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 379, + 548, + 641 + ], + "type": "text", + "content": "-Orthoplex—advance the concept further by observing stationary and maximally separated representations, as introduced in [48] and further detailed in [42]. Prior to these developments, [49] delved into the early energy-based investigations of symmetric and maximal separation in the representation space. The distinction between the natural emergence of a regular Simplex ETF and intentionally fixing the regular Simplex geometry at the beginning of training is that prior fixing can preserve regions in the representation space for future classes, as introduced in [50] and more recently in [51] and [52]. Our work takes advantage of this preservation for future classes, allowing third-party representation models to be trained from scratch and fine-tuned, while mitigating the interference in the representation space of the classes involved in both processes." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 642, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 548, + 715 + ], + "type": "text", + "content": "As neural collapse is related to the interaction between the neural network's final and penultimate layers, it offers a tool to examine training dynamics and convergence, as introduced in [53] and [54] under the name of Unconstrained Feature Model (UFM) and Layered Peeled Model (LPM), respectively. In both [55] and [56], the favorable conver" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28794" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "gence of fixing the final classifier according to the UFM is demonstrated. In [54], it is shown that training on imbalanced datasets does not necessarily result in NC. Additional observations from [57] suggest that NC can emerge in both imbalanced and long-tail scenarios when the classifier is fixed to a " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "-Simplex geometry. Further detailed results on NC are presented in [58]. Our proof is based on the assumption from the UFM and LPM that the backbone has sufficient expressiveness to allow for the independent study of each feature. Our proof is also based on the assumption of " + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 72, + 289, + 228 + ], + "type": "text", + "content": "-Simplex fixed classifier, whose inherent symmetry allows to reduce the extent of the analysis to a single pairwise class interaction, as it causes all the interactions to be identical." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 235, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 235, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 235, + 289, + 714 + ], + "type": "text", + "content": "Compatible Representations Learning. Compatible representations broadly refer to the ability to align different learned representations, as discussed in [59-63]. The distinction outlined in [27] is that the alignment of models should be achieved without wasting the information learned from new data. This capability is typically evaluated in a query and gallery setting, where query and gallery features are extracted from two different representation models. The model for the query is trained using an extended dataset that includes additional data not present in the one used for training the gallery's model. The study in [27] further presents a method called Backward Compatible Training (BCT), which applies regularization to a new model using the classifier from the previous learning phase. This approach implicitly aligns the current improved model with the previously trained classifier, which is kept fixed. Several other methods have adopted this basic working principle: The fundamental aspect of this principle is that the challenge of model alignment is primarily demanded by the new model, which must learn from both the additional and the old data how to compensate for the inadequate representations of the previously learned models. Conversely, as also recently highlighted in [41], methods such as [64] or the more recent [28, 65, 66] train a lightweight transformation to convert old representations into new ones for backward compatibility. However, these methods do not entirely eliminate the re-processing cost. As the number of chained mappings increases, the entire chain necessitates re-evaluation each time the representation model is updated. This makes them unsuitable for sequential learning and large gallery-sets. While its primary focus is on classification, the study in [37] is one of the first methods employing sequential chaining transformations for aligning representations within a common reference space. The works in [39] and [38] bypass the use of chaining transformations, focusing instead on aligning representations for compatibility purposes in lifelong learning scenarios. Both approaches leverage auxiliary losses to ensure similarity among previously learned representations. Additionally, [39] achieves alignment with an absolute reference through the use of fixed classifiers, in line with the" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 306, + 72, + 425, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 425, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 425, + 83 + ], + "type": "text", + "content": "neural collapse phenomenon." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 304, + 84, + 547, + 228 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 84, + 547, + 228 + ], + "spans": [ + { + "bbox": [ + 304, + 84, + 547, + 228 + ], + "type": "text", + "content": "The work in [41] argues that there is an inherent trade-off in the definition of compatibility introduced in [27], which inspires them to \"hold\" incompatible information of the new model on additional orthogonal dimensions to avoid this conflict. Their argument seems to be in line with the recent work [29] and [39] based on stationarity in which (nearly) orthogonal dimensions are pre-allocated from the beginning using a regular " + }, + { + "bbox": [ + 304, + 84, + 547, + 228 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 84, + 547, + 228 + ], + "type": "text", + "content": "-Simplex fixed classifier. In this paper, we establish a formal relationship among compatibility, neural collapse, and stationarity, showing that stationarity provides an optimal approximation to the compatibility definition formulated in [27]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 236, + 420, + 249 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 236, + 420, + 249 + ], + "spans": [ + { + "bbox": [ + 305, + 236, + 420, + 249 + ], + "type": "text", + "content": "3. Theoretical Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 256, + 473, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 256, + 473, + 269 + ], + "spans": [ + { + "bbox": [ + 306, + 256, + 473, + 269 + ], + "type": "text", + "content": "3.1. Stationarity and Compatibility" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": "Preliminaries. Let " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{G} = \\{\\mathbf{x}_i\\}_{i=1}^{N_g}" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " be a gallery-set composed of a set of " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "N_g" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " with class labels from " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{V} = \\{y_i\\}_{i=1}^L" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\Phi^\\mathcal{G} = \\{\\phi(\\mathbf{x}_i) \\in \\mathbb{R}^d | \\forall \\mathbf{x}_i \\in \\mathcal{G}\\}" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " be the set of feature vectors of the gallery-set " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{G}" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " obtained with representation model " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{Q} = \\{\\mathbf{x}_i\\}_{i=1}^{N_q}" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " be a query-set composed of " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "N_q" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " images " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i \\in \\mathbb{R}^D" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\Phi^\\mathcal{Q} = \\{\\phi(\\mathbf{x}_i) \\in \\mathbb{R}^d | \\forall \\mathbf{x}_i \\in \\mathcal{Q}\\}" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " be the set of feature vectors of the query-set " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathcal{Q}" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " obtained with " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": ". Visual search is performed using a distance function " + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "inline_equation", + "content": "\\mathrm{d}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 274, + 547, + 384 + ], + "type": "text", + "content": " to identify the closest gallery features to the query features." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_1, \\mathcal{T}_2, \\ldots, \\mathcal{T}_T" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " be a sequence of " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " tasks, where each task " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " is composed of labeled images " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "y_i \\in \\mathcal{K}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\mathcal{K}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " the set of classes in " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\mathcal{T}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ". At task " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ", the model " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " is finetuned starting from the previous representation model " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\phi_{t-1}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ". Compatibility between the current model " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " and a previous model " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\phi_k" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "k < t" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ", is achieved when the feature vector of any query image obtained with " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ", the set " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\Phi_t^{\\mathcal{Q}}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": ", can be compared with feature vectors in " + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "inline_equation", + "content": "\\Phi_k^{\\mathcal{G}}" + }, + { + "bbox": [ + 304, + 384, + 547, + 505 + ], + "type": "text", + "content": " without reprocessing the gallery-set. The following provides a formal definition of compatibility [27]:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": "Definition 1 (Compatibility) Given two representation models " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\phi_k" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": " learned after " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\phi_k" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "\\phi_k" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": " are compatible according to the distance function " + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "inline_equation", + "content": "d(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 509, + 547, + 556 + ], + "type": "text", + "content": " if it holds:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 348, + 560, + 547, + 575 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 560, + 547, + 575 + ], + "spans": [ + { + "bbox": [ + 348, + 560, + 547, + 575 + ], + "type": "interline_equation", + "content": "\\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right) \\leq \\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {k} \\left(\\mathbf {x} _ {j}\\right)\\right) \\tag {1a}", + "image_path": "d3ceebcc56d13009468742c078d62f51bcb8585a3fb698fb6220a7c42fd791eb.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 417, + 577, + 527, + 592 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 417, + 577, + 527, + 592 + ], + "spans": [ + { + "bbox": [ + 417, + 577, + 527, + 592 + ], + "type": "interline_equation", + "content": "\\forall (i, j) \\in \\left\\{(i, j) \\mid y _ {i} = y _ {j} \\right\\}", + "image_path": "3286aaecd6778e48354f47f646a55510d824da983ec9844124eb94ea1b83ae6d.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 424, + 594, + 443, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 424, + 594, + 443, + 603 + ], + "spans": [ + { + "bbox": [ + 424, + 594, + 443, + 603 + ], + "type": "text", + "content": "and" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 348, + 608, + 545, + 622 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 608, + 545, + 622 + ], + "spans": [ + { + "bbox": [ + 348, + 608, + 545, + 622 + ], + "type": "interline_equation", + "content": "\\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right) \\geq \\mathrm {d} \\left(\\phi_ {k} \\left(\\mathbf {x} _ {i}\\right), \\phi_ {k} \\left(\\mathbf {x} _ {j}\\right)\\right) \\tag {1b}", + "image_path": "3f61d07eb0b6a634d1b1ae6237157bdf4c01affa663d910a39d369a487e148cc.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 417, + 624, + 527, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 417, + 624, + 527, + 639 + ], + "spans": [ + { + "bbox": [ + 417, + 624, + 527, + 639 + ], + "type": "interline_equation", + "content": "\\forall (i, j) \\in \\left\\{(i, j) \\mid y _ {i} \\neq y _ {j} \\right\\}", + "image_path": "9b44fe8781130ee54c12a588874550749246c293eb61ca4c99e63d2ffe591770.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 639, + 535, + 652 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 639, + 535, + 652 + ], + "spans": [ + { + "bbox": [ + 316, + 639, + 535, + 652 + ], + "type": "interline_equation", + "content": "w i t h k < t, \\quad t = (2, 3, \\dots , T), \\quad k = (1, 2, \\dots , T - 1).", + "image_path": "1c0b34f89185e426e5c3e0ef9def026de26e44e067c8e18e90b60308d809c21a.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 548, + 714 + ], + "type": "text", + "content": "Main Result. In this paragraph, we state and prove that learning stationary feature representations according to a " + }, + { + "bbox": [ + 304, + 665, + 548, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 665, + 548, + 714 + ], + "type": "text", + "content": "-Simplex fixed classifier necessarily implies optimal approximation of the compatibility as defined in Eqs. 1a and 1b." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28795" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 130, + 83, + 232, + 183 + ], + "blocks": [ + { + "bbox": [ + 130, + 83, + 232, + 183 + ], + "lines": [ + { + "bbox": [ + 130, + 83, + 232, + 183 + ], + "spans": [ + { + "bbox": [ + 130, + 83, + 232, + 183 + ], + "type": "image", + "image_path": "2eff6fe739fb7df06c087bdb409f61e0c8800b5a50359107ffcac487911cfff6.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 167, + 192, + 215, + 202 + ], + "lines": [ + { + "bbox": [ + 167, + 192, + 215, + 202 + ], + "spans": [ + { + "bbox": [ + 167, + 192, + 215, + 202 + ], + "type": "text", + "content": "(a) Same class" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 262, + 80, + 496, + 183 + ], + "blocks": [ + { + "bbox": [ + 262, + 80, + 496, + 183 + ], + "lines": [ + { + "bbox": [ + 262, + 80, + 496, + 183 + ], + "spans": [ + { + "bbox": [ + 262, + 80, + 496, + 183 + ], + "type": "image", + "image_path": "7679c8255f67d0ca17852d3e5098ad24565751c03bcbdbc1f0d1a790d1cd8d74.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 350, + 192, + 410, + 202 + ], + "lines": [ + { + "bbox": [ + 350, + 192, + 410, + 202 + ], + "spans": [ + { + "bbox": [ + 350, + 192, + 410, + 202 + ], + "type": "text", + "content": "(b) Different class" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "lines": [ + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "spans": [ + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": "Figure 2. Key concepts and relationships underlying Theorem 1. Distances in feature space of two distinct samples within their hyperballs before and after model update, with the update process represented by a dotted arrow. (a): Distances between samples " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": " of the same class " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": " before (red) and after (cyan) model update. (b): Distances between samples " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_i" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_j" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "inline_equation", + "content": "y_j" + }, + { + "bbox": [ + 45, + 212, + 545, + 278 + ], + "type": "text", + "content": ", before (red) and after (cyan) model update. Compatibility is verified by computing the expected lengths of the segments and verifying if they satisfy the inequalities of the compatibility definition. A transparently colored instance shows counter-intuitive distance behavior. Expectation reveals the underlying pattern of approximation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 290, + 288, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 288, + 387 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 288, + 387 + ], + "type": "text", + "content": "The formulation involves examining the expected distance between feature points before and after a learning update in a high-dimensional space, where the feature points are assumed to be distributed in hyperballs (i.e., high dimensional ball) centered at the prototypes of the " + }, + { + "bbox": [ + 46, + 290, + 288, + 387 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 290, + 288, + 387 + ], + "type": "text", + "content": "-Simplex fixed classifier. This abstraction allows for mathematical manipulation and analysis of the cluster as a single entity rather than individual points." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": "Theorem 1 (Stationarity " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\Rightarrow" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " Compatibility) Let " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{W} = [\\mathbf{w}_1, \\mathbf{w}_2, \\ldots, \\mathbf{w}_K]" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " be the " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "d \\times K" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " matrix of a " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": "-Simplex fixed classifier with " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " pre-allocated classes. Given two tasks, " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_k" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_t" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ". The task " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_t" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " is derived from " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_k" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " by incorporating an additional training set " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\Delta \\mathcal{T}" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_t = \\mathcal{T}_k \\cup \\Delta \\mathcal{T}" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ". The combined task, " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_t" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ", comprises a set of classes each denoted by " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "y \\in \\{1, 2, \\ldots, K_t\\}" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "K_t < K" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ". Under the assumption that learning the new task " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_t" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " causes the hyperball " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_k(\\mathbf{w}_y)" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " with radius " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "r_k^y" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " to shrink into a smaller hyperball " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_t(\\mathbf{w}_y)" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "r_t^y \\leq r_k^y" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " for all " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " in the set " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\{1, 2, \\ldots, K_k\\}" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": ", then it necessarily follows that " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "inline_equation", + "content": "\\phi_k" + }, + { + "bbox": [ + 46, + 396, + 288, + 552 + ], + "type": "text", + "content": " optimally approximate the compatibility inequality constraints as defined in Def. 1 in expectation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 562, + 205, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 562, + 205, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 562, + 205, + 574 + ], + "type": "text", + "content": "The proof is available in the Appendix." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 588, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 588, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 588, + 287, + 649 + ], + "type": "text", + "content": "Discussion. The Theorem relies on two main assumptions: the use of a " + }, + { + "bbox": [ + 46, + 588, + 287, + 649 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 588, + 287, + 649 + ], + "type": "text", + "content": "-Simplex fixed classifier [42] and the model's sufficient expressiveness, as described in the UFM abstraction [53, 54]. The latter assumption enables us to consider features independently1. While the former allows focusing" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 291, + 547, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 291, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 306, + 291, + 547, + 338 + ], + "type": "text", + "content": "on a single pairwise class interaction, since interactions with all other classes are symmetrically similar and cannot change. Fig. 2 illustrates the key concepts and relationships presented in Theorem 1." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": "Without loss of generality, the Theorem considers two distinct hyperballs of different radius " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathrm{old}}(\\mathbf{w}_y)" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": " representing the semantic clusters of a generic class " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": ", respectively before and after a generic learning update. The assumption that features are distributed in hyperballs stems from the margin-based softmax loss" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": " introduced in [67]. This interpretation has since been utilized in various studies, such as SphereFace [68] and ArcFace [8]. Besides the margin formulation, empirical evidence, such as Neural Collapse [44], shows that class features not only cluster around their associated prototypes but also, with sufficient training epochs, collapse into them, resulting in hyperballs tightening around the prototypes. Due to the stationarity property induced by the " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": "-Simplex classifier " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathrm{old}}(\\mathbf{w}_y)" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": " hyperballs have the same center in the representation space on the classifier prototype " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_y" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": ". After the learning step, " + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "inline_equation", + "content": "\\mathcal{B}_{\\mathrm{new}}(\\mathbf{w}_y)" + }, + { + "bbox": [ + 304, + 339, + 547, + 555 + ], + "type": "text", + "content": " has a shorter radius (i.e., adding new information improves the discrimination capability of the model [69-72])." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "text", + "content": "In particular, Fig. 2a shows the case in which feature vectors are from samples of the same class. As defined in Eq. 1a compatibility requires that, after updating, the distance between " + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{new}}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "text", + "content": " (in the cyan hyperball) and " + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{old}}(\\mathbf{x}_j)" + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "text", + "content": " (in red hyperball) is less than or equal to distance between " + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{old}}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{old}}(\\mathbf{x}_j)" + }, + { + "bbox": [ + 304, + 555, + 547, + 651 + ], + "type": "text", + "content": ". The figure displays two configurations: one where the condition is met and another where it is not met (shown in transparent colors)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 317, + 652, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 652, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 317, + 652, + 545, + 664 + ], + "type": "text", + "content": "Fig. 2b shows the case in which the feature vectors are" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 48, + 654, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 654, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 48, + 654, + 287, + 713 + ], + "type": "text", + "content": "Essentially, the Neural Collapse phenomenon, which is observed across various networks and datasets, also appears in a two-layer neural network when assuming input feature independence (i.e., a UFM). This equivalence supports the assumption that: 1) real network backbones are typically expressive enough to learn features as independent entities, and 2) UFM can be used as a tool to study neural networks properties." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 673, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 673, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 673, + 547, + 713 + ], + "type": "text", + "content": "2The margin enforces the confinement of features within a hyperball or a hyperdisc (the local approximation of a hypercap) around class prototypes. A disc in high-dimensional space can be considered a hyperball when referring to its filled volume." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28796" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": "from samples of different classes. As defined in Eq. 1b compatibility requires that, after updating, the distance between " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{new}}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "y_i" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": " (in the cyan hyperball centered in " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{y_i}" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{old}}(\\mathbf{x}_j)" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": " of class " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "y_j" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": " (in the red hyperball centered in " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{y_j}" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": ") is greater than or equal to than the distance between " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{old}}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "inline_equation", + "content": "\\phi_{\\mathrm{old}}(\\mathbf{x}_j)" + }, + { + "bbox": [ + 47, + 72, + 289, + 204 + ], + "type": "text", + "content": ". The Theorem establishes that, on average, this condition cannot be optimally satisfied and that stationarity is the best approximation achievable under the given constraints. A detailed justification for this is provided in the proof of Theorem 1, with a clearer and more focused exposition presented as a Corollary in the Appendix." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 206, + 289, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 289, + 350 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 289, + 350 + ], + "type": "text", + "content": "Informally, the proof of the Theorem starts with the premise that, upon retraining a model, the probability of finding a class feature near the corresponding class prototype from the old model—an indicator of compatibility between the two models—is nearly zero. Subsequently, the proof establishes that the optimal approximation for a compatible representation is obtained when the average distance between the same hyperball in two distinct learned models is minimized. This minimization occurs when the two corresponding hyperballs are centered at the same class prototype and when adding more classes does not alter this distance, i.e., the stationarity condition." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 352, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 352, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 352, + 289, + 483 + ], + "type": "text", + "content": "Our formulation calculates the average distance between hyperballs based on the Ball Line Picking problem, which determines the expected length of a line segment that connects two random points inside a hyperball [73-78]. Differently from that problem, our theorem considers a line segment connecting two random points in two distinct hyperballs, each with a different radius. Specifically, we analyze the cases as shown in Fig. 2. These hyperballs represent the \"class-state\" before and after the learning step during each model update. Closed-form solutions are not available for this problem, except in a specific two-dimensional case [79]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 498, + 266, + 511 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 498, + 266, + 511 + ], + "spans": [ + { + "bbox": [ + 47, + 498, + 266, + 511 + ], + "type": "text", + "content": "3.2. Stationarity and Higher-Order Alignment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 520, + 288, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 288, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 288, + 699 + ], + "type": "text", + "content": "A specific challenge arises when fine-tuning stationary learned representation models, for example in the IAM-CL" + }, + { + "bbox": [ + 46, + 520, + 288, + 699 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 520, + 288, + 699 + ], + "type": "text", + "content": "R setting of Fig. 1. In this case the old and the new models align at the first-order statistics, an inherent property of stationarity [42]. The consequence is that cross-entropy based prediction errors may not fully capture higher-order dependencies in representation space. We conjecture that simple cross-entropy mostly focuses on prediction errors related to the forgetting of the internal representation which may not promote compatibility when the representation model is largely aligned. To address this problem, we show that adding the infoNCE loss function [45, 80] is equivalent to training with the cross-entropy loss under one of the compatibility constraints while capturing higher-order dependencies." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "The loss for training at task " + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": " the stationary representation" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "type": "text", + "content": "model " + }, + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 306, + 72, + 440, + 84 + ], + "type": "text", + "content": " assumes the form [42]:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 307, + 91, + 545, + 158 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 91, + 545, + 158 + ], + "spans": [ + { + "bbox": [ + 307, + 91, + 545, + 158 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {S C E}} \\left(\\phi_ {t}\\right) = \\\\ = - \\sum_ {B} \\log \\left(\\frac {\\exp \\left(\\mathbf {W} _ {y _ {i}} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right)}{\\sum_ {j = 1} ^ {K _ {t}} \\exp \\left(\\mathbf {W} _ {j} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right) + \\sum_ {j = K _ {t} + 1} ^ {K} \\exp \\left(\\mathbf {W} _ {j} ^ {\\top} \\phi_ {t} (\\mathbf {x} _ {i})\\right)}\\right) \\tag {2} \\\\ \\end{array}", + "image_path": "a9b08dda3b3fa87f1b56d84a473582305a040090d4f5168bfd16d9eb10ad924f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "spans": [ + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_j^\\top \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": "-th column of the " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": "-Simplex classifier matrix " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "\\mathbf{W} \\in \\mathbb{R}^{d \\times K}" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": ", being " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": " the number of preallocated classes, " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "K_t = |\\bigcup_{i=1}^t \\mathcal{K}_i|" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": " the number of classes learned until time " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "K_t < K" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": " is a mini-batch of samples of " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "\\mathcal{T}_t" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": ". The first term in the denominator accounts for the classes learned until " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": ". The second term accounts for future classes, preserving dedicated regions in the representation space. This ensures that adding new classes minimally impacts the representation of previously learned classes [29, 39, 50, 81]. We train the representation model " + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 304, + 159, + 547, + 292 + ], + "type": "text", + "content": " with the following convex combination, namely:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 300, + 545, + 327 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 300, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 318, + 300, + 545, + 327 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {H O C}} \\left(\\phi_ {t}\\right) = \\lambda \\mathcal {L} _ {\\mathrm {S C E}} \\left(\\phi_ {t}\\right) + (1 - \\lambda) \\mathcal {L} _ {\\mathrm {N C E}} \\left(\\phi_ {t}, \\phi_ {t - 1}\\right), \\tag {3} \\\\ \\text {w i t h} \\quad \\lambda \\in [ 0, 1 ] \\\\ \\end{array}", + "image_path": "76778b67750e46b8ce5b8c684f243b23b92cd48ab7901d7111a25a562d3b7588.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 335, + 527, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 527, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 527, + 348 + ], + "type": "text", + "content": "where: " + }, + { + "bbox": [ + 305, + 335, + 527, + 348 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{SCE}}(\\phi_t)" + }, + { + "bbox": [ + 305, + 335, + 527, + 348 + ], + "type": "text", + "content": " is the cross-entropy loss of Eq. 2, and" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 307, + 371, + 545, + 427 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 371, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 307, + 371, + 545, + 427 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {N C E}} \\left(\\phi_ {t}, \\phi_ {t - 1}\\right) = - \\sum_ {B} \\log \\left(\\frac {\\Delta \\left(\\phi_ {t - 1} \\left(\\mathbf {x} _ {i}\\right) , \\phi_ {t} \\left(\\mathbf {x} _ {i}\\right)\\right)}{\\sum_ {j \\neq i} \\Delta \\left(\\phi_ {t - 1} \\left(\\mathbf {x} _ {i}\\right) , \\phi_ {t} \\left(\\mathbf {x} _ {j}\\right)\\right)}\\right) \\tag {4}", + "image_path": "8922359e9253f30c7423cb7b81df7bb0c74c057c4ec1448af1bd53e4acc8c97b.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 435, + 327, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 327, + 445 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 327, + 445 + ], + "type": "text", + "content": "with" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 312, + 452, + 545, + 488 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 452, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 312, + 452, + 545, + 488 + ], + "type": "interline_equation", + "content": "\\Delta \\left(\\phi_ {t - 1} (\\mathbf {x} _ {i}), \\phi_ {t} (\\mathbf {x} _ {j})\\right) = \\exp \\left(\\tau \\cdot \\frac {\\phi_ {t - 1} (\\mathbf {x} _ {i}) \\phi_ {t} (\\mathbf {x} _ {j})}{\\left| \\left| \\phi_ {t - 1} (\\mathbf {x} _ {i}) \\phi_ {t} (\\mathbf {x} _ {j}) \\right|\\right|}\\right) \\tag {5}", + "image_path": "64c7b80c8b387729ba70cb59bf774746827868829e1fba48e95c119c7ea4a140.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "spans": [ + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "content": "is the contrastive loss [45, 80] based on " + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "content": "-scaled cosine similarity between " + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "inline_equation", + "content": "\\phi_{t-1}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "inline_equation", + "content": "\\phi_t(\\mathbf{x}_j)" + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "content": ". We show that training the representation model with the " + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{HOC}}" + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "content": " of Eq. 3 is both: (1) able to capture higher-order dependencies between old and new model representations and (2) equivalent to learning under the compatibility constraints in Def. 1a. We refer to this loss as the Higher-Order Compatibility loss (" + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{HOC}}" + }, + { + "bbox": [ + 304, + 488, + 547, + 571 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 572, + 547, + 643 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 572, + 547, + 643 + ], + "spans": [ + { + "bbox": [ + 304, + 572, + 547, + 643 + ], + "type": "text", + "content": "Through Theorem 1 presented in the previous section, we establish that the constraint of Eq. 1a cannot be exploited in combination with the constraint of Eq. 1b. Based on this result we show that, under no specific conditions, the constrained optimization problem using solely the inequality constraint of Eq. 1a:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 313, + 651, + 545, + 713 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 651, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 313, + 651, + 545, + 713 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname * {a r g m i n} _ {\\phi_ {t}} \\mathcal {L} _ {\\text {S C E}} (\\phi_ {t}) \\\\ \\mathrm {s . t .} \\quad \\mathrm {d} \\left(\\phi_ {k} (\\mathbf {x} _ {i}), \\phi_ {t} (\\mathbf {x} _ {j})\\right) - \\mathrm {d} \\left(\\phi_ {k} (\\mathbf {x} _ {i}), \\phi_ {k} (\\mathbf {x} _ {j})\\right) \\leq 0 \\\\ \\forall y _ {i} = y _ {j} \\tag {6} \\\\ \\end{array}", + "image_path": "c1ae1cf0ae93e4694c72951adb8e2e0b194d4413050e69c93103810fa9566952.jpg" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28797" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 85, + 73, + 251, + 196 + ], + "blocks": [ + { + "bbox": [ + 85, + 73, + 251, + 196 + ], + "lines": [ + { + "bbox": [ + 85, + 73, + 251, + 196 + ], + "spans": [ + { + "bbox": [ + 85, + 73, + 251, + 196 + ], + "type": "image", + "image_path": "51b5926c6a665b7911f4c226f04a454b67c1fc53c2dc604314acd5664d3fdb67.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "type": "text", + "content": "Figure 3. Training loss of a " + }, + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 205, + 287, + 239 + ], + "type": "text", + "content": "-Simplex fixed classifier during a model update. Values are the cross-entropy loss of Eq. 2 (red line) and the loss of Eq. 3 (blue line). Models are trained on MNIST." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 261, + 287, + 356 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 356 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 356 + ], + "type": "text", + "content": "can be transformed into a tractable form. Rooted in the work of [82], this transformation not only provides an approach to solve the tractability issue but, within the context of compatibility, it also allows preserving the optimality as outlined in the proof of Theorem 1. As shown in [82], the model for a constrained problem like Eq. 6 can be equivalently learned with a convex combination of the cross-entropy loss and the Kullback-Leibler divergence function." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": "On the other hand, as discussed in [83], the contrastive loss " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": " can be approximated as the Kullback-Leibler divergence between the product of the marginals of the joint distribution of " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\phi_{t - 1}" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": ". Moreover, " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": " also approximates the mutual information between " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\phi_t" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\phi_{t - 1}" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": ", thereby enabling to capture higher-order dependencies between consecutive updates of the model. As a consequence, training with the loss in Eq. 3 is equivalent to the optimal classifier for the constrained optimization problem stated in Eq. 6 and at the same time, thanks to the term " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{NCE}}(\\phi_t,\\phi_{t - 1})" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": ", takes into account higher-order variations between " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\phi_{t - 1}(\\mathbf{x}_i)" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\phi_t(\\mathbf{x}_j)" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": ". In the following, we call training the representation model using " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": "-Simplex with " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{HOC}}" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 357, + 288, + 525 + ], + "type": "text", + "content": "-Simplex-HOC." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": "In Fig. 3, we illustrate the effects of " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{HOC}}" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " compared to the cross-entropy loss. We use a toy example with the LeNet++ CNN architecture [84] with the " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": "-Simplex fixed classifier. The model is initially trained on the first five MNIST classes and then fine-tuned on all ten classes. The cross-entropy training error (red curve) converges rapidly to low values. In contrast, the convergence with the " + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{HOC}}" + }, + { + "bbox": [ + 46, + 525, + 287, + 634 + ], + "type": "text", + "content": " loss (blue curve) is more gradual, which allows for the capture of richer information during back-propagation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 645, + 194, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 194, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 194, + 658 + ], + "type": "text", + "content": "4. Experimental Verification" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "Referring to the IAM-CL" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 46, + 665, + 287, + 712 + ], + "type": "text", + "content": "R learning scenario presented in Fig. 1, this section provides empirical evidence to verify the practical implications of the theoretical results discussed earlier." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 428, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 428, + 85 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 428, + 85 + ], + "type": "text", + "content": "4.1. Datasets and Settings" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 547, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 547, + 198 + ], + "type": "text", + "content": "Pre-trained Models. We pre-train our models in a supervised manner using the ImageNet32 [85]. Three distinct models are pre-trained on ImageNet32 with 100, 300, and 600 classes. The model trained with 100 classes is used to initialize the model before fine-tuning on the sequence of tasks. The other two models are used to simulate the practice of downloading and fine-tuning pre-trained models and serve as third-party models that will replace the current one undergoing fine-tuning." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 547, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 547, + 258 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 547, + 258 + ], + "type": "text", + "content": "Fine-tuning. We replicate the fact that dataset size for training third-party models is typically significantly larger than the dataset size used for fine-tuning [86]. According to this, pre-trained models are fine-tuned with a reduced version of CIFAR100 [87] denoted in this paper as CIFAR100R." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 258, + 546, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 546, + 354 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 546, + 354 + ], + "type": "text", + "content": "We considered two distinct task sequences consisting of 7 and 31 tasks each. We fine-tune the pre-trained model with an initial task comprising 10 classes. Subsequently, for the sequences of 7 and 31 tasks, the respective tasks contain 15 and 3 classes each. The fine-tuning process incorporates incoming task data, consisting of 300 images per class, and utilizes an episodic memory that stores 20 images from each class of previous tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 449 + ], + "type": "text", + "content": "Model Replacement. In our experiments, we verify the impact of replacing the current fine-tuned model with two improved models pre-trained elsewhere. The two replacements occur while fine-tuning on CIFAR100R: at the third and fifth tasks in the shorter sequence, and at the eleventh and twenty-first tasks in the longer sequence. We also consider the challenging scenario of improved model replacement considering more sophisticated network architectures." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "spans": [ + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "type": "text", + "content": "-Simplex fixed classifier is pre-allocated with a number of classes " + }, + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 450, + 547, + 545 + ], + "type": "text", + "content": ", ensuring enough space to accommodate future classes for both pre-training and fine-tuning. Class assignments for pre-training are made from left to right, and for fine-tuning, from right to left. This straightforward convention is used to ensure that classes assigned for pre-training and fine-tuning remain distinct, without overlap. Other non-overlapping assignment methods could also be used." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 605 + ], + "type": "text", + "content": "Network Architectures. We use ResNet18 [88] as network architecture. In the scenario using more sophisticated network architectures, we initially replace ResNet18 with SENet18 [89], followed by a subsequent replacement with a RegNetY_400MF [90]." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "Hyper-parameters. The ResNet18, SENet18, and RegNetY_400MF models were pre-trained on ImageNet32 using the following hyper-parameters: 300 epochs, a batch size of 128, and an initial SGD optimizer learning rate of 0.1, which was adjusted using a Cosine Annealing schedule. For each task used for fine-tuning, the model is trained for 70 epochs with a batch size of 128, starting with a learning rate of 0.001 that was reduced by a factor of 10 after the 50th and 64th epochs. The " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "text", + "content": "-Simplex was pre-allocated with " + }, + { + "bbox": [ + 304, + 605, + 547, + 713 + ], + "type": "inline_equation", + "content": "K = 1024" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28798" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 60, + 71, + 285, + 220 + ], + "blocks": [ + { + "bbox": [ + 60, + 71, + 285, + 220 + ], + "lines": [ + { + "bbox": [ + 60, + 71, + 285, + 220 + ], + "spans": [ + { + "bbox": [ + 60, + 71, + 285, + 220 + ], + "type": "image", + "image_path": "daf12376188a7578eda5c33dac4097b5be3399f75659d393e2304cffba46cc02.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 221, + 206, + 232 + ], + "lines": [ + { + "bbox": [ + 135, + 221, + 206, + 232 + ], + "spans": [ + { + "bbox": [ + 135, + 221, + 206, + 232 + ], + "type": "text", + "content": "(a) Two replacements" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 285, + 72, + 534, + 220 + ], + "blocks": [ + { + "bbox": [ + 285, + 72, + 534, + 220 + ], + "lines": [ + { + "bbox": [ + 285, + 72, + 534, + 220 + ], + "spans": [ + { + "bbox": [ + 285, + 72, + 534, + 220 + ], + "type": "image", + "image_path": "c28a1e1b1bfff5061ec4cabfa7d32b1bda83e8b47436d44b711ecf395b07b51c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 390, + 221, + 456, + 232 + ], + "lines": [ + { + "bbox": [ + 390, + 221, + 456, + 232 + ], + "spans": [ + { + "bbox": [ + 390, + 221, + 456, + 232 + ], + "type": "text", + "content": "(b) No replacements" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 47, + 273, + 164, + 392 + ], + "blocks": [ + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "type": "text", + "content": "Figure 4. Average multi-model Accuracy " + }, + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "type": "inline_equation", + "content": "(AA_{t})" + }, + { + "bbox": [ + 46, + 240, + 546, + 264 + ], + "type": "text", + "content": " evaluated across 31 tasks using CIFAR100R/10, showing: (a) model replacements at tasks 11 and 21 (indicated by yellow markers); (b) no model replacement." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 273, + 164, + 392 + ], + "lines": [ + { + "bbox": [ + 47, + 273, + 164, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 273, + 164, + 392 + ], + "type": "image", + "image_path": "90def011759f1a932dda13471ce617d13616a3dad4114e20366884e0647f5724.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 84, + 393, + 127, + 403 + ], + "lines": [ + { + "bbox": [ + 84, + 393, + 127, + 403 + ], + "spans": [ + { + "bbox": [ + 84, + 393, + 127, + 403 + ], + "type": "text", + "content": "(a) CVS [38]" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "lines": [ + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "type": "text", + "content": "Figure 5. Compatibility Matrices for " + }, + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "type": "text", + "content": "-Simplex-HOC, CVS, BCT-ER, and " + }, + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 412, + 546, + 446 + ], + "type": "text", + "content": "-Simplex-FD on CIFAR100R/10 across 7 tasks. Model replacements at tasks 3 and 5 are highlighted in bold. Entries failing to meet compatibility criteria as defined in [27] are marked with a light-red background." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 164, + 274, + 280, + 392 + ], + "blocks": [ + { + "bbox": [ + 164, + 274, + 280, + 392 + ], + "lines": [ + { + "bbox": [ + 164, + 274, + 280, + 392 + ], + "spans": [ + { + "bbox": [ + 164, + 274, + 280, + 392 + ], + "type": "image", + "image_path": "d892ae816ee6affdd5d2a9603a05a8c50240f93018a036714cfdca4608f9c43e.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 194, + 393, + 250, + 403 + ], + "lines": [ + { + "bbox": [ + 194, + 393, + 250, + 403 + ], + "spans": [ + { + "bbox": [ + 194, + 393, + 250, + 403 + ], + "type": "text", + "content": "(b) BCT-ER [27]" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 280, + 274, + 395, + 392 + ], + "blocks": [ + { + "bbox": [ + 280, + 274, + 395, + 392 + ], + "lines": [ + { + "bbox": [ + 280, + 274, + 395, + 392 + ], + "spans": [ + { + "bbox": [ + 280, + 274, + 395, + 392 + ], + "type": "image", + "image_path": "3d3372b5327f7237a91ff50a6919172dc7b30f2fb41b1b5f4d5a90feeb70e99e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 301, + 393, + 375, + 403 + ], + "lines": [ + { + "bbox": [ + 301, + 393, + 375, + 403 + ], + "spans": [ + { + "bbox": [ + 301, + 393, + 375, + 403 + ], + "type": "text", + "content": "(c) " + }, + { + "bbox": [ + 301, + 393, + 375, + 403 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 301, + 393, + 375, + 403 + ], + "type": "text", + "content": " -Simplex-FD [39]" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 396, + 274, + 533, + 392 + ], + "blocks": [ + { + "bbox": [ + 396, + 274, + 533, + 392 + ], + "lines": [ + { + "bbox": [ + 396, + 274, + 533, + 392 + ], + "spans": [ + { + "bbox": [ + 396, + 274, + 533, + 392 + ], + "type": "image", + "image_path": "e57ccf828d516be7cdc327d2a959188689fb8eef1b91cd428fc917a96b7bd98e.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 398, + 393, + 511, + 403 + ], + "lines": [ + { + "bbox": [ + 398, + 393, + 511, + 403 + ], + "spans": [ + { + "bbox": [ + 398, + 393, + 511, + 403 + ], + "type": "text", + "content": "(d) " + }, + { + "bbox": [ + 398, + 393, + 511, + 403 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 398, + 393, + 511, + 403 + ], + "type": "text", + "content": "-Simplex-HOC (in this paper)" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 458, + 151, + 470 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 458, + 151, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 458, + 151, + 470 + ], + "type": "text", + "content": "classes (i.e., " + }, + { + "bbox": [ + 47, + 458, + 151, + 470 + ], + "type": "inline_equation", + "content": "d = K - 1" + }, + { + "bbox": [ + 47, + 458, + 151, + 470 + ], + "type": "text", + "content": ")." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 472, + 288, + 592 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 472, + 288, + 592 + ], + "spans": [ + { + "bbox": [ + 46, + 472, + 288, + 592 + ], + "type": "text", + "content": "Performance Evaluation. The evaluation focuses on the open-set recognition task, in which separated datasets for training and evaluation are required. The standard 1:N search protocol, applicable to re-identification and similar tasks [27], is employed in the evaluation. To ensure strict separation between datasets, the CIFAR10 dataset is utilized for evaluation during fine-tuning with CIFAR100R. Specifically, the test set of CIFAR10, comprising 10,000 images, is used as the gallery set, while its training set of 50,000 images serves as the query set." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "Following [27] and [29], we measure performance progression across the two sequences of tasks using two established metrics: Average Compatibility " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "(AC)" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " and Average multi-model Accuracy (referred shortly as to " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "AA_{t}" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": "). The metric " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "AC" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " quantifies the extent of compatibility across all possible pairs of model combinations by providing a normalized count of times in which compatibility is achieved. Conversely, " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "AA_{t}" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": " calculates the mean accuracy across all combinations of the previously learned models until task " + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 594, + 289, + 714 + ], + "type": "text", + "content": ", providing an overall measure of accuracy." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 457, + 487, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 457, + 487, + 470 + ], + "spans": [ + { + "bbox": [ + 306, + 457, + 487, + 470 + ], + "type": "text", + "content": "4.2. IAM-CL" + }, + { + "bbox": [ + 306, + 457, + 487, + 470 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 306, + 457, + 487, + 470 + ], + "type": "text", + "content": "R: Comparative Results" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "spans": [ + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "text", + "content": "We performed a comparative analysis of " + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "text", + "content": "-Simplex-HOC against FAN [37], CVS [38], " + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "text", + "content": "-Simplex-FD [39], and the lifelong adapted versions of BCT [27] (BCT-ER), LCE [28] (LCE-ER), and AdvBCT [36] (AdvBCT-ER). The experiments also incorporate a baseline method, Experience Replay (ER), in which the model is fine-tuned using cross-entropy loss on data of the new task and an episodic memory. Ablation studies of IAM-CL" + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "inline_equation", + "content": "^2" + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "text", + "content": "R with the " + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 486, + 547, + 594 + ], + "type": "text", + "content": "-Simplex-HOC are provided in the Appendix." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "Replacing: Same Architecture, Expanded Data. Fig. 4 presents the Average multi-model Accuracy at task " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "t(AA_{t})" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": " for learning scenarios with model replacement as depicted in Fig. 4a and for those without as depicted in Fig. 4b. The experiment involves fine-tuning a ResNet18 model across 31 tasks. The comparison provides insights into the performance benefits that can be obtained by replacing models when representations are trained in a compatible manner. The " + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 594, + 547, + 714 + ], + "type": "text", + "content": "-Simplex-HOC effectively incorporates improvements from model replacements, showing increased performance" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28799" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 70, + 283, + 228 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 283, + 228 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 283, + 228 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 283, + 228 + ], + "type": "image", + "image_path": "7d76aaa98ec5fdfdffd8fb2bee47ff1d1b2a129b99612185b842040c060d65cd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 236, + 288, + 270 + ], + "lines": [ + { + "bbox": [ + 46, + 236, + 288, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 236, + 288, + 270 + ], + "type": "text", + "content": "Figure 6. Plots of Average multi-model Accuracy " + }, + { + "bbox": [ + 46, + 236, + 288, + 270 + ], + "type": "inline_equation", + "content": "(AA_{t})" + }, + { + "bbox": [ + 46, + 236, + 288, + 270 + ], + "type": "text", + "content": " for 31 tasks on CIFAR100R/10, showing the impact of model replacements with different network architectures at tasks 11 and 21." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": "compared to the case without model replacement, as indicated in Fig. 4b. The " + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 293, + 287, + 400 + ], + "type": "text", + "content": "-Simplex-FD demonstrates a similar capability, though to a reduced extent. The other methods have a clear performance decay after model replacements and end up with a worse performance than the case without replacement. This can be attributed to the fact that after replacement, fine-tuning is applied to a model obtained by retraining the network from scratch, leading to an entirely different representation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "Further performance details, as indicated by the self and cross-test accuracy values, are shown according to the compatibility matrices [27, 29]. Fig. 5 shows these values for CVS, BCT-ER, " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex-FD, and " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex-HOC in the 7 tasks sequence. The values reveal that the " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex-HOC effectively leverages the improved expressive power of the models after replacement, except in one instance. This exception, where the model is not compatible and the cross-test accuracy falls below the self-test accuracy, is shown in Fig. 5d. Both CVS and BCT-ER score near zero cros-tests accuracy after model replacements as indicated by the values in the blue sub matrix blocks shown in Fig. 5a and Fig. 5b. This leads to mostly non-compatible representations. Although both " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex-HOC and " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex-FD utilize the " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex fixed classifier to learn stationary representations, the former shows better performance. This can be attributed to the high-order alignment achievable through the HOC loss. To provide a full evaluation of compatibility, the " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "AA_{t}" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": " of Fig. 4 is complemented with the Average Compatibility " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "AC" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": " in Tab. 1. We also report the Average multi-model Accuracy " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "AA_{7}" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "AA_{31}" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": " for methods compared at the end of the 7-th and 31-th task, respectively. It is observed that, in both instances, all models—with the exception of " + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 46, + 401, + 290, + 689 + ], + "type": "text", + "content": "-Simplex-HOC—fail to achieve significant compatibility performance." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Replacing: Different Architectures, Expanded Data. Fig. 6 shows the performance of the evaluated methods when" + } + ] + } + ], + "index": 4 + }, + { + "type": "table", + "bbox": [ + 310, + 70, + 543, + 198 + ], + "blocks": [ + { + "bbox": [ + 310, + 70, + 543, + 198 + ], + "lines": [ + { + "bbox": [ + 310, + 70, + 543, + 198 + ], + "spans": [ + { + "bbox": [ + 310, + 70, + 543, + 198 + ], + "type": "table", + "html": "
METHOD7 tasks31 tasks
\\( {AC} \\)\\( A{A}_{7} \\)\\( {AC} \\)\\( A{A}_{31} \\)
ER baseline×36.22<0.0131.30
FAN [37]×36.32<0.0130.79
BCT-ER [27]×35.59×29.88
LCE-ER [28]×34.89×29.30
AdvBCT-ER [36]×35.73×30.10
CVS [38]×36.310.0131.34
d-Simplex-FD [39]0.0556.580.2156.27
d-Simplex-HOC0.9568.130.6567.40
", + "image_path": "86641bcf4dacf1b6a4a0fc02e464eb5d2ecb4e0bc5cbea199e8696c8af1decab.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 205, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 305, + 205, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 305, + 205, + 547, + 251 + ], + "type": "text", + "content": "Table 1. Compatibility metrics with CIFAR100R/10 for 7 tasks with model replacements at task 3 and task 5, and 31 tasks with model replacements at task 11 and task 21. “×” indicates the case in which compatibility is not achieved." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "content": "the original ResNet18 is replaced first by a SENet18 and then by a more expressive RegNetY_400MF. It is observed that the change of network architecture not only does not adversely affect compatibility in the " + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "content": "-Simplex-HOC but takes advantage of their more expressive representation power. In particular, direct comparison of Fig. 6 with Fig. 5 shows that " + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "content": "-Simplex-HOC improves performance gradually with each model replacement. This is in contrast to " + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "content": "-SimplexFD, which does not demonstrate the same trends leading to a plateau around the 20-th task. Given the different feature sizes before and after the second model replacement with the RegNetY_400MF architecture—512 and 384, respectively—all methods except " + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "content": "-Simplex-HOC and " + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "inline_equation", + "content": "d" + }, + { + "bbox": [ + 304, + 276, + 547, + 468 + ], + "type": "text", + "content": "-Simplex-FD require non-trivial extensions to adapt to the changed feature size. According to this, for these methods, evaluation cannot be reported." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 485, + 379, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 485, + 379, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 485, + 379, + 498 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 507, + 547, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 507, + 547, + 639 + ], + "spans": [ + { + "bbox": [ + 304, + 507, + 547, + 639 + ], + "type": "text", + "content": "In this paper, we have investigated the concept of learning compatible representations through the principle of stationarity. We demonstrated that stationary representations optimally approximate compatibility according to its definition. We demonstrated that better model alignment through higher-order dependencies can be obtained by training with a loss derived from one of the compatibility inequality constraints. Finally, empirical evidence confirmed that stationary representations enable uninterrupted retrieval service allowing for fine-tuning and model replacement to occur concurrently and asynchronously with limited interference." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 641, + 547, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 677 + ], + "type": "text", + "content": "Acknowledgment: This work was partially supported by the European Commission under European Horizon 2020 Programme, grant number 951911 - AI4Media." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 713 + ], + "type": "text", + "content": "We acknowledge the CINECA award under the ISCRA initiative, for the availability of high-performance computing resources and support (ISCRA-C ID: HP10C4TIIM)." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28800" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 145 + ], + "type": "text", + "content": "[1] Sumit Chopra, Raia Hadsell, and Yann LeCun. 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Matching under large in-plane rotations. Two challenging pairs from AIMS [49]. The left images in each pair were taken by astronauts on the ISS and are geo-referenced by matching them with the satellite images on the right. We plot estimated inlier correspondences after homography estimation with RANSAC. Further qualitative examples are shown in the appendix." + ], + "image_footnote": [], + "bbox": [ + 84, + 255, + 320, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/e87f9cd549473b880a698c7fbe584fa9564f20ca104adba542db2670169b1db7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 255, + 478, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/bb3793dd397774b491e8830371d350084e2a713f5eb0d000e382543bf4b759e1.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 255, + 727, + 378 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6be77e114758ceb84df4dac9d5252d1fcd06f2f90266e3c0e7c3b9c5128b8198.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 728, + 255, + 883, + 378 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 453, + 313, + 468 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image keypoint descriptions that are discriminative and matchable over large changes in viewpoint are vital for 3D reconstruction. However, descriptions output by learned descriptors are typically not robust to camera rotation. While they can be made more robust by, e.g., data augmentation, this degrades performance on upright images. Another approach is test-time augmentation, which incurs a significant increase in runtime. Instead, we learn a linear transform in description space that encodes rotations of the input image. We call this linear transform a steerer since it allows us to transform the descriptions as if the image was rotated. From representation theory, we know all possible steers for the rotation group. Steerers can be optimized (A) given a fixed descriptor; (B) jointly with a descriptor or (C) we can optimize a descriptor given a fixed steerer. We perform experiments in these three settings and obtain state-of-the-art results on the rotation invariant image matching benchmarks AIMS and Roto-360. We publish code and model weights at this https url.", + "bbox": [ + 75, + 484, + 473, + 773 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 797, + 209, + 814 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Discriminative local descriptions are vital for multiple 3D vision tasks, and learned descriptors have recently been shown to outperform traditional handcrafted local features [17, 19, 23, 43]. One major weakness of learned descriptors compared to handcrafted features such as", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "SIFT [35] is the relative lack of robustness to non-upright images [55]. While images taken from ground level can sometimes be made upright by aligning with gravity as the canonical orientation, this is not always possible. For example, descriptors robust to rotation are vital in space applications [49], as well as medical applications [42], where no such canonical orientation exists. Even when a canonical orientation exists, it may be difficult or impossible to estimate. Rotation invariant matching is thus a key challenge.", + "bbox": [ + 496, + 453, + 892, + 590 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The most straightforward manner to get rotation invariant matching is to train or design a descriptor to be rotation invariant [17, 35]. However, this sacrifices distinctiveness in matching images with small relative rotations [41]. An alternative approach is to train a rotation-sensitive descriptor and perform test-time-augmentation, selecting the pair that produces the most matches. The obvious downside of TTA is computational cost. For example, testing all $45^{\\circ}$ rotations requires running the model eight times.", + "bbox": [ + 496, + 594, + 893, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we present an approach that maintains distinctiveness for small rotations and allows for rotation invariant matching when we have images with large rotations. We do this while adding only negligible additional runtime, running the descriptor only a single time. The main idea is to learn a linear transform in description space that corresponds to a rotation of the input image; see Figure 2. We call this linear transform a steerer as it allows us to modify keypoint descriptions as if they were describing rotated images—we can steer the descriptions without having to rerun the descriptor network. We show empi", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "4885", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/75408d11bc3061b8bae87c49bf6292333b2bf12fad984fb7d43165f2bab7ac91.jpg", + "image_caption": [ + "Figure 2. Overview of approach. A steerer (Definition 4.4) is a linear map that transforms the description of a keypoint into the description of the corresponding keypoint in a rotated image. Thus, a steerer makes the keypoint descriptor rotation equivariant, and we can obtain the descriptions of keypoints in arbitrarily rotated images while only running the descriptor once." + ], + "image_footnote": [], + "bbox": [ + 112, + 97, + 436, + 258 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "cally that approximate steers can be obtained for existing descriptors and motivate this theoretically. We also investigate jointly optimizing steers and descriptors and show how this enables nearly exact steering while not sacrificing performance on upright images. Using mathematical representation theory, we can describe all possible steers—they are representations of the rotation group. This enables the choice of a fixed steerer and training a descriptor for it, and in turn, the investigation of which steers give the best performance.", + "bbox": [ + 75, + 378, + 468, + 527 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Using our framework, we set a new state-of-the-art on the rotation invariant matching benchmarks AIMS [49] (Figure 1) and Roto-360 [31]. At the same time, we are with the same models able to perform on par with or even outperform existing non-invariant methods on upright images on the competitive MegaDepth-1500 benchmark [33, 50]. In summary, our main contributions are as follows.", + "bbox": [ + 76, + 530, + 468, + 635 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. We introduce a new framework of steerers for equivariant keypoint descriptors (Section 4) and theoretically motivate why steerers emerge in practice (Section 5).", + "2. We develop several settings for investigating steers (Section 5.1) and ways to apply them for rotation invariant matching (Section 5.2).", + "3. We conduct a large set of experiments, culminating in state-of-the-art on AIMS and Roto-360 (Section 6)." + ], + "bbox": [ + 76, + 635, + 468, + 755 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 76, + 768, + 215, + 784 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Classical keypoint descriptions are typically made rotation invariant by using keypoints with associated local rotation frames and computing the descriptions in these frames. Examples include SIFT [35], SURF [8], and ORB [45]. A canonical rotation frame can be used for patch-based neural network descriptors as well [53, 54]. Further, neural network-based approaches have been proposed for es", + "bbox": [ + 75, + 794, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "timating the keypoint rotation frame [29, 30, 37] and for both computing the rotation frame and the descriptions in that frame [31, 61]. Notably, [30, 31] use rotation equivariant ConvNets [15, 56, 59]. Equivariant ConvNets have also been used for rotation-robust keypoint detection without estimating the rotation frame [2, 46], keypoint description [2, 34] and end-to-end image matching [9]. In theory1, equivariant ConvNets guarantee that the predictions are consistent when rotating the image. They are one example of hard-coding equivariance into network layers using mathematical group theory, an idea that goes back to the 1990's [58] and has seen large recent interest [11, 20, 22].", + "bbox": [ + 496, + 90, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Neural networks can also be encouraged to learn equivariance rather than having it hard-coded in the layers. This can be done by enforcing group-specific invariants in the network output space [25, 48] (see also Section 5). Another approach is to specify a group representation on the output of the network and train the network to satisfy equivariance wrt. that representation [16, 28, 36, 60]. We will use this approach for keypoint descriptions in our Setting C. The benefits of not hard-coding equivariance are that arbitrary network architectures can be used (particularly pre-trained non-equivariant networks) and that one does not need to specify the group representations acting on each layer of the network. A special case of learning equivariance is rotation invariant descriptors through data augmentation [38, 52].", + "bbox": [ + 496, + 273, + 890, + 484 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "A recent line of work [10, 12, 24, 32] investigates to what extent neural networks exhibit equivariance without having been trained or hard-coded to do so. They find that many networks are approximately equivariant. One major limitation is that they only consider networks trained for image classification. We will empirically demonstrate a high level of equivariance in keypoint descriptors that were not explicitly trained to be equivariant and theoretically motivate why this happens (our Setting A).", + "bbox": [ + 496, + 486, + 890, + 622 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 500, + 638, + 637, + 654 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we are interested in finding linear mappings between keypoint descriptions where the images may have been rotated independently. We will, in particular, consider the group of quarter rotations $C_4$ and the group of continuous rotations $\\mathrm{SO}(2)$ .", + "bbox": [ + 496, + 666, + 890, + 742 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Ordinary typeset $g$ will denote an arbitrary group element, boldface $\\mathbf{g}$ will always mean the generator of $C_4$ for the remainder of the text so that the elements of $C_4$ are $\\mathbf{g}$ , $\\mathbf{g}^2$ , $\\mathbf{g}^3$ and the identity element $\\mathrm{id} = \\mathbf{g}^4$ . Boldface $\\mathbf{i}$ will denote the imaginary unit such that $\\mathbf{i}^2 = -1$ . Given matrices $X_1, X_2, \\ldots, X_J$ , the notation $\\oplus_{j=1}^{J} X_j$ will mean the block-diagonal matrix with blocks $X_1, X_2, \\ldots, X_J$ .", + "bbox": [ + 496, + 743, + 890, + 849 + ], + "page_idx": 1 + }, + { + "type": "page_footnote", + "text": "1It has been demonstrated that equivariant ConvNets can learn to break equivariance [18] when this benefits the task at hand. E.g., the end-to-end matcher SE2-LoFTR [9] is not perfectly consistent over rotations [9, 49].", + "bbox": [ + 500, + 862, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "4886", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Preliminaries on keypoint matching", + "text_level": 1, + "bbox": [ + 76, + 90, + 388, + 107 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The underlying task is to take two images of the same scene and detect 2D points that correspond to the same 3D point. A pair of such points that depict the same 3D point is called a correspondence. The approach for finding correspondences that will be explored is a three-stage approach:", + "bbox": [ + 75, + 114, + 467, + 190 + ], + "page_idx": 2 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. Detection. Detect $N$ keypoint locations in each image.", + "2. Description. Describe the keypoint locations with descriptors, i.e., feature vectors in $\\mathbb{R}^D$ .", + "3. Matching. Match the descriptors, typically by using mutual nearest neighbours in cosine distance." + ], + "bbox": [ + 76, + 191, + 467, + 267 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This classical setup includes SIFT [35] but also more recent deep learning-based approaches. In particular, we follow the method in DeDoDe [19], where the keypoint detector is first optimized to find good point tracks from SfM reconstructions and the keypoint descriptor is optimized by maximizing the matching likelihood obtained by a frozen keypoint detector as follows. If the $N$ descriptors (each normalized to unit length) in the two images are $y_{1} \\in \\mathbb{R}^{D \\times N}$ and $y_{2} \\in \\mathbb{R}^{D \\times N}$ we first form the $N \\times N$ matching matrix $Y = y_{1}^{T}y_{2}$ , and obtain a matrix of pairwise likelihoods by using the dual softmax [44, 50, 55]:", + "bbox": [ + 75, + 268, + 467, + 435 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\np \\left(y _ {1}, y _ {2}\\right) = \\frac {\\exp (\\iota Y)}{\\sum_ {\\text {c o l u m n s}} \\exp (\\iota Y)} \\cdot \\frac {\\exp (\\iota Y)}{\\sum_ {\\text {r o w s}} \\exp (\\iota Y)}. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 449, + 468, + 484 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here $\\iota = 20$ is the inverse temperature. The negative logarithm of the likelihood (1) is minimized for those pairs in the $N\\times N$ matrix that correspond to ground truth inliers.", + "bbox": [ + 75, + 496, + 467, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Preliminaries on group representations", + "text_level": 1, + "bbox": [ + 76, + 556, + 411, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 3.1. (Group representation) Given a group $G$ , a representation of $G$ on $\\mathbb{R}^D$ is a mapping $\\rho : G \\to \\mathrm{GL}(\\mathbb{R}, D)$ that preserves the group multiplication, i.e., $\\rho(gg') = \\rho(g)\\rho(g')$ for every $g, g' \\in G$ .", + "bbox": [ + 75, + 580, + 467, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Simply stated, $\\rho$ maps every element in the group to an invertible $D\\times D$ matrix. The point of using representations is that groups such as $C_4$ act differently on different quantities as we will illustrate in the following examples.", + "bbox": [ + 75, + 656, + 467, + 715 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Example 3.1. For $\\mathbb{R}^{n\\times n}$ (a square image grid), $C_4$ can be represented by permutations of the pixels in the obvious way so that the image is rotated anticlockwise by multiples of $90^{\\circ}$ . We denote this group representation by $P_{90}$ so that applying $P_{90}^{k}$ rotates the image by $k\\cdot 90^{\\circ}$ anticlockwise.", + "bbox": [ + 75, + 729, + 467, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Example 3.2. For $\\mathbb{R}^2$ (image coordinates), one possible representation of $C_4$ is $\\rho(\\mathbf{g}^k) = R_{90}^k = \\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)^k$ . Multiplication by $R_{90}^k$ corresponds to rotating image coordinates by $k \\cdot 90^\\circ$ if the center of the image is taken as $(0,0)$ .", + "bbox": [ + 75, + 820, + 467, + 883 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/10a662079dc70f77ddbf467c9da8a4de192d38afa0cf70f5726154224ecce7b2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 614, + 175 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/18d6455e65d469d95a3a04b8df5b0e1bbb4e21698e6d35db90f1f4e76bbfaaaa.jpg", + "image_caption": [ + "Figure 3. Equivariance of Upright SIFT. Left: A keypoint with its Upright SIFT description in an upright image and a rotated version. The small yellow squares are the subregions where histograms of gradient orientations are computed. Right: The Upright SIFT descriptions unravelled into the 128 bin histograms that constitute them. When we rotate the image, the subregions are permuted, and the histogram bins within each subregion are further permuted cyclically. Hence, Upright SIFT is rotation equivariant." + ], + "image_footnote": [], + "bbox": [ + 500, + 194, + 614, + 281 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/701ef7fa0a09cf869091b0a144f7348481b447f286bb088b63ed351579c7d81e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 633, + 95, + 890, + 275 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Equivariance and steerability", + "text_level": 1, + "bbox": [ + 498, + 415, + 769, + 431 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we will analyze the close connection between equivariance and steerability. We start with an example to introduce the former concept.", + "bbox": [ + 496, + 440, + 890, + 486 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Example 4.1. SIFT descriptions [35] are $128\\mathrm{dim}$ vectors designed to be invariant to rotation, scale and illumination and highly distinctive for leveraging feature matching. For an input image $I \\in \\mathbb{R}^{n \\times n}$ and $N$ keypoints with scale and orientation $x \\in \\mathbb{R}^{4 \\times N^2}$ , we get descriptions $y \\in \\mathbb{R}^{128 \\times N}$ . If $f$ is the SIFT descriptor, we write $f(I, x) = y$ . The descriptions consist of histograms of image gradients over patches around the keypoints $x$ . The patches are oriented by the keypoint orientations so that the descriptions are invariant to joint rotations of the image and keypoints:", + "bbox": [ + 496, + 491, + 890, + 643 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf \\left(P _ {9 0} ^ {k} I, \\left(\\oplus_ {b = 1} ^ {2} R _ {9 0}\\right) ^ {k} x\\right) = f (I, x).\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 648, + 813, + 667 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "If we discard the keypoint orientations, i.e., set the angle of each keypoint to 0, we get the Upright SIFT (UPSIFT) descriptor [1, 7], which is often used for upright images as it is more discriminative than SIFT. When we rotate an image $90^{\\circ}$ , then the gradient histograms, i.e., the UPSIFT descriptions are permuted by a specific permutation $P_{\\mathrm{UPSIFT}}$ , so if $f$ is the UPSIFT descriptor, we have", + "bbox": [ + 496, + 672, + 890, + 779 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf \\left(P _ {9 0} ^ {k} I, \\left(\\oplus_ {b = 1} ^ {2} R _ {9 0}\\right) ^ {k} x\\right) = P _ {\\text {U P S I F T}} ^ {k} f (I, x).\n$$\n", + "text_format": "latex", + "bbox": [ + 550, + 785, + 836, + 804 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We illustrate the permutation $P_{\\mathrm{UPSIFT}}$ in Figure 3. UPSIFT is not rotation invariant, but it is rotation equivariant when we rotate the input, the output changes predictably. Explicitly, the representation is $\\rho(\\mathbf{g}^k) = P_{\\mathrm{UPSIFT}}^k$ .", + "bbox": [ + 496, + 809, + 890, + 872 + ], + "page_idx": 2 + }, + { + "type": "page_footnote", + "text": "2The first two coordinates of each keypoint in $x$ are its location and the last two a vector for its orientation and scale, so $x$ is rotated by $\\oplus_{b = 1}^{2}R_{90}$", + "bbox": [ + 500, + 875, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "4887", + "bbox": [ + 480, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 4.1 (Equivariance). We say that a function $f: V \\to W$ is equivariant with respect to a group $G$ if", + "bbox": [ + 76, + 90, + 468, + 121 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\rho (g) f (v) = f \\left(\\rho_ {\\text {i n}} (g) v\\right), \\forall v \\in V, g \\in G, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 138, + 128, + 468, + 146 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for some group representations $\\rho_{\\mathrm{in}},\\rho$", + "bbox": [ + 76, + 152, + 326, + 167 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This work will mainly be concerned with the equivariance of learned keypoint descriptors of ordinary keypoints (without scale and orientation).", + "bbox": [ + 76, + 172, + 468, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 4.2 (Equivalence of keypoint descriptor). We say that a keypoint descriptor $f$ is equivariant with respect to a group $G$ transforming the input image by $\\rho_{\\mathrm{image}}$ and the input keypoint locations by $\\rho_{\\mathrm{keypoint}}$ if there exists $\\rho$ such that", + "bbox": [ + 76, + 224, + 468, + 299 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\rho (g) f (I, x) = f \\left(\\rho_ {\\text {i m a g e}} (g) I, \\rho_ {\\text {k e y p o i n t}} (g) x\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 308, + 468, + 325 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for all images, keypoints and group elements. We call the descriptor invariant if $\\rho(g)$ is the identity matrix for all $g$ . Invariance is a special type of equivariance.", + "bbox": [ + 76, + 332, + 468, + 378 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Example 4.2. A keypoint descriptor $f$ is equivariant under $90^{\\circ}$ rotations if there exists $\\rho$ of $C_4$ such that", + "bbox": [ + 76, + 383, + 468, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\rho \\left(\\mathbf {g} ^ {k}\\right) f (I, x) = f \\left(P _ {9 0} ^ {k} I, R _ {9 0} ^ {k} x\\right) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 420, + 468, + 438 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for $k \\in \\{0,1,2,3\\}$ , where $P_{90}$ and $R_{90}$ are the representations from Examples 3.1 and 3.2 that rotate images and coordinates in the ordinary manner.", + "bbox": [ + 76, + 445, + 468, + 489 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Both SIFT and Upright SIFT are equivariant. For SIFT, $\\rho (\\mathbf{g}^k)$ is the identity, so SIFT is invariant. For Upright SIFT, $\\rho (\\mathbf{g}^k)$ is $P_{\\mathrm{UPSIFT}}^k$ as explained in Example 4.1.", + "bbox": [ + 76, + 489, + 468, + 537 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "One aim of this work is to argue and demonstrate that learned keypoint descriptors, which are trained on upright data, will behave more like Upright SIFT than SIFT, i.e., they will be rotation equivariant but not invariant.", + "bbox": [ + 76, + 542, + 468, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 4.3 (Steerability, adapted from [21]). A real-valued function $\\phi : V \\to \\mathbb{R}$ is said to be steerable under a representation $\\rho_{\\mathrm{in}}$ of $G$ on $V$ , if there exist $D$ functions (for some $D$ ) $\\phi_j : V \\to \\mathbb{R}$ and $D$ functions $\\kappa_j : G \\to \\mathbb{R}$ such that $\\phi(\\rho_{\\mathrm{in}}(g)v) = \\sum_{j=1}^{D} \\kappa_j(g)\\phi_j(v)$ .", + "bbox": [ + 76, + 608, + 468, + 688 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that an equivariant function $f:V\\to \\mathbb{R}^{D}$ satisfies in each component $f_{d}$ that $f_{d}(\\rho_{\\mathrm{in}}(g)v) = \\sum_{j = 1}^{D}\\rho (g)_{dj}f_{j}(v)$ , so each component of $f$ is steerable, in the notation of Definition 4.3, $\\phi = f_d,\\phi_j = f_j,\\kappa_j(g) = \\rho (g)_{dj}$ . This motivates the definition of a steerer.", + "bbox": [ + 76, + 694, + 468, + 772 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 4.4 (Steerer). Given a function $f: V \\to W$ between vector spaces, and a representation $\\rho_{\\mathrm{in}}$ of $G$ on $V$ , a steerer is a representation $\\rho$ of $G$ on $W$ that makes $f$ equivariant, i.e. such that", + "bbox": [ + 76, + 777, + 468, + 838 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf \\left(\\rho_ {\\text {i n}} (g) v\\right) = \\rho (g) f (v). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 191, + 847, + 468, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Even if (5) only holds approximately or $\\rho$ is only approximately a representation, we will refer to $\\rho$ as a steerer.", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We will use the verb steer for multiplying a feature/description by a steerer; see Figure 2 for the broad idea.", + "bbox": [ + 500, + 90, + 890, + 121 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Example 4.3. As explained in Example 4.1, $P_{\\mathrm{UPSIFT}}$ is a steerer for Upright SIFT under $90^{\\circ}$ rotations. This has practical consequences. If we want to obtain the Upright SIFT descriptions for an image $I$ and the same image rotated $k \\cdot 90^{\\circ}$ , we only need to compute the descriptions for the original image. We can obtain the rotated ones by multiplying the descriptions by $P_{\\mathrm{UPSIFT}}^{k}$ . That is, we can steer the Upright SIFT descriptions with $P_{\\mathrm{UPSIFT}}$ .", + "bbox": [ + 498, + 127, + 890, + 248 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "It is known from representation theory [47] what all possible representations of $C_4$ are, and hence what all possible steerers for rotation equivariant descriptors are. As this result will be necessary for the remainder of the text, we collect it in a theorem. Similar results are also known for other groups e.g. the continuous rotation group SO(2), which we discuss in the next section.", + "bbox": [ + 498, + 255, + 890, + 359 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 4.1 (Representations of $C_4$ ). Let $\\rho$ be a representation of $C_4$ on $\\mathbb{R}^D$ . Then, there exists an invertible matrix $Q$ and $j_d \\in \\{0, 1, 2, 3\\}$ such that", + "bbox": [ + 498, + 367, + 890, + 412 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\rho \\left(\\mathbf {g} ^ {k}\\right) = Q ^ {- 1} \\operatorname {d i a g} \\left(\\mathbf {i} ^ {k j _ {1}}, \\mathbf {i} ^ {k j _ {2}}, \\dots , \\mathbf {i} ^ {k j _ {D}}\\right) Q. \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 417, + 890, + 436 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The diagonal in (6) contains the eigenvalues of $\\rho (\\mathbf{g}^k)$ .", + "bbox": [ + 519, + 443, + 874, + 459 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Example 4.4. The Upright SIFT steuerer $P_{\\mathrm{UPSIFT}}$ is diagonalizable with an equal amount of each eigenvalue $\\pm 1$ , $\\pm \\mathbf{i}$ .", + "bbox": [ + 498, + 464, + 890, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The complex eigenvalues must appear in conjugate pairs as we take $\\rho(\\mathbf{g})$ to be real-valued. It is then possible to do a change of basis so that each pair $\\mathbf{i}, -\\mathbf{i}$ on the diagonal in (6) is replaced by a block $\\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)$ . In this way, $\\rho(\\mathbf{g})$ can always be block-diagonalized: $\\rho(\\mathbf{g}) = Q^{-1}BQ$ where $Q$ and $B$ are real valued and $B$ is block-diagonal with blocks of sizes 1 and 2.", + "bbox": [ + 498, + 501, + 890, + 606 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Representation theory of SO(2)", + "text_level": 1, + "bbox": [ + 500, + 614, + 772, + 631 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "SO(2) is a one-parameter Lie group, i.e. a continuous group with one degree of freedom $\\alpha$ the rotation angle. A $D$ -dimensional representation of SO(2) is a map $\\varsigma : [0, 2\\pi) \\to \\mathrm{GL}(\\mathbb{R}, D)$ such that addition modulo $2\\pi$ on the input is encoded as matrix multiplication on the output—we will consistently use $\\varsigma$ for SO(2) representations to separate them from $C_4$ representations $\\rho$ ( $\\rho$ will also be used for representations of general groups). The most familiar is the two-dimensional representation $\\varsigma(\\alpha) = \\begin{pmatrix} \\cos(\\alpha) & -\\sin(\\alpha) \\\\ \\sin(\\alpha) & \\cos(\\alpha) \\end{pmatrix}$ which rotates 2D coordinates. Similar to the $C_4$ case in Theorem 4.1, we can write down a general representation for SO(2) as follows [57].", + "bbox": [ + 498, + 637, + 890, + 825 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Theorem 4.2 (Representations of $\\mathrm{SO}(2)$ ). Let $\\varsigma$ be a representation of $\\mathrm{SO}(2)$ on $\\mathbb{R}^D$ . Then there exists an invertible $Q$ and $j_d \\in \\mathbb{Z}$ such that", + "bbox": [ + 498, + 832, + 890, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\varsigma (\\alpha) = Q ^ {- 1} \\operatorname {d i a g} \\left(\\mathrm {e} ^ {\\mathbf {i} j _ {1} \\alpha}, \\mathrm {e} ^ {\\mathbf {i} j _ {2} \\alpha}, \\dots , \\mathrm {e} ^ {\\mathbf {i} j _ {D} \\alpha}\\right) Q. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 883, + 890, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "4888", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The $j_{d}$ 's are the frequencies of the eigenspaces of $\\varsigma$ . Complex eigenvalues appear in conjugate pairs so (7) can be rewritten as a block diagonal decomposition $\\varsigma(\\alpha) = Q^{-1}BQ$ where $Q$ and $B$ are real valued and $B$ is block-diagonal with minimal blocks. The admissible blocks (= real-valued irreducible representations) in $B$ are then the $1 \\times 1$ block (1) and the $2 \\times 2$ blocks", + "bbox": [ + 76, + 90, + 472, + 198 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left( \\begin{array}{c c} \\cos (j \\alpha) & - \\sin (j \\alpha) \\\\ \\sin (j \\alpha) & \\cos (j \\alpha) \\end{array} \\right) \\quad \\text {f o r} j \\in \\mathbb {Z} \\backslash \\{0 \\}. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 209, + 468, + 242 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We can write $\\varsigma (\\alpha) = \\exp \\left(\\alpha Q^{-1}\\mathrm{diag}(\\mathbf{i}j_1,\\ldots ,\\mathbf{i}j_D)Q\\right)$ where $\\mathrm{expm}$ is the matrix exponential. The quantity $\\mathrm{d}\\varsigma \\coloneqq$ $Q^{-1}\\mathrm{diag}(\\mathbf{i}j_1,\\dots ,\\mathbf{i}j_D)Q$ is called a Lie algebra representation of SO(2), here in its most general form. When training a steerer for SO(2) it is practical to train a $D\\times D$ matrix $\\mathrm{d}\\varsigma$ and steer using $\\varsigma (\\alpha) = \\exp \\mathrm{m}(\\alpha \\mathrm{d}\\varsigma)$ .", + "bbox": [ + 76, + 253, + 468, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Disentangling description space", + "text_level": 1, + "bbox": [ + 76, + 354, + 356, + 371 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "When we have a steerer, we get a description space on which rotations act—up to a change of basis—by a block-diagonal matrix $\\oplus_{j=1}^{J} B_{j}$ . The description space can then be thought of as being disentangled into different subspaces where rotations act in different ways $B_{j}$ [14, 60]. We detail what this means for keypoint descriptors in Appendix A.", + "bbox": [ + 76, + 378, + 468, + 470 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Descriptors and steerers", + "text_level": 1, + "bbox": [ + 76, + 482, + 305, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This work's crucial observation and assumption is that learned descriptors, while not invariant, are approximately equivariant so that they have a steerer. Or, as a weaker assumption, they can be trained to be equivariant. It may seem that this is a strong assumption. However, a seemingly less strong assumption turns out to be equivalent.", + "bbox": [ + 75, + 507, + 468, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Theorem 5.1. [Adapted from Shakerinava et al. [48], Gupta et al. [25]] Assume that we have a function $f: V \\to \\mathbb{S}^{D-1}$ and a group $G$ with representation $\\rho_{\\mathrm{in}}$ on $V$ such that, for all $v, v' \\in V$ and $g \\in G$", + "bbox": [ + 75, + 607, + 468, + 670 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\langle f \\left(\\rho_ {\\text {i n}} (g) v\\right), f \\left(\\rho_ {\\text {i n}} (g) v ^ {\\prime}\\right) \\rangle = \\langle f (v), f \\left(v ^ {\\prime}\\right) \\rangle . \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 133, + 680, + 468, + 699 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then there exists an orthogonal representation $\\rho(g)$ , such that $f$ is equivariant w.r.t. $G$ with representations $\\rho_{\\mathrm{in}}$ and $\\rho$ .", + "bbox": [ + 76, + 708, + 468, + 742 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We provide a proof in Appendix A. Since we match normalized keypoint descriptions by their cosine similarity, Theorem 5.1 is highly applicable to the image matching problem. If a keypoint descriptor $f$ is perfectly consistent in the matching scores when simultaneously rotating the images, then the scalar products in (9) will be equal so that the theorem tells us that $f$ has a steerer $\\rho$ . Furthermore, we can expect many local image features to appear in all orientations even over a dataset of upright images, thus encouraging (9) to hold for $f$ trained on large datasets.", + "bbox": [ + 75, + 750, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Three settings for investigating steerers", + "text_level": 1, + "bbox": [ + 498, + 90, + 836, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As $C_4$ is cyclic, all its representations are defined by $\\rho(\\mathbf{g})$ , where $\\mathbf{g}$ is the generator of $C_4$ . To find a steerer for a keypoint descriptor under $C_4$ hence comes down to finding a single matrix $\\rho(\\mathbf{g})$ that represents rotations by $90^\\circ$ in the description space. Similarly, for SO(2) we find the single matrix $\\mathrm{d}\\varsigma$ that defines the representation $\\varsigma$ .", + "bbox": [ + 496, + 113, + 890, + 204 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We will consider three settings. In each case we will optimize $\\rho (\\mathbf{g})$ and/or $f$ over the MegaDepth training set [33] with rotation augmentation and maximize", + "bbox": [ + 496, + 204, + 890, + 250 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\np \\left(f \\left(P _ {9 0} ^ {k _ {1}} I _ {1}, R _ {9 0} ^ {k _ {1}} x _ {1}\\right), \\rho (\\mathbf {g}) ^ {k} f \\left(P _ {9 0} ^ {k _ {2}} I _ {2}, R _ {9 0} ^ {k _ {2}} x _ {2}\\right)\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 258, + 890, + 284 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $p$ is the matching probability (1). The number of rotations $k_{1}$ and $k_{2}$ for each image are sampled independently during training, and $k = k_{1} - k_{2} \\mod 4$ is the number of rotations that aligns image $I_{2}$ to image $I_{1}$ . Thus, $\\rho(\\mathbf{g})^{k}$ aligns the relative rotation between descriptions in $I_{2}$ and $I_{1}$ . We optimize continuous steerers $\\varsigma$ analogously to (10).", + "bbox": [ + 496, + 291, + 890, + 382 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setting A: Fixed descriptor, optimized steerer. If a descriptor works equally well for upright images as well as images rotated the same amount from upright, then according to Theorem 5.1, we should expect that there exists a steerer $\\rho (\\mathbf{g})$ such that (4) holds. To find $\\rho (\\mathbf{g})$ we optimize it as a single $D\\times D$ linear layer by maximizing (10).", + "bbox": [ + 496, + 383, + 890, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setting B: Joint optimization of descriptor and steerer.", + "text_level": 1, + "bbox": [ + 498, + 474, + 883, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The aim is to find a steerer that is as good as possible for the given data. We will see in the experiments, by looking at the evolution of the eigenvalues of $\\rho(\\mathbf{g})$ during training, that this joint optimization has many local optima and is highly dependent on the initialization of $\\rho(\\mathbf{g})$ . However, looking at the eigenvalues of $\\rho(\\mathbf{g})$ does give knowledge about which descriptor dimensions are most important, as will be explained in Section 6.5.", + "bbox": [ + 496, + 489, + 890, + 609 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Setting C: Fixed steerer, optimized descriptor. To get the most precise control over the rotation behaviour of a descriptor, we can fix the steerer and optimize only the descriptor. This enables us to investigate how much influence the choice of steerer has on the descriptor. For instance, choosing the steerer as the identity leads to a rotation invariant descriptor. We will see in the experiments that this choice leads to suboptimal performance on upright images compared to other steers.", + "bbox": [ + 496, + 609, + 890, + 746 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.2. Matching with equivariant descriptions", + "text_level": 1, + "bbox": [ + 498, + 756, + 836, + 773 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "This section presents several approaches to rotation invariant matching using equivariant descriptors. Throughout, we will denote the $D$ -dimensional descriptions of $N$ keypoints in two images $I_1, I_2$ by $y_1, y_2 \\in \\mathbb{R}^{D \\times N}$ and will assume that we know the $C_4$ -steerer $\\rho(\\mathbf{g})$ that rotates descriptions $90^\\circ$ or the SO(2)-steerer $\\varsigma(\\alpha)$ through the Lie algebra generator $\\mathrm{d}\\varsigma$ . For matching we follow DeDoDe [19], as described in Section 3.1. The base similarity used is the cosine", + "bbox": [ + 496, + 780, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "4889", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/9b029575b1d80e46ff98ea59d1e11fa9a79522e63a5a5410c61a3cc7afe13a4b.jpg", + "table_caption": [ + "Table 1. Evaluation on Roto-360 [31]. We report the percentage of correct matches at three thresholds. We use the DeDoDe-SO2 detector with 5,000 keypoints in the last two rows. Matching strategies are Max Matches for the $C_4$ -descriptor and Max Sim. over $C_8$ for the SO(2)-descriptor. See Section 6.1 for the shorthands for our models." + ], + "table_footnote": [], + "table_body": "
DetectorDescriptor3px5px10px
SIFT [35]SIFT [35]787879
ORB [45]ORB [45]798587
SuperPoint [17]RELF, single [31]909193
SuperPoint [17]RELF, multiple [31]929394
SuperPoint [17]C4-B (ours)828283
SuperPoint [17]SO2-Spread-B (ours)969797
DeDoDe [19]C4-B (ours)828486
DeDoDe [19]SO2-Spread-B (ours)959798
", + "bbox": [ + 76, + 174, + 470, + 321 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "similarity, so we compute $y_1^T y_2$ for normalized descriptions to get an $N \\times N$ matrix of pairwise scores on which dual softmax (1) is applied. Matches are mutual most similar descriptions with similarity above 0.01.", + "bbox": [ + 75, + 349, + 468, + 411 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Max matches over steered descriptions. The first way of obtaining invariant matches is to match $y_{1}$ with $\\rho(\\mathbf{g})^{k}y_{2}$ for $k = 0,1,2,3$ and keep the matches from the $k$ that has the most matches. This is similar to matching the image $I_{1}$ with four different rotations of $I_{2}$ but alleviates the need for rerunning the descriptor network for each rotation.", + "bbox": [ + 75, + 417, + 468, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Max similarity over steered descriptions. A computationally cheaper version is to select the matching matrix not as $y_1^T y_2$ but as $\\max_k y_1^T \\rho(\\mathbf{g})^k y_2$ , where the max is elementwise over the matrix.", + "bbox": [ + 75, + 507, + 468, + 566 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SO(2)-steerers. To apply the above matching strategies to SO(2)-steerers $\\varsigma (\\alpha) = \\exp (\\alpha \\mathrm{d}\\varsigma)$ we discretize $\\varsigma$ . A $C_\\ell$ -steerer is obtained through $\\rho (\\mathbf{g}_\\ell) = \\exp \\left(\\frac{2\\pi}{\\ell}\\mathrm{d}\\varsigma\\right)$ , where $\\mathbf{g}_{\\ell}$ generates $C_\\ell$ . We will use $C_8$ in the experiments.", + "bbox": [ + 75, + 568, + 468, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Procrustes matcher. If all eigenvalues of $\\rho(\\mathbf{g})$ are $\\pm \\mathrm{i}$ , the steuer can be block-diagonalized with only the block $\\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)^3$ . The descriptions consist of $D/2$ two-dimensional quantities that all rotate with the same frequency as the image. We will refer to them as frequency 1 descriptions and view them reshaped as $y \\in \\mathbb{R}^{2 \\times (D/2) \\times N}$ . A 2D rotation matrix acts on these descriptions from the left when the image rotates, and we can find the optimal rotation matrix $R_{m,n}$ that aligns each pair $y_{1,m}, y_{2,n} \\in \\mathbb{R}^{2 \\times (D/2)}$ by solving the Procrustes problem via SVD. The matching matrix is obtained by computing $\\langle R_{m,n}y_{1,m}, y_{2,n} \\rangle$ for each pair. $R_{m,n}$ gives the relative rotation between each pair of keypoints, which can be useful e.g. for minimal relative pose solvers [4, 6] or for outlier filtering [13]. We leave exploring this per-correspondence geometry to future work.", + "bbox": [ + 75, + 628, + 468, + 854 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/a1f3ae7badf389a6b5955e85bb8af8805ba6de045f6aabc114b306bc87bc80f5.jpg", + "table_caption": [ + "Table 2. Evaluation on AIMS [49]. We report the average precision (AP) in percent on different splits of AIMS: \"North Up\" (N. Up) contains images with small rotations, \"All Others\" (A. O.) contains images with larger rotations and \"All\" contains all images. We use the DeDoDe-SO2 detector and 10,000 keypoints throughout. See Section 6.1 for the shorthands for our models." + ], + "table_footnote": [], + "table_body": "
MethodN. UpA. O.All
SE2-LoFTR [9]585152
C4-B, Max Matches (ours)525151
SO2-Spread-B, Max Sim. C8 (ours)605758
SO2-Freq1-B, Procrustes (ours)645960
", + "bbox": [ + 503, + 174, + 885, + 261 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6. Experiments", + "text_level": 1, + "bbox": [ + 500, + 282, + 632, + 301 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We train and evaluate a variety of descriptors and steerers. Experimental details are covered in Appendix C. We provide comparisons to TTA in performance and runtime in Appendix B, as well as experiments with more matching strategies and an explicit experiment to test the connection between Theorem 5.1 and rotation equivariance.", + "bbox": [ + 496, + 309, + 890, + 398 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We start by reporting results on two public benchmarks for rotation invariant image matching. Then, we will present ablation results for the MegaDepth benchmark, both for the standard version with upright images and a version where we have rotated the input images.", + "bbox": [ + 496, + 400, + 890, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "6.1. Models considered", + "text_level": 1, + "bbox": [ + 500, + 484, + 679, + 500 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our base models are the DeDoDe-B and DeDoDe-G descriptors introduced in [19]. These are both $D = 256$ dimensional descriptors. The focus will be on the smaller model DeDoDe-B, as this gives us the chance to do large-scale ablations. We train all models on MegaDepth [33]. To obtain rotation-consistent detections, we retrain two versions of the DeDoDe-detector, with data augmentation over $C_4$ and SO(2) respectively, denoted DeDoDe-{C4, SO2}.", + "bbox": [ + 496, + 507, + 890, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For Setting B (Section 5.1), we will see that the initialization of the steerer matters. Similarly, for Setting C, we can fix the steerer with different eigenvalue structures. Here, we introduce shorthand, which is used in the result tables. We will refer to the case of all eigenvalues 1 as $Inv$ for invariant. This case corresponds to the ordinary notion of data augmentation, where the descriptions for rotated images should be the same as for non-rotated images. The case when all eigenvalues are $\\pm \\mathbf{i}$ is denoted $Freq1$ for frequency 1 as explained in Section 5.2. For $C_4$ -steers, the case with an equal distribution of all eigenvalues $\\pm 1, \\pm \\mathbf{i}$ will be denoted $Perm$ , as this is the eigenvalue signature of a cyclic permutation of order 4. For SO(2)-steers, the case with an equal distribution of eigenvalues $0, \\pm \\mathbf{i}, \\pm 2\\mathbf{i}, \\ldots \\pm 6\\mathbf{i}$ will be denoted $Spread$ (the cutoff 6 was arbitrarily chosen). The $Perm$ and $Spread$ steers correspond to a broad range of frequencies in the description space. When none of the above labels ( $Inv$ , $Freq1$ , $Perm$ or", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "This also holds for $\\mathrm{SO}(2)$ steers, referring to eigenvalues and blocks of the Lie algebra generator $\\mathrm{d}\\varsigma$ .", + "bbox": [ + 75, + 873, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "4890", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/24afd456a089ac9ffb093fd785178f531455f6390e96e6f3a5d16be4b461acba.jpg", + "table_caption": [ + "Table 3. Evaluation on MegaDepth [33, 50]. The first section shows Setting A where we only optimize the steerer, the second section shows Setting B where we jointly optimize the descriptor and steerer and the third section shows the Setting C where we predefine the steerer and optimize only the descriptor. For MegaDepth-1500 we always use dual softmax matcher to evaluate the descriptors on upright images. We use 20,000 keypoints throughout. The best values for B- and G-models are highlighted in each column. See Section 6.1 for shorthand explanations for our models. A larger version of this table with more methods is available in Appendix B." + ], + "table_footnote": [], + "table_body": "
DetectorDescriptorMatching strategyMegaDepth-1500MegaDepth-C4MegaDepth-SO2
DeDoDeAUC @ 5°10°20°5°10°20°5°10°20°
OriginalBDual softmax496577121720121620
OriginalBMax matches C4-steered-11--11--11-436073304456
SO2BMax matches C8-steered506678405770345165
OriginalGDual softmax526981131721162228
OriginalGMax matches C4-steered-11--11--11-314557263950
C4C4-BMax matches C4-steered516779506779395568
SO2SO2-BMax matches C8-steered476376476376446174
SO2SO2-Spread-BMax matches C8-steered506679496678466376
SO2SO2-Spread-BMax similarity C8-steered496678476477436174
C4C4-Inv-BDual softmax486476476376395569
C4C4-Perm-BMax matches C4-steered506779506679395467
SO2SO2-Inv-BDual softmax466275456174436073
SO2SO2-Freq1-BMax matches C8-steered476477476476456275
SO2SO2-Freq1-BProcrustes476476466275456174
C4C4-Perm-GMax matches C4-steered526981536982446174
", + "bbox": [ + 96, + 160, + 870, + 426 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Spread) is attached to a descriptor and steerer trained jointly in Setting B, then we initialize the steerer with values uniformly in $(-D^{-1/2}, D^{-1/2})^4$ , the eigenvalues are then approximately uniformly distributed in the disk with radius $3^{-1/2}$ [51]. When a descriptor is trained with $k \\cdot 90^\\circ$ rotations, we append $C4$ to its name and when trained with continuous augmentations, we append $SO2$ to its name.", + "bbox": [ + 75, + 450, + 470, + 556 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.2. Roto-360", + "text_level": 1, + "bbox": [ + 76, + 566, + 184, + 580 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate on the Roto-360 benchmark [31], which consists of ten image pairs from HPatches [3] where the second image in each image pair is rotated by all multiples of $10^{\\circ}$ to obtain 360 image pairs in total. We report the average precision of the obtained matches and compare it to the current state-of-the-art RELF [31]. The results are shown in Table 1. We see that we outperform RELF when using methods trained for continuous rotations. Our matching runs around three times faster than RELF on Roto-360.", + "bbox": [ + 75, + 589, + 468, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.3.AIMS", + "text_level": 1, + "bbox": [ + 76, + 734, + 161, + 750 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The Astronaut Image Matching Subset (AIMS) [49] consists of images taken by astronauts from the ISS and satellite images covering the broad regions that the astronaut images could depict. The task consists of finding the pairs of astronaut images and satellite images that show the same locations on Earth. Pairs are found by setting a threshold for the number of matches between images after homography estimation with RANSAC.", + "bbox": [ + 75, + 758, + 470, + 878 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The relative rotations of the astronaut and satellite images are unknown, making the task suitable for rotation-invariant matchers. Indeed, in [49], the best performing method is the rotation invariant SE2-LoFTR [9], which we compare to. The AIMS can be split into \"North Up\" astronaut images, consisting of images with small rotations (between $0^{\\circ}$ and $90^{\\circ}$ ) and \"All Others\", consisting of images with large rotations. This split further enables the evaluation of rotation invariant matchers. We report the average precision over the whole dataset, as opposed to the approach in [49], where the score is computed over at most 100 true negatives per astronaut image. Results are shown in Table 2. Further, we plot precision-recall curves in Appendix B. We generally outperform SE2-LoFTR, particularly on the heavily rotated images in \"All Others\".", + "bbox": [ + 500, + 450, + 893, + 678 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6.4. MegaDepth-1500", + "text_level": 1, + "bbox": [ + 500, + 693, + 669, + 709 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate on a held-out part of MegaDepth (MegaDepth-1500 following [50]). Here, the task is to take two input images and output the relative pose between the cameras. The performance is measured by the AUC of the pose error. Additionally, we create two versions of MegaDepth with rotated images to evaluate the rotational robustness of our models. For MegaDepth-C4, the second image in every image pair is rotated ( $i \\mod 4$ ) $\\cdot 90^{\\circ}$ where $i$ is the index of the image pair. We visualize a pair in MegaDepth-C4 in Appendix B, illustrating the improvement from DeDoDe-B to DeDoDe-B with a steerer optimized in Setting A. For MegaDepth-SO2, the second image in every image pair is", + "bbox": [ + 498, + 719, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_footnote", + "text": "This is the standard initialization of a linear layer in Pytorch [26, 40].", + "bbox": [ + 94, + 886, + 467, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "4891", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/a1ec4834300c2564d345386d24d9c7689659dd06493c761622e795ff405be885.jpg", + "image_caption": [ + "Figure 4. Training evolution of eigenvalue distributions of steers. We plot the eigenvalue distribution of $C_4$ -steerers $\\rho(\\mathbf{g})$ (first three columns) and Lie algebra generators $\\mathrm{d}\\varsigma$ for SO(2)-steerers (last two columns) in the complex plane, with different initializations when trained jointly with a descriptor. The top row depicts the eigenvalues at the start, and the bottom row at the end of training. There are $D = 256$ eigenvalues in every plot—many congregate at the \"admissible\" eigenvalues as described in Section 4—but some do not, see the discussion in Section 6.5. These visualizations highlight the initialization sensitivity of the steerer. We show gif movies of the training evolution at this https url." + ], + "image_footnote": [], + "bbox": [ + 86, + 90, + 464, + 218 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "instead rotated ( $i \\mod 36) \\cdot 10^{\\circ}$ , thus requiring robustness under continuous rotations.", + "bbox": [ + 75, + 406, + 468, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "The results are presented in Table 3; for more methods, see Appendix B. We summarize the main takeaways:", + "bbox": [ + 76, + 438, + 468, + 468 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. It is possible to find steers for the original DeDoDe models (e.g. the second row of the table), even though they were not trained with any rotation augmentation.", + "2. The trained $C_4$ steers perform very well as their scores on MegaDepth-1500 and MegaDepth-C4 are the same.", + "3. Training DeDoDe-B jointly with a $C_4$ steerer (C4-B) or with a fixed steerer (C4-Perm-B) improves results on upright images—this can be attributed to the fact that training with a steerer enables using rotation augmentation.", + "4. The right equivariance for the task at hand is crucial—SO(2)-steerers outperform others on MegaDepth-SO2.", + "5. The eigenvalue distribution of the steerer is important-- invariant models are worse than others, and SO2-B and SO2-Freq1-B are worse than SO2-Spread-B.", + "6. DeDoDe-G can be made equivariant (C4-Perm-G), even though it has a frozen DINoV2 [39] ViT backbone." + ], + "bbox": [ + 76, + 469, + 468, + 710 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6.5. Training dynamics of steerer eigenvalues", + "text_level": 1, + "bbox": [ + 76, + 724, + 426, + 741 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This section aims to demonstrate that joint optimization of the steerer and descriptor does not necessarily lead to a good eigenvalue structure for the steerer. We plot the evolution of the eigenvalues of the steerer over the training epochs in Figure 4. For $C_4$ -steerers we plot the eigenvalues of $\\rho(\\mathbf{g})$ itself, while for $\\mathrm{SO}(2)$ -steerers we plot the eigenvalues $\\lambda_d$ of the Lie algebra generator $\\mathrm{d}\\varsigma$ , so that the eigenvalues of the steerer $\\varsigma(\\alpha)$ are $\\mathrm{e}^{\\alpha \\lambda_d}$ . It is clear from Figure 4 that the initialization of the steerer influences the final distribution of eigenvalues a lot and we saw in Table 3 that the eigenvalue", + "bbox": [ + 75, + 750, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "distribution of the steerer matters for performance. Thus, we think it is an important direction for future work to figure out how to get around this initialization sensitivity. The choice of eigenvalue structure is related to the problem of specifying which group representations to use in the layers of equivariant neural networks in general.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As a side effect of plotting the eigenvalues, we find that some of the steerer's eigenvalues have much lower absolute values than others. The steerer is applied to descriptions before they are normalized, so the absolute value of the maximum eigenvalue is unimportant, but the relative size of the eigenvalues tells us something about feature importance. Eigenvectors with small eigenvalues cannot be too important for matching, since they will be relatively down-scaled when applying the steerer in the optimization of (10). Indeed, small eigenvalues seem to correspond to unimportant dimensions of the descriptor—we maintain matching performance when projecting the descriptions to the span of the eigenvectors with large eigenvalues. This is related to PCA for dimensionality reduction, which has successfully been used for classical keypoint descriptors [27].", + "bbox": [ + 496, + 181, + 892, + 409 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 421, + 619, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We developed a new framework for rotation equivariant keypoint descriptors using steers—linear maps that encode image rotations in description space. After outlining the general theory of steers using representation theory, we designed a large set of experiments with steers in three settings: (A) optimizing a steerer for a fixed descriptor, (B) optimizing a steerer and a descriptor jointly and (C) optimizing a descriptor for a fixed steerer. Our best models obtained new state-of-the-art results on the rotation invariant matching benchmarks Roto-360 and AIMS.", + "bbox": [ + 496, + 446, + 893, + 599 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 611, + 668, + 628 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We thank Alex Stoken for help with the evaluation on AIMS. This work was supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP), funded by the Knut and Alice Wallenberg Foundation and by the strategic research environment ELLIIT, funded by the Swedish government. The computational resources were provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at C3SE, partially funded by the Swedish Research Council through grant agreement no. 2022-06725, and by the Berzelius resource, provided by the Knut and Alice Wallenberg Foundation at the National Supercomputer Centre.", + "bbox": [ + 496, + 637, + 893, + 819 + ], + "page_idx": 7 + }, + { + "type": "page_footnote", + "text": "The absolute values of the eigenvalues of a SO(2) steerer $\\varsigma (\\alpha)$ are $\\mathrm{e}^{\\alpha \\mathrm{Re}(\\lambda_d)}$ where $\\lambda_{d}$ are the eigenvalues of $\\mathrm{d}\\varsigma$ that are plotted in the two rightmost columns of Figure 4. Therefore, a lower real value of $\\lambda_{d}$ means a lower absolute value of the eigenvalue of the steerer.", + "bbox": [ + 496, + 849, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "4892", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Georges Baatz, Kevin Koser, David Chen, Radek Grzesczuk, and Marc Pollefeys. Handling urban location recognition as a 2d homothetic problem. In Computer Vision-ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI 11, pages 266-279. Springer, 2010. 3", + "[2] Piyush Bagad, Floor Eijkelboom, Mark Fokkema, Danilo de Goede, Paul Hilders, and Miltiadis Kofinas. C-3po: Towards rotation equivariant feature detection and description. 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Springer, 2016. 2" + ], + "bbox": [ + 78, + 90, + 468, + 558 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "4895", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/e8356a95-c6c3-4afe-8ccf-5c5531990c8a_model.json b/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/e8356a95-c6c3-4afe-8ccf-5c5531990c8a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..2b53d70aac48b2da682c43128db51e0288f1c007 --- /dev/null +++ b/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/e8356a95-c6c3-4afe-8ccf-5c5531990c8a_model.json @@ -0,0 +1,2686 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.14, + 0.131, + 0.833, + 0.154 + ], + "angle": 0, + "content": "Steerers: A framework for rotation equivariant keypoint descriptors" + }, + { + "type": "text", + "bbox": [ + 0.177, + 0.18, + 0.308, + 0.199 + ], + "angle": 0, + "content": "Georg Bökman†" + }, + { + "type": "text", + "bbox": [ + 0.344, + 0.181, + 0.463, + 0.198 + ], + "angle": 0, + "content": "Johan Edstedt" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.181, + 0.645, + 0.199 + ], + "angle": 0, + "content": "Michael Felsberg†" + }, + { + "type": "text", + "bbox": [ + 0.681, + 0.181, + 0.791, + 0.198 + ], + "angle": 0, + "content": "Fredrik Kahl†" + }, + { + "type": "text", + "bbox": [ + 0.232, + 0.199, + 0.521, + 0.218 + ], + "angle": 0, + "content": "†Chalmers University of Technology" + }, + { + "type": "text", + "bbox": [ + 0.557, + 0.2, + 0.735, + 0.218 + ], + "angle": 0, + "content": "\\(^{\\ddagger}\\)Linköping University" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.256, + 0.321, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.322, + 0.256, + 0.48, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.256, + 0.728, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.729, + 0.256, + 0.885, + 0.38 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.387, + 0.893, + 0.43 + ], + "angle": 0, + "content": "Figure 1. Matching under large in-plane rotations. Two challenging pairs from AIMS [49]. The left images in each pair were taken by astronauts on the ISS and are geo-referenced by matching them with the satellite images on the right. We plot estimated inlier correspondences after homography estimation with RANSAC. Further qualitative examples are shown in the appendix." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.454, + 0.314, + 0.469 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.474, + 0.775 + ], + "angle": 0, + "content": "Image keypoint descriptions that are discriminative and matchable over large changes in viewpoint are vital for 3D reconstruction. However, descriptions output by learned descriptors are typically not robust to camera rotation. While they can be made more robust by, e.g., data augmentation, this degrades performance on upright images. Another approach is test-time augmentation, which incurs a significant increase in runtime. Instead, we learn a linear transform in description space that encodes rotations of the input image. We call this linear transform a steerer since it allows us to transform the descriptions as if the image was rotated. From representation theory, we know all possible steers for the rotation group. Steerers can be optimized (A) given a fixed descriptor; (B) jointly with a descriptor or (C) we can optimize a descriptor given a fixed steerer. We perform experiments in these three settings and obtain state-of-the-art results on the rotation invariant image matching benchmarks AIMS and Roto-360. We publish code and model weights at this https url." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.799, + 0.21, + 0.815 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Discriminative local descriptions are vital for multiple 3D vision tasks, and learned descriptors have recently been shown to outperform traditional handcrafted local features [17, 19, 23, 43]. One major weakness of learned descriptors compared to handcrafted features such as" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.454, + 0.893, + 0.592 + ], + "angle": 0, + "content": "SIFT [35] is the relative lack of robustness to non-upright images [55]. While images taken from ground level can sometimes be made upright by aligning with gravity as the canonical orientation, this is not always possible. For example, descriptors robust to rotation are vital in space applications [49], as well as medical applications [42], where no such canonical orientation exists. Even when a canonical orientation exists, it may be difficult or impossible to estimate. Rotation invariant matching is thus a key challenge." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.895, + 0.732 + ], + "angle": 0, + "content": "The most straightforward manner to get rotation invariant matching is to train or design a descriptor to be rotation invariant [17, 35]. However, this sacrifices distinctiveness in matching images with small relative rotations [41]. An alternative approach is to train a rotation-sensitive descriptor and perform test-time-augmentation, selecting the pair that produces the most matches. The obvious downside of TTA is computational cost. For example, testing all \\(45^{\\circ}\\) rotations requires running the model eight times." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "In this paper, we present an approach that maintains distinctiveness for small rotations and allows for rotation invariant matching when we have images with large rotations. We do this while adding only negligible additional runtime, running the descriptor only a single time. The main idea is to learn a linear transform in description space that corresponds to a rotation of the input image; see Figure 2. We call this linear transform a steerer as it allows us to modify keypoint descriptions as if they were describing rotated images—we can steer the descriptions without having to rerun the descriptor network. We show empi" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4885" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.113, + 0.098, + 0.437, + 0.26 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.473, + 0.365 + ], + "angle": 0, + "content": "Figure 2. Overview of approach. A steerer (Definition 4.4) is a linear map that transforms the description of a keypoint into the description of the corresponding keypoint in a rotated image. Thus, a steerer makes the keypoint descriptor rotation equivariant, and we can obtain the descriptions of keypoints in arbitrarily rotated images while only running the descriptor once." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.38, + 0.47, + 0.529 + ], + "angle": 0, + "content": "cally that approximate steers can be obtained for existing descriptors and motivate this theoretically. We also investigate jointly optimizing steers and descriptors and show how this enables nearly exact steering while not sacrificing performance on upright images. Using mathematical representation theory, we can describe all possible steers—they are representations of the rotation group. This enables the choice of a fixed steerer and training a descriptor for it, and in turn, the investigation of which steers give the best performance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.531, + 0.47, + 0.636 + ], + "angle": 0, + "content": "Using our framework, we set a new state-of-the-art on the rotation invariant matching benchmarks AIMS [49] (Figure 1) and Roto-360 [31]. At the same time, we are with the same models able to perform on par with or even outperform existing non-invariant methods on upright images on the competitive MegaDepth-1500 benchmark [33, 50]. In summary, our main contributions are as follows." + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.636, + 0.469, + 0.681 + ], + "angle": 0, + "content": "1. We introduce a new framework of steerers for equivariant keypoint descriptors (Section 4) and theoretically motivate why steerers emerge in practice (Section 5)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.682, + 0.469, + 0.726 + ], + "angle": 0, + "content": "2. We develop several settings for investigating steers (Section 5.1) and ways to apply them for rotation invariant matching (Section 5.2)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.727, + 0.468, + 0.756 + ], + "angle": 0, + "content": "3. We conduct a large set of experiments, culminating in state-of-the-art on AIMS and Roto-360 (Section 6)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.636, + 0.469, + 0.756 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.77, + 0.216, + 0.785 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Classical keypoint descriptions are typically made rotation invariant by using keypoints with associated local rotation frames and computing the descriptions in these frames. Examples include SIFT [35], SURF [8], and ORB [45]. A canonical rotation frame can be used for patch-based neural network descriptors as well [53, 54]. Further, neural network-based approaches have been proposed for es" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.273 + ], + "angle": 0, + "content": "timating the keypoint rotation frame [29, 30, 37] and for both computing the rotation frame and the descriptions in that frame [31, 61]. Notably, [30, 31] use rotation equivariant ConvNets [15, 56, 59]. Equivariant ConvNets have also been used for rotation-robust keypoint detection without estimating the rotation frame [2, 46], keypoint description [2, 34] and end-to-end image matching [9]. In theory1, equivariant ConvNets guarantee that the predictions are consistent when rotating the image. They are one example of hard-coding equivariance into network layers using mathematical group theory, an idea that goes back to the 1990's [58] and has seen large recent interest [11, 20, 22]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.274, + 0.892, + 0.486 + ], + "angle": 0, + "content": "Neural networks can also be encouraged to learn equivariance rather than having it hard-coded in the layers. This can be done by enforcing group-specific invariants in the network output space [25, 48] (see also Section 5). Another approach is to specify a group representation on the output of the network and train the network to satisfy equivariance wrt. that representation [16, 28, 36, 60]. We will use this approach for keypoint descriptions in our Setting C. The benefits of not hard-coding equivariance are that arbitrary network architectures can be used (particularly pre-trained non-equivariant networks) and that one does not need to specify the group representations acting on each layer of the network. A special case of learning equivariance is rotation invariant descriptors through data augmentation [38, 52]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.487, + 0.892, + 0.623 + ], + "angle": 0, + "content": "A recent line of work [10, 12, 24, 32] investigates to what extent neural networks exhibit equivariance without having been trained or hard-coded to do so. They find that many networks are approximately equivariant. One major limitation is that they only consider networks trained for image classification. We will empirically demonstrate a high level of equivariance in keypoint descriptors that were not explicitly trained to be equivariant and theoretically motivate why this happens (our Setting A)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.64, + 0.638, + 0.655 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.667, + 0.891, + 0.743 + ], + "angle": 0, + "content": "In this work, we are interested in finding linear mappings between keypoint descriptions where the images may have been rotated independently. We will, in particular, consider the group of quarter rotations \\( C_4 \\) and the group of continuous rotations \\( \\mathrm{SO}(2) \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.744, + 0.892, + 0.85 + ], + "angle": 0, + "content": "Ordinary typeset \\( g \\) will denote an arbitrary group element, boldface \\( \\mathbf{g} \\) will always mean the generator of \\( C_4 \\) for the remainder of the text so that the elements of \\( C_4 \\) are \\( \\mathbf{g} \\), \\( \\mathbf{g}^2 \\), \\( \\mathbf{g}^3 \\) and the identity element \\( \\mathrm{id} = \\mathbf{g}^4 \\). Boldface \\( \\mathbf{i} \\) will denote the imaginary unit such that \\( \\mathbf{i}^2 = -1 \\). Given matrices \\( X_1, X_2, \\ldots, X_J \\), the notation \\( \\oplus_{j=1}^{J} X_j \\) will mean the block-diagonal matrix with blocks \\( X_1, X_2, \\ldots, X_J \\)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.863, + 0.892, + 0.901 + ], + "angle": 0, + "content": "1It has been demonstrated that equivariant ConvNets can learn to break equivariance [18] when this benefits the task at hand. E.g., the end-to-end matcher SE2-LoFTR [9] is not perfectly consistent over rotations [9, 49]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4886" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.077, + 0.091, + 0.389, + 0.108 + ], + "angle": 0, + "content": "3.1. Preliminaries on keypoint matching" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.116, + 0.468, + 0.191 + ], + "angle": 0, + "content": "The underlying task is to take two images of the same scene and detect 2D points that correspond to the same 3D point. A pair of such points that depict the same 3D point is called a correspondence. The approach for finding correspondences that will be explored is a three-stage approach:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.193, + 0.458, + 0.207 + ], + "angle": 0, + "content": "1. Detection. Detect \\(N\\) keypoint locations in each image." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.208, + 0.468, + 0.237 + ], + "angle": 0, + "content": "2. Description. Describe the keypoint locations with descriptors, i.e., feature vectors in \\(\\mathbb{R}^D\\)." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.238, + 0.468, + 0.268 + ], + "angle": 0, + "content": "3. Matching. Match the descriptors, typically by using mutual nearest neighbours in cosine distance." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.193, + 0.468, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.27, + 0.468, + 0.436 + ], + "angle": 0, + "content": "This classical setup includes SIFT [35] but also more recent deep learning-based approaches. In particular, we follow the method in DeDoDe [19], where the keypoint detector is first optimized to find good point tracks from SfM reconstructions and the keypoint descriptor is optimized by maximizing the matching likelihood obtained by a frozen keypoint detector as follows. If the \\(N\\) descriptors (each normalized to unit length) in the two images are \\(y_{1} \\in \\mathbb{R}^{D \\times N}\\) and \\(y_{2} \\in \\mathbb{R}^{D \\times N}\\) we first form the \\(N \\times N\\) matching matrix \\(Y = y_{1}^{T}y_{2}\\), and obtain a matrix of pairwise likelihoods by using the dual softmax [44, 50, 55]:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.45, + 0.469, + 0.485 + ], + "angle": 0, + "content": "\\[\np \\left(y _ {1}, y _ {2}\\right) = \\frac {\\exp (\\iota Y)}{\\sum_ {\\text {c o l u m n s}} \\exp (\\iota Y)} \\cdot \\frac {\\exp (\\iota Y)}{\\sum_ {\\text {r o w s}} \\exp (\\iota Y)}. \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.497, + 0.468, + 0.542 + ], + "angle": 0, + "content": "Here \\(\\iota = 20\\) is the inverse temperature. The negative logarithm of the likelihood (1) is minimized for those pairs in the \\(N\\times N\\) matrix that correspond to ground truth inliers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.413, + 0.573 + ], + "angle": 0, + "content": "3.2. Preliminaries on group representations" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.468, + 0.643 + ], + "angle": 0, + "content": "Definition 3.1. (Group representation) Given a group \\( G \\), a representation of \\( G \\) on \\( \\mathbb{R}^D \\) is a mapping \\( \\rho : G \\to \\mathrm{GL}(\\mathbb{R}, D) \\) that preserves the group multiplication, i.e., \\( \\rho(gg') = \\rho(g)\\rho(g') \\) for every \\( g, g' \\in G \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.468, + 0.717 + ], + "angle": 0, + "content": "Simply stated, \\(\\rho\\) maps every element in the group to an invertible \\(D\\times D\\) matrix. The point of using representations is that groups such as \\(C_4\\) act differently on different quantities as we will illustrate in the following examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.468, + 0.807 + ], + "angle": 0, + "content": "Example 3.1. For \\(\\mathbb{R}^{n\\times n}\\) (a square image grid), \\(C_4\\) can be represented by permutations of the pixels in the obvious way so that the image is rotated anticlockwise by multiples of \\(90^{\\circ}\\). We denote this group representation by \\(P_{90}\\) so that applying \\(P_{90}^{k}\\) rotates the image by \\(k\\cdot 90^{\\circ}\\) anticlockwise." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.821, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Example 3.2. For \\(\\mathbb{R}^2\\) (image coordinates), one possible representation of \\(C_4\\) is \\(\\rho(\\mathbf{g}^k) = R_{90}^k = \\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)^k\\). Multiplication by \\(R_{90}^k\\) corresponds to rotating image coordinates by \\(k \\cdot 90^\\circ\\) if the center of the image is taken as \\((0,0)\\)." + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.616, + 0.176 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.195, + 0.615, + 0.282 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.635, + 0.096, + 0.892, + 0.276 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.292, + 0.892, + 0.404 + ], + "angle": 0, + "content": "Figure 3. Equivariance of Upright SIFT. Left: A keypoint with its Upright SIFT description in an upright image and a rotated version. The small yellow squares are the subregions where histograms of gradient orientations are computed. Right: The Upright SIFT descriptions unravelled into the 128 bin histograms that constitute them. When we rotate the image, the subregions are permuted, and the histogram bins within each subregion are further permuted cyclically. Hence, Upright SIFT is rotation equivariant." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.416, + 0.771, + 0.433 + ], + "angle": 0, + "content": "4. Equivariance and steerability" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.441, + 0.892, + 0.487 + ], + "angle": 0, + "content": "In this section, we will analyze the close connection between equivariance and steerability. We start with an example to introduce the former concept." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Example 4.1. SIFT descriptions [35] are \\(128\\mathrm{dim}\\) vectors designed to be invariant to rotation, scale and illumination and highly distinctive for leveraging feature matching. For an input image \\(I \\in \\mathbb{R}^{n \\times n}\\) and \\(N\\) keypoints with scale and orientation \\(x \\in \\mathbb{R}^{4 \\times N^2}\\), we get descriptions \\(y \\in \\mathbb{R}^{128 \\times N}\\). If \\(f\\) is the SIFT descriptor, we write \\(f(I, x) = y\\). The descriptions consist of histograms of image gradients over patches around the keypoints \\(x\\). The patches are oriented by the keypoint orientations so that the descriptions are invariant to joint rotations of the image and keypoints:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.649, + 0.814, + 0.668 + ], + "angle": 0, + "content": "\\[\nf \\left(P _ {9 0} ^ {k} I, \\left(\\oplus_ {b = 1} ^ {2} R _ {9 0}\\right) ^ {k} x\\right) = f (I, x).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.78 + ], + "angle": 0, + "content": "If we discard the keypoint orientations, i.e., set the angle of each keypoint to 0, we get the Upright SIFT (UPSIFT) descriptor [1, 7], which is often used for upright images as it is more discriminative than SIFT. When we rotate an image \\(90^{\\circ}\\), then the gradient histograms, i.e., the UPSIFT descriptions are permuted by a specific permutation \\(P_{\\mathrm{UPSIFT}}\\), so if \\(f\\) is the UPSIFT descriptor, we have" + }, + { + "type": "equation", + "bbox": [ + 0.551, + 0.786, + 0.838, + 0.805 + ], + "angle": 0, + "content": "\\[\nf \\left(P _ {9 0} ^ {k} I, \\left(\\oplus_ {b = 1} ^ {2} R _ {9 0}\\right) ^ {k} x\\right) = P _ {\\text {U P S I F T}} ^ {k} f (I, x).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.873 + ], + "angle": 0, + "content": "We illustrate the permutation \\( P_{\\mathrm{UPSIFT}} \\) in Figure 3. UPSIFT is not rotation invariant, but it is rotation equivariant when we rotate the input, the output changes predictably. Explicitly, the representation is \\( \\rho(\\mathbf{g}^k) = P_{\\mathrm{UPSIFT}}^k \\)." + }, + { + "type": "page_footnote", + "bbox": [ + 0.5, + 0.875, + 0.892, + 0.902 + ], + "angle": 0, + "content": "2The first two coordinates of each keypoint in \\(x\\) are its location and the last two a vector for its orientation and scale, so \\(x\\) is rotated by \\(\\oplus_{b = 1}^{2}R_{90}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.482, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4887" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.47, + 0.122 + ], + "angle": 0, + "content": "Definition 4.1 (Equivariance). We say that a function \\( f: V \\to W \\) is equivariant with respect to a group \\( G \\) if" + }, + { + "type": "equation", + "bbox": [ + 0.14, + 0.129, + 0.469, + 0.147 + ], + "angle": 0, + "content": "\\[\n\\rho (g) f (v) = f \\left(\\rho_ {\\text {i n}} (g) v\\right), \\forall v \\in V, g \\in G, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.154, + 0.327, + 0.169 + ], + "angle": 0, + "content": "for some group representations \\(\\rho_{\\mathrm{in}},\\rho\\)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.174, + 0.469, + 0.22 + ], + "angle": 0, + "content": "This work will mainly be concerned with the equivariance of learned keypoint descriptors of ordinary keypoints (without scale and orientation)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.226, + 0.469, + 0.3 + ], + "angle": 0, + "content": "Definition 4.2 (Equivalence of keypoint descriptor). We say that a keypoint descriptor \\( f \\) is equivariant with respect to a group \\( G \\) transforming the input image by \\( \\rho_{\\mathrm{image}} \\) and the input keypoint locations by \\( \\rho_{\\mathrm{keypoint}} \\) if there exists \\( \\rho \\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.309, + 0.469, + 0.327 + ], + "angle": 0, + "content": "\\[\n\\rho (g) f (I, x) = f \\left(\\rho_ {\\text {i m a g e}} (g) I, \\rho_ {\\text {k e y p o i n t}} (g) x\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.333, + 0.469, + 0.379 + ], + "angle": 0, + "content": "for all images, keypoints and group elements. We call the descriptor invariant if \\(\\rho(g)\\) is the identity matrix for all \\(g\\). Invariance is a special type of equivariance." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.385, + 0.469, + 0.414 + ], + "angle": 0, + "content": "Example 4.2. A keypoint descriptor \\( f \\) is equivariant under \\( 90^{\\circ} \\) rotations if there exists \\( \\rho \\) of \\( C_4 \\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.421, + 0.469, + 0.439 + ], + "angle": 0, + "content": "\\[\n\\rho \\left(\\mathbf {g} ^ {k}\\right) f (I, x) = f \\left(P _ {9 0} ^ {k} I, R _ {9 0} ^ {k} x\\right) \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.446, + 0.469, + 0.49 + ], + "angle": 0, + "content": "for \\( k \\in \\{0,1,2,3\\} \\), where \\( P_{90} \\) and \\( R_{90} \\) are the representations from Examples 3.1 and 3.2 that rotate images and coordinates in the ordinary manner." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.491, + 0.469, + 0.538 + ], + "angle": 0, + "content": "Both SIFT and Upright SIFT are equivariant. For SIFT, \\(\\rho (\\mathbf{g}^k)\\) is the identity, so SIFT is invariant. For Upright SIFT, \\(\\rho (\\mathbf{g}^k)\\) is \\(P_{\\mathrm{UPSIFT}}^k\\) as explained in Example 4.1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.543, + 0.469, + 0.603 + ], + "angle": 0, + "content": "One aim of this work is to argue and demonstrate that learned keypoint descriptors, which are trained on upright data, will behave more like Upright SIFT than SIFT, i.e., they will be rotation equivariant but not invariant." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.609, + 0.469, + 0.689 + ], + "angle": 0, + "content": "Definition 4.3 (Steerability, adapted from [21]). A real-valued function \\(\\phi : V \\to \\mathbb{R}\\) is said to be steerable under a representation \\(\\rho_{\\mathrm{in}}\\) of \\(G\\) on \\(V\\), if there exist \\(D\\) functions (for some \\(D\\)) \\(\\phi_j : V \\to \\mathbb{R}\\) and \\(D\\) functions \\(\\kappa_j : G \\to \\mathbb{R}\\) such that \\(\\phi(\\rho_{\\mathrm{in}}(g)v) = \\sum_{j=1}^{D} \\kappa_j(g)\\phi_j(v)\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.695, + 0.469, + 0.773 + ], + "angle": 0, + "content": "Note that an equivariant function \\(f:V\\to \\mathbb{R}^{D}\\) satisfies in each component \\(f_{d}\\) that \\(f_{d}(\\rho_{\\mathrm{in}}(g)v) = \\sum_{j = 1}^{D}\\rho (g)_{dj}f_{j}(v)\\), so each component of \\(f\\) is steerable, in the notation of Definition 4.3, \\(\\phi = f_d,\\phi_j = f_j,\\kappa_j(g) = \\rho (g)_{dj}\\). This motivates the definition of a steerer." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.779, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Definition 4.4 (Steerer). Given a function \\( f: V \\to W \\) between vector spaces, and a representation \\( \\rho_{\\mathrm{in}} \\) of \\( G \\) on \\( V \\), a steerer is a representation \\( \\rho \\) of \\( G \\) on \\( W \\) that makes \\( f \\) equivariant, i.e. such that" + }, + { + "type": "equation", + "bbox": [ + 0.192, + 0.848, + 0.469, + 0.865 + ], + "angle": 0, + "content": "\\[\nf \\left(\\rho_ {\\text {i n}} (g) v\\right) = \\rho (g) f (v). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Even if (5) only holds approximately or \\(\\rho\\) is only approximately a representation, we will refer to \\(\\rho\\) as a steerer." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.092, + 0.891, + 0.122 + ], + "angle": 0, + "content": "We will use the verb steer for multiplying a feature/description by a steerer; see Figure 2 for the broad idea." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.128, + 0.892, + 0.249 + ], + "angle": 0, + "content": "Example 4.3. As explained in Example 4.1, \\( P_{\\mathrm{UPSIFT}} \\) is a steerer for Upright SIFT under \\( 90^{\\circ} \\) rotations. This has practical consequences. If we want to obtain the Upright SIFT descriptions for an image \\( I \\) and the same image rotated \\( k \\cdot 90^{\\circ} \\), we only need to compute the descriptions for the original image. We can obtain the rotated ones by multiplying the descriptions by \\( P_{\\mathrm{UPSIFT}}^{k} \\). That is, we can steer the Upright SIFT descriptions with \\( P_{\\mathrm{UPSIFT}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.256, + 0.892, + 0.36 + ], + "angle": 0, + "content": "It is known from representation theory [47] what all possible representations of \\( C_4 \\) are, and hence what all possible steerers for rotation equivariant descriptors are. As this result will be necessary for the remainder of the text, we collect it in a theorem. Similar results are also known for other groups e.g. the continuous rotation group SO(2), which we discuss in the next section." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.368, + 0.891, + 0.413 + ], + "angle": 0, + "content": "Theorem 4.1 (Representations of \\( C_4 \\)). Let \\( \\rho \\) be a representation of \\( C_4 \\) on \\( \\mathbb{R}^D \\). Then, there exists an invertible matrix \\( Q \\) and \\( j_d \\in \\{0, 1, 2, 3\\} \\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.419, + 0.891, + 0.437 + ], + "angle": 0, + "content": "\\[\n\\rho \\left(\\mathbf {g} ^ {k}\\right) = Q ^ {- 1} \\operatorname {d i a g} \\left(\\mathbf {i} ^ {k j _ {1}}, \\mathbf {i} ^ {k j _ {2}}, \\dots , \\mathbf {i} ^ {k j _ {D}}\\right) Q. \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.444, + 0.875, + 0.46 + ], + "angle": 0, + "content": "The diagonal in (6) contains the eigenvalues of \\(\\rho (\\mathbf{g}^k)\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.465, + 0.891, + 0.495 + ], + "angle": 0, + "content": "Example 4.4. The Upright SIFT steuerer \\( P_{\\mathrm{UPSIFT}} \\) is diagonalizable with an equal amount of each eigenvalue \\( \\pm 1 \\), \\( \\pm \\mathbf{i} \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.502, + 0.892, + 0.607 + ], + "angle": 0, + "content": "The complex eigenvalues must appear in conjugate pairs as we take \\(\\rho(\\mathbf{g})\\) to be real-valued. It is then possible to do a change of basis so that each pair \\(\\mathbf{i}, -\\mathbf{i}\\) on the diagonal in (6) is replaced by a block \\(\\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)\\). In this way, \\(\\rho(\\mathbf{g})\\) can always be block-diagonalized: \\(\\rho(\\mathbf{g}) = Q^{-1}BQ\\) where \\(Q\\) and \\(B\\) are real valued and \\(B\\) is block-diagonal with blocks of sizes 1 and 2." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.615, + 0.774, + 0.632 + ], + "angle": 0, + "content": "4.1. Representation theory of SO(2)" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.638, + 0.892, + 0.827 + ], + "angle": 0, + "content": "SO(2) is a one-parameter Lie group, i.e. a continuous group with one degree of freedom \\(\\alpha\\) the rotation angle. A \\(D\\)-dimensional representation of SO(2) is a map \\(\\varsigma : [0, 2\\pi) \\to \\mathrm{GL}(\\mathbb{R}, D)\\) such that addition modulo \\(2\\pi\\) on the input is encoded as matrix multiplication on the output—we will consistently use \\(\\varsigma\\) for SO(2) representations to separate them from \\(C_4\\) representations \\(\\rho\\) (\\(\\rho\\) will also be used for representations of general groups). The most familiar is the two-dimensional representation \\(\\varsigma(\\alpha) = \\begin{pmatrix} \\cos(\\alpha) & -\\sin(\\alpha) \\\\ \\sin(\\alpha) & \\cos(\\alpha) \\end{pmatrix}\\) which rotates 2D coordinates. Similar to the \\(C_4\\) case in Theorem 4.1, we can write down a general representation for SO(2) as follows [57]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.833, + 0.891, + 0.877 + ], + "angle": 0, + "content": "Theorem 4.2 (Representations of \\(\\mathrm{SO}(2)\\)). Let \\(\\varsigma\\) be a representation of \\(\\mathrm{SO}(2)\\) on \\(\\mathbb{R}^D\\). Then there exists an invertible \\(Q\\) and \\(j_d \\in \\mathbb{Z}\\) such that" + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.884, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\varsigma (\\alpha) = Q ^ {- 1} \\operatorname {d i a g} \\left(\\mathrm {e} ^ {\\mathbf {i} j _ {1} \\alpha}, \\mathrm {e} ^ {\\mathbf {i} j _ {2} \\alpha}, \\dots , \\mathrm {e} ^ {\\mathbf {i} j _ {D} \\alpha}\\right) Q. \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "4888" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.199 + ], + "angle": 0, + "content": "The \\(j_{d}\\)'s are the frequencies of the eigenspaces of \\(\\varsigma\\). Complex eigenvalues appear in conjugate pairs so (7) can be rewritten as a block diagonal decomposition \\(\\varsigma(\\alpha) = Q^{-1}BQ\\) where \\(Q\\) and \\(B\\) are real valued and \\(B\\) is block-diagonal with minimal blocks. The admissible blocks (= real-valued irreducible representations) in \\(B\\) are then the \\(1 \\times 1\\) block (1) and the \\(2 \\times 2\\) blocks" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.21, + 0.47, + 0.243 + ], + "angle": 0, + "content": "\\[\n\\left( \\begin{array}{c c} \\cos (j \\alpha) & - \\sin (j \\alpha) \\\\ \\sin (j \\alpha) & \\cos (j \\alpha) \\end{array} \\right) \\quad \\text {f o r} j \\in \\mathbb {Z} \\backslash \\{0 \\}. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.255, + 0.47, + 0.348 + ], + "angle": 0, + "content": "We can write \\(\\varsigma (\\alpha) = \\exp \\left(\\alpha Q^{-1}\\mathrm{diag}(\\mathbf{i}j_1,\\ldots ,\\mathbf{i}j_D)Q\\right)\\) where \\(\\mathrm{expm}\\) is the matrix exponential. The quantity \\(\\mathrm{d}\\varsigma \\coloneqq\\) \\(Q^{-1}\\mathrm{diag}(\\mathbf{i}j_1,\\dots ,\\mathbf{i}j_D)Q\\) is called a Lie algebra representation of SO(2), here in its most general form. When training a steerer for SO(2) it is practical to train a \\(D\\times D\\) matrix \\(\\mathrm{d}\\varsigma\\) and steer using \\(\\varsigma (\\alpha) = \\exp \\mathrm{m}(\\alpha \\mathrm{d}\\varsigma)\\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.355, + 0.357, + 0.372 + ], + "angle": 0, + "content": "4.2. Disentangling description space" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.379, + 0.47, + 0.471 + ], + "angle": 0, + "content": "When we have a steerer, we get a description space on which rotations act—up to a change of basis—by a block-diagonal matrix \\(\\oplus_{j=1}^{J} B_{j}\\). The description space can then be thought of as being disentangled into different subspaces where rotations act in different ways \\(B_{j}\\) [14, 60]. We detail what this means for keypoint descriptors in Appendix A." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.307, + 0.5 + ], + "angle": 0, + "content": "5. Descriptors and steerers" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.47, + 0.6 + ], + "angle": 0, + "content": "This work's crucial observation and assumption is that learned descriptors, while not invariant, are approximately equivariant so that they have a steerer. Or, as a weaker assumption, they can be trained to be equivariant. It may seem that this is a strong assumption. However, a seemingly less strong assumption turns out to be equivalent." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.47, + 0.671 + ], + "angle": 0, + "content": "Theorem 5.1. [Adapted from Shakerinava et al. [48], Gupta et al. [25]] Assume that we have a function \\( f: V \\to \\mathbb{S}^{D-1} \\) and a group \\( G \\) with representation \\( \\rho_{\\mathrm{in}} \\) on \\( V \\) such that, for all \\( v, v' \\in V \\) and \\( g \\in G \\)" + }, + { + "type": "equation", + "bbox": [ + 0.134, + 0.681, + 0.47, + 0.7 + ], + "angle": 0, + "content": "\\[\n\\langle f \\left(\\rho_ {\\text {i n}} (g) v\\right), f \\left(\\rho_ {\\text {i n}} (g) v ^ {\\prime}\\right) \\rangle = \\langle f (v), f \\left(v ^ {\\prime}\\right) \\rangle . \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.709, + 0.47, + 0.743 + ], + "angle": 0, + "content": "Then there exists an orthogonal representation \\(\\rho(g)\\), such that \\(f\\) is equivariant w.r.t. \\(G\\) with representations \\(\\rho_{\\mathrm{in}}\\) and \\(\\rho\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We provide a proof in Appendix A. Since we match normalized keypoint descriptions by their cosine similarity, Theorem 5.1 is highly applicable to the image matching problem. If a keypoint descriptor \\( f \\) is perfectly consistent in the matching scores when simultaneously rotating the images, then the scalar products in (9) will be equal so that the theorem tells us that \\( f \\) has a steerer \\( \\rho \\). Furthermore, we can expect many local image features to appear in all orientations even over a dataset of upright images, thus encouraging (9) to hold for \\( f \\) trained on large datasets." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.091, + 0.838, + 0.108 + ], + "angle": 0, + "content": "5.1. Three settings for investigating steerers" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.205 + ], + "angle": 0, + "content": "As \\( C_4 \\) is cyclic, all its representations are defined by \\( \\rho(\\mathbf{g}) \\), where \\( \\mathbf{g} \\) is the generator of \\( C_4 \\). To find a steerer for a keypoint descriptor under \\( C_4 \\) hence comes down to finding a single matrix \\( \\rho(\\mathbf{g}) \\) that represents rotations by \\( 90^\\circ \\) in the description space. Similarly, for SO(2) we find the single matrix \\( \\mathrm{d}\\varsigma \\) that defines the representation \\( \\varsigma \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.205, + 0.892, + 0.25 + ], + "angle": 0, + "content": "We will consider three settings. In each case we will optimize \\(\\rho (\\mathbf{g})\\) and/or \\(f\\) over the MegaDepth training set [33] with rotation augmentation and maximize" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.259, + 0.892, + 0.285 + ], + "angle": 0, + "content": "\\[\np \\left(f \\left(P _ {9 0} ^ {k _ {1}} I _ {1}, R _ {9 0} ^ {k _ {1}} x _ {1}\\right), \\rho (\\mathbf {g}) ^ {k} f \\left(P _ {9 0} ^ {k _ {2}} I _ {2}, R _ {9 0} ^ {k _ {2}} x _ {2}\\right)\\right) \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.292, + 0.892, + 0.383 + ], + "angle": 0, + "content": "where \\( p \\) is the matching probability (1). The number of rotations \\( k_{1} \\) and \\( k_{2} \\) for each image are sampled independently during training, and \\( k = k_{1} - k_{2} \\mod 4 \\) is the number of rotations that aligns image \\( I_{2} \\) to image \\( I_{1} \\). Thus, \\( \\rho(\\mathbf{g})^{k} \\) aligns the relative rotation between descriptions in \\( I_{2} \\) and \\( I_{1} \\). We optimize continuous steerers \\( \\varsigma \\) analogously to (10)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.384, + 0.892, + 0.475 + ], + "angle": 0, + "content": "Setting A: Fixed descriptor, optimized steerer. If a descriptor works equally well for upright images as well as images rotated the same amount from upright, then according to Theorem 5.1, we should expect that there exists a steerer \\(\\rho (\\mathbf{g})\\) such that (4) holds. To find \\(\\rho (\\mathbf{g})\\) we optimize it as a single \\(D\\times D\\) linear layer by maximizing (10)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.476, + 0.884, + 0.489 + ], + "angle": 0, + "content": "Setting B: Joint optimization of descriptor and steerer." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.49, + 0.892, + 0.61 + ], + "angle": 0, + "content": "The aim is to find a steerer that is as good as possible for the given data. We will see in the experiments, by looking at the evolution of the eigenvalues of \\(\\rho(\\mathbf{g})\\) during training, that this joint optimization has many local optima and is highly dependent on the initialization of \\(\\rho(\\mathbf{g})\\). However, looking at the eigenvalues of \\(\\rho(\\mathbf{g})\\) does give knowledge about which descriptor dimensions are most important, as will be explained in Section 6.5." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.611, + 0.892, + 0.747 + ], + "angle": 0, + "content": "Setting C: Fixed steerer, optimized descriptor. To get the most precise control over the rotation behaviour of a descriptor, we can fix the steerer and optimize only the descriptor. This enables us to investigate how much influence the choice of steerer has on the descriptor. For instance, choosing the steerer as the identity leads to a rotation invariant descriptor. We will see in the experiments that this choice leads to suboptimal performance on upright images compared to other steers." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.838, + 0.774 + ], + "angle": 0, + "content": "5.2. Matching with equivariant descriptions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.781, + 0.892, + 0.901 + ], + "angle": 0, + "content": "This section presents several approaches to rotation invariant matching using equivariant descriptors. Throughout, we will denote the \\(D\\)-dimensional descriptions of \\(N\\) keypoints in two images \\(I_1, I_2\\) by \\(y_1, y_2 \\in \\mathbb{R}^{D \\times N}\\) and will assume that we know the \\(C_4\\)-steerer \\(\\rho(\\mathbf{g})\\) that rotates descriptions \\(90^\\circ\\) or the SO(2)-steerer \\(\\varsigma(\\alpha)\\) through the Lie algebra generator \\(\\mathrm{d}\\varsigma\\). For matching we follow DeDoDe [19], as described in Section 3.1. The base similarity used is the cosine" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4889" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.08, + 0.472, + 0.162 + ], + "angle": 0, + "content": "Table 1. Evaluation on Roto-360 [31]. We report the percentage of correct matches at three thresholds. We use the DeDoDe-SO2 detector with 5,000 keypoints in the last two rows. Matching strategies are Max Matches for the \\( C_4 \\)-descriptor and Max Sim. over \\( C_8 \\) for the SO(2)-descriptor. See Section 6.1 for the shorthands for our models." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.175, + 0.472, + 0.323 + ], + "angle": 0, + "content": "
DetectorDescriptor3px5px10px
SIFT [35]SIFT [35]787879
ORB [45]ORB [45]798587
SuperPoint [17]RELF, single [31]909193
SuperPoint [17]RELF, multiple [31]929394
SuperPoint [17]C4-B (ours)828283
SuperPoint [17]SO2-Spread-B (ours)969797
DeDoDe [19]C4-B (ours)828486
DeDoDe [19]SO2-Spread-B (ours)959798
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.351, + 0.47, + 0.412 + ], + "angle": 0, + "content": "similarity, so we compute \\( y_1^T y_2 \\) for normalized descriptions to get an \\( N \\times N \\) matrix of pairwise scores on which dual softmax (1) is applied. Matches are mutual most similar descriptions with similarity above 0.01." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.418, + 0.47, + 0.508 + ], + "angle": 0, + "content": "Max matches over steered descriptions. The first way of obtaining invariant matches is to match \\( y_{1} \\) with \\( \\rho(\\mathbf{g})^{k}y_{2} \\) for \\( k = 0,1,2,3 \\) and keep the matches from the \\( k \\) that has the most matches. This is similar to matching the image \\( I_{1} \\) with four different rotations of \\( I_{2} \\) but alleviates the need for rerunning the descriptor network for each rotation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.469, + 0.568 + ], + "angle": 0, + "content": "Max similarity over steered descriptions. A computationally cheaper version is to select the matching matrix not as \\( y_1^T y_2 \\) but as \\( \\max_k y_1^T \\rho(\\mathbf{g})^k y_2 \\), where the max is elementwise over the matrix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.569, + 0.469, + 0.63 + ], + "angle": 0, + "content": "SO(2)-steerers. To apply the above matching strategies to SO(2)-steerers \\(\\varsigma (\\alpha) = \\exp (\\alpha \\mathrm{d}\\varsigma)\\) we discretize \\(\\varsigma\\). A \\(C_\\ell\\)-steerer is obtained through \\(\\rho (\\mathbf{g}_\\ell) = \\exp \\left(\\frac{2\\pi}{\\ell}\\mathrm{d}\\varsigma\\right)\\), where \\(\\mathbf{g}_{\\ell}\\) generates \\(C_\\ell\\). We will use \\(C_8\\) in the experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.63, + 0.469, + 0.856 + ], + "angle": 0, + "content": "Procrustes matcher. If all eigenvalues of \\(\\rho(\\mathbf{g})\\) are \\(\\pm \\mathrm{i}\\), the steuer can be block-diagonalized with only the block \\(\\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)^3\\). The descriptions consist of \\(D/2\\) two-dimensional quantities that all rotate with the same frequency as the image. We will refer to them as frequency 1 descriptions and view them reshaped as \\(y \\in \\mathbb{R}^{2 \\times (D/2) \\times N}\\). A 2D rotation matrix acts on these descriptions from the left when the image rotates, and we can find the optimal rotation matrix \\(R_{m,n}\\) that aligns each pair \\(y_{1,m}, y_{2,n} \\in \\mathbb{R}^{2 \\times (D/2)}\\) by solving the Procrustes problem via SVD. The matching matrix is obtained by computing \\(\\langle R_{m,n}y_{1,m}, y_{2,n} \\rangle\\) for each pair. \\(R_{m,n}\\) gives the relative rotation between each pair of keypoints, which can be useful e.g. for minimal relative pose solvers [4, 6] or for outlier filtering [13]. We leave exploring this per-correspondence geometry to future work." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.08, + 0.892, + 0.163 + ], + "angle": 0, + "content": "Table 2. Evaluation on AIMS [49]. We report the average precision (AP) in percent on different splits of AIMS: \"North Up\" (N. Up) contains images with small rotations, \"All Others\" (A. O.) contains images with larger rotations and \"All\" contains all images. We use the DeDoDe-SO2 detector and 10,000 keypoints throughout. See Section 6.1 for the shorthands for our models." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.175, + 0.887, + 0.262 + ], + "angle": 0, + "content": "
MethodN. UpA. O.All
SE2-LoFTR [9]585152
C4-B, Max Matches (ours)525151
SO2-Spread-B, Max Sim. C8 (ours)605758
SO2-Freq1-B, Procrustes (ours)645960
" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.284, + 0.633, + 0.302 + ], + "angle": 0, + "content": "6. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.31, + 0.892, + 0.4 + ], + "angle": 0, + "content": "We train and evaluate a variety of descriptors and steerers. Experimental details are covered in Appendix C. We provide comparisons to TTA in performance and runtime in Appendix B, as well as experiments with more matching strategies and an explicit experiment to test the connection between Theorem 5.1 and rotation equivariance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.401, + 0.892, + 0.476 + ], + "angle": 0, + "content": "We start by reporting results on two public benchmarks for rotation invariant image matching. Then, we will present ablation results for the MegaDepth benchmark, both for the standard version with upright images and a version where we have rotated the input images." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.485, + 0.68, + 0.5 + ], + "angle": 0, + "content": "6.1. Models considered" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.892, + 0.629 + ], + "angle": 0, + "content": "Our base models are the DeDoDe-B and DeDoDe-G descriptors introduced in [19]. These are both \\( D = 256 \\) dimensional descriptors. The focus will be on the smaller model DeDoDe-B, as this gives us the chance to do large-scale ablations. We train all models on MegaDepth [33]. To obtain rotation-consistent detections, we retrain two versions of the DeDoDe-detector, with data augmentation over \\( C_4 \\) and SO(2) respectively, denoted DeDoDe-{C4, SO2}." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "For Setting B (Section 5.1), we will see that the initialization of the steerer matters. Similarly, for Setting C, we can fix the steerer with different eigenvalue structures. Here, we introduce shorthand, which is used in the result tables. We will refer to the case of all eigenvalues 1 as \\(Inv\\) for invariant. This case corresponds to the ordinary notion of data augmentation, where the descriptions for rotated images should be the same as for non-rotated images. The case when all eigenvalues are \\(\\pm \\mathbf{i}\\) is denoted \\(Freq1\\) for frequency 1 as explained in Section 5.2. For \\(C_4\\)-steers, the case with an equal distribution of all eigenvalues \\(\\pm 1, \\pm \\mathbf{i}\\) will be denoted \\(Perm\\), as this is the eigenvalue signature of a cyclic permutation of order 4. For SO(2)-steers, the case with an equal distribution of eigenvalues \\(0, \\pm \\mathbf{i}, \\pm 2\\mathbf{i}, \\ldots \\pm 6\\mathbf{i}\\) will be denoted \\(Spread\\) (the cutoff 6 was arbitrarily chosen). The \\(Perm\\) and \\(Spread\\) steers correspond to a broad range of frequencies in the description space. When none of the above labels (\\(Inv\\), \\(Freq1\\), \\(Perm\\) or" + }, + { + "type": "page_footnote", + "bbox": [ + 0.076, + 0.874, + 0.469, + 0.901 + ], + "angle": 0, + "content": "This also holds for \\(\\mathrm{SO}(2)\\) steers, referring to eigenvalues and blocks of the Lie algebra generator \\(\\mathrm{d}\\varsigma\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4890" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.08, + 0.895, + 0.152 + ], + "angle": 0, + "content": "Table 3. Evaluation on MegaDepth [33, 50]. The first section shows Setting A where we only optimize the steerer, the second section shows Setting B where we jointly optimize the descriptor and steerer and the third section shows the Setting C where we predefine the steerer and optimize only the descriptor. For MegaDepth-1500 we always use dual softmax matcher to evaluate the descriptors on upright images. We use 20,000 keypoints throughout. The best values for B- and G-models are highlighted in each column. See Section 6.1 for shorthand explanations for our models. A larger version of this table with more methods is available in Appendix B." + }, + { + "type": "table", + "bbox": [ + 0.098, + 0.161, + 0.872, + 0.427 + ], + "angle": 0, + "content": "
DetectorDescriptorMatching strategyMegaDepth-1500MegaDepth-C4MegaDepth-SO2
DeDoDeAUC @ 5°10°20°5°10°20°5°10°20°
OriginalBDual softmax496577121720121620
OriginalBMax matches C4-steered-11--11--11-436073304456
SO2BMax matches C8-steered506678405770345165
OriginalGDual softmax526981131721162228
OriginalGMax matches C4-steered-11--11--11-314557263950
C4C4-BMax matches C4-steered516779506779395568
SO2SO2-BMax matches C8-steered476376476376446174
SO2SO2-Spread-BMax matches C8-steered506679496678466376
SO2SO2-Spread-BMax similarity C8-steered496678476477436174
C4C4-Inv-BDual softmax486476476376395569
C4C4-Perm-BMax matches C4-steered506779506679395467
SO2SO2-Inv-BDual softmax466275456174436073
SO2SO2-Freq1-BMax matches C8-steered476477476476456275
SO2SO2-Freq1-BProcrustes476476466275456174
C4C4-Perm-GMax matches C4-steered526981536982446174
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.451, + 0.471, + 0.558 + ], + "angle": 0, + "content": "Spread) is attached to a descriptor and steerer trained jointly in Setting B, then we initialize the steerer with values uniformly in \\((-D^{-1/2}, D^{-1/2})^4\\), the eigenvalues are then approximately uniformly distributed in the disk with radius \\(3^{-1/2}\\) [51]. When a descriptor is trained with \\(k \\cdot 90^\\circ\\) rotations, we append \\(C4\\) to its name and when trained with continuous augmentations, we append \\(SO2\\) to its name." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.567, + 0.185, + 0.581 + ], + "angle": 0, + "content": "6.2. Roto-360" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.47, + 0.727 + ], + "angle": 0, + "content": "We evaluate on the Roto-360 benchmark [31], which consists of ten image pairs from HPatches [3] where the second image in each image pair is rotated by all multiples of \\(10^{\\circ}\\) to obtain 360 image pairs in total. We report the average precision of the obtained matches and compare it to the current state-of-the-art RELF [31]. The results are shown in Table 1. We see that we outperform RELF when using methods trained for continuous rotations. Our matching runs around three times faster than RELF on Roto-360." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.736, + 0.163, + 0.75 + ], + "angle": 0, + "content": "6.3.AIMS" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.759, + 0.471, + 0.88 + ], + "angle": 0, + "content": "The Astronaut Image Matching Subset (AIMS) [49] consists of images taken by astronauts from the ISS and satellite images covering the broad regions that the astronaut images could depict. The task consists of finding the pairs of astronaut images and satellite images that show the same locations on Earth. Pairs are found by setting a threshold for the number of matches between images after homography estimation with RANSAC." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.451, + 0.895, + 0.679 + ], + "angle": 0, + "content": "The relative rotations of the astronaut and satellite images are unknown, making the task suitable for rotation-invariant matchers. Indeed, in [49], the best performing method is the rotation invariant SE2-LoFTR [9], which we compare to. The AIMS can be split into \"North Up\" astronaut images, consisting of images with small rotations (between \\(0^{\\circ}\\) and \\(90^{\\circ}\\)) and \"All Others\", consisting of images with large rotations. This split further enables the evaluation of rotation invariant matchers. We report the average precision over the whole dataset, as opposed to the approach in [49], where the score is computed over at most 100 true negatives per astronaut image. Results are shown in Table 2. Further, we plot precision-recall curves in Appendix B. We generally outperform SE2-LoFTR, particularly on the heavily rotated images in \"All Others\"." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.694, + 0.671, + 0.71 + ], + "angle": 0, + "content": "6.4. MegaDepth-1500" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We evaluate on a held-out part of MegaDepth (MegaDepth-1500 following [50]). Here, the task is to take two input images and output the relative pose between the cameras. The performance is measured by the AUC of the pose error. Additionally, we create two versions of MegaDepth with rotated images to evaluate the rotational robustness of our models. For MegaDepth-C4, the second image in every image pair is rotated (\\(i \\mod 4\\)) \\(\\cdot 90^{\\circ}\\) where \\(i\\) is the index of the image pair. We visualize a pair in MegaDepth-C4 in Appendix B, illustrating the improvement from DeDoDe-B to DeDoDe-B with a steerer optimized in Setting A. For MegaDepth-SO2, the second image in every image pair is" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.468, + 0.902 + ], + "angle": 0, + "content": "This is the standard initialization of a linear layer in Pytorch [26, 40]." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "4891" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.092, + 0.465, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.473, + 0.388 + ], + "angle": 0, + "content": "Figure 4. Training evolution of eigenvalue distributions of steers. We plot the eigenvalue distribution of \\( C_4 \\)-steerers \\( \\rho(\\mathbf{g}) \\) (first three columns) and Lie algebra generators \\( \\mathrm{d}\\varsigma \\) for SO(2)-steerers (last two columns) in the complex plane, with different initializations when trained jointly with a descriptor. The top row depicts the eigenvalues at the start, and the bottom row at the end of training. There are \\( D = 256 \\) eigenvalues in every plot—many congregate at the \"admissible\" eigenvalues as described in Section 4—but some do not, see the discussion in Section 6.5. These visualizations highlight the initialization sensitivity of the steerer. We show gif movies of the training evolution at this https url." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.407, + 0.47, + 0.437 + ], + "angle": 0, + "content": "instead rotated (\\(i \\mod 36) \\cdot 10^{\\circ}\\), thus requiring robustness under continuous rotations." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.439, + 0.469, + 0.469 + ], + "angle": 0, + "content": "The results are presented in Table 3; for more methods, see Appendix B. We summarize the main takeaways:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.47, + 0.469, + 0.516 + ], + "angle": 0, + "content": "1. It is possible to find steers for the original DeDoDe models (e.g. the second row of the table), even though they were not trained with any rotation augmentation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.516, + 0.469, + 0.546 + ], + "angle": 0, + "content": "2. The trained \\( C_4 \\) steers perform very well as their scores on MegaDepth-1500 and MegaDepth-C4 are the same." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.546, + 0.469, + 0.607 + ], + "angle": 0, + "content": "3. Training DeDoDe-B jointly with a \\( C_4 \\) steerer (C4-B) or with a fixed steerer (C4-Perm-B) improves results on upright images—this can be attributed to the fact that training with a steerer enables using rotation augmentation." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.607, + 0.469, + 0.637 + ], + "angle": 0, + "content": "4. The right equivariance for the task at hand is crucial—SO(2)-steerers outperform others on MegaDepth-SO2." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.637, + 0.469, + 0.682 + ], + "angle": 0, + "content": "5. The eigenvalue distribution of the steerer is important-- invariant models are worse than others, and SO2-B and SO2-Freq1-B are worse than SO2-Spread-B." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.682, + 0.469, + 0.712 + ], + "angle": 0, + "content": "6. DeDoDe-G can be made equivariant (C4-Perm-G), even though it has a frozen DINoV2 [39] ViT backbone." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.47, + 0.469, + 0.712 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.725, + 0.427, + 0.742 + ], + "angle": 0, + "content": "6.5. Training dynamics of steerer eigenvalues" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "This section aims to demonstrate that joint optimization of the steerer and descriptor does not necessarily lead to a good eigenvalue structure for the steerer. We plot the evolution of the eigenvalues of the steerer over the training epochs in Figure 4. For \\( C_4 \\)-steerers we plot the eigenvalues of \\( \\rho(\\mathbf{g}) \\) itself, while for \\( \\mathrm{SO}(2) \\)-steerers we plot the eigenvalues \\( \\lambda_d \\) of the Lie algebra generator \\( \\mathrm{d}\\varsigma \\), so that the eigenvalues of the steerer \\( \\varsigma(\\alpha) \\) are \\( \\mathrm{e}^{\\alpha \\lambda_d} \\). It is clear from Figure 4 that the initialization of the steerer influences the final distribution of eigenvalues a lot and we saw in Table 3 that the eigenvalue" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "distribution of the steerer matters for performance. Thus, we think it is an important direction for future work to figure out how to get around this initialization sensitivity. The choice of eigenvalue structure is related to the problem of specifying which group representations to use in the layers of equivariant neural networks in general." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.893, + 0.41 + ], + "angle": 0, + "content": "As a side effect of plotting the eigenvalues, we find that some of the steerer's eigenvalues have much lower absolute values than others. The steerer is applied to descriptions before they are normalized, so the absolute value of the maximum eigenvalue is unimportant, but the relative size of the eigenvalues tells us something about feature importance. Eigenvectors with small eigenvalues cannot be too important for matching, since they will be relatively down-scaled when applying the steerer in the optimization of (10). Indeed, small eigenvalues seem to correspond to unimportant dimensions of the descriptor—we maintain matching performance when projecting the descriptions to the span of the eigenvectors with large eigenvalues. This is related to PCA for dimensionality reduction, which has successfully been used for classical keypoint descriptors [27]." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.422, + 0.62, + 0.437 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.448, + 0.895, + 0.6 + ], + "angle": 0, + "content": "We developed a new framework for rotation equivariant keypoint descriptors using steers—linear maps that encode image rotations in description space. After outlining the general theory of steers using representation theory, we designed a large set of experiments with steers in three settings: (A) optimizing a steerer for a fixed descriptor, (B) optimizing a steerer and a descriptor jointly and (C) optimizing a descriptor for a fixed steerer. Our best models obtained new state-of-the-art results on the rotation invariant matching benchmarks Roto-360 and AIMS." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.612, + 0.669, + 0.63 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.638, + 0.894, + 0.82 + ], + "angle": 0, + "content": "We thank Alex Stoken for help with the evaluation on AIMS. This work was supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP), funded by the Knut and Alice Wallenberg Foundation and by the strategic research environment ELLIIT, funded by the Swedish government. The computational resources were provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at C3SE, partially funded by the Swedish Research Council through grant agreement no. 2022-06725, and by the Berzelius resource, provided by the Knut and Alice Wallenberg Foundation at the National Supercomputer Centre." + }, + { + "type": "page_footnote", + "bbox": [ + 0.498, + 0.851, + 0.894, + 0.901 + ], + "angle": 0, + "content": "The absolute values of the eigenvalues of a SO(2) steerer \\(\\varsigma (\\alpha)\\) are \\(\\mathrm{e}^{\\alpha \\mathrm{Re}(\\lambda_d)}\\) where \\(\\lambda_{d}\\) are the eigenvalues of \\(\\mathrm{d}\\varsigma\\) that are plotted in the two rightmost columns of Figure 4. Therefore, a lower real value of \\(\\lambda_{d}\\) means a lower absolute value of the eigenvalue of the steerer." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "4892" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.211 + ], + "angle": 0, + "content": "[1] Georges Baatz, Kevin Koser, David Chen, Radek Grzesczuk, and Marc Pollefeys. Handling urban location recognition as a 2d homothetic problem. In Computer Vision-ECCV 2010: 11th European Conference on Computer Vision, Heraklion, Crete, Greece, September 5-11, 2010, Proceedings, Part VI 11, pages 266-279. 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Springer, 2016. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.559 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.946, + 0.515, + 0.956 + ], + "angle": 0, + "content": "4895" + } + ] +] \ No newline at end of file diff --git a/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/e8356a95-c6c3-4afe-8ccf-5c5531990c8a_origin.pdf b/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/e8356a95-c6c3-4afe-8ccf-5c5531990c8a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..658c8f238690a6a989196ec2c7d88f1f931a0642 --- /dev/null +++ b/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/e8356a95-c6c3-4afe-8ccf-5c5531990c8a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4eab008e793cad1ec94c691026dd1c01f6387a6ce9a1df5e5a6015ca31e00a2b +size 6790112 diff --git a/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/full.md b/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/full.md new file mode 100644 index 0000000000000000000000000000000000000000..a4394c1b30f050e1cd4399cdd48f50adac6dbd85 --- /dev/null +++ b/2024/Steerers_ A Framework for Rotation Equivariant Keypoint Descriptors/full.md @@ -0,0 +1,384 @@ +# Steerers: A framework for rotation equivariant keypoint descriptors + +Georg Bökman† + +Johan Edstedt + +Michael Felsberg† + +Fredrik Kahl† + +†Chalmers University of Technology + +$^{\ddagger}$ Linköping University + +![](images/9a9ac4cee2a641ddfdd8fbf9fc5d742264dcf49bfc7c583b515d5919ce5936e3.jpg) +Figure 1. Matching under large in-plane rotations. Two challenging pairs from AIMS [49]. The left images in each pair were taken by astronauts on the ISS and are geo-referenced by matching them with the satellite images on the right. We plot estimated inlier correspondences after homography estimation with RANSAC. Further qualitative examples are shown in the appendix. + +![](images/e87f9cd549473b880a698c7fbe584fa9564f20ca104adba542db2670169b1db7.jpg) + +![](images/bb3793dd397774b491e8830371d350084e2a713f5eb0d000e382543bf4b759e1.jpg) + +![](images/6be77e114758ceb84df4dac9d5252d1fcd06f2f90266e3c0e7c3b9c5128b8198.jpg) + +# Abstract + +Image keypoint descriptions that are discriminative and matchable over large changes in viewpoint are vital for 3D reconstruction. However, descriptions output by learned descriptors are typically not robust to camera rotation. While they can be made more robust by, e.g., data augmentation, this degrades performance on upright images. Another approach is test-time augmentation, which incurs a significant increase in runtime. Instead, we learn a linear transform in description space that encodes rotations of the input image. We call this linear transform a steerer since it allows us to transform the descriptions as if the image was rotated. From representation theory, we know all possible steers for the rotation group. Steerers can be optimized (A) given a fixed descriptor; (B) jointly with a descriptor or (C) we can optimize a descriptor given a fixed steerer. We perform experiments in these three settings and obtain state-of-the-art results on the rotation invariant image matching benchmarks AIMS and Roto-360. We publish code and model weights at this https url. + +# 1. Introduction + +Discriminative local descriptions are vital for multiple 3D vision tasks, and learned descriptors have recently been shown to outperform traditional handcrafted local features [17, 19, 23, 43]. One major weakness of learned descriptors compared to handcrafted features such as + +SIFT [35] is the relative lack of robustness to non-upright images [55]. While images taken from ground level can sometimes be made upright by aligning with gravity as the canonical orientation, this is not always possible. For example, descriptors robust to rotation are vital in space applications [49], as well as medical applications [42], where no such canonical orientation exists. Even when a canonical orientation exists, it may be difficult or impossible to estimate. Rotation invariant matching is thus a key challenge. + +The most straightforward manner to get rotation invariant matching is to train or design a descriptor to be rotation invariant [17, 35]. However, this sacrifices distinctiveness in matching images with small relative rotations [41]. An alternative approach is to train a rotation-sensitive descriptor and perform test-time-augmentation, selecting the pair that produces the most matches. The obvious downside of TTA is computational cost. For example, testing all $45^{\circ}$ rotations requires running the model eight times. + +In this paper, we present an approach that maintains distinctiveness for small rotations and allows for rotation invariant matching when we have images with large rotations. We do this while adding only negligible additional runtime, running the descriptor only a single time. The main idea is to learn a linear transform in description space that corresponds to a rotation of the input image; see Figure 2. We call this linear transform a steerer as it allows us to modify keypoint descriptions as if they were describing rotated images—we can steer the descriptions without having to rerun the descriptor network. We show empi + +![](images/75408d11bc3061b8bae87c49bf6292333b2bf12fad984fb7d43165f2bab7ac91.jpg) +Figure 2. Overview of approach. A steerer (Definition 4.4) is a linear map that transforms the description of a keypoint into the description of the corresponding keypoint in a rotated image. Thus, a steerer makes the keypoint descriptor rotation equivariant, and we can obtain the descriptions of keypoints in arbitrarily rotated images while only running the descriptor once. + +cally that approximate steers can be obtained for existing descriptors and motivate this theoretically. We also investigate jointly optimizing steers and descriptors and show how this enables nearly exact steering while not sacrificing performance on upright images. Using mathematical representation theory, we can describe all possible steers—they are representations of the rotation group. This enables the choice of a fixed steerer and training a descriptor for it, and in turn, the investigation of which steers give the best performance. + +Using our framework, we set a new state-of-the-art on the rotation invariant matching benchmarks AIMS [49] (Figure 1) and Roto-360 [31]. At the same time, we are with the same models able to perform on par with or even outperform existing non-invariant methods on upright images on the competitive MegaDepth-1500 benchmark [33, 50]. In summary, our main contributions are as follows. + +1. We introduce a new framework of steerers for equivariant keypoint descriptors (Section 4) and theoretically motivate why steerers emerge in practice (Section 5). +2. We develop several settings for investigating steers (Section 5.1) and ways to apply them for rotation invariant matching (Section 5.2). +3. We conduct a large set of experiments, culminating in state-of-the-art on AIMS and Roto-360 (Section 6). + +# 2. Related work + +Classical keypoint descriptions are typically made rotation invariant by using keypoints with associated local rotation frames and computing the descriptions in these frames. Examples include SIFT [35], SURF [8], and ORB [45]. A canonical rotation frame can be used for patch-based neural network descriptors as well [53, 54]. Further, neural network-based approaches have been proposed for es + +timating the keypoint rotation frame [29, 30, 37] and for both computing the rotation frame and the descriptions in that frame [31, 61]. Notably, [30, 31] use rotation equivariant ConvNets [15, 56, 59]. Equivariant ConvNets have also been used for rotation-robust keypoint detection without estimating the rotation frame [2, 46], keypoint description [2, 34] and end-to-end image matching [9]. In theory1, equivariant ConvNets guarantee that the predictions are consistent when rotating the image. They are one example of hard-coding equivariance into network layers using mathematical group theory, an idea that goes back to the 1990's [58] and has seen large recent interest [11, 20, 22]. + +Neural networks can also be encouraged to learn equivariance rather than having it hard-coded in the layers. This can be done by enforcing group-specific invariants in the network output space [25, 48] (see also Section 5). Another approach is to specify a group representation on the output of the network and train the network to satisfy equivariance wrt. that representation [16, 28, 36, 60]. We will use this approach for keypoint descriptions in our Setting C. The benefits of not hard-coding equivariance are that arbitrary network architectures can be used (particularly pre-trained non-equivariant networks) and that one does not need to specify the group representations acting on each layer of the network. A special case of learning equivariance is rotation invariant descriptors through data augmentation [38, 52]. + +A recent line of work [10, 12, 24, 32] investigates to what extent neural networks exhibit equivariance without having been trained or hard-coded to do so. They find that many networks are approximately equivariant. One major limitation is that they only consider networks trained for image classification. We will empirically demonstrate a high level of equivariance in keypoint descriptors that were not explicitly trained to be equivariant and theoretically motivate why this happens (our Setting A). + +# 3. Preliminaries + +In this work, we are interested in finding linear mappings between keypoint descriptions where the images may have been rotated independently. We will, in particular, consider the group of quarter rotations $C_4$ and the group of continuous rotations $\mathrm{SO}(2)$ . + +Ordinary typeset $g$ will denote an arbitrary group element, boldface $\mathbf{g}$ will always mean the generator of $C_4$ for the remainder of the text so that the elements of $C_4$ are $\mathbf{g}$ , $\mathbf{g}^2$ , $\mathbf{g}^3$ and the identity element $\mathrm{id} = \mathbf{g}^4$ . Boldface $\mathbf{i}$ will denote the imaginary unit such that $\mathbf{i}^2 = -1$ . Given matrices $X_1, X_2, \ldots, X_J$ , the notation $\oplus_{j=1}^{J} X_j$ will mean the block-diagonal matrix with blocks $X_1, X_2, \ldots, X_J$ . + +# 3.1. Preliminaries on keypoint matching + +The underlying task is to take two images of the same scene and detect 2D points that correspond to the same 3D point. A pair of such points that depict the same 3D point is called a correspondence. The approach for finding correspondences that will be explored is a three-stage approach: + +1. Detection. Detect $N$ keypoint locations in each image. +2. Description. Describe the keypoint locations with descriptors, i.e., feature vectors in $\mathbb{R}^D$ . +3. Matching. Match the descriptors, typically by using mutual nearest neighbours in cosine distance. + +This classical setup includes SIFT [35] but also more recent deep learning-based approaches. In particular, we follow the method in DeDoDe [19], where the keypoint detector is first optimized to find good point tracks from SfM reconstructions and the keypoint descriptor is optimized by maximizing the matching likelihood obtained by a frozen keypoint detector as follows. If the $N$ descriptors (each normalized to unit length) in the two images are $y_{1} \in \mathbb{R}^{D \times N}$ and $y_{2} \in \mathbb{R}^{D \times N}$ we first form the $N \times N$ matching matrix $Y = y_{1}^{T}y_{2}$ , and obtain a matrix of pairwise likelihoods by using the dual softmax [44, 50, 55]: + +$$ +p \left(y _ {1}, y _ {2}\right) = \frac {\exp (\iota Y)}{\sum_ {\text {c o l u m n s}} \exp (\iota Y)} \cdot \frac {\exp (\iota Y)}{\sum_ {\text {r o w s}} \exp (\iota Y)}. \tag {1} +$$ + +Here $\iota = 20$ is the inverse temperature. The negative logarithm of the likelihood (1) is minimized for those pairs in the $N\times N$ matrix that correspond to ground truth inliers. + +# 3.2. Preliminaries on group representations + +Definition 3.1. (Group representation) Given a group $G$ , a representation of $G$ on $\mathbb{R}^D$ is a mapping $\rho : G \to \mathrm{GL}(\mathbb{R}, D)$ that preserves the group multiplication, i.e., $\rho(gg') = \rho(g)\rho(g')$ for every $g, g' \in G$ . + +Simply stated, $\rho$ maps every element in the group to an invertible $D\times D$ matrix. The point of using representations is that groups such as $C_4$ act differently on different quantities as we will illustrate in the following examples. + +Example 3.1. For $\mathbb{R}^{n\times n}$ (a square image grid), $C_4$ can be represented by permutations of the pixels in the obvious way so that the image is rotated anticlockwise by multiples of $90^{\circ}$ . We denote this group representation by $P_{90}$ so that applying $P_{90}^{k}$ rotates the image by $k\cdot 90^{\circ}$ anticlockwise. + +Example 3.2. For $\mathbb{R}^2$ (image coordinates), one possible representation of $C_4$ is $\rho(\mathbf{g}^k) = R_{90}^k = \left( \begin{array}{cc}0 & -1\\ 1 & 0 \end{array} \right)^k$ . Multiplication by $R_{90}^k$ corresponds to rotating image coordinates by $k \cdot 90^\circ$ if the center of the image is taken as $(0,0)$ . + +![](images/10a662079dc70f77ddbf467c9da8a4de192d38afa0cf70f5726154224ecce7b2.jpg) + +![](images/18d6455e65d469d95a3a04b8df5b0e1bbb4e21698e6d35db90f1f4e76bbfaaaa.jpg) +Figure 3. Equivariance of Upright SIFT. Left: A keypoint with its Upright SIFT description in an upright image and a rotated version. The small yellow squares are the subregions where histograms of gradient orientations are computed. Right: The Upright SIFT descriptions unravelled into the 128 bin histograms that constitute them. When we rotate the image, the subregions are permuted, and the histogram bins within each subregion are further permuted cyclically. Hence, Upright SIFT is rotation equivariant. + +![](images/701ef7fa0a09cf869091b0a144f7348481b447f286bb088b63ed351579c7d81e.jpg) + +# 4. Equivariance and steerability + +In this section, we will analyze the close connection between equivariance and steerability. We start with an example to introduce the former concept. + +Example 4.1. SIFT descriptions [35] are $128\mathrm{dim}$ vectors designed to be invariant to rotation, scale and illumination and highly distinctive for leveraging feature matching. For an input image $I \in \mathbb{R}^{n \times n}$ and $N$ keypoints with scale and orientation $x \in \mathbb{R}^{4 \times N^2}$ , we get descriptions $y \in \mathbb{R}^{128 \times N}$ . If $f$ is the SIFT descriptor, we write $f(I, x) = y$ . The descriptions consist of histograms of image gradients over patches around the keypoints $x$ . The patches are oriented by the keypoint orientations so that the descriptions are invariant to joint rotations of the image and keypoints: + +$$ +f \left(P _ {9 0} ^ {k} I, \left(\oplus_ {b = 1} ^ {2} R _ {9 0}\right) ^ {k} x\right) = f (I, x). +$$ + +If we discard the keypoint orientations, i.e., set the angle of each keypoint to 0, we get the Upright SIFT (UPSIFT) descriptor [1, 7], which is often used for upright images as it is more discriminative than SIFT. When we rotate an image $90^{\circ}$ , then the gradient histograms, i.e., the UPSIFT descriptions are permuted by a specific permutation $P_{\mathrm{UPSIFT}}$ , so if $f$ is the UPSIFT descriptor, we have + +$$ +f \left(P _ {9 0} ^ {k} I, \left(\oplus_ {b = 1} ^ {2} R _ {9 0}\right) ^ {k} x\right) = P _ {\text {U P S I F T}} ^ {k} f (I, x). +$$ + +We illustrate the permutation $P_{\mathrm{UPSIFT}}$ in Figure 3. UPSIFT is not rotation invariant, but it is rotation equivariant when we rotate the input, the output changes predictably. Explicitly, the representation is $\rho(\mathbf{g}^k) = P_{\mathrm{UPSIFT}}^k$ . + +Definition 4.1 (Equivariance). We say that a function $f: V \to W$ is equivariant with respect to a group $G$ if + +$$ +\rho (g) f (v) = f \left(\rho_ {\text {i n}} (g) v\right), \forall v \in V, g \in G, \tag {2} +$$ + +for some group representations $\rho_{\mathrm{in}},\rho$ + +This work will mainly be concerned with the equivariance of learned keypoint descriptors of ordinary keypoints (without scale and orientation). + +Definition 4.2 (Equivalence of keypoint descriptor). We say that a keypoint descriptor $f$ is equivariant with respect to a group $G$ transforming the input image by $\rho_{\mathrm{image}}$ and the input keypoint locations by $\rho_{\mathrm{keypoint}}$ if there exists $\rho$ such that + +$$ +\rho (g) f (I, x) = f \left(\rho_ {\text {i m a g e}} (g) I, \rho_ {\text {k e y p o i n t}} (g) x\right) \tag {3} +$$ + +for all images, keypoints and group elements. We call the descriptor invariant if $\rho(g)$ is the identity matrix for all $g$ . Invariance is a special type of equivariance. + +Example 4.2. A keypoint descriptor $f$ is equivariant under $90^{\circ}$ rotations if there exists $\rho$ of $C_4$ such that + +$$ +\rho \left(\mathbf {g} ^ {k}\right) f (I, x) = f \left(P _ {9 0} ^ {k} I, R _ {9 0} ^ {k} x\right) \tag {4} +$$ + +for $k \in \{0,1,2,3\}$ , where $P_{90}$ and $R_{90}$ are the representations from Examples 3.1 and 3.2 that rotate images and coordinates in the ordinary manner. + +Both SIFT and Upright SIFT are equivariant. For SIFT, $\rho (\mathbf{g}^k)$ is the identity, so SIFT is invariant. For Upright SIFT, $\rho (\mathbf{g}^k)$ is $P_{\mathrm{UPSIFT}}^k$ as explained in Example 4.1. + +One aim of this work is to argue and demonstrate that learned keypoint descriptors, which are trained on upright data, will behave more like Upright SIFT than SIFT, i.e., they will be rotation equivariant but not invariant. + +Definition 4.3 (Steerability, adapted from [21]). A real-valued function $\phi : V \to \mathbb{R}$ is said to be steerable under a representation $\rho_{\mathrm{in}}$ of $G$ on $V$ , if there exist $D$ functions (for some $D$ ) $\phi_j : V \to \mathbb{R}$ and $D$ functions $\kappa_j : G \to \mathbb{R}$ such that $\phi(\rho_{\mathrm{in}}(g)v) = \sum_{j=1}^{D} \kappa_j(g)\phi_j(v)$ . + +Note that an equivariant function $f:V\to \mathbb{R}^{D}$ satisfies in each component $f_{d}$ that $f_{d}(\rho_{\mathrm{in}}(g)v) = \sum_{j = 1}^{D}\rho (g)_{dj}f_{j}(v)$ , so each component of $f$ is steerable, in the notation of Definition 4.3, $\phi = f_d,\phi_j = f_j,\kappa_j(g) = \rho (g)_{dj}$ . This motivates the definition of a steerer. + +Definition 4.4 (Steerer). Given a function $f: V \to W$ between vector spaces, and a representation $\rho_{\mathrm{in}}$ of $G$ on $V$ , a steerer is a representation $\rho$ of $G$ on $W$ that makes $f$ equivariant, i.e. such that + +$$ +f \left(\rho_ {\text {i n}} (g) v\right) = \rho (g) f (v). \tag {5} +$$ + +Even if (5) only holds approximately or $\rho$ is only approximately a representation, we will refer to $\rho$ as a steerer. + +We will use the verb steer for multiplying a feature/description by a steerer; see Figure 2 for the broad idea. + +Example 4.3. As explained in Example 4.1, $P_{\mathrm{UPSIFT}}$ is a steerer for Upright SIFT under $90^{\circ}$ rotations. This has practical consequences. If we want to obtain the Upright SIFT descriptions for an image $I$ and the same image rotated $k \cdot 90^{\circ}$ , we only need to compute the descriptions for the original image. We can obtain the rotated ones by multiplying the descriptions by $P_{\mathrm{UPSIFT}}^{k}$ . That is, we can steer the Upright SIFT descriptions with $P_{\mathrm{UPSIFT}}$ . + +It is known from representation theory [47] what all possible representations of $C_4$ are, and hence what all possible steerers for rotation equivariant descriptors are. As this result will be necessary for the remainder of the text, we collect it in a theorem. Similar results are also known for other groups e.g. the continuous rotation group SO(2), which we discuss in the next section. + +Theorem 4.1 (Representations of $C_4$ ). Let $\rho$ be a representation of $C_4$ on $\mathbb{R}^D$ . Then, there exists an invertible matrix $Q$ and $j_d \in \{0, 1, 2, 3\}$ such that + +$$ +\rho \left(\mathbf {g} ^ {k}\right) = Q ^ {- 1} \operatorname {d i a g} \left(\mathbf {i} ^ {k j _ {1}}, \mathbf {i} ^ {k j _ {2}}, \dots , \mathbf {i} ^ {k j _ {D}}\right) Q. \tag {6} +$$ + +The diagonal in (6) contains the eigenvalues of $\rho (\mathbf{g}^k)$ . + +Example 4.4. The Upright SIFT steuerer $P_{\mathrm{UPSIFT}}$ is diagonalizable with an equal amount of each eigenvalue $\pm 1$ , $\pm \mathbf{i}$ . + +The complex eigenvalues must appear in conjugate pairs as we take $\rho(\mathbf{g})$ to be real-valued. It is then possible to do a change of basis so that each pair $\mathbf{i}, -\mathbf{i}$ on the diagonal in (6) is replaced by a block $\left( \begin{array}{cc}0 & -1\\ 1 & 0 \end{array} \right)$ . In this way, $\rho(\mathbf{g})$ can always be block-diagonalized: $\rho(\mathbf{g}) = Q^{-1}BQ$ where $Q$ and $B$ are real valued and $B$ is block-diagonal with blocks of sizes 1 and 2. + +# 4.1. Representation theory of SO(2) + +SO(2) is a one-parameter Lie group, i.e. a continuous group with one degree of freedom $\alpha$ the rotation angle. A $D$ -dimensional representation of SO(2) is a map $\varsigma : [0, 2\pi) \to \mathrm{GL}(\mathbb{R}, D)$ such that addition modulo $2\pi$ on the input is encoded as matrix multiplication on the output—we will consistently use $\varsigma$ for SO(2) representations to separate them from $C_4$ representations $\rho$ ( $\rho$ will also be used for representations of general groups). The most familiar is the two-dimensional representation $\varsigma(\alpha) = \begin{pmatrix} \cos(\alpha) & -\sin(\alpha) \\ \sin(\alpha) & \cos(\alpha) \end{pmatrix}$ which rotates 2D coordinates. Similar to the $C_4$ case in Theorem 4.1, we can write down a general representation for SO(2) as follows [57]. + +Theorem 4.2 (Representations of $\mathrm{SO}(2)$ ). Let $\varsigma$ be a representation of $\mathrm{SO}(2)$ on $\mathbb{R}^D$ . Then there exists an invertible $Q$ and $j_d \in \mathbb{Z}$ such that + +$$ +\varsigma (\alpha) = Q ^ {- 1} \operatorname {d i a g} \left(\mathrm {e} ^ {\mathbf {i} j _ {1} \alpha}, \mathrm {e} ^ {\mathbf {i} j _ {2} \alpha}, \dots , \mathrm {e} ^ {\mathbf {i} j _ {D} \alpha}\right) Q. \tag {7} +$$ + +The $j_{d}$ 's are the frequencies of the eigenspaces of $\varsigma$ . Complex eigenvalues appear in conjugate pairs so (7) can be rewritten as a block diagonal decomposition $\varsigma(\alpha) = Q^{-1}BQ$ where $Q$ and $B$ are real valued and $B$ is block-diagonal with minimal blocks. The admissible blocks (= real-valued irreducible representations) in $B$ are then the $1 \times 1$ block (1) and the $2 \times 2$ blocks + +$$ +\left( \begin{array}{c c} \cos (j \alpha) & - \sin (j \alpha) \\ \sin (j \alpha) & \cos (j \alpha) \end{array} \right) \quad \text {f o r} j \in \mathbb {Z} \backslash \{0 \}. \tag {8} +$$ + +We can write $\varsigma (\alpha) = \exp \left(\alpha Q^{-1}\mathrm{diag}(\mathbf{i}j_1,\ldots ,\mathbf{i}j_D)Q\right)$ where $\mathrm{expm}$ is the matrix exponential. The quantity $\mathrm{d}\varsigma \coloneqq$ $Q^{-1}\mathrm{diag}(\mathbf{i}j_1,\dots ,\mathbf{i}j_D)Q$ is called a Lie algebra representation of SO(2), here in its most general form. When training a steerer for SO(2) it is practical to train a $D\times D$ matrix $\mathrm{d}\varsigma$ and steer using $\varsigma (\alpha) = \exp \mathrm{m}(\alpha \mathrm{d}\varsigma)$ . + +# 4.2. Disentangling description space + +When we have a steerer, we get a description space on which rotations act—up to a change of basis—by a block-diagonal matrix $\oplus_{j=1}^{J} B_{j}$ . The description space can then be thought of as being disentangled into different subspaces where rotations act in different ways $B_{j}$ [14, 60]. We detail what this means for keypoint descriptors in Appendix A. + +# 5. Descriptors and steerers + +This work's crucial observation and assumption is that learned descriptors, while not invariant, are approximately equivariant so that they have a steerer. Or, as a weaker assumption, they can be trained to be equivariant. It may seem that this is a strong assumption. However, a seemingly less strong assumption turns out to be equivalent. + +Theorem 5.1. [Adapted from Shakerinava et al. [48], Gupta et al. [25]] Assume that we have a function $f: V \to \mathbb{S}^{D-1}$ and a group $G$ with representation $\rho_{\mathrm{in}}$ on $V$ such that, for all $v, v' \in V$ and $g \in G$ + +$$ +\langle f \left(\rho_ {\text {i n}} (g) v\right), f \left(\rho_ {\text {i n}} (g) v ^ {\prime}\right) \rangle = \langle f (v), f \left(v ^ {\prime}\right) \rangle . \tag {9} +$$ + +Then there exists an orthogonal representation $\rho(g)$ , such that $f$ is equivariant w.r.t. $G$ with representations $\rho_{\mathrm{in}}$ and $\rho$ . + +We provide a proof in Appendix A. Since we match normalized keypoint descriptions by their cosine similarity, Theorem 5.1 is highly applicable to the image matching problem. If a keypoint descriptor $f$ is perfectly consistent in the matching scores when simultaneously rotating the images, then the scalar products in (9) will be equal so that the theorem tells us that $f$ has a steerer $\rho$ . Furthermore, we can expect many local image features to appear in all orientations even over a dataset of upright images, thus encouraging (9) to hold for $f$ trained on large datasets. + +# 5.1. Three settings for investigating steerers + +As $C_4$ is cyclic, all its representations are defined by $\rho(\mathbf{g})$ , where $\mathbf{g}$ is the generator of $C_4$ . To find a steerer for a keypoint descriptor under $C_4$ hence comes down to finding a single matrix $\rho(\mathbf{g})$ that represents rotations by $90^\circ$ in the description space. Similarly, for SO(2) we find the single matrix $\mathrm{d}\varsigma$ that defines the representation $\varsigma$ . + +We will consider three settings. In each case we will optimize $\rho (\mathbf{g})$ and/or $f$ over the MegaDepth training set [33] with rotation augmentation and maximize + +$$ +p \left(f \left(P _ {9 0} ^ {k _ {1}} I _ {1}, R _ {9 0} ^ {k _ {1}} x _ {1}\right), \rho (\mathbf {g}) ^ {k} f \left(P _ {9 0} ^ {k _ {2}} I _ {2}, R _ {9 0} ^ {k _ {2}} x _ {2}\right)\right) \tag {10} +$$ + +where $p$ is the matching probability (1). The number of rotations $k_{1}$ and $k_{2}$ for each image are sampled independently during training, and $k = k_{1} - k_{2} \mod 4$ is the number of rotations that aligns image $I_{2}$ to image $I_{1}$ . Thus, $\rho(\mathbf{g})^{k}$ aligns the relative rotation between descriptions in $I_{2}$ and $I_{1}$ . We optimize continuous steerers $\varsigma$ analogously to (10). + +Setting A: Fixed descriptor, optimized steerer. If a descriptor works equally well for upright images as well as images rotated the same amount from upright, then according to Theorem 5.1, we should expect that there exists a steerer $\rho (\mathbf{g})$ such that (4) holds. To find $\rho (\mathbf{g})$ we optimize it as a single $D\times D$ linear layer by maximizing (10). + +# Setting B: Joint optimization of descriptor and steerer. + +The aim is to find a steerer that is as good as possible for the given data. We will see in the experiments, by looking at the evolution of the eigenvalues of $\rho(\mathbf{g})$ during training, that this joint optimization has many local optima and is highly dependent on the initialization of $\rho(\mathbf{g})$ . However, looking at the eigenvalues of $\rho(\mathbf{g})$ does give knowledge about which descriptor dimensions are most important, as will be explained in Section 6.5. + +Setting C: Fixed steerer, optimized descriptor. To get the most precise control over the rotation behaviour of a descriptor, we can fix the steerer and optimize only the descriptor. This enables us to investigate how much influence the choice of steerer has on the descriptor. For instance, choosing the steerer as the identity leads to a rotation invariant descriptor. We will see in the experiments that this choice leads to suboptimal performance on upright images compared to other steers. + +# 5.2. Matching with equivariant descriptions + +This section presents several approaches to rotation invariant matching using equivariant descriptors. Throughout, we will denote the $D$ -dimensional descriptions of $N$ keypoints in two images $I_1, I_2$ by $y_1, y_2 \in \mathbb{R}^{D \times N}$ and will assume that we know the $C_4$ -steerer $\rho(\mathbf{g})$ that rotates descriptions $90^\circ$ or the SO(2)-steerer $\varsigma(\alpha)$ through the Lie algebra generator $\mathrm{d}\varsigma$ . For matching we follow DeDoDe [19], as described in Section 3.1. The base similarity used is the cosine + +Table 1. Evaluation on Roto-360 [31]. We report the percentage of correct matches at three thresholds. We use the DeDoDe-SO2 detector with 5,000 keypoints in the last two rows. Matching strategies are Max Matches for the $C_4$ -descriptor and Max Sim. over $C_8$ for the SO(2)-descriptor. See Section 6.1 for the shorthands for our models. + +
DetectorDescriptor3px5px10px
SIFT [35]SIFT [35]787879
ORB [45]ORB [45]798587
SuperPoint [17]RELF, single [31]909193
SuperPoint [17]RELF, multiple [31]929394
SuperPoint [17]C4-B (ours)828283
SuperPoint [17]SO2-Spread-B (ours)969797
DeDoDe [19]C4-B (ours)828486
DeDoDe [19]SO2-Spread-B (ours)959798
+ +similarity, so we compute $y_1^T y_2$ for normalized descriptions to get an $N \times N$ matrix of pairwise scores on which dual softmax (1) is applied. Matches are mutual most similar descriptions with similarity above 0.01. + +Max matches over steered descriptions. The first way of obtaining invariant matches is to match $y_{1}$ with $\rho(\mathbf{g})^{k}y_{2}$ for $k = 0,1,2,3$ and keep the matches from the $k$ that has the most matches. This is similar to matching the image $I_{1}$ with four different rotations of $I_{2}$ but alleviates the need for rerunning the descriptor network for each rotation. + +Max similarity over steered descriptions. A computationally cheaper version is to select the matching matrix not as $y_1^T y_2$ but as $\max_k y_1^T \rho(\mathbf{g})^k y_2$ , where the max is elementwise over the matrix. + +SO(2)-steerers. To apply the above matching strategies to SO(2)-steerers $\varsigma (\alpha) = \exp (\alpha \mathrm{d}\varsigma)$ we discretize $\varsigma$ . A $C_\ell$ -steerer is obtained through $\rho (\mathbf{g}_\ell) = \exp \left(\frac{2\pi}{\ell}\mathrm{d}\varsigma\right)$ , where $\mathbf{g}_{\ell}$ generates $C_\ell$ . We will use $C_8$ in the experiments. + +Procrustes matcher. If all eigenvalues of $\rho(\mathbf{g})$ are $\pm \mathrm{i}$ , the steuer can be block-diagonalized with only the block $\left( \begin{array}{cc}0 & -1\\ 1 & 0 \end{array} \right)^3$ . The descriptions consist of $D/2$ two-dimensional quantities that all rotate with the same frequency as the image. We will refer to them as frequency 1 descriptions and view them reshaped as $y \in \mathbb{R}^{2 \times (D/2) \times N}$ . A 2D rotation matrix acts on these descriptions from the left when the image rotates, and we can find the optimal rotation matrix $R_{m,n}$ that aligns each pair $y_{1,m}, y_{2,n} \in \mathbb{R}^{2 \times (D/2)}$ by solving the Procrustes problem via SVD. The matching matrix is obtained by computing $\langle R_{m,n}y_{1,m}, y_{2,n} \rangle$ for each pair. $R_{m,n}$ gives the relative rotation between each pair of keypoints, which can be useful e.g. for minimal relative pose solvers [4, 6] or for outlier filtering [13]. We leave exploring this per-correspondence geometry to future work. + +Table 2. Evaluation on AIMS [49]. We report the average precision (AP) in percent on different splits of AIMS: "North Up" (N. Up) contains images with small rotations, "All Others" (A. O.) contains images with larger rotations and "All" contains all images. We use the DeDoDe-SO2 detector and 10,000 keypoints throughout. See Section 6.1 for the shorthands for our models. + +
MethodN. UpA. O.All
SE2-LoFTR [9]585152
C4-B, Max Matches (ours)525151
SO2-Spread-B, Max Sim. C8 (ours)605758
SO2-Freq1-B, Procrustes (ours)645960
+ +# 6. Experiments + +We train and evaluate a variety of descriptors and steerers. Experimental details are covered in Appendix C. We provide comparisons to TTA in performance and runtime in Appendix B, as well as experiments with more matching strategies and an explicit experiment to test the connection between Theorem 5.1 and rotation equivariance. + +We start by reporting results on two public benchmarks for rotation invariant image matching. Then, we will present ablation results for the MegaDepth benchmark, both for the standard version with upright images and a version where we have rotated the input images. + +# 6.1. Models considered + +Our base models are the DeDoDe-B and DeDoDe-G descriptors introduced in [19]. These are both $D = 256$ dimensional descriptors. The focus will be on the smaller model DeDoDe-B, as this gives us the chance to do large-scale ablations. We train all models on MegaDepth [33]. To obtain rotation-consistent detections, we retrain two versions of the DeDoDe-detector, with data augmentation over $C_4$ and SO(2) respectively, denoted DeDoDe-{C4, SO2}. + +For Setting B (Section 5.1), we will see that the initialization of the steerer matters. Similarly, for Setting C, we can fix the steerer with different eigenvalue structures. Here, we introduce shorthand, which is used in the result tables. We will refer to the case of all eigenvalues 1 as $Inv$ for invariant. This case corresponds to the ordinary notion of data augmentation, where the descriptions for rotated images should be the same as for non-rotated images. The case when all eigenvalues are $\pm \mathbf{i}$ is denoted $Freq1$ for frequency 1 as explained in Section 5.2. For $C_4$ -steers, the case with an equal distribution of all eigenvalues $\pm 1, \pm \mathbf{i}$ will be denoted $Perm$ , as this is the eigenvalue signature of a cyclic permutation of order 4. For SO(2)-steers, the case with an equal distribution of eigenvalues $0, \pm \mathbf{i}, \pm 2\mathbf{i}, \ldots \pm 6\mathbf{i}$ will be denoted $Spread$ (the cutoff 6 was arbitrarily chosen). The $Perm$ and $Spread$ steers correspond to a broad range of frequencies in the description space. When none of the above labels ( $Inv$ , $Freq1$ , $Perm$ or + +Table 3. Evaluation on MegaDepth [33, 50]. The first section shows Setting A where we only optimize the steerer, the second section shows Setting B where we jointly optimize the descriptor and steerer and the third section shows the Setting C where we predefine the steerer and optimize only the descriptor. For MegaDepth-1500 we always use dual softmax matcher to evaluate the descriptors on upright images. We use 20,000 keypoints throughout. The best values for B- and G-models are highlighted in each column. See Section 6.1 for shorthand explanations for our models. A larger version of this table with more methods is available in Appendix B. + +
DetectorDescriptorMatching strategyMegaDepth-1500MegaDepth-C4MegaDepth-SO2
DeDoDeAUC @ 5°10°20°5°10°20°5°10°20°
OriginalBDual softmax496577121720121620
OriginalBMax matches C4-steered-11--11--11-436073304456
SO2BMax matches C8-steered506678405770345165
OriginalGDual softmax526981131721162228
OriginalGMax matches C4-steered-11--11--11-314557263950
C4C4-BMax matches C4-steered516779506779395568
SO2SO2-BMax matches C8-steered476376476376446174
SO2SO2-Spread-BMax matches C8-steered506679496678466376
SO2SO2-Spread-BMax similarity C8-steered496678476477436174
C4C4-Inv-BDual softmax486476476376395569
C4C4-Perm-BMax matches C4-steered506779506679395467
SO2SO2-Inv-BDual softmax466275456174436073
SO2SO2-Freq1-BMax matches C8-steered476477476476456275
SO2SO2-Freq1-BProcrustes476476466275456174
C4C4-Perm-GMax matches C4-steered526981536982446174
+ +Spread) is attached to a descriptor and steerer trained jointly in Setting B, then we initialize the steerer with values uniformly in $(-D^{-1/2}, D^{-1/2})^4$ , the eigenvalues are then approximately uniformly distributed in the disk with radius $3^{-1/2}$ [51]. When a descriptor is trained with $k \cdot 90^\circ$ rotations, we append $C4$ to its name and when trained with continuous augmentations, we append $SO2$ to its name. + +# 6.2. Roto-360 + +We evaluate on the Roto-360 benchmark [31], which consists of ten image pairs from HPatches [3] where the second image in each image pair is rotated by all multiples of $10^{\circ}$ to obtain 360 image pairs in total. We report the average precision of the obtained matches and compare it to the current state-of-the-art RELF [31]. The results are shown in Table 1. We see that we outperform RELF when using methods trained for continuous rotations. Our matching runs around three times faster than RELF on Roto-360. + +# 6.3.AIMS + +The Astronaut Image Matching Subset (AIMS) [49] consists of images taken by astronauts from the ISS and satellite images covering the broad regions that the astronaut images could depict. The task consists of finding the pairs of astronaut images and satellite images that show the same locations on Earth. Pairs are found by setting a threshold for the number of matches between images after homography estimation with RANSAC. + +The relative rotations of the astronaut and satellite images are unknown, making the task suitable for rotation-invariant matchers. Indeed, in [49], the best performing method is the rotation invariant SE2-LoFTR [9], which we compare to. The AIMS can be split into "North Up" astronaut images, consisting of images with small rotations (between $0^{\circ}$ and $90^{\circ}$ ) and "All Others", consisting of images with large rotations. This split further enables the evaluation of rotation invariant matchers. We report the average precision over the whole dataset, as opposed to the approach in [49], where the score is computed over at most 100 true negatives per astronaut image. Results are shown in Table 2. Further, we plot precision-recall curves in Appendix B. We generally outperform SE2-LoFTR, particularly on the heavily rotated images in "All Others". + +# 6.4. MegaDepth-1500 + +We evaluate on a held-out part of MegaDepth (MegaDepth-1500 following [50]). Here, the task is to take two input images and output the relative pose between the cameras. The performance is measured by the AUC of the pose error. Additionally, we create two versions of MegaDepth with rotated images to evaluate the rotational robustness of our models. For MegaDepth-C4, the second image in every image pair is rotated ( $i \mod 4$ ) $\cdot 90^{\circ}$ where $i$ is the index of the image pair. We visualize a pair in MegaDepth-C4 in Appendix B, illustrating the improvement from DeDoDe-B to DeDoDe-B with a steerer optimized in Setting A. For MegaDepth-SO2, the second image in every image pair is + +![](images/a1ec4834300c2564d345386d24d9c7689659dd06493c761622e795ff405be885.jpg) +Figure 4. Training evolution of eigenvalue distributions of steers. We plot the eigenvalue distribution of $C_4$ -steerers $\rho(\mathbf{g})$ (first three columns) and Lie algebra generators $\mathrm{d}\varsigma$ for SO(2)-steerers (last two columns) in the complex plane, with different initializations when trained jointly with a descriptor. The top row depicts the eigenvalues at the start, and the bottom row at the end of training. There are $D = 256$ eigenvalues in every plot—many congregate at the "admissible" eigenvalues as described in Section 4—but some do not, see the discussion in Section 6.5. These visualizations highlight the initialization sensitivity of the steerer. We show gif movies of the training evolution at this https url. + +instead rotated ( $i \mod 36) \cdot 10^{\circ}$ , thus requiring robustness under continuous rotations. + +The results are presented in Table 3; for more methods, see Appendix B. We summarize the main takeaways: + +1. It is possible to find steers for the original DeDoDe models (e.g. the second row of the table), even though they were not trained with any rotation augmentation. +2. The trained $C_4$ steers perform very well as their scores on MegaDepth-1500 and MegaDepth-C4 are the same. +3. Training DeDoDe-B jointly with a $C_4$ steerer (C4-B) or with a fixed steerer (C4-Perm-B) improves results on upright images—this can be attributed to the fact that training with a steerer enables using rotation augmentation. +4. The right equivariance for the task at hand is crucial—SO(2)-steerers outperform others on MegaDepth-SO2. +5. The eigenvalue distribution of the steerer is important-- invariant models are worse than others, and SO2-B and SO2-Freq1-B are worse than SO2-Spread-B. +6. DeDoDe-G can be made equivariant (C4-Perm-G), even though it has a frozen DINoV2 [39] ViT backbone. + +# 6.5. Training dynamics of steerer eigenvalues + +This section aims to demonstrate that joint optimization of the steerer and descriptor does not necessarily lead to a good eigenvalue structure for the steerer. We plot the evolution of the eigenvalues of the steerer over the training epochs in Figure 4. For $C_4$ -steerers we plot the eigenvalues of $\rho(\mathbf{g})$ itself, while for $\mathrm{SO}(2)$ -steerers we plot the eigenvalues $\lambda_d$ of the Lie algebra generator $\mathrm{d}\varsigma$ , so that the eigenvalues of the steerer $\varsigma(\alpha)$ are $\mathrm{e}^{\alpha \lambda_d}$ . It is clear from Figure 4 that the initialization of the steerer influences the final distribution of eigenvalues a lot and we saw in Table 3 that the eigenvalue + +distribution of the steerer matters for performance. Thus, we think it is an important direction for future work to figure out how to get around this initialization sensitivity. The choice of eigenvalue structure is related to the problem of specifying which group representations to use in the layers of equivariant neural networks in general. + +As a side effect of plotting the eigenvalues, we find that some of the steerer's eigenvalues have much lower absolute values than others. The steerer is applied to descriptions before they are normalized, so the absolute value of the maximum eigenvalue is unimportant, but the relative size of the eigenvalues tells us something about feature importance. Eigenvectors with small eigenvalues cannot be too important for matching, since they will be relatively down-scaled when applying the steerer in the optimization of (10). Indeed, small eigenvalues seem to correspond to unimportant dimensions of the descriptor—we maintain matching performance when projecting the descriptions to the span of the eigenvectors with large eigenvalues. This is related to PCA for dimensionality reduction, which has successfully been used for classical keypoint descriptors [27]. + +# 7. Conclusion + +We developed a new framework for rotation equivariant keypoint descriptors using steers—linear maps that encode image rotations in description space. After outlining the general theory of steers using representation theory, we designed a large set of experiments with steers in three settings: (A) optimizing a steerer for a fixed descriptor, (B) optimizing a steerer and a descriptor jointly and (C) optimizing a descriptor for a fixed steerer. Our best models obtained new state-of-the-art results on the rotation invariant matching benchmarks Roto-360 and AIMS. + +# Acknowledgements + +We thank Alex Stoken for help with the evaluation on AIMS. This work was supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP), funded by the Knut and Alice Wallenberg Foundation and by the strategic research environment ELLIIT, funded by the Swedish government. The computational resources were provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at C3SE, partially funded by the Swedish Research Council through grant agreement no. 2022-06725, and by the Berzelius resource, provided by the Knut and Alice Wallenberg Foundation at the National Supercomputer Centre. + +# References + +[1] Georges Baatz, Kevin Koser, David Chen, Radek Grzesczuk, and Marc Pollefeys. Handling urban location recognition as a 2d homothetic problem. 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Matching under large in-plane rotations. Two challenging pairs from AIMS [49]. The left images in each pair were taken by astronauts on the ISS and are geo-referenced by matching them with the satellite images on the right. We plot estimated inlier correspondences after homography estimation with RANSAC. 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However, descriptions output by learned descriptors are typically not robust to camera rotation. While they can be made more robust by, e.g., data augmentation, this degrades performance on upright images. Another approach is test-time augmentation, which incurs a significant increase in runtime. Instead, we learn a linear transform in description space that encodes rotations of the input image. We call this linear transform a steerer since it allows us to transform the descriptions as if the image was rotated. From representation theory, we know all possible steers for the rotation group. Steerers can be optimized (A) given a fixed descriptor; (B) jointly with a descriptor or (C) we can optimize a descriptor given a fixed steerer. We perform experiments in these three settings and obtain state-of-the-art results on the rotation invariant image matching benchmarks AIMS and Roto-360. We publish code and model weights at this https url." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 632, + 128, + 645 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 632, + 128, + 645 + ], + "spans": [ + { + "bbox": [ + 47, + 632, + 128, + 645 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "Discriminative local descriptions are vital for multiple 3D vision tasks, and learned descriptors have recently been shown to outperform traditional handcrafted local features [17, 19, 23, 43]. One major weakness of learned descriptors compared to handcrafted features such as" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "spans": [ + { + "bbox": [ + 304, + 359, + 546, + 468 + ], + "type": "text", + "content": "SIFT [35] is the relative lack of robustness to non-upright images [55]. While images taken from ground level can sometimes be made upright by aligning with gravity as the canonical orientation, this is not always possible. For example, descriptors robust to rotation are vital in space applications [49], as well as medical applications [42], where no such canonical orientation exists. Even when a canonical orientation exists, it may be difficult or impossible to estimate. Rotation invariant matching is thus a key challenge." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "type": "text", + "content": "The most straightforward manner to get rotation invariant matching is to train or design a descriptor to be rotation invariant [17, 35]. However, this sacrifices distinctiveness in matching images with small relative rotations [41]. An alternative approach is to train a rotation-sensitive descriptor and perform test-time-augmentation, selecting the pair that produces the most matches. The obvious downside of TTA is computational cost. For example, testing all " + }, + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "type": "inline_equation", + "content": "45^{\\circ}" + }, + { + "bbox": [ + 304, + 471, + 547, + 579 + ], + "type": "text", + "content": " rotations requires running the model eight times." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "In this paper, we present an approach that maintains distinctiveness for small rotations and allows for rotation invariant matching when we have images with large rotations. We do this while adding only negligible additional runtime, running the descriptor only a single time. The main idea is to learn a linear transform in description space that corresponds to a rotation of the input image; see Figure 2. We call this linear transform a steerer as it allows us to modify keypoint descriptions as if they were describing rotated images—we can steer the descriptions without having to rerun the descriptor network. We show empi" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4885" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 69, + 77, + 267, + 205 + ], + "blocks": [ + { + "bbox": [ + 69, + 77, + 267, + 205 + ], + "lines": [ + { + "bbox": [ + 69, + 77, + 267, + 205 + ], + "spans": [ + { + "bbox": [ + 69, + 77, + 267, + 205 + ], + "type": "image", + "image_path": "75408d11bc3061b8bae87c49bf6292333b2bf12fad984fb7d43165f2bab7ac91.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 289, + 289 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 289, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 289, + 289 + ], + "type": "text", + "content": "Figure 2. Overview of approach. A steerer (Definition 4.4) is a linear map that transforms the description of a keypoint into the description of the corresponding keypoint in a rotated image. Thus, a steerer makes the keypoint descriptor rotation equivariant, and we can obtain the descriptions of keypoints in arbitrarily rotated images while only running the descriptor once." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 300, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 300, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 300, + 287, + 418 + ], + "type": "text", + "content": "cally that approximate steers can be obtained for existing descriptors and motivate this theoretically. We also investigate jointly optimizing steers and descriptors and show how this enables nearly exact steering while not sacrificing performance on upright images. Using mathematical representation theory, we can describe all possible steers—they are representations of the rotation group. This enables the choice of a fixed steerer and training a descriptor for it, and in turn, the investigation of which steers give the best performance." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 420, + 287, + 503 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 420, + 287, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 420, + 287, + 503 + ], + "type": "text", + "content": "Using our framework, we set a new state-of-the-art on the rotation invariant matching benchmarks AIMS [49] (Figure 1) and Roto-360 [31]. At the same time, we are with the same models able to perform on par with or even outperform existing non-invariant methods on upright images on the competitive MegaDepth-1500 benchmark [33, 50]. In summary, our main contributions are as follows." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 503, + 287, + 598 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 48, + 503, + 287, + 539 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 503, + 287, + 539 + ], + "spans": [ + { + "bbox": [ + 48, + 503, + 287, + 539 + ], + "type": "text", + "content": "1. We introduce a new framework of steerers for equivariant keypoint descriptors (Section 4) and theoretically motivate why steerers emerge in practice (Section 5)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 540, + 287, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 287, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 287, + 574 + ], + "type": "text", + "content": "2. We develop several settings for investigating steers (Section 5.1) and ways to apply them for rotation invariant matching (Section 5.2)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 575, + 286, + 598 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 286, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 286, + 598 + ], + "type": "text", + "content": "3. We conduct a large set of experiments, culminating in state-of-the-art on AIMS and Roto-360 (Section 6)." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 609, + 132, + 621 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 132, + 621 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 132, + 621 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 287, + 713 + ], + "type": "text", + "content": "Classical keypoint descriptions are typically made rotation invariant by using keypoints with associated local rotation frames and computing the descriptions in these frames. Examples include SIFT [35], SURF [8], and ORB [45]. A canonical rotation frame can be used for patch-based neural network descriptors as well [53, 54]. Further, neural network-based approaches have been proposed for es" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 216 + ], + "type": "text", + "content": "timating the keypoint rotation frame [29, 30, 37] and for both computing the rotation frame and the descriptions in that frame [31, 61]. Notably, [30, 31] use rotation equivariant ConvNets [15, 56, 59]. Equivariant ConvNets have also been used for rotation-robust keypoint detection without estimating the rotation frame [2, 46], keypoint description [2, 34] and end-to-end image matching [9]. In theory1, equivariant ConvNets guarantee that the predictions are consistent when rotating the image. They are one example of hard-coding equivariance into network layers using mathematical group theory, an idea that goes back to the 1990's [58] and has seen large recent interest [11, 20, 22]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 217, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 384 + ], + "type": "text", + "content": "Neural networks can also be encouraged to learn equivariance rather than having it hard-coded in the layers. This can be done by enforcing group-specific invariants in the network output space [25, 48] (see also Section 5). Another approach is to specify a group representation on the output of the network and train the network to satisfy equivariance wrt. that representation [16, 28, 36, 60]. We will use this approach for keypoint descriptions in our Setting C. The benefits of not hard-coding equivariance are that arbitrary network architectures can be used (particularly pre-trained non-equivariant networks) and that one does not need to specify the group representations acting on each layer of the network. A special case of learning equivariance is rotation invariant descriptors through data augmentation [38, 52]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 385, + 545, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 385, + 545, + 493 + ], + "spans": [ + { + "bbox": [ + 304, + 385, + 545, + 493 + ], + "type": "text", + "content": "A recent line of work [10, 12, 24, 32] investigates to what extent neural networks exhibit equivariance without having been trained or hard-coded to do so. They find that many networks are approximately equivariant. One major limitation is that they only consider networks trained for image classification. We will empirically demonstrate a high level of equivariance in keypoint descriptors that were not explicitly trained to be equivariant and theoretically motivate why this happens (our Setting A)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 506, + 390, + 518 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 390, + 518 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 390, + 518 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "text", + "content": "In this work, we are interested in finding linear mappings between keypoint descriptions where the images may have been rotated independently. We will, in particular, consider the group of quarter rotations " + }, + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "text", + "content": " and the group of continuous rotations " + }, + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)" + }, + { + "bbox": [ + 304, + 528, + 545, + 588 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": "Ordinary typeset " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " will denote an arbitrary group element, boldface " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " will always mean the generator of " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " for the remainder of the text so that the elements of " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{g}^2" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{g}^3" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " and the identity element " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathrm{id} = \\mathbf{g}^4" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": ". Boldface " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{i}" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " will denote the imaginary unit such that " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\mathbf{i}^2 = -1" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": ". Given matrices " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "X_1, X_2, \\ldots, X_J" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": ", the notation " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "\\oplus_{j=1}^{J} X_j" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": " will mean the block-diagonal matrix with blocks " + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "inline_equation", + "content": "X_1, X_2, \\ldots, X_J" + }, + { + "bbox": [ + 304, + 589, + 545, + 673 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 683, + 545, + 713 + ], + "type": "text", + "content": "1It has been demonstrated that equivariant ConvNets can learn to break equivariance [18] when this benefits the task at hand. E.g., the end-to-end matcher SE2-LoFTR [9] is not perfectly consistent over rotations [9, 49]." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4886" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 238, + 85 + ], + "type": "text", + "content": "3.1. Preliminaries on keypoint matching" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 91, + 286, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 91, + 286, + 151 + ], + "spans": [ + { + "bbox": [ + 46, + 91, + 286, + 151 + ], + "type": "text", + "content": "The underlying task is to take two images of the same scene and detect 2D points that correspond to the same 3D point. A pair of such points that depict the same 3D point is called a correspondence. The approach for finding correspondences that will be explored is a three-stage approach:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 152, + 286, + 212 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 152, + 280, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 152, + 280, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 152, + 280, + 163 + ], + "type": "text", + "content": "1. Detection. Detect " + }, + { + "bbox": [ + 47, + 152, + 280, + 163 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 152, + 280, + 163 + ], + "type": "text", + "content": " keypoint locations in each image." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 164, + 286, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 164, + 286, + 187 + ], + "spans": [ + { + "bbox": [ + 47, + 164, + 286, + 187 + ], + "type": "text", + "content": "2. Description. Describe the keypoint locations with descriptors, i.e., feature vectors in " + }, + { + "bbox": [ + 47, + 164, + 286, + 187 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^D" + }, + { + "bbox": [ + 47, + 164, + 286, + 187 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 188, + 286, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 188, + 286, + 212 + ], + "spans": [ + { + "bbox": [ + 47, + 188, + 286, + 212 + ], + "type": "text", + "content": "3. Matching. Match the descriptors, typically by using mutual nearest neighbours in cosine distance." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "content": "This classical setup includes SIFT [35] but also more recent deep learning-based approaches. In particular, we follow the method in DeDoDe [19], where the keypoint detector is first optimized to find good point tracks from SfM reconstructions and the keypoint descriptor is optimized by maximizing the matching likelihood obtained by a frozen keypoint detector as follows. If the " + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "content": " descriptors (each normalized to unit length) in the two images are " + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "inline_equation", + "content": "y_{1} \\in \\mathbb{R}^{D \\times N}" + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "inline_equation", + "content": "y_{2} \\in \\mathbb{R}^{D \\times N}" + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "content": " we first form the " + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "content": " matching matrix " + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "inline_equation", + "content": "Y = y_{1}^{T}y_{2}" + }, + { + "bbox": [ + 46, + 213, + 286, + 345 + ], + "type": "text", + "content": ", and obtain a matrix of pairwise likelihoods by using the dual softmax [44, 50, 55]:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 61, + 356, + 287, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 356, + 287, + 384 + ], + "spans": [ + { + "bbox": [ + 61, + 356, + 287, + 384 + ], + "type": "interline_equation", + "content": "p \\left(y _ {1}, y _ {2}\\right) = \\frac {\\exp (\\iota Y)}{\\sum_ {\\text {c o l u m n s}} \\exp (\\iota Y)} \\cdot \\frac {\\exp (\\iota Y)}{\\sum_ {\\text {r o w s}} \\exp (\\iota Y)}. \\tag {1}", + "image_path": "3d5fccf01367933f96c3fbb0f822963cde6b6be572e57bb0e52f642e2f37b82e.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "type": "text", + "content": "Here " + }, + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "type": "inline_equation", + "content": "\\iota = 20" + }, + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "type": "text", + "content": " is the inverse temperature. The negative logarithm of the likelihood (1) is minimized for those pairs in the " + }, + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "type": "inline_equation", + "content": "N\\times N" + }, + { + "bbox": [ + 46, + 393, + 286, + 429 + ], + "type": "text", + "content": " matrix that correspond to ground truth inliers." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 441, + 252, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 252, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 252, + 453 + ], + "type": "text", + "content": "3.2. Preliminaries on group representations" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": "Definition 3.1. (Group representation) Given a group " + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": ", a representation of " + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^D" + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": " is a mapping " + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "inline_equation", + "content": "\\rho : G \\to \\mathrm{GL}(\\mathbb{R}, D)" + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": " that preserves the group multiplication, i.e., " + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "inline_equation", + "content": "\\rho(gg') = \\rho(g)\\rho(g')" + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": " for every " + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "inline_equation", + "content": "g, g' \\in G" + }, + { + "bbox": [ + 46, + 460, + 286, + 509 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "text", + "content": "Simply stated, " + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "text", + "content": " maps every element in the group to an invertible " + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "inline_equation", + "content": "D\\times D" + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "text", + "content": " matrix. The point of using representations is that groups such as " + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 46, + 520, + 286, + 567 + ], + "type": "text", + "content": " act differently on different quantities as we will illustrate in the following examples." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": "Example 3.1. For " + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{n\\times n}" + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": " (a square image grid), " + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": " can be represented by permutations of the pixels in the obvious way so that the image is rotated anticlockwise by multiples of " + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": ". We denote this group representation by " + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "inline_equation", + "content": "P_{90}" + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": " so that applying " + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "inline_equation", + "content": "P_{90}^{k}" + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": " rotates the image by " + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "inline_equation", + "content": "k\\cdot 90^{\\circ}" + }, + { + "bbox": [ + 46, + 578, + 286, + 639 + ], + "type": "text", + "content": " anticlockwise." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": "Example 3.2. For " + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^2" + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": " (image coordinates), one possible representation of " + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g}^k) = R_{90}^k = \\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)^k" + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": ". Multiplication by " + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "inline_equation", + "content": "R_{90}^k" + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": " corresponds to rotating image coordinates by " + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "inline_equation", + "content": "k \\cdot 90^\\circ" + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": " if the center of the image is taken as " + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "inline_equation", + "content": "(0,0)" + }, + { + "bbox": [ + 46, + 650, + 286, + 700 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 376, + 139 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 376, + 139 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 376, + 139 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 376, + 139 + ], + "type": "image", + "image_path": "10a662079dc70f77ddbf467c9da8a4de192d38afa0cf70f5726154224ecce7b2.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 306, + 154, + 376, + 223 + ], + "blocks": [ + { + "bbox": [ + 306, + 154, + 376, + 223 + ], + "lines": [ + { + "bbox": [ + 306, + 154, + 376, + 223 + ], + "spans": [ + { + "bbox": [ + 306, + 154, + 376, + 223 + ], + "type": "image", + "image_path": "18d6455e65d469d95a3a04b8df5b0e1bbb4e21698e6d35db90f1f4e76bbfaaaa.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 231, + 545, + 319 + ], + "lines": [ + { + "bbox": [ + 304, + 231, + 545, + 319 + ], + "spans": [ + { + "bbox": [ + 304, + 231, + 545, + 319 + ], + "type": "text", + "content": "Figure 3. Equivariance of Upright SIFT. Left: A keypoint with its Upright SIFT description in an upright image and a rotated version. The small yellow squares are the subregions where histograms of gradient orientations are computed. Right: The Upright SIFT descriptions unravelled into the 128 bin histograms that constitute them. When we rotate the image, the subregions are permuted, and the histogram bins within each subregion are further permuted cyclically. Hence, Upright SIFT is rotation equivariant." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 15 + }, + { + "type": "image", + "bbox": [ + 388, + 76, + 545, + 218 + ], + "blocks": [ + { + "bbox": [ + 388, + 76, + 545, + 218 + ], + "lines": [ + { + "bbox": [ + 388, + 76, + 545, + 218 + ], + "spans": [ + { + "bbox": [ + 388, + 76, + 545, + 218 + ], + "type": "image", + "image_path": "701ef7fa0a09cf869091b0a144f7348481b447f286bb088b63ed351579c7d81e.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 329, + 471, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 329, + 471, + 342 + ], + "spans": [ + { + "bbox": [ + 305, + 329, + 471, + 342 + ], + "type": "text", + "content": "4. Equivariance and steerability" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 349, + 545, + 385 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 349, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 304, + 349, + 545, + 385 + ], + "type": "text", + "content": "In this section, we will analyze the close connection between equivariance and steerability. We start with an example to introduce the former concept." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": "Example 4.1. SIFT descriptions [35] are " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "128\\mathrm{dim}" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": " vectors designed to be invariant to rotation, scale and illumination and highly distinctive for leveraging feature matching. For an input image " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "I \\in \\mathbb{R}^{n \\times n}" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": " keypoints with scale and orientation " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^{4 \\times N^2}" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": ", we get descriptions " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{128 \\times N}" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": " is the SIFT descriptor, we write " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "f(I, x) = y" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": ". The descriptions consist of histograms of image gradients over patches around the keypoints " + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 389, + 545, + 510 + ], + "type": "text", + "content": ". The patches are oriented by the keypoint orientations so that the descriptions are invariant to joint rotations of the image and keypoints:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 352, + 514, + 498, + 529 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 514, + 498, + 529 + ], + "spans": [ + { + "bbox": [ + 352, + 514, + 498, + 529 + ], + "type": "interline_equation", + "content": "f \\left(P _ {9 0} ^ {k} I, \\left(\\oplus_ {b = 1} ^ {2} R _ {9 0}\\right) ^ {k} x\\right) = f (I, x).", + "image_path": "c2b9160e3758608680c83e740d132c616142fa5689c1b56504719cc7d154a2f4.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "text", + "content": "If we discard the keypoint orientations, i.e., set the angle of each keypoint to 0, we get the Upright SIFT (UPSIFT) descriptor [1, 7], which is often used for upright images as it is more discriminative than SIFT. When we rotate an image " + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "text", + "content": ", then the gradient histograms, i.e., the UPSIFT descriptions are permuted by a specific permutation " + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}" + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "text", + "content": ", so if " + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 533, + 545, + 617 + ], + "type": "text", + "content": " is the UPSIFT descriptor, we have" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 337, + 622, + 512, + 637 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 337, + 622, + 512, + 637 + ], + "spans": [ + { + "bbox": [ + 337, + 622, + 512, + 637 + ], + "type": "interline_equation", + "content": "f \\left(P _ {9 0} ^ {k} I, \\left(\\oplus_ {b = 1} ^ {2} R _ {9 0}\\right) ^ {k} x\\right) = P _ {\\text {U P S I F T}} ^ {k} f (I, x).", + "image_path": "cd5dbcfa5d889c891644f06d81c4092bd904e4d2d23fe3b2fbb44f46da1b46a3.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "type": "text", + "content": "We illustrate the permutation " + }, + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}" + }, + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "type": "text", + "content": " in Figure 3. UPSIFT is not rotation invariant, but it is rotation equivariant when we rotate the input, the output changes predictably. Explicitly, the representation is " + }, + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g}^k) = P_{\\mathrm{UPSIFT}}^k" + }, + { + "bbox": [ + 304, + 641, + 545, + 691 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "text", + "content": "2The first two coordinates of each keypoint in " + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "text", + "content": " are its location and the last two a vector for its orientation and scale, so " + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "text", + "content": " is rotated by " + }, + { + "bbox": [ + 306, + 693, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\oplus_{b = 1}^{2}R_{90}" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 315, + 757 + ], + "type": "text", + "content": "4887" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": "Definition 4.1 (Equivariance). We say that a function " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "f: V \\to W" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " is equivariant with respect to a group " + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 72, + 287, + 96 + ], + "type": "text", + "content": " if" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 85, + 102, + 287, + 116 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 85, + 102, + 287, + 116 + ], + "spans": [ + { + "bbox": [ + 85, + 102, + 287, + 116 + ], + "type": "interline_equation", + "content": "\\rho (g) f (v) = f \\left(\\rho_ {\\text {i n}} (g) v\\right), \\forall v \\in V, g \\in G, \\tag {2}", + "image_path": "6713b45540b83e4bc3c6a8735463624fb53083b35c77d354c5ec46f968f1c665.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 121, + 200, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 121, + 200, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 121, + 200, + 133 + ], + "type": "text", + "content": "for some group representations " + }, + { + "bbox": [ + 47, + 121, + 200, + 133 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{in}},\\rho" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 137, + 287, + 174 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 137, + 287, + 174 + ], + "spans": [ + { + "bbox": [ + 47, + 137, + 287, + 174 + ], + "type": "text", + "content": "This work will mainly be concerned with the equivariance of learned keypoint descriptors of ordinary keypoints (without scale and orientation)." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "content": "Definition 4.2 (Equivalence of keypoint descriptor). We say that a keypoint descriptor " + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "content": " is equivariant with respect to a group " + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "content": " transforming the input image by " + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{image}}" + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "content": " and the input keypoint locations by " + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{keypoint}}" + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "content": " if there exists " + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 178, + 287, + 237 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 81, + 244, + 287, + 258 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 244, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 81, + 244, + 287, + 258 + ], + "type": "interline_equation", + "content": "\\rho (g) f (I, x) = f \\left(\\rho_ {\\text {i m a g e}} (g) I, \\rho_ {\\text {k e y p o i n t}} (g) x\\right) \\tag {3}", + "image_path": "86da9386c64c3f198b33147543eb9a0a34616c43c679256344b24d36bdad8098.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "spans": [ + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "type": "text", + "content": "for all images, keypoints and group elements. We call the descriptor invariant if " + }, + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "type": "inline_equation", + "content": "\\rho(g)" + }, + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "type": "text", + "content": " is the identity matrix for all " + }, + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 47, + 263, + 287, + 300 + ], + "type": "text", + "content": ". Invariance is a special type of equivariance." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "text", + "content": "Example 4.2. A keypoint descriptor " + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "text", + "content": " is equivariant under " + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "text", + "content": " rotations if there exists " + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 47, + 304, + 287, + 327 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 102, + 333, + 287, + 347 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 333, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 102, + 333, + 287, + 347 + ], + "type": "interline_equation", + "content": "\\rho \\left(\\mathbf {g} ^ {k}\\right) f (I, x) = f \\left(P _ {9 0} ^ {k} I, R _ {9 0} ^ {k} x\\right) \\tag {4}", + "image_path": "0c7878c9906ae8858f67f1241e688e659e979a8815f6762842adef1cea587a46.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "inline_equation", + "content": "k \\in \\{0,1,2,3\\}" + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "inline_equation", + "content": "P_{90}" + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "inline_equation", + "content": "R_{90}" + }, + { + "bbox": [ + 47, + 353, + 287, + 388 + ], + "type": "text", + "content": " are the representations from Examples 3.1 and 3.2 that rotate images and coordinates in the ordinary manner." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "text", + "content": "Both SIFT and Upright SIFT are equivariant. For SIFT, " + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g}^k)" + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "text", + "content": " is the identity, so SIFT is invariant. For Upright SIFT, " + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g}^k)" + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}^k" + }, + { + "bbox": [ + 47, + 388, + 287, + 426 + ], + "type": "text", + "content": " as explained in Example 4.1." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 430, + 287, + 477 + ], + "type": "text", + "content": "One aim of this work is to argue and demonstrate that learned keypoint descriptors, which are trained on upright data, will behave more like Upright SIFT than SIFT, i.e., they will be rotation equivariant but not invariant." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": "Definition 4.3 (Steerability, adapted from [21]). A real-valued function " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\phi : V \\to \\mathbb{R}" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " is said to be steerable under a representation " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{in}}" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": ", if there exist " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " functions (for some " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\phi_j : V \\to \\mathbb{R}" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " functions " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\kappa_j : G \\to \\mathbb{R}" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": " such that " + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "inline_equation", + "content": "\\phi(\\rho_{\\mathrm{in}}(g)v) = \\sum_{j=1}^{D} \\kappa_j(g)\\phi_j(v)" + }, + { + "bbox": [ + 47, + 482, + 287, + 545 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "content": "Note that an equivariant function " + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "f:V\\to \\mathbb{R}^{D}" + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "content": " satisfies in each component " + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "f_{d}" + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "content": " that " + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "f_{d}(\\rho_{\\mathrm{in}}(g)v) = \\sum_{j = 1}^{D}\\rho (g)_{dj}f_{j}(v)" + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "content": ", so each component of " + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "content": " is steerable, in the notation of Definition 4.3, " + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "inline_equation", + "content": "\\phi = f_d,\\phi_j = f_j,\\kappa_j(g) = \\rho (g)_{dj}" + }, + { + "bbox": [ + 47, + 550, + 287, + 612 + ], + "type": "text", + "content": ". This motivates the definition of a steerer." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": "Definition 4.4 (Steerer). Given a function " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "f: V \\to W" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " between vector spaces, and a representation " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{in}}" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": ", a steerer is a representation " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "W" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " that makes " + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 616, + 287, + 664 + ], + "type": "text", + "content": " equivariant, i.e. such that" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 117, + 671, + 287, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 117, + 671, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 117, + 671, + 287, + 685 + ], + "type": "interline_equation", + "content": "f \\left(\\rho_ {\\text {i n}} (g) v\\right) = \\rho (g) f (v). \\tag {5}", + "image_path": "3839968734d7c9328b4b217ed8abdc9cd7f2e219b29ec2d7e506251181b7a10c.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Even if (5) only holds approximately or " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " is only approximately a representation, we will refer to " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " as a steerer." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 96 + ], + "type": "text", + "content": "We will use the verb steer for multiplying a feature/description by a steerer; see Figure 2 for the broad idea." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "spans": [ + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": "Example 4.3. As explained in Example 4.1, " + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}" + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": " is a steerer for Upright SIFT under " + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": " rotations. This has practical consequences. If we want to obtain the Upright SIFT descriptions for an image " + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": " and the same image rotated " + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "inline_equation", + "content": "k \\cdot 90^{\\circ}" + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": ", we only need to compute the descriptions for the original image. We can obtain the rotated ones by multiplying the descriptions by " + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}^{k}" + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": ". That is, we can steer the Upright SIFT descriptions with " + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}" + }, + { + "bbox": [ + 305, + 101, + 545, + 197 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 202, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 202, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 202, + 545, + 285 + ], + "type": "text", + "content": "It is known from representation theory [47] what all possible representations of " + }, + { + "bbox": [ + 305, + 202, + 545, + 285 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 305, + 202, + 545, + 285 + ], + "type": "text", + "content": " are, and hence what all possible steerers for rotation equivariant descriptors are. As this result will be necessary for the remainder of the text, we collect it in a theorem. Similar results are also known for other groups e.g. the continuous rotation group SO(2), which we discuss in the next section." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": "Theorem 4.1 (Representations of " + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": "). Let " + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": " be a representation of " + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^D" + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": ". Then, there exists an invertible matrix " + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "inline_equation", + "content": "j_d \\in \\{0, 1, 2, 3\\}" + }, + { + "bbox": [ + 305, + 291, + 545, + 327 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 340, + 331, + 545, + 346 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 331, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 340, + 331, + 545, + 346 + ], + "type": "interline_equation", + "content": "\\rho \\left(\\mathbf {g} ^ {k}\\right) = Q ^ {- 1} \\operatorname {d i a g} \\left(\\mathbf {i} ^ {k j _ {1}}, \\mathbf {i} ^ {k j _ {2}}, \\dots , \\mathbf {i} ^ {k j _ {D}}\\right) Q. \\tag {6}", + "image_path": "a68ba7a95dec822a7175b8c9dd7f69ea4154c1db39796e0eb93afdb9aa0abb03.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 351, + 535, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 351, + 535, + 364 + ], + "spans": [ + { + "bbox": [ + 318, + 351, + 535, + 364 + ], + "type": "text", + "content": "The diagonal in (6) contains the eigenvalues of " + }, + { + "bbox": [ + 318, + 351, + 535, + 364 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g}^k)" + }, + { + "bbox": [ + 318, + 351, + 535, + 364 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "content": "Example 4.4. The Upright SIFT steuerer " + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "inline_equation", + "content": "P_{\\mathrm{UPSIFT}}" + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "content": " is diagonalizable with an equal amount of each eigenvalue " + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\pm 1" + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "inline_equation", + "content": "\\pm \\mathbf{i}" + }, + { + "bbox": [ + 305, + 368, + 545, + 392 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "spans": [ + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": "The complex eigenvalues must appear in conjugate pairs as we take " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " to be real-valued. It is then possible to do a change of basis so that each pair " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\mathbf{i}, -\\mathbf{i}" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " on the diagonal in (6) is replaced by a block " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": ". In this way, " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " can always be block-diagonalized: " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g}) = Q^{-1}BQ" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " are real valued and " + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 305, + 397, + 545, + 480 + ], + "type": "text", + "content": " is block-diagonal with blocks of sizes 1 and 2." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 487, + 473, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 473, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 473, + 500 + ], + "type": "text", + "content": "4.1. Representation theory of SO(2)" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": "SO(2) is a one-parameter Lie group, i.e. a continuous group with one degree of freedom " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " the rotation angle. A " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": "-dimensional representation of SO(2) is a map " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\varsigma : [0, 2\\pi) \\to \\mathrm{GL}(\\mathbb{R}, D)" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " such that addition modulo " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "2\\pi" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " on the input is encoded as matrix multiplication on the output—we will consistently use " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\varsigma" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " for SO(2) representations to separate them from " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " representations " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " will also be used for representations of general groups). The most familiar is the two-dimensional representation " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\varsigma(\\alpha) = \\begin{pmatrix} \\cos(\\alpha) & -\\sin(\\alpha) \\\\ \\sin(\\alpha) & \\cos(\\alpha) \\end{pmatrix}" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " which rotates 2D coordinates. Similar to the " + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 305, + 505, + 545, + 654 + ], + "type": "text", + "content": " case in Theorem 4.1, we can write down a general representation for SO(2) as follows [57]." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "spans": [ + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": "Theorem 4.2 (Representations of " + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)" + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": "). Let " + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\varsigma" + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": " be a representation of " + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)" + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^D" + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": ". Then there exists an invertible " + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "inline_equation", + "content": "j_d \\in \\mathbb{Z}" + }, + { + "bbox": [ + 305, + 659, + 545, + 694 + ], + "type": "text", + "content": " such that" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 333, + 700, + 545, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 700, + 545, + 715 + ], + "spans": [ + { + "bbox": [ + 333, + 700, + 545, + 715 + ], + "type": "interline_equation", + "content": "\\varsigma (\\alpha) = Q ^ {- 1} \\operatorname {d i a g} \\left(\\mathrm {e} ^ {\\mathbf {i} j _ {1} \\alpha}, \\mathrm {e} ^ {\\mathbf {i} j _ {2} \\alpha}, \\dots , \\mathrm {e} ^ {\\mathbf {i} j _ {D} \\alpha}\\right) Q. \\tag {7}", + "image_path": "dffcdd7e66c540be08f94e6157cd4ea7f7e89a8c3e04dd74ef469fe21ad64114.jpg" + } + ] + } + ], + "index": 28 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4888" + } + ] + } + ], + "index": 29 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": "The " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "j_{d}" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": "'s are the frequencies of the eigenspaces of " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "\\varsigma" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": ". Complex eigenvalues appear in conjugate pairs so (7) can be rewritten as a block diagonal decomposition " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "\\varsigma(\\alpha) = Q^{-1}BQ" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " are real valued and " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " is block-diagonal with minimal blocks. The admissible blocks (= real-valued irreducible representations) in " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " are then the " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "1 \\times 1" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " block (1) and the " + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "inline_equation", + "content": "2 \\times 2" + }, + { + "bbox": [ + 47, + 72, + 289, + 157 + ], + "type": "text", + "content": " blocks" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 80, + 166, + 287, + 192 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 166, + 287, + 192 + ], + "spans": [ + { + "bbox": [ + 80, + 166, + 287, + 192 + ], + "type": "interline_equation", + "content": "\\left( \\begin{array}{c c} \\cos (j \\alpha) & - \\sin (j \\alpha) \\\\ \\sin (j \\alpha) & \\cos (j \\alpha) \\end{array} \\right) \\quad \\text {f o r} j \\in \\mathbb {Z} \\backslash \\{0 \\}. \\tag {8}", + "image_path": "5d8777b7ffef1649b61decaf4e3c1e6e952ced3b4b71e1a800e05a07e134b8ec.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "spans": [ + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": "We can write " + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\varsigma (\\alpha) = \\exp \\left(\\alpha Q^{-1}\\mathrm{diag}(\\mathbf{i}j_1,\\ldots ,\\mathbf{i}j_D)Q\\right)" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{expm}" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": " is the matrix exponential. The quantity " + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma \\coloneqq" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "Q^{-1}\\mathrm{diag}(\\mathbf{i}j_1,\\dots ,\\mathbf{i}j_D)Q" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": " is called a Lie algebra representation of SO(2), here in its most general form. When training a steerer for SO(2) it is practical to train a " + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "D\\times D" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": " matrix " + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": " and steer using " + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "inline_equation", + "content": "\\varsigma (\\alpha) = \\exp \\mathrm{m}(\\alpha \\mathrm{d}\\varsigma)" + }, + { + "bbox": [ + 47, + 201, + 287, + 275 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 281, + 218, + 294 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 281, + 218, + 294 + ], + "spans": [ + { + "bbox": [ + 47, + 281, + 218, + 294 + ], + "type": "text", + "content": "4.2. Disentangling description space" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "type": "text", + "content": "When we have a steerer, we get a description space on which rotations act—up to a change of basis—by a block-diagonal matrix " + }, + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "type": "inline_equation", + "content": "\\oplus_{j=1}^{J} B_{j}" + }, + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "type": "text", + "content": ". The description space can then be thought of as being disentangled into different subspaces where rotations act in different ways " + }, + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "type": "inline_equation", + "content": "B_{j}" + }, + { + "bbox": [ + 47, + 300, + 287, + 373 + ], + "type": "text", + "content": " [14, 60]. We detail what this means for keypoint descriptors in Appendix A." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 382, + 187, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 187, + 396 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 187, + 396 + ], + "type": "text", + "content": "5. Descriptors and steerers" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 402, + 287, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 475 + ], + "type": "text", + "content": "This work's crucial observation and assumption is that learned descriptors, while not invariant, are approximately equivariant so that they have a steerer. Or, as a weaker assumption, they can be trained to be equivariant. It may seem that this is a strong assumption. However, a seemingly less strong assumption turns out to be equivalent." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "content": "Theorem 5.1. [Adapted from Shakerinava et al. [48], Gupta et al. [25]] Assume that we have a function " + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "inline_equation", + "content": "f: V \\to \\mathbb{S}^{D-1}" + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "content": " and a group " + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "content": " with representation " + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{in}}" + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "content": " on " + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "content": " such that, for all " + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "inline_equation", + "content": "v, v' \\in V" + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 481, + 287, + 531 + ], + "type": "inline_equation", + "content": "g \\in G" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 82, + 539, + 287, + 554 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 82, + 539, + 287, + 554 + ], + "spans": [ + { + "bbox": [ + 82, + 539, + 287, + 554 + ], + "type": "interline_equation", + "content": "\\langle f \\left(\\rho_ {\\text {i n}} (g) v\\right), f \\left(\\rho_ {\\text {i n}} (g) v ^ {\\prime}\\right) \\rangle = \\langle f (v), f \\left(v ^ {\\prime}\\right) \\rangle . \\tag {9}", + "image_path": "ced8ae80c30a431489bb71761c7638d3a9b7af62b94f28ae1e24dc165de792cc.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "spans": [ + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "content": "Then there exists an orthogonal representation " + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\rho(g)" + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "content": " is equivariant w.r.t. " + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "inline_equation", + "content": "G" + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "content": " with representations " + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\rho_{\\mathrm{in}}" + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 47, + 561, + 287, + 588 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": "We provide a proof in Appendix A. Since we match normalized keypoint descriptions by their cosine similarity, Theorem 5.1 is highly applicable to the image matching problem. If a keypoint descriptor " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " is perfectly consistent in the matching scores when simultaneously rotating the images, then the scalar products in (9) will be equal so that the theorem tells us that " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " has a steerer " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\rho" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": ". Furthermore, we can expect many local image features to appear in all orientations even over a dataset of upright images, thus encouraging (9) to hold for " + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 46, + 594, + 288, + 715 + ], + "type": "text", + "content": " trained on large datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 72, + 512, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 512, + 85 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 512, + 85 + ], + "type": "text", + "content": "5.1. Three settings for investigating steerers" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": "As " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": " is cyclic, all its representations are defined by " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "\\mathbf{g}" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": " is the generator of " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": ". To find a steerer for a keypoint descriptor under " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": " hence comes down to finding a single matrix " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": " that represents rotations by " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "90^\\circ" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": " in the description space. Similarly, for SO(2) we find the single matrix " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": " that defines the representation " + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "inline_equation", + "content": "\\varsigma" + }, + { + "bbox": [ + 304, + 90, + 545, + 162 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "type": "text", + "content": "We will consider three settings. In each case we will optimize " + }, + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g})" + }, + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "type": "text", + "content": " and/or " + }, + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 304, + 162, + 545, + 198 + ], + "type": "text", + "content": " over the MegaDepth training set [33] with rotation augmentation and maximize" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 321, + 205, + 545, + 225 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 205, + 545, + 225 + ], + "spans": [ + { + "bbox": [ + 321, + 205, + 545, + 225 + ], + "type": "interline_equation", + "content": "p \\left(f \\left(P _ {9 0} ^ {k _ {1}} I _ {1}, R _ {9 0} ^ {k _ {1}} x _ {1}\\right), \\rho (\\mathbf {g}) ^ {k} f \\left(P _ {9 0} ^ {k _ {2}} I _ {2}, R _ {9 0} ^ {k _ {2}} x _ {2}\\right)\\right) \\tag {10}", + "image_path": "559ecd8fd0500ecb43863d3ed4aaf49a3ed897d542fd4292137168e9e9e19bc8.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " is the matching probability (1). The number of rotations " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "k_{1}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "k_{2}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " for each image are sampled independently during training, and " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "k = k_{1} - k_{2} \\mod 4" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " is the number of rotations that aligns image " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "I_{2}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " to image " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": ". Thus, " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})^{k}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " aligns the relative rotation between descriptions in " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "I_{2}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": ". We optimize continuous steerers " + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "inline_equation", + "content": "\\varsigma" + }, + { + "bbox": [ + 304, + 231, + 545, + 303 + ], + "type": "text", + "content": " analogously to (10)." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "text", + "content": "Setting A: Fixed descriptor, optimized steerer. If a descriptor works equally well for upright images as well as images rotated the same amount from upright, then according to Theorem 5.1, we should expect that there exists a steerer " + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g})" + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "text", + "content": " such that (4) holds. To find " + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g})" + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "text", + "content": " we optimize it as a single " + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "inline_equation", + "content": "D\\times D" + }, + { + "bbox": [ + 304, + 304, + 545, + 376 + ], + "type": "text", + "content": " linear layer by maximizing (10)." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 376, + 541, + 387 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 541, + 387 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 541, + 387 + ], + "type": "text", + "content": "Setting B: Joint optimization of descriptor and steerer." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "spans": [ + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "content": "The aim is to find a steerer that is as good as possible for the given data. We will see in the experiments, by looking at the evolution of the eigenvalues of " + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "content": " during training, that this joint optimization has many local optima and is highly dependent on the initialization of " + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "content": ". However, looking at the eigenvalues of " + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 304, + 388, + 545, + 483 + ], + "type": "text", + "content": " does give knowledge about which descriptor dimensions are most important, as will be explained in Section 6.5." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 483, + 545, + 591 + ], + "type": "text", + "content": "Setting C: Fixed steerer, optimized descriptor. To get the most precise control over the rotation behaviour of a descriptor, we can fix the steerer and optimize only the descriptor. This enables us to investigate how much influence the choice of steerer has on the descriptor. For instance, choosing the steerer as the identity leads to a rotation invariant descriptor. We will see in the experiments that this choice leads to suboptimal performance on upright images compared to other steers." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 599, + 512, + 613 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 512, + 613 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 512, + 613 + ], + "type": "text", + "content": "5.2. Matching with equivariant descriptions" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "This section presents several approaches to rotation invariant matching using equivariant descriptors. Throughout, we will denote the " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "-dimensional descriptions of " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " keypoints in two images " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "I_1, I_2" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "y_1, y_2 \\in \\mathbb{R}^{D \\times N}" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " and will assume that we know the " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": "-steerer " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " that rotates descriptions " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "90^\\circ" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " or the SO(2)-steerer " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\varsigma(\\alpha)" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": " through the Lie algebra generator " + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 304, + 618, + 545, + 713 + ], + "type": "text", + "content": ". For matching we follow DeDoDe [19], as described in Section 3.1. The base similarity used is the cosine" + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4889" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 138, + 288, + 255 + ], + "blocks": [ + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "lines": [ + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "spans": [ + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "type": "text", + "content": "Table 1. Evaluation on Roto-360 [31]. We report the percentage of correct matches at three thresholds. We use the DeDoDe-SO2 detector with 5,000 keypoints in the last two rows. Matching strategies are Max Matches for the " + }, + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "type": "text", + "content": "-descriptor and Max Sim. over " + }, + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "type": "inline_equation", + "content": "C_8" + }, + { + "bbox": [ + 46, + 63, + 288, + 128 + ], + "type": "text", + "content": " for the SO(2)-descriptor. See Section 6.1 for the shorthands for our models." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 138, + 288, + 255 + ], + "lines": [ + { + "bbox": [ + 47, + 138, + 288, + 255 + ], + "spans": [ + { + "bbox": [ + 47, + 138, + 288, + 255 + ], + "type": "table", + "html": "
DetectorDescriptor3px5px10px
SIFT [35]SIFT [35]787879
ORB [45]ORB [45]798587
SuperPoint [17]RELF, single [31]909193
SuperPoint [17]RELF, multiple [31]929394
SuperPoint [17]C4-B (ours)828283
SuperPoint [17]SO2-Spread-B (ours)969797
DeDoDe [19]C4-B (ours)828486
DeDoDe [19]SO2-Spread-B (ours)959798
", + "image_path": "9b029575b1d80e46ff98ea59d1e11fa9a79522e63a5a5410c61a3cc7afe13a4b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "type": "text", + "content": "similarity, so we compute " + }, + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "y_1^T y_2" + }, + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "type": "text", + "content": " for normalized descriptions to get an " + }, + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "type": "inline_equation", + "content": "N \\times N" + }, + { + "bbox": [ + 46, + 277, + 287, + 326 + ], + "type": "text", + "content": " matrix of pairwise scores on which dual softmax (1) is applied. Matches are mutual most similar descriptions with similarity above 0.01." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": "Max matches over steered descriptions. The first way of obtaining invariant matches is to match " + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "inline_equation", + "content": "y_{1}" + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})^{k}y_{2}" + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "inline_equation", + "content": "k = 0,1,2,3" + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": " and keep the matches from the " + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": " that has the most matches. This is similar to matching the image " + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "inline_equation", + "content": "I_{1}" + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": " with four different rotations of " + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "inline_equation", + "content": "I_{2}" + }, + { + "bbox": [ + 46, + 331, + 287, + 402 + ], + "type": "text", + "content": " but alleviates the need for rerunning the descriptor network for each rotation." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "type": "text", + "content": "Max similarity over steered descriptions. A computationally cheaper version is to select the matching matrix not as " + }, + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "type": "inline_equation", + "content": "y_1^T y_2" + }, + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "type": "text", + "content": " but as " + }, + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "type": "inline_equation", + "content": "\\max_k y_1^T \\rho(\\mathbf{g})^k y_2" + }, + { + "bbox": [ + 46, + 402, + 287, + 449 + ], + "type": "text", + "content": ", where the max is elementwise over the matrix." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "spans": [ + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": "SO(2)-steerers. To apply the above matching strategies to SO(2)-steerers " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\varsigma (\\alpha) = \\exp (\\alpha \\mathrm{d}\\varsigma)" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": " we discretize " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\varsigma" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": ". A " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "C_\\ell" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": "-steerer is obtained through " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\rho (\\mathbf{g}_\\ell) = \\exp \\left(\\frac{2\\pi}{\\ell}\\mathrm{d}\\varsigma\\right)" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "\\mathbf{g}_{\\ell}" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": " generates " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "C_\\ell" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": ". We will use " + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "inline_equation", + "content": "C_8" + }, + { + "bbox": [ + 46, + 450, + 287, + 498 + ], + "type": "text", + "content": " in the experiments." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": "Procrustes matcher. If all eigenvalues of " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\pm \\mathrm{i}" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": ", the steuer can be block-diagonalized with only the block " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\left( \\begin{array}{cc}0 & -1\\\\ 1 & 0 \\end{array} \\right)^3" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": ". The descriptions consist of " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "D/2" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": " two-dimensional quantities that all rotate with the same frequency as the image. We will refer to them as frequency 1 descriptions and view them reshaped as " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "y \\in \\mathbb{R}^{2 \\times (D/2) \\times N}" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": ". A 2D rotation matrix acts on these descriptions from the left when the image rotates, and we can find the optimal rotation matrix " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "R_{m,n}" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": " that aligns each pair " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "y_{1,m}, y_{2,n} \\in \\mathbb{R}^{2 \\times (D/2)}" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": " by solving the Procrustes problem via SVD. The matching matrix is obtained by computing " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "\\langle R_{m,n}y_{1,m}, y_{2,n} \\rangle" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": " for each pair. " + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "inline_equation", + "content": "R_{m,n}" + }, + { + "bbox": [ + 46, + 498, + 287, + 677 + ], + "type": "text", + "content": " gives the relative rotation between each pair of keypoints, which can be useful e.g. for minimal relative pose solvers [4, 6] or for outlier filtering [13]. We leave exploring this per-correspondence geometry to future work." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 308, + 138, + 542, + 207 + ], + "blocks": [ + { + "bbox": [ + 306, + 63, + 545, + 129 + ], + "lines": [ + { + "bbox": [ + 306, + 63, + 545, + 129 + ], + "spans": [ + { + "bbox": [ + 306, + 63, + 545, + 129 + ], + "type": "text", + "content": "Table 2. Evaluation on AIMS [49]. We report the average precision (AP) in percent on different splits of AIMS: \"North Up\" (N. Up) contains images with small rotations, \"All Others\" (A. O.) contains images with larger rotations and \"All\" contains all images. We use the DeDoDe-SO2 detector and 10,000 keypoints throughout. See Section 6.1 for the shorthands for our models." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 138, + 542, + 207 + ], + "lines": [ + { + "bbox": [ + 308, + 138, + 542, + 207 + ], + "spans": [ + { + "bbox": [ + 308, + 138, + 542, + 207 + ], + "type": "table", + "html": "
MethodN. UpA. O.All
SE2-LoFTR [9]585152
C4-B, Max Matches (ours)525151
SO2-Spread-B, Max Sim. C8 (ours)605758
SO2-Freq1-B, Procrustes (ours)645960
", + "image_path": "a1f3ae7badf389a6b5955e85bb8af8805ba6de045f6aabc114b306bc87bc80f5.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 224, + 387, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 224, + 387, + 239 + ], + "spans": [ + { + "bbox": [ + 306, + 224, + 387, + 239 + ], + "type": "text", + "content": "6. Experiments" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 245, + 545, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 245, + 545, + 316 + ], + "spans": [ + { + "bbox": [ + 304, + 245, + 545, + 316 + ], + "type": "text", + "content": "We train and evaluate a variety of descriptors and steerers. Experimental details are covered in Appendix C. We provide comparisons to TTA in performance and runtime in Appendix B, as well as experiments with more matching strategies and an explicit experiment to test the connection between Theorem 5.1 and rotation equivariance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 317, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 317, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 304, + 317, + 545, + 376 + ], + "type": "text", + "content": "We start by reporting results on two public benchmarks for rotation invariant image matching. Then, we will present ablation results for the MegaDepth benchmark, both for the standard version with upright images and a version where we have rotated the input images." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 384, + 416, + 396 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 384, + 416, + 396 + ], + "spans": [ + { + "bbox": [ + 306, + 384, + 416, + 396 + ], + "type": "text", + "content": "6.1. Models considered" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "type": "text", + "content": "Our base models are the DeDoDe-B and DeDoDe-G descriptors introduced in [19]. These are both " + }, + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "type": "inline_equation", + "content": "D = 256" + }, + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "type": "text", + "content": " dimensional descriptors. The focus will be on the smaller model DeDoDe-B, as this gives us the chance to do large-scale ablations. We train all models on MegaDepth [33]. To obtain rotation-consistent detections, we retrain two versions of the DeDoDe-detector, with data augmentation over " + }, + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 402, + 545, + 498 + ], + "type": "text", + "content": " and SO(2) respectively, denoted DeDoDe-{C4, SO2}." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "For Setting B (Section 5.1), we will see that the initialization of the steerer matters. Similarly, for Setting C, we can fix the steerer with different eigenvalue structures. Here, we introduce shorthand, which is used in the result tables. We will refer to the case of all eigenvalues 1 as " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Inv" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " for invariant. This case corresponds to the ordinary notion of data augmentation, where the descriptions for rotated images should be the same as for non-rotated images. The case when all eigenvalues are " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pm \\mathbf{i}" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " is denoted " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Freq1" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " for frequency 1 as explained in Section 5.2. For " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "-steers, the case with an equal distribution of all eigenvalues " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\pm 1, \\pm \\mathbf{i}" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " will be denoted " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Perm" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": ", as this is the eigenvalue signature of a cyclic permutation of order 4. For SO(2)-steers, the case with an equal distribution of eigenvalues " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "0, \\pm \\mathbf{i}, \\pm 2\\mathbf{i}, \\ldots \\pm 6\\mathbf{i}" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " will be denoted " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Spread" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " (the cutoff 6 was arbitrarily chosen). The " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Perm" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Spread" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " steers correspond to a broad range of frequencies in the description space. When none of the above labels (" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Inv" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Freq1" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "Perm" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " or" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "type": "text", + "content": "This also holds for " + }, + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)" + }, + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "type": "text", + "content": " steers, referring to eigenvalues and blocks of the Lie algebra generator " + }, + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 46, + 692, + 287, + 713 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4890" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 59, + 127, + 533, + 338 + ], + "blocks": [ + { + "bbox": [ + 46, + 63, + 547, + 120 + ], + "lines": [ + { + "bbox": [ + 46, + 63, + 547, + 120 + ], + "spans": [ + { + "bbox": [ + 46, + 63, + 547, + 120 + ], + "type": "text", + "content": "Table 3. Evaluation on MegaDepth [33, 50]. The first section shows Setting A where we only optimize the steerer, the second section shows Setting B where we jointly optimize the descriptor and steerer and the third section shows the Setting C where we predefine the steerer and optimize only the descriptor. For MegaDepth-1500 we always use dual softmax matcher to evaluate the descriptors on upright images. We use 20,000 keypoints throughout. The best values for B- and G-models are highlighted in each column. See Section 6.1 for shorthand explanations for our models. A larger version of this table with more methods is available in Appendix B." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 127, + 533, + 338 + ], + "lines": [ + { + "bbox": [ + 59, + 127, + 533, + 338 + ], + "spans": [ + { + "bbox": [ + 59, + 127, + 533, + 338 + ], + "type": "table", + "html": "
DetectorDescriptorMatching strategyMegaDepth-1500MegaDepth-C4MegaDepth-SO2
DeDoDeAUC @ 5°10°20°5°10°20°5°10°20°
OriginalBDual softmax496577121720121620
OriginalBMax matches C4-steered-11--11--11-436073304456
SO2BMax matches C8-steered506678405770345165
OriginalGDual softmax526981131721162228
OriginalGMax matches C4-steered-11--11--11-314557263950
C4C4-BMax matches C4-steered516779506779395568
SO2SO2-BMax matches C8-steered476376476376446174
SO2SO2-Spread-BMax matches C8-steered506679496678466376
SO2SO2-Spread-BMax similarity C8-steered496678476477436174
C4C4-Inv-BDual softmax486476476376395569
C4C4-Perm-BMax matches C4-steered506779506679395467
SO2SO2-Inv-BDual softmax466275456174436073
SO2SO2-Freq1-BMax matches C8-steered476477476476456275
SO2SO2-Freq1-BProcrustes476476466275456174
C4C4-Perm-GMax matches C4-steered526981536982446174
", + "image_path": "24afd456a089ac9ffb093fd785178f531455f6390e96e6f3a5d16be4b461acba.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "spans": [ + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "content": "Spread) is attached to a descriptor and steerer trained jointly in Setting B, then we initialize the steerer with values uniformly in " + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "inline_equation", + "content": "(-D^{-1/2}, D^{-1/2})^4" + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "content": ", the eigenvalues are then approximately uniformly distributed in the disk with radius " + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "inline_equation", + "content": "3^{-1/2}" + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "content": " [51]. When a descriptor is trained with " + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "inline_equation", + "content": "k \\cdot 90^\\circ" + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "content": " rotations, we append " + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "inline_equation", + "content": "C4" + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "content": " to its name and when trained with continuous augmentations, we append " + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "inline_equation", + "content": "SO2" + }, + { + "bbox": [ + 46, + 357, + 288, + 441 + ], + "type": "text", + "content": " to its name." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 449, + 113, + 460 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 113, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 113, + 460 + ], + "type": "text", + "content": "6.2. Roto-360" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "content": "We evaluate on the Roto-360 benchmark [31], which consists of ten image pairs from HPatches [3] where the second image in each image pair is rotated by all multiples of " + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "inline_equation", + "content": "10^{\\circ}" + }, + { + "bbox": [ + 46, + 467, + 287, + 575 + ], + "type": "text", + "content": " to obtain 360 image pairs in total. We report the average precision of the obtained matches and compare it to the current state-of-the-art RELF [31]. The results are shown in Table 1. We see that we outperform RELF when using methods trained for continuous rotations. Our matching runs around three times faster than RELF on Roto-360." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 582, + 99, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 582, + 99, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 582, + 99, + 594 + ], + "type": "text", + "content": "6.3.AIMS" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 601, + 288, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 601, + 288, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 601, + 288, + 696 + ], + "type": "text", + "content": "The Astronaut Image Matching Subset (AIMS) [49] consists of images taken by astronauts from the ISS and satellite images covering the broad regions that the astronaut images could depict. The task consists of finding the pairs of astronaut images and satellite images that show the same locations on Earth. Pairs are found by setting a threshold for the number of matches between images after homography estimation with RANSAC." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "spans": [ + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "type": "text", + "content": "The relative rotations of the astronaut and satellite images are unknown, making the task suitable for rotation-invariant matchers. Indeed, in [49], the best performing method is the rotation invariant SE2-LoFTR [9], which we compare to. The AIMS can be split into \"North Up\" astronaut images, consisting of images with small rotations (between " + }, + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "type": "inline_equation", + "content": "0^{\\circ}" + }, + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "type": "inline_equation", + "content": "90^{\\circ}" + }, + { + "bbox": [ + 306, + 357, + 547, + 537 + ], + "type": "text", + "content": ") and \"All Others\", consisting of images with large rotations. This split further enables the evaluation of rotation invariant matchers. We report the average precision over the whole dataset, as opposed to the approach in [49], where the score is computed over at most 100 true negatives per astronaut image. Results are shown in Table 2. Further, we plot precision-recall curves in Appendix B. We generally outperform SE2-LoFTR, particularly on the heavily rotated images in \"All Others\"." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 549, + 410, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 549, + 410, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 549, + 410, + 562 + ], + "type": "text", + "content": "6.4. MegaDepth-1500" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "text", + "content": "We evaluate on a held-out part of MegaDepth (MegaDepth-1500 following [50]). Here, the task is to take two input images and output the relative pose between the cameras. The performance is measured by the AUC of the pose error. Additionally, we create two versions of MegaDepth with rotated images to evaluate the rotational robustness of our models. For MegaDepth-C4, the second image in every image pair is rotated (" + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "i \\mod 4" + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "text", + "content": ") " + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\cdot 90^{\\circ}" + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 570, + 547, + 715 + ], + "type": "text", + "content": " is the index of the image pair. We visualize a pair in MegaDepth-C4 in Appendix B, illustrating the improvement from DeDoDe-B to DeDoDe-B with a steerer optimized in Setting A. For MegaDepth-SO2, the second image in every image pair is" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 286, + 714 + ], + "type": "text", + "content": "This is the standard initialization of a linear layer in Pytorch [26, 40]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "4891" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 72, + 284, + 173 + ], + "blocks": [ + { + "bbox": [ + 53, + 72, + 284, + 173 + ], + "lines": [ + { + "bbox": [ + 53, + 72, + 284, + 173 + ], + "spans": [ + { + "bbox": [ + 53, + 72, + 284, + 173 + ], + "type": "image", + "image_path": "a1ec4834300c2564d345386d24d9c7689659dd06493c761622e795ff405be885.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "text", + "content": "Figure 4. Training evolution of eigenvalue distributions of steers. We plot the eigenvalue distribution of " + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "text", + "content": "-steerers " + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "text", + "content": " (first three columns) and Lie algebra generators " + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "text", + "content": " for SO(2)-steerers (last two columns) in the complex plane, with different initializations when trained jointly with a descriptor. The top row depicts the eigenvalues at the start, and the bottom row at the end of training. There are " + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "inline_equation", + "content": "D = 256" + }, + { + "bbox": [ + 46, + 186, + 289, + 307 + ], + "type": "text", + "content": " eigenvalues in every plot—many congregate at the \"admissible\" eigenvalues as described in Section 4—but some do not, see the discussion in Section 6.5. These visualizations highlight the initialization sensitivity of the steerer. We show gif movies of the training evolution at this https url." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 322, + 287, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 322, + 287, + 346 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 287, + 346 + ], + "type": "text", + "content": "instead rotated (" + }, + { + "bbox": [ + 46, + 322, + 287, + 346 + ], + "type": "inline_equation", + "content": "i \\mod 36) \\cdot 10^{\\circ}" + }, + { + "bbox": [ + 46, + 322, + 287, + 346 + ], + "type": "text", + "content": ", thus requiring robustness under continuous rotations." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 347, + 287, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 287, + 371 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 287, + 371 + ], + "type": "text", + "content": "The results are presented in Table 3; for more methods, see Appendix B. We summarize the main takeaways:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 372, + 287, + 563 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 372, + 287, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 287, + 408 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 287, + 408 + ], + "type": "text", + "content": "1. It is possible to find steers for the original DeDoDe models (e.g. the second row of the table), even though they were not trained with any rotation augmentation." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 408, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 408, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 408, + 287, + 432 + ], + "type": "text", + "content": "2. The trained " + }, + { + "bbox": [ + 47, + 408, + 287, + 432 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 47, + 408, + 287, + 432 + ], + "type": "text", + "content": " steers perform very well as their scores on MegaDepth-1500 and MegaDepth-C4 are the same." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 432, + 287, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 432, + 287, + 480 + ], + "spans": [ + { + "bbox": [ + 47, + 432, + 287, + 480 + ], + "type": "text", + "content": "3. Training DeDoDe-B jointly with a " + }, + { + "bbox": [ + 47, + 432, + 287, + 480 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 47, + 432, + 287, + 480 + ], + "type": "text", + "content": " steerer (C4-B) or with a fixed steerer (C4-Perm-B) improves results on upright images—this can be attributed to the fact that training with a steerer enables using rotation augmentation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 480, + 287, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 480, + 287, + 504 + ], + "spans": [ + { + "bbox": [ + 47, + 480, + 287, + 504 + ], + "type": "text", + "content": "4. The right equivariance for the task at hand is crucial—SO(2)-steerers outperform others on MegaDepth-SO2." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 504, + 287, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 504, + 287, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 504, + 287, + 540 + ], + "type": "text", + "content": "5. The eigenvalue distribution of the steerer is important-- invariant models are worse than others, and SO2-B and SO2-Freq1-B are worse than SO2-Spread-B." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 540, + 287, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 540, + 287, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 540, + 287, + 563 + ], + "type": "text", + "content": "6. DeDoDe-G can be made equivariant (C4-Perm-G), even though it has a frozen DINoV2 [39] ViT backbone." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 574, + 261, + 587 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 261, + 587 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 261, + 587 + ], + "type": "text", + "content": "6.5. Training dynamics of steerer eigenvalues" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "This section aims to demonstrate that joint optimization of the steerer and descriptor does not necessarily lead to a good eigenvalue structure for the steerer. We plot the evolution of the eigenvalues of the steerer over the training epochs in Figure 4. For " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "C_4" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "-steerers we plot the eigenvalues of " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\rho(\\mathbf{g})" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " itself, while for " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{SO}(2)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": "-steerers we plot the eigenvalues " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\lambda_d" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " of the Lie algebra generator " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ", so that the eigenvalues of the steerer " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\varsigma(\\alpha)" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathrm{e}^{\\alpha \\lambda_d}" + }, + { + "bbox": [ + 46, + 594, + 289, + 715 + ], + "type": "text", + "content": ". It is clear from Figure 4 that the initialization of the steerer influences the final distribution of eigenvalues a lot and we saw in Table 3 that the eigenvalue" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "distribution of the steerer matters for performance. Thus, we think it is an important direction for future work to figure out how to get around this initialization sensitivity. The choice of eigenvalue structure is related to the problem of specifying which group representations to use in the layers of equivariant neural networks in general." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 144, + 546, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 546, + 324 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 546, + 324 + ], + "type": "text", + "content": "As a side effect of plotting the eigenvalues, we find that some of the steerer's eigenvalues have much lower absolute values than others. The steerer is applied to descriptions before they are normalized, so the absolute value of the maximum eigenvalue is unimportant, but the relative size of the eigenvalues tells us something about feature importance. Eigenvectors with small eigenvalues cannot be too important for matching, since they will be relatively down-scaled when applying the steerer in the optimization of (10). Indeed, small eigenvalues seem to correspond to unimportant dimensions of the descriptor—we maintain matching performance when projecting the descriptions to the span of the eigenvectors with large eigenvalues. This is related to PCA for dimensionality reduction, which has successfully been used for classical keypoint descriptors [27]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 334, + 379, + 346 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 334, + 379, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 334, + 379, + 346 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 354, + 547, + 475 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 354, + 547, + 475 + ], + "spans": [ + { + "bbox": [ + 304, + 354, + 547, + 475 + ], + "type": "text", + "content": "We developed a new framework for rotation equivariant keypoint descriptors using steers—linear maps that encode image rotations in description space. After outlining the general theory of steers using representation theory, we designed a large set of experiments with steers in three settings: (A) optimizing a steerer for a fixed descriptor, (B) optimizing a steerer and a descriptor jointly and (C) optimizing a descriptor for a fixed steerer. Our best models obtained new state-of-the-art results on the rotation invariant matching benchmarks Roto-360 and AIMS." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 484, + 409, + 498 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 484, + 409, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 484, + 409, + 498 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 505, + 547, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 505, + 547, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 505, + 547, + 649 + ], + "type": "text", + "content": "We thank Alex Stoken for help with the evaluation on AIMS. This work was supported by the Wallenberg Artificial Intelligence, Autonomous Systems and Software Program (WASP), funded by the Knut and Alice Wallenberg Foundation and by the strategic research environment ELLIIT, funded by the Swedish government. The computational resources were provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at C3SE, partially funded by the Swedish Research Council through grant agreement no. 2022-06725, and by the Berzelius resource, provided by the Knut and Alice Wallenberg Foundation at the National Supercomputer Centre." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": "The absolute values of the eigenvalues of a SO(2) steerer " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\varsigma (\\alpha)" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " are " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{e}^{\\alpha \\mathrm{Re}(\\lambda_d)}" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{d}" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " are the eigenvalues of " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\mathrm{d}\\varsigma" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " that are plotted in the two rightmost columns of Figure 4. Therefore, a lower real value of " + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{d}" + }, + { + "bbox": [ + 304, + 673, + 547, + 713 + ], + "type": "text", + "content": " means a lower absolute value of the eigenvalue of the steerer." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "4892" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 167 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 167 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 167 + ], + "type": "text", + "content": "[1] Georges Baatz, Kevin Koser, David Chen, Radek Grzesczuk, and Marc Pollefeys. 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Current passport-based methods that obfuscate model functionality for license-to-use and ownership verifications suffer from capacity and quality constraints, as they require retraining the owner model for new users. They are also vulnerable to advanced Expanded Residual Block ambiguity attacks. We propose Steganographic Passport, which uses an invertible steganographic network to decouple license-to-use from ownership verification by hiding the user's identity images into the owner-side passport and recovering them from their respective user-side passports. An irreversible and collision-resistant hash function is used to avoid exposing the owner-side passport from the derived user-side passports and increase the uniqueness of the model signature. To safeguard both the passport and model's weights against advanced ambiguity attacks, an activation-level obfuscation is proposed for the verification branch of the owner's model. By jointly training the verification and deployment branches, their weights become tightly coupled. The proposed method supports agile licensing of deep models by providing a strong ownership proof and license accountability without requiring a separate model retraining for the admission of every new user. Experiment results show that our Steganographic Passport outperforms other passport-based deep model protection methods in robustness against various known attacks.", + "bbox": [ + 75, + 323, + 473, + 731 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 736, + 209, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To foster Artificial Intelligence (AI) diffusion and application, AI as a Service (AIaaS) has emerged as a lucrative", + "bbox": [ + 75, + 753, + 468, + 785 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This research is supported by the National Research Foundation, Singapore, and Cyber Security Agency of Singapore under its National Cybersecurity Research & Development Programme (Development of Secured Components & Systems in Emerging Technologies through Hardware & Software Evaluation $<$ NRF-NCR25-DeSNTU-0001>). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the view of National Research Foundation, Singapore and Cyber Security Agency of Singapore.", + "bbox": [ + 75, + 790, + 468, + 887 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "†Corresponding author; *Both authors contributed equally.", + "bbox": [ + 96, + 887, + 419, + 900 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/baaebbbe3fc8a6fe92ef51104c1801eb09238162f1b8c73bdac4aead8612722e.jpg", + "image_caption": [ + "Figure 1. The conceptual overview. The owner holds the owner-side passport and the steganographic key, which are used to verify the licenses and reveal the user IDs, respectively. The verification branch of the deep model is trained with the constraint of the signature. Upon licensing, the user receives the user-side passport and the deployment branch of the deep model." + ], + "image_footnote": [], + "bbox": [ + 532, + 268, + 888, + 391 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "business model that offers across-the-broad access to high-performance machine learning models with subscription- or transaction-based payment schemes. The customers can submit inputs to the remote server and receive the inference or classification results of machine learning processes through application program interfaces (APIs). As complex models of high capabilities in AIaaS are offered as \"turnkey\" solutions to potentially anyone, they have huge potential to be misused and abused. Ownership and user license verifications are the first step towards accountability of responsible use of AI services.", + "bbox": [ + 496, + 477, + 892, + 643 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ownership verification has long been a primary tool to protect deployed deep models against intellectual property (IP) infringement and unauthorized model replication [13]. Numerous approaches have been proposed, such as watermarking [8, 27], fingerprinting [10, 23, 24], and backdoor embedding [11, 14, 26]. These approaches typically aim to enable the trained deep model to exhibit distinguishable characteristics under specific conditions without sacrificing its utility. To resist ambiguity attacks, passport-based ownership verification scheme [5, 6, 20, 30] embeds digital passports during model training to obfuscate the primary functionality until the obfuscated parameters are restored by a genuine passport. The passport scheme provides access control [5, 6] at the expense of some accuracy degradation. Each passport is tied to a user model, retraining is required to derive a new user model from the owner model for every new passport issued. The recent passport-aware normal", + "bbox": [ + 496, + 643, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "12302", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ization [30] avoids making structural changes to the target model by training it jointly with a passport-aware branch. The secret passport and passport-aware branch after training are kept by the model owner for future ownership verification and only the original passport-free target model is released to the end users. By forgoing the usage control, this method allows one deployed model to be used by various users but it also loses the accountability of inappropriate and unlawful use of the deployed model by different licensees. Besides, it has been demonstrated that the passports of existing methods can still be counterfeited by the more advanced ambiguity attack [3].", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In usage authorization, one major limitation of existing passport-based methods is the need to retrain the network to incorporate different parameter modulations for every new passport issued, which may cause uneven service quality for different end users. Besides, retraining to accommodate new user models is inflexible, non-scalable and not cost-effective for complex models. This pitfall motivates us to explore anti-forgery passports that allow fidelity verification of deployed model to hold authorized users accountable for misuse of their licensed models without having to retrain the owner model when admitting new users. To this end, we propose a novel Steganographic Passport to decouple user license verification from ownership verification, as illustrated in Fig. 1. For ownership verification, the uniqueness of the model weights is maintained by aligning them with the hashed output of the owner-side passport, which allows the model owner to prove the ownership and authenticity of the distributed model. For license verification, any licensed user's hidden identity (ID) image can be extracted using the user-side passport. Both owner-side and user-side passports will pass the fidelity assessment as their visual similarity is preserved by using steganography to hide the ID image. To increase the sensitivity of the deployed model against malicious tampering of passports and weights, we propose an activation-level obfuscation for the verification branch of the owner model. The weights of the deployment and verification branches are tightly coupled by training them jointly with a balance loss function. Our contributions can be summarized as follows.", + "bbox": [ + 75, + 276, + 472, + 715 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- A novel Steganographic Passport is designed based on key-based invertible steganographic network to allow both original model ownership and right-of-use of its deployed model by multiple licensees to be verified without requiring retraining.", + "- An activation-level obfuscation architecture is designed to thwart forgery by tampering with the user-side passports or model weights.", + "- Extensive experiments are conducted to demonstrate the state-of-the-art security performance of our steganographic passports—the credibility of its owner-side and user-side passport verifications and its robustness against" + ], + "bbox": [ + 76, + 719, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "various attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks.", + "bbox": [ + 511, + 90, + 890, + 121 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Background", + "text_level": 1, + "bbox": [ + 500, + 128, + 627, + 145 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The need to safeguard the deep model against misappropriation and IP theft arises from the enormous cost of designing and training a high-performance model from scratch. Given redundancy inherent in the numerous parameters of deep models, it is possible to embed a watermark into a model for ownership identification without significantly impairing its performance. The model can be watermarked either explicitly or implicitly. Explicit watermarking embeds the watermark by modifying the weights [7, 10, 23, 27] or feature maps [8] through a weight regularizer without compromising the original model performance. Implicit watermarking (a.k.a prediction watermarking) deliberately trains a backdoor into the protected model to classify inputs with specific triggers to the predefined labels [11, 14, 22, 26, 28]. However, these techniques are found to be vulnerable to ambiguity attacks as the embedded triggers can be replaced by attackers to forge the ownership with a substitute watermark. To mitigate this risk, model passports are introduced [5, 6], where the affine scale and bias factors of normalization functions are substituted with those derived from the passport images $\\{p_{\\gamma}, p_{\\beta}\\}$ .", + "bbox": [ + 496, + 147, + 890, + 464 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Let $x^{l}$ be the output of the $l$ -th convolutional layer, and $\\mu_{x^l}$ and $\\sigma_{x^l}$ be its mean and standard deviation, respectively. Then, the normalization function at the $l$ -layer with affine factors $\\gamma^l$ and $\\beta^l$ is given by:", + "bbox": [ + 496, + 464, + 890, + 526 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\tilde {x ^ {l}} + \\beta^ {l},\n$$\n", + "text_format": "latex", + "bbox": [ + 653, + 529, + 772, + 549 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\text {w h e r e} \\quad \\tilde {x ^ {l}} = \\frac {1}{\\sigma_ {x ^ {l}}} \\left(x ^ {l} - \\mu_ {x ^ {l}}\\right). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 596, + 550, + 890, + 584 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By substituting $\\gamma^l$ and $\\beta^l$ by the passport affine factors $\\gamma_{p_\\gamma}^l$ and $\\beta_{p_\\beta}^l$ , the following passport normalization [5] is obtained:", + "bbox": [ + 500, + 585, + 890, + 628 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {x _ {p} ^ {l}} = \\gamma_ {p _ {\\gamma}} ^ {l} \\cdot \\tilde {x} ^ {l} + \\beta_ {p _ {\\beta}} ^ {l}. \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 624, + 628, + 890, + 652 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The sign sequence of $\\gamma_{p_\\gamma}^l$ in Eq. (2) is constrained to match a self-defined binary signature sequence. As large magnitudes of $\\gamma_{p_\\gamma}^l$ can be penalized, the gradients are kept small to ensure that the signs of $\\gamma_{p_\\gamma}^l$ are lazy-to-flip so as to prevent the signature from being replaced by retraining the model. To minimize the influence of passport normalization on inference performance, Zhang et al. [30] proposed a dual-branch passport structure. Its normalization function is expressed in Eq. (3) and illustrated in Fig. 2a.", + "bbox": [ + 496, + 660, + 890, + 799 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\tilde {x ^ {l}} + \\beta^ {l}, \\\\ \\widehat {x _ {p} ^ {l}} = \\gamma_ {p _ {\\gamma}} ^ {l} \\cdot \\tilde {x ^ {l}} + \\beta_ {p _ {\\beta}} ^ {l}, \\end{array} \\right. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 609, + 806, + 890, + 848 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where the passport-free output $\\widehat{x^l}$ and the passport-aware output $\\widehat{x_p^l}$ are used for the deployment and ownership verification, respectively. Besides, a two-layer perception (TLP)", + "bbox": [ + 496, + 849, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "12303", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3176ae7e9907bd4170357b9063a52ee2da63634d45a27238944eaf0eb5cf4b72.jpg", + "image_caption": [ + "(a) Existing passport architecture" + ], + "image_footnote": [], + "bbox": [ + 83, + 66, + 272, + 162 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/c8d1a5e063f486cc3a2879b47887870014b090fc6dc9ad4412c497fe2a39c7e1.jpg", + "image_caption": [ + "(b) Proposed passport architecture", + "Figure 2. The existing and proposed passport architectures. The dual branches are enclosed in the dashed line box." + ], + "image_footnote": [], + "bbox": [ + 279, + 65, + 467, + 162 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "structure is also inserted before the affine factors to mitigate the strict limitations in managing the functionality of normalization layers.", + "bbox": [ + 75, + 214, + 468, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To protect against ambiguity attacks with oracle passports due to passport leakage, Liu et al. [20] used trapdoor normalization to establish a direct correlation between the signature and the passport through a hash function. The collision-intractable hash function makes it virtually impossible for the attackers to reverse engineer a counterfeit passport, even if they can compromise the signature. Recently, Chen et al. [3] proposed an advanced ambiguity attack called Expanded Residual Block (ERB) on passport-based methods. This attack exploits the extensive solution space of TLP to force-flip the signs of the scale factors according to their forged passport without compromising the model performance. In summary, existing model passport methods aim only to resist the diverse ambiguity attacks by obfuscating the normalization functionalities with immutable passports. They do not allow admission of new users and their right-of-use verification upon model deployment. This is an important measure to safeguard the interest of AIaaS providers against revenue extorts by unauthenticated usage.", + "bbox": [ + 75, + 260, + 468, + 561 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed method", + "text_level": 1, + "bbox": [ + 76, + 566, + 246, + 583 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem statement", + "text_level": 1, + "bbox": [ + 76, + 587, + 258, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider a practical licensing scenario of a deep model. Besides being able to detect and verify the ownership of a deployed model, the model owner should also be able to verify usage permission. If the passport images $\\{p_{\\gamma}, p_{\\beta}\\}$ are used as a unique proof to verify the ownership of the deployed model, they cannot be used to verify the usage permission granted to licensed users of that model. Although new backdoor triggers or watermarks can be added to verify each licensed user, the model needs to be retrained to learn the new features. This is very restrictive and impractical as it requires the model owner to fix the number of users and their identities upfront. Therefore, our aim is to enable the passport-based scheme to grant verifiable usage permission of a deployed deep model to ad hoc registered users without requiring retraining and without undermining the validity and robustness of the model's ownership proof.", + "bbox": [ + 75, + 604, + 468, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Steganographic passport framework", + "text_level": 1, + "bbox": [ + 76, + 854, + 393, + 869 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Recall that in existing passport approaches [5, 6, 20, 30], a forged passport image can also be used to pass the fi", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "delity assessment if it bears a high visual similarity to the genuine passport image. Inspired by advanced steganography techniques, we apply the art of imperceptible secret concealment to the passport-based scheme. The proposed Steganographic Passport follows the dual-branch setting, as illustrated in Fig. 2b.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We define an owner-side passport $p_{o} = \\{p_{o_{\\gamma}}, p_{o_{\\beta}}\\}$ as the genuine passport images selected and held only by the model owner for generating the affine scale and bias factors accordingly. By feeding $p_{o}$ into the model, the corresponding owner-side passport feature maps are sequentially generated across the $n$ passport layers. These feature maps are then transformed into the affine factors for obfuscating the verification branch, which will be described in Sec. 3.3. We also introduce a new user-side passport, $p_{u} = \\{p_{u_{\\gamma}}, p_{u_{\\beta}}\\}$ , which is obtained by hiding the ID image $\\mathrm{I}_u$ provided by a registered user into $p_{o}$ . The user-side passport $p_{u}$ fills the gap of existing passport-based limitation in meeting the goal of Sec. 3.1. The model owner can license the deployment branch of the model to multiple registered users by merely hiding each user's ID image into $p_{o}$ .", + "bbox": [ + 496, + 181, + 890, + 407 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Anti-forgery owner-side passport. To avoid user-side passports from exposing the visual content of the owner-side passports, the owner-side passport is irreversibly transformed to a unique model signature to ensure that the ownership cannot be forged by knowing any of the user-side passports. SHA-512 [25] is used as the one-way function for this mapping.", + "bbox": [ + 496, + 407, + 890, + 513 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Before training the target model, the model owner hashes the owner-side $p_{o_{\\gamma}}$ to a binary signature $\\xi^l$ of passport layer $l$ , as follows:", + "bbox": [ + 496, + 513, + 890, + 558 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\xi^ {l} = \\left\\{\\operatorname {S G N} (x) \\mid x \\in \\operatorname {H A S H} \\left(p _ {o _ {\\gamma}}\\right) \\right\\}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 573, + 561, + 890, + 580 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where SGN maps each bit of a binary input sequence from $\\{0,1\\}$ to $\\{-1,1\\}$ . If the desired length of $\\xi^l$ is shorter than 512 bits, the excess bits of the hash output are truncated from the beginning; Otherwise, we cycle the hash function's output until the required sequence length is obtained.", + "bbox": [ + 496, + 583, + 890, + 657 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "For a model with $n$ passport layers, its overall model signature is represented as $\\{\\xi^1, \\xi^2, \\dots, \\xi^n\\}$ . The strict avalanche criterion of the hash function ensures that even minor changes to the passport image will result in significantly different affine factors, which prevents force-flipping from forging the passport with high model performance fidelity. Together with the irreversibility property of SHA-512, the genuine model signature $\\xi$ can only be generated with the owner-side passport to thwart ownership impersonation fraud. The signature $\\{\\xi^1, \\xi^2, \\dots, \\xi^n\\}$ will be used to constrain the model's learning in the subsequent training phase to transform them into unique model's weights. A detailed exposition of this process is provided in Sec. 3.3.", + "bbox": [ + 496, + 659, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "License verification via key-based deep steganography. To support an agile licensing scheme that is capable of admitting and verifying any new user after the tar", + "bbox": [ + 496, + 856, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "12304", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "get model has finalized its training phase, we need to decouple the license verification from the ownership verification. To this end, we hide the user's ID into the owner-side passport by integrating the key-based scheme of Invertible Steganographic Network (ISN) [21] within the Deep Image Hiding Network (HiNet) framework [15]. The key-based ISN is divided into two processes: forward hiding pass $\\mathcal{H}_s$ and reverse revealing pass $\\mathcal{H}_s^{-1}$ . The forward hiding pass is used to obtain the user-side passport $p_u$ from the owner-side passport $p_o$ as follows:", + "bbox": [ + 75, + 90, + 472, + 242 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np _ {u} = \\mathcal {H} _ {s} \\left(p _ {o}, \\mathrm {I} _ {u}\\right), \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 244, + 468, + 262 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{I}_u$ denotes the user's ID image to be hidden into the owner-side passport $p_o$ .", + "bbox": [ + 75, + 263, + 468, + 294 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The reverse revealing pass is utilized for license verification. Using the private steganographic key $\\mathbf{k}_s$ , the model owner can reveal the hidden user's ID image from the underside passport $p_u$ :", + "bbox": [ + 75, + 294, + 468, + 354 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {I} _ {u} ^ {\\prime} = \\mathcal {H} _ {s} ^ {- 1} \\left(p _ {u}, \\mathbf {k} _ {s}\\right), \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 354, + 468, + 375 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathrm{I}_u^\\prime$ denotes the revealed ID image of the licensed user. The detailed architecture and algorithms of the hiding and revealing passes are given in the Appendix.", + "bbox": [ + 75, + 375, + 468, + 421 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Activation-level obfuscation", + "text_level": 1, + "bbox": [ + 76, + 429, + 326, + 443 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To counteract sophisticated ambiguity attacks, an activation-level obfuscation is proposed to safeguard the verification branch against alterations of both the passport and the model's weights.", + "bbox": [ + 75, + 445, + 468, + 505 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Immutable passport. As illustrated in Fig. 2b, the passport-affine factors of layer $l$ can be calculated from the passport feature maps $p_{o}^{l}$ by:", + "bbox": [ + 75, + 506, + 468, + 551 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\gamma_ {p _ {o _ {\\gamma}}} ^ {l} = \\Phi (\\Pi (p _ {o _ {\\gamma}} ^ {l})) \\text {, a n d} \\beta_ {p _ {o _ {\\beta}}} ^ {l} = \\Phi (\\Pi (p _ {o _ {\\beta}} ^ {l})) \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 551, + 468, + 579 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\Phi$ and $\\Pi$ denote the TLP and the global average pooling, respectively.", + "bbox": [ + 75, + 579, + 468, + 609 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by the controllable rectifiers of the Dynamic ReLU [2], we make $\\gamma_{p_{o\\gamma}}^l$ and $\\beta_{p_{o\\beta}}^l$ the dependent variables of the activation function. This can be incorporated into a dual-branch architecture as follows:", + "bbox": [ + 75, + 609, + 468, + 670 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} \\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\widetilde {x ^ {l}} + \\beta^ {l}, \\\\ \\widehat {x _ {p _ {o}} ^ {l}} = \\gamma_ {p _ {o \\gamma}} ^ {l} \\cdot \\left(\\gamma_ {t} ^ {l} \\cdot \\widetilde {x ^ {l}} + \\beta_ {t} ^ {l}\\right) + \\beta_ {p _ {o \\beta}} ^ {l}, \\end{array} \\right. \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 140, + 672, + 468, + 712 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\gamma^l$ and $\\beta^l$ denote the original affine factors used in the deployment branch, and $\\gamma_t^l$ and $\\beta_t^l$ denote the additional temporal affine factors used in the verification branch.", + "bbox": [ + 75, + 715, + 468, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To simplify the expressions, let $x_{t}^{l} = \\gamma_{t}^{l}\\cdot x^{l} + \\beta_{t}^{l}$ . By subjecting the outputs of Eq. (8) to an activation function (e.g. ReLU) before feeding them to the next layer, the final outputs of layer $l$ are given by:", + "bbox": [ + 75, + 763, + 468, + 825 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{ \\begin{array}{l} x _ {\\varphi} ^ {l} = \\max \\left(\\widehat {x ^ {l}}, 0\\right), \\\\ x _ {\\varphi_ {p o}} ^ {l} = \\max \\left(\\gamma_ {p _ {o \\gamma}} ^ {l} \\cdot \\widehat {x _ {t} ^ {l}} + \\beta_ {p _ {o \\beta}} ^ {l}, 0\\right). \\end{array} \\right. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 142, + 827, + 468, + 868 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The activation function used for the deployment branch (top expression) in Eq. (9) is a regular ReLU, whereas the", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "activation function used for the verification branch (bottom expression) can be viewed as a special case of Dynamic ReLU. This way, the changes in the affine factors due to any alterations of the owner-side passport $p_o$ will lead to apparent changes in the passport-aware output, $x_{\\varphi_{p_o}}^l$ , but not in the passport-free output, $x_{\\varphi}^{l}$ .", + "bbox": [ + 496, + 90, + 890, + 185 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Immutable deployment branch. Under the dual-branch setting, the deployment and verification branches share all the model's weights but the affine factors. The deployment branch has to be consistently updated according to the updated passport-derived affine factors in the verification branch. If the deployment branch cannot keep up with the updates, the shared weights will overfit the verification branch, causing gradient explosions. To keep the updates of the two branches in tandem, the following balance loss function is proposed to train the model by explicitly aligning the affine factors in Eq. (8):", + "bbox": [ + 496, + 184, + 890, + 349 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {b} = \\sum_ {l = 1} ^ {n} \\left(\\mathcal {L} _ {\\mathrm {y}} \\left(\\gamma^ {l}, \\gamma_ {t} ^ {l} \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l}\\right) + \\mathcal {L} _ {\\mathrm {y}} \\left(\\beta^ {l}, \\beta_ {t} ^ {l} \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l} + \\beta_ {p _ {o _ {\\beta}}} ^ {l}\\right)\\right), \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 508, + 349, + 890, + 386 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\ell_1$ norm is used for $\\mathcal{L}_y$ , and $n$ is the total number of passport layers.", + "bbox": [ + 496, + 385, + 890, + 414 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This loss function aims to strike an equilibrium performance between the two branches. After the model is trained, the verification branch is removed from the model before it is licensed to any user. As the model trained with the balance loss function will have negligible accuracy difference between the two branches, any modification on the deployment branch would amplify the mean absolute difference. By comparing the accuracy difference between the two branches, the integrity of the model can be validated.", + "bbox": [ + 496, + 415, + 890, + 550 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Immutable verification branch. During the target model's training phase, the owner uses the model signature $\\{\\xi^1,\\xi^2,\\dots ,\\xi^n\\}$ to constrain the update of model's weights with the following signature loss function:", + "bbox": [ + 500, + 551, + 890, + 612 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {s} = \\sum \\max \\left(\\epsilon - \\xi^ {l} \\cdot \\Pi \\left(p _ {o _ {\\gamma}} ^ {l}\\right) \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l}, 0\\right), \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 531, + 612, + 890, + 638 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\xi^l$ and $p_{o_\\gamma}^l$ denote the $l$ -th layer's signature and passport feature map, respectively, and $\\epsilon$ is a small constant.", + "bbox": [ + 496, + 638, + 890, + 670 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$\\mathcal{L}_s$ encourages the signs of the product $\\Pi \\left(p_{o_\\gamma}^l\\right) \\cdot \\gamma_{p_{o_\\gamma}}^l$ to align with that of $\\xi^l$ , while keeping the magnitude of this product low. Since $p_{o_\\gamma}^l$ and $\\gamma_{p_{o_\\gamma}}^l$ are the outputs of the convolution and TLP, respectively, the weights of the convolution layer and TLP become tightly coupled. The uniqueness of $\\xi^l$ in Eq. (11) contributes to the distinctiveness of the weights. Any adjustment to the TLP will directly affect the convolution output. This property helps to prevent advanced ambiguity attacks, especially ERB, which maliciously alter the weights of the TLP to force-flip the signs of the product to align it with the forged signature.", + "bbox": [ + 496, + 671, + 890, + 848 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Training objectives", + "text_level": 1, + "bbox": [ + 498, + 854, + 683, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The one-time training pipeline consists of training the key-based ISN and the target model.", + "bbox": [ + 496, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "12305", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training the key-based ISN. The key-based ISN is trained once independently of the target model to enhance the hiding invisibility and the revealing quality by the following loss function:", + "bbox": [ + 76, + 90, + 468, + 151 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I S N} = \\mathcal {L} _ {h} \\left(p _ {o}, p _ {u}\\right) + \\mathcal {L} _ {r} \\left(\\mathrm {I} _ {u}, \\mathrm {I} _ {u} ^ {\\prime}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 163, + 155, + 468, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Both $\\mathcal{L}_h$ and $\\mathcal{L}_r$ utilize the $\\ell_2$ norm for distance calculation. $p_o$ and $\\mathrm{I}_u$ are randomly sampled in the training phase.", + "bbox": [ + 76, + 176, + 468, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training the target model. Given a target model, we denote the models with only the weights of the deployment branch as $\\mathcal{M}$ , and those with only the weights of the $p_o$ -based verification branch as $\\mathcal{M}_{p_o}$ . Three loss functions are used to train the dual branches parallelly. The loss function for model performance is defined as:", + "bbox": [ + 76, + 207, + 468, + 296 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {f} = \\frac {1}{N _ {t r}} \\sum_ {i = 1} ^ {N _ {t r}} \\left(\\mathcal {L} _ {c} \\left(\\mathcal {M} \\left(x _ {i}\\right), y _ {i}\\right) + \\mathcal {L} _ {c} \\left(\\mathcal {M} _ {p _ {o}} \\left(x _ {i}\\right), y _ {i}\\right)\\right), \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 301, + 468, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_{i}$ and $y_{i}$ are respectively the $i$ -th sample and its label from $N_{tr}$ training samples, and $\\mathcal{L}_c$ is the cross-entropy loss.", + "bbox": [ + 76, + 345, + 468, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Together with the signature loss $\\mathcal{L}_s$ and the balance loss $\\mathcal{L}_b$ , the total loss is defined as:", + "bbox": [ + 76, + 375, + 468, + 402 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = \\mathcal {L} _ {f} + \\omega_ {s} \\mathcal {L} _ {s} + \\omega_ {b} \\mathcal {L} _ {b}, \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 409, + 468, + 426 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the signature and balance losses are weighted by $\\omega_{s}$ and $\\omega_{b}$ , respectively.", + "bbox": [ + 76, + 430, + 467, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.5. Inclusive verification chain", + "text_level": 1, + "bbox": [ + 76, + 469, + 318, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To confirm the ownership and legal usability of a deployed model M, we propose the following verification chain involving the model owner O, the licensed user U, and the deployed model M.", + "bbox": [ + 76, + 484, + 468, + 545 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ownership verification. The ownership verification comprises three tests: $\\mathcal{V}_O^{\\mathcal{I}}$ , $\\mathcal{V}_O^f$ and $\\mathcal{V}_O^s$ for the verification of the model integrity, performance fidelity and signature accuracy, respectively. By replacing the passport layers' affine factors with the ones derived from the owner-side passport $p_o$ , the deployed branch $\\mathbf{M}$ becomes a verifiable branch $\\mathbf{M}_{p_o}$ .", + "bbox": [ + 76, + 546, + 468, + 651 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $\\mathcal{F}(\\cdot ,\\cdot)$ denote the model performance. $\\nu_{O}^{\\mathcal{T}}$ tests if $\\mathbf{M}$ has been modified based on the absolute performance difference (AD):", + "bbox": [ + 76, + 651, + 468, + 696 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {O} ^ {\\mathcal {I}} \\Longleftrightarrow \\frac {1}{N _ {t}} \\left| \\sum_ {j = 1} ^ {N _ {t}} \\left(\\mathcal {F} \\left(\\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\\right) - \\mathcal {F} \\left(\\mathbf {M}, x _ {j} ^ {t}\\right)\\right) \\right| < \\tau_ {d}, \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 83, + 700, + 468, + 748 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_{j}^{t}$ is the $j$ -th sample from total $N_{t}$ test samples, and $\\tau_{d}$ is a small predefined passing threshold.", + "bbox": [ + 76, + 751, + 468, + 781 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mathcal{V}_O^f$ verifies the performance fidelity by:", + "bbox": [ + 96, + 780, + 359, + 797 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {O} ^ {f} \\Longleftrightarrow \\frac {1}{N _ {t}} \\sum_ {j = 1} ^ {N _ {t}} \\mathcal {F} \\left(\\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\\right) > \\tau_ {f}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 145, + 797, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau_{f}$ is the predefined minimum accuracy to pass the performance fidelity verification.", + "bbox": [ + 76, + 840, + 468, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To validate the signature accuracy, the owner uses Eq. (4) to transform $p_{o_{\\gamma}}$ into the model signature $\\xi =$", + "bbox": [ + 76, + 869, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\{\\xi^1,\\xi^2,\\dots ,\\xi^n\\}$ . By comparing each element of $\\xi$ with those of $\\xi^{*}$ extracted from $\\mathbf{M}_{p_o}$ $\\nu_{O}^{s}$ checks the sign agreement (SA) by:", + "bbox": [ + 500, + 90, + 890, + 133 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {O} ^ {s} \\Longleftrightarrow \\frac {1}{N _ {\\xi}} \\sum_ {b = 1} ^ {N _ {\\xi}} \\left(\\xi_ {b} \\wedge \\xi_ {b} ^ {*}\\right) \\geq \\tau_ {\\xi}, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 133, + 890, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N_{\\xi}$ is the total length of $\\xi$ . $\\tau_{\\xi}$ is a predefined error tolerance only for the post-distribution verification. Otherwise, the SA of an untainted pre-deployment model has to be $100\\%$ (i.e., $\\tau_{\\xi} = 1$ ) to satisfy $\\mathcal{V}_O^s$ .", + "bbox": [ + 496, + 176, + 890, + 236 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark 1: Before distributing the deployed model $\\mathbf{M}$ , the owner $\\mathbf{O}$ is required to disclose the evidence of compliance with $\\mathcal{V}_O^{\\mathcal{T}}$ , $\\mathcal{V}_O^f$ , and $\\mathcal{V}_O^s$ to establish the credibility of the ownership claim of $\\mathbf{M}$ .", + "bbox": [ + 496, + 237, + 890, + 296 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "License verification. Upon verifying that the model M deployed by the licensed user $\\mathbf{U}$ complies with the criteria set by $\\mathcal{V}_O^{\\mathcal{T}}$ , $\\mathcal{V}_O^f$ , and $\\mathcal{V}_O^s$ , a provable association between the licensed user $\\mathbf{U}$ and the model owner $\\mathbf{O}$ can be established by two license verification tests: $\\mathcal{V}_L^p$ for passport image similarity, and $\\mathcal{V}_L^I$ for ID image similarity.", + "bbox": [ + 496, + 297, + 890, + 387 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Upon receiving $p_u$ submitted by the user $\\mathbf{U}$ , the owner can compare the PSNR between the user and owner passport images by:", + "bbox": [ + 496, + 387, + 890, + 431 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {L} ^ {p} \\Longleftrightarrow \\operatorname {P S N R} \\left(p _ {o}, p _ {u}\\right) > \\tau_ {p}, \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 435, + 890, + 452 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tau_{p}$ is the predefined visual similarity threshold for successful verification.", + "bbox": [ + 496, + 454, + 890, + 483 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The reverse revealing pass is utilized for license verification. Using the private steganographic key $\\mathbf{k}_s$ , the model owner can reveal the hidden user's ID image $\\mathrm{I}_u^{\\prime}$ from the user-side passport $p_u$ by Eq. (6). $\\mathcal{V}_L^{\\mathrm{I}}$ tests the visual similarity between $\\mathrm{I}_u$ and the revealed ID image, $\\mathrm{I}_u^{\\prime}$ of the licensed user by comparing the PSNR with predefined threshold $\\tau_r$ :", + "bbox": [ + 496, + 484, + 890, + 575 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {V} _ {L} ^ {\\mathrm {I}} \\Longleftrightarrow \\operatorname {P S N R} \\left(\\mathrm {I} _ {u}, \\mathrm {I} _ {u} ^ {\\prime}\\right) > \\tau_ {r}. \\tag {19}\n$$\n", + "text_format": "latex", + "bbox": [ + 591, + 578, + 890, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark 2: Once $\\mathcal{V}_L^p$ and $\\mathcal{V}_L^{\\mathrm{I}}$ are satisfied, on the condition that the model $\\mathbf{M}$ passes the three ownership verification tests of the owner $\\mathbf{O}$ , the user $\\mathbf{U}$ is proven to be a legal licensee of $\\mathbf{M}$ .", + "bbox": [ + 496, + 597, + 890, + 657 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 662, + 624, + 680 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Setup", + "text_level": 1, + "bbox": [ + 500, + 688, + 580, + 703 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generally, we follow the settings on image classification tasks in existing passport approaches, including dual-branch DeepIPR [6], Passport-Aware Normalization (PAN) [30], and Trapdoor Normalization (TdN) [20]. AlexNet [17] and ResNet-18 [9], with Batch Normalization (BN) [12] and Group Normalization (GN) [29], are employed to evaluate and compare the performance. The datasets used in the classification experiments include CIFAR-10, CIFAR-100 [16], Caltech-101, and Caltech-256 [18]. Besides, DIV2K [1] is used to train the key-based ISN. For passport images $p_{\\gamma}$ and $p_{\\beta}$ , we randomly select them from the test set of COCO dataset [19]. For steganographic key image $\\mathbf{k}_s$ , we randomly select it from DTD", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "12306", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/2fe5f6ad52a7eb0fe085d15502c419ef03b7a1bd5af834b35685efb8535a8eb4.jpg", + "table_caption": [ + "Table 1. Inference performance (in %) for deployment/verification. $\\uparrow / \\downarrow$ denotes higher / lower value for better performance." + ], + "table_footnote": [], + "table_body": "
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18BN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean94.6993.8576.4273.5774.5870.7355.4349.5273.60-
DeepIPR93.04 / 94.0593.81 / 93.6960.76 / 62.8872.19 / 71.1573.84 / 73.2265.08 / 63.3341.53 / 44.1243.81 / 42.6768.01 / 68.141.30
PAN94.70 / 94.6193.63 / 93.6775.97 / 74.7072.19 / 71.4973.79 / 72.9468.36 / 65.3755.37 / 54.3344.73 / 43.5172.34 / 71.331.03
TdN94.65 / 94.6893.57 / 93.5776.00 / 75.6171.25 / 71.4274.12 / 73.0567.63 / 67.5154.90 / 54.2844.90 / 44.2772.13 / 71.800.38
Ours94.89 / 94.8993.79 / 93.8076.10 / 76.1070.84 / 70.8373.56 / 73.5667.01 / 67.0153.65 / 53.6544.01 / 44.0171.73 / 71.730.00
AlexNetBN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean91.2090.2768.4065.7271.5868.7044.2441.1867.66-
DeepIPR81.80 / 90.7689.90 / 90.2045.71 / 51.7764.89 / 64.1667.91 / 65.9567.80 / 67.0631.39 / 36.2540.69 / 39.7360.14 / 63.243.07
PAN91.51 / 91.2990.22 / 90.3968.46 / 66.4450.60 / 56.7171.03 / 70.9066.95 / 66.7144.93 / 41.1340.03 / 38.8466.47 / 65.311.32
TdN91.28 / 91.0290.08 / 89.8068.71 / 68.0764.54 / 63.7770.45 / 69.4468.31 / 66.3845.36 / 44.8242.39 / 37.8867.64 / 66.401.24
Ours91.39 / 91.3889.77 / 89.7767.86 / 67.8563.36 / 63.3471.98 / 71.9868.42 / 68.4246.10 / 46.0741.10 / 41.1267.50 / 67.490.01
", + "bbox": [ + 81, + 74, + 890, + 227 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "dataset [4]. For hyper-parameters $\\epsilon, \\omega_s$ , and $\\omega_b$ , we empirically set them as 0.1, 1, and 1. By default, the last three/five normalization layers of AlexNet/ResNet-18 are set as the passport layers.", + "bbox": [ + 75, + 247, + 468, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Verification assessment", + "text_level": 1, + "bbox": [ + 76, + 316, + 290, + 332 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We evaluate the effectiveness of the proposed steganographic passport by the verification and inference performances. All the models are trained with 200 epochs, utilizing a multi-step learning rate that decreases gradually from 0.01 to 0.0001. A twofold verification is adopted in our method, which entails a) an ownership verification $\\{\\mathcal{V}_O^{\\mathcal{T}},\\mathcal{V}_O^f,\\mathcal{V}_O^s\\}$ and b) a license verification $\\{\\mathcal{V}_L^p,\\mathcal{V}_L^1\\}$ .", + "bbox": [ + 75, + 340, + 468, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For ownership verification, our steganographic passport exhibits the lowest AD values of $0.00\\%$ on ResNet-18 and $0.01\\%$ on AlexNet for $\\mathcal{V}_O^T$ with the correct owner passport, as presented in Table 1. This is attributed to the effect of the balance loss function, which ensures that the updates of the affine factors of the two branches are more synchronized during training. For $\\mathcal{V}_O^f$ , due to the stronger anti-forgery passport constraint imposed by our method, there is a slight decrease in model inference performance compared to Tdn and PAN, but it still outperforms DeepIPR. As shown in Table 1, the average deployment and verification branch accuracies of our method on ResNet-18 are both $71.73\\%$ , which is only $0.40\\%$ and $0.07\\%$ lower than the accuracies of the deployment and verification branches, respectively of Tdn. The performance of our method peaks in several cases highlighted with the bold-printed percentages. For instance, it achieves the top score of $71.98\\%$ for AlexNet on Caltech-101. For $\\mathcal{V}_O^s$ , the SAs of all four methods achieve $100\\%$ in all the settings.", + "bbox": [ + 75, + 448, + 468, + 733 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "For license verification, a comparison of the visual images for $\\mathcal{V}_L^p$ and $\\mathcal{V}_L^{\\mathrm{I}}$ is presented in Fig. 3. A very high PSNR of 41.47 between the original ID image and the ID image revealed using the genuine steganographic key is obtained, indicating a high level of visual similarity between them. In contrast, using forged keys to reveal the ID image results in significantly lower PSNR. Specifically, a PSNR of only 15.48 is obtained for the revealed ID images by using a random noise-like forged passport image and 32.56 by using a steganographic key image selected randomly from the same distribution as the genuine key image. Further", + "bbox": [ + 75, + 734, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b78d92cb54e4db4835d0b97c7b6c2c1245227d264686b2a8163a047d8bd17414.jpg", + "image_caption": [ + "Figure 3. Hiding and revealing performance of the key-based ISN." + ], + "image_footnote": [], + "bbox": [ + 517, + 244, + 869, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "more, upon repeating this evaluation 100 times, the average PSNRs obtained from revealing the ID image by using random noise-like forged and randomly-selected key images are 15.68 and 35.89, respectively.", + "bbox": [ + 498, + 452, + 890, + 513 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on the above observations, we empirically set $\\tau_{d}$ , $\\tau_{\\xi}$ , $\\tau_{p}$ and $\\tau_{r}$ to $0.05\\%$ , $93\\%$ , 39 and 41 for $\\mathcal{V}_O^{\\mathcal{I}}$ , $\\mathcal{V}_O^s$ , $\\mathcal{V}_L^p$ and $\\mathcal{V}_L^i$ , respectively. For $\\mathcal{V}_O^f$ , $\\tau_{f}$ is calibrated according to the task as the same clean model trained for different tasks has different inference performance.", + "bbox": [ + 498, + 513, + 890, + 590 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Robustness against ownership ambiguity attacks", + "text_level": 1, + "bbox": [ + 498, + 595, + 890, + 625 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Ownership ambiguity attacks aim to falsely claim the ownership of a deep model by satisfying the conditions outlined in Remark 1. Owing to the avalanche criterion provided by the hash function, attacks that attempt to forge the genuine passport images by random selection [6, 20, 30] or tamper with the user-side passport images will fail on $\\mathcal{V}_O^s$ due to the significant signature deviation. Additionally, it is computationally intractable to reverse the uniformly random and collision-resistant cryptographically secure hash function to recover genuine passport images [20]. Thus, we specifically focus on the state-of-the-art ERB ownership ambiguity attack, under the strict assumption that the attacker has stolen both the deployment and verification branches, along with $10\\%$ of original training data. The individual version of ERB, i.e., IERB is used to attack the models with BN.", + "bbox": [ + 496, + 627, + 890, + 852 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ERB demonstrated its effectiveness by retraining the model to fit a forged passport. In ERB's original configuration, attackers directly fabricate the passport layer's affine", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "12307", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/1e8fb5d20c5f01ed34c5ed69c7bb2b2da27d3bd8e272c519518bbe4474ac1063.jpg", + "table_caption": [ + "Table 2. Inference performance fidelity (in %) for deployment/verification under ERB ambiguity attacks with BN. FSA and BDR refer to the forged signature accuracy and the bit difference rate between benign and forged signatures, respectively." + ], + "table_footnote": [], + "table_body": "
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR94.19 / 94.3910050.2262.92 / 64.0610049.4973.56 / 73.8910050.2346.05 / 46.3910049.3769.18 / 69.680.50
PAN94.64 / 94.7210048.7175.28 / 75.1010049.5773.11 / 73.0510049.3053.62 / 53.5810050.0874.16 / 74.110.90
TdN94.48 / 94.2410053.0975.91 / 66.6610048.2073.22 / 64.5499.9650.0454.49 / 34.6110051.7674.53 / 65.019.51
Ours94.70 / 92.8710049.5375.85 / 50.2799.9649.1873.00 / 50.0699.9251.0552.87 / 38.4410049.1873.82 / 57.9116.20
AlexNetERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR26.54 / 85.7210047.6146.61 / 51.9710050.1163.56 / 67.8310052.6532.61 / 34.3410051.0842.31 / 59.9717.64
PAN91.56 / 82.0610052.4368.36 / 60.2910049.8770.37 / 69.1710053.3844.41 / 40.1510052.5668.68 / 62.925.76
TdN90.16 / 53.1610051.3366.96 / 1.6598.9649.7870.26 / 37.1998.9649.9644.14 / 0.2895.3148.2467.88 / 23.0744.81
Ours84.90 / 16.1199.5750.2467.38 / 1.0296.7549.7271.26 / 35.8698.9650.3345.00 / 4.9310051.1767.14 / 14.4852.66
", + "bbox": [ + 80, + 116, + 888, + 241 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e2b34716823ce1e2f60f10756a312c684d7f847e2792dcc033fa7f8eef67dca9.jpg", + "image_caption": [ + "(a) Forged passport" + ], + "image_footnote": [], + "bbox": [ + 81, + 244, + 271, + 349 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/05ef9c3e491db277a86be35b486fb2c7100ed2a1e59a3bd266c2bca562cfb956.jpg", + "image_caption": [ + "(b) Forged steganographic key", + "Figure 4. Results of license ambiguity attacks on our method. Batch Normalization is used in the evaluated models. We set the Z-score as 2.33 for $98\\%$ confidence interval (CI)." + ], + "image_footnote": [], + "bbox": [ + 272, + 244, + 460, + 349 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "factors, leveraging the network's differentiable architecture to deduce the passport images. However, this possibility is denied by the hash functions of our method and TdN. Therefore, while maintaining the original settings of ERB for DeepIPR and PAN, the passport layer's affine factors in our method and TdN are to be derived from the corresponding hash-related functions. Table 2 displays the experimental results. To successfully meet the criteria of Remark 1, the attack must achieve $100\\%$ of forged SA (FSA) for $\\mathcal{V}_O^s$ . As evinced by the results presented in Sec. 4.2, the legitimate owner is able to comply with this stringent criteria. The experimental results show that the attacks on TdN and our method can only achieve $100\\%$ FSA for four and three model-dataset cases, respectively. Conversely, despite having around $50\\%$ BDR between the forged and genuine signatures, DeepIPR and PAN fail to withstand this attack with $100\\%$ FSA on all the model-dataset combinations. Besides, our method consistently produces the lowest mean performance fidelity of the verification branch for $\\mathcal{V}_O^f$ , especially for ResNet-18 $(57.91\\%)$ and AlexNet $(14.48\\%)$ . Furthermore, our method also exhibits the highest AD that surpasses $\\tau_d$ of $\\mathcal{V}_O^d$ by a significant margin. The results, taken holistically, corroborate that our method has the highest resilience against ambiguity attacks.", + "bbox": [ + 76, + 412, + 468, + 775 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Robustness against license ambiguity attacks", + "text_level": 1, + "bbox": [ + 75, + 790, + 455, + 806 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Two license ambiguity attacks are considered. The first attack is to reveal the attacker's ID image by manipulating the genuine user-side passports. The second attack is to reveal the attacker's ID image from the genuine user-side passport image by forging the steganographic key image.", + "bbox": [ + 75, + 806, + 467, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Forged user-side passport. To simulate this attack, we", + "bbox": [ + 96, + 885, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "retain the ISN's weights and forge user-side passports with the attacker's ID images by minimizing the reveal loss $\\mathcal{L}_r$ between the original forged ID images and revealed forged ID images. The attack was performed by randomly sampling 100 owner-side passport images to generate 100 corresponding user-side passport images, and then using the Adam optimizer on each user-side passport image for 1000 iterations with a learning rate of 0.001. The progression of the attack is depicted in Fig. 4a. The mean PSNR between the original forged ID images and their revealed forged ID images increases and the mean PSNR between the forged user-side passport images and genuine owner-side passport images decreases with iterations. As a result, it becomes impossible for the attacker to simultaneously satisfy the criteria of both $\\mathcal{V}_L^{\\mathrm{I}}$ and $\\mathcal{V}_L^p$ .", + "bbox": [ + 496, + 250, + 890, + 477 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Forged steganographic key. In this experiment, the attacker steals the key-based ISN to forge the steganographic key image. We initialize this attack by randomly sampling a noise vector from a Gaussian distribution 100 times. Correspondingly, we also randomly sample a target forged ID image from the distribution of genuine ID images 100 times, ensuring that there is no overlap between the forged and real images. The forged key images are obtained by an Adam optimizer with a learning rate of 0.001 over 1000 iterations. The progress of this process is depicted in Fig. 4b, where the shaded region marks the range of average PSNRs obtained over 100 rounds of attack. For the forged key images, the deviation is small and the purple shaded region is not visible for the scale of the plot. These observations indicate that this attack fails to satisfy the criteria of $\\nu_{L}^{\\mathbf{I}}$ .", + "bbox": [ + 496, + 478, + 890, + 705 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Robustness against removal attacks", + "text_level": 1, + "bbox": [ + 498, + 715, + 808, + 732 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We consider removal attacks that happen on the deployment branch when that branch is stolen by the attacker or abused by the licensed user. Unlike the pre-deployment model ownership claim in Sec 4.3, the model may be deliberately or maliciously altered after its deployment without compromising its utility, $\\tau_{\\xi}$ for $\\mathcal{V}_O^s$ needs not be infinitely close to 1 to claim the ownership of the deployed model.", + "bbox": [ + 496, + 733, + 890, + 839 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fine-tuning. We consider a transfer-learning task by fine-tuning the deployment branch of a pretrained dual-branch model for 100 epochs at a learning rate of 0.001. As shown in Table 3, our method has the second-highest", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "12308", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/7c98872ae404154900b66506603a682e0b9d4f234c46d9b78d92bd0d3899126e.jpg", + "table_caption": [ + "Table 3. The performance fidelity (in %) of deployment model under fine-tuning attacks. The value in bracket is the signature accuracy." + ], + "table_footnote": [], + "table_body": "
ResNet-18CIFAR-10 to CIFAR-10CIFAR-100 to CIFAR-10Caltech-101 to Caltech-256Caltech-256 to Caltech-101Mean
BNGNBNGNBNGNBNGN
DeepIPR73.81 (96.16)70.71 (95.23)92.10 (99.10)90.98 (99.45)48.53 (99.49)41.48 (99.30)76.05 (99.92)71.75 (100)70.68 (98.58)
PAN71.73 (74.30)68.15 (96.37)91.97 (78.71)90.46 (99.34)47.61 (81.29)39.51 (84.53)79.96 (100)71.64 (99.97)70.13 (89.31)
TdN70.77 (56.05)69.43 (62.70)91.86 (87.50)89.93 (73.87)46.55 (90.51)39.88 (82.30)77.12 (96.09)71.58 (82.81)69.64 (78.98)
Ours64.13 (98.60)65.11 (93.91)92.28 (96.17)90.22 (93.86)43.91 (98.24)37.48 (97.11)76.09 (99.09)69.04 (99.26)67.28 (97.03)
", + "bbox": [ + 81, + 74, + 888, + 148 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9b34983ef4904042e876220a6da169b5bbc64dbd3cdf0faaa6d9047f41b61ac7.jpg", + "image_caption": [ + "(a) CIFAR-10 with BN" + ], + "image_footnote": [], + "bbox": [ + 78, + 154, + 272, + 271 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0387e35ba150d7062f2105b64832fc8c79f8e5d78dfa5ddf53aa9319ec001062.jpg", + "image_caption": [ + "(b) CIFAR-10 with GN", + "Figure 5. The performance of our method under random and $\\ell_1$ norm pruning attacks." + ], + "image_footnote": [], + "bbox": [ + 272, + 156, + 467, + 271 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "average SA of $97.03\\%$ . Given the avalanche criterion of the hash function, a false passport will lead to substantially high signature bit errors. The model owner can still attest the ownership under $\\mathcal{V}_O^s$ with this small signature error. This is because both $\\mathcal{V}_O^f$ and $\\mathcal{V}_O^I$ can still be fulfilled by applying this slightly mismatched signature obtained from the fine-tuned deployment branch to the original dual branch model kept by the model owner. Compared to other passport-based methods, our method has the lowest average performance fidelity upon fine-tuning, making it less attractive to attack our model.", + "bbox": [ + 75, + 321, + 467, + 487 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Pruning. Two prune strategies, i.e., random pruning and $\\ell_1$ -norm pruning are evaluated. For each model, the pruning rate was increased from $0\\%$ to $100\\%$ with a step size of $10\\%$ . The results are shown in Fig. 5. The SA remains relatively high and stable even when the model performance starts to drop abruptly. For example, in Fig. 5a, a $100\\%$ signature detection accuracy is preserved at $80\\%$ pruning rate while the accuracy of the pruned model has fallen to around $50\\%$ . This implies that the pruned model can still pass $\\mathcal{V}_O^f$ and $\\mathcal{V}_O^s$ unless the pruning rate is so high that it renders the model unusable. Additionally, the large AD between the two branches also signifies that the model has been modified, as stated in Sec. 3.5.", + "bbox": [ + 75, + 489, + 467, + 685 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.6. Ablation study", + "text_level": 1, + "bbox": [ + 76, + 700, + 225, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This section investigates the variations of our method without the TLP structure and with other activation functions.", + "bbox": [ + 75, + 718, + 467, + 746 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Without TLP. We examine the inference performance fidelity when the TLP is removed from the BN variants of ResNet-18 and AlexNet, and compare their performances across different datasets. The results presented in Table 4 indicate that the drop in inference performance is trivial for models without TLP compared to their corresponding TLP counterparts. The higher AD of AlexNet, $0.23\\%$ as opposed to $0.00\\%$ of ResNet-18, implies that TLP has negligible impact on the performance fidelity of our method for complex networks but is essential to keep for simpler networks.", + "bbox": [ + 75, + 750, + 467, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f5849c9fce52964267c7247866e43d76cbca007b0093aeb0229f991a57365638.jpg", + "table_caption": [ + "Table 4. Inference performance fidelity (in %) for the deployment/verification branches of our method without TLP." + ], + "table_footnote": [], + "table_body": "
CIFAR-10CIFAR-100Caltech-101Caltech-256AD↓
ResNet-18BN↑BN↑BN↑BN↑
94.47 / 94.4775.19 / 75.2071.53 / 71.5350.46 / 50.460.00
AlexNetBN↑BN↑BN↑BN↑AD↓
91.05 / 91.2568.26 / 68.6570.11 / 70.1142.42 / 42.750.23
", + "bbox": [ + 503, + 183, + 888, + 242 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ce61446735d3779e1b14f948a02e3245badad5066c7a8578d8a204f5c79c8ccc.jpg", + "table_caption": [ + "Table 5. Performance (in %) integrating Sigmoid and LeakyReLU in our proposed passport architecture, trained on CIFAR-10. Dep/Ver refer to deployment/verification branch, respectively." + ], + "table_footnote": [], + "table_body": "
ResNet-18-BNInferenceAmbiguity attack (ERB)
Dep / VerSAADDep / VerFSAAD
Sigmoid94.60 / 94.661000.0694.49 / 17.7699.8476.73
LeakyReLU94.96 / 94.551000.4194.46 / 91.931002.53
", + "bbox": [ + 504, + 287, + 888, + 337 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "With other activation functions. To assess the impact of different activation functions on our method, we also incorporate Sigmoid and LeakyReLU into ResNet-18 with BN. For each activation function, the inference performance and robustness to the ERB attack are evaluated and presented in Table 5. Both activation functions demonstrate comparable performance fidelity between the deployment and verification branches, with SA of $100\\%$ for both activation functions, and AD of $0.06\\%$ and $0.41\\%$ for Sigmoid and LeakyReLU, respectively. The Sigmoid-based model is more resilient to ERB attack than the LeakyReLU-based model, with a significantly higher AD of $76.73\\%$ . Nonetheless, we can adapt the tamper threshold $\\tau_{d}$ to the activation function for higher ambiguity attack resistance.", + "bbox": [ + 496, + 344, + 890, + 555 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 564, + 617, + 579 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduce Steganographic Passport, a novel passport-based model IP licensing protection method that allows the original model ownership to be verified with the passport-aware branch and individual licensees to be verified from the passport-free deployed model without requiring retraining the model for the admission of each licensed user. Legal license verification is made possible by hiding and revealing the licensed user's ID image in a user-side passport of the deployed model by the invertible steganographic network without compromising the accuracy and security of original model ownership verification. Activation-level obfuscation is added to heighten the security of both passports against ambiguity attacks. The affine factors of the deployment and verification branches, as well as the signatures and model's weights are tightly coupled during training to safeguard the owner-side passport and the deployed model's weights against malicious tampering to succeed in forging the ownership or licenseship. The experimental results substantiate the resilience of our method against a range of attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks.", + "bbox": [ + 496, + 583, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "12309", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pages 126-135, 2017. 5", + "[2] Yinpeng Chen, Xiyang Dai, Mengchen Liu, Dongdong Chen, Lu Yuan, and Zicheng Liu. Dynamic ReLU. In European Conference on Computer Vision, pages 351-367. 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On the robustness of backdoor-based watermarking in deep neural networks. In Proceed-" + ], + "bbox": [ + 501, + 92, + 890, + 901 + ], + "page_idx": 8 + }, + { + "type": "page_number", + "text": "12310", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "ings of the 2021 ACM Workshop on Information Hiding and Multimedia Security, pages 177-188, 2021. 1, 2", + "[27] Yusuke Uchida, Yuki Nagai, Shigeyuki Sakazawa, and Shinichi Satoh. Embedding watermarks into deep neural networks. In Proceedings of the 2017 ACM on international conference on multimedia retrieval, pages 269-277, 2017. 1, 2", + "[28] Si Wang, Chaohui Xu, Yue Zheng, and Chip-Hong Chang. A buyer-traceable dnn model IP protection method against piracy and misappropriation. In 2022 IEEE 4th International Conference on Artificial Intelligence Circuits and Systems (AICAS), pages 308-311. IEEE, 2022. 2", + "[29] Yuxin Wu and Kaiming He. Group normalization. In Proceedings of the European conference on computer vision (ECCV), pages 3-19, 2018. 5", + "[30] Jie Zhang, Dongdong Chen, Jing Liao, Weiming Zhang, Gang Hua, and Nenghai Yu. Passport-aware normalization for deep model protection. Advances in Neural Information Processing Systems, 33:22619-22628, 2020. 1, 2, 3, 5, 6" + ], + "bbox": [ + 78, + 90, + 468, + 359 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "12311", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/723188cf-21a3-4072-a767-991efe3bf48f_model.json b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/723188cf-21a3-4072-a767-991efe3bf48f_model.json new file mode 100644 index 0000000000000000000000000000000000000000..70539c7c7b050842b9183d08ef910349c1932411 --- /dev/null +++ b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/723188cf-21a3-4072-a767-991efe3bf48f_model.json @@ -0,0 +1,2310 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.097, + 0.13, + 0.877, + 0.178 + ], + "angle": 0, + "content": "Steganographic Passport: An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining" + }, + { + "type": "text", + "bbox": [ + 0.203, + 0.204, + 0.773, + 0.223 + ], + "angle": 0, + "content": "Qi Cui* Ruohan Meng* Chaohui Xu Chip-Hong Chang†" + }, + { + "type": "text", + "bbox": [ + 0.155, + 0.223, + 0.816, + 0.24 + ], + "angle": 0, + "content": "School of Electrical and Electronic Engineering, Nanyang Technological University" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.243, + 0.868, + 0.258 + ], + "angle": 0, + "content": "qi.cui@ntu.edu.sg, ruohan.meng@ntu.edu.sg, chaohui001@e.ntu.edu.sg, echchang@ntu.edu.sg" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.732 + ], + "angle": 0, + "content": "Ensuring the legal usage of deep models is crucial to promoting trustable, accountable, and responsible artificial intelligence innovation. Current passport-based methods that obfuscate model functionality for license-to-use and ownership verifications suffer from capacity and quality constraints, as they require retraining the owner model for new users. They are also vulnerable to advanced Expanded Residual Block ambiguity attacks. We propose Steganographic Passport, which uses an invertible steganographic network to decouple license-to-use from ownership verification by hiding the user's identity images into the owner-side passport and recovering them from their respective user-side passports. An irreversible and collision-resistant hash function is used to avoid exposing the owner-side passport from the derived user-side passports and increase the uniqueness of the model signature. To safeguard both the passport and model's weights against advanced ambiguity attacks, an activation-level obfuscation is proposed for the verification branch of the owner's model. By jointly training the verification and deployment branches, their weights become tightly coupled. The proposed method supports agile licensing of deep models by providing a strong ownership proof and license accountability without requiring a separate model retraining for the admission of every new user. Experiment results show that our Steganographic Passport outperforms other passport-based deep model protection methods in robustness against various known attacks." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.737, + 0.21, + 0.751 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.754, + 0.47, + 0.786 + ], + "angle": 0, + "content": "To foster Artificial Intelligence (AI) diffusion and application, AI as a Service (AIaaS) has emerged as a lucrative" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.791, + 0.47, + 0.888 + ], + "angle": 0, + "content": "This research is supported by the National Research Foundation, Singapore, and Cyber Security Agency of Singapore under its National Cybersecurity Research & Development Programme (Development of Secured Components & Systems in Emerging Technologies through Hardware & Software Evaluation \\(<\\) NRF-NCR25-DeSNTU-0001>). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the view of National Research Foundation, Singapore and Cyber Security Agency of Singapore." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.888, + 0.42, + 0.901 + ], + "angle": 0, + "content": "†Corresponding author; *Both authors contributed equally." + }, + { + "type": "image", + "bbox": [ + 0.533, + 0.269, + 0.889, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.39, + 0.895, + 0.473 + ], + "angle": 0, + "content": "Figure 1. The conceptual overview. The owner holds the owner-side passport and the steganographic key, which are used to verify the licenses and reveal the user IDs, respectively. The verification branch of the deep model is trained with the constraint of the signature. Upon licensing, the user receives the user-side passport and the deployment branch of the deep model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.478, + 0.893, + 0.644 + ], + "angle": 0, + "content": "business model that offers across-the-broad access to high-performance machine learning models with subscription- or transaction-based payment schemes. The customers can submit inputs to the remote server and receive the inference or classification results of machine learning processes through application program interfaces (APIs). As complex models of high capabilities in AIaaS are offered as \"turnkey\" solutions to potentially anyone, they have huge potential to be misused and abused. Ownership and user license verifications are the first step towards accountability of responsible use of AI services." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Ownership verification has long been a primary tool to protect deployed deep models against intellectual property (IP) infringement and unauthorized model replication [13]. Numerous approaches have been proposed, such as watermarking [8, 27], fingerprinting [10, 23, 24], and backdoor embedding [11, 14, 26]. These approaches typically aim to enable the trained deep model to exhibit distinguishable characteristics under specific conditions without sacrificing its utility. To resist ambiguity attacks, passport-based ownership verification scheme [5, 6, 20, 30] embeds digital passports during model training to obfuscate the primary functionality until the obfuscated parameters are restored by a genuine passport. The passport scheme provides access control [5, 6] at the expense of some accuracy degradation. Each passport is tied to a user model, retraining is required to derive a new user model from the owner model for every new passport issued. The recent passport-aware normal" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "12302" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "ization [30] avoids making structural changes to the target model by training it jointly with a passport-aware branch. The secret passport and passport-aware branch after training are kept by the model owner for future ownership verification and only the original passport-free target model is released to the end users. By forgoing the usage control, this method allows one deployed model to be used by various users but it also loses the accountability of inappropriate and unlawful use of the deployed model by different licensees. Besides, it has been demonstrated that the passports of existing methods can still be counterfeited by the more advanced ambiguity attack [3]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.277, + 0.473, + 0.716 + ], + "angle": 0, + "content": "In usage authorization, one major limitation of existing passport-based methods is the need to retrain the network to incorporate different parameter modulations for every new passport issued, which may cause uneven service quality for different end users. Besides, retraining to accommodate new user models is inflexible, non-scalable and not cost-effective for complex models. This pitfall motivates us to explore anti-forgery passports that allow fidelity verification of deployed model to hold authorized users accountable for misuse of their licensed models without having to retrain the owner model when admitting new users. To this end, we propose a novel Steganographic Passport to decouple user license verification from ownership verification, as illustrated in Fig. 1. For ownership verification, the uniqueness of the model weights is maintained by aligning them with the hashed output of the owner-side passport, which allows the model owner to prove the ownership and authenticity of the distributed model. For license verification, any licensed user's hidden identity (ID) image can be extracted using the user-side passport. Both owner-side and user-side passports will pass the fidelity assessment as their visual similarity is preserved by using steganography to hide the ID image. To increase the sensitivity of the deployed model against malicious tampering of passports and weights, we propose an activation-level obfuscation for the verification branch of the owner model. The weights of the deployment and verification branches are tightly coupled by training them jointly with a balance loss function. Our contributions can be summarized as follows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.72, + 0.47, + 0.796 + ], + "angle": 0, + "content": "- A novel Steganographic Passport is designed based on key-based invertible steganographic network to allow both original model ownership and right-of-use of its deployed model by multiple licensees to be verified without requiring retraining." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.796, + 0.47, + 0.841 + ], + "angle": 0, + "content": "- An activation-level obfuscation architecture is designed to thwart forgery by tampering with the user-side passports or model weights." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.841, + 0.471, + 0.902 + ], + "angle": 0, + "content": "- Extensive experiments are conducted to demonstrate the state-of-the-art security performance of our steganographic passports—the credibility of its owner-side and user-side passport verifications and its robustness against" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "various attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.129, + 0.628, + 0.146 + ], + "angle": 0, + "content": "2. Background" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.148, + 0.892, + 0.465 + ], + "angle": 0, + "content": "The need to safeguard the deep model against misappropriation and IP theft arises from the enormous cost of designing and training a high-performance model from scratch. Given redundancy inherent in the numerous parameters of deep models, it is possible to embed a watermark into a model for ownership identification without significantly impairing its performance. The model can be watermarked either explicitly or implicitly. Explicit watermarking embeds the watermark by modifying the weights [7, 10, 23, 27] or feature maps [8] through a weight regularizer without compromising the original model performance. Implicit watermarking (a.k.a prediction watermarking) deliberately trains a backdoor into the protected model to classify inputs with specific triggers to the predefined labels [11, 14, 22, 26, 28]. However, these techniques are found to be vulnerable to ambiguity attacks as the embedded triggers can be replaced by attackers to forge the ownership with a substitute watermark. To mitigate this risk, model passports are introduced [5, 6], where the affine scale and bias factors of normalization functions are substituted with those derived from the passport images \\(\\{p_{\\gamma}, p_{\\beta}\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.465, + 0.892, + 0.527 + ], + "angle": 0, + "content": "Let \\( x^{l} \\) be the output of the \\( l \\)-th convolutional layer, and \\( \\mu_{x^l} \\) and \\( \\sigma_{x^l} \\) be its mean and standard deviation, respectively. Then, the normalization function at the \\( l \\)-layer with affine factors \\( \\gamma^l \\) and \\( \\beta^l \\) is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.654, + 0.53, + 0.774, + 0.55 + ], + "angle": 0, + "content": "\\[\n\\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\tilde {x ^ {l}} + \\beta^ {l},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.598, + 0.551, + 0.892, + 0.585 + ], + "angle": 0, + "content": "\\[\n\\text {w h e r e} \\quad \\tilde {x ^ {l}} = \\frac {1}{\\sigma_ {x ^ {l}}} \\left(x ^ {l} - \\mu_ {x ^ {l}}\\right). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.586, + 0.892, + 0.629 + ], + "angle": 0, + "content": "By substituting \\(\\gamma^l\\) and \\(\\beta^l\\) by the passport affine factors \\(\\gamma_{p_\\gamma}^l\\) and \\(\\beta_{p_\\beta}^l\\), the following passport normalization [5] is obtained:" + }, + { + "type": "equation", + "bbox": [ + 0.625, + 0.63, + 0.892, + 0.654 + ], + "angle": 0, + "content": "\\[\n\\widehat {x _ {p} ^ {l}} = \\gamma_ {p _ {\\gamma}} ^ {l} \\cdot \\tilde {x} ^ {l} + \\beta_ {p _ {\\beta}} ^ {l}. \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.661, + 0.892, + 0.8 + ], + "angle": 0, + "content": "The sign sequence of \\(\\gamma_{p_\\gamma}^l\\) in Eq. (2) is constrained to match a self-defined binary signature sequence. As large magnitudes of \\(\\gamma_{p_\\gamma}^l\\) can be penalized, the gradients are kept small to ensure that the signs of \\(\\gamma_{p_\\gamma}^l\\) are lazy-to-flip so as to prevent the signature from being replaced by retraining the model. To minimize the influence of passport normalization on inference performance, Zhang et al. [30] proposed a dual-branch passport structure. Its normalization function is expressed in Eq. (3) and illustrated in Fig. 2a." + }, + { + "type": "equation", + "bbox": [ + 0.611, + 0.807, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\tilde {x ^ {l}} + \\beta^ {l}, \\\\ \\widehat {x _ {p} ^ {l}} = \\gamma_ {p _ {\\gamma}} ^ {l} \\cdot \\tilde {x ^ {l}} + \\beta_ {p _ {\\beta}} ^ {l}, \\end{array} \\right. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.851, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where the passport-free output \\(\\widehat{x^l}\\) and the passport-aware output \\(\\widehat{x_p^l}\\) are used for the deployment and ownership verification, respectively. Besides, a two-layer perception (TLP)" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12303" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.067, + 0.273, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.166, + 0.264, + 0.178 + ], + "angle": 0, + "content": "(a) Existing passport architecture" + }, + { + "type": "image", + "bbox": [ + 0.28, + 0.066, + 0.468, + 0.164 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.282, + 0.166, + 0.462, + 0.178 + ], + "angle": 0, + "content": "(b) Proposed passport architecture" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.181, + 0.468, + 0.207 + ], + "angle": 0, + "content": "Figure 2. The existing and proposed passport architectures. The dual branches are enclosed in the dashed line box." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.215, + 0.469, + 0.259 + ], + "angle": 0, + "content": "structure is also inserted before the affine factors to mitigate the strict limitations in managing the functionality of normalization layers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.261, + 0.47, + 0.563 + ], + "angle": 0, + "content": "To protect against ambiguity attacks with oracle passports due to passport leakage, Liu et al. [20] used trapdoor normalization to establish a direct correlation between the signature and the passport through a hash function. The collision-intractable hash function makes it virtually impossible for the attackers to reverse engineer a counterfeit passport, even if they can compromise the signature. Recently, Chen et al. [3] proposed an advanced ambiguity attack called Expanded Residual Block (ERB) on passport-based methods. This attack exploits the extensive solution space of TLP to force-flip the signs of the scale factors according to their forged passport without compromising the model performance. In summary, existing model passport methods aim only to resist the diverse ambiguity attacks by obfuscating the normalization functionalities with immutable passports. They do not allow admission of new users and their right-of-use verification upon model deployment. This is an important measure to safeguard the interest of AIaaS providers against revenue extorts by unauthenticated usage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.567, + 0.248, + 0.584 + ], + "angle": 0, + "content": "3. Proposed method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.588, + 0.259, + 0.603 + ], + "angle": 0, + "content": "3.1. Problem statement" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.469, + 0.847 + ], + "angle": 0, + "content": "We consider a practical licensing scenario of a deep model. Besides being able to detect and verify the ownership of a deployed model, the model owner should also be able to verify usage permission. If the passport images \\(\\{p_{\\gamma}, p_{\\beta}\\}\\) are used as a unique proof to verify the ownership of the deployed model, they cannot be used to verify the usage permission granted to licensed users of that model. Although new backdoor triggers or watermarks can be added to verify each licensed user, the model needs to be retrained to learn the new features. This is very restrictive and impractical as it requires the model owner to fix the number of users and their identities upfront. Therefore, our aim is to enable the passport-based scheme to grant verifiable usage permission of a deployed deep model to ad hoc registered users without requiring retraining and without undermining the validity and robustness of the model's ownership proof." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.855, + 0.394, + 0.87 + ], + "angle": 0, + "content": "3.2. Steganographic passport framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Recall that in existing passport approaches [5, 6, 20, 30], a forged passport image can also be used to pass the fi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.182 + ], + "angle": 0, + "content": "delity assessment if it bears a high visual similarity to the genuine passport image. Inspired by advanced steganography techniques, we apply the art of imperceptible secret concealment to the passport-based scheme. The proposed Steganographic Passport follows the dual-branch setting, as illustrated in Fig. 2b." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.409 + ], + "angle": 0, + "content": "We define an owner-side passport \\( p_{o} = \\{p_{o_{\\gamma}}, p_{o_{\\beta}}\\} \\) as the genuine passport images selected and held only by the model owner for generating the affine scale and bias factors accordingly. By feeding \\( p_{o} \\) into the model, the corresponding owner-side passport feature maps are sequentially generated across the \\( n \\) passport layers. These feature maps are then transformed into the affine factors for obfuscating the verification branch, which will be described in Sec. 3.3. We also introduce a new user-side passport, \\( p_{u} = \\{p_{u_{\\gamma}}, p_{u_{\\beta}}\\} \\), which is obtained by hiding the ID image \\( \\mathrm{I}_u \\) provided by a registered user into \\( p_{o} \\). The user-side passport \\( p_{u} \\) fills the gap of existing passport-based limitation in meeting the goal of Sec. 3.1. The model owner can license the deployment branch of the model to multiple registered users by merely hiding each user's ID image into \\( p_{o} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.409, + 0.891, + 0.514 + ], + "angle": 0, + "content": "Anti-forgery owner-side passport. To avoid user-side passports from exposing the visual content of the owner-side passports, the owner-side passport is irreversibly transformed to a unique model signature to ensure that the ownership cannot be forged by knowing any of the user-side passports. SHA-512 [25] is used as the one-way function for this mapping." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.515, + 0.892, + 0.559 + ], + "angle": 0, + "content": "Before training the target model, the model owner hashes the owner-side \\( p_{o_{\\gamma}} \\) to a binary signature \\( \\xi^l \\) of passport layer \\( l \\), as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.575, + 0.563, + 0.891, + 0.581 + ], + "angle": 0, + "content": "\\[\n\\xi^ {l} = \\left\\{\\operatorname {S G N} (x) \\mid x \\in \\operatorname {H A S H} \\left(p _ {o _ {\\gamma}}\\right) \\right\\}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.659 + ], + "angle": 0, + "content": "where SGN maps each bit of a binary input sequence from \\(\\{0,1\\}\\) to \\(\\{-1,1\\}\\). If the desired length of \\(\\xi^l\\) is shorter than 512 bits, the excess bits of the hash output are truncated from the beginning; Otherwise, we cycle the hash function's output until the required sequence length is obtained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.855 + ], + "angle": 0, + "content": "For a model with \\( n \\) passport layers, its overall model signature is represented as \\( \\{\\xi^1, \\xi^2, \\dots, \\xi^n\\} \\). The strict avalanche criterion of the hash function ensures that even minor changes to the passport image will result in significantly different affine factors, which prevents force-flipping from forging the passport with high model performance fidelity. Together with the irreversibility property of SHA-512, the genuine model signature \\( \\xi \\) can only be generated with the owner-side passport to thwart ownership impersonation fraud. The signature \\( \\{\\xi^1, \\xi^2, \\dots, \\xi^n\\} \\) will be used to constrain the model's learning in the subsequent training phase to transform them into unique model's weights. A detailed exposition of this process is provided in Sec. 3.3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.857, + 0.892, + 0.901 + ], + "angle": 0, + "content": "License verification via key-based deep steganography. To support an agile licensing scheme that is capable of admitting and verifying any new user after the tar" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12304" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.243 + ], + "angle": 0, + "content": "get model has finalized its training phase, we need to decouple the license verification from the ownership verification. To this end, we hide the user's ID into the owner-side passport by integrating the key-based scheme of Invertible Steganographic Network (ISN) [21] within the Deep Image Hiding Network (HiNet) framework [15]. The key-based ISN is divided into two processes: forward hiding pass \\(\\mathcal{H}_s\\) and reverse revealing pass \\(\\mathcal{H}_s^{-1}\\). The forward hiding pass is used to obtain the user-side passport \\(p_u\\) from the owner-side passport \\(p_o\\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.213, + 0.246, + 0.47, + 0.263 + ], + "angle": 0, + "content": "\\[\np _ {u} = \\mathcal {H} _ {s} \\left(p _ {o}, \\mathrm {I} _ {u}\\right), \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.264, + 0.47, + 0.295 + ], + "angle": 0, + "content": "where \\(\\mathrm{I}_u\\) denotes the user's ID image to be hidden into the owner-side passport \\(p_o\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.295, + 0.47, + 0.355 + ], + "angle": 0, + "content": "The reverse revealing pass is utilized for license verification. Using the private steganographic key \\(\\mathbf{k}_s\\), the model owner can reveal the hidden user's ID image from the underside passport \\(p_u\\):" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.356, + 0.469, + 0.375 + ], + "angle": 0, + "content": "\\[\n\\mathrm {I} _ {u} ^ {\\prime} = \\mathcal {H} _ {s} ^ {- 1} \\left(p _ {u}, \\mathbf {k} _ {s}\\right), \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.376, + 0.47, + 0.422 + ], + "angle": 0, + "content": "where \\(\\mathrm{I}_u^\\prime\\) denotes the revealed ID image of the licensed user. The detailed architecture and algorithms of the hiding and revealing passes are given in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.43, + 0.328, + 0.444 + ], + "angle": 0, + "content": "3.3. Activation-level obfuscation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.446, + 0.47, + 0.506 + ], + "angle": 0, + "content": "To counteract sophisticated ambiguity attacks, an activation-level obfuscation is proposed to safeguard the verification branch against alterations of both the passport and the model's weights." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.553 + ], + "angle": 0, + "content": "Immutable passport. As illustrated in Fig. 2b, the passport-affine factors of layer \\( l \\) can be calculated from the passport feature maps \\( p_{o}^{l} \\) by:" + }, + { + "type": "equation", + "bbox": [ + 0.095, + 0.553, + 0.469, + 0.58 + ], + "angle": 0, + "content": "\\[\n\\gamma_ {p _ {o _ {\\gamma}}} ^ {l} = \\Phi (\\Pi (p _ {o _ {\\gamma}} ^ {l})) \\text {, a n d} \\beta_ {p _ {o _ {\\beta}}} ^ {l} = \\Phi (\\Pi (p _ {o _ {\\beta}} ^ {l})) \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.58, + 0.469, + 0.61 + ], + "angle": 0, + "content": "where \\(\\Phi\\) and \\(\\Pi\\) denote the TLP and the global average pooling, respectively." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.469, + 0.671 + ], + "angle": 0, + "content": "Inspired by the controllable rectifiers of the Dynamic ReLU [2], we make \\(\\gamma_{p_{o\\gamma}}^l\\) and \\(\\beta_{p_{o\\beta}}^l\\) the dependent variables of the activation function. This can be incorporated into a dual-branch architecture as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.141, + 0.673, + 0.469, + 0.713 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} \\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\widetilde {x ^ {l}} + \\beta^ {l}, \\\\ \\widehat {x _ {p _ {o}} ^ {l}} = \\gamma_ {p _ {o \\gamma}} ^ {l} \\cdot \\left(\\gamma_ {t} ^ {l} \\cdot \\widetilde {x ^ {l}} + \\beta_ {t} ^ {l}\\right) + \\beta_ {p _ {o \\beta}} ^ {l}, \\end{array} \\right. \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.716, + 0.469, + 0.763 + ], + "angle": 0, + "content": "where \\(\\gamma^l\\) and \\(\\beta^l\\) denote the original affine factors used in the deployment branch, and \\(\\gamma_t^l\\) and \\(\\beta_t^l\\) denote the additional temporal affine factors used in the verification branch." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.469, + 0.826 + ], + "angle": 0, + "content": "To simplify the expressions, let \\( x_{t}^{l} = \\gamma_{t}^{l}\\cdot x^{l} + \\beta_{t}^{l} \\). By subjecting the outputs of Eq. (8) to an activation function (e.g. ReLU) before feeding them to the next layer, the final outputs of layer \\( l \\) are given by:" + }, + { + "type": "equation", + "bbox": [ + 0.143, + 0.828, + 0.469, + 0.869 + ], + "angle": 0, + "content": "\\[\n\\left\\{ \\begin{array}{l} x _ {\\varphi} ^ {l} = \\max \\left(\\widehat {x ^ {l}}, 0\\right), \\\\ x _ {\\varphi_ {p o}} ^ {l} = \\max \\left(\\gamma_ {p _ {o \\gamma}} ^ {l} \\cdot \\widehat {x _ {t} ^ {l}} + \\beta_ {p _ {o \\beta}} ^ {l}, 0\\right). \\end{array} \\right. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.902 + ], + "angle": 0, + "content": "The activation function used for the deployment branch (top expression) in Eq. (9) is a regular ReLU, whereas the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.186 + ], + "angle": 0, + "content": "activation function used for the verification branch (bottom expression) can be viewed as a special case of Dynamic ReLU. This way, the changes in the affine factors due to any alterations of the owner-side passport \\( p_o \\) will lead to apparent changes in the passport-aware output, \\( x_{\\varphi_{p_o}}^l \\), but not in the passport-free output, \\( x_{\\varphi}^{l} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.185, + 0.892, + 0.35 + ], + "angle": 0, + "content": "Immutable deployment branch. Under the dual-branch setting, the deployment and verification branches share all the model's weights but the affine factors. The deployment branch has to be consistently updated according to the updated passport-derived affine factors in the verification branch. If the deployment branch cannot keep up with the updates, the shared weights will overfit the verification branch, causing gradient explosions. To keep the updates of the two branches in tandem, the following balance loss function is proposed to train the model by explicitly aligning the affine factors in Eq. (8):" + }, + { + "type": "equation", + "bbox": [ + 0.509, + 0.35, + 0.892, + 0.387 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {b} = \\sum_ {l = 1} ^ {n} \\left(\\mathcal {L} _ {\\mathrm {y}} \\left(\\gamma^ {l}, \\gamma_ {t} ^ {l} \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l}\\right) + \\mathcal {L} _ {\\mathrm {y}} \\left(\\beta^ {l}, \\beta_ {t} ^ {l} \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l} + \\beta_ {p _ {o _ {\\beta}}} ^ {l}\\right)\\right), \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.386, + 0.892, + 0.415 + ], + "angle": 0, + "content": "where \\(\\ell_1\\) norm is used for \\(\\mathcal{L}_y\\), and \\(n\\) is the total number of passport layers." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.892, + 0.551 + ], + "angle": 0, + "content": "This loss function aims to strike an equilibrium performance between the two branches. After the model is trained, the verification branch is removed from the model before it is licensed to any user. As the model trained with the balance loss function will have negligible accuracy difference between the two branches, any modification on the deployment branch would amplify the mean absolute difference. By comparing the accuracy difference between the two branches, the integrity of the model can be validated." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.552, + 0.892, + 0.613 + ], + "angle": 0, + "content": "Immutable verification branch. During the target model's training phase, the owner uses the model signature \\(\\{\\xi^1,\\xi^2,\\dots ,\\xi^n\\}\\) to constrain the update of model's weights with the following signature loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.532, + 0.613, + 0.892, + 0.639 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {s} = \\sum \\max \\left(\\epsilon - \\xi^ {l} \\cdot \\Pi \\left(p _ {o _ {\\gamma}} ^ {l}\\right) \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l}, 0\\right), \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.671 + ], + "angle": 0, + "content": "where \\(\\xi^l\\) and \\(p_{o_\\gamma}^l\\) denote the \\(l\\)-th layer's signature and passport feature map, respectively, and \\(\\epsilon\\) is a small constant." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.672, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\(\\mathcal{L}_s\\) encourages the signs of the product \\(\\Pi \\left(p_{o_\\gamma}^l\\right) \\cdot \\gamma_{p_{o_\\gamma}}^l\\) to align with that of \\(\\xi^l\\), while keeping the magnitude of this product low. Since \\(p_{o_\\gamma}^l\\) and \\(\\gamma_{p_{o_\\gamma}}^l\\) are the outputs of the convolution and TLP, respectively, the weights of the convolution layer and TLP become tightly coupled. The uniqueness of \\(\\xi^l\\) in Eq. (11) contributes to the distinctiveness of the weights. Any adjustment to the TLP will directly affect the convolution output. This property helps to prevent advanced ambiguity attacks, especially ERB, which maliciously alter the weights of the TLP to force-flip the signs of the product to align it with the forged signature." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.855, + 0.684, + 0.87 + ], + "angle": 0, + "content": "3.4. Training objectives" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The one-time training pipeline consists of training the key-based ISN and the target model." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12305" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.152 + ], + "angle": 0, + "content": "Training the key-based ISN. The key-based ISN is trained once independently of the target model to enhance the hiding invisibility and the revealing quality by the following loss function:" + }, + { + "type": "equation", + "bbox": [ + 0.164, + 0.156, + 0.469, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I S N} = \\mathcal {L} _ {h} \\left(p _ {o}, p _ {u}\\right) + \\mathcal {L} _ {r} \\left(\\mathrm {I} _ {u}, \\mathrm {I} _ {u} ^ {\\prime}\\right). \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.177, + 0.469, + 0.207 + ], + "angle": 0, + "content": "Both \\(\\mathcal{L}_h\\) and \\(\\mathcal{L}_r\\) utilize the \\(\\ell_2\\) norm for distance calculation. \\(p_o\\) and \\(\\mathrm{I}_u\\) are randomly sampled in the training phase." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.208, + 0.469, + 0.297 + ], + "angle": 0, + "content": "Training the target model. Given a target model, we denote the models with only the weights of the deployment branch as \\(\\mathcal{M}\\), and those with only the weights of the \\(p_o\\)-based verification branch as \\(\\mathcal{M}_{p_o}\\). Three loss functions are used to train the dual branches parallelly. The loss function for model performance is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.302, + 0.469, + 0.342 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {f} = \\frac {1}{N _ {t r}} \\sum_ {i = 1} ^ {N _ {t r}} \\left(\\mathcal {L} _ {c} \\left(\\mathcal {M} \\left(x _ {i}\\right), y _ {i}\\right) + \\mathcal {L} _ {c} \\left(\\mathcal {M} _ {p _ {o}} \\left(x _ {i}\\right), y _ {i}\\right)\\right), \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.346, + 0.469, + 0.376 + ], + "angle": 0, + "content": "where \\( x_{i} \\) and \\( y_{i} \\) are respectively the \\( i \\)-th sample and its label from \\( N_{tr} \\) training samples, and \\( \\mathcal{L}_c \\) is the cross-entropy loss." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.376, + 0.469, + 0.404 + ], + "angle": 0, + "content": "Together with the signature loss \\(\\mathcal{L}_s\\) and the balance loss \\(\\mathcal{L}_b\\), the total loss is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.41, + 0.469, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = \\mathcal {L} _ {f} + \\omega_ {s} \\mathcal {L} _ {s} + \\omega_ {b} \\mathcal {L} _ {b}, \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.431, + 0.468, + 0.461 + ], + "angle": 0, + "content": "where the signature and balance losses are weighted by \\(\\omega_{s}\\) and \\(\\omega_{b}\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.47, + 0.32, + 0.484 + ], + "angle": 0, + "content": "3.5. Inclusive verification chain" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.486, + 0.469, + 0.546 + ], + "angle": 0, + "content": "To confirm the ownership and legal usability of a deployed model M, we propose the following verification chain involving the model owner O, the licensed user U, and the deployed model M." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.547, + 0.469, + 0.652 + ], + "angle": 0, + "content": "Ownership verification. The ownership verification comprises three tests: \\(\\mathcal{V}_O^{\\mathcal{I}}\\), \\(\\mathcal{V}_O^f\\) and \\(\\mathcal{V}_O^s\\) for the verification of the model integrity, performance fidelity and signature accuracy, respectively. By replacing the passport layers' affine factors with the ones derived from the owner-side passport \\(p_o\\), the deployed branch \\(\\mathbf{M}\\) becomes a verifiable branch \\(\\mathbf{M}_{p_o}\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.652, + 0.469, + 0.697 + ], + "angle": 0, + "content": "Let \\(\\mathcal{F}(\\cdot ,\\cdot)\\) denote the model performance. \\(\\nu_{O}^{\\mathcal{T}}\\) tests if \\(\\mathbf{M}\\) has been modified based on the absolute performance difference (AD):" + }, + { + "type": "equation", + "bbox": [ + 0.084, + 0.701, + 0.469, + 0.749 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {O} ^ {\\mathcal {I}} \\Longleftrightarrow \\frac {1}{N _ {t}} \\left| \\sum_ {j = 1} ^ {N _ {t}} \\left(\\mathcal {F} \\left(\\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\\right) - \\mathcal {F} \\left(\\mathbf {M}, x _ {j} ^ {t}\\right)\\right) \\right| < \\tau_ {d}, \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.752, + 0.469, + 0.782 + ], + "angle": 0, + "content": "where \\( x_{j}^{t} \\) is the \\( j \\)-th sample from total \\( N_{t} \\) test samples, and \\( \\tau_{d} \\) is a small predefined passing threshold." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.781, + 0.36, + 0.798 + ], + "angle": 0, + "content": "\\(\\mathcal{V}_O^f\\) verifies the performance fidelity by:" + }, + { + "type": "equation", + "bbox": [ + 0.146, + 0.799, + 0.469, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {O} ^ {f} \\Longleftrightarrow \\frac {1}{N _ {t}} \\sum_ {j = 1} ^ {N _ {t}} \\mathcal {F} \\left(\\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\\right) > \\tau_ {f}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.841, + 0.469, + 0.871 + ], + "angle": 0, + "content": "where \\(\\tau_{f}\\) is the predefined minimum accuracy to pass the performance fidelity verification." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.902 + ], + "angle": 0, + "content": "To validate the signature accuracy, the owner uses Eq. (4) to transform \\( p_{o_{\\gamma}} \\) into the model signature \\( \\xi = \\)" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.091, + 0.892, + 0.135 + ], + "angle": 0, + "content": "\\(\\{\\xi^1,\\xi^2,\\dots ,\\xi^n\\}\\) . By comparing each element of \\(\\xi\\) with those of \\(\\xi^{*}\\) extracted from \\(\\mathbf{M}_{p_o}\\) \\(\\nu_{O}^{s}\\) checks the sign agreement (SA) by:" + }, + { + "type": "equation", + "bbox": [ + 0.583, + 0.134, + 0.892, + 0.174 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {O} ^ {s} \\Longleftrightarrow \\frac {1}{N _ {\\xi}} \\sum_ {b = 1} ^ {N _ {\\xi}} \\left(\\xi_ {b} \\wedge \\xi_ {b} ^ {*}\\right) \\geq \\tau_ {\\xi}, \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.177, + 0.892, + 0.237 + ], + "angle": 0, + "content": "where \\(N_{\\xi}\\) is the total length of \\(\\xi\\). \\(\\tau_{\\xi}\\) is a predefined error tolerance only for the post-distribution verification. Otherwise, the SA of an untainted pre-deployment model has to be \\(100\\%\\) (i.e., \\(\\tau_{\\xi} = 1\\)) to satisfy \\(\\mathcal{V}_O^s\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.238, + 0.892, + 0.297 + ], + "angle": 0, + "content": "Remark 1: Before distributing the deployed model \\(\\mathbf{M}\\), the owner \\(\\mathbf{O}\\) is required to disclose the evidence of compliance with \\(\\mathcal{V}_O^{\\mathcal{T}}\\), \\(\\mathcal{V}_O^f\\), and \\(\\mathcal{V}_O^s\\) to establish the credibility of the ownership claim of \\(\\mathbf{M}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.298, + 0.892, + 0.388 + ], + "angle": 0, + "content": "License verification. Upon verifying that the model M deployed by the licensed user \\(\\mathbf{U}\\) complies with the criteria set by \\(\\mathcal{V}_O^{\\mathcal{T}}\\), \\(\\mathcal{V}_O^f\\), and \\(\\mathcal{V}_O^s\\), a provable association between the licensed user \\(\\mathbf{U}\\) and the model owner \\(\\mathbf{O}\\) can be established by two license verification tests: \\(\\mathcal{V}_L^p\\) for passport image similarity, and \\(\\mathcal{V}_L^I\\) for ID image similarity." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.388, + 0.892, + 0.433 + ], + "angle": 0, + "content": "Upon receiving \\( p_u \\) submitted by the user \\( \\mathbf{U} \\), the owner can compare the PSNR between the user and owner passport images by:" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.436, + 0.892, + 0.453 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {L} ^ {p} \\Longleftrightarrow \\operatorname {P S N R} \\left(p _ {o}, p _ {u}\\right) > \\tau_ {p}, \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.455, + 0.892, + 0.484 + ], + "angle": 0, + "content": "where \\(\\tau_{p}\\) is the predefined visual similarity threshold for successful verification." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.892, + 0.576 + ], + "angle": 0, + "content": "The reverse revealing pass is utilized for license verification. Using the private steganographic key \\(\\mathbf{k}_s\\), the model owner can reveal the hidden user's ID image \\(\\mathrm{I}_u^{\\prime}\\) from the user-side passport \\(p_u\\) by Eq. (6). \\(\\mathcal{V}_L^{\\mathrm{I}}\\) tests the visual similarity between \\(\\mathrm{I}_u\\) and the revealed ID image, \\(\\mathrm{I}_u^{\\prime}\\) of the licensed user by comparing the PSNR with predefined threshold \\(\\tau_r\\):" + }, + { + "type": "equation", + "bbox": [ + 0.592, + 0.579, + 0.892, + 0.596 + ], + "angle": 0, + "content": "\\[\n\\mathcal {V} _ {L} ^ {\\mathrm {I}} \\Longleftrightarrow \\operatorname {P S N R} \\left(\\mathrm {I} _ {u}, \\mathrm {I} _ {u} ^ {\\prime}\\right) > \\tau_ {r}. \\tag {19}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.892, + 0.658 + ], + "angle": 0, + "content": "Remark 2: Once \\(\\mathcal{V}_L^p\\) and \\(\\mathcal{V}_L^{\\mathrm{I}}\\) are satisfied, on the condition that the model \\(\\mathbf{M}\\) passes the three ownership verification tests of the owner \\(\\mathbf{O}\\), the user \\(\\mathbf{U}\\) is proven to be a legal licensee of \\(\\mathbf{M}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.664, + 0.625, + 0.681 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.689, + 0.581, + 0.704 + ], + "angle": 0, + "content": "4.1. Setup" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Generally, we follow the settings on image classification tasks in existing passport approaches, including dual-branch DeepIPR [6], Passport-Aware Normalization (PAN) [30], and Trapdoor Normalization (TdN) [20]. AlexNet [17] and ResNet-18 [9], with Batch Normalization (BN) [12] and Group Normalization (GN) [29], are employed to evaluate and compare the performance. The datasets used in the classification experiments include CIFAR-10, CIFAR-100 [16], Caltech-101, and Caltech-256 [18]. Besides, DIV2K [1] is used to train the key-based ISN. For passport images \\( p_{\\gamma} \\) and \\( p_{\\beta} \\), we randomly select them from the test set of COCO dataset [19]. For steganographic key image \\( \\mathbf{k}_s \\), we randomly select it from DTD" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12306" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.114, + 0.061, + 0.85, + 0.074 + ], + "angle": 0, + "content": "Table 1. Inference performance (in %) for deployment/verification. \\( \\uparrow / \\downarrow \\) denotes higher / lower value for better performance." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.075, + 0.891, + 0.228 + ], + "angle": 0, + "content": "
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18BN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean94.6993.8576.4273.5774.5870.7355.4349.5273.60-
DeepIPR93.04 / 94.0593.81 / 93.6960.76 / 62.8872.19 / 71.1573.84 / 73.2265.08 / 63.3341.53 / 44.1243.81 / 42.6768.01 / 68.141.30
PAN94.70 / 94.6193.63 / 93.6775.97 / 74.7072.19 / 71.4973.79 / 72.9468.36 / 65.3755.37 / 54.3344.73 / 43.5172.34 / 71.331.03
TdN94.65 / 94.6893.57 / 93.5776.00 / 75.6171.25 / 71.4274.12 / 73.0567.63 / 67.5154.90 / 54.2844.90 / 44.2772.13 / 71.800.38
Ours94.89 / 94.8993.79 / 93.8076.10 / 76.1070.84 / 70.8373.56 / 73.5667.01 / 67.0153.65 / 53.6544.01 / 44.0171.73 / 71.730.00
AlexNetBN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean91.2090.2768.4065.7271.5868.7044.2441.1867.66-
DeepIPR81.80 / 90.7689.90 / 90.2045.71 / 51.7764.89 / 64.1667.91 / 65.9567.80 / 67.0631.39 / 36.2540.69 / 39.7360.14 / 63.243.07
PAN91.51 / 91.2990.22 / 90.3968.46 / 66.4450.60 / 56.7171.03 / 70.9066.95 / 66.7144.93 / 41.1340.03 / 38.8466.47 / 65.311.32
TdN91.28 / 91.0290.08 / 89.8068.71 / 68.0764.54 / 63.7770.45 / 69.4468.31 / 66.3845.36 / 44.8242.39 / 37.8867.64 / 66.401.24
Ours91.39 / 91.3889.77 / 89.7767.86 / 67.8563.36 / 63.3471.98 / 71.9868.42 / 68.4246.10 / 46.0741.10 / 41.1267.50 / 67.490.01
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.308 + ], + "angle": 0, + "content": "dataset [4]. For hyper-parameters \\(\\epsilon, \\omega_s\\), and \\(\\omega_b\\), we empirically set them as 0.1, 1, and 1. By default, the last three/five normalization layers of AlexNet/ResNet-18 are set as the passport layers." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.318, + 0.292, + 0.333 + ], + "angle": 0, + "content": "4.2. Verification assessment" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.469, + 0.448 + ], + "angle": 0, + "content": "We evaluate the effectiveness of the proposed steganographic passport by the verification and inference performances. All the models are trained with 200 epochs, utilizing a multi-step learning rate that decreases gradually from 0.01 to 0.0001. A twofold verification is adopted in our method, which entails a) an ownership verification \\(\\{\\mathcal{V}_O^{\\mathcal{T}},\\mathcal{V}_O^f,\\mathcal{V}_O^s\\}\\) and b) a license verification \\(\\{\\mathcal{V}_L^p,\\mathcal{V}_L^1\\}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.449, + 0.47, + 0.734 + ], + "angle": 0, + "content": "For ownership verification, our steganographic passport exhibits the lowest AD values of \\(0.00\\%\\) on ResNet-18 and \\(0.01\\%\\) on AlexNet for \\(\\mathcal{V}_O^T\\) with the correct owner passport, as presented in Table 1. This is attributed to the effect of the balance loss function, which ensures that the updates of the affine factors of the two branches are more synchronized during training. For \\(\\mathcal{V}_O^f\\), due to the stronger anti-forgery passport constraint imposed by our method, there is a slight decrease in model inference performance compared to Tdn and PAN, but it still outperforms DeepIPR. As shown in Table 1, the average deployment and verification branch accuracies of our method on ResNet-18 are both \\(71.73\\%\\), which is only \\(0.40\\%\\) and \\(0.07\\%\\) lower than the accuracies of the deployment and verification branches, respectively of Tdn. The performance of our method peaks in several cases highlighted with the bold-printed percentages. For instance, it achieves the top score of \\(71.98\\%\\) for AlexNet on Caltech-101. For \\(\\mathcal{V}_O^s\\), the SAs of all four methods achieve \\(100\\%\\) in all the settings." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.47, + 0.902 + ], + "angle": 0, + "content": "For license verification, a comparison of the visual images for \\(\\mathcal{V}_L^p\\) and \\(\\mathcal{V}_L^{\\mathrm{I}}\\) is presented in Fig. 3. A very high PSNR of 41.47 between the original ID image and the ID image revealed using the genuine steganographic key is obtained, indicating a high level of visual similarity between them. In contrast, using forged keys to reveal the ID image results in significantly lower PSNR. Specifically, a PSNR of only 15.48 is obtained for the revealed ID images by using a random noise-like forged passport image and 32.56 by using a steganographic key image selected randomly from the same distribution as the genuine key image. Further" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.245, + 0.87, + 0.427 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.43, + 0.892, + 0.446 + ], + "angle": 0, + "content": "Figure 3. Hiding and revealing performance of the key-based ISN." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.453, + 0.892, + 0.514 + ], + "angle": 0, + "content": "more, upon repeating this evaluation 100 times, the average PSNRs obtained from revealing the ID image by using random noise-like forged and randomly-selected key images are 15.68 and 35.89, respectively." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.514, + 0.892, + 0.591 + ], + "angle": 0, + "content": "Based on the above observations, we empirically set \\(\\tau_{d}\\), \\(\\tau_{\\xi}\\), \\(\\tau_{p}\\) and \\(\\tau_{r}\\) to \\(0.05\\%\\), \\(93\\%\\), 39 and 41 for \\(\\mathcal{V}_O^{\\mathcal{I}}\\), \\(\\mathcal{V}_O^s\\), \\(\\mathcal{V}_L^p\\) and \\(\\mathcal{V}_L^i\\), respectively. For \\(\\mathcal{V}_O^f\\), \\(\\tau_{f}\\) is calibrated according to the task as the same clean model trained for different tasks has different inference performance." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.596, + 0.892, + 0.626 + ], + "angle": 0, + "content": "4.3. Robustness against ownership ambiguity attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.853 + ], + "angle": 0, + "content": "Ownership ambiguity attacks aim to falsely claim the ownership of a deep model by satisfying the conditions outlined in Remark 1. Owing to the avalanche criterion provided by the hash function, attacks that attempt to forge the genuine passport images by random selection [6, 20, 30] or tamper with the user-side passport images will fail on \\(\\mathcal{V}_O^s\\) due to the significant signature deviation. Additionally, it is computationally intractable to reverse the uniformly random and collision-resistant cryptographically secure hash function to recover genuine passport images [20]. Thus, we specifically focus on the state-of-the-art ERB ownership ambiguity attack, under the strict assumption that the attacker has stolen both the deployment and verification branches, along with \\(10\\%\\) of original training data. The individual version of ERB, i.e., IERB is used to attack the models with BN." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "ERB demonstrated its effectiveness by retraining the model to fit a forged passport. In ERB's original configuration, attackers directly fabricate the passport layer's affine" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12307" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.892, + 0.117 + ], + "angle": 0, + "content": "Table 2. Inference performance fidelity (in %) for deployment/verification under ERB ambiguity attacks with BN. FSA and BDR refer to the forged signature accuracy and the bit difference rate between benign and forged signatures, respectively." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.117, + 0.89, + 0.242 + ], + "angle": 0, + "content": "
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR94.19 / 94.3910050.2262.92 / 64.0610049.4973.56 / 73.8910050.2346.05 / 46.3910049.3769.18 / 69.680.50
PAN94.64 / 94.7210048.7175.28 / 75.1010049.5773.11 / 73.0510049.3053.62 / 53.5810050.0874.16 / 74.110.90
TdN94.48 / 94.2410053.0975.91 / 66.6610048.2073.22 / 64.5499.9650.0454.49 / 34.6110051.7674.53 / 65.019.51
Ours94.70 / 92.8710049.5375.85 / 50.2799.9649.1873.00 / 50.0699.9251.0552.87 / 38.4410049.1873.82 / 57.9116.20
AlexNetERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR26.54 / 85.7210047.6146.61 / 51.9710050.1163.56 / 67.8310052.6532.61 / 34.3410051.0842.31 / 59.9717.64
PAN91.56 / 82.0610052.4368.36 / 60.2910049.8770.37 / 69.1710053.3844.41 / 40.1510052.5668.68 / 62.925.76
TdN90.16 / 53.1610051.3366.96 / 1.6598.9649.7870.26 / 37.1998.9649.9644.14 / 0.2895.3148.2467.88 / 23.0744.81
Ours84.90 / 16.1199.5750.2467.38 / 1.0296.7549.7271.26 / 35.8698.9650.3345.00 / 4.9310051.1767.14 / 14.4852.66
" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.245, + 0.272, + 0.35 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.126, + 0.353, + 0.228, + 0.365 + ], + "angle": 0, + "content": "(a) Forged passport" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.246, + 0.462, + 0.351 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.287, + 0.353, + 0.449, + 0.365 + ], + "angle": 0, + "content": "(b) Forged steganographic key" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.365, + 0.468, + 0.404 + ], + "angle": 0, + "content": "Figure 4. Results of license ambiguity attacks on our method. Batch Normalization is used in the evaluated models. We set the Z-score as 2.33 for \\(98\\%\\) confidence interval (CI)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.414, + 0.47, + 0.776 + ], + "angle": 0, + "content": "factors, leveraging the network's differentiable architecture to deduce the passport images. However, this possibility is denied by the hash functions of our method and TdN. Therefore, while maintaining the original settings of ERB for DeepIPR and PAN, the passport layer's affine factors in our method and TdN are to be derived from the corresponding hash-related functions. Table 2 displays the experimental results. To successfully meet the criteria of Remark 1, the attack must achieve \\(100\\%\\) of forged SA (FSA) for \\(\\mathcal{V}_O^s\\). As evinced by the results presented in Sec. 4.2, the legitimate owner is able to comply with this stringent criteria. The experimental results show that the attacks on TdN and our method can only achieve \\(100\\%\\) FSA for four and three model-dataset cases, respectively. Conversely, despite having around \\(50\\%\\) BDR between the forged and genuine signatures, DeepIPR and PAN fail to withstand this attack with \\(100\\%\\) FSA on all the model-dataset combinations. Besides, our method consistently produces the lowest mean performance fidelity of the verification branch for \\(\\mathcal{V}_O^f\\), especially for ResNet-18 \\((57.91\\%)\\) and AlexNet \\((14.48\\%)\\). Furthermore, our method also exhibits the highest AD that surpasses \\(\\tau_d\\) of \\(\\mathcal{V}_O^d\\) by a significant margin. The results, taken holistically, corroborate that our method has the highest resilience against ambiguity attacks." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.791, + 0.457, + 0.807 + ], + "angle": 0, + "content": "4.4. Robustness against license ambiguity attacks" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.808, + 0.468, + 0.884 + ], + "angle": 0, + "content": "Two license ambiguity attacks are considered. The first attack is to reveal the attacker's ID image by manipulating the genuine user-side passports. The second attack is to reveal the attacker's ID image from the genuine user-side passport image by forging the steganographic key image." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Forged user-side passport. To simulate this attack, we" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.478 + ], + "angle": 0, + "content": "retain the ISN's weights and forge user-side passports with the attacker's ID images by minimizing the reveal loss \\(\\mathcal{L}_r\\) between the original forged ID images and revealed forged ID images. The attack was performed by randomly sampling 100 owner-side passport images to generate 100 corresponding user-side passport images, and then using the Adam optimizer on each user-side passport image for 1000 iterations with a learning rate of 0.001. The progression of the attack is depicted in Fig. 4a. The mean PSNR between the original forged ID images and their revealed forged ID images increases and the mean PSNR between the forged user-side passport images and genuine owner-side passport images decreases with iterations. As a result, it becomes impossible for the attacker to simultaneously satisfy the criteria of both \\(\\mathcal{V}_L^{\\mathrm{I}}\\) and \\(\\mathcal{V}_L^p\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.479, + 0.892, + 0.706 + ], + "angle": 0, + "content": "Forged steganographic key. In this experiment, the attacker steals the key-based ISN to forge the steganographic key image. We initialize this attack by randomly sampling a noise vector from a Gaussian distribution 100 times. Correspondingly, we also randomly sample a target forged ID image from the distribution of genuine ID images 100 times, ensuring that there is no overlap between the forged and real images. The forged key images are obtained by an Adam optimizer with a learning rate of 0.001 over 1000 iterations. The progress of this process is depicted in Fig. 4b, where the shaded region marks the range of average PSNRs obtained over 100 rounds of attack. For the forged key images, the deviation is small and the purple shaded region is not visible for the scale of the plot. These observations indicate that this attack fails to satisfy the criteria of \\(\\nu_{L}^{\\mathbf{I}}\\)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.717, + 0.809, + 0.733 + ], + "angle": 0, + "content": "4.5. Robustness against removal attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.734, + 0.892, + 0.84 + ], + "angle": 0, + "content": "We consider removal attacks that happen on the deployment branch when that branch is stolen by the attacker or abused by the licensed user. Unlike the pre-deployment model ownership claim in Sec 4.3, the model may be deliberately or maliciously altered after its deployment without compromising its utility, \\(\\tau_{\\xi}\\) for \\(\\mathcal{V}_O^s\\) needs not be infinitely close to 1 to claim the ownership of the deployed model." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Fine-tuning. We consider a transfer-learning task by fine-tuning the deployment branch of a pretrained dual-branch model for 100 epochs at a learning rate of 0.001. As shown in Table 3, our method has the second-highest" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12308" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.084, + 0.061, + 0.885, + 0.074 + ], + "angle": 0, + "content": "Table 3. The performance fidelity (in %) of deployment model under fine-tuning attacks. The value in bracket is the signature accuracy." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.075, + 0.89, + 0.149 + ], + "angle": 0, + "content": "
ResNet-18CIFAR-10 to CIFAR-10CIFAR-100 to CIFAR-10Caltech-101 to Caltech-256Caltech-256 to Caltech-101Mean
BNGNBNGNBNGNBNGN
DeepIPR73.81 (96.16)70.71 (95.23)92.10 (99.10)90.98 (99.45)48.53 (99.49)41.48 (99.30)76.05 (99.92)71.75 (100)70.68 (98.58)
PAN71.73 (74.30)68.15 (96.37)91.97 (78.71)90.46 (99.34)47.61 (81.29)39.51 (84.53)79.96 (100)71.64 (99.97)70.13 (89.31)
TdN70.77 (56.05)69.43 (62.70)91.86 (87.50)89.93 (73.87)46.55 (90.51)39.88 (82.30)77.12 (96.09)71.58 (82.81)69.64 (78.98)
Ours64.13 (98.60)65.11 (93.91)92.28 (96.17)90.22 (93.86)43.91 (98.24)37.48 (97.11)76.09 (99.09)69.04 (99.26)67.28 (97.03)
" + }, + { + "type": "image", + "bbox": [ + 0.08, + 0.155, + 0.273, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.115, + 0.275, + 0.238, + 0.286 + ], + "angle": 0, + "content": "(a) CIFAR-10 with BN" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.157, + 0.468, + 0.272 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.309, + 0.275, + 0.434, + 0.286 + ], + "angle": 0, + "content": "(b) CIFAR-10 with GN" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.29, + 0.468, + 0.317 + ], + "angle": 0, + "content": "Figure 5. The performance of our method under random and \\(\\ell_1\\) norm pruning attacks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.322, + 0.468, + 0.488 + ], + "angle": 0, + "content": "average SA of \\(97.03\\%\\). Given the avalanche criterion of the hash function, a false passport will lead to substantially high signature bit errors. The model owner can still attest the ownership under \\(\\mathcal{V}_O^s\\) with this small signature error. This is because both \\(\\mathcal{V}_O^f\\) and \\(\\mathcal{V}_O^I\\) can still be fulfilled by applying this slightly mismatched signature obtained from the fine-tuned deployment branch to the original dual branch model kept by the model owner. Compared to other passport-based methods, our method has the lowest average performance fidelity upon fine-tuning, making it less attractive to attack our model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.468, + 0.686 + ], + "angle": 0, + "content": "Pruning. Two prune strategies, i.e., random pruning and \\(\\ell_1\\)-norm pruning are evaluated. For each model, the pruning rate was increased from \\(0\\%\\) to \\(100\\%\\) with a step size of \\(10\\%\\). The results are shown in Fig. 5. The SA remains relatively high and stable even when the model performance starts to drop abruptly. For example, in Fig. 5a, a \\(100\\%\\) signature detection accuracy is preserved at \\(80\\%\\) pruning rate while the accuracy of the pruned model has fallen to around \\(50\\%\\). This implies that the pruned model can still pass \\(\\mathcal{V}_O^f\\) and \\(\\mathcal{V}_O^s\\) unless the pruning rate is so high that it renders the model unusable. Additionally, the large AD between the two branches also signifies that the model has been modified, as stated in Sec. 3.5." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.701, + 0.227, + 0.717 + ], + "angle": 0, + "content": "4.6. Ablation study" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.719, + 0.468, + 0.747 + ], + "angle": 0, + "content": "This section investigates the variations of our method without the TLP structure and with other activation functions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Without TLP. We examine the inference performance fidelity when the TLP is removed from the BN variants of ResNet-18 and AlexNet, and compare their performances across different datasets. The results presented in Table 4 indicate that the drop in inference performance is trivial for models without TLP compared to their corresponding TLP counterparts. The higher AD of AlexNet, \\(0.23\\%\\) as opposed to \\(0.00\\%\\) of ResNet-18, implies that TLP has negligible impact on the performance fidelity of our method for complex networks but is essential to keep for simpler networks." + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.157, + 0.89, + 0.183 + ], + "angle": 0, + "content": "Table 4. Inference performance fidelity (in %) for the deployment/verification branches of our method without TLP." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.184, + 0.89, + 0.243 + ], + "angle": 0, + "content": "
CIFAR-10CIFAR-100Caltech-101Caltech-256AD↓
ResNet-18BN↑BN↑BN↑BN↑
94.47 / 94.4775.19 / 75.2071.53 / 71.5350.46 / 50.460.00
AlexNetBN↑BN↑BN↑BN↑AD↓
91.05 / 91.2568.26 / 68.6570.11 / 70.1142.42 / 42.750.23
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.248, + 0.892, + 0.289 + ], + "angle": 0, + "content": "Table 5. Performance (in %) integrating Sigmoid and LeakyReLU in our proposed passport architecture, trained on CIFAR-10. Dep/Ver refer to deployment/verification branch, respectively." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.289, + 0.889, + 0.338 + ], + "angle": 0, + "content": "
ResNet-18-BNInferenceAmbiguity attack (ERB)
Dep / VerSAADDep / VerFSAAD
Sigmoid94.60 / 94.661000.0694.49 / 17.7699.8476.73
LeakyReLU94.96 / 94.551000.4194.46 / 91.931002.53
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.345, + 0.892, + 0.556 + ], + "angle": 0, + "content": "With other activation functions. To assess the impact of different activation functions on our method, we also incorporate Sigmoid and LeakyReLU into ResNet-18 with BN. For each activation function, the inference performance and robustness to the ERB attack are evaluated and presented in Table 5. Both activation functions demonstrate comparable performance fidelity between the deployment and verification branches, with SA of \\(100\\%\\) for both activation functions, and AD of \\(0.06\\%\\) and \\(0.41\\%\\) for Sigmoid and LeakyReLU, respectively. The Sigmoid-based model is more resilient to ERB attack than the LeakyReLU-based model, with a significantly higher AD of \\(76.73\\%\\). Nonetheless, we can adapt the tamper threshold \\(\\tau_{d}\\) to the activation function for higher ambiguity attack resistance." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.565, + 0.618, + 0.58 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.584, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this paper, we introduce Steganographic Passport, a novel passport-based model IP licensing protection method that allows the original model ownership to be verified with the passport-aware branch and individual licensees to be verified from the passport-free deployed model without requiring retraining the model for the admission of each licensed user. Legal license verification is made possible by hiding and revealing the licensed user's ID image in a user-side passport of the deployed model by the invertible steganographic network without compromising the accuracy and security of original model ownership verification. Activation-level obfuscation is added to heighten the security of both passports against ambiguity attacks. The affine factors of the deployment and verification branches, as well as the signatures and model's weights are tightly coupled during training to safeguard the owner-side passport and the deployed model's weights against malicious tampering to succeed in forging the ownership or licenseship. The experimental results substantiate the resilience of our method against a range of attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "12309" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Eirikur Agustsson and Radu Timofte. 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Advances in Neural Information Processing Systems, 33:22619-22628, 2020. 1, 2, 3, 5, 6" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.36 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.518, + 0.956 + ], + "angle": 0, + "content": "12311" + } + ] +] \ No newline at end of file diff --git a/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/723188cf-21a3-4072-a767-991efe3bf48f_origin.pdf b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/723188cf-21a3-4072-a767-991efe3bf48f_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..19364e49c0578694b21671dea009517205fc46b9 --- /dev/null +++ b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/723188cf-21a3-4072-a767-991efe3bf48f_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a5ebf84119bdda2783689c39e75883e614a6bc4daf7f10e47df43861115ff4b9 +size 1402804 diff --git a/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/full.md b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/full.md new file mode 100644 index 0000000000000000000000000000000000000000..18e0749e9c68a314899d2453a3b6c0488df531c7 --- /dev/null +++ b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/full.md @@ -0,0 +1,382 @@ +# Steganographic Passport: An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining + +Qi Cui* Ruohan Meng* Chaohui Xu Chip-Hong Chang† + +School of Electrical and Electronic Engineering, Nanyang Technological University + +qi.cui@ntu.edu.sg, ruohan.meng@ntu.edu.sg, chaohui001@e.ntu.edu.sg, echchang@ntu.edu.sg + +# Abstract + +Ensuring the legal usage of deep models is crucial to promoting trustable, accountable, and responsible artificial intelligence innovation. Current passport-based methods that obfuscate model functionality for license-to-use and ownership verifications suffer from capacity and quality constraints, as they require retraining the owner model for new users. They are also vulnerable to advanced Expanded Residual Block ambiguity attacks. We propose Steganographic Passport, which uses an invertible steganographic network to decouple license-to-use from ownership verification by hiding the user's identity images into the owner-side passport and recovering them from their respective user-side passports. An irreversible and collision-resistant hash function is used to avoid exposing the owner-side passport from the derived user-side passports and increase the uniqueness of the model signature. To safeguard both the passport and model's weights against advanced ambiguity attacks, an activation-level obfuscation is proposed for the verification branch of the owner's model. By jointly training the verification and deployment branches, their weights become tightly coupled. The proposed method supports agile licensing of deep models by providing a strong ownership proof and license accountability without requiring a separate model retraining for the admission of every new user. Experiment results show that our Steganographic Passport outperforms other passport-based deep model protection methods in robustness against various known attacks. + +# 1. Introduction + +To foster Artificial Intelligence (AI) diffusion and application, AI as a Service (AIaaS) has emerged as a lucrative + +This research is supported by the National Research Foundation, Singapore, and Cyber Security Agency of Singapore under its National Cybersecurity Research & Development Programme (Development of Secured Components & Systems in Emerging Technologies through Hardware & Software Evaluation $<$ NRF-NCR25-DeSNTU-0001>). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the view of National Research Foundation, Singapore and Cyber Security Agency of Singapore. + +†Corresponding author; *Both authors contributed equally. + +![](images/baaebbbe3fc8a6fe92ef51104c1801eb09238162f1b8c73bdac4aead8612722e.jpg) +Figure 1. The conceptual overview. The owner holds the owner-side passport and the steganographic key, which are used to verify the licenses and reveal the user IDs, respectively. The verification branch of the deep model is trained with the constraint of the signature. Upon licensing, the user receives the user-side passport and the deployment branch of the deep model. + +business model that offers across-the-broad access to high-performance machine learning models with subscription- or transaction-based payment schemes. The customers can submit inputs to the remote server and receive the inference or classification results of machine learning processes through application program interfaces (APIs). As complex models of high capabilities in AIaaS are offered as "turnkey" solutions to potentially anyone, they have huge potential to be misused and abused. Ownership and user license verifications are the first step towards accountability of responsible use of AI services. + +Ownership verification has long been a primary tool to protect deployed deep models against intellectual property (IP) infringement and unauthorized model replication [13]. Numerous approaches have been proposed, such as watermarking [8, 27], fingerprinting [10, 23, 24], and backdoor embedding [11, 14, 26]. These approaches typically aim to enable the trained deep model to exhibit distinguishable characteristics under specific conditions without sacrificing its utility. To resist ambiguity attacks, passport-based ownership verification scheme [5, 6, 20, 30] embeds digital passports during model training to obfuscate the primary functionality until the obfuscated parameters are restored by a genuine passport. The passport scheme provides access control [5, 6] at the expense of some accuracy degradation. Each passport is tied to a user model, retraining is required to derive a new user model from the owner model for every new passport issued. The recent passport-aware normal + +ization [30] avoids making structural changes to the target model by training it jointly with a passport-aware branch. The secret passport and passport-aware branch after training are kept by the model owner for future ownership verification and only the original passport-free target model is released to the end users. By forgoing the usage control, this method allows one deployed model to be used by various users but it also loses the accountability of inappropriate and unlawful use of the deployed model by different licensees. Besides, it has been demonstrated that the passports of existing methods can still be counterfeited by the more advanced ambiguity attack [3]. + +In usage authorization, one major limitation of existing passport-based methods is the need to retrain the network to incorporate different parameter modulations for every new passport issued, which may cause uneven service quality for different end users. Besides, retraining to accommodate new user models is inflexible, non-scalable and not cost-effective for complex models. This pitfall motivates us to explore anti-forgery passports that allow fidelity verification of deployed model to hold authorized users accountable for misuse of their licensed models without having to retrain the owner model when admitting new users. To this end, we propose a novel Steganographic Passport to decouple user license verification from ownership verification, as illustrated in Fig. 1. For ownership verification, the uniqueness of the model weights is maintained by aligning them with the hashed output of the owner-side passport, which allows the model owner to prove the ownership and authenticity of the distributed model. For license verification, any licensed user's hidden identity (ID) image can be extracted using the user-side passport. Both owner-side and user-side passports will pass the fidelity assessment as their visual similarity is preserved by using steganography to hide the ID image. To increase the sensitivity of the deployed model against malicious tampering of passports and weights, we propose an activation-level obfuscation for the verification branch of the owner model. The weights of the deployment and verification branches are tightly coupled by training them jointly with a balance loss function. Our contributions can be summarized as follows. + +- A novel Steganographic Passport is designed based on key-based invertible steganographic network to allow both original model ownership and right-of-use of its deployed model by multiple licensees to be verified without requiring retraining. +- An activation-level obfuscation architecture is designed to thwart forgery by tampering with the user-side passports or model weights. +- Extensive experiments are conducted to demonstrate the state-of-the-art security performance of our steganographic passports—the credibility of its owner-side and user-side passport verifications and its robustness against + +various attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks. + +# 2. Background + +The need to safeguard the deep model against misappropriation and IP theft arises from the enormous cost of designing and training a high-performance model from scratch. Given redundancy inherent in the numerous parameters of deep models, it is possible to embed a watermark into a model for ownership identification without significantly impairing its performance. The model can be watermarked either explicitly or implicitly. Explicit watermarking embeds the watermark by modifying the weights [7, 10, 23, 27] or feature maps [8] through a weight regularizer without compromising the original model performance. Implicit watermarking (a.k.a prediction watermarking) deliberately trains a backdoor into the protected model to classify inputs with specific triggers to the predefined labels [11, 14, 22, 26, 28]. However, these techniques are found to be vulnerable to ambiguity attacks as the embedded triggers can be replaced by attackers to forge the ownership with a substitute watermark. To mitigate this risk, model passports are introduced [5, 6], where the affine scale and bias factors of normalization functions are substituted with those derived from the passport images $\{p_{\gamma}, p_{\beta}\}$ . + +Let $x^{l}$ be the output of the $l$ -th convolutional layer, and $\mu_{x^l}$ and $\sigma_{x^l}$ be its mean and standard deviation, respectively. Then, the normalization function at the $l$ -layer with affine factors $\gamma^l$ and $\beta^l$ is given by: + +$$ +\widehat {x ^ {l}} = \gamma^ {l} \cdot \tilde {x ^ {l}} + \beta^ {l}, +$$ + +$$ +\text {w h e r e} \quad \tilde {x ^ {l}} = \frac {1}{\sigma_ {x ^ {l}}} \left(x ^ {l} - \mu_ {x ^ {l}}\right). \tag {1} +$$ + +By substituting $\gamma^l$ and $\beta^l$ by the passport affine factors $\gamma_{p_\gamma}^l$ and $\beta_{p_\beta}^l$ , the following passport normalization [5] is obtained: + +$$ +\widehat {x _ {p} ^ {l}} = \gamma_ {p _ {\gamma}} ^ {l} \cdot \tilde {x} ^ {l} + \beta_ {p _ {\beta}} ^ {l}. \tag {2} +$$ + +The sign sequence of $\gamma_{p_\gamma}^l$ in Eq. (2) is constrained to match a self-defined binary signature sequence. As large magnitudes of $\gamma_{p_\gamma}^l$ can be penalized, the gradients are kept small to ensure that the signs of $\gamma_{p_\gamma}^l$ are lazy-to-flip so as to prevent the signature from being replaced by retraining the model. To minimize the influence of passport normalization on inference performance, Zhang et al. [30] proposed a dual-branch passport structure. Its normalization function is expressed in Eq. (3) and illustrated in Fig. 2a. + +$$ +\left\{ \begin{array}{l} \widehat {x ^ {l}} = \gamma^ {l} \cdot \tilde {x ^ {l}} + \beta^ {l}, \\ \widehat {x _ {p} ^ {l}} = \gamma_ {p _ {\gamma}} ^ {l} \cdot \tilde {x ^ {l}} + \beta_ {p _ {\beta}} ^ {l}, \end{array} \right. \tag {3} +$$ + +where the passport-free output $\widehat{x^l}$ and the passport-aware output $\widehat{x_p^l}$ are used for the deployment and ownership verification, respectively. Besides, a two-layer perception (TLP) + +![](images/3176ae7e9907bd4170357b9063a52ee2da63634d45a27238944eaf0eb5cf4b72.jpg) +(a) Existing passport architecture + +![](images/c8d1a5e063f486cc3a2879b47887870014b090fc6dc9ad4412c497fe2a39c7e1.jpg) +(b) Proposed passport architecture +Figure 2. The existing and proposed passport architectures. The dual branches are enclosed in the dashed line box. + +structure is also inserted before the affine factors to mitigate the strict limitations in managing the functionality of normalization layers. + +To protect against ambiguity attacks with oracle passports due to passport leakage, Liu et al. [20] used trapdoor normalization to establish a direct correlation between the signature and the passport through a hash function. The collision-intractable hash function makes it virtually impossible for the attackers to reverse engineer a counterfeit passport, even if they can compromise the signature. Recently, Chen et al. [3] proposed an advanced ambiguity attack called Expanded Residual Block (ERB) on passport-based methods. This attack exploits the extensive solution space of TLP to force-flip the signs of the scale factors according to their forged passport without compromising the model performance. In summary, existing model passport methods aim only to resist the diverse ambiguity attacks by obfuscating the normalization functionalities with immutable passports. They do not allow admission of new users and their right-of-use verification upon model deployment. This is an important measure to safeguard the interest of AIaaS providers against revenue extorts by unauthenticated usage. + +# 3. Proposed method + +# 3.1. Problem statement + +We consider a practical licensing scenario of a deep model. Besides being able to detect and verify the ownership of a deployed model, the model owner should also be able to verify usage permission. If the passport images $\{p_{\gamma}, p_{\beta}\}$ are used as a unique proof to verify the ownership of the deployed model, they cannot be used to verify the usage permission granted to licensed users of that model. Although new backdoor triggers or watermarks can be added to verify each licensed user, the model needs to be retrained to learn the new features. This is very restrictive and impractical as it requires the model owner to fix the number of users and their identities upfront. Therefore, our aim is to enable the passport-based scheme to grant verifiable usage permission of a deployed deep model to ad hoc registered users without requiring retraining and without undermining the validity and robustness of the model's ownership proof. + +# 3.2. Steganographic passport framework + +Recall that in existing passport approaches [5, 6, 20, 30], a forged passport image can also be used to pass the fi + +delity assessment if it bears a high visual similarity to the genuine passport image. Inspired by advanced steganography techniques, we apply the art of imperceptible secret concealment to the passport-based scheme. The proposed Steganographic Passport follows the dual-branch setting, as illustrated in Fig. 2b. + +We define an owner-side passport $p_{o} = \{p_{o_{\gamma}}, p_{o_{\beta}}\}$ as the genuine passport images selected and held only by the model owner for generating the affine scale and bias factors accordingly. By feeding $p_{o}$ into the model, the corresponding owner-side passport feature maps are sequentially generated across the $n$ passport layers. These feature maps are then transformed into the affine factors for obfuscating the verification branch, which will be described in Sec. 3.3. We also introduce a new user-side passport, $p_{u} = \{p_{u_{\gamma}}, p_{u_{\beta}}\}$ , which is obtained by hiding the ID image $\mathrm{I}_u$ provided by a registered user into $p_{o}$ . The user-side passport $p_{u}$ fills the gap of existing passport-based limitation in meeting the goal of Sec. 3.1. The model owner can license the deployment branch of the model to multiple registered users by merely hiding each user's ID image into $p_{o}$ . + +Anti-forgery owner-side passport. To avoid user-side passports from exposing the visual content of the owner-side passports, the owner-side passport is irreversibly transformed to a unique model signature to ensure that the ownership cannot be forged by knowing any of the user-side passports. SHA-512 [25] is used as the one-way function for this mapping. + +Before training the target model, the model owner hashes the owner-side $p_{o_{\gamma}}$ to a binary signature $\xi^l$ of passport layer $l$ , as follows: + +$$ +\xi^ {l} = \left\{\operatorname {S G N} (x) \mid x \in \operatorname {H A S H} \left(p _ {o _ {\gamma}}\right) \right\}, \tag {4} +$$ + +where SGN maps each bit of a binary input sequence from $\{0,1\}$ to $\{-1,1\}$ . If the desired length of $\xi^l$ is shorter than 512 bits, the excess bits of the hash output are truncated from the beginning; Otherwise, we cycle the hash function's output until the required sequence length is obtained. + +For a model with $n$ passport layers, its overall model signature is represented as $\{\xi^1, \xi^2, \dots, \xi^n\}$ . The strict avalanche criterion of the hash function ensures that even minor changes to the passport image will result in significantly different affine factors, which prevents force-flipping from forging the passport with high model performance fidelity. Together with the irreversibility property of SHA-512, the genuine model signature $\xi$ can only be generated with the owner-side passport to thwart ownership impersonation fraud. The signature $\{\xi^1, \xi^2, \dots, \xi^n\}$ will be used to constrain the model's learning in the subsequent training phase to transform them into unique model's weights. A detailed exposition of this process is provided in Sec. 3.3. + +License verification via key-based deep steganography. To support an agile licensing scheme that is capable of admitting and verifying any new user after the tar + +get model has finalized its training phase, we need to decouple the license verification from the ownership verification. To this end, we hide the user's ID into the owner-side passport by integrating the key-based scheme of Invertible Steganographic Network (ISN) [21] within the Deep Image Hiding Network (HiNet) framework [15]. The key-based ISN is divided into two processes: forward hiding pass $\mathcal{H}_s$ and reverse revealing pass $\mathcal{H}_s^{-1}$ . The forward hiding pass is used to obtain the user-side passport $p_u$ from the owner-side passport $p_o$ as follows: + +$$ +p _ {u} = \mathcal {H} _ {s} \left(p _ {o}, \mathrm {I} _ {u}\right), \tag {5} +$$ + +where $\mathrm{I}_u$ denotes the user's ID image to be hidden into the owner-side passport $p_o$ . + +The reverse revealing pass is utilized for license verification. Using the private steganographic key $\mathbf{k}_s$ , the model owner can reveal the hidden user's ID image from the underside passport $p_u$ : + +$$ +\mathrm {I} _ {u} ^ {\prime} = \mathcal {H} _ {s} ^ {- 1} \left(p _ {u}, \mathbf {k} _ {s}\right), \tag {6} +$$ + +where $\mathrm{I}_u^\prime$ denotes the revealed ID image of the licensed user. The detailed architecture and algorithms of the hiding and revealing passes are given in the Appendix. + +# 3.3. Activation-level obfuscation + +To counteract sophisticated ambiguity attacks, an activation-level obfuscation is proposed to safeguard the verification branch against alterations of both the passport and the model's weights. + +Immutable passport. As illustrated in Fig. 2b, the passport-affine factors of layer $l$ can be calculated from the passport feature maps $p_{o}^{l}$ by: + +$$ +\gamma_ {p _ {o _ {\gamma}}} ^ {l} = \Phi (\Pi (p _ {o _ {\gamma}} ^ {l})) \text {, a n d} \beta_ {p _ {o _ {\beta}}} ^ {l} = \Phi (\Pi (p _ {o _ {\beta}} ^ {l})) \tag {7} +$$ + +where $\Phi$ and $\Pi$ denote the TLP and the global average pooling, respectively. + +Inspired by the controllable rectifiers of the Dynamic ReLU [2], we make $\gamma_{p_{o\gamma}}^l$ and $\beta_{p_{o\beta}}^l$ the dependent variables of the activation function. This can be incorporated into a dual-branch architecture as follows: + +$$ +\left\{ \begin{array}{l} \widehat {x ^ {l}} = \gamma^ {l} \cdot \widetilde {x ^ {l}} + \beta^ {l}, \\ \widehat {x _ {p _ {o}} ^ {l}} = \gamma_ {p _ {o \gamma}} ^ {l} \cdot \left(\gamma_ {t} ^ {l} \cdot \widetilde {x ^ {l}} + \beta_ {t} ^ {l}\right) + \beta_ {p _ {o \beta}} ^ {l}, \end{array} \right. \tag {8} +$$ + +where $\gamma^l$ and $\beta^l$ denote the original affine factors used in the deployment branch, and $\gamma_t^l$ and $\beta_t^l$ denote the additional temporal affine factors used in the verification branch. + +To simplify the expressions, let $x_{t}^{l} = \gamma_{t}^{l}\cdot x^{l} + \beta_{t}^{l}$ . By subjecting the outputs of Eq. (8) to an activation function (e.g. ReLU) before feeding them to the next layer, the final outputs of layer $l$ are given by: + +$$ +\left\{ \begin{array}{l} x _ {\varphi} ^ {l} = \max \left(\widehat {x ^ {l}}, 0\right), \\ x _ {\varphi_ {p o}} ^ {l} = \max \left(\gamma_ {p _ {o \gamma}} ^ {l} \cdot \widehat {x _ {t} ^ {l}} + \beta_ {p _ {o \beta}} ^ {l}, 0\right). \end{array} \right. \tag {9} +$$ + +The activation function used for the deployment branch (top expression) in Eq. (9) is a regular ReLU, whereas the + +activation function used for the verification branch (bottom expression) can be viewed as a special case of Dynamic ReLU. This way, the changes in the affine factors due to any alterations of the owner-side passport $p_o$ will lead to apparent changes in the passport-aware output, $x_{\varphi_{p_o}}^l$ , but not in the passport-free output, $x_{\varphi}^{l}$ . + +Immutable deployment branch. Under the dual-branch setting, the deployment and verification branches share all the model's weights but the affine factors. The deployment branch has to be consistently updated according to the updated passport-derived affine factors in the verification branch. If the deployment branch cannot keep up with the updates, the shared weights will overfit the verification branch, causing gradient explosions. To keep the updates of the two branches in tandem, the following balance loss function is proposed to train the model by explicitly aligning the affine factors in Eq. (8): + +$$ +\mathcal {L} _ {b} = \sum_ {l = 1} ^ {n} \left(\mathcal {L} _ {\mathrm {y}} \left(\gamma^ {l}, \gamma_ {t} ^ {l} \cdot \gamma_ {p _ {o _ {\gamma}}} ^ {l}\right) + \mathcal {L} _ {\mathrm {y}} \left(\beta^ {l}, \beta_ {t} ^ {l} \cdot \gamma_ {p _ {o _ {\gamma}}} ^ {l} + \beta_ {p _ {o _ {\beta}}} ^ {l}\right)\right), \tag {10} +$$ + +where $\ell_1$ norm is used for $\mathcal{L}_y$ , and $n$ is the total number of passport layers. + +This loss function aims to strike an equilibrium performance between the two branches. After the model is trained, the verification branch is removed from the model before it is licensed to any user. As the model trained with the balance loss function will have negligible accuracy difference between the two branches, any modification on the deployment branch would amplify the mean absolute difference. By comparing the accuracy difference between the two branches, the integrity of the model can be validated. + +Immutable verification branch. During the target model's training phase, the owner uses the model signature $\{\xi^1,\xi^2,\dots ,\xi^n\}$ to constrain the update of model's weights with the following signature loss function: + +$$ +\mathcal {L} _ {s} = \sum \max \left(\epsilon - \xi^ {l} \cdot \Pi \left(p _ {o _ {\gamma}} ^ {l}\right) \cdot \gamma_ {p _ {o _ {\gamma}}} ^ {l}, 0\right), \tag {11} +$$ + +where $\xi^l$ and $p_{o_\gamma}^l$ denote the $l$ -th layer's signature and passport feature map, respectively, and $\epsilon$ is a small constant. + +$\mathcal{L}_s$ encourages the signs of the product $\Pi \left(p_{o_\gamma}^l\right) \cdot \gamma_{p_{o_\gamma}}^l$ to align with that of $\xi^l$ , while keeping the magnitude of this product low. Since $p_{o_\gamma}^l$ and $\gamma_{p_{o_\gamma}}^l$ are the outputs of the convolution and TLP, respectively, the weights of the convolution layer and TLP become tightly coupled. The uniqueness of $\xi^l$ in Eq. (11) contributes to the distinctiveness of the weights. Any adjustment to the TLP will directly affect the convolution output. This property helps to prevent advanced ambiguity attacks, especially ERB, which maliciously alter the weights of the TLP to force-flip the signs of the product to align it with the forged signature. + +# 3.4. Training objectives + +The one-time training pipeline consists of training the key-based ISN and the target model. + +Training the key-based ISN. The key-based ISN is trained once independently of the target model to enhance the hiding invisibility and the revealing quality by the following loss function: + +$$ +\mathcal {L} _ {I S N} = \mathcal {L} _ {h} \left(p _ {o}, p _ {u}\right) + \mathcal {L} _ {r} \left(\mathrm {I} _ {u}, \mathrm {I} _ {u} ^ {\prime}\right). \tag {12} +$$ + +Both $\mathcal{L}_h$ and $\mathcal{L}_r$ utilize the $\ell_2$ norm for distance calculation. $p_o$ and $\mathrm{I}_u$ are randomly sampled in the training phase. + +Training the target model. Given a target model, we denote the models with only the weights of the deployment branch as $\mathcal{M}$ , and those with only the weights of the $p_o$ -based verification branch as $\mathcal{M}_{p_o}$ . Three loss functions are used to train the dual branches parallelly. The loss function for model performance is defined as: + +$$ +\mathcal {L} _ {f} = \frac {1}{N _ {t r}} \sum_ {i = 1} ^ {N _ {t r}} \left(\mathcal {L} _ {c} \left(\mathcal {M} \left(x _ {i}\right), y _ {i}\right) + \mathcal {L} _ {c} \left(\mathcal {M} _ {p _ {o}} \left(x _ {i}\right), y _ {i}\right)\right), \tag {13} +$$ + +where $x_{i}$ and $y_{i}$ are respectively the $i$ -th sample and its label from $N_{tr}$ training samples, and $\mathcal{L}_c$ is the cross-entropy loss. + +Together with the signature loss $\mathcal{L}_s$ and the balance loss $\mathcal{L}_b$ , the total loss is defined as: + +$$ +\mathcal {L} _ {t} = \mathcal {L} _ {f} + \omega_ {s} \mathcal {L} _ {s} + \omega_ {b} \mathcal {L} _ {b}, \tag {14} +$$ + +where the signature and balance losses are weighted by $\omega_{s}$ and $\omega_{b}$ , respectively. + +# 3.5. Inclusive verification chain + +To confirm the ownership and legal usability of a deployed model M, we propose the following verification chain involving the model owner O, the licensed user U, and the deployed model M. + +Ownership verification. The ownership verification comprises three tests: $\mathcal{V}_O^{\mathcal{I}}$ , $\mathcal{V}_O^f$ and $\mathcal{V}_O^s$ for the verification of the model integrity, performance fidelity and signature accuracy, respectively. By replacing the passport layers' affine factors with the ones derived from the owner-side passport $p_o$ , the deployed branch $\mathbf{M}$ becomes a verifiable branch $\mathbf{M}_{p_o}$ . + +Let $\mathcal{F}(\cdot ,\cdot)$ denote the model performance. $\nu_{O}^{\mathcal{T}}$ tests if $\mathbf{M}$ has been modified based on the absolute performance difference (AD): + +$$ +\mathcal {V} _ {O} ^ {\mathcal {I}} \Longleftrightarrow \frac {1}{N _ {t}} \left| \sum_ {j = 1} ^ {N _ {t}} \left(\mathcal {F} \left(\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\right) - \mathcal {F} \left(\mathbf {M}, x _ {j} ^ {t}\right)\right) \right| < \tau_ {d}, \tag {15} +$$ + +where $x_{j}^{t}$ is the $j$ -th sample from total $N_{t}$ test samples, and $\tau_{d}$ is a small predefined passing threshold. + +$\mathcal{V}_O^f$ verifies the performance fidelity by: + +$$ +\mathcal {V} _ {O} ^ {f} \Longleftrightarrow \frac {1}{N _ {t}} \sum_ {j = 1} ^ {N _ {t}} \mathcal {F} \left(\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\right) > \tau_ {f}, \tag {16} +$$ + +where $\tau_{f}$ is the predefined minimum accuracy to pass the performance fidelity verification. + +To validate the signature accuracy, the owner uses Eq. (4) to transform $p_{o_{\gamma}}$ into the model signature $\xi =$ + +$\{\xi^1,\xi^2,\dots ,\xi^n\}$ . By comparing each element of $\xi$ with those of $\xi^{*}$ extracted from $\mathbf{M}_{p_o}$ $\nu_{O}^{s}$ checks the sign agreement (SA) by: + +$$ +\mathcal {V} _ {O} ^ {s} \Longleftrightarrow \frac {1}{N _ {\xi}} \sum_ {b = 1} ^ {N _ {\xi}} \left(\xi_ {b} \wedge \xi_ {b} ^ {*}\right) \geq \tau_ {\xi}, \tag {17} +$$ + +where $N_{\xi}$ is the total length of $\xi$ . $\tau_{\xi}$ is a predefined error tolerance only for the post-distribution verification. Otherwise, the SA of an untainted pre-deployment model has to be $100\%$ (i.e., $\tau_{\xi} = 1$ ) to satisfy $\mathcal{V}_O^s$ . + +Remark 1: Before distributing the deployed model $\mathbf{M}$ , the owner $\mathbf{O}$ is required to disclose the evidence of compliance with $\mathcal{V}_O^{\mathcal{T}}$ , $\mathcal{V}_O^f$ , and $\mathcal{V}_O^s$ to establish the credibility of the ownership claim of $\mathbf{M}$ . + +License verification. Upon verifying that the model M deployed by the licensed user $\mathbf{U}$ complies with the criteria set by $\mathcal{V}_O^{\mathcal{T}}$ , $\mathcal{V}_O^f$ , and $\mathcal{V}_O^s$ , a provable association between the licensed user $\mathbf{U}$ and the model owner $\mathbf{O}$ can be established by two license verification tests: $\mathcal{V}_L^p$ for passport image similarity, and $\mathcal{V}_L^I$ for ID image similarity. + +Upon receiving $p_u$ submitted by the user $\mathbf{U}$ , the owner can compare the PSNR between the user and owner passport images by: + +$$ +\mathcal {V} _ {L} ^ {p} \Longleftrightarrow \operatorname {P S N R} \left(p _ {o}, p _ {u}\right) > \tau_ {p}, \tag {18} +$$ + +where $\tau_{p}$ is the predefined visual similarity threshold for successful verification. + +The reverse revealing pass is utilized for license verification. Using the private steganographic key $\mathbf{k}_s$ , the model owner can reveal the hidden user's ID image $\mathrm{I}_u^{\prime}$ from the user-side passport $p_u$ by Eq. (6). $\mathcal{V}_L^{\mathrm{I}}$ tests the visual similarity between $\mathrm{I}_u$ and the revealed ID image, $\mathrm{I}_u^{\prime}$ of the licensed user by comparing the PSNR with predefined threshold $\tau_r$ : + +$$ +\mathcal {V} _ {L} ^ {\mathrm {I}} \Longleftrightarrow \operatorname {P S N R} \left(\mathrm {I} _ {u}, \mathrm {I} _ {u} ^ {\prime}\right) > \tau_ {r}. \tag {19} +$$ + +Remark 2: Once $\mathcal{V}_L^p$ and $\mathcal{V}_L^{\mathrm{I}}$ are satisfied, on the condition that the model $\mathbf{M}$ passes the three ownership verification tests of the owner $\mathbf{O}$ , the user $\mathbf{U}$ is proven to be a legal licensee of $\mathbf{M}$ . + +# 4. Experiment + +# 4.1. Setup + +Generally, we follow the settings on image classification tasks in existing passport approaches, including dual-branch DeepIPR [6], Passport-Aware Normalization (PAN) [30], and Trapdoor Normalization (TdN) [20]. AlexNet [17] and ResNet-18 [9], with Batch Normalization (BN) [12] and Group Normalization (GN) [29], are employed to evaluate and compare the performance. The datasets used in the classification experiments include CIFAR-10, CIFAR-100 [16], Caltech-101, and Caltech-256 [18]. Besides, DIV2K [1] is used to train the key-based ISN. For passport images $p_{\gamma}$ and $p_{\beta}$ , we randomly select them from the test set of COCO dataset [19]. For steganographic key image $\mathbf{k}_s$ , we randomly select it from DTD + +Table 1. Inference performance (in %) for deployment/verification. $\uparrow / \downarrow$ denotes higher / lower value for better performance. + +
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18BN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean94.6993.8576.4273.5774.5870.7355.4349.5273.60-
DeepIPR93.04 / 94.0593.81 / 93.6960.76 / 62.8872.19 / 71.1573.84 / 73.2265.08 / 63.3341.53 / 44.1243.81 / 42.6768.01 / 68.141.30
PAN94.70 / 94.6193.63 / 93.6775.97 / 74.7072.19 / 71.4973.79 / 72.9468.36 / 65.3755.37 / 54.3344.73 / 43.5172.34 / 71.331.03
TdN94.65 / 94.6893.57 / 93.5776.00 / 75.6171.25 / 71.4274.12 / 73.0567.63 / 67.5154.90 / 54.2844.90 / 44.2772.13 / 71.800.38
Ours94.89 / 94.8993.79 / 93.8076.10 / 76.1070.84 / 70.8373.56 / 73.5667.01 / 67.0153.65 / 53.6544.01 / 44.0171.73 / 71.730.00
AlexNetBN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean91.2090.2768.4065.7271.5868.7044.2441.1867.66-
DeepIPR81.80 / 90.7689.90 / 90.2045.71 / 51.7764.89 / 64.1667.91 / 65.9567.80 / 67.0631.39 / 36.2540.69 / 39.7360.14 / 63.243.07
PAN91.51 / 91.2990.22 / 90.3968.46 / 66.4450.60 / 56.7171.03 / 70.9066.95 / 66.7144.93 / 41.1340.03 / 38.8466.47 / 65.311.32
TdN91.28 / 91.0290.08 / 89.8068.71 / 68.0764.54 / 63.7770.45 / 69.4468.31 / 66.3845.36 / 44.8242.39 / 37.8867.64 / 66.401.24
Ours91.39 / 91.3889.77 / 89.7767.86 / 67.8563.36 / 63.3471.98 / 71.9868.42 / 68.4246.10 / 46.0741.10 / 41.1267.50 / 67.490.01
+ +dataset [4]. For hyper-parameters $\epsilon, \omega_s$ , and $\omega_b$ , we empirically set them as 0.1, 1, and 1. By default, the last three/five normalization layers of AlexNet/ResNet-18 are set as the passport layers. + +# 4.2. Verification assessment + +We evaluate the effectiveness of the proposed steganographic passport by the verification and inference performances. All the models are trained with 200 epochs, utilizing a multi-step learning rate that decreases gradually from 0.01 to 0.0001. A twofold verification is adopted in our method, which entails a) an ownership verification $\{\mathcal{V}_O^{\mathcal{T}},\mathcal{V}_O^f,\mathcal{V}_O^s\}$ and b) a license verification $\{\mathcal{V}_L^p,\mathcal{V}_L^1\}$ . + +For ownership verification, our steganographic passport exhibits the lowest AD values of $0.00\%$ on ResNet-18 and $0.01\%$ on AlexNet for $\mathcal{V}_O^T$ with the correct owner passport, as presented in Table 1. This is attributed to the effect of the balance loss function, which ensures that the updates of the affine factors of the two branches are more synchronized during training. For $\mathcal{V}_O^f$ , due to the stronger anti-forgery passport constraint imposed by our method, there is a slight decrease in model inference performance compared to Tdn and PAN, but it still outperforms DeepIPR. As shown in Table 1, the average deployment and verification branch accuracies of our method on ResNet-18 are both $71.73\%$ , which is only $0.40\%$ and $0.07\%$ lower than the accuracies of the deployment and verification branches, respectively of Tdn. The performance of our method peaks in several cases highlighted with the bold-printed percentages. For instance, it achieves the top score of $71.98\%$ for AlexNet on Caltech-101. For $\mathcal{V}_O^s$ , the SAs of all four methods achieve $100\%$ in all the settings. + +For license verification, a comparison of the visual images for $\mathcal{V}_L^p$ and $\mathcal{V}_L^{\mathrm{I}}$ is presented in Fig. 3. A very high PSNR of 41.47 between the original ID image and the ID image revealed using the genuine steganographic key is obtained, indicating a high level of visual similarity between them. In contrast, using forged keys to reveal the ID image results in significantly lower PSNR. Specifically, a PSNR of only 15.48 is obtained for the revealed ID images by using a random noise-like forged passport image and 32.56 by using a steganographic key image selected randomly from the same distribution as the genuine key image. Further + +![](images/b78d92cb54e4db4835d0b97c7b6c2c1245227d264686b2a8163a047d8bd17414.jpg) +Figure 3. Hiding and revealing performance of the key-based ISN. + +more, upon repeating this evaluation 100 times, the average PSNRs obtained from revealing the ID image by using random noise-like forged and randomly-selected key images are 15.68 and 35.89, respectively. + +Based on the above observations, we empirically set $\tau_{d}$ , $\tau_{\xi}$ , $\tau_{p}$ and $\tau_{r}$ to $0.05\%$ , $93\%$ , 39 and 41 for $\mathcal{V}_O^{\mathcal{I}}$ , $\mathcal{V}_O^s$ , $\mathcal{V}_L^p$ and $\mathcal{V}_L^i$ , respectively. For $\mathcal{V}_O^f$ , $\tau_{f}$ is calibrated according to the task as the same clean model trained for different tasks has different inference performance. + +# 4.3. Robustness against ownership ambiguity attacks + +Ownership ambiguity attacks aim to falsely claim the ownership of a deep model by satisfying the conditions outlined in Remark 1. Owing to the avalanche criterion provided by the hash function, attacks that attempt to forge the genuine passport images by random selection [6, 20, 30] or tamper with the user-side passport images will fail on $\mathcal{V}_O^s$ due to the significant signature deviation. Additionally, it is computationally intractable to reverse the uniformly random and collision-resistant cryptographically secure hash function to recover genuine passport images [20]. Thus, we specifically focus on the state-of-the-art ERB ownership ambiguity attack, under the strict assumption that the attacker has stolen both the deployment and verification branches, along with $10\%$ of original training data. The individual version of ERB, i.e., IERB is used to attack the models with BN. + +ERB demonstrated its effectiveness by retraining the model to fit a forged passport. In ERB's original configuration, attackers directly fabricate the passport layer's affine + +Table 2. Inference performance fidelity (in %) for deployment/verification under ERB ambiguity attacks with BN. FSA and BDR refer to the forged signature accuracy and the bit difference rate between benign and forged signatures, respectively. + +
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR94.19 / 94.3910050.2262.92 / 64.0610049.4973.56 / 73.8910050.2346.05 / 46.3910049.3769.18 / 69.680.50
PAN94.64 / 94.7210048.7175.28 / 75.1010049.5773.11 / 73.0510049.3053.62 / 53.5810050.0874.16 / 74.110.90
TdN94.48 / 94.2410053.0975.91 / 66.6610048.2073.22 / 64.5499.9650.0454.49 / 34.6110051.7674.53 / 65.019.51
Ours94.70 / 92.8710049.5375.85 / 50.2799.9649.1873.00 / 50.0699.9251.0552.87 / 38.4410049.1873.82 / 57.9116.20
AlexNetERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR26.54 / 85.7210047.6146.61 / 51.9710050.1163.56 / 67.8310052.6532.61 / 34.3410051.0842.31 / 59.9717.64
PAN91.56 / 82.0610052.4368.36 / 60.2910049.8770.37 / 69.1710053.3844.41 / 40.1510052.5668.68 / 62.925.76
TdN90.16 / 53.1610051.3366.96 / 1.6598.9649.7870.26 / 37.1998.9649.9644.14 / 0.2895.3148.2467.88 / 23.0744.81
Ours84.90 / 16.1199.5750.2467.38 / 1.0296.7549.7271.26 / 35.8698.9650.3345.00 / 4.9310051.1767.14 / 14.4852.66
+ +![](images/e2b34716823ce1e2f60f10756a312c684d7f847e2792dcc033fa7f8eef67dca9.jpg) +(a) Forged passport + +![](images/05ef9c3e491db277a86be35b486fb2c7100ed2a1e59a3bd266c2bca562cfb956.jpg) +(b) Forged steganographic key +Figure 4. Results of license ambiguity attacks on our method. Batch Normalization is used in the evaluated models. We set the Z-score as 2.33 for $98\%$ confidence interval (CI). + +factors, leveraging the network's differentiable architecture to deduce the passport images. However, this possibility is denied by the hash functions of our method and TdN. Therefore, while maintaining the original settings of ERB for DeepIPR and PAN, the passport layer's affine factors in our method and TdN are to be derived from the corresponding hash-related functions. Table 2 displays the experimental results. To successfully meet the criteria of Remark 1, the attack must achieve $100\%$ of forged SA (FSA) for $\mathcal{V}_O^s$ . As evinced by the results presented in Sec. 4.2, the legitimate owner is able to comply with this stringent criteria. The experimental results show that the attacks on TdN and our method can only achieve $100\%$ FSA for four and three model-dataset cases, respectively. Conversely, despite having around $50\%$ BDR between the forged and genuine signatures, DeepIPR and PAN fail to withstand this attack with $100\%$ FSA on all the model-dataset combinations. Besides, our method consistently produces the lowest mean performance fidelity of the verification branch for $\mathcal{V}_O^f$ , especially for ResNet-18 $(57.91\%)$ and AlexNet $(14.48\%)$ . Furthermore, our method also exhibits the highest AD that surpasses $\tau_d$ of $\mathcal{V}_O^d$ by a significant margin. The results, taken holistically, corroborate that our method has the highest resilience against ambiguity attacks. + +# 4.4. Robustness against license ambiguity attacks + +Two license ambiguity attacks are considered. The first attack is to reveal the attacker's ID image by manipulating the genuine user-side passports. The second attack is to reveal the attacker's ID image from the genuine user-side passport image by forging the steganographic key image. + +Forged user-side passport. To simulate this attack, we + +retain the ISN's weights and forge user-side passports with the attacker's ID images by minimizing the reveal loss $\mathcal{L}_r$ between the original forged ID images and revealed forged ID images. The attack was performed by randomly sampling 100 owner-side passport images to generate 100 corresponding user-side passport images, and then using the Adam optimizer on each user-side passport image for 1000 iterations with a learning rate of 0.001. The progression of the attack is depicted in Fig. 4a. The mean PSNR between the original forged ID images and their revealed forged ID images increases and the mean PSNR between the forged user-side passport images and genuine owner-side passport images decreases with iterations. As a result, it becomes impossible for the attacker to simultaneously satisfy the criteria of both $\mathcal{V}_L^{\mathrm{I}}$ and $\mathcal{V}_L^p$ . + +Forged steganographic key. In this experiment, the attacker steals the key-based ISN to forge the steganographic key image. We initialize this attack by randomly sampling a noise vector from a Gaussian distribution 100 times. Correspondingly, we also randomly sample a target forged ID image from the distribution of genuine ID images 100 times, ensuring that there is no overlap between the forged and real images. The forged key images are obtained by an Adam optimizer with a learning rate of 0.001 over 1000 iterations. The progress of this process is depicted in Fig. 4b, where the shaded region marks the range of average PSNRs obtained over 100 rounds of attack. For the forged key images, the deviation is small and the purple shaded region is not visible for the scale of the plot. These observations indicate that this attack fails to satisfy the criteria of $\nu_{L}^{\mathbf{I}}$ . + +# 4.5. Robustness against removal attacks + +We consider removal attacks that happen on the deployment branch when that branch is stolen by the attacker or abused by the licensed user. Unlike the pre-deployment model ownership claim in Sec 4.3, the model may be deliberately or maliciously altered after its deployment without compromising its utility, $\tau_{\xi}$ for $\mathcal{V}_O^s$ needs not be infinitely close to 1 to claim the ownership of the deployed model. + +Fine-tuning. We consider a transfer-learning task by fine-tuning the deployment branch of a pretrained dual-branch model for 100 epochs at a learning rate of 0.001. As shown in Table 3, our method has the second-highest + +Table 3. The performance fidelity (in %) of deployment model under fine-tuning attacks. The value in bracket is the signature accuracy. + +
ResNet-18CIFAR-10 to CIFAR-10CIFAR-100 to CIFAR-10Caltech-101 to Caltech-256Caltech-256 to Caltech-101Mean
BNGNBNGNBNGNBNGN
DeepIPR73.81 (96.16)70.71 (95.23)92.10 (99.10)90.98 (99.45)48.53 (99.49)41.48 (99.30)76.05 (99.92)71.75 (100)70.68 (98.58)
PAN71.73 (74.30)68.15 (96.37)91.97 (78.71)90.46 (99.34)47.61 (81.29)39.51 (84.53)79.96 (100)71.64 (99.97)70.13 (89.31)
TdN70.77 (56.05)69.43 (62.70)91.86 (87.50)89.93 (73.87)46.55 (90.51)39.88 (82.30)77.12 (96.09)71.58 (82.81)69.64 (78.98)
Ours64.13 (98.60)65.11 (93.91)92.28 (96.17)90.22 (93.86)43.91 (98.24)37.48 (97.11)76.09 (99.09)69.04 (99.26)67.28 (97.03)
+ +![](images/9b34983ef4904042e876220a6da169b5bbc64dbd3cdf0faaa6d9047f41b61ac7.jpg) +(a) CIFAR-10 with BN + +![](images/0387e35ba150d7062f2105b64832fc8c79f8e5d78dfa5ddf53aa9319ec001062.jpg) +(b) CIFAR-10 with GN +Figure 5. The performance of our method under random and $\ell_1$ norm pruning attacks. + +average SA of $97.03\%$ . Given the avalanche criterion of the hash function, a false passport will lead to substantially high signature bit errors. The model owner can still attest the ownership under $\mathcal{V}_O^s$ with this small signature error. This is because both $\mathcal{V}_O^f$ and $\mathcal{V}_O^I$ can still be fulfilled by applying this slightly mismatched signature obtained from the fine-tuned deployment branch to the original dual branch model kept by the model owner. Compared to other passport-based methods, our method has the lowest average performance fidelity upon fine-tuning, making it less attractive to attack our model. + +Pruning. Two prune strategies, i.e., random pruning and $\ell_1$ -norm pruning are evaluated. For each model, the pruning rate was increased from $0\%$ to $100\%$ with a step size of $10\%$ . The results are shown in Fig. 5. The SA remains relatively high and stable even when the model performance starts to drop abruptly. For example, in Fig. 5a, a $100\%$ signature detection accuracy is preserved at $80\%$ pruning rate while the accuracy of the pruned model has fallen to around $50\%$ . This implies that the pruned model can still pass $\mathcal{V}_O^f$ and $\mathcal{V}_O^s$ unless the pruning rate is so high that it renders the model unusable. Additionally, the large AD between the two branches also signifies that the model has been modified, as stated in Sec. 3.5. + +# 4.6. Ablation study + +This section investigates the variations of our method without the TLP structure and with other activation functions. + +Without TLP. We examine the inference performance fidelity when the TLP is removed from the BN variants of ResNet-18 and AlexNet, and compare their performances across different datasets. The results presented in Table 4 indicate that the drop in inference performance is trivial for models without TLP compared to their corresponding TLP counterparts. The higher AD of AlexNet, $0.23\%$ as opposed to $0.00\%$ of ResNet-18, implies that TLP has negligible impact on the performance fidelity of our method for complex networks but is essential to keep for simpler networks. + +Table 4. Inference performance fidelity (in %) for the deployment/verification branches of our method without TLP. + +
CIFAR-10CIFAR-100Caltech-101Caltech-256AD↓
ResNet-18BN↑BN↑BN↑BN↑
94.47 / 94.4775.19 / 75.2071.53 / 71.5350.46 / 50.460.00
AlexNetBN↑BN↑BN↑BN↑AD↓
91.05 / 91.2568.26 / 68.6570.11 / 70.1142.42 / 42.750.23
+ +Table 5. Performance (in %) integrating Sigmoid and LeakyReLU in our proposed passport architecture, trained on CIFAR-10. Dep/Ver refer to deployment/verification branch, respectively. + +
ResNet-18-BNInferenceAmbiguity attack (ERB)
Dep / VerSAADDep / VerFSAAD
Sigmoid94.60 / 94.661000.0694.49 / 17.7699.8476.73
LeakyReLU94.96 / 94.551000.4194.46 / 91.931002.53
+ +With other activation functions. To assess the impact of different activation functions on our method, we also incorporate Sigmoid and LeakyReLU into ResNet-18 with BN. For each activation function, the inference performance and robustness to the ERB attack are evaluated and presented in Table 5. Both activation functions demonstrate comparable performance fidelity between the deployment and verification branches, with SA of $100\%$ for both activation functions, and AD of $0.06\%$ and $0.41\%$ for Sigmoid and LeakyReLU, respectively. The Sigmoid-based model is more resilient to ERB attack than the LeakyReLU-based model, with a significantly higher AD of $76.73\%$ . Nonetheless, we can adapt the tamper threshold $\tau_{d}$ to the activation function for higher ambiguity attack resistance. + +# 5. Conclusion + +In this paper, we introduce Steganographic Passport, a novel passport-based model IP licensing protection method that allows the original model ownership to be verified with the passport-aware branch and individual licensees to be verified from the passport-free deployed model without requiring retraining the model for the admission of each licensed user. Legal license verification is made possible by hiding and revealing the licensed user's ID image in a user-side passport of the deployed model by the invertible steganographic network without compromising the accuracy and security of original model ownership verification. Activation-level obfuscation is added to heighten the security of both passports against ambiguity attacks. The affine factors of the deployment and verification branches, as well as the signatures and model's weights are tightly coupled during training to safeguard the owner-side passport and the deployed model's weights against malicious tampering to succeed in forging the ownership or licenseship. The experimental results substantiate the resilience of our method against a range of attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks. + +# References + +[1] Eirikur Agustsson and Radu Timofte. Ntire 2017 challenge on single image super-resolution: Dataset and study. In Proceedings of the IEEE conference on computer vision and pattern recognition workshops, pages 126-135, 2017. 5 +[2] Yinpeng Chen, Xiyang Dai, Mengchen Liu, Dongdong Chen, Lu Yuan, and Zicheng Liu. Dynamic ReLU. In European Conference on Computer Vision, pages 351-367. Springer, 2020. 4 +[3] Yiming Chen, Jinyu Tian, Xiangyu Chen, and Jiantao Zhou. Effective ambiguity attack against passport-based dnn intellectual property protection schemes through fully connected layer substitution. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 8123-8132, 2023. 2, 3 +[4] Mircea Cimpoi, Subhransu Maji, Iasonas Kokkinos, Sammy Mohamed, and Andrea Vedaldi. Describing textures in the wild. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 3606-3613, 2014. 6 +[5] Lixin Fan, Kam Woh Ng, and Chee Seng Chan. Rethinking deep neural network ownership verification: Embedding passports to defeat ambiguity attacks. Advances in neural information processing systems, 32, 2019. 1, 2, 3 +[6] Lixin Fan, Kam Woh Ng, Chee Seng Chan, and Qiang Yang. DeepIPR: Deep neural network ownership verification with passports. IEEE Transactions on Pattern Analysis and Machine Intelligence, 44(10):6122-6139, 2021. 1, 2, 3, 5, 6 +[7] Le Feng and Xinpeng Zhang. 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In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 4729-4737, 2019. 1, 2 +[11] Guang Hua, Andrew Beng Jin Teoh, Yong Xiang, and Hao Jiang. Unambiguous and high-fidelity backdoor watermarking for deep neural networks. IEEE Transactions on Neural Networks and Learning Systems, 2023. 1, 2 +[12] Sergey Ioffe and Christian Szegedy. Batch Normalization: Accelerating deep network training by reducing internal covariate shift. In International conference on machine learning, pages 448-456. pmlr, 2015. 5 +[13] Seyyed Ahmad Javadi, Chris Norval, Richard Cloete, and Jatinder Singh. Monitoring AI services for misuse. In Proceedings of the 2021 AAAI/ACM Conference on AI, Ethics, and Society, pages 597-607, 2021. 1 + +[14] Hengrui Jia, Christopher A Choquette-Choo, Varun Chandrasekaran, and Nicolas Papernot. Entangled watermarks as a defense against model extraction. In 30th USENIX Security Symposium (USENIX Security 21), pages 1937-1954, 2021. 1, 2 +[15] Junpeng Jing, Xin Deng, Mai Xu, Jianyi Wang, and Zhenyu Guan. HiNet: deep image hiding by invertible network. In Proceedings of the IEEE/CVF international conference on computer vision, pages 4733-4742, 2021. 4 +[16] Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images. 2009. 5 +[17] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural networks. Advances in neural information processing systems, 25, 2012. 5 +[18] Fei-Fei Li, Robert Fergus, and Pietro Perona. One-shot learning of object categories. IEEE transactions on pattern analysis and machine intelligence, 28(4):594–611, 2006. 5 +[19] Tsung-Yi Lin, Michael Maire, Serge Belongie, James Hays, Pietro Perona, Deva Ramanan, Piotr Dólar, and C Lawrence Zitnick. Microsoft COCO: Common objects in context. In Computer Vision-ECCV 2014: 13th European Conference, Zurich, Switzerland, September 6-12, 2014, Proceedings, Part V 13, pages 740-755. Springer, 2014. 5 +[20] Hanwen Liu, Zhenyu Weng, Yuesheng Zhu, and Yadong Mu. Trapdoor normalization with irreversible ownership verification. In International Conference on Machine Learning, pages 22177-22187. PMLR, 2023. 1, 3, 5, 6 +[21] Shao-Ping Lu, Rong Wang, Tao Zhong, and Paul L Rosin. Large-capacity image steganography based on invertible neural networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pages 10816-10825, 2021. 4 +[22] Ding Sheng Ong, Chee Seng Chan, Kam Woh Ng, Lixin Fan, and Qiang Yang. Protecting intellectual property of generative adversarial networks from ambiguity attacks. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 3630-3639, 2021. 2 +[23] Zirui Peng, Shaofeng Li, Guoxing Chen, Cheng Zhang, Haojin Zhu, and Minhui Xue. Fingerprinting deep neural networks globally via universal adversarial perturbations. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 13430-13439, 2022. 1, 2 +[24] Yuhui Quan, Huan Teng, Ruotao Xu, Jun Huang, and Hui Ji. Fingerprinting deep image restoration models. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 13285-13295, 2023. 1 +[25] Somitra Kumar Sanadhya and Palash Sarkar. New collision attacks against up to 24-step sha-2. In Progress in Cryptology-INDOCRYPT 2008: 9th International Conference on Cryptology in India, Kharagpur, India, December 14-17, 2008. Proceedings 9, pages 91-103. Springer, 2008. 3 +[26] Masoumeh Shafieinejad, Nils Lukas, Jiaqi Wang, Xinda Li, and Florian Kerschbaum. On the robustness of backdoor-based watermarking in deep neural networks. In Proceed- + +ings of the 2021 ACM Workshop on Information Hiding and Multimedia Security, pages 177-188, 2021. 1, 2 +[27] Yusuke Uchida, Yuki Nagai, Shigeyuki Sakazawa, and Shinichi Satoh. Embedding watermarks into deep neural networks. In Proceedings of the 2017 ACM on international conference on multimedia retrieval, pages 269-277, 2017. 1, 2 +[28] Si Wang, Chaohui Xu, Yue Zheng, and Chip-Hong Chang. A buyer-traceable dnn model IP protection method against piracy and misappropriation. In 2022 IEEE 4th International Conference on Artificial Intelligence Circuits and Systems (AICAS), pages 308-311. IEEE, 2022. 2 +[29] Yuxin Wu and Kaiming He. Group normalization. In Proceedings of the European conference on computer vision (ECCV), pages 3-19, 2018. 5 +[30] Jie Zhang, Dongdong Chen, Jing Liao, Weiming Zhang, Gang Hua, and Nenghai Yu. Passport-aware normalization for deep model protection. Advances in Neural Information Processing Systems, 33:22619-22628, 2020. 1, 2, 3, 5, 6 \ No newline at end of file diff --git a/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/images.zip b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..31cbcd1af299cc7713c8d1dd5695f2db3fccd493 --- /dev/null +++ b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c7e27132851cad8b92b408a9866db00fbec591e57a317028a66664d92db9fee6 +size 593655 diff --git a/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/layout.json b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..c82651028cd0f962148d6ea3dbe9c86d229c74ac --- /dev/null +++ b/2024/Steganographic Passport_ An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining/layout.json @@ -0,0 +1,11475 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 59, + 102, + 536, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 102, + 536, + 140 + ], + "spans": [ + { + "bbox": [ + 59, + 102, + 536, + 140 + ], + "type": "text", + "content": "Steganographic Passport: An Owner and User Verifiable Credential for Deep Model IP Protection Without Retraining" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 124, + 161, + 473, + 176 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 124, + 161, + 473, + 176 + ], + "spans": [ + { + "bbox": [ + 124, + 161, + 473, + 176 + ], + "type": "text", + "content": "Qi Cui* Ruohan Meng* Chaohui Xu Chip-Hong Chang†" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 94, + 176, + 499, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 176, + 499, + 190 + ], + "spans": [ + { + "bbox": [ + 94, + 176, + 499, + 190 + ], + "type": "text", + "content": "School of Electrical and Electronic Engineering, Nanyang Technological University" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 59, + 192, + 531, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 192, + 531, + 204 + ], + "spans": [ + { + "bbox": [ + 59, + 192, + 531, + 204 + ], + "type": "text", + "content": "qi.cui@ntu.edu.sg, ruohan.meng@ntu.edu.sg, chaohui001@e.ntu.edu.sg, echchang@ntu.edu.sg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 256, + 290, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 579 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 579 + ], + "type": "text", + "content": "Ensuring the legal usage of deep models is crucial to promoting trustable, accountable, and responsible artificial intelligence innovation. Current passport-based methods that obfuscate model functionality for license-to-use and ownership verifications suffer from capacity and quality constraints, as they require retraining the owner model for new users. They are also vulnerable to advanced Expanded Residual Block ambiguity attacks. We propose Steganographic Passport, which uses an invertible steganographic network to decouple license-to-use from ownership verification by hiding the user's identity images into the owner-side passport and recovering them from their respective user-side passports. An irreversible and collision-resistant hash function is used to avoid exposing the owner-side passport from the derived user-side passports and increase the uniqueness of the model signature. To safeguard both the passport and model's weights against advanced ambiguity attacks, an activation-level obfuscation is proposed for the verification branch of the owner's model. By jointly training the verification and deployment branches, their weights become tightly coupled. The proposed method supports agile licensing of deep models by providing a strong ownership proof and license accountability without requiring a separate model retraining for the admission of every new user. Experiment results show that our Steganographic Passport outperforms other passport-based deep model protection methods in robustness against various known attacks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 583, + 128, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 583, + 128, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 583, + 128, + 594 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 597, + 287, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 597, + 287, + 622 + ], + "spans": [ + { + "bbox": [ + 46, + 597, + 287, + 622 + ], + "type": "text", + "content": "To foster Artificial Intelligence (AI) diffusion and application, AI as a Service (AIaaS) has emerged as a lucrative" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 626, + 287, + 703 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 626, + 287, + 703 + ], + "spans": [ + { + "bbox": [ + 46, + 626, + 287, + 703 + ], + "type": "text", + "content": "This research is supported by the National Research Foundation, Singapore, and Cyber Security Agency of Singapore under its National Cybersecurity Research & Development Programme (Development of Secured Components & Systems in Emerging Technologies through Hardware & Software Evaluation " + }, + { + "bbox": [ + 46, + 626, + 287, + 703 + ], + "type": "inline_equation", + "content": "<" + }, + { + "bbox": [ + 46, + 626, + 287, + 703 + ], + "type": "text", + "content": " NRF-NCR25-DeSNTU-0001>). Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the view of National Research Foundation, Singapore and Cyber Security Agency of Singapore." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 59, + 703, + 257, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 257, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 257, + 713 + ], + "type": "text", + "content": "†Corresponding author; *Both authors contributed equally." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 326, + 213, + 544, + 310 + ], + "blocks": [ + { + "bbox": [ + 326, + 213, + 544, + 310 + ], + "lines": [ + { + "bbox": [ + 326, + 213, + 544, + 310 + ], + "spans": [ + { + "bbox": [ + 326, + 213, + 544, + 310 + ], + "type": "image", + "image_path": "baaebbbe3fc8a6fe92ef51104c1801eb09238162f1b8c73bdac4aead8612722e.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 308, + 547, + 374 + ], + "lines": [ + { + "bbox": [ + 304, + 308, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 308, + 547, + 374 + ], + "type": "text", + "content": "Figure 1. The conceptual overview. The owner holds the owner-side passport and the steganographic key, which are used to verify the licenses and reveal the user IDs, respectively. The verification branch of the deep model is trained with the constraint of the signature. Upon licensing, the user receives the user-side passport and the deployment branch of the deep model." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 378, + 546, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 378, + 546, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 378, + 546, + 510 + ], + "type": "text", + "content": "business model that offers across-the-broad access to high-performance machine learning models with subscription- or transaction-based payment schemes. The customers can submit inputs to the remote server and receive the inference or classification results of machine learning processes through application program interfaces (APIs). As complex models of high capabilities in AIaaS are offered as \"turnkey\" solutions to potentially anyone, they have huge potential to be misused and abused. Ownership and user license verifications are the first step towards accountability of responsible use of AI services." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 547, + 714 + ], + "type": "text", + "content": "Ownership verification has long been a primary tool to protect deployed deep models against intellectual property (IP) infringement and unauthorized model replication [13]. Numerous approaches have been proposed, such as watermarking [8, 27], fingerprinting [10, 23, 24], and backdoor embedding [11, 14, 26]. These approaches typically aim to enable the trained deep model to exhibit distinguishable characteristics under specific conditions without sacrificing its utility. To resist ambiguity attacks, passport-based ownership verification scheme [5, 6, 20, 30] embeds digital passports during model training to obfuscate the primary functionality until the obfuscated parameters are restored by a genuine passport. The passport scheme provides access control [5, 6] at the expense of some accuracy degradation. Each passport is tied to a user model, retraining is required to derive a new user model from the owner model for every new passport issued. The recent passport-aware normal" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "12302" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "ization [30] avoids making structural changes to the target model by training it jointly with a passport-aware branch. The secret passport and passport-aware branch after training are kept by the model owner for future ownership verification and only the original passport-free target model is released to the end users. By forgoing the usage control, this method allows one deployed model to be used by various users but it also loses the accountability of inappropriate and unlawful use of the deployed model by different licensees. Besides, it has been demonstrated that the passports of existing methods can still be counterfeited by the more advanced ambiguity attack [3]." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 219, + 289, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 219, + 289, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 219, + 289, + 567 + ], + "type": "text", + "content": "In usage authorization, one major limitation of existing passport-based methods is the need to retrain the network to incorporate different parameter modulations for every new passport issued, which may cause uneven service quality for different end users. Besides, retraining to accommodate new user models is inflexible, non-scalable and not cost-effective for complex models. This pitfall motivates us to explore anti-forgery passports that allow fidelity verification of deployed model to hold authorized users accountable for misuse of their licensed models without having to retrain the owner model when admitting new users. To this end, we propose a novel Steganographic Passport to decouple user license verification from ownership verification, as illustrated in Fig. 1. For ownership verification, the uniqueness of the model weights is maintained by aligning them with the hashed output of the owner-side passport, which allows the model owner to prove the ownership and authenticity of the distributed model. For license verification, any licensed user's hidden identity (ID) image can be extracted using the user-side passport. Both owner-side and user-side passports will pass the fidelity assessment as their visual similarity is preserved by using steganography to hide the ID image. To increase the sensitivity of the deployed model against malicious tampering of passports and weights, we propose an activation-level obfuscation for the verification branch of the owner model. The weights of the deployment and verification branches are tightly coupled by training them jointly with a balance loss function. Our contributions can be summarized as follows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 570, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 570, + 287, + 630 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 570, + 287, + 630 + ], + "spans": [ + { + "bbox": [ + 47, + 570, + 287, + 630 + ], + "type": "text", + "content": "- A novel Steganographic Passport is designed based on key-based invertible steganographic network to allow both original model ownership and right-of-use of its deployed model by multiple licensees to be verified without requiring retraining." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 47, + 630, + 287, + 666 + ], + "type": "text", + "content": "- An activation-level obfuscation architecture is designed to thwart forgery by tampering with the user-side passports or model weights." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 288, + 714 + ], + "type": "text", + "content": "- Extensive experiments are conducted to demonstrate the state-of-the-art security performance of our steganographic passports—the credibility of its owner-side and user-side passport verifications and its robustness against" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 313, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 313, + 72, + 545, + 96 + ], + "type": "text", + "content": "various attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 102, + 384, + 115 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 102, + 384, + 115 + ], + "spans": [ + { + "bbox": [ + 306, + 102, + 384, + 115 + ], + "type": "text", + "content": "2. Background" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 117, + 545, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 117, + 545, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 117, + 545, + 368 + ], + "type": "text", + "content": "The need to safeguard the deep model against misappropriation and IP theft arises from the enormous cost of designing and training a high-performance model from scratch. Given redundancy inherent in the numerous parameters of deep models, it is possible to embed a watermark into a model for ownership identification without significantly impairing its performance. The model can be watermarked either explicitly or implicitly. Explicit watermarking embeds the watermark by modifying the weights [7, 10, 23, 27] or feature maps [8] through a weight regularizer without compromising the original model performance. Implicit watermarking (a.k.a prediction watermarking) deliberately trains a backdoor into the protected model to classify inputs with specific triggers to the predefined labels [11, 14, 22, 26, 28]. However, these techniques are found to be vulnerable to ambiguity attacks as the embedded triggers can be replaced by attackers to forge the ownership with a substitute watermark. To mitigate this risk, model passports are introduced [5, 6], where the affine scale and bias factors of normalization functions are substituted with those derived from the passport images " + }, + { + "bbox": [ + 304, + 117, + 545, + 368 + ], + "type": "inline_equation", + "content": "\\{p_{\\gamma}, p_{\\beta}\\}" + }, + { + "bbox": [ + 304, + 117, + 545, + 368 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "x^{l}" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": " be the output of the " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": "-th convolutional layer, and " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\mu_{x^l}" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\sigma_{x^l}" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": " be its mean and standard deviation, respectively. Then, the normalization function at the " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": "-layer with affine factors " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\gamma^l" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "inline_equation", + "content": "\\beta^l" + }, + { + "bbox": [ + 304, + 368, + 545, + 417 + ], + "type": "text", + "content": " is given by:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 400, + 419, + 473, + 435 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 400, + 419, + 473, + 435 + ], + "spans": [ + { + "bbox": [ + 400, + 419, + 473, + 435 + ], + "type": "interline_equation", + "content": "\\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\tilde {x ^ {l}} + \\beta^ {l},", + "image_path": "66ca85a0ab18aa8f982b0087a18b8351d1e562ceb39fc265b4d495921899e01c.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 365, + 436, + 545, + 463 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 365, + 436, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 365, + 436, + 545, + 463 + ], + "type": "interline_equation", + "content": "\\text {w h e r e} \\quad \\tilde {x ^ {l}} = \\frac {1}{\\sigma_ {x ^ {l}}} \\left(x ^ {l} - \\mu_ {x ^ {l}}\\right). \\tag {1}", + "image_path": "7d717ee901c1de8287065a2a202177318227a138d3c8e40e9536610e0bb68582.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "text", + "content": "By substituting " + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\gamma^l" + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\beta^l" + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "text", + "content": " by the passport affine factors " + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\gamma_{p_\\gamma}^l" + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "inline_equation", + "content": "\\beta_{p_\\beta}^l" + }, + { + "bbox": [ + 306, + 464, + 545, + 498 + ], + "type": "text", + "content": ", the following passport normalization [5] is obtained:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 382, + 498, + 545, + 517 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 382, + 498, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 382, + 498, + 545, + 517 + ], + "type": "interline_equation", + "content": "\\widehat {x _ {p} ^ {l}} = \\gamma_ {p _ {\\gamma}} ^ {l} \\cdot \\tilde {x} ^ {l} + \\beta_ {p _ {\\beta}} ^ {l}. \\tag {2}", + "image_path": "4b44494c75c3de96ad8104eb4843a5f311f558d3953279391dff57f79b9af7a3.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "text", + "content": "The sign sequence of " + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\gamma_{p_\\gamma}^l" + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "text", + "content": " in Eq. (2) is constrained to match a self-defined binary signature sequence. As large magnitudes of " + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\gamma_{p_\\gamma}^l" + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "text", + "content": " can be penalized, the gradients are kept small to ensure that the signs of " + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "inline_equation", + "content": "\\gamma_{p_\\gamma}^l" + }, + { + "bbox": [ + 304, + 523, + 545, + 633 + ], + "type": "text", + "content": " are lazy-to-flip so as to prevent the signature from being replaced by retraining the model. To minimize the influence of passport normalization on inference performance, Zhang et al. [30] proposed a dual-branch passport structure. Its normalization function is expressed in Eq. (3) and illustrated in Fig. 2a." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 373, + 639, + 545, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 373, + 639, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 373, + 639, + 545, + 672 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\tilde {x ^ {l}} + \\beta^ {l}, \\\\ \\widehat {x _ {p} ^ {l}} = \\gamma_ {p _ {\\gamma}} ^ {l} \\cdot \\tilde {x ^ {l}} + \\beta_ {p _ {\\beta}} ^ {l}, \\end{array} \\right. \\tag {3}", + "image_path": "27916e02edcbb44928110f75ce0c6940f8a7481abb88748fa7700a3deb9717be.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "type": "text", + "content": "where the passport-free output " + }, + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{x^l}" + }, + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "type": "text", + "content": " and the passport-aware output " + }, + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\widehat{x_p^l}" + }, + { + "bbox": [ + 304, + 673, + 545, + 714 + ], + "type": "text", + "content": " are used for the deployment and ownership verification, respectively. Besides, a two-layer perception (TLP)" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12303" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 53, + 167, + 129 + ], + "blocks": [ + { + "bbox": [ + 51, + 53, + 167, + 129 + ], + "lines": [ + { + "bbox": [ + 51, + 53, + 167, + 129 + ], + "spans": [ + { + "bbox": [ + 51, + 53, + 167, + 129 + ], + "type": "image", + "image_path": "3176ae7e9907bd4170357b9063a52ee2da63634d45a27238944eaf0eb5cf4b72.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 131, + 161, + 140 + ], + "lines": [ + { + "bbox": [ + 54, + 131, + 161, + 140 + ], + "spans": [ + { + "bbox": [ + 54, + 131, + 161, + 140 + ], + "type": "text", + "content": "(a) Existing passport architecture" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 171, + 52, + 286, + 129 + ], + "blocks": [ + { + "bbox": [ + 171, + 52, + 286, + 129 + ], + "lines": [ + { + "bbox": [ + 171, + 52, + 286, + 129 + ], + "spans": [ + { + "bbox": [ + 171, + 52, + 286, + 129 + ], + "type": "image", + "image_path": "c8d1a5e063f486cc3a2879b47887870014b090fc6dc9ad4412c497fe2a39c7e1.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 172, + 131, + 282, + 140 + ], + "lines": [ + { + "bbox": [ + 172, + 131, + 282, + 140 + ], + "spans": [ + { + "bbox": [ + 172, + 131, + 282, + 140 + ], + "type": "text", + "content": "(b) Proposed passport architecture" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 47, + 143, + 286, + 163 + ], + "lines": [ + { + "bbox": [ + 47, + 143, + 286, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 143, + 286, + 163 + ], + "type": "text", + "content": "Figure 2. The existing and proposed passport architectures. The dual branches are enclosed in the dashed line box." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 170, + 287, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 170, + 287, + 205 + ], + "spans": [ + { + "bbox": [ + 46, + 170, + 287, + 205 + ], + "type": "text", + "content": "structure is also inserted before the affine factors to mitigate the strict limitations in managing the functionality of normalization layers." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 206, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 206, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 206, + 287, + 445 + ], + "type": "text", + "content": "To protect against ambiguity attacks with oracle passports due to passport leakage, Liu et al. [20] used trapdoor normalization to establish a direct correlation between the signature and the passport through a hash function. The collision-intractable hash function makes it virtually impossible for the attackers to reverse engineer a counterfeit passport, even if they can compromise the signature. Recently, Chen et al. [3] proposed an advanced ambiguity attack called Expanded Residual Block (ERB) on passport-based methods. This attack exploits the extensive solution space of TLP to force-flip the signs of the scale factors according to their forged passport without compromising the model performance. In summary, existing model passport methods aim only to resist the diverse ambiguity attacks by obfuscating the normalization functionalities with immutable passports. They do not allow admission of new users and their right-of-use verification upon model deployment. This is an important measure to safeguard the interest of AIaaS providers against revenue extorts by unauthenticated usage." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 449, + 151, + 462 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 449, + 151, + 462 + ], + "spans": [ + { + "bbox": [ + 47, + 449, + 151, + 462 + ], + "type": "text", + "content": "3. Proposed method" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 465, + 158, + 477 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 465, + 158, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 465, + 158, + 477 + ], + "type": "text", + "content": "3.1. Problem statement" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 479, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 670 + ], + "type": "text", + "content": "We consider a practical licensing scenario of a deep model. Besides being able to detect and verify the ownership of a deployed model, the model owner should also be able to verify usage permission. If the passport images " + }, + { + "bbox": [ + 46, + 479, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\{p_{\\gamma}, p_{\\beta}\\}" + }, + { + "bbox": [ + 46, + 479, + 287, + 670 + ], + "type": "text", + "content": " are used as a unique proof to verify the ownership of the deployed model, they cannot be used to verify the usage permission granted to licensed users of that model. Although new backdoor triggers or watermarks can be added to verify each licensed user, the model needs to be retrained to learn the new features. This is very restrictive and impractical as it requires the model owner to fix the number of users and their identities upfront. Therefore, our aim is to enable the passport-based scheme to grant verifiable usage permission of a deployed deep model to ad hoc registered users without requiring retraining and without undermining the validity and robustness of the model's ownership proof." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 677, + 241, + 689 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 241, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 241, + 689 + ], + "type": "text", + "content": "3.2. Steganographic passport framework" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Recall that in existing passport approaches [5, 6, 20, 30], a forged passport image can also be used to pass the fi" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "delity assessment if it bears a high visual similarity to the genuine passport image. Inspired by advanced steganography techniques, we apply the art of imperceptible secret concealment to the passport-based scheme. The proposed Steganographic Passport follows the dual-branch setting, as illustrated in Fig. 2b." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": "We define an owner-side passport " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "p_{o} = \\{p_{o_{\\gamma}}, p_{o_{\\beta}}\\}" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": " as the genuine passport images selected and held only by the model owner for generating the affine scale and bias factors accordingly. By feeding " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "p_{o}" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": " into the model, the corresponding owner-side passport feature maps are sequentially generated across the " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": " passport layers. These feature maps are then transformed into the affine factors for obfuscating the verification branch, which will be described in Sec. 3.3. We also introduce a new user-side passport, " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "p_{u} = \\{p_{u_{\\gamma}}, p_{u_{\\beta}}\\}" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": ", which is obtained by hiding the ID image " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": " provided by a registered user into " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "p_{o}" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": ". The user-side passport " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "p_{u}" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": " fills the gap of existing passport-based limitation in meeting the goal of Sec. 3.1. The model owner can license the deployment branch of the model to multiple registered users by merely hiding each user's ID image into " + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "inline_equation", + "content": "p_{o}" + }, + { + "bbox": [ + 304, + 144, + 545, + 323 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 323, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 407 + ], + "type": "text", + "content": "Anti-forgery owner-side passport. To avoid user-side passports from exposing the visual content of the owner-side passports, the owner-side passport is irreversibly transformed to a unique model signature to ensure that the ownership cannot be forged by knowing any of the user-side passports. SHA-512 [25] is used as the one-way function for this mapping." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "spans": [ + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "text", + "content": "Before training the target model, the model owner hashes the owner-side " + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "p_{o_{\\gamma}}" + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "text", + "content": " to a binary signature " + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "\\xi^l" + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "text", + "content": " of passport layer " + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 407, + 545, + 442 + ], + "type": "text", + "content": ", as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 351, + 445, + 545, + 460 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 351, + 445, + 545, + 460 + ], + "spans": [ + { + "bbox": [ + 351, + 445, + 545, + 460 + ], + "type": "interline_equation", + "content": "\\xi^ {l} = \\left\\{\\operatorname {S G N} (x) \\mid x \\in \\operatorname {H A S H} \\left(p _ {o _ {\\gamma}}\\right) \\right\\}, \\tag {4}", + "image_path": "aea9882877447d40e25efb9711e0270c906c26198bcd8bcf9bfc99d3f33ca6f8.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "content": "where SGN maps each bit of a binary input sequence from " + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\{0,1\\}" + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\{-1,1\\}" + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "content": ". If the desired length of " + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\xi^l" + }, + { + "bbox": [ + 304, + 462, + 545, + 521 + ], + "type": "text", + "content": " is shorter than 512 bits, the excess bits of the hash output are truncated from the beginning; Otherwise, we cycle the hash function's output until the required sequence length is obtained." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "text", + "content": "For a model with " + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "text", + "content": " passport layers, its overall model signature is represented as " + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\{\\xi^1, \\xi^2, \\dots, \\xi^n\\}" + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "text", + "content": ". The strict avalanche criterion of the hash function ensures that even minor changes to the passport image will result in significantly different affine factors, which prevents force-flipping from forging the passport with high model performance fidelity. Together with the irreversibility property of SHA-512, the genuine model signature " + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "text", + "content": " can only be generated with the owner-side passport to thwart ownership impersonation fraud. The signature " + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "inline_equation", + "content": "\\{\\xi^1, \\xi^2, \\dots, \\xi^n\\}" + }, + { + "bbox": [ + 304, + 522, + 545, + 677 + ], + "type": "text", + "content": " will be used to constrain the model's learning in the subsequent training phase to transform them into unique model's weights. A detailed exposition of this process is provided in Sec. 3.3." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 678, + 545, + 713 + ], + "type": "text", + "content": "License verification via key-based deep steganography. To support an agile licensing scheme that is capable of admitting and verifying any new user after the tar" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12304" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": "get model has finalized its training phase, we need to decouple the license verification from the ownership verification. To this end, we hide the user's ID into the owner-side passport by integrating the key-based scheme of Invertible Steganographic Network (ISN) [21] within the Deep Image Hiding Network (HiNet) framework [15]. The key-based ISN is divided into two processes: forward hiding pass " + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{H}_s" + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": " and reverse revealing pass " + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "\\mathcal{H}_s^{-1}" + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": ". The forward hiding pass is used to obtain the user-side passport " + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "p_u" + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": " from the owner-side passport " + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 46, + 72, + 289, + 192 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 130, + 194, + 287, + 208 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 194, + 287, + 208 + ], + "spans": [ + { + "bbox": [ + 130, + 194, + 287, + 208 + ], + "type": "interline_equation", + "content": "p _ {u} = \\mathcal {H} _ {s} \\left(p _ {o}, \\mathrm {I} _ {u}\\right), \\tag {5}", + "image_path": "6cb79df001cd15c4142ef2d882f1e9b5e29260de25a25b839825c78cbc8d6021.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "spans": [ + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u" + }, + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "type": "text", + "content": " denotes the user's ID image to be hidden into the owner-side passport " + }, + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 46, + 209, + 287, + 233 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "text", + "content": "The reverse revealing pass is utilized for license verification. Using the private steganographic key " + }, + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_s" + }, + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "text", + "content": ", the model owner can reveal the hidden user's ID image from the underside passport " + }, + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "inline_equation", + "content": "p_u" + }, + { + "bbox": [ + 46, + 233, + 287, + 281 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 126, + 281, + 287, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 281, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 126, + 281, + 287, + 297 + ], + "type": "interline_equation", + "content": "\\mathrm {I} _ {u} ^ {\\prime} = \\mathcal {H} _ {s} ^ {- 1} \\left(p _ {u}, \\mathbf {k} _ {s}\\right), \\tag {6}", + "image_path": "e5723172bb83136a454dfe269b28e624e61cbfdfca41830d33c7e31af930a682.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 297, + 287, + 334 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 287, + 334 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 287, + 334 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 297, + 287, + 334 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u^\\prime" + }, + { + "bbox": [ + 46, + 297, + 287, + 334 + ], + "type": "text", + "content": " denotes the revealed ID image of the licensed user. The detailed architecture and algorithms of the hiding and revealing passes are given in the Appendix." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 340, + 200, + 351 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 340, + 200, + 351 + ], + "spans": [ + { + "bbox": [ + 47, + 340, + 200, + 351 + ], + "type": "text", + "content": "3.3. Activation-level obfuscation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 353, + 287, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 353, + 287, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 353, + 287, + 400 + ], + "type": "text", + "content": "To counteract sophisticated ambiguity attacks, an activation-level obfuscation is proposed to safeguard the verification branch against alterations of both the passport and the model's weights." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "content": "Immutable passport. As illustrated in Fig. 2b, the passport-affine factors of layer " + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "content": " can be calculated from the passport feature maps " + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "inline_equation", + "content": "p_{o}^{l}" + }, + { + "bbox": [ + 46, + 401, + 287, + 437 + ], + "type": "text", + "content": " by:" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 58, + 437, + 287, + 459 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 437, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 58, + 437, + 287, + 459 + ], + "type": "interline_equation", + "content": "\\gamma_ {p _ {o _ {\\gamma}}} ^ {l} = \\Phi (\\Pi (p _ {o _ {\\gamma}} ^ {l})) \\text {, a n d} \\beta_ {p _ {o _ {\\beta}}} ^ {l} = \\Phi (\\Pi (p _ {o _ {\\beta}} ^ {l})) \\tag {7}", + "image_path": "737de56f81fa9183f2fe3a54e3955216efce4fdb2dca1572d07962ba39d045ad.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\Phi" + }, + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "inline_equation", + "content": "\\Pi" + }, + { + "bbox": [ + 46, + 459, + 287, + 483 + ], + "type": "text", + "content": " denote the TLP and the global average pooling, respectively." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "type": "text", + "content": "Inspired by the controllable rectifiers of the Dynamic ReLU [2], we make " + }, + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "type": "inline_equation", + "content": "\\gamma_{p_{o\\gamma}}^l" + }, + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "type": "inline_equation", + "content": "\\beta_{p_{o\\beta}}^l" + }, + { + "bbox": [ + 46, + 483, + 287, + 531 + ], + "type": "text", + "content": " the dependent variables of the activation function. This can be incorporated into a dual-branch architecture as follows:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 86, + 533, + 287, + 564 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 86, + 533, + 287, + 564 + ], + "spans": [ + { + "bbox": [ + 86, + 533, + 287, + 564 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} \\widehat {x ^ {l}} = \\gamma^ {l} \\cdot \\widetilde {x ^ {l}} + \\beta^ {l}, \\\\ \\widehat {x _ {p _ {o}} ^ {l}} = \\gamma_ {p _ {o \\gamma}} ^ {l} \\cdot \\left(\\gamma_ {t} ^ {l} \\cdot \\widetilde {x ^ {l}} + \\beta_ {t} ^ {l}\\right) + \\beta_ {p _ {o \\beta}} ^ {l}, \\end{array} \\right. \\tag {8}", + "image_path": "bbb5853ed6c505e8682dbecc429af98fc2ab828cdb4831e2b527cb4f08c3e3d6.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\gamma^l" + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\beta^l" + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": " denote the original affine factors used in the deployment branch, and " + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\gamma_t^l" + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "inline_equation", + "content": "\\beta_t^l" + }, + { + "bbox": [ + 46, + 567, + 287, + 604 + ], + "type": "text", + "content": " denote the additional temporal affine factors used in the verification branch." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "content": "To simplify the expressions, let " + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "inline_equation", + "content": "x_{t}^{l} = \\gamma_{t}^{l}\\cdot x^{l} + \\beta_{t}^{l}" + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "content": ". By subjecting the outputs of Eq. (8) to an activation function (e.g. ReLU) before feeding them to the next layer, the final outputs of layer " + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 605, + 287, + 654 + ], + "type": "text", + "content": " are given by:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 87, + 655, + 287, + 688 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 87, + 655, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 87, + 655, + 287, + 688 + ], + "type": "interline_equation", + "content": "\\left\\{ \\begin{array}{l} x _ {\\varphi} ^ {l} = \\max \\left(\\widehat {x ^ {l}}, 0\\right), \\\\ x _ {\\varphi_ {p o}} ^ {l} = \\max \\left(\\gamma_ {p _ {o \\gamma}} ^ {l} \\cdot \\widehat {x _ {t} ^ {l}} + \\beta_ {p _ {o \\beta}} ^ {l}, 0\\right). \\end{array} \\right. \\tag {9}", + "image_path": "5aafc900501baeb9e01a5d67e1f13ae96f16223b0bbe9e02426e52bd9d0cb953.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "The activation function used for the deployment branch (top expression) in Eq. (9) is a regular ReLU, whereas the" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "text", + "content": "activation function used for the verification branch (bottom expression) can be viewed as a special case of Dynamic ReLU. This way, the changes in the affine factors due to any alterations of the owner-side passport " + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "text", + "content": " will lead to apparent changes in the passport-aware output, " + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "inline_equation", + "content": "x_{\\varphi_{p_o}}^l" + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "text", + "content": ", but not in the passport-free output, " + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "inline_equation", + "content": "x_{\\varphi}^{l}" + }, + { + "bbox": [ + 304, + 72, + 545, + 147 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 146, + 545, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 146, + 545, + 277 + ], + "spans": [ + { + "bbox": [ + 304, + 146, + 545, + 277 + ], + "type": "text", + "content": "Immutable deployment branch. Under the dual-branch setting, the deployment and verification branches share all the model's weights but the affine factors. The deployment branch has to be consistently updated according to the updated passport-derived affine factors in the verification branch. If the deployment branch cannot keep up with the updates, the shared weights will overfit the verification branch, causing gradient explosions. To keep the updates of the two branches in tandem, the following balance loss function is proposed to train the model by explicitly aligning the affine factors in Eq. (8):" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 311, + 277, + 545, + 306 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 311, + 277, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 311, + 277, + 545, + 306 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {b} = \\sum_ {l = 1} ^ {n} \\left(\\mathcal {L} _ {\\mathrm {y}} \\left(\\gamma^ {l}, \\gamma_ {t} ^ {l} \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l}\\right) + \\mathcal {L} _ {\\mathrm {y}} \\left(\\beta^ {l}, \\beta_ {t} ^ {l} \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l} + \\beta_ {p _ {o _ {\\beta}}} ^ {l}\\right)\\right), \\tag {10}", + "image_path": "5834334e1b954c4f2b5f03c1743bf41aac1800627f641007cfc4dab10814160a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "spans": [ + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "content": " norm is used for " + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_y" + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 305, + 545, + 328 + ], + "type": "text", + "content": " is the total number of passport layers." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 329, + 545, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 545, + 436 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 545, + 436 + ], + "type": "text", + "content": "This loss function aims to strike an equilibrium performance between the two branches. After the model is trained, the verification branch is removed from the model before it is licensed to any user. As the model trained with the balance loss function will have negligible accuracy difference between the two branches, any modification on the deployment branch would amplify the mean absolute difference. By comparing the accuracy difference between the two branches, the integrity of the model can be validated." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 437, + 545, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 437, + 545, + 485 + ], + "spans": [ + { + "bbox": [ + 306, + 437, + 545, + 485 + ], + "type": "text", + "content": "Immutable verification branch. During the target model's training phase, the owner uses the model signature " + }, + { + "bbox": [ + 306, + 437, + 545, + 485 + ], + "type": "inline_equation", + "content": "\\{\\xi^1,\\xi^2,\\dots ,\\xi^n\\}" + }, + { + "bbox": [ + 306, + 437, + 545, + 485 + ], + "type": "text", + "content": " to constrain the update of model's weights with the following signature loss function:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 325, + 485, + 545, + 506 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 325, + 485, + 545, + 506 + ], + "spans": [ + { + "bbox": [ + 325, + 485, + 545, + 506 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {s} = \\sum \\max \\left(\\epsilon - \\xi^ {l} \\cdot \\Pi \\left(p _ {o _ {\\gamma}} ^ {l}\\right) \\cdot \\gamma_ {p _ {o _ {\\gamma}}} ^ {l}, 0\\right), \\tag {11}", + "image_path": "2683f7e8f06dd9bbec742a9f7f905c400c232e197bb21947b53ee5b272eb899d.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\xi^l" + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "inline_equation", + "content": "p_{o_\\gamma}^l" + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "text", + "content": "-th layer's signature and passport feature map, respectively, and " + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 506, + 545, + 531 + ], + "type": "text", + "content": " is a small constant." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "content": " encourages the signs of the product " + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\Pi \\left(p_{o_\\gamma}^l\\right) \\cdot \\gamma_{p_{o_\\gamma}}^l" + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "content": " to align with that of " + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\xi^l" + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "content": ", while keeping the magnitude of this product low. Since " + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "inline_equation", + "content": "p_{o_\\gamma}^l" + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\gamma_{p_{o_\\gamma}}^l" + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "content": " are the outputs of the convolution and TLP, respectively, the weights of the convolution layer and TLP become tightly coupled. The uniqueness of " + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "inline_equation", + "content": "\\xi^l" + }, + { + "bbox": [ + 304, + 532, + 545, + 672 + ], + "type": "text", + "content": " in Eq. (11) contributes to the distinctiveness of the weights. Any adjustment to the TLP will directly affect the convolution output. This property helps to prevent advanced ambiguity attacks, especially ERB, which maliciously alter the weights of the TLP to force-flip the signs of the product to align it with the forged signature." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 677, + 418, + 689 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 418, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 418, + 689 + ], + "type": "text", + "content": "3.4. Training objectives" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 689, + 545, + 713 + ], + "type": "text", + "content": "The one-time training pipeline consists of training the key-based ISN and the target model." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12305" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 120 + ], + "type": "text", + "content": "Training the key-based ISN. The key-based ISN is trained once independently of the target model to enhance the hiding invisibility and the revealing quality by the following loss function:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 100, + 123, + 287, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 100, + 123, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 100, + 123, + 287, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I S N} = \\mathcal {L} _ {h} \\left(p _ {o}, p _ {u}\\right) + \\mathcal {L} _ {r} \\left(\\mathrm {I} _ {u}, \\mathrm {I} _ {u} ^ {\\prime}\\right). \\tag {12}", + "image_path": "40d24dfaac4110a47377e6b6f69a9495b519beec301be246611ee52adfcbd05a.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "spans": [ + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "content": "Both " + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_h" + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r" + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "content": " utilize the " + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "content": " norm for distance calculation. " + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u" + }, + { + "bbox": [ + 47, + 140, + 287, + 163 + ], + "type": "text", + "content": " are randomly sampled in the training phase." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "spans": [ + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "text", + "content": "Training the target model. Given a target model, we denote the models with only the weights of the deployment branch as " + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{M}" + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "text", + "content": ", and those with only the weights of the " + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "text", + "content": "-based verification branch as " + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{p_o}" + }, + { + "bbox": [ + 47, + 164, + 287, + 235 + ], + "type": "text", + "content": ". Three loss functions are used to train the dual branches parallelly. The loss function for model performance is defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 239, + 287, + 270 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 239, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 47, + 239, + 287, + 270 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {f} = \\frac {1}{N _ {t r}} \\sum_ {i = 1} ^ {N _ {t r}} \\left(\\mathcal {L} _ {c} \\left(\\mathcal {M} \\left(x _ {i}\\right), y _ {i}\\right) + \\mathcal {L} _ {c} \\left(\\mathcal {M} _ {p _ {o}} \\left(x _ {i}\\right), y _ {i}\\right)\\right), \\tag {13}", + "image_path": "5934803ee17ca9525f61e80c8e262eb15e879d08bf7852243d33ec07c0be1a41.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "content": " are respectively the " + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "content": "-th sample and its label from " + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "inline_equation", + "content": "N_{tr}" + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "content": " training samples, and " + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_c" + }, + { + "bbox": [ + 47, + 274, + 287, + 297 + ], + "type": "text", + "content": " is the cross-entropy loss." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "spans": [ + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "type": "text", + "content": "Together with the signature loss " + }, + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_s" + }, + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "type": "text", + "content": " and the balance loss " + }, + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_b" + }, + { + "bbox": [ + 47, + 297, + 287, + 319 + ], + "type": "text", + "content": ", the total loss is defined as:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 113, + 324, + 287, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 324, + 287, + 338 + ], + "spans": [ + { + "bbox": [ + 113, + 324, + 287, + 338 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} = \\mathcal {L} _ {f} + \\omega_ {s} \\mathcal {L} _ {s} + \\omega_ {b} \\mathcal {L} _ {b}, \\tag {14}", + "image_path": "4784ed0a235a932a22df57cc093a9872d273ecebba59a6dfb26c7e29f9cededc.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "spans": [ + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "type": "text", + "content": "where the signature and balance losses are weighted by " + }, + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "type": "inline_equation", + "content": "\\omega_{s}" + }, + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "type": "inline_equation", + "content": "\\omega_{b}" + }, + { + "bbox": [ + 47, + 341, + 286, + 365 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 372, + 195, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 372, + 195, + 383 + ], + "spans": [ + { + "bbox": [ + 47, + 372, + 195, + 383 + ], + "type": "text", + "content": "3.5. Inclusive verification chain" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 384, + 287, + 432 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 384, + 287, + 432 + ], + "spans": [ + { + "bbox": [ + 47, + 384, + 287, + 432 + ], + "type": "text", + "content": "To confirm the ownership and legal usability of a deployed model M, we propose the following verification chain involving the model owner O, the licensed user U, and the deployed model M." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "spans": [ + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": "Ownership verification. The ownership verification comprises three tests: " + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^{\\mathcal{I}}" + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": " for the verification of the model integrity, performance fidelity and signature accuracy, respectively. By replacing the passport layers' affine factors with the ones derived from the owner-side passport " + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "inline_equation", + "content": "p_o" + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": ", the deployed branch " + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": " becomes a verifiable branch " + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{p_o}" + }, + { + "bbox": [ + 47, + 433, + 287, + 516 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathcal{F}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "text", + "content": " denote the model performance. " + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\nu_{O}^{\\mathcal{T}}" + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "text", + "content": " tests if " + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 47, + 516, + 287, + 552 + ], + "type": "text", + "content": " has been modified based on the absolute performance difference (AD):" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 51, + 555, + 287, + 593 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 51, + 555, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 51, + 555, + 287, + 593 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {O} ^ {\\mathcal {I}} \\Longleftrightarrow \\frac {1}{N _ {t}} \\left| \\sum_ {j = 1} ^ {N _ {t}} \\left(\\mathcal {F} \\left(\\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\\right) - \\mathcal {F} \\left(\\mathbf {M}, x _ {j} ^ {t}\\right)\\right) \\right| < \\tau_ {d}, \\tag {15}", + "image_path": "002d2970cdc7d61b9962b6dcdf11aba88c65fe608b9fb57422688280b67890d4.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "spans": [ + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "inline_equation", + "content": "x_{j}^{t}" + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "text", + "content": "-th sample from total " + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "inline_equation", + "content": "N_{t}" + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "text", + "content": " test samples, and " + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "inline_equation", + "content": "\\tau_{d}" + }, + { + "bbox": [ + 47, + 595, + 287, + 619 + ], + "type": "text", + "content": " is a small predefined passing threshold." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 59, + 618, + 220, + 632 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 618, + 220, + 632 + ], + "spans": [ + { + "bbox": [ + 59, + 618, + 220, + 632 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 59, + 618, + 220, + 632 + ], + "type": "text", + "content": " verifies the performance fidelity by:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 89, + 632, + 287, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 89, + 632, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 89, + 632, + 287, + 666 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {O} ^ {f} \\Longleftrightarrow \\frac {1}{N _ {t}} \\sum_ {j = 1} ^ {N _ {t}} \\mathcal {F} \\left(\\mathbf {M} _ {p _ {o}}, x _ {j} ^ {t}\\right) > \\tau_ {f}, \\tag {16}", + "image_path": "1af1ad232254895122a28d228dd22e1838294bb36052a1df80fccdc083d93595.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 47, + 666, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 689 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 666, + 287, + 689 + ], + "type": "inline_equation", + "content": "\\tau_{f}" + }, + { + "bbox": [ + 47, + 666, + 287, + 689 + ], + "type": "text", + "content": " is the predefined minimum accuracy to pass the performance fidelity verification." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": "To validate the signature accuracy, the owner uses Eq. (4) to transform " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "p_{o_{\\gamma}}" + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "text", + "content": " into the model signature " + }, + { + "bbox": [ + 47, + 689, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\xi =" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "inline_equation", + "content": "\\{\\xi^1,\\xi^2,\\dots ,\\xi^n\\}" + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "text", + "content": " . By comparing each element of " + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "text", + "content": " with those of " + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "inline_equation", + "content": "\\xi^{*}" + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "text", + "content": " extracted from " + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{p_o}" + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "inline_equation", + "content": "\\nu_{O}^{s}" + }, + { + "bbox": [ + 306, + 72, + 545, + 106 + ], + "type": "text", + "content": " checks the sign agreement (SA) by:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 356, + 106, + 545, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 106, + 545, + 137 + ], + "spans": [ + { + "bbox": [ + 356, + 106, + 545, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {O} ^ {s} \\Longleftrightarrow \\frac {1}{N _ {\\xi}} \\sum_ {b = 1} ^ {N _ {\\xi}} \\left(\\xi_ {b} \\wedge \\xi_ {b} ^ {*}\\right) \\geq \\tau_ {\\xi}, \\tag {17}", + "image_path": "d8ad08d73b1f6c2ff271ba7715b3b680aa67b52bf8234eb787f70b44c7a8a790.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "spans": [ + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "inline_equation", + "content": "N_{\\xi}" + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "content": " is the total length of " + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\xi" + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "content": ". 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Otherwise, the SA of an untainted pre-deployment model has to be " + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "content": " (i.e., " + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\tau_{\\xi} = 1" + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "content": ") to satisfy " + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 304, + 140, + 545, + 187 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "spans": [ + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": "Remark 1: Before distributing the deployed model " + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": ", the owner " + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": " is required to disclose the evidence of compliance with " + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": " to establish the credibility of the ownership claim of " + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 188, + 545, + 235 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": "License verification. Upon verifying that the model M deployed by the licensed user " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": " complies with the criteria set by " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^{\\mathcal{T}}" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": ", a provable association between the licensed user " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": " and the model owner " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": " can be established by two license verification tests: " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^p" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": " for passport image similarity, and " + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^I" + }, + { + "bbox": [ + 304, + 236, + 545, + 307 + ], + "type": "text", + "content": " for ID image similarity." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "spans": [ + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "text", + "content": "Upon receiving " + }, + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "inline_equation", + "content": "p_u" + }, + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "text", + "content": " submitted by the user " + }, + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 307, + 545, + 342 + ], + "type": "text", + "content": ", the owner can compare the PSNR between the user and owner passport images by:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 361, + 345, + 545, + 358 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 345, + 545, + 358 + ], + "spans": [ + { + "bbox": [ + 361, + 345, + 545, + 358 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {L} ^ {p} \\Longleftrightarrow \\operatorname {P S N R} \\left(p _ {o}, p _ {u}\\right) > \\tau_ {p}, \\tag {18}", + "image_path": "5e42d5d6169405d64da6ddfd0825ea96300d14ef748431ba15df1ae53a7454f0.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 360, + 545, + 383 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 360, + 545, + 383 + ], + "spans": [ + { + "bbox": [ + 304, + 360, + 545, + 383 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 360, + 545, + 383 + ], + "type": "inline_equation", + "content": "\\tau_{p}" + }, + { + "bbox": [ + 304, + 360, + 545, + 383 + ], + "type": "text", + "content": " is the predefined visual similarity threshold for successful verification." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": "The reverse revealing pass is utilized for license verification. Using the private steganographic key " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_s" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": ", the model owner can reveal the hidden user's ID image " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u^{\\prime}" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": " from the user-side passport " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "p_u" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": " by Eq. (6). " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^{\\mathrm{I}}" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": " tests the visual similarity between " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": " and the revealed ID image, " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\mathrm{I}_u^{\\prime}" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": " of the licensed user by comparing the PSNR with predefined threshold " + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "inline_equation", + "content": "\\tau_r" + }, + { + "bbox": [ + 304, + 384, + 545, + 456 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 362, + 458, + 545, + 472 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 362, + 458, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 362, + 458, + 545, + 472 + ], + "type": "interline_equation", + "content": "\\mathcal {V} _ {L} ^ {\\mathrm {I}} \\Longleftrightarrow \\operatorname {P S N R} \\left(\\mathrm {I} _ {u}, \\mathrm {I} _ {u} ^ {\\prime}\\right) > \\tau_ {r}. \\tag {19}", + "image_path": "54a24ddc311107b37990daa50a38ebc5acbebe7967c1655f0085010d33df68d3.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": "Remark 2: Once " + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^p" + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^{\\mathrm{I}}" + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": " are satisfied, on the condition that the model " + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": " passes the three ownership verification tests of the owner " + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{O}" + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": ", the user " + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{U}" + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": " is proven to be a legal licensee of " + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 304, + 473, + 545, + 521 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 525, + 382, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 382, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 382, + 539 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 306, + 545, + 355, + 557 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 545, + 355, + 557 + ], + "spans": [ + { + "bbox": [ + 306, + 545, + 355, + 557 + ], + "type": "text", + "content": "4.1. Setup" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Generally, we follow the settings on image classification tasks in existing passport approaches, including dual-branch DeepIPR [6], Passport-Aware Normalization (PAN) [30], and Trapdoor Normalization (TdN) [20]. AlexNet [17] and ResNet-18 [9], with Batch Normalization (BN) [12] and Group Normalization (GN) [29], are employed to evaluate and compare the performance. The datasets used in the classification experiments include CIFAR-10, CIFAR-100 [16], Caltech-101, and Caltech-256 [18]. Besides, DIV2K [1] is used to train the key-based ISN. For passport images " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{\\gamma}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "p_{\\beta}" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ", we randomly select them from the test set of COCO dataset [19]. For steganographic key image " + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{k}_s" + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": ", we randomly select it from DTD" + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12306" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 59, + 545, + 180 + ], + "blocks": [ + { + "bbox": [ + 69, + 48, + 520, + 58 + ], + "lines": [ + { + "bbox": [ + 69, + 48, + 520, + 58 + ], + "spans": [ + { + "bbox": [ + 69, + 48, + 520, + 58 + ], + "type": "text", + "content": "Table 1. Inference performance (in %) for deployment/verification. " + }, + { + "bbox": [ + 69, + 48, + 520, + 58 + ], + "type": "inline_equation", + "content": "\\uparrow / \\downarrow" + }, + { + "bbox": [ + 69, + 48, + 520, + 58 + ], + "type": "text", + "content": " denotes higher / lower value for better performance." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 59, + 545, + 180 + ], + "lines": [ + { + "bbox": [ + 50, + 59, + 545, + 180 + ], + "spans": [ + { + "bbox": [ + 50, + 59, + 545, + 180 + ], + "type": "table", + "html": "
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18BN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean94.6993.8576.4273.5774.5870.7355.4349.5273.60-
DeepIPR93.04 / 94.0593.81 / 93.6960.76 / 62.8872.19 / 71.1573.84 / 73.2265.08 / 63.3341.53 / 44.1243.81 / 42.6768.01 / 68.141.30
PAN94.70 / 94.6193.63 / 93.6775.97 / 74.7072.19 / 71.4973.79 / 72.9468.36 / 65.3755.37 / 54.3344.73 / 43.5172.34 / 71.331.03
TdN94.65 / 94.6893.57 / 93.5776.00 / 75.6171.25 / 71.4274.12 / 73.0567.63 / 67.5154.90 / 54.2844.90 / 44.2772.13 / 71.800.38
Ours94.89 / 94.8993.79 / 93.8076.10 / 76.1070.84 / 70.8373.56 / 73.5667.01 / 67.0153.65 / 53.6544.01 / 44.0171.73 / 71.730.00
AlexNetBN↑GN↑BN↑GN↑BN↑GN↑BN↑GN↑Mean↑AD↓
Clean91.2090.2768.4065.7271.5868.7044.2441.1867.66-
DeepIPR81.80 / 90.7689.90 / 90.2045.71 / 51.7764.89 / 64.1667.91 / 65.9567.80 / 67.0631.39 / 36.2540.69 / 39.7360.14 / 63.243.07
PAN91.51 / 91.2990.22 / 90.3968.46 / 66.4450.60 / 56.7171.03 / 70.9066.95 / 66.7144.93 / 41.1340.03 / 38.8466.47 / 65.311.32
TdN91.28 / 91.0290.08 / 89.8068.71 / 68.0764.54 / 63.7770.45 / 69.4468.31 / 66.3845.36 / 44.8242.39 / 37.8867.64 / 66.401.24
Ours91.39 / 91.3889.77 / 89.7767.86 / 67.8563.36 / 63.3471.98 / 71.9868.42 / 68.4246.10 / 46.0741.10 / 41.1267.50 / 67.490.01
", + "image_path": "2fe5f6ad52a7eb0fe085d15502c419ef03b7a1bd5af834b35685efb8535a8eb4.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "type": "text", + "content": "dataset [4]. For hyper-parameters " + }, + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "type": "inline_equation", + "content": "\\epsilon, \\omega_s" + }, + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "type": "inline_equation", + "content": "\\omega_b" + }, + { + "bbox": [ + 46, + 196, + 287, + 243 + ], + "type": "text", + "content": ", we empirically set them as 0.1, 1, and 1. By default, the last three/five normalization layers of AlexNet/ResNet-18 are set as the passport layers." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 251, + 178, + 263 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 251, + 178, + 263 + ], + "spans": [ + { + "bbox": [ + 47, + 251, + 178, + 263 + ], + "type": "text", + "content": "4.2. Verification assessment" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "type": "text", + "content": "We evaluate the effectiveness of the proposed steganographic passport by the verification and inference performances. All the models are trained with 200 epochs, utilizing a multi-step learning rate that decreases gradually from 0.01 to 0.0001. A twofold verification is adopted in our method, which entails a) an ownership verification " + }, + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}_O^{\\mathcal{T}},\\mathcal{V}_O^f,\\mathcal{V}_O^s\\}" + }, + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "type": "text", + "content": " and b) a license verification " + }, + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "type": "inline_equation", + "content": "\\{\\mathcal{V}_L^p,\\mathcal{V}_L^1\\}" + }, + { + "bbox": [ + 46, + 270, + 287, + 354 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": "For ownership verification, our steganographic passport exhibits the lowest AD values of " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "0.00\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " on ResNet-18 and " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "0.01\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " on AlexNet for " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^T" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " with the correct owner passport, as presented in Table 1. This is attributed to the effect of the balance loss function, which ensures that the updates of the affine factors of the two branches are more synchronized during training. For " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": ", due to the stronger anti-forgery passport constraint imposed by our method, there is a slight decrease in model inference performance compared to Tdn and PAN, but it still outperforms DeepIPR. As shown in Table 1, the average deployment and verification branch accuracies of our method on ResNet-18 are both " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "71.73\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": ", which is only " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "0.40\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "0.07\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " lower than the accuracies of the deployment and verification branches, respectively of Tdn. The performance of our method peaks in several cases highlighted with the bold-printed percentages. For instance, it achieves the top score of " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "71.98\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " for AlexNet on Caltech-101. For " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": ", the SAs of all four methods achieve " + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 355, + 287, + 581 + ], + "type": "text", + "content": " in all the settings." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": "For license verification, a comparison of the visual images for " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^p" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^{\\mathrm{I}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 714 + ], + "type": "text", + "content": " is presented in Fig. 3. A very high PSNR of 41.47 between the original ID image and the ID image revealed using the genuine steganographic key is obtained, indicating a high level of visual similarity between them. In contrast, using forged keys to reveal the ID image results in significantly lower PSNR. Specifically, a PSNR of only 15.48 is obtained for the revealed ID images by using a random noise-like forged passport image and 32.56 by using a steganographic key image selected randomly from the same distribution as the genuine key image. Further" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 317, + 194, + 532, + 338 + ], + "blocks": [ + { + "bbox": [ + 317, + 194, + 532, + 338 + ], + "lines": [ + { + "bbox": [ + 317, + 194, + 532, + 338 + ], + "spans": [ + { + "bbox": [ + 317, + 194, + 532, + 338 + ], + "type": "image", + "image_path": "b78d92cb54e4db4835d0b97c7b6c2c1245227d264686b2a8163a047d8bd17414.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 340, + 545, + 353 + ], + "lines": [ + { + "bbox": [ + 305, + 340, + 545, + 353 + ], + "spans": [ + { + "bbox": [ + 305, + 340, + 545, + 353 + ], + "type": "text", + "content": "Figure 3. Hiding and revealing performance of the key-based ISN." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 358, + 545, + 407 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 358, + 545, + 407 + ], + "spans": [ + { + "bbox": [ + 305, + 358, + 545, + 407 + ], + "type": "text", + "content": "more, upon repeating this evaluation 100 times, the average PSNRs obtained from revealing the ID image by using random noise-like forged and randomly-selected key images are 15.68 and 35.89, respectively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": "Based on the above observations, we empirically set " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\tau_{d}" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\tau_{\\xi}" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\tau_{p}" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\tau_{r}" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "0.05\\%" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "93\\%" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", 39 and 41 for " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^{\\mathcal{I}}" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^p" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^i" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", respectively. For " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "inline_equation", + "content": "\\tau_{f}" + }, + { + "bbox": [ + 305, + 407, + 545, + 468 + ], + "type": "text", + "content": " is calibrated according to the task as the same clean model trained for different tasks has different inference performance." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "type": "text", + "content": "4.3. Robustness against ownership ambiguity attacks" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "type": "text", + "content": "Ownership ambiguity attacks aim to falsely claim the ownership of a deep model by satisfying the conditions outlined in Remark 1. Owing to the avalanche criterion provided by the hash function, attacks that attempt to forge the genuine passport images by random selection [6, 20, 30] or tamper with the user-side passport images will fail on " + }, + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "type": "text", + "content": " due to the significant signature deviation. Additionally, it is computationally intractable to reverse the uniformly random and collision-resistant cryptographically secure hash function to recover genuine passport images [20]. Thus, we specifically focus on the state-of-the-art ERB ownership ambiguity attack, under the strict assumption that the attacker has stolen both the deployment and verification branches, along with " + }, + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 497, + 545, + 675 + ], + "type": "text", + "content": " of original training data. The individual version of ERB, i.e., IERB is used to attack the models with BN." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "ERB demonstrated its effectiveness by retraining the model to fit a forged passport. In ERB's original configuration, attackers directly fabricate the passport layer's affine" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12307" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 92, + 544, + 191 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 545, + 92 + ], + "type": "text", + "content": "Table 2. Inference performance fidelity (in %) for deployment/verification under ERB ambiguity attacks with BN. FSA and BDR refer to the forged signature accuracy and the bit difference rate between benign and forged signatures, respectively." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 92, + 544, + 191 + ], + "lines": [ + { + "bbox": [ + 49, + 92, + 544, + 191 + ], + "spans": [ + { + "bbox": [ + 49, + 92, + 544, + 191 + ], + "type": "table", + "html": "
CIFAR-10CIFAR-100Caltech-101Caltech-256
ResNet-18ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR94.19 / 94.3910050.2262.92 / 64.0610049.4973.56 / 73.8910050.2346.05 / 46.3910049.3769.18 / 69.680.50
PAN94.64 / 94.7210048.7175.28 / 75.1010049.5773.11 / 73.0510049.3053.62 / 53.5810050.0874.16 / 74.110.90
TdN94.48 / 94.2410053.0975.91 / 66.6610048.2073.22 / 64.5499.9650.0454.49 / 34.6110051.7674.53 / 65.019.51
Ours94.70 / 92.8710049.5375.85 / 50.2799.9649.1873.00 / 50.0699.9251.0552.87 / 38.4410049.1873.82 / 57.9116.20
AlexNetERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓ERB↓FSA↓BDR↓Mean↓AD↑
DeepIPR26.54 / 85.7210047.6146.61 / 51.9710050.1163.56 / 67.8310052.6532.61 / 34.3410051.0842.31 / 59.9717.64
PAN91.56 / 82.0610052.4368.36 / 60.2910049.8770.37 / 69.1710053.3844.41 / 40.1510052.5668.68 / 62.925.76
TdN90.16 / 53.1610051.3366.96 / 1.6598.9649.7870.26 / 37.1998.9649.9644.14 / 0.2895.3148.2467.88 / 23.0744.81
Ours84.90 / 16.1199.5750.2467.38 / 1.0296.7549.7271.26 / 35.8698.9650.3345.00 / 4.9310051.1767.14 / 14.4852.66
", + "image_path": "1e8fb5d20c5f01ed34c5ed69c7bb2b2da27d3bd8e272c519518bbe4474ac1063.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 50, + 194, + 166, + 277 + ], + "blocks": [ + { + "bbox": [ + 50, + 194, + 166, + 277 + ], + "lines": [ + { + "bbox": [ + 50, + 194, + 166, + 277 + ], + "spans": [ + { + "bbox": [ + 50, + 194, + 166, + 277 + ], + "type": "image", + "image_path": "e2b34716823ce1e2f60f10756a312c684d7f847e2792dcc033fa7f8eef67dca9.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 77, + 279, + 139, + 289 + ], + "lines": [ + { + "bbox": [ + 77, + 279, + 139, + 289 + ], + "spans": [ + { + "bbox": [ + 77, + 279, + 139, + 289 + ], + "type": "text", + "content": "(a) Forged passport" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 194, + 282, + 277 + ], + "blocks": [ + { + "bbox": [ + 167, + 194, + 282, + 277 + ], + "lines": [ + { + "bbox": [ + 167, + 194, + 282, + 277 + ], + "spans": [ + { + "bbox": [ + 167, + 194, + 282, + 277 + ], + "type": "image", + "image_path": "05ef9c3e491db277a86be35b486fb2c7100ed2a1e59a3bd266c2bca562cfb956.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 175, + 279, + 274, + 289 + ], + "lines": [ + { + "bbox": [ + 175, + 279, + 274, + 289 + ], + "spans": [ + { + "bbox": [ + 175, + 279, + 274, + 289 + ], + "type": "text", + "content": "(b) Forged steganographic key" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 289, + 286, + 319 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 286, + 319 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 286, + 319 + ], + "type": "text", + "content": "Figure 4. Results of license ambiguity attacks on our method. Batch Normalization is used in the evaluated models. We set the Z-score as 2.33 for " + }, + { + "bbox": [ + 46, + 289, + 286, + 319 + ], + "type": "inline_equation", + "content": "98\\%" + }, + { + "bbox": [ + 46, + 289, + 286, + 319 + ], + "type": "text", + "content": " confidence interval (CI)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "spans": [ + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": "factors, leveraging the network's differentiable architecture to deduce the passport images. However, this possibility is denied by the hash functions of our method and TdN. Therefore, while maintaining the original settings of ERB for DeepIPR and PAN, the passport layer's affine factors in our method and TdN are to be derived from the corresponding hash-related functions. Table 2 displays the experimental results. To successfully meet the criteria of Remark 1, the attack must achieve " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " of forged SA (FSA) for " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": ". As evinced by the results presented in Sec. 4.2, the legitimate owner is able to comply with this stringent criteria. The experimental results show that the attacks on TdN and our method can only achieve " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " FSA for four and three model-dataset cases, respectively. Conversely, despite having around " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " BDR between the forged and genuine signatures, DeepIPR and PAN fail to withstand this attack with " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " FSA on all the model-dataset combinations. Besides, our method consistently produces the lowest mean performance fidelity of the verification branch for " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": ", especially for ResNet-18 " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "(57.91\\%)" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " and AlexNet " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "(14.48\\%)" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": ". Furthermore, our method also exhibits the highest AD that surpasses " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\tau_d" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^d" + }, + { + "bbox": [ + 47, + 327, + 287, + 614 + ], + "type": "text", + "content": " by a significant margin. The results, taken holistically, corroborate that our method has the highest resilience against ambiguity attacks." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 626, + 279, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 626, + 279, + 639 + ], + "spans": [ + { + "bbox": [ + 46, + 626, + 279, + 639 + ], + "type": "text", + "content": "4.4. Robustness against license ambiguity attacks" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 639, + 286, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 639, + 286, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 639, + 286, + 700 + ], + "type": "text", + "content": "Two license ambiguity attacks are considered. The first attack is to reveal the attacker's ID image by manipulating the genuine user-side passports. The second attack is to reveal the attacker's ID image from the genuine user-side passport image by forging the steganographic key image." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 713 + ], + "type": "text", + "content": "Forged user-side passport. To simulate this attack, we" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "text", + "content": "retain the ISN's weights and forge user-side passports with the attacker's ID images by minimizing the reveal loss " + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_r" + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "text", + "content": " between the original forged ID images and revealed forged ID images. The attack was performed by randomly sampling 100 owner-side passport images to generate 100 corresponding user-side passport images, and then using the Adam optimizer on each user-side passport image for 1000 iterations with a learning rate of 0.001. The progression of the attack is depicted in Fig. 4a. The mean PSNR between the original forged ID images and their revealed forged ID images increases and the mean PSNR between the forged user-side passport images and genuine owner-side passport images decreases with iterations. As a result, it becomes impossible for the attacker to simultaneously satisfy the criteria of both " + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^{\\mathrm{I}}" + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_L^p" + }, + { + "bbox": [ + 304, + 198, + 545, + 378 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 379, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 379, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 379, + 545, + 559 + ], + "type": "text", + "content": "Forged steganographic key. In this experiment, the attacker steals the key-based ISN to forge the steganographic key image. We initialize this attack by randomly sampling a noise vector from a Gaussian distribution 100 times. Correspondingly, we also randomly sample a target forged ID image from the distribution of genuine ID images 100 times, ensuring that there is no overlap between the forged and real images. The forged key images are obtained by an Adam optimizer with a learning rate of 0.001 over 1000 iterations. The progress of this process is depicted in Fig. 4b, where the shaded region marks the range of average PSNRs obtained over 100 rounds of attack. For the forged key images, the deviation is small and the purple shaded region is not visible for the scale of the plot. These observations indicate that this attack fails to satisfy the criteria of " + }, + { + "bbox": [ + 304, + 379, + 545, + 559 + ], + "type": "inline_equation", + "content": "\\nu_{L}^{\\mathbf{I}}" + }, + { + "bbox": [ + 304, + 379, + 545, + 559 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 567, + 495, + 580 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 567, + 495, + 580 + ], + "spans": [ + { + "bbox": [ + 305, + 567, + 495, + 580 + ], + "type": "text", + "content": "4.5. Robustness against removal attacks" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "spans": [ + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "type": "text", + "content": "We consider removal attacks that happen on the deployment branch when that branch is stolen by the attacker or abused by the licensed user. Unlike the pre-deployment model ownership claim in Sec 4.3, the model may be deliberately or maliciously altered after its deployment without compromising its utility, " + }, + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\tau_{\\xi}" + }, + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 304, + 581, + 545, + 665 + ], + "type": "text", + "content": " needs not be infinitely close to 1 to claim the ownership of the deployed model." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Fine-tuning. We consider a transfer-learning task by fine-tuning the deployment branch of a pretrained dual-branch model for 100 epochs at a learning rate of 0.001. As shown in Table 3, our method has the second-highest" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12308" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 50, + 59, + 544, + 118 + ], + "blocks": [ + { + "bbox": [ + 51, + 48, + 541, + 58 + ], + "lines": [ + { + "bbox": [ + 51, + 48, + 541, + 58 + ], + "spans": [ + { + "bbox": [ + 51, + 48, + 541, + 58 + ], + "type": "text", + "content": "Table 3. The performance fidelity (in %) of deployment model under fine-tuning attacks. The value in bracket is the signature accuracy." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 59, + 544, + 118 + ], + "lines": [ + { + "bbox": [ + 50, + 59, + 544, + 118 + ], + "spans": [ + { + "bbox": [ + 50, + 59, + 544, + 118 + ], + "type": "table", + "html": "
ResNet-18CIFAR-10 to CIFAR-10CIFAR-100 to CIFAR-10Caltech-101 to Caltech-256Caltech-256 to Caltech-101Mean
BNGNBNGNBNGNBNGN
DeepIPR73.81 (96.16)70.71 (95.23)92.10 (99.10)90.98 (99.45)48.53 (99.49)41.48 (99.30)76.05 (99.92)71.75 (100)70.68 (98.58)
PAN71.73 (74.30)68.15 (96.37)91.97 (78.71)90.46 (99.34)47.61 (81.29)39.51 (84.53)79.96 (100)71.64 (99.97)70.13 (89.31)
TdN70.77 (56.05)69.43 (62.70)91.86 (87.50)89.93 (73.87)46.55 (90.51)39.88 (82.30)77.12 (96.09)71.58 (82.81)69.64 (78.98)
Ours64.13 (98.60)65.11 (93.91)92.28 (96.17)90.22 (93.86)43.91 (98.24)37.48 (97.11)76.09 (99.09)69.04 (99.26)67.28 (97.03)
", + "image_path": "7c98872ae404154900b66506603a682e0b9d4f234c46d9b78d92bd0d3899126e.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 48, + 122, + 167, + 215 + ], + "blocks": [ + { + "bbox": [ + 48, + 122, + 167, + 215 + ], + "lines": [ + { + "bbox": [ + 48, + 122, + 167, + 215 + ], + "spans": [ + { + "bbox": [ + 48, + 122, + 167, + 215 + ], + "type": "image", + "image_path": "9b34983ef4904042e876220a6da169b5bbc64dbd3cdf0faaa6d9047f41b61ac7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 70, + 217, + 145, + 226 + ], + "lines": [ + { + "bbox": [ + 70, + 217, + 145, + 226 + ], + "spans": [ + { + "bbox": [ + 70, + 217, + 145, + 226 + ], + "type": "text", + "content": "(a) CIFAR-10 with BN" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 167, + 124, + 286, + 215 + ], + "blocks": [ + { + "bbox": [ + 167, + 124, + 286, + 215 + ], + "lines": [ + { + "bbox": [ + 167, + 124, + 286, + 215 + ], + "spans": [ + { + "bbox": [ + 167, + 124, + 286, + 215 + ], + "type": "image", + "image_path": "0387e35ba150d7062f2105b64832fc8c79f8e5d78dfa5ddf53aa9319ec001062.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 189, + 217, + 265, + 226 + ], + "lines": [ + { + "bbox": [ + 189, + 217, + 265, + 226 + ], + "spans": [ + { + "bbox": [ + 189, + 217, + 265, + 226 + ], + "type": "text", + "content": "(b) CIFAR-10 with GN" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 229, + 286, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 229, + 286, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 229, + 286, + 251 + ], + "type": "text", + "content": "Figure 5. The performance of our method under random and " + }, + { + "bbox": [ + 46, + 229, + 286, + 251 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 229, + 286, + 251 + ], + "type": "text", + "content": " norm pruning attacks." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "text", + "content": "average SA of " + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "inline_equation", + "content": "97.03\\%" + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "text", + "content": ". Given the avalanche criterion of the hash function, a false passport will lead to substantially high signature bit errors. The model owner can still attest the ownership under " + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "text", + "content": " with this small signature error. This is because both " + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^I" + }, + { + "bbox": [ + 46, + 255, + 286, + 386 + ], + "type": "text", + "content": " can still be fulfilled by applying this slightly mismatched signature obtained from the fine-tuned deployment branch to the original dual branch model kept by the model owner. Compared to other passport-based methods, our method has the lowest average performance fidelity upon fine-tuning, making it less attractive to attack our model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": "Pruning. Two prune strategies, i.e., random pruning and " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "\\ell_1" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": "-norm pruning are evaluated. For each model, the pruning rate was increased from " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": " with a step size of " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": ". The results are shown in Fig. 5. The SA remains relatively high and stable even when the model performance starts to drop abruptly. For example, in Fig. 5a, a " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": " signature detection accuracy is preserved at " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "80\\%" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": " pruning rate while the accuracy of the pruned model has fallen to around " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "50\\%" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": ". This implies that the pruned model can still pass " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^f" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_O^s" + }, + { + "bbox": [ + 46, + 388, + 286, + 543 + ], + "type": "text", + "content": " unless the pruning rate is so high that it renders the model unusable. Additionally, the large AD between the two branches also signifies that the model has been modified, as stated in Sec. 3.5." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 555, + 138, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 138, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 138, + 567 + ], + "type": "text", + "content": "4.6. Ablation study" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 569, + 286, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 569, + 286, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 569, + 286, + 591 + ], + "type": "text", + "content": "This section investigates the variations of our method without the TLP structure and with other activation functions." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": "Without TLP. We examine the inference performance fidelity when the TLP is removed from the BN variants of ResNet-18 and AlexNet, and compare their performances across different datasets. The results presented in Table 4 indicate that the drop in inference performance is trivial for models without TLP compared to their corresponding TLP counterparts. The higher AD of AlexNet, " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "0.23\\%" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " as opposed to " + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "inline_equation", + "content": "0.00\\%" + }, + { + "bbox": [ + 46, + 594, + 286, + 713 + ], + "type": "text", + "content": " of ResNet-18, implies that TLP has negligible impact on the performance fidelity of our method for complex networks but is essential to keep for simpler networks." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 308, + 145, + 544, + 192 + ], + "blocks": [ + { + "bbox": [ + 306, + 124, + 544, + 144 + ], + "lines": [ + { + "bbox": [ + 306, + 124, + 544, + 144 + ], + "spans": [ + { + "bbox": [ + 306, + 124, + 544, + 144 + ], + "type": "text", + "content": "Table 4. Inference performance fidelity (in %) for the deployment/verification branches of our method without TLP." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 145, + 544, + 192 + ], + "lines": [ + { + "bbox": [ + 308, + 145, + 544, + 192 + ], + "spans": [ + { + "bbox": [ + 308, + 145, + 544, + 192 + ], + "type": "table", + "html": "
CIFAR-10CIFAR-100Caltech-101Caltech-256AD↓
ResNet-18BN↑BN↑BN↑BN↑
94.47 / 94.4775.19 / 75.2071.53 / 71.5350.46 / 50.460.00
AlexNetBN↑BN↑BN↑BN↑AD↓
91.05 / 91.2568.26 / 68.6570.11 / 70.1142.42 / 42.750.23
", + "image_path": "f5849c9fce52964267c7247866e43d76cbca007b0093aeb0229f991a57365638.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 309, + 228, + 544, + 267 + ], + "blocks": [ + { + "bbox": [ + 306, + 196, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 306, + 196, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 306, + 196, + 545, + 228 + ], + "type": "text", + "content": "Table 5. Performance (in %) integrating Sigmoid and LeakyReLU in our proposed passport architecture, trained on CIFAR-10. Dep/Ver refer to deployment/verification branch, respectively." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 228, + 544, + 267 + ], + "lines": [ + { + "bbox": [ + 309, + 228, + 544, + 267 + ], + "spans": [ + { + "bbox": [ + 309, + 228, + 544, + 267 + ], + "type": "table", + "html": "
ResNet-18-BNInferenceAmbiguity attack (ERB)
Dep / VerSAADDep / VerFSAAD
Sigmoid94.60 / 94.661000.0694.49 / 17.7699.8476.73
LeakyReLU94.96 / 94.551000.4194.46 / 91.931002.53
", + "image_path": "ce61446735d3779e1b14f948a02e3245badad5066c7a8578d8a204f5c79c8ccc.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "spans": [ + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "content": "With other activation functions. To assess the impact of different activation functions on our method, we also incorporate Sigmoid and LeakyReLU into ResNet-18 with BN. For each activation function, the inference performance and robustness to the ERB attack are evaluated and presented in Table 5. Both activation functions demonstrate comparable performance fidelity between the deployment and verification branches, with SA of " + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "inline_equation", + "content": "100\\%" + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "content": " for both activation functions, and AD of " + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "inline_equation", + "content": "0.06\\%" + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "inline_equation", + "content": "0.41\\%" + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "content": " for Sigmoid and LeakyReLU, respectively. The Sigmoid-based model is more resilient to ERB attack than the LeakyReLU-based model, with a significantly higher AD of " + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "inline_equation", + "content": "76.73\\%" + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "content": ". Nonetheless, we can adapt the tamper threshold " + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "inline_equation", + "content": "\\tau_{d}" + }, + { + "bbox": [ + 304, + 273, + 545, + 440 + ], + "type": "text", + "content": " to the activation function for higher ambiguity attack resistance." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 447, + 378, + 459 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 447, + 378, + 459 + ], + "spans": [ + { + "bbox": [ + 306, + 447, + 378, + 459 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 462, + 545, + 713 + ], + "type": "text", + "content": "In this paper, we introduce Steganographic Passport, a novel passport-based model IP licensing protection method that allows the original model ownership to be verified with the passport-aware branch and individual licensees to be verified from the passport-free deployed model without requiring retraining the model for the admission of each licensed user. Legal license verification is made possible by hiding and revealing the licensed user's ID image in a user-side passport of the deployed model by the invertible steganographic network without compromising the accuracy and security of original model ownership verification. Activation-level obfuscation is added to heighten the security of both passports against ambiguity attacks. The affine factors of the deployment and verification branches, as well as the signatures and model's weights are tightly coupled during training to safeguard the owner-side passport and the deployed model's weights against malicious tampering to succeed in forging the ownership or licenseship. The experimental results substantiate the resilience of our method against a range of attacks, including ownership ambiguity attacks, license ambiguity attacks, and removal attacks." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "12309" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 135 + ], + "type": "text", + "content": "[1] Eirikur Agustsson and Radu Timofte. 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Advances in Neural Information Processing Systems, 33:22619-22628, 2020. 1, 2, 3, 5, 6" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "12311" + } + ] + } + ], + "index": 6 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_content_list.json b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..b00e054e6b5276766e81626e8cb0e438b02650a0 --- /dev/null +++ b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_content_list.json @@ -0,0 +1,1595 @@ +[ + { + "type": "text", + "text": "StegoGAN: Leveraging Steganography for Non-Bijective Image-to-Image Translation", + "text_level": 1, + "bbox": [ + 251, + 130, + 717, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Sidi Wu $^{1*}$ Yizi Chen $^{1*}$ Samuel Mermet $^{2}$ Lorenz Hurni $^{1}$ Konrad Schindler $^{1}$ Nicolas Gonthier $^{3,2}$ Loic Landrieu $^{4,2}$", + "bbox": [ + 217, + 202, + 776, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ ETH Zurich $^{2}$ Univ Gustave Eiffel, IGN, ENSG, LASTIG $^{3}$ IGN $^{4}$ Univ Gustave Eiffel, CNRS, Ecole des Ponts, LIGM", + "bbox": [ + 86, + 244, + 898, + 263 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 297, + 312, + 314 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Most image-to-image translation models postulate that a unique correspondence exists between the semantic classes of the source and target domains. However, this assumption does not always hold in real-world scenarios due to divergent distributions, different class sets, and asymmetrical information representation. As conventional GANs attempt to generate images that match the distribution of the target domain, they may hallucinate spurious instances of classes absent from the source domain, thereby diminishing the usefulness and reliability of translated images. CycleGAN-based methods are also known to hide the mismatched information in the generated images to bypass cycle consistency objectives, a process known as steganography. In response to the challenge of non-bijective image translation, we introduce StegoGAN, a novel model that leverages steganography to prevent spurious features in generated images. Our approach enhances the semantic consistency of the translated images without requiring additional postprocessing or supervision. Our experimental evaluations demonstrate that StegoGAN outperforms existing GAN-based models across various non-bijective image-to-image translation tasks, both qualitatively and quantitatively. Our code and pretrained models are accessible at https://github.com/sian-wusidi/StegoGAN.", + "bbox": [ + 76, + 330, + 473, + 694 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 78, + 741, + 207, + 756 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Image-to-image translation is an active research subject with impactful applications ranging from changing the style of images [12, 36] to automatically creating maps from satellite images [36] or changing the modality of medical images [9]. When the source and target domains exhibit substantial differences, ensuring the semantic consistency between input images and their translation becomes particularly challeng-", + "bbox": [ + 75, + 767, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/02c4a3768175c9371ced9722a95b20d0aa1dabddf845933c309c417f2b68e07e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 488, + 301, + 888, + 549 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "(b) GAN models hallucinate spurious features.", + "bbox": [ + 486, + 546, + 733, + 558 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/34ed5233575711c28f251edc758ae15016cf15bdae7b4cf5ba0b2c5809e65447.jpg", + "image_caption": [], + "image_footnote": [ + "(c) CycleGAN models hide unmatched features by steganography.", + "Figure 1. Non-Bijective Translation. When image domains present classes without equivalence (a), GAN models tend to hallucinate spurious features when translating images (b). A related phenomenon is steganography, where CycleGAN-based models covertly encode features in low-amplitude patterns to bypass cycle consistency (c). Instead of disabling this phenomenon, we harness steganography to prevent the hallucination of spurious features." + ], + "bbox": [ + 496, + 561, + 885, + 662 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing [8]. Our work explores the surprisingly uncharted field of adversarial, non-bijective image-to-image translation.", + "bbox": [ + 496, + 808, + 892, + 840 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Non-Bijective Image Translation. Existing translation methods assume a one-to-one correspondence between classes of the source and target domains: horses to zebras [36], satellite image features to their cartographic repre", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 808, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution.", + "bbox": [ + 94, + 887, + 205, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7922", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sentation [6, 36], or distinct cell types viewed under varying medical imaging modalities [9]. However, as illustrated in Figure 1a, this assumption does not always hold. For instance, when considering a dataset with horses and one with zebras in their habitat, zebra images may include background elements with no equivalent in the source domain—like elephants. Similarly, in map translation toponyms (i.e., place names printed onto the map) do not have counterparts in satellite images [6]. We qualify classes of the target domain without equivalent in the source domain as unmatched.", + "bbox": [ + 75, + 90, + 472, + 241 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As illustrated in Figure 1b, by trying to reproduce the distribution of the target domain, GANs may hallucinate spurious features or textures in the generated images, i.e., objects without equivalent in the source image. This is particularly frequent for unmatched classes [8]. While this can be perfectly acceptable for some applications [23], adding nonexistent tumors in MRI scans or incorrect toponyms in maps can severely degrade the usefulness of the translation result. Instead of detecting and removing these artifacts in post-processing, we propose an approach that directly prevents their generation using steganography.", + "bbox": [ + 75, + 242, + 472, + 409 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GAN Steganography. To ensure its semantic consistency, CycleGAN [36] back-translates the generated image to the source image. However, unmatched classes of the source domain cannot be encoded into meaningful features in the images generated in the target domain. As shown in Figure 1c, these models can instead cheat by encoding the necessary information into quasi-invisible patterns in the generated images [7]. This process, known as steganography, allows GANs to perform seemingly impossible back-translation. For instance, in a map-to-satellite task, the model can restore the correct names of towns from satellite images that appear visually correct. This phenomenon is often viewed as a quirky optimization flaw, easily fixable by adding noise or blur [11, 20, 26].", + "bbox": [ + 75, + 412, + 472, + 625 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "StegoGAN. We propose StegoGAN, a model that leverages steganography to detect and mitigate semantic misalignment between domains. In settings where the domain mapping is non-bijective, StegoGAN experimentally demonstrates superior semantic consistency over other GAN-based models both visually and quantitatively, without requiring detection or inpainting steps. In addition, we publish three datasets from open-access sources as a benchmark for evaluating non-bijective image translation models.", + "bbox": [ + 75, + 628, + 472, + 765 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 780, + 218, + 796 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "GAN-Based Image Translation. GAN-based image translation models transfer the style of images between domains with an adversarial perceptual loss [13]. When pairs of aligned images from both domains are available, the translated images can also be supervised by their fidelity with target images [18]. In practice, such pairs are not always", + "bbox": [ + 75, + 809, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "available or even possible to obtain. In the absence of explicit equivalence between images, preserving the semantics of the input in the generated image is a priority. Multiple approaches have been proposed to address this challenge, such as density-based regularization [33], spatial mutual information [20, 26, 30], or cycle consistency losses [17, 21, 36].", + "bbox": [ + 496, + 90, + 893, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Asymmetric Image Translation. Translating between domains with different semantic distributions is challenging. Existing approaches include focusing the network's attention on the most discriminative part of the input image [29], augmenting the consistency loss with geometric transformations [11], replacing the consistency reconstruction term with a contrastive loss [20, 26], or ensuring that the translation is robust to small perturbations of the input [19]. However, these methods assume a bijective relationship between the classes of the source and target domains.", + "bbox": [ + 496, + 186, + 895, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Closest to our work is the model of Li et al. [23], which uses an auxiliary variable to model the information loss from information-rich domains (such as natural images) to information-poor domains (such as label maps). In turn, they use this variable to create realistic poor-to-rich domain translations. Our work differs as we precisely want to avoid the creation of spurious—albeit realistic—details when translating to a domain with unmatched classes.", + "bbox": [ + 496, + 338, + 893, + 459 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "CycleGAN Steganography. Chu et al. [7] discovered that, when faced with unmatched classes, CycleGAN [36] hides information in low-amplitude and high-frequency signals. The model uses these visually imperceptible patterns to recreate the source image and bypass the cycle loss. This contradicts the intention of the cycle consistency loss and makes the model more vulnerable to adversarial attacks [7]. Luckily, multiple approaches can prevent steganography, such as blurring [11], compressing [10], or adding noise [20] to the generated source images in the back-translation. Alternatively, the back-translation from poor to rich domains can be omitted in the cycle consistency loss [27, 35].", + "bbox": [ + 496, + 463, + 895, + 645 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "While steganography in CycleGAN can be problematic, it also offers an opportunity to analyse distribution differences. In StegAnomaly [3], a model is trained to translate healthy brain scans into a low-entropy domain with cycle consistency. When removing high-frequency components, the model error reveals anomalous structures. This approach, like ours, harnesses steganography for insightful domain analysis, albeit with a different goal.", + "bbox": [ + 496, + 646, + 893, + 767 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 500, + 782, + 599, + 799 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We consider two image domains $\\mathcal{X}$ and $\\mathcal{Y}$ with respective semantic class sets $\\kappa_{\\mathcal{X}}$ and $\\kappa_{\\mathcal{Y}}$ . The domains $\\mathcal{X}$ and $\\mathcal{Y}$ are considered bijective if there exists a function $\\phi$ from $\\kappa_{\\mathcal{X}}$ to $\\kappa_{\\mathcal{Y}}$ such that each class $k_{\\mathcal{X}}$ has a unique and natural semantically equivalent class $\\phi(k_{\\mathcal{X}})$ in $\\mathcal{Y}$ , and vice-versa. A class of $\\kappa_{\\mathcal{Y}}$ is said to be unmatched if it doesn't have an", + "bbox": [ + 496, + 809, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7923", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/59892bec01e1880155468227e0e9c721ea04fbf84afa568881098beb31237584.jpg", + "image_caption": [ + "(a) Backward cycle" + ], + "image_footnote": [], + "bbox": [ + 117, + 90, + 883, + 224 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ceaf0a91bdc12159b0bf74fa3b88172dae9a85f74c6f5454d5a8acd819097d2f.jpg", + "image_caption": [ + "Figure 2. Architecture. To avoid spurious generation of unmatched classes in non-bijective image translation, we propose to make the steganographic process explicit and in feature-space. Our model runs the backward cycle first (a), then the forward translation cycle (b). Thanks to our matchability disentanglement module (c), we can separate the matchable and unmatched information while translating images from domain $\\mathcal{V}$ to $\\mathcal{X}$ . We can then produce generated and reconstructed images with and without unmatched features. At inference time (d), our model operates like a normal image translation model." + ], + "image_footnote": [], + "bbox": [ + 106, + 250, + 272, + 344 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/93a947522354f24c0b3f00e0ddcc06966c57fc5db5c92061270e32ad685afeb8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 299, + 250, + 575, + 347 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/ac93ac8be3a35a6d0ba27a353d4b4fc625c2c1d75e06c0685f142a90012a6a30.jpg", + "image_caption": [ + "(b) Forward cycle", + "(d) Inference" + ], + "image_footnote": [], + "bbox": [ + 663, + 256, + 870, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "equivalent in $\\mathcal{K}_{\\mathcal{X}}$ . While this notion is somewhat subjective, many applications have obvious examples: toponyms are unmatched in satellite images, and tumors in scans of healthy patients.", + "bbox": [ + 75, + 443, + 470, + 505 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Objective. Our goal is to learn a mapping $G: \\mathcal{X} \\mapsto \\mathcal{Y}$ such that the translation $G(x)$ of any image $x \\in \\mathcal{X}$ aligns stylistically with images from $\\mathcal{Y}$ , while preserving the semantic content of $x$ . If $\\mathcal{K}_{\\mathcal{Y}}$ contains an unmatched class $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ , images translated from $\\mathcal{X}$ to $\\mathcal{Y}$ should not contain any instances of $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ . However, in an attempt to match the distribution of $\\mathcal{Y}$ , GAN models often create spurious instances of unmatched classes in their translated images. In this paper, we propose a method that employs steganography to prevent the generation of such spurious information.", + "bbox": [ + 75, + 508, + 472, + 660 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. CycleGAN", + "text_level": 1, + "bbox": [ + 76, + 672, + 197, + 690 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "CycleGAN [36] learns unpaired image translation by enforcing the consistency between the input image and its backtranslation from the generated image. It uses two generators $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}: \\mathcal{X} \\mapsto \\mathcal{Y}$ and $G_{\\mathcal{Y} \\mapsto \\mathcal{X}}: \\mathcal{Y} \\mapsto \\mathcal{X}$ , and two domain discriminators $D_{\\mathcal{X}}: \\mathcal{X} \\mapsto \\{0,1\\}$ , $D_{\\mathcal{Y}}: \\mathcal{Y} \\mapsto \\{0,1\\}$ which predict whether a sample is generated (0) or real (1).", + "bbox": [ + 75, + 696, + 470, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In the following, when considering images $x \\in \\mathcal{X}$ or $y \\in \\mathcal{Y}$ , we define the following short-hands: $x_{\\mathrm{gen}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}(y)$ and $y_{\\mathrm{gen}} := G_{\\mathcal{X} \\mapsto \\mathcal{Y}}(x)$ for the generated images, and $x_{\\mathrm{rec}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}(y_{\\mathrm{gen}})$ and $y_{\\mathrm{rec}} := G_{\\mathcal{X} \\mapsto \\mathcal{Y}}(x_{\\mathrm{gen}})$ for the reconstructed images. We now detail the losses of CycleGAN.", + "bbox": [ + 76, + 790, + 470, + 866 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Adversarial loss. The adversarial loss [13] encourages the discriminators $D_{\\mathcal{X}}$ and $D_{\\mathcal{Y}}$ to distinguish between authentic", + "bbox": [ + 75, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "and generated images, while pushing the generators $G_{\\mathcal{X}\\mapsto \\mathcal{Y}}$ and $G_{\\mathcal{Y}\\mapsto \\mathcal{X}}$ to create credible images:", + "bbox": [ + 498, + 443, + 890, + 474 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {G A N}} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\log (D _ {\\mathcal {Y}} (y)) + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\log (1 - D _ {\\mathcal {Y}} (y _ {\\text {g e n}})) \\\\ + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\log (D _ {\\mathcal {X}} (x)) + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\log (1 - D _ {\\mathcal {X}} (x _ {\\text {g e n}})). \\tag {1} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 500, + 890, + 536 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Cycle consistency. The cycle consistency loss ensures that the back-translation of $y_{\\mathrm{gen}}$ to domain $\\mathcal{X}$ is close to the original image $x$ , and likewise for $x_{\\mathrm{gen}}$ and $y$ :", + "bbox": [ + 498, + 549, + 890, + 597 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\text {c y c}} = \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| x _ {\\text {r e c}} - x \\| + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| y _ {\\text {r e c}} - y \\|, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 606, + 890, + 623 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $\\| \\cdot \\|$ the pixel-wise $L_{1}$ norm.", + "bbox": [ + 498, + 633, + 725, + 648 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Identity loss. The identity loss regularizes the generators to be close to identity, generally improving color composition:", + "bbox": [ + 498, + 652, + 893, + 683 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\mathrm {i d}} = \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} (x) - x \\| + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} (y) - y \\|. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 503, + 693, + 890, + 710 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Final Loss. The final objectives are:", + "bbox": [ + 500, + 720, + 743, + 734 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}}, G _ {\\mathcal {Y} \\mapsto \\mathcal {X}}\\right) = \\mathcal {L} _ {G A N} + \\lambda_ {\\text {c y c}} \\mathcal {L} _ {\\text {c y c}} + \\lambda_ {\\text {i d}} \\mathcal {L} _ {\\text {i d}}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 746, + 890, + 763 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} \\left(D _ {\\mathcal {X}}, D _ {\\mathcal {Y}}\\right) = - \\mathcal {L} _ {\\mathrm {G A N}}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 766, + 890, + 781 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "with $\\lambda_{\\mathrm{cyc}}$ and $\\lambda_{\\mathrm{id}}$ non-negative hyperparameters.", + "bbox": [ + 500, + 792, + 818, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. StegoGAN", + "text_level": 1, + "bbox": [ + 500, + 816, + 617, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce StegoGAN, a novel model building on the CycleGAN framework [36], designed specifically for scenarios where domains $\\mathcal{X}$ and $\\mathcal{Y}$ lack a bijective relationship. When generating images $y_{\\mathrm{gen}}$ in $\\mathcal{V}$ , the generator $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ may add", + "bbox": [ + 498, + 839, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7924", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "spurious instances of an unmatched class $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ in order to deceive the discriminator $D_{\\mathcal{Y}}$ . Our goal is to prevent the generation of such hallucinated instances. To achieve this, we leverage steganography to explicitly disentangle the matchable and unmatched information in the backward cycle ( $y \\mapsto x_{\\mathrm{gen}} \\mapsto y_{\\mathrm{rec}}$ ) and prevent the network from hallucinating in the forward translation ( $x \\mapsto y_{\\mathrm{gen}} \\mapsto x_{\\mathrm{rec}}$ ). See Figure 2 for the overall design of our approach.", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Steganography. In order to faithfully reconstruct $y$ with $y_{\\mathrm{rec}}$ , the translated image $x_{\\mathrm{gen}}$ must somehow contain information about the instances of the unmatched class $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ . CycleGAN methods typically achieve this by hiding low-amplitude and high-frequency patterns in $x_{\\mathrm{gen}}$ that will be decoded by $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ and translated back to instances of $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ in $y_{\\mathrm{rec}}$ . Adding low-intensity noise on each pixel is typically sufficient to destroy the hidden information and prevent steganography [7].", + "bbox": [ + 75, + 215, + 472, + 351 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Steganography is often viewed as an optimization flaw that undermines the consistency loss. However, in the case of non-bijective translation, this is the only way to let $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ reconstruct instances of $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ in $y_{\\mathrm{rec}}$ . Instead of disabling steganography, we propose to use it to our advantage to detect and prevent spurious generations. We adapt CycleGAN so that steganography takes place in feature-space instead of pixel-space, and in an explicit manner.", + "bbox": [ + 75, + 352, + 472, + 473 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Backward Cycle. We decompose the generators $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ and $G_{\\mathcal{Y} \\mapsto \\mathcal{X}}$ into two components: an encoder and a decoder, such that $G_{\\mathcal{X} \\mapsto \\mathcal{Y}} = G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{dec}} \\circ G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{enc}}$ and $G_{\\mathcal{Y} \\mapsto \\mathcal{X}} = G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{dec}} \\circ G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}$ . The encoders map their inputs to feature maps of spatial dimension $H \\times W$ , where each pixel has $C$ channels. In the following, we denote the intermediary representation of $y$ in $G_{\\mathcal{Y} \\mapsto \\mathcal{X}}$ by $z_{\\mathrm{gen}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}(y)$ . The feature map $z_{\\mathrm{gen}}$ encodes information about both matchable and unmatched classes, which we want to disentangle.", + "bbox": [ + 75, + 476, + 472, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We introduce a network $M$ : $\\mathbb{R}^{H \\times W \\times C} \\mapsto [0,1]^{H \\times W \\times C}$ that assigns an unmatchedability score between 0 and 1 to each pixel and channel. Here, a score of 1 indicates that the information does not have a counterpart in domain $\\mathcal{X}$ , while it does for 0. This process gives us the unmatchedability mask $M(z_{\\mathrm{gen}})$ , which we use to split $z_{\\mathrm{gen}}$ into its matchable and unmatched parts:", + "bbox": [ + 75, + 611, + 472, + 719 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {\\text {g e n}} ^ {\\text {u n m a t c h}} = M \\left(z _ {\\text {g e n}}\\right) \\odot z \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 729, + 468, + 750 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {\\text {g e n}} ^ {\\text {m a t c h}} = \\left(1 - M \\left(z _ {\\text {g e n}}\\right)\\right) \\odot z, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 751, + 468, + 771 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\odot$ the pixel-wise and channel-wise Hadamard product. In our model, the generated image $x_{\\mathrm{gen}}$ is computed using only the matchable part of the representation:", + "bbox": [ + 75, + 781, + 472, + 828 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {\\text {g e n}} = G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} ^ {\\text {d e c}} \\left(z _ {\\text {g e n}} ^ {\\text {m a t c h}}\\right). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 192, + 838, + 468, + 858 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We produce two reconstructions of $y$ : $y_{\\mathrm{rec}}^{\\mathrm{clean}}$ , which is a direct back-translation of $x_{\\mathrm{gen}}$ into the $\\mathcal{V}$ domain: $y_{\\mathrm{rec}}^{\\mathrm{clean}} =$", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$G_{\\mathcal{X}\\mapsto \\mathcal{Y}}(x_{\\mathrm{gen}})$ ; and $y_{\\mathrm{rec}}$ , which is generated by decoding a combination of the unmatched part of $z_{\\mathrm{gen}}$ and the features extracted by $G_{\\mathcal{X}\\mapsto \\mathcal{Y}}^{\\mathrm{enc}}$ from a noise-perturbed version of $x_{\\mathrm{gen}}$ :", + "bbox": [ + 496, + 90, + 893, + 138 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {\\text {r e c}} = G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {d e c}} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {e n c}} \\left(x _ {\\text {g e n}} + \\epsilon\\right) + z _ {\\text {g e n}} ^ {\\text {u n m a t c h}}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 539, + 148, + 893, + 169 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with $\\epsilon$ denoting random Gaussian noise of low amplitude applied to each pixel and channel of $x_{\\mathrm{gen}}$ . This noise is added to destroy potential steganographic information in $x_{\\mathrm{gen}}$ , therefore forcing $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ to rely only on $z_{\\mathrm{gen}}^{\\mathrm{unmatch}}$ to reconstruct unmatched features in $y_{\\mathrm{rec}}$ .", + "bbox": [ + 496, + 178, + 893, + 253 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The key mechanisms to disentangle matchable and unmatched information are twofold: (i) disturbing direct steganography with random noise, and (ii) explicitly providing unmatched information to $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ in feature-space.", + "bbox": [ + 496, + 255, + 893, + 316 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Forward Cycle. In the forward cycle $x \\to y_{\\mathrm{gen}} \\to x_{\\mathrm{rec}}$ , the generator $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ may create spurious instances of unmatched classes when translating $x$ to $\\mathcal{Y}$ to fulfill the expectations of the discriminator $D_y$ . To address this, we perform two distinct translations of $x$ in $\\mathcal{Y}$ : $y_{\\mathrm{gen}}$ has explicit access to the steganographic information $z_{\\mathrm{gen}}^{\\mathrm{unmatch}}$ extracted from the backward cycle, while $y_{\\mathrm{gen}}^{\\mathrm{clean}}$ does not:", + "bbox": [ + 496, + 319, + 893, + 428 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {\\text {g e n}} = G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {d e c}} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {e n c}} (x) + z _ {\\text {g e n}} ^ {\\text {u n m a t c h}}\\right) \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 439, + 890, + 459 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\ny _ {\\text {g e n}} ^ {\\text {c l e a n}} = G _ {\\chi \\mapsto y} (x). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 460, + 890, + 479 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The rationale is that $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{dec}}$ has explicit access to information about the unmatched classes of $y$ , so it is not incentivized to invent them. For consistency with the backward step, where the decoder of $G_{\\mathcal{Y} \\mapsto \\mathcal{X}}$ processes only matchable information as defined in (7), we use the same disentangle-ment approach for generating $x_{\\mathrm{rec}}$ :", + "bbox": [ + 496, + 492, + 893, + 584 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {\\text {r e c}} = G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} ^ {\\text {d e c}} \\left(\\left(1 - M \\left(z _ {\\text {r e c}}\\right)\\right) \\odot z _ {\\text {r e c}}\\right), \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 562, + 594, + 890, + 613 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $z_{\\mathrm{rec}} = G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}(y_{\\mathrm{gen}})$ is the intermediary representation of $y_{\\mathrm{gen}}$ in the forward cycle.", + "bbox": [ + 496, + 623, + 890, + 655 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Mask Regularization. To avoid degenerate behaviors of our explicit steganography mechanism, we enforce two priors on the unmatchedability masks: (i) given that a well-posed translation problem predominantly involves matchable features, the masks should be sparse; (ii) to improve the model's interpretability, we favor mask values near 0 or 1, representing clear decisions about matchability. To enforce these priors, we regularize the masks with the non-convex $L_{0.5}$ norm [34]:", + "bbox": [ + 496, + 657, + 893, + 779 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {r e g} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| M \\left(z _ {\\text {g e n}}\\right) \\| _ {0. 5} + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| M \\left(z _ {\\text {r e c}}\\right) \\| _ {0. 5}. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 791, + 890, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Matchable Consistency. The images $y_{\\mathrm{gen}}$ and $y_{\\mathrm{gen}}^{\\mathrm{clean}}$ , as well as $y_{\\mathrm{rec}}$ and $y_{\\mathrm{rec}}^{\\mathrm{clean}}$ , should be identical outside of unmatched regions. To enforce this constraint, we design a function $I$ which takes an unmatchedness mask $m$ as input, takes the channel-wise maximum values of all pixels, flips its", + "bbox": [ + 496, + 821, + 893, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7925", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a731982eda57a52a69994bdfbf56dab32ede3c9d21d049eaf0df8892facc4dc8.jpg", + "image_caption": [ + "Figure 3. Qualitative Comparison. We report reconstructions from the test sets of PlanIGN (top two rows), GoogleMap (row 3 and 4), and MRI (last two rows). Contrary to the other models, StegoGAN does not hallucinate spurious toponyms, highways (orange roads), or tumors (white areas) and shows better semantic correspondences during translation." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 890, + 579 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "value from [0, 1] to [1, 0], and upsamples the results to the dimensions of the input images.", + "bbox": [ + 75, + 657, + 468, + 688 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nI (m) = \\operatorname {u p s a m p l e} \\left(1 - \\max _ {c} m\\right). \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 696, + 470, + 722 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The obtained consistency masks $I(m)$ have values close to 1 for pixels with only matchable content, and close to 0 otherwise. This enables us to define a loss for $y_{\\mathrm{gen}}^{\\mathrm{clean}}$ and $y_{\\mathrm{rec}}^{\\mathrm{clean}}$ that focuses solely on regions with matchable features:", + "bbox": [ + 76, + 731, + 472, + 796 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {\\text {m a t c h}} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| I (M (z _ {\\text {g e n}})) \\odot (y _ {\\text {g e n}} - y _ {\\text {g e n}} ^ {\\text {c l e a n}}) \\| \\\\ + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| I (M (z _ {\\mathrm {r e c}})) \\odot (y _ {\\mathrm {r e c}} - y _ {\\mathrm {r e c}} ^ {\\text {c l e a n}}) \\|. \\tag {15} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 803, + 468, + 843 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Final Objective. In addition to the standard CycleGAN loss components (4-5), we integrate $\\mathcal{L}_{\\mathrm{match}}$ and $\\mathcal{L}_{\\mathrm{reg}}$ into the overall loss function $\\mathcal{L}(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}, G_{\\mathcal{Y} \\mapsto \\mathcal{X}})$ , weighted by", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "their respective coefficients $\\lambda_{\\mathrm{reg}}$ and $\\lambda_{\\mathrm{match}}$ . Crucially, our proposed approach remains unsupervised, requiring neither aligned images from $\\mathcal{X}$ and $\\mathcal{Y}$ nor specific annotations of unmatched features.", + "bbox": [ + 496, + 657, + 893, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 734, + 633, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we assess the improvements brought by our method for non-bijective image translation across various datasets and compare them with existing models, both qualitatively and quantitatively.", + "bbox": [ + 496, + 760, + 893, + 821 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation details. We follow the setting of CyleGAN [36] as our baseline model: the generators are Resnets [15] and the discriminator is based on PatchGAN [18]. We define the encoders as the first half of the generator's layers and the decoders as the second half. The", + "bbox": [ + 496, + 824, + 895, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7926", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/700ea251354a90565c44a0be7003610a7a1b2fe4d87f9e2a40cc88b51b08713a.jpg", + "image_caption": [ + "Figure 4. Results on GoogleMaps. We report the performance of several top-performing image translation models for different ratios of unmatched features in the target domain of the training set. StegoGAN handles higher ratios better than competing methods." + ], + "image_footnote": [], + "bbox": [ + 106, + 88, + 851, + 354 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "unmatchability mask predictor $M$ is defined as a small 3-layer convolutional neural network (CNN). We set $\\lambda_{\\mathrm{cyc}} = 10$ , $\\lambda_{\\mathrm{idt}} = 0.5$ as in [36] and $\\lambda_{\\mathrm{match}} = 1$ . The amplitude of the perturbation $\\epsilon$ is 0.01 as in [7]. The Appendix provides more architecture and training details.", + "bbox": [ + 75, + 419, + 473, + 494 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Datasets", + "text_level": 1, + "bbox": [ + 76, + 505, + 181, + 518 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We assess the performance of StegoGAN across several image translation tasks that feature unmatched classes. Each dataset follows a consistent structure: the training set includes images from the source domain $\\mathcal{X}$ devoid of a specific class (e.g., tumors, motorways, toponyms) while the target domain $\\mathcal{Y}$ does include that class. The test set comprises paired images from both domains, specifically excluding the unmatched class. This setup allows us to quantify the models' hallucinations: any generated instances of the unmatched class are necessarily spurious and due to its presence in the training set. We release all three curated datasets on the Zenodo platform and provide details below.", + "bbox": [ + 75, + 527, + 470, + 710 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "PlanIGN. $\\mathcal{X}$ : Aerial Photo, $\\mathcal{Y}$ : Maps, $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ : Text. We construct a dataset using open data from the French National Mapping Agency (IGN), comprising 1900 aerial (ortho-)images at 3m spatial resolution, and two versions of their corresponding topographic maps: one with and one without toponyms. This dataset presents a clear unmatched class: place names. The training set includes 1000 maps with toponyms and 1000 aerial images, while the test set comprises 900 map samples without toponyms and their corresponding aerial images.", + "bbox": [ + 75, + 713, + 470, + 866 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "GoogleMaps. $\\mathcal{X}$ : Aerial Photo, $\\mathcal{V}$ : Maps, $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ : Highways. The GoogleMaps dataset [18] is a standard bench", + "bbox": [ + 75, + 869, + 472, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "mark for image translation tasks [19, 20]. It contains 1096 map/image pairs for training and 1098 for testing. To create a controlled non-bijective scenario, we exclude all satellite images that show highways and sample the maps of the training set to contain varying proportions of maps with highways, ranging from $0\\%$ to $65\\%$ , for a fixed total of 548 maps. For the test set we selected 898 pairs without highways.", + "bbox": [ + 496, + 419, + 893, + 526 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Brats MRI $\\mathcal{X}$ : T1 Scans, $\\mathcal{V}$ : FLAIR, $k_{\\mathcal{Y}}^{\\mathrm{unmatch}}$ : Tumors. Lastly, we used a dataset of brain MRI scans [25] with two modalities: T1 (naive) and FLAIR (T2 Fluid Attenuated Inversion Recovery) [14]. We adapt the protocol that Cohen et al. [8] used for the Brats2013 datasets [24] to the more recent Brats2018 [2] dataset by varying the percentage of scans with tumors in the target domain. We selected transverse slices from the $60^{\\circ}$ to $100^{\\circ}$ range in the caudocranial direction [1] for both T1 and FLAIR scans. Each scan was classified as tumorous if more than $1\\%$ of its pixels were labeled as such, and as healthy if it contained no tumor pixels. The training set contains 800 images from each modality, with all source images (T1) being healthy and the target domain (FLAIR) comprising $60\\%$ tumorous scans. The test set contains 335 paired scans of healthy brains.", + "bbox": [ + 496, + 527, + 895, + 757 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Evaluation metrics", + "text_level": 1, + "bbox": [ + 500, + 767, + 684, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We use a broad range of metrics to evaluate the performance of StegoGAN and other image translation algorithms in the non-bijective setting:", + "bbox": [ + 496, + 790, + 892, + 835 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "FID and KID. The Fréchet Inception Distance (FID) [16] and Kernel Inception Distance (KID) [4] are widely used to quantify the similarity between the distributions of real and generated images in the target domain.", + "bbox": [ + 496, + 839, + 893, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7927", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/f5a838b30f53767576001886da22a62a09222e2e2d5d372ac5f6d5fce1bdb2ba.jpg", + "table_caption": [ + "Table 1. Quantitative Comparison on PlanIGN. Our model shows a remarkably better performance than other existing models." + ], + "table_footnote": [], + "table_body": "
MethodRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
CUT [26]30.546.755.868.42.8
CycleGAN [36]27.015.157.697.56.6
DRIT [21]34.833.636.976.43.8
GcGAN [11]32.754.556.9110.88.2
SRUNIT [19]32.348.852.860.22.2
StegoGAN (ours)22.566.174.858.42.4
", + "bbox": [ + 80, + 122, + 467, + 218 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "RMSE, $\\mathbf{Acc}(\\sigma_1)$ , and $\\mathbf{Acc}(\\sigma_2)$ . As the test sets comprise paired images from both domains, we can directly compare the Root Mean Square Error (RMSE) between the real and predicted images in the target domain. We count a predicted pixel as correctly predicted if it deviate by less than a fixed threshold in any of the color channels [11]. We use $\\sigma_1 = 5$ and $\\sigma_2 = 10$ for the GoogleMap dataset and $\\sigma_1 = 2$ and $\\sigma_2 = 5$ for the less colorful PlanIGN dataset.", + "bbox": [ + 75, + 229, + 468, + 349 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "pFPR and iFPR. In the GoogleMap dataset, highways are always depicted in orange, allowing us to label pixels where all color channels differ by less than 20 units from (240, 160, 30) as highways. In the Brats MRI dataset, we use a pretrained tumor detector [5] to find spurious tumors in the generated images. This allows us to compute the average false positive rate per pixel (pFPR) and per instance (iFPR) of the generated images.", + "bbox": [ + 75, + 354, + 470, + 476 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Results", + "text_level": 1, + "bbox": [ + 76, + 488, + 171, + 502 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Qualitative Results. Figure 3 showcases StegoGAN's qualitative performance against other image translation algorithms. Notably, StegoGAN effectively avoids generating unmatched classes such as texts, highways, and tumors, while producing high-quality image translations.", + "bbox": [ + 75, + 512, + 470, + 588 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Results. On the PlanIGN dataset (Table 1) and the Brats MRI dataset (Table 2), StegoGAN outperforms others in fidelity, achieving the lowest RMSE by a margin of 4.5 on PlanIGN and by 3.5 for Brats MRI. Furthermore, it significantly enhances pixel accuracy, with improvements of $+11.6$ in $\\mathrm{Acc}(\\sigma_1)$ and $+17.2$ in $\\mathrm{Acc}(\\sigma_2)$ on PlanIGN. In the MRI dataset, StegoGAN dramatically reduces false positive rates—over $20\\times$ lower than CycleGAN and $10\\times$ less than the next best model SRUNIT (for pFPR).", + "bbox": [ + 75, + 592, + 468, + 728 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On the GoogleMap dataset, as shown in Figure 4, StegoGAN's performance is on par with CycleGAN at $0\\%$ unmatched cases and remains stable even as this ratio increases, unlike other methods that degrade. Remarkably, StegoGAN maintains a consistent false positive rate of 0 across all tests, while this rate increases for all other methods.", + "bbox": [ + 75, + 729, + 470, + 834 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Unmatchability Masks. In Figure 5, we illustrate the emergent ability of the unmatchedability masks to trace the outline of unmatched class instances like toponyms, highways, and tumors. This aspect highlights the versatility of our", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9889fc1452ad659c6d8b6724170076e7d3fa9cd8fa370f98d79454b4a981cc8d.jpg", + "table_caption": [ + "Table 2. Quantitative Comparison on Brats MRI Flair $\\rightarrow$ T1. Our model outperforms competing method in terms of both reconstruction accuracy and consistency." + ], + "table_footnote": [], + "table_body": "
MethodRMSE↓pFPR(‰)↓iFPR↓FID↓KID↓
CUT [26]39.817.023.0103.98.8
CycleGAN [36]39.921.922.789.87.7
DRIT [21]53.018.541.2123.411.6
GcGAN [11]41.724.722.461.93.5
SRUNIT [19]42.515.121.858.92.9
StegoGAN (ours)36.31.14.258.52.4
", + "bbox": [ + 504, + 135, + 888, + 232 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/e3a0027370b66e1203ff5f025d36802aa4f78f746092ebffb624b4bfc011d4e1.jpg", + "image_caption": [ + "Figure 5. Unmatchability Masks. The unmatchedability masks predicted in the backward cycle follow the instances of unmatched features in the target domain: toponyms, highways, and tumors." + ], + "image_footnote": [], + "bbox": [ + 517, + 247, + 874, + 539 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/40215441befcdef672753fba249774f9449d1caddb9b44969f6ff920fd7de5b4.jpg", + "table_caption": [ + "Table 3. Ablation Study on Encoder Depth. We evaluate the impact of changing the depth of the encoder on the reconstruction fidelity and the quality of unmatchedability masks. Depth= -1 or 8 means no encoder or no decoder, respectively." + ], + "table_footnote": [], + "table_body": "
DepthMaskPrediction
mIOU↑Prec.↑recall↑RMSE↓A(σ1)↑A(σ2)↑FID↓KID↓
-126.627.181.222.464.374.258.82.5
125.225.881.222.566.174.858.42.4
327.127.980.422.861.673.462.93.0
530.833.469.524.252.770.662.32.6
847.360.160.024.553.570.762.72.7
", + "bbox": [ + 500, + 667, + 890, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "approach, which functions without explicit supervision or aligned images, offering a tool to explore the pairwise semantic differences between arbitrary datasets.", + "bbox": [ + 498, + 772, + 893, + 818 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Ablation study and analysis", + "text_level": 1, + "bbox": [ + 500, + 830, + 748, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We explore the impact of our main design choices, as well as further capabilities and limitations of our approach. See the Appendix for further ablations.", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7928", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a507aa641d769355d146cd0851f27dcf1a1355b352618a59250cb2fe32ccc7c.jpg", + "image_caption": [ + "Figure 6. Impact of Encoder Depth. We visualize the unmatchedability mask for encoders of different depths for the PlanIGN dataset. Shallower encoders consider more features as unmatched." + ], + "image_footnote": [], + "bbox": [ + 83, + 88, + 885, + 191 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Encoder Ablation. We conducted an ablation study on the definition of the intermediary representation $z$ by varying the depth at which the \"encoder\" ends and the \"decoder\" starts within the generator. Given that our generators consist of 9 consecutive convolutional blocks, we experimented with different configurations: -1 (indicating no decoder), 1 (the configuration used in our paper), as well as depths of 3, 5, and 8 (implying no decoder). We report in Table 3 the reconstruction error of these models, as well as the fidelity of the consistency mask with the toponym text mask. We observe that shallow encoders have better reconstruction accuracy while the consistency masks of deeper encoders better approximate the text masks.", + "bbox": [ + 75, + 265, + 472, + 460 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visualizing these masks in Figure 6, we observe that shallow encoders consider complex features such as highways and rivers as unmatched features, while deeper encoders do not. Shallower encoders seem more influenced by the variation in appearance (e.g., rivers being sometimes covered in vegetation or with varying colors) while deeper encoders focus on high-level semantics. We argue that both definitions are equally valid, and that varying the depth of the encoders can provide insights into the nature of the semantic mismatch between datasets.", + "bbox": [ + 75, + 465, + 470, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Parameterization. In Table 4, we analyze the effects of omitting the additional terms $\\mathcal{L}_{\\mathrm{reg}}$ and $\\mathcal{L}_{\\mathrm{match}}$ from the loss function $\\mathcal{L}$ in Equation (4). We show that while $\\mathcal{L}_{\\mathrm{match}}$ generally yields modest improvements across all metrics, $\\mathcal{L}_{\\mathrm{reg}}$ is pivotal, particularly for learning the target distribution. This outcome aligns with our expectations, as the absence of $\\mathcal{L}_{\\mathrm{reg}}$ allows the network to transmit all information, matchable or not, to the $G_{\\mathcal{Y} \\mapsto \\mathcal{X}}$ decoder without repercussions, impeding the training of the $G_{\\mathcal{X} \\mapsto \\mathcal{Y}}$ encoder.", + "bbox": [ + 75, + 630, + 468, + 767 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Limitations. We augment the CycleGAN framework with a module $M$ and two hyper-parameters $\\lambda_{\\mathrm{match}}$ and $\\lambda_{\\mathrm{reg}}$ , thereby adding to the complexity of its training dynamics. Moreover, the concept of unmatchedability, integral to our approach, is inherently subjective. Given enough semantic detail, any two distinct datasets could be considered unmatched. As a result, fine-tuning the hyperparameter $\\lambda_{\\mathrm{reg}}$ is essential to balance the elimination of hallucinations against the reten", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/09aea19f0466afc194d435dd90b2c494238ed274dc714dbdba2ae2f017de7533.jpg", + "table_caption": [ + "Table 4. Impact of Additional Loss Terms. We evaluate on the GoogleMap dataset the effect of removing our proposed losses. $\\mathcal{L}_{\\mathrm{match}}$ has a small impact while $\\mathcal{L}_{\\mathrm{reg}}$ is pivotal." + ], + "table_footnote": [], + "table_body": "
SettingsRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
LregLmatch
✓✓22.741.767.177.36.8
✓X24.141.564.788.07.5
X✓26.726.758.9271.126.6
XX25.025.061.0303.633.4
", + "bbox": [ + 503, + 316, + 888, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "tion of necessary details: increasing its value leads to more conservative masks and improves the visual appearance of the generated images, at the cost of more spurious features. Visualizing the consistency mask is often a useful form of guidance. More details on learning strategies can be found in the Appendix.", + "bbox": [ + 496, + 433, + 893, + 525 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We also acknowledge the potential of recent denoising diffusion models for image-to-image translation tasks [22, 32]. While our method is not confined to GANs and could be adapted to diffusion models with cycle consistency losses [28, 31], unpaired image translation with diffusion models is a nascent field with unique challenges. We plan to explore this area in future research.", + "bbox": [ + 496, + 531, + 893, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 672, + 627, + 688 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have introduced StegoGAN, a model built upon the CycleGAN framework, which leverages the mechanism of steganography to address the challenges of non-bijective image-to-image translation. Our model demonstrates an improved capability to handle divergent distributions between domains, as evidenced by its performance across various datasets, including aerial imagery, topographic maps, and MRI scans. We hope that our work will inspire further research in the little-studied area of non-bijective image translation. We find this research direction important to ensure image translation models are transferable and applicable in real-world scenarios, where datasets rarely conform to the level of curation typically found in research benchmarks.", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7929", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Simon Andermatt, Antal Horváth, Simon Pezold, and Philippe Cattin. Pathology segmentation using distributional differences to images of healthy origin. 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In Computer Vision (ICCV), 2017 IEEE International Conference on, 2017. 1, 2, 3, 5, 6, 7" + ], + "bbox": [ + 78, + 90, + 470, + 797 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7931", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_model.json b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_model.json new file mode 100644 index 0000000000000000000000000000000000000000..f0e13cfa6dec967c57136122097911f1d5a64bd2 --- /dev/null +++ b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_model.json @@ -0,0 +1,2046 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.809, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.253, + 0.131, + 0.718, + 0.177 + ], + "angle": 0, + "content": "StegoGAN: Leveraging Steganography for Non-Bijective Image-to-Image Translation" + }, + { + "type": "text", + "bbox": [ + 0.218, + 0.203, + 0.777, + 0.24 + ], + "angle": 0, + "content": "Sidi Wu \\(^{1*}\\) Yizi Chen \\(^{1*}\\) Samuel Mermet \\(^{2}\\) Lorenz Hurni \\(^{1}\\) Konrad Schindler \\(^{1}\\) Nicolas Gonthier \\(^{3,2}\\) Loic Landrieu \\(^{4,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.245, + 0.9, + 0.265 + ], + "angle": 0, + "content": "\\(^{1}\\) ETH Zurich \\(^{2}\\) Univ Gustave Eiffel, IGN, ENSG, LASTIG \\(^{3}\\) IGN \\(^{4}\\) Univ Gustave Eiffel, CNRS, Ecole des Ponts, LIGM" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.299, + 0.313, + 0.315 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.332, + 0.474, + 0.695 + ], + "angle": 0, + "content": "Most image-to-image translation models postulate that a unique correspondence exists between the semantic classes of the source and target domains. However, this assumption does not always hold in real-world scenarios due to divergent distributions, different class sets, and asymmetrical information representation. As conventional GANs attempt to generate images that match the distribution of the target domain, they may hallucinate spurious instances of classes absent from the source domain, thereby diminishing the usefulness and reliability of translated images. CycleGAN-based methods are also known to hide the mismatched information in the generated images to bypass cycle consistency objectives, a process known as steganography. In response to the challenge of non-bijective image translation, we introduce StegoGAN, a novel model that leverages steganography to prevent spurious features in generated images. Our approach enhances the semantic consistency of the translated images without requiring additional postprocessing or supervision. Our experimental evaluations demonstrate that StegoGAN outperforms existing GAN-based models across various non-bijective image-to-image translation tasks, both qualitatively and quantitatively. Our code and pretrained models are accessible at https://github.com/sian-wusidi/StegoGAN." + }, + { + "type": "title", + "bbox": [ + 0.079, + 0.742, + 0.208, + 0.757 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.768, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Image-to-image translation is an active research subject with impactful applications ranging from changing the style of images [12, 36] to automatically creating maps from satellite images [36] or changing the modality of medical images [9]. When the source and target domains exhibit substantial differences, ensuring the semantic consistency between input images and their translation becomes particularly challeng-" + }, + { + "type": "image", + "bbox": [ + 0.489, + 0.302, + 0.889, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.487, + 0.547, + 0.734, + 0.559 + ], + "angle": 0, + "content": "(b) GAN models hallucinate spurious features." + }, + { + "type": "image", + "bbox": [ + 0.497, + 0.563, + 0.887, + 0.664 + ], + "angle": 0, + "content": null + }, + { + "type": "image_footnote", + "bbox": [ + 0.503, + 0.67, + 0.861, + 0.684 + ], + "angle": 0, + "content": "(c) CycleGAN models hide unmatched features by steganography." + }, + { + "type": "image_footnote", + "bbox": [ + 0.498, + 0.701, + 0.894, + 0.799 + ], + "angle": 0, + "content": "Figure 1. Non-Bijective Translation. When image domains present classes without equivalence (a), GAN models tend to hallucinate spurious features when translating images (b). A related phenomenon is steganography, where CycleGAN-based models covertly encode features in low-amplitude patterns to bypass cycle consistency (c). Instead of disabling this phenomenon, we harness steganography to prevent the hallucination of spurious features." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.809, + 0.893, + 0.841 + ], + "angle": 0, + "content": "ing [8]. Our work explores the surprisingly uncharted field of adversarial, non-bijective image-to-image translation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Non-Bijective Image Translation. Existing translation methods assume a one-to-one correspondence between classes of the source and target domains: horses to zebras [36], satellite image features to their cartographic repre" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.888, + 0.206, + 0.9 + ], + "angle": 0, + "content": "*Equal contribution." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7922" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.242 + ], + "angle": 0, + "content": "sentation [6, 36], or distinct cell types viewed under varying medical imaging modalities [9]. However, as illustrated in Figure 1a, this assumption does not always hold. For instance, when considering a dataset with horses and one with zebras in their habitat, zebra images may include background elements with no equivalent in the source domain—like elephants. Similarly, in map translation toponyms (i.e., place names printed onto the map) do not have counterparts in satellite images [6]. We qualify classes of the target domain without equivalent in the source domain as unmatched." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.243, + 0.473, + 0.41 + ], + "angle": 0, + "content": "As illustrated in Figure 1b, by trying to reproduce the distribution of the target domain, GANs may hallucinate spurious features or textures in the generated images, i.e., objects without equivalent in the source image. This is particularly frequent for unmatched classes [8]. While this can be perfectly acceptable for some applications [23], adding nonexistent tumors in MRI scans or incorrect toponyms in maps can severely degrade the usefulness of the translation result. Instead of detecting and removing these artifacts in post-processing, we propose an approach that directly prevents their generation using steganography." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.413, + 0.473, + 0.626 + ], + "angle": 0, + "content": "GAN Steganography. To ensure its semantic consistency, CycleGAN [36] back-translates the generated image to the source image. However, unmatched classes of the source domain cannot be encoded into meaningful features in the images generated in the target domain. As shown in Figure 1c, these models can instead cheat by encoding the necessary information into quasi-invisible patterns in the generated images [7]. This process, known as steganography, allows GANs to perform seemingly impossible back-translation. For instance, in a map-to-satellite task, the model can restore the correct names of towns from satellite images that appear visually correct. This phenomenon is often viewed as a quirky optimization flaw, easily fixable by adding noise or blur [11, 20, 26]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.473, + 0.766 + ], + "angle": 0, + "content": "StegoGAN. We propose StegoGAN, a model that leverages steganography to detect and mitigate semantic misalignment between domains. In settings where the domain mapping is non-bijective, StegoGAN experimentally demonstrates superior semantic consistency over other GAN-based models both visually and quantitatively, without requiring detection or inpainting steps. In addition, we publish three datasets from open-access sources as a benchmark for evaluating non-bijective image translation models." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.781, + 0.22, + 0.797 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.473, + 0.903 + ], + "angle": 0, + "content": "GAN-Based Image Translation. GAN-based image translation models transfer the style of images between domains with an adversarial perceptual loss [13]. When pairs of aligned images from both domains are available, the translated images can also be supervised by their fidelity with target images [18]. In practice, such pairs are not always" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.183 + ], + "angle": 0, + "content": "available or even possible to obtain. In the absence of explicit equivalence between images, preserving the semantics of the input in the generated image is a priority. Multiple approaches have been proposed to address this challenge, such as density-based regularization [33], spatial mutual information [20, 26, 30], or cycle consistency losses [17, 21, 36]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.187, + 0.897, + 0.337 + ], + "angle": 0, + "content": "Asymmetric Image Translation. Translating between domains with different semantic distributions is challenging. Existing approaches include focusing the network's attention on the most discriminative part of the input image [29], augmenting the consistency loss with geometric transformations [11], replacing the consistency reconstruction term with a contrastive loss [20, 26], or ensuring that the translation is robust to small perturbations of the input [19]. However, these methods assume a bijective relationship between the classes of the source and target domains." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.339, + 0.895, + 0.46 + ], + "angle": 0, + "content": "Closest to our work is the model of Li et al. [23], which uses an auxiliary variable to model the information loss from information-rich domains (such as natural images) to information-poor domains (such as label maps). In turn, they use this variable to create realistic poor-to-rich domain translations. Our work differs as we precisely want to avoid the creation of spurious—albeit realistic—details when translating to a domain with unmatched classes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.464, + 0.897, + 0.646 + ], + "angle": 0, + "content": "CycleGAN Steganography. Chu et al. [7] discovered that, when faced with unmatched classes, CycleGAN [36] hides information in low-amplitude and high-frequency signals. The model uses these visually imperceptible patterns to recreate the source image and bypass the cycle loss. This contradicts the intention of the cycle consistency loss and makes the model more vulnerable to adversarial attacks [7]. Luckily, multiple approaches can prevent steganography, such as blurring [11], compressing [10], or adding noise [20] to the generated source images in the back-translation. Alternatively, the back-translation from poor to rich domains can be omitted in the cycle consistency loss [27, 35]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.647, + 0.895, + 0.768 + ], + "angle": 0, + "content": "While steganography in CycleGAN can be problematic, it also offers an opportunity to analyse distribution differences. In StegAnomaly [3], a model is trained to translate healthy brain scans into a low-entropy domain with cycle consistency. When removing high-frequency components, the model error reveals anomalous structures. This approach, like ours, harnesses steganography for insightful domain analysis, albeit with a different goal." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.784, + 0.6, + 0.8 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We consider two image domains \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) with respective semantic class sets \\(\\kappa_{\\mathcal{X}}\\) and \\(\\kappa_{\\mathcal{Y}}\\). The domains \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) are considered bijective if there exists a function \\(\\phi\\) from \\(\\kappa_{\\mathcal{X}}\\) to \\(\\kappa_{\\mathcal{Y}}\\) such that each class \\(k_{\\mathcal{X}}\\) has a unique and natural semantically equivalent class \\(\\phi(k_{\\mathcal{X}})\\) in \\(\\mathcal{Y}\\), and vice-versa. A class of \\(\\kappa_{\\mathcal{Y}}\\) is said to be unmatched if it doesn't have an" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7923" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.092, + 0.885, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.235, + 0.345, + 0.247 + ], + "angle": 0, + "content": "(a) Backward cycle" + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.25, + 0.273, + 0.345 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.3, + 0.25, + 0.576, + 0.348 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.659, + 0.235, + 0.756, + 0.248 + ], + "angle": 0, + "content": "(b) Forward cycle" + }, + { + "type": "image", + "bbox": [ + 0.664, + 0.257, + 0.871, + 0.333 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.753, + 0.336, + 0.824, + 0.347 + ], + "angle": 0, + "content": "(d) Inference" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.357, + 0.895, + 0.427 + ], + "angle": 0, + "content": "Figure 2. Architecture. To avoid spurious generation of unmatched classes in non-bijective image translation, we propose to make the steganographic process explicit and in feature-space. Our model runs the backward cycle first (a), then the forward translation cycle (b). Thanks to our matchability disentanglement module (c), we can separate the matchable and unmatched information while translating images from domain \\(\\mathcal{V}\\) to \\(\\mathcal{X}\\). We can then produce generated and reconstructed images with and without unmatched features. At inference time (d), our model operates like a normal image translation model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.471, + 0.506 + ], + "angle": 0, + "content": "equivalent in \\(\\mathcal{K}_{\\mathcal{X}}\\). While this notion is somewhat subjective, many applications have obvious examples: toponyms are unmatched in satellite images, and tumors in scans of healthy patients." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.473, + 0.661 + ], + "angle": 0, + "content": "Objective. Our goal is to learn a mapping \\( G: \\mathcal{X} \\mapsto \\mathcal{Y} \\) such that the translation \\( G(x) \\) of any image \\( x \\in \\mathcal{X} \\) aligns stylistically with images from \\( \\mathcal{Y} \\), while preserving the semantic content of \\( x \\). If \\( \\mathcal{K}_{\\mathcal{Y}} \\) contains an unmatched class \\( k_{\\mathcal{Y}}^{\\mathrm{unmatch}} \\), images translated from \\( \\mathcal{X} \\) to \\( \\mathcal{Y} \\) should not contain any instances of \\( k_{\\mathcal{Y}}^{\\mathrm{unmatch}} \\). However, in an attempt to match the distribution of \\( \\mathcal{Y} \\), GAN models often create spurious instances of unmatched classes in their translated images. In this paper, we propose a method that employs steganography to prevent the generation of such spurious information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.673, + 0.199, + 0.691 + ], + "angle": 0, + "content": "3.1. CycleGAN" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.698, + 0.471, + 0.789 + ], + "angle": 0, + "content": "CycleGAN [36] learns unpaired image translation by enforcing the consistency between the input image and its backtranslation from the generated image. It uses two generators \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}}: \\mathcal{X} \\mapsto \\mathcal{Y} \\) and \\( G_{\\mathcal{Y} \\mapsto \\mathcal{X}}: \\mathcal{Y} \\mapsto \\mathcal{X} \\), and two domain discriminators \\( D_{\\mathcal{X}}: \\mathcal{X} \\mapsto \\{0,1\\} \\), \\( D_{\\mathcal{Y}}: \\mathcal{Y} \\mapsto \\{0,1\\} \\) which predict whether a sample is generated (0) or real (1)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.791, + 0.471, + 0.867 + ], + "angle": 0, + "content": "In the following, when considering images \\( x \\in \\mathcal{X} \\) or \\( y \\in \\mathcal{Y} \\), we define the following short-hands: \\( x_{\\mathrm{gen}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}(y) \\) and \\( y_{\\mathrm{gen}} := G_{\\mathcal{X} \\mapsto \\mathcal{Y}}(x) \\) for the generated images, and \\( x_{\\mathrm{rec}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}(y_{\\mathrm{gen}}) \\) and \\( y_{\\mathrm{rec}} := G_{\\mathcal{X} \\mapsto \\mathcal{Y}}(x_{\\mathrm{gen}}) \\) for the reconstructed images. We now detail the losses of CycleGAN." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Adversarial loss. The adversarial loss [13] encourages the discriminators \\(D_{\\mathcal{X}}\\) and \\(D_{\\mathcal{Y}}\\) to distinguish between authentic" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.444, + 0.892, + 0.476 + ], + "angle": 0, + "content": "and generated images, while pushing the generators \\(G_{\\mathcal{X}\\mapsto \\mathcal{Y}}\\) and \\(G_{\\mathcal{Y}\\mapsto \\mathcal{X}}\\) to create credible images:" + }, + { + "type": "equation", + "bbox": [ + 0.501, + 0.501, + 0.892, + 0.537 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\mathrm {G A N}} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\log (D _ {\\mathcal {Y}} (y)) + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\log (1 - D _ {\\mathcal {Y}} (y _ {\\text {g e n}})) \\\\ + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\log (D _ {\\mathcal {X}} (x)) + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\log (1 - D _ {\\mathcal {X}} (x _ {\\text {g e n}})). \\tag {1} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.55, + 0.892, + 0.598 + ], + "angle": 0, + "content": "Cycle consistency. The cycle consistency loss ensures that the back-translation of \\( y_{\\mathrm{gen}} \\) to domain \\( \\mathcal{X} \\) is close to the original image \\( x \\), and likewise for \\( x_{\\mathrm{gen}} \\) and \\( y \\):" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.607, + 0.892, + 0.624 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\text {c y c}} = \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| x _ {\\text {r e c}} - x \\| + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| y _ {\\text {r e c}} - y \\|, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.634, + 0.726, + 0.65 + ], + "angle": 0, + "content": "with \\(\\| \\cdot \\|\\) the pixel-wise \\(L_{1}\\) norm." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.653, + 0.894, + 0.684 + ], + "angle": 0, + "content": "Identity loss. The identity loss regularizes the generators to be close to identity, generally improving color composition:" + }, + { + "type": "equation", + "bbox": [ + 0.504, + 0.694, + 0.892, + 0.712 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\mathrm {i d}} = \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} (x) - x \\| + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} (y) - y \\|. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.721, + 0.744, + 0.736 + ], + "angle": 0, + "content": "Final Loss. The final objectives are:" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.747, + 0.892, + 0.764 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}}, G _ {\\mathcal {Y} \\mapsto \\mathcal {X}}\\right) = \\mathcal {L} _ {G A N} + \\lambda_ {\\text {c y c}} \\mathcal {L} _ {\\text {c y c}} + \\lambda_ {\\text {i d}} \\mathcal {L} _ {\\text {i d}}, \\tag {4}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.767, + 0.892, + 0.782 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} \\left(D _ {\\mathcal {X}}, D _ {\\mathcal {Y}}\\right) = - \\mathcal {L} _ {\\mathrm {G A N}}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.793, + 0.819, + 0.809 + ], + "angle": 0, + "content": "with \\(\\lambda_{\\mathrm{cyc}}\\) and \\(\\lambda_{\\mathrm{id}}\\) non-negative hyperparameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.817, + 0.619, + 0.833 + ], + "angle": 0, + "content": "3.2. StegoGAN" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.84, + 0.894, + 0.903 + ], + "angle": 0, + "content": "We introduce StegoGAN, a novel model building on the CycleGAN framework [36], designed specifically for scenarios where domains \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) lack a bijective relationship. When generating images \\(y_{\\mathrm{gen}}\\) in \\(\\mathcal{V}\\), the generator \\(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}\\) may add" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7924" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.213 + ], + "angle": 0, + "content": "spurious instances of an unmatched class \\( k_{\\mathcal{Y}}^{\\mathrm{unmatch}} \\) in order to deceive the discriminator \\( D_{\\mathcal{Y}} \\). Our goal is to prevent the generation of such hallucinated instances. To achieve this, we leverage steganography to explicitly disentangle the matchable and unmatched information in the backward cycle (\\( y \\mapsto x_{\\mathrm{gen}} \\mapsto y_{\\mathrm{rec}} \\)) and prevent the network from hallucinating in the forward translation (\\( x \\mapsto y_{\\mathrm{gen}} \\mapsto x_{\\mathrm{rec}} \\)). See Figure 2 for the overall design of our approach." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.216, + 0.473, + 0.352 + ], + "angle": 0, + "content": "Steganography. In order to faithfully reconstruct \\( y \\) with \\( y_{\\mathrm{rec}} \\), the translated image \\( x_{\\mathrm{gen}} \\) must somehow contain information about the instances of the unmatched class \\( k_{\\mathcal{Y}}^{\\mathrm{unmatch}} \\). CycleGAN methods typically achieve this by hiding low-amplitude and high-frequency patterns in \\( x_{\\mathrm{gen}} \\) that will be decoded by \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}} \\) and translated back to instances of \\( k_{\\mathcal{Y}}^{\\mathrm{unmatch}} \\) in \\( y_{\\mathrm{rec}} \\). Adding low-intensity noise on each pixel is typically sufficient to destroy the hidden information and prevent steganography [7]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.353, + 0.473, + 0.474 + ], + "angle": 0, + "content": "Steganography is often viewed as an optimization flaw that undermines the consistency loss. However, in the case of non-bijective translation, this is the only way to let \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}} \\) reconstruct instances of \\( k_{\\mathcal{Y}}^{\\mathrm{unmatch}} \\) in \\( y_{\\mathrm{rec}} \\). Instead of disabling steganography, we propose to use it to our advantage to detect and prevent spurious generations. We adapt CycleGAN so that steganography takes place in feature-space instead of pixel-space, and in an explicit manner." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.473, + 0.612 + ], + "angle": 0, + "content": "Backward Cycle. We decompose the generators \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}} \\) and \\( G_{\\mathcal{Y} \\mapsto \\mathcal{X}} \\) into two components: an encoder and a decoder, such that \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}} = G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{dec}} \\circ G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{enc}} \\) and \\( G_{\\mathcal{Y} \\mapsto \\mathcal{X}} = G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{dec}} \\circ G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}} \\). The encoders map their inputs to feature maps of spatial dimension \\( H \\times W \\), where each pixel has \\( C \\) channels. In the following, we denote the intermediary representation of \\( y \\) in \\( G_{\\mathcal{Y} \\mapsto \\mathcal{X}} \\) by \\( z_{\\mathrm{gen}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}(y) \\). The feature map \\( z_{\\mathrm{gen}} \\) encodes information about both matchable and unmatched classes, which we want to disentangle." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.612, + 0.473, + 0.72 + ], + "angle": 0, + "content": "We introduce a network \\( M \\): \\( \\mathbb{R}^{H \\times W \\times C} \\mapsto [0,1]^{H \\times W \\times C} \\) that assigns an unmatchedability score between 0 and 1 to each pixel and channel. Here, a score of 1 indicates that the information does not have a counterpart in domain \\( \\mathcal{X} \\), while it does for 0. This process gives us the unmatchedability mask \\( M(z_{\\mathrm{gen}}) \\), which we use to split \\( z_{\\mathrm{gen}} \\) into its matchable and unmatched parts:" + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.731, + 0.47, + 0.75 + ], + "angle": 0, + "content": "\\[\nz _ {\\text {g e n}} ^ {\\text {u n m a t c h}} = M \\left(z _ {\\text {g e n}}\\right) \\odot z \\tag {6}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.752, + 0.47, + 0.772 + ], + "angle": 0, + "content": "\\[\nz _ {\\text {g e n}} ^ {\\text {m a t c h}} = \\left(1 - M \\left(z _ {\\text {g e n}}\\right)\\right) \\odot z, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.782, + 0.473, + 0.829 + ], + "angle": 0, + "content": "with \\(\\odot\\) the pixel-wise and channel-wise Hadamard product. In our model, the generated image \\(x_{\\mathrm{gen}}\\) is computed using only the matchable part of the representation:" + }, + { + "type": "equation", + "bbox": [ + 0.194, + 0.839, + 0.47, + 0.859 + ], + "angle": 0, + "content": "\\[\nx _ {\\text {g e n}} = G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} ^ {\\text {d e c}} \\left(z _ {\\text {g e n}} ^ {\\text {m a t c h}}\\right). \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We produce two reconstructions of \\( y \\): \\( y_{\\mathrm{rec}}^{\\mathrm{clean}} \\), which is a direct back-translation of \\( x_{\\mathrm{gen}} \\) into the \\( \\mathcal{V} \\) domain: \\( y_{\\mathrm{rec}}^{\\mathrm{clean}} = \\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.14 + ], + "angle": 0, + "content": "\\(G_{\\mathcal{X}\\mapsto \\mathcal{Y}}(x_{\\mathrm{gen}})\\); and \\(y_{\\mathrm{rec}}\\), which is generated by decoding a combination of the unmatched part of \\(z_{\\mathrm{gen}}\\) and the features extracted by \\(G_{\\mathcal{X}\\mapsto \\mathcal{Y}}^{\\mathrm{enc}}\\) from a noise-perturbed version of \\(x_{\\mathrm{gen}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.54, + 0.15, + 0.895, + 0.17 + ], + "angle": 0, + "content": "\\[\ny _ {\\text {r e c}} = G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {d e c}} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {e n c}} \\left(x _ {\\text {g e n}} + \\epsilon\\right) + z _ {\\text {g e n}} ^ {\\text {u n m a t c h}}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.179, + 0.895, + 0.255 + ], + "angle": 0, + "content": "with \\(\\epsilon\\) denoting random Gaussian noise of low amplitude applied to each pixel and channel of \\(x_{\\mathrm{gen}}\\). This noise is added to destroy potential steganographic information in \\(x_{\\mathrm{gen}}\\), therefore forcing \\(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}\\) to rely only on \\(z_{\\mathrm{gen}}^{\\mathrm{unmatch}}\\) to reconstruct unmatched features in \\(y_{\\mathrm{rec}}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.256, + 0.895, + 0.317 + ], + "angle": 0, + "content": "The key mechanisms to disentangle matchable and unmatched information are twofold: (i) disturbing direct steganography with random noise, and (ii) explicitly providing unmatched information to \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}} \\) in feature-space." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.32, + 0.895, + 0.429 + ], + "angle": 0, + "content": "Forward Cycle. In the forward cycle \\(x \\to y_{\\mathrm{gen}} \\to x_{\\mathrm{rec}}\\), the generator \\(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}\\) may create spurious instances of unmatched classes when translating \\(x\\) to \\(\\mathcal{Y}\\) to fulfill the expectations of the discriminator \\(D_y\\). To address this, we perform two distinct translations of \\(x\\) in \\(\\mathcal{Y}\\): \\(y_{\\mathrm{gen}}\\) has explicit access to the steganographic information \\(z_{\\mathrm{gen}}^{\\mathrm{unmatch}}\\) extracted from the backward cycle, while \\(y_{\\mathrm{gen}}^{\\mathrm{clean}}\\) does not:" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.44, + 0.892, + 0.46 + ], + "angle": 0, + "content": "\\[\ny _ {\\text {g e n}} = G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {d e c}} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {e n c}} (x) + z _ {\\text {g e n}} ^ {\\text {u n m a t c h}}\\right) \\tag {10}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.462, + 0.892, + 0.481 + ], + "angle": 0, + "content": "\\[\ny _ {\\text {g e n}} ^ {\\text {c l e a n}} = G _ {\\chi \\mapsto y} (x). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.895, + 0.585 + ], + "angle": 0, + "content": "The rationale is that \\( G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{dec}} \\) has explicit access to information about the unmatched classes of \\( y \\), so it is not incentivized to invent them. For consistency with the backward step, where the decoder of \\( G_{\\mathcal{Y} \\mapsto \\mathcal{X}} \\) processes only matchable information as defined in (7), we use the same disentangle-ment approach for generating \\( x_{\\mathrm{rec}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.563, + 0.595, + 0.892, + 0.614 + ], + "angle": 0, + "content": "\\[\nx _ {\\text {r e c}} = G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} ^ {\\text {d e c}} \\left(\\left(1 - M \\left(z _ {\\text {r e c}}\\right)\\right) \\odot z _ {\\text {r e c}}\\right), \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.624, + 0.892, + 0.656 + ], + "angle": 0, + "content": "where \\( z_{\\mathrm{rec}} = G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}(y_{\\mathrm{gen}}) \\) is the intermediary representation of \\( y_{\\mathrm{gen}} \\) in the forward cycle." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.895, + 0.78 + ], + "angle": 0, + "content": "Mask Regularization. To avoid degenerate behaviors of our explicit steganography mechanism, we enforce two priors on the unmatchedability masks: (i) given that a well-posed translation problem predominantly involves matchable features, the masks should be sparse; (ii) to improve the model's interpretability, we favor mask values near 0 or 1, representing clear decisions about matchability. To enforce these priors, we regularize the masks with the non-convex \\( L_{0.5} \\) norm [34]:" + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.792, + 0.892, + 0.81 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {r e g} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| M \\left(z _ {\\text {g e n}}\\right) \\| _ {0. 5} + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| M \\left(z _ {\\text {r e c}}\\right) \\| _ {0. 5}. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.823, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Matchable Consistency. The images \\( y_{\\mathrm{gen}} \\) and \\( y_{\\mathrm{gen}}^{\\mathrm{clean}} \\), as well as \\( y_{\\mathrm{rec}} \\) and \\( y_{\\mathrm{rec}}^{\\mathrm{clean}} \\), should be identical outside of unmatched regions. To enforce this constraint, we design a function \\( I \\) which takes an unmatchedness mask \\( m \\) as input, takes the channel-wise maximum values of all pixels, flips its" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7925" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.892, + 0.58 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.589, + 0.895, + 0.633 + ], + "angle": 0, + "content": "Figure 3. Qualitative Comparison. We report reconstructions from the test sets of PlanIGN (top two rows), GoogleMap (row 3 and 4), and MRI (last two rows). Contrary to the other models, StegoGAN does not hallucinate spurious toponyms, highways (orange roads), or tumors (white areas) and shows better semantic correspondences during translation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.658, + 0.47, + 0.689 + ], + "angle": 0, + "content": "value from [0, 1] to [1, 0], and upsamples the results to the dimensions of the input images." + }, + { + "type": "equation", + "bbox": [ + 0.154, + 0.697, + 0.472, + 0.723 + ], + "angle": 0, + "content": "\\[\nI (m) = \\operatorname {u p s a m p l e} \\left(1 - \\max _ {c} m\\right). \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.732, + 0.473, + 0.797 + ], + "angle": 0, + "content": "The obtained consistency masks \\( I(m) \\) have values close to 1 for pixels with only matchable content, and close to 0 otherwise. This enables us to define a loss for \\( y_{\\mathrm{gen}}^{\\mathrm{clean}} \\) and \\( y_{\\mathrm{rec}}^{\\mathrm{clean}} \\) that focuses solely on regions with matchable features:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.804, + 0.47, + 0.844 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {\\text {m a t c h}} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| I (M (z _ {\\text {g e n}})) \\odot (y _ {\\text {g e n}} - y _ {\\text {g e n}} ^ {\\text {c l e a n}}) \\| \\\\ + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| I (M (z _ {\\mathrm {r e c}})) \\odot (y _ {\\mathrm {r e c}} - y _ {\\mathrm {r e c}} ^ {\\text {c l e a n}}) \\|. \\tag {15} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Final Objective. In addition to the standard CycleGAN loss components (4-5), we integrate \\(\\mathcal{L}_{\\mathrm{match}}\\) and \\(\\mathcal{L}_{\\mathrm{reg}}\\) into the overall loss function \\(\\mathcal{L}(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}, G_{\\mathcal{Y} \\mapsto \\mathcal{X}})\\), weighted by" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.658, + 0.895, + 0.718 + ], + "angle": 0, + "content": "their respective coefficients \\(\\lambda_{\\mathrm{reg}}\\) and \\(\\lambda_{\\mathrm{match}}\\). Crucially, our proposed approach remains unsupervised, requiring neither aligned images from \\(\\mathcal{X}\\) and \\(\\mathcal{Y}\\) nor specific annotations of unmatched features." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.735, + 0.634, + 0.751 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.761, + 0.895, + 0.822 + ], + "angle": 0, + "content": "In this section, we assess the improvements brought by our method for non-bijective image translation across various datasets and compare them with existing models, both qualitatively and quantitatively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.897, + 0.902 + ], + "angle": 0, + "content": "Implementation details. We follow the setting of CyleGAN [36] as our baseline model: the generators are Resnets [15] and the discriminator is based on PatchGAN [18]. We define the encoders as the first half of the generator's layers and the decoders as the second half. The" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7926" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.852, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.365, + 0.895, + 0.396 + ], + "angle": 0, + "content": "Figure 4. Results on GoogleMaps. We report the performance of several top-performing image translation models for different ratios of unmatched features in the target domain of the training set. StegoGAN handles higher ratios better than competing methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.42, + 0.475, + 0.496 + ], + "angle": 0, + "content": "unmatchability mask predictor \\( M \\) is defined as a small 3-layer convolutional neural network (CNN). We set \\( \\lambda_{\\mathrm{cyc}} = 10 \\), \\( \\lambda_{\\mathrm{idt}} = 0.5 \\) as in [36] and \\( \\lambda_{\\mathrm{match}} = 1 \\). The amplitude of the perturbation \\( \\epsilon \\) is 0.01 as in [7]. The Appendix provides more architecture and training details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.506, + 0.182, + 0.52 + ], + "angle": 0, + "content": "4.1. Datasets" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.471, + 0.711 + ], + "angle": 0, + "content": "We assess the performance of StegoGAN across several image translation tasks that feature unmatched classes. Each dataset follows a consistent structure: the training set includes images from the source domain \\(\\mathcal{X}\\) devoid of a specific class (e.g., tumors, motorways, toponyms) while the target domain \\(\\mathcal{Y}\\) does include that class. The test set comprises paired images from both domains, specifically excluding the unmatched class. This setup allows us to quantify the models' hallucinations: any generated instances of the unmatched class are necessarily spurious and due to its presence in the training set. We release all three curated datasets on the Zenodo platform and provide details below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.714, + 0.472, + 0.867 + ], + "angle": 0, + "content": "PlanIGN. \\(\\mathcal{X}\\) : Aerial Photo, \\(\\mathcal{Y}\\) : Maps, \\(k_{\\mathcal{Y}}^{\\mathrm{unmatch}}\\) : Text. We construct a dataset using open data from the French National Mapping Agency (IGN), comprising 1900 aerial (ortho-)images at 3m spatial resolution, and two versions of their corresponding topographic maps: one with and one without toponyms. This dataset presents a clear unmatched class: place names. The training set includes 1000 maps with toponyms and 1000 aerial images, while the test set comprises 900 map samples without toponyms and their corresponding aerial images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.473, + 0.903 + ], + "angle": 0, + "content": "GoogleMaps. \\(\\mathcal{X}\\) : Aerial Photo, \\(\\mathcal{V}\\) : Maps, \\(k_{\\mathcal{Y}}^{\\mathrm{unmatch}}\\) : Highways. The GoogleMaps dataset [18] is a standard bench" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.895, + 0.527 + ], + "angle": 0, + "content": "mark for image translation tasks [19, 20]. It contains 1096 map/image pairs for training and 1098 for testing. To create a controlled non-bijective scenario, we exclude all satellite images that show highways and sample the maps of the training set to contain varying proportions of maps with highways, ranging from \\(0\\%\\) to \\(65\\%\\), for a fixed total of 548 maps. For the test set we selected 898 pairs without highways." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.897, + 0.758 + ], + "angle": 0, + "content": "Brats MRI \\(\\mathcal{X}\\) : T1 Scans, \\(\\mathcal{V}\\) : FLAIR, \\(k_{\\mathcal{Y}}^{\\mathrm{unmatch}}\\) : Tumors. Lastly, we used a dataset of brain MRI scans [25] with two modalities: T1 (naive) and FLAIR (T2 Fluid Attenuated Inversion Recovery) [14]. We adapt the protocol that Cohen et al. [8] used for the Brats2013 datasets [24] to the more recent Brats2018 [2] dataset by varying the percentage of scans with tumors in the target domain. We selected transverse slices from the \\(60^{\\circ}\\) to \\(100^{\\circ}\\) range in the caudocranial direction [1] for both T1 and FLAIR scans. Each scan was classified as tumorous if more than \\(1\\%\\) of its pixels were labeled as such, and as healthy if it contained no tumor pixels. The training set contains 800 images from each modality, with all source images (T1) being healthy and the target domain (FLAIR) comprising \\(60\\%\\) tumorous scans. The test set contains 335 paired scans of healthy brains." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.768, + 0.685, + 0.782 + ], + "angle": 0, + "content": "4.2. Evaluation metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.791, + 0.893, + 0.837 + ], + "angle": 0, + "content": "We use a broad range of metrics to evaluate the performance of StegoGAN and other image translation algorithms in the non-bijective setting:" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.902 + ], + "angle": 0, + "content": "FID and KID. The Fréchet Inception Distance (FID) [16] and Kernel Inception Distance (KID) [4] are widely used to quantify the similarity between the distributions of real and generated images in the target domain." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7927" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.089, + 0.47, + 0.118 + ], + "angle": 0, + "content": "Table 1. Quantitative Comparison on PlanIGN. Our model shows a remarkably better performance than other existing models." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.123, + 0.468, + 0.219 + ], + "angle": 0, + "content": "
MethodRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
CUT [26]30.546.755.868.42.8
CycleGAN [36]27.015.157.697.56.6
DRIT [21]34.833.636.976.43.8
GcGAN [11]32.754.556.9110.88.2
SRUNIT [19]32.348.852.860.22.2
StegoGAN (ours)22.566.174.858.42.4
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.23, + 0.47, + 0.351 + ], + "angle": 0, + "content": "RMSE, \\(\\mathbf{Acc}(\\sigma_1)\\), and \\(\\mathbf{Acc}(\\sigma_2)\\). As the test sets comprise paired images from both domains, we can directly compare the Root Mean Square Error (RMSE) between the real and predicted images in the target domain. We count a predicted pixel as correctly predicted if it deviate by less than a fixed threshold in any of the color channels [11]. We use \\(\\sigma_1 = 5\\) and \\(\\sigma_2 = 10\\) for the GoogleMap dataset and \\(\\sigma_1 = 2\\) and \\(\\sigma_2 = 5\\) for the less colorful PlanIGN dataset." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.356, + 0.471, + 0.477 + ], + "angle": 0, + "content": "pFPR and iFPR. In the GoogleMap dataset, highways are always depicted in orange, allowing us to label pixels where all color channels differ by less than 20 units from (240, 160, 30) as highways. In the Brats MRI dataset, we use a pretrained tumor detector [5] to find spurious tumors in the generated images. This allows us to compute the average false positive rate per pixel (pFPR) and per instance (iFPR) of the generated images." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.489, + 0.172, + 0.503 + ], + "angle": 0, + "content": "4.3. Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.471, + 0.589 + ], + "angle": 0, + "content": "Qualitative Results. Figure 3 showcases StegoGAN's qualitative performance against other image translation algorithms. Notably, StegoGAN effectively avoids generating unmatched classes such as texts, highways, and tumors, while producing high-quality image translations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.593, + 0.47, + 0.729 + ], + "angle": 0, + "content": "Quantitative Results. On the PlanIGN dataset (Table 1) and the Brats MRI dataset (Table 2), StegoGAN outperforms others in fidelity, achieving the lowest RMSE by a margin of 4.5 on PlanIGN and by 3.5 for Brats MRI. Furthermore, it significantly enhances pixel accuracy, with improvements of \\(+11.6\\) in \\(\\mathrm{Acc}(\\sigma_1)\\) and \\(+17.2\\) in \\(\\mathrm{Acc}(\\sigma_2)\\) on PlanIGN. In the MRI dataset, StegoGAN dramatically reduces false positive rates—over \\(20\\times\\) lower than CycleGAN and \\(10\\times\\) less than the next best model SRUNIT (for pFPR)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.731, + 0.471, + 0.835 + ], + "angle": 0, + "content": "On the GoogleMap dataset, as shown in Figure 4, StegoGAN's performance is on par with CycleGAN at \\(0\\%\\) unmatched cases and remains stable even as this ratio increases, unlike other methods that degrade. Remarkably, StegoGAN maintains a consistent false positive rate of 0 across all tests, while this rate increases for all other methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Unmatchability Masks. In Figure 5, we illustrate the emergent ability of the unmatchedability masks to trace the outline of unmatched class instances like toponyms, highways, and tumors. This aspect highlights the versatility of our" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.132 + ], + "angle": 0, + "content": "Table 2. Quantitative Comparison on Brats MRI Flair \\(\\rightarrow\\) T1. Our model outperforms competing method in terms of both reconstruction accuracy and consistency." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.136, + 0.89, + 0.233 + ], + "angle": 0, + "content": "
MethodRMSE↓pFPR(‰)↓iFPR↓FID↓KID↓
CUT [26]39.817.023.0103.98.8
CycleGAN [36]39.921.922.789.87.7
DRIT [21]53.018.541.2123.411.6
GcGAN [11]41.724.722.461.93.5
SRUNIT [19]42.515.121.858.92.9
StegoGAN (ours)36.31.14.258.52.4
" + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.248, + 0.875, + 0.54 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.549, + 0.892, + 0.592 + ], + "angle": 0, + "content": "Figure 5. Unmatchability Masks. The unmatchedability masks predicted in the backward cycle follow the instances of unmatched features in the target domain: toponyms, highways, and tumors." + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.608, + 0.892, + 0.664 + ], + "angle": 0, + "content": "Table 3. Ablation Study on Encoder Depth. We evaluate the impact of changing the depth of the encoder on the reconstruction fidelity and the quality of unmatchedability masks. Depth= -1 or 8 means no encoder or no decoder, respectively." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.669, + 0.892, + 0.763 + ], + "angle": 0, + "content": "
DepthMaskPrediction
mIOU↑Prec.↑recall↑RMSE↓A(σ1)↑A(σ2)↑FID↓KID↓
-126.627.181.222.464.374.258.82.5
125.225.881.222.566.174.858.42.4
327.127.980.422.861.673.462.93.0
530.833.469.524.252.770.662.32.6
847.360.160.024.553.570.762.72.7
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.773, + 0.894, + 0.819 + ], + "angle": 0, + "content": "approach, which functions without explicit supervision or aligned images, offering a tool to explore the pairwise semantic differences between arbitrary datasets." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.749, + 0.848 + ], + "angle": 0, + "content": "4.4. Ablation study and analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We explore the impact of our main design choices, as well as further capabilities and limitations of our approach. See the Appendix for further ablations." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7928" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.089, + 0.887, + 0.193 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.207, + 0.893, + 0.234 + ], + "angle": 0, + "content": "Figure 6. Impact of Encoder Depth. We visualize the unmatchedability mask for encoders of different depths for the PlanIGN dataset. Shallower encoders consider more features as unmatched." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.473, + 0.462 + ], + "angle": 0, + "content": "Encoder Ablation. We conducted an ablation study on the definition of the intermediary representation \\( z \\) by varying the depth at which the \"encoder\" ends and the \"decoder\" starts within the generator. Given that our generators consist of 9 consecutive convolutional blocks, we experimented with different configurations: -1 (indicating no decoder), 1 (the configuration used in our paper), as well as depths of 3, 5, and 8 (implying no decoder). We report in Table 3 the reconstruction error of these models, as well as the fidelity of the consistency mask with the toponym text mask. We observe that shallow encoders have better reconstruction accuracy while the consistency masks of deeper encoders better approximate the text masks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.466, + 0.471, + 0.618 + ], + "angle": 0, + "content": "Visualizing these masks in Figure 6, we observe that shallow encoders consider complex features such as highways and rivers as unmatched features, while deeper encoders do not. Shallower encoders seem more influenced by the variation in appearance (e.g., rivers being sometimes covered in vegetation or with varying colors) while deeper encoders focus on high-level semantics. We argue that both definitions are equally valid, and that varying the depth of the encoders can provide insights into the nature of the semantic mismatch between datasets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.631, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Parameterization. In Table 4, we analyze the effects of omitting the additional terms \\(\\mathcal{L}_{\\mathrm{reg}}\\) and \\(\\mathcal{L}_{\\mathrm{match}}\\) from the loss function \\(\\mathcal{L}\\) in Equation (4). We show that while \\(\\mathcal{L}_{\\mathrm{match}}\\) generally yields modest improvements across all metrics, \\(\\mathcal{L}_{\\mathrm{reg}}\\) is pivotal, particularly for learning the target distribution. This outcome aligns with our expectations, as the absence of \\(\\mathcal{L}_{\\mathrm{reg}}\\) allows the network to transmit all information, matchable or not, to the \\(G_{\\mathcal{Y} \\mapsto \\mathcal{X}}\\) decoder without repercussions, impeding the training of the \\(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}\\) encoder." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Limitations. We augment the CycleGAN framework with a module \\(M\\) and two hyper-parameters \\(\\lambda_{\\mathrm{match}}\\) and \\(\\lambda_{\\mathrm{reg}}\\), thereby adding to the complexity of its training dynamics. Moreover, the concept of unmatchedability, integral to our approach, is inherently subjective. Given enough semantic detail, any two distinct datasets could be considered unmatched. As a result, fine-tuning the hyperparameter \\(\\lambda_{\\mathrm{reg}}\\) is essential to balance the elimination of hallucinations against the reten" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.264, + 0.895, + 0.307 + ], + "angle": 0, + "content": "Table 4. Impact of Additional Loss Terms. We evaluate on the GoogleMap dataset the effect of removing our proposed losses. \\(\\mathcal{L}_{\\mathrm{match}}\\) has a small impact while \\(\\mathcal{L}_{\\mathrm{reg}}\\) is pivotal." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.317, + 0.89, + 0.408 + ], + "angle": 0, + "content": "
SettingsRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
LregLmatch
✓✓22.741.767.177.36.8
✓X24.141.564.788.07.5
X✓26.726.758.9271.126.6
XX25.025.061.0303.633.4
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.434, + 0.894, + 0.526 + ], + "angle": 0, + "content": "tion of necessary details: increasing its value leads to more conservative masks and improves the visual appearance of the generated images, at the cost of more spurious features. Visualizing the consistency mask is often a useful form of guidance. More details on learning strategies can be found in the Appendix." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.894, + 0.637 + ], + "angle": 0, + "content": "We also acknowledge the potential of recent denoising diffusion models for image-to-image translation tasks [22, 32]. While our method is not confined to GANs and could be adapted to diffusion models with cycle consistency losses [28, 31], unpaired image translation with diffusion models is a nascent field with unique challenges. We plan to explore this area in future research." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.673, + 0.628, + 0.689 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We have introduced StegoGAN, a model built upon the CycleGAN framework, which leverages the mechanism of steganography to address the challenges of non-bijective image-to-image translation. Our model demonstrates an improved capability to handle divergent distributions between domains, as evidenced by its performance across various datasets, including aerial imagery, topographic maps, and MRI scans. We hope that our work will inspire further research in the little-studied area of non-bijective image translation. We find this research direction important to ensure image translation models are transferable and applicable in real-world scenarios, where datasets rarely conform to the level of curation typically found in research benchmarks." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7929" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.473, + 0.226 + ], + "angle": 0, + "content": "[1] Simon Andermatt, Antal Horváth, Simon Pezold, and Philippe Cattin. Pathology segmentation using distributional differences to images of healthy origin. In *Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries: 4th International Workshop*, *BrainLes* 2018, Held in Conjunction with MICCAI*2018*, Granada, Spain, September 16, 2018, Revised Selected Papers, Part I 4, pages 228-238. 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In Computer Vision (ICCV), 2017 IEEE International Conference on, 2017. 1, 2, 3, 5, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.472, + 0.799 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7931" + } + ] +] \ No newline at end of file diff --git a/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_origin.pdf b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..9e551a7b4f17a1b7911a0935412c91717c5b73d7 --- /dev/null +++ b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/6c6dbef8-429a-42af-8789-b7a3716cc2bf_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:043ab325058b8035b5340b00d112afd9eac54959a3b5258803acdead1b7231a3 +size 6738613 diff --git a/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/full.md b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9723420438a360ee856bf9cfbaec8a915584fee8 --- /dev/null +++ b/2024/StegoGAN_ Leveraging Steganography for Non-Bijective Image-to-Image Translation/full.md @@ -0,0 +1,321 @@ +# StegoGAN: Leveraging Steganography for Non-Bijective Image-to-Image Translation + +Sidi Wu $^{1*}$ Yizi Chen $^{1*}$ Samuel Mermet $^{2}$ Lorenz Hurni $^{1}$ Konrad Schindler $^{1}$ Nicolas Gonthier $^{3,2}$ Loic Landrieu $^{4,2}$ + +$^{1}$ ETH Zurich $^{2}$ Univ Gustave Eiffel, IGN, ENSG, LASTIG $^{3}$ IGN $^{4}$ Univ Gustave Eiffel, CNRS, Ecole des Ponts, LIGM + +# Abstract + +Most image-to-image translation models postulate that a unique correspondence exists between the semantic classes of the source and target domains. However, this assumption does not always hold in real-world scenarios due to divergent distributions, different class sets, and asymmetrical information representation. As conventional GANs attempt to generate images that match the distribution of the target domain, they may hallucinate spurious instances of classes absent from the source domain, thereby diminishing the usefulness and reliability of translated images. CycleGAN-based methods are also known to hide the mismatched information in the generated images to bypass cycle consistency objectives, a process known as steganography. In response to the challenge of non-bijective image translation, we introduce StegoGAN, a novel model that leverages steganography to prevent spurious features in generated images. Our approach enhances the semantic consistency of the translated images without requiring additional postprocessing or supervision. Our experimental evaluations demonstrate that StegoGAN outperforms existing GAN-based models across various non-bijective image-to-image translation tasks, both qualitatively and quantitatively. Our code and pretrained models are accessible at https://github.com/sian-wusidi/StegoGAN. + +# 1. Introduction + +Image-to-image translation is an active research subject with impactful applications ranging from changing the style of images [12, 36] to automatically creating maps from satellite images [36] or changing the modality of medical images [9]. When the source and target domains exhibit substantial differences, ensuring the semantic consistency between input images and their translation becomes particularly challeng- + +![](images/02c4a3768175c9371ced9722a95b20d0aa1dabddf845933c309c417f2b68e07e.jpg) + +(b) GAN models hallucinate spurious features. + +![](images/34ed5233575711c28f251edc758ae15016cf15bdae7b4cf5ba0b2c5809e65447.jpg) +(c) CycleGAN models hide unmatched features by steganography. +Figure 1. Non-Bijective Translation. When image domains present classes without equivalence (a), GAN models tend to hallucinate spurious features when translating images (b). A related phenomenon is steganography, where CycleGAN-based models covertly encode features in low-amplitude patterns to bypass cycle consistency (c). Instead of disabling this phenomenon, we harness steganography to prevent the hallucination of spurious features. + +ing [8]. Our work explores the surprisingly uncharted field of adversarial, non-bijective image-to-image translation. + +Non-Bijective Image Translation. Existing translation methods assume a one-to-one correspondence between classes of the source and target domains: horses to zebras [36], satellite image features to their cartographic repre + +sentation [6, 36], or distinct cell types viewed under varying medical imaging modalities [9]. However, as illustrated in Figure 1a, this assumption does not always hold. For instance, when considering a dataset with horses and one with zebras in their habitat, zebra images may include background elements with no equivalent in the source domain—like elephants. Similarly, in map translation toponyms (i.e., place names printed onto the map) do not have counterparts in satellite images [6]. We qualify classes of the target domain without equivalent in the source domain as unmatched. + +As illustrated in Figure 1b, by trying to reproduce the distribution of the target domain, GANs may hallucinate spurious features or textures in the generated images, i.e., objects without equivalent in the source image. This is particularly frequent for unmatched classes [8]. While this can be perfectly acceptable for some applications [23], adding nonexistent tumors in MRI scans or incorrect toponyms in maps can severely degrade the usefulness of the translation result. Instead of detecting and removing these artifacts in post-processing, we propose an approach that directly prevents their generation using steganography. + +GAN Steganography. To ensure its semantic consistency, CycleGAN [36] back-translates the generated image to the source image. However, unmatched classes of the source domain cannot be encoded into meaningful features in the images generated in the target domain. As shown in Figure 1c, these models can instead cheat by encoding the necessary information into quasi-invisible patterns in the generated images [7]. This process, known as steganography, allows GANs to perform seemingly impossible back-translation. For instance, in a map-to-satellite task, the model can restore the correct names of towns from satellite images that appear visually correct. This phenomenon is often viewed as a quirky optimization flaw, easily fixable by adding noise or blur [11, 20, 26]. + +StegoGAN. We propose StegoGAN, a model that leverages steganography to detect and mitigate semantic misalignment between domains. In settings where the domain mapping is non-bijective, StegoGAN experimentally demonstrates superior semantic consistency over other GAN-based models both visually and quantitatively, without requiring detection or inpainting steps. In addition, we publish three datasets from open-access sources as a benchmark for evaluating non-bijective image translation models. + +# 2. Related Work + +GAN-Based Image Translation. GAN-based image translation models transfer the style of images between domains with an adversarial perceptual loss [13]. When pairs of aligned images from both domains are available, the translated images can also be supervised by their fidelity with target images [18]. In practice, such pairs are not always + +available or even possible to obtain. In the absence of explicit equivalence between images, preserving the semantics of the input in the generated image is a priority. Multiple approaches have been proposed to address this challenge, such as density-based regularization [33], spatial mutual information [20, 26, 30], or cycle consistency losses [17, 21, 36]. + +Asymmetric Image Translation. Translating between domains with different semantic distributions is challenging. Existing approaches include focusing the network's attention on the most discriminative part of the input image [29], augmenting the consistency loss with geometric transformations [11], replacing the consistency reconstruction term with a contrastive loss [20, 26], or ensuring that the translation is robust to small perturbations of the input [19]. However, these methods assume a bijective relationship between the classes of the source and target domains. + +Closest to our work is the model of Li et al. [23], which uses an auxiliary variable to model the information loss from information-rich domains (such as natural images) to information-poor domains (such as label maps). In turn, they use this variable to create realistic poor-to-rich domain translations. Our work differs as we precisely want to avoid the creation of spurious—albeit realistic—details when translating to a domain with unmatched classes. + +CycleGAN Steganography. Chu et al. [7] discovered that, when faced with unmatched classes, CycleGAN [36] hides information in low-amplitude and high-frequency signals. The model uses these visually imperceptible patterns to recreate the source image and bypass the cycle loss. This contradicts the intention of the cycle consistency loss and makes the model more vulnerable to adversarial attacks [7]. Luckily, multiple approaches can prevent steganography, such as blurring [11], compressing [10], or adding noise [20] to the generated source images in the back-translation. Alternatively, the back-translation from poor to rich domains can be omitted in the cycle consistency loss [27, 35]. + +While steganography in CycleGAN can be problematic, it also offers an opportunity to analyse distribution differences. In StegAnomaly [3], a model is trained to translate healthy brain scans into a low-entropy domain with cycle consistency. When removing high-frequency components, the model error reveals anomalous structures. This approach, like ours, harnesses steganography for insightful domain analysis, albeit with a different goal. + +# 3. Methods + +We consider two image domains $\mathcal{X}$ and $\mathcal{Y}$ with respective semantic class sets $\kappa_{\mathcal{X}}$ and $\kappa_{\mathcal{Y}}$ . The domains $\mathcal{X}$ and $\mathcal{Y}$ are considered bijective if there exists a function $\phi$ from $\kappa_{\mathcal{X}}$ to $\kappa_{\mathcal{Y}}$ such that each class $k_{\mathcal{X}}$ has a unique and natural semantically equivalent class $\phi(k_{\mathcal{X}})$ in $\mathcal{Y}$ , and vice-versa. A class of $\kappa_{\mathcal{Y}}$ is said to be unmatched if it doesn't have an + +![](images/59892bec01e1880155468227e0e9c721ea04fbf84afa568881098beb31237584.jpg) +(a) Backward cycle + +![](images/ceaf0a91bdc12159b0bf74fa3b88172dae9a85f74c6f5454d5a8acd819097d2f.jpg) +Figure 2. Architecture. To avoid spurious generation of unmatched classes in non-bijective image translation, we propose to make the steganographic process explicit and in feature-space. Our model runs the backward cycle first (a), then the forward translation cycle (b). Thanks to our matchability disentanglement module (c), we can separate the matchable and unmatched information while translating images from domain $\mathcal{V}$ to $\mathcal{X}$ . We can then produce generated and reconstructed images with and without unmatched features. At inference time (d), our model operates like a normal image translation model. + +![](images/93a947522354f24c0b3f00e0ddcc06966c57fc5db5c92061270e32ad685afeb8.jpg) + +![](images/ac93ac8be3a35a6d0ba27a353d4b4fc625c2c1d75e06c0685f142a90012a6a30.jpg) +(b) Forward cycle +(d) Inference + +equivalent in $\mathcal{K}_{\mathcal{X}}$ . While this notion is somewhat subjective, many applications have obvious examples: toponyms are unmatched in satellite images, and tumors in scans of healthy patients. + +Objective. Our goal is to learn a mapping $G: \mathcal{X} \mapsto \mathcal{Y}$ such that the translation $G(x)$ of any image $x \in \mathcal{X}$ aligns stylistically with images from $\mathcal{Y}$ , while preserving the semantic content of $x$ . If $\mathcal{K}_{\mathcal{Y}}$ contains an unmatched class $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ , images translated from $\mathcal{X}$ to $\mathcal{Y}$ should not contain any instances of $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ . However, in an attempt to match the distribution of $\mathcal{Y}$ , GAN models often create spurious instances of unmatched classes in their translated images. In this paper, we propose a method that employs steganography to prevent the generation of such spurious information. + +# 3.1. CycleGAN + +CycleGAN [36] learns unpaired image translation by enforcing the consistency between the input image and its backtranslation from the generated image. It uses two generators $G_{\mathcal{X} \mapsto \mathcal{Y}}: \mathcal{X} \mapsto \mathcal{Y}$ and $G_{\mathcal{Y} \mapsto \mathcal{X}}: \mathcal{Y} \mapsto \mathcal{X}$ , and two domain discriminators $D_{\mathcal{X}}: \mathcal{X} \mapsto \{0,1\}$ , $D_{\mathcal{Y}}: \mathcal{Y} \mapsto \{0,1\}$ which predict whether a sample is generated (0) or real (1). + +In the following, when considering images $x \in \mathcal{X}$ or $y \in \mathcal{Y}$ , we define the following short-hands: $x_{\mathrm{gen}} := G_{\mathcal{Y} \mapsto \mathcal{X}}(y)$ and $y_{\mathrm{gen}} := G_{\mathcal{X} \mapsto \mathcal{Y}}(x)$ for the generated images, and $x_{\mathrm{rec}} := G_{\mathcal{Y} \mapsto \mathcal{X}}(y_{\mathrm{gen}})$ and $y_{\mathrm{rec}} := G_{\mathcal{X} \mapsto \mathcal{Y}}(x_{\mathrm{gen}})$ for the reconstructed images. We now detail the losses of CycleGAN. + +Adversarial loss. The adversarial loss [13] encourages the discriminators $D_{\mathcal{X}}$ and $D_{\mathcal{Y}}$ to distinguish between authentic + +and generated images, while pushing the generators $G_{\mathcal{X}\mapsto \mathcal{Y}}$ and $G_{\mathcal{Y}\mapsto \mathcal{X}}$ to create credible images: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {G A N}} = \mathbb {E} _ {y \sim \mathcal {Y}} \log (D _ {\mathcal {Y}} (y)) + \mathbb {E} _ {x \sim \mathcal {X}} \log (1 - D _ {\mathcal {Y}} (y _ {\text {g e n}})) \\ + \mathbb {E} _ {x \sim \mathcal {X}} \log (D _ {\mathcal {X}} (x)) + \mathbb {E} _ {y \sim \mathcal {Y}} \log (1 - D _ {\mathcal {X}} (x _ {\text {g e n}})). \tag {1} \\ \end{array} +$$ + +Cycle consistency. The cycle consistency loss ensures that the back-translation of $y_{\mathrm{gen}}$ to domain $\mathcal{X}$ is close to the original image $x$ , and likewise for $x_{\mathrm{gen}}$ and $y$ : + +$$ +\mathcal {L} _ {\text {c y c}} = \mathbb {E} _ {x \sim \mathcal {X}} \| x _ {\text {r e c}} - x \| + \mathbb {E} _ {y \sim \mathcal {Y}} \| y _ {\text {r e c}} - y \|, \tag {2} +$$ + +with $\| \cdot \|$ the pixel-wise $L_{1}$ norm. + +Identity loss. The identity loss regularizes the generators to be close to identity, generally improving color composition: + +$$ +\mathcal {L} _ {\mathrm {i d}} = \mathbb {E} _ {x \sim \mathcal {X}} \| G _ {\mathcal {Y} \mapsto \mathcal {X}} (x) - x \| + \mathbb {E} _ {y \sim \mathcal {Y}} \| G _ {\mathcal {X} \mapsto \mathcal {Y}} (y) - y \|. \tag {3} +$$ + +Final Loss. The final objectives are: + +$$ +\mathcal {L} \left(G _ {\mathcal {X} \mapsto \mathcal {Y}}, G _ {\mathcal {Y} \mapsto \mathcal {X}}\right) = \mathcal {L} _ {G A N} + \lambda_ {\text {c y c}} \mathcal {L} _ {\text {c y c}} + \lambda_ {\text {i d}} \mathcal {L} _ {\text {i d}}, \tag {4} +$$ + +$$ +\mathcal {L} \left(D _ {\mathcal {X}}, D _ {\mathcal {Y}}\right) = - \mathcal {L} _ {\mathrm {G A N}}, \tag {5} +$$ + +with $\lambda_{\mathrm{cyc}}$ and $\lambda_{\mathrm{id}}$ non-negative hyperparameters. + +# 3.2. StegoGAN + +We introduce StegoGAN, a novel model building on the CycleGAN framework [36], designed specifically for scenarios where domains $\mathcal{X}$ and $\mathcal{Y}$ lack a bijective relationship. When generating images $y_{\mathrm{gen}}$ in $\mathcal{V}$ , the generator $G_{\mathcal{X} \mapsto \mathcal{Y}}$ may add + +spurious instances of an unmatched class $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ in order to deceive the discriminator $D_{\mathcal{Y}}$ . Our goal is to prevent the generation of such hallucinated instances. To achieve this, we leverage steganography to explicitly disentangle the matchable and unmatched information in the backward cycle ( $y \mapsto x_{\mathrm{gen}} \mapsto y_{\mathrm{rec}}$ ) and prevent the network from hallucinating in the forward translation ( $x \mapsto y_{\mathrm{gen}} \mapsto x_{\mathrm{rec}}$ ). See Figure 2 for the overall design of our approach. + +Steganography. In order to faithfully reconstruct $y$ with $y_{\mathrm{rec}}$ , the translated image $x_{\mathrm{gen}}$ must somehow contain information about the instances of the unmatched class $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ . CycleGAN methods typically achieve this by hiding low-amplitude and high-frequency patterns in $x_{\mathrm{gen}}$ that will be decoded by $G_{\mathcal{X} \mapsto \mathcal{Y}}$ and translated back to instances of $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ in $y_{\mathrm{rec}}$ . Adding low-intensity noise on each pixel is typically sufficient to destroy the hidden information and prevent steganography [7]. + +Steganography is often viewed as an optimization flaw that undermines the consistency loss. However, in the case of non-bijective translation, this is the only way to let $G_{\mathcal{X} \mapsto \mathcal{Y}}$ reconstruct instances of $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ in $y_{\mathrm{rec}}$ . Instead of disabling steganography, we propose to use it to our advantage to detect and prevent spurious generations. We adapt CycleGAN so that steganography takes place in feature-space instead of pixel-space, and in an explicit manner. + +Backward Cycle. We decompose the generators $G_{\mathcal{X} \mapsto \mathcal{Y}}$ and $G_{\mathcal{Y} \mapsto \mathcal{X}}$ into two components: an encoder and a decoder, such that $G_{\mathcal{X} \mapsto \mathcal{Y}} = G_{\mathcal{X} \mapsto \mathcal{Y}}^{\mathrm{dec}} \circ G_{\mathcal{X} \mapsto \mathcal{Y}}^{\mathrm{enc}}$ and $G_{\mathcal{Y} \mapsto \mathcal{X}} = G_{\mathcal{Y} \mapsto \mathcal{X}}^{\mathrm{dec}} \circ G_{\mathcal{Y} \mapsto \mathcal{X}}^{\mathrm{enc}}$ . The encoders map their inputs to feature maps of spatial dimension $H \times W$ , where each pixel has $C$ channels. In the following, we denote the intermediary representation of $y$ in $G_{\mathcal{Y} \mapsto \mathcal{X}}$ by $z_{\mathrm{gen}} := G_{\mathcal{Y} \mapsto \mathcal{X}}^{\mathrm{enc}}(y)$ . The feature map $z_{\mathrm{gen}}$ encodes information about both matchable and unmatched classes, which we want to disentangle. + +We introduce a network $M$ : $\mathbb{R}^{H \times W \times C} \mapsto [0,1]^{H \times W \times C}$ that assigns an unmatchedability score between 0 and 1 to each pixel and channel. Here, a score of 1 indicates that the information does not have a counterpart in domain $\mathcal{X}$ , while it does for 0. This process gives us the unmatchedability mask $M(z_{\mathrm{gen}})$ , which we use to split $z_{\mathrm{gen}}$ into its matchable and unmatched parts: + +$$ +z _ {\text {g e n}} ^ {\text {u n m a t c h}} = M \left(z _ {\text {g e n}}\right) \odot z \tag {6} +$$ + +$$ +z _ {\text {g e n}} ^ {\text {m a t c h}} = \left(1 - M \left(z _ {\text {g e n}}\right)\right) \odot z, \tag {7} +$$ + +with $\odot$ the pixel-wise and channel-wise Hadamard product. In our model, the generated image $x_{\mathrm{gen}}$ is computed using only the matchable part of the representation: + +$$ +x _ {\text {g e n}} = G _ {\mathcal {Y} \mapsto \mathcal {X}} ^ {\text {d e c}} \left(z _ {\text {g e n}} ^ {\text {m a t c h}}\right). \tag {8} +$$ + +We produce two reconstructions of $y$ : $y_{\mathrm{rec}}^{\mathrm{clean}}$ , which is a direct back-translation of $x_{\mathrm{gen}}$ into the $\mathcal{V}$ domain: $y_{\mathrm{rec}}^{\mathrm{clean}} =$ + +$G_{\mathcal{X}\mapsto \mathcal{Y}}(x_{\mathrm{gen}})$ ; and $y_{\mathrm{rec}}$ , which is generated by decoding a combination of the unmatched part of $z_{\mathrm{gen}}$ and the features extracted by $G_{\mathcal{X}\mapsto \mathcal{Y}}^{\mathrm{enc}}$ from a noise-perturbed version of $x_{\mathrm{gen}}$ : + +$$ +y _ {\text {r e c}} = G _ {\mathcal {X} \mapsto \mathcal {Y}} ^ {\text {d e c}} \left(G _ {\mathcal {X} \mapsto \mathcal {Y}} ^ {\text {e n c}} \left(x _ {\text {g e n}} + \epsilon\right) + z _ {\text {g e n}} ^ {\text {u n m a t c h}}\right), \tag {9} +$$ + +with $\epsilon$ denoting random Gaussian noise of low amplitude applied to each pixel and channel of $x_{\mathrm{gen}}$ . This noise is added to destroy potential steganographic information in $x_{\mathrm{gen}}$ , therefore forcing $G_{\mathcal{X} \mapsto \mathcal{Y}}$ to rely only on $z_{\mathrm{gen}}^{\mathrm{unmatch}}$ to reconstruct unmatched features in $y_{\mathrm{rec}}$ . + +The key mechanisms to disentangle matchable and unmatched information are twofold: (i) disturbing direct steganography with random noise, and (ii) explicitly providing unmatched information to $G_{\mathcal{X} \mapsto \mathcal{Y}}$ in feature-space. + +Forward Cycle. In the forward cycle $x \to y_{\mathrm{gen}} \to x_{\mathrm{rec}}$ , the generator $G_{\mathcal{X} \mapsto \mathcal{Y}}$ may create spurious instances of unmatched classes when translating $x$ to $\mathcal{Y}$ to fulfill the expectations of the discriminator $D_y$ . To address this, we perform two distinct translations of $x$ in $\mathcal{Y}$ : $y_{\mathrm{gen}}$ has explicit access to the steganographic information $z_{\mathrm{gen}}^{\mathrm{unmatch}}$ extracted from the backward cycle, while $y_{\mathrm{gen}}^{\mathrm{clean}}$ does not: + +$$ +y _ {\text {g e n}} = G _ {\mathcal {X} \mapsto \mathcal {Y}} ^ {\text {d e c}} \left(G _ {\mathcal {X} \mapsto \mathcal {Y}} ^ {\text {e n c}} (x) + z _ {\text {g e n}} ^ {\text {u n m a t c h}}\right) \tag {10} +$$ + +$$ +y _ {\text {g e n}} ^ {\text {c l e a n}} = G _ {\chi \mapsto y} (x). \tag {11} +$$ + +The rationale is that $G_{\mathcal{X} \mapsto \mathcal{Y}}^{\mathrm{dec}}$ has explicit access to information about the unmatched classes of $y$ , so it is not incentivized to invent them. For consistency with the backward step, where the decoder of $G_{\mathcal{Y} \mapsto \mathcal{X}}$ processes only matchable information as defined in (7), we use the same disentangle-ment approach for generating $x_{\mathrm{rec}}$ : + +$$ +x _ {\text {r e c}} = G _ {\mathcal {Y} \mapsto \mathcal {X}} ^ {\text {d e c}} \left(\left(1 - M \left(z _ {\text {r e c}}\right)\right) \odot z _ {\text {r e c}}\right), \tag {12} +$$ + +where $z_{\mathrm{rec}} = G_{\mathcal{Y} \mapsto \mathcal{X}}^{\mathrm{enc}}(y_{\mathrm{gen}})$ is the intermediary representation of $y_{\mathrm{gen}}$ in the forward cycle. + +Mask Regularization. To avoid degenerate behaviors of our explicit steganography mechanism, we enforce two priors on the unmatchedability masks: (i) given that a well-posed translation problem predominantly involves matchable features, the masks should be sparse; (ii) to improve the model's interpretability, we favor mask values near 0 or 1, representing clear decisions about matchability. To enforce these priors, we regularize the masks with the non-convex $L_{0.5}$ norm [34]: + +$$ +\mathcal {L} _ {r e g} = \mathbb {E} _ {y \sim \mathcal {Y}} \| M \left(z _ {\text {g e n}}\right) \| _ {0. 5} + \mathbb {E} _ {x \sim \mathcal {X}} \| M \left(z _ {\text {r e c}}\right) \| _ {0. 5}. \tag {13} +$$ + +Matchable Consistency. The images $y_{\mathrm{gen}}$ and $y_{\mathrm{gen}}^{\mathrm{clean}}$ , as well as $y_{\mathrm{rec}}$ and $y_{\mathrm{rec}}^{\mathrm{clean}}$ , should be identical outside of unmatched regions. To enforce this constraint, we design a function $I$ which takes an unmatchedness mask $m$ as input, takes the channel-wise maximum values of all pixels, flips its + +![](images/a731982eda57a52a69994bdfbf56dab32ede3c9d21d049eaf0df8892facc4dc8.jpg) +Figure 3. Qualitative Comparison. We report reconstructions from the test sets of PlanIGN (top two rows), GoogleMap (row 3 and 4), and MRI (last two rows). Contrary to the other models, StegoGAN does not hallucinate spurious toponyms, highways (orange roads), or tumors (white areas) and shows better semantic correspondences during translation. + +value from [0, 1] to [1, 0], and upsamples the results to the dimensions of the input images. + +$$ +I (m) = \operatorname {u p s a m p l e} \left(1 - \max _ {c} m\right). \tag {14} +$$ + +The obtained consistency masks $I(m)$ have values close to 1 for pixels with only matchable content, and close to 0 otherwise. This enables us to define a loss for $y_{\mathrm{gen}}^{\mathrm{clean}}$ and $y_{\mathrm{rec}}^{\mathrm{clean}}$ that focuses solely on regions with matchable features: + +$$ +\begin{array}{l} \mathcal {L} _ {\text {m a t c h}} = \mathbb {E} _ {y \sim \mathcal {Y}} \| I (M (z _ {\text {g e n}})) \odot (y _ {\text {g e n}} - y _ {\text {g e n}} ^ {\text {c l e a n}}) \| \\ + \mathbb {E} _ {x \sim \mathcal {X}} \| I (M (z _ {\mathrm {r e c}})) \odot (y _ {\mathrm {r e c}} - y _ {\mathrm {r e c}} ^ {\text {c l e a n}}) \|. \tag {15} \\ \end{array} +$$ + +Final Objective. In addition to the standard CycleGAN loss components (4-5), we integrate $\mathcal{L}_{\mathrm{match}}$ and $\mathcal{L}_{\mathrm{reg}}$ into the overall loss function $\mathcal{L}(G_{\mathcal{X} \mapsto \mathcal{Y}}, G_{\mathcal{Y} \mapsto \mathcal{X}})$ , weighted by + +their respective coefficients $\lambda_{\mathrm{reg}}$ and $\lambda_{\mathrm{match}}$ . Crucially, our proposed approach remains unsupervised, requiring neither aligned images from $\mathcal{X}$ and $\mathcal{Y}$ nor specific annotations of unmatched features. + +# 4. Experiments + +In this section, we assess the improvements brought by our method for non-bijective image translation across various datasets and compare them with existing models, both qualitatively and quantitatively. + +Implementation details. We follow the setting of CyleGAN [36] as our baseline model: the generators are Resnets [15] and the discriminator is based on PatchGAN [18]. We define the encoders as the first half of the generator's layers and the decoders as the second half. The + +![](images/700ea251354a90565c44a0be7003610a7a1b2fe4d87f9e2a40cc88b51b08713a.jpg) +Figure 4. Results on GoogleMaps. We report the performance of several top-performing image translation models for different ratios of unmatched features in the target domain of the training set. StegoGAN handles higher ratios better than competing methods. + +unmatchability mask predictor $M$ is defined as a small 3-layer convolutional neural network (CNN). We set $\lambda_{\mathrm{cyc}} = 10$ , $\lambda_{\mathrm{idt}} = 0.5$ as in [36] and $\lambda_{\mathrm{match}} = 1$ . The amplitude of the perturbation $\epsilon$ is 0.01 as in [7]. The Appendix provides more architecture and training details. + +# 4.1. Datasets + +We assess the performance of StegoGAN across several image translation tasks that feature unmatched classes. Each dataset follows a consistent structure: the training set includes images from the source domain $\mathcal{X}$ devoid of a specific class (e.g., tumors, motorways, toponyms) while the target domain $\mathcal{Y}$ does include that class. The test set comprises paired images from both domains, specifically excluding the unmatched class. This setup allows us to quantify the models' hallucinations: any generated instances of the unmatched class are necessarily spurious and due to its presence in the training set. We release all three curated datasets on the Zenodo platform and provide details below. + +PlanIGN. $\mathcal{X}$ : Aerial Photo, $\mathcal{Y}$ : Maps, $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ : Text. We construct a dataset using open data from the French National Mapping Agency (IGN), comprising 1900 aerial (ortho-)images at 3m spatial resolution, and two versions of their corresponding topographic maps: one with and one without toponyms. This dataset presents a clear unmatched class: place names. The training set includes 1000 maps with toponyms and 1000 aerial images, while the test set comprises 900 map samples without toponyms and their corresponding aerial images. + +GoogleMaps. $\mathcal{X}$ : Aerial Photo, $\mathcal{V}$ : Maps, $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ : Highways. The GoogleMaps dataset [18] is a standard bench + +mark for image translation tasks [19, 20]. It contains 1096 map/image pairs for training and 1098 for testing. To create a controlled non-bijective scenario, we exclude all satellite images that show highways and sample the maps of the training set to contain varying proportions of maps with highways, ranging from $0\%$ to $65\%$ , for a fixed total of 548 maps. For the test set we selected 898 pairs without highways. + +Brats MRI $\mathcal{X}$ : T1 Scans, $\mathcal{V}$ : FLAIR, $k_{\mathcal{Y}}^{\mathrm{unmatch}}$ : Tumors. Lastly, we used a dataset of brain MRI scans [25] with two modalities: T1 (naive) and FLAIR (T2 Fluid Attenuated Inversion Recovery) [14]. We adapt the protocol that Cohen et al. [8] used for the Brats2013 datasets [24] to the more recent Brats2018 [2] dataset by varying the percentage of scans with tumors in the target domain. We selected transverse slices from the $60^{\circ}$ to $100^{\circ}$ range in the caudocranial direction [1] for both T1 and FLAIR scans. Each scan was classified as tumorous if more than $1\%$ of its pixels were labeled as such, and as healthy if it contained no tumor pixels. The training set contains 800 images from each modality, with all source images (T1) being healthy and the target domain (FLAIR) comprising $60\%$ tumorous scans. The test set contains 335 paired scans of healthy brains. + +# 4.2. Evaluation metrics + +We use a broad range of metrics to evaluate the performance of StegoGAN and other image translation algorithms in the non-bijective setting: + +FID and KID. The Fréchet Inception Distance (FID) [16] and Kernel Inception Distance (KID) [4] are widely used to quantify the similarity between the distributions of real and generated images in the target domain. + +Table 1. Quantitative Comparison on PlanIGN. Our model shows a remarkably better performance than other existing models. + +
MethodRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
CUT [26]30.546.755.868.42.8
CycleGAN [36]27.015.157.697.56.6
DRIT [21]34.833.636.976.43.8
GcGAN [11]32.754.556.9110.88.2
SRUNIT [19]32.348.852.860.22.2
StegoGAN (ours)22.566.174.858.42.4
+ +RMSE, $\mathbf{Acc}(\sigma_1)$ , and $\mathbf{Acc}(\sigma_2)$ . As the test sets comprise paired images from both domains, we can directly compare the Root Mean Square Error (RMSE) between the real and predicted images in the target domain. We count a predicted pixel as correctly predicted if it deviate by less than a fixed threshold in any of the color channels [11]. We use $\sigma_1 = 5$ and $\sigma_2 = 10$ for the GoogleMap dataset and $\sigma_1 = 2$ and $\sigma_2 = 5$ for the less colorful PlanIGN dataset. + +pFPR and iFPR. In the GoogleMap dataset, highways are always depicted in orange, allowing us to label pixels where all color channels differ by less than 20 units from (240, 160, 30) as highways. In the Brats MRI dataset, we use a pretrained tumor detector [5] to find spurious tumors in the generated images. This allows us to compute the average false positive rate per pixel (pFPR) and per instance (iFPR) of the generated images. + +# 4.3. Results + +Qualitative Results. Figure 3 showcases StegoGAN's qualitative performance against other image translation algorithms. Notably, StegoGAN effectively avoids generating unmatched classes such as texts, highways, and tumors, while producing high-quality image translations. + +Quantitative Results. On the PlanIGN dataset (Table 1) and the Brats MRI dataset (Table 2), StegoGAN outperforms others in fidelity, achieving the lowest RMSE by a margin of 4.5 on PlanIGN and by 3.5 for Brats MRI. Furthermore, it significantly enhances pixel accuracy, with improvements of $+11.6$ in $\mathrm{Acc}(\sigma_1)$ and $+17.2$ in $\mathrm{Acc}(\sigma_2)$ on PlanIGN. In the MRI dataset, StegoGAN dramatically reduces false positive rates—over $20\times$ lower than CycleGAN and $10\times$ less than the next best model SRUNIT (for pFPR). + +On the GoogleMap dataset, as shown in Figure 4, StegoGAN's performance is on par with CycleGAN at $0\%$ unmatched cases and remains stable even as this ratio increases, unlike other methods that degrade. Remarkably, StegoGAN maintains a consistent false positive rate of 0 across all tests, while this rate increases for all other methods. + +Unmatchability Masks. In Figure 5, we illustrate the emergent ability of the unmatchedability masks to trace the outline of unmatched class instances like toponyms, highways, and tumors. This aspect highlights the versatility of our + +Table 2. Quantitative Comparison on Brats MRI Flair $\rightarrow$ T1. Our model outperforms competing method in terms of both reconstruction accuracy and consistency. + +
MethodRMSE↓pFPR(‰)↓iFPR↓FID↓KID↓
CUT [26]39.817.023.0103.98.8
CycleGAN [36]39.921.922.789.87.7
DRIT [21]53.018.541.2123.411.6
GcGAN [11]41.724.722.461.93.5
SRUNIT [19]42.515.121.858.92.9
StegoGAN (ours)36.31.14.258.52.4
+ +![](images/e3a0027370b66e1203ff5f025d36802aa4f78f746092ebffb624b4bfc011d4e1.jpg) +Figure 5. Unmatchability Masks. The unmatchedability masks predicted in the backward cycle follow the instances of unmatched features in the target domain: toponyms, highways, and tumors. + +Table 3. Ablation Study on Encoder Depth. We evaluate the impact of changing the depth of the encoder on the reconstruction fidelity and the quality of unmatchedability masks. Depth= -1 or 8 means no encoder or no decoder, respectively. + +
DepthMaskPrediction
mIOU↑Prec.↑recall↑RMSE↓A(σ1)↑A(σ2)↑FID↓KID↓
-126.627.181.222.464.374.258.82.5
125.225.881.222.566.174.858.42.4
327.127.980.422.861.673.462.93.0
530.833.469.524.252.770.662.32.6
847.360.160.024.553.570.762.72.7
+ +approach, which functions without explicit supervision or aligned images, offering a tool to explore the pairwise semantic differences between arbitrary datasets. + +# 4.4. Ablation study and analysis + +We explore the impact of our main design choices, as well as further capabilities and limitations of our approach. See the Appendix for further ablations. + +![](images/8a507aa641d769355d146cd0851f27dcf1a1355b352618a59250cb2fe32ccc7c.jpg) +Figure 6. Impact of Encoder Depth. We visualize the unmatchedability mask for encoders of different depths for the PlanIGN dataset. Shallower encoders consider more features as unmatched. + +Encoder Ablation. We conducted an ablation study on the definition of the intermediary representation $z$ by varying the depth at which the "encoder" ends and the "decoder" starts within the generator. Given that our generators consist of 9 consecutive convolutional blocks, we experimented with different configurations: -1 (indicating no decoder), 1 (the configuration used in our paper), as well as depths of 3, 5, and 8 (implying no decoder). We report in Table 3 the reconstruction error of these models, as well as the fidelity of the consistency mask with the toponym text mask. We observe that shallow encoders have better reconstruction accuracy while the consistency masks of deeper encoders better approximate the text masks. + +Visualizing these masks in Figure 6, we observe that shallow encoders consider complex features such as highways and rivers as unmatched features, while deeper encoders do not. Shallower encoders seem more influenced by the variation in appearance (e.g., rivers being sometimes covered in vegetation or with varying colors) while deeper encoders focus on high-level semantics. We argue that both definitions are equally valid, and that varying the depth of the encoders can provide insights into the nature of the semantic mismatch between datasets. + +Parameterization. In Table 4, we analyze the effects of omitting the additional terms $\mathcal{L}_{\mathrm{reg}}$ and $\mathcal{L}_{\mathrm{match}}$ from the loss function $\mathcal{L}$ in Equation (4). We show that while $\mathcal{L}_{\mathrm{match}}$ generally yields modest improvements across all metrics, $\mathcal{L}_{\mathrm{reg}}$ is pivotal, particularly for learning the target distribution. This outcome aligns with our expectations, as the absence of $\mathcal{L}_{\mathrm{reg}}$ allows the network to transmit all information, matchable or not, to the $G_{\mathcal{Y} \mapsto \mathcal{X}}$ decoder without repercussions, impeding the training of the $G_{\mathcal{X} \mapsto \mathcal{Y}}$ encoder. + +Limitations. We augment the CycleGAN framework with a module $M$ and two hyper-parameters $\lambda_{\mathrm{match}}$ and $\lambda_{\mathrm{reg}}$ , thereby adding to the complexity of its training dynamics. Moreover, the concept of unmatchedability, integral to our approach, is inherently subjective. Given enough semantic detail, any two distinct datasets could be considered unmatched. As a result, fine-tuning the hyperparameter $\lambda_{\mathrm{reg}}$ is essential to balance the elimination of hallucinations against the reten + +Table 4. Impact of Additional Loss Terms. We evaluate on the GoogleMap dataset the effect of removing our proposed losses. $\mathcal{L}_{\mathrm{match}}$ has a small impact while $\mathcal{L}_{\mathrm{reg}}$ is pivotal. + +
SettingsRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
LregLmatch
✓✓22.741.767.177.36.8
✓X24.141.564.788.07.5
X✓26.726.758.9271.126.6
XX25.025.061.0303.633.4
+ +tion of necessary details: increasing its value leads to more conservative masks and improves the visual appearance of the generated images, at the cost of more spurious features. Visualizing the consistency mask is often a useful form of guidance. More details on learning strategies can be found in the Appendix. + +We also acknowledge the potential of recent denoising diffusion models for image-to-image translation tasks [22, 32]. While our method is not confined to GANs and could be adapted to diffusion models with cycle consistency losses [28, 31], unpaired image translation with diffusion models is a nascent field with unique challenges. We plan to explore this area in future research. + +# 5. Conclusions + +We have introduced StegoGAN, a model built upon the CycleGAN framework, which leverages the mechanism of steganography to address the challenges of non-bijective image-to-image translation. Our model demonstrates an improved capability to handle divergent distributions between domains, as evidenced by its performance across various datasets, including aerial imagery, topographic maps, and MRI scans. We hope that our work will inspire further research in the little-studied area of non-bijective image translation. We find this research direction important to ensure image translation models are transferable and applicable in real-world scenarios, where datasets rarely conform to the level of curation typically found in research benchmarks. + +# References + +[1] Simon Andermatt, Antal Horváth, Simon Pezold, and Philippe Cattin. Pathology segmentation using distributional differences to images of healthy origin. In *Brainlesion: Glioma, Multiple Sclerosis, Stroke and Traumatic Brain Injuries: 4th International Workshop*, *BrainLes* 2018, Held in Conjunction with MICCAI*2018*, Granada, Spain, September 16, 2018, Revised Selected Papers, Part I 4, pages 228-238. Springer, 2019. 6 +[2] Spyridon Bakas, Mauricio Reyes, Andras Jakab, Stefan Bauer, Markus Rempfler, Alessandro Crimi, Russell Takeshi Shinohara, Christoph Berger, Sung Min Ha, Martin Rozycki, et al. Identifying the best machine learning algorithms for brain tumor segmentation, progression assessment, and overall survival prediction in the brats challenge. arXiv preprint arXiv:1811.02629, 2018. 6 +[3] Christoph Baur, Robert Graf, Benedikt Wiestler, Shadi Albarqouni, and Nassir Navab. Steganomaly: Inhibiting cyclegan steganography for unsupervised anomaly detection in brain mri. In International Conference on Medical Image Computing and Computer-Assisted Intervention, pages 718-727. Springer, 2020. 2 +[4] Mikołaj Binkowski, Danica J Sutherland, Michael Arbel, and Arthur Gretton. Demystifying mmd gans. arXiv preprint arXiv:1801.01401, 2018. 6 +[5] Mateusz Buda, Ashirbani Saha, and Maciej A Mazurowski. 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Advances in neural information processing systems, 27, 2014. 2, 3 +[14] Joseph V Hajnal, David J Bryant, Larry Kasuboski, Pradip M Pattany, Beatrice De Coene, Paul D Lewis, Jacqueline M Pennock, Angela Oatridge, Ian R Young, and Graeme M Bydder. Use of fluid attenuated inversion recovery (FLAIR) pulse sequences in MRI of the brain. Journal of computer assisted tomography, 1992. 6 +[15] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770-778, 2016. 5 +[16] Martin Heusel, Hubert Ramsauer, Thomas Unterthiner, Bernhard Nessler, and Sepp Hochreiter. Gans trained by a two time-scale update rule converge to a local nash equilibrium. Advances in neural information processing systems, 30, 2017. 6 +[17] Xun Huang, Ming-Yu Liu, Serge Belongie, and Jan Kautz. Multimodal unsupervised image-to-image translation. 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The multimodal brain tumor image segmentation benchmark (brats). IEEE transactions on medical imaging, 34(10):1993-2024, 2014. 6 +[26] Taesung Park, Alexei A. Efros, Richard Zhang, and Jun-Yan Zhu. Contrastive learning for unpaired image-to-image translation. In European Conference on Computer Vision, 2020. 2, 5, 6, 7 +[27] Luca Sestini, Benoit Rosa, Elena De Momi, Giancarlo Ferrigno, and Nicolas Padoy. Fun-sis: A fully unsupervised approach for surgical instrument segmentation. Medical Image Analysis, 85:102751, 2023. 2 +[28] Xuan Su, Jiaming Song, Chenlin Meng, and Stefano Ermon. Dual diffusion implicit bridges for image-to-image translation. In ICLR, 2023. 8 +[29] Hao Tang, Hong Liu, Dan Xu, Philip HS Torr, and Nicu Sebe. AttentionGAN: Unpaired image-to-image translation using attention-guided generative adversarial networks. IEEE transactions on neural networks and learning systems, 2021. 2 +[30] Weilun Wang, Wen gang Zhou, Jianmin Bao, Dong Chen, and Houqiang Li. Instance-wise hard negative example generation for contrastive learning in unpaired image-to-image translation. 2021 IEEE/CVF International Conference on Computer Vision (ICCV), pages 14000-14009, 2021. 2 +[31] Chen Henry Wu and Fernando De la Torre. A latent space of stochastic diffusion models for zero-shot image editing and guidance. In ICCV, 2023. 8 +[32] Bin Xia, Yulun Zhang, Shiyin Wang, Yitong Wang, Xinglong Wu, Yapeng Tian, Wenming Yang, Radu Timotfe, and Luc Van Gool. Diffi2i: Efficient diffusion model for image-to-image translation. arXiv preprint arXiv:2308.13767, 2023. 8 +[33] Shaoan Xie, Qirong Ho, and Kun Zhang. Unsupervised image-to-image translation with density changing regularization. Advances in Neural Information Processing Systems, 35:28545-28558, 2022. 2 +[34] Zongben Xu, Hai Zhang, Yao Wang, XiangYu Chang, and Yong Liang. L 1/2 regularization. Science China Information Sciences, 53:1159-1169, 2010. 4 +[35] Ran Yi, Yong-Jin Liu, Yu-Kun Lai, and Paul L Rosin. Unpaired portrait drawing generation via asymmetric cycle mapping. In IEEE Conference on Computer Vision and Pattern Recognition (CVPR '20), pages 8214-8222, 2020. 2 +[36] Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A Efros. Unpaired image-to-image translation using cycle-consistent adversarial networks. 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However, this assumption does not always hold in real-world scenarios due to divergent distributions, different class sets, and asymmetrical information representation. As conventional GANs attempt to generate images that match the distribution of the target domain, they may hallucinate spurious instances of classes absent from the source domain, thereby diminishing the usefulness and reliability of translated images. CycleGAN-based methods are also known to hide the mismatched information in the generated images to bypass cycle consistency objectives, a process known as steganography. In response to the challenge of non-bijective image translation, we introduce StegoGAN, a novel model that leverages steganography to prevent spurious features in generated images. Our approach enhances the semantic consistency of the translated images without requiring additional postprocessing or supervision. Our experimental evaluations demonstrate that StegoGAN outperforms existing GAN-based models across various non-bijective image-to-image translation tasks, both qualitatively and quantitatively. Our code and pretrained models are accessible at https://github.com/sian-wusidi/StegoGAN." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 48, + 587, + 127, + 599 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 587, + 127, + 599 + ], + "spans": [ + { + "bbox": [ + 48, + 587, + 127, + 599 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 608, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 608, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 46, + 608, + 288, + 693 + ], + "type": "text", + "content": "Image-to-image translation is an active research subject with impactful applications ranging from changing the style of images [12, 36] to automatically creating maps from satellite images [36] or changing the modality of medical images [9]. When the source and target domains exhibit substantial differences, ensuring the semantic consistency between input images and their translation becomes particularly challeng-" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 299, + 239, + 544, + 435 + ], + "blocks": [ + { + "bbox": [ + 299, + 239, + 544, + 435 + ], + "lines": [ + { + "bbox": [ + 299, + 239, + 544, + 435 + ], + "spans": [ + { + "bbox": [ + 299, + 239, + 544, + 435 + ], + "type": "image", + "image_path": "02c4a3768175c9371ced9722a95b20d0aa1dabddf845933c309c417f2b68e07e.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 298, + 433, + 449, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 433, + 449, + 442 + ], + "spans": [ + { + "bbox": [ + 298, + 433, + 449, + 442 + ], + "type": "text", + "content": "(b) GAN models hallucinate spurious features." + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 304, + 445, + 542, + 525 + ], + "blocks": [ + { + "bbox": [ + 304, + 445, + 542, + 525 + ], + "lines": [ + { + "bbox": [ + 304, + 445, + 542, + 525 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 542, + 525 + ], + "type": "image", + "image_path": "34ed5233575711c28f251edc758ae15016cf15bdae7b4cf5ba0b2c5809e65447.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 307, + 530, + 526, + 541 + ], + "lines": [ + { + "bbox": [ + 307, + 530, + 526, + 541 + ], + "spans": [ + { + "bbox": [ + 307, + 530, + 526, + 541 + ], + "type": "text", + "content": "(c) CycleGAN models hide unmatched features by steganography." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_footnote" + }, + { + "bbox": [ + 304, + 555, + 547, + 632 + ], + "lines": [ + { + "bbox": [ + 304, + 555, + 547, + 632 + ], + "spans": [ + { + "bbox": [ + 304, + 555, + 547, + 632 + ], + "type": "text", + "content": "Figure 1. Non-Bijective Translation. When image domains present classes without equivalence (a), GAN models tend to hallucinate spurious features when translating images (b). A related phenomenon is steganography, where CycleGAN-based models covertly encode features in low-amplitude patterns to bypass cycle consistency (c). Instead of disabling this phenomenon, we harness steganography to prevent the hallucination of spurious features." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 640, + 546, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 640, + 546, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 640, + 546, + 666 + ], + "type": "text", + "content": "ing [8]. Our work explores the surprisingly uncharted field of adversarial, non-bijective image-to-image translation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "Non-Bijective Image Translation. Existing translation methods assume a one-to-one correspondence between classes of the source and target domains: horses to zebras [36], satellite image features to their cartographic repre" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 495, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 703, + 126, + 712 + ], + "type": "text", + "content": "*Equal contribution." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7922" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 191 + ], + "type": "text", + "content": "sentation [6, 36], or distinct cell types viewed under varying medical imaging modalities [9]. However, as illustrated in Figure 1a, this assumption does not always hold. For instance, when considering a dataset with horses and one with zebras in their habitat, zebra images may include background elements with no equivalent in the source domain—like elephants. Similarly, in map translation toponyms (i.e., place names printed onto the map) do not have counterparts in satellite images [6]. We qualify classes of the target domain without equivalent in the source domain as unmatched." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 192, + 289, + 324 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 192, + 289, + 324 + ], + "spans": [ + { + "bbox": [ + 46, + 192, + 289, + 324 + ], + "type": "text", + "content": "As illustrated in Figure 1b, by trying to reproduce the distribution of the target domain, GANs may hallucinate spurious features or textures in the generated images, i.e., objects without equivalent in the source image. This is particularly frequent for unmatched classes [8]. While this can be perfectly acceptable for some applications [23], adding nonexistent tumors in MRI scans or incorrect toponyms in maps can severely degrade the usefulness of the translation result. Instead of detecting and removing these artifacts in post-processing, we propose an approach that directly prevents their generation using steganography." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 327, + 289, + 495 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 327, + 289, + 495 + ], + "spans": [ + { + "bbox": [ + 46, + 327, + 289, + 495 + ], + "type": "text", + "content": "GAN Steganography. To ensure its semantic consistency, CycleGAN [36] back-translates the generated image to the source image. However, unmatched classes of the source domain cannot be encoded into meaningful features in the images generated in the target domain. As shown in Figure 1c, these models can instead cheat by encoding the necessary information into quasi-invisible patterns in the generated images [7]. This process, known as steganography, allows GANs to perform seemingly impossible back-translation. For instance, in a map-to-satellite task, the model can restore the correct names of towns from satellite images that appear visually correct. This phenomenon is often viewed as a quirky optimization flaw, easily fixable by adding noise or blur [11, 20, 26]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 498, + 289, + 606 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 289, + 606 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 289, + 606 + ], + "type": "text", + "content": "StegoGAN. We propose StegoGAN, a model that leverages steganography to detect and mitigate semantic misalignment between domains. In settings where the domain mapping is non-bijective, StegoGAN experimentally demonstrates superior semantic consistency over other GAN-based models both visually and quantitatively, without requiring detection or inpainting steps. In addition, we publish three datasets from open-access sources as a benchmark for evaluating non-bijective image translation models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 618, + 134, + 631 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 618, + 134, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 618, + 134, + 631 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 289, + 715 + ], + "type": "text", + "content": "GAN-Based Image Translation. GAN-based image translation models transfer the style of images between domains with an adversarial perceptual loss [13]. When pairs of aligned images from both domains are available, the translated images can also be supervised by their fidelity with target images [18]. In practice, such pairs are not always" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 144 + ], + "type": "text", + "content": "available or even possible to obtain. In the absence of explicit equivalence between images, preserving the semantics of the input in the generated image is a priority. Multiple approaches have been proposed to address this challenge, such as density-based regularization [33], spatial mutual information [20, 26, 30], or cycle consistency losses [17, 21, 36]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 148, + 548, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 148, + 548, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 148, + 548, + 266 + ], + "type": "text", + "content": "Asymmetric Image Translation. Translating between domains with different semantic distributions is challenging. Existing approaches include focusing the network's attention on the most discriminative part of the input image [29], augmenting the consistency loss with geometric transformations [11], replacing the consistency reconstruction term with a contrastive loss [20, 26], or ensuring that the translation is robust to small perturbations of the input [19]. However, these methods assume a bijective relationship between the classes of the source and target domains." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 268, + 547, + 364 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 268, + 547, + 364 + ], + "spans": [ + { + "bbox": [ + 304, + 268, + 547, + 364 + ], + "type": "text", + "content": "Closest to our work is the model of Li et al. [23], which uses an auxiliary variable to model the information loss from information-rich domains (such as natural images) to information-poor domains (such as label maps). In turn, they use this variable to create realistic poor-to-rich domain translations. Our work differs as we precisely want to avoid the creation of spurious—albeit realistic—details when translating to a domain with unmatched classes." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 367, + 548, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 367, + 548, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 367, + 548, + 511 + ], + "type": "text", + "content": "CycleGAN Steganography. Chu et al. [7] discovered that, when faced with unmatched classes, CycleGAN [36] hides information in low-amplitude and high-frequency signals. The model uses these visually imperceptible patterns to recreate the source image and bypass the cycle loss. This contradicts the intention of the cycle consistency loss and makes the model more vulnerable to adversarial attacks [7]. Luckily, multiple approaches can prevent steganography, such as blurring [11], compressing [10], or adding noise [20] to the generated source images in the back-translation. Alternatively, the back-translation from poor to rich domains can be omitted in the cycle consistency loss [27, 35]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 512, + 547, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 512, + 547, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 512, + 547, + 608 + ], + "type": "text", + "content": "While steganography in CycleGAN can be problematic, it also offers an opportunity to analyse distribution differences. In StegAnomaly [3], a model is trained to translate healthy brain scans into a low-entropy domain with cycle consistency. When removing high-frequency components, the model error reveals anomalous structures. This approach, like ours, harnesses steganography for insightful domain analysis, albeit with a different goal." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 620, + 367, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 620, + 367, + 633 + ], + "spans": [ + { + "bbox": [ + 306, + 620, + 367, + 633 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": "We consider two image domains " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " with respective semantic class sets " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\kappa_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\kappa_{\\mathcal{Y}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ". The domains " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " are considered bijective if there exists a function " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\kappa_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\kappa_{\\mathcal{Y}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " such that each class " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{X}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " has a unique and natural semantically equivalent class " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\phi(k_{\\mathcal{X}})" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": ", and vice-versa. A class of " + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\kappa_{\\mathcal{Y}}" + }, + { + "bbox": [ + 304, + 641, + 547, + 715 + ], + "type": "text", + "content": " is said to be unmatched if it doesn't have an" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7923" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 72, + 541, + 178 + ], + "blocks": [ + { + "bbox": [ + 72, + 72, + 541, + 178 + ], + "lines": [ + { + "bbox": [ + 72, + 72, + 541, + 178 + ], + "spans": [ + { + "bbox": [ + 72, + 72, + 541, + 178 + ], + "type": "image", + "image_path": "59892bec01e1880155468227e0e9c721ea04fbf84afa568881098beb31237584.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 147, + 186, + 211, + 195 + ], + "lines": [ + { + "bbox": [ + 147, + 186, + 211, + 195 + ], + "spans": [ + { + "bbox": [ + 147, + 186, + 211, + 195 + ], + "type": "text", + "content": "(a) Backward cycle" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 65, + 198, + 167, + 273 + ], + "blocks": [ + { + "bbox": [ + 65, + 198, + 167, + 273 + ], + "lines": [ + { + "bbox": [ + 65, + 198, + 167, + 273 + ], + "spans": [ + { + "bbox": [ + 65, + 198, + 167, + 273 + ], + "type": "image", + "image_path": "ceaf0a91bdc12159b0bf74fa3b88172dae9a85f74c6f5454d5a8acd819097d2f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "lines": [ + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "type": "text", + "content": "Figure 2. Architecture. To avoid spurious generation of unmatched classes in non-bijective image translation, we propose to make the steganographic process explicit and in feature-space. Our model runs the backward cycle first (a), then the forward translation cycle (b). Thanks to our matchability disentanglement module (c), we can separate the matchable and unmatched information while translating images from domain " + }, + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 282, + 547, + 338 + ], + "type": "text", + "content": ". We can then produce generated and reconstructed images with and without unmatched features. At inference time (d), our model operates like a normal image translation model." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 183, + 198, + 352, + 275 + ], + "blocks": [ + { + "bbox": [ + 183, + 198, + 352, + 275 + ], + "lines": [ + { + "bbox": [ + 183, + 198, + 352, + 275 + ], + "spans": [ + { + "bbox": [ + 183, + 198, + 352, + 275 + ], + "type": "image", + "image_path": "93a947522354f24c0b3f00e0ddcc06966c57fc5db5c92061270e32ad685afeb8.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 406, + 203, + 533, + 263 + ], + "blocks": [ + { + "bbox": [ + 403, + 186, + 462, + 196 + ], + "lines": [ + { + "bbox": [ + 403, + 186, + 462, + 196 + ], + "spans": [ + { + "bbox": [ + 403, + 186, + 462, + 196 + ], + "type": "text", + "content": "(b) Forward cycle" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 406, + 203, + 533, + 263 + ], + "lines": [ + { + "bbox": [ + 406, + 203, + 533, + 263 + ], + "spans": [ + { + "bbox": [ + 406, + 203, + 533, + 263 + ], + "type": "image", + "image_path": "ac93ac8be3a35a6d0ba27a353d4b4fc625c2c1d75e06c0685f142a90012a6a30.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 460, + 266, + 504, + 274 + ], + "lines": [ + { + "bbox": [ + 460, + 266, + 504, + 274 + ], + "spans": [ + { + "bbox": [ + 460, + 266, + 504, + 274 + ], + "type": "text", + "content": "(d) Inference" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 351, + 288, + 400 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 288, + 400 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 288, + 400 + ], + "type": "text", + "content": "equivalent in " + }, + { + "bbox": [ + 46, + 351, + 288, + 400 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 351, + 288, + 400 + ], + "type": "text", + "content": ". While this notion is somewhat subjective, many applications have obvious examples: toponyms are unmatched in satellite images, and tumors in scans of healthy patients." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": "Objective. Our goal is to learn a mapping " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "G: \\mathcal{X} \\mapsto \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": " such that the translation " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "G(x)" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": " of any image " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": " aligns stylistically with images from " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": ", while preserving the semantic content of " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": ". If " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{K}_{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": " contains an unmatched class " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": ", images translated from " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": " should not contain any instances of " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": ". However, in an attempt to match the distribution of " + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 403, + 289, + 523 + ], + "type": "text", + "content": ", GAN models often create spurious instances of unmatched classes in their translated images. In this paper, we propose a method that employs steganography to prevent the generation of such spurious information." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 533, + 121, + 547 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 533, + 121, + 547 + ], + "spans": [ + { + "bbox": [ + 47, + 533, + 121, + 547 + ], + "type": "text", + "content": "3.1. CycleGAN" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "content": "CycleGAN [36] learns unpaired image translation by enforcing the consistency between the input image and its backtranslation from the generated image. It uses two generators " + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}: \\mathcal{X} \\mapsto \\mathcal{Y}" + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y} \\mapsto \\mathcal{X}}: \\mathcal{Y} \\mapsto \\mathcal{X}" + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "content": ", and two domain discriminators " + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "inline_equation", + "content": "D_{\\mathcal{X}}: \\mathcal{X} \\mapsto \\{0,1\\}" + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "inline_equation", + "content": "D_{\\mathcal{Y}}: \\mathcal{Y} \\mapsto \\{0,1\\}" + }, + { + "bbox": [ + 46, + 552, + 288, + 624 + ], + "type": "text", + "content": " which predict whether a sample is generated (0) or real (1)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": "In the following, when considering images " + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "inline_equation", + "content": "x \\in \\mathcal{X}" + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": " or " + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "inline_equation", + "content": "y \\in \\mathcal{Y}" + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": ", we define the following short-hands: " + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}(y)" + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}} := G_{\\mathcal{X} \\mapsto \\mathcal{Y}}(x)" + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": " for the generated images, and " + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{rec}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}(y_{\\mathrm{gen}})" + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}} := G_{\\mathcal{X} \\mapsto \\mathcal{Y}}(x_{\\mathrm{gen}})" + }, + { + "bbox": [ + 47, + 626, + 288, + 686 + ], + "type": "text", + "content": " for the reconstructed images. We now detail the losses of CycleGAN." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": "Adversarial loss. The adversarial loss [13] encourages the discriminators " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "D_{\\mathcal{X}}" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "inline_equation", + "content": "D_{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 689, + 288, + 714 + ], + "type": "text", + "content": " to distinguish between authentic" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "spans": [ + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "type": "text", + "content": "and generated images, while pushing the generators " + }, + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X}\\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y}\\mapsto \\mathcal{X}}" + }, + { + "bbox": [ + 305, + 351, + 545, + 376 + ], + "type": "text", + "content": " to create credible images:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 396, + 545, + 425 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 396, + 545, + 425 + ], + "spans": [ + { + "bbox": [ + 306, + 396, + 545, + 425 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\mathrm {G A N}} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\log (D _ {\\mathcal {Y}} (y)) + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\log (1 - D _ {\\mathcal {Y}} (y _ {\\text {g e n}})) \\\\ + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\log (D _ {\\mathcal {X}} (x)) + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\log (1 - D _ {\\mathcal {X}} (x _ {\\text {g e n}})). \\tag {1} \\\\ \\end{array}", + "image_path": "e2d7f1b808a388444c7b224c9a864e1332a7db276cde8a13f36f0d73a5d67b20.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "content": "Cycle consistency. The cycle consistency loss ensures that the back-translation of " + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}" + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "content": " to domain " + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "content": " is close to the original image " + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "content": ", and likewise for " + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 305, + 435, + 545, + 473 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 334, + 480, + 545, + 494 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 480, + 545, + 494 + ], + "spans": [ + { + "bbox": [ + 334, + 480, + 545, + 494 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\text {c y c}} = \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| x _ {\\text {r e c}} - x \\| + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| y _ {\\text {r e c}} - y \\|, \\tag {2}", + "image_path": "c6b9c148b8931a648d6fa135f4ff298e39edbf5b88710d356bcc53adbcc4ef44.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "type": "inline_equation", + "content": "\\| \\cdot \\|" + }, + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "type": "text", + "content": " the pixel-wise " + }, + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 305, + 502, + 444, + 514 + ], + "type": "text", + "content": " norm." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 517, + 547, + 541 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 517, + 547, + 541 + ], + "spans": [ + { + "bbox": [ + 305, + 517, + 547, + 541 + ], + "type": "text", + "content": "Identity loss. The identity loss regularizes the generators to be close to identity, generally improving color composition:" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 308, + 549, + 545, + 563 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 549, + 545, + 563 + ], + "spans": [ + { + "bbox": [ + 308, + 549, + 545, + 563 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\mathrm {i d}} = \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} (x) - x \\| + \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} (y) - y \\|. \\tag {3}", + "image_path": "e2a76d5ea1ca43b65801a0aa906eb3ab644389b925b8b6ffefe747195c2cdae4.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 571, + 455, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 571, + 455, + 582 + ], + "spans": [ + { + "bbox": [ + 306, + 571, + 455, + 582 + ], + "type": "text", + "content": "Final Loss. The final objectives are:" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 317, + 591, + 545, + 605 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 591, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 317, + 591, + 545, + 605 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}}, G _ {\\mathcal {Y} \\mapsto \\mathcal {X}}\\right) = \\mathcal {L} _ {G A N} + \\lambda_ {\\text {c y c}} \\mathcal {L} _ {\\text {c y c}} + \\lambda_ {\\text {i d}} \\mathcal {L} _ {\\text {i d}}, \\tag {4}", + "image_path": "74612d58592237cd0341037ea93acef74af12d1c2bef6265c57f72478ddf7574.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 345, + 607, + 545, + 619 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 345, + 607, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 345, + 607, + 545, + 619 + ], + "type": "interline_equation", + "content": "\\mathcal {L} \\left(D _ {\\mathcal {X}}, D _ {\\mathcal {Y}}\\right) = - \\mathcal {L} _ {\\mathrm {G A N}}, \\tag {5}", + "image_path": "851cfee4d9cac8ac0bfdffa52d2d3f301222417b0b0709d43199fb5e3b5fc10c.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{cyc}}" + }, + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{id}}" + }, + { + "bbox": [ + 306, + 628, + 501, + 640 + ], + "type": "text", + "content": " non-negative hyperparameters." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 647, + 378, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 647, + 378, + 659 + ], + "spans": [ + { + "bbox": [ + 306, + 647, + 378, + 659 + ], + "type": "text", + "content": "3.2. StegoGAN" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": "We introduce StegoGAN, a novel model building on the CycleGAN framework [36], designed specifically for scenarios where domains " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " lack a bijective relationship. When generating images " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": ", the generator " + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 305, + 665, + 547, + 715 + ], + "type": "text", + "content": " may add" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7924" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "spurious instances of an unmatched class " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " in order to deceive the discriminator " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "D_{\\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": ". Our goal is to prevent the generation of such hallucinated instances. To achieve this, we leverage steganography to explicitly disentangle the matchable and unmatched information in the backward cycle (" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "y \\mapsto x_{\\mathrm{gen}} \\mapsto y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": ") and prevent the network from hallucinating in the forward translation (" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "x \\mapsto y_{\\mathrm{gen}} \\mapsto x_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "). See Figure 2 for the overall design of our approach." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "spans": [ + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": "Steganography. In order to faithfully reconstruct " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": " with " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": ", the translated image " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": " must somehow contain information about the instances of the unmatched class " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": ". CycleGAN methods typically achieve this by hiding low-amplitude and high-frequency patterns in " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": " that will be decoded by " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": " and translated back to instances of " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 171, + 289, + 278 + ], + "type": "text", + "content": ". Adding low-intensity noise on each pixel is typically sufficient to destroy the hidden information and prevent steganography [7]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "spans": [ + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "text", + "content": "Steganography is often viewed as an optimization flaw that undermines the consistency loss. However, in the case of non-bijective translation, this is the only way to let " + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "text", + "content": " reconstruct instances of " + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 46, + 279, + 289, + 375 + ], + "type": "text", + "content": ". Instead of disabling steganography, we propose to use it to our advantage to detect and prevent spurious generations. We adapt CycleGAN so that steganography takes place in feature-space instead of pixel-space, and in an explicit manner." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": "Backward Cycle. We decompose the generators " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y} \\mapsto \\mathcal{X}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " into two components: an encoder and a decoder, such that " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}} = G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{dec}} \\circ G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{enc}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y} \\mapsto \\mathcal{X}} = G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{dec}} \\circ G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": ". The encoders map their inputs to feature maps of spatial dimension " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "H \\times W" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": ", where each pixel has " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " channels. In the following, we denote the intermediary representation of " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y} \\mapsto \\mathcal{X}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " by " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gen}} := G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}(y)" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": ". The feature map " + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gen}}" + }, + { + "bbox": [ + 46, + 377, + 289, + 484 + ], + "type": "text", + "content": " encodes information about both matchable and unmatched classes, which we want to disentangle." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "content": "We introduce a network " + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{H \\times W \\times C} \\mapsto [0,1]^{H \\times W \\times C}" + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "content": " that assigns an unmatchedability score between 0 and 1 to each pixel and channel. Here, a score of 1 indicates that the information does not have a counterpart in domain " + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "content": ", while it does for 0. This process gives us the unmatchedability mask " + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "inline_equation", + "content": "M(z_{\\mathrm{gen}})" + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "content": ", which we use to split " + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gen}}" + }, + { + "bbox": [ + 46, + 484, + 289, + 570 + ], + "type": "text", + "content": " into its matchable and unmatched parts:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 578, + 287, + 594 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 578, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 104, + 578, + 287, + 594 + ], + "type": "interline_equation", + "content": "z _ {\\text {g e n}} ^ {\\text {u n m a t c h}} = M \\left(z _ {\\text {g e n}}\\right) \\odot z \\tag {6}", + "image_path": "0b26ef2a479b5cecda2fad9fc51ab35ad2e994e78c0d6d45534cd52646afddc5.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 111, + 595, + 287, + 611 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 595, + 287, + 611 + ], + "spans": [ + { + "bbox": [ + 111, + 595, + 287, + 611 + ], + "type": "interline_equation", + "content": "z _ {\\text {g e n}} ^ {\\text {m a t c h}} = \\left(1 - M \\left(z _ {\\text {g e n}}\\right)\\right) \\odot z, \\tag {7}", + "image_path": "e1a3f5c4e1f58292a19f3ae6f90d72f1f5e77195d9a25a5c7d038b4c73de7692.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "spans": [ + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "type": "text", + "content": " the pixel-wise and channel-wise Hadamard product. In our model, the generated image " + }, + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 46, + 619, + 289, + 656 + ], + "type": "text", + "content": " is computed using only the matchable part of the representation:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 118, + 664, + 287, + 680 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 118, + 664, + 287, + 680 + ], + "spans": [ + { + "bbox": [ + 118, + 664, + 287, + 680 + ], + "type": "interline_equation", + "content": "x _ {\\text {g e n}} = G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} ^ {\\text {d e c}} \\left(z _ {\\text {g e n}} ^ {\\text {m a t c h}}\\right). \\tag {8}", + "image_path": "0a8c0cf8ef1693fcc55d0d1ff160618ba2267e2b5a5eb91b79f581151409e242.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "We produce two reconstructions of " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}^{\\mathrm{clean}}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": ", which is a direct back-translation of " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " into the " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " domain: " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}^{\\mathrm{clean}} =" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X}\\mapsto \\mathcal{Y}}(x_{\\mathrm{gen}})" + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "text", + "content": "; and " + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "text", + "content": ", which is generated by decoding a combination of the unmatched part of " + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "text", + "content": " and the features extracted by " + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X}\\mapsto \\mathcal{Y}}^{\\mathrm{enc}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "text", + "content": " from a noise-perturbed version of " + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 72, + 547, + 110 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 330, + 118, + 547, + 134 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 330, + 118, + 547, + 134 + ], + "spans": [ + { + "bbox": [ + 330, + 118, + 547, + 134 + ], + "type": "interline_equation", + "content": "y _ {\\text {r e c}} = G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {d e c}} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {e n c}} \\left(x _ {\\text {g e n}} + \\epsilon\\right) + z _ {\\text {g e n}} ^ {\\text {u n m a t c h}}\\right), \\tag {9}", + "image_path": "6b6c6497ba898ee0de46d24eb62b5cb1501111d9d7bbe54ca19c794de46332f7.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "spans": [ + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": "with " + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": " denoting random Gaussian noise of low amplitude applied to each pixel and channel of " + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": ". This noise is added to destroy potential steganographic information in " + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": ", therefore forcing " + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": " to rely only on " + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gen}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": " to reconstruct unmatched features in " + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 141, + 547, + 201 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 202, + 547, + 251 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 202, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 304, + 202, + 547, + 251 + ], + "type": "text", + "content": "The key mechanisms to disentangle matchable and unmatched information are twofold: (i) disturbing direct steganography with random noise, and (ii) explicitly providing unmatched information to " + }, + { + "bbox": [ + 304, + 202, + 547, + 251 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 304, + 202, + 547, + 251 + ], + "type": "text", + "content": " in feature-space." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "spans": [ + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": "Forward Cycle. In the forward cycle " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "x \\to y_{\\mathrm{gen}} \\to x_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": ", the generator " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " may create spurious instances of unmatched classes when translating " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " to fulfill the expectations of the discriminator " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "D_y" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": ". To address this, we perform two distinct translations of " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " has explicit access to the steganographic information " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{gen}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " extracted from the backward cycle, while " + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}^{\\mathrm{clean}}" + }, + { + "bbox": [ + 304, + 253, + 547, + 339 + ], + "type": "text", + "content": " does not:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 347, + 348, + 545, + 364 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 348, + 545, + 364 + ], + "spans": [ + { + "bbox": [ + 347, + 348, + 545, + 364 + ], + "type": "interline_equation", + "content": "y _ {\\text {g e n}} = G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {d e c}} \\left(G _ {\\mathcal {X} \\mapsto \\mathcal {Y}} ^ {\\text {e n c}} (x) + z _ {\\text {g e n}} ^ {\\text {u n m a t c h}}\\right) \\tag {10}", + "image_path": "d0e1da6564be73858e3c44d4d46a3d2903b964868479c270ccc33f57b4830a95.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 347, + 365, + 545, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 365, + 545, + 380 + ], + "spans": [ + { + "bbox": [ + 347, + 365, + 545, + 380 + ], + "type": "interline_equation", + "content": "y _ {\\text {g e n}} ^ {\\text {c l e a n}} = G _ {\\chi \\mapsto y} (x). \\tag {11}", + "image_path": "aeb9679c7964230448744dbb3b69b94581232e5516763ad5973727a146aa6263.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "text", + "content": "The rationale is that " + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}^{\\mathrm{dec}}" + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "text", + "content": " has explicit access to information about the unmatched classes of " + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "text", + "content": ", so it is not incentivized to invent them. For consistency with the backward step, where the decoder of " + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y} \\mapsto \\mathcal{X}}" + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "text", + "content": " processes only matchable information as defined in (7), we use the same disentangle-ment approach for generating " + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "inline_equation", + "content": "x_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 390, + 547, + 463 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 344, + 471, + 545, + 486 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 344, + 471, + 545, + 486 + ], + "spans": [ + { + "bbox": [ + 344, + 471, + 545, + 486 + ], + "type": "interline_equation", + "content": "x _ {\\text {r e c}} = G _ {\\mathcal {Y} \\mapsto \\mathcal {X}} ^ {\\text {d e c}} \\left(\\left(1 - M \\left(z _ {\\text {r e c}}\\right)\\right) \\odot z _ {\\text {r e c}}\\right), \\tag {12}", + "image_path": "9cf59cd6793feea57268d33bcf28e85cc4c44868b28cfdaeac288194f2c54b65.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "spans": [ + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "type": "inline_equation", + "content": "z_{\\mathrm{rec}} = G_{\\mathcal{Y} \\mapsto \\mathcal{X}}^{\\mathrm{enc}}(y_{\\mathrm{gen}})" + }, + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "type": "text", + "content": " is the intermediary representation of " + }, + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 494, + 545, + 519 + ], + "type": "text", + "content": " in the forward cycle." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 521, + 547, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 617 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 617 + ], + "type": "text", + "content": "Mask Regularization. To avoid degenerate behaviors of our explicit steganography mechanism, we enforce two priors on the unmatchedability masks: (i) given that a well-posed translation problem predominantly involves matchable features, the masks should be sparse; (ii) to improve the model's interpretability, we favor mask values near 0 or 1, representing clear decisions about matchability. To enforce these priors, we regularize the masks with the non-convex " + }, + { + "bbox": [ + 304, + 521, + 547, + 617 + ], + "type": "inline_equation", + "content": "L_{0.5}" + }, + { + "bbox": [ + 304, + 521, + 547, + 617 + ], + "type": "text", + "content": " norm [34]:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 313, + 627, + 545, + 641 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 627, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 313, + 627, + 545, + 641 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {r e g} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| M \\left(z _ {\\text {g e n}}\\right) \\| _ {0. 5} + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| M \\left(z _ {\\text {r e c}}\\right) \\| _ {0. 5}. \\tag {13}", + "image_path": "9596c3031280dc03102e0b2dd51efc7b4f2bf793e51bc383896d12ac52a904ac.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": "Matchable Consistency. The images " + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}" + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}^{\\mathrm{clean}}" + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": ", as well as " + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}" + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}^{\\mathrm{clean}}" + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": ", should be identical outside of unmatched regions. To enforce this constraint, we design a function " + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "inline_equation", + "content": "I" + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": " which takes an unmatchedness mask " + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 304, + 651, + 547, + 714 + ], + "type": "text", + "content": " as input, takes the channel-wise maximum values of all pixels, flips its" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7925" + } + ] + } + ], + "index": 23 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 545, + 459 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 545, + 459 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 545, + 459 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 545, + 459 + ], + "type": "image", + "image_path": "a731982eda57a52a69994bdfbf56dab32ede3c9d21d049eaf0df8892facc4dc8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 466, + 547, + 501 + ], + "lines": [ + { + "bbox": [ + 46, + 466, + 547, + 501 + ], + "spans": [ + { + "bbox": [ + 46, + 466, + 547, + 501 + ], + "type": "text", + "content": "Figure 3. Qualitative Comparison. We report reconstructions from the test sets of PlanIGN (top two rows), GoogleMap (row 3 and 4), and MRI (last two rows). Contrary to the other models, StegoGAN does not hallucinate spurious toponyms, highways (orange roads), or tumors (white areas) and shows better semantic correspondences during translation." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 521, + 287, + 545 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 521, + 287, + 545 + ], + "spans": [ + { + "bbox": [ + 46, + 521, + 287, + 545 + ], + "type": "text", + "content": "value from [0, 1] to [1, 0], and upsamples the results to the dimensions of the input images." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 94, + 552, + 288, + 572 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 552, + 288, + 572 + ], + "spans": [ + { + "bbox": [ + 94, + 552, + 288, + 572 + ], + "type": "interline_equation", + "content": "I (m) = \\operatorname {u p s a m p l e} \\left(1 - \\max _ {c} m\\right). \\tag {14}", + "image_path": "2bd768d9a946376c81ca9017090acd5c64ad4e1cdc35fa9452e7e5c65b6f0ea8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "spans": [ + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "text", + "content": "The obtained consistency masks " + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "inline_equation", + "content": "I(m)" + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "text", + "content": " have values close to 1 for pixels with only matchable content, and close to 0 otherwise. This enables us to define a loss for " + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{gen}}^{\\mathrm{clean}}" + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "inline_equation", + "content": "y_{\\mathrm{rec}}^{\\mathrm{clean}}" + }, + { + "bbox": [ + 47, + 579, + 289, + 631 + ], + "type": "text", + "content": " that focuses solely on regions with matchable features:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 636, + 287, + 668 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 636, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 61, + 636, + 287, + 668 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {\\text {m a t c h}} = \\mathbb {E} _ {y \\sim \\mathcal {Y}} \\| I (M (z _ {\\text {g e n}})) \\odot (y _ {\\text {g e n}} - y _ {\\text {g e n}} ^ {\\text {c l e a n}}) \\| \\\\ + \\mathbb {E} _ {x \\sim \\mathcal {X}} \\| I (M (z _ {\\mathrm {r e c}})) \\odot (y _ {\\mathrm {r e c}} - y _ {\\mathrm {r e c}} ^ {\\text {c l e a n}}) \\|. \\tag {15} \\\\ \\end{array}", + "image_path": "08dc369fa64ae44d797c24fd41d906d86c2091d7facb355fa64af4633f00c896.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Final Objective. In addition to the standard CycleGAN loss components (4-5), we integrate " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{match}}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": " into the overall loss function " + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(G_{\\mathcal{X} \\mapsto \\mathcal{Y}}, G_{\\mathcal{Y} \\mapsto \\mathcal{X}})" + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": ", weighted by" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "text", + "content": "their respective coefficients " + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{reg}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{match}}" + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "text", + "content": ". Crucially, our proposed approach remains unsupervised, requiring neither aligned images from " + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 304, + 521, + 547, + 568 + ], + "type": "text", + "content": " nor specific annotations of unmatched features." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 582, + 388, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 582, + 388, + 594 + ], + "spans": [ + { + "bbox": [ + 306, + 582, + 388, + 594 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 602, + 547, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 602, + 547, + 651 + ], + "spans": [ + { + "bbox": [ + 304, + 602, + 547, + 651 + ], + "type": "text", + "content": "In this section, we assess the improvements brought by our method for non-bijective image translation across various datasets and compare them with existing models, both qualitatively and quantitatively." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 653, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 548, + 714 + ], + "type": "text", + "content": "Implementation details. We follow the setting of CyleGAN [36] as our baseline model: the generators are Resnets [15] and the discriminator is based on PatchGAN [18]. We define the encoders as the first half of the generator's layers and the decoders as the second half. The" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7926" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 521, + 281 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 521, + 281 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 521, + 281 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 521, + 281 + ], + "type": "image", + "image_path": "700ea251354a90565c44a0be7003610a7a1b2fe4d87f9e2a40cc88b51b08713a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 289, + 547, + 313 + ], + "lines": [ + { + "bbox": [ + 46, + 289, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 547, + 313 + ], + "type": "text", + "content": "Figure 4. Results on GoogleMaps. We report the performance of several top-performing image translation models for different ratios of unmatched features in the target domain of the training set. StegoGAN handles higher ratios better than competing methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "content": "unmatchability mask predictor " + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "content": " is defined as a small 3-layer convolutional neural network (CNN). We set " + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{cyc}} = 10" + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{idt}} = 0.5" + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "content": " as in [36] and " + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{match}} = 1" + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "content": ". The amplitude of the perturbation " + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 332, + 290, + 392 + ], + "type": "text", + "content": " is 0.01 as in [7]. The Appendix provides more architecture and training details." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 400, + 111, + 411 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 400, + 111, + 411 + ], + "spans": [ + { + "bbox": [ + 47, + 400, + 111, + 411 + ], + "type": "text", + "content": "4.1. Datasets" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "content": "We assess the performance of StegoGAN across several image translation tasks that feature unmatched classes. Each dataset follows a consistent structure: the training set includes images from the source domain " + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "content": " devoid of a specific class (e.g., tumors, motorways, toponyms) while the target domain " + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 418, + 288, + 563 + ], + "type": "text", + "content": " does include that class. The test set comprises paired images from both domains, specifically excluding the unmatched class. This setup allows us to quantify the models' hallucinations: any generated instances of the unmatched class are necessarily spurious and due to its presence in the training set. We release all three curated datasets on the Zenodo platform and provide details below." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "spans": [ + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "text", + "content": "PlanIGN. " + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "text", + "content": " : Aerial Photo, " + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "inline_equation", + "content": "\\mathcal{Y}" + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "text", + "content": " : Maps, " + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 565, + 288, + 686 + ], + "type": "text", + "content": " : Text. We construct a dataset using open data from the French National Mapping Agency (IGN), comprising 1900 aerial (ortho-)images at 3m spatial resolution, and two versions of their corresponding topographic maps: one with and one without toponyms. This dataset presents a clear unmatched class: place names. The training set includes 1000 maps with toponyms and 1000 aerial images, while the test set comprises 900 map samples without toponyms and their corresponding aerial images." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": "GoogleMaps. " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " : Aerial Photo, " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " : Maps, " + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 46, + 689, + 289, + 715 + ], + "type": "text", + "content": " : Highways. The GoogleMaps dataset [18] is a standard bench" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "type": "text", + "content": "mark for image translation tasks [19, 20]. It contains 1096 map/image pairs for training and 1098 for testing. To create a controlled non-bijective scenario, we exclude all satellite images that show highways and sample the maps of the training set to contain varying proportions of maps with highways, ranging from " + }, + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "type": "inline_equation", + "content": "65\\%" + }, + { + "bbox": [ + 304, + 332, + 547, + 417 + ], + "type": "text", + "content": ", for a fixed total of 548 maps. For the test set we selected 898 pairs without highways." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": "Brats MRI " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "\\mathcal{X}" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " : T1 Scans, " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "\\mathcal{V}" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " : FLAIR, " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "k_{\\mathcal{Y}}^{\\mathrm{unmatch}}" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " : Tumors. Lastly, we used a dataset of brain MRI scans [25] with two modalities: T1 (naive) and FLAIR (T2 Fluid Attenuated Inversion Recovery) [14]. We adapt the protocol that Cohen et al. [8] used for the Brats2013 datasets [24] to the more recent Brats2018 [2] dataset by varying the percentage of scans with tumors in the target domain. We selected transverse slices from the " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "60^{\\circ}" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "100^{\\circ}" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " range in the caudocranial direction [1] for both T1 and FLAIR scans. Each scan was classified as tumorous if more than " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " of its pixels were labeled as such, and as healthy if it contained no tumor pixels. The training set contains 800 images from each modality, with all source images (T1) being healthy and the target domain (FLAIR) comprising " + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 418, + 548, + 600 + ], + "type": "text", + "content": " tumorous scans. The test set contains 335 paired scans of healthy brains." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 608, + 419, + 619 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 608, + 419, + 619 + ], + "spans": [ + { + "bbox": [ + 306, + 608, + 419, + 619 + ], + "type": "text", + "content": "4.2. Evaluation metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 626, + 546, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 626, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 626, + 546, + 662 + ], + "type": "text", + "content": "We use a broad range of metrics to evaluate the performance of StegoGAN and other image translation algorithms in the non-bijective setting:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 714 + ], + "type": "text", + "content": "FID and KID. The Fréchet Inception Distance (FID) [16] and Kernel Inception Distance (KID) [4] are widely used to quantify the similarity between the distributions of real and generated images in the target domain." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7927" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 49, + 97, + 286, + 173 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 287, + 93 + ], + "type": "text", + "content": "Table 1. Quantitative Comparison on PlanIGN. Our model shows a remarkably better performance than other existing models." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 97, + 286, + 173 + ], + "lines": [ + { + "bbox": [ + 49, + 97, + 286, + 173 + ], + "spans": [ + { + "bbox": [ + 49, + 97, + 286, + 173 + ], + "type": "table", + "html": "
MethodRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
CUT [26]30.546.755.868.42.8
CycleGAN [36]27.015.157.697.56.6
DRIT [21]34.833.636.976.43.8
GcGAN [11]32.754.556.9110.88.2
SRUNIT [19]32.348.852.860.22.2
StegoGAN (ours)22.566.174.858.42.4
", + "image_path": "f5a838b30f53767576001886da22a62a09222e2e2d5d372ac5f6d5fce1bdb2ba.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": "RMSE, " + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{Acc}(\\sigma_1)" + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\mathbf{Acc}(\\sigma_2)" + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": ". As the test sets comprise paired images from both domains, we can directly compare the Root Mean Square Error (RMSE) between the real and predicted images in the target domain. We count a predicted pixel as correctly predicted if it deviate by less than a fixed threshold in any of the color channels [11]. We use " + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_1 = 5" + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_2 = 10" + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": " for the GoogleMap dataset and " + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_1 = 2" + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "inline_equation", + "content": "\\sigma_2 = 5" + }, + { + "bbox": [ + 46, + 182, + 287, + 277 + ], + "type": "text", + "content": " for the less colorful PlanIGN dataset." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 281, + 288, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 281, + 288, + 377 + ], + "spans": [ + { + "bbox": [ + 46, + 281, + 288, + 377 + ], + "type": "text", + "content": "pFPR and iFPR. In the GoogleMap dataset, highways are always depicted in orange, allowing us to label pixels where all color channels differ by less than 20 units from (240, 160, 30) as highways. In the Brats MRI dataset, we use a pretrained tumor detector [5] to find spurious tumors in the generated images. This allows us to compute the average false positive rate per pixel (pFPR) and per instance (iFPR) of the generated images." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 387, + 105, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 105, + 398 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 105, + 398 + ], + "type": "text", + "content": "4.3. Results" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 406, + 288, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 288, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 288, + 466 + ], + "type": "text", + "content": "Qualitative Results. Figure 3 showcases StegoGAN's qualitative performance against other image translation algorithms. Notably, StegoGAN effectively avoids generating unmatched classes such as texts, highways, and tumors, while producing high-quality image translations." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "spans": [ + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": "Quantitative Results. On the PlanIGN dataset (Table 1) and the Brats MRI dataset (Table 2), StegoGAN outperforms others in fidelity, achieving the lowest RMSE by a margin of 4.5 on PlanIGN and by 3.5 for Brats MRI. Furthermore, it significantly enhances pixel accuracy, with improvements of " + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "inline_equation", + "content": "+11.6" + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{Acc}(\\sigma_1)" + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "inline_equation", + "content": "+17.2" + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "inline_equation", + "content": "\\mathrm{Acc}(\\sigma_2)" + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": " on PlanIGN. In the MRI dataset, StegoGAN dramatically reduces false positive rates—over " + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "inline_equation", + "content": "20\\times" + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": " lower than CycleGAN and " + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "inline_equation", + "content": "10\\times" + }, + { + "bbox": [ + 46, + 469, + 287, + 577 + ], + "type": "text", + "content": " less than the next best model SRUNIT (for pFPR)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 578, + 288, + 661 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 578, + 288, + 661 + ], + "spans": [ + { + "bbox": [ + 46, + 578, + 288, + 661 + ], + "type": "text", + "content": "On the GoogleMap dataset, as shown in Figure 4, StegoGAN's performance is on par with CycleGAN at " + }, + { + "bbox": [ + 46, + 578, + 288, + 661 + ], + "type": "inline_equation", + "content": "0\\%" + }, + { + "bbox": [ + 46, + 578, + 288, + 661 + ], + "type": "text", + "content": " unmatched cases and remains stable even as this ratio increases, unlike other methods that degrade. Remarkably, StegoGAN maintains a consistent false positive rate of 0 across all tests, while this rate increases for all other methods." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Unmatchability Masks. In Figure 5, we illustrate the emergent ability of the unmatchedability masks to trace the outline of unmatched class instances like toponyms, highways, and tumors. This aspect highlights the versatility of our" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 309, + 107, + 544, + 184 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "type": "text", + "content": "Table 2. Quantitative Comparison on Brats MRI Flair " + }, + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 305, + 70, + 547, + 104 + ], + "type": "text", + "content": " T1. Our model outperforms competing method in terms of both reconstruction accuracy and consistency." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 107, + 544, + 184 + ], + "lines": [ + { + "bbox": [ + 309, + 107, + 544, + 184 + ], + "spans": [ + { + "bbox": [ + 309, + 107, + 544, + 184 + ], + "type": "table", + "html": "
MethodRMSE↓pFPR(‰)↓iFPR↓FID↓KID↓
CUT [26]39.817.023.0103.98.8
CycleGAN [36]39.921.922.789.87.7
DRIT [21]53.018.541.2123.411.6
GcGAN [11]41.724.722.461.93.5
SRUNIT [19]42.515.121.858.92.9
StegoGAN (ours)36.31.14.258.52.4
", + "image_path": "9889fc1452ad659c6d8b6724170076e7d3fa9cd8fa370f98d79454b4a981cc8d.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 317, + 196, + 535, + 427 + ], + "blocks": [ + { + "bbox": [ + 317, + 196, + 535, + 427 + ], + "lines": [ + { + "bbox": [ + 317, + 196, + 535, + 427 + ], + "spans": [ + { + "bbox": [ + 317, + 196, + 535, + 427 + ], + "type": "image", + "image_path": "e3a0027370b66e1203ff5f025d36802aa4f78f746092ebffb624b4bfc011d4e1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 434, + 545, + 468 + ], + "lines": [ + { + "bbox": [ + 305, + 434, + 545, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 434, + 545, + 468 + ], + "type": "text", + "content": "Figure 5. Unmatchability Masks. The unmatchedability masks predicted in the backward cycle follow the instances of unmatched features in the target domain: toponyms, highways, and tumors." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 306, + 529, + 545, + 604 + ], + "blocks": [ + { + "bbox": [ + 305, + 481, + 545, + 525 + ], + "lines": [ + { + "bbox": [ + 305, + 481, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 305, + 481, + 545, + 525 + ], + "type": "text", + "content": "Table 3. Ablation Study on Encoder Depth. We evaluate the impact of changing the depth of the encoder on the reconstruction fidelity and the quality of unmatchedability masks. Depth= -1 or 8 means no encoder or no decoder, respectively." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 529, + 545, + 604 + ], + "lines": [ + { + "bbox": [ + 306, + 529, + 545, + 604 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 545, + 604 + ], + "type": "table", + "html": "
DepthMaskPrediction
mIOU↑Prec.↑recall↑RMSE↓A(σ1)↑A(σ2)↑FID↓KID↓
-126.627.181.222.464.374.258.82.5
125.225.881.222.566.174.858.42.4
327.127.980.422.861.673.462.93.0
530.833.469.524.252.770.662.32.6
847.360.160.024.553.570.762.72.7
", + "image_path": "40215441befcdef672753fba249774f9449d1caddb9b44969f6ff920fd7de5b4.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 612, + 547, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 612, + 547, + 648 + ], + "spans": [ + { + "bbox": [ + 305, + 612, + 547, + 648 + ], + "type": "text", + "content": "approach, which functions without explicit supervision or aligned images, offering a tool to explore the pairwise semantic differences between arbitrary datasets." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 658, + 458, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 458, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 458, + 671 + ], + "type": "text", + "content": "4.4. Ablation study and analysis" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "We explore the impact of our main design choices, as well as further capabilities and limitations of our approach. See the Appendix for further ablations." + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7928" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 70, + 542, + 152 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 542, + 152 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 542, + 152 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 542, + 152 + ], + "type": "image", + "image_path": "8a507aa641d769355d146cd0851f27dcf1a1355b352618a59250cb2fe32ccc7c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 163, + 546, + 185 + ], + "lines": [ + { + "bbox": [ + 46, + 163, + 546, + 185 + ], + "spans": [ + { + "bbox": [ + 46, + 163, + 546, + 185 + ], + "type": "text", + "content": "Figure 6. Impact of Encoder Depth. We visualize the unmatchedability mask for encoders of different depths for the PlanIGN dataset. Shallower encoders consider more features as unmatched." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 210, + 289, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 289, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 289, + 365 + ], + "type": "text", + "content": "Encoder Ablation. We conducted an ablation study on the definition of the intermediary representation " + }, + { + "bbox": [ + 46, + 210, + 289, + 365 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 210, + 289, + 365 + ], + "type": "text", + "content": " by varying the depth at which the \"encoder\" ends and the \"decoder\" starts within the generator. Given that our generators consist of 9 consecutive convolutional blocks, we experimented with different configurations: -1 (indicating no decoder), 1 (the configuration used in our paper), as well as depths of 3, 5, and 8 (implying no decoder). We report in Table 3 the reconstruction error of these models, as well as the fidelity of the consistency mask with the toponym text mask. We observe that shallow encoders have better reconstruction accuracy while the consistency masks of deeper encoders better approximate the text masks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 369, + 288, + 489 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 369, + 288, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 369, + 288, + 489 + ], + "type": "text", + "content": "Visualizing these masks in Figure 6, we observe that shallow encoders consider complex features such as highways and rivers as unmatched features, while deeper encoders do not. Shallower encoders seem more influenced by the variation in appearance (e.g., rivers being sometimes covered in vegetation or with varying colors) while deeper encoders focus on high-level semantics. We argue that both definitions are equally valid, and that varying the depth of the encoders can provide insights into the nature of the semantic mismatch between datasets." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": "Parameterization. In Table 4, we analyze the effects of omitting the additional terms " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{match}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " from the loss function " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " in Equation (4). We show that while " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{match}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " generally yields modest improvements across all metrics, " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " is pivotal, particularly for learning the target distribution. This outcome aligns with our expectations, as the absence of " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " allows the network to transmit all information, matchable or not, to the " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{Y} \\mapsto \\mathcal{X}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " decoder without repercussions, impeding the training of the " + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "inline_equation", + "content": "G_{\\mathcal{X} \\mapsto \\mathcal{Y}}" + }, + { + "bbox": [ + 46, + 499, + 287, + 608 + ], + "type": "text", + "content": " encoder." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "Limitations. We augment the CycleGAN framework with a module " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " and two hyper-parameters " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{match}}" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": ", thereby adding to the complexity of its training dynamics. Moreover, the concept of unmatchedability, integral to our approach, is inherently subjective. Given enough semantic detail, any two distinct datasets could be considered unmatched. As a result, fine-tuning the hyperparameter " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\lambda_{\\mathrm{reg}}" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " is essential to balance the elimination of hallucinations against the reten" + } + ] + } + ], + "index": 5 + }, + { + "type": "table", + "bbox": [ + 308, + 251, + 544, + 323 + ], + "blocks": [ + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "lines": [ + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "spans": [ + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "type": "text", + "content": "Table 4. Impact of Additional Loss Terms. We evaluate on the GoogleMap dataset the effect of removing our proposed losses. " + }, + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{match}}" + }, + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "type": "text", + "content": " has a small impact while " + }, + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_{\\mathrm{reg}}" + }, + { + "bbox": [ + 305, + 209, + 547, + 243 + ], + "type": "text", + "content": " is pivotal." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 251, + 544, + 323 + ], + "lines": [ + { + "bbox": [ + 308, + 251, + 544, + 323 + ], + "spans": [ + { + "bbox": [ + 308, + 251, + 544, + 323 + ], + "type": "table", + "html": "
SettingsRMSE↓Acc(σ1)↑Acc(σ2)↑FID↓KID↓
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", + "image_path": "09aea19f0466afc194d435dd90b2c494238ed274dc714dbdba2ae2f017de7533.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 343, + 547, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 343, + 547, + 416 + ], + "spans": [ + { + "bbox": [ + 304, + 343, + 547, + 416 + ], + "type": "text", + "content": "tion of necessary details: increasing its value leads to more conservative masks and improves the visual appearance of the generated images, at the cost of more spurious features. Visualizing the consistency mask is often a useful form of guidance. More details on learning strategies can be found in the Appendix." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 421, + 547, + 504 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 504 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 504 + ], + "type": "text", + "content": "We also acknowledge the potential of recent denoising diffusion models for image-to-image translation tasks [22, 32]. While our method is not confined to GANs and could be adapted to diffusion models with cycle consistency losses [28, 31], unpaired image translation with diffusion models is a nascent field with unique challenges. We plan to explore this area in future research." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 533, + 384, + 545 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 533, + 384, + 545 + ], + "spans": [ + { + "bbox": [ + 306, + 533, + 384, + 545 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": "We have introduced StegoGAN, a model built upon the CycleGAN framework, which leverages the mechanism of steganography to address the challenges of non-bijective image-to-image translation. Our model demonstrates an improved capability to handle divergent distributions between domains, as evidenced by its performance across various datasets, including aerial imagery, topographic maps, and MRI scans. We hope that our work will inspire further research in the little-studied area of non-bijective image translation. 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In Computer Vision (ICCV), 2017 IEEE International Conference on, 2017. 1, 2, 3, 5, 6, 7" + } + ] + } + ], + "index": 11 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7931" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_content_list.json b/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..f2417bbd6d3d30cb6cb450f70719404462c0cfd2 --- /dev/null +++ b/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_content_list.json @@ -0,0 +1,1700 @@ +[ + { + "type": "text", + "text": "Step Differences in Instructional Video", + "text_level": 1, + "bbox": [ + 287, + 130, + 679, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tushar Nagarajan, Lorenzo Torresani \nFAIR, Meta", + "bbox": [ + 336, + 180, + 630, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 251, + 312, + 266 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Comparing a user video to a reference how-to video is a key requirement for AR/VR technology delivering personalized assistance tailored to the user's progress. However, current approaches for language-based assistance can only answer questions about a single video. We propose an approach that first automatically generates large amounts of visual instruction tuning data involving pairs of videos from HowTo100M by leveraging existing step annotations and accompanying narrations, and then trains a video-conditioned language model to jointly reason across multiple raw videos. Our model achieves state-of-the-art performance at identifying differences between video pairs and ranking videos based on the severity of these differences, and shows promising ability to perform general reasoning over multiple videos.", + "bbox": [ + 75, + 282, + 473, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 540, + 207, + 556 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Instructional how-to videos are an important medium for learning new skills that offer in-depth visual demonstrations of complex procedural activities. In turn, they serve as a valuable resource for building AR/VR assistants that can guide a user through a procedural activity, by aligning user activity to a reference how-to video. Instructional videos have thus been the subject of several recent datasets and benchmarks that are driving new research [6, 9, 41, 45, 48, 59, 68, 69].", + "bbox": [ + 75, + 566, + 468, + 702 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A key requirement for such systems is the ability to compare and contrast the user's execution of a step in the activity with the reference video step, to highlight similarities and differences between them. For example, to let the user know that they used too much detergent (while doing laundry) or that the gravity is too thick (while cooking). This ability has direct value for personalized assistance applications such as progress tracking, mistake detection and surfacing user-activity driven tips.", + "bbox": [ + 75, + 704, + 468, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "More generally, reasoning about a video with respect to a reference video is a fundamental problem for video understanding that has value for fine-grained video retrieval [11, 53, 54, 57] (e.g., to browse internet videos for \"this movie", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ba73c7a2b1c5df3a56800e8daea03f7b3b6bbfa3168eee0d37a8d0df70c41b9b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 501, + 250, + 591, + 321 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d49aaa0de98fc1597f1127ed1c89a46a5daeef0caf580f9ede750ab1d5f2949f.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 591, + 251, + 683, + 320 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4cf44cf4c9b4567d2a8301ac9aa8caa1591ce2c3e8a0eab1feffd54f3d165fd0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 684, + 251, + 888, + 321 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/a80536d75100e187d2f06f5038494f2cb764248e6242707f766df6517a97bc13.jpg", + "image_caption": [ + "Figure 1. Main idea. Top: We train models to compare two videos showing the same high-level keystep and to describe their differences (e.g., in tools, ingredients, technique). Bottom: Once trained, such models can then help answer questions about a user's activity compared to a reference (e.g., an internet how-to video) like \"did I do this step right?\" or \"am I done yet?\"." + ], + "image_footnote": [], + "bbox": [ + 501, + 324, + 591, + 395 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/877c8747fdd842c7c6901897063f5df311ea85d0dc7e88f25dff59561a4b13f1.jpg", + "image_caption": [ + "Q: Am I done stirring the onions?" + ], + "image_footnote": [ + "A: No, keep stirring till they become golden brown like the video." + ], + "bbox": [ + 591, + 324, + 684, + 395 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "scene, but in a forest\"), step detection [6, 45, 46, 48, 69] (e.g., to recognize subtle variations in keysteps) and multi-video question answering and reasoning [5, 36] (e.g., to answer comparative questions like \"which video uses the least amount of oil?\").", + "bbox": [ + 496, + 520, + 893, + 595 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite its importance, there has been limited work on comparing videos. Prior work has explored change captioning in images [14, 16, 17, 34, 39, 70], however these works typically consider pixel-level differences (e.g., missing or moved objects; changed background objects) in static scenes (e.g., the same parking lot; the same tabletop), or in synthetically generated datasets [34]. They do not consider important semantic differences in activities (e.g., differences in tool use, subtle variations in actions and techniques or visual differences due to state changes), which together with the low-level visual differences, form a complete picture of human-object interactions.", + "bbox": [ + 496, + 597, + 893, + 777 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To address these limitations, we propose a video-conditioned language model (VCLM) approach to directly compare two videos of same step in a procedural activity. Specifically, we propose the difference question answering task: given a reference and a candidate video, a model must answer a question that involves reasoning across both videos (e.g., what are the differences in tools? techniques?; do the two videos show the same activity?). Such a model that", + "bbox": [ + 496, + 779, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18740", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "effectively relates user activity to a reference video, can then provide detailed context to answer more general questions such as \"what did I do wrong compared to the reference\" or \"am I done yet?\". See Fig. 1.", + "bbox": [ + 73, + 90, + 470, + 151 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An important practical question is how to source the supervision to train such a model, given that existing video datasets only contain individual videos with captions. Moreover, meaningful differences are not guaranteed to exist between arbitrary pairings of videos. We therefore automatically generate training data from existing large-scale instructional video datasets annotated with keysteps and speech narrations describing what instructors are doing [9, 29]. We pair clips of the same keystep (e.g., two videos of a person \"stir frying the rice until it is dark yellow\") but from distinct videos to allow for variations between them. For example the first video may use a cast iron pan versus a steel wok or the person may be tossing the food in the pan vs stirring with a spatula. We then leverage recent large language models [50] to generate questions and answers about the similarities and differences between the two videos given their visual descriptions, speech narrations, and visible objects as context. Inspired by work in visual instruction tuning of language models [27, 65], we finally fine-tune a video-pair conditioned language model with the collected dataset. The resulting model has the ability to cross-reference videos to compare them, and more generally answer questions that require joint reasoning about both videos simultaneously.", + "bbox": [ + 73, + 152, + 470, + 498 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To evaluate our model, we collect a manually annotated dataset of 6292 video pairs with $\\sim 36\\mathrm{k}$ difference captions spanning 5 categories, as well as scores for how severe the differences are. We set up the first benchmark for video comparisons and evaluate models on their ability to describe the differences in specific categories (e.g., \"What are the differences in tools? techniques?\") and to rank videos based on their differences (e.g., \"Which video shows the least different technique?\"). Our models trained with weak-supervision from automatically generated data achieve state-of-the-art results on our benchmark, highlighting its value for personalized assistance applications. Our benchmark will be hosted publicly, to allow the community to make progress towards this under-explored task.", + "bbox": [ + 73, + 500, + 470, + 710 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related work", + "text_level": 1, + "bbox": [ + 75, + 724, + 215, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Instructional video understanding Recent large-scale instructional video datasets [6, 9, 41, 45, 48, 59, 68, 69] have facilitated research in step captioning [63, 68], step detection [6, 45, 46, 48, 69], temporal grounding [2, 7, 13, 18, 28], vision-language representation learning [3, 25, 38, 66] and video question answering [56, 58, 60, 62] to name a few. In all these approaches, the goal is to process a single video and then caption, answer questions or temporally localize an action or text within it. While we are also interested in the space of procedural videos in the context of personalized", + "bbox": [ + 73, + 750, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "language-based assistance, in contrast, we develop methods to compare and contrast multiple videos — namely a reference video and a candidate video — in order to identify differences and answer comparative questions about them.", + "bbox": [ + 496, + 90, + 893, + 152 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual differences in images Prior work has studied visual differences in images in the context of attributes [8, 10, 33, 61] (e.g., which shoe is more formal) to facilitate fine-grained recognition. More relevant to our work, change captioning [14, 16, 17, 34, 39, 70] involves describing the differences between two images as a text caption. Other work defines differences as 2D bounding boxes [42, 43] or semantic maps [35] for regions that differ. More recently, VCLM models have been trained with \"spot-the-difference\" data from the above with a similar goal of identifying image differences [20]. In all these cases, the two images typically involve the same scene from multiple viewpoints or over time (e.g., surveillance footage) or are constructed from synthetic images (e.g., 3D geometric shapes re-arranged on a table). The resulting differences therefore focus on simple visual cues like missing or moved objects. More recent approaches use visual differences to retrieve videos [4], however they assume the difference is known (to retrieve a relevant video) rather than identifying and describing it. In contrast, we compare across distinct video clips that show the same high-level keystep. As a result, the difference captions characterize complex variations that arise naturally from the availability of tools and ingredients, differing skill / technique or personal preference.", + "bbox": [ + 496, + 172, + 895, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Visual instruction tuning of language models Given the recent success of large language models (LLMs), several efforts have tried to adapt them for use with various modalities including images, videos, audio etc., typically by aligning captions to modalities or instruction tuning [12, 21, 26, 27, 31, 32, 64, 65]. All these approaches typically use text captions or generate instruction tuning data based on a single image or video. In contrast, we generate instruction data for pairs of videos (a reference, and a target video) to allow vision conditioned language models to jointly reason about them both. Some approaches do train on multiple images interleaved with text [1, 19, 51], however they do not support instructions at inference, and instead rely on in-context few-shot prompting to respond. In contrast, our approach can respond to arbitrary questions about a video with respect to a reference clip.", + "bbox": [ + 496, + 556, + 895, + 800 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Approach", + "text_level": 1, + "bbox": [ + 500, + 814, + 609, + 830 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our goal is to train models to answer questions about a video in the context of a reference video, by jointly reasoning about the two. The problem is two-fold: where do we source data of pairs of videos with relevant questions", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18741", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/2061e3adb07d5eef315bc69de70a7f966bed2f324e4bafdd15adbda16c7e68f5.jpg", + "image_caption": [ + "Figure 2. Step differences framework. We first generate a comprehensive step description including information from action captions, object detections and ASR narrations (left panel). We then select pairs of clips with similar step descriptions, and automatically generate questions and answers that compare the two (center panel, Sec. 3.2). Finally, we instruction-tune an LLM to generate answers conditioned on the generated questions and encoded representations of both videos (right panel, Sec. 3.3). Once trained, the model directly operates on video clips to compare them, without the need for captions, ASR or object detections." + ], + "image_footnote": [], + "bbox": [ + 76, + 88, + 405, + 265 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/92c8fe4c27f749417afe435cb1692ac0a14976e406919a1b898f5e2632bc434b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 413, + 88, + 665, + 267 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/6b535b8e2793d592d13a276ae939b4e76b967d9c8310a90f2b278c88443999e0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 666, + 89, + 893, + 261 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "to train such models and what model architectures support training with multiple videos? For the former, we turn to automatically generating this data using large-language models (LLMs) parsing narrated video from existing datasets. For the latter, we use vision-conditioned language models (VCLMs) — a powerful class of models for single-video question answering — adapted to our multi-video setting. In the following, we first formally define our task (Sec. 3.1). Next, we describe our automatic training data generation pipeline (Sec. 3.2). Finally, we discuss training and downstream inference (Sec. 3.3).", + "bbox": [ + 75, + 375, + 473, + 541 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Task definition", + "text_level": 1, + "bbox": [ + 76, + 556, + 227, + 571 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We require models that collectively answer questions about two videos. Formally, given a reference video $V_{r}$ , a candidate video $V_{c}$ and a question $q$ , models must produce a corresponding answer $a$ . This formulation is an extension of standard video question answering or captioning [67] with a response that is additionally conditioned on a reference video. The questions can take various forms, for example \"How is the dough being prepared differently in Video 2\"; \"What is the similarity in mixing techniques between the two videos?\". Critically, these questions all share the assumption that a single video alone (either the reference or the candidate) is insufficient to answer the question — reasoning over both videos is required.", + "bbox": [ + 73, + 580, + 470, + 777 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In our experiments, we train models with a diverse set of automatically-generated question-answer pairs. At test time, we focus on step differences, where the $q$ is of the form \"what is the main difference between these videos in the category $g$ \" and $g$ is the difference category (e.g., ingredients, techniques, etc.). This structure captures a representative range of fine-grained differences, and allows for consistent evaluation of models as we will show.", + "bbox": [ + 75, + 780, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Step differences dataset generation", + "text_level": 1, + "bbox": [ + 500, + 375, + 803, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To train our models, we require a dataset of paired videos along with questions and answers (QA) relating the two in the form $(V_r, V_c, q, a)$ . However, current video datasets typically contain individual video clips annotated for actions, narrations, or single-video QA which is incompatible with our task definition. We therefore construct this from existing video datasets using large-language models, inspired by prior work on instruction tuning [12, 20, 27, 37, 49].", + "bbox": [ + 496, + 398, + 893, + 518 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Constructing this dataset from existing video datasets is non-trivial. On the one hand, selecting random pairs of videos showing very different content (e.g., sports vs. cooking) or near-identical videos (e.g., from repetitions of the same activity by the same participant) will lead to trivial differences. On the other hand, naively selecting video pairs of the same class in action recognition datasets (e.g., \"Bookbinding\" or \"Mowing the lawn\") will not highlight fine-grained differences of interest, and will instead focus on global differences (e.g., changes in actors or scenes). Moreover, these datasets do not come with text descriptions to construct differences from.", + "bbox": [ + 496, + 520, + 895, + 700 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We therefore propose to use videos from the large-scale procedural video dataset HowTo100M [29], specifically cooking-themed videos labeled for keysteps from HT-Step [9]. Instructional videos are an ideal data source as they are narrated and show the same high-level keystep, but with variations that arise naturally from availability of tools and ingredients, differing skill / technique or personal preference.", + "bbox": [ + 496, + 703, + 893, + 809 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Specifically, for two videos showing the same keystep (e.g., Slowly pour the sauce over the dumplings), we assume one is the reference $V_{r}$ and the other is the candidate video $V_{c}$ , with corresponding speech narrations. First, we generate descriptions of the actions and objects (including their attributes) using off-the-shelf captioning models [31]. These", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18742", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "models often hallucinate details in their generations, so we additionally filter object descriptions based on the scores of a pre-trained detection model [30] and filter action descriptions using visual grounding models [55]. Details about the filtering stage are in Supp. Finally, we aggregate the information from these three sources (ASR narration, filtered objects and actions) to synthesize a detailed step description for each video (Fig. 2, left panel). We then prompt a language model (in our case, Llama 2 [50]) to generate both questions and answers comparing the two videos based on their step descriptions. In short, the prompt takes the form: \"Video 1: {description1}. Video 2: {description2}. Summarize the differences and generate 3 question-answer pairs comparing the two videos.\" (Fig. 2, center panel). An overview of the data generation pipeline with examples at each stage can be seen in Fig. 2. See Supp. for more examples and full step description prompt details.", + "bbox": [ + 75, + 90, + 472, + 347 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The resulting dataset contains QA instances over video pairs across 87740 unique video clips. Note that the LLM-generated data is noisy — they may hallucinate details that are not present in the video, misunderstand the ASR narrations, produce irrelevant questions or incorrect answers to questions. Despite this, they offer valuable weak supervision to train our VCLM models, as our experiments will show.", + "bbox": [ + 75, + 347, + 472, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Paired video instruction tuning", + "text_level": 1, + "bbox": [ + 76, + 462, + 352, + 478 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We require a model that can generate natural language responses to video comparison questions in our dataset. To do this, we adapt a vision-conditioned language model (VCLM) to our multi-video setting via visual instruction tuning. In short, visual instruction tuning aligns the outputs of an image (or video) backbone to a powerful LLM to condition its responses on the visual content. This strategy has been successful in prior work for single image/video captioning and question answering [12, 21, 26, 27, 31, 64, 65]. We extend this to support comparisons across multiple videos. In our experiments, we use a Llama2 [50] LLM aligned with an Internvideo [55] backbone following prior work [31]. Note that it is possible to directly provide multiple videos to existing models by adding extra visual tokens to the input prompt, however their performance is degraded as they not trained to support this. We compare against such models.", + "bbox": [ + 75, + 484, + 470, + 726 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, for an instruction-tuning instance $(V_{r}, V_{c}, q, a)$ , we generate an instruction prompt in the Llama2 format as follows.", + "bbox": [ + 75, + 726, + 468, + 771 + ], + "page_idx": 3 + }, + { + "type": "code", + "sub_type": "code", + "code_caption": [], + "code_body": " [INST] <> You are a helpful AI assistant that answers questions about a pair of videos. Answer in a single sentence. Here is the first video: {V_r}. Here is the second video: {V_c}. > {q} [/INST] {a}", + "guess_lang": "txt", + "bbox": [ + 81, + 781, + 434, + 837 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We encode the text tokens in this prompt using the LLM's pre-trained text encoder. We encode each video into a sequence of spatiotemporal tokens using a pre-trained video", + "bbox": [ + 75, + 854, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/60b4463b907d0931fae58cc0f83294bbae16db278e174ea8161373bd15aede28.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 658, + 195 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e8b6ccee952803c831fea077dbc15be2e296cc6a50b1955517b6a385a25f9f90.jpg", + "image_caption": [ + "Difference Recognition" + ], + "image_footnote": [], + "bbox": [ + 669, + 104, + 885, + 195 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/f470fd08a878fe0e2f036c2e8a3ed71cf0e371f586bfa4d690dae7effb36c81b.jpg", + "image_caption": [ + "Figure 3. Evaluation tasks. We evaluate on describing (DiffCap), recognizing (DiffMCQ) and ranking (DiffRank) differences." + ], + "image_footnote": [], + "bbox": [ + 503, + 199, + 890, + 292 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "backbone $M_V$ , and then align them to the LLM's input space using a learnable projection module $M_{proj}$ . The resulting encoded instruction prompt is a sequence of tokens comprising a mix of text and visual tokens, which can then be processed by the LLM (Fig. 2, right panel).", + "bbox": [ + 496, + 359, + 893, + 435 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The model is trained using the original auto-regressive objective to maximize the probability of generating the answer tokens, conditioned on the question, reference and candidate video, and is trained using a standard cross-entropy loss.", + "bbox": [ + 496, + 436, + 893, + 497 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\np \\left(X _ {a} \\mid X _ {r}, X _ {c}, X _ {q}\\right) = \\prod_ {i = 1} ^ {\\left| X _ {a} \\right|} p _ {\\theta} \\left(X _ {a, i} \\mid X _ {r}, X _ {c}, X _ {q}, X _ {a, < i}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 518, + 890, + 577 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {r} = M _ {p r o j} \\left(M _ {V} \\left(V _ {r}\\right)\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 616, + 580, + 890, + 598 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nX _ {c} = M _ {p r o j} \\left(M _ {V} \\left(V _ {c}\\right)\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 617, + 601, + 890, + 618 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $X_{a,i}$ is the i-th answer token in the sequence, $X_{r}(X_{c})$ are the visual tokens corresponding to the reference (candidate) videos, $X_{q}, X_{a}$ are tokens of the question and answer, $X_{a, < i}$ are answer tokens that occur before $X_{a,i}$ and $\\theta$ are the learnable parameters in $\\mathcal{M}_{proj}$ .", + "bbox": [ + 496, + 628, + 890, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note that the video encoder and the LLM weights are frozen, and the loss is computed only for answer tokens. Only the projection layer is fine-tuned. Once trained, our model will be able to refer to each video, discuss their similarities and compare them. We evaluate our model by autoregressively generating text in response to various prompts coupled with reference and candidate videos.", + "bbox": [ + 496, + 704, + 893, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Describing, recognizing and ranking step differences in procedural videos", + "text_level": 1, + "bbox": [ + 500, + 818, + 890, + 849 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Finally, we use our trained models to identify and rank fine-grained differences between pairs of video. We cast these tasks into the paired-video QA framework as follows.", + "bbox": [ + 496, + 857, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18743", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/a3867a413d161cda4f42af8274476ebf138ead5c77cd72318d628358c5d0a4fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 80, + 88, + 174, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ingredients: The person oiled the baking dish with oil as opposed to vegetable ghee. Score: 4/5", + "bbox": [ + 178, + 95, + 478, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Tools/Equipment: The oil was applied to the pan with a pastry brush instead of bare hands; The baking dish used was a glass baking dish as opposed to ceramic. Score: 3/5", + "bbox": [ + 178, + 125, + 478, + 165 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Actions: The person skipped pressing the dough mixture into the baking dish after oiling it. Score: 3/5", + "bbox": [ + 178, + 170, + 475, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/9160aff5baa71ab5cbe00a41df2ba342036b6231c86dd33cd50ade7558bf90fd.jpg", + "image_caption": [ + "Figure 4. StepDiff dataset samples We annotate text describing differences in various categories and scores for how different the videos are in each category (1 = very different; 5 = nearly identical). More examples are in Supp." + ], + "image_footnote": [], + "bbox": [ + 80, + 210, + 174, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Tools/Equipment: The person mixes the cream mixture with green spatula instead of red. Score: 5/5", + "bbox": [ + 178, + 224, + 472, + 246 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Actions: The person continuously mixes the cream mixture instead of folding then shakes off the spatula. Score: 3/5", + "bbox": [ + 178, + 252, + 478, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visuals: The cream mixture has a thick and clumpy consistency instead of smooth and runny. Score: 2/5", + "bbox": [ + 178, + 289, + 470, + 310 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/d85e16b5ca31f0fbec5293661d1efd5bd09d2769fa15ed4126b878d495c06a9b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 88, + 596, + 205 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Ingredients: The person only cooks the regular potato fries as opposed to 6 varieties of potato fries. Score: 4/5", + "bbox": [ + 598, + 95, + 883, + 128 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Actions: The person skips transferring the potato fries in the tray. Score: 3/5", + "bbox": [ + 598, + 133, + 872, + 155 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visuals: The potato fries has a regular yellow color contrary to having green, red, orange and brown fries. Score: 2/5", + "bbox": [ + 598, + 160, + 877, + 191 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/3576d30116a6c73aa91a5ed9f09996af5c1821c7fd803d0f46577de1813dd8a2.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 500, + 212, + 596, + 329 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Tools/Equipment: The dough was flipped using a fork rather than a tong; The dough was deep-fried in a steel pan instead of a non-stick pan. Score: 3/5", + "bbox": [ + 598, + 220, + 890, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Technique: The dough was flipped once as opposed to three times. Score: 4/5", + "bbox": [ + 598, + 257, + 890, + 277 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Visuals: The deep-fried dough appears to have a flower design and has holes on it as opposed to full and lumpy. Score: 3/5", + "bbox": [ + 598, + 282, + 883, + 315 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Difference captioning (DiffCap) The goal is to generate a textual description of the differences between two videos in a specific category $g$ (e.g., ingredients, tools). The question $q$ takes the form \"what is the main difference between these videos in the category $g$ \". The difference caption is generated auto-regressively using the trained model.", + "bbox": [ + 75, + 383, + 468, + 474 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Difference recognition (DiffMCQ) The goal is to select the correct video pair that matches the difference caption, from a list of candidate video pairs $\\{(V_r^i,V_c^i)\\}_{i = 1..4}$ . This is a discriminative version of the captioning task above inspired by recent work in vision-language feature learning [24]. For this, we compute $p(a|V_r^i,V_c^i,q)$ — the likelihood of generating the difference text given the pair of videos following Eqn. 2 — and then select the pair with the highest score.", + "bbox": [ + 75, + 489, + 470, + 612 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Difference ranking (DiffRank) The goal is to rank video instances $\\{V_c^i\\}_{i=1..4}$ based on how different they are to a common reference video $V_r$ , in terms of a particular category of interest $g$ . For this, we set $q$ to be \"do these two videos show the same $g$ ? Answer YES or NO,\" and rank each candidate video based on the likelihood of generating \"YES\" as the response.", + "bbox": [ + 75, + 628, + 470, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Together, these tasks are a representative suite of problems for instructional video understanding that require comparing videos along various axes. DiffCap tests how accurately a model can describe differences in natural language, DiffMCQ tests how well it can discriminate differences between videos, and DiffRank tests how well the model can assess the severity of these differences to rank them. A model for these tasks can enable applications that guide user action (e.g., to follow a reference video tutorial) or help browse through large collections of videos (e.g., to find the perfect variation of a recipe). Fig. 3 illustrates these tasks.", + "bbox": [ + 75, + 734, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 500, + 382, + 632, + 398 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our VCLM model on the three step difference tasks from Sec. 3.4.", + "bbox": [ + 500, + 407, + 890, + 436 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Dataset We construct a test dataset from videos in HT-Step [9]. HTStep contains videos from a large-scale procedural video dataset, HowTo100M [29] (Cooking & Entertainment), with temporal segments (clips) annotated for keysteps (e.g., \"fry then onions until golden brown\"). We manually annotate pairs of clips, where each pair corresponds to instances of the same labeled keystep, but from distinct videos. Annotators are asked to identify the main differences across 5 categories (ingredients, tools/equipment, techniques, visual differences) and write difference captions of a consistent style — what happens in the target clip, compared to what happens in the reference (e.g., \"The person uses a deep fryer to fry the potatoes instead of shallow frying it in a pan\"). They are then asked to score the difference caption in each category on a scale of 1-5 based on how severe the difference is, where 1 is a significant difference (e.g., swapping out a critical ingredient that would change the dish entirely) and 5 is nearly identical (e.g., minor cosmetic differences that does not affect the activity). A rubric is used to ensure consistency in scoring.", + "bbox": [ + 496, + 459, + 893, + 761 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Note that this data is only used for evaluation — we exclude these pairs from the automatic training data generation pipeline described in Sec. 3.2 to ensure that the model has not seen these instances during training. In total, we collect 35988 difference captions across 6292 clip pairs, involving 8396 unique clips. See Fig. 4 for examples. Full collection details and dataset statistics are in Supp.", + "bbox": [ + 496, + 762, + 893, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Baselines We compare several classes of models.", + "bbox": [ + 500, + 885, + 836, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18744", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/8316641fcfa29d77ea2a8ac88ff45c7602b718ce69f6c938be0006a33447d13c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DIFFCAP
BLEUCIDERROGUE-L
VLEmb (CLIP) [40]---
VLEmb (InternVideo) [55]---
Socratic (BLIP-2) [22]0.1590.0360.169
Socratic (LLaVA) [27]0.1510.0310.166
Socratic (Step desc.)0.1410.0200.172
VCLM (LLaVA) [27]0.2110.0690.199
VCLM (AnyMAL) [31]0.2090.1150.196
Interleaved (IDEFICS) [19]0.2170.0800.210
Interleaved (AnyMAL)0.2070.1020.198
StepDiff0.2230.1040.215
", + "bbox": [ + 176, + 88, + 580, + 256 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/8e4d754bc4cd4b2dddd9306a52121ae6fcf335085deef3abfba2f579045e9bc5.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Acc %
0.396
0.451
0.335
0.332
0.392
0.381
0.471
0.376
0.497
0.541
", + "bbox": [ + 589, + 88, + 684, + 256 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/3e07b99a77c67bf9e93f3481e41288e6dd0148a3a6a5ab6bf43a47cbb6fe0b00.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DIFFRANK
τ
0.1270.170
0.0220.004
0.0130.013
0.0190.032
0.0810.014
0.181
", + "bbox": [ + 696, + 89, + 790, + 256 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Results. Our approach outperforms three classes of baselines built on top of state-of-the-art vision-language embedding and VCLM models. VLEmb baselines are excluded from DiffCap as they cannot generate text.", + "bbox": [ + 75, + 258, + 890, + 287 + ], + "page_idx": 5 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- VLEmbed is a class of vision-language model that embeds images or video in the same space as text, and then compares their similarity in the shared space. Video pair embeddings are calculated as the average of individual video embeddings1. We use CLIP [40] and InternVideo [55].", + "- Socratic is a class of VCLMs that first converts videos into text using a captioning model, and then prompts a text-only LLM with these captions. These models are powerful, but often require complex, manually engineered prompts. We use state-of-the-art visual captioners (BLIP-2 [22], LLaVA-1.5 [27]) as well our aggregate step descriptions from Sec. 3.2. We use Llama2 to process the captions regardless of which model generated them, for fair comparisons.", + "- VCLM is a class of visual instruction-tuned language model trained for video captioning and question answering (for a single video). We directly add extra tokens for the reference video into the prompt to be consistent with our paired-video QA task. We compare LLaVA-1.5 [27] and AnyMAL [31].", + "- Interleaved is a class of models that are trained with interleaved sequences of images/videos and text, and naturally support multiple videos as inputs, but are not explicitly trained to compare them. We compare the recently proposed IDEFICS [19] and a model we train on sequences of (video, ASR) pairs from HowTo100M (training details in Supp.)." + ], + "bbox": [ + 76, + 313, + 470, + 720 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "These baselines represent a spectrum of leading strategies for vision-language reasoning, including methods that directly embed video and language in the same space (VLEmbed), ones that explicitly convert videos to text and perform exclusively text-based reasoning (Socratic) and ones that perform joint vision-text reasoning on videos (VCLM, Interleaved). We ensure that each class of baselines include methods that have been trained on in-domain HowTo100M videos, while excluding the evaluation videos, to ensure fair comparisons with our approach. These are InternVideo,", + "bbox": [ + 75, + 722, + 470, + 873 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Socratic (Step desc.), VCLM (AnyMAL), and Interleaved (AnyMAL). Additional pretraining and implementation details are in Supp.", + "bbox": [ + 500, + 313, + 893, + 359 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details We use the Llama2-chat-70B [50] as the base LLM for all our experiments. Following prior work [31], $M_V$ is an Internvideo [55] video encoder that inputs 8 uniformly sampled frames from each video clip and generates 2048 spatio-temporal tokens. $M_{Proj}$ is a 2-layer Perceiver [15] module followed by a linear layer head to output 32 tokens in the LLM's input dimension. During training, all parameters are frozen except for $M_{Proj}$ . StepDiff models are initialized from Interleaved model weights before finetuning (interleaved data is retained during finetuning). For baselines, we use the largest available versions of models — InstructBLIP (Vicuna13B), LLaVA (Vicuna13B), AnyMAL (70B), IDEFICS (80B). Full implementation and training details are in Supp.", + "bbox": [ + 498, + 371, + 893, + 583 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Difference captioning", + "text_level": 1, + "bbox": [ + 500, + 590, + 700, + 606 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first evaluate how well our model can describe differences in video pairs (DiffCap). As mentioned in Sec. 3.1, $q$ is of the form \"what is the main difference between these videos in the category $g$ \" where $g$ is the difference category. Since there may be multiple annotated differences in the same category, we group them together and treat them as a ground truth set, resulting in a dataset with 22292 instances. We measure standard text generation metrics including CIDER [52] and ROUGE-L [23]. Outputs are postprocessed using simple string matching techniques to ensure difference captions are generated in the correct format (details in Supp). For the socratic baselines, we provide the generated caption instead of the video tokens in the prompt from Sec. 3.3. Table 1 (left) shows our results. The socratic models perform poorly as they are limited by the information contained in the base captions. It is infeasible to generate captions that exhaustively describe every aspect of a video, without knowing what is of interest, and without the risk of model hallucinations. The VCLM models perform better,", + "bbox": [ + 496, + 612, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_footnote", + "text": "1We evaluate other aggregation strategies in Supp.", + "bbox": [ + 94, + 886, + 359, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18745", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/bb5064d9fe927d66660d6f1aa3b0db838c0399961f8d400b971599349c815343.jpg", + "image_caption": [ + "Figure 5. Extended QA on video pairs. Our model which can describe differences (row 1) can be prompted (i.e., queried without any form of retraining) for comparative reasoning (e.g., \"why are they different?\"; \"how different are they?\" row 2-3), or to bootstrap mistake detection (row 4). A failure case is shown in row 5 due to model hallucination." + ], + "image_footnote": [], + "bbox": [ + 76, + 87, + 893, + 452 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "especially when trained to process multiple videos (i.e., interleaved models), however they still fall short of our approach that can explicitly compare and contrast videos. The example in Fig. 6 highlights the sensitivity of socratic models to input captions (e.g., the reference caption did not mention the use of hands), and shows how VCLM models tend to hallucinate details. Our approach can correctly describe the difference. See Supp for more examples.", + "bbox": [ + 75, + 527, + 473, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Difference recognition", + "text_level": 1, + "bbox": [ + 76, + 662, + 284, + 680 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "While the captioning metrics are informative, they are based on word overlap statistics, and do not always capture the semantics of the text well. To address this, we evaluate on DiffMCQ – the discriminative version of the captioning task. We adapt the same dataset from DiffCap, except we sample a single difference caption for each category if there are multiple differences present. Further, we sample three negative video pairs from other instances in the dataset that involve similar objects and actions (details in Supp). For the VLEmb bed baselines, we score each video pair using the cosine similarity between their average visual embeddings and the text embedding of the difference caption. We compare variants of this baseline considering only the reference or target in Supp. For all LLM-based baselines, we compute the", + "bbox": [ + 75, + 688, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "likelihood of generating the difference caption for each video pair, under each model as discussed in Sec. 3.1. We evaluate top-1 accuracy. Table 1 (center) shows our results. The joint feature embedding models capture some semantics, but are insufficient for identifying differences. Socratic models have a similar trend to captioning results, however models trained on step differences show large improvements, highlighting the value of careful curation for generating captions. Among VCLM models, ones that have seen in-domain HowTo100M videos during training have an edge over the others (i.e., LLaVA, IDEFICS), with interleaved models again being superior. Our model outperforms all these approaches with a $5\\%$ accuracy improvement over the strongest baseline. Fig. 7 shows performance increases by difference category, over the weakest baseline (Socratic). Our approach shows large relative improvements on most categories especially in technique and tool use (both $46\\%$ ), which require fine-grained action understanding.", + "bbox": [ + 496, + 527, + 895, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Difference ranking", + "text_level": 1, + "bbox": [ + 498, + 814, + 683, + 830 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Finally, we evaluate how well our model can rank videos based on the severity of differences compared to a common reference (DiffRank). Each reference video in the dataset is paired with four target videos, scored along each category", + "bbox": [ + 496, + 839, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18746", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/961448b3fd16f108256382e8be7d904bbcc42e7aaa3adf1472a63c20102bad34.jpg", + "image_caption": [ + "Figure 6. DiffCap baselines. Our approach can describe differences without relying on input captions (like Socratic) and is less prone to hallucinating details (like VCLM)." + ], + "image_footnote": [], + "bbox": [ + 80, + 88, + 184, + 215 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "What is the main difference in \"Tools\" between the two videos?", + "text_level": 1, + "bbox": [ + 187, + 90, + 467, + 112 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- Socratic: the person is using a rolling pin to roll out dough on a wooden surface, instead of a woman and young girl working together in a kitchen, ...", + "VCLM: the dough is rolled out on parchment paper, instead of directly on the counter.", + "- StepDiff: the dough is rolled out with a rolling pin, instead of being stretched with hands." + ], + "bbox": [ + 187, + 118, + 460, + 213 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/2430cc269ec99e6e627a7ef26add33532175981d8f73216c5ac31956cddb0fa4.jpg", + "image_caption": [ + "Figure 7. DiffMCQ performance by category. Improvements are reported over the weakest baseline (Socratic)." + ], + "image_footnote": [], + "bbox": [ + 83, + 284, + 460, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "axis. For example, some videos may be very similar in terms of technique, but very different in terms of ingredients. We only retain instances where there is a clear ranking (i.e., no more than one tie in scores) The resulting dataset contains 3932 instances involving 5746 unique clips.", + "bbox": [ + 76, + 506, + 468, + 580 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As discussed in Sec. 3.1, we rank each target video candidate based on the likelihood of producing the response \"YES\" when asked whether it is similar to the reference. We use the Kendall's $\\tau$ rank correlation metric to evaluate how well the generated ranking compares to the ground truth ranking annotators provide. Table 1 (right) shows our results. Unlike the previous tasks, the joint embedding models perform better than the LLM based baselines for two reasons. First, similarity in the embedding space directly translates to a score for ranking, rather than relying on computing \"YES\" token probability as a proxy for this. Second, there is a high correlation between the rankings across categories for the same set of instances ( $\\tau = 0.63$ ). For example, videos ranked low in similarity for tools when compared to a reference are often also ranked low for technique. Despite these issues, our approach is able to outperform all baselines, showcasing its versatility as a retrieval and ranking model.", + "bbox": [ + 76, + 580, + 468, + 838 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.4. Extending QA beyond atomic differences", + "text_level": 1, + "bbox": [ + 76, + 847, + 426, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Next, we show how our model can be prompted to answer questions beyond just \"describe the differences\". LLMs have", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ae6fff60d9ccc42866cea17a462ea2f037c3f3ff0c6e5e11c580541153c89b2c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DIFFCAP
BLEUCIDERROGUE-L
StepDiff0.2230.1040.215
w/o interleaved data0.2140.0940.210
w/o QA filtering0.2220.0960.212
w/ 13B LLM0.2160.1240.205
", + "bbox": [ + 501, + 89, + 743, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fb26ad30a555510868f73aff648b88005b9f028fb0ca41de45ef90b49147045e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
DIFFMCQDIFFRANK
Acc %τ
0.5410.181
0.4990.185
0.5160.120
0.5270.175
", + "bbox": [ + 750, + 89, + 888, + 148 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. Ablation experiments. Impact of retaining interleaved training data, careful filtering of QA training data and LLM size.", + "bbox": [ + 500, + 152, + 890, + 180 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "shown remarkable abilities for complex, multi-step reasoning in text – our training framework unlocks the same kind of reasoning for multiple videos, based on their differences. In Fig. 5, we show some examples of this. Our model is able to naturally describe differences as it was trained for this task (row 1), but also has the ability to perform comparative reasoning (row 2-3) or explain mistakes (row 4). We show a failure case in row 5, where the model hallucinates content – a characteristic feature of the LLM models it is built upon. Moreover, our model works with egocentric video (row 1, 4), despite being trained on largely third-person video content (HowTo100M), which is promising for AR/VR user assistance applications.", + "bbox": [ + 496, + 198, + 893, + 395 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.5. Ablation experiments", + "text_level": 1, + "bbox": [ + 500, + 404, + 700, + 420 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we ablate several design choices in our model in Table 2. As mentioned in Sec. 4, we finetune models on both interleaved ASR data as well as our generated pair QA data. Without the interleaved data, the model performance drops on two tasks, likely due to catastrophic forgetting (w/o interleaved data). Next, we show the importance of filtering the generated QA data (w/o QA filtering), given the high likelihood of hallucinations produced by the LLM. Finally, we swap out the 70B LLM model for a smaller sized one (w/13B LLM), causing the performance to drop, though not significantly.", + "bbox": [ + 496, + 428, + 890, + 594 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 608, + 617, + 625 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We proposed StepDiff, a video-conditioned language model (VCLM) that can compare and contrast videos to reveal fine-grained differences between them. We propose an approach that can automatically generate instruction-following paired-video QA training data from large-scale procedural video data, and a manually curated benchmark to evaluate models. Our experiments on describing and identifying differences, as well on ranking videos based on differences demonstrate the value of our approach for personalized assistance applications. Future work can leverage our work for personalized retrieval (e.g., retrieve content based on user-activity), or multi-video QA beyond instructional videos.", + "bbox": [ + 496, + 633, + 893, + 815 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements Thanks to Efi Mavroudi, Huiyu Wang, Triantafyllos Afouras and Yale Song for helpful discussions; Kumar Ashutosh and Suyog Jain for help with annotation tooling and collection; Austin Miller and Honey Manglani for managing the annotator workforce.", + "bbox": [ + 496, + 824, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18747", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. 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Springer, 2022. 1, 2" + ], + "bbox": [ + 503, + 92, + 893, + 441 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "18750", + "bbox": [ + 480, + 945, + 519, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_model.json b/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_model.json new file mode 100644 index 0000000000000000000000000000000000000000..ba8a99618d2ab76a7d18885cf9b6eb9938644609 --- /dev/null +++ b/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_model.json @@ -0,0 +1,2521 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.289, + 0.131, + 0.681, + 0.152 + ], + "angle": 0, + "content": "Step Differences in Instructional Video" + }, + { + "type": "text", + "bbox": [ + 0.337, + 0.181, + 0.632, + 0.216 + ], + "angle": 0, + "content": "Tushar Nagarajan, Lorenzo Torresani \nFAIR, Meta" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.252, + 0.313, + 0.267 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.284, + 0.474, + 0.496 + ], + "angle": 0, + "content": "Comparing a user video to a reference how-to video is a key requirement for AR/VR technology delivering personalized assistance tailored to the user's progress. However, current approaches for language-based assistance can only answer questions about a single video. We propose an approach that first automatically generates large amounts of visual instruction tuning data involving pairs of videos from HowTo100M by leveraging existing step annotations and accompanying narrations, and then trains a video-conditioned language model to jointly reason across multiple raw videos. Our model achieves state-of-the-art performance at identifying differences between video pairs and ranking videos based on the severity of these differences, and shows promising ability to perform general reasoning over multiple videos." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.541, + 0.208, + 0.557 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.703 + ], + "angle": 0, + "content": "Instructional how-to videos are an important medium for learning new skills that offer in-depth visual demonstrations of complex procedural activities. In turn, they serve as a valuable resource for building AR/VR assistants that can guide a user through a procedural activity, by aligning user activity to a reference how-to video. Instructional videos have thus been the subject of several recent datasets and benchmarks that are driving new research [6, 9, 41, 45, 48, 59, 68, 69]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.47, + 0.84 + ], + "angle": 0, + "content": "A key requirement for such systems is the ability to compare and contrast the user's execution of a step in the activity with the reference video step, to highlight similarities and differences between them. For example, to let the user know that they used too much detergent (while doing laundry) or that the gravity is too thick (while cooking). This ability has direct value for personalized assistance applications such as progress tracking, mistake detection and surfacing user-activity driven tips." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "More generally, reasoning about a video with respect to a reference video is a fundamental problem for video understanding that has value for fine-grained video retrieval [11, 53, 54, 57] (e.g., to browse internet videos for \"this movie" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.251, + 0.593, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.252, + 0.684, + 0.321 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.685, + 0.252, + 0.89, + 0.322 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.325, + 0.593, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.593, + 0.325, + 0.685, + 0.396 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.688, + 0.338, + 0.88, + 0.35 + ], + "angle": 0, + "content": "Q: Am I done stirring the onions?" + }, + { + "type": "image_footnote", + "bbox": [ + 0.689, + 0.355, + 0.883, + 0.376 + ], + "angle": 0, + "content": "A: No, keep stirring till they become golden brown like the video." + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.408, + 0.895, + 0.492 + ], + "angle": 0, + "content": "Figure 1. Main idea. Top: We train models to compare two videos showing the same high-level keystep and to describe their differences (e.g., in tools, ingredients, technique). Bottom: Once trained, such models can then help answer questions about a user's activity compared to a reference (e.g., an internet how-to video) like \"did I do this step right?\" or \"am I done yet?\"." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.895, + 0.596 + ], + "angle": 0, + "content": "scene, but in a forest\"), step detection [6, 45, 46, 48, 69] (e.g., to recognize subtle variations in keysteps) and multi-video question answering and reasoning [5, 36] (e.g., to answer comparative questions like \"which video uses the least amount of oil?\")." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.598, + 0.895, + 0.779 + ], + "angle": 0, + "content": "Despite its importance, there has been limited work on comparing videos. Prior work has explored change captioning in images [14, 16, 17, 34, 39, 70], however these works typically consider pixel-level differences (e.g., missing or moved objects; changed background objects) in static scenes (e.g., the same parking lot; the same tabletop), or in synthetically generated datasets [34]. They do not consider important semantic differences in activities (e.g., differences in tool use, subtle variations in actions and techniques or visual differences due to state changes), which together with the low-level visual differences, form a complete picture of human-object interactions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.895, + 0.901 + ], + "angle": 0, + "content": "To address these limitations, we propose a video-conditioned language model (VCLM) approach to directly compare two videos of same step in a procedural activity. Specifically, we propose the difference question answering task: given a reference and a candidate video, a model must answer a question that involves reasoning across both videos (e.g., what are the differences in tools? techniques?; do the two videos show the same activity?). Such a model that" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18740" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.075, + 0.092, + 0.471, + 0.152 + ], + "angle": 0, + "content": "effectively relates user activity to a reference video, can then provide detailed context to answer more general questions such as \"what did I do wrong compared to the reference\" or \"am I done yet?\". See Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.153, + 0.472, + 0.499 + ], + "angle": 0, + "content": "An important practical question is how to source the supervision to train such a model, given that existing video datasets only contain individual videos with captions. Moreover, meaningful differences are not guaranteed to exist between arbitrary pairings of videos. We therefore automatically generate training data from existing large-scale instructional video datasets annotated with keysteps and speech narrations describing what instructors are doing [9, 29]. We pair clips of the same keystep (e.g., two videos of a person \"stir frying the rice until it is dark yellow\") but from distinct videos to allow for variations between them. For example the first video may use a cast iron pan versus a steel wok or the person may be tossing the food in the pan vs stirring with a spatula. We then leverage recent large language models [50] to generate questions and answers about the similarities and differences between the two videos given their visual descriptions, speech narrations, and visible objects as context. Inspired by work in visual instruction tuning of language models [27, 65], we finally fine-tune a video-pair conditioned language model with the collected dataset. The resulting model has the ability to cross-reference videos to compare them, and more generally answer questions that require joint reasoning about both videos simultaneously." + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.5, + 0.472, + 0.711 + ], + "angle": 0, + "content": "To evaluate our model, we collect a manually annotated dataset of 6292 video pairs with \\(\\sim 36\\mathrm{k}\\) difference captions spanning 5 categories, as well as scores for how severe the differences are. We set up the first benchmark for video comparisons and evaluate models on their ability to describe the differences in specific categories (e.g., \"What are the differences in tools? techniques?\") and to rank videos based on their differences (e.g., \"Which video shows the least different technique?\"). Our models trained with weak-supervision from automatically generated data achieve state-of-the-art results on our benchmark, highlighting its value for personalized assistance applications. Our benchmark will be hosted publicly, to allow the community to make progress towards this under-explored task." + }, + { + "type": "title", + "bbox": [ + 0.076, + 0.725, + 0.216, + 0.74 + ], + "angle": 0, + "content": "2. Related work" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.75, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Instructional video understanding Recent large-scale instructional video datasets [6, 9, 41, 45, 48, 59, 68, 69] have facilitated research in step captioning [63, 68], step detection [6, 45, 46, 48, 69], temporal grounding [2, 7, 13, 18, 28], vision-language representation learning [3, 25, 38, 66] and video question answering [56, 58, 60, 62] to name a few. In all these approaches, the goal is to process a single video and then caption, answer questions or temporally localize an action or text within it. While we are also interested in the space of procedural videos in the context of personalized" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.153 + ], + "angle": 0, + "content": "language-based assistance, in contrast, we develop methods to compare and contrast multiple videos — namely a reference video and a candidate video — in order to identify differences and answer comparative questions about them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.173, + 0.897, + 0.537 + ], + "angle": 0, + "content": "Visual differences in images Prior work has studied visual differences in images in the context of attributes [8, 10, 33, 61] (e.g., which shoe is more formal) to facilitate fine-grained recognition. More relevant to our work, change captioning [14, 16, 17, 34, 39, 70] involves describing the differences between two images as a text caption. Other work defines differences as 2D bounding boxes [42, 43] or semantic maps [35] for regions that differ. More recently, VCLM models have been trained with \"spot-the-difference\" data from the above with a similar goal of identifying image differences [20]. In all these cases, the two images typically involve the same scene from multiple viewpoints or over time (e.g., surveillance footage) or are constructed from synthetic images (e.g., 3D geometric shapes re-arranged on a table). The resulting differences therefore focus on simple visual cues like missing or moved objects. More recent approaches use visual differences to retrieve videos [4], however they assume the difference is known (to retrieve a relevant video) rather than identifying and describing it. In contrast, we compare across distinct video clips that show the same high-level keystep. As a result, the difference captions characterize complex variations that arise naturally from the availability of tools and ingredients, differing skill / technique or personal preference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.558, + 0.897, + 0.801 + ], + "angle": 0, + "content": "Visual instruction tuning of language models Given the recent success of large language models (LLMs), several efforts have tried to adapt them for use with various modalities including images, videos, audio etc., typically by aligning captions to modalities or instruction tuning [12, 21, 26, 27, 31, 32, 64, 65]. All these approaches typically use text captions or generate instruction tuning data based on a single image or video. In contrast, we generate instruction data for pairs of videos (a reference, and a target video) to allow vision conditioned language models to jointly reason about them both. Some approaches do train on multiple images interleaved with text [1, 19, 51], however they do not support instructions at inference, and instead rely on in-context few-shot prompting to respond. In contrast, our approach can respond to arbitrary questions about a video with respect to a reference clip." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.815, + 0.61, + 0.832 + ], + "angle": 0, + "content": "3. Approach" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Our goal is to train models to answer questions about a video in the context of a reference video, by jointly reasoning about the two. The problem is two-fold: where do we source data of pairs of videos with relevant questions" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "18741" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.089, + 0.406, + 0.266 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.414, + 0.089, + 0.666, + 0.268 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.668, + 0.09, + 0.895, + 0.262 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.895, + 0.35 + ], + "angle": 0, + "content": "Figure 2. Step differences framework. We first generate a comprehensive step description including information from action captions, object detections and ASR narrations (left panel). We then select pairs of clips with similar step descriptions, and automatically generate questions and answers that compare the two (center panel, Sec. 3.2). Finally, we instruction-tune an LLM to generate answers conditioned on the generated questions and encoded representations of both videos (right panel, Sec. 3.3). Once trained, the model directly operates on video clips to compare them, without the need for captions, ASR or object detections." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.375, + 0.474, + 0.542 + ], + "angle": 0, + "content": "to train such models and what model architectures support training with multiple videos? For the former, we turn to automatically generating this data using large-language models (LLMs) parsing narrated video from existing datasets. For the latter, we use vision-conditioned language models (VCLMs) — a powerful class of models for single-video question answering — adapted to our multi-video setting. In the following, we first formally define our task (Sec. 3.1). Next, we describe our automatic training data generation pipeline (Sec. 3.2). Finally, we discuss training and downstream inference (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.557, + 0.228, + 0.572 + ], + "angle": 0, + "content": "3.1. Task definition" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.582, + 0.471, + 0.779 + ], + "angle": 0, + "content": "We require models that collectively answer questions about two videos. Formally, given a reference video \\( V_{r} \\), a candidate video \\( V_{c} \\) and a question \\( q \\), models must produce a corresponding answer \\( a \\). This formulation is an extension of standard video question answering or captioning [67] with a response that is additionally conditioned on a reference video. The questions can take various forms, for example \"How is the dough being prepared differently in Video 2\"; \"What is the similarity in mixing techniques between the two videos?\". Critically, these questions all share the assumption that a single video alone (either the reference or the candidate) is insufficient to answer the question — reasoning over both videos is required." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.473, + 0.901 + ], + "angle": 0, + "content": "In our experiments, we train models with a diverse set of automatically-generated question-answer pairs. At test time, we focus on step differences, where the \\( q \\) is of the form \"what is the main difference between these videos in the category \\( g \\)\" and \\( g \\) is the difference category (e.g., ingredients, techniques, etc.). This structure captures a representative range of fine-grained differences, and allows for consistent evaluation of models as we will show." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.375, + 0.805, + 0.391 + ], + "angle": 0, + "content": "3.2. Step differences dataset generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.399, + 0.895, + 0.52 + ], + "angle": 0, + "content": "To train our models, we require a dataset of paired videos along with questions and answers (QA) relating the two in the form \\((V_r, V_c, q, a)\\). However, current video datasets typically contain individual video clips annotated for actions, narrations, or single-video QA which is incompatible with our task definition. We therefore construct this from existing video datasets using large-language models, inspired by prior work on instruction tuning [12, 20, 27, 37, 49]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.521, + 0.896, + 0.702 + ], + "angle": 0, + "content": "Constructing this dataset from existing video datasets is non-trivial. On the one hand, selecting random pairs of videos showing very different content (e.g., sports vs. cooking) or near-identical videos (e.g., from repetitions of the same activity by the same participant) will lead to trivial differences. On the other hand, naively selecting video pairs of the same class in action recognition datasets (e.g., \"Bookbinding\" or \"Mowing the lawn\") will not highlight fine-grained differences of interest, and will instead focus on global differences (e.g., changes in actors or scenes). Moreover, these datasets do not come with text descriptions to construct differences from." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.81 + ], + "angle": 0, + "content": "We therefore propose to use videos from the large-scale procedural video dataset HowTo100M [29], specifically cooking-themed videos labeled for keysteps from HT-Step [9]. Instructional videos are an ideal data source as they are narrated and show the same high-level keystep, but with variations that arise naturally from availability of tools and ingredients, differing skill / technique or personal preference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Specifically, for two videos showing the same keystep (e.g., Slowly pour the sauce over the dumplings), we assume one is the reference \\( V_{r} \\) and the other is the candidate video \\( V_{c} \\), with corresponding speech narrations. First, we generate descriptions of the actions and objects (including their attributes) using off-the-shelf captioning models [31]. These" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18742" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.348 + ], + "angle": 0, + "content": "models often hallucinate details in their generations, so we additionally filter object descriptions based on the scores of a pre-trained detection model [30] and filter action descriptions using visual grounding models [55]. Details about the filtering stage are in Supp. Finally, we aggregate the information from these three sources (ASR narration, filtered objects and actions) to synthesize a detailed step description for each video (Fig. 2, left panel). We then prompt a language model (in our case, Llama 2 [50]) to generate both questions and answers comparing the two videos based on their step descriptions. In short, the prompt takes the form: \"Video 1: {description1}. Video 2: {description2}. Summarize the differences and generate 3 question-answer pairs comparing the two videos.\" (Fig. 2, center panel). An overview of the data generation pipeline with examples at each stage can be seen in Fig. 2. See Supp. for more examples and full step description prompt details." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.348, + 0.473, + 0.455 + ], + "angle": 0, + "content": "The resulting dataset contains QA instances over video pairs across 87740 unique video clips. Note that the LLM-generated data is noisy — they may hallucinate details that are not present in the video, misunderstand the ASR narrations, produce irrelevant questions or incorrect answers to questions. Despite this, they offer valuable weak supervision to train our VCLM models, as our experiments will show." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.463, + 0.353, + 0.479 + ], + "angle": 0, + "content": "3.3. Paired video instruction tuning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.486, + 0.472, + 0.727 + ], + "angle": 0, + "content": "We require a model that can generate natural language responses to video comparison questions in our dataset. To do this, we adapt a vision-conditioned language model (VCLM) to our multi-video setting via visual instruction tuning. In short, visual instruction tuning aligns the outputs of an image (or video) backbone to a powerful LLM to condition its responses on the visual content. This strategy has been successful in prior work for single image/video captioning and question answering [12, 21, 26, 27, 31, 64, 65]. We extend this to support comparisons across multiple videos. In our experiments, we use a Llama2 [50] LLM aligned with an Internvideo [55] backbone following prior work [31]. Note that it is possible to directly provide multiple videos to existing models by adding extra visual tokens to the input prompt, however their performance is degraded as they not trained to support this. We compare against such models." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.727, + 0.47, + 0.772 + ], + "angle": 0, + "content": "Specifically, for an instruction-tuning instance \\((V_{r}, V_{c}, q, a)\\), we generate an instruction prompt in the Llama2 format as follows." + }, + { + "type": "code", + "bbox": [ + 0.082, + 0.782, + 0.435, + 0.838 + ], + "angle": 0, + "content": " [INST] <> You are a helpful AI assistant that answers questions about a pair of videos. Answer in a single sentence. Here is the first video: {V_r}. Here is the second video: {V_c}. > {q} [/INST] {a}" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We encode the text tokens in this prompt using the LLM's pre-trained text encoder. We encode each video into a sequence of spatiotemporal tokens using a pre-trained video" + }, + { + "type": "image", + "bbox": [ + 0.501, + 0.089, + 0.66, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.718, + 0.092, + 0.838, + 0.102 + ], + "angle": 0, + "content": "Difference Recognition" + }, + { + "type": "image", + "bbox": [ + 0.67, + 0.106, + 0.886, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.2, + 0.891, + 0.294 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.307, + 0.894, + 0.336 + ], + "angle": 0, + "content": "Figure 3. Evaluation tasks. We evaluate on describing (DiffCap), recognizing (DiffMCQ) and ranking (DiffRank) differences." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.361, + 0.894, + 0.436 + ], + "angle": 0, + "content": "backbone \\( M_V \\), and then align them to the LLM's input space using a learnable projection module \\( M_{proj} \\). The resulting encoded instruction prompt is a sequence of tokens comprising a mix of text and visual tokens, which can then be processed by the LLM (Fig. 2, right panel)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.437, + 0.894, + 0.498 + ], + "angle": 0, + "content": "The model is trained using the original auto-regressive objective to maximize the probability of generating the answer tokens, conditioned on the question, reference and candidate video, and is trained using a standard cross-entropy loss." + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.52, + 0.892, + 0.578 + ], + "angle": 0, + "content": "\\[\np \\left(X _ {a} \\mid X _ {r}, X _ {c}, X _ {q}\\right) = \\prod_ {i = 1} ^ {\\left| X _ {a} \\right|} p _ {\\theta} \\left(X _ {a, i} \\mid X _ {r}, X _ {c}, X _ {q}, X _ {a, < i}\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.617, + 0.582, + 0.892, + 0.599 + ], + "angle": 0, + "content": "\\[\nX _ {r} = M _ {p r o j} \\left(M _ {V} \\left(V _ {r}\\right)\\right) \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.618, + 0.602, + 0.892, + 0.619 + ], + "angle": 0, + "content": "\\[\nX _ {c} = M _ {p r o j} \\left(M _ {V} \\left(V _ {c}\\right)\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.629, + 0.892, + 0.704 + ], + "angle": 0, + "content": "where \\(X_{a,i}\\) is the i-th answer token in the sequence, \\(X_{r}(X_{c})\\) are the visual tokens corresponding to the reference (candidate) videos, \\(X_{q}, X_{a}\\) are tokens of the question and answer, \\(X_{a, < i}\\) are answer tokens that occur before \\(X_{a,i}\\) and \\(\\theta\\) are the learnable parameters in \\(\\mathcal{M}_{proj}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.894, + 0.81 + ], + "angle": 0, + "content": "Note that the video encoder and the LLM weights are frozen, and the loss is computed only for answer tokens. Only the projection layer is fine-tuned. Once trained, our model will be able to refer to each video, discuss their similarities and compare them. We evaluate our model by autoregressively generating text in response to various prompts coupled with reference and candidate videos." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.819, + 0.892, + 0.851 + ], + "angle": 0, + "content": "3.4. Describing, recognizing and ranking step differences in procedural videos" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.858, + 0.894, + 0.903 + ], + "angle": 0, + "content": "Finally, we use our trained models to identify and rank fine-grained differences between pairs of video. We cast these tasks into the paired-video QA framework as follows." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18743" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.176, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.097, + 0.48, + 0.12 + ], + "angle": 0, + "content": "Ingredients: The person oiled the baking dish with oil as opposed to vegetable ghee. Score: 4/5" + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.125, + 0.48, + 0.166 + ], + "angle": 0, + "content": "Tools/Equipment: The oil was applied to the pan with a pastry brush instead of bare hands; The baking dish used was a glass baking dish as opposed to ceramic. Score: 3/5" + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.171, + 0.476, + 0.193 + ], + "angle": 0, + "content": "Actions: The person skipped pressing the dough mixture into the baking dish after oiling it. Score: 3/5" + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.212, + 0.176, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.226, + 0.473, + 0.247 + ], + "angle": 0, + "content": "Tools/Equipment: The person mixes the cream mixture with green spatula instead of red. Score: 5/5" + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.253, + 0.48, + 0.284 + ], + "angle": 0, + "content": "Actions: The person continuously mixes the cream mixture instead of folding then shakes off the spatula. Score: 3/5" + }, + { + "type": "text", + "bbox": [ + 0.179, + 0.29, + 0.472, + 0.311 + ], + "angle": 0, + "content": "Visuals: The cream mixture has a thick and clumpy consistency instead of smooth and runny. Score: 2/5" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.089, + 0.597, + 0.207 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.599, + 0.097, + 0.885, + 0.129 + ], + "angle": 0, + "content": "Ingredients: The person only cooks the regular potato fries as opposed to 6 varieties of potato fries. Score: 4/5" + }, + { + "type": "text", + "bbox": [ + 0.599, + 0.134, + 0.873, + 0.156 + ], + "angle": 0, + "content": "Actions: The person skips transferring the potato fries in the tray. Score: 3/5" + }, + { + "type": "text", + "bbox": [ + 0.599, + 0.161, + 0.879, + 0.192 + ], + "angle": 0, + "content": "Visuals: The potato fries has a regular yellow color contrary to having green, red, orange and brown fries. Score: 2/5" + }, + { + "type": "image", + "bbox": [ + 0.5, + 0.213, + 0.597, + 0.33 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.599, + 0.221, + 0.892, + 0.253 + ], + "angle": 0, + "content": "Tools/Equipment: The dough was flipped using a fork rather than a tong; The dough was deep-fried in a steel pan instead of a non-stick pan. Score: 3/5" + }, + { + "type": "text", + "bbox": [ + 0.599, + 0.258, + 0.891, + 0.279 + ], + "angle": 0, + "content": "Technique: The dough was flipped once as opposed to three times. Score: 4/5" + }, + { + "type": "text", + "bbox": [ + 0.599, + 0.284, + 0.884, + 0.316 + ], + "angle": 0, + "content": "Visuals: The deep-fried dough appears to have a flower design and has holes on it as opposed to full and lumpy. Score: 3/5" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.338, + 0.894, + 0.367 + ], + "angle": 0, + "content": "Figure 4. StepDiff dataset samples We annotate text describing differences in various categories and scores for how different the videos are in each category (1 = very different; 5 = nearly identical). More examples are in Supp." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.384, + 0.47, + 0.475 + ], + "angle": 0, + "content": "Difference captioning (DiffCap) The goal is to generate a textual description of the differences between two videos in a specific category \\( g \\) (e.g., ingredients, tools). The question \\( q \\) takes the form \"what is the main difference between these videos in the category \\( g \\)\". The difference caption is generated auto-regressively using the trained model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.491, + 0.471, + 0.613 + ], + "angle": 0, + "content": "Difference recognition (DiffMCQ) The goal is to select the correct video pair that matches the difference caption, from a list of candidate video pairs \\(\\{(V_r^i,V_c^i)\\}_{i = 1..4}\\). This is a discriminative version of the captioning task above inspired by recent work in vision-language feature learning [24]. For this, we compute \\(p(a|V_r^i,V_c^i,q)\\) — the likelihood of generating the difference text given the pair of videos following Eqn. 2 — and then select the pair with the highest score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.629, + 0.471, + 0.734 + ], + "angle": 0, + "content": "Difference ranking (DiffRank) The goal is to rank video instances \\(\\{V_c^i\\}_{i=1..4}\\) based on how different they are to a common reference video \\(V_r\\), in terms of a particular category of interest \\(g\\). For this, we set \\(q\\) to be \"do these two videos show the same \\(g\\)? Answer YES or NO,\" and rank each candidate video based on the likelihood of generating \"YES\" as the response." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Together, these tasks are a representative suite of problems for instructional video understanding that require comparing videos along various axes. DiffCap tests how accurately a model can describe differences in natural language, DiffMCQ tests how well it can discriminate differences between videos, and DiffRank tests how well the model can assess the severity of these differences to rank them. A model for these tasks can enable applications that guide user action (e.g., to follow a reference video tutorial) or help browse through large collections of videos (e.g., to find the perfect variation of a recipe). Fig. 3 illustrates these tasks." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.383, + 0.633, + 0.4 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.408, + 0.892, + 0.438 + ], + "angle": 0, + "content": "We evaluate our VCLM model on the three step difference tasks from Sec. 3.4." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.46, + 0.895, + 0.762 + ], + "angle": 0, + "content": "Dataset We construct a test dataset from videos in HT-Step [9]. HTStep contains videos from a large-scale procedural video dataset, HowTo100M [29] (Cooking & Entertainment), with temporal segments (clips) annotated for keysteps (e.g., \"fry then onions until golden brown\"). We manually annotate pairs of clips, where each pair corresponds to instances of the same labeled keystep, but from distinct videos. Annotators are asked to identify the main differences across 5 categories (ingredients, tools/equipment, techniques, visual differences) and write difference captions of a consistent style — what happens in the target clip, compared to what happens in the reference (e.g., \"The person uses a deep fryer to fry the potatoes instead of shallow frying it in a pan\"). They are then asked to score the difference caption in each category on a scale of 1-5 based on how severe the difference is, where 1 is a significant difference (e.g., swapping out a critical ingredient that would change the dish entirely) and 5 is nearly identical (e.g., minor cosmetic differences that does not affect the activity). A rubric is used to ensure consistency in scoring." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.894, + 0.87 + ], + "angle": 0, + "content": "Note that this data is only used for evaluation — we exclude these pairs from the automatic training data generation pipeline described in Sec. 3.2 to ensure that the model has not seen these instances during training. In total, we collect 35988 difference captions across 6292 clip pairs, involving 8396 unique clips. See Fig. 4 for examples. Full collection details and dataset statistics are in Supp." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.838, + 0.901 + ], + "angle": 0, + "content": "Baselines We compare several classes of models." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18744" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.178, + 0.089, + 0.581, + 0.257 + ], + "angle": 0, + "content": "
DIFFCAP
BLEUCIDERROGUE-L
VLEmb (CLIP) [40]---
VLEmb (InternVideo) [55]---
Socratic (BLIP-2) [22]0.1590.0360.169
Socratic (LLaVA) [27]0.1510.0310.166
Socratic (Step desc.)0.1410.0200.172
VCLM (LLaVA) [27]0.2110.0690.199
VCLM (AnyMAL) [31]0.2090.1150.196
Interleaved (IDEFICS) [19]0.2170.0800.210
Interleaved (AnyMAL)0.2070.1020.198
StepDiff0.2230.1040.215
" + }, + { + "type": "table", + "bbox": [ + 0.59, + 0.089, + 0.685, + 0.257 + ], + "angle": 0, + "content": "
Acc %
0.396
0.451
0.335
0.332
0.392
0.381
0.471
0.376
0.497
0.541
" + }, + { + "type": "table", + "bbox": [ + 0.697, + 0.09, + 0.791, + 0.257 + ], + "angle": 0, + "content": "
DIFFRANK
τ
0.1270.170
0.0220.004
0.0130.013
0.0190.032
0.0810.014
0.181
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.259, + 0.892, + 0.288 + ], + "angle": 0, + "content": "Table 1. Results. Our approach outperforms three classes of baselines built on top of state-of-the-art vision-language embedding and VCLM models. VLEmb baselines are excluded from DiffCap as they cannot generate text." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.314, + 0.47, + 0.389 + ], + "angle": 0, + "content": "- VLEmbed is a class of vision-language model that embeds images or video in the same space as text, and then compares their similarity in the shared space. Video pair embeddings are calculated as the average of individual video embeddings1. We use CLIP [40] and InternVideo [55]." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.39, + 0.471, + 0.525 + ], + "angle": 0, + "content": "- Socratic is a class of VCLMs that first converts videos into text using a captioning model, and then prompts a text-only LLM with these captions. These models are powerful, but often require complex, manually engineered prompts. We use state-of-the-art visual captioners (BLIP-2 [22], LLaVA-1.5 [27]) as well our aggregate step descriptions from Sec. 3.2. We use Llama2 to process the captions regardless of which model generated them, for fair comparisons." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.526, + 0.47, + 0.616 + ], + "angle": 0, + "content": "- VCLM is a class of visual instruction-tuned language model trained for video captioning and question answering (for a single video). We directly add extra tokens for the reference video into the prompt to be consistent with our paired-video QA task. We compare LLaVA-1.5 [27] and AnyMAL [31]." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.616, + 0.471, + 0.721 + ], + "angle": 0, + "content": "- Interleaved is a class of models that are trained with interleaved sequences of images/videos and text, and naturally support multiple videos as inputs, but are not explicitly trained to compare them. We compare the recently proposed IDEFICS [19] and a model we train on sequences of (video, ASR) pairs from HowTo100M (training details in Supp.)." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.314, + 0.471, + 0.721 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.723, + 0.471, + 0.874 + ], + "angle": 0, + "content": "These baselines represent a spectrum of leading strategies for vision-language reasoning, including methods that directly embed video and language in the same space (VLEmbed), ones that explicitly convert videos to text and perform exclusively text-based reasoning (Socratic) and ones that perform joint vision-text reasoning on videos (VCLM, Interleaved). We ensure that each class of baselines include methods that have been trained on in-domain HowTo100M videos, while excluding the evaluation videos, to ensure fair comparisons with our approach. These are InternVideo," + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.314, + 0.894, + 0.36 + ], + "angle": 0, + "content": "Socratic (Step desc.), VCLM (AnyMAL), and Interleaved (AnyMAL). Additional pretraining and implementation details are in Supp." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.372, + 0.895, + 0.584 + ], + "angle": 0, + "content": "Implementation details We use the Llama2-chat-70B [50] as the base LLM for all our experiments. Following prior work [31], \\( M_V \\) is an Internvideo [55] video encoder that inputs 8 uniformly sampled frames from each video clip and generates 2048 spatio-temporal tokens. \\( M_{Proj} \\) is a 2-layer Perceiver [15] module followed by a linear layer head to output 32 tokens in the LLM's input dimension. During training, all parameters are frozen except for \\( M_{Proj} \\). StepDiff models are initialized from Interleaved model weights before finetuning (interleaved data is retained during finetuning). For baselines, we use the largest available versions of models — InstructBLIP (Vicuna13B), LLaVA (Vicuna13B), AnyMAL (70B), IDEFICS (80B). Full implementation and training details are in Supp." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.591, + 0.702, + 0.607 + ], + "angle": 0, + "content": "4.1. Difference captioning" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.613, + 0.895, + 0.901 + ], + "angle": 0, + "content": "We first evaluate how well our model can describe differences in video pairs (DiffCap). As mentioned in Sec. 3.1, \\( q \\) is of the form \"what is the main difference between these videos in the category \\( g \\)\" where \\( g \\) is the difference category. Since there may be multiple annotated differences in the same category, we group them together and treat them as a ground truth set, resulting in a dataset with 22292 instances. We measure standard text generation metrics including CIDER [52] and ROUGE-L [23]. Outputs are postprocessed using simple string matching techniques to ensure difference captions are generated in the correct format (details in Supp). For the socratic baselines, we provide the generated caption instead of the video tokens in the prompt from Sec. 3.3. Table 1 (left) shows our results. The socratic models perform poorly as they are limited by the information contained in the base captions. It is infeasible to generate captions that exhaustively describe every aspect of a video, without knowing what is of interest, and without the risk of model hallucinations. The VCLM models perform better," + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.361, + 0.901 + ], + "angle": 0, + "content": "1We evaluate other aggregation strategies in Supp." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18745" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.078, + 0.088, + 0.895, + 0.453 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.468, + 0.893, + 0.511 + ], + "angle": 0, + "content": "Figure 5. Extended QA on video pairs. Our model which can describe differences (row 1) can be prompted (i.e., queried without any form of retraining) for comparative reasoning (e.g., \"why are they different?\"; \"how different are they?\" row 2-3), or to bootstrap mistake detection (row 4). A failure case is shown in row 5 due to model hallucination." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.475, + 0.651 + ], + "angle": 0, + "content": "especially when trained to process multiple videos (i.e., interleaved models), however they still fall short of our approach that can explicitly compare and contrast videos. The example in Fig. 6 highlights the sensitivity of socratic models to input captions (e.g., the reference caption did not mention the use of hands), and shows how VCLM models tend to hallucinate details. Our approach can correctly describe the difference. See Supp for more examples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.664, + 0.285, + 0.681 + ], + "angle": 0, + "content": "4.2. Difference recognition" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.473, + 0.903 + ], + "angle": 0, + "content": "While the captioning metrics are informative, they are based on word overlap statistics, and do not always capture the semantics of the text well. To address this, we evaluate on DiffMCQ – the discriminative version of the captioning task. We adapt the same dataset from DiffCap, except we sample a single difference caption for each category if there are multiple differences present. Further, we sample three negative video pairs from other instances in the dataset that involve similar objects and actions (details in Supp). For the VLEmb bed baselines, we score each video pair using the cosine similarity between their average visual embeddings and the text embedding of the difference caption. We compare variants of this baseline considering only the reference or target in Supp. For all LLM-based baselines, we compute the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.896, + 0.801 + ], + "angle": 0, + "content": "likelihood of generating the difference caption for each video pair, under each model as discussed in Sec. 3.1. We evaluate top-1 accuracy. Table 1 (center) shows our results. The joint feature embedding models capture some semantics, but are insufficient for identifying differences. Socratic models have a similar trend to captioning results, however models trained on step differences show large improvements, highlighting the value of careful curation for generating captions. Among VCLM models, ones that have seen in-domain HowTo100M videos during training have an edge over the others (i.e., LLaVA, IDEFICS), with interleaved models again being superior. Our model outperforms all these approaches with a \\(5\\%\\) accuracy improvement over the strongest baseline. Fig. 7 shows performance increases by difference category, over the weakest baseline (Socratic). Our approach shows large relative improvements on most categories especially in technique and tool use (both \\(46\\%\\)), which require fine-grained action understanding." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.815, + 0.684, + 0.832 + ], + "angle": 0, + "content": "4.3. Difference ranking" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Finally, we evaluate how well our model can rank videos based on the severity of differences compared to a common reference (DiffRank). Each reference video in the dataset is paired with four target videos, scored along each category" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18746" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.089, + 0.186, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.189, + 0.092, + 0.468, + 0.113 + ], + "angle": 0, + "content": "What is the main difference in \"Tools\" between the two videos?" + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.119, + 0.462, + 0.16 + ], + "angle": 0, + "content": "- Socratic: the person is using a rolling pin to roll out dough on a wooden surface, instead of a woman and young girl working together in a kitchen, ..." + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.166, + 0.45, + 0.188 + ], + "angle": 0, + "content": "VCLM: the dough is rolled out on parchment paper, instead of directly on the counter." + }, + { + "type": "text", + "bbox": [ + 0.189, + 0.193, + 0.456, + 0.214 + ], + "angle": 0, + "content": "- StepDiff: the dough is rolled out with a rolling pin, instead of being stretched with hands." + }, + { + "type": "list", + "bbox": [ + 0.189, + 0.119, + 0.462, + 0.214 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.234, + 0.471, + 0.276 + ], + "angle": 0, + "content": "Figure 6. DiffCap baselines. Our approach can describe differences without relying on input captions (like Socratic) and is less prone to hallucinating details (like VCLM)." + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.285, + 0.462, + 0.442 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.462, + 0.469, + 0.491 + ], + "angle": 0, + "content": "Figure 7. DiffMCQ performance by category. Improvements are reported over the weakest baseline (Socratic)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.507, + 0.469, + 0.581 + ], + "angle": 0, + "content": "axis. For example, some videos may be very similar in terms of technique, but very different in terms of ingredients. We only retain instances where there is a clear ranking (i.e., no more than one tie in scores) The resulting dataset contains 3932 instances involving 5746 unique clips." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.582, + 0.47, + 0.839 + ], + "angle": 0, + "content": "As discussed in Sec. 3.1, we rank each target video candidate based on the likelihood of producing the response \"YES\" when asked whether it is similar to the reference. We use the Kendall's \\(\\tau\\) rank correlation metric to evaluate how well the generated ranking compares to the ground truth ranking annotators provide. Table 1 (right) shows our results. Unlike the previous tasks, the joint embedding models perform better than the LLM based baselines for two reasons. First, similarity in the embedding space directly translates to a score for ranking, rather than relying on computing \"YES\" token probability as a proxy for this. Second, there is a high correlation between the rankings across categories for the same set of instances (\\(\\tau = 0.63\\)). For example, videos ranked low in similarity for tools when compared to a reference are often also ranked low for technique. Despite these issues, our approach is able to outperform all baselines, showcasing its versatility as a retrieval and ranking model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.428, + 0.865 + ], + "angle": 0, + "content": "4.4. Extending QA beyond atomic differences" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Next, we show how our model can be prompted to answer questions beyond just \"describe the differences\". LLMs have" + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.09, + 0.744, + 0.15 + ], + "angle": 0, + "content": "
DIFFCAP
BLEUCIDERROGUE-L
StepDiff0.2230.1040.215
w/o interleaved data0.2140.0940.210
w/o QA filtering0.2220.0960.212
w/ 13B LLM0.2160.1240.205
" + }, + { + "type": "table", + "bbox": [ + 0.75, + 0.09, + 0.889, + 0.15 + ], + "angle": 0, + "content": "
DIFFMCQDIFFRANK
Acc %τ
0.5410.181
0.4990.185
0.5160.120
0.5270.175
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.153, + 0.892, + 0.181 + ], + "angle": 0, + "content": "Table 2. Ablation experiments. Impact of retaining interleaved training data, careful filtering of QA training data and LLM size." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.895, + 0.396 + ], + "angle": 0, + "content": "shown remarkable abilities for complex, multi-step reasoning in text – our training framework unlocks the same kind of reasoning for multiple videos, based on their differences. In Fig. 5, we show some examples of this. Our model is able to naturally describe differences as it was trained for this task (row 1), but also has the ability to perform comparative reasoning (row 2-3) or explain mistakes (row 4). We show a failure case in row 5, where the model hallucinates content – a characteristic feature of the LLM models it is built upon. Moreover, our model works with egocentric video (row 1, 4), despite being trained on largely third-person video content (HowTo100M), which is promising for AR/VR user assistance applications." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.405, + 0.702, + 0.421 + ], + "angle": 0, + "content": "4.5. Ablation experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.429, + 0.892, + 0.595 + ], + "angle": 0, + "content": "Finally, we ablate several design choices in our model in Table 2. As mentioned in Sec. 4, we finetune models on both interleaved ASR data as well as our generated pair QA data. Without the interleaved data, the model performance drops on two tasks, likely due to catastrophic forgetting (w/o interleaved data). Next, we show the importance of filtering the generated QA data (w/o QA filtering), given the high likelihood of hallucinations produced by the LLM. Finally, we swap out the 70B LLM model for a smaller sized one (w/13B LLM), causing the performance to drop, though not significantly." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.609, + 0.619, + 0.625 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.894, + 0.816 + ], + "angle": 0, + "content": "We proposed StepDiff, a video-conditioned language model (VCLM) that can compare and contrast videos to reveal fine-grained differences between them. We propose an approach that can automatically generate instruction-following paired-video QA training data from large-scale procedural video data, and a manually curated benchmark to evaluate models. Our experiments on describing and identifying differences, as well on ranking videos based on differences demonstrate the value of our approach for personalized assistance applications. Future work can leverage our work for personalized retrieval (e.g., retrieve content based on user-activity), or multi-video QA beyond instructional videos." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgements Thanks to Efi Mavroudi, Huiyu Wang, Triantafyllos Afouras and Yale Song for helpful discussions; Kumar Ashutosh and Suyog Jain for help with annotation tooling and collection; Austin Miller and Honey Manglani for managing the annotator workforce." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18747" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.473, + 0.198 + ], + "angle": 0, + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. 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Springer, 2022. 1, 2" + }, + { + "type": "list", + "bbox": [ + 0.504, + 0.093, + 0.894, + 0.443 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18750" + } + ] +] \ No newline at end of file diff --git a/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_origin.pdf b/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..6900cc8f5cfc604210e3f058a72e0046a7bdf3eb --- /dev/null +++ b/2024/Step Differences in Instructional Video/ddcdbdd3-a745-4d02-aef0-ad93fd7b5b5b_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:22bb76bfaea165f061378ba26989d6ccd0df8c4ef9c5d4e5c8d4c510290a8fb0 +size 2636638 diff --git a/2024/Step Differences in Instructional Video/full.md b/2024/Step Differences in Instructional Video/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e8beaf834c951d73a79a354badce5b7e22e406d2 --- /dev/null +++ b/2024/Step Differences in Instructional Video/full.md @@ -0,0 +1,336 @@ +# Step Differences in Instructional Video + +Tushar Nagarajan, Lorenzo Torresani +FAIR, Meta + +# Abstract + +Comparing a user video to a reference how-to video is a key requirement for AR/VR technology delivering personalized assistance tailored to the user's progress. However, current approaches for language-based assistance can only answer questions about a single video. We propose an approach that first automatically generates large amounts of visual instruction tuning data involving pairs of videos from HowTo100M by leveraging existing step annotations and accompanying narrations, and then trains a video-conditioned language model to jointly reason across multiple raw videos. Our model achieves state-of-the-art performance at identifying differences between video pairs and ranking videos based on the severity of these differences, and shows promising ability to perform general reasoning over multiple videos. + +# 1. Introduction + +Instructional how-to videos are an important medium for learning new skills that offer in-depth visual demonstrations of complex procedural activities. In turn, they serve as a valuable resource for building AR/VR assistants that can guide a user through a procedural activity, by aligning user activity to a reference how-to video. Instructional videos have thus been the subject of several recent datasets and benchmarks that are driving new research [6, 9, 41, 45, 48, 59, 68, 69]. + +A key requirement for such systems is the ability to compare and contrast the user's execution of a step in the activity with the reference video step, to highlight similarities and differences between them. For example, to let the user know that they used too much detergent (while doing laundry) or that the gravity is too thick (while cooking). This ability has direct value for personalized assistance applications such as progress tracking, mistake detection and surfacing user-activity driven tips. + +More generally, reasoning about a video with respect to a reference video is a fundamental problem for video understanding that has value for fine-grained video retrieval [11, 53, 54, 57] (e.g., to browse internet videos for "this movie + +![](images/ba73c7a2b1c5df3a56800e8daea03f7b3b6bbfa3168eee0d37a8d0df70c41b9b.jpg) + +![](images/d49aaa0de98fc1597f1127ed1c89a46a5daeef0caf580f9ede750ab1d5f2949f.jpg) + +![](images/4cf44cf4c9b4567d2a8301ac9aa8caa1591ce2c3e8a0eab1feffd54f3d165fd0.jpg) + +![](images/a80536d75100e187d2f06f5038494f2cb764248e6242707f766df6517a97bc13.jpg) +Figure 1. Main idea. Top: We train models to compare two videos showing the same high-level keystep and to describe their differences (e.g., in tools, ingredients, technique). Bottom: Once trained, such models can then help answer questions about a user's activity compared to a reference (e.g., an internet how-to video) like "did I do this step right?" or "am I done yet?". + +Q: Am I done stirring the onions? +![](images/877c8747fdd842c7c6901897063f5df311ea85d0dc7e88f25dff59561a4b13f1.jpg) +A: No, keep stirring till they become golden brown like the video. + +scene, but in a forest"), step detection [6, 45, 46, 48, 69] (e.g., to recognize subtle variations in keysteps) and multi-video question answering and reasoning [5, 36] (e.g., to answer comparative questions like "which video uses the least amount of oil?"). + +Despite its importance, there has been limited work on comparing videos. Prior work has explored change captioning in images [14, 16, 17, 34, 39, 70], however these works typically consider pixel-level differences (e.g., missing or moved objects; changed background objects) in static scenes (e.g., the same parking lot; the same tabletop), or in synthetically generated datasets [34]. They do not consider important semantic differences in activities (e.g., differences in tool use, subtle variations in actions and techniques or visual differences due to state changes), which together with the low-level visual differences, form a complete picture of human-object interactions. + +To address these limitations, we propose a video-conditioned language model (VCLM) approach to directly compare two videos of same step in a procedural activity. Specifically, we propose the difference question answering task: given a reference and a candidate video, a model must answer a question that involves reasoning across both videos (e.g., what are the differences in tools? techniques?; do the two videos show the same activity?). Such a model that + +effectively relates user activity to a reference video, can then provide detailed context to answer more general questions such as "what did I do wrong compared to the reference" or "am I done yet?". See Fig. 1. + +An important practical question is how to source the supervision to train such a model, given that existing video datasets only contain individual videos with captions. Moreover, meaningful differences are not guaranteed to exist between arbitrary pairings of videos. We therefore automatically generate training data from existing large-scale instructional video datasets annotated with keysteps and speech narrations describing what instructors are doing [9, 29]. We pair clips of the same keystep (e.g., two videos of a person "stir frying the rice until it is dark yellow") but from distinct videos to allow for variations between them. For example the first video may use a cast iron pan versus a steel wok or the person may be tossing the food in the pan vs stirring with a spatula. We then leverage recent large language models [50] to generate questions and answers about the similarities and differences between the two videos given their visual descriptions, speech narrations, and visible objects as context. Inspired by work in visual instruction tuning of language models [27, 65], we finally fine-tune a video-pair conditioned language model with the collected dataset. The resulting model has the ability to cross-reference videos to compare them, and more generally answer questions that require joint reasoning about both videos simultaneously. + +To evaluate our model, we collect a manually annotated dataset of 6292 video pairs with $\sim 36\mathrm{k}$ difference captions spanning 5 categories, as well as scores for how severe the differences are. We set up the first benchmark for video comparisons and evaluate models on their ability to describe the differences in specific categories (e.g., "What are the differences in tools? techniques?") and to rank videos based on their differences (e.g., "Which video shows the least different technique?"). Our models trained with weak-supervision from automatically generated data achieve state-of-the-art results on our benchmark, highlighting its value for personalized assistance applications. Our benchmark will be hosted publicly, to allow the community to make progress towards this under-explored task. + +# 2. Related work + +Instructional video understanding Recent large-scale instructional video datasets [6, 9, 41, 45, 48, 59, 68, 69] have facilitated research in step captioning [63, 68], step detection [6, 45, 46, 48, 69], temporal grounding [2, 7, 13, 18, 28], vision-language representation learning [3, 25, 38, 66] and video question answering [56, 58, 60, 62] to name a few. In all these approaches, the goal is to process a single video and then caption, answer questions or temporally localize an action or text within it. While we are also interested in the space of procedural videos in the context of personalized + +language-based assistance, in contrast, we develop methods to compare and contrast multiple videos — namely a reference video and a candidate video — in order to identify differences and answer comparative questions about them. + +Visual differences in images Prior work has studied visual differences in images in the context of attributes [8, 10, 33, 61] (e.g., which shoe is more formal) to facilitate fine-grained recognition. More relevant to our work, change captioning [14, 16, 17, 34, 39, 70] involves describing the differences between two images as a text caption. Other work defines differences as 2D bounding boxes [42, 43] or semantic maps [35] for regions that differ. More recently, VCLM models have been trained with "spot-the-difference" data from the above with a similar goal of identifying image differences [20]. In all these cases, the two images typically involve the same scene from multiple viewpoints or over time (e.g., surveillance footage) or are constructed from synthetic images (e.g., 3D geometric shapes re-arranged on a table). The resulting differences therefore focus on simple visual cues like missing or moved objects. More recent approaches use visual differences to retrieve videos [4], however they assume the difference is known (to retrieve a relevant video) rather than identifying and describing it. In contrast, we compare across distinct video clips that show the same high-level keystep. As a result, the difference captions characterize complex variations that arise naturally from the availability of tools and ingredients, differing skill / technique or personal preference. + +Visual instruction tuning of language models Given the recent success of large language models (LLMs), several efforts have tried to adapt them for use with various modalities including images, videos, audio etc., typically by aligning captions to modalities or instruction tuning [12, 21, 26, 27, 31, 32, 64, 65]. All these approaches typically use text captions or generate instruction tuning data based on a single image or video. In contrast, we generate instruction data for pairs of videos (a reference, and a target video) to allow vision conditioned language models to jointly reason about them both. Some approaches do train on multiple images interleaved with text [1, 19, 51], however they do not support instructions at inference, and instead rely on in-context few-shot prompting to respond. In contrast, our approach can respond to arbitrary questions about a video with respect to a reference clip. + +# 3. Approach + +Our goal is to train models to answer questions about a video in the context of a reference video, by jointly reasoning about the two. The problem is two-fold: where do we source data of pairs of videos with relevant questions + +![](images/2061e3adb07d5eef315bc69de70a7f966bed2f324e4bafdd15adbda16c7e68f5.jpg) +Figure 2. Step differences framework. We first generate a comprehensive step description including information from action captions, object detections and ASR narrations (left panel). We then select pairs of clips with similar step descriptions, and automatically generate questions and answers that compare the two (center panel, Sec. 3.2). Finally, we instruction-tune an LLM to generate answers conditioned on the generated questions and encoded representations of both videos (right panel, Sec. 3.3). Once trained, the model directly operates on video clips to compare them, without the need for captions, ASR or object detections. + +![](images/92c8fe4c27f749417afe435cb1692ac0a14976e406919a1b898f5e2632bc434b.jpg) + +![](images/6b535b8e2793d592d13a276ae939b4e76b967d9c8310a90f2b278c88443999e0.jpg) + +to train such models and what model architectures support training with multiple videos? For the former, we turn to automatically generating this data using large-language models (LLMs) parsing narrated video from existing datasets. For the latter, we use vision-conditioned language models (VCLMs) — a powerful class of models for single-video question answering — adapted to our multi-video setting. In the following, we first formally define our task (Sec. 3.1). Next, we describe our automatic training data generation pipeline (Sec. 3.2). Finally, we discuss training and downstream inference (Sec. 3.3). + +# 3.1. Task definition + +We require models that collectively answer questions about two videos. Formally, given a reference video $V_{r}$ , a candidate video $V_{c}$ and a question $q$ , models must produce a corresponding answer $a$ . This formulation is an extension of standard video question answering or captioning [67] with a response that is additionally conditioned on a reference video. The questions can take various forms, for example "How is the dough being prepared differently in Video 2"; "What is the similarity in mixing techniques between the two videos?". Critically, these questions all share the assumption that a single video alone (either the reference or the candidate) is insufficient to answer the question — reasoning over both videos is required. + +In our experiments, we train models with a diverse set of automatically-generated question-answer pairs. At test time, we focus on step differences, where the $q$ is of the form "what is the main difference between these videos in the category $g$ " and $g$ is the difference category (e.g., ingredients, techniques, etc.). This structure captures a representative range of fine-grained differences, and allows for consistent evaluation of models as we will show. + +# 3.2. Step differences dataset generation + +To train our models, we require a dataset of paired videos along with questions and answers (QA) relating the two in the form $(V_r, V_c, q, a)$ . However, current video datasets typically contain individual video clips annotated for actions, narrations, or single-video QA which is incompatible with our task definition. We therefore construct this from existing video datasets using large-language models, inspired by prior work on instruction tuning [12, 20, 27, 37, 49]. + +Constructing this dataset from existing video datasets is non-trivial. On the one hand, selecting random pairs of videos showing very different content (e.g., sports vs. cooking) or near-identical videos (e.g., from repetitions of the same activity by the same participant) will lead to trivial differences. On the other hand, naively selecting video pairs of the same class in action recognition datasets (e.g., "Bookbinding" or "Mowing the lawn") will not highlight fine-grained differences of interest, and will instead focus on global differences (e.g., changes in actors or scenes). Moreover, these datasets do not come with text descriptions to construct differences from. + +We therefore propose to use videos from the large-scale procedural video dataset HowTo100M [29], specifically cooking-themed videos labeled for keysteps from HT-Step [9]. Instructional videos are an ideal data source as they are narrated and show the same high-level keystep, but with variations that arise naturally from availability of tools and ingredients, differing skill / technique or personal preference. + +Specifically, for two videos showing the same keystep (e.g., Slowly pour the sauce over the dumplings), we assume one is the reference $V_{r}$ and the other is the candidate video $V_{c}$ , with corresponding speech narrations. First, we generate descriptions of the actions and objects (including their attributes) using off-the-shelf captioning models [31]. These + +models often hallucinate details in their generations, so we additionally filter object descriptions based on the scores of a pre-trained detection model [30] and filter action descriptions using visual grounding models [55]. Details about the filtering stage are in Supp. Finally, we aggregate the information from these three sources (ASR narration, filtered objects and actions) to synthesize a detailed step description for each video (Fig. 2, left panel). We then prompt a language model (in our case, Llama 2 [50]) to generate both questions and answers comparing the two videos based on their step descriptions. In short, the prompt takes the form: "Video 1: {description1}. Video 2: {description2}. Summarize the differences and generate 3 question-answer pairs comparing the two videos." (Fig. 2, center panel). An overview of the data generation pipeline with examples at each stage can be seen in Fig. 2. See Supp. for more examples and full step description prompt details. + +The resulting dataset contains QA instances over video pairs across 87740 unique video clips. Note that the LLM-generated data is noisy — they may hallucinate details that are not present in the video, misunderstand the ASR narrations, produce irrelevant questions or incorrect answers to questions. Despite this, they offer valuable weak supervision to train our VCLM models, as our experiments will show. + +# 3.3. Paired video instruction tuning + +We require a model that can generate natural language responses to video comparison questions in our dataset. To do this, we adapt a vision-conditioned language model (VCLM) to our multi-video setting via visual instruction tuning. In short, visual instruction tuning aligns the outputs of an image (or video) backbone to a powerful LLM to condition its responses on the visual content. This strategy has been successful in prior work for single image/video captioning and question answering [12, 21, 26, 27, 31, 64, 65]. We extend this to support comparisons across multiple videos. In our experiments, we use a Llama2 [50] LLM aligned with an Internvideo [55] backbone following prior work [31]. Note that it is possible to directly provide multiple videos to existing models by adding extra visual tokens to the input prompt, however their performance is degraded as they not trained to support this. We compare against such models. + +Specifically, for an instruction-tuning instance $(V_{r}, V_{c}, q, a)$ , we generate an instruction prompt in the Llama2 format as follows. + +```txt + [INST] <> You are a helpful AI assistant that answers questions about a pair of videos. Answer in a single sentence. Here is the first video: {V_r}. Here is the second video: {V_c}. > {q} [/INST] {a} +``` + +We encode the text tokens in this prompt using the LLM's pre-trained text encoder. We encode each video into a sequence of spatiotemporal tokens using a pre-trained video + +![](images/60b4463b907d0931fae58cc0f83294bbae16db278e174ea8161373bd15aede28.jpg) + +![](images/e8b6ccee952803c831fea077dbc15be2e296cc6a50b1955517b6a385a25f9f90.jpg) +Difference Recognition + +![](images/f470fd08a878fe0e2f036c2e8a3ed71cf0e371f586bfa4d690dae7effb36c81b.jpg) +Figure 3. Evaluation tasks. We evaluate on describing (DiffCap), recognizing (DiffMCQ) and ranking (DiffRank) differences. + +backbone $M_V$ , and then align them to the LLM's input space using a learnable projection module $M_{proj}$ . The resulting encoded instruction prompt is a sequence of tokens comprising a mix of text and visual tokens, which can then be processed by the LLM (Fig. 2, right panel). + +The model is trained using the original auto-regressive objective to maximize the probability of generating the answer tokens, conditioned on the question, reference and candidate video, and is trained using a standard cross-entropy loss. + +$$ +p \left(X _ {a} \mid X _ {r}, X _ {c}, X _ {q}\right) = \prod_ {i = 1} ^ {\left| X _ {a} \right|} p _ {\theta} \left(X _ {a, i} \mid X _ {r}, X _ {c}, X _ {q}, X _ {a, < i}\right) \tag {1} +$$ + +$$ +X _ {r} = M _ {p r o j} \left(M _ {V} \left(V _ {r}\right)\right) \tag {2} +$$ + +$$ +X _ {c} = M _ {p r o j} \left(M _ {V} \left(V _ {c}\right)\right), \tag {3} +$$ + +where $X_{a,i}$ is the i-th answer token in the sequence, $X_{r}(X_{c})$ are the visual tokens corresponding to the reference (candidate) videos, $X_{q}, X_{a}$ are tokens of the question and answer, $X_{a, < i}$ are answer tokens that occur before $X_{a,i}$ and $\theta$ are the learnable parameters in $\mathcal{M}_{proj}$ . + +Note that the video encoder and the LLM weights are frozen, and the loss is computed only for answer tokens. Only the projection layer is fine-tuned. Once trained, our model will be able to refer to each video, discuss their similarities and compare them. We evaluate our model by autoregressively generating text in response to various prompts coupled with reference and candidate videos. + +# 3.4. Describing, recognizing and ranking step differences in procedural videos + +Finally, we use our trained models to identify and rank fine-grained differences between pairs of video. We cast these tasks into the paired-video QA framework as follows. + +![](images/a3867a413d161cda4f42af8274476ebf138ead5c77cd72318d628358c5d0a4fc.jpg) + +Ingredients: The person oiled the baking dish with oil as opposed to vegetable ghee. Score: 4/5 + +Tools/Equipment: The oil was applied to the pan with a pastry brush instead of bare hands; The baking dish used was a glass baking dish as opposed to ceramic. Score: 3/5 + +Actions: The person skipped pressing the dough mixture into the baking dish after oiling it. Score: 3/5 + +![](images/9160aff5baa71ab5cbe00a41df2ba342036b6231c86dd33cd50ade7558bf90fd.jpg) +Figure 4. StepDiff dataset samples We annotate text describing differences in various categories and scores for how different the videos are in each category (1 = very different; 5 = nearly identical). More examples are in Supp. + +Tools/Equipment: The person mixes the cream mixture with green spatula instead of red. Score: 5/5 + +Actions: The person continuously mixes the cream mixture instead of folding then shakes off the spatula. Score: 3/5 + +Visuals: The cream mixture has a thick and clumpy consistency instead of smooth and runny. Score: 2/5 + +![](images/d85e16b5ca31f0fbec5293661d1efd5bd09d2769fa15ed4126b878d495c06a9b.jpg) + +Ingredients: The person only cooks the regular potato fries as opposed to 6 varieties of potato fries. Score: 4/5 + +Actions: The person skips transferring the potato fries in the tray. Score: 3/5 + +Visuals: The potato fries has a regular yellow color contrary to having green, red, orange and brown fries. Score: 2/5 + +![](images/3576d30116a6c73aa91a5ed9f09996af5c1821c7fd803d0f46577de1813dd8a2.jpg) + +Tools/Equipment: The dough was flipped using a fork rather than a tong; The dough was deep-fried in a steel pan instead of a non-stick pan. Score: 3/5 + +Technique: The dough was flipped once as opposed to three times. Score: 4/5 + +Visuals: The deep-fried dough appears to have a flower design and has holes on it as opposed to full and lumpy. Score: 3/5 + +Difference captioning (DiffCap) The goal is to generate a textual description of the differences between two videos in a specific category $g$ (e.g., ingredients, tools). The question $q$ takes the form "what is the main difference between these videos in the category $g$ ". The difference caption is generated auto-regressively using the trained model. + +Difference recognition (DiffMCQ) The goal is to select the correct video pair that matches the difference caption, from a list of candidate video pairs $\{(V_r^i,V_c^i)\}_{i = 1..4}$ . This is a discriminative version of the captioning task above inspired by recent work in vision-language feature learning [24]. For this, we compute $p(a|V_r^i,V_c^i,q)$ — the likelihood of generating the difference text given the pair of videos following Eqn. 2 — and then select the pair with the highest score. + +Difference ranking (DiffRank) The goal is to rank video instances $\{V_c^i\}_{i=1..4}$ based on how different they are to a common reference video $V_r$ , in terms of a particular category of interest $g$ . For this, we set $q$ to be "do these two videos show the same $g$ ? Answer YES or NO," and rank each candidate video based on the likelihood of generating "YES" as the response. + +Together, these tasks are a representative suite of problems for instructional video understanding that require comparing videos along various axes. DiffCap tests how accurately a model can describe differences in natural language, DiffMCQ tests how well it can discriminate differences between videos, and DiffRank tests how well the model can assess the severity of these differences to rank them. A model for these tasks can enable applications that guide user action (e.g., to follow a reference video tutorial) or help browse through large collections of videos (e.g., to find the perfect variation of a recipe). Fig. 3 illustrates these tasks. + +# 4. Experiments + +We evaluate our VCLM model on the three step difference tasks from Sec. 3.4. + +Dataset We construct a test dataset from videos in HT-Step [9]. HTStep contains videos from a large-scale procedural video dataset, HowTo100M [29] (Cooking & Entertainment), with temporal segments (clips) annotated for keysteps (e.g., "fry then onions until golden brown"). We manually annotate pairs of clips, where each pair corresponds to instances of the same labeled keystep, but from distinct videos. Annotators are asked to identify the main differences across 5 categories (ingredients, tools/equipment, techniques, visual differences) and write difference captions of a consistent style — what happens in the target clip, compared to what happens in the reference (e.g., "The person uses a deep fryer to fry the potatoes instead of shallow frying it in a pan"). They are then asked to score the difference caption in each category on a scale of 1-5 based on how severe the difference is, where 1 is a significant difference (e.g., swapping out a critical ingredient that would change the dish entirely) and 5 is nearly identical (e.g., minor cosmetic differences that does not affect the activity). A rubric is used to ensure consistency in scoring. + +Note that this data is only used for evaluation — we exclude these pairs from the automatic training data generation pipeline described in Sec. 3.2 to ensure that the model has not seen these instances during training. In total, we collect 35988 difference captions across 6292 clip pairs, involving 8396 unique clips. See Fig. 4 for examples. Full collection details and dataset statistics are in Supp. + +Baselines We compare several classes of models. + +
DIFFCAP
BLEUCIDERROGUE-L
VLEmb (CLIP) [40]---
VLEmb (InternVideo) [55]---
Socratic (BLIP-2) [22]0.1590.0360.169
Socratic (LLaVA) [27]0.1510.0310.166
Socratic (Step desc.)0.1410.0200.172
VCLM (LLaVA) [27]0.2110.0690.199
VCLM (AnyMAL) [31]0.2090.1150.196
Interleaved (IDEFICS) [19]0.2170.0800.210
Interleaved (AnyMAL)0.2070.1020.198
StepDiff0.2230.1040.215
+ +
Acc %
0.396
0.451
0.335
0.332
0.392
0.381
0.471
0.376
0.497
0.541
+ +
DIFFRANK
τ
0.1270.170
0.0220.004
0.0130.013
0.0190.032
0.0810.014
0.181
+ +Table 1. Results. Our approach outperforms three classes of baselines built on top of state-of-the-art vision-language embedding and VCLM models. VLEmb baselines are excluded from DiffCap as they cannot generate text. + +- VLEmbed is a class of vision-language model that embeds images or video in the same space as text, and then compares their similarity in the shared space. Video pair embeddings are calculated as the average of individual video embeddings1. We use CLIP [40] and InternVideo [55]. +- Socratic is a class of VCLMs that first converts videos into text using a captioning model, and then prompts a text-only LLM with these captions. These models are powerful, but often require complex, manually engineered prompts. We use state-of-the-art visual captioners (BLIP-2 [22], LLaVA-1.5 [27]) as well our aggregate step descriptions from Sec. 3.2. We use Llama2 to process the captions regardless of which model generated them, for fair comparisons. +- VCLM is a class of visual instruction-tuned language model trained for video captioning and question answering (for a single video). We directly add extra tokens for the reference video into the prompt to be consistent with our paired-video QA task. We compare LLaVA-1.5 [27] and AnyMAL [31]. +- Interleaved is a class of models that are trained with interleaved sequences of images/videos and text, and naturally support multiple videos as inputs, but are not explicitly trained to compare them. We compare the recently proposed IDEFICS [19] and a model we train on sequences of (video, ASR) pairs from HowTo100M (training details in Supp.). + +These baselines represent a spectrum of leading strategies for vision-language reasoning, including methods that directly embed video and language in the same space (VLEmbed), ones that explicitly convert videos to text and perform exclusively text-based reasoning (Socratic) and ones that perform joint vision-text reasoning on videos (VCLM, Interleaved). We ensure that each class of baselines include methods that have been trained on in-domain HowTo100M videos, while excluding the evaluation videos, to ensure fair comparisons with our approach. These are InternVideo, + +Socratic (Step desc.), VCLM (AnyMAL), and Interleaved (AnyMAL). Additional pretraining and implementation details are in Supp. + +Implementation details We use the Llama2-chat-70B [50] as the base LLM for all our experiments. Following prior work [31], $M_V$ is an Internvideo [55] video encoder that inputs 8 uniformly sampled frames from each video clip and generates 2048 spatio-temporal tokens. $M_{Proj}$ is a 2-layer Perceiver [15] module followed by a linear layer head to output 32 tokens in the LLM's input dimension. During training, all parameters are frozen except for $M_{Proj}$ . StepDiff models are initialized from Interleaved model weights before finetuning (interleaved data is retained during finetuning). For baselines, we use the largest available versions of models — InstructBLIP (Vicuna13B), LLaVA (Vicuna13B), AnyMAL (70B), IDEFICS (80B). Full implementation and training details are in Supp. + +# 4.1. Difference captioning + +We first evaluate how well our model can describe differences in video pairs (DiffCap). As mentioned in Sec. 3.1, $q$ is of the form "what is the main difference between these videos in the category $g$ " where $g$ is the difference category. Since there may be multiple annotated differences in the same category, we group them together and treat them as a ground truth set, resulting in a dataset with 22292 instances. We measure standard text generation metrics including CIDER [52] and ROUGE-L [23]. Outputs are postprocessed using simple string matching techniques to ensure difference captions are generated in the correct format (details in Supp). For the socratic baselines, we provide the generated caption instead of the video tokens in the prompt from Sec. 3.3. Table 1 (left) shows our results. The socratic models perform poorly as they are limited by the information contained in the base captions. It is infeasible to generate captions that exhaustively describe every aspect of a video, without knowing what is of interest, and without the risk of model hallucinations. The VCLM models perform better, + +![](images/bb5064d9fe927d66660d6f1aa3b0db838c0399961f8d400b971599349c815343.jpg) +Figure 5. Extended QA on video pairs. Our model which can describe differences (row 1) can be prompted (i.e., queried without any form of retraining) for comparative reasoning (e.g., "why are they different?"; "how different are they?" row 2-3), or to bootstrap mistake detection (row 4). A failure case is shown in row 5 due to model hallucination. + +especially when trained to process multiple videos (i.e., interleaved models), however they still fall short of our approach that can explicitly compare and contrast videos. The example in Fig. 6 highlights the sensitivity of socratic models to input captions (e.g., the reference caption did not mention the use of hands), and shows how VCLM models tend to hallucinate details. Our approach can correctly describe the difference. See Supp for more examples. + +# 4.2. Difference recognition + +While the captioning metrics are informative, they are based on word overlap statistics, and do not always capture the semantics of the text well. To address this, we evaluate on DiffMCQ – the discriminative version of the captioning task. We adapt the same dataset from DiffCap, except we sample a single difference caption for each category if there are multiple differences present. Further, we sample three negative video pairs from other instances in the dataset that involve similar objects and actions (details in Supp). For the VLEmb bed baselines, we score each video pair using the cosine similarity between their average visual embeddings and the text embedding of the difference caption. We compare variants of this baseline considering only the reference or target in Supp. For all LLM-based baselines, we compute the + +likelihood of generating the difference caption for each video pair, under each model as discussed in Sec. 3.1. We evaluate top-1 accuracy. Table 1 (center) shows our results. The joint feature embedding models capture some semantics, but are insufficient for identifying differences. Socratic models have a similar trend to captioning results, however models trained on step differences show large improvements, highlighting the value of careful curation for generating captions. Among VCLM models, ones that have seen in-domain HowTo100M videos during training have an edge over the others (i.e., LLaVA, IDEFICS), with interleaved models again being superior. Our model outperforms all these approaches with a $5\%$ accuracy improvement over the strongest baseline. Fig. 7 shows performance increases by difference category, over the weakest baseline (Socratic). Our approach shows large relative improvements on most categories especially in technique and tool use (both $46\%$ ), which require fine-grained action understanding. + +# 4.3. Difference ranking + +Finally, we evaluate how well our model can rank videos based on the severity of differences compared to a common reference (DiffRank). Each reference video in the dataset is paired with four target videos, scored along each category + +![](images/961448b3fd16f108256382e8be7d904bbcc42e7aaa3adf1472a63c20102bad34.jpg) +Figure 6. DiffCap baselines. Our approach can describe differences without relying on input captions (like Socratic) and is less prone to hallucinating details (like VCLM). + +# What is the main difference in "Tools" between the two videos? + +- Socratic: the person is using a rolling pin to roll out dough on a wooden surface, instead of a woman and young girl working together in a kitchen, ... +VCLM: the dough is rolled out on parchment paper, instead of directly on the counter. +- StepDiff: the dough is rolled out with a rolling pin, instead of being stretched with hands. + +![](images/2430cc269ec99e6e627a7ef26add33532175981d8f73216c5ac31956cddb0fa4.jpg) +Figure 7. DiffMCQ performance by category. Improvements are reported over the weakest baseline (Socratic). + +axis. For example, some videos may be very similar in terms of technique, but very different in terms of ingredients. We only retain instances where there is a clear ranking (i.e., no more than one tie in scores) The resulting dataset contains 3932 instances involving 5746 unique clips. + +As discussed in Sec. 3.1, we rank each target video candidate based on the likelihood of producing the response "YES" when asked whether it is similar to the reference. We use the Kendall's $\tau$ rank correlation metric to evaluate how well the generated ranking compares to the ground truth ranking annotators provide. Table 1 (right) shows our results. Unlike the previous tasks, the joint embedding models perform better than the LLM based baselines for two reasons. First, similarity in the embedding space directly translates to a score for ranking, rather than relying on computing "YES" token probability as a proxy for this. Second, there is a high correlation between the rankings across categories for the same set of instances ( $\tau = 0.63$ ). For example, videos ranked low in similarity for tools when compared to a reference are often also ranked low for technique. Despite these issues, our approach is able to outperform all baselines, showcasing its versatility as a retrieval and ranking model. + +# 4.4. Extending QA beyond atomic differences + +Next, we show how our model can be prompted to answer questions beyond just "describe the differences". LLMs have + +
DIFFCAP
BLEUCIDERROGUE-L
StepDiff0.2230.1040.215
w/o interleaved data0.2140.0940.210
w/o QA filtering0.2220.0960.212
w/ 13B LLM0.2160.1240.205
+ +
DIFFMCQDIFFRANK
Acc %τ
0.5410.181
0.4990.185
0.5160.120
0.5270.175
+ +Table 2. Ablation experiments. Impact of retaining interleaved training data, careful filtering of QA training data and LLM size. + +shown remarkable abilities for complex, multi-step reasoning in text – our training framework unlocks the same kind of reasoning for multiple videos, based on their differences. In Fig. 5, we show some examples of this. Our model is able to naturally describe differences as it was trained for this task (row 1), but also has the ability to perform comparative reasoning (row 2-3) or explain mistakes (row 4). We show a failure case in row 5, where the model hallucinates content – a characteristic feature of the LLM models it is built upon. Moreover, our model works with egocentric video (row 1, 4), despite being trained on largely third-person video content (HowTo100M), which is promising for AR/VR user assistance applications. + +# 4.5. Ablation experiments + +Finally, we ablate several design choices in our model in Table 2. As mentioned in Sec. 4, we finetune models on both interleaved ASR data as well as our generated pair QA data. Without the interleaved data, the model performance drops on two tasks, likely due to catastrophic forgetting (w/o interleaved data). Next, we show the importance of filtering the generated QA data (w/o QA filtering), given the high likelihood of hallucinations produced by the LLM. Finally, we swap out the 70B LLM model for a smaller sized one (w/13B LLM), causing the performance to drop, though not significantly. + +# 5. Conclusion + +We proposed StepDiff, a video-conditioned language model (VCLM) that can compare and contrast videos to reveal fine-grained differences between them. We propose an approach that can automatically generate instruction-following paired-video QA training data from large-scale procedural video data, and a manually curated benchmark to evaluate models. Our experiments on describing and identifying differences, as well on ranking videos based on differences demonstrate the value of our approach for personalized assistance applications. Future work can leverage our work for personalized retrieval (e.g., retrieve content based on user-activity), or multi-video QA beyond instructional videos. + +Acknowledgements Thanks to Efi Mavroudi, Huiyu Wang, Triantafyllos Afouras and Yale Song for helpful discussions; Kumar Ashutosh and Suyog Jain for help with annotation tooling and collection; Austin Miller and Honey Manglani for managing the annotator workforce. + +# References + +[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. Flamingo: a visual language model for few-shot learning. 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Springer, 2022. 1, 2 \ No newline at end of file diff --git a/2024/Step Differences in Instructional Video/images.zip b/2024/Step Differences in Instructional Video/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..88a9777312bb102a70e2bad2e2ae4c6c8a1b7cf2 --- /dev/null +++ b/2024/Step Differences in Instructional Video/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cabbedcc070ce5cf1fe30fe5ae55e800c290bea5f74a5b9613d44c2778bdbd01 +size 570572 diff --git a/2024/Step Differences in Instructional Video/layout.json b/2024/Step Differences in Instructional Video/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d1b0efae59bb8571f89a719824b0b1bebadd1f0b --- /dev/null +++ b/2024/Step Differences in Instructional Video/layout.json @@ -0,0 +1,8584 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 176, + 103, + 416, + 120 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 176, + 103, + 416, + 120 + ], + "spans": [ + { + "bbox": [ + 176, + 103, + 416, + 120 + ], + "type": "text", + "content": "Step Differences in Instructional Video" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 206, + 143, + 386, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 206, + 143, + 386, + 171 + ], + "spans": [ + { + "bbox": [ + 206, + 143, + 386, + 171 + ], + "type": "text", + "content": "Tushar Nagarajan, Lorenzo Torresani \nFAIR, Meta" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 199, + 191, + 211 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 199, + 191, + 211 + ], + "spans": [ + { + "bbox": [ + 143, + 199, + 191, + 211 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 224, + 290, + 392 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 224, + 290, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 224, + 290, + 392 + ], + "type": "text", + "content": "Comparing a user video to a reference how-to video is a key requirement for AR/VR technology delivering personalized assistance tailored to the user's progress. However, current approaches for language-based assistance can only answer questions about a single video. We propose an approach that first automatically generates large amounts of visual instruction tuning data involving pairs of videos from HowTo100M by leveraging existing step annotations and accompanying narrations, and then trains a video-conditioned language model to jointly reason across multiple raw videos. Our model achieves state-of-the-art performance at identifying differences between video pairs and ranking videos based on the severity of these differences, and shows promising ability to perform general reasoning over multiple videos." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 428, + 127, + 441 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 428, + 127, + 441 + ], + "spans": [ + { + "bbox": [ + 47, + 428, + 127, + 441 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 449, + 287, + 556 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 556 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 556 + ], + "type": "text", + "content": "Instructional how-to videos are an important medium for learning new skills that offer in-depth visual demonstrations of complex procedural activities. In turn, they serve as a valuable resource for building AR/VR assistants that can guide a user through a procedural activity, by aligning user activity to a reference how-to video. Instructional videos have thus been the subject of several recent datasets and benchmarks that are driving new research [6, 9, 41, 45, 48, 59, 68, 69]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 558, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 287, + 665 + ], + "type": "text", + "content": "A key requirement for such systems is the ability to compare and contrast the user's execution of a step in the activity with the reference video step, to highlight similarities and differences between them. For example, to let the user know that they used too much detergent (while doing laundry) or that the gravity is too thick (while cooking). This ability has direct value for personalized assistance applications such as progress tracking, mistake detection and surfacing user-activity driven tips." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "More generally, reasoning about a video with respect to a reference video is a fundamental problem for video understanding that has value for fine-grained video retrieval [11, 53, 54, 57] (e.g., to browse internet videos for \"this movie" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 198, + 362, + 255 + ], + "blocks": [ + { + "bbox": [ + 307, + 198, + 362, + 255 + ], + "lines": [ + { + "bbox": [ + 307, + 198, + 362, + 255 + ], + "spans": [ + { + "bbox": [ + 307, + 198, + 362, + 255 + ], + "type": "image", + "image_path": "ba73c7a2b1c5df3a56800e8daea03f7b3b6bbfa3168eee0d37a8d0df70c41b9b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 362, + 199, + 418, + 254 + ], + "blocks": [ + { + "bbox": [ + 362, + 199, + 418, + 254 + ], + "lines": [ + { + "bbox": [ + 362, + 199, + 418, + 254 + ], + "spans": [ + { + "bbox": [ + 362, + 199, + 418, + 254 + ], + "type": "image", + "image_path": "d49aaa0de98fc1597f1127ed1c89a46a5daeef0caf580f9ede750ab1d5f2949f.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 419, + 199, + 544, + 255 + ], + "blocks": [ + { + "bbox": [ + 419, + 199, + 544, + 255 + ], + "lines": [ + { + "bbox": [ + 419, + 199, + 544, + 255 + ], + "spans": [ + { + "bbox": [ + 419, + 199, + 544, + 255 + ], + "type": "image", + "image_path": "4cf44cf4c9b4567d2a8301ac9aa8caa1591ce2c3e8a0eab1feffd54f3d165fd0.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 307, + 257, + 362, + 313 + ], + "blocks": [ + { + "bbox": [ + 307, + 257, + 362, + 313 + ], + "lines": [ + { + "bbox": [ + 307, + 257, + 362, + 313 + ], + "spans": [ + { + "bbox": [ + 307, + 257, + 362, + 313 + ], + "type": "image", + "image_path": "a80536d75100e187d2f06f5038494f2cb764248e6242707f766df6517a97bc13.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 323, + 547, + 389 + ], + "lines": [ + { + "bbox": [ + 304, + 323, + 547, + 389 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 547, + 389 + ], + "type": "text", + "content": "Figure 1. Main idea. Top: We train models to compare two videos showing the same high-level keystep and to describe their differences (e.g., in tools, ingredients, technique). Bottom: Once trained, such models can then help answer questions about a user's activity compared to a reference (e.g., an internet how-to video) like \"did I do this step right?\" or \"am I done yet?\"." + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_caption" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 362, + 257, + 419, + 313 + ], + "blocks": [ + { + "bbox": [ + 362, + 257, + 419, + 313 + ], + "lines": [ + { + "bbox": [ + 362, + 257, + 419, + 313 + ], + "spans": [ + { + "bbox": [ + 362, + 257, + 419, + 313 + ], + "type": "image", + "image_path": "877c8747fdd842c7c6901897063f5df311ea85d0dc7e88f25dff59561a4b13f1.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 421, + 267, + 538, + 277 + ], + "lines": [ + { + "bbox": [ + 421, + 267, + 538, + 277 + ], + "spans": [ + { + "bbox": [ + 421, + 267, + 538, + 277 + ], + "type": "text", + "content": "Q: Am I done stirring the onions?" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 421, + 281, + 540, + 297 + ], + "lines": [ + { + "bbox": [ + 421, + 281, + 540, + 297 + ], + "spans": [ + { + "bbox": [ + 421, + 281, + 540, + 297 + ], + "type": "text", + "content": "A: No, keep stirring till they become golden brown like the video." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_footnote" + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 412, + 547, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 547, + 472 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 547, + 472 + ], + "type": "text", + "content": "scene, but in a forest\"), step detection [6, 45, 46, 48, 69] (e.g., to recognize subtle variations in keysteps) and multi-video question answering and reasoning [5, 36] (e.g., to answer comparative questions like \"which video uses the least amount of oil?\")." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 473, + 547, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 473, + 547, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 473, + 547, + 616 + ], + "type": "text", + "content": "Despite its importance, there has been limited work on comparing videos. Prior work has explored change captioning in images [14, 16, 17, 34, 39, 70], however these works typically consider pixel-level differences (e.g., missing or moved objects; changed background objects) in static scenes (e.g., the same parking lot; the same tabletop), or in synthetically generated datasets [34]. They do not consider important semantic differences in activities (e.g., differences in tool use, subtle variations in actions and techniques or visual differences due to state changes), which together with the low-level visual differences, form a complete picture of human-object interactions." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 547, + 713 + ], + "type": "text", + "content": "To address these limitations, we propose a video-conditioned language model (VCLM) approach to directly compare two videos of same step in a procedural activity. Specifically, we propose the difference question answering task: given a reference and a candidate video, a model must answer a question that involves reasoning across both videos (e.g., what are the differences in tools? techniques?; do the two videos show the same activity?). Such a model that" + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18740" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 45, + 72, + 288, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 72, + 288, + 120 + ], + "spans": [ + { + "bbox": [ + 45, + 72, + 288, + 120 + ], + "type": "text", + "content": "effectively relates user activity to a reference video, can then provide detailed context to answer more general questions such as \"what did I do wrong compared to the reference\" or \"am I done yet?\". See Fig. 1." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 45, + 121, + 288, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 121, + 288, + 395 + ], + "spans": [ + { + "bbox": [ + 45, + 121, + 288, + 395 + ], + "type": "text", + "content": "An important practical question is how to source the supervision to train such a model, given that existing video datasets only contain individual videos with captions. Moreover, meaningful differences are not guaranteed to exist between arbitrary pairings of videos. We therefore automatically generate training data from existing large-scale instructional video datasets annotated with keysteps and speech narrations describing what instructors are doing [9, 29]. We pair clips of the same keystep (e.g., two videos of a person \"stir frying the rice until it is dark yellow\") but from distinct videos to allow for variations between them. For example the first video may use a cast iron pan versus a steel wok or the person may be tossing the food in the pan vs stirring with a spatula. We then leverage recent large language models [50] to generate questions and answers about the similarities and differences between the two videos given their visual descriptions, speech narrations, and visible objects as context. Inspired by work in visual instruction tuning of language models [27, 65], we finally fine-tune a video-pair conditioned language model with the collected dataset. The resulting model has the ability to cross-reference videos to compare them, and more generally answer questions that require joint reasoning about both videos simultaneously." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 45, + 396, + 288, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 396, + 288, + 563 + ], + "spans": [ + { + "bbox": [ + 45, + 396, + 288, + 563 + ], + "type": "text", + "content": "To evaluate our model, we collect a manually annotated dataset of 6292 video pairs with " + }, + { + "bbox": [ + 45, + 396, + 288, + 563 + ], + "type": "inline_equation", + "content": "\\sim 36\\mathrm{k}" + }, + { + "bbox": [ + 45, + 396, + 288, + 563 + ], + "type": "text", + "content": " difference captions spanning 5 categories, as well as scores for how severe the differences are. We set up the first benchmark for video comparisons and evaluate models on their ability to describe the differences in specific categories (e.g., \"What are the differences in tools? techniques?\") and to rank videos based on their differences (e.g., \"Which video shows the least different technique?\"). Our models trained with weak-supervision from automatically generated data achieve state-of-the-art results on our benchmark, highlighting its value for personalized assistance applications. Our benchmark will be hosted publicly, to allow the community to make progress towards this under-explored task." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 574, + 132, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 132, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 132, + 586 + ], + "type": "text", + "content": "2. Related work" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 594, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 594, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 594, + 288, + 715 + ], + "type": "text", + "content": "Instructional video understanding Recent large-scale instructional video datasets [6, 9, 41, 45, 48, 59, 68, 69] have facilitated research in step captioning [63, 68], step detection [6, 45, 46, 48, 69], temporal grounding [2, 7, 13, 18, 28], vision-language representation learning [3, 25, 38, 66] and video question answering [56, 58, 60, 62] to name a few. In all these approaches, the goal is to process a single video and then caption, answer questions or temporally localize an action or text within it. While we are also interested in the space of procedural videos in the context of personalized" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 121 + ], + "type": "text", + "content": "language-based assistance, in contrast, we develop methods to compare and contrast multiple videos — namely a reference video and a candidate video — in order to identify differences and answer comparative questions about them." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 137, + 548, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 137, + 548, + 425 + ], + "spans": [ + { + "bbox": [ + 304, + 137, + 548, + 425 + ], + "type": "text", + "content": "Visual differences in images Prior work has studied visual differences in images in the context of attributes [8, 10, 33, 61] (e.g., which shoe is more formal) to facilitate fine-grained recognition. More relevant to our work, change captioning [14, 16, 17, 34, 39, 70] involves describing the differences between two images as a text caption. Other work defines differences as 2D bounding boxes [42, 43] or semantic maps [35] for regions that differ. More recently, VCLM models have been trained with \"spot-the-difference\" data from the above with a similar goal of identifying image differences [20]. In all these cases, the two images typically involve the same scene from multiple viewpoints or over time (e.g., surveillance footage) or are constructed from synthetic images (e.g., 3D geometric shapes re-arranged on a table). The resulting differences therefore focus on simple visual cues like missing or moved objects. More recent approaches use visual differences to retrieve videos [4], however they assume the difference is known (to retrieve a relevant video) rather than identifying and describing it. In contrast, we compare across distinct video clips that show the same high-level keystep. As a result, the difference captions characterize complex variations that arise naturally from the availability of tools and ingredients, differing skill / technique or personal preference." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 441, + 548, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 441, + 548, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 441, + 548, + 634 + ], + "type": "text", + "content": "Visual instruction tuning of language models Given the recent success of large language models (LLMs), several efforts have tried to adapt them for use with various modalities including images, videos, audio etc., typically by aligning captions to modalities or instruction tuning [12, 21, 26, 27, 31, 32, 64, 65]. All these approaches typically use text captions or generate instruction tuning data based on a single image or video. In contrast, we generate instruction data for pairs of videos (a reference, and a target video) to allow vision conditioned language models to jointly reason about them both. Some approaches do train on multiple images interleaved with text [1, 19, 51], however they do not support instructions at inference, and instead rely on in-context few-shot prompting to respond. In contrast, our approach can respond to arbitrary questions about a video with respect to a reference clip." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 645, + 373, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 645, + 373, + 658 + ], + "spans": [ + { + "bbox": [ + 306, + 645, + 373, + 658 + ], + "type": "text", + "content": "3. Approach" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Our goal is to train models to answer questions about a video in the context of a reference video, by jointly reasoning about the two. The problem is two-fold: where do we source data of pairs of videos with relevant questions" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18741" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 70, + 248, + 210 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 248, + 210 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 248, + 210 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 248, + 210 + ], + "type": "image", + "image_path": "2061e3adb07d5eef315bc69de70a7f966bed2f324e4bafdd15adbda16c7e68f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 220, + 547, + 277 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 547, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 547, + 277 + ], + "type": "text", + "content": "Figure 2. Step differences framework. We first generate a comprehensive step description including information from action captions, object detections and ASR narrations (left panel). We then select pairs of clips with similar step descriptions, and automatically generate questions and answers that compare the two (center panel, Sec. 3.2). Finally, we instruction-tune an LLM to generate answers conditioned on the generated questions and encoded representations of both videos (right panel, Sec. 3.3). Once trained, the model directly operates on video clips to compare them, without the need for captions, ASR or object detections." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 253, + 70, + 407, + 212 + ], + "blocks": [ + { + "bbox": [ + 253, + 70, + 407, + 212 + ], + "lines": [ + { + "bbox": [ + 253, + 70, + 407, + 212 + ], + "spans": [ + { + "bbox": [ + 253, + 70, + 407, + 212 + ], + "type": "image", + "image_path": "92c8fe4c27f749417afe435cb1692ac0a14976e406919a1b898f5e2632bc434b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 408, + 71, + 547, + 207 + ], + "blocks": [ + { + "bbox": [ + 408, + 71, + 547, + 207 + ], + "lines": [ + { + "bbox": [ + 408, + 71, + 547, + 207 + ], + "spans": [ + { + "bbox": [ + 408, + 71, + 547, + 207 + ], + "type": "image", + "image_path": "6b535b8e2793d592d13a276ae939b4e76b967d9c8310a90f2b278c88443999e0.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 297, + 290, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 297, + 290, + 429 + ], + "spans": [ + { + "bbox": [ + 46, + 297, + 290, + 429 + ], + "type": "text", + "content": "to train such models and what model architectures support training with multiple videos? For the former, we turn to automatically generating this data using large-language models (LLMs) parsing narrated video from existing datasets. For the latter, we use vision-conditioned language models (VCLMs) — a powerful class of models for single-video question answering — adapted to our multi-video setting. In the following, we first formally define our task (Sec. 3.1). Next, we describe our automatic training data generation pipeline (Sec. 3.2). Finally, we discuss training and downstream inference (Sec. 3.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 441, + 139, + 453 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 139, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 139, + 453 + ], + "type": "text", + "content": "3.1. Task definition" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "spans": [ + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "text", + "content": "We require models that collectively answer questions about two videos. Formally, given a reference video " + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "inline_equation", + "content": "V_{r}" + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "text", + "content": ", a candidate video " + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "inline_equation", + "content": "V_{c}" + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "text", + "content": " and a question " + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "text", + "content": ", models must produce a corresponding answer " + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "inline_equation", + "content": "a" + }, + { + "bbox": [ + 45, + 460, + 288, + 616 + ], + "type": "text", + "content": ". This formulation is an extension of standard video question answering or captioning [67] with a response that is additionally conditioned on a reference video. The questions can take various forms, for example \"How is the dough being prepared differently in Video 2\"; \"What is the similarity in mixing techniques between the two videos?\". Critically, these questions all share the assumption that a single video alone (either the reference or the candidate) is insufficient to answer the question — reasoning over both videos is required." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "content": "In our experiments, we train models with a diverse set of automatically-generated question-answer pairs. At test time, we focus on step differences, where the " + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "content": " is of the form \"what is the main difference between these videos in the category " + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "content": "\" and " + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 618, + 289, + 713 + ], + "type": "text", + "content": " is the difference category (e.g., ingredients, techniques, etc.). This structure captures a representative range of fine-grained differences, and allows for consistent evaluation of models as we will show." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 297, + 492, + 309 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 297, + 492, + 309 + ], + "spans": [ + { + "bbox": [ + 306, + 297, + 492, + 309 + ], + "type": "text", + "content": "3.2. Step differences dataset generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 316, + 547, + 411 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 547, + 411 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 547, + 411 + ], + "type": "text", + "content": "To train our models, we require a dataset of paired videos along with questions and answers (QA) relating the two in the form " + }, + { + "bbox": [ + 304, + 316, + 547, + 411 + ], + "type": "inline_equation", + "content": "(V_r, V_c, q, a)" + }, + { + "bbox": [ + 304, + 316, + 547, + 411 + ], + "type": "text", + "content": ". However, current video datasets typically contain individual video clips annotated for actions, narrations, or single-video QA which is incompatible with our task definition. We therefore construct this from existing video datasets using large-language models, inspired by prior work on instruction tuning [12, 20, 27, 37, 49]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 412, + 548, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 412, + 548, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 412, + 548, + 555 + ], + "type": "text", + "content": "Constructing this dataset from existing video datasets is non-trivial. On the one hand, selecting random pairs of videos showing very different content (e.g., sports vs. cooking) or near-identical videos (e.g., from repetitions of the same activity by the same participant) will lead to trivial differences. On the other hand, naively selecting video pairs of the same class in action recognition datasets (e.g., \"Bookbinding\" or \"Mowing the lawn\") will not highlight fine-grained differences of interest, and will instead focus on global differences (e.g., changes in actors or scenes). Moreover, these datasets do not come with text descriptions to construct differences from." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 641 + ], + "type": "text", + "content": "We therefore propose to use videos from the large-scale procedural video dataset HowTo100M [29], specifically cooking-themed videos labeled for keysteps from HT-Step [9]. Instructional videos are an ideal data source as they are narrated and show the same high-level keystep, but with variations that arise naturally from availability of tools and ingredients, differing skill / technique or personal preference." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Specifically, for two videos showing the same keystep (e.g., Slowly pour the sauce over the dumplings), we assume one is the reference " + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "inline_equation", + "content": "V_{r}" + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": " and the other is the candidate video " + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "inline_equation", + "content": "V_{c}" + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": ", with corresponding speech narrations. First, we generate descriptions of the actions and objects (including their attributes) using off-the-shelf captioning models [31]. These" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18742" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 275 + ], + "type": "text", + "content": "models often hallucinate details in their generations, so we additionally filter object descriptions based on the scores of a pre-trained detection model [30] and filter action descriptions using visual grounding models [55]. Details about the filtering stage are in Supp. Finally, we aggregate the information from these three sources (ASR narration, filtered objects and actions) to synthesize a detailed step description for each video (Fig. 2, left panel). We then prompt a language model (in our case, Llama 2 [50]) to generate both questions and answers comparing the two videos based on their step descriptions. In short, the prompt takes the form: \"Video 1: {description1}. Video 2: {description2}. Summarize the differences and generate 3 question-answer pairs comparing the two videos.\" (Fig. 2, center panel). An overview of the data generation pipeline with examples at each stage can be seen in Fig. 2. See Supp. for more examples and full step description prompt details." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 275, + 289, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 275, + 289, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 275, + 289, + 360 + ], + "type": "text", + "content": "The resulting dataset contains QA instances over video pairs across 87740 unique video clips. Note that the LLM-generated data is noisy — they may hallucinate details that are not present in the video, misunderstand the ASR narrations, produce irrelevant questions or incorrect answers to questions. Despite this, they offer valuable weak supervision to train our VCLM models, as our experiments will show." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 366, + 216, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 366, + 216, + 379 + ], + "spans": [ + { + "bbox": [ + 47, + 366, + 216, + 379 + ], + "type": "text", + "content": "3.3. Paired video instruction tuning" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 384, + 288, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 384, + 288, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 384, + 288, + 575 + ], + "type": "text", + "content": "We require a model that can generate natural language responses to video comparison questions in our dataset. To do this, we adapt a vision-conditioned language model (VCLM) to our multi-video setting via visual instruction tuning. In short, visual instruction tuning aligns the outputs of an image (or video) backbone to a powerful LLM to condition its responses on the visual content. This strategy has been successful in prior work for single image/video captioning and question answering [12, 21, 26, 27, 31, 64, 65]. We extend this to support comparisons across multiple videos. In our experiments, we use a Llama2 [50] LLM aligned with an Internvideo [55] backbone following prior work [31]. Note that it is possible to directly provide multiple videos to existing models by adding extra visual tokens to the input prompt, however their performance is degraded as they not trained to support this. We compare against such models." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 575, + 287, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 575, + 287, + 611 + ], + "spans": [ + { + "bbox": [ + 46, + 575, + 287, + 611 + ], + "type": "text", + "content": "Specifically, for an instruction-tuning instance " + }, + { + "bbox": [ + 46, + 575, + 287, + 611 + ], + "type": "inline_equation", + "content": "(V_{r}, V_{c}, q, a)" + }, + { + "bbox": [ + 46, + 575, + 287, + 611 + ], + "type": "text", + "content": ", we generate an instruction prompt in the Llama2 format as follows." + } + ] + } + ], + "index": 4 + }, + { + "type": "code", + "bbox": [ + 50, + 619, + 266, + 663 + ], + "blocks": [ + { + "bbox": [ + 50, + 619, + 266, + 663 + ], + "lines": [ + { + "bbox": [ + 50, + 619, + 266, + 663 + ], + "spans": [ + { + "bbox": [ + 50, + 619, + 266, + 663 + ], + "type": "text", + "content": " [INST] <> You are a helpful AI assistant that answers questions about a pair of videos. Answer in a single sentence. Here is the first video: {V_r}. Here is the second video: {V_c}. > {q} [/INST] {a}" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "code_body" + } + ], + "index": 5, + "sub_type": "code", + "guess_lang": "txt" + }, + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 289, + 715 + ], + "type": "text", + "content": "We encode the text tokens in this prompt using the LLM's pre-trained text encoder. We encode each video into a sequence of spatiotemporal tokens using a pre-trained video" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 403, + 155 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 403, + 155 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 403, + 155 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 403, + 155 + ], + "type": "image", + "image_path": "60b4463b907d0931fae58cc0f83294bbae16db278e174ea8161373bd15aede28.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 410, + 83, + 542, + 155 + ], + "blocks": [ + { + "bbox": [ + 439, + 72, + 512, + 80 + ], + "lines": [ + { + "bbox": [ + 439, + 72, + 512, + 80 + ], + "spans": [ + { + "bbox": [ + 439, + 72, + 512, + 80 + ], + "type": "text", + "content": "Difference Recognition" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 410, + 83, + 542, + 155 + ], + "lines": [ + { + "bbox": [ + 410, + 83, + 542, + 155 + ], + "spans": [ + { + "bbox": [ + 410, + 83, + 542, + 155 + ], + "type": "image", + "image_path": "e8b6ccee952803c831fea077dbc15be2e296cc6a50b1955517b6a385a25f9f90.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 308, + 158, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 308, + 158, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 308, + 158, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 308, + 158, + 545, + 232 + ], + "type": "image", + "image_path": "f470fd08a878fe0e2f036c2e8a3ed71cf0e371f586bfa4d690dae7effb36c81b.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 243, + 547, + 266 + ], + "lines": [ + { + "bbox": [ + 305, + 243, + 547, + 266 + ], + "spans": [ + { + "bbox": [ + 305, + 243, + 547, + 266 + ], + "type": "text", + "content": "Figure 3. Evaluation tasks. We evaluate on describing (DiffCap), recognizing (DiffMCQ) and ranking (DiffRank) differences." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "type": "text", + "content": "backbone " + }, + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "type": "inline_equation", + "content": "M_V" + }, + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "type": "text", + "content": ", and then align them to the LLM's input space using a learnable projection module " + }, + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "type": "inline_equation", + "content": "M_{proj}" + }, + { + "bbox": [ + 304, + 285, + 547, + 345 + ], + "type": "text", + "content": ". The resulting encoded instruction prompt is a sequence of tokens comprising a mix of text and visual tokens, which can then be processed by the LLM (Fig. 2, right panel)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 346, + 547, + 394 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 547, + 394 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 547, + 394 + ], + "type": "text", + "content": "The model is trained using the original auto-regressive objective to maximize the probability of generating the answer tokens, conditioned on the question, reference and candidate video, and is trained using a standard cross-entropy loss." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 313, + 411, + 545, + 457 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 411, + 545, + 457 + ], + "spans": [ + { + "bbox": [ + 313, + 411, + 545, + 457 + ], + "type": "interline_equation", + "content": "p \\left(X _ {a} \\mid X _ {r}, X _ {c}, X _ {q}\\right) = \\prod_ {i = 1} ^ {\\left| X _ {a} \\right|} p _ {\\theta} \\left(X _ {a, i} \\mid X _ {r}, X _ {c}, X _ {q}, X _ {a, < i}\\right) \\tag {1}", + "image_path": "3f9b4fc21eff5914226566fd3f93b4bb60682389b1e635a8bc2b3bb2f60a4809.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 377, + 460, + 545, + 474 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 377, + 460, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 377, + 460, + 545, + 474 + ], + "type": "interline_equation", + "content": "X _ {r} = M _ {p r o j} \\left(M _ {V} \\left(V _ {r}\\right)\\right) \\tag {2}", + "image_path": "2bb9e196b4b3728903139433f2e89f42988ae236ad4c582ccf9f6c5c315dd666.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 378, + 476, + 545, + 490 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 378, + 476, + 545, + 490 + ], + "spans": [ + { + "bbox": [ + 378, + 476, + 545, + 490 + ], + "type": "interline_equation", + "content": "X _ {c} = M _ {p r o j} \\left(M _ {V} \\left(V _ {c}\\right)\\right), \\tag {3}", + "image_path": "f32694a0cc4d983c98015609589dd2479003159ecd53a0dfe7a8775420d83423.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "X_{a,i}" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": " is the i-th answer token in the sequence, " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "X_{r}(X_{c})" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": " are the visual tokens corresponding to the reference (candidate) videos, " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "X_{q}, X_{a}" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": " are tokens of the question and answer, " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "X_{a, < i}" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": " are answer tokens that occur before " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "X_{a,i}" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": " are the learnable parameters in " + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "inline_equation", + "content": "\\mathcal{M}_{proj}" + }, + { + "bbox": [ + 304, + 498, + 545, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 558, + 547, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 547, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 547, + 641 + ], + "type": "text", + "content": "Note that the video encoder and the LLM weights are frozen, and the loss is computed only for answer tokens. Only the projection layer is fine-tuned. Once trained, our model will be able to refer to each video, discuss their similarities and compare them. We evaluate our model by autoregressively generating text in response to various prompts coupled with reference and candidate videos." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 648, + 545, + 673 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 648, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 306, + 648, + 545, + 673 + ], + "type": "text", + "content": "3.4. Describing, recognizing and ranking step differences in procedural videos" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 679, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 679, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 679, + 547, + 715 + ], + "type": "text", + "content": "Finally, we use our trained models to identify and rank fine-grained differences between pairs of video. We cast these tasks into the paired-video QA framework as follows." + } + ] + } + ], + "index": 20 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18743" + } + ] + } + ], + "index": 21 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 107, + 163 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 107, + 163 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 107, + 163 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 107, + 163 + ], + "type": "image", + "image_path": "a3867a413d161cda4f42af8274476ebf138ead5c77cd72318d628358c5d0a4fc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 109, + 76, + 293, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 76, + 293, + 95 + ], + "spans": [ + { + "bbox": [ + 109, + 76, + 293, + 95 + ], + "type": "text", + "content": "Ingredients: The person oiled the baking dish with oil as opposed to vegetable ghee. Score: 4/5" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 109, + 99, + 293, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 99, + 293, + 131 + ], + "spans": [ + { + "bbox": [ + 109, + 99, + 293, + 131 + ], + "type": "text", + "content": "Tools/Equipment: The oil was applied to the pan with a pastry brush instead of bare hands; The baking dish used was a glass baking dish as opposed to ceramic. Score: 3/5" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 109, + 135, + 291, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 135, + 291, + 152 + ], + "spans": [ + { + "bbox": [ + 109, + 135, + 291, + 152 + ], + "type": "text", + "content": "Actions: The person skipped pressing the dough mixture into the baking dish after oiling it. Score: 3/5" + } + ] + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 49, + 167, + 107, + 261 + ], + "blocks": [ + { + "bbox": [ + 49, + 167, + 107, + 261 + ], + "lines": [ + { + "bbox": [ + 49, + 167, + 107, + 261 + ], + "spans": [ + { + "bbox": [ + 49, + 167, + 107, + 261 + ], + "type": "image", + "image_path": "9160aff5baa71ab5cbe00a41df2ba342036b6231c86dd33cd50ade7558bf90fd.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 267, + 547, + 290 + ], + "lines": [ + { + "bbox": [ + 46, + 267, + 547, + 290 + ], + "spans": [ + { + "bbox": [ + 46, + 267, + 547, + 290 + ], + "type": "text", + "content": "Figure 4. StepDiff dataset samples We annotate text describing differences in various categories and scores for how different the videos are in each category (1 = very different; 5 = nearly identical). More examples are in Supp." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 109, + 178, + 289, + 195 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 178, + 289, + 195 + ], + "spans": [ + { + "bbox": [ + 109, + 178, + 289, + 195 + ], + "type": "text", + "content": "Tools/Equipment: The person mixes the cream mixture with green spatula instead of red. Score: 5/5" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 109, + 200, + 293, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 200, + 293, + 224 + ], + "spans": [ + { + "bbox": [ + 109, + 200, + 293, + 224 + ], + "type": "text", + "content": "Actions: The person continuously mixes the cream mixture instead of folding then shakes off the spatula. Score: 3/5" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 109, + 229, + 288, + 246 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 109, + 229, + 288, + 246 + ], + "spans": [ + { + "bbox": [ + 109, + 229, + 288, + 246 + ], + "type": "text", + "content": "Visuals: The cream mixture has a thick and clumpy consistency instead of smooth and runny. Score: 2/5" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 306, + 70, + 365, + 163 + ], + "blocks": [ + { + "bbox": [ + 306, + 70, + 365, + 163 + ], + "lines": [ + { + "bbox": [ + 306, + 70, + 365, + 163 + ], + "spans": [ + { + "bbox": [ + 306, + 70, + 365, + 163 + ], + "type": "image", + "image_path": "d85e16b5ca31f0fbec5293661d1efd5bd09d2769fa15ed4126b878d495c06a9b.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 366, + 76, + 541, + 102 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 76, + 541, + 102 + ], + "spans": [ + { + "bbox": [ + 366, + 76, + 541, + 102 + ], + "type": "text", + "content": "Ingredients: The person only cooks the regular potato fries as opposed to 6 varieties of potato fries. Score: 4/5" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 366, + 106, + 534, + 123 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 106, + 534, + 123 + ], + "spans": [ + { + "bbox": [ + 366, + 106, + 534, + 123 + ], + "type": "text", + "content": "Actions: The person skips transferring the potato fries in the tray. Score: 3/5" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 366, + 127, + 537, + 152 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 127, + 537, + 152 + ], + "spans": [ + { + "bbox": [ + 366, + 127, + 537, + 152 + ], + "type": "text", + "content": "Visuals: The potato fries has a regular yellow color contrary to having green, red, orange and brown fries. Score: 2/5" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 306, + 168, + 365, + 261 + ], + "blocks": [ + { + "bbox": [ + 306, + 168, + 365, + 261 + ], + "lines": [ + { + "bbox": [ + 306, + 168, + 365, + 261 + ], + "spans": [ + { + "bbox": [ + 306, + 168, + 365, + 261 + ], + "type": "image", + "image_path": "3576d30116a6c73aa91a5ed9f09996af5c1821c7fd803d0f46577de1813dd8a2.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 366, + 175, + 545, + 200 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 175, + 545, + 200 + ], + "spans": [ + { + "bbox": [ + 366, + 175, + 545, + 200 + ], + "type": "text", + "content": "Tools/Equipment: The dough was flipped using a fork rather than a tong; The dough was deep-fried in a steel pan instead of a non-stick pan. Score: 3/5" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 366, + 204, + 545, + 220 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 204, + 545, + 220 + ], + "spans": [ + { + "bbox": [ + 366, + 204, + 545, + 220 + ], + "type": "text", + "content": "Technique: The dough was flipped once as opposed to three times. Score: 4/5" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 366, + 224, + 541, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 366, + 224, + 541, + 250 + ], + "spans": [ + { + "bbox": [ + 366, + 224, + 541, + 250 + ], + "type": "text", + "content": "Visuals: The deep-fried dough appears to have a flower design and has holes on it as opposed to full and lumpy. Score: 3/5" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "text", + "content": "Difference captioning (DiffCap) The goal is to generate a textual description of the differences between two videos in a specific category " + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "text", + "content": " (e.g., ingredients, tools). The question " + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "text", + "content": " takes the form \"what is the main difference between these videos in the category " + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 304, + 287, + 376 + ], + "type": "text", + "content": "\". The difference caption is generated auto-regressively using the trained model." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "type": "text", + "content": "Difference recognition (DiffMCQ) The goal is to select the correct video pair that matches the difference caption, from a list of candidate video pairs " + }, + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "type": "inline_equation", + "content": "\\{(V_r^i,V_c^i)\\}_{i = 1..4}" + }, + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "type": "text", + "content": ". This is a discriminative version of the captioning task above inspired by recent work in vision-language feature learning [24]. For this, we compute " + }, + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "type": "inline_equation", + "content": "p(a|V_r^i,V_c^i,q)" + }, + { + "bbox": [ + 46, + 388, + 288, + 485 + ], + "type": "text", + "content": " — the likelihood of generating the difference text given the pair of videos following Eqn. 2 — and then select the pair with the highest score." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "content": "Difference ranking (DiffRank) The goal is to rank video instances " + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "inline_equation", + "content": "\\{V_c^i\\}_{i=1..4}" + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "content": " based on how different they are to a common reference video " + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "inline_equation", + "content": "V_r" + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "content": ", in terms of a particular category of interest " + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "content": ". For this, we set " + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "content": " to be \"do these two videos show the same " + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 46, + 498, + 288, + 581 + ], + "type": "text", + "content": "? Answer YES or NO,\" and rank each candidate video based on the likelihood of generating \"YES\" as the response." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 714 + ], + "type": "text", + "content": "Together, these tasks are a representative suite of problems for instructional video understanding that require comparing videos along various axes. DiffCap tests how accurately a model can describe differences in natural language, DiffMCQ tests how well it can discriminate differences between videos, and DiffRank tests how well the model can assess the severity of these differences to rank them. A model for these tasks can enable applications that guide user action (e.g., to follow a reference video tutorial) or help browse through large collections of videos (e.g., to find the perfect variation of a recipe). Fig. 3 illustrates these tasks." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 303, + 387, + 316 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 303, + 387, + 316 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 387, + 316 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 323, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 545, + 346 + ], + "type": "text", + "content": "We evaluate our VCLM model on the three step difference tasks from Sec. 3.4." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 364, + 547, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 364, + 547, + 603 + ], + "spans": [ + { + "bbox": [ + 304, + 364, + 547, + 603 + ], + "type": "text", + "content": "Dataset We construct a test dataset from videos in HT-Step [9]. HTStep contains videos from a large-scale procedural video dataset, HowTo100M [29] (Cooking & Entertainment), with temporal segments (clips) annotated for keysteps (e.g., \"fry then onions until golden brown\"). We manually annotate pairs of clips, where each pair corresponds to instances of the same labeled keystep, but from distinct videos. Annotators are asked to identify the main differences across 5 categories (ingredients, tools/equipment, techniques, visual differences) and write difference captions of a consistent style — what happens in the target clip, compared to what happens in the reference (e.g., \"The person uses a deep fryer to fry the potatoes instead of shallow frying it in a pan\"). They are then asked to score the difference caption in each category on a scale of 1-5 based on how severe the difference is, where 1 is a significant difference (e.g., swapping out a critical ingredient that would change the dish entirely) and 5 is nearly identical (e.g., minor cosmetic differences that does not affect the activity). A rubric is used to ensure consistency in scoring." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 604, + 547, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 547, + 689 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 547, + 689 + ], + "type": "text", + "content": "Note that this data is only used for evaluation — we exclude these pairs from the automatic training data generation pipeline described in Sec. 3.2 to ensure that the model has not seen these instances during training. In total, we collect 35988 difference captions across 6292 clip pairs, involving 8396 unique clips. See Fig. 4 for examples. Full collection details and dataset statistics are in Supp." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 701, + 512, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 512, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 512, + 713 + ], + "type": "text", + "content": "Baselines We compare several classes of models." + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18744" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 108, + 70, + 355, + 203 + ], + "blocks": [ + { + "bbox": [ + 108, + 70, + 355, + 203 + ], + "lines": [ + { + "bbox": [ + 108, + 70, + 355, + 203 + ], + "spans": [ + { + "bbox": [ + 108, + 70, + 355, + 203 + ], + "type": "table", + "html": "
DIFFCAP
BLEUCIDERROGUE-L
VLEmb (CLIP) [40]---
VLEmb (InternVideo) [55]---
Socratic (BLIP-2) [22]0.1590.0360.169
Socratic (LLaVA) [27]0.1510.0310.166
Socratic (Step desc.)0.1410.0200.172
VCLM (LLaVA) [27]0.2110.0690.199
VCLM (AnyMAL) [31]0.2090.1150.196
Interleaved (IDEFICS) [19]0.2170.0800.210
Interleaved (AnyMAL)0.2070.1020.198
StepDiff0.2230.1040.215
", + "image_path": "8316641fcfa29d77ea2a8ac88ff45c7602b718ce69f6c938be0006a33447d13c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 361, + 70, + 419, + 203 + ], + "blocks": [ + { + "bbox": [ + 361, + 70, + 419, + 203 + ], + "lines": [ + { + "bbox": [ + 361, + 70, + 419, + 203 + ], + "spans": [ + { + "bbox": [ + 361, + 70, + 419, + 203 + ], + "type": "table", + "html": "
Acc %
0.396
0.451
0.335
0.332
0.392
0.381
0.471
0.376
0.497
0.541
", + "image_path": "8e4d754bc4cd4b2dddd9306a52121ae6fcf335085deef3abfba2f579045e9bc5.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 426, + 71, + 484, + 203 + ], + "blocks": [ + { + "bbox": [ + 426, + 71, + 484, + 203 + ], + "lines": [ + { + "bbox": [ + 426, + 71, + 484, + 203 + ], + "spans": [ + { + "bbox": [ + 426, + 71, + 484, + 203 + ], + "type": "table", + "html": "
DIFFRANK
τ
0.1270.170
0.0220.004
0.0130.013
0.0190.032
0.0810.014
0.181
", + "image_path": "3e07b99a77c67bf9e93f3481e41288e6dd0148a3a6a5ab6bf43a47cbb6fe0b00.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 205, + 545, + 228 + ], + "lines": [ + { + "bbox": [ + 46, + 205, + 545, + 228 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 545, + 228 + ], + "type": "text", + "content": "Table 1. Results. Our approach outperforms three classes of baselines built on top of state-of-the-art vision-language embedding and VCLM models. VLEmb baselines are excluded from DiffCap as they cannot generate text." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 248, + 288, + 571 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 47, + 248, + 287, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 248, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 47, + 248, + 287, + 308 + ], + "type": "text", + "content": "- VLEmbed is a class of vision-language model that embeds images or video in the same space as text, and then compares their similarity in the shared space. Video pair embeddings are calculated as the average of individual video embeddings1. We use CLIP [40] and InternVideo [55]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 308, + 288, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 308, + 288, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 308, + 288, + 415 + ], + "type": "text", + "content": "- Socratic is a class of VCLMs that first converts videos into text using a captioning model, and then prompts a text-only LLM with these captions. These models are powerful, but often require complex, manually engineered prompts. We use state-of-the-art visual captioners (BLIP-2 [22], LLaVA-1.5 [27]) as well our aggregate step descriptions from Sec. 3.2. We use Llama2 to process the captions regardless of which model generated them, for fair comparisons." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 416, + 287, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 416, + 287, + 487 + ], + "spans": [ + { + "bbox": [ + 47, + 416, + 287, + 487 + ], + "type": "text", + "content": "- VCLM is a class of visual instruction-tuned language model trained for video captioning and question answering (for a single video). We directly add extra tokens for the reference video into the prompt to be consistent with our paired-video QA task. We compare LLaVA-1.5 [27] and AnyMAL [31]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 487, + 288, + 571 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 487, + 288, + 571 + ], + "spans": [ + { + "bbox": [ + 47, + 487, + 288, + 571 + ], + "type": "text", + "content": "- Interleaved is a class of models that are trained with interleaved sequences of images/videos and text, and naturally support multiple videos as inputs, but are not explicitly trained to compare them. We compare the recently proposed IDEFICS [19] and a model we train on sequences of (video, ASR) pairs from HowTo100M (training details in Supp.)." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 572, + 288, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 572, + 288, + 692 + ], + "spans": [ + { + "bbox": [ + 46, + 572, + 288, + 692 + ], + "type": "text", + "content": "These baselines represent a spectrum of leading strategies for vision-language reasoning, including methods that directly embed video and language in the same space (VLEmbed), ones that explicitly convert videos to text and perform exclusively text-based reasoning (Socratic) and ones that perform joint vision-text reasoning on videos (VCLM, Interleaved). We ensure that each class of baselines include methods that have been trained on in-domain HowTo100M videos, while excluding the evaluation videos, to ensure fair comparisons with our approach. These are InternVideo," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 248, + 547, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 248, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 306, + 248, + 547, + 285 + ], + "type": "text", + "content": "Socratic (Step desc.), VCLM (AnyMAL), and Interleaved (AnyMAL). Additional pretraining and implementation details are in Supp." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "spans": [ + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "text", + "content": "Implementation details We use the Llama2-chat-70B [50] as the base LLM for all our experiments. Following prior work [31], " + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "inline_equation", + "content": "M_V" + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "text", + "content": " is an Internvideo [55] video encoder that inputs 8 uniformly sampled frames from each video clip and generates 2048 spatio-temporal tokens. " + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "inline_equation", + "content": "M_{Proj}" + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "text", + "content": " is a 2-layer Perceiver [15] module followed by a linear layer head to output 32 tokens in the LLM's input dimension. During training, all parameters are frozen except for " + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "inline_equation", + "content": "M_{Proj}" + }, + { + "bbox": [ + 305, + 294, + 547, + 462 + ], + "type": "text", + "content": ". StepDiff models are initialized from Interleaved model weights before finetuning (interleaved data is retained during finetuning). For baselines, we use the largest available versions of models — InstructBLIP (Vicuna13B), LLaVA (Vicuna13B), AnyMAL (70B), IDEFICS (80B). Full implementation and training details are in Supp." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 468, + 429, + 480 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 468, + 429, + 480 + ], + "spans": [ + { + "bbox": [ + 306, + 468, + 429, + 480 + ], + "type": "text", + "content": "4.1. Difference captioning" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "text", + "content": "We first evaluate how well our model can describe differences in video pairs (DiffCap). As mentioned in Sec. 3.1, " + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "inline_equation", + "content": "q" + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "text", + "content": " is of the form \"what is the main difference between these videos in the category " + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "text", + "content": "\" where " + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "inline_equation", + "content": "g" + }, + { + "bbox": [ + 304, + 485, + 547, + 713 + ], + "type": "text", + "content": " is the difference category. Since there may be multiple annotated differences in the same category, we group them together and treat them as a ground truth set, resulting in a dataset with 22292 instances. We measure standard text generation metrics including CIDER [52] and ROUGE-L [23]. Outputs are postprocessed using simple string matching techniques to ensure difference captions are generated in the correct format (details in Supp). For the socratic baselines, we provide the generated caption instead of the video tokens in the prompt from Sec. 3.3. Table 1 (left) shows our results. The socratic models perform poorly as they are limited by the information contained in the base captions. It is infeasible to generate captions that exhaustively describe every aspect of a video, without knowing what is of interest, and without the risk of model hallucinations. The VCLM models perform better," + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 58, + 702, + 220, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 220, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 220, + 713 + ], + "type": "text", + "content": "1We evaluate other aggregation strategies in Supp." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18745" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 47, + 69, + 547, + 358 + ], + "blocks": [ + { + "bbox": [ + 47, + 69, + 547, + 358 + ], + "lines": [ + { + "bbox": [ + 47, + 69, + 547, + 358 + ], + "spans": [ + { + "bbox": [ + 47, + 69, + 547, + 358 + ], + "type": "image", + "image_path": "bb5064d9fe927d66660d6f1aa3b0db838c0399961f8d400b971599349c815343.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 370, + 546, + 404 + ], + "lines": [ + { + "bbox": [ + 46, + 370, + 546, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 370, + 546, + 404 + ], + "type": "text", + "content": "Figure 5. Extended QA on video pairs. Our model which can describe differences (row 1) can be prompted (i.e., queried without any form of retraining) for comparative reasoning (e.g., \"why are they different?\"; \"how different are they?\" row 2-3), or to bootstrap mistake detection (row 4). A failure case is shown in row 5 due to model hallucination." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 418, + 290, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 290, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 290, + 515 + ], + "type": "text", + "content": "especially when trained to process multiple videos (i.e., interleaved models), however they still fall short of our approach that can explicitly compare and contrast videos. The example in Fig. 6 highlights the sensitivity of socratic models to input captions (e.g., the reference caption did not mention the use of hands), and shows how VCLM models tend to hallucinate details. Our approach can correctly describe the difference. See Supp for more examples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 525, + 174, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 525, + 174, + 539 + ], + "spans": [ + { + "bbox": [ + 47, + 525, + 174, + 539 + ], + "type": "text", + "content": "4.2. Difference recognition" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 289, + 715 + ], + "type": "text", + "content": "While the captioning metrics are informative, they are based on word overlap statistics, and do not always capture the semantics of the text well. To address this, we evaluate on DiffMCQ – the discriminative version of the captioning task. We adapt the same dataset from DiffCap, except we sample a single difference caption for each category if there are multiple differences present. Further, we sample three negative video pairs from other instances in the dataset that involve similar objects and actions (details in Supp). For the VLEmb bed baselines, we score each video pair using the cosine similarity between their average visual embeddings and the text embedding of the difference caption. We compare variants of this baseline considering only the reference or target in Supp. For all LLM-based baselines, we compute the" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "type": "text", + "content": "likelihood of generating the difference caption for each video pair, under each model as discussed in Sec. 3.1. We evaluate top-1 accuracy. Table 1 (center) shows our results. The joint feature embedding models capture some semantics, but are insufficient for identifying differences. Socratic models have a similar trend to captioning results, however models trained on step differences show large improvements, highlighting the value of careful curation for generating captions. Among VCLM models, ones that have seen in-domain HowTo100M videos during training have an edge over the others (i.e., LLaVA, IDEFICS), with interleaved models again being superior. Our model outperforms all these approaches with a " + }, + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "type": "inline_equation", + "content": "5\\%" + }, + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "type": "text", + "content": " accuracy improvement over the strongest baseline. Fig. 7 shows performance increases by difference category, over the weakest baseline (Socratic). Our approach shows large relative improvements on most categories especially in technique and tool use (both " + }, + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "type": "inline_equation", + "content": "46\\%" + }, + { + "bbox": [ + 304, + 418, + 548, + 634 + ], + "type": "text", + "content": "), which require fine-grained action understanding." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 645, + 418, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 645, + 418, + 658 + ], + "spans": [ + { + "bbox": [ + 305, + 645, + 418, + 658 + ], + "type": "text", + "content": "4.3. Difference ranking" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 715 + ], + "type": "text", + "content": "Finally, we evaluate how well our model can rank videos based on the severity of differences compared to a common reference (DiffRank). Each reference video in the dataset is paired with four target videos, scored along each category" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18746" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 70, + 113, + 171 + ], + "blocks": [ + { + "bbox": [ + 49, + 70, + 113, + 171 + ], + "lines": [ + { + "bbox": [ + 49, + 70, + 113, + 171 + ], + "spans": [ + { + "bbox": [ + 49, + 70, + 113, + 171 + ], + "type": "image", + "image_path": "961448b3fd16f108256382e8be7d904bbcc42e7aaa3adf1472a63c20102bad34.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 185, + 288, + 218 + ], + "lines": [ + { + "bbox": [ + 47, + 185, + 288, + 218 + ], + "spans": [ + { + "bbox": [ + 47, + 185, + 288, + 218 + ], + "type": "text", + "content": "Figure 6. DiffCap baselines. Our approach can describe differences without relying on input captions (like Socratic) and is less prone to hallucinating details (like VCLM)." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 72, + 286, + 89 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 72, + 286, + 89 + ], + "spans": [ + { + "bbox": [ + 115, + 72, + 286, + 89 + ], + "type": "text", + "content": "What is the main difference in \"Tools\" between the two videos?" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 94, + 282, + 169 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 115, + 94, + 282, + 126 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 94, + 282, + 126 + ], + "spans": [ + { + "bbox": [ + 115, + 94, + 282, + 126 + ], + "type": "text", + "content": "- Socratic: the person is using a rolling pin to roll out dough on a wooden surface, instead of a woman and young girl working together in a kitchen, ..." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 131, + 275, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 131, + 275, + 148 + ], + "spans": [ + { + "bbox": [ + 115, + 131, + 275, + 148 + ], + "type": "text", + "content": "VCLM: the dough is rolled out on parchment paper, instead of directly on the counter." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 115, + 152, + 279, + 169 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 152, + 279, + 169 + ], + "spans": [ + { + "bbox": [ + 115, + 152, + 279, + 169 + ], + "type": "text", + "content": "- StepDiff: the dough is rolled out with a rolling pin, instead of being stretched with hands." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "type": "image", + "bbox": [ + 51, + 225, + 282, + 350 + ], + "blocks": [ + { + "bbox": [ + 51, + 225, + 282, + 350 + ], + "lines": [ + { + "bbox": [ + 51, + 225, + 282, + 350 + ], + "spans": [ + { + "bbox": [ + 51, + 225, + 282, + 350 + ], + "type": "image", + "image_path": "2430cc269ec99e6e627a7ef26add33532175981d8f73216c5ac31956cddb0fa4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 365, + 287, + 388 + ], + "lines": [ + { + "bbox": [ + 47, + 365, + 287, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 365, + 287, + 388 + ], + "type": "text", + "content": "Figure 7. DiffMCQ performance by category. Improvements are reported over the weakest baseline (Socratic)." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 401, + 287, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 401, + 287, + 460 + ], + "spans": [ + { + "bbox": [ + 47, + 401, + 287, + 460 + ], + "type": "text", + "content": "axis. For example, some videos may be very similar in terms of technique, but very different in terms of ingredients. We only retain instances where there is a clear ranking (i.e., no more than one tie in scores) The resulting dataset contains 3932 instances involving 5746 unique clips." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "type": "text", + "content": "As discussed in Sec. 3.1, we rank each target video candidate based on the likelihood of producing the response \"YES\" when asked whether it is similar to the reference. We use the Kendall's " + }, + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "type": "text", + "content": " rank correlation metric to evaluate how well the generated ranking compares to the ground truth ranking annotators provide. Table 1 (right) shows our results. Unlike the previous tasks, the joint embedding models perform better than the LLM based baselines for two reasons. First, similarity in the embedding space directly translates to a score for ranking, rather than relying on computing \"YES\" token probability as a proxy for this. Second, there is a high correlation between the rankings across categories for the same set of instances (" + }, + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "type": "inline_equation", + "content": "\\tau = 0.63" + }, + { + "bbox": [ + 47, + 460, + 287, + 664 + ], + "type": "text", + "content": "). For example, videos ranked low in similarity for tools when compared to a reference are often also ranked low for technique. Despite these issues, our approach is able to outperform all baselines, showcasing its versatility as a retrieval and ranking model." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 671, + 261, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 261, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 261, + 685 + ], + "type": "text", + "content": "4.4. Extending QA beyond atomic differences" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Next, we show how our model can be prompted to answer questions beyond just \"describe the differences\". LLMs have" + } + ] + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 307, + 71, + 455, + 118 + ], + "blocks": [ + { + "bbox": [ + 307, + 71, + 455, + 118 + ], + "lines": [ + { + "bbox": [ + 307, + 71, + 455, + 118 + ], + "spans": [ + { + "bbox": [ + 307, + 71, + 455, + 118 + ], + "type": "table", + "html": "
DIFFCAP
BLEUCIDERROGUE-L
StepDiff0.2230.1040.215
w/o interleaved data0.2140.0940.210
w/o QA filtering0.2220.0960.212
w/ 13B LLM0.2160.1240.205
", + "image_path": "ae6fff60d9ccc42866cea17a462ea2f037c3f3ff0c6e5e11c580541153c89b2c.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "type": "table", + "bbox": [ + 459, + 71, + 544, + 118 + ], + "blocks": [ + { + "bbox": [ + 459, + 71, + 544, + 118 + ], + "lines": [ + { + "bbox": [ + 459, + 71, + 544, + 118 + ], + "spans": [ + { + "bbox": [ + 459, + 71, + 544, + 118 + ], + "type": "table", + "html": "
DIFFMCQDIFFRANK
Acc %τ
0.5410.181
0.4990.185
0.5160.120
0.5270.175
", + "image_path": "fb26ad30a555510868f73aff648b88005b9f028fb0ca41de45ef90b49147045e.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "table_body" + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 121, + 545, + 143 + ], + "lines": [ + { + "bbox": [ + 306, + 121, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 306, + 121, + 545, + 143 + ], + "type": "text", + "content": "Table 2. Ablation experiments. Impact of retaining interleaved training data, careful filtering of QA training data and LLM size." + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 157, + 547, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 547, + 313 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 547, + 313 + ], + "type": "text", + "content": "shown remarkable abilities for complex, multi-step reasoning in text – our training framework unlocks the same kind of reasoning for multiple videos, based on their differences. In Fig. 5, we show some examples of this. Our model is able to naturally describe differences as it was trained for this task (row 1), but also has the ability to perform comparative reasoning (row 2-3) or explain mistakes (row 4). We show a failure case in row 5, where the model hallucinates content – a characteristic feature of the LLM models it is built upon. Moreover, our model works with egocentric video (row 1, 4), despite being trained on largely third-person video content (HowTo100M), which is promising for AR/VR user assistance applications." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 320, + 429, + 333 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 320, + 429, + 333 + ], + "spans": [ + { + "bbox": [ + 306, + 320, + 429, + 333 + ], + "type": "text", + "content": "4.5. Ablation experiments" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 339, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 339, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 339, + 545, + 471 + ], + "type": "text", + "content": "Finally, we ablate several design choices in our model in Table 2. As mentioned in Sec. 4, we finetune models on both interleaved ASR data as well as our generated pair QA data. Without the interleaved data, the model performance drops on two tasks, likely due to catastrophic forgetting (w/o interleaved data). Next, we show the importance of filtering the generated QA data (w/o QA filtering), given the high likelihood of hallucinations produced by the LLM. Finally, we swap out the 70B LLM model for a smaller sized one (w/13B LLM), causing the performance to drop, though not significantly." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 482, + 378, + 495 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 482, + 378, + 495 + ], + "spans": [ + { + "bbox": [ + 306, + 482, + 378, + 495 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 304, + 502, + 547, + 646 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 547, + 646 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 547, + 646 + ], + "type": "text", + "content": "We proposed StepDiff, a video-conditioned language model (VCLM) that can compare and contrast videos to reveal fine-grained differences between them. We propose an approach that can automatically generate instruction-following paired-video QA training data from large-scale procedural video data, and a manually curated benchmark to evaluate models. Our experiments on describing and identifying differences, as well on ranking videos based on differences demonstrate the value of our approach for personalized assistance applications. Future work can leverage our work for personalized retrieval (e.g., retrieve content based on user-activity), or multi-video QA beyond instructional videos." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgements Thanks to Efi Mavroudi, Huiyu Wang, Triantafyllos Afouras and Yale Song for helpful discussions; Kumar Ashutosh and Suyog Jain for help with annotation tooling and collection; Austin Miller and Honey Manglani for managing the annotator workforce." + } + ] + } + ], + "index": 21 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18747" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 53, + 91, + 289, + 156 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 289, + 156 + ], + "type": "text", + "content": "[1] Jean-Baptiste Alayrac, Jeff Donahue, Pauline Luc, Antoine Miech, Iain Barr, Yana Hasson, Karel Lenc, Arthur Mensch, Katherine Millican, Malcolm Reynolds, et al. 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Springer, 2022. 1, 2" + } + ] + } + ], + "index": 20 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 318, + 757 + ], + "type": "text", + "content": "18750" + } + ] + } + ], + "index": 22 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_content_list.json b/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..12f2a2b8356591949b2f714c3f3b514cb2b3ce27 --- /dev/null +++ b/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_content_list.json @@ -0,0 +1,1386 @@ +[ + { + "type": "text", + "text": "StraightPCF: Straight Point Cloud Filtering", + "text_level": 1, + "bbox": [ + 259, + 130, + 709, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Dasith de Silva Edirimuni1, Xuequan Lu2*, Gang Li1, Lei Wei1, Antonio Robles-Kelly1, Hongdong Li3 \n1Deakin University, 2La Trobe University, 3Australian National University", + "bbox": [ + 86, + 179, + 895, + 215 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{dtdesilva, gang.li, lei.wei, antonio.robles-kelly}@deakin.edu.au,", + "bbox": [ + 199, + 218, + 781, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "b.lu@latrobe.edu.au, hongdong.li@anu.edu.au", + "bbox": [ + 295, + 237, + 679, + 250 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 286, + 313, + 301 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Point cloud filtering is a fundamental 3D vision task, which aims to remove noise while recovering the underlying clean surfaces. State-of-the-art methods remove noise by moving noisy points along stochastic trajectories to the clean surfaces. These methods often require regularization within the training objective and/or during post-processing, to ensure fidelity. In this paper, we introduce StraightPCF, a new deep learning based method for point cloud filtering. It works by moving noisy points along straight paths, thus reducing discretization errors while ensuring faster convergence to the clean surfaces. We model noisy patches as intermediate states between high noise patch variants and their clean counterparts, and design the VelocityModule to infer a constant flow velocity from the former to the latter. This constant flow leads to straight filtering trajectories. In addition, we introduce a DistanceModule that scales the straight trajectory using an estimated distance scalar to attain convergence near the clean surface. Our network is lightweight and only has $\\sim 530K$ parameters, being $17\\%$ of IterativePFN (a most recent point cloud filtering network). Extensive experiments on both synthetic and real-world data show our method achieves state-of-the-art results. Our method also demonstrates nice distributions of filtered points without the need for regularization. The implementation code can be found at: https://github.com/ddsdiri/StuartPCF.", + "bbox": [ + 76, + 318, + 473, + 710 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 742, + 209, + 758 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, point clouds have become increasingly popular as the representation-of-choice for storing and manipulating 3D data, with numerous applications in both computer vision [12, 20, 25, 38] and geometry modelling [16, 25, 40]. Point clouds are unordered sets of 3D coordinates which typically represent object surfaces and are captured using 3D sensors such as depth and Lidar devices. However,", + "bbox": [ + 76, + 768, + 468, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0e11c694f22c11639a21d581a7be698004f1330eeb71441eaf0f7ab481368725.jpg", + "image_caption": [ + "Figure 1. Filtered trajectories for the Isocahedron shape at $50\\mathrm{K}$ resolution and noise scale $\\sigma = 3\\%$ . Our StraightPCF filters points along much straighter paths, compared to ScoreDenoise [28]." + ], + "image_footnote": [], + "bbox": [ + 504, + 284, + 893, + 429 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "noisy artifacts may appear in point clouds as a result of sensor limitations and environmental factors. Removing this noise, known as filtering or denoising, is a fundamental 3D vision task. Filtering methods are broadly categorized into two groups: 1) conventional methods involving traditional optimization and 2) deep learning based methods. Conventional methods can further be subdivided into normal based methods which require surface normal information to reliably filter point clouds [2, 10, 13, 24, 30] and point based methods which directly filter point clouds [15, 21, 32]. While normal based methods are limited by the accuracy of normals, point based methods suffer from a loss of geometric details and still exhibit sensitivity to noise. Recently, many deep learning approaches have been proposed to overcome these shortcomings.", + "bbox": [ + 496, + 518, + 893, + 744 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep learning methods can be divided into 1) resampling, 2) displacement and 3) probability based methods. Resampling-based methods [26] show the least fidelity when recovering the underlying noise-free surfaces as their downsampling procedure results in the loss of crucial geometric information. By contrast, displacement and probability based methods show greater promise as they model the filtering objective as a reverse Markov process, which can be iteratively applied on the input to progressively remove noise. Early displacement based methods, such as", + "bbox": [ + 496, + 750, + 895, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author: X. Lu, supported by fund 3.2501.11.47.", + "bbox": [ + 94, + 886, + 434, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "20721", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "PointCleanNet [7, 35, 45], employ large networks ( $>1\\mathrm{M}$ parameters) that consume a large patch of points to filter a single, central point. This is time-consuming and resource intensive. More recently, IterativePFN [8] models the iterative filtering process internally using multiple IterationModules and filters all patch points simultaneously. However, incorporating multiple IterationModules results in a large network ( $>3.2\\mathrm{M}$ parameters) which requires a large amount of GPU memory to process. Probabilistic score based methods such as ScoreDenoise [6, 28] offer a more lightweight network but require a high number of iterations to recover the clean surface. At higher noise levels, they converge to surfaces that retain noticeable amounts of noise. DeepPSR [6] utilizes the score module of [28] but performs an additional Graph Laplacian Regularization [14] step on intermediate point clouds to obtain a better point distribution. More importantly, the iterative filtering objectives of current displacement and probabilistic methods move noisy points to the clean surface via stochastic trajectories and are error prone as incorrectly inferred displacements may result in significant changes to the distribution of filtered points.", + "bbox": [ + 76, + 90, + 472, + 407 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We propose StraightPCF, which moves noisy points along straight filtering trajectories towards the clean surfaces, as illustrated in Fig. 1. StraightPCF, illustrated in Fig. 2, is a lightweight network ( $\\sim 530K$ parameters, $17\\%$ of IterativePFN [8]) which filters all patch points simultaneously. Our technical contributions are as follows.", + "bbox": [ + 76, + 407, + 470, + 498 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We introduce the patch-wise VelocityModule that infers constant, straight flows to filter point cloud patches. The VelocityModule elegantly recovers the underlying clean surfaces with nice point distributions.", + "- To improve straightness of flows, we propose a novel straightening mechanism consisting of coupled VelocityModules. This coupled VelocityModule stack infers straighter filtering trajectories, leading to better results.", + "- Constant flows may lead to filtered points overshooting the clean surface. Therefore, we design the Distance-Module to infer a distance scalar that provides a magnitude to scale the flow velocity. Our architecture is the first to decompose filtering into a dual objective of inferring a vector field of flow velocities and a distance scalar." + ], + "bbox": [ + 76, + 500, + 468, + 709 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 723, + 218, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Conventional filtering. Early conventional methods were inspired by the Moving Least Squares (MLS) method of Levin [17] and require normal information for filtering. Notably, Alexa et al. [2] employed MLS optimization in recovering denoised surfaces from noisy point sets. The Implicit MLS (IMLS) method of Adamson and Alexa [1] further extended this approach to point-sampled cell complexes which allow for a well defined local geometry. The Algebraic Point Set Surface (APSS) method of Guennebaud and Gross [13] applied MLS optimization for the purpose of", + "bbox": [ + 76, + 750, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "fitting algebraic spheres to recover surfaces while being robust to point set density and underlying curvature. Furthermore, Digne proposed filtering the height map associated to a point set by considering handcrafted features that encode height variations around each point [9]. Digne and de Franchis designed a weighted projection scheme, that moves points to their filtered positions [10], based on the mesh bilateral filtering method of Fleishman, Drori and Cohen-Or [11]. Other normal based methods include the Moving Robust Principal Component Analysis (MRPCA) [30] of Mattei and Castrodad, the Graph Laplacian Regularization (GLR) [14] technique of Hu et al. and the Low Rank Matrix Approximation [24] of Lu et al. The main drawback of such methods is susceptibility to noise, during both the normal estimation and filtering steps.", + "bbox": [ + 496, + 90, + 893, + 318 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "By contrast, point based methods employ only point information for filtering. Cazals and Pouget [4] proposed a $N$ -dimensional polynomial surface fitting method that can be used to filter points. Meanwhile, the Locally Optimal Projection (LOP) [21] method of Lipman et al. downsampled and regularized noisy point clouds. It was extended by Huang et al. and Preiner et al. who developed Weighted-LOP (WLOP) [15] and Continuous-LOP (CLOP) [32], respectively. However, these methods do not effectively recover geometric details due to their downsampling step.", + "bbox": [ + 496, + 320, + 893, + 472 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Deep learning based filtering. While conventional methods rely on handcrafted features, convolutional neural network architectures have provided great improvements to feature generation. PointProNets [37] by Roveri et al. and Deep Feature Preserving (DFP) [23] by Lu et al. projected points onto 2D height maps before processing them using CNNs. PointNet [33], introduced by Qi et al., set the precedent for direct point set convolution and was later improved by PointNet++ [34]. Meanwhile, DGCNN [42] of Wang et al. reformulated point set convolution as a graph convolution task. PointCleanNet (PCN) [35] was one of the first methods to adopt the PointNet architecture and inferred the filtered displacement of a single central point by considering its neighborhood patch. Pointfilter [45] of Zhang et al. furthered this line of research using a bilateral filtering-inspired loss.", + "bbox": [ + 496, + 474, + 895, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Pistilli et al. introduced the first graph convolution-based mechanism, named GPDNet [31], while Luo and Hu proposed the DGCNN based DMRDenoise [26]. DMRDenoise filtered points by downsampling noisy inputs and upsampling these less noisy surfaces. Luo and Hu also proposed ScoreDenoise [28] where they formally expressed the filtering objective as the backward Langevin equation that iteratively removes noise using the inferred gradient-log of the probability distribution, i.e., the score, for point positions $\\mathbf{x}$ . This was extended by Chen et al. in their DeepPSR [6] which employs an additional graph laplacian regularization post-processing step. Mao et al. introduced the normalizing", + "bbox": [ + 496, + 719, + 895, + 902 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "20722", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/23a453b31e45605dc7c7ee97f800a9e3bbcfd9a0ceb10e21e882ac28de3c3e97.jpg", + "image_caption": [ + "Figure 2. Our StraightPCF network. It involves a coupled VelocityModule stack that infers a constant flow velocity $\\pmb{v}_{\\theta}^{k}$ for patch states $\\tilde{\\pmb{X}}_{(\\hat{t} + k)/T}$ . To ensure filtered points converge to the surface, the DistanceModule infers a distance scalar $d_{\\phi}$ that scales the velocity." + ], + "image_footnote": [], + "bbox": [ + 135, + 87, + 834, + 224 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "flows based filtering method PDFlow [29] that disentangles noise from the underlying clean representation at higher dimensions. The RePCDNet [5] method of Chen et al. sought to model iterative filtering via a recurrent neural network. By contrast, de Silva Edirimuni et al. proposed the graph convolution based IterativePFN [8] that models iterative filtering using individual IterationModules. The joint filtering and normal estimation method CFilter [7], developed by de Silva Edirimuni et al., exploited normals to improve filtered point positions. Ma et al. introduced learning implicit signed distance functions, by displacing noisy query points back to the surface along normals where the surface corresponds to the zero-level set of the function [3]. This has been exploited for normal estimation [18, 19].", + "bbox": [ + 75, + 291, + 472, + 501 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Score and displacement based methods are inspired by diffusive processes [27, 39] and their filtering objectives result in stochastic trajectories. Recent work by Liu, Gong and Liu focuses on Reflow [22], which explored the optimal transport problem of identifying straight paths given two samples from different distributions. The work of Wu et al. further extended this Reflow mechanism to point cloud generation, which attempts to generate point cloud shapes given initial samples from the normal distribution [43].", + "bbox": [ + 75, + 503, + 470, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Problem Statement and Motivation", + "text_level": 1, + "bbox": [ + 76, + 650, + 397, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Resampling methods demonstrate an inability to recover clean surfaces with high accuracy, unlike probabilistic and displacement based methods. A probabilistic score based method such as ScoreDenoise [28] and a displacement based method such as IterativePFN [8] share similar filtering objectives that may be expressed by,", + "bbox": [ + 75, + 675, + 468, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {x}} _ {t} ^ {i} = \\tilde {\\boldsymbol {x}} _ {t - 1} ^ {i} + F _ {\\theta} \\left(\\tilde {\\boldsymbol {x}} _ {t - 1} ^ {i}\\right), t = 1, \\dots , T \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 147, + 771, + 468, + 789 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\tilde{\\pmb{x}}_t^i$ is the $i$ -th filtered point at time $t$ and $F_{\\theta}$ represents the network with parameters $\\theta$ . The main difference between ScoreDenoise and IterativePFN lies in their training objectives, $\\mathcal{L}_S$ and $\\mathcal{L}_I$ , respectively. For a noisy point $\\pmb{x}^i \\in \\pmb{X}$ where $\\pmb{X}$ is the initial noisy patch, we have:", + "bbox": [ + 75, + 796, + 470, + 873 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {S} ^ {i} = \\mathbb {E} _ {\\boldsymbol {x} \\sim k N N (\\boldsymbol {x} ^ {i}, \\boldsymbol {X})} \\left[ \\left\\| s (\\boldsymbol {x}) - \\mathcal {S} ^ {i} (\\boldsymbol {x}) \\right\\| _ {2} ^ {2} \\right], \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 129, + 878, + 468, + 905 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {I} ^ {i} = \\sum_ {t = 0} ^ {T} \\left\\| \\boldsymbol {d} _ {t} ^ {i} - \\left(N N \\left(\\boldsymbol {x} _ {t - 1} ^ {i}, \\boldsymbol {Y} _ {t}\\right) - \\boldsymbol {x} _ {t - 1} ^ {i}\\right) \\right\\| _ {2} ^ {2}. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 303, + 892, + 344 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "ScoreDenoise is trained to predict a score $S^i(\\boldsymbol{x}) = \\text{Score}(\\boldsymbol{x} - \\boldsymbol{x}^i | \\boldsymbol{h}^i)$ for $\\boldsymbol{x}$ sampled from the k-nearest neighbors of $\\boldsymbol{x}^i$ . It is conditioned on the latent feature $\\boldsymbol{h}^i$ of $\\boldsymbol{x}^i$ and corresponds to the gradient-log of the noise-convolved probability distribution for point position $\\boldsymbol{x}$ . The ground truth target $s(\\boldsymbol{x}) = N N(\\boldsymbol{x}, \\boldsymbol{Y}) - \\boldsymbol{x}$ , where $\\boldsymbol{Y}$ is the clean patch. Ergo, $s(\\boldsymbol{x})$ is the displacement from $\\boldsymbol{x}$ to its nearest neighbor in $\\boldsymbol{Y}$ . Once this training objective has been optimized, score based methods infer aggregate scores, at each iteration $t$ , such that $F_{\\theta}(\\boldsymbol{x}_{t-1}^i) = \\alpha \\mathcal{E}^i(\\boldsymbol{x}_{t-1}^i) = (\\alpha / K) \\sum_{\\boldsymbol{x}_{t-1}^j \\in kNN(\\boldsymbol{x}_{t-1}^i)} S^j(\\boldsymbol{x}_{t-1}^i)$ where $\\alpha$ is the step discretization parameter. This score shifts points towards the clean surface along a stochastic filtered trajectory that is sensitive to the choice of $\\alpha$ , which must be kept relatively small ( $\\sim 0.2$ ). By contrast, IterativePFN internally models the iterative filtering objective and incorporates it within their training objective. They directly infer displacements $F_{\\theta}(\\tilde{\\boldsymbol{x}}_{t-1}^i) = \\boldsymbol{d}_t^i$ as the output of each IterationModule that models an iteration $t$ . From Eq. (3) we identify that the overall filtered trajectories inferred by IterativePFN will also be stochastic in nature as it uses an Adaptive Ground Truth (AGT), $Y_t = Y + \\sigma_t\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I)$ , within the training objective. Modelling the iterative filtering process internally results in a large network ( $>3.2M$ parameters). The AGT, while recovering the surface, causes clustering along the surface and fails to respect the original point distribution. This is illustrated in Fig. 3.", + "bbox": [ + 496, + 353, + 893, + 763 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Inspired by Reflow which focuses on optimal transport between samples of different distributions [22, 43], we pose filtering as an optimal transport problem between point cloud patches. These patches of $n$ points are sampled from 1) the clean surface (i.e., clean patch $\\mathbf{X}_1\\sim \\pi_1$ ) and 2) a high noise variant of the clean surface (i.e., high noise patch $\\mathbf{X}_0\\sim \\pi_0$ ). The goal is to determine a transport plan (coupling) such that $\\mathbf{X}_1 = V(\\mathbf{X}_0)$ where $V:\\mathbb{R}^{n\\times 3}\\to \\mathbb{R}^{n\\times 3}$ . The approximated flow velocity, $\\pmb{v}_{\\theta}:\\mathbb{R}^{n\\times 3}\\rightarrow \\mathbb{R}^{n\\times 3}$ sat", + "bbox": [ + 496, + 763, + 893, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "20723", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/33db8d260ff8ed94ab1d498b1bc9c0e412afd8df1bcc7797b2b9e6e8b214b6fc.jpg", + "image_caption": [ + "Figure 3. Our StraightPCF is able to recover a better distribution of filtered points, even at very high noise scales ( $\\sigma = 3\\%$ and $50\\mathrm{K}$ resolution) unseen during network training." + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 467, + 314 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "isfies this transport mapping and $(\\tilde{\\pmb{X}}_0,\\tilde{\\pmb{X}}_1)$ form a valid coupling. Consequently, the filtered trajectories are straight (see Fig. 4), unlike ScoreDenoise and IterativePFN. Moreover, our method recovers the underlying point distribution of the surface without clustering artifacts or distortion.", + "bbox": [ + 75, + 391, + 470, + 467 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4. Method", + "text_level": 1, + "bbox": [ + 76, + 479, + 168, + 496 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Previous methods such as ScoreDenoise [28] and IterativePFN [8] focus on filtering as a reverse Markov process where the forward process would correspond to adding noise. We formulate filtering as an optimal transport plan that moves noisy points back to the clean surface along the shortest (straight) path. We model noisy input patches as intermediate states between high noise variants and their corresponding clean counterparts. We design a graph convolution based VelocityModule that infers a constant flow velocity for each intermediate state. This encourages noisy points to move along straight filtering trajectories as shown in Fig. 4. We further improve the straightness of these trajectories via VelocityModule coupling. Finally, as the flow is constant, it may result in filtered points overshooting the clean surface. Therefore, we design a DistanceModule that scales the flow velocity appropriately and ensures convergence near the surface. The overall Straight-PCF architecture is illustrated in Fig. 2, which demonstrates the filtering process that utilizes both the coupled Velocity-Module and DistanceModule sub-networks to move points along straightened paths. The supplementary document provides additional methodology details.", + "bbox": [ + 75, + 505, + 470, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.1. Filtering via straight flows", + "text_level": 1, + "bbox": [ + 76, + 847, + 316, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In this section, we introduce the VelocityModule (VM) that moves noisy points along constant, straight flows to-", + "bbox": [ + 75, + 869, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/67cc5ddbe1bf6da4c2692472c3ee08c7670097fcb1eca29638cc4308999630a1.jpg", + "image_caption": [ + "Figure 4. StraightPCF models initial noisy patches (light blue) as being intermediate states of a linear interpolation between high noise variants (red) and the clean surfaces (dark blue) and encourages straight filtering trajectories." + ], + "image_footnote": [], + "bbox": [ + 540, + 88, + 854, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "wards the clean surface. Given a noisy patch $\\mathbf{X} = \\{\\pmb{x}^i | \\pmb{x}^i \\in kNN(\\pmb{x}^r, \\mathcal{P}_X, k)\\}$ centered around a reference point $\\pmb{x}^r$ in the noisy point cloud $\\mathcal{P}_X$ , the filtering objective aims to move $\\pmb{x}^i$ towards the underlying clean patch $\\mathbf{Y} = \\{\\pmb{y}^i | \\pmb{y}^i \\in \\mathcal{P}_Y\\}$ . For the filtering task, learning based methods are typically trained on noisy point clouds with Gaussian noise [6, 28, 29, 35, 45]. Iterative filtering depends on the ability of the method to filter patches from a higher noise level to a lower noise level, with the end result converging to the clean surface. Given the highest noise setting $\\sigma_H$ , intermediate noise scales at a time $t \\in [0,1]$ can be expressed as $\\sigma = (1 - t)\\sigma_H$ . Therefore, we model noisy patches $\\mathbf{X} = \\mathbf{Y} + \\sigma\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I)$ as intermediate states $X_t$ , of the filtering objective that moves points from a high noise variant, $X_0 = Y + \\sigma_H\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I)$ to the clean counterpart $X_1 = Y$ . Here, $\\sigma_H = 2\\%$ of the point cloud's bounding sphere radius and corresponds to the highest noise setting of our training set. We observe that intermediate states $X_t$ can be defined as a linear interpolation of $X_0$ and $X_1$ , that is, a straight path, such that,", + "bbox": [ + 498, + 266, + 892, + 569 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\boldsymbol {X} _ {t} = (1 - t) \\boldsymbol {X} _ {0} + t \\boldsymbol {X} _ {1} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 578, + 890, + 594 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Therefore, we intuit that the filtering objective can be reformulated as an optimal transport process that moves points from $\\mathbf{X}_0$ to $\\mathbf{X}_1$ . The flow of $\\mathbf{X}_t$ at time $t$ can be expressed via the ordinary differential equation (ODE):", + "bbox": [ + 498, + 604, + 890, + 664 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {d} \\boldsymbol {X} _ {t} = \\boldsymbol {v} \\left(\\boldsymbol {X} _ {t}\\right) \\mathrm {d} t, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 672, + 890, + 689 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\pmb{v}(\\pmb{X}_t)$ is the velocity field at $\\pmb{X}_t$ . For this ODE process, the linear interpolation of Eq. (4) can be used in the least squares optimization to determine the flow,", + "bbox": [ + 498, + 698, + 890, + 744 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {v} \\int_ {0} ^ {1} \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\| \\boldsymbol {v} (\\boldsymbol {X} _ {t}) - (\\boldsymbol {X} _ {1} - \\boldsymbol {X} _ {0}) \\| _ {2} ^ {2} \\right] d t, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 521, + 752, + 890, + 786 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where times $t$ are sampled uniformly along $[0,1]$ . However, the velocity field at an intermediate state $\\pmb{X}_t$ cannot be causally determined as both $\\pmb{X}_0$ and $\\pmb{X}_1$ are unknown, during filtering. To address this, our idea is to approximate the velocity field for each $\\pmb{X}_t$ by a neural network.", + "bbox": [ + 498, + 794, + 890, + 869 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Training objective for single VM. We use a DGCNN based graph neural network to model a VelocityModule $\\pmb{v}_{\\theta}$", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "20724", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "with parameters $\\theta$ to approximate the flow velocity. To train this VelocityModule, we define the following training objective.", + "bbox": [ + 75, + 90, + 468, + 135 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {A} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\| \\boldsymbol {v} _ {\\theta} (\\boldsymbol {X} _ {t}) - \\boldsymbol {\\delta} (\\boldsymbol {X} _ {1}, \\boldsymbol {X} _ {0}) \\| _ {2} ^ {2} \\right], \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 120, + 145, + 468, + 172 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\delta(X_1, X_0) = X_1 - X_0$ . Hence, at each intermediate state, the corresponding flow velocity is ideally a constant vector that leads to a straight path from $X_0$ to $X_1$ .", + "bbox": [ + 76, + 180, + 468, + 224 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Filtering objective for single VM. During inference, given a straight flow velocity $\\pmb{v}_{\\theta}$ , we can move points from $\\pmb{X}_{\\hat{t} /N}$ to $\\pmb{X}_{(\\hat{t} +1) / N}$ using the Euler method ODE solver:", + "bbox": [ + 76, + 224, + 468, + 273 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + 1) / N} = \\tilde {\\boldsymbol {X}} _ {\\hat {t} / N} + \\frac {1}{N} \\boldsymbol {v} _ {\\theta} (\\tilde {\\boldsymbol {X}} _ {\\hat {t} / N}), \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 282, + 468, + 311 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $N$ denotes the total number of filtering steps, $\\hat{t} \\in [0, \\dots, M, \\dots, N-1]$ is an integer time step and $\\tilde{\\pmb{X}}_0 = \\pmb{X}_0$ . In practice, filtering starts at an unknown time step $\\hat{t} = M$ . We do not know the noise scale of the input patch and need to model it as an intermediate state $\\tilde{\\pmb{X}}_{M/N}$ of a higher noise variant $\\pmb{X}_0$ . The full position update takes the form,", + "bbox": [ + 76, + 321, + 468, + 412 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {X}} _ {1} = \\tilde {\\boldsymbol {X}} _ {M / N} + \\frac {1}{N} \\sum_ {\\hat {t} = M} ^ {N - 1} \\boldsymbol {v} _ {\\theta} \\left(\\tilde {\\boldsymbol {X}} _ {\\hat {t} / N}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 422, + 468, + 464 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Eq. (9) poses two challenges:", + "bbox": [ + 76, + 473, + 272, + 488 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. The straightness of paths is crucial to reducing the number of total steps and improving efficiency. If paths are not sufficiently straight (i.e., they are curved), we need a higher number of steps to filter points effectively.", + "2. The starting time $t = M / N$ is unknown. Applying the Euler method for too many steps, $N$ , may lead to points not converging at the surface." + ], + "bbox": [ + 76, + 488, + 468, + 594 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Straighter flows via VelocityModule coupling", + "text_level": 1, + "bbox": [ + 76, + 603, + 457, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Given noisy initial data, the trajectories of points tend to be curved, with limited straightness. One way to improve straightness is to finetune the velocity network on the coupling $(\\tilde{X}_0,\\tilde{X}_1)$ to satisfy $\\tilde{X}_1 = V(\\tilde{X}_0)$ . For filtering, we aim to recover surfaces while preserving local geometric details [35]. Applying such finetuning requires the pre-computation of $\\tilde{X}_1$ for all possible surface patches and is infeasible due to the large number of patches in the training set. We propose a simple mechanism to straighten paths by coupling $K$ VelocityModules together.", + "bbox": [ + 75, + 626, + 468, + 776 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Training objective for coupled VMs. Given a noisy patch $\\mathbf{X}_t$ , we partition the trajectory from $\\mathbf{X}_t$ to $\\mathbf{X}_1$ into $K$ segments and obtain the velocity flow $\\pmb{v}_{\\theta}^{k}(\\tilde{\\pmb{X}}_{t_k})$ at times $t_k = (t(K - k) + k) / K$ where $k \\in \\{0, 1, \\dots, K - 1\\}$ . Intermediate positions at times $t_{k+1}$ are given by $\\tilde{\\pmb{X}}_{t_{k+1}} = \\tilde{\\pmb{X}}_{t_k} + (1 / K) \\pmb{v}_{\\theta}^{k}(\\tilde{\\pmb{X}}_{t_k})$ . We empirically find that two VelocityModules, i.e., $K = 2$ , provide the best balance between accuracy and efficiency. The Velocity Modules are", + "bbox": [ + 75, + 777, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "pretrained using the training objective of Eq. (7) and the coupled VMs are finetuned with the introduced objective,", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {B} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\sum_ {k = 0} ^ {K - 1} \\left\\| \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {k}}\\right) - \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1}, \\boldsymbol {X} _ {0}\\right) \\right\\| _ {2} ^ {2} \\right. \\tag {10} \\\\ \\left. + \\lambda_ {1} \\sum_ {k = 0} ^ {K - 2} \\left\\| \\boldsymbol {\\delta} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {k + 1}}, \\boldsymbol {X} _ {t _ {k + 1}}\\right) \\right\\| _ {2} ^ {2} \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 127, + 890, + 213 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "for $K \\geq 2$ , $\\lambda_{1} = 10$ and $\\tilde{\\pmb{X}}_{t_0} = \\pmb{X}_{t_0} = \\pmb{X}_t$ . The first term of $\\mathcal{L}_B$ encourages coupled VelocityModules to infer a constant velocity at times $t_k$ , while the second encourages filtered points $\\tilde{\\pmb{X}}_{t_k}$ to move closer to interpolated points $\\pmb{X}_{t_k}$ .", + "bbox": [ + 496, + 220, + 890, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Filtering objective for coupled VMs. At inference, we apply a modified form of the Euler method to filter points, similar to Eq. (8). We apply $K$ coupled VelocityModules $N$ times, resulting in $T = K \\cdot N$ total filtering steps. We adjust our earlier notation of integer time steps such that $\\hat{t} \\in \\{0, K, \\dots, \\hat{M}, \\dots, K(N - 1)\\}$ where $\\hat{M}$ is divisible by $K$ and $\\tilde{\\pmb{X}}_0 = \\pmb{X}_0$ . The sequential position update becomes,", + "bbox": [ + 498, + 282, + 890, + 387 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k + 1) / T} = \\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T} + \\frac {1}{T} \\boldsymbol {v} _ {\\theta} ^ {k} (\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 527, + 405, + 890, + 434 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The corresponding full position update across time steps $S = \\{\\hat{M},\\hat{M} +K,\\dots ,N(K - 1)\\}$ is,", + "bbox": [ + 498, + 438, + 890, + 468 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {X}} _ {1} = \\tilde {\\boldsymbol {X}} _ {\\hat {M} / T} + \\frac {1}{T} \\sum_ {\\hat {t} \\in \\mathcal {S}} \\sum_ {k = 0} ^ {K - 1} \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}\\right). \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 474, + 890, + 517 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Distance estimation to the clean surface", + "text_level": 1, + "bbox": [ + 500, + 537, + 838, + 551 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We now address the second challenge related to Eq. (9) and introduce the DistanceModule that scales the overall straight trajectory. This leads to better convergence near the surface. The DistanceModule estimates a distance scalar, corresponding to the standard deviation of initial noisy points from the clean surface. More specifically, the DistanceModule $\\mathcal{D}_{\\phi}(\\cdot)$ is used to approximate a mapping $d_{\\phi}:\\mathbb{R}^{n\\times 3}\\to \\mathbb{R}$ , such that,", + "bbox": [ + 496, + 560, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nd _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right) = \\operatorname {S i g m o i d} \\left(\\operatorname {M a x} \\left(\\mathcal {D} _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right)\\right)\\right). \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 686, + 890, + 705 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The distance $d_{\\phi}$ is then used to scale the output of VelocityModules, as illustrated in Fig. 5. The DistanceModule is embedded within the StraightPCF architecture (see Fig. 2). We keep the weights of the finetuned coupled VelocityModules fixed when training the DistanceModule. The respective training objective for optimizing the parameters $\\phi$ is,", + "bbox": [ + 496, + 712, + 890, + 803 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {C} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\left(d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right) - \\frac {\\| \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1} , \\boldsymbol {X} _ {t _ {0}}\\right) \\| _ {2}}{\\| \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1} , \\boldsymbol {X} _ {0}\\right) \\| _ {2}}\\right) ^ {2} \\right. \\tag {14} \\\\ \\left. + \\lambda_ {2} \\left\\| \\boldsymbol {\\delta} \\left(\\tilde {\\boldsymbol {X}} _ {1}, \\boldsymbol {X} _ {1}\\right) \\right\\| _ {2} ^ {2} \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 820, + 890, + 904 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "20725", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/ff1b43ea5fbd0dab3af9418da0884f34bc0aa62594119bcdf283fd60bedb1669.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Resolution10K (Sparse)50K (Dense)
Noise1%2%3%1%2%3%
MethodCDP2MCDP2MCDP2MCDP2MCDP2MCDP2M
PUNet dataset [44]PCN [35]3.5151.1487.4673.96513.0678.7371.0490.3461.4470.6082.2891.285
PointFilter [45]2.4610.4433.5340.8625.0891.8490.7580.1820.9070.2511.5990.710
Score [28]2.5210.4633.6861.0744.7081.9420.7160.1501.2880.5661.9281.041
PDFlow [29]2.1260.3813.2461.0104.4471.9990.6510.1641.1730.5811.9141.210
DeepPSR [6]2.3530.3063.3500.7344.0751.2420.6490.0760.9970.2961.3440.531
IterativePFN [8]2.0560.2183.0430.5554.2411.3760.6050.0590.8030.1821.9711.012
Ours1.8700.2392.6440.6043.2871.1260.5620.1110.7650.2661.3070.648
PCNet dataset [35]PCN [35]3.8471.2218.7523.04314.5255.8731.2930.2891.9130.5053.2491.076
Score [28]3.3690.8305.1321.1956.7761.9411.0660.1771.6590.3542.4940.657
PointFilter [45]3.0190.8864.8851.2757.0622.0321.0530.1861.3490.2572.2250.491
PDFlow [29]3.2430.6064.5450.9665.9341.4410.9690.1521.6460.4242.4500.569
DeepPSR [6]2.8730.7834.7571.1186.0311.6191.0100.1461.5150.3402.0930.573
IterativePFN [8]2.6210.6984.4391.0116.0261.5600.9130.1391.2510.2382.5290.716
Ours2.7470.5364.0460.7884.9211.0930.8770.1441.1730.2591.8160.445
", + "bbox": [ + 83, + 88, + 888, + 373 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative filtering results of recent state-of-the-art methods and our method on the synthetic PUNet and PCNet datasets. Note that our network is lightweight, with just $\\sim 530K$ parameters (17% of IterativePFN). CD and P2M values are multiplied by $10^{4}$", + "bbox": [ + 75, + 383, + 892, + 411 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/840f7a8b07a8c99c3ae93b25bb17ed31e970bae683d13969145a81e9130ccb6a.jpg", + "image_caption": [ + "Figure 5. Left: Filtering by coupled VelocityModules only. Right: Coupled VelocityModules and DistanceModule. Scaled trajectories (green lines) lead to better convergence at the surface." + ], + "image_footnote": [], + "bbox": [ + 84, + 433, + 465, + 523 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $t_0 = t$ and $\\tilde{\\pmb{X}}_{t_0} = \\pmb{X}_{t_0} = \\pmb{X}_t$ . The first term of $\\mathcal{L}_C$ encourages the DistanceModule to infer the relative distance of $\\pmb{X}_{t_0}$ from the clean surface, as compared to $\\pmb{X}_0$ . The last term encourages points to return to the clean surface. We set $\\lambda_{2} = 2\\times 10^{2}$ to ensure the loss contribution of the last term is of the same order as that of the first one. Consequently, Eq. (11) becomes,", + "bbox": [ + 75, + 602, + 468, + 709 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k + 1) / T} = \\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T} + \\frac {d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {\\hat {M} / T}\\right)}{T} \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}\\right). \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 86, + 720, + 468, + 768 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 782, + 209, + 800 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Next, we provide results on synthetic data under Gaussian noise and real-world Kinect [41] and Paris-Rue-Madame [38] data. The supplementary document contains additional results of both conventional and learning based methods on synthetic and real-world scanned data, as well as a comparison of testing times.", + "bbox": [ + 75, + 809, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Training and evaluation details", + "text_level": 1, + "bbox": [ + 498, + 436, + 774, + 454 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We follow the training procedure of ScoreDenoise [28], and train our model on the PUNet dataset [44] consisting of 40 point clouds for training and 20 point clouds for testing. To ensure consistency with ScoreDenoise's training settings, we add Gaussian noise sampled with standard deviation $\\sigma_{H} = 2\\%$ of the bounding sphere radius to each clean point cloud. Our training procedure only requires the high noise variants and the clean ground truth targets. All intermediate states at noise scales $\\sigma = (1 - t)\\sigma_{H}$ , with $t \\sim \\mathcal{U}(0,1)$ are created as linear interpolations between these two, initial and final states, as per Eq. (4). For testing, we also consider 10 test point clouds from the PCNet dataset [35] provided by ScoreDenoise. These synthetic point clouds contain Gaussian noise at scales of $1\\%$ , $2\\%$ and $3\\%$ of the point cloud's bounding sphere radius. We use two different sampling densities of 10K and 50K points to evaluate filtering ability across different sparsity settings. Moreover, to assess filtering results on real-world noisy point clouds, we compare methods on the Kinect v1 dataset that comprises of 71 point clouds [41] and 4 scenes extracted from the Paris-Rue-Madame dataset [38]. Finally, we provide a comparison on 4 scenes of the Kitti-360 dataset [20], in the supplementary document. Following [8, 28], all methods are only trained on PUNet with Gaussian noise.", + "bbox": [ + 496, + 460, + 890, + 823 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation. We train and test StraightPCF on a NVIDIA GeForce RTX 3090 GPU using PyTorch. We use the Adam optimizer with a learning rate of $1 \\times 10^{-4}$ . Similar to [8, 28], we use PyTorch3D [36] to compute Chamfer Distance (CD) and Point2Mesh (P2M) metric values.", + "bbox": [ + 496, + 824, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "20726", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/07a3f63a3bf81e1c259b8658043d6014b111944b8e4605b44c1147ff8ae1037f.jpg", + "image_caption": [ + "Figure 6. Visual filtering results for $50\\mathrm{K}$ resolution shapes $(\\sigma = 2\\%)$ within the PUNet and PCNet datasets. The darker (i.e., more blueish) the better. We achieve both strong point-wise P2M results while also ensuring well distributed points (illustrated by close-ups) unlike DeepPSR or IterativePFN which have holes indicating clustering." + ], + "image_footnote": [], + "bbox": [ + 86, + 85, + 890, + 397 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Performance on synthetic data", + "text_level": 1, + "bbox": [ + 76, + 474, + 346, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 1 and Fig. 6 illustrate filtering results on the synthetic PUNet and PCNet datasets. Our method has a clear edge over others in recovering the underlying clean point distribution demonstrated by superior CD results across all noise settings. We also achieve strong P2M results on the PUNet dataset. While IterativePFN [8] has marginally better P2M results on the PUNet data, this does not ensure a good distribution of points as evidenced by visual results in Fig. 6. Here, for noisy point clouds at $50\\mathrm{K}$ resolution and $2\\%$ noise, IterativePFN exhibits small holes, indicating clustering. Moreover, our network consists of only $530\\mathrm{K}$ parameters and is roughly $83\\%$ smaller than that of IterativePFN, given the latter's $3.2\\mathrm{M}$ parameters. DeepPSR [6], despite using a post-processing regularization step, also suffers from holes and poor point distributions. We also note that IterativePFN generalizes poorly to higher noise scales outside the training noise scales (where maximum noise is $\\sigma = 2\\%$ ). The ability of our method to generalize well across different data is demonstrated by the superior performance on the PCNet dataset. The PCNet shapes are unseen during training. Our method obtains both superior CD and P2M results over all other methods. At $10\\mathrm{K}$ resolution and $\\sigma = 3\\%$ noise, our method offers a $17.1\\%$ reduction in CD error and $24.1\\%$ reduction in P2M error. Our method also yields state-of-the-art results at $50\\mathrm{K}$ resolution where, for $\\sigma = 3\\%$ , the CD error improvement is $13.2\\%$ and P2M error", + "bbox": [ + 75, + 507, + 472, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "improvement is $9.4\\%$ . Visual filtering results in Fig. 6 indicate that our method outperforms others in recovering complex details such as the legs of the Camel which are closely situated. By contrast, methods such as Pointfilter [45] and PDFlow [29] flatten points between these close surfaces while IterativePFN does not recover the body well. Furthermore, on a complex shape as Netsuke, we outperform other methods which either cause clustering (e.g., PDFlow, IterativePFN) at this high noise scale or leave behind noise due to limited filtering ability (e.g., ScoreDenoise).", + "bbox": [ + 496, + 474, + 890, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Performance on real-world scanned data", + "text_level": 1, + "bbox": [ + 498, + 636, + 848, + 650 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Next we consider filtering results on scanned data. Table 2 provides quantitative results on the Kinect dataset and Fig. 7 illustrates visual results on the Paris-Rue-Madame dataset. Our method performs favorably on the Kinect data, obtaining a $1.82\\%$ reduction on CD errors, as compared to IterativePFN [8]. As this data is very sparse, our P2M result is marginally higher than Pointfilter [45] and Score-Denoise [28]. These methods focus on returning points to the surface yet succumb to clustering artifacts whereas our method both recovers surfaces while retaining good point distributions. The Paris-Rue-Madame dataset contains high noise scans due to outdoor environmental factors. In Fig. 7, we visualize filtering results for several most recent, state-of-the-art methods. In general, methods such as PDFlow [29] and DeepPSR [6] perform poorly in removing noisy artifacts while IterativePFN [8] causes points to", + "bbox": [ + 496, + 657, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "20727", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/06aadf5b8eca17d9b43a94229ca6d2d8412edec73af59083e5ab12d735f23b14.jpg", + "image_caption": [ + "Figure 7. Visual filtering results on two scenes of the RueMadame dataset. We show results for the most recent state-of-the-art methods." + ], + "image_footnote": [], + "bbox": [ + 84, + 85, + 883, + 296 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1a294babdfa6a490c3d3157afc4d3e5a24b3e8a1c0940b554fd307ab59b0a5ad.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodKinect
CDP2M
ScoreDenoise1.3220.652
Pointfilter1.3770.644
PDFlow1.3340.699
DeepPSR1.4310.715
IterativePFN1.3200.685
Ours1.2960.664
", + "bbox": [ + 158, + 344, + 387, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "cluster near the original scan lines. Our method, however, recovers the underlying clean surface and ensures a much better point distribution, as evidenced by the close-ups in Scene 1. In Scene 2, PDFlow and IterativePFN are not able to clean the surface of the parked vehicle whereas our method recovers the underlying shape with fewer noisy artifacts.", + "bbox": [ + 75, + 566, + 468, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Ablation Study and Discussion", + "text_level": 1, + "bbox": [ + 76, + 691, + 357, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We train and test several variant architectures in order to ascertain the impact of the proposed VelocityModule (VM) and DistanceModule (DM). The results are given in Table 3. Our coupled VM + DM architecture (V5) increases the parameter number to $\\sim 530K$ . Therefore, we train another Large VM with $\\sim 530K$ parameters (V3). We find that directly increasing the parameter number (V3) leads to very limited performance gain while V5 exhibits far superior performance. Furthermore, the coupled VM + DM architecture (V5) significantly outperforms the single VM (V1 and V2) architectures. Finally, there is a noticeable difference in performance with and without a DM as evidenced by the dis", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1ab66e50877495414dfada2d4a97cfee28a4027c4f1dc19fa32b29460eb7e417.jpg", + "table_caption": [ + "Table 2. Quantitative results on Kinect data. Our network is lightweight, with just $\\sim 530K$ parameters (17% of IterativePFN). CD and P2M values are multiplied by $10^{4}$ ." + ], + "table_footnote": [], + "table_body": "
Ablation10K points
1% noise2% noise3% noise
CDP2MCDP2MCDP2M
VI) VM w/o DM2.160.423.060.923.731.42
V2) VM w/ DM2.000.323.060.963.811.55
V3) Large VM2.170.412.990.843.541.29
V4) CVM w/o DM1.970.323.010.923.711.45
V5) CVM w/ DM1.870.242.640.603.291.13
", + "bbox": [ + 500, + 344, + 903, + 486 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. Ablation results for different VelocityModule (VM) and DistanceModule (DM) configurations.", + "bbox": [ + 498, + 496, + 890, + 523 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "parity between V4 and V5. We provide further ablations, including higher VM couplings, in the supplementary document.", + "bbox": [ + 498, + 553, + 890, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Limitation.** While our StraightPCF yields state-of-the-art results across multiple datasets, we observe relatively low performance on low density or high sparsity data, which is similar to current methods. We provide the visual results in the supplementary document due to space limit.", + "bbox": [ + 498, + 599, + 890, + 676 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "7. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 691, + 617, + 709 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Recent deep learning based filtering methods focus on moving noisy points along stochastic paths to remove noise from input point clouds. We propose the first study to consider filtering points along straight paths, leading to smaller discretization errors and fewer filtering iterations. This lightweight method, while being parameter efficient, delivers filtered point distributions closer to that of the ground truth distributions without requiring any regularization in loss function or post-processing. Our method achieves state-of-the-art performance on multiple synthetic and real-world datasets across standard filtering metrics, showcasing its superiority and effectiveness.", + "bbox": [ + 496, + 719, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "20728", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] A. Adamson and M. Alexa. Point-sampled cell complexes. ACM Trans. Graph., 25:671-680, 2006. 2", + "[2] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and Cláudio T. Silva. Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. Graph., 9:3–15, 2003. 1, 2", + "[3] Ma Baorui, Han Zhizhong, Liu Yu-Shen, and Zwicker Matthias. 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IEEE Transactions on Visualization and Computer Graphics, 27:2015-2027, 2021. 2, 4, 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 898 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "20730", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_model.json b/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..eb9ecd000fbd01b1b72675728c1516f3f71b2d8c --- /dev/null +++ b/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_model.json @@ -0,0 +1,1914 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.261, + 0.131, + 0.71, + 0.154 + ], + "angle": 0, + "content": "StraightPCF: Straight Point Cloud Filtering" + }, + { + "type": "text", + "bbox": [ + 0.088, + 0.18, + 0.896, + 0.217 + ], + "angle": 0, + "content": "Dasith de Silva Edirimuni1, Xuequan Lu2*, Gang Li1, Lei Wei1, Antonio Robles-Kelly1, Hongdong Li3 \n1Deakin University, 2La Trobe University, 3Australian National University" + }, + { + "type": "text", + "bbox": [ + 0.2, + 0.219, + 0.782, + 0.234 + ], + "angle": 0, + "content": "{dtdesilva, gang.li, lei.wei, antonio.robles-kelly}@deakin.edu.au," + }, + { + "type": "text", + "bbox": [ + 0.297, + 0.238, + 0.68, + 0.251 + ], + "angle": 0, + "content": "b.lu@latrobe.edu.au, hongdong.li@anu.edu.au" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.287, + 0.314, + 0.303 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.319, + 0.474, + 0.712 + ], + "angle": 0, + "content": "Point cloud filtering is a fundamental 3D vision task, which aims to remove noise while recovering the underlying clean surfaces. State-of-the-art methods remove noise by moving noisy points along stochastic trajectories to the clean surfaces. These methods often require regularization within the training objective and/or during post-processing, to ensure fidelity. In this paper, we introduce StraightPCF, a new deep learning based method for point cloud filtering. It works by moving noisy points along straight paths, thus reducing discretization errors while ensuring faster convergence to the clean surfaces. We model noisy patches as intermediate states between high noise patch variants and their clean counterparts, and design the VelocityModule to infer a constant flow velocity from the former to the latter. This constant flow leads to straight filtering trajectories. In addition, we introduce a DistanceModule that scales the straight trajectory using an estimated distance scalar to attain convergence near the clean surface. Our network is lightweight and only has \\(\\sim 530K\\) parameters, being \\(17\\%\\) of IterativePFN (a most recent point cloud filtering network). Extensive experiments on both synthetic and real-world data show our method achieves state-of-the-art results. Our method also demonstrates nice distributions of filtered points without the need for regularization. The implementation code can be found at: https://github.com/ddsdiri/StuartPCF." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.743, + 0.21, + 0.759 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.77, + 0.47, + 0.876 + ], + "angle": 0, + "content": "In recent years, point clouds have become increasingly popular as the representation-of-choice for storing and manipulating 3D data, with numerous applications in both computer vision [12, 20, 25, 38] and geometry modelling [16, 25, 40]. Point clouds are unordered sets of 3D coordinates which typically represent object surfaces and are captured using 3D sensors such as depth and Lidar devices. However," + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.285, + 0.895, + 0.43 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.441, + 0.895, + 0.484 + ], + "angle": 0, + "content": "Figure 1. Filtered trajectories for the Isocahedron shape at \\(50\\mathrm{K}\\) resolution and noise scale \\(\\sigma = 3\\%\\). Our StraightPCF filters points along much straighter paths, compared to ScoreDenoise [28]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.519, + 0.895, + 0.746 + ], + "angle": 0, + "content": "noisy artifacts may appear in point clouds as a result of sensor limitations and environmental factors. Removing this noise, known as filtering or denoising, is a fundamental 3D vision task. Filtering methods are broadly categorized into two groups: 1) conventional methods involving traditional optimization and 2) deep learning based methods. Conventional methods can further be subdivided into normal based methods which require surface normal information to reliably filter point clouds [2, 10, 13, 24, 30] and point based methods which directly filter point clouds [15, 21, 32]. While normal based methods are limited by the accuracy of normals, point based methods suffer from a loss of geometric details and still exhibit sensitivity to noise. Recently, many deep learning approaches have been proposed to overcome these shortcomings." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.896, + 0.902 + ], + "angle": 0, + "content": "Deep learning methods can be divided into 1) resampling, 2) displacement and 3) probability based methods. Resampling-based methods [26] show the least fidelity when recovering the underlying noise-free surfaces as their downsampling procedure results in the loss of crucial geometric information. By contrast, displacement and probability based methods show greater promise as they model the filtering objective as a reverse Markov process, which can be iteratively applied on the input to progressively remove noise. Early displacement based methods, such as" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.435, + 0.901 + ], + "angle": 0, + "content": "*Corresponding author: X. Lu, supported by fund 3.2501.11.47." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.958 + ], + "angle": 0, + "content": "20721" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.473, + 0.408 + ], + "angle": 0, + "content": "PointCleanNet [7, 35, 45], employ large networks (\\(>1\\mathrm{M}\\) parameters) that consume a large patch of points to filter a single, central point. This is time-consuming and resource intensive. More recently, IterativePFN [8] models the iterative filtering process internally using multiple IterationModules and filters all patch points simultaneously. However, incorporating multiple IterationModules results in a large network (\\(>3.2\\mathrm{M}\\) parameters) which requires a large amount of GPU memory to process. Probabilistic score based methods such as ScoreDenoise [6, 28] offer a more lightweight network but require a high number of iterations to recover the clean surface. At higher noise levels, they converge to surfaces that retain noticeable amounts of noise. DeepPSR [6] utilizes the score module of [28] but performs an additional Graph Laplacian Regularization [14] step on intermediate point clouds to obtain a better point distribution. More importantly, the iterative filtering objectives of current displacement and probabilistic methods move noisy points to the clean surface via stochastic trajectories and are error prone as incorrectly inferred displacements may result in significant changes to the distribution of filtered points." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.409, + 0.472, + 0.499 + ], + "angle": 0, + "content": "We propose StraightPCF, which moves noisy points along straight filtering trajectories towards the clean surfaces, as illustrated in Fig. 1. StraightPCF, illustrated in Fig. 2, is a lightweight network (\\(\\sim 530K\\) parameters, \\(17\\%\\) of IterativePFN [8]) which filters all patch points simultaneously. Our technical contributions are as follows." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.5, + 0.47, + 0.559 + ], + "angle": 0, + "content": "- We introduce the patch-wise VelocityModule that infers constant, straight flows to filter point cloud patches. The VelocityModule elegantly recovers the underlying clean surfaces with nice point distributions." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.561, + 0.47, + 0.62 + ], + "angle": 0, + "content": "- To improve straightness of flows, we propose a novel straightening mechanism consisting of coupled VelocityModules. This coupled VelocityModule stack infers straighter filtering trajectories, leading to better results." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.62, + 0.47, + 0.71 + ], + "angle": 0, + "content": "- Constant flows may lead to filtered points overshooting the clean surface. Therefore, we design the Distance-Module to infer a distance scalar that provides a magnitude to scale the flow velocity. Our architecture is the first to decompose filtering into a dual objective of inferring a vector field of flow velocities and a distance scalar." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.5, + 0.47, + 0.71 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.724, + 0.22, + 0.74 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.75, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Conventional filtering. Early conventional methods were inspired by the Moving Least Squares (MLS) method of Levin [17] and require normal information for filtering. Notably, Alexa et al. [2] employed MLS optimization in recovering denoised surfaces from noisy point sets. The Implicit MLS (IMLS) method of Adamson and Alexa [1] further extended this approach to point-sampled cell complexes which allow for a well defined local geometry. The Algebraic Point Set Surface (APSS) method of Guennebaud and Gross [13] applied MLS optimization for the purpose of" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.319 + ], + "angle": 0, + "content": "fitting algebraic spheres to recover surfaces while being robust to point set density and underlying curvature. Furthermore, Digne proposed filtering the height map associated to a point set by considering handcrafted features that encode height variations around each point [9]. Digne and de Franchis designed a weighted projection scheme, that moves points to their filtered positions [10], based on the mesh bilateral filtering method of Fleishman, Drori and Cohen-Or [11]. Other normal based methods include the Moving Robust Principal Component Analysis (MRPCA) [30] of Mattei and Castrodad, the Graph Laplacian Regularization (GLR) [14] technique of Hu et al. and the Low Rank Matrix Approximation [24] of Lu et al. The main drawback of such methods is susceptibility to noise, during both the normal estimation and filtering steps." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.321, + 0.895, + 0.473 + ], + "angle": 0, + "content": "By contrast, point based methods employ only point information for filtering. Cazals and Pouget [4] proposed a \\(N\\)-dimensional polynomial surface fitting method that can be used to filter points. Meanwhile, the Locally Optimal Projection (LOP) [21] method of Lipman et al. downsampled and regularized noisy point clouds. It was extended by Huang et al. and Preiner et al. who developed Weighted-LOP (WLOP) [15] and Continuous-LOP (CLOP) [32], respectively. However, these methods do not effectively recover geometric details due to their downsampling step." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.896, + 0.718 + ], + "angle": 0, + "content": "Deep learning based filtering. While conventional methods rely on handcrafted features, convolutional neural network architectures have provided great improvements to feature generation. PointProNets [37] by Roveri et al. and Deep Feature Preserving (DFP) [23] by Lu et al. projected points onto 2D height maps before processing them using CNNs. PointNet [33], introduced by Qi et al., set the precedent for direct point set convolution and was later improved by PointNet++ [34]. Meanwhile, DGCNN [42] of Wang et al. reformulated point set convolution as a graph convolution task. PointCleanNet (PCN) [35] was one of the first methods to adopt the PointNet architecture and inferred the filtered displacement of a single central point by considering its neighborhood patch. Pointfilter [45] of Zhang et al. furthered this line of research using a bilateral filtering-inspired loss." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.897, + 0.903 + ], + "angle": 0, + "content": "Pistilli et al. introduced the first graph convolution-based mechanism, named GPDNet [31], while Luo and Hu proposed the DGCNN based DMRDenoise [26]. DMRDenoise filtered points by downsampling noisy inputs and upsampling these less noisy surfaces. Luo and Hu also proposed ScoreDenoise [28] where they formally expressed the filtering objective as the backward Langevin equation that iteratively removes noise using the inferred gradient-log of the probability distribution, i.e., the score, for point positions \\( \\mathbf{x} \\). This was extended by Chen et al. in their DeepPSR [6] which employs an additional graph laplacian regularization post-processing step. Mao et al. introduced the normalizing" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20722" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.137, + 0.088, + 0.835, + 0.226 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.236, + 0.895, + 0.269 + ], + "angle": 0, + "content": "Figure 2. Our StraightPCF network. It involves a coupled VelocityModule stack that infers a constant flow velocity \\(\\pmb{v}_{\\theta}^{k}\\) for patch states \\(\\tilde{\\pmb{X}}_{(\\hat{t} + k)/T}\\). To ensure filtered points converge to the surface, the DistanceModule infers a distance scalar \\(d_{\\phi}\\) that scales the velocity." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.292, + 0.473, + 0.502 + ], + "angle": 0, + "content": "flows based filtering method PDFlow [29] that disentangles noise from the underlying clean representation at higher dimensions. The RePCDNet [5] method of Chen et al. sought to model iterative filtering via a recurrent neural network. By contrast, de Silva Edirimuni et al. proposed the graph convolution based IterativePFN [8] that models iterative filtering using individual IterationModules. The joint filtering and normal estimation method CFilter [7], developed by de Silva Edirimuni et al., exploited normals to improve filtered point positions. Ma et al. introduced learning implicit signed distance functions, by displacing noisy query points back to the surface along normals where the surface corresponds to the zero-level set of the function [3]. This has been exploited for normal estimation [18, 19]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.504, + 0.471, + 0.641 + ], + "angle": 0, + "content": "Score and displacement based methods are inspired by diffusive processes [27, 39] and their filtering objectives result in stochastic trajectories. Recent work by Liu, Gong and Liu focuses on Reflow [22], which explored the optimal transport problem of identifying straight paths given two samples from different distributions. The work of Wu et al. further extended this Reflow mechanism to point cloud generation, which attempts to generate point cloud shapes given initial samples from the normal distribution [43]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.651, + 0.398, + 0.667 + ], + "angle": 0, + "content": "3. Problem Statement and Motivation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.676, + 0.47, + 0.768 + ], + "angle": 0, + "content": "Resampling methods demonstrate an inability to recover clean surfaces with high accuracy, unlike probabilistic and displacement based methods. A probabilistic score based method such as ScoreDenoise [28] and a displacement based method such as IterativePFN [8] share similar filtering objectives that may be expressed by," + }, + { + "type": "equation", + "bbox": [ + 0.148, + 0.772, + 0.47, + 0.79 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {x}} _ {t} ^ {i} = \\tilde {\\boldsymbol {x}} _ {t - 1} ^ {i} + F _ {\\theta} \\left(\\tilde {\\boldsymbol {x}} _ {t - 1} ^ {i}\\right), t = 1, \\dots , T \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.797, + 0.471, + 0.874 + ], + "angle": 0, + "content": "where \\(\\tilde{\\pmb{x}}_t^i\\) is the \\(i\\)-th filtered point at time \\(t\\) and \\(F_{\\theta}\\) represents the network with parameters \\(\\theta\\). The main difference between ScoreDenoise and IterativePFN lies in their training objectives, \\(\\mathcal{L}_S\\) and \\(\\mathcal{L}_I\\), respectively. For a noisy point \\(\\pmb{x}^i \\in \\pmb{X}\\) where \\(\\pmb{X}\\) is the initial noisy patch, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.13, + 0.879, + 0.47, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {S} ^ {i} = \\mathbb {E} _ {\\boldsymbol {x} \\sim k N N (\\boldsymbol {x} ^ {i}, \\boldsymbol {X})} \\left[ \\left\\| s (\\boldsymbol {x}) - \\mathcal {S} ^ {i} (\\boldsymbol {x}) \\right\\| _ {2} ^ {2} \\right], \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.304, + 0.893, + 0.345 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {I} ^ {i} = \\sum_ {t = 0} ^ {T} \\left\\| \\boldsymbol {d} _ {t} ^ {i} - \\left(N N \\left(\\boldsymbol {x} _ {t - 1} ^ {i}, \\boldsymbol {Y} _ {t}\\right) - \\boldsymbol {x} _ {t - 1} ^ {i}\\right) \\right\\| _ {2} ^ {2}. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.354, + 0.895, + 0.765 + ], + "angle": 0, + "content": "ScoreDenoise is trained to predict a score \\( S^i(\\boldsymbol{x}) = \\text{Score}(\\boldsymbol{x} - \\boldsymbol{x}^i | \\boldsymbol{h}^i) \\) for \\( \\boldsymbol{x} \\) sampled from the k-nearest neighbors of \\( \\boldsymbol{x}^i \\). It is conditioned on the latent feature \\( \\boldsymbol{h}^i \\) of \\( \\boldsymbol{x}^i \\) and corresponds to the gradient-log of the noise-convolved probability distribution for point position \\( \\boldsymbol{x} \\). The ground truth target \\( s(\\boldsymbol{x}) = N N(\\boldsymbol{x}, \\boldsymbol{Y}) - \\boldsymbol{x} \\), where \\( \\boldsymbol{Y} \\) is the clean patch. Ergo, \\( s(\\boldsymbol{x}) \\) is the displacement from \\( \\boldsymbol{x} \\) to its nearest neighbor in \\( \\boldsymbol{Y} \\). Once this training objective has been optimized, score based methods infer aggregate scores, at each iteration \\( t \\), such that \\( F_{\\theta}(\\boldsymbol{x}_{t-1}^i) = \\alpha \\mathcal{E}^i(\\boldsymbol{x}_{t-1}^i) = (\\alpha / K) \\sum_{\\boldsymbol{x}_{t-1}^j \\in kNN(\\boldsymbol{x}_{t-1}^i)} S^j(\\boldsymbol{x}_{t-1}^i) \\) where \\( \\alpha \\) is the step discretization parameter. This score shifts points towards the clean surface along a stochastic filtered trajectory that is sensitive to the choice of \\( \\alpha \\), which must be kept relatively small (\\( \\sim 0.2 \\)). By contrast, IterativePFN internally models the iterative filtering objective and incorporates it within their training objective. They directly infer displacements \\( F_{\\theta}(\\tilde{\\boldsymbol{x}}_{t-1}^i) = \\boldsymbol{d}_t^i \\) as the output of each IterationModule that models an iteration \\( t \\). From Eq. (3) we identify that the overall filtered trajectories inferred by IterativePFN will also be stochastic in nature as it uses an Adaptive Ground Truth (AGT), \\( Y_t = Y + \\sigma_t\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I) \\), within the training objective. Modelling the iterative filtering process internally results in a large network (\\( >3.2M \\) parameters). The AGT, while recovering the surface, causes clustering along the surface and fails to respect the original point distribution. This is illustrated in Fig. 3." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Inspired by Reflow which focuses on optimal transport between samples of different distributions [22, 43], we pose filtering as an optimal transport problem between point cloud patches. These patches of \\(n\\) points are sampled from 1) the clean surface (i.e., clean patch \\(\\mathbf{X}_1\\sim \\pi_1\\)) and 2) a high noise variant of the clean surface (i.e., high noise patch \\(\\mathbf{X}_0\\sim \\pi_0\\)). The goal is to determine a transport plan (coupling) such that \\(\\mathbf{X}_1 = V(\\mathbf{X}_0)\\) where \\(V:\\mathbb{R}^{n\\times 3}\\to \\mathbb{R}^{n\\times 3}\\). The approximated flow velocity, \\(\\pmb{v}_{\\theta}:\\mathbb{R}^{n\\times 3}\\rightarrow \\mathbb{R}^{n\\times 3}\\) sat" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "20723" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.468, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.325, + 0.471, + 0.368 + ], + "angle": 0, + "content": "Figure 3. Our StraightPCF is able to recover a better distribution of filtered points, even at very high noise scales (\\(\\sigma = 3\\%\\) and \\(50\\mathrm{K}\\) resolution) unseen during network training." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.392, + 0.471, + 0.468 + ], + "angle": 0, + "content": "isfies this transport mapping and \\((\\tilde{\\pmb{X}}_0,\\tilde{\\pmb{X}}_1)\\) form a valid coupling. Consequently, the filtered trajectories are straight (see Fig. 4), unlike ScoreDenoise and IterativePFN. Moreover, our method recovers the underlying point distribution of the surface without clustering artifacts or distortion." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.481, + 0.169, + 0.497 + ], + "angle": 0, + "content": "4. Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.506, + 0.471, + 0.84 + ], + "angle": 0, + "content": "Previous methods such as ScoreDenoise [28] and IterativePFN [8] focus on filtering as a reverse Markov process where the forward process would correspond to adding noise. We formulate filtering as an optimal transport plan that moves noisy points back to the clean surface along the shortest (straight) path. We model noisy input patches as intermediate states between high noise variants and their corresponding clean counterparts. We design a graph convolution based VelocityModule that infers a constant flow velocity for each intermediate state. This encourages noisy points to move along straight filtering trajectories as shown in Fig. 4. We further improve the straightness of these trajectories via VelocityModule coupling. Finally, as the flow is constant, it may result in filtered points overshooting the clean surface. Therefore, we design a DistanceModule that scales the flow velocity appropriately and ensures convergence near the surface. The overall Straight-PCF architecture is illustrated in Fig. 2, which demonstrates the filtering process that utilizes both the coupled Velocity-Module and DistanceModule sub-networks to move points along straightened paths. The supplementary document provides additional methodology details." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.317, + 0.864 + ], + "angle": 0, + "content": "4.1. Filtering via straight flows" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.87, + 0.47, + 0.902 + ], + "angle": 0, + "content": "In this section, we introduce the VelocityModule (VM) that moves noisy points along constant, straight flows to-" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.089, + 0.855, + 0.177 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.187, + 0.894, + 0.243 + ], + "angle": 0, + "content": "Figure 4. StraightPCF models initial noisy patches (light blue) as being intermediate states of a linear interpolation between high noise variants (red) and the clean surfaces (dark blue) and encourages straight filtering trajectories." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.267, + 0.893, + 0.57 + ], + "angle": 0, + "content": "wards the clean surface. Given a noisy patch \\( \\mathbf{X} = \\{\\pmb{x}^i | \\pmb{x}^i \\in kNN(\\pmb{x}^r, \\mathcal{P}_X, k)\\} \\) centered around a reference point \\( \\pmb{x}^r \\) in the noisy point cloud \\( \\mathcal{P}_X \\), the filtering objective aims to move \\( \\pmb{x}^i \\) towards the underlying clean patch \\( \\mathbf{Y} = \\{\\pmb{y}^i | \\pmb{y}^i \\in \\mathcal{P}_Y\\} \\). For the filtering task, learning based methods are typically trained on noisy point clouds with Gaussian noise [6, 28, 29, 35, 45]. Iterative filtering depends on the ability of the method to filter patches from a higher noise level to a lower noise level, with the end result converging to the clean surface. Given the highest noise setting \\( \\sigma_H \\), intermediate noise scales at a time \\( t \\in [0,1] \\) can be expressed as \\( \\sigma = (1 - t)\\sigma_H \\). Therefore, we model noisy patches \\( \\mathbf{X} = \\mathbf{Y} + \\sigma\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I) \\) as intermediate states \\( X_t \\), of the filtering objective that moves points from a high noise variant, \\( X_0 = Y + \\sigma_H\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I) \\) to the clean counterpart \\( X_1 = Y \\). Here, \\( \\sigma_H = 2\\% \\) of the point cloud's bounding sphere radius and corresponds to the highest noise setting of our training set. We observe that intermediate states \\( X_t \\) can be defined as a linear interpolation of \\( X_0 \\) and \\( X_1 \\), that is, a straight path, such that," + }, + { + "type": "equation", + "bbox": [ + 0.613, + 0.579, + 0.891, + 0.595 + ], + "angle": 0, + "content": "\\[\n\\boldsymbol {X} _ {t} = (1 - t) \\boldsymbol {X} _ {0} + t \\boldsymbol {X} _ {1} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.605, + 0.892, + 0.665 + ], + "angle": 0, + "content": "Therefore, we intuit that the filtering objective can be reformulated as an optimal transport process that moves points from \\( \\mathbf{X}_0 \\) to \\( \\mathbf{X}_1 \\). The flow of \\( \\mathbf{X}_t \\) at time \\( t \\) can be expressed via the ordinary differential equation (ODE):" + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.674, + 0.891, + 0.69 + ], + "angle": 0, + "content": "\\[\n\\mathrm {d} \\boldsymbol {X} _ {t} = \\boldsymbol {v} \\left(\\boldsymbol {X} _ {t}\\right) \\mathrm {d} t, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.699, + 0.892, + 0.745 + ], + "angle": 0, + "content": "where \\(\\pmb{v}(\\pmb{X}_t)\\) is the velocity field at \\(\\pmb{X}_t\\). For this ODE process, the linear interpolation of Eq. (4) can be used in the least squares optimization to determine the flow," + }, + { + "type": "equation", + "bbox": [ + 0.522, + 0.753, + 0.892, + 0.787 + ], + "angle": 0, + "content": "\\[\n\\min _ {v} \\int_ {0} ^ {1} \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\| \\boldsymbol {v} (\\boldsymbol {X} _ {t}) - (\\boldsymbol {X} _ {1} - \\boldsymbol {X} _ {0}) \\| _ {2} ^ {2} \\right] d t, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.87 + ], + "angle": 0, + "content": "where times \\(t\\) are sampled uniformly along \\([0,1]\\). However, the velocity field at an intermediate state \\(\\pmb{X}_t\\) cannot be causally determined as both \\(\\pmb{X}_0\\) and \\(\\pmb{X}_1\\) are unknown, during filtering. To address this, our idea is to approximate the velocity field for each \\(\\pmb{X}_t\\) by a neural network." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Training objective for single VM. We use a DGCNN based graph neural network to model a VelocityModule \\(\\pmb{v}_{\\theta}\\)" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20724" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.136 + ], + "angle": 0, + "content": "with parameters \\(\\theta\\) to approximate the flow velocity. To train this VelocityModule, we define the following training objective." + }, + { + "type": "equation", + "bbox": [ + 0.122, + 0.146, + 0.469, + 0.173 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {A} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\| \\boldsymbol {v} _ {\\theta} (\\boldsymbol {X} _ {t}) - \\boldsymbol {\\delta} (\\boldsymbol {X} _ {1}, \\boldsymbol {X} _ {0}) \\| _ {2} ^ {2} \\right], \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.181, + 0.469, + 0.226 + ], + "angle": 0, + "content": "where \\(\\delta(X_1, X_0) = X_1 - X_0\\). Hence, at each intermediate state, the corresponding flow velocity is ideally a constant vector that leads to a straight path from \\(X_0\\) to \\(X_1\\)." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.226, + 0.469, + 0.274 + ], + "angle": 0, + "content": "Filtering objective for single VM. During inference, given a straight flow velocity \\(\\pmb{v}_{\\theta}\\), we can move points from \\(\\pmb{X}_{\\hat{t} /N}\\) to \\(\\pmb{X}_{(\\hat{t} +1) / N}\\) using the Euler method ODE solver:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.283, + 0.47, + 0.312 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + 1) / N} = \\tilde {\\boldsymbol {X}} _ {\\hat {t} / N} + \\frac {1}{N} \\boldsymbol {v} _ {\\theta} (\\tilde {\\boldsymbol {X}} _ {\\hat {t} / N}), \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.322, + 0.469, + 0.413 + ], + "angle": 0, + "content": "where \\(N\\) denotes the total number of filtering steps, \\(\\hat{t} \\in [0, \\dots, M, \\dots, N-1]\\) is an integer time step and \\(\\tilde{\\pmb{X}}_0 = \\pmb{X}_0\\). In practice, filtering starts at an unknown time step \\(\\hat{t} = M\\). We do not know the noise scale of the input patch and need to model it as an intermediate state \\(\\tilde{\\pmb{X}}_{M/N}\\) of a higher noise variant \\(\\pmb{X}_0\\). The full position update takes the form," + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.423, + 0.469, + 0.465 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {X}} _ {1} = \\tilde {\\boldsymbol {X}} _ {M / N} + \\frac {1}{N} \\sum_ {\\hat {t} = M} ^ {N - 1} \\boldsymbol {v} _ {\\theta} \\left(\\tilde {\\boldsymbol {X}} _ {\\hat {t} / N}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.474, + 0.274, + 0.489 + ], + "angle": 0, + "content": "Eq. (9) poses two challenges:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.489, + 0.469, + 0.549 + ], + "angle": 0, + "content": "1. The straightness of paths is crucial to reducing the number of total steps and improving efficiency. If paths are not sufficiently straight (i.e., they are curved), we need a higher number of steps to filter points effectively." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.55, + 0.469, + 0.595 + ], + "angle": 0, + "content": "2. The starting time \\( t = M / N \\) is unknown. Applying the Euler method for too many steps, \\( N \\), may lead to points not converging at the surface." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.489, + 0.469, + 0.595 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.604, + 0.458, + 0.62 + ], + "angle": 0, + "content": "4.2. Straighter flows via VelocityModule coupling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.627, + 0.469, + 0.777 + ], + "angle": 0, + "content": "Given noisy initial data, the trajectories of points tend to be curved, with limited straightness. One way to improve straightness is to finetune the velocity network on the coupling \\((\\tilde{X}_0,\\tilde{X}_1)\\) to satisfy \\(\\tilde{X}_1 = V(\\tilde{X}_0)\\). For filtering, we aim to recover surfaces while preserving local geometric details [35]. Applying such finetuning requires the pre-computation of \\(\\tilde{X}_1\\) for all possible surface patches and is infeasible due to the large number of patches in the training set. We propose a simple mechanism to straighten paths by coupling \\(K\\) VelocityModules together." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.778, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Training objective for coupled VMs. Given a noisy patch \\( \\mathbf{X}_t \\), we partition the trajectory from \\( \\mathbf{X}_t \\) to \\( \\mathbf{X}_1 \\) into \\( K \\) segments and obtain the velocity flow \\( \\pmb{v}_{\\theta}^{k}(\\tilde{\\pmb{X}}_{t_k}) \\) at times \\( t_k = (t(K - k) + k) / K \\) where \\( k \\in \\{0, 1, \\dots, K - 1\\} \\). Intermediate positions at times \\( t_{k+1} \\) are given by \\( \\tilde{\\pmb{X}}_{t_{k+1}} = \\tilde{\\pmb{X}}_{t_k} + (1 / K) \\pmb{v}_{\\theta}^{k}(\\tilde{\\pmb{X}}_{t_k}) \\). We empirically find that two VelocityModules, i.e., \\( K = 2 \\), provide the best balance between accuracy and efficiency. The Velocity Modules are" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "pretrained using the training objective of Eq. (7) and the coupled VMs are finetuned with the introduced objective," + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.128, + 0.892, + 0.214 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {B} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\sum_ {k = 0} ^ {K - 1} \\left\\| \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {k}}\\right) - \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1}, \\boldsymbol {X} _ {0}\\right) \\right\\| _ {2} ^ {2} \\right. \\tag {10} \\\\ \\left. + \\lambda_ {1} \\sum_ {k = 0} ^ {K - 2} \\left\\| \\boldsymbol {\\delta} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {k + 1}}, \\boldsymbol {X} _ {t _ {k + 1}}\\right) \\right\\| _ {2} ^ {2} \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.221, + 0.892, + 0.283 + ], + "angle": 0, + "content": "for \\(K \\geq 2\\), \\(\\lambda_{1} = 10\\) and \\(\\tilde{\\pmb{X}}_{t_0} = \\pmb{X}_{t_0} = \\pmb{X}_t\\). The first term of \\(\\mathcal{L}_B\\) encourages coupled VelocityModules to infer a constant velocity at times \\(t_k\\), while the second encourages filtered points \\(\\tilde{\\pmb{X}}_{t_k}\\) to move closer to interpolated points \\(\\pmb{X}_{t_k}\\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.283, + 0.892, + 0.388 + ], + "angle": 0, + "content": "Filtering objective for coupled VMs. At inference, we apply a modified form of the Euler method to filter points, similar to Eq. (8). We apply \\(K\\) coupled VelocityModules \\(N\\) times, resulting in \\(T = K \\cdot N\\) total filtering steps. We adjust our earlier notation of integer time steps such that \\(\\hat{t} \\in \\{0, K, \\dots, \\hat{M}, \\dots, K(N - 1)\\}\\) where \\(\\hat{M}\\) is divisible by \\(K\\) and \\(\\tilde{\\pmb{X}}_0 = \\pmb{X}_0\\). The sequential position update becomes," + }, + { + "type": "equation", + "bbox": [ + 0.529, + 0.406, + 0.891, + 0.435 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k + 1) / T} = \\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T} + \\frac {1}{T} \\boldsymbol {v} _ {\\theta} ^ {k} (\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.439, + 0.891, + 0.469 + ], + "angle": 0, + "content": "The corresponding full position update across time steps \\( S = \\{\\hat{M},\\hat{M} +K,\\dots ,N(K - 1)\\} \\) is," + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.476, + 0.891, + 0.518 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {X}} _ {1} = \\tilde {\\boldsymbol {X}} _ {\\hat {M} / T} + \\frac {1}{T} \\sum_ {\\hat {t} \\in \\mathcal {S}} \\sum_ {k = 0} ^ {K - 1} \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}\\right). \\tag {12}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.538, + 0.839, + 0.552 + ], + "angle": 0, + "content": "4.3. Distance estimation to the clean surface" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.561, + 0.892, + 0.682 + ], + "angle": 0, + "content": "We now address the second challenge related to Eq. (9) and introduce the DistanceModule that scales the overall straight trajectory. This leads to better convergence near the surface. The DistanceModule estimates a distance scalar, corresponding to the standard deviation of initial noisy points from the clean surface. More specifically, the DistanceModule \\(\\mathcal{D}_{\\phi}(\\cdot)\\) is used to approximate a mapping \\(d_{\\phi}:\\mathbb{R}^{n\\times 3}\\to \\mathbb{R}\\), such that," + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.688, + 0.891, + 0.707 + ], + "angle": 0, + "content": "\\[\nd _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right) = \\operatorname {S i g m o i d} \\left(\\operatorname {M a x} \\left(\\mathcal {D} _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right)\\right)\\right). \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.713, + 0.892, + 0.804 + ], + "angle": 0, + "content": "The distance \\( d_{\\phi} \\) is then used to scale the output of VelocityModules, as illustrated in Fig. 5. The DistanceModule is embedded within the StraightPCF architecture (see Fig. 2). We keep the weights of the finetuned coupled VelocityModules fixed when training the DistanceModule. The respective training objective for optimizing the parameters \\( \\phi \\) is," + }, + { + "type": "equation", + "bbox": [ + 0.512, + 0.821, + 0.891, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {C} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\left(d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right) - \\frac {\\| \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1} , \\boldsymbol {X} _ {t _ {0}}\\right) \\| _ {2}}{\\| \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1} , \\boldsymbol {X} _ {0}\\right) \\| _ {2}}\\right) ^ {2} \\right. \\tag {14} \\\\ \\left. + \\lambda_ {2} \\left\\| \\boldsymbol {\\delta} \\left(\\tilde {\\boldsymbol {X}} _ {1}, \\boldsymbol {X} _ {1}\\right) \\right\\| _ {2} ^ {2} \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20725" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.889, + 0.374 + ], + "angle": 0, + "content": "
Resolution10K (Sparse)50K (Dense)
Noise1%2%3%1%2%3%
MethodCDP2MCDP2MCDP2MCDP2MCDP2MCDP2M
PUNet dataset [44]PCN [35]3.5151.1487.4673.96513.0678.7371.0490.3461.4470.6082.2891.285
PointFilter [45]2.4610.4433.5340.8625.0891.8490.7580.1820.9070.2511.5990.710
Score [28]2.5210.4633.6861.0744.7081.9420.7160.1501.2880.5661.9281.041
PDFlow [29]2.1260.3813.2461.0104.4471.9990.6510.1641.1730.5811.9141.210
DeepPSR [6]2.3530.3063.3500.7344.0751.2420.6490.0760.9970.2961.3440.531
IterativePFN [8]2.0560.2183.0430.5554.2411.3760.6050.0590.8030.1821.9711.012
Ours1.8700.2392.6440.6043.2871.1260.5620.1110.7650.2661.3070.648
PCNet dataset [35]PCN [35]3.8471.2218.7523.04314.5255.8731.2930.2891.9130.5053.2491.076
Score [28]3.3690.8305.1321.1956.7761.9411.0660.1771.6590.3542.4940.657
PointFilter [45]3.0190.8864.8851.2757.0622.0321.0530.1861.3490.2572.2250.491
PDFlow [29]3.2430.6064.5450.9665.9341.4410.9690.1521.6460.4242.4500.569
DeepPSR [6]2.8730.7834.7571.1186.0311.6191.0100.1461.5150.3402.0930.573
IterativePFN [8]2.6210.6984.4391.0116.0261.5600.9130.1391.2510.2382.5290.716
Ours2.7470.5364.0460.7884.9211.0930.8770.1441.1730.2591.8160.445
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.384, + 0.893, + 0.412 + ], + "angle": 0, + "content": "Table 1. Quantitative filtering results of recent state-of-the-art methods and our method on the synthetic PUNet and PCNet datasets. Note that our network is lightweight, with just \\(\\sim 530K\\) parameters (17% of IterativePFN). CD and P2M values are multiplied by \\(10^{4}\\)" + }, + { + "type": "image", + "bbox": [ + 0.085, + 0.434, + 0.466, + 0.525 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.534, + 0.47, + 0.577 + ], + "angle": 0, + "content": "Figure 5. Left: Filtering by coupled VelocityModules only. Right: Coupled VelocityModules and DistanceModule. Scaled trajectories (green lines) lead to better convergence at the surface." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.603, + 0.47, + 0.71 + ], + "angle": 0, + "content": "where \\(t_0 = t\\) and \\(\\tilde{\\pmb{X}}_{t_0} = \\pmb{X}_{t_0} = \\pmb{X}_t\\). The first term of \\(\\mathcal{L}_C\\) encourages the DistanceModule to infer the relative distance of \\(\\pmb{X}_{t_0}\\) from the clean surface, as compared to \\(\\pmb{X}_0\\). The last term encourages points to return to the clean surface. We set \\(\\lambda_{2} = 2\\times 10^{2}\\) to ensure the loss contribution of the last term is of the same order as that of the first one. Consequently, Eq. (11) becomes," + }, + { + "type": "equation", + "bbox": [ + 0.088, + 0.722, + 0.469, + 0.769 + ], + "angle": 0, + "content": "\\[\n\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k + 1) / T} = \\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T} + \\frac {d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {\\hat {M} / T}\\right)}{T} \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}\\right). \\tag {15}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.784, + 0.21, + 0.801 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Next, we provide results on synthetic data under Gaussian noise and real-world Kinect [41] and Paris-Rue-Madame [38] data. The supplementary document contains additional results of both conventional and learning based methods on synthetic and real-world scanned data, as well as a comparison of testing times." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.438, + 0.776, + 0.455 + ], + "angle": 0, + "content": "5.1. Training and evaluation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.462, + 0.892, + 0.824 + ], + "angle": 0, + "content": "We follow the training procedure of ScoreDenoise [28], and train our model on the PUNet dataset [44] consisting of 40 point clouds for training and 20 point clouds for testing. To ensure consistency with ScoreDenoise's training settings, we add Gaussian noise sampled with standard deviation \\(\\sigma_{H} = 2\\%\\) of the bounding sphere radius to each clean point cloud. Our training procedure only requires the high noise variants and the clean ground truth targets. All intermediate states at noise scales \\(\\sigma = (1 - t)\\sigma_{H}\\), with \\(t \\sim \\mathcal{U}(0,1)\\) are created as linear interpolations between these two, initial and final states, as per Eq. (4). For testing, we also consider 10 test point clouds from the PCNet dataset [35] provided by ScoreDenoise. These synthetic point clouds contain Gaussian noise at scales of \\(1\\%\\), \\(2\\%\\) and \\(3\\%\\) of the point cloud's bounding sphere radius. We use two different sampling densities of 10K and 50K points to evaluate filtering ability across different sparsity settings. Moreover, to assess filtering results on real-world noisy point clouds, we compare methods on the Kinect v1 dataset that comprises of 71 point clouds [41] and 4 scenes extracted from the Paris-Rue-Madame dataset [38]. Finally, we provide a comparison on 4 scenes of the Kitti-360 dataset [20], in the supplementary document. Following [8, 28], all methods are only trained on PUNet with Gaussian noise." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.825, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Implementation. We train and test StraightPCF on a NVIDIA GeForce RTX 3090 GPU using PyTorch. We use the Adam optimizer with a learning rate of \\(1 \\times 10^{-4}\\). Similar to [8, 28], we use PyTorch3D [36] to compute Chamfer Distance (CD) and Point2Mesh (P2M) metric values." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "20726" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.086, + 0.892, + 0.398 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.407, + 0.893, + 0.449 + ], + "angle": 0, + "content": "Figure 6. Visual filtering results for \\(50\\mathrm{K}\\) resolution shapes \\((\\sigma = 2\\%)\\) within the PUNet and PCNet datasets. The darker (i.e., more blueish) the better. We achieve both strong point-wise P2M results while also ensuring well distributed points (illustrated by close-ups) unlike DeepPSR or IterativePFN which have holes indicating clustering." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.475, + 0.347, + 0.491 + ], + "angle": 0, + "content": "5.2. Performance on synthetic data" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.473, + 0.902 + ], + "angle": 0, + "content": "Table 1 and Fig. 6 illustrate filtering results on the synthetic PUNet and PCNet datasets. Our method has a clear edge over others in recovering the underlying clean point distribution demonstrated by superior CD results across all noise settings. We also achieve strong P2M results on the PUNet dataset. While IterativePFN [8] has marginally better P2M results on the PUNet data, this does not ensure a good distribution of points as evidenced by visual results in Fig. 6. Here, for noisy point clouds at \\(50\\mathrm{K}\\) resolution and \\(2\\%\\) noise, IterativePFN exhibits small holes, indicating clustering. Moreover, our network consists of only \\(530\\mathrm{K}\\) parameters and is roughly \\(83\\%\\) smaller than that of IterativePFN, given the latter's \\(3.2\\mathrm{M}\\) parameters. DeepPSR [6], despite using a post-processing regularization step, also suffers from holes and poor point distributions. We also note that IterativePFN generalizes poorly to higher noise scales outside the training noise scales (where maximum noise is \\(\\sigma = 2\\%\\)). The ability of our method to generalize well across different data is demonstrated by the superior performance on the PCNet dataset. The PCNet shapes are unseen during training. Our method obtains both superior CD and P2M results over all other methods. At \\(10\\mathrm{K}\\) resolution and \\(\\sigma = 3\\%\\) noise, our method offers a \\(17.1\\%\\) reduction in CD error and \\(24.1\\%\\) reduction in P2M error. Our method also yields state-of-the-art results at \\(50\\mathrm{K}\\) resolution where, for \\(\\sigma = 3\\%\\), the CD error improvement is \\(13.2\\%\\) and P2M error" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.475, + 0.892, + 0.627 + ], + "angle": 0, + "content": "improvement is \\(9.4\\%\\). Visual filtering results in Fig. 6 indicate that our method outperforms others in recovering complex details such as the legs of the Camel which are closely situated. By contrast, methods such as Pointfilter [45] and PDFlow [29] flatten points between these close surfaces while IterativePFN does not recover the body well. Furthermore, on a complex shape as Netsuke, we outperform other methods which either cause clustering (e.g., PDFlow, IterativePFN) at this high noise scale or leave behind noise due to limited filtering ability (e.g., ScoreDenoise)." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.637, + 0.849, + 0.651 + ], + "angle": 0, + "content": "5.3. Performance on real-world scanned data" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.659, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Next we consider filtering results on scanned data. Table 2 provides quantitative results on the Kinect dataset and Fig. 7 illustrates visual results on the Paris-Rue-Madame dataset. Our method performs favorably on the Kinect data, obtaining a \\(1.82\\%\\) reduction on CD errors, as compared to IterativePFN [8]. As this data is very sparse, our P2M result is marginally higher than Pointfilter [45] and Score-Denoise [28]. These methods focus on returning points to the surface yet succumb to clustering artifacts whereas our method both recovers surfaces while retaining good point distributions. The Paris-Rue-Madame dataset contains high noise scans due to outdoor environmental factors. In Fig. 7, we visualize filtering results for several most recent, state-of-the-art methods. In general, methods such as PDFlow [29] and DeepPSR [6] perform poorly in removing noisy artifacts while IterativePFN [8] causes points to" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "20727" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.086, + 0.087, + 0.885, + 0.297 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.082, + 0.306, + 0.885, + 0.321 + ], + "angle": 0, + "content": "Figure 7. Visual filtering results on two scenes of the RueMadame dataset. We show results for the most recent state-of-the-art methods." + }, + { + "type": "table", + "bbox": [ + 0.16, + 0.345, + 0.388, + 0.484 + ], + "angle": 0, + "content": "
MethodKinect
CDP2M
ScoreDenoise1.3220.652
Pointfilter1.3770.644
PDFlow1.3340.699
DeepPSR1.4310.715
IterativePFN1.3200.685
Ours1.2960.664
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.494, + 0.47, + 0.536 + ], + "angle": 0, + "content": "Table 2. Quantitative results on Kinect data. Our network is lightweight, with just \\(\\sim 530K\\) parameters (17% of IterativePFN). CD and P2M values are multiplied by \\(10^{4}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.567, + 0.47, + 0.673 + ], + "angle": 0, + "content": "cluster near the original scan lines. Our method, however, recovers the underlying clean surface and ensures a much better point distribution, as evidenced by the close-ups in Scene 1. In Scene 2, PDFlow and IterativePFN are not able to clean the surface of the parked vehicle whereas our method recovers the underlying shape with fewer noisy artifacts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.692, + 0.358, + 0.71 + ], + "angle": 0, + "content": "6. Ablation Study and Discussion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "We train and test several variant architectures in order to ascertain the impact of the proposed VelocityModule (VM) and DistanceModule (DM). The results are given in Table 3. Our coupled VM + DM architecture (V5) increases the parameter number to \\(\\sim 530K\\). Therefore, we train another Large VM with \\(\\sim 530K\\) parameters (V3). We find that directly increasing the parameter number (V3) leads to very limited performance gain while V5 exhibits far superior performance. Furthermore, the coupled VM + DM architecture (V5) significantly outperforms the single VM (V1 and V2) architectures. Finally, there is a noticeable difference in performance with and without a DM as evidenced by the dis" + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.345, + 0.905, + 0.487 + ], + "angle": 0, + "content": "
Ablation10K points
1% noise2% noise3% noise
CDP2MCDP2MCDP2M
VI) VM w/o DM2.160.423.060.923.731.42
V2) VM w/ DM2.000.323.060.963.811.55
V3) Large VM2.170.412.990.843.541.29
V4) CVM w/o DM1.970.323.010.923.711.45
V5) CVM w/ DM1.870.242.640.603.291.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.497, + 0.892, + 0.525 + ], + "angle": 0, + "content": "Table 3. Ablation results for different VelocityModule (VM) and DistanceModule (DM) configurations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.554, + 0.892, + 0.599 + ], + "angle": 0, + "content": "parity between V4 and V5. We provide further ablations, including higher VM couplings, in the supplementary document." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.601, + 0.892, + 0.678 + ], + "angle": 0, + "content": "**Limitation.** While our StraightPCF yields state-of-the-art results across multiple datasets, we observe relatively low performance on low density or high sparsity data, which is similar to current methods. We provide the visual results in the supplementary document due to space limit." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.693, + 0.619, + 0.71 + ], + "angle": 0, + "content": "7. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recent deep learning based filtering methods focus on moving noisy points along stochastic paths to remove noise from input point clouds. We propose the first study to consider filtering points along straight paths, leading to smaller discretization errors and fewer filtering iterations. This lightweight method, while being parameter efficient, delivers filtered point distributions closer to that of the ground truth distributions without requiring any regularization in loss function or post-processing. Our method achieves state-of-the-art performance on multiple synthetic and real-world datasets across standard filtering metrics, showcasing its superiority and effectiveness." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "20728" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.468, + 0.142 + ], + "angle": 0, + "content": "[1] A. Adamson and M. Alexa. Point-sampled cell complexes. ACM Trans. Graph., 25:671-680, 2006. 2" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.469, + 0.197 + ], + "angle": 0, + "content": "[2] M. Alexa, J. Behr, D. Cohen-Or, S. Fleishman, D. Levin, and Cláudio T. Silva. Computing and rendering point set surfaces. IEEE Trans. Vis. Comput. 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IEEE Transactions on Visualization and Computer Graphics, 27:2015-2027, 2021. 2, 4, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "20730" + } + ] +] \ No newline at end of file diff --git a/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_origin.pdf b/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1f406163633505e5900c5a0fa8de4f2a969fee96 --- /dev/null +++ b/2024/StraightPCF_ Straight Point Cloud Filtering/af60050a-e20e-4b9c-abbd-b5e0d81faed0_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4b7438a9b9dee7764274d0fb49a93d452bb0db5dc503a9fd68b6cdb525811671 +size 9679721 diff --git a/2024/StraightPCF_ Straight Point Cloud Filtering/full.md b/2024/StraightPCF_ Straight Point Cloud Filtering/full.md new file mode 100644 index 0000000000000000000000000000000000000000..041758351d1de62d90b18dcd91fe5e4307ab139d --- /dev/null +++ b/2024/StraightPCF_ Straight Point Cloud Filtering/full.md @@ -0,0 +1,286 @@ +# StraightPCF: Straight Point Cloud Filtering + +Dasith de Silva Edirimuni1, Xuequan Lu2*, Gang Li1, Lei Wei1, Antonio Robles-Kelly1, Hongdong Li3 +1Deakin University, 2La Trobe University, 3Australian National University + +{dtdesilva, gang.li, lei.wei, antonio.robles-kelly}@deakin.edu.au, + +b.lu@latrobe.edu.au, hongdong.li@anu.edu.au + +# Abstract + +Point cloud filtering is a fundamental 3D vision task, which aims to remove noise while recovering the underlying clean surfaces. State-of-the-art methods remove noise by moving noisy points along stochastic trajectories to the clean surfaces. These methods often require regularization within the training objective and/or during post-processing, to ensure fidelity. In this paper, we introduce StraightPCF, a new deep learning based method for point cloud filtering. It works by moving noisy points along straight paths, thus reducing discretization errors while ensuring faster convergence to the clean surfaces. We model noisy patches as intermediate states between high noise patch variants and their clean counterparts, and design the VelocityModule to infer a constant flow velocity from the former to the latter. This constant flow leads to straight filtering trajectories. In addition, we introduce a DistanceModule that scales the straight trajectory using an estimated distance scalar to attain convergence near the clean surface. Our network is lightweight and only has $\sim 530K$ parameters, being $17\%$ of IterativePFN (a most recent point cloud filtering network). Extensive experiments on both synthetic and real-world data show our method achieves state-of-the-art results. Our method also demonstrates nice distributions of filtered points without the need for regularization. The implementation code can be found at: https://github.com/ddsdiri/StuartPCF. + +# 1. Introduction + +In recent years, point clouds have become increasingly popular as the representation-of-choice for storing and manipulating 3D data, with numerous applications in both computer vision [12, 20, 25, 38] and geometry modelling [16, 25, 40]. Point clouds are unordered sets of 3D coordinates which typically represent object surfaces and are captured using 3D sensors such as depth and Lidar devices. However, + +![](images/0e11c694f22c11639a21d581a7be698004f1330eeb71441eaf0f7ab481368725.jpg) +Figure 1. Filtered trajectories for the Isocahedron shape at $50\mathrm{K}$ resolution and noise scale $\sigma = 3\%$ . Our StraightPCF filters points along much straighter paths, compared to ScoreDenoise [28]. + +noisy artifacts may appear in point clouds as a result of sensor limitations and environmental factors. Removing this noise, known as filtering or denoising, is a fundamental 3D vision task. Filtering methods are broadly categorized into two groups: 1) conventional methods involving traditional optimization and 2) deep learning based methods. Conventional methods can further be subdivided into normal based methods which require surface normal information to reliably filter point clouds [2, 10, 13, 24, 30] and point based methods which directly filter point clouds [15, 21, 32]. While normal based methods are limited by the accuracy of normals, point based methods suffer from a loss of geometric details and still exhibit sensitivity to noise. Recently, many deep learning approaches have been proposed to overcome these shortcomings. + +Deep learning methods can be divided into 1) resampling, 2) displacement and 3) probability based methods. Resampling-based methods [26] show the least fidelity when recovering the underlying noise-free surfaces as their downsampling procedure results in the loss of crucial geometric information. By contrast, displacement and probability based methods show greater promise as they model the filtering objective as a reverse Markov process, which can be iteratively applied on the input to progressively remove noise. Early displacement based methods, such as + +PointCleanNet [7, 35, 45], employ large networks ( $>1\mathrm{M}$ parameters) that consume a large patch of points to filter a single, central point. This is time-consuming and resource intensive. More recently, IterativePFN [8] models the iterative filtering process internally using multiple IterationModules and filters all patch points simultaneously. However, incorporating multiple IterationModules results in a large network ( $>3.2\mathrm{M}$ parameters) which requires a large amount of GPU memory to process. Probabilistic score based methods such as ScoreDenoise [6, 28] offer a more lightweight network but require a high number of iterations to recover the clean surface. At higher noise levels, they converge to surfaces that retain noticeable amounts of noise. DeepPSR [6] utilizes the score module of [28] but performs an additional Graph Laplacian Regularization [14] step on intermediate point clouds to obtain a better point distribution. More importantly, the iterative filtering objectives of current displacement and probabilistic methods move noisy points to the clean surface via stochastic trajectories and are error prone as incorrectly inferred displacements may result in significant changes to the distribution of filtered points. + +We propose StraightPCF, which moves noisy points along straight filtering trajectories towards the clean surfaces, as illustrated in Fig. 1. StraightPCF, illustrated in Fig. 2, is a lightweight network ( $\sim 530K$ parameters, $17\%$ of IterativePFN [8]) which filters all patch points simultaneously. Our technical contributions are as follows. + +- We introduce the patch-wise VelocityModule that infers constant, straight flows to filter point cloud patches. The VelocityModule elegantly recovers the underlying clean surfaces with nice point distributions. +- To improve straightness of flows, we propose a novel straightening mechanism consisting of coupled VelocityModules. This coupled VelocityModule stack infers straighter filtering trajectories, leading to better results. +- Constant flows may lead to filtered points overshooting the clean surface. Therefore, we design the Distance-Module to infer a distance scalar that provides a magnitude to scale the flow velocity. Our architecture is the first to decompose filtering into a dual objective of inferring a vector field of flow velocities and a distance scalar. + +# 2. Related Work + +Conventional filtering. Early conventional methods were inspired by the Moving Least Squares (MLS) method of Levin [17] and require normal information for filtering. Notably, Alexa et al. [2] employed MLS optimization in recovering denoised surfaces from noisy point sets. The Implicit MLS (IMLS) method of Adamson and Alexa [1] further extended this approach to point-sampled cell complexes which allow for a well defined local geometry. The Algebraic Point Set Surface (APSS) method of Guennebaud and Gross [13] applied MLS optimization for the purpose of + +fitting algebraic spheres to recover surfaces while being robust to point set density and underlying curvature. Furthermore, Digne proposed filtering the height map associated to a point set by considering handcrafted features that encode height variations around each point [9]. Digne and de Franchis designed a weighted projection scheme, that moves points to their filtered positions [10], based on the mesh bilateral filtering method of Fleishman, Drori and Cohen-Or [11]. Other normal based methods include the Moving Robust Principal Component Analysis (MRPCA) [30] of Mattei and Castrodad, the Graph Laplacian Regularization (GLR) [14] technique of Hu et al. and the Low Rank Matrix Approximation [24] of Lu et al. The main drawback of such methods is susceptibility to noise, during both the normal estimation and filtering steps. + +By contrast, point based methods employ only point information for filtering. Cazals and Pouget [4] proposed a $N$ -dimensional polynomial surface fitting method that can be used to filter points. Meanwhile, the Locally Optimal Projection (LOP) [21] method of Lipman et al. downsampled and regularized noisy point clouds. It was extended by Huang et al. and Preiner et al. who developed Weighted-LOP (WLOP) [15] and Continuous-LOP (CLOP) [32], respectively. However, these methods do not effectively recover geometric details due to their downsampling step. + +Deep learning based filtering. While conventional methods rely on handcrafted features, convolutional neural network architectures have provided great improvements to feature generation. PointProNets [37] by Roveri et al. and Deep Feature Preserving (DFP) [23] by Lu et al. projected points onto 2D height maps before processing them using CNNs. PointNet [33], introduced by Qi et al., set the precedent for direct point set convolution and was later improved by PointNet++ [34]. Meanwhile, DGCNN [42] of Wang et al. reformulated point set convolution as a graph convolution task. PointCleanNet (PCN) [35] was one of the first methods to adopt the PointNet architecture and inferred the filtered displacement of a single central point by considering its neighborhood patch. Pointfilter [45] of Zhang et al. furthered this line of research using a bilateral filtering-inspired loss. + +Pistilli et al. introduced the first graph convolution-based mechanism, named GPDNet [31], while Luo and Hu proposed the DGCNN based DMRDenoise [26]. DMRDenoise filtered points by downsampling noisy inputs and upsampling these less noisy surfaces. Luo and Hu also proposed ScoreDenoise [28] where they formally expressed the filtering objective as the backward Langevin equation that iteratively removes noise using the inferred gradient-log of the probability distribution, i.e., the score, for point positions $\mathbf{x}$ . This was extended by Chen et al. in their DeepPSR [6] which employs an additional graph laplacian regularization post-processing step. Mao et al. introduced the normalizing + +![](images/23a453b31e45605dc7c7ee97f800a9e3bbcfd9a0ceb10e21e882ac28de3c3e97.jpg) +Figure 2. Our StraightPCF network. It involves a coupled VelocityModule stack that infers a constant flow velocity $\pmb{v}_{\theta}^{k}$ for patch states $\tilde{\pmb{X}}_{(\hat{t} + k)/T}$ . To ensure filtered points converge to the surface, the DistanceModule infers a distance scalar $d_{\phi}$ that scales the velocity. + +flows based filtering method PDFlow [29] that disentangles noise from the underlying clean representation at higher dimensions. The RePCDNet [5] method of Chen et al. sought to model iterative filtering via a recurrent neural network. By contrast, de Silva Edirimuni et al. proposed the graph convolution based IterativePFN [8] that models iterative filtering using individual IterationModules. The joint filtering and normal estimation method CFilter [7], developed by de Silva Edirimuni et al., exploited normals to improve filtered point positions. Ma et al. introduced learning implicit signed distance functions, by displacing noisy query points back to the surface along normals where the surface corresponds to the zero-level set of the function [3]. This has been exploited for normal estimation [18, 19]. + +Score and displacement based methods are inspired by diffusive processes [27, 39] and their filtering objectives result in stochastic trajectories. Recent work by Liu, Gong and Liu focuses on Reflow [22], which explored the optimal transport problem of identifying straight paths given two samples from different distributions. The work of Wu et al. further extended this Reflow mechanism to point cloud generation, which attempts to generate point cloud shapes given initial samples from the normal distribution [43]. + +# 3. Problem Statement and Motivation + +Resampling methods demonstrate an inability to recover clean surfaces with high accuracy, unlike probabilistic and displacement based methods. A probabilistic score based method such as ScoreDenoise [28] and a displacement based method such as IterativePFN [8] share similar filtering objectives that may be expressed by, + +$$ +\tilde {\boldsymbol {x}} _ {t} ^ {i} = \tilde {\boldsymbol {x}} _ {t - 1} ^ {i} + F _ {\theta} \left(\tilde {\boldsymbol {x}} _ {t - 1} ^ {i}\right), t = 1, \dots , T \tag {1} +$$ + +where $\tilde{\pmb{x}}_t^i$ is the $i$ -th filtered point at time $t$ and $F_{\theta}$ represents the network with parameters $\theta$ . The main difference between ScoreDenoise and IterativePFN lies in their training objectives, $\mathcal{L}_S$ and $\mathcal{L}_I$ , respectively. For a noisy point $\pmb{x}^i \in \pmb{X}$ where $\pmb{X}$ is the initial noisy patch, we have: + +$$ +\mathcal {L} _ {S} ^ {i} = \mathbb {E} _ {\boldsymbol {x} \sim k N N (\boldsymbol {x} ^ {i}, \boldsymbol {X})} \left[ \left\| s (\boldsymbol {x}) - \mathcal {S} ^ {i} (\boldsymbol {x}) \right\| _ {2} ^ {2} \right], \tag {2} +$$ + +$$ +\mathcal {L} _ {I} ^ {i} = \sum_ {t = 0} ^ {T} \left\| \boldsymbol {d} _ {t} ^ {i} - \left(N N \left(\boldsymbol {x} _ {t - 1} ^ {i}, \boldsymbol {Y} _ {t}\right) - \boldsymbol {x} _ {t - 1} ^ {i}\right) \right\| _ {2} ^ {2}. \tag {3} +$$ + +ScoreDenoise is trained to predict a score $S^i(\boldsymbol{x}) = \text{Score}(\boldsymbol{x} - \boldsymbol{x}^i | \boldsymbol{h}^i)$ for $\boldsymbol{x}$ sampled from the k-nearest neighbors of $\boldsymbol{x}^i$ . It is conditioned on the latent feature $\boldsymbol{h}^i$ of $\boldsymbol{x}^i$ and corresponds to the gradient-log of the noise-convolved probability distribution for point position $\boldsymbol{x}$ . The ground truth target $s(\boldsymbol{x}) = N N(\boldsymbol{x}, \boldsymbol{Y}) - \boldsymbol{x}$ , where $\boldsymbol{Y}$ is the clean patch. Ergo, $s(\boldsymbol{x})$ is the displacement from $\boldsymbol{x}$ to its nearest neighbor in $\boldsymbol{Y}$ . Once this training objective has been optimized, score based methods infer aggregate scores, at each iteration $t$ , such that $F_{\theta}(\boldsymbol{x}_{t-1}^i) = \alpha \mathcal{E}^i(\boldsymbol{x}_{t-1}^i) = (\alpha / K) \sum_{\boldsymbol{x}_{t-1}^j \in kNN(\boldsymbol{x}_{t-1}^i)} S^j(\boldsymbol{x}_{t-1}^i)$ where $\alpha$ is the step discretization parameter. This score shifts points towards the clean surface along a stochastic filtered trajectory that is sensitive to the choice of $\alpha$ , which must be kept relatively small ( $\sim 0.2$ ). By contrast, IterativePFN internally models the iterative filtering objective and incorporates it within their training objective. They directly infer displacements $F_{\theta}(\tilde{\boldsymbol{x}}_{t-1}^i) = \boldsymbol{d}_t^i$ as the output of each IterationModule that models an iteration $t$ . From Eq. (3) we identify that the overall filtered trajectories inferred by IterativePFN will also be stochastic in nature as it uses an Adaptive Ground Truth (AGT), $Y_t = Y + \sigma_t\xi \wedge \xi \sim \mathcal{N}(0, I)$ , within the training objective. Modelling the iterative filtering process internally results in a large network ( $>3.2M$ parameters). The AGT, while recovering the surface, causes clustering along the surface and fails to respect the original point distribution. This is illustrated in Fig. 3. + +Inspired by Reflow which focuses on optimal transport between samples of different distributions [22, 43], we pose filtering as an optimal transport problem between point cloud patches. These patches of $n$ points are sampled from 1) the clean surface (i.e., clean patch $\mathbf{X}_1\sim \pi_1$ ) and 2) a high noise variant of the clean surface (i.e., high noise patch $\mathbf{X}_0\sim \pi_0$ ). The goal is to determine a transport plan (coupling) such that $\mathbf{X}_1 = V(\mathbf{X}_0)$ where $V:\mathbb{R}^{n\times 3}\to \mathbb{R}^{n\times 3}$ . The approximated flow velocity, $\pmb{v}_{\theta}:\mathbb{R}^{n\times 3}\rightarrow \mathbb{R}^{n\times 3}$ sat + +![](images/33db8d260ff8ed94ab1d498b1bc9c0e412afd8df1bcc7797b2b9e6e8b214b6fc.jpg) +Figure 3. Our StraightPCF is able to recover a better distribution of filtered points, even at very high noise scales ( $\sigma = 3\%$ and $50\mathrm{K}$ resolution) unseen during network training. + +isfies this transport mapping and $(\tilde{\pmb{X}}_0,\tilde{\pmb{X}}_1)$ form a valid coupling. Consequently, the filtered trajectories are straight (see Fig. 4), unlike ScoreDenoise and IterativePFN. Moreover, our method recovers the underlying point distribution of the surface without clustering artifacts or distortion. + +# 4. Method + +Previous methods such as ScoreDenoise [28] and IterativePFN [8] focus on filtering as a reverse Markov process where the forward process would correspond to adding noise. We formulate filtering as an optimal transport plan that moves noisy points back to the clean surface along the shortest (straight) path. We model noisy input patches as intermediate states between high noise variants and their corresponding clean counterparts. We design a graph convolution based VelocityModule that infers a constant flow velocity for each intermediate state. This encourages noisy points to move along straight filtering trajectories as shown in Fig. 4. We further improve the straightness of these trajectories via VelocityModule coupling. Finally, as the flow is constant, it may result in filtered points overshooting the clean surface. Therefore, we design a DistanceModule that scales the flow velocity appropriately and ensures convergence near the surface. The overall Straight-PCF architecture is illustrated in Fig. 2, which demonstrates the filtering process that utilizes both the coupled Velocity-Module and DistanceModule sub-networks to move points along straightened paths. The supplementary document provides additional methodology details. + +# 4.1. Filtering via straight flows + +In this section, we introduce the VelocityModule (VM) that moves noisy points along constant, straight flows to- + +![](images/67cc5ddbe1bf6da4c2692472c3ee08c7670097fcb1eca29638cc4308999630a1.jpg) +Figure 4. StraightPCF models initial noisy patches (light blue) as being intermediate states of a linear interpolation between high noise variants (red) and the clean surfaces (dark blue) and encourages straight filtering trajectories. + +wards the clean surface. Given a noisy patch $\mathbf{X} = \{\pmb{x}^i | \pmb{x}^i \in kNN(\pmb{x}^r, \mathcal{P}_X, k)\}$ centered around a reference point $\pmb{x}^r$ in the noisy point cloud $\mathcal{P}_X$ , the filtering objective aims to move $\pmb{x}^i$ towards the underlying clean patch $\mathbf{Y} = \{\pmb{y}^i | \pmb{y}^i \in \mathcal{P}_Y\}$ . For the filtering task, learning based methods are typically trained on noisy point clouds with Gaussian noise [6, 28, 29, 35, 45]. Iterative filtering depends on the ability of the method to filter patches from a higher noise level to a lower noise level, with the end result converging to the clean surface. Given the highest noise setting $\sigma_H$ , intermediate noise scales at a time $t \in [0,1]$ can be expressed as $\sigma = (1 - t)\sigma_H$ . Therefore, we model noisy patches $\mathbf{X} = \mathbf{Y} + \sigma\xi \wedge \xi \sim \mathcal{N}(0, I)$ as intermediate states $X_t$ , of the filtering objective that moves points from a high noise variant, $X_0 = Y + \sigma_H\xi \wedge \xi \sim \mathcal{N}(0, I)$ to the clean counterpart $X_1 = Y$ . Here, $\sigma_H = 2\%$ of the point cloud's bounding sphere radius and corresponds to the highest noise setting of our training set. We observe that intermediate states $X_t$ can be defined as a linear interpolation of $X_0$ and $X_1$ , that is, a straight path, such that, + +$$ +\boldsymbol {X} _ {t} = (1 - t) \boldsymbol {X} _ {0} + t \boldsymbol {X} _ {1} \tag {4} +$$ + +Therefore, we intuit that the filtering objective can be reformulated as an optimal transport process that moves points from $\mathbf{X}_0$ to $\mathbf{X}_1$ . The flow of $\mathbf{X}_t$ at time $t$ can be expressed via the ordinary differential equation (ODE): + +$$ +\mathrm {d} \boldsymbol {X} _ {t} = \boldsymbol {v} \left(\boldsymbol {X} _ {t}\right) \mathrm {d} t, \tag {5} +$$ + +where $\pmb{v}(\pmb{X}_t)$ is the velocity field at $\pmb{X}_t$ . For this ODE process, the linear interpolation of Eq. (4) can be used in the least squares optimization to determine the flow, + +$$ +\min _ {v} \int_ {0} ^ {1} \mathbb {E} _ {t \sim \mathcal {U} (0, 1)} \left[ \| \boldsymbol {v} (\boldsymbol {X} _ {t}) - (\boldsymbol {X} _ {1} - \boldsymbol {X} _ {0}) \| _ {2} ^ {2} \right] d t, \tag {6} +$$ + +where times $t$ are sampled uniformly along $[0,1]$ . However, the velocity field at an intermediate state $\pmb{X}_t$ cannot be causally determined as both $\pmb{X}_0$ and $\pmb{X}_1$ are unknown, during filtering. To address this, our idea is to approximate the velocity field for each $\pmb{X}_t$ by a neural network. + +Training objective for single VM. We use a DGCNN based graph neural network to model a VelocityModule $\pmb{v}_{\theta}$ + +with parameters $\theta$ to approximate the flow velocity. To train this VelocityModule, we define the following training objective. + +$$ +\mathcal {L} _ {A} = \mathbb {E} _ {t \sim \mathcal {U} (0, 1)} \left[ \| \boldsymbol {v} _ {\theta} (\boldsymbol {X} _ {t}) - \boldsymbol {\delta} (\boldsymbol {X} _ {1}, \boldsymbol {X} _ {0}) \| _ {2} ^ {2} \right], \tag {7} +$$ + +where $\delta(X_1, X_0) = X_1 - X_0$ . Hence, at each intermediate state, the corresponding flow velocity is ideally a constant vector that leads to a straight path from $X_0$ to $X_1$ . + +Filtering objective for single VM. During inference, given a straight flow velocity $\pmb{v}_{\theta}$ , we can move points from $\pmb{X}_{\hat{t} /N}$ to $\pmb{X}_{(\hat{t} +1) / N}$ using the Euler method ODE solver: + +$$ +\tilde {\boldsymbol {X}} _ {(\hat {t} + 1) / N} = \tilde {\boldsymbol {X}} _ {\hat {t} / N} + \frac {1}{N} \boldsymbol {v} _ {\theta} (\tilde {\boldsymbol {X}} _ {\hat {t} / N}), \tag {8} +$$ + +where $N$ denotes the total number of filtering steps, $\hat{t} \in [0, \dots, M, \dots, N-1]$ is an integer time step and $\tilde{\pmb{X}}_0 = \pmb{X}_0$ . In practice, filtering starts at an unknown time step $\hat{t} = M$ . We do not know the noise scale of the input patch and need to model it as an intermediate state $\tilde{\pmb{X}}_{M/N}$ of a higher noise variant $\pmb{X}_0$ . The full position update takes the form, + +$$ +\tilde {\boldsymbol {X}} _ {1} = \tilde {\boldsymbol {X}} _ {M / N} + \frac {1}{N} \sum_ {\hat {t} = M} ^ {N - 1} \boldsymbol {v} _ {\theta} \left(\tilde {\boldsymbol {X}} _ {\hat {t} / N}\right), \tag {9} +$$ + +Eq. (9) poses two challenges: + +1. The straightness of paths is crucial to reducing the number of total steps and improving efficiency. If paths are not sufficiently straight (i.e., they are curved), we need a higher number of steps to filter points effectively. +2. The starting time $t = M / N$ is unknown. Applying the Euler method for too many steps, $N$ , may lead to points not converging at the surface. + +# 4.2. Straighter flows via VelocityModule coupling + +Given noisy initial data, the trajectories of points tend to be curved, with limited straightness. One way to improve straightness is to finetune the velocity network on the coupling $(\tilde{X}_0,\tilde{X}_1)$ to satisfy $\tilde{X}_1 = V(\tilde{X}_0)$ . For filtering, we aim to recover surfaces while preserving local geometric details [35]. Applying such finetuning requires the pre-computation of $\tilde{X}_1$ for all possible surface patches and is infeasible due to the large number of patches in the training set. We propose a simple mechanism to straighten paths by coupling $K$ VelocityModules together. + +Training objective for coupled VMs. Given a noisy patch $\mathbf{X}_t$ , we partition the trajectory from $\mathbf{X}_t$ to $\mathbf{X}_1$ into $K$ segments and obtain the velocity flow $\pmb{v}_{\theta}^{k}(\tilde{\pmb{X}}_{t_k})$ at times $t_k = (t(K - k) + k) / K$ where $k \in \{0, 1, \dots, K - 1\}$ . Intermediate positions at times $t_{k+1}$ are given by $\tilde{\pmb{X}}_{t_{k+1}} = \tilde{\pmb{X}}_{t_k} + (1 / K) \pmb{v}_{\theta}^{k}(\tilde{\pmb{X}}_{t_k})$ . We empirically find that two VelocityModules, i.e., $K = 2$ , provide the best balance between accuracy and efficiency. The Velocity Modules are + +pretrained using the training objective of Eq. (7) and the coupled VMs are finetuned with the introduced objective, + +$$ +\begin{array}{l} \mathcal {L} _ {B} = \mathbb {E} _ {t \sim \mathcal {U} (0, 1)} \left[ \sum_ {k = 0} ^ {K - 1} \left\| \boldsymbol {v} _ {\theta} ^ {k} \left(\tilde {\boldsymbol {X}} _ {t _ {k}}\right) - \boldsymbol {\delta} \left(\boldsymbol {X} _ {1}, \boldsymbol {X} _ {0}\right) \right\| _ {2} ^ {2} \right. \tag {10} \\ \left. + \lambda_ {1} \sum_ {k = 0} ^ {K - 2} \left\| \boldsymbol {\delta} \left(\tilde {\boldsymbol {X}} _ {t _ {k + 1}}, \boldsymbol {X} _ {t _ {k + 1}}\right) \right\| _ {2} ^ {2} \right], \\ \end{array} +$$ + +for $K \geq 2$ , $\lambda_{1} = 10$ and $\tilde{\pmb{X}}_{t_0} = \pmb{X}_{t_0} = \pmb{X}_t$ . The first term of $\mathcal{L}_B$ encourages coupled VelocityModules to infer a constant velocity at times $t_k$ , while the second encourages filtered points $\tilde{\pmb{X}}_{t_k}$ to move closer to interpolated points $\pmb{X}_{t_k}$ . + +Filtering objective for coupled VMs. At inference, we apply a modified form of the Euler method to filter points, similar to Eq. (8). We apply $K$ coupled VelocityModules $N$ times, resulting in $T = K \cdot N$ total filtering steps. We adjust our earlier notation of integer time steps such that $\hat{t} \in \{0, K, \dots, \hat{M}, \dots, K(N - 1)\}$ where $\hat{M}$ is divisible by $K$ and $\tilde{\pmb{X}}_0 = \pmb{X}_0$ . The sequential position update becomes, + +$$ +\tilde {\boldsymbol {X}} _ {(\hat {t} + k + 1) / T} = \tilde {\boldsymbol {X}} _ {(\hat {t} + k) / T} + \frac {1}{T} \boldsymbol {v} _ {\theta} ^ {k} (\tilde {\boldsymbol {X}} _ {(\hat {t} + k) / T}). \tag {11} +$$ + +The corresponding full position update across time steps $S = \{\hat{M},\hat{M} +K,\dots ,N(K - 1)\}$ is, + +$$ +\tilde {\boldsymbol {X}} _ {1} = \tilde {\boldsymbol {X}} _ {\hat {M} / T} + \frac {1}{T} \sum_ {\hat {t} \in \mathcal {S}} \sum_ {k = 0} ^ {K - 1} \boldsymbol {v} _ {\theta} ^ {k} \left(\tilde {\boldsymbol {X}} _ {(\hat {t} + k) / T}\right). \tag {12} +$$ + +# 4.3. Distance estimation to the clean surface + +We now address the second challenge related to Eq. (9) and introduce the DistanceModule that scales the overall straight trajectory. This leads to better convergence near the surface. The DistanceModule estimates a distance scalar, corresponding to the standard deviation of initial noisy points from the clean surface. More specifically, the DistanceModule $\mathcal{D}_{\phi}(\cdot)$ is used to approximate a mapping $d_{\phi}:\mathbb{R}^{n\times 3}\to \mathbb{R}$ , such that, + +$$ +d _ {\phi} \left(\tilde {\boldsymbol {X}} _ {t _ {0}}\right) = \operatorname {S i g m o i d} \left(\operatorname {M a x} \left(\mathcal {D} _ {\phi} \left(\tilde {\boldsymbol {X}} _ {t _ {0}}\right)\right)\right). \tag {13} +$$ + +The distance $d_{\phi}$ is then used to scale the output of VelocityModules, as illustrated in Fig. 5. The DistanceModule is embedded within the StraightPCF architecture (see Fig. 2). We keep the weights of the finetuned coupled VelocityModules fixed when training the DistanceModule. The respective training objective for optimizing the parameters $\phi$ is, + +$$ +\begin{array}{l} \mathcal {L} _ {C} = \mathbb {E} _ {t \sim \mathcal {U} (0, 1)} \left[ \left(d _ {\phi} \left(\tilde {\boldsymbol {X}} _ {t _ {0}}\right) - \frac {\| \boldsymbol {\delta} \left(\boldsymbol {X} _ {1} , \boldsymbol {X} _ {t _ {0}}\right) \| _ {2}}{\| \boldsymbol {\delta} \left(\boldsymbol {X} _ {1} , \boldsymbol {X} _ {0}\right) \| _ {2}}\right) ^ {2} \right. \tag {14} \\ \left. + \lambda_ {2} \left\| \boldsymbol {\delta} \left(\tilde {\boldsymbol {X}} _ {1}, \boldsymbol {X} _ {1}\right) \right\| _ {2} ^ {2} \right], \\ \end{array} +$$ + +
Resolution10K (Sparse)50K (Dense)
Noise1%2%3%1%2%3%
MethodCDP2MCDP2MCDP2MCDP2MCDP2MCDP2M
PUNet dataset [44]PCN [35]3.5151.1487.4673.96513.0678.7371.0490.3461.4470.6082.2891.285
PointFilter [45]2.4610.4433.5340.8625.0891.8490.7580.1820.9070.2511.5990.710
Score [28]2.5210.4633.6861.0744.7081.9420.7160.1501.2880.5661.9281.041
PDFlow [29]2.1260.3813.2461.0104.4471.9990.6510.1641.1730.5811.9141.210
DeepPSR [6]2.3530.3063.3500.7344.0751.2420.6490.0760.9970.2961.3440.531
IterativePFN [8]2.0560.2183.0430.5554.2411.3760.6050.0590.8030.1821.9711.012
Ours1.8700.2392.6440.6043.2871.1260.5620.1110.7650.2661.3070.648
PCNet dataset [35]PCN [35]3.8471.2218.7523.04314.5255.8731.2930.2891.9130.5053.2491.076
Score [28]3.3690.8305.1321.1956.7761.9411.0660.1771.6590.3542.4940.657
PointFilter [45]3.0190.8864.8851.2757.0622.0321.0530.1861.3490.2572.2250.491
PDFlow [29]3.2430.6064.5450.9665.9341.4410.9690.1521.6460.4242.4500.569
DeepPSR [6]2.8730.7834.7571.1186.0311.6191.0100.1461.5150.3402.0930.573
IterativePFN [8]2.6210.6984.4391.0116.0261.5600.9130.1391.2510.2382.5290.716
Ours2.7470.5364.0460.7884.9211.0930.8770.1441.1730.2591.8160.445
+ +Table 1. Quantitative filtering results of recent state-of-the-art methods and our method on the synthetic PUNet and PCNet datasets. Note that our network is lightweight, with just $\sim 530K$ parameters (17% of IterativePFN). CD and P2M values are multiplied by $10^{4}$ + +![](images/840f7a8b07a8c99c3ae93b25bb17ed31e970bae683d13969145a81e9130ccb6a.jpg) +Figure 5. Left: Filtering by coupled VelocityModules only. Right: Coupled VelocityModules and DistanceModule. Scaled trajectories (green lines) lead to better convergence at the surface. + +where $t_0 = t$ and $\tilde{\pmb{X}}_{t_0} = \pmb{X}_{t_0} = \pmb{X}_t$ . The first term of $\mathcal{L}_C$ encourages the DistanceModule to infer the relative distance of $\pmb{X}_{t_0}$ from the clean surface, as compared to $\pmb{X}_0$ . The last term encourages points to return to the clean surface. We set $\lambda_{2} = 2\times 10^{2}$ to ensure the loss contribution of the last term is of the same order as that of the first one. Consequently, Eq. (11) becomes, + +$$ +\tilde {\boldsymbol {X}} _ {(\hat {t} + k + 1) / T} = \tilde {\boldsymbol {X}} _ {(\hat {t} + k) / T} + \frac {d _ {\phi} \left(\tilde {\boldsymbol {X}} _ {\hat {M} / T}\right)}{T} \boldsymbol {v} _ {\theta} ^ {k} \left(\tilde {\boldsymbol {X}} _ {(\hat {t} + k) / T}\right). \tag {15} +$$ + +# 5. Experiments + +Next, we provide results on synthetic data under Gaussian noise and real-world Kinect [41] and Paris-Rue-Madame [38] data. The supplementary document contains additional results of both conventional and learning based methods on synthetic and real-world scanned data, as well as a comparison of testing times. + +# 5.1. Training and evaluation details + +We follow the training procedure of ScoreDenoise [28], and train our model on the PUNet dataset [44] consisting of 40 point clouds for training and 20 point clouds for testing. To ensure consistency with ScoreDenoise's training settings, we add Gaussian noise sampled with standard deviation $\sigma_{H} = 2\%$ of the bounding sphere radius to each clean point cloud. Our training procedure only requires the high noise variants and the clean ground truth targets. All intermediate states at noise scales $\sigma = (1 - t)\sigma_{H}$ , with $t \sim \mathcal{U}(0,1)$ are created as linear interpolations between these two, initial and final states, as per Eq. (4). For testing, we also consider 10 test point clouds from the PCNet dataset [35] provided by ScoreDenoise. These synthetic point clouds contain Gaussian noise at scales of $1\%$ , $2\%$ and $3\%$ of the point cloud's bounding sphere radius. We use two different sampling densities of 10K and 50K points to evaluate filtering ability across different sparsity settings. Moreover, to assess filtering results on real-world noisy point clouds, we compare methods on the Kinect v1 dataset that comprises of 71 point clouds [41] and 4 scenes extracted from the Paris-Rue-Madame dataset [38]. Finally, we provide a comparison on 4 scenes of the Kitti-360 dataset [20], in the supplementary document. Following [8, 28], all methods are only trained on PUNet with Gaussian noise. + +Implementation. We train and test StraightPCF on a NVIDIA GeForce RTX 3090 GPU using PyTorch. We use the Adam optimizer with a learning rate of $1 \times 10^{-4}$ . Similar to [8, 28], we use PyTorch3D [36] to compute Chamfer Distance (CD) and Point2Mesh (P2M) metric values. + +![](images/07a3f63a3bf81e1c259b8658043d6014b111944b8e4605b44c1147ff8ae1037f.jpg) +Figure 6. Visual filtering results for $50\mathrm{K}$ resolution shapes $(\sigma = 2\%)$ within the PUNet and PCNet datasets. The darker (i.e., more blueish) the better. We achieve both strong point-wise P2M results while also ensuring well distributed points (illustrated by close-ups) unlike DeepPSR or IterativePFN which have holes indicating clustering. + +# 5.2. Performance on synthetic data + +Table 1 and Fig. 6 illustrate filtering results on the synthetic PUNet and PCNet datasets. Our method has a clear edge over others in recovering the underlying clean point distribution demonstrated by superior CD results across all noise settings. We also achieve strong P2M results on the PUNet dataset. While IterativePFN [8] has marginally better P2M results on the PUNet data, this does not ensure a good distribution of points as evidenced by visual results in Fig. 6. Here, for noisy point clouds at $50\mathrm{K}$ resolution and $2\%$ noise, IterativePFN exhibits small holes, indicating clustering. Moreover, our network consists of only $530\mathrm{K}$ parameters and is roughly $83\%$ smaller than that of IterativePFN, given the latter's $3.2\mathrm{M}$ parameters. DeepPSR [6], despite using a post-processing regularization step, also suffers from holes and poor point distributions. We also note that IterativePFN generalizes poorly to higher noise scales outside the training noise scales (where maximum noise is $\sigma = 2\%$ ). The ability of our method to generalize well across different data is demonstrated by the superior performance on the PCNet dataset. The PCNet shapes are unseen during training. Our method obtains both superior CD and P2M results over all other methods. At $10\mathrm{K}$ resolution and $\sigma = 3\%$ noise, our method offers a $17.1\%$ reduction in CD error and $24.1\%$ reduction in P2M error. Our method also yields state-of-the-art results at $50\mathrm{K}$ resolution where, for $\sigma = 3\%$ , the CD error improvement is $13.2\%$ and P2M error + +improvement is $9.4\%$ . Visual filtering results in Fig. 6 indicate that our method outperforms others in recovering complex details such as the legs of the Camel which are closely situated. By contrast, methods such as Pointfilter [45] and PDFlow [29] flatten points between these close surfaces while IterativePFN does not recover the body well. Furthermore, on a complex shape as Netsuke, we outperform other methods which either cause clustering (e.g., PDFlow, IterativePFN) at this high noise scale or leave behind noise due to limited filtering ability (e.g., ScoreDenoise). + +# 5.3. Performance on real-world scanned data + +Next we consider filtering results on scanned data. Table 2 provides quantitative results on the Kinect dataset and Fig. 7 illustrates visual results on the Paris-Rue-Madame dataset. Our method performs favorably on the Kinect data, obtaining a $1.82\%$ reduction on CD errors, as compared to IterativePFN [8]. As this data is very sparse, our P2M result is marginally higher than Pointfilter [45] and Score-Denoise [28]. These methods focus on returning points to the surface yet succumb to clustering artifacts whereas our method both recovers surfaces while retaining good point distributions. The Paris-Rue-Madame dataset contains high noise scans due to outdoor environmental factors. In Fig. 7, we visualize filtering results for several most recent, state-of-the-art methods. In general, methods such as PDFlow [29] and DeepPSR [6] perform poorly in removing noisy artifacts while IterativePFN [8] causes points to + +![](images/06aadf5b8eca17d9b43a94229ca6d2d8412edec73af59083e5ab12d735f23b14.jpg) +Figure 7. Visual filtering results on two scenes of the RueMadame dataset. We show results for the most recent state-of-the-art methods. + +
MethodKinect
CDP2M
ScoreDenoise1.3220.652
Pointfilter1.3770.644
PDFlow1.3340.699
DeepPSR1.4310.715
IterativePFN1.3200.685
Ours1.2960.664
+ +cluster near the original scan lines. Our method, however, recovers the underlying clean surface and ensures a much better point distribution, as evidenced by the close-ups in Scene 1. In Scene 2, PDFlow and IterativePFN are not able to clean the surface of the parked vehicle whereas our method recovers the underlying shape with fewer noisy artifacts. + +# 6. Ablation Study and Discussion + +We train and test several variant architectures in order to ascertain the impact of the proposed VelocityModule (VM) and DistanceModule (DM). The results are given in Table 3. Our coupled VM + DM architecture (V5) increases the parameter number to $\sim 530K$ . Therefore, we train another Large VM with $\sim 530K$ parameters (V3). We find that directly increasing the parameter number (V3) leads to very limited performance gain while V5 exhibits far superior performance. Furthermore, the coupled VM + DM architecture (V5) significantly outperforms the single VM (V1 and V2) architectures. Finally, there is a noticeable difference in performance with and without a DM as evidenced by the dis + +Table 2. Quantitative results on Kinect data. Our network is lightweight, with just $\sim 530K$ parameters (17% of IterativePFN). CD and P2M values are multiplied by $10^{4}$ . + +
Ablation10K points
1% noise2% noise3% noise
CDP2MCDP2MCDP2M
VI) VM w/o DM2.160.423.060.923.731.42
V2) VM w/ DM2.000.323.060.963.811.55
V3) Large VM2.170.412.990.843.541.29
V4) CVM w/o DM1.970.323.010.923.711.45
V5) CVM w/ DM1.870.242.640.603.291.13
+ +Table 3. Ablation results for different VelocityModule (VM) and DistanceModule (DM) configurations. + +parity between V4 and V5. We provide further ablations, including higher VM couplings, in the supplementary document. + +**Limitation.** While our StraightPCF yields state-of-the-art results across multiple datasets, we observe relatively low performance on low density or high sparsity data, which is similar to current methods. We provide the visual results in the supplementary document due to space limit. + +# 7. Conclusion + +Recent deep learning based filtering methods focus on moving noisy points along stochastic paths to remove noise from input point clouds. We propose the first study to consider filtering points along straight paths, leading to smaller discretization errors and fewer filtering iterations. 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IEEE Transactions on Visualization and Computer Graphics, 27:2015-2027, 2021. 2, 4, 6, 7 \ No newline at end of file diff --git a/2024/StraightPCF_ Straight Point Cloud Filtering/images.zip b/2024/StraightPCF_ Straight Point Cloud Filtering/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..660bce3982701e5506e2a4110c7cde01a722f34e --- /dev/null +++ b/2024/StraightPCF_ Straight Point Cloud Filtering/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:19c5dabb85dea20063ab47a5eaffc12b2f75b56f08a56a5c3b5776b8a587ce0d +size 841771 diff --git a/2024/StraightPCF_ Straight Point Cloud Filtering/layout.json b/2024/StraightPCF_ Straight Point Cloud Filtering/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..d9756c2ebb41b1b5c1da7b2c96f688ee4dbd9d66 --- /dev/null +++ b/2024/StraightPCF_ Straight Point Cloud Filtering/layout.json @@ -0,0 +1,9095 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 159, + 103, + 434, + 121 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 159, + 103, + 434, + 121 + ], + "spans": [ + { + "bbox": [ + 159, + 103, + 434, + 121 + ], + "type": "text", + "content": "StraightPCF: Straight Point Cloud Filtering" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 53, + 142, + 548, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 142, + 548, + 171 + ], + "spans": [ + { + "bbox": [ + 53, + 142, + 548, + 171 + ], + "type": "text", + "content": "Dasith de Silva Edirimuni1, Xuequan Lu2*, Gang Li1, Lei Wei1, Antonio Robles-Kelly1, Hongdong Li3 \n1Deakin University, 2La Trobe University, 3Australian National University" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 122, + 173, + 478, + 185 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 122, + 173, + 478, + 185 + ], + "spans": [ + { + "bbox": [ + 122, + 173, + 478, + 185 + ], + "type": "text", + "content": "{dtdesilva, gang.li, lei.wei, antonio.robles-kelly}@deakin.edu.au," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 181, + 188, + 416, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 181, + 188, + 416, + 198 + ], + "spans": [ + { + "bbox": [ + 181, + 188, + 416, + 198 + ], + "type": "text", + "content": "b.lu@latrobe.edu.au, hongdong.li@anu.edu.au" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "spans": [ + { + "bbox": [ + 143, + 227, + 192, + 239 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "spans": [ + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "type": "text", + "content": "Point cloud filtering is a fundamental 3D vision task, which aims to remove noise while recovering the underlying clean surfaces. State-of-the-art methods remove noise by moving noisy points along stochastic trajectories to the clean surfaces. These methods often require regularization within the training objective and/or during post-processing, to ensure fidelity. In this paper, we introduce StraightPCF, a new deep learning based method for point cloud filtering. It works by moving noisy points along straight paths, thus reducing discretization errors while ensuring faster convergence to the clean surfaces. We model noisy patches as intermediate states between high noise patch variants and their clean counterparts, and design the VelocityModule to infer a constant flow velocity from the former to the latter. This constant flow leads to straight filtering trajectories. In addition, we introduce a DistanceModule that scales the straight trajectory using an estimated distance scalar to attain convergence near the clean surface. Our network is lightweight and only has " + }, + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "type": "inline_equation", + "content": "\\sim 530K" + }, + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "type": "text", + "content": " parameters, being " + }, + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 47, + 252, + 290, + 563 + ], + "type": "text", + "content": " of IterativePFN (a most recent point cloud filtering network). Extensive experiments on both synthetic and real-world data show our method achieves state-of-the-art results. Our method also demonstrates nice distributions of filtered points without the need for regularization. The implementation code can be found at: https://github.com/ddsdiri/StuartPCF." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 588, + 128, + 601 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 609, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 609, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 609, + 287, + 693 + ], + "type": "text", + "content": "In recent years, point clouds have become increasingly popular as the representation-of-choice for storing and manipulating 3D data, with numerous applications in both computer vision [12, 20, 25, 38] and geometry modelling [16, 25, 40]. Point clouds are unordered sets of 3D coordinates which typically represent object surfaces and are captured using 3D sensors such as depth and Lidar devices. However," + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 309, + 225, + 547, + 340 + ], + "blocks": [ + { + "bbox": [ + 309, + 225, + 547, + 340 + ], + "lines": [ + { + "bbox": [ + 309, + 225, + 547, + 340 + ], + "spans": [ + { + "bbox": [ + 309, + 225, + 547, + 340 + ], + "type": "image", + "image_path": "0e11c694f22c11639a21d581a7be698004f1330eeb71441eaf0f7ab481368725.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "lines": [ + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "type": "text", + "content": "Figure 1. Filtered trajectories for the Isocahedron shape at " + }, + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "type": "text", + "content": " resolution and noise scale " + }, + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "type": "inline_equation", + "content": "\\sigma = 3\\%" + }, + { + "bbox": [ + 305, + 349, + 547, + 383 + ], + "type": "text", + "content": ". Our StraightPCF filters points along much straighter paths, compared to ScoreDenoise [28]." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 411, + 547, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 547, + 590 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 547, + 590 + ], + "type": "text", + "content": "noisy artifacts may appear in point clouds as a result of sensor limitations and environmental factors. Removing this noise, known as filtering or denoising, is a fundamental 3D vision task. Filtering methods are broadly categorized into two groups: 1) conventional methods involving traditional optimization and 2) deep learning based methods. Conventional methods can further be subdivided into normal based methods which require surface normal information to reliably filter point clouds [2, 10, 13, 24, 30] and point based methods which directly filter point clouds [15, 21, 32]. While normal based methods are limited by the accuracy of normals, point based methods suffer from a loss of geometric details and still exhibit sensitivity to noise. Recently, many deep learning approaches have been proposed to overcome these shortcomings." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 548, + 714 + ], + "type": "text", + "content": "Deep learning methods can be divided into 1) resampling, 2) displacement and 3) probability based methods. Resampling-based methods [26] show the least fidelity when recovering the underlying noise-free surfaces as their downsampling procedure results in the loss of crucial geometric information. By contrast, displacement and probability based methods show greater promise as they model the filtering objective as a reverse Markov process, which can be iteratively applied on the input to progressively remove noise. Early displacement based methods, such as" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 266, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 266, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 266, + 713 + ], + "type": "text", + "content": "*Corresponding author: X. Lu, supported by fund 3.2501.11.47." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20721" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "content": "PointCleanNet [7, 35, 45], employ large networks (" + }, + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "inline_equation", + "content": ">1\\mathrm{M}" + }, + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "content": " parameters) that consume a large patch of points to filter a single, central point. This is time-consuming and resource intensive. More recently, IterativePFN [8] models the iterative filtering process internally using multiple IterationModules and filters all patch points simultaneously. However, incorporating multiple IterationModules results in a large network (" + }, + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "inline_equation", + "content": ">3.2\\mathrm{M}" + }, + { + "bbox": [ + 47, + 72, + 289, + 323 + ], + "type": "text", + "content": " parameters) which requires a large amount of GPU memory to process. Probabilistic score based methods such as ScoreDenoise [6, 28] offer a more lightweight network but require a high number of iterations to recover the clean surface. At higher noise levels, they converge to surfaces that retain noticeable amounts of noise. DeepPSR [6] utilizes the score module of [28] but performs an additional Graph Laplacian Regularization [14] step on intermediate point clouds to obtain a better point distribution. More importantly, the iterative filtering objectives of current displacement and probabilistic methods move noisy points to the clean surface via stochastic trajectories and are error prone as incorrectly inferred displacements may result in significant changes to the distribution of filtered points." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "type": "text", + "content": "We propose StraightPCF, which moves noisy points along straight filtering trajectories towards the clean surfaces, as illustrated in Fig. 1. StraightPCF, illustrated in Fig. 2, is a lightweight network (" + }, + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "type": "inline_equation", + "content": "\\sim 530K" + }, + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "type": "text", + "content": " parameters, " + }, + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "type": "inline_equation", + "content": "17\\%" + }, + { + "bbox": [ + 47, + 323, + 288, + 395 + ], + "type": "text", + "content": " of IterativePFN [8]) which filters all patch points simultaneously. Our technical contributions are as follows." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 396, + 287, + 562 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 47, + 396, + 287, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 287, + 442 + ], + "type": "text", + "content": "- We introduce the patch-wise VelocityModule that infers constant, straight flows to filter point cloud patches. The VelocityModule elegantly recovers the underlying clean surfaces with nice point distributions." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 444, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 444, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 444, + 287, + 491 + ], + "type": "text", + "content": "- To improve straightness of flows, we propose a novel straightening mechanism consisting of coupled VelocityModules. This coupled VelocityModule stack infers straighter filtering trajectories, leading to better results." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 491, + 287, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 287, + 562 + ], + "type": "text", + "content": "- Constant flows may lead to filtered points overshooting the clean surface. Therefore, we design the Distance-Module to infer a distance scalar that provides a magnitude to scale the flow velocity. Our architecture is the first to decompose filtering into a dual objective of inferring a vector field of flow velocities and a distance scalar." + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 134, + 586 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 594, + 289, + 715 + ], + "type": "text", + "content": "Conventional filtering. Early conventional methods were inspired by the Moving Least Squares (MLS) method of Levin [17] and require normal information for filtering. Notably, Alexa et al. [2] employed MLS optimization in recovering denoised surfaces from noisy point sets. The Implicit MLS (IMLS) method of Adamson and Alexa [1] further extended this approach to point-sampled cell complexes which allow for a well defined local geometry. The Algebraic Point Set Surface (APSS) method of Guennebaud and Gross [13] applied MLS optimization for the purpose of" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 252 + ], + "type": "text", + "content": "fitting algebraic spheres to recover surfaces while being robust to point set density and underlying curvature. Furthermore, Digne proposed filtering the height map associated to a point set by considering handcrafted features that encode height variations around each point [9]. Digne and de Franchis designed a weighted projection scheme, that moves points to their filtered positions [10], based on the mesh bilateral filtering method of Fleishman, Drori and Cohen-Or [11]. Other normal based methods include the Moving Robust Principal Component Analysis (MRPCA) [30] of Mattei and Castrodad, the Graph Laplacian Regularization (GLR) [14] technique of Hu et al. and the Low Rank Matrix Approximation [24] of Lu et al. The main drawback of such methods is susceptibility to noise, during both the normal estimation and filtering steps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 254, + 547, + 374 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 254, + 547, + 374 + ], + "spans": [ + { + "bbox": [ + 304, + 254, + 547, + 374 + ], + "type": "text", + "content": "By contrast, point based methods employ only point information for filtering. Cazals and Pouget [4] proposed a " + }, + { + "bbox": [ + 304, + 254, + 547, + 374 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 254, + 547, + 374 + ], + "type": "text", + "content": "-dimensional polynomial surface fitting method that can be used to filter points. Meanwhile, the Locally Optimal Projection (LOP) [21] method of Lipman et al. downsampled and regularized noisy point clouds. It was extended by Huang et al. and Preiner et al. who developed Weighted-LOP (WLOP) [15] and Continuous-LOP (CLOP) [32], respectively. However, these methods do not effectively recover geometric details due to their downsampling step." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 376, + 548, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 548, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 548, + 568 + ], + "type": "text", + "content": "Deep learning based filtering. While conventional methods rely on handcrafted features, convolutional neural network architectures have provided great improvements to feature generation. PointProNets [37] by Roveri et al. and Deep Feature Preserving (DFP) [23] by Lu et al. projected points onto 2D height maps before processing them using CNNs. PointNet [33], introduced by Qi et al., set the precedent for direct point set convolution and was later improved by PointNet++ [34]. Meanwhile, DGCNN [42] of Wang et al. reformulated point set convolution as a graph convolution task. PointCleanNet (PCN) [35] was one of the first methods to adopt the PointNet architecture and inferred the filtered displacement of a single central point by considering its neighborhood patch. Pointfilter [45] of Zhang et al. furthered this line of research using a bilateral filtering-inspired loss." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": "Pistilli et al. introduced the first graph convolution-based mechanism, named GPDNet [31], while Luo and Hu proposed the DGCNN based DMRDenoise [26]. DMRDenoise filtered points by downsampling noisy inputs and upsampling these less noisy surfaces. Luo and Hu also proposed ScoreDenoise [28] where they formally expressed the filtering objective as the backward Langevin equation that iteratively removes noise using the inferred gradient-log of the probability distribution, i.e., the score, for point positions " + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 570, + 548, + 715 + ], + "type": "text", + "content": ". This was extended by Chen et al. in their DeepPSR [6] which employs an additional graph laplacian regularization post-processing step. Mao et al. introduced the normalizing" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20722" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 83, + 69, + 511, + 178 + ], + "blocks": [ + { + "bbox": [ + 83, + 69, + 511, + 178 + ], + "lines": [ + { + "bbox": [ + 83, + 69, + 511, + 178 + ], + "spans": [ + { + "bbox": [ + 83, + 69, + 511, + 178 + ], + "type": "image", + "image_path": "23a453b31e45605dc7c7ee97f800a9e3bbcfd9a0ceb10e21e882ac28de3c3e97.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "text", + "content": "Figure 2. Our StraightPCF network. It involves a coupled VelocityModule stack that infers a constant flow velocity " + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "inline_equation", + "content": "\\pmb{v}_{\\theta}^{k}" + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "text", + "content": " for patch states " + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_{(\\hat{t} + k)/T}" + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "text", + "content": ". To ensure filtered points converge to the surface, the DistanceModule infers a distance scalar " + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "inline_equation", + "content": "d_{\\phi}" + }, + { + "bbox": [ + 46, + 186, + 547, + 213 + ], + "type": "text", + "content": " that scales the velocity." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 231, + 289, + 397 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 231, + 289, + 397 + ], + "spans": [ + { + "bbox": [ + 46, + 231, + 289, + 397 + ], + "type": "text", + "content": "flows based filtering method PDFlow [29] that disentangles noise from the underlying clean representation at higher dimensions. The RePCDNet [5] method of Chen et al. sought to model iterative filtering via a recurrent neural network. By contrast, de Silva Edirimuni et al. proposed the graph convolution based IterativePFN [8] that models iterative filtering using individual IterationModules. The joint filtering and normal estimation method CFilter [7], developed by de Silva Edirimuni et al., exploited normals to improve filtered point positions. Ma et al. introduced learning implicit signed distance functions, by displacing noisy query points back to the surface along normals where the surface corresponds to the zero-level set of the function [3]. This has been exploited for normal estimation [18, 19]." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 399, + 288, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 288, + 507 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 288, + 507 + ], + "type": "text", + "content": "Score and displacement based methods are inspired by diffusive processes [27, 39] and their filtering objectives result in stochastic trajectories. Recent work by Liu, Gong and Liu focuses on Reflow [22], which explored the optimal transport problem of identifying straight paths given two samples from different distributions. The work of Wu et al. further extended this Reflow mechanism to point cloud generation, which attempts to generate point cloud shapes given initial samples from the normal distribution [43]." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 515, + 243, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 515, + 243, + 528 + ], + "spans": [ + { + "bbox": [ + 47, + 515, + 243, + 528 + ], + "type": "text", + "content": "3. Problem Statement and Motivation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 535, + 287, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 535, + 287, + 608 + ], + "spans": [ + { + "bbox": [ + 46, + 535, + 287, + 608 + ], + "type": "text", + "content": "Resampling methods demonstrate an inability to recover clean surfaces with high accuracy, unlike probabilistic and displacement based methods. A probabilistic score based method such as ScoreDenoise [28] and a displacement based method such as IterativePFN [8] share similar filtering objectives that may be expressed by," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 90, + 611, + 287, + 625 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 90, + 611, + 287, + 625 + ], + "spans": [ + { + "bbox": [ + 90, + 611, + 287, + 625 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {x}} _ {t} ^ {i} = \\tilde {\\boldsymbol {x}} _ {t - 1} ^ {i} + F _ {\\theta} \\left(\\tilde {\\boldsymbol {x}} _ {t - 1} ^ {i}\\right), t = 1, \\dots , T \\tag {1}", + "image_path": "5773aa531a7ab58cbc61c262c9c4d178012d5f55a505d41327dc4d12988a8f12.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "spans": [ + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{x}}_t^i" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": " is the " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": "-th filtered point at time " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "F_{\\theta}" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": " represents the network with parameters " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": ". The main difference between ScoreDenoise and IterativePFN lies in their training objectives, " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_S" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_I" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": ", respectively. For a noisy point " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\pmb{x}^i \\in \\pmb{X}" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "inline_equation", + "content": "\\pmb{X}" + }, + { + "bbox": [ + 46, + 631, + 288, + 692 + ], + "type": "text", + "content": " is the initial noisy patch, we have:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 79, + 696, + 287, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 79, + 696, + 287, + 717 + ], + "spans": [ + { + "bbox": [ + 79, + 696, + 287, + 717 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {S} ^ {i} = \\mathbb {E} _ {\\boldsymbol {x} \\sim k N N (\\boldsymbol {x} ^ {i}, \\boldsymbol {X})} \\left[ \\left\\| s (\\boldsymbol {x}) - \\mathcal {S} ^ {i} (\\boldsymbol {x}) \\right\\| _ {2} ^ {2} \\right], \\tag {2}", + "image_path": "be3508b2c7389874f10067bcff2f8ac919b795f6cddb884ad65412d98cf8e04b.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 332, + 240, + 546, + 273 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 240, + 546, + 273 + ], + "spans": [ + { + "bbox": [ + 332, + 240, + 546, + 273 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {I} ^ {i} = \\sum_ {t = 0} ^ {T} \\left\\| \\boldsymbol {d} _ {t} ^ {i} - \\left(N N \\left(\\boldsymbol {x} _ {t - 1} ^ {i}, \\boldsymbol {Y} _ {t}\\right) - \\boldsymbol {x} _ {t - 1} ^ {i}\\right) \\right\\| _ {2} ^ {2}. \\tag {3}", + "image_path": "ba31877ebcf89620b14b37f2dfe9468cb206933e87512af606a29a0e1bc1eff0.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": "ScoreDenoise is trained to predict a score " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "S^i(\\boldsymbol{x}) = \\text{Score}(\\boldsymbol{x} - \\boldsymbol{x}^i | \\boldsymbol{h}^i)" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " for " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " sampled from the k-nearest neighbors of " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}^i" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ". It is conditioned on the latent feature " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{h}^i" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}^i" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " and corresponds to the gradient-log of the noise-convolved probability distribution for point position " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ". The ground truth target " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "s(\\boldsymbol{x}) = N N(\\boldsymbol{x}, \\boldsymbol{Y}) - \\boldsymbol{x}" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{Y}" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " is the clean patch. Ergo, " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "s(\\boldsymbol{x})" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " is the displacement from " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{x}" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " to its nearest neighbor in " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\boldsymbol{Y}" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ". Once this training objective has been optimized, score based methods infer aggregate scores, at each iteration " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ", such that " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "F_{\\theta}(\\boldsymbol{x}_{t-1}^i) = \\alpha \\mathcal{E}^i(\\boldsymbol{x}_{t-1}^i) = (\\alpha / K) \\sum_{\\boldsymbol{x}_{t-1}^j \\in kNN(\\boldsymbol{x}_{t-1}^i)} S^j(\\boldsymbol{x}_{t-1}^i)" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " is the step discretization parameter. This score shifts points towards the clean surface along a stochastic filtered trajectory that is sensitive to the choice of " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ", which must be kept relatively small (" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "\\sim 0.2" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": "). By contrast, IterativePFN internally models the iterative filtering objective and incorporates it within their training objective. They directly infer displacements " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "F_{\\theta}(\\tilde{\\boldsymbol{x}}_{t-1}^i) = \\boldsymbol{d}_t^i" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " as the output of each IterationModule that models an iteration " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ". From Eq. (3) we identify that the overall filtered trajectories inferred by IterativePFN will also be stochastic in nature as it uses an Adaptive Ground Truth (AGT), " + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": "Y_t = Y + \\sigma_t\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": ", within the training objective. Modelling the iterative filtering process internally results in a large network (" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "inline_equation", + "content": ">3.2M" + }, + { + "bbox": [ + 304, + 280, + 547, + 605 + ], + "type": "text", + "content": " parameters). The AGT, while recovering the surface, causes clustering along the surface and fails to respect the original point distribution. This is illustrated in Fig. 3." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "Inspired by Reflow which focuses on optimal transport between samples of different distributions [22, 43], we pose filtering as an optimal transport problem between point cloud patches. These patches of " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " points are sampled from 1) the clean surface (i.e., clean patch " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1\\sim \\pi_1" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ") and 2) a high noise variant of the clean surface (i.e., high noise patch " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_0\\sim \\pi_0" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": "). The goal is to determine a transport plan (coupling) such that " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1 = V(\\mathbf{X}_0)" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "V:\\mathbb{R}^{n\\times 3}\\to \\mathbb{R}^{n\\times 3}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": ". The approximated flow velocity, " + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\pmb{v}_{\\theta}:\\mathbb{R}^{n\\times 3}\\rightarrow \\mathbb{R}^{n\\times 3}" + }, + { + "bbox": [ + 304, + 605, + 547, + 714 + ], + "type": "text", + "content": " sat" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "20723" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 69, + 286, + 249 + ], + "blocks": [ + { + "bbox": [ + 50, + 69, + 286, + 249 + ], + "lines": [ + { + "bbox": [ + 50, + 69, + 286, + 249 + ], + "spans": [ + { + "bbox": [ + 50, + 69, + 286, + 249 + ], + "type": "image", + "image_path": "33db8d260ff8ed94ab1d498b1bc9c0e412afd8df1bcc7797b2b9e6e8b214b6fc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "lines": [ + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "spans": [ + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "type": "text", + "content": "Figure 3. Our StraightPCF is able to recover a better distribution of filtered points, even at very high noise scales (" + }, + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "type": "inline_equation", + "content": "\\sigma = 3\\%" + }, + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 46, + 257, + 288, + 291 + ], + "type": "text", + "content": " resolution) unseen during network training." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 310, + 288, + 370 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 310, + 288, + 370 + ], + "spans": [ + { + "bbox": [ + 46, + 310, + 288, + 370 + ], + "type": "text", + "content": "isfies this transport mapping and " + }, + { + "bbox": [ + 46, + 310, + 288, + 370 + ], + "type": "inline_equation", + "content": "(\\tilde{\\pmb{X}}_0,\\tilde{\\pmb{X}}_1)" + }, + { + "bbox": [ + 46, + 310, + 288, + 370 + ], + "type": "text", + "content": " form a valid coupling. Consequently, the filtered trajectories are straight (see Fig. 4), unlike ScoreDenoise and IterativePFN. Moreover, our method recovers the underlying point distribution of the surface without clustering artifacts or distortion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 380, + 103, + 393 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 103, + 393 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 103, + 393 + ], + "type": "text", + "content": "4. Method" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 400, + 288, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 400, + 288, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 400, + 288, + 665 + ], + "type": "text", + "content": "Previous methods such as ScoreDenoise [28] and IterativePFN [8] focus on filtering as a reverse Markov process where the forward process would correspond to adding noise. We formulate filtering as an optimal transport plan that moves noisy points back to the clean surface along the shortest (straight) path. We model noisy input patches as intermediate states between high noise variants and their corresponding clean counterparts. We design a graph convolution based VelocityModule that infers a constant flow velocity for each intermediate state. This encourages noisy points to move along straight filtering trajectories as shown in Fig. 4. We further improve the straightness of these trajectories via VelocityModule coupling. Finally, as the flow is constant, it may result in filtered points overshooting the clean surface. Therefore, we design a DistanceModule that scales the flow velocity appropriately and ensures convergence near the surface. The overall Straight-PCF architecture is illustrated in Fig. 2, which demonstrates the filtering process that utilizes both the coupled Velocity-Module and DistanceModule sub-networks to move points along straightened paths. The supplementary document provides additional methodology details." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 671, + 194, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 194, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 194, + 684 + ], + "type": "text", + "content": "4.1. Filtering via straight flows" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 714 + ], + "type": "text", + "content": "In this section, we introduce the VelocityModule (VM) that moves noisy points along constant, straight flows to-" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 331, + 70, + 523, + 140 + ], + "blocks": [ + { + "bbox": [ + 331, + 70, + 523, + 140 + ], + "lines": [ + { + "bbox": [ + 331, + 70, + 523, + 140 + ], + "spans": [ + { + "bbox": [ + 331, + 70, + 523, + 140 + ], + "type": "image", + "image_path": "67cc5ddbe1bf6da4c2692472c3ee08c7670097fcb1eca29638cc4308999630a1.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 148, + 547, + 192 + ], + "lines": [ + { + "bbox": [ + 305, + 148, + 547, + 192 + ], + "spans": [ + { + "bbox": [ + 305, + 148, + 547, + 192 + ], + "type": "text", + "content": "Figure 4. StraightPCF models initial noisy patches (light blue) as being intermediate states of a linear interpolation between high noise variants (red) and the clean surfaces (dark blue) and encourages straight filtering trajectories." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "spans": [ + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": "wards the clean surface. Given a noisy patch " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\{\\pmb{x}^i | \\pmb{x}^i \\in kNN(\\pmb{x}^r, \\mathcal{P}_X, k)\\}" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " centered around a reference point " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\pmb{x}^r" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " in the noisy point cloud " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\mathcal{P}_X" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ", the filtering objective aims to move " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\pmb{x}^i" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " towards the underlying clean patch " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\mathbf{Y} = \\{\\pmb{y}^i | \\pmb{y}^i \\in \\mathcal{P}_Y\\}" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ". For the filtering task, learning based methods are typically trained on noisy point clouds with Gaussian noise [6, 28, 29, 35, 45]. Iterative filtering depends on the ability of the method to filter patches from a higher noise level to a lower noise level, with the end result converging to the clean surface. Given the highest noise setting " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\sigma_H" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ", intermediate noise scales at a time " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " can be expressed as " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\sigma = (1 - t)\\sigma_H" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ". Therefore, we model noisy patches " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = \\mathbf{Y} + \\sigma\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " as intermediate states " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "X_t" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ", of the filtering objective that moves points from a high noise variant, " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "X_0 = Y + \\sigma_H\\xi \\wedge \\xi \\sim \\mathcal{N}(0, I)" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " to the clean counterpart " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "X_1 = Y" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ". Here, " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "\\sigma_H = 2\\%" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " of the point cloud's bounding sphere radius and corresponds to the highest noise setting of our training set. We observe that intermediate states " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "X_t" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " can be defined as a linear interpolation of " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "inline_equation", + "content": "X_1" + }, + { + "bbox": [ + 305, + 211, + 546, + 451 + ], + "type": "text", + "content": ", that is, a straight path, such that," + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 375, + 458, + 545, + 471 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 458, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 375, + 458, + 545, + 471 + ], + "type": "interline_equation", + "content": "\\boldsymbol {X} _ {t} = (1 - t) \\boldsymbol {X} _ {0} + t \\boldsymbol {X} _ {1} \\tag {4}", + "image_path": "afe19a63f0c719752c87acf71afd3f0daf78b2cec8a5bfd99d7ce221ebd66591.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "spans": [ + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "text", + "content": "Therefore, we intuit that the filtering objective can be reformulated as an optimal transport process that moves points from " + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_0" + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1" + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "text", + "content": ". The flow of " + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t" + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 479, + 545, + 526 + ], + "type": "text", + "content": " can be expressed via the ordinary differential equation (ODE):" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 390, + 533, + 545, + 546 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 533, + 545, + 546 + ], + "spans": [ + { + "bbox": [ + 390, + 533, + 545, + 546 + ], + "type": "interline_equation", + "content": "\\mathrm {d} \\boldsymbol {X} _ {t} = \\boldsymbol {v} \\left(\\boldsymbol {X} _ {t}\\right) \\mathrm {d} t, \\tag {5}", + "image_path": "bc91ad8700e79bac1e468f0e47820b0838f9d3c30186c99ffd008fb8d23accf7.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "spans": [ + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{v}(\\pmb{X}_t)" + }, + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "type": "text", + "content": " is the velocity field at " + }, + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "type": "inline_equation", + "content": "\\pmb{X}_t" + }, + { + "bbox": [ + 305, + 553, + 545, + 590 + ], + "type": "text", + "content": ". For this ODE process, the linear interpolation of Eq. (4) can be used in the least squares optimization to determine the flow," + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 319, + 596, + 545, + 623 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 319, + 596, + 545, + 623 + ], + "spans": [ + { + "bbox": [ + 319, + 596, + 545, + 623 + ], + "type": "interline_equation", + "content": "\\min _ {v} \\int_ {0} ^ {1} \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\| \\boldsymbol {v} (\\boldsymbol {X} _ {t}) - (\\boldsymbol {X} _ {1} - \\boldsymbol {X} _ {0}) \\| _ {2} ^ {2} \\right] d t, \\tag {6}", + "image_path": "ca14a8c81b63e2f1a0f930391818641321cdf8f63c0b81a0b52995218dd365c3.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": "where times " + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": " are sampled uniformly along " + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "[0,1]" + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": ". However, the velocity field at an intermediate state " + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{X}_t" + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": " cannot be causally determined as both " + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{X}_0" + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{X}_1" + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": " are unknown, during filtering. To address this, our idea is to approximate the velocity field for each " + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "inline_equation", + "content": "\\pmb{X}_t" + }, + { + "bbox": [ + 305, + 629, + 545, + 689 + ], + "type": "text", + "content": " by a neural network." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Training objective for single VM. We use a DGCNN based graph neural network to model a VelocityModule " + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{v}_{\\theta}" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20724" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": "with parameters " + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 72, + 287, + 107 + ], + "type": "text", + "content": " to approximate the flow velocity. To train this VelocityModule, we define the following training objective." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 74, + 115, + 287, + 137 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 115, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 74, + 115, + 287, + 137 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {A} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\| \\boldsymbol {v} _ {\\theta} (\\boldsymbol {X} _ {t}) - \\boldsymbol {\\delta} (\\boldsymbol {X} _ {1}, \\boldsymbol {X} _ {0}) \\| _ {2} ^ {2} \\right], \\tag {7}", + "image_path": "175cbcb775e433995dd4c59986140988b6d5e9578d6e6c63819b0799e731e293.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "spans": [ + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "inline_equation", + "content": "\\delta(X_1, X_0) = X_1 - X_0" + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "text", + "content": ". Hence, at each intermediate state, the corresponding flow velocity is ideally a constant vector that leads to a straight path from " + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "inline_equation", + "content": "X_0" + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "inline_equation", + "content": "X_1" + }, + { + "bbox": [ + 47, + 143, + 287, + 178 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "spans": [ + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "text", + "content": "Filtering objective for single VM. During inference, given a straight flow velocity " + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\pmb{v}_{\\theta}" + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "text", + "content": ", we can move points from " + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\pmb{X}_{\\hat{t} /N}" + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "inline_equation", + "content": "\\pmb{X}_{(\\hat{t} +1) / N}" + }, + { + "bbox": [ + 47, + 178, + 287, + 217 + ], + "type": "text", + "content": " using the Euler method ODE solver:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 93, + 224, + 287, + 247 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 224, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 93, + 224, + 287, + 247 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + 1) / N} = \\tilde {\\boldsymbol {X}} _ {\\hat {t} / N} + \\frac {1}{N} \\boldsymbol {v} _ {\\theta} (\\tilde {\\boldsymbol {X}} _ {\\hat {t} / N}), \\tag {8}", + "image_path": "e269ab140644f03fce34f23ee6cdbe152a684a23f54154a56a94c986f16017de.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "spans": [ + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": " denotes the total number of filtering steps, " + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\hat{t} \\in [0, \\dots, M, \\dots, N-1]" + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": " is an integer time step and " + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_0 = \\pmb{X}_0" + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": ". In practice, filtering starts at an unknown time step " + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\hat{t} = M" + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": ". We do not know the noise scale of the input patch and need to model it as an intermediate state " + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_{M/N}" + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": " of a higher noise variant " + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "inline_equation", + "content": "\\pmb{X}_0" + }, + { + "bbox": [ + 47, + 255, + 287, + 327 + ], + "type": "text", + "content": ". The full position update takes the form," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 93, + 335, + 287, + 368 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 335, + 287, + 368 + ], + "spans": [ + { + "bbox": [ + 93, + 335, + 287, + 368 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {X}} _ {1} = \\tilde {\\boldsymbol {X}} _ {M / N} + \\frac {1}{N} \\sum_ {\\hat {t} = M} ^ {N - 1} \\boldsymbol {v} _ {\\theta} \\left(\\tilde {\\boldsymbol {X}} _ {\\hat {t} / N}\\right), \\tag {9}", + "image_path": "3bd06f99fc78e49654ff491650d688d20870d50180eb13bb78b3099652b00ad1.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 375, + 167, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 375, + 167, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 375, + 167, + 387 + ], + "type": "text", + "content": "Eq. (9) poses two challenges:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 387, + 287, + 471 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 387, + 287, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 287, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 287, + 434 + ], + "type": "text", + "content": "1. The straightness of paths is crucial to reducing the number of total steps and improving efficiency. If paths are not sufficiently straight (i.e., they are curved), we need a higher number of steps to filter points effectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "spans": [ + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "type": "text", + "content": "2. The starting time " + }, + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "type": "inline_equation", + "content": "t = M / N" + }, + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "type": "text", + "content": " is unknown. Applying the Euler method for too many steps, " + }, + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 435, + 287, + 471 + ], + "type": "text", + "content": ", may lead to points not converging at the surface." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 478, + 280, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 280, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 280, + 491 + ], + "type": "text", + "content": "4.2. Straighter flows via VelocityModule coupling" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "spans": [ + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": "Given noisy initial data, the trajectories of points tend to be curved, with limited straightness. One way to improve straightness is to finetune the velocity network on the coupling " + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "inline_equation", + "content": "(\\tilde{X}_0,\\tilde{X}_1)" + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": " to satisfy " + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\tilde{X}_1 = V(\\tilde{X}_0)" + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": ". For filtering, we aim to recover surfaces while preserving local geometric details [35]. Applying such finetuning requires the pre-computation of " + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "inline_equation", + "content": "\\tilde{X}_1" + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": " for all possible surface patches and is infeasible due to the large number of patches in the training set. We propose a simple mechanism to straighten paths by coupling " + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 496, + 287, + 615 + ], + "type": "text", + "content": " VelocityModules together." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": "Training objective for coupled VMs. Given a noisy patch " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": ", we partition the trajectory from " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_t" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_1" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " into " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " segments and obtain the velocity flow " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\pmb{v}_{\\theta}^{k}(\\tilde{\\pmb{X}}_{t_k})" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " at times " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "t_k = (t(K - k) + k) / K" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "k \\in \\{0, 1, \\dots, K - 1\\}" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": ". Intermediate positions at times " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "t_{k+1}" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": " are given by " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_{t_{k+1}} = \\tilde{\\pmb{X}}_{t_k} + (1 / K) \\pmb{v}_{\\theta}^{k}(\\tilde{\\pmb{X}}_{t_k})" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": ". We empirically find that two VelocityModules, i.e., " + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "inline_equation", + "content": "K = 2" + }, + { + "bbox": [ + 46, + 616, + 287, + 713 + ], + "type": "text", + "content": ", provide the best balance between accuracy and efficiency. The Velocity Modules are" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "pretrained using the training objective of Eq. (7) and the coupled VMs are finetuned with the introduced objective," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 315, + 101, + 545, + 169 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 101, + 545, + 169 + ], + "spans": [ + { + "bbox": [ + 315, + 101, + 545, + 169 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {B} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\sum_ {k = 0} ^ {K - 1} \\left\\| \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {k}}\\right) - \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1}, \\boldsymbol {X} _ {0}\\right) \\right\\| _ {2} ^ {2} \\right. \\tag {10} \\\\ \\left. + \\lambda_ {1} \\sum_ {k = 0} ^ {K - 2} \\left\\| \\boldsymbol {\\delta} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {k + 1}}, \\boldsymbol {X} _ {t _ {k + 1}}\\right) \\right\\| _ {2} ^ {2} \\right], \\\\ \\end{array}", + "image_path": "feabbb2437e805d7c835feb5a1890e215ae4467e7f588c0c13cc736650c3ddeb.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": "for " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "K \\geq 2" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\lambda_{1} = 10" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_{t_0} = \\pmb{X}_{t_0} = \\pmb{X}_t" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": ". The first term of " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_B" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": " encourages coupled VelocityModules to infer a constant velocity at times " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "t_k" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": ", while the second encourages filtered points " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_{t_k}" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": " to move closer to interpolated points " + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "inline_equation", + "content": "\\pmb{X}_{t_k}" + }, + { + "bbox": [ + 304, + 175, + 545, + 224 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "spans": [ + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": "Filtering objective for coupled VMs. At inference, we apply a modified form of the Euler method to filter points, similar to Eq. (8). We apply " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": " coupled VelocityModules " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": " times, resulting in " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "T = K \\cdot N" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": " total filtering steps. We adjust our earlier notation of integer time steps such that " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\hat{t} \\in \\{0, K, \\dots, \\hat{M}, \\dots, K(N - 1)\\}" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\hat{M}" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": " is divisible by " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_0 = \\pmb{X}_0" + }, + { + "bbox": [ + 305, + 224, + 545, + 307 + ], + "type": "text", + "content": ". The sequential position update becomes," + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 323, + 321, + 545, + 344 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 323, + 321, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 323, + 321, + 545, + 344 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k + 1) / T} = \\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T} + \\frac {1}{T} \\boldsymbol {v} _ {\\theta} ^ {k} (\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}). \\tag {11}", + "image_path": "475473521e604662a24c3b82e13aa40be00783a444e22274adfa1d87a138460f.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 347, + 545, + 371 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 347, + 545, + 371 + ], + "spans": [ + { + "bbox": [ + 305, + 347, + 545, + 371 + ], + "type": "text", + "content": "The corresponding full position update across time steps " + }, + { + "bbox": [ + 305, + 347, + 545, + 371 + ], + "type": "inline_equation", + "content": "S = \\{\\hat{M},\\hat{M} +K,\\dots ,N(K - 1)\\}" + }, + { + "bbox": [ + 305, + 347, + 545, + 371 + ], + "type": "text", + "content": " is," + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 328, + 376, + 545, + 410 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 376, + 545, + 410 + ], + "spans": [ + { + "bbox": [ + 328, + 376, + 545, + 410 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {X}} _ {1} = \\tilde {\\boldsymbol {X}} _ {\\hat {M} / T} + \\frac {1}{T} \\sum_ {\\hat {t} \\in \\mathcal {S}} \\sum_ {k = 0} ^ {K - 1} \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}\\right). \\tag {12}", + "image_path": "ff3b80d4426811c51f5b7dd6f2c4b33bcaa15d21f86020cf42f15dc1bed90aac.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 426, + 513, + 437 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 426, + 513, + 437 + ], + "spans": [ + { + "bbox": [ + 306, + 426, + 513, + 437 + ], + "type": "text", + "content": "4.3. Distance estimation to the clean surface" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "type": "text", + "content": "We now address the second challenge related to Eq. (9) and introduce the DistanceModule that scales the overall straight trajectory. This leads to better convergence near the surface. The DistanceModule estimates a distance scalar, corresponding to the standard deviation of initial noisy points from the clean surface. More specifically, the DistanceModule " + }, + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "type": "inline_equation", + "content": "\\mathcal{D}_{\\phi}(\\cdot)" + }, + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "type": "text", + "content": " is used to approximate a mapping " + }, + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "type": "inline_equation", + "content": "d_{\\phi}:\\mathbb{R}^{n\\times 3}\\to \\mathbb{R}" + }, + { + "bbox": [ + 304, + 444, + 545, + 540 + ], + "type": "text", + "content": ", such that," + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 346, + 544, + 545, + 559 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 544, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 346, + 544, + 545, + 559 + ], + "type": "interline_equation", + "content": "d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right) = \\operatorname {S i g m o i d} \\left(\\operatorname {M a x} \\left(\\mathcal {D} _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right)\\right)\\right). \\tag {13}", + "image_path": "f5a245fdf68b5d5c4ffb9d2f331a8a2cf74d8a2128c6919d5abc79261510547b.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "content": "The distance " + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "inline_equation", + "content": "d_{\\phi}" + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "content": " is then used to scale the output of VelocityModules, as illustrated in Fig. 5. The DistanceModule is embedded within the StraightPCF architecture (see Fig. 2). We keep the weights of the finetuned coupled VelocityModules fixed when training the DistanceModule. The respective training objective for optimizing the parameters " + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 564, + 545, + 636 + ], + "type": "text", + "content": " is," + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 313, + 650, + 545, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 650, + 545, + 716 + ], + "spans": [ + { + "bbox": [ + 313, + 650, + 545, + 716 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {C} = \\mathbb {E} _ {t \\sim \\mathcal {U} (0, 1)} \\left[ \\left(d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {t _ {0}}\\right) - \\frac {\\| \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1} , \\boldsymbol {X} _ {t _ {0}}\\right) \\| _ {2}}{\\| \\boldsymbol {\\delta} \\left(\\boldsymbol {X} _ {1} , \\boldsymbol {X} _ {0}\\right) \\| _ {2}}\\right) ^ {2} \\right. \\tag {14} \\\\ \\left. + \\lambda_ {2} \\left\\| \\boldsymbol {\\delta} \\left(\\tilde {\\boldsymbol {X}} _ {1}, \\boldsymbol {X} _ {1}\\right) \\right\\| _ {2} ^ {2} \\right], \\\\ \\end{array}", + "image_path": "e7dac70dd7726dd2fb97b590c7fe3c521c32bc3d92647d81b12fd7c2b20da28a.jpg" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20725" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 544, + 296 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 544, + 296 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 544, + 296 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 544, + 296 + ], + "type": "table", + "html": "
Resolution10K (Sparse)50K (Dense)
Noise1%2%3%1%2%3%
MethodCDP2MCDP2MCDP2MCDP2MCDP2MCDP2M
PUNet dataset [44]PCN [35]3.5151.1487.4673.96513.0678.7371.0490.3461.4470.6082.2891.285
PointFilter [45]2.4610.4433.5340.8625.0891.8490.7580.1820.9070.2511.5990.710
Score [28]2.5210.4633.6861.0744.7081.9420.7160.1501.2880.5661.9281.041
PDFlow [29]2.1260.3813.2461.0104.4471.9990.6510.1641.1730.5811.9141.210
DeepPSR [6]2.3530.3063.3500.7344.0751.2420.6490.0760.9970.2961.3440.531
IterativePFN [8]2.0560.2183.0430.5554.2411.3760.6050.0590.8030.1821.9711.012
Ours1.8700.2392.6440.6043.2871.1260.5620.1110.7650.2661.3070.648
PCNet dataset [35]PCN [35]3.8471.2218.7523.04314.5255.8731.2930.2891.9130.5053.2491.076
Score [28]3.3690.8305.1321.1956.7761.9411.0660.1771.6590.3542.4940.657
PointFilter [45]3.0190.8864.8851.2757.0622.0321.0530.1861.3490.2572.2250.491
PDFlow [29]3.2430.6064.5450.9665.9341.4410.9690.1521.6460.4242.4500.569
DeepPSR [6]2.8730.7834.7571.1186.0311.6191.0100.1461.5150.3402.0930.573
IterativePFN [8]2.6210.6984.4391.0116.0261.5600.9130.1391.2510.2382.5290.716
Ours2.7470.5364.0460.7884.9211.0930.8770.1441.1730.2591.8160.445
", + "image_path": "ff1b43ea5fbd0dab3af9418da0884f34bc0aa62594119bcdf283fd60bedb1669.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 304, + 546, + 326 + ], + "lines": [ + { + "bbox": [ + 46, + 304, + 546, + 326 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 546, + 326 + ], + "type": "text", + "content": "Table 1. Quantitative filtering results of recent state-of-the-art methods and our method on the synthetic PUNet and PCNet datasets. Note that our network is lightweight, with just " + }, + { + "bbox": [ + 46, + 304, + 546, + 326 + ], + "type": "inline_equation", + "content": "\\sim 530K" + }, + { + "bbox": [ + 46, + 304, + 546, + 326 + ], + "type": "text", + "content": " parameters (17% of IterativePFN). CD and P2M values are multiplied by " + }, + { + "bbox": [ + 46, + 304, + 546, + 326 + ], + "type": "inline_equation", + "content": "10^{4}" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 52, + 343, + 285, + 415 + ], + "blocks": [ + { + "bbox": [ + 52, + 343, + 285, + 415 + ], + "lines": [ + { + "bbox": [ + 52, + 343, + 285, + 415 + ], + "spans": [ + { + "bbox": [ + 52, + 343, + 285, + 415 + ], + "type": "image", + "image_path": "840f7a8b07a8c99c3ae93b25bb17ed31e970bae683d13969145a81e9130ccb6a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 422, + 287, + 456 + ], + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 456 + ], + "type": "text", + "content": "Figure 5. Left: Filtering by coupled VelocityModules only. Right: Coupled VelocityModules and DistanceModule. Scaled trajectories (green lines) lead to better convergence at the surface." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "spans": [ + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "inline_equation", + "content": "t_0 = t" + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "inline_equation", + "content": "\\tilde{\\pmb{X}}_{t_0} = \\pmb{X}_{t_0} = \\pmb{X}_t" + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": ". The first term of " + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_C" + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": " encourages the DistanceModule to infer the relative distance of " + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "inline_equation", + "content": "\\pmb{X}_{t_0}" + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": " from the clean surface, as compared to " + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "inline_equation", + "content": "\\pmb{X}_0" + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": ". The last term encourages points to return to the clean surface. We set " + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "inline_equation", + "content": "\\lambda_{2} = 2\\times 10^{2}" + }, + { + "bbox": [ + 46, + 477, + 287, + 562 + ], + "type": "text", + "content": " to ensure the loss contribution of the last term is of the same order as that of the first one. Consequently, Eq. (11) becomes," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 53, + 571, + 287, + 609 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 571, + 287, + 609 + ], + "spans": [ + { + "bbox": [ + 53, + 571, + 287, + 609 + ], + "type": "interline_equation", + "content": "\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k + 1) / T} = \\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T} + \\frac {d _ {\\phi} \\left(\\tilde {\\boldsymbol {X}} _ {\\hat {M} / T}\\right)}{T} \\boldsymbol {v} _ {\\theta} ^ {k} \\left(\\tilde {\\boldsymbol {X}} _ {(\\hat {t} + k) / T}\\right). \\tag {15}", + "image_path": "853c71b25e4cf1e8369cec3f49d1fa76a6c892e8811444240dd4fadba315aa75.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 620, + 128, + 634 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 620, + 128, + 634 + ], + "spans": [ + { + "bbox": [ + 47, + 620, + 128, + 634 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 287, + 714 + ], + "type": "text", + "content": "Next, we provide results on synthetic data under Gaussian noise and real-world Kinect [41] and Paris-Rue-Madame [38] data. The supplementary document contains additional results of both conventional and learning based methods on synthetic and real-world scanned data, as well as a comparison of testing times." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 346, + 474, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 346, + 474, + 360 + ], + "spans": [ + { + "bbox": [ + 305, + 346, + 474, + 360 + ], + "type": "text", + "content": "5.1. Training and evaluation details" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "spans": [ + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": "We follow the training procedure of ScoreDenoise [28], and train our model on the PUNet dataset [44] consisting of 40 point clouds for training and 20 point clouds for testing. To ensure consistency with ScoreDenoise's training settings, we add Gaussian noise sampled with standard deviation " + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\sigma_{H} = 2\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": " of the bounding sphere radius to each clean point cloud. Our training procedure only requires the high noise variants and the clean ground truth targets. All intermediate states at noise scales " + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "inline_equation", + "content": "\\sigma = (1 - t)\\sigma_{H}" + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": ", with " + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "inline_equation", + "content": "t \\sim \\mathcal{U}(0,1)" + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": " are created as linear interpolations between these two, initial and final states, as per Eq. (4). For testing, we also consider 10 test point clouds from the PCNet dataset [35] provided by ScoreDenoise. These synthetic point clouds contain Gaussian noise at scales of " + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 365, + 545, + 652 + ], + "type": "text", + "content": " of the point cloud's bounding sphere radius. We use two different sampling densities of 10K and 50K points to evaluate filtering ability across different sparsity settings. Moreover, to assess filtering results on real-world noisy point clouds, we compare methods on the Kinect v1 dataset that comprises of 71 point clouds [41] and 4 scenes extracted from the Paris-Rue-Madame dataset [38]. Finally, we provide a comparison on 4 scenes of the Kitti-360 dataset [20], in the supplementary document. Following [8, 28], all methods are only trained on PUNet with Gaussian noise." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "content": "Implementation. We train and test StraightPCF on a NVIDIA GeForce RTX 3090 GPU using PyTorch. We use the Adam optimizer with a learning rate of " + }, + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "inline_equation", + "content": "1 \\times 10^{-4}" + }, + { + "bbox": [ + 304, + 653, + 546, + 713 + ], + "type": "text", + "content": ". Similar to [8, 28], we use PyTorch3D [36] to compute Chamfer Distance (CD) and Point2Mesh (P2M) metric values." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "20726" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 68, + 545, + 315 + ], + "blocks": [ + { + "bbox": [ + 53, + 68, + 545, + 315 + ], + "lines": [ + { + "bbox": [ + 53, + 68, + 545, + 315 + ], + "spans": [ + { + "bbox": [ + 53, + 68, + 545, + 315 + ], + "type": "image", + "image_path": "07a3f63a3bf81e1c259b8658043d6014b111944b8e4605b44c1147ff8ae1037f.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "lines": [ + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "spans": [ + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "type": "text", + "content": "Figure 6. Visual filtering results for " + }, + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "type": "text", + "content": " resolution shapes " + }, + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "type": "inline_equation", + "content": "(\\sigma = 2\\%)" + }, + { + "bbox": [ + 46, + 322, + 546, + 355 + ], + "type": "text", + "content": " within the PUNet and PCNet datasets. The darker (i.e., more blueish) the better. We achieve both strong point-wise P2M results while also ensuring well distributed points (illustrated by close-ups) unlike DeepPSR or IterativePFN which have holes indicating clustering." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 376, + 212, + 388 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 376, + 212, + 388 + ], + "spans": [ + { + "bbox": [ + 47, + 376, + 212, + 388 + ], + "type": "text", + "content": "5.2. Performance on synthetic data" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": "Table 1 and Fig. 6 illustrate filtering results on the synthetic PUNet and PCNet datasets. Our method has a clear edge over others in recovering the underlying clean point distribution demonstrated by superior CD results across all noise settings. We also achieve strong P2M results on the PUNet dataset. While IterativePFN [8] has marginally better P2M results on the PUNet data, this does not ensure a good distribution of points as evidenced by visual results in Fig. 6. Here, for noisy point clouds at " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " resolution and " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "2\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " noise, IterativePFN exhibits small holes, indicating clustering. Moreover, our network consists of only " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "530\\mathrm{K}" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " parameters and is roughly " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "83\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " smaller than that of IterativePFN, given the latter's " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "3.2\\mathrm{M}" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " parameters. DeepPSR [6], despite using a post-processing regularization step, also suffers from holes and poor point distributions. We also note that IterativePFN generalizes poorly to higher noise scales outside the training noise scales (where maximum noise is " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\sigma = 2\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": "). The ability of our method to generalize well across different data is demonstrated by the superior performance on the PCNet dataset. The PCNet shapes are unseen during training. Our method obtains both superior CD and P2M results over all other methods. At " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "10\\mathrm{K}" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " resolution and " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\sigma = 3\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " noise, our method offers a " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "17.1\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " reduction in CD error and " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "24.1\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " reduction in P2M error. Our method also yields state-of-the-art results at " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "50\\mathrm{K}" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " resolution where, for " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\sigma = 3\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": ", the CD error improvement is " + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "inline_equation", + "content": "13.2\\%" + }, + { + "bbox": [ + 46, + 402, + 289, + 714 + ], + "type": "text", + "content": " and P2M error" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": "improvement is " + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "inline_equation", + "content": "9.4\\%" + }, + { + "bbox": [ + 304, + 376, + 545, + 496 + ], + "type": "text", + "content": ". Visual filtering results in Fig. 6 indicate that our method outperforms others in recovering complex details such as the legs of the Camel which are closely situated. By contrast, methods such as Pointfilter [45] and PDFlow [29] flatten points between these close surfaces while IterativePFN does not recover the body well. Furthermore, on a complex shape as Netsuke, we outperform other methods which either cause clustering (e.g., PDFlow, IterativePFN) at this high noise scale or leave behind noise due to limited filtering ability (e.g., ScoreDenoise)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 504, + 519, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 504, + 519, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 504, + 519, + 515 + ], + "type": "text", + "content": "5.3. Performance on real-world scanned data" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": "Next we consider filtering results on scanned data. Table 2 provides quantitative results on the Kinect dataset and Fig. 7 illustrates visual results on the Paris-Rue-Madame dataset. Our method performs favorably on the Kinect data, obtaining a " + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "inline_equation", + "content": "1.82\\%" + }, + { + "bbox": [ + 304, + 521, + 545, + 713 + ], + "type": "text", + "content": " reduction on CD errors, as compared to IterativePFN [8]. As this data is very sparse, our P2M result is marginally higher than Pointfilter [45] and Score-Denoise [28]. These methods focus on returning points to the surface yet succumb to clustering artifacts whereas our method both recovers surfaces while retaining good point distributions. The Paris-Rue-Madame dataset contains high noise scans due to outdoor environmental factors. In Fig. 7, we visualize filtering results for several most recent, state-of-the-art methods. In general, methods such as PDFlow [29] and DeepPSR [6] perform poorly in removing noisy artifacts while IterativePFN [8] causes points to" + } + ] + } + ], + "index": 6 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "20727" + } + ] + } + ], + "index": 7 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 52, + 68, + 541, + 235 + ], + "blocks": [ + { + "bbox": [ + 52, + 68, + 541, + 235 + ], + "lines": [ + { + "bbox": [ + 52, + 68, + 541, + 235 + ], + "spans": [ + { + "bbox": [ + 52, + 68, + 541, + 235 + ], + "type": "image", + "image_path": "06aadf5b8eca17d9b43a94229ca6d2d8412edec73af59083e5ab12d735f23b14.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 50, + 242, + 541, + 254 + ], + "lines": [ + { + "bbox": [ + 50, + 242, + 541, + 254 + ], + "spans": [ + { + "bbox": [ + 50, + 242, + 541, + 254 + ], + "type": "text", + "content": "Figure 7. Visual filtering results on two scenes of the RueMadame dataset. We show results for the most recent state-of-the-art methods." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 97, + 273, + 237, + 383 + ], + "blocks": [ + { + "bbox": [ + 97, + 273, + 237, + 383 + ], + "lines": [ + { + "bbox": [ + 97, + 273, + 237, + 383 + ], + "spans": [ + { + "bbox": [ + 97, + 273, + 237, + 383 + ], + "type": "table", + "html": "
MethodKinect
CDP2M
ScoreDenoise1.3220.652
Pointfilter1.3770.644
PDFlow1.3340.699
DeepPSR1.4310.715
IterativePFN1.3200.685
Ours1.2960.664
", + "image_path": "1a294babdfa6a490c3d3157afc4d3e5a24b3e8a1c0940b554fd307ab59b0a5ad.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 449, + 287, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 449, + 287, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 449, + 287, + 533 + ], + "type": "text", + "content": "cluster near the original scan lines. Our method, however, recovers the underlying clean surface and ensures a much better point distribution, as evidenced by the close-ups in Scene 1. In Scene 2, PDFlow and IterativePFN are not able to clean the surface of the parked vehicle whereas our method recovers the underlying shape with fewer noisy artifacts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 548, + 219, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 548, + 219, + 562 + ], + "spans": [ + { + "bbox": [ + 47, + 548, + 219, + 562 + ], + "type": "text", + "content": "6. Ablation Study and Discussion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "We train and test several variant architectures in order to ascertain the impact of the proposed VelocityModule (VM) and DistanceModule (DM). The results are given in Table 3. Our coupled VM + DM architecture (V5) increases the parameter number to " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sim 530K" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ". Therefore, we train another Large VM with " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\sim 530K" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": " parameters (V3). We find that directly increasing the parameter number (V3) leads to very limited performance gain while V5 exhibits far superior performance. Furthermore, the coupled VM + DM architecture (V5) significantly outperforms the single VM (V1 and V2) architectures. Finally, there is a noticeable difference in performance with and without a DM as evidenced by the dis" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 273, + 553, + 385 + ], + "blocks": [ + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "lines": [ + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "spans": [ + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "type": "text", + "content": "Table 2. Quantitative results on Kinect data. Our network is lightweight, with just " + }, + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "type": "inline_equation", + "content": "\\sim 530K" + }, + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "type": "text", + "content": " parameters (17% of IterativePFN). CD and P2M values are multiplied by " + }, + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "type": "inline_equation", + "content": "10^{4}" + }, + { + "bbox": [ + 46, + 391, + 287, + 424 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 273, + 553, + 385 + ], + "lines": [ + { + "bbox": [ + 306, + 273, + 553, + 385 + ], + "spans": [ + { + "bbox": [ + 306, + 273, + 553, + 385 + ], + "type": "table", + "html": "
Ablation10K points
1% noise2% noise3% noise
CDP2MCDP2MCDP2M
VI) VM w/o DM2.160.423.060.923.731.42
V2) VM w/ DM2.000.323.060.963.811.55
V3) Large VM2.170.412.990.843.541.29
V4) CVM w/o DM1.970.323.010.923.711.45
V5) CVM w/ DM1.870.242.640.603.291.13
", + "image_path": "1ab66e50877495414dfada2d4a97cfee28a4027c4f1dc19fa32b29460eb7e417.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 393, + 545, + 415 + ], + "lines": [ + { + "bbox": [ + 305, + 393, + 545, + 415 + ], + "spans": [ + { + "bbox": [ + 305, + 393, + 545, + 415 + ], + "type": "text", + "content": "Table 3. Ablation results for different VelocityModule (VM) and DistanceModule (DM) configurations." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 305, + 438, + 545, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 438, + 545, + 474 + ], + "spans": [ + { + "bbox": [ + 305, + 438, + 545, + 474 + ], + "type": "text", + "content": "parity between V4 and V5. We provide further ablations, including higher VM couplings, in the supplementary document." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 475, + 545, + 536 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 536 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 536 + ], + "type": "text", + "content": "**Limitation.** While our StraightPCF yields state-of-the-art results across multiple datasets, we observe relatively low performance on low density or high sparsity data, which is similar to current methods. We provide the visual results in the supplementary document due to space limit." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 548, + 378, + 562 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 548, + 378, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 548, + 378, + 562 + ], + "type": "text", + "content": "7. Conclusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 545, + 713 + ], + "type": "text", + "content": "Recent deep learning based filtering methods focus on moving noisy points along stochastic paths to remove noise from input point clouds. We propose the first study to consider filtering points along straight paths, leading to smaller discretization errors and fewer filtering iterations. This lightweight method, while being parameter efficient, delivers filtered point distributions closer to that of the ground truth distributions without requiring any regularization in loss function or post-processing. 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IEEE Transactions on Visualization and Computer Graphics, 27:2015-2027, 2021. 2, 4, 6, 7" + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "20730" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_content_list.json b/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e55811b138a3a7c92d3bfef4248ca8a0b5902a63 --- /dev/null +++ b/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_content_list.json @@ -0,0 +1,1541 @@ +[ + { + "type": "text", + "text": "Stratified Avatar Generation from Sparse Observations", + "text_level": 1, + "bbox": [ + 204, + 130, + 767, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Han Feng $^{1*,\\star}$ Wenchao Ma $^{2*}$ Quankai Gao $^{3}$ Xianwei Zheng $^{1}$ Nan Xue $^{1,4\\dagger,\\star}$ Huijuan Xu $^{2}$", + "bbox": [ + 88, + 178, + 883, + 200 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ Wuhan University $^{2}$ Pennsylvania State University", + "bbox": [ + 263, + 203, + 705, + 222 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "3University of Southern California 4Ant Group", + "bbox": [ + 277, + 222, + 691, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Project website: https://fhan235.github.io/SAGENet/", + "bbox": [ + 272, + 239, + 691, + 257 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3f30e37e45f7173f0b03808890c0f515ddbd58ee60c61398e582eecfbdd9837f.jpg", + "image_caption": [ + "(a) Sparse Observation" + ], + "image_footnote": [], + "bbox": [ + 91, + 290, + 246, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/03e8b5d8a9ff968ca9fedc567256134d1f9bd8cb6e2e25699ec4944a00767eca.jpg", + "image_caption": [ + "Figure 1. Stratified avatar generation from sparse observations. Given the sensory sparse observation of the body motion: 6-DoF poses of the head and hand marked by RGB axes in (a), our method leverages a disentangled body representation in (b) to reconstruct the upper-body conditioned on the sparse observation in (c), and lower-body conditioned on the upper-body reconstruction in (d) to accomplish the full-body reconstruction in (e)." + ], + "image_footnote": [], + "bbox": [ + 250, + 292, + 403, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5e71c0defd1f51f8b741735623483da121399e7c1a75d854cd46305c96cee9c9.jpg", + "image_caption": [ + "(b) Disentangled Body" + ], + "image_footnote": [], + "bbox": [ + 406, + 292, + 562, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/0bad81b4987a56ef05c1b02711db435f7852158bf8f6115c3d4b15f7e3bc2053.jpg", + "image_caption": [ + "(c) Upper-Body Recon." + ], + "image_footnote": [], + "bbox": [ + 563, + 292, + 720, + 390 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/63dd14f102de6df743ee2edc1f00db180b00ed2d6af010053d48d331c528ad9c.jpg", + "image_caption": [ + "(d) Lower-Body Recon.", + "(e) Full-Body Recon." + ], + "image_footnote": [], + "bbox": [ + 722, + 292, + 877, + 390 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 489, + 313, + 506 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Estimating 3D full-body avatars from AR/VR devices is essential for creating immersive experiences in AR/VR applications. This task is challenging due to the limited input from Head Mounted Devices, which capture only sparse observations from the head and hands. Predicting the full-body avatars, particularly the lower body, from these sparse observations presents significant difficulties. In this paper, we are inspired by the inherent property of the kinematic tree defined in the Skinned Multi-Person Linear (SMPL) model, where the upper body and lower body share only one common ancestor node, bringing the potential of decoupled reconstruction. We propose a stratified approach to decouple the conventional full-body avatar reconstruction pipeline into two stages, with the reconstruction of the upper body first and a subsequent reconstruction of the lower body conditioned on the previous stage. To implement this straightforward idea, we leverage the latent diffusion model as a powerful probabilistic generator, and train it to follow the latent distribution of decoupled motions explored by a VQ-VAE encoder-decoder model. Extensive experiments on AMASS mocap dataset demonstrate our state-of-the-art performance in the reconstruction of full-body motions.", + "bbox": [ + 75, + 512, + 472, + 845 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 486, + 632, + 502 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Generating 3D full-body avatars from observations of Head Mounted Devices (HMDs) is crucial for enhancing immersive AR/VR experiences. HMDs primarily track the head and hands, while leaving the rest of the body unmonitored. This limited motion tracking poses a challenging scenario for accurately reconstructing full-body 3D avatars, particularly in representing the lower body. The high degree of freedom in body movements compounds this difficulty, making the task of reasoning human motion from such sparse observations significantly complex.", + "bbox": [ + 496, + 516, + 890, + 669 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Tremendous efforts have been made to obtain more tracking signals by adding sensors at Pelvis [5, 10, 33] or both Pelvis and Legs [16, 19, 45, 49, 50]. While these approaches provide more data points for avatar construction, they can diminish the user's experience. Wearing extra devices can be cumbersome, potentially interfering with the user's comfort and immersion in the virtual environment. This trade-off highlights the need for innovative solutions that can deliver detailed body tracking without compromising the user's comfort and immersion in AR/VR settings. Accordingly, we are interested in the problem of generating 3D full-body avatars from sparse observations of HMDs that track the motion of the head and two hands, by developing a neural solution that learns the distribution of full-body poses given the sparse observations as the input condition.", + "bbox": [ + 496, + 672, + 892, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\star$ indicates the School of Computer Science, Wuhan University", + "bbox": [ + 99, + 862, + 434, + 875 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* indicates equal contributions.", + "bbox": [ + 102, + 876, + 267, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author: xuanan@ieee.org", + "bbox": [ + 102, + 888, + 352, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "153", + "bbox": [ + 486, + 945, + 511, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recent studies have attempted to address the challenge of sparse observations in HMD-based full-body avatar generation by employing regression-based techniques, as seen in [18, 53], or by adopting generation-based approaches like [7, 11]. These methods typically use deep neural networks to predict human motion within a single, expansive motion space. However, due to the limited data provided by sparse observations, these networks often struggle to fully capture the complexities of human kinematics across such a broad and unified motion space. This limitation frequently results in reconstructions that are unrealistic and lack physical plausibility.", + "bbox": [ + 75, + 90, + 472, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We introduce a new method for reconstructing full-body human motions from sparse observations, called Stratified Avatar Generation (SAGE). Instead of the upper-body motion prediction that has tracking signals of certain upper joints from sparse observations, predicting lower-body motion is not straightforward as no direct tracking signals about any lower-body joint is given. It is noteworthy that SMPL model [22] connects the upper and lower half-body by a single root joint, as shown in Fig. 1 (b), which motivates us to split the full-body motions into upper and lower half-body parts. The benefits are two-fold: 1) the smaller search space achieved by disentanglement facilitates learning and prediction; 2) our stratified design makes the modeling and inferring for lower-body motions more accurate and visually appealing by explicitly modeling the correlation and constraint between two half-body motions. To this end, we use VQ-VAE [43] to encode and reconstruct upper and lower body motions separately.", + "bbox": [ + 75, + 290, + 472, + 563 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With the disentangled latent representation of the upper and lower body motions, we aim to recover the accurate full-body motions from sparse observations with a body-customized latent diffusion model (LDM) [35] in a stratified manner. Specifically, as shown in Fig. 1 (c), Fig. 1(d), and Fig. 1(e), we first find the latent of upper-body motion condition on the sparse observations (i.e., tracking signals of the head and hands in Fig. 1(a)). Then, the latent of lower-body motion is inferred condition on both the predicted upper-body latent and sparse observations. Finally, a full-body decoder takes the two half-body latents as input and outputs the full-body motion.", + "bbox": [ + 75, + 580, + 470, + 762 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In the experiments, we comprehensively justified our intuitive design of disentangling the upper and lower body motion in a stratified manner. On the large-scale motion capture benchmark AMASS [25], our proposed SAGE is exhibiting superior performance in different evaluation settings and particularly performs well in terms of the evaluation metrics for lower-body motion estimation compared to previous state-of-the-art methods.", + "bbox": [ + 75, + 780, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 498, + 89, + 642, + 106 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Motion Reconstruction from Sparse Input", + "text_level": 1, + "bbox": [ + 500, + 114, + 859, + 132 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The task of reconstructing full human body motion from sparse observations has gained significant attention in recent decades within the research community [1, 3, 5, 7, 10, 11, 16, 18, 19, 45, 46, 48-50, 53]. For instance, recent works [16, 19, 45, 49, 50] focus on reconstructing full body motion from six inertial measurement units (IMUs). SIP [45] employs heuristic methods, while DIP [16] pioneers the use of deep neural networks for this task. PIP [50] and TIP [19] further enhance performance by incorporating physics constraints. With the rise of VR/AR applications, researchers turn their attention toward reconstructing full body motion from VR/AR devices, such as head-mounted devices (HMDs), which only provide information about the user's head and hands, posing additional challenges. LoBSTr [48], AvATARPoser [18], and AvATARJLM [53] approach this task as a regression problem, utilizing GRU [48] and Transformer Network [18, 53] to predict the full body pose from sparse observations of HMDs. Another line of methods employs generative models [5, 7, 10, 11]. For example, VAEHMD [10] and FLAG [5] utilize Variational AutoEncoder (VAE) [20] and Normalizing flow [34], respectively. Recent works [7, 11] leverage more powerful diffusion models [15, 37] for motion generation, yielding promising results due to the powerful ability of diffusion models in modeling the conditional probabilistic distribution of full-body motion.", + "bbox": [ + 496, + 138, + 890, + 531 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contrasting with previous methods that model full-body motion in a comprehensive, unified framework, our approach acknowledges the complexities such methods impose on deep learning models, particularly in capturing the intricate kinematics of human motion. Hence, we propose a stratified approach that decouples the conventional full-body avatar reconstruction pipeline, first for the upper body and then for the lower body under the condition of the upper-body.", + "bbox": [ + 496, + 532, + 890, + 669 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Human Motion Generation", + "text_level": 1, + "bbox": [ + 500, + 680, + 746, + 695 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Human motion generation is explored under various input conditions, including text [17, 30, 38, 39, 51], action labels [13, 29], 3D scenes and objects [14, 31, 47], and motion itself [8, 24, 27]. Our work shares similarities with two primary research streams. The first involves diffusion-based motion generation. For instance, [39] is the first to utilize a diffusion model [15, 37] for text-to-motion generation with a transformer network. [31] develops a hierarchical generation pipeline for human-object interaction by generating initial keyframes in the motion sequence and then interpolating between them. Secondly, our approach parallels works like PoseGPT [24], MotionGPT [17], and T2M-GPT [51] in terms of representing human motions with discrete la", + "bbox": [ + 496, + 704, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "154", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "tent. These studies also utilize a VQ-VAE [43] to encode human motion into a discrete latent space, facilitating the subsequent generation process.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The task we aim to address significantly deviates from traditional motion generation tasks like text-to-motion generation, which typically aims to create motions that align with textual descriptions. Our goal is distinctly different: we focus on accurately reconstructing human motion using solely sparse observations.", + "bbox": [ + 75, + 137, + 467, + 227 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. SAGE: Stratified Avatar Generation", + "text_level": 1, + "bbox": [ + 76, + 242, + 405, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "This section introduces the proposed SAGE Network, following our observation about the connection relationship between upper-body and lower-body motions. The overall architecture of our SAGE Net is shown in Fig. 2. Disentangled latent representations for upper-body and lower-body motions are learned in Fig. 2 (a). Subsequently, as illustrated in Fig. 2 (b), we employ a stratified latent diffusion process for full body motion reconstruction.", + "bbox": [ + 75, + 268, + 467, + 388 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Problem Statement and Notation", + "text_level": 1, + "bbox": [ + 76, + 400, + 366, + 415 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Input Signals. Our paper follows the common setting of Head Mounted Devices (HMDs) inputs for motion generation, in which three sensors mounted on the head and, left and right hands are employed to perceive the corresponding joint motions. Formally, the raw input signals are denoted by a time-dependent vector function $\\mathbf{X}(t) = (\\mathbf{x}_h(t),\\mathbf{x}_l(t),\\mathbf{x}_r(t))$ , where the subscripts $h$ , $l$ and $r$ indicate the head, left hand, and right hand, and all these functions are with six degree of freedom for 3D rotation and translation under the global coordinate system. Joint rotations are represented by a six-axis representation, which has been demonstrated to be more suitable for network learning in previous works [54]. Given a time interval with $T$ sampling points, the raw input signals can be denoted in a matrix $\\mathbf{X}_{\\mathrm{raw}}\\in \\mathbb{R}^{T\\times (3\\times (3 + 6))}$ . To enhance the input signals, we follow [18] to compute the positional velocities and angular velocities. This augmentation process adds a 9D input signal for each observed joint, resulting in an 18D input signal per joint at every timestamp. By combining these signals for all joints over all timestamps, we form the complete sparse input signal, represented as $\\mathbf{X}\\in \\mathbb{R}^{T\\times 54}$ .", + "bbox": [ + 75, + 424, + 468, + 741 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Kinematic Tree and SMPL Representation. As shown in Fig. 1 (b), SMPL [22] represents a human pose by a standard skeletal rig, which is widely adopted by current motion generation works. A pose $\\theta^j(t)$ represents the relative rotation of joint $j$ at $t$ th frame with respect to its parent in the kinematic tree. The global rotations $G(\\theta^j(t))$ can be calculated by:", + "bbox": [ + 75, + 762, + 467, + 867 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nG \\left(\\theta^ {j} (t)\\right) = \\prod_ {k \\in A (j)} \\theta^ {k} (t) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 189, + 869, + 467, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $A(j)$ denotes the ordered set of joint ancestors of joint $j$ .", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Articulated motion representation based on the human kinematic tree, is key for realistically simulating human motions and enables efficient control over joint parameters. However, such an intricate articulated motion representation poses a significant challenge for models to learn effectively. In this work, we seek to disentangle this complex representation to enable the model to focus on a limited set of motions and interactions, thereby simplifying the learning process.", + "bbox": [ + 496, + 122, + 890, + 258 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Nevertheless, separating full-body human motions into distinct parts is nontrivial due to the complex correlations among joints. We revisit the human kinematic tree defined in SMPL model, where the upper and lower half-body is connected solely via a root joint. This insight from SMPL model provides a natural solution to separate the articulated full-body motion into two distinct parts: upper-body motion and lower-body motion. Notably, the root joint is included in both two parts as a central element since the parameters of all other joints in each half-body are defined in the local coordinate system of the root joint.", + "bbox": [ + 496, + 260, + 890, + 426 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Outputs. As discussed in the last paragraph for SMPL representation [22], the problem of 3D body avatar generation comes down to the full-body motion estimation of 22 joints (including the root joint), denoted in the set function $\\Theta(t) = \\{\\theta^i(t) \\in \\mathrm{SE}(3) | t \\in \\{t_1, \\ldots, t_T\\}\\}$ as the expected output of our problem. Based on the discussion of SMPL model with the disentangling nature of upper and lower body, we redefine the set function $\\Theta(t)$ in the disentangled way by $\\Theta(t) = \\Theta_{\\mathrm{upper}}(t) \\cup \\Theta_{\\mathrm{lower}}(t)$ , where $\\Theta_{\\mathrm{upper}}(t) = \\{\\theta^0(t), \\ldots, \\theta_u^{b_u}(t)\\}$ , $\\Theta_{\\mathrm{lower}} = \\{\\theta^0(t), \\ldots, \\theta_l^{b_l}(t)\\}$ . These two subsets have only one intersected joint: root joint $\\theta^0$ , and $b_u = 13$ and $b_l = 8$ denote the number of rest joints in the upper and lower body, respectively. For the final output of our method, the dimension of the underlying motion variables is $22 \\times 6 = 132$ at every timestamp.", + "bbox": [ + 496, + 450, + 890, + 695 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. Disentangled Motion Representation", + "text_level": 1, + "bbox": [ + 500, + 708, + 815, + 724 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, our objective is to disentangle full-body human motions into upper-body and lower-body parts and encode them to discrete latent spaces. This can effectively reduce the complexity and burden of encoding since each encoding takes care of only half-body motions.", + "bbox": [ + 496, + 732, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We employ two autoencoders, i.e., VQ-VAE [43, 52], with identical architecture to learn the discrete latent spaces for upper-body and lower-body motions, respectively. As shown in Fig. 2 (a), our VQ-VAE model consists of an encoder and a decoder. The encoder $E$ takes the motion sequence $\\Theta = \\{\\theta_i\\}_{i=1}^T$ as input and encodes it into a series of", + "bbox": [ + 496, + 809, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "155", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/cfa8aacc89e0ef96131745c37cf456053d925ba2f16d305bb42053495f899a49.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 83, + 87, + 885, + 222 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/1505433cfb1c02e88ff88a4ef43df8a5594cbdc37afb0405c0f2f35b10444274.jpg", + "image_caption": [ + "Figure 2. The overall architecture of our SAGE Net. It mainly contains two components: (a) Disentangled VQ-VAE for discrete human motion latent learning. To facilitate visualization, we incorporate zero rotations as padding for the lower body in the Upper VQ-VAE, and vice versa for the Lower VQ-VAE. Consequently, in the visualizations of the Upper VQ-VAE, the lower body remains in a stationary pose, whereas in the visualizations of the Lower VQ-VAE, the upper body is maintained in a T-pose. (b) The stratified diffusion model, which models the conditional distribution of the latent space for upper and lower motion. This model sequentially infers the upper and lower body latents, capturing the correlation between upper and lower motions. By employing a dedicated full-body decoder on the concatenated upper and lower latents, we can obtain full-body motion." + ], + "image_footnote": [], + "bbox": [ + 83, + 222, + 885, + 393 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "continuous latent $E(\\Theta) = H$ , where $H = \\{h_i\\}_{i=1}^{T/l}$ , and $l$ is the temporal down-sampling rate of input motion sequence.", + "bbox": [ + 75, + 527, + 467, + 559 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To quantize the continuous latent, we define the discrete motion latent space by a codebook $C = \\{c_j\\}_{j=1}^N \\in \\mathbb{R}^{N \\times D}$ , where $N = 512$ is the number of entries in the codebook and $D = 384$ is the dimension of each element $c_j$ . The operation $Q$ quantizes the continuous latent $h_i$ into discrete latent $z_i$ by finding its most similar element in $C$ :", + "bbox": [ + 75, + 560, + 467, + 650 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nz _ {i} = Q \\left(h _ {i}\\right) = \\underset {c _ {j} \\in C} {\\arg \\min } \\left\\| h _ {i} - c _ {j} \\right\\| _ {2} \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 156, + 656, + 467, + 683 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since continuous latent from all data samples share the same codebook $C$ , all the real motions in the training set could be expressed by a finite number of bases in latent space.", + "bbox": [ + 75, + 686, + 467, + 746 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Subsequently, the quantified latents $Z$ are fed into the decoder to reconstruct the original motions, given by $\\hat{\\Theta} = D(Z)$ . The training process involves the joint optimization of the encoder and decoder by minimizing the following loss over the training dataset:", + "bbox": [ + 76, + 748, + 467, + 823 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} L o s s _ {v q} = \\operatorname {S m o o t h} _ {L _ {1}} (\\hat {\\Theta}, \\Theta) + \\| \\mathrm {s g} [ Z ] - H \\| _ {2} \\tag {3} \\\\ + \\beta \\| Z - \\operatorname {s g} [ H ] \\| _ {2} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 829, + 467, + 866 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Here, sg denotes the stop gradient operator, and $\\beta$ is a hyperparameter. We have two independent VQ-VAEs for", + "bbox": [ + 75, + 869, + 467, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "upper-body and lower-body motion encoding, which we refer to as VQ-VAE $_{up}$ and VQ-VAE $_{low}$ .", + "bbox": [ + 498, + 529, + 888, + 560 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Stratified Motion Diffusion", + "text_level": 1, + "bbox": [ + 500, + 570, + 743, + 584 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "After encoding and expressing different human motions as latents, we aim to properly sample from the latent space for full-body motion reconstructions and match the sparse observations.", + "bbox": [ + 498, + 594, + 890, + 652 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although disentangling the full-body motions into upper and lower parts enhances effectiveness and efficiency for motion representation learning, it's crucial to include the correlation between two body parts during generation. Otherwise, severe inconsistency would be witnessed in reconstructed full-body motions. To this end, we propose Stratified Motion Diffusion to sample upper-body and lower-body latent in a cascaded manner with explicit considerations of the correlations mentioned above.", + "bbox": [ + 496, + 655, + 890, + 789 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Since the sparse observations are all from the upper body (e.g., head and hand sensors), we first generate upper-body latent $z^{\\hat{u}p}$ by upper diffusion model conditioning on the sparse observations $X$ . Thus the training objective of the upper diffusion model is:", + "bbox": [ + 496, + 791, + 890, + 866 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nL _ {u p} := \\mathbb {E} _ {z ^ {u p}, \\epsilon \\sim \\mathcal {N} (0, 1), k} \\left[ \\| \\epsilon - \\epsilon_ {\\alpha} \\left(z _ {k} ^ {u p}, X, k\\right) \\| _ {2} ^ {2} \\right] \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 524, + 878, + 890, + 905 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "156", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\epsilon$ is the random noise from the normal distribution, $\\epsilon_{\\alpha}$ is the noise predictor of the diffusion model with network parameters $\\alpha$ , and $k$ is the diffusion time step.", + "bbox": [ + 75, + 90, + 468, + 136 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Compared with upper-body latent prediction, directly predicting the lower-body latent $z^{\\hat{low}}$ from the same sparse observations is more challenging due to the absence of direct tracking or supervision for any of the lower-body joints. To make the prediction more physically meaningful, as shown in Fig. 2 (b), we take both the sparse observations $X$ and the generated upper-body latent $z^{\\hat{up}}$ as conditions for lower-body latent prediction by lower diffusion model. This design considers the correlation between two half-body parts and allows more information to be involved for the lower-body inference. The objective for lower diffusion model training is as follows:", + "bbox": [ + 75, + 137, + 470, + 319 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {l o w} := \\mathbb {E} _ {z ^ {l o w}, \\epsilon \\sim \\mathcal {N} (0, 1), k} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\alpha} \\left(z _ {k} ^ {l o w}, (X, z ^ {\\hat {u}} p), k\\right) \\right\\| _ {2} ^ {2} \\right] \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 327, + 468, + 354 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Once two half-body latent $z^{\\hat{u}p}$ and $z^{\\hat{l}ow}$ are obtained, the full-body motions can be recovered with a decoder $\\hat{\\Theta} = D_{full}(z^{\\hat{u}p}, z^{\\hat{l}ow})$ . Instead of directly using pre-trained upper and lower decoders in Fig. 2 (a) to recover the corresponding half-body motions, we train this full-body decoder $E_{full}$ from scratch together with our stratified motion diffusion, which is further optimized to capture the correlations between half-body motions.", + "bbox": [ + 76, + 363, + 468, + 488 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Implementation Details", + "text_level": 1, + "bbox": [ + 76, + 500, + 294, + 513 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Since both sparse observations and human motion occur sequentially, we utilize the widely adopted sequential network, i.e., transformer [44], as the backbone network for the encoder and decoder in the disentangled VQ-VAE [43], and the denoise network in the stratified diffusion model. We set temporal down-sampling rate $l = 2$ to balance the computational cost and the performance. During the training of the latent diffusion model, instead of predicting noise $\\epsilon_{k}$ as formulated by the standard latent diffusion model [35], we follow [32, 39] and directly predict the latent $z$ itself, as we find that this operation can significantly reduce the sampled time steps during inference stage. For training decoders, i.e., $E_{up}, E_{low}$ and $E_{full}$ , in addition to the rotation-level reconstruction loss, we incorporate the forward kinematic loss proposed in [18] and the hand loss described in [53].", + "bbox": [ + 75, + 522, + 468, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For the inference stage, we evaluate our model in an online manner. Specifically, we fix the sequence length at 20 for both the input and the output of our model, and only the last pose in the output motion sequence is retained. Given a sparse observation sequence, we apply our model using a sliding window approach. For the first 20 poses in the motion sequence, we predict by padding the sparse observation sequence $x$ at the beginning with the first available observation. We make this choice considering the practicality and relevance of online inference in real-world application sce", + "bbox": [ + 75, + 750, + 470, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "narios. This allows the motion sequences to be predicted in a frame-by-frame manner.", + "bbox": [ + 498, + 90, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In addition, we employ a simple two-layer GRU [9] on the top of the full body decoder as a temporal memory to smooth the prediction of the output sequence with minimal computational expense, and we term it as a Refiner. To train this Refiner, we use the same velocity loss as [53]. Our model takes $0.74\\mathrm{ms}$ to infer 1 frame on a single NVIDIA RTX3090 GPU.", + "bbox": [ + 496, + 121, + 893, + 227 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 498, + 241, + 831, + 258 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Dataset and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 498, + 267, + 779, + 282 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We train and evaluate our method on AMASS [25], which unifies multiple motion capture datasets [2, 4, 6, 12, 23, 26, 28, 36, 40-42] as SMPL [22] representations.", + "bbox": [ + 496, + 290, + 890, + 335 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We report several metrics for evaluations and comparisons: mean per joint rotation error (MPJRE) and mean per joint position error (MPJPE) for measuring the average relative rotation and position error across all joints respectively, as well as the average position error of the root joints (Root PE), hand joints (Hand PE), upper-body joints (Upper PE), and lower-body joints (Lower PE).", + "bbox": [ + 496, + 337, + 890, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Besides the above reconstruction accuracy, we also evaluate the spatial and temporal consistency of the generated sequences, as it significantly contributes to the visual quality. Specifically, we calculate the mean per joint velocity error (MPJVE) and Jitter, where MPJVE measures the average velocity error of all body joints, and Jitter quantifies the average jerk (time derivative of acceleration) of all body joints. In both cases, lower values indicate better results.", + "bbox": [ + 496, + 443, + 890, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Quantitative and Qualitative Results", + "text_level": 1, + "bbox": [ + 498, + 574, + 816, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "For fair comparison, we follow two settings used in previous works [5, 10, 11, 18, 33, 53] for quantitative and qualitative assessment. Moreover, we propose a new setting in this paper for a more comprehensive evaluation on current methods.", + "bbox": [ + 496, + 598, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the first setting, as previous works [7, 11, 18, 53], subsets CMU [6], BMLrub [40], and HDM05 [28] datasets are randomly divided into $90\\%$ for training and $10\\%$ for testing. Besides sparse observations of three joints, we also evaluate the performance of all compared methods by using four joints as input, including the root joint as an additional input, the same as in [18]. We term this setting as S1 in the following.", + "bbox": [ + 496, + 672, + 890, + 794 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Tabs. 1 and 2 show that our method outperforms existing methods on most evaluation metrics, confirming its effectiveness. For the MPJVE metric, only AGRoL [11] surpasses our method when employing an offline strategy. In this scenario, specifically, AGRoL processes the entire sparse observation sequence in one pass and outputs the predicted full-body motions simultaneously. This enables", + "bbox": [ + 496, + 795, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "157", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/868b2fa3a49d389ce77e03455a7e137aeee3b36174b87219d570c380584a3690.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
Final IK [1]16.7718.0959.24-----
LoBSTr [48]10.699.0244.97-----
VAR-HMD [10]4.116.8337.99-----
Avatarposer [18]3.084.1827.702.121.817.593.3414.49
AvatarJLM [53]2.903.3520.791.241.426.142.948.39
AGRoL (Online) [11]2.964.2679.121.511.737.913.7884.79
AGRoL (Offline) [11]2.663.7118.591.311.556.843.367.26
Ours2.533.2820.621.181.396.012.956.55
", + "bbox": [ + 109, + 88, + 857, + 241 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Evaluation results under setting S1.", + "bbox": [ + 351, + 251, + 614, + 265 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/e543e74a0c1f506186a74bc54c6f6303e8614d77677fd13bab7b0702d64e405f.jpg", + "image_caption": [ + "Figure 3. Visualization results compared with other methods. All models are trained under setting S1." + ], + "image_footnote": [], + "bbox": [ + 86, + 300, + 883, + 688 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "each position in the sequence to utilize the information from both preceding and subsequent time steps, offering an advantage in this particular metric. However, it's important to note that, despite being competitive in metric numbers, offline inference has limited practical applicability in real-world scenarios where online processing capability is most important.", + "bbox": [ + 75, + 736, + 470, + 843 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The second setting follows [5, 10, 11, 33, 53], where we evaluate the methods on a larger benchmark from AMASS [25]. The subsets [2, 4, 6, 12, 21, 23, 26, 26, 28,", + "bbox": [ + 76, + 854, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "40-42, 42] are for training, and Transition [25] and HumanEva [36] subsets are for testing. We term this setting as S2 in the following.", + "bbox": [ + 496, + 736, + 890, + 781 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As shown in Tab. 3, our method achieves comparable performance with previous works on S2. However, we observe that the testing set of S2 is disproportionately small (i.e., only $1\\%$ of the training set). Such a small fraction cannot represent the overall data distribution of the large dataset and may not include sufficiently diverse motions to evaluate the models' scalability, causing unconvincing eval", + "bbox": [ + 496, + 794, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "158", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/49ea08a4bfa927992ef6f2057eccfe47e1be24c456081be4c9acb7f10776ec89.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMPJREMPJPEMPJVE
Final IK [1]12.399.5436.73
CoolMoves [3]4.585.5565.28
LoBSTr [48]8.095.5630.12
VAE-HMD [10]3.123.5128.23
AvatarPoser [18]2.592.6122.16
AvatarJLM [53]2.402.0917.82
AGRoL [11]2.252.1716.26
Ours2.101.8814.79
", + "bbox": [ + 102, + 88, + 444, + 241 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/b837406bb4dc04a62d08c5efb96769781cecde8a65db73b82e7691d357b79762.jpg", + "table_caption": [ + "Table 2. Evaluation results under setting S1 with the root joint as an additional input." + ], + "table_footnote": [], + "table_body": "
MethodMPJREMPJPEMPJVEJitter
VAEHMD†[10]-7.45--
Humor†[33]-5.50--
FLAG†[5]-4.96--
AvatarPoser [18]4.706.3834.0510.21
AGRoL [11]4.306.1724.408.32
AvatarJLM [53]4.304.9326.177.19
Ours4.625.8633.547.13
", + "bbox": [ + 76, + 295, + 467, + 444 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3. Evaluation result under setting S2. $\\dagger$ indicates that these methods use additional inputs of pelvis location and rotation for training and inference, which are not directly comparable methods. The results of AvatarPoser [18] is provided by [11].", + "bbox": [ + 75, + 452, + 468, + 510 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/647a5fadc46381cd914e812c96d7489a2f680eb28713777b7d65dfac25edc678.jpg", + "image_caption": [ + "Figure 4. Visualization results on real data." + ], + "image_footnote": [], + "bbox": [ + 94, + 531, + 455, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "uation results. We introduce a new setting, S3, which adopts the same training and testing splitting ratio used in S1. In this setting, we randomly select $90\\%$ of the samples from the 15 subsets of S2 for training, while the remaining $10\\%$ are for testing. We train and evaluate the compared methods with this new setting. Table 4 reveals that under S3, the performance differences between the compared methods are more significant than S1 and S2. Since the test set has more", + "bbox": [ + 75, + 779, + 470, + 900 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/6f2f1e59031f15aed1de9aebc5a030d4ccb3377d508c5f7c99051887b369e0c5.jpg", + "image_caption": [ + "Figure 5. The visualization comparison for disentanglement. The darker the red color, the greater the deviation is between the predicted result and the ground truth." + ], + "image_footnote": [], + "bbox": [ + 519, + 95, + 875, + 279 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "diverse motions in S3, this benchmark evaluates the models' scalability in a more objective way. In this context, our method outperforms existing methods in most metrics, especially in the critical metric of Lower PE, highlighting the superiority of our stratified design for lower-body modeling and inference.", + "bbox": [ + 496, + 345, + 890, + 435 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Fig. 3 presents a visual comparison between our SAGE Net and baseline methods, all trained under the S1 protocol, which is commonly used by baselines for releasing their trained checkpoints. These visualizations demonstrate the significant improvements that our model offers in reconstructing the lower body. For example, in the first row of samples, baseline methods typically reconstruct the feet too close to the ground, restricting the avatar's leg movements. Our model, however, overcomes this limitation, enabling more flexible leg movements. In the third row, for a subject climbing a ladder, the baseline methods often result in avatars with floating feet, failing to capture the detailed motion of climbing. In contrast, our SAGE Net accurately replicates complex foot movements, resulting in more realistic and precise climbing animations. We also evaluate our model on the real data, and for fair comparison, we directly use the real data release by [53]. As shown in Fig. 4, our method also achieves better reconstruction results on the real data.", + "bbox": [ + 496, + 438, + 892, + 724 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 738, + 653, + 753 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We perform ablation study under S1 to justify the design choice of each component in our SAGE Net.", + "bbox": [ + 496, + 762, + 890, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Disentangled Codebook: We establish a baseline using a unified motion representation to evaluate the disentangle strategy. Specifically, we developed a full-body VQ-VAE model that encodes full-body motion into a single, unified discrete codebook. Other components are the same as the original model. Results shown in the first and the last rows in Table 5, demonstrate that our approach employing dis", + "bbox": [ + 496, + 794, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "159", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/45bd30044f4451417fd97770496d7cd35bed84732dca4932e977465c83fea64f.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
AGRoL(Online) [11]3.094.31109.291.791.807.953.86121.78
AGRoL(Offline) [11]2.833.8017.761.621.666.903.5310.08
AvatarJLM [53]3.143.3915.750.691.486.133.045.33
AvATARposer [18]2.723.3721.002.121.635.872.9010.24
Ours2.412.9516.941.151.285.372.745.27
", + "bbox": [ + 107, + 88, + 859, + 196 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/55762c6acb0a0cd1096783f6cf2f36f65fa22f35705e520b2e2a981171242691.jpg", + "table_caption": [ + "Table 4. Evaluation results under setting S3." + ], + "table_footnote": [], + "table_body": "
MethodMPJREMPJPEMPJVEJitter
w/o Disentangle2.643.6233.1825.07
w/o Full-Body Decoder2.713.6926.0710.80
w/o Refiner2.543.2621.999.29
5 Part Disentanglement2.633.4820.327.16
Ours2.533.2820.626.55
", + "bbox": [ + 83, + 233, + 457, + 325 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/5970bc805e409734633e2d01e43bcbefba25cbc6d6366e71b3dc94644eab508c.jpg", + "table_caption": [ + "Table 5. Ablation results of different components in SAGE Net under setting S1." + ], + "table_footnote": [], + "table_body": "
MethodLowe PEJitter
Parallel Diffusion6.7314.71
Stratified Diffusion6.4610.83
", + "bbox": [ + 133, + 368, + 410, + 430 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 6. Evaluation results on the conditional strategy of the diffusion model under setting S1.", + "bbox": [ + 76, + 436, + 468, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "entangled latents significantly outperforms the baseline on all evaluation metrics. This demonstrates that the disentanglement can simplify the learning process by allowing the model to focus on a more limited set of movements and interactions. Additionally, Fig. 5 shows the visualization comparison between our model and baseline model, verifying that the disentangle can significantly improve the reconstruction results for the most challenging lower motions.", + "bbox": [ + 75, + 477, + 468, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Full-Body Decoder and Refiner: The second and third rows of Tab. 5 demonstrate the impact of the full-body decoder and the refiner, respectively. Compared with utilizing the upper and lower decoder from VQ-VAE $_{up}$ and VQ-VAE $_{low}$ , the full-body decoder facilitates the integration of features from both the upper and lower body, improving the overall accuracy of full-body motion reconstruction. On the other hand, the refiner acts as a temporal memory, smoothing out the motion sequence to yield better visualization results.", + "bbox": [ + 75, + 598, + 468, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Disentanglement Strategy: To investigate the optimal disentanglement strategy, we explore an extreme disentanglement configuration by following the path from the root (Pelvis) node to each leaf node along the kinematic tree. Specifically, we break down the body into five segments: the paths from the root to the left hand (a), right hand (b), head (c), left foot (d), and right foot (e). As reported in the last two rows of Tab. 5, the natural joint interconnections within the upper (or lower) body were disrupted when further disentangling the human body, resulting in perfor", + "bbox": [ + 75, + 750, + 468, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/97bd799511d336aadc985270c806201f8332af4be272527298ada78a57f93dfd.jpg", + "image_caption": [ + "Figure 6. Failure cases. All models are trained under setting S1." + ], + "image_footnote": [], + "bbox": [ + 516, + 234, + 879, + 391 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "mance drops and complicating the model design.", + "bbox": [ + 498, + 422, + 823, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Stratified Inference: Tab. 6 highlights the influence of our stratified design on the accuracy of lower body predictions. For comparison, we design a baseline that only uses the sparse observation for lower body latent generation without predicted upper body latent (term as Parallel Diffusion in the table). As we focus solely on the reconstruction quality of the lower body here, we use the decoding results on the generated lower latents from $\\mathrm{VQ - VAELow}$ to isolate the impact of other modules such as the full-body decoder and refiner. We report Lower PE and Jitter of the lower body for comparison. Results show that our stratified design markedly improves the accuracy of lower body predictions.", + "bbox": [ + 496, + 436, + 890, + 633 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "**Limitation:** In Fig. 6, both the previous state-of-the-art method and our model encounter difficulties in two main situations: (1) External Force-Induced Movements (the top row). (2) Unconventional Poses (the bottom row). The addition of more varied samples to the training dataset can potentially enhance the model's performance in these areas.", + "bbox": [ + 496, + 633, + 890, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 738, + 617, + 753 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We study the problem of human avatar generation from sparse observations. Our key finding is that the upper and lower body motions should be disentangled with respect to the input signals from the upper-body joints. Based on this, we propose a novel stratified solution where the upper-body motion is reconstructed first, and the lower-body motion is reconstructed next and conditioned on the upper-body motion. Our proposed stratified solution achieves superior performance on public available benchmarks.", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "160", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 106 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] RootMotion Final IK., 2018. 2, 6, 7", + "[2] Advanced Computing Center for the Arts and Design. ACCAD MoCap Dataset. 5, 6", + "[3] Karan Ahuja, Eyal Ofek, Mar González-Franco, Christian Holz, and Andrew D. Wilson. Coolmoves: User motion accentuation in virtual reality. Proc. ACM Interact. Mob. Wearable Ubiquitous Technol., 5(2): 52:1-52:23, 2021. 2, 7", + "[4] Ijaz Akhter and Michael J. Black. Pose-conditioned joint angle limits for 3d human pose reconstruction. 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On the continuity of rotation representations in neural networks. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5745-5753, 2019. 3" + ], + "bbox": [ + 78, + 90, + 468, + 703 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "163", + "bbox": [ + 486, + 945, + 509, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_model.json b/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_model.json new file mode 100644 index 0000000000000000000000000000000000000000..3d6e8fd91e2bbf49639321f73f6a51dfc82c194d --- /dev/null +++ b/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_model.json @@ -0,0 +1,2169 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.205, + 0.131, + 0.768, + 0.154 + ], + "angle": 0, + "content": "Stratified Avatar Generation from Sparse Observations" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.179, + 0.884, + 0.201 + ], + "angle": 0, + "content": "Han Feng\\(^{1*,\\star}\\) Wenchao Ma\\(^{2*}\\) Quankai Gao\\(^{3}\\) Xianwei Zheng\\(^{1}\\) Nan Xue\\(^{1,4\\dagger,\\star}\\) Huijuan Xu\\(^{2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.264, + 0.204, + 0.707, + 0.223 + ], + "angle": 0, + "content": "\\(^{1}\\)Wuhan University \\(^{2}\\)Pennsylvania State University" + }, + { + "type": "text", + "bbox": [ + 0.278, + 0.223, + 0.692, + 0.241 + ], + "angle": 0, + "content": "3University of Southern California 4Ant Group" + }, + { + "type": "text", + "bbox": [ + 0.274, + 0.241, + 0.692, + 0.258 + ], + "angle": 0, + "content": "Project website: https://fhan235.github.io/SAGENet/" + }, + { + "type": "image", + "bbox": [ + 0.092, + 0.291, + 0.247, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.102, + 0.394, + 0.239, + 0.408 + ], + "angle": 0, + "content": "(a) Sparse Observation" + }, + { + "type": "image", + "bbox": [ + 0.25, + 0.293, + 0.405, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.259, + 0.394, + 0.396, + 0.408 + ], + "angle": 0, + "content": "(b) Disentangled Body" + }, + { + "type": "image", + "bbox": [ + 0.408, + 0.293, + 0.563, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.415, + 0.394, + 0.555, + 0.408 + ], + "angle": 0, + "content": "(c) Upper-Body Recon." + }, + { + "type": "image", + "bbox": [ + 0.565, + 0.293, + 0.721, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.572, + 0.394, + 0.714, + 0.408 + ], + "angle": 0, + "content": "(d) Lower-Body Recon." + }, + { + "type": "image", + "bbox": [ + 0.723, + 0.293, + 0.879, + 0.391 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.738, + 0.394, + 0.864, + 0.408 + ], + "angle": 0, + "content": "(e) Full-Body Recon." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.418, + 0.895, + 0.475 + ], + "angle": 0, + "content": "Figure 1. Stratified avatar generation from sparse observations. Given the sensory sparse observation of the body motion: 6-DoF poses of the head and hand marked by RGB axes in (a), our method leverages a disentangled body representation in (b) to reconstruct the upper-body conditioned on the sparse observation in (c), and lower-body conditioned on the upper-body reconstruction in (d) to accomplish the full-body reconstruction in (e)." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.491, + 0.314, + 0.507 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.473, + 0.846 + ], + "angle": 0, + "content": "Estimating 3D full-body avatars from AR/VR devices is essential for creating immersive experiences in AR/VR applications. This task is challenging due to the limited input from Head Mounted Devices, which capture only sparse observations from the head and hands. Predicting the full-body avatars, particularly the lower body, from these sparse observations presents significant difficulties. In this paper, we are inspired by the inherent property of the kinematic tree defined in the Skinned Multi-Person Linear (SMPL) model, where the upper body and lower body share only one common ancestor node, bringing the potential of decoupled reconstruction. We propose a stratified approach to decouple the conventional full-body avatar reconstruction pipeline into two stages, with the reconstruction of the upper body first and a subsequent reconstruction of the lower body conditioned on the previous stage. To implement this straightforward idea, we leverage the latent diffusion model as a powerful probabilistic generator, and train it to follow the latent distribution of decoupled motions explored by a VQ-VAE encoder-decoder model. Extensive experiments on AMASS mocap dataset demonstrate our state-of-the-art performance in the reconstruction of full-body motions." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.487, + 0.633, + 0.503 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.517, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Generating 3D full-body avatars from observations of Head Mounted Devices (HMDs) is crucial for enhancing immersive AR/VR experiences. HMDs primarily track the head and hands, while leaving the rest of the body unmonitored. This limited motion tracking poses a challenging scenario for accurately reconstructing full-body 3D avatars, particularly in representing the lower body. The high degree of freedom in body movements compounds this difficulty, making the task of reasoning human motion from such sparse observations significantly complex." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Tremendous efforts have been made to obtain more tracking signals by adding sensors at Pelvis [5, 10, 33] or both Pelvis and Legs [16, 19, 45, 49, 50]. While these approaches provide more data points for avatar construction, they can diminish the user's experience. Wearing extra devices can be cumbersome, potentially interfering with the user's comfort and immersion in the virtual environment. This trade-off highlights the need for innovative solutions that can deliver detailed body tracking without compromising the user's comfort and immersion in AR/VR settings. Accordingly, we are interested in the problem of generating 3D full-body avatars from sparse observations of HMDs that track the motion of the head and two hands, by developing a neural solution that learns the distribution of full-body poses given the sparse observations as the input condition." + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.863, + 0.436, + 0.876 + ], + "angle": 0, + "content": "\\(\\star\\) indicates the School of Computer Science, Wuhan University" + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.877, + 0.269, + 0.888 + ], + "angle": 0, + "content": "* indicates equal contributions." + }, + { + "type": "page_footnote", + "bbox": [ + 0.103, + 0.889, + 0.354, + 0.9 + ], + "angle": 0, + "content": "† Corresponding author: xuanan@ieee.org" + }, + { + "type": "list", + "bbox": [ + 0.1, + 0.863, + 0.436, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.512, + 0.957 + ], + "angle": 0, + "content": "153" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.273 + ], + "angle": 0, + "content": "Recent studies have attempted to address the challenge of sparse observations in HMD-based full-body avatar generation by employing regression-based techniques, as seen in [18, 53], or by adopting generation-based approaches like [7, 11]. These methods typically use deep neural networks to predict human motion within a single, expansive motion space. However, due to the limited data provided by sparse observations, these networks often struggle to fully capture the complexities of human kinematics across such a broad and unified motion space. This limitation frequently results in reconstructions that are unrealistic and lack physical plausibility." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.291, + 0.473, + 0.564 + ], + "angle": 0, + "content": "We introduce a new method for reconstructing full-body human motions from sparse observations, called Stratified Avatar Generation (SAGE). Instead of the upper-body motion prediction that has tracking signals of certain upper joints from sparse observations, predicting lower-body motion is not straightforward as no direct tracking signals about any lower-body joint is given. It is noteworthy that SMPL model [22] connects the upper and lower half-body by a single root joint, as shown in Fig. 1 (b), which motivates us to split the full-body motions into upper and lower half-body parts. The benefits are two-fold: 1) the smaller search space achieved by disentanglement facilitates learning and prediction; 2) our stratified design makes the modeling and inferring for lower-body motions more accurate and visually appealing by explicitly modeling the correlation and constraint between two half-body motions. To this end, we use VQ-VAE [43] to encode and reconstruct upper and lower body motions separately." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.472, + 0.763 + ], + "angle": 0, + "content": "With the disentangled latent representation of the upper and lower body motions, we aim to recover the accurate full-body motions from sparse observations with a body-customized latent diffusion model (LDM) [35] in a stratified manner. Specifically, as shown in Fig. 1 (c), Fig. 1(d), and Fig. 1(e), we first find the latent of upper-body motion condition on the sparse observations (i.e., tracking signals of the head and hands in Fig. 1(a)). Then, the latent of lower-body motion is inferred condition on both the predicted upper-body latent and sparse observations. Finally, a full-body decoder takes the two half-body latents as input and outputs the full-body motion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.781, + 0.472, + 0.903 + ], + "angle": 0, + "content": "In the experiments, we comprehensively justified our intuitive design of disentangling the upper and lower body motion in a stratified manner. On the large-scale motion capture benchmark AMASS [25], our proposed SAGE is exhibiting superior performance in different evaluation settings and particularly performs well in terms of the evaluation metrics for lower-body motion estimation compared to previous state-of-the-art methods." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.09, + 0.643, + 0.107 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.115, + 0.86, + 0.133 + ], + "angle": 0, + "content": "2.1. Motion Reconstruction from Sparse Input" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.14, + 0.892, + 0.532 + ], + "angle": 0, + "content": "The task of reconstructing full human body motion from sparse observations has gained significant attention in recent decades within the research community [1, 3, 5, 7, 10, 11, 16, 18, 19, 45, 46, 48-50, 53]. For instance, recent works [16, 19, 45, 49, 50] focus on reconstructing full body motion from six inertial measurement units (IMUs). SIP [45] employs heuristic methods, while DIP [16] pioneers the use of deep neural networks for this task. PIP [50] and TIP [19] further enhance performance by incorporating physics constraints. With the rise of VR/AR applications, researchers turn their attention toward reconstructing full body motion from VR/AR devices, such as head-mounted devices (HMDs), which only provide information about the user's head and hands, posing additional challenges. LoBSTr [48], AvATARPoser [18], and AvATARJLM [53] approach this task as a regression problem, utilizing GRU [48] and Transformer Network [18, 53] to predict the full body pose from sparse observations of HMDs. Another line of methods employs generative models [5, 7, 10, 11]. For example, VAEHMD [10] and FLAG [5] utilize Variational AutoEncoder (VAE) [20] and Normalizing flow [34], respectively. Recent works [7, 11] leverage more powerful diffusion models [15, 37] for motion generation, yielding promising results due to the powerful ability of diffusion models in modeling the conditional probabilistic distribution of full-body motion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.533, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Contrasting with previous methods that model full-body motion in a comprehensive, unified framework, our approach acknowledges the complexities such methods impose on deep learning models, particularly in capturing the intricate kinematics of human motion. Hence, we propose a stratified approach that decouples the conventional full-body avatar reconstruction pipeline, first for the upper body and then for the lower body under the condition of the upper-body." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.681, + 0.747, + 0.696 + ], + "angle": 0, + "content": "2.2. Human Motion Generation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.705, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Human motion generation is explored under various input conditions, including text [17, 30, 38, 39, 51], action labels [13, 29], 3D scenes and objects [14, 31, 47], and motion itself [8, 24, 27]. Our work shares similarities with two primary research streams. The first involves diffusion-based motion generation. For instance, [39] is the first to utilize a diffusion model [15, 37] for text-to-motion generation with a transformer network. [31] develops a hierarchical generation pipeline for human-object interaction by generating initial keyframes in the motion sequence and then interpolating between them. Secondly, our approach parallels works like PoseGPT [24], MotionGPT [17], and T2M-GPT [51] in terms of representing human motions with discrete la" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "154" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "tent. These studies also utilize a VQ-VAE [43] to encode human motion into a discrete latent space, facilitating the subsequent generation process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.468, + 0.228 + ], + "angle": 0, + "content": "The task we aim to address significantly deviates from traditional motion generation tasks like text-to-motion generation, which typically aims to create motions that align with textual descriptions. Our goal is distinctly different: we focus on accurately reconstructing human motion using solely sparse observations." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.243, + 0.406, + 0.26 + ], + "angle": 0, + "content": "3. SAGE: Stratified Avatar Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.269, + 0.468, + 0.39 + ], + "angle": 0, + "content": "This section introduces the proposed SAGE Network, following our observation about the connection relationship between upper-body and lower-body motions. The overall architecture of our SAGE Net is shown in Fig. 2. Disentangled latent representations for upper-body and lower-body motions are learned in Fig. 2 (a). Subsequently, as illustrated in Fig. 2 (b), we employ a stratified latent diffusion process for full body motion reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.401, + 0.367, + 0.416 + ], + "angle": 0, + "content": "3.1. Problem Statement and Notation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.425, + 0.47, + 0.742 + ], + "angle": 0, + "content": "Input Signals. Our paper follows the common setting of Head Mounted Devices (HMDs) inputs for motion generation, in which three sensors mounted on the head and, left and right hands are employed to perceive the corresponding joint motions. Formally, the raw input signals are denoted by a time-dependent vector function \\(\\mathbf{X}(t) = (\\mathbf{x}_h(t),\\mathbf{x}_l(t),\\mathbf{x}_r(t))\\), where the subscripts \\(h\\), \\(l\\) and \\(r\\) indicate the head, left hand, and right hand, and all these functions are with six degree of freedom for 3D rotation and translation under the global coordinate system. Joint rotations are represented by a six-axis representation, which has been demonstrated to be more suitable for network learning in previous works [54]. Given a time interval with \\(T\\) sampling points, the raw input signals can be denoted in a matrix \\(\\mathbf{X}_{\\mathrm{raw}}\\in \\mathbb{R}^{T\\times (3\\times (3 + 6))}\\). To enhance the input signals, we follow [18] to compute the positional velocities and angular velocities. This augmentation process adds a 9D input signal for each observed joint, resulting in an 18D input signal per joint at every timestamp. By combining these signals for all joints over all timestamps, we form the complete sparse input signal, represented as \\(\\mathbf{X}\\in \\mathbb{R}^{T\\times 54}\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.763, + 0.468, + 0.868 + ], + "angle": 0, + "content": "Kinematic Tree and SMPL Representation. As shown in Fig. 1 (b), SMPL [22] represents a human pose by a standard skeletal rig, which is widely adopted by current motion generation works. A pose \\(\\theta^j(t)\\) represents the relative rotation of joint \\(j\\) at \\(t\\)th frame with respect to its parent in the kinematic tree. The global rotations \\(G(\\theta^j(t))\\) can be calculated by:" + }, + { + "type": "equation", + "bbox": [ + 0.19, + 0.87, + 0.468, + 0.904 + ], + "angle": 0, + "content": "\\[\nG \\left(\\theta^ {j} (t)\\right) = \\prod_ {k \\in A (j)} \\theta^ {k} (t) \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "where \\(A(j)\\) denotes the ordered set of joint ancestors of joint \\(j\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.123, + 0.892, + 0.259 + ], + "angle": 0, + "content": "Articulated motion representation based on the human kinematic tree, is key for realistically simulating human motions and enables efficient control over joint parameters. However, such an intricate articulated motion representation poses a significant challenge for models to learn effectively. In this work, we seek to disentangle this complex representation to enable the model to focus on a limited set of motions and interactions, thereby simplifying the learning process." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.261, + 0.892, + 0.427 + ], + "angle": 0, + "content": "Nevertheless, separating full-body human motions into distinct parts is nontrivial due to the complex correlations among joints. We revisit the human kinematic tree defined in SMPL model, where the upper and lower half-body is connected solely via a root joint. This insight from SMPL model provides a natural solution to separate the articulated full-body motion into two distinct parts: upper-body motion and lower-body motion. Notably, the root joint is included in both two parts as a central element since the parameters of all other joints in each half-body are defined in the local coordinate system of the root joint." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.452, + 0.892, + 0.696 + ], + "angle": 0, + "content": "The Outputs. As discussed in the last paragraph for SMPL representation [22], the problem of 3D body avatar generation comes down to the full-body motion estimation of 22 joints (including the root joint), denoted in the set function \\(\\Theta(t) = \\{\\theta^i(t) \\in \\mathrm{SE}(3) | t \\in \\{t_1, \\ldots, t_T\\}\\}\\) as the expected output of our problem. Based on the discussion of SMPL model with the disentangling nature of upper and lower body, we redefine the set function \\(\\Theta(t)\\) in the disentangled way by \\(\\Theta(t) = \\Theta_{\\mathrm{upper}}(t) \\cup \\Theta_{\\mathrm{lower}}(t)\\), where \\(\\Theta_{\\mathrm{upper}}(t) = \\{\\theta^0(t), \\ldots, \\theta_u^{b_u}(t)\\}\\), \\(\\Theta_{\\mathrm{lower}} = \\{\\theta^0(t), \\ldots, \\theta_l^{b_l}(t)\\}\\). These two subsets have only one intersected joint: root joint \\(\\theta^0\\), and \\(b_u = 13\\) and \\(b_l = 8\\) denote the number of rest joints in the upper and lower body, respectively. For the final output of our method, the dimension of the underlying motion variables is \\(22 \\times 6 = 132\\) at every timestamp." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.709, + 0.816, + 0.725 + ], + "angle": 0, + "content": "3.2. Disentangled Motion Representation" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.733, + 0.891, + 0.809 + ], + "angle": 0, + "content": "In this section, our objective is to disentangle full-body human motions into upper-body and lower-body parts and encode them to discrete latent spaces. This can effectively reduce the complexity and burden of encoding since each encoding takes care of only half-body motions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We employ two autoencoders, i.e., VQ-VAE [43, 52], with identical architecture to learn the discrete latent spaces for upper-body and lower-body motions, respectively. As shown in Fig. 2 (a), our VQ-VAE model consists of an encoder and a decoder. The encoder \\( E \\) takes the motion sequence \\( \\Theta = \\{\\theta_i\\}_{i=1}^T \\) as input and encodes it into a series of" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "155" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.088, + 0.887, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.223, + 0.887, + 0.395 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.406, + 0.892, + 0.504 + ], + "angle": 0, + "content": "Figure 2. The overall architecture of our SAGE Net. It mainly contains two components: (a) Disentangled VQ-VAE for discrete human motion latent learning. To facilitate visualization, we incorporate zero rotations as padding for the lower body in the Upper VQ-VAE, and vice versa for the Lower VQ-VAE. Consequently, in the visualizations of the Upper VQ-VAE, the lower body remains in a stationary pose, whereas in the visualizations of the Lower VQ-VAE, the upper body is maintained in a T-pose. (b) The stratified diffusion model, which models the conditional distribution of the latent space for upper and lower motion. This model sequentially infers the upper and lower body latents, capturing the correlation between upper and lower motions. By employing a dedicated full-body decoder on the concatenated upper and lower latents, we can obtain full-body motion." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.468, + 0.56 + ], + "angle": 0, + "content": "continuous latent \\( E(\\Theta) = H \\), where \\( H = \\{h_i\\}_{i=1}^{T/l} \\), and \\( l \\) is the temporal down-sampling rate of input motion sequence." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.561, + 0.468, + 0.651 + ], + "angle": 0, + "content": "To quantize the continuous latent, we define the discrete motion latent space by a codebook \\(C = \\{c_j\\}_{j=1}^N \\in \\mathbb{R}^{N \\times D}\\), where \\(N = 512\\) is the number of entries in the codebook and \\(D = 384\\) is the dimension of each element \\(c_j\\). The operation \\(Q\\) quantizes the continuous latent \\(h_i\\) into discrete latent \\(z_i\\) by finding its most similar element in \\(C\\):" + }, + { + "type": "equation", + "bbox": [ + 0.158, + 0.657, + 0.468, + 0.684 + ], + "angle": 0, + "content": "\\[\nz _ {i} = Q \\left(h _ {i}\\right) = \\underset {c _ {j} \\in C} {\\arg \\min } \\left\\| h _ {i} - c _ {j} \\right\\| _ {2} \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.688, + 0.468, + 0.747 + ], + "angle": 0, + "content": "Since continuous latent from all data samples share the same codebook \\( C \\), all the real motions in the training set could be expressed by a finite number of bases in latent space." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.749, + 0.468, + 0.824 + ], + "angle": 0, + "content": "Subsequently, the quantified latents \\( Z \\) are fed into the decoder to reconstruct the original motions, given by \\( \\hat{\\Theta} = D(Z) \\). The training process involves the joint optimization of the encoder and decoder by minimizing the following loss over the training dataset:" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.83, + 0.468, + 0.867 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} L o s s _ {v q} = \\operatorname {S m o o t h} _ {L _ {1}} (\\hat {\\Theta}, \\Theta) + \\| \\mathrm {s g} [ Z ] - H \\| _ {2} \\tag {3} \\\\ + \\beta \\| Z - \\operatorname {s g} [ H ] \\| _ {2} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.468, + 0.902 + ], + "angle": 0, + "content": "Here, sg denotes the stop gradient operator, and \\(\\beta\\) is a hyperparameter. We have two independent VQ-VAEs for" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.53, + 0.89, + 0.561 + ], + "angle": 0, + "content": "upper-body and lower-body motion encoding, which we refer to as VQ-VAE\\(_{up}\\) and VQ-VAE\\(_{low}\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.571, + 0.744, + 0.585 + ], + "angle": 0, + "content": "3.3. Stratified Motion Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.595, + 0.891, + 0.654 + ], + "angle": 0, + "content": "After encoding and expressing different human motions as latents, we aim to properly sample from the latent space for full-body motion reconstructions and match the sparse observations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.656, + 0.892, + 0.79 + ], + "angle": 0, + "content": "Although disentangling the full-body motions into upper and lower parts enhances effectiveness and efficiency for motion representation learning, it's crucial to include the correlation between two body parts during generation. Otherwise, severe inconsistency would be witnessed in reconstructed full-body motions. To this end, we propose Stratified Motion Diffusion to sample upper-body and lower-body latent in a cascaded manner with explicit considerations of the correlations mentioned above." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.792, + 0.891, + 0.867 + ], + "angle": 0, + "content": "Since the sparse observations are all from the upper body (e.g., head and hand sensors), we first generate upper-body latent \\( z^{\\hat{u}p} \\) by upper diffusion model conditioning on the sparse observations \\( X \\). Thus the training objective of the upper diffusion model is:" + }, + { + "type": "equation", + "bbox": [ + 0.526, + 0.879, + 0.891, + 0.906 + ], + "angle": 0, + "content": "\\[\nL _ {u p} := \\mathbb {E} _ {z ^ {u p}, \\epsilon \\sim \\mathcal {N} (0, 1), k} \\left[ \\| \\epsilon - \\epsilon_ {\\alpha} \\left(z _ {k} ^ {u p}, X, k\\right) \\| _ {2} ^ {2} \\right] \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "156" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "where \\(\\epsilon\\) is the random noise from the normal distribution, \\(\\epsilon_{\\alpha}\\) is the noise predictor of the diffusion model with network parameters \\(\\alpha\\), and \\(k\\) is the diffusion time step." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.138, + 0.471, + 0.32 + ], + "angle": 0, + "content": "Compared with upper-body latent prediction, directly predicting the lower-body latent \\( z^{\\hat{low}} \\) from the same sparse observations is more challenging due to the absence of direct tracking or supervision for any of the lower-body joints. To make the prediction more physically meaningful, as shown in Fig. 2 (b), we take both the sparse observations \\( X \\) and the generated upper-body latent \\( z^{\\hat{up}} \\) as conditions for lower-body latent prediction by lower diffusion model. This design considers the correlation between two half-body parts and allows more information to be involved for the lower-body inference. The objective for lower diffusion model training is as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.328, + 0.47, + 0.356 + ], + "angle": 0, + "content": "\\[\nL _ {l o w} := \\mathbb {E} _ {z ^ {l o w}, \\epsilon \\sim \\mathcal {N} (0, 1), k} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\alpha} \\left(z _ {k} ^ {l o w}, (X, z ^ {\\hat {u}} p), k\\right) \\right\\| _ {2} ^ {2} \\right] \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.364, + 0.47, + 0.489 + ], + "angle": 0, + "content": "Once two half-body latent \\( z^{\\hat{u}p} \\) and \\( z^{\\hat{l}ow} \\) are obtained, the full-body motions can be recovered with a decoder \\( \\hat{\\Theta} = D_{full}(z^{\\hat{u}p}, z^{\\hat{l}ow}) \\). Instead of directly using pre-trained upper and lower decoders in Fig. 2 (a) to recover the corresponding half-body motions, we train this full-body decoder \\( E_{full} \\) from scratch together with our stratified motion diffusion, which is further optimized to capture the correlations between half-body motions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.5, + 0.295, + 0.515 + ], + "angle": 0, + "content": "3.4. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.523, + 0.47, + 0.75 + ], + "angle": 0, + "content": "Since both sparse observations and human motion occur sequentially, we utilize the widely adopted sequential network, i.e., transformer [44], as the backbone network for the encoder and decoder in the disentangled VQ-VAE [43], and the denoise network in the stratified diffusion model. We set temporal down-sampling rate \\( l = 2 \\) to balance the computational cost and the performance. During the training of the latent diffusion model, instead of predicting noise \\( \\epsilon_{k} \\) as formulated by the standard latent diffusion model [35], we follow [32, 39] and directly predict the latent \\( z \\) itself, as we find that this operation can significantly reduce the sampled time steps during inference stage. For training decoders, i.e., \\( E_{up}, E_{low} \\) and \\( E_{full} \\), in addition to the rotation-level reconstruction loss, we incorporate the forward kinematic loss proposed in [18] and the hand loss described in [53]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.751, + 0.471, + 0.902 + ], + "angle": 0, + "content": "For the inference stage, we evaluate our model in an online manner. Specifically, we fix the sequence length at 20 for both the input and the output of our model, and only the last pose in the output motion sequence is retained. Given a sparse observation sequence, we apply our model using a sliding window approach. For the first 20 poses in the motion sequence, we predict by padding the sparse observation sequence \\( x \\) at the beginning with the first available observation. We make this choice considering the practicality and relevance of online inference in real-world application sce" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.121 + ], + "angle": 0, + "content": "narios. This allows the motion sequences to be predicted in a frame-by-frame manner." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.122, + 0.894, + 0.228 + ], + "angle": 0, + "content": "In addition, we employ a simple two-layer GRU [9] on the top of the full body decoder as a temporal memory to smooth the prediction of the output sequence with minimal computational expense, and we term it as a Refiner. To train this Refiner, we use the same velocity loss as [53]. Our model takes \\(0.74\\mathrm{ms}\\) to infer 1 frame on a single NVIDIA RTX3090 GPU." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.242, + 0.833, + 0.26 + ], + "angle": 0, + "content": "4. Experiments and Evaluation Metrics" + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.268, + 0.78, + 0.283 + ], + "angle": 0, + "content": "4.1. Dataset and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.291, + 0.892, + 0.337 + ], + "angle": 0, + "content": "We train and evaluate our method on AMASS [25], which unifies multiple motion capture datasets [2, 4, 6, 12, 23, 26, 28, 36, 40-42] as SMPL [22] representations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.338, + 0.892, + 0.442 + ], + "angle": 0, + "content": "We report several metrics for evaluations and comparisons: mean per joint rotation error (MPJRE) and mean per joint position error (MPJPE) for measuring the average relative rotation and position error across all joints respectively, as well as the average position error of the root joints (Root PE), hand joints (Hand PE), upper-body joints (Upper PE), and lower-body joints (Lower PE)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.565 + ], + "angle": 0, + "content": "Besides the above reconstruction accuracy, we also evaluate the spatial and temporal consistency of the generated sequences, as it significantly contributes to the visual quality. Specifically, we calculate the mean per joint velocity error (MPJVE) and Jitter, where MPJVE measures the average velocity error of all body joints, and Jitter quantifies the average jerk (time derivative of acceleration) of all body joints. In both cases, lower values indicate better results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.575, + 0.818, + 0.591 + ], + "angle": 0, + "content": "4.2. Quantitative and Qualitative Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.673 + ], + "angle": 0, + "content": "For fair comparison, we follow two settings used in previous works [5, 10, 11, 18, 33, 53] for quantitative and qualitative assessment. Moreover, we propose a new setting in this paper for a more comprehensive evaluation on current methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.674, + 0.892, + 0.795 + ], + "angle": 0, + "content": "In the first setting, as previous works [7, 11, 18, 53], subsets CMU [6], BMLrub [40], and HDM05 [28] datasets are randomly divided into \\(90\\%\\) for training and \\(10\\%\\) for testing. Besides sparse observations of three joints, we also evaluate the performance of all compared methods by using four joints as input, including the root joint as an additional input, the same as in [18]. We term this setting as S1 in the following." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Tabs. 1 and 2 show that our method outperforms existing methods on most evaluation metrics, confirming its effectiveness. For the MPJVE metric, only AGRoL [11] surpasses our method when employing an offline strategy. In this scenario, specifically, AGRoL processes the entire sparse observation sequence in one pass and outputs the predicted full-body motions simultaneously. This enables" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "157" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.859, + 0.242 + ], + "angle": 0, + "content": "
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
Final IK [1]16.7718.0959.24-----
LoBSTr [48]10.699.0244.97-----
VAR-HMD [10]4.116.8337.99-----
Avatarposer [18]3.084.1827.702.121.817.593.3414.49
AvatarJLM [53]2.903.3520.791.241.426.142.948.39
AGRoL (Online) [11]2.964.2679.121.511.737.913.7884.79
AGRoL (Offline) [11]2.663.7118.591.311.556.843.367.26
Ours2.533.2820.621.181.396.012.956.55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.352, + 0.252, + 0.616, + 0.266 + ], + "angle": 0, + "content": "Table 1. Evaluation results under setting S1." + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.301, + 0.884, + 0.689 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.182, + 0.696, + 0.785, + 0.71 + ], + "angle": 0, + "content": "Figure 3. Visualization results compared with other methods. All models are trained under setting S1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.737, + 0.471, + 0.844 + ], + "angle": 0, + "content": "each position in the sequence to utilize the information from both preceding and subsequent time steps, offering an advantage in this particular metric. However, it's important to note that, despite being competitive in metric numbers, offline inference has limited practical applicability in real-world scenarios where online processing capability is most important." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.471, + 0.901 + ], + "angle": 0, + "content": "The second setting follows [5, 10, 11, 33, 53], where we evaluate the methods on a larger benchmark from AMASS [25]. The subsets [2, 4, 6, 12, 21, 23, 26, 26, 28," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.737, + 0.892, + 0.782 + ], + "angle": 0, + "content": "40-42, 42] are for training, and Transition [25] and HumanEva [36] subsets are for testing. We term this setting as S2 in the following." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.893, + 0.901 + ], + "angle": 0, + "content": "As shown in Tab. 3, our method achieves comparable performance with previous works on S2. However, we observe that the testing set of S2 is disproportionately small (i.e., only \\(1\\%\\) of the training set). Such a small fraction cannot represent the overall data distribution of the large dataset and may not include sufficiently diverse motions to evaluate the models' scalability, causing unconvincing eval" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "158" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.104, + 0.089, + 0.445, + 0.242 + ], + "angle": 0, + "content": "
MethodMPJREMPJPEMPJVE
Final IK [1]12.399.5436.73
CoolMoves [3]4.585.5565.28
LoBSTr [48]8.095.5630.12
VAE-HMD [10]3.123.5128.23
AvatarPoser [18]2.592.6122.16
AvatarJLM [53]2.402.0917.82
AGRoL [11]2.252.1716.26
Ours2.101.8814.79
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.252, + 0.47, + 0.281 + ], + "angle": 0, + "content": "Table 2. Evaluation results under setting S1 with the root joint as an additional input." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.296, + 0.468, + 0.445 + ], + "angle": 0, + "content": "
MethodMPJREMPJPEMPJVEJitter
VAEHMD†[10]-7.45--
Humor†[33]-5.50--
FLAG†[5]-4.96--
AvatarPoser [18]4.706.3834.0510.21
AGRoL [11]4.306.1724.408.32
AvatarJLM [53]4.304.9326.177.19
Ours4.625.8633.547.13
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.453, + 0.47, + 0.511 + ], + "angle": 0, + "content": "Table 3. Evaluation result under setting S2. \\(\\dagger\\) indicates that these methods use additional inputs of pelvis location and rotation for training and inference, which are not directly comparable methods. The results of AvatarPoser [18] is provided by [11]." + }, + { + "type": "image", + "bbox": [ + 0.095, + 0.532, + 0.456, + 0.727 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.144, + 0.737, + 0.402, + 0.751 + ], + "angle": 0, + "content": "Figure 4. Visualization results on real data." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.471, + 0.901 + ], + "angle": 0, + "content": "uation results. We introduce a new setting, S3, which adopts the same training and testing splitting ratio used in S1. In this setting, we randomly select \\(90\\%\\) of the samples from the 15 subsets of S2 for training, while the remaining \\(10\\%\\) are for testing. We train and evaluate the compared methods with this new setting. Table 4 reveals that under S3, the performance differences between the compared methods are more significant than S1 and S2. Since the test set has more" + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.096, + 0.877, + 0.28 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.289, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Figure 5. The visualization comparison for disentanglement. The darker the red color, the greater the deviation is between the predicted result and the ground truth." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.892, + 0.436 + ], + "angle": 0, + "content": "diverse motions in S3, this benchmark evaluates the models' scalability in a more objective way. In this context, our method outperforms existing methods in most metrics, especially in the critical metric of Lower PE, highlighting the superiority of our stratified design for lower-body modeling and inference." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.439, + 0.893, + 0.726 + ], + "angle": 0, + "content": "Fig. 3 presents a visual comparison between our SAGE Net and baseline methods, all trained under the S1 protocol, which is commonly used by baselines for releasing their trained checkpoints. These visualizations demonstrate the significant improvements that our model offers in reconstructing the lower body. For example, in the first row of samples, baseline methods typically reconstruct the feet too close to the ground, restricting the avatar's leg movements. Our model, however, overcomes this limitation, enabling more flexible leg movements. In the third row, for a subject climbing a ladder, the baseline methods often result in avatars with floating feet, failing to capture the detailed motion of climbing. In contrast, our SAGE Net accurately replicates complex foot movements, resulting in more realistic and precise climbing animations. We also evaluate our model on the real data, and for fair comparison, we directly use the real data release by [53]. As shown in Fig. 4, our method also achieves better reconstruction results on the real data." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.655, + 0.755 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.763, + 0.892, + 0.793 + ], + "angle": 0, + "content": "We perform ablation study under S1 to justify the design choice of each component in our SAGE Net." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Disentangled Codebook: We establish a baseline using a unified motion representation to evaluate the disentangle strategy. Specifically, we developed a full-body VQ-VAE model that encodes full-body motion into a single, unified discrete codebook. Other components are the same as the original model. Results shown in the first and the last rows in Table 5, demonstrate that our approach employing dis" + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "159" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.109, + 0.089, + 0.861, + 0.198 + ], + "angle": 0, + "content": "
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
AGRoL(Online) [11]3.094.31109.291.791.807.953.86121.78
AGRoL(Offline) [11]2.833.8017.761.621.666.903.5310.08
AvatarJLM [53]3.143.3915.750.691.486.133.045.33
AvATARposer [18]2.723.3721.002.121.635.872.9010.24
Ours2.412.9516.941.151.285.372.745.27
" + }, + { + "type": "table_caption", + "bbox": [ + 0.352, + 0.207, + 0.616, + 0.221 + ], + "angle": 0, + "content": "Table 4. Evaluation results under setting S3." + }, + { + "type": "table", + "bbox": [ + 0.084, + 0.234, + 0.459, + 0.327 + ], + "angle": 0, + "content": "
MethodMPJREMPJPEMPJVEJitter
w/o Disentangle2.643.6233.1825.07
w/o Full-Body Decoder2.713.6926.0710.80
w/o Refiner2.543.2621.999.29
5 Part Disentanglement2.633.4820.327.16
Ours2.533.2820.626.55
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.334, + 0.47, + 0.362 + ], + "angle": 0, + "content": "Table 5. Ablation results of different components in SAGE Net under setting S1." + }, + { + "type": "table", + "bbox": [ + 0.134, + 0.369, + 0.411, + 0.431 + ], + "angle": 0, + "content": "
MethodLowe PEJitter
Parallel Diffusion6.7314.71
Stratified Diffusion6.4610.83
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.438, + 0.47, + 0.466 + ], + "angle": 0, + "content": "Table 6. Evaluation results on the conditional strategy of the diffusion model under setting S1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.478, + 0.469, + 0.599 + ], + "angle": 0, + "content": "entangled latents significantly outperforms the baseline on all evaluation metrics. This demonstrates that the disentanglement can simplify the learning process by allowing the model to focus on a more limited set of movements and interactions. Additionally, Fig. 5 shows the visualization comparison between our model and baseline model, verifying that the disentangle can significantly improve the reconstruction results for the most challenging lower motions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.749 + ], + "angle": 0, + "content": "Full-Body Decoder and Refiner: The second and third rows of Tab. 5 demonstrate the impact of the full-body decoder and the refiner, respectively. Compared with utilizing the upper and lower decoder from VQ-VAE\\(_{up}\\) and VQ-VAE\\(_{low}\\), the full-body decoder facilitates the integration of features from both the upper and lower body, improving the overall accuracy of full-body motion reconstruction. On the other hand, the refiner acts as a temporal memory, smoothing out the motion sequence to yield better visualization results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.75, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Disentanglement Strategy: To investigate the optimal disentanglement strategy, we explore an extreme disentanglement configuration by following the path from the root (Pelvis) node to each leaf node along the kinematic tree. Specifically, we break down the body into five segments: the paths from the root to the left hand (a), right hand (b), head (c), left foot (d), and right foot (e). As reported in the last two rows of Tab. 5, the natural joint interconnections within the upper (or lower) body were disrupted when further disentangling the human body, resulting in perfor" + }, + { + "type": "image", + "bbox": [ + 0.517, + 0.236, + 0.88, + 0.392 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.504, + 0.4, + 0.885, + 0.415 + ], + "angle": 0, + "content": "Figure 6. Failure cases. All models are trained under setting S1." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.424, + 0.824, + 0.438 + ], + "angle": 0, + "content": "mance drops and complicating the model design." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.438, + 0.892, + 0.635 + ], + "angle": 0, + "content": "Stratified Inference: Tab. 6 highlights the influence of our stratified design on the accuracy of lower body predictions. For comparison, we design a baseline that only uses the sparse observation for lower body latent generation without predicted upper body latent (term as Parallel Diffusion in the table). As we focus solely on the reconstruction quality of the lower body here, we use the decoding results on the generated lower latents from \\(\\mathrm{VQ - VAELow}\\) to isolate the impact of other modules such as the full-body decoder and refiner. We report Lower PE and Jitter of the lower body for comparison. Results show that our stratified design markedly improves the accuracy of lower body predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.635, + 0.892, + 0.727 + ], + "angle": 0, + "content": "**Limitation:** In Fig. 6, both the previous state-of-the-art method and our model encounter difficulties in two main situations: (1) External Force-Induced Movements (the top row). (2) Unconventional Poses (the bottom row). The addition of more varied samples to the training dataset can potentially enhance the model's performance in these areas." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.739, + 0.619, + 0.755 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We study the problem of human avatar generation from sparse observations. Our key finding is that the upper and lower body motions should be disentangled with respect to the input signals from the upper-body joints. Based on this, we propose a novel stratified solution where the upper-body motion is reconstructed first, and the lower-body motion is reconstructed next and conditioned on the upper-body motion. Our proposed stratified solution achieves superior performance on public available benchmarks." + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.957 + ], + "angle": 0, + "content": "160" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.079, + 0.09, + 0.176, + 0.107 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.352, + 0.13 + ], + "angle": 0, + "content": "[1] RootMotion Final IK., 2018. 2, 6, 7" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.132, + 0.468, + 0.162 + ], + "angle": 0, + "content": "[2] Advanced Computing Center for the Arts and Design. ACCAD MoCap Dataset. 5, 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.164, + 0.468, + 0.239 + ], + "angle": 0, + "content": "[3] Karan Ahuja, Eyal Ofek, Mar González-Franco, Christian Holz, and Andrew D. Wilson. Coolmoves: User motion accentuation in virtual reality. Proc. ACM Interact. Mob. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5745-5753, 2019. 3" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.091, + 0.47, + 0.704 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.488, + 0.946, + 0.511, + 0.956 + ], + "angle": 0, + "content": "163" + } + ] +] \ No newline at end of file diff --git a/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_origin.pdf b/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ce06a7ace797ba5eb357b15d4e438c7de57ce696 --- /dev/null +++ b/2024/Stratified Avatar Generation from Sparse Observations/efda3faf-6f32-487b-b0f2-cf234b098ea4_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:4031cae913ca0766b68967a5059654a2483aa8e1730c97f80ed961dcf68f3225 +size 8753504 diff --git a/2024/Stratified Avatar Generation from Sparse Observations/full.md b/2024/Stratified Avatar Generation from Sparse Observations/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f2a57316741ba330a89d68877faa00ab53e292e1 --- /dev/null +++ b/2024/Stratified Avatar Generation from Sparse Observations/full.md @@ -0,0 +1,295 @@ +# Stratified Avatar Generation from Sparse Observations + +Han Feng $^{1*,\star}$ Wenchao Ma $^{2*}$ Quankai Gao $^{3}$ Xianwei Zheng $^{1}$ Nan Xue $^{1,4\dagger,\star}$ Huijuan Xu $^{2}$ + +$^{1}$ Wuhan University $^{2}$ Pennsylvania State University + +3University of Southern California 4Ant Group + +Project website: https://fhan235.github.io/SAGENet/ + +![](images/3f30e37e45f7173f0b03808890c0f515ddbd58ee60c61398e582eecfbdd9837f.jpg) +(a) Sparse Observation + +![](images/03e8b5d8a9ff968ca9fedc567256134d1f9bd8cb6e2e25699ec4944a00767eca.jpg) +Figure 1. Stratified avatar generation from sparse observations. Given the sensory sparse observation of the body motion: 6-DoF poses of the head and hand marked by RGB axes in (a), our method leverages a disentangled body representation in (b) to reconstruct the upper-body conditioned on the sparse observation in (c), and lower-body conditioned on the upper-body reconstruction in (d) to accomplish the full-body reconstruction in (e). + +![](images/5e71c0defd1f51f8b741735623483da121399e7c1a75d854cd46305c96cee9c9.jpg) +(b) Disentangled Body + +![](images/0bad81b4987a56ef05c1b02711db435f7852158bf8f6115c3d4b15f7e3bc2053.jpg) +(c) Upper-Body Recon. + +![](images/63dd14f102de6df743ee2edc1f00db180b00ed2d6af010053d48d331c528ad9c.jpg) +(d) Lower-Body Recon. +(e) Full-Body Recon. + +# Abstract + +Estimating 3D full-body avatars from AR/VR devices is essential for creating immersive experiences in AR/VR applications. This task is challenging due to the limited input from Head Mounted Devices, which capture only sparse observations from the head and hands. Predicting the full-body avatars, particularly the lower body, from these sparse observations presents significant difficulties. In this paper, we are inspired by the inherent property of the kinematic tree defined in the Skinned Multi-Person Linear (SMPL) model, where the upper body and lower body share only one common ancestor node, bringing the potential of decoupled reconstruction. We propose a stratified approach to decouple the conventional full-body avatar reconstruction pipeline into two stages, with the reconstruction of the upper body first and a subsequent reconstruction of the lower body conditioned on the previous stage. To implement this straightforward idea, we leverage the latent diffusion model as a powerful probabilistic generator, and train it to follow the latent distribution of decoupled motions explored by a VQ-VAE encoder-decoder model. Extensive experiments on AMASS mocap dataset demonstrate our state-of-the-art performance in the reconstruction of full-body motions. + +# 1. Introduction + +Generating 3D full-body avatars from observations of Head Mounted Devices (HMDs) is crucial for enhancing immersive AR/VR experiences. HMDs primarily track the head and hands, while leaving the rest of the body unmonitored. This limited motion tracking poses a challenging scenario for accurately reconstructing full-body 3D avatars, particularly in representing the lower body. The high degree of freedom in body movements compounds this difficulty, making the task of reasoning human motion from such sparse observations significantly complex. + +Tremendous efforts have been made to obtain more tracking signals by adding sensors at Pelvis [5, 10, 33] or both Pelvis and Legs [16, 19, 45, 49, 50]. While these approaches provide more data points for avatar construction, they can diminish the user's experience. Wearing extra devices can be cumbersome, potentially interfering with the user's comfort and immersion in the virtual environment. This trade-off highlights the need for innovative solutions that can deliver detailed body tracking without compromising the user's comfort and immersion in AR/VR settings. Accordingly, we are interested in the problem of generating 3D full-body avatars from sparse observations of HMDs that track the motion of the head and two hands, by developing a neural solution that learns the distribution of full-body poses given the sparse observations as the input condition. + +Recent studies have attempted to address the challenge of sparse observations in HMD-based full-body avatar generation by employing regression-based techniques, as seen in [18, 53], or by adopting generation-based approaches like [7, 11]. These methods typically use deep neural networks to predict human motion within a single, expansive motion space. However, due to the limited data provided by sparse observations, these networks often struggle to fully capture the complexities of human kinematics across such a broad and unified motion space. This limitation frequently results in reconstructions that are unrealistic and lack physical plausibility. + +We introduce a new method for reconstructing full-body human motions from sparse observations, called Stratified Avatar Generation (SAGE). Instead of the upper-body motion prediction that has tracking signals of certain upper joints from sparse observations, predicting lower-body motion is not straightforward as no direct tracking signals about any lower-body joint is given. It is noteworthy that SMPL model [22] connects the upper and lower half-body by a single root joint, as shown in Fig. 1 (b), which motivates us to split the full-body motions into upper and lower half-body parts. The benefits are two-fold: 1) the smaller search space achieved by disentanglement facilitates learning and prediction; 2) our stratified design makes the modeling and inferring for lower-body motions more accurate and visually appealing by explicitly modeling the correlation and constraint between two half-body motions. To this end, we use VQ-VAE [43] to encode and reconstruct upper and lower body motions separately. + +With the disentangled latent representation of the upper and lower body motions, we aim to recover the accurate full-body motions from sparse observations with a body-customized latent diffusion model (LDM) [35] in a stratified manner. Specifically, as shown in Fig. 1 (c), Fig. 1(d), and Fig. 1(e), we first find the latent of upper-body motion condition on the sparse observations (i.e., tracking signals of the head and hands in Fig. 1(a)). Then, the latent of lower-body motion is inferred condition on both the predicted upper-body latent and sparse observations. Finally, a full-body decoder takes the two half-body latents as input and outputs the full-body motion. + +In the experiments, we comprehensively justified our intuitive design of disentangling the upper and lower body motion in a stratified manner. On the large-scale motion capture benchmark AMASS [25], our proposed SAGE is exhibiting superior performance in different evaluation settings and particularly performs well in terms of the evaluation metrics for lower-body motion estimation compared to previous state-of-the-art methods. + +# 2. Related Work + +# 2.1. Motion Reconstruction from Sparse Input + +The task of reconstructing full human body motion from sparse observations has gained significant attention in recent decades within the research community [1, 3, 5, 7, 10, 11, 16, 18, 19, 45, 46, 48-50, 53]. For instance, recent works [16, 19, 45, 49, 50] focus on reconstructing full body motion from six inertial measurement units (IMUs). SIP [45] employs heuristic methods, while DIP [16] pioneers the use of deep neural networks for this task. PIP [50] and TIP [19] further enhance performance by incorporating physics constraints. With the rise of VR/AR applications, researchers turn their attention toward reconstructing full body motion from VR/AR devices, such as head-mounted devices (HMDs), which only provide information about the user's head and hands, posing additional challenges. LoBSTr [48], AvATARPoser [18], and AvATARJLM [53] approach this task as a regression problem, utilizing GRU [48] and Transformer Network [18, 53] to predict the full body pose from sparse observations of HMDs. Another line of methods employs generative models [5, 7, 10, 11]. For example, VAEHMD [10] and FLAG [5] utilize Variational AutoEncoder (VAE) [20] and Normalizing flow [34], respectively. Recent works [7, 11] leverage more powerful diffusion models [15, 37] for motion generation, yielding promising results due to the powerful ability of diffusion models in modeling the conditional probabilistic distribution of full-body motion. + +Contrasting with previous methods that model full-body motion in a comprehensive, unified framework, our approach acknowledges the complexities such methods impose on deep learning models, particularly in capturing the intricate kinematics of human motion. Hence, we propose a stratified approach that decouples the conventional full-body avatar reconstruction pipeline, first for the upper body and then for the lower body under the condition of the upper-body. + +# 2.2. Human Motion Generation + +Human motion generation is explored under various input conditions, including text [17, 30, 38, 39, 51], action labels [13, 29], 3D scenes and objects [14, 31, 47], and motion itself [8, 24, 27]. Our work shares similarities with two primary research streams. The first involves diffusion-based motion generation. For instance, [39] is the first to utilize a diffusion model [15, 37] for text-to-motion generation with a transformer network. [31] develops a hierarchical generation pipeline for human-object interaction by generating initial keyframes in the motion sequence and then interpolating between them. Secondly, our approach parallels works like PoseGPT [24], MotionGPT [17], and T2M-GPT [51] in terms of representing human motions with discrete la + +tent. These studies also utilize a VQ-VAE [43] to encode human motion into a discrete latent space, facilitating the subsequent generation process. + +The task we aim to address significantly deviates from traditional motion generation tasks like text-to-motion generation, which typically aims to create motions that align with textual descriptions. Our goal is distinctly different: we focus on accurately reconstructing human motion using solely sparse observations. + +# 3. SAGE: Stratified Avatar Generation + +This section introduces the proposed SAGE Network, following our observation about the connection relationship between upper-body and lower-body motions. The overall architecture of our SAGE Net is shown in Fig. 2. Disentangled latent representations for upper-body and lower-body motions are learned in Fig. 2 (a). Subsequently, as illustrated in Fig. 2 (b), we employ a stratified latent diffusion process for full body motion reconstruction. + +# 3.1. Problem Statement and Notation + +Input Signals. Our paper follows the common setting of Head Mounted Devices (HMDs) inputs for motion generation, in which three sensors mounted on the head and, left and right hands are employed to perceive the corresponding joint motions. Formally, the raw input signals are denoted by a time-dependent vector function $\mathbf{X}(t) = (\mathbf{x}_h(t),\mathbf{x}_l(t),\mathbf{x}_r(t))$ , where the subscripts $h$ , $l$ and $r$ indicate the head, left hand, and right hand, and all these functions are with six degree of freedom for 3D rotation and translation under the global coordinate system. Joint rotations are represented by a six-axis representation, which has been demonstrated to be more suitable for network learning in previous works [54]. Given a time interval with $T$ sampling points, the raw input signals can be denoted in a matrix $\mathbf{X}_{\mathrm{raw}}\in \mathbb{R}^{T\times (3\times (3 + 6))}$ . To enhance the input signals, we follow [18] to compute the positional velocities and angular velocities. This augmentation process adds a 9D input signal for each observed joint, resulting in an 18D input signal per joint at every timestamp. By combining these signals for all joints over all timestamps, we form the complete sparse input signal, represented as $\mathbf{X}\in \mathbb{R}^{T\times 54}$ . + +Kinematic Tree and SMPL Representation. As shown in Fig. 1 (b), SMPL [22] represents a human pose by a standard skeletal rig, which is widely adopted by current motion generation works. A pose $\theta^j(t)$ represents the relative rotation of joint $j$ at $t$ th frame with respect to its parent in the kinematic tree. The global rotations $G(\theta^j(t))$ can be calculated by: + +$$ +G \left(\theta^ {j} (t)\right) = \prod_ {k \in A (j)} \theta^ {k} (t) \tag {1} +$$ + +where $A(j)$ denotes the ordered set of joint ancestors of joint $j$ . + +Articulated motion representation based on the human kinematic tree, is key for realistically simulating human motions and enables efficient control over joint parameters. However, such an intricate articulated motion representation poses a significant challenge for models to learn effectively. In this work, we seek to disentangle this complex representation to enable the model to focus on a limited set of motions and interactions, thereby simplifying the learning process. + +Nevertheless, separating full-body human motions into distinct parts is nontrivial due to the complex correlations among joints. We revisit the human kinematic tree defined in SMPL model, where the upper and lower half-body is connected solely via a root joint. This insight from SMPL model provides a natural solution to separate the articulated full-body motion into two distinct parts: upper-body motion and lower-body motion. Notably, the root joint is included in both two parts as a central element since the parameters of all other joints in each half-body are defined in the local coordinate system of the root joint. + +The Outputs. As discussed in the last paragraph for SMPL representation [22], the problem of 3D body avatar generation comes down to the full-body motion estimation of 22 joints (including the root joint), denoted in the set function $\Theta(t) = \{\theta^i(t) \in \mathrm{SE}(3) | t \in \{t_1, \ldots, t_T\}\}$ as the expected output of our problem. Based on the discussion of SMPL model with the disentangling nature of upper and lower body, we redefine the set function $\Theta(t)$ in the disentangled way by $\Theta(t) = \Theta_{\mathrm{upper}}(t) \cup \Theta_{\mathrm{lower}}(t)$ , where $\Theta_{\mathrm{upper}}(t) = \{\theta^0(t), \ldots, \theta_u^{b_u}(t)\}$ , $\Theta_{\mathrm{lower}} = \{\theta^0(t), \ldots, \theta_l^{b_l}(t)\}$ . These two subsets have only one intersected joint: root joint $\theta^0$ , and $b_u = 13$ and $b_l = 8$ denote the number of rest joints in the upper and lower body, respectively. For the final output of our method, the dimension of the underlying motion variables is $22 \times 6 = 132$ at every timestamp. + +# 3.2. Disentangled Motion Representation + +In this section, our objective is to disentangle full-body human motions into upper-body and lower-body parts and encode them to discrete latent spaces. This can effectively reduce the complexity and burden of encoding since each encoding takes care of only half-body motions. + +We employ two autoencoders, i.e., VQ-VAE [43, 52], with identical architecture to learn the discrete latent spaces for upper-body and lower-body motions, respectively. As shown in Fig. 2 (a), our VQ-VAE model consists of an encoder and a decoder. The encoder $E$ takes the motion sequence $\Theta = \{\theta_i\}_{i=1}^T$ as input and encodes it into a series of + +![](images/cfa8aacc89e0ef96131745c37cf456053d925ba2f16d305bb42053495f899a49.jpg) + +![](images/1505433cfb1c02e88ff88a4ef43df8a5594cbdc37afb0405c0f2f35b10444274.jpg) +Figure 2. The overall architecture of our SAGE Net. It mainly contains two components: (a) Disentangled VQ-VAE for discrete human motion latent learning. To facilitate visualization, we incorporate zero rotations as padding for the lower body in the Upper VQ-VAE, and vice versa for the Lower VQ-VAE. Consequently, in the visualizations of the Upper VQ-VAE, the lower body remains in a stationary pose, whereas in the visualizations of the Lower VQ-VAE, the upper body is maintained in a T-pose. (b) The stratified diffusion model, which models the conditional distribution of the latent space for upper and lower motion. This model sequentially infers the upper and lower body latents, capturing the correlation between upper and lower motions. By employing a dedicated full-body decoder on the concatenated upper and lower latents, we can obtain full-body motion. + +continuous latent $E(\Theta) = H$ , where $H = \{h_i\}_{i=1}^{T/l}$ , and $l$ is the temporal down-sampling rate of input motion sequence. + +To quantize the continuous latent, we define the discrete motion latent space by a codebook $C = \{c_j\}_{j=1}^N \in \mathbb{R}^{N \times D}$ , where $N = 512$ is the number of entries in the codebook and $D = 384$ is the dimension of each element $c_j$ . The operation $Q$ quantizes the continuous latent $h_i$ into discrete latent $z_i$ by finding its most similar element in $C$ : + +$$ +z _ {i} = Q \left(h _ {i}\right) = \underset {c _ {j} \in C} {\arg \min } \left\| h _ {i} - c _ {j} \right\| _ {2} \tag {2} +$$ + +Since continuous latent from all data samples share the same codebook $C$ , all the real motions in the training set could be expressed by a finite number of bases in latent space. + +Subsequently, the quantified latents $Z$ are fed into the decoder to reconstruct the original motions, given by $\hat{\Theta} = D(Z)$ . The training process involves the joint optimization of the encoder and decoder by minimizing the following loss over the training dataset: + +$$ +\begin{array}{l} L o s s _ {v q} = \operatorname {S m o o t h} _ {L _ {1}} (\hat {\Theta}, \Theta) + \| \mathrm {s g} [ Z ] - H \| _ {2} \tag {3} \\ + \beta \| Z - \operatorname {s g} [ H ] \| _ {2} \\ \end{array} +$$ + +Here, sg denotes the stop gradient operator, and $\beta$ is a hyperparameter. We have two independent VQ-VAEs for + +upper-body and lower-body motion encoding, which we refer to as VQ-VAE $_{up}$ and VQ-VAE $_{low}$ . + +# 3.3. Stratified Motion Diffusion + +After encoding and expressing different human motions as latents, we aim to properly sample from the latent space for full-body motion reconstructions and match the sparse observations. + +Although disentangling the full-body motions into upper and lower parts enhances effectiveness and efficiency for motion representation learning, it's crucial to include the correlation between two body parts during generation. Otherwise, severe inconsistency would be witnessed in reconstructed full-body motions. To this end, we propose Stratified Motion Diffusion to sample upper-body and lower-body latent in a cascaded manner with explicit considerations of the correlations mentioned above. + +Since the sparse observations are all from the upper body (e.g., head and hand sensors), we first generate upper-body latent $z^{\hat{u}p}$ by upper diffusion model conditioning on the sparse observations $X$ . Thus the training objective of the upper diffusion model is: + +$$ +L _ {u p} := \mathbb {E} _ {z ^ {u p}, \epsilon \sim \mathcal {N} (0, 1), k} \left[ \| \epsilon - \epsilon_ {\alpha} \left(z _ {k} ^ {u p}, X, k\right) \| _ {2} ^ {2} \right] \tag {4} +$$ + +where $\epsilon$ is the random noise from the normal distribution, $\epsilon_{\alpha}$ is the noise predictor of the diffusion model with network parameters $\alpha$ , and $k$ is the diffusion time step. + +Compared with upper-body latent prediction, directly predicting the lower-body latent $z^{\hat{low}}$ from the same sparse observations is more challenging due to the absence of direct tracking or supervision for any of the lower-body joints. To make the prediction more physically meaningful, as shown in Fig. 2 (b), we take both the sparse observations $X$ and the generated upper-body latent $z^{\hat{up}}$ as conditions for lower-body latent prediction by lower diffusion model. This design considers the correlation between two half-body parts and allows more information to be involved for the lower-body inference. The objective for lower diffusion model training is as follows: + +$$ +L _ {l o w} := \mathbb {E} _ {z ^ {l o w}, \epsilon \sim \mathcal {N} (0, 1), k} \left[ \left\| \epsilon - \epsilon_ {\alpha} \left(z _ {k} ^ {l o w}, (X, z ^ {\hat {u}} p), k\right) \right\| _ {2} ^ {2} \right] \tag {5} +$$ + +Once two half-body latent $z^{\hat{u}p}$ and $z^{\hat{l}ow}$ are obtained, the full-body motions can be recovered with a decoder $\hat{\Theta} = D_{full}(z^{\hat{u}p}, z^{\hat{l}ow})$ . Instead of directly using pre-trained upper and lower decoders in Fig. 2 (a) to recover the corresponding half-body motions, we train this full-body decoder $E_{full}$ from scratch together with our stratified motion diffusion, which is further optimized to capture the correlations between half-body motions. + +# 3.4. Implementation Details + +Since both sparse observations and human motion occur sequentially, we utilize the widely adopted sequential network, i.e., transformer [44], as the backbone network for the encoder and decoder in the disentangled VQ-VAE [43], and the denoise network in the stratified diffusion model. We set temporal down-sampling rate $l = 2$ to balance the computational cost and the performance. During the training of the latent diffusion model, instead of predicting noise $\epsilon_{k}$ as formulated by the standard latent diffusion model [35], we follow [32, 39] and directly predict the latent $z$ itself, as we find that this operation can significantly reduce the sampled time steps during inference stage. For training decoders, i.e., $E_{up}, E_{low}$ and $E_{full}$ , in addition to the rotation-level reconstruction loss, we incorporate the forward kinematic loss proposed in [18] and the hand loss described in [53]. + +For the inference stage, we evaluate our model in an online manner. Specifically, we fix the sequence length at 20 for both the input and the output of our model, and only the last pose in the output motion sequence is retained. Given a sparse observation sequence, we apply our model using a sliding window approach. For the first 20 poses in the motion sequence, we predict by padding the sparse observation sequence $x$ at the beginning with the first available observation. We make this choice considering the practicality and relevance of online inference in real-world application sce + +narios. This allows the motion sequences to be predicted in a frame-by-frame manner. + +In addition, we employ a simple two-layer GRU [9] on the top of the full body decoder as a temporal memory to smooth the prediction of the output sequence with minimal computational expense, and we term it as a Refiner. To train this Refiner, we use the same velocity loss as [53]. Our model takes $0.74\mathrm{ms}$ to infer 1 frame on a single NVIDIA RTX3090 GPU. + +# 4. Experiments and Evaluation Metrics + +# 4.1. Dataset and Evaluation Metrics + +We train and evaluate our method on AMASS [25], which unifies multiple motion capture datasets [2, 4, 6, 12, 23, 26, 28, 36, 40-42] as SMPL [22] representations. + +We report several metrics for evaluations and comparisons: mean per joint rotation error (MPJRE) and mean per joint position error (MPJPE) for measuring the average relative rotation and position error across all joints respectively, as well as the average position error of the root joints (Root PE), hand joints (Hand PE), upper-body joints (Upper PE), and lower-body joints (Lower PE). + +Besides the above reconstruction accuracy, we also evaluate the spatial and temporal consistency of the generated sequences, as it significantly contributes to the visual quality. Specifically, we calculate the mean per joint velocity error (MPJVE) and Jitter, where MPJVE measures the average velocity error of all body joints, and Jitter quantifies the average jerk (time derivative of acceleration) of all body joints. In both cases, lower values indicate better results. + +# 4.2. Quantitative and Qualitative Results + +For fair comparison, we follow two settings used in previous works [5, 10, 11, 18, 33, 53] for quantitative and qualitative assessment. Moreover, we propose a new setting in this paper for a more comprehensive evaluation on current methods. + +In the first setting, as previous works [7, 11, 18, 53], subsets CMU [6], BMLrub [40], and HDM05 [28] datasets are randomly divided into $90\%$ for training and $10\%$ for testing. Besides sparse observations of three joints, we also evaluate the performance of all compared methods by using four joints as input, including the root joint as an additional input, the same as in [18]. We term this setting as S1 in the following. + +Tabs. 1 and 2 show that our method outperforms existing methods on most evaluation metrics, confirming its effectiveness. For the MPJVE metric, only AGRoL [11] surpasses our method when employing an offline strategy. In this scenario, specifically, AGRoL processes the entire sparse observation sequence in one pass and outputs the predicted full-body motions simultaneously. This enables + +
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
Final IK [1]16.7718.0959.24-----
LoBSTr [48]10.699.0244.97-----
VAR-HMD [10]4.116.8337.99-----
Avatarposer [18]3.084.1827.702.121.817.593.3414.49
AvatarJLM [53]2.903.3520.791.241.426.142.948.39
AGRoL (Online) [11]2.964.2679.121.511.737.913.7884.79
AGRoL (Offline) [11]2.663.7118.591.311.556.843.367.26
Ours2.533.2820.621.181.396.012.956.55
+ +Table 1. Evaluation results under setting S1. + +![](images/e543e74a0c1f506186a74bc54c6f6303e8614d77677fd13bab7b0702d64e405f.jpg) +Figure 3. Visualization results compared with other methods. All models are trained under setting S1. + +each position in the sequence to utilize the information from both preceding and subsequent time steps, offering an advantage in this particular metric. However, it's important to note that, despite being competitive in metric numbers, offline inference has limited practical applicability in real-world scenarios where online processing capability is most important. + +The second setting follows [5, 10, 11, 33, 53], where we evaluate the methods on a larger benchmark from AMASS [25]. The subsets [2, 4, 6, 12, 21, 23, 26, 26, 28, + +40-42, 42] are for training, and Transition [25] and HumanEva [36] subsets are for testing. We term this setting as S2 in the following. + +As shown in Tab. 3, our method achieves comparable performance with previous works on S2. However, we observe that the testing set of S2 is disproportionately small (i.e., only $1\%$ of the training set). Such a small fraction cannot represent the overall data distribution of the large dataset and may not include sufficiently diverse motions to evaluate the models' scalability, causing unconvincing eval + +
MethodMPJREMPJPEMPJVE
Final IK [1]12.399.5436.73
CoolMoves [3]4.585.5565.28
LoBSTr [48]8.095.5630.12
VAE-HMD [10]3.123.5128.23
AvatarPoser [18]2.592.6122.16
AvatarJLM [53]2.402.0917.82
AGRoL [11]2.252.1716.26
Ours2.101.8814.79
+ +Table 2. Evaluation results under setting S1 with the root joint as an additional input. + +
MethodMPJREMPJPEMPJVEJitter
VAEHMD†[10]-7.45--
Humor†[33]-5.50--
FLAG†[5]-4.96--
AvatarPoser [18]4.706.3834.0510.21
AGRoL [11]4.306.1724.408.32
AvatarJLM [53]4.304.9326.177.19
Ours4.625.8633.547.13
+ +Table 3. Evaluation result under setting S2. $\dagger$ indicates that these methods use additional inputs of pelvis location and rotation for training and inference, which are not directly comparable methods. The results of AvatarPoser [18] is provided by [11]. + +![](images/647a5fadc46381cd914e812c96d7489a2f680eb28713777b7d65dfac25edc678.jpg) +Figure 4. Visualization results on real data. + +uation results. We introduce a new setting, S3, which adopts the same training and testing splitting ratio used in S1. In this setting, we randomly select $90\%$ of the samples from the 15 subsets of S2 for training, while the remaining $10\%$ are for testing. We train and evaluate the compared methods with this new setting. Table 4 reveals that under S3, the performance differences between the compared methods are more significant than S1 and S2. Since the test set has more + +![](images/6f2f1e59031f15aed1de9aebc5a030d4ccb3377d508c5f7c99051887b369e0c5.jpg) +Figure 5. The visualization comparison for disentanglement. The darker the red color, the greater the deviation is between the predicted result and the ground truth. + +diverse motions in S3, this benchmark evaluates the models' scalability in a more objective way. In this context, our method outperforms existing methods in most metrics, especially in the critical metric of Lower PE, highlighting the superiority of our stratified design for lower-body modeling and inference. + +Fig. 3 presents a visual comparison between our SAGE Net and baseline methods, all trained under the S1 protocol, which is commonly used by baselines for releasing their trained checkpoints. These visualizations demonstrate the significant improvements that our model offers in reconstructing the lower body. For example, in the first row of samples, baseline methods typically reconstruct the feet too close to the ground, restricting the avatar's leg movements. Our model, however, overcomes this limitation, enabling more flexible leg movements. In the third row, for a subject climbing a ladder, the baseline methods often result in avatars with floating feet, failing to capture the detailed motion of climbing. In contrast, our SAGE Net accurately replicates complex foot movements, resulting in more realistic and precise climbing animations. We also evaluate our model on the real data, and for fair comparison, we directly use the real data release by [53]. As shown in Fig. 4, our method also achieves better reconstruction results on the real data. + +# 4.3. Ablation Study + +We perform ablation study under S1 to justify the design choice of each component in our SAGE Net. + +Disentangled Codebook: We establish a baseline using a unified motion representation to evaluate the disentangle strategy. Specifically, we developed a full-body VQ-VAE model that encodes full-body motion into a single, unified discrete codebook. Other components are the same as the original model. Results shown in the first and the last rows in Table 5, demonstrate that our approach employing dis + +
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
AGRoL(Online) [11]3.094.31109.291.791.807.953.86121.78
AGRoL(Offline) [11]2.833.8017.761.621.666.903.5310.08
AvatarJLM [53]3.143.3915.750.691.486.133.045.33
AvATARposer [18]2.723.3721.002.121.635.872.9010.24
Ours2.412.9516.941.151.285.372.745.27
+ +Table 4. Evaluation results under setting S3. + +
MethodMPJREMPJPEMPJVEJitter
w/o Disentangle2.643.6233.1825.07
w/o Full-Body Decoder2.713.6926.0710.80
w/o Refiner2.543.2621.999.29
5 Part Disentanglement2.633.4820.327.16
Ours2.533.2820.626.55
+ +Table 5. Ablation results of different components in SAGE Net under setting S1. + +
MethodLowe PEJitter
Parallel Diffusion6.7314.71
Stratified Diffusion6.4610.83
+ +Table 6. Evaluation results on the conditional strategy of the diffusion model under setting S1. + +entangled latents significantly outperforms the baseline on all evaluation metrics. This demonstrates that the disentanglement can simplify the learning process by allowing the model to focus on a more limited set of movements and interactions. Additionally, Fig. 5 shows the visualization comparison between our model and baseline model, verifying that the disentangle can significantly improve the reconstruction results for the most challenging lower motions. + +Full-Body Decoder and Refiner: The second and third rows of Tab. 5 demonstrate the impact of the full-body decoder and the refiner, respectively. Compared with utilizing the upper and lower decoder from VQ-VAE $_{up}$ and VQ-VAE $_{low}$ , the full-body decoder facilitates the integration of features from both the upper and lower body, improving the overall accuracy of full-body motion reconstruction. On the other hand, the refiner acts as a temporal memory, smoothing out the motion sequence to yield better visualization results. + +Disentanglement Strategy: To investigate the optimal disentanglement strategy, we explore an extreme disentanglement configuration by following the path from the root (Pelvis) node to each leaf node along the kinematic tree. Specifically, we break down the body into five segments: the paths from the root to the left hand (a), right hand (b), head (c), left foot (d), and right foot (e). As reported in the last two rows of Tab. 5, the natural joint interconnections within the upper (or lower) body were disrupted when further disentangling the human body, resulting in perfor + +![](images/97bd799511d336aadc985270c806201f8332af4be272527298ada78a57f93dfd.jpg) +Figure 6. Failure cases. All models are trained under setting S1. + +mance drops and complicating the model design. + +Stratified Inference: Tab. 6 highlights the influence of our stratified design on the accuracy of lower body predictions. For comparison, we design a baseline that only uses the sparse observation for lower body latent generation without predicted upper body latent (term as Parallel Diffusion in the table). As we focus solely on the reconstruction quality of the lower body here, we use the decoding results on the generated lower latents from $\mathrm{VQ - VAELow}$ to isolate the impact of other modules such as the full-body decoder and refiner. We report Lower PE and Jitter of the lower body for comparison. Results show that our stratified design markedly improves the accuracy of lower body predictions. + +**Limitation:** In Fig. 6, both the previous state-of-the-art method and our model encounter difficulties in two main situations: (1) External Force-Induced Movements (the top row). (2) Unconventional Poses (the bottom row). The addition of more varied samples to the training dataset can potentially enhance the model's performance in these areas. + +# 5. Conclusion + +We study the problem of human avatar generation from sparse observations. Our key finding is that the upper and lower body motions should be disentangled with respect to the input signals from the upper-body joints. Based on this, we propose a novel stratified solution where the upper-body motion is reconstructed first, and the lower-body motion is reconstructed next and conditioned on the upper-body motion. Our proposed stratified solution achieves superior performance on public available benchmarks. + +# References + +[1] RootMotion Final IK., 2018. 2, 6, 7 +[2] Advanced Computing Center for the Arts and Design. ACCAD MoCap Dataset. 5, 6 +[3] Karan Ahuja, Eyal Ofek, Mar González-Franco, Christian Holz, and Andrew D. Wilson. Coolmoves: User motion accentuation in virtual reality. Proc. 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This task is challenging due to the limited input from Head Mounted Devices, which capture only sparse observations from the head and hands. Predicting the full-body avatars, particularly the lower body, from these sparse observations presents significant difficulties. In this paper, we are inspired by the inherent property of the kinematic tree defined in the Skinned Multi-Person Linear (SMPL) model, where the upper body and lower body share only one common ancestor node, bringing the potential of decoupled reconstruction. We propose a stratified approach to decouple the conventional full-body avatar reconstruction pipeline into two stages, with the reconstruction of the upper body first and a subsequent reconstruction of the lower body conditioned on the previous stage. To implement this straightforward idea, we leverage the latent diffusion model as a powerful probabilistic generator, and train it to follow the latent distribution of decoupled motions explored by a VQ-VAE encoder-decoder model. Extensive experiments on AMASS mocap dataset demonstrate our state-of-the-art performance in the reconstruction of full-body motions." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 385, + 387, + 398 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 387, + 398 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 387, + 398 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 409, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 409, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 409, + 545, + 530 + ], + "type": "text", + "content": "Generating 3D full-body avatars from observations of Head Mounted Devices (HMDs) is crucial for enhancing immersive AR/VR experiences. HMDs primarily track the head and hands, while leaving the rest of the body unmonitored. This limited motion tracking poses a challenging scenario for accurately reconstructing full-body 3D avatars, particularly in representing the lower body. The high degree of freedom in body movements compounds this difficulty, making the task of reasoning human motion from such sparse observations significantly complex." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 533, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 546, + 715 + ], + "type": "text", + "content": "Tremendous efforts have been made to obtain more tracking signals by adding sensors at Pelvis [5, 10, 33] or both Pelvis and Legs [16, 19, 45, 49, 50]. While these approaches provide more data points for avatar construction, they can diminish the user's experience. Wearing extra devices can be cumbersome, potentially interfering with the user's comfort and immersion in the virtual environment. This trade-off highlights the need for innovative solutions that can deliver detailed body tracking without compromising the user's comfort and immersion in AR/VR settings. Accordingly, we are interested in the problem of generating 3D full-body avatars from sparse observations of HMDs that track the motion of the head and two hands, by developing a neural solution that learns the distribution of full-body poses given the sparse observations as the input condition." + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 683, + 266, + 693 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 683, + 266, + 693 + ], + "spans": [ + { + "bbox": [ + 61, + 683, + 266, + 693 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 61, + 683, + 266, + 693 + ], + "type": "text", + "content": " indicates the School of Computer Science, Wuhan University" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 63, + 694, + 164, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 694, + 164, + 703 + ], + "spans": [ + { + "bbox": [ + 63, + 694, + 164, + 703 + ], + "type": "text", + "content": "* indicates equal contributions." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 63, + 704, + 216, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 704, + 216, + 712 + ], + "spans": [ + { + "bbox": [ + 63, + 704, + 216, + 712 + ], + "type": "text", + "content": "† Corresponding author: xuanan@ieee.org" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 313, + 757 + ], + "type": "text", + "content": "153" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 216 + ], + "type": "text", + "content": "Recent studies have attempted to address the challenge of sparse observations in HMD-based full-body avatar generation by employing regression-based techniques, as seen in [18, 53], or by adopting generation-based approaches like [7, 11]. These methods typically use deep neural networks to predict human motion within a single, expansive motion space. However, due to the limited data provided by sparse observations, these networks often struggle to fully capture the complexities of human kinematics across such a broad and unified motion space. This limitation frequently results in reconstructions that are unrealistic and lack physical plausibility." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 230, + 289, + 446 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 230, + 289, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 230, + 289, + 446 + ], + "type": "text", + "content": "We introduce a new method for reconstructing full-body human motions from sparse observations, called Stratified Avatar Generation (SAGE). Instead of the upper-body motion prediction that has tracking signals of certain upper joints from sparse observations, predicting lower-body motion is not straightforward as no direct tracking signals about any lower-body joint is given. It is noteworthy that SMPL model [22] connects the upper and lower half-body by a single root joint, as shown in Fig. 1 (b), which motivates us to split the full-body motions into upper and lower half-body parts. The benefits are two-fold: 1) the smaller search space achieved by disentanglement facilitates learning and prediction; 2) our stratified design makes the modeling and inferring for lower-body motions more accurate and visually appealing by explicitly modeling the correlation and constraint between two half-body motions. To this end, we use VQ-VAE [43] to encode and reconstruct upper and lower body motions separately." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 460, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 288, + 604 + ], + "type": "text", + "content": "With the disentangled latent representation of the upper and lower body motions, we aim to recover the accurate full-body motions from sparse observations with a body-customized latent diffusion model (LDM) [35] in a stratified manner. Specifically, as shown in Fig. 1 (c), Fig. 1(d), and Fig. 1(e), we first find the latent of upper-body motion condition on the sparse observations (i.e., tracking signals of the head and hands in Fig. 1(a)). Then, the latent of lower-body motion is inferred condition on both the predicted upper-body latent and sparse observations. Finally, a full-body decoder takes the two half-body latents as input and outputs the full-body motion." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 618, + 288, + 715 + ], + "type": "text", + "content": "In the experiments, we comprehensively justified our intuitive design of disentangling the upper and lower body motion in a stratified manner. On the large-scale motion capture benchmark AMASS [25], our proposed SAGE is exhibiting superior performance in different evaluation settings and particularly performs well in terms of the evaluation metrics for lower-body motion estimation compared to previous state-of-the-art methods." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 305, + 71, + 393, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 393, + 84 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 393, + 84 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 91, + 526, + 105 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 91, + 526, + 105 + ], + "spans": [ + { + "bbox": [ + 306, + 91, + 526, + 105 + ], + "type": "text", + "content": "2.1. Motion Reconstruction from Sparse Input" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 110, + 545, + 421 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 110, + 545, + 421 + ], + "spans": [ + { + "bbox": [ + 304, + 110, + 545, + 421 + ], + "type": "text", + "content": "The task of reconstructing full human body motion from sparse observations has gained significant attention in recent decades within the research community [1, 3, 5, 7, 10, 11, 16, 18, 19, 45, 46, 48-50, 53]. For instance, recent works [16, 19, 45, 49, 50] focus on reconstructing full body motion from six inertial measurement units (IMUs). SIP [45] employs heuristic methods, while DIP [16] pioneers the use of deep neural networks for this task. PIP [50] and TIP [19] further enhance performance by incorporating physics constraints. With the rise of VR/AR applications, researchers turn their attention toward reconstructing full body motion from VR/AR devices, such as head-mounted devices (HMDs), which only provide information about the user's head and hands, posing additional challenges. LoBSTr [48], AvATARPoser [18], and AvATARJLM [53] approach this task as a regression problem, utilizing GRU [48] and Transformer Network [18, 53] to predict the full body pose from sparse observations of HMDs. Another line of methods employs generative models [5, 7, 10, 11]. For example, VAEHMD [10] and FLAG [5] utilize Variational AutoEncoder (VAE) [20] and Normalizing flow [34], respectively. Recent works [7, 11] leverage more powerful diffusion models [15, 37] for motion generation, yielding promising results due to the powerful ability of diffusion models in modeling the conditional probabilistic distribution of full-body motion." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 422, + 545, + 530 + ], + "type": "text", + "content": "Contrasting with previous methods that model full-body motion in a comprehensive, unified framework, our approach acknowledges the complexities such methods impose on deep learning models, particularly in capturing the intricate kinematics of human motion. Hence, we propose a stratified approach that decouples the conventional full-body avatar reconstruction pipeline, first for the upper body and then for the lower body under the condition of the upper-body." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 539, + 457, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 539, + 457, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 539, + 457, + 551 + ], + "type": "text", + "content": "2.2. Human Motion Generation" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 558, + 545, + 713 + ], + "type": "text", + "content": "Human motion generation is explored under various input conditions, including text [17, 30, 38, 39, 51], action labels [13, 29], 3D scenes and objects [14, 31, 47], and motion itself [8, 24, 27]. Our work shares similarities with two primary research streams. The first involves diffusion-based motion generation. For instance, [39] is the first to utilize a diffusion model [15, 37] for text-to-motion generation with a transformer network. [31] develops a hierarchical generation pipeline for human-object interaction by generating initial keyframes in the motion sequence and then interpolating between them. Secondly, our approach parallels works like PoseGPT [24], MotionGPT [17], and T2M-GPT [51] in terms of representing human motions with discrete la" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "154" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "tent. These studies also utilize a VQ-VAE [43] to encode human motion into a discrete latent space, facilitating the subsequent generation process." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 286, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 286, + 180 + ], + "type": "text", + "content": "The task we aim to address significantly deviates from traditional motion generation tasks like text-to-motion generation, which typically aims to create motions that align with textual descriptions. Our goal is distinctly different: we focus on accurately reconstructing human motion using solely sparse observations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 192, + 248, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 192, + 248, + 205 + ], + "spans": [ + { + "bbox": [ + 47, + 192, + 248, + 205 + ], + "type": "text", + "content": "3. SAGE: Stratified Avatar Generation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 213, + 286, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 213, + 286, + 308 + ], + "spans": [ + { + "bbox": [ + 46, + 213, + 286, + 308 + ], + "type": "text", + "content": "This section introduces the proposed SAGE Network, following our observation about the connection relationship between upper-body and lower-body motions. The overall architecture of our SAGE Net is shown in Fig. 2. Disentangled latent representations for upper-body and lower-body motions are learned in Fig. 2 (a). Subsequently, as illustrated in Fig. 2 (b), we employ a stratified latent diffusion process for full body motion reconstruction." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 317, + 224, + 329 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 317, + 224, + 329 + ], + "spans": [ + { + "bbox": [ + 47, + 317, + 224, + 329 + ], + "type": "text", + "content": "3.1. Problem Statement and Notation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": "Input Signals. Our paper follows the common setting of Head Mounted Devices (HMDs) inputs for motion generation, in which three sensors mounted on the head and, left and right hands are employed to perceive the corresponding joint motions. Formally, the raw input signals are denoted by a time-dependent vector function " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{X}(t) = (\\mathbf{x}_h(t),\\mathbf{x}_l(t),\\mathbf{x}_r(t))" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": ", where the subscripts " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": " indicate the head, left hand, and right hand, and all these functions are with six degree of freedom for 3D rotation and translation under the global coordinate system. Joint rotations are represented by a six-axis representation, which has been demonstrated to be more suitable for network learning in previous works [54]. Given a time interval with " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": " sampling points, the raw input signals can be denoted in a matrix " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_{\\mathrm{raw}}\\in \\mathbb{R}^{T\\times (3\\times (3 + 6))}" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": ". To enhance the input signals, we follow [18] to compute the positional velocities and angular velocities. This augmentation process adds a 9D input signal for each observed joint, resulting in an 18D input signal per joint at every timestamp. By combining these signals for all joints over all timestamps, we form the complete sparse input signal, represented as " + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\in \\mathbb{R}^{T\\times 54}" + }, + { + "bbox": [ + 46, + 336, + 287, + 587 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "text", + "content": "Kinematic Tree and SMPL Representation. As shown in Fig. 1 (b), SMPL [22] represents a human pose by a standard skeletal rig, which is widely adopted by current motion generation works. A pose " + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "inline_equation", + "content": "\\theta^j(t)" + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "text", + "content": " represents the relative rotation of joint " + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "text", + "content": " at " + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "text", + "content": "th frame with respect to its parent in the kinematic tree. The global rotations " + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "inline_equation", + "content": "G(\\theta^j(t))" + }, + { + "bbox": [ + 46, + 604, + 286, + 687 + ], + "type": "text", + "content": " can be calculated by:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 689, + 286, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 116, + 689, + 286, + 715 + ], + "spans": [ + { + "bbox": [ + 116, + 689, + 286, + 715 + ], + "type": "interline_equation", + "content": "G \\left(\\theta^ {j} (t)\\right) = \\prod_ {k \\in A (j)} \\theta^ {k} (t) \\tag {1}", + "image_path": "6af0cd184ea975768ef6f068c31d0d1ec7e198ba3f342eec97de685e1520b2e4.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "A(j)" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": " denotes the ordered set of joint ancestors of joint " + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 97, + 545, + 205 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 97, + 545, + 205 + ], + "spans": [ + { + "bbox": [ + 304, + 97, + 545, + 205 + ], + "type": "text", + "content": "Articulated motion representation based on the human kinematic tree, is key for realistically simulating human motions and enables efficient control over joint parameters. However, such an intricate articulated motion representation poses a significant challenge for models to learn effectively. In this work, we seek to disentangle this complex representation to enable the model to focus on a limited set of motions and interactions, thereby simplifying the learning process." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 206, + 545, + 338 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 206, + 545, + 338 + ], + "spans": [ + { + "bbox": [ + 304, + 206, + 545, + 338 + ], + "type": "text", + "content": "Nevertheless, separating full-body human motions into distinct parts is nontrivial due to the complex correlations among joints. We revisit the human kinematic tree defined in SMPL model, where the upper and lower half-body is connected solely via a root joint. This insight from SMPL model provides a natural solution to separate the articulated full-body motion into two distinct parts: upper-body motion and lower-body motion. Notably, the root joint is included in both two parts as a central element since the parameters of all other joints in each half-body are defined in the local coordinate system of the root joint." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": "The Outputs. As discussed in the last paragraph for SMPL representation [22], the problem of 3D body avatar generation comes down to the full-body motion estimation of 22 joints (including the root joint), denoted in the set function " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\Theta(t) = \\{\\theta^i(t) \\in \\mathrm{SE}(3) | t \\in \\{t_1, \\ldots, t_T\\}\\}" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": " as the expected output of our problem. Based on the discussion of SMPL model with the disentangling nature of upper and lower body, we redefine the set function " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\Theta(t)" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": " in the disentangled way by " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\Theta(t) = \\Theta_{\\mathrm{upper}}(t) \\cup \\Theta_{\\mathrm{lower}}(t)" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\Theta_{\\mathrm{upper}}(t) = \\{\\theta^0(t), \\ldots, \\theta_u^{b_u}(t)\\}" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\Theta_{\\mathrm{lower}} = \\{\\theta^0(t), \\ldots, \\theta_l^{b_l}(t)\\}" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": ". These two subsets have only one intersected joint: root joint " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "\\theta^0" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "b_u = 13" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "b_l = 8" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": " denote the number of rest joints in the upper and lower body, respectively. For the final output of our method, the dimension of the underlying motion variables is " + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "inline_equation", + "content": "22 \\times 6 = 132" + }, + { + "bbox": [ + 304, + 357, + 545, + 551 + ], + "type": "text", + "content": " at every timestamp." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 561, + 499, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 561, + 499, + 574 + ], + "spans": [ + { + "bbox": [ + 306, + 561, + 499, + 574 + ], + "type": "text", + "content": "3.2. Disentangled Motion Representation" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 304, + 580, + 545, + 640 + ], + "type": "text", + "content": "In this section, our objective is to disentangle full-body human motions into upper-body and lower-body parts and encode them to discrete latent spaces. This can effectively reduce the complexity and burden of encoding since each encoding takes care of only half-body motions." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": "We employ two autoencoders, i.e., VQ-VAE [43, 52], with identical architecture to learn the discrete latent spaces for upper-body and lower-body motions, respectively. As shown in Fig. 2 (a), our VQ-VAE model consists of an encoder and a decoder. The encoder " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "E" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " takes the motion sequence " + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\Theta = \\{\\theta_i\\}_{i=1}^T" + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": " as input and encodes it into a series of" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "155" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 69, + 542, + 176 + ], + "blocks": [ + { + "bbox": [ + 51, + 69, + 542, + 176 + ], + "lines": [ + { + "bbox": [ + 51, + 69, + 542, + 176 + ], + "spans": [ + { + "bbox": [ + 51, + 69, + 542, + 176 + ], + "type": "image", + "image_path": "cfa8aacc89e0ef96131745c37cf456053d925ba2f16d305bb42053495f899a49.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 176, + 542, + 312 + ], + "blocks": [ + { + "bbox": [ + 51, + 176, + 542, + 312 + ], + "lines": [ + { + "bbox": [ + 51, + 176, + 542, + 312 + ], + "spans": [ + { + "bbox": [ + 51, + 176, + 542, + 312 + ], + "type": "image", + "image_path": "1505433cfb1c02e88ff88a4ef43df8a5594cbdc37afb0405c0f2f35b10444274.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 321, + 545, + 399 + ], + "lines": [ + { + "bbox": [ + 46, + 321, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 46, + 321, + 545, + 399 + ], + "type": "text", + "content": "Figure 2. The overall architecture of our SAGE Net. It mainly contains two components: (a) Disentangled VQ-VAE for discrete human motion latent learning. To facilitate visualization, we incorporate zero rotations as padding for the lower body in the Upper VQ-VAE, and vice versa for the Lower VQ-VAE. Consequently, in the visualizations of the Upper VQ-VAE, the lower body remains in a stationary pose, whereas in the visualizations of the Lower VQ-VAE, the upper body is maintained in a T-pose. (b) The stratified diffusion model, which models the conditional distribution of the latent space for upper and lower motion. This model sequentially infers the upper and lower body latents, capturing the correlation between upper and lower motions. By employing a dedicated full-body decoder on the concatenated upper and lower latents, we can obtain full-body motion." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "text", + "content": "continuous latent " + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "inline_equation", + "content": "E(\\Theta) = H" + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "inline_equation", + "content": "H = \\{h_i\\}_{i=1}^{T/l}" + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "inline_equation", + "content": "l" + }, + { + "bbox": [ + 46, + 418, + 286, + 443 + ], + "type": "text", + "content": " is the temporal down-sampling rate of input motion sequence." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": "To quantize the continuous latent, we define the discrete motion latent space by a codebook " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "C = \\{c_j\\}_{j=1}^N \\in \\mathbb{R}^{N \\times D}" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "N = 512" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": " is the number of entries in the codebook and " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "D = 384" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": " is the dimension of each element " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "c_j" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": ". The operation " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": " quantizes the continuous latent " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "h_i" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": " into discrete latent " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "z_i" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": " by finding its most similar element in " + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 444, + 286, + 515 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 96, + 520, + 286, + 541 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 96, + 520, + 286, + 541 + ], + "spans": [ + { + "bbox": [ + 96, + 520, + 286, + 541 + ], + "type": "interline_equation", + "content": "z _ {i} = Q \\left(h _ {i}\\right) = \\underset {c _ {j} \\in C} {\\arg \\min } \\left\\| h _ {i} - c _ {j} \\right\\| _ {2} \\tag {2}", + "image_path": "63037952f348a5d9534aea9278e0c61b8a4d387eef629e32b27924b20d059dc4.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 544, + 286, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 544, + 286, + 591 + ], + "spans": [ + { + "bbox": [ + 46, + 544, + 286, + 591 + ], + "type": "text", + "content": "Since continuous latent from all data samples share the same codebook " + }, + { + "bbox": [ + 46, + 544, + 286, + 591 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 544, + 286, + 591 + ], + "type": "text", + "content": ", all the real motions in the training set could be expressed by a finite number of bases in latent space." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "spans": [ + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "type": "text", + "content": "Subsequently, the quantified latents " + }, + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "type": "inline_equation", + "content": "Z" + }, + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "type": "text", + "content": " are fed into the decoder to reconstruct the original motions, given by " + }, + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "type": "inline_equation", + "content": "\\hat{\\Theta} = D(Z)" + }, + { + "bbox": [ + 47, + 593, + 286, + 652 + ], + "type": "text", + "content": ". The training process involves the joint optimization of the encoder and decoder by minimizing the following loss over the training dataset:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 75, + 657, + 286, + 686 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 657, + 286, + 686 + ], + "spans": [ + { + "bbox": [ + 75, + 657, + 286, + 686 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} L o s s _ {v q} = \\operatorname {S m o o t h} _ {L _ {1}} (\\hat {\\Theta}, \\Theta) + \\| \\mathrm {s g} [ Z ] - H \\| _ {2} \\tag {3} \\\\ + \\beta \\| Z - \\operatorname {s g} [ H ] \\| _ {2} \\\\ \\end{array}", + "image_path": "635dabdb19c7492741cc56eef5240a6f4a90a2e76763e3674561d15c009622a7.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "content": "Here, sg denotes the stop gradient operator, and " + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "inline_equation", + "content": "\\beta" + }, + { + "bbox": [ + 46, + 689, + 286, + 714 + ], + "type": "text", + "content": " is a hyperparameter. We have two independent VQ-VAEs for" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "spans": [ + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "type": "text", + "content": "upper-body and lower-body motion encoding, which we refer to as VQ-VAE" + }, + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "type": "inline_equation", + "content": "_{up}" + }, + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "type": "text", + "content": " and VQ-VAE" + }, + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "type": "inline_equation", + "content": "_{low}" + }, + { + "bbox": [ + 305, + 419, + 544, + 444 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 452, + 455, + 463 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 452, + 455, + 463 + ], + "spans": [ + { + "bbox": [ + 306, + 452, + 455, + 463 + ], + "type": "text", + "content": "3.3. Stratified Motion Diffusion" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 471, + 545, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 471, + 545, + 517 + ], + "spans": [ + { + "bbox": [ + 305, + 471, + 545, + 517 + ], + "type": "text", + "content": "After encoding and expressing different human motions as latents, we aim to properly sample from the latent space for full-body motion reconstructions and match the sparse observations." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 519, + 545, + 625 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 519, + 545, + 625 + ], + "spans": [ + { + "bbox": [ + 304, + 519, + 545, + 625 + ], + "type": "text", + "content": "Although disentangling the full-body motions into upper and lower parts enhances effectiveness and efficiency for motion representation learning, it's crucial to include the correlation between two body parts during generation. Otherwise, severe inconsistency would be witnessed in reconstructed full-body motions. To this end, we propose Stratified Motion Diffusion to sample upper-body and lower-body latent in a cascaded manner with explicit considerations of the correlations mentioned above." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "spans": [ + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "text", + "content": "Since the sparse observations are all from the upper body (e.g., head and hand sensors), we first generate upper-body latent " + }, + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "inline_equation", + "content": "z^{\\hat{u}p}" + }, + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "text", + "content": " by upper diffusion model conditioning on the sparse observations " + }, + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 304, + 627, + 545, + 686 + ], + "type": "text", + "content": ". Thus the training objective of the upper diffusion model is:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 321, + 696, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 321, + 696, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 321, + 696, + 545, + 717 + ], + "type": "interline_equation", + "content": "L _ {u p} := \\mathbb {E} _ {z ^ {u p}, \\epsilon \\sim \\mathcal {N} (0, 1), k} \\left[ \\| \\epsilon - \\epsilon_ {\\alpha} \\left(z _ {k} ^ {u p}, X, k\\right) \\| _ {2} ^ {2} \\right] \\tag {4}", + "image_path": "becd1bccc82a4a3ba5594e71639cdb8eb0175b73b7ac76afba0b7716e2d6c6b0.jpg" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "156" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " is the random noise from the normal distribution, " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\alpha}" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " is the noise predictor of the diffusion model with network parameters " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 46, + 72, + 287, + 108 + ], + "type": "text", + "content": " is the diffusion time step." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "spans": [ + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "text", + "content": "Compared with upper-body latent prediction, directly predicting the lower-body latent " + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "inline_equation", + "content": "z^{\\hat{low}}" + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "text", + "content": " from the same sparse observations is more challenging due to the absence of direct tracking or supervision for any of the lower-body joints. To make the prediction more physically meaningful, as shown in Fig. 2 (b), we take both the sparse observations " + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "inline_equation", + "content": "X" + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "text", + "content": " and the generated upper-body latent " + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "inline_equation", + "content": "z^{\\hat{up}}" + }, + { + "bbox": [ + 46, + 109, + 288, + 253 + ], + "type": "text", + "content": " as conditions for lower-body latent prediction by lower diffusion model. This design considers the correlation between two half-body parts and allows more information to be involved for the lower-body inference. The objective for lower diffusion model training is as follows:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 56, + 259, + 287, + 281 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 259, + 287, + 281 + ], + "spans": [ + { + "bbox": [ + 56, + 259, + 287, + 281 + ], + "type": "interline_equation", + "content": "L _ {l o w} := \\mathbb {E} _ {z ^ {l o w}, \\epsilon \\sim \\mathcal {N} (0, 1), k} \\left[ \\left\\| \\epsilon - \\epsilon_ {\\alpha} \\left(z _ {k} ^ {l o w}, (X, z ^ {\\hat {u}} p), k\\right) \\right\\| _ {2} ^ {2} \\right] \\tag {5}", + "image_path": "1ece2801b328283b7902110d5d4ada9a22886ad29f3737cf90a3578a2db27927.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "spans": [ + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "text", + "content": "Once two half-body latent " + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "inline_equation", + "content": "z^{\\hat{u}p}" + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "inline_equation", + "content": "z^{\\hat{l}ow}" + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "text", + "content": " are obtained, the full-body motions can be recovered with a decoder " + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "inline_equation", + "content": "\\hat{\\Theta} = D_{full}(z^{\\hat{u}p}, z^{\\hat{l}ow})" + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "text", + "content": ". Instead of directly using pre-trained upper and lower decoders in Fig. 2 (a) to recover the corresponding half-body motions, we train this full-body decoder " + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "inline_equation", + "content": "E_{full}" + }, + { + "bbox": [ + 47, + 288, + 287, + 387 + ], + "type": "text", + "content": " from scratch together with our stratified motion diffusion, which is further optimized to capture the correlations between half-body motions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 396, + 180, + 407 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 180, + 407 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 180, + 407 + ], + "type": "text", + "content": "3.4. Implementation Details" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "spans": [ + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "content": "Since both sparse observations and human motion occur sequentially, we utilize the widely adopted sequential network, i.e., transformer [44], as the backbone network for the encoder and decoder in the disentangled VQ-VAE [43], and the denoise network in the stratified diffusion model. We set temporal down-sampling rate " + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "inline_equation", + "content": "l = 2" + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "content": " to balance the computational cost and the performance. During the training of the latent diffusion model, instead of predicting noise " + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "inline_equation", + "content": "\\epsilon_{k}" + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "content": " as formulated by the standard latent diffusion model [35], we follow [32, 39] and directly predict the latent " + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "inline_equation", + "content": "z" + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "content": " itself, as we find that this operation can significantly reduce the sampled time steps during inference stage. For training decoders, i.e., " + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "inline_equation", + "content": "E_{up}, E_{low}" + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "inline_equation", + "content": "E_{full}" + }, + { + "bbox": [ + 46, + 414, + 287, + 594 + ], + "type": "text", + "content": ", in addition to the rotation-level reconstruction loss, we incorporate the forward kinematic loss proposed in [18] and the hand loss described in [53]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": "For the inference stage, we evaluate our model in an online manner. Specifically, we fix the sequence length at 20 for both the input and the output of our model, and only the last pose in the output motion sequence is retained. Given a sparse observation sequence, we apply our model using a sliding window approach. For the first 20 poses in the motion sequence, we predict by padding the sparse observation sequence " + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 594, + 288, + 714 + ], + "type": "text", + "content": " at the beginning with the first available observation. We make this choice considering the practicality and relevance of online inference in real-world application sce" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 95 + ], + "type": "text", + "content": "narios. This allows the motion sequences to be predicted in a frame-by-frame manner." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 96, + 547, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 96, + 547, + 180 + ], + "spans": [ + { + "bbox": [ + 304, + 96, + 547, + 180 + ], + "type": "text", + "content": "In addition, we employ a simple two-layer GRU [9] on the top of the full body decoder as a temporal memory to smooth the prediction of the output sequence with minimal computational expense, and we term it as a Refiner. To train this Refiner, we use the same velocity loss as [53]. Our model takes " + }, + { + "bbox": [ + 304, + 96, + 547, + 180 + ], + "type": "inline_equation", + "content": "0.74\\mathrm{ms}" + }, + { + "bbox": [ + 304, + 96, + 547, + 180 + ], + "type": "text", + "content": " to infer 1 frame on a single NVIDIA RTX3090 GPU." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 191, + 509, + 205 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 191, + 509, + 205 + ], + "spans": [ + { + "bbox": [ + 305, + 191, + 509, + 205 + ], + "type": "text", + "content": "4. Experiments and Evaluation Metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 212, + 477, + 224 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 212, + 477, + 224 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 477, + 224 + ], + "type": "text", + "content": "4.1. Dataset and Evaluation Metrics" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 230, + 545, + 266 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 230, + 545, + 266 + ], + "spans": [ + { + "bbox": [ + 304, + 230, + 545, + 266 + ], + "type": "text", + "content": "We train and evaluate our method on AMASS [25], which unifies multiple motion capture datasets [2, 4, 6, 12, 23, 26, 28, 36, 40-42] as SMPL [22] representations." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 267, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 267, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 304, + 267, + 545, + 350 + ], + "type": "text", + "content": "We report several metrics for evaluations and comparisons: mean per joint rotation error (MPJRE) and mean per joint position error (MPJPE) for measuring the average relative rotation and position error across all joints respectively, as well as the average position error of the root joints (Root PE), hand joints (Hand PE), upper-body joints (Upper PE), and lower-body joints (Lower PE)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 351, + 545, + 447 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 447 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 447 + ], + "type": "text", + "content": "Besides the above reconstruction accuracy, we also evaluate the spatial and temporal consistency of the generated sequences, as it significantly contributes to the visual quality. Specifically, we calculate the mean per joint velocity error (MPJVE) and Jitter, where MPJVE measures the average velocity error of all body joints, and Jitter quantifies the average jerk (time derivative of acceleration) of all body joints. In both cases, lower values indicate better results." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 455, + 500, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 455, + 500, + 468 + ], + "spans": [ + { + "bbox": [ + 305, + 455, + 500, + 468 + ], + "type": "text", + "content": "4.2. Quantitative and Qualitative Results" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "content": "For fair comparison, we follow two settings used in previous works [5, 10, 11, 18, 33, 53] for quantitative and qualitative assessment. Moreover, we propose a new setting in this paper for a more comprehensive evaluation on current methods." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "content": "In the first setting, as previous works [7, 11, 18, 53], subsets CMU [6], BMLrub [40], and HDM05 [28] datasets are randomly divided into " + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "content": " for training and " + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 533, + 545, + 629 + ], + "type": "text", + "content": " for testing. Besides sparse observations of three joints, we also evaluate the performance of all compared methods by using four joints as input, including the root joint as an additional input, the same as in [18]. We term this setting as S1 in the following." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 714 + ], + "type": "text", + "content": "Tabs. 1 and 2 show that our method outperforms existing methods on most evaluation metrics, confirming its effectiveness. For the MPJVE metric, only AGRoL [11] surpasses our method when employing an offline strategy. In this scenario, specifically, AGRoL processes the entire sparse observation sequence in one pass and outputs the predicted full-body motions simultaneously. This enables" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "157" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 525, + 191 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 525, + 191 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 525, + 191 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 525, + 191 + ], + "type": "table", + "html": "
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
Final IK [1]16.7718.0959.24-----
LoBSTr [48]10.699.0244.97-----
VAR-HMD [10]4.116.8337.99-----
Avatarposer [18]3.084.1827.702.121.817.593.3414.49
AvatarJLM [53]2.903.3520.791.241.426.142.948.39
AGRoL (Online) [11]2.964.2679.121.511.737.913.7884.79
AGRoL (Offline) [11]2.663.7118.591.311.556.843.367.26
Ours2.533.2820.621.181.396.012.956.55
", + "image_path": "868b2fa3a49d389ce77e03455a7e137aeee3b36174b87219d570c380584a3690.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 215, + 199, + 376, + 210 + ], + "lines": [ + { + "bbox": [ + 215, + 199, + 376, + 210 + ], + "spans": [ + { + "bbox": [ + 215, + 199, + 376, + 210 + ], + "type": "text", + "content": "Table 1. Evaluation results under setting S1." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 53, + 238, + 541, + 545 + ], + "blocks": [ + { + "bbox": [ + 53, + 238, + 541, + 545 + ], + "lines": [ + { + "bbox": [ + 53, + 238, + 541, + 545 + ], + "spans": [ + { + "bbox": [ + 53, + 238, + 541, + 545 + ], + "type": "image", + "image_path": "e543e74a0c1f506186a74bc54c6f6303e8614d77677fd13bab7b0702d64e405f.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 111, + 551, + 480, + 562 + ], + "lines": [ + { + "bbox": [ + 111, + 551, + 480, + 562 + ], + "spans": [ + { + "bbox": [ + 111, + 551, + 480, + 562 + ], + "type": "text", + "content": "Figure 3. Visualization results compared with other methods. All models are trained under setting S1." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 583, + 288, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 583, + 288, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 583, + 288, + 668 + ], + "type": "text", + "content": "each position in the sequence to utilize the information from both preceding and subsequent time steps, offering an advantage in this particular metric. However, it's important to note that, despite being competitive in metric numbers, offline inference has limited practical applicability in real-world scenarios where online processing capability is most important." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 288, + 713 + ], + "type": "text", + "content": "The second setting follows [5, 10, 11, 33, 53], where we evaluate the methods on a larger benchmark from AMASS [25]. The subsets [2, 4, 6, 12, 21, 23, 26, 26, 28," + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 583, + 545, + 619 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 583, + 545, + 619 + ], + "spans": [ + { + "bbox": [ + 304, + 583, + 545, + 619 + ], + "type": "text", + "content": "40-42, 42] are for training, and Transition [25] and HumanEva [36] subsets are for testing. We term this setting as S2 in the following." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": "As shown in Tab. 3, our method achieves comparable performance with previous works on S2. However, we observe that the testing set of S2 is disproportionately small (i.e., only " + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 629, + 546, + 713 + ], + "type": "text", + "content": " of the training set). Such a small fraction cannot represent the overall data distribution of the large dataset and may not include sufficiently diverse motions to evaluate the models' scalability, causing unconvincing eval" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "158" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 63, + 70, + 272, + 191 + ], + "blocks": [ + { + "bbox": [ + 63, + 70, + 272, + 191 + ], + "lines": [ + { + "bbox": [ + 63, + 70, + 272, + 191 + ], + "spans": [ + { + "bbox": [ + 63, + 70, + 272, + 191 + ], + "type": "table", + "html": "
MethodMPJREMPJPEMPJVE
Final IK [1]12.399.5436.73
CoolMoves [3]4.585.5565.28
LoBSTr [48]8.095.5630.12
VAE-HMD [10]3.123.5128.23
AvatarPoser [18]2.592.6122.16
AvatarJLM [53]2.402.0917.82
AGRoL [11]2.252.1716.26
Ours2.101.8814.79
", + "image_path": "49ea08a4bfa927992ef6f2057eccfe47e1be24c456081be4c9acb7f10776ec89.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 47, + 234, + 286, + 352 + ], + "blocks": [ + { + "bbox": [ + 47, + 199, + 287, + 222 + ], + "lines": [ + { + "bbox": [ + 47, + 199, + 287, + 222 + ], + "spans": [ + { + "bbox": [ + 47, + 199, + 287, + 222 + ], + "type": "text", + "content": "Table 2. Evaluation results under setting S1 with the root joint as an additional input." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 234, + 286, + 352 + ], + "lines": [ + { + "bbox": [ + 47, + 234, + 286, + 352 + ], + "spans": [ + { + "bbox": [ + 47, + 234, + 286, + 352 + ], + "type": "table", + "html": "
MethodMPJREMPJPEMPJVEJitter
VAEHMD†[10]-7.45--
Humor†[33]-5.50--
FLAG†[5]-4.96--
AvatarPoser [18]4.706.3834.0510.21
AGRoL [11]4.306.1724.408.32
AvatarJLM [53]4.304.9326.177.19
Ours4.625.8633.547.13
", + "image_path": "b837406bb4dc04a62d08c5efb96769781cecde8a65db73b82e7691d357b79762.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 358, + 287, + 404 + ], + "lines": [ + { + "bbox": [ + 46, + 358, + 287, + 404 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 287, + 404 + ], + "type": "text", + "content": "Table 3. Evaluation result under setting S2. " + }, + { + "bbox": [ + 46, + 358, + 287, + 404 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 358, + 287, + 404 + ], + "type": "text", + "content": " indicates that these methods use additional inputs of pelvis location and rotation for training and inference, which are not directly comparable methods. The results of AvatarPoser [18] is provided by [11]." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 58, + 421, + 279, + 575 + ], + "blocks": [ + { + "bbox": [ + 58, + 421, + 279, + 575 + ], + "lines": [ + { + "bbox": [ + 58, + 421, + 279, + 575 + ], + "spans": [ + { + "bbox": [ + 58, + 421, + 279, + 575 + ], + "type": "image", + "image_path": "647a5fadc46381cd914e812c96d7489a2f680eb28713777b7d65dfac25edc678.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 88, + 583, + 246, + 594 + ], + "lines": [ + { + "bbox": [ + 88, + 583, + 246, + 594 + ], + "spans": [ + { + "bbox": [ + 88, + 583, + 246, + 594 + ], + "type": "text", + "content": "Figure 4. Visualization results on real data." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": "uation results. We introduce a new setting, S3, which adopts the same training and testing splitting ratio used in S1. In this setting, we randomly select " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " of the samples from the 15 subsets of S2 for training, while the remaining " + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 617, + 288, + 713 + ], + "type": "text", + "content": " are for testing. We train and evaluate the compared methods with this new setting. Table 4 reveals that under S3, the performance differences between the compared methods are more significant than S1 and S2. Since the test set has more" + } + ] + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 318, + 76, + 536, + 221 + ], + "blocks": [ + { + "bbox": [ + 318, + 76, + 536, + 221 + ], + "lines": [ + { + "bbox": [ + 318, + 76, + 536, + 221 + ], + "spans": [ + { + "bbox": [ + 318, + 76, + 536, + 221 + ], + "type": "image", + "image_path": "6f2f1e59031f15aed1de9aebc5a030d4ccb3377d508c5f7c99051887b369e0c5.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 228, + 545, + 262 + ], + "lines": [ + { + "bbox": [ + 304, + 228, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 228, + 545, + 262 + ], + "type": "text", + "content": "Figure 5. The visualization comparison for disentanglement. The darker the red color, the greater the deviation is between the predicted result and the ground truth." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 274, + 545, + 345 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 345 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 345 + ], + "type": "text", + "content": "diverse motions in S3, this benchmark evaluates the models' scalability in a more objective way. In this context, our method outperforms existing methods in most metrics, especially in the critical metric of Lower PE, highlighting the superiority of our stratified design for lower-body modeling and inference." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 347, + 546, + 574 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 347, + 546, + 574 + ], + "spans": [ + { + "bbox": [ + 304, + 347, + 546, + 574 + ], + "type": "text", + "content": "Fig. 3 presents a visual comparison between our SAGE Net and baseline methods, all trained under the S1 protocol, which is commonly used by baselines for releasing their trained checkpoints. These visualizations demonstrate the significant improvements that our model offers in reconstructing the lower body. For example, in the first row of samples, baseline methods typically reconstruct the feet too close to the ground, restricting the avatar's leg movements. Our model, however, overcomes this limitation, enabling more flexible leg movements. In the third row, for a subject climbing a ladder, the baseline methods often result in avatars with floating feet, failing to capture the detailed motion of climbing. In contrast, our SAGE Net accurately replicates complex foot movements, resulting in more realistic and precise climbing animations. We also evaluate our model on the real data, and for fair comparison, we directly use the real data release by [53]. As shown in Fig. 4, our method also achieves better reconstruction results on the real data." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 585, + 400, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 400, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 400, + 597 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 604, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 604, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 604, + 545, + 628 + ], + "type": "text", + "content": "We perform ablation study under S1 to justify the design choice of each component in our SAGE Net." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 713 + ], + "type": "text", + "content": "Disentangled Codebook: We establish a baseline using a unified motion representation to evaluate the disentangle strategy. Specifically, we developed a full-body VQ-VAE model that encodes full-body motion into a single, unified discrete codebook. Other components are the same as the original model. Results shown in the first and the last rows in Table 5, demonstrate that our approach employing dis" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "159" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 66, + 70, + 526, + 156 + ], + "blocks": [ + { + "bbox": [ + 66, + 70, + 526, + 156 + ], + "lines": [ + { + "bbox": [ + 66, + 70, + 526, + 156 + ], + "spans": [ + { + "bbox": [ + 66, + 70, + 526, + 156 + ], + "type": "table", + "html": "
MethodMPJREMPJPEMPJVEHand PEUpper PELower PERoot PEJitter
AGRoL(Online) [11]3.094.31109.291.791.807.953.86121.78
AGRoL(Offline) [11]2.833.8017.761.621.666.903.5310.08
AvatarJLM [53]3.143.3915.750.691.486.133.045.33
AvATARposer [18]2.723.3721.002.121.635.872.9010.24
Ours2.412.9516.941.151.285.372.745.27
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MethodMPJREMPJPEMPJVEJitter
w/o Disentangle2.643.6233.1825.07
w/o Full-Body Decoder2.713.6926.0710.80
w/o Refiner2.543.2621.999.29
5 Part Disentanglement2.633.4820.327.16
Ours2.533.2820.626.55
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MethodLowe PEJitter
Parallel Diffusion6.7314.71
Stratified Diffusion6.4610.83
", + "image_path": "5970bc805e409734633e2d01e43bcbefba25cbc6d6366e71b3dc94644eab508c.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 287, + 369 + ], + "lines": [ + { + "bbox": [ + 47, + 346, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 287, + 369 + ], + "type": "text", + "content": "Table 6. Evaluation results on the conditional strategy of the diffusion model under setting S1." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 378, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 378, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 378, + 287, + 474 + ], + "type": "text", + "content": "entangled latents significantly outperforms the baseline on all evaluation metrics. This demonstrates that the disentanglement can simplify the learning process by allowing the model to focus on a more limited set of movements and interactions. Additionally, Fig. 5 shows the visualization comparison between our model and baseline model, verifying that the disentangle can significantly improve the reconstruction results for the most challenging lower motions." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": "Full-Body Decoder and Refiner: The second and third rows of Tab. 5 demonstrate the impact of the full-body decoder and the refiner, respectively. Compared with utilizing the upper and lower decoder from VQ-VAE" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "_{up}" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": " and VQ-VAE" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "inline_equation", + "content": "_{low}" + }, + { + "bbox": [ + 46, + 474, + 287, + 593 + ], + "type": "text", + "content": ", the full-body decoder facilitates the integration of features from both the upper and lower body, improving the overall accuracy of full-body motion reconstruction. On the other hand, the refiner acts as a temporal memory, smoothing out the motion sequence to yield better visualization results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 594, + 287, + 714 + ], + "type": "text", + "content": "Disentanglement Strategy: To investigate the optimal disentanglement strategy, we explore an extreme disentanglement configuration by following the path from the root (Pelvis) node to each leaf node along the kinematic tree. Specifically, we break down the body into five segments: the paths from the root to the left hand (a), right hand (b), head (c), left foot (d), and right foot (e). As reported in the last two rows of Tab. 5, the natural joint interconnections within the upper (or lower) body were disrupted when further disentangling the human body, resulting in perfor" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 316, + 186, + 538, + 310 + ], + "blocks": [ + { + "bbox": [ + 316, + 186, + 538, + 310 + ], + "lines": [ + { + "bbox": [ + 316, + 186, + 538, + 310 + ], + "spans": [ + { + "bbox": [ + 316, + 186, + 538, + 310 + ], + "type": "image", + "image_path": "97bd799511d336aadc985270c806201f8332af4be272527298ada78a57f93dfd.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 308, + 316, + 541, + 328 + ], + "lines": [ + { + "bbox": [ + 308, + 316, + 541, + 328 + ], + "spans": [ + { + "bbox": [ + 308, + 316, + 541, + 328 + ], + "type": "text", + "content": "Figure 6. Failure cases. All models are trained under setting S1." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 335, + 504, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 504, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 504, + 346 + ], + "type": "text", + "content": "mance drops and complicating the model design." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 346, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 346, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 346, + 545, + 502 + ], + "type": "text", + "content": "Stratified Inference: Tab. 6 highlights the influence of our stratified design on the accuracy of lower body predictions. For comparison, we design a baseline that only uses the sparse observation for lower body latent generation without predicted upper body latent (term as Parallel Diffusion in the table). As we focus solely on the reconstruction quality of the lower body here, we use the decoding results on the generated lower latents from " + }, + { + "bbox": [ + 304, + 346, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\mathrm{VQ - VAELow}" + }, + { + "bbox": [ + 304, + 346, + 545, + 502 + ], + "type": "text", + "content": " to isolate the impact of other modules such as the full-body decoder and refiner. We report Lower PE and Jitter of the lower body for comparison. Results show that our stratified design markedly improves the accuracy of lower body predictions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 502, + 545, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 502, + 545, + 575 + ], + "spans": [ + { + "bbox": [ + 304, + 502, + 545, + 575 + ], + "type": "text", + "content": "**Limitation:** In Fig. 6, both the previous state-of-the-art method and our model encounter difficulties in two main situations: (1) External Force-Induced Movements (the top row). (2) Unconventional Poses (the bottom row). The addition of more varied samples to the training dataset can potentially enhance the model's performance in these areas." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 585, + 378, + 597 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 585, + 378, + 597 + ], + "spans": [ + { + "bbox": [ + 306, + 585, + 378, + 597 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "We study the problem of human avatar generation from sparse observations. Our key finding is that the upper and lower body motions should be disentangled with respect to the input signals from the upper-body joints. Based on this, we propose a novel stratified solution where the upper-body motion is reconstructed first, and the lower-body motion is reconstructed next and conditioned on the upper-body motion. Our proposed stratified solution achieves superior performance on public available benchmarks." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "160" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 84 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 91, + 286, + 712 + ], + "type": "list", + "angle": 0, + "index": 12, + "blocks": [ + { + "bbox": [ + 53, + 91, + 215, + 102 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 215, + 102 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 215, + 102 + ], + "type": "text", + "content": "[1] RootMotion Final IK., 2018. 2, 6, 7" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 53, + 104, + 286, + 128 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 104, + 286, + 128 + ], + "spans": [ + { + "bbox": [ + 53, + 104, + 286, + 128 + ], + "type": "text", + "content": "[2] Advanced Computing Center for the Arts and Design. 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In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 5745-5753, 2019. 3" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "spans": [ + { + "bbox": [ + 298, + 749, + 312, + 757 + ], + "type": "text", + "content": "163" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_content_list.json b/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7175367480f5cf0a3235ac8b51222363a3339452 --- /dev/null +++ b/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_content_list.json @@ -0,0 +1,1569 @@ +[ + { + "type": "text", + "text": "Streaming Dense Video Captioning", + "text_level": 1, + "bbox": [ + 305, + 130, + 663, + 152 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Xingyi Zhou* Anurag Arnab* Shyamal Buch Shen Yan \nAustin Myers Xuehan Xiong Arsha Nagrani Cordelia Schmid \nGoogle", + "bbox": [ + 212, + 180, + 756, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "An ideal model for dense video captioning – predicting captions localized temporally in a video – should be able to handle long input videos, predict rich, detailed textual descriptions, and be able to produce outputs before processing the entire video. Current state-of-the-art models, however, process a fixed number of downsampled frames, and make a single full prediction after seeing the whole video. We propose a streaming dense video captioning model that consists of two novel components: First, we propose a new memory module, based on clustering incoming tokens, which can handle arbitrarily long videos as the memory is of a fixed size. Second, we develop a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. Our model achieves this streaming ability, and significantly improves the state-of-the-art on three dense video captioning benchmarks: ActivityNet, YouCook2 and ViTT. Our code is released at https://github.com/google-research/scenic.", + "bbox": [ + 75, + 301, + 473, + 575 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 604, + 209, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Video is ubiquitous in modern society, quickly becoming one of the most prevalent media formats for transmitting information. The majority of computer vision models designed for video understanding only process a handful of frames, mostly covering only a few seconds [28, 30, 36, 46, 55], and are typically limited to classifying these short segments into a fixed number of concepts. In order to achieve a comprehensive, fine-grained video understanding, we study the task of dense video captioning – jointly localizing events temporally in video and generating captions for them. Ideal models for this goal should be able to handle both long input sequences – to reason over long, untrimmed videos – and also to handle long output sequences in text space, to describe in detail all the events within the video.", + "bbox": [ + 75, + 631, + 468, + 843 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior work on dense video captioning does not handle either long inputs or long outputs. Given a video of", + "bbox": [ + 76, + 844, + 470, + 875 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/cd5124675d807cdcb6e7fa5108bb96f26737371ec465dce4ea175454eba34b72.jpg", + "image_caption": [ + "(a) Conventional global dense video captioning models [48, 56]." + ], + "image_footnote": [], + "bbox": [ + 501, + 253, + 890, + 323 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/11fdecd9bb4c60c54afb36dc9af135e82ddb4e8be75f9da8831b98674b18536a.jpg", + "image_caption": [ + "(b) Our streaming dense video captioning model.", + "Figure 1. Comparing our streaming model (b) to conventional global models (a). Conventional global models encode the entire video at once, and produce captions for all events at the end. Our model encodes images frame-by-frame, uses them to update a running memory, and predicts captions sequentially." + ], + "image_footnote": [], + "bbox": [ + 501, + 340, + 887, + 458 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "any length, state-of-the-art models either sample very few frames (e.g., 6 frames [45]) with large strides [10, 27, 45] (i.e., temporal downsampling), or keep one feature per-frame for all the frames [48, 56, 62] (i.e., spatial downsampling). With long textual output, current models solely rely on auto-regressive decoding [17] to generate multiple sentences at the end.", + "bbox": [ + 496, + 561, + 890, + 666 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this work, we design a streaming model for dense video captioning as shown in Fig. 1. Our streaming model does not require access to all input frames concurrently in order to process the video thanks to a memory mechanism. Moreover, our model can produce outputs causally without processing the entire input sequence, thanks to a new streaming decoding algorithm. Streaming models such as ours are inherently suited to processing long videos – as they ingest frames one at a time. Moreover, as the output is streamed, intermediate predictions are produced before processing the full video. This property means that streaming models can in theory be applied to process live video streams, as required for applications such as video conferencing, security and continuous monitoring among others.", + "bbox": [ + 496, + 670, + 892, + 882 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In order to develop our streaming model, we first propose", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Equal contribution. {zhouxy, aarnab} @google.com", + "bbox": [ + 94, + 886, + 377, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "18243", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/34ef85e03f5a1fda96e700972dc8731ea99e891dbee7c5b42d1f443777c1e32c.jpg", + "image_caption": [ + "Figure 2. Illustration of our framework. Each frame is passed through an image encoder, one at a time. A memory model, based on clustering, maintains compressed visual features from the beginning up to the current frame. At certain frames, denoted as \"decoding points\", we decode the representations from our memory into captions and their timestamps. Earlier text predictions, if available, are also passed as a prefix to the language decoder for the following decoding points. Our model can run on videos of arbitrary length, as the memory has a constant size, and can also output predictions before processing the whole video." + ], + "image_footnote": [], + "bbox": [ + 117, + 88, + 851, + 280 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "a novel memory mechanism, that takes frames once at a time. The memory model is based on K-means clustering, and uses a fixed number of cluster-center tokens to represent the video at each timestamp. We show that this method is simple and effective, and can process variable numbers of frames, with a fixed computational budget at decoding.", + "bbox": [ + 75, + 363, + 470, + 453 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We also develop a streaming decoding algorithm, and train our network such that given a \"decoding point\" (Fig. 2) at a particular timestamp, it predicts all event captions that ended before it given the memory features at that timestamp. Our network is thus trained to make predictions at any timestamp of the video, and not just at the end of the video as in conventional, non-streaming models. Furthermore, we provide predictions from earlier decoding points as contexts for later ones. This context avoids predicting duplicated events, and can be used as an \"explicit\" memory in natural language summarising the earlier video. Our streaming output is also motivated by the fact that as the video length grows, our memory will inevitably lose information over time as its size is bounded. We avert this issue by making predictions before we have processed the entire video, and still keep early information via language context.", + "bbox": [ + 75, + 454, + 468, + 696 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We evaluate our approach on three popular dense video captioning datasets, ActivityNet [26], YouCook2 [61] and ViTT [21]. Our results show that our streaming model significantly improves over the state-of-the-art, which inevitably uses fewer frames or fewer features, by up to 11.0 CIDEr points. We show that our method generalizes across both GIT [45] and Vid2Seq [56] architectures. Finally, our proposed memory can also be applied to paragraph captioning, improving baselines by 1-5 CIDEr points.", + "bbox": [ + 75, + 696, + 470, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 76, + 844, + 218, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Dense video captioning. Dense video captioning requires captioning events, and localizing them temporally. Tra", + "bbox": [ + 75, + 869, + 470, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ditionally, prior work used a two-stage approach, first localizing events in video, and then subsequently captioning them [22, 23, 26, 44, 47]. More recent end-to-end approaches include PDVC [63] which infers event captions and timestamps using a DETR-like [9] model. Vid2Seq [56] augments the vocabulary of a language model with timestamp tokens, allowing them to generate concatenated event captions in the same manner as a regular captioning model. We also use the output formulation of [56], as it integrates well with foundation vision-language models [45]. A related, but different problem, is that of audio description in movies [18, 19, 40], which requires generating captions for the visually impaired that must be complementary to speech, and often uses auxiliary, non-causal models to recognize characters or their speech [19].", + "bbox": [ + 496, + 363, + 890, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "As far as we are aware, all prior dense captioning models are not causal, as they encode the entire video at once. Moreover, to process long videos, they typically use visual features that are downsampled heavily (by selecting a few frames [10, 27, 45], or spatially pooling features per frame [48, 56, 62]). In contrast, we process videos in a streaming manner, processing long input sequences one frame at a time with a memory module, and streaming output sentences with a novel decoding algorithm.", + "bbox": [ + 496, + 594, + 890, + 731 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Models for long videos. A common way of processing longer videos is to use a memory mechanism to provide a compact representation of past events. With transformers, memory can easily be implemented by using tokens from past observations as inputs for the present time step [12, 33, 53]. Examples in vision include [20, 32, 50, 51] which preextract features offline and retrieve them during inference, and are thus not causal. MemViT [52] uses token activations from previous time steps as inputs to the current time step. However, this means that the sequence length grows over time and so it cannot handle arbitrarily long videos.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "18244", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "An alternate view of memory is to see it as a method of compressing previously observed tokens into a smaller, fixed-size set to be used at future time steps. Token Turing Machines [38] summarize past and current observations using the token summarization module of [37]. MovieChat [41] follows a similar idea, but uses a variant of Token Merging [5] instead to perform the summarization. TeSTra [59] uses an exponential moving average to integrate video features instead. The advantage of such approaches is that the memory bank has a fixed size, and therefore the computational cost remains bounded regardless of the length of the video. Our memory model has this same desirable property. However, our memory is based on clustering, using the centers from a K-means-like algorithm to summarize tokens from each time step, and we show experimentally that this outperforms other alternatives.", + "bbox": [ + 75, + 90, + 472, + 332 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Causal models in video. Our streaming model is causal, meaning that its output only depends on current and past frames, without access to future frames. Although we are not aware of prior causal models for dense video captioning, there are causal models in many other vision domains. Online action detection [13, 25, 59, 60] aims to predict action labels for videos in real-time without access to future frames. Analogously, online temporal action localization [6, 24, 39] models also predict start- and end-times after an action is observed. Most models for object tracking [3, 49] and video object/instance segmentation [8, 29, 31] are causal too.", + "bbox": [ + 75, + 333, + 472, + 515 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "A common theme in the above tasks is that the model must make a prediction at each frame of the video. In contrast, we focus on dense video captioning [26], which is challenging as the output captions do not have a one-to-one correspondence with the video frames. We address this problem by proposing a streaming decoding algorithm.", + "bbox": [ + 75, + 516, + 472, + 609 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Streaming Dense Video Captioning", + "text_level": 1, + "bbox": [ + 76, + 625, + 397, + 642 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a video $\\mathbf{V} \\in \\mathbb{R}^{T \\times H \\times W \\times 3}$ , our goal is to produce a set of temporally localized captions: $\\{(s, e, \\mathbf{c})_1, \\ldots, (s, e, \\mathbf{c})_{n_e}\\}$ , where $s \\in \\mathbb{R}$ and $e \\in \\mathbb{R}$ are the starting and ending timestamps ( $0 \\leq s < e \\leq T$ ), respectively, $\\mathbf{c} = [w_1, \\dots, w_n]$ is a sequence of word tokens, and $n_e$ the number of events. Each word token $w_i$ is an integer in the range $[0, |V|]$ , indexing the vocabulary $V$ . We begin by describing conventional captioning models (Sec. 3.1), before detailing how we develop a streaming model (Fig. 2) by streaming inputs with memory (Sec. 3.2) and outputs with decoding points (Sec. 3.3).", + "bbox": [ + 75, + 648, + 472, + 819 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 830, + 218, + 845 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Captioning models broadly consist of a vision encoder followed by a text decoder. We outline these approaches, and show how they can be extended to dense captioning next.", + "bbox": [ + 75, + 854, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Visual encoder. The first step is to encode the video into features $\\mathbf{f} = \\mathcal{F}(\\mathbf{V}),\\mathbf{f}\\in \\mathbb{R}^{N\\times D}$ , where $N$ is the feature resolution (i.e., number of tokens for transformer-based encoders), and $D$ is the feature dimension. The visual feature encoder $\\mathcal{F}$ can be a native video backbone [1, 4], or an image encoder [34, 57] applied to each individual frame. In the latter case, the video feature is a stack of image features, i.e. $N = T\\cdot N_{f}$ , where $N_{f}$ is the number of tokens per frame. We use a per-frame encoding, but instead of pre-extracting them from the whole video, we use a memory mechanism to process the features in a causal, streaming fashion (Sec. 3.2) that can generalize to longer video durations.", + "bbox": [ + 496, + 90, + 893, + 272 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Text decoder. Given the visual features, $\\mathbf{f}$ , and optional textual prefix tokens, $\\mathbf{p}$ , the text decoder, $\\mathcal{D}$ generates a sequence of word tokens, $\\mathbf{c}$ from them. We use an autoregressive [17, 42] decoder that generates the next word token, $w_{i}$ , conditioned on previous words, $\\mathbf{w}_{1:i-1}$ , and prefix if provided as $w_{i} = \\mathcal{D}(\\mathbf{f}, \\mathbf{p}, \\mathbf{w}_{1:i-1})$ . Note that prefix tokens are typically not used in captioning tasks, but are used in question-answering (QA) to encode the input question. Concretely, the text decoder, $\\mathcal{D}$ , is a sequence of transformer layers [42] operating on a concatenation of visual features $\\mathbf{f}$ and word embeddings of the prefix [35, 45]. This architecture is shown to be effective in both captioning and QA tasks across image and video [10, 27, 45].", + "bbox": [ + 496, + 280, + 893, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Dense video captioning with timestamps. Combining the above visual encoder and text decoder gives a basic architecture for video captioning. To extend it for captioning multiple events with starting and ending timestamps, Vid2Seq [56] introduced two main modifications: First, it augments the vocabulary, $V'$ , of the captioning model with time tokens, $w^s$ and $w^e$ , which represent the starting and ending times, respectively. A single event is therefore represented as $\\mathbf{c}' = [w^s, w^e, w_1, \\dots, w_n]$ , and $|V'| = |V| + |T|$ where $|V| \\leq w^s < w^e \\leq |V'|$ , and $|T|$ is the number of time tokens. Second, Vid2Seq concatenates all timed captions into a single long caption that is ordered by starting time: $\\mathbf{C} = [\\mathbf{c}_1', \\mathbf{c}_2', \\dots, \\mathbf{c}_{n_e}']$ where $n_e$ is the number of events. Therefore, dense video captioning can be formulated as standard video captioning with target $\\mathbf{C}$ .", + "bbox": [ + 496, + 484, + 893, + 712 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Despite its effectiveness, the (generalized) Vid2Seq [56] architecture has a number of key limitations: First, it forwards visual features from the whole video, f through the decoder, meaning that it does not scale effectively to longer videos and more tokens. In addition, as Vid2Seq predicts all event captions at once, after processing the whole video, it struggles with predicting long, detailed captions. To address these issues, we introduce streaming dense video captioning models, where we process the inputs once at a time using a memory module to bound computational costs, and stream the outputs such that we can make predictions before processing the whole video.", + "bbox": [ + 496, + 719, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "18245", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1: Updating memory tokens at a timestamp." + ], + "code_body": "Input : $\\mathbf{M}_{t - 1}\\in \\mathbb{R}^{K\\times D}$ : memory tokens $\\mathbf{W}_{t - 1}\\in \\mathbb{R}^K$ : weights of memory tokens $\\mathbf{f}_t\\in \\mathbb{R}^{N_f\\times D}$ : incoming tokens Hyperparameters: $\\tau$ : number of K-means iterations. Output : $\\mathbf{M}_t\\in \\mathbb{R}^{K\\times D}$ : updated memory tokens $\\mathbf{W}_t\\in \\mathbb{R}^K$ : updated weights of memory \n1 $\\mathbf{X}\\gets [\\mathbf{M}_{t - 1},\\mathbf{f}_t]$ // Concatenate memory and incoming tokens. \n2 $\\mathbf{W}\\gets [\\mathbf{W}_{t - 1},\\mathbf{1}]$ // Initialize incoming weights and concatenate. \n3 $\\mathbf{M}_t\\gets \\mathbf{M}_{t - 1}$ // Initialize new cluster centers as the old centers. \n4 for $i\\gets I$ : $\\tau$ do \n5 $\\mathbf{d}\\gets$ pairwise.l2_distance(X, $\\mathbf{M}_t$ ) // Shape $(K + N_{f},K)$ . \n6 $\\delta \\gets$ d.argmin(axis=1) // Assign each token to a center. \n7 $\\delta \\gets$ make_onehot(δ,K) // Binary. Shape $(K + N_{f},K)$ . \n8 $\\mathbf{W}_t\\gets \\delta^\\top \\mathbf{W}_t$ // Compute #tokens assigned to each center. \n9 $\\mathbf{A}\\gets \\delta^\\top /\\mathbf{W}_t$ // Weight matrix. “/” is elementwise div. \n10 $\\mathbf{M}_t\\gets \\mathbf{AX}$ // Compute new centers as a linear function. \n11 end \n12 return $\\mathbf{M}_t$ , $\\mathbf{W}_t$", + "bbox": [ + 78, + 111, + 468, + 335 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Streaming inputs using memory", + "text_level": 1, + "bbox": [ + 76, + 342, + 357, + 358 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The input visual features, $\\mathbf{f}$ , have dimensionality $\\mathbb{R}^{T\\cdot N_f\\times D}$ where typical values are $T > 64$ for a sparsely sampled (e.g. 1 FPS), few-minute-long video, and $N_{f} = 257$ tokens per-frame for a vision transformer such as CLIP [34]. Directly feeding all $T\\cdot N_{f}$ to the text decoder is prohibitively expensive, due to the quadratic complexity of self-attention. Therefore, existing methods aggressively downsample $\\mathbf{f}$ to reduce the number of tokens (by temporally sampling a few frames with large strides [10, 45], or spatially subsampling each frame to a single token [48, 56, 62]). Even so, we will reach memory limits with longer videos, and the information required for fine-grained localization and description is lost. Therefore, rather than aggressive downsampling, we use a memory mechanism to process all tokens frame-by-frame, which ensures that the computational cost is bounded irrespective of the length of the video.", + "bbox": [ + 75, + 366, + 468, + 608 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $K$ be a pre-defined memory size, the memory at each time $\\mathbf{M}_t$ would always be the constant size $K$ , i.e., $\\mathbf{M}_t \\in \\mathbb{R}^{K \\times D}, \\forall t$ . We interpret $\\mathbf{M}$ as being a summary of all relevant information in the video, and initialize it by taking the first $K$ tokens from $\\mathbf{f}$ . Therefore, we set $K$ as a multiple of $N_f$ , such that the initial memory is the features of the first $\\frac{K}{N_f}$ frames: $\\mathbf{M}_{K / N_f} = [\\mathbf{f}_1, \\dots, \\mathbf{f}_{K / N_f}]$ .", + "bbox": [ + 75, + 609, + 468, + 719 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we update the memory at each timestamp for each incoming frame $\\mathbf{f}_t$ . Our intuition is to keep as much diverse information in the original video as possible, while not increasing the storage budget (i.e. by keeping a constant memory size $K$ ). We thus propose a K-means-like clustering algorithm, to use the feature cluster centers as the approximate video features. To avoid the cluster centers biasing quickly to incoming features, we keep track of the number of merged tokens in each cluster center. We use this as a momentum weight, so that cluster centers that are merged from more tokens change slower. The detailed algorithm diagram is provided in Alg. 1, and illustrated in Fig. 3.", + "bbox": [ + 75, + 719, + 470, + 901 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/57de4c0239133ed7f7764b4672330c034520100cc596cb7d6d101084fd043c16.jpg", + "image_caption": [ + "Figure 3. Illustration of our clustering-based memory module. The current memory tokens are shown by blue squares. At each time step, the memory tokens evolve by integrating information from the incoming tokens (gray squares), using K-means iterations to produce the updated memory tokens (green circles)." + ], + "image_footnote": [], + "bbox": [ + 537, + 94, + 857, + 219 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The K-means algorithm is not differentiable with respect to the assignment of data points to cluster centers, $\\delta$ (Line 6 of Alg.1). However, the inputs and outputs of our memory module are the updated cluster centers, $\\mathbf{M}_t$ , which is a linear mapping of the input $\\mathbf{X} = [\\mathbf{M}_{t - 1},\\mathbf{f}_t]$ , as $\\mathbf{M}_t = \\mathbf{A}\\mathbf{X}$ where $\\mathbf{A}$ is a weight matrix computed from $\\mathbf{X}$ . Therefore, even though we cannot compute the gradient of $\\mathbf{A}$ with respect to $\\mathbf{X}$ , we can compute the gradient of $\\mathbf{M}_t$ with respect to the input $\\mathbf{X}$ , and thus to the input visual feature $\\mathbf{f}$ . As a result, we can use our memory module in any part of a neural network, and learn parameters in preceding layers.", + "bbox": [ + 496, + 310, + 890, + 478 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Streaming outputs with decoding points", + "text_level": 1, + "bbox": [ + 500, + 486, + 841, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The memory module from Sec. 3.2 enables us to efficiently ingest long input videos. However, it is still desirable for our model's text decoder to predict outputs before it has processed the entire input sequence: Streaming the output substantially decreases the latency of the model, as we do not have to wait for the model to process the entire input sequence to make predictions. This is particularly relevant for processing, for example, live video streams. Furthermore, streaming the output can in fact increase our model's accuracy: As we have a memory with a fixed size, $K$ , from which we decode outputs, we will inevitably lose information over time. We can therefore avert this issue by making predictions before we have processed the entire video.", + "bbox": [ + 496, + 508, + 890, + 705 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Decoding points As shown in Fig. 4, we define \"decoding points\", $d_{i}$ , as intermediate timestamps where we decode event captions given the features in our memory, $\\mathbf{M}_{d_i}$ . We train our model such that at each decoding point, $d_{i}$ the model predicts all event captions that finished before it. More specifically,", + "bbox": [ + 496, + 723, + 890, + 814 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {Y} _ {i} = \\left\\{\\left(w _ {j} ^ {s}, w _ {j} ^ {e}, \\mathbf {c} _ {j}\\right) \\mid w _ {j} ^ {e} \\leq d _ {i} \\right\\}, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 593, + 825, + 890, + 844 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{V}_i$ is the set of all event captions corresponding to the $i^{\\mathrm{th}}$ decoding point $d_{i}$ , and $w_{j}^{s}, w_{j}^{e}$ are the starting and ending time of the $j^{\\mathrm{th}}$ event.", + "bbox": [ + 496, + 853, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "18246", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/ebc3a539681804380bf14dbcdfa57cd40847dc17dea96132c34e8c3d3bf635bc.jpg", + "image_caption": [ + "Figure 4. Decoding point supervision in training. A decoding point, $d_i$ , can be at any frame. At each point, we take the memory features, $\\mathbf{M}_{d_i}$ , and predict all events that have finished before $d_i$ and are not in the prefix $\\mathbf{p}$ . Therefore, the union between the prefix and the prediction target covers all events finished before it." + ], + "image_footnote": [], + "bbox": [ + 106, + 89, + 434, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As decoding points are applied sequentially, later decoding points should have access to the predictions of earlier decoding points, and should not repeat them again. Therefore, from the second decoding point onwards, we concatenate the outputs of previous decoding points as the prefix to the text decoder, as shown in Fig. 4. Moreover, during training, we perform further data augmentation by randomly removing some of the previous event captions from the prefix, and adding them to the target instead, to increase robustness to potential errors in earlier predictions. We therefore denote our prefixes and captioning targets during training as", + "bbox": [ + 75, + 285, + 470, + 450 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {p} _ {i} = \\left[ \\mathbf {c} _ {1} ^ {\\prime}, \\mathbf {c} _ {2} ^ {\\prime}, \\dots , \\mathbf {c} _ {j - 1} ^ {\\prime} \\right] \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 462, + 468, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {y} _ {i} = \\left[ \\mathbf {c} _ {j} ^ {\\prime}, \\mathbf {c} _ {j + 1} ^ {\\prime}, \\dots , \\mathbf {c} _ {| \\mathcal {Y} _ {i} |} ^ {\\prime} \\right], \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 184, + 483, + 468, + 501 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $j < |\\mathcal{V}_i|$ is a randomly chosen splitting point to partition the target and context. During inference, we use the models actual predictions, $\\mathbf{p}_i = [\\hat{\\mathbf{y}}_1,\\hat{\\mathbf{y}}_2,\\dots ,\\hat{\\mathbf{y}}_{i - 1}]$ , instead.", + "bbox": [ + 75, + 512, + 468, + 558 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In practice, we uniformly sample decoding points during both training and inference, with a stride of $S$ frames. Since the model is trained to predict all event captions before the decoding point, it means that the exact location at inference time does not need to match the event boundaries closely. The number of decoding points can be also different between training and inference, as we will ablate. This method is both simple and scalable, as we show experimentally in the next section.", + "bbox": [ + 75, + 558, + 468, + 693 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experimental Evaluation", + "text_level": 1, + "bbox": [ + 76, + 707, + 310, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 732, + 266, + 750 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.1 Datasets and Evaluation Metrics", + "text_level": 1, + "bbox": [ + 76, + 756, + 357, + 768 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We evaluate our model on the three most popular dense video captioning datasets: ActivityNet Captions [26], YouCook2[61], and ViTT [21].", + "bbox": [ + 75, + 779, + 468, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ActivityNet Captions [26] contains 8,649 training videos and 4,267 validation videos (considering videos that are still online on YouTube). The videos are untrimmed, each containing multiple action events, with an average video length of 2 minutes and an average of 3.7 events. The", + "bbox": [ + 75, + 825, + 468, + 898 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "videos are selected from the ActivityNet [7], which covers a wide range of visual domains. Each video is carefully labeled by human annotators. We use this dataset for both dense captioning (predicting a sequence of captions with their start- and end-times) and paragraph captioning (predicting the aforementioned captions as a single paragraph without timestamps).", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "YouCook2 [61] contains 1,333 training videos and 456 validation videos. The videos are on average 5.3 minutes long, with an average of 7.8 events. This dataset focuses on cooking scenes, and most videos contain one main actor cooking while describing the recipe. The videos are manually annotated, aided by speech transcriptions obtained through Automatic Speech Recognition (ASR). As expected due to the annotation process, using ASR as an additional modality can be used to improve model predictions [56]. However, our work focuses on using visual-only inputs, to study our proposed streaming model. We also perform dense and paragraph captioning on this dataset.", + "bbox": [ + 496, + 196, + 890, + 378 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "ViTT [21] contains 4,608 training videos and 2,301 testing videos, which are on average 4.7 minutes long and contain 7 events per video. It is collected in a similar way as YouCook2, but focuses on more diverse domains. Again, we do not use the ASR inputs in our experiments.", + "bbox": [ + 496, + 378, + 890, + 455 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Evaluation Metrics For all datasets, we report standard dense captioning evaluation metrics following Vid2Seq [56] and PDVC [48]. The primary metric is CIDEr which has been adapted to jointly evaluate captioning and localisation. In particular, we average the CIDEr score [43] for positive ground-truth-prediction pairs with a temporal IoU above the thresholds, $\\{0.3, 0.5, 0.7, 0.9\\}$ . Similarly, we report ME-TEOR [2] averaged over multiple IoU thresholds. Finally, we report the recently proposed $\\mathrm{SODA}_c$ [16], which considers all event captions from the same video, and is therefore a more holistic measure.", + "bbox": [ + 496, + 455, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1.2 Implementation details", + "text_level": 1, + "bbox": [ + 500, + 646, + 714, + 661 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We implement our streaming model on two video captioning architectures, GIT [45] and Vid2Seq [56]. Both use a ViT-L [14] initialized from CLIP [34] as image encoder $\\mathcal{F}$ .", + "bbox": [ + 496, + 672, + 890, + 717 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "GIT [45] concatenates all tokens from all input frames, f, and feeds them to a 6-layer transformer language decoder. We apply our streaming input module before the language decoder, i.e., rather than concatenating frame features, we use our memory features instead. The original GIT paper pretrains the language decoder on in-house data [45]. As we do not have access to the original data or weights, we pretrain our GIT model on the WebLI dataset [11].", + "bbox": [ + 496, + 718, + 890, + 838 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Vid2Seq [56] pools all frame tokens spatially into 1 token per frame, and then applies a 12-layer temporal transformer [1] to obtain the final visual features. The language decoder is a 12-layer T5-Base decoder [35]. Vid2Seq pre", + "bbox": [ + 496, + 839, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "18247", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/28747a3885a382adbcbcf36e7151d4c33ef4a4f18f2442f4622fb3074942a4e8.jpg", + "table_caption": [], + "table_footnote": [ + "Table 1. Ablation on memory modules. We show CIDEr (averaged over multiple IoUs) on ActivityNet with GIT under different # input frames $T$ . The 2nd column shows the number of input tokens to the language decoder. $N_{f} = 257$ is the number of tokens per-frame. $K = 514$ is the number of memory tokens. Our module benefits from more frames, and outperforms other alternatives." + ], + "table_body": "
#TokensT=16T=32T=64T=128
No memoryT×Nf29.8---
Spatial poolingT27.627.327.927.4
Temporal poolingNf29.328.026.825.2
EMA [59]Nf28.226.322.016.3
MovieChat [41]K29.329.228.929.3
Clustering (ours)K29.829.230.630.4
", + "bbox": [ + 83, + 80, + 459, + 208 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/acc62d69816d4ac0125dcac1ee16fdfa108777293376a3e756752e6222550b82.jpg", + "table_caption": [], + "table_footnote": [ + "(a) #memory tokens. (b) K-means iterations.", + "Table 2. Ablation on memory module hyperparameters. We perform experiments on ActivityNet with GIT with 64 frames." + ], + "table_body": "
KCIDEr
25729.4
257 × 230.6
257 × 329.8
", + "bbox": [ + 81, + 324, + 202, + 402 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/9eb87edab471b4588606ce6c3b1ca0fbb0080ca298fd32fc4cf2dc229b853c81.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Iters.CIDEr
130.3
230.6
430.3
", + "bbox": [ + 218, + 324, + 321, + 402 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/d81846eaee43790b654d148b6bdc998c6a011c92cf89721980b924aef016022e.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Momentum term in clustering" + ], + "table_body": "
MomentumCIDEr
X29.7
✓30.6
", + "bbox": [ + 334, + 324, + 468, + 386 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "trains the temporal transformer and the T5 decoder on narrated videos from the YT-Temporal dataset [58]. We use their public, pretrained weights as our initialization. We apply our streaming input module before the temporal transformer, to ensure the intermediate features remain causal.", + "bbox": [ + 75, + 462, + 468, + 536 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "When finetuning our model for each dataset, we freeze the frame encoder following prior works [48, 56, 63]. We provide detailed training hyperparameters in the supplementary. For each architecture, the training hyperparameters are shared across the 3 datasets.", + "bbox": [ + 75, + 539, + 468, + 613 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Analysis of Streaming Modules", + "text_level": 1, + "bbox": [ + 76, + 627, + 352, + 643 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We first analyze each of the main components of our model: streaming the input with our memory module (Sec. 3.2), and then streaming outputs using decoding points (Sec. 3.3). Unless otherwise stated, we use the GIT [45] backbone for our experiments. Due to randomness in training and evaluation, for all ablation experiments (Tab. 1-Tab. 3), we repeat the same run 3 times and report the averaged metrics. When compared to other methods (Tab. 4, Tab. 5), we report results for the best model.", + "bbox": [ + 75, + 651, + 468, + 787 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2.1 Streaming inputs with memory", + "text_level": 1, + "bbox": [ + 76, + 814, + 346, + 830 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "As the GIT [45] architecture concatenates visual features, f, from multiple frames before passing it to the language decoder, it is limited by the number of frames that it can process. Our clustering-based memory module allows us", + "bbox": [ + 75, + 839, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/eda6dd09c865adf3d69f41fc4f63d636e60ffd8c0a479bc81ca0fa0262e6e1bd.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Number of decoding points12481620
CIDEr30.634.538.839.540.640.4
", + "bbox": [ + 506, + 80, + 883, + 118 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/84108b7c335aada6aae48daefceeb67f44640f6edbbb2604f2721a1b2aedcbdb.jpg", + "table_caption": [ + "(a) Number of decoding points during training." + ], + "table_footnote": [ + "(b) Context provided (c) Random masking (d) Decoding point after the first decoding prefix as augmentation stride during inference point. during training. (input 64 frames)." + ], + "table_body": "
PrefixCIDErAug. PrefixCIDErStrideCIDEr
None23.1×37.63240.6
Captions40.6✓40.62134.7
Captions & time39.3
", + "bbox": [ + 503, + 133, + 869, + 195 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 3. Ablation on streaming outputs. (a) Increasing the number of decoding points during training consistently improves accuracy, as it provides more supervision to the model. (b) It is critical to provide context after the first decoding point, so that the model does not repeat predictions. Providing captions alone, without timestamps is sufficient. (c) It is important to provide imperfect prefixes during training, to mimic model behavior in inference. (d) Stride used for decoding during inference.", + "bbox": [ + 500, + 234, + 890, + 345 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "to process more frames, and we consider the following approaches to evaluate it:", + "bbox": [ + 498, + 363, + 890, + 392 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "No memory: We simply concatenate all visual tokens from all frames as done in GIT [45]. Due to memory constraints, we can only feed up to 16 frames to the decoder.", + "bbox": [ + 498, + 393, + 890, + 439 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Spatial- or temporal-pooling: We pool the visual features, f, along either the spatial or temporal dimensions to reduce the number of tokens fed to the language decoder.", + "bbox": [ + 498, + 441, + 890, + 487 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "EMA: We use an exponential moving average of frame features, $\\mathbf{f}_t$ , at each time step, following TeSTra [59]. We sweep the decay rate from $\\{0.9, 0.99, 0.999\\}$ , finding 0.9 to perform best.", + "bbox": [ + 498, + 488, + 890, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "MovieChat [41]. Finally, the recent MovieChat paper maintains a memory of $K$ tokens. For each incoming frame, it sequentially processes each token, and merges the two most similar tokens in the memory bank such that the size remains fixed at $K$ . We implement this method using the author's public code.", + "bbox": [ + 498, + 549, + 890, + 640 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Tab. 1 compares the results of the different memory modules. For $T = 16$ , where we can feed all the tokens from the vision backbone, $\\mathbf{f}$ , into the decoder, \"no memory\" and our method both performs the best. We expected \"no memory\" to perform well, as it uses the most tokens, $T \\times N_f$ . However, our clustering-based method achieves the same performance, which suggests that it is able to effectively capture the relevant information in the video with $8 \\times$ fewer tokens, and is causal too. It is not possible to use \"no memory\" for $T > 16$ due to its computational cost.", + "bbox": [ + 496, + 642, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "With more frames, naively pooling along the spatial-, or temporal-dimensions actually performs worse. This is likely because we are averaging out information over longer temporal durations, and thus losing the details required for more detailed localization or captioning. Our method and MovieChat on the other hand, are able to leverage more frames to improve performance, as they keep diverse fea", + "bbox": [ + 496, + 795, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "18248", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/957c3ae4f0404034c0d4066a6cd516afe23a285f1fd708df58fd64ae81e7a683.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ActivityNetYouCook2ViTT
CIDErSODAMeteorF1CIDErSODAMeteorF1CIDErSODAMeteorF1
MT [62]9.3-5.0-6.1-3.2-----
E2ESG [63]----25.0-3.5-----
PDVC [48]29.36.07.6-28.94.95.7-----
GIT [45]29.85.77.850.612.13.13.417.715.17.13.432.5
Vid2Seq†[56]30.25.98.551.825.35.76.423.523.09.85.037.7
Streaming GIT (ours)41.26.69.050.915.43.23.616.618.58.34.033.9
Streaming Vid2Seq (ours)37.86.210.052.932.96.07.124.125.210.05.835.4
", + "bbox": [ + 109, + 88, + 856, + 243 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 4. Comparison to the state-of-the-art on dense video captioning We add our streaming model to both GIT [45] and Vid2Seq [56], denoted by Streaming GIT and Streaming Vid2Seq, respectively, achieving consistent and substantial improvements across three datasets. All models use only visual inputs. $^\\dagger$ denotes version with visual-only inputs.", + "bbox": [ + 75, + 246, + 890, + 289 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tures within the memory. Finally, our clustering method outperforms MovieChat and other memory modules for all numbers of frames that we considered, which is why we use it for all future experiments.", + "bbox": [ + 75, + 305, + 468, + 364 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We also ablate the hyperparameters of our memory module in Tab. 2. Following this experiment, we set $K = 257 \\times 2$ , or the number of tokens in two frames, and use 2 iterations of K-means, as it achieves the best performance. Our proposed momentum term (Sec. 3.2), which prevents cluster centers from becoming too biased towards incoming frame tokens, also improves CIDEr from 29.7 to 30.6.", + "bbox": [ + 75, + 364, + 468, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.2 Streaming outputs", + "text_level": 1, + "bbox": [ + 76, + 482, + 261, + 498 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We now analyze the effect of our streaming decoding method (Sec. 3.3), which enables us to predict event captions from intermediate features in our memory, and utilize previous prediction as the prefix to our text decoder. Table 3 analyses the effects of the number of decoding points during training, the impact of the prefix, and how we select decoding points during inference.", + "bbox": [ + 75, + 506, + 468, + 612 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3a shows that we achieve significant improvements by increasing the number of decoding points during training, improving the CIDEr score by 10 points, or $33\\%$ relative, compared to only making predictions at the end, as in conventional models. Streaming the output with decoding points can provide performance benefits for multiple reasons: First, as we have multiple decoding points, the required output caption is shorter at each decoding point, making the captioning task easier. Second, the visual features from our memory, M, may be aligned better with the target text, since M does not represent the visual features from the entire video as in baseline approaches, but only the features up to the decoding point. Finally, training with decoding points provides a stronger training signal to the model, as we provide training supervision at each decoding point. Moreover, it should aid generalization, as the network is being trained to make consistent predictions from more points along the timeline.", + "bbox": [ + 75, + 613, + 470, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Tab. 3b shows that it is essential to provide past predic", + "bbox": [ + 96, + 885, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "tions as the prefix. Without a prefix, the model is poor, underperforming our non-streaming baseline of only decoding at the end (30.6). This is because the model predicts duplicated predictions at each decoding point. Providing past captions outperforms this baseline substantially. We find that also adding previously predicted timestamps, does not improve over captions alone, suggesting that temporal boundaries of past events are not particularly informative for future events. Tab. 3c further shows that while training with a prefix, it is important to mimic inference behavior by including missing captions in earlier predictions.", + "bbox": [ + 496, + 305, + 890, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 3d examines the choice of decoding points during inference. We find that using a stride, $S = 32$ (which equates to a decoding point at the middle and end of a 64-frame clip), performs considerably better than $S = 21$ (three uniformly chosen points). We observed qualitatively that using too many decoding points during inference can sometimes still result in the model making duplicate predictions (even with past prediction as the prefix). Whilst it is also possible to remove duplicate predictions with non-maximal suppression (NMS [15]), it is more challenging for captioning models as we also require a calibrated score for each event caption to perform NMS. We therefore leave an investigation of NMS for dense video captioning to future work.", + "bbox": [ + 496, + 470, + 890, + 667 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2.3 Generalization to backbones and datasets", + "text_level": 1, + "bbox": [ + 500, + 679, + 843, + 694 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To show the generality of our method, we add our streaming modules onto both the GIT [45] and Vid2Seq [56] architectures, which we denote as Streaming GIT and Streaming Vid2Seq, respectively.", + "bbox": [ + 496, + 703, + 890, + 763 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The last two rows of Tab. 4 shows that we improve substantially over both baselines consistently on three datasets. Our GIT baseline can process a maximum of $N_{f} = 16$ frames due to memory limitations, and our improvement also stems from the fact that we use $N_{f} = 64$ for our Streaming GIT thanks to our memory module. Vid2Seq pools visual tokens spatially such that it only uses a single token per frame. Therefore, our Streaming Vid2Seq does not use more frames than the baseline, and the improvement is due", + "bbox": [ + 496, + 763, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "18249", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/495c75ac89baf3470019768c9c7fe62336985d0d020796bba5b8735fa73f8982.jpg", + "image_caption": [ + "Figure 5. Qualitative results on ActivityNet validation. Results from the ground truth (top), the baseline (middle), and our model (bottom). We show outputs from two decoding points in green and blue respectively. Our model captures more details than the baseline." + ], + "image_footnote": [], + "bbox": [ + 83, + 80, + 883, + 284 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "to our streaming of output event captions, which improves performance significantly as shown in Tab. 3.", + "bbox": [ + 75, + 329, + 468, + 358 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Finally, we observe that our Vid2Seq baseline performs substantially better than the GIT baseline on YouCook2. This difference is due to the pretraining: We used the public, pretrained Vid2Seq checkpoint [56] which was pretrained on YT-Temporal [58] - a dataset with a similar domain to YouCook2. Note that this is the same experimental protocol as Vid2Seq [56], the current state-of-the-art.", + "bbox": [ + 75, + 359, + 468, + 465 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. State-of-the-art Comparison", + "text_level": 1, + "bbox": [ + 76, + 479, + 331, + 494 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Tab. 4 also compares our method to the state-of-the-art among dense video captioning methods using only video frames as inputs. We achieved substantial gains over prior, published works, notably improving CIDEr on ActivityNet by 11.0 points, and YouCook2 by 4.0 points, respectively. We also achieved improvements, albeit smaller, on SODA and Meteor. Our improvements on localization (F1) are smaller, showing the gains are more from better captioning qualities. Fig. 5 visualizes an example on ActivityNet.", + "bbox": [ + 75, + 503, + 468, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We note that it is possible to further improve results, particularly on YouCook2, by using Automatic Speech Recognition (ASR) as an additional input modality [56]. This is primarily because the spoken utterances of the actors are well aligned with the visual content, and because ASR was used in the annotation procedure of the dataset itself. However, integrating multiple modalities such as ASR is orthogonal to the main focus of this work.", + "bbox": [ + 75, + 641, + 468, + 761 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Paragraph captioning. In addition to dense captioning, we also compare with state-of-the-art models on the same datasets for paragraph captioning, which aims to predict the captions throughout the entire video, but without any timestamps. Therefore, we only apply our streaming input model here, as the timestamps needed to assign decoding points during training are not available in this setting.", + "bbox": [ + 75, + 763, + 468, + 868 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We train our Streaming GIT model for paragraph captioning, on both ActivityNet [26] and Youcook2 [61]. Tab. 5", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/fce93c77f2ad962c1081a019b8ca86adb353f4cc1b63bed8df2a006a20c2563c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
ActivityNetYouCook2
MFT [54]19.1-
PDVC [48]20.5-
Vid2Seq [56]†28.026.6
GIT [45]32.528.4
Ours33.433.9
", + "bbox": [ + 542, + 324, + 844, + 438 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 5. State-of-the-art comparison on paragraph captioning. We report CIDEr on ActivityNet and YouCook2 validation set. We compare models that do not require action proposal inputs and only takes visual inputs. $\\dagger$ denotes version with visual-only inputs. Our model achieves the best performance on both datasets. shows that we achieve state-of-the-art results on this task too. The GIT baseline is our model trained on the same setting as our full model, but uses 16 input frames with all tokens concatenated for the decoder. This baseline already outperforms the state-of-the-art from visual-only inputs. Our model uses more input frames (64 frames), and further boosts the performance by 0.9 and 5.5 points on the two datasets, respectively, showing the benefits of our memory module which is consistent with our results in Tab. 1.", + "bbox": [ + 496, + 439, + 892, + 646 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion and Future Work", + "text_level": 1, + "bbox": [ + 500, + 670, + 769, + 686 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We have proposed a streaming model for dense video captioning with two novel components: A clustering-based memory that can efficiently handle arbitrarily long videos with bounded computation, and a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. We achieve this streaming ability while also improving the state-of-the-art on five dense- and paragraphCaptioning tasks.", + "bbox": [ + 496, + 699, + 890, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Future work is to develop a benchmark for dense video captioning which requires reasoning over longer videos than current datasets, to better evaluate the abilities of streaming models such as ours.", + "bbox": [ + 496, + 823, + 890, + 882 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. We thank Chen Sun for helpful discussions.", + "bbox": [ + 500, + 886, + 883, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "18250", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. ViViT: A Video Vision Transformer. In ICCV, 2021. 3, 5", + "[2] Satanjeev Banerjee and Alon Lavie. Meteor: An automatic metric for mt evaluation with improved correlation with human judgments. In ACL Workshops, 2005. 5", + "[3] Philipp Bergmann, Tim Meinhardt, and Laura Leal-Taixe. Tracking without bells and whistles. In ICCV, pages 941-951, 2019. 3", + "[4] Gedas Bertasius, Heng Wang, and Lorenzo Torresani. Is space-time attention all you need for video understanding? 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ACL, 2022. 2, 6, 7" + ], + "bbox": [ + 501, + 92, + 890, + 844 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "18252", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_model.json b/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_model.json new file mode 100644 index 0000000000000000000000000000000000000000..890794e14a72520590b98b3a5a6552c7882fbcdf --- /dev/null +++ b/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_model.json @@ -0,0 +1,2310 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.307, + 0.131, + 0.664, + 0.154 + ], + "angle": 0, + "content": "Streaming Dense Video Captioning" + }, + { + "type": "text", + "bbox": [ + 0.213, + 0.181, + 0.758, + 0.234 + ], + "angle": 0, + "content": "Xingyi Zhou* Anurag Arnab* Shyamal Buch Shen Yan \nAustin Myers Xuehan Xiong Arsha Nagrani Cordelia Schmid \nGoogle" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.302, + 0.474, + 0.576 + ], + "angle": 0, + "content": "An ideal model for dense video captioning – predicting captions localized temporally in a video – should be able to handle long input videos, predict rich, detailed textual descriptions, and be able to produce outputs before processing the entire video. Current state-of-the-art models, however, process a fixed number of downsampled frames, and make a single full prediction after seeing the whole video. We propose a streaming dense video captioning model that consists of two novel components: First, we propose a new memory module, based on clustering incoming tokens, which can handle arbitrarily long videos as the memory is of a fixed size. Second, we develop a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. Our model achieves this streaming ability, and significantly improves the state-of-the-art on three dense video captioning benchmarks: ActivityNet, YouCook2 and ViTT. Our code is released at https://github.com/google-research/scenic." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.605, + 0.21, + 0.621 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.632, + 0.47, + 0.844 + ], + "angle": 0, + "content": "Video is ubiquitous in modern society, quickly becoming one of the most prevalent media formats for transmitting information. The majority of computer vision models designed for video understanding only process a handful of frames, mostly covering only a few seconds [28, 30, 36, 46, 55], and are typically limited to classifying these short segments into a fixed number of concepts. In order to achieve a comprehensive, fine-grained video understanding, we study the task of dense video captioning – jointly localizing events temporally in video and generating captions for them. Ideal models for this goal should be able to handle both long input sequences – to reason over long, untrimmed videos – and also to handle long output sequences in text space, to describe in detail all the events within the video." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.845, + 0.471, + 0.875 + ], + "angle": 0, + "content": "Prior work on dense video captioning does not handle either long inputs or long outputs. Given a video of" + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.255, + 0.891, + 0.324 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.521, + 0.327, + 0.872, + 0.34 + ], + "angle": 0, + "content": "(a) Conventional global dense video captioning models [48, 56]." + }, + { + "type": "image", + "bbox": [ + 0.503, + 0.342, + 0.888, + 0.459 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.56, + 0.461, + 0.834, + 0.473 + ], + "angle": 0, + "content": "(b) Our streaming dense video captioning model." + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.475, + 0.893, + 0.545 + ], + "angle": 0, + "content": "Figure 1. Comparing our streaming model (b) to conventional global models (a). Conventional global models encode the entire video at once, and produce captions for all events at the end. Our model encodes images frame-by-frame, uses them to update a running memory, and predicts captions sequentially." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.562, + 0.892, + 0.667 + ], + "angle": 0, + "content": "any length, state-of-the-art models either sample very few frames (e.g., 6 frames [45]) with large strides [10, 27, 45] (i.e., temporal downsampling), or keep one feature per-frame for all the frames [48, 56, 62] (i.e., spatial downsampling). With long textual output, current models solely rely on auto-regressive decoding [17] to generate multiple sentences at the end." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.893, + 0.883 + ], + "angle": 0, + "content": "In this work, we design a streaming model for dense video captioning as shown in Fig. 1. Our streaming model does not require access to all input frames concurrently in order to process the video thanks to a memory mechanism. Moreover, our model can produce outputs causally without processing the entire input sequence, thanks to a new streaming decoding algorithm. Streaming models such as ours are inherently suited to processing long videos – as they ingest frames one at a time. Moreover, as the output is streamed, intermediate predictions are produced before processing the full video. This property means that streaming models can in theory be applied to process live video streams, as required for applications such as video conferencing, security and continuous monitoring among others." + }, + { + "type": "text", + "bbox": [ + 0.519, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "In order to develop our streaming model, we first propose" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.378, + 0.901 + ], + "angle": 0, + "content": "*Equal contribution. {zhouxy, aarnab} @google.com" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18243" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.089, + 0.852, + 0.281 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.282, + 0.895, + 0.354 + ], + "angle": 0, + "content": "Figure 2. Illustration of our framework. Each frame is passed through an image encoder, one at a time. A memory model, based on clustering, maintains compressed visual features from the beginning up to the current frame. At certain frames, denoted as \"decoding points\", we decode the representations from our memory into captions and their timestamps. Earlier text predictions, if available, are also passed as a prefix to the language decoder for the following decoding points. Our model can run on videos of arbitrary length, as the memory has a constant size, and can also output predictions before processing the whole video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.364, + 0.471, + 0.454 + ], + "angle": 0, + "content": "a novel memory mechanism, that takes frames once at a time. The memory model is based on K-means clustering, and uses a fixed number of cluster-center tokens to represent the video at each timestamp. We show that this method is simple and effective, and can process variable numbers of frames, with a fixed computational budget at decoding." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.697 + ], + "angle": 0, + "content": "We also develop a streaming decoding algorithm, and train our network such that given a \"decoding point\" (Fig. 2) at a particular timestamp, it predicts all event captions that ended before it given the memory features at that timestamp. Our network is thus trained to make predictions at any timestamp of the video, and not just at the end of the video as in conventional, non-streaming models. Furthermore, we provide predictions from earlier decoding points as contexts for later ones. This context avoids predicting duplicated events, and can be used as an \"explicit\" memory in natural language summarising the earlier video. Our streaming output is also motivated by the fact that as the video length grows, our memory will inevitably lose information over time as its size is bounded. We avert this issue by making predictions before we have processed the entire video, and still keep early information via language context." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.697, + 0.471, + 0.833 + ], + "angle": 0, + "content": "We evaluate our approach on three popular dense video captioning datasets, ActivityNet [26], YouCook2 [61] and ViTT [21]. Our results show that our streaming model significantly improves over the state-of-the-art, which inevitably uses fewer frames or fewer features, by up to 11.0 CIDEr points. We show that our method generalizes across both GIT [45] and Vid2Seq [56] architectures. Finally, our proposed memory can also be applied to paragraph captioning, improving baselines by 1-5 CIDEr points." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.845, + 0.22, + 0.86 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Dense video captioning. Dense video captioning requires captioning events, and localizing them temporally. Tra" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.364, + 0.892, + 0.59 + ], + "angle": 0, + "content": "ditionally, prior work used a two-stage approach, first localizing events in video, and then subsequently captioning them [22, 23, 26, 44, 47]. More recent end-to-end approaches include PDVC [63] which infers event captions and timestamps using a DETR-like [9] model. Vid2Seq [56] augments the vocabulary of a language model with timestamp tokens, allowing them to generate concatenated event captions in the same manner as a regular captioning model. We also use the output formulation of [56], as it integrates well with foundation vision-language models [45]. A related, but different problem, is that of audio description in movies [18, 19, 40], which requires generating captions for the visually impaired that must be complementary to speech, and often uses auxiliary, non-causal models to recognize characters or their speech [19]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.732 + ], + "angle": 0, + "content": "As far as we are aware, all prior dense captioning models are not causal, as they encode the entire video at once. Moreover, to process long videos, they typically use visual features that are downsampled heavily (by selecting a few frames [10, 27, 45], or spatially pooling features per frame [48, 56, 62]). In contrast, we process videos in a streaming manner, processing long input sequences one frame at a time with a memory module, and streaming output sentences with a novel decoding algorithm." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Models for long videos. A common way of processing longer videos is to use a memory mechanism to provide a compact representation of past events. With transformers, memory can easily be implemented by using tokens from past observations as inputs for the present time step [12, 33, 53]. Examples in vision include [20, 32, 50, 51] which preextract features offline and retrieve them during inference, and are thus not causal. MemViT [52] uses token activations from previous time steps as inputs to the current time step. However, this means that the sequence length grows over time and so it cannot handle arbitrarily long videos." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18244" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.333 + ], + "angle": 0, + "content": "An alternate view of memory is to see it as a method of compressing previously observed tokens into a smaller, fixed-size set to be used at future time steps. Token Turing Machines [38] summarize past and current observations using the token summarization module of [37]. MovieChat [41] follows a similar idea, but uses a variant of Token Merging [5] instead to perform the summarization. TeSTra [59] uses an exponential moving average to integrate video features instead. The advantage of such approaches is that the memory bank has a fixed size, and therefore the computational cost remains bounded regardless of the length of the video. Our memory model has this same desirable property. However, our memory is based on clustering, using the centers from a K-means-like algorithm to summarize tokens from each time step, and we show experimentally that this outperforms other alternatives." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.334, + 0.473, + 0.516 + ], + "angle": 0, + "content": "Causal models in video. Our streaming model is causal, meaning that its output only depends on current and past frames, without access to future frames. Although we are not aware of prior causal models for dense video captioning, there are causal models in many other vision domains. Online action detection [13, 25, 59, 60] aims to predict action labels for videos in real-time without access to future frames. Analogously, online temporal action localization [6, 24, 39] models also predict start- and end-times after an action is observed. Most models for object tracking [3, 49] and video object/instance segmentation [8, 29, 31] are causal too." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.517, + 0.473, + 0.61 + ], + "angle": 0, + "content": "A common theme in the above tasks is that the model must make a prediction at each frame of the video. In contrast, we focus on dense video captioning [26], which is challenging as the output captions do not have a one-to-one correspondence with the video frames. We address this problem by proposing a streaming decoding algorithm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.625, + 0.398, + 0.643 + ], + "angle": 0, + "content": "3. Streaming Dense Video Captioning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.65, + 0.473, + 0.82 + ], + "angle": 0, + "content": "Given a video \\(\\mathbf{V} \\in \\mathbb{R}^{T \\times H \\times W \\times 3}\\), our goal is to produce a set of temporally localized captions: \\(\\{(s, e, \\mathbf{c})_1, \\ldots, (s, e, \\mathbf{c})_{n_e}\\}\\), where \\(s \\in \\mathbb{R}\\) and \\(e \\in \\mathbb{R}\\) are the starting and ending timestamps (\\(0 \\leq s < e \\leq T\\)), respectively, \\(\\mathbf{c} = [w_1, \\dots, w_n]\\) is a sequence of word tokens, and \\(n_e\\) the number of events. Each word token \\(w_i\\) is an integer in the range \\([0, |V|]\\), indexing the vocabulary \\(V\\). We begin by describing conventional captioning models (Sec. 3.1), before detailing how we develop a streaming model (Fig. 2) by streaming inputs with memory (Sec. 3.2) and outputs with decoding points (Sec. 3.3)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.831, + 0.22, + 0.847 + ], + "angle": 0, + "content": "3.1. Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.472, + 0.903 + ], + "angle": 0, + "content": "Captioning models broadly consist of a vision encoder followed by a text decoder. We outline these approaches, and show how they can be extended to dense captioning next." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.273 + ], + "angle": 0, + "content": "Visual encoder. The first step is to encode the video into features \\(\\mathbf{f} = \\mathcal{F}(\\mathbf{V}),\\mathbf{f}\\in \\mathbb{R}^{N\\times D}\\), where \\(N\\) is the feature resolution (i.e., number of tokens for transformer-based encoders), and \\(D\\) is the feature dimension. The visual feature encoder \\(\\mathcal{F}\\) can be a native video backbone [1, 4], or an image encoder [34, 57] applied to each individual frame. In the latter case, the video feature is a stack of image features, i.e. \\(N = T\\cdot N_{f}\\), where \\(N_{f}\\) is the number of tokens per frame. We use a per-frame encoding, but instead of pre-extracting them from the whole video, we use a memory mechanism to process the features in a causal, streaming fashion (Sec. 3.2) that can generalize to longer video durations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.895, + 0.478 + ], + "angle": 0, + "content": "Text decoder. Given the visual features, \\(\\mathbf{f}\\), and optional textual prefix tokens, \\(\\mathbf{p}\\), the text decoder, \\(\\mathcal{D}\\) generates a sequence of word tokens, \\(\\mathbf{c}\\) from them. We use an autoregressive [17, 42] decoder that generates the next word token, \\(w_{i}\\), conditioned on previous words, \\(\\mathbf{w}_{1:i-1}\\), and prefix if provided as \\(w_{i} = \\mathcal{D}(\\mathbf{f}, \\mathbf{p}, \\mathbf{w}_{1:i-1})\\). Note that prefix tokens are typically not used in captioning tasks, but are used in question-answering (QA) to encode the input question. Concretely, the text decoder, \\(\\mathcal{D}\\), is a sequence of transformer layers [42] operating on a concatenation of visual features \\(\\mathbf{f}\\) and word embeddings of the prefix [35, 45]. This architecture is shown to be effective in both captioning and QA tasks across image and video [10, 27, 45]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.485, + 0.895, + 0.713 + ], + "angle": 0, + "content": "Dense video captioning with timestamps. Combining the above visual encoder and text decoder gives a basic architecture for video captioning. To extend it for captioning multiple events with starting and ending timestamps, Vid2Seq [56] introduced two main modifications: First, it augments the vocabulary, \\( V' \\), of the captioning model with time tokens, \\( w^s \\) and \\( w^e \\), which represent the starting and ending times, respectively. A single event is therefore represented as \\( \\mathbf{c}' = [w^s, w^e, w_1, \\dots, w_n] \\), and \\( |V'| = |V| + |T| \\) where \\( |V| \\leq w^s < w^e \\leq |V'| \\), and \\( |T| \\) is the number of time tokens. Second, Vid2Seq concatenates all timed captions into a single long caption that is ordered by starting time: \\( \\mathbf{C} = [\\mathbf{c}_1', \\mathbf{c}_2', \\dots, \\mathbf{c}_{n_e}'] \\) where \\( n_e \\) is the number of events. Therefore, dense video captioning can be formulated as standard video captioning with target \\( \\mathbf{C} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Despite its effectiveness, the (generalized) Vid2Seq [56] architecture has a number of key limitations: First, it forwards visual features from the whole video, f through the decoder, meaning that it does not scale effectively to longer videos and more tokens. In addition, as Vid2Seq predicts all event captions at once, after processing the whole video, it struggles with predicting long, detailed captions. To address these issues, we introduce streaming dense video captioning models, where we process the inputs once at a time using a memory module to bound computational costs, and stream the outputs such that we can make predictions before processing the whole video." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18245" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.088, + 0.096, + 0.424, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: Updating memory tokens at a timestamp." + }, + { + "type": "algorithm", + "bbox": [ + 0.08, + 0.112, + 0.47, + 0.337 + ], + "angle": 0, + "content": "Input : \\(\\mathbf{M}_{t - 1}\\in \\mathbb{R}^{K\\times D}\\) : memory tokens \\(\\mathbf{W}_{t - 1}\\in \\mathbb{R}^K\\) : weights of memory tokens \\(\\mathbf{f}_t\\in \\mathbb{R}^{N_f\\times D}\\) : incoming tokens Hyperparameters: \\(\\tau\\) : number of K-means iterations. Output : \\(\\mathbf{M}_t\\in \\mathbb{R}^{K\\times D}\\) : updated memory tokens \\(\\mathbf{W}_t\\in \\mathbb{R}^K\\) : updated weights of memory \n1 \\(\\mathbf{X}\\gets [\\mathbf{M}_{t - 1},\\mathbf{f}_t]\\) // Concatenate memory and incoming tokens. \n2 \\(\\mathbf{W}\\gets [\\mathbf{W}_{t - 1},\\mathbf{1}]\\) // Initialize incoming weights and concatenate. \n3 \\(\\mathbf{M}_t\\gets \\mathbf{M}_{t - 1}\\) // Initialize new cluster centers as the old centers. \n4 for \\(i\\gets I\\) : \\(\\tau\\) do \n5 \\(\\mathbf{d}\\gets\\) pairwise.l2_distance(X, \\(\\mathbf{M}_t\\)) // Shape \\((K + N_{f},K)\\). \n6 \\(\\delta \\gets\\) d.argmin(axis=1) // Assign each token to a center. \n7 \\(\\delta \\gets\\) make_onehot(δ,K) // Binary. Shape \\((K + N_{f},K)\\). \n8 \\(\\mathbf{W}_t\\gets \\delta^\\top \\mathbf{W}_t\\) // Compute #tokens assigned to each center. \n9 \\(\\mathbf{A}\\gets \\delta^\\top /\\mathbf{W}_t\\) // Weight matrix. “/” is elementwise div. \n10 \\(\\mathbf{M}_t\\gets \\mathbf{AX}\\) // Compute new centers as a linear function. \n11 end \n12 return \\(\\mathbf{M}_t\\) , \\(\\mathbf{W}_t\\)" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.343, + 0.359, + 0.359 + ], + "angle": 0, + "content": "3.2. Streaming inputs using memory" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.367, + 0.47, + 0.609 + ], + "angle": 0, + "content": "The input visual features, \\(\\mathbf{f}\\), have dimensionality \\(\\mathbb{R}^{T\\cdot N_f\\times D}\\) where typical values are \\(T > 64\\) for a sparsely sampled (e.g. 1 FPS), few-minute-long video, and \\(N_{f} = 257\\) tokens per-frame for a vision transformer such as CLIP [34]. Directly feeding all \\(T\\cdot N_{f}\\) to the text decoder is prohibitively expensive, due to the quadratic complexity of self-attention. Therefore, existing methods aggressively downsample \\(\\mathbf{f}\\) to reduce the number of tokens (by temporally sampling a few frames with large strides [10, 45], or spatially subsampling each frame to a single token [48, 56, 62]). Even so, we will reach memory limits with longer videos, and the information required for fine-grained localization and description is lost. Therefore, rather than aggressive downsampling, we use a memory mechanism to process all tokens frame-by-frame, which ensures that the computational cost is bounded irrespective of the length of the video." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.611, + 0.47, + 0.72 + ], + "angle": 0, + "content": "Let \\(K\\) be a pre-defined memory size, the memory at each time \\(\\mathbf{M}_t\\) would always be the constant size \\(K\\), i.e., \\(\\mathbf{M}_t \\in \\mathbb{R}^{K \\times D}, \\forall t\\). We interpret \\(\\mathbf{M}\\) as being a summary of all relevant information in the video, and initialize it by taking the first \\(K\\) tokens from \\(\\mathbf{f}\\). Therefore, we set \\(K\\) as a multiple of \\(N_f\\), such that the initial memory is the features of the first \\(\\frac{K}{N_f}\\) frames: \\(\\mathbf{M}_{K / N_f} = [\\mathbf{f}_1, \\dots, \\mathbf{f}_{K / N_f}]\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Next, we update the memory at each timestamp for each incoming frame \\(\\mathbf{f}_t\\). Our intuition is to keep as much diverse information in the original video as possible, while not increasing the storage budget (i.e. by keeping a constant memory size \\(K\\)). We thus propose a K-means-like clustering algorithm, to use the feature cluster centers as the approximate video features. To avoid the cluster centers biasing quickly to incoming features, we keep track of the number of merged tokens in each cluster center. We use this as a momentum weight, so that cluster centers that are merged from more tokens change slower. The detailed algorithm diagram is provided in Alg. 1, and illustrated in Fig. 3." + }, + { + "type": "image", + "bbox": [ + 0.539, + 0.095, + 0.858, + 0.22 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.226, + 0.892, + 0.296 + ], + "angle": 0, + "content": "Figure 3. Illustration of our clustering-based memory module. The current memory tokens are shown by blue squares. At each time step, the memory tokens evolve by integrating information from the incoming tokens (gray squares), using K-means iterations to produce the updated memory tokens (green circles)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.311, + 0.892, + 0.479 + ], + "angle": 0, + "content": "The K-means algorithm is not differentiable with respect to the assignment of data points to cluster centers, \\(\\delta\\) (Line 6 of Alg.1). However, the inputs and outputs of our memory module are the updated cluster centers, \\(\\mathbf{M}_t\\), which is a linear mapping of the input \\(\\mathbf{X} = [\\mathbf{M}_{t - 1},\\mathbf{f}_t]\\), as \\(\\mathbf{M}_t = \\mathbf{A}\\mathbf{X}\\) where \\(\\mathbf{A}\\) is a weight matrix computed from \\(\\mathbf{X}\\). Therefore, even though we cannot compute the gradient of \\(\\mathbf{A}\\) with respect to \\(\\mathbf{X}\\), we can compute the gradient of \\(\\mathbf{M}_t\\) with respect to the input \\(\\mathbf{X}\\), and thus to the input visual feature \\(\\mathbf{f}\\). As a result, we can use our memory module in any part of a neural network, and learn parameters in preceding layers." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.487, + 0.842, + 0.504 + ], + "angle": 0, + "content": "3.3. Streaming outputs with decoding points" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.51, + 0.892, + 0.707 + ], + "angle": 0, + "content": "The memory module from Sec. 3.2 enables us to efficiently ingest long input videos. However, it is still desirable for our model's text decoder to predict outputs before it has processed the entire input sequence: Streaming the output substantially decreases the latency of the model, as we do not have to wait for the model to process the entire input sequence to make predictions. This is particularly relevant for processing, for example, live video streams. Furthermore, streaming the output can in fact increase our model's accuracy: As we have a memory with a fixed size, \\( K \\), from which we decode outputs, we will inevitably lose information over time. We can therefore avert this issue by making predictions before we have processed the entire video." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.724, + 0.892, + 0.815 + ], + "angle": 0, + "content": "Decoding points As shown in Fig. 4, we define \"decoding points\", \\( d_{i} \\), as intermediate timestamps where we decode event captions given the features in our memory, \\( \\mathbf{M}_{d_i} \\). We train our model such that at each decoding point, \\( d_{i} \\) the model predicts all event captions that finished before it. More specifically," + }, + { + "type": "equation", + "bbox": [ + 0.594, + 0.826, + 0.892, + 0.845 + ], + "angle": 0, + "content": "\\[\n\\mathcal {Y} _ {i} = \\left\\{\\left(w _ {j} ^ {s}, w _ {j} ^ {e}, \\mathbf {c} _ {j}\\right) \\mid w _ {j} ^ {e} \\leq d _ {i} \\right\\}, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.854, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\(\\mathcal{V}_i\\) is the set of all event captions corresponding to the \\(i^{\\mathrm{th}}\\) decoding point \\(d_{i}\\), and \\(w_{j}^{s}, w_{j}^{e}\\) are the starting and ending time of the \\(j^{\\mathrm{th}}\\) event." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18246" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.09, + 0.435, + 0.198 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.2, + 0.47, + 0.268 + ], + "angle": 0, + "content": "Figure 4. Decoding point supervision in training. A decoding point, \\( d_i \\), can be at any frame. At each point, we take the memory features, \\( \\mathbf{M}_{d_i} \\), and predict all events that have finished before \\( d_i \\) and are not in the prefix \\( \\mathbf{p} \\). Therefore, the union between the prefix and the prediction target covers all events finished before it." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.286, + 0.471, + 0.452 + ], + "angle": 0, + "content": "As decoding points are applied sequentially, later decoding points should have access to the predictions of earlier decoding points, and should not repeat them again. Therefore, from the second decoding point onwards, we concatenate the outputs of previous decoding points as the prefix to the text decoder, as shown in Fig. 4. Moreover, during training, we perform further data augmentation by randomly removing some of the previous event captions from the prefix, and adding them to the target instead, to increase robustness to potential errors in earlier predictions. We therefore denote our prefixes and captioning targets during training as" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.463, + 0.469, + 0.481 + ], + "angle": 0, + "content": "\\[\n\\mathbf {p} _ {i} = \\left[ \\mathbf {c} _ {1} ^ {\\prime}, \\mathbf {c} _ {2} ^ {\\prime}, \\dots , \\mathbf {c} _ {j - 1} ^ {\\prime} \\right] \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.185, + 0.484, + 0.469, + 0.502 + ], + "angle": 0, + "content": "\\[\n\\mathbf {y} _ {i} = \\left[ \\mathbf {c} _ {j} ^ {\\prime}, \\mathbf {c} _ {j + 1} ^ {\\prime}, \\dots , \\mathbf {c} _ {| \\mathcal {Y} _ {i} |} ^ {\\prime} \\right], \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.513, + 0.469, + 0.559 + ], + "angle": 0, + "content": "where \\(j < |\\mathcal{V}_i|\\) is a randomly chosen splitting point to partition the target and context. During inference, we use the models actual predictions, \\(\\mathbf{p}_i = [\\hat{\\mathbf{y}}_1,\\hat{\\mathbf{y}}_2,\\dots ,\\hat{\\mathbf{y}}_{i - 1}]\\), instead." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.559, + 0.469, + 0.694 + ], + "angle": 0, + "content": "In practice, we uniformly sample decoding points during both training and inference, with a stride of \\( S \\) frames. Since the model is trained to predict all event captions before the decoding point, it means that the exact location at inference time does not need to match the event boundaries closely. The number of decoding points can be also different between training and inference, as we will ablate. This method is both simple and scalable, as we show experimentally in the next section." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.708, + 0.312, + 0.725 + ], + "angle": 0, + "content": "4. Experimental Evaluation" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.733, + 0.267, + 0.75 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.757, + 0.358, + 0.77 + ], + "angle": 0, + "content": "4.1.1 Datasets and Evaluation Metrics" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.469, + 0.825 + ], + "angle": 0, + "content": "We evaluate our model on the three most popular dense video captioning datasets: ActivityNet Captions [26], YouCook2[61], and ViTT [21]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.469, + 0.9 + ], + "angle": 0, + "content": "ActivityNet Captions [26] contains 8,649 training videos and 4,267 validation videos (considering videos that are still online on YouTube). The videos are untrimmed, each containing multiple action events, with an average video length of 2 minutes and an average of 3.7 events. The" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "videos are selected from the ActivityNet [7], which covers a wide range of visual domains. Each video is carefully labeled by human annotators. We use this dataset for both dense captioning (predicting a sequence of captions with their start- and end-times) and paragraph captioning (predicting the aforementioned captions as a single paragraph without timestamps)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.379 + ], + "angle": 0, + "content": "YouCook2 [61] contains 1,333 training videos and 456 validation videos. The videos are on average 5.3 minutes long, with an average of 7.8 events. This dataset focuses on cooking scenes, and most videos contain one main actor cooking while describing the recipe. The videos are manually annotated, aided by speech transcriptions obtained through Automatic Speech Recognition (ASR). As expected due to the annotation process, using ASR as an additional modality can be used to improve model predictions [56]. However, our work focuses on using visual-only inputs, to study our proposed streaming model. We also perform dense and paragraph captioning on this dataset." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.456 + ], + "angle": 0, + "content": "ViTT [21] contains 4,608 training videos and 2,301 testing videos, which are on average 4.7 minutes long and contain 7 events per video. It is collected in a similar way as YouCook2, but focuses on more diverse domains. Again, we do not use the ASR inputs in our experiments." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.457, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Evaluation Metrics For all datasets, we report standard dense captioning evaluation metrics following Vid2Seq [56] and PDVC [48]. The primary metric is CIDEr which has been adapted to jointly evaluate captioning and localisation. In particular, we average the CIDEr score [43] for positive ground-truth-prediction pairs with a temporal IoU above the thresholds, \\(\\{0.3, 0.5, 0.7, 0.9\\}\\). Similarly, we report ME-TEOR [2] averaged over multiple IoU thresholds. Finally, we report the recently proposed \\(\\mathrm{SODA}_c\\) [16], which considers all event captions from the same video, and is therefore a more holistic measure." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.647, + 0.715, + 0.662 + ], + "angle": 0, + "content": "4.1.2 Implementation details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.891, + 0.718 + ], + "angle": 0, + "content": "We implement our streaming model on two video captioning architectures, GIT [45] and Vid2Seq [56]. Both use a ViT-L [14] initialized from CLIP [34] as image encoder \\(\\mathcal{F}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.719, + 0.892, + 0.839 + ], + "angle": 0, + "content": "GIT [45] concatenates all tokens from all input frames, f, and feeds them to a 6-layer transformer language decoder. We apply our streaming input module before the language decoder, i.e., rather than concatenating frame features, we use our memory features instead. The original GIT paper pretrains the language decoder on in-house data [45]. As we do not have access to the original data or weights, we pretrain our GIT model on the WebLI dataset [11]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Vid2Seq [56] pools all frame tokens spatially into 1 token per frame, and then applies a 12-layer temporal transformer [1] to obtain the final visual features. The language decoder is a 12-layer T5-Base decoder [35]. Vid2Seq pre" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "18247" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.081, + 0.46, + 0.209 + ], + "angle": 0, + "content": "
#TokensT=16T=32T=64T=128
No memoryT×Nf29.8---
Spatial poolingT27.627.327.927.4
Temporal poolingNf29.328.026.825.2
EMA [59]Nf28.226.322.016.3
MovieChat [41]K29.329.228.929.3
Clustering (ours)K29.829.230.630.4
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.21, + 0.47, + 0.294 + ], + "angle": 0, + "content": "Table 1. Ablation on memory modules. We show CIDEr (averaged over multiple IoUs) on ActivityNet with GIT under different # input frames \\( T \\). The 2nd column shows the number of input tokens to the language decoder. \\( N_{f} = 257 \\) is the number of tokens per-frame. \\( K = 514 \\) is the number of memory tokens. Our module benefits from more frames, and outperforms other alternatives." + }, + { + "type": "table", + "bbox": [ + 0.082, + 0.325, + 0.203, + 0.403 + ], + "angle": 0, + "content": "
KCIDEr
25729.4
257 × 230.6
257 × 329.8
" + }, + { + "type": "table", + "bbox": [ + 0.22, + 0.325, + 0.323, + 0.403 + ], + "angle": 0, + "content": "
Iters.CIDEr
130.3
230.6
430.3
" + }, + { + "type": "table", + "bbox": [ + 0.336, + 0.325, + 0.469, + 0.387 + ], + "angle": 0, + "content": "
MomentumCIDEr
X29.7
✓30.6
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.338, + 0.389, + 0.465, + 0.414 + ], + "angle": 0, + "content": "(c) Momentum term in clustering" + }, + { + "type": "table_footnote", + "bbox": [ + 0.086, + 0.404, + 0.333, + 0.416 + ], + "angle": 0, + "content": "(a) #memory tokens. (b) K-means iterations." + }, + { + "type": "table_footnote", + "bbox": [ + 0.076, + 0.418, + 0.469, + 0.446 + ], + "angle": 0, + "content": "Table 2. Ablation on memory module hyperparameters. We perform experiments on ActivityNet with GIT with 64 frames." + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.404, + 0.469, + 0.446 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.463, + 0.469, + 0.537 + ], + "angle": 0, + "content": "trains the temporal transformer and the T5 decoder on narrated videos from the YT-Temporal dataset [58]. We use their public, pretrained weights as our initialization. We apply our streaming input module before the temporal transformer, to ensure the intermediate features remain causal." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.54, + 0.469, + 0.614 + ], + "angle": 0, + "content": "When finetuning our model for each dataset, we freeze the frame encoder following prior works [48, 56, 63]. We provide detailed training hyperparameters in the supplementary. For each architecture, the training hyperparameters are shared across the 3 datasets." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.628, + 0.353, + 0.645 + ], + "angle": 0, + "content": "4.2. Analysis of Streaming Modules" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.652, + 0.469, + 0.788 + ], + "angle": 0, + "content": "We first analyze each of the main components of our model: streaming the input with our memory module (Sec. 3.2), and then streaming outputs using decoding points (Sec. 3.3). Unless otherwise stated, we use the GIT [45] backbone for our experiments. Due to randomness in training and evaluation, for all ablation experiments (Tab. 1-Tab. 3), we repeat the same run 3 times and report the averaged metrics. When compared to other methods (Tab. 4, Tab. 5), we report results for the best model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.348, + 0.831 + ], + "angle": 0, + "content": "4.2.1 Streaming inputs with memory" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.469, + 0.901 + ], + "angle": 0, + "content": "As the GIT [45] architecture concatenates visual features, f, from multiple frames before passing it to the language decoder, it is limited by the number of frames that it can process. Our clustering-based memory module allows us" + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.081, + 0.885, + 0.119 + ], + "angle": 0, + "content": "
Number of decoding points12481620
CIDEr30.634.538.839.540.640.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.573, + 0.121, + 0.82, + 0.134 + ], + "angle": 0, + "content": "(a) Number of decoding points during training." + }, + { + "type": "table", + "bbox": [ + 0.504, + 0.135, + 0.87, + 0.196 + ], + "angle": 0, + "content": "
PrefixCIDErAug. PrefixCIDErStrideCIDEr
None23.1×37.63240.6
Captions40.6✓40.62134.7
Captions & time39.3
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.5, + 0.198, + 0.888, + 0.234 + ], + "angle": 0, + "content": "(b) Context provided (c) Random masking (d) Decoding point after the first decoding prefix as augmentation stride during inference point. during training. (input 64 frames)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.236, + 0.892, + 0.346 + ], + "angle": 0, + "content": "Table 3. Ablation on streaming outputs. (a) Increasing the number of decoding points during training consistently improves accuracy, as it provides more supervision to the model. (b) It is critical to provide context after the first decoding point, so that the model does not repeat predictions. Providing captions alone, without timestamps is sufficient. (c) It is important to provide imperfect prefixes during training, to mimic model behavior in inference. (d) Stride used for decoding during inference." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.364, + 0.891, + 0.393 + ], + "angle": 0, + "content": "to process more frames, and we consider the following approaches to evaluate it:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.395, + 0.891, + 0.44 + ], + "angle": 0, + "content": "No memory: We simply concatenate all visual tokens from all frames as done in GIT [45]. Due to memory constraints, we can only feed up to 16 frames to the decoder." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.442, + 0.891, + 0.488 + ], + "angle": 0, + "content": "Spatial- or temporal-pooling: We pool the visual features, f, along either the spatial or temporal dimensions to reduce the number of tokens fed to the language decoder." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.489, + 0.891, + 0.548 + ], + "angle": 0, + "content": "EMA: We use an exponential moving average of frame features, \\(\\mathbf{f}_t\\), at each time step, following TeSTra [59]. We sweep the decay rate from \\(\\{0.9, 0.99, 0.999\\}\\), finding 0.9 to perform best." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.55, + 0.892, + 0.641 + ], + "angle": 0, + "content": "MovieChat [41]. Finally, the recent MovieChat paper maintains a memory of \\( K \\) tokens. For each incoming frame, it sequentially processes each token, and merges the two most similar tokens in the memory bank such that the size remains fixed at \\( K \\). We implement this method using the author's public code." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.794 + ], + "angle": 0, + "content": "Tab. 1 compares the results of the different memory modules. For \\( T = 16 \\), where we can feed all the tokens from the vision backbone, \\( \\mathbf{f} \\), into the decoder, \"no memory\" and our method both performs the best. We expected \"no memory\" to perform well, as it uses the most tokens, \\( T \\times N_f \\). However, our clustering-based method achieves the same performance, which suggests that it is able to effectively capture the relevant information in the video with \\( 8 \\times \\) fewer tokens, and is causal too. It is not possible to use \"no memory\" for \\( T > 16 \\) due to its computational cost." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.796, + 0.892, + 0.901 + ], + "angle": 0, + "content": "With more frames, naively pooling along the spatial-, or temporal-dimensions actually performs worse. This is likely because we are averaging out information over longer temporal durations, and thus losing the details required for more detailed localization or captioning. Our method and MovieChat on the other hand, are able to leverage more frames to improve performance, as they keep diverse fea" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "18248" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.11, + 0.089, + 0.857, + 0.244 + ], + "angle": 0, + "content": "
ActivityNetYouCook2ViTT
CIDErSODAMeteorF1CIDErSODAMeteorF1CIDErSODAMeteorF1
MT [62]9.3-5.0-6.1-3.2-----
E2ESG [63]----25.0-3.5-----
PDVC [48]29.36.07.6-28.94.95.7-----
GIT [45]29.85.77.850.612.13.13.417.715.17.13.432.5
Vid2Seq†[56]30.25.98.551.825.35.76.423.523.09.85.037.7
Streaming GIT (ours)41.26.69.050.915.43.23.616.618.58.34.033.9
Streaming Vid2Seq (ours)37.86.210.052.932.96.07.124.125.210.05.835.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.247, + 0.892, + 0.29 + ], + "angle": 0, + "content": "Table 4. Comparison to the state-of-the-art on dense video captioning We add our streaming model to both GIT [45] and Vid2Seq [56], denoted by Streaming GIT and Streaming Vid2Seq, respectively, achieving consistent and substantial improvements across three datasets. All models use only visual inputs. \\(^\\dagger\\) denotes version with visual-only inputs." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.306, + 0.47, + 0.366 + ], + "angle": 0, + "content": "tures within the memory. Finally, our clustering method outperforms MovieChat and other memory modules for all numbers of frames that we considered, which is why we use it for all future experiments." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.366, + 0.47, + 0.472 + ], + "angle": 0, + "content": "We also ablate the hyperparameters of our memory module in Tab. 2. Following this experiment, we set \\( K = 257 \\times 2 \\), or the number of tokens in two frames, and use 2 iterations of K-means, as it achieves the best performance. Our proposed momentum term (Sec. 3.2), which prevents cluster centers from becoming too biased towards incoming frame tokens, also improves CIDEr from 29.7 to 30.6." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.483, + 0.262, + 0.499 + ], + "angle": 0, + "content": "4.2.2 Streaming outputs" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.507, + 0.47, + 0.613 + ], + "angle": 0, + "content": "We now analyze the effect of our streaming decoding method (Sec. 3.3), which enables us to predict event captions from intermediate features in our memory, and utilize previous prediction as the prefix to our text decoder. Table 3 analyses the effects of the number of decoding points during training, the impact of the prefix, and how we select decoding points during inference." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.471, + 0.885 + ], + "angle": 0, + "content": "Table 3a shows that we achieve significant improvements by increasing the number of decoding points during training, improving the CIDEr score by 10 points, or \\(33\\%\\) relative, compared to only making predictions at the end, as in conventional models. Streaming the output with decoding points can provide performance benefits for multiple reasons: First, as we have multiple decoding points, the required output caption is shorter at each decoding point, making the captioning task easier. Second, the visual features from our memory, M, may be aligned better with the target text, since M does not represent the visual features from the entire video as in baseline approaches, but only the features up to the decoding point. Finally, training with decoding points provides a stronger training signal to the model, as we provide training supervision at each decoding point. Moreover, it should aid generalization, as the network is being trained to make consistent predictions from more points along the timeline." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Tab. 3b shows that it is essential to provide past predic" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.306, + 0.892, + 0.472 + ], + "angle": 0, + "content": "tions as the prefix. Without a prefix, the model is poor, underperforming our non-streaming baseline of only decoding at the end (30.6). This is because the model predicts duplicated predictions at each decoding point. Providing past captions outperforms this baseline substantially. We find that also adding previously predicted timestamps, does not improve over captions alone, suggesting that temporal boundaries of past events are not particularly informative for future events. Tab. 3c further shows that while training with a prefix, it is important to mimic inference behavior by including missing captions in earlier predictions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.472, + 0.892, + 0.669 + ], + "angle": 0, + "content": "Table 3d examines the choice of decoding points during inference. We find that using a stride, \\( S = 32 \\) (which equates to a decoding point at the middle and end of a 64-frame clip), performs considerably better than \\( S = 21 \\) (three uniformly chosen points). We observed qualitatively that using too many decoding points during inference can sometimes still result in the model making duplicate predictions (even with past prediction as the prefix). Whilst it is also possible to remove duplicate predictions with non-maximal suppression (NMS [15]), it is more challenging for captioning models as we also require a calibrated score for each event caption to perform NMS. We therefore leave an investigation of NMS for dense video captioning to future work." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.844, + 0.695 + ], + "angle": 0, + "content": "4.2.3 Generalization to backbones and datasets" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.765 + ], + "angle": 0, + "content": "To show the generality of our method, we add our streaming modules onto both the GIT [45] and Vid2Seq [56] architectures, which we denote as Streaming GIT and Streaming Vid2Seq, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The last two rows of Tab. 4 shows that we improve substantially over both baselines consistently on three datasets. Our GIT baseline can process a maximum of \\( N_{f} = 16 \\) frames due to memory limitations, and our improvement also stems from the fact that we use \\( N_{f} = 64 \\) for our Streaming GIT thanks to our memory module. Vid2Seq pools visual tokens spatially such that it only uses a single token per frame. Therefore, our Streaming Vid2Seq does not use more frames than the baseline, and the improvement is due" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18249" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.081, + 0.885, + 0.285 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.286, + 0.893, + 0.315 + ], + "angle": 0, + "content": "Figure 5. Qualitative results on ActivityNet validation. Results from the ground truth (top), the baseline (middle), and our model (bottom). We show outputs from two decoding points in green and blue respectively. Our model captures more details than the baseline." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.359 + ], + "angle": 0, + "content": "to our streaming of output event captions, which improves performance significantly as shown in Tab. 3." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.361, + 0.47, + 0.466 + ], + "angle": 0, + "content": "Finally, we observe that our Vid2Seq baseline performs substantially better than the GIT baseline on YouCook2. This difference is due to the pretraining: We used the public, pretrained Vid2Seq checkpoint [56] which was pretrained on YT-Temporal [58] - a dataset with a similar domain to YouCook2. Note that this is the same experimental protocol as Vid2Seq [56], the current state-of-the-art." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.48, + 0.333, + 0.496 + ], + "angle": 0, + "content": "4.3. State-of-the-art Comparison" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.505, + 0.47, + 0.64 + ], + "angle": 0, + "content": "Tab. 4 also compares our method to the state-of-the-art among dense video captioning methods using only video frames as inputs. We achieved substantial gains over prior, published works, notably improving CIDEr on ActivityNet by 11.0 points, and YouCook2 by 4.0 points, respectively. We also achieved improvements, albeit smaller, on SODA and Meteor. Our improvements on localization (F1) are smaller, showing the gains are more from better captioning qualities. Fig. 5 visualizes an example on ActivityNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.642, + 0.47, + 0.762 + ], + "angle": 0, + "content": "We note that it is possible to further improve results, particularly on YouCook2, by using Automatic Speech Recognition (ASR) as an additional input modality [56]. This is primarily because the spoken utterances of the actors are well aligned with the visual content, and because ASR was used in the annotation procedure of the dataset itself. However, integrating multiple modalities such as ASR is orthogonal to the main focus of this work." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.764, + 0.47, + 0.869 + ], + "angle": 0, + "content": "Paragraph captioning. In addition to dense captioning, we also compare with state-of-the-art models on the same datasets for paragraph captioning, which aims to predict the captions throughout the entire video, but without any timestamps. Therefore, we only apply our streaming input model here, as the timestamps needed to assign decoding points during training are not available in this setting." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We train our Streaming GIT model for paragraph captioning, on both ActivityNet [26] and Youcook2 [61]. Tab. 5" + }, + { + "type": "table", + "bbox": [ + 0.544, + 0.325, + 0.846, + 0.439 + ], + "angle": 0, + "content": "
ActivityNetYouCook2
MFT [54]19.1-
PDVC [48]20.5-
Vid2Seq [56]†28.026.6
GIT [45]32.528.4
Ours33.433.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.498, + 0.44, + 0.893, + 0.647 + ], + "angle": 0, + "content": "Table 5. State-of-the-art comparison on paragraph captioning. We report CIDEr on ActivityNet and YouCook2 validation set. We compare models that do not require action proposal inputs and only takes visual inputs. \\(\\dagger\\) denotes version with visual-only inputs. Our model achieves the best performance on both datasets. shows that we achieve state-of-the-art results on this task too. The GIT baseline is our model trained on the same setting as our full model, but uses 16 input frames with all tokens concatenated for the decoder. This baseline already outperforms the state-of-the-art from visual-only inputs. Our model uses more input frames (64 frames), and further boosts the performance by 0.9 and 5.5 points on the two datasets, respectively, showing the benefits of our memory module which is consistent with our results in Tab. 1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.671, + 0.771, + 0.687 + ], + "angle": 0, + "content": "5. Conclusion and Future Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.7, + 0.892, + 0.82 + ], + "angle": 0, + "content": "We have proposed a streaming model for dense video captioning with two novel components: A clustering-based memory that can efficiently handle arbitrarily long videos with bounded computation, and a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. We achieve this streaming ability while also improving the state-of-the-art on five dense- and paragraphCaptioning tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.824, + 0.892, + 0.883 + ], + "angle": 0, + "content": "Future work is to develop a benchmark for dense video captioning which requires reasoning over longer videos than current datasets, to better evaluate the abilities of streaming models such as ours." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.887, + 0.885, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments. We thank Chen Sun for helpful discussions." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18250" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.156 + ], + "angle": 0, + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. ViViT: A Video Vision Transformer. In ICCV, 2021. 3, 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.157, + 0.47, + 0.199 + ], + "angle": 0, + "content": "[2] Satanjeev Banerjee and Alon Lavie. Meteor: An automatic metric for mt evaluation with improved correlation with human judgments. In ACL Workshops, 2005. 5" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.2, + 0.471, + 0.24 + ], + "angle": 0, + "content": "[3] Philipp Bergmann, Tim Meinhardt, and Laura Leal-Taixe. 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ACL, 2022. 2, 6, 7" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.845 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "18252" + } + ] +] \ No newline at end of file diff --git a/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_origin.pdf b/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..11d85e7d494569c83bf796674f57619b1b940924 --- /dev/null +++ b/2024/Streaming Dense Video Captioning/d7bbec97-020a-4518-8c20-5703b1fc127a_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:fd882a3ce049240c71005b0b40d15128595e88e53342c0f296ff87d934697e59 +size 749122 diff --git a/2024/Streaming Dense Video Captioning/full.md b/2024/Streaming Dense Video Captioning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..9a36dac35d7d3d638f516182901238ecc2174954 --- /dev/null +++ b/2024/Streaming Dense Video Captioning/full.md @@ -0,0 +1,329 @@ +# Streaming Dense Video Captioning + +Xingyi Zhou* Anurag Arnab* Shyamal Buch Shen Yan +Austin Myers Xuehan Xiong Arsha Nagrani Cordelia Schmid +Google + +# Abstract + +An ideal model for dense video captioning – predicting captions localized temporally in a video – should be able to handle long input videos, predict rich, detailed textual descriptions, and be able to produce outputs before processing the entire video. Current state-of-the-art models, however, process a fixed number of downsampled frames, and make a single full prediction after seeing the whole video. We propose a streaming dense video captioning model that consists of two novel components: First, we propose a new memory module, based on clustering incoming tokens, which can handle arbitrarily long videos as the memory is of a fixed size. Second, we develop a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. Our model achieves this streaming ability, and significantly improves the state-of-the-art on three dense video captioning benchmarks: ActivityNet, YouCook2 and ViTT. Our code is released at https://github.com/google-research/scenic. + +# 1. Introduction + +Video is ubiquitous in modern society, quickly becoming one of the most prevalent media formats for transmitting information. The majority of computer vision models designed for video understanding only process a handful of frames, mostly covering only a few seconds [28, 30, 36, 46, 55], and are typically limited to classifying these short segments into a fixed number of concepts. In order to achieve a comprehensive, fine-grained video understanding, we study the task of dense video captioning – jointly localizing events temporally in video and generating captions for them. Ideal models for this goal should be able to handle both long input sequences – to reason over long, untrimmed videos – and also to handle long output sequences in text space, to describe in detail all the events within the video. + +Prior work on dense video captioning does not handle either long inputs or long outputs. Given a video of + +![](images/cd5124675d807cdcb6e7fa5108bb96f26737371ec465dce4ea175454eba34b72.jpg) +(a) Conventional global dense video captioning models [48, 56]. + +![](images/11fdecd9bb4c60c54afb36dc9af135e82ddb4e8be75f9da8831b98674b18536a.jpg) +(b) Our streaming dense video captioning model. +Figure 1. Comparing our streaming model (b) to conventional global models (a). Conventional global models encode the entire video at once, and produce captions for all events at the end. Our model encodes images frame-by-frame, uses them to update a running memory, and predicts captions sequentially. + +any length, state-of-the-art models either sample very few frames (e.g., 6 frames [45]) with large strides [10, 27, 45] (i.e., temporal downsampling), or keep one feature per-frame for all the frames [48, 56, 62] (i.e., spatial downsampling). With long textual output, current models solely rely on auto-regressive decoding [17] to generate multiple sentences at the end. + +In this work, we design a streaming model for dense video captioning as shown in Fig. 1. Our streaming model does not require access to all input frames concurrently in order to process the video thanks to a memory mechanism. Moreover, our model can produce outputs causally without processing the entire input sequence, thanks to a new streaming decoding algorithm. Streaming models such as ours are inherently suited to processing long videos – as they ingest frames one at a time. Moreover, as the output is streamed, intermediate predictions are produced before processing the full video. This property means that streaming models can in theory be applied to process live video streams, as required for applications such as video conferencing, security and continuous monitoring among others. + +In order to develop our streaming model, we first propose + +![](images/34ef85e03f5a1fda96e700972dc8731ea99e891dbee7c5b42d1f443777c1e32c.jpg) +Figure 2. Illustration of our framework. Each frame is passed through an image encoder, one at a time. A memory model, based on clustering, maintains compressed visual features from the beginning up to the current frame. At certain frames, denoted as "decoding points", we decode the representations from our memory into captions and their timestamps. Earlier text predictions, if available, are also passed as a prefix to the language decoder for the following decoding points. Our model can run on videos of arbitrary length, as the memory has a constant size, and can also output predictions before processing the whole video. + +a novel memory mechanism, that takes frames once at a time. The memory model is based on K-means clustering, and uses a fixed number of cluster-center tokens to represent the video at each timestamp. We show that this method is simple and effective, and can process variable numbers of frames, with a fixed computational budget at decoding. + +We also develop a streaming decoding algorithm, and train our network such that given a "decoding point" (Fig. 2) at a particular timestamp, it predicts all event captions that ended before it given the memory features at that timestamp. Our network is thus trained to make predictions at any timestamp of the video, and not just at the end of the video as in conventional, non-streaming models. Furthermore, we provide predictions from earlier decoding points as contexts for later ones. This context avoids predicting duplicated events, and can be used as an "explicit" memory in natural language summarising the earlier video. Our streaming output is also motivated by the fact that as the video length grows, our memory will inevitably lose information over time as its size is bounded. We avert this issue by making predictions before we have processed the entire video, and still keep early information via language context. + +We evaluate our approach on three popular dense video captioning datasets, ActivityNet [26], YouCook2 [61] and ViTT [21]. Our results show that our streaming model significantly improves over the state-of-the-art, which inevitably uses fewer frames or fewer features, by up to 11.0 CIDEr points. We show that our method generalizes across both GIT [45] and Vid2Seq [56] architectures. Finally, our proposed memory can also be applied to paragraph captioning, improving baselines by 1-5 CIDEr points. + +# 2. Related Work + +Dense video captioning. Dense video captioning requires captioning events, and localizing them temporally. Tra + +ditionally, prior work used a two-stage approach, first localizing events in video, and then subsequently captioning them [22, 23, 26, 44, 47]. More recent end-to-end approaches include PDVC [63] which infers event captions and timestamps using a DETR-like [9] model. Vid2Seq [56] augments the vocabulary of a language model with timestamp tokens, allowing them to generate concatenated event captions in the same manner as a regular captioning model. We also use the output formulation of [56], as it integrates well with foundation vision-language models [45]. A related, but different problem, is that of audio description in movies [18, 19, 40], which requires generating captions for the visually impaired that must be complementary to speech, and often uses auxiliary, non-causal models to recognize characters or their speech [19]. + +As far as we are aware, all prior dense captioning models are not causal, as they encode the entire video at once. Moreover, to process long videos, they typically use visual features that are downsampled heavily (by selecting a few frames [10, 27, 45], or spatially pooling features per frame [48, 56, 62]). In contrast, we process videos in a streaming manner, processing long input sequences one frame at a time with a memory module, and streaming output sentences with a novel decoding algorithm. + +Models for long videos. A common way of processing longer videos is to use a memory mechanism to provide a compact representation of past events. With transformers, memory can easily be implemented by using tokens from past observations as inputs for the present time step [12, 33, 53]. Examples in vision include [20, 32, 50, 51] which preextract features offline and retrieve them during inference, and are thus not causal. MemViT [52] uses token activations from previous time steps as inputs to the current time step. However, this means that the sequence length grows over time and so it cannot handle arbitrarily long videos. + +An alternate view of memory is to see it as a method of compressing previously observed tokens into a smaller, fixed-size set to be used at future time steps. Token Turing Machines [38] summarize past and current observations using the token summarization module of [37]. MovieChat [41] follows a similar idea, but uses a variant of Token Merging [5] instead to perform the summarization. TeSTra [59] uses an exponential moving average to integrate video features instead. The advantage of such approaches is that the memory bank has a fixed size, and therefore the computational cost remains bounded regardless of the length of the video. Our memory model has this same desirable property. However, our memory is based on clustering, using the centers from a K-means-like algorithm to summarize tokens from each time step, and we show experimentally that this outperforms other alternatives. + +Causal models in video. Our streaming model is causal, meaning that its output only depends on current and past frames, without access to future frames. Although we are not aware of prior causal models for dense video captioning, there are causal models in many other vision domains. Online action detection [13, 25, 59, 60] aims to predict action labels for videos in real-time without access to future frames. Analogously, online temporal action localization [6, 24, 39] models also predict start- and end-times after an action is observed. Most models for object tracking [3, 49] and video object/instance segmentation [8, 29, 31] are causal too. + +A common theme in the above tasks is that the model must make a prediction at each frame of the video. In contrast, we focus on dense video captioning [26], which is challenging as the output captions do not have a one-to-one correspondence with the video frames. We address this problem by proposing a streaming decoding algorithm. + +# 3. Streaming Dense Video Captioning + +Given a video $\mathbf{V} \in \mathbb{R}^{T \times H \times W \times 3}$ , our goal is to produce a set of temporally localized captions: $\{(s, e, \mathbf{c})_1, \ldots, (s, e, \mathbf{c})_{n_e}\}$ , where $s \in \mathbb{R}$ and $e \in \mathbb{R}$ are the starting and ending timestamps ( $0 \leq s < e \leq T$ ), respectively, $\mathbf{c} = [w_1, \dots, w_n]$ is a sequence of word tokens, and $n_e$ the number of events. Each word token $w_i$ is an integer in the range $[0, |V|]$ , indexing the vocabulary $V$ . We begin by describing conventional captioning models (Sec. 3.1), before detailing how we develop a streaming model (Fig. 2) by streaming inputs with memory (Sec. 3.2) and outputs with decoding points (Sec. 3.3). + +# 3.1. Preliminaries + +Captioning models broadly consist of a vision encoder followed by a text decoder. We outline these approaches, and show how they can be extended to dense captioning next. + +Visual encoder. The first step is to encode the video into features $\mathbf{f} = \mathcal{F}(\mathbf{V}),\mathbf{f}\in \mathbb{R}^{N\times D}$ , where $N$ is the feature resolution (i.e., number of tokens for transformer-based encoders), and $D$ is the feature dimension. The visual feature encoder $\mathcal{F}$ can be a native video backbone [1, 4], or an image encoder [34, 57] applied to each individual frame. In the latter case, the video feature is a stack of image features, i.e. $N = T\cdot N_{f}$ , where $N_{f}$ is the number of tokens per frame. We use a per-frame encoding, but instead of pre-extracting them from the whole video, we use a memory mechanism to process the features in a causal, streaming fashion (Sec. 3.2) that can generalize to longer video durations. + +Text decoder. Given the visual features, $\mathbf{f}$ , and optional textual prefix tokens, $\mathbf{p}$ , the text decoder, $\mathcal{D}$ generates a sequence of word tokens, $\mathbf{c}$ from them. We use an autoregressive [17, 42] decoder that generates the next word token, $w_{i}$ , conditioned on previous words, $\mathbf{w}_{1:i-1}$ , and prefix if provided as $w_{i} = \mathcal{D}(\mathbf{f}, \mathbf{p}, \mathbf{w}_{1:i-1})$ . Note that prefix tokens are typically not used in captioning tasks, but are used in question-answering (QA) to encode the input question. Concretely, the text decoder, $\mathcal{D}$ , is a sequence of transformer layers [42] operating on a concatenation of visual features $\mathbf{f}$ and word embeddings of the prefix [35, 45]. This architecture is shown to be effective in both captioning and QA tasks across image and video [10, 27, 45]. + +Dense video captioning with timestamps. Combining the above visual encoder and text decoder gives a basic architecture for video captioning. To extend it for captioning multiple events with starting and ending timestamps, Vid2Seq [56] introduced two main modifications: First, it augments the vocabulary, $V'$ , of the captioning model with time tokens, $w^s$ and $w^e$ , which represent the starting and ending times, respectively. A single event is therefore represented as $\mathbf{c}' = [w^s, w^e, w_1, \dots, w_n]$ , and $|V'| = |V| + |T|$ where $|V| \leq w^s < w^e \leq |V'|$ , and $|T|$ is the number of time tokens. Second, Vid2Seq concatenates all timed captions into a single long caption that is ordered by starting time: $\mathbf{C} = [\mathbf{c}_1', \mathbf{c}_2', \dots, \mathbf{c}_{n_e}']$ where $n_e$ is the number of events. Therefore, dense video captioning can be formulated as standard video captioning with target $\mathbf{C}$ . + +Despite its effectiveness, the (generalized) Vid2Seq [56] architecture has a number of key limitations: First, it forwards visual features from the whole video, f through the decoder, meaning that it does not scale effectively to longer videos and more tokens. In addition, as Vid2Seq predicts all event captions at once, after processing the whole video, it struggles with predicting long, detailed captions. To address these issues, we introduce streaming dense video captioning models, where we process the inputs once at a time using a memory module to bound computational costs, and stream the outputs such that we can make predictions before processing the whole video. + +Algorithm 1: Updating memory tokens at a timestamp. +Input : $\mathbf{M}_{t - 1}\in \mathbb{R}^{K\times D}$ : memory tokens $\mathbf{W}_{t - 1}\in \mathbb{R}^K$ : weights of memory tokens $\mathbf{f}_t\in \mathbb{R}^{N_f\times D}$ : incoming tokens Hyperparameters: $\tau$ : number of K-means iterations. Output : $\mathbf{M}_t\in \mathbb{R}^{K\times D}$ : updated memory tokens $\mathbf{W}_t\in \mathbb{R}^K$ : updated weights of memory +1 $\mathbf{X}\gets [\mathbf{M}_{t - 1},\mathbf{f}_t]$ // Concatenate memory and incoming tokens. +2 $\mathbf{W}\gets [\mathbf{W}_{t - 1},\mathbf{1}]$ // Initialize incoming weights and concatenate. +3 $\mathbf{M}_t\gets \mathbf{M}_{t - 1}$ // Initialize new cluster centers as the old centers. +4 for $i\gets I$ : $\tau$ do +5 $\mathbf{d}\gets$ pairwise.l2_distance(X, $\mathbf{M}_t$ ) // Shape $(K + N_{f},K)$ . +6 $\delta \gets$ d.argmin(axis=1) // Assign each token to a center. +7 $\delta \gets$ make_onehot(δ,K) // Binary. Shape $(K + N_{f},K)$ . +8 $\mathbf{W}_t\gets \delta^\top \mathbf{W}_t$ // Compute #tokens assigned to each center. +9 $\mathbf{A}\gets \delta^\top /\mathbf{W}_t$ // Weight matrix. “/” is elementwise div. +10 $\mathbf{M}_t\gets \mathbf{AX}$ // Compute new centers as a linear function. +11 end +12 return $\mathbf{M}_t$ , $\mathbf{W}_t$ + +# 3.2. Streaming inputs using memory + +The input visual features, $\mathbf{f}$ , have dimensionality $\mathbb{R}^{T\cdot N_f\times D}$ where typical values are $T > 64$ for a sparsely sampled (e.g. 1 FPS), few-minute-long video, and $N_{f} = 257$ tokens per-frame for a vision transformer such as CLIP [34]. Directly feeding all $T\cdot N_{f}$ to the text decoder is prohibitively expensive, due to the quadratic complexity of self-attention. Therefore, existing methods aggressively downsample $\mathbf{f}$ to reduce the number of tokens (by temporally sampling a few frames with large strides [10, 45], or spatially subsampling each frame to a single token [48, 56, 62]). Even so, we will reach memory limits with longer videos, and the information required for fine-grained localization and description is lost. Therefore, rather than aggressive downsampling, we use a memory mechanism to process all tokens frame-by-frame, which ensures that the computational cost is bounded irrespective of the length of the video. + +Let $K$ be a pre-defined memory size, the memory at each time $\mathbf{M}_t$ would always be the constant size $K$ , i.e., $\mathbf{M}_t \in \mathbb{R}^{K \times D}, \forall t$ . We interpret $\mathbf{M}$ as being a summary of all relevant information in the video, and initialize it by taking the first $K$ tokens from $\mathbf{f}$ . Therefore, we set $K$ as a multiple of $N_f$ , such that the initial memory is the features of the first $\frac{K}{N_f}$ frames: $\mathbf{M}_{K / N_f} = [\mathbf{f}_1, \dots, \mathbf{f}_{K / N_f}]$ . + +Next, we update the memory at each timestamp for each incoming frame $\mathbf{f}_t$ . Our intuition is to keep as much diverse information in the original video as possible, while not increasing the storage budget (i.e. by keeping a constant memory size $K$ ). We thus propose a K-means-like clustering algorithm, to use the feature cluster centers as the approximate video features. To avoid the cluster centers biasing quickly to incoming features, we keep track of the number of merged tokens in each cluster center. We use this as a momentum weight, so that cluster centers that are merged from more tokens change slower. The detailed algorithm diagram is provided in Alg. 1, and illustrated in Fig. 3. + +![](images/57de4c0239133ed7f7764b4672330c034520100cc596cb7d6d101084fd043c16.jpg) +Figure 3. Illustration of our clustering-based memory module. The current memory tokens are shown by blue squares. At each time step, the memory tokens evolve by integrating information from the incoming tokens (gray squares), using K-means iterations to produce the updated memory tokens (green circles). + +The K-means algorithm is not differentiable with respect to the assignment of data points to cluster centers, $\delta$ (Line 6 of Alg.1). However, the inputs and outputs of our memory module are the updated cluster centers, $\mathbf{M}_t$ , which is a linear mapping of the input $\mathbf{X} = [\mathbf{M}_{t - 1},\mathbf{f}_t]$ , as $\mathbf{M}_t = \mathbf{A}\mathbf{X}$ where $\mathbf{A}$ is a weight matrix computed from $\mathbf{X}$ . Therefore, even though we cannot compute the gradient of $\mathbf{A}$ with respect to $\mathbf{X}$ , we can compute the gradient of $\mathbf{M}_t$ with respect to the input $\mathbf{X}$ , and thus to the input visual feature $\mathbf{f}$ . As a result, we can use our memory module in any part of a neural network, and learn parameters in preceding layers. + +# 3.3. Streaming outputs with decoding points + +The memory module from Sec. 3.2 enables us to efficiently ingest long input videos. However, it is still desirable for our model's text decoder to predict outputs before it has processed the entire input sequence: Streaming the output substantially decreases the latency of the model, as we do not have to wait for the model to process the entire input sequence to make predictions. This is particularly relevant for processing, for example, live video streams. Furthermore, streaming the output can in fact increase our model's accuracy: As we have a memory with a fixed size, $K$ , from which we decode outputs, we will inevitably lose information over time. We can therefore avert this issue by making predictions before we have processed the entire video. + +Decoding points As shown in Fig. 4, we define "decoding points", $d_{i}$ , as intermediate timestamps where we decode event captions given the features in our memory, $\mathbf{M}_{d_i}$ . We train our model such that at each decoding point, $d_{i}$ the model predicts all event captions that finished before it. More specifically, + +$$ +\mathcal {Y} _ {i} = \left\{\left(w _ {j} ^ {s}, w _ {j} ^ {e}, \mathbf {c} _ {j}\right) \mid w _ {j} ^ {e} \leq d _ {i} \right\}, \tag {1} +$$ + +where $\mathcal{V}_i$ is the set of all event captions corresponding to the $i^{\mathrm{th}}$ decoding point $d_{i}$ , and $w_{j}^{s}, w_{j}^{e}$ are the starting and ending time of the $j^{\mathrm{th}}$ event. + +![](images/ebc3a539681804380bf14dbcdfa57cd40847dc17dea96132c34e8c3d3bf635bc.jpg) +Figure 4. Decoding point supervision in training. A decoding point, $d_i$ , can be at any frame. At each point, we take the memory features, $\mathbf{M}_{d_i}$ , and predict all events that have finished before $d_i$ and are not in the prefix $\mathbf{p}$ . Therefore, the union between the prefix and the prediction target covers all events finished before it. + +As decoding points are applied sequentially, later decoding points should have access to the predictions of earlier decoding points, and should not repeat them again. Therefore, from the second decoding point onwards, we concatenate the outputs of previous decoding points as the prefix to the text decoder, as shown in Fig. 4. Moreover, during training, we perform further data augmentation by randomly removing some of the previous event captions from the prefix, and adding them to the target instead, to increase robustness to potential errors in earlier predictions. We therefore denote our prefixes and captioning targets during training as + +$$ +\mathbf {p} _ {i} = \left[ \mathbf {c} _ {1} ^ {\prime}, \mathbf {c} _ {2} ^ {\prime}, \dots , \mathbf {c} _ {j - 1} ^ {\prime} \right] \tag {2} +$$ + +$$ +\mathbf {y} _ {i} = \left[ \mathbf {c} _ {j} ^ {\prime}, \mathbf {c} _ {j + 1} ^ {\prime}, \dots , \mathbf {c} _ {| \mathcal {Y} _ {i} |} ^ {\prime} \right], \tag {3} +$$ + +where $j < |\mathcal{V}_i|$ is a randomly chosen splitting point to partition the target and context. During inference, we use the models actual predictions, $\mathbf{p}_i = [\hat{\mathbf{y}}_1,\hat{\mathbf{y}}_2,\dots ,\hat{\mathbf{y}}_{i - 1}]$ , instead. + +In practice, we uniformly sample decoding points during both training and inference, with a stride of $S$ frames. Since the model is trained to predict all event captions before the decoding point, it means that the exact location at inference time does not need to match the event boundaries closely. The number of decoding points can be also different between training and inference, as we will ablate. This method is both simple and scalable, as we show experimentally in the next section. + +# 4. Experimental Evaluation + +# 4.1. Experimental Setup + +# 4.1.1 Datasets and Evaluation Metrics + +We evaluate our model on the three most popular dense video captioning datasets: ActivityNet Captions [26], YouCook2[61], and ViTT [21]. + +ActivityNet Captions [26] contains 8,649 training videos and 4,267 validation videos (considering videos that are still online on YouTube). The videos are untrimmed, each containing multiple action events, with an average video length of 2 minutes and an average of 3.7 events. The + +videos are selected from the ActivityNet [7], which covers a wide range of visual domains. Each video is carefully labeled by human annotators. We use this dataset for both dense captioning (predicting a sequence of captions with their start- and end-times) and paragraph captioning (predicting the aforementioned captions as a single paragraph without timestamps). + +YouCook2 [61] contains 1,333 training videos and 456 validation videos. The videos are on average 5.3 minutes long, with an average of 7.8 events. This dataset focuses on cooking scenes, and most videos contain one main actor cooking while describing the recipe. The videos are manually annotated, aided by speech transcriptions obtained through Automatic Speech Recognition (ASR). As expected due to the annotation process, using ASR as an additional modality can be used to improve model predictions [56]. However, our work focuses on using visual-only inputs, to study our proposed streaming model. We also perform dense and paragraph captioning on this dataset. + +ViTT [21] contains 4,608 training videos and 2,301 testing videos, which are on average 4.7 minutes long and contain 7 events per video. It is collected in a similar way as YouCook2, but focuses on more diverse domains. Again, we do not use the ASR inputs in our experiments. + +Evaluation Metrics For all datasets, we report standard dense captioning evaluation metrics following Vid2Seq [56] and PDVC [48]. The primary metric is CIDEr which has been adapted to jointly evaluate captioning and localisation. In particular, we average the CIDEr score [43] for positive ground-truth-prediction pairs with a temporal IoU above the thresholds, $\{0.3, 0.5, 0.7, 0.9\}$ . Similarly, we report ME-TEOR [2] averaged over multiple IoU thresholds. Finally, we report the recently proposed $\mathrm{SODA}_c$ [16], which considers all event captions from the same video, and is therefore a more holistic measure. + +# 4.1.2 Implementation details + +We implement our streaming model on two video captioning architectures, GIT [45] and Vid2Seq [56]. Both use a ViT-L [14] initialized from CLIP [34] as image encoder $\mathcal{F}$ . + +GIT [45] concatenates all tokens from all input frames, f, and feeds them to a 6-layer transformer language decoder. We apply our streaming input module before the language decoder, i.e., rather than concatenating frame features, we use our memory features instead. The original GIT paper pretrains the language decoder on in-house data [45]. As we do not have access to the original data or weights, we pretrain our GIT model on the WebLI dataset [11]. + +Vid2Seq [56] pools all frame tokens spatially into 1 token per frame, and then applies a 12-layer temporal transformer [1] to obtain the final visual features. The language decoder is a 12-layer T5-Base decoder [35]. Vid2Seq pre + +
#TokensT=16T=32T=64T=128
No memoryT×Nf29.8---
Spatial poolingT27.627.327.927.4
Temporal poolingNf29.328.026.825.2
EMA [59]Nf28.226.322.016.3
MovieChat [41]K29.329.228.929.3
Clustering (ours)K29.829.230.630.4
+ +Table 1. Ablation on memory modules. We show CIDEr (averaged over multiple IoUs) on ActivityNet with GIT under different # input frames $T$ . The 2nd column shows the number of input tokens to the language decoder. $N_{f} = 257$ is the number of tokens per-frame. $K = 514$ is the number of memory tokens. Our module benefits from more frames, and outperforms other alternatives. + +
KCIDEr
25729.4
257 × 230.6
257 × 329.8
+ +(a) #memory tokens. (b) K-means iterations. +Table 2. Ablation on memory module hyperparameters. We perform experiments on ActivityNet with GIT with 64 frames. + +
Iters.CIDEr
130.3
230.6
430.3
+ +
MomentumCIDEr
X29.7
✓30.6
+ +(c) Momentum term in clustering + +trains the temporal transformer and the T5 decoder on narrated videos from the YT-Temporal dataset [58]. We use their public, pretrained weights as our initialization. We apply our streaming input module before the temporal transformer, to ensure the intermediate features remain causal. + +When finetuning our model for each dataset, we freeze the frame encoder following prior works [48, 56, 63]. We provide detailed training hyperparameters in the supplementary. For each architecture, the training hyperparameters are shared across the 3 datasets. + +# 4.2. Analysis of Streaming Modules + +We first analyze each of the main components of our model: streaming the input with our memory module (Sec. 3.2), and then streaming outputs using decoding points (Sec. 3.3). Unless otherwise stated, we use the GIT [45] backbone for our experiments. Due to randomness in training and evaluation, for all ablation experiments (Tab. 1-Tab. 3), we repeat the same run 3 times and report the averaged metrics. When compared to other methods (Tab. 4, Tab. 5), we report results for the best model. + +# 4.2.1 Streaming inputs with memory + +As the GIT [45] architecture concatenates visual features, f, from multiple frames before passing it to the language decoder, it is limited by the number of frames that it can process. Our clustering-based memory module allows us + +
Number of decoding points12481620
CIDEr30.634.538.839.540.640.4
+ +(a) Number of decoding points during training. + +
PrefixCIDErAug. PrefixCIDErStrideCIDEr
None23.1×37.63240.6
Captions40.6✓40.62134.7
Captions & time39.3
+ +(b) Context provided (c) Random masking (d) Decoding point after the first decoding prefix as augmentation stride during inference point. during training. (input 64 frames). + +Table 3. Ablation on streaming outputs. (a) Increasing the number of decoding points during training consistently improves accuracy, as it provides more supervision to the model. (b) It is critical to provide context after the first decoding point, so that the model does not repeat predictions. Providing captions alone, without timestamps is sufficient. (c) It is important to provide imperfect prefixes during training, to mimic model behavior in inference. (d) Stride used for decoding during inference. + +to process more frames, and we consider the following approaches to evaluate it: + +No memory: We simply concatenate all visual tokens from all frames as done in GIT [45]. Due to memory constraints, we can only feed up to 16 frames to the decoder. + +Spatial- or temporal-pooling: We pool the visual features, f, along either the spatial or temporal dimensions to reduce the number of tokens fed to the language decoder. + +EMA: We use an exponential moving average of frame features, $\mathbf{f}_t$ , at each time step, following TeSTra [59]. We sweep the decay rate from $\{0.9, 0.99, 0.999\}$ , finding 0.9 to perform best. + +MovieChat [41]. Finally, the recent MovieChat paper maintains a memory of $K$ tokens. For each incoming frame, it sequentially processes each token, and merges the two most similar tokens in the memory bank such that the size remains fixed at $K$ . We implement this method using the author's public code. + +Tab. 1 compares the results of the different memory modules. For $T = 16$ , where we can feed all the tokens from the vision backbone, $\mathbf{f}$ , into the decoder, "no memory" and our method both performs the best. We expected "no memory" to perform well, as it uses the most tokens, $T \times N_f$ . However, our clustering-based method achieves the same performance, which suggests that it is able to effectively capture the relevant information in the video with $8 \times$ fewer tokens, and is causal too. It is not possible to use "no memory" for $T > 16$ due to its computational cost. + +With more frames, naively pooling along the spatial-, or temporal-dimensions actually performs worse. This is likely because we are averaging out information over longer temporal durations, and thus losing the details required for more detailed localization or captioning. Our method and MovieChat on the other hand, are able to leverage more frames to improve performance, as they keep diverse fea + +
ActivityNetYouCook2ViTT
CIDErSODAMeteorF1CIDErSODAMeteorF1CIDErSODAMeteorF1
MT [62]9.3-5.0-6.1-3.2-----
E2ESG [63]----25.0-3.5-----
PDVC [48]29.36.07.6-28.94.95.7-----
GIT [45]29.85.77.850.612.13.13.417.715.17.13.432.5
Vid2Seq†[56]30.25.98.551.825.35.76.423.523.09.85.037.7
Streaming GIT (ours)41.26.69.050.915.43.23.616.618.58.34.033.9
Streaming Vid2Seq (ours)37.86.210.052.932.96.07.124.125.210.05.835.4
+ +Table 4. Comparison to the state-of-the-art on dense video captioning We add our streaming model to both GIT [45] and Vid2Seq [56], denoted by Streaming GIT and Streaming Vid2Seq, respectively, achieving consistent and substantial improvements across three datasets. All models use only visual inputs. $^\dagger$ denotes version with visual-only inputs. + +tures within the memory. Finally, our clustering method outperforms MovieChat and other memory modules for all numbers of frames that we considered, which is why we use it for all future experiments. + +We also ablate the hyperparameters of our memory module in Tab. 2. Following this experiment, we set $K = 257 \times 2$ , or the number of tokens in two frames, and use 2 iterations of K-means, as it achieves the best performance. Our proposed momentum term (Sec. 3.2), which prevents cluster centers from becoming too biased towards incoming frame tokens, also improves CIDEr from 29.7 to 30.6. + +# 4.2.2 Streaming outputs + +We now analyze the effect of our streaming decoding method (Sec. 3.3), which enables us to predict event captions from intermediate features in our memory, and utilize previous prediction as the prefix to our text decoder. Table 3 analyses the effects of the number of decoding points during training, the impact of the prefix, and how we select decoding points during inference. + +Table 3a shows that we achieve significant improvements by increasing the number of decoding points during training, improving the CIDEr score by 10 points, or $33\%$ relative, compared to only making predictions at the end, as in conventional models. Streaming the output with decoding points can provide performance benefits for multiple reasons: First, as we have multiple decoding points, the required output caption is shorter at each decoding point, making the captioning task easier. Second, the visual features from our memory, M, may be aligned better with the target text, since M does not represent the visual features from the entire video as in baseline approaches, but only the features up to the decoding point. Finally, training with decoding points provides a stronger training signal to the model, as we provide training supervision at each decoding point. Moreover, it should aid generalization, as the network is being trained to make consistent predictions from more points along the timeline. + +Tab. 3b shows that it is essential to provide past predic + +tions as the prefix. Without a prefix, the model is poor, underperforming our non-streaming baseline of only decoding at the end (30.6). This is because the model predicts duplicated predictions at each decoding point. Providing past captions outperforms this baseline substantially. We find that also adding previously predicted timestamps, does not improve over captions alone, suggesting that temporal boundaries of past events are not particularly informative for future events. Tab. 3c further shows that while training with a prefix, it is important to mimic inference behavior by including missing captions in earlier predictions. + +Table 3d examines the choice of decoding points during inference. We find that using a stride, $S = 32$ (which equates to a decoding point at the middle and end of a 64-frame clip), performs considerably better than $S = 21$ (three uniformly chosen points). We observed qualitatively that using too many decoding points during inference can sometimes still result in the model making duplicate predictions (even with past prediction as the prefix). Whilst it is also possible to remove duplicate predictions with non-maximal suppression (NMS [15]), it is more challenging for captioning models as we also require a calibrated score for each event caption to perform NMS. We therefore leave an investigation of NMS for dense video captioning to future work. + +# 4.2.3 Generalization to backbones and datasets + +To show the generality of our method, we add our streaming modules onto both the GIT [45] and Vid2Seq [56] architectures, which we denote as Streaming GIT and Streaming Vid2Seq, respectively. + +The last two rows of Tab. 4 shows that we improve substantially over both baselines consistently on three datasets. Our GIT baseline can process a maximum of $N_{f} = 16$ frames due to memory limitations, and our improvement also stems from the fact that we use $N_{f} = 64$ for our Streaming GIT thanks to our memory module. Vid2Seq pools visual tokens spatially such that it only uses a single token per frame. Therefore, our Streaming Vid2Seq does not use more frames than the baseline, and the improvement is due + +![](images/495c75ac89baf3470019768c9c7fe62336985d0d020796bba5b8735fa73f8982.jpg) +Figure 5. Qualitative results on ActivityNet validation. Results from the ground truth (top), the baseline (middle), and our model (bottom). We show outputs from two decoding points in green and blue respectively. Our model captures more details than the baseline. + +to our streaming of output event captions, which improves performance significantly as shown in Tab. 3. + +Finally, we observe that our Vid2Seq baseline performs substantially better than the GIT baseline on YouCook2. This difference is due to the pretraining: We used the public, pretrained Vid2Seq checkpoint [56] which was pretrained on YT-Temporal [58] - a dataset with a similar domain to YouCook2. Note that this is the same experimental protocol as Vid2Seq [56], the current state-of-the-art. + +# 4.3. State-of-the-art Comparison + +Tab. 4 also compares our method to the state-of-the-art among dense video captioning methods using only video frames as inputs. We achieved substantial gains over prior, published works, notably improving CIDEr on ActivityNet by 11.0 points, and YouCook2 by 4.0 points, respectively. We also achieved improvements, albeit smaller, on SODA and Meteor. Our improvements on localization (F1) are smaller, showing the gains are more from better captioning qualities. Fig. 5 visualizes an example on ActivityNet. + +We note that it is possible to further improve results, particularly on YouCook2, by using Automatic Speech Recognition (ASR) as an additional input modality [56]. This is primarily because the spoken utterances of the actors are well aligned with the visual content, and because ASR was used in the annotation procedure of the dataset itself. However, integrating multiple modalities such as ASR is orthogonal to the main focus of this work. + +Paragraph captioning. In addition to dense captioning, we also compare with state-of-the-art models on the same datasets for paragraph captioning, which aims to predict the captions throughout the entire video, but without any timestamps. Therefore, we only apply our streaming input model here, as the timestamps needed to assign decoding points during training are not available in this setting. + +We train our Streaming GIT model for paragraph captioning, on both ActivityNet [26] and Youcook2 [61]. Tab. 5 + +
ActivityNetYouCook2
MFT [54]19.1-
PDVC [48]20.5-
Vid2Seq [56]†28.026.6
GIT [45]32.528.4
Ours33.433.9
+ +Table 5. State-of-the-art comparison on paragraph captioning. We report CIDEr on ActivityNet and YouCook2 validation set. We compare models that do not require action proposal inputs and only takes visual inputs. $\dagger$ denotes version with visual-only inputs. Our model achieves the best performance on both datasets. shows that we achieve state-of-the-art results on this task too. The GIT baseline is our model trained on the same setting as our full model, but uses 16 input frames with all tokens concatenated for the decoder. This baseline already outperforms the state-of-the-art from visual-only inputs. Our model uses more input frames (64 frames), and further boosts the performance by 0.9 and 5.5 points on the two datasets, respectively, showing the benefits of our memory module which is consistent with our results in Tab. 1. + +# 5. Conclusion and Future Work + +We have proposed a streaming model for dense video captioning with two novel components: A clustering-based memory that can efficiently handle arbitrarily long videos with bounded computation, and a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. We achieve this streaming ability while also improving the state-of-the-art on five dense- and paragraphCaptioning tasks. + +Future work is to develop a benchmark for dense video captioning which requires reasoning over longer videos than current datasets, to better evaluate the abilities of streaming models such as ours. + +Acknowledgments. We thank Chen Sun for helpful discussions. + +# References + +[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. ViViT: A Video Vision Transformer. In ICCV, 2021. 3, 5 +[2] Satanjeev Banerjee and Alon Lavie. 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Current state-of-the-art models, however, process a fixed number of downsampled frames, and make a single full prediction after seeing the whole video. We propose a streaming dense video captioning model that consists of two novel components: First, we propose a new memory module, based on clustering incoming tokens, which can handle arbitrarily long videos as the memory is of a fixed size. Second, we develop a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. Our model achieves this streaming ability, and significantly improves the state-of-the-art on three dense video captioning benchmarks: ActivityNet, YouCook2 and ViTT. Our code is released at https://github.com/google-research/scenic." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 479, + 128, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 128, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 128, + 491 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 500, + 287, + 668 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 500, + 287, + 668 + ], + "spans": [ + { + "bbox": [ + 46, + 500, + 287, + 668 + ], + "type": "text", + "content": "Video is ubiquitous in modern society, quickly becoming one of the most prevalent media formats for transmitting information. The majority of computer vision models designed for video understanding only process a handful of frames, mostly covering only a few seconds [28, 30, 36, 46, 55], and are typically limited to classifying these short segments into a fixed number of concepts. In order to achieve a comprehensive, fine-grained video understanding, we study the task of dense video captioning – jointly localizing events temporally in video and generating captions for them. Ideal models for this goal should be able to handle both long input sequences – to reason over long, untrimmed videos – and also to handle long output sequences in text space, to describe in detail all the events within the video." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 669, + 288, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 288, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 288, + 693 + ], + "type": "text", + "content": "Prior work on dense video captioning does not handle either long inputs or long outputs. Given a video of" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 307, + 201, + 545, + 256 + ], + "blocks": [ + { + "bbox": [ + 307, + 201, + 545, + 256 + ], + "lines": [ + { + "bbox": [ + 307, + 201, + 545, + 256 + ], + "spans": [ + { + "bbox": [ + 307, + 201, + 545, + 256 + ], + "type": "image", + "image_path": "cd5124675d807cdcb6e7fa5108bb96f26737371ec465dce4ea175454eba34b72.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 318, + 258, + 533, + 269 + ], + "lines": [ + { + "bbox": [ + 318, + 258, + 533, + 269 + ], + "spans": [ + { + "bbox": [ + 318, + 258, + 533, + 269 + ], + "type": "text", + "content": "(a) Conventional global dense video captioning models [48, 56]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 307, + 270, + 543, + 363 + ], + "blocks": [ + { + "bbox": [ + 307, + 270, + 543, + 363 + ], + "lines": [ + { + "bbox": [ + 307, + 270, + 543, + 363 + ], + "spans": [ + { + "bbox": [ + 307, + 270, + 543, + 363 + ], + "type": "image", + "image_path": "11fdecd9bb4c60c54afb36dc9af135e82ddb4e8be75f9da8831b98674b18536a.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 342, + 365, + 510, + 374 + ], + "lines": [ + { + "bbox": [ + 342, + 365, + 510, + 374 + ], + "spans": [ + { + "bbox": [ + 342, + 365, + 510, + 374 + ], + "type": "text", + "content": "(b) Our streaming dense video captioning model." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 376, + 546, + 431 + ], + "lines": [ + { + "bbox": [ + 305, + 376, + 546, + 431 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 546, + 431 + ], + "type": "text", + "content": "Figure 1. Comparing our streaming model (b) to conventional global models (a). Conventional global models encode the entire video at once, and produce captions for all events at the end. Our model encodes images frame-by-frame, uses them to update a running memory, and predicts captions sequentially." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 445, + 545, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 445, + 545, + 528 + ], + "spans": [ + { + "bbox": [ + 304, + 445, + 545, + 528 + ], + "type": "text", + "content": "any length, state-of-the-art models either sample very few frames (e.g., 6 frames [45]) with large strides [10, 27, 45] (i.e., temporal downsampling), or keep one feature per-frame for all the frames [48, 56, 62] (i.e., spatial downsampling). With long textual output, current models solely rely on auto-regressive decoding [17] to generate multiple sentences at the end." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 531, + 546, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 546, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 546, + 699 + ], + "type": "text", + "content": "In this work, we design a streaming model for dense video captioning as shown in Fig. 1. Our streaming model does not require access to all input frames concurrently in order to process the video thanks to a memory mechanism. Moreover, our model can produce outputs causally without processing the entire input sequence, thanks to a new streaming decoding algorithm. Streaming models such as ours are inherently suited to processing long videos – as they ingest frames one at a time. Moreover, as the output is streamed, intermediate predictions are produced before processing the full video. This property means that streaming models can in theory be applied to process live video streams, as required for applications such as video conferencing, security and continuous monitoring among others." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "In order to develop our streaming model, we first propose" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 231, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 231, + 713 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 231, + 713 + ], + "type": "text", + "content": "*Equal contribution. {zhouxy, aarnab} @google.com" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18243" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 70, + 521, + 222 + ], + "blocks": [ + { + "bbox": [ + 72, + 70, + 521, + 222 + ], + "lines": [ + { + "bbox": [ + 72, + 70, + 521, + 222 + ], + "spans": [ + { + "bbox": [ + 72, + 70, + 521, + 222 + ], + "type": "image", + "image_path": "34ef85e03f5a1fda96e700972dc8731ea99e891dbee7c5b42d1f443777c1e32c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 223, + 547, + 280 + ], + "lines": [ + { + "bbox": [ + 46, + 223, + 547, + 280 + ], + "spans": [ + { + "bbox": [ + 46, + 223, + 547, + 280 + ], + "type": "text", + "content": "Figure 2. Illustration of our framework. Each frame is passed through an image encoder, one at a time. A memory model, based on clustering, maintains compressed visual features from the beginning up to the current frame. At certain frames, denoted as \"decoding points\", we decode the representations from our memory into captions and their timestamps. Earlier text predictions, if available, are also passed as a prefix to the language decoder for the following decoding points. Our model can run on videos of arbitrary length, as the memory has a constant size, and can also output predictions before processing the whole video." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 288, + 288, + 359 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 288, + 288, + 359 + ], + "spans": [ + { + "bbox": [ + 46, + 288, + 288, + 359 + ], + "type": "text", + "content": "a novel memory mechanism, that takes frames once at a time. The memory model is based on K-means clustering, and uses a fixed number of cluster-center tokens to represent the video at each timestamp. We show that this method is simple and effective, and can process variable numbers of frames, with a fixed computational budget at decoding." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 360, + 287, + 552 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 552 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 552 + ], + "type": "text", + "content": "We also develop a streaming decoding algorithm, and train our network such that given a \"decoding point\" (Fig. 2) at a particular timestamp, it predicts all event captions that ended before it given the memory features at that timestamp. Our network is thus trained to make predictions at any timestamp of the video, and not just at the end of the video as in conventional, non-streaming models. Furthermore, we provide predictions from earlier decoding points as contexts for later ones. This context avoids predicting duplicated events, and can be used as an \"explicit\" memory in natural language summarising the earlier video. Our streaming output is also motivated by the fact that as the video length grows, our memory will inevitably lose information over time as its size is bounded. We avert this issue by making predictions before we have processed the entire video, and still keep early information via language context." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 552, + 288, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 552, + 288, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 552, + 288, + 659 + ], + "type": "text", + "content": "We evaluate our approach on three popular dense video captioning datasets, ActivityNet [26], YouCook2 [61] and ViTT [21]. Our results show that our streaming model significantly improves over the state-of-the-art, which inevitably uses fewer frames or fewer features, by up to 11.0 CIDEr points. We show that our method generalizes across both GIT [45] and Vid2Seq [56] architectures. Finally, our proposed memory can also be applied to paragraph captioning, improving baselines by 1-5 CIDEr points." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "spans": [ + { + "bbox": [ + 47, + 669, + 134, + 681 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 288, + 715 + ], + "type": "text", + "content": "Dense video captioning. Dense video captioning requires captioning events, and localizing them temporally. Tra" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 288, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 288, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 304, + 288, + 545, + 467 + ], + "type": "text", + "content": "ditionally, prior work used a two-stage approach, first localizing events in video, and then subsequently captioning them [22, 23, 26, 44, 47]. More recent end-to-end approaches include PDVC [63] which infers event captions and timestamps using a DETR-like [9] model. Vid2Seq [56] augments the vocabulary of a language model with timestamp tokens, allowing them to generate concatenated event captions in the same manner as a regular captioning model. We also use the output formulation of [56], as it integrates well with foundation vision-language models [45]. A related, but different problem, is that of audio description in movies [18, 19, 40], which requires generating captions for the visually impaired that must be complementary to speech, and often uses auxiliary, non-causal models to recognize characters or their speech [19]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 471, + 545, + 579 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 579 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 579 + ], + "type": "text", + "content": "As far as we are aware, all prior dense captioning models are not causal, as they encode the entire video at once. Moreover, to process long videos, they typically use visual features that are downsampled heavily (by selecting a few frames [10, 27, 45], or spatially pooling features per frame [48, 56, 62]). In contrast, we process videos in a streaming manner, processing long input sequences one frame at a time with a memory module, and streaming output sentences with a novel decoding algorithm." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "Models for long videos. A common way of processing longer videos is to use a memory mechanism to provide a compact representation of past events. With transformers, memory can easily be implemented by using tokens from past observations as inputs for the present time step [12, 33, 53]. Examples in vision include [20, 32, 50, 51] which preextract features offline and retrieve them during inference, and are thus not causal. MemViT [52] uses token activations from previous time steps as inputs to the current time step. However, this means that the sequence length grows over time and so it cannot handle arbitrarily long videos." + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18244" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 263 + ], + "type": "text", + "content": "An alternate view of memory is to see it as a method of compressing previously observed tokens into a smaller, fixed-size set to be used at future time steps. Token Turing Machines [38] summarize past and current observations using the token summarization module of [37]. MovieChat [41] follows a similar idea, but uses a variant of Token Merging [5] instead to perform the summarization. TeSTra [59] uses an exponential moving average to integrate video features instead. The advantage of such approaches is that the memory bank has a fixed size, and therefore the computational cost remains bounded regardless of the length of the video. Our memory model has this same desirable property. However, our memory is based on clustering, using the centers from a K-means-like algorithm to summarize tokens from each time step, and we show experimentally that this outperforms other alternatives." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 264, + 289, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 264, + 289, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 264, + 289, + 408 + ], + "type": "text", + "content": "Causal models in video. Our streaming model is causal, meaning that its output only depends on current and past frames, without access to future frames. Although we are not aware of prior causal models for dense video captioning, there are causal models in many other vision domains. Online action detection [13, 25, 59, 60] aims to predict action labels for videos in real-time without access to future frames. Analogously, online temporal action localization [6, 24, 39] models also predict start- and end-times after an action is observed. Most models for object tracking [3, 49] and video object/instance segmentation [8, 29, 31] are causal too." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 409, + 289, + 483 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 409, + 289, + 483 + ], + "spans": [ + { + "bbox": [ + 46, + 409, + 289, + 483 + ], + "type": "text", + "content": "A common theme in the above tasks is that the model must make a prediction at each frame of the video. In contrast, we focus on dense video captioning [26], which is challenging as the output captions do not have a one-to-one correspondence with the video frames. We address this problem by proposing a streaming decoding algorithm." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 495, + 243, + 509 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 243, + 509 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 243, + 509 + ], + "type": "text", + "content": "3. Streaming Dense Video Captioning" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": "Given a video " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "\\mathbf{V} \\in \\mathbb{R}^{T \\times H \\times W \\times 3}" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": ", our goal is to produce a set of temporally localized captions: " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "\\{(s, e, \\mathbf{c})_1, \\ldots, (s, e, \\mathbf{c})_{n_e}\\}" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "s \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "e \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": " are the starting and ending timestamps (" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "0 \\leq s < e \\leq T" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": "), respectively, " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "\\mathbf{c} = [w_1, \\dots, w_n]" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": " is a sequence of word tokens, and " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "n_e" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": " the number of events. Each word token " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "w_i" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": " is an integer in the range " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "[0, |V|]" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": ", indexing the vocabulary " + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "inline_equation", + "content": "V" + }, + { + "bbox": [ + 46, + 514, + 289, + 649 + ], + "type": "text", + "content": ". We begin by describing conventional captioning models (Sec. 3.1), before detailing how we develop a streaming model (Fig. 2) by streaming inputs with memory (Sec. 3.2) and outputs with decoding points (Sec. 3.3)." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 658, + 134, + 670 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 658, + 134, + 670 + ], + "spans": [ + { + "bbox": [ + 47, + 658, + 134, + 670 + ], + "type": "text", + "content": "3.1. Preliminaries" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 288, + 715 + ], + "type": "text", + "content": "Captioning models broadly consist of a vision encoder followed by a text decoder. We outline these approaches, and show how they can be extended to dense captioning next." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": "Visual encoder. The first step is to encode the video into features " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathbf{f} = \\mathcal{F}(\\mathbf{V}),\\mathbf{f}\\in \\mathbb{R}^{N\\times D}" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " is the feature resolution (i.e., number of tokens for transformer-based encoders), and " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " is the feature dimension. The visual feature encoder " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " can be a native video backbone [1, 4], or an image encoder [34, 57] applied to each individual frame. In the latter case, the video feature is a stack of image features, i.e. " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "N = T\\cdot N_{f}" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "inline_equation", + "content": "N_{f}" + }, + { + "bbox": [ + 304, + 72, + 547, + 216 + ], + "type": "text", + "content": " is the number of tokens per frame. We use a per-frame encoding, but instead of pre-extracting them from the whole video, we use a memory mechanism to process the features in a causal, streaming fashion (Sec. 3.2) that can generalize to longer video durations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": "Text decoder. Given the visual features, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": ", and optional textual prefix tokens, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": ", the text decoder, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": " generates a sequence of word tokens, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{c}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": " from them. We use an autoregressive [17, 42] decoder that generates the next word token, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "w_{i}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": ", conditioned on previous words, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{w}_{1:i-1}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": ", and prefix if provided as " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "w_{i} = \\mathcal{D}(\\mathbf{f}, \\mathbf{p}, \\mathbf{w}_{1:i-1})" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": ". Note that prefix tokens are typically not used in captioning tasks, but are used in question-answering (QA) to encode the input question. Concretely, the text decoder, " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathcal{D}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": ", is a sequence of transformer layers [42] operating on a concatenation of visual features " + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 222, + 547, + 378 + ], + "type": "text", + "content": " and word embeddings of the prefix [35, 45]. This architecture is shown to be effective in both captioning and QA tasks across image and video [10, 27, 45]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": "Dense video captioning with timestamps. Combining the above visual encoder and text decoder gives a basic architecture for video captioning. To extend it for captioning multiple events with starting and ending timestamps, Vid2Seq [56] introduced two main modifications: First, it augments the vocabulary, " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "V'" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": ", of the captioning model with time tokens, " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "w^s" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "w^e" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": ", which represent the starting and ending times, respectively. A single event is therefore represented as " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{c}' = [w^s, w^e, w_1, \\dots, w_n]" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "|V'| = |V| + |T|" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "|V| \\leq w^s < w^e \\leq |V'|" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "|T|" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": " is the number of time tokens. Second, Vid2Seq concatenates all timed captions into a single long caption that is ordered by starting time: " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{C} = [\\mathbf{c}_1', \\mathbf{c}_2', \\dots, \\mathbf{c}_{n_e}']" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "n_e" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": " is the number of events. Therefore, dense video captioning can be formulated as standard video captioning with target " + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "inline_equation", + "content": "\\mathbf{C}" + }, + { + "bbox": [ + 304, + 384, + 547, + 564 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 715 + ], + "type": "text", + "content": "Despite its effectiveness, the (generalized) Vid2Seq [56] architecture has a number of key limitations: First, it forwards visual features from the whole video, f through the decoder, meaning that it does not scale effectively to longer videos and more tokens. In addition, as Vid2Seq predicts all event captions at once, after processing the whole video, it struggles with predicting long, detailed captions. To address these issues, we introduce streaming dense video captioning models, where we process the inputs once at a time using a memory module to bound computational costs, and stream the outputs such that we can make predictions before processing the whole video." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18245" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 48, + 88, + 287, + 266 + ], + "blocks": [ + { + "bbox": [ + 53, + 76, + 259, + 87 + ], + "lines": [ + { + "bbox": [ + 53, + 76, + 259, + 87 + ], + "spans": [ + { + "bbox": [ + 53, + 76, + 259, + 87 + ], + "type": "text", + "content": "Algorithm 1: Updating memory tokens at a timestamp." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "lines": [ + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "spans": [ + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": "Input : " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{t - 1}\\in \\mathbb{R}^{K\\times D}" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : memory tokens " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_{t - 1}\\in \\mathbb{R}^K" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : weights of memory tokens " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_t\\in \\mathbb{R}^{N_f\\times D}" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : incoming tokens Hyperparameters: " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : number of K-means iterations. Output : " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t\\in \\mathbb{R}^{K\\times D}" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : updated memory tokens " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t\\in \\mathbb{R}^K" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : updated weights of memory \n1 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{X}\\gets [\\mathbf{M}_{t - 1},\\mathbf{f}_t]" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " // Concatenate memory and incoming tokens. \n2 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{W}\\gets [\\mathbf{W}_{t - 1},\\mathbf{1}]" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " // Initialize incoming weights and concatenate. \n3 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t\\gets \\mathbf{M}_{t - 1}" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " // Initialize new cluster centers as the old centers. \n4 for " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "i\\gets I" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " : " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\tau" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " do \n5 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{d}\\gets" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " pairwise.l2_distance(X, " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": ") // Shape " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "(K + N_{f},K)" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": ". \n6 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\delta \\gets" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " d.argmin(axis=1) // Assign each token to a center. \n7 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\delta \\gets" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " make_onehot(δ,K) // Binary. Shape " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "(K + N_{f},K)" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": ". \n8 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t\\gets \\delta^\\top \\mathbf{W}_t" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " // Compute #tokens assigned to each center. \n9 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{A}\\gets \\delta^\\top /\\mathbf{W}_t" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " // Weight matrix. “/” is elementwise div. \n10 " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t\\gets \\mathbf{AX}" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " // Compute new centers as a linear function. \n11 end \n12 return " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t" + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "text", + "content": " , " + }, + { + "bbox": [ + 48, + 88, + 287, + 266 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_t" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 271, + 219, + 284 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 219, + 284 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 219, + 284 + ], + "type": "text", + "content": "3.2. Streaming inputs using memory" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "spans": [ + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": "The input visual features, " + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": ", have dimensionality " + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{T\\cdot N_f\\times D}" + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": " where typical values are " + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "inline_equation", + "content": "T > 64" + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": " for a sparsely sampled (e.g. 1 FPS), few-minute-long video, and " + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "inline_equation", + "content": "N_{f} = 257" + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": " tokens per-frame for a vision transformer such as CLIP [34]. Directly feeding all " + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "inline_equation", + "content": "T\\cdot N_{f}" + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": " to the text decoder is prohibitively expensive, due to the quadratic complexity of self-attention. Therefore, existing methods aggressively downsample " + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 290, + 287, + 482 + ], + "type": "text", + "content": " to reduce the number of tokens (by temporally sampling a few frames with large strides [10, 45], or spatially subsampling each frame to a single token [48, 56, 62]). Even so, we will reach memory limits with longer videos, and the information required for fine-grained localization and description is lost. Therefore, rather than aggressive downsampling, we use a memory mechanism to process all tokens frame-by-frame, which ensures that the computational cost is bounded irrespective of the length of the video." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "spans": [ + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": " be a pre-defined memory size, the memory at each time " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": " would always be the constant size " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": ", i.e., " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t \\in \\mathbb{R}^{K \\times D}, \\forall t" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": ". We interpret " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": " as being a summary of all relevant information in the video, and initialize it by taking the first " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": " tokens from " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": ". Therefore, we set " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": " as a multiple of " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "N_f" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": ", such that the initial memory is the features of the first " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\frac{K}{N_f}" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": " frames: " + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{K / N_f} = [\\mathbf{f}_1, \\dots, \\mathbf{f}_{K / N_f}]" + }, + { + "bbox": [ + 46, + 483, + 287, + 570 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "Next, we update the memory at each timestamp for each incoming frame " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_t" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": ". Our intuition is to keep as much diverse information in the original video as possible, while not increasing the storage budget (i.e. by keeping a constant memory size " + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 570, + 288, + 714 + ], + "type": "text", + "content": "). We thus propose a K-means-like clustering algorithm, to use the feature cluster centers as the approximate video features. To avoid the cluster centers biasing quickly to incoming features, we keep track of the number of merged tokens in each cluster center. We use this as a momentum weight, so that cluster centers that are merged from more tokens change slower. The detailed algorithm diagram is provided in Alg. 1, and illustrated in Fig. 3." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 329, + 75, + 525, + 174 + ], + "blocks": [ + { + "bbox": [ + 329, + 75, + 525, + 174 + ], + "lines": [ + { + "bbox": [ + 329, + 75, + 525, + 174 + ], + "spans": [ + { + "bbox": [ + 329, + 75, + 525, + 174 + ], + "type": "image", + "image_path": "57de4c0239133ed7f7764b4672330c034520100cc596cb7d6d101084fd043c16.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 178, + 545, + 234 + ], + "lines": [ + { + "bbox": [ + 304, + 178, + 545, + 234 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 545, + 234 + ], + "type": "text", + "content": "Figure 3. Illustration of our clustering-based memory module. The current memory tokens are shown by blue squares. At each time step, the memory tokens evolve by integrating information from the incoming tokens (gray squares), using K-means iterations to produce the updated memory tokens (green circles)." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "spans": [ + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": "The K-means algorithm is not differentiable with respect to the assignment of data points to cluster centers, " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": " (Line 6 of Alg.1). However, the inputs and outputs of our memory module are the updated cluster centers, " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": ", which is a linear mapping of the input " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{X} = [\\mathbf{M}_{t - 1},\\mathbf{f}_t]" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": ", as " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t = \\mathbf{A}\\mathbf{X}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": " is a weight matrix computed from " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": ". Therefore, even though we cannot compute the gradient of " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{A}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": " with respect to " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": ", we can compute the gradient of " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_t" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": " with respect to the input " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{X}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": ", and thus to the input visual feature " + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 246, + 545, + 379 + ], + "type": "text", + "content": ". As a result, we can use our memory module in any part of a neural network, and learn parameters in preceding layers." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 385, + 515, + 399 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 385, + 515, + 399 + ], + "spans": [ + { + "bbox": [ + 306, + 385, + 515, + 399 + ], + "type": "text", + "content": "3.3. Streaming outputs with decoding points" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "text", + "content": "The memory module from Sec. 3.2 enables us to efficiently ingest long input videos. However, it is still desirable for our model's text decoder to predict outputs before it has processed the entire input sequence: Streaming the output substantially decreases the latency of the model, as we do not have to wait for the model to process the entire input sequence to make predictions. This is particularly relevant for processing, for example, live video streams. Furthermore, streaming the output can in fact increase our model's accuracy: As we have a memory with a fixed size, " + }, + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 304, + 403, + 545, + 559 + ], + "type": "text", + "content": ", from which we decode outputs, we will inevitably lose information over time. We can therefore avert this issue by making predictions before we have processed the entire video." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "spans": [ + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "text", + "content": "Decoding points As shown in Fig. 4, we define \"decoding points\", " + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "text", + "content": ", as intermediate timestamps where we decode event captions given the features in our memory, " + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{d_i}" + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "text", + "content": ". We train our model such that at each decoding point, " + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 304, + 573, + 545, + 645 + ], + "type": "text", + "content": " the model predicts all event captions that finished before it. More specifically," + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 363, + 654, + 545, + 669 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 363, + 654, + 545, + 669 + ], + "spans": [ + { + "bbox": [ + 363, + 654, + 545, + 669 + ], + "type": "interline_equation", + "content": "\\mathcal {Y} _ {i} = \\left\\{\\left(w _ {j} ^ {s}, w _ {j} ^ {e}, \\mathbf {c} _ {j}\\right) \\mid w _ {j} ^ {e} \\leq d _ {i} \\right\\}, \\tag {1}", + "image_path": "ff697fa849631fb15002d041444ea8401c13627f10a374775f286bafaeb9eb35.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{V}_i" + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "content": " is the set of all event captions corresponding to the " + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "inline_equation", + "content": "i^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "content": " decoding point " + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "inline_equation", + "content": "d_{i}" + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "inline_equation", + "content": "w_{j}^{s}, w_{j}^{e}" + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "content": " are the starting and ending time of the " + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "inline_equation", + "content": "j^{\\mathrm{th}}" + }, + { + "bbox": [ + 304, + 676, + 545, + 713 + ], + "type": "text", + "content": " event." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18246" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 71, + 266, + 156 + ], + "blocks": [ + { + "bbox": [ + 65, + 71, + 266, + 156 + ], + "lines": [ + { + "bbox": [ + 65, + 71, + 266, + 156 + ], + "spans": [ + { + "bbox": [ + 65, + 71, + 266, + 156 + ], + "type": "image", + "image_path": "ebc3a539681804380bf14dbcdfa57cd40847dc17dea96132c34e8c3d3bf635bc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "lines": [ + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "spans": [ + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "text", + "content": "Figure 4. Decoding point supervision in training. A decoding point, " + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "text", + "content": ", can be at any frame. At each point, we take the memory features, " + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{M}_{d_i}" + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "text", + "content": ", and predict all events that have finished before " + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "inline_equation", + "content": "d_i" + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "text", + "content": " and are not in the prefix " + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "inline_equation", + "content": "\\mathbf{p}" + }, + { + "bbox": [ + 46, + 158, + 287, + 212 + ], + "type": "text", + "content": ". Therefore, the union between the prefix and the prediction target covers all events finished before it." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 226, + 288, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 226, + 288, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 226, + 288, + 357 + ], + "type": "text", + "content": "As decoding points are applied sequentially, later decoding points should have access to the predictions of earlier decoding points, and should not repeat them again. Therefore, from the second decoding point onwards, we concatenate the outputs of previous decoding points as the prefix to the text decoder, as shown in Fig. 4. Moreover, during training, we perform further data augmentation by randomly removing some of the previous event captions from the prefix, and adding them to the target instead, to increase robustness to potential errors in earlier predictions. We therefore denote our prefixes and captioning targets during training as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 366, + 287, + 380 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 366, + 287, + 380 + ], + "spans": [ + { + "bbox": [ + 112, + 366, + 287, + 380 + ], + "type": "interline_equation", + "content": "\\mathbf {p} _ {i} = \\left[ \\mathbf {c} _ {1} ^ {\\prime}, \\mathbf {c} _ {2} ^ {\\prime}, \\dots , \\mathbf {c} _ {j - 1} ^ {\\prime} \\right] \\tag {2}", + "image_path": "23e3e7750a94990ec97d0d8b00df6bb2b038f719e632b737cb2e4407986a7380.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 113, + 383, + 287, + 397 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 113, + 383, + 287, + 397 + ], + "spans": [ + { + "bbox": [ + 113, + 383, + 287, + 397 + ], + "type": "interline_equation", + "content": "\\mathbf {y} _ {i} = \\left[ \\mathbf {c} _ {j} ^ {\\prime}, \\mathbf {c} _ {j + 1} ^ {\\prime}, \\dots , \\mathbf {c} _ {| \\mathcal {Y} _ {i} |} ^ {\\prime} \\right], \\tag {3}", + "image_path": "0cc4dda4bb10aa5d2713822fbc004c62467d9c3366243924aac40e76885824cb.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "spans": [ + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "type": "inline_equation", + "content": "j < |\\mathcal{V}_i|" + }, + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "type": "text", + "content": " is a randomly chosen splitting point to partition the target and context. During inference, we use the models actual predictions, " + }, + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "type": "inline_equation", + "content": "\\mathbf{p}_i = [\\hat{\\mathbf{y}}_1,\\hat{\\mathbf{y}}_2,\\dots ,\\hat{\\mathbf{y}}_{i - 1}]" + }, + { + "bbox": [ + 46, + 406, + 287, + 442 + ], + "type": "text", + "content": ", instead." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 442, + 287, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 442, + 287, + 549 + ], + "spans": [ + { + "bbox": [ + 46, + 442, + 287, + 549 + ], + "type": "text", + "content": "In practice, we uniformly sample decoding points during both training and inference, with a stride of " + }, + { + "bbox": [ + 46, + 442, + 287, + 549 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 442, + 287, + 549 + ], + "type": "text", + "content": " frames. Since the model is trained to predict all event captions before the decoding point, it means that the exact location at inference time does not need to match the event boundaries closely. The number of decoding points can be also different between training and inference, as we will ablate. This method is both simple and scalable, as we show experimentally in the next section." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 560, + 190, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 560, + 190, + 574 + ], + "spans": [ + { + "bbox": [ + 47, + 560, + 190, + 574 + ], + "type": "text", + "content": "4. Experimental Evaluation" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 580, + 163, + 594 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 580, + 163, + 594 + ], + "spans": [ + { + "bbox": [ + 47, + 580, + 163, + 594 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 599, + 219, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 599, + 219, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 599, + 219, + 609 + ], + "type": "text", + "content": "4.1.1 Datasets and Evaluation Metrics" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 287, + 653 + ], + "type": "text", + "content": "We evaluate our model on the three most popular dense video captioning datasets: ActivityNet Captions [26], YouCook2[61], and ViTT [21]." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 712 + ], + "type": "text", + "content": "ActivityNet Captions [26] contains 8,649 training videos and 4,267 validation videos (considering videos that are still online on YouTube). The videos are untrimmed, each containing multiple action events, with an average video length of 2 minutes and an average of 3.7 events. The" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "videos are selected from the ActivityNet [7], which covers a wide range of visual domains. Each video is carefully labeled by human annotators. We use this dataset for both dense captioning (predicting a sequence of captions with their start- and end-times) and paragraph captioning (predicting the aforementioned captions as a single paragraph without timestamps)." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 156, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 300 + ], + "type": "text", + "content": "YouCook2 [61] contains 1,333 training videos and 456 validation videos. The videos are on average 5.3 minutes long, with an average of 7.8 events. This dataset focuses on cooking scenes, and most videos contain one main actor cooking while describing the recipe. The videos are manually annotated, aided by speech transcriptions obtained through Automatic Speech Recognition (ASR). As expected due to the annotation process, using ASR as an additional modality can be used to improve model predictions [56]. However, our work focuses on using visual-only inputs, to study our proposed streaming model. We also perform dense and paragraph captioning on this dataset." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 361 + ], + "type": "text", + "content": "ViTT [21] contains 4,608 training videos and 2,301 testing videos, which are on average 4.7 minutes long and contain 7 events per video. It is collected in a similar way as YouCook2, but focuses on more diverse domains. Again, we do not use the ASR inputs in our experiments." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "content": "Evaluation Metrics For all datasets, we report standard dense captioning evaluation metrics following Vid2Seq [56] and PDVC [48]. The primary metric is CIDEr which has been adapted to jointly evaluate captioning and localisation. In particular, we average the CIDEr score [43] for positive ground-truth-prediction pairs with a temporal IoU above the thresholds, " + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\{0.3, 0.5, 0.7, 0.9\\}" + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "content": ". Similarly, we report ME-TEOR [2] averaged over multiple IoU thresholds. Finally, we report the recently proposed " + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\mathrm{SODA}_c" + }, + { + "bbox": [ + 304, + 361, + 545, + 492 + ], + "type": "text", + "content": " [16], which considers all event captions from the same video, and is therefore a more holistic measure." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 512, + 437, + 524 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 512, + 437, + 524 + ], + "spans": [ + { + "bbox": [ + 306, + 512, + 437, + 524 + ], + "type": "text", + "content": "4.1.2 Implementation details" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "content": "We implement our streaming model on two video captioning architectures, GIT [45] and Vid2Seq [56]. Both use a ViT-L [14] initialized from CLIP [34] as image encoder " + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 533, + 545, + 568 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 569, + 545, + 664 + ], + "type": "text", + "content": "GIT [45] concatenates all tokens from all input frames, f, and feeds them to a 6-layer transformer language decoder. We apply our streaming input module before the language decoder, i.e., rather than concatenating frame features, we use our memory features instead. The original GIT paper pretrains the language decoder on in-house data [45]. As we do not have access to the original data or weights, we pretrain our GIT model on the WebLI dataset [11]." + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 545, + 713 + ], + "type": "text", + "content": "Vid2Seq [56] pools all frame tokens spatially into 1 token per frame, and then applies a 12-layer temporal transformer [1] to obtain the final visual features. The language decoder is a 12-layer T5-Base decoder [35]. Vid2Seq pre" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18247" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 64, + 281, + 165 + ], + "blocks": [ + { + "bbox": [ + 51, + 64, + 281, + 165 + ], + "lines": [ + { + "bbox": [ + 51, + 64, + 281, + 165 + ], + "spans": [ + { + "bbox": [ + 51, + 64, + 281, + 165 + ], + "type": "table", + "html": "
#TokensT=16T=32T=64T=128
No memoryT×Nf29.8---
Spatial poolingT27.627.327.927.4
Temporal poolingNf29.328.026.825.2
EMA [59]Nf28.226.322.016.3
MovieChat [41]K29.329.228.929.3
Clustering (ours)K29.829.230.630.4
", + "image_path": "28747a3885a382adbcbcf36e7151d4c33ef4a4f18f2442f4622fb3074942a4e8.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "text", + "content": "Table 1. Ablation on memory modules. We show CIDEr (averaged over multiple IoUs) on ActivityNet with GIT under different # input frames " + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "text", + "content": ". The 2nd column shows the number of input tokens to the language decoder. " + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "inline_equation", + "content": "N_{f} = 257" + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "text", + "content": " is the number of tokens per-frame. " + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "inline_equation", + "content": "K = 514" + }, + { + "bbox": [ + 46, + 166, + 287, + 232 + ], + "type": "text", + "content": " is the number of memory tokens. Our module benefits from more frames, and outperforms other alternatives." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 50, + 257, + 124, + 319 + ], + "blocks": [ + { + "bbox": [ + 50, + 257, + 124, + 319 + ], + "lines": [ + { + "bbox": [ + 50, + 257, + 124, + 319 + ], + "spans": [ + { + "bbox": [ + 50, + 257, + 124, + 319 + ], + "type": "table", + "html": "
KCIDEr
25729.4
257 × 230.6
257 × 329.8
", + "image_path": "acc62d69816d4ac0125dcac1ee16fdfa108777293376a3e756752e6222550b82.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 52, + 319, + 203, + 329 + ], + "lines": [ + { + "bbox": [ + 52, + 319, + 203, + 329 + ], + "spans": [ + { + "bbox": [ + 52, + 319, + 203, + 329 + ], + "type": "text", + "content": "(a) #memory tokens. (b) K-means iterations." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "table_footnote" + }, + { + "bbox": [ + 46, + 331, + 287, + 353 + ], + "lines": [ + { + "bbox": [ + 46, + 331, + 287, + 353 + ], + "spans": [ + { + "bbox": [ + 46, + 331, + 287, + 353 + ], + "type": "text", + "content": "Table 2. Ablation on memory module hyperparameters. We perform experiments on ActivityNet with GIT with 64 frames." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 134, + 257, + 197, + 319 + ], + "blocks": [ + { + "bbox": [ + 134, + 257, + 197, + 319 + ], + "lines": [ + { + "bbox": [ + 134, + 257, + 197, + 319 + ], + "spans": [ + { + "bbox": [ + 134, + 257, + 197, + 319 + ], + "type": "table", + "html": "
Iters.CIDEr
130.3
230.6
430.3
", + "image_path": "9eb87edab471b4588606ce6c3b1ca0fbb0080ca298fd32fc4cf2dc229b853c81.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 205, + 257, + 287, + 306 + ], + "blocks": [ + { + "bbox": [ + 205, + 257, + 287, + 306 + ], + "lines": [ + { + "bbox": [ + 205, + 257, + 287, + 306 + ], + "spans": [ + { + "bbox": [ + 205, + 257, + 287, + 306 + ], + "type": "table", + "html": "
MomentumCIDEr
X29.7
✓30.6
", + "image_path": "d81846eaee43790b654d148b6bdc998c6a011c92cf89721980b924aef016022e.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 206, + 308, + 284, + 327 + ], + "lines": [ + { + "bbox": [ + 206, + 308, + 284, + 327 + ], + "spans": [ + { + "bbox": [ + 206, + 308, + 284, + 327 + ], + "type": "text", + "content": "(c) Momentum term in clustering" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 366, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 366, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 366, + 287, + 425 + ], + "type": "text", + "content": "trains the temporal transformer and the T5 decoder on narrated videos from the YT-Temporal dataset [58]. We use their public, pretrained weights as our initialization. We apply our streaming input module before the temporal transformer, to ensure the intermediate features remain causal." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 427, + 287, + 486 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 427, + 287, + 486 + ], + "spans": [ + { + "bbox": [ + 46, + 427, + 287, + 486 + ], + "type": "text", + "content": "When finetuning our model for each dataset, we freeze the frame encoder following prior works [48, 56, 63]. We provide detailed training hyperparameters in the supplementary. For each architecture, the training hyperparameters are shared across the 3 datasets." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 497, + 216, + 510 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 497, + 216, + 510 + ], + "spans": [ + { + "bbox": [ + 47, + 497, + 216, + 510 + ], + "type": "text", + "content": "4.2. Analysis of Streaming Modules" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 516, + 287, + 624 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 516, + 287, + 624 + ], + "spans": [ + { + "bbox": [ + 46, + 516, + 287, + 624 + ], + "type": "text", + "content": "We first analyze each of the main components of our model: streaming the input with our memory module (Sec. 3.2), and then streaming outputs using decoding points (Sec. 3.3). Unless otherwise stated, we use the GIT [45] backbone for our experiments. Due to randomness in training and evaluation, for all ablation experiments (Tab. 1-Tab. 3), we repeat the same run 3 times and report the averaged metrics. When compared to other methods (Tab. 4, Tab. 5), we report results for the best model." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 645, + 212, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 212, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 212, + 658 + ], + "type": "text", + "content": "4.2.1 Streaming inputs with memory" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 713 + ], + "type": "text", + "content": "As the GIT [45] architecture concatenates visual features, f, from multiple frames before passing it to the language decoder, it is limited by the number of frames that it can process. Our clustering-based memory module allows us" + } + ] + } + ], + "index": 14 + }, + { + "type": "table", + "bbox": [ + 310, + 64, + 541, + 94 + ], + "blocks": [ + { + "bbox": [ + 310, + 64, + 541, + 94 + ], + "lines": [ + { + "bbox": [ + 310, + 64, + 541, + 94 + ], + "spans": [ + { + "bbox": [ + 310, + 64, + 541, + 94 + ], + "type": "table", + "html": "
Number of decoding points12481620
CIDEr30.634.538.839.540.640.4
", + "image_path": "eda6dd09c865adf3d69f41fc4f63d636e60ffd8c0a479bc81ca0fa0262e6e1bd.jpg" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "table_body" + } + ], + "index": 15 + }, + { + "type": "table", + "bbox": [ + 308, + 106, + 532, + 155 + ], + "blocks": [ + { + "bbox": [ + 350, + 95, + 501, + 106 + ], + "lines": [ + { + "bbox": [ + 350, + 95, + 501, + 106 + ], + "spans": [ + { + "bbox": [ + 350, + 95, + 501, + 106 + ], + "type": "text", + "content": "(a) Number of decoding points during training." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 308, + 106, + 532, + 155 + ], + "lines": [ + { + "bbox": [ + 308, + 106, + 532, + 155 + ], + "spans": [ + { + "bbox": [ + 308, + 106, + 532, + 155 + ], + "type": "table", + "html": "
PrefixCIDErAug. PrefixCIDErStrideCIDEr
None23.1×37.63240.6
Captions40.6✓40.62134.7
Captions & time39.3
", + "image_path": "84108b7c335aada6aae48daefceeb67f44640f6edbbb2604f2721a1b2aedcbdb.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 306, + 156, + 543, + 185 + ], + "lines": [ + { + "bbox": [ + 306, + 156, + 543, + 185 + ], + "spans": [ + { + "bbox": [ + 306, + 156, + 543, + 185 + ], + "type": "text", + "content": "(b) Context provided (c) Random masking (d) Decoding point after the first decoding prefix as augmentation stride during inference point. during training. (input 64 frames)." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 186, + 545, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 186, + 545, + 274 + ], + "spans": [ + { + "bbox": [ + 306, + 186, + 545, + 274 + ], + "type": "text", + "content": "Table 3. Ablation on streaming outputs. (a) Increasing the number of decoding points during training consistently improves accuracy, as it provides more supervision to the model. (b) It is critical to provide context after the first decoding point, so that the model does not repeat predictions. Providing captions alone, without timestamps is sufficient. (c) It is important to provide imperfect prefixes during training, to mimic model behavior in inference. (d) Stride used for decoding during inference." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 288, + 545, + 311 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 288, + 545, + 311 + ], + "spans": [ + { + "bbox": [ + 305, + 288, + 545, + 311 + ], + "type": "text", + "content": "to process more frames, and we consider the following approaches to evaluate it:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 312, + 545, + 348 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 348 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 348 + ], + "type": "text", + "content": "No memory: We simply concatenate all visual tokens from all frames as done in GIT [45]. Due to memory constraints, we can only feed up to 16 frames to the decoder." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 350, + 545, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 350, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 305, + 350, + 545, + 386 + ], + "type": "text", + "content": "Spatial- or temporal-pooling: We pool the visual features, f, along either the spatial or temporal dimensions to reduce the number of tokens fed to the language decoder." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "spans": [ + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "type": "text", + "content": "EMA: We use an exponential moving average of frame features, " + }, + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\mathbf{f}_t" + }, + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "type": "text", + "content": ", at each time step, following TeSTra [59]. We sweep the decay rate from " + }, + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "type": "inline_equation", + "content": "\\{0.9, 0.99, 0.999\\}" + }, + { + "bbox": [ + 305, + 387, + 545, + 434 + ], + "type": "text", + "content": ", finding 0.9 to perform best." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "spans": [ + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "type": "text", + "content": "MovieChat [41]. Finally, the recent MovieChat paper maintains a memory of " + }, + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "type": "text", + "content": " tokens. For each incoming frame, it sequentially processes each token, and merges the two most similar tokens in the memory bank such that the size remains fixed at " + }, + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 305, + 435, + 545, + 507 + ], + "type": "text", + "content": ". We implement this method using the author's public code." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": "Tab. 1 compares the results of the different memory modules. For " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "T = 16" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": ", where we can feed all the tokens from the vision backbone, " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "\\mathbf{f}" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": ", into the decoder, \"no memory\" and our method both performs the best. We expected \"no memory\" to perform well, as it uses the most tokens, " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "T \\times N_f" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": ". However, our clustering-based method achieves the same performance, which suggests that it is able to effectively capture the relevant information in the video with " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "8 \\times" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": " fewer tokens, and is causal too. It is not possible to use \"no memory\" for " + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "inline_equation", + "content": "T > 16" + }, + { + "bbox": [ + 304, + 509, + 545, + 628 + ], + "type": "text", + "content": " due to its computational cost." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 630, + 545, + 713 + ], + "type": "text", + "content": "With more frames, naively pooling along the spatial-, or temporal-dimensions actually performs worse. This is likely because we are averaging out information over longer temporal durations, and thus losing the details required for more detailed localization or captioning. Our method and MovieChat on the other hand, are able to leverage more frames to improve performance, as they keep diverse fea" + } + ] + } + ], + "index": 26 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "18248" + } + ] + } + ], + "index": 27 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 67, + 70, + 524, + 193 + ], + "blocks": [ + { + "bbox": [ + 67, + 70, + 524, + 193 + ], + "lines": [ + { + "bbox": [ + 67, + 70, + 524, + 193 + ], + "spans": [ + { + "bbox": [ + 67, + 70, + 524, + 193 + ], + "type": "table", + "html": "
ActivityNetYouCook2ViTT
CIDErSODAMeteorF1CIDErSODAMeteorF1CIDErSODAMeteorF1
MT [62]9.3-5.0-6.1-3.2-----
E2ESG [63]----25.0-3.5-----
PDVC [48]29.36.07.6-28.94.95.7-----
GIT [45]29.85.77.850.612.13.13.417.715.17.13.432.5
Vid2Seq†[56]30.25.98.551.825.35.76.423.523.09.85.037.7
Streaming GIT (ours)41.26.69.050.915.43.23.616.618.58.34.033.9
Streaming Vid2Seq (ours)37.86.210.052.932.96.07.124.125.210.05.835.4
", + "image_path": "957c3ae4f0404034c0d4066a6cd516afe23a285f1fd708df58fd64ae81e7a683.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 195, + 545, + 229 + ], + "lines": [ + { + "bbox": [ + 46, + 195, + 545, + 229 + ], + "spans": [ + { + "bbox": [ + 46, + 195, + 545, + 229 + ], + "type": "text", + "content": "Table 4. Comparison to the state-of-the-art on dense video captioning We add our streaming model to both GIT [45] and Vid2Seq [56], denoted by Streaming GIT and Streaming Vid2Seq, respectively, achieving consistent and substantial improvements across three datasets. All models use only visual inputs. " + }, + { + "bbox": [ + 46, + 195, + 545, + 229 + ], + "type": "inline_equation", + "content": "^\\dagger" + }, + { + "bbox": [ + 46, + 195, + 545, + 229 + ], + "type": "text", + "content": " denotes version with visual-only inputs." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 242, + 287, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 242, + 287, + 289 + ], + "spans": [ + { + "bbox": [ + 46, + 242, + 287, + 289 + ], + "type": "text", + "content": "tures within the memory. Finally, our clustering method outperforms MovieChat and other memory modules for all numbers of frames that we considered, which is why we use it for all future experiments." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "spans": [ + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": "We also ablate the hyperparameters of our memory module in Tab. 2. Following this experiment, we set " + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "inline_equation", + "content": "K = 257 \\times 2" + }, + { + "bbox": [ + 46, + 289, + 287, + 373 + ], + "type": "text", + "content": ", or the number of tokens in two frames, and use 2 iterations of K-means, as it achieves the best performance. Our proposed momentum term (Sec. 3.2), which prevents cluster centers from becoming too biased towards incoming frame tokens, also improves CIDEr from 29.7 to 30.6." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 382, + 160, + 395 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 382, + 160, + 395 + ], + "spans": [ + { + "bbox": [ + 47, + 382, + 160, + 395 + ], + "type": "text", + "content": "4.2.2 Streaming outputs" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 287, + 485 + ], + "type": "text", + "content": "We now analyze the effect of our streaming decoding method (Sec. 3.3), which enables us to predict event captions from intermediate features in our memory, and utilize previous prediction as the prefix to our text decoder. Table 3 analyses the effects of the number of decoding points during training, the impact of the prefix, and how we select decoding points during inference." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "type": "text", + "content": "Table 3a shows that we achieve significant improvements by increasing the number of decoding points during training, improving the CIDEr score by 10 points, or " + }, + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "type": "inline_equation", + "content": "33\\%" + }, + { + "bbox": [ + 46, + 486, + 288, + 700 + ], + "type": "text", + "content": " relative, compared to only making predictions at the end, as in conventional models. Streaming the output with decoding points can provide performance benefits for multiple reasons: First, as we have multiple decoding points, the required output caption is shorter at each decoding point, making the captioning task easier. Second, the visual features from our memory, M, may be aligned better with the target text, since M does not represent the visual features from the entire video as in baseline approaches, but only the features up to the decoding point. Finally, training with decoding points provides a stronger training signal to the model, as we provide training supervision at each decoding point. Moreover, it should aid generalization, as the network is being trained to make consistent predictions from more points along the timeline." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 714 + ], + "type": "text", + "content": "Tab. 3b shows that it is essential to provide past predic" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 242, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 242, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 242, + 545, + 373 + ], + "type": "text", + "content": "tions as the prefix. Without a prefix, the model is poor, underperforming our non-streaming baseline of only decoding at the end (30.6). This is because the model predicts duplicated predictions at each decoding point. Providing past captions outperforms this baseline substantially. We find that also adding previously predicted timestamps, does not improve over captions alone, suggesting that temporal boundaries of past events are not particularly informative for future events. Tab. 3c further shows that while training with a prefix, it is important to mimic inference behavior by including missing captions in earlier predictions." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "text", + "content": "Table 3d examines the choice of decoding points during inference. We find that using a stride, " + }, + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "inline_equation", + "content": "S = 32" + }, + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "text", + "content": " (which equates to a decoding point at the middle and end of a 64-frame clip), performs considerably better than " + }, + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "inline_equation", + "content": "S = 21" + }, + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "text", + "content": " (three uniformly chosen points). We observed qualitatively that using too many decoding points during inference can sometimes still result in the model making duplicate predictions (even with past prediction as the prefix). Whilst it is also possible to remove duplicate predictions with non-maximal suppression (NMS [15]), it is more challenging for captioning models as we also require a calibrated score for each event caption to perform NMS. We therefore leave an investigation of NMS for dense video captioning to future work." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 538, + 516, + 550 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 516, + 550 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 516, + 550 + ], + "type": "text", + "content": "4.2.3 Generalization to backbones and datasets" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 605 + ], + "type": "text", + "content": "To show the generality of our method, we add our streaming modules onto both the GIT [45] and Vid2Seq [56] architectures, which we denote as Streaming GIT and Streaming Vid2Seq, respectively." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": "The last two rows of Tab. 4 shows that we improve substantially over both baselines consistently on three datasets. Our GIT baseline can process a maximum of " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{f} = 16" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " frames due to memory limitations, and our improvement also stems from the fact that we use " + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "inline_equation", + "content": "N_{f} = 64" + }, + { + "bbox": [ + 304, + 605, + 545, + 713 + ], + "type": "text", + "content": " for our Streaming GIT thanks to our memory module. Vid2Seq pools visual tokens spatially such that it only uses a single token per frame. Therefore, our Streaming Vid2Seq does not use more frames than the baseline, and the improvement is due" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18249" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 64, + 541, + 225 + ], + "blocks": [ + { + "bbox": [ + 51, + 64, + 541, + 225 + ], + "lines": [ + { + "bbox": [ + 51, + 64, + 541, + 225 + ], + "spans": [ + { + "bbox": [ + 51, + 64, + 541, + 225 + ], + "type": "image", + "image_path": "495c75ac89baf3470019768c9c7fe62336985d0d020796bba5b8735fa73f8982.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 226, + 546, + 249 + ], + "lines": [ + { + "bbox": [ + 46, + 226, + 546, + 249 + ], + "spans": [ + { + "bbox": [ + 46, + 226, + 546, + 249 + ], + "type": "text", + "content": "Figure 5. Qualitative results on ActivityNet validation. Results from the ground truth (top), the baseline (middle), and our model (bottom). We show outputs from two decoding points in green and blue respectively. Our model captures more details than the baseline." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 261, + 287, + 284 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 284 + ], + "type": "text", + "content": "to our streaming of output event captions, which improves performance significantly as shown in Tab. 3." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 285, + 287, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 285, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 46, + 285, + 287, + 369 + ], + "type": "text", + "content": "Finally, we observe that our Vid2Seq baseline performs substantially better than the GIT baseline on YouCook2. This difference is due to the pretraining: We used the public, pretrained Vid2Seq checkpoint [56] which was pretrained on YT-Temporal [58] - a dataset with a similar domain to YouCook2. Note that this is the same experimental protocol as Vid2Seq [56], the current state-of-the-art." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 380, + 203, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 380, + 203, + 392 + ], + "spans": [ + { + "bbox": [ + 47, + 380, + 203, + 392 + ], + "type": "text", + "content": "4.3. State-of-the-art Comparison" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 399, + 287, + 506 + ], + "type": "text", + "content": "Tab. 4 also compares our method to the state-of-the-art among dense video captioning methods using only video frames as inputs. We achieved substantial gains over prior, published works, notably improving CIDEr on ActivityNet by 11.0 points, and YouCook2 by 4.0 points, respectively. We also achieved improvements, albeit smaller, on SODA and Meteor. Our improvements on localization (F1) are smaller, showing the gains are more from better captioning qualities. Fig. 5 visualizes an example on ActivityNet." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 508, + 287, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 508, + 287, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 508, + 287, + 603 + ], + "type": "text", + "content": "We note that it is possible to further improve results, particularly on YouCook2, by using Automatic Speech Recognition (ASR) as an additional input modality [56]. This is primarily because the spoken utterances of the actors are well aligned with the visual content, and because ASR was used in the annotation procedure of the dataset itself. However, integrating multiple modalities such as ASR is orthogonal to the main focus of this work." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 287, + 688 + ], + "type": "text", + "content": "Paragraph captioning. In addition to dense captioning, we also compare with state-of-the-art models on the same datasets for paragraph captioning, which aims to predict the captions throughout the entire video, but without any timestamps. Therefore, we only apply our streaming input model here, as the timestamps needed to assign decoding points during training are not available in this setting." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "We train our Streaming GIT model for paragraph captioning, on both ActivityNet [26] and Youcook2 [61]. Tab. 5" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 332, + 257, + 517, + 347 + ], + "blocks": [ + { + "bbox": [ + 332, + 257, + 517, + 347 + ], + "lines": [ + { + "bbox": [ + 332, + 257, + 517, + 347 + ], + "spans": [ + { + "bbox": [ + 332, + 257, + 517, + 347 + ], + "type": "table", + "html": "
ActivityNetYouCook2
MFT [54]19.1-
PDVC [48]20.5-
Vid2Seq [56]†28.026.6
GIT [45]32.528.4
Ours33.433.9
", + "image_path": "fce93c77f2ad962c1081a019b8ca86adb353f4cc1b63bed8df2a006a20c2563c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 348, + 546, + 512 + ], + "lines": [ + { + "bbox": [ + 304, + 348, + 546, + 512 + ], + "spans": [ + { + "bbox": [ + 304, + 348, + 546, + 512 + ], + "type": "text", + "content": "Table 5. State-of-the-art comparison on paragraph captioning. We report CIDEr on ActivityNet and YouCook2 validation set. We compare models that do not require action proposal inputs and only takes visual inputs. " + }, + { + "bbox": [ + 304, + 348, + 546, + 512 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 304, + 348, + 546, + 512 + ], + "type": "text", + "content": " denotes version with visual-only inputs. Our model achieves the best performance on both datasets. shows that we achieve state-of-the-art results on this task too. The GIT baseline is our model trained on the same setting as our full model, but uses 16 input frames with all tokens concatenated for the decoder. This baseline already outperforms the state-of-the-art from visual-only inputs. Our model uses more input frames (64 frames), and further boosts the performance by 0.9 and 5.5 points on the two datasets, respectively, showing the benefits of our memory module which is consistent with our results in Tab. 1." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 531, + 471, + 544 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 531, + 471, + 544 + ], + "spans": [ + { + "bbox": [ + 306, + 531, + 471, + 544 + ], + "type": "text", + "content": "5. Conclusion and Future Work" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 554, + 545, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 554, + 545, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 554, + 545, + 649 + ], + "type": "text", + "content": "We have proposed a streaming model for dense video captioning with two novel components: A clustering-based memory that can efficiently handle arbitrarily long videos with bounded computation, and a streaming decoding algorithm that enables our model to make predictions before the entire video has been processed. We achieve this streaming ability while also improving the state-of-the-art on five dense- and paragraphCaptioning tasks." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 652, + 545, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 652, + 545, + 699 + ], + "spans": [ + { + "bbox": [ + 304, + 652, + 545, + 699 + ], + "type": "text", + "content": "Future work is to develop a benchmark for dense video captioning which requires reasoning over longer videos than current datasets, to better evaluate the abilities of streaming models such as ours." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 702, + 541, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 702, + 541, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 702, + 541, + 713 + ], + "type": "text", + "content": "Acknowledgments. We thank Chen Sun for helpful discussions." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18250" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 123 + ], + "type": "text", + "content": "[1] Anurag Arnab, Mostafa Dehghani, Georg Heigold, Chen Sun, Mario Lucic, and Cordelia Schmid. 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ACL, 2022. 2, 6, 7" + } + ] + } + ], + "index": 31 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "18252" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/d9ff698c-3801-40b5-9c86-560933f80c96_content_list.json b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/d9ff698c-3801-40b5-9c86-560933f80c96_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..09a2a188e80441d36d8781b33c35424fe67bb63c --- /dev/null +++ b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/d9ff698c-3801-40b5-9c86-560933f80c96_content_list.json @@ -0,0 +1,1521 @@ +[ + { + "type": "text", + "text": "StreamingFlow: Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation", + "text_level": 1, + "bbox": [ + 127, + 130, + 844, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Yining Shi $^{1,3*}$ Kun Jiang $^{1\\dagger}$ Ke Wang $^{2}$ Jiusi Li $^{1}$ Yunlong Wang $^{1}$ Mengmeng Yang $^{1}$ Dange Yang $^{1\\dagger}$ $^{1}$ School of Vehicle and Mobility, Tsinghua University $^{2}$ KargoBot, Inc $^{3}$ DiDi Chuxing", + "bbox": [ + 88, + 202, + 879, + 241 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 273, + 313, + 289 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Predicting the future occupancy states of the surrounding environment is a vital task for autonomous driving. However, current best-performing single-modality methods or multi-modality fusion perception methods are only able to predict uniform snapshots of future occupancy states and require strictly synchronized sensory data for sensor fusion. We propose a novel framework, StreamingFlow, to lift these strong limitations. StreamingFlow is a novel BEV occupancy predictor that ingests asynchronous multisensor data streams for fusion and performs streaming forecasting of the future occupancy map at any future times-tamps. By integrating neural ordinary differential equations (N-ODE) into recurrent neural networks, StreamingFlow learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV features as part of the fusion process, and propagates BEV states to the desired future time point. It shows good zero-shot generalization ability of prediction, reflected in the interpolation of the observed prediction time horizon and the reasonable inference of the unseen farther future period. Extensive experiments on two large-scale datasets, nuScenes [2] and Lyft L5 [14], demonstrate that StreamingFlow significantly outperforms previous vision-based, LiDAR-based methods, and shows superior performance compared to state-of-the-art fusion-based methods.", + "bbox": [ + 73, + 306, + 473, + 684 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 715, + 209, + 729 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Occupancy grid is gaining more traction in the self-driving community, due to its versatility in downstream tasks, e.g., irregularly shaped object representation, robot navigation, etc. With the help of modern deep learning technologies, occupancy grid maps (OGMs) have evolved significantly. For example, not just LiDAR point clouds, camera images can now be used to construct high-quality occupancy grid maps [26]. In addition to its fine-grained geometric infor", + "bbox": [ + 75, + 741, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/7b84382c7eea5f301e3a763ecea1acb2762dbc9325fe17705b76498bcaff359d.jpg", + "image_caption": [ + "Figure 1. Comparison between conventional synchronized BEV fusion (top) and our asynchronous BEV fusion (bottom). We formulate fusion with an update-predict-update approach." + ], + "image_footnote": [], + "bbox": [ + 514, + 273, + 879, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "mation, occupancy grids can also represent rich semantic and motion cues [1, 9-11]. Such cues grant occupancy networks the ability to predict the occupancy state of the environment at desired future timestamps. While trajectory forecasting only contains object-level information, the occupancy grid conveys a much more comprehensive understanding of the surrounding environment, which is the key to achieving better intelligence and driving safety.", + "bbox": [ + 496, + 550, + 890, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the great potential of occupancy-based prediction, we notice that existing methods can only predict at fixed frequencies [1, 9-11, 33]. This comes from the fact that sensors sample the environment at predetermined frequencies, e.g., motors in mechanical LiDARs spin at $10\\mathrm{Hz}$ and many cameras captures images at 30FPS. Thus, previous algorithms predict at the same intervals as they are trained with ground-truth labels of future intervals. If future occupancy can be predicted at any given timestamps in a continuous manner, self-driving algorithms can have shorter latency and more rapid responses. Streaming forecasting can also relax the sensor synchronization constraints, as the continuous forecasting model can update the prediction as new sensory data come in. Compared with discrete snapshot-based prediction, streaming motion forecast", + "bbox": [ + 496, + 674, + 892, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Work done during internship at DiDi Chuxing.", + "bbox": [ + 93, + 875, + 354, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding author: Kun Jiang, Dange Yang.", + "bbox": [ + 93, + 887, + 359, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "14833", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ing [24] naturally has safety advantages.", + "bbox": [ + 76, + 90, + 344, + 104 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We noticed several challenges in fulfilling such a streaming forecasting paradigm. Firstly, sensory data and ground truth annotations are collected at a fixed frequency. Streaming forecasting aims to achieve temporally dense and continuous prediction, with data only sparsely and uniformly sampled in the temporal domain. Secondly, mainstream network architectures are not designed for such streaming requirements. Forecasting at any given timestamp requires delicate modeling of the temporal dynamics, but how to embed the temporal dynamics into the widely adopted BEV feature representation remains under-explored.", + "bbox": [ + 75, + 107, + 467, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To this end, we propose to use the neural ordinary differential equation (N-ODE) framework for such temporal dynamics modeling. N-ODE is originally proposed for learning continuous implicit processes in dynamic systems. In our application, by representing the continuous motion trends of the driving scenarios into a time series of implicit spatial BEV features, the neural ODE framework not only allows streaming occupancy predictions on any temporal horizon with one fixed model, but also relaxes the sensor synchronization constraints.", + "bbox": [ + 75, + 273, + 467, + 425 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "With such flexibility, we propose a novel method, StreamingFlow, that performs asynchronous multi-modal sensor fusion to achieve streaming occupancy forecasting. Toward the goal of streaming modeling of temporal BEV features, StreamingFlow integrates neural ordinary differential equations (N-ODE) onto wrapped-based recurrent neural networks. It learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV feature as part of the fusion process, and propagates BEV states to the desired future time point. A graphical illustration of fusion strategies between conventional BEV-based fusion and ours is illustrated in Fig. 1.", + "bbox": [ + 75, + 426, + 467, + 606 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 96, + 608, + 419, + 622 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1. To the best of our knowledge, we propose the first streaming occupancy flow prediction framework that supports asynchronous multi-sensor fusion;", + "2. We design a novel temporal feature propagation strategy that achieves high performance on dense continuous occupancy prediction with only temporally sparse labels;", + "3. Our proposed method achieves state-of-the-art performance on the widely used nuScenes [2] and Lyft L5 [14] datasets, validating the effectiveness and robustness of our proposed algorithms." + ], + "bbox": [ + 76, + 623, + 467, + 773 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 76, + 790, + 225, + 806 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Occupancy forecasting", + "text_level": 1, + "bbox": [ + 76, + 816, + 287, + 832 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Occupancy flow prediction, first proposed in [23], is a valuable supplement to trajectory-set prediction [3, 22]. The advantages of occupancy flow are a non-parametric distribution output and fine-grained grid flow. Recent LiDAR-", + "bbox": [ + 75, + 839, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "based methods [21, 30, 32] attach displacement vectors to non-empty BEV grids to describe short-term motion in future 1.0s. These networks typically have a BEV-based spatial-temporal backbone and several shared heads that indicate the classification, motion, and displacement of each grid. STPN [32] and BE-STI [30] are effective BEV-based spatial-temporal feature extractors for binary-occupied grids which consist of only 2D convolutional blocks. Vision-centric pipelines usually formulate the prediction task as future instance segmentation on BEV grids. FIERY [9] is the first vision-centric stochastic future prediction method. StretchBEV [1] uses a variational autoencoder for decoupling learning of temporal dynamics and BEV decoder. End-to-end driving frameworks [10, 11, 33, 34] conduct planning based on occupancy prediction. UniAD [11] and TBP-Former [6] models temporal future with video transformers. One major bottleneck of video transformers is prediction of long-term sequence length [28]. Position encoding enables video transformer to interpolate shorter sequences but few video transformers can generalize to the unseen longer sequence length. Unlike all prior works that predict discrete near-future snapshots, We focus on the streaming flow prediction which adapt the predictor to a more distant future and finer granularity.", + "bbox": [ + 496, + 90, + 890, + 454 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Multi-sensor Spatial-temporal Fusion", + "text_level": 1, + "bbox": [ + 500, + 460, + 823, + 478 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Spatial multi-modal fusion is widely investigated in the feature level. BEVFusion and its variants [7, 8, 20] combine multi-modal input features in a shared BEV space. [4, 16] support feature interaction in 3D voxel space. Temporal fusion is a common aggregator for perception tasks. LiDAR-based networks [30, 32] typically employ data-level temporal fusion, which transforms multi-frame point clouds to the current ego's coordinate as inputs via ego pose or registration methods. Most vision-centric methods align the BEV feature maps from multiple time steps based on ego pose, and then concatenate them for fusion [9, 12, 17, 25] or support their interactions of multi-frame BEV features through attention [13, 18, 27]. Prior spatial fusion methods usually assume strict synchronization. CoBEVFlow [31] is most similar to our approach in that they predict BEV flow to interpolate asynchronous data timestamps from roadside unit to vehicle system, but short-term flow information cannot support long-term prediction. To this end, we provide a flexible spatio-temporal fusion framework which predicts the future frames and triggers update process as fusion when asynchronous sensor data arrives.", + "bbox": [ + 496, + 484, + 890, + 801 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 500, + 819, + 633, + 837 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "3.1. Framework", + "text_level": 1, + "bbox": [ + 500, + 845, + 625, + 859 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "The pipeline of StreamingFlow is depicted in Fig. 2. Given multi-modal data streams from the previous few seconds,", + "bbox": [ + 500, + 869, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "14834", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1fc171bf9fb2ba64ca5df4aab6be3a4ad7dd79ffad212b24c7dcaab73f19e7ac.jpg", + "image_caption": [ + "Figure 2. The framework of StreamingFlow. Raw data streams are encoded to BEV features, respectively. The SpatialGRU-ODE process operates on the timeline with two stages split by the present timestamp, asynchronous multi-sensor deep feature via the SpatialGRU-ODE update process and continuous occupancy flow prediction via SpatialGRU-ODE predict process." + ], + "image_footnote": [], + "bbox": [ + 117, + 87, + 848, + 262 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "the task is defined as predicting the future several seconds' instance occupancy and flow on uniformly-shaped BEV grids. The framework includes three phases: 1) BEV encoders for LiDAR and camera branches, respectively, 2) asynchronous multi-sensor fusion, and 3) streaming occupancy prediction. As the data stream runs, modality-specific encoders map raw data to BEV features. The BEV state starts from zeroed features and fuses every incoming BEV feature in a trigger mode instead of a matching mode in conventional fusion. The BEV state propagates until a new BEV feature is received. The incoming BEV feature is fused to the BEV state and state continues to propagate until next incoming observation.", + "bbox": [ + 75, + 328, + 472, + 525 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The SpatialGRU-ODE is the core for streaming prediction. The SpatialGRU-ODE iterates for ODE steps, updates when a new measurement occurs within a certain ODE step, and performs future prediction. In the training stage, the loss comes from the supervision of decoded BEV grids at the timestamps with labels, as well as an auxiliary probabilistic loss from Kullback-Leibler divergence (KLD) between updated BEV features and latent observations. In the inference process, SpatialGRU-ODE predicts via a variable ODE step only related to the required timestamps for evaluation and application.", + "bbox": [ + 75, + 526, + 468, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The BEV decoder, loss functions, and post-processing techniques follow standard practices, and we leave the details in the supplementary materials.", + "bbox": [ + 75, + 694, + 470, + 739 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. BEV Encoders", + "text_level": 1, + "bbox": [ + 76, + 753, + 227, + 768 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "LiDAR branch. We adopt the popular pillar representations for point cloud features. We observed that a very lightweight pillar-net encoder is sufficient for high accuracy. Heavier backbones consisting of sparse convolutional modules or voxel transformers can be trivially integrated for performance at the cost of additional computation.", + "bbox": [ + 75, + 777, + 468, + 868 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Camera branch. As a baseline for algorithms aligned with previous work, we adopt the Lift-splat-shoot", + "bbox": [ + 76, + 869, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(LSS [26]) settings with depth supervision for depth-based view transformation. We adopt accelerated BEV pool operators to speed up the inference stage. Other BEV mapping methods are trivially compatible with our framework.", + "bbox": [ + 496, + 328, + 893, + 390 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. SpatialGRU-ODE", + "text_level": 1, + "bbox": [ + 500, + 396, + 676, + 412 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Gate Recurrent Unit (GRU) consists of reset gate $(r_t)$ , update gate $(z_t)$ , and update vector $(g_t)$ . The update process follows the formula,", + "bbox": [ + 496, + 419, + 893, + 464 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nr _ {t} = \\sigma \\left(W _ {r} x _ {t} + U _ {r} h _ {t - 1} + b _ {r}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 469, + 756, + 484 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nz _ {t} = \\sigma \\left(W _ {z} x _ {t} + U _ {z} h _ {t - 1} + b _ {z}\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 487, + 890, + 502 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ng _ {t} = \\tanh \\left(W _ {h} x _ {t} + U _ {h} \\left(r _ {t} \\odot h _ {t - 1}\\right) + b _ {h}\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 566, + 505, + 823, + 520 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Neural-ODE on GRU blocks focuses N-ODE's ability to model continuous time series given sporadic sensor data coming from non-uniform time intervals. SpatialGRU-ODE is highly inspired by GRU-ODE-Bayes [5], which serves as the foundation component of the proposed spatiotemporal fusion and flow predictor. Eq. (1) formulates the general process of GRU blocks. With regard to $h_t$ as a BEV feature, SpatialGRU has its state variable $h_t$ with shape $[B, C, H, W]$ where $B, C, H, W$ are the batch size, embedded dims, height, and width. $\\sigma$ is the sigmoid function, and $\\tanh$ denotes a CNN block in SpatialGRU settings. $x_t$ is the input state at timestamp $t$ with the same shape as $h_t$ . For simplicity, the update gate $W_r = U_r$ , the reset gate $W_z = U_z$ , and the GRU init bias $b_r = b_z$ . $r_t \\odot h_{t-1}$ is the matrix multiplication between reset gate and state. In summary, the update state $h_t$ is calculated as,", + "bbox": [ + 496, + 523, + 890, + 767 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nh _ {t} = z _ {t} \\cdot h _ {t - 1} + \\left(1 - z _ {t}\\right) \\cdot g _ {t} = G R U \\left(h _ {t - 1}, g _ {t}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 544, + 772, + 890, + 787 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The amount of change of the state variable is calculated as:", + "bbox": [ + 500, + 792, + 890, + 808 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\Delta h _ {t} = h _ {t} - h _ {t - 1} = z _ {t} \\cdot h _ {t - 1} + (1 - z _ {t}) \\cdot g _ {t} - h _ {t - 1} \\tag {3} \\\\ = \\left(1 - z _ {t}\\right) \\cdot \\left(g _ {t} - h _ {t - 1}\\right) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 825, + 890, + 854 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The derivatives of the state variable are calculated as:", + "bbox": [ + 500, + 859, + 852, + 875 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\frac {\\Delta h (t)}{d t} = (1 - z (t)) \\cdot (g (t) - h (t)) \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 877, + 890, + 905 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "14835", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "code", + "sub_type": "algorithm", + "code_caption": [ + "Algorithm 1 The pseudo-code of SpatialGRU-ODE" + ], + "code_body": "Input: state-timestamp pairs $[t,m[t]],t\\in [t_0,\\dots,t_{present}]$ ODE step $\\Delta t$ \nOutput: $loss_{KLD}$ , state-timestamp pairs $[t,h[t]],t\\in$ $[t_0,\\dots,t_{present},\\dots,t_{future}]$ 1: Initialize current time $T = t_0$ KL divergence loss $loss_{KLD} = 0$ , current state feature $h = h_0$ \n2: for $t_{obs}$ in $[t_0,\\dots,t_{present}]$ do \n3: while $T < t_{obs}$ do \n4: $h = \\mathrm{ODE\\_Predict}(h,\\Delta t)$ \n5: $T + = \\Delta t$ \n6: end while \n7: $h,loss = \\mathrm{ODE\\_Update}(h,m[t_{obs}])$ \n8: $loss_{KLD} + = loss$ \n9: save $h[t_{obs}] = h$ \n10: end for \n11: for $t_{predict}$ in $[t_{present} + 1,\\dots,t_{future}]$ do \n12: while $T < t_{predict}$ do \n13: $h = \\mathrm{ODE\\_Predict}(h,\\Delta t)$ \n14: $T + = \\Delta t$ \n15: end while \n16: save $h[t_{predict}] = h$ \n17: end for", + "bbox": [ + 76, + 125, + 468, + 458 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "GRU-ODE-Bayes has proven the convergence of this process, as is also applicable to the initial state of SpatialGRU-ODE. If $h_0 \\in [-1, 1]$ , then $h_j(t) \\in [-1, 1]$ , where $j$ is the index of elements in $h(t)$ , as $\\left.\\frac{dh(t)_j}{dt}\\right|_{t: h(t)_j = 1} \\leq 0$ and $\\left.\\frac{dh(t)_j}{dt}\\right|_{t: h(t)_j = -1} \\geq 0$ .", + "bbox": [ + 76, + 488, + 468, + 582 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "N-ODE has several nice properties when implemented on GRU models. The learned parametric derivative makes training not constrained by supervision from fixed future timestamps states, which greatly increases flexibility. On the other hand, unlike RNNs, which require emission intervals for updating, the GRU-ODE continuously defined dynamic model can naturally combine data observed at any given time.", + "bbox": [ + 75, + 582, + 468, + 700 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The pseudo-code for SpatialGRU-ODE is shown in Algorithm 1. Given state-timestamp pairs $[t, m[t]]$ from previous multisensor features, The expected output is the states $[t, h[t]]$ of each measured past timestamp and anticipated future timestamp $t \\in [t_0, \\dots, t_{\\text{present}}, \\dots, t_{\\text{future}}}$ . The ode step may be variable or constant. During the update procedure, a KL divergence loss $loss_{KLD}$ is gathered to quantify the similarity between updated state feature $h$ and observed feature $m[t_{obs}]$ .", + "bbox": [ + 76, + 702, + 468, + 839 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.4. Asynchronous Modality-agnostic Fusion", + "text_level": 1, + "bbox": [ + 76, + 847, + 421, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Asynchronous modality-agnostic fusion attempts to fuse Li-DAR and camera BEV features in a way similar to the", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Beyasian predict-then-update process. The proposed strategy is able to eliminate two crucial limits for multi-sensor fusion, which are strict multi-modal synchronizations and fixed interval data flow.", + "bbox": [ + 496, + 90, + 890, + 150 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/e14a5b1d9b60760d9d1ead4b364e17927f63b3b96d6e7b34f5a4380868841a5f.jpg", + "image_caption": [ + "Figure 3. Illustration of the measurement update process of SpatialGRU-ODE in temporal-agnostic fusion." + ], + "image_footnote": [], + "bbox": [ + 517, + 165, + 872, + 348 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Fig. 3 presents the network structure for the SpatialGRU-ODE update process. After raw data is encoded to BEV maps by different BEV encoders, BEV features from different modalities are agnostic on the source, ordered chronologically, and formulated as multiple timestamp-BEV-feature pairs $[t,h_t]$ . The output retains the same shape as the input, but the hidden features are as $\\frac{1}{4}$ size of the input for the sake of eliminating memory storage. In order not to degrade the ultimate performance, both state and observation in BEV feature space with shape $[B,C,H,W]$ are implicitly encoded into a smaller feature space $[B,C,H/4,W/4]$ and finally implicit decoded in the same way for occupancy flow decoder. The temporal propagator runs the subsequent ODE step till the arrival of the next observation. When a new observation occurs, the predicted state and new observation are processed into the distribution module with CNN blocks to obtain the mean and variance of BEV features both with the size $[1,H/4,W/4]$ . Means and variances of both features are estimated using KL divergence, an auxiliary loss that reflects the similarity between predicted and measured characteristics. Probabilistic auxiliary loss is calculated as follows:", + "bbox": [ + 496, + 409, + 892, + 741 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {l o s s} _ {K L D} = \\sum_ {j = 1} ^ {H \\times W} D _ {K L} \\left(p _ {\\text {s t a t e}, j} \\| p _ {\\text {m e a s}, j}\\right) \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 753, + 890, + 797 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The core module for the updated BEV feature is a dual-pathway SpatialGRU module, which first propagates the observed and predicted features respectively, then mixes the two hidden states distributions and finally undergoes the weighted summation of two features after the trusting gate and softmax function to generate the final new state.", + "bbox": [ + 496, + 809, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "14836", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.5. Streaming Occupancy Flow Predictor", + "text_level": 1, + "bbox": [ + 76, + 90, + 401, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The occupancy flow predictor handles multi-frame BEV features from past and present timestamp-agnostic fusion as input and propagates to future steps in an ODE-enabled variational recurrent neural network. Particularly, the granularity of temporal prediction is decoupled from the training granularity and only related to the minimal ODE step in this method. If we set the variable ODE step, the prediction enables arbitrary granularity.", + "bbox": [ + 75, + 116, + 468, + 238 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/345e8d046350eae63292687e4b3c056783bc03772cb1d61d99af6b7c66933626.jpg", + "image_caption": [ + "Figure 4. Illustration of streaming prediction process of SpatialGRU-ODE." + ], + "image_footnote": [], + "bbox": [ + 91, + 255, + 439, + 411 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Fig. 4 illustrates the SpatialGRU-ODE procedure. Similar to the update process, the states are implicitly encoded into a smaller feature space. Except for the initial input which is the first BEV feature, the input with shape $[H / 4,W / 4,C]$ is inherited from the last ODE step. The core module, SpatialGRU-ODE, computes the derivatives of BEV features in unit time intervals via a recurrent block specified in Eq. (4). SpatialGRU-ODE may employ either Euler or Midpoint solver for the update and fixed or variable ODE time step. To obtain the projected states, the derivatives are multiplied by delta time $dt$ and added to the initial states. A CNN block is used to infer the next input from the current state in order to make the subsequent prediction. Only states near to the needed timestamps with supervision (closer than half of the minimum ode step) are preserved and decoded in the BEV decoder for supervision. Thus, the prediction time step $dt$ is not always constant and uniform, and supervision signals are not required for each future timestamp.", + "bbox": [ + 75, + 470, + 468, + 758 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 781, + 209, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we seek to answer two questions with the following experiments: (1) Whether the model works as well as published state-of-the-art algorithms for standard occupancy forecasting tasks. (2) Whether we are able to generalize to streaming forecasting settings with one model trained with temporally-sparse occupancy labels.", + "bbox": [ + 75, + 810, + 467, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Datasets and Metrics", + "text_level": 1, + "bbox": [ + 500, + 90, + 697, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The NuScenes [2] dataset is a public large-scale autonomous driving dataset collected by Motional. NuScenes dataset provides a full sensor suite including 1 top LiDAR, 6 cameras, 5 radars, GPS, and IMU, with $360^{\\circ}$ coverage of the surroundings. It contains 1000 scenes, each lasting 20 seconds, of which annotations of 850 scenes at $2\\mathrm{Hz}$ are available. We use the training and validation splits as same as previous works [1, 9, 10, 30, 34], with 28130 samples for training and 6019 samples for validation.", + "bbox": [ + 496, + 113, + 890, + 250 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The Lyft L5 dataset [14] is another large-scale autonomous dataset provided by Lyft. This dataset contains 180 scenes, each lasting 25-45s in length and annotated at $5\\mathrm{Hz}$ . We use 6 ring cameras and the top LiDAR from its sensor suite, which has a $360^{\\circ}$ field of view. We use training and validation splits from the practice of FIERY [9], which include 16000 training samples and 4000 validation samples.", + "bbox": [ + 496, + 250, + 890, + 369 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The occupancy flow prediction is formulated as a video panoptic prediction task [15]. We use Intersection over Union (IoU) to measure the semantic segmentation quality of each frame, and video panoptic quality (PQ), recognition quality (RQ), and segmentation quality (SQ) to measure both the accuracy and consistency of instance segmentation. VPQ is computed as:", + "bbox": [ + 496, + 369, + 890, + 476 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathrm {V P Q} = \\sum_ {t = 0} ^ {H} \\frac {\\sum_ {\\left(p _ {t} , q _ {t}\\right) \\cdot T P _ {t}} \\operatorname {I o U} \\left(p _ {t} \\cdot q _ {t}\\right)}{\\left| T P _ {t} \\right| + \\frac {1}{2} \\left| F P _ {t} \\right| + \\frac {1}{2} \\left| F N _ {t} \\right|} \\tag {6} \\\\ = \\sum_ {t = 0} ^ {H} \\frac {\\left| T P _ {t} \\right|}{\\left| T P _ {t} \\right| + \\frac {1}{2} \\left| F P _ {t} \\right| + \\frac {1}{2} \\left| F N _ {t} \\right|} = \\mathrm {S Q} \\cdot \\mathrm {R Q} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 547, + 486, + 890, + 566 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 574, + 718, + 590 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Task details. The standard occupancy prediction task is to take the past 1.0s sensor data for input, which is 3 keyframes in nuScenes (5 keyframes in Lyft), predict the motion in the future 2s, which is 4 keyframes in nuScenes and 10 keyframes in Lyft.", + "bbox": [ + 496, + 598, + 890, + 672 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Data details. The BEV occupancy labels are from 3D bounding boxes labels projected to BEV. The perception range is set as $[100m, 100m]$ and the grid resolution is set as $0.5m$ . Images are resized to $224 \\times 480$ pixels for each frame. Each point cloud is densified by aggregating point clouds of adjacent sweeps. Point clouds are voxelized to $200 \\times 200 \\times 13$ voxels. StreamingFlow adopts an asynchronous data stream as input, with LiDAR streams every 0.2s and camera streams every 0.5s as input. For larger models fairly compared with the state-of-the-art, we use images with size $320 \\times 800$ and aggregated LiDAR streams, each with 10 sweeps.", + "bbox": [ + 496, + 674, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Model details. The framework is implemented on Pytorch 1.10.2 and Pytorch Lightning 1.2.5. The optimizer is AdamW with a learning rate of $1e - 4$ . The learning strategy", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "14837", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/47d7983c3d8d3aec94297de1ce45062ae6703f7363e69f67d3a08a60e30ef6bd.jpg", + "image_caption": [ + "Figure 5. Visualization of StreamingFlow for diverse driving scenarios. Different colors represent different instances of the agents, and lighter colors represent the future occupancy of the agents. (top): samples from Lyft dataset, highway (left), and urban (right). (middle and bottom): samples from nuScenes dataset, sunny (middle left), overcast after rain (middle right), rainy (bottom left), and night (bottom right). StreamingFlow works well in all challenging driving scenarios." + ], + "image_footnote": [], + "bbox": [ + 78, + 87, + 385, + 291 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/230bb776870702404520a5208daf4d0ff668457ccbc8b8c2171cb65680e6f550.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 395, + 87, + 880, + 291 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "is cosine annealing with a weight decay of 0.01. All models are trained on 8 A6000 GPUs for 20 epochs with a total batch size 16. The image backbone is EfficientNet-b4 [29] for tiny and base model and Effi-b7 for small model.", + "bbox": [ + 75, + 383, + 468, + 444 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.3. Comparison with the State-of-the-art", + "text_level": 1, + "bbox": [ + 76, + 452, + 398, + 469 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons of methods implemented in the nuScenes dataset are shown in Tab. 1. All methods are trained for a standard instance flow segmentation and prediction task. Fig. 5 illustrates some examples covering diverse scenarios.", + "bbox": [ + 75, + 476, + 468, + 537 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "StreamingFlow achieves competitive performance while significantly outperforming other single-modality methods. StreamingFlow surpasses the best vision-based BEVerse [34] with a larger backbone Swin-small [19] by $+7.0$ IoU and $+10.0$ VPQ, and the best LiDAR-based BE-STI [30] $+7.7$ IoU and 5.1VPQ. Compared to FusionAD, StreamingFlow-base uses the same LiDAR backbone(SpConv), similar image backbone(Effi-B4 vs. ResNet101) but a half smaller image size $(800\\times 320$ vs. $1600\\times 900)$ , and is $+1.6$ VPQ and 2.4 IoU higher than the latest fusion-based FusionAD [33].", + "bbox": [ + 75, + 537, + 468, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Comparisons of methods implemented in the Lyft L5 dataset are shown in Tab. 2. StreamingFlow achieves the best of all metrics while surpassing baseline methods by a large margin: $+20.6$ IoU and $+23.5$ VPQ against STP3 [10]. Moreover, it surpasses our reproduced BEVFusion with lightweight encoders by $+2.3$ mIoU and 0.2 VPQ.", + "bbox": [ + 75, + 702, + 468, + 794 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.4. Streaming Forecasting Results", + "text_level": 1, + "bbox": [ + 76, + 801, + 348, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We design three experiments on nuScenes dataset for demonstration of the streaming occupancy prediction: (1) Extension of the prediction temporal horizons to unseen future; (2) Prediction at any desired future time point; (3) Data streams input at different frame rates. Experiments are con", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "duced on models loaded from the checkpoints trained on standard instance forecasting tasks.", + "bbox": [ + 498, + 383, + 890, + 412 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Extension of the temporal horizons of unseen future. Tab. 3 shows the prediction result of StreamingFlow which extends the temporal horizons from 2.0s to 8.0s. Baselines reported in [1] are trained for different lengths of temporal horizons. StreamingFlow shows excellent performance in variable prediction length without retraining. Similar to prior arts which extend prediction horizons to farther future, StreamingFlow shows a similar gradual performance decay. We then compare zero-shot Streamingflow with the model trained with the longest future 8s groundtruth labels in Tab. 4. The zero-shot long-term prediction results are only $-0.9$ IoU and $-1.8$ VPQ less than fully supervised models, which demonstrates great generalization ability of foreseeing the unseen future.", + "bbox": [ + 496, + 415, + 892, + 626 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Streaming prediction at any desired time point. Since nuScenes do not provide labels for non-keyframes, we adopt the practice of MotionNet and interpolate the box instances between two adjacent keyframes. We randomly choose to predict at a list of time points and report the results in Tab. 5. To simply illustrate the capability, we designed the main task to predict uniformly spaced temporal horizons, but this framework can predict uneven and arbitrary future snapshots. The prediction results are stable generally. There is a slight decline as the forecast becomes denser.", + "bbox": [ + 496, + 627, + 890, + 792 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We provide demo videos as supplementary materials to show the effectiveness of streaming prediction. We provide a finer granularity of streaming perception at any future time. In the video, we visualize the prediction results every 0.05s from the current to the future 2s to 3s, with a total of 40 to 60 frames.", + "bbox": [ + 496, + 794, + 890, + 883 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Asynchronous multi-modal data streams as input.", + "bbox": [ + 519, + 885, + 890, + 901 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "14838", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/15d791cc68e3f4cffbc854e101929b7a88e15ced7526c2c88ac19cd3301f348a.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodModalityImage backboneLiDAR backboneFuture Semantic Seg. IoU↑Future Instance Seg.
PQ↑SQ↑RQ↑
Static*CEffi-B4-32.227.670.139.1
FIERY*[9]CEffi-B4-37.030.270.242.9
StretchBEV[1]CEffi-B4-37.129.0--
BEVerse[34]CSwin-tiny-38.733.370.647.2
BEVerse[34]CSwin-small-40.836.170.751.1
ST-P3 Gaus.[10]CEffi-B4-38.631.770.245.2
ST-P3 Ber.[10]CEffi-B4-38.932.170.445.6
UniAD[11]CEffi-B4-40.233.5--
MotionNet[32]L-STPN37.238.975.651.4
BE-STI[30]L-BESTI-STPN40.141.075.554.3
StreamingFlow-tinyLCEffi-B4PillarNet47.846.175.860.8
StreamingFlow-smallLCEffi-B7PillarNet51.148.075.164.0
FusionAD[33]LCResNet-101VoxelNet51.551.1--
StreamingFlow-baseLCEffi-B4VoxelNet53.952.778.766.9
", + "bbox": [ + 76, + 88, + 893, + 339 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/f08d62559ae3476610715a84b8994be22afea7e2e6031623b0aca97ffe4962d7.jpg", + "table_caption": [ + "Table 1. Comparison with the state-of-the-art methods for instance-aware occupancy flow prediction on nuScenes[2] validation set. 'C' denotes vision-only methods, 'L' denotes LiDAR-based methods, and 'LC' denotes a LiDAR-camera fusion methods. $*$ : reported in [9]." + ], + "table_footnote": [], + "table_body": "
MethodIoU↑PQ↑SQ↑RQ↑
Static*24.120.7--
Extrapolation model*24.821.2--
FIERY*[9]36.327.2--
ST-P3[10]36.332.471.145.5
BEVFusion-tiny†54.655.778.071.4
StreamingFlow-tiny56.955.978.171.6
", + "bbox": [ + 78, + 401, + 468, + 521 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/46d66007d32688afcf711996e0dd96c61db5775661a71d9c1e25a25f555148d3.jpg", + "table_caption": [ + "Table 2. Comparison with the state-of-the-art methods for future instance segmentation (2.0s) on Lyft L5 AV [14] validation set. $\\star$ results reported in [9]. $\\dagger$ : results of BEVFusion with LSS-based image encoder and pillar-based encoder reproduced by us." + ], + "table_footnote": [], + "table_body": "
MethodPredIoU↑PQ↑SQ↑RQ↑
FIERY2s35.829.0--
4s30.123.6--
6s26.720.9--
StretchBEV2s37.129.0--
4s32.523.8--
6s28.421.0--
StreamingFlow2s47.846.175.860.8
3s44.441.174.155.4
4s41.738.473.652.1
5s39.135.873.248.9
6s36.733.672.946.0
8s32.529.872.640.1
", + "bbox": [ + 80, + 590, + 468, + 800 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We validate asynchronous data streams as input and standard occupancy forecasting as output. We test multiple settings of data stream frame rate and report the results in Tab.", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/633bd89e1a221b608098772c8f03b89277f097fa798c697ca9e35723a20155c0.jpg", + "table_caption": [ + "Table 3. Comparison of occupancy flow prediction for any temporal horizons." + ], + "table_footnote": [], + "table_body": "
Schedule2s3s4s6s8s
ZS.47.8/46.144.4/41.141.7/38.436.7/33.632.5/29.8
Sup.48.2/46.946.0/45.241.9/38.737.8/34.233.6/31.6
", + "bbox": [ + 500, + 401, + 893, + 458 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/1a6b73b51f15bb18bd37af3d77d207b6d86bf608aafdbe1ebf10e0c1a1cc465c.jpg", + "table_caption": [ + "Table 4. ZS: zero-shot inference of StreamingFlow. Sup: StreamingFlow trained with the longest prediction horizons 8s. Each value is given in the format of 'IoU/PQ'." + ], + "table_footnote": [], + "table_body": "
Prediction IntervalIoU↑PQ↑SQ↑RQ↑
0.547.846.175.860.8
0.2543.440.174.154.1
0.645.644.375.258.9
", + "bbox": [ + 501, + 515, + 890, + 584 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "6. The model performs the best when the inference uses the training configuration. Denser inputs lead to similar forecasting accuracy.", + "bbox": [ + 500, + 638, + 890, + 684 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/dd43ad3948b974162fc276db6a2603d2dd4e8f11b88f4642172cfc128f25e62d.jpg", + "table_caption": [ + "Table 5. Prediction results at any desired intervals. For example, prediction at the interval of 0.6 means prediction at [0.6, 1.2, 1.8]." + ], + "table_footnote": [], + "table_body": "
LiDAR streamCam streamIoU↑PQ↑SQ↑RQ↑
5247.846.175.860.8
10247.645.875.660.5
10447.145.475.160.4
", + "bbox": [ + 501, + 696, + 890, + 767 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Prediction results with multi-modal data stream of different frame rates. Frame rates are shown in Hz.", + "bbox": [ + 500, + 777, + 888, + 805 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.5. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 832, + 653, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Effect of different fusion strategies. We compare SpatialGRU-ODE with fusion strategies at different stages and the implementation details are in supplementary", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "14839", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "material. As shown in Tab. 7, asynchronous fusion is inferior to synchronous fusion and SpatialGRU-ODE for both datasets. For nuScenes dataset, the ordinary temporally-synchronized fusion approach performs the best. SpatialGRU-ODE performs $-2.4$ IoU and $-0.9$ VPQ, slightly less than BEVFusion [20]. For Lyft dataset, SpatialGRU-ODE outperforms synchronized fusion. It performs $+2.3$ IoU and $+0.2$ VPQ more than BEVFusion [20].", + "bbox": [ + 75, + 90, + 472, + 212 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/09785962bbf527609f9a79087c1c71413010e6b567eecfb38511de7241366f3b.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Fusion modeIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Spatial then temporal50.247.075.663.0
Temporal then spatial44.742.774.657.2
SpatialGRU-ODE47.846.175.860.8
Lyft L5 AV dataset
Spatial then temporal54.655.778.071.4
Temporal then spatial50.450.275.266.7
SpatialGRU-ODE56.955.978.171.9
", + "bbox": [ + 78, + 223, + 468, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of ODE solvers. ODE solvers are vital tools for a N-ODE framework. We test two basic ode solvers, Euler, and midpoint solver as compared in Tab. 8 on two datasets. In both cases, the midpoint solver yields superior VPQ, surpassing the Euler solver by 3.2 points on nuScenes dataset and 0.8 points on Lyft dataset. On nuScenes dataset, the midpoint solver shows similar IoU with the Euler solver, but on Lyft dataset, the midpoint solver performs worse semantic segmentation by $-1.9$ .", + "bbox": [ + 75, + 483, + 468, + 619 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/b456ad393e93772a2eae27415c1406b0b712b6739ae51cfee0f7bdb43988713b.jpg", + "table_caption": [ + "Table 7. Comparison with the baseline fusion methods for future instance segmentation (2.0s) on nuScenes validation set. StreamingFlow-ODE is compared with different fusion modes. Spatial fusion is conducted in the same way as BEVFusion [20]. 'Spatial Then Temporal' is for synchronous mode, and 'Temporal Then Spatial' is for asynchronous mode." + ], + "table_footnote": [], + "table_body": "
ODE SolverIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Euler47.842.973.558.6
Midpoint47.846.175.860.8
Lyft L5 AV dataset
Euler56.955.978.171.5
Midpoint55.056.778.272.4
", + "bbox": [ + 81, + 631, + 465, + 765 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Effect of ODE update intervals. We ablate different ODE update intervals which determine the minimum granularity of occupancy prediction. The ODE step is set to 0.05, 0.1, 0.5 and variable for comparison. Variable means the ODE step is the next timestamp minus the current timestamp. In general, the finer a single update is divided during the ODE update process, the higher the final prediction ac", + "bbox": [ + 75, + 794, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "curacy. It is also intuitive that a higher update frequency may eliminate continuous errors. As shown in Tab. 9, the predictor with interval $0.05s$ surpasses interval $0.1s$ by 0.1 IoU and 3.1 VPQ, and interval $0.5s$ by 0.5 IoU and 3.1 VPQ. Remarkably, the variable time step update also shows nice performance, which is $+0.5$ IoU and $-2.2$ VPQ when compared to the predictor with ODE step $0.05s$ . A variable time step updater strikes a good balance between precision and inference speed, so it is more favorable for long-term prediction to 8s future.", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/6f3e50c482e252939135c0311bb7ce833bb37e649be5400890c783d12e4be995.jpg", + "table_caption": [ + "Table 8. Comparison with prediction using different ODE solvers." + ], + "table_footnote": [], + "table_body": "
StepIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
0.0547.846.175.860.8
0.147.743.073.758.4
0.547.342.173.357.4
Variable48.243.973.958.8
Lyft L5 dataset
0.0556.955.978.171.9
Variable54.053.577.469.7
", + "bbox": [ + 506, + 253, + 885, + 412 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 9. Comparison of prediction under different ode steps.", + "bbox": [ + 514, + 422, + 874, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 443, + 619, + 458 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We present StreamingFlow as the first practice for fusion-based streaming occupancy forecasting. Starting from the motivation of fusing and predicting from non-ideal data streams, the streaming feature brings a more flexible temporal scene understanding and generalizes occupancy forecasting well to any temporal horizon. The advantage of SpatialGRU-ODE is that it decouples the supervision in the training process and outputs in the inference process, by modeling the derivatives of BEV grids and propagating future grid states to required timestamps. We hope that this work will inspire more Neural-ODE applications and insights into the streaming automotive perception.", + "bbox": [ + 496, + 468, + 890, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 662, + 679, + 680 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the National Natural Science Foundation of China under Grants (52372414, U22A20104, 52102464). This work was also sponsored by Tsinghua University-DiDi Joint Research Center for Future Mobility and Tsinghua University-Zongmu Technology Joint Research Center.", + "bbox": [ + 496, + 686, + 890, + 777 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 791, + 596, + 806 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Adil Kaan Akan and Fatma Güney. 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Beverse: Unified perception and prediction in birds-eye-view for vision-centric autonomous driving. arXiv preprint arXiv:2205.09743, 2022. 2, 5, 6, 7" + ], + "bbox": [ + 78, + 90, + 468, + 723 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "14842", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/d9ff698c-3801-40b5-9c86-560933f80c96_model.json b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/d9ff698c-3801-40b5-9c86-560933f80c96_model.json new file mode 100644 index 0000000000000000000000000000000000000000..96045395a5c763f272006e35f80891d054d005bd --- /dev/null +++ b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/d9ff698c-3801-40b5-9c86-560933f80c96_model.json @@ -0,0 +1,1969 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.128, + 0.131, + 0.845, + 0.177 + ], + "angle": 0, + "content": "StreamingFlow: Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation" + }, + { + "type": "text", + "bbox": [ + 0.089, + 0.203, + 0.88, + 0.242 + ], + "angle": 0, + "content": "Yining Shi\\(^{1,3*}\\) Kun Jiang\\(^{1\\dagger}\\) Ke Wang\\(^{2}\\) Jiusi Li\\(^{1}\\) Yunlong Wang\\(^{1}\\) Mengmeng Yang\\(^{1}\\) Dange Yang\\(^{1\\dagger}\\) \n\\(^{1}\\) School of Vehicle and Mobility, Tsinghua University \\(^{2}\\) KargoBot, Inc \\(^{3}\\) DiDi Chuxing" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.274, + 0.314, + 0.29 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.307, + 0.474, + 0.685 + ], + "angle": 0, + "content": "Predicting the future occupancy states of the surrounding environment is a vital task for autonomous driving. However, current best-performing single-modality methods or multi-modality fusion perception methods are only able to predict uniform snapshots of future occupancy states and require strictly synchronized sensory data for sensor fusion. We propose a novel framework, StreamingFlow, to lift these strong limitations. StreamingFlow is a novel BEV occupancy predictor that ingests asynchronous multisensor data streams for fusion and performs streaming forecasting of the future occupancy map at any future times-tamps. By integrating neural ordinary differential equations (N-ODE) into recurrent neural networks, StreamingFlow learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV features as part of the fusion process, and propagates BEV states to the desired future time point. It shows good zero-shot generalization ability of prediction, reflected in the interpolation of the observed prediction time horizon and the reasonable inference of the unseen farther future period. Extensive experiments on two large-scale datasets, nuScenes [2] and Lyft L5 [14], demonstrate that StreamingFlow significantly outperforms previous vision-based, LiDAR-based methods, and shows superior performance compared to state-of-the-art fusion-based methods." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.716, + 0.21, + 0.731 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.742, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Occupancy grid is gaining more traction in the self-driving community, due to its versatility in downstream tasks, e.g., irregularly shaped object representation, robot navigation, etc. With the help of modern deep learning technologies, occupancy grid maps (OGMs) have evolved significantly. For example, not just LiDAR point clouds, camera images can now be used to construct high-quality occupancy grid maps [26]. In addition to its fine-grained geometric infor" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.274, + 0.88, + 0.48 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.491, + 0.892, + 0.534 + ], + "angle": 0, + "content": "Figure 1. Comparison between conventional synchronized BEV fusion (top) and our asynchronous BEV fusion (bottom). We formulate fusion with an update-predict-update approach." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.673 + ], + "angle": 0, + "content": "mation, occupancy grids can also represent rich semantic and motion cues [1, 9-11]. Such cues grant occupancy networks the ability to predict the occupancy state of the environment at desired future timestamps. While trajectory forecasting only contains object-level information, the occupancy grid conveys a much more comprehensive understanding of the surrounding environment, which is the key to achieving better intelligence and driving safety." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Despite the great potential of occupancy-based prediction, we notice that existing methods can only predict at fixed frequencies [1, 9-11, 33]. This comes from the fact that sensors sample the environment at predetermined frequencies, e.g., motors in mechanical LiDARs spin at \\(10\\mathrm{Hz}\\) and many cameras captures images at 30FPS. Thus, previous algorithms predict at the same intervals as they are trained with ground-truth labels of future intervals. If future occupancy can be predicted at any given timestamps in a continuous manner, self-driving algorithms can have shorter latency and more rapid responses. Streaming forecasting can also relax the sensor synchronization constraints, as the continuous forecasting model can update the prediction as new sensory data come in. Compared with discrete snapshot-based prediction, streaming motion forecast" + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.875, + 0.355, + 0.888 + ], + "angle": 0, + "content": "*Work done during internship at DiDi Chuxing." + }, + { + "type": "page_footnote", + "bbox": [ + 0.094, + 0.888, + 0.36, + 0.901 + ], + "angle": 0, + "content": "† Corresponding author: Kun Jiang, Dange Yang." + }, + { + "type": "list", + "bbox": [ + 0.094, + 0.875, + 0.36, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14833" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.345, + 0.106 + ], + "angle": 0, + "content": "ing [24] naturally has safety advantages." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.108, + 0.468, + 0.273 + ], + "angle": 0, + "content": "We noticed several challenges in fulfilling such a streaming forecasting paradigm. Firstly, sensory data and ground truth annotations are collected at a fixed frequency. Streaming forecasting aims to achieve temporally dense and continuous prediction, with data only sparsely and uniformly sampled in the temporal domain. Secondly, mainstream network architectures are not designed for such streaming requirements. Forecasting at any given timestamp requires delicate modeling of the temporal dynamics, but how to embed the temporal dynamics into the widely adopted BEV feature representation remains under-explored." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.275, + 0.468, + 0.426 + ], + "angle": 0, + "content": "To this end, we propose to use the neural ordinary differential equation (N-ODE) framework for such temporal dynamics modeling. N-ODE is originally proposed for learning continuous implicit processes in dynamic systems. In our application, by representing the continuous motion trends of the driving scenarios into a time series of implicit spatial BEV features, the neural ODE framework not only allows streaming occupancy predictions on any temporal horizon with one fixed model, but also relaxes the sensor synchronization constraints." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.427, + 0.468, + 0.607 + ], + "angle": 0, + "content": "With such flexibility, we propose a novel method, StreamingFlow, that performs asynchronous multi-modal sensor fusion to achieve streaming occupancy forecasting. Toward the goal of streaming modeling of temporal BEV features, StreamingFlow integrates neural ordinary differential equations (N-ODE) onto wrapped-based recurrent neural networks. It learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV feature as part of the fusion process, and propagates BEV states to the desired future time point. A graphical illustration of fusion strategies between conventional BEV-based fusion and ours is illustrated in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.609, + 0.421, + 0.623 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.079, + 0.624, + 0.468, + 0.667 + ], + "angle": 0, + "content": "1. To the best of our knowledge, we propose the first streaming occupancy flow prediction framework that supports asynchronous multi-sensor fusion;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.669, + 0.468, + 0.713 + ], + "angle": 0, + "content": "2. We design a novel temporal feature propagation strategy that achieves high performance on dense continuous occupancy prediction with only temporally sparse labels;" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.715, + 0.468, + 0.774 + ], + "angle": 0, + "content": "3. Our proposed method achieves state-of-the-art performance on the widely used nuScenes [2] and Lyft L5 [14] datasets, validating the effectiveness and robustness of our proposed algorithms." + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.624, + 0.468, + 0.774 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.791, + 0.227, + 0.807 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.288, + 0.833 + ], + "angle": 0, + "content": "2.1. Occupancy forecasting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Occupancy flow prediction, first proposed in [23], is a valuable supplement to trajectory-set prediction [3, 22]. The advantages of occupancy flow are a non-parametric distribution output and fine-grained grid flow. Recent LiDAR-" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.455 + ], + "angle": 0, + "content": "based methods [21, 30, 32] attach displacement vectors to non-empty BEV grids to describe short-term motion in future 1.0s. These networks typically have a BEV-based spatial-temporal backbone and several shared heads that indicate the classification, motion, and displacement of each grid. STPN [32] and BE-STI [30] are effective BEV-based spatial-temporal feature extractors for binary-occupied grids which consist of only 2D convolutional blocks. Vision-centric pipelines usually formulate the prediction task as future instance segmentation on BEV grids. FIERY [9] is the first vision-centric stochastic future prediction method. StretchBEV [1] uses a variational autoencoder for decoupling learning of temporal dynamics and BEV decoder. End-to-end driving frameworks [10, 11, 33, 34] conduct planning based on occupancy prediction. UniAD [11] and TBP-Former [6] models temporal future with video transformers. One major bottleneck of video transformers is prediction of long-term sequence length [28]. Position encoding enables video transformer to interpolate shorter sequences but few video transformers can generalize to the unseen longer sequence length. Unlike all prior works that predict discrete near-future snapshots, We focus on the streaming flow prediction which adapt the predictor to a more distant future and finer granularity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.462, + 0.825, + 0.479 + ], + "angle": 0, + "content": "2.2. Multi-sensor Spatial-temporal Fusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.486, + 0.892, + 0.803 + ], + "angle": 0, + "content": "Spatial multi-modal fusion is widely investigated in the feature level. BEVFusion and its variants [7, 8, 20] combine multi-modal input features in a shared BEV space. [4, 16] support feature interaction in 3D voxel space. Temporal fusion is a common aggregator for perception tasks. LiDAR-based networks [30, 32] typically employ data-level temporal fusion, which transforms multi-frame point clouds to the current ego's coordinate as inputs via ego pose or registration methods. Most vision-centric methods align the BEV feature maps from multiple time steps based on ego pose, and then concatenate them for fusion [9, 12, 17, 25] or support their interactions of multi-frame BEV features through attention [13, 18, 27]. Prior spatial fusion methods usually assume strict synchronization. CoBEVFlow [31] is most similar to our approach in that they predict BEV flow to interpolate asynchronous data timestamps from roadside unit to vehicle system, but short-term flow information cannot support long-term prediction. To this end, we provide a flexible spatio-temporal fusion framework which predicts the future frames and triggers update process as fusion when asynchronous sensor data arrives." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.82, + 0.634, + 0.838 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.846, + 0.627, + 0.861 + ], + "angle": 0, + "content": "3.1. Framework" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The pipeline of StreamingFlow is depicted in Fig. 2. Given multi-modal data streams from the previous few seconds," + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14834" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.118, + 0.088, + 0.849, + 0.263 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.273, + 0.895, + 0.318 + ], + "angle": 0, + "content": "Figure 2. The framework of StreamingFlow. Raw data streams are encoded to BEV features, respectively. The SpatialGRU-ODE process operates on the timeline with two stages split by the present timestamp, asynchronous multi-sensor deep feature via the SpatialGRU-ODE update process and continuous occupancy flow prediction via SpatialGRU-ODE predict process." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.329, + 0.473, + 0.526 + ], + "angle": 0, + "content": "the task is defined as predicting the future several seconds' instance occupancy and flow on uniformly-shaped BEV grids. The framework includes three phases: 1) BEV encoders for LiDAR and camera branches, respectively, 2) asynchronous multi-sensor fusion, and 3) streaming occupancy prediction. As the data stream runs, modality-specific encoders map raw data to BEV features. The BEV state starts from zeroed features and fuses every incoming BEV feature in a trigger mode instead of a matching mode in conventional fusion. The BEV state propagates until a new BEV feature is received. The incoming BEV feature is fused to the BEV state and state continues to propagate until next incoming observation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.527, + 0.47, + 0.693 + ], + "angle": 0, + "content": "The SpatialGRU-ODE is the core for streaming prediction. The SpatialGRU-ODE iterates for ODE steps, updates when a new measurement occurs within a certain ODE step, and performs future prediction. In the training stage, the loss comes from the supervision of decoded BEV grids at the timestamps with labels, as well as an auxiliary probabilistic loss from Kullback-Leibler divergence (KLD) between updated BEV features and latent observations. In the inference process, SpatialGRU-ODE predicts via a variable ODE step only related to the required timestamps for evaluation and application." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.695, + 0.471, + 0.741 + ], + "angle": 0, + "content": "The BEV decoder, loss functions, and post-processing techniques follow standard practices, and we leave the details in the supplementary materials." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.754, + 0.228, + 0.769 + ], + "angle": 0, + "content": "3.2. BEV Encoders" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.779, + 0.47, + 0.869 + ], + "angle": 0, + "content": "LiDAR branch. We adopt the popular pillar representations for point cloud features. We observed that a very lightweight pillar-net encoder is sufficient for high accuracy. Heavier backbones consisting of sparse convolutional modules or voxel transformers can be trivially integrated for performance at the cost of additional computation." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Camera branch. As a baseline for algorithms aligned with previous work, we adopt the Lift-splat-shoot" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.329, + 0.895, + 0.391 + ], + "angle": 0, + "content": "(LSS [26]) settings with depth supervision for depth-based view transformation. We adopt accelerated BEV pool operators to speed up the inference stage. Other BEV mapping methods are trivially compatible with our framework." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.397, + 0.677, + 0.414 + ], + "angle": 0, + "content": "3.3. SpatialGRU-ODE" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.42, + 0.894, + 0.465 + ], + "angle": 0, + "content": "Gate Recurrent Unit (GRU) consists of reset gate \\((r_t)\\), update gate \\((z_t)\\), and update vector \\((g_t)\\). The update process follows the formula," + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.47, + 0.757, + 0.485 + ], + "angle": 0, + "content": "\\[\nr _ {t} = \\sigma \\left(W _ {r} x _ {t} + U _ {r} h _ {t - 1} + b _ {r}\\right)\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.568, + 0.488, + 0.892, + 0.503 + ], + "angle": 0, + "content": "\\[\nz _ {t} = \\sigma \\left(W _ {z} x _ {t} + U _ {z} h _ {t - 1} + b _ {z}\\right) \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.567, + 0.506, + 0.825, + 0.521 + ], + "angle": 0, + "content": "\\[\ng _ {t} = \\tanh \\left(W _ {h} x _ {t} + U _ {h} \\left(r _ {t} \\odot h _ {t - 1}\\right) + b _ {h}\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.525, + 0.892, + 0.768 + ], + "angle": 0, + "content": "Neural-ODE on GRU blocks focuses N-ODE's ability to model continuous time series given sporadic sensor data coming from non-uniform time intervals. SpatialGRU-ODE is highly inspired by GRU-ODE-Bayes [5], which serves as the foundation component of the proposed spatiotemporal fusion and flow predictor. Eq. (1) formulates the general process of GRU blocks. With regard to \\( h_t \\) as a BEV feature, SpatialGRU has its state variable \\( h_t \\) with shape \\( [B, C, H, W] \\) where \\( B, C, H, W \\) are the batch size, embedded dims, height, and width. \\( \\sigma \\) is the sigmoid function, and \\( \\tanh \\) denotes a CNN block in SpatialGRU settings. \\( x_t \\) is the input state at timestamp \\( t \\) with the same shape as \\( h_t \\). For simplicity, the update gate \\( W_r = U_r \\), the reset gate \\( W_z = U_z \\), and the GRU init bias \\( b_r = b_z \\). \\( r_t \\odot h_{t-1} \\) is the matrix multiplication between reset gate and state. In summary, the update state \\( h_t \\) is calculated as," + }, + { + "type": "equation", + "bbox": [ + 0.545, + 0.773, + 0.891, + 0.789 + ], + "angle": 0, + "content": "\\[\nh _ {t} = z _ {t} \\cdot h _ {t - 1} + \\left(1 - z _ {t}\\right) \\cdot g _ {t} = G R U \\left(h _ {t - 1}, g _ {t}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.794, + 0.892, + 0.809 + ], + "angle": 0, + "content": "The amount of change of the state variable is calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.827, + 0.892, + 0.856 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\Delta h _ {t} = h _ {t} - h _ {t - 1} = z _ {t} \\cdot h _ {t - 1} + (1 - z _ {t}) \\cdot g _ {t} - h _ {t - 1} \\tag {3} \\\\ = \\left(1 - z _ {t}\\right) \\cdot \\left(g _ {t} - h _ {t - 1}\\right) \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.861, + 0.853, + 0.875 + ], + "angle": 0, + "content": "The derivatives of the state variable are calculated as:" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.878, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\frac {\\Delta h (t)}{d t} = (1 - z (t)) \\cdot (g (t) - h (t)) \\tag {4}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14835" + } + ], + [ + { + "type": "code_caption", + "bbox": [ + 0.079, + 0.106, + 0.423, + 0.122 + ], + "angle": 0, + "content": "Algorithm 1 The pseudo-code of SpatialGRU-ODE" + }, + { + "type": "algorithm", + "bbox": [ + 0.078, + 0.125, + 0.47, + 0.459 + ], + "angle": 0, + "content": "Input: state-timestamp pairs \\([t,m[t]],t\\in [t_0,\\dots,t_{present}]\\) ODE step \\(\\Delta t\\) \nOutput: \\(loss_{KLD}\\) , state-timestamp pairs \\([t,h[t]],t\\in\\) \\([t_0,\\dots,t_{present},\\dots,t_{future}]\\) 1: Initialize current time \\(T = t_0\\) KL divergence loss \\(loss_{KLD} = 0\\) , current state feature \\(h = h_0\\) \n2: for \\(t_{obs}\\) in \\([t_0,\\dots,t_{present}]\\) do \n3: while \\(T < t_{obs}\\) do \n4: \\(h = \\mathrm{ODE\\_Predict}(h,\\Delta t)\\) \n5: \\(T + = \\Delta t\\) \n6: end while \n7: \\(h,loss = \\mathrm{ODE\\_Update}(h,m[t_{obs}])\\) \n8: \\(loss_{KLD} + = loss\\) \n9: save \\(h[t_{obs}] = h\\) \n10: end for \n11: for \\(t_{predict}\\) in \\([t_{present} + 1,\\dots,t_{future}]\\) do \n12: while \\(T < t_{predict}\\) do \n13: \\(h = \\mathrm{ODE\\_Predict}(h,\\Delta t)\\) \n14: \\(T + = \\Delta t\\) \n15: end while \n16: save \\(h[t_{predict}] = h\\) \n17: end for" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.489, + 0.47, + 0.583 + ], + "angle": 0, + "content": "GRU-ODE-Bayes has proven the convergence of this process, as is also applicable to the initial state of SpatialGRU-ODE. If \\( h_0 \\in [-1, 1] \\), then \\( h_j(t) \\in [-1, 1] \\), where \\( j \\) is the index of elements in \\( h(t) \\), as \\( \\left.\\frac{dh(t)_j}{dt}\\right|_{t: h(t)_j = 1} \\leq 0 \\) and \\( \\left.\\frac{dh(t)_j}{dt}\\right|_{t: h(t)_j = -1} \\geq 0 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.583, + 0.469, + 0.702 + ], + "angle": 0, + "content": "N-ODE has several nice properties when implemented on GRU models. The learned parametric derivative makes training not constrained by supervision from fixed future timestamps states, which greatly increases flexibility. On the other hand, unlike RNNs, which require emission intervals for updating, the GRU-ODE continuously defined dynamic model can naturally combine data observed at any given time." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.703, + 0.469, + 0.84 + ], + "angle": 0, + "content": "The pseudo-code for SpatialGRU-ODE is shown in Algorithm 1. Given state-timestamp pairs \\([t, m[t]]\\) from previous multisensor features, The expected output is the states \\([t, h[t]]\\) of each measured past timestamp and anticipated future timestamp \\( t \\in [t_0, \\dots, t_{\\text{present}}, \\dots, t_{\\text{future}}} \\). The ode step may be variable or constant. During the update procedure, a KL divergence loss \\( loss_{KLD} \\) is gathered to quantify the similarity between updated state feature \\( h \\) and observed feature \\( m[t_{obs}] \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.848, + 0.423, + 0.865 + ], + "angle": 0, + "content": "3.4. Asynchronous Modality-agnostic Fusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Asynchronous modality-agnostic fusion attempts to fuse Li-DAR and camera BEV features in a way similar to the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.151 + ], + "angle": 0, + "content": "Beyasian predict-then-update process. The proposed strategy is able to eliminate two crucial limits for multi-sensor fusion, which are strict multi-modal synchronizations and fixed interval data flow." + }, + { + "type": "image", + "bbox": [ + 0.519, + 0.166, + 0.874, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.361, + 0.893, + 0.39 + ], + "angle": 0, + "content": "Figure 3. Illustration of the measurement update process of SpatialGRU-ODE in temporal-agnostic fusion." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.41, + 0.893, + 0.742 + ], + "angle": 0, + "content": "Fig. 3 presents the network structure for the SpatialGRU-ODE update process. After raw data is encoded to BEV maps by different BEV encoders, BEV features from different modalities are agnostic on the source, ordered chronologically, and formulated as multiple timestamp-BEV-feature pairs \\([t,h_t]\\). The output retains the same shape as the input, but the hidden features are as \\(\\frac{1}{4}\\) size of the input for the sake of eliminating memory storage. In order not to degrade the ultimate performance, both state and observation in BEV feature space with shape \\([B,C,H,W]\\) are implicitly encoded into a smaller feature space \\([B,C,H/4,W/4]\\) and finally implicit decoded in the same way for occupancy flow decoder. The temporal propagator runs the subsequent ODE step till the arrival of the next observation. When a new observation occurs, the predicted state and new observation are processed into the distribution module with CNN blocks to obtain the mean and variance of BEV features both with the size \\([1,H/4,W/4]\\). Means and variances of both features are estimated using KL divergence, an auxiliary loss that reflects the similarity between predicted and measured characteristics. Probabilistic auxiliary loss is calculated as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.754, + 0.892, + 0.799 + ], + "angle": 0, + "content": "\\[\n\\operatorname {l o s s} _ {K L D} = \\sum_ {j = 1} ^ {H \\times W} D _ {K L} \\left(p _ {\\text {s t a t e}, j} \\| p _ {\\text {m e a s}, j}\\right) \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The core module for the updated BEV feature is a dual-pathway SpatialGRU module, which first propagates the observed and predicted features respectively, then mixes the two hidden states distributions and finally undergoes the weighted summation of two features after the trusting gate and softmax function to generate the final new state." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14836" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.402, + 0.108 + ], + "angle": 0, + "content": "3.5. Streaming Occupancy Flow Predictor" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.117, + 0.47, + 0.239 + ], + "angle": 0, + "content": "The occupancy flow predictor handles multi-frame BEV features from past and present timestamp-agnostic fusion as input and propagates to future steps in an ODE-enabled variational recurrent neural network. Particularly, the granularity of temporal prediction is decoupled from the training granularity and only related to the minimal ODE step in this method. If we set the variable ODE step, the prediction enables arbitrary granularity." + }, + { + "type": "image", + "bbox": [ + 0.093, + 0.256, + 0.441, + 0.412 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.422, + 0.473, + 0.451 + ], + "angle": 0, + "content": "Figure 4. Illustration of streaming prediction process of SpatialGRU-ODE." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.472, + 0.47, + 0.76 + ], + "angle": 0, + "content": "Fig. 4 illustrates the SpatialGRU-ODE procedure. Similar to the update process, the states are implicitly encoded into a smaller feature space. Except for the initial input which is the first BEV feature, the input with shape \\([H / 4,W / 4,C]\\) is inherited from the last ODE step. The core module, SpatialGRU-ODE, computes the derivatives of BEV features in unit time intervals via a recurrent block specified in Eq. (4). SpatialGRU-ODE may employ either Euler or Midpoint solver for the update and fixed or variable ODE time step. To obtain the projected states, the derivatives are multiplied by delta time \\(dt\\) and added to the initial states. A CNN block is used to infer the next input from the current state in order to make the subsequent prediction. Only states near to the needed timestamps with supervision (closer than half of the minimum ode step) are preserved and decoded in the BEV decoder for supervision. Thus, the prediction time step \\(dt\\) is not always constant and uniform, and supervision signals are not required for each future timestamp." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.782, + 0.21, + 0.8 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.468, + 0.902 + ], + "angle": 0, + "content": "In this section, we seek to answer two questions with the following experiments: (1) Whether the model works as well as published state-of-the-art algorithms for standard occupancy forecasting tasks. (2) Whether we are able to generalize to streaming forecasting settings with one model trained with temporally-sparse occupancy labels." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.091, + 0.698, + 0.106 + ], + "angle": 0, + "content": "4.1. Datasets and Metrics" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.114, + 0.892, + 0.25 + ], + "angle": 0, + "content": "The NuScenes [2] dataset is a public large-scale autonomous driving dataset collected by Motional. NuScenes dataset provides a full sensor suite including 1 top LiDAR, 6 cameras, 5 radars, GPS, and IMU, with \\(360^{\\circ}\\) coverage of the surroundings. It contains 1000 scenes, each lasting 20 seconds, of which annotations of 850 scenes at \\(2\\mathrm{Hz}\\) are available. We use the training and validation splits as same as previous works [1, 9, 10, 30, 34], with 28130 samples for training and 6019 samples for validation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.251, + 0.892, + 0.37 + ], + "angle": 0, + "content": "The Lyft L5 dataset [14] is another large-scale autonomous dataset provided by Lyft. This dataset contains 180 scenes, each lasting 25-45s in length and annotated at \\(5\\mathrm{Hz}\\). We use 6 ring cameras and the top LiDAR from its sensor suite, which has a \\(360^{\\circ}\\) field of view. We use training and validation splits from the practice of FIERY [9], which include 16000 training samples and 4000 validation samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.892, + 0.477 + ], + "angle": 0, + "content": "The occupancy flow prediction is formulated as a video panoptic prediction task [15]. We use Intersection over Union (IoU) to measure the semantic segmentation quality of each frame, and video panoptic quality (PQ), recognition quality (RQ), and segmentation quality (SQ) to measure both the accuracy and consistency of instance segmentation. VPQ is computed as:" + }, + { + "type": "equation", + "bbox": [ + 0.549, + 0.487, + 0.892, + 0.567 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathrm {V P Q} = \\sum_ {t = 0} ^ {H} \\frac {\\sum_ {\\left(p _ {t} , q _ {t}\\right) \\cdot T P _ {t}} \\operatorname {I o U} \\left(p _ {t} \\cdot q _ {t}\\right)}{\\left| T P _ {t} \\right| + \\frac {1}{2} \\left| F P _ {t} \\right| + \\frac {1}{2} \\left| F N _ {t} \\right|} \\tag {6} \\\\ = \\sum_ {t = 0} ^ {H} \\frac {\\left| T P _ {t} \\right|}{\\left| T P _ {t} \\right| + \\frac {1}{2} \\left| F P _ {t} \\right| + \\frac {1}{2} \\left| F N _ {t} \\right|} = \\mathrm {S Q} \\cdot \\mathrm {R Q} \\\\ \\end{array}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.719, + 0.592 + ], + "angle": 0, + "content": "4.2. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.674 + ], + "angle": 0, + "content": "Task details. The standard occupancy prediction task is to take the past 1.0s sensor data for input, which is 3 keyframes in nuScenes (5 keyframes in Lyft), predict the motion in the future 2s, which is 4 keyframes in nuScenes and 10 keyframes in Lyft." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.856 + ], + "angle": 0, + "content": "Data details. The BEV occupancy labels are from 3D bounding boxes labels projected to BEV. The perception range is set as \\([100m, 100m]\\) and the grid resolution is set as \\(0.5m\\). Images are resized to \\(224 \\times 480\\) pixels for each frame. Each point cloud is densified by aggregating point clouds of adjacent sweeps. Point clouds are voxelized to \\(200 \\times 200 \\times 13\\) voxels. StreamingFlow adopts an asynchronous data stream as input, with LiDAR streams every 0.2s and camera streams every 0.5s as input. For larger models fairly compared with the state-of-the-art, we use images with size \\(320 \\times 800\\) and aggregated LiDAR streams, each with 10 sweeps." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Model details. The framework is implemented on Pytorch 1.10.2 and Pytorch Lightning 1.2.5. The optimizer is AdamW with a learning rate of \\( 1e - 4 \\). The learning strategy" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14837" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.08, + 0.088, + 0.387, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.396, + 0.088, + 0.882, + 0.292 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.302, + 0.895, + 0.359 + ], + "angle": 0, + "content": "Figure 5. Visualization of StreamingFlow for diverse driving scenarios. Different colors represent different instances of the agents, and lighter colors represent the future occupancy of the agents. (top): samples from Lyft dataset, highway (left), and urban (right). (middle and bottom): samples from nuScenes dataset, sunny (middle left), overcast after rain (middle right), rainy (bottom left), and night (bottom right). StreamingFlow works well in all challenging driving scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.385, + 0.47, + 0.445 + ], + "angle": 0, + "content": "is cosine annealing with a weight decay of 0.01. All models are trained on 8 A6000 GPUs for 20 epochs with a total batch size 16. The image backbone is EfficientNet-b4 [29] for tiny and base model and Effi-b7 for small model." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.453, + 0.4, + 0.47 + ], + "angle": 0, + "content": "4.3. Comparison with the State-of-the-art" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.47, + 0.538 + ], + "angle": 0, + "content": "Comparisons of methods implemented in the nuScenes dataset are shown in Tab. 1. All methods are trained for a standard instance flow segmentation and prediction task. Fig. 5 illustrates some examples covering diverse scenarios." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.702 + ], + "angle": 0, + "content": "StreamingFlow achieves competitive performance while significantly outperforming other single-modality methods. StreamingFlow surpasses the best vision-based BEVerse [34] with a larger backbone Swin-small [19] by \\(+7.0\\) IoU and \\(+10.0\\) VPQ, and the best LiDAR-based BE-STI [30] \\(+7.7\\) IoU and 5.1VPQ. Compared to FusionAD, StreamingFlow-base uses the same LiDAR backbone(SpConv), similar image backbone(Effi-B4 vs. ResNet101) but a half smaller image size \\((800\\times 320\\) vs. \\(1600\\times 900)\\), and is \\(+1.6\\) VPQ and 2.4 IoU higher than the latest fusion-based FusionAD [33]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.703, + 0.47, + 0.795 + ], + "angle": 0, + "content": "Comparisons of methods implemented in the Lyft L5 dataset are shown in Tab. 2. StreamingFlow achieves the best of all metrics while surpassing baseline methods by a large margin: \\(+20.6\\) IoU and \\(+23.5\\) VPQ against STP3 [10]. Moreover, it surpasses our reproduced BEVFusion with lightweight encoders by \\(+2.3\\) mIoU and 0.2 VPQ." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.349, + 0.818 + ], + "angle": 0, + "content": "4.4. Streaming Forecasting Results" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "We design three experiments on nuScenes dataset for demonstration of the streaming occupancy prediction: (1) Extension of the prediction temporal horizons to unseen future; (2) Prediction at any desired future time point; (3) Data streams input at different frame rates. Experiments are con" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.385, + 0.892, + 0.414 + ], + "angle": 0, + "content": "duced on models loaded from the checkpoints trained on standard instance forecasting tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.416, + 0.893, + 0.627 + ], + "angle": 0, + "content": "Extension of the temporal horizons of unseen future. Tab. 3 shows the prediction result of StreamingFlow which extends the temporal horizons from 2.0s to 8.0s. Baselines reported in [1] are trained for different lengths of temporal horizons. StreamingFlow shows excellent performance in variable prediction length without retraining. Similar to prior arts which extend prediction horizons to farther future, StreamingFlow shows a similar gradual performance decay. We then compare zero-shot Streamingflow with the model trained with the longest future 8s groundtruth labels in Tab. 4. The zero-shot long-term prediction results are only \\(-0.9\\) IoU and \\(-1.8\\) VPQ less than fully supervised models, which demonstrates great generalization ability of foreseeing the unseen future." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.628, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Streaming prediction at any desired time point. Since nuScenes do not provide labels for non-keyframes, we adopt the practice of MotionNet and interpolate the box instances between two adjacent keyframes. We randomly choose to predict at a list of time points and report the results in Tab. 5. To simply illustrate the capability, we designed the main task to predict uniformly spaced temporal horizons, but this framework can predict uneven and arbitrary future snapshots. The prediction results are stable generally. There is a slight decline as the forecast becomes denser." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.795, + 0.892, + 0.884 + ], + "angle": 0, + "content": "We provide demo videos as supplementary materials to show the effectiveness of streaming prediction. We provide a finer granularity of streaming perception at any future time. In the video, we visualize the prediction results every 0.05s from the current to the future 2s to 3s, with a total of 40 to 60 frames." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Asynchronous multi-modal data streams as input." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14838" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.078, + 0.089, + 0.895, + 0.34 + ], + "angle": 0, + "content": "
MethodModalityImage backboneLiDAR backboneFuture Semantic Seg. IoU↑Future Instance Seg.
PQ↑SQ↑RQ↑
Static*CEffi-B4-32.227.670.139.1
FIERY*[9]CEffi-B4-37.030.270.242.9
StretchBEV[1]CEffi-B4-37.129.0--
BEVerse[34]CSwin-tiny-38.733.370.647.2
BEVerse[34]CSwin-small-40.836.170.751.1
ST-P3 Gaus.[10]CEffi-B4-38.631.770.245.2
ST-P3 Ber.[10]CEffi-B4-38.932.170.445.6
UniAD[11]CEffi-B4-40.233.5--
MotionNet[32]L-STPN37.238.975.651.4
BE-STI[30]L-BESTI-STPN40.141.075.554.3
StreamingFlow-tinyLCEffi-B4PillarNet47.846.175.860.8
StreamingFlow-smallLCEffi-B7PillarNet51.148.075.164.0
FusionAD[33]LCResNet-101VoxelNet51.551.1--
StreamingFlow-baseLCEffi-B4VoxelNet53.952.778.766.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.35, + 0.891, + 0.379 + ], + "angle": 0, + "content": "Table 1. Comparison with the state-of-the-art methods for instance-aware occupancy flow prediction on nuScenes[2] validation set. 'C' denotes vision-only methods, 'L' denotes LiDAR-based methods, and 'LC' denotes a LiDAR-camera fusion methods. \\(*\\): reported in [9]." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.402, + 0.47, + 0.522 + ], + "angle": 0, + "content": "
MethodIoU↑PQ↑SQ↑RQ↑
Static*24.120.7--
Extrapolation model*24.821.2--
FIERY*[9]36.327.2--
ST-P3[10]36.332.471.145.5
BEVFusion-tiny†54.655.778.071.4
StreamingFlow-tiny56.955.978.171.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.533, + 0.47, + 0.589 + ], + "angle": 0, + "content": "Table 2. Comparison with the state-of-the-art methods for future instance segmentation (2.0s) on Lyft L5 AV [14] validation set. \\(\\star\\) results reported in [9]. \\(\\dagger\\) : results of BEVFusion with LSS-based image encoder and pillar-based encoder reproduced by us." + }, + { + "type": "table", + "bbox": [ + 0.081, + 0.592, + 0.469, + 0.801 + ], + "angle": 0, + "content": "
MethodPredIoU↑PQ↑SQ↑RQ↑
FIERY2s35.829.0--
4s30.123.6--
6s26.720.9--
StretchBEV2s37.129.0--
4s32.523.8--
6s28.421.0--
StreamingFlow2s47.846.175.860.8
3s44.441.174.155.4
4s41.738.473.652.1
5s39.135.873.248.9
6s36.733.672.946.0
8s32.529.872.640.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.812, + 0.469, + 0.839 + ], + "angle": 0, + "content": "Table 3. Comparison of occupancy flow prediction for any temporal horizons." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "We validate asynchronous data streams as input and standard occupancy forecasting as output. We test multiple settings of data stream frame rate and report the results in Tab." + }, + { + "type": "table", + "bbox": [ + 0.501, + 0.402, + 0.895, + 0.459 + ], + "angle": 0, + "content": "
Schedule2s3s4s6s8s
ZS.47.8/46.144.4/41.141.7/38.436.7/33.632.5/29.8
Sup.48.2/46.946.0/45.241.9/38.737.8/34.233.6/31.6
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.46, + 0.892, + 0.502 + ], + "angle": 0, + "content": "Table 4. ZS: zero-shot inference of StreamingFlow. Sup: StreamingFlow trained with the longest prediction horizons 8s. Each value is given in the format of 'IoU/PQ'." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.516, + 0.891, + 0.585 + ], + "angle": 0, + "content": "
Prediction IntervalIoU↑PQ↑SQ↑RQ↑
0.547.846.175.860.8
0.2543.440.174.154.1
0.645.644.375.258.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.597, + 0.891, + 0.625 + ], + "angle": 0, + "content": "Table 5. Prediction results at any desired intervals. For example, prediction at the interval of 0.6 means prediction at [0.6, 1.2, 1.8]." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.64, + 0.891, + 0.685 + ], + "angle": 0, + "content": "6. The model performs the best when the inference uses the training configuration. Denser inputs lead to similar forecasting accuracy." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.698, + 0.891, + 0.768 + ], + "angle": 0, + "content": "
LiDAR streamCam streamIoU↑PQ↑SQ↑RQ↑
5247.846.175.860.8
10247.645.875.660.5
10447.145.475.160.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.5, + 0.779, + 0.89, + 0.806 + ], + "angle": 0, + "content": "Table 6. Prediction results with multi-modal data stream of different frame rates. Frame rates are shown in Hz." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.833, + 0.654, + 0.849 + ], + "angle": 0, + "content": "4.5. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Effect of different fusion strategies. We compare SpatialGRU-ODE with fusion strategies at different stages and the implementation details are in supplementary" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "14839" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.213 + ], + "angle": 0, + "content": "material. As shown in Tab. 7, asynchronous fusion is inferior to synchronous fusion and SpatialGRU-ODE for both datasets. For nuScenes dataset, the ordinary temporally-synchronized fusion approach performs the best. SpatialGRU-ODE performs \\(-2.4\\) IoU and \\(-0.9\\) VPQ, slightly less than BEVFusion [20]. For Lyft dataset, SpatialGRU-ODE outperforms synchronized fusion. It performs \\(+2.3\\) IoU and \\(+0.2\\) VPQ more than BEVFusion [20]." + }, + { + "type": "table", + "bbox": [ + 0.08, + 0.224, + 0.47, + 0.386 + ], + "angle": 0, + "content": "
Fusion modeIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Spatial then temporal50.247.075.663.0
Temporal then spatial44.742.774.657.2
SpatialGRU-ODE47.846.175.860.8
Lyft L5 AV dataset
Spatial then temporal54.655.778.071.4
Temporal then spatial50.450.275.266.7
SpatialGRU-ODE56.955.978.171.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.395, + 0.471, + 0.478 + ], + "angle": 0, + "content": "Table 7. Comparison with the baseline fusion methods for future instance segmentation (2.0s) on nuScenes validation set. StreamingFlow-ODE is compared with different fusion modes. Spatial fusion is conducted in the same way as BEVFusion [20]. 'Spatial Then Temporal' is for synchronous mode, and 'Temporal Then Spatial' is for asynchronous mode." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.484, + 0.47, + 0.621 + ], + "angle": 0, + "content": "Effect of ODE solvers. ODE solvers are vital tools for a N-ODE framework. We test two basic ode solvers, Euler, and midpoint solver as compared in Tab. 8 on two datasets. In both cases, the midpoint solver yields superior VPQ, surpassing the Euler solver by 3.2 points on nuScenes dataset and 0.8 points on Lyft dataset. On nuScenes dataset, the midpoint solver shows similar IoU with the Euler solver, but on Lyft dataset, the midpoint solver performs worse semantic segmentation by \\(-1.9\\)." + }, + { + "type": "table", + "bbox": [ + 0.083, + 0.632, + 0.467, + 0.766 + ], + "angle": 0, + "content": "
ODE SolverIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Euler47.842.973.558.6
Midpoint47.846.175.860.8
Lyft L5 AV dataset
Euler56.955.978.171.5
Midpoint55.056.778.272.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.776, + 0.468, + 0.79 + ], + "angle": 0, + "content": "Table 8. Comparison with prediction using different ODE solvers." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.903 + ], + "angle": 0, + "content": "Effect of ODE update intervals. We ablate different ODE update intervals which determine the minimum granularity of occupancy prediction. The ODE step is set to 0.05, 0.1, 0.5 and variable for comparison. Variable means the ODE step is the next timestamp minus the current timestamp. In general, the finer a single update is divided during the ODE update process, the higher the final prediction ac" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "curacy. It is also intuitive that a higher update frequency may eliminate continuous errors. As shown in Tab. 9, the predictor with interval \\(0.05s\\) surpasses interval \\(0.1s\\) by 0.1 IoU and 3.1 VPQ, and interval \\(0.5s\\) by 0.5 IoU and 3.1 VPQ. Remarkably, the variable time step update also shows nice performance, which is \\(+0.5\\) IoU and \\(-2.2\\) VPQ when compared to the predictor with ODE step \\(0.05s\\). A variable time step updater strikes a good balance between precision and inference speed, so it is more favorable for long-term prediction to 8s future." + }, + { + "type": "table", + "bbox": [ + 0.508, + 0.254, + 0.887, + 0.414 + ], + "angle": 0, + "content": "
StepIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
0.0547.846.175.860.8
0.147.743.073.758.4
0.547.342.173.357.4
Variable48.243.973.958.8
Lyft L5 dataset
0.0556.955.978.171.9
Variable54.053.577.469.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.515, + 0.424, + 0.875, + 0.438 + ], + "angle": 0, + "content": "Table 9. Comparison of prediction under different ode steps." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.444, + 0.62, + 0.459 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.469, + 0.892, + 0.651 + ], + "angle": 0, + "content": "We present StreamingFlow as the first practice for fusion-based streaming occupancy forecasting. Starting from the motivation of fusing and predicting from non-ideal data streams, the streaming feature brings a more flexible temporal scene understanding and generalizes occupancy forecasting well to any temporal horizon. The advantage of SpatialGRU-ODE is that it decouples the supervision in the training process and outputs in the inference process, by modeling the derivatives of BEV grids and propagating future grid states to required timestamps. We hope that this work will inspire more Neural-ODE applications and insights into the streaming automotive perception." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.663, + 0.681, + 0.681 + ], + "angle": 0, + "content": "6. Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.779 + ], + "angle": 0, + "content": "This work was supported in part by the National Natural Science Foundation of China under Grants (52372414, U22A20104, 52102464). This work was also sponsored by Tsinghua University-DiDi Joint Research Center for Future Mobility and Tsinghua University-Zongmu Technology Joint Research Center." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.792, + 0.597, + 0.807 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.816, + 0.892, + 0.871 + ], + "angle": 0, + "content": "[1] Adil Kaan Akan and Fatma Güney. Stretchbev: Stretching future instance prediction spatially and temporally. 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However, current best-performing single-modality methods or multi-modality fusion perception methods are only able to predict uniform snapshots of future occupancy states and require strictly synchronized sensory data for sensor fusion. We propose a novel framework, StreamingFlow, to lift these strong limitations. StreamingFlow is a novel BEV occupancy predictor that ingests asynchronous multisensor data streams for fusion and performs streaming forecasting of the future occupancy map at any future times-tamps. By integrating neural ordinary differential equations (N-ODE) into recurrent neural networks, StreamingFlow learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV features as part of the fusion process, and propagates BEV states to the desired future time point. It shows good zero-shot generalization ability of prediction, reflected in the interpolation of the observed prediction time horizon and the reasonable inference of the unseen farther future period. Extensive experiments on two large-scale datasets, nuScenes [2] and Lyft L5 [14], demonstrate that StreamingFlow significantly outperforms previous vision-based, LiDAR-based methods, and shows superior performance compared to state-of-the-art fusion-based methods. + +# 1. Introduction + +Occupancy grid is gaining more traction in the self-driving community, due to its versatility in downstream tasks, e.g., irregularly shaped object representation, robot navigation, etc. With the help of modern deep learning technologies, occupancy grid maps (OGMs) have evolved significantly. For example, not just LiDAR point clouds, camera images can now be used to construct high-quality occupancy grid maps [26]. In addition to its fine-grained geometric infor + +![](images/7b84382c7eea5f301e3a763ecea1acb2762dbc9325fe17705b76498bcaff359d.jpg) +Figure 1. Comparison between conventional synchronized BEV fusion (top) and our asynchronous BEV fusion (bottom). We formulate fusion with an update-predict-update approach. + +mation, occupancy grids can also represent rich semantic and motion cues [1, 9-11]. Such cues grant occupancy networks the ability to predict the occupancy state of the environment at desired future timestamps. While trajectory forecasting only contains object-level information, the occupancy grid conveys a much more comprehensive understanding of the surrounding environment, which is the key to achieving better intelligence and driving safety. + +Despite the great potential of occupancy-based prediction, we notice that existing methods can only predict at fixed frequencies [1, 9-11, 33]. This comes from the fact that sensors sample the environment at predetermined frequencies, e.g., motors in mechanical LiDARs spin at $10\mathrm{Hz}$ and many cameras captures images at 30FPS. Thus, previous algorithms predict at the same intervals as they are trained with ground-truth labels of future intervals. If future occupancy can be predicted at any given timestamps in a continuous manner, self-driving algorithms can have shorter latency and more rapid responses. Streaming forecasting can also relax the sensor synchronization constraints, as the continuous forecasting model can update the prediction as new sensory data come in. Compared with discrete snapshot-based prediction, streaming motion forecast + +ing [24] naturally has safety advantages. + +We noticed several challenges in fulfilling such a streaming forecasting paradigm. Firstly, sensory data and ground truth annotations are collected at a fixed frequency. Streaming forecasting aims to achieve temporally dense and continuous prediction, with data only sparsely and uniformly sampled in the temporal domain. Secondly, mainstream network architectures are not designed for such streaming requirements. Forecasting at any given timestamp requires delicate modeling of the temporal dynamics, but how to embed the temporal dynamics into the widely adopted BEV feature representation remains under-explored. + +To this end, we propose to use the neural ordinary differential equation (N-ODE) framework for such temporal dynamics modeling. N-ODE is originally proposed for learning continuous implicit processes in dynamic systems. In our application, by representing the continuous motion trends of the driving scenarios into a time series of implicit spatial BEV features, the neural ODE framework not only allows streaming occupancy predictions on any temporal horizon with one fixed model, but also relaxes the sensor synchronization constraints. + +With such flexibility, we propose a novel method, StreamingFlow, that performs asynchronous multi-modal sensor fusion to achieve streaming occupancy forecasting. Toward the goal of streaming modeling of temporal BEV features, StreamingFlow integrates neural ordinary differential equations (N-ODE) onto wrapped-based recurrent neural networks. It learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV feature as part of the fusion process, and propagates BEV states to the desired future time point. A graphical illustration of fusion strategies between conventional BEV-based fusion and ours is illustrated in Fig. 1. + +Our contributions can be summarized as follows: + +1. To the best of our knowledge, we propose the first streaming occupancy flow prediction framework that supports asynchronous multi-sensor fusion; +2. We design a novel temporal feature propagation strategy that achieves high performance on dense continuous occupancy prediction with only temporally sparse labels; +3. Our proposed method achieves state-of-the-art performance on the widely used nuScenes [2] and Lyft L5 [14] datasets, validating the effectiveness and robustness of our proposed algorithms. + +# 2. Related Works + +# 2.1. Occupancy forecasting + +Occupancy flow prediction, first proposed in [23], is a valuable supplement to trajectory-set prediction [3, 22]. The advantages of occupancy flow are a non-parametric distribution output and fine-grained grid flow. Recent LiDAR- + +based methods [21, 30, 32] attach displacement vectors to non-empty BEV grids to describe short-term motion in future 1.0s. These networks typically have a BEV-based spatial-temporal backbone and several shared heads that indicate the classification, motion, and displacement of each grid. STPN [32] and BE-STI [30] are effective BEV-based spatial-temporal feature extractors for binary-occupied grids which consist of only 2D convolutional blocks. Vision-centric pipelines usually formulate the prediction task as future instance segmentation on BEV grids. FIERY [9] is the first vision-centric stochastic future prediction method. StretchBEV [1] uses a variational autoencoder for decoupling learning of temporal dynamics and BEV decoder. End-to-end driving frameworks [10, 11, 33, 34] conduct planning based on occupancy prediction. UniAD [11] and TBP-Former [6] models temporal future with video transformers. One major bottleneck of video transformers is prediction of long-term sequence length [28]. Position encoding enables video transformer to interpolate shorter sequences but few video transformers can generalize to the unseen longer sequence length. Unlike all prior works that predict discrete near-future snapshots, We focus on the streaming flow prediction which adapt the predictor to a more distant future and finer granularity. + +# 2.2. Multi-sensor Spatial-temporal Fusion + +Spatial multi-modal fusion is widely investigated in the feature level. BEVFusion and its variants [7, 8, 20] combine multi-modal input features in a shared BEV space. [4, 16] support feature interaction in 3D voxel space. Temporal fusion is a common aggregator for perception tasks. LiDAR-based networks [30, 32] typically employ data-level temporal fusion, which transforms multi-frame point clouds to the current ego's coordinate as inputs via ego pose or registration methods. Most vision-centric methods align the BEV feature maps from multiple time steps based on ego pose, and then concatenate them for fusion [9, 12, 17, 25] or support their interactions of multi-frame BEV features through attention [13, 18, 27]. Prior spatial fusion methods usually assume strict synchronization. CoBEVFlow [31] is most similar to our approach in that they predict BEV flow to interpolate asynchronous data timestamps from roadside unit to vehicle system, but short-term flow information cannot support long-term prediction. To this end, we provide a flexible spatio-temporal fusion framework which predicts the future frames and triggers update process as fusion when asynchronous sensor data arrives. + +# 3. Methodology + +# 3.1. Framework + +The pipeline of StreamingFlow is depicted in Fig. 2. Given multi-modal data streams from the previous few seconds, + +![](images/1fc171bf9fb2ba64ca5df4aab6be3a4ad7dd79ffad212b24c7dcaab73f19e7ac.jpg) +Figure 2. The framework of StreamingFlow. Raw data streams are encoded to BEV features, respectively. The SpatialGRU-ODE process operates on the timeline with two stages split by the present timestamp, asynchronous multi-sensor deep feature via the SpatialGRU-ODE update process and continuous occupancy flow prediction via SpatialGRU-ODE predict process. + +the task is defined as predicting the future several seconds' instance occupancy and flow on uniformly-shaped BEV grids. The framework includes three phases: 1) BEV encoders for LiDAR and camera branches, respectively, 2) asynchronous multi-sensor fusion, and 3) streaming occupancy prediction. As the data stream runs, modality-specific encoders map raw data to BEV features. The BEV state starts from zeroed features and fuses every incoming BEV feature in a trigger mode instead of a matching mode in conventional fusion. The BEV state propagates until a new BEV feature is received. The incoming BEV feature is fused to the BEV state and state continues to propagate until next incoming observation. + +The SpatialGRU-ODE is the core for streaming prediction. The SpatialGRU-ODE iterates for ODE steps, updates when a new measurement occurs within a certain ODE step, and performs future prediction. In the training stage, the loss comes from the supervision of decoded BEV grids at the timestamps with labels, as well as an auxiliary probabilistic loss from Kullback-Leibler divergence (KLD) between updated BEV features and latent observations. In the inference process, SpatialGRU-ODE predicts via a variable ODE step only related to the required timestamps for evaluation and application. + +The BEV decoder, loss functions, and post-processing techniques follow standard practices, and we leave the details in the supplementary materials. + +# 3.2. BEV Encoders + +LiDAR branch. We adopt the popular pillar representations for point cloud features. We observed that a very lightweight pillar-net encoder is sufficient for high accuracy. Heavier backbones consisting of sparse convolutional modules or voxel transformers can be trivially integrated for performance at the cost of additional computation. + +Camera branch. As a baseline for algorithms aligned with previous work, we adopt the Lift-splat-shoot + +(LSS [26]) settings with depth supervision for depth-based view transformation. We adopt accelerated BEV pool operators to speed up the inference stage. Other BEV mapping methods are trivially compatible with our framework. + +# 3.3. SpatialGRU-ODE + +Gate Recurrent Unit (GRU) consists of reset gate $(r_t)$ , update gate $(z_t)$ , and update vector $(g_t)$ . The update process follows the formula, + +$$ +r _ {t} = \sigma \left(W _ {r} x _ {t} + U _ {r} h _ {t - 1} + b _ {r}\right) +$$ + +$$ +z _ {t} = \sigma \left(W _ {z} x _ {t} + U _ {z} h _ {t - 1} + b _ {z}\right) \tag {1} +$$ + +$$ +g _ {t} = \tanh \left(W _ {h} x _ {t} + U _ {h} \left(r _ {t} \odot h _ {t - 1}\right) + b _ {h}\right) +$$ + +Neural-ODE on GRU blocks focuses N-ODE's ability to model continuous time series given sporadic sensor data coming from non-uniform time intervals. SpatialGRU-ODE is highly inspired by GRU-ODE-Bayes [5], which serves as the foundation component of the proposed spatiotemporal fusion and flow predictor. Eq. (1) formulates the general process of GRU blocks. With regard to $h_t$ as a BEV feature, SpatialGRU has its state variable $h_t$ with shape $[B, C, H, W]$ where $B, C, H, W$ are the batch size, embedded dims, height, and width. $\sigma$ is the sigmoid function, and $\tanh$ denotes a CNN block in SpatialGRU settings. $x_t$ is the input state at timestamp $t$ with the same shape as $h_t$ . For simplicity, the update gate $W_r = U_r$ , the reset gate $W_z = U_z$ , and the GRU init bias $b_r = b_z$ . $r_t \odot h_{t-1}$ is the matrix multiplication between reset gate and state. In summary, the update state $h_t$ is calculated as, + +$$ +h _ {t} = z _ {t} \cdot h _ {t - 1} + \left(1 - z _ {t}\right) \cdot g _ {t} = G R U \left(h _ {t - 1}, g _ {t}\right) \tag {2} +$$ + +The amount of change of the state variable is calculated as: + +$$ +\begin{array}{l} \Delta h _ {t} = h _ {t} - h _ {t - 1} = z _ {t} \cdot h _ {t - 1} + (1 - z _ {t}) \cdot g _ {t} - h _ {t - 1} \tag {3} \\ = \left(1 - z _ {t}\right) \cdot \left(g _ {t} - h _ {t - 1}\right) \\ \end{array} +$$ + +The derivatives of the state variable are calculated as: + +$$ +\frac {\Delta h (t)}{d t} = (1 - z (t)) \cdot (g (t) - h (t)) \tag {4} +$$ + +Algorithm 1 The pseudo-code of SpatialGRU-ODE +Input: state-timestamp pairs $[t,m[t]],t\in [t_0,\dots,t_{present}]$ ODE step $\Delta t$ +Output: $loss_{KLD}$ , state-timestamp pairs $[t,h[t]],t\in$ $[t_0,\dots,t_{present},\dots,t_{future}]$ 1: Initialize current time $T = t_0$ KL divergence loss $loss_{KLD} = 0$ , current state feature $h = h_0$ +2: for $t_{obs}$ in $[t_0,\dots,t_{present}]$ do +3: while $T < t_{obs}$ do +4: $h = \mathrm{ODE\_Predict}(h,\Delta t)$ +5: $T + = \Delta t$ +6: end while +7: $h,loss = \mathrm{ODE\_Update}(h,m[t_{obs}])$ +8: $loss_{KLD} + = loss$ +9: save $h[t_{obs}] = h$ +10: end for +11: for $t_{predict}$ in $[t_{present} + 1,\dots,t_{future}]$ do +12: while $T < t_{predict}$ do +13: $h = \mathrm{ODE\_Predict}(h,\Delta t)$ +14: $T + = \Delta t$ +15: end while +16: save $h[t_{predict}] = h$ +17: end for + +GRU-ODE-Bayes has proven the convergence of this process, as is also applicable to the initial state of SpatialGRU-ODE. If $h_0 \in [-1, 1]$ , then $h_j(t) \in [-1, 1]$ , where $j$ is the index of elements in $h(t)$ , as $\left.\frac{dh(t)_j}{dt}\right|_{t: h(t)_j = 1} \leq 0$ and $\left.\frac{dh(t)_j}{dt}\right|_{t: h(t)_j = -1} \geq 0$ . + +N-ODE has several nice properties when implemented on GRU models. The learned parametric derivative makes training not constrained by supervision from fixed future timestamps states, which greatly increases flexibility. On the other hand, unlike RNNs, which require emission intervals for updating, the GRU-ODE continuously defined dynamic model can naturally combine data observed at any given time. + +The pseudo-code for SpatialGRU-ODE is shown in Algorithm 1. Given state-timestamp pairs $[t, m[t]]$ from previous multisensor features, The expected output is the states $[t, h[t]]$ of each measured past timestamp and anticipated future timestamp $t \in [t_0, \dots, t_{\text{present}}, \dots, t_{\text{future}}}$ . The ode step may be variable or constant. During the update procedure, a KL divergence loss $loss_{KLD}$ is gathered to quantify the similarity between updated state feature $h$ and observed feature $m[t_{obs}]$ . + +# 3.4. Asynchronous Modality-agnostic Fusion + +Asynchronous modality-agnostic fusion attempts to fuse Li-DAR and camera BEV features in a way similar to the + +Beyasian predict-then-update process. The proposed strategy is able to eliminate two crucial limits for multi-sensor fusion, which are strict multi-modal synchronizations and fixed interval data flow. + +![](images/e14a5b1d9b60760d9d1ead4b364e17927f63b3b96d6e7b34f5a4380868841a5f.jpg) +Figure 3. Illustration of the measurement update process of SpatialGRU-ODE in temporal-agnostic fusion. + +Fig. 3 presents the network structure for the SpatialGRU-ODE update process. After raw data is encoded to BEV maps by different BEV encoders, BEV features from different modalities are agnostic on the source, ordered chronologically, and formulated as multiple timestamp-BEV-feature pairs $[t,h_t]$ . The output retains the same shape as the input, but the hidden features are as $\frac{1}{4}$ size of the input for the sake of eliminating memory storage. In order not to degrade the ultimate performance, both state and observation in BEV feature space with shape $[B,C,H,W]$ are implicitly encoded into a smaller feature space $[B,C,H/4,W/4]$ and finally implicit decoded in the same way for occupancy flow decoder. The temporal propagator runs the subsequent ODE step till the arrival of the next observation. When a new observation occurs, the predicted state and new observation are processed into the distribution module with CNN blocks to obtain the mean and variance of BEV features both with the size $[1,H/4,W/4]$ . Means and variances of both features are estimated using KL divergence, an auxiliary loss that reflects the similarity between predicted and measured characteristics. Probabilistic auxiliary loss is calculated as follows: + +$$ +\operatorname {l o s s} _ {K L D} = \sum_ {j = 1} ^ {H \times W} D _ {K L} \left(p _ {\text {s t a t e}, j} \| p _ {\text {m e a s}, j}\right) \tag {5} +$$ + +The core module for the updated BEV feature is a dual-pathway SpatialGRU module, which first propagates the observed and predicted features respectively, then mixes the two hidden states distributions and finally undergoes the weighted summation of two features after the trusting gate and softmax function to generate the final new state. + +# 3.5. Streaming Occupancy Flow Predictor + +The occupancy flow predictor handles multi-frame BEV features from past and present timestamp-agnostic fusion as input and propagates to future steps in an ODE-enabled variational recurrent neural network. Particularly, the granularity of temporal prediction is decoupled from the training granularity and only related to the minimal ODE step in this method. If we set the variable ODE step, the prediction enables arbitrary granularity. + +![](images/345e8d046350eae63292687e4b3c056783bc03772cb1d61d99af6b7c66933626.jpg) +Figure 4. Illustration of streaming prediction process of SpatialGRU-ODE. + +Fig. 4 illustrates the SpatialGRU-ODE procedure. Similar to the update process, the states are implicitly encoded into a smaller feature space. Except for the initial input which is the first BEV feature, the input with shape $[H / 4,W / 4,C]$ is inherited from the last ODE step. The core module, SpatialGRU-ODE, computes the derivatives of BEV features in unit time intervals via a recurrent block specified in Eq. (4). SpatialGRU-ODE may employ either Euler or Midpoint solver for the update and fixed or variable ODE time step. To obtain the projected states, the derivatives are multiplied by delta time $dt$ and added to the initial states. A CNN block is used to infer the next input from the current state in order to make the subsequent prediction. Only states near to the needed timestamps with supervision (closer than half of the minimum ode step) are preserved and decoded in the BEV decoder for supervision. Thus, the prediction time step $dt$ is not always constant and uniform, and supervision signals are not required for each future timestamp. + +# 4. Experiments + +In this section, we seek to answer two questions with the following experiments: (1) Whether the model works as well as published state-of-the-art algorithms for standard occupancy forecasting tasks. (2) Whether we are able to generalize to streaming forecasting settings with one model trained with temporally-sparse occupancy labels. + +# 4.1. Datasets and Metrics + +The NuScenes [2] dataset is a public large-scale autonomous driving dataset collected by Motional. NuScenes dataset provides a full sensor suite including 1 top LiDAR, 6 cameras, 5 radars, GPS, and IMU, with $360^{\circ}$ coverage of the surroundings. It contains 1000 scenes, each lasting 20 seconds, of which annotations of 850 scenes at $2\mathrm{Hz}$ are available. We use the training and validation splits as same as previous works [1, 9, 10, 30, 34], with 28130 samples for training and 6019 samples for validation. + +The Lyft L5 dataset [14] is another large-scale autonomous dataset provided by Lyft. This dataset contains 180 scenes, each lasting 25-45s in length and annotated at $5\mathrm{Hz}$ . We use 6 ring cameras and the top LiDAR from its sensor suite, which has a $360^{\circ}$ field of view. We use training and validation splits from the practice of FIERY [9], which include 16000 training samples and 4000 validation samples. + +The occupancy flow prediction is formulated as a video panoptic prediction task [15]. We use Intersection over Union (IoU) to measure the semantic segmentation quality of each frame, and video panoptic quality (PQ), recognition quality (RQ), and segmentation quality (SQ) to measure both the accuracy and consistency of instance segmentation. VPQ is computed as: + +$$ +\begin{array}{l} \mathrm {V P Q} = \sum_ {t = 0} ^ {H} \frac {\sum_ {\left(p _ {t} , q _ {t}\right) \cdot T P _ {t}} \operatorname {I o U} \left(p _ {t} \cdot q _ {t}\right)}{\left| T P _ {t} \right| + \frac {1}{2} \left| F P _ {t} \right| + \frac {1}{2} \left| F N _ {t} \right|} \tag {6} \\ = \sum_ {t = 0} ^ {H} \frac {\left| T P _ {t} \right|}{\left| T P _ {t} \right| + \frac {1}{2} \left| F P _ {t} \right| + \frac {1}{2} \left| F N _ {t} \right|} = \mathrm {S Q} \cdot \mathrm {R Q} \\ \end{array} +$$ + +# 4.2. Implementation Details + +Task details. The standard occupancy prediction task is to take the past 1.0s sensor data for input, which is 3 keyframes in nuScenes (5 keyframes in Lyft), predict the motion in the future 2s, which is 4 keyframes in nuScenes and 10 keyframes in Lyft. + +Data details. The BEV occupancy labels are from 3D bounding boxes labels projected to BEV. The perception range is set as $[100m, 100m]$ and the grid resolution is set as $0.5m$ . Images are resized to $224 \times 480$ pixels for each frame. Each point cloud is densified by aggregating point clouds of adjacent sweeps. Point clouds are voxelized to $200 \times 200 \times 13$ voxels. StreamingFlow adopts an asynchronous data stream as input, with LiDAR streams every 0.2s and camera streams every 0.5s as input. For larger models fairly compared with the state-of-the-art, we use images with size $320 \times 800$ and aggregated LiDAR streams, each with 10 sweeps. + +Model details. The framework is implemented on Pytorch 1.10.2 and Pytorch Lightning 1.2.5. The optimizer is AdamW with a learning rate of $1e - 4$ . The learning strategy + +![](images/47d7983c3d8d3aec94297de1ce45062ae6703f7363e69f67d3a08a60e30ef6bd.jpg) +Figure 5. Visualization of StreamingFlow for diverse driving scenarios. Different colors represent different instances of the agents, and lighter colors represent the future occupancy of the agents. (top): samples from Lyft dataset, highway (left), and urban (right). (middle and bottom): samples from nuScenes dataset, sunny (middle left), overcast after rain (middle right), rainy (bottom left), and night (bottom right). StreamingFlow works well in all challenging driving scenarios. + +![](images/230bb776870702404520a5208daf4d0ff668457ccbc8b8c2171cb65680e6f550.jpg) + +is cosine annealing with a weight decay of 0.01. All models are trained on 8 A6000 GPUs for 20 epochs with a total batch size 16. The image backbone is EfficientNet-b4 [29] for tiny and base model and Effi-b7 for small model. + +# 4.3. Comparison with the State-of-the-art + +Comparisons of methods implemented in the nuScenes dataset are shown in Tab. 1. All methods are trained for a standard instance flow segmentation and prediction task. Fig. 5 illustrates some examples covering diverse scenarios. + +StreamingFlow achieves competitive performance while significantly outperforming other single-modality methods. StreamingFlow surpasses the best vision-based BEVerse [34] with a larger backbone Swin-small [19] by $+7.0$ IoU and $+10.0$ VPQ, and the best LiDAR-based BE-STI [30] $+7.7$ IoU and 5.1VPQ. Compared to FusionAD, StreamingFlow-base uses the same LiDAR backbone(SpConv), similar image backbone(Effi-B4 vs. ResNet101) but a half smaller image size $(800\times 320$ vs. $1600\times 900)$ , and is $+1.6$ VPQ and 2.4 IoU higher than the latest fusion-based FusionAD [33]. + +Comparisons of methods implemented in the Lyft L5 dataset are shown in Tab. 2. StreamingFlow achieves the best of all metrics while surpassing baseline methods by a large margin: $+20.6$ IoU and $+23.5$ VPQ against STP3 [10]. Moreover, it surpasses our reproduced BEVFusion with lightweight encoders by $+2.3$ mIoU and 0.2 VPQ. + +# 4.4. Streaming Forecasting Results + +We design three experiments on nuScenes dataset for demonstration of the streaming occupancy prediction: (1) Extension of the prediction temporal horizons to unseen future; (2) Prediction at any desired future time point; (3) Data streams input at different frame rates. Experiments are con + +duced on models loaded from the checkpoints trained on standard instance forecasting tasks. + +Extension of the temporal horizons of unseen future. Tab. 3 shows the prediction result of StreamingFlow which extends the temporal horizons from 2.0s to 8.0s. Baselines reported in [1] are trained for different lengths of temporal horizons. StreamingFlow shows excellent performance in variable prediction length without retraining. Similar to prior arts which extend prediction horizons to farther future, StreamingFlow shows a similar gradual performance decay. We then compare zero-shot Streamingflow with the model trained with the longest future 8s groundtruth labels in Tab. 4. The zero-shot long-term prediction results are only $-0.9$ IoU and $-1.8$ VPQ less than fully supervised models, which demonstrates great generalization ability of foreseeing the unseen future. + +Streaming prediction at any desired time point. Since nuScenes do not provide labels for non-keyframes, we adopt the practice of MotionNet and interpolate the box instances between two adjacent keyframes. We randomly choose to predict at a list of time points and report the results in Tab. 5. To simply illustrate the capability, we designed the main task to predict uniformly spaced temporal horizons, but this framework can predict uneven and arbitrary future snapshots. The prediction results are stable generally. There is a slight decline as the forecast becomes denser. + +We provide demo videos as supplementary materials to show the effectiveness of streaming prediction. We provide a finer granularity of streaming perception at any future time. In the video, we visualize the prediction results every 0.05s from the current to the future 2s to 3s, with a total of 40 to 60 frames. + +Asynchronous multi-modal data streams as input. + +
MethodModalityImage backboneLiDAR backboneFuture Semantic Seg. IoU↑Future Instance Seg.
PQ↑SQ↑RQ↑
Static*CEffi-B4-32.227.670.139.1
FIERY*[9]CEffi-B4-37.030.270.242.9
StretchBEV[1]CEffi-B4-37.129.0--
BEVerse[34]CSwin-tiny-38.733.370.647.2
BEVerse[34]CSwin-small-40.836.170.751.1
ST-P3 Gaus.[10]CEffi-B4-38.631.770.245.2
ST-P3 Ber.[10]CEffi-B4-38.932.170.445.6
UniAD[11]CEffi-B4-40.233.5--
MotionNet[32]L-STPN37.238.975.651.4
BE-STI[30]L-BESTI-STPN40.141.075.554.3
StreamingFlow-tinyLCEffi-B4PillarNet47.846.175.860.8
StreamingFlow-smallLCEffi-B7PillarNet51.148.075.164.0
FusionAD[33]LCResNet-101VoxelNet51.551.1--
StreamingFlow-baseLCEffi-B4VoxelNet53.952.778.766.9
+ +Table 1. Comparison with the state-of-the-art methods for instance-aware occupancy flow prediction on nuScenes[2] validation set. 'C' denotes vision-only methods, 'L' denotes LiDAR-based methods, and 'LC' denotes a LiDAR-camera fusion methods. $*$ : reported in [9]. + +
MethodIoU↑PQ↑SQ↑RQ↑
Static*24.120.7--
Extrapolation model*24.821.2--
FIERY*[9]36.327.2--
ST-P3[10]36.332.471.145.5
BEVFusion-tiny†54.655.778.071.4
StreamingFlow-tiny56.955.978.171.6
+ +Table 2. Comparison with the state-of-the-art methods for future instance segmentation (2.0s) on Lyft L5 AV [14] validation set. $\star$ results reported in [9]. $\dagger$ : results of BEVFusion with LSS-based image encoder and pillar-based encoder reproduced by us. + +
MethodPredIoU↑PQ↑SQ↑RQ↑
FIERY2s35.829.0--
4s30.123.6--
6s26.720.9--
StretchBEV2s37.129.0--
4s32.523.8--
6s28.421.0--
StreamingFlow2s47.846.175.860.8
3s44.441.174.155.4
4s41.738.473.652.1
5s39.135.873.248.9
6s36.733.672.946.0
8s32.529.872.640.1
+ +We validate asynchronous data streams as input and standard occupancy forecasting as output. We test multiple settings of data stream frame rate and report the results in Tab. + +Table 3. Comparison of occupancy flow prediction for any temporal horizons. + +
Schedule2s3s4s6s8s
ZS.47.8/46.144.4/41.141.7/38.436.7/33.632.5/29.8
Sup.48.2/46.946.0/45.241.9/38.737.8/34.233.6/31.6
+ +Table 4. ZS: zero-shot inference of StreamingFlow. Sup: StreamingFlow trained with the longest prediction horizons 8s. Each value is given in the format of 'IoU/PQ'. + +
Prediction IntervalIoU↑PQ↑SQ↑RQ↑
0.547.846.175.860.8
0.2543.440.174.154.1
0.645.644.375.258.9
+ +6. The model performs the best when the inference uses the training configuration. Denser inputs lead to similar forecasting accuracy. + +Table 5. Prediction results at any desired intervals. For example, prediction at the interval of 0.6 means prediction at [0.6, 1.2, 1.8]. + +
LiDAR streamCam streamIoU↑PQ↑SQ↑RQ↑
5247.846.175.860.8
10247.645.875.660.5
10447.145.475.160.4
+ +Table 6. Prediction results with multi-modal data stream of different frame rates. Frame rates are shown in Hz. + +# 4.5. Ablation Study + +Effect of different fusion strategies. We compare SpatialGRU-ODE with fusion strategies at different stages and the implementation details are in supplementary + +material. As shown in Tab. 7, asynchronous fusion is inferior to synchronous fusion and SpatialGRU-ODE for both datasets. For nuScenes dataset, the ordinary temporally-synchronized fusion approach performs the best. SpatialGRU-ODE performs $-2.4$ IoU and $-0.9$ VPQ, slightly less than BEVFusion [20]. For Lyft dataset, SpatialGRU-ODE outperforms synchronized fusion. It performs $+2.3$ IoU and $+0.2$ VPQ more than BEVFusion [20]. + +
Fusion modeIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Spatial then temporal50.247.075.663.0
Temporal then spatial44.742.774.657.2
SpatialGRU-ODE47.846.175.860.8
Lyft L5 AV dataset
Spatial then temporal54.655.778.071.4
Temporal then spatial50.450.275.266.7
SpatialGRU-ODE56.955.978.171.9
+ +Effect of ODE solvers. ODE solvers are vital tools for a N-ODE framework. We test two basic ode solvers, Euler, and midpoint solver as compared in Tab. 8 on two datasets. In both cases, the midpoint solver yields superior VPQ, surpassing the Euler solver by 3.2 points on nuScenes dataset and 0.8 points on Lyft dataset. On nuScenes dataset, the midpoint solver shows similar IoU with the Euler solver, but on Lyft dataset, the midpoint solver performs worse semantic segmentation by $-1.9$ . + +Table 7. Comparison with the baseline fusion methods for future instance segmentation (2.0s) on nuScenes validation set. StreamingFlow-ODE is compared with different fusion modes. Spatial fusion is conducted in the same way as BEVFusion [20]. 'Spatial Then Temporal' is for synchronous mode, and 'Temporal Then Spatial' is for asynchronous mode. + +
ODE SolverIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Euler47.842.973.558.6
Midpoint47.846.175.860.8
Lyft L5 AV dataset
Euler56.955.978.171.5
Midpoint55.056.778.272.4
+ +Effect of ODE update intervals. We ablate different ODE update intervals which determine the minimum granularity of occupancy prediction. The ODE step is set to 0.05, 0.1, 0.5 and variable for comparison. Variable means the ODE step is the next timestamp minus the current timestamp. In general, the finer a single update is divided during the ODE update process, the higher the final prediction ac + +curacy. It is also intuitive that a higher update frequency may eliminate continuous errors. As shown in Tab. 9, the predictor with interval $0.05s$ surpasses interval $0.1s$ by 0.1 IoU and 3.1 VPQ, and interval $0.5s$ by 0.5 IoU and 3.1 VPQ. Remarkably, the variable time step update also shows nice performance, which is $+0.5$ IoU and $-2.2$ VPQ when compared to the predictor with ODE step $0.05s$ . A variable time step updater strikes a good balance between precision and inference speed, so it is more favorable for long-term prediction to 8s future. + +Table 8. Comparison with prediction using different ODE solvers. + +
StepIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
0.0547.846.175.860.8
0.147.743.073.758.4
0.547.342.173.357.4
Variable48.243.973.958.8
Lyft L5 dataset
0.0556.955.978.171.9
Variable54.053.577.469.7
+ +Table 9. Comparison of prediction under different ode steps. + +# 5. Conclusion + +We present StreamingFlow as the first practice for fusion-based streaming occupancy forecasting. Starting from the motivation of fusing and predicting from non-ideal data streams, the streaming feature brings a more flexible temporal scene understanding and generalizes occupancy forecasting well to any temporal horizon. The advantage of SpatialGRU-ODE is that it decouples the supervision in the training process and outputs in the inference process, by modeling the derivatives of BEV grids and propagating future grid states to required timestamps. We hope that this work will inspire more Neural-ODE applications and insights into the streaming automotive perception. + +# 6. Acknowledgement + +This work was supported in part by the National Natural Science Foundation of China under Grants (52372414, U22A20104, 52102464). 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Be-sti: Spatial-temporal integrated network for class-agnostic motion prediction with bidirectional enhancement. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 17093–17102, 2022. 2, 5, 6, 7 +[31] Sizhe Wei, Yuxi Wei, Yue Hu, Yifan Lu, Yiqi Zhong, Siheng Chen, and Ya Zhang. Asynchrony-robust collaborative perception via bird's eye view flow. Advances in Neural Information Processing Systems, 36, 2024. 2 +[32] Pengxiang Wu, Siheng Chen, and DImitris N. Metaxas. MotionNet: Joint Perception and Motion Prediction for Autonomous Driving Based on Bird's Eye View Maps. Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pages 11382-11392, 2020. 2, 7 +[33] Tengju Ye, Wei Jing, Chunyong Hu, Shikun Huang, Lingping Gao, Fangzhen Li, Jingke Wang, Ke Guo, Wencong Xiao, Weibo Mao, et al. Fusionad: Multi-modality fusion for prediction and planning tasks of autonomous driving. arXiv preprint arXiv:2308.01006, 2023. 1, 2, 6, 7 +[34] Yunpeng Zhang, Zheng Zhu, Wenzhao Zheng, Junjie Huang, Guan Huang, Jie Zhou, and Jiwen Lu. Beverse: Unified perception and prediction in birds-eye-view for vision-centric autonomous driving. arXiv preprint arXiv:2205.09743, 2022. 2, 5, 6, 7 \ No newline at end of file diff --git a/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/images.zip b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..d6f00b6dd3b842b3bb9aa83e0ce4d31995539481 --- /dev/null +++ b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:7fc9f72fc042e2d228dc29c48ceca77ad2746226439c6c54450012d1ccfe53d4 +size 609332 diff --git a/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/layout.json b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..771a1d838e99f0a5176cbc87bbcfb5afd0891ccb --- /dev/null +++ b/2024/StreamingFlow_ Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation/layout.json @@ -0,0 +1,8119 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 78, + 103, + 517, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 103, + 517, + 140 + ], + "spans": [ + { + "bbox": [ + 78, + 103, + 517, + 140 + ], + "type": "text", + "content": "StreamingFlow: Streaming Occupancy Forecasting with Asynchronous Multi-modal Data Streams via Neural Ordinary Differential Equation" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "spans": [ + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": "Yining Shi" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1,3*}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " Kun Jiang" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " Ke Wang" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " Jiusi Li" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " Yunlong Wang" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " Mengmeng Yang" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " Dange Yang" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1\\dagger}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " School of Vehicle and Mobility, Tsinghua University " + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " KargoBot, Inc " + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "inline_equation", + "content": "^{3}" + }, + { + "bbox": [ + 54, + 160, + 538, + 191 + ], + "type": "text", + "content": " DiDi Chuxing" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "spans": [ + { + "bbox": [ + 143, + 217, + 192, + 229 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 45, + 243, + 290, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 243, + 290, + 542 + ], + "spans": [ + { + "bbox": [ + 45, + 243, + 290, + 542 + ], + "type": "text", + "content": "Predicting the future occupancy states of the surrounding environment is a vital task for autonomous driving. However, current best-performing single-modality methods or multi-modality fusion perception methods are only able to predict uniform snapshots of future occupancy states and require strictly synchronized sensory data for sensor fusion. We propose a novel framework, StreamingFlow, to lift these strong limitations. StreamingFlow is a novel BEV occupancy predictor that ingests asynchronous multisensor data streams for fusion and performs streaming forecasting of the future occupancy map at any future times-tamps. By integrating neural ordinary differential equations (N-ODE) into recurrent neural networks, StreamingFlow learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV features as part of the fusion process, and propagates BEV states to the desired future time point. It shows good zero-shot generalization ability of prediction, reflected in the interpolation of the observed prediction time horizon and the reasonable inference of the unseen farther future period. Extensive experiments on two large-scale datasets, nuScenes [2] and Lyft L5 [14], demonstrate that StreamingFlow significantly outperforms previous vision-based, LiDAR-based methods, and shows superior performance compared to state-of-the-art fusion-based methods." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 567, + 128, + 578 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 567, + 128, + 578 + ], + "spans": [ + { + "bbox": [ + 47, + 567, + 128, + 578 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 587, + 287, + 684 + ], + "type": "text", + "content": "Occupancy grid is gaining more traction in the self-driving community, due to its versatility in downstream tasks, e.g., irregularly shaped object representation, robot navigation, etc. With the help of modern deep learning technologies, occupancy grid maps (OGMs) have evolved significantly. For example, not just LiDAR point clouds, camera images can now be used to construct high-quality occupancy grid maps [26]. In addition to its fine-grained geometric infor" + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 315, + 217, + 538, + 380 + ], + "blocks": [ + { + "bbox": [ + 315, + 217, + 538, + 380 + ], + "lines": [ + { + "bbox": [ + 315, + 217, + 538, + 380 + ], + "spans": [ + { + "bbox": [ + 315, + 217, + 538, + 380 + ], + "type": "image", + "image_path": "7b84382c7eea5f301e3a763ecea1acb2762dbc9325fe17705b76498bcaff359d.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 388, + 545, + 422 + ], + "lines": [ + { + "bbox": [ + 305, + 388, + 545, + 422 + ], + "spans": [ + { + "bbox": [ + 305, + 388, + 545, + 422 + ], + "type": "text", + "content": "Figure 1. Comparison between conventional synchronized BEV fusion (top) and our asynchronous BEV fusion (bottom). We formulate fusion with an update-predict-update approach." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 436, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 533 + ], + "type": "text", + "content": "mation, occupancy grids can also represent rich semantic and motion cues [1, 9-11]. Such cues grant occupancy networks the ability to predict the occupancy state of the environment at desired future timestamps. While trajectory forecasting only contains object-level information, the occupancy grid conveys a much more comprehensive understanding of the surrounding environment, which is the key to achieving better intelligence and driving safety." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": "Despite the great potential of occupancy-based prediction, we notice that existing methods can only predict at fixed frequencies [1, 9-11, 33]. This comes from the fact that sensors sample the environment at predetermined frequencies, e.g., motors in mechanical LiDARs spin at " + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "inline_equation", + "content": "10\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 534, + 546, + 713 + ], + "type": "text", + "content": " and many cameras captures images at 30FPS. Thus, previous algorithms predict at the same intervals as they are trained with ground-truth labels of future intervals. If future occupancy can be predicted at any given timestamps in a continuous manner, self-driving algorithms can have shorter latency and more rapid responses. Streaming forecasting can also relax the sensor synchronization constraints, as the continuous forecasting model can update the prediction as new sensory data come in. Compared with discrete snapshot-based prediction, streaming motion forecast" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 57, + 693, + 217, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 693, + 217, + 703 + ], + "spans": [ + { + "bbox": [ + 57, + 693, + 217, + 703 + ], + "type": "text", + "content": "*Work done during internship at DiDi Chuxing." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 57, + 703, + 220, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 57, + 703, + 220, + 713 + ], + "spans": [ + { + "bbox": [ + 57, + 703, + 220, + 713 + ], + "type": "text", + "content": "† Corresponding author: Kun Jiang, Dange Yang." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14833" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 211, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 211, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 211, + 83 + ], + "type": "text", + "content": "ing [24] naturally has safety advantages." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 85, + 286, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 85, + 286, + 216 + ], + "spans": [ + { + "bbox": [ + 46, + 85, + 286, + 216 + ], + "type": "text", + "content": "We noticed several challenges in fulfilling such a streaming forecasting paradigm. Firstly, sensory data and ground truth annotations are collected at a fixed frequency. Streaming forecasting aims to achieve temporally dense and continuous prediction, with data only sparsely and uniformly sampled in the temporal domain. Secondly, mainstream network architectures are not designed for such streaming requirements. Forecasting at any given timestamp requires delicate modeling of the temporal dynamics, but how to embed the temporal dynamics into the widely adopted BEV feature representation remains under-explored." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 217, + 286, + 337 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 217, + 286, + 337 + ], + "spans": [ + { + "bbox": [ + 46, + 217, + 286, + 337 + ], + "type": "text", + "content": "To this end, we propose to use the neural ordinary differential equation (N-ODE) framework for such temporal dynamics modeling. N-ODE is originally proposed for learning continuous implicit processes in dynamic systems. In our application, by representing the continuous motion trends of the driving scenarios into a time series of implicit spatial BEV features, the neural ODE framework not only allows streaming occupancy predictions on any temporal horizon with one fixed model, but also relaxes the sensor synchronization constraints." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 338, + 286, + 480 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 286, + 480 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 286, + 480 + ], + "type": "text", + "content": "With such flexibility, we propose a novel method, StreamingFlow, that performs asynchronous multi-modal sensor fusion to achieve streaming occupancy forecasting. Toward the goal of streaming modeling of temporal BEV features, StreamingFlow integrates neural ordinary differential equations (N-ODE) onto wrapped-based recurrent neural networks. It learns derivatives of BEV features over temporal horizons, updates the implicit sensor's BEV feature as part of the fusion process, and propagates BEV states to the desired future time point. A graphical illustration of fusion strategies between conventional BEV-based fusion and ours is illustrated in Fig. 1." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 482, + 257, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 482, + 257, + 493 + ], + "spans": [ + { + "bbox": [ + 59, + 482, + 257, + 493 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 494, + 286, + 613 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 48, + 494, + 286, + 528 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 494, + 286, + 528 + ], + "spans": [ + { + "bbox": [ + 48, + 494, + 286, + 528 + ], + "type": "text", + "content": "1. To the best of our knowledge, we propose the first streaming occupancy flow prediction framework that supports asynchronous multi-sensor fusion;" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 529, + 286, + 564 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 529, + 286, + 564 + ], + "spans": [ + { + "bbox": [ + 47, + 529, + 286, + 564 + ], + "type": "text", + "content": "2. We design a novel temporal feature propagation strategy that achieves high performance on dense continuous occupancy prediction with only temporally sparse labels;" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 566, + 286, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 286, + 613 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 286, + 613 + ], + "type": "text", + "content": "3. Our proposed method achieves state-of-the-art performance on the widely used nuScenes [2] and Lyft L5 [14] datasets, validating the effectiveness and robustness of our proposed algorithms." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 47, + 626, + 138, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 626, + 138, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 626, + 138, + 639 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 647, + 176, + 659 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 176, + 659 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 176, + 659 + ], + "type": "text", + "content": "2.1. Occupancy forecasting" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 286, + 713 + ], + "type": "text", + "content": "Occupancy flow prediction, first proposed in [23], is a valuable supplement to trajectory-set prediction [3, 22]. The advantages of occupancy flow are a non-parametric distribution output and fine-grained grid flow. Recent LiDAR-" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 72, + 545, + 360 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 360 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 360 + ], + "type": "text", + "content": "based methods [21, 30, 32] attach displacement vectors to non-empty BEV grids to describe short-term motion in future 1.0s. These networks typically have a BEV-based spatial-temporal backbone and several shared heads that indicate the classification, motion, and displacement of each grid. STPN [32] and BE-STI [30] are effective BEV-based spatial-temporal feature extractors for binary-occupied grids which consist of only 2D convolutional blocks. Vision-centric pipelines usually formulate the prediction task as future instance segmentation on BEV grids. FIERY [9] is the first vision-centric stochastic future prediction method. StretchBEV [1] uses a variational autoencoder for decoupling learning of temporal dynamics and BEV decoder. End-to-end driving frameworks [10, 11, 33, 34] conduct planning based on occupancy prediction. UniAD [11] and TBP-Former [6] models temporal future with video transformers. One major bottleneck of video transformers is prediction of long-term sequence length [28]. Position encoding enables video transformer to interpolate shorter sequences but few video transformers can generalize to the unseen longer sequence length. Unlike all prior works that predict discrete near-future snapshots, We focus on the streaming flow prediction which adapt the predictor to a more distant future and finer granularity." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 365, + 504, + 379 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 365, + 504, + 379 + ], + "spans": [ + { + "bbox": [ + 306, + 365, + 504, + 379 + ], + "type": "text", + "content": "2.2. Multi-sensor Spatial-temporal Fusion" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 384, + 545, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 384, + 545, + 635 + ], + "spans": [ + { + "bbox": [ + 304, + 384, + 545, + 635 + ], + "type": "text", + "content": "Spatial multi-modal fusion is widely investigated in the feature level. BEVFusion and its variants [7, 8, 20] combine multi-modal input features in a shared BEV space. [4, 16] support feature interaction in 3D voxel space. Temporal fusion is a common aggregator for perception tasks. LiDAR-based networks [30, 32] typically employ data-level temporal fusion, which transforms multi-frame point clouds to the current ego's coordinate as inputs via ego pose or registration methods. Most vision-centric methods align the BEV feature maps from multiple time steps based on ego pose, and then concatenate them for fusion [9, 12, 17, 25] or support their interactions of multi-frame BEV features through attention [13, 18, 27]. Prior spatial fusion methods usually assume strict synchronization. CoBEVFlow [31] is most similar to our approach in that they predict BEV flow to interpolate asynchronous data timestamps from roadside unit to vehicle system, but short-term flow information cannot support long-term prediction. To this end, we provide a flexible spatio-temporal fusion framework which predicts the future frames and triggers update process as fusion when asynchronous sensor data arrives." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 649, + 388, + 663 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 649, + 388, + 663 + ], + "spans": [ + { + "bbox": [ + 306, + 649, + 388, + 663 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 670, + 383, + 681 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 383, + 681 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 383, + 681 + ], + "type": "text", + "content": "3.1. Framework" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 713 + ], + "type": "text", + "content": "The pipeline of StreamingFlow is depicted in Fig. 2. Given multi-modal data streams from the previous few seconds," + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14834" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 69, + 519, + 208 + ], + "blocks": [ + { + "bbox": [ + 72, + 69, + 519, + 208 + ], + "lines": [ + { + "bbox": [ + 72, + 69, + 519, + 208 + ], + "spans": [ + { + "bbox": [ + 72, + 69, + 519, + 208 + ], + "type": "image", + "image_path": "1fc171bf9fb2ba64ca5df4aab6be3a4ad7dd79ffad212b24c7dcaab73f19e7ac.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 216, + 547, + 251 + ], + "lines": [ + { + "bbox": [ + 46, + 216, + 547, + 251 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 547, + 251 + ], + "type": "text", + "content": "Figure 2. The framework of StreamingFlow. Raw data streams are encoded to BEV features, respectively. The SpatialGRU-ODE process operates on the timeline with two stages split by the present timestamp, asynchronous multi-sensor deep feature via the SpatialGRU-ODE update process and continuous occupancy flow prediction via SpatialGRU-ODE predict process." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 260, + 289, + 416 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 260, + 289, + 416 + ], + "spans": [ + { + "bbox": [ + 46, + 260, + 289, + 416 + ], + "type": "text", + "content": "the task is defined as predicting the future several seconds' instance occupancy and flow on uniformly-shaped BEV grids. The framework includes three phases: 1) BEV encoders for LiDAR and camera branches, respectively, 2) asynchronous multi-sensor fusion, and 3) streaming occupancy prediction. As the data stream runs, modality-specific encoders map raw data to BEV features. The BEV state starts from zeroed features and fuses every incoming BEV feature in a trigger mode instead of a matching mode in conventional fusion. The BEV state propagates until a new BEV feature is received. The incoming BEV feature is fused to the BEV state and state continues to propagate until next incoming observation." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 417, + 287, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 417, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 46, + 417, + 287, + 548 + ], + "type": "text", + "content": "The SpatialGRU-ODE is the core for streaming prediction. The SpatialGRU-ODE iterates for ODE steps, updates when a new measurement occurs within a certain ODE step, and performs future prediction. In the training stage, the loss comes from the supervision of decoded BEV grids at the timestamps with labels, as well as an auxiliary probabilistic loss from Kullback-Leibler divergence (KLD) between updated BEV features and latent observations. In the inference process, SpatialGRU-ODE predicts via a variable ODE step only related to the required timestamps for evaluation and application." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 550, + 288, + 586 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 550, + 288, + 586 + ], + "spans": [ + { + "bbox": [ + 46, + 550, + 288, + 586 + ], + "type": "text", + "content": "The BEV decoder, loss functions, and post-processing techniques follow standard practices, and we leave the details in the supplementary materials." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 597, + 139, + 609 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 597, + 139, + 609 + ], + "spans": [ + { + "bbox": [ + 47, + 597, + 139, + 609 + ], + "type": "text", + "content": "3.2. BEV Encoders" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "spans": [ + { + "bbox": [ + 46, + 616, + 287, + 688 + ], + "type": "text", + "content": "LiDAR branch. We adopt the popular pillar representations for point cloud features. We observed that a very lightweight pillar-net encoder is sufficient for high accuracy. Heavier backbones consisting of sparse convolutional modules or voxel transformers can be trivially integrated for performance at the cost of additional computation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 288, + 714 + ], + "type": "text", + "content": "Camera branch. As a baseline for algorithms aligned with previous work, we adopt the Lift-splat-shoot" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 260, + 547, + 309 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 260, + 547, + 309 + ], + "spans": [ + { + "bbox": [ + 304, + 260, + 547, + 309 + ], + "type": "text", + "content": "(LSS [26]) settings with depth supervision for depth-based view transformation. We adopt accelerated BEV pool operators to speed up the inference stage. Other BEV mapping methods are trivially compatible with our framework." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 314, + 414, + 327 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 314, + 414, + 327 + ], + "spans": [ + { + "bbox": [ + 306, + 314, + 414, + 327 + ], + "type": "text", + "content": "3.3. SpatialGRU-ODE" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "spans": [ + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "text", + "content": "Gate Recurrent Unit (GRU) consists of reset gate " + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "inline_equation", + "content": "(r_t)" + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "text", + "content": ", update gate " + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "inline_equation", + "content": "(z_t)" + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "text", + "content": ", and update vector " + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "inline_equation", + "content": "(g_t)" + }, + { + "bbox": [ + 304, + 332, + 547, + 368 + ], + "type": "text", + "content": ". The update process follows the formula," + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 347, + 372, + 463, + 384 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 372, + 463, + 384 + ], + "spans": [ + { + "bbox": [ + 347, + 372, + 463, + 384 + ], + "type": "interline_equation", + "content": "r _ {t} = \\sigma \\left(W _ {r} x _ {t} + U _ {r} h _ {t - 1} + b _ {r}\\right)", + "image_path": "e8b7f6f2921b0b07bab1cfa1095f37fa9e08f0bf50cb6c8e36359110b5af6bbe.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 347, + 386, + 545, + 398 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 386, + 545, + 398 + ], + "spans": [ + { + "bbox": [ + 347, + 386, + 545, + 398 + ], + "type": "interline_equation", + "content": "z _ {t} = \\sigma \\left(W _ {z} x _ {t} + U _ {z} h _ {t - 1} + b _ {z}\\right) \\tag {1}", + "image_path": "59f0ea741e23daf14c8a961f93496ebab218cc19b397e657970818773d57dc2d.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 347, + 400, + 504, + 412 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 347, + 400, + 504, + 412 + ], + "spans": [ + { + "bbox": [ + 347, + 400, + 504, + 412 + ], + "type": "interline_equation", + "content": "g _ {t} = \\tanh \\left(W _ {h} x _ {t} + U _ {h} \\left(r _ {t} \\odot h _ {t - 1}\\right) + b _ {h}\\right)", + "image_path": "bd9a99e018fbabffb6418936ed5e03acaedc5663f105d9a32f4873803be11818.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": "Neural-ODE on GRU blocks focuses N-ODE's ability to model continuous time series given sporadic sensor data coming from non-uniform time intervals. SpatialGRU-ODE is highly inspired by GRU-ODE-Bayes [5], which serves as the foundation component of the proposed spatiotemporal fusion and flow predictor. Eq. (1) formulates the general process of GRU blocks. With regard to " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " as a BEV feature, SpatialGRU has its state variable " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " with shape " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "[B, C, H, W]" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "B, C, H, W" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " are the batch size, embedded dims, height, and width. " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " is the sigmoid function, and " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "\\tanh" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " denotes a CNN block in SpatialGRU settings. " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "x_t" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " is the input state at timestamp " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " with the same shape as " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": ". For simplicity, the update gate " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "W_r = U_r" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": ", the reset gate " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "W_z = U_z" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": ", and the GRU init bias " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "b_r = b_z" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "r_t \\odot h_{t-1}" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " is the matrix multiplication between reset gate and state. In summary, the update state " + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "inline_equation", + "content": "h_t" + }, + { + "bbox": [ + 304, + 415, + 545, + 608 + ], + "type": "text", + "content": " is calculated as," + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 333, + 612, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 333, + 612, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 333, + 612, + 545, + 624 + ], + "type": "interline_equation", + "content": "h _ {t} = z _ {t} \\cdot h _ {t - 1} + \\left(1 - z _ {t}\\right) \\cdot g _ {t} = G R U \\left(h _ {t - 1}, g _ {t}\\right) \\tag {2}", + "image_path": "cb13bcbae418148e49c0d0b59bb9c5662b9aabd9b224ff00ca2dea9152725a69.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 628, + 545, + 640 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 628, + 545, + 640 + ], + "spans": [ + { + "bbox": [ + 306, + 628, + 545, + 640 + ], + "type": "text", + "content": "The amount of change of the state variable is calculated as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 654, + 545, + 677 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 654, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 320, + 654, + 545, + 677 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\Delta h _ {t} = h _ {t} - h _ {t - 1} = z _ {t} \\cdot h _ {t - 1} + (1 - z _ {t}) \\cdot g _ {t} - h _ {t - 1} \\tag {3} \\\\ = \\left(1 - z _ {t}\\right) \\cdot \\left(g _ {t} - h _ {t - 1}\\right) \\\\ \\end{array}", + "image_path": "da4631a538045dd3e146d6974b55eb5b537ebfc794634462a949124d711aa6d8.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 681, + 522, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 681, + 522, + 693 + ], + "spans": [ + { + "bbox": [ + 306, + 681, + 522, + 693 + ], + "type": "text", + "content": "The derivatives of the state variable are calculated as:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 358, + 695, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 695, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 358, + 695, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\frac {\\Delta h (t)}{d t} = (1 - z (t)) \\cdot (g (t) - h (t)) \\tag {4}", + "image_path": "4e8fe572240275a99a7f9a44daff3eba9df21f0f6730e4ab5aaf021668f7c788.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14835" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "code", + "bbox": [ + 47, + 99, + 287, + 363 + ], + "blocks": [ + { + "bbox": [ + 48, + 83, + 258, + 96 + ], + "lines": [ + { + "bbox": [ + 48, + 83, + 258, + 96 + ], + "spans": [ + { + "bbox": [ + 48, + 83, + 258, + 96 + ], + "type": "text", + "content": "Algorithm 1 The pseudo-code of SpatialGRU-ODE" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "code_caption" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "lines": [ + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "spans": [ + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": "Input: state-timestamp pairs " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "[t,m[t]],t\\in [t_0,\\dots,t_{present}]" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " ODE step " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "\\Delta t" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \nOutput: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "loss_{KLD}" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " , state-timestamp pairs " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "[t,h[t]],t\\in" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "[t_0,\\dots,t_{present},\\dots,t_{future}]" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " 1: Initialize current time " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "T = t_0" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " KL divergence loss " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "loss_{KLD} = 0" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " , current state feature " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "h = h_0" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n2: for " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "t_{obs}" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "[t_0,\\dots,t_{present}]" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " do \n3: while " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "T < t_{obs}" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " do \n4: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "h = \\mathrm{ODE\\_Predict}(h,\\Delta t)" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n5: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "T + = \\Delta t" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n6: end while \n7: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "h,loss = \\mathrm{ODE\\_Update}(h,m[t_{obs}])" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n8: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "loss_{KLD} + = loss" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n9: save " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "h[t_{obs}] = h" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n10: end for \n11: for " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "t_{predict}" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "[t_{present} + 1,\\dots,t_{future}]" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " do \n12: while " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "T < t_{predict}" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " do \n13: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "h = \\mathrm{ODE\\_Predict}(h,\\Delta t)" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n14: " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "T + = \\Delta t" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n15: end while \n16: save " + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "inline_equation", + "content": "h[t_{predict}] = h" + }, + { + "bbox": [ + 47, + 99, + 287, + 363 + ], + "type": "text", + "content": " \n17: end for" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "code_body" + } + ], + "index": 1, + "sub_type": "algorithm" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "spans": [ + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": "GRU-ODE-Bayes has proven the convergence of this process, as is also applicable to the initial state of SpatialGRU-ODE. If " + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "inline_equation", + "content": "h_0 \\in [-1, 1]" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": ", then " + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "inline_equation", + "content": "h_j(t) \\in [-1, 1]" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": " is the index of elements in " + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "inline_equation", + "content": "h(t)" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": ", as " + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\left.\\frac{dh(t)_j}{dt}\\right|_{t: h(t)_j = 1} \\leq 0" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "inline_equation", + "content": "\\left.\\frac{dh(t)_j}{dt}\\right|_{t: h(t)_j = -1} \\geq 0" + }, + { + "bbox": [ + 47, + 387, + 287, + 461 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 461, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 461, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 461, + 287, + 555 + ], + "type": "text", + "content": "N-ODE has several nice properties when implemented on GRU models. The learned parametric derivative makes training not constrained by supervision from fixed future timestamps states, which greatly increases flexibility. On the other hand, unlike RNNs, which require emission intervals for updating, the GRU-ODE continuously defined dynamic model can naturally combine data observed at any given time." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": "The pseudo-code for SpatialGRU-ODE is shown in Algorithm 1. Given state-timestamp pairs " + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "inline_equation", + "content": "[t, m[t]]" + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": " from previous multisensor features, The expected output is the states " + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "inline_equation", + "content": "[t, h[t]]" + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": " of each measured past timestamp and anticipated future timestamp " + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "inline_equation", + "content": "t \\in [t_0, \\dots, t_{\\text{present}}, \\dots, t_{\\text{future}}}" + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": ". The ode step may be variable or constant. During the update procedure, a KL divergence loss " + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "inline_equation", + "content": "loss_{KLD}" + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": " is gathered to quantify the similarity between updated state feature " + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": " and observed feature " + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "inline_equation", + "content": "m[t_{obs}]" + }, + { + "bbox": [ + 47, + 556, + 287, + 665 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 671, + 258, + 685 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 671, + 258, + 685 + ], + "spans": [ + { + "bbox": [ + 47, + 671, + 258, + 685 + ], + "type": "text", + "content": "3.4. Asynchronous Modality-agnostic Fusion" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "Asynchronous modality-agnostic fusion attempts to fuse Li-DAR and camera BEV features in a way similar to the" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 119 + ], + "type": "text", + "content": "Beyasian predict-then-update process. The proposed strategy is able to eliminate two crucial limits for multi-sensor fusion, which are strict multi-modal synchronizations and fixed interval data flow." + } + ] + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 317, + 131, + 534, + 276 + ], + "blocks": [ + { + "bbox": [ + 317, + 131, + 534, + 276 + ], + "lines": [ + { + "bbox": [ + 317, + 131, + 534, + 276 + ], + "spans": [ + { + "bbox": [ + 317, + 131, + 534, + 276 + ], + "type": "image", + "image_path": "e14a5b1d9b60760d9d1ead4b364e17927f63b3b96d6e7b34f5a4380868841a5f.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 285, + 546, + 308 + ], + "lines": [ + { + "bbox": [ + 305, + 285, + 546, + 308 + ], + "spans": [ + { + "bbox": [ + 305, + 285, + 546, + 308 + ], + "type": "text", + "content": "Figure 3. Illustration of the measurement update process of SpatialGRU-ODE in temporal-agnostic fusion." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "spans": [ + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "content": "Fig. 3 presents the network structure for the SpatialGRU-ODE update process. After raw data is encoded to BEV maps by different BEV encoders, BEV features from different modalities are agnostic on the source, ordered chronologically, and formulated as multiple timestamp-BEV-feature pairs " + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "inline_equation", + "content": "[t,h_t]" + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "content": ". The output retains the same shape as the input, but the hidden features are as " + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "inline_equation", + "content": "\\frac{1}{4}" + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "content": " size of the input for the sake of eliminating memory storage. In order not to degrade the ultimate performance, both state and observation in BEV feature space with shape " + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "inline_equation", + "content": "[B,C,H,W]" + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "content": " are implicitly encoded into a smaller feature space " + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "inline_equation", + "content": "[B,C,H/4,W/4]" + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "content": " and finally implicit decoded in the same way for occupancy flow decoder. The temporal propagator runs the subsequent ODE step till the arrival of the next observation. When a new observation occurs, the predicted state and new observation are processed into the distribution module with CNN blocks to obtain the mean and variance of BEV features both with the size " + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "inline_equation", + "content": "[1,H/4,W/4]" + }, + { + "bbox": [ + 304, + 324, + 546, + 587 + ], + "type": "text", + "content": ". Means and variances of both features are estimated using KL divergence, an auxiliary loss that reflects the similarity between predicted and measured characteristics. Probabilistic auxiliary loss is calculated as follows:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 340, + 597, + 545, + 632 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 597, + 545, + 632 + ], + "spans": [ + { + "bbox": [ + 340, + 597, + 545, + 632 + ], + "type": "interline_equation", + "content": "\\operatorname {l o s s} _ {K L D} = \\sum_ {j = 1} ^ {H \\times W} D _ {K L} \\left(p _ {\\text {s t a t e}, j} \\| p _ {\\text {m e a s}, j}\\right) \\tag {5}", + "image_path": "2583ddce5954cf440ddbb86d033c5cedd67ce343815e702365df59ef2d2ae1bc.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 713 + ], + "type": "text", + "content": "The core module for the updated BEV feature is a dual-pathway SpatialGRU module, which first propagates the observed and predicted features respectively, then mixes the two hidden states distributions and finally undergoes the weighted summation of two features after the trusting gate and softmax function to generate the final new state." + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14836" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 246, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 246, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 246, + 85 + ], + "type": "text", + "content": "3.5. Streaming Occupancy Flow Predictor" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 92, + 287, + 189 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 92, + 287, + 189 + ], + "spans": [ + { + "bbox": [ + 46, + 92, + 287, + 189 + ], + "type": "text", + "content": "The occupancy flow predictor handles multi-frame BEV features from past and present timestamp-agnostic fusion as input and propagates to future steps in an ODE-enabled variational recurrent neural network. Particularly, the granularity of temporal prediction is decoupled from the training granularity and only related to the minimal ODE step in this method. If we set the variable ODE step, the prediction enables arbitrary granularity." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 56, + 202, + 269, + 326 + ], + "blocks": [ + { + "bbox": [ + 56, + 202, + 269, + 326 + ], + "lines": [ + { + "bbox": [ + 56, + 202, + 269, + 326 + ], + "spans": [ + { + "bbox": [ + 56, + 202, + 269, + 326 + ], + "type": "image", + "image_path": "345e8d046350eae63292687e4b3c056783bc03772cb1d61d99af6b7c66933626.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 334, + 289, + 357 + ], + "lines": [ + { + "bbox": [ + 46, + 334, + 289, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 334, + 289, + 357 + ], + "type": "text", + "content": "Figure 4. Illustration of streaming prediction process of SpatialGRU-ODE." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "spans": [ + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "text", + "content": "Fig. 4 illustrates the SpatialGRU-ODE procedure. Similar to the update process, the states are implicitly encoded into a smaller feature space. Except for the initial input which is the first BEV feature, the input with shape " + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "inline_equation", + "content": "[H / 4,W / 4,C]" + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "text", + "content": " is inherited from the last ODE step. The core module, SpatialGRU-ODE, computes the derivatives of BEV features in unit time intervals via a recurrent block specified in Eq. (4). SpatialGRU-ODE may employ either Euler or Midpoint solver for the update and fixed or variable ODE time step. To obtain the projected states, the derivatives are multiplied by delta time " + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "inline_equation", + "content": "dt" + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "text", + "content": " and added to the initial states. A CNN block is used to infer the next input from the current state in order to make the subsequent prediction. Only states near to the needed timestamps with supervision (closer than half of the minimum ode step) are preserved and decoded in the BEV decoder for supervision. Thus, the prediction time step " + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "inline_equation", + "content": "dt" + }, + { + "bbox": [ + 46, + 373, + 287, + 601 + ], + "type": "text", + "content": " is not always constant and uniform, and supervision signals are not required for each future timestamp." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 619, + 128, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 619, + 128, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 619, + 128, + 633 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 286, + 714 + ], + "type": "text", + "content": "In this section, we seek to answer two questions with the following experiments: (1) Whether the model works as well as published state-of-the-art algorithms for standard occupancy forecasting tasks. (2) Whether we are able to generalize to streaming forecasting settings with one model trained with temporally-sparse occupancy labels." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 72, + 427, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 72, + 427, + 83 + ], + "spans": [ + { + "bbox": [ + 306, + 72, + 427, + 83 + ], + "type": "text", + "content": "4.1. Datasets and Metrics" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "spans": [ + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "type": "text", + "content": "The NuScenes [2] dataset is a public large-scale autonomous driving dataset collected by Motional. NuScenes dataset provides a full sensor suite including 1 top LiDAR, 6 cameras, 5 radars, GPS, and IMU, with " + }, + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "type": "text", + "content": " coverage of the surroundings. It contains 1000 scenes, each lasting 20 seconds, of which annotations of 850 scenes at " + }, + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "type": "inline_equation", + "content": "2\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 90, + 545, + 198 + ], + "type": "text", + "content": " are available. We use the training and validation splits as same as previous works [1, 9, 10, 30, 34], with 28130 samples for training and 6019 samples for validation." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "spans": [ + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "content": "The Lyft L5 dataset [14] is another large-scale autonomous dataset provided by Lyft. This dataset contains 180 scenes, each lasting 25-45s in length and annotated at " + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "inline_equation", + "content": "5\\mathrm{Hz}" + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "content": ". We use 6 ring cameras and the top LiDAR from its sensor suite, which has a " + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "inline_equation", + "content": "360^{\\circ}" + }, + { + "bbox": [ + 304, + 198, + 545, + 293 + ], + "type": "text", + "content": " field of view. We use training and validation splits from the practice of FIERY [9], which include 16000 training samples and 4000 validation samples." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 293, + 545, + 377 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 545, + 377 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 545, + 377 + ], + "type": "text", + "content": "The occupancy flow prediction is formulated as a video panoptic prediction task [15]. We use Intersection over Union (IoU) to measure the semantic segmentation quality of each frame, and video panoptic quality (PQ), recognition quality (RQ), and segmentation quality (SQ) to measure both the accuracy and consistency of instance segmentation. VPQ is computed as:" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 335, + 385, + 545, + 449 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 335, + 385, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 335, + 385, + 545, + 449 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathrm {V P Q} = \\sum_ {t = 0} ^ {H} \\frac {\\sum_ {\\left(p _ {t} , q _ {t}\\right) \\cdot T P _ {t}} \\operatorname {I o U} \\left(p _ {t} \\cdot q _ {t}\\right)}{\\left| T P _ {t} \\right| + \\frac {1}{2} \\left| F P _ {t} \\right| + \\frac {1}{2} \\left| F N _ {t} \\right|} \\tag {6} \\\\ = \\sum_ {t = 0} ^ {H} \\frac {\\left| T P _ {t} \\right|}{\\left| T P _ {t} \\right| + \\frac {1}{2} \\left| F P _ {t} \\right| + \\frac {1}{2} \\left| F N _ {t} \\right|} = \\mathrm {S Q} \\cdot \\mathrm {R Q} \\\\ \\end{array}", + "image_path": "dd77a074f41ea7230b87c0eecf26fb798b99650979ada2aa5686d1516eac8740.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 455, + 440, + 468 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 440, + 468 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 440, + 468 + ], + "type": "text", + "content": "4.2. Implementation Details" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 533 + ], + "type": "text", + "content": "Task details. The standard occupancy prediction task is to take the past 1.0s sensor data for input, which is 3 keyframes in nuScenes (5 keyframes in Lyft), predict the motion in the future 2s, which is 4 keyframes in nuScenes and 10 keyframes in Lyft." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "content": "Data details. The BEV occupancy labels are from 3D bounding boxes labels projected to BEV. The perception range is set as " + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "inline_equation", + "content": "[100m, 100m]" + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "content": " and the grid resolution is set as " + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "inline_equation", + "content": "0.5m" + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "content": ". Images are resized to " + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "inline_equation", + "content": "224 \\times 480" + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "content": " pixels for each frame. Each point cloud is densified by aggregating point clouds of adjacent sweeps. Point clouds are voxelized to " + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "inline_equation", + "content": "200 \\times 200 \\times 13" + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "content": " voxels. StreamingFlow adopts an asynchronous data stream as input, with LiDAR streams every 0.2s and camera streams every 0.5s as input. For larger models fairly compared with the state-of-the-art, we use images with size " + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "inline_equation", + "content": "320 \\times 800" + }, + { + "bbox": [ + 304, + 534, + 545, + 677 + ], + "type": "text", + "content": " and aggregated LiDAR streams, each with 10 sweeps." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "Model details. The framework is implemented on Pytorch 1.10.2 and Pytorch Lightning 1.2.5. The optimizer is AdamW with a learning rate of " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "1e - 4" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": ". The learning strategy" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "14837" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 48, + 69, + 236, + 231 + ], + "blocks": [ + { + "bbox": [ + 48, + 69, + 236, + 231 + ], + "lines": [ + { + "bbox": [ + 48, + 69, + 236, + 231 + ], + "spans": [ + { + "bbox": [ + 48, + 69, + 236, + 231 + ], + "type": "image", + "image_path": "47d7983c3d8d3aec94297de1ce45062ae6703f7363e69f67d3a08a60e30ef6bd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 239, + 547, + 284 + ], + "lines": [ + { + "bbox": [ + 46, + 239, + 547, + 284 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 547, + 284 + ], + "type": "text", + "content": "Figure 5. Visualization of StreamingFlow for diverse driving scenarios. Different colors represent different instances of the agents, and lighter colors represent the future occupancy of the agents. (top): samples from Lyft dataset, highway (left), and urban (right). (middle and bottom): samples from nuScenes dataset, sunny (middle left), overcast after rain (middle right), rainy (bottom left), and night (bottom right). StreamingFlow works well in all challenging driving scenarios." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 242, + 69, + 539, + 231 + ], + "blocks": [ + { + "bbox": [ + 242, + 69, + 539, + 231 + ], + "lines": [ + { + "bbox": [ + 242, + 69, + 539, + 231 + ], + "spans": [ + { + "bbox": [ + 242, + 69, + 539, + 231 + ], + "type": "image", + "image_path": "230bb776870702404520a5208daf4d0ff668457ccbc8b8c2171cb65680e6f550.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 304, + 287, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 304, + 287, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 304, + 287, + 352 + ], + "type": "text", + "content": "is cosine annealing with a weight decay of 0.01. All models are trained on 8 A6000 GPUs for 20 epochs with a total batch size 16. The image backbone is EfficientNet-b4 [29] for tiny and base model and Effi-b7 for small model." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 358, + 244, + 372 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 358, + 244, + 372 + ], + "spans": [ + { + "bbox": [ + 47, + 358, + 244, + 372 + ], + "type": "text", + "content": "4.3. Comparison with the State-of-the-art" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 377, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 287, + 426 + ], + "type": "text", + "content": "Comparisons of methods implemented in the nuScenes dataset are shown in Tab. 1. All methods are trained for a standard instance flow segmentation and prediction task. Fig. 5 illustrates some examples covering diverse scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": "StreamingFlow achieves competitive performance while significantly outperforming other single-modality methods. StreamingFlow surpasses the best vision-based BEVerse [34] with a larger backbone Swin-small [19] by " + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "inline_equation", + "content": "+7.0" + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "inline_equation", + "content": "+10.0" + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": " VPQ, and the best LiDAR-based BE-STI [30] " + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "inline_equation", + "content": "+7.7" + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": " IoU and 5.1VPQ. Compared to FusionAD, StreamingFlow-base uses the same LiDAR backbone(SpConv), similar image backbone(Effi-B4 vs. ResNet101) but a half smaller image size " + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "inline_equation", + "content": "(800\\times 320" + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": " vs. " + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "inline_equation", + "content": "1600\\times 900)" + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": ", and is " + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "inline_equation", + "content": "+1.6" + }, + { + "bbox": [ + 46, + 426, + 287, + 555 + ], + "type": "text", + "content": " VPQ and 2.4 IoU higher than the latest fusion-based FusionAD [33]." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "text", + "content": "Comparisons of methods implemented in the Lyft L5 dataset are shown in Tab. 2. StreamingFlow achieves the best of all metrics while surpassing baseline methods by a large margin: " + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "inline_equation", + "content": "+20.6" + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "inline_equation", + "content": "+23.5" + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "text", + "content": " VPQ against STP3 [10]. Moreover, it surpasses our reproduced BEVFusion with lightweight encoders by " + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "inline_equation", + "content": "+2.3" + }, + { + "bbox": [ + 46, + 556, + 287, + 629 + ], + "type": "text", + "content": " mIoU and 0.2 VPQ." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 635, + 213, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 213, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 213, + 647 + ], + "type": "text", + "content": "4.4. Streaming Forecasting Results" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "We design three experiments on nuScenes dataset for demonstration of the streaming occupancy prediction: (1) Extension of the prediction temporal horizons to unseen future; (2) Prediction at any desired future time point; (3) Data streams input at different frame rates. Experiments are con" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 545, + 327 + ], + "type": "text", + "content": "duced on models loaded from the checkpoints trained on standard instance forecasting tasks." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "type": "text", + "content": "Extension of the temporal horizons of unseen future. Tab. 3 shows the prediction result of StreamingFlow which extends the temporal horizons from 2.0s to 8.0s. Baselines reported in [1] are trained for different lengths of temporal horizons. StreamingFlow shows excellent performance in variable prediction length without retraining. Similar to prior arts which extend prediction horizons to farther future, StreamingFlow shows a similar gradual performance decay. We then compare zero-shot Streamingflow with the model trained with the longest future 8s groundtruth labels in Tab. 4. The zero-shot long-term prediction results are only " + }, + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "type": "inline_equation", + "content": "-0.9" + }, + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "type": "inline_equation", + "content": "-1.8" + }, + { + "bbox": [ + 304, + 329, + 546, + 496 + ], + "type": "text", + "content": " VPQ less than fully supervised models, which demonstrates great generalization ability of foreseeing the unseen future." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 497, + 545, + 628 + ], + "type": "text", + "content": "Streaming prediction at any desired time point. Since nuScenes do not provide labels for non-keyframes, we adopt the practice of MotionNet and interpolate the box instances between two adjacent keyframes. We randomly choose to predict at a list of time points and report the results in Tab. 5. To simply illustrate the capability, we designed the main task to predict uniformly spaced temporal horizons, but this framework can predict uneven and arbitrary future snapshots. The prediction results are stable generally. There is a slight decline as the forecast becomes denser." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 629, + 545, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 629, + 545, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 629, + 545, + 700 + ], + "type": "text", + "content": "We provide demo videos as supplementary materials to show the effectiveness of streaming prediction. We provide a finer granularity of streaming perception at any future time. In the video, we visualize the prediction results every 0.05s from the current to the future 2s to 3s, with a total of 40 to 60 frames." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 701, + 545, + 714 + ], + "type": "text", + "content": "Asynchronous multi-modal data streams as input." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14838" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 47, + 70, + 547, + 269 + ], + "blocks": [ + { + "bbox": [ + 47, + 70, + 547, + 269 + ], + "lines": [ + { + "bbox": [ + 47, + 70, + 547, + 269 + ], + "spans": [ + { + "bbox": [ + 47, + 70, + 547, + 269 + ], + "type": "table", + "html": "
MethodModalityImage backboneLiDAR backboneFuture Semantic Seg. IoU↑Future Instance Seg.
PQ↑SQ↑RQ↑
Static*CEffi-B4-32.227.670.139.1
FIERY*[9]CEffi-B4-37.030.270.242.9
StretchBEV[1]CEffi-B4-37.129.0--
BEVerse[34]CSwin-tiny-38.733.370.647.2
BEVerse[34]CSwin-small-40.836.170.751.1
ST-P3 Gaus.[10]CEffi-B4-38.631.770.245.2
ST-P3 Ber.[10]CEffi-B4-38.932.170.445.6
UniAD[11]CEffi-B4-40.233.5--
MotionNet[32]L-STPN37.238.975.651.4
BE-STI[30]L-BESTI-STPN40.141.075.554.3
StreamingFlow-tinyLCEffi-B4PillarNet47.846.175.860.8
StreamingFlow-smallLCEffi-B7PillarNet51.148.075.164.0
FusionAD[33]LCResNet-101VoxelNet51.551.1--
StreamingFlow-baseLCEffi-B4VoxelNet53.952.778.766.9
", + "image_path": "15d791cc68e3f4cffbc854e101929b7a88e15ced7526c2c88ac19cd3301f348a.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 318, + 287, + 413 + ], + "blocks": [ + { + "bbox": [ + 46, + 277, + 545, + 300 + ], + "lines": [ + { + "bbox": [ + 46, + 277, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 46, + 277, + 545, + 300 + ], + "type": "text", + "content": "Table 1. Comparison with the state-of-the-art methods for instance-aware occupancy flow prediction on nuScenes[2] validation set. 'C' denotes vision-only methods, 'L' denotes LiDAR-based methods, and 'LC' denotes a LiDAR-camera fusion methods. " + }, + { + "bbox": [ + 46, + 277, + 545, + 300 + ], + "type": "inline_equation", + "content": "*" + }, + { + "bbox": [ + 46, + 277, + 545, + 300 + ], + "type": "text", + "content": ": reported in [9]." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 318, + 287, + 413 + ], + "lines": [ + { + "bbox": [ + 48, + 318, + 287, + 413 + ], + "spans": [ + { + "bbox": [ + 48, + 318, + 287, + 413 + ], + "type": "table", + "html": "
MethodIoU↑PQ↑SQ↑RQ↑
Static*24.120.7--
Extrapolation model*24.821.2--
FIERY*[9]36.327.2--
ST-P3[10]36.332.471.145.5
BEVFusion-tiny†54.655.778.071.4
StreamingFlow-tiny56.955.978.171.6
", + "image_path": "f08d62559ae3476610715a84b8994be22afea7e2e6031623b0aca97ffe4962d7.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 49, + 468, + 287, + 634 + ], + "blocks": [ + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "lines": [ + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "type": "text", + "content": "Table 2. Comparison with the state-of-the-art methods for future instance segmentation (2.0s) on Lyft L5 AV [14] validation set. " + }, + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "type": "inline_equation", + "content": "\\star" + }, + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "type": "text", + "content": " results reported in [9]. " + }, + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "type": "inline_equation", + "content": "\\dagger" + }, + { + "bbox": [ + 46, + 422, + 287, + 466 + ], + "type": "text", + "content": " : results of BEVFusion with LSS-based image encoder and pillar-based encoder reproduced by us." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 49, + 468, + 287, + 634 + ], + "lines": [ + { + "bbox": [ + 49, + 468, + 287, + 634 + ], + "spans": [ + { + "bbox": [ + 49, + 468, + 287, + 634 + ], + "type": "table", + "html": "
MethodPredIoU↑PQ↑SQ↑RQ↑
FIERY2s35.829.0--
4s30.123.6--
6s26.720.9--
StretchBEV2s37.129.0--
4s32.523.8--
6s28.421.0--
StreamingFlow2s47.846.175.860.8
3s44.441.174.155.4
4s41.738.473.652.1
5s39.135.873.248.9
6s36.733.672.946.0
8s32.529.872.640.1
", + "image_path": "46d66007d32688afcf711996e0dd96c61db5775661a71d9c1e25a25f555148d3.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "We validate asynchronous data streams as input and standard occupancy forecasting as output. We test multiple settings of data stream frame rate and report the results in Tab." + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 306, + 318, + 547, + 363 + ], + "blocks": [ + { + "bbox": [ + 46, + 643, + 287, + 664 + ], + "lines": [ + { + "bbox": [ + 46, + 643, + 287, + 664 + ], + "spans": [ + { + "bbox": [ + 46, + 643, + 287, + 664 + ], + "type": "text", + "content": "Table 3. Comparison of occupancy flow prediction for any temporal horizons." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 306, + 318, + 547, + 363 + ], + "lines": [ + { + "bbox": [ + 306, + 318, + 547, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 318, + 547, + 363 + ], + "type": "table", + "html": "
Schedule2s3s4s6s8s
ZS.47.8/46.144.4/41.141.7/38.436.7/33.632.5/29.8
Sup.48.2/46.946.0/45.241.9/38.737.8/34.233.6/31.6
", + "image_path": "633bd89e1a221b608098772c8f03b89277f097fa798c697ca9e35723a20155c0.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_body" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 307, + 408, + 545, + 463 + ], + "blocks": [ + { + "bbox": [ + 306, + 364, + 545, + 397 + ], + "lines": [ + { + "bbox": [ + 306, + 364, + 545, + 397 + ], + "spans": [ + { + "bbox": [ + 306, + 364, + 545, + 397 + ], + "type": "text", + "content": "Table 4. ZS: zero-shot inference of StreamingFlow. Sup: StreamingFlow trained with the longest prediction horizons 8s. Each value is given in the format of 'IoU/PQ'." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 408, + 545, + 463 + ], + "lines": [ + { + "bbox": [ + 307, + 408, + 545, + 463 + ], + "spans": [ + { + "bbox": [ + 307, + 408, + 545, + 463 + ], + "type": "table", + "html": "
Prediction IntervalIoU↑PQ↑SQ↑RQ↑
0.547.846.175.860.8
0.2543.440.174.154.1
0.645.644.375.258.9
", + "image_path": "1a6b73b51f15bb18bd37af3d77d207b6d86bf608aafdbe1ebf10e0c1a1cc465c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_body" + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 506, + 545, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 506, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 306, + 506, + 545, + 542 + ], + "type": "text", + "content": "6. The model performs the best when the inference uses the training configuration. Denser inputs lead to similar forecasting accuracy." + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 307, + 552, + 545, + 608 + ], + "blocks": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "lines": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "spans": [ + { + "bbox": [ + 305, + 472, + 545, + 495 + ], + "type": "text", + "content": "Table 5. Prediction results at any desired intervals. For example, prediction at the interval of 0.6 means prediction at [0.6, 1.2, 1.8]." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 552, + 545, + 608 + ], + "lines": [ + { + "bbox": [ + 307, + 552, + 545, + 608 + ], + "spans": [ + { + "bbox": [ + 307, + 552, + 545, + 608 + ], + "type": "table", + "html": "
LiDAR streamCam streamIoU↑PQ↑SQ↑RQ↑
5247.846.175.860.8
10247.645.875.660.5
10447.145.475.160.4
", + "image_path": "dd43ad3948b974162fc276db6a2603d2dd4e8f11b88f4642172cfc128f25e62d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_body" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 616, + 544, + 638 + ], + "lines": [ + { + "bbox": [ + 306, + 616, + 544, + 638 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 544, + 638 + ], + "type": "text", + "content": "Table 6. Prediction results with multi-modal data stream of different frame rates. Frame rates are shown in Hz." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 659, + 400, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 659, + 400, + 672 + ], + "spans": [ + { + "bbox": [ + 306, + 659, + 400, + 672 + ], + "type": "text", + "content": "4.5. Ablation Study" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "Effect of different fusion strategies. We compare SpatialGRU-ODE with fusion strategies at different stages and the implementation details are in supplementary" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 749, + 317, + 757 + ], + "type": "text", + "content": "14839" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": "material. As shown in Tab. 7, asynchronous fusion is inferior to synchronous fusion and SpatialGRU-ODE for both datasets. For nuScenes dataset, the ordinary temporally-synchronized fusion approach performs the best. SpatialGRU-ODE performs " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "-2.4" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "-0.9" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " VPQ, slightly less than BEVFusion [20]. For Lyft dataset, SpatialGRU-ODE outperforms synchronized fusion. It performs " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "+2.3" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "inline_equation", + "content": "+0.2" + }, + { + "bbox": [ + 46, + 72, + 289, + 168 + ], + "type": "text", + "content": " VPQ more than BEVFusion [20]." + } + ] + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 177, + 287, + 305 + ], + "blocks": [ + { + "bbox": [ + 48, + 177, + 287, + 305 + ], + "lines": [ + { + "bbox": [ + 48, + 177, + 287, + 305 + ], + "spans": [ + { + "bbox": [ + 48, + 177, + 287, + 305 + ], + "type": "table", + "html": "
Fusion modeIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Spatial then temporal50.247.075.663.0
Temporal then spatial44.742.774.657.2
SpatialGRU-ODE47.846.175.860.8
Lyft L5 AV dataset
Spatial then temporal54.655.778.071.4
Temporal then spatial50.450.275.266.7
SpatialGRU-ODE56.955.978.171.9
", + "image_path": "09785962bbf527609f9a79087c1c71413010e6b567eecfb38511de7241366f3b.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 383, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 383, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 383, + 287, + 491 + ], + "type": "text", + "content": "Effect of ODE solvers. ODE solvers are vital tools for a N-ODE framework. We test two basic ode solvers, Euler, and midpoint solver as compared in Tab. 8 on two datasets. In both cases, the midpoint solver yields superior VPQ, surpassing the Euler solver by 3.2 points on nuScenes dataset and 0.8 points on Lyft dataset. On nuScenes dataset, the midpoint solver shows similar IoU with the Euler solver, but on Lyft dataset, the midpoint solver performs worse semantic segmentation by " + }, + { + "bbox": [ + 46, + 383, + 287, + 491 + ], + "type": "inline_equation", + "content": "-1.9" + }, + { + "bbox": [ + 46, + 383, + 287, + 491 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 3 + }, + { + "type": "table", + "bbox": [ + 50, + 500, + 285, + 606 + ], + "blocks": [ + { + "bbox": [ + 46, + 312, + 288, + 378 + ], + "lines": [ + { + "bbox": [ + 46, + 312, + 288, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 288, + 378 + ], + "type": "text", + "content": "Table 7. Comparison with the baseline fusion methods for future instance segmentation (2.0s) on nuScenes validation set. StreamingFlow-ODE is compared with different fusion modes. Spatial fusion is conducted in the same way as BEVFusion [20]. 'Spatial Then Temporal' is for synchronous mode, and 'Temporal Then Spatial' is for asynchronous mode." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 50, + 500, + 285, + 606 + ], + "lines": [ + { + "bbox": [ + 50, + 500, + 285, + 606 + ], + "spans": [ + { + "bbox": [ + 50, + 500, + 285, + 606 + ], + "type": "table", + "html": "
ODE SolverIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
Euler47.842.973.558.6
Midpoint47.846.175.860.8
Lyft L5 AV dataset
Euler56.955.978.171.5
Midpoint55.056.778.272.4
", + "image_path": "b456ad393e93772a2eae27415c1406b0b712b6739ae51cfee0f7bdb43988713b.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 715 + ], + "type": "text", + "content": "Effect of ODE update intervals. We ablate different ODE update intervals which determine the minimum granularity of occupancy prediction. The ODE step is set to 0.05, 0.1, 0.5 and variable for comparison. Variable means the ODE step is the next timestamp minus the current timestamp. In general, the finer a single update is divided during the ODE update process, the higher the final prediction ac" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "curacy. It is also intuitive that a higher update frequency may eliminate continuous errors. As shown in Tab. 9, the predictor with interval " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "0.05s" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " surpasses interval " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "0.1s" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " by 0.1 IoU and 3.1 VPQ, and interval " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "0.5s" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " by 0.5 IoU and 3.1 VPQ. Remarkably, the variable time step update also shows nice performance, which is " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "+0.5" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " IoU and " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "-2.2" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": " VPQ when compared to the predictor with ODE step " + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "inline_equation", + "content": "0.05s" + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": ". A variable time step updater strikes a good balance between precision and inference speed, so it is more favorable for long-term prediction to 8s future." + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 310, + 201, + 542, + 327 + ], + "blocks": [ + { + "bbox": [ + 47, + 614, + 286, + 625 + ], + "lines": [ + { + "bbox": [ + 47, + 614, + 286, + 625 + ], + "spans": [ + { + "bbox": [ + 47, + 614, + 286, + 625 + ], + "type": "text", + "content": "Table 8. Comparison with prediction using different ODE solvers." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 310, + 201, + 542, + 327 + ], + "lines": [ + { + "bbox": [ + 310, + 201, + 542, + 327 + ], + "spans": [ + { + "bbox": [ + 310, + 201, + 542, + 327 + ], + "type": "table", + "html": "
StepIoU↑PQ↑SQ↑RQ↑
nuScenes dataset
0.0547.846.175.860.8
0.147.743.073.758.4
0.547.342.173.357.4
Variable48.243.973.958.8
Lyft L5 dataset
0.0556.955.978.171.9
Variable54.053.577.469.7
", + "image_path": "6f3e50c482e252939135c0311bb7ce833bb37e649be5400890c783d12e4be995.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 315, + 335, + 535, + 346 + ], + "lines": [ + { + "bbox": [ + 315, + 335, + 535, + 346 + ], + "spans": [ + { + "bbox": [ + 315, + 335, + 535, + 346 + ], + "type": "text", + "content": "Table 9. Comparison of prediction under different ode steps." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 306, + 351, + 379, + 363 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 351, + 379, + 363 + ], + "spans": [ + { + "bbox": [ + 306, + 351, + 379, + 363 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 371, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 371, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 371, + 545, + 515 + ], + "type": "text", + "content": "We present StreamingFlow as the first practice for fusion-based streaming occupancy forecasting. Starting from the motivation of fusing and predicting from non-ideal data streams, the streaming feature brings a more flexible temporal scene understanding and generalizes occupancy forecasting well to any temporal horizon. The advantage of SpatialGRU-ODE is that it decouples the supervision in the training process and outputs in the inference process, by modeling the derivatives of BEV grids and propagating future grid states to required timestamps. We hope that this work will inspire more Neural-ODE applications and insights into the streaming automotive perception." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 525, + 416, + 539 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 525, + 416, + 539 + ], + "spans": [ + { + "bbox": [ + 306, + 525, + 416, + 539 + ], + "type": "text", + "content": "6. Acknowledgement" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "type": "text", + "content": "This work was supported in part by the National Natural Science Foundation of China under Grants (52372414, U22A20104, 52102464). This work was also sponsored by Tsinghua University-DiDi Joint Research Center for Future Mobility and Tsinghua University-Zongmu Technology Joint Research Center." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 627, + 365, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 627, + 365, + 639 + ], + "spans": [ + { + "bbox": [ + 306, + 627, + 365, + 639 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 310, + 646, + 545, + 712 + ], + "type": "list", + "angle": 0, + "index": 17, + "blocks": [ + { + "bbox": [ + 310, + 646, + 545, + 689 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 646, + 545, + 689 + ], + "spans": [ + { + "bbox": [ + 310, + 646, + 545, + 689 + ], + "type": "text", + "content": "[1] Adil Kaan Akan and Fatma Güney. Stretchbev: Stretching future instance prediction spatially and temporally. 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StrokeFaceNeRF enables versatile high-quality color stroke-based appearance editing for facial NeRFs. Users can draw strokes over a rendered facial image from any angle and define the editing region using masks. The third column showcases the photo-realistic free-view rendering results with exceptional color correspondence." + ], + "image_footnote": [], + "bbox": [ + 99, + 304, + 870, + 494 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 553, + 313, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Current 3D-aware facial NeRF generation approaches control the facial appearance by text, lighting conditions or reference images, limiting precise manipulation of local facial regions and interactivity. Color stroke, a user-friendly and effective tool to depict appearance, is challenging to edit 3D faces because of the lack of texture, coarse geometry representation and detailed editing operations. To solve the above problems, we introduce StrokeFaceNeRF, a novel stroke-based method for editing facial NeRF appearance. In order to infer the missing texture and 3D geometry information, 2D edited stroke maps are firstly encoded into the EG3D's latent space, followed by a transformer-based editing module to achieve effective appearance changes while preserving the original geometry in editing regions. Notably, we design a novel geometry loss function to ensure surface density remains consistent during training. To further enhance the local manipulation accuracy, we propose a stereo fusion approach which lifts the 2D mask (inferred from strokes or drawn by users) into 3D mask volume, al", + "bbox": [ + 75, + 585, + 472, + 872 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "lowing explicit blending of the original and edited faces. Extensive experiments validate that the proposed method outperforms existing 2D and 3D methods in both editing reality and geometry retention.", + "bbox": [ + 500, + 554, + 892, + 614 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 648, + 632, + 664 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Realistic 3D human face generation is a popular topic and has wide range applications in character design, virtual meeting and education. Traditional 3D facial modeling methods rely on software like Maya and Zbursh to construct mesh models while employing texture mapping for facial appearances. However, these methods are time-consuming and labor-intensive, especially when editing local appearance details and aiming for photorealistic results. Neural Radiance Field (NeRF) [23], a new 3D representation technique, easily render photo-realistic images with the input of multi-view images. The further combination of Generative Adversarial Networks (GAN) [10] with NeRF [5, 11, 24, 30] has enabled the generation of high-quality facial NeRF through random sampling. Nevertheless, precise control over appearance details remains a challenge.", + "bbox": [ + 496, + 674, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding Author", + "bbox": [ + 80, + 887, + 210, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7538", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Efforts to enhance controllability involve disentangling geometry and appearance during facial NeRF generation. Sun et al. introduced the FE-NeRF [32] that employs separate latent codes to control the intricacies of facial geometry and appearance. Subsequent advancements [16, 31] utilize decoupling techniques based on triplane representations, leading to the facial generation results with significantly enhanced quality. Despite their success in good geometry and appearance swapping, these methods heavily rely on random sampling or reference images for global appearance editing. This reliance poses challenges in the obtainment of desired reference images and precludes precise control over localized appearance attributes, such as selective hair color alteration.", + "bbox": [ + 75, + 90, + 472, + 301 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Compared to reference images, colored strokes, functioning as an interactive tool, offer a precise depiction of local appearance details. In stroke-based image editing, one category of methods [17, 26] relies on conditional GAN and completion framework to edit local regions with the stroke guidance. However, artifacts may arise in the editing boundary and result in less realistic images for large-area editing operations, as shown in Figure 6. Another category of methods [22, 27] employs pre-trained facial generation models as decoders, mapping colored strokes to the latent space of the generation model to generate edited facial results. However, these methods struggle to preserve the unchanged geometric features of the input face during editing, as demonstrated in Figure 6. Importantly, these techniques are specifically tailored for 2D facial image editing and cannot be directly applied to 3D facial radiance fields.", + "bbox": [ + 75, + 301, + 472, + 542 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "This paper presents StrokeFaceNeRF, a framework for editing facial NeRF appearance based on colored strokes, enabling precise modifications of color and lighting in 3D faces. Leveraging 2D facial image generation techniques such as StyleGAN2 [21] and semantic segmentation methods [38], we construct a dataset of faces with identical geometry but varying appearances, generating corresponding colored stroke maps using bilateral filtering and semantic clustering algorithms. To achieve appearance editing, directly encoding edited stroke maps into the latent space of the pre-trained facial NeRF generation model [5] leads to texture smoothness and undesirable geometry distortion due to high-frequency information absence and user's inaccurate drawing of strokes. To solve this problem, we propose a transformer-based editing network, which fuses the original and stroke-encoded latent codes to modify appearance while preserving the original geometry in edited regions. Furthermore, we introduce a geometry loss term during training to ensure surface density remains unchanged, improving detail preservation. To further maintain unchanged features in non-edited areas for precise editing, we design a volumetric fusion algorithm that integrates localized regions before and after editing in 3D space, enabling local-", + "bbox": [ + 75, + 545, + 472, + 893 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ized appearance editing effects in facial models. Our contributions are summarized as follows", + "bbox": [ + 498, + 90, + 816, + 119 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose the first color stroke-based facial NeRF editing framework to generate free-view realistic appearance editing facial images.", + "- We design a novel geometry density loss to train the transformer-based latent editing network, which effectively preserves the geometry detail during facial appearance modifications.", + "- We introduce a volumetric fusion algorithm to precisely edit local regions while maintaining the 3D consistency in unedited regions." + ], + "bbox": [ + 500, + 121, + 890, + 272 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 292, + 640, + 309 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Facial Image Editing with Colored Strokes", + "text_level": 1, + "bbox": [ + 500, + 318, + 862, + 335 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Existing 2D facial image editing methods using colored strokes can be divided into two categories. One group of methods utilizes conditional Generative Adversarial Networks (cGANs) to accomplish stroke-guided image generation. Sangkloy et al. [29] utilize sketches and colored strokes to directly generate realistic images through a translation network. However, this method fails to achieve localized area editing. To solve this problem, FaceShop [26] utilizes image completion techniques and 2D mask marking for localized facial image editing based on sketches and colored strokes. Jo et al. [18] further introduced SC-FEGAN that employs gated convolutions and new style losses for training, enabling a broader range of editing operations. Xiao et al. [36] design a hair generation network with self-attention mechanisms, achieving more natural and realistic hair editing effects. However, these methods are sensitive to input conditions and result in smooth edits lacking texture information in edited regions. Additionally, they tend to produce artifacts at the editing boundary due to the image completion techniques.", + "bbox": [ + 496, + 340, + 890, + 643 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Another category of methods utilizes pre-trained generative models to generate high quality faces instead of pixelwise translation. Bau et al. [3] first utilize reverse optimization to achieve image shape and color editing in the GAN's latent space. pSp [27] further designs an image encoding network to map various types of input images, such as sketches and color strokes, into StyleGAN2's latent space to generate corresponding facial images. In order to generate highly editable latent codes, Tov et al. [34] further constrained the latent codes with a discriminator. However, these methods, as they represent the entire image with latent vectors, struggle to achieve localized editing effects. Instead of GAN dependence, Meng et al. [22] employed pre-trained diffusion models to achieve facial image editing based on colored stroke maps. Images with user-drawn strokes are added Gaussian noise, then progressively denoised to synthesize realistic facial images. However, it is", + "bbox": [ + 496, + 643, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7539", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ed19e967ddc010a416c336e52113dbc352b8d11f8b3232dd849538ec88390936.jpg", + "image_caption": [ + "Figure 2. 3D Facial Appearance Editing Framework. Given the original latent code $w$ , free-view images are rendered by EG3D. Users introduce editing operations, resulting in the creation of a color stroke image $C_{\\mathrm{edit}}$ . This stroke map is encoded by Color Encoder $E_{c}$ to generate $w_{c}$ , which is fused with original latent code $w$ by latent fusion network to generate $w_{\\mathrm{edit}}$ . Utilizing an additional 2D mask, the volumetric fusion approach facilitates targeted appearance editing within specific regions." + ], + "image_footnote": [], + "bbox": [ + 101, + 88, + 470, + 300 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/8fd18f8e3a238858f24822341956ddb4686569ee346e964549491c47cb1e42ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 473, + 88, + 870, + 300 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "challenging to directly apply this method to facial neural radiance field editing. Additionally, because of the direct input of coarse stroke maps, it is challenging for the above methods to maintain geometric features while performing appearance modification in editing regions.", + "bbox": [ + 75, + 367, + 470, + 444 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Editing Facial NeRF", + "text_level": 1, + "bbox": [ + 76, + 454, + 272, + 470 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Combining generative adversarial networks with neural radiance fields enables the synthesis of realistic facial images from arbitrary viewpoints. Graf [30] first adds extra latent codes to NeRF's fully connected network to support face generation and use multiscale discriminators for supervision. Giraffe [24] designs a new framework that employs volume rendering to obtain feature maps and a convolutional framework to generate facial images. StyleSDF [25] and GRAM [7] utilize representation methods based on SDF and implicit planes, respectively, producing higher-quality and more 3D consistent results. EG3D [5] propose a facial NeRF generation framework based on triplane representation and StyleGAN2 [21] generator. However, these methods can only synthesize faces through random sampling and lack the ability for editing.", + "bbox": [ + 75, + 478, + 468, + 704 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "To generate controllable facial NeRF, Jo et al. [17] use sketches, black-and-white images, and text as control conditions. Gao et al. [9] propose a facial NeRF generation and editing framework based on sketches to enhance synthesis quality and achieve fine editing. However, this method can only edit facial geometry. Another line of work decouples facial NeRF's geometry and appearance using semantic segmentation. FE-NeRF [32] achieves geometric editing through reverse latent code optimization and appearance editing through random sampling. IDE-3D [31] constructs geometry triplanes and appearance triplanes, and designs a semantic map encoder to generate higher-quality facial results. NeRFFaceEditing [16] apply AdaIN [14] to triplanes", + "bbox": [ + 75, + 704, + 470, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "features, enabling the disentanglement of geometry and appearance control. Although the above methods achieve effective appearance modification, reference images or latent codes are required instead of user's flexible interaction. More importantly, the above methods are designed for the global appearance editing and cannot be directly utilized for local editing.", + "bbox": [ + 496, + 367, + 893, + 473 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Methodology", + "text_level": 1, + "bbox": [ + 498, + 497, + 635, + 515 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We propose a framework, StrokeFaceNeRF, enables users to utilize colored strokes for facial NeRF appearance editing. We employ the EG3D [5] generator architecture, a proficient 3D-aware Generative Adversarial Network (GAN) that combines the StyleGAN2 [21] architecture and neural rendering to produce high-quality 3D shapes. Given a latent code, a triplane representation can be obtained from a StyleGAN2 backbone. The neural renderer then aggregates features from these triplanes and predicts feature images based on a specified camera pose. Subsequently, a super-resolution module is applied to upsample and refine these raw neurally rendered images, resulting in high-quality, multiview-consistent images. More details of the generator can be found in [5].", + "bbox": [ + 496, + 523, + 890, + 734 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Our method comprises three key components: dataset construction, colored stroke editing network, and 3D local fusion module. Initially, we introduce a dataset construction approach to acquire facial images with consistent geometry but varying appearances, along with their corresponding colored stroke images as detailed in Section 3.1. Subsequently, an appearance editing network, described in Section 3.2, is established within the latent space of EG3D to predict the 3D faces. Additionally, in Section 3.3, we propose a 3D local fusion method to enable effective appearance editing while meticulously preserving features in", + "bbox": [ + 496, + 734, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7540", + "bbox": [ + 482, + 944, + 516, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "non-edited regions.", + "bbox": [ + 76, + 90, + 207, + 104 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Dataset Construction", + "text_level": 1, + "bbox": [ + 76, + 122, + 276, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To supervise the training of network models, the training data needs to simulate the process of facial appearance editing based on colored strokes. Thus, the training tuples include original faces, edited faces, and corresponding colored stroke maps. Dataset construction involves three steps as shown in Figure 3: (1) building a collection of facial latent codes in EG3D's latent space, obtained through random sampling and real images inversion; (2) constructing facial tuples with identical geometry but different appearances. Two different methods were employed: one based on semantic segmentation and the other based on StyleGAN2 generative networks; (3) generating colored stroke maps using bilateral filtering and semantic clustering methods.", + "bbox": [ + 75, + 145, + 468, + 340 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We utilize two approaches to synthesize paired images with the same geometry but different appearance, indicated as the edited ground truth faces. Semantic Segmentation-Based Augmentation. Given the original rendered facial images, we utilize BiSeNet [38] to get semantic segmentation masks. Then, for each local semantic region, we represent it into HSV space, where the Hue channel is uniformly replaced with random color, while the Saturation and Value channels are added random perturbation. Finally, these regions are merged into original images to imitate appearance editing. StyleGAN2-Based Augmentation. We further utilize pre-trained generator to synthesize more diverse and realistic training images. Given the original rendered images, ReStyle [2] encodes them into StyleGAN2 latent space, followed with style mixing to change the facial appearance while preserving the same geometry. More details can be found in Supplementary.", + "bbox": [ + 75, + 340, + 468, + 598 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "With the paired appearance modification images, corresponding color strokes are required to imitate real editing situation. Typically, users drawn strokes are simple and monochromatic. Therefore, synthesized color stroke images must preserve the original image's color and geometric layout while eliminating high-frequency texture features and local details. To achieve this objective, we employ the bilateral filtering method [33] to effectively preserves the edge features of the facial image while eliminating high-frequency details. Specially, the initial image undergoes median filtering, followed by iterative application of bilateral filtering, as explained in the Supplementary. Nevertheless, some regions still exhibit smooth transitions between different colored areas after filtering, posing challenges for users aiming to replicate specific effects. To tackle this issue, we employ a pixel value clustering technique based on semantic information. Initially, the facial image undergoes semantic segmentation. Within the hair area, clustering allows all pixel colors to be replaced by the nearest cluster center color, thereby eliminating smooth transition regions.", + "bbox": [ + 75, + 598, + 468, + 900 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/2da12d65a8b1e146d8aff06e23ee124b1aa2e1c042f22399ffe959067c008dd2.jpg", + "image_caption": [ + "Figure 3. Dataset construction pipeline. Given EG3D rendering images, the appearance is changed by two different approaches. Then, the color stroke images are synthesized by image filter and cluster." + ], + "image_footnote": [], + "bbox": [ + 511, + 87, + 883, + 215 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The same methodology is applied to the facial area, yielding the final color stroke image.", + "bbox": [ + 498, + 284, + 890, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Appearance Editing Network", + "text_level": 1, + "bbox": [ + 500, + 323, + 759, + 339 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In our framework, the target face NeRF to be edited is represented as a latent code $w$ within EG3D's latent space. The latent code can be obtained either by random sampling in EG3D or by applying PTI [28] to invert real images. Utilizing StyleGAN generator and volume rendering, free view facial images can be generated, followed by the approaches in Section 3.1 to extract color stroke images. Users then modify these color stroke images to obtain the edited color stroke image $C_{\\mathrm{edit}}$ . As illustrated in Figure 2, the input to the appearance editing network consists of the original latent variable $w$ , the edited color stroke image $C_{\\mathrm{edit}}$ , and the output is the edited latent variable $w_{\\mathrm{edit}}$ .", + "bbox": [ + 496, + 345, + 890, + 526 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The appearance editing network comprises two main components: the Color Encoder $E_{c}$ and the Latent Fusion Network $F_{l}$ . Specifically, given the edited color stroke image $C_{\\mathrm{edit}}$ , the color encoder that has a similar structure to [27], predicts the latent code $w_{c}$ . While this latent code generates facial results with color editing effects, it fails to preserve the original facial features, such as the geometric structure of the hair and the original skin color in non-edited areas, as shown in Figure 2. Therefore, a latent code fusion network is designed to utilize the information from the original latent variable $w$ , thus better preserving the original facial features. The latent fusion network $F_{l}$ adopts a cross-attention transformer block to predict the fused latent variable $w_{\\mathrm{edit}}$ . This design implicitly extracts the color information from $w_{c}$ and geometry information from $w$ , guaranteeing a thorough integration of both color-edited and original facial features. In this configuration, the latent code $w_{c}$ is employed as query tokens, whereas the original latent code $w$ serves as key and value tokens. We also normalize over queries instead of keys as described in [13] to ensure a continuous refinement of $w_{c}$ during the fusion process with value tokens while mitigating the potential influence of $w$ being too large.", + "bbox": [ + 496, + 527, + 892, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nw _ {\\text {e d i t}} = F _ {l} \\left(w, E _ {c} \\left(C _ {\\text {e d i t}}\\right)\\right) \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 612, + 885, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7541", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Volumetric Local Fusion", + "text_level": 1, + "bbox": [ + 76, + 90, + 302, + 104 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "While direct rendering by $w_{\\mathrm{edit}}$ yields good editing effects within targeted editing areas, as depicted in Figure 7, noticeable undesirable discrepancies emerge in unedited regions. Moreover, intricate editing tasks, such as selectively dyeing specific portions of hair or drawing specific patterns on faces, pose challenges for the latent code-based representation because of its overarching global control inherited from StyleGAN2 backbone. To address these issues, we propose a volumetric fusion approach to enable more refined editing operations.", + "bbox": [ + 75, + 112, + 468, + 263 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In order to facilitate local editing, our method introduces support for an additional 2D mask input that indicates the editing region. This 2D mask is further lifted into 3D mask volume to support volumetric fusion. Specifically, we propose a depth guidance approach to sample a set of points near the facial surface. In the volume rendering, for each ray $r_{i,j}$ of the pixel at the $i$ th row and $j$ th column, the camera's position and ray direction are denoted as $o_{i,j}$ and $d_{i,j}$ , respectively. After rendering the original faces, we get the corresponding depth value $D[i,j]$ . Then, for each ray, we uniformly sample $K$ points with offset $\\triangle x_k$ within range $[-0.1, 0.1]$ . The sampled 3D points set $S$ for the original face is denoted as:", + "bbox": [ + 75, + 265, + 470, + 460 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS = \\cup_ {i, j} \\cup_ {k = 1} ^ {K} \\left(o _ {i, j} + \\left(D [ i, j ] + \\triangle x _ {k}\\right) \\cdot d _ {i, j}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 119, + 465, + 468, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where the default value of $K$ is 5. Notably, as illustrated in Figure 2, we selectively employ the rays corresponding to pixels within the 2D mask regions.", + "bbox": [ + 75, + 491, + 468, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, this generated 3D point set undergoes a transformation into a 3D volumetric mask. Specifically, we initialize a $256 \\times 256 \\times 256$ 3D volume with zero values throughout the space. The coordinates of the 3D points, along with their neighboring positions, are designated as 1, indicating 3D editing regions. To ensure smoother boundaries, we utilize a three-dimensional dilation and Gaussian filtering, yielding the 3D mask denoted as $M_{\\mathrm{3D}}$ . Additionally, We implement a mask padding strategy, which introduces direction offsets to the camera poses and extends the mask boundary. This prevents incomplete editing artifacts during view changes. Further details regarding the padding technique are available in the Supplemental material.", + "bbox": [ + 75, + 537, + 468, + 733 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To render realistic editing images, the original latent variable $w$ and the edited latent variable $w_{\\mathrm{edit}}$ are used to synthesize the original and edited triplane features, respectively. For the sampling points $h$ in space during volume rendering, the corresponding original feature $f_{h}$ and edited feature $f_{\\mathrm{edit}}(h)$ are generated. To achieve the editing fusion effect, the features are fused based on the 3D mask $M_{3\\mathrm{D}}$ :", + "bbox": [ + 75, + 734, + 468, + 839 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nf _ {\\text {f u s i o n}} (h) = f _ {\\text {e d i t}} (h) \\cdot M _ {\\mathrm {3 D}} [ h ] + f (h) \\cdot \\left(1 - M _ {\\mathrm {3 D}} [ h ]\\right) \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 88, + 845, + 468, + 864 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The fused features $f_{\\mathrm{fusion}}$ are passed through the decoder of EG3D to obtain color and density information. Afterward,", + "bbox": [ + 76, + 869, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "they are processed through the volume rendering and upsampling modules to generate the final edited faces.", + "bbox": [ + 498, + 90, + 890, + 121 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.4. Training Strategy", + "text_level": 1, + "bbox": [ + 500, + 130, + 671, + 147 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "During the training of Appearance Editing Network, the geometry details should be preserved while the appearance editing effectiveness should not be influenced. This is nontrivial because the 2D supervision lacks detailed 3D structure constrain and the synthesized training data has minor geometry distortion because of Style-mixing's limitation. To solve this problem, we train our network with the follow strategy.", + "bbox": [ + 496, + 152, + 890, + 273 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Geometry Density Loss. Based on our NeRF representation, we design a novel density loss to enforce the 3D geometry consistency between the original and edited faces. Specifically, leveraging the 3D points generation approach described in Equation 2, a collection of 3D points is generated. Notably, we use all the rays during the rendering instead of rays in specific regions. These 3D sample points are further projected onto triplane space to query corresponding triplane features that are subsequently decoded into color and density through volume rendering. We minimize the density value between the original and edited faces to effectively preserve the facial geometry while decoupling the appearance:", + "bbox": [ + 496, + 273, + 890, + 470 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {\\text {d e n s i t y}} = \\sum_ {x \\in S, x ^ {\\prime} \\in S ^ {\\prime}} | | \\psi_ {\\text {d e n s i t y}} (\\mathcal {F} (x)) - \\psi_ {\\text {d e n s i t y}} \\left(\\mathcal {F} ^ {\\prime} \\left(x ^ {\\prime}\\right)\\right) | | _ {1} \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 506, + 479, + 890, + 526 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\mathcal{F}$ denotes the triplane query process and $\\psi_{\\mathrm{density}}$ denotes density decoder. $x^{\\prime}$ and $S^{\\prime}$ are the 3D points and set for edited faces. These points are sampled with the same offset but new depth map $D_{\\mathrm{edit}}$ of edited faces. Edited triplane features $\\mathcal{F}^{\\prime}$ synthesized by $w_{\\mathrm{edit}}$ are used for density calculation.", + "bbox": [ + 496, + 527, + 890, + 616 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We also utilizes the same loss functions as the pSp framework [27] to match the original stroke distribution. The loss function includes the per-pixel $L_{2}$ loss between the ground truth image $I_{GT}$ (obtained in Sec.3.1) and the edited image generated by EG3D $G$ :", + "bbox": [ + 496, + 617, + 890, + 693 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {i m g} = \\left\\| I _ {G T} - G \\left(w _ {\\text {e d i t}}\\right) \\right\\| _ {2} \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 703, + 890, + 720 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Here, $||.||_2$ denotes the Euclidean distance. To better constrain the reconstruction quality, a perceptual distance loss term is further employed:", + "bbox": [ + 496, + 729, + 890, + 776 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {L P I P S} = \\left\\| F \\left(I _ {G T}\\right) - F \\left(G \\left(w _ {\\text {e d i t}}\\right)\\right) \\right\\| _ {2} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 563, + 786, + 890, + 804 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Where $F$ represents an image feature extraction method based on VGG [19]. In order to better constrain the images generated to preserve the identity features of the original faces, an identity constraint term is employed:", + "bbox": [ + 496, + 813, + 890, + 875 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nL _ {I D} = 1 - \\left\\langle R \\left(I _ {G T}, R \\left(G \\left(w _ {\\text {e d i t}}\\right)\\right) \\right\\rangle \\right. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 578, + 883, + 890, + 902 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7542", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/c3ec3475b6cd87e09504c27162a0852cb56236dd503df313ee5c861f942ef244.jpg", + "image_caption": [ + "(a) Original image" + ], + "image_footnote": [], + "bbox": [ + 107, + 87, + 281, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/78b11e960855559575145ebfeecf05df5839088edb177da6ea79d4aa56cc075b.jpg", + "image_caption": [ + "(b) Input 1" + ], + "image_footnote": [], + "bbox": [ + 282, + 88, + 397, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/6928445405f711a5a2c4dfe226cfa38ad23a8583f0fc9f3229b2e25d725d682b.jpg", + "image_caption": [ + "(c) Results 1" + ], + "image_footnote": [], + "bbox": [ + 398, + 88, + 571, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/508b0a089bd9546f23ca28602fd00f929618b30618ad8f63b979d285f532b55c.jpg", + "image_caption": [ + "(d) Input 2" + ], + "image_footnote": [], + "bbox": [ + 571, + 88, + 687, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/c8f6d9bb838c63452e397465f84c735dd8e09b712d2c57199a299e0c4d010b17.jpg", + "image_caption": [ + "(e) Results 2" + ], + "image_footnote": [], + "bbox": [ + 687, + 88, + 861, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/07ce8394c4c060c6f22f4a6cb4814ef1cbb0bb1efced83e750885a6ac11c716d.jpg", + "image_caption": [ + "Figure 4. Color stroke-based facial NeRF appearance editing results. Given the original faces (a), users drawn the editing color strokes (b) (d), our methods generate the corresponding editing results (c)(e). Additional masks are shown in top left corner, which is the same as stroke's shape in the first two rows, and drawn by users in the last row.", + "(a) Real image", + "Figure 5. Real image appearance editing results." + ], + "image_footnote": [], + "bbox": [ + 84, + 420, + 168, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/48f34321224258c320eb50eaae134c947e60d5116e9f20b7fe8796a8dd71064d.jpg", + "image_caption": [ + "(b) Inversion" + ], + "image_footnote": [], + "bbox": [ + 169, + 420, + 254, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/a8afbad18069f82a9f0b32a8873c8351fc8f483accef60a713b0678ebbdd534e.jpg", + "image_caption": [ + "(c) Stroke" + ], + "image_footnote": [], + "bbox": [ + 254, + 420, + 336, + 549 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/dbadcbd7e2c93f21c3bf30b28c6c63835d08b76394a83338e1a90fac4834c53f.jpg", + "image_caption": [ + "(d) Result" + ], + "image_footnote": [], + "bbox": [ + 338, + 420, + 462, + 549 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "$R$ represents the pre-trained facial recognition network, ArcFace [6], and $\\langle .\\rangle$ denotes cosine similarity. Regularization constraints are added to ensure that the edited latent variables are as close as possible to the mean latent variables $\\overline{w}$ , making the generated faces more natural.", + "bbox": [ + 75, + 589, + 467, + 664 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL _ {r e g} = \\left\\| w _ {\\mathrm {e d i t}} - \\bar {w} \\right\\| _ {2} \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 675, + 468, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The overall loss function is given by:", + "bbox": [ + 76, + 700, + 323, + 715 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nL = \\alpha_ {1} L _ {\\text {d e n s i t y}} + \\alpha_ {2} L _ {i m g} + \\alpha_ {3} L _ {L P I P S} + \\alpha_ {4} L _ {I D} + \\alpha_ {5} L _ {r e g} \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 726, + 467, + 755 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Here, $\\alpha_{1},\\alpha_{2},\\alpha_{3},\\alpha_{4}$ and $\\alpha_{5}$ represent the weighting coefficients for each loss term, with values of 0.05, 2.0, 2.0, 0.2, and 0.005, respectively. In the first stage training, we set $\\alpha_{1} = 0$ because only appearance is expected to be encoded in this stage.", + "bbox": [ + 75, + 757, + 468, + 832 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 845, + 207, + 861 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Dataset: Our training dataset comprises original faces generated by EG3D random sampling and real images in", + "bbox": [ + 75, + 869, + 468, + 900 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "version [1] of CelebA-HQ [20], amounting to 47,134 examples. Appearance-edited faces and corresponding color stroke images are constructed using the method detailed in Section 3.1, resulting in 94,268 paired samples in total.", + "bbox": [ + 498, + 422, + 890, + 484 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Training details: We use a single NVIDIA GeForce RTX 3090 GPU to train our framework. The batch size is 4, with the Ranger optimizer [37] and a learning rate of 1e-4. Each training stage involved 30k iterations, completing the final network training process.", + "bbox": [ + 498, + 486, + 890, + 561 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation metrics: We use the following common metrics: Fréchet Inception Distance (FID) [12], Kernel Inception Distance (KID) [4] and Identity Consistency (ID) from [15]. To evaluate the geometry consistency in both 2D and 3D methods, we computed the Structural Similarity Index (SSIM) [35] metric for the edges obtained using the Sobel [8] operator in the edited regions of the generated images compared to the real images, denoted as E-SSIM. A higher E-SSIM value in the edited regions indicates a better preservation of the geometry in those areas.", + "bbox": [ + 498, + 564, + 890, + 715 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Results", + "text_level": 1, + "bbox": [ + 500, + 726, + 591, + 739 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Figure 4 illustrates the 3D facial NeRF appearance editing based on color strokes. Benefit from the 3D representation in our framework, users can select arbitrary view point to render images. Then, users could draw color strokes, which are overlaid on extracted strokes extracted based on methods described in Section 3.1 to serve as the edited stroke image. Our framework takes an additional 2D mask inputs, which either have the same shape with drawing strokes, or additionally drawn by users. As shown in Figure 4(c)(e), our method allows the precise control over the skin, hair,", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7543", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/74b07006572a5b4f6cb9ade34abcb4d82da6a872dfff5f9b784ce4e28de9eaa8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 88, + 212, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/67123b544404afd7363474c63f3bcb3229562c8f8af2ca86662d995af6e84925.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 170, + 210, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f86ec15e5f53033bec90ef1f0723941d5b5479860ae637607957ed0402dc8a21.jpg", + "image_caption": [ + "(a) Original image" + ], + "image_footnote": [], + "bbox": [ + 106, + 253, + 210, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8c47c9e765f41dafe2ada58b4d0fb38a4d58e8e3381b26e4d6619846ae2f7d88.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 88, + 321, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eaf73983b4522ad7be18aa89e977d847a0a59abea9755073183eb9cac764a049.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 215, + 170, + 321, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/9c5b81a344eafcb8180a0fccfefb1b7795ca372d7a9a7ca0358517787a38002d.jpg", + "image_caption": [ + "(b) Input", + "(c) SC-FEGAN[18]" + ], + "image_footnote": [], + "bbox": [ + 215, + 253, + 321, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8a8fbfcbd8e557cdf57fbcf125cbc5f678231060000b391dec2a03881b07ae6d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 88, + 429, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3943e34c26f182814a519d23deaf4c0a8f0e9e318702480b2d4e0317b5d1845a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 170, + 429, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f43730c1a0cc8592f3e6bfcfdcc123d3790f7fa5534aa5c9db8494c447fa81ce.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 321, + 253, + 429, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/476555c808c2989c461b46007fe212e243e65ab112febc7832d4a17ad98822fc.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 431, + 88, + 537, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/de7d9ed5cac85a3783db91d8f7c743d96d888094634aaee21852ebe0390a9db7.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 431, + 170, + 537, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/14224d46fe984d73fce57ff4e83a5473c1dc0a2c8613f360cbb51d2ef30a1c83.jpg", + "image_caption": [ + "(d) SDEdit[22]", + "Figure 6. Comparison with existing color stroke-based facial editing methods. SC-FEAGN[18] and SDEdit[22] are 2D image editing approaches that generate texture smoothness. pSp[27] and pSp-mixing globally changes the 3D faces. Our method generates the best results on realism and identity preservation." + ], + "image_footnote": [], + "bbox": [ + 431, + 253, + 537, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/58ebcb8f374fa0602f3c855932047319015cb82e844b8dfe991af976bed100bf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 540, + 88, + 647, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/69d4990dbebf7d319d13ddee03d1c4ed88724b6a5308b3857c7a15b49684d724.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 540, + 170, + 647, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/133d4a9b43f6871bf57245a6e27d66f24a7a9ad4c65f10e8183ea3ce13863e38.jpg", + "image_caption": [ + "(e) psp[27]" + ], + "image_footnote": [], + "bbox": [ + 540, + 253, + 647, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/8395397de1d0b172c69c44fd69be736ddb5c672c40b7541268c10126c8a3218d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 88, + 754, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/ff6783d5247c40cad95b546eec635b4c8a9348c25d96a603990c38fd22614181.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 648, + 170, + 754, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/cb1f717825b68dc76e46daccacd8ac986747e845b3c6f22539ab73ac21c44d87.jpg", + "image_caption": [ + "(f) PSP-mixing" + ], + "image_footnote": [], + "bbox": [ + 648, + 253, + 754, + 335 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/16e93cfb71062d4d67081f7cf63307a9cdb4a490245cdd00186aa5f81a9925ff.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 88, + 864, + 170 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/bcb68074f50d18b4c551a4f6bb0f17db78facb69134fa6b697e55844b4ffb439.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 756, + 170, + 864, + 253 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/3212ccf48b1e6a44a65d45bb2f9d5e1f53ffd11e9350edaa1dd48908dbea0ede.jpg", + "image_caption": [ + "(g) Ours" + ], + "image_footnote": [], + "bbox": [ + 756, + 253, + 864, + 335 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "and lip colors. It is noteworthy that the geometric details are well preserved as the original faces during appearance editing, as demonstrated by the wrinkle details in the 1st row and hair structure in the 3rd row. Unedited regions, such as hair (1st row) and background, also retain the same as the original faces. The 3rd row of Figure 4 showcases more complex local appearance editing results. To achieve diverse editing effects, users draw finer masks (c) to mark local areas, such as a cluster of hair or specific facial patterns. The 3D local fusion algorithm enables editing in marked areas, resulting in more complex and diverse editing effects.", + "bbox": [ + 75, + 404, + 468, + 570 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "As shown in Figure 5, given a real facial image, the original facial image is reconstructed in latent space using the PTI algorithm [28] (b). Similarly, users draw color stroke images (c) and edit area masks (d). Our method generates corresponding facial NeRF appearance editing results and obtains multi-view facial outcomes.", + "bbox": [ + 75, + 571, + 468, + 660 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.2. Comparisons", + "text_level": 1, + "bbox": [ + 76, + 679, + 215, + 695 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9ec5a1611052ff0382ad87a731d97d06e6ecbffc332b3c7cce16eaa90287021d.jpg", + "table_caption": [ + "Table 1. Quantitative evaluation using FID, KID $\\times 10^{2}$ , mean and std value of identity consistency (ID), E-SSIM $\\times 10^{2}$ on baseline models and our methods." + ], + "table_footnote": [], + "table_body": "
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
SC-FEGAN [18]47.183.410.50 ± 0.3774.36
SDEdit [22]37.612.520.41±0.4174.52
pSp [27]40.392.490.66 ± 0.1178.94
pSp-mixing31.322.000.73±0.0981.50
Ours16.860.830.85±0.1084.30
", + "bbox": [ + 76, + 747, + 491, + 853 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Since there are no prior works on 3D-aware stroke-based image synthesis, we retrained the pSp [27] model on EG3D using our dataset. To ensure fair comparisons, we further", + "bbox": [ + 75, + 854, + 468, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "applied style-mixing on pSp's predicted latent code by replacing 7-14 layers with original latent codes. We also compare with 2D image editing methods, including SC-FEGAN [18] and SDEdit [22]. Officially released codebases were used for all comparisons. As shown in Figure 6, given the original faces(a), color strokes and masks(b), since the editing areas are too large to complete, SC-FEGAN [18] generates less realistic results(c), with facial details appearing blurry in larger editing areas. Based on diffusion prior knowledge, SDEdit [22] generates more realistic results(d). However, the texture is still too smooth due to the geometry information absence of color stokes. Different from 2D image completion frameworks, pSp [27] predicts a latent code, which, however, totally modify the geometry compared with original faces. Unedited regions, such as background, are also changed. Even utilizing the style-mixing approach (f), there are also undesirable changes and the degree of editing has been largely affected. Compared with existing approaches, our method generates more realistic faces, which shows good faithfulness to the color strokes and precisely preserve the geometry details, even the sophisticated curly hair structure is well maintained.", + "bbox": [ + 496, + 404, + 892, + 736 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative Comparison. To further validate the superiority of our method, we conduct a quantitation evaluation. We generated 1000 facial editing examples in FFHQ datasets, following the data generation method outlined in Section 3.1. We calculated the relevant metrics between all algorithm-generated results and real images. As shown in Table 1, our method has achieved the best results on all metrics, which proves that our method generates more realistic faces (FID, KID). The original identity feature (ID) and geometry details (E-SSIM) are also better preserved.", + "bbox": [ + 496, + 737, + 892, + 888 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7544", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/f9183214cf3d7d16b8b4d5365394ebee080385fdb4a00be666b60da0a6a76c0f.jpg", + "image_caption": [ + "(a) Original" + ], + "image_footnote": [], + "bbox": [ + 81, + 87, + 158, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f06f17cfa4b09ca2340b65ead99872db8e6b72595e985b4e3304b33d21554659.jpg", + "image_caption": [ + "(b) Input" + ], + "image_footnote": [], + "bbox": [ + 158, + 88, + 235, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/ff322c874765249561a27bba03a1b3d7124c25e688184a4a806fd4ebe1eaf9d0.jpg", + "image_caption": [ + "(c) $\\mathrm{w / o}L_{\\mathrm{den}}$ (d)", + "(d) depth loss" + ], + "image_footnote": [], + "bbox": [ + 235, + 88, + 310, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f0bdb7045a7ec81875397c5c3ac078958781ed4cede721592f2ad5f16542764f.jpg", + "image_caption": [ + "Figure 7. The results of ablation study for density loss. w/o $L_{\\mathrm{den}}$ method is trained without geometry density loss while depth loss method is trained with an alternative depth image loss." + ], + "image_footnote": [], + "bbox": [ + 312, + 88, + 387, + 205 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8286044f9080c8cbb9ef64aff66504f3d6d2cbb421d923aaf431786054b594cf.jpg", + "image_caption": [ + "(e) Ours" + ], + "image_footnote": [], + "bbox": [ + 388, + 88, + 465, + 205 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 76, + 275, + 228, + 291 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/f40ff44da129518afce175ad0bf8185878104c0d529c91bc7a38ce78185e2ced.jpg", + "table_caption": [ + "Table 2. Ablation study comparison. All models are trained on the datasets described in Section 3.1 and evaluated on 1000 randomly sampled EG3D data. Metric calculations follow the methods outlined in Table 1." + ], + "table_footnote": [], + "table_body": "
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
w/o density loss21.441.070.67 ± 0.2277.35
w/ depth loss23.141.230.75 ± 0.1780.10
w/o mask fusion28.331.720.82± 0.0782.97
Ours16.860.830.85± 0.1084.30
", + "bbox": [ + 78, + 356, + 488, + 448 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conduct ablation experiments on EG3D random sampled data to justify the necessity of each component. To validate the effectiveness of the proposed geometry density loss, we presents the results of training without density loss $L_{\\mathrm{den}}$ and with an alternative depth image loss. Specifically, we employed MSE Loss between the original depth image and the generated one to constrain the network. The results in Figure 7 (d)(e) and Table 2 demonstrate the superiority of our density loss in preserving facial geometry features and maintaining identity consistency.", + "bbox": [ + 75, + 454, + 468, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Figure 8 indicates our volumetric local fusion module' effectiveness in maintaining consistency for non-edited areas between and the original and edited face. As shown in Figure 8 (d), without using 3D local fusion, non-edited areas undergo significant changes, such as brightening hair in the first row and reddening the face in the second row. In contrast, our method (Figure 8 (e)) perfectly maintains consistency in non-edited areas without affecting the editing effects in edited regions. Figures 8 (d) and (f) display computed heatmap differences between pre-edited and post-edited images.", + "bbox": [ + 75, + 604, + 468, + 772 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 76, + 784, + 194, + 799 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this study, we propose a facial NeRF appearance editing method based on color strokes, enabling the modification of facial appearance features while preserving the original facial geometry. Initially, a data construction approach is introduced, leveraging StyleGAN2 and semantic segmentation networks to create paired data with consistent", + "bbox": [ + 75, + 809, + 470, + 901 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4556c6165592b4241cefe0d786acc3fac8415e20740cc55289ea01c53f4a4e0b.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 506, + 89, + 568, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/6e417872e10068b59d700d337ef29a3ef10bcc02cbd7fbdffd7190f681d81294.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 568, + 90, + 627, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/f2974eebc124580a519598949f414e757276e2e8acf2b0e6ac9569b76bb260f8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 627, + 90, + 687, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5225b37d466883a633df03f4d6e576f26786980b82af404b295c4d764210a57d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 689, + 90, + 750, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/9271a7d13660916fa3d802564aa332e789cf683a9d06c89acf6fb44ed397b8a3.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 750, + 90, + 810, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/61916c2d9fb896db130a8e42d22aba0df1d3acfe38c0d269dec6167a4efeeec9.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 812, + 90, + 883, + 137 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/673e8d2c91b533995b55cd7c4a30c0b094ab55b79e9fb40e07f84f0058e9f5f5.jpg", + "image_caption": [ + "(a) Original", + "Figure 8. The results of ablation study for local region fusion. w/o fusion are the results without 3D local fusion method. Corresponding heat map indicates the difference between the edited images and the original images." + ], + "image_footnote": [], + "bbox": [ + 506, + 138, + 568, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4c583743e7ed4249acaea525266b3552882a76821d6907c6c4887931f113503e.jpg", + "image_caption": [ + "(b) Input" + ], + "image_footnote": [], + "bbox": [ + 568, + 138, + 627, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/20c5bdb5cb39ef3ba2bef4b955570e8018b93f29ca01dd91d053478427173624.jpg", + "image_caption": [ + "(c) w/o fusion", + "(d) Heatmap 1" + ], + "image_footnote": [], + "bbox": [ + 629, + 138, + 691, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/53821119905fb97514467bed4e000c5c09227fa280b520bfd69176fbf9b8b163.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 692, + 138, + 750, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/4a658de7ebfbd012de9ed0c063855794bbb9e2c4c8ec93e82020d93d319f5f8d.jpg", + "image_caption": [ + "(e)ours" + ], + "image_footnote": [], + "bbox": [ + 751, + 138, + 812, + 184 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/342e71844b914566dc4f096b0a1c9d11700161143fddd7715da7dbb2de4a58bc.jpg", + "image_caption": [ + "(f) Heatmap 2" + ], + "image_footnote": [], + "bbox": [ + 813, + 138, + 879, + 184 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "geometry and diverse appearances, along with corresponding color strokes. Subsequently, an appearance editing network is constructed within the pre-trained generative network's latent space. The network employs a color stroke encoder to extract color features from input stroke images and utilizes a latent variable fusion network to achieve appearance editing while preserving geometric features. To maintain unchanged regions, a 3D local fusion method is introduced, enabling effective editing of localized appearance while preserving the facial identity features. Experimental results demonstrate the superiority of our method in generating higher-quality digital facial results compared to existing approaches.", + "bbox": [ + 496, + 277, + 890, + 474 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Despite achieving high-quality color editing results through color strokes, our method faces several challenges. Firstly, for highly detailed areas such as eyeballs, our method struggles to yield effective editing results. Handling these regions separately through segmentation and dedicated data processing could enhance editing outcomes. Additionally, due to limitations in the training dataset, our method encounters difficulties in handling overly complex color strokes, such as rainbow-colored hair, tending to average color strokes instead. To address this, generating distinct colors separately, followed by mask creation and blending, could yield superior results. Future research endeavors could extend the proposed algorithm from 3D digital faces to other types of 3D models, achieving more generalized editing effects. Moreover, combining color strokes with line drawings and semantic segmentation maps could enable simultaneous editing of 3D digital facial geometry and appearance.", + "bbox": [ + 496, + 474, + 892, + 748 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 784, + 658, + 801 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by National Natural Science Foundation of China (No. 62102403), and the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (No. VRLAB2022C07). We would like to thank Professor Lin Gao for his helpful discussions and generous support.", + "bbox": [ + 496, + 809, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7545", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE/CVF international conference on computer vision, pages 4432-4441, 2019. 6", + "[2] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. Restyle: A residual-based stylegan encoder via iterative refinement. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 6711–6720, 2021. 4", + "[3] David Bau, Hendrik Strobelt, William S. 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International Journal of Computer Vision, 129: 3051-3068, 2021. 2, 4" + ], + "bbox": [ + 78, + 90, + 468, + 867 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "7547", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/7fe1ba34-6e33-48a7-bca3-a74b49e199ac_model.json b/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/7fe1ba34-6e33-48a7-bca3-a74b49e199ac_model.json new file mode 100644 index 0000000000000000000000000000000000000000..98b7537dc1dd8e42b7c0310ad4c094bde32a0b82 --- /dev/null +++ b/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/7fe1ba34-6e33-48a7-bca3-a74b49e199ac_model.json @@ -0,0 +1,2585 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.176, + 0.131, + 0.795, + 0.175 + ], + "angle": 0, + "content": "StrokeFaceNeRF: Stroke-based Facial Appearance Editing in Neural Radiance Field" + }, + { + "type": "text", + "bbox": [ + 0.203, + 0.203, + 0.768, + 0.275 + ], + "angle": 0, + "content": "Xiao-Juan Li\\(^{1,2}\\) Dingxi Zhang\\(^{2,1}\\) Shu-Yu Chen\\(^{1}\\) Feng-Lin Liu\\(^{1,2*}\\) \n\\(^{1}\\)Beijing Key Laboratory of Mobile Computing and Pervasive Device, Institute of Computing Technology, Chinese Academy of Sciences \n\\(^{2}\\)University of Chinese Academy of Sciences" + }, + { + "type": "text", + "bbox": [ + 0.131, + 0.278, + 0.835, + 0.293 + ], + "angle": 0, + "content": "{lixiaojuan,chenshuyu,liufenglin21s}@ict.ac.cn zhangdingxi20a@mails.ucas.ac.cn" + }, + { + "type": "image", + "bbox": [ + 0.1, + 0.305, + 0.871, + 0.495 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.498, + 0.893, + 0.54 + ], + "angle": 0, + "content": "Figure 1. StrokeFaceNeRF enables versatile high-quality color stroke-based appearance editing for facial NeRFs. Users can draw strokes over a rendered facial image from any angle and define the editing region using masks. The third column showcases the photo-realistic free-view rendering results with exceptional color correspondence." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.554, + 0.314, + 0.57 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.473, + 0.873 + ], + "angle": 0, + "content": "Current 3D-aware facial NeRF generation approaches control the facial appearance by text, lighting conditions or reference images, limiting precise manipulation of local facial regions and interactivity. Color stroke, a user-friendly and effective tool to depict appearance, is challenging to edit 3D faces because of the lack of texture, coarse geometry representation and detailed editing operations. To solve the above problems, we introduce StrokeFaceNeRF, a novel stroke-based method for editing facial NeRF appearance. In order to infer the missing texture and 3D geometry information, 2D edited stroke maps are firstly encoded into the EG3D's latent space, followed by a transformer-based editing module to achieve effective appearance changes while preserving the original geometry in editing regions. Notably, we design a novel geometry loss function to ensure surface density remains consistent during training. To further enhance the local manipulation accuracy, we propose a stereo fusion approach which lifts the 2D mask (inferred from strokes or drawn by users) into 3D mask volume, al" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.555, + 0.893, + 0.616 + ], + "angle": 0, + "content": "lowing explicit blending of the original and edited faces. Extensive experiments validate that the proposed method outperforms existing 2D and 3D methods in both editing reality and geometry retention." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.649, + 0.633, + 0.665 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Realistic 3D human face generation is a popular topic and has wide range applications in character design, virtual meeting and education. Traditional 3D facial modeling methods rely on software like Maya and Zbursh to construct mesh models while employing texture mapping for facial appearances. However, these methods are time-consuming and labor-intensive, especially when editing local appearance details and aiming for photorealistic results. Neural Radiance Field (NeRF) [23], a new 3D representation technique, easily render photo-realistic images with the input of multi-view images. The further combination of Generative Adversarial Networks (GAN) [10] with NeRF [5, 11, 24, 30] has enabled the generation of high-quality facial NeRF through random sampling. Nevertheless, precise control over appearance details remains a challenge." + }, + { + "type": "page_footnote", + "bbox": [ + 0.081, + 0.888, + 0.212, + 0.9 + ], + "angle": 0, + "content": "*Corresponding Author" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7538" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.302 + ], + "angle": 0, + "content": "Efforts to enhance controllability involve disentangling geometry and appearance during facial NeRF generation. Sun et al. introduced the FE-NeRF [32] that employs separate latent codes to control the intricacies of facial geometry and appearance. Subsequent advancements [16, 31] utilize decoupling techniques based on triplane representations, leading to the facial generation results with significantly enhanced quality. Despite their success in good geometry and appearance swapping, these methods heavily rely on random sampling or reference images for global appearance editing. This reliance poses challenges in the obtainment of desired reference images and precludes precise control over localized appearance attributes, such as selective hair color alteration." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.303, + 0.473, + 0.544 + ], + "angle": 0, + "content": "Compared to reference images, colored strokes, functioning as an interactive tool, offer a precise depiction of local appearance details. In stroke-based image editing, one category of methods [17, 26] relies on conditional GAN and completion framework to edit local regions with the stroke guidance. However, artifacts may arise in the editing boundary and result in less realistic images for large-area editing operations, as shown in Figure 6. Another category of methods [22, 27] employs pre-trained facial generation models as decoders, mapping colored strokes to the latent space of the generation model to generate edited facial results. However, these methods struggle to preserve the unchanged geometric features of the input face during editing, as demonstrated in Figure 6. Importantly, these techniques are specifically tailored for 2D facial image editing and cannot be directly applied to 3D facial radiance fields." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.546, + 0.473, + 0.894 + ], + "angle": 0, + "content": "This paper presents StrokeFaceNeRF, a framework for editing facial NeRF appearance based on colored strokes, enabling precise modifications of color and lighting in 3D faces. Leveraging 2D facial image generation techniques such as StyleGAN2 [21] and semantic segmentation methods [38], we construct a dataset of faces with identical geometry but varying appearances, generating corresponding colored stroke maps using bilateral filtering and semantic clustering algorithms. To achieve appearance editing, directly encoding edited stroke maps into the latent space of the pre-trained facial NeRF generation model [5] leads to texture smoothness and undesirable geometry distortion due to high-frequency information absence and user's inaccurate drawing of strokes. To solve this problem, we propose a transformer-based editing network, which fuses the original and stroke-encoded latent codes to modify appearance while preserving the original geometry in edited regions. Furthermore, we introduce a geometry loss term during training to ensure surface density remains unchanged, improving detail preservation. To further maintain unchanged features in non-edited areas for precise editing, we design a volumetric fusion algorithm that integrates localized regions before and after editing in 3D space, enabling local-" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.818, + 0.121 + ], + "angle": 0, + "content": "ized appearance editing effects in facial models. Our contributions are summarized as follows" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.122, + 0.892, + 0.167 + ], + "angle": 0, + "content": "- We propose the first color stroke-based facial NeRF editing framework to generate free-view realistic appearance editing facial images." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.168, + 0.892, + 0.227 + ], + "angle": 0, + "content": "- We design a novel geometry density loss to train the transformer-based latent editing network, which effectively preserves the geometry detail during facial appearance modifications." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.228, + 0.892, + 0.273 + ], + "angle": 0, + "content": "- We introduce a volumetric fusion algorithm to precisely edit local regions while maintaining the 3D consistency in unedited regions." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.122, + 0.892, + 0.273 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.294, + 0.642, + 0.31 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.319, + 0.864, + 0.336 + ], + "angle": 0, + "content": "2.1. Facial Image Editing with Colored Strokes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.342, + 0.892, + 0.644 + ], + "angle": 0, + "content": "Existing 2D facial image editing methods using colored strokes can be divided into two categories. One group of methods utilizes conditional Generative Adversarial Networks (cGANs) to accomplish stroke-guided image generation. Sangkloy et al. [29] utilize sketches and colored strokes to directly generate realistic images through a translation network. However, this method fails to achieve localized area editing. To solve this problem, FaceShop [26] utilizes image completion techniques and 2D mask marking for localized facial image editing based on sketches and colored strokes. Jo et al. [18] further introduced SC-FEGAN that employs gated convolutions and new style losses for training, enabling a broader range of editing operations. Xiao et al. [36] design a hair generation network with self-attention mechanisms, achieving more natural and realistic hair editing effects. However, these methods are sensitive to input conditions and result in smooth edits lacking texture information in edited regions. Additionally, they tend to produce artifacts at the editing boundary due to the image completion techniques." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.645, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Another category of methods utilizes pre-trained generative models to generate high quality faces instead of pixelwise translation. Bau et al. [3] first utilize reverse optimization to achieve image shape and color editing in the GAN's latent space. pSp [27] further designs an image encoding network to map various types of input images, such as sketches and color strokes, into StyleGAN2's latent space to generate corresponding facial images. In order to generate highly editable latent codes, Tov et al. [34] further constrained the latent codes with a discriminator. However, these methods, as they represent the entire image with latent vectors, struggle to achieve localized editing effects. Instead of GAN dependence, Meng et al. [22] employed pre-trained diffusion models to achieve facial image editing based on colored stroke maps. Images with user-drawn strokes are added Gaussian noise, then progressively denoised to synthesize realistic facial images. However, it is" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7539" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.102, + 0.089, + 0.472, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.475, + 0.089, + 0.871, + 0.301 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.304, + 0.895, + 0.361 + ], + "angle": 0, + "content": "Figure 2. 3D Facial Appearance Editing Framework. Given the original latent code \\( w \\), free-view images are rendered by EG3D. Users introduce editing operations, resulting in the creation of a color stroke image \\( C_{\\mathrm{edit}} \\). This stroke map is encoded by Color Encoder \\( E_{c} \\) to generate \\( w_{c} \\), which is fused with original latent code \\( w \\) by latent fusion network to generate \\( w_{\\mathrm{edit}} \\). Utilizing an additional 2D mask, the volumetric fusion approach facilitates targeted appearance editing within specific regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.368, + 0.471, + 0.445 + ], + "angle": 0, + "content": "challenging to directly apply this method to facial neural radiance field editing. Additionally, because of the direct input of coarse stroke maps, it is challenging for the above methods to maintain geometric features while performing appearance modification in editing regions." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.455, + 0.273, + 0.472 + ], + "angle": 0, + "content": "2.2. Editing Facial NeRF" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.479, + 0.47, + 0.705 + ], + "angle": 0, + "content": "Combining generative adversarial networks with neural radiance fields enables the synthesis of realistic facial images from arbitrary viewpoints. Graf [30] first adds extra latent codes to NeRF's fully connected network to support face generation and use multiscale discriminators for supervision. Giraffe [24] designs a new framework that employs volume rendering to obtain feature maps and a convolutional framework to generate facial images. StyleSDF [25] and GRAM [7] utilize representation methods based on SDF and implicit planes, respectively, producing higher-quality and more 3D consistent results. EG3D [5] propose a facial NeRF generation framework based on triplane representation and StyleGAN2 [21] generator. However, these methods can only synthesize faces through random sampling and lack the ability for editing." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.705, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To generate controllable facial NeRF, Jo et al. [17] use sketches, black-and-white images, and text as control conditions. Gao et al. [9] propose a facial NeRF generation and editing framework based on sketches to enhance synthesis quality and achieve fine editing. However, this method can only edit facial geometry. Another line of work decouples facial NeRF's geometry and appearance using semantic segmentation. FE-NeRF [32] achieves geometric editing through reverse latent code optimization and appearance editing through random sampling. IDE-3D [31] constructs geometry triplanes and appearance triplanes, and designs a semantic map encoder to generate higher-quality facial results. NeRFFaceEditing [16] apply AdaIN [14] to triplanes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.368, + 0.895, + 0.474 + ], + "angle": 0, + "content": "features, enabling the disentanglement of geometry and appearance control. Although the above methods achieve effective appearance modification, reference images or latent codes are required instead of user's flexible interaction. More importantly, the above methods are designed for the global appearance editing and cannot be directly utilized for local editing." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.498, + 0.637, + 0.516 + ], + "angle": 0, + "content": "3. Methodology" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.735 + ], + "angle": 0, + "content": "We propose a framework, StrokeFaceNeRF, enables users to utilize colored strokes for facial NeRF appearance editing. We employ the EG3D [5] generator architecture, a proficient 3D-aware Generative Adversarial Network (GAN) that combines the StyleGAN2 [21] architecture and neural rendering to produce high-quality 3D shapes. Given a latent code, a triplane representation can be obtained from a StyleGAN2 backbone. The neural renderer then aggregates features from these triplanes and predicts feature images based on a specified camera pose. Subsequently, a super-resolution module is applied to upsample and refine these raw neurally rendered images, resulting in high-quality, multiview-consistent images. More details of the generator can be found in [5]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.736, + 0.893, + 0.903 + ], + "angle": 0, + "content": "Our method comprises three key components: dataset construction, colored stroke editing network, and 3D local fusion module. Initially, we introduce a dataset construction approach to acquire facial images with consistent geometry but varying appearances, along with their corresponding colored stroke images as detailed in Section 3.1. Subsequently, an appearance editing network, described in Section 3.2, is established within the latent space of EG3D to predict the 3D faces. Additionally, in Section 3.3, we propose a 3D local fusion method to enable effective appearance editing while meticulously preserving features in" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.517, + 0.957 + ], + "angle": 0, + "content": "7540" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.208, + 0.106 + ], + "angle": 0, + "content": "non-edited regions." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.123, + 0.277, + 0.137 + ], + "angle": 0, + "content": "3.1. Dataset Construction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.146, + 0.469, + 0.341 + ], + "angle": 0, + "content": "To supervise the training of network models, the training data needs to simulate the process of facial appearance editing based on colored strokes. Thus, the training tuples include original faces, edited faces, and corresponding colored stroke maps. Dataset construction involves three steps as shown in Figure 3: (1) building a collection of facial latent codes in EG3D's latent space, obtained through random sampling and real images inversion; (2) constructing facial tuples with identical geometry but different appearances. Two different methods were employed: one based on semantic segmentation and the other based on StyleGAN2 generative networks; (3) generating colored stroke maps using bilateral filtering and semantic clustering methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.469, + 0.599 + ], + "angle": 0, + "content": "We utilize two approaches to synthesize paired images with the same geometry but different appearance, indicated as the edited ground truth faces. Semantic Segmentation-Based Augmentation. Given the original rendered facial images, we utilize BiSeNet [38] to get semantic segmentation masks. Then, for each local semantic region, we represent it into HSV space, where the Hue channel is uniformly replaced with random color, while the Saturation and Value channels are added random perturbation. Finally, these regions are merged into original images to imitate appearance editing. StyleGAN2-Based Augmentation. We further utilize pre-trained generator to synthesize more diverse and realistic training images. Given the original rendered images, ReStyle [2] encodes them into StyleGAN2 latent space, followed with style mixing to change the facial appearance while preserving the same geometry. More details can be found in Supplementary." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.599, + 0.469, + 0.901 + ], + "angle": 0, + "content": "With the paired appearance modification images, corresponding color strokes are required to imitate real editing situation. Typically, users drawn strokes are simple and monochromatic. Therefore, synthesized color stroke images must preserve the original image's color and geometric layout while eliminating high-frequency texture features and local details. To achieve this objective, we employ the bilateral filtering method [33] to effectively preserves the edge features of the facial image while eliminating high-frequency details. Specially, the initial image undergoes median filtering, followed by iterative application of bilateral filtering, as explained in the Supplementary. Nevertheless, some regions still exhibit smooth transitions between different colored areas after filtering, posing challenges for users aiming to replicate specific effects. To tackle this issue, we employ a pixel value clustering technique based on semantic information. Initially, the facial image undergoes semantic segmentation. Within the hair area, clustering allows all pixel colors to be replaced by the nearest cluster center color, thereby eliminating smooth transition regions." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.088, + 0.885, + 0.216 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.222, + 0.892, + 0.277 + ], + "angle": 0, + "content": "Figure 3. Dataset construction pipeline. Given EG3D rendering images, the appearance is changed by two different approaches. Then, the color stroke images are synthesized by image filter and cluster." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.285, + 0.892, + 0.316 + ], + "angle": 0, + "content": "The same methodology is applied to the facial area, yielding the final color stroke image." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.324, + 0.761, + 0.34 + ], + "angle": 0, + "content": "3.2. Appearance Editing Network" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.347, + 0.892, + 0.527 + ], + "angle": 0, + "content": "In our framework, the target face NeRF to be edited is represented as a latent code \\( w \\) within EG3D's latent space. The latent code can be obtained either by random sampling in EG3D or by applying PTI [28] to invert real images. Utilizing StyleGAN generator and volume rendering, free view facial images can be generated, followed by the approaches in Section 3.1 to extract color stroke images. Users then modify these color stroke images to obtain the edited color stroke image \\( C_{\\mathrm{edit}} \\). As illustrated in Figure 2, the input to the appearance editing network consists of the original latent variable \\( w \\), the edited color stroke image \\( C_{\\mathrm{edit}} \\), and the output is the edited latent variable \\( w_{\\mathrm{edit}} \\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.529, + 0.893, + 0.875 + ], + "angle": 0, + "content": "The appearance editing network comprises two main components: the Color Encoder \\( E_{c} \\) and the Latent Fusion Network \\( F_{l} \\). Specifically, given the edited color stroke image \\( C_{\\mathrm{edit}} \\), the color encoder that has a similar structure to [27], predicts the latent code \\( w_{c} \\). While this latent code generates facial results with color editing effects, it fails to preserve the original facial features, such as the geometric structure of the hair and the original skin color in non-edited areas, as shown in Figure 2. Therefore, a latent code fusion network is designed to utilize the information from the original latent variable \\( w \\), thus better preserving the original facial features. The latent fusion network \\( F_{l} \\) adopts a cross-attention transformer block to predict the fused latent variable \\( w_{\\mathrm{edit}} \\). This design implicitly extracts the color information from \\( w_{c} \\) and geometry information from \\( w \\), guaranteeing a thorough integration of both color-edited and original facial features. In this configuration, the latent code \\( w_{c} \\) is employed as query tokens, whereas the original latent code \\( w \\) serves as key and value tokens. We also normalize over queries instead of keys as described in [13] to ensure a continuous refinement of \\( w_{c} \\) during the fusion process with value tokens while mitigating the potential influence of \\( w \\) being too large." + }, + { + "type": "equation", + "bbox": [ + 0.614, + 0.886, + 0.891, + 0.902 + ], + "angle": 0, + "content": "\\[\nw _ {\\text {e d i t}} = F _ {l} \\left(w, E _ {c} \\left(C _ {\\text {e d i t}}\\right)\\right) \\tag {1}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7541" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.303, + 0.106 + ], + "angle": 0, + "content": "3.3. Volumetric Local Fusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.113, + 0.469, + 0.265 + ], + "angle": 0, + "content": "While direct rendering by \\( w_{\\mathrm{edit}} \\) yields good editing effects within targeted editing areas, as depicted in Figure 7, noticeable undesirable discrepancies emerge in unedited regions. Moreover, intricate editing tasks, such as selectively dyeing specific portions of hair or drawing specific patterns on faces, pose challenges for the latent code-based representation because of its overarching global control inherited from StyleGAN2 backbone. To address these issues, we propose a volumetric fusion approach to enable more refined editing operations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.266, + 0.471, + 0.462 + ], + "angle": 0, + "content": "In order to facilitate local editing, our method introduces support for an additional 2D mask input that indicates the editing region. This 2D mask is further lifted into 3D mask volume to support volumetric fusion. Specifically, we propose a depth guidance approach to sample a set of points near the facial surface. In the volume rendering, for each ray \\( r_{i,j} \\) of the pixel at the \\( i \\)th row and \\( j \\)th column, the camera's position and ray direction are denoted as \\( o_{i,j} \\) and \\( d_{i,j} \\), respectively. After rendering the original faces, we get the corresponding depth value \\( D[i,j] \\). Then, for each ray, we uniformly sample \\( K \\) points with offset \\( \\triangle x_k \\) within range \\( [-0.1, 0.1] \\). The sampled 3D points set \\( S \\) for the original face is denoted as:" + }, + { + "type": "equation", + "bbox": [ + 0.12, + 0.467, + 0.469, + 0.487 + ], + "angle": 0, + "content": "\\[\nS = \\cup_ {i, j} \\cup_ {k = 1} ^ {K} \\left(o _ {i, j} + \\left(D [ i, j ] + \\triangle x _ {k}\\right) \\cdot d _ {i, j}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.492, + 0.469, + 0.538 + ], + "angle": 0, + "content": "where the default value of \\( K \\) is 5. Notably, as illustrated in Figure 2, we selectively employ the rays corresponding to pixels within the 2D mask regions." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.469, + 0.734 + ], + "angle": 0, + "content": "Subsequently, this generated 3D point set undergoes a transformation into a 3D volumetric mask. Specifically, we initialize a \\(256 \\times 256 \\times 256\\) 3D volume with zero values throughout the space. The coordinates of the 3D points, along with their neighboring positions, are designated as 1, indicating 3D editing regions. To ensure smoother boundaries, we utilize a three-dimensional dilation and Gaussian filtering, yielding the 3D mask denoted as \\(M_{\\mathrm{3D}}\\). Additionally, We implement a mask padding strategy, which introduces direction offsets to the camera poses and extends the mask boundary. This prevents incomplete editing artifacts during view changes. Further details regarding the padding technique are available in the Supplemental material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.469, + 0.84 + ], + "angle": 0, + "content": "To render realistic editing images, the original latent variable \\( w \\) and the edited latent variable \\( w_{\\mathrm{edit}} \\) are used to synthesize the original and edited triplane features, respectively. For the sampling points \\( h \\) in space during volume rendering, the corresponding original feature \\( f_{h} \\) and edited feature \\( f_{\\mathrm{edit}}(h) \\) are generated. To achieve the editing fusion effect, the features are fused based on the 3D mask \\( M_{3\\mathrm{D}} \\):" + }, + { + "type": "equation", + "bbox": [ + 0.089, + 0.847, + 0.469, + 0.865 + ], + "angle": 0, + "content": "\\[\nf _ {\\text {f u s i o n}} (h) = f _ {\\text {e d i t}} (h) \\cdot M _ {\\mathrm {3 D}} [ h ] + f (h) \\cdot \\left(1 - M _ {\\mathrm {3 D}} [ h ]\\right) \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "The fused features \\( f_{\\mathrm{fusion}} \\) are passed through the decoder of EG3D to obtain color and density information. Afterward," + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.122 + ], + "angle": 0, + "content": "they are processed through the volume rendering and upsampling modules to generate the final edited faces." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.131, + 0.673, + 0.148 + ], + "angle": 0, + "content": "3.4. Training Strategy" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.154, + 0.892, + 0.274 + ], + "angle": 0, + "content": "During the training of Appearance Editing Network, the geometry details should be preserved while the appearance editing effectiveness should not be influenced. This is nontrivial because the 2D supervision lacks detailed 3D structure constrain and the synthesized training data has minor geometry distortion because of Style-mixing's limitation. To solve this problem, we train our network with the follow strategy." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.275, + 0.892, + 0.472 + ], + "angle": 0, + "content": "Geometry Density Loss. Based on our NeRF representation, we design a novel density loss to enforce the 3D geometry consistency between the original and edited faces. Specifically, leveraging the 3D points generation approach described in Equation 2, a collection of 3D points is generated. Notably, we use all the rays during the rendering instead of rays in specific regions. These 3D sample points are further projected onto triplane space to query corresponding triplane features that are subsequently decoded into color and density through volume rendering. We minimize the density value between the original and edited faces to effectively preserve the facial geometry while decoupling the appearance:" + }, + { + "type": "equation", + "bbox": [ + 0.508, + 0.481, + 0.892, + 0.527 + ], + "angle": 0, + "content": "\\[\nL _ {\\text {d e n s i t y}} = \\sum_ {x \\in S, x ^ {\\prime} \\in S ^ {\\prime}} | | \\psi_ {\\text {d e n s i t y}} (\\mathcal {F} (x)) - \\psi_ {\\text {d e n s i t y}} \\left(\\mathcal {F} ^ {\\prime} \\left(x ^ {\\prime}\\right)\\right) | | _ {1} \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.528, + 0.892, + 0.617 + ], + "angle": 0, + "content": "where \\(\\mathcal{F}\\) denotes the triplane query process and \\(\\psi_{\\mathrm{density}}\\) denotes density decoder. \\(x^{\\prime}\\) and \\(S^{\\prime}\\) are the 3D points and set for edited faces. These points are sampled with the same offset but new depth map \\(D_{\\mathrm{edit}}\\) of edited faces. Edited triplane features \\(\\mathcal{F}^{\\prime}\\) synthesized by \\(w_{\\mathrm{edit}}\\) are used for density calculation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.618, + 0.892, + 0.694 + ], + "angle": 0, + "content": "We also utilizes the same loss functions as the pSp framework [27] to match the original stroke distribution. The loss function includes the per-pixel \\( L_{2} \\) loss between the ground truth image \\( I_{GT} \\) (obtained in Sec.3.1) and the edited image generated by EG3D \\( G \\):" + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.704, + 0.891, + 0.722 + ], + "angle": 0, + "content": "\\[\nL _ {i m g} = \\left\\| I _ {G T} - G \\left(w _ {\\text {e d i t}}\\right) \\right\\| _ {2} \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.731, + 0.892, + 0.777 + ], + "angle": 0, + "content": "Here, \\(||.||_2\\) denotes the Euclidean distance. To better constrain the reconstruction quality, a perceptual distance loss term is further employed:" + }, + { + "type": "equation", + "bbox": [ + 0.565, + 0.787, + 0.891, + 0.805 + ], + "angle": 0, + "content": "\\[\nL _ {L P I P S} = \\left\\| F \\left(I _ {G T}\\right) - F \\left(G \\left(w _ {\\text {e d i t}}\\right)\\right) \\right\\| _ {2} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.814, + 0.892, + 0.876 + ], + "angle": 0, + "content": "Where \\( F \\) represents an image feature extraction method based on VGG [19]. In order to better constrain the images generated to preserve the identity features of the original faces, an identity constraint term is employed:" + }, + { + "type": "equation", + "bbox": [ + 0.58, + 0.885, + 0.891, + 0.903 + ], + "angle": 0, + "content": "\\[\nL _ {I D} = 1 - \\left\\langle R \\left(I _ {G T}, R \\left(G \\left(w _ {\\text {e d i t}}\\right)\\right) \\right\\rangle \\right. \\tag {7}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7542" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.109, + 0.088, + 0.282, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.147, + 0.357, + 0.245, + 0.37 + ], + "angle": 0, + "content": "(a) Original image" + }, + { + "type": "image", + "bbox": [ + 0.283, + 0.089, + 0.398, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.312, + 0.357, + 0.369, + 0.369 + ], + "angle": 0, + "content": "(b) Input 1" + }, + { + "type": "image", + "bbox": [ + 0.399, + 0.089, + 0.573, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.452, + 0.357, + 0.518, + 0.369 + ], + "angle": 0, + "content": "(c) Results 1" + }, + { + "type": "image", + "bbox": [ + 0.573, + 0.089, + 0.688, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.602, + 0.357, + 0.659, + 0.369 + ], + "angle": 0, + "content": "(d) Input 2" + }, + { + "type": "image", + "bbox": [ + 0.689, + 0.089, + 0.862, + 0.355 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.741, + 0.357, + 0.808, + 0.369 + ], + "angle": 0, + "content": "(e) Results 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.374, + 0.892, + 0.416 + ], + "angle": 0, + "content": "Figure 4. Color stroke-based facial NeRF appearance editing results. Given the original faces (a), users drawn the editing color strokes (b) (d), our methods generate the corresponding editing results (c)(e). Additional masks are shown in top left corner, which is the same as stroke's shape in the first two rows, and drawn by users in the last row." + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.421, + 0.169, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.088, + 0.552, + 0.168, + 0.564 + ], + "angle": 0, + "content": "(a) Real image" + }, + { + "type": "image", + "bbox": [ + 0.171, + 0.421, + 0.255, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.179, + 0.552, + 0.246, + 0.563 + ], + "angle": 0, + "content": "(b) Inversion" + }, + { + "type": "image", + "bbox": [ + 0.255, + 0.421, + 0.338, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.269, + 0.552, + 0.323, + 0.563 + ], + "angle": 0, + "content": "(c) Stroke" + }, + { + "type": "image", + "bbox": [ + 0.339, + 0.421, + 0.463, + 0.55 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.374, + 0.552, + 0.428, + 0.563 + ], + "angle": 0, + "content": "(d) Result" + }, + { + "type": "image_caption", + "bbox": [ + 0.129, + 0.569, + 0.416, + 0.583 + ], + "angle": 0, + "content": "Figure 5. Real image appearance editing results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.59, + 0.468, + 0.665 + ], + "angle": 0, + "content": "\\(R\\) represents the pre-trained facial recognition network, ArcFace [6], and \\(\\langle .\\rangle\\) denotes cosine similarity. Regularization constraints are added to ensure that the edited latent variables are as close as possible to the mean latent variables \\(\\overline{w}\\), making the generated faces more natural." + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.676, + 0.469, + 0.693 + ], + "angle": 0, + "content": "\\[\nL _ {r e g} = \\left\\| w _ {\\mathrm {e d i t}} - \\bar {w} \\right\\| _ {2} \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.702, + 0.324, + 0.716 + ], + "angle": 0, + "content": "The overall loss function is given by:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.727, + 0.468, + 0.756 + ], + "angle": 0, + "content": "\\[\nL = \\alpha_ {1} L _ {\\text {d e n s i t y}} + \\alpha_ {2} L _ {i m g} + \\alpha_ {3} L _ {L P I P S} + \\alpha_ {4} L _ {I D} + \\alpha_ {5} L _ {r e g} \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.758, + 0.469, + 0.833 + ], + "angle": 0, + "content": "Here, \\(\\alpha_{1},\\alpha_{2},\\alpha_{3},\\alpha_{4}\\) and \\(\\alpha_{5}\\) represent the weighting coefficients for each loss term, with values of 0.05, 2.0, 2.0, 0.2, and 0.005, respectively. In the first stage training, we set \\(\\alpha_{1} = 0\\) because only appearance is expected to be encoded in this stage." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.846, + 0.209, + 0.862 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Dataset: Our training dataset comprises original faces generated by EG3D random sampling and real images in" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.424, + 0.892, + 0.485 + ], + "angle": 0, + "content": "version [1] of CelebA-HQ [20], amounting to 47,134 examples. Appearance-edited faces and corresponding color stroke images are constructed using the method detailed in Section 3.1, resulting in 94,268 paired samples in total." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.487, + 0.892, + 0.563 + ], + "angle": 0, + "content": "Training details: We use a single NVIDIA GeForce RTX 3090 GPU to train our framework. The batch size is 4, with the Ranger optimizer [37] and a learning rate of 1e-4. Each training stage involved 30k iterations, completing the final network training process." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.565, + 0.892, + 0.716 + ], + "angle": 0, + "content": "Evaluation metrics: We use the following common metrics: Fréchet Inception Distance (FID) [12], Kernel Inception Distance (KID) [4] and Identity Consistency (ID) from [15]. To evaluate the geometry consistency in both 2D and 3D methods, we computed the Structural Similarity Index (SSIM) [35] metric for the edges obtained using the Sobel [8] operator in the edited regions of the generated images compared to the real images, denoted as E-SSIM. A higher E-SSIM value in the edited regions indicates a better preservation of the geometry in those areas." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.727, + 0.593, + 0.74 + ], + "angle": 0, + "content": "4.1. Results" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Figure 4 illustrates the 3D facial NeRF appearance editing based on color strokes. Benefit from the 3D representation in our framework, users can select arbitrary view point to render images. Then, users could draw color strokes, which are overlaid on extracted strokes extracted based on methods described in Section 3.1 to serve as the edited stroke image. Our framework takes an additional 2D mask inputs, which either have the same shape with drawing strokes, or additionally drawn by users. As shown in Figure 4(c)(e), our method allows the precise control over the skin, hair," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7543" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.213, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.171, + 0.212, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.107, + 0.254, + 0.212, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.111, + 0.339, + 0.21, + 0.351 + ], + "angle": 0, + "content": "(a) Original image" + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.089, + 0.322, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.171, + 0.322, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.216, + 0.254, + 0.322, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.245, + 0.339, + 0.293, + 0.351 + ], + "angle": 0, + "content": "(b) Input" + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.089, + 0.43, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.171, + 0.43, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.323, + 0.254, + 0.43, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.324, + 0.338, + 0.43, + 0.351 + ], + "angle": 0, + "content": "(c) SC-FEGAN[18]" + }, + { + "type": "image", + "bbox": [ + 0.432, + 0.089, + 0.539, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.432, + 0.171, + 0.539, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.432, + 0.254, + 0.539, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.445, + 0.339, + 0.526, + 0.351 + ], + "angle": 0, + "content": "(d) SDEdit[22]" + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.089, + 0.648, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.171, + 0.648, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.541, + 0.254, + 0.648, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.564, + 0.339, + 0.624, + 0.351 + ], + "angle": 0, + "content": "(e) psp[27]" + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.089, + 0.756, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.171, + 0.756, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.65, + 0.254, + 0.756, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.663, + 0.339, + 0.741, + 0.351 + ], + "angle": 0, + "content": "(f) PSP-mixing" + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.089, + 0.865, + 0.171 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.171, + 0.865, + 0.254 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.758, + 0.254, + 0.865, + 0.336 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.788, + 0.339, + 0.834, + 0.351 + ], + "angle": 0, + "content": "(g) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.355, + 0.894, + 0.397 + ], + "angle": 0, + "content": "Figure 6. Comparison with existing color stroke-based facial editing methods. SC-FEAGN[18] and SDEdit[22] are 2D image editing approaches that generate texture smoothness. pSp[27] and pSp-mixing globally changes the 3D faces. Our method generates the best results on realism and identity preservation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.405, + 0.469, + 0.571 + ], + "angle": 0, + "content": "and lip colors. It is noteworthy that the geometric details are well preserved as the original faces during appearance editing, as demonstrated by the wrinkle details in the 1st row and hair structure in the 3rd row. Unedited regions, such as hair (1st row) and background, also retain the same as the original faces. The 3rd row of Figure 4 showcases more complex local appearance editing results. To achieve diverse editing effects, users draw finer masks (c) to mark local areas, such as a cluster of hair or specific facial patterns. The 3D local fusion algorithm enables editing in marked areas, resulting in more complex and diverse editing effects." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.572, + 0.47, + 0.661 + ], + "angle": 0, + "content": "As shown in Figure 5, given a real facial image, the original facial image is reconstructed in latent space using the PTI algorithm [28] (b). Similarly, users draw color stroke images (c) and edit area masks (d). Our method generates corresponding facial NeRF appearance editing results and obtains multi-view facial outcomes." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.68, + 0.217, + 0.696 + ], + "angle": 0, + "content": "4.2. Comparisons" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.702, + 0.47, + 0.744 + ], + "angle": 0, + "content": "Table 1. Quantitative evaluation using FID, KID \\(\\times 10^{2}\\), mean and std value of identity consistency (ID), E-SSIM \\(\\times 10^{2}\\) on baseline models and our methods." + }, + { + "type": "table", + "bbox": [ + 0.078, + 0.748, + 0.493, + 0.854 + ], + "angle": 0, + "content": "
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
SC-FEGAN [18]47.183.410.50 ± 0.3774.36
SDEdit [22]37.612.520.41±0.4174.52
pSp [27]40.392.490.66 ± 0.1178.94
pSp-mixing31.322.000.73±0.0981.50
Ours16.860.830.85±0.1084.30
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.901 + ], + "angle": 0, + "content": "Since there are no prior works on 3D-aware stroke-based image synthesis, we retrained the pSp [27] model on EG3D using our dataset. To ensure fair comparisons, we further" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.893, + 0.737 + ], + "angle": 0, + "content": "applied style-mixing on pSp's predicted latent code by replacing 7-14 layers with original latent codes. We also compare with 2D image editing methods, including SC-FEGAN [18] and SDEdit [22]. Officially released codebases were used for all comparisons. As shown in Figure 6, given the original faces(a), color strokes and masks(b), since the editing areas are too large to complete, SC-FEGAN [18] generates less realistic results(c), with facial details appearing blurry in larger editing areas. Based on diffusion prior knowledge, SDEdit [22] generates more realistic results(d). However, the texture is still too smooth due to the geometry information absence of color stokes. Different from 2D image completion frameworks, pSp [27] predicts a latent code, which, however, totally modify the geometry compared with original faces. Unedited regions, such as background, are also changed. Even utilizing the style-mixing approach (f), there are also undesirable changes and the degree of editing has been largely affected. Compared with existing approaches, our method generates more realistic faces, which shows good faithfulness to the color strokes and precisely preserve the geometry details, even the sophisticated curly hair structure is well maintained." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.738, + 0.893, + 0.889 + ], + "angle": 0, + "content": "Quantitative Comparison. To further validate the superiority of our method, we conduct a quantitation evaluation. We generated 1000 facial editing examples in FFHQ datasets, following the data generation method outlined in Section 3.1. We calculated the relevant metrics between all algorithm-generated results and real images. As shown in Table 1, our method has achieved the best results on all metrics, which proves that our method generates more realistic faces (FID, KID). The original identity feature (ID) and geometry details (E-SSIM) are also better preserved." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7544" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.082, + 0.088, + 0.159, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.208, + 0.153, + 0.22 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image", + "bbox": [ + 0.16, + 0.089, + 0.236, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.174, + 0.208, + 0.222, + 0.22 + ], + "angle": 0, + "content": "(b) Input" + }, + { + "type": "image", + "bbox": [ + 0.236, + 0.089, + 0.312, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.241, + 0.208, + 0.335, + 0.22 + ], + "angle": 0, + "content": "(c) \\(\\mathrm{w / o}L_{\\mathrm{den}}\\) (d)" + }, + { + "type": "image", + "bbox": [ + 0.313, + 0.089, + 0.388, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.311, + 0.208, + 0.387, + 0.22 + ], + "angle": 0, + "content": "(d) depth loss" + }, + { + "type": "image", + "bbox": [ + 0.39, + 0.089, + 0.466, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.405, + 0.208, + 0.45, + 0.22 + ], + "angle": 0, + "content": "(e) Ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.224, + 0.47, + 0.267 + ], + "angle": 0, + "content": "Figure 7. The results of ablation study for density loss. w/o \\( L_{\\mathrm{den}} \\) method is trained without geometry density loss while depth loss method is trained with an alternative depth image loss." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.276, + 0.23, + 0.292 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.299, + 0.47, + 0.354 + ], + "angle": 0, + "content": "Table 2. Ablation study comparison. All models are trained on the datasets described in Section 3.1 and evaluated on 1000 randomly sampled EG3D data. Metric calculations follow the methods outlined in Table 1." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.357, + 0.49, + 0.449 + ], + "angle": 0, + "content": "
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
w/o density loss21.441.070.67 ± 0.2277.35
w/ depth loss23.141.230.75 ± 0.1780.10
w/o mask fusion28.331.720.82± 0.0782.97
Ours16.860.830.85± 0.1084.30
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.455, + 0.47, + 0.606 + ], + "angle": 0, + "content": "We conduct ablation experiments on EG3D random sampled data to justify the necessity of each component. To validate the effectiveness of the proposed geometry density loss, we presents the results of training without density loss \\( L_{\\mathrm{den}} \\) and with an alternative depth image loss. Specifically, we employed MSE Loss between the original depth image and the generated one to constrain the network. The results in Figure 7 (d)(e) and Table 2 demonstrate the superiority of our density loss in preserving facial geometry features and maintaining identity consistency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.606, + 0.47, + 0.773 + ], + "angle": 0, + "content": "Figure 8 indicates our volumetric local fusion module' effectiveness in maintaining consistency for non-edited areas between and the original and edited face. As shown in Figure 8 (d), without using 3D local fusion, non-edited areas undergo significant changes, such as brightening hair in the first row and reddening the face in the second row. In contrast, our method (Figure 8 (e)) perfectly maintains consistency in non-edited areas without affecting the editing effects in edited regions. Figures 8 (d) and (f) display computed heatmap differences between pre-edited and post-edited images." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.785, + 0.196, + 0.8 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.81, + 0.471, + 0.902 + ], + "angle": 0, + "content": "In this study, we propose a facial NeRF appearance editing method based on color strokes, enabling the modification of facial appearance features while preserving the original facial geometry. Initially, a data construction approach is introduced, leveraging StyleGAN2 and semantic segmentation networks to create paired data with consistent" + }, + { + "type": "image", + "bbox": [ + 0.507, + 0.09, + 0.569, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.091, + 0.628, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.629, + 0.091, + 0.689, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.69, + 0.091, + 0.75, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.751, + 0.091, + 0.812, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.813, + 0.091, + 0.885, + 0.138 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.508, + 0.139, + 0.569, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.569, + 0.139, + 0.629, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.139, + 0.692, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.693, + 0.139, + 0.751, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.752, + 0.139, + 0.813, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.814, + 0.139, + 0.88, + 0.185 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.515, + 0.188, + 0.562, + 0.199 + ], + "angle": 0, + "content": "(a) Original" + }, + { + "type": "image_caption", + "bbox": [ + 0.581, + 0.188, + 0.619, + 0.199 + ], + "angle": 0, + "content": "(b) Input" + }, + { + "type": "image_caption", + "bbox": [ + 0.634, + 0.188, + 0.689, + 0.199 + ], + "angle": 0, + "content": "(c) w/o fusion" + }, + { + "type": "image_caption", + "bbox": [ + 0.69, + 0.188, + 0.749, + 0.199 + ], + "angle": 0, + "content": "(d) Heatmap 1" + }, + { + "type": "image_caption", + "bbox": [ + 0.765, + 0.188, + 0.8, + 0.199 + ], + "angle": 0, + "content": "(e)ours" + }, + { + "type": "image_caption", + "bbox": [ + 0.817, + 0.188, + 0.871, + 0.199 + ], + "angle": 0, + "content": "(f) Heatmap 2" + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.202, + 0.892, + 0.259 + ], + "angle": 0, + "content": "Figure 8. The results of ablation study for local region fusion. w/o fusion are the results without 3D local fusion method. Corresponding heat map indicates the difference between the edited images and the original images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.279, + 0.892, + 0.476 + ], + "angle": 0, + "content": "geometry and diverse appearances, along with corresponding color strokes. Subsequently, an appearance editing network is constructed within the pre-trained generative network's latent space. The network employs a color stroke encoder to extract color features from input stroke images and utilizes a latent variable fusion network to achieve appearance editing while preserving geometric features. To maintain unchanged regions, a 3D local fusion method is introduced, enabling effective editing of localized appearance while preserving the facial identity features. Experimental results demonstrate the superiority of our method in generating higher-quality digital facial results compared to existing approaches." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.476, + 0.893, + 0.749 + ], + "angle": 0, + "content": "Despite achieving high-quality color editing results through color strokes, our method faces several challenges. Firstly, for highly detailed areas such as eyeballs, our method struggles to yield effective editing results. Handling these regions separately through segmentation and dedicated data processing could enhance editing outcomes. Additionally, due to limitations in the training dataset, our method encounters difficulties in handling overly complex color strokes, such as rainbow-colored hair, tending to average color strokes instead. To address this, generating distinct colors separately, followed by mask creation and blending, could yield superior results. Future research endeavors could extend the proposed algorithm from 3D digital faces to other types of 3D models, achieving more generalized editing effects. Moreover, combining color strokes with line drawings and semantic segmentation maps could enable simultaneous editing of 3D digital facial geometry and appearance." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.785, + 0.66, + 0.802 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.902 + ], + "angle": 0, + "content": "This work was supported by National Natural Science Foundation of China (No. 62102403), and the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (No. VRLAB2022C07). We would like to thank Professor Lin Gao for his helpful discussions and generous support." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7545" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.171 + ], + "angle": 0, + "content": "[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE/CVF international conference on computer vision, pages 4432-4441, 2019. 6" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.173, + 0.472, + 0.228 + ], + "angle": 0, + "content": "[2] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. Restyle: A residual-based stylegan encoder via iterative refinement. 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International Journal of Computer Vision, 129: 3051-3068, 2021. 2, 4" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.868 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "7547" + } + ] +] \ No newline at end of file diff --git a/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/7fe1ba34-6e33-48a7-bca3-a74b49e199ac_origin.pdf b/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/7fe1ba34-6e33-48a7-bca3-a74b49e199ac_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..7c1c3e24099fc7615091bd553cd5c920c490b852 --- /dev/null +++ b/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/7fe1ba34-6e33-48a7-bca3-a74b49e199ac_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c60eb1f85c5efef14436f548f3c1b36c35f042ba2327c215dfe89db1d56416a7 +size 9953367 diff --git a/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/full.md b/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/full.md new file mode 100644 index 0000000000000000000000000000000000000000..dab3b2caa14dc13907ddf7a928aace68a6cde735 --- /dev/null +++ b/2024/StrokeFaceNeRF_ Stroke-based Facial Appearance Editing in Neural Radiance Field/full.md @@ -0,0 +1,376 @@ +# StrokeFaceNeRF: Stroke-based Facial Appearance Editing in Neural Radiance Field + +Xiao-Juan Li $^{1,2}$ Dingxi Zhang $^{2,1}$ Shu-Yu Chen $^{1}$ Feng-Lin Liu $^{1,2*}$ $^{1}$ Beijing Key Laboratory of Mobile Computing and Pervasive Device, Institute of Computing Technology, Chinese Academy of Sciences + $^{2}$ University of Chinese Academy of Sciences + +{lixiaojuan,chenshuyu,liufenglin21s}@ict.ac.cn zhangdingxi20a@mails.ucas.ac.cn + +![](images/7eb1ffa65cb45fa9e7659cc360130b9500c7e64f5ca1139d18a36dbef67dfb29.jpg) +Figure 1. StrokeFaceNeRF enables versatile high-quality color stroke-based appearance editing for facial NeRFs. Users can draw strokes over a rendered facial image from any angle and define the editing region using masks. The third column showcases the photo-realistic free-view rendering results with exceptional color correspondence. + +# Abstract + +Current 3D-aware facial NeRF generation approaches control the facial appearance by text, lighting conditions or reference images, limiting precise manipulation of local facial regions and interactivity. Color stroke, a user-friendly and effective tool to depict appearance, is challenging to edit 3D faces because of the lack of texture, coarse geometry representation and detailed editing operations. To solve the above problems, we introduce StrokeFaceNeRF, a novel stroke-based method for editing facial NeRF appearance. In order to infer the missing texture and 3D geometry information, 2D edited stroke maps are firstly encoded into the EG3D's latent space, followed by a transformer-based editing module to achieve effective appearance changes while preserving the original geometry in editing regions. Notably, we design a novel geometry loss function to ensure surface density remains consistent during training. To further enhance the local manipulation accuracy, we propose a stereo fusion approach which lifts the 2D mask (inferred from strokes or drawn by users) into 3D mask volume, al + +lowing explicit blending of the original and edited faces. Extensive experiments validate that the proposed method outperforms existing 2D and 3D methods in both editing reality and geometry retention. + +# 1. Introduction + +Realistic 3D human face generation is a popular topic and has wide range applications in character design, virtual meeting and education. Traditional 3D facial modeling methods rely on software like Maya and Zbursh to construct mesh models while employing texture mapping for facial appearances. However, these methods are time-consuming and labor-intensive, especially when editing local appearance details and aiming for photorealistic results. Neural Radiance Field (NeRF) [23], a new 3D representation technique, easily render photo-realistic images with the input of multi-view images. The further combination of Generative Adversarial Networks (GAN) [10] with NeRF [5, 11, 24, 30] has enabled the generation of high-quality facial NeRF through random sampling. Nevertheless, precise control over appearance details remains a challenge. + +Efforts to enhance controllability involve disentangling geometry and appearance during facial NeRF generation. Sun et al. introduced the FE-NeRF [32] that employs separate latent codes to control the intricacies of facial geometry and appearance. Subsequent advancements [16, 31] utilize decoupling techniques based on triplane representations, leading to the facial generation results with significantly enhanced quality. Despite their success in good geometry and appearance swapping, these methods heavily rely on random sampling or reference images for global appearance editing. This reliance poses challenges in the obtainment of desired reference images and precludes precise control over localized appearance attributes, such as selective hair color alteration. + +Compared to reference images, colored strokes, functioning as an interactive tool, offer a precise depiction of local appearance details. In stroke-based image editing, one category of methods [17, 26] relies on conditional GAN and completion framework to edit local regions with the stroke guidance. However, artifacts may arise in the editing boundary and result in less realistic images for large-area editing operations, as shown in Figure 6. Another category of methods [22, 27] employs pre-trained facial generation models as decoders, mapping colored strokes to the latent space of the generation model to generate edited facial results. However, these methods struggle to preserve the unchanged geometric features of the input face during editing, as demonstrated in Figure 6. Importantly, these techniques are specifically tailored for 2D facial image editing and cannot be directly applied to 3D facial radiance fields. + +This paper presents StrokeFaceNeRF, a framework for editing facial NeRF appearance based on colored strokes, enabling precise modifications of color and lighting in 3D faces. Leveraging 2D facial image generation techniques such as StyleGAN2 [21] and semantic segmentation methods [38], we construct a dataset of faces with identical geometry but varying appearances, generating corresponding colored stroke maps using bilateral filtering and semantic clustering algorithms. To achieve appearance editing, directly encoding edited stroke maps into the latent space of the pre-trained facial NeRF generation model [5] leads to texture smoothness and undesirable geometry distortion due to high-frequency information absence and user's inaccurate drawing of strokes. To solve this problem, we propose a transformer-based editing network, which fuses the original and stroke-encoded latent codes to modify appearance while preserving the original geometry in edited regions. Furthermore, we introduce a geometry loss term during training to ensure surface density remains unchanged, improving detail preservation. To further maintain unchanged features in non-edited areas for precise editing, we design a volumetric fusion algorithm that integrates localized regions before and after editing in 3D space, enabling local- + +ized appearance editing effects in facial models. Our contributions are summarized as follows + +- We propose the first color stroke-based facial NeRF editing framework to generate free-view realistic appearance editing facial images. +- We design a novel geometry density loss to train the transformer-based latent editing network, which effectively preserves the geometry detail during facial appearance modifications. +- We introduce a volumetric fusion algorithm to precisely edit local regions while maintaining the 3D consistency in unedited regions. + +# 2. Related Work + +# 2.1. Facial Image Editing with Colored Strokes + +Existing 2D facial image editing methods using colored strokes can be divided into two categories. One group of methods utilizes conditional Generative Adversarial Networks (cGANs) to accomplish stroke-guided image generation. Sangkloy et al. [29] utilize sketches and colored strokes to directly generate realistic images through a translation network. However, this method fails to achieve localized area editing. To solve this problem, FaceShop [26] utilizes image completion techniques and 2D mask marking for localized facial image editing based on sketches and colored strokes. Jo et al. [18] further introduced SC-FEGAN that employs gated convolutions and new style losses for training, enabling a broader range of editing operations. Xiao et al. [36] design a hair generation network with self-attention mechanisms, achieving more natural and realistic hair editing effects. However, these methods are sensitive to input conditions and result in smooth edits lacking texture information in edited regions. Additionally, they tend to produce artifacts at the editing boundary due to the image completion techniques. + +Another category of methods utilizes pre-trained generative models to generate high quality faces instead of pixelwise translation. Bau et al. [3] first utilize reverse optimization to achieve image shape and color editing in the GAN's latent space. pSp [27] further designs an image encoding network to map various types of input images, such as sketches and color strokes, into StyleGAN2's latent space to generate corresponding facial images. In order to generate highly editable latent codes, Tov et al. [34] further constrained the latent codes with a discriminator. However, these methods, as they represent the entire image with latent vectors, struggle to achieve localized editing effects. Instead of GAN dependence, Meng et al. [22] employed pre-trained diffusion models to achieve facial image editing based on colored stroke maps. Images with user-drawn strokes are added Gaussian noise, then progressively denoised to synthesize realistic facial images. However, it is + +![](images/ed19e967ddc010a416c336e52113dbc352b8d11f8b3232dd849538ec88390936.jpg) +Figure 2. 3D Facial Appearance Editing Framework. Given the original latent code $w$ , free-view images are rendered by EG3D. Users introduce editing operations, resulting in the creation of a color stroke image $C_{\mathrm{edit}}$ . This stroke map is encoded by Color Encoder $E_{c}$ to generate $w_{c}$ , which is fused with original latent code $w$ by latent fusion network to generate $w_{\mathrm{edit}}$ . Utilizing an additional 2D mask, the volumetric fusion approach facilitates targeted appearance editing within specific regions. + +![](images/8fd18f8e3a238858f24822341956ddb4686569ee346e964549491c47cb1e42ce.jpg) + +challenging to directly apply this method to facial neural radiance field editing. Additionally, because of the direct input of coarse stroke maps, it is challenging for the above methods to maintain geometric features while performing appearance modification in editing regions. + +# 2.2. Editing Facial NeRF + +Combining generative adversarial networks with neural radiance fields enables the synthesis of realistic facial images from arbitrary viewpoints. Graf [30] first adds extra latent codes to NeRF's fully connected network to support face generation and use multiscale discriminators for supervision. Giraffe [24] designs a new framework that employs volume rendering to obtain feature maps and a convolutional framework to generate facial images. StyleSDF [25] and GRAM [7] utilize representation methods based on SDF and implicit planes, respectively, producing higher-quality and more 3D consistent results. EG3D [5] propose a facial NeRF generation framework based on triplane representation and StyleGAN2 [21] generator. However, these methods can only synthesize faces through random sampling and lack the ability for editing. + +To generate controllable facial NeRF, Jo et al. [17] use sketches, black-and-white images, and text as control conditions. Gao et al. [9] propose a facial NeRF generation and editing framework based on sketches to enhance synthesis quality and achieve fine editing. However, this method can only edit facial geometry. Another line of work decouples facial NeRF's geometry and appearance using semantic segmentation. FE-NeRF [32] achieves geometric editing through reverse latent code optimization and appearance editing through random sampling. IDE-3D [31] constructs geometry triplanes and appearance triplanes, and designs a semantic map encoder to generate higher-quality facial results. NeRFFaceEditing [16] apply AdaIN [14] to triplanes + +features, enabling the disentanglement of geometry and appearance control. Although the above methods achieve effective appearance modification, reference images or latent codes are required instead of user's flexible interaction. More importantly, the above methods are designed for the global appearance editing and cannot be directly utilized for local editing. + +# 3. Methodology + +We propose a framework, StrokeFaceNeRF, enables users to utilize colored strokes for facial NeRF appearance editing. We employ the EG3D [5] generator architecture, a proficient 3D-aware Generative Adversarial Network (GAN) that combines the StyleGAN2 [21] architecture and neural rendering to produce high-quality 3D shapes. Given a latent code, a triplane representation can be obtained from a StyleGAN2 backbone. The neural renderer then aggregates features from these triplanes and predicts feature images based on a specified camera pose. Subsequently, a super-resolution module is applied to upsample and refine these raw neurally rendered images, resulting in high-quality, multiview-consistent images. More details of the generator can be found in [5]. + +Our method comprises three key components: dataset construction, colored stroke editing network, and 3D local fusion module. Initially, we introduce a dataset construction approach to acquire facial images with consistent geometry but varying appearances, along with their corresponding colored stroke images as detailed in Section 3.1. Subsequently, an appearance editing network, described in Section 3.2, is established within the latent space of EG3D to predict the 3D faces. Additionally, in Section 3.3, we propose a 3D local fusion method to enable effective appearance editing while meticulously preserving features in + +non-edited regions. + +# 3.1. Dataset Construction + +To supervise the training of network models, the training data needs to simulate the process of facial appearance editing based on colored strokes. Thus, the training tuples include original faces, edited faces, and corresponding colored stroke maps. Dataset construction involves three steps as shown in Figure 3: (1) building a collection of facial latent codes in EG3D's latent space, obtained through random sampling and real images inversion; (2) constructing facial tuples with identical geometry but different appearances. Two different methods were employed: one based on semantic segmentation and the other based on StyleGAN2 generative networks; (3) generating colored stroke maps using bilateral filtering and semantic clustering methods. + +We utilize two approaches to synthesize paired images with the same geometry but different appearance, indicated as the edited ground truth faces. Semantic Segmentation-Based Augmentation. Given the original rendered facial images, we utilize BiSeNet [38] to get semantic segmentation masks. Then, for each local semantic region, we represent it into HSV space, where the Hue channel is uniformly replaced with random color, while the Saturation and Value channels are added random perturbation. Finally, these regions are merged into original images to imitate appearance editing. StyleGAN2-Based Augmentation. We further utilize pre-trained generator to synthesize more diverse and realistic training images. Given the original rendered images, ReStyle [2] encodes them into StyleGAN2 latent space, followed with style mixing to change the facial appearance while preserving the same geometry. More details can be found in Supplementary. + +With the paired appearance modification images, corresponding color strokes are required to imitate real editing situation. Typically, users drawn strokes are simple and monochromatic. Therefore, synthesized color stroke images must preserve the original image's color and geometric layout while eliminating high-frequency texture features and local details. To achieve this objective, we employ the bilateral filtering method [33] to effectively preserves the edge features of the facial image while eliminating high-frequency details. Specially, the initial image undergoes median filtering, followed by iterative application of bilateral filtering, as explained in the Supplementary. Nevertheless, some regions still exhibit smooth transitions between different colored areas after filtering, posing challenges for users aiming to replicate specific effects. To tackle this issue, we employ a pixel value clustering technique based on semantic information. Initially, the facial image undergoes semantic segmentation. Within the hair area, clustering allows all pixel colors to be replaced by the nearest cluster center color, thereby eliminating smooth transition regions. + +![](images/2da12d65a8b1e146d8aff06e23ee124b1aa2e1c042f22399ffe959067c008dd2.jpg) +Figure 3. Dataset construction pipeline. Given EG3D rendering images, the appearance is changed by two different approaches. Then, the color stroke images are synthesized by image filter and cluster. + +The same methodology is applied to the facial area, yielding the final color stroke image. + +# 3.2. Appearance Editing Network + +In our framework, the target face NeRF to be edited is represented as a latent code $w$ within EG3D's latent space. The latent code can be obtained either by random sampling in EG3D or by applying PTI [28] to invert real images. Utilizing StyleGAN generator and volume rendering, free view facial images can be generated, followed by the approaches in Section 3.1 to extract color stroke images. Users then modify these color stroke images to obtain the edited color stroke image $C_{\mathrm{edit}}$ . As illustrated in Figure 2, the input to the appearance editing network consists of the original latent variable $w$ , the edited color stroke image $C_{\mathrm{edit}}$ , and the output is the edited latent variable $w_{\mathrm{edit}}$ . + +The appearance editing network comprises two main components: the Color Encoder $E_{c}$ and the Latent Fusion Network $F_{l}$ . Specifically, given the edited color stroke image $C_{\mathrm{edit}}$ , the color encoder that has a similar structure to [27], predicts the latent code $w_{c}$ . While this latent code generates facial results with color editing effects, it fails to preserve the original facial features, such as the geometric structure of the hair and the original skin color in non-edited areas, as shown in Figure 2. Therefore, a latent code fusion network is designed to utilize the information from the original latent variable $w$ , thus better preserving the original facial features. The latent fusion network $F_{l}$ adopts a cross-attention transformer block to predict the fused latent variable $w_{\mathrm{edit}}$ . This design implicitly extracts the color information from $w_{c}$ and geometry information from $w$ , guaranteeing a thorough integration of both color-edited and original facial features. In this configuration, the latent code $w_{c}$ is employed as query tokens, whereas the original latent code $w$ serves as key and value tokens. We also normalize over queries instead of keys as described in [13] to ensure a continuous refinement of $w_{c}$ during the fusion process with value tokens while mitigating the potential influence of $w$ being too large. + +$$ +w _ {\text {e d i t}} = F _ {l} \left(w, E _ {c} \left(C _ {\text {e d i t}}\right)\right) \tag {1} +$$ + +# 3.3. Volumetric Local Fusion + +While direct rendering by $w_{\mathrm{edit}}$ yields good editing effects within targeted editing areas, as depicted in Figure 7, noticeable undesirable discrepancies emerge in unedited regions. Moreover, intricate editing tasks, such as selectively dyeing specific portions of hair or drawing specific patterns on faces, pose challenges for the latent code-based representation because of its overarching global control inherited from StyleGAN2 backbone. To address these issues, we propose a volumetric fusion approach to enable more refined editing operations. + +In order to facilitate local editing, our method introduces support for an additional 2D mask input that indicates the editing region. This 2D mask is further lifted into 3D mask volume to support volumetric fusion. Specifically, we propose a depth guidance approach to sample a set of points near the facial surface. In the volume rendering, for each ray $r_{i,j}$ of the pixel at the $i$ th row and $j$ th column, the camera's position and ray direction are denoted as $o_{i,j}$ and $d_{i,j}$ , respectively. After rendering the original faces, we get the corresponding depth value $D[i,j]$ . Then, for each ray, we uniformly sample $K$ points with offset $\triangle x_k$ within range $[-0.1, 0.1]$ . The sampled 3D points set $S$ for the original face is denoted as: + +$$ +S = \cup_ {i, j} \cup_ {k = 1} ^ {K} \left(o _ {i, j} + \left(D [ i, j ] + \triangle x _ {k}\right) \cdot d _ {i, j}\right) \tag {2} +$$ + +where the default value of $K$ is 5. Notably, as illustrated in Figure 2, we selectively employ the rays corresponding to pixels within the 2D mask regions. + +Subsequently, this generated 3D point set undergoes a transformation into a 3D volumetric mask. Specifically, we initialize a $256 \times 256 \times 256$ 3D volume with zero values throughout the space. The coordinates of the 3D points, along with their neighboring positions, are designated as 1, indicating 3D editing regions. To ensure smoother boundaries, we utilize a three-dimensional dilation and Gaussian filtering, yielding the 3D mask denoted as $M_{\mathrm{3D}}$ . Additionally, We implement a mask padding strategy, which introduces direction offsets to the camera poses and extends the mask boundary. This prevents incomplete editing artifacts during view changes. Further details regarding the padding technique are available in the Supplemental material. + +To render realistic editing images, the original latent variable $w$ and the edited latent variable $w_{\mathrm{edit}}$ are used to synthesize the original and edited triplane features, respectively. For the sampling points $h$ in space during volume rendering, the corresponding original feature $f_{h}$ and edited feature $f_{\mathrm{edit}}(h)$ are generated. To achieve the editing fusion effect, the features are fused based on the 3D mask $M_{3\mathrm{D}}$ : + +$$ +f _ {\text {f u s i o n}} (h) = f _ {\text {e d i t}} (h) \cdot M _ {\mathrm {3 D}} [ h ] + f (h) \cdot \left(1 - M _ {\mathrm {3 D}} [ h ]\right) \tag {3} +$$ + +The fused features $f_{\mathrm{fusion}}$ are passed through the decoder of EG3D to obtain color and density information. Afterward, + +they are processed through the volume rendering and upsampling modules to generate the final edited faces. + +# 3.4. Training Strategy + +During the training of Appearance Editing Network, the geometry details should be preserved while the appearance editing effectiveness should not be influenced. This is nontrivial because the 2D supervision lacks detailed 3D structure constrain and the synthesized training data has minor geometry distortion because of Style-mixing's limitation. To solve this problem, we train our network with the follow strategy. + +Geometry Density Loss. Based on our NeRF representation, we design a novel density loss to enforce the 3D geometry consistency between the original and edited faces. Specifically, leveraging the 3D points generation approach described in Equation 2, a collection of 3D points is generated. Notably, we use all the rays during the rendering instead of rays in specific regions. These 3D sample points are further projected onto triplane space to query corresponding triplane features that are subsequently decoded into color and density through volume rendering. We minimize the density value between the original and edited faces to effectively preserve the facial geometry while decoupling the appearance: + +$$ +L _ {\text {d e n s i t y}} = \sum_ {x \in S, x ^ {\prime} \in S ^ {\prime}} | | \psi_ {\text {d e n s i t y}} (\mathcal {F} (x)) - \psi_ {\text {d e n s i t y}} \left(\mathcal {F} ^ {\prime} \left(x ^ {\prime}\right)\right) | | _ {1} \tag {4} +$$ + +where $\mathcal{F}$ denotes the triplane query process and $\psi_{\mathrm{density}}$ denotes density decoder. $x^{\prime}$ and $S^{\prime}$ are the 3D points and set for edited faces. These points are sampled with the same offset but new depth map $D_{\mathrm{edit}}$ of edited faces. Edited triplane features $\mathcal{F}^{\prime}$ synthesized by $w_{\mathrm{edit}}$ are used for density calculation. + +We also utilizes the same loss functions as the pSp framework [27] to match the original stroke distribution. The loss function includes the per-pixel $L_{2}$ loss between the ground truth image $I_{GT}$ (obtained in Sec.3.1) and the edited image generated by EG3D $G$ : + +$$ +L _ {i m g} = \left\| I _ {G T} - G \left(w _ {\text {e d i t}}\right) \right\| _ {2} \tag {5} +$$ + +Here, $||.||_2$ denotes the Euclidean distance. To better constrain the reconstruction quality, a perceptual distance loss term is further employed: + +$$ +L _ {L P I P S} = \left\| F \left(I _ {G T}\right) - F \left(G \left(w _ {\text {e d i t}}\right)\right) \right\| _ {2} \tag {6} +$$ + +Where $F$ represents an image feature extraction method based on VGG [19]. In order to better constrain the images generated to preserve the identity features of the original faces, an identity constraint term is employed: + +$$ +L _ {I D} = 1 - \left\langle R \left(I _ {G T}, R \left(G \left(w _ {\text {e d i t}}\right)\right) \right\rangle \right. \tag {7} +$$ + +![](images/c3ec3475b6cd87e09504c27162a0852cb56236dd503df313ee5c861f942ef244.jpg) +(a) Original image + +![](images/78b11e960855559575145ebfeecf05df5839088edb177da6ea79d4aa56cc075b.jpg) +(b) Input 1 + +![](images/6928445405f711a5a2c4dfe226cfa38ad23a8583f0fc9f3229b2e25d725d682b.jpg) +(c) Results 1 + +![](images/508b0a089bd9546f23ca28602fd00f929618b30618ad8f63b979d285f532b55c.jpg) +(d) Input 2 + +![](images/c8f6d9bb838c63452e397465f84c735dd8e09b712d2c57199a299e0c4d010b17.jpg) +(e) Results 2 + +![](images/07ce8394c4c060c6f22f4a6cb4814ef1cbb0bb1efced83e750885a6ac11c716d.jpg) +Figure 4. Color stroke-based facial NeRF appearance editing results. Given the original faces (a), users drawn the editing color strokes (b) (d), our methods generate the corresponding editing results (c)(e). Additional masks are shown in top left corner, which is the same as stroke's shape in the first two rows, and drawn by users in the last row. +(a) Real image +Figure 5. Real image appearance editing results. + +![](images/48f34321224258c320eb50eaae134c947e60d5116e9f20b7fe8796a8dd71064d.jpg) +(b) Inversion + +![](images/a8afbad18069f82a9f0b32a8873c8351fc8f483accef60a713b0678ebbdd534e.jpg) +(c) Stroke + +![](images/dbadcbd7e2c93f21c3bf30b28c6c63835d08b76394a83338e1a90fac4834c53f.jpg) +(d) Result + +$R$ represents the pre-trained facial recognition network, ArcFace [6], and $\langle .\rangle$ denotes cosine similarity. Regularization constraints are added to ensure that the edited latent variables are as close as possible to the mean latent variables $\overline{w}$ , making the generated faces more natural. + +$$ +L _ {r e g} = \left\| w _ {\mathrm {e d i t}} - \bar {w} \right\| _ {2} \tag {8} +$$ + +The overall loss function is given by: + +$$ +L = \alpha_ {1} L _ {\text {d e n s i t y}} + \alpha_ {2} L _ {i m g} + \alpha_ {3} L _ {L P I P S} + \alpha_ {4} L _ {I D} + \alpha_ {5} L _ {r e g} \tag {9} +$$ + +Here, $\alpha_{1},\alpha_{2},\alpha_{3},\alpha_{4}$ and $\alpha_{5}$ represent the weighting coefficients for each loss term, with values of 0.05, 2.0, 2.0, 0.2, and 0.005, respectively. In the first stage training, we set $\alpha_{1} = 0$ because only appearance is expected to be encoded in this stage. + +# 4. Experiments + +Dataset: Our training dataset comprises original faces generated by EG3D random sampling and real images in + +version [1] of CelebA-HQ [20], amounting to 47,134 examples. Appearance-edited faces and corresponding color stroke images are constructed using the method detailed in Section 3.1, resulting in 94,268 paired samples in total. + +Training details: We use a single NVIDIA GeForce RTX 3090 GPU to train our framework. The batch size is 4, with the Ranger optimizer [37] and a learning rate of 1e-4. Each training stage involved 30k iterations, completing the final network training process. + +Evaluation metrics: We use the following common metrics: Fréchet Inception Distance (FID) [12], Kernel Inception Distance (KID) [4] and Identity Consistency (ID) from [15]. To evaluate the geometry consistency in both 2D and 3D methods, we computed the Structural Similarity Index (SSIM) [35] metric for the edges obtained using the Sobel [8] operator in the edited regions of the generated images compared to the real images, denoted as E-SSIM. A higher E-SSIM value in the edited regions indicates a better preservation of the geometry in those areas. + +# 4.1. Results + +Figure 4 illustrates the 3D facial NeRF appearance editing based on color strokes. Benefit from the 3D representation in our framework, users can select arbitrary view point to render images. Then, users could draw color strokes, which are overlaid on extracted strokes extracted based on methods described in Section 3.1 to serve as the edited stroke image. Our framework takes an additional 2D mask inputs, which either have the same shape with drawing strokes, or additionally drawn by users. As shown in Figure 4(c)(e), our method allows the precise control over the skin, hair, + +![](images/74b07006572a5b4f6cb9ade34abcb4d82da6a872dfff5f9b784ce4e28de9eaa8.jpg) + +![](images/67123b544404afd7363474c63f3bcb3229562c8f8af2ca86662d995af6e84925.jpg) + +![](images/f86ec15e5f53033bec90ef1f0723941d5b5479860ae637607957ed0402dc8a21.jpg) +(a) Original image + +![](images/8c47c9e765f41dafe2ada58b4d0fb38a4d58e8e3381b26e4d6619846ae2f7d88.jpg) + +![](images/eaf73983b4522ad7be18aa89e977d847a0a59abea9755073183eb9cac764a049.jpg) + +![](images/9c5b81a344eafcb8180a0fccfefb1b7795ca372d7a9a7ca0358517787a38002d.jpg) +(b) Input +(c) SC-FEGAN[18] + +![](images/8a8fbfcbd8e557cdf57fbcf125cbc5f678231060000b391dec2a03881b07ae6d.jpg) + +![](images/3943e34c26f182814a519d23deaf4c0a8f0e9e318702480b2d4e0317b5d1845a.jpg) + +![](images/f43730c1a0cc8592f3e6bfcfdcc123d3790f7fa5534aa5c9db8494c447fa81ce.jpg) + +![](images/476555c808c2989c461b46007fe212e243e65ab112febc7832d4a17ad98822fc.jpg) + +![](images/de7d9ed5cac85a3783db91d8f7c743d96d888094634aaee21852ebe0390a9db7.jpg) + +![](images/14224d46fe984d73fce57ff4e83a5473c1dc0a2c8613f360cbb51d2ef30a1c83.jpg) +(d) SDEdit[22] +Figure 6. Comparison with existing color stroke-based facial editing methods. SC-FEAGN[18] and SDEdit[22] are 2D image editing approaches that generate texture smoothness. pSp[27] and pSp-mixing globally changes the 3D faces. Our method generates the best results on realism and identity preservation. + +![](images/58ebcb8f374fa0602f3c855932047319015cb82e844b8dfe991af976bed100bf.jpg) + +![](images/69d4990dbebf7d319d13ddee03d1c4ed88724b6a5308b3857c7a15b49684d724.jpg) + +![](images/133d4a9b43f6871bf57245a6e27d66f24a7a9ad4c65f10e8183ea3ce13863e38.jpg) +(e) psp[27] + +![](images/8395397de1d0b172c69c44fd69be736ddb5c672c40b7541268c10126c8a3218d.jpg) + +![](images/ff6783d5247c40cad95b546eec635b4c8a9348c25d96a603990c38fd22614181.jpg) + +![](images/cb1f717825b68dc76e46daccacd8ac986747e845b3c6f22539ab73ac21c44d87.jpg) +(f) PSP-mixing + +![](images/16e93cfb71062d4d67081f7cf63307a9cdb4a490245cdd00186aa5f81a9925ff.jpg) + +![](images/bcb68074f50d18b4c551a4f6bb0f17db78facb69134fa6b697e55844b4ffb439.jpg) + +![](images/3212ccf48b1e6a44a65d45bb2f9d5e1f53ffd11e9350edaa1dd48908dbea0ede.jpg) +(g) Ours + +and lip colors. It is noteworthy that the geometric details are well preserved as the original faces during appearance editing, as demonstrated by the wrinkle details in the 1st row and hair structure in the 3rd row. Unedited regions, such as hair (1st row) and background, also retain the same as the original faces. The 3rd row of Figure 4 showcases more complex local appearance editing results. To achieve diverse editing effects, users draw finer masks (c) to mark local areas, such as a cluster of hair or specific facial patterns. The 3D local fusion algorithm enables editing in marked areas, resulting in more complex and diverse editing effects. + +As shown in Figure 5, given a real facial image, the original facial image is reconstructed in latent space using the PTI algorithm [28] (b). Similarly, users draw color stroke images (c) and edit area masks (d). Our method generates corresponding facial NeRF appearance editing results and obtains multi-view facial outcomes. + +# 4.2. Comparisons + +Table 1. Quantitative evaluation using FID, KID $\times 10^{2}$ , mean and std value of identity consistency (ID), E-SSIM $\times 10^{2}$ on baseline models and our methods. + +
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
SC-FEGAN [18]47.183.410.50 ± 0.3774.36
SDEdit [22]37.612.520.41±0.4174.52
pSp [27]40.392.490.66 ± 0.1178.94
pSp-mixing31.322.000.73±0.0981.50
Ours16.860.830.85±0.1084.30
+ +Since there are no prior works on 3D-aware stroke-based image synthesis, we retrained the pSp [27] model on EG3D using our dataset. To ensure fair comparisons, we further + +applied style-mixing on pSp's predicted latent code by replacing 7-14 layers with original latent codes. We also compare with 2D image editing methods, including SC-FEGAN [18] and SDEdit [22]. Officially released codebases were used for all comparisons. As shown in Figure 6, given the original faces(a), color strokes and masks(b), since the editing areas are too large to complete, SC-FEGAN [18] generates less realistic results(c), with facial details appearing blurry in larger editing areas. Based on diffusion prior knowledge, SDEdit [22] generates more realistic results(d). However, the texture is still too smooth due to the geometry information absence of color stokes. Different from 2D image completion frameworks, pSp [27] predicts a latent code, which, however, totally modify the geometry compared with original faces. Unedited regions, such as background, are also changed. Even utilizing the style-mixing approach (f), there are also undesirable changes and the degree of editing has been largely affected. Compared with existing approaches, our method generates more realistic faces, which shows good faithfulness to the color strokes and precisely preserve the geometry details, even the sophisticated curly hair structure is well maintained. + +Quantitative Comparison. To further validate the superiority of our method, we conduct a quantitation evaluation. We generated 1000 facial editing examples in FFHQ datasets, following the data generation method outlined in Section 3.1. We calculated the relevant metrics between all algorithm-generated results and real images. As shown in Table 1, our method has achieved the best results on all metrics, which proves that our method generates more realistic faces (FID, KID). The original identity feature (ID) and geometry details (E-SSIM) are also better preserved. + +![](images/f9183214cf3d7d16b8b4d5365394ebee080385fdb4a00be666b60da0a6a76c0f.jpg) +(a) Original + +![](images/f06f17cfa4b09ca2340b65ead99872db8e6b72595e985b4e3304b33d21554659.jpg) +(b) Input + +![](images/ff322c874765249561a27bba03a1b3d7124c25e688184a4a806fd4ebe1eaf9d0.jpg) +(c) $\mathrm{w / o}L_{\mathrm{den}}$ (d) +(d) depth loss + +![](images/f0bdb7045a7ec81875397c5c3ac078958781ed4cede721592f2ad5f16542764f.jpg) +Figure 7. The results of ablation study for density loss. w/o $L_{\mathrm{den}}$ method is trained without geometry density loss while depth loss method is trained with an alternative depth image loss. + +![](images/8286044f9080c8cbb9ef64aff66504f3d6d2cbb421d923aaf431786054b594cf.jpg) +(e) Ours + +# 4.3. Ablation Study + +Table 2. Ablation study comparison. All models are trained on the datasets described in Section 3.1 and evaluated on 1000 randomly sampled EG3D data. Metric calculations follow the methods outlined in Table 1. + +
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
w/o density loss21.441.070.67 ± 0.2277.35
w/ depth loss23.141.230.75 ± 0.1780.10
w/o mask fusion28.331.720.82± 0.0782.97
Ours16.860.830.85± 0.1084.30
+ +We conduct ablation experiments on EG3D random sampled data to justify the necessity of each component. To validate the effectiveness of the proposed geometry density loss, we presents the results of training without density loss $L_{\mathrm{den}}$ and with an alternative depth image loss. Specifically, we employed MSE Loss between the original depth image and the generated one to constrain the network. The results in Figure 7 (d)(e) and Table 2 demonstrate the superiority of our density loss in preserving facial geometry features and maintaining identity consistency. + +Figure 8 indicates our volumetric local fusion module' effectiveness in maintaining consistency for non-edited areas between and the original and edited face. As shown in Figure 8 (d), without using 3D local fusion, non-edited areas undergo significant changes, such as brightening hair in the first row and reddening the face in the second row. In contrast, our method (Figure 8 (e)) perfectly maintains consistency in non-edited areas without affecting the editing effects in edited regions. Figures 8 (d) and (f) display computed heatmap differences between pre-edited and post-edited images. + +# 5. Conclusion + +In this study, we propose a facial NeRF appearance editing method based on color strokes, enabling the modification of facial appearance features while preserving the original facial geometry. Initially, a data construction approach is introduced, leveraging StyleGAN2 and semantic segmentation networks to create paired data with consistent + +![](images/4556c6165592b4241cefe0d786acc3fac8415e20740cc55289ea01c53f4a4e0b.jpg) + +![](images/6e417872e10068b59d700d337ef29a3ef10bcc02cbd7fbdffd7190f681d81294.jpg) + +![](images/f2974eebc124580a519598949f414e757276e2e8acf2b0e6ac9569b76bb260f8.jpg) + +![](images/5225b37d466883a633df03f4d6e576f26786980b82af404b295c4d764210a57d.jpg) + +![](images/9271a7d13660916fa3d802564aa332e789cf683a9d06c89acf6fb44ed397b8a3.jpg) + +![](images/61916c2d9fb896db130a8e42d22aba0df1d3acfe38c0d269dec6167a4efeeec9.jpg) + +![](images/673e8d2c91b533995b55cd7c4a30c0b094ab55b79e9fb40e07f84f0058e9f5f5.jpg) +(a) Original +Figure 8. The results of ablation study for local region fusion. w/o fusion are the results without 3D local fusion method. Corresponding heat map indicates the difference between the edited images and the original images. + +![](images/4c583743e7ed4249acaea525266b3552882a76821d6907c6c4887931f113503e.jpg) +(b) Input + +![](images/20c5bdb5cb39ef3ba2bef4b955570e8018b93f29ca01dd91d053478427173624.jpg) +(c) w/o fusion +(d) Heatmap 1 + +![](images/53821119905fb97514467bed4e000c5c09227fa280b520bfd69176fbf9b8b163.jpg) + +![](images/4a658de7ebfbd012de9ed0c063855794bbb9e2c4c8ec93e82020d93d319f5f8d.jpg) +(e)ours + +![](images/342e71844b914566dc4f096b0a1c9d11700161143fddd7715da7dbb2de4a58bc.jpg) +(f) Heatmap 2 + +geometry and diverse appearances, along with corresponding color strokes. Subsequently, an appearance editing network is constructed within the pre-trained generative network's latent space. The network employs a color stroke encoder to extract color features from input stroke images and utilizes a latent variable fusion network to achieve appearance editing while preserving geometric features. To maintain unchanged regions, a 3D local fusion method is introduced, enabling effective editing of localized appearance while preserving the facial identity features. Experimental results demonstrate the superiority of our method in generating higher-quality digital facial results compared to existing approaches. + +Despite achieving high-quality color editing results through color strokes, our method faces several challenges. Firstly, for highly detailed areas such as eyeballs, our method struggles to yield effective editing results. Handling these regions separately through segmentation and dedicated data processing could enhance editing outcomes. Additionally, due to limitations in the training dataset, our method encounters difficulties in handling overly complex color strokes, such as rainbow-colored hair, tending to average color strokes instead. To address this, generating distinct colors separately, followed by mask creation and blending, could yield superior results. Future research endeavors could extend the proposed algorithm from 3D digital faces to other types of 3D models, achieving more generalized editing effects. Moreover, combining color strokes with line drawings and semantic segmentation maps could enable simultaneous editing of 3D digital facial geometry and appearance. + +# Acknowledgement + +This work was supported by National Natural Science Foundation of China (No. 62102403), and the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (No. VRLAB2022C07). We would like to thank Professor Lin Gao for his helpful discussions and generous support. + +# References + +[1] Rameen Abdul, Yipeng Qin, and Peter Wonka. Image2stylegan: How to embed images into the stylegan latent space? In Proceedings of the IEEE/CVF international conference on computer vision, pages 4432-4441, 2019. 6 +[2] Yuval Alaluf, Or Patashnik, and Daniel Cohen-Or. 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Bisenet v2: Bilateral network with guided aggregation for real-time semantic segmentation. 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StrokeFaceNeRF enables versatile high-quality color stroke-based appearance editing for facial NeRFs. Users can draw strokes over a rendered facial image from any angle and define the editing region using masks. The third column showcases the photo-realistic free-view rendering results with exceptional color correspondence." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 143, + 438, + 192, + 451 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 438, + 192, + 451 + ], + "spans": [ + { + "bbox": [ + 143, + 438, + 192, + 451 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 464, + 289, + 691 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 289, + 691 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 289, + 691 + ], + "type": "text", + "content": "Current 3D-aware facial NeRF generation approaches control the facial appearance by text, lighting conditions or reference images, limiting precise manipulation of local facial regions and interactivity. Color stroke, a user-friendly and effective tool to depict appearance, is challenging to edit 3D faces because of the lack of texture, coarse geometry representation and detailed editing operations. To solve the above problems, we introduce StrokeFaceNeRF, a novel stroke-based method for editing facial NeRF appearance. In order to infer the missing texture and 3D geometry information, 2D edited stroke maps are firstly encoded into the EG3D's latent space, followed by a transformer-based editing module to achieve effective appearance changes while preserving the original geometry in editing regions. Notably, we design a novel geometry loss function to ensure surface density remains consistent during training. To further enhance the local manipulation accuracy, we propose a stereo fusion approach which lifts the 2D mask (inferred from strokes or drawn by users) into 3D mask volume, al" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 439, + 546, + 487 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 439, + 546, + 487 + ], + "spans": [ + { + "bbox": [ + 306, + 439, + 546, + 487 + ], + "type": "text", + "content": "lowing explicit blending of the original and edited faces. Extensive experiments validate that the proposed method outperforms existing 2D and 3D methods in both editing reality and geometry retention." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 514, + 387, + 526 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 514, + 387, + 526 + ], + "spans": [ + { + "bbox": [ + 306, + 514, + 387, + 526 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 547, + 715 + ], + "type": "text", + "content": "Realistic 3D human face generation is a popular topic and has wide range applications in character design, virtual meeting and education. Traditional 3D facial modeling methods rely on software like Maya and Zbursh to construct mesh models while employing texture mapping for facial appearances. However, these methods are time-consuming and labor-intensive, especially when editing local appearance details and aiming for photorealistic results. Neural Radiance Field (NeRF) [23], a new 3D representation technique, easily render photo-realistic images with the input of multi-view images. The further combination of Generative Adversarial Networks (GAN) [10] with NeRF [5, 11, 24, 30] has enabled the generation of high-quality facial NeRF through random sampling. Nevertheless, precise control over appearance details remains a challenge." + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 49, + 703, + 129, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 703, + 129, + 712 + ], + "spans": [ + { + "bbox": [ + 49, + 703, + 129, + 712 + ], + "type": "text", + "content": "*Corresponding Author" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7538" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 239 + ], + "type": "text", + "content": "Efforts to enhance controllability involve disentangling geometry and appearance during facial NeRF generation. Sun et al. introduced the FE-NeRF [32] that employs separate latent codes to control the intricacies of facial geometry and appearance. Subsequent advancements [16, 31] utilize decoupling techniques based on triplane representations, leading to the facial generation results with significantly enhanced quality. Despite their success in good geometry and appearance swapping, these methods heavily rely on random sampling or reference images for global appearance editing. This reliance poses challenges in the obtainment of desired reference images and precludes precise control over localized appearance attributes, such as selective hair color alteration." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 239, + 289, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 239, + 289, + 430 + ], + "spans": [ + { + "bbox": [ + 46, + 239, + 289, + 430 + ], + "type": "text", + "content": "Compared to reference images, colored strokes, functioning as an interactive tool, offer a precise depiction of local appearance details. In stroke-based image editing, one category of methods [17, 26] relies on conditional GAN and completion framework to edit local regions with the stroke guidance. However, artifacts may arise in the editing boundary and result in less realistic images for large-area editing operations, as shown in Figure 6. Another category of methods [22, 27] employs pre-trained facial generation models as decoders, mapping colored strokes to the latent space of the generation model to generate edited facial results. However, these methods struggle to preserve the unchanged geometric features of the input face during editing, as demonstrated in Figure 6. Importantly, these techniques are specifically tailored for 2D facial image editing and cannot be directly applied to 3D facial radiance fields." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 432, + 289, + 708 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 432, + 289, + 708 + ], + "spans": [ + { + "bbox": [ + 46, + 432, + 289, + 708 + ], + "type": "text", + "content": "This paper presents StrokeFaceNeRF, a framework for editing facial NeRF appearance based on colored strokes, enabling precise modifications of color and lighting in 3D faces. Leveraging 2D facial image generation techniques such as StyleGAN2 [21] and semantic segmentation methods [38], we construct a dataset of faces with identical geometry but varying appearances, generating corresponding colored stroke maps using bilateral filtering and semantic clustering algorithms. To achieve appearance editing, directly encoding edited stroke maps into the latent space of the pre-trained facial NeRF generation model [5] leads to texture smoothness and undesirable geometry distortion due to high-frequency information absence and user's inaccurate drawing of strokes. To solve this problem, we propose a transformer-based editing network, which fuses the original and stroke-encoded latent codes to modify appearance while preserving the original geometry in edited regions. Furthermore, we introduce a geometry loss term during training to ensure surface density remains unchanged, improving detail preservation. To further maintain unchanged features in non-edited areas for precise editing, we design a volumetric fusion algorithm that integrates localized regions before and after editing in 3D space, enabling local-" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 305, + 72, + 500, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 500, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 500, + 95 + ], + "type": "text", + "content": "ized appearance editing effects in facial models. Our contributions are summarized as follows" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 306, + 96, + 545, + 216 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 306, + 96, + 545, + 132 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 96, + 545, + 132 + ], + "spans": [ + { + "bbox": [ + 306, + 96, + 545, + 132 + ], + "type": "text", + "content": "- We propose the first color stroke-based facial NeRF editing framework to generate free-view realistic appearance editing facial images." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 133, + 545, + 179 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 133, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 306, + 133, + 545, + 179 + ], + "type": "text", + "content": "- We design a novel geometry density loss to train the transformer-based latent editing network, which effectively preserves the geometry detail during facial appearance modifications." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 180, + 545, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 180, + 545, + 216 + ], + "spans": [ + { + "bbox": [ + 306, + 180, + 545, + 216 + ], + "type": "text", + "content": "- We introduce a volumetric fusion algorithm to precisely edit local regions while maintaining the 3D consistency in unedited regions." + } + ] + } + ], + "index": 6 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 232, + 392, + 245 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 232, + 392, + 245 + ], + "spans": [ + { + "bbox": [ + 306, + 232, + 392, + 245 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 252, + 528, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 252, + 528, + 266 + ], + "spans": [ + { + "bbox": [ + 306, + 252, + 528, + 266 + ], + "type": "text", + "content": "2.1. Facial Image Editing with Colored Strokes" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 270, + 545, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 270, + 545, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 270, + 545, + 510 + ], + "type": "text", + "content": "Existing 2D facial image editing methods using colored strokes can be divided into two categories. One group of methods utilizes conditional Generative Adversarial Networks (cGANs) to accomplish stroke-guided image generation. Sangkloy et al. [29] utilize sketches and colored strokes to directly generate realistic images through a translation network. However, this method fails to achieve localized area editing. To solve this problem, FaceShop [26] utilizes image completion techniques and 2D mask marking for localized facial image editing based on sketches and colored strokes. Jo et al. [18] further introduced SC-FEGAN that employs gated convolutions and new style losses for training, enabling a broader range of editing operations. Xiao et al. [36] design a hair generation network with self-attention mechanisms, achieving more natural and realistic hair editing effects. However, these methods are sensitive to input conditions and result in smooth edits lacking texture information in edited regions. Additionally, they tend to produce artifacts at the editing boundary due to the image completion techniques." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 510, + 545, + 713 + ], + "type": "text", + "content": "Another category of methods utilizes pre-trained generative models to generate high quality faces instead of pixelwise translation. Bau et al. [3] first utilize reverse optimization to achieve image shape and color editing in the GAN's latent space. pSp [27] further designs an image encoding network to map various types of input images, such as sketches and color strokes, into StyleGAN2's latent space to generate corresponding facial images. In order to generate highly editable latent codes, Tov et al. [34] further constrained the latent codes with a discriminator. However, these methods, as they represent the entire image with latent vectors, struggle to achieve localized editing effects. Instead of GAN dependence, Meng et al. [22] employed pre-trained diffusion models to achieve facial image editing based on colored stroke maps. Images with user-drawn strokes are added Gaussian noise, then progressively denoised to synthesize realistic facial images. However, it is" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7539" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 62, + 70, + 288, + 238 + ], + "blocks": [ + { + "bbox": [ + 62, + 70, + 288, + 238 + ], + "lines": [ + { + "bbox": [ + 62, + 70, + 288, + 238 + ], + "spans": [ + { + "bbox": [ + 62, + 70, + 288, + 238 + ], + "type": "image", + "image_path": "ed19e967ddc010a416c336e52113dbc352b8d11f8b3232dd849538ec88390936.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "lines": [ + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": "Figure 2. 3D Facial Appearance Editing Framework. Given the original latent code " + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": ", free-view images are rendered by EG3D. Users introduce editing operations, resulting in the creation of a color stroke image " + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{edit}}" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": ". This stroke map is encoded by Color Encoder " + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "inline_equation", + "content": "E_{c}" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": " to generate " + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "inline_equation", + "content": "w_{c}" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": ", which is fused with original latent code " + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": " by latent fusion network to generate " + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{edit}}" + }, + { + "bbox": [ + 46, + 240, + 547, + 285 + ], + "type": "text", + "content": ". Utilizing an additional 2D mask, the volumetric fusion approach facilitates targeted appearance editing within specific regions." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 290, + 70, + 533, + 238 + ], + "blocks": [ + { + "bbox": [ + 290, + 70, + 533, + 238 + ], + "lines": [ + { + "bbox": [ + 290, + 70, + 533, + 238 + ], + "spans": [ + { + "bbox": [ + 290, + 70, + 533, + 238 + ], + "type": "image", + "image_path": "8fd18f8e3a238858f24822341956ddb4686569ee346e964549491c47cb1e42ce.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 291, + 288, + 352 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 291, + 288, + 352 + ], + "spans": [ + { + "bbox": [ + 46, + 291, + 288, + 352 + ], + "type": "text", + "content": "challenging to directly apply this method to facial neural radiance field editing. Additionally, because of the direct input of coarse stroke maps, it is challenging for the above methods to maintain geometric features while performing appearance modification in editing regions." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 360, + 167, + 373 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 360, + 167, + 373 + ], + "spans": [ + { + "bbox": [ + 47, + 360, + 167, + 373 + ], + "type": "text", + "content": "2.2. Editing Facial NeRF" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 379, + 287, + 558 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 379, + 287, + 558 + ], + "spans": [ + { + "bbox": [ + 46, + 379, + 287, + 558 + ], + "type": "text", + "content": "Combining generative adversarial networks with neural radiance fields enables the synthesis of realistic facial images from arbitrary viewpoints. Graf [30] first adds extra latent codes to NeRF's fully connected network to support face generation and use multiscale discriminators for supervision. Giraffe [24] designs a new framework that employs volume rendering to obtain feature maps and a convolutional framework to generate facial images. StyleSDF [25] and GRAM [7] utilize representation methods based on SDF and implicit planes, respectively, producing higher-quality and more 3D consistent results. EG3D [5] propose a facial NeRF generation framework based on triplane representation and StyleGAN2 [21] generator. However, these methods can only synthesize faces through random sampling and lack the ability for editing." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 558, + 288, + 715 + ], + "type": "text", + "content": "To generate controllable facial NeRF, Jo et al. [17] use sketches, black-and-white images, and text as control conditions. Gao et al. [9] propose a facial NeRF generation and editing framework based on sketches to enhance synthesis quality and achieve fine editing. However, this method can only edit facial geometry. Another line of work decouples facial NeRF's geometry and appearance using semantic segmentation. FE-NeRF [32] achieves geometric editing through reverse latent code optimization and appearance editing through random sampling. IDE-3D [31] constructs geometry triplanes and appearance triplanes, and designs a semantic map encoder to generate higher-quality facial results. NeRFFaceEditing [16] apply AdaIN [14] to triplanes" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 291, + 547, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 291, + 547, + 375 + ], + "spans": [ + { + "bbox": [ + 304, + 291, + 547, + 375 + ], + "type": "text", + "content": "features, enabling the disentanglement of geometry and appearance control. Although the above methods achieve effective appearance modification, reference images or latent codes are required instead of user's flexible interaction. More importantly, the above methods are designed for the global appearance editing and cannot be directly utilized for local editing." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 394, + 389, + 408 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 394, + 389, + 408 + ], + "spans": [ + { + "bbox": [ + 305, + 394, + 389, + 408 + ], + "type": "text", + "content": "3. Methodology" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 415, + 545, + 582 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 582 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 582 + ], + "type": "text", + "content": "We propose a framework, StrokeFaceNeRF, enables users to utilize colored strokes for facial NeRF appearance editing. We employ the EG3D [5] generator architecture, a proficient 3D-aware Generative Adversarial Network (GAN) that combines the StyleGAN2 [21] architecture and neural rendering to produce high-quality 3D shapes. Given a latent code, a triplane representation can be obtained from a StyleGAN2 backbone. The neural renderer then aggregates features from these triplanes and predicts feature images based on a specified camera pose. Subsequently, a super-resolution module is applied to upsample and refine these raw neurally rendered images, resulting in high-quality, multiview-consistent images. More details of the generator can be found in [5]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 546, + 715 + ], + "type": "text", + "content": "Our method comprises three key components: dataset construction, colored stroke editing network, and 3D local fusion module. Initially, we introduce a dataset construction approach to acquire facial images with consistent geometry but varying appearances, along with their corresponding colored stroke images as detailed in Section 3.1. Subsequently, an appearance editing network, described in Section 3.2, is established within the latent space of EG3D to predict the 3D faces. Additionally, in Section 3.3, we propose a 3D local fusion method to enable effective appearance editing while meticulously preserving features in" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 316, + 757 + ], + "type": "text", + "content": "7540" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 127, + 83 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 127, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 127, + 83 + ], + "type": "text", + "content": "non-edited regions." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 97, + 169, + 108 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 97, + 169, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 97, + 169, + 108 + ], + "type": "text", + "content": "3.1. Dataset Construction" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 115, + 287, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 115, + 287, + 270 + ], + "spans": [ + { + "bbox": [ + 46, + 115, + 287, + 270 + ], + "type": "text", + "content": "To supervise the training of network models, the training data needs to simulate the process of facial appearance editing based on colored strokes. Thus, the training tuples include original faces, edited faces, and corresponding colored stroke maps. Dataset construction involves three steps as shown in Figure 3: (1) building a collection of facial latent codes in EG3D's latent space, obtained through random sampling and real images inversion; (2) constructing facial tuples with identical geometry but different appearances. Two different methods were employed: one based on semantic segmentation and the other based on StyleGAN2 generative networks; (3) generating colored stroke maps using bilateral filtering and semantic clustering methods." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 270, + 287, + 474 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 287, + 474 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 287, + 474 + ], + "type": "text", + "content": "We utilize two approaches to synthesize paired images with the same geometry but different appearance, indicated as the edited ground truth faces. Semantic Segmentation-Based Augmentation. Given the original rendered facial images, we utilize BiSeNet [38] to get semantic segmentation masks. Then, for each local semantic region, we represent it into HSV space, where the Hue channel is uniformly replaced with random color, while the Saturation and Value channels are added random perturbation. Finally, these regions are merged into original images to imitate appearance editing. StyleGAN2-Based Augmentation. We further utilize pre-trained generator to synthesize more diverse and realistic training images. Given the original rendered images, ReStyle [2] encodes them into StyleGAN2 latent space, followed with style mixing to change the facial appearance while preserving the same geometry. More details can be found in Supplementary." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 474, + 287, + 713 + ], + "type": "text", + "content": "With the paired appearance modification images, corresponding color strokes are required to imitate real editing situation. Typically, users drawn strokes are simple and monochromatic. Therefore, synthesized color stroke images must preserve the original image's color and geometric layout while eliminating high-frequency texture features and local details. To achieve this objective, we employ the bilateral filtering method [33] to effectively preserves the edge features of the facial image while eliminating high-frequency details. Specially, the initial image undergoes median filtering, followed by iterative application of bilateral filtering, as explained in the Supplementary. Nevertheless, some regions still exhibit smooth transitions between different colored areas after filtering, posing challenges for users aiming to replicate specific effects. To tackle this issue, we employ a pixel value clustering technique based on semantic information. Initially, the facial image undergoes semantic segmentation. Within the hair area, clustering allows all pixel colors to be replaced by the nearest cluster center color, thereby eliminating smooth transition regions." + } + ] + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 313, + 69, + 541, + 171 + ], + "blocks": [ + { + "bbox": [ + 313, + 69, + 541, + 171 + ], + "lines": [ + { + "bbox": [ + 313, + 69, + 541, + 171 + ], + "spans": [ + { + "bbox": [ + 313, + 69, + 541, + 171 + ], + "type": "image", + "image_path": "2da12d65a8b1e146d8aff06e23ee124b1aa2e1c042f22399ffe959067c008dd2.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 175, + 545, + 219 + ], + "lines": [ + { + "bbox": [ + 304, + 175, + 545, + 219 + ], + "spans": [ + { + "bbox": [ + 304, + 175, + 545, + 219 + ], + "type": "text", + "content": "Figure 3. Dataset construction pipeline. Given EG3D rendering images, the appearance is changed by two different approaches. Then, the color stroke images are synthesized by image filter and cluster." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 225, + 545, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 225, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 305, + 225, + 545, + 250 + ], + "type": "text", + "content": "The same methodology is applied to the facial area, yielding the final color stroke image." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 256, + 465, + 269 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 256, + 465, + 269 + ], + "spans": [ + { + "bbox": [ + 306, + 256, + 465, + 269 + ], + "type": "text", + "content": "3.2. Appearance Editing Network" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": "In our framework, the target face NeRF to be edited is represented as a latent code " + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": " within EG3D's latent space. The latent code can be obtained either by random sampling in EG3D or by applying PTI [28] to invert real images. Utilizing StyleGAN generator and volume rendering, free view facial images can be generated, followed by the approaches in Section 3.1 to extract color stroke images. Users then modify these color stroke images to obtain the edited color stroke image " + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": ". As illustrated in Figure 2, the input to the appearance editing network consists of the original latent variable " + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": ", the edited color stroke image " + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": ", and the output is the edited latent variable " + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 274, + 545, + 417 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": "The appearance editing network comprises two main components: the Color Encoder " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "E_{c}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " and the Latent Fusion Network " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "F_{l}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ". Specifically, given the edited color stroke image " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "C_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ", the color encoder that has a similar structure to [27], predicts the latent code " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w_{c}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ". While this latent code generates facial results with color editing effects, it fails to preserve the original facial features, such as the geometric structure of the hair and the original skin color in non-edited areas, as shown in Figure 2. Therefore, a latent code fusion network is designed to utilize the information from the original latent variable " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ", thus better preserving the original facial features. The latent fusion network " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "F_{l}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " adopts a cross-attention transformer block to predict the fused latent variable " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ". This design implicitly extracts the color information from " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w_{c}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " and geometry information from " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": ", guaranteeing a thorough integration of both color-edited and original facial features. In this configuration, the latent code " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w_{c}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " is employed as query tokens, whereas the original latent code " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " serves as key and value tokens. We also normalize over queries instead of keys as described in [13] to ensure a continuous refinement of " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w_{c}" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " during the fusion process with value tokens while mitigating the potential influence of " + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 418, + 546, + 693 + ], + "type": "text", + "content": " being too large." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 375, + 701, + 545, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 375, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 375, + 701, + 545, + 714 + ], + "type": "interline_equation", + "content": "w _ {\\text {e d i t}} = F _ {l} \\left(w, E _ {c} \\left(C _ {\\text {e d i t}}\\right)\\right) \\tag {1}", + "image_path": "da9b855d1b37ef888c011b4c056e54c6551b094b6e359daa42a253a59e9cd954.jpg" + } + ] + } + ], + "index": 11 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7541" + } + ] + } + ], + "index": 12 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 185, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 185, + 83 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 185, + 83 + ], + "type": "text", + "content": "3.3. Volumetric Local Fusion" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": "While direct rendering by " + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{edit}}" + }, + { + "bbox": [ + 46, + 89, + 287, + 209 + ], + "type": "text", + "content": " yields good editing effects within targeted editing areas, as depicted in Figure 7, noticeable undesirable discrepancies emerge in unedited regions. Moreover, intricate editing tasks, such as selectively dyeing specific portions of hair or drawing specific patterns on faces, pose challenges for the latent code-based representation because of its overarching global control inherited from StyleGAN2 backbone. To address these issues, we propose a volumetric fusion approach to enable more refined editing operations." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "spans": [ + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": "In order to facilitate local editing, our method introduces support for an additional 2D mask input that indicates the editing region. This 2D mask is further lifted into 3D mask volume to support volumetric fusion. Specifically, we propose a depth guidance approach to sample a set of points near the facial surface. In the volume rendering, for each ray " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "r_{i,j}" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": " of the pixel at the " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": "th row and " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "j" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": "th column, the camera's position and ray direction are denoted as " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "o_{i,j}" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "d_{i,j}" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": ", respectively. After rendering the original faces, we get the corresponding depth value " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "D[i,j]" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": ". Then, for each ray, we uniformly sample " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": " points with offset " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "\\triangle x_k" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": " within range " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "[-0.1, 0.1]" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": ". The sampled 3D points set " + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 210, + 288, + 365 + ], + "type": "text", + "content": " for the original face is denoted as:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 73, + 369, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 73, + 369, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 73, + 369, + 287, + 385 + ], + "type": "interline_equation", + "content": "S = \\cup_ {i, j} \\cup_ {k = 1} ^ {K} \\left(o _ {i, j} + \\left(D [ i, j ] + \\triangle x _ {k}\\right) \\cdot d _ {i, j}\\right) \\tag {2}", + "image_path": "1150017f5b5808cd8ad1b289d40fbfd1d6ab0896b8640af31e6baa0bfccd3130.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 389, + 287, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 389, + 287, + 426 + ], + "spans": [ + { + "bbox": [ + 46, + 389, + 287, + 426 + ], + "type": "text", + "content": "where the default value of " + }, + { + "bbox": [ + 46, + 389, + 287, + 426 + ], + "type": "inline_equation", + "content": "K" + }, + { + "bbox": [ + 46, + 389, + 287, + 426 + ], + "type": "text", + "content": " is 5. Notably, as illustrated in Figure 2, we selectively employ the rays corresponding to pixels within the 2D mask regions." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "text", + "content": "Subsequently, this generated 3D point set undergoes a transformation into a 3D volumetric mask. Specifically, we initialize a " + }, + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "inline_equation", + "content": "256 \\times 256 \\times 256" + }, + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "text", + "content": " 3D volume with zero values throughout the space. The coordinates of the 3D points, along with their neighboring positions, are designated as 1, indicating 3D editing regions. To ensure smoother boundaries, we utilize a three-dimensional dilation and Gaussian filtering, yielding the 3D mask denoted as " + }, + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "inline_equation", + "content": "M_{\\mathrm{3D}}" + }, + { + "bbox": [ + 46, + 426, + 287, + 581 + ], + "type": "text", + "content": ". Additionally, We implement a mask padding strategy, which introduces direction offsets to the camera poses and extends the mask boundary. This prevents incomplete editing artifacts during view changes. Further details regarding the padding technique are available in the Supplemental material." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": "To render realistic editing images, the original latent variable " + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": " and the edited latent variable " + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{edit}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": " are used to synthesize the original and edited triplane features, respectively. For the sampling points " + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": " in space during volume rendering, the corresponding original feature " + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "inline_equation", + "content": "f_{h}" + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": " and edited feature " + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{edit}}(h)" + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": " are generated. To achieve the editing fusion effect, the features are fused based on the 3D mask " + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "inline_equation", + "content": "M_{3\\mathrm{D}}" + }, + { + "bbox": [ + 46, + 582, + 287, + 665 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 54, + 670, + 287, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 54, + 670, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 54, + 670, + 287, + 685 + ], + "type": "interline_equation", + "content": "f _ {\\text {f u s i o n}} (h) = f _ {\\text {e d i t}} (h) \\cdot M _ {\\mathrm {3 D}} [ h ] + f (h) \\cdot \\left(1 - M _ {\\mathrm {3 D}} [ h ]\\right) \\tag {3}", + "image_path": "8026617718b433f59c66fd5ea48f9aa04abeea89eba703fbc9584760d6bd5cc9.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "The fused features " + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "inline_equation", + "content": "f_{\\mathrm{fusion}}" + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": " are passed through the decoder of EG3D to obtain color and density information. Afterward," + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 96 + ], + "type": "text", + "content": "they are processed through the volume rendering and upsampling modules to generate the final edited faces." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 103, + 411, + 117 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 103, + 411, + 117 + ], + "spans": [ + { + "bbox": [ + 306, + 103, + 411, + 117 + ], + "type": "text", + "content": "3.4. Training Strategy" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 121, + 545, + 217 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 121, + 545, + 217 + ], + "spans": [ + { + "bbox": [ + 304, + 121, + 545, + 217 + ], + "type": "text", + "content": "During the training of Appearance Editing Network, the geometry details should be preserved while the appearance editing effectiveness should not be influenced. This is nontrivial because the 2D supervision lacks detailed 3D structure constrain and the synthesized training data has minor geometry distortion because of Style-mixing's limitation. To solve this problem, we train our network with the follow strategy." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 217, + 545, + 373 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 217, + 545, + 373 + ], + "spans": [ + { + "bbox": [ + 304, + 217, + 545, + 373 + ], + "type": "text", + "content": "Geometry Density Loss. Based on our NeRF representation, we design a novel density loss to enforce the 3D geometry consistency between the original and edited faces. Specifically, leveraging the 3D points generation approach described in Equation 2, a collection of 3D points is generated. Notably, we use all the rays during the rendering instead of rays in specific regions. These 3D sample points are further projected onto triplane space to query corresponding triplane features that are subsequently decoded into color and density through volume rendering. We minimize the density value between the original and edited faces to effectively preserve the facial geometry while decoupling the appearance:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 310, + 380, + 545, + 417 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 310, + 380, + 545, + 417 + ], + "spans": [ + { + "bbox": [ + 310, + 380, + 545, + 417 + ], + "type": "interline_equation", + "content": "L _ {\\text {d e n s i t y}} = \\sum_ {x \\in S, x ^ {\\prime} \\in S ^ {\\prime}} | | \\psi_ {\\text {d e n s i t y}} (\\mathcal {F} (x)) - \\psi_ {\\text {d e n s i t y}} \\left(\\mathcal {F} ^ {\\prime} \\left(x ^ {\\prime}\\right)\\right) | | _ {1} \\tag {4}", + "image_path": "45950985dae98a3ee70f412f18f52f2342f0830f35f400bd9474690540da3feb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{F}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " denotes the triplane query process and " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\psi_{\\mathrm{density}}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " denotes density decoder. " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "x^{\\prime}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "S^{\\prime}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " are the 3D points and set for edited faces. These points are sampled with the same offset but new depth map " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "D_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " of edited faces. Edited triplane features " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "\\mathcal{F}^{\\prime}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " synthesized by " + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "inline_equation", + "content": "w_{\\mathrm{edit}}" + }, + { + "bbox": [ + 304, + 418, + 545, + 488 + ], + "type": "text", + "content": " are used for density calculation." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 489, + 545, + 549 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 489, + 545, + 549 + ], + "spans": [ + { + "bbox": [ + 304, + 489, + 545, + 549 + ], + "type": "text", + "content": "We also utilizes the same loss functions as the pSp framework [27] to match the original stroke distribution. 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Color stroke-based facial NeRF appearance editing results. Given the original faces (a), users drawn the editing color strokes (b) (d), our methods generate the corresponding editing results (c)(e). 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Regularization constraints are added to ensure that the edited latent variables are as close as possible to the mean latent variables " + }, + { + "bbox": [ + 46, + 467, + 286, + 526 + ], + "type": "inline_equation", + "content": "\\overline{w}" + }, + { + "bbox": [ + 46, + 467, + 286, + 526 + ], + "type": "text", + "content": ", making the generated faces more natural." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 123, + 535, + 287, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 535, + 287, + 548 + ], + "spans": [ + { + "bbox": [ + 123, + 535, + 287, + 548 + ], + "type": "interline_equation", + "content": "L _ {r e g} = \\left\\| w _ {\\mathrm {e d i t}} - \\bar {w} \\right\\| _ {2} \\tag {8}", + "image_path": "396228a8c452b6cf844b25c0e787c25b8b1410225fa4418b9b915a54b00fe2eb.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 47, + 555, + 198, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 198, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 198, + 567 + ], + "type": "text", + "content": "The overall loss function is given by:" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 47, + 575, + 286, + 598 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 575, + 286, + 598 + ], + "spans": [ + { + "bbox": [ + 47, + 575, + 286, + 598 + ], + "type": "interline_equation", + "content": "L = \\alpha_ {1} L _ {\\text {d e n s i t y}} + \\alpha_ {2} L _ {i m g} + \\alpha_ {3} L _ {L P I P S} + \\alpha_ {4} L _ {I D} + \\alpha_ {5} L _ {r e g} \\tag {9}", + "image_path": "c505e1c17120dc68cfeee9e824b059dd9d4d5906266afc6188399b5ce2de0879.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "spans": [ + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\alpha_{1},\\alpha_{2},\\alpha_{3},\\alpha_{4}" + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\alpha_{5}" + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "text", + "content": " represent the weighting coefficients for each loss term, with values of 0.05, 2.0, 2.0, 0.2, and 0.005, respectively. In the first stage training, we set " + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "inline_equation", + "content": "\\alpha_{1} = 0" + }, + { + "bbox": [ + 46, + 600, + 287, + 659 + ], + "type": "text", + "content": " because only appearance is expected to be encoded in this stage." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 47, + 670, + 127, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 127, + 682 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 127, + 682 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 713 + ], + "type": "text", + "content": "Dataset: Our training dataset comprises original faces generated by EG3D random sampling and real images in" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 335, + 545, + 384 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 335, + 545, + 384 + ], + "spans": [ + { + "bbox": [ + 305, + 335, + 545, + 384 + ], + "type": "text", + "content": "version [1] of CelebA-HQ [20], amounting to 47,134 examples. Appearance-edited faces and corresponding color stroke images are constructed using the method detailed in Section 3.1, resulting in 94,268 paired samples in total." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 385, + 545, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 385, + 545, + 445 + ], + "spans": [ + { + "bbox": [ + 305, + 385, + 545, + 445 + ], + "type": "text", + "content": "Training details: We use a single NVIDIA GeForce RTX 3090 GPU to train our framework. The batch size is 4, with the Ranger optimizer [37] and a learning rate of 1e-4. Each training stage involved 30k iterations, completing the final network training process." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 447, + 545, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 447, + 545, + 567 + ], + "spans": [ + { + "bbox": [ + 305, + 447, + 545, + 567 + ], + "type": "text", + "content": "Evaluation metrics: We use the following common metrics: Fréchet Inception Distance (FID) [12], Kernel Inception Distance (KID) [4] and Identity Consistency (ID) from [15]. To evaluate the geometry consistency in both 2D and 3D methods, we computed the Structural Similarity Index (SSIM) [35] metric for the edges obtained using the Sobel [8] operator in the edited regions of the generated images compared to the real images, denoted as E-SSIM. A higher E-SSIM value in the edited regions indicates a better preservation of the geometry in those areas." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 575, + 362, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 575, + 362, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 575, + 362, + 586 + ], + "type": "text", + "content": "4.1. Results" + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Figure 4 illustrates the 3D facial NeRF appearance editing based on color strokes. Benefit from the 3D representation in our framework, users can select arbitrary view point to render images. Then, users could draw color strokes, which are overlaid on extracted strokes extracted based on methods described in Section 3.1 to serve as the edited stroke image. Our framework takes an additional 2D mask inputs, which either have the same shape with drawing strokes, or additionally drawn by users. 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"type": "text", + "content": "(g) Ours" + } + ] + } + ], + "index": 27, + "angle": 0, + "type": "image_caption" + } + ], + "index": 26 + }, + { + "bbox": [ + 46, + 320, + 287, + 452 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 320, + 287, + 452 + ], + "spans": [ + { + "bbox": [ + 46, + 320, + 287, + 452 + ], + "type": "text", + "content": "and lip colors. It is noteworthy that the geometric details are well preserved as the original faces during appearance editing, as demonstrated by the wrinkle details in the 1st row and hair structure in the 3rd row. Unedited regions, such as hair (1st row) and background, also retain the same as the original faces. The 3rd row of Figure 4 showcases more complex local appearance editing results. To achieve diverse editing effects, users draw finer masks (c) to mark local areas, such as a cluster of hair or specific facial patterns. The 3D local fusion algorithm enables editing in marked areas, resulting in more complex and diverse editing effects." + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 46, + 453, + 287, + 523 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 453, + 287, + 523 + ], + "spans": [ + { + "bbox": [ + 46, + 453, + 287, + 523 + ], + "type": "text", + "content": "As shown in Figure 5, given a real facial image, the original facial image is reconstructed in latent space using the PTI algorithm [28] (b). Similarly, users draw color stroke images (c) and edit area masks (d). Our method generates corresponding facial NeRF appearance editing results and obtains multi-view facial outcomes." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 47, + 538, + 132, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 538, + 132, + 551 + ], + "spans": [ + { + "bbox": [ + 47, + 538, + 132, + 551 + ], + "type": "text", + "content": "4.2. Comparisons" + } + ] + } + ], + "index": 31 + }, + { + "type": "table", + "bbox": [ + 47, + 592, + 301, + 676 + ], + "blocks": [ + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "type": "text", + "content": "Table 1. Quantitative evaluation using FID, KID " + }, + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\times 10^{2}" + }, + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "type": "text", + "content": ", mean and std value of identity consistency (ID), E-SSIM " + }, + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "type": "inline_equation", + "content": "\\times 10^{2}" + }, + { + "bbox": [ + 46, + 555, + 287, + 589 + ], + "type": "text", + "content": " on baseline models and our methods." + } + ] + } + ], + "index": 32, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 47, + 592, + 301, + 676 + ], + "lines": [ + { + "bbox": [ + 47, + 592, + 301, + 676 + ], + "spans": [ + { + "bbox": [ + 47, + 592, + 301, + 676 + ], + "type": "table", + "html": "
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
SC-FEGAN [18]47.183.410.50 ± 0.3774.36
SDEdit [22]37.612.520.41±0.4174.52
pSp [27]40.392.490.66 ± 0.1178.94
pSp-mixing31.322.000.73±0.0981.50
Ours16.860.830.85±0.1084.30
", + "image_path": "9ec5a1611052ff0382ad87a731d97d06e6ecbffc332b3c7cce16eaa90287021d.jpg" + } + ] + } + ], + "index": 33, + "angle": 0, + "type": "table_body" + } + ], + "index": 33 + }, + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 713 + ], + "type": "text", + "content": "Since there are no prior works on 3D-aware stroke-based image synthesis, we retrained the pSp [27] model on EG3D using our dataset. To ensure fair comparisons, we further" + } + ] + } + ], + "index": 34 + }, + { + "bbox": [ + 304, + 320, + 546, + 583 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 546, + 583 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 546, + 583 + ], + "type": "text", + "content": "applied style-mixing on pSp's predicted latent code by replacing 7-14 layers with original latent codes. We also compare with 2D image editing methods, including SC-FEGAN [18] and SDEdit [22]. Officially released codebases were used for all comparisons. As shown in Figure 6, given the original faces(a), color strokes and masks(b), since the editing areas are too large to complete, SC-FEGAN [18] generates less realistic results(c), with facial details appearing blurry in larger editing areas. Based on diffusion prior knowledge, SDEdit [22] generates more realistic results(d). However, the texture is still too smooth due to the geometry information absence of color stokes. Different from 2D image completion frameworks, pSp [27] predicts a latent code, which, however, totally modify the geometry compared with original faces. Unedited regions, such as background, are also changed. Even utilizing the style-mixing approach (f), there are also undesirable changes and the degree of editing has been largely affected. Compared with existing approaches, our method generates more realistic faces, which shows good faithfulness to the color strokes and precisely preserve the geometry details, even the sophisticated curly hair structure is well maintained." + } + ] + } + ], + "index": 35 + }, + { + "bbox": [ + 304, + 584, + 546, + 704 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 584, + 546, + 704 + ], + "spans": [ + { + "bbox": [ + 304, + 584, + 546, + 704 + ], + "type": "text", + "content": "Quantitative Comparison. To further validate the superiority of our method, we conduct a quantitation evaluation. We generated 1000 facial editing examples in FFHQ datasets, following the data generation method outlined in Section 3.1. We calculated the relevant metrics between all algorithm-generated results and real images. As shown in Table 1, our method has achieved the best results on all metrics, which proves that our method generates more realistic faces (FID, KID). 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The results of ablation study for density loss. w/o " + }, + { + "bbox": [ + 47, + 177, + 287, + 211 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{den}}" + }, + { + "bbox": [ + 47, + 177, + 287, + 211 + ], + "type": "text", + "content": " method is trained without geometry density loss while depth loss method is trained with an alternative depth image loss." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 238, + 70, + 285, + 163 + ], + "blocks": [ + { + "bbox": [ + 238, + 70, + 285, + 163 + ], + "lines": [ + { + "bbox": [ + 238, + 70, + 285, + 163 + ], + "spans": [ + { + "bbox": [ + 238, + 70, + 285, + 163 + ], + "type": "image", + "image_path": "8286044f9080c8cbb9ef64aff66504f3d6d2cbb421d923aaf431786054b594cf.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 247, + 164, + 275, + 174 + ], + "lines": [ + { + "bbox": [ + 247, + 164, + 275, + 174 + ], + "spans": [ + { + "bbox": [ + 247, + 164, + 275, + 174 + ], + "type": "text", + "content": "(e) Ours" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 218, + 140, + 231 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 140, + 231 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 140, + 231 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 11 + }, + { + "type": "table", + "bbox": [ + 48, + 282, + 299, + 355 + ], + "blocks": [ + { + "bbox": [ + 47, + 236, + 287, + 280 + ], + "lines": [ + { + "bbox": [ + 47, + 236, + 287, + 280 + ], + "spans": [ + { + "bbox": [ + 47, + 236, + 287, + 280 + ], + "type": "text", + "content": "Table 2. Ablation study comparison. All models are trained on the datasets described in Section 3.1 and evaluated on 1000 randomly sampled EG3D data. Metric calculations follow the methods outlined in Table 1." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 282, + 299, + 355 + ], + "lines": [ + { + "bbox": [ + 48, + 282, + 299, + 355 + ], + "spans": [ + { + "bbox": [ + 48, + 282, + 299, + 355 + ], + "type": "table", + "html": "
FID (↓)KID(↓)ID(↑)E-SSIM(↑)
w/o density loss21.441.070.67 ± 0.2277.35
w/ depth loss23.141.230.75 ± 0.1780.10
w/o mask fusion28.331.720.82± 0.0782.97
Ours16.860.830.85± 0.1084.30
", + "image_path": "f40ff44da129518afce175ad0bf8185878104c0d529c91bc7a38ce78185e2ced.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "table_body" + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 360, + 287, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 360, + 287, + 479 + ], + "spans": [ + { + "bbox": [ + 46, + 360, + 287, + 479 + ], + "type": "text", + "content": "We conduct ablation experiments on EG3D random sampled data to justify the necessity of each component. To validate the effectiveness of the proposed geometry density loss, we presents the results of training without density loss " + }, + { + "bbox": [ + 46, + 360, + 287, + 479 + ], + "type": "inline_equation", + "content": "L_{\\mathrm{den}}" + }, + { + "bbox": [ + 46, + 360, + 287, + 479 + ], + "type": "text", + "content": " and with an alternative depth image loss. Specifically, we employed MSE Loss between the original depth image and the generated one to constrain the network. The results in Figure 7 (d)(e) and Table 2 demonstrate the superiority of our density loss in preserving facial geometry features and maintaining identity consistency." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 46, + 479, + 287, + 612 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 287, + 612 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 287, + 612 + ], + "type": "text", + "content": "Figure 8 indicates our volumetric local fusion module' effectiveness in maintaining consistency for non-edited areas between and the original and edited face. As shown in Figure 8 (d), without using 3D local fusion, non-edited areas undergo significant changes, such as brightening hair in the first row and reddening the face in the second row. In contrast, our method (Figure 8 (e)) perfectly maintains consistency in non-edited areas without affecting the editing effects in edited regions. Figures 8 (d) and (f) display computed heatmap differences between pre-edited and post-edited images." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 47, + 621, + 119, + 633 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 621, + 119, + 633 + ], + "spans": [ + { + "bbox": [ + 47, + 621, + 119, + 633 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 641, + 288, + 714 + ], + "type": "text", + "content": "In this study, we propose a facial NeRF appearance editing method based on color strokes, enabling the modification of facial appearance features while preserving the original facial geometry. 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Subsequently, an appearance editing network is constructed within the pre-trained generative network's latent space. The network employs a color stroke encoder to extract color features from input stroke images and utilizes a latent variable fusion network to achieve appearance editing while preserving geometric features. To maintain unchanged regions, a 3D local fusion method is introduced, enabling effective editing of localized appearance while preserving the facial identity features. Experimental results demonstrate the superiority of our method in generating higher-quality digital facial results compared to existing approaches." + } + ] + } + ], + "index": 37 + }, + { + "bbox": [ + 304, + 376, + 546, + 593 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 376, + 546, + 593 + ], + "spans": [ + { + "bbox": [ + 304, + 376, + 546, + 593 + ], + "type": "text", + "content": "Despite achieving high-quality color editing results through color strokes, our method faces several challenges. Firstly, for highly detailed areas such as eyeballs, our method struggles to yield effective editing results. Handling these regions separately through segmentation and dedicated data processing could enhance editing outcomes. Additionally, due to limitations in the training dataset, our method encounters difficulties in handling overly complex color strokes, such as rainbow-colored hair, tending to average color strokes instead. To address this, generating distinct colors separately, followed by mask creation and blending, could yield superior results. Future research endeavors could extend the proposed algorithm from 3D digital faces to other types of 3D models, achieving more generalized editing effects. Moreover, combining color strokes with line drawings and semantic segmentation maps could enable simultaneous editing of 3D digital facial geometry and appearance." + } + ] + } + ], + "index": 38 + }, + { + "bbox": [ + 306, + 621, + 403, + 635 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 621, + 403, + 635 + ], + "spans": [ + { + "bbox": [ + 306, + 621, + 403, + 635 + ], + "type": "text", + "content": "Acknowledgement" + } + ] + } + ], + "index": 39 + }, + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 714 + ], + "type": "text", + "content": "This work was supported by National Natural Science Foundation of China (No. 62102403), and the Open Project Program of State Key Laboratory of Virtual Reality Technology and Systems, Beihang University (No. VRLAB2022C07). 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International Journal of Computer Vision, 129: 3051-3068, 2021. 2, 4" + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7547" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_content_list.json b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..9fb61487a443dbcd5bf3a91d4e32b7f51a939d67 --- /dev/null +++ b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_content_list.json @@ -0,0 +1,1609 @@ +[ + { + "type": "text", + "text": "Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning", + "text_level": 1, + "bbox": [ + 81, + 128, + 888, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhengwei Fang $^{1,2}$ , Rui Wang $^{1,2,3*}$ , Tao Huang $^{1,2}$ , Liping Jing $^{1,2}$", + "bbox": [ + 235, + 202, + 730, + 220 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{1}$ School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China", + "bbox": [ + 127, + 220, + 841, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{2}$ Beijing Key Lab of Traffic Data Analysis and Mining, Beijing, China", + "bbox": [ + 207, + 238, + 763, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "$^{3}$ Collaborative Innovation Center of Railway Traffic Safety, Beijing, China", + "bbox": [ + 191, + 256, + 779, + 275 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jankinfmail@gmail.com, {rui.wang,thuang,lpjing}@bjtu.edu.cn", + "bbox": [ + 223, + 277, + 745, + 292 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 325, + 313, + 343 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Strong adversarial examples are crucial for evaluating and enhancing the robustness of deep neural networks. However, the performance of popular attacks is usually sensitive, for instance, to minor image transformations, stemming from limited information — typically only one input example, a handful of white-box source models, and undefined defense strategies. Hence, the crafted adversarial examples are prone to overfit the source model, which hampers their transferability to unknown architectures. In this paper, we propose an approach named Multiple Asymptotically Normal Distribution Attacks (MultiANDA) which explicitly characterize adversarial perturbations from a learned distribution. Specifically, we approximate the posterior distribution over the perturbations by taking advantage of the asymptotic normality property of stochastic gradient ascent (SGA), then employ the deep ensemble strategy as an effective proxy for Bayesian marginalization in this process, aiming to estimate a mixture of Gaussians that facilitates a more thorough exploration of the potential optimization space. The approximated posterior essentially describes the stationary distribution of SGA iterations, which captures the geometric information around the local optimum. Thus, MultiANDA allows drawing an unlimited number of adversarial perturbations for each input and reliably maintains the transferability. Our proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without defenses through extensive experiments on seven normally trained and seven defense models.", + "bbox": [ + 76, + 358, + 473, + 795 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 823, + 209, + 838 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Albeit the excellent performance of deep neural networks (DNNs) across a broad spectrum of tasks in machine vi-", + "bbox": [ + 76, + 848, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/85b7c52b134c3f4ca34c2f89014f3ca3148ae881f3cd64b120c8382df4800db8.jpg", + "image_caption": [ + "Figure 1. Perturbation visualization of the adversarial examples generated by ANDA/MultiANDA that fool all selected normally trained (first row) and defense (second row) models." + ], + "image_footnote": [], + "bbox": [ + 514, + 327, + 883, + 444 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "sion and natural language processing, a rich stream of work [8, 14, 39, 50, 51] shows the non-negligible vulnerability of DNNs to adversarial attacks, which craft imperceptible perturbations to synthesize malicious inputs for triggering unexpected model predictions. Such severe degradation of model robustness and stability greatly hinders the application of DNNs in security- or safety-critical domains [1, 2, 11]. Fortunately, studying how to create potent adversarial examples aids in evaluating DNN-based systems and enhancing their robustness by devising defensive strategies, such as adversarial training [14, 29].", + "bbox": [ + 496, + 522, + 892, + 686 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "This paper focuses on the black-box and transfer-based threat model. The corresponding adversarial attack algorithms intend to synthesize the adversarial examples that can successfully fool the unknown DNNs without accessing any information on model architectures and outputs. Researchers implement such attacks by maximizing the nonconcave loss function of a substitute model trained for the same task with, for example, one step [14], or iterative steps [20] of gradient ascent optimization. However, prior work has shown the generated adversarial examples trend to overfit the substitute model, which hardly attacks other models [21]. Meanwhile, they are often sensitive to minor transformations [4, 26, 27].", + "bbox": [ + 496, + 688, + 893, + 883 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Hence, researchers have been exploring various data", + "bbox": [ + 517, + 885, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "*Corresponding author.", + "bbox": [ + 94, + 886, + 220, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "24841", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "augmentation strategies [4, 9, 25, 49] and improved SGA optimization methods [8, 17, 25, 45] to enhance the performance of transferable attacks. Nonetheless, these efforts exhibit limited generalization capabilities on unknown DNN architectures, particularly those trained with defense strategies. This suggests that a deterministic optimization procedure, initiated from a single image, is insufficient to thoroughly explore the high-dimensional perturbation space. Furthermore, the projected gradient descent (PGD) method proposed by Madry et al. [29] initializes the attack algorithm with random restarts around the legitimate image. However, these random samples represent homogeneous deviations from the original input, lacking diversity [10], which limits the transferability of adversarial examples.", + "bbox": [ + 75, + 90, + 472, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To resolve these issues, in this paper, we propose Multiple Asymptotically Normal Distribution Attacks (MultiANDA), a novel method that explicitly characterizes perturbations inferred from a learned distribution. Firstly, we formulate a single ANDA by taking advantage of the nice property of stochastic gradient ascent (SGA), the asymptotic normality [5, 18, 28, 30], to learn the true optimal posterior distribution of adversarial perturbations. Specifically, ANDA calculates and stores the first two moments of iterations captured along the optimizing trajectory to approximate the distribution of the adversarial perturbation as a Gaussian one. Moreover, we apply the deep ensemble strategy [22] on ANDA to devise a mixture of Gaussians, approximating the Bayesian posterior. As each Gaussians positioned at a different basin of attraction, the proposed MultiANDA leads to a further improved generalization performance of the attacks with more diverse adversarial examples. As shown in Figure 1, the perturbations crafted by our proposed method focus more on the semantic and decisive areas of objects than the baseline approach. In particular, the contributions of this work are the following:", + "bbox": [ + 75, + 304, + 472, + 622 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose MultiANDA, an approximate Bayesian inference method to realize transfer-based adversarial attacks. We learn the perturbation distribution instead of finding a specific adversary for each input example. Thus, a good approximation of the true perturbation posterior boosts the generalization (i.e., transferability) of the generated adversarial examples.", + "- We devise a stochastic adversarial attacking process instead of the original deterministic one initialized from one input by random image translations. In this way, we profit the asymptotic normality of SGA for a better perturbation distribution learning. Adopting the deep ensemble strategy, an effective mechanism for approximating Bayesian marginalization [47], MultiANDA accurately and efficiently estimate the posterior distribution over the perturbations by using the geometry information along the attacking trajectory.", + "- The learned distributions of perturbation allow draw" + ], + "bbox": [ + 75, + 625, + 472, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ing an unlimited number of adversarial examples for one input. We experimentally validate that the sampled adversaries have comparably high attack success rates with the singly generated ones, even on the defense models. This result demonstrates the great potential of our method for designing defense strategies grounded in adversarial training.", + "bbox": [ + 496, + 90, + 890, + 181 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "- Extensive experiment results show that the proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without advanced defenses. Significantly, MultiANDA is more advantageous when attacking the advanced defense models. Thus, ANDA and MultiANDA are expected to benchmark new defense methods in the future. Our code is available at https://github.com/CLIAgroup/ANDA.", + "bbox": [ + 496, + 181, + 890, + 303 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work and Preliminaries", + "text_level": 1, + "bbox": [ + 498, + 316, + 795, + 333 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our study mainly focuses on the black-box and transfer-based threat model, as they may bring more security and safety risks due to their practical applicability [8, 34].", + "bbox": [ + 496, + 343, + 890, + 388 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Black-Box Adversarial Attacks", + "text_level": 1, + "bbox": [ + 498, + 398, + 774, + 414 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Essentially, the adversarial attack algorithms intend to maximize the loss function $\\mathcal{L}(\\cdot)$ , e.g., the cross entropy loss for classification tasks, to search for the adversaries $x_{adv}$ [14, 39], with the constraints of $l_{\\infty}$ norm bound $\\varepsilon$ , as shown in (1):", + "bbox": [ + 496, + 422, + 890, + 498 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {x _ {a d v}} \\mathcal {L} (x _ {a d v}, y) \\quad \\text {s . t .} | | x _ {a d v} - x | | _ {\\infty} \\leq \\varepsilon , \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 511, + 890, + 534 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $x$ , $x_{adv}$ , $y$ are the legitimate input, the adversarial example and the true label, respectively.", + "bbox": [ + 496, + 544, + 890, + 574 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Among prior work, the fast gradient sign method (FGSM) [14] and its iterative version, the basic iterative method (BIM) [20] resort to linearizing the non-concave loss function and realize the attack with one-step update or iterative updates, as shown in (2):", + "bbox": [ + 496, + 575, + 890, + 650 + ], + "page_idx": 1 + }, + { + "type": "equation", + "text": "\n$$\nx _ {a d v} ^ {(t + 1)} = \\Phi (x _ {a d v} ^ {(t)} + \\alpha \\cdot \\operatorname {s i g n} (\\underbrace {\\nabla_ {x} \\mathcal {L} (x _ {a d v} ^ {(t)} , y)})), \\quad (2)\n$$\n", + "text_format": "latex", + "bbox": [ + 542, + 661, + 890, + 700 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $x_{adv}^{(t + 1)}$ , $\\delta^{(t)}$ are the adversarial example and perturbation at the $t$ -th step, $x_{adv}^{(0)}$ is the legitimate input, and $\\Phi (\\cdot)$ is the projection function on the $\\varepsilon$ -ball.", + "bbox": [ + 496, + 713, + 890, + 763 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "These attacks are more effective under white-box scenarios, whereas they tend to overfit the model parameters and hardly transfer to unknown architectures [21]. Thus, many works have been proposed to improve the transferability of adversarial examples, which can be divided into three categories. The first group focuses on the iterative optimizing process by considering momentum [8], Nesterov accelerated gradient [25], and variance reducing [45] to search for the optimal solutions. The second group attempts to attack", + "bbox": [ + 496, + 763, + 890, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "24842", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "the mid-layers by disrupting the critical object-aware features [12, 16, 31, 46, 52]", + "bbox": [ + 76, + 90, + 468, + 119 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Moreover, the third stream of methods adopt the commonly used generalization techniques by introducing diversity. These techniques encompass data augmentation [15, 19], such as resize and padding [49], translation [9]; and other integrated augmentation strategies, including combining multiple linear transformations [4], modifying the pixel values with multiple scales [25], integrating more information from other images [7], and using the sum of the gradients from intensity augmented images [17].", + "bbox": [ + 75, + 122, + 467, + 257 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Similar to our study, existing attack approaches also try to determine the explicit adversarial distributions. PGD [29] resolves the inner maximization problem by the random restart strategy. However, the uniformly drawn samples tend to lie densely around the natural image [10]. Li et al. [23] propose $\\mathcal{N}$ attack to define and learn an adversarial distribution. However, their work is under a query-based threat model, i.e., it has to access the output scores for each input from the black-box defense model, which weakens its scalability in real-world applications. Additionally, Dong et al. [10] propose to formulate the adversarial perturbations via a learned distribution for adversarial distributional training (ADT). Similar to $\\mathcal{N}$ attack, ADT crafts the adversarial examples centered with the natural input $x$ , which may fail in generating adversarial examples once the input is a little bit far away from the boundary. Conversely, ANDA generates adversaries around the optimal $x_{adv}^{*}$ . In this case, the adversaries are more prone to successful attacks. From the facets of implementation, ADT focuses on learning a distribution from a large amount of training data for adversarial training. Our proposed method tries to collect the trajectory information during the optimization process for each natural input. Thus, these crucial differences make two approaches suitable for distinct tasks: inner maximization problem for adversarial training (ADT) and transfer-based black-box attack (ANDA and MultiANDA).", + "bbox": [ + 75, + 258, + 468, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.2. Asymptotic Normality of SGD", + "text_level": 1, + "bbox": [ + 76, + 664, + 344, + 681 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Maddox et al. [28] point out that the trajectory of stochastic gradient descent (SGD) can be regarded as the Bayesian posterior distribution over the random variables to be optimized, e.g., the model parameters in the case of the DNN training. Following this theory, they propose a Gaussian posterior approximation method (SWAG) based on the first two moments of SGD iterations for model calibration or uncertainty quantification. In the prior work, Mandt et al. [30] provide a more detailed analysis of the stationary distribution of SGD iterations with a constant learning rate, also termed the asymptotic normality of SGD [44]. Such analysis can be traced back to the work by Ruppert [36], Polyak and Juditsky [35] known as Polyak-Ruppert averaging, and still an active research subject for SGD [5]. Furthermore,", + "bbox": [ + 75, + 688, + 467, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "inspired by deep ensembles [22], Wilson and Izmailov [47] carried out an extensive empirical study, demonstrating that applying SWAG only with multiple randomly initialized models can significantly improve the model performance. They emphasize that this benefits from the multimodal effects of the mixture Gaussian distributions and, in turn, boosts the contribution of each additional sample in the optimization procedure. In this paper, we adopt these theories to innovatively model the posterior distribution of perturbations to search for potent adversarial examples.", + "bbox": [ + 496, + 90, + 890, + 242 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Proposed Method", + "text_level": 1, + "bbox": [ + 498, + 260, + 671, + 277 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Drawing on the comprehensive research previously discussed, we hypothesize that utilizing the asymptotic normality of SGD (SGA in our problem formulation) to marginalize an approximate Bayesian posterior could enhance generalization (transferability in our context) beyond what is achievable with a fixed set of parameter (one specific adversarial perturbation). However, optimizing the objective (1) using attack algorithms such as BIM (2) is a deterministic gradient ascent process. In this process, no gradient noise is introduced to form a stationary distribution of SGD. Thus, to bridge this gap, we exploit random data augmentation in the standard optimization process, devising a novel attack method for accurately and efficiently estimating the posterior distribution over perturbations.", + "bbox": [ + 496, + 286, + 890, + 498 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In Section 3.1, we first empirically analyze the asymptotically normal distribution property in the stochastic adversarial attack process, then proceed to formalize the optimization objective for the task of adversarial example generation. Finally, inspired by the advantageous properties of SGD and the effective multimodal inference of the ensemble strategy, we introduce the new attack methods ANDA and MultiANDA in Sections 3.2 and 3.3, respectively.", + "bbox": [ + 496, + 500, + 890, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Asymptotic Normality of Stochastic BIM", + "text_level": 1, + "bbox": [ + 498, + 633, + 849, + 650 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Under specific conditions—decaying learning rates, smooth gradients, and a full rank stationary distribution—it has been theoretically established that SGD asymptotically converges to a Gaussian distribution centered at the local optimum [3, 5, 28]. Expanding on this, Mandt et al. [30] demonstrated that under certain assumptions, SGD with a constant and sufficiently small learning rate in its final search phase, i.e., when updates are proximal to the local optimum, converges to a stationary distribution. This convergence implies that iterations during this phase can approximate the posterior distribution of the optimized variables. Crucially, the gradient noise, introduced by the randomness of the sampled training batches, is instrumental in forming this distribution, provided the learning rate is adequately small [28]. These theoretical underpinnings motivate our approach in the algorithm design.", + "bbox": [ + 496, + 659, + 890, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "24843", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/44c3e6dc25cf12378b8ba55c4c682c790db4f22a8504cda03cc6d65757437d10.jpg", + "image_caption": [ + "a. Stochastic BIM" + ], + "image_footnote": [], + "bbox": [ + 83, + 90, + 467, + 169 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/66491600190cf1b1e4e3176e435b39afae2394344c086b39326269500bf70928.jpg", + "image_caption": [ + "b. ANDA implementation", + "Figure 2. Asymptotically normal distribution examples with iterative trajectories of adversarial perturbations generated by stochastic BIM (a) and the proposed approach (b)." + ], + "image_footnote": [], + "bbox": [ + 83, + 181, + 465, + 258 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As demonstrated in (2), the optimization process, beginning from a specific input, is a deterministic gradient ascent, differing from a standard SGA approach. Therefore, we introduce stochastic gradient noises to emulate Gaussian limiting distributions by integrating a random data augmentation technique AUG, like image translation used in our experiments, at each iterative step:", + "bbox": [ + 75, + 345, + 468, + 450 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nx _ {a d v} ^ {(t + 1)} = \\Phi (x _ {a d v} ^ {(t)} + \\alpha \\cdot \\operatorname {s i g n} (\\underbrace {\\nabla_ {x} \\mathcal {L} (\\mathrm {A U G} (x _ {a d v} ^ {(t)} , y))} _ {\\delta^ {(t)}})). \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 89, + 460, + 468, + 500 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Notably, a small constant learning rate schedule $(\\alpha = \\epsilon / T)$ is commonly adopted, where $\\epsilon \\in \\mathbb{R}$ is a sufficiently small number used to restrict the $L_{\\infty}$ -norm for creating invisible adversarial perturbations, and $T$ is the number of iterative steps. Hence, we speculate the devised stochastic BIM shown in (3) can be used as an approximate Bayesian inference algorithm. In particular, Mandt et al. [30] assume that the gradients along the optimizing trajectory follow the Gaussian distribution stemming from the central limit theorem. We visualized the adversarial perturbations $\\delta^{(t)}$ —the loss gradients in our task—using the t-SNE technique [43] to examine their distribution. 300 iterative steps for 3 randomly-drawn ImageNet [37] images shown in Fig. 2 a illustrates the Gaussian-shaped distributions which underpins our conjecture of the asymptotically normality of stochastic BIM algorithm. We notice the obvious increased gradient noise along the optimizing trajectory, which may due to the use of the sign() function and projection operations. Nevertheless, this does not affect the convergence of perturbations. Importantly, the first 10 steps converging with tight covariance justifies another speculation that the small value of $T$ (often $= 10$ for non-targeted attacks) and the non-trivial first step in our task (e.g., referring to strong attack performance of FGSM) indicate that the early iterates of are fairly close to the local optimum (i.e., the final search phase discussed above).", + "bbox": [ + 75, + 508, + 470, + 900 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Inspired by the results of this empirical study, we propose employing $n$ image transformations $\\mathsf{AUG}_i(\\cdot)$ to form a minibatch for an adversarial attack, thereby further enhancing stochasticity. Then, the optimization objective is formulated as", + "bbox": [ + 498, + 90, + 890, + 165 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {x _ {a d v}} \\sum_ {i = 1} ^ {n} \\mathcal {L} (\\mathrm {A U G} _ {i} (x _ {a d v}), y) \\quad \\text {s . t .} \\| x _ {a d v} - x \\| _ {\\infty} \\leq \\varepsilon . \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 509, + 176, + 890, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Furthermore, optimizing (4) to craft just one optimal adversarial example does not sufficiently explore the high-dimensional potential perturbation space. To further improve the transferability of adversarial examples to unknown architectures, we propose to explicitly model the adversarial perturbation $(\\delta)$ via a distribution $(\\Pi_{\\delta})$ . Thus, our optimization objective is formalized as", + "bbox": [ + 498, + 224, + 890, + 330 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\Pi_ {\\delta}} \\mathbb {E} _ {\\delta \\sim \\Pi_ {\\delta}} \\sum_ {i = 1} ^ {n} \\mathcal {L} (\\mathrm {A U G} _ {i} (x + \\delta), y), \\text {s . t .} \\| \\delta \\| _ {\\infty} \\leq \\varepsilon. \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 514, + 343, + 890, + 382 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Objective (5) aims to maximize the expected loss over the adversarial perturbation distribution. It is noteworthy that (5) is a generalized version of (4) and is expected to characterize sufficient information about perturbations for transferable adversarial example generation.", + "bbox": [ + 498, + 393, + 890, + 469 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Asymptotically Normal Distribution Attack", + "text_level": 1, + "bbox": [ + 500, + 479, + 867, + 494 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To better solve the optimization problem formulated in (5), we take advantage of the asymptotically normality of SGA and iteratively search for the adversarial examples similarly to (2). We omit the projection function $\\Phi(\\cdot)$ and $\\mathrm{sign}(\\cdot)$ because they do not effect the asymptotic normality of SGA as discussed in the previous subsection. Then, we calculate the gradient of the adversary with each transformation and denote it as the augmentation-aware perturbation $\\delta_i^{(t)}$ :", + "bbox": [ + 498, + 502, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {i} ^ {(t)} = \\nabla_ {x ^ {(t)}} \\mathcal {L} \\left(\\underset {\\text {A U G} _ {i}} {\\mathrm {A U G}} \\left(x _ {a d v} ^ {(t)}\\right), y\\right). \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 589, + 637, + 890, + 657 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Let $S$ be a set of samples augmented in each iteration, i.e., $S = \\{\\mathrm{AUG}_i(x_{adv}^{(t)})\\}_{i=1}^n$ . Here $S$ can be taken as a minibatch to form a stochastic gradient $\\hat{\\delta}_S$ which is a sum of contributions from all samples in $S$ . Hence, referring to the central limit theorem, $\\hat{\\delta}_S$ can be taken as a function of sample $z \\in S$ ,", + "bbox": [ + 498, + 669, + 890, + 763 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\hat {\\delta} _ {S} (z) \\approx \\delta (z) + \\frac {1}{\\sqrt {n}} \\Delta \\delta (z), \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 599, + 775, + 890, + 806 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the gradient noises $\\Delta \\delta (z)$ at each update can be conveniently assumed following a Gaussian distribution with covariance $C(z)$ ,", + "bbox": [ + 498, + 818, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\delta (z) \\sim \\mathcal {N} (0, C (z)), \\quad \\hat {\\delta} _ {S} (z) \\sim \\mathcal {N} (\\delta (z), \\frac {1}{n} C (z)). \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 511, + 875, + 890, + 905 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "24844", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Algorithm 1: Asymptotically Normal Distribution Attack (ANDA)", + "text_level": 1, + "bbox": [ + 86, + 95, + 424, + 123 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "Input: $x$ : clean image $x \\in \\mathbb{R}^d$ ; $y$ : ground-truth label; $f$ : pre-trained source model;", + "Parameters: $T$ : # iterations; $\\epsilon$ : perturbation magnitude; $n$ : # batch samples for augmentation; $M$ : # sampling examples;" + ], + "bbox": [ + 96, + 128, + 433, + 190 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output: $x_{adv}$ : Adversarial examples;", + "bbox": [ + 96, + 193, + 325, + 205 + ], + "page_idx": 4 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "1: Initialize $\\alpha \\leftarrow \\epsilon /T,\\bar{\\delta}^{(0)}\\leftarrow \\mathbf{0}^d$ $\\mathbf{D}\\gets \\emptyset ,x_0\\gets x$", + "2: for $t = 0$ to $T - 1$ do", + "3: Calculate the mean of gradients and store the deviation of gradients throughout previous $t$ iterations:" + ], + "bbox": [ + 104, + 205, + 480, + 253 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\delta_ {i} ^ {(t)} = \\nabla_ {x ^ {(t)}} J (f (\\mathrm {A U G} _ {i} (x ^ {(t)})), y), i = 1, \\dots , n\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 263, + 455, + 281 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\delta} ^ {(t + 1)} = \\frac {(t \\times n) \\bar {\\delta} ^ {(t)} + \\sum_ {i = 1} ^ {n} \\delta_ {i} ^ {(t)}}{(t + 1) \\times n}\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 297, + 418, + 329 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\text {A P P E N D - C O L S} (\\mathbf {D}, \\{\\delta_ {i} ^ {(t)} - \\bar {\\delta} ^ {(t + 1)} \\}), i = 1, \\dots , n\n$$\n", + "text_format": "latex", + "bbox": [ + 161, + 345, + 465, + 363 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4: Update the adversarial example along the average direction:", + "bbox": [ + 102, + 372, + 434, + 395 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx ^ {(t + 1)} = \\operatorname {C l i p} _ {x, e} \\left\\{x ^ {(t)} + \\alpha \\cdot \\operatorname {S i g n} (\\bar {\\delta} ^ {(t + 1)}) \\right\\}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 402, + 442, + 420 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5: end for", + "text_level": 1, + "bbox": [ + 104, + 430, + 171, + 441 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "6: Output option (a): Craft one $x_{adv}$", + "bbox": [ + 104, + 441, + 323, + 455 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nx _ {a d v} = x ^ {(T)}\n$$\n", + "text_format": "latex", + "bbox": [ + 263, + 460, + 343, + 477 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Output option (b): Craft M $x_{adv}$ by sampling from the learned perturbation distribution $\\mathcal{N}(\\bar{\\delta},\\sigma)$", + "bbox": [ + 120, + 482, + 446, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nC = \\text {N U M S} _ {-} \\operatorname {C O L S} (\\mathbf {D}) = n \\times T\n$$\n", + "text_format": "latex", + "bbox": [ + 205, + 517, + 401, + 531 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\delta} = \\bar {\\delta} ^ {(T)}, \\quad \\sigma = \\frac {\\mathbf {D} \\mathbf {D} ^ {T}}{C - 1}\n$$\n", + "text_format": "latex", + "bbox": [ + 207, + 535, + 357, + 564 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generate adversarial examples", + "bbox": [ + 120, + 566, + 305, + 580 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\{\\delta_ {m} \\} _ {m = 1} ^ {M} \\sim \\mathcal {N} (\\bar {\\delta}, \\sigma),\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 587, + 274, + 606 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\{x _ {a d v} ^ {m} \\right\\} _ {m = 1} ^ {M} = \\left\\{\\operatorname {C l i p} _ {x, \\epsilon} \\left\\{x ^ {(T - 1)} + \\alpha \\cdot \\operatorname {S i g n} \\left(\\delta_ {m}\\right) \\right\\} \\right\\} _ {m = 1} ^ {M}\n$$\n", + "text_format": "latex", + "bbox": [ + 132, + 607, + 477, + 626 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this case, the expectation of the stochastic gradient is the full gradient, i.e., $\\delta (z) = \\mathbb{E}[\\hat{\\delta}_S(z)]$ . Hence, the prior distribution over adversarial perturbations is naturally a Gaussian one at each iteration. Benefiting from the asymptotic normality of SGD [30], we propose a novel method to approximate the posterior distribution of perturbations. Our main idea is to estimate the mean and covariance matrix of the stationary distribution of stochastic gradient ascent during the optimizing procedure. The iterative averaging is adopted to approximate the mean of adversarial perturbations using the sequence of stochastic gradients", + "bbox": [ + 75, + 679, + 468, + 845 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\bar {\\delta} ^ {(t + 1)} = \\frac {(t \\times n) \\bar {\\delta} ^ {(t)} + \\sum_ {i = 1} ^ {n} \\delta_ {i} ^ {(t)}}{(t + 1) \\times n}. \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 153, + 867, + 468, + 904 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then, $\\bar{\\delta} = \\bar{\\delta}^{(T)}$ , where $n$ is the augmented samples in the $t$ -th iteration ( $t = 0, \\dots, T - 1$ ) and $T$ is the total iterations.", + "bbox": [ + 498, + 89, + 890, + 119 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Let $\\mathbf{D}$ be the deviation matrix with column $\\mathbf{D}_j = \\delta_i^{(t)} - \\bar{\\delta}^{(t + 1)}$ , where $j = t\\times n + i$ and $i = 1,\\dots ,n$ . Thus, the covariance matrix of the posterior distribution is estimated by considering all stochastic gradients in iterative processing,", + "bbox": [ + 498, + 121, + 890, + 184 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\sigma = \\frac {\\mathbf {D} \\mathbf {D} ^ {T}}{n \\times T - 1}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 637, + 194, + 890, + 226 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the adversarial example can be iteratively obtained by (3). Note that, ANDA allows to craft one or an unlimited number of adversarial examples for one input by sampling perturbations from the estimated distribution $\\mathcal{N}(\\bar{\\delta},\\sigma)$ . The complete procedure for the proposed ANDA method is shown in Algorithm 1. Following the empirical study in Section 3.1, we visualized the perturbations $\\delta_i^{(t)}$ of 10 iterates with multiple data augmentations (shown in Fig. 2 b), which validate our previous hypothesis.", + "bbox": [ + 496, + 236, + 890, + 375 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Multiple Implementations of ANDA", + "text_level": 1, + "bbox": [ + 498, + 383, + 808, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the proposed ANDA, we find a solution to approximating the true posterior distribution centered at the the optimal $x_{adv}^{*}$ for the maximization problem introduced in (2). Nevertheless, only exploring the unimodal optimization space largely limits the diversity of generated adversarial examples. Profiting the excellent generalization capability of Bayesian marginalization approximated with the deep ensemble strategy, we propose MultiANDA via multiple (e.g., K times) repeats of ANDA by add random initial values on origin sample $x$ . Especially, we average the adversarial perturbation $\\bar{\\delta}_k$ from each ANDA process, and obtain $\\bar{\\delta}_{mean} = \\frac{1}{K}\\sum_{k=0}^{K-1}\\bar{\\delta}_k$ . This realizes the multimodal marginalization of this Gaussian mixture distribution. Similarly, adversarial examples can be iteratively obtained by (2). MultiANDA also enables producing infinite adversarial examples with high effectiveness by sampling from each approximated Gaussian distribution $\\mathcal{N}(\\bar{\\delta}_k,\\sigma_k)$ . Remarkable improvements of the attacking ability, especially on the defense models are shown in Sections 4.2 and 4.3.", + "bbox": [ + 496, + 407, + 890, + 694 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 498, + 709, + 632, + 724 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In this section, we present the results of an extensive empirical study to validate the performance of the proposed methods. We first specify the experimental settings in Section 4.1. Then, the results of ANDA and MultiANDA compared with the state-of-the-art approaches on various types of DNNs with or without defenses are presented in Section 4.2 and 4.3. Section 4.4 shows the attacking effectiveness of the multiple adversarial examples generated from each input via the proposed methods. Due to page limitations, more detailed experiment settings, results and the ablation study are presented in Appendix.", + "bbox": [ + 496, + 734, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "24845", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/7806891fb793441aaeaa90e92998f13ef28916d175fb2ea9b54d3f4b318bec3e.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AttackInc-v3Inc-v3 =>ResNet-50 =>
ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM100.0*20.315.715.634.321.533.299.7*63.920.943.440.4
TIM64.3*35.930.625.470.445.347.377.0*47.630.868.854.3
SIM100.0*38.231.135.942.236.948.6100.0*83.735.350.954.6
DIM100.0*31.725.531.445.533.561.999.9*83.647.561.163.5
FIA98.3*78.475.381.283.579.686.299.6*94.580.488.387.4
TAIG99.7*53.345.956.754.252.562.4100.0*86.151.958.764.8
NI-FGSM100.0*40.035.239.956.943.059.699.7*85.448.167.065.0
MI-FGSM100.0*40.235.140.357.143.258.599.7*85.948.667.465.1
VMI-FGSM100.0*63.059.368.670.365.375.399.9*93.468.376.478.4
VNI-FGSM100.0*62.458.767.769.764.675.499.8*92.967.975.678.0
ANDA100.0*76.172.882.377.077.195.6100.0*98.994.089.594.5
MultiANDA100.0*79.276.084.578.879.696.5100.0*99.295.090.195.2
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM36.325.620.699.3*37.830.123.518.713.79.999.9*16.5
TIM43.436.532.036.0*66.242.841.534.830.223.6100.0*46.0
SIM58.947.841.499.6*49.849.537.734.425.223.6100.0*30.2
DIM54.641.436.698.2*50.045.731.726.419.216.499.9*23.4
FIA82.275.372.489.2*80.777.757.450.740.942.7100.0*47.9
TAIG73.963.458.495.0*57.463.348.843.634.733.9100.0*40.3
NI-FGSM61.949.544.799.2*64.755.243.639.529.230.499.9*35.7
MI-FGSM60.349.343.098.8*64.654.344.739.428.930.899.9*36.0
VMI-FGSM81.169.666.499.3*73.572.762.756.746.548.6100.0*53.6
VNI-FGSM80.970.065.899.4*73.872.663.256.746.648.8100.0*53.8
ANDA93.086.483.799.8*82.886.574.464.156.461.5100.0*64.1
MultiANDA93.987.185.699.8*84.387.775.466.158.663.5100.0*65.9
", + "bbox": [ + 86, + 107, + 885, + 452 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. The success rates $(\\%)$ of the proposed and baseline attacks on five normally trained models. Sign \\* indicates the results on white-box source models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix.", + "bbox": [ + 75, + 463, + 893, + 506 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Experimental Setup", + "text_level": 1, + "bbox": [ + 76, + 531, + 267, + 547 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The datasets, models, and baseline methods employed in our experiments are detailed below.", + "bbox": [ + 75, + 556, + 470, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets: Following the prior work [8, 13, 46], we implemented our experiments on ImageNet1k dataset [33] containing 1000 images, which are randomly drawn from the ImageNet dataset [37].", + "bbox": [ + 75, + 590, + 468, + 652 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Models: We considered two categories of target models for evaluation: seven normally trained models and seven advanced defense models. The first category includes Inception-v3 (Inc-v3) [40], Resnet-v2-50 (ResNet-50), Resnet-v2-101 (ResNet-101), Resnet-v2-152 (ResNet-152) [15], Inception-v4 (Inc-v4), Inception-ResNet-v2 (IncRes-v2) [41] and VGG-19 [38], where Inc-v3, ResNet-50, IncRes-v2 and VGG-19 are also used as the white-box source models to generate adversarial examples. The defense models contain three adversarially trained models: Inc-v3ens3, Inc-v3ens4 and IncRes-v2ens [42]; the High-level representation Guided Denoiser (HGD) [24]; the Neural Representation Purifier (NRP) [32]; the Randomized Smoothing (RS) [6]; and the 'Rand-3' submission in the NIPS 2017 defense competition (NIPS-r3).", + "bbox": [ + 75, + 655, + 470, + 882 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Baselines: Three streams of transfer-based attack meth", + "bbox": [ + 96, + 885, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ods are used as baseline methods. The first stream focuses on the data augmentations including DIM [49], TIM [9], SIM [45] and a recent work Transferable Attack based on Integrated Gradients (TAIG) [17]. For the second group, we choose the feature importance-aware (FIA)[46], which considers the middle-layer information of the source model and achieves the competitive performance. The last stream focuses on the optimization enhanced methods, including BIM [20], its accelerated version: MI-FGSM [8], NIFGSM [25], and the approaches using variance reduction strategy, VMI-FGSM, VNI-FGSM [45].", + "bbox": [ + 496, + 531, + 893, + 700 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Attack Normally Trained Models", + "text_level": 1, + "bbox": [ + 498, + 709, + 790, + 726 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We cross-validated our method by generating and testing the adversarial examples on the selected source (on rows) and target (on columns) networks (shown in Table 1). To be a fair comparison, our proposed methods generated one adversarial example for each input, aligned with the first output option of Algorithm 1, in the following experiments if not specified. From the Table 1, we observe that ANDA and MultiANDA significantly outperforms other methods in almost all cases, no matter in white-box or black-box settings. As the numerical results demonstrate, they consistently defeat all other methods when taking IncRes-v2,", + "bbox": [ + 496, + 734, + 893, + 902 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "24846", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "ResNet-50 and VGG-19 as source models, and for Inc-v3, ANDA is competitive with the current SOTA methods, and MultiANDA always keep higher success rate.", + "bbox": [ + 76, + 90, + 468, + 136 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We further investigated the adversarial examples generated with ResNet-50, shown in Figure 3. The other six models were used as black-box targets for evaluating the performance of these examples. A higher number of successfully deceived target models implies more capable adversaries and therefore stronger attacks. The rightmost bars show that ANDA, MultiANDA generated 840, 863/1000 adversaries that fooled all six targeted models, respectively, while 517/1000 are for VMI-FGSM. Naturally, the remaining sets of bars for this baseline method are higher, meaning that it deceived fewer targeted models. Moreover, we visualized the generated examples and the perturbations by these three methods (see Figure 1). The results show that the perturbations crafted by ANDA and MultiANDA focus more on the semantic areas of objects than VMI-FGSM, which dominates the decision of the prediction model. More visualization results are provided in Appendix.", + "bbox": [ + 75, + 136, + 470, + 393 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b19830786b2310d37a5ab60424bc29314f6767050ab7fead2787ba0dea426979.jpg", + "image_caption": [ + "Figure 3. Most examples crafted by our proposed methods successfully deceived all 6 black-box models." + ], + "image_footnote": [], + "bbox": [ + 102, + 406, + 444, + 555 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Attack Defense Models", + "text_level": 1, + "bbox": [ + 76, + 619, + 290, + 635 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We evaluate our proposed method targeting on the selected advanced defenses models. As shown in Table 2, the success rates of our proposed methods consistently improve over these various defense models in most cases. They provide a significant performance increase in general compared with the other attacks, especially reaches the overall optimal success rates with the source model ResNet-50. An intriguing finding is that using ResNet-50 as the source model always yields the best attacking performance. This aligns with the conclusion drawn by Wu et al. [48] that the skip connections in ResNet-like neural networks enhance black-box attack transferability.", + "bbox": [ + 75, + 643, + 467, + 824 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Notably, the fluctuating performance and the generally reduced effectiveness of all baseline methods can be observed with the source model VGG-19. The average maximum attack success rate in this context is only $28.3\\%$ , suggesting that the feature extraction capabilities of VGG-19", + "bbox": [ + 75, + 825, + 467, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "are not optimal, thereby leading to diminished transferability for black-box attacks. This observation highlights the critical role of source model selection in maximizing the transferability of adversarial attacks. Hence, the choice of source models and enhancing their capability for generalized feature extraction become promising directions for the future research.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Similarly, we visualized the generated examples and the perturbations by VMI-FGSM, ANDA and MultiANDA that fool the defense models. The perturbed area by our proposed methods concentrates more on the informative region of images than the baseline method. Details are illustrated in Appendix. These compelling results of ANDA and MultiANDA on defenses valid their overall generalization ability in generating transferable and diverse adversaries.", + "bbox": [ + 496, + 196, + 890, + 318 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fef9d131670076b83f8b39917693333ed54814ebd3c9aaeb18d449ef9cdaef6c.jpg", + "image_caption": [ + "Figure 4. Attack success rates of sampled adversaries with single $\\{\\widetilde{\\delta}\\}$ , multiple $\\{\\delta_m\\}_{m=1}^{20}$ and the succeeded $Suc.\\{\\delta_m\\}_{m=1}^{20}$ generated by ANDA and MultiANDA. $\\{\\delta_m\\}_{m=1}^{20}$ means the 20 adversarial examples sampled from the learned perturbation distribution for each input image; whereas $Suc.\\{\\delta_m\\}_{m=1}^{20}$ are the 20 sampled adversarial examples for the input image whose corresponding single adversarial example has succeeded in the attack." + ], + "image_footnote": [], + "bbox": [ + 503, + 333, + 887, + 503 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.4. Attack Performance of Sampled Adversaries", + "text_level": 1, + "bbox": [ + 498, + 650, + 877, + 666 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "The analysis presented above shows the effectiveness of the single optimum adversarial example per input generated, denoted as $\\bar{\\delta}$ , referring to Step 6 (a) shown in Algorithm 1. Besides, MultiANDA/ANDA allows learning the distribution of the perturbations $\\mathcal{N}(\\bar{\\delta},\\sigma)$ via Step 6 (b), and generate any number of adversarial examples for each input by sampling $M$ adversaries, denoted as $\\{\\delta_m\\}_{m = 1}^M$ . To verify the attack performance of these sampled adversaries, we drawn $20(M = 20)$ adversarial examples for each input image, i.e., $\\{\\delta_m\\}_{m = 1}^{20}$ . Meanwhile, we analyzed the adversaries sampled for the input images whose corresponding adversaries $\\bar{\\delta}$ succeeded in the attack, denoted as $Suc.\\{\\delta_m\\}_{m = 1}^{20}$ . Experiment results show in Figure 4 that the sampled adversaries have competitive attack success rates compared with the single adversary generated with $\\bar{\\delta}$ ,", + "bbox": [ + 496, + 674, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "24847", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/ed410254e2f78c753738a240359d8285a6cb3cb3360aa1e5a35a5f6a017f6325.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
AttackInc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.ResNet-50
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.14.63.713.44.87.512.37.17.413.78.19.7
TIM27.521.316.922.821.121.934.027.424.231.130.629.5
SIM18.18.48.615.210.812.221.413.115.216.115.116.2
DIM13.16.75.812.88.69.420.812.016.915.715.316.1
FIA37.421.311.623.529.224.644.427.230.025.935.332.6
TAIG38.023.922.829.628.528.639.230.429.729.634.432.7
MI-FGSM18.39.05.515.712.012.126.315.517.318.020.219.5
NI-FGSM18.68.66.215.312.212.226.215.717.518.919.819.6
VMI-FGSM36.921.219.124.727.725.947.431.337.727.138.736.4
VNI-FGSM36.422.018.925.327.427.146.530.437.427.138.736.4
ANDA44.425.936.523.237.020.371.450.772.432.967.441.6
MultiANDA54.436.752.824.346.929.979.764.882.334.476.350.1
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.17.05.113.06.08.49.64.43.913.44.67.2
TIM27.921.418.423.923.823.123.027.415.031.130.625.4
SIM23.816.415.918.318.118.511.45.68.713.47.49.3
DIM16.210.111.714.912.313.010.74.75.613.65.98.1
FIA48.934.724.230.842.836.313.38.37.114.69.810.6
TAIG49.041.212.216.513.326.417.710.236.934.141.928.2
MI-FGSM22.013.313.416.417.016.413.06.97.215.58.910.3
NI-FGSM21.613.813.415.516.616.213.96.87.214.69.310.4
VMI-FGSM49.238.836.025.239.237.721.911.615.918.415.916.7
VNI-FGSM49.937.735.425.639.338.421.611.916.818.615.722.9
ANDA63.347.357.828.557.932.620.910.822.215.416.23.7
MultiANDA70.361.969.931.267.841.824.613.731.216.221.37.9
", + "bbox": [ + 86, + 95, + 883, + 441 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 2. The success rates $(\\%)$ of the proposed and baseline attacks on five defense models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix.", + "bbox": [ + 75, + 452, + 892, + 483 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "even on the defense models. This confirms the well approximation of the perturbation distributions and the great potential of our method for adversarial training or defense model designing.", + "bbox": [ + 75, + 507, + 470, + 569 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions and Perspectives", + "text_level": 1, + "bbox": [ + 76, + 585, + 346, + 604 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this work, we present the Multiple Asymptotically Normal Distribution Attacks (MultiANDA) to generate transferable adversarial examples. Our primary goal is to efficiently approximate the posterior distribution of adversarial perturbations to achieve better generalization across unknown deep learning models. We leverage the statistical information of gradients along the optimization trajectory to estimate the stationary distribution of the perturbations. With this learned distribution's aid, MultiANDA can significantly improve the transferability of adversarial examples to black-box target models. Extensive experiments demonstrate that MultiANDA outperforms popular and recently proposed black-box and transfer-based methods, further highlighting the insufficiency of current defense techniques. Notably, the computational overhead of both ANDA and MultiANDA, largely depending on the number of batch samples during augmentation, is on par with similar baseline methods (refer to Appendix for the computational overhead analysis). Compared to the potential risks", + "bbox": [ + 73, + 613, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "these algorithms might pose if misused, their computational cost is relatively negligible. We advocate for the development of advanced deep learning models which align better with human visual preferences, thereby avoiding the fundamental defects present in modern models.", + "bbox": [ + 496, + 507, + 893, + 584 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 603, + 668, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China under Grant 62176020, the Joint Foundation of the Ministry of Education (8091B042235), the Beijing Natural Science Foundation under Grant L211016, the Talent Fund of Beijing Jiaotong University under Grant 2023XKRC041, and the Fundamental Research Funds for the Central Universities (Science and technology leading talent team project) under Grant 2022JBXT003. We also thank Huafeng Liu and Zhekun Liu for their helpful advice and support.", + "bbox": [ + 496, + 630, + 893, + 782 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 500, + 801, + 596, + 818 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Erin E Alves, Devesh Bhatt, Brendan Hall, Kevin Driscoll, Anitha Murugesan, and John Rushby. Considerations in assuring safety of increasingly autonomous systems. Technical report, 2018. NASA technical report. 1", + "[2] Dario Amodei, Chris Olah, Jacob Steinhardt, Paul Chris" + ], + "bbox": [ + 506, + 827, + 890, + 901 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "24848", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 7 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "tiano, John Schulman, and Dan Mané. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 452-467, 2018. 3" + ], + "bbox": [ + 501, + 92, + 890, + 625 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "24850", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_model.json b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8b924a31538d6d14fd8852bcf13cac7bbf627ce4 --- /dev/null +++ b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_model.json @@ -0,0 +1,2233 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.082, + 0.13, + 0.89, + 0.178 + ], + "angle": 0, + "content": "Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning" + }, + { + "type": "text", + "bbox": [ + 0.236, + 0.203, + 0.732, + 0.222 + ], + "angle": 0, + "content": "Zhengwei Fang\\(^{1,2}\\), Rui Wang\\(^{1,2,3*}\\), Tao Huang\\(^{1,2}\\), Liping Jing\\(^{1,2}\\)" + }, + { + "type": "text", + "bbox": [ + 0.129, + 0.222, + 0.842, + 0.24 + ], + "angle": 0, + "content": "\\(^{1}\\)School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.208, + 0.239, + 0.764, + 0.258 + ], + "angle": 0, + "content": "\\(^{2}\\)Beijing Key Lab of Traffic Data Analysis and Mining, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.192, + 0.257, + 0.78, + 0.276 + ], + "angle": 0, + "content": "\\(^{3}\\)Collaborative Innovation Center of Railway Traffic Safety, Beijing, China" + }, + { + "type": "text", + "bbox": [ + 0.225, + 0.278, + 0.746, + 0.293 + ], + "angle": 0, + "content": "jankinfmail@gmail.com, {rui.wang,thuang,lpjing}@bjtu.edu.cn" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.327, + 0.314, + 0.344 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.359, + 0.474, + 0.796 + ], + "angle": 0, + "content": "Strong adversarial examples are crucial for evaluating and enhancing the robustness of deep neural networks. However, the performance of popular attacks is usually sensitive, for instance, to minor image transformations, stemming from limited information — typically only one input example, a handful of white-box source models, and undefined defense strategies. Hence, the crafted adversarial examples are prone to overfit the source model, which hampers their transferability to unknown architectures. In this paper, we propose an approach named Multiple Asymptotically Normal Distribution Attacks (MultiANDA) which explicitly characterize adversarial perturbations from a learned distribution. Specifically, we approximate the posterior distribution over the perturbations by taking advantage of the asymptotic normality property of stochastic gradient ascent (SGA), then employ the deep ensemble strategy as an effective proxy for Bayesian marginalization in this process, aiming to estimate a mixture of Gaussians that facilitates a more thorough exploration of the potential optimization space. The approximated posterior essentially describes the stationary distribution of SGA iterations, which captures the geometric information around the local optimum. Thus, MultiANDA allows drawing an unlimited number of adversarial perturbations for each input and reliably maintains the transferability. Our proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without defenses through extensive experiments on seven normally trained and seven defense models." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.824, + 0.21, + 0.839 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.849, + 0.47, + 0.88 + ], + "angle": 0, + "content": "Albeit the excellent performance of deep neural networks (DNNs) across a broad spectrum of tasks in machine vi-" + }, + { + "type": "image", + "bbox": [ + 0.515, + 0.328, + 0.885, + 0.445 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.453, + 0.895, + 0.496 + ], + "angle": 0, + "content": "Figure 1. Perturbation visualization of the adversarial examples generated by ANDA/MultiANDA that fool all selected normally trained (first row) and defense (second row) models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.523, + 0.893, + 0.688 + ], + "angle": 0, + "content": "sion and natural language processing, a rich stream of work [8, 14, 39, 50, 51] shows the non-negligible vulnerability of DNNs to adversarial attacks, which craft imperceptible perturbations to synthesize malicious inputs for triggering unexpected model predictions. Such severe degradation of model robustness and stability greatly hinders the application of DNNs in security- or safety-critical domains [1, 2, 11]. Fortunately, studying how to create potent adversarial examples aids in evaluating DNN-based systems and enhancing their robustness by devising defensive strategies, such as adversarial training [14, 29]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.895, + 0.885 + ], + "angle": 0, + "content": "This paper focuses on the black-box and transfer-based threat model. The corresponding adversarial attack algorithms intend to synthesize the adversarial examples that can successfully fool the unknown DNNs without accessing any information on model architectures and outputs. Researchers implement such attacks by maximizing the nonconcave loss function of a substitute model trained for the same task with, for example, one step [14], or iterative steps [20] of gradient ascent optimization. However, prior work has shown the generated adversarial examples trend to overfit the substitute model, which hardly attacks other models [21]. Meanwhile, they are often sensitive to minor transformations [4, 26, 27]." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Hence, researchers have been exploring various data" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.222, + 0.9 + ], + "angle": 0, + "content": "*Corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24841" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.304 + ], + "angle": 0, + "content": "augmentation strategies [4, 9, 25, 49] and improved SGA optimization methods [8, 17, 25, 45] to enhance the performance of transferable attacks. Nonetheless, these efforts exhibit limited generalization capabilities on unknown DNN architectures, particularly those trained with defense strategies. This suggests that a deterministic optimization procedure, initiated from a single image, is insufficient to thoroughly explore the high-dimensional perturbation space. Furthermore, the projected gradient descent (PGD) method proposed by Madry et al. [29] initializes the attack algorithm with random restarts around the legitimate image. However, these random samples represent homogeneous deviations from the original input, lacking diversity [10], which limits the transferability of adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.305, + 0.473, + 0.623 + ], + "angle": 0, + "content": "To resolve these issues, in this paper, we propose Multiple Asymptotically Normal Distribution Attacks (MultiANDA), a novel method that explicitly characterizes perturbations inferred from a learned distribution. Firstly, we formulate a single ANDA by taking advantage of the nice property of stochastic gradient ascent (SGA), the asymptotic normality [5, 18, 28, 30], to learn the true optimal posterior distribution of adversarial perturbations. Specifically, ANDA calculates and stores the first two moments of iterations captured along the optimizing trajectory to approximate the distribution of the adversarial perturbation as a Gaussian one. Moreover, we apply the deep ensemble strategy [22] on ANDA to devise a mixture of Gaussians, approximating the Bayesian posterior. As each Gaussians positioned at a different basin of attraction, the proposed MultiANDA leads to a further improved generalization performance of the attacks with more diverse adversarial examples. As shown in Figure 1, the perturbations crafted by our proposed method focus more on the semantic and decisive areas of objects than the baseline approach. In particular, the contributions of this work are the following:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.625, + 0.473, + 0.731 + ], + "angle": 0, + "content": "- We propose MultiANDA, an approximate Bayesian inference method to realize transfer-based adversarial attacks. We learn the perturbation distribution instead of finding a specific adversary for each input example. Thus, a good approximation of the true perturbation posterior boosts the generalization (i.e., transferability) of the generated adversarial examples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.473, + 0.884 + ], + "angle": 0, + "content": "- We devise a stochastic adversarial attacking process instead of the original deterministic one initialized from one input by random image translations. In this way, we profit the asymptotic normality of SGA for a better perturbation distribution learning. Adopting the deep ensemble strategy, an effective mechanism for approximating Bayesian marginalization [47], MultiANDA accurately and efficiently estimate the posterior distribution over the perturbations by using the geometry information along the attacking trajectory." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.472, + 0.902 + ], + "angle": 0, + "content": "- The learned distributions of perturbation allow draw" + }, + { + "type": "list", + "bbox": [ + 0.076, + 0.625, + 0.473, + 0.902 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.183 + ], + "angle": 0, + "content": "ing an unlimited number of adversarial examples for one input. We experimentally validate that the sampled adversaries have comparably high attack success rates with the singly generated ones, even on the defense models. This result demonstrates the great potential of our method for designing defense strategies grounded in adversarial training." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.183, + 0.892, + 0.304 + ], + "angle": 0, + "content": "- Extensive experiment results show that the proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without advanced defenses. Significantly, MultiANDA is more advantageous when attacking the advanced defense models. Thus, ANDA and MultiANDA are expected to benchmark new defense methods in the future. Our code is available at https://github.com/CLIAgroup/ANDA." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.318, + 0.796, + 0.334 + ], + "angle": 0, + "content": "2. Related Work and Preliminaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.344, + 0.892, + 0.39 + ], + "angle": 0, + "content": "Our study mainly focuses on the black-box and transfer-based threat model, as they may bring more security and safety risks due to their practical applicability [8, 34]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.399, + 0.776, + 0.415 + ], + "angle": 0, + "content": "2.1. Black-Box Adversarial Attacks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.423, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Essentially, the adversarial attack algorithms intend to maximize the loss function \\(\\mathcal{L}(\\cdot)\\), e.g., the cross entropy loss for classification tasks, to search for the adversaries \\(x_{adv}\\) [14, 39], with the constraints of \\(l_{\\infty}\\) norm bound \\(\\varepsilon\\), as shown in (1):" + }, + { + "type": "equation", + "bbox": [ + 0.557, + 0.512, + 0.892, + 0.535 + ], + "angle": 0, + "content": "\\[\n\\max _ {x _ {a d v}} \\mathcal {L} (x _ {a d v}, y) \\quad \\text {s . t .} | | x _ {a d v} - x | | _ {\\infty} \\leq \\varepsilon , \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.545, + 0.892, + 0.575 + ], + "angle": 0, + "content": "where \\(x\\), \\(x_{adv}\\), \\(y\\) are the legitimate input, the adversarial example and the true label, respectively." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.576, + 0.892, + 0.651 + ], + "angle": 0, + "content": "Among prior work, the fast gradient sign method (FGSM) [14] and its iterative version, the basic iterative method (BIM) [20] resort to linearizing the non-concave loss function and realize the attack with one-step update or iterative updates, as shown in (2):" + }, + { + "type": "equation", + "bbox": [ + 0.543, + 0.662, + 0.892, + 0.702 + ], + "angle": 0, + "content": "\\[\nx _ {a d v} ^ {(t + 1)} = \\Phi (x _ {a d v} ^ {(t)} + \\alpha \\cdot \\operatorname {s i g n} (\\underbrace {\\nabla_ {x} \\mathcal {L} (x _ {a d v} ^ {(t)} , y)})), \\quad (2)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.714, + 0.892, + 0.764 + ], + "angle": 0, + "content": "where \\(x_{adv}^{(t + 1)}\\), \\(\\delta^{(t)}\\) are the adversarial example and perturbation at the \\(t\\)-th step, \\(x_{adv}^{(0)}\\) is the legitimate input, and \\(\\Phi (\\cdot)\\) is the projection function on the \\(\\varepsilon\\)-ball." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.765, + 0.892, + 0.902 + ], + "angle": 0, + "content": "These attacks are more effective under white-box scenarios, whereas they tend to overfit the model parameters and hardly transfer to unknown architectures [21]. Thus, many works have been proposed to improve the transferability of adversarial examples, which can be divided into three categories. The first group focuses on the iterative optimizing process by considering momentum [8], Nesterov accelerated gradient [25], and variance reducing [45] to search for the optimal solutions. The second group attempts to attack" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "24842" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.121 + ], + "angle": 0, + "content": "the mid-layers by disrupting the critical object-aware features [12, 16, 31, 46, 52]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.123, + 0.468, + 0.258 + ], + "angle": 0, + "content": "Moreover, the third stream of methods adopt the commonly used generalization techniques by introducing diversity. These techniques encompass data augmentation [15, 19], such as resize and padding [49], translation [9]; and other integrated augmentation strategies, including combining multiple linear transformations [4], modifying the pixel values with multiple scales [25], integrating more information from other images [7], and using the sum of the gradients from intensity augmented images [17]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.26, + 0.47, + 0.651 + ], + "angle": 0, + "content": "Similar to our study, existing attack approaches also try to determine the explicit adversarial distributions. PGD [29] resolves the inner maximization problem by the random restart strategy. However, the uniformly drawn samples tend to lie densely around the natural image [10]. Li et al. [23] propose \\(\\mathcal{N}\\) attack to define and learn an adversarial distribution. However, their work is under a query-based threat model, i.e., it has to access the output scores for each input from the black-box defense model, which weakens its scalability in real-world applications. Additionally, Dong et al. [10] propose to formulate the adversarial perturbations via a learned distribution for adversarial distributional training (ADT). Similar to \\(\\mathcal{N}\\) attack, ADT crafts the adversarial examples centered with the natural input \\(x\\), which may fail in generating adversarial examples once the input is a little bit far away from the boundary. Conversely, ANDA generates adversaries around the optimal \\(x_{adv}^{*}\\). In this case, the adversaries are more prone to successful attacks. From the facets of implementation, ADT focuses on learning a distribution from a large amount of training data for adversarial training. Our proposed method tries to collect the trajectory information during the optimization process for each natural input. Thus, these crucial differences make two approaches suitable for distinct tasks: inner maximization problem for adversarial training (ADT) and transfer-based black-box attack (ANDA and MultiANDA)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.665, + 0.345, + 0.682 + ], + "angle": 0, + "content": "2.2. Asymptotic Normality of SGD" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.689, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Maddox et al. [28] point out that the trajectory of stochastic gradient descent (SGD) can be regarded as the Bayesian posterior distribution over the random variables to be optimized, e.g., the model parameters in the case of the DNN training. Following this theory, they propose a Gaussian posterior approximation method (SWAG) based on the first two moments of SGD iterations for model calibration or uncertainty quantification. In the prior work, Mandt et al. [30] provide a more detailed analysis of the stationary distribution of SGD iterations with a constant learning rate, also termed the asymptotic normality of SGD [44]. Such analysis can be traced back to the work by Ruppert [36], Polyak and Juditsky [35] known as Polyak-Ruppert averaging, and still an active research subject for SGD [5]. Furthermore," + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.243 + ], + "angle": 0, + "content": "inspired by deep ensembles [22], Wilson and Izmailov [47] carried out an extensive empirical study, demonstrating that applying SWAG only with multiple randomly initialized models can significantly improve the model performance. They emphasize that this benefits from the multimodal effects of the mixture Gaussian distributions and, in turn, boosts the contribution of each additional sample in the optimization procedure. In this paper, we adopt these theories to innovatively model the posterior distribution of perturbations to search for potent adversarial examples." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.261, + 0.673, + 0.278 + ], + "angle": 0, + "content": "3. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.287, + 0.892, + 0.499 + ], + "angle": 0, + "content": "Drawing on the comprehensive research previously discussed, we hypothesize that utilizing the asymptotic normality of SGD (SGA in our problem formulation) to marginalize an approximate Bayesian posterior could enhance generalization (transferability in our context) beyond what is achievable with a fixed set of parameter (one specific adversarial perturbation). However, optimizing the objective (1) using attack algorithms such as BIM (2) is a deterministic gradient ascent process. In this process, no gradient noise is introduced to form a stationary distribution of SGD. Thus, to bridge this gap, we exploit random data augmentation in the standard optimization process, devising a novel attack method for accurately and efficiently estimating the posterior distribution over perturbations." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.5, + 0.892, + 0.621 + ], + "angle": 0, + "content": "In Section 3.1, we first empirically analyze the asymptotically normal distribution property in the stochastic adversarial attack process, then proceed to formalize the optimization objective for the task of adversarial example generation. Finally, inspired by the advantageous properties of SGD and the effective multimodal inference of the ensemble strategy, we introduce the new attack methods ANDA and MultiANDA in Sections 3.2 and 3.3, respectively." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.635, + 0.85, + 0.651 + ], + "angle": 0, + "content": "3.1. Asymptotic Normality of Stochastic BIM" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.66, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Under specific conditions—decaying learning rates, smooth gradients, and a full rank stationary distribution—it has been theoretically established that SGD asymptotically converges to a Gaussian distribution centered at the local optimum [3, 5, 28]. Expanding on this, Mandt et al. [30] demonstrated that under certain assumptions, SGD with a constant and sufficiently small learning rate in its final search phase, i.e., when updates are proximal to the local optimum, converges to a stationary distribution. This convergence implies that iterations during this phase can approximate the posterior distribution of the optimized variables. Crucially, the gradient noise, introduced by the randomness of the sampled training batches, is instrumental in forming this distribution, provided the learning rate is adequately small [28]. These theoretical underpinnings motivate our approach in the algorithm design." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "24843" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.092, + 0.468, + 0.17 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.235, + 0.171, + 0.31, + 0.18 + ], + "angle": 0, + "content": "a. Stochastic BIM" + }, + { + "type": "image", + "bbox": [ + 0.084, + 0.182, + 0.466, + 0.259 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.222, + 0.259, + 0.326, + 0.268 + ], + "angle": 0, + "content": "b. ANDA implementation" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.279, + 0.471, + 0.322 + ], + "angle": 0, + "content": "Figure 2. Asymptotically normal distribution examples with iterative trajectories of adversarial perturbations generated by stochastic BIM (a) and the proposed approach (b)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.347, + 0.47, + 0.452 + ], + "angle": 0, + "content": "As demonstrated in (2), the optimization process, beginning from a specific input, is a deterministic gradient ascent, differing from a standard SGA approach. Therefore, we introduce stochastic gradient noises to emulate Gaussian limiting distributions by integrating a random data augmentation technique AUG, like image translation used in our experiments, at each iterative step:" + }, + { + "type": "equation", + "bbox": [ + 0.09, + 0.461, + 0.47, + 0.5 + ], + "angle": 0, + "content": "\\[\nx _ {a d v} ^ {(t + 1)} = \\Phi (x _ {a d v} ^ {(t)} + \\alpha \\cdot \\operatorname {s i g n} (\\underbrace {\\nabla_ {x} \\mathcal {L} (\\mathrm {A U G} (x _ {a d v} ^ {(t)} , y))} _ {\\delta^ {(t)}})). \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.509, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Notably, a small constant learning rate schedule \\((\\alpha = \\epsilon / T)\\) is commonly adopted, where \\(\\epsilon \\in \\mathbb{R}\\) is a sufficiently small number used to restrict the \\(L_{\\infty}\\)-norm for creating invisible adversarial perturbations, and \\(T\\) is the number of iterative steps. Hence, we speculate the devised stochastic BIM shown in (3) can be used as an approximate Bayesian inference algorithm. In particular, Mandt et al. [30] assume that the gradients along the optimizing trajectory follow the Gaussian distribution stemming from the central limit theorem. We visualized the adversarial perturbations \\(\\delta^{(t)}\\)—the loss gradients in our task—using the t-SNE technique [43] to examine their distribution. 300 iterative steps for 3 randomly-drawn ImageNet [37] images shown in Fig. 2 a illustrates the Gaussian-shaped distributions which underpins our conjecture of the asymptotically normality of stochastic BIM algorithm. We notice the obvious increased gradient noise along the optimizing trajectory, which may due to the use of the sign() function and projection operations. Nevertheless, this does not affect the convergence of perturbations. Importantly, the first 10 steps converging with tight covariance justifies another speculation that the small value of \\(T\\) (often \\(= 10\\) for non-targeted attacks) and the non-trivial first step in our task (e.g., referring to strong attack performance of FGSM) indicate that the early iterates of are fairly close to the local optimum (i.e., the final search phase discussed above)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.092, + 0.892, + 0.166 + ], + "angle": 0, + "content": "Inspired by the results of this empirical study, we propose employing \\( n \\) image transformations \\( \\mathsf{AUG}_i(\\cdot) \\) to form a minibatch for an adversarial attack, thereby further enhancing stochasticity. Then, the optimization objective is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.51, + 0.177, + 0.892, + 0.215 + ], + "angle": 0, + "content": "\\[\n\\max _ {x _ {a d v}} \\sum_ {i = 1} ^ {n} \\mathcal {L} (\\mathrm {A U G} _ {i} (x _ {a d v}), y) \\quad \\text {s . t .} \\| x _ {a d v} - x \\| _ {\\infty} \\leq \\varepsilon . \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.226, + 0.892, + 0.332 + ], + "angle": 0, + "content": "Furthermore, optimizing (4) to craft just one optimal adversarial example does not sufficiently explore the high-dimensional potential perturbation space. To further improve the transferability of adversarial examples to unknown architectures, we propose to explicitly model the adversarial perturbation \\((\\delta)\\) via a distribution \\((\\Pi_{\\delta})\\). Thus, our optimization objective is formalized as" + }, + { + "type": "equation", + "bbox": [ + 0.515, + 0.344, + 0.892, + 0.383 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\Pi_ {\\delta}} \\mathbb {E} _ {\\delta \\sim \\Pi_ {\\delta}} \\sum_ {i = 1} ^ {n} \\mathcal {L} (\\mathrm {A U G} _ {i} (x + \\delta), y), \\text {s . t .} \\| \\delta \\| _ {\\infty} \\leq \\varepsilon. \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.394, + 0.892, + 0.47 + ], + "angle": 0, + "content": "Objective (5) aims to maximize the expected loss over the adversarial perturbation distribution. It is noteworthy that (5) is a generalized version of (4) and is expected to characterize sufficient information about perturbations for transferable adversarial example generation." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.48, + 0.869, + 0.496 + ], + "angle": 0, + "content": "3.2. Asymptotically Normal Distribution Attack" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.503, + 0.892, + 0.627 + ], + "angle": 0, + "content": "To better solve the optimization problem formulated in (5), we take advantage of the asymptotically normality of SGA and iteratively search for the adversarial examples similarly to (2). We omit the projection function \\(\\Phi(\\cdot)\\) and \\(\\mathrm{sign}(\\cdot)\\) because they do not effect the asymptotic normality of SGA as discussed in the previous subsection. Then, we calculate the gradient of the adversary with each transformation and denote it as the augmentation-aware perturbation \\(\\delta_i^{(t)}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.59, + 0.638, + 0.892, + 0.659 + ], + "angle": 0, + "content": "\\[\n\\delta_ {i} ^ {(t)} = \\nabla_ {x ^ {(t)}} \\mathcal {L} \\left(\\underset {\\text {A U G} _ {i}} {\\mathrm {A U G}} \\left(x _ {a d v} ^ {(t)}\\right), y\\right). \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.67, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Let \\( S \\) be a set of samples augmented in each iteration, i.e., \\( S = \\{\\mathrm{AUG}_i(x_{adv}^{(t)})\\}_{i=1}^n \\). Here \\( S \\) can be taken as a minibatch to form a stochastic gradient \\( \\hat{\\delta}_S \\) which is a sum of contributions from all samples in \\( S \\). Hence, referring to the central limit theorem, \\( \\hat{\\delta}_S \\) can be taken as a function of sample \\( z \\in S \\)," + }, + { + "type": "equation", + "bbox": [ + 0.601, + 0.776, + 0.892, + 0.807 + ], + "angle": 0, + "content": "\\[\n\\hat {\\delta} _ {S} (z) \\approx \\delta (z) + \\frac {1}{\\sqrt {n}} \\Delta \\delta (z), \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.819, + 0.892, + 0.865 + ], + "angle": 0, + "content": "where the gradient noises \\(\\Delta \\delta (z)\\) at each update can be conveniently assumed following a Gaussian distribution with covariance \\(C(z)\\)," + }, + { + "type": "equation", + "bbox": [ + 0.513, + 0.876, + 0.892, + 0.906 + ], + "angle": 0, + "content": "\\[\n\\Delta \\delta (z) \\sim \\mathcal {N} (0, C (z)), \\quad \\hat {\\delta} _ {S} (z) \\sim \\mathcal {N} (\\delta (z), \\frac {1}{n} C (z)). \\tag {8}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24844" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.088, + 0.096, + 0.425, + 0.124 + ], + "angle": 0, + "content": "Algorithm 1: Asymptotically Normal Distribution Attack (ANDA)" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.129, + 0.434, + 0.154 + ], + "angle": 0, + "content": "Input: \\(x\\): clean image \\(x \\in \\mathbb{R}^d\\); \\(y\\): ground-truth label; \\(f\\): pre-trained source model;" + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.156, + 0.434, + 0.191 + ], + "angle": 0, + "content": "Parameters: \\(T\\): # iterations; \\(\\epsilon\\): perturbation magnitude; \\(n\\): # batch samples for augmentation; \\(M\\): # sampling examples;" + }, + { + "type": "list", + "bbox": [ + 0.097, + 0.129, + 0.434, + 0.191 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.098, + 0.194, + 0.326, + 0.206 + ], + "angle": 0, + "content": "Output: \\( x_{adv} \\): Adversarial examples;" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.207, + 0.423, + 0.22 + ], + "angle": 0, + "content": "1: Initialize \\(\\alpha \\leftarrow \\epsilon /T,\\bar{\\delta}^{(0)}\\leftarrow \\mathbf{0}^d\\) \\(\\mathbf{D}\\gets \\emptyset ,x_0\\gets x\\)" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.22, + 0.258, + 0.231 + ], + "angle": 0, + "content": "2: for \\( t = 0 \\) to \\( T - 1 \\) do" + }, + { + "type": "text", + "bbox": [ + 0.106, + 0.231, + 0.482, + 0.255 + ], + "angle": 0, + "content": "3: Calculate the mean of gradients and store the deviation of gradients throughout previous \\(t\\) iterations:" + }, + { + "type": "list", + "bbox": [ + 0.106, + 0.207, + 0.482, + 0.255 + ], + "angle": 0, + "content": null + }, + { + "type": "equation", + "bbox": [ + 0.17, + 0.264, + 0.457, + 0.282 + ], + "angle": 0, + "content": "\\[\n\\delta_ {i} ^ {(t)} = \\nabla_ {x ^ {(t)}} J (f (\\mathrm {A U G} _ {i} (x ^ {(t)})), y), i = 1, \\dots , n\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.207, + 0.298, + 0.419, + 0.33 + ], + "angle": 0, + "content": "\\[\n\\bar {\\delta} ^ {(t + 1)} = \\frac {(t \\times n) \\bar {\\delta} ^ {(t)} + \\sum_ {i = 1} ^ {n} \\delta_ {i} ^ {(t)}}{(t + 1) \\times n}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.162, + 0.346, + 0.466, + 0.364 + ], + "angle": 0, + "content": "\\[\n\\text {A P P E N D - C O L S} (\\mathbf {D}, \\{\\delta_ {i} ^ {(t)} - \\bar {\\delta} ^ {(t + 1)} \\}), i = 1, \\dots , n\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.104, + 0.373, + 0.435, + 0.396 + ], + "angle": 0, + "content": "4: Update the adversarial example along the average direction:" + }, + { + "type": "equation", + "bbox": [ + 0.167, + 0.403, + 0.443, + 0.421 + ], + "angle": 0, + "content": "\\[\nx ^ {(t + 1)} = \\operatorname {C l i p} _ {x, e} \\left\\{x ^ {(t)} + \\alpha \\cdot \\operatorname {S i g n} (\\bar {\\delta} ^ {(t + 1)}) \\right\\}\n\\]" + }, + { + "type": "title", + "bbox": [ + 0.105, + 0.431, + 0.172, + 0.442 + ], + "angle": 0, + "content": "5: end for" + }, + { + "type": "text", + "bbox": [ + 0.105, + 0.442, + 0.324, + 0.456 + ], + "angle": 0, + "content": "6: Output option (a): Craft one \\( x_{adv} \\)" + }, + { + "type": "equation", + "bbox": [ + 0.264, + 0.462, + 0.344, + 0.478 + ], + "angle": 0, + "content": "\\[\nx _ {a d v} = x ^ {(T)}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.121, + 0.483, + 0.447, + 0.51 + ], + "angle": 0, + "content": "Output option (b): Craft M \\(x_{adv}\\) by sampling from the learned perturbation distribution \\(\\mathcal{N}(\\bar{\\delta},\\sigma)\\)" + }, + { + "type": "equation", + "bbox": [ + 0.206, + 0.518, + 0.403, + 0.532 + ], + "angle": 0, + "content": "\\[\nC = \\text {N U M S} _ {-} \\operatorname {C O L S} (\\mathbf {D}) = n \\times T\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.208, + 0.536, + 0.358, + 0.565 + ], + "angle": 0, + "content": "\\[\n\\bar {\\delta} = \\bar {\\delta} ^ {(T)}, \\quad \\sigma = \\frac {\\mathbf {D} \\mathbf {D} ^ {T}}{C - 1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.122, + 0.568, + 0.307, + 0.582 + ], + "angle": 0, + "content": "Generate adversarial examples" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.588, + 0.275, + 0.607 + ], + "angle": 0, + "content": "\\[\n\\{\\delta_ {m} \\} _ {m = 1} ^ {M} \\sim \\mathcal {N} (\\bar {\\delta}, \\sigma),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.133, + 0.608, + 0.478, + 0.627 + ], + "angle": 0, + "content": "\\[\n\\left\\{x _ {a d v} ^ {m} \\right\\} _ {m = 1} ^ {M} = \\left\\{\\operatorname {C l i p} _ {x, \\epsilon} \\left\\{x ^ {(T - 1)} + \\alpha \\cdot \\operatorname {S i g n} \\left(\\delta_ {m}\\right) \\right\\} \\right\\} _ {m = 1} ^ {M}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.68, + 0.47, + 0.846 + ], + "angle": 0, + "content": "In this case, the expectation of the stochastic gradient is the full gradient, i.e., \\(\\delta (z) = \\mathbb{E}[\\hat{\\delta}_S(z)]\\). Hence, the prior distribution over adversarial perturbations is naturally a Gaussian one at each iteration. Benefiting from the asymptotic normality of SGD [30], we propose a novel method to approximate the posterior distribution of perturbations. Our main idea is to estimate the mean and covariance matrix of the stationary distribution of stochastic gradient ascent during the optimizing procedure. The iterative averaging is adopted to approximate the mean of adversarial perturbations using the sequence of stochastic gradients" + }, + { + "type": "equation", + "bbox": [ + 0.155, + 0.868, + 0.469, + 0.905 + ], + "angle": 0, + "content": "\\[\n\\bar {\\delta} ^ {(t + 1)} = \\frac {(t \\times n) \\bar {\\delta} ^ {(t)} + \\sum_ {i = 1} ^ {n} \\delta_ {i} ^ {(t)}}{(t + 1) \\times n}. \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.121 + ], + "angle": 0, + "content": "Then, \\(\\bar{\\delta} = \\bar{\\delta}^{(T)}\\), where \\(n\\) is the augmented samples in the \\(t\\)-th iteration (\\(t = 0, \\dots, T - 1\\)) and \\(T\\) is the total iterations." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.122, + 0.892, + 0.185 + ], + "angle": 0, + "content": "Let \\(\\mathbf{D}\\) be the deviation matrix with column \\(\\mathbf{D}_j = \\delta_i^{(t)} - \\bar{\\delta}^{(t + 1)}\\), where \\(j = t\\times n + i\\) and \\(i = 1,\\dots ,n\\). Thus, the covariance matrix of the posterior distribution is estimated by considering all stochastic gradients in iterative processing," + }, + { + "type": "equation", + "bbox": [ + 0.638, + 0.195, + 0.891, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\sigma = \\frac {\\mathbf {D} \\mathbf {D} ^ {T}}{n \\times T - 1}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.237, + 0.892, + 0.376 + ], + "angle": 0, + "content": "Finally, the adversarial example can be iteratively obtained by (3). Note that, ANDA allows to craft one or an unlimited number of adversarial examples for one input by sampling perturbations from the estimated distribution \\(\\mathcal{N}(\\bar{\\delta},\\sigma)\\). The complete procedure for the proposed ANDA method is shown in Algorithm 1. Following the empirical study in Section 3.1, we visualized the perturbations \\(\\delta_i^{(t)}\\) of 10 iterates with multiple data augmentations (shown in Fig. 2 b), which validate our previous hypothesis." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.385, + 0.81, + 0.401 + ], + "angle": 0, + "content": "3.3. Multiple Implementations of ANDA" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.408, + 0.892, + 0.695 + ], + "angle": 0, + "content": "With the proposed ANDA, we find a solution to approximating the true posterior distribution centered at the the optimal \\( x_{adv}^{*} \\) for the maximization problem introduced in (2). Nevertheless, only exploring the unimodal optimization space largely limits the diversity of generated adversarial examples. Profiting the excellent generalization capability of Bayesian marginalization approximated with the deep ensemble strategy, we propose MultiANDA via multiple (e.g., K times) repeats of ANDA by add random initial values on origin sample \\( x \\). Especially, we average the adversarial perturbation \\( \\bar{\\delta}_k \\) from each ANDA process, and obtain \\( \\bar{\\delta}_{mean} = \\frac{1}{K}\\sum_{k=0}^{K-1}\\bar{\\delta}_k \\). This realizes the multimodal marginalization of this Gaussian mixture distribution. Similarly, adversarial examples can be iteratively obtained by (2). MultiANDA also enables producing infinite adversarial examples with high effectiveness by sampling from each approximated Gaussian distribution \\( \\mathcal{N}(\\bar{\\delta}_k,\\sigma_k) \\). Remarkable improvements of the attacking ability, especially on the defense models are shown in Sections 4.2 and 4.3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.71, + 0.633, + 0.726 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.892, + 0.901 + ], + "angle": 0, + "content": "In this section, we present the results of an extensive empirical study to validate the performance of the proposed methods. We first specify the experimental settings in Section 4.1. Then, the results of ANDA and MultiANDA compared with the state-of-the-art approaches on various types of DNNs with or without defenses are presented in Section 4.2 and 4.3. Section 4.4 shows the attacking effectiveness of the multiple adversarial examples generated from each input via the proposed methods. Due to page limitations, more detailed experiment settings, results and the ablation study are presented in Appendix." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "24845" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.108, + 0.887, + 0.453 + ], + "angle": 0, + "content": "
AttackInc-v3Inc-v3 =>ResNet-50 =>
ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM100.0*20.315.715.634.321.533.299.7*63.920.943.440.4
TIM64.3*35.930.625.470.445.347.377.0*47.630.868.854.3
SIM100.0*38.231.135.942.236.948.6100.0*83.735.350.954.6
DIM100.0*31.725.531.445.533.561.999.9*83.647.561.163.5
FIA98.3*78.475.381.283.579.686.299.6*94.580.488.387.4
TAIG99.7*53.345.956.754.252.562.4100.0*86.151.958.764.8
NI-FGSM100.0*40.035.239.956.943.059.699.7*85.448.167.065.0
MI-FGSM100.0*40.235.140.357.143.258.599.7*85.948.667.465.1
VMI-FGSM100.0*63.059.368.670.365.375.399.9*93.468.376.478.4
VNI-FGSM100.0*62.458.767.769.764.675.499.8*92.967.975.678.0
ANDA100.0*76.172.882.377.077.195.6100.0*98.994.089.594.5
MultiANDA100.0*79.276.084.578.879.696.5100.0*99.295.090.195.2
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM36.325.620.699.3*37.830.123.518.713.79.999.9*16.5
TIM43.436.532.036.0*66.242.841.534.830.223.6100.0*46.0
SIM58.947.841.499.6*49.849.537.734.425.223.6100.0*30.2
DIM54.641.436.698.2*50.045.731.726.419.216.499.9*23.4
FIA82.275.372.489.2*80.777.757.450.740.942.7100.0*47.9
TAIG73.963.458.495.0*57.463.348.843.634.733.9100.0*40.3
NI-FGSM61.949.544.799.2*64.755.243.639.529.230.499.9*35.7
MI-FGSM60.349.343.098.8*64.654.344.739.428.930.899.9*36.0
VMI-FGSM81.169.666.499.3*73.572.762.756.746.548.6100.0*53.6
VNI-FGSM80.970.065.899.4*73.872.663.256.746.648.8100.0*53.8
ANDA93.086.483.799.8*82.886.574.464.156.461.5100.0*64.1
MultiANDA93.987.185.699.8*84.387.775.466.158.663.5100.0*65.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.464, + 0.895, + 0.507 + ], + "angle": 0, + "content": "Table 1. The success rates \\((\\%)\\) of the proposed and baseline attacks on five normally trained models. Sign \\* indicates the results on white-box source models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.532, + 0.268, + 0.549 + ], + "angle": 0, + "content": "4.1. Experimental Setup" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.558, + 0.471, + 0.589 + ], + "angle": 0, + "content": "The datasets, models, and baseline methods employed in our experiments are detailed below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.592, + 0.47, + 0.653 + ], + "angle": 0, + "content": "Datasets: Following the prior work [8, 13, 46], we implemented our experiments on ImageNet1k dataset [33] containing 1000 images, which are randomly drawn from the ImageNet dataset [37]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.656, + 0.471, + 0.883 + ], + "angle": 0, + "content": "Models: We considered two categories of target models for evaluation: seven normally trained models and seven advanced defense models. The first category includes Inception-v3 (Inc-v3) [40], Resnet-v2-50 (ResNet-50), Resnet-v2-101 (ResNet-101), Resnet-v2-152 (ResNet-152) [15], Inception-v4 (Inc-v4), Inception-ResNet-v2 (IncRes-v2) [41] and VGG-19 [38], where Inc-v3, ResNet-50, IncRes-v2 and VGG-19 are also used as the white-box source models to generate adversarial examples. The defense models contain three adversarially trained models: Inc-v3ens3, Inc-v3ens4 and IncRes-v2ens [42]; the High-level representation Guided Denoiser (HGD) [24]; the Neural Representation Purifier (NRP) [32]; the Randomized Smoothing (RS) [6]; and the 'Rand-3' submission in the NIPS 2017 defense competition (NIPS-r3)." + }, + { + "type": "text", + "bbox": [ + 0.097, + 0.886, + 0.47, + 0.9 + ], + "angle": 0, + "content": "Baselines: Three streams of transfer-based attack meth" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.532, + 0.895, + 0.701 + ], + "angle": 0, + "content": "ods are used as baseline methods. The first stream focuses on the data augmentations including DIM [49], TIM [9], SIM [45] and a recent work Transferable Attack based on Integrated Gradients (TAIG) [17]. For the second group, we choose the feature importance-aware (FIA)[46], which considers the middle-layer information of the source model and achieves the competitive performance. The last stream focuses on the optimization enhanced methods, including BIM [20], its accelerated version: MI-FGSM [8], NIFGSM [25], and the approaches using variance reduction strategy, VMI-FGSM, VNI-FGSM [45]." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.71, + 0.792, + 0.727 + ], + "angle": 0, + "content": "4.2. Attack Normally Trained Models" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.895, + 0.903 + ], + "angle": 0, + "content": "We cross-validated our method by generating and testing the adversarial examples on the selected source (on rows) and target (on columns) networks (shown in Table 1). To be a fair comparison, our proposed methods generated one adversarial example for each input, aligned with the first output option of Algorithm 1, in the following experiments if not specified. From the Table 1, we observe that ANDA and MultiANDA significantly outperforms other methods in almost all cases, no matter in white-box or black-box settings. As the numerical results demonstrate, they consistently defeat all other methods when taking IncRes-v2," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "24846" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.137 + ], + "angle": 0, + "content": "ResNet-50 and VGG-19 as source models, and for Inc-v3, ANDA is competitive with the current SOTA methods, and MultiANDA always keep higher success rate." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.137, + 0.471, + 0.395 + ], + "angle": 0, + "content": "We further investigated the adversarial examples generated with ResNet-50, shown in Figure 3. The other six models were used as black-box targets for evaluating the performance of these examples. A higher number of successfully deceived target models implies more capable adversaries and therefore stronger attacks. The rightmost bars show that ANDA, MultiANDA generated 840, 863/1000 adversaries that fooled all six targeted models, respectively, while 517/1000 are for VMI-FGSM. Naturally, the remaining sets of bars for this baseline method are higher, meaning that it deceived fewer targeted models. Moreover, we visualized the generated examples and the perturbations by these three methods (see Figure 1). The results show that the perturbations crafted by ANDA and MultiANDA focus more on the semantic areas of objects than VMI-FGSM, which dominates the decision of the prediction model. More visualization results are provided in Appendix." + }, + { + "type": "image", + "bbox": [ + 0.104, + 0.407, + 0.445, + 0.556 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.571, + 0.468, + 0.599 + ], + "angle": 0, + "content": "Figure 3. Most examples crafted by our proposed methods successfully deceived all 6 black-box models." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.621, + 0.291, + 0.636 + ], + "angle": 0, + "content": "4.3. Attack Defense Models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.644, + 0.468, + 0.825 + ], + "angle": 0, + "content": "We evaluate our proposed method targeting on the selected advanced defenses models. As shown in Table 2, the success rates of our proposed methods consistently improve over these various defense models in most cases. They provide a significant performance increase in general compared with the other attacks, especially reaches the overall optimal success rates with the source model ResNet-50. An intriguing finding is that using ResNet-50 as the source model always yields the best attacking performance. This aligns with the conclusion drawn by Wu et al. [48] that the skip connections in ResNet-like neural networks enhance black-box attack transferability." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Notably, the fluctuating performance and the generally reduced effectiveness of all baseline methods can be observed with the source model VGG-19. The average maximum attack success rate in this context is only \\(28.3\\%\\), suggesting that the feature extraction capabilities of VGG-19" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.197 + ], + "angle": 0, + "content": "are not optimal, thereby leading to diminished transferability for black-box attacks. This observation highlights the critical role of source model selection in maximizing the transferability of adversarial attacks. Hence, the choice of source models and enhancing their capability for generalized feature extraction become promising directions for the future research." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.198, + 0.892, + 0.319 + ], + "angle": 0, + "content": "Similarly, we visualized the generated examples and the perturbations by VMI-FGSM, ANDA and MultiANDA that fool the defense models. The perturbed area by our proposed methods concentrates more on the informative region of images than the baseline method. Details are illustrated in Appendix. These compelling results of ANDA and MultiANDA on defenses valid their overall generalization ability in generating transferable and diverse adversaries." + }, + { + "type": "image", + "bbox": [ + 0.504, + 0.334, + 0.888, + 0.505 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.622 + ], + "angle": 0, + "content": "Figure 4. Attack success rates of sampled adversaries with single \\(\\{\\widetilde{\\delta}\\}\\), multiple \\(\\{\\delta_m\\}_{m=1}^{20}\\) and the succeeded \\(Suc.\\{\\delta_m\\}_{m=1}^{20}\\) generated by ANDA and MultiANDA. \\(\\{\\delta_m\\}_{m=1}^{20}\\) means the 20 adversarial examples sampled from the learned perturbation distribution for each input image; whereas \\(Suc.\\{\\delta_m\\}_{m=1}^{20}\\) are the 20 sampled adversarial examples for the input image whose corresponding single adversarial example has succeeded in the attack." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.651, + 0.878, + 0.667 + ], + "angle": 0, + "content": "4.4. Attack Performance of Sampled Adversaries" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.675, + 0.892, + 0.901 + ], + "angle": 0, + "content": "The analysis presented above shows the effectiveness of the single optimum adversarial example per input generated, denoted as \\(\\bar{\\delta}\\), referring to Step 6 (a) shown in Algorithm 1. Besides, MultiANDA/ANDA allows learning the distribution of the perturbations \\(\\mathcal{N}(\\bar{\\delta},\\sigma)\\) via Step 6 (b), and generate any number of adversarial examples for each input by sampling \\(M\\) adversaries, denoted as \\(\\{\\delta_m\\}_{m = 1}^M\\). To verify the attack performance of these sampled adversaries, we drawn \\(20(M = 20)\\) adversarial examples for each input image, i.e., \\(\\{\\delta_m\\}_{m = 1}^{20}\\). Meanwhile, we analyzed the adversaries sampled for the input images whose corresponding adversaries \\(\\bar{\\delta}\\) succeeded in the attack, denoted as \\(Suc.\\{\\delta_m\\}_{m = 1}^{20}\\). Experiment results show in Figure 4 that the sampled adversaries have competitive attack success rates compared with the single adversary generated with \\(\\bar{\\delta}\\)," + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.518, + 0.956 + ], + "angle": 0, + "content": "24847" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.087, + 0.097, + 0.884, + 0.442 + ], + "angle": 0, + "content": "
AttackInc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.ResNet-50
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.14.63.713.44.87.512.37.17.413.78.19.7
TIM27.521.316.922.821.121.934.027.424.231.130.629.5
SIM18.18.48.615.210.812.221.413.115.216.115.116.2
DIM13.16.75.812.88.69.420.812.016.915.715.316.1
FIA37.421.311.623.529.224.644.427.230.025.935.332.6
TAIG38.023.922.829.628.528.639.230.429.729.634.432.7
MI-FGSM18.39.05.515.712.012.126.315.517.318.020.219.5
NI-FGSM18.68.66.215.312.212.226.215.717.518.919.819.6
VMI-FGSM36.921.219.124.727.725.947.431.337.727.138.736.4
VNI-FGSM36.422.018.925.327.427.146.530.437.427.138.736.4
ANDA44.425.936.523.237.020.371.450.772.432.967.441.6
MultiANDA54.436.752.824.346.929.979.764.882.334.476.350.1
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.17.05.113.06.08.49.64.43.913.44.67.2
TIM27.921.418.423.923.823.123.027.415.031.130.625.4
SIM23.816.415.918.318.118.511.45.68.713.47.49.3
DIM16.210.111.714.912.313.010.74.75.613.65.98.1
FIA48.934.724.230.842.836.313.38.37.114.69.810.6
TAIG49.041.212.216.513.326.417.710.236.934.141.928.2
MI-FGSM22.013.313.416.417.016.413.06.97.215.58.910.3
NI-FGSM21.613.813.415.516.616.213.96.87.214.69.310.4
VMI-FGSM49.238.836.025.239.237.721.911.615.918.415.916.7
VNI-FGSM49.937.735.425.639.338.421.611.916.818.615.722.9
ANDA63.347.357.828.557.932.620.910.822.215.416.23.7
MultiANDA70.361.969.931.267.841.824.613.731.216.221.37.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.453, + 0.893, + 0.484 + ], + "angle": 0, + "content": "Table 2. The success rates \\((\\%)\\) of the proposed and baseline attacks on five defense models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.508, + 0.471, + 0.57 + ], + "angle": 0, + "content": "even on the defense models. This confirms the well approximation of the perturbation distributions and the great potential of our method for adversarial training or defense model designing." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.587, + 0.348, + 0.605 + ], + "angle": 0, + "content": "5. Conclusions and Perspectives" + }, + { + "type": "text", + "bbox": [ + 0.075, + 0.614, + 0.471, + 0.903 + ], + "angle": 0, + "content": "In this work, we present the Multiple Asymptotically Normal Distribution Attacks (MultiANDA) to generate transferable adversarial examples. Our primary goal is to efficiently approximate the posterior distribution of adversarial perturbations to achieve better generalization across unknown deep learning models. We leverage the statistical information of gradients along the optimization trajectory to estimate the stationary distribution of the perturbations. With this learned distribution's aid, MultiANDA can significantly improve the transferability of adversarial examples to black-box target models. Extensive experiments demonstrate that MultiANDA outperforms popular and recently proposed black-box and transfer-based methods, further highlighting the insufficiency of current defense techniques. Notably, the computational overhead of both ANDA and MultiANDA, largely depending on the number of batch samples during augmentation, is on par with similar baseline methods (refer to Appendix for the computational overhead analysis). Compared to the potential risks" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.508, + 0.895, + 0.585 + ], + "angle": 0, + "content": "these algorithms might pose if misused, their computational cost is relatively negligible. We advocate for the development of advanced deep learning models which align better with human visual preferences, thereby avoiding the fundamental defects present in modern models." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.604, + 0.669, + 0.623 + ], + "angle": 0, + "content": "Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.631, + 0.894, + 0.783 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China under Grant 62176020, the Joint Foundation of the Ministry of Education (8091B042235), the Beijing Natural Science Foundation under Grant L211016, the Talent Fund of Beijing Jiaotong University under Grant 2023XKRC041, and the Fundamental Research Funds for the Central Universities (Science and technology leading talent team project) under Grant 2022JBXT003. We also thank Huafeng Liu and Zhekun Liu for their helpful advice and support." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.803, + 0.597, + 0.819 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.508, + 0.828, + 0.892, + 0.884 + ], + "angle": 0, + "content": "[1] Erin E Alves, Devesh Bhatt, Brendan Hall, Kevin Driscoll, Anitha Murugesan, and John Rushby. Considerations in assuring safety of increasingly autonomous systems. Technical report, 2018. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 452-467, 2018. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.093, + 0.892, + 0.625 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "24850" + } + ] +] \ No newline at end of file diff --git a/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_origin.pdf b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f69dcbc40b2de3e59a6b02ac9e49000f39c0ebff --- /dev/null +++ b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/6823fc5a-81c6-4d57-a39f-933f81a96ddc_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d015bea0df64d2eb9f669fd450ac989eae8b9ba677be71630bdc8fa2b2b935cf +size 1347336 diff --git a/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/full.md b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/full.md new file mode 100644 index 0000000000000000000000000000000000000000..df61f3b35176e56b44dbc02a9bfa01d81356986d --- /dev/null +++ b/2024/Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning/full.md @@ -0,0 +1,337 @@ +# Strong Transferable Adversarial Attacks via Ensembled Asymptotically Normal Distribution Learning + +Zhengwei Fang $^{1,2}$ , Rui Wang $^{1,2,3*}$ , Tao Huang $^{1,2}$ , Liping Jing $^{1,2}$ + +$^{1}$ School of Computer Science and Technology, Beijing Jiaotong University, Beijing, China + +$^{2}$ Beijing Key Lab of Traffic Data Analysis and Mining, Beijing, China + +$^{3}$ Collaborative Innovation Center of Railway Traffic Safety, Beijing, China + +jankinfmail@gmail.com, {rui.wang,thuang,lpjing}@bjtu.edu.cn + +# Abstract + +Strong adversarial examples are crucial for evaluating and enhancing the robustness of deep neural networks. However, the performance of popular attacks is usually sensitive, for instance, to minor image transformations, stemming from limited information — typically only one input example, a handful of white-box source models, and undefined defense strategies. Hence, the crafted adversarial examples are prone to overfit the source model, which hampers their transferability to unknown architectures. In this paper, we propose an approach named Multiple Asymptotically Normal Distribution Attacks (MultiANDA) which explicitly characterize adversarial perturbations from a learned distribution. Specifically, we approximate the posterior distribution over the perturbations by taking advantage of the asymptotic normality property of stochastic gradient ascent (SGA), then employ the deep ensemble strategy as an effective proxy for Bayesian marginalization in this process, aiming to estimate a mixture of Gaussians that facilitates a more thorough exploration of the potential optimization space. The approximated posterior essentially describes the stationary distribution of SGA iterations, which captures the geometric information around the local optimum. Thus, MultiANDA allows drawing an unlimited number of adversarial perturbations for each input and reliably maintains the transferability. Our proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without defenses through extensive experiments on seven normally trained and seven defense models. + +# 1. Introduction + +Albeit the excellent performance of deep neural networks (DNNs) across a broad spectrum of tasks in machine vi- + +![](images/85b7c52b134c3f4ca34c2f89014f3ca3148ae881f3cd64b120c8382df4800db8.jpg) +Figure 1. Perturbation visualization of the adversarial examples generated by ANDA/MultiANDA that fool all selected normally trained (first row) and defense (second row) models. + +sion and natural language processing, a rich stream of work [8, 14, 39, 50, 51] shows the non-negligible vulnerability of DNNs to adversarial attacks, which craft imperceptible perturbations to synthesize malicious inputs for triggering unexpected model predictions. Such severe degradation of model robustness and stability greatly hinders the application of DNNs in security- or safety-critical domains [1, 2, 11]. Fortunately, studying how to create potent adversarial examples aids in evaluating DNN-based systems and enhancing their robustness by devising defensive strategies, such as adversarial training [14, 29]. + +This paper focuses on the black-box and transfer-based threat model. The corresponding adversarial attack algorithms intend to synthesize the adversarial examples that can successfully fool the unknown DNNs without accessing any information on model architectures and outputs. Researchers implement such attacks by maximizing the nonconcave loss function of a substitute model trained for the same task with, for example, one step [14], or iterative steps [20] of gradient ascent optimization. However, prior work has shown the generated adversarial examples trend to overfit the substitute model, which hardly attacks other models [21]. Meanwhile, they are often sensitive to minor transformations [4, 26, 27]. + +Hence, researchers have been exploring various data + +augmentation strategies [4, 9, 25, 49] and improved SGA optimization methods [8, 17, 25, 45] to enhance the performance of transferable attacks. Nonetheless, these efforts exhibit limited generalization capabilities on unknown DNN architectures, particularly those trained with defense strategies. This suggests that a deterministic optimization procedure, initiated from a single image, is insufficient to thoroughly explore the high-dimensional perturbation space. Furthermore, the projected gradient descent (PGD) method proposed by Madry et al. [29] initializes the attack algorithm with random restarts around the legitimate image. However, these random samples represent homogeneous deviations from the original input, lacking diversity [10], which limits the transferability of adversarial examples. + +To resolve these issues, in this paper, we propose Multiple Asymptotically Normal Distribution Attacks (MultiANDA), a novel method that explicitly characterizes perturbations inferred from a learned distribution. Firstly, we formulate a single ANDA by taking advantage of the nice property of stochastic gradient ascent (SGA), the asymptotic normality [5, 18, 28, 30], to learn the true optimal posterior distribution of adversarial perturbations. Specifically, ANDA calculates and stores the first two moments of iterations captured along the optimizing trajectory to approximate the distribution of the adversarial perturbation as a Gaussian one. Moreover, we apply the deep ensemble strategy [22] on ANDA to devise a mixture of Gaussians, approximating the Bayesian posterior. As each Gaussians positioned at a different basin of attraction, the proposed MultiANDA leads to a further improved generalization performance of the attacks with more diverse adversarial examples. As shown in Figure 1, the perturbations crafted by our proposed method focus more on the semantic and decisive areas of objects than the baseline approach. In particular, the contributions of this work are the following: + +- We propose MultiANDA, an approximate Bayesian inference method to realize transfer-based adversarial attacks. We learn the perturbation distribution instead of finding a specific adversary for each input example. Thus, a good approximation of the true perturbation posterior boosts the generalization (i.e., transferability) of the generated adversarial examples. +- We devise a stochastic adversarial attacking process instead of the original deterministic one initialized from one input by random image translations. In this way, we profit the asymptotic normality of SGA for a better perturbation distribution learning. Adopting the deep ensemble strategy, an effective mechanism for approximating Bayesian marginalization [47], MultiANDA accurately and efficiently estimate the posterior distribution over the perturbations by using the geometry information along the attacking trajectory. +- The learned distributions of perturbation allow draw + +ing an unlimited number of adversarial examples for one input. We experimentally validate that the sampled adversaries have comparably high attack success rates with the singly generated ones, even on the defense models. This result demonstrates the great potential of our method for designing defense strategies grounded in adversarial training. + +- Extensive experiment results show that the proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without advanced defenses. Significantly, MultiANDA is more advantageous when attacking the advanced defense models. Thus, ANDA and MultiANDA are expected to benchmark new defense methods in the future. Our code is available at https://github.com/CLIAgroup/ANDA. + +# 2. Related Work and Preliminaries + +Our study mainly focuses on the black-box and transfer-based threat model, as they may bring more security and safety risks due to their practical applicability [8, 34]. + +# 2.1. Black-Box Adversarial Attacks + +Essentially, the adversarial attack algorithms intend to maximize the loss function $\mathcal{L}(\cdot)$ , e.g., the cross entropy loss for classification tasks, to search for the adversaries $x_{adv}$ [14, 39], with the constraints of $l_{\infty}$ norm bound $\varepsilon$ , as shown in (1): + +$$ +\max _ {x _ {a d v}} \mathcal {L} (x _ {a d v}, y) \quad \text {s . t .} | | x _ {a d v} - x | | _ {\infty} \leq \varepsilon , \tag {1} +$$ + +where $x$ , $x_{adv}$ , $y$ are the legitimate input, the adversarial example and the true label, respectively. + +Among prior work, the fast gradient sign method (FGSM) [14] and its iterative version, the basic iterative method (BIM) [20] resort to linearizing the non-concave loss function and realize the attack with one-step update or iterative updates, as shown in (2): + +$$ +x _ {a d v} ^ {(t + 1)} = \Phi (x _ {a d v} ^ {(t)} + \alpha \cdot \operatorname {s i g n} (\underbrace {\nabla_ {x} \mathcal {L} (x _ {a d v} ^ {(t)} , y)})), \quad (2) +$$ + +where $x_{adv}^{(t + 1)}$ , $\delta^{(t)}$ are the adversarial example and perturbation at the $t$ -th step, $x_{adv}^{(0)}$ is the legitimate input, and $\Phi (\cdot)$ is the projection function on the $\varepsilon$ -ball. + +These attacks are more effective under white-box scenarios, whereas they tend to overfit the model parameters and hardly transfer to unknown architectures [21]. Thus, many works have been proposed to improve the transferability of adversarial examples, which can be divided into three categories. The first group focuses on the iterative optimizing process by considering momentum [8], Nesterov accelerated gradient [25], and variance reducing [45] to search for the optimal solutions. The second group attempts to attack + +the mid-layers by disrupting the critical object-aware features [12, 16, 31, 46, 52] + +Moreover, the third stream of methods adopt the commonly used generalization techniques by introducing diversity. These techniques encompass data augmentation [15, 19], such as resize and padding [49], translation [9]; and other integrated augmentation strategies, including combining multiple linear transformations [4], modifying the pixel values with multiple scales [25], integrating more information from other images [7], and using the sum of the gradients from intensity augmented images [17]. + +Similar to our study, existing attack approaches also try to determine the explicit adversarial distributions. PGD [29] resolves the inner maximization problem by the random restart strategy. However, the uniformly drawn samples tend to lie densely around the natural image [10]. Li et al. [23] propose $\mathcal{N}$ attack to define and learn an adversarial distribution. However, their work is under a query-based threat model, i.e., it has to access the output scores for each input from the black-box defense model, which weakens its scalability in real-world applications. Additionally, Dong et al. [10] propose to formulate the adversarial perturbations via a learned distribution for adversarial distributional training (ADT). Similar to $\mathcal{N}$ attack, ADT crafts the adversarial examples centered with the natural input $x$ , which may fail in generating adversarial examples once the input is a little bit far away from the boundary. Conversely, ANDA generates adversaries around the optimal $x_{adv}^{*}$ . In this case, the adversaries are more prone to successful attacks. From the facets of implementation, ADT focuses on learning a distribution from a large amount of training data for adversarial training. Our proposed method tries to collect the trajectory information during the optimization process for each natural input. Thus, these crucial differences make two approaches suitable for distinct tasks: inner maximization problem for adversarial training (ADT) and transfer-based black-box attack (ANDA and MultiANDA). + +# 2.2. Asymptotic Normality of SGD + +Maddox et al. [28] point out that the trajectory of stochastic gradient descent (SGD) can be regarded as the Bayesian posterior distribution over the random variables to be optimized, e.g., the model parameters in the case of the DNN training. Following this theory, they propose a Gaussian posterior approximation method (SWAG) based on the first two moments of SGD iterations for model calibration or uncertainty quantification. In the prior work, Mandt et al. [30] provide a more detailed analysis of the stationary distribution of SGD iterations with a constant learning rate, also termed the asymptotic normality of SGD [44]. Such analysis can be traced back to the work by Ruppert [36], Polyak and Juditsky [35] known as Polyak-Ruppert averaging, and still an active research subject for SGD [5]. Furthermore, + +inspired by deep ensembles [22], Wilson and Izmailov [47] carried out an extensive empirical study, demonstrating that applying SWAG only with multiple randomly initialized models can significantly improve the model performance. They emphasize that this benefits from the multimodal effects of the mixture Gaussian distributions and, in turn, boosts the contribution of each additional sample in the optimization procedure. In this paper, we adopt these theories to innovatively model the posterior distribution of perturbations to search for potent adversarial examples. + +# 3. Proposed Method + +Drawing on the comprehensive research previously discussed, we hypothesize that utilizing the asymptotic normality of SGD (SGA in our problem formulation) to marginalize an approximate Bayesian posterior could enhance generalization (transferability in our context) beyond what is achievable with a fixed set of parameter (one specific adversarial perturbation). However, optimizing the objective (1) using attack algorithms such as BIM (2) is a deterministic gradient ascent process. In this process, no gradient noise is introduced to form a stationary distribution of SGD. Thus, to bridge this gap, we exploit random data augmentation in the standard optimization process, devising a novel attack method for accurately and efficiently estimating the posterior distribution over perturbations. + +In Section 3.1, we first empirically analyze the asymptotically normal distribution property in the stochastic adversarial attack process, then proceed to formalize the optimization objective for the task of adversarial example generation. Finally, inspired by the advantageous properties of SGD and the effective multimodal inference of the ensemble strategy, we introduce the new attack methods ANDA and MultiANDA in Sections 3.2 and 3.3, respectively. + +# 3.1. Asymptotic Normality of Stochastic BIM + +Under specific conditions—decaying learning rates, smooth gradients, and a full rank stationary distribution—it has been theoretically established that SGD asymptotically converges to a Gaussian distribution centered at the local optimum [3, 5, 28]. Expanding on this, Mandt et al. [30] demonstrated that under certain assumptions, SGD with a constant and sufficiently small learning rate in its final search phase, i.e., when updates are proximal to the local optimum, converges to a stationary distribution. This convergence implies that iterations during this phase can approximate the posterior distribution of the optimized variables. Crucially, the gradient noise, introduced by the randomness of the sampled training batches, is instrumental in forming this distribution, provided the learning rate is adequately small [28]. These theoretical underpinnings motivate our approach in the algorithm design. + +![](images/44c3e6dc25cf12378b8ba55c4c682c790db4f22a8504cda03cc6d65757437d10.jpg) +a. Stochastic BIM + +![](images/66491600190cf1b1e4e3176e435b39afae2394344c086b39326269500bf70928.jpg) +b. ANDA implementation +Figure 2. Asymptotically normal distribution examples with iterative trajectories of adversarial perturbations generated by stochastic BIM (a) and the proposed approach (b). + +As demonstrated in (2), the optimization process, beginning from a specific input, is a deterministic gradient ascent, differing from a standard SGA approach. Therefore, we introduce stochastic gradient noises to emulate Gaussian limiting distributions by integrating a random data augmentation technique AUG, like image translation used in our experiments, at each iterative step: + +$$ +x _ {a d v} ^ {(t + 1)} = \Phi (x _ {a d v} ^ {(t)} + \alpha \cdot \operatorname {s i g n} (\underbrace {\nabla_ {x} \mathcal {L} (\mathrm {A U G} (x _ {a d v} ^ {(t)} , y))} _ {\delta^ {(t)}})). \tag {3} +$$ + +Notably, a small constant learning rate schedule $(\alpha = \epsilon / T)$ is commonly adopted, where $\epsilon \in \mathbb{R}$ is a sufficiently small number used to restrict the $L_{\infty}$ -norm for creating invisible adversarial perturbations, and $T$ is the number of iterative steps. Hence, we speculate the devised stochastic BIM shown in (3) can be used as an approximate Bayesian inference algorithm. In particular, Mandt et al. [30] assume that the gradients along the optimizing trajectory follow the Gaussian distribution stemming from the central limit theorem. We visualized the adversarial perturbations $\delta^{(t)}$ —the loss gradients in our task—using the t-SNE technique [43] to examine their distribution. 300 iterative steps for 3 randomly-drawn ImageNet [37] images shown in Fig. 2 a illustrates the Gaussian-shaped distributions which underpins our conjecture of the asymptotically normality of stochastic BIM algorithm. We notice the obvious increased gradient noise along the optimizing trajectory, which may due to the use of the sign() function and projection operations. Nevertheless, this does not affect the convergence of perturbations. Importantly, the first 10 steps converging with tight covariance justifies another speculation that the small value of $T$ (often $= 10$ for non-targeted attacks) and the non-trivial first step in our task (e.g., referring to strong attack performance of FGSM) indicate that the early iterates of are fairly close to the local optimum (i.e., the final search phase discussed above). + +Inspired by the results of this empirical study, we propose employing $n$ image transformations $\mathsf{AUG}_i(\cdot)$ to form a minibatch for an adversarial attack, thereby further enhancing stochasticity. Then, the optimization objective is formulated as + +$$ +\max _ {x _ {a d v}} \sum_ {i = 1} ^ {n} \mathcal {L} (\mathrm {A U G} _ {i} (x _ {a d v}), y) \quad \text {s . t .} \| x _ {a d v} - x \| _ {\infty} \leq \varepsilon . \tag {4} +$$ + +Furthermore, optimizing (4) to craft just one optimal adversarial example does not sufficiently explore the high-dimensional potential perturbation space. To further improve the transferability of adversarial examples to unknown architectures, we propose to explicitly model the adversarial perturbation $(\delta)$ via a distribution $(\Pi_{\delta})$ . Thus, our optimization objective is formalized as + +$$ +\max _ {\Pi_ {\delta}} \mathbb {E} _ {\delta \sim \Pi_ {\delta}} \sum_ {i = 1} ^ {n} \mathcal {L} (\mathrm {A U G} _ {i} (x + \delta), y), \text {s . t .} \| \delta \| _ {\infty} \leq \varepsilon. \tag {5} +$$ + +Objective (5) aims to maximize the expected loss over the adversarial perturbation distribution. It is noteworthy that (5) is a generalized version of (4) and is expected to characterize sufficient information about perturbations for transferable adversarial example generation. + +# 3.2. Asymptotically Normal Distribution Attack + +To better solve the optimization problem formulated in (5), we take advantage of the asymptotically normality of SGA and iteratively search for the adversarial examples similarly to (2). We omit the projection function $\Phi(\cdot)$ and $\mathrm{sign}(\cdot)$ because they do not effect the asymptotic normality of SGA as discussed in the previous subsection. Then, we calculate the gradient of the adversary with each transformation and denote it as the augmentation-aware perturbation $\delta_i^{(t)}$ : + +$$ +\delta_ {i} ^ {(t)} = \nabla_ {x ^ {(t)}} \mathcal {L} \left(\underset {\text {A U G} _ {i}} {\mathrm {A U G}} \left(x _ {a d v} ^ {(t)}\right), y\right). \tag {6} +$$ + +Let $S$ be a set of samples augmented in each iteration, i.e., $S = \{\mathrm{AUG}_i(x_{adv}^{(t)})\}_{i=1}^n$ . Here $S$ can be taken as a minibatch to form a stochastic gradient $\hat{\delta}_S$ which is a sum of contributions from all samples in $S$ . Hence, referring to the central limit theorem, $\hat{\delta}_S$ can be taken as a function of sample $z \in S$ , + +$$ +\hat {\delta} _ {S} (z) \approx \delta (z) + \frac {1}{\sqrt {n}} \Delta \delta (z), \tag {7} +$$ + +where the gradient noises $\Delta \delta (z)$ at each update can be conveniently assumed following a Gaussian distribution with covariance $C(z)$ , + +$$ +\Delta \delta (z) \sim \mathcal {N} (0, C (z)), \quad \hat {\delta} _ {S} (z) \sim \mathcal {N} (\delta (z), \frac {1}{n} C (z)). \tag {8} +$$ + +# Algorithm 1: Asymptotically Normal Distribution Attack (ANDA) + +Input: $x$ : clean image $x \in \mathbb{R}^d$ ; $y$ : ground-truth label; $f$ : pre-trained source model; +Parameters: $T$ : # iterations; $\epsilon$ : perturbation magnitude; $n$ : # batch samples for augmentation; $M$ : # sampling examples; + +Output: $x_{adv}$ : Adversarial examples; + +1: Initialize $\alpha \leftarrow \epsilon /T,\bar{\delta}^{(0)}\leftarrow \mathbf{0}^d$ $\mathbf{D}\gets \emptyset ,x_0\gets x$ +2: for $t = 0$ to $T - 1$ do +3: Calculate the mean of gradients and store the deviation of gradients throughout previous $t$ iterations: + +$$ +\delta_ {i} ^ {(t)} = \nabla_ {x ^ {(t)}} J (f (\mathrm {A U G} _ {i} (x ^ {(t)})), y), i = 1, \dots , n +$$ + +$$ +\bar {\delta} ^ {(t + 1)} = \frac {(t \times n) \bar {\delta} ^ {(t)} + \sum_ {i = 1} ^ {n} \delta_ {i} ^ {(t)}}{(t + 1) \times n} +$$ + +$$ +\text {A P P E N D - C O L S} (\mathbf {D}, \{\delta_ {i} ^ {(t)} - \bar {\delta} ^ {(t + 1)} \}), i = 1, \dots , n +$$ + +4: Update the adversarial example along the average direction: + +$$ +x ^ {(t + 1)} = \operatorname {C l i p} _ {x, e} \left\{x ^ {(t)} + \alpha \cdot \operatorname {S i g n} (\bar {\delta} ^ {(t + 1)}) \right\} +$$ + +# 5: end for + +6: Output option (a): Craft one $x_{adv}$ + +$$ +x _ {a d v} = x ^ {(T)} +$$ + +Output option (b): Craft M $x_{adv}$ by sampling from the learned perturbation distribution $\mathcal{N}(\bar{\delta},\sigma)$ + +$$ +C = \text {N U M S} _ {-} \operatorname {C O L S} (\mathbf {D}) = n \times T +$$ + +$$ +\bar {\delta} = \bar {\delta} ^ {(T)}, \quad \sigma = \frac {\mathbf {D} \mathbf {D} ^ {T}}{C - 1} +$$ + +Generate adversarial examples + +$$ +\{\delta_ {m} \} _ {m = 1} ^ {M} \sim \mathcal {N} (\bar {\delta}, \sigma), +$$ + +$$ +\left\{x _ {a d v} ^ {m} \right\} _ {m = 1} ^ {M} = \left\{\operatorname {C l i p} _ {x, \epsilon} \left\{x ^ {(T - 1)} + \alpha \cdot \operatorname {S i g n} \left(\delta_ {m}\right) \right\} \right\} _ {m = 1} ^ {M} +$$ + +In this case, the expectation of the stochastic gradient is the full gradient, i.e., $\delta (z) = \mathbb{E}[\hat{\delta}_S(z)]$ . Hence, the prior distribution over adversarial perturbations is naturally a Gaussian one at each iteration. Benefiting from the asymptotic normality of SGD [30], we propose a novel method to approximate the posterior distribution of perturbations. Our main idea is to estimate the mean and covariance matrix of the stationary distribution of stochastic gradient ascent during the optimizing procedure. The iterative averaging is adopted to approximate the mean of adversarial perturbations using the sequence of stochastic gradients + +$$ +\bar {\delta} ^ {(t + 1)} = \frac {(t \times n) \bar {\delta} ^ {(t)} + \sum_ {i = 1} ^ {n} \delta_ {i} ^ {(t)}}{(t + 1) \times n}. \tag {9} +$$ + +Then, $\bar{\delta} = \bar{\delta}^{(T)}$ , where $n$ is the augmented samples in the $t$ -th iteration ( $t = 0, \dots, T - 1$ ) and $T$ is the total iterations. + +Let $\mathbf{D}$ be the deviation matrix with column $\mathbf{D}_j = \delta_i^{(t)} - \bar{\delta}^{(t + 1)}$ , where $j = t\times n + i$ and $i = 1,\dots ,n$ . Thus, the covariance matrix of the posterior distribution is estimated by considering all stochastic gradients in iterative processing, + +$$ +\sigma = \frac {\mathbf {D} \mathbf {D} ^ {T}}{n \times T - 1}. \tag {10} +$$ + +Finally, the adversarial example can be iteratively obtained by (3). Note that, ANDA allows to craft one or an unlimited number of adversarial examples for one input by sampling perturbations from the estimated distribution $\mathcal{N}(\bar{\delta},\sigma)$ . The complete procedure for the proposed ANDA method is shown in Algorithm 1. Following the empirical study in Section 3.1, we visualized the perturbations $\delta_i^{(t)}$ of 10 iterates with multiple data augmentations (shown in Fig. 2 b), which validate our previous hypothesis. + +# 3.3. Multiple Implementations of ANDA + +With the proposed ANDA, we find a solution to approximating the true posterior distribution centered at the the optimal $x_{adv}^{*}$ for the maximization problem introduced in (2). Nevertheless, only exploring the unimodal optimization space largely limits the diversity of generated adversarial examples. Profiting the excellent generalization capability of Bayesian marginalization approximated with the deep ensemble strategy, we propose MultiANDA via multiple (e.g., K times) repeats of ANDA by add random initial values on origin sample $x$ . Especially, we average the adversarial perturbation $\bar{\delta}_k$ from each ANDA process, and obtain $\bar{\delta}_{mean} = \frac{1}{K}\sum_{k=0}^{K-1}\bar{\delta}_k$ . This realizes the multimodal marginalization of this Gaussian mixture distribution. Similarly, adversarial examples can be iteratively obtained by (2). MultiANDA also enables producing infinite adversarial examples with high effectiveness by sampling from each approximated Gaussian distribution $\mathcal{N}(\bar{\delta}_k,\sigma_k)$ . Remarkable improvements of the attacking ability, especially on the defense models are shown in Sections 4.2 and 4.3. + +# 4. Experiments + +In this section, we present the results of an extensive empirical study to validate the performance of the proposed methods. We first specify the experimental settings in Section 4.1. Then, the results of ANDA and MultiANDA compared with the state-of-the-art approaches on various types of DNNs with or without defenses are presented in Section 4.2 and 4.3. Section 4.4 shows the attacking effectiveness of the multiple adversarial examples generated from each input via the proposed methods. Due to page limitations, more detailed experiment settings, results and the ablation study are presented in Appendix. + +
AttackInc-v3Inc-v3 =>ResNet-50 =>
ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM100.0*20.315.715.634.321.533.299.7*63.920.943.440.4
TIM64.3*35.930.625.470.445.347.377.0*47.630.868.854.3
SIM100.0*38.231.135.942.236.948.6100.0*83.735.350.954.6
DIM100.0*31.725.531.445.533.561.999.9*83.647.561.163.5
FIA98.3*78.475.381.283.579.686.299.6*94.580.488.387.4
TAIG99.7*53.345.956.754.252.562.4100.0*86.151.958.764.8
NI-FGSM100.0*40.035.239.956.943.059.699.7*85.448.167.065.0
MI-FGSM100.0*40.235.140.357.143.258.599.7*85.948.667.465.1
VMI-FGSM100.0*63.059.368.670.365.375.399.9*93.468.376.478.4
VNI-FGSM100.0*62.458.767.769.764.675.499.8*92.967.975.678.0
ANDA100.0*76.172.882.377.077.195.6100.0*98.994.089.594.5
MultiANDA100.0*79.276.084.578.879.696.5100.0*99.295.090.195.2
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM36.325.620.699.3*37.830.123.518.713.79.999.9*16.5
TIM43.436.532.036.0*66.242.841.534.830.223.6100.0*46.0
SIM58.947.841.499.6*49.849.537.734.425.223.6100.0*30.2
DIM54.641.436.698.2*50.045.731.726.419.216.499.9*23.4
FIA82.275.372.489.2*80.777.757.450.740.942.7100.0*47.9
TAIG73.963.458.495.0*57.463.348.843.634.733.9100.0*40.3
NI-FGSM61.949.544.799.2*64.755.243.639.529.230.499.9*35.7
MI-FGSM60.349.343.098.8*64.654.344.739.428.930.899.9*36.0
VMI-FGSM81.169.666.499.3*73.572.762.756.746.548.6100.0*53.6
VNI-FGSM80.970.065.899.4*73.872.663.256.746.648.8100.0*53.8
ANDA93.086.483.799.8*82.886.574.464.156.461.5100.0*64.1
MultiANDA93.987.185.699.8*84.387.775.466.158.663.5100.0*65.9
+ +Table 1. The success rates $(\%)$ of the proposed and baseline attacks on five normally trained models. Sign \* indicates the results on white-box source models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix. + +# 4.1. Experimental Setup + +The datasets, models, and baseline methods employed in our experiments are detailed below. + +Datasets: Following the prior work [8, 13, 46], we implemented our experiments on ImageNet1k dataset [33] containing 1000 images, which are randomly drawn from the ImageNet dataset [37]. + +Models: We considered two categories of target models for evaluation: seven normally trained models and seven advanced defense models. The first category includes Inception-v3 (Inc-v3) [40], Resnet-v2-50 (ResNet-50), Resnet-v2-101 (ResNet-101), Resnet-v2-152 (ResNet-152) [15], Inception-v4 (Inc-v4), Inception-ResNet-v2 (IncRes-v2) [41] and VGG-19 [38], where Inc-v3, ResNet-50, IncRes-v2 and VGG-19 are also used as the white-box source models to generate adversarial examples. The defense models contain three adversarially trained models: Inc-v3ens3, Inc-v3ens4 and IncRes-v2ens [42]; the High-level representation Guided Denoiser (HGD) [24]; the Neural Representation Purifier (NRP) [32]; the Randomized Smoothing (RS) [6]; and the 'Rand-3' submission in the NIPS 2017 defense competition (NIPS-r3). + +Baselines: Three streams of transfer-based attack meth + +ods are used as baseline methods. The first stream focuses on the data augmentations including DIM [49], TIM [9], SIM [45] and a recent work Transferable Attack based on Integrated Gradients (TAIG) [17]. For the second group, we choose the feature importance-aware (FIA)[46], which considers the middle-layer information of the source model and achieves the competitive performance. The last stream focuses on the optimization enhanced methods, including BIM [20], its accelerated version: MI-FGSM [8], NIFGSM [25], and the approaches using variance reduction strategy, VMI-FGSM, VNI-FGSM [45]. + +# 4.2. Attack Normally Trained Models + +We cross-validated our method by generating and testing the adversarial examples on the selected source (on rows) and target (on columns) networks (shown in Table 1). To be a fair comparison, our proposed methods generated one adversarial example for each input, aligned with the first output option of Algorithm 1, in the following experiments if not specified. From the Table 1, we observe that ANDA and MultiANDA significantly outperforms other methods in almost all cases, no matter in white-box or black-box settings. As the numerical results demonstrate, they consistently defeat all other methods when taking IncRes-v2, + +ResNet-50 and VGG-19 as source models, and for Inc-v3, ANDA is competitive with the current SOTA methods, and MultiANDA always keep higher success rate. + +We further investigated the adversarial examples generated with ResNet-50, shown in Figure 3. The other six models were used as black-box targets for evaluating the performance of these examples. A higher number of successfully deceived target models implies more capable adversaries and therefore stronger attacks. The rightmost bars show that ANDA, MultiANDA generated 840, 863/1000 adversaries that fooled all six targeted models, respectively, while 517/1000 are for VMI-FGSM. Naturally, the remaining sets of bars for this baseline method are higher, meaning that it deceived fewer targeted models. Moreover, we visualized the generated examples and the perturbations by these three methods (see Figure 1). The results show that the perturbations crafted by ANDA and MultiANDA focus more on the semantic areas of objects than VMI-FGSM, which dominates the decision of the prediction model. More visualization results are provided in Appendix. + +![](images/b19830786b2310d37a5ab60424bc29314f6767050ab7fead2787ba0dea426979.jpg) +Figure 3. Most examples crafted by our proposed methods successfully deceived all 6 black-box models. + +# 4.3. Attack Defense Models + +We evaluate our proposed method targeting on the selected advanced defenses models. As shown in Table 2, the success rates of our proposed methods consistently improve over these various defense models in most cases. They provide a significant performance increase in general compared with the other attacks, especially reaches the overall optimal success rates with the source model ResNet-50. An intriguing finding is that using ResNet-50 as the source model always yields the best attacking performance. This aligns with the conclusion drawn by Wu et al. [48] that the skip connections in ResNet-like neural networks enhance black-box attack transferability. + +Notably, the fluctuating performance and the generally reduced effectiveness of all baseline methods can be observed with the source model VGG-19. The average maximum attack success rate in this context is only $28.3\%$ , suggesting that the feature extraction capabilities of VGG-19 + +are not optimal, thereby leading to diminished transferability for black-box attacks. This observation highlights the critical role of source model selection in maximizing the transferability of adversarial attacks. Hence, the choice of source models and enhancing their capability for generalized feature extraction become promising directions for the future research. + +Similarly, we visualized the generated examples and the perturbations by VMI-FGSM, ANDA and MultiANDA that fool the defense models. The perturbed area by our proposed methods concentrates more on the informative region of images than the baseline method. Details are illustrated in Appendix. These compelling results of ANDA and MultiANDA on defenses valid their overall generalization ability in generating transferable and diverse adversaries. + +![](images/fef9d131670076b83f8b39917693333ed54814ebd3c9aaeb18d449ef9cdaef6c.jpg) +Figure 4. Attack success rates of sampled adversaries with single $\{\widetilde{\delta}\}$ , multiple $\{\delta_m\}_{m=1}^{20}$ and the succeeded $Suc.\{\delta_m\}_{m=1}^{20}$ generated by ANDA and MultiANDA. $\{\delta_m\}_{m=1}^{20}$ means the 20 adversarial examples sampled from the learned perturbation distribution for each input image; whereas $Suc.\{\delta_m\}_{m=1}^{20}$ are the 20 sampled adversarial examples for the input image whose corresponding single adversarial example has succeeded in the attack. + +# 4.4. Attack Performance of Sampled Adversaries + +The analysis presented above shows the effectiveness of the single optimum adversarial example per input generated, denoted as $\bar{\delta}$ , referring to Step 6 (a) shown in Algorithm 1. Besides, MultiANDA/ANDA allows learning the distribution of the perturbations $\mathcal{N}(\bar{\delta},\sigma)$ via Step 6 (b), and generate any number of adversarial examples for each input by sampling $M$ adversaries, denoted as $\{\delta_m\}_{m = 1}^M$ . To verify the attack performance of these sampled adversaries, we drawn $20(M = 20)$ adversarial examples for each input image, i.e., $\{\delta_m\}_{m = 1}^{20}$ . Meanwhile, we analyzed the adversaries sampled for the input images whose corresponding adversaries $\bar{\delta}$ succeeded in the attack, denoted as $Suc.\{\delta_m\}_{m = 1}^{20}$ . Experiment results show in Figure 4 that the sampled adversaries have competitive attack success rates compared with the single adversary generated with $\bar{\delta}$ , + +
AttackInc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.ResNet-50
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.14.63.713.44.87.512.37.17.413.78.19.7
TIM27.521.316.922.821.121.934.027.424.231.130.629.5
SIM18.18.48.615.210.812.221.413.115.216.115.116.2
DIM13.16.75.812.88.69.420.812.016.915.715.316.1
FIA37.421.311.623.529.224.644.427.230.025.935.332.6
TAIG38.023.922.829.628.528.639.230.429.729.634.432.7
MI-FGSM18.39.05.515.712.012.126.315.517.318.020.219.5
NI-FGSM18.68.66.215.312.212.226.215.717.518.919.819.6
VMI-FGSM36.921.219.124.727.725.947.431.337.727.138.736.4
VNI-FGSM36.422.018.925.327.427.146.530.437.427.138.736.4
ANDA44.425.936.523.237.020.371.450.772.432.967.441.6
MultiANDA54.436.752.824.346.929.979.764.882.334.476.350.1
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.17.05.113.06.08.49.64.43.913.44.67.2
TIM27.921.418.423.923.823.123.027.415.031.130.625.4
SIM23.816.415.918.318.118.511.45.68.713.47.49.3
DIM16.210.111.714.912.313.010.74.75.613.65.98.1
FIA48.934.724.230.842.836.313.38.37.114.69.810.6
TAIG49.041.212.216.513.326.417.710.236.934.141.928.2
MI-FGSM22.013.313.416.417.016.413.06.97.215.58.910.3
NI-FGSM21.613.813.415.516.616.213.96.87.214.69.310.4
VMI-FGSM49.238.836.025.239.237.721.911.615.918.415.916.7
VNI-FGSM49.937.735.425.639.338.421.611.916.818.615.722.9
ANDA63.347.357.828.557.932.620.910.822.215.416.23.7
MultiANDA70.361.969.931.267.841.824.613.731.216.221.37.9
+ +Table 2. The success rates $(\%)$ of the proposed and baseline attacks on five defense models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix. + +even on the defense models. This confirms the well approximation of the perturbation distributions and the great potential of our method for adversarial training or defense model designing. + +# 5. Conclusions and Perspectives + +In this work, we present the Multiple Asymptotically Normal Distribution Attacks (MultiANDA) to generate transferable adversarial examples. Our primary goal is to efficiently approximate the posterior distribution of adversarial perturbations to achieve better generalization across unknown deep learning models. We leverage the statistical information of gradients along the optimization trajectory to estimate the stationary distribution of the perturbations. With this learned distribution's aid, MultiANDA can significantly improve the transferability of adversarial examples to black-box target models. Extensive experiments demonstrate that MultiANDA outperforms popular and recently proposed black-box and transfer-based methods, further highlighting the insufficiency of current defense techniques. Notably, the computational overhead of both ANDA and MultiANDA, largely depending on the number of batch samples during augmentation, is on par with similar baseline methods (refer to Appendix for the computational overhead analysis). Compared to the potential risks + +these algorithms might pose if misused, their computational cost is relatively negligible. We advocate for the development of advanced deep learning models which align better with human visual preferences, thereby avoiding the fundamental defects present in modern models. + +# Acknowledgements + +This work was supported by the National Natural Science Foundation of China under Grant 62176020, the Joint Foundation of the Ministry of Education (8091B042235), the Beijing Natural Science Foundation under Grant L211016, the Talent Fund of Beijing Jiaotong University under Grant 2023XKRC041, and the Fundamental Research Funds for the Central Universities (Science and technology leading talent team project) under Grant 2022JBXT003. We also thank Huafeng Liu and Zhekun Liu for their helpful advice and support. + +# References + +[1] Erin E Alves, Devesh Bhatt, Brendan Hall, Kevin Driscoll, Anitha Murugesan, and John Rushby. Considerations in assuring safety of increasingly autonomous systems. Technical report, 2018. 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However, the performance of popular attacks is usually sensitive, for instance, to minor image transformations, stemming from limited information — typically only one input example, a handful of white-box source models, and undefined defense strategies. Hence, the crafted adversarial examples are prone to overfit the source model, which hampers their transferability to unknown architectures. In this paper, we propose an approach named Multiple Asymptotically Normal Distribution Attacks (MultiANDA) which explicitly characterize adversarial perturbations from a learned distribution. Specifically, we approximate the posterior distribution over the perturbations by taking advantage of the asymptotic normality property of stochastic gradient ascent (SGA), then employ the deep ensemble strategy as an effective proxy for Bayesian marginalization in this process, aiming to estimate a mixture of Gaussians that facilitates a more thorough exploration of the potential optimization space. The approximated posterior essentially describes the stationary distribution of SGA iterations, which captures the geometric information around the local optimum. Thus, MultiANDA allows drawing an unlimited number of adversarial perturbations for each input and reliably maintains the transferability. Our proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without defenses through extensive experiments on seven normally trained and seven defense models." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 652, + 128, + 664 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 652, + 128, + 664 + ], + "spans": [ + { + "bbox": [ + 47, + 652, + 128, + 664 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 47, + 672, + 287, + 696 + ], + "type": "text", + "content": "Albeit the excellent performance of deep neural networks (DNNs) across a broad spectrum of tasks in machine vi-" + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 315, + 259, + 541, + 352 + ], + "blocks": [ + { + "bbox": [ + 315, + 259, + 541, + 352 + ], + "lines": [ + { + "bbox": [ + 315, + 259, + 541, + 352 + ], + "spans": [ + { + "bbox": [ + 315, + 259, + 541, + 352 + ], + "type": "image", + "image_path": "85b7c52b134c3f4ca34c2f89014f3ca3148ae881f3cd64b120c8382df4800db8.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 358, + 547, + 392 + ], + "lines": [ + { + "bbox": [ + 305, + 358, + 547, + 392 + ], + "spans": [ + { + "bbox": [ + 305, + 358, + 547, + 392 + ], + "type": "text", + "content": "Figure 1. Perturbation visualization of the adversarial examples generated by ANDA/MultiANDA that fool all selected normally trained (first row) and defense (second row) models." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 414, + 546, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 414, + 546, + 544 + ], + "spans": [ + { + "bbox": [ + 304, + 414, + 546, + 544 + ], + "type": "text", + "content": "sion and natural language processing, a rich stream of work [8, 14, 39, 50, 51] shows the non-negligible vulnerability of DNNs to adversarial attacks, which craft imperceptible perturbations to synthesize malicious inputs for triggering unexpected model predictions. Such severe degradation of model robustness and stability greatly hinders the application of DNNs in security- or safety-critical domains [1, 2, 11]. Fortunately, studying how to create potent adversarial examples aids in evaluating DNN-based systems and enhancing their robustness by devising defensive strategies, such as adversarial training [14, 29]." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 545, + 547, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 547, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 547, + 700 + ], + "type": "text", + "content": "This paper focuses on the black-box and transfer-based threat model. The corresponding adversarial attack algorithms intend to synthesize the adversarial examples that can successfully fool the unknown DNNs without accessing any information on model architectures and outputs. Researchers implement such attacks by maximizing the nonconcave loss function of a substitute model trained for the same task with, for example, one step [14], or iterative steps [20] of gradient ascent optimization. However, prior work has shown the generated adversarial examples trend to overfit the substitute model, which hardly attacks other models [21]. Meanwhile, they are often sensitive to minor transformations [4, 26, 27]." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 317, + 701, + 545, + 714 + ], + "type": "text", + "content": "Hence, researchers have been exploring various data" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 135, + 712 + ], + "type": "text", + "content": "*Corresponding author." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24841" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 240 + ], + "type": "text", + "content": "augmentation strategies [4, 9, 25, 49] and improved SGA optimization methods [8, 17, 25, 45] to enhance the performance of transferable attacks. Nonetheless, these efforts exhibit limited generalization capabilities on unknown DNN architectures, particularly those trained with defense strategies. This suggests that a deterministic optimization procedure, initiated from a single image, is insufficient to thoroughly explore the high-dimensional perturbation space. Furthermore, the projected gradient descent (PGD) method proposed by Madry et al. [29] initializes the attack algorithm with random restarts around the legitimate image. However, these random samples represent homogeneous deviations from the original input, lacking diversity [10], which limits the transferability of adversarial examples." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 241, + 289, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 241, + 289, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 241, + 289, + 493 + ], + "type": "text", + "content": "To resolve these issues, in this paper, we propose Multiple Asymptotically Normal Distribution Attacks (MultiANDA), a novel method that explicitly characterizes perturbations inferred from a learned distribution. Firstly, we formulate a single ANDA by taking advantage of the nice property of stochastic gradient ascent (SGA), the asymptotic normality [5, 18, 28, 30], to learn the true optimal posterior distribution of adversarial perturbations. Specifically, ANDA calculates and stores the first two moments of iterations captured along the optimizing trajectory to approximate the distribution of the adversarial perturbation as a Gaussian one. Moreover, we apply the deep ensemble strategy [22] on ANDA to devise a mixture of Gaussians, approximating the Bayesian posterior. As each Gaussians positioned at a different basin of attraction, the proposed MultiANDA leads to a further improved generalization performance of the attacks with more diverse adversarial examples. As shown in Figure 1, the perturbations crafted by our proposed method focus more on the semantic and decisive areas of objects than the baseline approach. In particular, the contributions of this work are the following:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 495, + 289, + 714 + ], + "type": "list", + "angle": 0, + "index": 5, + "blocks": [ + { + "bbox": [ + 46, + 495, + 289, + 578 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 289, + 578 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 289, + 578 + ], + "type": "text", + "content": "- We propose MultiANDA, an approximate Bayesian inference method to realize transfer-based adversarial attacks. We learn the perturbation distribution instead of finding a specific adversary for each input example. Thus, a good approximation of the true perturbation posterior boosts the generalization (i.e., transferability) of the generated adversarial examples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 580, + 289, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 289, + 700 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 289, + 700 + ], + "type": "text", + "content": "- We devise a stochastic adversarial attacking process instead of the original deterministic one initialized from one input by random image translations. In this way, we profit the asymptotic normality of SGA for a better perturbation distribution learning. Adopting the deep ensemble strategy, an effective mechanism for approximating Bayesian marginalization [47], MultiANDA accurately and efficiently estimate the posterior distribution over the perturbations by using the geometry information along the attacking trajectory." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 288, + 714 + ], + "type": "text", + "content": "- The learned distributions of perturbation allow draw" + } + ] + } + ], + "index": 4 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 144 + ], + "type": "text", + "content": "ing an unlimited number of adversarial examples for one input. We experimentally validate that the sampled adversaries have comparably high attack success rates with the singly generated ones, even on the defense models. This result demonstrates the great potential of our method for designing defense strategies grounded in adversarial training." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 144, + 545, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 144, + 545, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 144, + 545, + 240 + ], + "type": "text", + "content": "- Extensive experiment results show that the proposed method outperforms ten state-of-the-art black-box attacks on deep learning models with or without advanced defenses. Significantly, MultiANDA is more advantageous when attacking the advanced defense models. Thus, ANDA and MultiANDA are expected to benchmark new defense methods in the future. Our code is available at https://github.com/CLIAgroup/ANDA." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 251, + 487, + 264 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 251, + 487, + 264 + ], + "spans": [ + { + "bbox": [ + 305, + 251, + 487, + 264 + ], + "type": "text", + "content": "2. Related Work and Preliminaries" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 272, + 545, + 308 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 272, + 545, + 308 + ], + "spans": [ + { + "bbox": [ + 304, + 272, + 545, + 308 + ], + "type": "text", + "content": "Our study mainly focuses on the black-box and transfer-based threat model, as they may bring more security and safety risks due to their practical applicability [8, 34]." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 316, + 474, + 328 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 316, + 474, + 328 + ], + "spans": [ + { + "bbox": [ + 305, + 316, + 474, + 328 + ], + "type": "text", + "content": "2.1. Black-Box Adversarial Attacks" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "text", + "content": "Essentially, the adversarial attack algorithms intend to maximize the loss function " + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\mathcal{L}(\\cdot)" + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "text", + "content": ", e.g., the cross entropy loss for classification tasks, to search for the adversaries " + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "inline_equation", + "content": "x_{adv}" + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "text", + "content": " [14, 39], with the constraints of " + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "inline_equation", + "content": "l_{\\infty}" + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "text", + "content": " norm bound " + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 335, + 545, + 395 + ], + "type": "text", + "content": ", as shown in (1):" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 340, + 405, + 545, + 423 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 340, + 405, + 545, + 423 + ], + "spans": [ + { + "bbox": [ + 340, + 405, + 545, + 423 + ], + "type": "interline_equation", + "content": "\\max _ {x _ {a d v}} \\mathcal {L} (x _ {a d v}, y) \\quad \\text {s . t .} | | x _ {a d v} - x | | _ {\\infty} \\leq \\varepsilon , \\tag {1}", + "image_path": "fdd56b9ac166bfaad41847d7003638dc13160941df8f59d97d06a4ed4542f773.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "spans": [ + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "inline_equation", + "content": "x_{adv}" + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 304, + 431, + 545, + 455 + ], + "type": "text", + "content": " are the legitimate input, the adversarial example and the true label, respectively." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 456, + 545, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 515 + ], + "type": "text", + "content": "Among prior work, the fast gradient sign method (FGSM) [14] and its iterative version, the basic iterative method (BIM) [20] resort to linearizing the non-concave loss function and realize the attack with one-step update or iterative updates, as shown in (2):" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 332, + 524, + 545, + 555 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 332, + 524, + 545, + 555 + ], + "spans": [ + { + "bbox": [ + 332, + 524, + 545, + 555 + ], + "type": "interline_equation", + "content": "x _ {a d v} ^ {(t + 1)} = \\Phi (x _ {a d v} ^ {(t)} + \\alpha \\cdot \\operatorname {s i g n} (\\underbrace {\\nabla_ {x} \\mathcal {L} (x _ {a d v} ^ {(t)} , y)})), \\quad (2)", + "image_path": "88e7c499d9d231df23e053aa9a46662df98d0ff35148f527fb0851bfb7a4f1cf.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "inline_equation", + "content": "x_{adv}^{(t + 1)}" + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\delta^{(t)}" + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": " are the adversarial example and perturbation at the " + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": "-th step, " + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "inline_equation", + "content": "x_{adv}^{(0)}" + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": " is the legitimate input, and " + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\Phi (\\cdot)" + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": " is the projection function on the " + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 304, + 565, + 545, + 605 + ], + "type": "text", + "content": "-ball." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 605, + 545, + 714 + ], + "type": "text", + "content": "These attacks are more effective under white-box scenarios, whereas they tend to overfit the model parameters and hardly transfer to unknown architectures [21]. Thus, many works have been proposed to improve the transferability of adversarial examples, which can be divided into three categories. The first group focuses on the iterative optimizing process by considering momentum [8], Nesterov accelerated gradient [25], and variance reducing [45] to search for the optimal solutions. The second group attempts to attack" + } + ] + } + ], + "index": 17 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24842" + } + ] + } + ], + "index": 18 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 95 + ], + "type": "text", + "content": "the mid-layers by disrupting the critical object-aware features [12, 16, 31, 46, 52]" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 97, + 286, + 204 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 97, + 286, + 204 + ], + "spans": [ + { + "bbox": [ + 46, + 97, + 286, + 204 + ], + "type": "text", + "content": "Moreover, the third stream of methods adopt the commonly used generalization techniques by introducing diversity. These techniques encompass data augmentation [15, 19], such as resize and padding [49], translation [9]; and other integrated augmentation strategies, including combining multiple linear transformations [4], modifying the pixel values with multiple scales [25], integrating more information from other images [7], and using the sum of the gradients from intensity augmented images [17]." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "spans": [ + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "text", + "content": "Similar to our study, existing attack approaches also try to determine the explicit adversarial distributions. PGD [29] resolves the inner maximization problem by the random restart strategy. However, the uniformly drawn samples tend to lie densely around the natural image [10]. Li et al. [23] propose " + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "text", + "content": " attack to define and learn an adversarial distribution. However, their work is under a query-based threat model, i.e., it has to access the output scores for each input from the black-box defense model, which weakens its scalability in real-world applications. Additionally, Dong et al. [10] propose to formulate the adversarial perturbations via a learned distribution for adversarial distributional training (ADT). Similar to " + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "inline_equation", + "content": "\\mathcal{N}" + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "text", + "content": " attack, ADT crafts the adversarial examples centered with the natural input " + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "text", + "content": ", which may fail in generating adversarial examples once the input is a little bit far away from the boundary. Conversely, ANDA generates adversaries around the optimal " + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "inline_equation", + "content": "x_{adv}^{*}" + }, + { + "bbox": [ + 46, + 205, + 287, + 515 + ], + "type": "text", + "content": ". In this case, the adversaries are more prone to successful attacks. From the facets of implementation, ADT focuses on learning a distribution from a large amount of training data for adversarial training. Our proposed method tries to collect the trajectory information during the optimization process for each natural input. Thus, these crucial differences make two approaches suitable for distinct tasks: inner maximization problem for adversarial training (ADT) and transfer-based black-box attack (ANDA and MultiANDA)." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 526, + 211, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 526, + 211, + 540 + ], + "spans": [ + { + "bbox": [ + 47, + 526, + 211, + 540 + ], + "type": "text", + "content": "2.2. Asymptotic Normality of SGD" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 545, + 286, + 713 + ], + "type": "text", + "content": "Maddox et al. [28] point out that the trajectory of stochastic gradient descent (SGD) can be regarded as the Bayesian posterior distribution over the random variables to be optimized, e.g., the model parameters in the case of the DNN training. Following this theory, they propose a Gaussian posterior approximation method (SWAG) based on the first two moments of SGD iterations for model calibration or uncertainty quantification. In the prior work, Mandt et al. [30] provide a more detailed analysis of the stationary distribution of SGD iterations with a constant learning rate, also termed the asymptotic normality of SGD [44]. Such analysis can be traced back to the work by Ruppert [36], Polyak and Juditsky [35] known as Polyak-Ruppert averaging, and still an active research subject for SGD [5]. Furthermore," + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 192 + ], + "type": "text", + "content": "inspired by deep ensembles [22], Wilson and Izmailov [47] carried out an extensive empirical study, demonstrating that applying SWAG only with multiple randomly initialized models can significantly improve the model performance. They emphasize that this benefits from the multimodal effects of the mixture Gaussian distributions and, in turn, boosts the contribution of each additional sample in the optimization procedure. In this paper, we adopt these theories to innovatively model the posterior distribution of perturbations to search for potent adversarial examples." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 206, + 411, + 220 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 206, + 411, + 220 + ], + "spans": [ + { + "bbox": [ + 305, + 206, + 411, + 220 + ], + "type": "text", + "content": "3. Proposed Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 227, + 545, + 395 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 227, + 545, + 395 + ], + "spans": [ + { + "bbox": [ + 304, + 227, + 545, + 395 + ], + "type": "text", + "content": "Drawing on the comprehensive research previously discussed, we hypothesize that utilizing the asymptotic normality of SGD (SGA in our problem formulation) to marginalize an approximate Bayesian posterior could enhance generalization (transferability in our context) beyond what is achievable with a fixed set of parameter (one specific adversarial perturbation). However, optimizing the objective (1) using attack algorithms such as BIM (2) is a deterministic gradient ascent process. In this process, no gradient noise is introduced to form a stationary distribution of SGD. Thus, to bridge this gap, we exploit random data augmentation in the standard optimization process, devising a novel attack method for accurately and efficiently estimating the posterior distribution over perturbations." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 396, + 545, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 396, + 545, + 491 + ], + "spans": [ + { + "bbox": [ + 304, + 396, + 545, + 491 + ], + "type": "text", + "content": "In Section 3.1, we first empirically analyze the asymptotically normal distribution property in the stochastic adversarial attack process, then proceed to formalize the optimization objective for the task of adversarial example generation. Finally, inspired by the advantageous properties of SGD and the effective multimodal inference of the ensemble strategy, we introduce the new attack methods ANDA and MultiANDA in Sections 3.2 and 3.3, respectively." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 305, + 502, + 520, + 515 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 502, + 520, + 515 + ], + "spans": [ + { + "bbox": [ + 305, + 502, + 520, + 515 + ], + "type": "text", + "content": "3.1. Asymptotic Normality of Stochastic BIM" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 522, + 545, + 713 + ], + "type": "text", + "content": "Under specific conditions—decaying learning rates, smooth gradients, and a full rank stationary distribution—it has been theoretically established that SGD asymptotically converges to a Gaussian distribution centered at the local optimum [3, 5, 28]. Expanding on this, Mandt et al. [30] demonstrated that under certain assumptions, SGD with a constant and sufficiently small learning rate in its final search phase, i.e., when updates are proximal to the local optimum, converges to a stationary distribution. This convergence implies that iterations during this phase can approximate the posterior distribution of the optimized variables. Crucially, the gradient noise, introduced by the randomness of the sampled training batches, is instrumental in forming this distribution, provided the learning rate is adequately small [28]. These theoretical underpinnings motivate our approach in the algorithm design." + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24843" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 72, + 286, + 134 + ], + "blocks": [ + { + "bbox": [ + 51, + 72, + 286, + 134 + ], + "lines": [ + { + "bbox": [ + 51, + 72, + 286, + 134 + ], + "spans": [ + { + "bbox": [ + 51, + 72, + 286, + 134 + ], + "type": "image", + "image_path": "44c3e6dc25cf12378b8ba55c4c682c790db4f22a8504cda03cc6d65757437d10.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 143, + 135, + 189, + 142 + ], + "lines": [ + { + "bbox": [ + 143, + 135, + 189, + 142 + ], + "spans": [ + { + "bbox": [ + 143, + 135, + 189, + 142 + ], + "type": "text", + "content": "a. Stochastic BIM" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 51, + 144, + 285, + 205 + ], + "blocks": [ + { + "bbox": [ + 51, + 144, + 285, + 205 + ], + "lines": [ + { + "bbox": [ + 51, + 144, + 285, + 205 + ], + "spans": [ + { + "bbox": [ + 51, + 144, + 285, + 205 + ], + "type": "image", + "image_path": "66491600190cf1b1e4e3176e435b39afae2394344c086b39326269500bf70928.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 135, + 205, + 199, + 212 + ], + "lines": [ + { + "bbox": [ + 135, + 205, + 199, + 212 + ], + "spans": [ + { + "bbox": [ + 135, + 205, + 199, + 212 + ], + "type": "text", + "content": "b. ANDA implementation" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 220, + 288, + 255 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 288, + 255 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 288, + 255 + ], + "type": "text", + "content": "Figure 2. Asymptotically normal distribution examples with iterative trajectories of adversarial perturbations generated by stochastic BIM (a) and the proposed approach (b)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 274, + 287, + 357 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 274, + 287, + 357 + ], + "spans": [ + { + "bbox": [ + 46, + 274, + 287, + 357 + ], + "type": "text", + "content": "As demonstrated in (2), the optimization process, beginning from a specific input, is a deterministic gradient ascent, differing from a standard SGA approach. Therefore, we introduce stochastic gradient noises to emulate Gaussian limiting distributions by integrating a random data augmentation technique AUG, like image translation used in our experiments, at each iterative step:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 55, + 365, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 55, + 365, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 55, + 365, + 287, + 396 + ], + "type": "interline_equation", + "content": "x _ {a d v} ^ {(t + 1)} = \\Phi (x _ {a d v} ^ {(t)} + \\alpha \\cdot \\operatorname {s i g n} (\\underbrace {\\nabla_ {x} \\mathcal {L} (\\mathrm {A U G} (x _ {a d v} ^ {(t)} , y))} _ {\\delta^ {(t)}})). \\tag {3}", + "image_path": "a186032ed9cc7717422a5d0132a8e4f404998978a6d75862c44a2464eb441dce.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": "Notably, a small constant learning rate schedule " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "(\\alpha = \\epsilon / T)" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": " is commonly adopted, where " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\epsilon \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": " is a sufficiently small number used to restrict the " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": "-norm for creating invisible adversarial perturbations, and " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": " is the number of iterative steps. Hence, we speculate the devised stochastic BIM shown in (3) can be used as an approximate Bayesian inference algorithm. In particular, Mandt et al. [30] assume that the gradients along the optimizing trajectory follow the Gaussian distribution stemming from the central limit theorem. We visualized the adversarial perturbations " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "\\delta^{(t)}" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": "—the loss gradients in our task—using the t-SNE technique [43] to examine their distribution. 300 iterative steps for 3 randomly-drawn ImageNet [37] images shown in Fig. 2 a illustrates the Gaussian-shaped distributions which underpins our conjecture of the asymptotically normality of stochastic BIM algorithm. We notice the obvious increased gradient noise along the optimizing trajectory, which may due to the use of the sign() function and projection operations. Nevertheless, this does not affect the convergence of perturbations. Importantly, the first 10 steps converging with tight covariance justifies another speculation that the small value of " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": " (often " + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "inline_equation", + "content": "= 10" + }, + { + "bbox": [ + 46, + 403, + 288, + 713 + ], + "type": "text", + "content": " for non-targeted attacks) and the non-trivial first step in our task (e.g., referring to strong attack performance of FGSM) indicate that the early iterates of are fairly close to the local optimum (i.e., the final search phase discussed above)." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "text", + "content": "Inspired by the results of this empirical study, we propose employing " + }, + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "text", + "content": " image transformations " + }, + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "inline_equation", + "content": "\\mathsf{AUG}_i(\\cdot)" + }, + { + "bbox": [ + 305, + 72, + 545, + 131 + ], + "type": "text", + "content": " to form a minibatch for an adversarial attack, thereby further enhancing stochasticity. Then, the optimization objective is formulated as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 312, + 140, + 545, + 170 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 140, + 545, + 170 + ], + "spans": [ + { + "bbox": [ + 312, + 140, + 545, + 170 + ], + "type": "interline_equation", + "content": "\\max _ {x _ {a d v}} \\sum_ {i = 1} ^ {n} \\mathcal {L} (\\mathrm {A U G} _ {i} (x _ {a d v}), y) \\quad \\text {s . t .} \\| x _ {a d v} - x \\| _ {\\infty} \\leq \\varepsilon . \\tag {4}", + "image_path": "236c9165cd8f8588953e62ea39ed6cd8bc6b97a09b1103cb997bdfaca6e5b0a6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "type": "text", + "content": "Furthermore, optimizing (4) to craft just one optimal adversarial example does not sufficiently explore the high-dimensional potential perturbation space. To further improve the transferability of adversarial examples to unknown architectures, we propose to explicitly model the adversarial perturbation " + }, + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "type": "inline_equation", + "content": "(\\delta)" + }, + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "type": "text", + "content": " via a distribution " + }, + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "type": "inline_equation", + "content": "(\\Pi_{\\delta})" + }, + { + "bbox": [ + 305, + 178, + 545, + 262 + ], + "type": "text", + "content": ". Thus, our optimization objective is formalized as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 315, + 272, + 545, + 303 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 315, + 272, + 545, + 303 + ], + "spans": [ + { + "bbox": [ + 315, + 272, + 545, + 303 + ], + "type": "interline_equation", + "content": "\\max _ {\\Pi_ {\\delta}} \\mathbb {E} _ {\\delta \\sim \\Pi_ {\\delta}} \\sum_ {i = 1} ^ {n} \\mathcal {L} (\\mathrm {A U G} _ {i} (x + \\delta), y), \\text {s . t .} \\| \\delta \\| _ {\\infty} \\leq \\varepsilon. \\tag {5}", + "image_path": "5f1bfeb86303ca86a952f04ed8cb4bcb1730a9b299f2370a392159d738134460.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 312, + 545, + 372 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 312, + 545, + 372 + ], + "spans": [ + { + "bbox": [ + 305, + 312, + 545, + 372 + ], + "type": "text", + "content": "Objective (5) aims to maximize the expected loss over the adversarial perturbation distribution. It is noteworthy that (5) is a generalized version of (4) and is expected to characterize sufficient information about perturbations for transferable adversarial example generation." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 380, + 531, + 392 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 380, + 531, + 392 + ], + "spans": [ + { + "bbox": [ + 306, + 380, + 531, + 392 + ], + "type": "text", + "content": "3.2. Asymptotically Normal Distribution Attack" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "text", + "content": "To better solve the optimization problem formulated in (5), we take advantage of the asymptotically normality of SGA and iteratively search for the adversarial examples similarly to (2). We omit the projection function " + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\Phi(\\cdot)" + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\mathrm{sign}(\\cdot)" + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "text", + "content": " because they do not effect the asymptotic normality of SGA as discussed in the previous subsection. Then, we calculate the gradient of the adversary with each transformation and denote it as the augmentation-aware perturbation " + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\delta_i^{(t)}" + }, + { + "bbox": [ + 305, + 398, + 545, + 496 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 361, + 505, + 545, + 521 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 361, + 505, + 545, + 521 + ], + "spans": [ + { + "bbox": [ + 361, + 505, + 545, + 521 + ], + "type": "interline_equation", + "content": "\\delta_ {i} ^ {(t)} = \\nabla_ {x ^ {(t)}} \\mathcal {L} \\left(\\underset {\\text {A U G} _ {i}} {\\mathrm {A U G}} \\left(x _ {a d v} ^ {(t)}\\right), y\\right). \\tag {6}", + "image_path": "c700afd82ee94666c4b6fbb0666223d323fa983bc145a896b0b0f4abb4729dcb.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": " be a set of samples augmented in each iteration, i.e., " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "S = \\{\\mathrm{AUG}_i(x_{adv}^{(t)})\\}_{i=1}^n" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": ". Here " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": " can be taken as a minibatch to form a stochastic gradient " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\hat{\\delta}_S" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": " which is a sum of contributions from all samples in " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": ". Hence, referring to the central limit theorem, " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\hat{\\delta}_S" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": " can be taken as a function of sample " + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "inline_equation", + "content": "z \\in S" + }, + { + "bbox": [ + 305, + 530, + 545, + 605 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 367, + 614, + 545, + 639 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 367, + 614, + 545, + 639 + ], + "spans": [ + { + "bbox": [ + 367, + 614, + 545, + 639 + ], + "type": "interline_equation", + "content": "\\hat {\\delta} _ {S} (z) \\approx \\delta (z) + \\frac {1}{\\sqrt {n}} \\Delta \\delta (z), \\tag {7}", + "image_path": "ce714e31b44f2dd58b2371d6eabbc237102216b0d45cb1fea1ec5683538e1dd1.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "type": "text", + "content": "where the gradient noises " + }, + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "type": "inline_equation", + "content": "\\Delta \\delta (z)" + }, + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "type": "text", + "content": " at each update can be conveniently assumed following a Gaussian distribution with covariance " + }, + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "type": "inline_equation", + "content": "C(z)" + }, + { + "bbox": [ + 305, + 648, + 545, + 685 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 313, + 693, + 545, + 717 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 693, + 545, + 717 + ], + "spans": [ + { + "bbox": [ + 313, + 693, + 545, + 717 + ], + "type": "interline_equation", + "content": "\\Delta \\delta (z) \\sim \\mathcal {N} (0, C (z)), \\quad \\hat {\\delta} _ {S} (z) \\sim \\mathcal {N} (\\delta (z), \\frac {1}{n} C (z)). \\tag {8}", + "image_path": "dcb2c1128bab0e79222ed9834f33c007fb88c582be94e2a32220fee57eadd474.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24844" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 53, + 76, + 260, + 98 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 76, + 260, + 98 + ], + "spans": [ + { + "bbox": [ + 53, + 76, + 260, + 98 + ], + "type": "text", + "content": "Algorithm 1: Asymptotically Normal Distribution Attack (ANDA)" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 102, + 265, + 151 + ], + "type": "list", + "angle": 0, + "index": 3, + "blocks": [ + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "spans": [ + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "text", + "content": "Input: " + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "text", + "content": ": clean image " + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "inline_equation", + "content": "x \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "text", + "content": "; " + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "text", + "content": ": ground-truth label; " + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 59, + 102, + 265, + 121 + ], + "type": "text", + "content": ": pre-trained source model;" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "spans": [ + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "text", + "content": "Parameters: " + }, + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "text", + "content": ": # iterations; " + }, + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "text", + "content": ": perturbation magnitude; " + }, + { + "bbox": [ + 59, + 123, + 265, + 151 + ], + "type": "inline_equation", + 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+ "type": "text", + "content": " to " + }, + { + "bbox": [ + 64, + 174, + 157, + 182 + ], + "type": "inline_equation", + "content": "T - 1" + }, + { + "bbox": [ + 64, + 174, + 157, + 182 + ], + "type": "text", + "content": " do" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 64, + 182, + 294, + 201 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 182, + 294, + 201 + ], + "spans": [ + { + "bbox": [ + 64, + 182, + 294, + 201 + ], + "type": "text", + "content": "3: Calculate the mean of gradients and store the deviation of gradients throughout previous " + }, + { + "bbox": [ + 64, + 182, + 294, + 201 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 64, + 182, + 294, + 201 + ], + "type": "text", + "content": " iterations:" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 104, + 209, + 279, + 223 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 209, + 279, + 223 + ], + "spans": [ + { + "bbox": [ + 104, + 209, + 279, + 223 + ], + "type": "interline_equation", + "content": "\\delta_ {i} ^ {(t)} = \\nabla_ {x ^ {(t)}} J (f (\\mathrm {A U G} _ {i} (x ^ {(t)})), y), i = 1, \\dots , n", + "image_path": "d70d0e250b0b88e79a2ad40b6a6f785d862cd5f735d87f789ad0ebafd9ac13e3.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 236, + 256, + 261 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 236, + 256, + 261 + ], + "spans": [ + { + "bbox": [ + 126, + 236, + 256, + 261 + ], + "type": "interline_equation", + "content": "\\bar {\\delta} ^ {(t + 1)} = \\frac {(t \\times n) \\bar {\\delta} ^ {(t)} + \\sum_ {i = 1} ^ {n} \\delta_ {i} ^ {(t)}}{(t + 1) \\times n}", + "image_path": "85d800ade349bcab3ded1902c4eaebc6ea26503445102c5764b72df16cc3d6c4.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 99, + 274, + 285, + 288 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 99, 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\\operatorname {C l i p} _ {x, e} \\left\\{x ^ {(t)} + \\alpha \\cdot \\operatorname {S i g n} (\\bar {\\delta} ^ {(t + 1)}) \\right\\}", + "image_path": "d12e0e3dc54a860eeb2288fab115b1f1180ba3b44c410c431f8e771d458a1919.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 64, + 341, + 105, + 350 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 341, + 105, + 350 + ], + "spans": [ + { + "bbox": [ + 64, + 341, + 105, + 350 + ], + "type": "text", + "content": "5: end for" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 64, + 350, + 198, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 64, + 350, + 198, + 361 + ], + "spans": [ + { + "bbox": [ + 64, + 350, + 198, + 361 + ], + "type": "text", + "content": "6: Output option (a): Craft one " + }, + { + "bbox": [ + 64, + 350, + 198, + 361 + ], + "type": "inline_equation", + "content": "x_{adv}" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 161, + 365, + 210, + 378 + ], + 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+ } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 126, + 410, + 246, + 421 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 126, + 410, + 246, + 421 + ], + "spans": [ + { + "bbox": [ + 126, + 410, + 246, + 421 + ], + "type": "interline_equation", + "content": "C = \\text {N U M S} _ {-} \\operatorname {C O L S} (\\mathbf {D}) = n \\times T", + "image_path": "9402081f4608dae78d6875d256741bc1bffbccd9f705427cc03a41f40abfba14.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 127, + 424, + 219, + 447 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 424, + 219, + 447 + ], + "spans": [ + { + "bbox": [ + 127, + 424, + 219, + 447 + ], + "type": "interline_equation", + "content": "\\bar {\\delta} = \\bar {\\delta} ^ {(T)}, \\quad \\sigma = \\frac {\\mathbf {D} \\mathbf {D} ^ {T}}{C - 1}", + "image_path": "a2465783252c1b20dba067c40c620d18658a848cffd3c6f7593e3c868df56464.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 74, + 449, + 187, + 460 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 74, + 449, + 187, + 460 + ], + "spans": [ + { + "bbox": [ + 74, + 449, + 187, + 460 + ], + "type": "text", + "content": "Generate adversarial examples" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 80, + 465, + 168, + 480 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 465, + 168, + 480 + ], + "spans": [ + { + "bbox": [ + 80, + 465, + 168, + 480 + ], + "type": "interline_equation", + "content": "\\{\\delta_ {m} \\} _ {m = 1} ^ {M} \\sim \\mathcal {N} (\\bar {\\delta}, \\sigma),", + "image_path": "0168c8b6d7b2904ff97b0c386c5fab1a7683adc0d47cd23f014191e58a67ce51.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 81, + 481, + 292, + 496 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 81, + 481, + 292, + 496 + ], + "spans": [ + { + "bbox": [ + 81, + 481, + 292, + 496 + ], + "type": "interline_equation", + "content": "\\left\\{x _ {a d v} ^ {m} \\right\\} _ {m = 1} ^ {M} = \\left\\{\\operatorname {C l i p} _ {x, \\epsilon} \\left\\{x ^ {(T - 1)} + \\alpha \\cdot \\operatorname {S i g n} \\left(\\delta_ {m}\\right) \\right\\} \\right\\} _ {m = 1} ^ {M}", + "image_path": "cc8fd56bb821a684c8801e668949bce1a61125b0165921fe16fa15c9e6096522.jpg" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 538, + 287, + 670 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 538, + 287, + 670 + ], + "spans": [ + { + "bbox": [ + 46, + 538, + 287, + 670 + ], + "type": "text", + "content": "In this case, the expectation of the stochastic gradient is the full gradient, i.e., " + }, + { + "bbox": [ + 46, + 538, + 287, + 670 + ], + "type": "inline_equation", + "content": "\\delta (z) = \\mathbb{E}[\\hat{\\delta}_S(z)]" + }, + { + "bbox": [ + 46, + 538, + 287, + 670 + ], + "type": "text", + "content": ". Hence, the prior distribution over adversarial perturbations is naturally a Gaussian one at each iteration. Benefiting from the asymptotic normality of SGD [30], we propose a novel method to approximate the posterior distribution of perturbations. Our main idea is to estimate the mean and covariance matrix of the stationary distribution of stochastic gradient ascent during the optimizing procedure. The iterative averaging is adopted to approximate the mean of adversarial perturbations using the sequence of stochastic gradients" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 94, + 687, + 287, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 94, + 687, + 287, + 716 + ], + "spans": [ + { + "bbox": [ + 94, + 687, + 287, + 716 + ], + "type": "interline_equation", + "content": "\\bar {\\delta} ^ {(t + 1)} = \\frac {(t \\times n) \\bar {\\delta} ^ {(t)} + \\sum_ {i = 1} ^ {n} \\delta_ {i} ^ {(t)}}{(t + 1) \\times n}. \\tag {9}", + "image_path": "13b63a9392ba67a7fffa9c356876c027c0e832116173914deacb1a306dbe26ee.jpg" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "content": "Then, " + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "inline_equation", + "content": "\\bar{\\delta} = \\bar{\\delta}^{(T)}" + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "content": " is the augmented samples in the " + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "content": "-th iteration (" + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "inline_equation", + "content": "t = 0, \\dots, T - 1" + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "content": ") and " + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 305, + 71, + 545, + 95 + ], + "type": "text", + "content": " is the total iterations." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "spans": [ + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "content": "Let " + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "content": " be the deviation matrix with column " + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "inline_equation", + "content": "\\mathbf{D}_j = \\delta_i^{(t)} - \\bar{\\delta}^{(t + 1)}" + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "inline_equation", + "content": "j = t\\times n + i" + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "inline_equation", + "content": "i = 1,\\dots ,n" + }, + { + "bbox": [ + 305, + 96, + 545, + 146 + ], + "type": "text", + "content": ". Thus, the covariance matrix of the posterior distribution is estimated by considering all stochastic gradients in iterative processing," + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 390, + 154, + 545, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 390, + 154, + 545, + 179 + ], + "spans": [ + { + "bbox": [ + 390, + 154, + 545, + 179 + ], + "type": "interline_equation", + "content": "\\sigma = \\frac {\\mathbf {D} \\mathbf {D} ^ {T}}{n \\times T - 1}. \\tag {10}", + "image_path": "a2d321ca317f87fdd9391dcc4f55ac83ad1c1b367845d852340a537dd7e7ceed.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "spans": [ + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "type": "text", + "content": "Finally, the adversarial example can be iteratively obtained by (3). Note that, ANDA allows to craft one or an unlimited number of adversarial examples for one input by sampling perturbations from the estimated distribution " + }, + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\bar{\\delta},\\sigma)" + }, + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "type": "text", + "content": ". The complete procedure for the proposed ANDA method is shown in Algorithm 1. Following the empirical study in Section 3.1, we visualized the perturbations " + }, + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "type": "inline_equation", + "content": "\\delta_i^{(t)}" + }, + { + "bbox": [ + 304, + 187, + 545, + 297 + ], + "type": "text", + "content": " of 10 iterates with multiple data augmentations (shown in Fig. 2 b), which validate our previous hypothesis." + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 304, + 495, + 317 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 304, + 495, + 317 + ], + "spans": [ + { + "bbox": [ + 305, + 304, + 495, + 317 + ], + "type": "text", + "content": "3.3. Multiple Implementations of ANDA" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "content": "With the proposed ANDA, we find a solution to approximating the true posterior distribution centered at the the optimal " + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "inline_equation", + "content": "x_{adv}^{*}" + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "content": " for the maximization problem introduced in (2). Nevertheless, only exploring the unimodal optimization space largely limits the diversity of generated adversarial examples. Profiting the excellent generalization capability of Bayesian marginalization approximated with the deep ensemble strategy, we propose MultiANDA via multiple (e.g., K times) repeats of ANDA by add random initial values on origin sample " + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "content": ". Especially, we average the adversarial perturbation " + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\bar{\\delta}_k" + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "content": " from each ANDA process, and obtain " + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\bar{\\delta}_{mean} = \\frac{1}{K}\\sum_{k=0}^{K-1}\\bar{\\delta}_k" + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "content": ". This realizes the multimodal marginalization of this Gaussian mixture distribution. Similarly, adversarial examples can be iteratively obtained by (2). MultiANDA also enables producing infinite adversarial examples with high effectiveness by sampling from each approximated Gaussian distribution " + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\bar{\\delta}_k,\\sigma_k)" + }, + { + "bbox": [ + 304, + 323, + 545, + 550 + ], + "type": "text", + "content": ". Remarkable improvements of the attacking ability, especially on the defense models are shown in Sections 4.2 and 4.3." + } + ] + } + ], + "index": 30 + }, + { + "bbox": [ + 305, + 562, + 387, + 574 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 387, + 574 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 387, + 574 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 31 + }, + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 545, + 713 + ], + "type": "text", + "content": "In this section, we present the results of an extensive empirical study to validate the performance of the proposed methods. We first specify the experimental settings in Section 4.1. Then, the results of ANDA and MultiANDA compared with the state-of-the-art approaches on various types of DNNs with or without defenses are presented in Section 4.2 and 4.3. Section 4.4 shows the attacking effectiveness of the multiple adversarial examples generated from each input via the proposed methods. Due to page limitations, more detailed experiment settings, results and the ablation study are presented in Appendix." + } + ] + } + ], + "index": 32 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24845" + } + ] + } + ], + "index": 33 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 85, + 542, + 358 + ], + "blocks": [ + { + "bbox": [ + 53, + 85, + 542, + 358 + ], + "lines": [ + { + "bbox": [ + 53, + 85, + 542, + 358 + ], + "spans": [ + { + "bbox": [ + 53, + 85, + 542, + 358 + ], + "type": "table", + "html": "
AttackInc-v3Inc-v3 =>ResNet-50 =>
ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM100.0*20.315.715.634.321.533.299.7*63.920.943.440.4
TIM64.3*35.930.625.470.445.347.377.0*47.630.868.854.3
SIM100.0*38.231.135.942.236.948.6100.0*83.735.350.954.6
DIM100.0*31.725.531.445.533.561.999.9*83.647.561.163.5
FIA98.3*78.475.381.283.579.686.299.6*94.580.488.387.4
TAIG99.7*53.345.956.754.252.562.4100.0*86.151.958.764.8
NI-FGSM100.0*40.035.239.956.943.059.699.7*85.448.167.065.0
MI-FGSM100.0*40.235.140.357.143.258.599.7*85.948.667.465.1
VMI-FGSM100.0*63.059.368.670.365.375.399.9*93.468.376.478.4
VNI-FGSM100.0*62.458.767.769.764.675.499.8*92.967.975.678.0
ANDA100.0*76.172.882.377.077.195.6100.0*98.994.089.594.5
MultiANDA100.0*79.276.084.578.879.696.5100.0*99.295.090.195.2
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.Inc-v3ResNet-50ResNet-152IncRes-v2VGG-19Avg.
BIM36.325.620.699.3*37.830.123.518.713.79.999.9*16.5
TIM43.436.532.036.0*66.242.841.534.830.223.6100.0*46.0
SIM58.947.841.499.6*49.849.537.734.425.223.6100.0*30.2
DIM54.641.436.698.2*50.045.731.726.419.216.499.9*23.4
FIA82.275.372.489.2*80.777.757.450.740.942.7100.0*47.9
TAIG73.963.458.495.0*57.463.348.843.634.733.9100.0*40.3
NI-FGSM61.949.544.799.2*64.755.243.639.529.230.499.9*35.7
MI-FGSM60.349.343.098.8*64.654.344.739.428.930.899.9*36.0
VMI-FGSM81.169.666.499.3*73.572.762.756.746.548.6100.0*53.6
VNI-FGSM80.970.065.899.4*73.872.663.256.746.648.8100.0*53.8
ANDA93.086.483.799.8*82.886.574.464.156.461.5100.0*64.1
MultiANDA93.987.185.699.8*84.387.775.466.158.663.5100.0*65.9
", + "image_path": "7806891fb793441aaeaa90e92998f13ef28916d175fb2ea9b54d3f4b318bec3e.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 367, + 547, + 401 + ], + "lines": [ + { + "bbox": [ + 46, + 367, + 547, + 401 + ], + "spans": [ + { + "bbox": [ + 46, + 367, + 547, + 401 + ], + "type": "text", + "content": "Table 1. The success rates " + }, + { + "bbox": [ + 46, + 367, + 547, + 401 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 367, + 547, + 401 + ], + "type": "text", + "content": " of the proposed and baseline attacks on five normally trained models. Sign \\* indicates the results on white-box source models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 47, + 421, + 164, + 434 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 421, + 164, + 434 + ], + "spans": [ + { + "bbox": [ + 47, + 421, + 164, + 434 + ], + "type": "text", + "content": "4.1. Experimental Setup" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 441, + 288, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 441, + 288, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 441, + 288, + 466 + ], + "type": "text", + "content": "The datasets, models, and baseline methods employed in our experiments are detailed below." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 517 + ], + "type": "text", + "content": "Datasets: Following the prior work [8, 13, 46], we implemented our experiments on ImageNet1k dataset [33] containing 1000 images, which are randomly drawn from the ImageNet dataset [37]." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 519, + 288, + 699 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 519, + 288, + 699 + ], + "spans": [ + { + "bbox": [ + 46, + 519, + 288, + 699 + ], + "type": "text", + "content": "Models: We considered two categories of target models for evaluation: seven normally trained models and seven advanced defense models. The first category includes Inception-v3 (Inc-v3) [40], Resnet-v2-50 (ResNet-50), Resnet-v2-101 (ResNet-101), Resnet-v2-152 (ResNet-152) [15], Inception-v4 (Inc-v4), Inception-ResNet-v2 (IncRes-v2) [41] and VGG-19 [38], where Inc-v3, ResNet-50, IncRes-v2 and VGG-19 are also used as the white-box source models to generate adversarial examples. The defense models contain three adversarially trained models: Inc-v3ens3, Inc-v3ens4 and IncRes-v2ens [42]; the High-level representation Guided Denoiser (HGD) [24]; the Neural Representation Purifier (NRP) [32]; the Randomized Smoothing (RS) [6]; and the 'Rand-3' submission in the NIPS 2017 defense competition (NIPS-r3)." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 701, + 287, + 712 + ], + "type": "text", + "content": "Baselines: Three streams of transfer-based attack meth" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 421, + 547, + 555 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 421, + 547, + 555 + ], + "spans": [ + { + "bbox": [ + 304, + 421, + 547, + 555 + ], + "type": "text", + "content": "ods are used as baseline methods. The first stream focuses on the data augmentations including DIM [49], TIM [9], SIM [45] and a recent work Transferable Attack based on Integrated Gradients (TAIG) [17]. For the second group, we choose the feature importance-aware (FIA)[46], which considers the middle-layer information of the source model and achieves the competitive performance. The last stream focuses on the optimization enhanced methods, including BIM [20], its accelerated version: MI-FGSM [8], NIFGSM [25], and the approaches using variance reduction strategy, VMI-FGSM, VNI-FGSM [45]." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 562, + 484, + 575 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 562, + 484, + 575 + ], + "spans": [ + { + "bbox": [ + 305, + 562, + 484, + 575 + ], + "type": "text", + "content": "4.2. Attack Normally Trained Models" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 547, + 715 + ], + "type": "text", + "content": "We cross-validated our method by generating and testing the adversarial examples on the selected source (on rows) and target (on columns) networks (shown in Table 1). To be a fair comparison, our proposed methods generated one adversarial example for each input, aligned with the first output option of Algorithm 1, in the following experiments if not specified. From the Table 1, we observe that ANDA and MultiANDA significantly outperforms other methods in almost all cases, no matter in white-box or black-box settings. As the numerical results demonstrate, they consistently defeat all other methods when taking IncRes-v2," + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "24846" + } + ] + } + ], + "index": 10 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 108 + ], + "type": "text", + "content": "ResNet-50 and VGG-19 as source models, and for Inc-v3, ANDA is competitive with the current SOTA methods, and MultiANDA always keep higher success rate." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 108, + 288, + 312 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 108, + 288, + 312 + ], + "spans": [ + { + "bbox": [ + 46, + 108, + 288, + 312 + ], + "type": "text", + "content": "We further investigated the adversarial examples generated with ResNet-50, shown in Figure 3. The other six models were used as black-box targets for evaluating the performance of these examples. A higher number of successfully deceived target models implies more capable adversaries and therefore stronger attacks. The rightmost bars show that ANDA, MultiANDA generated 840, 863/1000 adversaries that fooled all six targeted models, respectively, while 517/1000 are for VMI-FGSM. Naturally, the remaining sets of bars for this baseline method are higher, meaning that it deceived fewer targeted models. Moreover, we visualized the generated examples and the perturbations by these three methods (see Figure 1). The results show that the perturbations crafted by ANDA and MultiANDA focus more on the semantic areas of objects than VMI-FGSM, which dominates the decision of the prediction model. More visualization results are provided in Appendix." + } + ] + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 63, + 322, + 272, + 440 + ], + "blocks": [ + { + "bbox": [ + 63, + 322, + 272, + 440 + ], + "lines": [ + { + "bbox": [ + 63, + 322, + 272, + 440 + ], + "spans": [ + { + "bbox": [ + 63, + 322, + 272, + 440 + ], + "type": "image", + "image_path": "b19830786b2310d37a5ab60424bc29314f6767050ab7fead2787ba0dea426979.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "lines": [ + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "spans": [ + { + "bbox": [ + 47, + 452, + 286, + 474 + ], + "type": "text", + "content": "Figure 3. Most examples crafted by our proposed methods successfully deceived all 6 black-box models." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 491, + 178, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 491, + 178, + 503 + ], + "spans": [ + { + "bbox": [ + 47, + 491, + 178, + 503 + ], + "type": "text", + "content": "4.3. Attack Defense Models" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 510, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 510, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 46, + 510, + 286, + 653 + ], + "type": "text", + "content": "We evaluate our proposed method targeting on the selected advanced defenses models. As shown in Table 2, the success rates of our proposed methods consistently improve over these various defense models in most cases. They provide a significant performance increase in general compared with the other attacks, especially reaches the overall optimal success rates with the source model ResNet-50. An intriguing finding is that using ResNet-50 as the source model always yields the best attacking performance. This aligns with the conclusion drawn by Wu et al. [48] that the skip connections in ResNet-like neural networks enhance black-box attack transferability." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": "Notably, the fluctuating performance and the generally reduced effectiveness of all baseline methods can be observed with the source model VGG-19. The average maximum attack success rate in this context is only " + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "inline_equation", + "content": "28.3\\%" + }, + { + "bbox": [ + 46, + 654, + 286, + 713 + ], + "type": "text", + "content": ", suggesting that the feature extraction capabilities of VGG-19" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "are not optimal, thereby leading to diminished transferability for black-box attacks. This observation highlights the critical role of source model selection in maximizing the transferability of adversarial attacks. Hence, the choice of source models and enhancing their capability for generalized feature extraction become promising directions for the future research." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 156, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 252 + ], + "type": "text", + "content": "Similarly, we visualized the generated examples and the perturbations by VMI-FGSM, ANDA and MultiANDA that fool the defense models. The perturbed area by our proposed methods concentrates more on the informative region of images than the baseline method. Details are illustrated in Appendix. These compelling results of ANDA and MultiANDA on defenses valid their overall generalization ability in generating transferable and diverse adversaries." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 308, + 264, + 543, + 399 + ], + "blocks": [ + { + "bbox": [ + 308, + 264, + 543, + 399 + ], + "lines": [ + { + "bbox": [ + 308, + 264, + 543, + 399 + ], + "spans": [ + { + "bbox": [ + 308, + 264, + 543, + 399 + ], + "type": "image", + "image_path": "fef9d131670076b83f8b39917693333ed54814ebd3c9aaeb18d449ef9cdaef6c.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "text", + "content": "Figure 4. Attack success rates of sampled adversaries with single " + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\{\\widetilde{\\delta}\\}" + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "text", + "content": ", multiple " + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\{\\delta_m\\}_{m=1}^{20}" + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "text", + "content": " and the succeeded " + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "inline_equation", + "content": "Suc.\\{\\delta_m\\}_{m=1}^{20}" + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "text", + "content": " generated by ANDA and MultiANDA. " + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\{\\delta_m\\}_{m=1}^{20}" + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "text", + "content": " means the 20 adversarial examples sampled from the learned perturbation distribution for each input image; whereas " + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "inline_equation", + "content": "Suc.\\{\\delta_m\\}_{m=1}^{20}" + }, + { + "bbox": [ + 304, + 415, + 545, + 492 + ], + "type": "text", + "content": " are the 20 sampled adversarial examples for the input image whose corresponding single adversarial example has succeeded in the attack." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 305, + 515, + 537, + 528 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 515, + 537, + 528 + ], + "spans": [ + { + "bbox": [ + 305, + 515, + 537, + 528 + ], + "type": "text", + "content": "4.4. Attack Performance of Sampled Adversaries" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "The analysis presented above shows the effectiveness of the single optimum adversarial example per input generated, denoted as " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{\\delta}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ", referring to Step 6 (a) shown in Algorithm 1. Besides, MultiANDA/ANDA allows learning the distribution of the perturbations " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{N}(\\bar{\\delta},\\sigma)" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " via Step 6 (b), and generate any number of adversarial examples for each input by sampling " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " adversaries, denoted as " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\delta_m\\}_{m = 1}^M" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". To verify the attack performance of these sampled adversaries, we drawn " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "20(M = 20)" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " adversarial examples for each input image, i.e., " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\{\\delta_m\\}_{m = 1}^{20}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". Meanwhile, we analyzed the adversaries sampled for the input images whose corresponding adversaries " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{\\delta}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": " succeeded in the attack, denoted as " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "Suc.\\{\\delta_m\\}_{m = 1}^{20}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": ". Experiment results show in Figure 4 that the sampled adversaries have competitive attack success rates compared with the single adversary generated with " + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\bar{\\delta}" + }, + { + "bbox": [ + 304, + 534, + 545, + 713 + ], + "type": "text", + "content": "," + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "24847" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 76, + 541, + 350 + ], + "blocks": [ + { + "bbox": [ + 53, + 76, + 541, + 350 + ], + "lines": [ + { + "bbox": [ + 53, + 76, + 541, + 350 + ], + "spans": [ + { + "bbox": [ + 53, + 76, + 541, + 350 + ], + "type": "table", + "html": "
AttackInc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.ResNet-50
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.14.63.713.44.87.512.37.17.413.78.19.7
TIM27.521.316.922.821.121.934.027.424.231.130.629.5
SIM18.18.48.615.210.812.221.413.115.216.115.116.2
DIM13.16.75.812.88.69.420.812.016.915.715.316.1
FIA37.421.311.623.529.224.644.427.230.025.935.332.6
TAIG38.023.922.829.628.528.639.230.429.729.634.432.7
MI-FGSM18.39.05.515.712.012.126.315.517.318.020.219.5
NI-FGSM18.68.66.215.312.212.226.215.717.518.919.819.6
VMI-FGSM36.921.219.124.727.725.947.431.337.727.138.736.4
VNI-FGSM36.422.018.925.327.427.146.530.437.427.138.736.4
ANDA44.425.936.523.237.020.371.450.772.432.967.441.6
MultiANDA54.436.752.824.346.929.979.764.882.334.476.350.1
AttackIncRes-v2 =>VGG-19 =>
Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.Inc-v3ens3IncRes-v2ensHGDNRPNIPS-r3Avg.
BIM11.17.05.113.06.08.49.64.43.913.44.67.2
TIM27.921.418.423.923.823.123.027.415.031.130.625.4
SIM23.816.415.918.318.118.511.45.68.713.47.49.3
DIM16.210.111.714.912.313.010.74.75.613.65.98.1
FIA48.934.724.230.842.836.313.38.37.114.69.810.6
TAIG49.041.212.216.513.326.417.710.236.934.141.928.2
MI-FGSM22.013.313.416.417.016.413.06.97.215.58.910.3
NI-FGSM21.613.813.415.516.616.213.96.87.214.69.310.4
VMI-FGSM49.238.836.025.239.237.721.911.615.918.415.916.7
VNI-FGSM49.937.735.425.639.338.421.611.916.818.615.722.9
ANDA63.347.357.828.557.932.620.910.822.215.416.23.7
MultiANDA70.361.969.931.267.841.824.613.731.216.221.37.9
", + "image_path": "ed410254e2f78c753738a240359d8285a6cb3cb3360aa1e5a35a5f6a017f6325.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 358, + 546, + 383 + ], + "lines": [ + { + "bbox": [ + 46, + 358, + 546, + 383 + ], + "spans": [ + { + "bbox": [ + 46, + 358, + 546, + 383 + ], + "type": "text", + "content": "Table 2. The success rates " + }, + { + "bbox": [ + 46, + 358, + 546, + 383 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 358, + 546, + 383 + ], + "type": "text", + "content": " of the proposed and baseline attacks on five defense models. The best/second results are shown in bold/underlined. Due to the space limit, performance on five target models are presented here. See full results on seven targets in Appendix." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 402, + 288, + 451 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 402, + 288, + 451 + ], + "spans": [ + { + "bbox": [ + 46, + 402, + 288, + 451 + ], + "type": "text", + "content": "even on the defense models. This confirms the well approximation of the perturbation distributions and the great potential of our method for adversarial training or defense model designing." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 464, + 212, + 479 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 464, + 212, + 479 + ], + "spans": [ + { + "bbox": [ + 47, + 464, + 212, + 479 + ], + "type": "text", + "content": "5. Conclusions and Perspectives" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 45, + 486, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 45, + 486, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 45, + 486, + 288, + 715 + ], + "type": "text", + "content": "In this work, we present the Multiple Asymptotically Normal Distribution Attacks (MultiANDA) to generate transferable adversarial examples. Our primary goal is to efficiently approximate the posterior distribution of adversarial perturbations to achieve better generalization across unknown deep learning models. We leverage the statistical information of gradients along the optimization trajectory to estimate the stationary distribution of the perturbations. With this learned distribution's aid, MultiANDA can significantly improve the transferability of adversarial examples to black-box target models. Extensive experiments demonstrate that MultiANDA outperforms popular and recently proposed black-box and transfer-based methods, further highlighting the insufficiency of current defense techniques. Notably, the computational overhead of both ANDA and MultiANDA, largely depending on the number of batch samples during augmentation, is on par with similar baseline methods (refer to Appendix for the computational overhead analysis). Compared to the potential risks" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 304, + 402, + 547, + 463 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 402, + 547, + 463 + ], + "spans": [ + { + "bbox": [ + 304, + 402, + 547, + 463 + ], + "type": "text", + "content": "these algorithms might pose if misused, their computational cost is relatively negligible. We advocate for the development of advanced deep learning models which align better with human visual preferences, thereby avoiding the fundamental defects present in modern models." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 478, + 409, + 493 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 478, + 409, + 493 + ], + "spans": [ + { + "bbox": [ + 306, + 478, + 409, + 493 + ], + "type": "text", + "content": "Acknowledgements" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 499, + 547, + 620 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 499, + 547, + 620 + ], + "spans": [ + { + "bbox": [ + 304, + 499, + 547, + 620 + ], + "type": "text", + "content": "This work was supported by the National Natural Science Foundation of China under Grant 62176020, the Joint Foundation of the Ministry of Education (8091B042235), the Beijing Natural Science Foundation under Grant L211016, the Talent Fund of Beijing Jiaotong University under Grant 2023XKRC041, and the Fundamental Research Funds for the Central Universities (Science and technology leading talent team project) under Grant 2022JBXT003. 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In Proceedings of the European Conference on Computer Vision (ECCV), pages 452-467, 2018. 3" + } + ] + } + ], + "index": 23 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "24850" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/89aa68d1-2eb8-4184-895d-0bf0c9b627f5_content_list.json b/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/89aa68d1-2eb8-4184-895d-0bf0c9b627f5_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..c03a300a9ed0f03ff7a3e05c1a9d6a034a3b920f --- /dev/null +++ b/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/89aa68d1-2eb8-4184-895d-0bf0c9b627f5_content_list.json @@ -0,0 +1,1751 @@ +[ + { + "type": "text", + "text": "Stronger, Fewer, & Superior: Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation", + "text_level": 1, + "bbox": [ + 142, + 130, + 828, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Zhixiang Wei $^{1*}$ Lin Chen $^{1,2*}$ Yi Jin $^{1*}$ Xiaoxiao Ma $^{1}$ Tianle Liu $^{1}$ Pengyang Ling $^{1,2}$ Ben Wang $^{1}$ Huaian Chen $^{1\\dagger}$ Jinjin Zheng $^{1}$", + "bbox": [ + 91, + 200, + 869, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 University of Science and Technology of China 2 Shanghai AI Laboratory", + "bbox": [ + 228, + 239, + 740, + 257 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{zhixiangwei,chlin,xiao_xiao,tleliu,lpyang27,wblzgrsn,anchen}@mail.ustc.edu.cn", + "bbox": [ + 142, + 258, + 826, + 273 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{jinyi08,jjzheng}@ustc.edu.cn", + "bbox": [ + 352, + 277, + 611, + 292 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/2a052c6bc911146c85a9904975836381ec4cda938a05d23222bce8cfbd6e343c.jpg", + "image_caption": [ + "(a) Stronger pre-trained models" + ], + "image_footnote": [], + "bbox": [ + 86, + 316, + 274, + 486 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/d3d09cc155492ee58c97ddda441d967a0aa96d424e5d0bbe05d4abfbb98768cb.jpg", + "image_caption": [ + "(b) Fewer trainable parameters" + ], + "image_footnote": [], + "bbox": [ + 272, + 329, + 529, + 484 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/6a25ece895207d03080e12a89faec354b0c11195a1a47d529389f784687169aa.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 537, + 329, + 715, + 404 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/3211a8e6af4ca7b62cd876ddb75eb24e86011234c68724d54ca70f7d330a486d.jpg", + "image_caption": [ + "Figure 1. Vision Foundation Models (VFMs) are stronger pre-trained models that serve as robust backbones, effortlessly outperforming previous state-of-the-art Domain Generalized Semantic Segmentation (DGSS), as shown in (a). Yet, the extensive parameters of VFMs make them challenging to train. To address this, we introduce a robust fine-tuning approach to efficiently harness VFMs for DGSS. As illustrated in (b) and (c), the proposed methods achieve superior generalizability with fewer trainable parameters within backbones." + ], + "image_footnote": [], + "bbox": [ + 537, + 407, + 715, + 479 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/54470b2982c6f094e33b8038d913cf27f2e076b4f0a4e751bd32040c2a923f6d.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 723, + 329, + 903, + 402 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/96d62aa4037bf6737f4b1b934d944d61445b14686e187c8843244fd6c8ffa9e2.jpg", + "image_caption": [ + "(c) Superior generalization ability" + ], + "image_footnote": [], + "bbox": [ + 723, + 407, + 903, + 479 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 578, + 313, + 594 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In this paper, we first assess and harness various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we introduce a robust fine-tuning approach, namely \"Rein\", to parameter-efficiently harness VFMs for DGSS. Built upon a set of trainable tokens, each linked to distinct instances, Rein precisely refines and forwards the feature maps from each layer to the next layer within the backbone. This process produces diverse refinements for different categories within a single image. With fewer trainable parameters, Rein efficiently fine-tunes VFMs for DGSS tasks, surprisingly surpassing full parameter fine-tuning. Extensive experiments across various settings demonstrate that Rein significantly outperforms state-of-the-art methods. Remarkably, with just an extra $1\\%$ of trainable parameters", + "bbox": [ + 75, + 607, + 472, + 864 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "within the frozen backbone, Rein achieves a mIoU of $78.4\\%$ on the Cityscapes, without accessing any real urban-scene datasets. Code is available at https://github.com/wloves/Rein.git.", + "bbox": [ + 500, + 580, + 893, + 640 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 501, + 646, + 632, + 661 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Prior works [32, 34, 36, 56, 63, 66, 72] in Domain Generalized Semantic Segmentation (DGSS) focus on improving prediction accuracy across multiple unseen domains without accessing their data, thus enabling a high generalization for real applications. Since models are fine-tuned using datasets [11, 57] that are either limited in scale or different in image style from the target domain, complex data augmentation approaches [4, 53, 73] and domain invariant feature extraction strategies [9, 51, 62, 67] have been widely explored in previous DGSS. These methods result in enhanced generalization when applied to classic backbones, e.g., VGGNet [61], MobileNetV2 [60], and ResNet [23].", + "bbox": [ + 496, + 672, + 890, + 853 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "In recent years, large-scale Vision Foundation Models (VFMs) like CLIP [55], MAE [24], SAM [38], EVA02 [17, 18], and DINOv2 [50] have significantly advanced the", + "bbox": [ + 498, + 854, + 893, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* indicates equal contributions.", + "bbox": [ + 94, + 875, + 261, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 96, + 887, + 230, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "28619", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/80e57834bae4ef1d990d50b0cf8ef2c3ac73e8c940d8c3477e06e272de8ece5c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
Previous DGSS methodsFrozen backbone of VFs
MethodsGTR[53]AdvStyle[73]WildNet[40]SPC[27]PASTA[4]TLDR[37]CLIP-ViT-L[55]MAE-L[24]SAM-H[38]EVA02-L[17]DINOv2-L[50]
PublicationsTIP21NIPS22CVPR22CVPR23ICCV23ICCV23ICML21CVPR22ICCV23arXiv23arXiv23
mIoU (Citys)43.743.445.846.745.347.653.743.357.056.563.3
mIoU (BDD)39.640.341.743.742.344.948.737.847.153.656.1
mIoU (Map)39.142.047.145.548.648.855.048.058.458.663.9
mIoU (Average)40.841.944.945.345.447.152.443.054.256.261.1
", + "bbox": [ + 84, + 88, + 890, + 178 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Table 1. Performance benchmarking of multiple VFMs and previous DGSS methods under the GTAV $\\rightarrow$ Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting. Without specialized design, frozen VFMs demonstrate stronger performance.", + "bbox": [ + 76, + 181, + 890, + 209 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "boundaries of performance in a variety of computer vision challenges. Giving the remarkable generalization of these VFMs across various unseen scenes, two intuitive questions emerge: How do VFMs perform in the context of DGSS? And How to harness VFMs for DGSS? We attempt to answer these questions as follows:", + "bbox": [ + 75, + 224, + 467, + 315 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Stronger: We begin by evaluating and comparing the performance of various VFMs against existing DGSS methods. To ensure a fair comparison, we use image encoders from a variety of VFMs as the backbone for feature extraction in all cases. These backbones are coupled with the widely-used decode head, i.e., Mask2Former [8], to generate semantic predictions. As illustrated in Tab. 1, while previous DGSS methods have showcased commendable results, they perform less effectively compared to frozen VFs. This finding clearly demonstrates the powerful potential of VFs in DGSS, outperforming traditional backbones like ResNet [23] and MobileNetV2 [60], thereby establishing VFs as a meaningful benchmark in the field.", + "bbox": [ + 75, + 319, + 467, + 515 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fewer: Although VFMs have exhibited impressive generalization capabilities, fine-tuning them for DGSS tasks poses a challenge. The datasets [11, 57] commonly used in DGSS tasks are significantly smaller in scale compared to ImageNet [12], and fine-tuning VFs with their huge number of trainable parameters on these datasets result in limited generalizability [33]. To address this issue, instead of the difficult task of large datasets collection, we resort to fine-tuning VFs with fewer trainable parameters. However, most existing parameter-efficient fine-tuning strategies, which fine-tune a large-scale model with fewer trainable parameters, are primarily designed for adapting large language models [25, 26, 41, 43, 44, 70, 74] or classification networks [6, 28]. These methods are not developed for refining features for distinct instances within a single image, thereby limiting their effectiveness in DGSS contexts.", + "bbox": [ + 75, + 518, + 467, + 760 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Superior: In this work, we introduce a robust and efficient fine-tuning approach, namely \"Rein\". Tailored for DGSS tasks, Rein employs fewer trainable parameters to harness stronger VFMs for achieving superior generalization. At its core, Rein comprises a set of randomly initialized tokens, each directly linked to different instances. These tokens, through a dot-product operation with VFMs features, generate an attention-like similarity map. This map enables Rein to perform precise refinement tailored to", + "bbox": [ + 75, + 763, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "each instance within an image, significantly boosting VFMs in the context of DGSS. Moreover, to reduce the number of trainable parameters, we employ shared weights across MLPs in different layers and design our learnable tokens by multiplying two low-rank matrices. Extensive experiments on various DGSS settings demonstrate that the proposed Rein outperforms existing DGSS methods by a large margin with fewer trainable parameters. In a nutshell, the main contributions of this paper are as follows:", + "bbox": [ + 496, + 224, + 890, + 359 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We first assess various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Our extensive experiments in the DGSS framework highlight the impressive generalization capabilities of VFMs. The findings confirm that VFMs serve as Stronger backbones, thereby establishing a significant benchmark in this field.", + "- We present a robust fine-tuning method, namely \"Rein\", to parameter-efficiently harness VFMs. At its core, Rein consists of a set of learnable tokens, each directly linked to instances. With deliberate design, this linkage enables Rein to refine features at an instance-level within each layer. As a result, Rein reinforces the ability of VFMs in DGSS tasks, achieving this with Fewer trainable parameters while preserving the pre-trained knowledge.", + "- Comprehensive experiments across various DGSS settings demonstrate that Rein employs Fewer trainable parameters to effectively leverage Stronger VFMs for achieving Superior generalizability. This performance surpasses existing DGSS methods by a large margin. Notably, Rein is designed to integrate smoothly with existing plain vision transformers, improving their generalization ability and making training more efficient." + ], + "bbox": [ + 500, + 362, + 890, + 708 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Works", + "text_level": 1, + "bbox": [ + 500, + 724, + 648, + 739 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Domain Generalized Semantic Segmentation. Domain Generalized Semantic Segmentation (DGSS) focuses on enhancing model generalizability. This field involves training models on a set of source domain to enhance their performance on distinct and unseen target domain. Various approaches [5, 13, 20, 21, 27, 29-31, 42, 54, 65] have been proposed to address this issue, with methods including splitting the learned features into domain-invariant and domain-specific components [62, 67], or employing meta-learning to train more robust models [35]. A standard scenario in", + "bbox": [ + 496, + 750, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "28620", + "bbox": [ + 478, + 945, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/5b496184cd146f7472386c83ef7fa6c6ec38bc5c84985692e9d5d300b65bb8db.jpg", + "image_caption": [ + "Figure 2. An overview of proposed Rein. Rein primarily consists of a collection of low-rank learnable tokens, denoted as $T = \\{T_1, T_2, \\ldots, T_N\\}$ . These tokens establish direct connections to distinct instances, facilitating instance-level feature refinement. This mechanism results in the generation of an enhancement feature map $f_i' = f_i + \\text{Rein}(f_i)$ for each layer within backbone. All parameters of MLPs are layer-shared to reduce the number of parameters. $M_f$ , $M_Q$ , and $M_S$ are features module, queries module, and segmentation module, respectively. The notation max & avg & last refers to the equation Eq. (8) and Eq. (10)." + ], + "image_footnote": [], + "bbox": [ + 86, + 99, + 890, + 292 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/fd2f61f42b356b038d0c9ba7f8063b43b27c45572c246fd21a99211e37a17d5c.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BackboneFine-tune \nMethodTrainable \nParams*mIoU
CitysBDDMapAvg.
CLIP [55] \n(ViT-Large)Full304.15M51.347.654.351.1
Freeze0.00M53.748.755.052.4
Rein2.99M57.154.760.557.4
MAE [24] \n(Large)Full330.94M53.750.858.154.2
Freeze0.00M43.337.848.043.0
Rein2.99M55.049.358.654.3
SAM [38] \n(Huge)Full632.18M57.651.761.556.9
Freeze0.00M57.047.158.454.2
Rein4.51M59.652.062.157.9
EVA02 [17, 18] \n(Large)Full304.24M62.156.264.660.9
Freeze0.00M56.553.658.656.2
Rein2.99M65.360.564.963.6
DINOV2 [50] \n(Large)Full304.20M63.757.464.261.7
Freeze0.00M63.356.163.961.1
Rein2.99M66.460.466.164.3
", + "bbox": [ + 84, + 378, + 467, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Table 2. Performance Comparison with the proposed Rein across Multiple VFMs as Backbones under the GTAV $\\rightarrow$ Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones.", + "bbox": [ + 75, + 637, + 470, + 694 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "DGSS is generalizing from one urban-scene dataset to another, for instance, from the synthetic GTAV [57] dataset to the real-world Cityscapes [11]. In this classic setting, certain techniques [9, 51, 52] have achieved notable performance through learning feature normalization/whitening schemes, while others [40] have improved segmentation results through feature-level style transfer and the introduction of additional data. Additionally, strong data augmentation [4, 16, 53, 73] often simply and effectively enhances model robustness. However, most of previous DGSS methods generally utilize outdated backbones like ResNet [23], VGGNet [61], MobileNetV2 [60], and ShuffleNetV2 [47], thereby leaving the efficacy of stronger Vision Foundation", + "bbox": [ + 75, + 703, + 472, + 902 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Models (VFMs) in DGSS relatively unexplored.", + "bbox": [ + 498, + 381, + 818, + 397 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Vision Foundation Models. The concept of a Foundation Model, initially introduced by Bommasani et al. [2] in the field of Natural Language Processing (NLP), defined as \"the base models trained on large-scale data in a self-supervised or semi-supervised manner that can be adapted for several other downstream tasks\". While models like the ViT [14] and Swin Transformer [45] have demonstrated excellent performance, the quest for a Vision Foundation Model (VFM) similar to their NLP counterparts is ongoing. This pursuit has yielded significant advancements with the advent of models such as CLIP [55], which learn high-quality visual representation by exploring contrastive learning with large-scale image text pairs; MAE [24], utilizing a masked image modeling for learning latent image representations; SAM [38], which develops a promptable model and pre-train it on a broad dataset for segmentation task; EVA02 [17, 18], which integrates Masked Image Modeling pre-training with CLIP's vision features; and DINOv2 [50], which is pretrained on extensive, curated datasets without explicit supervision. These VFs have shown remarkable performance in downstream applications. Yet, a dedicated investigation into their performance in the specific context of DGSS tasks remains unexplored.", + "bbox": [ + 496, + 398, + 890, + 746 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Parameter-Efficient Fine-tuning. In the realm of NLP, parameter-efficient fine-tuning (PEFT) has achieved notable success by freezing most parameters of VFMs and fine-tuning a select few. Various approaches have been developed, such as BitFit [70], which adjusts only the model's bias terms; Prompt-tuning [41], introducing soft prompts to adapt frozen language models; Adapter-tuning [25], adding lightweight modules to each transformer layer; and notably, LoRA [26], which injects trainable rank decomposition matrices into transformer layers, yielding significant influence.", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "28621", + "bbox": [ + 478, + 944, + 517, + 957 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/e5649f764e1f92661a59238300a7ff1f0e191b7cd75db40af9b1536cb4028ff7.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
TargetACDC[59] (test)Cityscapes-C[48] (level-5)
Night Snow Fog RainAllBlurNoiseDigitalWeatherAvg.
MotionDefocGlassGaussGaussImpulShotSpeckBrightContrSaturJPEGSnowSpattFogFrost
HGFormer52.768.669.972.067.264.167.261.563.627.235.732.963.179.972.978.053.655.475.875.543.2
Ours70.679.576.478.277.668.571.769.768.76.223.013.163.781.578.980.668.863.873.679.547.9
", + "bbox": [ + 84, + 88, + 890, + 157 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/246a83c336da90fbdeda68de17a6668e0bbbc41f83399474b54cee47645864fe.jpg", + "table_caption": [ + "Table 3. Results on Cityscapes $\\rightarrow$ ACDC (test) and Cityscapes-C (level-5) datasets, utilizing a batch size of 8." + ], + "table_footnote": [], + "table_body": "
BackboneFine-tune \nMethodTrainable \nParams*mIoU
CitysBDDMapAvg.
EVA02 \n(Large) \n[17, 18]Full304.24M62.156.264.660.9
+AdvStyle [73]304.24M63.156.464.061.2
+PASTA [4]304.24M61.857.163.660.8
+GTR-LTR [53]304.24M59.857.463.260.1
Freeze0.00M56.553.658.656.2
+AdvStyle [73]0.00M51.451.656.553.2
+PASTA [4]0.00M57.852.358.556.2
+GTR-LTR [53]0.00M52.552.857.154.1
+LoRA [26]1.18M55.552.758.355.5
+AdaptFormer [6]3.17M63.759.964.262.6
+VPT [28]3.69M62.257.762.560.8
+Rein (ours)2.99M65.360.564.963.6
DINOv2 \n(Large) \n[50]Full304.20M63.757.464.261.7
+AdvStyle [73]304.20M60.858.062.560.4
+PASTA [4]304.20M62.557.264.761.5
+GTR-LTR [4]304.20M62.757.464.561.6
Freeze0.00M63.356.163.961.1
+AdvStyle [73]0.00M61.555.163.960.1
+PASTA [4]0.00M62.157.264.561.3
+GTR-LTR [4]0.00M60.257.762.260.0
+LoRA [26]0.79M65.258.364.662.7
+AdaptFormer [6]3.17M64.959.064.262.7
+VPT [28]3.69M65.259.465.563.3
+Rein (ours)2.99M66.460.466.164.3
", + "bbox": [ + 84, + 181, + 467, + 558 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The application of PEFT methods is also expanding into the field of computer vision [15, 39], with notable examples such as Visual Prompt Tuning (VPT) [28], which prepends prompts into the input sequence of transformer layers; AdaptFormer [6], replacing the MLP block in the transformer encoder with an AdaptMLP; LP-FT [39] find that fine-tuning can achieve worse accuracy than linear probing out-of-distribution; and Prompt-ICM [19], applying large-scale pre-trained models to the task of image coding for machines. Contrasting with these methods, we aim to refine feature maps for each instance within an image, thereby achieving superior performance in the realm of DGSS.", + "bbox": [ + 75, + 627, + 470, + 809 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3. Methods", + "text_level": 1, + "bbox": [ + 76, + 821, + 174, + 835 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.1. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 845, + 205, + 863 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Driven by the motivation that Leveraging Stronger pretrained models and Fewer trainable parameters for Su", + "bbox": [ + 76, + 869, + 468, + 902 + ], + "page_idx": 3 + }, + { + "type": "table", + "img_path": "images/6312da5214a1ee700bef437ad1e45812e02164d4526f9eb005146c3bd2e53051.jpg", + "table_caption": [ + "Table 4. Performance Comparison of the proposed Rein against other DGSS and PEFT methods under the GTAV $\\rightarrow$ Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones." + ], + "table_footnote": [], + "table_body": "
Source DomainCityscapes mIoU
GTAV66.4
+Synthia68.1
+UrbanSyn78.4
+1/16 of Cityscapes Training set82.5
", + "bbox": [ + 517, + 181, + 874, + 268 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Table 5. Synthetic data + 1/16 of Citys. → Citys. val set.", + "bbox": [ + 519, + 271, + 870, + 286 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "perior generalizability, we choose to fine-tune VFMs with a reduced parameter set. A straightforward thought might involve a smaller decode head; however, this method merely acts as a passive receiver of feature maps from the backbone, lacking the flexibility to effectively adapt a frozen backbone for generating task-specific or scene-specific features. In contrast, we propose to embed a mechanism, named \"Rein\", between the layers within the backbone. Rein actively refines and forwards the feature maps from each layer to the subsequent one. This approach allows us to more effectively utilize the powerful capabilities of VFMs, much like using rein to control a horse.", + "bbox": [ + 496, + 296, + 890, + 477 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Given a pre-trained VFM with parameters $\\Phi_M$ , consisting of a sequence of layers $L_{1}, L_{2}, \\ldots, L_{N}$ , a decode head $\\mathcal{H}$ parameterized by $\\theta_h$ , and the Rein strategy with parameters $\\theta_R$ , the optimization objective can be written as:", + "bbox": [ + 498, + 478, + 890, + 539 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\underset {\\theta_ {R}, \\theta_ {h}} {\\arg \\min } \\sum_ {i = 1} ^ {N _ {d}} \\operatorname {L o s s} \\left(\\mathcal {H} _ {\\theta_ {h}} \\left(\\mathcal {F} _ {\\Phi_ {M}, \\theta_ {R}} \\left(x _ {i}\\right)\\right), y _ {i}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 547, + 890, + 589 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $x_{i}$ and $y_{i}$ denote the input image and its corresponding ground truth, respectively, and $N_{d}$ signifies the total number of samples. $\\mathcal{F}_{\\Phi_M,\\theta_R}$ represents the forward process of VFM after applying the Rein strategy.", + "bbox": [ + 496, + 598, + 890, + 659 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Core of Rein", + "text_level": 1, + "bbox": [ + 500, + 667, + 635, + 681 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "For simple implementation across different VFMs, we opt not to modify MLP weights at specific positions as described in the [6, 26]. Instead, our approach focuses on refining the output feature maps at each layer within the VFMs, as illustrated in Fig. 2. Precisely, for the features $f_{i}$ produced by the $i$ -th layer $L_{i}$ , Rein produces enhanced feature maps for the next layer as follows:", + "bbox": [ + 496, + 690, + 890, + 796 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {1} = L _ {1} (E m b e d (x)) \\quad f _ {1} \\in \\mathbb {R} ^ {n \\times c},\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 806, + 799, + 821 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {i + 1} = L _ {i + 1} \\left(f _ {i} + \\Delta f _ {i}\\right) \\quad i = 1, 2, \\dots , N - 1, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 825, + 890, + 840 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nf _ {o u t} = f _ {N} + \\Delta f _ {N},\n$$\n", + "text_format": "latex", + "bbox": [ + 519, + 844, + 653, + 859 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $f_{i}^{\\prime} = f_{i} + \\Delta f_{i}$ symbolizes the refined feature map, $x$ is the input image, $\\text{Embed}$ denotes the patch embedding", + "bbox": [ + 500, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "28622", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "layer in VFMs, $n$ represents the number of patches, $N$ denotes the number of layers, and $c$ is the dimensionality of $f_{1}, f_{2}, \\ldots, f_{N}$ . Note that the layers $L_{1}, L_{2}, \\ldots, L_{N}$ are kept frozen, and our focus is on training an efficient module, Rein, to generate $\\Delta f_{i}$ as follows:", + "bbox": [ + 76, + 90, + 468, + 167 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta f _ {i} = \\operatorname {R e i n} (f _ {i}) \\quad \\Delta f _ {i} \\in \\mathbb {R} ^ {n \\times c}, i = 1, 2, \\dots , N. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 91, + 178, + 468, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In the context of DGSS, an ideal $\\Delta f_{i}$ should assist VFMs to bridge two types of gaps. The first is gap in scene between pre-training dataset and target scene, exemplified by the contrast between ImageNet [12] and urban-scene images [11, 57]. The second is task divergence between pretraining and fine-tuning, such as the differences between masked image modeling and semantic segmentation tasks.", + "bbox": [ + 75, + 207, + 468, + 313 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To establish this dual bridge, Rein starts with a set of learnable tokens $T = \\{T_{i} \\in \\mathbb{R}^{m \\times c} \\mid i \\in \\mathbb{N}, 1 \\leq i \\leq N\\}$ , where each token sequence $T_{i}$ is randomly initialized, and $m$ denotes the sequence length of $T_{i}$ . Rein freezes the backbone and embeds knowledge learned from the finetuning dataset into these tokens, thereby bridging the gap in scene relative to the pre-training dataset. Moreover, considering the essential need in semantic segmentation to discern multiple instances within a single image, Rein implements an attention-inspired mechanism, which enables VFMs to make tailored adjustments to the features of distinct instances, thereby aiding VFMs in adapting to the differences between semantic segmentation and pre-training tasks. Specifically, Rein employs a dot-product operation to generate a similarity map $S_{i}$ , which captures the associations between feature vectors in $f_{i}$ and the tokens in $T$ :", + "bbox": [ + 75, + 313, + 468, + 554 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} = f _ {i} \\times T _ {i} ^ {\\mathrm {T}} \\quad S _ {i} \\in \\mathbb {R} ^ {n \\times m}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 568, + 468, + 585 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $T_{i}$ represents the token sequence of the $i$ -th layer, $m$ indicates the number of tokens in $T_{i}$ . As $S$ quantitatively evaluates the relationships between various tokens and feature vectors, Rein can apply a softmax function to align each patch with a unique instance:", + "bbox": [ + 75, + 593, + 468, + 667 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nS _ {i} = \\operatorname {S o f t m a x} \\left(\\frac {f _ {i} \\times T _ {i} ^ {\\mathrm {T}}}{\\sqrt {c}}\\right). \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 679, + 468, + 714 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Leveraging the feature-to-token similarity map $S_{i}$ , we can preliminarily estimates of $\\Delta f_{i}$ using the equation:", + "bbox": [ + 76, + 724, + 468, + 753 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta \\bar {f} _ {i} = S _ {i} (:, 2: m) \\times \\left[ T _ {i} (2: m) \\times W _ {T _ {i}} + b _ {T _ {i}} \\right], \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 102, + 765, + 468, + 782 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{T_i}$ and $b_{T_i}$ denote the weights and biases of a MLP, respectively. This MLP enables the transformation of $T_i$ across different feature spaces during the computation of $S_i$ and $\\Delta \\bar{f}_i$ . Optionally, Rein can pre-calculate $T_i \\times W_{T_i} + b_{T_i}$ to reduce inference time. The sum of $S_i$ equals one due to the softmax function; however, this can induce unneeded changes when all features are precise. To", + "bbox": [ + 76, + 794, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "avoid this, $S_{i}(:,2:m)$ is designed to choose columns 2 to m of $S_{i}$ , and $T_{i}(2:m)$ denotes the selection of rows 2 to m of $T_{i}$ . This strategic selection allows models to sidestep unnecessary adjustments by assigning a high value to the first token and subsequently discarding it. This approach allows the sum of each row in $S_{i}$ to vary from 0 to 1, thus reducing the risk of inappropriate changes.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To enhance the flexibility in feature adjustment, Rein utilizes a MLP composed of $W_{f_i}$ and $b_{f_i}$ to produce the final feature modifications $\\Delta f_i$ :", + "bbox": [ + 496, + 196, + 890, + 242 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\Delta f _ {i} = \\left(\\Delta \\bar {f} _ {i} + f _ {i}\\right) \\times W _ {f _ {i}} + b _ {f _ {i}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 584, + 252, + 890, + 270 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Benefiting from these instance-level $\\Delta f_{i}$ adjustments, Rein is capable of generating diverse modifications for various categories within a single image. The details of Rein will be explained in the next section.", + "bbox": [ + 496, + 280, + 890, + 340 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3. Details of Rein", + "text_level": 1, + "bbox": [ + 500, + 349, + 648, + 364 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Linking tokens to instances. At the core of Rein, we establish an implicit yet effective linkage between tokens and instances, which has demonstrated notable performance, as detailed in Sec. 4. This connection is further reinforced by utilizing object queries, a key component in DETR[3]-style decode heads [7, 8, 71], as intermediaries. These queries are empirically proven to establish a direct association with instances. Specifically, we generate layer-wise queries $Q_{i}$ from our learnable tokens $T_{i}$ via linear transformation:", + "bbox": [ + 496, + 373, + 890, + 508 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {i} = T _ {i} \\times W _ {Q _ {i}} + b _ {Q _ {i}} \\quad Q _ {i} \\in \\mathbb {R} ^ {m \\times c ^ {\\prime}}, \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 518, + 890, + 537 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $W_{Q_i}$ and $b_{Q_i}$ signify the weights and biases, respectively, and $c'$ denotes the dimension of $Q_i$ . However, due to the complexity arising from the large numbers of various layers in VFMs, transforming the diverse $Q_i$ into a single query $Q$ poses computational challenges. To address this, Rein computes both the maximal component $Q_{\\text{max}} \\in \\mathbb{R}^{m \\times c'}$ and the average component $Q_{\\text{avg}} \\in \\mathbb{R}^{m \\times c'}$ using the following equation:", + "bbox": [ + 496, + 547, + 890, + 667 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {m a x} (j, k) = \\max _ {i = 1, 2, \\dots , N} Q _ {i} (j, k),\n$$\n", + "text_format": "latex", + "bbox": [ + 581, + 679, + 808, + 702 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ _ {a v g} (j, k) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} Q _ {i} (j, k). \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 588, + 705, + 890, + 747 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Subsequently, $Q$ is derived as:", + "bbox": [ + 500, + 756, + 702, + 771 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nQ = \\operatorname {C o n c a t} \\left(\\left[ Q _ {\\max }, Q _ {\\text {a v g}}, Q _ {N} \\right]\\right) \\times W _ {Q} + b _ {Q}. \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 782, + 890, + 799 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "By mapping $T$ onto $Q$ , which subsequently links to instances, Rein achieves enhanced performance with a marginal increase in parameters.", + "bbox": [ + 496, + 809, + 890, + 854 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Layer-shared MLP weights. To address the redundancy of parameters in the layer-specific MLP weights, specifically $W_{T_i}$ in Eq. (6), $W_{f_i}$ in Eq. (7), and $W_{Q_i}$ in Eq. (8), which", + "bbox": [ + 496, + 854, + 890, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "28623", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "collectively contribute to a substantial trainable parameter count, we adopt a new strategy. Since the learnable $T_{i}$ is capable of producing distinct $\\Delta f_{i}$ for each layer, we design the role of the MLP to primarily perform consistent linear transformations across different feature spaces for each layer within the backbone. To this end, we employ shared MLP weights across layers as outlined in the equations:", + "bbox": [ + 75, + 90, + 472, + 196 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\left[ W _ {T _ {1}}, b _ {T _ {1}} \\right] = \\left[ W _ {T _ {2}}, b _ {T _ {2}} \\right] = \\dots = \\left[ W _ {T _ {N}}, b _ {T _ {N}} \\right], \\\\ \\left[ W _ {f _ {1}}, b _ {f _ {1}} \\right] = \\left[ W _ {f _ {2}}, b _ {f _ {2}} \\right] = \\dots = \\left[ W _ {f _ {N}}, b _ {f _ {N}} \\right], \\tag {11} \\\\ \\left[ W _ {Q _ {1}}, b _ {Q _ {1}} \\right] = \\left[ W _ {Q _ {2}}, b _ {Q _ {2}} \\right] = \\dots = \\left[ W _ {Q _ {N}}, b _ {Q _ {N}} \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 96, + 207, + 467, + 263 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Low-rank token sequence. Recognizing the potential for information overlap among diverse learnable tokens, such as the high similarity between tokens representing a car's headlight and a bicycle's light, Rein adopts a strategy to generate a low-rank token sequence $T$ as follows:", + "bbox": [ + 75, + 272, + 468, + 348 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\nT i = A _ {i} \\times B _ {i}, \\quad A \\in \\mathbb {R} ^ {m \\times r}, B \\in \\mathbb {R} ^ {r \\times c}, \\tag {12}\n$$\n", + "text_format": "latex", + "bbox": [ + 114, + 358, + 468, + 375 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $c$ denotes the dimension of $T_{i}$ , $m$ is the length of sequence $T_{i}$ , and $r$ represents the rank, with $r \\ll c$ . Here, matrices $A$ and $B$ are constructed as low-rank matrices. To reduce inference time, Rein can precompute and store $T$ . By implementing this low-rank token sequence approach, Rein significantly reduces the number of parameters.", + "bbox": [ + 75, + 386, + 468, + 477 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4. Experiments", + "text_level": 1, + "bbox": [ + 76, + 489, + 209, + 507 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.1. Settings", + "text_level": 1, + "bbox": [ + 76, + 513, + 174, + 530 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Visual Foundation Models. To thoroughly assess the influence of Visual Foundation Models (VFMs) within the context of DGSS, we analyze five distinct VFMs, each with different training strategies and datasets. Our selection includes CLIP [55], a language-image pre-training model; MAE [24], known for its masked pre-training approach; SAM [38], which leverages a large-scale segmentation dataset; EVA02 [17, 18] combines CLIP with masked image modeling; and DINOv2 [50], based on self-supervised pretraining with curated dataset. For balancing precision and efficiency, we mainly employ the ViT-Large architecture for these VFMs, except SAM, which utilizes a ViT-Huge image encoder, as described in its original paper [38]. We establish two fundamental baselines for VFMs: \"Full\", where we fine-tune the entire network, and \"Freeze\", in which all backbone parameters are fixed, with training solely on the segmentation head. More details about VFMs and PEFT methods are available in the supplementary material.", + "bbox": [ + 75, + 537, + 468, + 809 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Datasets. We evaluate VFs and proposed methods on both real-world datasets (Cityscapes [11], BDD100K [68], Mapillary [49]) and synthetic datasets (GTAV [57], Synthia [58], UrbanSyn [22]). In detail, Cityscapes (denoted as Citys) is an autonomous driving dataset that contains 2975 training images and 500 validation images, each with the", + "bbox": [ + 75, + 810, + 468, + 901 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "resolution of $2048 \\times 1024$ . BDD100K (shortened to BDD) and Mapillary (denoted by Map) offer 1,000 ( $1280 \\times 720$ ) and 2,000 ( $1902 \\times 1080$ ) validation images, respectively. GTAV, a synthetic dataset, presents 24,966 labeled images obtained from the game. Synthia, a synthetic dataset, provides 25,000 images created by photo-realistic rendering. UrbanSyn, a synthetic dataset consists of 7,539 images.", + "bbox": [ + 496, + 90, + 890, + 196 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation details. We utilize the MMSegmentation [10] codebase for our implementation. For superior performance, mask2former [8], a widely-used segmentation head, is integrated with various VFMs that serve as the backbone. Additional experiments involving other decode heads are detailed in the supplementary material. For the training phase, the AdamW optimizer [46] is employed, setting the learning rate at 1e-5 for the backbone and 1e-4 for both the decode head and the proposed Rein. Aiming to efficient training process, we utilize a configuration of 40,000 iterations with a batch size of 4, and crop images to a resolution of $512 \\times 512$ . Our approach includes only basic data augmentation, following Mask2Former [8]. Thanks to our streamlined training configuration and reduced number of trainable parameters, Rein can fine-tune models like DINOv2-Large or EVA02-Large on a single RTX 3090Ti GPU within 12 hours for superior generalization ability.", + "bbox": [ + 496, + 198, + 892, + 455 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4.2. Comparison with State-of-The-Art Methods", + "text_level": 1, + "bbox": [ + 498, + 467, + 872, + 483 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section, we comprehensively evaluate Rein over five datasets within three generalization settings: $GTAV \\rightarrow Citys + BDD + Map$ , $GTAV + Synthia \\rightarrow Citys + BDD + Map$ , and $Citys \\rightarrow BDD + Map$ . Rein is benchmarked against state-of-the-art (SOTA) methods, which can be classified into two groups, including domain generalized semantic segmentation (DGSS) methods[4, 9, 13, 27, 35, 40, 51, 53, 54, 64, 69, 73], and parameter-efficient fine-tuning (PEFT) approaches [6, 26, 28].", + "bbox": [ + 496, + 491, + 890, + 628 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Investigation of various VFMs. Our analysis of VFMs and proposed Rein in the $GTAV \\rightarrow Citys + BDD + Map$ setting is presented in Tables 1 and 2. In this setup, models are fine-tuned using GTAV and evaluated on Cityscapes, BDD100K, and Mapillary. Note that, due to the fixed and relatively small number of trainable parameters in the decode head (20.6M), the count of trainable parameters presented in the tables are focused solely on the backbone and the PEFT module. Our results, as detailed in Table 1, indicate that frozen VFMs significantly outperform previous DGSS methods without specialized design. Moreover, as shown in Table 2, VFMs with full parameter fine-tuning exhibit enhanced performance relative to their frozen counterparts. Remarkably, Rein achieves even superior generalization capabilities, surpassing the full parameter fine-tuning with merely an extra $1\\%$ of trainable parameters compared to the original backbone. Visual samples for qualitative comparison are given in Fig. 3.", + "bbox": [ + 496, + 628, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "28624", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/b8cbc0eeac34d701a218b4f67fae5989e784d6fa90f82f1a71a9b0362c46cfdc.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
BackboneFine-tune \nMethodTrainable \nParams*roadside.build.wallfencepolelightsignvegeterr.skypers.ridercartruckbustrainmoto.bicy.mIoU
EVA02 \n(Large) \n[17, 18]Full304.24M89.346.989.947.745.650.156.842.288.848.489.975.849.090.545.369.255.944.455.162.2
Freeze0.00M93.152.788.047.431.141.746.039.685.741.489.567.539.789.047.072.846.319.235.256.5
Rein-core52.84M91.153.890.050.347.746.656.442.987.844.290.473.544.291.858.177.257.343.457.363.4
+ Rein-link59.33M90.948.590.052.649.449.157.239.888.946.590.574.444.091.052.380.767.344.360.364.1
+ Rein-share5.02M92.754.390.051.848.648.855.345.088.946.789.873.743.390.649.581.169.641.750.263.4
+ Rein-lora2.99M91.751.890.152.848.448.256.042.089.144.190.274.247.091.154.584.178.947.259.465.3
DINOv2 \n(Large) \n[50]Full304.20M89.044.589.651.146.449.260.038.989.147.591.775.848.291.752.582.981.030.449.963.7
Freeze0.00M92.155.290.257.248.549.556.747.789.347.891.174.246.792.262.677.547.729.647.261.1
Rein-core52.84M92.457.890.656.850.750.557.544.889.847.091.175.947.291.960.180.359.837.952.364.9
+ Rein-link59.33M91.255.590.655.652.551.159.745.189.847.191.175.847.192.664.682.265.540.452.765.8
+ Rein-share5.02M93.561.290.757.753.252.458.050.189.749.990.774.845.091.758.580.166.336.950.765.8
+ Rein-lora2.99M92.459.190.758.353.751.858.246.489.849.490.873.943.392.364.381.670.940.454.066.4
", + "bbox": [ + 83, + 88, + 893, + 252 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 6. Ablation Study about Rein under Cityscapes $\\rightarrow$ BDD100K generalization in terms of mIoU. Components are sequentially incorporated. To better illustrate the gains contributed by each component, we employ varying shades of yellow to demonstrate the relative performance of the Freeze and Rein methods. The best results across all methods are highlighted.", + "bbox": [ + 75, + 253, + 893, + 295 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/b6207aeca8a25d9645477044f648597374345989031f87272ff74114086093ab.jpg", + "image_caption": [ + "Figure 3. Qualitative Comparison under GTAV $\\rightarrow$ Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting." + ], + "image_footnote": [], + "bbox": [ + 80, + 296, + 890, + 489 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparing Rein with SOTA. We conduct a comprehensive performance comparison of the proposed Rein against existing DGSS and PEFT methods under the $GTAV \\rightarrow Citys + BDD + Map$ setting, as detailed in Table 4. Owing to the robust feature extraction capabilities inherent in VFMs, DGSS methods, which typically enhance generalizability through strong data augmentation or consistency constraints, (e.g., AdvStyle, PASTA, and GTR), do not exhibit significant performance improvement. On the other hand, PEFT methods have demonstrated notable advancements. For instance, AdaptFormer outperforms the \"Freeze\" baseline using EVA02 as the backbone, while VPT shows improved performance over \"Full\" with DINOv2. Employing the same backbones (DINOv2 and EVA02), proposed Rein achieves superior performance and surpass previous DGSS and PEFT methods.", + "bbox": [ + 75, + 518, + 472, + 761 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Real-to-Real generalization of Rein. The generalization from one real-world dataset to others is pivotal for practical applications in the field. To this end, we conduct experiments under the $\\text{Citys} \\rightarrow \\text{ACDC}$ , $\\text{Citys} \\rightarrow \\text{Cityscapes-C}$ , and $\\text{Citys} \\rightarrow \\text{BDD} + \\text{Map}$ generalization setting. As shown in Table 3 and 7, Rein, when coupled with the DINOv2-Large, demonstrates superior performance across all datasets. This underscores the effectiveness of Rein in generalizing to diverse real-world scenarios.", + "bbox": [ + 75, + 763, + 472, + 900 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Synthetic-to-real generalization of Rein. As Tab. 5 illustrates, trained on synthetic UrbanSyn+GTAV+Synthia datasets, Rein achieved a $78.4\\%$ mIoU on the Cityscapes validation set. Further improvement is possible with additional synthetic data and higher-quality images generated by diffusion models, like [1]. This result can also be a valuable pre-trained weight for data-efficient training, reaching an $82.5\\%$ mIoU with 1/16 of Cityscapes training set. This is a significant performance for semi-supervised semantic segmentation.", + "bbox": [ + 496, + 518, + 890, + 669 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "More backbones. We extend our analysis to integrating Rein with Convolutional Networks, such as ResNet and ConvNeXt, and smaller scale architectures like DINOv2-S/B. As shown in Table 8, our findings reveal that Rein exhibits remarkable performance with diverse backbones.", + "bbox": [ + 496, + 670, + 890, + 746 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Studies and Analysis", + "text_level": 1, + "bbox": [ + 498, + 756, + 767, + 772 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We conduct extensive ablation studies within two settings: $GTAV \\to Citys$ and $GTAV \\to Citys + BDD + Map$ .", + "bbox": [ + 496, + 779, + 890, + 809 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Analysis of the key components. Table 6 is dedicated to thoroughly examining the effectiveness of each component within Rein. In the $GTAV \\rightarrow City$ generalization setting, we sequentially incorporate different components of Rein and assess their impact. Interestingly, we observe that the \"Freeze\" occasionally exhibit better recognition for specific", + "bbox": [ + 496, + 810, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "28625", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/c0c6f9d027767733c46e4aefa4956546158278e9ca45b071fc7046dfe779ef58.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodsBackboneTrainable \nParameters*mIoU
BDDMapAvg.
IBN [51]ResNet50 [23]23.58M48.657.052.8
DRPC [69]ResNet50 [23]23.58M49.956.353.1
GTR [53]ResNet50 [23]23.58M50.857.254.0
SAN-SAW [54]ResNet50 [23]23.58M53.059.856.4
WildNet [40]ResNet101 [23]42.62M50.958.854.9
HGFformer [13]Swin-L [45]196.03M61.572.166.8
FreezeEVA02-L [17]0.00M57.863.860.8
Rein (Ours)EVA02-L [17]2.99M64.169.566.8
FreezeDINOv2-L [50]0.00M63.469.766.7
Rein (Ours)DINOv2-L [50]2.99M65.072.368.7
", + "bbox": [ + 84, + 88, + 460, + 241 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/1c4333575eec7a487aba464df46c50173d2fec487d71aa4bff1952407590f90a.jpg", + "table_caption": [ + "Table 7. Performance Comparison of the Rein against other DGSS methods under Cityscapes $\\rightarrow$ BDD100K (BDD) +Mapillary (Map) generalization. The best results are highlighted." + ], + "table_footnote": [], + "table_body": "
Avg. mIoUResNet (50)ResNet (101)ConvNeXt (Large)DINOv2 (S)DINOv2 (B)
Full38.946.152.251.856.7
Ours46.646.355.555.759.1
", + "bbox": [ + 78, + 292, + 475, + 363 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 8. Results for ConvNets and smaller backbones.", + "bbox": [ + 104, + 364, + 439, + 378 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "categories, e.g., 'road, sidewalk', compared to the \"Full\". This suggests that VFMs lose some pre-training knowledge during fine-tuning, and \"Freeze\" helps to prevent. Similarly, our methods mitigate this knowledge forgetting. Furthermore, our methods show improved recognition capabilities for the majority of the 19 categories. For example, in recognizing 'wall, motorcycle, bicycle', our approach significantly outperforms both the \"Full\" and \"Freeze\" baselines.", + "bbox": [ + 75, + 395, + 468, + 516 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Overall, \"Rein-core\" boosts the average performance across 19 classes. Furthermore, \"Rein-link\" further boosts accuracy for certain objects, including 'car, bus, train, motorcycle', especially for DINOv2. Employing layer-shared MLP weights and low-rank token sequence efficiently reduces the number of trainable parameters and positively influences the performance of the model.", + "bbox": [ + 75, + 517, + 468, + 622 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study on token length $m$ . The core component of Rein is learnable tokens $T \\in \\mathbb{R}^{m \\times c}$ . We explored various lengths $m$ for the token sequence, ranging from 25 to 200. As demonstrated in Fig. 4, models with $m = 100$ and $m = 150$ both achieve a strong mIoU of $64.3\\%$ . We ultimately selected $m = 100$ as the most suitable parameter.", + "bbox": [ + 75, + 625, + 468, + 715 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Study on rank $r$ . As shown in Table 9, we turn attention to the effect of rank $r$ on model performance. With DINOv2 as the backbone, the optimal results are observed at $r = 16$ and $r = 32$ . Consequently, unlike LoRA [26], we opt for a comparatively higher value of $r = 16$ for our model.", + "bbox": [ + 75, + 717, + 468, + 792 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Speed, memory, and storage. For practical applications, training speed, GPU memory usage, and model storage requirements are crucial. As shown in Table 10, compared to \"Full\" baseline, proposed Rein improves training speed and reduces GPU memory usage. A significant advantage of Rein is that models trained under different settings can share the same backbone parameters. This means that for switch", + "bbox": [ + 75, + 795, + 468, + 900 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/173f2792a7339754674956c94d977fbf46165e65729e7068944f6cbba93dee21.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 498, + 87, + 890, + 238 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/3dcff3a289a06846e00fd97866d8333d6f390346e619d47b961083ff230a11dc.jpg", + "table_caption": [ + "Figure 4. Ablation study on token length $m$ ." + ], + "table_footnote": [], + "table_body": "
Rank r \nParams48163264
2.67M2.77M2.99M3.42M4.28M
DINOv2 \n(Large) \n[50]Citys65.866.166.466.166.4
BDD60.260.360.460.761.0
Map65.265.166.165.965.0
Avg.63.763.964.364.364.1
", + "bbox": [ + 501, + 258, + 890, + 353 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/528f0374bf24f337110489f23834719ffb454659ca232b07f9a7b7a7103d093e.jpg", + "table_caption": [ + "Table 9. Ablation study on lora dim $r$ ." + ], + "table_footnote": [], + "table_body": "
VFMsMethodTraining TimeGPU MemoryStorage
DINOv2 (Large)Full11.2 h14.7 GB1.22 GB
Rein9.5 h10.0 GB1.23 GB
", + "bbox": [ + 527, + 372, + 864, + 436 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 10. Training Time, GPU Memory, and Storage.", + "bbox": [ + 535, + 439, + 854, + 453 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "in diverse tasks and settings, we can only store and swap the rein weights (0.01GB) and head weights (0.08GB), rather than all parameters.", + "bbox": [ + 496, + 465, + 890, + 511 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusions", + "text_level": 1, + "bbox": [ + 500, + 522, + 625, + 537 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we assess and harness Vision Foundation Models (VFMs) in the context of DGSS. Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we first investigate the performance of VFMs under diverse DGSS settings. Subsequently, we introduce a robust fine-tuning approach, namely Rein, to parameter-efficiently harness VFMs for DGSS. With a fewer trainable parameters, Rein significantly enhance generalizability of VFMs, outperforming SOTA methods by a large margin. Rein can be seamlessly integrated as a plug-and-play adapter for existing VFMs, improving generalization with efficient training. Extensive experiments demonstrate the substantial potential of VFMs in the DGSS field, validating the effectiveness of proposed Rein in harnessing VFMs for DGSS.", + "bbox": [ + 496, + 546, + 890, + 773 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Acknowledgements", + "text_level": 1, + "bbox": [ + 500, + 786, + 687, + 803 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported in part by the Anhui Provincial Key Research and Development Plan 202304a05020072, in part by the Postdoctoral Fellowship Program of CPSFGZB20230713, and in part by the National Natural Science Foundation of China under Grant 61727809.", + "bbox": [ + 496, + 811, + 890, + 886 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "28626", + "bbox": [ + 478, + 945, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 90, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Yasser Benigmim, Subhankar Roy, Slim Essid, Vicky Kalogeiton, and Stephane Lathuilière. Collaborating foundation models for domain generalized semantic segmentation, 2023. 7", + "[2] Rishi Bommasani, Drew A. 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Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.143, + 0.131, + 0.83, + 0.177 + ], + "angle": 0, + "content": "Stronger, Fewer, & Superior: Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation" + }, + { + "type": "text", + "bbox": [ + 0.093, + 0.202, + 0.87, + 0.24 + ], + "angle": 0, + "content": "Zhixiang Wei\\(^{1*}\\) Lin Chen\\(^{1,2*}\\) Yi Jin\\(^{1*}\\) Xiaoxiao Ma\\(^{1}\\) Tianle Liu\\(^{1}\\) Pengyang Ling\\(^{1,2}\\) Ben Wang\\(^{1}\\) Huaian Chen\\(^{1\\dagger}\\) Jinjin Zheng\\(^{1}\\)" + }, + { + "type": "text", + "bbox": [ + 0.229, + 0.24, + 0.741, + 0.258 + ], + "angle": 0, + "content": "1 University of Science and Technology of China 2 Shanghai AI Laboratory" + }, + { + "type": "text", + "bbox": [ + 0.143, + 0.259, + 0.828, + 0.275 + ], + "angle": 0, + "content": "{zhixiangwei,chlin,xiao_xiao,tleliu,lpyang27,wblzgrsn,anchen}@mail.ustc.edu.cn" + }, + { + "type": "text", + "bbox": [ + 0.354, + 0.278, + 0.612, + 0.293 + ], + "angle": 0, + "content": "{jinyi08,jjzheng}@ustc.edu.cn" + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.318, + 0.275, + 0.487 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.096, + 0.49, + 0.268, + 0.503 + ], + "angle": 0, + "content": "(a) Stronger pre-trained models" + }, + { + "type": "image", + "bbox": [ + 0.274, + 0.33, + 0.53, + 0.485 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.331, + 0.49, + 0.498, + 0.503 + ], + "angle": 0, + "content": "(b) Fewer trainable parameters" + }, + { + "type": "image", + "bbox": [ + 0.538, + 0.33, + 0.717, + 0.405 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.538, + 0.408, + 0.717, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.33, + 0.904, + 0.404 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.725, + 0.408, + 0.904, + 0.481 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.633, + 0.49, + 0.818, + 0.504 + ], + "angle": 0, + "content": "(c) Superior generalization ability" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.507, + 0.895, + 0.564 + ], + "angle": 0, + "content": "Figure 1. Vision Foundation Models (VFMs) are stronger pre-trained models that serve as robust backbones, effortlessly outperforming previous state-of-the-art Domain Generalized Semantic Segmentation (DGSS), as shown in (a). Yet, the extensive parameters of VFMs make them challenging to train. To address this, we introduce a robust fine-tuning approach to efficiently harness VFMs for DGSS. As illustrated in (b) and (c), the proposed methods achieve superior generalizability with fewer trainable parameters within backbones." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.579, + 0.314, + 0.595 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.608, + 0.473, + 0.865 + ], + "angle": 0, + "content": "In this paper, we first assess and harness various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we introduce a robust fine-tuning approach, namely \"Rein\", to parameter-efficiently harness VFMs for DGSS. Built upon a set of trainable tokens, each linked to distinct instances, Rein precisely refines and forwards the feature maps from each layer to the next layer within the backbone. This process produces diverse refinements for different categories within a single image. With fewer trainable parameters, Rein efficiently fine-tunes VFMs for DGSS tasks, surprisingly surpassing full parameter fine-tuning. Extensive experiments across various settings demonstrate that Rein significantly outperforms state-of-the-art methods. Remarkably, with just an extra \\(1\\%\\) of trainable parameters" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.581, + 0.894, + 0.641 + ], + "angle": 0, + "content": "within the frozen backbone, Rein achieves a mIoU of \\(78.4\\%\\) on the Cityscapes, without accessing any real urban-scene datasets. Code is available at https://github.com/wloves/Rein.git." + }, + { + "type": "title", + "bbox": [ + 0.502, + 0.647, + 0.633, + 0.662 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.673, + 0.892, + 0.854 + ], + "angle": 0, + "content": "Prior works [32, 34, 36, 56, 63, 66, 72] in Domain Generalized Semantic Segmentation (DGSS) focus on improving prediction accuracy across multiple unseen domains without accessing their data, thus enabling a high generalization for real applications. Since models are fine-tuned using datasets [11, 57] that are either limited in scale or different in image style from the target domain, complex data augmentation approaches [4, 53, 73] and domain invariant feature extraction strategies [9, 51, 62, 67] have been widely explored in previous DGSS. These methods result in enhanced generalization when applied to classic backbones, e.g., VGGNet [61], MobileNetV2 [60], and ResNet [23]." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.894, + 0.901 + ], + "angle": 0, + "content": "In recent years, large-scale Vision Foundation Models (VFMs) like CLIP [55], MAE [24], SAM [38], EVA02 [17, 18], and DINOv2 [50] have significantly advanced the" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.262, + 0.888 + ], + "angle": 0, + "content": "* indicates equal contributions." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.231, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.262, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28619" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.891, + 0.179 + ], + "angle": 0, + "content": "
Previous DGSS methodsFrozen backbone of VFs
MethodsGTR[53]AdvStyle[73]WildNet[40]SPC[27]PASTA[4]TLDR[37]CLIP-ViT-L[55]MAE-L[24]SAM-H[38]EVA02-L[17]DINOv2-L[50]
PublicationsTIP21NIPS22CVPR22CVPR23ICCV23ICCV23ICML21CVPR22ICCV23arXiv23arXiv23
mIoU (Citys)43.743.445.846.745.347.653.743.357.056.563.3
mIoU (BDD)39.640.341.743.742.344.948.737.847.153.656.1
mIoU (Map)39.142.047.145.548.648.855.048.058.458.663.9
mIoU (Average)40.841.944.945.345.447.152.443.054.256.261.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.182, + 0.891, + 0.21 + ], + "angle": 0, + "content": "Table 1. Performance benchmarking of multiple VFMs and previous DGSS methods under the GTAV \\(\\rightarrow\\) Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting. Without specialized design, frozen VFMs demonstrate stronger performance." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.226, + 0.468, + 0.316 + ], + "angle": 0, + "content": "boundaries of performance in a variety of computer vision challenges. Giving the remarkable generalization of these VFMs across various unseen scenes, two intuitive questions emerge: How do VFMs perform in the context of DGSS? And How to harness VFMs for DGSS? We attempt to answer these questions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.32, + 0.468, + 0.516 + ], + "angle": 0, + "content": "Stronger: We begin by evaluating and comparing the performance of various VFMs against existing DGSS methods. To ensure a fair comparison, we use image encoders from a variety of VFMs as the backbone for feature extraction in all cases. These backbones are coupled with the widely-used decode head, i.e., Mask2Former [8], to generate semantic predictions. As illustrated in Tab. 1, while previous DGSS methods have showcased commendable results, they perform less effectively compared to frozen VFs. This finding clearly demonstrates the powerful potential of VFs in DGSS, outperforming traditional backbones like ResNet [23] and MobileNetV2 [60], thereby establishing VFs as a meaningful benchmark in the field." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.468, + 0.761 + ], + "angle": 0, + "content": "Fewer: Although VFMs have exhibited impressive generalization capabilities, fine-tuning them for DGSS tasks poses a challenge. The datasets [11, 57] commonly used in DGSS tasks are significantly smaller in scale compared to ImageNet [12], and fine-tuning VFs with their huge number of trainable parameters on these datasets result in limited generalizability [33]. To address this issue, instead of the difficult task of large datasets collection, we resort to fine-tuning VFs with fewer trainable parameters. However, most existing parameter-efficient fine-tuning strategies, which fine-tune a large-scale model with fewer trainable parameters, are primarily designed for adapting large language models [25, 26, 41, 43, 44, 70, 74] or classification networks [6, 28]. These methods are not developed for refining features for distinct instances within a single image, thereby limiting their effectiveness in DGSS contexts." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.468, + 0.901 + ], + "angle": 0, + "content": "Superior: In this work, we introduce a robust and efficient fine-tuning approach, namely \"Rein\". Tailored for DGSS tasks, Rein employs fewer trainable parameters to harness stronger VFMs for achieving superior generalization. At its core, Rein comprises a set of randomly initialized tokens, each directly linked to different instances. These tokens, through a dot-product operation with VFMs features, generate an attention-like similarity map. This map enables Rein to perform precise refinement tailored to" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.226, + 0.892, + 0.361 + ], + "angle": 0, + "content": "each instance within an image, significantly boosting VFMs in the context of DGSS. Moreover, to reduce the number of trainable parameters, we employ shared weights across MLPs in different layers and design our learnable tokens by multiplying two low-rank matrices. Extensive experiments on various DGSS settings demonstrate that the proposed Rein outperforms existing DGSS methods by a large margin with fewer trainable parameters. In a nutshell, the main contributions of this paper are as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.363, + 0.892, + 0.466 + ], + "angle": 0, + "content": "- We first assess various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Our extensive experiments in the DGSS framework highlight the impressive generalization capabilities of VFMs. The findings confirm that VFMs serve as Stronger backbones, thereby establishing a significant benchmark in this field." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.468, + 0.892, + 0.588 + ], + "angle": 0, + "content": "- We present a robust fine-tuning method, namely \"Rein\", to parameter-efficiently harness VFMs. At its core, Rein consists of a set of learnable tokens, each directly linked to instances. With deliberate design, this linkage enables Rein to refine features at an instance-level within each layer. As a result, Rein reinforces the ability of VFMs in DGSS tasks, achieving this with Fewer trainable parameters while preserving the pre-trained knowledge." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.589, + 0.892, + 0.709 + ], + "angle": 0, + "content": "- Comprehensive experiments across various DGSS settings demonstrate that Rein employs Fewer trainable parameters to effectively leverage Stronger VFMs for achieving Superior generalizability. This performance surpasses existing DGSS methods by a large margin. Notably, Rein is designed to integrate smoothly with existing plain vision transformers, improving their generalization ability and making training more efficient." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.363, + 0.892, + 0.709 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.725, + 0.649, + 0.74 + ], + "angle": 0, + "content": "2. Related Works" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Domain Generalized Semantic Segmentation. Domain Generalized Semantic Segmentation (DGSS) focuses on enhancing model generalizability. This field involves training models on a set of source domain to enhance their performance on distinct and unseen target domain. Various approaches [5, 13, 20, 21, 27, 29-31, 42, 54, 65] have been proposed to address this issue, with methods including splitting the learned features into domain-invariant and domain-specific components [62, 67], or employing meta-learning to train more robust models [35]. A standard scenario in" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28620" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.088, + 0.1, + 0.891, + 0.293 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.3, + 0.897, + 0.373 + ], + "angle": 0, + "content": "Figure 2. An overview of proposed Rein. Rein primarily consists of a collection of low-rank learnable tokens, denoted as \\( T = \\{T_1, T_2, \\ldots, T_N\\} \\). These tokens establish direct connections to distinct instances, facilitating instance-level feature refinement. This mechanism results in the generation of an enhancement feature map \\( f_i' = f_i + \\text{Rein}(f_i) \\) for each layer within backbone. All parameters of MLPs are layer-shared to reduce the number of parameters. \\( M_f \\), \\( M_Q \\), and \\( M_S \\) are features module, queries module, and segmentation module, respectively. The notation max & avg & last refers to the equation Eq. (8) and Eq. (10)." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.379, + 0.468, + 0.636 + ], + "angle": 0, + "content": "
BackboneFine-tune \nMethodTrainable \nParams*mIoU
CitysBDDMapAvg.
CLIP [55] \n(ViT-Large)Full304.15M51.347.654.351.1
Freeze0.00M53.748.755.052.4
Rein2.99M57.154.760.557.4
MAE [24] \n(Large)Full330.94M53.750.858.154.2
Freeze0.00M43.337.848.043.0
Rein2.99M55.049.358.654.3
SAM [38] \n(Huge)Full632.18M57.651.761.556.9
Freeze0.00M57.047.158.454.2
Rein4.51M59.652.062.157.9
EVA02 [17, 18] \n(Large)Full304.24M62.156.264.660.9
Freeze0.00M56.553.658.656.2
Rein2.99M65.360.564.963.6
DINOV2 [50] \n(Large)Full304.20M63.757.464.261.7
Freeze0.00M63.356.163.961.1
Rein2.99M66.460.466.164.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.638, + 0.472, + 0.695 + ], + "angle": 0, + "content": "Table 2. Performance Comparison with the proposed Rein across Multiple VFMs as Backbones under the GTAV \\(\\rightarrow\\) Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.473, + 0.903 + ], + "angle": 0, + "content": "DGSS is generalizing from one urban-scene dataset to another, for instance, from the synthetic GTAV [57] dataset to the real-world Cityscapes [11]. In this classic setting, certain techniques [9, 51, 52] have achieved notable performance through learning feature normalization/whitening schemes, while others [40] have improved segmentation results through feature-level style transfer and the introduction of additional data. Additionally, strong data augmentation [4, 16, 53, 73] often simply and effectively enhances model robustness. However, most of previous DGSS methods generally utilize outdated backbones like ResNet [23], VGGNet [61], MobileNetV2 [60], and ShuffleNetV2 [47], thereby leaving the efficacy of stronger Vision Foundation" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.382, + 0.82, + 0.398 + ], + "angle": 0, + "content": "Models (VFMs) in DGSS relatively unexplored." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.4, + 0.892, + 0.747 + ], + "angle": 0, + "content": "Vision Foundation Models. The concept of a Foundation Model, initially introduced by Bommasani et al. [2] in the field of Natural Language Processing (NLP), defined as \"the base models trained on large-scale data in a self-supervised or semi-supervised manner that can be adapted for several other downstream tasks\". While models like the ViT [14] and Swin Transformer [45] have demonstrated excellent performance, the quest for a Vision Foundation Model (VFM) similar to their NLP counterparts is ongoing. This pursuit has yielded significant advancements with the advent of models such as CLIP [55], which learn high-quality visual representation by exploring contrastive learning with large-scale image text pairs; MAE [24], utilizing a masked image modeling for learning latent image representations; SAM [38], which develops a promptable model and pre-train it on a broad dataset for segmentation task; EVA02 [17, 18], which integrates Masked Image Modeling pre-training with CLIP's vision features; and DINOv2 [50], which is pretrained on extensive, curated datasets without explicit supervision. These VFs have shown remarkable performance in downstream applications. Yet, a dedicated investigation into their performance in the specific context of DGSS tasks remains unexplored." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Parameter-Efficient Fine-tuning. In the realm of NLP, parameter-efficient fine-tuning (PEFT) has achieved notable success by freezing most parameters of VFMs and fine-tuning a select few. Various approaches have been developed, such as BitFit [70], which adjusts only the model's bias terms; Prompt-tuning [41], introducing soft prompts to adapt frozen language models; Adapter-tuning [25], adding lightweight modules to each transformer layer; and notably, LoRA [26], which injects trainable rank decomposition matrices into transformer layers, yielding significant influence." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.958 + ], + "angle": 0, + "content": "28621" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.085, + 0.089, + 0.891, + 0.158 + ], + "angle": 0, + "content": "
TargetACDC[59] (test)Cityscapes-C[48] (level-5)
Night Snow Fog RainAllBlurNoiseDigitalWeatherAvg.
MotionDefocGlassGaussGaussImpulShotSpeckBrightContrSaturJPEGSnowSpattFogFrost
HGFormer52.768.669.972.067.264.167.261.563.627.235.732.963.179.972.978.053.655.475.875.543.2
Ours70.679.576.478.277.668.571.769.768.76.223.013.163.781.578.980.668.863.873.679.547.9
" + }, + { + "type": "table_caption", + "bbox": [ + 0.152, + 0.159, + 0.816, + 0.173 + ], + "angle": 0, + "content": "Table 3. Results on Cityscapes \\( \\rightarrow \\) ACDC (test) and Cityscapes-C (level-5) datasets, utilizing a batch size of 8." + }, + { + "type": "table", + "bbox": [ + 0.086, + 0.183, + 0.468, + 0.559 + ], + "angle": 0, + "content": "
BackboneFine-tune \nMethodTrainable \nParams*mIoU
CitysBDDMapAvg.
EVA02 \n(Large) \n[17, 18]Full304.24M62.156.264.660.9
+AdvStyle [73]304.24M63.156.464.061.2
+PASTA [4]304.24M61.857.163.660.8
+GTR-LTR [53]304.24M59.857.463.260.1
Freeze0.00M56.553.658.656.2
+AdvStyle [73]0.00M51.451.656.553.2
+PASTA [4]0.00M57.852.358.556.2
+GTR-LTR [53]0.00M52.552.857.154.1
+LoRA [26]1.18M55.552.758.355.5
+AdaptFormer [6]3.17M63.759.964.262.6
+VPT [28]3.69M62.257.762.560.8
+Rein (ours)2.99M65.360.564.963.6
DINOv2 \n(Large) \n[50]Full304.20M63.757.464.261.7
+AdvStyle [73]304.20M60.858.062.560.4
+PASTA [4]304.20M62.557.264.761.5
+GTR-LTR [4]304.20M62.757.464.561.6
Freeze0.00M63.356.163.961.1
+AdvStyle [73]0.00M61.555.163.960.1
+PASTA [4]0.00M62.157.264.561.3
+GTR-LTR [4]0.00M60.257.762.260.0
+LoRA [26]0.79M65.258.364.662.7
+AdaptFormer [6]3.17M64.959.064.262.7
+VPT [28]3.69M65.259.465.563.3
+Rein (ours)2.99M66.460.466.164.3
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.561, + 0.47, + 0.618 + ], + "angle": 0, + "content": "Table 4. Performance Comparison of the proposed Rein against other DGSS and PEFT methods under the GTAV \\(\\rightarrow\\) Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.471, + 0.81 + ], + "angle": 0, + "content": "The application of PEFT methods is also expanding into the field of computer vision [15, 39], with notable examples such as Visual Prompt Tuning (VPT) [28], which prepends prompts into the input sequence of transformer layers; AdaptFormer [6], replacing the MLP block in the transformer encoder with an AdaptMLP; LP-FT [39] find that fine-tuning can achieve worse accuracy than linear probing out-of-distribution; and Prompt-ICM [19], applying large-scale pre-trained models to the task of image coding for machines. Contrasting with these methods, we aim to refine feature maps for each instance within an image, thereby achieving superior performance in the realm of DGSS." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.822, + 0.176, + 0.837 + ], + "angle": 0, + "content": "3. Methods" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.847, + 0.207, + 0.864 + ], + "angle": 0, + "content": "3.1. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Driven by the motivation that Leveraging Stronger pretrained models and Fewer trainable parameters for Su" + }, + { + "type": "table", + "bbox": [ + 0.518, + 0.183, + 0.875, + 0.27 + ], + "angle": 0, + "content": "
Source DomainCityscapes mIoU
GTAV66.4
+Synthia68.1
+UrbanSyn78.4
+1/16 of Cityscapes Training set82.5
" + }, + { + "type": "table_caption", + "bbox": [ + 0.521, + 0.272, + 0.871, + 0.287 + ], + "angle": 0, + "content": "Table 5. Synthetic data + 1/16 of Citys. → Citys. val set." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.892, + 0.478 + ], + "angle": 0, + "content": "perior generalizability, we choose to fine-tune VFMs with a reduced parameter set. A straightforward thought might involve a smaller decode head; however, this method merely acts as a passive receiver of feature maps from the backbone, lacking the flexibility to effectively adapt a frozen backbone for generating task-specific or scene-specific features. In contrast, we propose to embed a mechanism, named \"Rein\", between the layers within the backbone. Rein actively refines and forwards the feature maps from each layer to the subsequent one. This approach allows us to more effectively utilize the powerful capabilities of VFMs, much like using rein to control a horse." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.479, + 0.892, + 0.54 + ], + "angle": 0, + "content": "Given a pre-trained VFM with parameters \\(\\Phi_M\\), consisting of a sequence of layers \\(L_{1}, L_{2}, \\ldots, L_{N}\\), a decode head \\(\\mathcal{H}\\) parameterized by \\(\\theta_h\\), and the Rein strategy with parameters \\(\\theta_R\\), the optimization objective can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.548, + 0.892, + 0.59 + ], + "angle": 0, + "content": "\\[\n\\underset {\\theta_ {R}, \\theta_ {h}} {\\arg \\min } \\sum_ {i = 1} ^ {N _ {d}} \\operatorname {L o s s} \\left(\\mathcal {H} _ {\\theta_ {h}} \\left(\\mathcal {F} _ {\\Phi_ {M}, \\theta_ {R}} \\left(x _ {i}\\right)\\right), y _ {i}\\right), \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.599, + 0.892, + 0.66 + ], + "angle": 0, + "content": "where \\( x_{i} \\) and \\( y_{i} \\) denote the input image and its corresponding ground truth, respectively, and \\( N_{d} \\) signifies the total number of samples. \\( \\mathcal{F}_{\\Phi_M,\\theta_R} \\) represents the forward process of VFM after applying the Rein strategy." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.668, + 0.636, + 0.683 + ], + "angle": 0, + "content": "3.2. Core of Rein" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.691, + 0.892, + 0.797 + ], + "angle": 0, + "content": "For simple implementation across different VFMs, we opt not to modify MLP weights at specific positions as described in the [6, 26]. Instead, our approach focuses on refining the output feature maps at each layer within the VFMs, as illustrated in Fig. 2. Precisely, for the features \\( f_{i} \\) produced by the \\( i \\)-th layer \\( L_{i} \\), Rein produces enhanced feature maps for the next layer as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.534, + 0.807, + 0.8, + 0.823 + ], + "angle": 0, + "content": "\\[\nf _ {1} = L _ {1} (E m b e d (x)) \\quad f _ {1} \\in \\mathbb {R} ^ {n \\times c},\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.518, + 0.826, + 0.891, + 0.842 + ], + "angle": 0, + "content": "\\[\nf _ {i + 1} = L _ {i + 1} \\left(f _ {i} + \\Delta f _ {i}\\right) \\quad i = 1, 2, \\dots , N - 1, \\tag {2}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.521, + 0.845, + 0.654, + 0.861 + ], + "angle": 0, + "content": "\\[\nf _ {o u t} = f _ {N} + \\Delta f _ {N},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\( f_{i}^{\\prime} = f_{i} + \\Delta f_{i} \\) symbolizes the refined feature map, \\( x \\) is the input image, \\( \\text{Embed} \\) denotes the patch embedding" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28622" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "layer in VFMs, \\( n \\) represents the number of patches, \\( N \\) denotes the number of layers, and \\( c \\) is the dimensionality of \\( f_{1}, f_{2}, \\ldots, f_{N} \\). Note that the layers \\( L_{1}, L_{2}, \\ldots, L_{N} \\) are kept frozen, and our focus is on training an efficient module, Rein, to generate \\( \\Delta f_{i} \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.092, + 0.179, + 0.47, + 0.196 + ], + "angle": 0, + "content": "\\[\n\\Delta f _ {i} = \\operatorname {R e i n} (f _ {i}) \\quad \\Delta f _ {i} \\in \\mathbb {R} ^ {n \\times c}, i = 1, 2, \\dots , N. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.208, + 0.469, + 0.314 + ], + "angle": 0, + "content": "In the context of DGSS, an ideal \\(\\Delta f_{i}\\) should assist VFMs to bridge two types of gaps. The first is gap in scene between pre-training dataset and target scene, exemplified by the contrast between ImageNet [12] and urban-scene images [11, 57]. The second is task divergence between pretraining and fine-tuning, such as the differences between masked image modeling and semantic segmentation tasks." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.555 + ], + "angle": 0, + "content": "To establish this dual bridge, Rein starts with a set of learnable tokens \\( T = \\{T_{i} \\in \\mathbb{R}^{m \\times c} \\mid i \\in \\mathbb{N}, 1 \\leq i \\leq N\\} \\), where each token sequence \\( T_{i} \\) is randomly initialized, and \\( m \\) denotes the sequence length of \\( T_{i} \\). Rein freezes the backbone and embeds knowledge learned from the finetuning dataset into these tokens, thereby bridging the gap in scene relative to the pre-training dataset. Moreover, considering the essential need in semantic segmentation to discern multiple instances within a single image, Rein implements an attention-inspired mechanism, which enables VFMs to make tailored adjustments to the features of distinct instances, thereby aiding VFMs in adapting to the differences between semantic segmentation and pre-training tasks. Specifically, Rein employs a dot-product operation to generate a similarity map \\( S_{i} \\), which captures the associations between feature vectors in \\( f_{i} \\) and the tokens in \\( T \\):" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.569, + 0.469, + 0.587 + ], + "angle": 0, + "content": "\\[\nS _ {i} = f _ {i} \\times T _ {i} ^ {\\mathrm {T}} \\quad S _ {i} \\in \\mathbb {R} ^ {n \\times m}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.594, + 0.469, + 0.669 + ], + "angle": 0, + "content": "where \\( T_{i} \\) represents the token sequence of the \\( i \\)-th layer, \\( m \\) indicates the number of tokens in \\( T_{i} \\). As \\( S \\) quantitatively evaluates the relationships between various tokens and feature vectors, Rein can apply a softmax function to align each patch with a unique instance:" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.68, + 0.469, + 0.715 + ], + "angle": 0, + "content": "\\[\nS _ {i} = \\operatorname {S o f t m a x} \\left(\\frac {f _ {i} \\times T _ {i} ^ {\\mathrm {T}}}{\\sqrt {c}}\\right). \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.725, + 0.469, + 0.755 + ], + "angle": 0, + "content": "Leveraging the feature-to-token similarity map \\( S_{i} \\), we can preliminarily estimates of \\( \\Delta f_{i} \\) using the equation:" + }, + { + "type": "equation", + "bbox": [ + 0.104, + 0.766, + 0.469, + 0.784 + ], + "angle": 0, + "content": "\\[\n\\Delta \\bar {f} _ {i} = S _ {i} (:, 2: m) \\times \\left[ T _ {i} (2: m) \\times W _ {T _ {i}} + b _ {T _ {i}} \\right], \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.795, + 0.469, + 0.901 + ], + "angle": 0, + "content": "where \\( W_{T_i} \\) and \\( b_{T_i} \\) denote the weights and biases of a MLP, respectively. This MLP enables the transformation of \\( T_i \\) across different feature spaces during the computation of \\( S_i \\) and \\( \\Delta \\bar{f}_i \\). Optionally, Rein can pre-calculate \\( T_i \\times W_{T_i} + b_{T_i} \\) to reduce inference time. The sum of \\( S_i \\) equals one due to the softmax function; however, this can induce unneeded changes when all features are precise. To" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "avoid this, \\( S_{i}(:,2:m) \\) is designed to choose columns 2 to m of \\( S_{i} \\), and \\( T_{i}(2:m) \\) denotes the selection of rows 2 to m of \\( T_{i} \\). This strategic selection allows models to sidestep unnecessary adjustments by assigning a high value to the first token and subsequently discarding it. This approach allows the sum of each row in \\( S_{i} \\) to vary from 0 to 1, thus reducing the risk of inappropriate changes." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.197, + 0.892, + 0.243 + ], + "angle": 0, + "content": "To enhance the flexibility in feature adjustment, Rein utilizes a MLP composed of \\( W_{f_i} \\) and \\( b_{f_i} \\) to produce the final feature modifications \\( \\Delta f_i \\):" + }, + { + "type": "equation", + "bbox": [ + 0.586, + 0.253, + 0.892, + 0.271 + ], + "angle": 0, + "content": "\\[\n\\Delta f _ {i} = \\left(\\Delta \\bar {f} _ {i} + f _ {i}\\right) \\times W _ {f _ {i}} + b _ {f _ {i}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.281, + 0.892, + 0.341 + ], + "angle": 0, + "content": "Benefiting from these instance-level \\(\\Delta f_{i}\\) adjustments, Rein is capable of generating diverse modifications for various categories within a single image. The details of Rein will be explained in the next section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.351, + 0.65, + 0.365 + ], + "angle": 0, + "content": "3.3. Details of Rein" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.374, + 0.892, + 0.51 + ], + "angle": 0, + "content": "Linking tokens to instances. At the core of Rein, we establish an implicit yet effective linkage between tokens and instances, which has demonstrated notable performance, as detailed in Sec. 4. This connection is further reinforced by utilizing object queries, a key component in DETR[3]-style decode heads [7, 8, 71], as intermediaries. These queries are empirically proven to establish a direct association with instances. Specifically, we generate layer-wise queries \\( Q_{i} \\) from our learnable tokens \\( T_{i} \\) via linear transformation:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.52, + 0.891, + 0.538 + ], + "angle": 0, + "content": "\\[\nQ _ {i} = T _ {i} \\times W _ {Q _ {i}} + b _ {Q _ {i}} \\quad Q _ {i} \\in \\mathbb {R} ^ {m \\times c ^ {\\prime}}, \\tag {8}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.548, + 0.892, + 0.669 + ], + "angle": 0, + "content": "where \\( W_{Q_i} \\) and \\( b_{Q_i} \\) signify the weights and biases, respectively, and \\( c' \\) denotes the dimension of \\( Q_i \\). However, due to the complexity arising from the large numbers of various layers in VFMs, transforming the diverse \\( Q_i \\) into a single query \\( Q \\) poses computational challenges. To address this, Rein computes both the maximal component \\( Q_{\\text{max}} \\in \\mathbb{R}^{m \\times c'} \\) and the average component \\( Q_{\\text{avg}} \\in \\mathbb{R}^{m \\times c'} \\) using the following equation:" + }, + { + "type": "equation", + "bbox": [ + 0.582, + 0.68, + 0.809, + 0.703 + ], + "angle": 0, + "content": "\\[\nQ _ {m a x} (j, k) = \\max _ {i = 1, 2, \\dots , N} Q _ {i} (j, k),\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.589, + 0.706, + 0.891, + 0.748 + ], + "angle": 0, + "content": "\\[\nQ _ {a v g} (j, k) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} Q _ {i} (j, k). \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.757, + 0.704, + 0.772 + ], + "angle": 0, + "content": "Subsequently, \\(Q\\) is derived as:" + }, + { + "type": "equation", + "bbox": [ + 0.524, + 0.783, + 0.891, + 0.8 + ], + "angle": 0, + "content": "\\[\nQ = \\operatorname {C o n c a t} \\left(\\left[ Q _ {\\max }, Q _ {\\text {a v g}}, Q _ {N} \\right]\\right) \\times W _ {Q} + b _ {Q}. \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.81, + 0.892, + 0.856 + ], + "angle": 0, + "content": "By mapping \\( T \\) onto \\( Q \\), which subsequently links to instances, Rein achieves enhanced performance with a marginal increase in parameters." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Layer-shared MLP weights. To address the redundancy of parameters in the layer-specific MLP weights, specifically \\( W_{T_i} \\) in Eq. (6), \\( W_{f_i} \\) in Eq. (7), and \\( W_{Q_i} \\) in Eq. (8), which" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28623" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.473, + 0.198 + ], + "angle": 0, + "content": "collectively contribute to a substantial trainable parameter count, we adopt a new strategy. Since the learnable \\( T_{i} \\) is capable of producing distinct \\( \\Delta f_{i} \\) for each layer, we design the role of the MLP to primarily perform consistent linear transformations across different feature spaces for each layer within the backbone. To this end, we employ shared MLP weights across layers as outlined in the equations:" + }, + { + "type": "equation", + "bbox": [ + 0.098, + 0.208, + 0.468, + 0.264 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\left[ W _ {T _ {1}}, b _ {T _ {1}} \\right] = \\left[ W _ {T _ {2}}, b _ {T _ {2}} \\right] = \\dots = \\left[ W _ {T _ {N}}, b _ {T _ {N}} \\right], \\\\ \\left[ W _ {f _ {1}}, b _ {f _ {1}} \\right] = \\left[ W _ {f _ {2}}, b _ {f _ {2}} \\right] = \\dots = \\left[ W _ {f _ {N}}, b _ {f _ {N}} \\right], \\tag {11} \\\\ \\left[ W _ {Q _ {1}}, b _ {Q _ {1}} \\right] = \\left[ W _ {Q _ {2}}, b _ {Q _ {2}} \\right] = \\dots = \\left[ W _ {Q _ {N}}, b _ {Q _ {N}} \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.273, + 0.47, + 0.349 + ], + "angle": 0, + "content": "Low-rank token sequence. Recognizing the potential for information overlap among diverse learnable tokens, such as the high similarity between tokens representing a car's headlight and a bicycle's light, Rein adopts a strategy to generate a low-rank token sequence \\( T \\) as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.115, + 0.359, + 0.469, + 0.376 + ], + "angle": 0, + "content": "\\[\nT i = A _ {i} \\times B _ {i}, \\quad A \\in \\mathbb {R} ^ {m \\times r}, B \\in \\mathbb {R} ^ {r \\times c}, \\tag {12}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.387, + 0.47, + 0.478 + ], + "angle": 0, + "content": "where \\( c \\) denotes the dimension of \\( T_{i} \\), \\( m \\) is the length of sequence \\( T_{i} \\), and \\( r \\) represents the rank, with \\( r \\ll c \\). Here, matrices \\( A \\) and \\( B \\) are constructed as low-rank matrices. To reduce inference time, Rein can precompute and store \\( T \\). By implementing this low-rank token sequence approach, Rein significantly reduces the number of parameters." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.491, + 0.21, + 0.508 + ], + "angle": 0, + "content": "4. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.515, + 0.176, + 0.531 + ], + "angle": 0, + "content": "4.1. Settings" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.538, + 0.47, + 0.81 + ], + "angle": 0, + "content": "Visual Foundation Models. To thoroughly assess the influence of Visual Foundation Models (VFMs) within the context of DGSS, we analyze five distinct VFMs, each with different training strategies and datasets. Our selection includes CLIP [55], a language-image pre-training model; MAE [24], known for its masked pre-training approach; SAM [38], which leverages a large-scale segmentation dataset; EVA02 [17, 18] combines CLIP with masked image modeling; and DINOv2 [50], based on self-supervised pretraining with curated dataset. For balancing precision and efficiency, we mainly employ the ViT-Large architecture for these VFMs, except SAM, which utilizes a ViT-Huge image encoder, as described in its original paper [38]. We establish two fundamental baselines for VFMs: \"Full\", where we fine-tune the entire network, and \"Freeze\", in which all backbone parameters are fixed, with training solely on the segmentation head. More details about VFMs and PEFT methods are available in the supplementary material." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.811, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Datasets. We evaluate VFs and proposed methods on both real-world datasets (Cityscapes [11], BDD100K [68], Mapillary [49]) and synthetic datasets (GTAV [57], Synthia [58], UrbanSyn [22]). In detail, Cityscapes (denoted as Citys) is an autonomous driving dataset that contains 2975 training images and 500 validation images, each with the" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.198 + ], + "angle": 0, + "content": "resolution of \\(2048 \\times 1024\\). BDD100K (shortened to BDD) and Mapillary (denoted by Map) offer 1,000 (\\(1280 \\times 720\\)) and 2,000 (\\(1902 \\times 1080\\)) validation images, respectively. GTAV, a synthetic dataset, presents 24,966 labeled images obtained from the game. Synthia, a synthetic dataset, provides 25,000 images created by photo-realistic rendering. UrbanSyn, a synthetic dataset consists of 7,539 images." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.893, + 0.456 + ], + "angle": 0, + "content": "Implementation details. We utilize the MMSegmentation [10] codebase for our implementation. For superior performance, mask2former [8], a widely-used segmentation head, is integrated with various VFMs that serve as the backbone. Additional experiments involving other decode heads are detailed in the supplementary material. For the training phase, the AdamW optimizer [46] is employed, setting the learning rate at 1e-5 for the backbone and 1e-4 for both the decode head and the proposed Rein. Aiming to efficient training process, we utilize a configuration of 40,000 iterations with a batch size of 4, and crop images to a resolution of \\(512 \\times 512\\). Our approach includes only basic data augmentation, following Mask2Former [8]. Thanks to our streamlined training configuration and reduced number of trainable parameters, Rein can fine-tune models like DINOv2-Large or EVA02-Large on a single RTX 3090Ti GPU within 12 hours for superior generalization ability." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.468, + 0.874, + 0.484 + ], + "angle": 0, + "content": "4.2. Comparison with State-of-The-Art Methods" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.492, + 0.892, + 0.629 + ], + "angle": 0, + "content": "In this section, we comprehensively evaluate Rein over five datasets within three generalization settings: \\(GTAV \\rightarrow Citys + BDD + Map\\), \\(GTAV + Synthia \\rightarrow Citys + BDD + Map\\), and \\(Citys \\rightarrow BDD + Map\\). Rein is benchmarked against state-of-the-art (SOTA) methods, which can be classified into two groups, including domain generalized semantic segmentation (DGSS) methods[4, 9, 13, 27, 35, 40, 51, 53, 54, 64, 69, 73], and parameter-efficient fine-tuning (PEFT) approaches [6, 26, 28]." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.63, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Investigation of various VFMs. Our analysis of VFMs and proposed Rein in the \\(GTAV \\rightarrow Citys + BDD + Map\\) setting is presented in Tables 1 and 2. In this setup, models are fine-tuned using GTAV and evaluated on Cityscapes, BDD100K, and Mapillary. Note that, due to the fixed and relatively small number of trainable parameters in the decode head (20.6M), the count of trainable parameters presented in the tables are focused solely on the backbone and the PEFT module. Our results, as detailed in Table 1, indicate that frozen VFMs significantly outperform previous DGSS methods without specialized design. Moreover, as shown in Table 2, VFMs with full parameter fine-tuning exhibit enhanced performance relative to their frozen counterparts. Remarkably, Rein achieves even superior generalization capabilities, surpassing the full parameter fine-tuning with merely an extra \\(1\\%\\) of trainable parameters compared to the original backbone. Visual samples for qualitative comparison are given in Fig. 3." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.521, + 0.958 + ], + "angle": 0, + "content": "28624" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.084, + 0.089, + 0.894, + 0.253 + ], + "angle": 0, + "content": "
BackboneFine-tune \nMethodTrainable \nParams*roadside.build.wallfencepolelightsignvegeterr.skypers.ridercartruckbustrainmoto.bicy.mIoU
EVA02 \n(Large) \n[17, 18]Full304.24M89.346.989.947.745.650.156.842.288.848.489.975.849.090.545.369.255.944.455.162.2
Freeze0.00M93.152.788.047.431.141.746.039.685.741.489.567.539.789.047.072.846.319.235.256.5
Rein-core52.84M91.153.890.050.347.746.656.442.987.844.290.473.544.291.858.177.257.343.457.363.4
+ Rein-link59.33M90.948.590.052.649.449.157.239.888.946.590.574.444.091.052.380.767.344.360.364.1
+ Rein-share5.02M92.754.390.051.848.648.855.345.088.946.789.873.743.390.649.581.169.641.750.263.4
+ Rein-lora2.99M91.751.890.152.848.448.256.042.089.144.190.274.247.091.154.584.178.947.259.465.3
DINOv2 \n(Large) \n[50]Full304.20M89.044.589.651.146.449.260.038.989.147.591.775.848.291.752.582.981.030.449.963.7
Freeze0.00M92.155.290.257.248.549.556.747.789.347.891.174.246.792.262.677.547.729.647.261.1
Rein-core52.84M92.457.890.656.850.750.557.544.889.847.091.175.947.291.960.180.359.837.952.364.9
+ Rein-link59.33M91.255.590.655.652.551.159.745.189.847.191.175.847.192.664.682.265.540.452.765.8
+ Rein-share5.02M93.561.290.757.753.252.458.050.189.749.990.774.845.091.758.580.166.336.950.765.8
+ Rein-lora2.99M92.459.190.758.353.751.858.246.489.849.490.873.943.392.364.381.670.940.454.066.4
" + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.254, + 0.895, + 0.296 + ], + "angle": 0, + "content": "Table 6. Ablation Study about Rein under Cityscapes \\( \\rightarrow \\) BDD100K generalization in terms of mIoU. Components are sequentially incorporated. To better illustrate the gains contributed by each component, we employ varying shades of yellow to demonstrate the relative performance of the Freeze and Rein methods. The best results across all methods are highlighted." + }, + { + "type": "image", + "bbox": [ + 0.081, + 0.297, + 0.891, + 0.491 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.089, + 0.493, + 0.881, + 0.508 + ], + "angle": 0, + "content": "Figure 3. Qualitative Comparison under GTAV \\(\\rightarrow\\) Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.52, + 0.473, + 0.762 + ], + "angle": 0, + "content": "Comparing Rein with SOTA. We conduct a comprehensive performance comparison of the proposed Rein against existing DGSS and PEFT methods under the \\(GTAV \\rightarrow Citys + BDD + Map\\) setting, as detailed in Table 4. Owing to the robust feature extraction capabilities inherent in VFMs, DGSS methods, which typically enhance generalizability through strong data augmentation or consistency constraints, (e.g., AdvStyle, PASTA, and GTR), do not exhibit significant performance improvement. On the other hand, PEFT methods have demonstrated notable advancements. For instance, AdaptFormer outperforms the \"Freeze\" baseline using EVA02 as the backbone, while VPT shows improved performance over \"Full\" with DINOv2. Employing the same backbones (DINOv2 and EVA02), proposed Rein achieves superior performance and surpass previous DGSS and PEFT methods." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.901 + ], + "angle": 0, + "content": "Real-to-Real generalization of Rein. The generalization from one real-world dataset to others is pivotal for practical applications in the field. To this end, we conduct experiments under the \\( \\text{Citys} \\rightarrow \\text{ACDC} \\), \\( \\text{Citys} \\rightarrow \\text{Cityscapes-C} \\), and \\( \\text{Citys} \\rightarrow \\text{BDD} + \\text{Map} \\) generalization setting. As shown in Table 3 and 7, Rein, when coupled with the DINOv2-Large, demonstrates superior performance across all datasets. This underscores the effectiveness of Rein in generalizing to diverse real-world scenarios." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.52, + 0.892, + 0.67 + ], + "angle": 0, + "content": "Synthetic-to-real generalization of Rein. As Tab. 5 illustrates, trained on synthetic UrbanSyn+GTAV+Synthia datasets, Rein achieved a \\(78.4\\%\\) mIoU on the Cityscapes validation set. Further improvement is possible with additional synthetic data and higher-quality images generated by diffusion models, like [1]. This result can also be a valuable pre-trained weight for data-efficient training, reaching an \\(82.5\\%\\) mIoU with 1/16 of Cityscapes training set. This is a significant performance for semi-supervised semantic segmentation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.671, + 0.892, + 0.747 + ], + "angle": 0, + "content": "More backbones. We extend our analysis to integrating Rein with Convolutional Networks, such as ResNet and ConvNeXt, and smaller scale architectures like DINOv2-S/B. As shown in Table 8, our findings reveal that Rein exhibits remarkable performance with diverse backbones." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.757, + 0.768, + 0.773 + ], + "angle": 0, + "content": "4.3. Ablation Studies and Analysis" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.892, + 0.81 + ], + "angle": 0, + "content": "We conduct extensive ablation studies within two settings: \\(GTAV \\to Citys\\) and \\(GTAV \\to Citys + BDD + Map\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Analysis of the key components. Table 6 is dedicated to thoroughly examining the effectiveness of each component within Rein. In the \\(GTAV \\rightarrow City\\) generalization setting, we sequentially incorporate different components of Rein and assess their impact. Interestingly, we observe that the \"Freeze\" occasionally exhibit better recognition for specific" + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28625" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.086, + 0.089, + 0.462, + 0.242 + ], + "angle": 0, + "content": "
MethodsBackboneTrainable \nParameters*mIoU
BDDMapAvg.
IBN [51]ResNet50 [23]23.58M48.657.052.8
DRPC [69]ResNet50 [23]23.58M49.956.353.1
GTR [53]ResNet50 [23]23.58M50.857.254.0
SAN-SAW [54]ResNet50 [23]23.58M53.059.856.4
WildNet [40]ResNet101 [23]42.62M50.958.854.9
HGFformer [13]Swin-L [45]196.03M61.572.166.8
FreezeEVA02-L [17]0.00M57.863.860.8
Rein (Ours)EVA02-L [17]2.99M64.169.566.8
FreezeDINOv2-L [50]0.00M63.469.766.7
Rein (Ours)DINOv2-L [50]2.99M65.072.368.7
" + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.244, + 0.47, + 0.287 + ], + "angle": 0, + "content": "Table 7. Performance Comparison of the Rein against other DGSS methods under Cityscapes \\(\\rightarrow\\) BDD100K (BDD) +Mapillary (Map) generalization. The best results are highlighted." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.293, + 0.477, + 0.364 + ], + "angle": 0, + "content": "
Avg. mIoUResNet (50)ResNet (101)ConvNeXt (Large)DINOv2 (S)DINOv2 (B)
Full38.946.152.251.856.7
Ours46.646.355.555.759.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.105, + 0.365, + 0.441, + 0.379 + ], + "angle": 0, + "content": "Table 8. Results for ConvNets and smaller backbones." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.396, + 0.469, + 0.517 + ], + "angle": 0, + "content": "categories, e.g., 'road, sidewalk', compared to the \"Full\". This suggests that VFMs lose some pre-training knowledge during fine-tuning, and \"Freeze\" helps to prevent. Similarly, our methods mitigate this knowledge forgetting. Furthermore, our methods show improved recognition capabilities for the majority of the 19 categories. For example, in recognizing 'wall, motorcycle, bicycle', our approach significantly outperforms both the \"Full\" and \"Freeze\" baselines." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.518, + 0.469, + 0.623 + ], + "angle": 0, + "content": "Overall, \"Rein-core\" boosts the average performance across 19 classes. Furthermore, \"Rein-link\" further boosts accuracy for certain objects, including 'car, bus, train, motorcycle', especially for DINOv2. Employing layer-shared MLP weights and low-rank token sequence efficiently reduces the number of trainable parameters and positively influences the performance of the model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.626, + 0.469, + 0.716 + ], + "angle": 0, + "content": "Study on token length \\( m \\). The core component of Rein is learnable tokens \\( T \\in \\mathbb{R}^{m \\times c} \\). We explored various lengths \\( m \\) for the token sequence, ranging from 25 to 200. As demonstrated in Fig. 4, models with \\( m = 100 \\) and \\( m = 150 \\) both achieve a strong mIoU of \\( 64.3\\% \\). We ultimately selected \\( m = 100 \\) as the most suitable parameter." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.718, + 0.469, + 0.794 + ], + "angle": 0, + "content": "Study on rank \\( r \\). As shown in Table 9, we turn attention to the effect of rank \\( r \\) on model performance. With DINOv2 as the backbone, the optimal results are observed at \\( r = 16 \\) and \\( r = 32 \\). Consequently, unlike LoRA [26], we opt for a comparatively higher value of \\( r = 16 \\) for our model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.796, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Speed, memory, and storage. For practical applications, training speed, GPU memory usage, and model storage requirements are crucial. As shown in Table 10, compared to \"Full\" baseline, proposed Rein improves training speed and reduces GPU memory usage. A significant advantage of Rein is that models trained under different settings can share the same backbone parameters. This means that for switch" + }, + { + "type": "image", + "bbox": [ + 0.499, + 0.088, + 0.892, + 0.239 + ], + "angle": 0, + "content": null + }, + { + "type": "table_caption", + "bbox": [ + 0.563, + 0.242, + 0.828, + 0.256 + ], + "angle": 0, + "content": "Figure 4. Ablation study on token length \\( m \\)." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.259, + 0.892, + 0.354 + ], + "angle": 0, + "content": "
Rank r \nParams48163264
2.67M2.77M2.99M3.42M4.28M
DINOv2 \n(Large) \n[50]Citys65.866.166.466.166.4
BDD60.260.360.460.761.0
Map65.265.166.165.965.0
Avg.63.763.964.364.364.1
" + }, + { + "type": "table_caption", + "bbox": [ + 0.581, + 0.356, + 0.81, + 0.37 + ], + "angle": 0, + "content": "Table 9. Ablation study on lora dim \\( r \\) ." + }, + { + "type": "table", + "bbox": [ + 0.529, + 0.373, + 0.865, + 0.438 + ], + "angle": 0, + "content": "
VFMsMethodTraining TimeGPU MemoryStorage
DINOv2 (Large)Full11.2 h14.7 GB1.22 GB
Rein9.5 h10.0 GB1.23 GB
" + }, + { + "type": "table_caption", + "bbox": [ + 0.536, + 0.44, + 0.855, + 0.454 + ], + "angle": 0, + "content": "Table 10. Training Time, GPU Memory, and Storage." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.466, + 0.892, + 0.512 + ], + "angle": 0, + "content": "in diverse tasks and settings, we can only store and swap the rein weights (0.01GB) and head weights (0.08GB), rather than all parameters." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.523, + 0.627, + 0.538 + ], + "angle": 0, + "content": "5. Conclusions" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.547, + 0.892, + 0.774 + ], + "angle": 0, + "content": "In this paper, we assess and harness Vision Foundation Models (VFMs) in the context of DGSS. Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we first investigate the performance of VFMs under diverse DGSS settings. Subsequently, we introduce a robust fine-tuning approach, namely Rein, to parameter-efficiently harness VFMs for DGSS. With a fewer trainable parameters, Rein significantly enhance generalizability of VFMs, outperforming SOTA methods by a large margin. Rein can be seamlessly integrated as a plug-and-play adapter for existing VFMs, improving generalization with efficient training. Extensive experiments demonstrate the substantial potential of VFMs in the DGSS field, validating the effectiveness of proposed Rein in harnessing VFMs for DGSS." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.787, + 0.688, + 0.804 + ], + "angle": 0, + "content": "6. Acknowledgements" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.812, + 0.892, + 0.887 + ], + "angle": 0, + "content": "This work was supported in part by the Anhui Provincial Key Research and Development Plan 202304a05020072, in part by the Postdoctoral Fellowship Program of CPSFGZB20230713, and in part by the National Natural Science Foundation of China under Grant 61727809." + }, + { + "type": "page_number", + "bbox": [ + 0.479, + 0.946, + 0.521, + 0.957 + ], + "angle": 0, + "content": "28626" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.091, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Yasser Benigmim, Subhankar Roy, Slim Essid, Vicky Kalogeiton, and Stephane Lathuilière. 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International Journal of Computer Vision, 130(9):2337-2348, 2022. 2" + }, + { + "type": "list", + "bbox": [ + 0.08, + 0.092, + 0.47, + 0.653 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.946, + 0.519, + 0.957 + ], + "angle": 0, + "content": "28630" + } + ] +] \ No newline at end of file diff --git a/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/89aa68d1-2eb8-4184-895d-0bf0c9b627f5_origin.pdf b/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/89aa68d1-2eb8-4184-895d-0bf0c9b627f5_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..b6c312708fee18301e5393e8b1d21d6290588ade --- /dev/null +++ b/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/89aa68d1-2eb8-4184-895d-0bf0c9b627f5_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:34e1ad3f6f3d5931821a52cd2cad6478f4a6709439104d78224c41481332bbd7 +size 853542 diff --git a/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/full.md b/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..cc9a371fb7eae1cd22d1bfaa5229f8230e77dd42 --- /dev/null +++ b/2024/Stronger Fewer & Superior_ Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation/full.md @@ -0,0 +1,392 @@ +# Stronger, Fewer, & Superior: Harnessing Vision Foundation Models for Domain Generalized Semantic Segmentation + +Zhixiang Wei $^{1*}$ Lin Chen $^{1,2*}$ Yi Jin $^{1*}$ Xiaoxiao Ma $^{1}$ Tianle Liu $^{1}$ Pengyang Ling $^{1,2}$ Ben Wang $^{1}$ Huaian Chen $^{1\dagger}$ Jinjin Zheng $^{1}$ + +1 University of Science and Technology of China 2 Shanghai AI Laboratory + +{zhixiangwei,chlin,xiao_xiao,tleliu,lpyang27,wblzgrsn,anchen}@mail.ustc.edu.cn + +{jinyi08,jjzheng}@ustc.edu.cn + +![](images/2a052c6bc911146c85a9904975836381ec4cda938a05d23222bce8cfbd6e343c.jpg) +(a) Stronger pre-trained models + +![](images/d3d09cc155492ee58c97ddda441d967a0aa96d424e5d0bbe05d4abfbb98768cb.jpg) +(b) Fewer trainable parameters + +![](images/6a25ece895207d03080e12a89faec354b0c11195a1a47d529389f784687169aa.jpg) + +![](images/3211a8e6af4ca7b62cd876ddb75eb24e86011234c68724d54ca70f7d330a486d.jpg) +Figure 1. Vision Foundation Models (VFMs) are stronger pre-trained models that serve as robust backbones, effortlessly outperforming previous state-of-the-art Domain Generalized Semantic Segmentation (DGSS), as shown in (a). Yet, the extensive parameters of VFMs make them challenging to train. To address this, we introduce a robust fine-tuning approach to efficiently harness VFMs for DGSS. As illustrated in (b) and (c), the proposed methods achieve superior generalizability with fewer trainable parameters within backbones. + +![](images/54470b2982c6f094e33b8038d913cf27f2e076b4f0a4e751bd32040c2a923f6d.jpg) + +![](images/96d62aa4037bf6737f4b1b934d944d61445b14686e187c8843244fd6c8ffa9e2.jpg) +(c) Superior generalization ability + +# Abstract + +In this paper, we first assess and harness various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we introduce a robust fine-tuning approach, namely "Rein", to parameter-efficiently harness VFMs for DGSS. Built upon a set of trainable tokens, each linked to distinct instances, Rein precisely refines and forwards the feature maps from each layer to the next layer within the backbone. This process produces diverse refinements for different categories within a single image. With fewer trainable parameters, Rein efficiently fine-tunes VFMs for DGSS tasks, surprisingly surpassing full parameter fine-tuning. Extensive experiments across various settings demonstrate that Rein significantly outperforms state-of-the-art methods. Remarkably, with just an extra $1\%$ of trainable parameters + +within the frozen backbone, Rein achieves a mIoU of $78.4\%$ on the Cityscapes, without accessing any real urban-scene datasets. Code is available at https://github.com/wloves/Rein.git. + +# 1. Introduction + +Prior works [32, 34, 36, 56, 63, 66, 72] in Domain Generalized Semantic Segmentation (DGSS) focus on improving prediction accuracy across multiple unseen domains without accessing their data, thus enabling a high generalization for real applications. Since models are fine-tuned using datasets [11, 57] that are either limited in scale or different in image style from the target domain, complex data augmentation approaches [4, 53, 73] and domain invariant feature extraction strategies [9, 51, 62, 67] have been widely explored in previous DGSS. These methods result in enhanced generalization when applied to classic backbones, e.g., VGGNet [61], MobileNetV2 [60], and ResNet [23]. + +In recent years, large-scale Vision Foundation Models (VFMs) like CLIP [55], MAE [24], SAM [38], EVA02 [17, 18], and DINOv2 [50] have significantly advanced the + +
Previous DGSS methodsFrozen backbone of VFs
MethodsGTR[53]AdvStyle[73]WildNet[40]SPC[27]PASTA[4]TLDR[37]CLIP-ViT-L[55]MAE-L[24]SAM-H[38]EVA02-L[17]DINOv2-L[50]
PublicationsTIP21NIPS22CVPR22CVPR23ICCV23ICCV23ICML21CVPR22ICCV23arXiv23arXiv23
mIoU (Citys)43.743.445.846.745.347.653.743.357.056.563.3
mIoU (BDD)39.640.341.743.742.344.948.737.847.153.656.1
mIoU (Map)39.142.047.145.548.648.855.048.058.458.663.9
mIoU (Average)40.841.944.945.345.447.152.443.054.256.261.1
+ +Table 1. Performance benchmarking of multiple VFMs and previous DGSS methods under the GTAV $\rightarrow$ Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting. Without specialized design, frozen VFMs demonstrate stronger performance. + +boundaries of performance in a variety of computer vision challenges. Giving the remarkable generalization of these VFMs across various unseen scenes, two intuitive questions emerge: How do VFMs perform in the context of DGSS? And How to harness VFMs for DGSS? We attempt to answer these questions as follows: + +Stronger: We begin by evaluating and comparing the performance of various VFMs against existing DGSS methods. To ensure a fair comparison, we use image encoders from a variety of VFMs as the backbone for feature extraction in all cases. These backbones are coupled with the widely-used decode head, i.e., Mask2Former [8], to generate semantic predictions. As illustrated in Tab. 1, while previous DGSS methods have showcased commendable results, they perform less effectively compared to frozen VFs. This finding clearly demonstrates the powerful potential of VFs in DGSS, outperforming traditional backbones like ResNet [23] and MobileNetV2 [60], thereby establishing VFs as a meaningful benchmark in the field. + +Fewer: Although VFMs have exhibited impressive generalization capabilities, fine-tuning them for DGSS tasks poses a challenge. The datasets [11, 57] commonly used in DGSS tasks are significantly smaller in scale compared to ImageNet [12], and fine-tuning VFs with their huge number of trainable parameters on these datasets result in limited generalizability [33]. To address this issue, instead of the difficult task of large datasets collection, we resort to fine-tuning VFs with fewer trainable parameters. However, most existing parameter-efficient fine-tuning strategies, which fine-tune a large-scale model with fewer trainable parameters, are primarily designed for adapting large language models [25, 26, 41, 43, 44, 70, 74] or classification networks [6, 28]. These methods are not developed for refining features for distinct instances within a single image, thereby limiting their effectiveness in DGSS contexts. + +Superior: In this work, we introduce a robust and efficient fine-tuning approach, namely "Rein". Tailored for DGSS tasks, Rein employs fewer trainable parameters to harness stronger VFMs for achieving superior generalization. At its core, Rein comprises a set of randomly initialized tokens, each directly linked to different instances. These tokens, through a dot-product operation with VFMs features, generate an attention-like similarity map. This map enables Rein to perform precise refinement tailored to + +each instance within an image, significantly boosting VFMs in the context of DGSS. Moreover, to reduce the number of trainable parameters, we employ shared weights across MLPs in different layers and design our learnable tokens by multiplying two low-rank matrices. Extensive experiments on various DGSS settings demonstrate that the proposed Rein outperforms existing DGSS methods by a large margin with fewer trainable parameters. In a nutshell, the main contributions of this paper are as follows: + +- We first assess various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Our extensive experiments in the DGSS framework highlight the impressive generalization capabilities of VFMs. The findings confirm that VFMs serve as Stronger backbones, thereby establishing a significant benchmark in this field. +- We present a robust fine-tuning method, namely "Rein", to parameter-efficiently harness VFMs. At its core, Rein consists of a set of learnable tokens, each directly linked to instances. With deliberate design, this linkage enables Rein to refine features at an instance-level within each layer. As a result, Rein reinforces the ability of VFMs in DGSS tasks, achieving this with Fewer trainable parameters while preserving the pre-trained knowledge. +- Comprehensive experiments across various DGSS settings demonstrate that Rein employs Fewer trainable parameters to effectively leverage Stronger VFMs for achieving Superior generalizability. This performance surpasses existing DGSS methods by a large margin. Notably, Rein is designed to integrate smoothly with existing plain vision transformers, improving their generalization ability and making training more efficient. + +# 2. Related Works + +Domain Generalized Semantic Segmentation. Domain Generalized Semantic Segmentation (DGSS) focuses on enhancing model generalizability. This field involves training models on a set of source domain to enhance their performance on distinct and unseen target domain. Various approaches [5, 13, 20, 21, 27, 29-31, 42, 54, 65] have been proposed to address this issue, with methods including splitting the learned features into domain-invariant and domain-specific components [62, 67], or employing meta-learning to train more robust models [35]. A standard scenario in + +![](images/5b496184cd146f7472386c83ef7fa6c6ec38bc5c84985692e9d5d300b65bb8db.jpg) +Figure 2. An overview of proposed Rein. Rein primarily consists of a collection of low-rank learnable tokens, denoted as $T = \{T_1, T_2, \ldots, T_N\}$ . These tokens establish direct connections to distinct instances, facilitating instance-level feature refinement. This mechanism results in the generation of an enhancement feature map $f_i' = f_i + \text{Rein}(f_i)$ for each layer within backbone. All parameters of MLPs are layer-shared to reduce the number of parameters. $M_f$ , $M_Q$ , and $M_S$ are features module, queries module, and segmentation module, respectively. The notation max & avg & last refers to the equation Eq. (8) and Eq. (10). + +
BackboneFine-tune +MethodTrainable +Params*mIoU
CitysBDDMapAvg.
CLIP [55] +(ViT-Large)Full304.15M51.347.654.351.1
Freeze0.00M53.748.755.052.4
Rein2.99M57.154.760.557.4
MAE [24] +(Large)Full330.94M53.750.858.154.2
Freeze0.00M43.337.848.043.0
Rein2.99M55.049.358.654.3
SAM [38] +(Huge)Full632.18M57.651.761.556.9
Freeze0.00M57.047.158.454.2
Rein4.51M59.652.062.157.9
EVA02 [17, 18] +(Large)Full304.24M62.156.264.660.9
Freeze0.00M56.553.658.656.2
Rein2.99M65.360.564.963.6
DINOV2 [50] +(Large)Full304.20M63.757.464.261.7
Freeze0.00M63.356.163.961.1
Rein2.99M66.460.466.164.3
+ +Table 2. Performance Comparison with the proposed Rein across Multiple VFMs as Backbones under the GTAV $\rightarrow$ Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones. + +DGSS is generalizing from one urban-scene dataset to another, for instance, from the synthetic GTAV [57] dataset to the real-world Cityscapes [11]. In this classic setting, certain techniques [9, 51, 52] have achieved notable performance through learning feature normalization/whitening schemes, while others [40] have improved segmentation results through feature-level style transfer and the introduction of additional data. Additionally, strong data augmentation [4, 16, 53, 73] often simply and effectively enhances model robustness. However, most of previous DGSS methods generally utilize outdated backbones like ResNet [23], VGGNet [61], MobileNetV2 [60], and ShuffleNetV2 [47], thereby leaving the efficacy of stronger Vision Foundation + +Models (VFMs) in DGSS relatively unexplored. + +Vision Foundation Models. The concept of a Foundation Model, initially introduced by Bommasani et al. [2] in the field of Natural Language Processing (NLP), defined as "the base models trained on large-scale data in a self-supervised or semi-supervised manner that can be adapted for several other downstream tasks". While models like the ViT [14] and Swin Transformer [45] have demonstrated excellent performance, the quest for a Vision Foundation Model (VFM) similar to their NLP counterparts is ongoing. This pursuit has yielded significant advancements with the advent of models such as CLIP [55], which learn high-quality visual representation by exploring contrastive learning with large-scale image text pairs; MAE [24], utilizing a masked image modeling for learning latent image representations; SAM [38], which develops a promptable model and pre-train it on a broad dataset for segmentation task; EVA02 [17, 18], which integrates Masked Image Modeling pre-training with CLIP's vision features; and DINOv2 [50], which is pretrained on extensive, curated datasets without explicit supervision. These VFs have shown remarkable performance in downstream applications. Yet, a dedicated investigation into their performance in the specific context of DGSS tasks remains unexplored. + +Parameter-Efficient Fine-tuning. In the realm of NLP, parameter-efficient fine-tuning (PEFT) has achieved notable success by freezing most parameters of VFMs and fine-tuning a select few. Various approaches have been developed, such as BitFit [70], which adjusts only the model's bias terms; Prompt-tuning [41], introducing soft prompts to adapt frozen language models; Adapter-tuning [25], adding lightweight modules to each transformer layer; and notably, LoRA [26], which injects trainable rank decomposition matrices into transformer layers, yielding significant influence. + +
TargetACDC[59] (test)Cityscapes-C[48] (level-5)
Night Snow Fog RainAllBlurNoiseDigitalWeatherAvg.
MotionDefocGlassGaussGaussImpulShotSpeckBrightContrSaturJPEGSnowSpattFogFrost
HGFormer52.768.669.972.067.264.167.261.563.627.235.732.963.179.972.978.053.655.475.875.543.2
Ours70.679.576.478.277.668.571.769.768.76.223.013.163.781.578.980.668.863.873.679.547.9
+ +Table 3. Results on Cityscapes $\rightarrow$ ACDC (test) and Cityscapes-C (level-5) datasets, utilizing a batch size of 8. + +
BackboneFine-tune +MethodTrainable +Params*mIoU
CitysBDDMapAvg.
EVA02 +(Large) +[17, 18]Full304.24M62.156.264.660.9
+AdvStyle [73]304.24M63.156.464.061.2
+PASTA [4]304.24M61.857.163.660.8
+GTR-LTR [53]304.24M59.857.463.260.1
Freeze0.00M56.553.658.656.2
+AdvStyle [73]0.00M51.451.656.553.2
+PASTA [4]0.00M57.852.358.556.2
+GTR-LTR [53]0.00M52.552.857.154.1
+LoRA [26]1.18M55.552.758.355.5
+AdaptFormer [6]3.17M63.759.964.262.6
+VPT [28]3.69M62.257.762.560.8
+Rein (ours)2.99M65.360.564.963.6
DINOv2 +(Large) +[50]Full304.20M63.757.464.261.7
+AdvStyle [73]304.20M60.858.062.560.4
+PASTA [4]304.20M62.557.264.761.5
+GTR-LTR [4]304.20M62.757.464.561.6
Freeze0.00M63.356.163.961.1
+AdvStyle [73]0.00M61.555.163.960.1
+PASTA [4]0.00M62.157.264.561.3
+GTR-LTR [4]0.00M60.257.762.260.0
+LoRA [26]0.79M65.258.364.662.7
+AdaptFormer [6]3.17M64.959.064.262.7
+VPT [28]3.69M65.259.465.563.3
+Rein (ours)2.99M66.460.466.164.3
+ +The application of PEFT methods is also expanding into the field of computer vision [15, 39], with notable examples such as Visual Prompt Tuning (VPT) [28], which prepends prompts into the input sequence of transformer layers; AdaptFormer [6], replacing the MLP block in the transformer encoder with an AdaptMLP; LP-FT [39] find that fine-tuning can achieve worse accuracy than linear probing out-of-distribution; and Prompt-ICM [19], applying large-scale pre-trained models to the task of image coding for machines. Contrasting with these methods, we aim to refine feature maps for each instance within an image, thereby achieving superior performance in the realm of DGSS. + +# 3. Methods + +# 3.1. Preliminary + +Driven by the motivation that Leveraging Stronger pretrained models and Fewer trainable parameters for Su + +Table 4. Performance Comparison of the proposed Rein against other DGSS and PEFT methods under the GTAV $\rightarrow$ Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones. + +
Source DomainCityscapes mIoU
GTAV66.4
+Synthia68.1
+UrbanSyn78.4
+1/16 of Cityscapes Training set82.5
+ +Table 5. Synthetic data + 1/16 of Citys. → Citys. val set. + +perior generalizability, we choose to fine-tune VFMs with a reduced parameter set. A straightforward thought might involve a smaller decode head; however, this method merely acts as a passive receiver of feature maps from the backbone, lacking the flexibility to effectively adapt a frozen backbone for generating task-specific or scene-specific features. In contrast, we propose to embed a mechanism, named "Rein", between the layers within the backbone. Rein actively refines and forwards the feature maps from each layer to the subsequent one. This approach allows us to more effectively utilize the powerful capabilities of VFMs, much like using rein to control a horse. + +Given a pre-trained VFM with parameters $\Phi_M$ , consisting of a sequence of layers $L_{1}, L_{2}, \ldots, L_{N}$ , a decode head $\mathcal{H}$ parameterized by $\theta_h$ , and the Rein strategy with parameters $\theta_R$ , the optimization objective can be written as: + +$$ +\underset {\theta_ {R}, \theta_ {h}} {\arg \min } \sum_ {i = 1} ^ {N _ {d}} \operatorname {L o s s} \left(\mathcal {H} _ {\theta_ {h}} \left(\mathcal {F} _ {\Phi_ {M}, \theta_ {R}} \left(x _ {i}\right)\right), y _ {i}\right), \tag {1} +$$ + +where $x_{i}$ and $y_{i}$ denote the input image and its corresponding ground truth, respectively, and $N_{d}$ signifies the total number of samples. $\mathcal{F}_{\Phi_M,\theta_R}$ represents the forward process of VFM after applying the Rein strategy. + +# 3.2. Core of Rein + +For simple implementation across different VFMs, we opt not to modify MLP weights at specific positions as described in the [6, 26]. Instead, our approach focuses on refining the output feature maps at each layer within the VFMs, as illustrated in Fig. 2. Precisely, for the features $f_{i}$ produced by the $i$ -th layer $L_{i}$ , Rein produces enhanced feature maps for the next layer as follows: + +$$ +f _ {1} = L _ {1} (E m b e d (x)) \quad f _ {1} \in \mathbb {R} ^ {n \times c}, +$$ + +$$ +f _ {i + 1} = L _ {i + 1} \left(f _ {i} + \Delta f _ {i}\right) \quad i = 1, 2, \dots , N - 1, \tag {2} +$$ + +$$ +f _ {o u t} = f _ {N} + \Delta f _ {N}, +$$ + +where $f_{i}^{\prime} = f_{i} + \Delta f_{i}$ symbolizes the refined feature map, $x$ is the input image, $\text{Embed}$ denotes the patch embedding + +layer in VFMs, $n$ represents the number of patches, $N$ denotes the number of layers, and $c$ is the dimensionality of $f_{1}, f_{2}, \ldots, f_{N}$ . Note that the layers $L_{1}, L_{2}, \ldots, L_{N}$ are kept frozen, and our focus is on training an efficient module, Rein, to generate $\Delta f_{i}$ as follows: + +$$ +\Delta f _ {i} = \operatorname {R e i n} (f _ {i}) \quad \Delta f _ {i} \in \mathbb {R} ^ {n \times c}, i = 1, 2, \dots , N. \tag {3} +$$ + +In the context of DGSS, an ideal $\Delta f_{i}$ should assist VFMs to bridge two types of gaps. The first is gap in scene between pre-training dataset and target scene, exemplified by the contrast between ImageNet [12] and urban-scene images [11, 57]. The second is task divergence between pretraining and fine-tuning, such as the differences between masked image modeling and semantic segmentation tasks. + +To establish this dual bridge, Rein starts with a set of learnable tokens $T = \{T_{i} \in \mathbb{R}^{m \times c} \mid i \in \mathbb{N}, 1 \leq i \leq N\}$ , where each token sequence $T_{i}$ is randomly initialized, and $m$ denotes the sequence length of $T_{i}$ . Rein freezes the backbone and embeds knowledge learned from the finetuning dataset into these tokens, thereby bridging the gap in scene relative to the pre-training dataset. Moreover, considering the essential need in semantic segmentation to discern multiple instances within a single image, Rein implements an attention-inspired mechanism, which enables VFMs to make tailored adjustments to the features of distinct instances, thereby aiding VFMs in adapting to the differences between semantic segmentation and pre-training tasks. Specifically, Rein employs a dot-product operation to generate a similarity map $S_{i}$ , which captures the associations between feature vectors in $f_{i}$ and the tokens in $T$ : + +$$ +S _ {i} = f _ {i} \times T _ {i} ^ {\mathrm {T}} \quad S _ {i} \in \mathbb {R} ^ {n \times m}, \tag {4} +$$ + +where $T_{i}$ represents the token sequence of the $i$ -th layer, $m$ indicates the number of tokens in $T_{i}$ . As $S$ quantitatively evaluates the relationships between various tokens and feature vectors, Rein can apply a softmax function to align each patch with a unique instance: + +$$ +S _ {i} = \operatorname {S o f t m a x} \left(\frac {f _ {i} \times T _ {i} ^ {\mathrm {T}}}{\sqrt {c}}\right). \tag {5} +$$ + +Leveraging the feature-to-token similarity map $S_{i}$ , we can preliminarily estimates of $\Delta f_{i}$ using the equation: + +$$ +\Delta \bar {f} _ {i} = S _ {i} (:, 2: m) \times \left[ T _ {i} (2: m) \times W _ {T _ {i}} + b _ {T _ {i}} \right], \tag {6} +$$ + +where $W_{T_i}$ and $b_{T_i}$ denote the weights and biases of a MLP, respectively. This MLP enables the transformation of $T_i$ across different feature spaces during the computation of $S_i$ and $\Delta \bar{f}_i$ . Optionally, Rein can pre-calculate $T_i \times W_{T_i} + b_{T_i}$ to reduce inference time. The sum of $S_i$ equals one due to the softmax function; however, this can induce unneeded changes when all features are precise. To + +avoid this, $S_{i}(:,2:m)$ is designed to choose columns 2 to m of $S_{i}$ , and $T_{i}(2:m)$ denotes the selection of rows 2 to m of $T_{i}$ . This strategic selection allows models to sidestep unnecessary adjustments by assigning a high value to the first token and subsequently discarding it. This approach allows the sum of each row in $S_{i}$ to vary from 0 to 1, thus reducing the risk of inappropriate changes. + +To enhance the flexibility in feature adjustment, Rein utilizes a MLP composed of $W_{f_i}$ and $b_{f_i}$ to produce the final feature modifications $\Delta f_i$ : + +$$ +\Delta f _ {i} = \left(\Delta \bar {f} _ {i} + f _ {i}\right) \times W _ {f _ {i}} + b _ {f _ {i}}. \tag {7} +$$ + +Benefiting from these instance-level $\Delta f_{i}$ adjustments, Rein is capable of generating diverse modifications for various categories within a single image. The details of Rein will be explained in the next section. + +# 3.3. Details of Rein + +Linking tokens to instances. At the core of Rein, we establish an implicit yet effective linkage between tokens and instances, which has demonstrated notable performance, as detailed in Sec. 4. This connection is further reinforced by utilizing object queries, a key component in DETR[3]-style decode heads [7, 8, 71], as intermediaries. These queries are empirically proven to establish a direct association with instances. Specifically, we generate layer-wise queries $Q_{i}$ from our learnable tokens $T_{i}$ via linear transformation: + +$$ +Q _ {i} = T _ {i} \times W _ {Q _ {i}} + b _ {Q _ {i}} \quad Q _ {i} \in \mathbb {R} ^ {m \times c ^ {\prime}}, \tag {8} +$$ + +where $W_{Q_i}$ and $b_{Q_i}$ signify the weights and biases, respectively, and $c'$ denotes the dimension of $Q_i$ . However, due to the complexity arising from the large numbers of various layers in VFMs, transforming the diverse $Q_i$ into a single query $Q$ poses computational challenges. To address this, Rein computes both the maximal component $Q_{\text{max}} \in \mathbb{R}^{m \times c'}$ and the average component $Q_{\text{avg}} \in \mathbb{R}^{m \times c'}$ using the following equation: + +$$ +Q _ {m a x} (j, k) = \max _ {i = 1, 2, \dots , N} Q _ {i} (j, k), +$$ + +$$ +Q _ {a v g} (j, k) = \frac {1}{N} \sum_ {i = 1} ^ {N} Q _ {i} (j, k). \tag {9} +$$ + +Subsequently, $Q$ is derived as: + +$$ +Q = \operatorname {C o n c a t} \left(\left[ Q _ {\max }, Q _ {\text {a v g}}, Q _ {N} \right]\right) \times W _ {Q} + b _ {Q}. \tag {10} +$$ + +By mapping $T$ onto $Q$ , which subsequently links to instances, Rein achieves enhanced performance with a marginal increase in parameters. + +Layer-shared MLP weights. To address the redundancy of parameters in the layer-specific MLP weights, specifically $W_{T_i}$ in Eq. (6), $W_{f_i}$ in Eq. (7), and $W_{Q_i}$ in Eq. (8), which + +collectively contribute to a substantial trainable parameter count, we adopt a new strategy. Since the learnable $T_{i}$ is capable of producing distinct $\Delta f_{i}$ for each layer, we design the role of the MLP to primarily perform consistent linear transformations across different feature spaces for each layer within the backbone. To this end, we employ shared MLP weights across layers as outlined in the equations: + +$$ +\begin{array}{l} \left[ W _ {T _ {1}}, b _ {T _ {1}} \right] = \left[ W _ {T _ {2}}, b _ {T _ {2}} \right] = \dots = \left[ W _ {T _ {N}}, b _ {T _ {N}} \right], \\ \left[ W _ {f _ {1}}, b _ {f _ {1}} \right] = \left[ W _ {f _ {2}}, b _ {f _ {2}} \right] = \dots = \left[ W _ {f _ {N}}, b _ {f _ {N}} \right], \tag {11} \\ \left[ W _ {Q _ {1}}, b _ {Q _ {1}} \right] = \left[ W _ {Q _ {2}}, b _ {Q _ {2}} \right] = \dots = \left[ W _ {Q _ {N}}, b _ {Q _ {N}} \right]. \\ \end{array} +$$ + +Low-rank token sequence. Recognizing the potential for information overlap among diverse learnable tokens, such as the high similarity between tokens representing a car's headlight and a bicycle's light, Rein adopts a strategy to generate a low-rank token sequence $T$ as follows: + +$$ +T i = A _ {i} \times B _ {i}, \quad A \in \mathbb {R} ^ {m \times r}, B \in \mathbb {R} ^ {r \times c}, \tag {12} +$$ + +where $c$ denotes the dimension of $T_{i}$ , $m$ is the length of sequence $T_{i}$ , and $r$ represents the rank, with $r \ll c$ . Here, matrices $A$ and $B$ are constructed as low-rank matrices. To reduce inference time, Rein can precompute and store $T$ . By implementing this low-rank token sequence approach, Rein significantly reduces the number of parameters. + +# 4. Experiments + +# 4.1. Settings + +Visual Foundation Models. To thoroughly assess the influence of Visual Foundation Models (VFMs) within the context of DGSS, we analyze five distinct VFMs, each with different training strategies and datasets. Our selection includes CLIP [55], a language-image pre-training model; MAE [24], known for its masked pre-training approach; SAM [38], which leverages a large-scale segmentation dataset; EVA02 [17, 18] combines CLIP with masked image modeling; and DINOv2 [50], based on self-supervised pretraining with curated dataset. For balancing precision and efficiency, we mainly employ the ViT-Large architecture for these VFMs, except SAM, which utilizes a ViT-Huge image encoder, as described in its original paper [38]. We establish two fundamental baselines for VFMs: "Full", where we fine-tune the entire network, and "Freeze", in which all backbone parameters are fixed, with training solely on the segmentation head. More details about VFMs and PEFT methods are available in the supplementary material. + +Datasets. We evaluate VFs and proposed methods on both real-world datasets (Cityscapes [11], BDD100K [68], Mapillary [49]) and synthetic datasets (GTAV [57], Synthia [58], UrbanSyn [22]). In detail, Cityscapes (denoted as Citys) is an autonomous driving dataset that contains 2975 training images and 500 validation images, each with the + +resolution of $2048 \times 1024$ . BDD100K (shortened to BDD) and Mapillary (denoted by Map) offer 1,000 ( $1280 \times 720$ ) and 2,000 ( $1902 \times 1080$ ) validation images, respectively. GTAV, a synthetic dataset, presents 24,966 labeled images obtained from the game. Synthia, a synthetic dataset, provides 25,000 images created by photo-realistic rendering. UrbanSyn, a synthetic dataset consists of 7,539 images. + +Implementation details. We utilize the MMSegmentation [10] codebase for our implementation. For superior performance, mask2former [8], a widely-used segmentation head, is integrated with various VFMs that serve as the backbone. Additional experiments involving other decode heads are detailed in the supplementary material. For the training phase, the AdamW optimizer [46] is employed, setting the learning rate at 1e-5 for the backbone and 1e-4 for both the decode head and the proposed Rein. Aiming to efficient training process, we utilize a configuration of 40,000 iterations with a batch size of 4, and crop images to a resolution of $512 \times 512$ . Our approach includes only basic data augmentation, following Mask2Former [8]. Thanks to our streamlined training configuration and reduced number of trainable parameters, Rein can fine-tune models like DINOv2-Large or EVA02-Large on a single RTX 3090Ti GPU within 12 hours for superior generalization ability. + +# 4.2. Comparison with State-of-The-Art Methods + +In this section, we comprehensively evaluate Rein over five datasets within three generalization settings: $GTAV \rightarrow Citys + BDD + Map$ , $GTAV + Synthia \rightarrow Citys + BDD + Map$ , and $Citys \rightarrow BDD + Map$ . Rein is benchmarked against state-of-the-art (SOTA) methods, which can be classified into two groups, including domain generalized semantic segmentation (DGSS) methods[4, 9, 13, 27, 35, 40, 51, 53, 54, 64, 69, 73], and parameter-efficient fine-tuning (PEFT) approaches [6, 26, 28]. + +Investigation of various VFMs. Our analysis of VFMs and proposed Rein in the $GTAV \rightarrow Citys + BDD + Map$ setting is presented in Tables 1 and 2. In this setup, models are fine-tuned using GTAV and evaluated on Cityscapes, BDD100K, and Mapillary. Note that, due to the fixed and relatively small number of trainable parameters in the decode head (20.6M), the count of trainable parameters presented in the tables are focused solely on the backbone and the PEFT module. Our results, as detailed in Table 1, indicate that frozen VFMs significantly outperform previous DGSS methods without specialized design. Moreover, as shown in Table 2, VFMs with full parameter fine-tuning exhibit enhanced performance relative to their frozen counterparts. Remarkably, Rein achieves even superior generalization capabilities, surpassing the full parameter fine-tuning with merely an extra $1\%$ of trainable parameters compared to the original backbone. Visual samples for qualitative comparison are given in Fig. 3. + +
BackboneFine-tune +MethodTrainable +Params*roadside.build.wallfencepolelightsignvegeterr.skypers.ridercartruckbustrainmoto.bicy.mIoU
EVA02 +(Large) +[17, 18]Full304.24M89.346.989.947.745.650.156.842.288.848.489.975.849.090.545.369.255.944.455.162.2
Freeze0.00M93.152.788.047.431.141.746.039.685.741.489.567.539.789.047.072.846.319.235.256.5
Rein-core52.84M91.153.890.050.347.746.656.442.987.844.290.473.544.291.858.177.257.343.457.363.4
+ Rein-link59.33M90.948.590.052.649.449.157.239.888.946.590.574.444.091.052.380.767.344.360.364.1
+ Rein-share5.02M92.754.390.051.848.648.855.345.088.946.789.873.743.390.649.581.169.641.750.263.4
+ Rein-lora2.99M91.751.890.152.848.448.256.042.089.144.190.274.247.091.154.584.178.947.259.465.3
DINOv2 +(Large) +[50]Full304.20M89.044.589.651.146.449.260.038.989.147.591.775.848.291.752.582.981.030.449.963.7
Freeze0.00M92.155.290.257.248.549.556.747.789.347.891.174.246.792.262.677.547.729.647.261.1
Rein-core52.84M92.457.890.656.850.750.557.544.889.847.091.175.947.291.960.180.359.837.952.364.9
+ Rein-link59.33M91.255.590.655.652.551.159.745.189.847.191.175.847.192.664.682.265.540.452.765.8
+ Rein-share5.02M93.561.290.757.753.252.458.050.189.749.990.774.845.091.758.580.166.336.950.765.8
+ Rein-lora2.99M92.459.190.758.353.751.858.246.489.849.490.873.943.392.364.381.670.940.454.066.4
+ +Table 6. Ablation Study about Rein under Cityscapes $\rightarrow$ BDD100K generalization in terms of mIoU. Components are sequentially incorporated. To better illustrate the gains contributed by each component, we employ varying shades of yellow to demonstrate the relative performance of the Freeze and Rein methods. The best results across all methods are highlighted. + +![](images/b6207aeca8a25d9645477044f648597374345989031f87272ff74114086093ab.jpg) +Figure 3. Qualitative Comparison under GTAV $\rightarrow$ Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting. + +Comparing Rein with SOTA. We conduct a comprehensive performance comparison of the proposed Rein against existing DGSS and PEFT methods under the $GTAV \rightarrow Citys + BDD + Map$ setting, as detailed in Table 4. Owing to the robust feature extraction capabilities inherent in VFMs, DGSS methods, which typically enhance generalizability through strong data augmentation or consistency constraints, (e.g., AdvStyle, PASTA, and GTR), do not exhibit significant performance improvement. On the other hand, PEFT methods have demonstrated notable advancements. For instance, AdaptFormer outperforms the "Freeze" baseline using EVA02 as the backbone, while VPT shows improved performance over "Full" with DINOv2. Employing the same backbones (DINOv2 and EVA02), proposed Rein achieves superior performance and surpass previous DGSS and PEFT methods. + +Real-to-Real generalization of Rein. The generalization from one real-world dataset to others is pivotal for practical applications in the field. To this end, we conduct experiments under the $\text{Citys} \rightarrow \text{ACDC}$ , $\text{Citys} \rightarrow \text{Cityscapes-C}$ , and $\text{Citys} \rightarrow \text{BDD} + \text{Map}$ generalization setting. As shown in Table 3 and 7, Rein, when coupled with the DINOv2-Large, demonstrates superior performance across all datasets. This underscores the effectiveness of Rein in generalizing to diverse real-world scenarios. + +Synthetic-to-real generalization of Rein. As Tab. 5 illustrates, trained on synthetic UrbanSyn+GTAV+Synthia datasets, Rein achieved a $78.4\%$ mIoU on the Cityscapes validation set. Further improvement is possible with additional synthetic data and higher-quality images generated by diffusion models, like [1]. This result can also be a valuable pre-trained weight for data-efficient training, reaching an $82.5\%$ mIoU with 1/16 of Cityscapes training set. This is a significant performance for semi-supervised semantic segmentation. + +More backbones. We extend our analysis to integrating Rein with Convolutional Networks, such as ResNet and ConvNeXt, and smaller scale architectures like DINOv2-S/B. As shown in Table 8, our findings reveal that Rein exhibits remarkable performance with diverse backbones. + +# 4.3. Ablation Studies and Analysis + +We conduct extensive ablation studies within two settings: $GTAV \to Citys$ and $GTAV \to Citys + BDD + Map$ . + +Analysis of the key components. Table 6 is dedicated to thoroughly examining the effectiveness of each component within Rein. In the $GTAV \rightarrow City$ generalization setting, we sequentially incorporate different components of Rein and assess their impact. Interestingly, we observe that the "Freeze" occasionally exhibit better recognition for specific + +
MethodsBackboneTrainable +Parameters*mIoU
BDDMapAvg.
IBN [51]ResNet50 [23]23.58M48.657.052.8
DRPC [69]ResNet50 [23]23.58M49.956.353.1
GTR [53]ResNet50 [23]23.58M50.857.254.0
SAN-SAW [54]ResNet50 [23]23.58M53.059.856.4
WildNet [40]ResNet101 [23]42.62M50.958.854.9
HGFformer [13]Swin-L [45]196.03M61.572.166.8
FreezeEVA02-L [17]0.00M57.863.860.8
Rein (Ours)EVA02-L [17]2.99M64.169.566.8
FreezeDINOv2-L [50]0.00M63.469.766.7
Rein (Ours)DINOv2-L [50]2.99M65.072.368.7
+ +Table 7. Performance Comparison of the Rein against other DGSS methods under Cityscapes $\rightarrow$ BDD100K (BDD) +Mapillary (Map) generalization. The best results are highlighted. + +
Avg. mIoUResNet (50)ResNet (101)ConvNeXt (Large)DINOv2 (S)DINOv2 (B)
Full38.946.152.251.856.7
Ours46.646.355.555.759.1
+ +Table 8. Results for ConvNets and smaller backbones. + +categories, e.g., 'road, sidewalk', compared to the "Full". This suggests that VFMs lose some pre-training knowledge during fine-tuning, and "Freeze" helps to prevent. Similarly, our methods mitigate this knowledge forgetting. Furthermore, our methods show improved recognition capabilities for the majority of the 19 categories. For example, in recognizing 'wall, motorcycle, bicycle', our approach significantly outperforms both the "Full" and "Freeze" baselines. + +Overall, "Rein-core" boosts the average performance across 19 classes. Furthermore, "Rein-link" further boosts accuracy for certain objects, including 'car, bus, train, motorcycle', especially for DINOv2. Employing layer-shared MLP weights and low-rank token sequence efficiently reduces the number of trainable parameters and positively influences the performance of the model. + +Study on token length $m$ . The core component of Rein is learnable tokens $T \in \mathbb{R}^{m \times c}$ . We explored various lengths $m$ for the token sequence, ranging from 25 to 200. As demonstrated in Fig. 4, models with $m = 100$ and $m = 150$ both achieve a strong mIoU of $64.3\%$ . We ultimately selected $m = 100$ as the most suitable parameter. + +Study on rank $r$ . As shown in Table 9, we turn attention to the effect of rank $r$ on model performance. With DINOv2 as the backbone, the optimal results are observed at $r = 16$ and $r = 32$ . Consequently, unlike LoRA [26], we opt for a comparatively higher value of $r = 16$ for our model. + +Speed, memory, and storage. For practical applications, training speed, GPU memory usage, and model storage requirements are crucial. As shown in Table 10, compared to "Full" baseline, proposed Rein improves training speed and reduces GPU memory usage. A significant advantage of Rein is that models trained under different settings can share the same backbone parameters. This means that for switch + +![](images/173f2792a7339754674956c94d977fbf46165e65729e7068944f6cbba93dee21.jpg) + +Figure 4. Ablation study on token length $m$ . + +
Rank r +Params48163264
2.67M2.77M2.99M3.42M4.28M
DINOv2 +(Large) +[50]Citys65.866.166.466.166.4
BDD60.260.360.460.761.0
Map65.265.166.165.965.0
Avg.63.763.964.364.364.1
+ +Table 9. Ablation study on lora dim $r$ . + +
VFMsMethodTraining TimeGPU MemoryStorage
DINOv2 (Large)Full11.2 h14.7 GB1.22 GB
Rein9.5 h10.0 GB1.23 GB
+ +Table 10. Training Time, GPU Memory, and Storage. + +in diverse tasks and settings, we can only store and swap the rein weights (0.01GB) and head weights (0.08GB), rather than all parameters. + +# 5. Conclusions + +In this paper, we assess and harness Vision Foundation Models (VFMs) in the context of DGSS. Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we first investigate the performance of VFMs under diverse DGSS settings. Subsequently, we introduce a robust fine-tuning approach, namely Rein, to parameter-efficiently harness VFMs for DGSS. With a fewer trainable parameters, Rein significantly enhance generalizability of VFMs, outperforming SOTA methods by a large margin. Rein can be seamlessly integrated as a plug-and-play adapter for existing VFMs, improving generalization with efficient training. Extensive experiments demonstrate the substantial potential of VFMs in the DGSS field, validating the effectiveness of proposed Rein in harnessing VFMs for DGSS. + +# 6. Acknowledgements + +This work was supported in part by the Anhui Provincial Key Research and Development Plan 202304a05020072, in part by the Postdoctoral Fellowship Program of CPSFGZB20230713, and in part by the National Natural Science Foundation of China under Grant 61727809. + +# References + +[1] Yasser Benigmim, Subhankar Roy, Slim Essid, Vicky Kalogeiton, and Stephane Lathuilière. Collaborating foundation models for domain generalized semantic segmentation, 2023. 7 +[2] Rishi Bommasani, Drew A. Hudson, Ehsan Adeli, Russ Altman, Simran Arora, Sydney von Arx, Michael S. 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"3211a8e6af4ca7b62cd876ddb75eb24e86011234c68724d54ca70f7d330a486d.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 401, + 547, + 446 + ], + "lines": [ + { + "bbox": [ + 46, + 401, + 547, + 446 + ], + "spans": [ + { + "bbox": [ + 46, + 401, + 547, + 446 + ], + "type": "text", + "content": "Figure 1. Vision Foundation Models (VFMs) are stronger pre-trained models that serve as robust backbones, effortlessly outperforming previous state-of-the-art Domain Generalized Semantic Segmentation (DGSS), as shown in (a). Yet, the extensive parameters of VFMs make them challenging to train. To address this, we introduce a robust fine-tuning approach to efficiently harness VFMs for DGSS. As illustrated in (b) and (c), the proposed methods achieve superior generalizability with fewer trainable parameters within backbones." + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 443, + 261, + 553, + 319 + ], + "blocks": [ + { + "bbox": [ + 443, + 261, + 553, + 319 + ], + "lines": [ + { + "bbox": [ + 443, + 261, + 553, + 319 + ], + "spans": [ + { + "bbox": [ + 443, + 261, + 553, + 319 + ], + "type": "image", + "image_path": "54470b2982c6f094e33b8038d913cf27f2e076b4f0a4e751bd32040c2a923f6d.jpg" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_body" + } + ], + "index": 13 + }, + { + "type": "image", + "bbox": [ + 443, + 323, + 553, + 380 + ], + "blocks": [ + { + "bbox": [ + 443, + 323, + 553, + 380 + ], + "lines": [ + { + "bbox": [ + 443, + 323, + 553, + 380 + ], + "spans": [ + { + "bbox": [ + 443, + 323, + 553, + 380 + ], + "type": "image", + "image_path": "96d62aa4037bf6737f4b1b934d944d61445b14686e187c8843244fd6c8ffa9e2.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 387, + 388, + 500, + 399 + ], + "lines": [ + { + "bbox": [ + 387, + 388, + 500, + 399 + ], + "spans": [ + { + "bbox": [ + 387, + 388, + 500, + 399 + ], + "type": "text", + "content": "(c) Superior generalization ability" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "bbox": [ + 143, + 458, + 192, + 471 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 458, + 192, + 471 + ], + "spans": [ + { + "bbox": [ + 143, + 458, + 192, + 471 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 481, + 289, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 481, + 289, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 481, + 289, + 685 + ], + "type": "text", + "content": "In this paper, we first assess and harness various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we introduce a robust fine-tuning approach, namely \"Rein\", to parameter-efficiently harness VFMs for DGSS. Built upon a set of trainable tokens, each linked to distinct instances, Rein precisely refines and forwards the feature maps from each layer to the next layer within the backbone. This process produces diverse refinements for different categories within a single image. With fewer trainable parameters, Rein efficiently fine-tunes VFMs for DGSS tasks, surprisingly surpassing full parameter fine-tuning. Extensive experiments across various settings demonstrate that Rein significantly outperforms state-of-the-art methods. Remarkably, with just an extra " + }, + { + "bbox": [ + 46, + 481, + 289, + 685 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 46, + 481, + 289, + 685 + ], + "type": "text", + "content": " of trainable parameters" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 460, + 547, + 507 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 460, + 547, + 507 + ], + "spans": [ + { + "bbox": [ + 306, + 460, + 547, + 507 + ], + "type": "text", + "content": "within the frozen backbone, Rein achieves a mIoU of " + }, + { + "bbox": [ + 306, + 460, + 547, + 507 + ], + "type": "inline_equation", + "content": "78.4\\%" + }, + { + "bbox": [ + 306, + 460, + 547, + 507 + ], + "type": "text", + "content": " on the Cityscapes, without accessing any real urban-scene datasets. Code is available at https://github.com/wloves/Rein.git." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 307, + 512, + 387, + 524 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 307, + 512, + 387, + 524 + ], + "spans": [ + { + "bbox": [ + 307, + 512, + 387, + 524 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 533, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 533, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 533, + 545, + 676 + ], + "type": "text", + "content": "Prior works [32, 34, 36, 56, 63, 66, 72] in Domain Generalized Semantic Segmentation (DGSS) focus on improving prediction accuracy across multiple unseen domains without accessing their data, thus enabling a high generalization for real applications. Since models are fine-tuned using datasets [11, 57] that are either limited in scale or different in image style from the target domain, complex data augmentation approaches [4, 53, 73] and domain invariant feature extraction strategies [9, 51, 62, 67] have been widely explored in previous DGSS. These methods result in enhanced generalization when applied to classic backbones, e.g., VGGNet [61], MobileNetV2 [60], and ResNet [23]." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 713 + ], + "type": "text", + "content": "In recent years, large-scale Vision Foundation Models (VFMs) like CLIP [55], MAE [24], SAM [38], EVA02 [17, 18], and DINOv2 [50] have significantly advanced the" + } + ] + } + ], + "index": 22 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 160, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 160, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 160, + 703 + ], + "type": "text", + "content": "* indicates equal contributions." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 59, + 703, + 141, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 141, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 141, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28619" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 545, + 141 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 545, + 141 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 545, + 141 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 545, + 141 + ], + "type": "table", + "html": "
Previous DGSS methodsFrozen backbone of VFs
MethodsGTR[53]AdvStyle[73]WildNet[40]SPC[27]PASTA[4]TLDR[37]CLIP-ViT-L[55]MAE-L[24]SAM-H[38]EVA02-L[17]DINOv2-L[50]
PublicationsTIP21NIPS22CVPR22CVPR23ICCV23ICCV23ICML21CVPR22ICCV23arXiv23arXiv23
mIoU (Citys)43.743.445.846.745.347.653.743.357.056.563.3
mIoU (BDD)39.640.341.743.742.344.948.737.847.153.656.1
mIoU (Map)39.142.047.145.548.648.855.048.058.458.663.9
mIoU (Average)40.841.944.945.345.447.152.443.054.256.261.1
", + "image_path": "80e57834bae4ef1d990d50b0cf8ef2c3ac73e8c940d8c3477e06e272de8ece5c.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "lines": [ + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "spans": [ + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "type": "text", + "content": "Table 1. Performance benchmarking of multiple VFMs and previous DGSS methods under the GTAV " + }, + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 144, + 545, + 166 + ], + "type": "text", + "content": " Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting. Without specialized design, frozen VFMs demonstrate stronger performance." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 178, + 286, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 178, + 286, + 250 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 286, + 250 + ], + "type": "text", + "content": "boundaries of performance in a variety of computer vision challenges. Giving the remarkable generalization of these VFMs across various unseen scenes, two intuitive questions emerge: How do VFMs perform in the context of DGSS? And How to harness VFMs for DGSS? We attempt to answer these questions as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 253, + 286, + 408 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 253, + 286, + 408 + ], + "spans": [ + { + "bbox": [ + 46, + 253, + 286, + 408 + ], + "type": "text", + "content": "Stronger: We begin by evaluating and comparing the performance of various VFMs against existing DGSS methods. To ensure a fair comparison, we use image encoders from a variety of VFMs as the backbone for feature extraction in all cases. These backbones are coupled with the widely-used decode head, i.e., Mask2Former [8], to generate semantic predictions. As illustrated in Tab. 1, while previous DGSS methods have showcased commendable results, they perform less effectively compared to frozen VFs. This finding clearly demonstrates the powerful potential of VFs in DGSS, outperforming traditional backbones like ResNet [23] and MobileNetV2 [60], thereby establishing VFs as a meaningful benchmark in the field." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 411, + 286, + 602 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 286, + 602 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 286, + 602 + ], + "type": "text", + "content": "Fewer: Although VFMs have exhibited impressive generalization capabilities, fine-tuning them for DGSS tasks poses a challenge. The datasets [11, 57] commonly used in DGSS tasks are significantly smaller in scale compared to ImageNet [12], and fine-tuning VFs with their huge number of trainable parameters on these datasets result in limited generalizability [33]. To address this issue, instead of the difficult task of large datasets collection, we resort to fine-tuning VFs with fewer trainable parameters. However, most existing parameter-efficient fine-tuning strategies, which fine-tune a large-scale model with fewer trainable parameters, are primarily designed for adapting large language models [25, 26, 41, 43, 44, 70, 74] or classification networks [6, 28]. These methods are not developed for refining features for distinct instances within a single image, thereby limiting their effectiveness in DGSS contexts." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 286, + 713 + ], + "type": "text", + "content": "Superior: In this work, we introduce a robust and efficient fine-tuning approach, namely \"Rein\". Tailored for DGSS tasks, Rein employs fewer trainable parameters to harness stronger VFMs for achieving superior generalization. At its core, Rein comprises a set of randomly initialized tokens, each directly linked to different instances. These tokens, through a dot-product operation with VFMs features, generate an attention-like similarity map. This map enables Rein to perform precise refinement tailored to" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 178, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 178, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 304, + 178, + 545, + 285 + ], + "type": "text", + "content": "each instance within an image, significantly boosting VFMs in the context of DGSS. Moreover, to reduce the number of trainable parameters, we employ shared weights across MLPs in different layers and design our learnable tokens by multiplying two low-rank matrices. Extensive experiments on various DGSS settings demonstrate that the proposed Rein outperforms existing DGSS methods by a large margin with fewer trainable parameters. In a nutshell, the main contributions of this paper are as follows:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 287, + 545, + 561 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 306, + 287, + 545, + 369 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 287, + 545, + 369 + ], + "spans": [ + { + "bbox": [ + 306, + 287, + 545, + 369 + ], + "type": "text", + "content": "- We first assess various Vision Foundation Models (VFMs) in the context of Domain Generalized Semantic Segmentation (DGSS). Our extensive experiments in the DGSS framework highlight the impressive generalization capabilities of VFMs. The findings confirm that VFMs serve as Stronger backbones, thereby establishing a significant benchmark in this field." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 370, + 545, + 465 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 545, + 465 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 545, + 465 + ], + "type": "text", + "content": "- We present a robust fine-tuning method, namely \"Rein\", to parameter-efficiently harness VFMs. At its core, Rein consists of a set of learnable tokens, each directly linked to instances. With deliberate design, this linkage enables Rein to refine features at an instance-level within each layer. As a result, Rein reinforces the ability of VFMs in DGSS tasks, achieving this with Fewer trainable parameters while preserving the pre-trained knowledge." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 306, + 466, + 545, + 561 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 466, + 545, + 561 + ], + "spans": [ + { + "bbox": [ + 306, + 466, + 545, + 561 + ], + "type": "text", + "content": "- Comprehensive experiments across various DGSS settings demonstrate that Rein employs Fewer trainable parameters to effectively leverage Stronger VFMs for achieving Superior generalizability. This performance surpasses existing DGSS methods by a large margin. Notably, Rein is designed to integrate smoothly with existing plain vision transformers, improving their generalization ability and making training more efficient." + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 574, + 397, + 586 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 574, + 397, + 586 + ], + "spans": [ + { + "bbox": [ + 306, + 574, + 397, + 586 + ], + "type": "text", + "content": "2. Related Works" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 545, + 713 + ], + "type": "text", + "content": "Domain Generalized Semantic Segmentation. Domain Generalized Semantic Segmentation (DGSS) focuses on enhancing model generalizability. This field involves training models on a set of source domain to enhance their performance on distinct and unseen target domain. Various approaches [5, 13, 20, 21, 27, 29-31, 42, 54, 65] have been proposed to address this issue, with methods including splitting the learned features into domain-invariant and domain-specific components [62, 67], or employing meta-learning to train more robust models [35]. A standard scenario in" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28620" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 79, + 545, + 232 + ], + "blocks": [ + { + "bbox": [ + 53, + 79, + 545, + 232 + ], + "lines": [ + { + "bbox": [ + 53, + 79, + 545, + 232 + ], + "spans": [ + { + "bbox": [ + 53, + 79, + 545, + 232 + ], + "type": "image", + "image_path": "5b496184cd146f7472386c83ef7fa6c6ec38bc5c84985692e9d5d300b65bb8db.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "lines": [ + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "spans": [ + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "text", + "content": "Figure 2. An overview of proposed Rein. Rein primarily consists of a collection of low-rank learnable tokens, denoted as " + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "inline_equation", + "content": "T = \\{T_1, T_2, \\ldots, T_N\\}" + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "text", + "content": ". These tokens establish direct connections to distinct instances, facilitating instance-level feature refinement. This mechanism results in the generation of an enhancement feature map " + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "inline_equation", + "content": "f_i' = f_i + \\text{Rein}(f_i)" + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "text", + "content": " for each layer within backbone. All parameters of MLPs are layer-shared to reduce the number of parameters. " + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "inline_equation", + "content": "M_f" + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "inline_equation", + "content": "M_Q" + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "inline_equation", + "content": "M_S" + }, + { + "bbox": [ + 46, + 237, + 548, + 295 + ], + "type": "text", + "content": " are features module, queries module, and segmentation module, respectively. The notation max & avg & last refers to the equation Eq. (8) and Eq. (10)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 300, + 286, + 503 + ], + "blocks": [ + { + "bbox": [ + 52, + 300, + 286, + 503 + ], + "lines": [ + { + "bbox": [ + 52, + 300, + 286, + 503 + ], + "spans": [ + { + "bbox": [ + 52, + 300, + 286, + 503 + ], + "type": "table", + "html": "
BackboneFine-tune \nMethodTrainable \nParams*mIoU
CitysBDDMapAvg.
CLIP [55] \n(ViT-Large)Full304.15M51.347.654.351.1
Freeze0.00M53.748.755.052.4
Rein2.99M57.154.760.557.4
MAE [24] \n(Large)Full330.94M53.750.858.154.2
Freeze0.00M43.337.848.043.0
Rein2.99M55.049.358.654.3
SAM [38] \n(Huge)Full632.18M57.651.761.556.9
Freeze0.00M57.047.158.454.2
Rein4.51M59.652.062.157.9
EVA02 [17, 18] \n(Large)Full304.24M62.156.264.660.9
Freeze0.00M56.553.658.656.2
Rein2.99M65.360.564.963.6
DINOV2 [50] \n(Large)Full304.20M63.757.464.261.7
Freeze0.00M63.356.163.961.1
Rein2.99M66.460.466.164.3
", + "image_path": "fd2f61f42b356b038d0c9ba7f8063b43b27c45572c246fd21a99211e37a17d5c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 505, + 288, + 550 + ], + "lines": [ + { + "bbox": [ + 46, + 505, + 288, + 550 + ], + "spans": [ + { + "bbox": [ + 46, + 505, + 288, + 550 + ], + "type": "text", + "content": "Table 2. Performance Comparison with the proposed Rein across Multiple VFMs as Backbones under the GTAV " + }, + { + "bbox": [ + 46, + 505, + 288, + 550 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 505, + 288, + 550 + ], + "type": "text", + "content": " Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 289, + 715 + ], + "type": "text", + "content": "DGSS is generalizing from one urban-scene dataset to another, for instance, from the synthetic GTAV [57] dataset to the real-world Cityscapes [11]. In this classic setting, certain techniques [9, 51, 52] have achieved notable performance through learning feature normalization/whitening schemes, while others [40] have improved segmentation results through feature-level style transfer and the introduction of additional data. Additionally, strong data augmentation [4, 16, 53, 73] often simply and effectively enhances model robustness. However, most of previous DGSS methods generally utilize outdated backbones like ResNet [23], VGGNet [61], MobileNetV2 [60], and ShuffleNetV2 [47], thereby leaving the efficacy of stronger Vision Foundation" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 305, + 302, + 501, + 315 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 302, + 501, + 315 + ], + "spans": [ + { + "bbox": [ + 305, + 302, + 501, + 315 + ], + "type": "text", + "content": "Models (VFMs) in DGSS relatively unexplored." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 316, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 316, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 316, + 545, + 591 + ], + "type": "text", + "content": "Vision Foundation Models. The concept of a Foundation Model, initially introduced by Bommasani et al. [2] in the field of Natural Language Processing (NLP), defined as \"the base models trained on large-scale data in a self-supervised or semi-supervised manner that can be adapted for several other downstream tasks\". While models like the ViT [14] and Swin Transformer [45] have demonstrated excellent performance, the quest for a Vision Foundation Model (VFM) similar to their NLP counterparts is ongoing. This pursuit has yielded significant advancements with the advent of models such as CLIP [55], which learn high-quality visual representation by exploring contrastive learning with large-scale image text pairs; MAE [24], utilizing a masked image modeling for learning latent image representations; SAM [38], which develops a promptable model and pre-train it on a broad dataset for segmentation task; EVA02 [17, 18], which integrates Masked Image Modeling pre-training with CLIP's vision features; and DINOv2 [50], which is pretrained on extensive, curated datasets without explicit supervision. These VFs have shown remarkable performance in downstream applications. Yet, a dedicated investigation into their performance in the specific context of DGSS tasks remains unexplored." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Parameter-Efficient Fine-tuning. In the realm of NLP, parameter-efficient fine-tuning (PEFT) has achieved notable success by freezing most parameters of VFMs and fine-tuning a select few. Various approaches have been developed, such as BitFit [70], which adjusts only the model's bias terms; Prompt-tuning [41], introducing soft prompts to adapt frozen language models; Adapter-tuning [25], adding lightweight modules to each transformer layer; and notably, LoRA [26], which injects trainable rank decomposition matrices into transformer layers, yielding significant influence." + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 758 + ], + "type": "text", + "content": "28621" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 545, + 125 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 545, + 125 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 545, + 125 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 545, + 125 + ], + "type": "table", + "html": "
TargetACDC[59] (test)Cityscapes-C[48] (level-5)
Night Snow Fog RainAllBlurNoiseDigitalWeatherAvg.
MotionDefocGlassGaussGaussImpulShotSpeckBrightContrSaturJPEGSnowSpattFogFrost
HGFormer52.768.669.972.067.264.167.261.563.627.235.732.963.179.972.978.053.655.475.875.543.2
Ours70.679.576.478.277.668.571.769.768.76.223.013.163.781.578.980.668.863.873.679.547.9
", + "image_path": "e5649f764e1f92661a59238300a7ff1f0e191b7cd75db40af9b1536cb4028ff7.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 52, + 144, + 286, + 442 + ], + "blocks": [ + { + "bbox": [ + 93, + 125, + 499, + 137 + ], + "lines": [ + { + "bbox": [ + 93, + 125, + 499, + 137 + ], + "spans": [ + { + "bbox": [ + 93, + 125, + 499, + 137 + ], + "type": "text", + "content": "Table 3. Results on Cityscapes " + }, + { + "bbox": [ + 93, + 125, + 499, + 137 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 93, + 125, + 499, + 137 + ], + "type": "text", + "content": " ACDC (test) and Cityscapes-C (level-5) datasets, utilizing a batch size of 8." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 52, + 144, + 286, + 442 + ], + "lines": [ + { + "bbox": [ + 52, + 144, + 286, + 442 + ], + "spans": [ + { + "bbox": [ + 52, + 144, + 286, + 442 + ], + "type": "table", + "html": "
BackboneFine-tune \nMethodTrainable \nParams*mIoU
CitysBDDMapAvg.
EVA02 \n(Large) \n[17, 18]Full304.24M62.156.264.660.9
+AdvStyle [73]304.24M63.156.464.061.2
+PASTA [4]304.24M61.857.163.660.8
+GTR-LTR [53]304.24M59.857.463.260.1
Freeze0.00M56.553.658.656.2
+AdvStyle [73]0.00M51.451.656.553.2
+PASTA [4]0.00M57.852.358.556.2
+GTR-LTR [53]0.00M52.552.857.154.1
+LoRA [26]1.18M55.552.758.355.5
+AdaptFormer [6]3.17M63.759.964.262.6
+VPT [28]3.69M62.257.762.560.8
+Rein (ours)2.99M65.360.564.963.6
DINOv2 \n(Large) \n[50]Full304.20M63.757.464.261.7
+AdvStyle [73]304.20M60.858.062.560.4
+PASTA [4]304.20M62.557.264.761.5
+GTR-LTR [4]304.20M62.757.464.561.6
Freeze0.00M63.356.163.961.1
+AdvStyle [73]0.00M61.555.163.960.1
+PASTA [4]0.00M62.157.264.561.3
+GTR-LTR [4]0.00M60.257.762.260.0
+LoRA [26]0.79M65.258.364.662.7
+AdaptFormer [6]3.17M64.959.064.262.7
+VPT [28]3.69M65.259.465.563.3
+Rein (ours)2.99M66.460.466.164.3
", + "image_path": "246a83c336da90fbdeda68de17a6668e0bbbc41f83399474b54cee47645864fe.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 497, + 288, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 288, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 288, + 641 + ], + "type": "text", + "content": "The application of PEFT methods is also expanding into the field of computer vision [15, 39], with notable examples such as Visual Prompt Tuning (VPT) [28], which prepends prompts into the input sequence of transformer layers; AdaptFormer [6], replacing the MLP block in the transformer encoder with an AdaptMLP; LP-FT [39] find that fine-tuning can achieve worse accuracy than linear probing out-of-distribution; and Prompt-ICM [19], applying large-scale pre-trained models to the task of image coding for machines. Contrasting with these methods, we aim to refine feature maps for each instance within an image, thereby achieving superior performance in the realm of DGSS." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 651, + 107, + 662 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 651, + 107, + 662 + ], + "spans": [ + { + "bbox": [ + 47, + 651, + 107, + 662 + ], + "type": "text", + "content": "3. Methods" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 670, + 126, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 126, + 684 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 126, + 684 + ], + "type": "text", + "content": "3.1. Preliminary" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 715 + ], + "type": "text", + "content": "Driven by the motivation that Leveraging Stronger pretrained models and Fewer trainable parameters for Su" + } + ] + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 317, + 144, + 535, + 213 + ], + "blocks": [ + { + "bbox": [ + 46, + 444, + 287, + 489 + ], + "lines": [ + { + "bbox": [ + 46, + 444, + 287, + 489 + ], + "spans": [ + { + "bbox": [ + 46, + 444, + 287, + 489 + ], + "type": "text", + "content": "Table 4. Performance Comparison of the proposed Rein against other DGSS and PEFT methods under the GTAV " + }, + { + "bbox": [ + 46, + 444, + 287, + 489 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 444, + 287, + 489 + ], + "type": "text", + "content": " Cityscapes (Cities) + BDD100K (BDD) + Mapillary (Map) generalization setting. Mark * denotes trainable parameters in backbones." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 317, + 144, + 535, + 213 + ], + "lines": [ + { + "bbox": [ + 317, + 144, + 535, + 213 + ], + "spans": [ + { + "bbox": [ + 317, + 144, + 535, + 213 + ], + "type": "table", + "html": "
Source DomainCityscapes mIoU
GTAV66.4
+Synthia68.1
+UrbanSyn78.4
+1/16 of Cityscapes Training set82.5
", + "image_path": "6312da5214a1ee700bef437ad1e45812e02164d4526f9eb005146c3bd2e53051.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "table_body" + } + ], + "index": 8 + }, + { + "bbox": [ + 318, + 215, + 533, + 227 + ], + "lines": [ + { + "bbox": [ + 318, + 215, + 533, + 227 + ], + "spans": [ + { + "bbox": [ + 318, + 215, + 533, + 227 + ], + "type": "text", + "content": "Table 5. Synthetic data + 1/16 of Citys. → Citys. val set." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 545, + 378 + ], + "type": "text", + "content": "perior generalizability, we choose to fine-tune VFMs with a reduced parameter set. A straightforward thought might involve a smaller decode head; however, this method merely acts as a passive receiver of feature maps from the backbone, lacking the flexibility to effectively adapt a frozen backbone for generating task-specific or scene-specific features. In contrast, we propose to embed a mechanism, named \"Rein\", between the layers within the backbone. Rein actively refines and forwards the feature maps from each layer to the subsequent one. This approach allows us to more effectively utilize the powerful capabilities of VFMs, much like using rein to control a horse." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "spans": [ + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": "Given a pre-trained VFM with parameters " + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\Phi_M" + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": ", consisting of a sequence of layers " + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "inline_equation", + "content": "L_{1}, L_{2}, \\ldots, L_{N}" + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": ", a decode head " + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": " parameterized by " + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\theta_h" + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": ", and the Rein strategy with parameters " + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "inline_equation", + "content": "\\theta_R" + }, + { + "bbox": [ + 305, + 379, + 545, + 427 + ], + "type": "text", + "content": ", the optimization objective can be written as:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 339, + 434, + 545, + 467 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 434, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 339, + 434, + 545, + 467 + ], + "type": "interline_equation", + "content": "\\underset {\\theta_ {R}, \\theta_ {h}} {\\arg \\min } \\sum_ {i = 1} ^ {N _ {d}} \\operatorname {L o s s} \\left(\\mathcal {H} _ {\\theta_ {h}} \\left(\\mathcal {F} _ {\\Phi_ {M}, \\theta_ {R}} \\left(x _ {i}\\right)\\right), y _ {i}\\right), \\tag {1}", + "image_path": "385d8f12629a28764dc38e306668b951bebb75095c3a1cf3f4f7c6c82b2e1d2e.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "spans": [ + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "inline_equation", + "content": "x_{i}" + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "inline_equation", + "content": "y_{i}" + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "text", + "content": " denote the input image and its corresponding ground truth, respectively, and " + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "inline_equation", + "content": "N_{d}" + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "text", + "content": " signifies the total number of samples. " + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "inline_equation", + "content": "\\mathcal{F}_{\\Phi_M,\\theta_R}" + }, + { + "bbox": [ + 304, + 474, + 545, + 522 + ], + "type": "text", + "content": " represents the forward process of VFM after applying the Rein strategy." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 529, + 389, + 540 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 389, + 540 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 389, + 540 + ], + "type": "text", + "content": "3.2. Core of Rein" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "spans": [ + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "text", + "content": "For simple implementation across different VFMs, we opt not to modify MLP weights at specific positions as described in the [6, 26]. Instead, our approach focuses on refining the output feature maps at each layer within the VFMs, as illustrated in Fig. 2. Precisely, for the features " + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "text", + "content": " produced by the " + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "text", + "content": "-th layer " + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "inline_equation", + "content": "L_{i}" + }, + { + "bbox": [ + 304, + 547, + 545, + 631 + ], + "type": "text", + "content": ", Rein produces enhanced feature maps for the next layer as follows:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 326, + 639, + 489, + 651 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 639, + 489, + 651 + ], + "spans": [ + { + "bbox": [ + 326, + 639, + 489, + 651 + ], + "type": "interline_equation", + "content": "f _ {1} = L _ {1} (E m b e d (x)) \\quad f _ {1} \\in \\mathbb {R} ^ {n \\times c},", + "image_path": "c499ccac37232fd110cebf07ea26c1d3e4f5eea11409a9fe01f6bb8c4f61194f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 654, + 545, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 654, + 545, + 666 + ], + "spans": [ + { + "bbox": [ + 317, + 654, + 545, + 666 + ], + "type": "interline_equation", + "content": "f _ {i + 1} = L _ {i + 1} \\left(f _ {i} + \\Delta f _ {i}\\right) \\quad i = 1, 2, \\dots , N - 1, \\tag {2}", + "image_path": "32292f583b898eba1a6fc218f5d42773144d247b31cea3222baff1b6c31e23fd.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 318, + 669, + 400, + 681 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 669, + 400, + 681 + ], + "spans": [ + { + "bbox": [ + 318, + 669, + 400, + 681 + ], + "type": "interline_equation", + "content": "f _ {o u t} = f _ {N} + \\Delta f _ {N},", + "image_path": "73c74a85fe44ce932a5ecca21f43a5eee197db269bb0b283fea7f38ee545f1e4.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "f_{i}^{\\prime} = f_{i} + \\Delta f_{i}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " symbolizes the refined feature map, " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "x" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " is the input image, " + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\text{Embed}" + }, + { + "bbox": [ + 306, + 689, + 545, + 714 + ], + "type": "text", + "content": " denotes the patch embedding" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28622" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": "layer in VFMs, " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "n" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " represents the number of patches, " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " denotes the number of layers, and " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " is the dimensionality of " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "f_{1}, f_{2}, \\ldots, f_{N}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": ". Note that the layers " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "L_{1}, L_{2}, \\ldots, L_{N}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " are kept frozen, and our focus is on training an efficient module, Rein, to generate " + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\Delta f_{i}" + }, + { + "bbox": [ + 47, + 72, + 287, + 133 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 56, + 141, + 287, + 155 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 56, + 141, + 287, + 155 + ], + "spans": [ + { + "bbox": [ + 56, + 141, + 287, + 155 + ], + "type": "interline_equation", + "content": "\\Delta f _ {i} = \\operatorname {R e i n} (f _ {i}) \\quad \\Delta f _ {i} \\in \\mathbb {R} ^ {n \\times c}, i = 1, 2, \\dots , N. \\tag {3}", + "image_path": "f438093fe2107d21a1670aeb1d478dafde34b3343146b547575eb910226e7ea3.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 164, + 287, + 248 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 164, + 287, + 248 + ], + "spans": [ + { + "bbox": [ + 46, + 164, + 287, + 248 + ], + "type": "text", + "content": "In the context of DGSS, an ideal " + }, + { + "bbox": [ + 46, + 164, + 287, + 248 + ], + "type": "inline_equation", + "content": "\\Delta f_{i}" + }, + { + "bbox": [ + 46, + 164, + 287, + 248 + ], + "type": "text", + "content": " should assist VFMs to bridge two types of gaps. The first is gap in scene between pre-training dataset and target scene, exemplified by the contrast between ImageNet [12] and urban-scene images [11, 57]. The second is task divergence between pretraining and fine-tuning, such as the differences between masked image modeling and semantic segmentation tasks." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": "To establish this dual bridge, Rein starts with a set of learnable tokens " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "T = \\{T_{i} \\in \\mathbb{R}^{m \\times c} \\mid i \\in \\mathbb{N}, 1 \\leq i \\leq N\\}" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": ", where each token sequence " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": " is randomly initialized, and " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": " denotes the sequence length of " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": ". Rein freezes the backbone and embeds knowledge learned from the finetuning dataset into these tokens, thereby bridging the gap in scene relative to the pre-training dataset. Moreover, considering the essential need in semantic segmentation to discern multiple instances within a single image, Rein implements an attention-inspired mechanism, which enables VFMs to make tailored adjustments to the features of distinct instances, thereby aiding VFMs in adapting to the differences between semantic segmentation and pre-training tasks. Specifically, Rein employs a dot-product operation to generate a similarity map " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": ", which captures the associations between feature vectors in " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "f_{i}" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": " and the tokens in " + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 248, + 287, + 439 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 102, + 450, + 287, + 464 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 450, + 287, + 464 + ], + "spans": [ + { + "bbox": [ + 102, + 450, + 287, + 464 + ], + "type": "interline_equation", + "content": "S _ {i} = f _ {i} \\times T _ {i} ^ {\\mathrm {T}} \\quad S _ {i} \\in \\mathbb {R} ^ {n \\times m}, \\tag {4}", + "image_path": "7f4cc8cc06b6df1d67b019ce15f92e7463aaf98dd77892928718b004fa39637d.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "content": " represents the token sequence of the " + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "content": "-th layer, " + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "content": " indicates the number of tokens in " + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "content": ". As " + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 470, + 287, + 529 + ], + "type": "text", + "content": " quantitatively evaluates the relationships between various tokens and feature vectors, Rein can apply a softmax function to align each patch with a unique instance:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 111, + 538, + 287, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 538, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 111, + 538, + 287, + 566 + ], + "type": "interline_equation", + "content": "S _ {i} = \\operatorname {S o f t m a x} \\left(\\frac {f _ {i} \\times T _ {i} ^ {\\mathrm {T}}}{\\sqrt {c}}\\right). \\tag {5}", + "image_path": "86892a47d794b5cb592203263d8c1541521c75135eac3acfaf803afddab4c4d0.jpg" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "spans": [ + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "text", + "content": "Leveraging the feature-to-token similarity map " + }, + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "text", + "content": ", we can preliminarily estimates of " + }, + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "inline_equation", + "content": "\\Delta f_{i}" + }, + { + "bbox": [ + 47, + 574, + 287, + 597 + ], + "type": "text", + "content": " using the equation:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 63, + 606, + 287, + 620 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 63, + 606, + 287, + 620 + ], + "spans": [ + { + "bbox": [ + 63, + 606, + 287, + 620 + ], + "type": "interline_equation", + "content": "\\Delta \\bar {f} _ {i} = S _ {i} (:, 2: m) \\times \\left[ T _ {i} (2: m) \\times W _ {T _ {i}} + b _ {T _ {i}} \\right], \\tag {6}", + "image_path": "dbc5a32693bdf72bdc0b5aae391234fdf158ec3dbfa96547b5ced9bd60e5b69e.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "W_{T_i}" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "b_{T_i}" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": " denote the weights and biases of a MLP, respectively. This MLP enables the transformation of " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "T_i" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": " across different feature spaces during the computation of " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "S_i" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\Delta \\bar{f}_i" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": ". Optionally, Rein can pre-calculate " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "T_i \\times W_{T_i} + b_{T_i}" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": " to reduce inference time. The sum of " + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "inline_equation", + "content": "S_i" + }, + { + "bbox": [ + 47, + 629, + 287, + 713 + ], + "type": "text", + "content": " equals one due to the softmax function; however, this can induce unneeded changes when all features are precise. To" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "avoid this, " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "S_{i}(:,2:m)" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " is designed to choose columns 2 to m of " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "T_{i}(2:m)" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " denotes the selection of rows 2 to m of " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ". This strategic selection allows models to sidestep unnecessary adjustments by assigning a high value to the first token and subsequently discarding it. This approach allows the sum of each row in " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "S_{i}" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": " to vary from 0 to 1, thus reducing the risk of inappropriate changes." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "spans": [ + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": "To enhance the flexibility in feature adjustment, Rein utilizes a MLP composed of " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "W_{f_i}" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "b_{f_i}" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": " to produce the final feature modifications " + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "inline_equation", + "content": "\\Delta f_i" + }, + { + "bbox": [ + 304, + 156, + 545, + 192 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 358, + 200, + 545, + 214 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 358, + 200, + 545, + 214 + ], + "spans": [ + { + "bbox": [ + 358, + 200, + 545, + 214 + ], + "type": "interline_equation", + "content": "\\Delta f _ {i} = \\left(\\Delta \\bar {f} _ {i} + f _ {i}\\right) \\times W _ {f _ {i}} + b _ {f _ {i}}. \\tag {7}", + "image_path": "8ee1d90b8142668920700a87292a7a0dcce6f5b7aa73b6352844c15311c2624b.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 222, + 545, + 270 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 222, + 545, + 270 + ], + "spans": [ + { + "bbox": [ + 304, + 222, + 545, + 270 + ], + "type": "text", + "content": "Benefiting from these instance-level " + }, + { + "bbox": [ + 304, + 222, + 545, + 270 + ], + "type": "inline_equation", + "content": "\\Delta f_{i}" + }, + { + "bbox": [ + 304, + 222, + 545, + 270 + ], + "type": "text", + "content": " adjustments, Rein is capable of generating diverse modifications for various categories within a single image. The details of Rein will be explained in the next section." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 277, + 397, + 289 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 277, + 397, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 397, + 289 + ], + "type": "text", + "content": "3.3. Details of Rein" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "spans": [ + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "type": "text", + "content": "Linking tokens to instances. At the core of Rein, we establish an implicit yet effective linkage between tokens and instances, which has demonstrated notable performance, as detailed in Sec. 4. This connection is further reinforced by utilizing object queries, a key component in DETR[3]-style decode heads [7, 8, 71], as intermediaries. These queries are empirically proven to establish a direct association with instances. Specifically, we generate layer-wise queries " + }, + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "type": "inline_equation", + "content": "Q_{i}" + }, + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "type": "text", + "content": " from our learnable tokens " + }, + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 304, + 296, + 545, + 403 + ], + "type": "text", + "content": " via linear transformation:" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 341, + 411, + 545, + 426 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 411, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 341, + 411, + 545, + 426 + ], + "type": "interline_equation", + "content": "Q _ {i} = T _ {i} \\times W _ {Q _ {i}} + b _ {Q _ {i}} \\quad Q _ {i} \\in \\mathbb {R} ^ {m \\times c ^ {\\prime}}, \\tag {8}", + "image_path": "ac4285b038599ad60b70c864162a2884ec437b141d5d41f88f8dc8fe6c767d59.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "W_{Q_i}" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "b_{Q_i}" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " signify the weights and biases, respectively, and " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "c'" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " denotes the dimension of " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q_i" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": ". However, due to the complexity arising from the large numbers of various layers in VFMs, transforming the diverse " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q_i" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " into a single query " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " poses computational challenges. To address this, Rein computes both the maximal component " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q_{\\text{max}} \\in \\mathbb{R}^{m \\times c'}" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " and the average component " + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "inline_equation", + "content": "Q_{\\text{avg}} \\in \\mathbb{R}^{m \\times c'}" + }, + { + "bbox": [ + 304, + 434, + 545, + 529 + ], + "type": "text", + "content": " using the following equation:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 356, + 538, + 495, + 556 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 356, + 538, + 495, + 556 + ], + "spans": [ + { + "bbox": [ + 356, + 538, + 495, + 556 + ], + "type": "interline_equation", + "content": "Q _ {m a x} (j, k) = \\max _ {i = 1, 2, \\dots , N} Q _ {i} (j, k),", + "image_path": "57491a3ede0b94f6c2d292fa218606a1bc24e8af06ef17c37af9da7c3182e159.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 360, + 559, + 545, + 592 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 360, + 559, + 545, + 592 + ], + "spans": [ + { + "bbox": [ + 360, + 559, + 545, + 592 + ], + "type": "interline_equation", + "content": "Q _ {a v g} (j, k) = \\frac {1}{N} \\sum_ {i = 1} ^ {N} Q _ {i} (j, k). \\tag {9}", + "image_path": "aef5a1141cda26d6816812c790696772b180039ee56dc71ea2e0278ab728d42a.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 306, + 599, + 430, + 611 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 599, + 430, + 611 + ], + "spans": [ + { + "bbox": [ + 306, + 599, + 430, + 611 + ], + "type": "text", + "content": "Subsequently, " + }, + { + "bbox": [ + 306, + 599, + 430, + 611 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 306, + 599, + 430, + 611 + ], + "type": "text", + "content": " is derived as:" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 320, + 620, + 545, + 633 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 620, + 545, + 633 + ], + "spans": [ + { + "bbox": [ + 320, + 620, + 545, + 633 + ], + "type": "interline_equation", + "content": "Q = \\operatorname {C o n c a t} \\left(\\left[ Q _ {\\max }, Q _ {\\text {a v g}}, Q _ {N} \\right]\\right) \\times W _ {Q} + b _ {Q}. \\tag {10}", + "image_path": "d1a1ef828a5bf20547025ee5b5a0ef786ee722b47f48fd62f3e149530b8c2d73.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "spans": [ + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "content": "By mapping " + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "content": " onto " + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "inline_equation", + "content": "Q" + }, + { + "bbox": [ + 304, + 641, + 545, + 677 + ], + "type": "text", + "content": ", which subsequently links to instances, Rein achieves enhanced performance with a marginal increase in parameters." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": "Layer-shared MLP weights. To address the redundancy of parameters in the layer-specific MLP weights, specifically " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "W_{T_i}" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " in Eq. (6), " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "W_{f_i}" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " in Eq. (7), and " + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "W_{Q_i}" + }, + { + "bbox": [ + 304, + 677, + 545, + 714 + ], + "type": "text", + "content": " in Eq. (8), which" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28623" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": "collectively contribute to a substantial trainable parameter count, we adopt a new strategy. Since the learnable " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " is capable of producing distinct " + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "inline_equation", + "content": "\\Delta f_{i}" + }, + { + "bbox": [ + 46, + 72, + 289, + 156 + ], + "type": "text", + "content": " for each layer, we design the role of the MLP to primarily perform consistent linear transformations across different feature spaces for each layer within the backbone. To this end, we employ shared MLP weights across layers as outlined in the equations:" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 59, + 164, + 286, + 209 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 164, + 286, + 209 + ], + "spans": [ + { + "bbox": [ + 59, + 164, + 286, + 209 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\left[ W _ {T _ {1}}, b _ {T _ {1}} \\right] = \\left[ W _ {T _ {2}}, b _ {T _ {2}} \\right] = \\dots = \\left[ W _ {T _ {N}}, b _ {T _ {N}} \\right], \\\\ \\left[ W _ {f _ {1}}, b _ {f _ {1}} \\right] = \\left[ W _ {f _ {2}}, b _ {f _ {2}} \\right] = \\dots = \\left[ W _ {f _ {N}}, b _ {f _ {N}} \\right], \\tag {11} \\\\ \\left[ W _ {Q _ {1}}, b _ {Q _ {1}} \\right] = \\left[ W _ {Q _ {2}}, b _ {Q _ {2}} \\right] = \\dots = \\left[ W _ {Q _ {N}}, b _ {Q _ {N}} \\right]. \\\\ \\end{array}", + "image_path": "9ca36581a5fec2fb60966566594999040e20f22401d28f7b60306d9711a2f227.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 216, + 287, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 216, + 287, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 216, + 287, + 276 + ], + "type": "text", + "content": "Low-rank token sequence. Recognizing the potential for information overlap among diverse learnable tokens, such as the high similarity between tokens representing a car's headlight and a bicycle's light, Rein adopts a strategy to generate a low-rank token sequence " + }, + { + "bbox": [ + 46, + 216, + 287, + 276 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 216, + 287, + 276 + ], + "type": "text", + "content": " as follows:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 70, + 284, + 287, + 297 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 70, + 284, + 287, + 297 + ], + "spans": [ + { + "bbox": [ + 70, + 284, + 287, + 297 + ], + "type": "interline_equation", + "content": "T i = A _ {i} \\times B _ {i}, \\quad A \\in \\mathbb {R} ^ {m \\times r}, B \\in \\mathbb {R} ^ {r \\times c}, \\tag {12}", + "image_path": "10372fe726b0cd004c8fab1ff92e9d3517b5155dcea4758f18f30b6ad2a49c85.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "spans": [ + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": " denotes the dimension of " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": " is the length of sequence " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "T_{i}" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": " represents the rank, with " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "r \\ll c" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": ". Here, matrices " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "A" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": " are constructed as low-rank matrices. To reduce inference time, Rein can precompute and store " + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 306, + 287, + 378 + ], + "type": "text", + "content": ". By implementing this low-rank token sequence approach, Rein significantly reduces the number of parameters." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 388, + 128, + 402 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 388, + 128, + 402 + ], + "spans": [ + { + "bbox": [ + 47, + 388, + 128, + 402 + ], + "type": "text", + "content": "4. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 407, + 107, + 420 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 407, + 107, + 420 + ], + "spans": [ + { + "bbox": [ + 47, + 407, + 107, + 420 + ], + "type": "text", + "content": "4.1. Settings" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 426, + 287, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 287, + 641 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 287, + 641 + ], + "type": "text", + "content": "Visual Foundation Models. To thoroughly assess the influence of Visual Foundation Models (VFMs) within the context of DGSS, we analyze five distinct VFMs, each with different training strategies and datasets. Our selection includes CLIP [55], a language-image pre-training model; MAE [24], known for its masked pre-training approach; SAM [38], which leverages a large-scale segmentation dataset; EVA02 [17, 18] combines CLIP with masked image modeling; and DINOv2 [50], based on self-supervised pretraining with curated dataset. For balancing precision and efficiency, we mainly employ the ViT-Large architecture for these VFMs, except SAM, which utilizes a ViT-Huge image encoder, as described in its original paper [38]. We establish two fundamental baselines for VFMs: \"Full\", where we fine-tune the entire network, and \"Freeze\", in which all backbone parameters are fixed, with training solely on the segmentation head. More details about VFMs and PEFT methods are available in the supplementary material." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 642, + 287, + 714 + ], + "type": "text", + "content": "Datasets. We evaluate VFs and proposed methods on both real-world datasets (Cityscapes [11], BDD100K [68], Mapillary [49]) and synthetic datasets (GTAV [57], Synthia [58], UrbanSyn [22]). In detail, Cityscapes (denoted as Citys) is an autonomous driving dataset that contains 2975 training images and 500 validation images, each with the" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": "resolution of " + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "2048 \\times 1024" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ". BDD100K (shortened to BDD) and Mapillary (denoted by Map) offer 1,000 (" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "1280 \\times 720" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ") and 2,000 (" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "inline_equation", + "content": "1902 \\times 1080" + }, + { + "bbox": [ + 304, + 72, + 545, + 156 + ], + "type": "text", + "content": ") validation images, respectively. GTAV, a synthetic dataset, presents 24,966 labeled images obtained from the game. Synthia, a synthetic dataset, provides 25,000 images created by photo-realistic rendering. UrbanSyn, a synthetic dataset consists of 7,539 images." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 157, + 546, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 546, + 361 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 546, + 361 + ], + "type": "text", + "content": "Implementation details. We utilize the MMSegmentation [10] codebase for our implementation. For superior performance, mask2former [8], a widely-used segmentation head, is integrated with various VFMs that serve as the backbone. Additional experiments involving other decode heads are detailed in the supplementary material. For the training phase, the AdamW optimizer [46] is employed, setting the learning rate at 1e-5 for the backbone and 1e-4 for both the decode head and the proposed Rein. Aiming to efficient training process, we utilize a configuration of 40,000 iterations with a batch size of 4, and crop images to a resolution of " + }, + { + "bbox": [ + 304, + 157, + 546, + 361 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 157, + 546, + 361 + ], + "type": "text", + "content": ". Our approach includes only basic data augmentation, following Mask2Former [8]. Thanks to our streamlined training configuration and reduced number of trainable parameters, Rein can fine-tune models like DINOv2-Large or EVA02-Large on a single RTX 3090Ti GPU within 12 hours for superior generalization ability." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 370, + 534, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 370, + 534, + 383 + ], + "spans": [ + { + "bbox": [ + 305, + 370, + 534, + 383 + ], + "type": "text", + "content": "4.2. Comparison with State-of-The-Art Methods" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "spans": [ + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "text", + "content": "In this section, we comprehensively evaluate Rein over five datasets within three generalization settings: " + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "inline_equation", + "content": "GTAV \\rightarrow Citys + BDD + Map" + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "inline_equation", + "content": "GTAV + Synthia \\rightarrow Citys + BDD + Map" + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "inline_equation", + "content": "Citys \\rightarrow BDD + Map" + }, + { + "bbox": [ + 304, + 389, + 545, + 498 + ], + "type": "text", + "content": ". Rein is benchmarked against state-of-the-art (SOTA) methods, which can be classified into two groups, including domain generalized semantic segmentation (DGSS) methods[4, 9, 13, 27, 35, 40, 51, 53, 54, 64, 69, 73], and parameter-efficient fine-tuning (PEFT) approaches [6, 26, 28]." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": "Investigation of various VFMs. Our analysis of VFMs and proposed Rein in the " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "GTAV \\rightarrow Citys + BDD + Map" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " setting is presented in Tables 1 and 2. In this setup, models are fine-tuned using GTAV and evaluated on Cityscapes, BDD100K, and Mapillary. Note that, due to the fixed and relatively small number of trainable parameters in the decode head (20.6M), the count of trainable parameters presented in the tables are focused solely on the backbone and the PEFT module. Our results, as detailed in Table 1, indicate that frozen VFMs significantly outperform previous DGSS methods without specialized design. Moreover, as shown in Table 2, VFMs with full parameter fine-tuning exhibit enhanced performance relative to their frozen counterparts. Remarkably, Rein achieves even superior generalization capabilities, surpassing the full parameter fine-tuning with merely an extra " + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "inline_equation", + "content": "1\\%" + }, + { + "bbox": [ + 304, + 498, + 546, + 713 + ], + "type": "text", + "content": " of trainable parameters compared to the original backbone. Visual samples for qualitative comparison are given in Fig. 3." + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "28624" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 51, + 70, + 547, + 200 + ], + "blocks": [ + { + "bbox": [ + 51, + 70, + 547, + 200 + ], + "lines": [ + { + "bbox": [ + 51, + 70, + 547, + 200 + ], + "spans": [ + { + "bbox": [ + 51, + 70, + 547, + 200 + ], + "type": "table", + "html": "
BackboneFine-tune \nMethodTrainable \nParams*roadside.build.wallfencepolelightsignvegeterr.skypers.ridercartruckbustrainmoto.bicy.mIoU
EVA02 \n(Large) \n[17, 18]Full304.24M89.346.989.947.745.650.156.842.288.848.489.975.849.090.545.369.255.944.455.162.2
Freeze0.00M93.152.788.047.431.141.746.039.685.741.489.567.539.789.047.072.846.319.235.256.5
Rein-core52.84M91.153.890.050.347.746.656.442.987.844.290.473.544.291.858.177.257.343.457.363.4
+ Rein-link59.33M90.948.590.052.649.449.157.239.888.946.590.574.444.091.052.380.767.344.360.364.1
+ Rein-share5.02M92.754.390.051.848.648.855.345.088.946.789.873.743.390.649.581.169.641.750.263.4
+ Rein-lora2.99M91.751.890.152.848.448.256.042.089.144.190.274.247.091.154.584.178.947.259.465.3
DINOv2 \n(Large) \n[50]Full304.20M89.044.589.651.146.449.260.038.989.147.591.775.848.291.752.582.981.030.449.963.7
Freeze0.00M92.155.290.257.248.549.556.747.789.347.891.174.246.792.262.677.547.729.647.261.1
Rein-core52.84M92.457.890.656.850.750.557.544.889.847.091.175.947.291.960.180.359.837.952.364.9
+ Rein-link59.33M91.255.590.655.652.551.159.745.189.847.191.175.847.192.664.682.265.540.452.765.8
+ Rein-share5.02M93.561.290.757.753.252.458.050.189.749.990.774.845.091.758.580.166.336.950.765.8
+ Rein-lora2.99M92.459.190.758.353.751.858.246.489.849.490.873.943.392.364.381.670.940.454.066.4
", + "image_path": "b8cbc0eeac34d701a218b4f67fae5989e784d6fa90f82f1a71a9b0362c46cfdc.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "type": "text", + "content": "Table 6. Ablation Study about Rein under Cityscapes " + }, + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 46, + 201, + 547, + 234 + ], + "type": "text", + "content": " BDD100K generalization in terms of mIoU. Components are sequentially incorporated. To better illustrate the gains contributed by each component, we employ varying shades of yellow to demonstrate the relative performance of the Freeze and Rein methods. The best results across all methods are highlighted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 49, + 235, + 545, + 388 + ], + "blocks": [ + { + "bbox": [ + 49, + 235, + 545, + 388 + ], + "lines": [ + { + "bbox": [ + 49, + 235, + 545, + 388 + ], + "spans": [ + { + "bbox": [ + 49, + 235, + 545, + 388 + ], + "type": "image", + "image_path": "b6207aeca8a25d9645477044f648597374345989031f87272ff74114086093ab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 54, + 390, + 539, + 402 + ], + "lines": [ + { + "bbox": [ + 54, + 390, + 539, + 402 + ], + "spans": [ + { + "bbox": [ + 54, + 390, + 539, + 402 + ], + "type": "text", + "content": "Figure 3. Qualitative Comparison under GTAV " + }, + { + "bbox": [ + 54, + 390, + 539, + 402 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 54, + 390, + 539, + 402 + ], + "type": "text", + "content": " Cityscapes (Citys) + BDD100K (BDD) + Mapillary (Map) generalization setting." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 411, + 289, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 411, + 289, + 603 + ], + "spans": [ + { + "bbox": [ + 46, + 411, + 289, + 603 + ], + "type": "text", + "content": "Comparing Rein with SOTA. We conduct a comprehensive performance comparison of the proposed Rein against existing DGSS and PEFT methods under the " + }, + { + "bbox": [ + 46, + 411, + 289, + 603 + ], + "type": "inline_equation", + "content": "GTAV \\rightarrow Citys + BDD + Map" + }, + { + "bbox": [ + 46, + 411, + 289, + 603 + ], + "type": "text", + "content": " setting, as detailed in Table 4. Owing to the robust feature extraction capabilities inherent in VFMs, DGSS methods, which typically enhance generalizability through strong data augmentation or consistency constraints, (e.g., AdvStyle, PASTA, and GTR), do not exhibit significant performance improvement. On the other hand, PEFT methods have demonstrated notable advancements. For instance, AdaptFormer outperforms the \"Freeze\" baseline using EVA02 as the backbone, while VPT shows improved performance over \"Full\" with DINOv2. Employing the same backbones (DINOv2 and EVA02), proposed Rein achieves superior performance and surpass previous DGSS and PEFT methods." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "text", + "content": "Real-to-Real generalization of Rein. The generalization from one real-world dataset to others is pivotal for practical applications in the field. To this end, we conduct experiments under the " + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\text{Citys} \\rightarrow \\text{ACDC}" + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\text{Citys} \\rightarrow \\text{Cityscapes-C}" + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "inline_equation", + "content": "\\text{Citys} \\rightarrow \\text{BDD} + \\text{Map}" + }, + { + "bbox": [ + 46, + 605, + 289, + 713 + ], + "type": "text", + "content": " generalization setting. As shown in Table 3 and 7, Rein, when coupled with the DINOv2-Large, demonstrates superior performance across all datasets. This underscores the effectiveness of Rein in generalizing to diverse real-world scenarios." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": "Synthetic-to-real generalization of Rein. As Tab. 5 illustrates, trained on synthetic UrbanSyn+GTAV+Synthia datasets, Rein achieved a " + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "inline_equation", + "content": "78.4\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": " mIoU on the Cityscapes validation set. Further improvement is possible with additional synthetic data and higher-quality images generated by diffusion models, like [1]. This result can also be a valuable pre-trained weight for data-efficient training, reaching an " + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "inline_equation", + "content": "82.5\\%" + }, + { + "bbox": [ + 304, + 411, + 545, + 530 + ], + "type": "text", + "content": " mIoU with 1/16 of Cityscapes training set. This is a significant performance for semi-supervised semantic segmentation." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 531, + 545, + 591 + ], + "type": "text", + "content": "More backbones. We extend our analysis to integrating Rein with Convolutional Networks, such as ResNet and ConvNeXt, and smaller scale architectures like DINOv2-S/B. As shown in Table 8, our findings reveal that Rein exhibits remarkable performance with diverse backbones." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 305, + 599, + 470, + 612 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 599, + 470, + 612 + ], + "spans": [ + { + "bbox": [ + 305, + 599, + 470, + 612 + ], + "type": "text", + "content": "4.3. Ablation Studies and Analysis" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "type": "text", + "content": "We conduct extensive ablation studies within two settings: " + }, + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "type": "inline_equation", + "content": "GTAV \\to Citys" + }, + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "type": "inline_equation", + "content": "GTAV \\to Citys + BDD + Map" + }, + { + "bbox": [ + 304, + 617, + 545, + 641 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": "Analysis of the key components. Table 6 is dedicated to thoroughly examining the effectiveness of each component within Rein. In the " + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "inline_equation", + "content": "GTAV \\rightarrow City" + }, + { + "bbox": [ + 304, + 642, + 545, + 713 + ], + "type": "text", + "content": " generalization setting, we sequentially incorporate different components of Rein and assess their impact. Interestingly, we observe that the \"Freeze\" occasionally exhibit better recognition for specific" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "28625" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 52, + 70, + 282, + 191 + ], + "blocks": [ + { + "bbox": [ + 52, + 70, + 282, + 191 + ], + "lines": [ + { + "bbox": [ + 52, + 70, + 282, + 191 + ], + "spans": [ + { + "bbox": [ + 52, + 70, + 282, + 191 + ], + "type": "table", + "html": "
MethodsBackboneTrainable \nParameters*mIoU
BDDMapAvg.
IBN [51]ResNet50 [23]23.58M48.657.052.8
DRPC [69]ResNet50 [23]23.58M49.956.353.1
GTR [53]ResNet50 [23]23.58M50.857.254.0
SAN-SAW [54]ResNet50 [23]23.58M53.059.856.4
WildNet [40]ResNet101 [23]42.62M50.958.854.9
HGFformer [13]Swin-L [45]196.03M61.572.166.8
FreezeEVA02-L [17]0.00M57.863.860.8
Rein (Ours)EVA02-L [17]2.99M64.169.566.8
FreezeDINOv2-L [50]0.00M63.469.766.7
Rein (Ours)DINOv2-L [50]2.99M65.072.368.7
", + "image_path": "c0c6f9d027767733c46e4aefa4956546158278e9ca45b071fc7046dfe779ef58.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 48, + 232, + 291, + 288 + ], + "blocks": [ + { + "bbox": [ + 47, + 193, + 287, + 227 + ], + "lines": [ + { + "bbox": [ + 47, + 193, + 287, + 227 + ], + "spans": [ + { + "bbox": [ + 47, + 193, + 287, + 227 + ], + "type": "text", + "content": "Table 7. Performance Comparison of the Rein against other DGSS methods under Cityscapes " + }, + { + "bbox": [ + 47, + 193, + 287, + 227 + ], + "type": "inline_equation", + "content": "\\rightarrow" + }, + { + "bbox": [ + 47, + 193, + 287, + 227 + ], + "type": "text", + "content": " BDD100K (BDD) +Mapillary (Map) generalization. The best results are highlighted." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 232, + 291, + 288 + ], + "lines": [ + { + "bbox": [ + 48, + 232, + 291, + 288 + ], + "spans": [ + { + "bbox": [ + 48, + 232, + 291, + 288 + ], + "type": "table", + "html": "
Avg. mIoUResNet (50)ResNet (101)ConvNeXt (Large)DINOv2 (S)DINOv2 (B)
Full38.946.152.251.856.7
Ours46.646.355.555.759.1
", + "image_path": "1c4333575eec7a487aba464df46c50173d2fec487d71aa4bff1952407590f90a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + } + ], + "index": 2 + }, + { + "bbox": [ + 64, + 289, + 269, + 300 + ], + "lines": [ + { + "bbox": [ + 64, + 289, + 269, + 300 + ], + "spans": [ + { + "bbox": [ + 64, + 289, + 269, + 300 + ], + "type": "text", + "content": "Table 8. Results for ConvNets and smaller backbones." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 46, + 313, + 287, + 409 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 313, + 287, + 409 + ], + "spans": [ + { + "bbox": [ + 46, + 313, + 287, + 409 + ], + "type": "text", + "content": "categories, e.g., 'road, sidewalk', compared to the \"Full\". This suggests that VFMs lose some pre-training knowledge during fine-tuning, and \"Freeze\" helps to prevent. Similarly, our methods mitigate this knowledge forgetting. Furthermore, our methods show improved recognition capabilities for the majority of the 19 categories. For example, in recognizing 'wall, motorcycle, bicycle', our approach significantly outperforms both the \"Full\" and \"Freeze\" baselines." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 410, + 287, + 493 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 410, + 287, + 493 + ], + "spans": [ + { + "bbox": [ + 46, + 410, + 287, + 493 + ], + "type": "text", + "content": "Overall, \"Rein-core\" boosts the average performance across 19 classes. Furthermore, \"Rein-link\" further boosts accuracy for certain objects, including 'car, bus, train, motorcycle', especially for DINOv2. Employing layer-shared MLP weights and low-rank token sequence efficiently reduces the number of trainable parameters and positively influences the performance of the model." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "spans": [ + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": "Study on token length " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": ". The core component of Rein is learnable tokens " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}^{m \\times c}" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": ". We explored various lengths " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": " for the token sequence, ranging from 25 to 200. As demonstrated in Fig. 4, models with " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "m = 100" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "m = 150" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": " both achieve a strong mIoU of " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "64.3\\%" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": ". We ultimately selected " + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "inline_equation", + "content": "m = 100" + }, + { + "bbox": [ + 46, + 495, + 287, + 567 + ], + "type": "text", + "content": " as the most suitable parameter." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "content": "Study on rank " + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "content": ". As shown in Table 9, we turn attention to the effect of rank " + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "inline_equation", + "content": "r" + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "content": " on model performance. With DINOv2 as the backbone, the optimal results are observed at " + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "inline_equation", + "content": "r = 16" + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "inline_equation", + "content": "r = 32" + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "content": ". Consequently, unlike LoRA [26], we opt for a comparatively higher value of " + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "inline_equation", + "content": "r = 16" + }, + { + "bbox": [ + 46, + 568, + 287, + 628 + ], + "type": "text", + "content": " for our model." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 630, + 287, + 713 + ], + "type": "text", + "content": "Speed, memory, and storage. For practical applications, training speed, GPU memory usage, and model storage requirements are crucial. As shown in Table 10, compared to \"Full\" baseline, proposed Rein improves training speed and reduces GPU memory usage. A significant advantage of Rein is that models trained under different settings can share the same backbone parameters. This means that for switch" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 305, + 69, + 545, + 189 + ], + "blocks": [ + { + "bbox": [ + 305, + 69, + 545, + 189 + ], + "lines": [ + { + "bbox": [ + 305, + 69, + 545, + 189 + ], + "spans": [ + { + "bbox": [ + 305, + 69, + 545, + 189 + ], + "type": "image", + "image_path": "173f2792a7339754674956c94d977fbf46165e65729e7068944f6cbba93dee21.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 307, + 205, + 545, + 280 + ], + "blocks": [ + { + "bbox": [ + 344, + 191, + 506, + 202 + ], + "lines": [ + { + "bbox": [ + 344, + 191, + 506, + 202 + ], + "spans": [ + { + "bbox": [ + 344, + 191, + 506, + 202 + ], + "type": "text", + "content": "Figure 4. Ablation study on token length " + }, + { + "bbox": [ + 344, + 191, + 506, + 202 + ], + "type": "inline_equation", + "content": "m" + }, + { + "bbox": [ + 344, + 191, + 506, + 202 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 205, + 545, + 280 + ], + "lines": [ + { + "bbox": [ + 307, + 205, + 545, + 280 + ], + "spans": [ + { + "bbox": [ + 307, + 205, + 545, + 280 + ], + "type": "table", + "html": "
Rank r \nParams48163264
2.67M2.77M2.99M3.42M4.28M
DINOv2 \n(Large) \n[50]Citys65.866.166.466.166.4
BDD60.260.360.460.761.0
Map65.265.166.165.965.0
Avg.63.763.964.364.364.1
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VFMsMethodTraining TimeGPU MemoryStorage
DINOv2 (Large)Full11.2 h14.7 GB1.22 GB
Rein9.5 h10.0 GB1.23 GB
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Training Time, GPU Memory, and Storage." + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "text" + }, + { + "bbox": [ + 304, + 369, + 545, + 405 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 369, + 545, + 405 + ], + "spans": [ + { + "bbox": [ + 304, + 369, + 545, + 405 + ], + "type": "text", + "content": "in diverse tasks and settings, we can only store and swap the rein weights (0.01GB) and head weights (0.08GB), rather than all parameters." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 414, + 383, + 426 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 414, + 383, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 414, + 383, + 426 + ], + "type": "text", + "content": "5. Conclusions" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 433, + 545, + 613 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 433, + 545, + 613 + ], + "spans": [ + { + "bbox": [ + 304, + 433, + 545, + 613 + ], + "type": "text", + "content": "In this paper, we assess and harness Vision Foundation Models (VFMs) in the context of DGSS. Driven by the motivation that Leveraging Stronger pre-trained models and Fewer trainable parameters for Superior generalizability, we first investigate the performance of VFMs under diverse DGSS settings. Subsequently, we introduce a robust fine-tuning approach, namely Rein, to parameter-efficiently harness VFMs for DGSS. With a fewer trainable parameters, Rein significantly enhance generalizability of VFMs, outperforming SOTA methods by a large margin. Rein can be seamlessly integrated as a plug-and-play adapter for existing VFMs, improving generalization with efficient training. Extensive experiments demonstrate the substantial potential of VFMs in the DGSS field, validating the effectiveness of proposed Rein in harnessing VFMs for DGSS." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 623, + 421, + 636 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 623, + 421, + 636 + ], + "spans": [ + { + "bbox": [ + 306, + 623, + 421, + 636 + ], + "type": "text", + "content": "6. Acknowledgements" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 643, + 545, + 702 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 643, + 545, + 702 + ], + "spans": [ + { + "bbox": [ + 304, + 643, + 545, + 702 + ], + "type": "text", + "content": "This work was supported in part by the Anhui Provincial Key Research and Development Plan 202304a05020072, in part by the Postdoctoral Fellowship Program of CPSFGZB20230713, and in part by the National Natural Science Foundation of China under Grant 61727809." + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 318, + 757 + ], + "type": "text", + "content": "28626" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 72, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 53, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 7, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Yasser Benigmim, Subhankar Roy, Slim Essid, Vicky Kalogeiton, and Stephane Lathuilière. 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International Journal of Computer Vision, 130(9):2337-2348, 2022. 2" + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 749, + 317, + 757 + ], + "type": "text", + "content": "28630" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 11 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/14a78d05-b6ef-4749-8f8e-25cfaadc10a0_content_list.json b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/14a78d05-b6ef-4749-8f8e-25cfaadc10a0_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6ef389c480ee80415865fca5a801efff79da4c9c --- /dev/null +++ b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/14a78d05-b6ef-4749-8f8e-25cfaadc10a0_content_list.json @@ -0,0 +1,1620 @@ +[ + { + "type": "text", + "text": "Structure Matters: Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting", + "text_level": 1, + "bbox": [ + 207, + 128, + 759, + 174 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Haipeng Liu $^{1}$ Yang Wang $^{1*}$ Biao Qian $^{1}$ Meng Wang $^{1}$ Yong Rui $^{2}$ $^{1}$ Hefei University of Technology, China \n $^{2}$ Lenovo Research, China \nhpliu.hfut@hotmail.com, yangwang@hfut.edu.cn, \n{hfutqian,eric.mengwang}@gmail.com, yongrui@lenovo.com", + "bbox": [ + 204, + 200, + 764, + 272 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 305, + 313, + 321 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Denoising diffusion probabilistic models (DDPMs) for image inpainting aim to add the noise to the texture of the image during the forward process and recover the masked regions with the unmasked ones of the texture via the reverse denoising process. Despite the meaningful semantics generation, the existing arts suffer from the semantic discrepancy between the masked and unmasked regions, since the semantically dense unmasked texture fails to be completely degraded while the masked regions turn to the pure noise in diffusion process, leading to the large discrepancy between them. In this paper, we aim to answer how the unmasked semantics guide the texture denoising process; together with how to tackle the semantic discrepancy, to facilitate the consistent and meaningful semantics generation. To this end, we propose a novel structure-guided diffusion model for image inpainting named StrDiffusion, to reformulate the conventional texture denoising process under the structure guidance to derive a simplified denoising objective for image inpainting, while revealing: 1) the semantically sparse structure is beneficial to tackle the semantic discrepancy in the early stage, while the dense texture generates the reasonable semantics in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance for the texture denoising process, benefiting from the time-dependent sparsity of the structure semantics. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective by exploiting the consistency of the denoised structure between masked and unmasked regions. Besides, we devise an adaptive resampling strategy as a formal criterion as whether the structure is competent to guide the texture denoising process, while regulate their semantic correlations. Extensive experiments validate the merits of StrDiffusion over the state-of-the-arts. Our code is available at https://github.com/htyjers/StrDiffusion.", + "bbox": [ + 75, + 340, + 473, + 859 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/5de2aacc1979775bafe9672c3a8d61e73ba9e491c6791db16b5c068aed0e5c74.jpg", + "image_caption": [ + "Figure 1. Existing arts, e.g., IR-SDE [23] (a), suffer from the semantic discrepancy $(\\bigcirc)$ between the masked and unmasked regions despite of the meaningful semantics for the masked regions during the denoising process. Our StrDiffusion (b) tackles the semantic discrepancy issue via the guidance of the auxiliary sparse structure, yielding the consistent and meaningful denoised results. The experiments are conducted on PSV [6]." + ], + "image_footnote": [], + "bbox": [ + 521, + 303, + 870, + 545 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 500, + 667, + 630, + 683 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, image inpainting has supported a wide range of applications, e.g., photo restoration and image editing, which aims to recover the masked regions of an image with the semantic information of unmasked regions, where the principle mainly covers two aspects: the reasonable semantics for the masked regions and their semantic consistency with the unmasked regions. The prior work mainly involves the diffusion-based [2, 8] and patch-based [1, 4, 10] scheme, which tends to inpaint the small mask or repeated patterns of the image via simple color information, while fails to handle irregular or complicated masks. To address such issue, substantial attention [15, 17, 31, 36] has shifted to the convolutional neural networks (CNNs), which devote themselves to encoding the local semantics", + "bbox": [ + 496, + 694, + 890, + 900 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Yang Wang is the corresponding author.", + "bbox": [ + 94, + 886, + 313, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "8038", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/17d9bc8e73ebc98be727619a45b83a36440a4c29ad5db49c9661353ad3719a27.jpg", + "image_caption": [ + "Figure 2. Illustration of the motivating experiments about whether the sparse structure is beneficial to alleviating the discrepancy issue during the denoising process for image inpainting. Apart from the dense texture for IR-SDE [23] (a), the unmasked semantics combined with the Gaussian noise is further set as the sparse structure, e.g., the grayscale map (b) and edge map (c). Our StrDiffusion (d) can tackle the semantic discrepancy via the progressively sparse structure. The shadow area indicates the discrepancy between the masked and unmasked regions during the denoising process. The PSNR (higher is better) reflects the recovered semantics for the masked (unmasked) regions compared to the completed image (i.e., ground truth) by calculating the semantic similarity between them. The inpainted results are obtained by combining the masked regions of denoised results with the original masked images." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 277, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/3a2952ee5f24ce8356912ee76b5eb57e8417cfb00ce4904e10971ddcb9417dde.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 88, + 480, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/d8b01cdab815110b946aef9f03487503226d82016e1f023bfe37f3e19677b73a.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 483, + 88, + 689, + 215 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/806eb5f61cead4ae60744c9d4d7fe0b1870af1e904d1702514b0e6df3d4e514e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 694, + 89, + 888, + 215 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "around the masked regions, while ignore the global information from the unmasked regions, incurring that the regions far away from the mask boundary remain bury. Recently, self-attention mechanism [5, 14, 16, 32, 35] is proposed to globally associate the masked regions with unmasked ones in the form of the segmented image patches, enhancing the semantic consistency between them. However, such strategies suffer from poor semantic correlation between the varied patches inside the masked regions. To this end, the semantically sparse structure is exploited [3, 7, 9, 13, 18, 20, 27, 28, 33, 34] to strength their correlations, which, however, implies the heavy reliance on the semantic consistency between the structure and texture, hence inevitably bears the artifact in the inpainted output.", + "bbox": [ + 75, + 329, + 468, + 536 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Fortunately, the denoising diffusion probabilistic models (DDPMs) [12, 25] have emerged as the powerful generative models to deliver remarkable gains in the semantics generation and mode converge, hence well remedy the poor semantics generation for image inpainting [22, 23, 29, 38]. Specifically, instead of focusing on the training process, [22] proposed to adopt the pre-trained DDPMs as the prior and develop a resampling strategy to condition the reverse denoising process during the inference process. Further, [23] attempted to model the diffusion process for image inpainting by exploiting the semantics from the unmasked regions, yielding an optimal reverse solution to the denoising process. These methods mostly exhibit the semantically meaningful inpainted results with the advantages of DDPMs, whereas overlook the semantic consistency between the masked and unmasked regions. The intuition is that the semantically dense unmasked texture is degraded into the combination of the unmasked texture and the Gaussian noise, while the masked regions turn to the pure noise during the diffusion process, leading to the large discrepancy between them (see Fig.1(a) and Fig.2(a)), and motivates the followings:", + "bbox": [ + 75, + 537, + 470, + 863 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(1) How does the unmasked semantics guide the texture denoising process for image inpainting? Our motivating ex", + "bbox": [ + 63, + 869, + 470, + 901 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "periments (see Fig.2) suggest that, when the unmasked semantics combined with the noise turns to be sparser, e.g., utilizing the grayscale or edge map of the masked image as an alternative, the discrepancy issue is largely alleviated, meanwhile, bears the large semantic information loss in the inpainted results; see Fig.2(b)(c). Therefore, the invariable semantics from the unmasked regions over time fail to guide the texture denoising process well.", + "bbox": [ + 511, + 329, + 890, + 446 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "(2) Following (1), one naturally wonders how to yield the denoised results with consistent and meaningful semantics. It is apparent that the sparse structure benefits the semantic consistency in the early stage while the dense texture tends to generate the meaningful semantics in the late stage during denoising process, implying a balance between the consistent and reasonable semantics of the denoised results. To further yield the desirable results, we take into account the guidance of the structure as an auxiliary over the texture denoising process; see Fig.1(b).", + "bbox": [ + 486, + 446, + 890, + 595 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To answer the above questions, we propose a novel structure-guided texture diffusion model, named StrDiffusion, for image inpainting, to tackle the semantic discrepancy between masked and unmasked regions, together with the reasonable semantics for masked regions; technically, we reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective for image inpainting. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective during the denoising process, which exploits the time-dependent consistency of the denoised structure between the masked and unmasked regions to mitigate the discrepancy issue. Our StrDiffusion reveals: 1) the semantically sparse structure encourages the consistent semantics for the denoised results in the early stage, while the dense texture carries out the semantic generation in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance to the texture denoising process, benefiting from the time-dependent sparsity of the structure se", + "bbox": [ + 496, + 606, + 892, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "8039", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/6e9cb9a46f390a2116ea21f7923ae8253e61d18944f5756490cd952966e9e8e1.jpg", + "image_caption": [ + "Figure 3. Illustration of the proposed StrDiffusion pipeline. Our basic idea is to tackle the semantic discrepancy between masked and unmasked regions via the guidance of the progressively sparse structure (a), which guides the texture denoising network (b) to generate the consistent and meaningful denoised results." + ], + "image_footnote": [], + "bbox": [ + 140, + 88, + 834, + 244 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "mantics. Concurrently, we remark that whether the structure guides the texture well greatly depends on the semantic correlation between them. As inspired, an adaptive resampling strategy comes up to monitor the semantic correlation and regulate it via the resampling iteration. Extensive experiments on typical datasets validate the merits of StrDiffusion over the state-of-the-arts.", + "bbox": [ + 75, + 303, + 470, + 405 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. Structure-Guided Texture Diffusion Models", + "text_level": 1, + "bbox": [ + 76, + 421, + 468, + 438 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Central to our method lies in three aspects: 1) how to tackle the semantic discrepancy between the masked and unmasked regions (Sec.2.2); 2) structure-guided denoising network for image inpainting (Sec.2.3); and 3) more insights on whether the structure guides the texture well (Sec.2.4). Before shedding light on our technique, we elaborate the DDPMs for image inpainting.", + "bbox": [ + 75, + 446, + 468, + 551 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.1. Preliminaries: Denoising Diffusion Probabilistic Models for Image Inpainting", + "text_level": 1, + "bbox": [ + 76, + 561, + 468, + 593 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Given a completed image $I_{gt} \\in \\mathbb{R}^{3 \\times H \\times W}$ and the binary mask $M \\in \\{0,1\\}^{1 \\times H \\times W}$ (0 for masked regions, 1 for unmasked regions), image inpainting aims to recover the masked image $I_{m} = I_{gt} \\odot M$ towards a inpainted image. For diffusion models, the inpainted results are obtained by merging the masked regions of denoised results with the original masked images. The typical DDPMs for inpainting [23] basically involve the forward texture diffusion process and reverse texture denoising process:", + "bbox": [ + 75, + 599, + 468, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Forward Texture Diffusion Process. During the forward diffusion process, the semantic information from unmasked regions is utilized to guide the texture denoising process for image inpainting. Specifically, for the diffusion process with $T$ timesteps, we set the initial texture state $y_{0} = I_{gt}$ and the terminal texture state $y_{T}$ as the combination of the masked image $\\mu_{y} = I_{m}$ and the Gaussian noise $\\varepsilon$ . For any state $t \\in [0,T]$ , the diffusion process $\\{y_t\\}_{t=0}^T$ via the mean-reverting stochastic differential equation (SDE) [26] is defined as", + "bbox": [ + 75, + 732, + 470, + 869 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {d} y = \\theta_ {t} (\\mu_ {y} - y) d t + \\eta_ {t} \\mathrm {d} w, \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 183, + 883, + 468, + 898 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\theta_{t}$ and $\\eta_{t}$ are time-dependent positive parameters that characterize the speed of the mean-reversion and the stochastic volatility during the diffusion process, which are constrained by $\\eta_t^2 /\\theta_t = 2\\lambda^2$ for the stationary variance since $\\lambda$ is fixed as the noise level applied to $y_{T}$ . In particular, $\\theta_{t}$ can be adjusted to construct different noise schedules for the texture; $w$ is a standard Wiener process [25] (known as Brownian motion), which brings the randomness to the differential equation.", + "bbox": [ + 496, + 303, + 890, + 434 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Reverse Texture Denoising Process. To recover the completed image $y_{0}$ from the terminal texture state $y_{T}$ , we reverse the diffusion process by simulating the SDE backward in time, formulated as", + "bbox": [ + 496, + 434, + 890, + 488 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {d} y = \\left[ \\theta_ {t} \\left(\\mu_ {y} - y\\right) - \\eta_ {t} ^ {2} \\nabla_ {y} \\log q _ {t} (y) \\right] \\mathrm {d} t + \\eta_ {t} \\mathrm {d} \\hat {w}, \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 545, + 498, + 890, + 516 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\hat{w}$ is a reverse-time Wiener process and $q_{t}(y)$ stands for the marginal probability density function of texture $y_{t}$ at time $t$ . The score function $\\nabla_y\\log p_t(y)$ is unknown, which can be approximated by training a conditional time-dependent neural network $\\epsilon_{\\phi}(y_{t},t)$ [12]. Alternatively, we find the optimal reverse texture state $y_{t - 1}^{*}$ from $y_{t}$ in $(t - 1)$ -th timestep via the maximum likelihood learning, which is achieved by minimizing the negative log-likelihood:", + "bbox": [ + 496, + 523, + 890, + 633 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\ny _ {t - 1} ^ {*} = \\arg \\min _ {y _ {t - 1}} [ - \\log q (y _ {t - 1} | y _ {t}, y _ {0}) ]. \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 575, + 640, + 890, + 662 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "By solving the above objective, we have:", + "bbox": [ + 503, + 670, + 774, + 684 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} y _ {t - 1} ^ {*} = \\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\theta} _ {t}}} e ^ {- \\theta_ {t} ^ {\\prime}} \\left(y _ {t} - \\mu_ {y}\\right) \\\\ + \\frac {1 - e ^ {- 2 \\theta_ {t} ^ {\\prime}}}{1 - e ^ {- 2 \\overline {{\\theta}} _ {t}}} e ^ {- \\overline {{\\theta}} _ {t} - 1} (y _ {0} - \\mu_ {y}) + \\mu_ {y}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 557, + 693, + 890, + 761 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\theta_t' = \\int_{t-1}^t \\theta_i \\, \\mathrm{d}i$ and $\\overline{\\theta}_t = \\int_0^t \\theta_z \\, \\mathrm{d}z$ . Thus, we can optimize $\\epsilon_\\phi$ via the following training objective:", + "bbox": [ + 498, + 768, + 890, + 803 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\beta} ^ {t} (\\phi) = \\sum_ {t = 1} ^ {T} \\beta_ {t} \\mathbb {E} \\left[ \\| y _ {t} - \\left(\\mathrm {d} y _ {t}\\right) _ {\\epsilon_ {\\phi}} - y _ {t - 1} ^ {*} \\| _ {p} \\right], \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 811, + 890, + 848 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\beta_{t}$ is positive weight; $(\\mathrm{dy}_t)_{\\epsilon_\\phi}$ denotes the reverse-time SDE in Eq.(2) and its score is predicted via the noise network $\\epsilon_{\\phi}(y_t,t)$ . $||\\cdot ||_p$ stands for the $\\ell_p$ norm.", + "bbox": [ + 498, + 854, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "8040", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f4a5acfa802c13011525c7f36d67b3ba5900df6644f9b6b496386e13469862c3.jpg", + "image_caption": [ + "Figure 4. Illustration of the diffusion process for the dense texture (a) and sparse structure (b). In particular, the semantic sparsity of the structure is strengthened over time." + ], + "image_footnote": [], + "bbox": [ + 99, + 88, + 450, + 222 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2. Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting", + "text_level": 1, + "bbox": [ + 76, + 275, + 468, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Based on the above, the existing diffusion models for image inpainting [23] suffer from the semantic discrepancy between the masked and unmasked regions, owing to the dense semantics of the texture. As opposed to the texture, the previous work [20, 34] suggests that the structure are generally considered to be sparse, which motivates us to tackle the discrepancy issue via the structure.", + "bbox": [ + 75, + 313, + 468, + 417 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2.1 Structure Matters: Sparse Semantics benefits the Semantic Consistency", + "text_level": 1, + "bbox": [ + 76, + 435, + 468, + 465 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To validate such intuition, we design a series of motivation experiments over [23], where we replace the masked image $\\mu_y$ in the terminal texture state $y_{T}$ with the masked image $\\mu_x$ from the sparse structure, e.g., the grayscale map and edge map. Our motivation experiments (see Fig.2) reveal the followings:", + "bbox": [ + 75, + 473, + 468, + 561 + ], + "page_idx": 3 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "(1) With the dense semantics, the texture performs well in producing meaningful semantics, while suffers from the large semantic discrepancy between the masked and un-masked regions; see Fig.1(a) and Fig.2(a).", + "(2) The semantically sparse structure benefits the consistent semantics, while incurs the semantics loss in the inpainted results; see the grayscale and edge map version of [23] in Fig.2(b)(c)." + ], + "bbox": [ + 63, + 561, + 468, + 679 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The above observations indicate that, unlike [23] that fixes the texture guidance from the unmasked regions, the structure guidance from the unmasked regions varies to the texture over time; meanwhile, merely involving the semantics of either dense texture or sparse structure fails to obtain the desirable inpainted results, since it actually attempts to perform the trade-off between the consistent and meaningful semantics. Motivated by that, we propose to exploit structure as an auxiliary, which exhibits the sparser semantics than the texture, so as to tackle the discrepancy issue, as remarked below.", + "bbox": [ + 75, + 680, + 468, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 1. Strengthening the semantic sparsity of the structure over time. Throughout the texture diffusion process, the semantic discrepancy between the masked and un-masked regions progressively increases as the timestep goes", + "bbox": [ + 75, + 840, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "towards to a totally masked status (see Fig.4(a)). To decrease the semantic discrepancy, we aim to strengthen the semantic sparsity of the structure over time, as opposed to the texture, during diffusion process. Concretely, the sparse grayscale map is degraded into the combination of the sparser masked edge map and the Gaussian noise via the noise schedule; see Fig.4(b).", + "bbox": [ + 496, + 90, + 890, + 194 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Our basic idea is to tackle the semantic discrepancy issue via the guidance of the structure during the denoising process, thus simplify the texture denoising objective, i.e., the optimal solution (the ground truth) to the denoising process, which is discussed in the next.", + "bbox": [ + 496, + 195, + 890, + 267 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "2.2.2 Optimal Solution to the Denoising Process Under the Guidance of the Structure", + "text_level": 1, + "bbox": [ + 500, + 287, + 890, + 315 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As per the above observations, during the texture diffusion process, the distribution of the added noise in each timestep is disturbed by the semantic discrepancy between the masked and unmasked regions, incurring the difficulty to estimate such noise distribution via a noise-prediction network during the denoising process. Instead of focusing on texture, we exploit both structure and texture for diffusion process, where the sparsity of structure alleviates the semantic discrepancy, and the texture attempts to preserve the meaningful semantic. Unlike the diffusion process to simultaneously exploit structure and texture, for denoising process, the structure firstly generates the consistent semantics $(x_{t - 1})$ between masked and unmasked regions, which subsequently guides the texture to generate the meaningful semantics $(y_{t - 1})$ ; see Fig.3. By the assistance of structure for StrDiffusion, the texture diffusion process generates both consistent and meaningful inpainting output.", + "bbox": [ + 496, + 325, + 892, + 575 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Remark 2. Different from the typical DDPMs for inpainting [22, 23], our StrDiffusion exploits the semantic consistency of the denoised structure to guide the texture denoising process, yielding both consistent and meaningful denoised results. In particular, we view the structure as an auxiliary to guide the texture rather than the inverse; the reason is two-fold: 1) during the inference denoising process, the masked regions mainly focus on the texture to be inpainted rather than the structure; 2) the structure focuses on the consistency between the masked and unmasked regions, lacking the meaningful semantics, hence still relies on the texture for inpainting.", + "bbox": [ + 496, + 575, + 890, + 752 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Thanks to the guidance of the structure, the reverse transition for the texture in Eq.(3) can be reformulated via Bayes' rule as follows:", + "bbox": [ + 496, + 752, + 890, + 792 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{r l} q \\left(y _ {t - 1} \\mid y _ {t}, x _ {t - 1}\\right) & = \\frac {q \\left(y _ {t - 1} \\mid y _ {t}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1} , y _ {t}\\right)}{q \\left(x _ {t - 1} \\mid y _ {t}\\right)} \\\\ & = \\frac {q \\left(y _ {t} \\mid y _ {t - 1}\\right) q \\left(y _ {t - 1}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1}\\right)}{q \\left(x _ {t - 1} , y _ {t}\\right)}, \\end{array} \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 522, + 801, + 890, + 864 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where the texture $y_{t}$ and $y_{t - 1}$ , together with the structure $x_{t - 1}$ , are actually conditioned on their initial states, i.e.,", + "bbox": [ + 500, + 872, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "8041", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$y_{0}$ and $x_0$ , during the diffusion process, hence $q(y_{t - 1}) = q(y_{t - 1}|y_0)$ and $q(x_{t - 1},y_t) = q(x_{t - 1})q(y_t|x_{t - 1}) =$ $q(x_{t - 1}|x_0)q(y_t|x_{t - 1},y_0)$ . Eq.(6) can thus be simplified as", + "bbox": [ + 76, + 90, + 468, + 133 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} q \\left(y _ {t - 1} \\mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\\right) \\\\ = \\frac {q \\left(y _ {t} \\mid y _ {t - 1}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1}\\right)}{q \\left(y _ {t} \\mid x _ {t - 1} , y _ {0}\\right)} \\times \\frac {q \\left(y _ {t - 1} \\mid y _ {0}\\right)}{q \\left(x _ {t - 1} \\mid x _ {0}\\right)} \\tag {7} \\\\ \\approx \\frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 143, + 145, + 467, + 220 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $q(y_{t}|y_{t - 1})\\approx q(y_{t}|x_{t - 1},y_{0})$ and $q(x_{t - 1}|y_{t - 1})\\approx 1$ , since the texture $y_{t}$ can be obtained via the conditioned auxiliary structure $x_{t - 1}$ during the diffusion process and initial texture $y_{0}$ as Remarked above. Based on Eq.(7), the optimal reverse state is naturally acquired by minimizing the negative log-likelihood (see the supplementary material for more inference details):", + "bbox": [ + 76, + 229, + 468, + 325 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {y} _ {t - 1} ^ {*} = \\underset {y _ {t - 1}} {\\arg \\min } \\left[ - \\log q \\left(y _ {t - 1} \\mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\\right) \\right] \\tag {8} \\\\ = \\arg \\min _ {y _ {t - 1}} [ - \\log \\frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})} ], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 335, + 468, + 388 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde{y}_{t - 1}^{*}$ denotes the ideal state reversed from $\\tilde{y}_t$ under the structure guidance. To solve the above objective, we compute its gradient and setting it to be zero:", + "bbox": [ + 76, + 398, + 468, + 440 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\tilde {y} _ {t - 1} ^ {*}} \\left\\{- \\log q \\left(\\tilde {y} _ {t - 1} ^ {*} \\mid y _ {t}, y _ {0}, x _ {t - 1} ^ {*}, x _ {0}\\right) \\right\\} = \\\\ - \\nabla_ {\\tilde {y} _ {t - 1} ^ {*}} \\log q \\left(\\tilde {y} _ {t - 1} ^ {*} \\mid y _ {0}\\right) + \\nabla_ {x _ {t - 1} ^ {*}} \\log q \\left(x _ {t - 1} ^ {*} \\mid x _ {0}\\right) = 0, \\tag {9} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 450, + 468, + 486 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $x_{t - 1}^{*}$ is the ideal state reversed from $x_{t}$ for the structure, similar in spirit to Eq.(4), given as", + "bbox": [ + 76, + 494, + 467, + 523 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} x _ {t - 1} ^ {*} = \\frac {1 - e ^ {- 2 \\bar {\\delta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}} \\left(x _ {t} - \\mu_ {x}\\right) \\tag {10} \\\\ + \\frac {1 - e ^ {- 2 \\delta_ {t} ^ {\\prime}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\bar {\\delta} _ {t - 1}} (x _ {0} - \\mu_ {x}) + \\mu_ {x}, \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 534, + 468, + 599 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where structure $\\mu_{x}$ is the masked version of its initial state $x_0$ and $\\delta_t$ is time-dependent parameter that characterizes the speed of the mean-reversion. To simplify the notation, we have $\\delta_t' = \\int_{t-1}^t \\delta_i \\, \\mathrm{d}i$ , $\\overline{\\delta}_{t-1} = \\int_0^{t-1} \\delta_z \\, \\mathrm{d}z$ and $\\overline{\\delta}_t = \\overline{\\delta}_{t-1} + \\delta_t'$ . Since Eq.(9) is linear, we can derive $\\tilde{y}_{t-1}^*$ as", + "bbox": [ + 76, + 609, + 468, + 684 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {y} _ {t - 1} ^ {*} = \\underbrace {\\left(\\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}}\\right) \\left(x _ {t} - \\mu_ {x}\\right)} _ {\\text {C o n s i s t e n c y t e r m f o r m a s k e d r e g i o n s}} \\\\ - \\underbrace {\\left(\\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}}\\right) e ^ {- \\bar {\\delta} _ {t}} \\left(x _ {0} - \\mu_ {x}\\right)} _ {\\text {B a l i n c e t e r m f o r m a x i k e d r e g i o n s}} \\tag {11} \\\\ + \\underbrace {e ^ {- \\overline {{\\theta}} _ {t - 1}} (y _ {0} - \\mu_ {y})} _ {\\text {S e m a n t i c s t e r m f o r m a k e d r e g i o n s}} + \\underbrace {\\mu_ {y}} _ {\\text {U n m a x k e d r e g i o n s}}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 695, + 468, + 840 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Remark 3. Eq.(11) implies that the ideal reverse state $\\tilde{y}_{t - 1}^{*}$ focuses more on the semantic consistency based on the semantic generation for image inpainting, to alleviate", + "bbox": [ + 76, + 856, + 468, + 900 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "the semantic discrepancy issues. Under the guidance of the sparse structure, $\\tilde{y}_{t-1}^{*}$ tends to maintain the consistency between masked and unmasked regions in the early stage of the denoising process, while recovering the reasonable semantics in the late stage. Specifically, $\\tilde{y}_{t-1}^{*}$ is mainly composed of four parts: 1) the consistency term for the structure $x_{t} - \\mu_{x}$ is utilized to form the masked regions inside the denoised texture and keep the semantic consistency with the unmasked regions; 2) the semantics term for the texture $y_{0} - \\mu_{y}$ progressively provides meaningful semantics for masked regions as the denoising process progresses; 3) the negative balance term $x_{0} - \\mu_{x}$ adaptively surpasses the semantic information from $y_{0} - \\mu_{y}$ in the early stage and the consistency information from $x_{t} - \\mu_{x}$ in the late stage; 4) the unmasked texture $\\mu_{y}$ retains the semantics of the unmasked regions for the denoised texture. All four parts together constitute the optimal solution to the structure-guided denoising process in the $(t-1)$ -th timestep, i.e., the ground truth to optimize the noise-prediction network, thus yielding the denoised results with the consistent and desirable semantics (see Fig.6), as discussed in the next section.", + "bbox": [ + 496, + 90, + 890, + 400 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "2.3. Structure-Guided Denoising Process: How does the Structure Guide the Texture Denoising Process?", + "text_level": 1, + "bbox": [ + 500, + 407, + 890, + 453 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "With the above optimal solution (i.e., the ground truth) in Eq.(11), the goal of the structure-guided denoising process is to estimate it via a noise-prediction neural network $\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)$ under the guidance of the structure, where $\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)$ is trained to predict the mean of the noise with the fixed variance of noise [25]. Unlike the conventional texture denoising process in [23], the structure denoising network is pre-trained as an auxiliary to obtain the denoised structure, e.g., $x_{t - 1}$ in the $t$ -th timestep. To fulfill the structure guidance, a multi-scale spatially adaptive normalization strategy is devised to condition a time-dependent noise network $\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)$ for the texture, which deploys the spatially adaptive normalization and denormalization strategy [24] to incorporate the statistical information over the feature map across varied layers; see Fig.3. Formally, given $x_{t - 1}$ from a pre-trained structure denoising network, we achieve the structure guidance by reconstructing the feature map on the $k$ -th layer of CNNs in time-dependent noise network $\\tilde{\\epsilon}_{\\phi}$ for the texture (i.e., $F_{k}^{t}\\in \\mathbb{R}^{C_{k}\\times H_{k}\\times W_{k}}$ ) as", + "bbox": [ + 496, + 458, + 890, + 717 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\tilde {F} _ {k} ^ {t} = \\operatorname {c o n v} _ {\\gamma} \\left(x _ {t - 1}\\right) \\frac {F _ {k} ^ {t} - \\mu_ {k} ^ {t}}{\\sigma_ {k} ^ {t}} + \\operatorname {c o n v} _ {\\beta} \\left(x _ {t - 1}\\right), \\\\ \\mu_ {k} ^ {t} (h _ {k}, w _ {k}) = \\frac {1}{C _ {k}} \\sum_ {c _ {k} = 1} ^ {C _ {k}} F _ {k} ^ {t} (h _ {k}, w _ {k}, c _ {k}), \\\\ \\sigma_ {k} ^ {t} (h _ {k}, w _ {k}) = \\sqrt {\\frac {1}{C _ {k}} \\sum_ {c _ {k} = 1} ^ {C _ {k}} \\left(F _ {k} ^ {t} \\left(h _ {k} , w _ {k} , c _ {k}\\right) - \\mu_ {k} ^ {t} \\left(h _ {k} , w _ {k}\\right)\\right) ^ {2}}, \\\\ h _ {k} = 1, 2, \\dots , H _ {k}, w _ {k} = 1, 2, \\dots , W _ {k}, \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 516, + 724, + 890, + 872 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $conv_{\\gamma}(\\cdot)$ and $conv_{\\beta}(\\cdot)$ denote the mappings that convert the input $x_{t-1}$ to the scaling and bias values.", + "bbox": [ + 500, + 872, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "8042", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "$\\mu_k^t (h_k,w_k)$ and $\\sigma_k^t (h_k,w_k)$ are the statistical mean and variance of the pixels across different channels at the position $(h_k,w_k)$ . Based on that, we turn to optimize the noise network $\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)$ to estimate the optimal solution $\\tilde{y}_{t - 1}^{*}$ (i.e., the ground truth) to the denoising process. To this end, the overall training objective is formulated as", + "bbox": [ + 76, + 90, + 468, + 172 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {\\tilde {\\beta}} ^ {t} (\\phi) = \\sum_ {t = 1} ^ {T} \\tilde {\\beta} _ {t} \\mathbb {E} [ \\| \\underbrace {y _ {t} - (\\mathrm {d} y _ {t}) _ {\\tilde {\\epsilon} _ {\\phi}}} _ {\\text {D e n o i s e d} y _ {t - 1}} - \\tilde {y} _ {t - 1} ^ {*} \\| _ {p} ], \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 137, + 181, + 468, + 226 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\tilde{\\beta}_t$ is positive weight; $(\\mathrm{dy}_t)_{\\tilde{\\epsilon}_{\\phi}}$ denotes the estimated reverse noise by the noise-prediction network. By minimizing Eq.(13), the inpainted results with consistent and meaningful semantics can be generated during the structure-guided denoising process.", + "bbox": [ + 76, + 236, + 468, + 311 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2.4. More Insights on Eq.(13)", + "text_level": 1, + "bbox": [ + 76, + 319, + 305, + 335 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "To validate the effectiveness of the guidance from the structure to the texture denoising process, we provide more insights on Eq.(13) by studying the semantic correlation between the denoised texture and structure during inference.", + "bbox": [ + 76, + 342, + 468, + 401 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2.4.1 Correlation Measure via a Discriminator", + "text_level": 1, + "bbox": [ + 76, + 419, + 415, + 431 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Apart from the semantic structure sparsity, the semantic correlation between the structure and texture is crucial to achieve the semantic consistency between the masked and unmasked regions. To measure such semantic correlation, we adopt a discriminator network $D$ to yield the correlation score $D(y_{t - 1},x_{t - 1},t - 1)$ (abbreviated as $D(y_{t - 1},x_{t - 1})$ ) where the denoised texture $y_{t - 1}$ and structure $x_{t - 1}$ , together with the timestep $t - 1$ , serve as the inputs. To this end, we present a discriminator loss and a triplet loss to optimize $D$ , as described below:", + "bbox": [ + 76, + 441, + 468, + 588 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Discriminator Loss. During the denoising process, to provide the desirable guidance for the texture, the current structure $x_{t-1}$ is expected to be closely correlated with the texture $y_{t-1}$ in the current timestep, instead of the previous one $y_t$ . Hence, we aim to discriminate $y_{t-1}$ and $y_t$ via a discriminator loss below:", + "bbox": [ + 76, + 588, + 468, + 667 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {d i s} = - \\mathbb {E} _ {y _ {t - 1}} [ \\log (D (y _ {t - 1}, x _ {t - 1})) ] \\tag {14} \\\\ - \\mathbb {E} _ {y _ {t}} \\left[ \\log \\left(1 - D \\left(y _ {t}, x _ {t - 1}\\right)\\right) \\right]. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 675, + 468, + 708 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Triplet Loss. Since the unmasked regions almost possess much denser semantics information compared to the masked ones during the denoising process, to well evaluate the correlation, Eq.(14) is encouraged to focus more on the unmasked regions, which is achieved via a triplet loss:", + "bbox": [ + 76, + 723, + 468, + 792 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {t r i} = \\max (\\| D (\\bar {y} _ {t - 1}, x _ {t - 1}) - D (y _ {t - 1}, x _ {t - 1})) \\| _ {2} \\tag {15} \\\\ - \\| D \\left(\\bar {y} _ {t - 1}, x _ {t - 1}\\right) - D \\left(y _ {t}, x _ {t - 1}\\right) \\| _ {2} + \\alpha , 0), \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 799, + 467, + 833 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\bar{y}_{t-1} = y_{t-1} \\odot M + y_t \\odot (1 - M)$ is constructed to associate the unmasked regions of $y_{t-1}$ and the masked ones of $y_t$ . $\\alpha$ is a margin parameter and $||\\cdot||_2$ denotes the $\\ell_2$ norm.", + "bbox": [ + 76, + 840, + 468, + 898 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/4df6491798eaee1af14361f5391668593dc6f2b94c741b9f49056a8aed9047af.jpg", + "image_caption": [ + "Figure 5. Illustration of the adaptive resampling strategy, which adaptively regulates the semantic correlation between the denoised texture and structure according to the score from the discriminator." + ], + "image_footnote": [], + "bbox": [ + 524, + 88, + 869, + 207 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Total Loss. In summary, we finalize the total loss as", + "bbox": [ + 500, + 263, + 846, + 279 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {d i s}} + \\lambda_ {\\text {t r i}} \\mathcal {L} _ {\\text {t r i}}, \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 292, + 890, + 306 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "where $\\lambda_{tri}$ denotes the balance parameter, which is empirically set as 1 in our experiments. With Eq.(16) to be minimized, $D$ can be trained to evaluate the semantic correlation, where the small score value from $D$ indicates that the correlation between the texture and structure is not strong, weakening the guidance of the structure. To enhance the semantic correlation, an adaptive resampling strategy comes up, which is elaborated in the next section.", + "bbox": [ + 498, + 321, + 890, + 436 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "2.4.2 Adaptive Resampling Strategy", + "text_level": 1, + "bbox": [ + 500, + 459, + 764, + 474 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Different from the previous work [22] that directly performs the resampling strategy without the clear measurement, we devise an adaptive resampling strategy, which regulates the semantic correlation between the texture $(e.g., y_{t-1})$ and structure $(e.g., x_{t-1})$ according to the score value from a discriminator in Sec.2.4.1. Specifically, when the score value of the semantic correlation between $y_{t-1}$ and $x_{t-1}$ is smaller than a specific threshold $\\Delta$ (see the supplementary material for more intuitions), we first obtain $\\tilde{x}_t$ by adding the noise to $x_{t-1}$ , then receive a updated $\\tilde{x}_{t-1}$ by denoising $\\tilde{x}_t$ , which are described as follows:", + "bbox": [ + 498, + 483, + 890, + 645 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {t} = x _ {t - 1} + \\delta_ {t - 1} \\left(\\mu_ {x} - x _ {t - 1}\\right) d t + \\sigma_ {t - 1} \\mathrm {d} w, \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 532, + 657, + 888, + 679 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\tilde {x} _ {t - 1} = \\tilde {x} _ {t} - (\\mathrm {d} x _ {t}) _ {\\bar {\\epsilon} _ {\\varphi}}.\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 676, + 681, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Based on Eq.(17), $\\tilde{x}_{t - 1}$ is utilized to generate an updated $\\tilde{y}_{t - 1}$ via the trained noise network $\\tilde{\\epsilon}_{\\phi}(y_t,\\tilde{x}_{t - 1},t)$ . Following that, we evaluate the correlation between $\\tilde{y}_{t - 1}$ and $\\tilde{x}_{t - 1}$ again, and repeat the above procedure; see Fig.5.", + "bbox": [ + 500, + 704, + 890, + 763 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3. Experiments", + "text_level": 1, + "bbox": [ + 500, + 777, + 632, + 795 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "3.1. Implementation Details", + "text_level": 1, + "bbox": [ + 500, + 803, + 715, + 818 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We experimentally evaluate StrDiffusion over three typical datasets, including: Paris StreetView (PSV) [6] is a collection of street view images in Paris, consisting of 14.9k images for training and 100 images for validation; CelebA [21] is the human face dataset with 30k aligned face images,", + "bbox": [ + 498, + 825, + 890, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "8043", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fc42c73d370088e6b511259be2b6d5ae782110ffd5e717490e8df90fb6b142dd.jpg", + "image_caption": [ + "Figure 6. Illustration of the denoised results for IR-SDE [23] (a) and StrDiffusion (b) in the varied timesteps during the denoising process." + ], + "image_footnote": [], + "bbox": [ + 125, + 89, + 531, + 194 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/70eca2aa58a7335286ed107ac72939091c65d890998cbdbd209c5822b0744d6c.jpg", + "image_caption": [ + "Table 1. Comparison of quantitative results (i.e., PSNR, SSIM [30] and FID [11]) under varied mask ratios on Places2 with irregular mask dataset. ↑: Higher is better; ↓: Lower is better; -: no results are reported. The percentage (\\%) represents the ratios of varied irregular masked regions to the completed image. The best results are reported with **boldface**." + ], + "image_footnote": [], + "bbox": [ + 535, + 88, + 844, + 195 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/76e9257e04f8000ae1dd58f21dd0dfb58471672070ce6c81f3da0751576df070.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MetricsPSNR↑SSIM↑FID↓
MethodVenue10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%
RFR [15]CVPR' 2027.2624.8322.7521.110.9290.8910.8300.75617.8822.9430.6838.69
PENNet [35]CVPR' 1926.7823.5321.8020.480.9460.8940.8410.78120.4037.2253.7467.08
HiFill [32]CVPR' 2027.5024.6422.8121.230.9540.9140.8730.81616.9529.3042.8857.12
FAR [3]ECCV' 2228.3625.4823.6022.180.9420.9030.8610.818----
HAN [5]ECCV' 2228.9325.4423.0621.380.9570.9030.8390.76212.0120.1528.8537.63
CMT [14]ICCV' 2329.2825.8823.5621.700.9600.9240.8850.841----
MEDFE [13]ECCV' 2028.1325.0222.9821.530.9580.9190.8740.82514.4127.5238.4553.05
CTSDF [9]ICCV' 2128.9125.3622.9421.210.9520.9010.8340.75515.7227.8842.4457.78
ZITS [7]CVPR' 2228.3125.4023.5122.110.9420.9020.8600.817----
RePaint* [22]CVPR' 2229.1626.0224.0122.110.9670.9330.9150.86211.1620.6228.4941.16
IR-SDE [23]ICML' 2328.9825.3723.9321.680.9610.9280.9080.86412.0321.3429.3739.77
StrDiffusion (Ours)-29.4526.2824.4322.370.9730.9410.9170.8748.75016.1623.7236.93
", + "bbox": [ + 158, + 273, + 805, + 393 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "which is split into 26k training images and 4k validation images; Places2 [37] contains more than 1.8M natural images from varied scenes. The network is trained using $256 \\times 256$ images with irregular masks [19]. The noise-prediction network is constructed by removing group normalization layers and self-attention layers in the U-Net in DDPM [12] for inference efficiency. We adopt the Adam optimizer with $\\beta_{1} = 0.9$ and $\\beta_{2} = 0.99$ . We set the timestep $T = 100$ for the diffusion model. All the experiments are implemented with the pytorch framework and run on 4 NVIDIA 2080TI GPU.", + "bbox": [ + 75, + 402, + 472, + 550 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.2. Why can StrDiffusion Work?", + "text_level": 1, + "bbox": [ + 76, + 561, + 338, + 578 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "In this section, the core goal is to confirm that the intuition of StrDiffusion — the progressively sparse structure over time is beneficial to alleviate the semantic discrepancy issue between the masked and unmasked regions during the denoising process. We conduct the experiments on PSV and Places2 dataset. Fig.6 illustrates that, as the denoising process progresses, the denoised results from IR-SDE [23] always address the clear semantic discrepancy between the masked and unmasked regions (see Fig.6(a)); while for StrDiffusion, such discrepancy progressively degraded until vanished, yielding the consistent semantics (see Fig.6(b)), confirming our proposals in Sec.2.2.2 — the guidance of the structure benefits the consistent semantics between the masked and unmasked regions while the texture retains the reasonable semantics in the inpainted results; see the supplementary material for more results.", + "bbox": [ + 75, + 585, + 468, + 821 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "3.3. Comparison with State-of-the-arts", + "text_level": 1, + "bbox": [ + 76, + 832, + 377, + 848 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To validate the superiority of StrDiffusion, we compare it with the typical inpainting models, including: RFR [15] adopts the CNNs to encoding the local information;", + "bbox": [ + 75, + 854, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/002052159238cc066b08f3cb3d02a7c953c19da628d9e82723a205b24fef3127.jpg", + "image_caption": [ + "Figure 7. Comparison of the inpainted results with the state-of-the-arts under varied irregular masks on PSV, CelebA and Places2. Our StrDiffusion delivers the desirable inpainted results (marked as the red box) against others." + ], + "image_footnote": [], + "bbox": [ + 522, + 400, + 870, + 632 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "PENNet[35], HiFill[32], FAR[3], HAN[5] and CMT[14] globally associate the masked regions with unmasked ones via self-attention mechanism; MEDFE[13], CTSDG[9], ZITS[7] and DGTS[20] focus on the guidance of the structure, while ignore the semantic consistency between the structure and texture; RePaint[22] and IR-SDE[23] benefit from DDPMs whereas overlook the semantic consistency. For fair comparison, we reproduce RePaint by utilizing the pre-trained models from IR-SDE, denoted as RePaint*. Notably, the inpainted results are obtained by merging the masked regions from the denoised results with the original masked image.", + "bbox": [ + 496, + 705, + 892, + 883 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Quantitative and Qualitative analysis. The quantitative", + "bbox": [ + 500, + 885, + 890, + 901 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "8044", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/27c785229cfa990ca01cb1020e3aeae67f4fc034aa753a2afea252b4f19b2e80.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 106, + 88, + 271, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/5a893a139a8f49b7c786a65050dbcb1b021a5c40fa4763aaa0948467b66debb8.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 88, + 442, + 165 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/062ca8284d7044edfbc63efd528a7951e2f5871334c6abe05f887860231f4a60.jpg", + "image_caption": [ + "Figure 8. Ablation study about the progressive sparsity for the structure over time on the PSV dataset. The KL divergence (lower is better) measures the distribution difference between the masked (unmasked) regions and the completed image (i.e., ground truth)." + ], + "image_footnote": [], + "bbox": [ + 104, + 166, + 269, + 241 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a03fa08bbd391d4ade3d5e9aa03403c17428ba382e59e97d9e9ed468a35aa1f0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 277, + 165, + 441, + 242 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "results in Table 1 apart from the qualitative results in Fig.7 summarize our findings below: StrDiffusion enjoys a much smaller FID score, together with larger PSNR and SSIM than the competitors, confirming that StrDiffusion effectively addresses semantic discrepancy between the masked and unmasked regions, while yielding the reasonable semantics. Notably, RePaint* and IR-SDE still remain the large performance margins (at most $1.2\\%$ for PSNR, $1.4\\%$ for SSIM and $10\\%$ for FID) compared to StrDiffusion, owing to the semantic discrepancy (e.g., the white wall in the row 1 of Fig.7) in the denoised results incurred by the dense texture. Albeit MEDFE, CTSDG and ZITS focus on the guidance of the structure similar to StrDiffusion, they suffer from a performance loss due to the semantic discrepancy between the structure and texture, e.g., the woman's face for CTSDG in the row 4 of Fig.7, which further verifies our proposal in Sec.2.2 — the progressively sparse structure provides the time-dependent guidance for texture denoising process; see the supplementary material for more results.", + "bbox": [ + 75, + 311, + 472, + 592 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.4. Ablation Studies", + "text_level": 1, + "bbox": [ + 76, + 602, + 241, + 617 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.4.1 Why Should the Semantic Sparsity of the Structure be Strengthened over Time?", + "text_level": 1, + "bbox": [ + 76, + 625, + 468, + 655 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Recalling Sec.2.2, the progressive sparsity for the structure is utilized to mitigate the semantic discrepancy, by setting the initial structure state as the grayscale and the terminal structure state as the combination of the edge and the noise during the structure diffusion process, denoted as gray2edge. To shed more light on the semantic sparsity of the structure, we replace the initial and terminal structure state, yielding several alternatives as gray2gray, edge2edge and edge2gray; and perform the experiments on the PSV dataset. The structure sparsity of gray2gray and edge2edge is fixed over time. Fig.8 illustrates that gray2edge (Fig.8(d)) exhibits better consistency with meaningful semantics in the inpainted results against others, especially for edge2gray, implying the benefits of strengthening structure sparsity over time. Notably, for gray2gray, the discrepancy issue in the denoised re", + "bbox": [ + 75, + 664, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/c79d6c8df32b804171015f6221aa810898e870339f6ec8f7ca675d6314179b06.jpg", + "table_caption": [ + "Table 2. Ablation study about the adaptive resampling strategy on the PSV dataset. The best results are reported with **boldface**." + ], + "table_footnote": [], + "table_body": "
CasesHard maskEasy mask
PSNR↑SSIM↑FID↓PSNR↑SSIM↑FID↓
A24.650.85155.7327.690.91333.73
B25.470.86346.4428.310.92128.43
C25.590.86747.3128.640.92528.20
D25.940.87542.2828.850.92926.74
", + "bbox": [ + 519, + 127, + 864, + 204 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "sults still suffers (Fig.8(b)), while edge2edge receives the poor semantics (Fig.8(a)), which attributes to their invariant semantic sparsity over time, indicating time-dependent impacts of the unmasked semantics on the texture denoising process (Sec.2.2.1); see the supplementary material for more results.", + "bbox": [ + 496, + 214, + 893, + 303 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "3.4.2 How does Adaptive Resampling Strategy Benefit Inpainting?", + "text_level": 1, + "bbox": [ + 498, + 329, + 892, + 359 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To verify the effectiveness of the adaptive resampling strategy (Sec.2.4), we perform the ablation study on the PSV dataset from the following cases: A: refining the inpainted results of IR-SDE[23] via the resampling strategy in Repaint; B: removes the discriminator, which performs the adaptive resampling strategy without considering the semantic correlation between the texture and structure; C: StrDiffusion without the adaptive resampling strategy; D: the proposed StrDiffusion. Table 2 suggests that case D delivers great gains (at most $13.45\\%$ ) to other cases, which is evidenced that the adaptive resampling strategy succeeds in regulating the semantic correlation for the desirable results (Sec.2.4); case D upgrades beyond case A despite of the combination with the resampling strategy, which, in turn, verifies the necessity of the time-dependent guidance from the structure. In particular, case B bears a large performance degradation (at most $4.16\\%$ ), confirming the importance of adaptively resampling strategy as per the semantic correlation between the structure and texture in Sec.2.4.1.", + "bbox": [ + 496, + 369, + 893, + 650 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "4. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 667, + 619, + 683 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we propose a structure-guided diffusion model for inpainting (StrDiffusion), to reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective; while revealing: 1) the semantics from the unmasked regions essentially offer the time-dependent guidance for the texture denoising process; 2) the progressively sparse structure well tackle the semantic discrepancy in the inpainted results. Extensive experiments verify the superiority of StrDiffusion to the state-of-the-arts.", + "bbox": [ + 496, + 694, + 893, + 840 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments This work was supported by the National Natural Science Foundation of China (U21A20470, 62172136, 72188101), the Institute of Advanced Medicine and Frontier Technology under (2023IHM01080).", + "bbox": [ + 496, + 840, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "8045", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 174, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. Patchmatch: A randomized correspondence algorithm for structural image editing. ACM Trans. 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Designing a better asymmetric vqgan for stablediffusion. arXiv preprint arXiv:2306.04632, 2023. 2" + ], + "bbox": [ + 78, + 92, + 468, + 792 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "8047", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/14a78d05-b6ef-4749-8f8e-25cfaadc10a0_model.json b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/14a78d05-b6ef-4749-8f8e-25cfaadc10a0_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0d1553c7271b4709a43a884dad9b8f4207c02bda --- /dev/null +++ b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/14a78d05-b6ef-4749-8f8e-25cfaadc10a0_model.json @@ -0,0 +1,2057 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.208, + 0.13, + 0.761, + 0.175 + ], + "angle": 0, + "content": "Structure Matters: Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.205, + 0.201, + 0.765, + 0.273 + ], + "angle": 0, + "content": "Haipeng Liu\\(^{1}\\) Yang Wang\\(^{1*}\\) Biao Qian\\(^{1}\\) Meng Wang\\(^{1}\\) Yong Rui\\(^{2}\\) \n\\(^{1}\\)Hefei University of Technology, China \n\\(^{2}\\)Lenovo Research, China \nhpliu.hfut@hotmail.com, yangwang@hfut.edu.cn, \n{hfutqian,eric.mengwang}@gmail.com, yongrui@lenovo.com" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.306, + 0.314, + 0.323 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.342, + 0.474, + 0.86 + ], + "angle": 0, + "content": "Denoising diffusion probabilistic models (DDPMs) for image inpainting aim to add the noise to the texture of the image during the forward process and recover the masked regions with the unmasked ones of the texture via the reverse denoising process. Despite the meaningful semantics generation, the existing arts suffer from the semantic discrepancy between the masked and unmasked regions, since the semantically dense unmasked texture fails to be completely degraded while the masked regions turn to the pure noise in diffusion process, leading to the large discrepancy between them. In this paper, we aim to answer how the unmasked semantics guide the texture denoising process; together with how to tackle the semantic discrepancy, to facilitate the consistent and meaningful semantics generation. To this end, we propose a novel structure-guided diffusion model for image inpainting named StrDiffusion, to reformulate the conventional texture denoising process under the structure guidance to derive a simplified denoising objective for image inpainting, while revealing: 1) the semantically sparse structure is beneficial to tackle the semantic discrepancy in the early stage, while the dense texture generates the reasonable semantics in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance for the texture denoising process, benefiting from the time-dependent sparsity of the structure semantics. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective by exploiting the consistency of the denoised structure between masked and unmasked regions. Besides, we devise an adaptive resampling strategy as a formal criterion as whether the structure is competent to guide the texture denoising process, while regulate their semantic correlations. Extensive experiments validate the merits of StrDiffusion over the state-of-the-arts. Our code is available at https://github.com/htyjers/StrDiffusion." + }, + { + "type": "image", + "bbox": [ + 0.522, + 0.304, + 0.872, + 0.546 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.551, + 0.892, + 0.646 + ], + "angle": 0, + "content": "Figure 1. Existing arts, e.g., IR-SDE [23] (a), suffer from the semantic discrepancy \\((\\bigcirc)\\) between the masked and unmasked regions despite of the meaningful semantics for the masked regions during the denoising process. Our StrDiffusion (b) tackles the semantic discrepancy issue via the guidance of the auxiliary sparse structure, yielding the consistent and meaningful denoised results. The experiments are conducted on PSV [6]." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.669, + 0.631, + 0.684 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.695, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Recently, image inpainting has supported a wide range of applications, e.g., photo restoration and image editing, which aims to recover the masked regions of an image with the semantic information of unmasked regions, where the principle mainly covers two aspects: the reasonable semantics for the masked regions and their semantic consistency with the unmasked regions. The prior work mainly involves the diffusion-based [2, 8] and patch-based [1, 4, 10] scheme, which tends to inpaint the small mask or repeated patterns of the image via simple color information, while fails to handle irregular or complicated masks. To address such issue, substantial attention [15, 17, 31, 36] has shifted to the convolutional neural networks (CNNs), which devote themselves to encoding the local semantics" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.887, + 0.314, + 0.9 + ], + "angle": 0, + "content": "* Yang Wang is the corresponding author." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8038" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.278, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.089, + 0.482, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.484, + 0.089, + 0.69, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.695, + 0.09, + 0.89, + 0.217 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.226, + 0.894, + 0.321 + ], + "angle": 0, + "content": "Figure 2. Illustration of the motivating experiments about whether the sparse structure is beneficial to alleviating the discrepancy issue during the denoising process for image inpainting. Apart from the dense texture for IR-SDE [23] (a), the unmasked semantics combined with the Gaussian noise is further set as the sparse structure, e.g., the grayscale map (b) and edge map (c). Our StrDiffusion (d) can tackle the semantic discrepancy via the progressively sparse structure. The shadow area indicates the discrepancy between the masked and unmasked regions during the denoising process. The PSNR (higher is better) reflects the recovered semantics for the masked (unmasked) regions compared to the completed image (i.e., ground truth) by calculating the semantic similarity between them. The inpainted results are obtained by combining the masked regions of denoised results with the original masked images." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.33, + 0.47, + 0.537 + ], + "angle": 0, + "content": "around the masked regions, while ignore the global information from the unmasked regions, incurring that the regions far away from the mask boundary remain bury. Recently, self-attention mechanism [5, 14, 16, 32, 35] is proposed to globally associate the masked regions with unmasked ones in the form of the segmented image patches, enhancing the semantic consistency between them. However, such strategies suffer from poor semantic correlation between the varied patches inside the masked regions. To this end, the semantically sparse structure is exploited [3, 7, 9, 13, 18, 20, 27, 28, 33, 34] to strength their correlations, which, however, implies the heavy reliance on the semantic consistency between the structure and texture, hence inevitably bears the artifact in the inpainted output." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.539, + 0.471, + 0.864 + ], + "angle": 0, + "content": "Fortunately, the denoising diffusion probabilistic models (DDPMs) [12, 25] have emerged as the powerful generative models to deliver remarkable gains in the semantics generation and mode converge, hence well remedy the poor semantics generation for image inpainting [22, 23, 29, 38]. Specifically, instead of focusing on the training process, [22] proposed to adopt the pre-trained DDPMs as the prior and develop a resampling strategy to condition the reverse denoising process during the inference process. Further, [23] attempted to model the diffusion process for image inpainting by exploiting the semantics from the unmasked regions, yielding an optimal reverse solution to the denoising process. These methods mostly exhibit the semantically meaningful inpainted results with the advantages of DDPMs, whereas overlook the semantic consistency between the masked and unmasked regions. The intuition is that the semantically dense unmasked texture is degraded into the combination of the unmasked texture and the Gaussian noise, while the masked regions turn to the pure noise during the diffusion process, leading to the large discrepancy between them (see Fig.1(a) and Fig.2(a)), and motivates the followings:" + }, + { + "type": "text", + "bbox": [ + 0.064, + 0.871, + 0.471, + 0.902 + ], + "angle": 0, + "content": "(1) How does the unmasked semantics guide the texture denoising process for image inpainting? Our motivating ex" + }, + { + "type": "text", + "bbox": [ + 0.512, + 0.33, + 0.892, + 0.448 + ], + "angle": 0, + "content": "periments (see Fig.2) suggest that, when the unmasked semantics combined with the noise turns to be sparser, e.g., utilizing the grayscale or edge map of the masked image as an alternative, the discrepancy issue is largely alleviated, meanwhile, bears the large semantic information loss in the inpainted results; see Fig.2(b)(c). Therefore, the invariable semantics from the unmasked regions over time fail to guide the texture denoising process well." + }, + { + "type": "text", + "bbox": [ + 0.488, + 0.448, + 0.892, + 0.596 + ], + "angle": 0, + "content": "(2) Following (1), one naturally wonders how to yield the denoised results with consistent and meaningful semantics. It is apparent that the sparse structure benefits the semantic consistency in the early stage while the dense texture tends to generate the meaningful semantics in the late stage during denoising process, implying a balance between the consistent and reasonable semantics of the denoised results. To further yield the desirable results, we take into account the guidance of the structure as an auxiliary over the texture denoising process; see Fig.1(b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.607, + 0.893, + 0.901 + ], + "angle": 0, + "content": "To answer the above questions, we propose a novel structure-guided texture diffusion model, named StrDiffusion, for image inpainting, to tackle the semantic discrepancy between masked and unmasked regions, together with the reasonable semantics for masked regions; technically, we reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective for image inpainting. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective during the denoising process, which exploits the time-dependent consistency of the denoised structure between the masked and unmasked regions to mitigate the discrepancy issue. Our StrDiffusion reveals: 1) the semantically sparse structure encourages the consistent semantics for the denoised results in the early stage, while the dense texture carries out the semantic generation in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance to the texture denoising process, benefiting from the time-dependent sparsity of the structure se" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.956 + ], + "angle": 0, + "content": "8039" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.089, + 0.835, + 0.246 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.254, + 0.895, + 0.294 + ], + "angle": 0, + "content": "Figure 3. Illustration of the proposed StrDiffusion pipeline. Our basic idea is to tackle the semantic discrepancy between masked and unmasked regions via the guidance of the progressively sparse structure (a), which guides the texture denoising network (b) to generate the consistent and meaningful denoised results." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.304, + 0.471, + 0.406 + ], + "angle": 0, + "content": "mantics. Concurrently, we remark that whether the structure guides the texture well greatly depends on the semantic correlation between them. As inspired, an adaptive resampling strategy comes up to monitor the semantic correlation and regulate it via the resampling iteration. Extensive experiments on typical datasets validate the merits of StrDiffusion over the state-of-the-arts." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.422, + 0.469, + 0.439 + ], + "angle": 0, + "content": "2. Structure-Guided Texture Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.448, + 0.47, + 0.552 + ], + "angle": 0, + "content": "Central to our method lies in three aspects: 1) how to tackle the semantic discrepancy between the masked and unmasked regions (Sec.2.2); 2) structure-guided denoising network for image inpainting (Sec.2.3); and 3) more insights on whether the structure guides the texture well (Sec.2.4). Before shedding light on our technique, we elaborate the DDPMs for image inpainting." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.562, + 0.469, + 0.594 + ], + "angle": 0, + "content": "2.1. Preliminaries: Denoising Diffusion Probabilistic Models for Image Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.6, + 0.47, + 0.734 + ], + "angle": 0, + "content": "Given a completed image \\( I_{gt} \\in \\mathbb{R}^{3 \\times H \\times W} \\) and the binary mask \\( M \\in \\{0,1\\}^{1 \\times H \\times W} \\) (0 for masked regions, 1 for unmasked regions), image inpainting aims to recover the masked image \\( I_{m} = I_{gt} \\odot M \\) towards a inpainted image. For diffusion models, the inpainted results are obtained by merging the masked regions of denoised results with the original masked images. The typical DDPMs for inpainting [23] basically involve the forward texture diffusion process and reverse texture denoising process:" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.733, + 0.471, + 0.87 + ], + "angle": 0, + "content": "Forward Texture Diffusion Process. During the forward diffusion process, the semantic information from unmasked regions is utilized to guide the texture denoising process for image inpainting. Specifically, for the diffusion process with \\(T\\) timesteps, we set the initial texture state \\(y_{0} = I_{gt}\\) and the terminal texture state \\(y_{T}\\) as the combination of the masked image \\(\\mu_{y} = I_{m}\\) and the Gaussian noise \\(\\varepsilon\\). For any state \\(t \\in [0,T]\\), the diffusion process \\(\\{y_t\\}_{t=0}^T\\) via the mean-reverting stochastic differential equation (SDE) [26] is defined as" + }, + { + "type": "equation", + "bbox": [ + 0.184, + 0.884, + 0.47, + 0.9 + ], + "angle": 0, + "content": "\\[\n\\mathrm {d} y = \\theta_ {t} (\\mu_ {y} - y) d t + \\eta_ {t} \\mathrm {d} w, \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.304, + 0.892, + 0.435 + ], + "angle": 0, + "content": "where \\(\\theta_{t}\\) and \\(\\eta_{t}\\) are time-dependent positive parameters that characterize the speed of the mean-reversion and the stochastic volatility during the diffusion process, which are constrained by \\(\\eta_t^2 /\\theta_t = 2\\lambda^2\\) for the stationary variance since \\(\\lambda\\) is fixed as the noise level applied to \\(y_{T}\\). In particular, \\(\\theta_{t}\\) can be adjusted to construct different noise schedules for the texture; \\(w\\) is a standard Wiener process [25] (known as Brownian motion), which brings the randomness to the differential equation." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.435, + 0.892, + 0.489 + ], + "angle": 0, + "content": "Reverse Texture Denoising Process. To recover the completed image \\( y_{0} \\) from the terminal texture state \\( y_{T} \\), we reverse the diffusion process by simulating the SDE backward in time, formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.547, + 0.499, + 0.892, + 0.517 + ], + "angle": 0, + "content": "\\[\n\\mathrm {d} y = \\left[ \\theta_ {t} \\left(\\mu_ {y} - y\\right) - \\eta_ {t} ^ {2} \\nabla_ {y} \\log q _ {t} (y) \\right] \\mathrm {d} t + \\eta_ {t} \\mathrm {d} \\hat {w}, \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.524, + 0.892, + 0.634 + ], + "angle": 0, + "content": "where \\(\\hat{w}\\) is a reverse-time Wiener process and \\(q_{t}(y)\\) stands for the marginal probability density function of texture \\(y_{t}\\) at time \\(t\\). The score function \\(\\nabla_y\\log p_t(y)\\) is unknown, which can be approximated by training a conditional time-dependent neural network \\(\\epsilon_{\\phi}(y_{t},t)\\) [12]. Alternatively, we find the optimal reverse texture state \\(y_{t - 1}^{*}\\) from \\(y_{t}\\) in \\((t - 1)\\)-th timestep via the maximum likelihood learning, which is achieved by minimizing the negative log-likelihood:" + }, + { + "type": "equation", + "bbox": [ + 0.576, + 0.641, + 0.892, + 0.663 + ], + "angle": 0, + "content": "\\[\ny _ {t - 1} ^ {*} = \\arg \\min _ {y _ {t - 1}} [ - \\log q (y _ {t - 1} | y _ {t}, y _ {0}) ]. \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.504, + 0.671, + 0.776, + 0.685 + ], + "angle": 0, + "content": "By solving the above objective, we have:" + }, + { + "type": "equation", + "bbox": [ + 0.558, + 0.694, + 0.891, + 0.762 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} y _ {t - 1} ^ {*} = \\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\theta} _ {t}}} e ^ {- \\theta_ {t} ^ {\\prime}} \\left(y _ {t} - \\mu_ {y}\\right) \\\\ + \\frac {1 - e ^ {- 2 \\theta_ {t} ^ {\\prime}}}{1 - e ^ {- 2 \\overline {{\\theta}} _ {t}}} e ^ {- \\overline {{\\theta}} _ {t} - 1} (y _ {0} - \\mu_ {y}) + \\mu_ {y}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.77, + 0.892, + 0.804 + ], + "angle": 0, + "content": "where \\(\\theta_t' = \\int_{t-1}^t \\theta_i \\, \\mathrm{d}i\\) and \\(\\overline{\\theta}_t = \\int_0^t \\theta_z \\, \\mathrm{d}z\\). Thus, we can optimize \\(\\epsilon_\\phi\\) via the following training objective:" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.812, + 0.892, + 0.849 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\beta} ^ {t} (\\phi) = \\sum_ {t = 1} ^ {T} \\beta_ {t} \\mathbb {E} \\left[ \\| y _ {t} - \\left(\\mathrm {d} y _ {t}\\right) _ {\\epsilon_ {\\phi}} - y _ {t - 1} ^ {*} \\| _ {p} \\right], \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.902 + ], + "angle": 0, + "content": "where \\(\\beta_{t}\\) is positive weight; \\((\\mathrm{dy}_t)_{\\epsilon_\\phi}\\) denotes the reverse-time SDE in Eq.(2) and its score is predicted via the noise network \\(\\epsilon_{\\phi}(y_t,t)\\). \\(||\\cdot ||_p\\) stands for the \\(\\ell_p\\) norm." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8040" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.1, + 0.089, + 0.452, + 0.223 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.227, + 0.473, + 0.27 + ], + "angle": 0, + "content": "Figure 4. Illustration of the diffusion process for the dense texture (a) and sparse structure (b). In particular, the semantic sparsity of the structure is strengthened over time." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.276, + 0.47, + 0.308 + ], + "angle": 0, + "content": "2.2. Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.314, + 0.47, + 0.418 + ], + "angle": 0, + "content": "Based on the above, the existing diffusion models for image inpainting [23] suffer from the semantic discrepancy between the masked and unmasked regions, owing to the dense semantics of the texture. As opposed to the texture, the previous work [20, 34] suggests that the structure are generally considered to be sparse, which motivates us to tackle the discrepancy issue via the structure." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.436, + 0.47, + 0.466 + ], + "angle": 0, + "content": "2.2.1 Structure Matters: Sparse Semantics benefits the Semantic Consistency" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.474, + 0.47, + 0.562 + ], + "angle": 0, + "content": "To validate such intuition, we design a series of motivation experiments over [23], where we replace the masked image \\(\\mu_y\\) in the terminal texture state \\(y_{T}\\) with the masked image \\(\\mu_x\\) from the sparse structure, e.g., the grayscale map and edge map. Our motivation experiments (see Fig.2) reveal the followings:" + }, + { + "type": "text", + "bbox": [ + 0.065, + 0.563, + 0.47, + 0.621 + ], + "angle": 0, + "content": "(1) With the dense semantics, the texture performs well in producing meaningful semantics, while suffers from the large semantic discrepancy between the masked and un-masked regions; see Fig.1(a) and Fig.2(a)." + }, + { + "type": "text", + "bbox": [ + 0.065, + 0.621, + 0.47, + 0.68 + ], + "angle": 0, + "content": "(2) The semantically sparse structure benefits the consistent semantics, while incurs the semantics loss in the inpainted results; see the grayscale and edge map version of [23] in Fig.2(b)(c)." + }, + { + "type": "list", + "bbox": [ + 0.065, + 0.563, + 0.47, + 0.68 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.681, + 0.47, + 0.841 + ], + "angle": 0, + "content": "The above observations indicate that, unlike [23] that fixes the texture guidance from the unmasked regions, the structure guidance from the unmasked regions varies to the texture over time; meanwhile, merely involving the semantics of either dense texture or sparse structure fails to obtain the desirable inpainted results, since it actually attempts to perform the trade-off between the consistent and meaningful semantics. Motivated by that, we propose to exploit structure as an auxiliary, which exhibits the sparser semantics than the texture, so as to tackle the discrepancy issue, as remarked below." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.842, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Remark 1. Strengthening the semantic sparsity of the structure over time. Throughout the texture diffusion process, the semantic discrepancy between the masked and un-masked regions progressively increases as the timestep goes" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.195 + ], + "angle": 0, + "content": "towards to a totally masked status (see Fig.4(a)). To decrease the semantic discrepancy, we aim to strengthen the semantic sparsity of the structure over time, as opposed to the texture, during diffusion process. Concretely, the sparse grayscale map is degraded into the combination of the sparser masked edge map and the Gaussian noise via the noise schedule; see Fig.4(b)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.196, + 0.892, + 0.268 + ], + "angle": 0, + "content": "Our basic idea is to tackle the semantic discrepancy issue via the guidance of the structure during the denoising process, thus simplify the texture denoising objective, i.e., the optimal solution (the ground truth) to the denoising process, which is discussed in the next." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.288, + 0.892, + 0.316 + ], + "angle": 0, + "content": "2.2.2 Optimal Solution to the Denoising Process Under the Guidance of the Structure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.326, + 0.893, + 0.576 + ], + "angle": 0, + "content": "As per the above observations, during the texture diffusion process, the distribution of the added noise in each timestep is disturbed by the semantic discrepancy between the masked and unmasked regions, incurring the difficulty to estimate such noise distribution via a noise-prediction network during the denoising process. Instead of focusing on texture, we exploit both structure and texture for diffusion process, where the sparsity of structure alleviates the semantic discrepancy, and the texture attempts to preserve the meaningful semantic. Unlike the diffusion process to simultaneously exploit structure and texture, for denoising process, the structure firstly generates the consistent semantics \\((x_{t - 1})\\) between masked and unmasked regions, which subsequently guides the texture to generate the meaningful semantics \\((y_{t - 1})\\); see Fig.3. By the assistance of structure for StrDiffusion, the texture diffusion process generates both consistent and meaningful inpainting output." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.577, + 0.892, + 0.753 + ], + "angle": 0, + "content": "Remark 2. Different from the typical DDPMs for inpainting [22, 23], our StrDiffusion exploits the semantic consistency of the denoised structure to guide the texture denoising process, yielding both consistent and meaningful denoised results. In particular, we view the structure as an auxiliary to guide the texture rather than the inverse; the reason is two-fold: 1) during the inference denoising process, the masked regions mainly focus on the texture to be inpainted rather than the structure; 2) the structure focuses on the consistency between the masked and unmasked regions, lacking the meaningful semantics, hence still relies on the texture for inpainting." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.753, + 0.892, + 0.793 + ], + "angle": 0, + "content": "Thanks to the guidance of the structure, the reverse transition for the texture in Eq.(3) can be reformulated via Bayes' rule as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.523, + 0.803, + 0.892, + 0.865 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{r l} q \\left(y _ {t - 1} \\mid y _ {t}, x _ {t - 1}\\right) & = \\frac {q \\left(y _ {t - 1} \\mid y _ {t}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1} , y _ {t}\\right)}{q \\left(x _ {t - 1} \\mid y _ {t}\\right)} \\\\ & = \\frac {q \\left(y _ {t} \\mid y _ {t - 1}\\right) q \\left(y _ {t - 1}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1}\\right)}{q \\left(x _ {t - 1} , y _ {t}\\right)}, \\end{array} \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.873, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where the texture \\( y_{t} \\) and \\( y_{t - 1} \\), together with the structure \\( x_{t - 1} \\), are actually conditioned on their initial states, i.e.," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "8041" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.135 + ], + "angle": 0, + "content": "\\(y_{0}\\) and \\(x_0\\) , during the diffusion process, hence \\(q(y_{t - 1}) = q(y_{t - 1}|y_0)\\) and \\(q(x_{t - 1},y_t) = q(x_{t - 1})q(y_t|x_{t - 1}) =\\) \\(q(x_{t - 1}|x_0)q(y_t|x_{t - 1},y_0)\\) . Eq.(6) can thus be simplified as" + }, + { + "type": "equation", + "bbox": [ + 0.145, + 0.146, + 0.468, + 0.222 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} q \\left(y _ {t - 1} \\mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\\right) \\\\ = \\frac {q \\left(y _ {t} \\mid y _ {t - 1}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1}\\right)}{q \\left(y _ {t} \\mid x _ {t - 1} , y _ {0}\\right)} \\times \\frac {q \\left(y _ {t - 1} \\mid y _ {0}\\right)}{q \\left(x _ {t - 1} \\mid x _ {0}\\right)} \\tag {7} \\\\ \\approx \\frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.231, + 0.469, + 0.326 + ], + "angle": 0, + "content": "where \\( q(y_{t}|y_{t - 1})\\approx q(y_{t}|x_{t - 1},y_{0}) \\) and \\( q(x_{t - 1}|y_{t - 1})\\approx 1 \\), since the texture \\( y_{t} \\) can be obtained via the conditioned auxiliary structure \\( x_{t - 1} \\) during the diffusion process and initial texture \\( y_{0} \\) as Remarked above. Based on Eq.(7), the optimal reverse state is naturally acquired by minimizing the negative log-likelihood (see the supplementary material for more inference details):" + }, + { + "type": "equation", + "bbox": [ + 0.131, + 0.337, + 0.469, + 0.39 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {y} _ {t - 1} ^ {*} = \\underset {y _ {t - 1}} {\\arg \\min } \\left[ - \\log q \\left(y _ {t - 1} \\mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\\right) \\right] \\tag {8} \\\\ = \\arg \\min _ {y _ {t - 1}} [ - \\log \\frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})} ], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.399, + 0.469, + 0.441 + ], + "angle": 0, + "content": "where \\(\\tilde{y}_{t - 1}^{*}\\) denotes the ideal state reversed from \\(\\tilde{y}_t\\) under the structure guidance. To solve the above objective, we compute its gradient and setting it to be zero:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.451, + 0.469, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\tilde {y} _ {t - 1} ^ {*}} \\left\\{- \\log q \\left(\\tilde {y} _ {t - 1} ^ {*} \\mid y _ {t}, y _ {0}, x _ {t - 1} ^ {*}, x _ {0}\\right) \\right\\} = \\\\ - \\nabla_ {\\tilde {y} _ {t - 1} ^ {*}} \\log q \\left(\\tilde {y} _ {t - 1} ^ {*} \\mid y _ {0}\\right) + \\nabla_ {x _ {t - 1} ^ {*}} \\log q \\left(x _ {t - 1} ^ {*} \\mid x _ {0}\\right) = 0, \\tag {9} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.496, + 0.468, + 0.524 + ], + "angle": 0, + "content": "where \\(x_{t - 1}^{*}\\) is the ideal state reversed from \\(x_{t}\\) for the structure, similar in spirit to Eq.(4), given as" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.535, + 0.469, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} x _ {t - 1} ^ {*} = \\frac {1 - e ^ {- 2 \\bar {\\delta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}} \\left(x _ {t} - \\mu_ {x}\\right) \\tag {10} \\\\ + \\frac {1 - e ^ {- 2 \\delta_ {t} ^ {\\prime}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\bar {\\delta} _ {t - 1}} (x _ {0} - \\mu_ {x}) + \\mu_ {x}, \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.61, + 0.469, + 0.685 + ], + "angle": 0, + "content": "where structure \\(\\mu_{x}\\) is the masked version of its initial state \\(x_0\\) and \\(\\delta_t\\) is time-dependent parameter that characterizes the speed of the mean-reversion. To simplify the notation, we have \\(\\delta_t' = \\int_{t-1}^t \\delta_i \\, \\mathrm{d}i\\), \\(\\overline{\\delta}_{t-1} = \\int_0^{t-1} \\delta_z \\, \\mathrm{d}z\\) and \\(\\overline{\\delta}_t = \\overline{\\delta}_{t-1} + \\delta_t'\\). Since Eq.(9) is linear, we can derive \\(\\tilde{y}_{t-1}^*\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.113, + 0.696, + 0.469, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {y} _ {t - 1} ^ {*} = \\underbrace {\\left(\\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}}\\right) \\left(x _ {t} - \\mu_ {x}\\right)} _ {\\text {C o n s i s t e n c y t e r m f o r m a s k e d r e g i o n s}} \\\\ - \\underbrace {\\left(\\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}}\\right) e ^ {- \\bar {\\delta} _ {t}} \\left(x _ {0} - \\mu_ {x}\\right)} _ {\\text {B a l i n c e t e r m f o r m a x i k e d r e g i o n s}} \\tag {11} \\\\ + \\underbrace {e ^ {- \\overline {{\\theta}} _ {t - 1}} (y _ {0} - \\mu_ {y})} _ {\\text {S e m a n t i c s t e r m f o r m a k e d r e g i o n s}} + \\underbrace {\\mu_ {y}} _ {\\text {U n m a x k e d r e g i o n s}}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.857, + 0.469, + 0.901 + ], + "angle": 0, + "content": "Remark 3. Eq.(11) implies that the ideal reverse state \\(\\tilde{y}_{t - 1}^{*}\\) focuses more on the semantic consistency based on the semantic generation for image inpainting, to alleviate" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.401 + ], + "angle": 0, + "content": "the semantic discrepancy issues. Under the guidance of the sparse structure, \\(\\tilde{y}_{t-1}^{*}\\) tends to maintain the consistency between masked and unmasked regions in the early stage of the denoising process, while recovering the reasonable semantics in the late stage. Specifically, \\(\\tilde{y}_{t-1}^{*}\\) is mainly composed of four parts: 1) the consistency term for the structure \\(x_{t} - \\mu_{x}\\) is utilized to form the masked regions inside the denoised texture and keep the semantic consistency with the unmasked regions; 2) the semantics term for the texture \\(y_{0} - \\mu_{y}\\) progressively provides meaningful semantics for masked regions as the denoising process progresses; 3) the negative balance term \\(x_{0} - \\mu_{x}\\) adaptively surpasses the semantic information from \\(y_{0} - \\mu_{y}\\) in the early stage and the consistency information from \\(x_{t} - \\mu_{x}\\) in the late stage; 4) the unmasked texture \\(\\mu_{y}\\) retains the semantics of the unmasked regions for the denoised texture. All four parts together constitute the optimal solution to the structure-guided denoising process in the \\((t-1)\\)-th timestep, i.e., the ground truth to optimize the noise-prediction network, thus yielding the denoised results with the consistent and desirable semantics (see Fig.6), as discussed in the next section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.408, + 0.892, + 0.454 + ], + "angle": 0, + "content": "2.3. Structure-Guided Denoising Process: How does the Structure Guide the Texture Denoising Process?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.459, + 0.892, + 0.718 + ], + "angle": 0, + "content": "With the above optimal solution (i.e., the ground truth) in Eq.(11), the goal of the structure-guided denoising process is to estimate it via a noise-prediction neural network \\(\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)\\) under the guidance of the structure, where \\(\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)\\) is trained to predict the mean of the noise with the fixed variance of noise [25]. Unlike the conventional texture denoising process in [23], the structure denoising network is pre-trained as an auxiliary to obtain the denoised structure, e.g., \\(x_{t - 1}\\) in the \\(t\\) -th timestep. To fulfill the structure guidance, a multi-scale spatially adaptive normalization strategy is devised to condition a time-dependent noise network \\(\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)\\) for the texture, which deploys the spatially adaptive normalization and denormalization strategy [24] to incorporate the statistical information over the feature map across varied layers; see Fig.3. Formally, given \\(x_{t - 1}\\) from a pre-trained structure denoising network, we achieve the structure guidance by reconstructing the feature map on the \\(k\\) -th layer of CNNs in time-dependent noise network \\(\\tilde{\\epsilon}_{\\phi}\\) for the texture (i.e., \\(F_{k}^{t}\\in \\mathbb{R}^{C_{k}\\times H_{k}\\times W_{k}}\\) ) as" + }, + { + "type": "equation", + "bbox": [ + 0.517, + 0.726, + 0.891, + 0.873 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\tilde {F} _ {k} ^ {t} = \\operatorname {c o n v} _ {\\gamma} \\left(x _ {t - 1}\\right) \\frac {F _ {k} ^ {t} - \\mu_ {k} ^ {t}}{\\sigma_ {k} ^ {t}} + \\operatorname {c o n v} _ {\\beta} \\left(x _ {t - 1}\\right), \\\\ \\mu_ {k} ^ {t} (h _ {k}, w _ {k}) = \\frac {1}{C _ {k}} \\sum_ {c _ {k} = 1} ^ {C _ {k}} F _ {k} ^ {t} (h _ {k}, w _ {k}, c _ {k}), \\\\ \\sigma_ {k} ^ {t} (h _ {k}, w _ {k}) = \\sqrt {\\frac {1}{C _ {k}} \\sum_ {c _ {k} = 1} ^ {C _ {k}} \\left(F _ {k} ^ {t} \\left(h _ {k} , w _ {k} , c _ {k}\\right) - \\mu_ {k} ^ {t} \\left(h _ {k} , w _ {k}\\right)\\right) ^ {2}}, \\\\ h _ {k} = 1, 2, \\dots , H _ {k}, w _ {k} = 1, 2, \\dots , W _ {k}, \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.873, + 0.892, + 0.901 + ], + "angle": 0, + "content": "where \\( conv_{\\gamma}(\\cdot) \\) and \\( conv_{\\beta}(\\cdot) \\) denote the mappings that convert the input \\( x_{t-1} \\) to the scaling and bias values." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8042" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.091, + 0.47, + 0.174 + ], + "angle": 0, + "content": "\\(\\mu_k^t (h_k,w_k)\\) and \\(\\sigma_k^t (h_k,w_k)\\) are the statistical mean and variance of the pixels across different channels at the position \\((h_k,w_k)\\). Based on that, we turn to optimize the noise network \\(\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)\\) to estimate the optimal solution \\(\\tilde{y}_{t - 1}^{*}\\) (i.e., the ground truth) to the denoising process. To this end, the overall training objective is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.138, + 0.183, + 0.469, + 0.227 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {\\tilde {\\beta}} ^ {t} (\\phi) = \\sum_ {t = 1} ^ {T} \\tilde {\\beta} _ {t} \\mathbb {E} [ \\| \\underbrace {y _ {t} - (\\mathrm {d} y _ {t}) _ {\\tilde {\\epsilon} _ {\\phi}}} _ {\\text {D e n o i s e d} y _ {t - 1}} - \\tilde {y} _ {t - 1} ^ {*} \\| _ {p} ], \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.237, + 0.469, + 0.312 + ], + "angle": 0, + "content": "where \\(\\tilde{\\beta}_t\\) is positive weight; \\((\\mathrm{dy}_t)_{\\tilde{\\epsilon}_{\\phi}}\\) denotes the estimated reverse noise by the noise-prediction network. By minimizing Eq.(13), the inpainted results with consistent and meaningful semantics can be generated during the structure-guided denoising process." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.32, + 0.307, + 0.336 + ], + "angle": 0, + "content": "2.4. More Insights on Eq.(13)" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.343, + 0.469, + 0.402 + ], + "angle": 0, + "content": "To validate the effectiveness of the guidance from the structure to the texture denoising process, we provide more insights on Eq.(13) by studying the semantic correlation between the denoised texture and structure during inference." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.42, + 0.416, + 0.433 + ], + "angle": 0, + "content": "2.4.1 Correlation Measure via a Discriminator" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.443, + 0.469, + 0.589 + ], + "angle": 0, + "content": "Apart from the semantic structure sparsity, the semantic correlation between the structure and texture is crucial to achieve the semantic consistency between the masked and unmasked regions. To measure such semantic correlation, we adopt a discriminator network \\( D \\) to yield the correlation score \\( D(y_{t - 1},x_{t - 1},t - 1) \\) (abbreviated as \\( D(y_{t - 1},x_{t - 1}) \\)) where the denoised texture \\( y_{t - 1} \\) and structure \\( x_{t - 1} \\), together with the timestep \\( t - 1 \\), serve as the inputs. To this end, we present a discriminator loss and a triplet loss to optimize \\( D \\), as described below:" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.589, + 0.469, + 0.669 + ], + "angle": 0, + "content": "Discriminator Loss. During the denoising process, to provide the desirable guidance for the texture, the current structure \\( x_{t-1} \\) is expected to be closely correlated with the texture \\( y_{t-1} \\) in the current timestep, instead of the previous one \\( y_t \\). Hence, we aim to discriminate \\( y_{t-1} \\) and \\( y_t \\) via a discriminator loss below:" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.676, + 0.469, + 0.709 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {d i s} = - \\mathbb {E} _ {y _ {t - 1}} [ \\log (D (y _ {t - 1}, x _ {t - 1})) ] \\tag {14} \\\\ - \\mathbb {E} _ {y _ {t}} \\left[ \\log \\left(1 - D \\left(y _ {t}, x _ {t - 1}\\right)\\right) \\right]. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.724, + 0.469, + 0.793 + ], + "angle": 0, + "content": "Triplet Loss. Since the unmasked regions almost possess much denser semantics information compared to the masked ones during the denoising process, to well evaluate the correlation, Eq.(14) is encouraged to focus more on the unmasked regions, which is achieved via a triplet loss:" + }, + { + "type": "equation", + "bbox": [ + 0.1, + 0.8, + 0.468, + 0.834 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {t r i} = \\max (\\| D (\\bar {y} _ {t - 1}, x _ {t - 1}) - D (y _ {t - 1}, x _ {t - 1})) \\| _ {2} \\tag {15} \\\\ - \\| D \\left(\\bar {y} _ {t - 1}, x _ {t - 1}\\right) - D \\left(y _ {t}, x _ {t - 1}\\right) \\| _ {2} + \\alpha , 0), \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.842, + 0.469, + 0.9 + ], + "angle": 0, + "content": "where \\( \\bar{y}_{t-1} = y_{t-1} \\odot M + y_t \\odot (1 - M) \\) is constructed to associate the unmasked regions of \\( y_{t-1} \\) and the masked ones of \\( y_t \\). \\( \\alpha \\) is a margin parameter and \\( ||\\cdot||_2 \\) denotes the \\( \\ell_2 \\) norm." + }, + { + "type": "image", + "bbox": [ + 0.526, + 0.089, + 0.87, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.214, + 0.892, + 0.255 + ], + "angle": 0, + "content": "Figure 5. Illustration of the adaptive resampling strategy, which adaptively regulates the semantic correlation between the denoised texture and structure according to the score from the discriminator." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.265, + 0.847, + 0.28 + ], + "angle": 0, + "content": "Total Loss. In summary, we finalize the total loss as" + }, + { + "type": "equation", + "bbox": [ + 0.627, + 0.293, + 0.891, + 0.308 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\text {d i s}} + \\lambda_ {\\text {t r i}} \\mathcal {L} _ {\\text {t r i}}, \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.322, + 0.892, + 0.438 + ], + "angle": 0, + "content": "where \\(\\lambda_{tri}\\) denotes the balance parameter, which is empirically set as 1 in our experiments. With Eq.(16) to be minimized, \\(D\\) can be trained to evaluate the semantic correlation, where the small score value from \\(D\\) indicates that the correlation between the texture and structure is not strong, weakening the guidance of the structure. To enhance the semantic correlation, an adaptive resampling strategy comes up, which is elaborated in the next section." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.46, + 0.766, + 0.475 + ], + "angle": 0, + "content": "2.4.2 Adaptive Resampling Strategy" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.484, + 0.892, + 0.646 + ], + "angle": 0, + "content": "Different from the previous work [22] that directly performs the resampling strategy without the clear measurement, we devise an adaptive resampling strategy, which regulates the semantic correlation between the texture \\((e.g., y_{t-1})\\) and structure \\((e.g., x_{t-1})\\) according to the score value from a discriminator in Sec.2.4.1. Specifically, when the score value of the semantic correlation between \\(y_{t-1}\\) and \\(x_{t-1}\\) is smaller than a specific threshold \\(\\Delta\\) (see the supplementary material for more intuitions), we first obtain \\(\\tilde{x}_t\\) by adding the noise to \\(x_{t-1}\\), then receive a updated \\(\\tilde{x}_{t-1}\\) by denoising \\(\\tilde{x}_t\\), which are described as follows:" + }, + { + "type": "equation", + "bbox": [ + 0.533, + 0.658, + 0.89, + 0.68 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {t} = x _ {t - 1} + \\delta_ {t - 1} \\left(\\mu_ {x} - x _ {t - 1}\\right) d t + \\sigma_ {t - 1} \\mathrm {d} w, \\tag {17}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.536, + 0.678, + 0.682, + 0.693 + ], + "angle": 0, + "content": "\\[\n\\tilde {x} _ {t - 1} = \\tilde {x} _ {t} - (\\mathrm {d} x _ {t}) _ {\\bar {\\epsilon} _ {\\varphi}}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.705, + 0.892, + 0.765 + ], + "angle": 0, + "content": "Based on Eq.(17), \\(\\tilde{x}_{t - 1}\\) is utilized to generate an updated \\(\\tilde{y}_{t - 1}\\) via the trained noise network \\(\\tilde{\\epsilon}_{\\phi}(y_t,\\tilde{x}_{t - 1},t)\\). Following that, we evaluate the correlation between \\(\\tilde{y}_{t - 1}\\) and \\(\\tilde{x}_{t - 1}\\) again, and repeat the above procedure; see Fig.5." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.779, + 0.633, + 0.796 + ], + "angle": 0, + "content": "3. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.804, + 0.717, + 0.819 + ], + "angle": 0, + "content": "3.1. Implementation Details" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.827, + 0.892, + 0.901 + ], + "angle": 0, + "content": "We experimentally evaluate StrDiffusion over three typical datasets, including: Paris StreetView (PSV) [6] is a collection of street view images in Paris, consisting of 14.9k images for training and 100 images for validation; CelebA [21] is the human face dataset with 30k aligned face images," + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8043" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.126, + 0.09, + 0.532, + 0.195 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.536, + 0.089, + 0.846, + 0.196 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.201, + 0.892, + 0.216 + ], + "angle": 0, + "content": "Figure 6. Illustration of the denoised results for IR-SDE [23] (a) and StrDiffusion (b) in the varied timesteps during the denoising process." + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.222, + 0.893, + 0.264 + ], + "angle": 0, + "content": "Table 1. Comparison of quantitative results (i.e., PSNR, SSIM [30] and FID [11]) under varied mask ratios on Places2 with irregular mask dataset. ↑: Higher is better; ↓: Lower is better; -: no results are reported. The percentage (\\%) represents the ratios of varied irregular masked regions to the completed image. The best results are reported with **boldface**." + }, + { + "type": "table", + "bbox": [ + 0.159, + 0.274, + 0.806, + 0.395 + ], + "angle": 0, + "content": "
MetricsPSNR↑SSIM↑FID↓
MethodVenue10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%
RFR [15]CVPR' 2027.2624.8322.7521.110.9290.8910.8300.75617.8822.9430.6838.69
PENNet [35]CVPR' 1926.7823.5321.8020.480.9460.8940.8410.78120.4037.2253.7467.08
HiFill [32]CVPR' 2027.5024.6422.8121.230.9540.9140.8730.81616.9529.3042.8857.12
FAR [3]ECCV' 2228.3625.4823.6022.180.9420.9030.8610.818----
HAN [5]ECCV' 2228.9325.4423.0621.380.9570.9030.8390.76212.0120.1528.8537.63
CMT [14]ICCV' 2329.2825.8823.5621.700.9600.9240.8850.841----
MEDFE [13]ECCV' 2028.1325.0222.9821.530.9580.9190.8740.82514.4127.5238.4553.05
CTSDF [9]ICCV' 2128.9125.3622.9421.210.9520.9010.8340.75515.7227.8842.4457.78
ZITS [7]CVPR' 2228.3125.4023.5122.110.9420.9020.8600.817----
RePaint* [22]CVPR' 2229.1626.0224.0122.110.9670.9330.9150.86211.1620.6228.4941.16
IR-SDE [23]ICML' 2328.9825.3723.9321.680.9610.9280.9080.86412.0321.3429.3739.77
StrDiffusion (Ours)-29.4526.2824.4322.370.9730.9410.9170.8748.75016.1623.7236.93
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.403, + 0.473, + 0.551 + ], + "angle": 0, + "content": "which is split into 26k training images and 4k validation images; Places2 [37] contains more than 1.8M natural images from varied scenes. The network is trained using \\(256 \\times 256\\) images with irregular masks [19]. The noise-prediction network is constructed by removing group normalization layers and self-attention layers in the U-Net in DDPM [12] for inference efficiency. We adopt the Adam optimizer with \\(\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.99\\). We set the timestep \\(T = 100\\) for the diffusion model. All the experiments are implemented with the pytorch framework and run on 4 NVIDIA 2080TI GPU." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.562, + 0.339, + 0.579 + ], + "angle": 0, + "content": "3.2. Why can StrDiffusion Work?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.586, + 0.47, + 0.822 + ], + "angle": 0, + "content": "In this section, the core goal is to confirm that the intuition of StrDiffusion — the progressively sparse structure over time is beneficial to alleviate the semantic discrepancy issue between the masked and unmasked regions during the denoising process. We conduct the experiments on PSV and Places2 dataset. Fig.6 illustrates that, as the denoising process progresses, the denoised results from IR-SDE [23] always address the clear semantic discrepancy between the masked and unmasked regions (see Fig.6(a)); while for StrDiffusion, such discrepancy progressively degraded until vanished, yielding the consistent semantics (see Fig.6(b)), confirming our proposals in Sec.2.2.2 — the guidance of the structure benefits the consistent semantics between the masked and unmasked regions while the texture retains the reasonable semantics in the inpainted results; see the supplementary material for more results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.833, + 0.379, + 0.849 + ], + "angle": 0, + "content": "3.3. Comparison with State-of-the-arts" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.856, + 0.47, + 0.903 + ], + "angle": 0, + "content": "To validate the superiority of StrDiffusion, we compare it with the typical inpainting models, including: RFR [15] adopts the CNNs to encoding the local information;" + }, + { + "type": "image", + "bbox": [ + 0.523, + 0.401, + 0.871, + 0.633 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.639, + 0.892, + 0.695 + ], + "angle": 0, + "content": "Figure 7. Comparison of the inpainted results with the state-of-the-arts under varied irregular masks on PSV, CelebA and Places2. Our StrDiffusion delivers the desirable inpainted results (marked as the red box) against others." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.707, + 0.893, + 0.884 + ], + "angle": 0, + "content": "PENNet[35], HiFill[32], FAR[3], HAN[5] and CMT[14] globally associate the masked regions with unmasked ones via self-attention mechanism; MEDFE[13], CTSDG[9], ZITS[7] and DGTS[20] focus on the guidance of the structure, while ignore the semantic consistency between the structure and texture; RePaint[22] and IR-SDE[23] benefit from DDPMs whereas overlook the semantic consistency. For fair comparison, we reproduce RePaint by utilizing the pre-trained models from IR-SDE, denoted as RePaint*. Notably, the inpainted results are obtained by merging the masked regions from the denoised results with the original masked image." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Quantitative and Qualitative analysis. The quantitative" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8044" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.107, + 0.089, + 0.272, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.089, + 0.444, + 0.166 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.106, + 0.167, + 0.27, + 0.242 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.278, + 0.166, + 0.442, + 0.243 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.248, + 0.47, + 0.303 + ], + "angle": 0, + "content": "Figure 8. Ablation study about the progressive sparsity for the structure over time on the PSV dataset. The KL divergence (lower is better) measures the distribution difference between the masked (unmasked) regions and the completed image (i.e., ground truth)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.312, + 0.473, + 0.593 + ], + "angle": 0, + "content": "results in Table 1 apart from the qualitative results in Fig.7 summarize our findings below: StrDiffusion enjoys a much smaller FID score, together with larger PSNR and SSIM than the competitors, confirming that StrDiffusion effectively addresses semantic discrepancy between the masked and unmasked regions, while yielding the reasonable semantics. Notably, RePaint* and IR-SDE still remain the large performance margins (at most \\(1.2\\%\\) for PSNR, \\(1.4\\%\\) for SSIM and \\(10\\%\\) for FID) compared to StrDiffusion, owing to the semantic discrepancy (e.g., the white wall in the row 1 of Fig.7) in the denoised results incurred by the dense texture. Albeit MEDFE, CTSDG and ZITS focus on the guidance of the structure similar to StrDiffusion, they suffer from a performance loss due to the semantic discrepancy between the structure and texture, e.g., the woman's face for CTSDG in the row 4 of Fig.7, which further verifies our proposal in Sec.2.2 — the progressively sparse structure provides the time-dependent guidance for texture denoising process; see the supplementary material for more results." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.603, + 0.242, + 0.618 + ], + "angle": 0, + "content": "3.4. Ablation Studies" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.626, + 0.47, + 0.656 + ], + "angle": 0, + "content": "3.4.1 Why Should the Semantic Sparsity of the Structure be Strengthened over Time?" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.665, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Recalling Sec.2.2, the progressive sparsity for the structure is utilized to mitigate the semantic discrepancy, by setting the initial structure state as the grayscale and the terminal structure state as the combination of the edge and the noise during the structure diffusion process, denoted as gray2edge. To shed more light on the semantic sparsity of the structure, we replace the initial and terminal structure state, yielding several alternatives as gray2gray, edge2edge and edge2gray; and perform the experiments on the PSV dataset. The structure sparsity of gray2gray and edge2edge is fixed over time. Fig.8 illustrates that gray2edge (Fig.8(d)) exhibits better consistency with meaningful semantics in the inpainted results against others, especially for edge2gray, implying the benefits of strengthening structure sparsity over time. Notably, for gray2gray, the discrepancy issue in the denoised re" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.09, + 0.894, + 0.119 + ], + "angle": 0, + "content": "Table 2. Ablation study about the adaptive resampling strategy on the PSV dataset. The best results are reported with **boldface**." + }, + { + "type": "table", + "bbox": [ + 0.521, + 0.128, + 0.866, + 0.205 + ], + "angle": 0, + "content": "
CasesHard maskEasy mask
PSNR↑SSIM↑FID↓PSNR↑SSIM↑FID↓
A24.650.85155.7327.690.91333.73
B25.470.86346.4428.310.92128.43
C25.590.86747.3128.640.92528.20
D25.940.87542.2828.850.92926.74
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.215, + 0.895, + 0.304 + ], + "angle": 0, + "content": "sults still suffers (Fig.8(b)), while edge2edge receives the poor semantics (Fig.8(a)), which attributes to their invariant semantic sparsity over time, indicating time-dependent impacts of the unmasked semantics on the texture denoising process (Sec.2.2.1); see the supplementary material for more results." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.33, + 0.893, + 0.361 + ], + "angle": 0, + "content": "3.4.2 How does Adaptive Resampling Strategy Benefit Inpainting?" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.371, + 0.895, + 0.651 + ], + "angle": 0, + "content": "To verify the effectiveness of the adaptive resampling strategy (Sec.2.4), we perform the ablation study on the PSV dataset from the following cases: A: refining the inpainted results of IR-SDE[23] via the resampling strategy in Repaint; B: removes the discriminator, which performs the adaptive resampling strategy without considering the semantic correlation between the texture and structure; C: StrDiffusion without the adaptive resampling strategy; D: the proposed StrDiffusion. Table 2 suggests that case D delivers great gains (at most \\(13.45\\%\\)) to other cases, which is evidenced that the adaptive resampling strategy succeeds in regulating the semantic correlation for the desirable results (Sec.2.4); case D upgrades beyond case A despite of the combination with the resampling strategy, which, in turn, verifies the necessity of the time-dependent guidance from the structure. In particular, case B bears a large performance degradation (at most \\(4.16\\%\\)), confirming the importance of adaptively resampling strategy as per the semantic correlation between the structure and texture in Sec.2.4.1." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.668, + 0.62, + 0.684 + ], + "angle": 0, + "content": "4. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.695, + 0.894, + 0.841 + ], + "angle": 0, + "content": "In this paper, we propose a structure-guided diffusion model for inpainting (StrDiffusion), to reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective; while revealing: 1) the semantics from the unmasked regions essentially offer the time-dependent guidance for the texture denoising process; 2) the progressively sparse structure well tackle the semantic discrepancy in the inpainted results. Extensive experiments verify the superiority of StrDiffusion to the state-of-the-arts." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.842, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Acknowledgments This work was supported by the National Natural Science Foundation of China (U21A20470, 62172136, 72188101), the Institute of Advanced Medicine and Frontier Technology under (2023IHM01080)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "8045" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.175, + 0.106 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.169 + ], + "angle": 0, + "content": "[1] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. Patchmatch: A randomized correspondence algorithm for structural image editing. ACM Trans. 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Despite the meaningful semantics generation, the existing arts suffer from the semantic discrepancy between the masked and unmasked regions, since the semantically dense unmasked texture fails to be completely degraded while the masked regions turn to the pure noise in diffusion process, leading to the large discrepancy between them. In this paper, we aim to answer how the unmasked semantics guide the texture denoising process; together with how to tackle the semantic discrepancy, to facilitate the consistent and meaningful semantics generation. To this end, we propose a novel structure-guided diffusion model for image inpainting named StrDiffusion, to reformulate the conventional texture denoising process under the structure guidance to derive a simplified denoising objective for image inpainting, while revealing: 1) the semantically sparse structure is beneficial to tackle the semantic discrepancy in the early stage, while the dense texture generates the reasonable semantics in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance for the texture denoising process, benefiting from the time-dependent sparsity of the structure semantics. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective by exploiting the consistency of the denoised structure between masked and unmasked regions. Besides, we devise an adaptive resampling strategy as a formal criterion as whether the structure is competent to guide the texture denoising process, while regulate their semantic correlations. Extensive experiments validate the merits of StrDiffusion over the state-of-the-arts. Our code is available at https://github.com/htyjers/StrDiffusion. + +![](images/5de2aacc1979775bafe9672c3a8d61e73ba9e491c6791db16b5c068aed0e5c74.jpg) +Figure 1. Existing arts, e.g., IR-SDE [23] (a), suffer from the semantic discrepancy $(\bigcirc)$ between the masked and unmasked regions despite of the meaningful semantics for the masked regions during the denoising process. Our StrDiffusion (b) tackles the semantic discrepancy issue via the guidance of the auxiliary sparse structure, yielding the consistent and meaningful denoised results. The experiments are conducted on PSV [6]. + +# 1. Introduction + +Recently, image inpainting has supported a wide range of applications, e.g., photo restoration and image editing, which aims to recover the masked regions of an image with the semantic information of unmasked regions, where the principle mainly covers two aspects: the reasonable semantics for the masked regions and their semantic consistency with the unmasked regions. The prior work mainly involves the diffusion-based [2, 8] and patch-based [1, 4, 10] scheme, which tends to inpaint the small mask or repeated patterns of the image via simple color information, while fails to handle irregular or complicated masks. To address such issue, substantial attention [15, 17, 31, 36] has shifted to the convolutional neural networks (CNNs), which devote themselves to encoding the local semantics + +![](images/17d9bc8e73ebc98be727619a45b83a36440a4c29ad5db49c9661353ad3719a27.jpg) +Figure 2. Illustration of the motivating experiments about whether the sparse structure is beneficial to alleviating the discrepancy issue during the denoising process for image inpainting. Apart from the dense texture for IR-SDE [23] (a), the unmasked semantics combined with the Gaussian noise is further set as the sparse structure, e.g., the grayscale map (b) and edge map (c). Our StrDiffusion (d) can tackle the semantic discrepancy via the progressively sparse structure. The shadow area indicates the discrepancy between the masked and unmasked regions during the denoising process. The PSNR (higher is better) reflects the recovered semantics for the masked (unmasked) regions compared to the completed image (i.e., ground truth) by calculating the semantic similarity between them. The inpainted results are obtained by combining the masked regions of denoised results with the original masked images. + +![](images/3a2952ee5f24ce8356912ee76b5eb57e8417cfb00ce4904e10971ddcb9417dde.jpg) + +![](images/d8b01cdab815110b946aef9f03487503226d82016e1f023bfe37f3e19677b73a.jpg) + +![](images/806eb5f61cead4ae60744c9d4d7fe0b1870af1e904d1702514b0e6df3d4e514e.jpg) + +around the masked regions, while ignore the global information from the unmasked regions, incurring that the regions far away from the mask boundary remain bury. Recently, self-attention mechanism [5, 14, 16, 32, 35] is proposed to globally associate the masked regions with unmasked ones in the form of the segmented image patches, enhancing the semantic consistency between them. However, such strategies suffer from poor semantic correlation between the varied patches inside the masked regions. To this end, the semantically sparse structure is exploited [3, 7, 9, 13, 18, 20, 27, 28, 33, 34] to strength their correlations, which, however, implies the heavy reliance on the semantic consistency between the structure and texture, hence inevitably bears the artifact in the inpainted output. + +Fortunately, the denoising diffusion probabilistic models (DDPMs) [12, 25] have emerged as the powerful generative models to deliver remarkable gains in the semantics generation and mode converge, hence well remedy the poor semantics generation for image inpainting [22, 23, 29, 38]. Specifically, instead of focusing on the training process, [22] proposed to adopt the pre-trained DDPMs as the prior and develop a resampling strategy to condition the reverse denoising process during the inference process. Further, [23] attempted to model the diffusion process for image inpainting by exploiting the semantics from the unmasked regions, yielding an optimal reverse solution to the denoising process. These methods mostly exhibit the semantically meaningful inpainted results with the advantages of DDPMs, whereas overlook the semantic consistency between the masked and unmasked regions. The intuition is that the semantically dense unmasked texture is degraded into the combination of the unmasked texture and the Gaussian noise, while the masked regions turn to the pure noise during the diffusion process, leading to the large discrepancy between them (see Fig.1(a) and Fig.2(a)), and motivates the followings: + +(1) How does the unmasked semantics guide the texture denoising process for image inpainting? Our motivating ex + +periments (see Fig.2) suggest that, when the unmasked semantics combined with the noise turns to be sparser, e.g., utilizing the grayscale or edge map of the masked image as an alternative, the discrepancy issue is largely alleviated, meanwhile, bears the large semantic information loss in the inpainted results; see Fig.2(b)(c). Therefore, the invariable semantics from the unmasked regions over time fail to guide the texture denoising process well. + +(2) Following (1), one naturally wonders how to yield the denoised results with consistent and meaningful semantics. It is apparent that the sparse structure benefits the semantic consistency in the early stage while the dense texture tends to generate the meaningful semantics in the late stage during denoising process, implying a balance between the consistent and reasonable semantics of the denoised results. To further yield the desirable results, we take into account the guidance of the structure as an auxiliary over the texture denoising process; see Fig.1(b). + +To answer the above questions, we propose a novel structure-guided texture diffusion model, named StrDiffusion, for image inpainting, to tackle the semantic discrepancy between masked and unmasked regions, together with the reasonable semantics for masked regions; technically, we reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective for image inpainting. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective during the denoising process, which exploits the time-dependent consistency of the denoised structure between the masked and unmasked regions to mitigate the discrepancy issue. Our StrDiffusion reveals: 1) the semantically sparse structure encourages the consistent semantics for the denoised results in the early stage, while the dense texture carries out the semantic generation in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance to the texture denoising process, benefiting from the time-dependent sparsity of the structure se + +![](images/6e9cb9a46f390a2116ea21f7923ae8253e61d18944f5756490cd952966e9e8e1.jpg) +Figure 3. Illustration of the proposed StrDiffusion pipeline. Our basic idea is to tackle the semantic discrepancy between masked and unmasked regions via the guidance of the progressively sparse structure (a), which guides the texture denoising network (b) to generate the consistent and meaningful denoised results. + +mantics. Concurrently, we remark that whether the structure guides the texture well greatly depends on the semantic correlation between them. As inspired, an adaptive resampling strategy comes up to monitor the semantic correlation and regulate it via the resampling iteration. Extensive experiments on typical datasets validate the merits of StrDiffusion over the state-of-the-arts. + +# 2. Structure-Guided Texture Diffusion Models + +Central to our method lies in three aspects: 1) how to tackle the semantic discrepancy between the masked and unmasked regions (Sec.2.2); 2) structure-guided denoising network for image inpainting (Sec.2.3); and 3) more insights on whether the structure guides the texture well (Sec.2.4). Before shedding light on our technique, we elaborate the DDPMs for image inpainting. + +# 2.1. Preliminaries: Denoising Diffusion Probabilistic Models for Image Inpainting + +Given a completed image $I_{gt} \in \mathbb{R}^{3 \times H \times W}$ and the binary mask $M \in \{0,1\}^{1 \times H \times W}$ (0 for masked regions, 1 for unmasked regions), image inpainting aims to recover the masked image $I_{m} = I_{gt} \odot M$ towards a inpainted image. For diffusion models, the inpainted results are obtained by merging the masked regions of denoised results with the original masked images. The typical DDPMs for inpainting [23] basically involve the forward texture diffusion process and reverse texture denoising process: + +Forward Texture Diffusion Process. During the forward diffusion process, the semantic information from unmasked regions is utilized to guide the texture denoising process for image inpainting. Specifically, for the diffusion process with $T$ timesteps, we set the initial texture state $y_{0} = I_{gt}$ and the terminal texture state $y_{T}$ as the combination of the masked image $\mu_{y} = I_{m}$ and the Gaussian noise $\varepsilon$ . For any state $t \in [0,T]$ , the diffusion process $\{y_t\}_{t=0}^T$ via the mean-reverting stochastic differential equation (SDE) [26] is defined as + +$$ +\mathrm {d} y = \theta_ {t} (\mu_ {y} - y) d t + \eta_ {t} \mathrm {d} w, \tag {1} +$$ + +where $\theta_{t}$ and $\eta_{t}$ are time-dependent positive parameters that characterize the speed of the mean-reversion and the stochastic volatility during the diffusion process, which are constrained by $\eta_t^2 /\theta_t = 2\lambda^2$ for the stationary variance since $\lambda$ is fixed as the noise level applied to $y_{T}$ . In particular, $\theta_{t}$ can be adjusted to construct different noise schedules for the texture; $w$ is a standard Wiener process [25] (known as Brownian motion), which brings the randomness to the differential equation. + +Reverse Texture Denoising Process. To recover the completed image $y_{0}$ from the terminal texture state $y_{T}$ , we reverse the diffusion process by simulating the SDE backward in time, formulated as + +$$ +\mathrm {d} y = \left[ \theta_ {t} \left(\mu_ {y} - y\right) - \eta_ {t} ^ {2} \nabla_ {y} \log q _ {t} (y) \right] \mathrm {d} t + \eta_ {t} \mathrm {d} \hat {w}, \tag {2} +$$ + +where $\hat{w}$ is a reverse-time Wiener process and $q_{t}(y)$ stands for the marginal probability density function of texture $y_{t}$ at time $t$ . The score function $\nabla_y\log p_t(y)$ is unknown, which can be approximated by training a conditional time-dependent neural network $\epsilon_{\phi}(y_{t},t)$ [12]. Alternatively, we find the optimal reverse texture state $y_{t - 1}^{*}$ from $y_{t}$ in $(t - 1)$ -th timestep via the maximum likelihood learning, which is achieved by minimizing the negative log-likelihood: + +$$ +y _ {t - 1} ^ {*} = \arg \min _ {y _ {t - 1}} [ - \log q (y _ {t - 1} | y _ {t}, y _ {0}) ]. \tag {3} +$$ + +By solving the above objective, we have: + +$$ +\begin{array}{l} y _ {t - 1} ^ {*} = \frac {1 - e ^ {- 2 \bar {\theta} _ {t - 1}}}{1 - e ^ {- 2 \bar {\theta} _ {t}}} e ^ {- \theta_ {t} ^ {\prime}} \left(y _ {t} - \mu_ {y}\right) \\ + \frac {1 - e ^ {- 2 \theta_ {t} ^ {\prime}}}{1 - e ^ {- 2 \overline {{\theta}} _ {t}}} e ^ {- \overline {{\theta}} _ {t} - 1} (y _ {0} - \mu_ {y}) + \mu_ {y}, \\ \end{array} +$$ + +where $\theta_t' = \int_{t-1}^t \theta_i \, \mathrm{d}i$ and $\overline{\theta}_t = \int_0^t \theta_z \, \mathrm{d}z$ . Thus, we can optimize $\epsilon_\phi$ via the following training objective: + +$$ +\mathcal {L} _ {\beta} ^ {t} (\phi) = \sum_ {t = 1} ^ {T} \beta_ {t} \mathbb {E} \left[ \| y _ {t} - \left(\mathrm {d} y _ {t}\right) _ {\epsilon_ {\phi}} - y _ {t - 1} ^ {*} \| _ {p} \right], \tag {5} +$$ + +where $\beta_{t}$ is positive weight; $(\mathrm{dy}_t)_{\epsilon_\phi}$ denotes the reverse-time SDE in Eq.(2) and its score is predicted via the noise network $\epsilon_{\phi}(y_t,t)$ . $||\cdot ||_p$ stands for the $\ell_p$ norm. + +![](images/f4a5acfa802c13011525c7f36d67b3ba5900df6644f9b6b496386e13469862c3.jpg) +Figure 4. Illustration of the diffusion process for the dense texture (a) and sparse structure (b). In particular, the semantic sparsity of the structure is strengthened over time. + +# 2.2. Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting + +Based on the above, the existing diffusion models for image inpainting [23] suffer from the semantic discrepancy between the masked and unmasked regions, owing to the dense semantics of the texture. As opposed to the texture, the previous work [20, 34] suggests that the structure are generally considered to be sparse, which motivates us to tackle the discrepancy issue via the structure. + +# 2.2.1 Structure Matters: Sparse Semantics benefits the Semantic Consistency + +To validate such intuition, we design a series of motivation experiments over [23], where we replace the masked image $\mu_y$ in the terminal texture state $y_{T}$ with the masked image $\mu_x$ from the sparse structure, e.g., the grayscale map and edge map. Our motivation experiments (see Fig.2) reveal the followings: + +(1) With the dense semantics, the texture performs well in producing meaningful semantics, while suffers from the large semantic discrepancy between the masked and un-masked regions; see Fig.1(a) and Fig.2(a). +(2) The semantically sparse structure benefits the consistent semantics, while incurs the semantics loss in the inpainted results; see the grayscale and edge map version of [23] in Fig.2(b)(c). + +The above observations indicate that, unlike [23] that fixes the texture guidance from the unmasked regions, the structure guidance from the unmasked regions varies to the texture over time; meanwhile, merely involving the semantics of either dense texture or sparse structure fails to obtain the desirable inpainted results, since it actually attempts to perform the trade-off between the consistent and meaningful semantics. Motivated by that, we propose to exploit structure as an auxiliary, which exhibits the sparser semantics than the texture, so as to tackle the discrepancy issue, as remarked below. + +Remark 1. Strengthening the semantic sparsity of the structure over time. Throughout the texture diffusion process, the semantic discrepancy between the masked and un-masked regions progressively increases as the timestep goes + +towards to a totally masked status (see Fig.4(a)). To decrease the semantic discrepancy, we aim to strengthen the semantic sparsity of the structure over time, as opposed to the texture, during diffusion process. Concretely, the sparse grayscale map is degraded into the combination of the sparser masked edge map and the Gaussian noise via the noise schedule; see Fig.4(b). + +Our basic idea is to tackle the semantic discrepancy issue via the guidance of the structure during the denoising process, thus simplify the texture denoising objective, i.e., the optimal solution (the ground truth) to the denoising process, which is discussed in the next. + +# 2.2.2 Optimal Solution to the Denoising Process Under the Guidance of the Structure + +As per the above observations, during the texture diffusion process, the distribution of the added noise in each timestep is disturbed by the semantic discrepancy between the masked and unmasked regions, incurring the difficulty to estimate such noise distribution via a noise-prediction network during the denoising process. Instead of focusing on texture, we exploit both structure and texture for diffusion process, where the sparsity of structure alleviates the semantic discrepancy, and the texture attempts to preserve the meaningful semantic. Unlike the diffusion process to simultaneously exploit structure and texture, for denoising process, the structure firstly generates the consistent semantics $(x_{t - 1})$ between masked and unmasked regions, which subsequently guides the texture to generate the meaningful semantics $(y_{t - 1})$ ; see Fig.3. By the assistance of structure for StrDiffusion, the texture diffusion process generates both consistent and meaningful inpainting output. + +Remark 2. Different from the typical DDPMs for inpainting [22, 23], our StrDiffusion exploits the semantic consistency of the denoised structure to guide the texture denoising process, yielding both consistent and meaningful denoised results. In particular, we view the structure as an auxiliary to guide the texture rather than the inverse; the reason is two-fold: 1) during the inference denoising process, the masked regions mainly focus on the texture to be inpainted rather than the structure; 2) the structure focuses on the consistency between the masked and unmasked regions, lacking the meaningful semantics, hence still relies on the texture for inpainting. + +Thanks to the guidance of the structure, the reverse transition for the texture in Eq.(3) can be reformulated via Bayes' rule as follows: + +$$ +\begin{array}{r l} q \left(y _ {t - 1} \mid y _ {t}, x _ {t - 1}\right) & = \frac {q \left(y _ {t - 1} \mid y _ {t}\right) q \left(x _ {t - 1} \mid y _ {t - 1} , y _ {t}\right)}{q \left(x _ {t - 1} \mid y _ {t}\right)} \\ & = \frac {q \left(y _ {t} \mid y _ {t - 1}\right) q \left(y _ {t - 1}\right) q \left(x _ {t - 1} \mid y _ {t - 1}\right)}{q \left(x _ {t - 1} , y _ {t}\right)}, \end{array} \tag {6} +$$ + +where the texture $y_{t}$ and $y_{t - 1}$ , together with the structure $x_{t - 1}$ , are actually conditioned on their initial states, i.e., + +$y_{0}$ and $x_0$ , during the diffusion process, hence $q(y_{t - 1}) = q(y_{t - 1}|y_0)$ and $q(x_{t - 1},y_t) = q(x_{t - 1})q(y_t|x_{t - 1}) =$ $q(x_{t - 1}|x_0)q(y_t|x_{t - 1},y_0)$ . Eq.(6) can thus be simplified as + +$$ +\begin{array}{l} q \left(y _ {t - 1} \mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\right) \\ = \frac {q \left(y _ {t} \mid y _ {t - 1}\right) q \left(x _ {t - 1} \mid y _ {t - 1}\right)}{q \left(y _ {t} \mid x _ {t - 1} , y _ {0}\right)} \times \frac {q \left(y _ {t - 1} \mid y _ {0}\right)}{q \left(x _ {t - 1} \mid x _ {0}\right)} \tag {7} \\ \approx \frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})}, \\ \end{array} +$$ + +where $q(y_{t}|y_{t - 1})\approx q(y_{t}|x_{t - 1},y_{0})$ and $q(x_{t - 1}|y_{t - 1})\approx 1$ , since the texture $y_{t}$ can be obtained via the conditioned auxiliary structure $x_{t - 1}$ during the diffusion process and initial texture $y_{0}$ as Remarked above. Based on Eq.(7), the optimal reverse state is naturally acquired by minimizing the negative log-likelihood (see the supplementary material for more inference details): + +$$ +\begin{array}{l} \tilde {y} _ {t - 1} ^ {*} = \underset {y _ {t - 1}} {\arg \min } \left[ - \log q \left(y _ {t - 1} \mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\right) \right] \tag {8} \\ = \arg \min _ {y _ {t - 1}} [ - \log \frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})} ], \\ \end{array} +$$ + +where $\tilde{y}_{t - 1}^{*}$ denotes the ideal state reversed from $\tilde{y}_t$ under the structure guidance. To solve the above objective, we compute its gradient and setting it to be zero: + +$$ +\begin{array}{l} \nabla_ {\tilde {y} _ {t - 1} ^ {*}} \left\{- \log q \left(\tilde {y} _ {t - 1} ^ {*} \mid y _ {t}, y _ {0}, x _ {t - 1} ^ {*}, x _ {0}\right) \right\} = \\ - \nabla_ {\tilde {y} _ {t - 1} ^ {*}} \log q \left(\tilde {y} _ {t - 1} ^ {*} \mid y _ {0}\right) + \nabla_ {x _ {t - 1} ^ {*}} \log q \left(x _ {t - 1} ^ {*} \mid x _ {0}\right) = 0, \tag {9} \\ \end{array} +$$ + +where $x_{t - 1}^{*}$ is the ideal state reversed from $x_{t}$ for the structure, similar in spirit to Eq.(4), given as + +$$ +\begin{array}{l} x _ {t - 1} ^ {*} = \frac {1 - e ^ {- 2 \bar {\delta} _ {t - 1}}}{1 - e ^ {- 2 \bar {\delta} _ {t}}} e ^ {- \delta_ {t} ^ {\prime}} \left(x _ {t} - \mu_ {x}\right) \tag {10} \\ + \frac {1 - e ^ {- 2 \delta_ {t} ^ {\prime}}}{1 - e ^ {- 2 \bar {\delta} _ {t}}} e ^ {- \bar {\delta} _ {t - 1}} (x _ {0} - \mu_ {x}) + \mu_ {x}, \\ \end{array} +$$ + +where structure $\mu_{x}$ is the masked version of its initial state $x_0$ and $\delta_t$ is time-dependent parameter that characterizes the speed of the mean-reversion. To simplify the notation, we have $\delta_t' = \int_{t-1}^t \delta_i \, \mathrm{d}i$ , $\overline{\delta}_{t-1} = \int_0^{t-1} \delta_z \, \mathrm{d}z$ and $\overline{\delta}_t = \overline{\delta}_{t-1} + \delta_t'$ . Since Eq.(9) is linear, we can derive $\tilde{y}_{t-1}^*$ as + +$$ +\begin{array}{l} \tilde {y} _ {t - 1} ^ {*} = \underbrace {\left(\frac {1 - e ^ {- 2 \bar {\theta} _ {t - 1}}}{1 - e ^ {- 2 \bar {\delta} _ {t}}} e ^ {- \delta_ {t} ^ {\prime}}\right) \left(x _ {t} - \mu_ {x}\right)} _ {\text {C o n s i s t e n c y t e r m f o r m a s k e d r e g i o n s}} \\ - \underbrace {\left(\frac {1 - e ^ {- 2 \bar {\theta} _ {t - 1}}}{1 - e ^ {- 2 \bar {\delta} _ {t}}} e ^ {- \delta_ {t} ^ {\prime}}\right) e ^ {- \bar {\delta} _ {t}} \left(x _ {0} - \mu_ {x}\right)} _ {\text {B a l i n c e t e r m f o r m a x i k e d r e g i o n s}} \tag {11} \\ + \underbrace {e ^ {- \overline {{\theta}} _ {t - 1}} (y _ {0} - \mu_ {y})} _ {\text {S e m a n t i c s t e r m f o r m a k e d r e g i o n s}} + \underbrace {\mu_ {y}} _ {\text {U n m a x k e d r e g i o n s}}. \\ \end{array} +$$ + +Remark 3. Eq.(11) implies that the ideal reverse state $\tilde{y}_{t - 1}^{*}$ focuses more on the semantic consistency based on the semantic generation for image inpainting, to alleviate + +the semantic discrepancy issues. Under the guidance of the sparse structure, $\tilde{y}_{t-1}^{*}$ tends to maintain the consistency between masked and unmasked regions in the early stage of the denoising process, while recovering the reasonable semantics in the late stage. Specifically, $\tilde{y}_{t-1}^{*}$ is mainly composed of four parts: 1) the consistency term for the structure $x_{t} - \mu_{x}$ is utilized to form the masked regions inside the denoised texture and keep the semantic consistency with the unmasked regions; 2) the semantics term for the texture $y_{0} - \mu_{y}$ progressively provides meaningful semantics for masked regions as the denoising process progresses; 3) the negative balance term $x_{0} - \mu_{x}$ adaptively surpasses the semantic information from $y_{0} - \mu_{y}$ in the early stage and the consistency information from $x_{t} - \mu_{x}$ in the late stage; 4) the unmasked texture $\mu_{y}$ retains the semantics of the unmasked regions for the denoised texture. All four parts together constitute the optimal solution to the structure-guided denoising process in the $(t-1)$ -th timestep, i.e., the ground truth to optimize the noise-prediction network, thus yielding the denoised results with the consistent and desirable semantics (see Fig.6), as discussed in the next section. + +# 2.3. Structure-Guided Denoising Process: How does the Structure Guide the Texture Denoising Process? + +With the above optimal solution (i.e., the ground truth) in Eq.(11), the goal of the structure-guided denoising process is to estimate it via a noise-prediction neural network $\tilde{\epsilon}_{\phi}(y_t,x_{t - 1},t)$ under the guidance of the structure, where $\tilde{\epsilon}_{\phi}(y_t,x_{t - 1},t)$ is trained to predict the mean of the noise with the fixed variance of noise [25]. Unlike the conventional texture denoising process in [23], the structure denoising network is pre-trained as an auxiliary to obtain the denoised structure, e.g., $x_{t - 1}$ in the $t$ -th timestep. To fulfill the structure guidance, a multi-scale spatially adaptive normalization strategy is devised to condition a time-dependent noise network $\tilde{\epsilon}_{\phi}(y_t,x_{t - 1},t)$ for the texture, which deploys the spatially adaptive normalization and denormalization strategy [24] to incorporate the statistical information over the feature map across varied layers; see Fig.3. Formally, given $x_{t - 1}$ from a pre-trained structure denoising network, we achieve the structure guidance by reconstructing the feature map on the $k$ -th layer of CNNs in time-dependent noise network $\tilde{\epsilon}_{\phi}$ for the texture (i.e., $F_{k}^{t}\in \mathbb{R}^{C_{k}\times H_{k}\times W_{k}}$ ) as + +$$ +\begin{array}{l} \tilde {F} _ {k} ^ {t} = \operatorname {c o n v} _ {\gamma} \left(x _ {t - 1}\right) \frac {F _ {k} ^ {t} - \mu_ {k} ^ {t}}{\sigma_ {k} ^ {t}} + \operatorname {c o n v} _ {\beta} \left(x _ {t - 1}\right), \\ \mu_ {k} ^ {t} (h _ {k}, w _ {k}) = \frac {1}{C _ {k}} \sum_ {c _ {k} = 1} ^ {C _ {k}} F _ {k} ^ {t} (h _ {k}, w _ {k}, c _ {k}), \\ \sigma_ {k} ^ {t} (h _ {k}, w _ {k}) = \sqrt {\frac {1}{C _ {k}} \sum_ {c _ {k} = 1} ^ {C _ {k}} \left(F _ {k} ^ {t} \left(h _ {k} , w _ {k} , c _ {k}\right) - \mu_ {k} ^ {t} \left(h _ {k} , w _ {k}\right)\right) ^ {2}}, \\ h _ {k} = 1, 2, \dots , H _ {k}, w _ {k} = 1, 2, \dots , W _ {k}, \tag {12} \\ \end{array} +$$ + +where $conv_{\gamma}(\cdot)$ and $conv_{\beta}(\cdot)$ denote the mappings that convert the input $x_{t-1}$ to the scaling and bias values. + +$\mu_k^t (h_k,w_k)$ and $\sigma_k^t (h_k,w_k)$ are the statistical mean and variance of the pixels across different channels at the position $(h_k,w_k)$ . Based on that, we turn to optimize the noise network $\tilde{\epsilon}_{\phi}(y_t,x_{t - 1},t)$ to estimate the optimal solution $\tilde{y}_{t - 1}^{*}$ (i.e., the ground truth) to the denoising process. To this end, the overall training objective is formulated as + +$$ +\mathcal {L} _ {\tilde {\beta}} ^ {t} (\phi) = \sum_ {t = 1} ^ {T} \tilde {\beta} _ {t} \mathbb {E} [ \| \underbrace {y _ {t} - (\mathrm {d} y _ {t}) _ {\tilde {\epsilon} _ {\phi}}} _ {\text {D e n o i s e d} y _ {t - 1}} - \tilde {y} _ {t - 1} ^ {*} \| _ {p} ], \tag {13} +$$ + +where $\tilde{\beta}_t$ is positive weight; $(\mathrm{dy}_t)_{\tilde{\epsilon}_{\phi}}$ denotes the estimated reverse noise by the noise-prediction network. By minimizing Eq.(13), the inpainted results with consistent and meaningful semantics can be generated during the structure-guided denoising process. + +# 2.4. More Insights on Eq.(13) + +To validate the effectiveness of the guidance from the structure to the texture denoising process, we provide more insights on Eq.(13) by studying the semantic correlation between the denoised texture and structure during inference. + +# 2.4.1 Correlation Measure via a Discriminator + +Apart from the semantic structure sparsity, the semantic correlation between the structure and texture is crucial to achieve the semantic consistency between the masked and unmasked regions. To measure such semantic correlation, we adopt a discriminator network $D$ to yield the correlation score $D(y_{t - 1},x_{t - 1},t - 1)$ (abbreviated as $D(y_{t - 1},x_{t - 1})$ ) where the denoised texture $y_{t - 1}$ and structure $x_{t - 1}$ , together with the timestep $t - 1$ , serve as the inputs. To this end, we present a discriminator loss and a triplet loss to optimize $D$ , as described below: + +Discriminator Loss. During the denoising process, to provide the desirable guidance for the texture, the current structure $x_{t-1}$ is expected to be closely correlated with the texture $y_{t-1}$ in the current timestep, instead of the previous one $y_t$ . Hence, we aim to discriminate $y_{t-1}$ and $y_t$ via a discriminator loss below: + +$$ +\begin{array}{l} \mathcal {L} _ {d i s} = - \mathbb {E} _ {y _ {t - 1}} [ \log (D (y _ {t - 1}, x _ {t - 1})) ] \tag {14} \\ - \mathbb {E} _ {y _ {t}} \left[ \log \left(1 - D \left(y _ {t}, x _ {t - 1}\right)\right) \right]. \\ \end{array} +$$ + +Triplet Loss. Since the unmasked regions almost possess much denser semantics information compared to the masked ones during the denoising process, to well evaluate the correlation, Eq.(14) is encouraged to focus more on the unmasked regions, which is achieved via a triplet loss: + +$$ +\begin{array}{l} \mathcal {L} _ {t r i} = \max (\| D (\bar {y} _ {t - 1}, x _ {t - 1}) - D (y _ {t - 1}, x _ {t - 1})) \| _ {2} \tag {15} \\ - \| D \left(\bar {y} _ {t - 1}, x _ {t - 1}\right) - D \left(y _ {t}, x _ {t - 1}\right) \| _ {2} + \alpha , 0), \\ \end{array} +$$ + +where $\bar{y}_{t-1} = y_{t-1} \odot M + y_t \odot (1 - M)$ is constructed to associate the unmasked regions of $y_{t-1}$ and the masked ones of $y_t$ . $\alpha$ is a margin parameter and $||\cdot||_2$ denotes the $\ell_2$ norm. + +![](images/4df6491798eaee1af14361f5391668593dc6f2b94c741b9f49056a8aed9047af.jpg) +Figure 5. Illustration of the adaptive resampling strategy, which adaptively regulates the semantic correlation between the denoised texture and structure according to the score from the discriminator. + +Total Loss. In summary, we finalize the total loss as + +$$ +\mathcal {L} = \mathcal {L} _ {\text {d i s}} + \lambda_ {\text {t r i}} \mathcal {L} _ {\text {t r i}}, \tag {16} +$$ + +where $\lambda_{tri}$ denotes the balance parameter, which is empirically set as 1 in our experiments. With Eq.(16) to be minimized, $D$ can be trained to evaluate the semantic correlation, where the small score value from $D$ indicates that the correlation between the texture and structure is not strong, weakening the guidance of the structure. To enhance the semantic correlation, an adaptive resampling strategy comes up, which is elaborated in the next section. + +# 2.4.2 Adaptive Resampling Strategy + +Different from the previous work [22] that directly performs the resampling strategy without the clear measurement, we devise an adaptive resampling strategy, which regulates the semantic correlation between the texture $(e.g., y_{t-1})$ and structure $(e.g., x_{t-1})$ according to the score value from a discriminator in Sec.2.4.1. Specifically, when the score value of the semantic correlation between $y_{t-1}$ and $x_{t-1}$ is smaller than a specific threshold $\Delta$ (see the supplementary material for more intuitions), we first obtain $\tilde{x}_t$ by adding the noise to $x_{t-1}$ , then receive a updated $\tilde{x}_{t-1}$ by denoising $\tilde{x}_t$ , which are described as follows: + +$$ +\tilde {x} _ {t} = x _ {t - 1} + \delta_ {t - 1} \left(\mu_ {x} - x _ {t - 1}\right) d t + \sigma_ {t - 1} \mathrm {d} w, \tag {17} +$$ + +$$ +\tilde {x} _ {t - 1} = \tilde {x} _ {t} - (\mathrm {d} x _ {t}) _ {\bar {\epsilon} _ {\varphi}}. +$$ + +Based on Eq.(17), $\tilde{x}_{t - 1}$ is utilized to generate an updated $\tilde{y}_{t - 1}$ via the trained noise network $\tilde{\epsilon}_{\phi}(y_t,\tilde{x}_{t - 1},t)$ . Following that, we evaluate the correlation between $\tilde{y}_{t - 1}$ and $\tilde{x}_{t - 1}$ again, and repeat the above procedure; see Fig.5. + +# 3. Experiments + +# 3.1. Implementation Details + +We experimentally evaluate StrDiffusion over three typical datasets, including: Paris StreetView (PSV) [6] is a collection of street view images in Paris, consisting of 14.9k images for training and 100 images for validation; CelebA [21] is the human face dataset with 30k aligned face images, + +![](images/fc42c73d370088e6b511259be2b6d5ae782110ffd5e717490e8df90fb6b142dd.jpg) +Figure 6. Illustration of the denoised results for IR-SDE [23] (a) and StrDiffusion (b) in the varied timesteps during the denoising process. + +![](images/70eca2aa58a7335286ed107ac72939091c65d890998cbdbd209c5822b0744d6c.jpg) +Table 1. Comparison of quantitative results (i.e., PSNR, SSIM [30] and FID [11]) under varied mask ratios on Places2 with irregular mask dataset. ↑: Higher is better; ↓: Lower is better; -: no results are reported. The percentage (\%) represents the ratios of varied irregular masked regions to the completed image. The best results are reported with **boldface**. + +
MetricsPSNR↑SSIM↑FID↓
MethodVenue10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%
RFR [15]CVPR' 2027.2624.8322.7521.110.9290.8910.8300.75617.8822.9430.6838.69
PENNet [35]CVPR' 1926.7823.5321.8020.480.9460.8940.8410.78120.4037.2253.7467.08
HiFill [32]CVPR' 2027.5024.6422.8121.230.9540.9140.8730.81616.9529.3042.8857.12
FAR [3]ECCV' 2228.3625.4823.6022.180.9420.9030.8610.818----
HAN [5]ECCV' 2228.9325.4423.0621.380.9570.9030.8390.76212.0120.1528.8537.63
CMT [14]ICCV' 2329.2825.8823.5621.700.9600.9240.8850.841----
MEDFE [13]ECCV' 2028.1325.0222.9821.530.9580.9190.8740.82514.4127.5238.4553.05
CTSDF [9]ICCV' 2128.9125.3622.9421.210.9520.9010.8340.75515.7227.8842.4457.78
ZITS [7]CVPR' 2228.3125.4023.5122.110.9420.9020.8600.817----
RePaint* [22]CVPR' 2229.1626.0224.0122.110.9670.9330.9150.86211.1620.6228.4941.16
IR-SDE [23]ICML' 2328.9825.3723.9321.680.9610.9280.9080.86412.0321.3429.3739.77
StrDiffusion (Ours)-29.4526.2824.4322.370.9730.9410.9170.8748.75016.1623.7236.93
+ +which is split into 26k training images and 4k validation images; Places2 [37] contains more than 1.8M natural images from varied scenes. The network is trained using $256 \times 256$ images with irregular masks [19]. The noise-prediction network is constructed by removing group normalization layers and self-attention layers in the U-Net in DDPM [12] for inference efficiency. We adopt the Adam optimizer with $\beta_{1} = 0.9$ and $\beta_{2} = 0.99$ . We set the timestep $T = 100$ for the diffusion model. All the experiments are implemented with the pytorch framework and run on 4 NVIDIA 2080TI GPU. + +# 3.2. Why can StrDiffusion Work? + +In this section, the core goal is to confirm that the intuition of StrDiffusion — the progressively sparse structure over time is beneficial to alleviate the semantic discrepancy issue between the masked and unmasked regions during the denoising process. We conduct the experiments on PSV and Places2 dataset. Fig.6 illustrates that, as the denoising process progresses, the denoised results from IR-SDE [23] always address the clear semantic discrepancy between the masked and unmasked regions (see Fig.6(a)); while for StrDiffusion, such discrepancy progressively degraded until vanished, yielding the consistent semantics (see Fig.6(b)), confirming our proposals in Sec.2.2.2 — the guidance of the structure benefits the consistent semantics between the masked and unmasked regions while the texture retains the reasonable semantics in the inpainted results; see the supplementary material for more results. + +# 3.3. Comparison with State-of-the-arts + +To validate the superiority of StrDiffusion, we compare it with the typical inpainting models, including: RFR [15] adopts the CNNs to encoding the local information; + +![](images/002052159238cc066b08f3cb3d02a7c953c19da628d9e82723a205b24fef3127.jpg) +Figure 7. Comparison of the inpainted results with the state-of-the-arts under varied irregular masks on PSV, CelebA and Places2. Our StrDiffusion delivers the desirable inpainted results (marked as the red box) against others. + +PENNet[35], HiFill[32], FAR[3], HAN[5] and CMT[14] globally associate the masked regions with unmasked ones via self-attention mechanism; MEDFE[13], CTSDG[9], ZITS[7] and DGTS[20] focus on the guidance of the structure, while ignore the semantic consistency between the structure and texture; RePaint[22] and IR-SDE[23] benefit from DDPMs whereas overlook the semantic consistency. For fair comparison, we reproduce RePaint by utilizing the pre-trained models from IR-SDE, denoted as RePaint*. Notably, the inpainted results are obtained by merging the masked regions from the denoised results with the original masked image. + +Quantitative and Qualitative analysis. The quantitative + +![](images/27c785229cfa990ca01cb1020e3aeae67f4fc034aa753a2afea252b4f19b2e80.jpg) + +![](images/5a893a139a8f49b7c786a65050dbcb1b021a5c40fa4763aaa0948467b66debb8.jpg) + +![](images/062ca8284d7044edfbc63efd528a7951e2f5871334c6abe05f887860231f4a60.jpg) +Figure 8. Ablation study about the progressive sparsity for the structure over time on the PSV dataset. The KL divergence (lower is better) measures the distribution difference between the masked (unmasked) regions and the completed image (i.e., ground truth). + +![](images/a03fa08bbd391d4ade3d5e9aa03403c17428ba382e59e97d9e9ed468a35aa1f0.jpg) + +results in Table 1 apart from the qualitative results in Fig.7 summarize our findings below: StrDiffusion enjoys a much smaller FID score, together with larger PSNR and SSIM than the competitors, confirming that StrDiffusion effectively addresses semantic discrepancy between the masked and unmasked regions, while yielding the reasonable semantics. Notably, RePaint* and IR-SDE still remain the large performance margins (at most $1.2\%$ for PSNR, $1.4\%$ for SSIM and $10\%$ for FID) compared to StrDiffusion, owing to the semantic discrepancy (e.g., the white wall in the row 1 of Fig.7) in the denoised results incurred by the dense texture. Albeit MEDFE, CTSDG and ZITS focus on the guidance of the structure similar to StrDiffusion, they suffer from a performance loss due to the semantic discrepancy between the structure and texture, e.g., the woman's face for CTSDG in the row 4 of Fig.7, which further verifies our proposal in Sec.2.2 — the progressively sparse structure provides the time-dependent guidance for texture denoising process; see the supplementary material for more results. + +# 3.4. Ablation Studies + +# 3.4.1 Why Should the Semantic Sparsity of the Structure be Strengthened over Time? + +Recalling Sec.2.2, the progressive sparsity for the structure is utilized to mitigate the semantic discrepancy, by setting the initial structure state as the grayscale and the terminal structure state as the combination of the edge and the noise during the structure diffusion process, denoted as gray2edge. To shed more light on the semantic sparsity of the structure, we replace the initial and terminal structure state, yielding several alternatives as gray2gray, edge2edge and edge2gray; and perform the experiments on the PSV dataset. The structure sparsity of gray2gray and edge2edge is fixed over time. Fig.8 illustrates that gray2edge (Fig.8(d)) exhibits better consistency with meaningful semantics in the inpainted results against others, especially for edge2gray, implying the benefits of strengthening structure sparsity over time. Notably, for gray2gray, the discrepancy issue in the denoised re + +Table 2. Ablation study about the adaptive resampling strategy on the PSV dataset. The best results are reported with **boldface**. + +
CasesHard maskEasy mask
PSNR↑SSIM↑FID↓PSNR↑SSIM↑FID↓
A24.650.85155.7327.690.91333.73
B25.470.86346.4428.310.92128.43
C25.590.86747.3128.640.92528.20
D25.940.87542.2828.850.92926.74
+ +sults still suffers (Fig.8(b)), while edge2edge receives the poor semantics (Fig.8(a)), which attributes to their invariant semantic sparsity over time, indicating time-dependent impacts of the unmasked semantics on the texture denoising process (Sec.2.2.1); see the supplementary material for more results. + +# 3.4.2 How does Adaptive Resampling Strategy Benefit Inpainting? + +To verify the effectiveness of the adaptive resampling strategy (Sec.2.4), we perform the ablation study on the PSV dataset from the following cases: A: refining the inpainted results of IR-SDE[23] via the resampling strategy in Repaint; B: removes the discriminator, which performs the adaptive resampling strategy without considering the semantic correlation between the texture and structure; C: StrDiffusion without the adaptive resampling strategy; D: the proposed StrDiffusion. Table 2 suggests that case D delivers great gains (at most $13.45\%$ ) to other cases, which is evidenced that the adaptive resampling strategy succeeds in regulating the semantic correlation for the desirable results (Sec.2.4); case D upgrades beyond case A despite of the combination with the resampling strategy, which, in turn, verifies the necessity of the time-dependent guidance from the structure. In particular, case B bears a large performance degradation (at most $4.16\%$ ), confirming the importance of adaptively resampling strategy as per the semantic correlation between the structure and texture in Sec.2.4.1. + +# 4. Conclusion + +In this paper, we propose a structure-guided diffusion model for inpainting (StrDiffusion), to reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective; while revealing: 1) the semantics from the unmasked regions essentially offer the time-dependent guidance for the texture denoising process; 2) the progressively sparse structure well tackle the semantic discrepancy in the inpainted results. Extensive experiments verify the superiority of StrDiffusion to the state-of-the-arts. + +Acknowledgments This work was supported by the National Natural Science Foundation of China (U21A20470, 62172136, 72188101), the Institute of Advanced Medicine and Frontier Technology under (2023IHM01080). + +# References + +[1] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. Patchmatch: A randomized correspondence algorithm for structural image editing. ACM Trans. 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Designing a better asymmetric vqgan for stablediffusion. arXiv preprint arXiv:2306.04632, 2023. 2 \ No newline at end of file diff --git a/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/images.zip b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..b83c4b642745a0ea75b9691eb4907d0e94b757aa --- /dev/null +++ b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:68f663a158ea76e85e932d900ac2ef3eda875a7d2addb50810f095303ec0b045 +size 712789 diff --git a/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/layout.json b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..bd91c3245c8ea99e7d74ce92d8af29352bd94cd4 --- /dev/null +++ b/2024/Structure Matters_ Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting/layout.json @@ -0,0 +1,9249 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 127, + 102, + 465, + 138 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 127, + 102, + 465, + 138 + ], + "spans": [ + { + "bbox": [ + 127, + 102, + 465, + 138 + ], + "type": "text", + "content": "Structure Matters: Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "spans": [ + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": "Haipeng Liu" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": " Yang Wang" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{1*}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": " Biao Qian" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": " Meng Wang" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": " Yong Rui" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{1}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": "Hefei University of Technology, China \n" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "inline_equation", + "content": "^{2}" + }, + { + "bbox": [ + 125, + 159, + 468, + 216 + ], + "type": "text", + "content": "Lenovo Research, China \nhpliu.hfut@hotmail.com, yangwang@hfut.edu.cn, \n{hfutqian,eric.mengwang}@gmail.com, yongrui@lenovo.com" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 143, + 242, + 192, + 255 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 242, + 192, + 255 + ], + "spans": [ + { + "bbox": [ + 143, + 242, + 192, + 255 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 270, + 290, + 681 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 270, + 290, + 681 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 290, + 681 + ], + "type": "text", + "content": "Denoising diffusion probabilistic models (DDPMs) for image inpainting aim to add the noise to the texture of the image during the forward process and recover the masked regions with the unmasked ones of the texture via the reverse denoising process. Despite the meaningful semantics generation, the existing arts suffer from the semantic discrepancy between the masked and unmasked regions, since the semantically dense unmasked texture fails to be completely degraded while the masked regions turn to the pure noise in diffusion process, leading to the large discrepancy between them. In this paper, we aim to answer how the unmasked semantics guide the texture denoising process; together with how to tackle the semantic discrepancy, to facilitate the consistent and meaningful semantics generation. To this end, we propose a novel structure-guided diffusion model for image inpainting named StrDiffusion, to reformulate the conventional texture denoising process under the structure guidance to derive a simplified denoising objective for image inpainting, while revealing: 1) the semantically sparse structure is beneficial to tackle the semantic discrepancy in the early stage, while the dense texture generates the reasonable semantics in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance for the texture denoising process, benefiting from the time-dependent sparsity of the structure semantics. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective by exploiting the consistency of the denoised structure between masked and unmasked regions. Besides, we devise an adaptive resampling strategy as a formal criterion as whether the structure is competent to guide the texture denoising process, while regulate their semantic correlations. Extensive experiments validate the merits of StrDiffusion over the state-of-the-arts. Our code is available at https://github.com/htyjers/StrDiffusion." + } + ] + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 319, + 240, + 533, + 432 + ], + "blocks": [ + { + "bbox": [ + 319, + 240, + 533, + 432 + ], + "lines": [ + { + "bbox": [ + 319, + 240, + 533, + 432 + ], + "spans": [ + { + "bbox": [ + 319, + 240, + 533, + 432 + ], + "type": "image", + "image_path": "5de2aacc1979775bafe9672c3a8d61e73ba9e491c6791db16b5c068aed0e5c74.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 436, + 545, + 511 + ], + "lines": [ + { + "bbox": [ + 304, + 436, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 304, + 436, + 545, + 511 + ], + "type": "text", + "content": "Figure 1. Existing arts, e.g., IR-SDE [23] (a), suffer from the semantic discrepancy " + }, + { + "bbox": [ + 304, + 436, + 545, + 511 + ], + "type": "inline_equation", + "content": "(\\bigcirc)" + }, + { + "bbox": [ + 304, + 436, + 545, + 511 + ], + "type": "text", + "content": " between the masked and unmasked regions despite of the meaningful semantics for the masked regions during the denoising process. Our StrDiffusion (b) tackles the semantic discrepancy issue via the guidance of the auxiliary sparse structure, yielding the consistent and meaningful denoised results. The experiments are conducted on PSV [6]." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_caption" + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 529, + 386, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 386, + 541 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 386, + 541 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 550, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 550, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 550, + 545, + 713 + ], + "type": "text", + "content": "Recently, image inpainting has supported a wide range of applications, e.g., photo restoration and image editing, which aims to recover the masked regions of an image with the semantic information of unmasked regions, where the principle mainly covers two aspects: the reasonable semantics for the masked regions and their semantic consistency with the unmasked regions. The prior work mainly involves the diffusion-based [2, 8] and patch-based [1, 4, 10] scheme, which tends to inpaint the small mask or repeated patterns of the image via simple color information, while fails to handle irregular or complicated masks. To address such issue, substantial attention [15, 17, 31, 36] has shifted to the convolutional neural networks (CNNs), which devote themselves to encoding the local semantics" + } + ] + } + ], + "index": 9 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 702, + 192, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 702, + 192, + 712 + ], + "spans": [ + { + "bbox": [ + 58, + 702, + 192, + 712 + ], + "type": "text", + "content": "* Yang Wang is the corresponding author." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8038" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 170, + 171 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 170, + 171 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 170, + 171 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 170, + 171 + ], + "type": "image", + "image_path": "17d9bc8e73ebc98be727619a45b83a36440a4c29ad5db49c9661353ad3719a27.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 178, + 547, + 254 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 547, + 254 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 547, + 254 + ], + "type": "text", + "content": "Figure 2. Illustration of the motivating experiments about whether the sparse structure is beneficial to alleviating the discrepancy issue during the denoising process for image inpainting. Apart from the dense texture for IR-SDE [23] (a), the unmasked semantics combined with the Gaussian noise is further set as the sparse structure, e.g., the grayscale map (b) and edge map (c). Our StrDiffusion (d) can tackle the semantic discrepancy via the progressively sparse structure. The shadow area indicates the discrepancy between the masked and unmasked regions during the denoising process. The PSNR (higher is better) reflects the recovered semantics for the masked (unmasked) regions compared to the completed image (i.e., ground truth) by calculating the semantic similarity between them. The inpainted results are obtained by combining the masked regions of denoised results with the original masked images." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 173, + 70, + 294, + 171 + ], + "blocks": [ + { + "bbox": [ + 173, + 70, + 294, + 171 + ], + "lines": [ + { + "bbox": [ + 173, + 70, + 294, + 171 + ], + "spans": [ + { + "bbox": [ + 173, + 70, + 294, + 171 + ], + "type": "image", + "image_path": "3a2952ee5f24ce8356912ee76b5eb57e8417cfb00ce4904e10971ddcb9417dde.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 296, + 70, + 422, + 171 + ], + "blocks": [ + { + "bbox": [ + 296, + 70, + 422, + 171 + ], + "lines": [ + { + "bbox": [ + 296, + 70, + 422, + 171 + ], + "spans": [ + { + "bbox": [ + 296, + 70, + 422, + 171 + ], + "type": "image", + "image_path": "d8b01cdab815110b946aef9f03487503226d82016e1f023bfe37f3e19677b73a.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 425, + 71, + 544, + 171 + ], + "blocks": [ + { + "bbox": [ + 425, + 71, + 544, + 171 + ], + "lines": [ + { + "bbox": [ + 425, + 71, + 544, + 171 + ], + "spans": [ + { + "bbox": [ + 425, + 71, + 544, + 171 + ], + "type": "image", + "image_path": "806eb5f61cead4ae60744c9d4d7fe0b1870af1e904d1702514b0e6df3d4e514e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 261, + 287, + 425 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 261, + 287, + 425 + ], + "spans": [ + { + "bbox": [ + 46, + 261, + 287, + 425 + ], + "type": "text", + "content": "around the masked regions, while ignore the global information from the unmasked regions, incurring that the regions far away from the mask boundary remain bury. Recently, self-attention mechanism [5, 14, 16, 32, 35] is proposed to globally associate the masked regions with unmasked ones in the form of the segmented image patches, enhancing the semantic consistency between them. However, such strategies suffer from poor semantic correlation between the varied patches inside the masked regions. To this end, the semantically sparse structure is exploited [3, 7, 9, 13, 18, 20, 27, 28, 33, 34] to strength their correlations, which, however, implies the heavy reliance on the semantic consistency between the structure and texture, hence inevitably bears the artifact in the inpainted output." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 426, + 288, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 426, + 288, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 426, + 288, + 684 + ], + "type": "text", + "content": "Fortunately, the denoising diffusion probabilistic models (DDPMs) [12, 25] have emerged as the powerful generative models to deliver remarkable gains in the semantics generation and mode converge, hence well remedy the poor semantics generation for image inpainting [22, 23, 29, 38]. Specifically, instead of focusing on the training process, [22] proposed to adopt the pre-trained DDPMs as the prior and develop a resampling strategy to condition the reverse denoising process during the inference process. Further, [23] attempted to model the diffusion process for image inpainting by exploiting the semantics from the unmasked regions, yielding an optimal reverse solution to the denoising process. These methods mostly exhibit the semantically meaningful inpainted results with the advantages of DDPMs, whereas overlook the semantic consistency between the masked and unmasked regions. The intuition is that the semantically dense unmasked texture is degraded into the combination of the unmasked texture and the Gaussian noise, while the masked regions turn to the pure noise during the diffusion process, leading to the large discrepancy between them (see Fig.1(a) and Fig.2(a)), and motivates the followings:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 39, + 689, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 39, + 689, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 39, + 689, + 288, + 714 + ], + "type": "text", + "content": "(1) How does the unmasked semantics guide the texture denoising process for image inpainting? Our motivating ex" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 313, + 261, + 545, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 261, + 545, + 354 + ], + "spans": [ + { + "bbox": [ + 313, + 261, + 545, + 354 + ], + "type": "text", + "content": "periments (see Fig.2) suggest that, when the unmasked semantics combined with the noise turns to be sparser, e.g., utilizing the grayscale or edge map of the masked image as an alternative, the discrepancy issue is largely alleviated, meanwhile, bears the large semantic information loss in the inpainted results; see Fig.2(b)(c). Therefore, the invariable semantics from the unmasked regions over time fail to guide the texture denoising process well." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 298, + 354, + 545, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 298, + 354, + 545, + 472 + ], + "spans": [ + { + "bbox": [ + 298, + 354, + 545, + 472 + ], + "type": "text", + "content": "(2) Following (1), one naturally wonders how to yield the denoised results with consistent and meaningful semantics. It is apparent that the sparse structure benefits the semantic consistency in the early stage while the dense texture tends to generate the meaningful semantics in the late stage during denoising process, implying a balance between the consistent and reasonable semantics of the denoised results. To further yield the desirable results, we take into account the guidance of the structure as an auxiliary over the texture denoising process; see Fig.1(b)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 480, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 480, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 480, + 546, + 713 + ], + "type": "text", + "content": "To answer the above questions, we propose a novel structure-guided texture diffusion model, named StrDiffusion, for image inpainting, to tackle the semantic discrepancy between masked and unmasked regions, together with the reasonable semantics for masked regions; technically, we reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective for image inpainting. For the denoising process, a structure-guided neural network is trained to estimate the simplified denoising objective during the denoising process, which exploits the time-dependent consistency of the denoised structure between the masked and unmasked regions to mitigate the discrepancy issue. Our StrDiffusion reveals: 1) the semantically sparse structure encourages the consistent semantics for the denoised results in the early stage, while the dense texture carries out the semantic generation in the late stage; 2) the semantics from the unmasked regions essentially offer the time-dependent structure guidance to the texture denoising process, benefiting from the time-dependent sparsity of the structure se" + } + ] + } + ], + "index": 10 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8039" + } + ] + } + ], + "index": 11 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 70, + 511, + 194 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 511, + 194 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 511, + 194 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 511, + 194 + ], + "type": "image", + "image_path": "6e9cb9a46f390a2116ea21f7923ae8253e61d18944f5756490cd952966e9e8e1.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 201, + 547, + 232 + ], + "lines": [ + { + "bbox": [ + 46, + 201, + 547, + 232 + ], + "spans": [ + { + "bbox": [ + 46, + 201, + 547, + 232 + ], + "type": "text", + "content": "Figure 3. Illustration of the proposed StrDiffusion pipeline. Our basic idea is to tackle the semantic discrepancy between masked and unmasked regions via the guidance of the progressively sparse structure (a), which guides the texture denoising network (b) to generate the consistent and meaningful denoised results." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 240, + 288, + 321 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 240, + 288, + 321 + ], + "spans": [ + { + "bbox": [ + 46, + 240, + 288, + 321 + ], + "type": "text", + "content": "mantics. Concurrently, we remark that whether the structure guides the texture well greatly depends on the semantic correlation between them. As inspired, an adaptive resampling strategy comes up to monitor the semantic correlation and regulate it via the resampling iteration. Extensive experiments on typical datasets validate the merits of StrDiffusion over the state-of-the-arts." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 334, + 287, + 347 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 334, + 287, + 347 + ], + "spans": [ + { + "bbox": [ + 47, + 334, + 287, + 347 + ], + "type": "text", + "content": "2. Structure-Guided Texture Diffusion Models" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 354, + 287, + 437 + ], + "type": "text", + "content": "Central to our method lies in three aspects: 1) how to tackle the semantic discrepancy between the masked and unmasked regions (Sec.2.2); 2) structure-guided denoising network for image inpainting (Sec.2.3); and 3) more insights on whether the structure guides the texture well (Sec.2.4). Before shedding light on our technique, we elaborate the DDPMs for image inpainting." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 445, + 287, + 470 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 287, + 470 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 287, + 470 + ], + "type": "text", + "content": "2.1. Preliminaries: Denoising Diffusion Probabilistic Models for Image Inpainting" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "spans": [ + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "text", + "content": "Given a completed image " + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "inline_equation", + "content": "I_{gt} \\in \\mathbb{R}^{3 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "text", + "content": " and the binary mask " + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "inline_equation", + "content": "M \\in \\{0,1\\}^{1 \\times H \\times W}" + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "text", + "content": " (0 for masked regions, 1 for unmasked regions), image inpainting aims to recover the masked image " + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "inline_equation", + "content": "I_{m} = I_{gt} \\odot M" + }, + { + "bbox": [ + 46, + 475, + 287, + 581 + ], + "type": "text", + "content": " towards a inpainted image. For diffusion models, the inpainted results are obtained by merging the masked regions of denoised results with the original masked images. The typical DDPMs for inpainting [23] basically involve the forward texture diffusion process and reverse texture denoising process:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "spans": [ + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": "Forward Texture Diffusion Process. During the forward diffusion process, the semantic information from unmasked regions is utilized to guide the texture denoising process for image inpainting. Specifically, for the diffusion process with " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "T" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": " timesteps, we set the initial texture state " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "y_{0} = I_{gt}" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": " and the terminal texture state " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "y_{T}" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": " as the combination of the masked image " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\mu_{y} = I_{m}" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": " and the Gaussian noise " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\varepsilon" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": ". For any state " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "t \\in [0,T]" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": ", the diffusion process " + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "inline_equation", + "content": "\\{y_t\\}_{t=0}^T" + }, + { + "bbox": [ + 46, + 580, + 288, + 689 + ], + "type": "text", + "content": " via the mean-reverting stochastic differential equation (SDE) [26] is defined as" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 112, + 700, + 287, + 712 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 112, + 700, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 112, + 700, + 287, + 712 + ], + "type": "interline_equation", + "content": "\\mathrm {d} y = \\theta_ {t} (\\mu_ {y} - y) d t + \\eta_ {t} \\mathrm {d} w, \\tag {1}", + "image_path": "01123134ab9df0a3de0db265da58bfefb04074864cbf4e0950d61663abc6a727.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "spans": [ + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\eta_{t}" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": " are time-dependent positive parameters that characterize the speed of the mean-reversion and the stochastic volatility during the diffusion process, which are constrained by " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\eta_t^2 /\\theta_t = 2\\lambda^2" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": " for the stationary variance since " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": " is fixed as the noise level applied to " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "y_{T}" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": ". In particular, " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "\\theta_{t}" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": " can be adjusted to construct different noise schedules for the texture; " + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "inline_equation", + "content": "w" + }, + { + "bbox": [ + 304, + 240, + 545, + 344 + ], + "type": "text", + "content": " is a standard Wiener process [25] (known as Brownian motion), which brings the randomness to the differential equation." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "spans": [ + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "type": "text", + "content": "Reverse Texture Denoising Process. To recover the completed image " + }, + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "type": "inline_equation", + "content": "y_{0}" + }, + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "type": "text", + "content": " from the terminal texture state " + }, + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "type": "inline_equation", + "content": "y_{T}" + }, + { + "bbox": [ + 304, + 344, + 545, + 387 + ], + "type": "text", + "content": ", we reverse the diffusion process by simulating the SDE backward in time, formulated as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 334, + 395, + 545, + 409 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 334, + 395, + 545, + 409 + ], + "spans": [ + { + "bbox": [ + 334, + 395, + 545, + 409 + ], + "type": "interline_equation", + "content": "\\mathrm {d} y = \\left[ \\theta_ {t} \\left(\\mu_ {y} - y\\right) - \\eta_ {t} ^ {2} \\nabla_ {y} \\log q _ {t} (y) \\right] \\mathrm {d} t + \\eta_ {t} \\mathrm {d} \\hat {w}, \\tag {2}", + "image_path": "270f29ddecba068fbbdf8c0260fa39fea86c70e69ba54937347e16c4b18573df.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "spans": [ + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\hat{w}" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " is a reverse-time Wiener process and " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "q_{t}(y)" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " stands for the marginal probability density function of texture " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " at time " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": ". The score function " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\nabla_y\\log p_t(y)" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " is unknown, which can be approximated by training a conditional time-dependent neural network " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}(y_{t},t)" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " [12]. Alternatively, we find the optimal reverse texture state " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "y_{t - 1}^{*}" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": " in " + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "inline_equation", + "content": "(t - 1)" + }, + { + "bbox": [ + 304, + 415, + 545, + 502 + ], + "type": "text", + "content": "-th timestep via the maximum likelihood learning, which is achieved by minimizing the negative log-likelihood:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 352, + 507, + 545, + 525 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 352, + 507, + 545, + 525 + ], + "spans": [ + { + "bbox": [ + 352, + 507, + 545, + 525 + ], + "type": "interline_equation", + "content": "y _ {t - 1} ^ {*} = \\arg \\min _ {y _ {t - 1}} [ - \\log q (y _ {t - 1} | y _ {t}, y _ {0}) ]. \\tag {3}", + "image_path": "6054c6e91c80557c40d1f61805217dadc1f9e3af632a688b60ff7348eb37c3eb.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 308, + 531, + 474, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 308, + 531, + 474, + 542 + ], + "spans": [ + { + "bbox": [ + 308, + 531, + 474, + 542 + ], + "type": "text", + "content": "By solving the above objective, we have:" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 341, + 549, + 545, + 603 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 341, + 549, + 545, + 603 + ], + "spans": [ + { + "bbox": [ + 341, + 549, + 545, + 603 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} y _ {t - 1} ^ {*} = \\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\theta} _ {t}}} e ^ {- \\theta_ {t} ^ {\\prime}} \\left(y _ {t} - \\mu_ {y}\\right) \\\\ + \\frac {1 - e ^ {- 2 \\theta_ {t} ^ {\\prime}}}{1 - e ^ {- 2 \\overline {{\\theta}} _ {t}}} e ^ {- \\overline {{\\theta}} _ {t} - 1} (y _ {0} - \\mu_ {y}) + \\mu_ {y}, \\\\ \\end{array}", + "image_path": "c863915ccc57094707365f4a481b1c79c00556be141e73c3f62d63056e8ecc70.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "spans": [ + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\theta_t' = \\int_{t-1}^t \\theta_i \\, \\mathrm{d}i" + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\overline{\\theta}_t = \\int_0^t \\theta_z \\, \\mathrm{d}z" + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "text", + "content": ". Thus, we can optimize " + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "inline_equation", + "content": "\\epsilon_\\phi" + }, + { + "bbox": [ + 305, + 609, + 545, + 636 + ], + "type": "text", + "content": " via the following training objective:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 339, + 643, + 545, + 672 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 643, + 545, + 672 + ], + "spans": [ + { + "bbox": [ + 339, + 643, + 545, + 672 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\beta} ^ {t} (\\phi) = \\sum_ {t = 1} ^ {T} \\beta_ {t} \\mathbb {E} \\left[ \\| y _ {t} - \\left(\\mathrm {d} y _ {t}\\right) _ {\\epsilon_ {\\phi}} - y _ {t - 1} ^ {*} \\| _ {p} \\right], \\tag {5}", + "image_path": "27b2e47a2c7811f047cfc65e184ecfe47c32c87c9fed3b214044ec715d86d6f2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\beta_{t}" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " is positive weight; " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "(\\mathrm{dy}_t)_{\\epsilon_\\phi}" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " denotes the reverse-time SDE in Eq.(2) and its score is predicted via the noise network " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\epsilon_{\\phi}(y_t,t)" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "||\\cdot ||_p" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " stands for the " + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "inline_equation", + "content": "\\ell_p" + }, + { + "bbox": [ + 305, + 677, + 545, + 714 + ], + "type": "text", + "content": " norm." + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8040" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 61, + 70, + 276, + 176 + ], + "blocks": [ + { + "bbox": [ + 61, + 70, + 276, + 176 + ], + "lines": [ + { + "bbox": [ + 61, + 70, + 276, + 176 + ], + "spans": [ + { + "bbox": [ + 61, + 70, + 276, + 176 + ], + "type": "image", + "image_path": "f4a5acfa802c13011525c7f36d67b3ba5900df6644f9b6b496386e13469862c3.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 179, + 289, + 213 + ], + "lines": [ + { + "bbox": [ + 47, + 179, + 289, + 213 + ], + "spans": [ + { + "bbox": [ + 47, + 179, + 289, + 213 + ], + "type": "text", + "content": "Figure 4. Illustration of the diffusion process for the dense texture (a) and sparse structure (b). In particular, the semantic sparsity of the structure is strengthened over time." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 218, + 287, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 218, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 47, + 218, + 287, + 243 + ], + "type": "text", + "content": "2.2. Tackling the Semantic Discrepancy in Diffusion Models for Image Inpainting" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 248, + 287, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 248, + 287, + 331 + ], + "spans": [ + { + "bbox": [ + 46, + 248, + 287, + 331 + ], + "type": "text", + "content": "Based on the above, the existing diffusion models for image inpainting [23] suffer from the semantic discrepancy between the masked and unmasked regions, owing to the dense semantics of the texture. As opposed to the texture, the previous work [20, 34] suggests that the structure are generally considered to be sparse, which motivates us to tackle the discrepancy issue via the structure." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 345, + 287, + 369 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 345, + 287, + 369 + ], + "spans": [ + { + "bbox": [ + 47, + 345, + 287, + 369 + ], + "type": "text", + "content": "2.2.1 Structure Matters: Sparse Semantics benefits the Semantic Consistency" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "spans": [ + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "text", + "content": "To validate such intuition, we design a series of motivation experiments over [23], where we replace the masked image " + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mu_y" + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "text", + "content": " in the terminal texture state " + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "inline_equation", + "content": "y_{T}" + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "text", + "content": " with the masked image " + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "inline_equation", + "content": "\\mu_x" + }, + { + "bbox": [ + 46, + 375, + 287, + 445 + ], + "type": "text", + "content": " from the sparse structure, e.g., the grayscale map and edge map. Our motivation experiments (see Fig.2) reveal the followings:" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 39, + 445, + 287, + 538 + ], + "type": "list", + "angle": 0, + "index": 8, + "blocks": [ + { + "bbox": [ + 39, + 445, + 287, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 39, + 445, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 39, + 445, + 287, + 491 + ], + "type": "text", + "content": "(1) With the dense semantics, the texture performs well in producing meaningful semantics, while suffers from the large semantic discrepancy between the masked and un-masked regions; see Fig.1(a) and Fig.2(a)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 39, + 491, + 287, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 39, + 491, + 287, + 538 + ], + "spans": [ + { + "bbox": [ + 39, + 491, + 287, + 538 + ], + "type": "text", + "content": "(2) The semantically sparse structure benefits the consistent semantics, while incurs the semantics loss in the inpainted results; see the grayscale and edge map version of [23] in Fig.2(b)(c)." + } + ] + } + ], + "index": 7 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 46, + 539, + 287, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 539, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 46, + 539, + 287, + 666 + ], + "type": "text", + "content": "The above observations indicate that, unlike [23] that fixes the texture guidance from the unmasked regions, the structure guidance from the unmasked regions varies to the texture over time; meanwhile, merely involving the semantics of either dense texture or sparse structure fails to obtain the desirable inpainted results, since it actually attempts to perform the trade-off between the consistent and meaningful semantics. Motivated by that, we propose to exploit structure as an auxiliary, which exhibits the sparser semantics than the texture, so as to tackle the discrepancy issue, as remarked below." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 666, + 287, + 714 + ], + "type": "text", + "content": "Remark 1. Strengthening the semantic sparsity of the structure over time. Throughout the texture diffusion process, the semantic discrepancy between the masked and un-masked regions progressively increases as the timestep goes" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 154 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 154 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 154 + ], + "type": "text", + "content": "towards to a totally masked status (see Fig.4(a)). To decrease the semantic discrepancy, we aim to strengthen the semantic sparsity of the structure over time, as opposed to the texture, during diffusion process. Concretely, the sparse grayscale map is degraded into the combination of the sparser masked edge map and the Gaussian noise via the noise schedule; see Fig.4(b)." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 155, + 545, + 212 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 155, + 545, + 212 + ], + "spans": [ + { + "bbox": [ + 304, + 155, + 545, + 212 + ], + "type": "text", + "content": "Our basic idea is to tackle the semantic discrepancy issue via the guidance of the structure during the denoising process, thus simplify the texture denoising objective, i.e., the optimal solution (the ground truth) to the denoising process, which is discussed in the next." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 228, + 545, + 250 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 228, + 545, + 250 + ], + "spans": [ + { + "bbox": [ + 306, + 228, + 545, + 250 + ], + "type": "text", + "content": "2.2.2 Optimal Solution to the Denoising Process Under the Guidance of the Structure" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "spans": [ + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "type": "text", + "content": "As per the above observations, during the texture diffusion process, the distribution of the added noise in each timestep is disturbed by the semantic discrepancy between the masked and unmasked regions, incurring the difficulty to estimate such noise distribution via a noise-prediction network during the denoising process. Instead of focusing on texture, we exploit both structure and texture for diffusion process, where the sparsity of structure alleviates the semantic discrepancy, and the texture attempts to preserve the meaningful semantic. Unlike the diffusion process to simultaneously exploit structure and texture, for denoising process, the structure firstly generates the consistent semantics " + }, + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "type": "inline_equation", + "content": "(x_{t - 1})" + }, + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "type": "text", + "content": " between masked and unmasked regions, which subsequently guides the texture to generate the meaningful semantics " + }, + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "type": "inline_equation", + "content": "(y_{t - 1})" + }, + { + "bbox": [ + 304, + 258, + 546, + 456 + ], + "type": "text", + "content": "; see Fig.3. By the assistance of structure for StrDiffusion, the texture diffusion process generates both consistent and meaningful inpainting output." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 456, + 545, + 596 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 456, + 545, + 596 + ], + "spans": [ + { + "bbox": [ + 304, + 456, + 545, + 596 + ], + "type": "text", + "content": "Remark 2. Different from the typical DDPMs for inpainting [22, 23], our StrDiffusion exploits the semantic consistency of the denoised structure to guide the texture denoising process, yielding both consistent and meaningful denoised results. In particular, we view the structure as an auxiliary to guide the texture rather than the inverse; the reason is two-fold: 1) during the inference denoising process, the masked regions mainly focus on the texture to be inpainted rather than the structure; 2) the structure focuses on the consistency between the masked and unmasked regions, lacking the meaningful semantics, hence still relies on the texture for inpainting." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 596, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 596, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 596, + 545, + 628 + ], + "type": "text", + "content": "Thanks to the guidance of the structure, the reverse transition for the texture in Eq.(3) can be reformulated via Bayes' rule as follows:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 320, + 635, + 545, + 685 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 320, + 635, + 545, + 685 + ], + "spans": [ + { + "bbox": [ + 320, + 635, + 545, + 685 + ], + "type": "interline_equation", + "content": "\\begin{array}{r l} q \\left(y _ {t - 1} \\mid y _ {t}, x _ {t - 1}\\right) & = \\frac {q \\left(y _ {t - 1} \\mid y _ {t}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1} , y _ {t}\\right)}{q \\left(x _ {t - 1} \\mid y _ {t}\\right)} \\\\ & = \\frac {q \\left(y _ {t} \\mid y _ {t - 1}\\right) q \\left(y _ {t - 1}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1}\\right)}{q \\left(x _ {t - 1} , y _ {t}\\right)}, \\end{array} \\tag {6}", + "image_path": "ca70ab6b8058732ef184b539d6891d6da022116319e709e61df4eb9f99d0f239.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": "where the texture " + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "inline_equation", + "content": "y_{t - 1}" + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": ", together with the structure " + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": ", are actually conditioned on their initial states, i.e.," + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "8041" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "y_{0}" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": " , during the diffusion process, hence " + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "q(y_{t - 1}) = q(y_{t - 1}|y_0)" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "q(x_{t - 1},y_t) = q(x_{t - 1})q(y_t|x_{t - 1}) =" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "inline_equation", + "content": "q(x_{t - 1}|x_0)q(y_t|x_{t - 1},y_0)" + }, + { + "bbox": [ + 47, + 72, + 287, + 106 + ], + "type": "text", + "content": " . Eq.(6) can thus be simplified as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 88, + 115, + 286, + 175 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 88, + 115, + 286, + 175 + ], + "spans": [ + { + "bbox": [ + 88, + 115, + 286, + 175 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} q \\left(y _ {t - 1} \\mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\\right) \\\\ = \\frac {q \\left(y _ {t} \\mid y _ {t - 1}\\right) q \\left(x _ {t - 1} \\mid y _ {t - 1}\\right)}{q \\left(y _ {t} \\mid x _ {t - 1} , y _ {0}\\right)} \\times \\frac {q \\left(y _ {t - 1} \\mid y _ {0}\\right)}{q \\left(x _ {t - 1} \\mid x _ {0}\\right)} \\tag {7} \\\\ \\approx \\frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})}, \\\\ \\end{array}", + "image_path": "486d1f36b81386d8587bfa3289b0ce4e33db696b71b80ebc4338c4cb9023b1eb.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "spans": [ + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "inline_equation", + "content": "q(y_{t}|y_{t - 1})\\approx q(y_{t}|x_{t - 1},y_{0})" + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "inline_equation", + "content": "q(x_{t - 1}|y_{t - 1})\\approx 1" + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "content": ", since the texture " + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "inline_equation", + "content": "y_{t}" + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "content": " can be obtained via the conditioned auxiliary structure " + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "content": " during the diffusion process and initial texture " + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "inline_equation", + "content": "y_{0}" + }, + { + "bbox": [ + 47, + 182, + 287, + 258 + ], + "type": "text", + "content": " as Remarked above. Based on Eq.(7), the optimal reverse state is naturally acquired by minimizing the negative log-likelihood (see the supplementary material for more inference details):" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 80, + 266, + 287, + 308 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 266, + 287, + 308 + ], + "spans": [ + { + "bbox": [ + 80, + 266, + 287, + 308 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {y} _ {t - 1} ^ {*} = \\underset {y _ {t - 1}} {\\arg \\min } \\left[ - \\log q \\left(y _ {t - 1} \\mid y _ {t}, y _ {0}, x _ {t - 1}, x _ {0}\\right) \\right] \\tag {8} \\\\ = \\arg \\min _ {y _ {t - 1}} [ - \\log \\frac {q (y _ {t - 1} | y _ {0})}{q (x _ {t - 1} | x _ {0})} ], \\\\ \\end{array}", + "image_path": "ee925cf355a4c15f8ae645233292601401640f079f6bf27a1ffab07150ffc4a8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "spans": [ + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t - 1}^{*}" + }, + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "type": "text", + "content": " denotes the ideal state reversed from " + }, + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "type": "inline_equation", + "content": "\\tilde{y}_t" + }, + { + "bbox": [ + 47, + 316, + 287, + 349 + ], + "type": "text", + "content": " under the structure guidance. To solve the above objective, we compute its gradient and setting it to be zero:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 61, + 357, + 287, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 357, + 287, + 385 + ], + "spans": [ + { + "bbox": [ + 61, + 357, + 287, + 385 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {\\tilde {y} _ {t - 1} ^ {*}} \\left\\{- \\log q \\left(\\tilde {y} _ {t - 1} ^ {*} \\mid y _ {t}, y _ {0}, x _ {t - 1} ^ {*}, x _ {0}\\right) \\right\\} = \\\\ - \\nabla_ {\\tilde {y} _ {t - 1} ^ {*}} \\log q \\left(\\tilde {y} _ {t - 1} ^ {*} \\mid y _ {0}\\right) + \\nabla_ {x _ {t - 1} ^ {*}} \\log q \\left(x _ {t - 1} ^ {*} \\mid x _ {0}\\right) = 0, \\tag {9} \\\\ \\end{array}", + "image_path": "e4ce369b3c986a3908e3e5e43c2b01fe45f58f0533548dcdc1ea9a3565b0957b.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "spans": [ + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "type": "inline_equation", + "content": "x_{t - 1}^{*}" + }, + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "type": "text", + "content": " is the ideal state reversed from " + }, + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "type": "inline_equation", + "content": "x_{t}" + }, + { + "bbox": [ + 47, + 392, + 286, + 415 + ], + "type": "text", + "content": " for the structure, similar in spirit to Eq.(4), given as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 84, + 423, + 287, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 423, + 287, + 475 + ], + "spans": [ + { + "bbox": [ + 84, + 423, + 287, + 475 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} x _ {t - 1} ^ {*} = \\frac {1 - e ^ {- 2 \\bar {\\delta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}} \\left(x _ {t} - \\mu_ {x}\\right) \\tag {10} \\\\ + \\frac {1 - e ^ {- 2 \\delta_ {t} ^ {\\prime}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\bar {\\delta} _ {t - 1}} (x _ {0} - \\mu_ {x}) + \\mu_ {x}, \\\\ \\end{array}", + "image_path": "3fdd5f6a1509845211f90d529666a3d258f7673964c1fd9c07464c0c32ce8c41.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": "where structure " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\mu_{x}" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": " is the masked version of its initial state " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "x_0" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\delta_t" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": " is time-dependent parameter that characterizes the speed of the mean-reversion. To simplify the notation, we have " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\delta_t' = \\int_{t-1}^t \\delta_i \\, \\mathrm{d}i" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\overline{\\delta}_{t-1} = \\int_0^{t-1} \\delta_z \\, \\mathrm{d}z" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\overline{\\delta}_t = \\overline{\\delta}_{t-1} + \\delta_t'" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": ". Since Eq.(9) is linear, we can derive " + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t-1}^*" + }, + { + "bbox": [ + 47, + 483, + 287, + 542 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 69, + 551, + 287, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 551, + 287, + 666 + ], + "spans": [ + { + "bbox": [ + 69, + 551, + 287, + 666 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {y} _ {t - 1} ^ {*} = \\underbrace {\\left(\\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}}\\right) \\left(x _ {t} - \\mu_ {x}\\right)} _ {\\text {C o n s i s t e n c y t e r m f o r m a s k e d r e g i o n s}} \\\\ - \\underbrace {\\left(\\frac {1 - e ^ {- 2 \\bar {\\theta} _ {t - 1}}}{1 - e ^ {- 2 \\bar {\\delta} _ {t}}} e ^ {- \\delta_ {t} ^ {\\prime}}\\right) e ^ {- \\bar {\\delta} _ {t}} \\left(x _ {0} - \\mu_ {x}\\right)} _ {\\text {B a l i n c e t e r m f o r m a x i k e d r e g i o n s}} \\tag {11} \\\\ + \\underbrace {e ^ {- \\overline {{\\theta}} _ {t - 1}} (y _ {0} - \\mu_ {y})} _ {\\text {S e m a n t i c s t e r m f o r m a k e d r e g i o n s}} + \\underbrace {\\mu_ {y}} _ {\\text {U n m a x k e d r e g i o n s}}. \\\\ \\end{array}", + "image_path": "faf5e892d563dcb3bbb37608db72ee93af98a7c3e17d90ffac638eec9a4646d6.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "type": "text", + "content": "Remark 3. Eq.(11) implies that the ideal reverse state " + }, + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t - 1}^{*}" + }, + { + "bbox": [ + 47, + 678, + 287, + 713 + ], + "type": "text", + "content": " focuses more on the semantic consistency based on the semantic generation for image inpainting, to alleviate" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": "the semantic discrepancy issues. Under the guidance of the sparse structure, " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t-1}^{*}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " tends to maintain the consistency between masked and unmasked regions in the early stage of the denoising process, while recovering the reasonable semantics in the late stage. Specifically, " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t-1}^{*}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " is mainly composed of four parts: 1) the consistency term for the structure " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "x_{t} - \\mu_{x}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " is utilized to form the masked regions inside the denoised texture and keep the semantic consistency with the unmasked regions; 2) the semantics term for the texture " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "y_{0} - \\mu_{y}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " progressively provides meaningful semantics for masked regions as the denoising process progresses; 3) the negative balance term " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "x_{0} - \\mu_{x}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " adaptively surpasses the semantic information from " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "y_{0} - \\mu_{y}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " in the early stage and the consistency information from " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "x_{t} - \\mu_{x}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " in the late stage; 4) the unmasked texture " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "\\mu_{y}" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": " retains the semantics of the unmasked regions for the denoised texture. All four parts together constitute the optimal solution to the structure-guided denoising process in the " + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "inline_equation", + "content": "(t-1)" + }, + { + "bbox": [ + 304, + 72, + 545, + 317 + ], + "type": "text", + "content": "-th timestep, i.e., the ground truth to optimize the noise-prediction network, thus yielding the denoised results with the consistent and desirable semantics (see Fig.6), as discussed in the next section." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 323, + 545, + 359 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 323, + 545, + 359 + ], + "spans": [ + { + "bbox": [ + 306, + 323, + 545, + 359 + ], + "type": "text", + "content": "2.3. Structure-Guided Denoising Process: How does the Structure Guide the Texture Denoising Process?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "spans": [ + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": "With the above optimal solution (i.e., the ground truth) in Eq.(11), the goal of the structure-guided denoising process is to estimate it via a noise-prediction neural network " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " under the guidance of the structure, where " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " is trained to predict the mean of the noise with the fixed variance of noise [25]. Unlike the conventional texture denoising process in [23], the structure denoising network is pre-trained as an auxiliary to obtain the denoised structure, e.g., " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " in the " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " -th timestep. To fulfill the structure guidance, a multi-scale spatially adaptive normalization strategy is devised to condition a time-dependent noise network " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " for the texture, which deploys the spatially adaptive normalization and denormalization strategy [24] to incorporate the statistical information over the feature map across varied layers; see Fig.3. Formally, given " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " from a pre-trained structure denoising network, we achieve the structure guidance by reconstructing the feature map on the " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " -th layer of CNNs in time-dependent noise network " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " for the texture (i.e., " + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "inline_equation", + "content": "F_{k}^{t}\\in \\mathbb{R}^{C_{k}\\times H_{k}\\times W_{k}}" + }, + { + "bbox": [ + 304, + 363, + 545, + 568 + ], + "type": "text", + "content": " ) as" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 316, + 574, + 545, + 691 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 316, + 574, + 545, + 691 + ], + "spans": [ + { + "bbox": [ + 316, + 574, + 545, + 691 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\tilde {F} _ {k} ^ {t} = \\operatorname {c o n v} _ {\\gamma} \\left(x _ {t - 1}\\right) \\frac {F _ {k} ^ {t} - \\mu_ {k} ^ {t}}{\\sigma_ {k} ^ {t}} + \\operatorname {c o n v} _ {\\beta} \\left(x _ {t - 1}\\right), \\\\ \\mu_ {k} ^ {t} (h _ {k}, w _ {k}) = \\frac {1}{C _ {k}} \\sum_ {c _ {k} = 1} ^ {C _ {k}} F _ {k} ^ {t} (h _ {k}, w _ {k}, c _ {k}), \\\\ \\sigma_ {k} ^ {t} (h _ {k}, w _ {k}) = \\sqrt {\\frac {1}{C _ {k}} \\sum_ {c _ {k} = 1} ^ {C _ {k}} \\left(F _ {k} ^ {t} \\left(h _ {k} , w _ {k} , c _ {k}\\right) - \\mu_ {k} ^ {t} \\left(h _ {k} , w _ {k}\\right)\\right) ^ {2}}, \\\\ h _ {k} = 1, 2, \\dots , H _ {k}, w _ {k} = 1, 2, \\dots , W _ {k}, \\tag {12} \\\\ \\end{array}", + "image_path": "92614ff46dc5b9376eaa2e08789c51ca02073f4bb6740828111bd757bda8a421.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "inline_equation", + "content": "conv_{\\gamma}(\\cdot)" + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "inline_equation", + "content": "conv_{\\beta}(\\cdot)" + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": " denote the mappings that convert the input " + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 306, + 691, + 545, + 713 + ], + "type": "text", + "content": " to the scaling and bias values." + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8042" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "inline_equation", + "content": "\\mu_k^t (h_k,w_k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "inline_equation", + "content": "\\sigma_k^t (h_k,w_k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "text", + "content": " are the statistical mean and variance of the pixels across different channels at the position " + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "inline_equation", + "content": "(h_k,w_k)" + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "text", + "content": ". Based on that, we turn to optimize the noise network " + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}(y_t,x_{t - 1},t)" + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "text", + "content": " to estimate the optimal solution " + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t - 1}^{*}" + }, + { + "bbox": [ + 47, + 72, + 287, + 137 + ], + "type": "text", + "content": " (i.e., the ground truth) to the denoising process. To this end, the overall training objective is formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 84, + 144, + 287, + 179 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 84, + 144, + 287, + 179 + ], + "spans": [ + { + "bbox": [ + 84, + 144, + 287, + 179 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {\\tilde {\\beta}} ^ {t} (\\phi) = \\sum_ {t = 1} ^ {T} \\tilde {\\beta} _ {t} \\mathbb {E} [ \\| \\underbrace {y _ {t} - (\\mathrm {d} y _ {t}) _ {\\tilde {\\epsilon} _ {\\phi}}} _ {\\text {D e n o i s e d} y _ {t - 1}} - \\tilde {y} _ {t - 1} ^ {*} \\| _ {p} ], \\tag {13}", + "image_path": "3b49fc392511e8ab5890ddda109ad4302597440b840600ca9943feb529a3c04d.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "spans": [ + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "type": "inline_equation", + "content": "\\tilde{\\beta}_t" + }, + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "type": "text", + "content": " is positive weight; " + }, + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "type": "inline_equation", + "content": "(\\mathrm{dy}_t)_{\\tilde{\\epsilon}_{\\phi}}" + }, + { + "bbox": [ + 47, + 187, + 287, + 247 + ], + "type": "text", + "content": " denotes the estimated reverse noise by the noise-prediction network. By minimizing Eq.(13), the inpainted results with consistent and meaningful semantics can be generated during the structure-guided denoising process." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 253, + 187, + 266 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 253, + 187, + 266 + ], + "spans": [ + { + "bbox": [ + 47, + 253, + 187, + 266 + ], + "type": "text", + "content": "2.4. More Insights on Eq.(13)" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 271, + 287, + 318 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 271, + 287, + 318 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 287, + 318 + ], + "type": "text", + "content": "To validate the effectiveness of the guidance from the structure to the texture denoising process, we provide more insights on Eq.(13) by studying the semantic correlation between the denoised texture and structure during inference." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 332, + 254, + 342 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 332, + 254, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 332, + 254, + 342 + ], + "type": "text", + "content": "2.4.1 Correlation Measure via a Discriminator" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "spans": [ + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": "Apart from the semantic structure sparsity, the semantic correlation between the structure and texture is crucial to achieve the semantic consistency between the masked and unmasked regions. To measure such semantic correlation, we adopt a discriminator network " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": " to yield the correlation score " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "D(y_{t - 1},x_{t - 1},t - 1)" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": " (abbreviated as " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "D(y_{t - 1},x_{t - 1})" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": ") where the denoised texture " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "y_{t - 1}" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": " and structure " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "x_{t - 1}" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": ", together with the timestep " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "t - 1" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": ", serve as the inputs. To this end, we present a discriminator loss and a triplet loss to optimize " + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 47, + 350, + 287, + 466 + ], + "type": "text", + "content": ", as described below:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "content": "Discriminator Loss. During the denoising process, to provide the desirable guidance for the texture, the current structure " + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "content": " is expected to be closely correlated with the texture " + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "inline_equation", + "content": "y_{t-1}" + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "content": " in the current timestep, instead of the previous one " + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "inline_equation", + "content": "y_t" + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "content": ". Hence, we aim to discriminate " + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "inline_equation", + "content": "y_{t-1}" + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "inline_equation", + "content": "y_t" + }, + { + "bbox": [ + 47, + 466, + 287, + 529 + ], + "type": "text", + "content": " via a discriminator loss below:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 93, + 535, + 287, + 561 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 535, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 93, + 535, + 287, + 561 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {d i s} = - \\mathbb {E} _ {y _ {t - 1}} [ \\log (D (y _ {t - 1}, x _ {t - 1})) ] \\tag {14} \\\\ - \\mathbb {E} _ {y _ {t}} \\left[ \\log \\left(1 - D \\left(y _ {t}, x _ {t - 1}\\right)\\right) \\right]. \\\\ \\end{array}", + "image_path": "6f2971243b6995cb10be0bce9fb3b856bc6ab4ca9fd7716cddbbb5b1376418f1.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 573, + 287, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 573, + 287, + 628 + ], + "spans": [ + { + "bbox": [ + 47, + 573, + 287, + 628 + ], + "type": "text", + "content": "Triplet Loss. Since the unmasked regions almost possess much denser semantics information compared to the masked ones during the denoising process, to well evaluate the correlation, Eq.(14) is encouraged to focus more on the unmasked regions, which is achieved via a triplet loss:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 61, + 633, + 286, + 660 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 633, + 286, + 660 + ], + "spans": [ + { + "bbox": [ + 61, + 633, + 286, + 660 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {t r i} = \\max (\\| D (\\bar {y} _ {t - 1}, x _ {t - 1}) - D (y _ {t - 1}, x _ {t - 1})) \\| _ {2} \\tag {15} \\\\ - \\| D \\left(\\bar {y} _ {t - 1}, x _ {t - 1}\\right) - D \\left(y _ {t}, x _ {t - 1}\\right) \\| _ {2} + \\alpha , 0), \\\\ \\end{array}", + "image_path": "b8dd58d40b0c8482736b79a795bbb09f7562704b75d9d751e3ccfe56a0d12691.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "spans": [ + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\bar{y}_{t-1} = y_{t-1} \\odot M + y_t \\odot (1 - M)" + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": " is constructed to associate the unmasked regions of " + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "inline_equation", + "content": "y_{t-1}" + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": " and the masked ones of " + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "inline_equation", + "content": "y_t" + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": ". " + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": " is a margin parameter and " + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "inline_equation", + "content": "||\\cdot||_2" + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "inline_equation", + "content": "\\ell_2" + }, + { + "bbox": [ + 47, + 666, + 287, + 712 + ], + "type": "text", + "content": " norm." + } + ] + } + ], + "index": 11 + }, + { + "type": "image", + "bbox": [ + 321, + 70, + 532, + 164 + ], + "blocks": [ + { + "bbox": [ + 321, + 70, + 532, + 164 + ], + "lines": [ + { + "bbox": [ + 321, + 70, + 532, + 164 + ], + "spans": [ + { + "bbox": [ + 321, + 70, + 532, + 164 + ], + "type": "image", + "image_path": "4df6491798eaee1af14361f5391668593dc6f2b94c741b9f49056a8aed9047af.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 169, + 545, + 201 + ], + "lines": [ + { + "bbox": [ + 305, + 169, + 545, + 201 + ], + "spans": [ + { + "bbox": [ + 305, + 169, + 545, + 201 + ], + "type": "text", + "content": "Figure 5. Illustration of the adaptive resampling strategy, which adaptively regulates the semantic correlation between the denoised texture and structure according to the score from the discriminator." + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 209, + 518, + 221 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 209, + 518, + 221 + ], + "spans": [ + { + "bbox": [ + 306, + 209, + 518, + 221 + ], + "type": "text", + "content": "Total Loss. In summary, we finalize the total loss as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 383, + 232, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 232, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 383, + 232, + 545, + 243 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\mathcal {L} _ {\\text {d i s}} + \\lambda_ {\\text {t r i}} \\mathcal {L} _ {\\text {t r i}}, \\tag {16}", + "image_path": "6db0fb5340ba24c6e2ef7d92b662778ff5dd5c3441ca65df2e31f07d662ba820.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "spans": [ + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "inline_equation", + "content": "\\lambda_{tri}" + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "text", + "content": " denotes the balance parameter, which is empirically set as 1 in our experiments. With Eq.(16) to be minimized, " + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "text", + "content": " can be trained to evaluate the semantic correlation, where the small score value from " + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "inline_equation", + "content": "D" + }, + { + "bbox": [ + 305, + 255, + 545, + 346 + ], + "type": "text", + "content": " indicates that the correlation between the texture and structure is not strong, weakening the guidance of the structure. To enhance the semantic correlation, an adaptive resampling strategy comes up, which is elaborated in the next section." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 306, + 364, + 468, + 376 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 364, + 468, + 376 + ], + "spans": [ + { + "bbox": [ + 306, + 364, + 468, + 376 + ], + "type": "text", + "content": "2.4.2 Adaptive Resampling Strategy" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "spans": [ + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": "Different from the previous work [22] that directly performs the resampling strategy without the clear measurement, we devise an adaptive resampling strategy, which regulates the semantic correlation between the texture " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "(e.g., y_{t-1})" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " and structure " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "(e.g., x_{t-1})" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " according to the score value from a discriminator in Sec.2.4.1. Specifically, when the score value of the semantic correlation between " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "y_{t-1}" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " is smaller than a specific threshold " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "\\Delta" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " (see the supplementary material for more intuitions), we first obtain " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "\\tilde{x}_t" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " by adding the noise to " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "x_{t-1}" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": ", then receive a updated " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{t-1}" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": " by denoising " + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "inline_equation", + "content": "\\tilde{x}_t" + }, + { + "bbox": [ + 305, + 383, + 545, + 511 + ], + "type": "text", + "content": ", which are described as follows:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 326, + 521, + 544, + 538 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 326, + 521, + 544, + 538 + ], + "spans": [ + { + "bbox": [ + 326, + 521, + 544, + 538 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {t} = x _ {t - 1} + \\delta_ {t - 1} \\left(\\mu_ {x} - x _ {t - 1}\\right) d t + \\sigma_ {t - 1} \\mathrm {d} w, \\tag {17}", + "image_path": "0fb34f070e3efdf32a75a66f4835f2fe565a05f266f14454b35962e17f87c268.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 328, + 536, + 417, + 548 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 536, + 417, + 548 + ], + "spans": [ + { + "bbox": [ + 328, + 536, + 417, + 548 + ], + "type": "interline_equation", + "content": "\\tilde {x} _ {t - 1} = \\tilde {x} _ {t} - (\\mathrm {d} x _ {t}) _ {\\bar {\\epsilon} _ {\\varphi}}.", + "image_path": "10812a76af1abb1bbe88c531def3826979d5c9ddcf509fdec14e2ce41af4e505.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "spans": [ + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "content": "Based on Eq.(17), " + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{t - 1}" + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "content": " is utilized to generate an updated " + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t - 1}" + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "content": " via the trained noise network " + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\tilde{\\epsilon}_{\\phi}(y_t,\\tilde{x}_{t - 1},t)" + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "content": ". Following that, we evaluate the correlation between " + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\tilde{y}_{t - 1}" + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "inline_equation", + "content": "\\tilde{x}_{t - 1}" + }, + { + "bbox": [ + 306, + 558, + 545, + 605 + ], + "type": "text", + "content": " again, and repeat the above procedure; see Fig.5." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 306, + 616, + 387, + 630 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 616, + 387, + 630 + ], + "spans": [ + { + "bbox": [ + 306, + 616, + 387, + 630 + ], + "type": "text", + "content": "3. Experiments" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 306, + 636, + 438, + 648 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 636, + 438, + 648 + ], + "spans": [ + { + "bbox": [ + 306, + 636, + 438, + 648 + ], + "type": "text", + "content": "3.1. Implementation Details" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 654, + 545, + 713 + ], + "type": "text", + "content": "We experimentally evaluate StrDiffusion over three typical datasets, including: Paris StreetView (PSV) [6] is a collection of street view images in Paris, consisting of 14.9k images for training and 100 images for validation; CelebA [21] is the human face dataset with 30k aligned face images," + } + ] + } + ], + "index": 24 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8043" + } + ] + } + ], + "index": 25 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 77, + 71, + 325, + 154 + ], + "blocks": [ + { + "bbox": [ + 77, + 71, + 325, + 154 + ], + "lines": [ + { + "bbox": [ + 77, + 71, + 325, + 154 + ], + "spans": [ + { + "bbox": [ + 77, + 71, + 325, + 154 + ], + "type": "image", + "image_path": "fc42c73d370088e6b511259be2b6d5ae782110ffd5e717490e8df90fb6b142dd.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 159, + 545, + 171 + ], + "lines": [ + { + "bbox": [ + 46, + 159, + 545, + 171 + ], + "spans": [ + { + "bbox": [ + 46, + 159, + 545, + 171 + ], + "type": "text", + "content": "Figure 6. Illustration of the denoised results for IR-SDE [23] (a) and StrDiffusion (b) in the varied timesteps during the denoising process." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 328, + 70, + 517, + 155 + ], + "blocks": [ + { + "bbox": [ + 328, + 70, + 517, + 155 + ], + "lines": [ + { + "bbox": [ + 328, + 70, + 517, + 155 + ], + "spans": [ + { + "bbox": [ + 328, + 70, + 517, + 155 + ], + "type": "image", + "image_path": "70eca2aa58a7335286ed107ac72939091c65d890998cbdbd209c5822b0744d6c.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 175, + 546, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 175, + 546, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 175, + 546, + 209 + ], + "type": "text", + "content": "Table 1. Comparison of quantitative results (i.e., PSNR, SSIM [30] and FID [11]) under varied mask ratios on Places2 with irregular mask dataset. ↑: Higher is better; ↓: Lower is better; -: no results are reported. The percentage (\\%) represents the ratios of varied irregular masked regions to the completed image. The best results are reported with **boldface**." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 97, + 217, + 493, + 312 + ], + "blocks": [ + { + "bbox": [ + 97, + 217, + 493, + 312 + ], + "lines": [ + { + "bbox": [ + 97, + 217, + 493, + 312 + ], + "spans": [ + { + "bbox": [ + 97, + 217, + 493, + 312 + ], + "type": "table", + "html": "
MetricsPSNR↑SSIM↑FID↓
MethodVenue10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%10-20%20-30%30-40%40-50%
RFR [15]CVPR' 2027.2624.8322.7521.110.9290.8910.8300.75617.8822.9430.6838.69
PENNet [35]CVPR' 1926.7823.5321.8020.480.9460.8940.8410.78120.4037.2253.7467.08
HiFill [32]CVPR' 2027.5024.6422.8121.230.9540.9140.8730.81616.9529.3042.8857.12
FAR [3]ECCV' 2228.3625.4823.6022.180.9420.9030.8610.818----
HAN [5]ECCV' 2228.9325.4423.0621.380.9570.9030.8390.76212.0120.1528.8537.63
CMT [14]ICCV' 2329.2825.8823.5621.700.9600.9240.8850.841----
MEDFE [13]ECCV' 2028.1325.0222.9821.530.9580.9190.8740.82514.4127.5238.4553.05
CTSDF [9]ICCV' 2128.9125.3622.9421.210.9520.9010.8340.75515.7227.8842.4457.78
ZITS [7]CVPR' 2228.3125.4023.5122.110.9420.9020.8600.817----
RePaint* [22]CVPR' 2229.1626.0224.0122.110.9670.9330.9150.86211.1620.6228.4941.16
IR-SDE [23]ICML' 2328.9825.3723.9321.680.9610.9280.9080.86412.0321.3429.3739.77
StrDiffusion (Ours)-29.4526.2824.4322.370.9730.9410.9170.8748.75016.1623.7236.93
", + "image_path": "76e9257e04f8000ae1dd58f21dd0dfb58471672070ce6c81f3da0751576df070.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_body" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "spans": [ + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "text", + "content": "which is split into 26k training images and 4k validation images; Places2 [37] contains more than 1.8M natural images from varied scenes. The network is trained using " + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "text", + "content": " images with irregular masks [19]. The noise-prediction network is constructed by removing group normalization layers and self-attention layers in the U-Net in DDPM [12] for inference efficiency. We adopt the Adam optimizer with " + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "inline_equation", + "content": "\\beta_{1} = 0.9" + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.99" + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "text", + "content": ". We set the timestep " + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "inline_equation", + "content": "T = 100" + }, + { + "bbox": [ + 46, + 319, + 289, + 436 + ], + "type": "text", + "content": " for the diffusion model. All the experiments are implemented with the pytorch framework and run on 4 NVIDIA 2080TI GPU." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 445, + 207, + 458 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 445, + 207, + 458 + ], + "spans": [ + { + "bbox": [ + 47, + 445, + 207, + 458 + ], + "type": "text", + "content": "3.2. Why can StrDiffusion Work?" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 464, + 287, + 651 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 464, + 287, + 651 + ], + "spans": [ + { + "bbox": [ + 46, + 464, + 287, + 651 + ], + "type": "text", + "content": "In this section, the core goal is to confirm that the intuition of StrDiffusion — the progressively sparse structure over time is beneficial to alleviate the semantic discrepancy issue between the masked and unmasked regions during the denoising process. We conduct the experiments on PSV and Places2 dataset. Fig.6 illustrates that, as the denoising process progresses, the denoised results from IR-SDE [23] always address the clear semantic discrepancy between the masked and unmasked regions (see Fig.6(a)); while for StrDiffusion, such discrepancy progressively degraded until vanished, yielding the consistent semantics (see Fig.6(b)), confirming our proposals in Sec.2.2.2 — the guidance of the structure benefits the consistent semantics between the masked and unmasked regions while the texture retains the reasonable semantics in the inpainted results; see the supplementary material for more results." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 659, + 231, + 672 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 231, + 672 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 231, + 672 + ], + "type": "text", + "content": "3.3. Comparison with State-of-the-arts" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 677, + 287, + 715 + ], + "type": "text", + "content": "To validate the superiority of StrDiffusion, we compare it with the typical inpainting models, including: RFR [15] adopts the CNNs to encoding the local information;" + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 320, + 317, + 533, + 501 + ], + "blocks": [ + { + "bbox": [ + 320, + 317, + 533, + 501 + ], + "lines": [ + { + "bbox": [ + 320, + 317, + 533, + 501 + ], + "spans": [ + { + "bbox": [ + 320, + 317, + 533, + 501 + ], + "type": "image", + "image_path": "002052159238cc066b08f3cb3d02a7c953c19da628d9e82723a205b24fef3127.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 506, + 545, + 550 + ], + "lines": [ + { + "bbox": [ + 304, + 506, + 545, + 550 + ], + "spans": [ + { + "bbox": [ + 304, + 506, + 545, + 550 + ], + "type": "text", + "content": "Figure 7. Comparison of the inpainted results with the state-of-the-arts under varied irregular masks on PSV, CelebA and Places2. Our StrDiffusion delivers the desirable inpainted results (marked as the red box) against others." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 559, + 546, + 700 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 559, + 546, + 700 + ], + "spans": [ + { + "bbox": [ + 304, + 559, + 546, + 700 + ], + "type": "text", + "content": "PENNet[35], HiFill[32], FAR[3], HAN[5] and CMT[14] globally associate the masked regions with unmasked ones via self-attention mechanism; MEDFE[13], CTSDG[9], ZITS[7] and DGTS[20] focus on the guidance of the structure, while ignore the semantic consistency between the structure and texture; RePaint[22] and IR-SDE[23] benefit from DDPMs whereas overlook the semantic consistency. For fair comparison, we reproduce RePaint by utilizing the pre-trained models from IR-SDE, denoted as RePaint*. Notably, the inpainted results are obtained by merging the masked regions from the denoised results with the original masked image." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 714 + ], + "type": "text", + "content": "Quantitative and Qualitative analysis. The quantitative" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8044" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 65, + 70, + 166, + 131 + ], + "blocks": [ + { + "bbox": [ + 65, + 70, + 166, + 131 + ], + "lines": [ + { + "bbox": [ + 65, + 70, + 166, + 131 + ], + "spans": [ + { + "bbox": [ + 65, + 70, + 166, + 131 + ], + "type": "image", + "image_path": "27c785229cfa990ca01cb1020e3aeae67f4fc034aa753a2afea252b4f19b2e80.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 170, + 70, + 271, + 131 + ], + "blocks": [ + { + "bbox": [ + 170, + 70, + 271, + 131 + ], + "lines": [ + { + "bbox": [ + 170, + 70, + 271, + 131 + ], + "spans": [ + { + "bbox": [ + 170, + 70, + 271, + 131 + ], + "type": "image", + "image_path": "5a893a139a8f49b7c786a65050dbcb1b021a5c40fa4763aaa0948467b66debb8.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 64, + 132, + 165, + 191 + ], + "blocks": [ + { + "bbox": [ + 64, + 132, + 165, + 191 + ], + "lines": [ + { + "bbox": [ + 64, + 132, + 165, + 191 + ], + "spans": [ + { + "bbox": [ + 64, + 132, + 165, + 191 + ], + "type": "image", + "image_path": "062ca8284d7044edfbc63efd528a7951e2f5871334c6abe05f887860231f4a60.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 196, + 287, + 239 + ], + "lines": [ + { + "bbox": [ + 46, + 196, + 287, + 239 + ], + "spans": [ + { + "bbox": [ + 46, + 196, + 287, + 239 + ], + "type": "text", + "content": "Figure 8. Ablation study about the progressive sparsity for the structure over time on the PSV dataset. The KL divergence (lower is better) measures the distribution difference between the masked (unmasked) regions and the completed image (i.e., ground truth)." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 170, + 131, + 270, + 192 + ], + "blocks": [ + { + "bbox": [ + 170, + 131, + 270, + 192 + ], + "lines": [ + { + "bbox": [ + 170, + 131, + 270, + 192 + ], + "spans": [ + { + "bbox": [ + 170, + 131, + 270, + 192 + ], + "type": "image", + "image_path": "a03fa08bbd391d4ade3d5e9aa03403c17428ba382e59e97d9e9ed468a35aa1f0.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "spans": [ + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "text", + "content": "results in Table 1 apart from the qualitative results in Fig.7 summarize our findings below: StrDiffusion enjoys a much smaller FID score, together with larger PSNR and SSIM than the competitors, confirming that StrDiffusion effectively addresses semantic discrepancy between the masked and unmasked regions, while yielding the reasonable semantics. Notably, RePaint* and IR-SDE still remain the large performance margins (at most " + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "inline_equation", + "content": "1.2\\%" + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "text", + "content": " for PSNR, " + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "inline_equation", + "content": "1.4\\%" + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "text", + "content": " for SSIM and " + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 46, + 247, + 289, + 469 + ], + "type": "text", + "content": " for FID) compared to StrDiffusion, owing to the semantic discrepancy (e.g., the white wall in the row 1 of Fig.7) in the denoised results incurred by the dense texture. Albeit MEDFE, CTSDG and ZITS focus on the guidance of the structure similar to StrDiffusion, they suffer from a performance loss due to the semantic discrepancy between the structure and texture, e.g., the woman's face for CTSDG in the row 4 of Fig.7, which further verifies our proposal in Sec.2.2 — the progressively sparse structure provides the time-dependent guidance for texture denoising process; see the supplementary material for more results." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 477, + 148, + 489 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 477, + 148, + 489 + ], + "spans": [ + { + "bbox": [ + 47, + 477, + 148, + 489 + ], + "type": "text", + "content": "3.4. Ablation Studies" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "spans": [ + { + "bbox": [ + 47, + 495, + 287, + 519 + ], + "type": "text", + "content": "3.4.1 Why Should the Semantic Sparsity of the Structure be Strengthened over Time?" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 526, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 526, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 526, + 289, + 715 + ], + "type": "text", + "content": "Recalling Sec.2.2, the progressive sparsity for the structure is utilized to mitigate the semantic discrepancy, by setting the initial structure state as the grayscale and the terminal structure state as the combination of the edge and the noise during the structure diffusion process, denoted as gray2edge. To shed more light on the semantic sparsity of the structure, we replace the initial and terminal structure state, yielding several alternatives as gray2gray, edge2edge and edge2gray; and perform the experiments on the PSV dataset. The structure sparsity of gray2gray and edge2edge is fixed over time. Fig.8 illustrates that gray2edge (Fig.8(d)) exhibits better consistency with meaningful semantics in the inpainted results against others, especially for edge2gray, implying the benefits of strengthening structure sparsity over time. Notably, for gray2gray, the discrepancy issue in the denoised re" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 318, + 101, + 529, + 162 + ], + "blocks": [ + { + "bbox": [ + 305, + 71, + 547, + 94 + ], + "lines": [ + { + "bbox": [ + 305, + 71, + 547, + 94 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 547, + 94 + ], + "type": "text", + "content": "Table 2. Ablation study about the adaptive resampling strategy on the PSV dataset. The best results are reported with **boldface**." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 318, + 101, + 529, + 162 + ], + "lines": [ + { + "bbox": [ + 318, + 101, + 529, + 162 + ], + "spans": [ + { + "bbox": [ + 318, + 101, + 529, + 162 + ], + "type": "table", + "html": "
CasesHard maskEasy mask
PSNR↑SSIM↑FID↓PSNR↑SSIM↑FID↓
A24.650.85155.7327.690.91333.73
B25.470.86346.4428.310.92128.43
C25.590.86747.3128.640.92528.20
D25.940.87542.2828.850.92926.74
", + "image_path": "c79d6c8df32b804171015f6221aa810898e870339f6ec8f7ca675d6314179b06.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 170, + 547, + 240 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 170, + 547, + 240 + ], + "spans": [ + { + "bbox": [ + 304, + 170, + 547, + 240 + ], + "type": "text", + "content": "sults still suffers (Fig.8(b)), while edge2edge receives the poor semantics (Fig.8(a)), which attributes to their invariant semantic sparsity over time, indicating time-dependent impacts of the unmasked semantics on the texture denoising process (Sec.2.2.1); see the supplementary material for more results." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 261, + 546, + 285 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 261, + 546, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 261, + 546, + 285 + ], + "type": "text", + "content": "3.4.2 How does Adaptive Resampling Strategy Benefit Inpainting?" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "spans": [ + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "type": "text", + "content": "To verify the effectiveness of the adaptive resampling strategy (Sec.2.4), we perform the ablation study on the PSV dataset from the following cases: A: refining the inpainted results of IR-SDE[23] via the resampling strategy in Repaint; B: removes the discriminator, which performs the adaptive resampling strategy without considering the semantic correlation between the texture and structure; C: StrDiffusion without the adaptive resampling strategy; D: the proposed StrDiffusion. Table 2 suggests that case D delivers great gains (at most " + }, + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "type": "inline_equation", + "content": "13.45\\%" + }, + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "type": "text", + "content": ") to other cases, which is evidenced that the adaptive resampling strategy succeeds in regulating the semantic correlation for the desirable results (Sec.2.4); case D upgrades beyond case A despite of the combination with the resampling strategy, which, in turn, verifies the necessity of the time-dependent guidance from the structure. In particular, case B bears a large performance degradation (at most " + }, + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "type": "inline_equation", + "content": "4.16\\%" + }, + { + "bbox": [ + 304, + 293, + 547, + 515 + ], + "type": "text", + "content": "), confirming the importance of adaptively resampling strategy as per the semantic correlation between the structure and texture in Sec.2.4.1." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 529, + 379, + 541 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 529, + 379, + 541 + ], + "spans": [ + { + "bbox": [ + 306, + 529, + 379, + 541 + ], + "type": "text", + "content": "4. Conclusion" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 550, + 547, + 666 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 550, + 547, + 666 + ], + "spans": [ + { + "bbox": [ + 304, + 550, + 547, + 666 + ], + "type": "text", + "content": "In this paper, we propose a structure-guided diffusion model for inpainting (StrDiffusion), to reformulate the conventional texture denoising process under the guidance of the structure to derive a simplified denoising objective; while revealing: 1) the semantics from the unmasked regions essentially offer the time-dependent guidance for the texture denoising process; 2) the progressively sparse structure well tackle the semantic discrepancy in the inpainted results. Extensive experiments verify the superiority of StrDiffusion to the state-of-the-arts." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 666, + 547, + 713 + ], + "type": "text", + "content": "Acknowledgments This work was supported by the National Natural Science Foundation of China (U21A20470, 62172136, 72188101), the Institute of Advanced Medicine and Frontier Technology under (2023IHM01080)." + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "8045" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 107, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 713 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 133 + ], + "type": "text", + "content": "[1] Connelly Barnes, Eli Shechtman, Adam Finkelstein, and Dan B Goldman. 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Comparisons of X-ray novel view synthesis. On the collected X3D dataset, our method surpasses state-of-the-art algorithms including InTo (InTomo [56]), NeRF [35], NeAT [43], NAF [59], and TeRF (TensoRF [15]) by 10.91, 15.03, 5.13, and 13.76 dB in PSNR on the scenes of medicine, biology, security, and industry. The average gains are over 12 dB. The visual comparisons of our method and the second-best algorithms on four scenes (pelvis, bonsai, box, and engine) show that our method yields more perceptually pleasing results." + ], + "image_footnote": [], + "bbox": [ + 71, + 250, + 272, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/ee8cbd8640bf3e18cd465835b2ad0b07418ca0c0d80aabfc8db74e9ba9617633.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 282, + 250, + 483, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c04c291c866ee00a9b1b769292fc86033a73abe2ab9502e9eb3d0d6b8accc4a0.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 491, + 250, + 681, + 433 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f31fe9b543acb74771c17d593abfaa09e919449e64242c45b7033d7428112540.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 697, + 250, + 888, + 433 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 508, + 313, + 523 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "X-ray, known for its ability to reveal internal structures of objects, is expected to provide richer information for 3D reconstruction than visible light. Yet, existing NeRF algorithms overlook this nature of X-ray, leading to their limitations in capturing structural contents of imaged objects. In this paper, we propose a framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), for sparse-view X-ray 3D reconstruction. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. Lineformer captures internal structures of objects in 3D space by modeling the dependencies within each line segment of an X-ray. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy to extract contextual and geometric information in 2D projection. Plus, we collect a larger-scale dataset X3D covering wider X-ray applications. Experiments on X3D show that SAX-NeRF surpasses previous NeRF-based methods by 12.56 and 2.49 dB on novel view synthesis and CT reconstruction. https://github.com/caiyuanhao1998/SAX-NeRF", + "bbox": [ + 75, + 529, + 473, + 816 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 824, + 209, + 839 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Compared with natural light, X-ray has stronger penetrating power to reveal more internal structures of imaged ob", + "bbox": [ + 75, + 845, + 468, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "jects. Hence, X-ray is widely used for prospective imaging [20, 21, 26, 27] in medicine, biology, security, industry, etc. However, X-ray is harmful to human body because of its ionizing radiation. To reduce X-ray exposure, this paper studies the low-dose X-ray 3D reconstruction problem by decreasing X-ray imaging projections in the circular cone beam X-ray scanning scenario [9, 10, 16, 24, 45]. We focus on two tasks, i.e., novel view synthesis (NVS) and computed tomography (CT) reconstruction. NVS aims to create new projections of a scene from viewpoints not originally captured. CT reconstruction retrieves the 3D CT volume of the scanned object from multi-view X-ray projections. These two tasks are complementary with an overall objective to reconstruct 3D representations from 2D projections.", + "bbox": [ + 500, + 508, + 892, + 722 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "A majority of existing deep learning-based methods employ a powerful model such as convolutional neural network (CNN) to learn a brute-force mapping from 2D X-ray projections to 3D CT volumes. These methods require a large number of projection-CT pairs for training. Yet, CT volumes are not accessible in practice. Collecting even a small projection-CT dataset is tedious, labor-intensive, and harmful to health. Plus, these paired learning-based methods fail in generalizing from one application to another due to the large domain discrepancy between different CT datasets.", + "bbox": [ + 496, + 727, + 893, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Recently, the emergence of NeRF [35] provides a more", + "bbox": [ + 519, + 883, + 890, + 901 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "$\\dagger =$ advisor, $* =$ corresponding authors", + "bbox": [ + 99, + 885, + 372, + 901 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11174", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/4c3f83cc13d9dd71a2b2952e5b9e467b88f97a9d190cfeb3f18bddd8b4911f81.jpg", + "image_caption": [ + "(a)Visible Light Imaging" + ], + "image_footnote": [], + "bbox": [ + 80, + 102, + 259, + 205 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/e007bbb8b952588231c750b93a74f0bc25b0b18bf521d75b9ef0daee57b5f6cf.jpg", + "image_caption": [ + "(b) X-ray Imaging", + "Figure 2. Visible light vs. X-ray. Visible light imaging relies on reflection. X-ray imaging is based on penetration and attenuation." + ], + "image_footnote": [], + "bbox": [ + 284, + 95, + 467, + 207 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "reasonable solution to X-ray 3D reconstruction. Compared with paired learning-based algorithms, NeRF-based methods do not require CT volumes for training. Instead, they only need projections of just one scene. Although RGB NeRF algorithms have been well developed, directly applying them for X-ray scenes may achieve suboptimal results due to the fundamental differences between visible light and X-ray imaging. As compared in Fig. 2, visible light imaging relies on the reflection off the surface of an object. It mainly captures external features. In contrast, X-rays penetrate the object and attenuate, thereby forming an image. X-ray imaging primarily reveals internal structures, which provide key clues for X-ray 3D reconstruction.", + "bbox": [ + 75, + 277, + 467, + 474 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Nonetheless, current NeRF-based methods overlook this critical property of X-ray imaging. Firstly, they learn NeRF by a simple multilayer perceptron (MLP). X-ray attenuates differently when penetrating different structures. However, MLP treats each point on an X-ray equally, showing limitations in modeling 3D structures of objects. Secondly, previous methods mainly adopt a naive pixel-level ray sampling strategy in the training phase. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system. As a result, the contextual information and geometric structures in 2D projection are not well extracted. Plus, X-ray projections are spatially sparse. Sampling X-rays on uninformative regions may lead to low efficiency. Besides, existing methods mainly study X-ray 3D reconstruction in limited medical scenes while their performance on other applications is still under-explored.", + "bbox": [ + 75, + 476, + 467, + 717 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "To tackle these issues, we propose a novel framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), with the key insight of capturing 2D and 3D structures in X-ray imaging. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. It partitions an X-ray into different line segments and then samples points on each one. By computing self-attention within every piece of the X-ray, Lineformer can model internal dependencies and learn complex 3D structures of different parts penetrated by the X-ray. Unlike vanilla Transformer [49] whose computational cost is quadratic to the number of input points, Lineformer is more", + "bbox": [ + 75, + 719, + 467, + 900 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "efficient by enjoying linear computational complexity. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy. It uses a binary mask to segment informative foreground regions on the projection. We crop nonoverlapping patches from these informative regions and then sample X-rays that land on the pixels inside these patches to help Lineformer perceive local contextual information and 2D structures. For the informative regions outside the patches, we randomly sample X-rays to help Lineformer perceive the scene's 2D global shape and geometry. Besides, we collect a larger-scale dataset, X3D, to evaluate the performance of X-ray 3D reconstruction algorithms in wider application scenarios. As shown in Fig. 1, our SAX-NeRF surpasses state-of-the-art (SOTA) NeRF-based methods by large margins on the NVs task. The average improvements on all scenes of X3D are over 12 dB.", + "bbox": [ + 496, + 90, + 890, + 330 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Our contributions can be summarized as follows:", + "bbox": [ + 517, + 333, + 843, + 345 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We propose a novel method, SAX-NeRF, for sparse-view X-ray 3D reconstruction without CT data for training.", + "- We present a new Transformer, Lineformer, to capture complex internal structures of imaged objects in 3D space. To our knowledge, it is the first attempt to explore the potential of Transformer in X-ray neural rendering.", + "- We design an MLG sampling strategy to extract geometric and contextual information of objects in 2D projection.", + "- We establish a larger-scale benchmark, X3D, for X-ray 3D reconstruction. Experiments show that our method outperforms SOTA methods on NVs and CT reconstruction tasks across different application scenarios of X-ray." + ], + "bbox": [ + 500, + 349, + 890, + 537 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 549, + 640, + 565 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.1. Neural Rendering", + "text_level": 1, + "bbox": [ + 500, + 574, + 674, + 589 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "NeRF [35] represents objects via an implicit function of color and volume density, yielding high-quality results on the NVS task. Follow-up works improve NeRF with more fine-grained details [6, 7] and broader applications [17, 47, 50]. Meanwhile, to reduce the computational cost of NeRF, learnable feature encodings [15, 18, 36] are designed to embed input point positions. However, applying existing RGB NeRF methods for X-ray rendering [22, 43, 59] may achieve suboptimal results due to the differences between visible light and X-ray imaging. For instance, NAF [59] follows NeRF to employ an MLP model for medical X-ray neural rendering, showing limitations in capturing complex structures of imaged objects in 3D space and 2D projection.", + "bbox": [ + 496, + 595, + 890, + 792 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2.2. Cone Beam CT Reconstruction", + "text_level": 1, + "bbox": [ + 500, + 801, + 774, + 816 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Traditional cone beam CT Reconstruction algorithms are mainly divided into two categories: analytical methods [25, 54] and optimization-based methods [2, 34, 37, 44, 46, 57]. Analytical methods predict the CT volume by solving the Radon transformation [40] and its inverse. These methods", + "bbox": [ + 496, + 825, + 890, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11175", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/ce3eb0745cb73f93d1000b3a20161e20d3b6ce624d3a3c0316317c88a2a9cabf.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 89, + 90, + 885, + 233 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/061820d749da2ade9762222d455dd3c145de189774ba4473ba8e24685943ec14.jpg", + "image_caption": [ + "Figure 3. Overview of our method. (a) SAX-NeRF uses (i) MLG strategy to sample an X-ray batch $\\mathcal{R}$ . Then $N$ point positions $\\mathbf{P}$ on each X-ray $\\mathbf{r} \\in \\mathcal{R}$ are sampled and input into (ii) Lineformer to produce the radiodensity $\\mathbf{D}$ . (b) Line Segment-based Attention Block (LSAB) is the basic unit of Lineformer. It captures inner structural dependencies by (c) Line Segment-based Multi-head Self-Attention (LS-MSA)." + ], + "image_footnote": [], + "bbox": [ + 86, + 243, + 885, + 375 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "can achieve good results when given hundreds of projections but fail in handling sparse-view cases. Optimization-based algorithms treat the reconstruction as a maximum a posteriori (MAP) problem based on hand-crafted image priors and solve it by iteratively minimizing the energy function, which takes a long time. Recently, CNNs [3, 30, 33, 53, 56] and diffusion models [19] have been applied to CT reconstruction and achieve good results. Yet, these methods require a number of data pairs for training. To avoid the above restrictions, we develop NeRF-based algorithms.", + "bbox": [ + 75, + 443, + 472, + 595 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2.3. Vision Transformer", + "text_level": 1, + "bbox": [ + 76, + 604, + 264, + 619 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Transformer [49] is first proposed for machine translation. In recent years, it has achieved great success in computer vision including image classification [1, 5, 23], object detection [48, 58, 63], semantic segmentation [52, 61, 62], image restoration [12-14, 55] and generation [28, 29, 60], etc. Nonetheless, directly applying vanilla Transformer for X-ray neural rendering will suffer from expensive computational cost with respect to the number of input points. The potential of Transformer for X-ray neural rendering still remains under-explored. We aim to fill this research gap.", + "bbox": [ + 75, + 627, + 468, + 779 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Method", + "text_level": 1, + "bbox": [ + 76, + 792, + 166, + 806 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Overall Framework", + "text_level": 1, + "bbox": [ + 76, + 816, + 266, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Fig. 3 illustrates the pipeline of our method. The left part of Fig. 3 (a) depicts the scenario of circular cone beam X-ray scanning where a scanner emits cone-shaped X-ray beams and captures sparse-view projections at equal angular inter", + "bbox": [ + 75, + 839, + 470, + 901 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "vals. We first use (i) Masked Local-Global (MLG) strategy to sample a batch of X-rays $\\mathcal{R}$ landing on the projections for training. Then $N$ point positions $\\mathbf{P} = \\{\\mathbf{p}_1,\\dots ,\\mathbf{p}_N\\} \\in \\mathbb{R}^{N\\times 3}$ are sampled on each X-ray $\\mathbf{r}\\in \\mathcal{R}$ and fed into (ii) Lineformer. The basic unit of Lineformer is Line Segmentbased Attention Block (LSAB). As shown in Fig. 3 (b), an LSAB consists of a fully connected $(fc)$ layer, two layer normalization (LN), a feed-forward network (FFN), and a Line Segment-based Multi-head Self-Attention (LS-MSA). The details of LS-MSA are depicted in Fig. 3 (c).", + "bbox": [ + 496, + 443, + 890, + 594 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Firstly, we review RGB NeRF. An MLP with weights $\\Theta$ is usually employed to learn the mapping function $F_{\\Theta}$ from the point position $(x,y,z)\\in \\mathbb{R}^3$ at the view direction $(\\theta ,\\phi)$ to the color $(R,G,B)\\in \\mathbb{R}^3$ and volume density $\\sigma \\in \\mathbb{R}$ as", + "bbox": [ + 496, + 594, + 890, + 656 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\Theta}: (x, y, z, \\theta , \\phi) \\rightarrow (R, G, B, \\sigma). \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 583, + 664, + 890, + 680 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "As shown in Fig. 2, visible light of specific wavelengths reflects off the surface of the object, thus revealing its color. In contrast, X-rays penetrate the object, thereby not reflecting the color information. Instead, it records the radiodensity property that denotes the degree to which a substance blocks or attenuates the passage of X-rays or other ionizing radiation. Since the radiodensity only depends on the point position, we aim to model the neural radiodensity fields as", + "bbox": [ + 496, + 688, + 890, + 810 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nF _ {\\Theta_ {L}}: (x, y, z) \\rightarrow \\rho , \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 627, + 816, + 890, + 832 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $F_{\\Theta_L}$ represents the mapping function of our Lineformer with weights $\\Theta_L$ and $\\rho \\in \\mathbb{R}$ denotes the radiodensity. According to the Beer-Lambert law, the intensity of an X-ray is reduced by the exponential integration of the", + "bbox": [ + 496, + 839, + 892, + 900 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11176", + "bbox": [ + 478, + 944, + 519, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "traversed object's radiodensity. Hence, the ground-truth intensity $I_{gt}(\\mathbf{r}) \\in \\mathbb{R}$ of the X-ray $\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d} \\in \\mathbb{R}^3$ with the near and far bounds $t_n$ and $t_f \\in \\mathbb{R}$ can be formulated as", + "bbox": [ + 76, + 90, + 468, + 137 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {g t} (\\mathbf {r}) = I _ {0} \\cdot \\exp \\left(- \\int_ {t _ {n}} ^ {t _ {f}} \\rho (\\mathbf {r} (t)) d t\\right), \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 158, + 145, + 468, + 176 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I_0$ is the initial intensity. By discretizing Eq. (3), we derive the predicted projection intensity $I_{pred}(\\mathbf{r})\\in \\mathbb{R}$ as", + "bbox": [ + 76, + 184, + 468, + 215 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\nI _ {p r e d} (\\mathbf {r}) = I _ {0} \\cdot \\exp \\left(- \\sum_ {i = 1} ^ {N} \\rho_ {i} \\delta_ {i}\\right), \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 171, + 224, + 468, + 261 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\rho_{i}$ denotes the predicted radiodensity of the $i$ -th sampled point and $\\delta_{i} = ||\\mathbf{p}_{i + 1} - \\mathbf{p}_{i}||$ is the distance between adjacent points. Eventually, the training objective is to minimize the total squared error $\\mathcal{L}$ between the predicted and ground-truth intensities in the training X-ray batch $\\mathcal{R}$ as", + "bbox": [ + 76, + 270, + 468, + 345 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left| \\left| I _ {p r e d} (\\mathbf {r}) - I _ {g t} (\\mathbf {r}) \\right| \\right| _ {2} ^ {2}, \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 354, + 468, + 387 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $I_{gt}(\\mathbf{r})$ is obtained from the pixel value on projection. $\\mathcal{L}$ is depicted by the red pixels in the right part of Fig. 3 (a).", + "bbox": [ + 76, + 397, + 467, + 429 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2. Line Segment-based Transfomer", + "text_level": 1, + "bbox": [ + 76, + 438, + 362, + 454 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As aforementioned, X-ray imaging reveals internal structures of imaged objects, which provide key clues for 3D reconstruction. Yet, previous methods overlook this important imaging property. Specifically, similar to RGB NeRF algorithms, existing X-ray NeRF methods [56, 59] mainly adopt a simple MLP model to learn the implicit neural representations. X-ray attenuates differently when penetrating different structural contents. Yet, the MLP model treats each sampled point on an X-ray equally, showing limitations in modeling the 3D structures penetrated by the X-ray.", + "bbox": [ + 75, + 460, + 468, + 611 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Towards this issue, we propose a Line Segment-based Transformer (Lineformer), as shown in Fig. 3 (a) (ii). The point position $\\mathbf{P}$ is firstly fed into a hash encoding [36] module $\\mathcal{H}$ to produce point feature $\\mathbf{F} \\in \\mathbb{R}^{N \\times C}$ as $\\mathbf{F} = \\mathcal{H}(\\mathbf{P})$ . Then $\\mathbf{F}$ undergoes four LSABs with a skip connection and two $fc$ layers to derive the point radiodensity $\\mathbf{D} \\in \\mathbb{R}^N$ .", + "bbox": [ + 75, + 613, + 468, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "LSAB is the basic unit of Lineformer. Its most important component is the LS-MSA mechanism, which captures internal structural dependencies by computing self-attention within each line segment of an X-ray. As illustrated in Fig. 3 (c), the input point feature $\\mathbf{X} \\in \\mathbb{R}^{N \\times C}$ is firstly partitioned into $M$ segments along the point dimension as", + "bbox": [ + 75, + 703, + 468, + 794 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {X} = \\left[ \\begin{array}{l l l l} \\mathbf {X} _ {1}, & \\mathbf {X} _ {2}, & \\dots , & \\mathbf {X} _ {M} \\end{array} \\right] ^ {\\mathrm {T}}, \\tag {6}\n$$\n", + "text_format": "latex", + "bbox": [ + 181, + 801, + 468, + 820 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{X}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}$ and $i = 1,2,\\dots ,M$ . Then each $\\mathbf{X}_i$ is linearly projected into query $\\mathbf{Q}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}$ ,key $\\mathbf{K}_i\\in$ $\\mathbb{R}^{\\frac{N}{M}\\times C}$ , and value $\\mathbf{V}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}$ by three $fc$ layers as", + "bbox": [ + 76, + 828, + 468, + 875 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {Q} _ {i}}, \\quad \\mathbf {K} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {K} _ {i}}, \\quad \\mathbf {V} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {V} _ {i}}, \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 112, + 883, + 468, + 901 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}^{\\mathbf{Q}_i}$ , $\\mathbf{W}^{\\mathbf{K}_i}$ , and $\\mathbf{W}^{\\mathbf{V}_i} \\in \\mathbb{R}^{C \\times C}$ are learnable parameters of the $fc$ layers; biases are omitted for simplification. Subsequently, $\\mathbf{W}^{\\mathbf{Q}_i}$ , $\\mathbf{W}^{\\mathbf{K}_i}$ , and $\\mathbf{W}^{\\mathbf{V}_i}$ are uniformly split into $k$ heads along the channel dimension as", + "bbox": [ + 498, + 89, + 890, + 151 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Q} _ {i} = \\left[ \\begin{array}{c} \\mathbf {Q} _ {i} ^ {1}, \\quad \\mathbf {Q} _ {i} ^ {2}, \\quad \\dots , \\quad \\mathbf {Q} _ {i} ^ {k} \\end{array} \\right],\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 157, + 781, + 174 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {K} _ {i} = \\left[ \\mathbf {K} _ {i} ^ {1}, \\mathbf {K} _ {i} ^ {2}, \\dots , \\mathbf {K} _ {i} ^ {k} \\right], \\tag {8}\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 176, + 890, + 193 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {V} _ {i} = \\left[ \\begin{array}{c} \\mathbf {V} _ {i} ^ {1}, \\mathbf {V} _ {i} ^ {2}, \\dots , \\mathbf {V} _ {i} ^ {k} \\end{array} \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 607, + 196, + 782, + 214 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The dimension for each head is $d_h = C / k$ . Fig. 3 (b) illustrates the situation with $k = 1$ for simplicity. Then the self-attention within each head $\\mathbf{H}_i^j$ is computed as", + "bbox": [ + 498, + 220, + 890, + 266 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {H} _ {i} ^ {j} = \\operatorname {A t t n} \\left(\\mathbf {Q} _ {i} ^ {j}, \\mathbf {K} _ {i} ^ {j}, \\mathbf {V} _ {i} ^ {j}\\right) = \\mathbf {V} _ {i} ^ {j} \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {K} _ {i} ^ {j} {} ^ {\\mathrm {T}} \\mathbf {Q} _ {i} ^ {j}}{\\alpha_ {i} ^ {j}}\\right), \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 537, + 270, + 890, + 306 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\alpha_{i}^{j}\\in \\mathbb{R}$ is a learnable parameter that adaptively scales the inner product before the softmax function. Successively, $k$ heads are concatenated in channel dimension to pass through an $fc$ layer and then plus a positional embedding $\\mathbf{E}_i\\in \\mathbb{R}_{M}^{\\frac{N}{M}\\times C}$ to derive the $i$ -th output $\\mathbf{Y}_i\\in \\mathbb{R}_{M}^{\\frac{N}{M}\\times C}$ as", + "bbox": [ + 498, + 310, + 890, + 386 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} _ {i} = \\left[ \\mathbf {H} _ {i} ^ {1}, \\mathbf {H} _ {i} ^ {2}, \\dots , \\mathbf {H} _ {i} ^ {k} \\right] \\mathbf {W} _ {i} + \\mathbf {E} _ {i}, \\tag {10}\n$$\n", + "text_format": "latex", + "bbox": [ + 576, + 393, + 890, + 411 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbf{W}_i\\in \\mathbb{R}^{C\\times C}$ are learnable parameters of the $fc$ layer. Finally, we group the outputs of $M$ segments in point dimension to obtain the output feature $\\mathbf{Y}\\in \\mathbb{R}^{N\\times C}$ as", + "bbox": [ + 498, + 417, + 890, + 463 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {Y} = \\left[ \\begin{array}{l l l l} \\mathbf {Y} _ {1}, & \\mathbf {Y} _ {2}, & \\dots , & \\mathbf {Y} _ {M} \\end{array} \\right] ^ {\\mathrm {T}}. \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 602, + 468, + 890, + 486 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "By capturing the interactions of points within each line segment, the proposed Lineformer is more capable of perceiving the complex internal 3D structures of different parts penetrated by the X-ray and therefore modeling the implicit neural radiodensity fields in Eq. (2) more accurately.", + "bbox": [ + 498, + 491, + 890, + 566 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Complexity Analysis. We analyze the computational complexity of our LS-MSA and compare it with the global multi-head self-attention (G-MSA) mechanism of vanilla Transformer. The computational cost of LS-MSA primarily comes from the two matrix multiplication, i.e., $\\mathbb{R}^{d_h\\times \\frac{N}{M}\\times}$ $\\mathbb{R}_{M}^{N\\times d_{h}}$ and $\\mathbb{R}_{M}^{N\\times d_{h}}\\times \\mathbb{R}^{d_{h}\\times d_{h}}$ , in Eq. (9) performed $k\\times M$ times. Thus, the complexity of LS-MSA is formulated as", + "bbox": [ + 498, + 573, + 890, + 679 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {O} (\\text {L S - M S A}) = k M \\cdot \\left[ d _ {h} \\cdot \\left(d _ {h} \\cdot \\frac {N}{M}\\right) + \\frac {N}{M} \\cdot \\left(d _ {h} \\cdot d _ {h}\\right) \\right], \\tag {12} \\\\ = 2 k M d _ {h} ^ {2} \\frac {N}{M} = 2 N k \\left(\\frac {C}{k}\\right) ^ {2} = \\frac {2 N C ^ {2}}{k}. \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 513, + 686, + 890, + 742 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "While the complexity of G-MSA is formulated as", + "bbox": [ + 500, + 751, + 826, + 766 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {O} (\\mathrm {G} - \\mathrm {M S A}) = 2 N ^ {2} C. \\tag {13}\n$$\n", + "text_format": "latex", + "bbox": [ + 625, + 771, + 890, + 787 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Compare Eq. (12) with Eq. (13). $\\mathcal{O}(\\mathrm{G - MSA})$ is quadratic to the number of input points $(N)$ . This heavy computational burden impedes the application of Transformer for X-ray 3D reconstruction. In contrast, $\\mathcal{O}(\\mathrm{LS - MSA})$ is linear to $N$ . This significantly reduced cost allows for the integration of LS-MSA into each basic unit LSAB of Lineformer, thereby further exploring the tremendous potential of Transformer.", + "bbox": [ + 498, + 794, + 890, + 900 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11177", + "bbox": [ + 478, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.3. Masked Local-Global Ray Sampling", + "text_level": 1, + "bbox": [ + 76, + 90, + 392, + 107 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As shown in Fig. 4 (a), existing NeRF algorithms mainly adopt a naive pixel-level ray sampling strategy. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system for training. This naive strategy has two drawbacks. Firstly, it shows limitations in extracting local contextual and geometric representations in 2D projection because the semantic information from neighbor pixels is not captured. Secondly, X-ray images are spatially sparse. Some randomly sampled X-rays may land on the background dark regions of the projection, such as the pixel $p_{bg}$ in Fig. 4 (a). These X-rays do not penetrate the object and thus are not imaged on the projection. In other words, these X-rays are uninformative because they do not characterize the radiodensity property of the object. Learning with these X-rays will degrade the model efficiency.", + "bbox": [ + 75, + 113, + 468, + 339 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To address these problems, we propose a Masked Local-Global (MLG) ray sampling strategy, as shown in Fig. 4 (b). MLG first uses a mask $\\mathbf{M} \\in \\mathbb{R}^{H \\times W}$ to segment the imaged foreground regions. $\\mathbf{M}$ is derived by binarizing the projection $\\mathbf{I} \\in \\mathbb{R}^{H \\times W}$ with a threshold $T \\in \\mathbb{R}$ as $\\mathbf{M} = \\mathbf{1}_{\\mathbf{I} > T}$ . Subsequently, to avoid redundant sampling, we partition $\\mathbf{M}$ into a set $\\mathcal{W} \\in \\mathbb{R}^{\\frac{HW}{S^2} \\times S \\times S}$ of $\\frac{HW}{S^2}$ non-overlapping windows with size $S \\times S$ . Let $\\mathcal{W}_f$ denote the set of windows that are entirely contained in the foreground regions as", + "bbox": [ + 75, + 339, + 470, + 478 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {W} _ {f} = \\left\\{\\mathbf {w} \\in \\mathcal {W} \\mid \\mathbf {w} = \\mathbf {1} _ {S \\times S} \\right\\}. \\tag {14}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 483, + 468, + 500 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To capture local semantic information of the object, we perform patch-level sampling. Specifically, we randomly select $N_{l}$ windows $\\mathcal{W}_l = \\{\\mathbf{w}_1,\\dots ,\\mathbf{w}_{N_l}\\}$ from $\\mathcal{W}_f$ as shown in the red patches of Fig. 4 (b). Then the X-ray set $\\mathcal{R}_l$ corresponding to the pixels within $\\mathcal{W}_l$ can be formulated as", + "bbox": [ + 76, + 503, + 468, + 579 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {l} = \\bigcup_ {i = 1} ^ {N _ {l}} \\bigcup_ {p \\in \\mathbf {w} _ {i}} \\operatorname {R a y} (p), \\tag {15}\n$$\n", + "text_format": "latex", + "bbox": [ + 200, + 580, + 468, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\operatorname{Ray}(p)$ is a function that maps from a pixel $p$ to its corresponding X-ray. Furthermore, to assist the model in better capturing global contextual representations and perceiving the overall geometric shape of the imaged object, we perform pixel-level sampling. Particularly, we randomly select $N_g$ pixels $\\mathcal{P}$ from the foreground regions excluding the area of $\\mathcal{W}_l$ to avoid repeated ray sampling, as depicted in the blue pixels of Fig. 4 (b). $\\mathcal{P}$ can be formulated as", + "bbox": [ + 75, + 619, + 468, + 741 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {P} = \\{p \\in (\\mathbf {M} - \\mathcal {W} _ {l}) \\mid p = 1 \\}. \\tag {16}\n$$\n", + "text_format": "latex", + "bbox": [ + 174, + 746, + 468, + 762 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Then the X-ray set $\\mathcal{R}_g$ corresponding to $\\mathcal{P}$ is obtained by", + "bbox": [ + 76, + 765, + 455, + 780 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} _ {g} = \\bigcup_ {p \\in \\mathcal {P}} \\operatorname {R a y} (p). \\tag {17}\n$$\n", + "text_format": "latex", + "bbox": [ + 212, + 782, + 468, + 811 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Finally, the training X-ray batch is the union of $\\mathcal{R}_l$ and $\\mathcal{R}_g$ :", + "bbox": [ + 76, + 811, + 468, + 828 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {R} = \\mathcal {R} _ {l} \\bigcup \\mathcal {R} _ {g}. \\tag {18}\n$$\n", + "text_format": "latex", + "bbox": [ + 220, + 830, + 468, + 849 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Using MLG ray sampling strategy, the model can more effectively capture the contextual information and model the geometric structures of the imaged object on 2D projection.", + "bbox": [ + 76, + 854, + 468, + 901 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/25caeb2a5c978ab24ebb3b4eadb9c370710b763dfaff4d77be357094d30c810a.jpg", + "image_caption": [ + "Pixel-level Sampling", + "(a) Naive Sampling", + "Figure 4. Comparison of ray sampling. (a) The naive strategy samples X-rays that land on scattered pixels. (b) Our MLG strategy performs pixel- and patch-level sampling on foreground regions." + ], + "image_footnote": [], + "bbox": [ + 508, + 117, + 666, + 239 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/2e2f320bfe45a6cb2d6440876ca0518ec4475e24573982ebd78c3083246817fd.jpg", + "image_caption": [ + "Patch-level Sampling", + "(b) Our MLG Sampling" + ], + "image_footnote": [], + "bbox": [ + 714, + 117, + 870, + 239 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4. Experiment", + "text_level": 1, + "bbox": [ + 500, + 330, + 622, + 347 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.1. Experimental Settings", + "text_level": 1, + "bbox": [ + 500, + 354, + 705, + 372 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "X3D Dataset. Previous methods mainly conduct X-ray 3D reconstruction research on limited medical applications. For example, NAF [59] is evaluated on five medical scenes. The performance of NeRF-based methods on other X-ray applications is under-explored. To fill this research gap, we collect a larger-scale dataset, X3D, containing 15 scenes and covering 4 applications, i.e., medicine, biology, security, and industry. We collect the CT volumes of X3D from public datasets. Specifically, the chest, backpack, carp, and pancreas datasets are collected from LIDC-IDRI [4], MIDA [11], $\\mathrm{D}^2\\mathrm{VR}$ [41], and DeepOrgan [42], respectively. The teapot, aneurism, bonsai, and foot datasets are obtained from VOLVIS [39] and the rest are from the open scientific visualization dataset [32]. Then we use the tomographic method TIGRE [8] to generate projections by scanning CT volumes with $3\\%$ noise in the range of $0^{\\circ}\\sim 180^{\\circ}$ .", + "bbox": [ + 496, + 378, + 890, + 621 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Implementation Details. We implement our SAX-NeRF by PyTorch [38]. The model is trained with the Adam [31] optimizer $(\\beta_{1} = 0.9$ and $\\beta_{2} = 0.999)$ for 3000 iterations. The learning rate is initially set to $1\\times 10^{-4}$ and is halved every 1500 iterations during the training procedure. The batch size of X-rays is set to 2048, 1024 of which is from patchlevel sampling and the other 1024 is from pixel-level sampling. We uniformly sample 320 points along each X-ray. For each scene, we use its 50 projections to train, another 50 projections to test the performance of NVs, and its CT volume to evaluate the results of CT reconstruction. All experiments are conducted on an RTX 8000 GPU. We adopt the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) [51] as the evaluation metrics.", + "bbox": [ + 496, + 625, + 892, + 835 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.2. Main Results", + "text_level": 1, + "bbox": [ + 500, + 845, + 637, + 861 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Novel View Synthesis. Tab. 1 lists the quantitative results of PSNR and SSIM on the NVs task. We compare our", + "bbox": [ + 498, + 869, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11178", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/978a946bc5f4785d37420ce0c120cd172c5ac2206382b08167c4f0a2cf49dd11.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodInTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw26.910.993734.840.998132.680.991134.060.996439.890.998842.750.9992
Leg42.530.997645.920.998947.710.998141.400.996950.870.998856.860.9996
Box34.650.996335.670.998536.140.995735.430.997735.980.995539.670.9992
Carp24.040.964820.620.946731.260.962037.350.997329.600.959359.880.9999
Foot39.480.997941.050.998938.240.996337.730.992938.350.991346.640.9994
Head34.830.997729.760.999127.740.929534.430.987830.170.953153.060.9995
Pelvis38.720.996140.790.997237.700.986641.570.994843.760.997553.270.9995
Chest28.950.991536.160.998840.770.999023.610.940242.370.999347.420.9994
Bonsai39.260.995337.670.998347.020.998547.800.998949.030.998955.330.9995
Teapot41.510.997834.660.999329.290.966944.180.999334.920.998552.620.9996
Engine23.990.951721.070.933430.360.885439.720.991831.680.919558.800.9998
Pancreas20.030.853719.850.856037.530.901729.240.803136.230.884449.880.9978
Abdomen27.640.964624.620.955926.740.856327.380.873037.590.985554.220.9996
Aneurism20.810.962124.970.979235.410.993647.990.999739.620.999052.910.9998
Backpack36.090.991839.750.996241.600.996943.160.997742.020.998247.170.9989
Average31.960.976832.490.977036.010.963837.670.971238.810.978551.370.9994
", + "bbox": [ + 78, + 88, + 895, + 330 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Table 1. Quantitative comparisons on the novel view synthesis task. The best results are in bold and the second-best results are underlined.", + "bbox": [ + 76, + 339, + 890, + 354 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/b729bab158293fb1dbe9c4b7a9769d38ea3fa39b07848e00c41c192dd6dcd10b.jpg", + "image_caption": [ + "Figure 5. Qualitative results of novel view synthesis on the scenes of backpack (top) and carp (bottom). Please zoom in for a better view." + ], + "image_footnote": [], + "bbox": [ + 76, + 362, + 888, + 565 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "SAX-NeRF with five SOTA NeRF-based algorithms including InTomo [56], NeRF [35], NeAT [43], TensoRF [15], and NAF [59]. The input and output of all methods are set the same as Eq. (2) for fair comparison. It can be observed that our SAX-NeRF significantly outperforms SOTA methods on all scenes. Specifically, when compared with the recent best general RGB NeRF algorithm TensoRF, our SAX-NeRF is 13.70 dB (51.37 - 37.67) and 0.0282 (0.9994 - 0.9712) higher in PSNR and SSIM. When compared with the recent best medical NeRF method NAF, SAX-NeRF surpasses it by 12.56 dB in PSNR and 0.0209 in SSIM. The average improvements of our method on the scenes of medicine, biology, security, and industry are 10.91, 15.03, 5.13, and 13.76 dB, as shown in the bar charts of Fig. 1.", + "bbox": [ + 75, + 604, + 472, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The qualitative results are depicted in Fig. 5. As can be observed from the zoomed-in patches, previous methods are less effective in synthesizing novel projections. They either produce blurry images or fail to reconstruct structural contents. In contrast, our SAX-NeRF yields more vi", + "bbox": [ + 75, + 824, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "sually pleasing results with clearer textures and more fine-grained details while preserving more complete geometric structures. More visual comparisons are shown in Fig. 1.", + "bbox": [ + 496, + 604, + 890, + 651 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "CT Reconstruction. Tab. 2 reports the quantitative results on the CT reconstruction task. For fairness, we do not compare projection-CT paired learning-based algorithms, but instead focus on comparing methods that only require X-ray projections of single scenes for training or direct processing. In addition to the five SOTA NeRF-based algorithms. We also compare SAX-NeRF with an analytical method (FDK [25]) and two optimization-based algorithms (ASDPOCS [46] and SART [2]). Our method yields the best results on all scenes. In particular, SAX-NeRF dramatically outperforms previous NeRF-based, optimization-based, and analytical algorithms by over 2.49, 4.92, and $12.13\\mathrm{dB}$", + "bbox": [ + 496, + 656, + 892, + 838 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Fig. 6 displays the visual comparisons in four application scenarios including medicine (head), biology (carp), security (box), and industry (teapot). Other methods either produce over-smooth images blurring the structural contents or", + "bbox": [ + 496, + 839, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11179", + "bbox": [ + 478, + 944, + 519, + 957 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/0bf052b5730b63006dd5cacf8ede3da6ab685a4fae91c678fad5977cb4756926.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
MethodFDK [25]ASD-POCS [46]SART [2]InTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw28.580.781633.250.932533.130.930131.950.916232.170.911432.530.913931.900.897134.140.935835.470.9525
Leg28.480.669035.390.982635.300.980936.410.988239.270.993840.290.990240.700.992341.280.994043.470.9973
Box24.140.561631.270.922631.200.920030.590.914033.580.949431.580.929832.170.931431.780.930935.330.9602
Carp32.320.817737.630.977736.890.968232.470.949332.990.952936.850.957637.520.968737.930.971142.720.9902
Foot24.530.600029.980.920830.290.929631.430.912730.030.907230.860.922130.460.915331.630.936332.250.9403
Head26.170.715535.270.970734.880.959731.070.930334.150.967235.560.967935.530.967236.460.974339.700.9888
Pelvis26.910.636734.260.949334.380.948130.380.904231.720.917033.730.937035.130.952836.010.965440.400.9870
Chest22.890.786131.130.942232.170.959422.040.746028.400.892531.200.949730.130.930833.050.958134.380.9718
Bonsai24.530.727632.700.952933.020.960028.900.881131.770.938233.200.947633.470.952133.850.958536.510.9761
Teapot31.070.805937.350.980037.380.978736.150.978641.670.994540.850.987242.710.994242.560.992644.320.9970
Engine23.020.540530.810.958030.440.944227.490.926436.850.985836.630.980435.210.972837.840.985938.770.9917
Pancreas9.6410.123218.300.770118.360.700816.010.786517.730.861419.060.854119.750.773719.410.812622.980.9531
Abdomen22.630.603031.460.923131.400.917028.050.875429.710.904931.140.906031.510.907334.450.950135.010.9598
Aneurism28.070.729534.730.986434.760.986430.320.965231.970.935335.800.981937.360.988937.730.987141.460.9956
Backpack23.840.535131.340.930931.320.929428.770.875330.280.919231.900.934533.160.936233.260.950135.970.9688
Average25.120.642232.320.940032.330.934230.290.918932.150.935433.410.944733.780.938734.760.953537.250.9753
", + "bbox": [ + 78, + 88, + 893, + 309 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Table 2. Quantitative comparisons on the CT reconstruction task. The best results are in bold and the second-best results are underlined.", + "bbox": [ + 81, + 315, + 885, + 329 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/fffa8548d9cafe24f8c56f1e86799decb22064712733488cae606b7b5248dcb3.jpg", + "image_caption": [ + "Figure 6. Visual results of CT reconstruction on the scenes of head, carp, box, and teapot (top to bottom). Please zoom in for a better view." + ], + "image_footnote": [], + "bbox": [ + 76, + 342, + 895, + 758 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "introduce distracting artifacts. In contrast, our SAX-NeRF is more favorable to reconstruct vivid high-frequency details such as sharp edges while maintaining spatial smoothness of homogeneous regions within complex structures.", + "bbox": [ + 75, + 803, + 468, + 864 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "These results convincingly demonstrate the advantages of the proposed SAX-NeRF in X-ray 3D reconstruction.", + "bbox": [ + 75, + 869, + 468, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "4.3. Ablation Study", + "text_level": 1, + "bbox": [ + 500, + 801, + 653, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "To reliably evaluate the effectiveness of our approaches, we conduct ablation study on all scenes of X3D and report the average PSNR / SSIM results in the following part.", + "bbox": [ + 498, + 832, + 890, + 878 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Break-down Ablation. We adopt a baseline model that", + "bbox": [ + 500, + 885, + 890, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11180", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/92d05c569df9901a93c3d15b585af9a2d5217c83f5a15f19c8be0f627008df26.jpg", + "table_caption": [], + "table_footnote": [ + "(a) Break-down ablation to higher performance." + ], + "table_body": "
BaselineLS-MSAMLGNVSCT
✓37.97 / 0.974834.21 / 0.9513
✓✓47.95 / 0.994536.86 / 0.9717
✓✓43.51 / 0.986135.30 / 0.9601
✓✓✓51.37 / 0.999437.25 / 0.9753
", + "bbox": [ + 86, + 88, + 370, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ec8177249147826ffe1ec58ab617bfc8406d51470f563b49a286e78c5ea2ad92.jpg", + "table_caption": [], + "table_footnote": [ + "(b) Analysis of the line segment quantity." + ], + "table_body": "
Num204080160320
NVS45.77647.83250.14851.36550.620
0.98920.99390.99910.99940.9992
CT35.84536.78737.08837.24937.186
0.96700.97110.97450.97530.9749
", + "bbox": [ + 377, + 88, + 620, + 148 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/99633630747b5fbdfa5d3ec99bedd2c63d974af488cf376002173827680816ab.jpg", + "table_caption": [], + "table_footnote": [ + "(c) Analysis of the sampling patch size." + ], + "table_body": "
Size2×24×48×816×1632×32
NVS48.51551.36550.29750.40849.629
0.99760.99940.99920.99920.9989
CT36.98237.24937.11837.16337.014
0.97330.97530.97480.97490.9741
", + "bbox": [ + 627, + 88, + 880, + 148 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Table 3. We conduct ablation study on all scenes of X3D. Average PSNR and SSIM are reported on the NVS and CT reconstruction tasks.", + "bbox": [ + 76, + 171, + 890, + 185 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/37d29e76fa6019250888d16677472cbcd006c4ae51469c8baaa566a395287cf4.jpg", + "image_caption": [ + "Figure 7. Visual analysis. Using LS-MSA and MLG captures more structures." + ], + "image_footnote": [], + "bbox": [ + 70, + 198, + 240, + 310 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8bc9b8c7388cee82de450fb57cac29e8f796f3358dbe9207912d300daf493b4e.jpg", + "image_caption": [ + "Baseline" + ], + "image_footnote": [], + "bbox": [ + 245, + 198, + 321, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3d4d0966e70bd153c18468eed69983b88549ee69d4b9b0dd8448368b015d304f.jpg", + "image_caption": [ + "+LS-MSA" + ], + "image_footnote": [], + "bbox": [ + 325, + 198, + 390, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/0659a48c5efd32ffad9f34a02d77bc3b706972ed4bee1127e23b8e29e7fb313f.jpg", + "image_caption": [ + "+MLG" + ], + "image_footnote": [], + "bbox": [ + 393, + 198, + 457, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/aab49d6735a06e58237e5decf7a593ebbdeb7d588f8b839ebdfcc0a303b2d635.jpg", + "image_caption": [ + "Ground Truth" + ], + "image_footnote": [], + "bbox": [ + 462, + 198, + 524, + 247 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/51a11f1bea466f5588eec2ed57c8ba529d975bd3106d2631dbcc78427dc084de.jpg", + "image_caption": [ + "Figure 8. Analysis of the number of training projections." + ], + "image_footnote": [], + "bbox": [ + 534, + 198, + 710, + 314 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/8f3c05475387af9ed35caa088283853164756ecd099d495e7b4af6aa7626c3cd.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 710, + 198, + 883, + 314 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "is derived by directly removing the LS-MSA module and MLG sampling strategy from our SAX-NeRF to conduct the break-down ablation study. The results are listed in Tab. 3a. The baseline model yields 37.97 and 34.21 dB on NVS and CT reconstruction. When using LS-MSA, the baseline model gains by 9.98 and 2.65 dB. When we apply MLG sampling, the model achieves 5.54 and 1.09 dB improvements. When jointly exploiting the two techniques, the model is improved by 13.40 and 3.04 dB on the NVS and CT reconstruction tasks. This evidence clearly exhibits the efficacy of Lineformer and MLG sampling strategy.", + "bbox": [ + 75, + 356, + 468, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Visual Analysis. To intuitively show the effectiveness of the two proposed approaches, we further conduct visual analysis on the scene of bonsai. As depicted in Fig. 7, the baseline model fails to preserve the geometry like the tree branches in the projection and blurs high-frequency details such as the edges of the basin in the CT slice. When successively using LS-MSA and MLG sampling, the model reconstructs more structural contents and fine-grained textures.", + "bbox": [ + 75, + 527, + 468, + 648 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Parameter Analysis. We conduct parameter analysis regarding the number of line segments $M$ in Eq. (6) and the patch size $S$ in Eq. (14). Please note that we keep the total number of sampled points and X-rays unchanged for fair comparison. When analyzing one parameter, we fix the other at its optimal value. The results are reported in Tab. 3b and 3c. It is clear that, when using different $M$ and $S$ , our SAX-NeRF stably outperforms the baseline model by over 7.81 and 1.64 dB on NVS and CT reconstruction. This evidence suggests the reliability of our method. The model's performance yields its maximum when $M = 160$ and $S = 4$ .", + "bbox": [ + 75, + 654, + 468, + 820 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Robustness Analysis. We conduct robustness analysis regarding the number of training projections to compare the performance of different methods when given fewer X-ray projection views. The results are plotted as two line charts in Fig. 8, where the vertical axis is PSNR (in dB per", + "bbox": [ + 75, + 825, + 468, + 902 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "formance) and the horizontal axis is the number of training projections. Our SAX-NeRF reliably surpasses SOTA methods by large margins when given different numbers of training projections on both NVs (left) and CT reconstruction (right) tasks. Surprisingly, when using even only $60\\%$ of training projections, SAX-NeRF still outperforms other algorithms on the NVS task. These results clearly exhibit the superiority and robustness of our proposed method.", + "bbox": [ + 496, + 356, + 890, + 477 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Lineformer vs. vanilla Transformer. We replace LS-MSA with G-MSA to conduct comparative experiments. The experimental results show that our Lineformer significantly outperforms vanilla Transformer by 5.30 and $1.28\\mathrm{dB}$ on the NVS and CT reconstruction tasks while only requiring $3.41\\%$ of vanilla Transformer's computational complexity.", + "bbox": [ + 496, + 479, + 890, + 571 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 582, + 617, + 598 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we focus on studying a core problem in sparse-view X-ray 3D reconstruction, i.e., how to effectively capture the various and complex structures penetrated by X-rays. To this end, we propose a novel framework SAX-NeRF. To model 3D structural dependencies in space, we design a Transformer, Lineformer, as the backbone of SAX-NeRF. Lineformer partitions an X-ray into different line segments and then computes self-attention within each piece of the X-ray. In addition, to extract 2D geometry and contextual representations in projection, we present an MLG ray sampling strategy that contains pixel- and patch-level sampling on the informative foreground regions. Besides, we also collect a larger-scale dataset, X3D, covering wider X-ray application scenarios. Comprehensive experiments on X3D show that SAX-NeRF significantly surpasses SOTA algorithms on the NVs and CT reconstruction tasks.", + "bbox": [ + 496, + 608, + 890, + 849 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgements: This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and the Patrick J. McGovern Foundation Award.", + "bbox": [ + 496, + 854, + 890, + 898 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11181", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Alaaeldin Ali, Hugo Touvron, Mathilde Caron, Piotr Bojanowski, Matthijs Douze, Armand Joulin, Ivan Laptev, Natalia Neverova, Gabriel Synnaeve, Jakob Verbeek, et al. Xcit: Cross-covariance image transformers. 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In ICLR, 2021. 3" + ], + "bbox": [ + 501, + 90, + 890, + 883 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11183", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/e0ae7df8-d3f1-46c2-a34a-52862215b941_model.json b/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/e0ae7df8-d3f1-46c2-a34a-52862215b941_model.json new file mode 100644 index 0000000000000000000000000000000000000000..478c4dca43fd289079d0da20b89fbffcb0ada2e3 --- /dev/null +++ b/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/e0ae7df8-d3f1-46c2-a34a-52862215b941_model.json @@ -0,0 +1,2596 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.044 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.204, + 0.131, + 0.768, + 0.154 + ], + "angle": 0, + "content": "Structure-Aware Sparse-View X-ray 3D Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.177, + 0.181, + 0.795, + 0.219 + ], + "angle": 0, + "content": "Yuanhao Cai, Jiahao Wang, Alan Yuille\\(^{\\dagger,*}\\), Zongwei Zhou\\(^{*}\\), Angtian Wang Johns Hopkins University" + }, + { + "type": "image", + "bbox": [ + 0.073, + 0.25, + 0.273, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.284, + 0.251, + 0.485, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.492, + 0.25, + 0.682, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.699, + 0.25, + 0.889, + 0.434 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.439, + 0.895, + 0.496 + ], + "angle": 0, + "content": "Figure 1. Comparisons of X-ray novel view synthesis. On the collected X3D dataset, our method surpasses state-of-the-art algorithms including InTo (InTomo [56]), NeRF [35], NeAT [43], NAF [59], and TeRF (TensoRF [15]) by 10.91, 15.03, 5.13, and 13.76 dB in PSNR on the scenes of medicine, biology, security, and industry. The average gains are over 12 dB. The visual comparisons of our method and the second-best algorithms on four scenes (pelvis, bonsai, box, and engine) show that our method yields more perceptually pleasing results." + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.51, + 0.314, + 0.525 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.53, + 0.474, + 0.818 + ], + "angle": 0, + "content": "X-ray, known for its ability to reveal internal structures of objects, is expected to provide richer information for 3D reconstruction than visible light. Yet, existing NeRF algorithms overlook this nature of X-ray, leading to their limitations in capturing structural contents of imaged objects. In this paper, we propose a framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), for sparse-view X-ray 3D reconstruction. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. Lineformer captures internal structures of objects in 3D space by modeling the dependencies within each line segment of an X-ray. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy to extract contextual and geometric information in 2D projection. Plus, we collect a larger-scale dataset X3D covering wider X-ray applications. Experiments on X3D show that SAX-NeRF surpasses previous NeRF-based methods by 12.56 and 2.49 dB on novel view synthesis and CT reconstruction. https://github.com/caiyuanhao1998/SAX-NeRF" + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.825, + 0.21, + 0.84 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.847, + 0.47, + 0.879 + ], + "angle": 0, + "content": "Compared with natural light, X-ray has stronger penetrating power to reveal more internal structures of imaged ob" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.51, + 0.893, + 0.723 + ], + "angle": 0, + "content": "jects. Hence, X-ray is widely used for prospective imaging [20, 21, 26, 27] in medicine, biology, security, industry, etc. However, X-ray is harmful to human body because of its ionizing radiation. To reduce X-ray exposure, this paper studies the low-dose X-ray 3D reconstruction problem by decreasing X-ray imaging projections in the circular cone beam X-ray scanning scenario [9, 10, 16, 24, 45]. We focus on two tasks, i.e., novel view synthesis (NVS) and computed tomography (CT) reconstruction. NVS aims to create new projections of a scene from viewpoints not originally captured. CT reconstruction retrieves the 3D CT volume of the scanned object from multi-view X-ray projections. These two tasks are complementary with an overall objective to reconstruct 3D representations from 2D projections." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.728, + 0.895, + 0.88 + ], + "angle": 0, + "content": "A majority of existing deep learning-based methods employ a powerful model such as convolutional neural network (CNN) to learn a brute-force mapping from 2D X-ray projections to 3D CT volumes. These methods require a large number of projection-CT pairs for training. Yet, CT volumes are not accessible in practice. Collecting even a small projection-CT dataset is tedious, labor-intensive, and harmful to health. Plus, these paired learning-based methods fail in generalizing from one application to another due to the large domain discrepancy between different CT datasets." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.885, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Recently, the emergence of NeRF [35] provides a more" + }, + { + "type": "page_footnote", + "bbox": [ + 0.1, + 0.886, + 0.374, + 0.902 + ], + "angle": 0, + "content": "\\(\\dagger =\\) advisor, \\(* =\\) corresponding authors" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11174" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.081, + 0.103, + 0.26, + 0.206 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.099, + 0.216, + 0.237, + 0.23 + ], + "angle": 0, + "content": "(a)Visible Light Imaging" + }, + { + "type": "image", + "bbox": [ + 0.285, + 0.096, + 0.468, + 0.208 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.321, + 0.216, + 0.422, + 0.228 + ], + "angle": 0, + "content": "(b) X-ray Imaging" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.235, + 0.47, + 0.264 + ], + "angle": 0, + "content": "Figure 2. Visible light vs. X-ray. Visible light imaging relies on reflection. X-ray imaging is based on penetration and attenuation." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.279, + 0.468, + 0.475 + ], + "angle": 0, + "content": "reasonable solution to X-ray 3D reconstruction. Compared with paired learning-based algorithms, NeRF-based methods do not require CT volumes for training. Instead, they only need projections of just one scene. Although RGB NeRF algorithms have been well developed, directly applying them for X-ray scenes may achieve suboptimal results due to the fundamental differences between visible light and X-ray imaging. As compared in Fig. 2, visible light imaging relies on the reflection off the surface of an object. It mainly captures external features. In contrast, X-rays penetrate the object and attenuate, thereby forming an image. X-ray imaging primarily reveals internal structures, which provide key clues for X-ray 3D reconstruction." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.477, + 0.468, + 0.718 + ], + "angle": 0, + "content": "Nonetheless, current NeRF-based methods overlook this critical property of X-ray imaging. Firstly, they learn NeRF by a simple multilayer perceptron (MLP). X-ray attenuates differently when penetrating different structures. However, MLP treats each point on an X-ray equally, showing limitations in modeling 3D structures of objects. Secondly, previous methods mainly adopt a naive pixel-level ray sampling strategy in the training phase. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system. As a result, the contextual information and geometric structures in 2D projection are not well extracted. Plus, X-ray projections are spatially sparse. Sampling X-rays on uninformative regions may lead to low efficiency. Besides, existing methods mainly study X-ray 3D reconstruction in limited medical scenes while their performance on other applications is still under-explored." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.72, + 0.468, + 0.901 + ], + "angle": 0, + "content": "To tackle these issues, we propose a novel framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), with the key insight of capturing 2D and 3D structures in X-ray imaging. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. It partitions an X-ray into different line segments and then samples points on each one. By computing self-attention within every piece of the X-ray, Lineformer can model internal dependencies and learn complex 3D structures of different parts penetrated by the X-ray. Unlike vanilla Transformer [49] whose computational cost is quadratic to the number of input points, Lineformer is more" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.892, + 0.332 + ], + "angle": 0, + "content": "efficient by enjoying linear computational complexity. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy. It uses a binary mask to segment informative foreground regions on the projection. We crop nonoverlapping patches from these informative regions and then sample X-rays that land on the pixels inside these patches to help Lineformer perceive local contextual information and 2D structures. For the informative regions outside the patches, we randomly sample X-rays to help Lineformer perceive the scene's 2D global shape and geometry. Besides, we collect a larger-scale dataset, X3D, to evaluate the performance of X-ray 3D reconstruction algorithms in wider application scenarios. As shown in Fig. 1, our SAX-NeRF surpasses state-of-the-art (SOTA) NeRF-based methods by large margins on the NVs task. The average improvements on all scenes of X3D are over 12 dB." + }, + { + "type": "text", + "bbox": [ + 0.518, + 0.334, + 0.844, + 0.347 + ], + "angle": 0, + "content": "Our contributions can be summarized as follows:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.35, + 0.891, + 0.38 + ], + "angle": 0, + "content": "- We propose a novel method, SAX-NeRF, for sparse-view X-ray 3D reconstruction without CT data for training." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.383, + 0.891, + 0.442 + ], + "angle": 0, + "content": "- We present a new Transformer, Lineformer, to capture complex internal structures of imaged objects in 3D space. To our knowledge, it is the first attempt to explore the potential of Transformer in X-ray neural rendering." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.445, + 0.891, + 0.474 + ], + "angle": 0, + "content": "- We design an MLG sampling strategy to extract geometric and contextual information of objects in 2D projection." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.478, + 0.891, + 0.538 + ], + "angle": 0, + "content": "- We establish a larger-scale benchmark, X3D, for X-ray 3D reconstruction. Experiments show that our method outperforms SOTA methods on NVs and CT reconstruction tasks across different application scenarios of X-ray." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.35, + 0.891, + 0.538 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.55, + 0.642, + 0.566 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.575, + 0.676, + 0.59 + ], + "angle": 0, + "content": "2.1. Neural Rendering" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.597, + 0.892, + 0.793 + ], + "angle": 0, + "content": "NeRF [35] represents objects via an implicit function of color and volume density, yielding high-quality results on the NVS task. Follow-up works improve NeRF with more fine-grained details [6, 7] and broader applications [17, 47, 50]. Meanwhile, to reduce the computational cost of NeRF, learnable feature encodings [15, 18, 36] are designed to embed input point positions. However, applying existing RGB NeRF methods for X-ray rendering [22, 43, 59] may achieve suboptimal results due to the differences between visible light and X-ray imaging. For instance, NAF [59] follows NeRF to employ an MLP model for medical X-ray neural rendering, showing limitations in capturing complex structures of imaged objects in 3D space and 2D projection." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.802, + 0.776, + 0.817 + ], + "angle": 0, + "content": "2.2. Cone Beam CT Reconstruction" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.826, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Traditional cone beam CT Reconstruction algorithms are mainly divided into two categories: analytical methods [25, 54] and optimization-based methods [2, 34, 37, 44, 46, 57]. Analytical methods predict the CT volume by solving the Radon transformation [40] and its inverse. These methods" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11175" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.091, + 0.092, + 0.887, + 0.234 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.088, + 0.244, + 0.887, + 0.376 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.383, + 0.893, + 0.425 + ], + "angle": 0, + "content": "Figure 3. Overview of our method. (a) SAX-NeRF uses (i) MLG strategy to sample an X-ray batch \\(\\mathcal{R}\\). Then \\(N\\) point positions \\(\\mathbf{P}\\) on each X-ray \\(\\mathbf{r} \\in \\mathcal{R}\\) are sampled and input into (ii) Lineformer to produce the radiodensity \\(\\mathbf{D}\\). (b) Line Segment-based Attention Block (LSAB) is the basic unit of Lineformer. It captures inner structural dependencies by (c) Line Segment-based Multi-head Self-Attention (LS-MSA)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.444, + 0.473, + 0.596 + ], + "angle": 0, + "content": "can achieve good results when given hundreds of projections but fail in handling sparse-view cases. Optimization-based algorithms treat the reconstruction as a maximum a posteriori (MAP) problem based on hand-crafted image priors and solve it by iteratively minimizing the energy function, which takes a long time. Recently, CNNs [3, 30, 33, 53, 56] and diffusion models [19] have been applied to CT reconstruction and achieve good results. Yet, these methods require a number of data pairs for training. To avoid the above restrictions, we develop NeRF-based algorithms." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.605, + 0.265, + 0.62 + ], + "angle": 0, + "content": "2.3. Vision Transformer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.628, + 0.47, + 0.78 + ], + "angle": 0, + "content": "Transformer [49] is first proposed for machine translation. In recent years, it has achieved great success in computer vision including image classification [1, 5, 23], object detection [48, 58, 63], semantic segmentation [52, 61, 62], image restoration [12-14, 55] and generation [28, 29, 60], etc. Nonetheless, directly applying vanilla Transformer for X-ray neural rendering will suffer from expensive computational cost with respect to the number of input points. The potential of Transformer for X-ray neural rendering still remains under-explored. We aim to fill this research gap." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.793, + 0.168, + 0.807 + ], + "angle": 0, + "content": "3. Method" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.817, + 0.267, + 0.832 + ], + "angle": 0, + "content": "3.1. Overall Framework" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.471, + 0.902 + ], + "angle": 0, + "content": "Fig. 3 illustrates the pipeline of our method. The left part of Fig. 3 (a) depicts the scenario of circular cone beam X-ray scanning where a scanner emits cone-shaped X-ray beams and captures sparse-view projections at equal angular inter" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.444, + 0.892, + 0.595 + ], + "angle": 0, + "content": "vals. We first use (i) Masked Local-Global (MLG) strategy to sample a batch of X-rays \\(\\mathcal{R}\\) landing on the projections for training. Then \\(N\\) point positions \\(\\mathbf{P} = \\{\\mathbf{p}_1,\\dots ,\\mathbf{p}_N\\} \\in \\mathbb{R}^{N\\times 3}\\) are sampled on each X-ray \\(\\mathbf{r}\\in \\mathcal{R}\\) and fed into (ii) Lineformer. The basic unit of Lineformer is Line Segmentbased Attention Block (LSAB). As shown in Fig. 3 (b), an LSAB consists of a fully connected \\((fc)\\) layer, two layer normalization (LN), a feed-forward network (FFN), and a Line Segment-based Multi-head Self-Attention (LS-MSA). The details of LS-MSA are depicted in Fig. 3 (c)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.595, + 0.892, + 0.657 + ], + "angle": 0, + "content": "Firstly, we review RGB NeRF. An MLP with weights \\(\\Theta\\) is usually employed to learn the mapping function \\(F_{\\Theta}\\) from the point position \\((x,y,z)\\in \\mathbb{R}^3\\) at the view direction \\((\\theta ,\\phi)\\) to the color \\((R,G,B)\\in \\mathbb{R}^3\\) and volume density \\(\\sigma \\in \\mathbb{R}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.584, + 0.665, + 0.891, + 0.681 + ], + "angle": 0, + "content": "\\[\nF _ {\\Theta}: (x, y, z, \\theta , \\phi) \\rightarrow (R, G, B, \\sigma). \\tag {1}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.689, + 0.892, + 0.811 + ], + "angle": 0, + "content": "As shown in Fig. 2, visible light of specific wavelengths reflects off the surface of the object, thus revealing its color. In contrast, X-rays penetrate the object, thereby not reflecting the color information. Instead, it records the radiodensity property that denotes the degree to which a substance blocks or attenuates the passage of X-rays or other ionizing radiation. Since the radiodensity only depends on the point position, we aim to model the neural radiodensity fields as" + }, + { + "type": "equation", + "bbox": [ + 0.629, + 0.818, + 0.891, + 0.833 + ], + "angle": 0, + "content": "\\[\nF _ {\\Theta_ {L}}: (x, y, z) \\rightarrow \\rho , \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.893, + 0.901 + ], + "angle": 0, + "content": "where \\(F_{\\Theta_L}\\) represents the mapping function of our Lineformer with weights \\(\\Theta_L\\) and \\(\\rho \\in \\mathbb{R}\\) denotes the radiodensity. According to the Beer-Lambert law, the intensity of an X-ray is reduced by the exponential integration of the" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11176" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.47, + 0.138 + ], + "angle": 0, + "content": "traversed object's radiodensity. Hence, the ground-truth intensity \\( I_{gt}(\\mathbf{r}) \\in \\mathbb{R} \\) of the X-ray \\( \\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d} \\in \\mathbb{R}^3 \\) with the near and far bounds \\( t_n \\) and \\( t_f \\in \\mathbb{R} \\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.16, + 0.146, + 0.47, + 0.178 + ], + "angle": 0, + "content": "\\[\nI _ {g t} (\\mathbf {r}) = I _ {0} \\cdot \\exp \\left(- \\int_ {t _ {n}} ^ {t _ {f}} \\rho (\\mathbf {r} (t)) d t\\right), \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.185, + 0.469, + 0.217 + ], + "angle": 0, + "content": "where \\(I_0\\) is the initial intensity. By discretizing Eq. (3), we derive the predicted projection intensity \\(I_{pred}(\\mathbf{r})\\in \\mathbb{R}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.172, + 0.225, + 0.469, + 0.262 + ], + "angle": 0, + "content": "\\[\nI _ {p r e d} (\\mathbf {r}) = I _ {0} \\cdot \\exp \\left(- \\sum_ {i = 1} ^ {N} \\rho_ {i} \\delta_ {i}\\right), \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.271, + 0.469, + 0.347 + ], + "angle": 0, + "content": "where \\(\\rho_{i}\\) denotes the predicted radiodensity of the \\(i\\)-th sampled point and \\(\\delta_{i} = ||\\mathbf{p}_{i + 1} - \\mathbf{p}_{i}||\\) is the distance between adjacent points. Eventually, the training objective is to minimize the total squared error \\(\\mathcal{L}\\) between the predicted and ground-truth intensities in the training X-ray batch \\(\\mathcal{R}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.356, + 0.469, + 0.388 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left| \\left| I _ {p r e d} (\\mathbf {r}) - I _ {g t} (\\mathbf {r}) \\right| \\right| _ {2} ^ {2}, \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.398, + 0.468, + 0.43 + ], + "angle": 0, + "content": "where \\(I_{gt}(\\mathbf{r})\\) is obtained from the pixel value on projection. \\(\\mathcal{L}\\) is depicted by the red pixels in the right part of Fig. 3 (a)." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.439, + 0.364, + 0.455 + ], + "angle": 0, + "content": "3.2. Line Segment-based Transfomer" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.462, + 0.469, + 0.612 + ], + "angle": 0, + "content": "As aforementioned, X-ray imaging reveals internal structures of imaged objects, which provide key clues for 3D reconstruction. Yet, previous methods overlook this important imaging property. Specifically, similar to RGB NeRF algorithms, existing X-ray NeRF methods [56, 59] mainly adopt a simple MLP model to learn the implicit neural representations. X-ray attenuates differently when penetrating different structural contents. Yet, the MLP model treats each sampled point on an X-ray equally, showing limitations in modeling the 3D structures penetrated by the X-ray." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.614, + 0.469, + 0.704 + ], + "angle": 0, + "content": "Towards this issue, we propose a Line Segment-based Transformer (Lineformer), as shown in Fig. 3 (a) (ii). The point position \\(\\mathbf{P}\\) is firstly fed into a hash encoding [36] module \\(\\mathcal{H}\\) to produce point feature \\(\\mathbf{F} \\in \\mathbb{R}^{N \\times C}\\) as \\(\\mathbf{F} = \\mathcal{H}(\\mathbf{P})\\). Then \\(\\mathbf{F}\\) undergoes four LSABs with a skip connection and two \\(fc\\) layers to derive the point radiodensity \\(\\mathbf{D} \\in \\mathbb{R}^N\\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.704, + 0.469, + 0.795 + ], + "angle": 0, + "content": "LSAB is the basic unit of Lineformer. Its most important component is the LS-MSA mechanism, which captures internal structural dependencies by computing self-attention within each line segment of an X-ray. As illustrated in Fig. 3 (c), the input point feature \\(\\mathbf{X} \\in \\mathbb{R}^{N \\times C}\\) is firstly partitioned into \\(M\\) segments along the point dimension as" + }, + { + "type": "equation", + "bbox": [ + 0.182, + 0.803, + 0.469, + 0.821 + ], + "angle": 0, + "content": "\\[\n\\mathbf {X} = \\left[ \\begin{array}{l l l l} \\mathbf {X} _ {1}, & \\mathbf {X} _ {2}, & \\dots , & \\mathbf {X} _ {M} \\end{array} \\right] ^ {\\mathrm {T}}, \\tag {6}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.829, + 0.469, + 0.876 + ], + "angle": 0, + "content": "where \\(\\mathbf{X}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}\\) and \\(i = 1,2,\\dots ,M\\) . Then each \\(\\mathbf{X}_i\\) is linearly projected into query \\(\\mathbf{Q}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}\\) ,key \\(\\mathbf{K}_i\\in\\) \\(\\mathbb{R}^{\\frac{N}{M}\\times C}\\) , and value \\(\\mathbf{V}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}\\) by three \\(fc\\) layers as" + }, + { + "type": "equation", + "bbox": [ + 0.114, + 0.884, + 0.469, + 0.902 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {Q} _ {i}}, \\quad \\mathbf {K} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {K} _ {i}}, \\quad \\mathbf {V} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {V} _ {i}}, \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.09, + 0.892, + 0.152 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}^{\\mathbf{Q}_i}\\), \\(\\mathbf{W}^{\\mathbf{K}_i}\\), and \\(\\mathbf{W}^{\\mathbf{V}_i} \\in \\mathbb{R}^{C \\times C}\\) are learnable parameters of the \\(fc\\) layers; biases are omitted for simplification. Subsequently, \\(\\mathbf{W}^{\\mathbf{Q}_i}\\), \\(\\mathbf{W}^{\\mathbf{K}_i}\\), and \\(\\mathbf{W}^{\\mathbf{V}_i}\\) are uniformly split into \\(k\\) heads along the channel dimension as" + }, + { + "type": "equation", + "bbox": [ + 0.608, + 0.158, + 0.782, + 0.175 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Q} _ {i} = \\left[ \\begin{array}{c} \\mathbf {Q} _ {i} ^ {1}, \\quad \\mathbf {Q} _ {i} ^ {2}, \\quad \\dots , \\quad \\mathbf {Q} _ {i} ^ {k} \\end{array} \\right],\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.178, + 0.891, + 0.194 + ], + "angle": 0, + "content": "\\[\n\\mathbf {K} _ {i} = \\left[ \\mathbf {K} _ {i} ^ {1}, \\mathbf {K} _ {i} ^ {2}, \\dots , \\mathbf {K} _ {i} ^ {k} \\right], \\tag {8}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.609, + 0.198, + 0.783, + 0.215 + ], + "angle": 0, + "content": "\\[\n\\mathbf {V} _ {i} = \\left[ \\begin{array}{c} \\mathbf {V} _ {i} ^ {1}, \\mathbf {V} _ {i} ^ {2}, \\dots , \\mathbf {V} _ {i} ^ {k} \\end{array} \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.221, + 0.892, + 0.267 + ], + "angle": 0, + "content": "The dimension for each head is \\( d_h = C / k \\). Fig. 3 (b) illustrates the situation with \\( k = 1 \\) for simplicity. Then the self-attention within each head \\( \\mathbf{H}_i^j \\) is computed as" + }, + { + "type": "equation", + "bbox": [ + 0.539, + 0.271, + 0.891, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\mathbf {H} _ {i} ^ {j} = \\operatorname {A t t n} \\left(\\mathbf {Q} _ {i} ^ {j}, \\mathbf {K} _ {i} ^ {j}, \\mathbf {V} _ {i} ^ {j}\\right) = \\mathbf {V} _ {i} ^ {j} \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {K} _ {i} ^ {j} {} ^ {\\mathrm {T}} \\mathbf {Q} _ {i} ^ {j}}{\\alpha_ {i} ^ {j}}\\right), \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.311, + 0.892, + 0.387 + ], + "angle": 0, + "content": "where \\(\\alpha_{i}^{j}\\in \\mathbb{R}\\) is a learnable parameter that adaptively scales the inner product before the softmax function. Successively, \\(k\\) heads are concatenated in channel dimension to pass through an \\(fc\\) layer and then plus a positional embedding \\(\\mathbf{E}_i\\in \\mathbb{R}_{M}^{\\frac{N}{M}\\times C}\\) to derive the \\(i\\)-th output \\(\\mathbf{Y}_i\\in \\mathbb{R}_{M}^{\\frac{N}{M}\\times C}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.577, + 0.394, + 0.891, + 0.412 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} _ {i} = \\left[ \\mathbf {H} _ {i} ^ {1}, \\mathbf {H} _ {i} ^ {2}, \\dots , \\mathbf {H} _ {i} ^ {k} \\right] \\mathbf {W} _ {i} + \\mathbf {E} _ {i}, \\tag {10}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.419, + 0.892, + 0.464 + ], + "angle": 0, + "content": "where \\(\\mathbf{W}_i\\in \\mathbb{R}^{C\\times C}\\) are learnable parameters of the \\(fc\\) layer. Finally, we group the outputs of \\(M\\) segments in point dimension to obtain the output feature \\(\\mathbf{Y}\\in \\mathbb{R}^{N\\times C}\\) as" + }, + { + "type": "equation", + "bbox": [ + 0.604, + 0.469, + 0.891, + 0.487 + ], + "angle": 0, + "content": "\\[\n\\mathbf {Y} = \\left[ \\begin{array}{l l l l} \\mathbf {Y} _ {1}, & \\mathbf {Y} _ {2}, & \\dots , & \\mathbf {Y} _ {M} \\end{array} \\right] ^ {\\mathrm {T}}. \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.492, + 0.892, + 0.568 + ], + "angle": 0, + "content": "By capturing the interactions of points within each line segment, the proposed Lineformer is more capable of perceiving the complex internal 3D structures of different parts penetrated by the X-ray and therefore modeling the implicit neural radiodensity fields in Eq. (2) more accurately." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.574, + 0.892, + 0.68 + ], + "angle": 0, + "content": "Complexity Analysis. We analyze the computational complexity of our LS-MSA and compare it with the global multi-head self-attention (G-MSA) mechanism of vanilla Transformer. The computational cost of LS-MSA primarily comes from the two matrix multiplication, i.e., \\(\\mathbb{R}^{d_h\\times \\frac{N}{M}\\times}\\) \\(\\mathbb{R}_{M}^{N\\times d_{h}}\\) and \\(\\mathbb{R}_{M}^{N\\times d_{h}}\\times \\mathbb{R}^{d_{h}\\times d_{h}}\\), in Eq. (9) performed \\(k\\times M\\) times. Thus, the complexity of LS-MSA is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.514, + 0.687, + 0.892, + 0.743 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {O} (\\text {L S - M S A}) = k M \\cdot \\left[ d _ {h} \\cdot \\left(d _ {h} \\cdot \\frac {N}{M}\\right) + \\frac {N}{M} \\cdot \\left(d _ {h} \\cdot d _ {h}\\right) \\right], \\tag {12} \\\\ = 2 k M d _ {h} ^ {2} \\frac {N}{M} = 2 N k \\left(\\frac {C}{k}\\right) ^ {2} = \\frac {2 N C ^ {2}}{k}. \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.752, + 0.828, + 0.767 + ], + "angle": 0, + "content": "While the complexity of G-MSA is formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.626, + 0.772, + 0.891, + 0.789 + ], + "angle": 0, + "content": "\\[\n\\mathcal {O} (\\mathrm {G} - \\mathrm {M S A}) = 2 N ^ {2} C. \\tag {13}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.795, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Compare Eq. (12) with Eq. (13). \\(\\mathcal{O}(\\mathrm{G - MSA})\\) is quadratic to the number of input points \\((N)\\). This heavy computational burden impedes the application of Transformer for X-ray 3D reconstruction. In contrast, \\(\\mathcal{O}(\\mathrm{LS - MSA})\\) is linear to \\(N\\). This significantly reduced cost allows for the integration of LS-MSA into each basic unit LSAB of Lineformer, thereby further exploring the tremendous potential of Transformer." + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11177" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.078, + 0.091, + 0.393, + 0.108 + ], + "angle": 0, + "content": "3.3. Masked Local-Global Ray Sampling" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.114, + 0.47, + 0.34 + ], + "angle": 0, + "content": "As shown in Fig. 4 (a), existing NeRF algorithms mainly adopt a naive pixel-level ray sampling strategy. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system for training. This naive strategy has two drawbacks. Firstly, it shows limitations in extracting local contextual and geometric representations in 2D projection because the semantic information from neighbor pixels is not captured. Secondly, X-ray images are spatially sparse. Some randomly sampled X-rays may land on the background dark regions of the projection, such as the pixel \\( p_{bg} \\) in Fig. 4 (a). These X-rays do not penetrate the object and thus are not imaged on the projection. In other words, these X-rays are uninformative because they do not characterize the radiodensity property of the object. Learning with these X-rays will degrade the model efficiency." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.34, + 0.471, + 0.479 + ], + "angle": 0, + "content": "To address these problems, we propose a Masked Local-Global (MLG) ray sampling strategy, as shown in Fig. 4 (b). MLG first uses a mask \\(\\mathbf{M} \\in \\mathbb{R}^{H \\times W}\\) to segment the imaged foreground regions. \\(\\mathbf{M}\\) is derived by binarizing the projection \\(\\mathbf{I} \\in \\mathbb{R}^{H \\times W}\\) with a threshold \\(T \\in \\mathbb{R}\\) as \\(\\mathbf{M} = \\mathbf{1}_{\\mathbf{I} > T}\\). Subsequently, to avoid redundant sampling, we partition \\(\\mathbf{M}\\) into a set \\(\\mathcal{W} \\in \\mathbb{R}^{\\frac{HW}{S^2} \\times S \\times S}\\) of \\(\\frac{HW}{S^2}\\) non-overlapping windows with size \\(S \\times S\\). Let \\(\\mathcal{W}_f\\) denote the set of windows that are entirely contained in the foreground regions as" + }, + { + "type": "equation", + "bbox": [ + 0.176, + 0.484, + 0.469, + 0.5 + ], + "angle": 0, + "content": "\\[\n\\mathcal {W} _ {f} = \\left\\{\\mathbf {w} \\in \\mathcal {W} \\mid \\mathbf {w} = \\mathbf {1} _ {S \\times S} \\right\\}. \\tag {14}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.504, + 0.47, + 0.58 + ], + "angle": 0, + "content": "To capture local semantic information of the object, we perform patch-level sampling. Specifically, we randomly select \\(N_{l}\\) windows \\(\\mathcal{W}_l = \\{\\mathbf{w}_1,\\dots ,\\mathbf{w}_{N_l}\\}\\) from \\(\\mathcal{W}_f\\) as shown in the red patches of Fig. 4 (b). Then the X-ray set \\(\\mathcal{R}_l\\) corresponding to the pixels within \\(\\mathcal{W}_l\\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.201, + 0.582, + 0.469, + 0.62 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {l} = \\bigcup_ {i = 1} ^ {N _ {l}} \\bigcup_ {p \\in \\mathbf {w} _ {i}} \\operatorname {R a y} (p), \\tag {15}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.469, + 0.742 + ], + "angle": 0, + "content": "where \\(\\operatorname{Ray}(p)\\) is a function that maps from a pixel \\(p\\) to its corresponding X-ray. Furthermore, to assist the model in better capturing global contextual representations and perceiving the overall geometric shape of the imaged object, we perform pixel-level sampling. Particularly, we randomly select \\(N_g\\) pixels \\(\\mathcal{P}\\) from the foreground regions excluding the area of \\(\\mathcal{W}_l\\) to avoid repeated ray sampling, as depicted in the blue pixels of Fig. 4 (b). \\(\\mathcal{P}\\) can be formulated as" + }, + { + "type": "equation", + "bbox": [ + 0.175, + 0.747, + 0.469, + 0.763 + ], + "angle": 0, + "content": "\\[\n\\mathcal {P} = \\{p \\in (\\mathbf {M} - \\mathcal {W} _ {l}) \\mid p = 1 \\}. \\tag {16}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.766, + 0.456, + 0.781 + ], + "angle": 0, + "content": "Then the X-ray set \\(\\mathcal{R}_g\\) corresponding to \\(\\mathcal{P}\\) is obtained by" + }, + { + "type": "equation", + "bbox": [ + 0.214, + 0.783, + 0.469, + 0.812 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} _ {g} = \\bigcup_ {p \\in \\mathcal {P}} \\operatorname {R a y} (p). \\tag {17}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.813, + 0.469, + 0.829 + ], + "angle": 0, + "content": "Finally, the training X-ray batch is the union of \\(\\mathcal{R}_l\\) and \\(\\mathcal{R}_g\\):" + }, + { + "type": "equation", + "bbox": [ + 0.222, + 0.832, + 0.469, + 0.851 + ], + "angle": 0, + "content": "\\[\n\\mathcal {R} = \\mathcal {R} _ {l} \\bigcup \\mathcal {R} _ {g}. \\tag {18}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.856, + 0.469, + 0.902 + ], + "angle": 0, + "content": "Using MLG ray sampling strategy, the model can more effectively capture the contextual information and model the geometric structures of the imaged object on 2D projection." + }, + { + "type": "image_caption", + "bbox": [ + 0.525, + 0.098, + 0.648, + 0.11 + ], + "angle": 0, + "content": "Pixel-level Sampling" + }, + { + "type": "image", + "bbox": [ + 0.509, + 0.118, + 0.668, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.527, + 0.25, + 0.647, + 0.264 + ], + "angle": 0, + "content": "(a) Naive Sampling" + }, + { + "type": "image_caption", + "bbox": [ + 0.729, + 0.098, + 0.856, + 0.11 + ], + "angle": 0, + "content": "Patch-level Sampling" + }, + { + "type": "image", + "bbox": [ + 0.715, + 0.118, + 0.872, + 0.24 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.724, + 0.25, + 0.864, + 0.264 + ], + "angle": 0, + "content": "(b) Our MLG Sampling" + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.271, + 0.892, + 0.313 + ], + "angle": 0, + "content": "Figure 4. Comparison of ray sampling. (a) The naive strategy samples X-rays that land on scattered pixels. (b) Our MLG strategy performs pixel- and patch-level sampling on foreground regions." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.331, + 0.624, + 0.348 + ], + "angle": 0, + "content": "4. Experiment" + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.356, + 0.706, + 0.373 + ], + "angle": 0, + "content": "4.1. Experimental Settings" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.38, + 0.892, + 0.622 + ], + "angle": 0, + "content": "X3D Dataset. Previous methods mainly conduct X-ray 3D reconstruction research on limited medical applications. For example, NAF [59] is evaluated on five medical scenes. The performance of NeRF-based methods on other X-ray applications is under-explored. To fill this research gap, we collect a larger-scale dataset, X3D, containing 15 scenes and covering 4 applications, i.e., medicine, biology, security, and industry. We collect the CT volumes of X3D from public datasets. Specifically, the chest, backpack, carp, and pancreas datasets are collected from LIDC-IDRI [4], MIDA [11], \\(\\mathrm{D}^2\\mathrm{VR}\\) [41], and DeepOrgan [42], respectively. The teapot, aneurism, bonsai, and foot datasets are obtained from VOLVIS [39] and the rest are from the open scientific visualization dataset [32]. Then we use the tomographic method TIGRE [8] to generate projections by scanning CT volumes with \\(3\\%\\) noise in the range of \\(0^{\\circ}\\sim 180^{\\circ}\\)." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.625, + 0.893, + 0.837 + ], + "angle": 0, + "content": "Implementation Details. We implement our SAX-NeRF by PyTorch [38]. The model is trained with the Adam [31] optimizer \\((\\beta_{1} = 0.9\\) and \\(\\beta_{2} = 0.999)\\) for 3000 iterations. The learning rate is initially set to \\(1\\times 10^{-4}\\) and is halved every 1500 iterations during the training procedure. The batch size of X-rays is set to 2048, 1024 of which is from patchlevel sampling and the other 1024 is from pixel-level sampling. We uniformly sample 320 points along each X-ray. For each scene, we use its 50 projections to train, another 50 projections to test the performance of NVs, and its CT volume to evaluate the results of CT reconstruction. All experiments are conducted on an RTX 8000 GPU. We adopt the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) [51] as the evaluation metrics." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.847, + 0.638, + 0.862 + ], + "angle": 0, + "content": "4.2. Main Results" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Novel View Synthesis. Tab. 1 lists the quantitative results of PSNR and SSIM on the NVs task. We compare our" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11178" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.897, + 0.332 + ], + "angle": 0, + "content": "
MethodInTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw26.910.993734.840.998132.680.991134.060.996439.890.998842.750.9992
Leg42.530.997645.920.998947.710.998141.400.996950.870.998856.860.9996
Box34.650.996335.670.998536.140.995735.430.997735.980.995539.670.9992
Carp24.040.964820.620.946731.260.962037.350.997329.600.959359.880.9999
Foot39.480.997941.050.998938.240.996337.730.992938.350.991346.640.9994
Head34.830.997729.760.999127.740.929534.430.987830.170.953153.060.9995
Pelvis38.720.996140.790.997237.700.986641.570.994843.760.997553.270.9995
Chest28.950.991536.160.998840.770.999023.610.940242.370.999347.420.9994
Bonsai39.260.995337.670.998347.020.998547.800.998949.030.998955.330.9995
Teapot41.510.997834.660.999329.290.966944.180.999334.920.998552.620.9996
Engine23.990.951721.070.933430.360.885439.720.991831.680.919558.800.9998
Pancreas20.030.853719.850.856037.530.901729.240.803136.230.884449.880.9978
Abdomen27.640.964624.620.955926.740.856327.380.873037.590.985554.220.9996
Aneurism20.810.962124.970.979235.410.993647.990.999739.620.999052.910.9998
Backpack36.090.991839.750.996241.600.996943.160.997742.020.998247.170.9989
Average31.960.976832.490.977036.010.963837.670.971238.810.978551.370.9994
" + }, + { + "type": "table_caption", + "bbox": [ + 0.078, + 0.34, + 0.892, + 0.355 + ], + "angle": 0, + "content": "Table 1. Quantitative comparisons on the novel view synthesis task. The best results are in bold and the second-best results are underlined." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.363, + 0.889, + 0.566 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.079, + 0.572, + 0.889, + 0.587 + ], + "angle": 0, + "content": "Figure 5. Qualitative results of novel view synthesis on the scenes of backpack (top) and carp (bottom). Please zoom in for a better view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.605, + 0.473, + 0.818 + ], + "angle": 0, + "content": "SAX-NeRF with five SOTA NeRF-based algorithms including InTomo [56], NeRF [35], NeAT [43], TensoRF [15], and NAF [59]. The input and output of all methods are set the same as Eq. (2) for fair comparison. It can be observed that our SAX-NeRF significantly outperforms SOTA methods on all scenes. Specifically, when compared with the recent best general RGB NeRF algorithm TensoRF, our SAX-NeRF is 13.70 dB (51.37 - 37.67) and 0.0282 (0.9994 - 0.9712) higher in PSNR and SSIM. When compared with the recent best medical NeRF method NAF, SAX-NeRF surpasses it by 12.56 dB in PSNR and 0.0209 in SSIM. The average improvements of our method on the scenes of medicine, biology, security, and industry are 10.91, 15.03, 5.13, and 13.76 dB, as shown in the bar charts of Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.471, + 0.903 + ], + "angle": 0, + "content": "The qualitative results are depicted in Fig. 5. As can be observed from the zoomed-in patches, previous methods are less effective in synthesizing novel projections. They either produce blurry images or fail to reconstruct structural contents. In contrast, our SAX-NeRF yields more vi" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.606, + 0.892, + 0.652 + ], + "angle": 0, + "content": "sually pleasing results with clearer textures and more fine-grained details while preserving more complete geometric structures. More visual comparisons are shown in Fig. 1." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.657, + 0.893, + 0.839 + ], + "angle": 0, + "content": "CT Reconstruction. Tab. 2 reports the quantitative results on the CT reconstruction task. For fairness, we do not compare projection-CT paired learning-based algorithms, but instead focus on comparing methods that only require X-ray projections of single scenes for training or direct processing. In addition to the five SOTA NeRF-based algorithms. We also compare SAX-NeRF with an analytical method (FDK [25]) and two optimization-based algorithms (ASDPOCS [46] and SART [2]). Our method yields the best results on all scenes. In particular, SAX-NeRF dramatically outperforms previous NeRF-based, optimization-based, and analytical algorithms by over 2.49, 4.92, and \\(12.13\\mathrm{dB}\\)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.84, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Fig. 6 displays the visual comparisons in four application scenarios including medicine (head), biology (carp), security (box), and industry (teapot). Other methods either produce over-smooth images blurring the structural contents or" + }, + { + "type": "page_number", + "bbox": [ + 0.48, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11179" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.08, + 0.089, + 0.895, + 0.31 + ], + "angle": 0, + "content": "
MethodFDK [25]ASD-POCS [46]SART [2]InTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw28.580.781633.250.932533.130.930131.950.916232.170.911432.530.913931.900.897134.140.935835.470.9525
Leg28.480.669035.390.982635.300.980936.410.988239.270.993840.290.990240.700.992341.280.994043.470.9973
Box24.140.561631.270.922631.200.920030.590.914033.580.949431.580.929832.170.931431.780.930935.330.9602
Carp32.320.817737.630.977736.890.968232.470.949332.990.952936.850.957637.520.968737.930.971142.720.9902
Foot24.530.600029.980.920830.290.929631.430.912730.030.907230.860.922130.460.915331.630.936332.250.9403
Head26.170.715535.270.970734.880.959731.070.930334.150.967235.560.967935.530.967236.460.974339.700.9888
Pelvis26.910.636734.260.949334.380.948130.380.904231.720.917033.730.937035.130.952836.010.965440.400.9870
Chest22.890.786131.130.942232.170.959422.040.746028.400.892531.200.949730.130.930833.050.958134.380.9718
Bonsai24.530.727632.700.952933.020.960028.900.881131.770.938233.200.947633.470.952133.850.958536.510.9761
Teapot31.070.805937.350.980037.380.978736.150.978641.670.994540.850.987242.710.994242.560.992644.320.9970
Engine23.020.540530.810.958030.440.944227.490.926436.850.985836.630.980435.210.972837.840.985938.770.9917
Pancreas9.6410.123218.300.770118.360.700816.010.786517.730.861419.060.854119.750.773719.410.812622.980.9531
Abdomen22.630.603031.460.923131.400.917028.050.875429.710.904931.140.906031.510.907334.450.950135.010.9598
Aneurism28.070.729534.730.986434.760.986430.320.965231.970.935335.800.981937.360.988937.730.987141.460.9956
Backpack23.840.535131.340.930931.320.929428.770.875330.280.919231.900.934533.160.936233.260.950135.970.9688
Average25.120.642232.320.940032.330.934230.290.918932.150.935433.410.944733.780.938734.760.953537.250.9753
" + }, + { + "type": "table_caption", + "bbox": [ + 0.082, + 0.316, + 0.886, + 0.33 + ], + "angle": 0, + "content": "Table 2. Quantitative comparisons on the CT reconstruction task. The best results are in bold and the second-best results are underlined." + }, + { + "type": "image", + "bbox": [ + 0.078, + 0.343, + 0.896, + 0.759 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.767, + 0.891, + 0.781 + ], + "angle": 0, + "content": "Figure 6. Visual results of CT reconstruction on the scenes of head, carp, box, and teapot (top to bottom). Please zoom in for a better view." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.804, + 0.47, + 0.866 + ], + "angle": 0, + "content": "introduce distracting artifacts. In contrast, our SAX-NeRF is more favorable to reconstruct vivid high-frequency details such as sharp edges while maintaining spatial smoothness of homogeneous regions within complex structures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.871, + 0.47, + 0.903 + ], + "angle": 0, + "content": "These results convincingly demonstrate the advantages of the proposed SAX-NeRF in X-ray 3D reconstruction." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.803, + 0.655, + 0.82 + ], + "angle": 0, + "content": "4.3. Ablation Study" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.833, + 0.892, + 0.879 + ], + "angle": 0, + "content": "To reliably evaluate the effectiveness of our approaches, we conduct ablation study on all scenes of X3D and report the average PSNR / SSIM results in the following part." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.886, + 0.892, + 0.901 + ], + "angle": 0, + "content": "Break-down Ablation. We adopt a baseline model that" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11180" + } + ], + [ + { + "type": "table", + "bbox": [ + 0.088, + 0.089, + 0.372, + 0.149 + ], + "angle": 0, + "content": "
BaselineLS-MSAMLGNVSCT
✓37.97 / 0.974834.21 / 0.9513
✓✓47.95 / 0.994536.86 / 0.9717
✓✓43.51 / 0.986135.30 / 0.9601
✓✓✓51.37 / 0.999437.25 / 0.9753
" + }, + { + "type": "table", + "bbox": [ + 0.378, + 0.089, + 0.622, + 0.149 + ], + "angle": 0, + "content": "
Num204080160320
NVS45.77647.83250.14851.36550.620
0.98920.99390.99910.99940.9992
CT35.84536.78737.08837.24937.186
0.96700.97110.97450.97530.9749
" + }, + { + "type": "table", + "bbox": [ + 0.629, + 0.089, + 0.882, + 0.15 + ], + "angle": 0, + "content": "
Size2×24×48×816×1632×32
NVS48.51551.36550.29750.40849.629
0.99760.99940.99920.99920.9989
CT36.98237.24937.11837.16337.014
0.97330.97530.97480.97490.9741
" + }, + { + "type": "table_footnote", + "bbox": [ + 0.082, + 0.153, + 0.369, + 0.168 + ], + "angle": 0, + "content": "(a) Break-down ablation to higher performance." + }, + { + "type": "table_footnote", + "bbox": [ + 0.374, + 0.154, + 0.617, + 0.168 + ], + "angle": 0, + "content": "(b) Analysis of the line segment quantity." + }, + { + "type": "table_footnote", + "bbox": [ + 0.634, + 0.154, + 0.868, + 0.168 + ], + "angle": 0, + "content": "(c) Analysis of the sampling patch size." + }, + { + "type": "table_caption", + "bbox": [ + 0.077, + 0.172, + 0.892, + 0.186 + ], + "angle": 0, + "content": "Table 3. We conduct ablation study on all scenes of X3D. Average PSNR and SSIM are reported on the NVS and CT reconstruction tasks." + }, + { + "type": "image", + "bbox": [ + 0.071, + 0.199, + 0.241, + 0.311 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.246, + 0.199, + 0.323, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.274, + 0.251, + 0.308, + 0.259 + ], + "angle": 0, + "content": "Baseline" + }, + { + "type": "image", + "bbox": [ + 0.326, + 0.199, + 0.391, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.341, + 0.251, + 0.379, + 0.259 + ], + "angle": 0, + "content": "+LS-MSA" + }, + { + "type": "image", + "bbox": [ + 0.395, + 0.199, + 0.458, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.414, + 0.251, + 0.441, + 0.259 + ], + "angle": 0, + "content": "+MLG" + }, + { + "type": "image", + "bbox": [ + 0.463, + 0.199, + 0.526, + 0.248 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.466, + 0.251, + 0.521, + 0.259 + ], + "angle": 0, + "content": "Ground Truth" + }, + { + "type": "image", + "bbox": [ + 0.535, + 0.199, + 0.712, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.712, + 0.199, + 0.884, + 0.315 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.067, + 0.324, + 0.53, + 0.338 + ], + "angle": 0, + "content": "Figure 7. Visual analysis. Using LS-MSA and MLG captures more structures." + }, + { + "type": "image_caption", + "bbox": [ + 0.542, + 0.325, + 0.878, + 0.339 + ], + "angle": 0, + "content": "Figure 8. Analysis of the number of training projections." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.357, + 0.47, + 0.523 + ], + "angle": 0, + "content": "is derived by directly removing the LS-MSA module and MLG sampling strategy from our SAX-NeRF to conduct the break-down ablation study. The results are listed in Tab. 3a. The baseline model yields 37.97 and 34.21 dB on NVS and CT reconstruction. When using LS-MSA, the baseline model gains by 9.98 and 2.65 dB. When we apply MLG sampling, the model achieves 5.54 and 1.09 dB improvements. When jointly exploiting the two techniques, the model is improved by 13.40 and 3.04 dB on the NVS and CT reconstruction tasks. This evidence clearly exhibits the efficacy of Lineformer and MLG sampling strategy." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.528, + 0.47, + 0.65 + ], + "angle": 0, + "content": "Visual Analysis. To intuitively show the effectiveness of the two proposed approaches, we further conduct visual analysis on the scene of bonsai. As depicted in Fig. 7, the baseline model fails to preserve the geometry like the tree branches in the projection and blurs high-frequency details such as the edges of the basin in the CT slice. When successively using LS-MSA and MLG sampling, the model reconstructs more structural contents and fine-grained textures." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.655, + 0.47, + 0.821 + ], + "angle": 0, + "content": "Parameter Analysis. We conduct parameter analysis regarding the number of line segments \\( M \\) in Eq. (6) and the patch size \\( S \\) in Eq. (14). Please note that we keep the total number of sampled points and X-rays unchanged for fair comparison. When analyzing one parameter, we fix the other at its optimal value. The results are reported in Tab. 3b and 3c. It is clear that, when using different \\( M \\) and \\( S \\), our SAX-NeRF stably outperforms the baseline model by over 7.81 and 1.64 dB on NVS and CT reconstruction. This evidence suggests the reliability of our method. The model's performance yields its maximum when \\( M = 160 \\) and \\( S = 4 \\)." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.47, + 0.903 + ], + "angle": 0, + "content": "Robustness Analysis. We conduct robustness analysis regarding the number of training projections to compare the performance of different methods when given fewer X-ray projection views. The results are plotted as two line charts in Fig. 8, where the vertical axis is PSNR (in dB per" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.357, + 0.892, + 0.478 + ], + "angle": 0, + "content": "formance) and the horizontal axis is the number of training projections. Our SAX-NeRF reliably surpasses SOTA methods by large margins when given different numbers of training projections on both NVs (left) and CT reconstruction (right) tasks. Surprisingly, when using even only \\(60\\%\\) of training projections, SAX-NeRF still outperforms other algorithms on the NVS task. These results clearly exhibit the superiority and robustness of our proposed method." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.481, + 0.892, + 0.572 + ], + "angle": 0, + "content": "Lineformer vs. vanilla Transformer. We replace LS-MSA with G-MSA to conduct comparative experiments. The experimental results show that our Lineformer significantly outperforms vanilla Transformer by 5.30 and \\(1.28\\mathrm{dB}\\) on the NVS and CT reconstruction tasks while only requiring \\(3.41\\%\\) of vanilla Transformer's computational complexity." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.583, + 0.619, + 0.599 + ], + "angle": 0, + "content": "5. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.609, + 0.892, + 0.85 + ], + "angle": 0, + "content": "In this paper, we focus on studying a core problem in sparse-view X-ray 3D reconstruction, i.e., how to effectively capture the various and complex structures penetrated by X-rays. To this end, we propose a novel framework SAX-NeRF. To model 3D structural dependencies in space, we design a Transformer, Lineformer, as the backbone of SAX-NeRF. Lineformer partitions an X-ray into different line segments and then computes self-attention within each piece of the X-ray. In addition, to extract 2D geometry and contextual representations in projection, we present an MLG ray sampling strategy that contains pixel- and patch-level sampling on the informative foreground regions. Besides, we also collect a larger-scale dataset, X3D, covering wider X-ray application scenarios. Comprehensive experiments on X3D show that SAX-NeRF significantly surpasses SOTA algorithms on the NVs and CT reconstruction tasks." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.892, + 0.9 + ], + "angle": 0, + "content": "Acknowledgements: This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and the Patrick J. 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In ICLR, 2021. 3" + }, + { + "type": "list", + "bbox": [ + 0.503, + 0.092, + 0.892, + 0.884 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.956 + ], + "angle": 0, + "content": "11183" + } + ] +] \ No newline at end of file diff --git a/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/e0ae7df8-d3f1-46c2-a34a-52862215b941_origin.pdf b/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/e0ae7df8-d3f1-46c2-a34a-52862215b941_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2a88e795a562474b4b91e06fdcd15a22eae4cf0b --- /dev/null +++ b/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/e0ae7df8-d3f1-46c2-a34a-52862215b941_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:95570cec7c09179706afd02bd2787c0c0a51e3fdc8487c7e0873c4796503e7e8 +size 6085822 diff --git a/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/full.md b/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/full.md new file mode 100644 index 0000000000000000000000000000000000000000..5ba2a8cbf2f69071850bc041237bbddee4424828 --- /dev/null +++ b/2024/Structure-Aware Sparse-View X-ray 3D Reconstruction/full.md @@ -0,0 +1,390 @@ +# Structure-Aware Sparse-View X-ray 3D Reconstruction + +Yuanhao Cai, Jiahao Wang, Alan Yuille $^{\dagger,*}$ , Zongwei Zhou $^{*}$ , Angtian Wang Johns Hopkins University + +![](images/62173cd3d03eed777ab6f147f75ca5444274c98273d29904e300410883f0f6fe.jpg) +Figure 1. Comparisons of X-ray novel view synthesis. On the collected X3D dataset, our method surpasses state-of-the-art algorithms including InTo (InTomo [56]), NeRF [35], NeAT [43], NAF [59], and TeRF (TensoRF [15]) by 10.91, 15.03, 5.13, and 13.76 dB in PSNR on the scenes of medicine, biology, security, and industry. The average gains are over 12 dB. The visual comparisons of our method and the second-best algorithms on four scenes (pelvis, bonsai, box, and engine) show that our method yields more perceptually pleasing results. + +![](images/ee8cbd8640bf3e18cd465835b2ad0b07418ca0c0d80aabfc8db74e9ba9617633.jpg) + +![](images/c04c291c866ee00a9b1b769292fc86033a73abe2ab9502e9eb3d0d6b8accc4a0.jpg) + +![](images/f31fe9b543acb74771c17d593abfaa09e919449e64242c45b7033d7428112540.jpg) + +# Abstract + +X-ray, known for its ability to reveal internal structures of objects, is expected to provide richer information for 3D reconstruction than visible light. Yet, existing NeRF algorithms overlook this nature of X-ray, leading to their limitations in capturing structural contents of imaged objects. In this paper, we propose a framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), for sparse-view X-ray 3D reconstruction. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. Lineformer captures internal structures of objects in 3D space by modeling the dependencies within each line segment of an X-ray. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy to extract contextual and geometric information in 2D projection. Plus, we collect a larger-scale dataset X3D covering wider X-ray applications. Experiments on X3D show that SAX-NeRF surpasses previous NeRF-based methods by 12.56 and 2.49 dB on novel view synthesis and CT reconstruction. https://github.com/caiyuanhao1998/SAX-NeRF + +# 1. Introduction + +Compared with natural light, X-ray has stronger penetrating power to reveal more internal structures of imaged ob + +jects. Hence, X-ray is widely used for prospective imaging [20, 21, 26, 27] in medicine, biology, security, industry, etc. However, X-ray is harmful to human body because of its ionizing radiation. To reduce X-ray exposure, this paper studies the low-dose X-ray 3D reconstruction problem by decreasing X-ray imaging projections in the circular cone beam X-ray scanning scenario [9, 10, 16, 24, 45]. We focus on two tasks, i.e., novel view synthesis (NVS) and computed tomography (CT) reconstruction. NVS aims to create new projections of a scene from viewpoints not originally captured. CT reconstruction retrieves the 3D CT volume of the scanned object from multi-view X-ray projections. These two tasks are complementary with an overall objective to reconstruct 3D representations from 2D projections. + +A majority of existing deep learning-based methods employ a powerful model such as convolutional neural network (CNN) to learn a brute-force mapping from 2D X-ray projections to 3D CT volumes. These methods require a large number of projection-CT pairs for training. Yet, CT volumes are not accessible in practice. Collecting even a small projection-CT dataset is tedious, labor-intensive, and harmful to health. Plus, these paired learning-based methods fail in generalizing from one application to another due to the large domain discrepancy between different CT datasets. + +Recently, the emergence of NeRF [35] provides a more + +![](images/4c3f83cc13d9dd71a2b2952e5b9e467b88f97a9d190cfeb3f18bddd8b4911f81.jpg) +(a)Visible Light Imaging + +![](images/e007bbb8b952588231c750b93a74f0bc25b0b18bf521d75b9ef0daee57b5f6cf.jpg) +(b) X-ray Imaging +Figure 2. Visible light vs. X-ray. Visible light imaging relies on reflection. X-ray imaging is based on penetration and attenuation. + +reasonable solution to X-ray 3D reconstruction. Compared with paired learning-based algorithms, NeRF-based methods do not require CT volumes for training. Instead, they only need projections of just one scene. Although RGB NeRF algorithms have been well developed, directly applying them for X-ray scenes may achieve suboptimal results due to the fundamental differences between visible light and X-ray imaging. As compared in Fig. 2, visible light imaging relies on the reflection off the surface of an object. It mainly captures external features. In contrast, X-rays penetrate the object and attenuate, thereby forming an image. X-ray imaging primarily reveals internal structures, which provide key clues for X-ray 3D reconstruction. + +Nonetheless, current NeRF-based methods overlook this critical property of X-ray imaging. Firstly, they learn NeRF by a simple multilayer perceptron (MLP). X-ray attenuates differently when penetrating different structures. However, MLP treats each point on an X-ray equally, showing limitations in modeling 3D structures of objects. Secondly, previous methods mainly adopt a naive pixel-level ray sampling strategy in the training phase. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system. As a result, the contextual information and geometric structures in 2D projection are not well extracted. Plus, X-ray projections are spatially sparse. Sampling X-rays on uninformative regions may lead to low efficiency. Besides, existing methods mainly study X-ray 3D reconstruction in limited medical scenes while their performance on other applications is still under-explored. + +To tackle these issues, we propose a novel framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), with the key insight of capturing 2D and 3D structures in X-ray imaging. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. It partitions an X-ray into different line segments and then samples points on each one. By computing self-attention within every piece of the X-ray, Lineformer can model internal dependencies and learn complex 3D structures of different parts penetrated by the X-ray. Unlike vanilla Transformer [49] whose computational cost is quadratic to the number of input points, Lineformer is more + +efficient by enjoying linear computational complexity. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy. It uses a binary mask to segment informative foreground regions on the projection. We crop nonoverlapping patches from these informative regions and then sample X-rays that land on the pixels inside these patches to help Lineformer perceive local contextual information and 2D structures. For the informative regions outside the patches, we randomly sample X-rays to help Lineformer perceive the scene's 2D global shape and geometry. Besides, we collect a larger-scale dataset, X3D, to evaluate the performance of X-ray 3D reconstruction algorithms in wider application scenarios. As shown in Fig. 1, our SAX-NeRF surpasses state-of-the-art (SOTA) NeRF-based methods by large margins on the NVs task. The average improvements on all scenes of X3D are over 12 dB. + +Our contributions can be summarized as follows: + +- We propose a novel method, SAX-NeRF, for sparse-view X-ray 3D reconstruction without CT data for training. +- We present a new Transformer, Lineformer, to capture complex internal structures of imaged objects in 3D space. To our knowledge, it is the first attempt to explore the potential of Transformer in X-ray neural rendering. +- We design an MLG sampling strategy to extract geometric and contextual information of objects in 2D projection. +- We establish a larger-scale benchmark, X3D, for X-ray 3D reconstruction. Experiments show that our method outperforms SOTA methods on NVs and CT reconstruction tasks across different application scenarios of X-ray. + +# 2. Related Work + +# 2.1. Neural Rendering + +NeRF [35] represents objects via an implicit function of color and volume density, yielding high-quality results on the NVS task. Follow-up works improve NeRF with more fine-grained details [6, 7] and broader applications [17, 47, 50]. Meanwhile, to reduce the computational cost of NeRF, learnable feature encodings [15, 18, 36] are designed to embed input point positions. However, applying existing RGB NeRF methods for X-ray rendering [22, 43, 59] may achieve suboptimal results due to the differences between visible light and X-ray imaging. For instance, NAF [59] follows NeRF to employ an MLP model for medical X-ray neural rendering, showing limitations in capturing complex structures of imaged objects in 3D space and 2D projection. + +# 2.2. Cone Beam CT Reconstruction + +Traditional cone beam CT Reconstruction algorithms are mainly divided into two categories: analytical methods [25, 54] and optimization-based methods [2, 34, 37, 44, 46, 57]. Analytical methods predict the CT volume by solving the Radon transformation [40] and its inverse. These methods + +![](images/ce3eb0745cb73f93d1000b3a20161e20d3b6ce624d3a3c0316317c88a2a9cabf.jpg) + +![](images/061820d749da2ade9762222d455dd3c145de189774ba4473ba8e24685943ec14.jpg) +Figure 3. Overview of our method. (a) SAX-NeRF uses (i) MLG strategy to sample an X-ray batch $\mathcal{R}$ . Then $N$ point positions $\mathbf{P}$ on each X-ray $\mathbf{r} \in \mathcal{R}$ are sampled and input into (ii) Lineformer to produce the radiodensity $\mathbf{D}$ . (b) Line Segment-based Attention Block (LSAB) is the basic unit of Lineformer. It captures inner structural dependencies by (c) Line Segment-based Multi-head Self-Attention (LS-MSA). + +can achieve good results when given hundreds of projections but fail in handling sparse-view cases. Optimization-based algorithms treat the reconstruction as a maximum a posteriori (MAP) problem based on hand-crafted image priors and solve it by iteratively minimizing the energy function, which takes a long time. Recently, CNNs [3, 30, 33, 53, 56] and diffusion models [19] have been applied to CT reconstruction and achieve good results. Yet, these methods require a number of data pairs for training. To avoid the above restrictions, we develop NeRF-based algorithms. + +# 2.3. Vision Transformer + +Transformer [49] is first proposed for machine translation. In recent years, it has achieved great success in computer vision including image classification [1, 5, 23], object detection [48, 58, 63], semantic segmentation [52, 61, 62], image restoration [12-14, 55] and generation [28, 29, 60], etc. Nonetheless, directly applying vanilla Transformer for X-ray neural rendering will suffer from expensive computational cost with respect to the number of input points. The potential of Transformer for X-ray neural rendering still remains under-explored. We aim to fill this research gap. + +# 3. Method + +# 3.1. Overall Framework + +Fig. 3 illustrates the pipeline of our method. The left part of Fig. 3 (a) depicts the scenario of circular cone beam X-ray scanning where a scanner emits cone-shaped X-ray beams and captures sparse-view projections at equal angular inter + +vals. We first use (i) Masked Local-Global (MLG) strategy to sample a batch of X-rays $\mathcal{R}$ landing on the projections for training. Then $N$ point positions $\mathbf{P} = \{\mathbf{p}_1,\dots ,\mathbf{p}_N\} \in \mathbb{R}^{N\times 3}$ are sampled on each X-ray $\mathbf{r}\in \mathcal{R}$ and fed into (ii) Lineformer. The basic unit of Lineformer is Line Segmentbased Attention Block (LSAB). As shown in Fig. 3 (b), an LSAB consists of a fully connected $(fc)$ layer, two layer normalization (LN), a feed-forward network (FFN), and a Line Segment-based Multi-head Self-Attention (LS-MSA). The details of LS-MSA are depicted in Fig. 3 (c). + +Firstly, we review RGB NeRF. An MLP with weights $\Theta$ is usually employed to learn the mapping function $F_{\Theta}$ from the point position $(x,y,z)\in \mathbb{R}^3$ at the view direction $(\theta ,\phi)$ to the color $(R,G,B)\in \mathbb{R}^3$ and volume density $\sigma \in \mathbb{R}$ as + +$$ +F _ {\Theta}: (x, y, z, \theta , \phi) \rightarrow (R, G, B, \sigma). \tag {1} +$$ + +As shown in Fig. 2, visible light of specific wavelengths reflects off the surface of the object, thus revealing its color. In contrast, X-rays penetrate the object, thereby not reflecting the color information. Instead, it records the radiodensity property that denotes the degree to which a substance blocks or attenuates the passage of X-rays or other ionizing radiation. Since the radiodensity only depends on the point position, we aim to model the neural radiodensity fields as + +$$ +F _ {\Theta_ {L}}: (x, y, z) \rightarrow \rho , \tag {2} +$$ + +where $F_{\Theta_L}$ represents the mapping function of our Lineformer with weights $\Theta_L$ and $\rho \in \mathbb{R}$ denotes the radiodensity. According to the Beer-Lambert law, the intensity of an X-ray is reduced by the exponential integration of the + +traversed object's radiodensity. Hence, the ground-truth intensity $I_{gt}(\mathbf{r}) \in \mathbb{R}$ of the X-ray $\mathbf{r}(t) = \mathbf{o} + t\mathbf{d} \in \mathbb{R}^3$ with the near and far bounds $t_n$ and $t_f \in \mathbb{R}$ can be formulated as + +$$ +I _ {g t} (\mathbf {r}) = I _ {0} \cdot \exp \left(- \int_ {t _ {n}} ^ {t _ {f}} \rho (\mathbf {r} (t)) d t\right), \tag {3} +$$ + +where $I_0$ is the initial intensity. By discretizing Eq. (3), we derive the predicted projection intensity $I_{pred}(\mathbf{r})\in \mathbb{R}$ as + +$$ +I _ {p r e d} (\mathbf {r}) = I _ {0} \cdot \exp \left(- \sum_ {i = 1} ^ {N} \rho_ {i} \delta_ {i}\right), \tag {4} +$$ + +where $\rho_{i}$ denotes the predicted radiodensity of the $i$ -th sampled point and $\delta_{i} = ||\mathbf{p}_{i + 1} - \mathbf{p}_{i}||$ is the distance between adjacent points. Eventually, the training objective is to minimize the total squared error $\mathcal{L}$ between the predicted and ground-truth intensities in the training X-ray batch $\mathcal{R}$ as + +$$ +\mathcal {L} = \sum_ {\mathbf {r} \in \mathcal {R}} \left| \left| I _ {p r e d} (\mathbf {r}) - I _ {g t} (\mathbf {r}) \right| \right| _ {2} ^ {2}, \tag {5} +$$ + +where $I_{gt}(\mathbf{r})$ is obtained from the pixel value on projection. $\mathcal{L}$ is depicted by the red pixels in the right part of Fig. 3 (a). + +# 3.2. Line Segment-based Transfomer + +As aforementioned, X-ray imaging reveals internal structures of imaged objects, which provide key clues for 3D reconstruction. Yet, previous methods overlook this important imaging property. Specifically, similar to RGB NeRF algorithms, existing X-ray NeRF methods [56, 59] mainly adopt a simple MLP model to learn the implicit neural representations. X-ray attenuates differently when penetrating different structural contents. Yet, the MLP model treats each sampled point on an X-ray equally, showing limitations in modeling the 3D structures penetrated by the X-ray. + +Towards this issue, we propose a Line Segment-based Transformer (Lineformer), as shown in Fig. 3 (a) (ii). The point position $\mathbf{P}$ is firstly fed into a hash encoding [36] module $\mathcal{H}$ to produce point feature $\mathbf{F} \in \mathbb{R}^{N \times C}$ as $\mathbf{F} = \mathcal{H}(\mathbf{P})$ . Then $\mathbf{F}$ undergoes four LSABs with a skip connection and two $fc$ layers to derive the point radiodensity $\mathbf{D} \in \mathbb{R}^N$ . + +LSAB is the basic unit of Lineformer. Its most important component is the LS-MSA mechanism, which captures internal structural dependencies by computing self-attention within each line segment of an X-ray. As illustrated in Fig. 3 (c), the input point feature $\mathbf{X} \in \mathbb{R}^{N \times C}$ is firstly partitioned into $M$ segments along the point dimension as + +$$ +\mathbf {X} = \left[ \begin{array}{l l l l} \mathbf {X} _ {1}, & \mathbf {X} _ {2}, & \dots , & \mathbf {X} _ {M} \end{array} \right] ^ {\mathrm {T}}, \tag {6} +$$ + +where $\mathbf{X}_i\in \mathbb{R}^{\frac{N}{M}\times C}$ and $i = 1,2,\dots ,M$ . Then each $\mathbf{X}_i$ is linearly projected into query $\mathbf{Q}_i\in \mathbb{R}^{\frac{N}{M}\times C}$ ,key $\mathbf{K}_i\in$ $\mathbb{R}^{\frac{N}{M}\times C}$ , and value $\mathbf{V}_i\in \mathbb{R}^{\frac{N}{M}\times C}$ by three $fc$ layers as + +$$ +\mathbf {Q} _ {i} = \mathbf {X} _ {i} \mathbf {W} ^ {\mathbf {Q} _ {i}}, \quad \mathbf {K} _ {i} = \mathbf {X} _ {i} \mathbf {W} ^ {\mathbf {K} _ {i}}, \quad \mathbf {V} _ {i} = \mathbf {X} _ {i} \mathbf {W} ^ {\mathbf {V} _ {i}}, \tag {7} +$$ + +where $\mathbf{W}^{\mathbf{Q}_i}$ , $\mathbf{W}^{\mathbf{K}_i}$ , and $\mathbf{W}^{\mathbf{V}_i} \in \mathbb{R}^{C \times C}$ are learnable parameters of the $fc$ layers; biases are omitted for simplification. Subsequently, $\mathbf{W}^{\mathbf{Q}_i}$ , $\mathbf{W}^{\mathbf{K}_i}$ , and $\mathbf{W}^{\mathbf{V}_i}$ are uniformly split into $k$ heads along the channel dimension as + +$$ +\mathbf {Q} _ {i} = \left[ \begin{array}{c} \mathbf {Q} _ {i} ^ {1}, \quad \mathbf {Q} _ {i} ^ {2}, \quad \dots , \quad \mathbf {Q} _ {i} ^ {k} \end{array} \right], +$$ + +$$ +\mathbf {K} _ {i} = \left[ \mathbf {K} _ {i} ^ {1}, \mathbf {K} _ {i} ^ {2}, \dots , \mathbf {K} _ {i} ^ {k} \right], \tag {8} +$$ + +$$ +\mathbf {V} _ {i} = \left[ \begin{array}{c} \mathbf {V} _ {i} ^ {1}, \mathbf {V} _ {i} ^ {2}, \dots , \mathbf {V} _ {i} ^ {k} \end{array} \right]. +$$ + +The dimension for each head is $d_h = C / k$ . Fig. 3 (b) illustrates the situation with $k = 1$ for simplicity. Then the self-attention within each head $\mathbf{H}_i^j$ is computed as + +$$ +\mathbf {H} _ {i} ^ {j} = \operatorname {A t t n} \left(\mathbf {Q} _ {i} ^ {j}, \mathbf {K} _ {i} ^ {j}, \mathbf {V} _ {i} ^ {j}\right) = \mathbf {V} _ {i} ^ {j} \operatorname {s o f t m a x} \left(\frac {\mathbf {K} _ {i} ^ {j} {} ^ {\mathrm {T}} \mathbf {Q} _ {i} ^ {j}}{\alpha_ {i} ^ {j}}\right), \tag {9} +$$ + +where $\alpha_{i}^{j}\in \mathbb{R}$ is a learnable parameter that adaptively scales the inner product before the softmax function. Successively, $k$ heads are concatenated in channel dimension to pass through an $fc$ layer and then plus a positional embedding $\mathbf{E}_i\in \mathbb{R}_{M}^{\frac{N}{M}\times C}$ to derive the $i$ -th output $\mathbf{Y}_i\in \mathbb{R}_{M}^{\frac{N}{M}\times C}$ as + +$$ +\mathbf {Y} _ {i} = \left[ \mathbf {H} _ {i} ^ {1}, \mathbf {H} _ {i} ^ {2}, \dots , \mathbf {H} _ {i} ^ {k} \right] \mathbf {W} _ {i} + \mathbf {E} _ {i}, \tag {10} +$$ + +where $\mathbf{W}_i\in \mathbb{R}^{C\times C}$ are learnable parameters of the $fc$ layer. Finally, we group the outputs of $M$ segments in point dimension to obtain the output feature $\mathbf{Y}\in \mathbb{R}^{N\times C}$ as + +$$ +\mathbf {Y} = \left[ \begin{array}{l l l l} \mathbf {Y} _ {1}, & \mathbf {Y} _ {2}, & \dots , & \mathbf {Y} _ {M} \end{array} \right] ^ {\mathrm {T}}. \tag {11} +$$ + +By capturing the interactions of points within each line segment, the proposed Lineformer is more capable of perceiving the complex internal 3D structures of different parts penetrated by the X-ray and therefore modeling the implicit neural radiodensity fields in Eq. (2) more accurately. + +Complexity Analysis. We analyze the computational complexity of our LS-MSA and compare it with the global multi-head self-attention (G-MSA) mechanism of vanilla Transformer. The computational cost of LS-MSA primarily comes from the two matrix multiplication, i.e., $\mathbb{R}^{d_h\times \frac{N}{M}\times}$ $\mathbb{R}_{M}^{N\times d_{h}}$ and $\mathbb{R}_{M}^{N\times d_{h}}\times \mathbb{R}^{d_{h}\times d_{h}}$ , in Eq. (9) performed $k\times M$ times. Thus, the complexity of LS-MSA is formulated as + +$$ +\begin{array}{l} \mathcal {O} (\text {L S - M S A}) = k M \cdot \left[ d _ {h} \cdot \left(d _ {h} \cdot \frac {N}{M}\right) + \frac {N}{M} \cdot \left(d _ {h} \cdot d _ {h}\right) \right], \tag {12} \\ = 2 k M d _ {h} ^ {2} \frac {N}{M} = 2 N k \left(\frac {C}{k}\right) ^ {2} = \frac {2 N C ^ {2}}{k}. \\ \end{array} +$$ + +While the complexity of G-MSA is formulated as + +$$ +\mathcal {O} (\mathrm {G} - \mathrm {M S A}) = 2 N ^ {2} C. \tag {13} +$$ + +Compare Eq. (12) with Eq. (13). $\mathcal{O}(\mathrm{G - MSA})$ is quadratic to the number of input points $(N)$ . This heavy computational burden impedes the application of Transformer for X-ray 3D reconstruction. In contrast, $\mathcal{O}(\mathrm{LS - MSA})$ is linear to $N$ . This significantly reduced cost allows for the integration of LS-MSA into each basic unit LSAB of Lineformer, thereby further exploring the tremendous potential of Transformer. + +# 3.3. Masked Local-Global Ray Sampling + +As shown in Fig. 4 (a), existing NeRF algorithms mainly adopt a naive pixel-level ray sampling strategy. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system for training. This naive strategy has two drawbacks. Firstly, it shows limitations in extracting local contextual and geometric representations in 2D projection because the semantic information from neighbor pixels is not captured. Secondly, X-ray images are spatially sparse. Some randomly sampled X-rays may land on the background dark regions of the projection, such as the pixel $p_{bg}$ in Fig. 4 (a). These X-rays do not penetrate the object and thus are not imaged on the projection. In other words, these X-rays are uninformative because they do not characterize the radiodensity property of the object. Learning with these X-rays will degrade the model efficiency. + +To address these problems, we propose a Masked Local-Global (MLG) ray sampling strategy, as shown in Fig. 4 (b). MLG first uses a mask $\mathbf{M} \in \mathbb{R}^{H \times W}$ to segment the imaged foreground regions. $\mathbf{M}$ is derived by binarizing the projection $\mathbf{I} \in \mathbb{R}^{H \times W}$ with a threshold $T \in \mathbb{R}$ as $\mathbf{M} = \mathbf{1}_{\mathbf{I} > T}$ . Subsequently, to avoid redundant sampling, we partition $\mathbf{M}$ into a set $\mathcal{W} \in \mathbb{R}^{\frac{HW}{S^2} \times S \times S}$ of $\frac{HW}{S^2}$ non-overlapping windows with size $S \times S$ . Let $\mathcal{W}_f$ denote the set of windows that are entirely contained in the foreground regions as + +$$ +\mathcal {W} _ {f} = \left\{\mathbf {w} \in \mathcal {W} \mid \mathbf {w} = \mathbf {1} _ {S \times S} \right\}. \tag {14} +$$ + +To capture local semantic information of the object, we perform patch-level sampling. Specifically, we randomly select $N_{l}$ windows $\mathcal{W}_l = \{\mathbf{w}_1,\dots ,\mathbf{w}_{N_l}\}$ from $\mathcal{W}_f$ as shown in the red patches of Fig. 4 (b). Then the X-ray set $\mathcal{R}_l$ corresponding to the pixels within $\mathcal{W}_l$ can be formulated as + +$$ +\mathcal {R} _ {l} = \bigcup_ {i = 1} ^ {N _ {l}} \bigcup_ {p \in \mathbf {w} _ {i}} \operatorname {R a y} (p), \tag {15} +$$ + +where $\operatorname{Ray}(p)$ is a function that maps from a pixel $p$ to its corresponding X-ray. Furthermore, to assist the model in better capturing global contextual representations and perceiving the overall geometric shape of the imaged object, we perform pixel-level sampling. Particularly, we randomly select $N_g$ pixels $\mathcal{P}$ from the foreground regions excluding the area of $\mathcal{W}_l$ to avoid repeated ray sampling, as depicted in the blue pixels of Fig. 4 (b). $\mathcal{P}$ can be formulated as + +$$ +\mathcal {P} = \{p \in (\mathbf {M} - \mathcal {W} _ {l}) \mid p = 1 \}. \tag {16} +$$ + +Then the X-ray set $\mathcal{R}_g$ corresponding to $\mathcal{P}$ is obtained by + +$$ +\mathcal {R} _ {g} = \bigcup_ {p \in \mathcal {P}} \operatorname {R a y} (p). \tag {17} +$$ + +Finally, the training X-ray batch is the union of $\mathcal{R}_l$ and $\mathcal{R}_g$ : + +$$ +\mathcal {R} = \mathcal {R} _ {l} \bigcup \mathcal {R} _ {g}. \tag {18} +$$ + +Using MLG ray sampling strategy, the model can more effectively capture the contextual information and model the geometric structures of the imaged object on 2D projection. + +![](images/25caeb2a5c978ab24ebb3b4eadb9c370710b763dfaff4d77be357094d30c810a.jpg) +Pixel-level Sampling +(a) Naive Sampling +Figure 4. Comparison of ray sampling. (a) The naive strategy samples X-rays that land on scattered pixels. (b) Our MLG strategy performs pixel- and patch-level sampling on foreground regions. + +![](images/2e2f320bfe45a6cb2d6440876ca0518ec4475e24573982ebd78c3083246817fd.jpg) +Patch-level Sampling +(b) Our MLG Sampling + +# 4. Experiment + +# 4.1. Experimental Settings + +X3D Dataset. Previous methods mainly conduct X-ray 3D reconstruction research on limited medical applications. For example, NAF [59] is evaluated on five medical scenes. The performance of NeRF-based methods on other X-ray applications is under-explored. To fill this research gap, we collect a larger-scale dataset, X3D, containing 15 scenes and covering 4 applications, i.e., medicine, biology, security, and industry. We collect the CT volumes of X3D from public datasets. Specifically, the chest, backpack, carp, and pancreas datasets are collected from LIDC-IDRI [4], MIDA [11], $\mathrm{D}^2\mathrm{VR}$ [41], and DeepOrgan [42], respectively. The teapot, aneurism, bonsai, and foot datasets are obtained from VOLVIS [39] and the rest are from the open scientific visualization dataset [32]. Then we use the tomographic method TIGRE [8] to generate projections by scanning CT volumes with $3\%$ noise in the range of $0^{\circ}\sim 180^{\circ}$ . + +Implementation Details. We implement our SAX-NeRF by PyTorch [38]. The model is trained with the Adam [31] optimizer $(\beta_{1} = 0.9$ and $\beta_{2} = 0.999)$ for 3000 iterations. The learning rate is initially set to $1\times 10^{-4}$ and is halved every 1500 iterations during the training procedure. The batch size of X-rays is set to 2048, 1024 of which is from patchlevel sampling and the other 1024 is from pixel-level sampling. We uniformly sample 320 points along each X-ray. For each scene, we use its 50 projections to train, another 50 projections to test the performance of NVs, and its CT volume to evaluate the results of CT reconstruction. All experiments are conducted on an RTX 8000 GPU. We adopt the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) [51] as the evaluation metrics. + +# 4.2. Main Results + +Novel View Synthesis. Tab. 1 lists the quantitative results of PSNR and SSIM on the NVs task. We compare our + +
MethodInTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw26.910.993734.840.998132.680.991134.060.996439.890.998842.750.9992
Leg42.530.997645.920.998947.710.998141.400.996950.870.998856.860.9996
Box34.650.996335.670.998536.140.995735.430.997735.980.995539.670.9992
Carp24.040.964820.620.946731.260.962037.350.997329.600.959359.880.9999
Foot39.480.997941.050.998938.240.996337.730.992938.350.991346.640.9994
Head34.830.997729.760.999127.740.929534.430.987830.170.953153.060.9995
Pelvis38.720.996140.790.997237.700.986641.570.994843.760.997553.270.9995
Chest28.950.991536.160.998840.770.999023.610.940242.370.999347.420.9994
Bonsai39.260.995337.670.998347.020.998547.800.998949.030.998955.330.9995
Teapot41.510.997834.660.999329.290.966944.180.999334.920.998552.620.9996
Engine23.990.951721.070.933430.360.885439.720.991831.680.919558.800.9998
Pancreas20.030.853719.850.856037.530.901729.240.803136.230.884449.880.9978
Abdomen27.640.964624.620.955926.740.856327.380.873037.590.985554.220.9996
Aneurism20.810.962124.970.979235.410.993647.990.999739.620.999052.910.9998
Backpack36.090.991839.750.996241.600.996943.160.997742.020.998247.170.9989
Average31.960.976832.490.977036.010.963837.670.971238.810.978551.370.9994
+ +Table 1. Quantitative comparisons on the novel view synthesis task. The best results are in bold and the second-best results are underlined. + +![](images/b729bab158293fb1dbe9c4b7a9769d38ea3fa39b07848e00c41c192dd6dcd10b.jpg) +Figure 5. Qualitative results of novel view synthesis on the scenes of backpack (top) and carp (bottom). Please zoom in for a better view. + +SAX-NeRF with five SOTA NeRF-based algorithms including InTomo [56], NeRF [35], NeAT [43], TensoRF [15], and NAF [59]. The input and output of all methods are set the same as Eq. (2) for fair comparison. It can be observed that our SAX-NeRF significantly outperforms SOTA methods on all scenes. Specifically, when compared with the recent best general RGB NeRF algorithm TensoRF, our SAX-NeRF is 13.70 dB (51.37 - 37.67) and 0.0282 (0.9994 - 0.9712) higher in PSNR and SSIM. When compared with the recent best medical NeRF method NAF, SAX-NeRF surpasses it by 12.56 dB in PSNR and 0.0209 in SSIM. The average improvements of our method on the scenes of medicine, biology, security, and industry are 10.91, 15.03, 5.13, and 13.76 dB, as shown in the bar charts of Fig. 1. + +The qualitative results are depicted in Fig. 5. As can be observed from the zoomed-in patches, previous methods are less effective in synthesizing novel projections. They either produce blurry images or fail to reconstruct structural contents. In contrast, our SAX-NeRF yields more vi + +sually pleasing results with clearer textures and more fine-grained details while preserving more complete geometric structures. More visual comparisons are shown in Fig. 1. + +CT Reconstruction. Tab. 2 reports the quantitative results on the CT reconstruction task. For fairness, we do not compare projection-CT paired learning-based algorithms, but instead focus on comparing methods that only require X-ray projections of single scenes for training or direct processing. In addition to the five SOTA NeRF-based algorithms. We also compare SAX-NeRF with an analytical method (FDK [25]) and two optimization-based algorithms (ASDPOCS [46] and SART [2]). Our method yields the best results on all scenes. In particular, SAX-NeRF dramatically outperforms previous NeRF-based, optimization-based, and analytical algorithms by over 2.49, 4.92, and $12.13\mathrm{dB}$ + +Fig. 6 displays the visual comparisons in four application scenarios including medicine (head), biology (carp), security (box), and industry (teapot). Other methods either produce over-smooth images blurring the structural contents or + +
MethodFDK [25]ASD-POCS [46]SART [2]InTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw28.580.781633.250.932533.130.930131.950.916232.170.911432.530.913931.900.897134.140.935835.470.9525
Leg28.480.669035.390.982635.300.980936.410.988239.270.993840.290.990240.700.992341.280.994043.470.9973
Box24.140.561631.270.922631.200.920030.590.914033.580.949431.580.929832.170.931431.780.930935.330.9602
Carp32.320.817737.630.977736.890.968232.470.949332.990.952936.850.957637.520.968737.930.971142.720.9902
Foot24.530.600029.980.920830.290.929631.430.912730.030.907230.860.922130.460.915331.630.936332.250.9403
Head26.170.715535.270.970734.880.959731.070.930334.150.967235.560.967935.530.967236.460.974339.700.9888
Pelvis26.910.636734.260.949334.380.948130.380.904231.720.917033.730.937035.130.952836.010.965440.400.9870
Chest22.890.786131.130.942232.170.959422.040.746028.400.892531.200.949730.130.930833.050.958134.380.9718
Bonsai24.530.727632.700.952933.020.960028.900.881131.770.938233.200.947633.470.952133.850.958536.510.9761
Teapot31.070.805937.350.980037.380.978736.150.978641.670.994540.850.987242.710.994242.560.992644.320.9970
Engine23.020.540530.810.958030.440.944227.490.926436.850.985836.630.980435.210.972837.840.985938.770.9917
Pancreas9.6410.123218.300.770118.360.700816.010.786517.730.861419.060.854119.750.773719.410.812622.980.9531
Abdomen22.630.603031.460.923131.400.917028.050.875429.710.904931.140.906031.510.907334.450.950135.010.9598
Aneurism28.070.729534.730.986434.760.986430.320.965231.970.935335.800.981937.360.988937.730.987141.460.9956
Backpack23.840.535131.340.930931.320.929428.770.875330.280.919231.900.934533.160.936233.260.950135.970.9688
Average25.120.642232.320.940032.330.934230.290.918932.150.935433.410.944733.780.938734.760.953537.250.9753
+ +Table 2. Quantitative comparisons on the CT reconstruction task. The best results are in bold and the second-best results are underlined. + +![](images/fffa8548d9cafe24f8c56f1e86799decb22064712733488cae606b7b5248dcb3.jpg) +Figure 6. Visual results of CT reconstruction on the scenes of head, carp, box, and teapot (top to bottom). Please zoom in for a better view. + +introduce distracting artifacts. In contrast, our SAX-NeRF is more favorable to reconstruct vivid high-frequency details such as sharp edges while maintaining spatial smoothness of homogeneous regions within complex structures. + +These results convincingly demonstrate the advantages of the proposed SAX-NeRF in X-ray 3D reconstruction. + +# 4.3. Ablation Study + +To reliably evaluate the effectiveness of our approaches, we conduct ablation study on all scenes of X3D and report the average PSNR / SSIM results in the following part. + +Break-down Ablation. We adopt a baseline model that + +
BaselineLS-MSAMLGNVSCT
✓37.97 / 0.974834.21 / 0.9513
✓✓47.95 / 0.994536.86 / 0.9717
✓✓43.51 / 0.986135.30 / 0.9601
✓✓✓51.37 / 0.999437.25 / 0.9753
+ +(a) Break-down ablation to higher performance. + +
Num204080160320
NVS45.77647.83250.14851.36550.620
0.98920.99390.99910.99940.9992
CT35.84536.78737.08837.24937.186
0.96700.97110.97450.97530.9749
+ +(b) Analysis of the line segment quantity. + +
Size2×24×48×816×1632×32
NVS48.51551.36550.29750.40849.629
0.99760.99940.99920.99920.9989
CT36.98237.24937.11837.16337.014
0.97330.97530.97480.97490.9741
+ +(c) Analysis of the sampling patch size. + +Table 3. We conduct ablation study on all scenes of X3D. Average PSNR and SSIM are reported on the NVS and CT reconstruction tasks. + +![](images/37d29e76fa6019250888d16677472cbcd006c4ae51469c8baaa566a395287cf4.jpg) +Figure 7. Visual analysis. Using LS-MSA and MLG captures more structures. + +![](images/8bc9b8c7388cee82de450fb57cac29e8f796f3358dbe9207912d300daf493b4e.jpg) +Baseline + +![](images/3d4d0966e70bd153c18468eed69983b88549ee69d4b9b0dd8448368b015d304f.jpg) ++LS-MSA + +![](images/0659a48c5efd32ffad9f34a02d77bc3b706972ed4bee1127e23b8e29e7fb313f.jpg) ++MLG + +![](images/aab49d6735a06e58237e5decf7a593ebbdeb7d588f8b839ebdfcc0a303b2d635.jpg) +Ground Truth + +![](images/51a11f1bea466f5588eec2ed57c8ba529d975bd3106d2631dbcc78427dc084de.jpg) +Figure 8. Analysis of the number of training projections. + +![](images/8f3c05475387af9ed35caa088283853164756ecd099d495e7b4af6aa7626c3cd.jpg) + +is derived by directly removing the LS-MSA module and MLG sampling strategy from our SAX-NeRF to conduct the break-down ablation study. The results are listed in Tab. 3a. The baseline model yields 37.97 and 34.21 dB on NVS and CT reconstruction. When using LS-MSA, the baseline model gains by 9.98 and 2.65 dB. When we apply MLG sampling, the model achieves 5.54 and 1.09 dB improvements. When jointly exploiting the two techniques, the model is improved by 13.40 and 3.04 dB on the NVS and CT reconstruction tasks. This evidence clearly exhibits the efficacy of Lineformer and MLG sampling strategy. + +Visual Analysis. To intuitively show the effectiveness of the two proposed approaches, we further conduct visual analysis on the scene of bonsai. As depicted in Fig. 7, the baseline model fails to preserve the geometry like the tree branches in the projection and blurs high-frequency details such as the edges of the basin in the CT slice. When successively using LS-MSA and MLG sampling, the model reconstructs more structural contents and fine-grained textures. + +Parameter Analysis. We conduct parameter analysis regarding the number of line segments $M$ in Eq. (6) and the patch size $S$ in Eq. (14). Please note that we keep the total number of sampled points and X-rays unchanged for fair comparison. When analyzing one parameter, we fix the other at its optimal value. The results are reported in Tab. 3b and 3c. It is clear that, when using different $M$ and $S$ , our SAX-NeRF stably outperforms the baseline model by over 7.81 and 1.64 dB on NVS and CT reconstruction. This evidence suggests the reliability of our method. The model's performance yields its maximum when $M = 160$ and $S = 4$ . + +Robustness Analysis. We conduct robustness analysis regarding the number of training projections to compare the performance of different methods when given fewer X-ray projection views. The results are plotted as two line charts in Fig. 8, where the vertical axis is PSNR (in dB per + +formance) and the horizontal axis is the number of training projections. Our SAX-NeRF reliably surpasses SOTA methods by large margins when given different numbers of training projections on both NVs (left) and CT reconstruction (right) tasks. Surprisingly, when using even only $60\%$ of training projections, SAX-NeRF still outperforms other algorithms on the NVS task. These results clearly exhibit the superiority and robustness of our proposed method. + +Lineformer vs. vanilla Transformer. We replace LS-MSA with G-MSA to conduct comparative experiments. The experimental results show that our Lineformer significantly outperforms vanilla Transformer by 5.30 and $1.28\mathrm{dB}$ on the NVS and CT reconstruction tasks while only requiring $3.41\%$ of vanilla Transformer's computational complexity. + +# 5. Conclusion + +In this paper, we focus on studying a core problem in sparse-view X-ray 3D reconstruction, i.e., how to effectively capture the various and complex structures penetrated by X-rays. To this end, we propose a novel framework SAX-NeRF. To model 3D structural dependencies in space, we design a Transformer, Lineformer, as the backbone of SAX-NeRF. Lineformer partitions an X-ray into different line segments and then computes self-attention within each piece of the X-ray. In addition, to extract 2D geometry and contextual representations in projection, we present an MLG ray sampling strategy that contains pixel- and patch-level sampling on the informative foreground regions. 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Comparisons of X-ray novel view synthesis. On the collected X3D dataset, our method surpasses state-of-the-art algorithms including InTo (InTomo [56]), NeRF [35], NeAT [43], NAF [59], and TeRF (TensoRF [15]) by 10.91, 15.03, 5.13, and 13.76 dB in PSNR on the scenes of medicine, biology, security, and industry. The average gains are over 12 dB. The visual comparisons of our method and the second-best algorithms on four scenes (pelvis, bonsai, box, and engine) show that our method yields more perceptually pleasing results." + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "type": "image", + "bbox": [ + 173, + 198, + 296, + 343 + ], + "blocks": [ + { + "bbox": [ + 173, + 198, + 296, + 343 + ], + "lines": [ + { + "bbox": [ + 173, + 198, + 296, + 343 + ], + "spans": [ + { + "bbox": [ + 173, + 198, + 296, + 343 + ], + "type": "image", + "image_path": "ee8cbd8640bf3e18cd465835b2ad0b07418ca0c0d80aabfc8db74e9ba9617633.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 301, + 198, + 417, + 343 + ], + "blocks": [ + { + "bbox": [ + 301, + 198, + 417, + 343 + ], + "lines": [ + { + "bbox": [ + 301, + 198, + 417, + 343 + ], + "spans": [ + { + "bbox": [ + 301, + 198, + 417, + 343 + ], + "type": "image", + "image_path": "c04c291c866ee00a9b1b769292fc86033a73abe2ab9502e9eb3d0d6b8accc4a0.jpg" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_body" + } + ], + "index": 6 + }, + { + "type": "image", + "bbox": [ + 427, + 198, + 544, + 343 + ], + "blocks": [ + { + "bbox": [ + 427, + 198, + 544, + 343 + ], + "lines": [ + { + "bbox": [ + 427, + 198, + 544, + 343 + ], + "spans": [ + { + "bbox": [ + 427, + 198, + 544, + 343 + ], + "type": "image", + "image_path": "f31fe9b543acb74771c17d593abfaa09e919449e64242c45b7033d7428112540.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + } + ], + "index": 7 + }, + { + "bbox": [ + 143, + 403, + 192, + 415 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 403, + 192, + 415 + ], + "spans": [ + { + "bbox": [ + 143, + 403, + 192, + 415 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 419, + 290, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 419, + 290, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 419, + 290, + 647 + ], + "type": "text", + "content": "X-ray, known for its ability to reveal internal structures of objects, is expected to provide richer information for 3D reconstruction than visible light. Yet, existing NeRF algorithms overlook this nature of X-ray, leading to their limitations in capturing structural contents of imaged objects. In this paper, we propose a framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), for sparse-view X-ray 3D reconstruction. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. Lineformer captures internal structures of objects in 3D space by modeling the dependencies within each line segment of an X-ray. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy to extract contextual and geometric information in 2D projection. Plus, we collect a larger-scale dataset X3D covering wider X-ray applications. 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Introduction" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 670, + 287, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 670, + 287, + 696 + ], + "spans": [ + { + "bbox": [ + 46, + 670, + 287, + 696 + ], + "type": "text", + "content": "Compared with natural light, X-ray has stronger penetrating power to reveal more internal structures of imaged ob" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 403, + 546, + 572 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 403, + 546, + 572 + ], + "spans": [ + { + "bbox": [ + 306, + 403, + 546, + 572 + ], + "type": "text", + "content": "jects. Hence, X-ray is widely used for prospective imaging [20, 21, 26, 27] in medicine, biology, security, industry, etc. However, X-ray is harmful to human body because of its ionizing radiation. To reduce X-ray exposure, this paper studies the low-dose X-ray 3D reconstruction problem by decreasing X-ray imaging projections in the circular cone beam X-ray scanning scenario [9, 10, 16, 24, 45]. We focus on two tasks, i.e., novel view synthesis (NVS) and computed tomography (CT) reconstruction. NVS aims to create new projections of a scene from viewpoints not originally captured. CT reconstruction retrieves the 3D CT volume of the scanned object from multi-view X-ray projections. These two tasks are complementary with an overall objective to reconstruct 3D representations from 2D projections." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "spans": [ + { + "bbox": [ + 304, + 576, + 547, + 696 + ], + "type": "text", + "content": "A majority of existing deep learning-based methods employ a powerful model such as convolutional neural network (CNN) to learn a brute-force mapping from 2D X-ray projections to 3D CT volumes. These methods require a large number of projection-CT pairs for training. Yet, CT volumes are not accessible in practice. Collecting even a small projection-CT dataset is tedious, labor-intensive, and harmful to health. Plus, these paired learning-based methods fail in generalizing from one application to another due to the large domain discrepancy between different CT datasets." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 318, + 700, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 700, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 318, + 700, + 545, + 714 + ], + "type": "text", + "content": "Recently, the emergence of NeRF [35] provides a more" + } + ] + } + ], + "index": 15 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 61, + 701, + 228, + 714 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 701, + 228, + 714 + ], + "spans": [ + { + "bbox": [ + 61, + 701, + 228, + 714 + ], + "type": "inline_equation", + "content": "\\dagger =" + }, + { + "bbox": [ + 61, + 701, + 228, + 714 + ], + "type": "text", + "content": " advisor, " + }, + { + "bbox": [ + 61, + 701, + 228, + 714 + ], + "type": "inline_equation", + "content": "* =" + }, + { + "bbox": [ + 61, + 701, + 228, + 714 + ], + "type": "text", + "content": " corresponding authors" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11174" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 49, + 81, + 159, + 163 + ], + "blocks": [ + { + "bbox": [ + 49, + 81, + 159, + 163 + ], + "lines": [ + { + "bbox": [ + 49, + 81, + 159, + 163 + ], + "spans": [ + { + "bbox": [ + 49, + 81, + 159, + 163 + ], + "type": "image", + "image_path": "4c3f83cc13d9dd71a2b2952e5b9e467b88f97a9d190cfeb3f18bddd8b4911f81.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 60, + 171, + 145, + 182 + ], + "lines": [ + { + "bbox": [ + 60, + 171, + 145, + 182 + ], + "spans": [ + { + "bbox": [ + 60, + 171, + 145, + 182 + ], + "type": "text", + "content": "(a)Visible Light Imaging" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 174, + 76, + 286, + 164 + ], + "blocks": [ + { + "bbox": [ + 174, + 76, + 286, + 164 + ], + "lines": [ + { + "bbox": [ + 174, + 76, + 286, + 164 + ], + "spans": [ + { + "bbox": [ + 174, + 76, + 286, + 164 + ], + "type": "image", + "image_path": "e007bbb8b952588231c750b93a74f0bc25b0b18bf521d75b9ef0daee57b5f6cf.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 196, + 171, + 258, + 180 + ], + "lines": [ + { + "bbox": [ + 196, + 171, + 258, + 180 + ], + "spans": [ + { + "bbox": [ + 196, + 171, + 258, + 180 + ], + "type": "text", + "content": "(b) X-ray Imaging" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 186, + 287, + 209 + ], + "lines": [ + { + "bbox": [ + 46, + 186, + 287, + 209 + ], + "spans": [ + { + "bbox": [ + 46, + 186, + 287, + 209 + ], + "type": "text", + "content": "Figure 2. Visible light vs. X-ray. Visible light imaging relies on reflection. X-ray imaging is based on penetration and attenuation." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 220, + 286, + 376 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 220, + 286, + 376 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 286, + 376 + ], + "type": "text", + "content": "reasonable solution to X-ray 3D reconstruction. Compared with paired learning-based algorithms, NeRF-based methods do not require CT volumes for training. Instead, they only need projections of just one scene. Although RGB NeRF algorithms have been well developed, directly applying them for X-ray scenes may achieve suboptimal results due to the fundamental differences between visible light and X-ray imaging. As compared in Fig. 2, visible light imaging relies on the reflection off the surface of an object. It mainly captures external features. In contrast, X-rays penetrate the object and attenuate, thereby forming an image. X-ray imaging primarily reveals internal structures, which provide key clues for X-ray 3D reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 377, + 286, + 568 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 377, + 286, + 568 + ], + "spans": [ + { + "bbox": [ + 46, + 377, + 286, + 568 + ], + "type": "text", + "content": "Nonetheless, current NeRF-based methods overlook this critical property of X-ray imaging. Firstly, they learn NeRF by a simple multilayer perceptron (MLP). X-ray attenuates differently when penetrating different structures. However, MLP treats each point on an X-ray equally, showing limitations in modeling 3D structures of objects. Secondly, previous methods mainly adopt a naive pixel-level ray sampling strategy in the training phase. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system. As a result, the contextual information and geometric structures in 2D projection are not well extracted. Plus, X-ray projections are spatially sparse. Sampling X-rays on uninformative regions may lead to low efficiency. Besides, existing methods mainly study X-ray 3D reconstruction in limited medical scenes while their performance on other applications is still under-explored." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 570, + 286, + 713 + ], + "type": "text", + "content": "To tackle these issues, we propose a novel framework, Structure-Aware X-ray Neural Radiodensity Fields (SAX-NeRF), with the key insight of capturing 2D and 3D structures in X-ray imaging. Firstly, we design a Line Segment-based Transformer (Lineformer) as the backbone of SAX-NeRF. It partitions an X-ray into different line segments and then samples points on each one. By computing self-attention within every piece of the X-ray, Lineformer can model internal dependencies and learn complex 3D structures of different parts penetrated by the X-ray. Unlike vanilla Transformer [49] whose computational cost is quadratic to the number of input points, Lineformer is more" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 545, + 262 + ], + "type": "text", + "content": "efficient by enjoying linear computational complexity. Secondly, we present a Masked Local-Global (MLG) ray sampling strategy. It uses a binary mask to segment informative foreground regions on the projection. We crop nonoverlapping patches from these informative regions and then sample X-rays that land on the pixels inside these patches to help Lineformer perceive local contextual information and 2D structures. For the informative regions outside the patches, we randomly sample X-rays to help Lineformer perceive the scene's 2D global shape and geometry. Besides, we collect a larger-scale dataset, X3D, to evaluate the performance of X-ray 3D reconstruction algorithms in wider application scenarios. As shown in Fig. 1, our SAX-NeRF surpasses state-of-the-art (SOTA) NeRF-based methods by large margins on the NVs task. The average improvements on all scenes of X3D are over 12 dB." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 317, + 264, + 516, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 264, + 516, + 274 + ], + "spans": [ + { + "bbox": [ + 317, + 264, + 516, + 274 + ], + "type": "text", + "content": "Our contributions can be summarized as follows:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 306, + 277, + 545, + 426 + ], + "type": "list", + "angle": 0, + "index": 14, + "blocks": [ + { + "bbox": [ + 306, + 277, + 545, + 300 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 277, + 545, + 300 + ], + "spans": [ + { + "bbox": [ + 306, + 277, + 545, + 300 + ], + "type": "text", + "content": "- We propose a novel method, SAX-NeRF, for sparse-view X-ray 3D reconstruction without CT data for training." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 303, + 545, + 350 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 303, + 545, + 350 + ], + "spans": [ + { + "bbox": [ + 306, + 303, + 545, + 350 + ], + "type": "text", + "content": "- We present a new Transformer, Lineformer, to capture complex internal structures of imaged objects in 3D space. To our knowledge, it is the first attempt to explore the potential of Transformer in X-ray neural rendering." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 352, + 545, + 375 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 545, + 375 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 545, + 375 + ], + "type": "text", + "content": "- We design an MLG sampling strategy to extract geometric and contextual information of objects in 2D projection." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 306, + 378, + 545, + 426 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 378, + 545, + 426 + ], + "spans": [ + { + "bbox": [ + 306, + 378, + 545, + 426 + ], + "type": "text", + "content": "- We establish a larger-scale benchmark, X3D, for X-ray 3D reconstruction. Experiments show that our method outperforms SOTA methods on NVs and CT reconstruction tasks across different application scenarios of X-ray." + } + ] + } + ], + "index": 13 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 435, + 392, + 448 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 435, + 392, + 448 + ], + "spans": [ + { + "bbox": [ + 306, + 435, + 392, + 448 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 455, + 413, + 467 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 455, + 413, + 467 + ], + "spans": [ + { + "bbox": [ + 306, + 455, + 413, + 467 + ], + "type": "text", + "content": "2.1. Neural Rendering" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 472, + 545, + 628 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 472, + 545, + 628 + ], + "spans": [ + { + "bbox": [ + 304, + 472, + 545, + 628 + ], + "type": "text", + "content": "NeRF [35] represents objects via an implicit function of color and volume density, yielding high-quality results on the NVS task. Follow-up works improve NeRF with more fine-grained details [6, 7] and broader applications [17, 47, 50]. Meanwhile, to reduce the computational cost of NeRF, learnable feature encodings [15, 18, 36] are designed to embed input point positions. However, applying existing RGB NeRF methods for X-ray rendering [22, 43, 59] may achieve suboptimal results due to the differences between visible light and X-ray imaging. For instance, NAF [59] follows NeRF to employ an MLP model for medical X-ray neural rendering, showing limitations in capturing complex structures of imaged objects in 3D space and 2D projection." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 635, + 474, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 474, + 647 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 474, + 647 + ], + "type": "text", + "content": "2.2. Cone Beam CT Reconstruction" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 654, + 545, + 713 + ], + "type": "text", + "content": "Traditional cone beam CT Reconstruction algorithms are mainly divided into two categories: analytical methods [25, 54] and optimization-based methods [2, 34, 37, 44, 46, 57]. Analytical methods predict the CT volume by solving the Radon transformation [40] and its inverse. These methods" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11175" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 55, + 72, + 542, + 185 + ], + "blocks": [ + { + "bbox": [ + 55, + 72, + 542, + 185 + ], + "lines": [ + { + "bbox": [ + 55, + 72, + 542, + 185 + ], + "spans": [ + { + "bbox": [ + 55, + 72, + 542, + 185 + ], + "type": "image", + "image_path": "ce3eb0745cb73f93d1000b3a20161e20d3b6ce624d3a3c0316317c88a2a9cabf.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 53, + 193, + 542, + 297 + ], + "blocks": [ + { + "bbox": [ + 53, + 193, + 542, + 297 + ], + "lines": [ + { + "bbox": [ + 53, + 193, + 542, + 297 + ], + "spans": [ + { + "bbox": [ + 53, + 193, + 542, + 297 + ], + "type": "image", + "image_path": "061820d749da2ade9762222d455dd3c145de189774ba4473ba8e24685943ec14.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "lines": [ + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "text", + "content": "Figure 3. Overview of our method. (a) SAX-NeRF uses (i) MLG strategy to sample an X-ray batch " + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "text", + "content": " point positions " + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "text", + "content": " on each X-ray " + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "inline_equation", + "content": "\\mathbf{r} \\in \\mathcal{R}" + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "text", + "content": " are sampled and input into (ii) Lineformer to produce the radiodensity " + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "inline_equation", + "content": "\\mathbf{D}" + }, + { + "bbox": [ + 46, + 303, + 546, + 336 + ], + "type": "text", + "content": ". (b) Line Segment-based Attention Block (LSAB) is the basic unit of Lineformer. It captures inner structural dependencies by (c) Line Segment-based Multi-head Self-Attention (LS-MSA)." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_caption" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 351, + 289, + 472 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 351, + 289, + 472 + ], + "spans": [ + { + "bbox": [ + 46, + 351, + 289, + 472 + ], + "type": "text", + "content": "can achieve good results when given hundreds of projections but fail in handling sparse-view cases. Optimization-based algorithms treat the reconstruction as a maximum a posteriori (MAP) problem based on hand-crafted image priors and solve it by iteratively minimizing the energy function, which takes a long time. Recently, CNNs [3, 30, 33, 53, 56] and diffusion models [19] have been applied to CT reconstruction and achieve good results. Yet, these methods require a number of data pairs for training. To avoid the above restrictions, we develop NeRF-based algorithms." + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 479, + 162, + 491 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 162, + 491 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 162, + 491 + ], + "type": "text", + "content": "2.3. Vision Transformer" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 497, + 287, + 617 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 497, + 287, + 617 + ], + "spans": [ + { + "bbox": [ + 46, + 497, + 287, + 617 + ], + "type": "text", + "content": "Transformer [49] is first proposed for machine translation. In recent years, it has achieved great success in computer vision including image classification [1, 5, 23], object detection [48, 58, 63], semantic segmentation [52, 61, 62], image restoration [12-14, 55] and generation [28, 29, 60], etc. Nonetheless, directly applying vanilla Transformer for X-ray neural rendering will suffer from expensive computational cost with respect to the number of input points. The potential of Transformer for X-ray neural rendering still remains under-explored. We aim to fill this research gap." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 628, + 102, + 639 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 628, + 102, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 628, + 102, + 639 + ], + "type": "text", + "content": "3. Method" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 647, + 163, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 647, + 163, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 647, + 163, + 658 + ], + "type": "text", + "content": "3.1. Overall Framework" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 288, + 714 + ], + "type": "text", + "content": "Fig. 3 illustrates the pipeline of our method. The left part of Fig. 3 (a) depicts the scenario of circular cone beam X-ray scanning where a scanner emits cone-shaped X-ray beams and captures sparse-view projections at equal angular inter" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "spans": [ + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": "vals. We first use (i) Masked Local-Global (MLG) strategy to sample a batch of X-rays " + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": " landing on the projections for training. Then " + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": " point positions " + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{P} = \\{\\mathbf{p}_1,\\dots ,\\mathbf{p}_N\\} \\in \\mathbb{R}^{N\\times 3}" + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": " are sampled on each X-ray " + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "inline_equation", + "content": "\\mathbf{r}\\in \\mathcal{R}" + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": " and fed into (ii) Lineformer. The basic unit of Lineformer is Line Segmentbased Attention Block (LSAB). As shown in Fig. 3 (b), an LSAB consists of a fully connected " + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "inline_equation", + "content": "(fc)" + }, + { + "bbox": [ + 304, + 351, + 545, + 471 + ], + "type": "text", + "content": " layer, two layer normalization (LN), a feed-forward network (FFN), and a Line Segment-based Multi-head Self-Attention (LS-MSA). The details of LS-MSA are depicted in Fig. 3 (c)." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "spans": [ + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": "Firstly, we review RGB NeRF. An MLP with weights " + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\Theta" + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": " is usually employed to learn the mapping function " + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "inline_equation", + "content": "F_{\\Theta}" + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": " from the point position " + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "inline_equation", + "content": "(x,y,z)\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": " at the view direction " + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "inline_equation", + "content": "(\\theta ,\\phi)" + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": " to the color " + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "inline_equation", + "content": "(R,G,B)\\in \\mathbb{R}^3" + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": " and volume density " + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "inline_equation", + "content": "\\sigma \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 471, + 545, + 520 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 357, + 526, + 545, + 539 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 357, + 526, + 545, + 539 + ], + "spans": [ + { + "bbox": [ + 357, + 526, + 545, + 539 + ], + "type": "interline_equation", + "content": "F _ {\\Theta}: (x, y, z, \\theta , \\phi) \\rightarrow (R, G, B, \\sigma). \\tag {1}", + "image_path": "c21e88498e747ad4c902ce568e66fef5440805457366ef64c6eaae8630d1b9dd.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 545, + 545, + 642 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 545, + 545, + 642 + ], + "spans": [ + { + "bbox": [ + 304, + 545, + 545, + 642 + ], + "type": "text", + "content": "As shown in Fig. 2, visible light of specific wavelengths reflects off the surface of the object, thus revealing its color. In contrast, X-rays penetrate the object, thereby not reflecting the color information. Instead, it records the radiodensity property that denotes the degree to which a substance blocks or attenuates the passage of X-rays or other ionizing radiation. Since the radiodensity only depends on the point position, we aim to model the neural radiodensity fields as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 384, + 647, + 545, + 659 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 384, + 647, + 545, + 659 + ], + "spans": [ + { + "bbox": [ + 384, + 647, + 545, + 659 + ], + "type": "interline_equation", + "content": "F _ {\\Theta_ {L}}: (x, y, z) \\rightarrow \\rho , \\tag {2}", + "image_path": "926f7e89335ff6d014329f2422563c2e7d0a6b0dda4a9fa230f5ef05aa395fb6.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "inline_equation", + "content": "F_{\\Theta_L}" + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": " represents the mapping function of our Lineformer with weights " + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\Theta_L" + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "inline_equation", + "content": "\\rho \\in \\mathbb{R}" + }, + { + "bbox": [ + 304, + 665, + 546, + 713 + ], + "type": "text", + "content": " denotes the radiodensity. According to the Beer-Lambert law, the intensity of an X-ray is reduced by the exponential integration of the" + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 757 + ], + "type": "text", + "content": "11176" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": "traversed object's radiodensity. Hence, the ground-truth intensity " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "I_{gt}(\\mathbf{r}) \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " of the X-ray " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "\\mathbf{r}(t) = \\mathbf{o} + t\\mathbf{d} \\in \\mathbb{R}^3" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " with the near and far bounds " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "t_n" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "inline_equation", + "content": "t_f \\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 72, + 287, + 109 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 97, + 115, + 287, + 140 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 97, + 115, + 287, + 140 + ], + "spans": [ + { + "bbox": [ + 97, + 115, + 287, + 140 + ], + "type": "interline_equation", + "content": "I _ {g t} (\\mathbf {r}) = I _ {0} \\cdot \\exp \\left(- \\int_ {t _ {n}} ^ {t _ {f}} \\rho (\\mathbf {r} (t)) d t\\right), \\tag {3}", + "image_path": "338e6d087cb57edfbadef04b79f54f7a26ca191a463a17590fd04335a38ed4d2.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "spans": [ + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "inline_equation", + "content": "I_0" + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "content": " is the initial intensity. By discretizing Eq. (3), we derive the predicted projection intensity " + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "inline_equation", + "content": "I_{pred}(\\mathbf{r})\\in \\mathbb{R}" + }, + { + "bbox": [ + 47, + 146, + 287, + 171 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 178, + 287, + 207 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 105, + 178, + 287, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 287, + 207 + ], + "type": "interline_equation", + "content": "I _ {p r e d} (\\mathbf {r}) = I _ {0} \\cdot \\exp \\left(- \\sum_ {i = 1} ^ {N} \\rho_ {i} \\delta_ {i}\\right), \\tag {4}", + "image_path": "9e415eb513b6f854d5dc7f32503b0cb6bd629297b4e213752a21754a1095cb10.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "spans": [ + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\rho_{i}" + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "content": " denotes the predicted radiodensity of the " + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "content": "-th sampled point and " + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\delta_{i} = ||\\mathbf{p}_{i + 1} - \\mathbf{p}_{i}||" + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "content": " is the distance between adjacent points. Eventually, the training objective is to minimize the total squared error " + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "content": " between the predicted and ground-truth intensities in the training X-ray batch " + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 214, + 287, + 274 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 102, + 281, + 287, + 307 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 281, + 287, + 307 + ], + "spans": [ + { + "bbox": [ + 102, + 281, + 287, + 307 + ], + "type": "interline_equation", + "content": "\\mathcal {L} = \\sum_ {\\mathbf {r} \\in \\mathcal {R}} \\left| \\left| I _ {p r e d} (\\mathbf {r}) - I _ {g t} (\\mathbf {r}) \\right| \\right| _ {2} ^ {2}, \\tag {5}", + "image_path": "2fbf78ef14838cc1c8d82a14babe0826e5d24b8e936d7baecbea32f89285b413.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "spans": [ + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "type": "inline_equation", + "content": "I_{gt}(\\mathbf{r})" + }, + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "type": "text", + "content": " is obtained from the pixel value on projection. " + }, + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "type": "inline_equation", + "content": "\\mathcal{L}" + }, + { + "bbox": [ + 47, + 315, + 286, + 340 + ], + "type": "text", + "content": " is depicted by the red pixels in the right part of Fig. 3 (a)." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 347, + 222, + 360 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 347, + 222, + 360 + ], + "spans": [ + { + "bbox": [ + 47, + 347, + 222, + 360 + ], + "type": "text", + "content": "3.2. Line Segment-based Transfomer" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "spans": [ + { + "bbox": [ + 46, + 365, + 287, + 484 + ], + "type": "text", + "content": "As aforementioned, X-ray imaging reveals internal structures of imaged objects, which provide key clues for 3D reconstruction. Yet, previous methods overlook this important imaging property. Specifically, similar to RGB NeRF algorithms, existing X-ray NeRF methods [56, 59] mainly adopt a simple MLP model to learn the implicit neural representations. X-ray attenuates differently when penetrating different structural contents. Yet, the MLP model treats each sampled point on an X-ray equally, showing limitations in modeling the 3D structures penetrated by the X-ray." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "spans": [ + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": "Towards this issue, we propose a Line Segment-based Transformer (Lineformer), as shown in Fig. 3 (a) (ii). The point position " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{P}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " is firstly fed into a hash encoding [36] module " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathcal{H}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " to produce point feature " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{F} \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{F} = \\mathcal{H}(\\mathbf{P})" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": ". Then " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{F}" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " undergoes four LSABs with a skip connection and two " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "fc" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": " layers to derive the point radiodensity " + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "inline_equation", + "content": "\\mathbf{D} \\in \\mathbb{R}^N" + }, + { + "bbox": [ + 46, + 486, + 287, + 557 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "spans": [ + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "type": "text", + "content": "LSAB is the basic unit of Lineformer. Its most important component is the LS-MSA mechanism, which captures internal structural dependencies by computing self-attention within each line segment of an X-ray. As illustrated in Fig. 3 (c), the input point feature " + }, + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "type": "inline_equation", + "content": "\\mathbf{X} \\in \\mathbb{R}^{N \\times C}" + }, + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "type": "text", + "content": " is firstly partitioned into " + }, + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 557, + 287, + 629 + ], + "type": "text", + "content": " segments along the point dimension as" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 111, + 635, + 287, + 650 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 111, + 635, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 111, + 635, + 287, + 650 + ], + "type": "interline_equation", + "content": "\\mathbf {X} = \\left[ \\begin{array}{l l l l} \\mathbf {X} _ {1}, & \\mathbf {X} _ {2}, & \\dots , & \\mathbf {X} _ {M} \\end{array} \\right] ^ {\\mathrm {T}}, \\tag {6}", + "image_path": "db5e688c8e43603c0dc6a8aa6c6ee0c6723f8f48ed9f72e050c7d1ebd15fbd5f.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "spans": [ + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "i = 1,2,\\dots ,M" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " . Then each " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{X}_i" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " is linearly projected into query " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{Q}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " ,key " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{K}_i\\in" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{\\frac{N}{M}\\times C}" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " , and value " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "\\mathbf{V}_i\\in \\mathbb{R}^{\\frac{N}{M}\\times C}" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " by three " + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "inline_equation", + "content": "fc" + }, + { + "bbox": [ + 47, + 656, + 287, + 693 + ], + "type": "text", + "content": " layers as" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 69, + 700, + 287, + 714 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 69, + 700, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 69, + 700, + 287, + 714 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {Q} _ {i}}, \\quad \\mathbf {K} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {K} _ {i}}, \\quad \\mathbf {V} _ {i} = \\mathbf {X} _ {i} \\mathbf {W} ^ {\\mathbf {V} _ {i}}, \\tag {7}", + "image_path": "2678f25fe09f318eede9ebb1f5c572d8af6df274f44062c2122d54dd95b5ab68.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "spans": [ + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathbf{Q}_i}" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathbf{K}_i}" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathbf{V}_i} \\in \\mathbb{R}^{C \\times C}" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": " are learnable parameters of the " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "fc" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": " layers; biases are omitted for simplification. Subsequently, " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathbf{Q}_i}" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": ", " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathbf{K}_i}" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "\\mathbf{W}^{\\mathbf{V}_i}" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": " are uniformly split into " + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 71, + 545, + 120 + ], + "type": "text", + "content": " heads along the channel dimension as" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 372, + 125, + 478, + 138 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 125, + 478, + 138 + ], + "spans": [ + { + "bbox": [ + 372, + 125, + 478, + 138 + ], + "type": "interline_equation", + "content": "\\mathbf {Q} _ {i} = \\left[ \\begin{array}{c} \\mathbf {Q} _ {i} ^ {1}, \\quad \\mathbf {Q} _ {i} ^ {2}, \\quad \\dots , \\quad \\mathbf {Q} _ {i} ^ {k} \\end{array} \\right],", + "image_path": "2d62662142b4d0ae9981f4eb3ed15487182369f3947e814dc7da29fca42e2462.jpg" + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 372, + 140, + 545, + 153 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 140, + 545, + 153 + ], + "spans": [ + { + "bbox": [ + 372, + 140, + 545, + 153 + ], + "type": "interline_equation", + "content": "\\mathbf {K} _ {i} = \\left[ \\mathbf {K} _ {i} ^ {1}, \\mathbf {K} _ {i} ^ {2}, \\dots , \\mathbf {K} _ {i} ^ {k} \\right], \\tag {8}", + "image_path": "b06a9df0f884d13809250f2ab61fb9ce874e62467c9d8e646cb7aed4bff68f0f.jpg" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 372, + 156, + 479, + 170 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 372, + 156, + 479, + 170 + ], + "spans": [ + { + "bbox": [ + 372, + 156, + 479, + 170 + ], + "type": "interline_equation", + "content": "\\mathbf {V} _ {i} = \\left[ \\begin{array}{c} \\mathbf {V} _ {i} ^ {1}, \\mathbf {V} _ {i} ^ {2}, \\dots , \\mathbf {V} _ {i} ^ {k} \\end{array} \\right].", + "image_path": "094ffe2de61feada9058fa9d1decf5e92161b2e4fbf5789401a50c1d842a9746.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "spans": [ + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "text", + "content": "The dimension for each head is " + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "inline_equation", + "content": "d_h = C / k" + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "text", + "content": ". Fig. 3 (b) illustrates the situation with " + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "inline_equation", + "content": "k = 1" + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "text", + "content": " for simplicity. Then the self-attention within each head " + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "inline_equation", + "content": "\\mathbf{H}_i^j" + }, + { + "bbox": [ + 305, + 175, + 545, + 211 + ], + "type": "text", + "content": " is computed as" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 329, + 214, + 545, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 329, + 214, + 545, + 243 + ], + "spans": [ + { + "bbox": [ + 329, + 214, + 545, + 243 + ], + "type": "interline_equation", + "content": "\\mathbf {H} _ {i} ^ {j} = \\operatorname {A t t n} \\left(\\mathbf {Q} _ {i} ^ {j}, \\mathbf {K} _ {i} ^ {j}, \\mathbf {V} _ {i} ^ {j}\\right) = \\mathbf {V} _ {i} ^ {j} \\operatorname {s o f t m a x} \\left(\\frac {\\mathbf {K} _ {i} ^ {j} {} ^ {\\mathrm {T}} \\mathbf {Q} _ {i} ^ {j}}{\\alpha_ {i} ^ {j}}\\right), \\tag {9}", + "image_path": "4d4871e7b2bc388df4d8c8d0448fda1c9e80a09751bc831294fdcc0adf94451c.jpg" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "spans": [ + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "inline_equation", + "content": "\\alpha_{i}^{j}\\in \\mathbb{R}" + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": " is a learnable parameter that adaptively scales the inner product before the softmax function. Successively, " + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": " heads are concatenated in channel dimension to pass through an " + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "inline_equation", + "content": "fc" + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": " layer and then plus a positional embedding " + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{E}_i\\in \\mathbb{R}_{M}^{\\frac{N}{M}\\times C}" + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": " to derive the " + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "inline_equation", + "content": "i" + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": "-th output " + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}_i\\in \\mathbb{R}_{M}^{\\frac{N}{M}\\times C}" + }, + { + "bbox": [ + 305, + 246, + 545, + 306 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 353, + 312, + 545, + 326 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 353, + 312, + 545, + 326 + ], + "spans": [ + { + "bbox": [ + 353, + 312, + 545, + 326 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} _ {i} = \\left[ \\mathbf {H} _ {i} ^ {1}, \\mathbf {H} _ {i} ^ {2}, \\dots , \\mathbf {H} _ {i} ^ {k} \\right] \\mathbf {W} _ {i} + \\mathbf {E} _ {i}, \\tag {10}", + "image_path": "399fae10bb041ecef999dc66867e3364a4581842960e154aa4d323d215e1f92b.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{W}_i\\in \\mathbb{R}^{C\\times C}" + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "text", + "content": " are learnable parameters of the " + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "inline_equation", + "content": "fc" + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "text", + "content": " layer. Finally, we group the outputs of " + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "text", + "content": " segments in point dimension to obtain the output feature " + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "inline_equation", + "content": "\\mathbf{Y}\\in \\mathbb{R}^{N\\times C}" + }, + { + "bbox": [ + 305, + 331, + 545, + 367 + ], + "type": "text", + "content": " as" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 369, + 371, + 545, + 385 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 369, + 371, + 545, + 385 + ], + "spans": [ + { + "bbox": [ + 369, + 371, + 545, + 385 + ], + "type": "interline_equation", + "content": "\\mathbf {Y} = \\left[ \\begin{array}{l l l l} \\mathbf {Y} _ {1}, & \\mathbf {Y} _ {2}, & \\dots , & \\mathbf {Y} _ {M} \\end{array} \\right] ^ {\\mathrm {T}}. \\tag {11}", + "image_path": "338590a030827c764f6910c7b2f2fbaeb7be0411f1a85a2290f6a265e408595f.jpg" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 305, + 389, + 545, + 449 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 389, + 545, + 449 + ], + "spans": [ + { + "bbox": [ + 305, + 389, + 545, + 449 + ], + "type": "text", + "content": "By capturing the interactions of points within each line segment, the proposed Lineformer is more capable of perceiving the complex internal 3D structures of different parts penetrated by the X-ray and therefore modeling the implicit neural radiodensity fields in Eq. (2) more accurately." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "spans": [ + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "text", + "content": "Complexity Analysis. We analyze the computational complexity of our LS-MSA and compare it with the global multi-head self-attention (G-MSA) mechanism of vanilla Transformer. The computational cost of LS-MSA primarily comes from the two matrix multiplication, i.e., " + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathbb{R}^{d_h\\times \\frac{N}{M}\\times}" + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathbb{R}_{M}^{N\\times d_{h}}" + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "inline_equation", + "content": "\\mathbb{R}_{M}^{N\\times d_{h}}\\times \\mathbb{R}^{d_{h}\\times d_{h}}" + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "text", + "content": ", in Eq. (9) performed " + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "inline_equation", + "content": "k\\times M" + }, + { + "bbox": [ + 305, + 454, + 545, + 538 + ], + "type": "text", + "content": " times. Thus, the complexity of LS-MSA is formulated as" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 314, + 544, + 545, + 588 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 314, + 544, + 545, + 588 + ], + "spans": [ + { + "bbox": [ + 314, + 544, + 545, + 588 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {O} (\\text {L S - M S A}) = k M \\cdot \\left[ d _ {h} \\cdot \\left(d _ {h} \\cdot \\frac {N}{M}\\right) + \\frac {N}{M} \\cdot \\left(d _ {h} \\cdot d _ {h}\\right) \\right], \\tag {12} \\\\ = 2 k M d _ {h} ^ {2} \\frac {N}{M} = 2 N k \\left(\\frac {C}{k}\\right) ^ {2} = \\frac {2 N C ^ {2}}{k}. \\\\ \\end{array}", + "image_path": "a06366137479c2fb0a6c39cc8494d811f44cf00ad37f25b7a70ebd28b85caf72.jpg" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 306, + 595, + 506, + 607 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 595, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 306, + 595, + 506, + 607 + ], + "type": "text", + "content": "While the complexity of G-MSA is formulated as" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 383, + 611, + 545, + 624 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 383, + 611, + 545, + 624 + ], + "spans": [ + { + "bbox": [ + 383, + 611, + 545, + 624 + ], + "type": "interline_equation", + "content": "\\mathcal {O} (\\mathrm {G} - \\mathrm {M S A}) = 2 N ^ {2} C. \\tag {13}", + "image_path": "ab9e0d71494c5931eb6ccfd05d99d6ba6a42a88f6097f7f1c8c53a3a2d9eea1e.jpg" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": "Compare Eq. (12) with Eq. (13). " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\mathrm{G - MSA})" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " is quadratic to the number of input points " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "(N)" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": ". This heavy computational burden impedes the application of Transformer for X-ray 3D reconstruction. In contrast, " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\mathrm{LS - MSA})" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": " is linear to " + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "inline_equation", + "content": "N" + }, + { + "bbox": [ + 305, + 629, + 545, + 713 + ], + "type": "text", + "content": ". This significantly reduced cost allows for the integration of LS-MSA into each basic unit LSAB of Lineformer, thereby further exploring the tremendous potential of Transformer." + } + ] + } + ], + "index": 29 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 317, + 757 + ], + "type": "text", + "content": "11177" + } + ] + } + ], + "index": 30 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 240, + 85 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 240, + 85 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 240, + 85 + ], + "type": "text", + "content": "3.3. Masked Local-Global Ray Sampling" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "spans": [ + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "type": "text", + "content": "As shown in Fig. 4 (a), existing NeRF algorithms mainly adopt a naive pixel-level ray sampling strategy. They randomly sample X-rays corresponding to scattered pixels on the whole image coordinate system for training. This naive strategy has two drawbacks. Firstly, it shows limitations in extracting local contextual and geometric representations in 2D projection because the semantic information from neighbor pixels is not captured. Secondly, X-ray images are spatially sparse. Some randomly sampled X-rays may land on the background dark regions of the projection, such as the pixel " + }, + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "type": "inline_equation", + "content": "p_{bg}" + }, + { + "bbox": [ + 46, + 90, + 287, + 269 + ], + "type": "text", + "content": " in Fig. 4 (a). These X-rays do not penetrate the object and thus are not imaged on the projection. In other words, these X-rays are uninformative because they do not characterize the radiodensity property of the object. Learning with these X-rays will degrade the model efficiency." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "spans": [ + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": "To address these problems, we propose a Masked Local-Global (MLG) ray sampling strategy, as shown in Fig. 4 (b). MLG first uses a mask " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " to segment the imaged foreground regions. " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " is derived by binarizing the projection " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{I} \\in \\mathbb{R}^{H \\times W}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " with a threshold " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "T \\in \\mathbb{R}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " as " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M} = \\mathbf{1}_{\\mathbf{I} > T}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": ". Subsequently, to avoid redundant sampling, we partition " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathbf{M}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " into a set " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathcal{W} \\in \\mathbb{R}^{\\frac{HW}{S^2} \\times S \\times S}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " of " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\frac{HW}{S^2}" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " non-overlapping windows with size " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "S \\times S" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": ". Let " + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_f" + }, + { + "bbox": [ + 46, + 269, + 288, + 379 + ], + "type": "text", + "content": " denote the set of windows that are entirely contained in the foreground regions as" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 383, + 287, + 396 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 383, + 287, + 396 + ], + "spans": [ + { + "bbox": [ + 107, + 383, + 287, + 396 + ], + "type": "interline_equation", + "content": "\\mathcal {W} _ {f} = \\left\\{\\mathbf {w} \\in \\mathcal {W} \\mid \\mathbf {w} = \\mathbf {1} _ {S \\times S} \\right\\}. \\tag {14}", + "image_path": "78ce218928d12883ae578d598471cd2e7ddb4781fcc5941cc37e80e57ff9c2b2.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "spans": [ + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "content": "To capture local semantic information of the object, we perform patch-level sampling. Specifically, we randomly select " + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "N_{l}" + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "content": " windows " + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_l = \\{\\mathbf{w}_1,\\dots ,\\mathbf{w}_{N_l}\\}" + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_f" + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "content": " as shown in the red patches of Fig. 4 (b). Then the X-ray set " + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_l" + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "content": " corresponding to the pixels within " + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_l" + }, + { + "bbox": [ + 47, + 399, + 287, + 459 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 123, + 460, + 287, + 491 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 123, + 460, + 287, + 491 + ], + "spans": [ + { + "bbox": [ + 123, + 460, + 287, + 491 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {l} = \\bigcup_ {i = 1} ^ {N _ {l}} \\bigcup_ {p \\in \\mathbf {w} _ {i}} \\operatorname {R a y} (p), \\tag {15}", + "image_path": "a947d5a1a48c267815fd858e05b0c9081a3b50a742a19b491d98c4fa5b49ec42.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\operatorname{Ray}(p)" + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": " is a function that maps from a pixel " + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "inline_equation", + "content": "p" + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": " to its corresponding X-ray. Furthermore, to assist the model in better capturing global contextual representations and perceiving the overall geometric shape of the imaged object, we perform pixel-level sampling. Particularly, we randomly select " + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "inline_equation", + "content": "N_g" + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": " pixels " + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": " from the foreground regions excluding the area of " + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{W}_l" + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": " to avoid repeated ray sampling, as depicted in the blue pixels of Fig. 4 (b). " + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 46, + 491, + 287, + 587 + ], + "type": "text", + "content": " can be formulated as" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 107, + 591, + 287, + 604 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 107, + 591, + 287, + 604 + ], + "spans": [ + { + "bbox": [ + 107, + 591, + 287, + 604 + ], + "type": "interline_equation", + "content": "\\mathcal {P} = \\{p \\in (\\mathbf {M} - \\mathcal {W} _ {l}) \\mid p = 1 \\}. \\tag {16}", + "image_path": "9f8befaf6946339af4f8e82843856a56d2837450b02d1dad183dcce8b6a492a8.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "spans": [ + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "type": "text", + "content": "Then the X-ray set " + }, + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_g" + }, + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "type": "text", + "content": " corresponding to " + }, + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "type": "inline_equation", + "content": "\\mathcal{P}" + }, + { + "bbox": [ + 47, + 606, + 279, + 618 + ], + "type": "text", + "content": " is obtained by" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 130, + 620, + 287, + 643 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 130, + 620, + 287, + 643 + ], + "spans": [ + { + "bbox": [ + 130, + 620, + 287, + 643 + ], + "type": "interline_equation", + "content": "\\mathcal {R} _ {g} = \\bigcup_ {p \\in \\mathcal {P}} \\operatorname {R a y} (p). \\tag {17}", + "image_path": "b8d375c7d1af00c66cc3be82cb3f491fcbe869d8daf9e0c170e67a6bc1a49323.jpg" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "spans": [ + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "type": "text", + "content": "Finally, the training X-ray batch is the union of " + }, + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_l" + }, + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "type": "inline_equation", + "content": "\\mathcal{R}_g" + }, + { + "bbox": [ + 47, + 643, + 287, + 656 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 135, + 658, + 287, + 673 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 135, + 658, + 287, + 673 + ], + "spans": [ + { + "bbox": [ + 135, + 658, + 287, + 673 + ], + "type": "interline_equation", + "content": "\\mathcal {R} = \\mathcal {R} _ {l} \\bigcup \\mathcal {R} _ {g}. \\tag {18}", + "image_path": "e31ffb2504b6dbe8639d9ee725788b59ee32b197b70b93c0ff6e0e45a8436f60.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 677, + 287, + 714 + ], + "type": "text", + "content": "Using MLG ray sampling strategy, the model can more effectively capture the contextual information and model the geometric structures of the imaged object on 2D projection." + } + ] + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 311, + 93, + 408, + 190 + ], + "blocks": [ + { + "bbox": [ + 321, + 77, + 396, + 87 + ], + "lines": [ + { + "bbox": [ + 321, + 77, + 396, + 87 + ], + "spans": [ + { + "bbox": [ + 321, + 77, + 396, + 87 + ], + "type": "text", + "content": "Pixel-level Sampling" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 311, + 93, + 408, + 190 + ], + "lines": [ + { + "bbox": [ + 311, + 93, + 408, + 190 + ], + "spans": [ + { + "bbox": [ + 311, + 93, + 408, + 190 + ], + "type": "image", + "image_path": "25caeb2a5c978ab24ebb3b4eadb9c370710b763dfaff4d77be357094d30c810a.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 322, + 198, + 395, + 209 + ], + "lines": [ + { + "bbox": [ + 322, + 198, + 395, + 209 + ], + "spans": [ + { + "bbox": [ + 322, + 198, + 395, + 209 + ], + "type": "text", + "content": "(a) Naive Sampling" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 305, + 214, + 545, + 247 + ], + "lines": [ + { + "bbox": [ + 305, + 214, + 545, + 247 + ], + "spans": [ + { + "bbox": [ + 305, + 214, + 545, + 247 + ], + "type": "text", + "content": "Figure 4. Comparison of ray sampling. (a) The naive strategy samples X-rays that land on scattered pixels. (b) Our MLG strategy performs pixel- and patch-level sampling on foreground regions." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 437, + 93, + 533, + 190 + ], + "blocks": [ + { + "bbox": [ + 446, + 77, + 523, + 87 + ], + "lines": [ + { + "bbox": [ + 446, + 77, + 523, + 87 + ], + "spans": [ + { + "bbox": [ + 446, + 77, + 523, + 87 + ], + "type": "text", + "content": "Patch-level Sampling" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 437, + 93, + 533, + 190 + ], + "lines": [ + { + "bbox": [ + 437, + 93, + 533, + 190 + ], + "spans": [ + { + "bbox": [ + 437, + 93, + 533, + 190 + ], + "type": "image", + "image_path": "2e2f320bfe45a6cb2d6440876ca0518ec4475e24573982ebd78c3083246817fd.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 443, + 198, + 528, + 209 + ], + "lines": [ + { + "bbox": [ + 443, + 198, + 528, + 209 + ], + "spans": [ + { + "bbox": [ + 443, + 198, + 528, + 209 + ], + "type": "text", + "content": "(b) Our MLG Sampling" + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 262, + 381, + 275 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 262, + 381, + 275 + ], + "spans": [ + { + "bbox": [ + 306, + 262, + 381, + 275 + ], + "type": "text", + "content": "4. Experiment" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 306, + 281, + 432, + 295 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 281, + 432, + 295 + ], + "spans": [ + { + "bbox": [ + 306, + 281, + 432, + 295 + ], + "type": "text", + "content": "4.1. Experimental Settings" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "spans": [ + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "text", + "content": "X3D Dataset. Previous methods mainly conduct X-ray 3D reconstruction research on limited medical applications. For example, NAF [59] is evaluated on five medical scenes. The performance of NeRF-based methods on other X-ray applications is under-explored. To fill this research gap, we collect a larger-scale dataset, X3D, containing 15 scenes and covering 4 applications, i.e., medicine, biology, security, and industry. We collect the CT volumes of X3D from public datasets. Specifically, the chest, backpack, carp, and pancreas datasets are collected from LIDC-IDRI [4], MIDA [11], " + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "inline_equation", + "content": "\\mathrm{D}^2\\mathrm{VR}" + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "text", + "content": " [41], and DeepOrgan [42], respectively. The teapot, aneurism, bonsai, and foot datasets are obtained from VOLVIS [39] and the rest are from the open scientific visualization dataset [32]. Then we use the tomographic method TIGRE [8] to generate projections by scanning CT volumes with " + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "inline_equation", + "content": "3\\%" + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "text", + "content": " noise in the range of " + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "inline_equation", + "content": "0^{\\circ}\\sim 180^{\\circ}" + }, + { + "bbox": [ + 304, + 300, + 545, + 492 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "text", + "content": "Implementation Details. We implement our SAX-NeRF by PyTorch [38]. The model is trained with the Adam [31] optimizer " + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "inline_equation", + "content": "(\\beta_{1} = 0.9" + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "inline_equation", + "content": "\\beta_{2} = 0.999)" + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "text", + "content": " for 3000 iterations. The learning rate is initially set to " + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "inline_equation", + "content": "1\\times 10^{-4}" + }, + { + "bbox": [ + 304, + 495, + 546, + 662 + ], + "type": "text", + "content": " and is halved every 1500 iterations during the training procedure. The batch size of X-rays is set to 2048, 1024 of which is from patchlevel sampling and the other 1024 is from pixel-level sampling. We uniformly sample 320 points along each X-ray. For each scene, we use its 50 projections to train, another 50 projections to test the performance of NVs, and its CT volume to evaluate the results of CT reconstruction. All experiments are conducted on an RTX 8000 GPU. We adopt the peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) [51] as the evaluation metrics." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 670, + 390, + 682 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 670, + 390, + 682 + ], + "spans": [ + { + "bbox": [ + 306, + 670, + 390, + 682 + ], + "type": "text", + "content": "4.2. Main Results" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 713 + ], + "type": "text", + "content": "Novel View Synthesis. Tab. 1 lists the quantitative results of PSNR and SSIM on the NVs task. We compare our" + } + ] + } + ], + "index": 25 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11178" + } + ] + } + ], + "index": 26 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 548, + 262 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 548, + 262 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 548, + 262 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 548, + 262 + ], + "type": "table", + "html": "
MethodInTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw26.910.993734.840.998132.680.991134.060.996439.890.998842.750.9992
Leg42.530.997645.920.998947.710.998141.400.996950.870.998856.860.9996
Box34.650.996335.670.998536.140.995735.430.997735.980.995539.670.9992
Carp24.040.964820.620.946731.260.962037.350.997329.600.959359.880.9999
Foot39.480.997941.050.998938.240.996337.730.992938.350.991346.640.9994
Head34.830.997729.760.999127.740.929534.430.987830.170.953153.060.9995
Pelvis38.720.996140.790.997237.700.986641.570.994843.760.997553.270.9995
Chest28.950.991536.160.998840.770.999023.610.940242.370.999347.420.9994
Bonsai39.260.995337.670.998347.020.998547.800.998949.030.998955.330.9995
Teapot41.510.997834.660.999329.290.966944.180.999334.920.998552.620.9996
Engine23.990.951721.070.933430.360.885439.720.991831.680.919558.800.9998
Pancreas20.030.853719.850.856037.530.901729.240.803136.230.884449.880.9978
Abdomen27.640.964624.620.955926.740.856327.380.873037.590.985554.220.9996
Aneurism20.810.962124.970.979235.410.993647.990.999739.620.999052.910.9998
Backpack36.090.991839.750.996241.600.996943.160.997742.020.998247.170.9989
Average31.960.976832.490.977036.010.963837.670.971238.810.978551.370.9994
", + "image_path": "978a946bc5f4785d37420ce0c120cd172c5ac2206382b08167c4f0a2cf49dd11.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 269, + 545, + 281 + ], + "lines": [ + { + "bbox": [ + 47, + 269, + 545, + 281 + ], + "spans": [ + { + "bbox": [ + 47, + 269, + 545, + 281 + ], + "type": "text", + "content": "Table 1. Quantitative comparisons on the novel view synthesis task. The best results are in bold and the second-best results are underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 47, + 287, + 544, + 448 + ], + "blocks": [ + { + "bbox": [ + 47, + 287, + 544, + 448 + ], + "lines": [ + { + "bbox": [ + 47, + 287, + 544, + 448 + ], + "spans": [ + { + "bbox": [ + 47, + 287, + 544, + 448 + ], + "type": "image", + "image_path": "b729bab158293fb1dbe9c4b7a9769d38ea3fa39b07848e00c41c192dd6dcd10b.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 48, + 453, + 544, + 464 + ], + "lines": [ + { + "bbox": [ + 48, + 453, + 544, + 464 + ], + "spans": [ + { + "bbox": [ + 48, + 453, + 544, + 464 + ], + "type": "text", + "content": "Figure 5. Qualitative results of novel view synthesis on the scenes of backpack (top) and carp (bottom). Please zoom in for a better view." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "spans": [ + { + "bbox": [ + 46, + 479, + 289, + 647 + ], + "type": "text", + "content": "SAX-NeRF with five SOTA NeRF-based algorithms including InTomo [56], NeRF [35], NeAT [43], TensoRF [15], and NAF [59]. The input and output of all methods are set the same as Eq. (2) for fair comparison. It can be observed that our SAX-NeRF significantly outperforms SOTA methods on all scenes. Specifically, when compared with the recent best general RGB NeRF algorithm TensoRF, our SAX-NeRF is 13.70 dB (51.37 - 37.67) and 0.0282 (0.9994 - 0.9712) higher in PSNR and SSIM. When compared with the recent best medical NeRF method NAF, SAX-NeRF surpasses it by 12.56 dB in PSNR and 0.0209 in SSIM. The average improvements of our method on the scenes of medicine, biology, security, and industry are 10.91, 15.03, 5.13, and 13.76 dB, as shown in the bar charts of Fig. 1." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 288, + 715 + ], + "type": "text", + "content": "The qualitative results are depicted in Fig. 5. As can be observed from the zoomed-in patches, previous methods are less effective in synthesizing novel projections. They either produce blurry images or fail to reconstruct structural contents. In contrast, our SAX-NeRF yields more vi" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 479, + 545, + 516 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 479, + 545, + 516 + ], + "spans": [ + { + "bbox": [ + 304, + 479, + 545, + 516 + ], + "type": "text", + "content": "sually pleasing results with clearer textures and more fine-grained details while preserving more complete geometric structures. More visual comparisons are shown in Fig. 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 520, + 546, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 520, + 546, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 520, + 546, + 664 + ], + "type": "text", + "content": "CT Reconstruction. Tab. 2 reports the quantitative results on the CT reconstruction task. For fairness, we do not compare projection-CT paired learning-based algorithms, but instead focus on comparing methods that only require X-ray projections of single scenes for training or direct processing. In addition to the five SOTA NeRF-based algorithms. We also compare SAX-NeRF with an analytical method (FDK [25]) and two optimization-based algorithms (ASDPOCS [46] and SART [2]). Our method yields the best results on all scenes. In particular, SAX-NeRF dramatically outperforms previous NeRF-based, optimization-based, and analytical algorithms by over 2.49, 4.92, and " + }, + { + "bbox": [ + 304, + 520, + 546, + 664 + ], + "type": "inline_equation", + "content": "12.13\\mathrm{dB}" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 665, + 547, + 713 + ], + "type": "text", + "content": "Fig. 6 displays the visual comparisons in four application scenarios including medicine (head), biology (carp), security (box), and industry (teapot). Other methods either produce over-smooth images blurring the structural contents or" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 293, + 748, + 318, + 758 + ], + "type": "text", + "content": "11179" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 48, + 70, + 547, + 245 + ], + "blocks": [ + { + "bbox": [ + 48, + 70, + 547, + 245 + ], + "lines": [ + { + "bbox": [ + 48, + 70, + 547, + 245 + ], + "spans": [ + { + "bbox": [ + 48, + 70, + 547, + 245 + ], + "type": "table", + "html": "
MethodFDK [25]ASD-POCS [46]SART [2]InTomo [56]NeRF [35]NeAT [43]TensoRF [15]NAF [59]SAX-NeRF
ScenePSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIMPSNRSSIM
Jaw28.580.781633.250.932533.130.930131.950.916232.170.911432.530.913931.900.897134.140.935835.470.9525
Leg28.480.669035.390.982635.300.980936.410.988239.270.993840.290.990240.700.992341.280.994043.470.9973
Box24.140.561631.270.922631.200.920030.590.914033.580.949431.580.929832.170.931431.780.930935.330.9602
Carp32.320.817737.630.977736.890.968232.470.949332.990.952936.850.957637.520.968737.930.971142.720.9902
Foot24.530.600029.980.920830.290.929631.430.912730.030.907230.860.922130.460.915331.630.936332.250.9403
Head26.170.715535.270.970734.880.959731.070.930334.150.967235.560.967935.530.967236.460.974339.700.9888
Pelvis26.910.636734.260.949334.380.948130.380.904231.720.917033.730.937035.130.952836.010.965440.400.9870
Chest22.890.786131.130.942232.170.959422.040.746028.400.892531.200.949730.130.930833.050.958134.380.9718
Bonsai24.530.727632.700.952933.020.960028.900.881131.770.938233.200.947633.470.952133.850.958536.510.9761
Teapot31.070.805937.350.980037.380.978736.150.978641.670.994540.850.987242.710.994242.560.992644.320.9970
Engine23.020.540530.810.958030.440.944227.490.926436.850.985836.630.980435.210.972837.840.985938.770.9917
Pancreas9.6410.123218.300.770118.360.700816.010.786517.730.861419.060.854119.750.773719.410.812622.980.9531
Abdomen22.630.603031.460.923131.400.917028.050.875429.710.904931.140.906031.510.907334.450.950135.010.9598
Aneurism28.070.729534.730.986434.760.986430.320.965231.970.935335.800.981937.360.988937.730.987141.460.9956
Backpack23.840.535131.340.930931.320.929428.770.875330.280.919231.900.934533.160.936233.260.950135.970.9688
Average25.120.642232.320.940032.330.934230.290.918932.150.935433.410.944733.780.938734.760.953537.250.9753
", + "image_path": "0bf052b5730b63006dd5cacf8ede3da6ab685a4fae91c678fad5977cb4756926.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_body" + } + ], + "index": 0 + }, + { + "bbox": [ + 50, + 250, + 542, + 261 + ], + "lines": [ + { + "bbox": [ + 50, + 250, + 542, + 261 + ], + "spans": [ + { + "bbox": [ + 50, + 250, + 542, + 261 + ], + "type": "text", + "content": "Table 2. Quantitative comparisons on the CT reconstruction task. The best results are in bold and the second-best results are underlined." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 47, + 271, + 548, + 601 + ], + "blocks": [ + { + "bbox": [ + 47, + 271, + 548, + 601 + ], + "lines": [ + { + "bbox": [ + 47, + 271, + 548, + 601 + ], + "spans": [ + { + "bbox": [ + 47, + 271, + 548, + 601 + ], + "type": "image", + "image_path": "fffa8548d9cafe24f8c56f1e86799decb22064712733488cae606b7b5248dcb3.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 607, + 545, + 618 + ], + "lines": [ + { + "bbox": [ + 46, + 607, + 545, + 618 + ], + "spans": [ + { + "bbox": [ + 46, + 607, + 545, + 618 + ], + "type": "text", + "content": "Figure 6. Visual results of CT reconstruction on the scenes of head, carp, box, and teapot (top to bottom). Please zoom in for a better view." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 636, + 287, + 685 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 636, + 287, + 685 + ], + "spans": [ + { + "bbox": [ + 46, + 636, + 287, + 685 + ], + "type": "text", + "content": "introduce distracting artifacts. In contrast, our SAX-NeRF is more favorable to reconstruct vivid high-frequency details such as sharp edges while maintaining spatial smoothness of homogeneous regions within complex structures." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 689, + 287, + 715 + ], + "type": "text", + "content": "These results convincingly demonstrate the advantages of the proposed SAX-NeRF in X-ray 3D reconstruction." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 635, + 400, + 649 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 635, + 400, + 649 + ], + "spans": [ + { + "bbox": [ + 306, + 635, + 400, + 649 + ], + "type": "text", + "content": "4.3. Ablation Study" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 305, + 659, + 545, + 696 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 659, + 545, + 696 + ], + "spans": [ + { + "bbox": [ + 305, + 659, + 545, + 696 + ], + "type": "text", + "content": "To reliably evaluate the effectiveness of our approaches, we conduct ablation study on all scenes of X3D and report the average PSNR / SSIM results in the following part." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 306, + 701, + 545, + 713 + ], + "type": "text", + "content": "Break-down Ablation. We adopt a baseline model that" + } + ] + } + ], + "index": 8 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11180" + } + ] + } + ], + "index": 9 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 53, + 70, + 227, + 118 + ], + "blocks": [ + { + "bbox": [ + 53, + 70, + 227, + 118 + ], + "lines": [ + { + "bbox": [ + 53, + 70, + 227, + 118 + ], + "spans": [ + { + "bbox": [ + 53, + 70, + 227, + 118 + ], + "type": "table", + "html": "
BaselineLS-MSAMLGNVSCT
✓37.97 / 0.974834.21 / 0.9513
✓✓47.95 / 0.994536.86 / 0.9717
✓✓43.51 / 0.986135.30 / 0.9601
✓✓✓51.37 / 0.999437.25 / 0.9753
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Num204080160320
NVS45.77647.83250.14851.36550.620
0.98920.99390.99910.99940.9992
CT35.84536.78737.08837.24937.186
0.96700.97110.97450.97530.9749
", + "image_path": "ec8177249147826ffe1ec58ab617bfc8406d51470f563b49a286e78c5ea2ad92.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 228, + 121, + 377, + 133 + ], + "lines": [ + { + "bbox": [ + 228, + 121, + 377, + 133 + ], + "spans": [ + { + "bbox": [ + 228, + 121, + 377, + 133 + ], + "type": "text", + "content": "(b) Analysis of the line segment quantity." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 1 + }, + { + "type": "table", + "bbox": [ + 384, + 70, + 539, + 118 + ], + "blocks": [ + { + "bbox": [ + 384, + 70, + 539, + 118 + ], + "lines": [ + { + "bbox": [ + 384, + 70, + 539, + 118 + ], + "spans": [ + { + "bbox": [ + 384, + 70, + 539, + 118 + ], + "type": "table", + "html": "
Size2×24×48×816×1632×32
NVS48.51551.36550.29750.40849.629
0.99760.99940.99920.99920.9989
CT36.98237.24937.11837.16337.014
0.97330.97530.97480.97490.9741
", + "image_path": "99633630747b5fbdfa5d3ec99bedd2c63d974af488cf376002173827680816ab.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_body" + }, + { + "bbox": [ + 388, + 121, + 531, + 133 + ], + "lines": [ + { + "bbox": [ + 388, + 121, + 531, + 133 + ], + "spans": [ + { + "bbox": [ + 388, + 121, + 531, + 133 + ], + "type": "text", + "content": "(c) Analysis of the sampling patch size." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_footnote" + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 136, + 545, + 147 + ], + "lines": [ + { + "bbox": [ + 47, + 136, + 545, + 147 + ], + "spans": [ + { + "bbox": [ + 47, + 136, + 545, + 147 + ], + "type": "text", + "content": "Table 3. We conduct ablation study on all scenes of X3D. Average PSNR and SSIM are reported on the NVS and CT reconstruction tasks." + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "text" + }, + { + "type": "image", + "bbox": [ + 43, + 157, + 147, + 246 + ], + "blocks": [ + { + "bbox": [ + 43, + 157, + 147, + 246 + ], + "lines": [ + { + "bbox": [ + 43, + 157, + 147, + 246 + ], + "spans": [ + { + "bbox": [ + 43, + 157, + 147, + 246 + ], + "type": "image", + "image_path": "37d29e76fa6019250888d16677472cbcd006c4ae51469c8baaa566a395287cf4.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 41, + 256, + 324, + 267 + ], + "lines": [ + { + "bbox": [ + 41, + 256, + 324, + 267 + ], + "spans": [ + { + "bbox": [ + 41, + 256, + 324, + 267 + ], + "type": "text", + "content": "Figure 7. Visual analysis. Using LS-MSA and MLG captures more structures." + } + ] + } + ], + "index": 18, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "image", + "bbox": [ + 150, + 157, + 197, + 196 + ], + "blocks": [ + { + "bbox": [ + 150, + 157, + 197, + 196 + ], + "lines": [ + { + "bbox": [ + 150, + 157, + 197, + 196 + ], + "spans": [ + { + "bbox": [ + 150, + 157, + 197, + 196 + ], + "type": "image", + "image_path": "8bc9b8c7388cee82de450fb57cac29e8f796f3358dbe9207912d300daf493b4e.jpg" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 167, + 198, + 188, + 205 + ], + "lines": [ + { + "bbox": [ + 167, + 198, + 188, + 205 + ], + "spans": [ + { + "bbox": [ + 167, + 198, + 188, + 205 + ], + "type": "text", + "content": "Baseline" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 199, + 157, + 239, + 196 + ], + "blocks": [ + { + "bbox": [ + 199, + 157, + 239, + 196 + ], + "lines": [ + { + "bbox": [ + 199, + 157, + 239, + 196 + ], + "spans": [ + { + "bbox": [ + 199, + 157, + 239, + 196 + ], + "type": "image", + "image_path": "3d4d0966e70bd153c18468eed69983b88549ee69d4b9b0dd8448368b015d304f.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 208, + 198, + 231, + 205 + ], + "lines": [ + { + "bbox": [ + 208, + 198, + 231, + 205 + ], + "spans": [ + { + "bbox": [ + 208, + 198, + 231, + 205 + ], + "type": "text", + "content": "+LS-MSA" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 241, + 157, + 280, + 196 + ], + "blocks": [ + { + "bbox": [ + 241, + 157, + 280, + 196 + ], + "lines": [ + { + "bbox": [ + 241, + 157, + 280, + 196 + ], + "spans": [ + { + "bbox": [ + 241, + 157, + 280, + 196 + ], + "type": "image", + "image_path": "0659a48c5efd32ffad9f34a02d77bc3b706972ed4bee1127e23b8e29e7fb313f.jpg" + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 253, + 198, + 269, + 205 + ], + "lines": [ + { + "bbox": [ + 253, + 198, + 269, + 205 + ], + "spans": [ + { + "bbox": [ + 253, + 198, + 269, + 205 + ], + "type": "text", + "content": "+MLG" + } + ] + } + ], + "index": 13, + "angle": 0, + "type": "image_caption" + } + ], + "index": 12 + }, + { + "type": "image", + "bbox": [ + 283, + 157, + 321, + 196 + ], + "blocks": [ + { + "bbox": [ + 283, + 157, + 321, + 196 + ], + "lines": [ + { + "bbox": [ + 283, + 157, + 321, + 196 + ], + "spans": [ + { + "bbox": [ + 283, + 157, + 321, + 196 + ], + "type": "image", + "image_path": "aab49d6735a06e58237e5decf7a593ebbdeb7d588f8b839ebdfcc0a303b2d635.jpg" + } + ] + } + ], + "index": 14, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 285, + 198, + 318, + 205 + ], + "lines": [ + { + "bbox": [ + 285, + 198, + 318, + 205 + ], + "spans": [ + { + "bbox": [ + 285, + 198, + 318, + 205 + ], + "type": "text", + "content": "Ground Truth" + } + ] + } + ], + "index": 15, + "angle": 0, + "type": "image_caption" + } + ], + "index": 14 + }, + { + "type": "image", + "bbox": [ + 327, + 157, + 435, + 249 + ], + "blocks": [ + { + "bbox": [ + 327, + 157, + 435, + 249 + ], + "lines": [ + { + "bbox": [ + 327, + 157, + 435, + 249 + ], + "spans": [ + { + "bbox": [ + 327, + 157, + 435, + 249 + ], + "type": "image", + "image_path": "51a11f1bea466f5588eec2ed57c8ba529d975bd3106d2631dbcc78427dc084de.jpg" + } + ] + } + ], + "index": 16, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 331, + 257, + 537, + 268 + ], + "lines": [ + { + "bbox": [ + 331, + 257, + 537, + 268 + ], + "spans": [ + { + "bbox": [ + 331, + 257, + 537, + 268 + ], + "type": "text", + "content": "Figure 8. Analysis of the number of training projections." + } + ] + } + ], + "index": 19, + "angle": 0, + "type": "image_caption" + } + ], + "index": 16 + }, + { + "type": "image", + "bbox": [ + 435, + 157, + 541, + 249 + ], + "blocks": [ + { + "bbox": [ + 435, + 157, + 541, + 249 + ], + "lines": [ + { + "bbox": [ + 435, + 157, + 541, + 249 + ], + "spans": [ + { + "bbox": [ + 435, + 157, + 541, + 249 + ], + "type": "image", + "image_path": "8f3c05475387af9ed35caa088283853164756ecd099d495e7b4af6aa7626c3cd.jpg" + } + ] + } + ], + "index": 17, + "angle": 0, + "type": "image_body" + } + ], + "index": 17 + }, + { + "bbox": [ + 46, + 282, + 287, + 414 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 282, + 287, + 414 + ], + "spans": [ + { + "bbox": [ + 46, + 282, + 287, + 414 + ], + "type": "text", + "content": "is derived by directly removing the LS-MSA module and MLG sampling strategy from our SAX-NeRF to conduct the break-down ablation study. The results are listed in Tab. 3a. The baseline model yields 37.97 and 34.21 dB on NVS and CT reconstruction. When using LS-MSA, the baseline model gains by 9.98 and 2.65 dB. When we apply MLG sampling, the model achieves 5.54 and 1.09 dB improvements. When jointly exploiting the two techniques, the model is improved by 13.40 and 3.04 dB on the NVS and CT reconstruction tasks. This evidence clearly exhibits the efficacy of Lineformer and MLG sampling strategy." + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 46, + 418, + 287, + 514 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 287, + 514 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 287, + 514 + ], + "type": "text", + "content": "Visual Analysis. To intuitively show the effectiveness of the two proposed approaches, we further conduct visual analysis on the scene of bonsai. As depicted in Fig. 7, the baseline model fails to preserve the geometry like the tree branches in the projection and blurs high-frequency details such as the edges of the basin in the CT slice. When successively using LS-MSA and MLG sampling, the model reconstructs more structural contents and fine-grained textures." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "spans": [ + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": "Parameter Analysis. We conduct parameter analysis regarding the number of line segments " + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": " in Eq. (6) and the patch size " + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": " in Eq. (14). Please note that we keep the total number of sampled points and X-rays unchanged for fair comparison. When analyzing one parameter, we fix the other at its optimal value. The results are reported in Tab. 3b and 3c. It is clear that, when using different " + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "inline_equation", + "content": "M" + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "inline_equation", + "content": "S" + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": ", our SAX-NeRF stably outperforms the baseline model by over 7.81 and 1.64 dB on NVS and CT reconstruction. This evidence suggests the reliability of our method. The model's performance yields its maximum when " + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "inline_equation", + "content": "M = 160" + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "inline_equation", + "content": "S = 4" + }, + { + "bbox": [ + 46, + 518, + 287, + 650 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 287, + 715 + ], + "type": "text", + "content": "Robustness Analysis. We conduct robustness analysis regarding the number of training projections to compare the performance of different methods when given fewer X-ray projection views. The results are plotted as two line charts in Fig. 8, where the vertical axis is PSNR (in dB per" + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "spans": [ + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "type": "text", + "content": "formance) and the horizontal axis is the number of training projections. Our SAX-NeRF reliably surpasses SOTA methods by large margins when given different numbers of training projections on both NVs (left) and CT reconstruction (right) tasks. Surprisingly, when using even only " + }, + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "type": "inline_equation", + "content": "60\\%" + }, + { + "bbox": [ + 304, + 282, + 545, + 378 + ], + "type": "text", + "content": " of training projections, SAX-NeRF still outperforms other algorithms on the NVS task. These results clearly exhibit the superiority and robustness of our proposed method." + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "spans": [ + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "type": "text", + "content": "Lineformer vs. vanilla Transformer. We replace LS-MSA with G-MSA to conduct comparative experiments. The experimental results show that our Lineformer significantly outperforms vanilla Transformer by 5.30 and " + }, + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "type": "inline_equation", + "content": "1.28\\mathrm{dB}" + }, + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "type": "text", + "content": " on the NVS and CT reconstruction tasks while only requiring " + }, + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "type": "inline_equation", + "content": "3.41\\%" + }, + { + "bbox": [ + 304, + 380, + 545, + 453 + ], + "type": "text", + "content": " of vanilla Transformer's computational complexity." + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 461, + 378, + 474 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 461, + 378, + 474 + ], + "spans": [ + { + "bbox": [ + 306, + 461, + 378, + 474 + ], + "type": "text", + "content": "5. Conclusion" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 304, + 482, + 545, + 673 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 482, + 545, + 673 + ], + "spans": [ + { + "bbox": [ + 304, + 482, + 545, + 673 + ], + "type": "text", + "content": "In this paper, we focus on studying a core problem in sparse-view X-ray 3D reconstruction, i.e., how to effectively capture the various and complex structures penetrated by X-rays. To this end, we propose a novel framework SAX-NeRF. To model 3D structural dependencies in space, we design a Transformer, Lineformer, as the backbone of SAX-NeRF. Lineformer partitions an X-ray into different line segments and then computes self-attention within each piece of the X-ray. In addition, to extract 2D geometry and contextual representations in projection, we present an MLG ray sampling strategy that contains pixel- and patch-level sampling on the informative foreground regions. Besides, we also collect a larger-scale dataset, X3D, covering wider X-ray application scenarios. Comprehensive experiments on X3D show that SAX-NeRF significantly surpasses SOTA algorithms on the NVs and CT reconstruction tasks." + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 545, + 712 + ], + "type": "text", + "content": "Acknowledgements: This work was supported by the Lustgarten Foundation for Pancreatic Cancer Research and the Patrick J. 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In ICLR, 2021. 3" + } + ] + } + ], + "index": 30 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11183" + } + ] + } + ], + "index": 32 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 9 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Structure-Guided Adversarial Training of Diffusion Models/b70a5045-dbc8-47eb-880e-4252d02e0e55_content_list.json b/2024/Structure-Guided Adversarial Training of Diffusion Models/b70a5045-dbc8-47eb-880e-4252d02e0e55_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..6870d0c75100d60c0fc7b865098975b9a9c81d69 --- /dev/null +++ b/2024/Structure-Guided Adversarial Training of Diffusion Models/b70a5045-dbc8-47eb-880e-4252d02e0e55_content_list.json @@ -0,0 +1,1768 @@ +[ + { + "type": "text", + "text": "Structure-Guided Adversarial Training of Diffusion Models", + "text_level": 1, + "bbox": [ + 181, + 130, + 785, + 151 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Ling Yang*† Haotian Qian* Zhilong Zhang Jingwei Liu Bin Cui† Peking University", + "bbox": [ + 205, + 179, + 767, + 217 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "yangling0818@163.com, zzmqht@gmail.com, {zzl2018math, bin.cui}@pku.edu", + "bbox": [ + 166, + 219, + 795, + 233 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 268, + 313, + 284 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models have demonstrated exceptional efficacy in various generative applications. While existing models focus on minimizing a weighted sum of denoising score matching losses for data distribution modeling, their training primarily emphasizes instance-level optimization, overlooking valuable structural information within each minibatch, indicative of pair-wise relationships among samples. To address this limitation, we introduce Structure-guided Adversarial training of Diffusion Models (SADM). In this pioneering approach, we compel the model to learn manifold structures between samples in each training batch. To ensure the model captures authentic manifold structures in the data distribution, we advocate adversarial training of the diffusion generator against a novel structure discriminator in a minimax game, distinguishing real manifold structures from the generated ones. SADM substantially outperforms existing methods in image generation and cross-domain fine-tuning tasks across 12 datasets, establishing a new state-of-the-art FID of 1.58 and 2.11 on ImageNet for class-conditional image generation at resolutions of $256 \\times 256$ and $512 \\times 512$ , respectively.", + "bbox": [ + 73, + 301, + 473, + 619 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 651, + 209, + 667 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Diffusion models [20, 56-59, 73] have achieved remarkable generation quality in various tasks, including image generation [12, 50-52, 67, 74, 75, 79], audio synthesis [4, 33, 49], and interdisciplinary applications [21, 24, 71]. Starting from tractable noise distribution, diffusion models generate data by progressively removing noise. This involves the model learning to reverse a pre-defined diffusion process that sequentially introduces varying levels of noise to the data. The model is parameterized and undergoes training by optimizing the weighted sum of denoising score matching losses [20] for various noise levels [57], aiming to learn the recovery of clean images from corrupted images.", + "bbox": [ + 75, + 678, + 472, + 861 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/43b4ceb76b4fd49eef9bc4ec1fd6858e690585ed89054d30f90d4b8a07fbbc92.jpg", + "image_caption": [ + "Figure 1. Comparison between previous instance-level training and our structure-guided training for diffusion models." + ], + "image_footnote": [], + "bbox": [ + 519, + 260, + 867, + 455 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Aiming to maximally model the data distribution, recent works [28, 42, 60, 63, 72, 76] attempt to improve the precision of training diffusion models. For instance, many approaches design effective weighting schemes [8, 17, 30, 42, 60, 76] for maximum likelihood training or add an extra regularization term [10, 37, 46] to the denoising score loss. There are also some works to enhance the model expressiveness by incorporating other generative models, such as VAE [31, 51, 63], GAN [69], and Normalizing Flows [29, 43, 78]. However, their improved training of diffusion models primarily concentrates on instance-level optimization, overlooking the valuable structural information among batch samples. This oversight is significant, as the incorporation of structural details is crucial for aligning the learned distribution with the underlying data distribution.", + "bbox": [ + 496, + 505, + 893, + 733 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "To mitigate the challenges posed by existing instance-level training methods, we propose Structure-guided Adversarial training of Diffusion Models (SADM). In contrast to conventional instance-level training illustrated in Fig. 1, our approach guides diffusion training at a structural level. During batch training, the model is facilitated to learn manifold structures within batch samples, represented by pair-wise relationships in a low-dimensional feature space. To accurately learn real manifold structures in the data distribution, we introduce a novel structure discriminator that distinguishes genuine manifold structures from generated", + "bbox": [ + 496, + 734, + 895, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 810, + 44 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "* Contributed equally.", + "bbox": [ + 94, + 875, + 212, + 887 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "† Corresponding authors.", + "bbox": [ + 96, + 887, + 225, + 898 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "7256", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/c3da61ceb96c9c48998e873fce396c9e2d03035d70e207073349b0a35a8af68c.jpg", + "image_caption": [ + "FID: 4.59, Recall: 0.52" + ], + "image_footnote": [], + "bbox": [ + 81, + 101, + 341, + 434 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/1af0dfa1ed8cd7a702fbab03141c03e4f6d6223a7e4e6991a80689a376f58bfc.jpg", + "image_caption": [ + "FID: 3.14, Recall: 0.61" + ], + "image_footnote": [], + "bbox": [ + 354, + 101, + 614, + 435 + ], + "page_idx": 1 + }, + { + "type": "image", + "img_path": "images/9894ee3ed38a8a57851f764bfd53b19d035a91847226a7f973449cd16e15eff7.jpg", + "image_caption": [ + "Figure 2. Generated samples on ImageNet $256 \\times 256$ with (i) ADM with Classifier Guidance (ADM-G) [12], (ii) ADM optimized by our Structure-guided Adversarial Training, and (iii) real samples in ground truth classes. We can significantly improve diffusion models qualitatively and quantitatively, and our generated sample distribution is overall more similar to real sample distribution. See Appendix C for more synthesis samples of our SOTA model." + ], + "image_footnote": [], + "bbox": [ + 629, + 101, + 888, + 434 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "ones. For clarity, we alternatively refer to the diffusion models optimized through our structure-guided training as joint sample diffusion, a concept theoretically proven to enhance diffusion model optimization.", + "bbox": [ + 75, + 527, + 470, + 588 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We assess the performance of our model across two pivotal tasks: image generation and cross-domain fine-tuning. The former involves training the diffusion model from scratch to evaluate its capability in capturing the entire data distribution. The latter leverages a pre-trained diffusion model, constructed on a large-scale source dataset, and fine-tunes it on a target dataset to assess transferability. Our extensive experiments consistently demonstrate that our approach significantly improves the model's ability to effectively capture the underlying data distribution (Fig. 2). SADM achieves state-of-the-art results across 12 image datasets, including ImageNet [11]. Furthermore, we observe its potential for facilitating rapid adaptation to new domains in cross-domain fine-tuning tasks. We summarize our contributions as follows:", + "bbox": [ + 75, + 594, + 468, + 819 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- To the best of our knowledge, we are the first to propose Structure-guided Adversarial Training to optimize diffusion models from a structural perspective.", + "- We theoretically show that SADM is superior in capturing real data distribution, and can generalize to various image" + ], + "bbox": [ + 76, + 825, + 468, + 900 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "and latent-based diffusion architectures (e.g., DiT [47]).", + "- We substantially outperform existing methods on image generation and cross-domain fine-tuning tasks, achieving a new state-of-the-art FID of 1.58 and 2.11 on ImageNet at resolutions of $256 \\times 256$ and $512 \\times 512$ , respectively." + ], + "bbox": [ + 500, + 529, + 890, + 604 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 614, + 638, + 631 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we focus on improving the training of diffusion models. Here, we review previous related works and compare our SADM with them.", + "bbox": [ + 498, + 641, + 893, + 686 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Modifying Training Objectives of Diffusion Models A line of research modifies training objectives to achieve state-of-the-art likelihood [8, 42, 60, 74]. Song et al. [60] propose likelihood weighting to enable approximate maximum likelihood training of score-based diffusion models [57-59] while ContextDiff [76] introduces an effective shifting scheme for facilitating the diffusion and training processes of diffusion probabilistic models [20, 56] to achieve improved sample quality with stable training. Lai et al. [37] and [10] introduce an extra regularization term to the denoising score loss to satisfy some properties of the diffusion process. However, these improvements mainly focus on sample-level optimization, neglecting the rich structural information within batch", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "7257", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "samples, which is critical for aligning the learned distribution and data distribution. Hence, we enforce the model to maximally learn the manifold structures of samples.", + "bbox": [ + 76, + 90, + 472, + 137 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Combining Additional Models for Diffusion Training Another line of research incorporates other models to improve the stability and precision of diffusion training. For example, INDM [29] expands the linear diffusion to trainable nonlinear diffusion through a normalizing flow to improve the training curve of diffusion models. Jolicoeur-Martineau et al. [26], Kim et al. [28] improve diffusion models with adversarial learning while Xiao et al. [69] model each denoising step using a multimodal conditional GAN. LSGM [63] and LDM [51] conduct diffusion process in the semantic latent space obtained with a pre-trained VAE. Although these combinations strengthen the model expressiveness for capturing data distribution, they are still limited in modeling the underlying manifold structures within training samples. We propose a novel structure discriminator for adversarially learn the diffusion model from a structural perspective.", + "bbox": [ + 76, + 155, + 472, + 398 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminary", + "text_level": 1, + "bbox": [ + 76, + 411, + 202, + 428 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Diffusion Models We consider diffusion models [20, 56, 57] specified in continuous time [4, 31, 59, 62]. Given samples $\\mathbf{x}_0$ from a data distribution $q_0(\\mathbf{x}_0)$ , noise scheduling functions $\\alpha_{t},\\sigma_{t}$ , a diffusion model has latent variables $\\mathbf{x} = \\{\\mathbf{x}_t\\mid t\\in [0,1]\\}$ , and the forward process is defined with $q(\\mathbf{x}_t|\\mathbf{x}_0)$ , a Gaussian process satisfying the following Markovian structure:", + "bbox": [ + 76, + 436, + 472, + 541 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\alpha_ {t} \\mathbf {x} _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 553, + 468, + 571 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {s}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\left(\\alpha_ {t} / \\alpha_ {s}\\right) \\mathbf {x} _ {s}, \\sigma_ {t \\mid s} ^ {2} \\mathbf {I}\\right) \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 148, + 574, + 468, + 592 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $0 \\leq s < t \\leq 1$ and $\\sigma_{t|s}^2 = (1 - e^{\\lambda_t - \\lambda_s})\\sigma_t^2$ , and $\\lambda_t = \\log [\\alpha_t^2 /\\sigma_t^2 ]$ denotes the log signal-to-noise-ratio [31]. The goal of the diffusion model is to denoise $\\mathbf{x}_t \\sim q(\\mathbf{x}_t|\\mathbf{x}_0)$ by estimating $\\hat{\\mathbf{x}}_{\\theta}(\\mathbf{x}_t) \\approx \\mathbf{x}_0$ . We train this denoising model $\\hat{\\mathbf{x}}_{\\theta}$ using a weighted mean squared error loss", + "bbox": [ + 76, + 604, + 470, + 684 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbb {E} _ {\\mathbf {x} _ {0}, \\boldsymbol {\\epsilon}, t} \\left[ w \\left(\\lambda_ {t}\\right) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t}) - \\mathbf {x} _ {0} \\| _ {2} ^ {2} \\right] \\tag {3}\n$$\n", + "text_format": "latex", + "bbox": [ + 166, + 695, + 468, + 714 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "over uniformly sampled times $t \\in [0,1]$ . This loss can be justified as a weighted variational lower bound on the data log likelihood under the diffusion model [31] or as a form of denoising score matching [57, 64]. $w(\\lambda_t)$ is a pre-specified weighting function [31].", + "bbox": [ + 75, + 724, + 468, + 801 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. Proposed Method", + "text_level": 1, + "bbox": [ + 76, + 814, + 250, + 830 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce the proposed SADM in detail (Fig. 3). In order to maximally learn the structural information between real samples, we propose structure-guided training of diffusion models in Sec. 4.1. Then we design a novel structure", + "bbox": [ + 75, + 839, + 472, + 900 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "discriminator for adversarially optimizing the training procedure from a structural perspective in Sec. 4.2. Finally, we alternatively interpret our structure-guided training of diffusion models as joint sample diffusion with theoretical analysis for betwen understanding in Sec. 4.3.", + "bbox": [ + 496, + 90, + 893, + 167 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Beyond Instance-Level Training", + "text_level": 1, + "bbox": [ + 498, + 175, + 782, + 191 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We first review the previous instance-level training methods for diffusion models. Generally, they train the diffusion model with a finite sample version of Eq. (3):", + "bbox": [ + 496, + 198, + 892, + 244 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathcal {L} _ {t} = w \\left(\\lambda_ {t}\\right) \\frac {\\sum_ {i \\in B} \\left| \\left| \\mathbf {x} _ {0} ^ {i} - \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) \\right| \\right| ^ {2}}{| B |}, \\tag {4}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 252, + 892, + 286 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\mathbf{x}_0^i, \\mathbf{x}_t^i$ denote the $i^{th}$ ground truth samples and generated samples in the mini-batch $B$ at time step $t$ . However, this objective function encourages the diffusion model to denoise by considering only the instance-level information, neglecting the group-level (structural) information in the mini-batch. Therefore, we enforce the sample predictions of the denoising network to maximally preserve the manifold structures between batch samples.", + "bbox": [ + 496, + 296, + 893, + 417 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Structural Constraint in Manifold More concretely, ground truth samples $\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}$ are first projected from pixel space into embedding space using off-the-shelf pre-trained networks $\\Psi (\\cdot):\\mathbb{R}^{m\\times n}\\to \\mathbb{R}^d$ e.g., an Inception-V3 feature extractor pre-trained on ImageNet [61] (we conduct ablation study in Appendix B). Then, the pair-wise relationships $\\mathcal{R}(\\Psi (\\mathbf{x}_0^i),\\Psi (\\mathbf{x}_0^j))$ are calculated within batch samples $\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}$ , which contain rich structural information in a low-dimensional manifold. This structural information can be expressed with an affinity matrix $\\mathcal{M}(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|})$ defined as:", + "bbox": [ + 496, + 435, + 893, + 592 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\left[ \\begin{array}{c c c c} \\mathcal {R} (\\Psi_ {1}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {1}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {1}, \\Psi_ {| B |}) \\\\ \\mathcal {R} (\\Psi_ {2}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {2}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {2}, \\Psi_ {| B |}) \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {| B |}) \\end{array} \\right] \\tag {5}\n$$\n", + "text_format": "latex", + "bbox": [ + 517, + 599, + 890, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\Psi_{i}$ is a short-hand for $\\Psi (\\mathbf{x}_0^i)$ , and $\\mathcal{R}(\\cdot ,\\cdot)$ denotes the relational function, such as Euclidean distance. Kindly note that many off-the-shelf pre-trained networks are open-source and only work well on clean images, and thus fail to provide meaningful embeddings when the input is noisy. Therefore, we use the predicted clean samples $\\hat{\\mathbf{x}}_0^i$ for computing affinity matrix, and regularize the denoising network to minimize the structural distance between $\\mathcal{M}(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|})$ and $\\mathcal{M}(\\{\\hat{\\mathbf{x}}_0^i\\}_{i = 1}^{|B|})$ . Adding this structural constraint into Eq. (4), the training objective for denoising network is:", + "bbox": [ + 496, + 685, + 893, + 838 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {t} = \\frac {\\sum_ {i \\in B} \\left| \\left| \\mathbf {x} _ {0} ^ {i} - \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) \\right| \\right| ^ {2}}{| B |} \\tag {6} \\\\ + \\mathcal {D} (\\mathcal {M} (\\{\\mathbf {x} _ {0} ^ {i} \\} _ {i = 1} ^ {| B |}), \\mathcal {M} (\\{\\hat {\\mathbf {x}} _ {0} ^ {i} \\} _ {i = 1} ^ {| B |})) \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 568, + 845, + 892, + 902 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "7258", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/f7c7ccaeacfa297fc582e8005d7845092fb876aa9c76e0ac7a3d3ab000d6a6be.jpg", + "image_caption": [ + "Figure 3. Overview of SADM. We minimize the structural distance between the generated samples (fake) and ground truth samples (real) in the manifold space for optimizing the denoiser, and maximize their structural distance for optimizing the encoder in structure discriminator. The denoiser and the structure discriminator are adversarially trained." + ], + "image_footnote": [], + "bbox": [ + 117, + 85, + 851, + 400 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathcal{D}(\\cdot, \\cdot)$ denotes the distance metric between ground truth and predicted affinity matrices. In this way, the diffusion generator (denoiser) is optimized not only to make correct prediction for each instance, but also to preserve the manifold structures of batch samples.", + "bbox": [ + 75, + 474, + 470, + 551 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Structure-Guided Adversarial Training", + "text_level": 1, + "bbox": [ + 76, + 556, + 416, + 574 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "As demonstrated above, we aim to maximally learn data distribution by aligning the manifold structures of denoiser's predicted samples to those of ground truth samples in each training batch. At every training iteration, the manifold structures can be diverse and the denoiser tend to merely focus on some easy-to-learn structures, ultimately leading to trivial solutions that fail to capture the whole data distribution. In order to mitigate this problem and improve the expressiveness of denoiser, we adversarially learn the denoising network against a structure discriminator in a minimax game (Fig. 3), which is trained to distinguish the manifold structures between the real and generated batch samples.", + "bbox": [ + 75, + 580, + 470, + 762 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Structure Discriminator Normally, the discriminator in adversarial learning [15] would output the discrete value (0 or 1) to determine whether the input is real or fake. However, such discrete discriminator can not be applied in distinguishing manifold structures, because the generated and real sample sets would share similar pair-wise sample relations despite their different feature spaces. Thus, instead of learning a classification-based discriminator, we design a", + "bbox": [ + 75, + 779, + 472, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "novel comparison-based structure discriminator to address this issue.", + "bbox": [ + 498, + 474, + 890, + 503 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Specifically, as illustrated in Fig. 3, the structure discriminator consists of the aforementioned neural network $\\Psi_{\\phi}$ with trainable parameters $\\phi$ and the distance measure function $\\mathcal{D}(\\cdot ,\\cdot)$ that outputs continuous value. It projects both real and generated samples into the embedding space, then the structure discriminator is trained against the denoiser for finding a better manifold (or embedding space) to distinguish real sample set from generated set by maximizing their structural distance:", + "bbox": [ + 496, + 508, + 893, + 643 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\phi} \\frac {\\eta_ {t} \\sum_ {i , j \\in B} \\mathcal {D} \\left(\\mathcal {R} \\left(\\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) , \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right)\\right) , \\mathcal {R} \\left(\\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) , \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right)\\right)\\right)}{| B | ^ {2}}. \\tag {7}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 660, + 946, + 709 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where we choose $\\eta_t = \\frac{1}{t}$ as a time-dependent weighting factor. We can use simple measurements for $\\mathcal{D}(\\cdot, \\cdot)$ ( $L_2$ distance) and $\\mathcal{R}(\\cdot, \\cdot)$ (cosine similarity), as the critical semantic information has been already encoded by $\\Psi_\\phi$ . Conversely, the denoiser is adversarially optimized for generating more realistic sample set to fool the structure discriminator by minimizing the structural distance.", + "bbox": [ + 496, + 709, + 893, + 816 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Final Optimization Objective The final training objective of our SADM consists of normal denoising score matching loss (Eq. (3)) and adversarial structural distance loss (Eq. (7))", + "bbox": [ + 496, + 854, + 893, + 902 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "7259", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "at timestep $t$ , which can be written as:", + "bbox": [ + 76, + 90, + 331, + 104 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathcal {L} _ {t} (\\theta) = \\frac {w (\\lambda_ {t}) \\sum_ {i \\in B} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2}}{| B |} \\\\ + \\max _ {\\phi} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right) - \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2}}{| B | ^ {2}}. \\tag {8} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 114, + 488, + 200 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "In training, we iteratively optimize the feature extractor and the denoising network in Eq. (8). In an iteration, we first freeze $\\theta$ and update $\\phi$ by ascending along its gradient", + "bbox": [ + 76, + 203, + 468, + 248 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\nabla_ {\\phi} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right) - \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2}}{| B | ^ {2}}, \\tag {9}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 258, + 468, + 306 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "then we freeze $\\phi$ and update $\\theta$ by descending along its gradient", + "bbox": [ + 76, + 306, + 470, + 338 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\theta} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} (\\mathbf {x} _ {0} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\mathbf {x} _ {0} ^ {j}) - \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}) \\| _ {2} ^ {2}}{| B | ^ {2}} \\\\ + \\nabla_ {\\theta} \\frac {w \\left(\\lambda_ {t}\\right) \\sum_ {i \\in B} \\left\\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) - \\mathbf {x} _ {0} ^ {i} \\right\\| _ {2} ^ {2}}{| B |}. \\tag {10} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 80, + 345, + 468, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The proposed training algorithm is presented in Algorithm 1.", + "bbox": [ + 76, + 431, + 470, + 446 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Generalizing to Latent Diffusion Our proposed training algorithm applies not only to image diffusion but also to latent diffusion, such as LDM [51] and LSGM [63]. In this case, the intermediate results $\\mathbf{x}_t$ are latent codes rather than images. We can use the latent decoder (e.g., VAE decoder [32]) to project the generated latent codes to images and then use the same algorithm in the image domain.", + "bbox": [ + 76, + 465, + 468, + 571 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "4.3. Interpreting as Joint Sample Diffusion", + "text_level": 1, + "bbox": [ + 76, + 580, + 406, + 595 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Relation-Conditioned Diffusion Process For better understanding of our proposed structure-guided training, we interpret it as a joint sample diffusion model that simultaneously perturbs and denoises a set of samples conditioned on the relation variable. Formally, let $\\mathbf{y}_0 = (\\mathbf{x}_0^i,\\mathbf{x}_0^j)$ , where $\\mathbf{x}_0^i,\\mathbf{x}_0^j$ are independent random variables sampled from ground truth distribution $q_{0}$ . And the relation variable that encodes the structure information is defined as $\\mathcal{R} = \\mathcal{R}(\\mathbf{x}_0^i,\\mathbf{x}_0^j) + \\gamma \\epsilon$ , where $\\gamma \\epsilon$ denote a small gaussian noise added to the relation to avoid degenerated distribution. Then the forward diffusion jointly perturbs $\\mathbf{y}_0$ , conditioned on $\\mathcal{R}$ :", + "bbox": [ + 76, + 603, + 470, + 785 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nq (\\mathbf {y} _ {t} | \\mathbf {y} _ {0}, \\mathcal {R}) = \\mathcal {N} (\\mathbf {y} _ {t}; \\alpha_ {t} \\mathbf {y} _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}). \\tag {11}\n$$\n", + "text_format": "latex", + "bbox": [ + 151, + 796, + 468, + 814 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To reverse the diffusion process, we need to predict $\\mathbf{y}_0$ , or equivalently, learn the conditional score function $\\nabla_y\\log q_t(y_t|\\mathcal{R})$ [12, 19]. This formulation allows us to utilize the auxiliary structural information $\\mathcal{R}$ in the sampling process, which usually leads to better performance [13, 55].", + "bbox": [ + 76, + 824, + 472, + 901 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Algorithm 1: SADM, our proposed algorithm.", + "bbox": [ + 509, + 94, + 818, + 109 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "input : $\\{\\alpha_{t}\\}_{t\\in [0,1]}$ $\\{\\sigma_t\\}_{t\\in [0,1]}$ the noise schedule, $|B|$ the batch size, $w(\\lambda_t)$ $\\eta_t$ the scaling factors for denoising score matching loss and adversarial loss, pre-trained encoder $\\Psi_{\\phi}$ for structure discriminator.", + "bbox": [ + 519, + 112, + 867, + 186 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Initialize denoising network parameters $\\theta$", + "bbox": [ + 519, + 188, + 799, + 203 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "while $\\theta$ has not converged do", + "bbox": [ + 519, + 204, + 717, + 218 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sample a minibatch $\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}\\sim q_0$ and", + "bbox": [ + 545, + 218, + 802, + 237 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\{\\boldsymbol {\\epsilon} ^ {j} \\} _ {j = 1} ^ {| B |} \\sim \\mathcal {N} (\\mathbf {0}, \\boldsymbol {I})\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 237, + 687, + 255 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sample $t\\sim U[0,1]$", + "bbox": [ + 545, + 255, + 674, + 268 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Sample $\\{\\mathbf{x}_t^i = \\alpha_t\\mathbf{x}_0^i +\\sigma_t\\pmb {\\epsilon}^i\\}_{i = 1}^{|B|}$", + "bbox": [ + 545, + 270, + 763, + 287 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Freeze $\\phi$ and update $\\theta$ with its gradient", + "bbox": [ + 545, + 287, + 803, + 301 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {\\theta} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} (\\mathbf {\\hat {x}} _ {0} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\mathbf {\\hat {x}} _ {0} ^ {j}) - \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}) \\| _ {2} ^ {2}}{| B | ^ {2}} \\\\ + \\nabla_ {\\theta} \\frac {w (\\lambda_ {t}) \\sum_ {i \\in B} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2}}{| B |} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 555, + 301, + 872, + 348 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Adversarily train denoising network and structure discriminator by iteratively updating their parameters $\\theta, \\phi$ according to Eqs. (9) and (10).", + "bbox": [ + 519, + 349, + 859, + 395 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "output: Denoising network $\\theta$ .", + "bbox": [ + 519, + 396, + 720, + 410 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Learning Conditional Score To approximate the conditional score function, first we decompose it with Bayes' rule,", + "bbox": [ + 500, + 448, + 893, + 479 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\nabla_ {y} \\log q _ {t} \\left(y _ {t} | \\mathcal {R}\\right) = \\nabla_ {y} \\log q _ {t} \\left(y _ {t}\\right) + \\nabla_ {y} \\log q _ {t} \\left(\\mathcal {R} \\mid y _ {t}\\right) \\\\ = \\Sigma_ {s = i, j} \\nabla_ {x} \\log q _ {t} \\left(x _ {t} ^ {s}\\right) + \\nabla_ {y} \\log q _ {t} (\\mathcal {R} | y _ {t}). \\tag {12} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 506, + 893, + 554 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To approximate the first term on the right side of Eq. (12), we only need to learn $\\hat{\\mathbf{x}}_{\\theta ,t}^{i},\\hat{\\mathbf{x}}_{\\theta ,t}^{j}$ , as in standard diffusion models [59]. However, the second term is intractable since $q_{t}(\\mathcal{R}|y_{t})$ involves the intractable posterior $q(\\mathbf{y}_0|\\mathbf{y}_t)$ . Note that", + "bbox": [ + 500, + 555, + 893, + 616 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} q _ {t} (\\mathcal {R} | y _ {t}) = \\int g (\\mathcal {R} | \\mathbf {y} _ {0}) q \\left(\\mathbf {y} _ {0} \\mid \\mathbf {y} _ {t}\\right) d \\mathbf {y} _ {0} \\tag {13} \\\\ = \\mathbb {E} _ {\\mathbf {y} _ {0}} \\left[ g (\\mathcal {R} | \\mathbf {y} _ {0}) | \\mathbf {y} _ {t} \\right], \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 631, + 890, + 681 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $g(\\mathcal{R}|\\mathbf{y}_0)$ is the density function of Gaussian distribution with mean $\\mathcal{R}(\\mathbf{x}_0^i,\\mathbf{x}_0^j)$ and variance $\\gamma^2$ , by the definition of $\\mathcal{R}$ . As a result, we can use $g(\\mathcal{R}|\\hat{\\mathbf{y}}_{0,t}) = g(\\mathcal{R} | (\\hat{\\mathbf{x}}_{\\theta ,t}^i,\\hat{\\mathbf{x}}_{\\theta ,t}^j))$ to approximate $q_{t}(\\mathcal{R}|y_{t})$ , and train it with $L_{2}$ loss:", + "bbox": [ + 498, + 698, + 893, + 761 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {y} _ {t}} \\| \\mathbb {E} _ {\\mathbf {y} _ {0}} [ g (\\mathcal {R} | \\mathbf {y} _ {0}) | \\mathbf {y} _ {t} ] - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) \\| _ {2} ^ {2} \\\\ = \\mathbb {E} _ {\\mathbf {y} _ {t}} \\| \\mathbb {E} _ {\\mathbf {y} _ {0}} [ g (\\mathcal {R} | \\mathbf {y} _ {0}) - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) | \\mathbf {y} _ {t} ] \\| _ {2} ^ {2} \\\\ \\leq \\mathbb {E} _ {\\mathbf {y} _ {0}, \\mathbf {y} _ {t}} \\| g (\\mathcal {R} | \\mathbf {y} _ {0}) - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) \\| _ {2} ^ {2} \\quad (J e s s e n I n e q u a l i t y) \\\\ \\leq w (\\gamma) \\mathbb {E} _ {\\mathbf {y} _ {0}, \\mathbf {y} _ {t}} \\| \\mathcal {R} \\left(\\mathbf {x} _ {0} ^ {i}, \\mathbf {x} _ {0} ^ {j}\\right) - \\mathcal {R} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}, \\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2} = \\mathcal {L} _ {t} ^ {\\text {s t r u c t u r e}}, \\tag {14} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 500, + 776, + 895, + 869 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $w(\\gamma)$ is a weighting scalar that depends only on $\\gamma$ . The objective function is the sum of the denoising score", + "bbox": [ + 500, + 869, + 893, + 901 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "7260", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3517c9625ccfc43ac0993a41aaa3146267a6d97f8404367ecc29dbf03b4da552.jpg", + "table_caption": [ + "Table 1. Quantitative results for class-conditional generation on ImageNet ${256} \\times {256}$ and ${512} \\times {512}$ ." + ], + "table_footnote": [], + "table_body": "
ModelImageNet 256×256ImageNet 512×512
FID ↓IS ↑Precision ↑Recall ↑FID ↓IS ↑Precision ↑Recall ↑
BigGAN-deep [2]6.95171.400.870.288.43177.900.880.29
StyleGAN-XL [54]2.30265.120.780.532.41267.750.770.52
ADM-G, ADM-U [12]3.94215.840.830.533.85221.720.840.53
LDM-4-G [51]3.60247.670.870.48----
RIN+NoiseSchedule [6]3.52186.20--3.95216.00--
SimpleDiffusion [22]2.44256.30--3.02248.70--
DiT-G++ [28]1.83281.530.780.64----
MDT-G [14]1.79283.010.810.61----
DiT-XL/2-G [47]2.27278.240.830.573.04240.820.840.54
DiT-SADM (Ours)1.58298.460.860.662.11251.820.870.63
", + "bbox": [ + 120, + 114, + 846, + 323 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "matching objective and $\\mathcal{L}_t^{\\mathrm{structure}}$ :", + "bbox": [ + 76, + 347, + 294, + 364 + ], + "page_idx": 5 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {i}, \\boldsymbol {\\epsilon} ^ {i}, t} w (\\lambda_ {t}) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2} + \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {j}, \\boldsymbol {\\epsilon} ^ {j}, t} w (\\lambda_ {t}) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {j}) - \\mathbf {x} _ {0} ^ {j} \\| _ {2} ^ {2} \\\\ + \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {i}, \\epsilon^ {i}, \\mathbf {x} _ {0} ^ {j}, \\epsilon^ {j}, t} \\left[ \\mathcal {L} _ {t} ^ {\\text {s t r u c t u r e}} \\right], \\tag {15} \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 369, + 496, + 426 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "which is a variational upper bound of negative log likelihood of the joint sample. Our objective in Eq. (6) can be viewed as a finite-sample version of Eq. (15), which trains the conditional diffusion model to utilize the structural information.", + "bbox": [ + 75, + 426, + 470, + 487 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 76, + 500, + 209, + 517 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.1. Image Generation", + "text_level": 1, + "bbox": [ + 76, + 523, + 253, + 540 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Experiment Setup We experiment on CIFAR-10 [35], CelebA/FFHQ 64x64 [41], and ImageNet 256x256 [11]. We utilize our SADM to facilitate the training of the diffusion backbones from Karras et al. [27], Vahdat et al. [63] on CIFAR-10 and FFHQ, from Kim et al. [30] on CelebA, and from Peebles and Xie [47] (DiT, Diffusion Transformer) on ImageNet.", + "bbox": [ + 75, + 547, + 470, + 654 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Evaluation Metrics We use Frechet Inception Distance (FID) [18] as the primary metric for capturing both quality and diversity due to its alignment with human judgement. We follow the evaluation procedure of ADM [12] for fair comparisons. For completeness, we also use Inception Score (IS) [53], Precision and Recall [36] as the main metrics for measuring diversity and distribution coverage.", + "bbox": [ + 75, + 671, + 468, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Implementation Details We train the denoising network from scratch and use the feature extractor of Inception-V3 [61] pre-trained on ImageNet for initializing the encoder of our structure discriminator. At the beginning of training, we freeze the pre-trained discriminator encoder and train the denoiser with structure-guided training objective in Eq. (6) until convergence, then we adversarially tune the denoiser and", + "bbox": [ + 75, + 794, + 470, + 900 + ], + "page_idx": 5 + }, + { + "type": "table", + "img_path": "images/bd66c0e8fc144a5daedfaacdd334bad5f24af716d0e95414c3d9419df8121420.jpg", + "table_caption": [ + "Table 2. Performance on CIFAR-10." + ], + "table_footnote": [], + "table_body": "
ModelDiffusion SpaceNFE↓UnconditionalConditional
NLL↓FID↓FID↓
VDM [31]Data10002.497.41-
DDPM [20]Data10003.753.17-
iDDPM [44]Data10003.372.90-
Soft Truncation [30]Data20002.912.47-
INDM [29]Latent20003.092.28-
CLD-SGM [13]Data3123.312.25-
NCSN++ [59]Data20003.452.20-
LSGM [63]Latent1383.432.10-
NCSN++-G [3]Data2000--2.25
EDM [27]Data352.601.971.79
LSGM-G++ [28]Latent1383.421.94-
EDM-G++ [28]Data352.551.771.64
SADMLatent1382.511.781.73
SADMData352.281.541.47
", + "bbox": [ + 504, + 366, + 893, + 580 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "encoder with the objective in Eq. (8) for 3 or 4 rounds (500k steps) until they achieve a balance. This training paradigm keeps the same for unconditional and class-conditional generation tasks, and can be easily generalized to score-based diffusion models [59, 63] by adding our structural constraint into the final objective functions.", + "bbox": [ + 496, + 599, + 893, + 691 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Main Results Our SADM achieves new state-of-the-art FIDs on all datasets including CIFAR-10, CelebA, FFHQ, and ImageNet. On ImageNet $256 \\times 256$ and $512 \\times 512$ , we consistently achieve SOTA FIDs of 1.43 and 2.18 for class-conditional generation as illustrated in Tab. 1. Notably, We significantly improve the generation performance of DiT and outperform the previous best FID of MDT [14] solely through improved training algorithm without increasing the model complexity and inference time. From Tab. 2, we find that our SADM works well for both image diffusion (based on EDM) and latent diffusion (based on LSGM). In experiments, for fair comparisons, we use the same hyperpa", + "bbox": [ + 496, + 719, + 893, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "7261", + "bbox": [ + 482, + 944, + 513, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/fbb4982394ab41458bf3ea034e5b4ccf698b7a9b345d11fd583f45d35c0ea898.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 140, + 88, + 359, + 202 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/416ebc9789490f5432d059b6eb0b91168b7b4e7fadd00c6af9eec8fa6310ab88.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 375, + 88, + 594, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/eeca27ba0bbdcafc5cdb07682ce1d3c3e4705e32369e2edf7111c10cc2779f60.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 612, + 88, + 831, + 200 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/5f30182207199252dd477699781aefbdfd9dd204b8448aae506529b191a5b2a2.jpg", + "image_caption": [ + "ADM-G" + ], + "image_footnote": [], + "bbox": [ + 140, + 210, + 357, + 324 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/1fcd867034e108e61787fe6e43395c1d09c2d80efba015f61fce5a3aab48c058.jpg", + "image_caption": [ + "MDT", + "Figure 4. Qualitative comparison with ADM-G [12] and previous SOTA method MDT [14]. Our SADM can synthesize more realistic and high-quality samples while maintaining satisfying diversity." + ], + "image_footnote": [], + "bbox": [ + 375, + 210, + 594, + 324 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/4a71bcc15a34f599226a49cc344f0b4c7990e3924fd3f3b0cadbedced3ee202d.jpg", + "image_caption": [ + "SADM (Ours)" + ], + "image_footnote": [], + "bbox": [ + 612, + 210, + 830, + 324 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/5dfad3e60131faa8305f271dc4ed69616f193054b49df96070857e4942109cc1.jpg", + "table_caption": [ + "Table 3. FID performance on CelebA/FFHQ ${64} \\times {64}$ ." + ], + "table_footnote": [], + "table_body": "
ModelDiffusion SpaceNFE↓CelebAFFHQ
DDPM++ [59]Data1312.32-
Soft Truncation [30]Data1311.90-
Soft Diffusion [9]Data3001.85-
INDM [29]Latent1321.75-
EDM [27]Data79-2.39
Soft Truncation-G++ [28]Data1311.34-
EDM-G++ [28]Data71-1.98
SADMLatent1311.281.85
SADMData711.161.71
", + "bbox": [ + 78, + 410, + 480, + 571 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "rameters as EDM and LSGM to evaluate the effectiveness of our proposed training algorithm. And we also achieve significant performance improvement on facial datasets as demonstrated in Tab. 3. For qualitative results, we compare our SADM with ADM-G [12] and previous SOTA method MDT [14] in Fig. 4. These remarkable results demonstrate our SADM has the potential for generalizing to arbitrary diffusion architectures and can better learn the whole data distribution.", + "bbox": [ + 75, + 590, + 470, + 726 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2. Cross-Domain Fine-Tuning", + "text_level": 1, + "bbox": [ + 76, + 739, + 323, + 757 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Experiment Setup We conduct cross-domain fine-tuning tasks on diffusion image generation for evaluating the transferability of proposed model, where we pre-train a diffusion model in source domain and adapt it to a target domain by fine-tuning. Following Xie et al. [70], we use ImageNet as source dataset, and choose eight commonly-used fine-grained datasets as target datasets: Food101 [1], SUN397 [68], DF-20M mini [48], Caltech101 [16], CUB-200-2011 [65], ArtBench-10 [40], Oxford Flowers [45] and Stanford", + "bbox": [ + 75, + 763, + 472, + 902 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Cars [34]. More details about datasets are in Appendix A.", + "bbox": [ + 498, + 390, + 880, + 406 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Implementation Details For fair comparison, we follow Xie et al. [70] to set all the hyper-parameters in both pretraining and fine-tuning stages, and use Diffusion Transformer (DiT) [47] as the diffusion backbone. We pretrain DiT on ImageNet $256 \\times 256$ with a learning rate of 0.0001 using DDPM objective. For target datasets, we fine-tune the pre-trained DiT with 24k structure-guide training steps and 4k adversarial training steps. We experiment with two fine-tuning settings, full and parameter-efficient, for comprehensive evaluations. In parameter-efficient setting, following Xie et al. [70], we freeze most of parameters in the pre-trained diffusion model and fine-tune the bias term, normalization, and class condition module.", + "bbox": [ + 496, + 430, + 895, + 626 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Main Results We achieve SOTA performance on all datasets in fine-tuning tasks as illustrated in Tab. 4. Remarkably, we significantly surpass DDPM in full fine-tuning and outperform DiffFit in parameter-efficient fine-tuning. The results sufficiently demonstrate our superior capability of capturing the whole data distribution, which enables better adaptation to new domains. Among all datasets, we achieve the best improvement over other methods on ArtBench-10 which has distinct distribution from ImageNet, demonstrating the out-of-distribution generalization ability of our SADM. More qualitative results are in Appendix C.", + "bbox": [ + 496, + 651, + 895, + 819 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.3. Model Analysis", + "text_level": 1, + "bbox": [ + 500, + 830, + 655, + 847 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Heatmap Analysis To evaluate the ability to capture data distribution, we perform heatmap analysis in Fig. 5, where we provide DDPM and our SADM with 8 randomly-selected", + "bbox": [ + 498, + 854, + 893, + 902 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "7262", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/9caaf40884ffb692bfc7329ee15210a9a0dc0e85951b590a6476d107b55e52cb.jpg", + "table_caption": [ + "Table 4. FID performance comparisons on 8 downstream datasets, all the models are pretrained on ImageNet ${256} \\times {256}$ ." + ], + "table_footnote": [], + "table_body": "
Dataset MethodFoodSUNDF-20MCaltechCUB-BirdArtBenchOxford FlowersStandard CarsAverage FID
AdaptFormer [5]13.6711.4722.3835.767.7338.4321.2410.7320.17
BitFit [77]9.179.1117.7834.218.8124.5320.3110.6416.82
VPT [25]18.4714.5432.8942.7817.2940.7425.5922.1226.80
LoRA [23]33.7532.53120.2586.0556.0380.99164.1376.2481.25
DiffFit [70]6.968.5517.3533.845.4820.8720.189.9015.39
Full Fine-tuning with DDPM10.467.9617.2635.255.6825.3121.059.7916.59
SADM (parameter-efficient)5.747.9216.5832.035.0418.2319.379.2614.27
SADM (full)6.207.3515.1232.864.6919.8418.188.9314.15
", + "bbox": [ + 104, + 114, + 859, + 275 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "noisy images in test batch and visualize the correlations between their denoised outputs. We observe that compared to DDPM, the overall heatmap pattern of our SADM is more closer to that of label affinity. The phenomenon demonstrates our SADM can precisely learn the manifold structures within real data samples.", + "bbox": [ + 75, + 292, + 473, + 383 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/75fe677ff2742e4bab0a292bcd160c917009458342bcf4aa5eca451e666ce36e.jpg", + "image_caption": [ + "Figure 5. Heatmap visualization with 8 denoised samples." + ], + "image_footnote": [], + "bbox": [ + 81, + 385, + 464, + 638 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Ablation Study We conduct ablation study to validate the effectiveness of our algorithm in Tab. 5. Here, we base on DDPM [20] architecture, and progressively add our model components (structural guidance and structure discriminator) into it for evaluating FID score on three datasets. We observe that each component can consistently improve the DDPM on all datasets, and the performance improvement of our structural guidance is more significant. The results fully demonstrate the effectiveness of our algorithm. More ablation studies about our model are in Appendix B.", + "bbox": [ + 75, + 667, + 472, + 819 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Contributing to Better Convergence To investigate the contribution of our structure-guided training to model convergence, we plot the training curve in Fig. 6. We conclude that compared to previous SOTA methods DiT [47] and MDT", + "bbox": [ + 75, + 839, + 472, + 902 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/ee1f5c69fce0fea6b3f59e56b1523df037d1990e138212e5cb9e6b1a0bdf3ecb.jpg", + "table_caption": [ + "Table 5. Ablation study with FID performance. SG denotes structural guidance, SAT denotes SG+Structure Discriminator." + ], + "table_footnote": [], + "table_body": "
Model \nDatasetDDPM+ Our SG+ Our SAT
ImageNet4.593.573.14
CIFAR-103.172.642.33
CelebA2.321.821.64
", + "bbox": [ + 514, + 323, + 870, + 407 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "[14], the proposed structure-guided training enables faster and better model convergence because we optimize the diffusion models from a structural perspective, which essentially contributes to capturing the whole data distribution.", + "bbox": [ + 498, + 412, + 893, + 473 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/b9b8bba44d38199487c87681e9a0144b516318cd94b1fbf1423367b4017d1d4c.jpg", + "image_caption": [ + "Figure 6. Comparison with SOTA methods on model convergence." + ], + "image_footnote": [], + "bbox": [ + 560, + 486, + 810, + 631 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 657, + 619, + 672 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We propose structure-guided adversarial training for optimizing diffusion models from a structural perspective. The proposed training algorithm can easily generalize to both image and latent diffusion models, and consistently improve existing diffusion models with theoretical derivations and empirical results. We achieve new SOTA performance on image generation and cross-domain fine-tuning tasks across 12 image datasets. For future work, we will extend our method to more challenging diffusion-based applications (e.g., text-to-image/video generation).", + "bbox": [ + 496, + 683, + 893, + 835 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgement", + "text_level": 1, + "bbox": [ + 500, + 847, + 660, + 864 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "This work was supported by the National Natural Science Foundation of China (No.U23B2048 and U22B2037).", + "bbox": [ + 500, + 871, + 893, + 900 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "7263", + "bbox": [ + 482, + 944, + 514, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 118, + 171, + 132 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. 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Realcompo: Dynamic equilibrium between realism and compositionality improves text-to-image diffusion models. arXiv preprint arXiv:2402.12908, 2024. 1" + ], + "bbox": [ + 501, + 90, + 893, + 316 + ], + "page_idx": 10 + }, + { + "type": "page_number", + "text": "7266", + "bbox": [ + 482, + 945, + 514, + 955 + ], + "page_idx": 10 + } +] \ No newline at end of file diff --git a/2024/Structure-Guided Adversarial Training of Diffusion Models/b70a5045-dbc8-47eb-880e-4252d02e0e55_model.json b/2024/Structure-Guided Adversarial Training of Diffusion Models/b70a5045-dbc8-47eb-880e-4252d02e0e55_model.json new file mode 100644 index 0000000000000000000000000000000000000000..e6fbd84cd926e876bf4a156f8eb767e73d1155fa --- /dev/null +++ b/2024/Structure-Guided Adversarial Training of Diffusion Models/b70a5045-dbc8-47eb-880e-4252d02e0e55_model.json @@ -0,0 +1,2686 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.0, + 0.812, + 0.045 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.183, + 0.131, + 0.787, + 0.152 + ], + "angle": 0, + "content": "Structure-Guided Adversarial Training of Diffusion Models" + }, + { + "type": "text", + "bbox": [ + 0.207, + 0.18, + 0.768, + 0.218 + ], + "angle": 0, + "content": "Ling Yang*† Haotian Qian* Zhilong Zhang Jingwei Liu Bin Cui† Peking University" + }, + { + "type": "text", + "bbox": [ + 0.168, + 0.22, + 0.796, + 0.234 + ], + "angle": 0, + "content": "yangling0818@163.com, zzmqht@gmail.com, {zzl2018math, bin.cui}@pku.edu" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.269, + 0.314, + 0.285 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.074, + 0.302, + 0.474, + 0.62 + ], + "angle": 0, + "content": "Diffusion models have demonstrated exceptional efficacy in various generative applications. While existing models focus on minimizing a weighted sum of denoising score matching losses for data distribution modeling, their training primarily emphasizes instance-level optimization, overlooking valuable structural information within each minibatch, indicative of pair-wise relationships among samples. To address this limitation, we introduce Structure-guided Adversarial training of Diffusion Models (SADM). In this pioneering approach, we compel the model to learn manifold structures between samples in each training batch. To ensure the model captures authentic manifold structures in the data distribution, we advocate adversarial training of the diffusion generator against a novel structure discriminator in a minimax game, distinguishing real manifold structures from the generated ones. SADM substantially outperforms existing methods in image generation and cross-domain fine-tuning tasks across 12 datasets, establishing a new state-of-the-art FID of 1.58 and 2.11 on ImageNet for class-conditional image generation at resolutions of \\(256 \\times 256\\) and \\(512 \\times 512\\), respectively." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.652, + 0.21, + 0.669 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.679, + 0.473, + 0.862 + ], + "angle": 0, + "content": "Diffusion models [20, 56-59, 73] have achieved remarkable generation quality in various tasks, including image generation [12, 50-52, 67, 74, 75, 79], audio synthesis [4, 33, 49], and interdisciplinary applications [21, 24, 71]. Starting from tractable noise distribution, diffusion models generate data by progressively removing noise. This involves the model learning to reverse a pre-defined diffusion process that sequentially introduces varying levels of noise to the data. The model is parameterized and undergoes training by optimizing the weighted sum of denoising score matching losses [20] for various noise levels [57], aiming to learn the recovery of clean images from corrupted images." + }, + { + "type": "image", + "bbox": [ + 0.52, + 0.261, + 0.868, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.459, + 0.892, + 0.488 + ], + "angle": 0, + "content": "Figure 1. Comparison between previous instance-level training and our structure-guided training for diffusion models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.506, + 0.895, + 0.734 + ], + "angle": 0, + "content": "Aiming to maximally model the data distribution, recent works [28, 42, 60, 63, 72, 76] attempt to improve the precision of training diffusion models. For instance, many approaches design effective weighting schemes [8, 17, 30, 42, 60, 76] for maximum likelihood training or add an extra regularization term [10, 37, 46] to the denoising score loss. There are also some works to enhance the model expressiveness by incorporating other generative models, such as VAE [31, 51, 63], GAN [69], and Normalizing Flows [29, 43, 78]. However, their improved training of diffusion models primarily concentrates on instance-level optimization, overlooking the valuable structural information among batch samples. This oversight is significant, as the incorporation of structural details is crucial for aligning the learned distribution with the underlying data distribution." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.735, + 0.896, + 0.903 + ], + "angle": 0, + "content": "To mitigate the challenges posed by existing instance-level training methods, we propose Structure-guided Adversarial training of Diffusion Models (SADM). In contrast to conventional instance-level training illustrated in Fig. 1, our approach guides diffusion training at a structural level. During batch training, the model is facilitated to learn manifold structures within batch samples, represented by pair-wise relationships in a low-dimensional feature space. To accurately learn real manifold structures in the data distribution, we introduce a novel structure discriminator that distinguishes genuine manifold structures from generated" + }, + { + "type": "page_footnote", + "bbox": [ + 0.096, + 0.875, + 0.213, + 0.888 + ], + "angle": 0, + "content": "* Contributed equally." + }, + { + "type": "page_footnote", + "bbox": [ + 0.097, + 0.888, + 0.227, + 0.9 + ], + "angle": 0, + "content": "† Corresponding authors." + }, + { + "type": "list", + "bbox": [ + 0.096, + 0.875, + 0.227, + 0.9 + ], + "angle": 0, + "content": null + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7256" + } + ], + [ + { + "type": "image_caption", + "bbox": [ + 0.145, + 0.088, + 0.275, + 0.099 + ], + "angle": 0, + "content": "FID: 4.59, Recall: 0.52" + }, + { + "type": "image_caption", + "bbox": [ + 0.42, + 0.087, + 0.55, + 0.098 + ], + "angle": 0, + "content": "FID: 3.14, Recall: 0.61" + }, + { + "type": "image", + "bbox": [ + 0.082, + 0.102, + 0.342, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.356, + 0.102, + 0.615, + 0.436 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.63, + 0.102, + 0.889, + 0.435 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.441, + 0.893, + 0.496 + ], + "angle": 0, + "content": "Figure 2. Generated samples on ImageNet \\(256 \\times 256\\) with (i) ADM with Classifier Guidance (ADM-G) [12], (ii) ADM optimized by our Structure-guided Adversarial Training, and (iii) real samples in ground truth classes. We can significantly improve diffusion models qualitatively and quantitatively, and our generated sample distribution is overall more similar to real sample distribution. See Appendix C for more synthesis samples of our SOTA model." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.529, + 0.471, + 0.589 + ], + "angle": 0, + "content": "ones. For clarity, we alternatively refer to the diffusion models optimized through our structure-guided training as joint sample diffusion, a concept theoretically proven to enhance diffusion model optimization." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.595, + 0.47, + 0.82 + ], + "angle": 0, + "content": "We assess the performance of our model across two pivotal tasks: image generation and cross-domain fine-tuning. The former involves training the diffusion model from scratch to evaluate its capability in capturing the entire data distribution. The latter leverages a pre-trained diffusion model, constructed on a large-scale source dataset, and fine-tunes it on a target dataset to assess transferability. Our extensive experiments consistently demonstrate that our approach significantly improves the model's ability to effectively capture the underlying data distribution (Fig. 2). SADM achieves state-of-the-art results across 12 image datasets, including ImageNet [11]. Furthermore, we observe its potential for facilitating rapid adaptation to new domains in cross-domain fine-tuning tasks. We summarize our contributions as follows:" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.826, + 0.47, + 0.87 + ], + "angle": 0, + "content": "- To the best of our knowledge, we are the first to propose Structure-guided Adversarial Training to optimize diffusion models from a structural perspective." + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.871, + 0.47, + 0.901 + ], + "angle": 0, + "content": "- We theoretically show that SADM is superior in capturing real data distribution, and can generalize to various image" + }, + { + "type": "list", + "bbox": [ + 0.078, + 0.826, + 0.47, + 0.901 + ], + "angle": 0, + "content": null + }, + { + "type": "text", + "bbox": [ + 0.513, + 0.53, + 0.882, + 0.544 + ], + "angle": 0, + "content": "and latent-based diffusion architectures (e.g., DiT [47])." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.546, + 0.891, + 0.605 + ], + "angle": 0, + "content": "- We substantially outperform existing methods on image generation and cross-domain fine-tuning tasks, achieving a new state-of-the-art FID of 1.58 and 2.11 on ImageNet at resolutions of \\(256 \\times 256\\) and \\(512 \\times 512\\), respectively." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.53, + 0.891, + 0.605 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.616, + 0.64, + 0.632 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.642, + 0.894, + 0.687 + ], + "angle": 0, + "content": "In this work, we focus on improving the training of diffusion models. Here, we review previous related works and compare our SADM with them." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.894, + 0.901 + ], + "angle": 0, + "content": "Modifying Training Objectives of Diffusion Models A line of research modifies training objectives to achieve state-of-the-art likelihood [8, 42, 60, 74]. Song et al. [60] propose likelihood weighting to enable approximate maximum likelihood training of score-based diffusion models [57-59] while ContextDiff [76] introduces an effective shifting scheme for facilitating the diffusion and training processes of diffusion probabilistic models [20, 56] to achieve improved sample quality with stable training. Lai et al. [37] and [10] introduce an extra regularization term to the denoising score loss to satisfy some properties of the diffusion process. However, these improvements mainly focus on sample-level optimization, neglecting the rich structural information within batch" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.515, + 0.957 + ], + "angle": 0, + "content": "7257" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.473, + 0.138 + ], + "angle": 0, + "content": "samples, which is critical for aligning the learned distribution and data distribution. Hence, we enforce the model to maximally learn the manifold structures of samples." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.156, + 0.473, + 0.399 + ], + "angle": 0, + "content": "Combining Additional Models for Diffusion Training Another line of research incorporates other models to improve the stability and precision of diffusion training. For example, INDM [29] expands the linear diffusion to trainable nonlinear diffusion through a normalizing flow to improve the training curve of diffusion models. Jolicoeur-Martineau et al. [26], Kim et al. [28] improve diffusion models with adversarial learning while Xiao et al. [69] model each denoising step using a multimodal conditional GAN. LSGM [63] and LDM [51] conduct diffusion process in the semantic latent space obtained with a pre-trained VAE. Although these combinations strengthen the model expressiveness for capturing data distribution, they are still limited in modeling the underlying manifold structures within training samples. We propose a novel structure discriminator for adversarially learn the diffusion model from a structural perspective." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.412, + 0.204, + 0.429 + ], + "angle": 0, + "content": "3. Preliminary" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.437, + 0.473, + 0.542 + ], + "angle": 0, + "content": "Diffusion Models We consider diffusion models [20, 56, 57] specified in continuous time [4, 31, 59, 62]. Given samples \\(\\mathbf{x}_0\\) from a data distribution \\(q_0(\\mathbf{x}_0)\\), noise scheduling functions \\(\\alpha_{t},\\sigma_{t}\\), a diffusion model has latent variables \\(\\mathbf{x} = \\{\\mathbf{x}_t\\mid t\\in [0,1]\\}\\), and the forward process is defined with \\(q(\\mathbf{x}_t|\\mathbf{x}_0)\\), a Gaussian process satisfying the following Markovian structure:" + }, + { + "type": "equation", + "bbox": [ + 0.149, + 0.554, + 0.47, + 0.572 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\alpha_ {t} \\mathbf {x} _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {1}\n\\]" + }, + { + "type": "equation", + "bbox": [ + 0.15, + 0.575, + 0.47, + 0.593 + ], + "angle": 0, + "content": "\\[\nq \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {s}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\left(\\alpha_ {t} / \\alpha_ {s}\\right) \\mathbf {x} _ {s}, \\sigma_ {t \\mid s} ^ {2} \\mathbf {I}\\right) \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.606, + 0.472, + 0.685 + ], + "angle": 0, + "content": "where \\(0 \\leq s < t \\leq 1\\) and \\(\\sigma_{t|s}^2 = (1 - e^{\\lambda_t - \\lambda_s})\\sigma_t^2\\), and \\(\\lambda_t = \\log [\\alpha_t^2 /\\sigma_t^2 ]\\) denotes the log signal-to-noise-ratio [31]. The goal of the diffusion model is to denoise \\(\\mathbf{x}_t \\sim q(\\mathbf{x}_t|\\mathbf{x}_0)\\) by estimating \\(\\hat{\\mathbf{x}}_{\\theta}(\\mathbf{x}_t) \\approx \\mathbf{x}_0\\). We train this denoising model \\(\\hat{\\mathbf{x}}_{\\theta}\\) using a weighted mean squared error loss" + }, + { + "type": "equation", + "bbox": [ + 0.168, + 0.696, + 0.47, + 0.715 + ], + "angle": 0, + "content": "\\[\n\\mathbb {E} _ {\\mathbf {x} _ {0}, \\boldsymbol {\\epsilon}, t} \\left[ w \\left(\\lambda_ {t}\\right) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t}) - \\mathbf {x} _ {0} \\| _ {2} ^ {2} \\right] \\tag {3}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.725, + 0.47, + 0.802 + ], + "angle": 0, + "content": "over uniformly sampled times \\( t \\in [0,1] \\). This loss can be justified as a weighted variational lower bound on the data log likelihood under the diffusion model [31] or as a form of denoising score matching [57, 64]. \\( w(\\lambda_t) \\) is a pre-specified weighting function [31]." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.815, + 0.251, + 0.832 + ], + "angle": 0, + "content": "4. Proposed Method" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.901 + ], + "angle": 0, + "content": "We introduce the proposed SADM in detail (Fig. 3). In order to maximally learn the structural information between real samples, we propose structure-guided training of diffusion models in Sec. 4.1. Then we design a novel structure" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.168 + ], + "angle": 0, + "content": "discriminator for adversarially optimizing the training procedure from a structural perspective in Sec. 4.2. Finally, we alternatively interpret our structure-guided training of diffusion models as joint sample diffusion with theoretical analysis for betwen understanding in Sec. 4.3." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.176, + 0.783, + 0.192 + ], + "angle": 0, + "content": "4.1. Beyond Instance-Level Training" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.199, + 0.893, + 0.245 + ], + "angle": 0, + "content": "We first review the previous instance-level training methods for diffusion models. Generally, they train the diffusion model with a finite sample version of Eq. (3):" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.253, + 0.893, + 0.287 + ], + "angle": 0, + "content": "\\[\n\\mathcal {L} _ {t} = w \\left(\\lambda_ {t}\\right) \\frac {\\sum_ {i \\in B} \\left| \\left| \\mathbf {x} _ {0} ^ {i} - \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) \\right| \\right| ^ {2}}{| B |}, \\tag {4}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.297, + 0.895, + 0.419 + ], + "angle": 0, + "content": "where \\(\\mathbf{x}_0^i, \\mathbf{x}_t^i\\) denote the \\(i^{th}\\) ground truth samples and generated samples in the mini-batch \\(B\\) at time step \\(t\\). However, this objective function encourages the diffusion model to denoise by considering only the instance-level information, neglecting the group-level (structural) information in the mini-batch. Therefore, we enforce the sample predictions of the denoising network to maximally preserve the manifold structures between batch samples." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.436, + 0.895, + 0.593 + ], + "angle": 0, + "content": "Structural Constraint in Manifold More concretely, ground truth samples \\(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}\\) are first projected from pixel space into embedding space using off-the-shelf pre-trained networks \\(\\Psi (\\cdot):\\mathbb{R}^{m\\times n}\\to \\mathbb{R}^d\\) e.g., an Inception-V3 feature extractor pre-trained on ImageNet [61] (we conduct ablation study in Appendix B). Then, the pair-wise relationships \\(\\mathcal{R}(\\Psi (\\mathbf{x}_0^i),\\Psi (\\mathbf{x}_0^j))\\) are calculated within batch samples \\(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}\\) , which contain rich structural information in a low-dimensional manifold. This structural information can be expressed with an affinity matrix \\(\\mathcal{M}(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|})\\) defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.519, + 0.601, + 0.892, + 0.685 + ], + "angle": 0, + "content": "\\[\n\\left[ \\begin{array}{c c c c} \\mathcal {R} (\\Psi_ {1}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {1}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {1}, \\Psi_ {| B |}) \\\\ \\mathcal {R} (\\Psi_ {2}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {2}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {2}, \\Psi_ {| B |}) \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {| B |}) \\end{array} \\right] \\tag {5}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.686, + 0.895, + 0.839 + ], + "angle": 0, + "content": "where \\(\\Psi_{i}\\) is a short-hand for \\(\\Psi (\\mathbf{x}_0^i)\\), and \\(\\mathcal{R}(\\cdot ,\\cdot)\\) denotes the relational function, such as Euclidean distance. Kindly note that many off-the-shelf pre-trained networks are open-source and only work well on clean images, and thus fail to provide meaningful embeddings when the input is noisy. Therefore, we use the predicted clean samples \\(\\hat{\\mathbf{x}}_0^i\\) for computing affinity matrix, and regularize the denoising network to minimize the structural distance between \\(\\mathcal{M}(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|})\\) and \\(\\mathcal{M}(\\{\\hat{\\mathbf{x}}_0^i\\}_{i = 1}^{|B|})\\). Adding this structural constraint into Eq. (4), the training objective for denoising network is:" + }, + { + "type": "equation", + "bbox": [ + 0.57, + 0.847, + 0.893, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {t} = \\frac {\\sum_ {i \\in B} \\left| \\left| \\mathbf {x} _ {0} ^ {i} - \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) \\right| \\right| ^ {2}}{| B |} \\tag {6} \\\\ + \\mathcal {D} (\\mathcal {M} (\\{\\mathbf {x} _ {0} ^ {i} \\} _ {i = 1} ^ {| B |}), \\mathcal {M} (\\{\\hat {\\mathbf {x}} _ {0} ^ {i} \\} _ {i = 1} ^ {| B |})) \\\\ \\end{array}\n\\]" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7258" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.119, + 0.086, + 0.852, + 0.401 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.411, + 0.897, + 0.455 + ], + "angle": 0, + "content": "Figure 3. Overview of SADM. We minimize the structural distance between the generated samples (fake) and ground truth samples (real) in the manifold space for optimizing the denoiser, and maximize their structural distance for optimizing the encoder in structure discriminator. The denoiser and the structure discriminator are adversarially trained." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.475, + 0.472, + 0.552 + ], + "angle": 0, + "content": "where \\(\\mathcal{D}(\\cdot, \\cdot)\\) denotes the distance metric between ground truth and predicted affinity matrices. In this way, the diffusion generator (denoiser) is optimized not only to make correct prediction for each instance, but also to preserve the manifold structures of batch samples." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.558, + 0.418, + 0.575 + ], + "angle": 0, + "content": "4.2. Structure-Guided Adversarial Training" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.472, + 0.763 + ], + "angle": 0, + "content": "As demonstrated above, we aim to maximally learn data distribution by aligning the manifold structures of denoiser's predicted samples to those of ground truth samples in each training batch. At every training iteration, the manifold structures can be diverse and the denoiser tend to merely focus on some easy-to-learn structures, ultimately leading to trivial solutions that fail to capture the whole data distribution. In order to mitigate this problem and improve the expressiveness of denoiser, we adversarially learn the denoising network against a structure discriminator in a minimax game (Fig. 3), which is trained to distinguish the manifold structures between the real and generated batch samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.78, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Structure Discriminator Normally, the discriminator in adversarial learning [15] would output the discrete value (0 or 1) to determine whether the input is real or fake. However, such discrete discriminator can not be applied in distinguishing manifold structures, because the generated and real sample sets would share similar pair-wise sample relations despite their different feature spaces. Thus, instead of learning a classification-based discriminator, we design a" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.475, + 0.892, + 0.504 + ], + "angle": 0, + "content": "novel comparison-based structure discriminator to address this issue." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.509, + 0.895, + 0.645 + ], + "angle": 0, + "content": "Specifically, as illustrated in Fig. 3, the structure discriminator consists of the aforementioned neural network \\(\\Psi_{\\phi}\\) with trainable parameters \\(\\phi\\) and the distance measure function \\(\\mathcal{D}(\\cdot ,\\cdot)\\) that outputs continuous value. It projects both real and generated samples into the embedding space, then the structure discriminator is trained against the denoiser for finding a better manifold (or embedding space) to distinguish real sample set from generated set by maximizing their structural distance:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.661, + 0.947, + 0.71 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\phi} \\frac {\\eta_ {t} \\sum_ {i , j \\in B} \\mathcal {D} \\left(\\mathcal {R} \\left(\\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) , \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right)\\right) , \\mathcal {R} \\left(\\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) , \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right)\\right)\\right)}{| B | ^ {2}}. \\tag {7}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.71, + 0.895, + 0.817 + ], + "angle": 0, + "content": "where we choose \\(\\eta_t = \\frac{1}{t}\\) as a time-dependent weighting factor. We can use simple measurements for \\(\\mathcal{D}(\\cdot, \\cdot)\\) (\\(L_2\\) distance) and \\(\\mathcal{R}(\\cdot, \\cdot)\\) (cosine similarity), as the critical semantic information has been already encoded by \\(\\Psi_\\phi\\). Conversely, the denoiser is adversarially optimized for generating more realistic sample set to fool the structure discriminator by minimizing the structural distance." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Final Optimization Objective The final training objective of our SADM consists of normal denoising score matching loss (Eq. (3)) and adversarial structural distance loss (Eq. (7))" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7259" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.078, + 0.092, + 0.332, + 0.106 + ], + "angle": 0, + "content": "at timestep \\(t\\), which can be written as:" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.116, + 0.49, + 0.202 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathcal {L} _ {t} (\\theta) = \\frac {w (\\lambda_ {t}) \\sum_ {i \\in B} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2}}{| B |} \\\\ + \\max _ {\\phi} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right) - \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2}}{| B | ^ {2}}. \\tag {8} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.204, + 0.47, + 0.249 + ], + "angle": 0, + "content": "In training, we iteratively optimize the feature extractor and the denoising network in Eq. (8). In an iteration, we first freeze \\(\\theta\\) and update \\(\\phi\\) by ascending along its gradient" + }, + { + "type": "equation", + "bbox": [ + 0.079, + 0.259, + 0.47, + 0.307 + ], + "angle": 0, + "content": "\\[\n\\nabla_ {\\phi} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right) - \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2}}{| B | ^ {2}}, \\tag {9}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.308, + 0.471, + 0.339 + ], + "angle": 0, + "content": "then we freeze \\(\\phi\\) and update \\(\\theta\\) by descending along its gradient" + }, + { + "type": "equation", + "bbox": [ + 0.081, + 0.346, + 0.47, + 0.431 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\theta} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} (\\mathbf {x} _ {0} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\mathbf {x} _ {0} ^ {j}) - \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}) \\| _ {2} ^ {2}}{| B | ^ {2}} \\\\ + \\nabla_ {\\theta} \\frac {w \\left(\\lambda_ {t}\\right) \\sum_ {i \\in B} \\left\\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) - \\mathbf {x} _ {0} ^ {i} \\right\\| _ {2} ^ {2}}{| B |}. \\tag {10} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.078, + 0.433, + 0.471, + 0.448 + ], + "angle": 0, + "content": "The proposed training algorithm is presented in Algorithm 1." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.466, + 0.47, + 0.572 + ], + "angle": 0, + "content": "Generalizing to Latent Diffusion Our proposed training algorithm applies not only to image diffusion but also to latent diffusion, such as LDM [51] and LSGM [63]. In this case, the intermediate results \\(\\mathbf{x}_t\\) are latent codes rather than images. We can use the latent decoder (e.g., VAE decoder [32]) to project the generated latent codes to images and then use the same algorithm in the image domain." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.581, + 0.408, + 0.597 + ], + "angle": 0, + "content": "4.3. Interpreting as Joint Sample Diffusion" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.604, + 0.472, + 0.786 + ], + "angle": 0, + "content": "Relation-Conditioned Diffusion Process For better understanding of our proposed structure-guided training, we interpret it as a joint sample diffusion model that simultaneously perturbs and denoises a set of samples conditioned on the relation variable. Formally, let \\(\\mathbf{y}_0 = (\\mathbf{x}_0^i,\\mathbf{x}_0^j)\\), where \\(\\mathbf{x}_0^i,\\mathbf{x}_0^j\\) are independent random variables sampled from ground truth distribution \\(q_{0}\\). And the relation variable that encodes the structure information is defined as \\(\\mathcal{R} = \\mathcal{R}(\\mathbf{x}_0^i,\\mathbf{x}_0^j) + \\gamma \\epsilon\\), where \\(\\gamma \\epsilon\\) denote a small gaussian noise added to the relation to avoid degenerated distribution. Then the forward diffusion jointly perturbs \\(\\mathbf{y}_0\\), conditioned on \\(\\mathcal{R}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.152, + 0.797, + 0.47, + 0.815 + ], + "angle": 0, + "content": "\\[\nq (\\mathbf {y} _ {t} | \\mathbf {y} _ {0}, \\mathcal {R}) = \\mathcal {N} (\\mathbf {y} _ {t}; \\alpha_ {t} \\mathbf {y} _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}). \\tag {11}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.825, + 0.473, + 0.902 + ], + "angle": 0, + "content": "To reverse the diffusion process, we need to predict \\(\\mathbf{y}_0\\), or equivalently, learn the conditional score function \\(\\nabla_y\\log q_t(y_t|\\mathcal{R})\\) [12, 19]. This formulation allows us to utilize the auxiliary structural information \\(\\mathcal{R}\\) in the sampling process, which usually leads to better performance [13, 55]." + }, + { + "type": "text", + "bbox": [ + 0.51, + 0.095, + 0.82, + 0.11 + ], + "angle": 0, + "content": "Algorithm 1: SADM, our proposed algorithm." + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.113, + 0.868, + 0.187 + ], + "angle": 0, + "content": "input : \\(\\{\\alpha_{t}\\}_{t\\in [0,1]}\\) \\(\\{\\sigma_t\\}_{t\\in [0,1]}\\) the noise schedule, \\(|B|\\) the batch size, \\(w(\\lambda_t)\\) \\(\\eta_t\\) the scaling factors for denoising score matching loss and adversarial loss, pre-trained encoder \\(\\Psi_{\\phi}\\) for structure discriminator." + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.189, + 0.8, + 0.204 + ], + "angle": 0, + "content": "Initialize denoising network parameters \\(\\theta\\)" + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.205, + 0.718, + 0.219 + ], + "angle": 0, + "content": "while \\(\\theta\\) has not converged do" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.219, + 0.803, + 0.238 + ], + "angle": 0, + "content": "Sample a minibatch \\(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}\\sim q_0\\) and" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.238, + 0.688, + 0.256 + ], + "angle": 0, + "content": "\\[\n\\{\\boldsymbol {\\epsilon} ^ {j} \\} _ {j = 1} ^ {| B |} \\sim \\mathcal {N} (\\mathbf {0}, \\boldsymbol {I})\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.256, + 0.675, + 0.27 + ], + "angle": 0, + "content": "Sample \\(t\\sim U[0,1]\\)" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.271, + 0.764, + 0.288 + ], + "angle": 0, + "content": "Sample \\(\\{\\mathbf{x}_t^i = \\alpha_t\\mathbf{x}_0^i +\\sigma_t\\pmb {\\epsilon}^i\\}_{i = 1}^{|B|}\\)" + }, + { + "type": "text", + "bbox": [ + 0.547, + 0.289, + 0.805, + 0.302 + ], + "angle": 0, + "content": "Freeze \\(\\phi\\) and update \\(\\theta\\) with its gradient" + }, + { + "type": "equation", + "bbox": [ + 0.556, + 0.302, + 0.873, + 0.349 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {\\theta} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} (\\mathbf {\\hat {x}} _ {0} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\mathbf {\\hat {x}} _ {0} ^ {j}) - \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}) \\| _ {2} ^ {2}}{| B | ^ {2}} \\\\ + \\nabla_ {\\theta} \\frac {w (\\lambda_ {t}) \\sum_ {i \\in B} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2}}{| B |} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.52, + 0.351, + 0.86, + 0.396 + ], + "angle": 0, + "content": "Adversarily train denoising network and structure discriminator by iteratively updating their parameters \\(\\theta, \\phi\\) according to Eqs. (9) and (10)." + }, + { + "type": "text", + "bbox": [ + 0.521, + 0.397, + 0.721, + 0.411 + ], + "angle": 0, + "content": "output: Denoising network \\(\\theta\\)." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.449, + 0.895, + 0.48 + ], + "angle": 0, + "content": "Learning Conditional Score To approximate the conditional score function, first we decompose it with Bayes' rule," + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.507, + 0.894, + 0.555 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\nabla_ {y} \\log q _ {t} \\left(y _ {t} | \\mathcal {R}\\right) = \\nabla_ {y} \\log q _ {t} \\left(y _ {t}\\right) + \\nabla_ {y} \\log q _ {t} \\left(\\mathcal {R} \\mid y _ {t}\\right) \\\\ = \\Sigma_ {s = i, j} \\nabla_ {x} \\log q _ {t} \\left(x _ {t} ^ {s}\\right) + \\nabla_ {y} \\log q _ {t} (\\mathcal {R} | y _ {t}). \\tag {12} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.556, + 0.894, + 0.617 + ], + "angle": 0, + "content": "To approximate the first term on the right side of Eq. (12), we only need to learn \\(\\hat{\\mathbf{x}}_{\\theta ,t}^{i},\\hat{\\mathbf{x}}_{\\theta ,t}^{j}\\) , as in standard diffusion models [59]. However, the second term is intractable since \\(q_{t}(\\mathcal{R}|y_{t})\\) involves the intractable posterior \\(q(\\mathbf{y}_0|\\mathbf{y}_t)\\) . Note that" + }, + { + "type": "equation", + "bbox": [ + 0.573, + 0.632, + 0.892, + 0.683 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} q _ {t} (\\mathcal {R} | y _ {t}) = \\int g (\\mathcal {R} | \\mathbf {y} _ {0}) q \\left(\\mathbf {y} _ {0} \\mid \\mathbf {y} _ {t}\\right) d \\mathbf {y} _ {0} \\tag {13} \\\\ = \\mathbb {E} _ {\\mathbf {y} _ {0}} \\left[ g (\\mathcal {R} | \\mathbf {y} _ {0}) | \\mathbf {y} _ {t} \\right], \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.699, + 0.894, + 0.762 + ], + "angle": 0, + "content": "where \\(g(\\mathcal{R}|\\mathbf{y}_0)\\) is the density function of Gaussian distribution with mean \\(\\mathcal{R}(\\mathbf{x}_0^i,\\mathbf{x}_0^j)\\) and variance \\(\\gamma^2\\), by the definition of \\(\\mathcal{R}\\). As a result, we can use \\(g(\\mathcal{R}|\\hat{\\mathbf{y}}_{0,t}) = g(\\mathcal{R} | (\\hat{\\mathbf{x}}_{\\theta ,t}^i,\\hat{\\mathbf{x}}_{\\theta ,t}^j))\\) to approximate \\(q_{t}(\\mathcal{R}|y_{t})\\), and train it with \\(L_{2}\\) loss:" + }, + { + "type": "equation", + "bbox": [ + 0.5, + 0.777, + 0.897, + 0.87 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {y} _ {t}} \\| \\mathbb {E} _ {\\mathbf {y} _ {0}} [ g (\\mathcal {R} | \\mathbf {y} _ {0}) | \\mathbf {y} _ {t} ] - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) \\| _ {2} ^ {2} \\\\ = \\mathbb {E} _ {\\mathbf {y} _ {t}} \\| \\mathbb {E} _ {\\mathbf {y} _ {0}} [ g (\\mathcal {R} | \\mathbf {y} _ {0}) - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) | \\mathbf {y} _ {t} ] \\| _ {2} ^ {2} \\\\ \\leq \\mathbb {E} _ {\\mathbf {y} _ {0}, \\mathbf {y} _ {t}} \\| g (\\mathcal {R} | \\mathbf {y} _ {0}) - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) \\| _ {2} ^ {2} \\quad (J e s s e n I n e q u a l i t y) \\\\ \\leq w (\\gamma) \\mathbb {E} _ {\\mathbf {y} _ {0}, \\mathbf {y} _ {t}} \\| \\mathcal {R} \\left(\\mathbf {x} _ {0} ^ {i}, \\mathbf {x} _ {0} ^ {j}\\right) - \\mathcal {R} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}, \\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2} = \\mathcal {L} _ {t} ^ {\\text {s t r u c t u r e}}, \\tag {14} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.871, + 0.894, + 0.902 + ], + "angle": 0, + "content": "where \\( w(\\gamma) \\) is a weighting scalar that depends only on \\( \\gamma \\). The objective function is the sum of the denoising score" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7260" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.191, + 0.089, + 0.777, + 0.104 + ], + "angle": 0, + "content": "Table 1. Quantitative results for class-conditional generation on ImageNet \\( {256} \\times {256} \\) and \\( {512} \\times {512} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.121, + 0.115, + 0.847, + 0.324 + ], + "angle": 0, + "content": "
ModelImageNet 256×256ImageNet 512×512
FID ↓IS ↑Precision ↑Recall ↑FID ↓IS ↑Precision ↑Recall ↑
BigGAN-deep [2]6.95171.400.870.288.43177.900.880.29
StyleGAN-XL [54]2.30265.120.780.532.41267.750.770.52
ADM-G, ADM-U [12]3.94215.840.830.533.85221.720.840.53
LDM-4-G [51]3.60247.670.870.48----
RIN+NoiseSchedule [6]3.52186.20--3.95216.00--
SimpleDiffusion [22]2.44256.30--3.02248.70--
DiT-G++ [28]1.83281.530.780.64----
MDT-G [14]1.79283.010.810.61----
DiT-XL/2-G [47]2.27278.240.830.573.04240.820.840.54
DiT-SADM (Ours)1.58298.460.860.662.11251.820.870.63
" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.348, + 0.295, + 0.365 + ], + "angle": 0, + "content": "matching objective and \\(\\mathcal{L}_t^{\\mathrm{structure}}\\):" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.371, + 0.497, + 0.427 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {i}, \\boldsymbol {\\epsilon} ^ {i}, t} w (\\lambda_ {t}) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2} + \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {j}, \\boldsymbol {\\epsilon} ^ {j}, t} w (\\lambda_ {t}) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {j}) - \\mathbf {x} _ {0} ^ {j} \\| _ {2} ^ {2} \\\\ + \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {i}, \\epsilon^ {i}, \\mathbf {x} _ {0} ^ {j}, \\epsilon^ {j}, t} \\left[ \\mathcal {L} _ {t} ^ {\\text {s t r u c t u r e}} \\right], \\tag {15} \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.428, + 0.471, + 0.488 + ], + "angle": 0, + "content": "which is a variational upper bound of negative log likelihood of the joint sample. Our objective in Eq. (6) can be viewed as a finite-sample version of Eq. (15), which trains the conditional diffusion model to utilize the structural information." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.501, + 0.21, + 0.518 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.525, + 0.254, + 0.541 + ], + "angle": 0, + "content": "5.1. Image Generation" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.548, + 0.471, + 0.655 + ], + "angle": 0, + "content": "Experiment Setup We experiment on CIFAR-10 [35], CelebA/FFHQ 64x64 [41], and ImageNet 256x256 [11]. We utilize our SADM to facilitate the training of the diffusion backbones from Karras et al. [27], Vahdat et al. [63] on CIFAR-10 and FFHQ, from Kim et al. [30] on CelebA, and from Peebles and Xie [47] (DiT, Diffusion Transformer) on ImageNet." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.672, + 0.47, + 0.779 + ], + "angle": 0, + "content": "Evaluation Metrics We use Frechet Inception Distance (FID) [18] as the primary metric for capturing both quality and diversity due to its alignment with human judgement. We follow the evaluation procedure of ADM [12] for fair comparisons. For completeness, we also use Inception Score (IS) [53], Precision and Recall [36] as the main metrics for measuring diversity and distribution coverage." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.795, + 0.471, + 0.901 + ], + "angle": 0, + "content": "Implementation Details We train the denoising network from scratch and use the feature extractor of Inception-V3 [61] pre-trained on ImageNet for initializing the encoder of our structure discriminator. At the beginning of training, we freeze the pre-trained discriminator encoder and train the denoiser with structure-guided training objective in Eq. (6) until convergence, then we adversarially tune the denoiser and" + }, + { + "type": "table_caption", + "bbox": [ + 0.587, + 0.347, + 0.805, + 0.36 + ], + "angle": 0, + "content": "Table 2. Performance on CIFAR-10." + }, + { + "type": "table", + "bbox": [ + 0.505, + 0.367, + 0.895, + 0.581 + ], + "angle": 0, + "content": "
ModelDiffusion SpaceNFE↓UnconditionalConditional
NLL↓FID↓FID↓
VDM [31]Data10002.497.41-
DDPM [20]Data10003.753.17-
iDDPM [44]Data10003.372.90-
Soft Truncation [30]Data20002.912.47-
INDM [29]Latent20003.092.28-
CLD-SGM [13]Data3123.312.25-
NCSN++ [59]Data20003.452.20-
LSGM [63]Latent1383.432.10-
NCSN++-G [3]Data2000--2.25
EDM [27]Data352.601.971.79
LSGM-G++ [28]Latent1383.421.94-
EDM-G++ [28]Data352.551.771.64
SADMLatent1382.511.781.73
SADMData352.281.541.47
" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.601, + 0.894, + 0.692 + ], + "angle": 0, + "content": "encoder with the objective in Eq. (8) for 3 or 4 rounds (500k steps) until they achieve a balance. This training paradigm keeps the same for unconditional and class-conditional generation tasks, and can be easily generalized to score-based diffusion models [59, 63] by adding our structural constraint into the final objective functions." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.72, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Main Results Our SADM achieves new state-of-the-art FIDs on all datasets including CIFAR-10, CelebA, FFHQ, and ImageNet. On ImageNet \\(256 \\times 256\\) and \\(512 \\times 512\\), we consistently achieve SOTA FIDs of 1.43 and 2.18 for class-conditional generation as illustrated in Tab. 1. Notably, We significantly improve the generation performance of DiT and outperform the previous best FID of MDT [14] solely through improved training algorithm without increasing the model complexity and inference time. From Tab. 2, we find that our SADM works well for both image diffusion (based on EDM) and latent diffusion (based on LSGM). In experiments, for fair comparisons, we use the same hyperpa" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.514, + 0.957 + ], + "angle": 0, + "content": "7261" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.141, + 0.089, + 0.36, + 0.203 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.089, + 0.596, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.089, + 0.832, + 0.202 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.141, + 0.212, + 0.359, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.227, + 0.327, + 0.271, + 0.337 + ], + "angle": 0, + "content": "ADM-G" + }, + { + "type": "image", + "bbox": [ + 0.377, + 0.212, + 0.595, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.471, + 0.327, + 0.5, + 0.337 + ], + "angle": 0, + "content": "MDT" + }, + { + "type": "image", + "bbox": [ + 0.614, + 0.212, + 0.831, + 0.325 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.686, + 0.326, + 0.764, + 0.338 + ], + "angle": 0, + "content": "SADM (Ours)" + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.341, + 0.895, + 0.371 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison with ADM-G [12] and previous SOTA method MDT [14]. Our SADM can synthesize more realistic and high-quality samples while maintaining satisfying diversity." + }, + { + "type": "table_caption", + "bbox": [ + 0.112, + 0.389, + 0.434, + 0.404 + ], + "angle": 0, + "content": "Table 3. FID performance on CelebA/FFHQ \\( {64} \\times {64} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.079, + 0.411, + 0.481, + 0.572 + ], + "angle": 0, + "content": "
ModelDiffusion SpaceNFE↓CelebAFFHQ
DDPM++ [59]Data1312.32-
Soft Truncation [30]Data1311.90-
Soft Diffusion [9]Data3001.85-
INDM [29]Latent1321.75-
EDM [27]Data79-2.39
Soft Truncation-G++ [28]Data1311.34-
EDM-G++ [28]Data71-1.98
SADMLatent1311.281.85
SADMData711.161.71
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.471, + 0.727 + ], + "angle": 0, + "content": "rameters as EDM and LSGM to evaluate the effectiveness of our proposed training algorithm. And we also achieve significant performance improvement on facial datasets as demonstrated in Tab. 3. For qualitative results, we compare our SADM with ADM-G [12] and previous SOTA method MDT [14] in Fig. 4. These remarkable results demonstrate our SADM has the potential for generalizing to arbitrary diffusion architectures and can better learn the whole data distribution." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.741, + 0.325, + 0.758 + ], + "angle": 0, + "content": "5.2. Cross-Domain Fine-Tuning" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.765, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Experiment Setup We conduct cross-domain fine-tuning tasks on diffusion image generation for evaluating the transferability of proposed model, where we pre-train a diffusion model in source domain and adapt it to a target domain by fine-tuning. Following Xie et al. [70], we use ImageNet as source dataset, and choose eight commonly-used fine-grained datasets as target datasets: Food101 [1], SUN397 [68], DF-20M mini [48], Caltech101 [16], CUB-200-2011 [65], ArtBench-10 [40], Oxford Flowers [45] and Stanford" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.391, + 0.882, + 0.407 + ], + "angle": 0, + "content": "Cars [34]. More details about datasets are in Appendix A." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.431, + 0.896, + 0.627 + ], + "angle": 0, + "content": "Implementation Details For fair comparison, we follow Xie et al. [70] to set all the hyper-parameters in both pretraining and fine-tuning stages, and use Diffusion Transformer (DiT) [47] as the diffusion backbone. We pretrain DiT on ImageNet \\(256 \\times 256\\) with a learning rate of 0.0001 using DDPM objective. For target datasets, we fine-tune the pre-trained DiT with 24k structure-guide training steps and 4k adversarial training steps. We experiment with two fine-tuning settings, full and parameter-efficient, for comprehensive evaluations. In parameter-efficient setting, following Xie et al. [70], we freeze most of parameters in the pre-trained diffusion model and fine-tune the bias term, normalization, and class condition module." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.652, + 0.896, + 0.82 + ], + "angle": 0, + "content": "Main Results We achieve SOTA performance on all datasets in fine-tuning tasks as illustrated in Tab. 4. Remarkably, we significantly surpass DDPM in full fine-tuning and outperform DiffFit in parameter-efficient fine-tuning. The results sufficiently demonstrate our superior capability of capturing the whole data distribution, which enables better adaptation to new domains. Among all datasets, we achieve the best improvement over other methods on ArtBench-10 which has distinct distribution from ImageNet, demonstrating the out-of-distribution generalization ability of our SADM. More qualitative results are in Appendix C." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.831, + 0.656, + 0.848 + ], + "angle": 0, + "content": "5.3. Model Analysis" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Heatmap Analysis To evaluate the ability to capture data distribution, we perform heatmap analysis in Fig. 5, where we provide DDPM and our SADM with 8 randomly-selected" + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7262" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.089, + 0.838, + 0.105 + ], + "angle": 0, + "content": "Table 4. FID performance comparisons on 8 downstream datasets, all the models are pretrained on ImageNet \\( {256} \\times {256} \\) ." + }, + { + "type": "table", + "bbox": [ + 0.105, + 0.115, + 0.86, + 0.276 + ], + "angle": 0, + "content": "
Dataset MethodFoodSUNDF-20MCaltechCUB-BirdArtBenchOxford FlowersStandard CarsAverage FID
AdaptFormer [5]13.6711.4722.3835.767.7338.4321.2410.7320.17
BitFit [77]9.179.1117.7834.218.8124.5320.3110.6416.82
VPT [25]18.4714.5432.8942.7817.2940.7425.5922.1226.80
LoRA [23]33.7532.53120.2586.0556.0380.99164.1376.2481.25
DiffFit [70]6.968.5517.3533.845.4820.8720.189.9015.39
Full Fine-tuning with DDPM10.467.9617.2635.255.6825.3121.059.7916.59
SADM (parameter-efficient)5.747.9216.5832.035.0418.2319.379.2614.27
SADM (full)6.207.3515.1232.864.6919.8418.188.9314.15
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.293, + 0.475, + 0.384 + ], + "angle": 0, + "content": "noisy images in test batch and visualize the correlations between their denoised outputs. We observe that compared to DDPM, the overall heatmap pattern of our SADM is more closer to that of label affinity. The phenomenon demonstrates our SADM can precisely learn the manifold structures within real data samples." + }, + { + "type": "image", + "bbox": [ + 0.083, + 0.386, + 0.465, + 0.64 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.1, + 0.649, + 0.446, + 0.665 + ], + "angle": 0, + "content": "Figure 5. Heatmap visualization with 8 denoised samples." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.669, + 0.473, + 0.82 + ], + "angle": 0, + "content": "Ablation Study We conduct ablation study to validate the effectiveness of our algorithm in Tab. 5. Here, we base on DDPM [20] architecture, and progressively add our model components (structural guidance and structure discriminator) into it for evaluating FID score on three datasets. We observe that each component can consistently improve the DDPM on all datasets, and the performance improvement of our structural guidance is more significant. The results fully demonstrate the effectiveness of our algorithm. More ablation studies about our model are in Appendix B." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.473, + 0.903 + ], + "angle": 0, + "content": "Contributing to Better Convergence To investigate the contribution of our structure-guided training to model convergence, we plot the training curve in Fig. 6. We conclude that compared to previous SOTA methods DiT [47] and MDT" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.291, + 0.895, + 0.32 + ], + "angle": 0, + "content": "Table 5. Ablation study with FID performance. SG denotes structural guidance, SAT denotes SG+Structure Discriminator." + }, + { + "type": "table", + "bbox": [ + 0.515, + 0.324, + 0.872, + 0.409 + ], + "angle": 0, + "content": "
Model \nDatasetDDPM+ Our SG+ Our SAT
ImageNet4.593.573.14
CIFAR-103.172.642.33
CelebA2.321.821.64
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.413, + 0.895, + 0.474 + ], + "angle": 0, + "content": "[14], the proposed structure-guided training enables faster and better model convergence because we optimize the diffusion models from a structural perspective, which essentially contributes to capturing the whole data distribution." + }, + { + "type": "image", + "bbox": [ + 0.561, + 0.487, + 0.811, + 0.632 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.499, + 0.641, + 0.892, + 0.656 + ], + "angle": 0, + "content": "Figure 6. Comparison with SOTA methods on model convergence." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.659, + 0.62, + 0.674 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.684, + 0.895, + 0.836 + ], + "angle": 0, + "content": "We propose structure-guided adversarial training for optimizing diffusion models from a structural perspective. The proposed training algorithm can easily generalize to both image and latent diffusion models, and consistently improve existing diffusion models with theoretical derivations and empirical results. We achieve new SOTA performance on image generation and cross-domain fine-tuning tasks across 12 image datasets. For future work, we will extend our method to more challenging diffusion-based applications (e.g., text-to-image/video generation)." + }, + { + "type": "title", + "bbox": [ + 0.501, + 0.848, + 0.661, + 0.866 + ], + "angle": 0, + "content": "Acknowledgement" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.872, + 0.895, + 0.901 + ], + "angle": 0, + "content": "This work was supported by the National Natural Science Foundation of China (No.U23B2048 and U22B2037)." + }, + { + "type": "page_number", + "bbox": [ + 0.483, + 0.945, + 0.516, + 0.957 + ], + "angle": 0, + "content": "7263" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.119, + 0.173, + 0.133 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.144, + 0.47, + 0.185 + ], + "angle": 0, + "content": "[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. 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While existing models focus on minimizing a weighted sum of denoising score matching losses for data distribution modeling, their training primarily emphasizes instance-level optimization, overlooking valuable structural information within each minibatch, indicative of pair-wise relationships among samples. To address this limitation, we introduce Structure-guided Adversarial training of Diffusion Models (SADM). In this pioneering approach, we compel the model to learn manifold structures between samples in each training batch. To ensure the model captures authentic manifold structures in the data distribution, we advocate adversarial training of the diffusion generator against a novel structure discriminator in a minimax game, distinguishing real manifold structures from the generated ones. SADM substantially outperforms existing methods in image generation and cross-domain fine-tuning tasks across 12 datasets, establishing a new state-of-the-art FID of 1.58 and 2.11 on ImageNet for class-conditional image generation at resolutions of $256 \times 256$ and $512 \times 512$ , respectively. + +# 1. Introduction + +Diffusion models [20, 56-59, 73] have achieved remarkable generation quality in various tasks, including image generation [12, 50-52, 67, 74, 75, 79], audio synthesis [4, 33, 49], and interdisciplinary applications [21, 24, 71]. Starting from tractable noise distribution, diffusion models generate data by progressively removing noise. This involves the model learning to reverse a pre-defined diffusion process that sequentially introduces varying levels of noise to the data. The model is parameterized and undergoes training by optimizing the weighted sum of denoising score matching losses [20] for various noise levels [57], aiming to learn the recovery of clean images from corrupted images. + +![](images/43b4ceb76b4fd49eef9bc4ec1fd6858e690585ed89054d30f90d4b8a07fbbc92.jpg) +Figure 1. Comparison between previous instance-level training and our structure-guided training for diffusion models. + +Aiming to maximally model the data distribution, recent works [28, 42, 60, 63, 72, 76] attempt to improve the precision of training diffusion models. For instance, many approaches design effective weighting schemes [8, 17, 30, 42, 60, 76] for maximum likelihood training or add an extra regularization term [10, 37, 46] to the denoising score loss. There are also some works to enhance the model expressiveness by incorporating other generative models, such as VAE [31, 51, 63], GAN [69], and Normalizing Flows [29, 43, 78]. However, their improved training of diffusion models primarily concentrates on instance-level optimization, overlooking the valuable structural information among batch samples. This oversight is significant, as the incorporation of structural details is crucial for aligning the learned distribution with the underlying data distribution. + +To mitigate the challenges posed by existing instance-level training methods, we propose Structure-guided Adversarial training of Diffusion Models (SADM). In contrast to conventional instance-level training illustrated in Fig. 1, our approach guides diffusion training at a structural level. During batch training, the model is facilitated to learn manifold structures within batch samples, represented by pair-wise relationships in a low-dimensional feature space. To accurately learn real manifold structures in the data distribution, we introduce a novel structure discriminator that distinguishes genuine manifold structures from generated + +![](images/c3da61ceb96c9c48998e873fce396c9e2d03035d70e207073349b0a35a8af68c.jpg) +FID: 4.59, Recall: 0.52 + +![](images/1af0dfa1ed8cd7a702fbab03141c03e4f6d6223a7e4e6991a80689a376f58bfc.jpg) +FID: 3.14, Recall: 0.61 + +![](images/9894ee3ed38a8a57851f764bfd53b19d035a91847226a7f973449cd16e15eff7.jpg) +Figure 2. Generated samples on ImageNet $256 \times 256$ with (i) ADM with Classifier Guidance (ADM-G) [12], (ii) ADM optimized by our Structure-guided Adversarial Training, and (iii) real samples in ground truth classes. We can significantly improve diffusion models qualitatively and quantitatively, and our generated sample distribution is overall more similar to real sample distribution. See Appendix C for more synthesis samples of our SOTA model. + +ones. For clarity, we alternatively refer to the diffusion models optimized through our structure-guided training as joint sample diffusion, a concept theoretically proven to enhance diffusion model optimization. + +We assess the performance of our model across two pivotal tasks: image generation and cross-domain fine-tuning. The former involves training the diffusion model from scratch to evaluate its capability in capturing the entire data distribution. The latter leverages a pre-trained diffusion model, constructed on a large-scale source dataset, and fine-tunes it on a target dataset to assess transferability. Our extensive experiments consistently demonstrate that our approach significantly improves the model's ability to effectively capture the underlying data distribution (Fig. 2). SADM achieves state-of-the-art results across 12 image datasets, including ImageNet [11]. Furthermore, we observe its potential for facilitating rapid adaptation to new domains in cross-domain fine-tuning tasks. We summarize our contributions as follows: + +- To the best of our knowledge, we are the first to propose Structure-guided Adversarial Training to optimize diffusion models from a structural perspective. +- We theoretically show that SADM is superior in capturing real data distribution, and can generalize to various image + +and latent-based diffusion architectures (e.g., DiT [47]). +- We substantially outperform existing methods on image generation and cross-domain fine-tuning tasks, achieving a new state-of-the-art FID of 1.58 and 2.11 on ImageNet at resolutions of $256 \times 256$ and $512 \times 512$ , respectively. + +# 2. Related Work + +In this work, we focus on improving the training of diffusion models. Here, we review previous related works and compare our SADM with them. + +Modifying Training Objectives of Diffusion Models A line of research modifies training objectives to achieve state-of-the-art likelihood [8, 42, 60, 74]. Song et al. [60] propose likelihood weighting to enable approximate maximum likelihood training of score-based diffusion models [57-59] while ContextDiff [76] introduces an effective shifting scheme for facilitating the diffusion and training processes of diffusion probabilistic models [20, 56] to achieve improved sample quality with stable training. Lai et al. [37] and [10] introduce an extra regularization term to the denoising score loss to satisfy some properties of the diffusion process. However, these improvements mainly focus on sample-level optimization, neglecting the rich structural information within batch + +samples, which is critical for aligning the learned distribution and data distribution. Hence, we enforce the model to maximally learn the manifold structures of samples. + +Combining Additional Models for Diffusion Training Another line of research incorporates other models to improve the stability and precision of diffusion training. For example, INDM [29] expands the linear diffusion to trainable nonlinear diffusion through a normalizing flow to improve the training curve of diffusion models. Jolicoeur-Martineau et al. [26], Kim et al. [28] improve diffusion models with adversarial learning while Xiao et al. [69] model each denoising step using a multimodal conditional GAN. LSGM [63] and LDM [51] conduct diffusion process in the semantic latent space obtained with a pre-trained VAE. Although these combinations strengthen the model expressiveness for capturing data distribution, they are still limited in modeling the underlying manifold structures within training samples. We propose a novel structure discriminator for adversarially learn the diffusion model from a structural perspective. + +# 3. Preliminary + +Diffusion Models We consider diffusion models [20, 56, 57] specified in continuous time [4, 31, 59, 62]. Given samples $\mathbf{x}_0$ from a data distribution $q_0(\mathbf{x}_0)$ , noise scheduling functions $\alpha_{t},\sigma_{t}$ , a diffusion model has latent variables $\mathbf{x} = \{\mathbf{x}_t\mid t\in [0,1]\}$ , and the forward process is defined with $q(\mathbf{x}_t|\mathbf{x}_0)$ , a Gaussian process satisfying the following Markovian structure: + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {0}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \alpha_ {t} \mathbf {x} _ {0}, \sigma_ {t} ^ {2} \mathbf {I}\right), \tag {1} +$$ + +$$ +q \left(\mathbf {x} _ {t} \mid \mathbf {x} _ {s}\right) = \mathcal {N} \left(\mathbf {x} _ {t}; \left(\alpha_ {t} / \alpha_ {s}\right) \mathbf {x} _ {s}, \sigma_ {t \mid s} ^ {2} \mathbf {I}\right) \tag {2} +$$ + +where $0 \leq s < t \leq 1$ and $\sigma_{t|s}^2 = (1 - e^{\lambda_t - \lambda_s})\sigma_t^2$ , and $\lambda_t = \log [\alpha_t^2 /\sigma_t^2 ]$ denotes the log signal-to-noise-ratio [31]. The goal of the diffusion model is to denoise $\mathbf{x}_t \sim q(\mathbf{x}_t|\mathbf{x}_0)$ by estimating $\hat{\mathbf{x}}_{\theta}(\mathbf{x}_t) \approx \mathbf{x}_0$ . We train this denoising model $\hat{\mathbf{x}}_{\theta}$ using a weighted mean squared error loss + +$$ +\mathbb {E} _ {\mathbf {x} _ {0}, \boldsymbol {\epsilon}, t} \left[ w \left(\lambda_ {t}\right) \| \hat {\mathbf {x}} _ {\theta} (\mathbf {x} _ {t}) - \mathbf {x} _ {0} \| _ {2} ^ {2} \right] \tag {3} +$$ + +over uniformly sampled times $t \in [0,1]$ . This loss can be justified as a weighted variational lower bound on the data log likelihood under the diffusion model [31] or as a form of denoising score matching [57, 64]. $w(\lambda_t)$ is a pre-specified weighting function [31]. + +# 4. Proposed Method + +We introduce the proposed SADM in detail (Fig. 3). In order to maximally learn the structural information between real samples, we propose structure-guided training of diffusion models in Sec. 4.1. Then we design a novel structure + +discriminator for adversarially optimizing the training procedure from a structural perspective in Sec. 4.2. Finally, we alternatively interpret our structure-guided training of diffusion models as joint sample diffusion with theoretical analysis for betwen understanding in Sec. 4.3. + +# 4.1. Beyond Instance-Level Training + +We first review the previous instance-level training methods for diffusion models. Generally, they train the diffusion model with a finite sample version of Eq. (3): + +$$ +\mathcal {L} _ {t} = w \left(\lambda_ {t}\right) \frac {\sum_ {i \in B} \left| \left| \mathbf {x} _ {0} ^ {i} - \hat {\mathbf {x}} _ {\theta} \left(\mathbf {x} _ {t} ^ {i}\right) \right| \right| ^ {2}}{| B |}, \tag {4} +$$ + +where $\mathbf{x}_0^i, \mathbf{x}_t^i$ denote the $i^{th}$ ground truth samples and generated samples in the mini-batch $B$ at time step $t$ . However, this objective function encourages the diffusion model to denoise by considering only the instance-level information, neglecting the group-level (structural) information in the mini-batch. Therefore, we enforce the sample predictions of the denoising network to maximally preserve the manifold structures between batch samples. + +Structural Constraint in Manifold More concretely, ground truth samples $\{\mathbf{x}_0^i\}_{i = 1}^{|B|}$ are first projected from pixel space into embedding space using off-the-shelf pre-trained networks $\Psi (\cdot):\mathbb{R}^{m\times n}\to \mathbb{R}^d$ e.g., an Inception-V3 feature extractor pre-trained on ImageNet [61] (we conduct ablation study in Appendix B). Then, the pair-wise relationships $\mathcal{R}(\Psi (\mathbf{x}_0^i),\Psi (\mathbf{x}_0^j))$ are calculated within batch samples $\{\mathbf{x}_0^i\}_{i = 1}^{|B|}$ , which contain rich structural information in a low-dimensional manifold. This structural information can be expressed with an affinity matrix $\mathcal{M}(\{\mathbf{x}_0^i\}_{i = 1}^{|B|})$ defined as: + +$$ +\left[ \begin{array}{c c c c} \mathcal {R} (\Psi_ {1}, \Psi_ {1}) & \mathcal {R} (\Psi_ {1}, \Psi_ {2}) & \dots & \mathcal {R} (\Psi_ {1}, \Psi_ {| B |}) \\ \mathcal {R} (\Psi_ {2}, \Psi_ {1}) & \mathcal {R} (\Psi_ {2}, \Psi_ {2}) & \dots & \mathcal {R} (\Psi_ {2}, \Psi_ {| B |}) \\ \vdots & \vdots & \ddots & \vdots \\ \mathcal {R} (\Psi_ {| B |}, \Psi_ {1}) & \mathcal {R} (\Psi_ {| B |}, \Psi_ {2}) & \dots & \mathcal {R} (\Psi_ {| B |}, \Psi_ {| B |}) \end{array} \right] \tag {5} +$$ + +where $\Psi_{i}$ is a short-hand for $\Psi (\mathbf{x}_0^i)$ , and $\mathcal{R}(\cdot ,\cdot)$ denotes the relational function, such as Euclidean distance. Kindly note that many off-the-shelf pre-trained networks are open-source and only work well on clean images, and thus fail to provide meaningful embeddings when the input is noisy. Therefore, we use the predicted clean samples $\hat{\mathbf{x}}_0^i$ for computing affinity matrix, and regularize the denoising network to minimize the structural distance between $\mathcal{M}(\{\mathbf{x}_0^i\}_{i = 1}^{|B|})$ and $\mathcal{M}(\{\hat{\mathbf{x}}_0^i\}_{i = 1}^{|B|})$ . Adding this structural constraint into Eq. (4), the training objective for denoising network is: + +$$ +\begin{array}{l} \mathcal {L} _ {t} = \frac {\sum_ {i \in B} \left| \left| \mathbf {x} _ {0} ^ {i} - \hat {\mathbf {x}} _ {\theta} \left(\mathbf {x} _ {t} ^ {i}\right) \right| \right| ^ {2}}{| B |} \tag {6} \\ + \mathcal {D} (\mathcal {M} (\{\mathbf {x} _ {0} ^ {i} \} _ {i = 1} ^ {| B |}), \mathcal {M} (\{\hat {\mathbf {x}} _ {0} ^ {i} \} _ {i = 1} ^ {| B |})) \\ \end{array} +$$ + +![](images/f7c7ccaeacfa297fc582e8005d7845092fb876aa9c76e0ac7a3d3ab000d6a6be.jpg) +Figure 3. Overview of SADM. We minimize the structural distance between the generated samples (fake) and ground truth samples (real) in the manifold space for optimizing the denoiser, and maximize their structural distance for optimizing the encoder in structure discriminator. The denoiser and the structure discriminator are adversarially trained. + +where $\mathcal{D}(\cdot, \cdot)$ denotes the distance metric between ground truth and predicted affinity matrices. In this way, the diffusion generator (denoiser) is optimized not only to make correct prediction for each instance, but also to preserve the manifold structures of batch samples. + +# 4.2. Structure-Guided Adversarial Training + +As demonstrated above, we aim to maximally learn data distribution by aligning the manifold structures of denoiser's predicted samples to those of ground truth samples in each training batch. At every training iteration, the manifold structures can be diverse and the denoiser tend to merely focus on some easy-to-learn structures, ultimately leading to trivial solutions that fail to capture the whole data distribution. In order to mitigate this problem and improve the expressiveness of denoiser, we adversarially learn the denoising network against a structure discriminator in a minimax game (Fig. 3), which is trained to distinguish the manifold structures between the real and generated batch samples. + +Structure Discriminator Normally, the discriminator in adversarial learning [15] would output the discrete value (0 or 1) to determine whether the input is real or fake. However, such discrete discriminator can not be applied in distinguishing manifold structures, because the generated and real sample sets would share similar pair-wise sample relations despite their different feature spaces. Thus, instead of learning a classification-based discriminator, we design a + +novel comparison-based structure discriminator to address this issue. + +Specifically, as illustrated in Fig. 3, the structure discriminator consists of the aforementioned neural network $\Psi_{\phi}$ with trainable parameters $\phi$ and the distance measure function $\mathcal{D}(\cdot ,\cdot)$ that outputs continuous value. It projects both real and generated samples into the embedding space, then the structure discriminator is trained against the denoiser for finding a better manifold (or embedding space) to distinguish real sample set from generated set by maximizing their structural distance: + +$$ +\max _ {\phi} \frac {\eta_ {t} \sum_ {i , j \in B} \mathcal {D} \left(\mathcal {R} \left(\Psi_ {\phi} \left(\mathbf {x} _ {0} ^ {i}\right) , \Psi_ {\phi} \left(\mathbf {x} _ {0} ^ {j}\right)\right) , \mathcal {R} \left(\Psi_ {\phi} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {i}\right) , \Psi_ {\phi} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {j}\right)\right)\right)}{| B | ^ {2}}. \tag {7} +$$ + +where we choose $\eta_t = \frac{1}{t}$ as a time-dependent weighting factor. We can use simple measurements for $\mathcal{D}(\cdot, \cdot)$ ( $L_2$ distance) and $\mathcal{R}(\cdot, \cdot)$ (cosine similarity), as the critical semantic information has been already encoded by $\Psi_\phi$ . Conversely, the denoiser is adversarially optimized for generating more realistic sample set to fool the structure discriminator by minimizing the structural distance. + +Final Optimization Objective The final training objective of our SADM consists of normal denoising score matching loss (Eq. (3)) and adversarial structural distance loss (Eq. (7)) + +at timestep $t$ , which can be written as: + +$$ +\begin{array}{l} \mathcal {L} _ {t} (\theta) = \frac {w (\lambda_ {t}) \sum_ {i \in B} \| \hat {\mathbf {x}} _ {\theta} (\mathbf {x} _ {t} ^ {i}) - \mathbf {x} _ {0} ^ {i} \| _ {2} ^ {2}}{| B |} \\ + \max _ {\phi} \frac {\sum_ {i , j \in B} \eta_ {t} \| \Psi_ {\phi} \left(\mathbf {x} _ {0} ^ {i}\right) ^ {T} \Psi_ {\phi} \left(\mathbf {x} _ {0} ^ {j}\right) - \Psi_ {\phi} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {i}\right) ^ {T} \Psi_ {\phi} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {j}\right) \| _ {2} ^ {2}}{| B | ^ {2}}. \tag {8} \\ \end{array} +$$ + +In training, we iteratively optimize the feature extractor and the denoising network in Eq. (8). In an iteration, we first freeze $\theta$ and update $\phi$ by ascending along its gradient + +$$ +\nabla_ {\phi} \frac {\sum_ {i , j \in B} \eta_ {t} \| \Psi_ {\phi} \left(\mathbf {x} _ {0} ^ {i}\right) ^ {T} \Psi_ {\phi} \left(\mathbf {x} _ {0} ^ {j}\right) - \Psi_ {\phi} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {i}\right) ^ {T} \Psi_ {\phi} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {j}\right) \| _ {2} ^ {2}}{| B | ^ {2}}, \tag {9} +$$ + +then we freeze $\phi$ and update $\theta$ by descending along its gradient + +$$ +\begin{array}{l} \nabla_ {\theta} \frac {\sum_ {i , j \in B} \eta_ {t} \| \Psi_ {\phi} (\mathbf {x} _ {0} ^ {i}) ^ {T} \Psi_ {\phi} (\mathbf {x} _ {0} ^ {j}) - \Psi_ {\phi} (\hat {\mathbf {x}} _ {\theta , t} ^ {i}) ^ {T} \Psi_ {\phi} (\hat {\mathbf {x}} _ {\theta , t} ^ {j}) \| _ {2} ^ {2}}{| B | ^ {2}} \\ + \nabla_ {\theta} \frac {w \left(\lambda_ {t}\right) \sum_ {i \in B} \left\| \hat {\mathbf {x}} _ {\theta} \left(\mathbf {x} _ {t} ^ {i}\right) - \mathbf {x} _ {0} ^ {i} \right\| _ {2} ^ {2}}{| B |}. \tag {10} \\ \end{array} +$$ + +The proposed training algorithm is presented in Algorithm 1. + +Generalizing to Latent Diffusion Our proposed training algorithm applies not only to image diffusion but also to latent diffusion, such as LDM [51] and LSGM [63]. In this case, the intermediate results $\mathbf{x}_t$ are latent codes rather than images. We can use the latent decoder (e.g., VAE decoder [32]) to project the generated latent codes to images and then use the same algorithm in the image domain. + +# 4.3. Interpreting as Joint Sample Diffusion + +Relation-Conditioned Diffusion Process For better understanding of our proposed structure-guided training, we interpret it as a joint sample diffusion model that simultaneously perturbs and denoises a set of samples conditioned on the relation variable. Formally, let $\mathbf{y}_0 = (\mathbf{x}_0^i,\mathbf{x}_0^j)$ , where $\mathbf{x}_0^i,\mathbf{x}_0^j$ are independent random variables sampled from ground truth distribution $q_{0}$ . And the relation variable that encodes the structure information is defined as $\mathcal{R} = \mathcal{R}(\mathbf{x}_0^i,\mathbf{x}_0^j) + \gamma \epsilon$ , where $\gamma \epsilon$ denote a small gaussian noise added to the relation to avoid degenerated distribution. Then the forward diffusion jointly perturbs $\mathbf{y}_0$ , conditioned on $\mathcal{R}$ : + +$$ +q (\mathbf {y} _ {t} | \mathbf {y} _ {0}, \mathcal {R}) = \mathcal {N} (\mathbf {y} _ {t}; \alpha_ {t} \mathbf {y} _ {0}, \sigma_ {t} ^ {2} \mathbf {I}). \tag {11} +$$ + +To reverse the diffusion process, we need to predict $\mathbf{y}_0$ , or equivalently, learn the conditional score function $\nabla_y\log q_t(y_t|\mathcal{R})$ [12, 19]. This formulation allows us to utilize the auxiliary structural information $\mathcal{R}$ in the sampling process, which usually leads to better performance [13, 55]. + +Algorithm 1: SADM, our proposed algorithm. + +input : $\{\alpha_{t}\}_{t\in [0,1]}$ $\{\sigma_t\}_{t\in [0,1]}$ the noise schedule, $|B|$ the batch size, $w(\lambda_t)$ $\eta_t$ the scaling factors for denoising score matching loss and adversarial loss, pre-trained encoder $\Psi_{\phi}$ for structure discriminator. + +Initialize denoising network parameters $\theta$ + +while $\theta$ has not converged do + +Sample a minibatch $\{\mathbf{x}_0^i\}_{i = 1}^{|B|}\sim q_0$ and + +$$ +\{\boldsymbol {\epsilon} ^ {j} \} _ {j = 1} ^ {| B |} \sim \mathcal {N} (\mathbf {0}, \boldsymbol {I}) +$$ + +Sample $t\sim U[0,1]$ + +Sample $\{\mathbf{x}_t^i = \alpha_t\mathbf{x}_0^i +\sigma_t\pmb {\epsilon}^i\}_{i = 1}^{|B|}$ + +Freeze $\phi$ and update $\theta$ with its gradient + +$$ +\begin{array}{l} \nabla_ {\theta} \frac {\sum_ {i , j \in B} \eta_ {t} \| \Psi_ {\phi} (\mathbf {\hat {x}} _ {0} ^ {i}) ^ {T} \Psi_ {\phi} (\mathbf {\hat {x}} _ {0} ^ {j}) - \Psi_ {\phi} (\hat {\mathbf {x}} _ {\theta , t} ^ {i}) ^ {T} \Psi_ {\phi} (\hat {\mathbf {x}} _ {\theta , t} ^ {j}) \| _ {2} ^ {2}}{| B | ^ {2}} \\ + \nabla_ {\theta} \frac {w (\lambda_ {t}) \sum_ {i \in B} \| \hat {\mathbf {x}} _ {\theta} (\mathbf {x} _ {t} ^ {i}) - \mathbf {x} _ {0} ^ {i} \| _ {2} ^ {2}}{| B |} \\ \end{array} +$$ + +Adversarily train denoising network and structure discriminator by iteratively updating their parameters $\theta, \phi$ according to Eqs. (9) and (10). + +output: Denoising network $\theta$ . + +Learning Conditional Score To approximate the conditional score function, first we decompose it with Bayes' rule, + +$$ +\begin{array}{l} \nabla_ {y} \log q _ {t} \left(y _ {t} | \mathcal {R}\right) = \nabla_ {y} \log q _ {t} \left(y _ {t}\right) + \nabla_ {y} \log q _ {t} \left(\mathcal {R} \mid y _ {t}\right) \\ = \Sigma_ {s = i, j} \nabla_ {x} \log q _ {t} \left(x _ {t} ^ {s}\right) + \nabla_ {y} \log q _ {t} (\mathcal {R} | y _ {t}). \tag {12} \\ \end{array} +$$ + +To approximate the first term on the right side of Eq. (12), we only need to learn $\hat{\mathbf{x}}_{\theta ,t}^{i},\hat{\mathbf{x}}_{\theta ,t}^{j}$ , as in standard diffusion models [59]. However, the second term is intractable since $q_{t}(\mathcal{R}|y_{t})$ involves the intractable posterior $q(\mathbf{y}_0|\mathbf{y}_t)$ . Note that + +$$ +\begin{array}{l} q _ {t} (\mathcal {R} | y _ {t}) = \int g (\mathcal {R} | \mathbf {y} _ {0}) q \left(\mathbf {y} _ {0} \mid \mathbf {y} _ {t}\right) d \mathbf {y} _ {0} \tag {13} \\ = \mathbb {E} _ {\mathbf {y} _ {0}} \left[ g (\mathcal {R} | \mathbf {y} _ {0}) | \mathbf {y} _ {t} \right], \\ \end{array} +$$ + +where $g(\mathcal{R}|\mathbf{y}_0)$ is the density function of Gaussian distribution with mean $\mathcal{R}(\mathbf{x}_0^i,\mathbf{x}_0^j)$ and variance $\gamma^2$ , by the definition of $\mathcal{R}$ . As a result, we can use $g(\mathcal{R}|\hat{\mathbf{y}}_{0,t}) = g(\mathcal{R} | (\hat{\mathbf{x}}_{\theta ,t}^i,\hat{\mathbf{x}}_{\theta ,t}^j))$ to approximate $q_{t}(\mathcal{R}|y_{t})$ , and train it with $L_{2}$ loss: + +$$ +\begin{array}{l} \mathbb {E} _ {\mathbf {y} _ {t}} \| \mathbb {E} _ {\mathbf {y} _ {0}} [ g (\mathcal {R} | \mathbf {y} _ {0}) | \mathbf {y} _ {t} ] - g (\mathcal {R} | \hat {\mathbf {y}} _ {0} (\mathbf {y} _ {t})) \| _ {2} ^ {2} \\ = \mathbb {E} _ {\mathbf {y} _ {t}} \| \mathbb {E} _ {\mathbf {y} _ {0}} [ g (\mathcal {R} | \mathbf {y} _ {0}) - g (\mathcal {R} | \hat {\mathbf {y}} _ {0} (\mathbf {y} _ {t})) | \mathbf {y} _ {t} ] \| _ {2} ^ {2} \\ \leq \mathbb {E} _ {\mathbf {y} _ {0}, \mathbf {y} _ {t}} \| g (\mathcal {R} | \mathbf {y} _ {0}) - g (\mathcal {R} | \hat {\mathbf {y}} _ {0} (\mathbf {y} _ {t})) \| _ {2} ^ {2} \quad (J e s s e n I n e q u a l i t y) \\ \leq w (\gamma) \mathbb {E} _ {\mathbf {y} _ {0}, \mathbf {y} _ {t}} \| \mathcal {R} \left(\mathbf {x} _ {0} ^ {i}, \mathbf {x} _ {0} ^ {j}\right) - \mathcal {R} \left(\hat {\mathbf {x}} _ {\theta , t} ^ {i}, \hat {\mathbf {x}} _ {\theta , t} ^ {j}\right) \| _ {2} ^ {2} = \mathcal {L} _ {t} ^ {\text {s t r u c t u r e}}, \tag {14} \\ \end{array} +$$ + +where $w(\gamma)$ is a weighting scalar that depends only on $\gamma$ . The objective function is the sum of the denoising score + +Table 1. Quantitative results for class-conditional generation on ImageNet ${256} \times {256}$ and ${512} \times {512}$ . + +
ModelImageNet 256×256ImageNet 512×512
FID ↓IS ↑Precision ↑Recall ↑FID ↓IS ↑Precision ↑Recall ↑
BigGAN-deep [2]6.95171.400.870.288.43177.900.880.29
StyleGAN-XL [54]2.30265.120.780.532.41267.750.770.52
ADM-G, ADM-U [12]3.94215.840.830.533.85221.720.840.53
LDM-4-G [51]3.60247.670.870.48----
RIN+NoiseSchedule [6]3.52186.20--3.95216.00--
SimpleDiffusion [22]2.44256.30--3.02248.70--
DiT-G++ [28]1.83281.530.780.64----
MDT-G [14]1.79283.010.810.61----
DiT-XL/2-G [47]2.27278.240.830.573.04240.820.840.54
DiT-SADM (Ours)1.58298.460.860.662.11251.820.870.63
+ +matching objective and $\mathcal{L}_t^{\mathrm{structure}}$ : + +$$ +\begin{array}{l} \mathbb {E} _ {\mathbf {x} _ {0} ^ {i}, \boldsymbol {\epsilon} ^ {i}, t} w (\lambda_ {t}) \| \hat {\mathbf {x}} _ {\theta} (\mathbf {x} _ {t} ^ {i}) - \mathbf {x} _ {0} ^ {i} \| _ {2} ^ {2} + \mathbb {E} _ {\mathbf {x} _ {0} ^ {j}, \boldsymbol {\epsilon} ^ {j}, t} w (\lambda_ {t}) \| \hat {\mathbf {x}} _ {\theta} (\mathbf {x} _ {t} ^ {j}) - \mathbf {x} _ {0} ^ {j} \| _ {2} ^ {2} \\ + \mathbb {E} _ {\mathbf {x} _ {0} ^ {i}, \epsilon^ {i}, \mathbf {x} _ {0} ^ {j}, \epsilon^ {j}, t} \left[ \mathcal {L} _ {t} ^ {\text {s t r u c t u r e}} \right], \tag {15} \\ \end{array} +$$ + +which is a variational upper bound of negative log likelihood of the joint sample. Our objective in Eq. (6) can be viewed as a finite-sample version of Eq. (15), which trains the conditional diffusion model to utilize the structural information. + +# 5. Experiments + +# 5.1. Image Generation + +Experiment Setup We experiment on CIFAR-10 [35], CelebA/FFHQ 64x64 [41], and ImageNet 256x256 [11]. We utilize our SADM to facilitate the training of the diffusion backbones from Karras et al. [27], Vahdat et al. [63] on CIFAR-10 and FFHQ, from Kim et al. [30] on CelebA, and from Peebles and Xie [47] (DiT, Diffusion Transformer) on ImageNet. + +Evaluation Metrics We use Frechet Inception Distance (FID) [18] as the primary metric for capturing both quality and diversity due to its alignment with human judgement. We follow the evaluation procedure of ADM [12] for fair comparisons. For completeness, we also use Inception Score (IS) [53], Precision and Recall [36] as the main metrics for measuring diversity and distribution coverage. + +Implementation Details We train the denoising network from scratch and use the feature extractor of Inception-V3 [61] pre-trained on ImageNet for initializing the encoder of our structure discriminator. At the beginning of training, we freeze the pre-trained discriminator encoder and train the denoiser with structure-guided training objective in Eq. (6) until convergence, then we adversarially tune the denoiser and + +Table 2. Performance on CIFAR-10. + +
ModelDiffusion SpaceNFE↓UnconditionalConditional
NLL↓FID↓FID↓
VDM [31]Data10002.497.41-
DDPM [20]Data10003.753.17-
iDDPM [44]Data10003.372.90-
Soft Truncation [30]Data20002.912.47-
INDM [29]Latent20003.092.28-
CLD-SGM [13]Data3123.312.25-
NCSN++ [59]Data20003.452.20-
LSGM [63]Latent1383.432.10-
NCSN++-G [3]Data2000--2.25
EDM [27]Data352.601.971.79
LSGM-G++ [28]Latent1383.421.94-
EDM-G++ [28]Data352.551.771.64
SADMLatent1382.511.781.73
SADMData352.281.541.47
+ +encoder with the objective in Eq. (8) for 3 or 4 rounds (500k steps) until they achieve a balance. This training paradigm keeps the same for unconditional and class-conditional generation tasks, and can be easily generalized to score-based diffusion models [59, 63] by adding our structural constraint into the final objective functions. + +Main Results Our SADM achieves new state-of-the-art FIDs on all datasets including CIFAR-10, CelebA, FFHQ, and ImageNet. On ImageNet $256 \times 256$ and $512 \times 512$ , we consistently achieve SOTA FIDs of 1.43 and 2.18 for class-conditional generation as illustrated in Tab. 1. Notably, We significantly improve the generation performance of DiT and outperform the previous best FID of MDT [14] solely through improved training algorithm without increasing the model complexity and inference time. From Tab. 2, we find that our SADM works well for both image diffusion (based on EDM) and latent diffusion (based on LSGM). In experiments, for fair comparisons, we use the same hyperpa + +![](images/fbb4982394ab41458bf3ea034e5b4ccf698b7a9b345d11fd583f45d35c0ea898.jpg) + +![](images/416ebc9789490f5432d059b6eb0b91168b7b4e7fadd00c6af9eec8fa6310ab88.jpg) + +![](images/eeca27ba0bbdcafc5cdb07682ce1d3c3e4705e32369e2edf7111c10cc2779f60.jpg) + +![](images/5f30182207199252dd477699781aefbdfd9dd204b8448aae506529b191a5b2a2.jpg) +ADM-G + +![](images/1fcd867034e108e61787fe6e43395c1d09c2d80efba015f61fce5a3aab48c058.jpg) +MDT +Figure 4. Qualitative comparison with ADM-G [12] and previous SOTA method MDT [14]. Our SADM can synthesize more realistic and high-quality samples while maintaining satisfying diversity. + +![](images/4a71bcc15a34f599226a49cc344f0b4c7990e3924fd3f3b0cadbedced3ee202d.jpg) +SADM (Ours) + +Table 3. FID performance on CelebA/FFHQ ${64} \times {64}$ . + +
ModelDiffusion SpaceNFE↓CelebAFFHQ
DDPM++ [59]Data1312.32-
Soft Truncation [30]Data1311.90-
Soft Diffusion [9]Data3001.85-
INDM [29]Latent1321.75-
EDM [27]Data79-2.39
Soft Truncation-G++ [28]Data1311.34-
EDM-G++ [28]Data71-1.98
SADMLatent1311.281.85
SADMData711.161.71
+ +rameters as EDM and LSGM to evaluate the effectiveness of our proposed training algorithm. And we also achieve significant performance improvement on facial datasets as demonstrated in Tab. 3. For qualitative results, we compare our SADM with ADM-G [12] and previous SOTA method MDT [14] in Fig. 4. These remarkable results demonstrate our SADM has the potential for generalizing to arbitrary diffusion architectures and can better learn the whole data distribution. + +# 5.2. Cross-Domain Fine-Tuning + +Experiment Setup We conduct cross-domain fine-tuning tasks on diffusion image generation for evaluating the transferability of proposed model, where we pre-train a diffusion model in source domain and adapt it to a target domain by fine-tuning. Following Xie et al. [70], we use ImageNet as source dataset, and choose eight commonly-used fine-grained datasets as target datasets: Food101 [1], SUN397 [68], DF-20M mini [48], Caltech101 [16], CUB-200-2011 [65], ArtBench-10 [40], Oxford Flowers [45] and Stanford + +Cars [34]. More details about datasets are in Appendix A. + +Implementation Details For fair comparison, we follow Xie et al. [70] to set all the hyper-parameters in both pretraining and fine-tuning stages, and use Diffusion Transformer (DiT) [47] as the diffusion backbone. We pretrain DiT on ImageNet $256 \times 256$ with a learning rate of 0.0001 using DDPM objective. For target datasets, we fine-tune the pre-trained DiT with 24k structure-guide training steps and 4k adversarial training steps. We experiment with two fine-tuning settings, full and parameter-efficient, for comprehensive evaluations. In parameter-efficient setting, following Xie et al. [70], we freeze most of parameters in the pre-trained diffusion model and fine-tune the bias term, normalization, and class condition module. + +Main Results We achieve SOTA performance on all datasets in fine-tuning tasks as illustrated in Tab. 4. Remarkably, we significantly surpass DDPM in full fine-tuning and outperform DiffFit in parameter-efficient fine-tuning. The results sufficiently demonstrate our superior capability of capturing the whole data distribution, which enables better adaptation to new domains. Among all datasets, we achieve the best improvement over other methods on ArtBench-10 which has distinct distribution from ImageNet, demonstrating the out-of-distribution generalization ability of our SADM. More qualitative results are in Appendix C. + +# 5.3. Model Analysis + +Heatmap Analysis To evaluate the ability to capture data distribution, we perform heatmap analysis in Fig. 5, where we provide DDPM and our SADM with 8 randomly-selected + +Table 4. FID performance comparisons on 8 downstream datasets, all the models are pretrained on ImageNet ${256} \times {256}$ . + +
Dataset MethodFoodSUNDF-20MCaltechCUB-BirdArtBenchOxford FlowersStandard CarsAverage FID
AdaptFormer [5]13.6711.4722.3835.767.7338.4321.2410.7320.17
BitFit [77]9.179.1117.7834.218.8124.5320.3110.6416.82
VPT [25]18.4714.5432.8942.7817.2940.7425.5922.1226.80
LoRA [23]33.7532.53120.2586.0556.0380.99164.1376.2481.25
DiffFit [70]6.968.5517.3533.845.4820.8720.189.9015.39
Full Fine-tuning with DDPM10.467.9617.2635.255.6825.3121.059.7916.59
SADM (parameter-efficient)5.747.9216.5832.035.0418.2319.379.2614.27
SADM (full)6.207.3515.1232.864.6919.8418.188.9314.15
+ +noisy images in test batch and visualize the correlations between their denoised outputs. We observe that compared to DDPM, the overall heatmap pattern of our SADM is more closer to that of label affinity. The phenomenon demonstrates our SADM can precisely learn the manifold structures within real data samples. + +![](images/75fe677ff2742e4bab0a292bcd160c917009458342bcf4aa5eca451e666ce36e.jpg) +Figure 5. Heatmap visualization with 8 denoised samples. + +Ablation Study We conduct ablation study to validate the effectiveness of our algorithm in Tab. 5. Here, we base on DDPM [20] architecture, and progressively add our model components (structural guidance and structure discriminator) into it for evaluating FID score on three datasets. We observe that each component can consistently improve the DDPM on all datasets, and the performance improvement of our structural guidance is more significant. The results fully demonstrate the effectiveness of our algorithm. More ablation studies about our model are in Appendix B. + +Contributing to Better Convergence To investigate the contribution of our structure-guided training to model convergence, we plot the training curve in Fig. 6. We conclude that compared to previous SOTA methods DiT [47] and MDT + +Table 5. Ablation study with FID performance. SG denotes structural guidance, SAT denotes SG+Structure Discriminator. + +
Model +DatasetDDPM+ Our SG+ Our SAT
ImageNet4.593.573.14
CIFAR-103.172.642.33
CelebA2.321.821.64
+ +[14], the proposed structure-guided training enables faster and better model convergence because we optimize the diffusion models from a structural perspective, which essentially contributes to capturing the whole data distribution. + +![](images/b9b8bba44d38199487c87681e9a0144b516318cd94b1fbf1423367b4017d1d4c.jpg) +Figure 6. Comparison with SOTA methods on model convergence. + +# 6. Conclusion + +We propose structure-guided adversarial training for optimizing diffusion models from a structural perspective. The proposed training algorithm can easily generalize to both image and latent diffusion models, and consistently improve existing diffusion models with theoretical derivations and empirical results. We achieve new SOTA performance on image generation and cross-domain fine-tuning tasks across 12 image datasets. For future work, we will extend our method to more challenging diffusion-based applications (e.g., text-to-image/video generation). + +# Acknowledgement + +This work was supported by the National Natural Science Foundation of China (No.U23B2048 and U22B2037). + +# References + +[1] Lukas Bossard, Matthieu Guillaumin, and Luc Van Gool. Food-101-mining discriminative components with random forests. In ECCV, 2014. 7, 12 +[2] Andrew Brock, Jeff Donahue, and Karen Simonyan. Large scale gan training for high fidelity natural image synthesis. In International Conference on Learning Representations, 2018. 6 +[3] Chen-Hao Chao, Wei-Fang Sun, Bo-Wun Cheng, Yi-Chen Lo, Chia-Che Chang, Yu-Lun Liu, Yu-Lin Chang, Chia-Ping Chen, and Chun-Yi Lee. Denoising likelihood score matching for conditional score-based data generation. In International Conference on Learning Representations, 2022. 6 +[4] Nanxin Chen, Yu Zhang, Heiga Zen, Ron J Weiss, Mohammad Norouzi, and William Chan. 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While existing models focus on minimizing a weighted sum of denoising score matching losses for data distribution modeling, their training primarily emphasizes instance-level optimization, overlooking valuable structural information within each minibatch, indicative of pair-wise relationships among samples. To address this limitation, we introduce Structure-guided Adversarial training of Diffusion Models (SADM). In this pioneering approach, we compel the model to learn manifold structures between samples in each training batch. To ensure the model captures authentic manifold structures in the data distribution, we advocate adversarial training of the diffusion generator against a novel structure discriminator in a minimax game, distinguishing real manifold structures from the generated ones. 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Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 537, + 289, + 682 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 537, + 289, + 682 + ], + "spans": [ + { + "bbox": [ + 46, + 537, + 289, + 682 + ], + "type": "text", + "content": "Diffusion models [20, 56-59, 73] have achieved remarkable generation quality in various tasks, including image generation [12, 50-52, 67, 74, 75, 79], audio synthesis [4, 33, 49], and interdisciplinary applications [21, 24, 71]. Starting from tractable noise distribution, diffusion models generate data by progressively removing noise. This involves the model learning to reverse a pre-defined diffusion process that sequentially introduces varying levels of noise to the data. The model is parameterized and undergoes training by optimizing the weighted sum of denoising score matching losses [20] for various noise levels [57], aiming to learn the recovery of clean images from corrupted images." + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 318, + 206, + 531, + 361 + ], + "blocks": [ + { + "bbox": [ + 318, + 206, + 531, + 361 + ], + "lines": [ + { + "bbox": [ + 318, + 206, + 531, + 361 + ], + "spans": [ + { + "bbox": [ + 318, + 206, + 531, + 361 + ], + "type": "image", + "image_path": "43b4ceb76b4fd49eef9bc4ec1fd6858e690585ed89054d30f90d4b8a07fbbc92.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 305, + 363, + 545, + 386 + ], + "lines": [ + { + "bbox": [ + 305, + 363, + 545, + 386 + ], + "spans": [ + { + "bbox": [ + 305, + 363, + 545, + 386 + ], + "type": "text", + "content": "Figure 1. Comparison between previous instance-level training and our structure-guided training for diffusion models." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 400, + 547, + 581 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 400, + 547, + 581 + ], + "spans": [ + { + "bbox": [ + 304, + 400, + 547, + 581 + ], + "type": "text", + "content": "Aiming to maximally model the data distribution, recent works [28, 42, 60, 63, 72, 76] attempt to improve the precision of training diffusion models. For instance, many approaches design effective weighting schemes [8, 17, 30, 42, 60, 76] for maximum likelihood training or add an extra regularization term [10, 37, 46] to the denoising score loss. There are also some works to enhance the model expressiveness by incorporating other generative models, such as VAE [31, 51, 63], GAN [69], and Normalizing Flows [29, 43, 78]. However, their improved training of diffusion models primarily concentrates on instance-level optimization, overlooking the valuable structural information among batch samples. This oversight is significant, as the incorporation of structural details is crucial for aligning the learned distribution with the underlying data distribution." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 582, + 548, + 715 + ], + "type": "text", + "content": "To mitigate the challenges posed by existing instance-level training methods, we propose Structure-guided Adversarial training of Diffusion Models (SADM). In contrast to conventional instance-level training illustrated in Fig. 1, our approach guides diffusion training at a structural level. During batch training, the model is facilitated to learn manifold structures within batch samples, represented by pair-wise relationships in a low-dimensional feature space. To accurately learn real manifold structures in the data distribution, we introduce a novel structure discriminator that distinguishes genuine manifold structures from generated" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 496, + 35 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 58, + 693, + 130, + 703 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 693, + 130, + 703 + ], + "spans": [ + { + "bbox": [ + 58, + 693, + 130, + 703 + ], + "type": "text", + "content": "* Contributed equally." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "spans": [ + { + "bbox": [ + 59, + 703, + 138, + 712 + ], + "type": "text", + "content": "† Corresponding authors." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7256" + } + ] + } + ], + "index": 16 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 50, + 80, + 209, + 344 + ], + "blocks": [ + { + "bbox": [ + 88, + 69, + 168, + 78 + ], + "lines": [ + { + "bbox": [ + 88, + 69, + 168, + 78 + ], + "spans": [ + { + "bbox": [ + 88, + 69, + 168, + 78 + ], + "type": "text", + "content": "FID: 4.59, Recall: 0.52" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 50, + 80, + 209, + 344 + ], + "lines": [ + { + "bbox": [ + 50, + 80, + 209, + 344 + ], + "spans": [ + { + "bbox": [ + 50, + 80, + 209, + 344 + ], + "type": "image", + "image_path": "c3da61ceb96c9c48998e873fce396c9e2d03035d70e207073349b0a35a8af68c.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 217, + 80, + 376, + 345 + ], + "blocks": [ + { + "bbox": [ + 257, + 68, + 336, + 77 + ], + "lines": [ + { + "bbox": [ + 257, + 68, + 336, + 77 + ], + "spans": [ + { + "bbox": [ + 257, + 68, + 336, + 77 + ], + "type": "text", + "content": "FID: 3.14, Recall: 0.61" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 217, + 80, + 376, + 345 + ], + "lines": [ + { + "bbox": [ + 217, + 80, + 376, + 345 + ], + "spans": [ + { + "bbox": [ + 217, + 80, + 376, + 345 + ], + "type": "image", + "image_path": "1af0dfa1ed8cd7a702fbab03141c03e4f6d6223a7e4e6991a80689a376f58bfc.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 385, + 80, + 544, + 344 + ], + "blocks": [ + { + "bbox": [ + 385, + 80, + 544, + 344 + ], + "lines": [ + { + "bbox": [ + 385, + 80, + 544, + 344 + ], + "spans": [ + { + "bbox": [ + 385, + 80, + 544, + 344 + ], + "type": "image", + "image_path": "9894ee3ed38a8a57851f764bfd53b19d035a91847226a7f973449cd16e15eff7.jpg" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 349, + 546, + 392 + ], + "lines": [ + { + "bbox": [ + 46, + 349, + 546, + 392 + ], + "spans": [ + { + "bbox": [ + 46, + 349, + 546, + 392 + ], + "type": "text", + "content": "Figure 2. Generated samples on ImageNet " + }, + { + "bbox": [ + 46, + 349, + 546, + 392 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 46, + 349, + 546, + 392 + ], + "type": "text", + "content": " with (i) ADM with Classifier Guidance (ADM-G) [12], (ii) ADM optimized by our Structure-guided Adversarial Training, and (iii) real samples in ground truth classes. We can significantly improve diffusion models qualitatively and quantitatively, and our generated sample distribution is overall more similar to real sample distribution. See Appendix C for more synthesis samples of our SOTA model." + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_caption" + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 418, + 288, + 466 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 418, + 288, + 466 + ], + "spans": [ + { + "bbox": [ + 46, + 418, + 288, + 466 + ], + "type": "text", + "content": "ones. For clarity, we alternatively refer to the diffusion models optimized through our structure-guided training as joint sample diffusion, a concept theoretically proven to enhance diffusion model optimization." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 471, + 287, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 471, + 287, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 471, + 287, + 649 + ], + "type": "text", + "content": "We assess the performance of our model across two pivotal tasks: image generation and cross-domain fine-tuning. The former involves training the diffusion model from scratch to evaluate its capability in capturing the entire data distribution. The latter leverages a pre-trained diffusion model, constructed on a large-scale source dataset, and fine-tunes it on a target dataset to assess transferability. Our extensive experiments consistently demonstrate that our approach significantly improves the model's ability to effectively capture the underlying data distribution (Fig. 2). SADM achieves state-of-the-art results across 12 image datasets, including ImageNet [11]. Furthermore, we observe its potential for facilitating rapid adaptation to new domains in cross-domain fine-tuning tasks. We summarize our contributions as follows:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 654, + 287, + 713 + ], + "type": "list", + "angle": 0, + "index": 10, + "blocks": [ + { + "bbox": [ + 47, + 654, + 287, + 689 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 654, + 287, + 689 + ], + "spans": [ + { + "bbox": [ + 47, + 654, + 287, + 689 + ], + "type": "text", + "content": "- To the best of our knowledge, we are the first to propose Structure-guided Adversarial Training to optimize diffusion models from a structural perspective." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 689, + 287, + 713 + ], + "type": "text", + "content": "- We theoretically show that SADM is superior in capturing real data distribution, and can generalize to various image" + } + ] + } + ], + "index": 9 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 419, + 545, + 479 + ], + "type": "list", + "angle": 0, + "index": 13, + "blocks": [ + { + "bbox": [ + 313, + 419, + 539, + 430 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 313, + 419, + 539, + 430 + ], + "spans": [ + { + "bbox": [ + 313, + 419, + 539, + 430 + ], + "type": "text", + "content": "and latent-based diffusion architectures (e.g., DiT [47])." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "spans": [ + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "text", + "content": "- We substantially outperform existing methods on image generation and cross-domain fine-tuning tasks, achieving a new state-of-the-art FID of 1.58 and 2.11 on ImageNet at resolutions of " + }, + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 306, + 432, + 545, + 479 + ], + "type": "text", + "content": ", respectively." + } + ] + } + ], + "index": 12 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 487, + 391, + 500 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 487, + 391, + 500 + ], + "spans": [ + { + "bbox": [ + 306, + 487, + 391, + 500 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 508, + 547, + 544 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 508, + 547, + 544 + ], + "spans": [ + { + "bbox": [ + 305, + 508, + 547, + 544 + ], + "type": "text", + "content": "In this work, we focus on improving the training of diffusion models. Here, we review previous related works and compare our SADM with them." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": "Modifying Training Objectives of Diffusion Models A line of research modifies training objectives to achieve state-of-the-art likelihood [8, 42, 60, 74]. Song et al. [60] propose likelihood weighting to enable approximate maximum likelihood training of score-based diffusion models [57-59] while ContextDiff [76] introduces an effective shifting scheme for facilitating the diffusion and training processes of diffusion probabilistic models [20, 56] to achieve improved sample quality with stable training. Lai et al. [37] and [10] introduce an extra regularization term to the denoising score loss to satisfy some properties of the diffusion process. However, these improvements mainly focus on sample-level optimization, neglecting the rich structural information within batch" + } + ] + } + ], + "index": 16 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7257" + } + ] + } + ], + "index": 17 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 289, + 109 + ], + "type": "text", + "content": "samples, which is critical for aligning the learned distribution and data distribution. Hence, we enforce the model to maximally learn the manifold structures of samples." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 123, + 289, + 316 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 123, + 289, + 316 + ], + "spans": [ + { + "bbox": [ + 47, + 123, + 289, + 316 + ], + "type": "text", + "content": "Combining Additional Models for Diffusion Training Another line of research incorporates other models to improve the stability and precision of diffusion training. For example, INDM [29] expands the linear diffusion to trainable nonlinear diffusion through a normalizing flow to improve the training curve of diffusion models. Jolicoeur-Martineau et al. [26], Kim et al. [28] improve diffusion models with adversarial learning while Xiao et al. [69] model each denoising step using a multimodal conditional GAN. LSGM [63] and LDM [51] conduct diffusion process in the semantic latent space obtained with a pre-trained VAE. Although these combinations strengthen the model expressiveness for capturing data distribution, they are still limited in modeling the underlying manifold structures within training samples. We propose a novel structure discriminator for adversarially learn the diffusion model from a structural perspective." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 326, + 124, + 339 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 326, + 124, + 339 + ], + "spans": [ + { + "bbox": [ + 47, + 326, + 124, + 339 + ], + "type": "text", + "content": "3. Preliminary" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "content": "Diffusion Models We consider diffusion models [20, 56, 57] specified in continuous time [4, 31, 59, 62]. Given samples " + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0" + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "content": " from a data distribution " + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "inline_equation", + "content": "q_0(\\mathbf{x}_0)" + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "content": ", noise scheduling functions " + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\alpha_{t},\\sigma_{t}" + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "content": ", a diffusion model has latent variables " + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "inline_equation", + "content": "\\mathbf{x} = \\{\\mathbf{x}_t\\mid t\\in [0,1]\\}" + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "content": ", and the forward process is defined with " + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "inline_equation", + "content": "q(\\mathbf{x}_t|\\mathbf{x}_0)" + }, + { + "bbox": [ + 47, + 346, + 289, + 429 + ], + "type": "text", + "content": ", a Gaussian process satisfying the following Markovian structure:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 91, + 438, + 287, + 453 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 438, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 91, + 438, + 287, + 453 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {0}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\alpha_ {t} \\mathbf {x} _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}\\right), \\tag {1}", + "image_path": "00250cb354aaeee4dfab1148f8f9cecdb3dfcc09a1558050f04fcb499674245b.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 91, + 455, + 287, + 469 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 91, + 455, + 287, + 469 + ], + "spans": [ + { + "bbox": [ + 91, + 455, + 287, + 469 + ], + "type": "interline_equation", + "content": "q \\left(\\mathbf {x} _ {t} \\mid \\mathbf {x} _ {s}\\right) = \\mathcal {N} \\left(\\mathbf {x} _ {t}; \\left(\\alpha_ {t} / \\alpha_ {s}\\right) \\mathbf {x} _ {s}, \\sigma_ {t \\mid s} ^ {2} \\mathbf {I}\\right) \\tag {2}", + "image_path": "b007b20fa3d31f47bb89b088f21abe4f1c3aa01bd69b47e2055b87bb9611fd7f.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "spans": [ + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "inline_equation", + "content": "0 \\leq s < t \\leq 1" + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "inline_equation", + "content": "\\sigma_{t|s}^2 = (1 - e^{\\lambda_t - \\lambda_s})\\sigma_t^2" + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "inline_equation", + "content": "\\lambda_t = \\log [\\alpha_t^2 /\\sigma_t^2 ]" + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": " denotes the log signal-to-noise-ratio [31]. The goal of the diffusion model is to denoise " + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t \\sim q(\\mathbf{x}_t|\\mathbf{x}_0)" + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": " by estimating " + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_{\\theta}(\\mathbf{x}_t) \\approx \\mathbf{x}_0" + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": ". We train this denoising model " + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_{\\theta}" + }, + { + "bbox": [ + 47, + 479, + 288, + 542 + ], + "type": "text", + "content": " using a weighted mean squared error loss" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 102, + 551, + 287, + 566 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 102, + 551, + 287, + 566 + ], + "spans": [ + { + "bbox": [ + 102, + 551, + 287, + 566 + ], + "type": "interline_equation", + "content": "\\mathbb {E} _ {\\mathbf {x} _ {0}, \\boldsymbol {\\epsilon}, t} \\left[ w \\left(\\lambda_ {t}\\right) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t}) - \\mathbf {x} _ {0} \\| _ {2} ^ {2} \\right] \\tag {3}", + "image_path": "8fed4c4d4f48e4a71a93eea7ea7105e16c1e96bcd865d90093727a1c5f8e6002.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "spans": [ + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": "over uniformly sampled times " + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "inline_equation", + "content": "t \\in [0,1]" + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": ". This loss can be justified as a weighted variational lower bound on the data log likelihood under the diffusion model [31] or as a form of denoising score matching [57, 64]. " + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "inline_equation", + "content": "w(\\lambda_t)" + }, + { + "bbox": [ + 46, + 574, + 287, + 635 + ], + "type": "text", + "content": " is a pre-specified weighting function [31]." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 645, + 153, + 658 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 645, + 153, + 658 + ], + "spans": [ + { + "bbox": [ + 47, + 645, + 153, + 658 + ], + "type": "text", + "content": "4. Proposed Method" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 46, + 665, + 289, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 713 + ], + "type": "text", + "content": "We introduce the proposed SADM in detail (Fig. 3). In order to maximally learn the structural information between real samples, we propose structure-guided training of diffusion models in Sec. 4.1. Then we design a novel structure" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 133 + ], + "type": "text", + "content": "discriminator for adversarially optimizing the training procedure from a structural perspective in Sec. 4.2. Finally, we alternatively interpret our structure-guided training of diffusion models as joint sample diffusion with theoretical analysis for betwen understanding in Sec. 4.3." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 139, + 479, + 152 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 139, + 479, + 152 + ], + "spans": [ + { + "bbox": [ + 305, + 139, + 479, + 152 + ], + "type": "text", + "content": "4.1. Beyond Instance-Level Training" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 157, + 546, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 157, + 546, + 194 + ], + "spans": [ + { + "bbox": [ + 304, + 157, + 546, + 194 + ], + "type": "text", + "content": "We first review the previous instance-level training methods for diffusion models. Generally, they train the diffusion model with a finite sample version of Eq. (3):" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 350, + 200, + 546, + 227 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 200, + 546, + 227 + ], + "spans": [ + { + "bbox": [ + 350, + 200, + 546, + 227 + ], + "type": "interline_equation", + "content": "\\mathcal {L} _ {t} = w \\left(\\lambda_ {t}\\right) \\frac {\\sum_ {i \\in B} \\left| \\left| \\mathbf {x} _ {0} ^ {i} - \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) \\right| \\right| ^ {2}}{| B |}, \\tag {4}", + "image_path": "cb401f896b2e5659562d4a86e9b2558aa0550e533f1c7c779248ed07ef905416.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "spans": [ + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^i, \\mathbf{x}_t^i" + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "text", + "content": " denote the " + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "inline_equation", + "content": "i^{th}" + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "text", + "content": " ground truth samples and generated samples in the mini-batch " + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "inline_equation", + "content": "B" + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "text", + "content": " at time step " + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "inline_equation", + "content": "t" + }, + { + "bbox": [ + 304, + 235, + 547, + 331 + ], + "type": "text", + "content": ". However, this objective function encourages the diffusion model to denoise by considering only the instance-level information, neglecting the group-level (structural) information in the mini-batch. Therefore, we enforce the sample predictions of the denoising network to maximally preserve the manifold structures between batch samples." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "spans": [ + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "content": "Structural Constraint in Manifold More concretely, ground truth samples " + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}" + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "content": " are first projected from pixel space into embedding space using off-the-shelf pre-trained networks " + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "inline_equation", + "content": "\\Psi (\\cdot):\\mathbb{R}^{m\\times n}\\to \\mathbb{R}^d" + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "content": " e.g., an Inception-V3 feature extractor pre-trained on ImageNet [61] (we conduct ablation study in Appendix B). Then, the pair-wise relationships " + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\Psi (\\mathbf{x}_0^i),\\Psi (\\mathbf{x}_0^j))" + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "content": " are calculated within batch samples " + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "inline_equation", + "content": "\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|}" + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "content": " , which contain rich structural information in a low-dimensional manifold. This structural information can be expressed with an affinity matrix " + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|})" + }, + { + "bbox": [ + 304, + 345, + 547, + 469 + ], + "type": "text", + "content": " defined as:" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 317, + 475, + 545, + 542 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 317, + 475, + 545, + 542 + ], + "spans": [ + { + "bbox": [ + 317, + 475, + 545, + 542 + ], + "type": "interline_equation", + "content": "\\left[ \\begin{array}{c c c c} \\mathcal {R} (\\Psi_ {1}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {1}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {1}, \\Psi_ {| B |}) \\\\ \\mathcal {R} (\\Psi_ {2}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {2}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {2}, \\Psi_ {| B |}) \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {1}) & \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {2}) & \\dots & \\mathcal {R} (\\Psi_ {| B |}, \\Psi_ {| B |}) \\end{array} \\right] \\tag {5}", + "image_path": "43172fb2da13e47d9349a8f47ea31e7d58ba3931823c0439c674c9e35f7cb1b2.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "spans": [ + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "inline_equation", + "content": "\\Psi_{i}" + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": " is a short-hand for " + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "inline_equation", + "content": "\\Psi (\\mathbf{x}_0^i)" + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": ", and " + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": " denotes the relational function, such as Euclidean distance. Kindly note that many off-the-shelf pre-trained networks are open-source and only work well on clean images, and thus fail to provide meaningful embeddings when the input is noisy. Therefore, we use the predicted clean samples " + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_0^i" + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": " for computing affinity matrix, and regularize the denoising network to minimize the structural distance between " + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\{\\mathbf{x}_0^i\\}_{i = 1}^{|B|})" + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "inline_equation", + "content": "\\mathcal{M}(\\{\\hat{\\mathbf{x}}_0^i\\}_{i = 1}^{|B|})" + }, + { + "bbox": [ + 304, + 543, + 547, + 664 + ], + "type": "text", + "content": ". Adding this structural constraint into Eq. (4), the training objective for denoising network is:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 348, + 670, + 546, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 348, + 670, + 546, + 715 + ], + "spans": [ + { + "bbox": [ + 348, + 670, + 546, + 715 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathcal {L} _ {t} = \\frac {\\sum_ {i \\in B} \\left| \\left| \\mathbf {x} _ {0} ^ {i} - \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) \\right| \\right| ^ {2}}{| B |} \\tag {6} \\\\ + \\mathcal {D} (\\mathcal {M} (\\{\\mathbf {x} _ {0} ^ {i} \\} _ {i = 1} ^ {| B |}), \\mathcal {M} (\\{\\hat {\\mathbf {x}} _ {0} ^ {i} \\} _ {i = 1} ^ {| B |})) \\\\ \\end{array}", + "image_path": "f0707b56a74781c23afd43c30b678a9a2f59dbce34f90c3d54ccccbb5225b96c.jpg" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7258" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 72, + 68, + 521, + 317 + ], + "blocks": [ + { + "bbox": [ + 72, + 68, + 521, + 317 + ], + "lines": [ + { + "bbox": [ + 72, + 68, + 521, + 317 + ], + "spans": [ + { + "bbox": [ + 72, + 68, + 521, + 317 + ], + "type": "image", + "image_path": "f7c7ccaeacfa297fc582e8005d7845092fb876aa9c76e0ac7a3d3ab000d6a6be.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 325, + 548, + 360 + ], + "lines": [ + { + "bbox": [ + 46, + 325, + 548, + 360 + ], + "spans": [ + { + "bbox": [ + 46, + 325, + 548, + 360 + ], + "type": "text", + "content": "Figure 3. Overview of SADM. We minimize the structural distance between the generated samples (fake) and ground truth samples (real) in the manifold space for optimizing the denoiser, and maximize their structural distance for optimizing the encoder in structure discriminator. The denoiser and the structure discriminator are adversarially trained." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "spans": [ + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 46, + 376, + 288, + 437 + ], + "type": "text", + "content": " denotes the distance metric between ground truth and predicted affinity matrices. In this way, the diffusion generator (denoiser) is optimized not only to make correct prediction for each instance, but also to preserve the manifold structures of batch samples." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 441, + 255, + 455 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 441, + 255, + 455 + ], + "spans": [ + { + "bbox": [ + 47, + 441, + 255, + 455 + ], + "type": "text", + "content": "4.2. Structure-Guided Adversarial Training" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 460, + 288, + 604 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 288, + 604 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 288, + 604 + ], + "type": "text", + "content": "As demonstrated above, we aim to maximally learn data distribution by aligning the manifold structures of denoiser's predicted samples to those of ground truth samples in each training batch. At every training iteration, the manifold structures can be diverse and the denoiser tend to merely focus on some easy-to-learn structures, ultimately leading to trivial solutions that fail to capture the whole data distribution. In order to mitigate this problem and improve the expressiveness of denoiser, we adversarially learn the denoising network against a structure discriminator in a minimax game (Fig. 3), which is trained to distinguish the manifold structures between the real and generated batch samples." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 617, + 289, + 715 + ], + "type": "text", + "content": "Structure Discriminator Normally, the discriminator in adversarial learning [15] would output the discrete value (0 or 1) to determine whether the input is real or fake. However, such discrete discriminator can not be applied in distinguishing manifold structures, because the generated and real sample sets would share similar pair-wise sample relations despite their different feature spaces. Thus, instead of learning a classification-based discriminator, we design a" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 305, + 376, + 545, + 399 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 376, + 545, + 399 + ], + "spans": [ + { + "bbox": [ + 305, + 376, + 545, + 399 + ], + "type": "text", + "content": "novel comparison-based structure discriminator to address this issue." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "spans": [ + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "text", + "content": "Specifically, as illustrated in Fig. 3, the structure discriminator consists of the aforementioned neural network " + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "inline_equation", + "content": "\\Psi_{\\phi}" + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "text", + "content": " with trainable parameters " + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "text", + "content": " and the distance measure function " + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot ,\\cdot)" + }, + { + "bbox": [ + 304, + 403, + 547, + 510 + ], + "type": "text", + "content": " that outputs continuous value. It projects both real and generated samples into the embedding space, then the structure discriminator is trained against the denoiser for finding a better manifold (or embedding space) to distinguish real sample set from generated set by maximizing their structural distance:" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 523, + 579, + 562 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 523, + 579, + 562 + ], + "spans": [ + { + "bbox": [ + 306, + 523, + 579, + 562 + ], + "type": "interline_equation", + "content": "\\max _ {\\phi} \\frac {\\eta_ {t} \\sum_ {i , j \\in B} \\mathcal {D} \\left(\\mathcal {R} \\left(\\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) , \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right)\\right) , \\mathcal {R} \\left(\\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) , \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right)\\right)\\right)}{| B | ^ {2}}. \\tag {7}", + "image_path": "2065445dfd7dcd548e98f66a5d10780b1953be0a3f4b0371a6e9b83884bc0d01.jpg" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "spans": [ + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "content": "where we choose " + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\eta_t = \\frac{1}{t}" + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "content": " as a time-dependent weighting factor. We can use simple measurements for " + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{D}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "content": " (" + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "inline_equation", + "content": "L_2" + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "content": " distance) and " + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\cdot, \\cdot)" + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "content": " (cosine similarity), as the critical semantic information has been already encoded by " + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "inline_equation", + "content": "\\Psi_\\phi" + }, + { + "bbox": [ + 304, + 562, + 547, + 647 + ], + "type": "text", + "content": ". Conversely, the denoiser is adversarially optimized for generating more realistic sample set to fool the structure discriminator by minimizing the structural distance." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 677, + 547, + 715 + ], + "type": "text", + "content": "Final Optimization Objective The final training objective of our SADM consists of normal denoising score matching loss (Eq. (3)) and adversarial structural distance loss (Eq. 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(8). In an iteration, we first freeze " + }, + { + "bbox": [ + 47, + 161, + 287, + 197 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 161, + 287, + 197 + ], + "type": "text", + "content": " and update " + }, + { + "bbox": [ + 47, + 161, + 287, + 197 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 161, + 287, + 197 + ], + "type": "text", + "content": " by ascending along its gradient" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 205, + 287, + 243 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 205, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 48, + 205, + 287, + 243 + ], + "type": "interline_equation", + "content": "\\nabla_ {\\phi} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\mathbf {x} _ {0} ^ {j}\\right) - \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}\\right) ^ {T} \\Psi_ {\\phi} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2}}{| B | ^ {2}}, \\tag {9}", + "image_path": "d4d744fb6bd1b92e5aa5861159fcab61597be547227b03c6a4f1300fd306aab8.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "spans": [ + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "type": "text", + "content": "then we freeze " + }, + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "type": "inline_equation", + "content": "\\phi" + }, + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "type": "text", + "content": " and update " + }, + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 47, + 243, + 288, + 268 + ], + "type": "text", + "content": " by descending along its gradient" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 49, + 274, + 287, + 341 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 49, + 274, + 287, + 341 + ], + "spans": [ + { + "bbox": [ + 49, + 274, + 287, + 341 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {\\theta} \\frac {\\sum_ {i , j \\in B} \\eta_ {t} \\| \\Psi_ {\\phi} (\\mathbf {x} _ {0} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\mathbf {x} _ {0} ^ {j}) - \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}) \\| _ {2} ^ {2}}{| B | ^ {2}} \\\\ + \\nabla_ {\\theta} \\frac {w \\left(\\lambda_ {t}\\right) \\sum_ {i \\in B} \\left\\| \\hat {\\mathbf {x}} _ {\\theta} \\left(\\mathbf {x} _ {t} ^ {i}\\right) - \\mathbf {x} _ {0} ^ {i} \\right\\| _ {2} ^ {2}}{| B |}. \\tag {10} \\\\ \\end{array}", + "image_path": "7c6be2f2d2ffc71f38626bffb9a525600d08dcde9d625e1ac09393aa37c1ee33.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 342, + 288, + 354 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 342, + 288, + 354 + ], + "spans": [ + { + "bbox": [ + 47, + 342, + 288, + 354 + ], + "type": "text", + "content": "The proposed training algorithm is presented in Algorithm 1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 369, + 287, + 453 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 369, + 287, + 453 + ], + "spans": [ + { + "bbox": [ + 47, + 369, + 287, + 453 + ], + "type": "text", + "content": "Generalizing to Latent Diffusion Our proposed training algorithm applies not only to image diffusion but also to latent diffusion, such as LDM [51] and LSGM [63]. In this case, the intermediate results " + }, + { + "bbox": [ + 47, + 369, + 287, + 453 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_t" + }, + { + "bbox": [ + 47, + 369, + 287, + 453 + ], + "type": "text", + "content": " are latent codes rather than images. We can use the latent decoder (e.g., VAE decoder [32]) to project the generated latent codes to images and then use the same algorithm in the image domain." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 460, + 249, + 472 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 460, + 249, + 472 + ], + "spans": [ + { + "bbox": [ + 47, + 460, + 249, + 472 + ], + "type": "text", + "content": "4.3. Interpreting as Joint Sample Diffusion" + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "spans": [ + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": "Relation-Conditioned Diffusion Process For better understanding of our proposed structure-guided training, we interpret it as a joint sample diffusion model that simultaneously perturbs and denoises a set of samples conditioned on the relation variable. Formally, let " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_0 = (\\mathbf{x}_0^i,\\mathbf{x}_0^j)" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{x}_0^i,\\mathbf{x}_0^j" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": " are independent random variables sampled from ground truth distribution " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "q_{0}" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": ". And the relation variable that encodes the structure information is defined as " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{R} = \\mathcal{R}(\\mathbf{x}_0^i,\\mathbf{x}_0^j) + \\gamma \\epsilon" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "\\gamma \\epsilon" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": " denote a small gaussian noise added to the relation to avoid degenerated distribution. Then the forward diffusion jointly perturbs " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_0" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": ", conditioned on " + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 478, + 288, + 622 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 93, + 631, + 287, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 93, + 631, + 287, + 645 + ], + "spans": [ + { + "bbox": [ + 93, + 631, + 287, + 645 + ], + "type": "interline_equation", + "content": "q (\\mathbf {y} _ {t} | \\mathbf {y} _ {0}, \\mathcal {R}) = \\mathcal {N} (\\mathbf {y} _ {t}; \\alpha_ {t} \\mathbf {y} _ {0}, \\sigma_ {t} ^ {2} \\mathbf {I}). \\tag {11}", + "image_path": "db3c5663c38733ce75eb82169b8b62c348fb948c907051cd54243334c46db17e.jpg" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "spans": [ + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "text", + "content": "To reverse the diffusion process, we need to predict " + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathbf{y}_0" + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "text", + "content": ", or equivalently, learn the conditional score function " + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\nabla_y\\log q_t(y_t|\\mathcal{R})" + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "text", + "content": " [12, 19]. This formulation allows us to utilize the auxiliary structural information " + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 47, + 653, + 289, + 714 + ], + "type": "text", + "content": " in the sampling process, which usually leads to better performance [13, 55]." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 312, + 75, + 501, + 87 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 312, + 75, + 501, + 87 + ], + "spans": [ + { + "bbox": [ + 312, + 75, + 501, + 87 + ], + "type": "text", + "content": "Algorithm 1: SADM, our proposed algorithm." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 318, + 89, + 531, + 148 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 89, + 531, + 148 + ], + "spans": [ + { + "bbox": [ + 318, + 89, + 531, + 148 + ], + "type": "text", + "content": "input : " + }, + { + "bbox": [ + 318, + 89, + 531, + 148 + ], + "type": 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\\| \\Psi_ {\\phi} (\\mathbf {\\hat {x}} _ {0} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\mathbf {\\hat {x}} _ {0} ^ {j}) - \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}) ^ {T} \\Psi_ {\\phi} (\\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}) \\| _ {2} ^ {2}}{| B | ^ {2}} \\\\ + \\nabla_ {\\theta} \\frac {w (\\lambda_ {t}) \\sum_ {i \\in B} \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2}}{| B |} \\\\ \\end{array}", + "image_path": "3b11fcfa53d55785cb702a1ef6adbea8f200ad0474199d8f838a2a2366396951.jpg" + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 318, + 277, + 526, + 313 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 277, + 526, + 313 + ], + "spans": [ + { + "bbox": [ + 318, + 277, + 526, + 313 + ], + "type": "text", + "content": "Adversarily train denoising network and structure discriminator by iteratively updating their parameters " + }, + { + "bbox": [ + 318, + 277, + 526, + 313 + ], + "type": "inline_equation", + "content": "\\theta, \\phi" + }, + { + "bbox": [ + 318, + 277, + 526, + 313 + ], + "type": "text", + "content": " according to Eqs. (9) and (10)." + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 318, + 314, + 441, + 325 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 318, + 314, + 441, + 325 + ], + "spans": [ + { + "bbox": [ + 318, + 314, + 441, + 325 + ], + "type": "text", + "content": "output: Denoising network " + }, + { + "bbox": [ + 318, + 314, + 441, + 325 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 318, + 314, + 441, + 325 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 355, + 547, + 380 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 355, + 547, + 380 + ], + "spans": [ + { + "bbox": [ + 306, + 355, + 547, + 380 + ], + "type": "text", + "content": "Learning Conditional Score To approximate the conditional score function, first we decompose it with Bayes' rule," + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 306, + 401, + 547, + 439 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 401, + 547, + 439 + ], + "spans": [ + { + "bbox": [ + 306, + 401, + 547, + 439 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\nabla_ {y} \\log q _ {t} \\left(y _ {t} | \\mathcal {R}\\right) = \\nabla_ {y} \\log q _ {t} \\left(y _ {t}\\right) + \\nabla_ {y} \\log q _ {t} \\left(\\mathcal {R} \\mid y _ {t}\\right) \\\\ = \\Sigma_ {s = i, j} \\nabla_ {x} \\log q _ {t} \\left(x _ {t} ^ {s}\\right) + \\nabla_ {y} \\log q _ {t} (\\mathcal {R} | y _ {t}). \\tag {12} \\\\ \\end{array}", + "image_path": "783e4263337fbc5d494d44c6d6728b229498fa17a9e92ef90aae1acde295377a.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "spans": [ + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "text", + "content": "To approximate the first term on the right side of Eq. (12), we only need to learn " + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{x}}_{\\theta ,t}^{i},\\hat{\\mathbf{x}}_{\\theta ,t}^{j}" + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "text", + "content": " , as in standard diffusion models [59]. However, the second term is intractable since " + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "inline_equation", + "content": "q_{t}(\\mathcal{R}|y_{t})" + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "text", + "content": " involves the intractable posterior " + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "inline_equation", + "content": "q(\\mathbf{y}_0|\\mathbf{y}_t)" + }, + { + "bbox": [ + 306, + 440, + 547, + 488 + ], + "type": "text", + "content": " . Note that" + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 350, + 500, + 545, + 540 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 500, + 545, + 540 + ], + "spans": [ + { + "bbox": [ + 350, + 500, + 545, + 540 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} q _ {t} (\\mathcal {R} | y _ {t}) = \\int g (\\mathcal {R} | \\mathbf {y} _ {0}) q \\left(\\mathbf {y} _ {0} \\mid \\mathbf {y} _ {t}\\right) d \\mathbf {y} _ {0} \\tag {13} \\\\ = \\mathbb {E} _ {\\mathbf {y} _ {0}} \\left[ g (\\mathcal {R} | \\mathbf {y} _ {0}) | \\mathbf {y} _ {t} \\right], \\\\ \\end{array}", + "image_path": "7944bb0e35cb46f467a6889fb22123b227f20a3d382cbe6294d5d017ba0c990a.jpg" + } + ] + } + ], + "index": 27 + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "spans": [ + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "g(\\mathcal{R}|\\mathbf{y}_0)" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": " is the density function of Gaussian distribution with mean " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "\\mathcal{R}(\\mathbf{x}_0^i,\\mathbf{x}_0^j)" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": " and variance " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "\\gamma^2" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": ", by the definition of " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "\\mathcal{R}" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": ". As a result, we can use " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "g(\\mathcal{R}|\\hat{\\mathbf{y}}_{0,t}) = g(\\mathcal{R} | (\\hat{\\mathbf{x}}_{\\theta ,t}^i,\\hat{\\mathbf{x}}_{\\theta ,t}^j))" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": " to approximate " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "q_{t}(\\mathcal{R}|y_{t})" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": ", and train it with " + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 305, + 553, + 547, + 603 + ], + "type": "text", + "content": " loss:" + } + ] + } + ], + "index": 28 + }, + { + "bbox": [ + 306, + 615, + 548, + 689 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 615, + 548, + 689 + ], + "spans": [ + { + "bbox": [ + 306, + 615, + 548, + 689 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {\\mathbf {y} _ {t}} \\| \\mathbb {E} _ {\\mathbf {y} _ {0}} [ g (\\mathcal {R} | \\mathbf {y} _ {0}) | \\mathbf {y} _ {t} ] - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) \\| _ {2} ^ {2} \\\\ = \\mathbb {E} _ {\\mathbf {y} _ {t}} \\| \\mathbb {E} _ {\\mathbf {y} _ {0}} [ g (\\mathcal {R} | \\mathbf {y} _ {0}) - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) | \\mathbf {y} _ {t} ] \\| _ {2} ^ {2} \\\\ \\leq \\mathbb {E} _ {\\mathbf {y} _ {0}, \\mathbf {y} _ {t}} \\| g (\\mathcal {R} | \\mathbf {y} _ {0}) - g (\\mathcal {R} | \\hat {\\mathbf {y}} _ {0} (\\mathbf {y} _ {t})) \\| _ {2} ^ {2} \\quad (J e s s e n I n e q u a l i t y) \\\\ \\leq w (\\gamma) \\mathbb {E} _ {\\mathbf {y} _ {0}, \\mathbf {y} _ {t}} \\| \\mathcal {R} \\left(\\mathbf {x} _ {0} ^ {i}, \\mathbf {x} _ {0} ^ {j}\\right) - \\mathcal {R} \\left(\\hat {\\mathbf {x}} _ {\\theta , t} ^ {i}, \\hat {\\mathbf {x}} _ {\\theta , t} ^ {j}\\right) \\| _ {2} ^ {2} = \\mathcal {L} _ {t} ^ {\\text {s t r u c t u r e}}, \\tag {14} \\\\ \\end{array}", + "image_path": "f330a4fe8c37bf2d2b1cefa9333998d9cfd3dbc3359ed42436f5e8d368a14c81.jpg" + } + ] + } + ], + "index": 29 + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "inline_equation", + "content": "w(\\gamma)" + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": " is a weighting scalar that depends only on " + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "inline_equation", + "content": "\\gamma" + }, + { + "bbox": [ + 306, + 689, + 547, + 714 + ], + "type": "text", + "content": ". The objective function is the sum of the denoising score" + } + ] + } + ], + "index": 30 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7260" + } + ] + } + ], + "index": 31 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 74, + 91, + 518, + 256 + ], + "blocks": [ + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "lines": [ + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "spans": [ + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "type": "text", + "content": "Table 1. Quantitative results for class-conditional generation on ImageNet " + }, + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "type": "inline_equation", + "content": "{512} \\times {512}" + }, + { + "bbox": [ + 116, + 70, + 475, + 82 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 74, + 91, + 518, + 256 + ], + "lines": [ + { + "bbox": [ + 74, + 91, + 518, + 256 + ], + "spans": [ + { + "bbox": [ + 74, + 91, + 518, + 256 + ], + "type": "table", + "html": "
ModelImageNet 256×256ImageNet 512×512
FID ↓IS ↑Precision ↑Recall ↑FID ↓IS ↑Precision ↑Recall ↑
BigGAN-deep [2]6.95171.400.870.288.43177.900.880.29
StyleGAN-XL [54]2.30265.120.780.532.41267.750.770.52
ADM-G, ADM-U [12]3.94215.840.830.533.85221.720.840.53
LDM-4-G [51]3.60247.670.870.48----
RIN+NoiseSchedule [6]3.52186.20--3.95216.00--
SimpleDiffusion [22]2.44256.30--3.02248.70--
DiT-G++ [28]1.83281.530.780.64----
MDT-G [14]1.79283.010.810.61----
DiT-XL/2-G [47]2.27278.240.830.573.04240.820.840.54
DiT-SADM (Ours)1.58298.460.860.662.11251.820.870.63
", + "image_path": "3517c9625ccfc43ac0993a41aaa3146267a6d97f8404367ecc29dbf03b4da552.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 275, + 180, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 275, + 180, + 289 + ], + "spans": [ + { + "bbox": [ + 47, + 275, + 180, + 289 + ], + "type": "text", + "content": "matching objective and " + }, + { + "bbox": [ + 47, + 275, + 180, + 289 + ], + "type": "inline_equation", + "content": "\\mathcal{L}_t^{\\mathrm{structure}}" + }, + { + "bbox": [ + 47, + 275, + 180, + 289 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 293, + 304, + 338 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 293, + 304, + 338 + ], + "spans": [ + { + "bbox": [ + 47, + 293, + 304, + 338 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {i}, \\boldsymbol {\\epsilon} ^ {i}, t} w (\\lambda_ {t}) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {i}) - \\mathbf {x} _ {0} ^ {i} \\| _ {2} ^ {2} + \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {j}, \\boldsymbol {\\epsilon} ^ {j}, t} w (\\lambda_ {t}) \\| \\hat {\\mathbf {x}} _ {\\theta} (\\mathbf {x} _ {t} ^ {j}) - \\mathbf {x} _ {0} ^ {j} \\| _ {2} ^ {2} \\\\ + \\mathbb {E} _ {\\mathbf {x} _ {0} ^ {i}, \\epsilon^ {i}, \\mathbf {x} _ {0} ^ {j}, \\epsilon^ {j}, t} \\left[ \\mathcal {L} _ {t} ^ {\\text {s t r u c t u r e}} \\right], \\tag {15} \\\\ \\end{array}", + "image_path": "417e098ad0090e5de3337fa72f161ec0c274b0f294550895283b1e24863bdd0f.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 338, + 288, + 386 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 338, + 288, + 386 + ], + "spans": [ + { + "bbox": [ + 46, + 338, + 288, + 386 + ], + "type": "text", + "content": "which is a variational upper bound of negative log likelihood of the joint sample. Our objective in Eq. (6) can be viewed as a finite-sample version of Eq. (15), which trains the conditional diffusion model to utilize the structural information." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 396, + 128, + 410 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 396, + 128, + 410 + ], + "spans": [ + { + "bbox": [ + 47, + 396, + 128, + 410 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 415, + 155, + 428 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 415, + 155, + 428 + ], + "spans": [ + { + "bbox": [ + 47, + 415, + 155, + 428 + ], + "type": "text", + "content": "5.1. Image Generation" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 434, + 288, + 518 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 434, + 288, + 518 + ], + "spans": [ + { + "bbox": [ + 46, + 434, + 288, + 518 + ], + "type": "text", + "content": "Experiment Setup We experiment on CIFAR-10 [35], CelebA/FFHQ 64x64 [41], and ImageNet 256x256 [11]. We utilize our SADM to facilitate the training of the diffusion backbones from Karras et al. [27], Vahdat et al. [63] on CIFAR-10 and FFHQ, from Kim et al. [30] on CelebA, and from Peebles and Xie [47] (DiT, Diffusion Transformer) on ImageNet." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 532, + 287, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 532, + 287, + 616 + ], + "spans": [ + { + "bbox": [ + 46, + 532, + 287, + 616 + ], + "type": "text", + "content": "Evaluation Metrics We use Frechet Inception Distance (FID) [18] as the primary metric for capturing both quality and diversity due to its alignment with human judgement. We follow the evaluation procedure of ADM [12] for fair comparisons. For completeness, we also use Inception Score (IS) [53], Precision and Recall [36] as the main metrics for measuring diversity and distribution coverage." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "spans": [ + { + "bbox": [ + 46, + 629, + 288, + 713 + ], + "type": "text", + "content": "Implementation Details We train the denoising network from scratch and use the feature extractor of Inception-V3 [61] pre-trained on ImageNet for initializing the encoder of our structure discriminator. At the beginning of training, we freeze the pre-trained discriminator encoder and train the denoiser with structure-guided training objective in Eq. (6) until convergence, then we adversarially tune the denoiser and" + } + ] + } + ], + "index": 9 + }, + { + "type": "table", + "bbox": [ + 309, + 290, + 547, + 460 + ], + "blocks": [ + { + "bbox": [ + 359, + 274, + 492, + 285 + ], + "lines": [ + { + "bbox": [ + 359, + 274, + 492, + 285 + ], + "spans": [ + { + "bbox": [ + 359, + 274, + 492, + 285 + ], + "type": "text", + "content": "Table 2. Performance on CIFAR-10." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 309, + 290, + 547, + 460 + ], + "lines": [ + { + "bbox": [ + 309, + 290, + 547, + 460 + ], + "spans": [ + { + "bbox": [ + 309, + 290, + 547, + 460 + ], + "type": "table", + "html": "
ModelDiffusion SpaceNFE↓UnconditionalConditional
NLL↓FID↓FID↓
VDM [31]Data10002.497.41-
DDPM [20]Data10003.753.17-
iDDPM [44]Data10003.372.90-
Soft Truncation [30]Data20002.912.47-
INDM [29]Latent20003.092.28-
CLD-SGM [13]Data3123.312.25-
NCSN++ [59]Data20003.452.20-
LSGM [63]Latent1383.432.10-
NCSN++-G [3]Data2000--2.25
EDM [27]Data352.601.971.79
LSGM-G++ [28]Latent1383.421.94-
EDM-G++ [28]Data352.551.771.64
SADMLatent1382.511.781.73
SADMData352.281.541.47
", + "image_path": "bd66c0e8fc144a5daedfaacdd334bad5f24af716d0e95414c3d9419df8121420.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 475, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 475, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 475, + 547, + 548 + ], + "type": "text", + "content": "encoder with the objective in Eq. (8) for 3 or 4 rounds (500k steps) until they achieve a balance. This training paradigm keeps the same for unconditional and class-conditional generation tasks, and can be easily generalized to score-based diffusion models [59, 63] by adding our structural constraint into the final objective functions." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": "Main Results Our SADM achieves new state-of-the-art FIDs on all datasets including CIFAR-10, CelebA, FFHQ, and ImageNet. On ImageNet " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "inline_equation", + "content": "512 \\times 512" + }, + { + "bbox": [ + 304, + 570, + 547, + 713 + ], + "type": "text", + "content": ", we consistently achieve SOTA FIDs of 1.43 and 2.18 for class-conditional generation as illustrated in Tab. 1. Notably, We significantly improve the generation performance of DiT and outperform the previous best FID of MDT [14] solely through improved training algorithm without increasing the model complexity and inference time. From Tab. 2, we find that our SADM works well for both image diffusion (based on EDM) and latent diffusion (based on LSGM). In experiments, for fair comparisons, we use the same hyperpa" + } + ] + } + ], + "index": 13 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 314, + 757 + ], + "type": "text", + "content": "7261" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 86, + 70, + 220, + 160 + ], + "blocks": [ + { + "bbox": [ + 86, + 70, + 220, + 160 + ], + "lines": [ + { + "bbox": [ + 86, + 70, + 220, + 160 + ], + "spans": [ + { + "bbox": [ + 86, + 70, + 220, + 160 + ], + "type": "image", + "image_path": "fbb4982394ab41458bf3ea034e5b4ccf698b7a9b345d11fd583f45d35c0ea898.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 230, + 70, + 364, + 159 + ], + "blocks": [ + { + "bbox": [ + 230, + 70, + 364, + 159 + ], + "lines": [ + { + "bbox": [ + 230, + 70, + 364, + 159 + ], + "spans": [ + { + "bbox": [ + 230, + 70, + 364, + 159 + ], + "type": "image", + "image_path": "416ebc9789490f5432d059b6eb0b91168b7b4e7fadd00c6af9eec8fa6310ab88.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 375, + 70, + 509, + 159 + ], + "blocks": [ + { + "bbox": [ + 375, + 70, + 509, + 159 + ], + "lines": [ + { + "bbox": [ + 375, + 70, + 509, + 159 + ], + "spans": [ + { + "bbox": [ + 375, + 70, + 509, + 159 + ], + "type": "image", + "image_path": "eeca27ba0bbdcafc5cdb07682ce1d3c3e4705e32369e2edf7111c10cc2779f60.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 86, + 167, + 219, + 257 + ], + "blocks": [ + { + "bbox": [ + 86, + 167, + 219, + 257 + ], + "lines": [ + { + "bbox": [ + 86, + 167, + 219, + 257 + ], + "spans": [ + { + "bbox": [ + 86, + 167, + 219, + 257 + ], + "type": "image", + "image_path": "5f30182207199252dd477699781aefbdfd9dd204b8448aae506529b191a5b2a2.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 138, + 258, + 165, + 266 + ], + "lines": [ + { + "bbox": [ + 138, + 258, + 165, + 266 + ], + "spans": [ + { + "bbox": [ + 138, + 258, + 165, + 266 + ], + "type": "text", + "content": "ADM-G" + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "type": "image", + "bbox": [ + 230, + 167, + 364, + 257 + ], + "blocks": [ + { + "bbox": [ + 230, + 167, + 364, + 257 + ], + "lines": [ + { + "bbox": [ + 230, + 167, + 364, + 257 + ], + "spans": [ + { + "bbox": [ + 230, + 167, + 364, + 257 + ], + "type": "image", + "image_path": "1fcd867034e108e61787fe6e43395c1d09c2d80efba015f61fce5a3aab48c058.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 288, + 258, + 306, + 266 + ], + "lines": [ + { + "bbox": [ + 288, + 258, + 306, + 266 + ], + "spans": [ + { + "bbox": [ + 288, + 258, + 306, + 266 + ], + "type": "text", + "content": "MDT" + } + ] + } + ], + "index": 6, + "angle": 0, + "type": "image_caption" + }, + { + "bbox": [ + 46, + 270, + 547, + 293 + ], + "lines": [ + { + "bbox": [ + 46, + 270, + 547, + 293 + ], + "spans": [ + { + "bbox": [ + 46, + 270, + 547, + 293 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison with ADM-G [12] and previous SOTA method MDT [14]. Our SADM can synthesize more realistic and high-quality samples while maintaining satisfying diversity." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_caption" + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 375, + 167, + 508, + 257 + ], + "blocks": [ + { + "bbox": [ + 375, + 167, + 508, + 257 + ], + "lines": [ + { + "bbox": [ + 375, + 167, + 508, + 257 + ], + "spans": [ + { + "bbox": [ + 375, + 167, + 508, + 257 + ], + "type": "image", + "image_path": "4a71bcc15a34f599226a49cc344f0b4c7990e3924fd3f3b0cadbedced3ee202d.jpg" + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 419, + 258, + 467, + 267 + ], + "lines": [ + { + "bbox": [ + 419, + 258, + 467, + 267 + ], + "spans": [ + { + "bbox": [ + 419, + 258, + 467, + 267 + ], + "type": "text", + "content": "SADM (Ours)" + } + ] + } + ], + "index": 8, + "angle": 0, + "type": "image_caption" + } + ], + "index": 7 + }, + { + "type": "table", + "bbox": [ + 48, + 325, + 294, + 453 + ], + "blocks": [ + { + "bbox": [ + 68, + 308, + 265, + 319 + ], + "lines": [ + { + "bbox": [ + 68, + 308, + 265, + 319 + ], + "spans": [ + { + "bbox": [ + 68, + 308, + 265, + 319 + ], + "type": "text", + "content": "Table 3. FID performance on CelebA/FFHQ " + }, + { + "bbox": [ + 68, + 308, + 265, + 319 + ], + "type": "inline_equation", + "content": "{64} \\times {64}" + }, + { + "bbox": [ + 68, + 308, + 265, + 319 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 48, + 325, + 294, + 453 + ], + "lines": [ + { + "bbox": [ + 48, + 325, + 294, + 453 + ], + "spans": [ + { + "bbox": [ + 48, + 325, + 294, + 453 + ], + "type": "table", + "html": "
ModelDiffusion SpaceNFE↓CelebAFFHQ
DDPM++ [59]Data1312.32-
Soft Truncation [30]Data1311.90-
Soft Diffusion [9]Data3001.85-
INDM [29]Latent1321.75-
EDM [27]Data79-2.39
Soft Truncation-G++ [28]Data1311.34-
EDM-G++ [28]Data71-1.98
SADMLatent1311.281.85
SADMData711.161.71
", + "image_path": "5dfad3e60131faa8305f271dc4ed69616f193054b49df96070857e4942109cc1.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "table_body" + } + ], + "index": 11 + }, + { + "bbox": [ + 46, + 468, + 288, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 288, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 288, + 575 + ], + "type": "text", + "content": "rameters as EDM and LSGM to evaluate the effectiveness of our proposed training algorithm. And we also achieve significant performance improvement on facial datasets as demonstrated in Tab. 3. For qualitative results, we compare our SADM with ADM-G [12] and previous SOTA method MDT [14] in Fig. 4. These remarkable results demonstrate our SADM has the potential for generalizing to arbitrary diffusion architectures and can better learn the whole data distribution." + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 47, + 586, + 198, + 600 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 586, + 198, + 600 + ], + "spans": [ + { + "bbox": [ + 47, + 586, + 198, + 600 + ], + "type": "text", + "content": "5.2. Cross-Domain Fine-Tuning" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 605, + 289, + 715 + ], + "type": "text", + "content": "Experiment Setup We conduct cross-domain fine-tuning tasks on diffusion image generation for evaluating the transferability of proposed model, where we pre-train a diffusion model in source domain and adapt it to a target domain by fine-tuning. Following Xie et al. [70], we use ImageNet as source dataset, and choose eight commonly-used fine-grained datasets as target datasets: Food101 [1], SUN397 [68], DF-20M mini [48], Caltech101 [16], CUB-200-2011 [65], ArtBench-10 [40], Oxford Flowers [45] and Stanford" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 309, + 539, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 309, + 539, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 309, + 539, + 322 + ], + "type": "text", + "content": "Cars [34]. More details about datasets are in Appendix A." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 304, + 341, + 548, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 341, + 548, + 496 + ], + "spans": [ + { + "bbox": [ + 304, + 341, + 548, + 496 + ], + "type": "text", + "content": "Implementation Details For fair comparison, we follow Xie et al. [70] to set all the hyper-parameters in both pretraining and fine-tuning stages, and use Diffusion Transformer (DiT) [47] as the diffusion backbone. We pretrain DiT on ImageNet " + }, + { + "bbox": [ + 304, + 341, + 548, + 496 + ], + "type": "inline_equation", + "content": "256 \\times 256" + }, + { + "bbox": [ + 304, + 341, + 548, + 496 + ], + "type": "text", + "content": " with a learning rate of 0.0001 using DDPM objective. For target datasets, we fine-tune the pre-trained DiT with 24k structure-guide training steps and 4k adversarial training steps. We experiment with two fine-tuning settings, full and parameter-efficient, for comprehensive evaluations. In parameter-efficient setting, following Xie et al. [70], we freeze most of parameters in the pre-trained diffusion model and fine-tune the bias term, normalization, and class condition module." + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 516, + 548, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 516, + 548, + 649 + ], + "spans": [ + { + "bbox": [ + 304, + 516, + 548, + 649 + ], + "type": "text", + "content": "Main Results We achieve SOTA performance on all datasets in fine-tuning tasks as illustrated in Tab. 4. Remarkably, we significantly surpass DDPM in full fine-tuning and outperform DiffFit in parameter-efficient fine-tuning. The results sufficiently demonstrate our superior capability of capturing the whole data distribution, which enables better adaptation to new domains. Among all datasets, we achieve the best improvement over other methods on ArtBench-10 which has distinct distribution from ImageNet, demonstrating the out-of-distribution generalization ability of our SADM. More qualitative results are in Appendix C." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 306, + 658, + 401, + 671 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 658, + 401, + 671 + ], + "spans": [ + { + "bbox": [ + 306, + 658, + 401, + 671 + ], + "type": "text", + "content": "5.3. Model Analysis" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 547, + 715 + ], + "type": "text", + "content": "Heatmap Analysis To evaluate the ability to capture data distribution, we perform heatmap analysis in Fig. 5, where we provide DDPM and our SADM with 8 randomly-selected" + } + ] + } + ], + "index": 19 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 748, + 315, + 757 + ], + "type": "text", + "content": "7262" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 64, + 91, + 526, + 218 + ], + "blocks": [ + { + "bbox": [ + 79, + 70, + 512, + 83 + ], + "lines": [ + { + "bbox": [ + 79, + 70, + 512, + 83 + ], + "spans": [ + { + "bbox": [ + 79, + 70, + 512, + 83 + ], + "type": "text", + "content": "Table 4. FID performance comparisons on 8 downstream datasets, all the models are pretrained on ImageNet " + }, + { + "bbox": [ + 79, + 70, + 512, + 83 + ], + "type": "inline_equation", + "content": "{256} \\times {256}" + }, + { + "bbox": [ + 79, + 70, + 512, + 83 + ], + "type": "text", + "content": " ." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 64, + 91, + 526, + 218 + ], + "lines": [ + { + "bbox": [ + 64, + 91, + 526, + 218 + ], + "spans": [ + { + "bbox": [ + 64, + 91, + 526, + 218 + ], + "type": "table", + "html": "
Dataset MethodFoodSUNDF-20MCaltechCUB-BirdArtBenchOxford FlowersStandard CarsAverage FID
AdaptFormer [5]13.6711.4722.3835.767.7338.4321.2410.7320.17
BitFit [77]9.179.1117.7834.218.8124.5320.3110.6416.82
VPT [25]18.4714.5432.8942.7817.2940.7425.5922.1226.80
LoRA [23]33.7532.53120.2586.0556.0380.99164.1376.2481.25
DiffFit [70]6.968.5517.3533.845.4820.8720.189.9015.39
Full Fine-tuning with DDPM10.467.9617.2635.255.6825.3121.059.7916.59
SADM (parameter-efficient)5.747.9216.5832.035.0418.2319.379.2614.27
SADM (full)6.207.3515.1232.864.6919.8418.188.9314.15
", + "image_path": "9caaf40884ffb692bfc7329ee15210a9a0dc0e85951b590a6476d107b55e52cb.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 232, + 290, + 304 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 232, + 290, + 304 + ], + "spans": [ + { + "bbox": [ + 46, + 232, + 290, + 304 + ], + "type": "text", + "content": "noisy images in test batch and visualize the correlations between their denoised outputs. We observe that compared to DDPM, the overall heatmap pattern of our SADM is more closer to that of label affinity. The phenomenon demonstrates our SADM can precisely learn the manifold structures within real data samples." + } + ] + } + ], + "index": 2 + }, + { + "type": "image", + "bbox": [ + 50, + 305, + 284, + 506 + ], + "blocks": [ + { + "bbox": [ + 50, + 305, + 284, + 506 + ], + "lines": [ + { + "bbox": [ + 50, + 305, + 284, + 506 + ], + "spans": [ + { + "bbox": [ + 50, + 305, + 284, + 506 + ], + "type": "image", + "image_path": "75fe677ff2742e4bab0a292bcd160c917009458342bcf4aa5eca451e666ce36e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 61, + 514, + 272, + 526 + ], + "lines": [ + { + "bbox": [ + 61, + 514, + 272, + 526 + ], + "spans": [ + { + "bbox": [ + 61, + 514, + 272, + 526 + ], + "type": "text", + "content": "Figure 5. Heatmap visualization with 8 denoised samples." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "image_caption" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 529, + 289, + 649 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 529, + 289, + 649 + ], + "spans": [ + { + "bbox": [ + 46, + 529, + 289, + 649 + ], + "type": "text", + "content": "Ablation Study We conduct ablation study to validate the effectiveness of our algorithm in Tab. 5. Here, we base on DDPM [20] architecture, and progressively add our model components (structural guidance and structure discriminator) into it for evaluating FID score on three datasets. We observe that each component can consistently improve the DDPM on all datasets, and the performance improvement of our structural guidance is more significant. The results fully demonstrate the effectiveness of our algorithm. More ablation studies about our model are in Appendix B." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 289, + 715 + ], + "type": "text", + "content": "Contributing to Better Convergence To investigate the contribution of our structure-guided training to model convergence, we plot the training curve in Fig. 6. We conclude that compared to previous SOTA methods DiT [47] and MDT" + } + ] + } + ], + "index": 6 + }, + { + "type": "table", + "bbox": [ + 315, + 256, + 533, + 323 + ], + "blocks": [ + { + "bbox": [ + 305, + 230, + 547, + 253 + ], + "lines": [ + { + "bbox": [ + 305, + 230, + 547, + 253 + ], + "spans": [ + { + "bbox": [ + 305, + 230, + 547, + 253 + ], + "type": "text", + "content": "Table 5. Ablation study with FID performance. SG denotes structural guidance, SAT denotes SG+Structure Discriminator." + } + ] + } + ], + "index": 7, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 315, + 256, + 533, + 323 + ], + "lines": [ + { + "bbox": [ + 315, + 256, + 533, + 323 + ], + "spans": [ + { + "bbox": [ + 315, + 256, + 533, + 323 + ], + "type": "table", + "html": "
Model \nDatasetDDPM+ Our SG+ Our SAT
ImageNet4.593.573.14
CIFAR-103.172.642.33
CelebA2.321.821.64
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Comparison with SOTA methods on model convergence." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 521, + 379, + 533 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 521, + 379, + 533 + ], + "spans": [ + { + "bbox": [ + 306, + 521, + 379, + 533 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 541, + 547, + 662 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 541, + 547, + 662 + ], + "spans": [ + { + "bbox": [ + 304, + 541, + 547, + 662 + ], + "type": "text", + "content": "We propose structure-guided adversarial training for optimizing diffusion models from a structural perspective. The proposed training algorithm can easily generalize to both image and latent diffusion models, and consistently improve existing diffusion models with theoretical derivations and empirical results. We achieve new SOTA performance on image generation and cross-domain fine-tuning tasks across 12 image datasets. 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Realcompo: Dynamic equilibrium between realism and compositionality improves text-to-image diffusion models. arXiv preprint arXiv:2402.12908, 2024. 1" + } + ] + } + ], + "index": 18 + } + ], + "sub_type": "ref_text" + } + ], + "discarded_blocks": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "spans": [ + { + "bbox": [ + 295, + 749, + 315, + 757 + ], + "type": "text", + "content": "7266" + } + ] + } + ], + "index": 20 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 10 + } + ], + "_backend": "vlm", + "_version_name": "2.6.4" +} \ No newline at end of file diff --git a/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/25726c0b-b33a-4e50-8b53-f013deb7f334_content_list.json b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/25726c0b-b33a-4e50-8b53-f013deb7f334_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..ec4b92aa9696f7d8af5306de692aa731c3d18251 --- /dev/null +++ b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/25726c0b-b33a-4e50-8b53-f013deb7f334_content_list.json @@ -0,0 +1,1632 @@ +[ + { + "type": "text", + "text": "Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training", + "text_level": 1, + "bbox": [ + 250, + 130, + 722, + 176 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Shizhan Gong, Qi Dou, Farzan Farnia \nThe Chinese University of Hong Kong", + "bbox": [ + 331, + 203, + 637, + 239 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "{szgong22, qdou, farnia}@cse.cuhk.edu.hk", + "bbox": [ + 308, + 241, + 661, + 255 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract", + "text_level": 1, + "bbox": [ + 233, + 291, + 313, + 306 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Gradient-based saliency maps have been widely used to explain the decisions of deep neural network classifiers. However, standard gradient-based interpretation maps, including the simple gradient and integrated gradient algorithms, often lack desired structures such as sparsity and connectedness in their application to real-world computer vision models. A frequently used approach to inducing sparsity structures into gradient-based saliency maps is to alter the simple gradient scheme using sparsification or norm-based regularization. A drawback with such post-processing methods is their frequently-observed significant loss in fidelity to the original simple gradient map. In this work, we propose to apply adversarial training as an in-processing scheme to train neural networks with structured simple gradient maps. We show a duality relation between the regularized norms of the adversarial perturbations and gradient-based maps, based on which we design adversarial training loss functions promoting sparsity and group-sparsity properties in simple gradient maps. We present several numerical results to show the influence of our proposed norm-based adversarial training methods on the standard gradient-based maps of standard neural network architectures on benchmark image datasets1.", + "bbox": [ + 75, + 323, + 473, + 672 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Introduction", + "text_level": 1, + "bbox": [ + 76, + 700, + 209, + 715 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Deep neural networks have attained remarkable results in various computer vision tasks including image classification [17], object detection [44], and semantic segmentation [10]. However, understanding and explaining the decision-making process of these complex models remains a challenge, which is required for high-risk applications such as medical imaging [27], autonomous driving [16], and face recognition [37]. To interpret the predictions of neural network classifiers, several explanation methodolo", + "bbox": [ + 75, + 727, + 468, + 863 + ], + "page_idx": 0 + }, + { + "type": "image", + "img_path": "images/f3981a5d6a987fccd9bb558f7f9e7bb8f913b9937e3f65296b796d98e9c809cf.jpg", + "image_caption": [ + "Figure 1. The original simple gradient map could be dense and noisy. Post-processing methods such as sparsification enhance the sparsity at the expense of lower fidelity to the original map. Our proposed in-processing strategy with adversarial training results in higher sparsity without losing fidelity to the simple-grad map. (We use the Gini index as a sparsity measure, and relative $\\mathrm{AOPC}_{\\mathrm{MoRF}}$ with respect to simple gradient as a fidelity score.)" + ], + "image_footnote": [], + "bbox": [ + 504, + 292, + 888, + 515 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "gies have been proposed in the literature. Among these explanation methods, gradient-based saliency maps have been frequently applied to interpret image classifiers. The saliency maps provide insight into the regions of the input image contributing to the classifier's decision and potentially prompt the empirical understanding of phenomena from data-driven models.", + "bbox": [ + 496, + 642, + 893, + 746 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Despite the widespread use of standard gradient-based interpretation maps such as simple gradients [29] and integrated gradients [32], they often lack desired structures such as sparsity and connectedness. When applied to real-world computer vision tasks, the generated saliency maps have been frequently observed to be noisy and dense. Such unstructured behavior could hinder the application of gradient-based maps for detecting the influential features in the classifier's decision-making process. To obtain more structured saliency maps, several post-processing", + "bbox": [ + 496, + 750, + 893, + 902 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "CVF", + "bbox": [ + 106, + 2, + 181, + 42 + ], + "page_idx": 0 + }, + { + "type": "header", + "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.", + "bbox": [ + 236, + 0, + 807, + 46 + ], + "page_idx": 0 + }, + { + "type": "page_footnote", + "text": "The paper's code is available at: https://github.com/peterant330/AdvGrad", + "bbox": [ + 76, + 875, + 467, + 900 + ], + "page_idx": 0 + }, + { + "type": "page_number", + "text": "11009", + "bbox": [ + 480, + 944, + 519, + 957 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "schemes [18, 30, 31, 42, 43] have been proposed in the literature, which denoise the saliency map to gain higher sparsity. However, a drawback of these post-processing methods is the deviation from the original simple gradient map that alters the definition of the interpretation map. For example, Adebayo et al. [1] conducted a sanity check and found several interpretation methods such as Guided Propagation and Integrated Gradients lacked sensitivity to the model or the data-generating process. Arun et al. [2] demonstrated similar findings on medical imaging applications. To illustrate the fidelity vs. sparsity trade-off in such post-processing schemes, we display an example in Fig. 1, where the simple gradient map looks to contain significant noise scattered over the background. A post-processing sparsification of the gradient map could raise the sparsity of the map; however, the sparsity comes at the cost of a considerable drop (more than $82\\%$ ) in the fidelity score.", + "bbox": [ + 75, + 90, + 472, + 348 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "In this work, we propose a unified adversarial training (AT) framework to address the unstructured nature of standard simple-gradient maps, where we apply a norm-regularized adversarial training with a properly-designed norm function as an in-processing scheme to promote the sparsity structures in the simple gradient map. AT with standard $L_{2}$ and $L_{\\infty}$ -norm perturbations [19] has been successfully and widely utilized in the literature to enhance the adversarial robustness [33] and interpretability [26] of deep neural networks. In our analysis, we extend the understanding of the influence of AT algorithms on the interpretability of a trained model, where we provide a convex duality framework to understand the influence of the norm function constrained in AT on the regularized norm of gradient maps and hence the interpretability of neural nets.", + "bbox": [ + 75, + 351, + 472, + 577 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Specifically, we show a duality relation between the regularized norm of adversarial perturbations and the norm of input-based gradients. This duality relationship allows us to design norm-regularized adversarial training methods, which translates into the regularization of standard sparsity-inducing norms, e.g. the group norm [41] and the elastic net [45], of the simple gradient maps. As we show in this work, the special cases of our proposed framework can promote desired characteristics such as sparsity and connectedness in simple gradient maps. Importantly, unlike the sparsity-regularizing post-processing schemes, the gained sparsity properties of our proposed AT methods do not cost any loss in fidelity to the simple-gradient map, because we do not alter the definition of the interpretation map and only regularize the training process toward networks with more structured gradient maps.", + "bbox": [ + 75, + 580, + 472, + 823 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We conduct several numerical experiments on benchmark image datasets to validate the efficacy of our proposed AT-based methodology. The numerical results reveal the impact of our proposed norm-based AT methods on standard gradient-based maps, showing the enhanced spar", + "bbox": [ + 75, + 824, + 472, + 902 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "sity and connectedness properties. We empirically analyze the performance of the trained neural nets in terms of several factors including interpretability, robustness, and stability. Our numerical results indicate the improvements in the mentioned structure-related factors offered by our designed norm-regularized AT methods. Finally, we utilize the shown duality relation to propose an interpretation harmonization scheme for aligning simple gradient maps with expert gaze maps, which performs satisfactorily in our numerical experiments. Our work's main contributions can be summarized as:", + "bbox": [ + 496, + 90, + 893, + 256 + ], + "page_idx": 1 + }, + { + "type": "list", + "sub_type": "text", + "list_items": [ + "- We show a duality relation between the regularized norms of adversarial perturbations and gradient maps, and develop a unified AT framework for regularizing gradient maps.", + "- We derive special cases of our proposed AT-based framework leading to the regularization of the elastic net and group-norm of gradient map.", + "- We leverage the duality framework to propose an interpretation harmonization scheme for aligning gradient maps with human attention.", + "- We provide numerical results showing the efficacy of the AT-based framework in improving the sparsity and stability of interpretation maps." + ], + "bbox": [ + 500, + 258, + 890, + 455 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2. Related Work", + "text_level": 1, + "bbox": [ + 500, + 467, + 640, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Gradient-based Interpretation. Using the gradient of the output of a deep neural network w.r.t. an input image is a widely-used approach to generate saliency maps [29]. This method has been utilized in several related works and multiple variants of this approach are proposed in the literature, including SmoothGrad [30], Integrated Gradients [32], DeepLIFT [28], and GradCAM [24]. The vanilla gradient-based maps without post-processing are often noisy and difficult to interpret. A group of methods are proposed to improve the visual quality by sparsifying the gradient-based maps: Guided Propagation [31] removes the noise artifacts from saliency maps by suppressing negative activations in the back-propagation. Sparsified-SmoothGrad [18] applies a sparsification to the saliency map to promote sparsity and robustness. MoreauGrad [43] generates saliency maps using an optimization problem with sparsity regularization. One drawback of the discussed methods is that they are all post-processing schemes, which may compromise the fidelity to the original simple-gradient map. On the other hand, our proposed framework is an in-processing scheme that remains faithful to the simple gradient map.", + "bbox": [ + 496, + 492, + 890, + 809 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Adversarial Training and Interpretability. Adversarial training (AT) involves training the networks using adversarial examples [19]. Fast Gradient Sign Method (FGSM) [9] generates adversarial samples using a single iteration to create the adversarial training example for training the classifier. Projected gradient descent (PGD) [19] uses several", + "bbox": [ + 496, + 810, + 893, + 901 + ], + "page_idx": 1 + }, + { + "type": "page_number", + "text": "11010", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "gradient-based steps to generate more effective adversarial examples in order to make the trained model more robust to norm-constrained adversarial attacks. While the primary objective of AT is to improve the trained model's robustness against adversarial attacks, several studies have shown that AT can also improve the visual quality of interpretation maps [15, 22, 26]. Specifically, AT has been empirically shown to suppress irrelevant features [14], and the standard $\\ell_{\\infty}$ -norm-based AT will lead to higher sparsity and stability of the interpretation maps [3]. Building upon and extending these findings, our work provides a unified duality framework that connects the perturbation norm constrained by the AT algorithm and the norm penalized for the interpretation map. Specifically, we discuss novel variants of AT methods that lead to the regularization of the elastic net and group norms of the interpretation maps which have not been studied in these related works.", + "bbox": [ + 75, + 90, + 472, + 349 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. Preliminaries", + "text_level": 1, + "bbox": [ + 76, + 359, + 217, + 376 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1. Gradient-based Saliency Maps", + "text_level": 1, + "bbox": [ + 76, + 383, + 349, + 401 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Throughout this work, our analysis mainly focuses on the standard simple gradient as the gradient-based interpretation. We use $\\mathbf{x} \\in \\mathbb{R}^d$ and $\\mathbf{y} \\in \\mathbb{R}^C$ to denote the input and output of the neural network classifier. Note that $\\mathbf{y}$ denotes the output of the neural net's post-softmax layer and contains the assigned likelihood for each of the $C$ classes in the classification task. The neural net function $f_{\\theta}: \\mathbb{R}^{d} \\to \\mathbb{R}^{C}$ maps the input vector to the output vector, where $\\theta$ denotes the parameters of the neural net. The simple gradient generates a saliency map by taking derivatives of the output of the neural network with respect to the input:", + "bbox": [ + 75, + 407, + 472, + 575 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\operatorname {S G} \\left(f _ {\\theta , c}, \\mathbf {x}\\right) := \\nabla_ {\\mathbf {x}} f _ {\\theta , c} (\\mathbf {x}).\n$$\n", + "text_format": "latex", + "bbox": [ + 179, + 583, + 364, + 599 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Here, $c$ can be chosen as ground-truth label $y$ or the label $c$ with the maximum likelihood assigned by the classifier. In our analysis, we assume $\\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})$ denotes the saliency map corresponding to the ground-truth label of sample $\\mathbf{x}$ .", + "bbox": [ + 75, + 608, + 470, + 671 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.2. FGSM and PGD", + "text_level": 1, + "bbox": [ + 76, + 676, + 243, + 691 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We consider two of the most widely used forms of adversarial training, FGSM and PGD, in this work. These methods first generate adversarial samples by calculating the gradient of the loss function with respect to the input data and then perturb the data by taking one or multiple small steps in the direction of the sign of the gradient. The perturbation is usually bounded by $l_{\\infty}$ -norm. The parameters of the network are then updated to minimize the loss with respect to these adversarial samples. We can use the following objective to summarize the optimization problem where $\\hat{P}$ is the empirical distribution of training samples", + "bbox": [ + 75, + 700, + 468, + 867 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {(\\mathbf {x}, y) \\sim \\widehat {P}} \\left[ \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x} + \\delta), y\\right) \\right]. \\tag {1}\n$$\n", + "text_format": "latex", + "bbox": [ + 130, + 875, + 468, + 902 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/9d5e163c1d6242813230ece938e65c84667121ef21bdde53df0107545e7ee40c.jpg", + "table_caption": [ + "Table 1. Summary of regularized norm $h$ on perturbation $\\delta$ and the resulting regularized function ${h}^{\\star }$ of the input gradient ${\\nabla }_{\\mathbf{x}}\\mathcal{L}\\left( {{f}_{\\theta }\\left( \\mathbf{x}\\right) ,y}\\right)$ . Detailed description can be found in Section 4.3." + ], + "table_footnote": [], + "table_body": "
h(δ)h*(∇xL(fθ(x),y))
I(||δ||∞ ≤ ε)ε||∇xL(fθ(x),y)||1
I(||δ||2,∞ ≤ ε)ε||∇xL(fθ(x),y)||2,1
∑iPQε1,ε2(δi)ε1||∇xL(fθ(x),y)||1 + ε2||∇xL(fθ(x),y)||2
1/4ε||W ⊙ δ||2ε||W ⊙ ∇xL(fθ(x),y)||2
", + "bbox": [ + 501, + 138, + 893, + 250 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "FGSM generates adversarial samples by taking one step in the direction of the sign of the gradient:", + "bbox": [ + 498, + 267, + 893, + 297 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {\\mathrm {F G S M}} ^ {*} = \\mathbf {x} + \\epsilon \\cdot \\operatorname {s i g n} \\left(\\nabla_ {\\mathbf {x}} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x}), y\\right)\\right)\n$$\n", + "text_format": "latex", + "bbox": [ + 560, + 304, + 830, + 321 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "PGD, on the other hand, iteratively updates the samples with a stepsize $\\alpha$ :", + "bbox": [ + 498, + 328, + 890, + 359 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\n\\mathbf {x} _ {t + 1} = \\Pi_ {\\mathbf {x} + S} \\big (\\mathbf {x} _ {t} + \\alpha \\mathrm {s i g n} (\\nabla_ {\\mathbf {x} _ {t}} \\mathcal {L} (f _ {\\theta} (\\mathbf {x} _ {t}), y)) \\big),\n$$\n", + "text_format": "latex", + "bbox": [ + 535, + 364, + 854, + 383 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $S = \\{\\mathbf{z}:\\| \\mathbf{z}\\|_{\\infty}\\leq \\epsilon \\}$ denotes the $\\epsilon$ -radius $L_{\\infty}$ -ball.", + "bbox": [ + 498, + 388, + 885, + 406 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.3. Fenchel Conjugate", + "text_level": 1, + "bbox": [ + 500, + 412, + 681, + 429 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "The Fenchel conjugate is an essential operation in convex analysis which has many applications to various computer vision algorithms. For a function $f: \\mathcal{X} \\to \\mathbb{R}$ , its Fenchel conjugate $f^{\\star}: \\mathcal{X} \\to \\mathbb{R}$ is defined as:", + "bbox": [ + 498, + 436, + 893, + 496 + ], + "page_idx": 2 + }, + { + "type": "equation", + "text": "\n$$\nf ^ {\\star} (z) = \\sup \\left\\{\\langle x, z \\rangle - f (x): x \\in \\mathcal {X} \\right\\},\n$$\n", + "text_format": "latex", + "bbox": [ + 565, + 503, + 825, + 522 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\langle \\cdot ,\\cdot \\rangle$ denotes the inner product, and sup represents the supremum. Note that for a convex $f$ $f$ will be the Fenchel conjugate of $f^{\\star}$ . Furthermore, for every function $f$ , the Fenchel conjugate $f^{\\star}$ is guaranteed to be convex.", + "bbox": [ + 498, + 527, + 890, + 589 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. An Adversarial Training Methodology for Regularizing Interpretation Maps", + "text_level": 1, + "bbox": [ + 498, + 599, + 890, + 635 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "In this section, we show a duality relation between the input gradient and the perturbation vectors, which is based on the linear approximation of the loss function $\\ell\\big(f(\\mathbf{x} + \\delta),y\\big)$ around data point $\\mathbf{x}$ . In the approximation, the first-order term $\\langle \\nabla_{\\mathbf{x}}\\ell \\big(f(\\mathbf{x}),y\\big),\\delta \\rangle$ is the inner product of the perturbation vector and the input-based gradient of the loss function. Therefore, as will be explained in the section, to penalize a norm of the saliency map in the adversarial training process, we propose to constrain the dual norm of the perturbation vector. We summarize three variants of the norm constraint on the perturbation and its effect on the simple gradient saliency maps in Table 1.", + "bbox": [ + 496, + 642, + 890, + 825 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4.1. Rethinking the Impact of $\\ell_{\\infty}$ -Norm-Based Adversarial Training on Saliency Maps", + "text_level": 1, + "bbox": [ + 498, + 830, + 890, + 863 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We perform a first-order analysis by means of Fenchel conjugate to indicate how $L_{\\infty}$ -norm-based adversarial training", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 2 + }, + { + "type": "page_number", + "text": "11011", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "could lead to higher sparsity in gradient-based maps. Under a small enough perturbation norm bound $\\epsilon$ and twice-differentiable loss function, the objective of adversarial training in Eq. 1 can be approximated by first-order Taylor expansion as", + "bbox": [ + 75, + 90, + 468, + 167 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {E q.} 1 = \\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\hat {P}} \\left[ \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x}), y\\right) \\right. \\\\ + \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} \\left\\{\\delta^ {T} \\nabla_ {\\mathbf {x}} \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) \\right\\} \\biggr ] + \\mathcal {O} (\\epsilon^ {2}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 84, + 172, + 459, + 232 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Using the common cross-entropy loss or hinge loss, the derivative of the loss with respect to the predicted log-its at every training sample will be $\\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta},(\\mathbf{x}),y) = -f_{\\theta ,y}(\\mathbf{x})\\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})$ , so we can build the connection between the objective and the saliency map:", + "bbox": [ + 76, + 238, + 468, + 315 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\operatorname {E q.} 1 = \\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\hat {P}} \\left[ \\mathcal {L} \\left(f _ {\\theta , y} (\\mathbf {x})\\right) \\right. \\\\ \\left. + f _ {\\theta , y} (\\mathbf {x}) \\max _ {| | \\delta | | _ {\\infty} \\leq \\epsilon} \\left\\{- \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) \\right\\} \\right] + \\mathcal {O} (\\epsilon^ {2}). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 78, + 321, + 464, + 380 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Note we can leverage Fenchel conjugate operation to transform the maximization subproblem in the above problem into an unconstrained optimization:", + "bbox": [ + 76, + 386, + 468, + 431 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} - \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) = \\max _ {\\delta} - \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) - \\mathbb {I} (\\| \\delta \\| _ {\\infty} \\leq \\epsilon), \\tag {2}\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 436, + 470, + 476 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "where $\\mathbb{I}(\\mathrm{condition}) = 0$ if the condition holds and $+\\infty$ otherwise. With the concept of Fenchel conjugate, the optimal value of the optimization problem defined in Eq. 2 is $\\epsilon \\| \\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})\\| _1$ . Hence, we successfully transform the original minimax optimization problem into a regularized optimization within an approximation error $\\mathcal{O}(\\epsilon^2)$ :", + "bbox": [ + 76, + 477, + 468, + 568 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\mathrm {E q .} 1 \\approx \\underset {\\theta} {\\min } \\mathbb {E} _ {\\mathbf {x}, y \\sim \\widehat {P}} \\Big [ \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + \\epsilon f _ {\\theta , y} (\\mathbf {x}) \\| \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) \\| _ {1} \\Big ].\n$$\n", + "text_format": "latex", + "bbox": [ + 76, + 575, + 468, + 602 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Hence, we find that adversarial training with $L_{\\infty}$ -norm is approximately equivalent to applying $L_{1}$ -norm regularization to the simple gradient saliency map, therefore promoting the sparsity of the saliency maps.", + "bbox": [ + 76, + 608, + 468, + 667 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.2. Adversarial Training with Fenchel Conjugate Regularization: a Unified Approach", + "text_level": 1, + "bbox": [ + 76, + 676, + 468, + 708 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Next, we consider adversarial training with a general norm-based regularization penalty. Here our goal is to promote a structured saliency map through a regularization function $h^{\\star}(\\mathbf{z})$ . Note that for a convex $h$ , the Fenchel conjugate of $h^{\\star}(\\mathbf{z})$ will be $h(\\mathbf{x})$ . Therefore, we consider the min-max optimization with the adversarial penalty function $-h(\\delta)$ :", + "bbox": [ + 76, + 714, + 468, + 806 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\widehat {P}} \\left[ \\max _ {\\delta} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x} + \\delta), y\\right) - h (\\delta) \\right].\n$$\n", + "text_format": "latex", + "bbox": [ + 122, + 813, + 421, + 840 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Following our analysis for the $L_{\\infty}$ -norm-based adversarial training, we define the first-order approximate loss:", + "bbox": [ + 76, + 845, + 468, + 876 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\widehat {\\mathcal {L}} (f _ {\\theta} (\\mathbf {x}), y, \\delta) := \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + \\delta^ {T} \\nabla_ {x} \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y),\n$$\n", + "text_format": "latex", + "bbox": [ + 99, + 882, + 444, + 902 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To measure how well $\\widehat{\\mathcal{L}}(f_{\\theta}(\\mathbf{x}), y, \\delta)$ approximates the adversarial loss, we observe the approximation error can be simply bounded for the class of $\\lambda$ -smooth functions.", + "bbox": [ + 498, + 90, + 890, + 136 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Definition 1 We call $g: \\mathbb{R}^d \\to \\mathbb{R}$ a smooth if for every $\\mathbf{x}$ and $\\mathbf{z}$ : $\\| \\nabla g(\\mathbf{x}) - \\nabla g(\\mathbf{z}) \\|_2 \\leq \\lambda \\| \\mathbf{x} - \\mathbf{z} \\|_2$ .", + "bbox": [ + 498, + 148, + 890, + 180 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Observation 1 The approximation error of the first-order Taylor series expansion of adversarial loss under an $\\epsilon$ - $L_2$ -norm bounded perturbation $\\|\\delta\\| \\leq \\epsilon$ can be bounded as", + "bbox": [ + 498, + 195, + 890, + 241 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left| \\widehat {\\mathcal {L}} (f _ {\\theta} (\\mathbf {x}), y, \\delta) - \\mathcal {L} (f _ {\\theta} (\\mathbf {x} + \\delta), y) \\right| \\leq \\frac {\\lambda \\epsilon^ {2}}{2}\n$$\n", + "text_format": "latex", + "bbox": [ + 553, + 253, + 836, + 285 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "The observation shows $\\widehat{\\mathcal{L}}(f_{\\theta}(\\mathbf{x}), y, \\delta)$ can be a good approximation of the adversarial loss under a small $\\|\\delta\\|$ . Combining the approximate loss with $h(\\delta)$ regularization, we can derive the following equivalence by Fenchel conjugate:", + "bbox": [ + 498, + 299, + 890, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 1 Using Fenchel conjugate $h^{\\star}$ , we can reduce the maximization of the approximate adversarial loss as", + "bbox": [ + 498, + 375, + 890, + 404 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\begin{array}{l} \\max _ {\\delta} \\left\\{\\widehat {\\mathcal {L}} \\left(f _ {\\theta} (\\mathbf {x}), y, \\delta\\right) - h (\\delta) \\right\\} \\tag {3} \\\\ = \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + h ^ {\\star} \\bigl (\\nabla_ {\\mathbf {x}} \\mathcal {L} \\bigl (f _ {\\theta} (\\mathbf {x}), y \\bigr) \\bigr). \\\\ \\end{array}\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 416, + 890, + 463 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "In a scenario that the neural network completely fits the training data, we have that $\\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta}(\\mathbf{x}),y) = -f_{\\theta ,y}(\\mathbf{x})\\nabla_{x}f_{\\theta}(\\mathbf{x})\\approx -\\nabla_{x}f_{\\theta}(\\mathbf{x})$ . Therefore, to enforce the gradient map $\\nabla_{x}f_{\\theta}(\\mathbf{x})$ to satisfy a bounded penalty function $h^\\star$ , we can conduct adversarial training with an additive penalty term $-h(\\delta)$ . The optimal perturbation $\\delta^{*}$ can be derived via the standard gradient ascent algorithm to maximize the regularized adversarial loss or be approximated with the analytic solution to the approximate optimization problem.", + "bbox": [ + 498, + 476, + 890, + 626 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "4.3. Special Cases of the Fenchel Conjugate-based Duality Framework", + "text_level": 1, + "bbox": [ + 498, + 638, + 890, + 669 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Leveraging the duality framework in the previous section, we derive regularization penalty terms to penalize other sparsity norms different from $l_{1}$ -norm and discuss their influence on the saliency maps.", + "bbox": [ + 498, + 676, + 890, + 737 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "$L_{2,1}$ -group-norm penalty. The $L_{2,1}$ -group-norm of $\\mathbf{x} \\in \\mathbb{R}^d$ for disjoint variable subsets $S_1, \\dots, S_t \\subseteq \\{1, \\dots, d\\}$ is defined as the special case $p = 1$ of the following definition:", + "bbox": [ + 500, + 739, + 890, + 784 + ], + "page_idx": 3 + }, + { + "type": "equation", + "text": "\n$$\n\\left\\| \\mathbf {x} \\right\\| _ {2, p} := \\left\\| \\left[ \\left\\| \\mathbf {x} _ {S _ {1}} \\right\\| _ {2}, \\dots , \\left\\| \\mathbf {x} _ {S _ {t}} \\right\\| _ {2} \\right] \\right\\| _ {p}.\n$$\n", + "text_format": "latex", + "bbox": [ + 571, + 796, + 818, + 814 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "To apply the duality framework to the group norm (with coefficient $\\epsilon > 0$ ), we derive its Fenchel conjugate as follows.", + "bbox": [ + 498, + 827, + 890, + 857 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Proposition 2 The Fenchel conjugate of the above $L_{2,1}$ -group-norm is $h(\\mathbf{z}) = \\mathbb{I}(\\| \\mathbf{z}\\|_{2,\\infty}\\leq \\epsilon)$ .", + "bbox": [ + 498, + 869, + 890, + 901 + ], + "page_idx": 3 + }, + { + "type": "page_number", + "text": "11012", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Different from $L_{1}$ -norm inducing pixel-level sparsity, $L_{2,1}$ -group-norm will induce sparsity of the patch basis. Under this regularization, the more influential patches are expected to be highlighted in the saliency map. This effect could further lead to a connected saliency map, which will be desired when adjacent pixels belonging have similar effects on the prediction of the classifier.", + "bbox": [ + 76, + 90, + 467, + 195 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Elastic net penalty. The elastic net penalty $h^{\\star}(\\mathbf{x})$ linearly combines the $L_{1}$ and $L_{2}^{2}$ penalty terms:", + "bbox": [ + 76, + 196, + 467, + 227 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nh ^ {\\star} (\\mathbf {x}) = \\epsilon_ {1} \\| \\mathbf {x} \\| _ {1} + \\epsilon_ {2} \\| \\mathbf {x} \\| _ {2} ^ {2}, \\epsilon_ {1} > 0, \\epsilon_ {2} > 0.\n$$\n", + "text_format": "latex", + "bbox": [ + 127, + 234, + 415, + 253 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 3 The Fenchel conjugate of the above elastic net penalty $h^{\\star}$ is $h(\\mathbf{z}) = \\sum_{i} PQ_{\\epsilon_1, \\epsilon_2}(\\mathbf{z}_i)$ where $PQ_{\\epsilon_1, \\epsilon_2}$ is the piece-wise quadratic function defined as:", + "bbox": [ + 76, + 273, + 467, + 319 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nP Q _ {\\epsilon_ {1}, \\epsilon_ {2}} (\\mathbf {z} _ {i}) = \\left\\{ \\begin{array}{c l} \\frac {1}{4 \\epsilon_ {2}} (\\mathbf {z} _ {i} - \\epsilon_ {1}) ^ {2} & \\text {i f} \\epsilon_ {1} < \\mathbf {z} _ {i} \\\\ 0 & \\text {i f} - \\epsilon_ {1} \\leq \\mathbf {z} _ {i} \\leq \\epsilon_ {1} \\\\ \\frac {1}{4 \\epsilon_ {2}} (\\mathbf {z} _ {i} + \\epsilon_ {1}) ^ {2} & \\text {i f} \\mathbf {z} _ {i} < - \\epsilon_ {1}. \\end{array} \\right.\n$$\n", + "text_format": "latex", + "bbox": [ + 94, + 327, + 447, + 385 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The linear combination of the $L_{1}$ -norm and $L_{2}^{2}$ -norm penalty terms in the elastic net results in a strongly convex regularization function, which is known to promote the stability of the sparsity pattern. Therefore, one can expect that the elastic net-regularized maps could possess higher robustness and stability than the $L_{1}$ -norm regularized maps. Interpretation harmonization. The purpose of interpretation harmonization is to align the saliency map generated by the neural network with some reference attention map. The reference attention map can be manually labeled by domain experts, or based on some physical principle behind the classification task. Through interpretation harmonization, the network could be enabled to analyze the phenomenon in a similar way as a human, which would help diminish the potential bias or shortcuts learned by the neural net [6, 7].", + "bbox": [ + 75, + 393, + 467, + 619 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To achieve this goal, we leverage $L_{2}$ -norm regularization to diminish the importance scores of unrelated features. Specifically, assume $\\mathbf{A} \\in \\mathbb{R}^{d}$ is the expert's attention map with non-negative entries. A greater value implies a more important feature. We define $\\hat{\\mathbf{A}} := \\max(\\mathbf{A}) - \\mathbf{A} + \\sigma$ , where $\\sigma$ is small enough so that the ordinal relation is reverted and all elements are positive. To diminish the importance score of the background region, we use the penalty term:", + "bbox": [ + 75, + 619, + 467, + 741 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nh ^ {\\star} (\\mathbf {x}) = \\epsilon \\| \\sqrt {\\tilde {\\mathbf {A}}} \\odot \\mathbf {x} \\| _ {2} ^ {2}, \\epsilon > 0\n$$\n", + "text_format": "latex", + "bbox": [ + 169, + 750, + 372, + 772 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\odot$ denotes Hadamard product. By adding this regularization term, the importance score of unrelated features is pushed to 0 while important features remain unaffected.", + "bbox": [ + 76, + 779, + 467, + 824 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Proposition 4 The Fenchel conjugate of the above weighted $L_{2}$ -norm square regularization is:", + "bbox": [ + 76, + 832, + 467, + 862 + ], + "page_idx": 4 + }, + { + "type": "equation", + "text": "\n$$\nh (\\mathbf {z}) = \\frac {1}{4 \\epsilon} \\left\\| \\frac {1}{\\sqrt {\\tilde {\\mathbf {A}}}} \\odot \\mathbf {z} \\right\\| _ {2} ^ {2}.\n$$\n", + "text_format": "latex", + "bbox": [ + 187, + 869, + 356, + 904 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/1acfe4b86480d4afef7b923b424c20fe1a1770161add98138388d7b1eff50356.jpg", + "image_caption": [ + "Figure 2. Qualitative results based on the synthesized dataset." + ], + "image_footnote": [], + "bbox": [ + 509, + 93, + 883, + 252 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "The derivation requires the weight term $\\tilde{\\mathbf{A}}$ to be positive. However, a positive weight only leads to the diminishing of the importance score of unrelated features. It does not explicitly promote larger scores for important features. Empirically, we have found that using $\\delta^{*}$ in the opposite direction to the gradients for important pixels helps increase the attribution scores for important features and results in better alignment. Therefore, in our numerical experiment, we set $\\tilde{\\mathbf{A}} = \\frac{1}{2}\\max (\\mathbf{A}) - \\mathbf{A}$ and $\\delta^{*} = 2\\epsilon \\tilde{\\mathbf{A}}\\odot \\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta}(\\mathbf{x}),y)$ .", + "bbox": [ + 498, + 291, + 890, + 430 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5. Experiments", + "text_level": 1, + "bbox": [ + 500, + 444, + 632, + 460 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "We conducted comprehensive numerical experiments to evaluate the performance of our proposed adversarial training-based methods. Firstly, we evaluate saliency maps' accuracy on a synthesized dataset with ground truth interpretation. Next, we assessed the visual quality, sparsity, interpretability, robustness, and stability of the saliency maps on Imagenette. Finally, we demonstrated the effectiveness of our interpretation harmonization strategy on the CUB-GHA dataset. Our quantitative results include adversarial training with one normalized step and multi-step gradient ascent. The main text focuses on the results of one normalized step, while detailed training settings and complete numerical results can be found in the Appendix.", + "bbox": [ + 496, + 470, + 890, + 667 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "5.1. Results on synthesized dataset", + "text_level": 1, + "bbox": [ + 500, + 679, + 766, + 695 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "To illustrate how adversarial training can improve the model's interpretability, we first conducted experiments on a synthesized dataset with ground-truth for the saliency maps proposed by [35]. There are three regions on the ground-truth of the synthesized dataset (Fig. 2): background without any classification information (white region); localization information describes the location of an object (light red region); and distinguishing features crucial for classification (dark red area). We trained ResNet-34 [12] with standard training and regularized adversarial training.", + "bbox": [ + 496, + 703, + 890, + 853 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "As the ground-truth was a ternary class, we reported the five-band-score reflects pixel accuracy, recall, precision, and the false positive rate (FPR) based on ternary classifi", + "bbox": [ + 498, + 854, + 890, + 900 + ], + "page_idx": 4 + }, + { + "type": "page_number", + "text": "11013", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/04d79e7cd7c3a81bbf7f379ecbde73e7e72fc13740a89bb166a07edddf5e2d97.jpg", + "table_caption": [ + "Table 2. Comparison of five-band-scores and binary scores of standard training and adversarial training." + ], + "table_footnote": [], + "table_body": "
MethodsFive-band-scoresBinary scores
Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)
standard89.819.8632.581.2188.6644.4716.2210.22
\\( L_1 \\)-norm89.826.4129.200.7694.6065.0630.844.70
group-norm89.847.5427.350.9194.2763.7829.774.99
elastic net89.918.3526.830.9294.6365.6531.294.66
harmonization90.1411.3743.311.1493.8267.0528.155.54
", + "bbox": [ + 127, + 109, + 843, + 210 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/065f3927a0594365ba1f1b5a7cc109567da861a9505e0cabf34ec3dd22ee175d.jpg", + "image_caption": [ + "Figure 3. Images optimized for maximizing class-logit activations." + ], + "image_footnote": [], + "bbox": [ + 84, + 229, + 464, + 348 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "cation. The results are listed in Table 2, where the method's name corresponds to the penalty term $h^{\\star}$ in Eq. 3. The harmonization training achieved the best scores in terms of most of the metrics, showing the effectiveness of the proposed harmonization method. We also noticed that adversarial training-based methods consistently achieved higher accuracy and lower FPR compared with stranded training but led to lower recall and precision, because the adversarial training raised the sparsity of gradient maps. The importance scores of the localization area, which was less important compared with distinguishing features, were also diminished. Therefore, following [11], we also converted the ternary classification task to a binary classification task by considering the background and localization information as one class. The results suggested that adversarial training could significantly improve the accuracy of saliency maps in detecting distinguishing features.", + "bbox": [ + 75, + 382, + 468, + 638 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We visualized the saliency maps in Fig. 2 for qualitative evaluation (we only show results with elastic net regularization here and leave the rest in the Appendix). We discovered that the saliency map of standard training was activated more clearly in the region of the localization information than it was in the region of the distinguishing feature. In contrast, the saliency map with adversarial training was activated more significantly for the distinguishing features, especially on the boundaries. Moreover, the saliency maps looked more sparse and less noisy.", + "bbox": [ + 75, + 638, + 468, + 790 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5.2. Results on ImageNette", + "text_level": 1, + "bbox": [ + 76, + 801, + 285, + 816 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We performed numerical experiments on ImageNette, a ten-class subset of ImageNet [4], to examine the properties of the proposed adversarial training. Specifically, we studied the sparsity, interpretability, adversarial robustness, and stability of the saliency maps generated for EfficientNet [34]", + "bbox": [ + 75, + 825, + 470, + 902 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "classifiers with the proposed adversarial training methods.", + "bbox": [ + 496, + 229, + 883, + 244 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Sparsity. We trained the neural network models with different regularization coefficients and used the Gini Index [13] as a measure of the sparsity of the saliency map. The results are shown in Table 3. All the proposed adversarial training-based methods led to more sparse saliency maps than standard training, with zero or only minor drops in clean accuracy. The $L_{1}$ -norm-based method attained the highest sparsity. Also, the sparsity increased with the regularization coefficient $\\epsilon$ . The gradient maps visualized in Fig. 4 suggest that standard training could lead to miscellaneous points in the background. On the other hand, the gradient maps with our proposed adversarial training methods seem to have higher visual quality.", + "bbox": [ + 496, + 246, + 890, + 443 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Interpretability. To show that the proposed training methods can improve the interpretability of the model, we calculated the DiffROAR score [26] for the methods. DiffROAR measures the difference in the predictive power of the dataset, where the top and bottom $k\\%$ of the pixels are removed according to the importance score. A higher DiffROAR score shows the model captures the task-related features from the inputs. To this end, we measured the DiffROAR score for each method with $k$ from $10\\%$ to $90\\%$ in increments of $10\\%$ . Each measurement was repeated with three different initializations, and the final DiffROAR score was the average of the 27 measurements. The results are shown in Table 3. Compared with standard training, the proposed methods can improve the model's interpretability, especially under the elastic net regularization, which achieved the highest DiffROAR score.", + "bbox": [ + 496, + 444, + 892, + 685 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also visualized the learned feature for each model, using the optimization-based feature visualization technique of deep-dream [20]. The results (Fig. 3) also show that class-specific features identified with the proposed norm-regularized adversarial training methods look more meaningful to human perception.", + "bbox": [ + 496, + 686, + 890, + 777 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Robustness. To assess the robustness of interpretation maps under the standard and proposed training methods, we adopted an $L_{2}$ -norm bounded interpretation attack method proposed by [18]. We gradually increased the strength of the attack and measured the robustness through similarity measures of the saliency maps before and after the attack. We adopted two metrics as robustness measures: 1) top-k intersection ratio [8], which is the ratio of pix", + "bbox": [ + 496, + 779, + 892, + 900 + ], + "page_idx": 5 + }, + { + "type": "page_number", + "text": "11014", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/d731715a60311aff5f8345a45bb88573111aac8a58645a910709ca7452e8c178.jpg", + "image_caption": [ + "Figure 4. Qualitative comparison of saliency maps generated by networks with different adversarial training protocols (fast, iterative) and standard training with additional regularization on input gradients (penalty)." + ], + "image_footnote": [], + "bbox": [ + 83, + 89, + 885, + 362 + ], + "page_idx": 6 + }, + { + "type": "table", + "img_path": "images/daab8f5f28bbc00a0359861cbf7b3b0d3a7efb7c198999fd92f6d5e0f096068e.jpg", + "table_caption": [ + "Table 3. Quantitative evaluation on ImageNette." + ], + "table_footnote": [], + "table_body": "
MethodsDiffROAR (%) (↑)Gini (%) (↑)Acc. (%) (↑)
standard1.8146.5389.04
L1-norm (ε=0.01)2.9556.7390.46
L1-norm (ε=0.05)2.1262.0484.13
L1-norm (ε=0.10)1.9765.5378.85
group-norm (ε=0.10)2.5750.0786.83
group-norm (ε=0.50)1.3249.1587.57
group-norm (ε=1.00)0.4052.7083.80
elastic net (ε1=0.01, ε2=0.01)2.6057.1087.72
elastic net (ε1=0.01, ε2=0.05)3.2457.3587.67
elastic net (ε1=0.01, ε2=0.10)3.1454.4487.19
elastic net (ε1=0.05, ε2=0.01)2.3160.0584.59
elastic net (ε1=0.05, ε2=0.05)2.1161.8484.69
elastic net (ε1=0.05, ε2=0.10)2.1760.2584.54
", + "bbox": [ + 86, + 422, + 460, + 638 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "els that remain salient after the interpretation attack, and 2) the structural similarity index measure (SSIM) [38]. We compared the proposed training methods with the baseline standard training and three post-processing-based baselines, SmoothGrad, Sparsified-SmoothGrad (Sparsified-S.), and MoreauGrad (Fig. 5). Standard training seemed vulnerable to minor attacks, even when combined with the Smooth-based post-processing. In contrast, the neural nets trained by the proposed methods displayed significantly higher robustness to the attacks. We also observed that the elastic net and group-norm-based training methods performed slightly more robustly than the $L_{1}$ -norm-based method.", + "bbox": [ + 75, + 656, + 468, + 837 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Stability. We evaluated the algorithmic stability as the magnitude of perturbation in the saliency maps under classifiers trained with different training data or random initialization. As pointed out by [39], standard training with different", + "bbox": [ + 75, + 839, + 468, + 901 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "initializations can result in large discrepancies in saliency maps. We examined if the proposed training methods can alleviate this issue. To this end, we switched $10\\%$ of the training data with the test data and initialized two networks with different random seeds. Then we trained these two networks with the same training process. We used SSIM and top-k overlap to measure the similarities of the generated saliency maps, where the top-k overlap was defined as the Dice score of the top-k masks. As shown in Fig. 5, adversarial training could significantly improve stability. It even brings more improvement than post-processing methods. Note for Sparsified-SmoothGrad, the high SSIM is due to the sparsity of the saliency maps. Through studying top-k overlap, the activated regions were actually different. Among the three variants of adversarial training, the elastic net could achieve the best stability, as the incorporation of $L_2^2$ term could increase the smoothness of the objective function, making the optimization process less sensitive to the perturbation of the training data.", + "bbox": [ + 496, + 404, + 893, + 691 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Comparison of different training protocols. We also conducted experiments to see how different training protocols affect the numerical results. Specifically, we compared one-step optimization (fast), multiple-step optimization (iterative), and free adversarial training (free, in Appendix) [25]. As a baseline, we also studied standard training with norm regularization directly applied to the objective function (penalty). We visualized a few saliency maps in Fig. 4 for comparison. Standard training with regularization failed to generate structured saliency maps, showing the challenge of network optimization with regularization in the objective function, which further certified the superiority of adversarial training. Visually, fast, and iterative", + "bbox": [ + 496, + 703, + 893, + 900 + ], + "page_idx": 6 + }, + { + "type": "page_number", + "text": "11015", + "bbox": [ + 480, + 944, + 517, + 955 + ], + "page_idx": 6 + }, + { + "type": "image", + "img_path": "images/11844bd43c7a9166772627b28faaf5c0da9d559c88eeb4b92efb79e13c9479f5.jpg", + "image_caption": [ + "Figure 5. Quantitative robustness and stability comparison. Left/Middle: Comparison of SSIM/top-k intersection of saliency maps before and after the attack. Right: Comparison of SSIM/top-k overlap of saliency maps generated by networks with different stochastic training." + ], + "image_footnote": [], + "bbox": [ + 86, + 94, + 349, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/1627768cf21021453c9d71fd3f2af1f51333d21fbe1ad0d866f9efd5359f9234.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 352, + 94, + 614, + 218 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/3887241b624cd18016a21a8813a8867a30e5c739adb2815e1c588b475066db8e.jpg", + "image_caption": [], + "image_footnote": [], + "bbox": [ + 625, + 94, + 880, + 217 + ], + "page_idx": 7 + }, + { + "type": "table", + "img_path": "images/0465bcfc76cf331e23cb8771ff72878dc8707d7b23f91465ca6e55b7c8d382f5.jpg", + "table_caption": [ + "Table 4. Top-k overlap $(\\%)$ between gaze map and saliency map on CUB-GHA dataset." + ], + "table_footnote": [], + "table_body": "
€0.00.10.51.05.0
top 5% overlap33.4235.0738.7442.6350.62
top 10% overlap41.8142.9945.6047.0652.60
accuracy (%)67.5867.5066.5666.6564.99
", + "bbox": [ + 96, + 311, + 450, + 383 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "training achieved comparable quality. However, for $L_{1}$ -norm, interactive training would lose sparsity compared to fast training, but for the elastic net, the trend was the opposite. The Fenchel conjugate of elastic net regularization is differentiable everywhere due to the square term, making its optimization easier compared with $L_{1}$ -norm.", + "bbox": [ + 75, + 436, + 468, + 527 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3. Harmonization with gaze maps", + "text_level": 1, + "bbox": [ + 76, + 559, + 352, + 575 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We conducted experiments on the CUB-GHA [21] to verify the effectiveness of our interpretation harmonization strategy on real-world data. CUB-GHA is an extension of CUB [36], which includes gaze maps collected from domain experts for bird category classification. The gaze map is a type of human attention map reflecting how human experts would conduct this task. We aim to harmonize the saliency maps with human attention so that the network could make the decision more similar to humans.", + "bbox": [ + 75, + 590, + 468, + 726 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To do this, we normalized the gaze map and used the attention score as the weights for the $l_{2}$ -norm perturbation during adversarial training. The results are shown in Fig. 6. The original saliency maps highlighted the whole body of the bird, while the gaze maps were more focused on a specific part (e.g. head) of the bird. After harmonization, the saliency maps showed better alignment with the gaze maps. We also calculated the top-k overlap between saliency maps and gaze maps (Table 4). The results showed an increasing trend of the overlap as we raised the coefficient $\\epsilon$ , while the trade-off of accuracy was in a reasonable range.", + "bbox": [ + 75, + 734, + 470, + 902 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/207aee0309b4cfef0716060fa525b27d45945f62c2337027fda8e177b4f133a3.jpg", + "image_caption": [ + "Figure 6. Qualitative results based on CUB-GHA dataset." + ], + "image_footnote": [], + "bbox": [ + 511, + 281, + 883, + 470 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6. Conclusion", + "text_level": 1, + "bbox": [ + 500, + 505, + 619, + 522 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "In this paper, we introduced a duality framework to analyze the impact of norm-regularized adversarial training on the gradient-based saliency maps of a trained neural net classifier. Leveraging this duality framework, we proposed several variants of norm-regularized adversarial training, designed to promote certain structures in the gradient-based interpretation maps, including sparsity, group sparsity, and consistency with human attention. We provided experimental results on several benchmark datasets to validate the effectiveness of our proposed methods, which demonstrated that properly designed adversarial training methods can enhance model interpretability as well as the stability and robustness of the gradient-based maps. An interesting future direction is to develop a similar adversarial training-based regularization framework for structured interpretation maps according to integrated gradients, DeepLIFT, and GradCam. Another relevant future direction is to explore other forms of penalty terms in order to expand the methodology to domains beyond computer vision.", + "bbox": [ + 496, + 530, + 890, + 818 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Acknowledgments. The work of Farzan Farnia is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by a CUHK Direct Research Grant with CUHK Project No. 4055164.", + "bbox": [ + 496, + 820, + 893, + 897 + ], + "page_idx": 7 + }, + { + "type": "page_number", + "text": "11016", + "bbox": [ + 480, + 944, + 519, + 955 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "References", + "text_level": 1, + "bbox": [ + 78, + 89, + 173, + 104 + ], + "page_idx": 8 + }, + { + "type": "list", + "sub_type": "ref_text", + "list_items": [ + "[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 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Journal of the Royal Statistical Society Series B: Statistical Methodology, 67(2):301-320, 2005. 2" + ], + "bbox": [ + 501, + 92, + 893, + 174 + ], + "page_idx": 9 + }, + { + "type": "page_number", + "text": "11018", + "bbox": [ + 480, + 945, + 517, + 955 + ], + "page_idx": 9 + } +] \ No newline at end of file diff --git a/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/25726c0b-b33a-4e50-8b53-f013deb7f334_model.json b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/25726c0b-b33a-4e50-8b53-f013deb7f334_model.json new file mode 100644 index 0000000000000000000000000000000000000000..9abbfda30dcb3152111412d5bd52c1c2bf962350 --- /dev/null +++ b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/25726c0b-b33a-4e50-8b53-f013deb7f334_model.json @@ -0,0 +1,2178 @@ +[ + [ + { + "type": "header", + "bbox": [ + 0.107, + 0.003, + 0.182, + 0.043 + ], + "angle": 0, + "content": "CVF" + }, + { + "type": "header", + "bbox": [ + 0.237, + 0.001, + 0.808, + 0.047 + ], + "angle": 0, + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + }, + { + "type": "title", + "bbox": [ + 0.25, + 0.131, + 0.723, + 0.177 + ], + "angle": 0, + "content": "Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training" + }, + { + "type": "text", + "bbox": [ + 0.333, + 0.204, + 0.638, + 0.24 + ], + "angle": 0, + "content": "Shizhan Gong, Qi Dou, Farzan Farnia \nThe Chinese University of Hong Kong" + }, + { + "type": "text", + "bbox": [ + 0.31, + 0.242, + 0.662, + 0.256 + ], + "angle": 0, + "content": "{szgong22, qdou, farnia}@cse.cuhk.edu.hk" + }, + { + "type": "title", + "bbox": [ + 0.235, + 0.292, + 0.314, + 0.308 + ], + "angle": 0, + "content": "Abstract" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.324, + 0.474, + 0.673 + ], + "angle": 0, + "content": "Gradient-based saliency maps have been widely used to explain the decisions of deep neural network classifiers. However, standard gradient-based interpretation maps, including the simple gradient and integrated gradient algorithms, often lack desired structures such as sparsity and connectedness in their application to real-world computer vision models. A frequently used approach to inducing sparsity structures into gradient-based saliency maps is to alter the simple gradient scheme using sparsification or norm-based regularization. A drawback with such post-processing methods is their frequently-observed significant loss in fidelity to the original simple gradient map. In this work, we propose to apply adversarial training as an in-processing scheme to train neural networks with structured simple gradient maps. We show a duality relation between the regularized norms of the adversarial perturbations and gradient-based maps, based on which we design adversarial training loss functions promoting sparsity and group-sparsity properties in simple gradient maps. We present several numerical results to show the influence of our proposed norm-based adversarial training methods on the standard gradient-based maps of standard neural network architectures on benchmark image datasets1." + }, + { + "type": "title", + "bbox": [ + 0.078, + 0.702, + 0.21, + 0.717 + ], + "angle": 0, + "content": "1. Introduction" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.728, + 0.47, + 0.864 + ], + "angle": 0, + "content": "Deep neural networks have attained remarkable results in various computer vision tasks including image classification [17], object detection [44], and semantic segmentation [10]. However, understanding and explaining the decision-making process of these complex models remains a challenge, which is required for high-risk applications such as medical imaging [27], autonomous driving [16], and face recognition [37]. To interpret the predictions of neural network classifiers, several explanation methodolo" + }, + { + "type": "image", + "bbox": [ + 0.505, + 0.293, + 0.889, + 0.516 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.498, + 0.529, + 0.895, + 0.628 + ], + "angle": 0, + "content": "Figure 1. The original simple gradient map could be dense and noisy. Post-processing methods such as sparsification enhance the sparsity at the expense of lower fidelity to the original map. Our proposed in-processing strategy with adversarial training results in higher sparsity without losing fidelity to the simple-grad map. (We use the Gini index as a sparsity measure, and relative \\(\\mathrm{AOPC}_{\\mathrm{MoRF}}\\) with respect to simple gradient as a fidelity score.)" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.894, + 0.747 + ], + "angle": 0, + "content": "gies have been proposed in the literature. Among these explanation methods, gradient-based saliency maps have been frequently applied to interpret image classifiers. The saliency maps provide insight into the regions of the input image contributing to the classifier's decision and potentially prompt the empirical understanding of phenomena from data-driven models." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.75, + 0.895, + 0.903 + ], + "angle": 0, + "content": "Despite the widespread use of standard gradient-based interpretation maps such as simple gradients [29] and integrated gradients [32], they often lack desired structures such as sparsity and connectedness. When applied to real-world computer vision tasks, the generated saliency maps have been frequently observed to be noisy and dense. Such unstructured behavior could hinder the application of gradient-based maps for detecting the influential features in the classifier's decision-making process. To obtain more structured saliency maps, several post-processing" + }, + { + "type": "page_footnote", + "bbox": [ + 0.077, + 0.875, + 0.468, + 0.901 + ], + "angle": 0, + "content": "The paper's code is available at: https://github.com/peterant330/AdvGrad" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.958 + ], + "angle": 0, + "content": "11009" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.349 + ], + "angle": 0, + "content": "schemes [18, 30, 31, 42, 43] have been proposed in the literature, which denoise the saliency map to gain higher sparsity. However, a drawback of these post-processing methods is the deviation from the original simple gradient map that alters the definition of the interpretation map. For example, Adebayo et al. [1] conducted a sanity check and found several interpretation methods such as Guided Propagation and Integrated Gradients lacked sensitivity to the model or the data-generating process. Arun et al. [2] demonstrated similar findings on medical imaging applications. To illustrate the fidelity vs. sparsity trade-off in such post-processing schemes, we display an example in Fig. 1, where the simple gradient map looks to contain significant noise scattered over the background. A post-processing sparsification of the gradient map could raise the sparsity of the map; however, the sparsity comes at the cost of a considerable drop (more than \\(82\\%\\)) in the fidelity score." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.352, + 0.473, + 0.578 + ], + "angle": 0, + "content": "In this work, we propose a unified adversarial training (AT) framework to address the unstructured nature of standard simple-gradient maps, where we apply a norm-regularized adversarial training with a properly-designed norm function as an in-processing scheme to promote the sparsity structures in the simple gradient map. AT with standard \\( L_{2} \\) and \\( L_{\\infty} \\)-norm perturbations [19] has been successfully and widely utilized in the literature to enhance the adversarial robustness [33] and interpretability [26] of deep neural networks. In our analysis, we extend the understanding of the influence of AT algorithms on the interpretability of a trained model, where we provide a convex duality framework to understand the influence of the norm function constrained in AT on the regularized norm of gradient maps and hence the interpretability of neural nets." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.581, + 0.473, + 0.824 + ], + "angle": 0, + "content": "Specifically, we show a duality relation between the regularized norm of adversarial perturbations and the norm of input-based gradients. This duality relationship allows us to design norm-regularized adversarial training methods, which translates into the regularization of standard sparsity-inducing norms, e.g. the group norm [41] and the elastic net [45], of the simple gradient maps. As we show in this work, the special cases of our proposed framework can promote desired characteristics such as sparsity and connectedness in simple gradient maps. Importantly, unlike the sparsity-regularizing post-processing schemes, the gained sparsity properties of our proposed AT methods do not cost any loss in fidelity to the simple-gradient map, because we do not alter the definition of the interpretation map and only regularize the training process toward networks with more structured gradient maps." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.825, + 0.473, + 0.903 + ], + "angle": 0, + "content": "We conduct several numerical experiments on benchmark image datasets to validate the efficacy of our proposed AT-based methodology. The numerical results reveal the impact of our proposed norm-based AT methods on standard gradient-based maps, showing the enhanced spar" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.092, + 0.895, + 0.257 + ], + "angle": 0, + "content": "sity and connectedness properties. We empirically analyze the performance of the trained neural nets in terms of several factors including interpretability, robustness, and stability. Our numerical results indicate the improvements in the mentioned structure-related factors offered by our designed norm-regularized AT methods. Finally, we utilize the shown duality relation to propose an interpretation harmonization scheme for aligning simple gradient maps with expert gaze maps, which performs satisfactorily in our numerical experiments. Our work's main contributions can be summarized as:" + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.259, + 0.892, + 0.319 + ], + "angle": 0, + "content": "- We show a duality relation between the regularized norms of adversarial perturbations and gradient maps, and develop a unified AT framework for regularizing gradient maps." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.32, + 0.892, + 0.365 + ], + "angle": 0, + "content": "- We derive special cases of our proposed AT-based framework leading to the regularization of the elastic net and group-norm of gradient map." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.365, + 0.892, + 0.409 + ], + "angle": 0, + "content": "- We leverage the duality framework to propose an interpretation harmonization scheme for aligning gradient maps with human attention." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.41, + 0.892, + 0.456 + ], + "angle": 0, + "content": "- We provide numerical results showing the efficacy of the AT-based framework in improving the sparsity and stability of interpretation maps." + }, + { + "type": "list", + "bbox": [ + 0.5, + 0.259, + 0.892, + 0.456 + ], + "angle": 0, + "content": null + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.468, + 0.642, + 0.484 + ], + "angle": 0, + "content": "2. Related Work" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.493, + 0.892, + 0.81 + ], + "angle": 0, + "content": "Gradient-based Interpretation. Using the gradient of the output of a deep neural network w.r.t. an input image is a widely-used approach to generate saliency maps [29]. This method has been utilized in several related works and multiple variants of this approach are proposed in the literature, including SmoothGrad [30], Integrated Gradients [32], DeepLIFT [28], and GradCAM [24]. The vanilla gradient-based maps without post-processing are often noisy and difficult to interpret. A group of methods are proposed to improve the visual quality by sparsifying the gradient-based maps: Guided Propagation [31] removes the noise artifacts from saliency maps by suppressing negative activations in the back-propagation. Sparsified-SmoothGrad [18] applies a sparsification to the saliency map to promote sparsity and robustness. MoreauGrad [43] generates saliency maps using an optimization problem with sparsity regularization. One drawback of the discussed methods is that they are all post-processing schemes, which may compromise the fidelity to the original simple-gradient map. On the other hand, our proposed framework is an in-processing scheme that remains faithful to the simple gradient map." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.811, + 0.895, + 0.902 + ], + "angle": 0, + "content": "Adversarial Training and Interpretability. Adversarial training (AT) involves training the networks using adversarial examples [19]. Fast Gradient Sign Method (FGSM) [9] generates adversarial samples using a single iteration to create the adversarial training example for training the classifier. Projected gradient descent (PGD) [19] uses several" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.521, + 0.957 + ], + "angle": 0, + "content": "11010" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.091, + 0.473, + 0.35 + ], + "angle": 0, + "content": "gradient-based steps to generate more effective adversarial examples in order to make the trained model more robust to norm-constrained adversarial attacks. While the primary objective of AT is to improve the trained model's robustness against adversarial attacks, several studies have shown that AT can also improve the visual quality of interpretation maps [15, 22, 26]. Specifically, AT has been empirically shown to suppress irrelevant features [14], and the standard \\(\\ell_{\\infty}\\)-norm-based AT will lead to higher sparsity and stability of the interpretation maps [3]. Building upon and extending these findings, our work provides a unified duality framework that connects the perturbation norm constrained by the AT algorithm and the norm penalized for the interpretation map. Specifically, we discuss novel variants of AT methods that lead to the regularization of the elastic net and group norms of the interpretation maps which have not been studied in these related works." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.361, + 0.218, + 0.377 + ], + "angle": 0, + "content": "3. Preliminaries" + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.385, + 0.351, + 0.402 + ], + "angle": 0, + "content": "3.1. Gradient-based Saliency Maps" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.409, + 0.473, + 0.576 + ], + "angle": 0, + "content": "Throughout this work, our analysis mainly focuses on the standard simple gradient as the gradient-based interpretation. We use \\(\\mathbf{x} \\in \\mathbb{R}^d\\) and \\(\\mathbf{y} \\in \\mathbb{R}^C\\) to denote the input and output of the neural network classifier. Note that \\(\\mathbf{y}\\) denotes the output of the neural net's post-softmax layer and contains the assigned likelihood for each of the \\(C\\) classes in the classification task. The neural net function \\(f_{\\theta}: \\mathbb{R}^{d} \\to \\mathbb{R}^{C}\\) maps the input vector to the output vector, where \\(\\theta\\) denotes the parameters of the neural net. The simple gradient generates a saliency map by taking derivatives of the output of the neural network with respect to the input:" + }, + { + "type": "equation", + "bbox": [ + 0.181, + 0.584, + 0.366, + 0.601 + ], + "angle": 0, + "content": "\\[\n\\operatorname {S G} \\left(f _ {\\theta , c}, \\mathbf {x}\\right) := \\nabla_ {\\mathbf {x}} f _ {\\theta , c} (\\mathbf {x}).\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.609, + 0.471, + 0.672 + ], + "angle": 0, + "content": "Here, \\( c \\) can be chosen as ground-truth label \\( y \\) or the label \\( c \\) with the maximum likelihood assigned by the classifier. In our analysis, we assume \\( \\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x}) \\) denotes the saliency map corresponding to the ground-truth label of sample \\( \\mathbf{x} \\)." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.245, + 0.693 + ], + "angle": 0, + "content": "3.2. FGSM and PGD" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.701, + 0.47, + 0.868 + ], + "angle": 0, + "content": "We consider two of the most widely used forms of adversarial training, FGSM and PGD, in this work. These methods first generate adversarial samples by calculating the gradient of the loss function with respect to the input data and then perturb the data by taking one or multiple small steps in the direction of the sign of the gradient. The perturbation is usually bounded by \\( l_{\\infty} \\)-norm. The parameters of the network are then updated to minimize the loss with respect to these adversarial samples. We can use the following objective to summarize the optimization problem where \\( \\hat{P} \\) is the empirical distribution of training samples" + }, + { + "type": "equation", + "bbox": [ + 0.132, + 0.875, + 0.47, + 0.904 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {(\\mathbf {x}, y) \\sim \\widehat {P}} \\left[ \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x} + \\delta), y\\right) \\right]. \\tag {1}\n\\]" + }, + { + "type": "table_caption", + "bbox": [ + 0.499, + 0.089, + 0.895, + 0.133 + ], + "angle": 0, + "content": "Table 1. Summary of regularized norm \\( h \\) on perturbation \\( \\delta \\) and the resulting regularized function \\( {h}^{\\star } \\) of the input gradient \\( {\\nabla }_{\\mathbf{x}}\\mathcal{L}\\left( {{f}_{\\theta }\\left( \\mathbf{x}\\right) ,y}\\right) \\) . Detailed description can be found in Section 4.3." + }, + { + "type": "table", + "bbox": [ + 0.502, + 0.139, + 0.895, + 0.251 + ], + "angle": 0, + "content": "
h(δ)h*(∇xL(fθ(x),y))
I(||δ||∞ ≤ ε)ε||∇xL(fθ(x),y)||1
I(||δ||2,∞ ≤ ε)ε||∇xL(fθ(x),y)||2,1
∑iPQε1,ε2(δi)ε1||∇xL(fθ(x),y)||1 + ε2||∇xL(fθ(x),y)||2
1/4ε||W ⊙ δ||2ε||W ⊙ ∇xL(fθ(x),y)||2
" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.268, + 0.895, + 0.299 + ], + "angle": 0, + "content": "FGSM generates adversarial samples by taking one step in the direction of the sign of the gradient:" + }, + { + "type": "equation", + "bbox": [ + 0.562, + 0.305, + 0.831, + 0.323 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {\\mathrm {F G S M}} ^ {*} = \\mathbf {x} + \\epsilon \\cdot \\operatorname {s i g n} \\left(\\nabla_ {\\mathbf {x}} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x}), y\\right)\\right)\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.329, + 0.892, + 0.36 + ], + "angle": 0, + "content": "PGD, on the other hand, iteratively updates the samples with a stepsize \\(\\alpha\\):" + }, + { + "type": "equation", + "bbox": [ + 0.537, + 0.366, + 0.855, + 0.385 + ], + "angle": 0, + "content": "\\[\n\\mathbf {x} _ {t + 1} = \\Pi_ {\\mathbf {x} + S} \\big (\\mathbf {x} _ {t} + \\alpha \\mathrm {s i g n} (\\nabla_ {\\mathbf {x} _ {t}} \\mathcal {L} (f _ {\\theta} (\\mathbf {x} _ {t}), y)) \\big),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.39, + 0.887, + 0.407 + ], + "angle": 0, + "content": "where \\(S = \\{\\mathbf{z}:\\| \\mathbf{z}\\|_{\\infty}\\leq \\epsilon \\}\\) denotes the \\(\\epsilon\\) -radius \\(L_{\\infty}\\) -ball." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.413, + 0.682, + 0.43 + ], + "angle": 0, + "content": "3.3. Fenchel Conjugate" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.437, + 0.894, + 0.497 + ], + "angle": 0, + "content": "The Fenchel conjugate is an essential operation in convex analysis which has many applications to various computer vision algorithms. For a function \\( f: \\mathcal{X} \\to \\mathbb{R} \\), its Fenchel conjugate \\( f^{\\star}: \\mathcal{X} \\to \\mathbb{R} \\) is defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.566, + 0.504, + 0.826, + 0.523 + ], + "angle": 0, + "content": "\\[\nf ^ {\\star} (z) = \\sup \\left\\{\\langle x, z \\rangle - f (x): x \\in \\mathcal {X} \\right\\},\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.529, + 0.892, + 0.59 + ], + "angle": 0, + "content": "where \\(\\langle \\cdot ,\\cdot \\rangle\\) denotes the inner product, and sup represents the supremum. Note that for a convex \\(f\\) \\(f\\) will be the Fenchel conjugate of \\(f^{\\star}\\) . Furthermore, for every function \\(f\\) , the Fenchel conjugate \\(f^{\\star}\\) is guaranteed to be convex." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.601, + 0.892, + 0.636 + ], + "angle": 0, + "content": "4. An Adversarial Training Methodology for Regularizing Interpretation Maps" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.643, + 0.892, + 0.826 + ], + "angle": 0, + "content": "In this section, we show a duality relation between the input gradient and the perturbation vectors, which is based on the linear approximation of the loss function \\(\\ell\\big(f(\\mathbf{x} + \\delta),y\\big)\\) around data point \\(\\mathbf{x}\\). In the approximation, the first-order term \\(\\langle \\nabla_{\\mathbf{x}}\\ell \\big(f(\\mathbf{x}),y\\big),\\delta \\rangle\\) is the inner product of the perturbation vector and the input-based gradient of the loss function. Therefore, as will be explained in the section, to penalize a norm of the saliency map in the adversarial training process, we propose to constrain the dual norm of the perturbation vector. We summarize three variants of the norm constraint on the perturbation and its effect on the simple gradient saliency maps in Table 1." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.832, + 0.892, + 0.864 + ], + "angle": 0, + "content": "4.1. Rethinking the Impact of \\(\\ell_{\\infty}\\)-Norm-Based Adversarial Training on Saliency Maps" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "We perform a first-order analysis by means of Fenchel conjugate to indicate how \\( L_{\\infty} \\)-norm-based adversarial training" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.518, + 0.957 + ], + "angle": 0, + "content": "11011" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.076, + 0.092, + 0.47, + 0.168 + ], + "angle": 0, + "content": "could lead to higher sparsity in gradient-based maps. Under a small enough perturbation norm bound \\(\\epsilon\\) and twice-differentiable loss function, the objective of adversarial training in Eq. 1 can be approximated by first-order Taylor expansion as" + }, + { + "type": "equation", + "bbox": [ + 0.085, + 0.174, + 0.46, + 0.233 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {E q.} 1 = \\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\hat {P}} \\left[ \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x}), y\\right) \\right. \\\\ + \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} \\left\\{\\delta^ {T} \\nabla_ {\\mathbf {x}} \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) \\right\\} \\biggr ] + \\mathcal {O} (\\epsilon^ {2}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.239, + 0.469, + 0.316 + ], + "angle": 0, + "content": "Using the common cross-entropy loss or hinge loss, the derivative of the loss with respect to the predicted log-its at every training sample will be \\(\\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta},(\\mathbf{x}),y) = -f_{\\theta ,y}(\\mathbf{x})\\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})\\), so we can build the connection between the objective and the saliency map:" + }, + { + "type": "equation", + "bbox": [ + 0.08, + 0.322, + 0.465, + 0.381 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\operatorname {E q.} 1 = \\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\hat {P}} \\left[ \\mathcal {L} \\left(f _ {\\theta , y} (\\mathbf {x})\\right) \\right. \\\\ \\left. + f _ {\\theta , y} (\\mathbf {x}) \\max _ {| | \\delta | | _ {\\infty} \\leq \\epsilon} \\left\\{- \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) \\right\\} \\right] + \\mathcal {O} (\\epsilon^ {2}). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.387, + 0.469, + 0.432 + ], + "angle": 0, + "content": "Note we can leverage Fenchel conjugate operation to transform the maximization subproblem in the above problem into an unconstrained optimization:" + }, + { + "type": "equation", + "bbox": [ + 0.078, + 0.438, + 0.472, + 0.477 + ], + "angle": 0, + "content": "\\[\n\\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} - \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) = \\max _ {\\delta} - \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) - \\mathbb {I} (\\| \\delta \\| _ {\\infty} \\leq \\epsilon), \\tag {2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.478, + 0.469, + 0.569 + ], + "angle": 0, + "content": "where \\(\\mathbb{I}(\\mathrm{condition}) = 0\\) if the condition holds and \\(+\\infty\\) otherwise. With the concept of Fenchel conjugate, the optimal value of the optimization problem defined in Eq. 2 is \\(\\epsilon \\| \\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})\\| _1\\). Hence, we successfully transform the original minimax optimization problem into a regularized optimization within an approximation error \\(\\mathcal{O}(\\epsilon^2)\\):" + }, + { + "type": "equation", + "bbox": [ + 0.077, + 0.576, + 0.469, + 0.603 + ], + "angle": 0, + "content": "\\[\n\\mathrm {E q .} 1 \\approx \\underset {\\theta} {\\min } \\mathbb {E} _ {\\mathbf {x}, y \\sim \\widehat {P}} \\Big [ \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + \\epsilon f _ {\\theta , y} (\\mathbf {x}) \\| \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) \\| _ {1} \\Big ].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.609, + 0.469, + 0.669 + ], + "angle": 0, + "content": "Hence, we find that adversarial training with \\( L_{\\infty} \\)-norm is approximately equivalent to applying \\( L_{1} \\)-norm regularization to the simple gradient saliency map, therefore promoting the sparsity of the saliency maps." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.677, + 0.469, + 0.709 + ], + "angle": 0, + "content": "4.2. Adversarial Training with Fenchel Conjugate Regularization: a Unified Approach" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.715, + 0.469, + 0.807 + ], + "angle": 0, + "content": "Next, we consider adversarial training with a general norm-based regularization penalty. Here our goal is to promote a structured saliency map through a regularization function \\( h^{\\star}(\\mathbf{z}) \\). Note that for a convex \\( h \\), the Fenchel conjugate of \\( h^{\\star}(\\mathbf{z}) \\) will be \\( h(\\mathbf{x}) \\). Therefore, we consider the min-max optimization with the adversarial penalty function \\( -h(\\delta) \\):" + }, + { + "type": "equation", + "bbox": [ + 0.124, + 0.814, + 0.422, + 0.841 + ], + "angle": 0, + "content": "\\[\n\\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\widehat {P}} \\left[ \\max _ {\\delta} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x} + \\delta), y\\right) - h (\\delta) \\right].\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.847, + 0.469, + 0.877 + ], + "angle": 0, + "content": "Following our analysis for the \\(L_{\\infty}\\)-norm-based adversarial training, we define the first-order approximate loss:" + }, + { + "type": "equation", + "bbox": [ + 0.101, + 0.883, + 0.445, + 0.903 + ], + "angle": 0, + "content": "\\[\n\\widehat {\\mathcal {L}} (f _ {\\theta} (\\mathbf {x}), y, \\delta) := \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + \\delta^ {T} \\nabla_ {x} \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y),\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.091, + 0.892, + 0.137 + ], + "angle": 0, + "content": "To measure how well \\(\\widehat{\\mathcal{L}}(f_{\\theta}(\\mathbf{x}), y, \\delta)\\) approximates the adversarial loss, we observe the approximation error can be simply bounded for the class of \\(\\lambda\\)-smooth functions." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.15, + 0.892, + 0.181 + ], + "angle": 0, + "content": "Definition 1 We call \\( g: \\mathbb{R}^d \\to \\mathbb{R} \\) a smooth if for every \\( \\mathbf{x} \\) and \\( \\mathbf{z} \\): \\( \\| \\nabla g(\\mathbf{x}) - \\nabla g(\\mathbf{z}) \\|_2 \\leq \\lambda \\| \\mathbf{x} - \\mathbf{z} \\|_2 \\)." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.196, + 0.892, + 0.242 + ], + "angle": 0, + "content": "Observation 1 The approximation error of the first-order Taylor series expansion of adversarial loss under an \\(\\epsilon\\)-\\(L_2\\)-norm bounded perturbation \\(\\|\\delta\\| \\leq \\epsilon\\) can be bounded as" + }, + { + "type": "equation", + "bbox": [ + 0.555, + 0.255, + 0.837, + 0.286 + ], + "angle": 0, + "content": "\\[\n\\left| \\widehat {\\mathcal {L}} (f _ {\\theta} (\\mathbf {x}), y, \\delta) - \\mathcal {L} (f _ {\\theta} (\\mathbf {x} + \\delta), y) \\right| \\leq \\frac {\\lambda \\epsilon^ {2}}{2}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.3, + 0.892, + 0.362 + ], + "angle": 0, + "content": "The observation shows \\(\\widehat{\\mathcal{L}}(f_{\\theta}(\\mathbf{x}), y, \\delta)\\) can be a good approximation of the adversarial loss under a small \\(\\|\\delta\\|\\). Combining the approximate loss with \\(h(\\delta)\\) regularization, we can derive the following equivalence by Fenchel conjugate:" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.375, + 0.892, + 0.405 + ], + "angle": 0, + "content": "Proposition 1 Using Fenchel conjugate \\( h^{\\star} \\), we can reduce the maximization of the approximate adversarial loss as" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.417, + 0.891, + 0.464 + ], + "angle": 0, + "content": "\\[\n\\begin{array}{l} \\max _ {\\delta} \\left\\{\\widehat {\\mathcal {L}} \\left(f _ {\\theta} (\\mathbf {x}), y, \\delta\\right) - h (\\delta) \\right\\} \\tag {3} \\\\ = \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + h ^ {\\star} \\bigl (\\nabla_ {\\mathbf {x}} \\mathcal {L} \\bigl (f _ {\\theta} (\\mathbf {x}), y \\bigr) \\bigr). \\\\ \\end{array}\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.477, + 0.892, + 0.627 + ], + "angle": 0, + "content": "In a scenario that the neural network completely fits the training data, we have that \\(\\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta}(\\mathbf{x}),y) = -f_{\\theta ,y}(\\mathbf{x})\\nabla_{x}f_{\\theta}(\\mathbf{x})\\approx -\\nabla_{x}f_{\\theta}(\\mathbf{x})\\) . Therefore, to enforce the gradient map \\(\\nabla_{x}f_{\\theta}(\\mathbf{x})\\) to satisfy a bounded penalty function \\(h^\\star\\) , we can conduct adversarial training with an additive penalty term \\(-h(\\delta)\\) . The optimal perturbation \\(\\delta^{*}\\) can be derived via the standard gradient ascent algorithm to maximize the regularized adversarial loss or be approximated with the analytic solution to the approximate optimization problem." + }, + { + "type": "title", + "bbox": [ + 0.499, + 0.639, + 0.892, + 0.67 + ], + "angle": 0, + "content": "4.3. Special Cases of the Fenchel Conjugate-based Duality Framework" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.678, + 0.892, + 0.738 + ], + "angle": 0, + "content": "Leveraging the duality framework in the previous section, we derive regularization penalty terms to penalize other sparsity norms different from \\( l_{1} \\)-norm and discuss their influence on the saliency maps." + }, + { + "type": "text", + "bbox": [ + 0.5, + 0.74, + 0.892, + 0.785 + ], + "angle": 0, + "content": "\\(L_{2,1}\\)-group-norm penalty. The \\(L_{2,1}\\)-group-norm of \\(\\mathbf{x} \\in \\mathbb{R}^d\\) for disjoint variable subsets \\(S_1, \\dots, S_t \\subseteq \\{1, \\dots, d\\}\\) is defined as the special case \\(p = 1\\) of the following definition:" + }, + { + "type": "equation", + "bbox": [ + 0.572, + 0.797, + 0.819, + 0.815 + ], + "angle": 0, + "content": "\\[\n\\left\\| \\mathbf {x} \\right\\| _ {2, p} := \\left\\| \\left[ \\left\\| \\mathbf {x} _ {S _ {1}} \\right\\| _ {2}, \\dots , \\left\\| \\mathbf {x} _ {S _ {t}} \\right\\| _ {2} \\right] \\right\\| _ {p}.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.828, + 0.892, + 0.858 + ], + "angle": 0, + "content": "To apply the duality framework to the group norm (with coefficient \\(\\epsilon > 0\\)), we derive its Fenchel conjugate as follows." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.871, + 0.892, + 0.902 + ], + "angle": 0, + "content": "Proposition 2 The Fenchel conjugate of the above \\(L_{2,1}\\)-group-norm is \\(h(\\mathbf{z}) = \\mathbb{I}(\\| \\mathbf{z}\\|_{2,\\infty}\\leq \\epsilon)\\)." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11012" + } + ], + [ + { + "type": "text", + "bbox": [ + 0.077, + 0.092, + 0.468, + 0.196 + ], + "angle": 0, + "content": "Different from \\( L_{1} \\)-norm inducing pixel-level sparsity, \\( L_{2,1} \\)-group-norm will induce sparsity of the patch basis. Under this regularization, the more influential patches are expected to be highlighted in the saliency map. This effect could further lead to a connected saliency map, which will be desired when adjacent pixels belonging have similar effects on the prediction of the classifier." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.197, + 0.468, + 0.228 + ], + "angle": 0, + "content": "Elastic net penalty. The elastic net penalty \\( h^{\\star}(\\mathbf{x}) \\) linearly combines the \\( L_{1} \\) and \\( L_{2}^{2} \\) penalty terms:" + }, + { + "type": "equation", + "bbox": [ + 0.129, + 0.236, + 0.416, + 0.254 + ], + "angle": 0, + "content": "\\[\nh ^ {\\star} (\\mathbf {x}) = \\epsilon_ {1} \\| \\mathbf {x} \\| _ {1} + \\epsilon_ {2} \\| \\mathbf {x} \\| _ {2} ^ {2}, \\epsilon_ {1} > 0, \\epsilon_ {2} > 0.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.274, + 0.468, + 0.32 + ], + "angle": 0, + "content": "Proposition 3 The Fenchel conjugate of the above elastic net penalty \\( h^{\\star} \\) is \\( h(\\mathbf{z}) = \\sum_{i} PQ_{\\epsilon_1, \\epsilon_2}(\\mathbf{z}_i) \\) where \\( PQ_{\\epsilon_1, \\epsilon_2} \\) is the piece-wise quadratic function defined as:" + }, + { + "type": "equation", + "bbox": [ + 0.096, + 0.328, + 0.449, + 0.386 + ], + "angle": 0, + "content": "\\[\nP Q _ {\\epsilon_ {1}, \\epsilon_ {2}} (\\mathbf {z} _ {i}) = \\left\\{ \\begin{array}{c l} \\frac {1}{4 \\epsilon_ {2}} (\\mathbf {z} _ {i} - \\epsilon_ {1}) ^ {2} & \\text {i f} \\epsilon_ {1} < \\mathbf {z} _ {i} \\\\ 0 & \\text {i f} - \\epsilon_ {1} \\leq \\mathbf {z} _ {i} \\leq \\epsilon_ {1} \\\\ \\frac {1}{4 \\epsilon_ {2}} (\\mathbf {z} _ {i} + \\epsilon_ {1}) ^ {2} & \\text {i f} \\mathbf {z} _ {i} < - \\epsilon_ {1}. \\end{array} \\right.\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.394, + 0.468, + 0.621 + ], + "angle": 0, + "content": "The linear combination of the \\(L_{1}\\)-norm and \\(L_{2}^{2}\\)-norm penalty terms in the elastic net results in a strongly convex regularization function, which is known to promote the stability of the sparsity pattern. Therefore, one can expect that the elastic net-regularized maps could possess higher robustness and stability than the \\(L_{1}\\)-norm regularized maps. Interpretation harmonization. The purpose of interpretation harmonization is to align the saliency map generated by the neural network with some reference attention map. The reference attention map can be manually labeled by domain experts, or based on some physical principle behind the classification task. Through interpretation harmonization, the network could be enabled to analyze the phenomenon in a similar way as a human, which would help diminish the potential bias or shortcuts learned by the neural net [6, 7]." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.621, + 0.468, + 0.742 + ], + "angle": 0, + "content": "To achieve this goal, we leverage \\( L_{2} \\)-norm regularization to diminish the importance scores of unrelated features. Specifically, assume \\( \\mathbf{A} \\in \\mathbb{R}^{d} \\) is the expert's attention map with non-negative entries. A greater value implies a more important feature. We define \\( \\hat{\\mathbf{A}} := \\max(\\mathbf{A}) - \\mathbf{A} + \\sigma \\), where \\( \\sigma \\) is small enough so that the ordinal relation is reverted and all elements are positive. To diminish the importance score of the background region, we use the penalty term:" + }, + { + "type": "equation", + "bbox": [ + 0.171, + 0.75, + 0.374, + 0.773 + ], + "angle": 0, + "content": "\\[\nh ^ {\\star} (\\mathbf {x}) = \\epsilon \\| \\sqrt {\\tilde {\\mathbf {A}}} \\odot \\mathbf {x} \\| _ {2} ^ {2}, \\epsilon > 0\n\\]" + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.78, + 0.468, + 0.825 + ], + "angle": 0, + "content": "where \\(\\odot\\) denotes Hadamard product. By adding this regularization term, the importance score of unrelated features is pushed to 0 while important features remain unaffected." + }, + { + "type": "text", + "bbox": [ + 0.077, + 0.833, + 0.468, + 0.863 + ], + "angle": 0, + "content": "Proposition 4 The Fenchel conjugate of the above weighted \\(L_{2}\\)-norm square regularization is:" + }, + { + "type": "equation", + "bbox": [ + 0.188, + 0.87, + 0.357, + 0.905 + ], + "angle": 0, + "content": "\\[\nh (\\mathbf {z}) = \\frac {1}{4 \\epsilon} \\left\\| \\frac {1}{\\sqrt {\\tilde {\\mathbf {A}}}} \\odot \\mathbf {z} \\right\\| _ {2} ^ {2}.\n\\]" + }, + { + "type": "image", + "bbox": [ + 0.511, + 0.094, + 0.885, + 0.253 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.511, + 0.268, + 0.879, + 0.282 + ], + "angle": 0, + "content": "Figure 2. Qualitative results based on the synthesized dataset." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.292, + 0.892, + 0.431 + ], + "angle": 0, + "content": "The derivation requires the weight term \\(\\tilde{\\mathbf{A}}\\) to be positive. However, a positive weight only leads to the diminishing of the importance score of unrelated features. It does not explicitly promote larger scores for important features. Empirically, we have found that using \\(\\delta^{*}\\) in the opposite direction to the gradients for important pixels helps increase the attribution scores for important features and results in better alignment. Therefore, in our numerical experiment, we set \\(\\tilde{\\mathbf{A}} = \\frac{1}{2}\\max (\\mathbf{A}) - \\mathbf{A}\\) and \\(\\delta^{*} = 2\\epsilon \\tilde{\\mathbf{A}}\\odot \\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta}(\\mathbf{x}),y)\\)." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.445, + 0.633, + 0.461 + ], + "angle": 0, + "content": "5. Experiments" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.471, + 0.892, + 0.669 + ], + "angle": 0, + "content": "We conducted comprehensive numerical experiments to evaluate the performance of our proposed adversarial training-based methods. Firstly, we evaluate saliency maps' accuracy on a synthesized dataset with ground truth interpretation. Next, we assessed the visual quality, sparsity, interpretability, robustness, and stability of the saliency maps on Imagenette. Finally, we demonstrated the effectiveness of our interpretation harmonization strategy on the CUB-GHA dataset. Our quantitative results include adversarial training with one normalized step and multi-step gradient ascent. The main text focuses on the results of one normalized step, while detailed training settings and complete numerical results can be found in the Appendix." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.68, + 0.767, + 0.696 + ], + "angle": 0, + "content": "5.1. Results on synthesized dataset" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.892, + 0.854 + ], + "angle": 0, + "content": "To illustrate how adversarial training can improve the model's interpretability, we first conducted experiments on a synthesized dataset with ground-truth for the saliency maps proposed by [35]. There are three regions on the ground-truth of the synthesized dataset (Fig. 2): background without any classification information (white region); localization information describes the location of an object (light red region); and distinguishing features crucial for classification (dark red area). We trained ResNet-34 [12] with standard training and regularized adversarial training." + }, + { + "type": "text", + "bbox": [ + 0.499, + 0.856, + 0.892, + 0.901 + ], + "angle": 0, + "content": "As the ground-truth was a ternary class, we reported the five-band-score reflects pixel accuracy, recall, precision, and the false positive rate (FPR) based on ternary classifi" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11013" + } + ], + [ + { + "type": "table_caption", + "bbox": [ + 0.178, + 0.09, + 0.792, + 0.104 + ], + "angle": 0, + "content": "Table 2. Comparison of five-band-scores and binary scores of standard training and adversarial training." + }, + { + "type": "table", + "bbox": [ + 0.128, + 0.11, + 0.844, + 0.212 + ], + "angle": 0, + "content": "
MethodsFive-band-scoresBinary scores
Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)
standard89.819.8632.581.2188.6644.4716.2210.22
\\( L_1 \\)-norm89.826.4129.200.7694.6065.0630.844.70
group-norm89.847.5427.350.9194.2763.7829.774.99
elastic net89.918.3526.830.9294.6365.6531.294.66
harmonization90.1411.3743.311.1493.8267.0528.155.54
" + }, + { + "type": "image", + "bbox": [ + 0.086, + 0.231, + 0.465, + 0.349 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.077, + 0.359, + 0.468, + 0.373 + ], + "angle": 0, + "content": "Figure 3. Images optimized for maximizing class-logit activations." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.383, + 0.47, + 0.639 + ], + "angle": 0, + "content": "cation. The results are listed in Table 2, where the method's name corresponds to the penalty term \\( h^{\\star} \\) in Eq. 3. The harmonization training achieved the best scores in terms of most of the metrics, showing the effectiveness of the proposed harmonization method. We also noticed that adversarial training-based methods consistently achieved higher accuracy and lower FPR compared with stranded training but led to lower recall and precision, because the adversarial training raised the sparsity of gradient maps. The importance scores of the localization area, which was less important compared with distinguishing features, were also diminished. Therefore, following [11], we also converted the ternary classification task to a binary classification task by considering the background and localization information as one class. The results suggested that adversarial training could significantly improve the accuracy of saliency maps in detecting distinguishing features." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.64, + 0.47, + 0.791 + ], + "angle": 0, + "content": "We visualized the saliency maps in Fig. 2 for qualitative evaluation (we only show results with elastic net regularization here and leave the rest in the Appendix). We discovered that the saliency map of standard training was activated more clearly in the region of the localization information than it was in the region of the distinguishing feature. In contrast, the saliency map with adversarial training was activated more significantly for the distinguishing features, especially on the boundaries. Moreover, the saliency maps looked more sparse and less noisy." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.802, + 0.287, + 0.817 + ], + "angle": 0, + "content": "5.2. Results on ImageNette" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.826, + 0.471, + 0.903 + ], + "angle": 0, + "content": "We performed numerical experiments on ImageNette, a ten-class subset of ImageNet [4], to examine the properties of the proposed adversarial training. Specifically, we studied the sparsity, interpretability, adversarial robustness, and stability of the saliency maps generated for EfficientNet [34]" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.231, + 0.884, + 0.246 + ], + "angle": 0, + "content": "classifiers with the proposed adversarial training methods." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.247, + 0.892, + 0.444 + ], + "angle": 0, + "content": "Sparsity. We trained the neural network models with different regularization coefficients and used the Gini Index [13] as a measure of the sparsity of the saliency map. The results are shown in Table 3. All the proposed adversarial training-based methods led to more sparse saliency maps than standard training, with zero or only minor drops in clean accuracy. The \\( L_{1} \\)-norm-based method attained the highest sparsity. Also, the sparsity increased with the regularization coefficient \\( \\epsilon \\). The gradient maps visualized in Fig. 4 suggest that standard training could lead to miscellaneous points in the background. On the other hand, the gradient maps with our proposed adversarial training methods seem to have higher visual quality." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.445, + 0.893, + 0.686 + ], + "angle": 0, + "content": "Interpretability. To show that the proposed training methods can improve the interpretability of the model, we calculated the DiffROAR score [26] for the methods. DiffROAR measures the difference in the predictive power of the dataset, where the top and bottom \\( k\\% \\) of the pixels are removed according to the importance score. A higher DiffROAR score shows the model captures the task-related features from the inputs. To this end, we measured the DiffROAR score for each method with \\( k \\) from \\( 10\\% \\) to \\( 90\\% \\) in increments of \\( 10\\% \\). Each measurement was repeated with three different initializations, and the final DiffROAR score was the average of the 27 measurements. The results are shown in Table 3. Compared with standard training, the proposed methods can improve the model's interpretability, especially under the elastic net regularization, which achieved the highest DiffROAR score." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.688, + 0.892, + 0.779 + ], + "angle": 0, + "content": "We also visualized the learned feature for each model, using the optimization-based feature visualization technique of deep-dream [20]. The results (Fig. 3) also show that class-specific features identified with the proposed norm-regularized adversarial training methods look more meaningful to human perception." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.78, + 0.893, + 0.901 + ], + "angle": 0, + "content": "Robustness. To assess the robustness of interpretation maps under the standard and proposed training methods, we adopted an \\(L_{2}\\)-norm bounded interpretation attack method proposed by [18]. We gradually increased the strength of the attack and measured the robustness through similarity measures of the saliency maps before and after the attack. We adopted two metrics as robustness measures: 1) top-k intersection ratio [8], which is the ratio of pix" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11014" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.084, + 0.09, + 0.887, + 0.363 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.369, + 0.893, + 0.397 + ], + "angle": 0, + "content": "Figure 4. Qualitative comparison of saliency maps generated by networks with different adversarial training protocols (fast, iterative) and standard training with additional regularization on input gradients (penalty)." + }, + { + "type": "table_caption", + "bbox": [ + 0.13, + 0.404, + 0.416, + 0.419 + ], + "angle": 0, + "content": "Table 3. Quantitative evaluation on ImageNette." + }, + { + "type": "table", + "bbox": [ + 0.088, + 0.424, + 0.462, + 0.64 + ], + "angle": 0, + "content": "
MethodsDiffROAR (%) (↑)Gini (%) (↑)Acc. (%) (↑)
standard1.8146.5389.04
L1-norm (ε=0.01)2.9556.7390.46
L1-norm (ε=0.05)2.1262.0484.13
L1-norm (ε=0.10)1.9765.5378.85
group-norm (ε=0.10)2.5750.0786.83
group-norm (ε=0.50)1.3249.1587.57
group-norm (ε=1.00)0.4052.7083.80
elastic net (ε1=0.01, ε2=0.01)2.6057.1087.72
elastic net (ε1=0.01, ε2=0.05)3.2457.3587.67
elastic net (ε1=0.01, ε2=0.10)3.1454.4487.19
elastic net (ε1=0.05, ε2=0.01)2.3160.0584.59
elastic net (ε1=0.05, ε2=0.05)2.1161.8484.69
elastic net (ε1=0.05, ε2=0.10)2.1760.2584.54
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.657, + 0.47, + 0.838 + ], + "angle": 0, + "content": "els that remain salient after the interpretation attack, and 2) the structural similarity index measure (SSIM) [38]. We compared the proposed training methods with the baseline standard training and three post-processing-based baselines, SmoothGrad, Sparsified-SmoothGrad (Sparsified-S.), and MoreauGrad (Fig. 5). Standard training seemed vulnerable to minor attacks, even when combined with the Smooth-based post-processing. In contrast, the neural nets trained by the proposed methods displayed significantly higher robustness to the attacks. We also observed that the elastic net and group-norm-based training methods performed slightly more robustly than the \\( L_{1} \\)-norm-based method." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.84, + 0.47, + 0.902 + ], + "angle": 0, + "content": "Stability. We evaluated the algorithmic stability as the magnitude of perturbation in the saliency maps under classifiers trained with different training data or random initialization. As pointed out by [39], standard training with different" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.405, + 0.895, + 0.693 + ], + "angle": 0, + "content": "initializations can result in large discrepancies in saliency maps. We examined if the proposed training methods can alleviate this issue. To this end, we switched \\(10\\%\\) of the training data with the test data and initialized two networks with different random seeds. Then we trained these two networks with the same training process. We used SSIM and top-k overlap to measure the similarities of the generated saliency maps, where the top-k overlap was defined as the Dice score of the top-k masks. As shown in Fig. 5, adversarial training could significantly improve stability. It even brings more improvement than post-processing methods. Note for Sparsified-SmoothGrad, the high SSIM is due to the sparsity of the saliency maps. Through studying top-k overlap, the activated regions were actually different. Among the three variants of adversarial training, the elastic net could achieve the best stability, as the incorporation of \\(L_2^2\\) term could increase the smoothness of the objective function, making the optimization process less sensitive to the perturbation of the training data." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.704, + 0.895, + 0.901 + ], + "angle": 0, + "content": "Comparison of different training protocols. We also conducted experiments to see how different training protocols affect the numerical results. Specifically, we compared one-step optimization (fast), multiple-step optimization (iterative), and free adversarial training (free, in Appendix) [25]. As a baseline, we also studied standard training with norm regularization directly applied to the objective function (penalty). We visualized a few saliency maps in Fig. 4 for comparison. Standard training with regularization failed to generate structured saliency maps, showing the challenge of network optimization with regularization in the objective function, which further certified the superiority of adversarial training. Visually, fast, and iterative" + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.519, + 0.957 + ], + "angle": 0, + "content": "11015" + } + ], + [ + { + "type": "image", + "bbox": [ + 0.087, + 0.095, + 0.351, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.353, + 0.095, + 0.615, + 0.219 + ], + "angle": 0, + "content": null + }, + { + "type": "image", + "bbox": [ + 0.626, + 0.095, + 0.882, + 0.218 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.076, + 0.226, + 0.894, + 0.255 + ], + "angle": 0, + "content": "Figure 5. Quantitative robustness and stability comparison. Left/Middle: Comparison of SSIM/top-k intersection of saliency maps before and after the attack. Right: Comparison of SSIM/top-k overlap of saliency maps generated by networks with different stochastic training." + }, + { + "type": "table_caption", + "bbox": [ + 0.076, + 0.279, + 0.47, + 0.307 + ], + "angle": 0, + "content": "Table 4. Top-k overlap \\((\\%)\\) between gaze map and saliency map on CUB-GHA dataset." + }, + { + "type": "table", + "bbox": [ + 0.097, + 0.313, + 0.452, + 0.384 + ], + "angle": 0, + "content": "
€0.00.10.51.05.0
top 5% overlap33.4235.0738.7442.6350.62
top 10% overlap41.8142.9945.6047.0652.60
accuracy (%)67.5867.5066.5666.6564.99
" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.437, + 0.47, + 0.528 + ], + "angle": 0, + "content": "training achieved comparable quality. However, for \\( L_{1} \\)-norm, interactive training would lose sparsity compared to fast training, but for the elastic net, the trend was the opposite. The Fenchel conjugate of elastic net regularization is differentiable everywhere due to the square term, making its optimization easier compared with \\( L_{1} \\)-norm." + }, + { + "type": "title", + "bbox": [ + 0.077, + 0.56, + 0.353, + 0.577 + ], + "angle": 0, + "content": "5.3. Harmonization with gaze maps" + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.591, + 0.47, + 0.727 + ], + "angle": 0, + "content": "We conducted experiments on the CUB-GHA [21] to verify the effectiveness of our interpretation harmonization strategy on real-world data. CUB-GHA is an extension of CUB [36], which includes gaze maps collected from domain experts for bird category classification. The gaze map is a type of human attention map reflecting how human experts would conduct this task. We aim to harmonize the saliency maps with human attention so that the network could make the decision more similar to humans." + }, + { + "type": "text", + "bbox": [ + 0.076, + 0.735, + 0.471, + 0.903 + ], + "angle": 0, + "content": "To do this, we normalized the gaze map and used the attention score as the weights for the \\( l_{2} \\)-norm perturbation during adversarial training. The results are shown in Fig. 6. The original saliency maps highlighted the whole body of the bird, while the gaze maps were more focused on a specific part (e.g. head) of the bird. After harmonization, the saliency maps showed better alignment with the gaze maps. We also calculated the top-k overlap between saliency maps and gaze maps (Table 4). The results showed an increasing trend of the overlap as we raised the coefficient \\( \\epsilon \\), while the trade-off of accuracy was in a reasonable range." + }, + { + "type": "image", + "bbox": [ + 0.513, + 0.282, + 0.885, + 0.472 + ], + "angle": 0, + "content": null + }, + { + "type": "image_caption", + "bbox": [ + 0.524, + 0.484, + 0.868, + 0.499 + ], + "angle": 0, + "content": "Figure 6. Qualitative results based on CUB-GHA dataset." + }, + { + "type": "title", + "bbox": [ + 0.5, + 0.506, + 0.62, + 0.523 + ], + "angle": 0, + "content": "6. Conclusion" + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.531, + 0.892, + 0.819 + ], + "angle": 0, + "content": "In this paper, we introduced a duality framework to analyze the impact of norm-regularized adversarial training on the gradient-based saliency maps of a trained neural net classifier. Leveraging this duality framework, we proposed several variants of norm-regularized adversarial training, designed to promote certain structures in the gradient-based interpretation maps, including sparsity, group sparsity, and consistency with human attention. We provided experimental results on several benchmark datasets to validate the effectiveness of our proposed methods, which demonstrated that properly designed adversarial training methods can enhance model interpretability as well as the stability and robustness of the gradient-based maps. An interesting future direction is to develop a similar adversarial training-based regularization framework for structured interpretation maps according to integrated gradients, DeepLIFT, and GradCam. Another relevant future direction is to explore other forms of penalty terms in order to expand the methodology to domains beyond computer vision." + }, + { + "type": "text", + "bbox": [ + 0.498, + 0.821, + 0.894, + 0.898 + ], + "angle": 0, + "content": "Acknowledgments. The work of Farzan Farnia is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by a CUHK Direct Research Grant with CUHK Project No. 4055164." + }, + { + "type": "page_number", + "bbox": [ + 0.481, + 0.945, + 0.52, + 0.957 + ], + "angle": 0, + "content": "11016" + } + ], + [ + { + "type": "title", + "bbox": [ + 0.08, + 0.09, + 0.174, + 0.105 + ], + "angle": 0, + "content": "References" + }, + { + "type": "ref_text", + "bbox": [ + 0.087, + 0.115, + 0.47, + 0.17 + ], + "angle": 0, + "content": "[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 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However, standard gradient-based interpretation maps, including the simple gradient and integrated gradient algorithms, often lack desired structures such as sparsity and connectedness in their application to real-world computer vision models. A frequently used approach to inducing sparsity structures into gradient-based saliency maps is to alter the simple gradient scheme using sparsification or norm-based regularization. A drawback with such post-processing methods is their frequently-observed significant loss in fidelity to the original simple gradient map. In this work, we propose to apply adversarial training as an in-processing scheme to train neural networks with structured simple gradient maps. We show a duality relation between the regularized norms of the adversarial perturbations and gradient-based maps, based on which we design adversarial training loss functions promoting sparsity and group-sparsity properties in simple gradient maps. We present several numerical results to show the influence of our proposed norm-based adversarial training methods on the standard gradient-based maps of standard neural network architectures on benchmark image datasets1. + +# 1. Introduction + +Deep neural networks have attained remarkable results in various computer vision tasks including image classification [17], object detection [44], and semantic segmentation [10]. However, understanding and explaining the decision-making process of these complex models remains a challenge, which is required for high-risk applications such as medical imaging [27], autonomous driving [16], and face recognition [37]. To interpret the predictions of neural network classifiers, several explanation methodolo + +![](images/f3981a5d6a987fccd9bb558f7f9e7bb8f913b9937e3f65296b796d98e9c809cf.jpg) +Figure 1. The original simple gradient map could be dense and noisy. Post-processing methods such as sparsification enhance the sparsity at the expense of lower fidelity to the original map. Our proposed in-processing strategy with adversarial training results in higher sparsity without losing fidelity to the simple-grad map. (We use the Gini index as a sparsity measure, and relative $\mathrm{AOPC}_{\mathrm{MoRF}}$ with respect to simple gradient as a fidelity score.) + +gies have been proposed in the literature. Among these explanation methods, gradient-based saliency maps have been frequently applied to interpret image classifiers. The saliency maps provide insight into the regions of the input image contributing to the classifier's decision and potentially prompt the empirical understanding of phenomena from data-driven models. + +Despite the widespread use of standard gradient-based interpretation maps such as simple gradients [29] and integrated gradients [32], they often lack desired structures such as sparsity and connectedness. When applied to real-world computer vision tasks, the generated saliency maps have been frequently observed to be noisy and dense. Such unstructured behavior could hinder the application of gradient-based maps for detecting the influential features in the classifier's decision-making process. To obtain more structured saliency maps, several post-processing + +schemes [18, 30, 31, 42, 43] have been proposed in the literature, which denoise the saliency map to gain higher sparsity. However, a drawback of these post-processing methods is the deviation from the original simple gradient map that alters the definition of the interpretation map. For example, Adebayo et al. [1] conducted a sanity check and found several interpretation methods such as Guided Propagation and Integrated Gradients lacked sensitivity to the model or the data-generating process. Arun et al. [2] demonstrated similar findings on medical imaging applications. To illustrate the fidelity vs. sparsity trade-off in such post-processing schemes, we display an example in Fig. 1, where the simple gradient map looks to contain significant noise scattered over the background. A post-processing sparsification of the gradient map could raise the sparsity of the map; however, the sparsity comes at the cost of a considerable drop (more than $82\%$ ) in the fidelity score. + +In this work, we propose a unified adversarial training (AT) framework to address the unstructured nature of standard simple-gradient maps, where we apply a norm-regularized adversarial training with a properly-designed norm function as an in-processing scheme to promote the sparsity structures in the simple gradient map. AT with standard $L_{2}$ and $L_{\infty}$ -norm perturbations [19] has been successfully and widely utilized in the literature to enhance the adversarial robustness [33] and interpretability [26] of deep neural networks. In our analysis, we extend the understanding of the influence of AT algorithms on the interpretability of a trained model, where we provide a convex duality framework to understand the influence of the norm function constrained in AT on the regularized norm of gradient maps and hence the interpretability of neural nets. + +Specifically, we show a duality relation between the regularized norm of adversarial perturbations and the norm of input-based gradients. This duality relationship allows us to design norm-regularized adversarial training methods, which translates into the regularization of standard sparsity-inducing norms, e.g. the group norm [41] and the elastic net [45], of the simple gradient maps. As we show in this work, the special cases of our proposed framework can promote desired characteristics such as sparsity and connectedness in simple gradient maps. Importantly, unlike the sparsity-regularizing post-processing schemes, the gained sparsity properties of our proposed AT methods do not cost any loss in fidelity to the simple-gradient map, because we do not alter the definition of the interpretation map and only regularize the training process toward networks with more structured gradient maps. + +We conduct several numerical experiments on benchmark image datasets to validate the efficacy of our proposed AT-based methodology. The numerical results reveal the impact of our proposed norm-based AT methods on standard gradient-based maps, showing the enhanced spar + +sity and connectedness properties. We empirically analyze the performance of the trained neural nets in terms of several factors including interpretability, robustness, and stability. Our numerical results indicate the improvements in the mentioned structure-related factors offered by our designed norm-regularized AT methods. Finally, we utilize the shown duality relation to propose an interpretation harmonization scheme for aligning simple gradient maps with expert gaze maps, which performs satisfactorily in our numerical experiments. Our work's main contributions can be summarized as: + +- We show a duality relation between the regularized norms of adversarial perturbations and gradient maps, and develop a unified AT framework for regularizing gradient maps. +- We derive special cases of our proposed AT-based framework leading to the regularization of the elastic net and group-norm of gradient map. +- We leverage the duality framework to propose an interpretation harmonization scheme for aligning gradient maps with human attention. +- We provide numerical results showing the efficacy of the AT-based framework in improving the sparsity and stability of interpretation maps. + +# 2. Related Work + +Gradient-based Interpretation. Using the gradient of the output of a deep neural network w.r.t. an input image is a widely-used approach to generate saliency maps [29]. This method has been utilized in several related works and multiple variants of this approach are proposed in the literature, including SmoothGrad [30], Integrated Gradients [32], DeepLIFT [28], and GradCAM [24]. The vanilla gradient-based maps without post-processing are often noisy and difficult to interpret. A group of methods are proposed to improve the visual quality by sparsifying the gradient-based maps: Guided Propagation [31] removes the noise artifacts from saliency maps by suppressing negative activations in the back-propagation. Sparsified-SmoothGrad [18] applies a sparsification to the saliency map to promote sparsity and robustness. MoreauGrad [43] generates saliency maps using an optimization problem with sparsity regularization. One drawback of the discussed methods is that they are all post-processing schemes, which may compromise the fidelity to the original simple-gradient map. On the other hand, our proposed framework is an in-processing scheme that remains faithful to the simple gradient map. + +Adversarial Training and Interpretability. Adversarial training (AT) involves training the networks using adversarial examples [19]. Fast Gradient Sign Method (FGSM) [9] generates adversarial samples using a single iteration to create the adversarial training example for training the classifier. Projected gradient descent (PGD) [19] uses several + +gradient-based steps to generate more effective adversarial examples in order to make the trained model more robust to norm-constrained adversarial attacks. While the primary objective of AT is to improve the trained model's robustness against adversarial attacks, several studies have shown that AT can also improve the visual quality of interpretation maps [15, 22, 26]. Specifically, AT has been empirically shown to suppress irrelevant features [14], and the standard $\ell_{\infty}$ -norm-based AT will lead to higher sparsity and stability of the interpretation maps [3]. Building upon and extending these findings, our work provides a unified duality framework that connects the perturbation norm constrained by the AT algorithm and the norm penalized for the interpretation map. Specifically, we discuss novel variants of AT methods that lead to the regularization of the elastic net and group norms of the interpretation maps which have not been studied in these related works. + +# 3. Preliminaries + +# 3.1. Gradient-based Saliency Maps + +Throughout this work, our analysis mainly focuses on the standard simple gradient as the gradient-based interpretation. We use $\mathbf{x} \in \mathbb{R}^d$ and $\mathbf{y} \in \mathbb{R}^C$ to denote the input and output of the neural network classifier. Note that $\mathbf{y}$ denotes the output of the neural net's post-softmax layer and contains the assigned likelihood for each of the $C$ classes in the classification task. The neural net function $f_{\theta}: \mathbb{R}^{d} \to \mathbb{R}^{C}$ maps the input vector to the output vector, where $\theta$ denotes the parameters of the neural net. The simple gradient generates a saliency map by taking derivatives of the output of the neural network with respect to the input: + +$$ +\operatorname {S G} \left(f _ {\theta , c}, \mathbf {x}\right) := \nabla_ {\mathbf {x}} f _ {\theta , c} (\mathbf {x}). +$$ + +Here, $c$ can be chosen as ground-truth label $y$ or the label $c$ with the maximum likelihood assigned by the classifier. In our analysis, we assume $\nabla_{\mathbf{x}}f_{\theta}(\mathbf{x})$ denotes the saliency map corresponding to the ground-truth label of sample $\mathbf{x}$ . + +# 3.2. FGSM and PGD + +We consider two of the most widely used forms of adversarial training, FGSM and PGD, in this work. These methods first generate adversarial samples by calculating the gradient of the loss function with respect to the input data and then perturb the data by taking one or multiple small steps in the direction of the sign of the gradient. The perturbation is usually bounded by $l_{\infty}$ -norm. The parameters of the network are then updated to minimize the loss with respect to these adversarial samples. We can use the following objective to summarize the optimization problem where $\hat{P}$ is the empirical distribution of training samples + +$$ +\min _ {\theta} \mathbb {E} _ {(\mathbf {x}, y) \sim \widehat {P}} \left[ \max _ {\| \delta \| _ {\infty} \leq \epsilon} \mathcal {L} \left(f _ {\theta} (\mathbf {x} + \delta), y\right) \right]. \tag {1} +$$ + +Table 1. Summary of regularized norm $h$ on perturbation $\delta$ and the resulting regularized function ${h}^{\star }$ of the input gradient ${\nabla }_{\mathbf{x}}\mathcal{L}\left( {{f}_{\theta }\left( \mathbf{x}\right) ,y}\right)$ . Detailed description can be found in Section 4.3. + +
h(δ)h*(∇xL(fθ(x),y))
I(||δ||∞ ≤ ε)ε||∇xL(fθ(x),y)||1
I(||δ||2,∞ ≤ ε)ε||∇xL(fθ(x),y)||2,1
∑iPQε1,ε2(δi)ε1||∇xL(fθ(x),y)||1 + ε2||∇xL(fθ(x),y)||2
1/4ε||W ⊙ δ||2ε||W ⊙ ∇xL(fθ(x),y)||2
+ +FGSM generates adversarial samples by taking one step in the direction of the sign of the gradient: + +$$ +\mathbf {x} _ {\mathrm {F G S M}} ^ {*} = \mathbf {x} + \epsilon \cdot \operatorname {s i g n} \left(\nabla_ {\mathbf {x}} \mathcal {L} \left(f _ {\theta} (\mathbf {x}), y\right)\right) +$$ + +PGD, on the other hand, iteratively updates the samples with a stepsize $\alpha$ : + +$$ +\mathbf {x} _ {t + 1} = \Pi_ {\mathbf {x} + S} \big (\mathbf {x} _ {t} + \alpha \mathrm {s i g n} (\nabla_ {\mathbf {x} _ {t}} \mathcal {L} (f _ {\theta} (\mathbf {x} _ {t}), y)) \big), +$$ + +where $S = \{\mathbf{z}:\| \mathbf{z}\|_{\infty}\leq \epsilon \}$ denotes the $\epsilon$ -radius $L_{\infty}$ -ball. + +# 3.3. Fenchel Conjugate + +The Fenchel conjugate is an essential operation in convex analysis which has many applications to various computer vision algorithms. For a function $f: \mathcal{X} \to \mathbb{R}$ , its Fenchel conjugate $f^{\star}: \mathcal{X} \to \mathbb{R}$ is defined as: + +$$ +f ^ {\star} (z) = \sup \left\{\langle x, z \rangle - f (x): x \in \mathcal {X} \right\}, +$$ + +where $\langle \cdot ,\cdot \rangle$ denotes the inner product, and sup represents the supremum. Note that for a convex $f$ $f$ will be the Fenchel conjugate of $f^{\star}$ . Furthermore, for every function $f$ , the Fenchel conjugate $f^{\star}$ is guaranteed to be convex. + +# 4. An Adversarial Training Methodology for Regularizing Interpretation Maps + +In this section, we show a duality relation between the input gradient and the perturbation vectors, which is based on the linear approximation of the loss function $\ell\big(f(\mathbf{x} + \delta),y\big)$ around data point $\mathbf{x}$ . In the approximation, the first-order term $\langle \nabla_{\mathbf{x}}\ell \big(f(\mathbf{x}),y\big),\delta \rangle$ is the inner product of the perturbation vector and the input-based gradient of the loss function. Therefore, as will be explained in the section, to penalize a norm of the saliency map in the adversarial training process, we propose to constrain the dual norm of the perturbation vector. We summarize three variants of the norm constraint on the perturbation and its effect on the simple gradient saliency maps in Table 1. + +# 4.1. Rethinking the Impact of $\ell_{\infty}$ -Norm-Based Adversarial Training on Saliency Maps + +We perform a first-order analysis by means of Fenchel conjugate to indicate how $L_{\infty}$ -norm-based adversarial training + +could lead to higher sparsity in gradient-based maps. Under a small enough perturbation norm bound $\epsilon$ and twice-differentiable loss function, the objective of adversarial training in Eq. 1 can be approximated by first-order Taylor expansion as + +$$ +\begin{array}{l} \operatorname {E q.} 1 = \min _ {\theta} \mathbb {E} _ {\mathbf {x}, y \sim \hat {P}} \left[ \mathcal {L} \left(f _ {\theta} (\mathbf {x}), y\right) \right. \\ + \max _ {\| \delta \| _ {\infty} \leq \epsilon} \left\{\delta^ {T} \nabla_ {\mathbf {x}} \mathcal {L} (f _ {\theta} (\mathbf {x}), y) \right\} \biggr ] + \mathcal {O} (\epsilon^ {2}). \\ \end{array} +$$ + +Using the common cross-entropy loss or hinge loss, the derivative of the loss with respect to the predicted log-its at every training sample will be $\nabla_{\mathbf{x}}\mathcal{L}(f_{\theta},(\mathbf{x}),y) = -f_{\theta ,y}(\mathbf{x})\nabla_{\mathbf{x}}f_{\theta}(\mathbf{x})$ , so we can build the connection between the objective and the saliency map: + +$$ +\begin{array}{l} \operatorname {E q.} 1 = \min _ {\theta} \mathbb {E} _ {\mathbf {x}, y \sim \hat {P}} \left[ \mathcal {L} \left(f _ {\theta , y} (\mathbf {x})\right) \right. \\ \left. + f _ {\theta , y} (\mathbf {x}) \max _ {| | \delta | | _ {\infty} \leq \epsilon} \left\{- \delta^ {T} \nabla_ {\mathbf {x}} f _ {\theta} (\mathbf {x}) \right\} \right] + \mathcal {O} (\epsilon^ {2}). \\ \end{array} +$$ + +Note we can leverage Fenchel conjugate operation to transform the maximization subproblem in the above problem into an unconstrained optimization: + +$$ +\max _ {\| \delta \| _ {\infty} \leq \epsilon} - \delta^ {T} \nabla_ {\mathbf {x}} f _ {\theta} (\mathbf {x}) = \max _ {\delta} - \delta^ {T} \nabla_ {\mathbf {x}} f _ {\theta} (\mathbf {x}) - \mathbb {I} (\| \delta \| _ {\infty} \leq \epsilon), \tag {2} +$$ + +where $\mathbb{I}(\mathrm{condition}) = 0$ if the condition holds and $+\infty$ otherwise. With the concept of Fenchel conjugate, the optimal value of the optimization problem defined in Eq. 2 is $\epsilon \| \nabla_{\mathbf{x}}f_{\theta}(\mathbf{x})\| _1$ . Hence, we successfully transform the original minimax optimization problem into a regularized optimization within an approximation error $\mathcal{O}(\epsilon^2)$ : + +$$ +\mathrm {E q .} 1 \approx \underset {\theta} {\min } \mathbb {E} _ {\mathbf {x}, y \sim \widehat {P}} \Big [ \mathcal {L} (f _ {\theta} (\mathbf {x}), y) + \epsilon f _ {\theta , y} (\mathbf {x}) \| \nabla_ {\mathbf {x}} f _ {\theta} (\mathbf {x}) \| _ {1} \Big ]. +$$ + +Hence, we find that adversarial training with $L_{\infty}$ -norm is approximately equivalent to applying $L_{1}$ -norm regularization to the simple gradient saliency map, therefore promoting the sparsity of the saliency maps. + +# 4.2. Adversarial Training with Fenchel Conjugate Regularization: a Unified Approach + +Next, we consider adversarial training with a general norm-based regularization penalty. Here our goal is to promote a structured saliency map through a regularization function $h^{\star}(\mathbf{z})$ . Note that for a convex $h$ , the Fenchel conjugate of $h^{\star}(\mathbf{z})$ will be $h(\mathbf{x})$ . Therefore, we consider the min-max optimization with the adversarial penalty function $-h(\delta)$ : + +$$ +\min _ {\theta} \mathbb {E} _ {\mathbf {x}, y \sim \widehat {P}} \left[ \max _ {\delta} \mathcal {L} \left(f _ {\theta} (\mathbf {x} + \delta), y\right) - h (\delta) \right]. +$$ + +Following our analysis for the $L_{\infty}$ -norm-based adversarial training, we define the first-order approximate loss: + +$$ +\widehat {\mathcal {L}} (f _ {\theta} (\mathbf {x}), y, \delta) := \mathcal {L} (f _ {\theta} (\mathbf {x}), y) + \delta^ {T} \nabla_ {x} \mathcal {L} (f _ {\theta} (\mathbf {x}), y), +$$ + +To measure how well $\widehat{\mathcal{L}}(f_{\theta}(\mathbf{x}), y, \delta)$ approximates the adversarial loss, we observe the approximation error can be simply bounded for the class of $\lambda$ -smooth functions. + +Definition 1 We call $g: \mathbb{R}^d \to \mathbb{R}$ a smooth if for every $\mathbf{x}$ and $\mathbf{z}$ : $\| \nabla g(\mathbf{x}) - \nabla g(\mathbf{z}) \|_2 \leq \lambda \| \mathbf{x} - \mathbf{z} \|_2$ . + +Observation 1 The approximation error of the first-order Taylor series expansion of adversarial loss under an $\epsilon$ - $L_2$ -norm bounded perturbation $\|\delta\| \leq \epsilon$ can be bounded as + +$$ +\left| \widehat {\mathcal {L}} (f _ {\theta} (\mathbf {x}), y, \delta) - \mathcal {L} (f _ {\theta} (\mathbf {x} + \delta), y) \right| \leq \frac {\lambda \epsilon^ {2}}{2} +$$ + +The observation shows $\widehat{\mathcal{L}}(f_{\theta}(\mathbf{x}), y, \delta)$ can be a good approximation of the adversarial loss under a small $\|\delta\|$ . Combining the approximate loss with $h(\delta)$ regularization, we can derive the following equivalence by Fenchel conjugate: + +Proposition 1 Using Fenchel conjugate $h^{\star}$ , we can reduce the maximization of the approximate adversarial loss as + +$$ +\begin{array}{l} \max _ {\delta} \left\{\widehat {\mathcal {L}} \left(f _ {\theta} (\mathbf {x}), y, \delta\right) - h (\delta) \right\} \tag {3} \\ = \mathcal {L} (f _ {\theta} (\mathbf {x}), y) + h ^ {\star} \bigl (\nabla_ {\mathbf {x}} \mathcal {L} \bigl (f _ {\theta} (\mathbf {x}), y \bigr) \bigr). \\ \end{array} +$$ + +In a scenario that the neural network completely fits the training data, we have that $\nabla_{\mathbf{x}}\mathcal{L}(f_{\theta}(\mathbf{x}),y) = -f_{\theta ,y}(\mathbf{x})\nabla_{x}f_{\theta}(\mathbf{x})\approx -\nabla_{x}f_{\theta}(\mathbf{x})$ . Therefore, to enforce the gradient map $\nabla_{x}f_{\theta}(\mathbf{x})$ to satisfy a bounded penalty function $h^\star$ , we can conduct adversarial training with an additive penalty term $-h(\delta)$ . The optimal perturbation $\delta^{*}$ can be derived via the standard gradient ascent algorithm to maximize the regularized adversarial loss or be approximated with the analytic solution to the approximate optimization problem. + +# 4.3. Special Cases of the Fenchel Conjugate-based Duality Framework + +Leveraging the duality framework in the previous section, we derive regularization penalty terms to penalize other sparsity norms different from $l_{1}$ -norm and discuss their influence on the saliency maps. + +$L_{2,1}$ -group-norm penalty. The $L_{2,1}$ -group-norm of $\mathbf{x} \in \mathbb{R}^d$ for disjoint variable subsets $S_1, \dots, S_t \subseteq \{1, \dots, d\}$ is defined as the special case $p = 1$ of the following definition: + +$$ +\left\| \mathbf {x} \right\| _ {2, p} := \left\| \left[ \left\| \mathbf {x} _ {S _ {1}} \right\| _ {2}, \dots , \left\| \mathbf {x} _ {S _ {t}} \right\| _ {2} \right] \right\| _ {p}. +$$ + +To apply the duality framework to the group norm (with coefficient $\epsilon > 0$ ), we derive its Fenchel conjugate as follows. + +Proposition 2 The Fenchel conjugate of the above $L_{2,1}$ -group-norm is $h(\mathbf{z}) = \mathbb{I}(\| \mathbf{z}\|_{2,\infty}\leq \epsilon)$ . + +Different from $L_{1}$ -norm inducing pixel-level sparsity, $L_{2,1}$ -group-norm will induce sparsity of the patch basis. Under this regularization, the more influential patches are expected to be highlighted in the saliency map. This effect could further lead to a connected saliency map, which will be desired when adjacent pixels belonging have similar effects on the prediction of the classifier. + +Elastic net penalty. The elastic net penalty $h^{\star}(\mathbf{x})$ linearly combines the $L_{1}$ and $L_{2}^{2}$ penalty terms: + +$$ +h ^ {\star} (\mathbf {x}) = \epsilon_ {1} \| \mathbf {x} \| _ {1} + \epsilon_ {2} \| \mathbf {x} \| _ {2} ^ {2}, \epsilon_ {1} > 0, \epsilon_ {2} > 0. +$$ + +Proposition 3 The Fenchel conjugate of the above elastic net penalty $h^{\star}$ is $h(\mathbf{z}) = \sum_{i} PQ_{\epsilon_1, \epsilon_2}(\mathbf{z}_i)$ where $PQ_{\epsilon_1, \epsilon_2}$ is the piece-wise quadratic function defined as: + +$$ +P Q _ {\epsilon_ {1}, \epsilon_ {2}} (\mathbf {z} _ {i}) = \left\{ \begin{array}{c l} \frac {1}{4 \epsilon_ {2}} (\mathbf {z} _ {i} - \epsilon_ {1}) ^ {2} & \text {i f} \epsilon_ {1} < \mathbf {z} _ {i} \\ 0 & \text {i f} - \epsilon_ {1} \leq \mathbf {z} _ {i} \leq \epsilon_ {1} \\ \frac {1}{4 \epsilon_ {2}} (\mathbf {z} _ {i} + \epsilon_ {1}) ^ {2} & \text {i f} \mathbf {z} _ {i} < - \epsilon_ {1}. \end{array} \right. +$$ + +The linear combination of the $L_{1}$ -norm and $L_{2}^{2}$ -norm penalty terms in the elastic net results in a strongly convex regularization function, which is known to promote the stability of the sparsity pattern. Therefore, one can expect that the elastic net-regularized maps could possess higher robustness and stability than the $L_{1}$ -norm regularized maps. Interpretation harmonization. The purpose of interpretation harmonization is to align the saliency map generated by the neural network with some reference attention map. The reference attention map can be manually labeled by domain experts, or based on some physical principle behind the classification task. Through interpretation harmonization, the network could be enabled to analyze the phenomenon in a similar way as a human, which would help diminish the potential bias or shortcuts learned by the neural net [6, 7]. + +To achieve this goal, we leverage $L_{2}$ -norm regularization to diminish the importance scores of unrelated features. Specifically, assume $\mathbf{A} \in \mathbb{R}^{d}$ is the expert's attention map with non-negative entries. A greater value implies a more important feature. We define $\hat{\mathbf{A}} := \max(\mathbf{A}) - \mathbf{A} + \sigma$ , where $\sigma$ is small enough so that the ordinal relation is reverted and all elements are positive. To diminish the importance score of the background region, we use the penalty term: + +$$ +h ^ {\star} (\mathbf {x}) = \epsilon \| \sqrt {\tilde {\mathbf {A}}} \odot \mathbf {x} \| _ {2} ^ {2}, \epsilon > 0 +$$ + +where $\odot$ denotes Hadamard product. By adding this regularization term, the importance score of unrelated features is pushed to 0 while important features remain unaffected. + +Proposition 4 The Fenchel conjugate of the above weighted $L_{2}$ -norm square regularization is: + +$$ +h (\mathbf {z}) = \frac {1}{4 \epsilon} \left\| \frac {1}{\sqrt {\tilde {\mathbf {A}}}} \odot \mathbf {z} \right\| _ {2} ^ {2}. +$$ + +![](images/1acfe4b86480d4afef7b923b424c20fe1a1770161add98138388d7b1eff50356.jpg) +Figure 2. Qualitative results based on the synthesized dataset. + +The derivation requires the weight term $\tilde{\mathbf{A}}$ to be positive. However, a positive weight only leads to the diminishing of the importance score of unrelated features. It does not explicitly promote larger scores for important features. Empirically, we have found that using $\delta^{*}$ in the opposite direction to the gradients for important pixels helps increase the attribution scores for important features and results in better alignment. Therefore, in our numerical experiment, we set $\tilde{\mathbf{A}} = \frac{1}{2}\max (\mathbf{A}) - \mathbf{A}$ and $\delta^{*} = 2\epsilon \tilde{\mathbf{A}}\odot \nabla_{\mathbf{x}}\mathcal{L}(f_{\theta}(\mathbf{x}),y)$ . + +# 5. Experiments + +We conducted comprehensive numerical experiments to evaluate the performance of our proposed adversarial training-based methods. Firstly, we evaluate saliency maps' accuracy on a synthesized dataset with ground truth interpretation. Next, we assessed the visual quality, sparsity, interpretability, robustness, and stability of the saliency maps on Imagenette. Finally, we demonstrated the effectiveness of our interpretation harmonization strategy on the CUB-GHA dataset. Our quantitative results include adversarial training with one normalized step and multi-step gradient ascent. The main text focuses on the results of one normalized step, while detailed training settings and complete numerical results can be found in the Appendix. + +# 5.1. Results on synthesized dataset + +To illustrate how adversarial training can improve the model's interpretability, we first conducted experiments on a synthesized dataset with ground-truth for the saliency maps proposed by [35]. There are three regions on the ground-truth of the synthesized dataset (Fig. 2): background without any classification information (white region); localization information describes the location of an object (light red region); and distinguishing features crucial for classification (dark red area). We trained ResNet-34 [12] with standard training and regularized adversarial training. + +As the ground-truth was a ternary class, we reported the five-band-score reflects pixel accuracy, recall, precision, and the false positive rate (FPR) based on ternary classifi + +Table 2. Comparison of five-band-scores and binary scores of standard training and adversarial training. + +
MethodsFive-band-scoresBinary scores
Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)
standard89.819.8632.581.2188.6644.4716.2210.22
\( L_1 \)-norm89.826.4129.200.7694.6065.0630.844.70
group-norm89.847.5427.350.9194.2763.7829.774.99
elastic net89.918.3526.830.9294.6365.6531.294.66
harmonization90.1411.3743.311.1493.8267.0528.155.54
+ +![](images/065f3927a0594365ba1f1b5a7cc109567da861a9505e0cabf34ec3dd22ee175d.jpg) +Figure 3. Images optimized for maximizing class-logit activations. + +cation. The results are listed in Table 2, where the method's name corresponds to the penalty term $h^{\star}$ in Eq. 3. The harmonization training achieved the best scores in terms of most of the metrics, showing the effectiveness of the proposed harmonization method. We also noticed that adversarial training-based methods consistently achieved higher accuracy and lower FPR compared with stranded training but led to lower recall and precision, because the adversarial training raised the sparsity of gradient maps. The importance scores of the localization area, which was less important compared with distinguishing features, were also diminished. Therefore, following [11], we also converted the ternary classification task to a binary classification task by considering the background and localization information as one class. The results suggested that adversarial training could significantly improve the accuracy of saliency maps in detecting distinguishing features. + +We visualized the saliency maps in Fig. 2 for qualitative evaluation (we only show results with elastic net regularization here and leave the rest in the Appendix). We discovered that the saliency map of standard training was activated more clearly in the region of the localization information than it was in the region of the distinguishing feature. In contrast, the saliency map with adversarial training was activated more significantly for the distinguishing features, especially on the boundaries. Moreover, the saliency maps looked more sparse and less noisy. + +# 5.2. Results on ImageNette + +We performed numerical experiments on ImageNette, a ten-class subset of ImageNet [4], to examine the properties of the proposed adversarial training. Specifically, we studied the sparsity, interpretability, adversarial robustness, and stability of the saliency maps generated for EfficientNet [34] + +classifiers with the proposed adversarial training methods. + +Sparsity. We trained the neural network models with different regularization coefficients and used the Gini Index [13] as a measure of the sparsity of the saliency map. The results are shown in Table 3. All the proposed adversarial training-based methods led to more sparse saliency maps than standard training, with zero or only minor drops in clean accuracy. The $L_{1}$ -norm-based method attained the highest sparsity. Also, the sparsity increased with the regularization coefficient $\epsilon$ . The gradient maps visualized in Fig. 4 suggest that standard training could lead to miscellaneous points in the background. On the other hand, the gradient maps with our proposed adversarial training methods seem to have higher visual quality. + +Interpretability. To show that the proposed training methods can improve the interpretability of the model, we calculated the DiffROAR score [26] for the methods. DiffROAR measures the difference in the predictive power of the dataset, where the top and bottom $k\%$ of the pixels are removed according to the importance score. A higher DiffROAR score shows the model captures the task-related features from the inputs. To this end, we measured the DiffROAR score for each method with $k$ from $10\%$ to $90\%$ in increments of $10\%$ . Each measurement was repeated with three different initializations, and the final DiffROAR score was the average of the 27 measurements. The results are shown in Table 3. Compared with standard training, the proposed methods can improve the model's interpretability, especially under the elastic net regularization, which achieved the highest DiffROAR score. + +We also visualized the learned feature for each model, using the optimization-based feature visualization technique of deep-dream [20]. The results (Fig. 3) also show that class-specific features identified with the proposed norm-regularized adversarial training methods look more meaningful to human perception. + +Robustness. To assess the robustness of interpretation maps under the standard and proposed training methods, we adopted an $L_{2}$ -norm bounded interpretation attack method proposed by [18]. We gradually increased the strength of the attack and measured the robustness through similarity measures of the saliency maps before and after the attack. We adopted two metrics as robustness measures: 1) top-k intersection ratio [8], which is the ratio of pix + +![](images/d731715a60311aff5f8345a45bb88573111aac8a58645a910709ca7452e8c178.jpg) +Figure 4. Qualitative comparison of saliency maps generated by networks with different adversarial training protocols (fast, iterative) and standard training with additional regularization on input gradients (penalty). + +Table 3. Quantitative evaluation on ImageNette. + +
MethodsDiffROAR (%) (↑)Gini (%) (↑)Acc. (%) (↑)
standard1.8146.5389.04
L1-norm (ε=0.01)2.9556.7390.46
L1-norm (ε=0.05)2.1262.0484.13
L1-norm (ε=0.10)1.9765.5378.85
group-norm (ε=0.10)2.5750.0786.83
group-norm (ε=0.50)1.3249.1587.57
group-norm (ε=1.00)0.4052.7083.80
elastic net (ε1=0.01, ε2=0.01)2.6057.1087.72
elastic net (ε1=0.01, ε2=0.05)3.2457.3587.67
elastic net (ε1=0.01, ε2=0.10)3.1454.4487.19
elastic net (ε1=0.05, ε2=0.01)2.3160.0584.59
elastic net (ε1=0.05, ε2=0.05)2.1161.8484.69
elastic net (ε1=0.05, ε2=0.10)2.1760.2584.54
+ +els that remain salient after the interpretation attack, and 2) the structural similarity index measure (SSIM) [38]. We compared the proposed training methods with the baseline standard training and three post-processing-based baselines, SmoothGrad, Sparsified-SmoothGrad (Sparsified-S.), and MoreauGrad (Fig. 5). Standard training seemed vulnerable to minor attacks, even when combined with the Smooth-based post-processing. In contrast, the neural nets trained by the proposed methods displayed significantly higher robustness to the attacks. We also observed that the elastic net and group-norm-based training methods performed slightly more robustly than the $L_{1}$ -norm-based method. + +Stability. We evaluated the algorithmic stability as the magnitude of perturbation in the saliency maps under classifiers trained with different training data or random initialization. As pointed out by [39], standard training with different + +initializations can result in large discrepancies in saliency maps. We examined if the proposed training methods can alleviate this issue. To this end, we switched $10\%$ of the training data with the test data and initialized two networks with different random seeds. Then we trained these two networks with the same training process. We used SSIM and top-k overlap to measure the similarities of the generated saliency maps, where the top-k overlap was defined as the Dice score of the top-k masks. As shown in Fig. 5, adversarial training could significantly improve stability. It even brings more improvement than post-processing methods. Note for Sparsified-SmoothGrad, the high SSIM is due to the sparsity of the saliency maps. Through studying top-k overlap, the activated regions were actually different. Among the three variants of adversarial training, the elastic net could achieve the best stability, as the incorporation of $L_2^2$ term could increase the smoothness of the objective function, making the optimization process less sensitive to the perturbation of the training data. + +Comparison of different training protocols. We also conducted experiments to see how different training protocols affect the numerical results. Specifically, we compared one-step optimization (fast), multiple-step optimization (iterative), and free adversarial training (free, in Appendix) [25]. As a baseline, we also studied standard training with norm regularization directly applied to the objective function (penalty). We visualized a few saliency maps in Fig. 4 for comparison. Standard training with regularization failed to generate structured saliency maps, showing the challenge of network optimization with regularization in the objective function, which further certified the superiority of adversarial training. Visually, fast, and iterative + +![](images/11844bd43c7a9166772627b28faaf5c0da9d559c88eeb4b92efb79e13c9479f5.jpg) +Figure 5. Quantitative robustness and stability comparison. Left/Middle: Comparison of SSIM/top-k intersection of saliency maps before and after the attack. Right: Comparison of SSIM/top-k overlap of saliency maps generated by networks with different stochastic training. + +![](images/1627768cf21021453c9d71fd3f2af1f51333d21fbe1ad0d866f9efd5359f9234.jpg) + +![](images/3887241b624cd18016a21a8813a8867a30e5c739adb2815e1c588b475066db8e.jpg) + +Table 4. Top-k overlap $(\%)$ between gaze map and saliency map on CUB-GHA dataset. + +
€0.00.10.51.05.0
top 5% overlap33.4235.0738.7442.6350.62
top 10% overlap41.8142.9945.6047.0652.60
accuracy (%)67.5867.5066.5666.6564.99
+ +training achieved comparable quality. However, for $L_{1}$ -norm, interactive training would lose sparsity compared to fast training, but for the elastic net, the trend was the opposite. The Fenchel conjugate of elastic net regularization is differentiable everywhere due to the square term, making its optimization easier compared with $L_{1}$ -norm. + +# 5.3. Harmonization with gaze maps + +We conducted experiments on the CUB-GHA [21] to verify the effectiveness of our interpretation harmonization strategy on real-world data. CUB-GHA is an extension of CUB [36], which includes gaze maps collected from domain experts for bird category classification. The gaze map is a type of human attention map reflecting how human experts would conduct this task. We aim to harmonize the saliency maps with human attention so that the network could make the decision more similar to humans. + +To do this, we normalized the gaze map and used the attention score as the weights for the $l_{2}$ -norm perturbation during adversarial training. The results are shown in Fig. 6. The original saliency maps highlighted the whole body of the bird, while the gaze maps were more focused on a specific part (e.g. head) of the bird. After harmonization, the saliency maps showed better alignment with the gaze maps. We also calculated the top-k overlap between saliency maps and gaze maps (Table 4). The results showed an increasing trend of the overlap as we raised the coefficient $\epsilon$ , while the trade-off of accuracy was in a reasonable range. + +![](images/207aee0309b4cfef0716060fa525b27d45945f62c2337027fda8e177b4f133a3.jpg) +Figure 6. Qualitative results based on CUB-GHA dataset. + +# 6. Conclusion + +In this paper, we introduced a duality framework to analyze the impact of norm-regularized adversarial training on the gradient-based saliency maps of a trained neural net classifier. Leveraging this duality framework, we proposed several variants of norm-regularized adversarial training, designed to promote certain structures in the gradient-based interpretation maps, including sparsity, group sparsity, and consistency with human attention. We provided experimental results on several benchmark datasets to validate the effectiveness of our proposed methods, which demonstrated that properly designed adversarial training methods can enhance model interpretability as well as the stability and robustness of the gradient-based maps. An interesting future direction is to develop a similar adversarial training-based regularization framework for structured interpretation maps according to integrated gradients, DeepLIFT, and GradCam. Another relevant future direction is to explore other forms of penalty terms in order to expand the methodology to domains beyond computer vision. + +Acknowledgments. The work of Farzan Farnia is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by a CUHK Direct Research Grant with CUHK Project No. 4055164. + +# References + +[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. Sanity checks for saliency maps. Advances in neural information processing systems, 31, 2018. 2, 4 +[2] Nishanth Arun, Nathan Gaw, Praveer Singh, Ken Chang, Mehak Aggarwal, Bryan Chen, Katharina Hoebel, Sharut Gupta, Jay Patel, Mishka Gidwani, et al. Assessing the trustworthiness of saliency maps for localizing abnormalities in medical imaging. 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Journal of the Royal Statistical Society Series B: Statistical Methodology, 67(2):301-320, 2005. 2 \ No newline at end of file diff --git a/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/images.zip b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..0f689447f3b2106e443794684537f39be1722653 --- /dev/null +++ b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c241d43ae4e20da9e4d629e85cf82ede7c541c2631a2cccf39e6950620cdd00d +size 557070 diff --git a/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/layout.json b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4ff39b0852355eda1e9517283441390f9b847dca --- /dev/null +++ b/2024/Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training/layout.json @@ -0,0 +1,8995 @@ +{ + "pdf_info": [ + { + "para_blocks": [ + { + "bbox": [ + 153, + 103, + 442, + 140 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 153, + 103, + 442, + 140 + ], + "spans": [ + { + "bbox": [ + 153, + 103, + 442, + 140 + ], + "type": "text", + "content": "Structured Gradient-based Interpretations via Norm-Regularized Adversarial Training" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 203, + 161, + 390, + 190 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 203, + 161, + 390, + 190 + ], + "spans": [ + { + "bbox": [ + 203, + 161, + 390, + 190 + ], + "type": "text", + "content": "Shizhan Gong, Qi Dou, Farzan Farnia \nThe Chinese University of Hong Kong" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 189, + 191, + 405, + 202 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 189, + 191, + 405, + 202 + ], + "spans": [ + { + "bbox": [ + 189, + 191, + 405, + 202 + ], + "type": "text", + "content": "{szgong22, qdou, farnia}@cse.cuhk.edu.hk" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "spans": [ + { + "bbox": [ + 143, + 231, + 192, + 243 + ], + "type": "text", + "content": "Abstract" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "spans": [ + { + "bbox": [ + 46, + 256, + 290, + 533 + ], + "type": "text", + "content": "Gradient-based saliency maps have been widely used to explain the decisions of deep neural network classifiers. However, standard gradient-based interpretation maps, including the simple gradient and integrated gradient algorithms, often lack desired structures such as sparsity and connectedness in their application to real-world computer vision models. A frequently used approach to inducing sparsity structures into gradient-based saliency maps is to alter the simple gradient scheme using sparsification or norm-based regularization. A drawback with such post-processing methods is their frequently-observed significant loss in fidelity to the original simple gradient map. In this work, we propose to apply adversarial training as an in-processing scheme to train neural networks with structured simple gradient maps. We show a duality relation between the regularized norms of the adversarial perturbations and gradient-based maps, based on which we design adversarial training loss functions promoting sparsity and group-sparsity properties in simple gradient maps. We present several numerical results to show the influence of our proposed norm-based adversarial training methods on the standard gradient-based maps of standard neural network architectures on benchmark image datasets1." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "spans": [ + { + "bbox": [ + 47, + 555, + 128, + 567 + ], + "type": "text", + "content": "1. Introduction" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 576, + 287, + 684 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 576, + 287, + 684 + ], + "spans": [ + { + "bbox": [ + 46, + 576, + 287, + 684 + ], + "type": "text", + "content": "Deep neural networks have attained remarkable results in various computer vision tasks including image classification [17], object detection [44], and semantic segmentation [10]. However, understanding and explaining the decision-making process of these complex models remains a challenge, which is required for high-risk applications such as medical imaging [27], autonomous driving [16], and face recognition [37]. To interpret the predictions of neural network classifiers, several explanation methodolo" + } + ] + } + ], + "index": 8 + }, + { + "type": "image", + "bbox": [ + 309, + 232, + 544, + 408 + ], + "blocks": [ + { + "bbox": [ + 309, + 232, + 544, + 408 + ], + "lines": [ + { + "bbox": [ + 309, + 232, + 544, + 408 + ], + "spans": [ + { + "bbox": [ + 309, + 232, + 544, + 408 + ], + "type": "image", + "image_path": "f3981a5d6a987fccd9bb558f7f9e7bb8f913b9937e3f65296b796d98e9c809cf.jpg" + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 304, + 418, + 547, + 497 + ], + "lines": [ + { + "bbox": [ + 304, + 418, + 547, + 497 + ], + "spans": [ + { + "bbox": [ + 304, + 418, + 547, + 497 + ], + "type": "text", + "content": "Figure 1. The original simple gradient map could be dense and noisy. Post-processing methods such as sparsification enhance the sparsity at the expense of lower fidelity to the original map. Our proposed in-processing strategy with adversarial training results in higher sparsity without losing fidelity to the simple-grad map. (We use the Gini index as a sparsity measure, and relative " + }, + { + "bbox": [ + 304, + 418, + 547, + 497 + ], + "type": "inline_equation", + "content": "\\mathrm{AOPC}_{\\mathrm{MoRF}}" + }, + { + "bbox": [ + 304, + 418, + 547, + 497 + ], + "type": "text", + "content": " with respect to simple gradient as a fidelity score.)" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_caption" + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 509, + 547, + 591 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 547, + 591 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 547, + 591 + ], + "type": "text", + "content": "gies have been proposed in the literature. Among these explanation methods, gradient-based saliency maps have been frequently applied to interpret image classifiers. The saliency maps provide insight into the regions of the input image contributing to the classifier's decision and potentially prompt the empirical understanding of phenomena from data-driven models." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "spans": [ + { + "bbox": [ + 304, + 594, + 547, + 715 + ], + "type": "text", + "content": "Despite the widespread use of standard gradient-based interpretation maps such as simple gradients [29] and integrated gradients [32], they often lack desired structures such as sparsity and connectedness. When applied to real-world computer vision tasks, the generated saliency maps have been frequently observed to be noisy and dense. Such unstructured behavior could hinder the application of gradient-based maps for detecting the influential features in the classifier's decision-making process. To obtain more structured saliency maps, several post-processing" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "spans": [ + { + "bbox": [ + 65, + 2, + 111, + 34 + ], + "type": "text", + "content": "CVF" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "header", + "angle": 0, + "lines": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "spans": [ + { + "bbox": [ + 145, + 0, + 494, + 37 + ], + "type": "text", + "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "page_footnote", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "spans": [ + { + "bbox": [ + 47, + 693, + 286, + 713 + ], + "type": "text", + "content": "The paper's code is available at: https://github.com/peterant330/AdvGrad" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 758 + ], + "type": "text", + "content": "11009" + } + ] + } + ], + "index": 14 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 0 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": "schemes [18, 30, 31, 42, 43] have been proposed in the literature, which denoise the saliency map to gain higher sparsity. However, a drawback of these post-processing methods is the deviation from the original simple gradient map that alters the definition of the interpretation map. For example, Adebayo et al. [1] conducted a sanity check and found several interpretation methods such as Guided Propagation and Integrated Gradients lacked sensitivity to the model or the data-generating process. Arun et al. [2] demonstrated similar findings on medical imaging applications. To illustrate the fidelity vs. sparsity trade-off in such post-processing schemes, we display an example in Fig. 1, where the simple gradient map looks to contain significant noise scattered over the background. A post-processing sparsification of the gradient map could raise the sparsity of the map; however, the sparsity comes at the cost of a considerable drop (more than " + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "inline_equation", + "content": "82\\%" + }, + { + "bbox": [ + 46, + 72, + 289, + 276 + ], + "type": "text", + "content": ") in the fidelity score." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "spans": [ + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "type": "text", + "content": "In this work, we propose a unified adversarial training (AT) framework to address the unstructured nature of standard simple-gradient maps, where we apply a norm-regularized adversarial training with a properly-designed norm function as an in-processing scheme to promote the sparsity structures in the simple gradient map. AT with standard " + }, + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 46, + 278, + 289, + 457 + ], + "type": "text", + "content": "-norm perturbations [19] has been successfully and widely utilized in the literature to enhance the adversarial robustness [33] and interpretability [26] of deep neural networks. In our analysis, we extend the understanding of the influence of AT algorithms on the interpretability of a trained model, where we provide a convex duality framework to understand the influence of the norm function constrained in AT on the regularized norm of gradient maps and hence the interpretability of neural nets." + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 46, + 460, + 289, + 652 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 460, + 289, + 652 + ], + "spans": [ + { + "bbox": [ + 46, + 460, + 289, + 652 + ], + "type": "text", + "content": "Specifically, we show a duality relation between the regularized norm of adversarial perturbations and the norm of input-based gradients. This duality relationship allows us to design norm-regularized adversarial training methods, which translates into the regularization of standard sparsity-inducing norms, e.g. the group norm [41] and the elastic net [45], of the simple gradient maps. As we show in this work, the special cases of our proposed framework can promote desired characteristics such as sparsity and connectedness in simple gradient maps. Importantly, unlike the sparsity-regularizing post-processing schemes, the gained sparsity properties of our proposed AT methods do not cost any loss in fidelity to the simple-gradient map, because we do not alter the definition of the interpretation map and only regularize the training process toward networks with more structured gradient maps." + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 653, + 289, + 715 + ], + "type": "text", + "content": "We conduct several numerical experiments on benchmark image datasets to validate the efficacy of our proposed AT-based methodology. The numerical results reveal the impact of our proposed norm-based AT methods on standard gradient-based maps, showing the enhanced spar" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 304, + 72, + 547, + 203 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 72, + 547, + 203 + ], + "spans": [ + { + "bbox": [ + 304, + 72, + 547, + 203 + ], + "type": "text", + "content": "sity and connectedness properties. We empirically analyze the performance of the trained neural nets in terms of several factors including interpretability, robustness, and stability. Our numerical results indicate the improvements in the mentioned structure-related factors offered by our designed norm-regularized AT methods. Finally, we utilize the shown duality relation to propose an interpretation harmonization scheme for aligning simple gradient maps with expert gaze maps, which performs satisfactorily in our numerical experiments. Our work's main contributions can be summarized as:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 306, + 205, + 545, + 361 + ], + "type": "list", + "angle": 0, + "index": 9, + "blocks": [ + { + "bbox": [ + 306, + 205, + 545, + 252 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 205, + 545, + 252 + ], + "spans": [ + { + "bbox": [ + 306, + 205, + 545, + 252 + ], + "type": "text", + "content": "- We show a duality relation between the regularized norms of adversarial perturbations and gradient maps, and develop a unified AT framework for regularizing gradient maps." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 306, + 253, + 545, + 289 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 253, + 545, + 289 + ], + "spans": [ + { + "bbox": [ + 306, + 253, + 545, + 289 + ], + "type": "text", + "content": "- We derive special cases of our proposed AT-based framework leading to the regularization of the elastic net and group-norm of gradient map." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 306, + 289, + 545, + 323 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 289, + 545, + 323 + ], + "spans": [ + { + "bbox": [ + 306, + 289, + 545, + 323 + ], + "type": "text", + "content": "- We leverage the duality framework to propose an interpretation harmonization scheme for aligning gradient maps with human attention." + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 306, + 324, + 545, + 361 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 324, + 545, + 361 + ], + "spans": [ + { + "bbox": [ + 306, + 324, + 545, + 361 + ], + "type": "text", + "content": "- We provide numerical results showing the efficacy of the AT-based framework in improving the sparsity and stability of interpretation maps." + } + ] + } + ], + "index": 8 + } + ], + "sub_type": "text" + }, + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "spans": [ + { + "bbox": [ + 306, + 370, + 392, + 383 + ], + "type": "text", + "content": "2. Related Work" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 390, + 545, + 641 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 390, + 545, + 641 + ], + "spans": [ + { + "bbox": [ + 304, + 390, + 545, + 641 + ], + "type": "text", + "content": "Gradient-based Interpretation. Using the gradient of the output of a deep neural network w.r.t. an input image is a widely-used approach to generate saliency maps [29]. This method has been utilized in several related works and multiple variants of this approach are proposed in the literature, including SmoothGrad [30], Integrated Gradients [32], DeepLIFT [28], and GradCAM [24]. The vanilla gradient-based maps without post-processing are often noisy and difficult to interpret. A group of methods are proposed to improve the visual quality by sparsifying the gradient-based maps: Guided Propagation [31] removes the noise artifacts from saliency maps by suppressing negative activations in the back-propagation. Sparsified-SmoothGrad [18] applies a sparsification to the saliency map to promote sparsity and robustness. MoreauGrad [43] generates saliency maps using an optimization problem with sparsity regularization. One drawback of the discussed methods is that they are all post-processing schemes, which may compromise the fidelity to the original simple-gradient map. On the other hand, our proposed framework is an in-processing scheme that remains faithful to the simple gradient map." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "spans": [ + { + "bbox": [ + 304, + 642, + 547, + 714 + ], + "type": "text", + "content": "Adversarial Training and Interpretability. Adversarial training (AT) involves training the networks using adversarial examples [19]. Fast Gradient Sign Method (FGSM) [9] generates adversarial samples using a single iteration to create the adversarial training example for training the classifier. Projected gradient descent (PGD) [19] uses several" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11010" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 1 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "gradient-based steps to generate more effective adversarial examples in order to make the trained model more robust to norm-constrained adversarial attacks. While the primary objective of AT is to improve the trained model's robustness against adversarial attacks, several studies have shown that AT can also improve the visual quality of interpretation maps [15, 22, 26]. Specifically, AT has been empirically shown to suppress irrelevant features [14], and the standard " + }, + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 46, + 72, + 289, + 277 + ], + "type": "text", + "content": "-norm-based AT will lead to higher sparsity and stability of the interpretation maps [3]. Building upon and extending these findings, our work provides a unified duality framework that connects the perturbation norm constrained by the AT algorithm and the norm penalized for the interpretation map. Specifically, we discuss novel variants of AT methods that lead to the regularization of the elastic net and group norms of the interpretation maps which have not been studied in these related works." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 285, + 133, + 298 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 285, + 133, + 298 + ], + "spans": [ + { + "bbox": [ + 47, + 285, + 133, + 298 + ], + "type": "text", + "content": "3. Preliminaries" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 304, + 214, + 318 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 304, + 214, + 318 + ], + "spans": [ + { + "bbox": [ + 47, + 304, + 214, + 318 + ], + "type": "text", + "content": "3.1. Gradient-based Saliency Maps" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "spans": [ + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": "Throughout this work, our analysis mainly focuses on the standard simple gradient as the gradient-based interpretation. We use " + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{y} \\in \\mathbb{R}^C" + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": " to denote the input and output of the neural network classifier. Note that " + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\mathbf{y}" + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": " denotes the output of the neural net's post-softmax layer and contains the assigned likelihood for each of the " + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "inline_equation", + "content": "C" + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": " classes in the classification task. The neural net function " + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "inline_equation", + "content": "f_{\\theta}: \\mathbb{R}^{d} \\to \\mathbb{R}^{C}" + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": " maps the input vector to the output vector, where " + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "inline_equation", + "content": "\\theta" + }, + { + "bbox": [ + 46, + 323, + 289, + 456 + ], + "type": "text", + "content": " denotes the parameters of the neural net. The simple gradient generates a saliency map by taking derivatives of the output of the neural network with respect to the input:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 110, + 462, + 223, + 475 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 110, + 462, + 223, + 475 + ], + "spans": [ + { + "bbox": [ + 110, + 462, + 223, + 475 + ], + "type": "interline_equation", + "content": "\\operatorname {S G} \\left(f _ {\\theta , c}, \\mathbf {x}\\right) := \\nabla_ {\\mathbf {x}} f _ {\\theta , c} (\\mathbf {x}).", + "image_path": "0b312aa55b9d8d6fd723e68ec6ce56cb882415cd92bb5635364a98860a37d3c7.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "spans": [ + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "content": "Here, " + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "content": " can be chosen as ground-truth label " + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "inline_equation", + "content": "y" + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "content": " or the label " + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "inline_equation", + "content": "c" + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "content": " with the maximum likelihood assigned by the classifier. In our analysis, we assume " + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})" + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "content": " denotes the saliency map corresponding to the ground-truth label of sample " + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 46, + 482, + 288, + 532 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 536, + 149, + 548 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 149, + 548 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 149, + 548 + ], + "type": "text", + "content": "3.2. FGSM and PGD" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "spans": [ + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "text", + "content": "We consider two of the most widely used forms of adversarial training, FGSM and PGD, in this work. These methods first generate adversarial samples by calculating the gradient of the loss function with respect to the input data and then perturb the data by taking one or multiple small steps in the direction of the sign of the gradient. The perturbation is usually bounded by " + }, + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "inline_equation", + "content": "l_{\\infty}" + }, + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "text", + "content": "-norm. The parameters of the network are then updated to minimize the loss with respect to these adversarial samples. We can use the following objective to summarize the optimization problem where " + }, + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "inline_equation", + "content": "\\hat{P}" + }, + { + "bbox": [ + 46, + 555, + 287, + 687 + ], + "type": "text", + "content": " is the empirical distribution of training samples" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 80, + 693, + 287, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 80, + 693, + 287, + 715 + ], + "spans": [ + { + "bbox": [ + 80, + 693, + 287, + 715 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {(\\mathbf {x}, y) \\sim \\widehat {P}} \\left[ \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x} + \\delta), y\\right) \\right]. \\tag {1}", + "image_path": "401ac485b2d1ac35b7ad67279a8e0529d2004df553350c536f89458ef6e7d234.jpg" + } + ] + } + ], + "index": 8 + }, + { + "type": "table", + "bbox": [ + 307, + 110, + 547, + 198 + ], + "blocks": [ + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "lines": [ + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "spans": [ + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": "Table 1. Summary of regularized norm " + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": " on perturbation " + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "\\delta" + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": " and the resulting regularized function " + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "{h}^{\\star }" + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": " of the input gradient " + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "inline_equation", + "content": "{\\nabla }_{\\mathbf{x}}\\mathcal{L}\\left( {{f}_{\\theta }\\left( \\mathbf{x}\\right) ,y}\\right)" + }, + { + "bbox": [ + 305, + 70, + 547, + 105 + ], + "type": "text", + "content": " . Detailed description can be found in Section 4.3." + } + ] + } + ], + "index": 9, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 307, + 110, + 547, + 198 + ], + "lines": [ + { + "bbox": [ + 307, + 110, + 547, + 198 + ], + "spans": [ + { + "bbox": [ + 307, + 110, + 547, + 198 + ], + "type": "table", + "html": "
h(δ)h*(∇xL(fθ(x),y))
I(||δ||∞ ≤ ε)ε||∇xL(fθ(x),y)||1
I(||δ||2,∞ ≤ ε)ε||∇xL(fθ(x),y)||2,1
∑iPQε1,ε2(δi)ε1||∇xL(fθ(x),y)||1 + ε2||∇xL(fθ(x),y)||2
1/4ε||W ⊙ δ||2ε||W ⊙ ∇xL(fθ(x),y)||2
", + "image_path": "9d5e163c1d6242813230ece938e65c84667121ef21bdde53df0107545e7ee40c.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "table_body" + } + ], + "index": 10 + }, + { + "bbox": [ + 305, + 212, + 547, + 236 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 212, + 547, + 236 + ], + "spans": [ + { + "bbox": [ + 305, + 212, + 547, + 236 + ], + "type": "text", + "content": "FGSM generates adversarial samples by taking one step in the direction of the sign of the gradient:" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 343, + 241, + 508, + 255 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 343, + 241, + 508, + 255 + ], + "spans": [ + { + "bbox": [ + 343, + 241, + 508, + 255 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {\\mathrm {F G S M}} ^ {*} = \\mathbf {x} + \\epsilon \\cdot \\operatorname {s i g n} \\left(\\nabla_ {\\mathbf {x}} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x}), y\\right)\\right)", + "image_path": "48d462e9d33e38273b975328f5a2d8b50b82d33bf26577cfe1c16ff4dea09ead.jpg" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "spans": [ + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "content": "PGD, on the other hand, iteratively updates the samples with a stepsize " + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "inline_equation", + "content": "\\alpha" + }, + { + "bbox": [ + 305, + 260, + 545, + 285 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 328, + 289, + 523, + 304 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 328, + 289, + 523, + 304 + ], + "spans": [ + { + "bbox": [ + 328, + 289, + 523, + 304 + ], + "type": "interline_equation", + "content": "\\mathbf {x} _ {t + 1} = \\Pi_ {\\mathbf {x} + S} \\big (\\mathbf {x} _ {t} + \\alpha \\mathrm {s i g n} (\\nabla_ {\\mathbf {x} _ {t}} \\mathcal {L} (f _ {\\theta} (\\mathbf {x} _ {t}), y)) \\big),", + "image_path": "98e3a65df02ebdc57028b498d534a00e69153e268765b3011dc1710c8e85d557.jpg" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "spans": [ + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "inline_equation", + "content": "S = \\{\\mathbf{z}:\\| \\mathbf{z}\\|_{\\infty}\\leq \\epsilon \\}" + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "text", + "content": " denotes the " + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "text", + "content": " -radius " + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 305, + 308, + 542, + 322 + ], + "type": "text", + "content": " -ball." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 327, + 417, + 340 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 327, + 417, + 340 + ], + "spans": [ + { + "bbox": [ + 306, + 327, + 417, + 340 + ], + "type": "text", + "content": "3.3. 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For a function " + }, + { + "bbox": [ + 305, + 346, + 547, + 393 + ], + "type": "inline_equation", + "content": "f: \\mathcal{X} \\to \\mathbb{R}" + }, + { + "bbox": [ + 305, + 346, + 547, + 393 + ], + "type": "text", + "content": ", its Fenchel conjugate " + }, + { + "bbox": [ + 305, + 346, + 547, + 393 + ], + "type": "inline_equation", + "content": "f^{\\star}: \\mathcal{X} \\to \\mathbb{R}" + }, + { + "bbox": [ + 305, + 346, + 547, + 393 + ], + "type": "text", + "content": " is defined as:" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 346, + 399, + 505, + 414 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 346, + 399, + 505, + 414 + ], + "spans": [ + { + "bbox": [ + 346, + 399, + 505, + 414 + ], + "type": "interline_equation", + "content": "f ^ {\\star} (z) = \\sup \\left\\{\\langle x, z \\rangle - f (x): x \\in \\mathcal {X} \\right\\},", + "image_path": "d5c3e621ebb4d49301e6764c5c0615a428162b392cf976d0c77a0bef3c5b58ae.jpg" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "spans": [ + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "\\langle \\cdot ,\\cdot \\rangle" + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "content": " denotes the inner product, and sup represents the supremum. Note that for a convex " + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "content": " will be the Fenchel conjugate of " + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "f^{\\star}" + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "content": " . Furthermore, for every function " + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "f" + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "content": " , the Fenchel conjugate " + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "inline_equation", + "content": "f^{\\star}" + }, + { + "bbox": [ + 305, + 418, + 545, + 467 + ], + "type": "text", + "content": " is guaranteed to be convex." + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 305, + 475, + 545, + 503 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 475, + 545, + 503 + ], + "spans": [ + { + "bbox": [ + 305, + 475, + 545, + 503 + ], + "type": "text", + "content": "4. An Adversarial Training Methodology for Regularizing Interpretation Maps" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "spans": [ + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "text", + "content": "In this section, we show a duality relation between the input gradient and the perturbation vectors, which is based on the linear approximation of the loss function " + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\ell\\big(f(\\mathbf{x} + \\delta),y\\big)" + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "text", + "content": " around data point " + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "text", + "content": ". In the approximation, the first-order term " + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "inline_equation", + "content": "\\langle \\nabla_{\\mathbf{x}}\\ell \\big(f(\\mathbf{x}),y\\big),\\delta \\rangle" + }, + { + "bbox": [ + 304, + 509, + 545, + 654 + ], + "type": "text", + "content": " is the inner product of the perturbation vector and the input-based gradient of the loss function. Therefore, as will be explained in the section, to penalize a norm of the saliency map in the adversarial training process, we propose to constrain the dual norm of the perturbation vector. We summarize three variants of the norm constraint on the perturbation and its effect on the simple gradient saliency maps in Table 1." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 658, + 545, + 684 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 658, + 545, + 684 + ], + "spans": [ + { + "bbox": [ + 305, + 658, + 545, + 684 + ], + "type": "text", + "content": "4.1. Rethinking the Impact of " + }, + { + "bbox": [ + 305, + 658, + 545, + 684 + ], + "type": "inline_equation", + "content": "\\ell_{\\infty}" + }, + { + "bbox": [ + 305, + 658, + 545, + 684 + ], + "type": "text", + "content": "-Norm-Based Adversarial Training on Saliency Maps" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "We perform a first-order analysis by means of Fenchel conjugate to indicate how " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "-norm-based adversarial training" + } + ] + } + ], + "index": 23 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11011" + } + ] + } + ], + "index": 24 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 2 + }, + { + "para_blocks": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "spans": [ + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": "could lead to higher sparsity in gradient-based maps. Under a small enough perturbation norm bound " + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 72, + 287, + 133 + ], + "type": "text", + "content": " and twice-differentiable loss function, the objective of adversarial training in Eq. 1 can be approximated by first-order Taylor expansion as" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 52, + 137, + 281, + 184 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 52, + 137, + 281, + 184 + ], + "spans": [ + { + "bbox": [ + 52, + 137, + 281, + 184 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {E q.} 1 = \\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\hat {P}} \\left[ \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x}), y\\right) \\right. \\\\ + \\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} \\left\\{\\delta^ {T} \\nabla_ {\\mathbf {x}} \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) \\right\\} \\biggr ] + \\mathcal {O} (\\epsilon^ {2}). \\\\ \\end{array}", + "image_path": "4876e8b428f851680cb4ffa9631a7b8830a7e61e1c4453149fc2fee11321805b.jpg" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 47, + 189, + 287, + 250 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 189, + 287, + 250 + ], + "spans": [ + { + "bbox": [ + 47, + 189, + 287, + 250 + ], + "type": "text", + "content": "Using the common cross-entropy loss or hinge loss, the derivative of the loss with respect to the predicted log-its at every training sample will be " + }, + { + "bbox": [ + 47, + 189, + 287, + 250 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta},(\\mathbf{x}),y) = -f_{\\theta ,y}(\\mathbf{x})\\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 189, + 287, + 250 + ], + "type": "text", + "content": ", so we can build the connection between the objective and the saliency map:" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 48, + 255, + 284, + 301 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 255, + 284, + 301 + ], + "spans": [ + { + "bbox": [ + 48, + 255, + 284, + 301 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\operatorname {E q.} 1 = \\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\hat {P}} \\left[ \\mathcal {L} \\left(f _ {\\theta , y} (\\mathbf {x})\\right) \\right. \\\\ \\left. + f _ {\\theta , y} (\\mathbf {x}) \\max _ {| | \\delta | | _ {\\infty} \\leq \\epsilon} \\left\\{- \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) \\right\\} \\right] + \\mathcal {O} (\\epsilon^ {2}). \\\\ \\end{array}", + "image_path": "fc96cd3b58ad448ff486a5e878af927954ce0ae6232bdb2749eb165920d2cefd.jpg" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 47, + 306, + 287, + 342 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 306, + 287, + 342 + ], + "spans": [ + { + "bbox": [ + 47, + 306, + 287, + 342 + ], + "type": "text", + "content": "Note we can leverage Fenchel conjugate operation to transform the maximization subproblem in the above problem into an unconstrained optimization:" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 47, + 346, + 288, + 377 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 346, + 288, + 377 + ], + "spans": [ + { + "bbox": [ + 47, + 346, + 288, + 377 + ], + "type": "interline_equation", + "content": "\\max _ {\\| \\delta \\| _ {\\infty} \\leq \\epsilon} - \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) = \\max _ {\\delta} - \\delta^ {T} \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) - \\mathbb {I} (\\| \\delta \\| _ {\\infty} \\leq \\epsilon), \\tag {2}", + "image_path": "edc45f21f389ed14f5c5611a856d1889bae72af41da65f1d0bcb4b55d25bdd5c.jpg" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "spans": [ + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "inline_equation", + "content": "\\mathbb{I}(\\mathrm{condition}) = 0" + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "text", + "content": " if the condition holds and " + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "inline_equation", + "content": "+\\infty" + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "text", + "content": " otherwise. With the concept of Fenchel conjugate, the optimal value of the optimization problem defined in Eq. 2 is " + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "inline_equation", + "content": "\\epsilon \\| \\nabla_{\\mathbf{x}}f_{\\theta}(\\mathbf{x})\\| _1" + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "text", + "content": ". Hence, we successfully transform the original minimax optimization problem into a regularized optimization within an approximation error " + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "inline_equation", + "content": "\\mathcal{O}(\\epsilon^2)" + }, + { + "bbox": [ + 47, + 378, + 287, + 450 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 456, + 287, + 477 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 456, + 287, + 477 + ], + "spans": [ + { + "bbox": [ + 47, + 456, + 287, + 477 + ], + "type": "interline_equation", + "content": "\\mathrm {E q .} 1 \\approx \\underset {\\theta} {\\min } \\mathbb {E} _ {\\mathbf {x}, y \\sim \\widehat {P}} \\Big [ \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + \\epsilon f _ {\\theta , y} (\\mathbf {x}) \\| \\nabla_ {\\mathbf {x}} f _ {\\theta} (\\mathbf {x}) \\| _ {1} \\Big ].", + "image_path": "150dbde6d7003ac973a837369f8e7d0a17a80f1402638ae8715b41d8550fdd40.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "spans": [ + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "type": "text", + "content": "Hence, we find that adversarial training with " + }, + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "type": "text", + "content": "-norm is approximately equivalent to applying " + }, + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 482, + 287, + 529 + ], + "type": "text", + "content": "-norm regularization to the simple gradient saliency map, therefore promoting the sparsity of the saliency maps." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 536, + 287, + 561 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 536, + 287, + 561 + ], + "spans": [ + { + "bbox": [ + 47, + 536, + 287, + 561 + ], + "type": "text", + "content": "4.2. Adversarial Training with Fenchel Conjugate Regularization: a Unified Approach" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "spans": [ + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": "Next, we consider adversarial training with a general norm-based regularization penalty. Here our goal is to promote a structured saliency map through a regularization function " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "h^{\\star}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ". Note that for a convex " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "h" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ", the Fenchel conjugate of " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "h^{\\star}(\\mathbf{z})" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": " will be " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "h(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ". Therefore, we consider the min-max optimization with the adversarial penalty function " + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "inline_equation", + "content": "-h(\\delta)" + }, + { + "bbox": [ + 47, + 566, + 287, + 639 + ], + "type": "text", + "content": ":" + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 75, + 644, + 258, + 666 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 75, + 644, + 258, + 666 + ], + "spans": [ + { + "bbox": [ + 75, + 644, + 258, + 666 + ], + "type": "interline_equation", + "content": "\\min _ {\\theta} \\mathbb {E} _ {\\mathbf {x}, y \\sim \\widehat {P}} \\left[ \\max _ {\\delta} \\mathcal {L} \\left(f _ {\\theta} (\\mathbf {x} + \\delta), y\\right) - h (\\delta) \\right].", + "image_path": "f3934809a2b68357b3e2ece23163363383239673c0710d79fc150153b0caa48a.jpg" + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 47, + 670, + 287, + 694 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 670, + 287, + 694 + ], + "spans": [ + { + "bbox": [ + 47, + 670, + 287, + 694 + ], + "type": "text", + "content": "Following our analysis for the " + }, + { + "bbox": [ + 47, + 670, + 287, + 694 + ], + "type": "inline_equation", + "content": "L_{\\infty}" + }, + { + "bbox": [ + 47, + 670, + 287, + 694 + ], + "type": "text", + "content": "-norm-based adversarial training, we define the first-order approximate loss:" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 61, + 699, + 272, + 715 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 61, + 699, + 272, + 715 + ], + "spans": [ + { + "bbox": [ + 61, + 699, + 272, + 715 + ], + "type": "interline_equation", + "content": "\\widehat {\\mathcal {L}} (f _ {\\theta} (\\mathbf {x}), y, \\delta) := \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + \\delta^ {T} \\nabla_ {x} \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y),", + "image_path": "6b7e01c8a502cf470aa44474c0ac8a3a8f81a23433d9791ea247a3f09bb12960.jpg" + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "spans": [ + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "To measure how well " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{L}}(f_{\\theta}(\\mathbf{x}), y, \\delta)" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": " approximates the adversarial loss, we observe the approximation error can be simply bounded for the class of " + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "inline_equation", + "content": "\\lambda" + }, + { + "bbox": [ + 305, + 72, + 545, + 108 + ], + "type": "text", + "content": "-smooth functions." + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "spans": [ + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "content": "Definition 1 We call " + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "inline_equation", + "content": "g: \\mathbb{R}^d \\to \\mathbb{R}" + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "content": " a smooth if for every " + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "inline_equation", + "content": "\\mathbf{x}" + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "inline_equation", + "content": "\\mathbf{z}" + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "content": ": " + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "inline_equation", + "content": "\\| \\nabla g(\\mathbf{x}) - \\nabla g(\\mathbf{z}) \\|_2 \\leq \\lambda \\| \\mathbf{x} - \\mathbf{z} \\|_2" + }, + { + "bbox": [ + 305, + 118, + 545, + 143 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "spans": [ + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "text", + "content": "Observation 1 The approximation error of the first-order Taylor series expansion of adversarial loss under an " + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "text", + "content": "-" + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "inline_equation", + "content": "L_2" + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "text", + "content": "-norm bounded perturbation " + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "inline_equation", + "content": "\\|\\delta\\| \\leq \\epsilon" + }, + { + "bbox": [ + 305, + 155, + 545, + 191 + ], + "type": "text", + "content": " can be bounded as" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 339, + 201, + 512, + 226 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 339, + 201, + 512, + 226 + ], + "spans": [ + { + "bbox": [ + 339, + 201, + 512, + 226 + ], + "type": "interline_equation", + "content": "\\left| \\widehat {\\mathcal {L}} (f _ {\\theta} (\\mathbf {x}), y, \\delta) - \\mathcal {L} (f _ {\\theta} (\\mathbf {x} + \\delta), y) \\right| \\leq \\frac {\\lambda \\epsilon^ {2}}{2}", + "image_path": "a2773eafb902d42ffdf6d10a3d6c5db2f0b44e682e87d89fd9828b9f300669fb.jpg" + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "spans": [ + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "text", + "content": "The observation shows " + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "inline_equation", + "content": "\\widehat{\\mathcal{L}}(f_{\\theta}(\\mathbf{x}), y, \\delta)" + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "text", + "content": " can be a good approximation of the adversarial loss under a small " + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "inline_equation", + "content": "\\|\\delta\\|" + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "text", + "content": ". Combining the approximate loss with " + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "inline_equation", + "content": "h(\\delta)" + }, + { + "bbox": [ + 305, + 237, + 545, + 286 + ], + "type": "text", + "content": " regularization, we can derive the following equivalence by Fenchel conjugate:" + } + ] + } + ], + "index": 18 + }, + { + "bbox": [ + 305, + 297, + 545, + 320 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 297, + 545, + 320 + ], + "spans": [ + { + "bbox": [ + 305, + 297, + 545, + 320 + ], + "type": "text", + "content": "Proposition 1 Using Fenchel conjugate " + }, + { + "bbox": [ + 305, + 297, + 545, + 320 + ], + "type": "inline_equation", + "content": "h^{\\star}" + }, + { + "bbox": [ + 305, + 297, + 545, + 320 + ], + "type": "text", + "content": ", we can reduce the maximization of the approximate adversarial loss as" + } + ] + } + ], + "index": 19 + }, + { + "bbox": [ + 350, + 330, + 545, + 367 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 330, + 545, + 367 + ], + "spans": [ + { + "bbox": [ + 350, + 330, + 545, + 367 + ], + "type": "interline_equation", + "content": "\\begin{array}{l} \\max _ {\\delta} \\left\\{\\widehat {\\mathcal {L}} \\left(f _ {\\theta} (\\mathbf {x}), y, \\delta\\right) - h (\\delta) \\right\\} \\tag {3} \\\\ = \\mathcal {L} (f _ {\\theta} (\\mathbf {x}), y) + h ^ {\\star} \\bigl (\\nabla_ {\\mathbf {x}} \\mathcal {L} \\bigl (f _ {\\theta} (\\mathbf {x}), y \\bigr) \\bigr). \\\\ \\end{array}", + "image_path": "2d04381dde1cb268b8baeb5b195fc251058a1a8085d86c1068679492c96c1139.jpg" + } + ] + } + ], + "index": 20 + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "spans": [ + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "content": "In a scenario that the neural network completely fits the training data, we have that " + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta}(\\mathbf{x}),y) = -f_{\\theta ,y}(\\mathbf{x})\\nabla_{x}f_{\\theta}(\\mathbf{x})\\approx -\\nabla_{x}f_{\\theta}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "content": " . Therefore, to enforce the gradient map " + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\nabla_{x}f_{\\theta}(\\mathbf{x})" + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "content": " to satisfy a bounded penalty function " + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "inline_equation", + "content": "h^\\star" + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "content": " , we can conduct adversarial training with an additive penalty term " + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "inline_equation", + "content": "-h(\\delta)" + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "content": " . The optimal perturbation " + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "inline_equation", + "content": "\\delta^{*}" + }, + { + "bbox": [ + 305, + 377, + 545, + 496 + ], + "type": "text", + "content": " can be derived via the standard gradient ascent algorithm to maximize the regularized adversarial loss or be approximated with the analytic solution to the approximate optimization problem." + } + ] + } + ], + "index": 21 + }, + { + "bbox": [ + 305, + 506, + 545, + 530 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 506, + 545, + 530 + ], + "spans": [ + { + "bbox": [ + 305, + 506, + 545, + 530 + ], + "type": "text", + "content": "4.3. Special Cases of the Fenchel Conjugate-based Duality Framework" + } + ] + } + ], + "index": 22 + }, + { + "bbox": [ + 305, + 536, + 545, + 584 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 536, + 545, + 584 + ], + "spans": [ + { + "bbox": [ + 305, + 536, + 545, + 584 + ], + "type": "text", + "content": "Leveraging the duality framework in the previous section, we derive regularization penalty terms to penalize other sparsity norms different from " + }, + { + "bbox": [ + 305, + 536, + 545, + 584 + ], + "type": "inline_equation", + "content": "l_{1}" + }, + { + "bbox": [ + 305, + 536, + 545, + 584 + ], + "type": "text", + "content": "-norm and discuss their influence on the saliency maps." + } + ] + } + ], + "index": 23 + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "spans": [ + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "inline_equation", + "content": "L_{2,1}" + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "text", + "content": "-group-norm penalty. The " + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "inline_equation", + "content": "L_{2,1}" + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "text", + "content": "-group-norm of " + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "inline_equation", + "content": "\\mathbf{x} \\in \\mathbb{R}^d" + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "text", + "content": " for disjoint variable subsets " + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "inline_equation", + "content": "S_1, \\dots, S_t \\subseteq \\{1, \\dots, d\\}" + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "text", + "content": " is defined as the special case " + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "inline_equation", + "content": "p = 1" + }, + { + "bbox": [ + 306, + 586, + 545, + 621 + ], + "type": "text", + "content": " of the following definition:" + } + ] + } + ], + "index": 24 + }, + { + "bbox": [ + 350, + 631, + 501, + 645 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 350, + 631, + 501, + 645 + ], + "spans": [ + { + "bbox": [ + 350, + 631, + 501, + 645 + ], + "type": "interline_equation", + "content": "\\left\\| \\mathbf {x} \\right\\| _ {2, p} := \\left\\| \\left[ \\left\\| \\mathbf {x} _ {S _ {1}} \\right\\| _ {2}, \\dots , \\left\\| \\mathbf {x} _ {S _ {t}} \\right\\| _ {2} \\right] \\right\\| _ {p}.", + "image_path": "e85f9db02b333a8a5f93701cc067182c05d9a6a5979b7c361291b7172f564a9b.jpg" + } + ] + } + ], + "index": 25 + }, + { + "bbox": [ + 305, + 655, + 545, + 679 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 655, + 545, + 679 + ], + "spans": [ + { + "bbox": [ + 305, + 655, + 545, + 679 + ], + "type": "text", + "content": "To apply the duality framework to the group norm (with coefficient " + }, + { + "bbox": [ + 305, + 655, + 545, + 679 + ], + "type": "inline_equation", + "content": "\\epsilon > 0" + }, + { + "bbox": [ + 305, + 655, + 545, + 679 + ], + "type": "text", + "content": "), we derive its Fenchel conjugate as follows." + } + ] + } + ], + "index": 26 + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "spans": [ + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "Proposition 2 The Fenchel conjugate of the above " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "L_{2,1}" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "-group-norm is " + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "inline_equation", + "content": "h(\\mathbf{z}) = \\mathbb{I}(\\| \\mathbf{z}\\|_{2,\\infty}\\leq \\epsilon)" + }, + { + "bbox": [ + 305, + 689, + 545, + 714 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 27 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11012" + } + ] + } + ], + "index": 28 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 3 + }, + { + "para_blocks": [ + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "spans": [ + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "type": "text", + "content": "Different from " + }, + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "type": "text", + "content": "-norm inducing pixel-level sparsity, " + }, + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "type": "inline_equation", + "content": "L_{2,1}" + }, + { + "bbox": [ + 47, + 72, + 286, + 155 + ], + "type": "text", + "content": "-group-norm will induce sparsity of the patch basis. Under this regularization, the more influential patches are expected to be highlighted in the saliency map. This effect could further lead to a connected saliency map, which will be desired when adjacent pixels belonging have similar effects on the prediction of the classifier." + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "spans": [ + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "text", + "content": "Elastic net penalty. The elastic net penalty " + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "inline_equation", + "content": "h^{\\star}(\\mathbf{x})" + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "text", + "content": " linearly combines the " + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "inline_equation", + "content": "L_{2}^{2}" + }, + { + "bbox": [ + 47, + 156, + 286, + 180 + ], + "type": "text", + "content": " penalty terms:" + } + ] + } + ], + "index": 1 + }, + { + "bbox": [ + 78, + 186, + 254, + 201 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 78, + 186, + 254, + 201 + ], + "spans": [ + { + "bbox": [ + 78, + 186, + 254, + 201 + ], + "type": "interline_equation", + "content": "h ^ {\\star} (\\mathbf {x}) = \\epsilon_ {1} \\| \\mathbf {x} \\| _ {1} + \\epsilon_ {2} \\| \\mathbf {x} \\| _ {2} ^ {2}, \\epsilon_ {1} > 0, \\epsilon_ {2} > 0.", + "image_path": "dfb80f05cf13ef267df125b37edf69f90e46466b52e452618c346025159b8f54.jpg" + } + ] + } + ], + "index": 2 + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "spans": [ + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "text", + "content": "Proposition 3 The Fenchel conjugate of the above elastic net penalty " + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "inline_equation", + "content": "h^{\\star}" + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "text", + "content": " is " + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "inline_equation", + "content": "h(\\mathbf{z}) = \\sum_{i} PQ_{\\epsilon_1, \\epsilon_2}(\\mathbf{z}_i)" + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "text", + "content": " where " + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "inline_equation", + "content": "PQ_{\\epsilon_1, \\epsilon_2}" + }, + { + "bbox": [ + 47, + 217, + 286, + 253 + ], + "type": "text", + "content": " is the piece-wise quadratic function defined as:" + } + ] + } + ], + "index": 3 + }, + { + "bbox": [ + 58, + 259, + 274, + 305 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 58, + 259, + 274, + 305 + ], + "spans": [ + { + "bbox": [ + 58, + 259, + 274, + 305 + ], + "type": "interline_equation", + "content": "P Q _ {\\epsilon_ {1}, \\epsilon_ {2}} (\\mathbf {z} _ {i}) = \\left\\{ \\begin{array}{c l} \\frac {1}{4 \\epsilon_ {2}} (\\mathbf {z} _ {i} - \\epsilon_ {1}) ^ {2} & \\text {i f} \\epsilon_ {1} < \\mathbf {z} _ {i} \\\\ 0 & \\text {i f} - \\epsilon_ {1} \\leq \\mathbf {z} _ {i} \\leq \\epsilon_ {1} \\\\ \\frac {1}{4 \\epsilon_ {2}} (\\mathbf {z} _ {i} + \\epsilon_ {1}) ^ {2} & \\text {i f} \\mathbf {z} _ {i} < - \\epsilon_ {1}. \\end{array} \\right.", + "image_path": "a38f01139c79043e0a2ccded53e236419f4c5db25bb538f7341d8d5126102398.jpg" + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "spans": [ + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "text", + "content": "The linear combination of the " + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "text", + "content": "-norm and " + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "inline_equation", + "content": "L_{2}^{2}" + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "text", + "content": "-norm penalty terms in the elastic net results in a strongly convex regularization function, which is known to promote the stability of the sparsity pattern. Therefore, one can expect that the elastic net-regularized maps could possess higher robustness and stability than the " + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 312, + 286, + 491 + ], + "type": "text", + "content": "-norm regularized maps. Interpretation harmonization. The purpose of interpretation harmonization is to align the saliency map generated by the neural network with some reference attention map. The reference attention map can be manually labeled by domain experts, or based on some physical principle behind the classification task. Through interpretation harmonization, the network could be enabled to analyze the phenomenon in a similar way as a human, which would help diminish the potential bias or shortcuts learned by the neural net [6, 7]." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "spans": [ + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "text", + "content": "To achieve this goal, we leverage " + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "text", + "content": "-norm regularization to diminish the importance scores of unrelated features. Specifically, assume " + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "inline_equation", + "content": "\\mathbf{A} \\in \\mathbb{R}^{d}" + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "text", + "content": " is the expert's attention map with non-negative entries. A greater value implies a more important feature. We define " + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "inline_equation", + "content": "\\hat{\\mathbf{A}} := \\max(\\mathbf{A}) - \\mathbf{A} + \\sigma" + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "text", + "content": ", where " + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "inline_equation", + "content": "\\sigma" + }, + { + "bbox": [ + 46, + 491, + 286, + 587 + ], + "type": "text", + "content": " is small enough so that the ordinal relation is reverted and all elements are positive. To diminish the importance score of the background region, we use the penalty term:" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 594, + 228, + 612 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 104, + 594, + 228, + 612 + ], + "spans": [ + { + "bbox": [ + 104, + 594, + 228, + 612 + ], + "type": "interline_equation", + "content": "h ^ {\\star} (\\mathbf {x}) = \\epsilon \\| \\sqrt {\\tilde {\\mathbf {A}}} \\odot \\mathbf {x} \\| _ {2} ^ {2}, \\epsilon > 0", + "image_path": "fd426c9b05826369ea825d5fa90e4126f82198ed4226827ea70778de91f4ac4f.jpg" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 47, + 617, + 286, + 653 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 617, + 286, + 653 + ], + "spans": [ + { + "bbox": [ + 47, + 617, + 286, + 653 + ], + "type": "text", + "content": "where " + }, + { + "bbox": [ + 47, + 617, + 286, + 653 + ], + "type": "inline_equation", + "content": "\\odot" + }, + { + "bbox": [ + 47, + 617, + 286, + 653 + ], + "type": "text", + "content": " denotes Hadamard product. By adding this regularization term, the importance score of unrelated features is pushed to 0 while important features remain unaffected." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 47, + 659, + 286, + 683 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 659, + 286, + 683 + ], + "spans": [ + { + "bbox": [ + 47, + 659, + 286, + 683 + ], + "type": "text", + "content": "Proposition 4 The Fenchel conjugate of the above weighted " + }, + { + "bbox": [ + 47, + 659, + 286, + 683 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 47, + 659, + 286, + 683 + ], + "type": "text", + "content": "-norm square regularization is:" + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 689, + 218, + 716 + ], + "type": "interline_equation", + "angle": 0, + "lines": [ + { + "bbox": [ + 115, + 689, + 218, + 716 + ], + "spans": [ + { + "bbox": [ + 115, + 689, + 218, + 716 + ], + "type": "interline_equation", + "content": "h (\\mathbf {z}) = \\frac {1}{4 \\epsilon} \\left\\| \\frac {1}{\\sqrt {\\tilde {\\mathbf {A}}}} \\odot \\mathbf {z} \\right\\| _ {2} ^ {2}.", + "image_path": "b3672772a02a5ccf492ca875ea92380692cedbe32d466bc76291a20b7222fdc6.jpg" + } + ] + } + ], + "index": 10 + }, + { + "type": "image", + "bbox": [ + 312, + 74, + 541, + 200 + ], + "blocks": [ + { + "bbox": [ + 312, + 74, + 541, + 200 + ], + "lines": [ + { + "bbox": [ + 312, + 74, + 541, + 200 + ], + "spans": [ + { + "bbox": [ + 312, + 74, + 541, + 200 + ], + "type": "image", + "image_path": "1acfe4b86480d4afef7b923b424c20fe1a1770161add98138388d7b1eff50356.jpg" + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 312, + 212, + 537, + 223 + ], + "lines": [ + { + "bbox": [ + 312, + 212, + 537, + 223 + ], + "spans": [ + { + "bbox": [ + 312, + 212, + 537, + 223 + ], + "type": "text", + "content": "Figure 2. Qualitative results based on the synthesized dataset." + } + ] + } + ], + "index": 12, + "angle": 0, + "type": "image_caption" + } + ], + "index": 11 + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "spans": [ + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "text", + "content": "The derivation requires the weight term " + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{A}}" + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "text", + "content": " to be positive. However, a positive weight only leads to the diminishing of the importance score of unrelated features. It does not explicitly promote larger scores for important features. Empirically, we have found that using " + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\delta^{*}" + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "text", + "content": " in the opposite direction to the gradients for important pixels helps increase the attribution scores for important features and results in better alignment. Therefore, in our numerical experiment, we set " + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\tilde{\\mathbf{A}} = \\frac{1}{2}\\max (\\mathbf{A}) - \\mathbf{A}" + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "text", + "content": " and " + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "inline_equation", + "content": "\\delta^{*} = 2\\epsilon \\tilde{\\mathbf{A}}\\odot \\nabla_{\\mathbf{x}}\\mathcal{L}(f_{\\theta}(\\mathbf{x}),y)" + }, + { + "bbox": [ + 305, + 231, + 545, + 341 + ], + "type": "text", + "content": "." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 306, + 352, + 387, + 365 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 352, + 387, + 365 + ], + "spans": [ + { + "bbox": [ + 306, + 352, + 387, + 365 + ], + "type": "text", + "content": "5. Experiments" + } + ] + } + ], + "index": 14 + }, + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "spans": [ + { + "bbox": [ + 304, + 373, + 545, + 529 + ], + "type": "text", + "content": "We conducted comprehensive numerical experiments to evaluate the performance of our proposed adversarial training-based methods. Firstly, we evaluate saliency maps' accuracy on a synthesized dataset with ground truth interpretation. Next, we assessed the visual quality, sparsity, interpretability, robustness, and stability of the saliency maps on Imagenette. Finally, we demonstrated the effectiveness of our interpretation harmonization strategy on the CUB-GHA dataset. Our quantitative results include adversarial training with one normalized step and multi-step gradient ascent. The main text focuses on the results of one normalized step, while detailed training settings and complete numerical results can be found in the Appendix." + } + ] + } + ], + "index": 15 + }, + { + "bbox": [ + 306, + 538, + 469, + 551 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 538, + 469, + 551 + ], + "spans": [ + { + "bbox": [ + 306, + 538, + 469, + 551 + ], + "type": "text", + "content": "5.1. Results on synthesized dataset" + } + ] + } + ], + "index": 16 + }, + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 545, + 676 + ], + "type": "text", + "content": "To illustrate how adversarial training can improve the model's interpretability, we first conducted experiments on a synthesized dataset with ground-truth for the saliency maps proposed by [35]. There are three regions on the ground-truth of the synthesized dataset (Fig. 2): background without any classification information (white region); localization information describes the location of an object (light red region); and distinguishing features crucial for classification (dark red area). We trained ResNet-34 [12] with standard training and regularized adversarial training." + } + ] + } + ], + "index": 17 + }, + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "spans": [ + { + "bbox": [ + 305, + 677, + 545, + 713 + ], + "type": "text", + "content": "As the ground-truth was a ternary class, we reported the five-band-score reflects pixel accuracy, recall, precision, and the false positive rate (FPR) based on ternary classifi" + } + ] + } + ], + "index": 18 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11013" + } + ] + } + ], + "index": 19 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 4 + }, + { + "para_blocks": [ + { + "type": "table", + "bbox": [ + 78, + 87, + 516, + 167 + ], + "blocks": [ + { + "bbox": [ + 108, + 71, + 484, + 82 + ], + "lines": [ + { + "bbox": [ + 108, + 71, + 484, + 82 + ], + "spans": [ + { + "bbox": [ + 108, + 71, + 484, + 82 + ], + "type": "text", + "content": "Table 2. Comparison of five-band-scores and binary scores of standard training and adversarial training." + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 78, + 87, + 516, + 167 + ], + "lines": [ + { + "bbox": [ + 78, + 87, + 516, + 167 + ], + "spans": [ + { + "bbox": [ + 78, + 87, + 516, + 167 + ], + "type": "table", + "html": "
MethodsFive-band-scoresBinary scores
Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)Pixel_acc(↑)Recall (↑)Precision (↑)FPR (↓)
standard89.819.8632.581.2188.6644.4716.2210.22
\\( L_1 \\)-norm89.826.4129.200.7694.6065.0630.844.70
group-norm89.847.5427.350.9194.2763.7829.774.99
elastic net89.918.3526.830.9294.6365.6531.294.66
harmonization90.1411.3743.311.1493.8267.0528.155.54
", + "image_path": "04d79e7cd7c3a81bbf7f379ecbde73e7e72fc13740a89bb166a07edddf5e2d97.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "table_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 52, + 182, + 284, + 276 + ], + "blocks": [ + { + "bbox": [ + 52, + 182, + 284, + 276 + ], + "lines": [ + { + "bbox": [ + 52, + 182, + 284, + 276 + ], + "spans": [ + { + "bbox": [ + 52, + 182, + 284, + 276 + ], + "type": "image", + "image_path": "065f3927a0594365ba1f1b5a7cc109567da861a9505e0cabf34ec3dd22ee175d.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 47, + 284, + 286, + 295 + ], + "lines": [ + { + "bbox": [ + 47, + 284, + 286, + 295 + ], + "spans": [ + { + "bbox": [ + 47, + 284, + 286, + 295 + ], + "type": "text", + "content": "Figure 3. Images optimized for maximizing class-logit activations." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 2 + }, + { + "bbox": [ + 46, + 303, + 287, + 506 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 303, + 287, + 506 + ], + "spans": [ + { + "bbox": [ + 46, + 303, + 287, + 506 + ], + "type": "text", + "content": "cation. The results are listed in Table 2, where the method's name corresponds to the penalty term " + }, + { + "bbox": [ + 46, + 303, + 287, + 506 + ], + "type": "inline_equation", + "content": "h^{\\star}" + }, + { + "bbox": [ + 46, + 303, + 287, + 506 + ], + "type": "text", + "content": " in Eq. 3. The harmonization training achieved the best scores in terms of most of the metrics, showing the effectiveness of the proposed harmonization method. We also noticed that adversarial training-based methods consistently achieved higher accuracy and lower FPR compared with stranded training but led to lower recall and precision, because the adversarial training raised the sparsity of gradient maps. The importance scores of the localization area, which was less important compared with distinguishing features, were also diminished. Therefore, following [11], we also converted the ternary classification task to a binary classification task by considering the background and localization information as one class. The results suggested that adversarial training could significantly improve the accuracy of saliency maps in detecting distinguishing features." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 506, + 287, + 626 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 506, + 287, + 626 + ], + "spans": [ + { + "bbox": [ + 46, + 506, + 287, + 626 + ], + "type": "text", + "content": "We visualized the saliency maps in Fig. 2 for qualitative evaluation (we only show results with elastic net regularization here and leave the rest in the Appendix). We discovered that the saliency map of standard training was activated more clearly in the region of the localization information than it was in the region of the distinguishing feature. In contrast, the saliency map with adversarial training was activated more significantly for the distinguishing features, especially on the boundaries. Moreover, the saliency maps looked more sparse and less noisy." + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 47, + 635, + 175, + 647 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 635, + 175, + 647 + ], + "spans": [ + { + "bbox": [ + 47, + 635, + 175, + 647 + ], + "type": "text", + "content": "5.2. Results on ImageNette" + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 654, + 288, + 715 + ], + "type": "text", + "content": "We performed numerical experiments on ImageNette, a ten-class subset of ImageNet [4], to examine the properties of the proposed adversarial training. Specifically, we studied the sparsity, interpretability, adversarial robustness, and stability of the saliency maps generated for EfficientNet [34]" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 304, + 182, + 541, + 194 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 182, + 541, + 194 + ], + "spans": [ + { + "bbox": [ + 304, + 182, + 541, + 194 + ], + "type": "text", + "content": "classifiers with the proposed adversarial training methods." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "spans": [ + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "type": "text", + "content": "Sparsity. We trained the neural network models with different regularization coefficients and used the Gini Index [13] as a measure of the sparsity of the saliency map. The results are shown in Table 3. All the proposed adversarial training-based methods led to more sparse saliency maps than standard training, with zero or only minor drops in clean accuracy. The " + }, + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "type": "text", + "content": "-norm-based method attained the highest sparsity. Also, the sparsity increased with the regularization coefficient " + }, + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 304, + 195, + 545, + 351 + ], + "type": "text", + "content": ". The gradient maps visualized in Fig. 4 suggest that standard training could lead to miscellaneous points in the background. On the other hand, the gradient maps with our proposed adversarial training methods seem to have higher visual quality." + } + ] + } + ], + "index": 9 + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "spans": [ + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "content": "Interpretability. To show that the proposed training methods can improve the interpretability of the model, we calculated the DiffROAR score [26] for the methods. DiffROAR measures the difference in the predictive power of the dataset, where the top and bottom " + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "inline_equation", + "content": "k\\%" + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "content": " of the pixels are removed according to the importance score. A higher DiffROAR score shows the model captures the task-related features from the inputs. To this end, we measured the DiffROAR score for each method with " + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "inline_equation", + "content": "k" + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "content": " from " + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "content": " to " + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "inline_equation", + "content": "90\\%" + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "content": " in increments of " + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 352, + 546, + 543 + ], + "type": "text", + "content": ". Each measurement was repeated with three different initializations, and the final DiffROAR score was the average of the 27 measurements. The results are shown in Table 3. Compared with standard training, the proposed methods can improve the model's interpretability, especially under the elastic net regularization, which achieved the highest DiffROAR score." + } + ] + } + ], + "index": 10 + }, + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "spans": [ + { + "bbox": [ + 304, + 544, + 545, + 616 + ], + "type": "text", + "content": "We also visualized the learned feature for each model, using the optimization-based feature visualization technique of deep-dream [20]. The results (Fig. 3) also show that class-specific features identified with the proposed norm-regularized adversarial training methods look more meaningful to human perception." + } + ] + } + ], + "index": 11 + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "Robustness. To assess the robustness of interpretation maps under the standard and proposed training methods, we adopted an " + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "inline_equation", + "content": "L_{2}" + }, + { + "bbox": [ + 304, + 617, + 546, + 713 + ], + "type": "text", + "content": "-norm bounded interpretation attack method proposed by [18]. We gradually increased the strength of the attack and measured the robustness through similarity measures of the saliency maps before and after the attack. We adopted two metrics as robustness measures: 1) top-k intersection ratio [8], which is the ratio of pix" + } + ] + } + ], + "index": 12 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11014" + } + ] + } + ], + "index": 13 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 5 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 51, + 71, + 542, + 287 + ], + "blocks": [ + { + "bbox": [ + 51, + 71, + 542, + 287 + ], + "lines": [ + { + "bbox": [ + 51, + 71, + 542, + 287 + ], + "spans": [ + { + "bbox": [ + 51, + 71, + 542, + 287 + ], + "type": "image", + "image_path": "d731715a60311aff5f8345a45bb88573111aac8a58645a910709ca7452e8c178.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 292, + 546, + 314 + ], + "lines": [ + { + "bbox": [ + 46, + 292, + 546, + 314 + ], + "spans": [ + { + "bbox": [ + 46, + 292, + 546, + 314 + ], + "type": "text", + "content": "Figure 4. Qualitative comparison of saliency maps generated by networks with different adversarial training protocols (fast, iterative) and standard training with additional regularization on input gradients (penalty)." + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "table", + "bbox": [ + 53, + 335, + 282, + 506 + ], + "blocks": [ + { + "bbox": [ + 79, + 319, + 254, + 331 + ], + "lines": [ + { + "bbox": [ + 79, + 319, + 254, + 331 + ], + "spans": [ + { + "bbox": [ + 79, + 319, + 254, + 331 + ], + "type": "text", + "content": "Table 3. Quantitative evaluation on ImageNette." + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 53, + 335, + 282, + 506 + ], + "lines": [ + { + "bbox": [ + 53, + 335, + 282, + 506 + ], + "spans": [ + { + "bbox": [ + 53, + 335, + 282, + 506 + ], + "type": "table", + "html": "
MethodsDiffROAR (%) (↑)Gini (%) (↑)Acc. (%) (↑)
standard1.8146.5389.04
L1-norm (ε=0.01)2.9556.7390.46
L1-norm (ε=0.05)2.1262.0484.13
L1-norm (ε=0.10)1.9765.5378.85
group-norm (ε=0.10)2.5750.0786.83
group-norm (ε=0.50)1.3249.1587.57
group-norm (ε=1.00)0.4052.7083.80
elastic net (ε1=0.01, ε2=0.01)2.6057.1087.72
elastic net (ε1=0.01, ε2=0.05)3.2457.3587.67
elastic net (ε1=0.01, ε2=0.10)3.1454.4487.19
elastic net (ε1=0.05, ε2=0.01)2.3160.0584.59
elastic net (ε1=0.05, ε2=0.05)2.1161.8484.69
elastic net (ε1=0.05, ε2=0.10)2.1760.2584.54
", + "image_path": "daab8f5f28bbc00a0359861cbf7b3b0d3a7efb7c198999fd92f6d5e0f096068e.jpg" + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "table_body" + } + ], + "index": 3 + }, + { + "bbox": [ + 46, + 520, + 287, + 663 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 520, + 287, + 663 + ], + "spans": [ + { + "bbox": [ + 46, + 520, + 287, + 663 + ], + "type": "text", + "content": "els that remain salient after the interpretation attack, and 2) the structural similarity index measure (SSIM) [38]. We compared the proposed training methods with the baseline standard training and three post-processing-based baselines, SmoothGrad, Sparsified-SmoothGrad (Sparsified-S.), and MoreauGrad (Fig. 5). Standard training seemed vulnerable to minor attacks, even when combined with the Smooth-based post-processing. In contrast, the neural nets trained by the proposed methods displayed significantly higher robustness to the attacks. We also observed that the elastic net and group-norm-based training methods performed slightly more robustly than the " + }, + { + "bbox": [ + 46, + 520, + 287, + 663 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 520, + 287, + 663 + ], + "type": "text", + "content": "-norm-based method." + } + ] + } + ], + "index": 4 + }, + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "spans": [ + { + "bbox": [ + 46, + 665, + 287, + 714 + ], + "type": "text", + "content": "Stability. We evaluated the algorithmic stability as the magnitude of perturbation in the saliency maps under classifiers trained with different training data or random initialization. As pointed out by [39], standard training with different" + } + ] + } + ], + "index": 5 + }, + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "spans": [ + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "type": "text", + "content": "initializations can result in large discrepancies in saliency maps. We examined if the proposed training methods can alleviate this issue. To this end, we switched " + }, + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "type": "inline_equation", + "content": "10\\%" + }, + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "type": "text", + "content": " of the training data with the test data and initialized two networks with different random seeds. Then we trained these two networks with the same training process. We used SSIM and top-k overlap to measure the similarities of the generated saliency maps, where the top-k overlap was defined as the Dice score of the top-k masks. As shown in Fig. 5, adversarial training could significantly improve stability. It even brings more improvement than post-processing methods. Note for Sparsified-SmoothGrad, the high SSIM is due to the sparsity of the saliency maps. Through studying top-k overlap, the activated regions were actually different. Among the three variants of adversarial training, the elastic net could achieve the best stability, as the incorporation of " + }, + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "type": "inline_equation", + "content": "L_2^2" + }, + { + "bbox": [ + 304, + 320, + 547, + 548 + ], + "type": "text", + "content": " term could increase the smoothness of the objective function, making the optimization process less sensitive to the perturbation of the training data." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "spans": [ + { + "bbox": [ + 304, + 557, + 547, + 713 + ], + "type": "text", + "content": "Comparison of different training protocols. We also conducted experiments to see how different training protocols affect the numerical results. Specifically, we compared one-step optimization (fast), multiple-step optimization (iterative), and free adversarial training (free, in Appendix) [25]. As a baseline, we also studied standard training with norm regularization directly applied to the objective function (penalty). We visualized a few saliency maps in Fig. 4 for comparison. Standard training with regularization failed to generate structured saliency maps, showing the challenge of network optimization with regularization in the objective function, which further certified the superiority of adversarial training. Visually, fast, and iterative" + } + ] + } + ], + "index": 7 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 317, + 757 + ], + "type": "text", + "content": "11015" + } + ] + } + ], + "index": 8 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 6 + }, + { + "para_blocks": [ + { + "type": "image", + "bbox": [ + 53, + 75, + 214, + 173 + ], + "blocks": [ + { + "bbox": [ + 53, + 75, + 214, + 173 + ], + "lines": [ + { + "bbox": [ + 53, + 75, + 214, + 173 + ], + "spans": [ + { + "bbox": [ + 53, + 75, + 214, + 173 + ], + "type": "image", + "image_path": "11844bd43c7a9166772627b28faaf5c0da9d559c88eeb4b92efb79e13c9479f5.jpg" + } + ] + } + ], + "index": 0, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 46, + 178, + 547, + 201 + ], + "lines": [ + { + "bbox": [ + 46, + 178, + 547, + 201 + ], + "spans": [ + { + "bbox": [ + 46, + 178, + 547, + 201 + ], + "type": "text", + "content": "Figure 5. Quantitative robustness and stability comparison. Left/Middle: Comparison of SSIM/top-k intersection of saliency maps before and after the attack. Right: Comparison of SSIM/top-k overlap of saliency maps generated by networks with different stochastic training." + } + ] + } + ], + "index": 3, + "angle": 0, + "type": "image_caption" + } + ], + "index": 0 + }, + { + "type": "image", + "bbox": [ + 216, + 75, + 376, + 173 + ], + "blocks": [ + { + "bbox": [ + 216, + 75, + 376, + 173 + ], + "lines": [ + { + "bbox": [ + 216, + 75, + 376, + 173 + ], + "spans": [ + { + "bbox": [ + 216, + 75, + 376, + 173 + ], + "type": "image", + "image_path": "1627768cf21021453c9d71fd3f2af1f51333d21fbe1ad0d866f9efd5359f9234.jpg" + } + ] + } + ], + "index": 1, + "angle": 0, + "type": "image_body" + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 383, + 75, + 539, + 172 + ], + "blocks": [ + { + "bbox": [ + 383, + 75, + 539, + 172 + ], + "lines": [ + { + "bbox": [ + 383, + 75, + 539, + 172 + ], + "spans": [ + { + "bbox": [ + 383, + 75, + 539, + 172 + ], + "type": "image", + "image_path": "3887241b624cd18016a21a8813a8867a30e5c739adb2815e1c588b475066db8e.jpg" + } + ] + } + ], + "index": 2, + "angle": 0, + "type": "image_body" + } + ], + "index": 2 + }, + { + "type": "table", + "bbox": [ + 59, + 247, + 276, + 304 + ], + "blocks": [ + { + "bbox": [ + 46, + 220, + 287, + 243 + ], + "lines": [ + { + "bbox": [ + 46, + 220, + 287, + 243 + ], + "spans": [ + { + "bbox": [ + 46, + 220, + 287, + 243 + ], + "type": "text", + "content": "Table 4. Top-k overlap " + }, + { + "bbox": [ + 46, + 220, + 287, + 243 + ], + "type": "inline_equation", + "content": "(\\%)" + }, + { + "bbox": [ + 46, + 220, + 287, + 243 + ], + "type": "text", + "content": " between gaze map and saliency map on CUB-GHA dataset." + } + ] + } + ], + "index": 4, + "angle": 0, + "type": "table_caption" + }, + { + "bbox": [ + 59, + 247, + 276, + 304 + ], + "lines": [ + { + "bbox": [ + 59, + 247, + 276, + 304 + ], + "spans": [ + { + "bbox": [ + 59, + 247, + 276, + 304 + ], + "type": "table", + "html": "
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top 5% overlap33.4235.0738.7442.6350.62
top 10% overlap41.8142.9945.6047.0652.60
accuracy (%)67.5867.5066.5666.6564.99
", + "image_path": "0465bcfc76cf331e23cb8771ff72878dc8707d7b23f91465ca6e55b7c8d382f5.jpg" + } + ] + } + ], + "index": 5, + "angle": 0, + "type": "table_body" + } + ], + "index": 5 + }, + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "spans": [ + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "type": "text", + "content": "training achieved comparable quality. However, for " + }, + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "type": "text", + "content": "-norm, interactive training would lose sparsity compared to fast training, but for the elastic net, the trend was the opposite. The Fenchel conjugate of elastic net regularization is differentiable everywhere due to the square term, making its optimization easier compared with " + }, + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "type": "inline_equation", + "content": "L_{1}" + }, + { + "bbox": [ + 46, + 346, + 287, + 418 + ], + "type": "text", + "content": "-norm." + } + ] + } + ], + "index": 6 + }, + { + "bbox": [ + 47, + 443, + 216, + 456 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 47, + 443, + 216, + 456 + ], + "spans": [ + { + "bbox": [ + 47, + 443, + 216, + 456 + ], + "type": "text", + "content": "5.3. Harmonization with gaze maps" + } + ] + } + ], + "index": 7 + }, + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "spans": [ + { + "bbox": [ + 46, + 468, + 287, + 575 + ], + "type": "text", + "content": "We conducted experiments on the CUB-GHA [21] to verify the effectiveness of our interpretation harmonization strategy on real-world data. CUB-GHA is an extension of CUB [36], which includes gaze maps collected from domain experts for bird category classification. The gaze map is a type of human attention map reflecting how human experts would conduct this task. We aim to harmonize the saliency maps with human attention so that the network could make the decision more similar to humans." + } + ] + } + ], + "index": 8 + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "spans": [ + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "To do this, we normalized the gaze map and used the attention score as the weights for the " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "l_{2}" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": "-norm perturbation during adversarial training. The results are shown in Fig. 6. The original saliency maps highlighted the whole body of the bird, while the gaze maps were more focused on a specific part (e.g. head) of the bird. After harmonization, the saliency maps showed better alignment with the gaze maps. We also calculated the top-k overlap between saliency maps and gaze maps (Table 4). The results showed an increasing trend of the overlap as we raised the coefficient " + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "inline_equation", + "content": "\\epsilon" + }, + { + "bbox": [ + 46, + 582, + 288, + 715 + ], + "type": "text", + "content": ", while the trade-off of accuracy was in a reasonable range." + } + ] + } + ], + "index": 9 + }, + { + "type": "image", + "bbox": [ + 313, + 223, + 541, + 373 + ], + "blocks": [ + { + "bbox": [ + 313, + 223, + 541, + 373 + ], + "lines": [ + { + "bbox": [ + 313, + 223, + 541, + 373 + ], + "spans": [ + { + "bbox": [ + 313, + 223, + 541, + 373 + ], + "type": "image", + "image_path": "207aee0309b4cfef0716060fa525b27d45945f62c2337027fda8e177b4f133a3.jpg" + } + ] + } + ], + "index": 10, + "angle": 0, + "type": "image_body" + }, + { + "bbox": [ + 320, + 383, + 531, + 395 + ], + "lines": [ + { + "bbox": [ + 320, + 383, + 531, + 395 + ], + "spans": [ + { + "bbox": [ + 320, + 383, + 531, + 395 + ], + "type": "text", + "content": "Figure 6. Qualitative results based on CUB-GHA dataset." + } + ] + } + ], + "index": 11, + "angle": 0, + "type": "image_caption" + } + ], + "index": 10 + }, + { + "bbox": [ + 306, + 400, + 379, + 414 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 306, + 400, + 379, + 414 + ], + "spans": [ + { + "bbox": [ + 306, + 400, + 379, + 414 + ], + "type": "text", + "content": "6. Conclusion" + } + ] + } + ], + "index": 12 + }, + { + "bbox": [ + 304, + 420, + 545, + 648 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 420, + 545, + 648 + ], + "spans": [ + { + "bbox": [ + 304, + 420, + 545, + 648 + ], + "type": "text", + "content": "In this paper, we introduced a duality framework to analyze the impact of norm-regularized adversarial training on the gradient-based saliency maps of a trained neural net classifier. Leveraging this duality framework, we proposed several variants of norm-regularized adversarial training, designed to promote certain structures in the gradient-based interpretation maps, including sparsity, group sparsity, and consistency with human attention. We provided experimental results on several benchmark datasets to validate the effectiveness of our proposed methods, which demonstrated that properly designed adversarial training methods can enhance model interpretability as well as the stability and robustness of the gradient-based maps. An interesting future direction is to develop a similar adversarial training-based regularization framework for structured interpretation maps according to integrated gradients, DeepLIFT, and GradCam. Another relevant future direction is to explore other forms of penalty terms in order to expand the methodology to domains beyond computer vision." + } + ] + } + ], + "index": 13 + }, + { + "bbox": [ + 304, + 650, + 547, + 711 + ], + "type": "text", + "angle": 0, + "lines": [ + { + "bbox": [ + 304, + 650, + 547, + 711 + ], + "spans": [ + { + "bbox": [ + 304, + 650, + 547, + 711 + ], + "type": "text", + "content": "Acknowledgments. The work of Farzan Farnia is partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China, Project 14209920, and is partially supported by a CUHK Direct Research Grant with CUHK Project No. 4055164." + } + ] + } + ], + "index": 14 + } + ], + "discarded_blocks": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "page_number", + "angle": 0, + "lines": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "spans": [ + { + "bbox": [ + 294, + 748, + 318, + 757 + ], + "type": "text", + "content": "11016" + } + ] + } + ], + "index": 15 + } + ], + "page_size": [ + 612, + 792 + ], + "page_idx": 7 + }, + { + "para_blocks": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "title", + "angle": 0, + "lines": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "spans": [ + { + "bbox": [ + 48, + 71, + 106, + 83 + ], + "type": "text", + "content": "References" + } + ] + } + ], + "index": 0 + }, + { + "bbox": [ + 48, + 91, + 288, + 714 + ], + "type": "list", + "angle": 0, + "index": 15, + "blocks": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "ref_text", + "angle": 0, + "lines": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "spans": [ + { + "bbox": [ + 53, + 91, + 287, + 134 + ], + "type": "text", + "content": "[1] Julius Adebayo, Justin Gilmer, Michael Muelly, Ian Goodfellow, Moritz Hardt, and Been Kim. 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